LMFDB - Embedded newform 441.2.h.g.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$0.474636 + 0.274031i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.g.214.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69963 q^{2} +(0.175815 - 1.72310i) q^{3} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(-2.93818 - 0.605896i) q^{9} +O(q^{10})$	\(q-1.69963 q^{2} +(0.175815 - 1.72310i) q^{3} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(-2.93818 - 0.605896i) q^{9} +(-0.806704 - 1.39725i) q^{10} +(0.294182 - 0.509538i) q^{11} +(0.156253 - 1.53138i) q^{12} +(2.50987 - 4.34722i) q^{13} +(1.50000 - 0.673310i) q^{15} -4.98762 q^{16} +(3.79121 + 6.56657i) q^{17} +(4.99381 + 1.02980i) q^{18} +(2.23061 - 3.86353i) q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.23855 - 2.14523i) q^{23} +(0.332068 - 3.25449i) q^{24} +(2.04944 - 3.54974i) q^{25} +(-4.26584 + 7.38866i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(-2.73855 - 4.74331i) q^{29} +(-2.54944 + 1.14438i) q^{30} -6.07463 q^{31} +4.69963 q^{32} +(-0.826266 - 0.596491i) q^{33} +(-6.44364 - 11.1607i) q^{34} +(-2.61126 - 0.538481i) q^{36} +(3.49381 - 6.05146i) q^{37} +(-3.79121 + 6.56657i) q^{38} +(-7.04944 - 5.08907i) q^{39} +(0.896461 + 1.55272i) q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +(0.261450 - 0.452845i) q^{44} +(-0.896461 - 2.70303i) q^{45} +(2.10507 + 3.64610i) q^{46} -7.47680 q^{47} +(-0.876899 + 8.59419i) q^{48} +(-3.48329 + 6.03323i) q^{50} +(11.9814 - 5.37815i) q^{51} +(2.23061 - 3.86353i) q^{52} +(-3.46108 - 5.99476i) q^{53} +(2.65244 - 8.42380i) q^{54} +0.558517 q^{55} +(-6.26509 - 4.52284i) q^{57} +(4.65452 + 8.06186i) q^{58} +10.4302 q^{59} +(1.33310 - 0.598395i) q^{60} +11.6529 q^{61} +10.3246 q^{62} +1.98762 q^{64} +4.76509 q^{65} +(1.40434 + 1.01381i) q^{66} -11.8640 q^{67} +(3.36938 + 5.83594i) q^{68} +(-3.91421 + 1.75699i) q^{69} +4.30037 q^{71} +(-5.54944 - 1.14438i) q^{72} +(-2.23061 - 3.86353i) q^{73} +(-5.93818 + 10.2852i) q^{74} +(-5.75625 - 4.15550i) q^{75} +(1.98242 - 3.43366i) q^{76} +(11.9814 + 8.64953i) q^{78} -1.33379 q^{79} +(-2.36730 - 4.10029i) q^{80} +(8.26578 + 3.56046i) q^{81} +(-0.896461 + 1.55272i) q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(5.93818 + 10.2852i) q^{86} +(-8.65469 + 3.88486i) q^{87} +(0.555632 - 0.962383i) q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.52365 + 4.59415i) q^{90} +(-1.10074 - 1.90654i) q^{92} +(-1.06801 + 10.4672i) q^{93} +12.7078 q^{94} +4.23491 q^{95} +(0.826266 - 8.09795i) q^{96} +(1.70317 + 2.94997i) q^{97} +(-1.17309 + 1.31887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	$ 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.69963			−1.20182			−0.600909	−	0.799317i	$-0.705195\pi$
$2$	−1.69963			−1.20182			−0.600909	+	0.799317i	$0.705195\pi$
$3$	0.175815	−	1.72310i	0.101507	−	0.994835i
$3$	0.175815	−	1.72310i	0.101507	−	0.994835i
$4$	0.888736			0.444368
$5$	0.474636	+	0.822093i	0.212263	+	0.367651i	0.952423	−	0.304781i	$-0.0985832\pi$
$5$	0.474636	+	0.822093i	0.212263	+	0.367651i	−0.740159	+	0.672432i	$0.765250\pi$
$6$	−0.298820	+	2.92864i	−0.121993	+	1.19561i
$7$		0			0
$7$		0			0
$8$	1.88874			0.667769
$9$	−2.93818	−	0.605896i	−0.979393	−	0.201965i
$10$	−0.806704	−	1.39725i	−0.255102	−	0.441850i
$11$	0.294182	−	0.509538i	0.0886992	−	0.153632i	−0.818262	−	0.574845i	$-0.805062\pi$
$11$	0.294182	−	0.509538i	0.0886992	−	0.153632i	0.906962	+	0.421213i	$0.138396\pi$
$12$	0.156253	−	1.53138i	0.0451064	−	0.442073i
$13$	2.50987	−	4.34722i	0.696112	−	1.20570i	−0.273692	−	0.961817i	$-0.588245\pi$
$13$	2.50987	−	4.34722i	0.696112	−	1.20570i	0.969804	−	0.243885i	$-0.0784218\pi$
$14$		0			0
$15$	1.50000	−	0.673310i	0.387298	−	0.173848i
$16$	−4.98762			−1.24691
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.800171	+	0.599772i	$0.204742\pi$
$17$	3.79121	+	6.56657i	0.919503	+	1.59263i	0.119332	+	0.992854i	$0.461925\pi$
$18$	4.99381	+	1.02980i	1.17705	+	0.242726i
$19$	2.23061	−	3.86353i	0.511737	−	0.886355i	−0.488170	−	0.872748i	$-0.662336\pi$
$19$	2.23061	−	3.86353i	0.511737	−	0.886355i	0.999907	−	0.0136063i	$-0.00433116\pi$
$20$	0.421826	+	0.730623i	0.0943231	+	0.163372i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−1.23855	−	2.14523i	−0.258256	−	0.447312i	0.707519	−	0.706694i	$-0.249814\pi$
$23$	−1.23855	−	2.14523i	−0.258256	−	0.447312i	−0.965775	+	0.259382i	$0.916481\pi$
$24$	0.332068	−	3.25449i	0.0677832	−	0.664320i
$25$	2.04944	−	3.54974i	0.409888	−	0.709948i
$26$	−4.26584	+	7.38866i	−0.836601	+	1.44904i
$27$	−1.56060	+	4.95626i	−0.300337	+	0.953833i
$28$		0			0
$29$	−2.73855	−	4.74331i	−0.508536	−	0.880810i	−0.999951	−	0.00988468i	$-0.996854\pi$
$29$	−2.73855	−	4.74331i	−0.508536	−	0.880810i	0.491415	−	0.870925i	$-0.336480\pi$
$30$	−2.54944	+	1.14438i	−0.465462	+	0.208934i
$31$	−6.07463			−1.09104			−0.545518	−	0.838099i	$-0.683667\pi$
$31$	−6.07463			−1.09104			−0.545518	+	0.838099i	$0.683667\pi$
$32$	4.69963			0.830785
$33$	−0.826266	−	0.596491i	−0.143834	−	0.103836i
$34$	−6.44364	−	11.1607i	−1.10508	−	1.91405i
$35$		0			0
$36$	−2.61126	−	0.538481i	−0.435211	−	0.0897469i
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	−0.421730	−	0.906721i	$-0.638577\pi$
$37$	3.49381	−	6.05146i	0.574379	−	0.994853i	0.996109	−	0.0881319i	$-0.0280897\pi$
$38$	−3.79121	+	6.56657i	−0.615015	+	1.06524i
$39$	−7.04944	−	5.08907i	−1.12881	−	0.814904i
$40$	0.896461	+	1.55272i	0.141743	+	0.245506i
$41$	0.527445	−	0.913562i	0.0823731	−	0.142674i	−0.821896	−	0.569638i	$-0.807083\pi$
$41$	0.527445	−	0.913562i	0.0823731	−	0.142674i	0.904269	+	0.426964i	$0.140417\pi$
$42$		0			0
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	−0.999266	−	0.0382990i	$-0.987806\pi$
$43$	−3.49381	−	6.05146i	−0.532801	−	0.922838i	0.466465	−	0.884540i	$-0.345527\pi$
$44$	0.261450	−	0.452845i	0.0394151	−	0.0682689i
$45$	−0.896461	−	2.70303i	−0.133637	−	0.402945i
$46$	2.10507	+	3.64610i	0.310376	+	0.537587i
$47$	−7.47680			−1.09060			−0.545301	−	0.838240i	$-0.683585\pi$
$47$	−7.47680			−1.09060			−0.545301	+	0.838240i	$0.683585\pi$
$48$	−0.876899	+	8.59419i	−0.126569	+	1.24046i
$49$		0			0
$50$	−3.48329	+	6.03323i	−0.492612	+	0.853228i
$51$	11.9814	−	5.37815i	1.67774	−	0.753091i
$52$	2.23061	−	3.86353i	0.309330	−	0.535775i
$53$	−3.46108	−	5.99476i	−0.475416	−	0.823444i	0.524188	−	0.851603i	$-0.324369\pi$
$53$	−3.46108	−	5.99476i	−0.475416	−	0.823444i	−0.999603	+	0.0281586i	$0.991036\pi$
$54$	2.65244	−	8.42380i	0.360951	−	1.14633i
$55$	0.558517			0.0753104
$56$		0			0
$57$	−6.26509	−	4.52284i	−0.829832	−	0.599065i
$58$	4.65452	+	8.06186i	0.611168	+	1.05857i
$59$	10.4302			1.35790			0.678950	−	0.734184i	$-0.262435\pi$
$59$	10.4302			1.35790			0.678950	+	0.734184i	$0.262435\pi$
$60$	1.33310	−	0.598395i	0.172103	−	0.0772525i
$61$	11.6529			1.49200			0.745999	−	0.665947i	$-0.231972\pi$
$61$	11.6529			1.49200			0.745999	+	0.665947i	$0.231972\pi$
$62$	10.3246			1.31123
$63$		0			0
$64$	1.98762			0.248453
$65$	4.76509			0.591037
$66$	1.40434	+	1.01381i	0.172863	+	0.124792i
$67$	−11.8640			−1.44942			−0.724708	−	0.689056i	$-0.758025\pi$
$67$	−11.8640			−1.44942			−0.724708	+	0.689056i	$0.758025\pi$
$68$	3.36938	+	5.83594i	0.408598	+	0.707712i
$69$	−3.91421	+	1.75699i	−0.471216	+	0.211516i
$70$		0			0
$71$	4.30037			0.510360			0.255180	−	0.966894i	$-0.417865\pi$
$71$	4.30037			0.510360			0.255180	+	0.966894i	$0.417865\pi$
$72$	−5.54944	−	1.14438i	−0.654008	−	0.134866i
$73$	−2.23061	−	3.86353i	−0.261073	−	0.452192i	0.705454	−	0.708756i	$-0.250743\pi$
$73$	−2.23061	−	3.86353i	−0.261073	−	0.452192i	−0.966527	+	0.256563i	$0.917410\pi$
$74$	−5.93818	+	10.2852i	−0.690299	+	1.19563i
$75$	−5.75625	−	4.15550i	−0.664674	−	0.479836i
$76$	1.98242	−	3.43366i	0.227400	−	0.393868i
$77$		0			0
$78$	11.9814	+	8.64953i	1.35663	+	0.979367i
$79$	−1.33379			−0.150063			−0.0750317	−	0.997181i	$-0.523906\pi$
$79$	−1.33379			−0.150063			−0.0750317	+	0.997181i	$0.523906\pi$
$80$	−2.36730	−	4.10029i	−0.264672	−	0.458426i
$81$	8.26578	+	3.56046i	0.918420	+	0.395607i
$82$	−0.896461	+	1.55272i	−0.0989976	+	0.171469i
$83$	2.84194	+	4.92238i	0.311943	+	0.540301i	0.978783	−	0.204900i	$-0.0656868\pi$
$83$	2.84194	+	4.92238i	0.311943	+	0.540301i	−0.666840	+	0.745201i	$0.732353\pi$
$84$		0			0
$85$	−3.59888	+	6.23345i	−0.390354	+	0.676113i
$86$	5.93818	+	10.2852i	0.640330	+	1.10908i
$87$	−8.65469	+	3.88486i	−0.927880	+	0.416501i
$88$	0.555632	−	0.962383i	0.0592306	−	0.102590i
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	−0.887516	−	0.460777i	$-0.847571\pi$
$89$	−0.421826	+	0.730623i	−0.0447134	+	0.0774459i	0.842803	+	0.538223i	$0.180904\pi$
$90$	1.52365	+	4.59415i	0.160607	+	0.484266i
$91$		0			0
$92$	−1.10074	−	1.90654i	−0.114760	−	0.198771i
$93$	−1.06801	+	10.4672i	−0.110748	+	1.08540i
$94$	12.7078			1.31071
$95$	4.23491			0.434492
$96$	0.826266	−	8.09795i	0.0843304	−	0.826494i
$97$	1.70317	+	2.94997i	0.172930	+	0.299524i	0.939443	−	0.342705i	$-0.111343\pi$
$97$	1.70317	+	2.94997i	0.172930	+	0.299524i	−0.766513	+	0.642229i	$0.778010\pi$
$98$		0			0
$99$	−1.17309	+	1.31887i	−0.117900	+	0.132551i
$100$	1.82141	−	3.15478i	0.182141	−	0.315478i
$101$	4.79329	−	8.30222i	0.476950	−	0.826102i	−0.522701	−	0.852516i	$-0.675076\pi$
$101$	4.79329	−	8.30222i	0.476950	−	0.826102i	0.999651	+	0.0264143i	$0.00840890\pi$
$102$	−20.3640	+	9.14085i	−2.01633	+	0.905079i
$103$	5.82644	+	10.0917i	0.574096	+	0.994364i	0.996139	+	0.0877882i	$0.0279799\pi$
$103$	5.82644	+	10.0917i	0.574096	+	0.994364i	−0.422043	+	0.906576i	$0.638687\pi$
$104$	4.74048	−	8.21075i	0.464842	−	0.805130i
$105$		0			0
$106$	5.88255	+	10.1889i	0.571363	+	0.989630i
$107$	1.89926	−	3.28961i	0.183608	−	0.318018i	−0.759499	−	0.650509i	$-0.774556\pi$
$107$	1.89926	−	3.28961i	0.183608	−	0.318018i	0.943107	+	0.332491i	$0.107889\pi$
$108$	−1.38696	+	4.40481i	−0.133460	+	0.423853i
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	0.990195	+	0.139690i	$0.0446106\pi$
$109$	6.43199	+	11.1405i	0.616073	+	1.06707i	−0.374123	+	0.927379i	$0.622056\pi$
$110$	−0.949271			−0.0905094
$111$	−9.81303	−	7.08414i	−0.931411	−	0.672397i
$112$		0			0
$113$	−4.51052	+	7.81245i	−0.424314	+	0.734934i	−0.996356	−	0.0852908i	$-0.972818\pi$
$113$	−4.51052	+	7.81245i	−0.424314	+	0.734934i	0.572042	+	0.820224i	$0.306151\pi$
$114$	10.6483	+	7.68715i	0.997307	+	0.719968i
$115$	1.17572	−	2.03641i	0.109636	−	0.189896i
$116$	−2.43385	−	4.21555i	−0.225977	−	0.391404i
$117$	−10.0084	+	11.2522i	−0.925277	+	1.04027i
$118$	−17.7275			−1.63195
$119$		0			0
$120$	2.83310	−	1.27171i	0.258626	−	0.116090i
$121$	5.32691	+	9.22649i	0.484265	+	0.838771i
$122$	−19.8056			−1.79311
$123$	−1.48143	−	1.06946i	−0.133576	−	0.0964301i
$124$	−5.39874			−0.484821
$125$	8.63731			0.772544
$126$		0			0
$127$	6.43268			0.570808			0.285404	−	0.958407i	$-0.407872\pi$
$127$	6.43268			0.570808			0.285404	+	0.958407i	$0.407872\pi$
$128$	−12.7775			−1.12938
$129$	−11.0416	+	4.95626i	−0.972155	+	0.436375i
$130$	−8.09888			−0.710319
$131$	−3.31657	−	5.74447i	−0.289770	−	0.501897i	0.683984	−	0.729497i	$-0.260246\pi$
$131$	−3.31657	−	5.74447i	−0.289770	−	0.501897i	−0.973755	+	0.227600i	$0.926912\pi$
$132$	−0.734332	−	0.530123i	−0.0639154	−	0.0461413i
$133$		0			0
$134$	20.1643			1.74193
$135$	−4.81522	+	1.06946i	−0.414428	+	0.0920446i
$136$	7.16059	+	12.4025i	0.614016	+	1.06351i
$137$	−7.01671	+	12.1533i	−0.599478	+	1.03833i	0.393420	+	0.919359i	$0.371292\pi$
$137$	−7.01671	+	12.1533i	−0.599478	+	1.03833i	−0.992898	+	0.118968i	$0.962042\pi$
$138$	6.65271	−	2.98622i	0.566316	−	0.254204i
$139$	−4.40254	+	7.62541i	−0.373418	+	0.646779i	−0.990089	−	0.140442i	$-0.955148\pi$
$139$	−4.40254	+	7.62541i	−0.373418	+	0.646779i	0.616671	+	0.787221i	$0.288481\pi$
$140$		0			0
$141$	−1.31453	+	12.8833i	−0.110704	+	1.08497i
$142$	−7.30903			−0.613360
$143$	−1.47672	−	2.55775i	−0.123489	−	0.213890i
$144$	14.6545	+	3.02198i	1.22121	+	0.251831i
$145$	2.59963	−	4.50268i	0.215887	−	0.373928i
$146$	3.79121	+	6.56657i	0.313763	+	0.543453i
$147$		0			0
$148$	3.10507	−	5.37815i	0.255236	−	0.442081i
$149$	2.18292	+	3.78092i	0.178832	+	0.309745i	0.941481	−	0.337067i	$-0.109435\pi$
$149$	2.18292	+	3.78092i	0.178832	+	0.309745i	−0.762649	+	0.646813i	$0.776102\pi$
$150$	9.78348	+	7.06281i	0.798818	+	0.576676i
$151$	6.32691	−	10.9585i	0.514877	−	0.891793i	−0.484974	−	0.874529i	$-0.661171\pi$
$151$	6.32691	−	10.9585i	0.514877	−	0.891793i	0.999851	−	0.0172645i	$-0.00549573\pi$
$152$	4.21303	−	7.29719i	0.341722	−	0.591880i
$153$	−7.16059	−	21.5908i	−0.578899	−	1.74551i
$154$		0			0
$155$	−2.88323	−	4.99391i	−0.231587	−	0.401120i
$156$	−6.26509	−	4.52284i	−0.501609	−	0.362117i
$157$	11.2739			0.899754			0.449877	−	0.893091i	$-0.351468\pi$
$157$	11.2739			0.899754			0.449877	+	0.893091i	$0.351468\pi$
$158$	2.26695			0.180349
$159$	−10.9381	+	4.90983i	−0.867449	+	0.389375i
$160$	2.23061	+	3.86353i	0.176345	+	0.305439i
$161$		0			0
$162$	−14.0488	−	6.05146i	−1.10377	−	0.475447i
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	−0.831553	−	0.555446i	$-0.812548\pi$
$163$	0.833104	−	1.44298i	0.0652537	−	0.113023i	0.896807	+	0.442423i	$0.145881\pi$
$164$	0.468760	−	0.811916i	0.0366040	−	0.0634000i
$165$	0.0981957	−	0.962383i	0.00764453	−	0.0749214i
$166$	−4.83024	−	8.36622i	−0.374899	−	0.649344i
$167$	−1.95135	+	3.37984i	−0.151000	+	0.261540i	−0.931595	−	0.363497i	$-0.881583\pi$
$167$	−1.95135	+	3.37984i	−0.151000	+	0.261540i	0.780595	+	0.625037i	$0.214916\pi$
$168$		0			0
$169$	−6.09888	−	10.5636i	−0.469145	−	0.812583i
$170$	6.11677	−	10.5945i	0.469134	−	0.812565i
$171$	−8.89483	+	10.0002i	−0.680204	+	0.764736i
$172$	−3.10507	−	5.37815i	−0.236760	−	0.410080i
$173$	16.1141			1.22513			0.612566	−	0.790419i	$-0.290137\pi$
$173$	16.1141			1.22513			0.612566	+	0.790419i	$0.290137\pi$
$174$	14.7098	−	6.60282i	1.11514	−	0.500559i
$175$		0			0
$176$	−1.46727	+	2.54138i	−0.110599	+	0.191564i
$177$	1.83379	−	17.9724i	0.137836	−	1.35089i
$178$	0.716947	−	1.24179i	0.0537374	−	0.0930760i
$179$	−7.14400	−	12.3738i	−0.533967	−	0.924859i	−0.999213	−	0.0396767i	$-0.987367\pi$
$179$	−7.14400	−	12.3738i	−0.533967	−	0.924859i	0.465245	−	0.885182i	$-0.345966\pi$
$180$	−0.796717	−	2.40228i	−0.0593838	−	0.179056i
$181$	12.8873			0.957905			0.478952	−	0.877841i	$-0.341017\pi$
$181$	12.8873			0.957905			0.478952	+	0.877841i	$0.341017\pi$
$182$		0			0
$183$	2.04875	−	20.0791i	0.151448	−	1.48429i
$184$	−2.33929	−	4.05178i	−0.172455	−	0.298701i
$185$	6.63315			0.487679
$186$	1.81522	−	17.7904i	0.133099	−	1.30445i
$187$	4.46122			0.326237
$188$	−6.64490			−0.484629
$189$		0			0
$190$	−7.19777			−0.522181
$191$	−2.16435			−0.156607			−0.0783034	−	0.996930i	$-0.524950\pi$
$191$	−2.16435			−0.156607			−0.0783034	+	0.996930i	$0.524950\pi$
$192$	0.349454	−	3.42488i	0.0252197	−	0.247169i
$193$	10.4313			0.750861			0.375431	−	0.926850i	$-0.377495\pi$
$193$	10.4313			0.750861			0.375431	+	0.926850i	$0.377495\pi$
$194$	−2.89475	−	5.01385i	−0.207831	−	0.359973i
$195$	0.837775	−	8.21075i	0.0599943	−	0.587984i
$196$		0			0
$197$	−18.7848			−1.33836			−0.669179	−	0.743101i	$-0.733354\pi$
$197$	−18.7848			−1.33836			−0.669179	+	0.743101i	$0.733354\pi$
$198$	1.99381	−	2.24159i	0.141694	−	0.159303i
$199$	−4.21303	−	7.29719i	−0.298654	−	0.517284i	0.677174	−	0.735823i	$-0.263204\pi$
$199$	−4.21303	−	7.29719i	−0.298654	−	0.517284i	−0.975828	+	0.218539i	$0.929871\pi$
$200$	3.87085	−	6.70452i	0.273711	−	0.474081i
$201$	−2.08587	+	20.4429i	−0.147126	+	1.44193i
$202$	−8.14681	+	14.1107i	−0.573208	+	0.992825i
$203$		0			0
$204$	10.6483	−	4.77975i	0.745532	−	0.334650i
$205$	1.00138			0.0699392
$206$	−9.90278	−	17.1521i	−0.689960	−	1.19505i
$207$	2.33929	+	7.05350i	0.162592	+	0.490252i
$208$	−12.5183	+	21.6823i	−0.867986	+	1.50340i
$209$	−1.31241	−	2.27316i	−0.0907814	−	0.157238i
$210$		0			0
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	−0.991948	−	0.126646i	$-0.959579\pi$
$211$	−5.61126	+	9.71899i	−0.386295	+	0.669083i	0.605653	+	0.795729i	$0.292912\pi$
$212$	−3.07598	−	5.32776i	−0.211259	−	0.365912i
$213$	0.756071	−	7.40999i	0.0518051	−	0.507724i
$214$	−3.22803	+	5.59111i	−0.220664	+	0.382200i
$215$	3.31657	−	5.74447i	0.226188	−	0.391770i
$216$	−2.94756	+	9.36107i	−0.200556	+	0.636940i
$217$		0			0
$218$	−10.9320	−	18.9348i	−0.740408	−	1.28242i
$219$	−7.04944	+	3.16431i	−0.476357	+	0.213824i
$220$	0.496374			0.0334655
$221$	38.0617			2.56031
$222$	16.6785	+	12.0404i	1.11939	+	0.808099i
$223$	10.3774	+	17.9742i	0.694923	+	1.20364i	0.970206	+	0.242279i	$0.0778951\pi$
$223$	10.3774	+	17.9742i	0.694923	+	1.20364i	−0.275283	+	0.961363i	$0.588772\pi$
$224$		0			0
$225$	−8.17240	+	9.18801i	−0.544826	+	0.612534i
$226$	7.66621	−	13.2783i	0.509949	−	0.883257i
$227$	5.21512	−	9.03284i	0.346139	−	0.599531i	−0.639421	−	0.768857i	$-0.720826\pi$
$227$	5.21512	−	9.03284i	0.346139	−	0.599531i	0.985560	+	0.169326i	$0.0541591\pi$
$228$	−5.56801	−	4.01961i	−0.368751	−	0.266205i
$229$	−7.52961	−	13.0417i	−0.497570	−	0.861817i	0.502426	−	0.864620i	$-0.332441\pi$
$229$	−7.52961	−	13.0417i	−0.497570	−	0.861817i	−0.999996	+	0.00280316i	$0.999108\pi$
$230$	−1.99829	+	3.46113i	−0.131763	+	0.228220i
$231$		0			0
$232$	−5.17240	−	8.95886i	−0.339585	−	0.588178i
$233$	−2.19344	+	3.79915i	−0.143697	+	0.248890i	−0.928886	−	0.370366i	$-0.879232\pi$
$233$	−2.19344	+	3.79915i	−0.143697	+	0.248890i	0.785189	+	0.619256i	$0.212566\pi$
$234$	17.0106	−	19.1245i	1.11202	−	1.25021i
$235$	−3.54875	−	6.14662i	−0.231495	−	0.400961i
$236$	9.26972			0.603407
$237$	−0.234501	+	2.29826i	−0.0152325	+	0.149288i
$238$		0			0
$239$	4.77561	−	8.27160i	0.308909	−	0.535046i	−0.669215	−	0.743069i	$-0.733370\pi$
$239$	4.77561	−	8.27160i	0.308909	−	0.535046i	0.978124	+	0.208023i	$0.0667029\pi$
$240$	−7.48143	+	3.35822i	−0.482924	+	0.216772i
$241$	−5.26792	+	9.12431i	−0.339337	+	0.587749i	−0.984308	−	0.176458i	$-0.943536\pi$
$241$	−5.26792	+	9.12431i	−0.339337	+	0.587749i	0.644971	+	0.764207i	$0.276869\pi$
$242$	−9.05377	−	15.6816i	−0.581999	−	1.00805i
$243$	7.58829	−	13.6168i	0.486789	−	0.873519i
$244$	10.3563			0.662996
$245$		0			0
$246$	2.51788	+	1.81769i	0.160534	+	0.115892i
$247$	−11.1971	−	19.3939i	−0.712453	−	1.23401i
$248$	−11.4734			−0.728560
$249$	8.98143	−	4.03153i	0.569175	−	0.255488i
$250$	−14.6802			−0.928458
$251$	−24.4346			−1.54230			−0.771148	−	0.636656i	$-0.780317\pi$
$251$	−24.4346			−1.54230			−0.771148	+	0.636656i	$0.780317\pi$
$252$		0			0
$253$	−1.45744			−0.0916282
$254$	−10.9332			−0.686007
$255$	10.1081	+	7.29719i	0.632997	+	0.456968i
$256$	17.7417			1.10886
$257$	−2.00416	−	3.47131i	−0.125016	−	0.216534i	0.796723	−	0.604345i	$-0.206565\pi$
$257$	−2.00416	−	3.47131i	−0.125016	−	0.216534i	−0.921739	+	0.387810i	$0.873232\pi$
$258$	18.7665	−	8.42380i	1.16835	−	0.524443i
$259$		0			0
$260$	4.23491			0.262638
$261$	5.17240	+	15.5960i	0.320163	+	0.965366i
$262$	5.63694	+	9.76347i	0.348251	+	0.603189i
$263$	−8.84362	+	15.3176i	−0.545321	+	0.944524i	0.453265	+	0.891376i	$0.350259\pi$
$263$	−8.84362	+	15.3176i	−0.545321	+	0.944524i	−0.998587	+	0.0531485i	$0.983074\pi$
$264$	−1.56060	−	1.12661i	−0.0960482	−	0.0693383i
$265$	3.28550	−	5.69066i	0.201827	−	0.349574i
$266$		0			0
$267$	1.18478	+	0.855304i	0.0725072	+	0.0523438i
$268$	−10.5439			−0.644074
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	0.997191	−	0.0749032i	$-0.0238648\pi$
$269$	7.11366	+	12.3212i	0.433727	+	0.751238i	−0.563463	+	0.826141i	$0.690531\pi$
$270$	8.18409	−	1.81769i	0.498068	−	0.110621i
$271$	2.69937	−	4.67545i	0.163975	−	0.284013i	−0.772316	−	0.635239i	$-0.780902\pi$
$271$	2.69937	−	4.67545i	0.163975	−	0.284013i	0.936291	+	0.351226i	$0.114235\pi$
$272$	−18.9091	−	32.7515i	−1.14653	−	1.98585i
$273$		0			0
$274$	11.9258	−	20.6561i	0.720464	−	1.24788i
$275$	−1.20582	−	2.08854i	−0.0727136	−	0.125944i
$276$	−3.47870	+	1.56150i	−0.209393	+	0.0939911i
$277$	−3.83310	+	6.63913i	−0.230309	+	0.398907i	−0.957899	−	0.287105i	$-0.907307\pi$
$277$	−3.83310	+	6.63913i	−0.230309	+	0.398907i	0.727590	+	0.686012i	$0.240640\pi$
$278$	7.48267	−	12.9604i	0.448781	−	0.777311i
$279$	17.8483	+	3.68059i	1.06855	+	0.220351i
$280$		0			0
$281$	11.3312	+	19.6263i	0.675965	+	1.17081i	0.976186	+	0.216936i	$0.0696065\pi$
$281$	11.3312	+	19.6263i	0.675965	+	1.17081i	−0.300220	+	0.953870i	$0.597060\pi$
$282$	2.23422	−	21.8968i	0.133046	−	1.30394i
$283$	−31.8492			−1.89324			−0.946619	−	0.322353i	$-0.895526\pi$
$283$	−31.8492			−1.89324			−0.946619	+	0.322353i	$0.895526\pi$
$284$	3.82189			0.226788
$285$	0.744561	−	7.29719i	0.0441040	−	0.432248i
$286$	2.50987	+	4.34722i	0.148412	+	0.257057i
$287$		0			0
$288$	−13.8083	−	2.84748i	−0.813664	−	0.167790i
$289$	−20.2465	+	35.0680i	−1.19097	+	2.06282i
$290$	−4.41840	+	7.65289i	−0.259457	+	0.449393i
$291$	5.38255	−	2.41608i	0.315530	−	0.141633i
$292$	−1.98242	−	3.43366i	−0.116013	−	0.200940i
$293$	−13.7468	+	23.8102i	−0.803097	+	1.39100i	0.114472	+	0.993427i	$0.463483\pi$
$293$	−13.7468	+	23.8102i	−0.803097	+	1.39100i	−0.917568	+	0.397578i	$0.869851\pi$
$294$		0			0
$295$	4.95056	+	8.57462i	0.288233	+	0.499234i
$296$	6.59888	−	11.4296i	0.383552	−	0.664332i
$297$	2.06630	+	2.25323i	0.119899	+	0.130746i
$298$	−3.71015	−	6.42617i	−0.214923	−	0.372258i
$299$	−12.4344			−0.719099
$300$	−5.11578	−	3.69314i	−0.295360	−	0.213224i
$301$		0			0
$302$	−10.7534	+	18.6254i	−0.618789	+	1.07177i
$303$	−13.4629	−	9.71899i	−0.773421	−	0.558342i
$304$	−11.1254	+	19.2698i	−0.638088	+	1.10520i
$305$	5.53087	+	9.57975i	0.316697	+	0.548535i
$306$	12.1703	+	36.6964i	0.695732	+	2.09779i
$307$	14.8176			0.845683			0.422841	−	0.906204i	$-0.361033\pi$
$307$	14.8176			0.845683			0.422841	+	0.906204i	$0.361033\pi$
$308$		0			0
$309$	18.4134	−	8.26530i	1.04750	−	0.470196i
$310$	4.90043	+	8.48779i	0.278326	+	0.482074i
$311$	29.0635			1.64804			0.824021	−	0.566559i	$-0.191726\pi$
$311$	29.0635			1.64804			0.824021	+	0.566559i	$0.191726\pi$
$312$	−13.3145	−	9.61192i	−0.753787	−	0.544168i
$313$	−24.4780			−1.38358			−0.691790	−	0.722099i	$-0.743178\pi$
$313$	−24.4780			−1.38358			−0.691790	+	0.722099i	$0.743178\pi$
$314$	−19.1614			−1.08134
$315$		0			0
$316$	−1.18539			−0.0666834
$317$	−7.38688			−0.414888			−0.207444	−	0.978247i	$-0.566515\pi$
$317$	−7.38688			−0.414888			−0.207444	+	0.978247i	$0.566515\pi$
$318$	18.5907	−	8.34488i	1.04252	−	0.467958i
$319$	−3.22253			−0.180427
$320$	0.943395	+	1.63401i	0.0527374	+	0.0913438i
$321$	−5.33442	−	3.85098i	−0.297738	−	0.214941i
$322$		0			0
$323$	33.8268			1.88218
$324$	7.34610	+	3.16431i	0.408116	+	0.175795i
$325$	−10.2877	−	17.8188i	−0.570657	−	0.988407i
$326$	−1.41597	+	2.45253i	−0.0784231	+	0.135833i
$327$	20.3271	−	9.12431i	1.12409	−	0.504576i
$328$	0.996205	−	1.72548i	0.0550062	−	0.0952736i
$329$		0			0
$330$	−0.166896	+	1.63569i	−0.00918734	+	0.0900419i
$331$	20.0617			1.10269			0.551347	−	0.834276i	$-0.314114\pi$
$331$	20.0617			1.10269			0.551347	+	0.834276i	$0.314114\pi$
$332$	2.52573	+	4.37470i	0.138618	+	0.240093i
$333$	−13.9320	+	15.6634i	−0.763468	+	0.858348i
$334$	3.31657	−	5.74447i	0.181475	−	0.314324i
$335$	−5.63106	−	9.75329i	−0.307658	−	0.532879i
$336$		0			0
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	−0.939986	−	0.341214i	$-0.889162\pi$
$337$	−3.20327	+	5.54823i	−0.174493	+	0.302231i	0.765493	+	0.643445i	$0.222495\pi$
$338$	10.3658	+	17.9542i	0.563827	+	0.976577i
$339$	12.6687	+	9.14565i	0.688067	+	0.496723i
$340$	−3.19846	+	5.53989i	−0.173461	+	0.300443i
$341$	−1.78705	+	3.09526i	−0.0967740	+	0.167617i
$342$	15.1179	−	16.9967i	0.817482	−	0.919074i
$343$		0			0
$344$	−6.59888	−	11.4296i	−0.355788	−	0.616243i
$345$	−3.30223	−	2.38392i	−0.177786	−	0.128346i
$346$	−27.3880			−1.47239
$347$	−29.1927			−1.56714			−0.783572	−	0.621300i	$-0.786605\pi$
$347$	−29.1927			−1.56714			−0.783572	+	0.621300i	$0.786605\pi$
$348$	−7.69174	+	3.45262i	−0.412320	+	0.185080i
$349$	2.17192	+	3.76188i	0.116260	+	0.201369i	0.918283	−	0.395925i	$-0.129576\pi$
$349$	2.17192	+	3.76188i	0.116260	+	0.201369i	−0.802022	+	0.597294i	$0.796243\pi$
$350$		0			0
$351$	17.6291	+	19.2238i	0.940970	+	1.02609i
$352$	1.38255	−	2.39464i	0.0736899	−	0.127635i
$353$	−12.8503	+	22.2574i	−0.683955	+	1.18464i	0.289809	+	0.957084i	$0.406408\pi$
$353$	−12.8503	+	22.2574i	−0.683955	+	1.18464i	−0.973764	+	0.227560i	$0.926925\pi$
$354$	−3.11677	+	30.5464i	−0.165654	+	1.62352i
$355$	2.04111	+	3.53530i	0.108331	+	0.187635i
$356$	−0.374892	+	0.649331i	−0.0198692	+	0.0344145i
$357$		0			0
$358$	12.1421	+	21.0308i	0.641732	+	1.11151i
$359$	−10.3436	+	17.9157i	−0.545916	+	0.945554i	0.452633	+	0.891697i	$0.350485\pi$
$359$	−10.3436	+	17.9157i	−0.545916	+	0.945554i	−0.998549	+	0.0538567i	$0.982849\pi$
$360$	−1.69318	−	5.10532i	−0.0892383	−	0.269074i
$361$	−0.451246	−	0.781582i	−0.0237498	−	0.0411359i
$362$	−21.9036			−1.15123
$363$	16.8348	−	7.55667i	0.883595	−	0.396622i
$364$		0			0
$365$	2.11745	−	3.66754i	0.110833	−	0.191968i
$366$	−3.48212	+	34.1271i	−0.182013	+	1.78385i
$367$	1.42391	−	2.46628i	0.0743273	−	0.128739i	−0.826466	−	0.562986i	$-0.809652\pi$
$367$	1.42391	−	2.46628i	0.0743273	−	0.128739i	0.900794	+	0.434248i	$0.142986\pi$
$368$	6.17742	+	10.6996i	0.322020	+	0.557755i
$369$	−2.10325	+	2.36463i	−0.109491	+	0.123098i
$370$	−11.2739			−0.586101
$371$		0			0
$372$	−0.949180	+	9.30259i	−0.0492127	+	0.482317i
$373$	−10.7163	−	18.5612i	−0.554871	−	0.961065i	−0.997914	−	0.0645641i	$-0.979434\pi$
$373$	−10.7163	−	18.5612i	−0.554871	−	0.961065i	0.443043	−	0.896501i	$-0.353899\pi$
$374$	−7.58242			−0.392077
$375$	1.51857	−	14.8830i	0.0784186	−	0.768554i
$376$	−14.1217			−0.728271
$377$	−27.4936			−1.41599
$378$		0			0
$379$	27.0494			1.38943			0.694716	−	0.719284i	$-0.255530\pi$
$379$	27.0494			1.38943			0.694716	+	0.719284i	$0.255530\pi$
$380$	3.76371			0.193074
$381$	1.13096	−	11.0842i	0.0579409	−	0.567859i
$382$	3.67859			0.188213
$383$	7.21340	+	12.4940i	0.368588	+	0.638412i	0.989345	−	0.145590i	$-0.0465081\pi$
$383$	7.21340	+	12.4940i	0.368588	+	0.638412i	−0.620757	+	0.784003i	$0.713175\pi$
$384$	−2.24647	+	22.0169i	−0.114640	+	1.12355i
$385$		0			0
$386$	−17.7293			−0.902399
$387$	6.59888	+	19.8971i	0.335440	+	1.01143i
$388$	1.51366	+	2.62174i	0.0768446	+	0.133099i
$389$	3.05377	−	5.28929i	0.154832	−	0.268178i	−0.778166	−	0.628059i	$-0.783850\pi$
$389$	3.05377	−	5.28929i	0.154832	−	0.268178i	0.932998	+	0.359882i	$0.117183\pi$
$390$	−1.42391	+	13.9552i	−0.0721023	+	0.706650i
$391$	9.39120	−	16.2660i	0.474933	−	0.822609i
$392$		0			0
$393$	−10.4814	+	4.70484i	−0.528718	+	0.237328i
$394$	31.9271			1.60846
$395$	−0.633065	−	1.09650i	−0.0318530	−	0.0551710i
$396$	−1.04256	+	1.17213i	−0.0523908	+	0.0589016i
$397$	6.44364	−	11.1607i	0.323397	−	0.560140i	−0.657789	−	0.753202i	$-0.728508\pi$
$397$	6.44364	−	11.1607i	0.323397	−	0.560140i	0.981187	+	0.193061i	$0.0618417\pi$
$398$	7.16059	+	12.4025i	0.358928	+	0.621682i
$399$		0			0
$400$	−10.2218	+	17.7047i	−0.511092	+	0.885237i
$401$	−4.19530	−	7.26647i	−0.209503	−	0.362870i	0.742055	−	0.670339i	$-0.233851\pi$
$401$	−4.19530	−	7.26647i	−0.209503	−	0.362870i	−0.951558	+	0.307469i	$0.900518\pi$
$402$	3.54520	−	34.7453i	0.176818	−	1.73294i
$403$	−15.2465	+	26.4078i	−0.759483	+	1.31546i
$404$	4.25997	−	7.37848i	0.211941	−	0.367093i
$405$	0.996205	+	8.48516i	0.0495018	+	0.421631i
$406$		0			0
$407$	−2.05563	−	3.56046i	−0.101894	−	0.176485i
$408$	22.6298	−	10.1579i	1.12034	−	0.502891i
$409$	6.81266			0.336864			0.168432	−	0.985713i	$-0.446130\pi$
$409$	6.81266			0.336864			0.168432	+	0.985713i	$0.446130\pi$
$410$	−1.70197			−0.0840543
$411$	19.7078	+	14.2273i	0.972112	+	0.701779i
$412$	5.17817	+	8.96885i	0.255110	+	0.441864i
$413$		0			0
$414$	−3.97593	−	11.9883i	−0.195406	−	0.589194i
$415$	−2.69777	+	4.67267i	−0.132428	+	0.229372i
$416$	11.7955	−	20.4303i	0.578320	−	1.00168i
$417$	12.3654	+	8.92669i	0.605534	+	0.437142i
$418$	2.23061	+	3.86353i	0.109103	+	0.188971i
$419$	5.16231	−	8.94137i	0.252195	−	0.436815i	−0.711935	−	0.702246i	$-0.752181\pi$
$419$	5.16231	−	8.94137i	0.252195	−	0.436815i	0.964130	+	0.265431i	$0.0855142\pi$
$420$		0			0
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	0.825283	−	0.564720i	$-0.191016\pi$
$421$	−1.56801	−	2.71588i	−0.0764202	−	0.132364i	−0.901703	+	0.432356i	$0.857682\pi$
$422$	9.53706	−	16.5187i	0.464257	−	0.804117i
$423$	21.9682	+	4.53016i	1.06813	+	0.220264i
$424$	−6.53706	−	11.3225i	−0.317468	−	0.549870i
$425$	31.0795			1.50757
$426$	−1.28504	+	12.5942i	−0.0622603	+	0.610192i
$427$		0			0
$428$	1.68794	−	2.92359i	0.0815895	−	0.141317i
$429$	−4.66690	+	2.09485i	−0.225320	+	0.101140i
$430$	−5.63694	+	9.76347i	−0.271837	+	0.470836i
$431$	−15.9363	−	27.6025i	−0.767625	−	1.32957i	−0.938847	−	0.344334i	$-0.888105\pi$
$431$	−15.9363	−	27.6025i	−0.767625	−	1.32957i	0.171222	−	0.985233i	$-0.445229\pi$
$432$	7.78367	−	24.7200i	0.374492	−	1.18934i
$433$	7.48855			0.359877			0.179938	−	0.983678i	$-0.442410\pi$
$433$	7.48855			0.359877			0.179938	+	0.983678i	$0.442410\pi$
$434$		0			0
$435$	−7.30154	−	5.27107i	−0.350082	−	0.252728i
$436$	5.71634	+	9.90099i	0.273763	+	0.474171i
$437$	−11.0509			−0.528636
$438$	11.9814	−	5.37815i	0.572495	−	0.256978i
$439$	2.28930			0.109262			0.0546311	−	0.998507i	$-0.482602\pi$
$439$	2.28930			0.109262			0.0546311	+	0.998507i	$0.482602\pi$
$440$	1.05489			0.0502900
$441$		0			0
$442$	−64.6908			−3.07703
$443$	37.3497			1.77454			0.887270	−	0.461251i	$-0.152599\pi$
$443$	37.3497			1.77454			0.887270	+	0.461251i	$0.152599\pi$
$444$	−8.72119	−	6.29593i	−0.413889	−	0.298791i
$445$	−0.800854			−0.0379641
$446$	−17.6378	−	30.5495i	−0.835172	−	1.44656i
$447$	6.89872	−	3.09665i	0.326298	−	0.146467i
$448$		0			0
$449$	−6.20286			−0.292731			−0.146366	−	0.989231i	$-0.546758\pi$
$449$	−6.20286			−0.292731			−0.146366	+	0.989231i	$0.546758\pi$
$450$	13.8900	−	15.6162i	0.654783	−	0.736155i
$451$	−0.310330	−	0.537507i	−0.0146129	−	0.0253102i
$452$	−4.00866	+	6.94320i	−0.188552	+	0.326581i
$453$	−17.7703	−	12.8286i	−0.834923	−	0.602741i
$454$	−8.86376	+	15.3525i	−0.415997	+	0.720527i
$455$		0			0
$456$	−11.8331	−	8.54245i	−0.554136	−	0.400037i
$457$	20.1716			0.943589			0.471795	−	0.881709i	$-0.343606\pi$
$457$	20.1716			0.943589			0.471795	+	0.881709i	$0.343606\pi$
$458$	12.7975	+	22.1660i	0.597989	+	1.03575i
$459$	−38.4622	+	8.54245i	−1.79526	+	0.398728i
$460$	1.04490	−	1.80983i	0.0487189	−	0.0843836i
$461$	11.2680	+	19.5168i	0.524803	+	0.908986i	0.999583	+	0.0288813i	$0.00919447\pi$
$461$	11.2680	+	19.5168i	0.524803	+	0.908986i	−0.474780	+	0.880105i	$0.657472\pi$
$462$		0			0
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	−0.342966	−	0.939348i	$-0.611432\pi$
$463$	13.8145	−	23.9275i	0.642016	−	1.11200i	0.984982	−	0.172656i	$-0.0552350\pi$
$464$	13.6588	+	23.6578i	0.634096	+	1.09829i
$465$	−9.11194	+	4.09011i	−0.422556	+	0.189674i
$466$	3.72803	−	6.45714i	0.172698	−	0.299121i
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	−0.999227	−	0.0393016i	$-0.987487\pi$
$467$	−10.0612	+	17.4265i	−0.465577	+	0.806404i	0.533650	+	0.845705i	$0.320820\pi$
$468$	−8.89483	+	10.0002i	−0.411164	+	0.462261i
$469$		0			0
$470$	6.03156	+	10.4470i	0.278215	+	0.481883i
$471$	1.98212	−	19.4261i	0.0913312	−	0.895106i
$472$	19.6999			0.906764
$473$	−4.11126			−0.189036
$474$	0.398564	−	3.90619i	0.0183067	−	0.179417i
$475$	−9.14301	−	15.8362i	−0.419510	−	0.726613i
$476$		0			0
$477$	6.53706	+	19.7107i	0.299312	+	0.902493i
$478$	−8.11677	+	14.0586i	−0.371252	+	0.643028i
$479$	4.79329	−	8.30222i	0.219011	−	0.379338i	−0.735495	−	0.677530i	$-0.763050\pi$
$479$	4.79329	−	8.30222i	0.219011	−	0.379338i	0.954506	+	0.298192i	$0.0963836\pi$
$480$	7.04944	−	3.16431i	0.321762	−	0.144430i
$481$	−17.5380	−	30.3767i	−0.799664	−	1.38506i
$482$	8.95351	−	15.5079i	0.407821	−	0.706367i
$483$		0			0
$484$	4.73422	+	8.19991i	0.215192	+	0.372723i
$485$	−1.61677	+	2.80032i	−0.0734135	+	0.127156i
$486$	−12.8973	+	23.1435i	−0.585032	+	1.04981i
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	0.679046	−	0.734096i	$-0.262394\pi$
$487$	−6.53706	−	11.3225i	−0.296223	−	0.513073i	−0.975269	+	0.221023i	$0.929060\pi$
$488$	22.0092			0.996311
$489$	−2.33993	−	1.68922i	−0.105815	−	0.0763893i
$490$		0			0
$491$	−7.67054	+	13.2858i	−0.346167	+	0.599578i	−0.985565	−	0.169298i	$-0.945850\pi$
$491$	−7.67054	+	13.2858i	−0.346167	+	0.599578i	0.639398	+	0.768876i	$0.279183\pi$
$492$	−1.31660	−	0.950469i	−0.0593569	−	0.0428505i
$493$	20.7648	−	35.9657i	0.935201	−	1.61982i
$494$	19.0309	+	32.9624i	0.856239	+	1.48305i
$495$	−1.64102	−	0.338403i	−0.0737585	−	0.0152101i
$496$	30.2979			1.36042
$497$		0			0
$498$	−15.2651	+	6.85210i	−0.684045	+	0.307050i
$499$	−2.43268	−	4.21352i	−0.108902	−	0.188623i	0.806424	−	0.591338i	$-0.201400\pi$
$499$	−2.43268	−	4.21352i	−0.108902	−	0.188623i	−0.915326	+	0.402715i	$0.868067\pi$
$500$	7.67628			0.343294
$501$	5.48074	+	3.95661i	0.244861	+	0.176768i
$502$	41.5297			1.85356
$503$	16.0085			0.713783			0.356892	−	0.934146i	$-0.383837\pi$
$503$	16.0085			0.713783			0.356892	+	0.934146i	$0.383837\pi$
$504$		0			0
$505$	9.10026			0.404956
$506$	2.47710			0.110121
$507$	−19.2744	+	8.65178i	−0.856007	+	0.384239i
$508$	5.71695			0.253649
$509$	15.5925	+	27.0071i	0.691127	+	1.19707i	0.971469	+	0.237167i	$0.0762188\pi$
$509$	15.5925	+	27.0071i	0.691127	+	1.19707i	−0.280342	+	0.959900i	$0.590448\pi$
$510$	−17.1801	−	12.4025i	−0.760747	−	0.549192i
$511$		0			0
$512$	−4.59937			−0.203265
$513$	15.6676	+	17.0849i	0.691741	+	0.754317i
$514$	3.40633	+	5.89994i	0.150247	+	0.260235i
$515$	−5.53087	+	9.57975i	−0.243719	+	0.422134i
$516$	−9.81303	+	4.40481i	−0.431994	+	0.193911i
$517$	−2.19954	+	3.80971i	−0.0967356	+	0.167551i
$518$		0			0
$519$	2.83310	−	27.7663i	0.124359	−	1.21880i
$520$	9.00000			0.394676
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	0.539652	−	0.841888i	$-0.318556\pi$
$521$	−10.4830	−	18.1572i	−0.459270	−	0.795480i	−0.998923	+	0.0464085i	$0.985222\pi$
$522$	−8.79115	−	26.5073i	−0.384778	−	1.16019i
$523$	−21.7821	+	37.7277i	−0.952465	+	1.64972i	−0.212401	+	0.977183i	$0.568128\pi$
$523$	−21.7821	+	37.7277i	−0.952465	+	1.64972i	−0.740064	+	0.672536i	$0.765205\pi$
$524$	−2.94756	−	5.10532i	−0.128765	−	0.223027i
$525$		0			0
$526$	15.0309	−	26.0342i	0.655377	−	1.13515i
$527$	−23.0302	−	39.8894i	−1.00321	−	1.73761i
$528$	4.12110	+	2.97507i	0.179348	+	0.129473i
$529$	8.43199	−	14.6046i	0.366608	−	0.634984i
$530$	−5.58413	+	9.67200i	−0.242559	+	0.420125i
$531$	−30.6459	−	6.31963i	−1.32992	−	0.274249i
$532$		0			0
$533$	−2.64764	−	4.58584i	−0.114682	−	0.198635i
$534$	−2.01368	−	1.45370i	−0.0871405	−	0.0629077i
$535$	3.60582			0.155893
$536$	−22.4079			−0.967875
$537$	−22.5773	+	10.1344i	−0.974283	+	0.437330i
$538$	−12.0906	−	20.9415i	−0.521262	−	0.902852i
$539$		0			0
$540$	−4.27946	+	0.950469i	−0.184159	+	0.0409017i
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	−0.952363	−	0.304967i	$-0.901355\pi$
$541$	−4.93268	+	8.54365i	−0.212072	+	0.367320i	0.740291	+	0.672287i	$0.234688\pi$
$542$	−4.58793	+	7.94652i	−0.197068	+	0.341332i
$543$	2.26578	−	22.2061i	0.0972340	−	0.952957i
$544$	17.8173	+	30.8604i	0.763909	+	1.32313i
$545$	−6.10570	+	10.5754i	−0.261539	+	0.453000i
$546$		0			0
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	0.859882	−	0.510492i	$-0.170537\pi$
$547$	−0.284350	−	0.492509i	−0.0121579	−	0.0210582i	−0.872040	+	0.489434i	$0.837203\pi$
$548$	−6.23600	+	10.8011i	−0.266389	+	0.461399i
$549$	−34.2382	−	7.06043i	−1.46125	−	0.301332i
$550$	2.04944	+	3.54974i	0.0873885	+	0.151361i
$551$	−24.4346			−1.04095
$552$	−7.39292	+	3.31848i	−0.314663	+	0.141244i
$553$		0			0
$554$	6.51485	−	11.2841i	0.276789	−	0.479413i
$555$	1.16621	−	11.4296i	0.0495028	−	0.485160i
$556$	−3.91269	+	6.77698i	−0.165935	+	0.287408i
$557$	1.29349	+	2.24040i	0.0548071	+	0.0949286i	0.892127	−	0.451784i	$-0.149212\pi$
$557$	1.29349	+	2.24040i	0.0548071	+	0.0949286i	−0.837320	+	0.546713i	$0.815879\pi$
$558$	−30.3355	−	6.25564i	−1.28421	−	0.264822i
$559$	−35.0760			−1.48356
$560$		0			0
$561$	0.784350	−	7.68715i	0.0331153	−	0.324552i
$562$	−19.2589	−	33.3574i	−0.812388	−	1.40710i
$563$	−33.2831			−1.40272			−0.701358	−	0.712809i	$-0.747422\pi$
$563$	−33.2831			−1.40272			−0.701358	+	0.712809i	$0.747422\pi$
$564$	−1.16827	+	11.4499i	−0.0491932	+	0.482126i
$565$	−8.56341			−0.360265
$566$	54.1318			2.27533
$567$		0			0
$568$	8.12227			0.340803
$569$	−5.35346			−0.224429			−0.112214	−	0.993684i	$-0.535794\pi$
$569$	−5.35346			−0.224429			−0.112214	+	0.993684i	$0.535794\pi$
$570$	−1.26548	+	12.4025i	−0.0530050	+	0.519484i
$571$	4.90112			0.205105			0.102553	−	0.994728i	$-0.467299\pi$
$571$	4.90112			0.205105			0.102553	+	0.994728i	$0.467299\pi$
$572$	−1.31241	−	2.27316i	−0.0548747	−	0.0950457i
$573$	−0.380525	+	3.72940i	−0.0158967	+	0.155798i
$574$		0			0
$575$	−10.1533			−0.423424
$576$	−5.83998	−	1.20429i	−0.243333	−	0.0501788i
$577$	18.0378	+	31.2425i	0.750925	+	1.30064i	0.947375	+	0.320127i	$0.103725\pi$
$577$	18.0378	+	31.2425i	0.750925	+	1.30064i	−0.196450	+	0.980514i	$0.562941\pi$
$578$	34.4116	−	59.6026i	1.43133	−	2.47914i
$579$	1.83398	−	17.9742i	0.0762176	−	0.746983i
$580$	2.31038	−	4.00170i	0.0959333	−	0.166161i
$581$		0			0
$582$	−9.14833	+	4.10644i	−0.379210	+	0.170217i
$583$	−4.07275			−0.168676
$584$	−4.21303	−	7.29719i	−0.174337	−	0.301960i
$585$	−14.0007	−	2.88715i	−0.578857	−	0.119369i
$586$	23.3645	−	40.4684i	0.965177	−	1.67174i
$587$	−0.527445	−	0.913562i	−0.0217700	−	0.0377068i	0.854935	−	0.518735i	$-0.173597\pi$
$587$	−0.527445	−	0.913562i	−0.0217700	−	0.0377068i	−0.876705	+	0.481028i	$0.840263\pi$
$588$		0			0
$589$	−13.5501	+	23.4695i	−0.558323	+	0.967045i
$590$	−8.41411	−	14.5737i	−0.346403	−	0.599988i
$591$	−3.30264	+	32.3681i	−0.135853	+	1.33145i
$592$	−17.4258	+	30.1824i	−0.716196	+	1.24049i
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	−0.668796	−	0.743446i	$-0.733190\pi$
$593$	7.53548	−	13.0518i	0.309445	−	0.535975i	0.978241	+	0.207471i	$0.0665233\pi$
$594$	−3.51195	−	3.82965i	−0.144097	−	0.157132i
$595$		0			0
$596$	1.94004	+	3.36024i	0.0794670	+	0.137641i
$597$	−13.3145	+	5.97654i	−0.544928	+	0.244604i
$598$	21.1338			0.864227
$599$	42.0566			1.71839			0.859194	−	0.511650i	$-0.170965\pi$
$599$	42.0566			1.71839			0.859194	+	0.511650i	$0.170965\pi$
$600$	−10.8720	−	7.84864i	−0.443849	−	0.320420i
$601$	−9.44989	−	16.3677i	−0.385469	−	0.667652i	0.606365	−	0.795186i	$-0.292627\pi$
$601$	−9.44989	−	16.3677i	−0.385469	−	0.667652i	−0.991834	+	0.127534i	$0.959294\pi$
$602$		0			0
$603$	34.8585	+	7.18833i	1.41955	+	0.292732i
$604$	5.62296	−	9.73924i	0.228795	−	0.396284i
$605$	−5.05669	+	8.75844i	−0.205583	+	0.356081i
$606$	22.8819	+	16.5187i	0.929512	+	0.671025i
$607$	14.7213	+	25.4980i	0.597518	+	1.03493i	0.993186	+	0.116538i	$0.0371796\pi$
$607$	14.7213	+	25.4980i	0.597518	+	1.03493i	−0.395668	+	0.918393i	$0.629487\pi$
$608$	10.4830	−	18.1572i	0.425143	−	0.736370i
$609$		0			0
$610$	−9.40043	−	16.2820i	−0.380612	−	0.659240i
$611$	−18.7658	+	32.5033i	−0.759182	+	1.31494i
$612$	−6.36387	−	19.1885i	−0.257244	−	0.775650i
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	0.959454	−	0.281865i	$-0.0909531\pi$
$613$	5.83379	+	10.1044i	0.235625	+	0.408114i	−0.723829	+	0.689979i	$0.757620\pi$
$614$	−25.1843			−1.01636
$615$	0.176057	−	1.72548i	0.00709932	−	0.0695780i
$616$		0			0
$617$	16.4054	−	28.4151i	0.660458	−	1.14395i	−0.320037	−	0.947405i	$-0.603695\pi$
$617$	16.4054	−	28.4151i	0.660458	−	1.14395i	0.980495	−	0.196542i	$-0.0629713\pi$
$618$	−31.2960	+	14.0479i	−1.25891	+	0.565091i
$619$	12.0806	−	20.9242i	0.485560	−	0.841014i	−0.514303	−	0.857609i	$-0.671949\pi$
$619$	12.0806	−	20.9242i	0.485560	−	0.841014i	0.999862	+	0.0165947i	$0.00528250\pi$
$620$	−2.56243	−	4.43827i	−0.102910	−	0.178245i
$621$	12.5652	−	2.79073i	0.504224	−	0.111988i
$622$	−49.3972			−1.98065
$623$		0			0
$624$	35.1599	+	25.3824i	1.40752	+	1.01611i
$625$	−6.14764	−	10.6480i	−0.245906	−	0.425921i
$626$	41.6035			1.66281
$627$	−4.14764	+	1.86176i	−0.165641	+	0.0743517i
$628$	10.0195			0.399822
$629$	52.9830			2.11257
$630$		0			0
$631$	−11.1003			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$631$	−11.1003			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$632$	−2.51918			−0.100208
$633$	15.7603	+	11.3775i	0.626416	+	0.452217i
$634$	12.5549			0.498620
$635$	3.05318	+	5.28826i	0.121162	+	0.209858i
$636$	−9.72109	+	4.36354i	−0.385466	+	0.173026i
$637$		0			0
$638$	5.47710			0.216840
$639$	−12.6353	−	2.60558i	−0.499843	−	0.103075i
$640$	−6.06464	−	10.5043i	−0.239726	−	0.415218i
$641$	−3.65019	+	6.32231i	−0.144174	+	0.249716i	−0.929064	−	0.369918i	$-0.879386\pi$
$641$	−3.65019	+	6.32231i	−0.144174	+	0.249716i	0.784891	+	0.619634i	$0.212719\pi$
$642$	9.06653	+	6.54523i	0.357827	+	0.258320i
$643$	−10.6256	+	18.4041i	−0.419033	+	0.725787i	−0.995842	−	0.0910922i	$-0.970964\pi$
$643$	−10.6256	+	18.4041i	−0.419033	+	0.725787i	0.576809	+	0.816879i	$0.304298\pi$
$644$		0			0
$645$	−9.31522	−	6.72477i	−0.366787	−	0.264787i
$646$	−57.4930			−2.26203
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	0.650011	−	0.759924i	$-0.274764\pi$
$647$	−8.47300	−	14.6757i	−0.333108	−	0.576960i	−0.983120	+	0.182964i	$0.941431\pi$
$648$	15.6119	+	6.72477i	0.613292	+	0.264174i
$649$	3.06839	−	5.31460i	0.120445	−	0.208616i
$650$	17.4852	+	30.2853i	0.685826	+	1.18789i
$651$		0			0
$652$	0.740409	−	1.28243i	0.0289967	−	0.0502237i
$653$	1.86652	+	3.23292i	0.0730427	+	0.126514i	0.900233	−	0.435408i	$-0.143396\pi$
$653$	1.86652	+	3.23292i	0.0730427	+	0.126514i	−0.827191	+	0.561921i	$0.810062\pi$
$654$	−34.5486	+	15.5079i	−1.35096	+	0.606408i
$655$	3.14833	−	5.45306i	0.123015	−	0.213069i
$656$	−2.63070	+	4.55650i	−0.102711	+	0.177902i
$657$	4.21303	+	12.7033i	0.164366	+	0.495601i
$658$		0			0
$659$	11.7992	+	20.4368i	0.459632	+	0.796105i	0.998941	−	0.0460022i	$-0.0146481\pi$
$659$	11.7992	+	20.4368i	0.459632	+	0.796105i	−0.539310	+	0.842107i	$0.681315\pi$
$660$	0.0872701	−	0.855304i	0.00339698	−	0.0332927i
$661$	34.5175			1.34258			0.671288	−	0.741197i	$-0.265742\pi$
$661$	34.5175			1.34258			0.671288	+	0.741197i	$0.265742\pi$
$662$	−34.0975			−1.32524
$663$	6.69183	−	65.5844i	0.259889	−	2.54709i
$664$	5.36767	+	9.29708i	0.208306	+	0.360796i
$665$		0			0
$666$	23.6792	−	26.6219i	0.917550	−	1.03158i
$667$	−6.78366	+	11.7496i	−0.262664	+	0.454948i
$668$	−1.73424	+	3.00379i	−0.0670996	+	0.116220i
$669$	32.7960	−	14.7212i	1.26797	−	0.569156i
$670$	9.57072	+	16.5770i	0.369749	+	0.640424i
$671$	3.42807	−	5.93759i	0.132339	−	0.229218i
$672$		0			0
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	0.999464	−	0.0327353i	$-0.0104218\pi$
$673$	12.2287	+	21.1808i	0.471382	+	0.816458i	−0.528082	+	0.849194i	$0.677088\pi$
$674$	5.44437	−	9.42992i	0.209709	−	0.363227i
$675$	14.3951	+	15.6973i	0.554067	+	0.604189i
$676$	−5.42030	−	9.38823i	−0.208473	−	0.361086i
$677$	−8.32045			−0.319781			−0.159890	−	0.987135i	$-0.551114\pi$
$677$	−8.32045			−0.319781			−0.159890	+	0.987135i	$0.551114\pi$
$678$	−21.5320	−	15.5442i	−0.826931	−	0.596971i
$679$		0			0
$680$	−6.79734	+	11.7733i	−0.260666	+	0.451487i
$681$	−14.6476	−	10.5743i	−0.561299	−	0.405208i
$682$	3.03731	−	5.26078i	0.116305	−	0.201446i
$683$	21.2312	+	36.7735i	0.812389	+	1.40710i	0.911188	+	0.411991i	$0.135167\pi$
$683$	21.2312	+	36.7735i	0.812389	+	1.40710i	−0.0987988	+	0.995107i	$0.531500\pi$
$684$	−7.90515	+	8.88756i	−0.302261	+	0.339824i
$685$	−13.3215			−0.508989
$686$		0			0
$687$	−23.7960	+	10.6814i	−0.907873	+	0.407520i
$688$	17.4258	+	30.1824i	0.664352	+	1.15069i
$689$	−34.7474			−1.32377
$690$	5.61256	+	4.05178i	0.213667	+	0.154248i
$691$	35.3929			1.34641			0.673204	−	0.739456i	$-0.264917\pi$
$691$	35.3929			1.34641			0.673204	+	0.739456i	$0.264917\pi$
$692$	14.3212			0.544410
$693$		0			0
$694$	49.6167			1.88342
$695$	−8.35840			−0.317052
$696$	−16.3464	+	7.33748i	−0.619610	+	0.278126i
$697$	7.99862			0.302969
$698$	−3.69146	−	6.39380i	−0.139724	−	0.242009i
$699$	6.16069	+	4.44747i	0.233019	+	0.168219i
$700$		0			0
$701$	−7.00372			−0.264527			−0.132263	−	0.991215i	$-0.542224\pi$
$701$	−7.00372			−0.264527			−0.132263	+	0.991215i	$0.542224\pi$
$702$	−29.9629	−	32.6734i	−1.13088	−	1.23318i
$703$	−15.5867	−	26.9969i	−0.587862	−	1.01821i
$704$	0.584722	−	1.01277i	0.0220375	−	0.0381701i
$705$	−11.2152	+	5.03420i	−0.422389	+	0.189599i
$706$	21.8408	−	37.8294i	0.821989	−	1.42373i
$707$		0			0
$708$	1.62976	−	15.9727i	0.0612500	−	0.600291i
$709$	−2.22253			−0.0834688			−0.0417344	−	0.999129i	$-0.513288\pi$
$709$	−2.22253			−0.0834688			−0.0417344	+	0.999129i	$0.513288\pi$
$710$	−3.46913	−	6.00870i	−0.130194	−	0.225503i
$711$	3.91892	+	0.808139i	0.146971	+	0.0303076i
$712$	−0.796717	+	1.37995i	−0.0298582	+	0.0517160i
$713$	7.52373	+	13.0315i	0.281766	+	0.488033i
$714$		0			0
$715$	1.40180	−	2.42800i	0.0524245	−	0.0908019i
$716$	−6.34913	−	10.9970i	−0.237278	−	0.410977i
$717$	−13.4132	−	9.68315i	−0.500926	−	0.361624i
$718$	17.5803	−	30.4500i	0.656092	−	1.13638i
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	−0.999854	−	0.0170686i	$-0.994567\pi$
$719$	−13.0088	+	22.5319i	−0.485145	+	0.840296i	0.514709	+	0.857365i	$0.327900\pi$
$720$	4.47121	+	13.4817i	0.166632	+	0.502434i
$721$		0			0
$722$	0.766951	+	1.32840i	0.0285430	+	0.0494379i
$723$	14.7960	+	10.6814i	0.550268	+	0.397245i
$724$	11.4534			0.425662
$725$	−22.4500			−0.833772
$726$	−28.6128	+	12.8435i	−1.06192	+	0.476668i
$727$	0.685875	+	1.18797i	0.0254377	+	0.0440594i	0.878464	−	0.477809i	$-0.158569\pi$
$727$	0.685875	+	1.18797i	0.0254377	+	0.0440594i	−0.853026	+	0.521868i	$0.825235\pi$
$728$		0			0
$729$	−22.1291	−	15.4695i	−0.819595	−	0.572943i
$730$	−3.59888	+	6.23345i	−0.133201	+	0.230710i
$731$	26.4915	−	45.8847i	0.979824	−	1.69711i
$732$	1.82080	−	17.8450i	0.0672987	−	0.659572i
$733$	0.400087	+	0.692971i	0.0147776	+	0.0255955i	0.873320	−	0.487148i	$-0.161963\pi$
$733$	0.400087	+	0.692971i	0.0147776	+	0.0255955i	−0.858542	+	0.512743i	$0.828629\pi$
$734$	−2.42011	+	4.19176i	−0.0893280	+	0.154721i
$735$		0			0
$736$	−5.82072	−	10.0818i	−0.214555	−	0.371620i
$737$	−3.49017	+	6.04515i	−0.128562	+	0.222676i
$738$	3.57475	−	4.01899i	0.131588	−	0.147941i
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	0.812396	−	0.583106i	$-0.198163\pi$
$739$	−2.68547	−	4.65136i	−0.0987865	−	0.171103i	−0.911183	+	0.412003i	$0.864829\pi$
$740$	5.89511			0.216709
$741$	−35.3864	+	15.8840i	−1.29995	+	0.583513i
$742$		0			0
$743$	6.63162	−	11.4863i	0.243290	−	0.421391i	−0.718359	−	0.695672i	$-0.755107\pi$
$743$	6.63162	−	11.4863i	0.243290	−	0.421391i	0.961650	+	0.274281i	$0.0884399\pi$
$744$	−2.01719	+	19.7698i	−0.0739539	+	0.724797i
$745$	−2.07218	+	3.58912i	−0.0759188	+	0.131495i
$746$	18.2138	+	31.5472i	0.666854	+	1.15503i
$747$	−5.36767	−	16.1847i	−0.196393	−	0.592169i
$748$	3.96485			0.144969
$749$		0			0
$750$	−2.58100	+	25.2955i	−0.0942449	+	0.923662i
$751$	−2.77816	−	4.81191i	−0.101377	−	0.175589i	0.810875	−	0.585219i	$-0.198991\pi$
$751$	−2.77816	−	4.81191i	−0.101377	−	0.175589i	−0.912252	+	0.409629i	$0.865658\pi$
$752$	37.2914			1.35988
$753$	−4.29596	+	42.1033i	−0.156554	+	1.53433i
$754$	46.7289			1.70177
$755$	12.0119			0.437158
$756$		0			0
$757$	−13.3942			−0.486819			−0.243410	−	0.969924i	$-0.578266\pi$
$757$	−13.3942			−0.486819			−0.243410	+	0.969924i	$0.578266\pi$
$758$	−45.9739			−1.66985
$759$	−0.256239	+	2.51132i	−0.00930090	+	0.0911550i
$760$	7.99862			0.290141
$761$	6.42191	+	11.1231i	0.232794	+	0.403211i	0.958629	−	0.284658i	$-0.0918799\pi$
$761$	6.42191	+	11.1231i	0.232794	+	0.403211i	−0.725835	+	0.687868i	$0.758547\pi$
$762$	−1.92221	+	18.8390i	−0.0696345	+	0.682464i
$763$		0			0
$764$	−1.92353			−0.0695910
$765$	14.3510	−	16.1344i	0.518861	−	0.583342i
$766$	−12.2601	−	21.2351i	−0.442975	−	0.767256i
$767$	26.1785	−	45.3425i	0.945251	−	1.63722i
$768$	3.11926	−	30.5708i	0.112557	−	1.10313i
$769$	−1.48259	+	2.56793i	−0.0534636	+	0.0926018i	−0.891519	−	0.452984i	$-0.850359\pi$
$769$	−1.48259	+	2.56793i	−0.0534636	+	0.0926018i	0.838055	+	0.545586i	$0.183693\pi$
$770$		0			0
$771$	−6.33379	+	2.84307i	−0.228106	+	0.102391i
$772$	9.27067			0.333659
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	0.985662	−	0.168732i	$-0.0539673\pi$
$773$	9.63939	+	16.6959i	0.346705	+	0.600510i	−0.638957	+	0.769242i	$0.720634\pi$
$774$	−11.2156	−	33.8177i	−0.403138	−	1.21555i
$775$	−12.4496	+	21.5633i	−0.447203	+	0.774578i
$776$	3.21683	+	5.57171i	0.115477	+	0.200013i
$777$		0			0
$778$	−5.19028	+	8.98983i	−0.186080	+	0.322301i
$779$	−2.35305	−	4.07560i	−0.0843068	−	0.146024i
$780$	0.744561	−	7.29719i	0.0266596	−	0.261281i
$781$	1.26509	−	2.19120i	0.0452685	−	0.0784074i
$782$	−15.9616	+	27.6462i	−0.570784	+	0.988627i
$783$	27.7829	−	6.17058i	0.992878	−	0.220518i
$784$		0			0
$785$	5.35098	+	9.26818i	0.190985	+	0.330795i
$786$	17.8145	−	7.99647i	0.635423	−	0.285225i
$787$	13.6453			0.486402			0.243201	−	0.969976i	$-0.421803\pi$
$787$	13.6453			0.486402			0.243201	+	0.969976i	$0.421803\pi$
$788$	−16.6947			−0.594724
$789$	24.8390	+	17.9316i	0.884292	+	0.638380i
$790$	1.07598	+	1.86364i	0.0382815	+	0.0663055i
$791$		0			0
$792$	−2.21565	+	2.49100i	−0.0787297	+	0.0885137i
$793$	29.2472	−	50.6577i	1.03860	−	1.79891i
$794$	−10.9518	+	18.9691i	−0.388665	+	0.673187i
$795$	−9.22795	−	6.66177i	−0.327282	−	0.236268i
$796$	−3.74427	−	6.48527i	−0.132712	−	0.229864i
$797$	11.4792	−	19.8826i	0.406616	−	0.704279i	−0.587892	−	0.808939i	$-0.700042\pi$
$797$	11.4792	−	19.8826i	0.406616	−	0.704279i	0.994508	+	0.104660i	$0.0333755\pi$
$798$		0			0
$799$	−28.3461	−	49.0969i	−1.00281	−	1.73692i
$800$	9.63162	−	16.6824i	0.340529	−	0.589814i
$801$	1.68208	−	1.89112i	0.0594334	−	0.0668194i
$802$	7.13045	+	12.3503i	0.251785	+	0.436104i
$803$	−2.62482			−0.0926279
$804$	−1.85378	+	18.1683i	−0.0653779	+	0.640747i
$805$		0			0
$806$	25.9134	−	44.8834i	0.912761	−	1.58095i
$807$	22.4814	−	10.0913i	0.791384	−	0.355231i
$808$	9.05326	−	15.6807i	0.318492	−	0.551645i
$809$	−19.7291	−	34.1718i	−0.693639	−	1.20142i	−0.970637	−	0.240548i	$-0.922673\pi$
$809$	−19.7291	−	34.1718i	−0.693639	−	1.20142i	0.276998	−	0.960870i	$-0.410660\pi$
$810$	−1.69318	−	14.4216i	−0.0594922	−	0.506724i
$811$	−0.496374			−0.0174300			−0.00871502	−	0.999962i	$-0.502774\pi$
$811$	−0.496374			−0.0174300			−0.00871502	+	0.999962i	$0.502774\pi$
$812$		0			0
$813$	−7.58169	−	5.47331i	−0.265902	−	0.191957i
$814$	3.49381	+	6.05146i	0.122458	+	0.212103i
$815$	1.58168			0.0554039
$816$	−59.7588	+	26.8242i	−2.09198	+	0.939033i
$817$	−31.1733			−1.09062
$818$	−11.5790			−0.404850
$819$		0			0
$820$	0.889960			0.0310788
$821$	47.1038			1.64393			0.821967	−	0.569534i	$-0.192876\pi$
$821$	47.1038			1.64393			0.821967	+	0.569534i	$0.192876\pi$
$822$	−33.4959	−	24.1810i	−1.16830	−	0.843411i
$823$	−2.19777			−0.0766094			−0.0383047	−	0.999266i	$-0.512196\pi$
$823$	−2.19777			−0.0766094			−0.0383047	+	0.999266i	$0.512196\pi$
$824$	11.0046	+	19.0605i	0.383364	+	0.664005i
$825$	−3.81077	+	1.71055i	−0.132674	+	0.0595538i
$826$		0			0
$827$	−55.3360			−1.92422			−0.962110	−	0.272661i	$-0.912096\pi$
$827$	−55.3360			−1.92422			−0.962110	+	0.272661i	$0.912096\pi$
$828$	2.07901	+	6.26870i	0.0722507	+	0.217852i
$829$	10.1603	+	17.5982i	0.352882	+	0.611209i	0.986753	−	0.162229i	$-0.0518684\pi$
$829$	10.1603	+	17.5982i	0.352882	+	0.611209i	−0.633871	+	0.773439i	$0.718535\pi$
$830$	4.58520	−	7.94181i	0.159155	−	0.275664i
$831$	10.7660	+	7.77210i	0.373468	+	0.269611i
$832$	4.98867	−	8.64062i	0.172951	−	0.299560i
$833$		0			0
$834$	−21.0165	−	15.1721i	−0.727742	−	0.525365i
$835$	−3.70472			−0.128207
$836$	−1.16639	−	2.02024i	−0.0403403	−	0.0698715i
$837$	9.48005	−	30.1075i	0.327679	−	1.04067i
$838$	−8.77400	+	15.1970i	−0.303093	+	0.524972i
$839$	−12.2760	−	21.2626i	−0.423813	−	0.734066i	0.572496	−	0.819908i	$-0.305975\pi$
$839$	−12.2760	−	21.2626i	−0.423813	−	0.734066i	−0.996309	+	0.0858417i	$0.972642\pi$
$840$		0			0
$841$	−0.499311	+	0.864833i	−0.0172176	+	0.0298218i
$842$	2.66504	+	4.61598i	0.0918432	+	0.159077i
$843$	35.8104	−	16.0743i	1.23337	−	0.553629i
$844$	−4.98693	+	8.63762i	−0.171657	+	0.297319i
$845$	5.78949	−	10.0277i	0.199165	−	0.344963i
$846$	−37.3377	−	7.69959i	−1.28370	−	0.264717i
$847$		0			0
$848$	17.2625	+	29.8996i	0.592798	+	1.02676i
$849$	−5.59957	+	54.8795i	−0.192177	+	1.88346i
$850$	−52.8235			−1.81183
$851$	−17.3090			−0.593346
$852$	0.671947	−	6.58552i	0.0230205	−	0.225616i
$853$	−26.7708	−	46.3684i	−0.916614	−	1.58762i	−0.804521	−	0.593925i	$-0.797578\pi$
$853$	−26.7708	−	46.3684i	−0.916614	−	1.58762i	−0.112093	−	0.993698i	$-0.535756\pi$
$854$		0			0
$855$	−12.4429	−	2.56591i	−0.425539	−	0.0877524i
$856$	3.58719	−	6.21320i	0.122608	−	0.212363i
$857$	−27.0777	+	46.8999i	−0.924955	+	1.60207i	−0.133322	+	0.991073i	$0.542564\pi$
$857$	−27.0777	+	46.8999i	−0.924955	+	1.60207i	−0.791633	+	0.610996i	$0.790769\pi$
$858$	7.93199	−	3.56046i	0.270794	−	0.121552i
$859$	0.896461	+	1.55272i	0.0305869	+	0.0529780i	0.880914	−	0.473277i	$-0.156929\pi$
$859$	0.896461	+	1.55272i	0.0305869	+	0.0529780i	−0.850327	+	0.526255i	$0.823596\pi$
$860$	2.94756	−	5.10532i	0.100511	−	0.174090i
$861$		0			0
$862$	27.0858	+	46.9140i	0.922547	+	1.59790i
$863$	16.2854	−	28.2072i	0.554363	−	0.960185i	−0.443590	−	0.896230i	$-0.646295\pi$
$863$	16.2854	−	28.2072i	0.554363	−	0.960185i	0.997953	−	0.0639549i	$-0.0203714\pi$
$864$	−7.33423	+	23.2926i	−0.249516	+	0.792430i
$865$	7.64833	+	13.2473i	0.260051	+	0.450421i
$866$	−12.7277			−0.432506
$867$	56.8662	+	41.0524i	1.93128	+	1.39421i
$868$		0			0
$869$	−0.392378	+	0.679618i	−0.0133105	+	0.0230545i
$870$	12.4099	+	8.95886i	0.420735	+	0.303734i
$871$	−29.7770	+	51.5753i	−1.00896	+	1.74756i
$872$	12.1483	+	21.0415i	0.411394	+	0.712556i
$873$	−3.21683	−	9.69947i	−0.108873	−	0.328277i
$874$	18.7824			0.635324
$875$		0			0
$876$	−6.26509	+	2.81223i	−0.211678	+	0.0950166i
$877$	18.3647	+	31.8085i	0.620131	+	1.07410i	0.989461	+	0.144800i	$0.0462538\pi$
$877$	18.3647	+	31.8085i	0.620131	+	1.07410i	−0.369330	+	0.929298i	$0.620413\pi$
$878$	−3.89095			−0.131313
$879$	38.6105	+	27.8734i	1.30230	+	0.940145i
$880$	−2.78567			−0.0939049
$881$	−25.3721			−0.854807			−0.427403	−	0.904061i	$-0.640572\pi$
$881$	−25.3721			−0.854807			−0.427403	+	0.904061i	$0.640572\pi$
$882$		0			0
$883$	−16.9381			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$883$	−16.9381			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$884$	33.8268			1.13772
$885$	15.6453	−	7.02278i	0.525913	−	0.236068i
$886$	−63.4807			−2.13267
$887$	−24.0069	−	41.5811i	−0.806071	−	1.39616i	−0.915566	−	0.402169i	$-0.868256\pi$
$887$	−24.0069	−	41.5811i	−0.806071	−	1.39616i	0.109494	−	0.993987i	$-0.465077\pi$
$888$	−18.5342	−	13.3801i	−0.621968	−	0.449006i
$889$		0			0
$890$	1.36115			0.0456260
$891$	4.24583	−	3.16431i	0.142241	−	0.106008i
$892$	9.22279	+	15.9743i	0.308802	+	0.534860i
$893$	−16.6778	+	28.8868i	−0.558102	+	0.966661i
$894$	−11.7253	+	5.26316i	−0.392151	+	0.176026i
$895$	6.78159	−	11.7461i	0.226684	−	0.392627i
$896$		0			0
$897$	−2.18615	+	21.4258i	−0.0729936	+	0.715385i
$898$	10.5426			0.351810
$899$	16.6357	+	28.8138i	0.554831	+	0.960995i
$900$	−7.26310	+	8.16572i	−0.242103	+	0.272191i
$901$	26.2433	−	45.4548i	0.874292	−	1.51432i
$902$	0.527445	+	0.913562i	0.0175620	+	0.0304183i
$903$		0			0
$904$	−8.51918	+	14.7557i	−0.283344	+	0.490766i
$905$	6.11677	+	10.5945i	0.203328	+	0.352175i
$906$	30.2030	+	21.8039i	1.00343	+	0.724385i
$907$	12.3887	−	21.4579i	0.411361	−	0.712499i	−0.583678	−	0.811985i	$-0.698387\pi$
$907$	12.3887	−	21.4579i	0.411361	−	0.712499i	0.995039	+	0.0994869i	$0.0317201\pi$
$908$	4.63486	−	8.02781i	0.153813	−	0.266412i
$909$	−19.1138	+	21.4892i	−0.633965	+	0.712751i
$910$		0			0
$911$	−15.7916	−	27.3519i	−0.523200	−	0.906209i	−0.999635	−	0.0269997i	$-0.991405\pi$
$911$	−15.7916	−	27.3519i	−0.523200	−	0.906209i	0.476435	−	0.879210i	$-0.341929\pi$
$912$	31.2479	+	22.5582i	1.03472	+	0.746977i
$913$	3.34419			0.110676
$914$	−34.2843			−1.13402
$915$	17.4793	−	7.84601i	0.577849	−	0.259381i
$916$	−6.69183	−	11.5906i	−0.221104	−	0.382964i
$917$		0			0
$918$	65.3714	−	14.5190i	2.15758	−	0.479198i
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	−0.878856	−	0.477087i	$-0.841693\pi$
$919$	−0.796041	+	1.37878i	−0.0262590	+	0.0454819i	0.852597	+	0.522569i	$0.175026\pi$
$920$	2.22062	−	3.84623i	0.0732118	−	0.126807i
$921$	2.60515	−	25.5322i	0.0858426	−	0.841315i
$922$	−19.1514	−	33.1712i	−0.630718	−	1.09244i
$923$	10.7934	−	18.6947i	0.355268	−	0.615342i
$924$		0			0
$925$	−14.3207	−	24.8042i	−0.470863	−	0.815558i
$926$	−23.4796	+	40.6678i	−0.771587	+	1.33643i
$927$	−11.0046	−	33.1814i	−0.361439	−	1.08982i
$928$	−12.8702	−	22.2918i	−0.422484	−	0.731764i
$929$	27.0711			0.888175			0.444087	−	0.895983i	$-0.353528\pi$
$929$	27.0711			0.888175			0.444087	+	0.895983i	$0.353528\pi$
$930$	15.4869	−	6.95167i	0.507836	−	0.227954i
$931$		0			0
$932$	−1.94939	+	3.37644i	−0.0638543	+	0.110599i
$933$	5.10981	−	50.0795i	0.167288	−	1.63953i
$934$	17.1003	−	29.6186i	0.559540	−	0.969151i
$935$	2.11745	+	3.66754i	0.0692482	+	0.119941i
$936$	−18.9032	+	21.2524i	−0.617871	+	0.694657i
$937$	32.6624			1.06704			0.533518	−	0.845789i	$-0.320870\pi$
$937$	32.6624			1.06704			0.533518	+	0.845789i	$0.320870\pi$
$938$		0			0
$939$	−4.30361	+	42.1782i	−0.140443	+	1.37643i
$940$	−3.15390	−	5.46272i	−0.102869	−	0.178174i
$941$	4.72285			0.153961			0.0769803	−	0.997033i	$-0.475472\pi$
$941$	4.72285			0.153961			0.0769803	+	0.997033i	$0.475472\pi$
$942$	−3.36887	+	33.0171i	−0.109764	+	1.07576i
$943$	−2.61307			−0.0850933
$944$	−52.0220			−1.69317
$945$		0			0
$946$	6.98762			0.227187
$947$	56.7810			1.84514			0.922568	−	0.385835i	$-0.126087\pi$
$947$	56.7810			1.84514			0.922568	+	0.385835i	$0.126087\pi$
$948$	−0.208409	+	2.04255i	−0.00676882	+	0.0663389i
$949$	−22.3942			−0.726945
$950$	15.5397	+	26.9156i	0.504175	+	0.873257i
$951$	−1.29872	+	12.7284i	−0.0421140	+	0.412745i
$952$		0			0
$953$	−47.1693			−1.52796			−0.763982	−	0.645238i	$-0.776758\pi$
$953$	−47.1693			−1.52796			−0.763982	+	0.645238i	$0.776758\pi$
$954$	−11.1106	−	33.5009i	−0.359718	−	1.08463i
$955$	−1.02728	−	1.77930i	−0.0332419	−	0.0575766i
$956$	4.24426	−	7.35127i	0.137269	−	0.237757i
$957$	−0.566569	+	5.55275i	−0.0183146	+	0.179495i
$958$	−8.14681	+	14.1107i	−0.263211	+	0.455896i
$959$		0			0
$960$	2.98143	−	1.33829i	0.0962253	−	0.0431930i
$961$	5.90112			0.190359
$962$	29.8081	+	51.6291i	0.961052	+	1.66459i
$963$	−7.57351	+	8.51470i	−0.244053	+	0.274382i
$964$	−4.68179	+	8.10910i	−0.150790	+	0.261177i
$965$	4.95107	+	8.57550i	0.159380	+	0.276055i
$966$		0			0
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	0.179680	+	0.983725i	$0.442494\pi$
$967$	−23.6985	+	41.0469i	−0.762091	+	1.31998i	−0.941771	+	0.336255i	$0.890840\pi$
$968$	10.0611	+	17.4264i	0.323377	+	0.560106i
$969$	5.94727	−	58.2872i	0.191054	−	1.87245i
$970$	2.74790	−	4.75950i	0.0882297	−	0.152818i
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	−0.988776	−	0.149408i	$-0.952263\pi$
$971$	−11.3736	+	19.6997i	−0.364997	+	0.632193i	0.623779	+	0.781601i	$0.285597\pi$
$972$	6.74399	−	12.1018i	0.216314	−	0.388164i
$973$		0			0
$974$	11.1106	+	19.2441i	0.356006	+	0.616620i
$975$	−32.5123	+	14.5939i	−1.04123	+	0.467379i
$976$	−58.1202			−1.86038
$977$	35.6849			1.14166			0.570831	−	0.821068i	$-0.306621\pi$
$977$	35.6849			1.14166			0.570831	+	0.821068i	$0.306621\pi$
$978$	3.97701	+	2.87105i	0.127171	+	0.0918060i
$979$	0.248187	+	0.429872i	0.00793209	+	0.0137388i
$980$		0			0
$981$	−12.1483	−	36.6300i	−0.387866	−	1.16951i
$982$	13.0371	−	22.5809i	0.416029	−	0.720584i
$983$	−12.0067	+	20.7962i	−0.382954	+	0.663296i	−0.991483	−	0.130236i	$-0.958427\pi$
$983$	−12.0067	+	20.7962i	−0.382954	+	0.663296i	0.608529	+	0.793532i	$0.291760\pi$
$984$	−2.79803	−	2.01993i	−0.0891980	−	0.0643930i
$985$	−8.91591	−	15.4428i	−0.284085	−	0.492049i
$986$	−35.2925	+	61.1284i	−1.12394	+	1.94672i
$987$		0			0
$988$	−9.95125	−	17.2361i	−0.316591	−	0.548352i
$989$	−8.65452	+	14.9901i	−0.275198	+	0.476656i
$990$	2.78913	+	0.575159i	0.0886443	+	0.0182798i
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	0.966508	+	0.256635i	$0.0826139\pi$
$991$	22.2095	+	38.4679i	0.705507	+	1.22197i	−0.261002	+	0.965338i	$0.584053\pi$
$992$	−28.5485			−0.906416
$993$	3.52716	−	34.5685i	0.111931	−	1.09700i
$994$		0			0
$995$	3.99931	−	6.92701i	0.126787	−	0.219601i
$996$	7.98212	−	3.58296i	0.252923	−	0.113530i
$997$	−4.52336	+	7.83470i	−0.143256	+	0.248127i	−0.928721	−	0.370779i	$-0.879091\pi$
$997$	−4.52336	+	7.83470i	−0.143256	+	0.248127i	0.785465	+	0.618906i	$0.212424\pi$
$998$	4.13465	+	7.16142i	0.130880	+	0.226691i
$999$	24.5402	+	26.7601i	0.776417	+	0.846653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.g.373.2		12
3.2	odd	2		1323.2.h.g.226.5		12
7.2	even	3		441.2.f.g.148.6	yes	12
7.3	odd	6		441.2.g.g.67.6		12
7.4	even	3		441.2.g.g.67.5		12
7.5	odd	6		441.2.f.g.148.5	✓	12
7.6	odd	2	inner	441.2.h.g.373.1		12
9.2	odd	6		1323.2.g.g.667.2		12
9.7	even	3		441.2.g.g.79.5		12
21.2	odd	6		1323.2.f.g.442.1		12
21.5	even	6		1323.2.f.g.442.2		12
21.11	odd	6		1323.2.g.g.361.2		12
21.17	even	6		1323.2.g.g.361.1		12
21.20	even	2		1323.2.h.g.226.6		12
63.2	odd	6		1323.2.f.g.883.1		12
63.5	even	6		3969.2.a.bd.1.5		6
63.11	odd	6		1323.2.h.g.802.5		12
63.16	even	3		441.2.f.g.295.6	yes	12
63.20	even	6		1323.2.g.g.667.1		12
63.23	odd	6		3969.2.a.bd.1.6		6
63.25	even	3	inner	441.2.h.g.214.2		12
63.34	odd	6		441.2.g.g.79.6		12
63.38	even	6		1323.2.h.g.802.6		12
63.40	odd	6		3969.2.a.be.1.2		6
63.47	even	6		1323.2.f.g.883.2		12
63.52	odd	6	inner	441.2.h.g.214.1		12
63.58	even	3		3969.2.a.be.1.1		6
63.61	odd	6		441.2.f.g.295.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.5	✓	12	7.5	odd	6
441.2.f.g.148.6	yes	12	7.2	even	3
441.2.f.g.295.5	yes	12	63.61	odd	6
441.2.f.g.295.6	yes	12	63.16	even	3
441.2.g.g.67.5		12	7.4	even	3
441.2.g.g.67.6		12	7.3	odd	6
441.2.g.g.79.5		12	9.7	even	3
441.2.g.g.79.6		12	63.34	odd	6
441.2.h.g.214.1		12	63.52	odd	6	inner
441.2.h.g.214.2		12	63.25	even	3	inner
441.2.h.g.373.1		12	7.6	odd	2	inner
441.2.h.g.373.2		12	1.1	even	1	trivial
1323.2.f.g.442.1		12	21.2	odd	6
1323.2.f.g.442.2		12	21.5	even	6
1323.2.f.g.883.1		12	63.2	odd	6
1323.2.f.g.883.2		12	63.47	even	6
1323.2.g.g.361.1		12	21.17	even	6
1323.2.g.g.361.2		12	21.11	odd	6
1323.2.g.g.667.1		12	63.20	even	6
1323.2.g.g.667.2		12	9.2	odd	6
1323.2.h.g.226.5		12	3.2	odd	2
1323.2.h.g.226.6		12	21.20	even	2
1323.2.h.g.802.5		12	63.11	odd	6
1323.2.h.g.802.6		12	63.38	even	6
3969.2.a.bd.1.5		6	63.5	even	6
3969.2.a.bd.1.6		6	63.23	odd	6
3969.2.a.be.1.1		6	63.58	even	3
3969.2.a.be.1.2		6	63.40	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.69963 q^{2} +(0.175815 - 1.72310i) q^{3} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(-2.93818 - 0.605896i) q^{9} +O(q^{10})\)	\(q-1.69963 q^{2} +(0.175815 - 1.72310i) q^{3} +0.888736 q^{4} +(0.474636 + 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(-2.93818 - 0.605896i) q^{9} +(-0.806704 - 1.39725i) q^{10} +(0.294182 - 0.509538i) q^{11} +(0.156253 - 1.53138i) q^{12} +(2.50987 - 4.34722i) q^{13} +(1.50000 - 0.673310i) q^{15} -4.98762 q^{16} +(3.79121 + 6.56657i) q^{17} +(4.99381 + 1.02980i) q^{18} +(2.23061 - 3.86353i) q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.23855 - 2.14523i) q^{23} +(0.332068 - 3.25449i) q^{24} +(2.04944 - 3.54974i) q^{25} +(-4.26584 + 7.38866i) q^{26} +(-1.56060 + 4.95626i) q^{27} +(-2.73855 - 4.74331i) q^{29} +(-2.54944 + 1.14438i) q^{30} -6.07463 q^{31} +4.69963 q^{32} +(-0.826266 - 0.596491i) q^{33} +(-6.44364 - 11.1607i) q^{34} +(-2.61126 - 0.538481i) q^{36} +(3.49381 - 6.05146i) q^{37} +(-3.79121 + 6.56657i) q^{38} +(-7.04944 - 5.08907i) q^{39} +(0.896461 + 1.55272i) q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} +(0.261450 - 0.452845i) q^{44} +(-0.896461 - 2.70303i) q^{45} +(2.10507 + 3.64610i) q^{46} -7.47680 q^{47} +(-0.876899 + 8.59419i) q^{48} +(-3.48329 + 6.03323i) q^{50} +(11.9814 - 5.37815i) q^{51} +(2.23061 - 3.86353i) q^{52} +(-3.46108 - 5.99476i) q^{53} +(2.65244 - 8.42380i) q^{54} +0.558517 q^{55} +(-6.26509 - 4.52284i) q^{57} +(4.65452 + 8.06186i) q^{58} +10.4302 q^{59} +(1.33310 - 0.598395i) q^{60} +11.6529 q^{61} +10.3246 q^{62} +1.98762 q^{64} +4.76509 q^{65} +(1.40434 + 1.01381i) q^{66} -11.8640 q^{67} +(3.36938 + 5.83594i) q^{68} +(-3.91421 + 1.75699i) q^{69} +4.30037 q^{71} +(-5.54944 - 1.14438i) q^{72} +(-2.23061 - 3.86353i) q^{73} +(-5.93818 + 10.2852i) q^{74} +(-5.75625 - 4.15550i) q^{75} +(1.98242 - 3.43366i) q^{76} +(11.9814 + 8.64953i) q^{78} -1.33379 q^{79} +(-2.36730 - 4.10029i) q^{80} +(8.26578 + 3.56046i) q^{81} +(-0.896461 + 1.55272i) q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(5.93818 + 10.2852i) q^{86} +(-8.65469 + 3.88486i) q^{87} +(0.555632 - 0.962383i) q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.52365 + 4.59415i) q^{90} +(-1.10074 - 1.90654i) q^{92} +(-1.06801 + 10.4672i) q^{93} +12.7078 q^{94} +4.23491 q^{95} +(0.826266 - 8.09795i) q^{96} +(1.70317 + 2.94997i) q^{97} +(-1.17309 + 1.31887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8	\( 12 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 8 q^{11} + 18 q^{15} + 12 q^{16} + 24 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} + 6 q^{30} + 32 q^{32} - 30 q^{36} + 6 q^{37} - 48 q^{39} - 6 q^{43} + 14 q^{44} - 12 q^{46} - 56 q^{50} + 36 q^{51} - 28 q^{53} - 6 q^{57} - 18 q^{58} + 18 q^{60} - 48 q^{64} - 12 q^{65} + 76 q^{71} - 30 q^{72} - 36 q^{74} + 36 q^{78} - 12 q^{79} + 24 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} - 84 q^{93} + 120 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 8 * q^11 + 18 * q^15 + 12 * q^16 + 24 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 + 6 * q^30 + 32 * q^32 - 30 * q^36 + 6 * q^37 - 48 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 + 36 * q^51 - 28 * q^53 - 6 * q^57 - 18 * q^58 + 18 * q^60 - 48 * q^64 - 12 * q^65 + 76 * q^71 - 30 * q^72 - 36 * q^74 + 36 * q^78 - 12 * q^79 + 24 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 - 84 * q^93 + 120 * q^95 - 48 * q^99

Introduction

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