LMFDB - Embedded newform 156.2.h.b.155.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(155,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.h (of order $2$, degree $1$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 43x^{12} + 517x^{8} + 1804x^{4} + 16 $ x^16 + 43x^12 + 517x^8 + 1804*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.11
Root			$-1.58894 - 1.58894i$ of defining polynomial
Character	$\chi$	$=$	156.155
Dual form			156.2.h.b.155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599676 + 1.28078i) q^{2} +(-1.62493 + 0.599676i) q^{3} +(-1.28078 + 1.53610i) q^{4} -2.13578 q^{5} +(-1.74248 - 1.72156i) q^{6} -1.52162 q^{7} +(-2.73546 - 0.719224i) q^{8} +(2.28078 - 1.94886i) q^{9} +O(q^{10})$	\(q+(0.599676 + 1.28078i) q^{2} +(-1.62493 + 0.599676i) q^{3} +(-1.28078 + 1.53610i) q^{4} -2.13578 q^{5} +(-1.74248 - 1.72156i) q^{6} -1.52162 q^{7} +(-2.73546 - 0.719224i) q^{8} +(2.28078 - 1.94886i) q^{9} +(-1.28078 - 2.73546i) q^{10} +2.00000i q^{11} +(1.16000 - 3.26411i) q^{12} +(1.56155 + 3.24985i) q^{13} +(-0.912482 - 1.94886i) q^{14} +(3.47049 - 1.28078i) q^{15} +(-0.719224 - 3.93481i) q^{16} +6.94097i q^{17} +(3.86378 + 1.75248i) q^{18} -5.41935 q^{19} +(2.73546 - 3.28078i) q^{20} +(2.47253 - 0.912482i) q^{21} +(-2.56155 + 1.19935i) q^{22} +5.07482 q^{23} +(4.87622 - 0.471702i) q^{24} -0.438447 q^{25} +(-3.22591 + 3.94886i) q^{26} +(-2.53741 + 4.53448i) q^{27} +(1.94886 - 2.33737i) q^{28} -3.04325i q^{29} +(3.72156 + 3.67686i) q^{30} +5.41935 q^{31} +(4.60831 - 3.28078i) q^{32} +(-1.19935 - 3.24985i) q^{33} +(-8.88983 + 4.16234i) q^{34} +3.24985 q^{35} +(0.0724861 + 5.99956i) q^{36} +1.82496i q^{37} +(-3.24985 - 6.94097i) q^{38} +(-4.48627 - 4.34435i) q^{39} +(5.84233 + 1.53610i) q^{40} +5.73384 q^{41} +(2.65140 + 2.61956i) q^{42} +3.07221i q^{43} +(-3.07221 - 2.56155i) q^{44} +(-4.87123 + 4.16234i) q^{45} +(3.04325 + 6.49971i) q^{46} -5.68466i q^{47} +(3.52830 + 5.96248i) q^{48} -4.68466 q^{49} +(-0.262926 - 0.561553i) q^{50} +(-4.16234 - 11.2786i) q^{51} +(-6.99211 - 1.76363i) q^{52} +(-7.32929 - 0.530631i) q^{54} -4.27156i q^{55} +(4.16234 + 1.09439i) q^{56} +(8.80604 - 3.24985i) q^{57} +(3.89772 - 1.82496i) q^{58} +11.1231i q^{59} +(-2.47751 + 6.97141i) q^{60} -5.12311 q^{61} +(3.24985 + 6.94097i) q^{62} +(-3.47049 + 2.96543i) q^{63} +(6.96543 + 3.93481i) q^{64} +(-3.33513 - 6.94097i) q^{65} +(3.44311 - 3.48496i) q^{66} +8.46260 q^{67} +(-10.6620 - 8.88983i) q^{68} +(-8.24621 + 3.04325i) q^{69} +(1.94886 + 4.16234i) q^{70} -2.31534i q^{71} +(-7.64063 + 3.69063i) q^{72} -10.1496i q^{73} +(-2.33737 + 1.09439i) q^{74} +(0.712445 - 0.262926i) q^{75} +(6.94097 - 8.32467i) q^{76} -3.04325i q^{77} +(2.87383 - 8.35111i) q^{78} -9.06897i q^{79} +(1.53610 + 8.40388i) q^{80} +(1.40388 - 8.88983i) q^{81} +(3.43845 + 7.34376i) q^{82} +6.00000i q^{83} +(-1.76509 + 4.96674i) q^{84} -14.8244i q^{85} +(-3.93481 + 1.84233i) q^{86} +(1.82496 + 4.94506i) q^{87} +(1.43845 - 5.47091i) q^{88} -11.3524 q^{89} +(-8.25219 - 3.74291i) q^{90} +(-2.37610 - 4.94506i) q^{91} +(-6.49971 + 7.79544i) q^{92} +(-8.80604 + 3.24985i) q^{93} +(7.28078 - 3.40896i) q^{94} +11.5745 q^{95} +(-5.52076 + 8.09452i) q^{96} +16.6493i q^{97} +(-2.80928 - 6.00000i) q^{98} +(3.89772 + 4.56155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 + 20 * q^9	$ 16 q - 4 q^{4} + 20 q^{9} - 4 q^{10} + 10 q^{12} - 8 q^{13} - 28 q^{16} - 8 q^{22} - 40 q^{25} + 18 q^{30} - 22 q^{36} + 44 q^{40} - 34 q^{42} + 46 q^{48} + 24 q^{49} - 32 q^{52} - 16 q^{61} - 4 q^{64} - 28 q^{66} + 34 q^{78} - 60 q^{81} + 88 q^{82} + 56 q^{88} - 22 q^{90} + 100 q^{94}+O(q^{100}) $ 16 * q - 4 * q^4 + 20 * q^9 - 4 * q^10 + 10 * q^12 - 8 * q^13 - 28 * q^16 - 8 * q^22 - 40 * q^25 + 18 * q^30 - 22 * q^36 + 44 * q^40 - 34 * q^42 + 46 * q^48 + 24 * q^49 - 32 * q^52 - 16 * q^61 - 4 * q^64 - 28 * q^66 + 34 * q^78 - 60 * q^81 + 88 * q^82 + 56 * q^88 - 22 * q^90 + 100 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.599676	+	1.28078i	0.424035	+	0.905646i
$2$	0.599676	+	1.28078i	0.424035	+	0.905646i
$3$	−1.62493	+	0.599676i	−0.938152	+	0.346223i
$3$	−1.62493	+	0.599676i	−0.938152	+	0.346223i
$4$	−1.28078	+	1.53610i	−0.640388	+	0.768051i
$5$	−2.13578			−0.955149			−0.477575	−	0.878591i	$-0.658484\pi$
$5$	−2.13578			−0.955149			−0.477575	+	0.878591i	$0.658484\pi$
$6$	−1.74248	−	1.72156i	−0.711365	−	0.702823i
$7$	−1.52162			−0.575120			−0.287560	−	0.957763i	$-0.592844\pi$
$7$	−1.52162			−0.575120			−0.287560	+	0.957763i	$0.592844\pi$
$8$	−2.73546	−	0.719224i	−0.967130	−	0.254284i
$9$	2.28078	−	1.94886i	0.760259	−	0.649620i
$10$	−1.28078	−	2.73546i	−0.405017	−	0.865027i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	1.16000	−	3.26411i	0.334864	−	0.942266i
$13$	1.56155	+	3.24985i	0.433097	+	0.901347i
$13$	1.56155	+	3.24985i	0.433097	+	0.901347i
$14$	−0.912482	−	1.94886i	−0.243871	−	0.520855i
$15$	3.47049	−	1.28078i	0.896076	−	0.330695i
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$			6.94097i			1.68343i	0.539920	+	0.841716i	$0.318455\pi$
$17$			6.94097i			1.68343i	−0.539920	+	0.841716i	$0.681545\pi$
$18$	3.86378	+	1.75248i	0.910702	+	0.413063i
$19$	−5.41935			−1.24328			−0.621642	−	0.783302i	$-0.713534\pi$
$19$	−5.41935			−1.24328			−0.621642	+	0.783302i	$0.713534\pi$
$20$	2.73546	−	3.28078i	0.611666	−	0.733604i
$21$	2.47253	−	0.912482i	0.539550	−	0.199120i
$22$	−2.56155	+	1.19935i	−0.546125	+	0.255703i
$23$	5.07482			1.05817			0.529086	−	0.848568i	$-0.322535\pi$
$23$	5.07482			1.05817			0.529086	+	0.848568i	$0.322535\pi$
$24$	4.87622	−	0.471702i	0.995354	−	0.0962858i
$25$	−0.438447			−0.0876894
$26$	−3.22591	+	3.94886i	−0.632653	+	0.774435i
$27$	−2.53741	+	4.53448i	−0.488325	+	0.872662i
$28$	1.94886	−	2.33737i	0.368300	−	0.441722i
$29$		−	3.04325i		−	0.565117i	−0.959250	−	0.282559i	$-0.908817\pi$
$29$		−	3.04325i		−	0.565117i	0.959250	−	0.282559i	$-0.0911832\pi$
$30$	3.72156	+	3.67686i	0.679460	+	0.671301i
$31$	5.41935			0.973343			0.486672	−	0.873585i	$-0.338211\pi$
$31$	5.41935			0.973343			0.486672	+	0.873585i	$0.338211\pi$
$32$	4.60831	−	3.28078i	0.814642	−	0.579965i
$33$	−1.19935	−	3.24985i	−0.208781	−	0.565727i
$34$	−8.88983	+	4.16234i	−1.52459	+	0.713835i
$35$	3.24985			0.549326
$36$	0.0724861	+	5.99956i	0.0120810	+	0.999927i
$37$			1.82496i			0.300022i	0.988684	+	0.150011i	$0.0479310\pi$
$37$			1.82496i			0.300022i	−0.988684	+	0.150011i	$0.952069\pi$
$38$	−3.24985	−	6.94097i	−0.527196	−	1.12597i
$39$	−4.48627	−	4.34435i	−0.718378	−	0.695653i
$40$	5.84233	+	1.53610i	0.923753	+	0.242879i
$41$	5.73384			0.895475			0.447737	−	0.894165i	$-0.352230\pi$
$41$	5.73384			0.895475			0.447737	+	0.894165i	$0.352230\pi$
$42$	2.65140	+	2.61956i	0.409120	+	0.404207i
$43$			3.07221i			0.468507i	0.972176	+	0.234253i	$0.0752646\pi$
$43$			3.07221i			0.468507i	−0.972176	+	0.234253i	$0.924735\pi$
$44$	−3.07221	−	2.56155i	−0.463152	−	0.386169i
$45$	−4.87123	+	4.16234i	−0.726161	+	0.620485i
$46$	3.04325	+	6.49971i	0.448703	+	0.958330i
$47$		−	5.68466i		−	0.829193i	−0.910005	−	0.414596i	$-0.863923\pi$
$47$		−	5.68466i		−	0.829193i	0.910005	−	0.414596i	$-0.136077\pi$
$48$	3.52830	+	5.96248i	0.509266	+	0.860609i
$49$	−4.68466			−0.669237
$50$	−0.262926	−	0.561553i	−0.0371834	−	0.0794156i
$51$	−4.16234	−	11.2786i	−0.582844	−	1.57932i
$52$	−6.99211	−	1.76363i	−0.969631	−	0.244572i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−7.32929	−	0.530631i	−0.997389	−	0.0722097i
$55$		−	4.27156i		−	0.575977i
$56$	4.16234	+	1.09439i	0.556216	+	0.146244i
$57$	8.80604	−	3.24985i	1.16639	−	0.430454i
$58$	3.89772	−	1.82496i	0.511796	−	0.239630i
$59$			11.1231i			1.44811i	0.689745	+	0.724053i	$0.257723\pi$
$59$			11.1231i			1.44811i	−0.689745	+	0.724053i	$0.742277\pi$
$60$	−2.47751	+	6.97141i	−0.319845	+	0.900005i
$61$	−5.12311			−0.655946			−0.327973	−	0.944687i	$-0.606366\pi$
$61$	−5.12311			−0.655946			−0.327973	+	0.944687i	$0.606366\pi$
$62$	3.24985	+	6.94097i	0.412732	+	0.881504i
$63$	−3.47049	+	2.96543i	−0.437240	+	0.373610i
$64$	6.96543	+	3.93481i	0.870679	+	0.491851i
$65$	−3.33513	−	6.94097i	−0.413672	−	0.860922i
$66$	3.44311	−	3.48496i	0.423818	−	0.428969i
$67$	8.46260			1.03387			0.516935	−	0.856024i	$-0.327073\pi$
$67$	8.46260			1.03387			0.516935	+	0.856024i	$0.327073\pi$
$68$	−10.6620	−	8.88983i	−1.29296	−	1.07805i
$69$	−8.24621	+	3.04325i	−0.992727	+	0.366364i
$70$	1.94886	+	4.16234i	0.232933	+	0.497494i
$71$		−	2.31534i		−	0.274780i	−0.990517	−	0.137390i	$-0.956129\pi$
$71$		−	2.31534i		−	0.274780i	0.990517	−	0.137390i	$-0.0438714\pi$
$72$	−7.64063	+	3.69063i	−0.900457	+	0.434945i
$73$		−	10.1496i		−	1.18793i	−0.804493	−	0.593963i	$-0.797563\pi$
$73$		−	10.1496i		−	1.18793i	0.804493	−	0.593963i	$-0.202437\pi$
$74$	−2.33737	+	1.09439i	−0.271714	+	0.127220i
$75$	0.712445	−	0.262926i	0.0822660	−	0.0303601i
$76$	6.94097	−	8.32467i	0.796184	−	0.954906i
$77$		−	3.04325i		−	0.346810i
$78$	2.87383	−	8.35111i	0.325397	−	0.945577i
$79$		−	9.06897i		−	1.02034i	−0.860074	−	0.510169i	$-0.829583\pi$
$79$		−	9.06897i		−	1.02034i	0.860074	−	0.510169i	$-0.170417\pi$
$80$	1.53610	+	8.40388i	0.171742	+	0.939583i
$81$	1.40388	−	8.88983i	0.155987	−	0.987759i
$82$	3.43845	+	7.34376i	0.379713	+	0.810983i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	−1.76509	+	4.96674i	−0.192587	+	0.541916i
$85$		−	14.8244i		−	1.60793i
$86$	−3.93481	+	1.84233i	−0.424301	+	0.198663i
$87$	1.82496	+	4.94506i	0.195657	+	0.530166i
$88$	1.43845	−	5.47091i	0.153339	−	0.583201i
$89$	−11.3524			−1.20335			−0.601676	−	0.798740i	$-0.705500\pi$
$89$	−11.3524			−1.20335			−0.601676	+	0.798740i	$0.705500\pi$
$90$	−8.25219	−	3.74291i	−0.869857	−	0.394537i
$91$	−2.37610	−	4.94506i	−0.249083	−	0.518383i
$92$	−6.49971	+	7.79544i	−0.677641	+	0.812731i
$93$	−8.80604	+	3.24985i	−0.913144	+	0.336994i
$94$	7.28078	−	3.40896i	0.750955	−	0.351607i
$95$	11.5745			1.18752
$96$	−5.52076	+	8.09452i	−0.563460	+	0.826143i
$97$			16.6493i			1.69049i	0.534383	+	0.845243i	$0.320544\pi$
$97$			16.6493i			1.69049i	−0.534383	+	0.845243i	$0.679456\pi$
$98$	−2.80928	−	6.00000i	−0.283780	−	0.606092i
$99$	3.89772	+	4.56155i	0.391736	+	0.458453i
$100$	0.561553	−	0.673500i	0.0561553	−	0.0673500i
$101$			6.08650i			0.605629i	0.953049	+	0.302815i	$0.0979263\pi$
$101$			6.08650i			0.605629i	−0.953049	+	0.302815i	$0.902074\pi$
$102$	11.9493	−	12.0945i	1.18315	−	1.19754i
$103$			19.4849i			1.91991i	0.280157	+	0.959954i	$0.409613\pi$
$103$			19.4849i			1.91991i	−0.280157	+	0.959954i	$0.590387\pi$
$104$	−1.93419	−	10.0129i	−0.189663	−	0.981849i
$105$	−5.28078	+	1.94886i	−0.515351	+	0.190189i
$106$		0			0
$107$	−10.1496			−0.981203			−0.490601	−	0.871384i	$-0.663223\pi$
$107$	−10.1496			−0.981203			−0.490601	+	0.871384i	$0.663223\pi$
$108$	−3.71558	−	9.70538i	−0.357532	−	0.933901i
$109$		−	8.32467i		−	0.797359i	−0.917090	−	0.398680i	$-0.869469\pi$
$109$		−	8.32467i		−	0.797359i	0.917090	−	0.398680i	$-0.130531\pi$
$110$	5.47091	−	2.56155i	0.521631	−	0.244234i
$111$	−1.09439	−	2.96543i	−0.103875	−	0.281467i
$112$	1.09439	+	5.98730i	0.103410	+	0.565747i
$113$			10.8387i			1.01962i	0.860287	+	0.509809i	$0.170284\pi$
$113$			10.8387i			1.01962i	−0.860287	+	0.509809i	$0.829716\pi$
$114$	9.44311	+	9.32971i	0.884429	+	0.873808i
$115$	−10.8387			−1.01071
$116$	4.67474	+	3.89772i	0.434039	+	0.361894i
$117$	9.89507	+	4.36894i	0.914799	+	0.403909i
$118$	−14.2462	+	6.67026i	−1.31147	+	0.614048i
$119$		−	10.5616i		−	0.968176i
$120$	−10.4145	+	1.00745i	−0.950712	+	0.0919674i
$121$	7.00000			0.636364
$122$	−3.07221	−	6.56155i	−0.278144	−	0.594055i
$123$	−9.31707	+	3.43845i	−0.840092	+	0.310034i
$124$	−6.94097	+	8.32467i	−0.623318	+	0.747578i
$125$	11.6153			1.03891
$126$	−5.87923	−	2.66661i	−0.523763	−	0.237561i
$127$			6.67026i			0.591890i	0.955205	+	0.295945i	$0.0956346\pi$
$127$			6.67026i			0.591890i	−0.955205	+	0.295945i	$0.904365\pi$
$128$	−0.862603	+	11.2808i	−0.0762440	+	0.997089i
$129$	−1.84233	−	4.99211i	−0.162208	−	0.439531i
$130$	6.88983	−	8.43390i	0.604278	−	0.739702i
$131$	1.82496			0.159448			0.0797240	−	0.996817i	$-0.474596\pi$
$131$	1.82496			0.159448			0.0797240	+	0.996817i	$0.474596\pi$
$132$	6.52821	+	2.32001i	0.568208	+	0.201931i
$133$	8.24621			0.715037
$134$	5.07482	+	10.8387i	0.438398	+	0.936320i
$135$	5.41935	−	9.68466i	0.466423	−	0.833523i
$136$	4.99211	−	18.9867i	0.428070	−	1.62810i
$137$	8.95369			0.764965			0.382483	−	0.923963i	$-0.375069\pi$
$137$	8.95369			0.764965			0.382483	+	0.923963i	$0.375069\pi$
$138$	−8.84278	−	8.73659i	−0.752747	−	0.743708i
$139$		−	6.81791i		−	0.578288i	−0.957286	−	0.289144i	$-0.906629\pi$
$139$		−	6.81791i		−	0.578288i	0.957286	−	0.289144i	$-0.0933706\pi$
$140$	−4.16234	+	4.99211i	−0.351782	+	0.421910i
$141$	3.40896	+	9.23716i	0.287086	+	0.777909i
$142$	2.96543	−	1.38846i	0.248854	−	0.116517i
$143$	−6.49971	+	3.12311i	−0.543533	+	0.261167i
$144$	−9.30878	−	7.57275i	−0.775732	−	0.631063i
$145$			6.49971i			0.539771i
$146$	12.9994	−	6.08650i	1.07584	−	0.503722i
$147$	7.61223	−	2.80928i	0.627846	−	0.231705i
$148$	−2.80333	−	2.33737i	−0.230433	−	0.192131i
$149$	−0.410574			−0.0336355			−0.0168177	−	0.999859i	$-0.505354\pi$
$149$	−0.410574			−0.0336355			−0.0168177	+	0.999859i	$0.505354\pi$
$150$	0.763986	+	0.754812i	0.0623792	+	0.0616301i
$151$	17.1125			1.39260			0.696298	−	0.717753i	$-0.254829\pi$
$151$	17.1125			1.39260			0.696298	+	0.717753i	$0.254829\pi$
$152$	14.8244	+	3.89772i	1.20242	+	0.316147i
$153$	13.5270	+	15.8308i	1.09359	+	1.27984i
$154$	3.89772	−	1.82496i	0.314087	−	0.147060i
$155$	−11.5745			−0.929688
$156$	12.4193	−	1.32723i	0.994338	−	0.106264i
$157$	6.24621			0.498502			0.249251	−	0.968439i	$-0.419816\pi$
$157$	6.24621			0.498502			0.249251	+	0.968439i	$0.419816\pi$
$158$	11.6153	−	5.43845i	0.924065	−	0.432660i
$159$		0			0
$160$	−9.84233	+	7.00701i	−0.778104	+	0.553953i
$161$	−7.72197			−0.608576
$162$	12.2278	−	3.53296i	0.960704	−	0.277576i
$163$	13.2148			1.03506			0.517531	−	0.855664i	$-0.326851\pi$
$163$	13.2148			1.03506			0.517531	+	0.855664i	$0.326851\pi$
$164$	−7.34376	+	8.80776i	−0.573452	+	0.687771i
$165$	2.56155	+	6.94097i	0.199417	+	0.540354i
$166$	−7.68466	+	3.59806i	−0.596445	+	0.279263i
$167$		−	17.3693i		−	1.34408i	−0.740516	−	0.672039i	$-0.765419\pi$
$167$		−	17.3693i		−	1.34408i	0.740516	−	0.672039i	$-0.234581\pi$
$168$	−7.41977	+	0.717754i	−0.572448	+	0.0553759i
$169$	−8.12311	+	10.1496i	−0.624854	+	0.780741i
$170$	18.9867	−	8.88983i	1.45621	−	0.681819i
$171$	−12.3603	+	10.5616i	−0.945217	+	0.807662i
$172$	−4.71922	−	3.93481i	−0.359837	−	0.300026i
$173$		−	7.79544i		−	0.592677i	−0.955083	−	0.296338i	$-0.904234\pi$
$173$		−	7.79544i		−	0.592677i	0.955083	−	0.296338i	$-0.0957656\pi$
$174$	−5.23913	+	5.30281i	−0.397177	+	0.402005i
$175$	0.667152			0.0504320
$176$	7.86962	−	1.43845i	0.593195	−	0.108427i
$177$	−6.67026	−	18.0742i	−0.501368	−	1.35854i
$178$	−6.80776	−	14.5399i	−0.510263	−	1.08981i
$179$	−1.82496			−0.136404			−0.0682021	−	0.997672i	$-0.521726\pi$
$179$	−1.82496			−0.136404			−0.0682021	+	0.997672i	$0.521726\pi$
$180$	−0.154814	−	12.8137i	−0.0115392	−	0.955080i
$181$	19.3693			1.43971			0.719855	−	0.694124i	$-0.244208\pi$
$181$	19.3693			1.43971			0.719855	+	0.694124i	$0.244208\pi$
$182$	4.90862	−	6.00868i	0.363851	−	0.445393i
$183$	8.32467	−	3.07221i	0.615378	−	0.227104i
$184$	−13.8819	−	3.64993i	−1.02339	−	0.269076i
$185$		−	3.89772i		−	0.286566i
$186$	−9.44311	−	9.32971i	−0.692403	−	0.684088i
$187$	−13.8819			−1.01515
$188$	8.73222	+	7.28078i	0.636863	+	0.531005i
$189$	3.86098	−	6.89978i	0.280845	−	0.501885i
$190$	6.94097	+	14.8244i	0.503551	+	1.07547i
$191$	−11.5745			−0.837503			−0.418752	−	0.908101i	$-0.637532\pi$
$191$	−11.5745			−0.837503			−0.418752	+	0.908101i	$0.637532\pi$
$192$	−13.6779	−	2.21677i	−0.987120	−	0.159982i
$193$			19.4991i			1.40358i	0.712385	+	0.701789i	$0.247615\pi$
$193$			19.4991i			1.40358i	−0.712385	+	0.701789i	$0.752385\pi$
$194$	−21.3241	+	9.98422i	−1.53098	+	0.716825i
$195$	9.58168	+	9.27857i	0.686159	+	0.664452i
$196$	6.00000	−	7.19612i	0.428571	−	0.514008i
$197$	8.28019			0.589939			0.294970	−	0.955507i	$-0.404690\pi$
$197$	8.28019			0.589939			0.294970	+	0.955507i	$0.404690\pi$
$198$	−3.50496	+	7.72757i	−0.249086	+	0.549174i
$199$			5.61856i			0.398289i	0.979970	+	0.199145i	$0.0638163\pi$
$199$			5.61856i			0.398289i	−0.979970	+	0.199145i	$0.936184\pi$
$200$	1.19935	+	0.315342i	0.0848071	+	0.0222980i
$201$	−13.7511	+	5.07482i	−0.969928	+	0.357950i
$202$	−7.79544	+	3.64993i	−0.548486	+	0.256808i
$203$			4.63068i			0.325010i
$204$	22.6561	+	8.05155i	1.58624	+	0.563721i
$205$	−12.2462			−0.855312
$206$	−24.9559	+	11.6847i	−1.73876	+	0.814109i
$207$	11.5745	−	9.89012i	0.804485	−	0.687411i
$208$	11.6644	−	8.48178i	0.808784	−	0.588106i
$209$		−	10.8387i		−	0.749728i
$210$	−5.66281	−	5.59481i	−0.390771	−	0.386078i
$211$			1.19935i			0.0825669i	0.999147	+	0.0412834i	$0.0131447\pi$
$211$			1.19935i			0.0825669i	−0.999147	+	0.0412834i	$0.986855\pi$
$212$		0			0
$213$	1.38846	+	3.76226i	0.0951354	+	0.257786i
$214$	−6.08650	−	12.9994i	−0.416064	−	0.888622i
$215$		−	6.56155i		−	0.447494i
$216$	10.2023	−	10.5789i	0.694177	−	0.719804i
$217$	−8.24621			−0.559789
$218$	10.6620	−	4.99211i	0.722125	−	0.338108i
$219$	6.08650	+	16.4924i	0.411287	+	1.11445i
$220$	6.56155	+	5.47091i	0.442380	+	0.368849i
$221$	−22.5571	+	10.8387i	−1.51736	+	0.729089i
$222$	3.14178	−	3.17997i	0.210862	−	0.213425i
$223$	−29.2855			−1.96110			−0.980551	−	0.196263i	$-0.937120\pi$
$223$	−29.2855			−1.96110			−0.980551	+	0.196263i	$0.937120\pi$
$224$	−7.01212	+	4.99211i	−0.468517	+	0.333549i
$225$	−1.00000	+	0.854473i	−0.0666667	+	0.0569648i
$226$	−13.8819	+	6.49971i	−0.923413	+	0.432354i
$227$		−	7.75379i		−	0.514637i	−0.966327	−	0.257319i	$-0.917161\pi$
$227$		−	7.75379i		−	0.514637i	0.966327	−	0.257319i	$-0.0828390\pi$
$228$	−6.28646	+	17.6893i	−0.416331	+	1.17150i
$229$		−	27.8238i		−	1.83865i	−0.393501	−	0.919324i	$-0.628736\pi$
$229$		−	27.8238i		−	1.83865i	0.393501	−	0.919324i	$-0.371264\pi$
$230$	−6.49971	−	13.8819i	−0.428578	−	0.915348i
$231$	1.82496	+	4.94506i	0.120074	+	0.325361i
$232$	−2.18878	+	8.32467i	−0.143700	+	0.546542i
$233$		−	11.6932i		−	0.766045i	−0.923739	−	0.383022i	$-0.874883\pi$
$233$		−	11.6932i		−	0.766045i	0.923739	−	0.383022i	$-0.125117\pi$
$234$	0.338201	+	15.2933i	0.0221089	+	0.999756i
$235$			12.1412i			0.792003i
$236$	−17.0862	−	14.2462i	−1.11222	−	0.927349i
$237$	5.43845	+	14.7364i	0.353265	+	0.957233i
$238$	13.5270	−	6.33351i	0.876824	−	0.410541i
$239$			19.9309i			1.28922i	0.764511	+	0.644610i	$0.222980\pi$
$239$			19.9309i			1.28922i	−0.764511	+	0.644610i	$0.777020\pi$
$240$	−7.53566	−	12.7345i	−0.486425	−	0.822010i
$241$		−	3.64993i		−	0.235113i	−0.993066	−	0.117556i	$-0.962494\pi$
$241$		−	3.64993i		−	0.235113i	0.993066	−	0.117556i	$-0.0375061\pi$
$242$	4.19773	+	8.96543i	0.269841	+	0.576320i
$243$	3.04982	+	15.2872i	0.195646	+	0.980675i
$244$	6.56155	−	7.86962i	0.420060	−	0.503801i
$245$	10.0054			0.639221
$246$	−9.99111	−	9.87113i	−0.637010	−	0.629360i
$247$	−8.46260	−	17.6121i	−0.538462	−	1.12063i
$248$	−14.8244	−	3.89772i	−0.941349	−	0.247506i
$249$	−3.59806	−	9.74956i	−0.228018	−	0.617853i
$250$	6.96543	+	14.8766i	0.440533	+	0.940881i
$251$	−18.0742			−1.14084			−0.570418	−	0.821355i	$-0.693219\pi$
$251$	−18.0742			−1.14084			−0.570418	+	0.821355i	$0.693219\pi$
$252$	−0.110297	−	9.12908i	−0.00694804	−	0.575078i
$253$			10.1496i			0.638102i
$254$	−8.54312	+	4.00000i	−0.536043	+	0.250982i
$255$	8.88983	+	24.0885i	0.556703	+	1.50848i
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$		−	2.18878i		−	0.136532i	−0.997667	−	0.0682661i	$-0.978253\pi$
$257$		−	2.18878i		−	0.136532i	0.997667	−	0.0682661i	$-0.0217467\pi$
$258$	5.28898	−	5.35326i	0.329277	−	0.333280i
$259$		−	2.77691i		−	0.172549i
$260$	14.9336	+	3.76673i	0.926143	+	0.233602i
$261$	−5.93087	−	6.94097i	−0.367112	−	0.429635i
$262$	1.09439	+	2.33737i	0.0676115	+	0.144403i
$263$	3.64993			0.225064			0.112532	−	0.993648i	$-0.464104\pi$
$263$	3.64993			0.225064			0.112532	+	0.993648i	$0.464104\pi$
$264$	0.943405	+	9.75243i	0.0580625	+	0.600221i
$265$		0			0
$266$	4.94506	+	10.5616i	0.303201	+	0.647570i
$267$	18.4468	−	6.80776i	1.12893	−	0.416628i
$268$	−10.8387	+	12.9994i	−0.662079	+	0.794066i
$269$		−	18.6341i		−	1.13614i	−0.822979	−	0.568072i	$-0.807690\pi$
$269$		−	18.6341i		−	1.13614i	0.822979	−	0.568072i	$-0.192310\pi$
$270$	15.6537	+	1.13331i	0.952656	+	0.0689710i
$271$	7.60812			0.462161			0.231080	−	0.972935i	$-0.425774\pi$
$271$	7.60812			0.462161			0.231080	+	0.972935i	$0.425774\pi$
$272$	27.3114	−	4.99211i	1.65600	−	0.302691i
$273$	6.82642	+	6.61047i	0.413154	+	0.400084i
$274$	5.36932	+	11.4677i	0.324372	+	0.692788i
$275$		−	0.876894i		−	0.0528787i
$276$	5.88681	−	16.5648i	0.354344	−	0.997081i
$277$	−3.75379			−0.225543			−0.112772	−	0.993621i	$-0.535973\pi$
$277$	−3.75379			−0.225543			−0.112772	+	0.993621i	$0.535973\pi$
$278$	8.73222	−	4.08854i	0.523724	−	0.245214i
$279$	12.3603	−	10.5616i	0.739993	−	0.632304i
$280$	−8.88983	−	2.33737i	−0.531269	−	0.139685i
$281$	17.2015			1.02616			0.513078	−	0.858342i	$-0.328505\pi$
$281$	17.2015			1.02616			0.513078	+	0.858342i	$0.328505\pi$
$282$	−9.78646	+	9.90541i	−0.582775	+	0.589859i
$283$		−	16.5604i		−	0.984412i	−0.870479	−	0.492206i	$-0.836191\pi$
$283$		−	16.5604i		−	0.984412i	0.870479	−	0.492206i	$-0.163809\pi$
$284$	3.55660	+	2.96543i	0.211046	+	0.175966i
$285$	−18.8078	+	6.94097i	−1.11408	+	0.411148i
$286$	−7.89772	−	6.45182i	−0.467002	−	0.381504i
$287$	−8.72475			−0.515006
$288$	4.11674	−	16.4637i	0.242581	−	0.970131i
$289$	−31.1771			−1.83395
$290$	−8.32467	+	3.89772i	−0.488842	+	0.228882i
$291$	−9.98422	−	27.0540i	−0.585285	−	1.58593i
$292$	15.5909	+	12.9994i	0.912388	+	0.760733i
$293$	−2.66163			−0.155494			−0.0777471	−	0.996973i	$-0.524773\pi$
$293$	−2.66163			−0.155494			−0.0777471	+	0.996973i	$0.524773\pi$
$294$	8.16293	+	8.06490i	0.476072	+	0.470355i
$295$		−	23.7565i		−	1.38316i
$296$	1.31256	−	4.99211i	0.0762909	−	0.290161i
$297$	−9.06897	−	5.07482i	−0.526235	−	0.294471i
$298$	−0.246211	−	0.525853i	−0.0142626	−	0.0304618i
$299$	7.92460	+	16.4924i	0.458291	+	0.953781i
$300$	−0.508600	+	1.43114i	−0.0293641	+	0.0826268i
$301$		−	4.67474i		−	0.269448i
$302$	10.2620	+	21.9173i	0.590510	+	1.26120i
$303$	−3.64993	−	9.89012i	−0.209683	−	0.568172i
$304$	3.89772	+	21.3241i	0.223550	+	1.22302i
$305$	10.9418			0.626527
$306$	−12.1639	+	26.8184i	−0.695364	+	1.53311i
$307$	2.37610			0.135611			0.0678055	−	0.997699i	$-0.478400\pi$
$307$	2.37610			0.135611			0.0678055	+	0.997699i	$0.478400\pi$
$308$	4.67474	+	3.89772i	0.266368	+	0.222093i
$309$	−11.6847	−	31.6616i	−0.664717	−	1.80117i
$310$	−6.94097	−	14.8244i	−0.394221	−	0.841968i
$311$	24.5739			1.39346			0.696730	−	0.717333i	$-0.254637\pi$
$311$	24.5739			1.39346			0.696730	+	0.717333i	$0.254637\pi$
$312$	9.14743	+	15.1104i	0.517872	+	0.855458i
$313$	7.43845			0.420446			0.210223	−	0.977653i	$-0.432581\pi$
$313$	7.43845			0.420446			0.210223	+	0.977653i	$0.432581\pi$
$314$	3.74571	+	8.00000i	0.211382	+	0.451466i
$315$	7.41219	−	6.33351i	0.417630	−	0.356853i
$316$	13.9309	+	11.6153i	0.783673	+	0.653413i
$317$	0.410574			0.0230601			0.0115301	−	0.999934i	$-0.496330\pi$
$317$	0.410574			0.0230601			0.0115301	+	0.999934i	$0.496330\pi$
$318$		0			0
$319$	6.08650			0.340778
$320$	−14.8766	−	8.40388i	−0.831629	−	0.469791i
$321$	16.4924	−	6.08650i	0.920517	−	0.339715i
$322$	−4.63068	−	9.89012i	−0.258058	−	0.551155i
$323$		−	37.6155i		−	2.09298i
$324$	11.8576	+	13.5424i	0.658758	+	0.752355i
$325$	−0.684658	−	1.42489i	−0.0379780	−	0.0790386i
$326$	7.92460	+	16.9252i	0.438903	+	0.937400i
$327$	4.99211	+	13.5270i	0.276064	+	0.748044i
$328$	−15.6847	−	4.12391i	−0.866040	−	0.227705i
$329$			8.64992i			0.476885i
$330$	−7.35373	+	7.44311i	−0.404809	+	0.409730i
$331$	−5.41935			−0.297874			−0.148937	−	0.988847i	$-0.547585\pi$
$331$	−5.41935			−0.297874			−0.148937	+	0.988847i	$0.547585\pi$
$332$	−9.21662	−	7.68466i	−0.505828	−	0.421750i
$333$	3.55660	+	4.16234i	0.194901	+	0.228095i
$334$	22.2462	−	10.4160i	1.21726	−	0.569936i
$335$	−18.0742			−0.987501
$336$	−5.36874	−	9.07265i	−0.292889	−	0.494954i
$337$	−9.68466			−0.527557			−0.263778	−	0.964583i	$-0.584969\pi$
$337$	−9.68466			−0.527557			−0.263778	+	0.964583i	$0.584969\pi$
$338$	−17.8707	−	4.31738i	−0.972035	−	0.234835i
$339$	−6.49971	−	17.6121i	−0.353016	−	0.956557i
$340$	22.7718	+	18.9867i	1.23497	+	1.02970i
$341$			10.8387i			0.586948i
$342$	−20.9392	−	9.49729i	−1.13226	−	0.513555i
$343$	17.7797			0.960012
$344$	2.20960	−	8.40388i	0.119134	−	0.453107i
$345$	17.6121	−	6.49971i	0.948203	−	0.349933i
$346$	9.98422	−	4.67474i	0.536755	−	0.251316i
$347$	19.8992			1.06825			0.534123	−	0.845407i	$-0.320642\pi$
$347$	19.8992			1.06825			0.534123	+	0.845407i	$0.320642\pi$
$348$	−9.93349	−	3.53018i	−0.532491	−	0.189238i
$349$			1.82496i			0.0976881i	0.998806	+	0.0488441i	$0.0155537\pi$
$349$			1.82496i			0.0976881i	−0.998806	+	0.0488441i	$0.984446\pi$
$350$	0.400075	+	0.854473i	0.0213849	+	0.0456735i
$351$	−18.6987	−	1.16537i	−0.998064	−	0.0622030i
$352$	6.56155	+	9.21662i	0.349732	+	0.491247i
$353$	−26.5658			−1.41395			−0.706977	−	0.707237i	$-0.749942\pi$
$353$	−26.5658			−1.41395			−0.706977	+	0.707237i	$0.749942\pi$
$354$	19.1491	−	19.3818i	1.01776	−	1.03013i
$355$			4.94506i			0.262456i
$356$	14.5399	−	17.4384i	0.770612	−	0.924236i
$357$	6.33351	+	17.1618i	0.335205	+	0.908296i
$358$	−1.09439	−	2.33737i	−0.0578402	−	0.123534i
$359$		−	11.1231i		−	0.587055i	−0.955951	−	0.293528i	$-0.905171\pi$
$359$		−	11.1231i		−	0.587055i	0.955951	−	0.293528i	$-0.0948292\pi$
$360$	16.3187	−	7.88238i	0.860071	−	0.415438i
$361$	10.3693			0.545754
$362$	11.6153	+	24.8078i	0.610488	+	1.30387i
$363$	−11.3745	+	4.19773i	−0.597006	+	0.220324i
$364$	10.6394	+	2.68358i	0.557654	+	0.140658i
$365$			21.6774i			1.13465i
$366$	8.92692	+	8.81972i	0.466618	+	0.461014i
$367$			21.8836i			1.14232i	0.820840	+	0.571158i	$0.193506\pi$
$367$			21.8836i			1.14232i	−0.820840	+	0.571158i	$0.806494\pi$
$368$	−3.64993	−	19.9684i	−0.190266	−	1.04093i
$369$	13.0776	−	11.1745i	0.680793	−	0.581719i
$370$	4.99211	−	2.33737i	0.259527	−	0.121514i
$371$		0			0
$372$	6.28646	−	17.6893i	0.325938	−	0.917149i
$373$	−0.876894			−0.0454039			−0.0227019	−	0.999742i	$-0.507227\pi$
$373$	−0.876894			−0.0454039			−0.0227019	+	0.999742i	$0.507227\pi$
$374$	−8.32467	−	17.7797i	−0.430459	−	0.919365i
$375$	−18.8741	+	6.96543i	−0.974652	+	0.359694i
$376$	−4.08854	+	15.5501i	−0.210850	+	0.801937i
$377$	9.89012	−	4.75219i	0.509367	−	0.244750i
$378$	11.1524	+	0.807421i	0.573619	+	0.0415292i
$379$	8.46260			0.434694			0.217347	−	0.976094i	$-0.430260\pi$
$379$	8.46260			0.434694			0.217347	+	0.976094i	$0.430260\pi$
$380$	−14.8244	+	17.7797i	−0.760475	+	0.912078i
$381$	−4.00000	−	10.8387i	−0.204926	−	0.555283i
$382$	−6.94097	−	14.8244i	−0.355131	−	0.758481i
$383$			19.4384i			0.993258i	0.867963	+	0.496629i	$0.165429\pi$
$383$			19.4384i			0.993258i	−0.867963	+	0.496629i	$0.834571\pi$
$384$	−5.36315	−	18.8477i	−0.273687	−	0.961819i
$385$			6.49971i			0.331256i
$386$	−24.9740	+	11.6932i	−1.27114	+	0.595166i
$387$	5.98730	+	7.00701i	0.304352	+	0.356187i
$388$	−25.5751	−	21.3241i	−1.29838	−	1.08257i
$389$			32.5161i			1.64863i	0.566131	+	0.824315i	$0.308440\pi$
$389$			32.5161i			1.64863i	−0.566131	+	0.824315i	$0.691560\pi$
$390$	−6.13787	+	17.8361i	−0.310803	+	0.903168i
$391$			35.2242i			1.78136i
$392$	12.8147	+	3.36932i	0.647239	+	0.170176i
$393$	−2.96543	+	1.09439i	−0.149586	+	0.0552046i
$394$	4.96543	+	10.6051i	0.250155	+	0.534276i
$395$			19.3693i			0.974576i
$396$	−11.9991	+	0.144972i	−0.602979	+	0.00728513i
$397$		−	3.64993i		−	0.183185i	−0.995797	−	0.0915924i	$-0.970804\pi$
$397$		−	3.64993i		−	0.183185i	0.995797	−	0.0915924i	$-0.0291957\pi$
$398$	−7.19612	+	3.36932i	−0.360709	+	0.168889i
$399$	−13.3995	+	4.94506i	−0.670814	+	0.247563i
$400$	0.315342	+	1.72521i	0.0157671	+	0.0862603i
$401$	15.8545			0.791737			0.395868	−	0.918307i	$-0.370444\pi$
$401$	15.8545			0.791737			0.395868	+	0.918307i	$0.370444\pi$
$402$	−14.7459	−	14.5688i	−0.735460	−	0.726628i
$403$	8.46260	+	17.6121i	0.421552	+	0.877321i
$404$	−9.34949	−	7.79544i	−0.465154	−	0.387838i
$405$	−2.99838	+	18.9867i	−0.148991	+	0.943458i
$406$	−5.93087	+	2.77691i	−0.294344	+	0.137816i
$407$	−3.64993			−0.180920
$408$	3.27407	+	33.8457i	0.162091	+	1.67561i
$409$			2.84978i			0.140912i	0.997515	+	0.0704562i	$0.0224455\pi$
$409$			2.84978i			0.140912i	−0.997515	+	0.0704562i	$0.977554\pi$
$410$	−7.34376	−	15.6847i	−0.362683	−	0.774610i
$411$	−14.5491	+	5.36932i	−0.717654	+	0.264849i
$412$	−29.9309	−	24.9559i	−1.47459	−	1.22949i
$413$		−	16.9252i		−	0.832834i
$414$	19.6080	+	8.89351i	0.963681	+	0.437092i
$415$		−	12.8147i		−	0.629048i
$416$	17.8582	+	9.85323i	0.875568	+	0.483094i
$417$	4.08854	+	11.0786i	0.200217	+	0.542522i
$418$	13.8819	−	6.49971i	0.678988	−	0.317911i
$419$	35.1237			1.71590			0.857951	−	0.513731i	$-0.171737\pi$
$419$	35.1237			1.71590			0.857951	+	0.513731i	$0.171737\pi$
$420$	3.76984	−	10.6079i	0.183950	−	0.517611i
$421$		−	8.32467i		−	0.405720i	−0.979208	−	0.202860i	$-0.934976\pi$
$421$		−	8.32467i		−	0.405720i	0.979208	−	0.202860i	$-0.0650236\pi$
$422$	−1.53610	+	0.719224i	−0.0747763	+	0.0350113i
$423$	−11.0786	−	12.9654i	−0.538660	−	0.630401i
$424$		0			0
$425$		−	3.04325i		−	0.147619i
$426$	−3.98599	+	4.03444i	−0.193122	+	0.195469i
$427$	7.79544			0.377248
$428$	12.9994	−	15.5909i	0.628351	−	0.753614i
$429$	8.68870	−	8.97254i	0.419494	−	0.433198i
$430$	8.40388	−	3.93481i	0.405271	−	0.189753i
$431$			9.19224i			0.442774i	0.975186	+	0.221387i	$0.0710585\pi$
$431$			9.19224i			0.442774i	−0.975186	+	0.221387i	$0.928942\pi$
$432$	19.6673	+	6.72291i	0.946243	+	0.323456i
$433$	36.1771			1.73856			0.869280	−	0.494320i	$-0.164583\pi$
$433$	36.1771			1.73856			0.869280	+	0.494320i	$0.164583\pi$
$434$	−4.94506	−	10.5616i	−0.237370	−	0.506971i
$435$	−3.89772	−	10.5616i	−0.186881	−	0.506388i
$436$	12.7876	+	10.6620i	0.612413	+	0.510619i
$437$	−27.5022			−1.31561
$438$	−17.4732	+	17.6856i	−0.834901	+	0.845049i
$439$		−	25.6294i		−	1.22322i	−0.791159	−	0.611611i	$-0.790522\pi$
$439$		−	25.6294i		−	1.22322i	0.791159	−	0.611611i	$-0.209478\pi$
$440$	−3.07221	+	11.6847i	−0.146462	+	0.557044i
$441$	−10.6847	+	9.12975i	−0.508793	+	0.434750i
$442$	−27.4089	−	22.3910i	−1.30371	−	1.06503i
$443$	1.82496			0.0867067			0.0433533	−	0.999060i	$-0.486196\pi$
$443$	1.82496			0.0867067			0.0433533	+	0.999060i	$0.486196\pi$
$444$	5.95688	+	2.11697i	0.282701	+	0.100467i
$445$	24.2462			1.14938
$446$	−17.5618	−	37.5082i	−0.831577	−	1.77606i
$447$	0.667152	−	0.246211i	0.0315552	−	0.0116454i
$448$	−10.5988	−	5.98730i	−0.500745	−	0.282873i
$449$	−14.2770			−0.673771			−0.336886	−	0.941546i	$-0.609374\pi$
$449$	−14.2770			−0.673771			−0.336886	+	0.941546i	$0.609374\pi$
$450$	−1.69406	−	0.768369i	−0.0798590	−	0.0362213i
$451$			11.4677i			0.539992i
$452$	−16.6493	−	13.8819i	−0.783119	−	0.652952i
$453$	−27.8066	+	10.2620i	−1.30647	+	0.482149i
$454$	9.93087	−	4.64976i	0.466079	−	0.218224i
$455$	5.07482	+	10.5616i	0.237911	+	0.495133i
$456$	−26.4259	+	2.55632i	−1.23751	+	0.119711i
$457$		−	6.49971i		−	0.304044i	−0.988377	−	0.152022i	$-0.951422\pi$
$457$		−	6.49971i		−	0.304044i	0.988377	−	0.152022i	$-0.0485784\pi$
$458$	35.6361	−	16.6853i	1.66516	−	0.779652i
$459$	−31.4737	−	17.6121i	−1.46907	−	0.822062i
$460$	13.8819	−	16.6493i	0.647249	−	0.776280i
$461$	−25.0711			−1.16768			−0.583839	−	0.811869i	$-0.698450\pi$
$461$	−25.0711			−1.16768			−0.583839	+	0.811869i	$0.698450\pi$
$462$	−5.23913	+	5.30281i	−0.243746	+	0.246709i
$463$	−27.0967			−1.25929			−0.629646	−	0.776882i	$-0.716800\pi$
$463$	−27.0967			−1.25929			−0.629646	+	0.776882i	$0.716800\pi$
$464$	−11.9746	+	2.18878i	−0.555907	+	0.101611i
$465$	18.8078	−	6.94097i	0.872189	−	0.321880i
$466$	14.9763	−	7.01212i	0.693765	−	0.324830i
$467$	−10.7744			−0.498579			−0.249289	−	0.968429i	$-0.580197\pi$
$467$	−10.7744			−0.498579			−0.249289	+	0.968429i	$0.580197\pi$
$468$	−19.3845	+	9.60420i	−0.896049	+	0.443954i
$469$	−12.8769			−0.594600
$470$	−15.5501	+	7.28078i	−0.717274	+	0.335837i
$471$	−10.1496	+	3.74571i	−0.467671	+	0.172593i
$472$	8.00000	−	30.4268i	0.368230	−	1.40051i
$473$	−6.14441			−0.282520
$474$	−15.6127	+	15.8025i	−0.717117	+	0.725834i
$475$	2.37610			0.109023
$476$	16.2236	+	13.5270i	0.743609	+	0.620008i
$477$		0			0
$478$	−25.5270	+	11.9521i	−1.16758	+	0.546675i
$479$			7.43845i			0.339871i	0.985455	+	0.169936i	$0.0543560\pi$
$479$			7.43845i			0.339871i	−0.985455	+	0.169936i	$0.945644\pi$
$480$	11.7911	−	17.2881i	0.538189	−	0.789090i
$481$	−5.93087	+	2.84978i	−0.270424	+	0.129939i
$482$	4.67474	−	2.18878i	0.212929	−	0.0996960i
$483$	12.5476	−	4.63068i	0.570937	−	0.210703i
$484$	−8.96543	+	10.7527i	−0.407520	+	0.488760i
$485$		−	35.5593i		−	1.61467i
$486$	−17.7506	+	13.0735i	−0.805183	+	0.593026i
$487$	−5.41935			−0.245574			−0.122787	−	0.992433i	$-0.539183\pi$
$487$	−5.41935			−0.245574			−0.122787	+	0.992433i	$0.539183\pi$
$488$	14.0140	+	3.68466i	0.634385	+	0.166797i
$489$	−21.4731	+	7.92460i	−0.971046	+	0.358363i
$490$	6.00000	+	12.8147i	0.271052	+	0.578908i
$491$	22.7490			1.02665			0.513324	−	0.858195i	$-0.328414\pi$
$491$	22.7490			1.02665			0.513324	+	0.858195i	$0.328414\pi$
$492$	6.65127	−	18.7159i	0.299863	−	0.843776i
$493$	21.1231			0.951337
$494$	17.4823	−	21.4002i	0.786567	−	0.962843i
$495$	−8.32467	−	9.74247i	−0.374166	−	0.437891i
$496$	−3.89772	−	21.3241i	−0.175013	−	0.957480i
$497$			3.52308i			0.158032i
$498$	10.3293	−	10.4549i	0.462869	−	0.468495i
$499$	5.41935			0.242603			0.121302	−	0.992616i	$-0.461293\pi$
$499$	5.41935			0.242603			0.121302	+	0.992616i	$0.461293\pi$
$500$	−14.8766	+	17.8423i	−0.665303	+	0.797933i
$501$	10.4160	+	28.2239i	0.465351	+	1.26095i
$502$	−10.8387	−	23.1491i	−0.483755	−	1.03319i
$503$	−22.3489			−0.996488			−0.498244	−	0.867037i	$-0.666022\pi$
$503$	−22.3489			−0.996488			−0.498244	+	0.867037i	$0.666022\pi$
$504$	11.6262	−	5.61576i	0.517871	−	0.250146i
$505$		−	12.9994i		−	0.578466i
$506$	−12.9994	+	6.08650i	−0.577895	+	0.270578i
$507$	7.11296	−	21.3637i	0.315897	−	0.948793i
$508$	−10.2462	−	8.54312i	−0.454602	−	0.379040i
$509$	32.9407			1.46007			0.730036	−	0.683408i	$-0.239503\pi$
$509$	32.9407			1.46007			0.730036	+	0.683408i	$0.239503\pi$
$510$	−25.5210	+	25.8312i	−1.13009	+	1.14383i
$511$			15.4439i			0.683200i
$512$	−16.2236	−	15.7732i	−0.716990	−	0.697083i
$513$	13.7511	−	24.5739i	0.607126	−	1.08497i
$514$	2.80333	−	1.31256i	0.123650	−	0.0578944i
$515$		−	41.6155i		−	1.83380i
$516$	10.0280	+	3.56377i	0.441458	+	0.156886i
$517$	11.3693			0.500022
$518$	3.55660	−	1.66525i	0.156268	−	0.0731668i
$519$	4.67474	+	12.6670i	0.205198	+	0.556021i
$520$	4.13100	+	21.3854i	0.181156	+	0.937813i
$521$			14.7364i			0.645614i	0.946465	+	0.322807i	$0.104626\pi$
$521$			14.7364i			0.645614i	−0.946465	+	0.322807i	$0.895374\pi$
$522$	5.33323	−	11.7585i	0.233429	−	0.514654i
$523$		−	19.4849i		−	0.852017i	−0.904719	−	0.426008i	$-0.859919\pi$
$523$		−	19.4849i		−	0.852017i	0.904719	−	0.426008i	$-0.140081\pi$
$524$	−2.33737	+	2.80333i	−0.102109	+	0.122464i
$525$	−1.08407	+	0.400075i	−0.0473128	+	0.0174607i
$526$	2.18878	+	4.67474i	0.0954352	+	0.203829i
$527$			37.6155i			1.63856i
$528$	−11.9250	+	7.05660i	−0.518967	+	0.307099i
$529$	2.75379			0.119730
$530$		0			0
$531$	21.6774	+	25.3693i	0.940718	+	1.10093i
$532$	−10.5616	+	12.6670i	−0.457901	+	0.549185i
$533$	8.95369	+	18.6341i	0.387827	+	0.807134i
$534$	19.7813	+	19.5438i	0.856022	+	0.845743i
$535$	21.6774			0.937195
$536$	−23.1491	−	6.08650i	−0.999887	−	0.262897i
$537$	2.96543	−	1.09439i	0.127968	−	0.0472263i
$538$	23.8662	−	11.1745i	1.02894	−	0.481765i
$539$		−	9.36932i		−	0.403565i
$540$	7.93566	+	20.7286i	0.341496	+	0.892015i
$541$			21.3241i			0.916794i	0.888747	+	0.458397i	$0.151576\pi$
$541$			21.3241i			0.916794i	−0.888747	+	0.458397i	$0.848424\pi$
$542$	4.56241	+	9.74430i	0.195972	+	0.418554i
$543$	−31.4737	+	11.6153i	−1.35067	+	0.498461i
$544$	22.7718	+	31.9861i	0.976332	+	1.37139i
$545$			17.7797i			0.761597i
$546$	−4.37289	+	12.7073i	−0.187142	+	0.543821i
$547$		−	24.6606i		−	1.05441i	−0.849738	−	0.527205i	$-0.823240\pi$
$547$		−	24.6606i		−	1.05441i	0.849738	−	0.527205i	$-0.176760\pi$
$548$	−11.4677	+	13.7538i	−0.489875	+	0.587533i
$549$	−11.6847	+	9.98422i	−0.498689	+	0.426116i
$550$	1.12311	−	0.525853i	0.0478894	−	0.0224224i
$551$			16.4924i			0.702601i
$552$	24.7459	−	2.39380i	1.05326	−	0.101887i
$553$			13.7996i			0.586817i
$554$	−2.25106	−	4.80776i	−0.0956383	−	0.204262i
$555$	2.33737	+	6.33351i	0.0992159	+	0.268843i
$556$	10.4730	+	8.73222i	0.444155	+	0.370329i
$557$	18.4009			0.779670			0.389835	−	0.920885i	$-0.372532\pi$
$557$	18.4009			0.779670			0.389835	+	0.920885i	$0.372532\pi$
$558$	20.9392	+	9.49729i	0.886426	+	0.402052i
$559$	−9.98422	+	4.79741i	−0.422288	+	0.202909i
$560$	−2.33737	−	12.7876i	−0.0987720	−	0.540373i
$561$	22.5571	−	8.32467i	0.952363	−	0.351468i
$562$	10.3153	+	22.0313i	0.435126	+	0.929334i
$563$	−11.1745			−0.470947			−0.235474	−	0.971881i	$-0.575664\pi$
$563$	−11.1745			−0.470947			−0.235474	+	0.971881i	$0.575664\pi$
$564$	−18.5553	−	6.59422i	−0.781320	−	0.277667i
$565$		−	23.1491i		−	0.973888i
$566$	21.2101	−	9.93087i	0.891529	−	0.417426i
$567$	−2.13618	+	13.5270i	−0.0897112	+	0.568080i
$568$	−1.66525	+	6.33351i	−0.0698723	+	0.265748i
$569$		−	2.18878i		−	0.0917583i	−0.998947	−	0.0458791i	$-0.985391\pi$
$569$		−	2.18878i		−	0.0917583i	0.998947	−	0.0458791i	$-0.0146089\pi$
$570$	−20.1684	−	19.9262i	−0.844762	−	0.834617i
$571$			22.0313i			0.921981i	0.887405	+	0.460990i	$0.152506\pi$
$571$			22.0313i			0.921981i	−0.887405	+	0.460990i	$0.847494\pi$
$572$	3.52726	−	13.9842i	0.147482	−	0.584710i
$573$	18.8078	−	6.94097i	0.785706	−	0.289963i
$574$	−5.23203	−	11.1745i	−0.218381	−	0.466413i
$575$	−2.22504			−0.0927906
$576$	23.5550	−	4.60025i	0.981458	−	0.191677i
$577$			23.1491i			0.963708i	0.876252	+	0.481854i	$0.160036\pi$
$577$			23.1491i			0.963708i	−0.876252	+	0.481854i	$0.839964\pi$
$578$	−18.6962	−	39.9309i	−0.777658	−	1.66091i
$579$	−11.6932	−	31.6847i	−0.485951	−	1.31677i
$580$	−9.98422	−	8.32467i	−0.414572	−	0.345663i
$581$		−	9.12975i		−	0.378766i
$582$	28.6628	−	29.0112i	1.18811	−	1.20255i
$583$		0			0
$584$	−7.29986	+	27.7639i	−0.302070	+	1.14888i
$585$	−21.1337	−	9.33109i	−0.873770	−	0.385793i
$586$	−1.59612	−	3.40896i	−0.0659350	−	0.140823i
$587$		−	15.6155i		−	0.644522i	−0.946651	−	0.322261i	$-0.895557\pi$
$587$		−	15.6155i		−	0.644522i	0.946651	−	0.322261i	$-0.104443\pi$
$588$	−5.43422	+	15.2912i	−0.224104	+	0.630599i
$589$	−29.3693			−1.21014
$590$	30.4268	−	14.2462i	1.25265	−	0.586507i
$591$	−13.4547	+	4.96543i	−0.553453	+	0.204251i
$592$	7.18089	−	1.31256i	0.295133	−	0.0539458i
$593$	31.3632			1.28793			0.643966	−	0.765054i	$-0.277288\pi$
$593$	31.3632			1.28793			0.643966	+	0.765054i	$0.277288\pi$
$594$	1.06126	−	14.6586i	0.0435441	−	0.601448i
$595$			22.5571i			0.924753i
$596$	0.525853	−	0.630683i	0.0215398	−	0.0258338i
$597$	−3.36932	−	9.12975i	−0.137897	−	0.373656i
$598$	−16.3709	+	20.0398i	−0.669456	+	0.819487i
$599$	33.2987			1.36055			0.680274	−	0.732958i	$-0.261861\pi$
$599$	33.2987			1.36055			0.680274	+	0.732958i	$0.261861\pi$
$600$	−2.13796	+	0.206817i	−0.0872820	+	0.00844325i
$601$	2.80776			0.114531			0.0572655	−	0.998359i	$-0.481762\pi$
$601$	2.80776			0.114531			0.0572655	+	0.998359i	$0.481762\pi$
$602$	5.98730	−	2.80333i	0.244024	−	0.114255i
$603$	19.3013	−	16.4924i	0.786009	−	0.671623i
$604$	−21.9173	+	26.2866i	−0.891802	+	1.06959i
$605$	−14.9505			−0.607822
$606$	10.4783	−	10.6056i	0.425650	−	0.430824i
$607$		−	13.3405i		−	0.541475i	−0.962653	−	0.270738i	$-0.912732\pi$
$607$		−	13.3405i		−	0.541475i	0.962653	−	0.270738i	$-0.0872676\pi$
$608$	−24.9740	+	17.7797i	−1.01283	+	0.721061i
$609$	−2.77691	−	7.52452i	−0.112526	−	0.304909i
$610$	6.56155	+	14.0140i	0.265670	+	0.567411i
$611$	18.4743	−	8.87689i	0.747391	−	0.359121i
$612$	−41.6428	+	0.503124i	−1.68331	+	0.0203376i
$613$		−	6.49971i		−	0.262521i	−0.991348	−	0.131260i	$-0.958098\pi$
$613$		−	6.49971i		−	0.262521i	0.991348	−	0.131260i	$-0.0419024\pi$
$614$	1.42489	+	3.04325i	0.0575039	+	0.122816i
$615$	19.8992	−	7.34376i	0.802413	−	0.296129i
$616$	−2.18878	+	8.32467i	−0.0881883	+	0.335411i
$617$	−18.5485			−0.746735			−0.373368	−	0.927684i	$-0.621797\pi$
$617$	−18.5485			−0.746735			−0.373368	+	0.927684i	$0.621797\pi$
$618$	33.5444	−	33.9522i	1.34935	−	1.36576i
$619$	−4.08504			−0.164192			−0.0820959	−	0.996624i	$-0.526161\pi$
$619$	−4.08504			−0.164192			−0.0820959	+	0.996624i	$0.526161\pi$
$620$	14.8244	−	17.7797i	0.595362	−	0.714048i
$621$	−12.8769	+	23.0117i	−0.516732	+	0.923427i
$622$	14.7364	+	31.4737i	0.590876	+	1.26198i
$623$	17.2741			0.692072
$624$	−13.8676	+	20.7772i	−0.555146	+	0.831753i
$625$	−22.6155			−0.904621
$626$	4.46066	+	9.52699i	0.178284	+	0.380775i
$627$	6.49971	+	17.6121i	0.259573	+	0.703359i
$628$	−8.00000	+	9.59482i	−0.319235	+	0.382875i
$629$	−12.6670			−0.505067
$630$	12.5567	+	5.69530i	0.500272	+	0.226906i
$631$	−30.9945			−1.23387			−0.616935	−	0.787014i	$-0.711626\pi$
$631$	−30.9945			−1.23387			−0.616935	+	0.787014i	$0.711626\pi$
$632$	−6.52262	+	24.8078i	−0.259456	+	0.986800i
$633$	−0.719224	−	1.94886i	−0.0285866	−	0.0774603i
$634$	0.246211	+	0.525853i	0.00977830	+	0.0208843i
$635$		−	14.2462i		−	0.565344i
$636$		0			0
$637$	−7.31534	−	15.2245i	−0.289844	−	0.603215i
$638$	3.64993	+	7.79544i	0.144502	+	0.308625i
$639$	−4.51228	−	5.28078i	−0.178503	−	0.208904i
$640$	1.84233	−	24.0932i	0.0728245	−	0.952369i
$641$		−	1.33430i		−	0.0527018i	−0.999653	−	0.0263509i	$-0.991611\pi$
$641$		−	1.33430i		−	0.0527018i	0.999653	−	0.0263509i	$-0.00838873\pi$
$642$	17.6856	+	17.4732i	0.697993	+	0.689611i
$643$	1.04179			0.0410843			0.0205422	−	0.999789i	$-0.493461\pi$
$643$	1.04179			0.0410843			0.0205422	+	0.999789i	$0.493461\pi$
$644$	9.89012	−	11.8617i	0.389725	−	0.467418i
$645$	3.93481	+	10.6620i	0.154933	+	0.419818i
$646$	48.1771	−	22.5571i	1.89550	−	0.887499i
$647$	−33.2987			−1.30911			−0.654553	−	0.756016i	$-0.727143\pi$
$647$	−33.2987			−1.30911			−0.654553	+	0.756016i	$0.727143\pi$
$648$	−10.2340	+	23.3080i	−0.402031	+	0.915626i
$649$	−22.2462			−0.873240
$650$	1.41439	−	1.73137i	0.0554770	−	0.0679098i
$651$	13.3995	−	4.94506i	0.525168	−	0.193812i
$652$	−16.9252	+	20.2993i	−0.662842	+	0.794981i
$653$			26.4296i			1.03427i	0.855904	+	0.517135i	$0.173001\pi$
$653$			26.4296i			1.03427i	−0.855904	+	0.517135i	$0.826999\pi$
$654$	−14.3314	+	14.5056i	−0.560402	+	0.567214i
$655$	−3.89772			−0.152297
$656$	−4.12391	−	22.5616i	−0.161012	−	0.880881i
$657$	−19.7802	−	23.1491i	−0.771700	−	0.903131i
$658$	−11.0786	+	5.18715i	−0.431889	+	0.202216i
$659$	23.7738			0.926096			0.463048	−	0.886333i	$-0.346756\pi$
$659$	23.7738			0.926096			0.463048	+	0.886333i	$0.346756\pi$
$660$	−13.9428	−	4.95502i	−0.542724	−	0.192874i
$661$		−	29.6488i		−	1.15320i	−0.817025	−	0.576602i	$-0.804378\pi$
$661$		−	29.6488i		−	1.15320i	0.817025	−	0.576602i	$-0.195622\pi$
$662$	−3.24985	−	6.94097i	−0.126309	−	0.269769i
$663$	30.1540	−	31.1391i	1.17108	−	1.20934i
$664$	4.31534	−	16.4127i	0.167468	−	0.636938i
$665$	−17.6121			−0.682967
$666$	−3.19821	+	7.05127i	−0.123928	+	0.273231i
$667$		−	15.4439i		−	0.597992i
$668$	26.6811	+	22.2462i	1.03232	+	0.860732i
$669$	47.5868	−	17.5618i	1.83981	−	0.678980i
$670$	−10.8387	−	23.1491i	−0.418735	−	0.894326i
$671$		−	10.2462i		−	0.395551i
$672$	8.40053	−	12.3168i	0.324057	−	0.475131i
$673$	−11.6847			−0.450410			−0.225205	−	0.974311i	$-0.572305\pi$
$673$	−11.6847			−0.450410			−0.225205	+	0.974311i	$0.572305\pi$
$674$	−5.80766	−	12.4039i	−0.223703	−	0.477780i
$675$	1.11252	−	1.98813i	0.0428209	−	0.0765232i
$676$	−5.18701	−	25.4773i	−0.199500	−	0.979898i
$677$		−	29.4728i		−	1.13273i	−0.824154	−	0.566366i	$-0.808349\pi$
$677$		−	29.4728i		−	1.13273i	0.824154	−	0.566366i	$-0.191651\pi$
$678$	18.6594	−	18.8862i	0.716611	−	0.725321i
$679$		−	25.3341i		−	0.972232i
$680$	−10.6620	+	40.5514i	−0.408871	+	1.55508i
$681$	4.64976	+	12.5993i	0.178179	+	0.482808i
$682$	−13.8819	+	6.49971i	−0.531567	+	0.248887i
$683$			38.9848i			1.49171i	0.666106	+	0.745857i	$0.267960\pi$
$683$			38.9848i			1.49171i	−0.666106	+	0.745857i	$0.732040\pi$
$684$	−0.392827	−	32.5137i	−0.0150201	−	1.24319i
$685$	−19.1231			−0.730656
$686$	10.6620	+	22.7718i	0.407079	+	0.869430i
$687$	16.6853	+	45.2116i	0.636583	+	1.72493i
$688$	12.0885	−	2.20960i	0.460871	−	0.0842403i
$689$		0			0
$690$	18.8862	+	18.6594i	0.718986	+	0.710352i
$691$	31.4743			1.19734			0.598669	−	0.800996i	$-0.295696\pi$
$691$	31.4743			1.19734			0.598669	+	0.800996i	$0.295696\pi$
$692$	11.9746	+	9.98422i	0.455206	+	0.379543i
$693$	−5.93087	−	6.94097i	−0.225295	−	0.263666i
$694$	11.9331	+	25.4864i	0.452974	+	0.967452i
$695$			14.5616i			0.552351i
$696$	−1.43551	−	14.8395i	−0.0544128	−	0.562492i
$697$			39.7984i			1.50747i
$698$	−2.33737	+	1.09439i	−0.0884708	+	0.0414232i
$699$	7.01212	+	19.0005i	0.265223	+	0.718667i
$700$	−0.854473	+	1.02481i	−0.0322960	+	0.0387343i
$701$		−	26.4296i		−	0.998231i	−0.866535	−	0.499116i	$-0.833658\pi$
$701$		−	26.4296i		−	0.998231i	0.866535	−	0.499116i	$-0.166342\pi$
$702$	−9.72059	−	24.6477i	−0.366880	−	0.930268i
$703$		−	9.89012i		−	0.373013i
$704$	−7.86962	+	13.9309i	−0.296597	+	0.525039i
$705$	−7.28078	−	19.7285i	−0.274210	−	0.743019i
$706$	−15.9309	−	34.0248i	−0.599566	−	1.28054i
$707$		−	9.26137i		−	0.348310i
$708$	36.3070	+	12.9028i	1.36450	+	0.484919i
$709$			23.9492i			0.899431i	0.893172	+	0.449716i	$0.148475\pi$
$709$			23.9492i			0.899431i	−0.893172	+	0.449716i	$0.851525\pi$
$710$	−6.33351	+	2.96543i	−0.237693	+	0.111291i
$711$	−17.6742	−	20.6843i	−0.662833	−	0.775722i
$712$	31.0540	+	8.16491i	1.16380	+	0.305993i
$713$	27.5022			1.02997
$714$	−18.1823	+	18.4033i	−0.680456	+	0.688727i
$715$	13.8819	−	6.67026i	0.519155	−	0.249454i
$716$	2.33737	−	2.80333i	0.0873517	−	0.104765i
$717$	−11.9521	−	32.3862i	−0.446358	−	1.20949i
$718$	14.2462	−	6.67026i	0.531664	−	0.248932i
$719$	31.0737			1.15885			0.579426	−	0.815025i	$-0.303277\pi$
$719$	31.0737			1.15885			0.579426	+	0.815025i	$0.303277\pi$
$720$	19.8815	+	16.1737i	0.740940	+	0.602759i
$721$		−	29.6488i		−	1.10418i
$722$	6.21823	+	13.2808i	0.231419	+	0.494259i
$723$	2.18878	+	5.93087i	0.0814015	+	0.220571i
$724$	−24.8078	+	29.7533i	−0.921973	+	1.10577i
$725$			1.33430i			0.0495548i
$726$	−12.1974	−	12.0509i	−0.452687	−	0.447251i
$727$			5.32326i			0.197429i	0.995116	+	0.0987145i	$0.0314730\pi$
$727$			5.32326i			0.197429i	−0.995116	+	0.0987145i	$0.968527\pi$
$728$	2.94311	+	15.2359i	0.109079	+	0.564681i
$729$	−14.1231	−	23.0117i	−0.523078	−	0.852285i
$730$	−27.7639	+	12.9994i	−1.02759	+	0.481130i
$731$	−21.3241			−0.788700
$732$	−5.94282	+	16.7224i	−0.219653	+	0.618076i
$733$			5.47489i			0.202220i	0.994875	+	0.101110i	$0.0322394\pi$
$733$			5.47489i			0.202220i	−0.994875	+	0.101110i	$0.967761\pi$
$734$	−28.0281	+	13.1231i	−1.03453	+	0.484383i
$735$	−16.2580	+	6.00000i	−0.599687	+	0.221313i
$736$	23.3863	−	16.6493i	0.862032	−	0.613703i
$737$			16.9252i			0.623447i
$738$	22.1543	+	10.0484i	0.815511	+	0.369888i
$739$	−23.6788			−0.871040			−0.435520	−	0.900179i	$-0.643436\pi$
$739$	−23.6788			−0.871040			−0.435520	+	0.900179i	$0.643436\pi$
$740$	5.98730	+	4.99211i	0.220098	+	0.183514i
$741$	24.3127	+	23.5435i	0.893148	+	0.864893i
$742$		0			0
$743$		−	12.5616i		−	0.460839i	−0.973091	−	0.230419i	$-0.925990\pi$
$743$		−	12.5616i		−	0.460839i	0.973091	−	0.230419i	$-0.0740098\pi$
$744$	26.4259	−	2.55632i	0.968821	−	0.0937192i
$745$	0.876894			0.0321269
$746$	−0.525853	−	1.12311i	−0.0192528	−	0.0411198i
$747$	11.6932	+	13.6847i	0.427831	+	0.500695i
$748$	17.7797	−	21.3241i	0.650089	−	0.779686i
$749$	15.4439			0.564309
$750$	−20.2395	−	19.9964i	−0.739042	−	0.730167i
$751$		−	38.6746i		−	1.41126i	−0.708583	−	0.705628i	$-0.750665\pi$
$751$		−	38.6746i		−	1.41126i	0.708583	−	0.705628i	$-0.249335\pi$
$752$	−22.3680	+	4.08854i	−0.815679	+	0.149094i
$753$	29.3693	−	10.8387i	1.07028	−	0.394984i
$754$	12.0174	+	9.81725i	0.437647	+	0.357523i
$755$	−36.5485			−1.33014
$756$	5.65372	+	14.7680i	0.205624	+	0.537105i
$757$	−4.49242			−0.163280			−0.0816399	−	0.996662i	$-0.526016\pi$
$757$	−4.49242			−0.163280			−0.0816399	+	0.996662i	$0.526016\pi$
$758$	5.07482	+	10.8387i	0.184326	+	0.393679i
$759$	−6.08650	−	16.4924i	−0.220926	−	0.598637i
$760$	−31.6616	−	8.32467i	−1.14849	−	0.301968i
$761$	−23.3459			−0.846289			−0.423145	−	0.906062i	$-0.639074\pi$
$761$	−23.3459			−0.846289			−0.423145	+	0.906062i	$0.639074\pi$
$762$	11.4832	−	11.6228i	0.415994	−	0.421050i
$763$			12.6670i			0.458577i
$764$	14.8244	−	17.7797i	0.536327	−	0.643246i
$765$	−28.8907	−	33.8111i	−1.04454	−	1.22244i
$766$	−24.8963	+	11.6568i	−0.899540	+	0.421177i
$767$	−36.1485	+	17.3693i	−1.30525	+	0.627170i
$768$	20.9236	−	18.1715i	0.755014	−	0.655709i
$769$			28.8486i			1.04031i	0.854073	+	0.520154i	$0.174125\pi$
$769$			28.8486i			1.04031i	−0.854073	+	0.520154i	$0.825875\pi$
$770$	−8.32467	+	3.89772i	−0.300000	+	0.140464i
$771$	1.31256	+	3.55660i	0.0472706	+	0.128088i
$772$	−29.9527	−	24.9740i	−1.07802	−	0.898835i
$773$	2.13578			0.0768186			0.0384093	−	0.999262i	$-0.487771\pi$
$773$	2.13578			0.0768186			0.0384093	+	0.999262i	$0.487771\pi$
$774$	−5.38397	+	11.8703i	−0.193523	+	0.426670i
$775$	−2.37610			−0.0853519
$776$	11.9746	−	45.5435i	0.429863	−	1.63492i
$777$	1.66525	+	4.51228i	0.0597404	+	0.161877i
$778$	−41.6458	+	19.4991i	−1.49308	+	0.699078i
$779$	−31.0737			−1.11333
$780$	−26.5248	+	2.83467i	−0.949741	+	0.101498i
$781$	4.63068			0.165699
$782$	−45.1143	+	21.1231i	−1.61328	+	0.755361i
$783$	13.7996	+	7.72197i	0.493156	+	0.275961i
$784$	3.36932	+	18.4332i	0.120333	+	0.658330i
$785$	−13.3405			−0.476144
$786$	−3.17997	−	3.14178i	−0.113426	−	0.112064i
$787$	−39.2697			−1.39981			−0.699907	−	0.714234i	$-0.746775\pi$
$787$	−39.2697			−1.39981			−0.699907	+	0.714234i	$0.746775\pi$
$788$	−10.6051	+	12.7192i	−0.377790	+	0.453104i
$789$	−5.93087	+	2.18878i	−0.211145	+	0.0779225i
$790$	−24.8078	+	11.6153i	−0.882621	+	0.413255i
$791$		−	16.4924i		−	0.586403i
$792$	−7.38127	−	15.2813i	−0.262282	−	0.542996i
$793$	−8.00000	−	16.6493i	−0.284088	−	0.591236i
$794$	4.67474	−	2.18878i	0.165900	−	0.0776768i
$795$		0			0
$796$	−8.63068	−	7.19612i	−0.305906	−	0.255060i
$797$			15.2162i			0.538987i	0.963002	+	0.269494i	$0.0868563\pi$
$797$			15.2162i			0.538987i	−0.963002	+	0.269494i	$0.913144\pi$
$798$	−14.3689	−	14.1963i	−0.508653	−	0.502544i
$799$	39.4571			1.39589
$800$	−2.02050	+	1.43845i	−0.0714355	+	0.0508568i
$801$	−25.8923	+	22.1242i	−0.914859	+	0.781722i
$802$	9.50758	+	20.3061i	0.335724	+	0.717033i
$803$	20.2993			0.716346
$804$	9.81664	−	27.6228i	0.346206	−	0.974182i
$805$	16.4924			0.581282
$806$	−17.4823	+	21.4002i	−0.615789	+	0.753792i
$807$	11.1745	+	30.2791i	0.393359	+	1.06588i
$808$	4.37755	−	16.6493i	0.154002	−	0.585722i
$809$		−	11.3185i		−	0.397938i	−0.980006	−	0.198969i	$-0.936241\pi$
$809$		−	11.3185i		−	0.397938i	0.980006	−	0.198969i	$-0.0637593\pi$
$810$	−26.1158	+	7.54563i	−0.917616	+	0.265126i
$811$	−24.0535			−0.844632			−0.422316	−	0.906449i	$-0.638783\pi$
$811$	−24.0535			−0.844632			−0.422316	+	0.906449i	$0.638783\pi$
$812$	−7.11321	−	5.93087i	−0.249625	−	0.208133i
$813$	−12.3626	+	4.56241i	−0.433577	+	0.160011i
$814$	−2.18878	−	4.67474i	−0.0767166	−	0.163850i
$815$	−28.2239			−0.988639
$816$	−41.3854	+	24.4898i	−1.44878	+	0.857315i
$817$		−	16.6493i		−	0.582487i
$818$	−3.64993	+	1.70895i	−0.127617	+	0.0597519i
$819$	−15.0566	−	6.64789i	−0.526119	−	0.232296i
$820$	15.6847	−	18.8114i	0.547732	−	0.656924i
$821$	−9.85775			−0.344038			−0.172019	−	0.985094i	$-0.555029\pi$
$821$	−9.85775			−0.344038			−0.172019	+	0.985094i	$0.555029\pi$
$822$	−15.6016	−	15.4143i	−0.544170	−	0.537635i
$823$			9.59482i			0.334454i	0.985918	+	0.167227i	$0.0534814\pi$
$823$			9.59482i			0.334454i	−0.985918	+	0.167227i	$0.946519\pi$
$824$	14.0140	−	53.3002i	0.488202	−	1.85680i
$825$	0.525853	+	1.42489i	0.0183078	+	0.0496083i
$826$	21.6774	−	10.1496i	0.754253	−	0.353151i
$827$		−	13.5076i		−	0.469704i	−0.972031	−	0.234852i	$-0.924539\pi$
$827$		−	13.5076i		−	0.469704i	0.972031	−	0.234852i	$-0.0754606\pi$
$828$	0.367854	+	30.4467i	0.0127838	+	1.05810i
$829$	24.0000			0.833554			0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000			0.833554			0.416777	+	0.909009i	$0.363160\pi$
$830$	16.4127	−	7.68466i	0.569694	−	0.266738i
$831$	6.09963	−	2.25106i	0.211594	−	0.0780884i
$832$	−1.91066	+	28.7811i	−0.0662402	+	0.997804i
$833$		−	32.5161i		−	1.12662i
$834$	−11.7374	+	11.8801i	−0.406434	+	0.411374i
$835$			37.0970i			1.28380i
$836$	16.6493	+	13.8819i	0.575830	+	0.480117i
$837$	−13.7511	+	24.5739i	−0.475308	+	0.849400i
$838$	21.0628	+	44.9856i	0.727603	+	1.55400i
$839$		−	19.1231i		−	0.660203i	−0.943945	−	0.330101i	$-0.892917\pi$
$839$		−	19.1231i		−	0.660203i	0.943945	−	0.330101i	$-0.107083\pi$
$840$	15.8470	−	1.53296i	0.546773	−	0.0528923i
$841$	19.7386			0.680643
$842$	10.6620	−	4.99211i	0.367438	−	0.172039i
$843$	−27.9512	+	10.3153i	−0.962691	+	0.355279i
$844$	−1.84233	−	1.53610i	−0.0634156	−	0.0528748i
$845$	17.3492	−	21.6774i	0.596829	−	0.745725i
$846$	9.96224	−	21.9643i	0.342509	−	0.755148i
$847$	−10.6514			−0.365985
$848$		0			0
$849$	9.93087	+	26.9094i	0.340827	+	0.923529i
$850$	3.89772	−	1.82496i	0.133691	−	0.0625958i
$851$			9.26137i			0.317476i
$852$	−7.55752	−	2.68580i	−0.258916	−	0.0920142i
$853$			21.3241i			0.730123i	0.930983	+	0.365061i	$0.118952\pi$
$853$			21.3241i			0.730123i	−0.930983	+	0.365061i	$0.881048\pi$
$854$	4.67474	+	9.98422i	0.159966	+	0.341653i
$855$	26.3989	−	22.5571i	0.902824	−	0.771438i
$856$	27.7639	+	7.29986i	0.948950	+	0.249504i
$857$		−	49.4413i		−	1.68888i	−0.535649	−	0.844441i	$-0.679933\pi$
$857$		−	49.4413i		−	1.68888i	0.535649	−	0.844441i	$-0.320067\pi$
$858$	16.7022	+	5.74766i	0.570205	+	0.196222i
$859$			9.06897i			0.309429i	0.987959	+	0.154715i	$0.0494458\pi$
$859$			9.06897i			0.309429i	−0.987959	+	0.154715i	$0.950554\pi$
$860$	10.0792	+	8.40388i	0.343699	+	0.286570i
$861$	14.1771	−	5.23203i	0.483154	−	0.178307i
$862$	−11.7732	+	5.51237i	−0.400997	+	0.187752i
$863$			0.561553i			0.0191155i	0.999954	+	0.00955774i	$0.00304237\pi$
$863$			0.561553i			0.0191155i	−0.999954	+	0.00955774i	$0.996958\pi$
$864$	3.18347	+	29.2210i	0.108304	+	0.994118i
$865$			16.6493i			0.566095i
$866$	21.6945	+	46.3348i	0.737211	+	1.57452i
$867$	50.6605	−	18.6962i	1.72052	−	0.634955i
$868$	10.5616	−	12.6670i	0.358482	−	0.429947i
$869$	18.1379			0.615287
$870$	11.1896	−	11.3256i	0.379364	−	0.383975i
$871$	13.2148	+	27.5022i	0.447766	+	0.931877i
$872$	−5.98730	+	22.7718i	−0.202756	+	0.771150i
$873$	32.4473	+	37.9734i	1.09817	+	1.28521i
$874$	−16.4924	−	35.2242i	−0.557865	−	1.19148i
$875$	−17.6742			−0.597496
$876$	−33.1295	−	11.7736i	−1.11934	−	0.397794i
$877$		−	14.8244i		−	0.500584i	−0.968170	−	0.250292i	$-0.919473\pi$
$877$		−	14.8244i		−	0.500584i	0.968170	−	0.250292i	$-0.0805266\pi$
$878$	32.8255	−	15.3693i	1.10781	−	0.518689i
$879$	4.32496	−	1.59612i	0.145877	−	0.0538357i
$880$	−16.8078	+	3.07221i	−0.566590	+	0.103564i
$881$			43.8346i			1.47683i	0.674349	+	0.738413i	$0.264424\pi$
$881$			43.8346i			1.47683i	−0.674349	+	0.738413i	$0.735576\pi$
$882$	−18.1005	−	8.20976i	−0.609476	−	0.276437i
$883$		−	47.6606i		−	1.60391i	−0.597386	−	0.801954i	$-0.703794\pi$
$883$		−	47.6606i		−	1.60391i	0.597386	−	0.801954i	$-0.296206\pi$
$884$	12.2413	−	48.5320i	0.411720	−	1.63231i
$885$	14.2462	+	38.6026i	0.478881	+	1.29761i
$886$	1.09439	+	2.33737i	0.0367667	+	0.0785255i
$887$	−34.7236			−1.16590			−0.582952	−	0.812507i	$-0.698102\pi$
$887$	−34.7236			−1.16590			−0.582952	+	0.812507i	$0.698102\pi$
$888$	0.860840	+	8.89893i	0.0288879	+	0.298628i
$889$		−	10.1496i		−	0.340408i
$890$	14.5399	+	31.0540i	0.487378	+	1.04093i
$891$	17.7797	+	2.80776i	0.595641	+	0.0940636i
$892$	37.5082	−	44.9856i	1.25587	−	1.50623i
$893$			30.8071i			1.03092i
$894$	0.715417	+	0.706826i	0.0239271	+	0.0236398i
$895$	3.89772			0.130286
$896$	1.31256	−	17.1651i	0.0438495	−	0.573446i
$897$	−22.7670	−	22.0468i	−0.760168	−	0.736121i
$898$	−8.56155	−	18.2856i	−0.285703	−	0.610198i
$899$		−	16.4924i		−	0.550053i
$900$	−0.0317813	−	2.63049i	−0.00105938	−	0.0876830i
$901$		0			0
$902$	−14.6875	+	6.87689i	−0.489041	+	0.228976i
$903$	2.80333	+	7.59612i	0.0932891	+	0.252783i
$904$	7.79544	−	29.6488i	0.259273	−	0.986103i
$905$	−41.3686			−1.37514
$906$	−29.8182	−	29.4602i	−0.990645	−	0.978748i
$907$			31.3308i			1.04032i	0.854068	+	0.520161i	$0.174128\pi$
$907$			31.3308i			1.04032i	−0.854068	+	0.520161i	$0.825872\pi$
$908$	11.9106	+	9.93087i	0.395268	+	0.329567i
$909$	11.8617	+	13.8819i	0.393429	+	0.460435i
$910$	−10.4837	+	12.8332i	−0.347533	+	0.425417i
$911$	8.72475			0.289064			0.144532	−	0.989500i	$-0.453832\pi$
$911$	8.72475			0.289064			0.144532	+	0.989500i	$0.453832\pi$
$912$	−19.1211	−	32.3127i	−0.633162	−	1.06998i
$913$	−12.0000			−0.397142
$914$	8.32467	−	3.89772i	0.275356	−	0.128925i
$915$	−17.7797	+	6.56155i	−0.587778	+	0.216918i
$916$	42.7402	+	35.6361i	1.41218	+	1.17745i
$917$	−2.77691			−0.0917017
$918$	3.68309	−	50.8724i	0.121560	−	1.67904i
$919$			47.2824i			1.55970i	0.625964	+	0.779852i	$0.284706\pi$
$919$			47.2824i			1.55970i	−0.625964	+	0.779852i	$0.715294\pi$
$920$	29.6488	+	7.79544i	0.977491	+	0.257008i
$921$	−3.86098	+	1.42489i	−0.127224	+	0.0469517i
$922$	−15.0346	−	32.1105i	−0.495137	−	1.05750i
$923$	7.52452	−	3.61553i	0.247673	−	0.119007i
$924$	−9.93349	−	3.53018i	−0.326788	−	0.116134i
$925$		−	0.800151i		−	0.0263088i
$926$	−16.2493	−	34.7049i	−0.533984	−	1.14047i
$927$	37.9734	+	44.4408i	1.24721	+	1.45963i
$928$	−9.98422	−	14.0242i	−0.327748	−	0.460368i
$929$	9.77484			0.320702			0.160351	−	0.987060i	$-0.448737\pi$
$929$	9.77484			0.320702			0.160351	+	0.987060i	$0.448737\pi$
$930$	20.1684	+	19.9262i	0.661348	+	0.653406i
$931$	25.3878			0.832051
$932$	17.9619	+	14.9763i	0.588362	+	0.490566i
$933$	−39.9309	+	14.7364i	−1.30728	+	0.482449i
$934$	−6.46114	−	13.7996i	−0.211415	−	0.451536i
$935$	29.6488			0.969618
$936$	−23.9253	−	19.0678i	−0.782022	−	0.623251i
$937$	55.8617			1.82492			0.912462	−	0.409162i	$-0.134179\pi$
$937$	55.8617			1.82492			0.912462	+	0.409162i	$0.134179\pi$
$938$	−7.72197	−	16.4924i	−0.252131	−	0.538497i
$939$	−12.0869	+	4.46066i	−0.394442	+	0.145568i
$940$	−18.6501	−	15.5501i	−0.608299	−	0.507189i
$941$	49.4182			1.61099			0.805494	−	0.592604i	$-0.201900\pi$
$941$	49.4182			1.61099			0.805494	+	0.592604i	$0.201900\pi$
$942$	−10.8839	−	10.7532i	−0.354617	−	0.350358i
$943$	29.0982			0.947567
$944$	43.7673	−	8.00000i	1.42450	−	0.260378i
$945$	−8.24621	+	14.7364i	−0.268249	+	0.479376i
$946$	−3.68466	−	7.86962i	−0.119799	−	0.255863i
$947$			2.00000i			0.0649913i	0.999472	+	0.0324956i	$0.0103455\pi$
$947$			2.00000i			0.0649913i	−0.999472	+	0.0324956i	$0.989654\pi$
$948$	−29.6021	−	10.5200i	−0.961431	−	0.341675i
$949$	32.9848	−	15.8492i	1.07073	−	0.514487i
$950$	1.42489	+	3.04325i	0.0462295	+	0.0987360i
$951$	−0.667152	+	0.246211i	−0.0216339	+	0.00798395i
$952$	−7.59612	+	28.8907i	−0.246192	+	0.936352i
$953$			29.9527i			0.970262i	0.874442	+	0.485131i	$0.161228\pi$
$953$			29.9527i			0.970262i	−0.874442	+	0.485131i	$0.838772\pi$
$954$		0			0
$955$	24.7206			0.799941
$956$	−30.6159	−	25.5270i	−0.990188	−	0.825602i
$957$	−9.89012	+	3.64993i	−0.319702	+	0.117985i
$958$	−9.52699	+	4.46066i	−0.307803	+	0.144117i
$959$	−13.6242			−0.439947
$960$	29.2131	+	4.73453i	0.942847	+	0.152806i
$961$	−1.63068			−0.0526027
$962$	−7.20653	−	5.88717i	−0.232348	−	0.189810i
$963$	−23.1491	+	19.7802i	−0.745968	+	0.637409i
$964$	5.60667	+	4.67474i	0.180579	+	0.150563i
$965$		−	41.6458i		−	1.34063i
$966$	13.4554	+	13.2938i	0.432920	+	0.427721i
$967$	−38.7899			−1.24740			−0.623700	−	0.781664i	$-0.714371\pi$
$967$	−38.7899			−1.24740			−0.623700	+	0.781664i	$0.714371\pi$
$968$	−19.1482	−	5.03457i	−0.615446	−	0.161817i
$969$	22.5571	+	61.1225i	0.724640	+	1.96354i
$970$	45.5435	−	21.3241i	1.46232	−	0.684675i
$971$	6.09963			0.195747			0.0978733	−	0.995199i	$-0.468796\pi$
$971$	6.09963			0.195747			0.0978733	+	0.995199i	$0.468796\pi$
$972$	−27.3889	−	14.8947i	−0.878498	−	0.477746i
$973$			10.3743i			0.332585i
$974$	−3.24985	−	6.94097i	−0.104132	−	0.222403i
$975$	1.96699	+	1.90477i	0.0629942	+	0.0610014i
$976$	3.68466	+	20.1584i	0.117943	+	0.645256i
$977$	28.9645			0.926656			0.463328	−	0.886187i	$-0.346655\pi$
$977$	28.9645			0.926656			0.463328	+	0.886187i	$0.346655\pi$
$978$	−23.0265	−	22.7500i	−0.736307	−	0.727465i
$979$		−	22.7048i		−	0.725648i
$980$	−12.8147	+	15.3693i	−0.409350	+	0.490955i
$981$	−16.2236	−	18.9867i	−0.517981	−	0.606199i
$982$	13.6420	+	29.1364i	0.435335	+	0.929779i
$983$		−	35.9309i		−	1.14602i	−0.819550	−	0.573008i	$-0.805776\pi$
$983$		−	35.9309i		−	1.14602i	0.819550	−	0.573008i	$-0.194224\pi$
$984$	27.9594	−	2.70466i	0.891314	−	0.0862215i
$985$	−17.6847			−0.563480
$986$	12.6670	+	27.0540i	0.403400	+	0.861574i
$987$	−5.18715	−	14.0555i	−0.165109	−	0.447391i
$988$	37.8927	+	9.55773i	1.20553	+	0.304072i
$989$			15.5909i			0.495761i
$990$	7.48582	−	16.5044i	0.237915	−	0.524543i
$991$		−	47.8083i		−	1.51868i	−0.650694	−	0.759340i	$-0.725522\pi$
$991$		−	47.8083i		−	1.51868i	0.650694	−	0.759340i	$-0.274478\pi$
$992$	24.9740	−	17.7797i	0.792926	−	0.564505i
$993$	8.80604	−	3.24985i	0.279451	−	0.103131i
$994$	−4.51228	+	2.11271i	−0.143121	+	0.0670110i
$995$		−	12.0000i		−	0.380426i
$996$	19.5846	+	6.96002i	0.620563	+	0.220537i
$997$	10.0000			0.316703			0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000			0.316703			0.158352	+	0.987383i	$0.449382\pi$
$998$	3.24985	+	6.94097i	0.102872	+	0.219713i
$999$	−8.27528	−	4.63068i	−0.261818	−	0.146508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.h.b.155.11	yes	16
3.2	odd	2	inner	156.2.h.b.155.6	yes	16
4.3	odd	2	inner	156.2.h.b.155.10	yes	16
12.11	even	2	inner	156.2.h.b.155.7	yes	16
13.12	even	2	inner	156.2.h.b.155.5	✓	16
39.38	odd	2	inner	156.2.h.b.155.12	yes	16
52.51	odd	2	inner	156.2.h.b.155.8	yes	16
156.155	even	2	inner	156.2.h.b.155.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.h.b.155.5	✓	16	13.12	even	2	inner
156.2.h.b.155.6	yes	16	3.2	odd	2	inner
156.2.h.b.155.7	yes	16	12.11	even	2	inner
156.2.h.b.155.8	yes	16	52.51	odd	2	inner
156.2.h.b.155.9	yes	16	156.155	even	2	inner
156.2.h.b.155.10	yes	16	4.3	odd	2	inner
156.2.h.b.155.11	yes	16	1.1	even	1	trivial
156.2.h.b.155.12	yes	16	39.38	odd	2	inner

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599676 + 1.28078i) q^{2} +(-1.62493 + 0.599676i) q^{3} +(-1.28078 + 1.53610i) q^{4} -2.13578 q^{5} +(-1.74248 - 1.72156i) q^{6} -1.52162 q^{7} +(-2.73546 - 0.719224i) q^{8} +(2.28078 - 1.94886i) q^{9} +O(q^{10})\)	\(q+(0.599676 + 1.28078i) q^{2} +(-1.62493 + 0.599676i) q^{3} +(-1.28078 + 1.53610i) q^{4} -2.13578 q^{5} +(-1.74248 - 1.72156i) q^{6} -1.52162 q^{7} +(-2.73546 - 0.719224i) q^{8} +(2.28078 - 1.94886i) q^{9} +(-1.28078 - 2.73546i) q^{10} +2.00000i q^{11} +(1.16000 - 3.26411i) q^{12} +(1.56155 + 3.24985i) q^{13} +(-0.912482 - 1.94886i) q^{14} +(3.47049 - 1.28078i) q^{15} +(-0.719224 - 3.93481i) q^{16} +6.94097i q^{17} +(3.86378 + 1.75248i) q^{18} -5.41935 q^{19} +(2.73546 - 3.28078i) q^{20} +(2.47253 - 0.912482i) q^{21} +(-2.56155 + 1.19935i) q^{22} +5.07482 q^{23} +(4.87622 - 0.471702i) q^{24} -0.438447 q^{25} +(-3.22591 + 3.94886i) q^{26} +(-2.53741 + 4.53448i) q^{27} +(1.94886 - 2.33737i) q^{28} -3.04325i q^{29} +(3.72156 + 3.67686i) q^{30} +5.41935 q^{31} +(4.60831 - 3.28078i) q^{32} +(-1.19935 - 3.24985i) q^{33} +(-8.88983 + 4.16234i) q^{34} +3.24985 q^{35} +(0.0724861 + 5.99956i) q^{36} +1.82496i q^{37} +(-3.24985 - 6.94097i) q^{38} +(-4.48627 - 4.34435i) q^{39} +(5.84233 + 1.53610i) q^{40} +5.73384 q^{41} +(2.65140 + 2.61956i) q^{42} +3.07221i q^{43} +(-3.07221 - 2.56155i) q^{44} +(-4.87123 + 4.16234i) q^{45} +(3.04325 + 6.49971i) q^{46} -5.68466i q^{47} +(3.52830 + 5.96248i) q^{48} -4.68466 q^{49} +(-0.262926 - 0.561553i) q^{50} +(-4.16234 - 11.2786i) q^{51} +(-6.99211 - 1.76363i) q^{52} +(-7.32929 - 0.530631i) q^{54} -4.27156i q^{55} +(4.16234 + 1.09439i) q^{56} +(8.80604 - 3.24985i) q^{57} +(3.89772 - 1.82496i) q^{58} +11.1231i q^{59} +(-2.47751 + 6.97141i) q^{60} -5.12311 q^{61} +(3.24985 + 6.94097i) q^{62} +(-3.47049 + 2.96543i) q^{63} +(6.96543 + 3.93481i) q^{64} +(-3.33513 - 6.94097i) q^{65} +(3.44311 - 3.48496i) q^{66} +8.46260 q^{67} +(-10.6620 - 8.88983i) q^{68} +(-8.24621 + 3.04325i) q^{69} +(1.94886 + 4.16234i) q^{70} -2.31534i q^{71} +(-7.64063 + 3.69063i) q^{72} -10.1496i q^{73} +(-2.33737 + 1.09439i) q^{74} +(0.712445 - 0.262926i) q^{75} +(6.94097 - 8.32467i) q^{76} -3.04325i q^{77} +(2.87383 - 8.35111i) q^{78} -9.06897i q^{79} +(1.53610 + 8.40388i) q^{80} +(1.40388 - 8.88983i) q^{81} +(3.43845 + 7.34376i) q^{82} +6.00000i q^{83} +(-1.76509 + 4.96674i) q^{84} -14.8244i q^{85} +(-3.93481 + 1.84233i) q^{86} +(1.82496 + 4.94506i) q^{87} +(1.43845 - 5.47091i) q^{88} -11.3524 q^{89} +(-8.25219 - 3.74291i) q^{90} +(-2.37610 - 4.94506i) q^{91} +(-6.49971 + 7.79544i) q^{92} +(-8.80604 + 3.24985i) q^{93} +(7.28078 - 3.40896i) q^{94} +11.5745 q^{95} +(-5.52076 + 8.09452i) q^{96} +16.6493i q^{97} +(-2.80928 - 6.00000i) q^{98} +(3.89772 + 4.56155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 + 20 * q^9	\( 16 q - 4 q^{4} + 20 q^{9} - 4 q^{10} + 10 q^{12} - 8 q^{13} - 28 q^{16} - 8 q^{22} - 40 q^{25} + 18 q^{30} - 22 q^{36} + 44 q^{40} - 34 q^{42} + 46 q^{48} + 24 q^{49} - 32 q^{52} - 16 q^{61} - 4 q^{64} - 28 q^{66} + 34 q^{78} - 60 q^{81} + 88 q^{82} + 56 q^{88} - 22 q^{90} + 100 q^{94}+O(q^{100}) \) 16 * q - 4 * q^4 + 20 * q^9 - 4 * q^10 + 10 * q^12 - 8 * q^13 - 28 * q^16 - 8 * q^22 - 40 * q^25 + 18 * q^30 - 22 * q^36 + 44 * q^40 - 34 * q^42 + 46 * q^48 + 24 * q^49 - 32 * q^52 - 16 * q^61 - 4 * q^64 - 28 * q^66 + 34 * q^78 - 60 * q^81 + 88 * q^82 + 56 * q^88 - 22 * q^90 + 100 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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