LMFDB - Embedded newform 225.2.p.b.32.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.4
Root			$2.24352 - 0.601150i$ of defining polynomial
Character	$\chi$	$=$	225.32
Dual form			225.2.p.b.218.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24352 + 0.601150i) q^{2} +(-0.173261 - 1.72336i) q^{3} +(2.93996 + 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(0.201351 - 0.751454i) q^{7} +(2.29074 + 2.29074i) q^{8} +(-2.93996 + 0.597183i) q^{9} +O(q^{10})$	\(q+(2.24352 + 0.601150i) q^{2} +(-0.173261 - 1.72336i) q^{3} +(2.93996 + 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(0.201351 - 0.751454i) q^{7} +(2.29074 + 2.29074i) q^{8} +(-2.93996 + 0.597183i) q^{9} +(-0.220188 + 0.127126i) q^{11} +(2.41583 - 5.36071i) q^{12} +(0.992714 + 3.70486i) q^{13} +(0.903473 - 1.56486i) q^{14} +(0.367473 + 0.636483i) q^{16} +(-3.93311 + 3.93311i) q^{17} +(-6.95487 - 0.427565i) q^{18} +0.440377i q^{19} +(-1.32991 - 0.216804i) q^{21} +(-0.570419 + 0.152843i) q^{22} +(3.42258 - 0.917076i) q^{23} +(3.55088 - 4.34467i) q^{24} +8.90871i q^{26} +(1.53854 + 4.96315i) q^{27} +(1.86747 - 1.86747i) q^{28} +(-2.76265 - 4.78505i) q^{29} +(-0.0971829 + 0.168326i) q^{31} +(-1.23512 - 4.60955i) q^{32} +(0.257234 + 0.357439i) q^{33} +(-11.1884 + 6.45964i) q^{34} +(-9.65702 - 3.23456i) q^{36} +(0.123005 + 0.123005i) q^{37} +(-0.264732 + 0.987995i) q^{38} +(6.21282 - 2.35271i) q^{39} +(-3.88223 - 2.24141i) q^{41} +(-2.85336 - 1.28588i) q^{42} +(-1.33488 - 0.357680i) q^{43} -0.863127 q^{44} +8.22993 q^{46} +(-4.17348 - 1.11828i) q^{47} +(1.03322 - 0.743568i) q^{48} +(5.53804 + 3.19739i) q^{49} +(7.45964 + 6.09673i) q^{51} +(-3.37004 + 12.5772i) q^{52} +(-0.938022 - 0.938022i) q^{53} +(0.468157 + 12.0598i) q^{54} +(2.18263 - 1.26014i) q^{56} +(0.758929 - 0.0763000i) q^{57} +(-3.32153 - 12.3961i) q^{58} +(-4.02279 + 6.96768i) q^{59} +(-1.44186 - 2.49737i) q^{61} +(-0.319221 + 0.319221i) q^{62} +(-0.143210 + 2.32949i) q^{63} -12.5540i q^{64} +(0.362236 + 0.956558i) q^{66} +(12.9666 - 3.47438i) q^{67} +(-18.2392 + 4.88718i) q^{68} +(-2.17345 - 5.73945i) q^{69} -2.15986i q^{71} +(-8.10268 - 5.36670i) q^{72} +(9.18432 - 9.18432i) q^{73} +(0.202021 + 0.349910i) q^{74} +(-0.747490 + 1.29469i) q^{76} +(0.0511939 + 0.191058i) q^{77} +(15.3529 - 1.54353i) q^{78} +(11.9729 - 6.91256i) q^{79} +(8.28675 - 3.51139i) q^{81} +(-7.36245 - 7.36245i) q^{82} +(1.39384 - 5.20187i) q^{83} +(-3.54190 - 2.89477i) q^{84} +(-2.77981 - 1.60493i) q^{86} +(-7.76772 + 5.59011i) q^{87} +(-0.795606 - 0.213182i) q^{88} +0.285526 q^{89} +2.98392 q^{91} +(11.6189 + 3.11327i) q^{92} +(0.306924 + 0.138317i) q^{93} +(-8.69105 - 5.01778i) q^{94} +(-7.72993 + 2.92722i) q^{96} +(2.34065 - 8.73543i) q^{97} +(10.5026 + 10.5026i) q^{98} +(0.571428 - 0.505238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.24352	+	0.601150i	1.58641	+	0.425077i	0.940903	−	0.338677i	$-0.109979\pi$
$2$	2.24352	+	0.601150i	1.58641	+	0.425077i	0.645507	+	0.763754i	$0.276646\pi$
$3$	−0.173261	−	1.72336i	−0.100032	−	0.994984i
$3$	−0.173261	−	1.72336i	−0.100032	−	0.994984i
$4$	2.93996	+	1.69739i	1.46998	+	0.848694i
$5$		0			0
$5$		0			0
$6$	0.647285	−	3.97056i	0.264253	−	1.62097i
$7$	0.201351	−	0.751454i	0.0761037	−	0.284023i	−0.917378	−	0.398018i	$-0.869698\pi$
$7$	0.201351	−	0.751454i	0.0761037	−	0.284023i	0.993481	+	0.113995i	$0.0363648\pi$
$8$	2.29074	+	2.29074i	0.809899	+	0.809899i
$9$	−2.93996	+	0.597183i	−0.979987	+	0.199061i
$10$		0			0
$11$	−0.220188	+	0.127126i	−0.0663893	+	0.0383299i	−0.532827	−	0.846224i	$-0.678870\pi$
$11$	−0.220188	+	0.127126i	−0.0663893	+	0.0383299i	0.466438	+	0.884554i	$0.345537\pi$
$12$	2.41583	−	5.36071i	0.697391	−	1.54750i
$13$	0.992714	+	3.70486i	0.275329	+	1.02754i	0.955620	+	0.294601i	$0.0951868\pi$
$13$	0.992714	+	3.70486i	0.275329	+	1.02754i	−0.680291	+	0.732942i	$0.738147\pi$
$14$	0.903473	−	1.56486i	0.241463	−	0.418227i
$15$		0			0
$16$	0.367473	+	0.636483i	0.0918684	+	0.159121i
$17$	−3.93311	+	3.93311i	−0.953920	+	0.953920i	−0.998984	−	0.0450642i	$-0.985651\pi$
$17$	−3.93311	+	3.93311i	−0.953920	+	0.953920i	0.0450642	+	0.998984i	$0.485651\pi$
$18$	−6.95487	−	0.427565i	−1.63928	−	0.100778i
$19$			0.440377i			0.101029i	0.998723	+	0.0505147i	$0.0160862\pi$
$19$			0.440377i			0.101029i	−0.998723	+	0.0505147i	$0.983914\pi$
$20$		0			0
$21$	−1.32991	−	0.216804i	−0.290211	−	0.0473105i
$22$	−0.570419	+	0.152843i	−0.121614	+	0.0325863i
$23$	3.42258	−	0.917076i	0.713656	−	0.191224i	0.116317	−	0.993212i	$-0.462891\pi$
$23$	3.42258	−	0.917076i	0.713656	−	0.191224i	0.597339	+	0.801989i	$0.296225\pi$
$24$	3.55088	−	4.34467i	0.724821	−	0.886853i
$25$		0			0
$26$			8.90871i			1.74714i
$27$	1.53854	+	4.96315i	0.296093	+	0.955159i
$28$	1.86747	−	1.86747i	0.352919	−	0.352919i
$29$	−2.76265	−	4.78505i	−0.513011	−	0.888561i	−0.999886	−	0.0150897i	$-0.995197\pi$
$29$	−2.76265	−	4.78505i	−0.513011	−	0.888561i	0.486875	−	0.873472i	$-0.338137\pi$
$30$		0			0
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	−0.874621	−	0.484808i	$-0.838890\pi$
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	0.857166	+	0.515040i	$0.172223\pi$
$32$	−1.23512	−	4.60955i	−0.218341	−	0.814861i
$33$	0.257234	+	0.357439i	0.0447787	+	0.0622221i
$34$	−11.1884	+	6.45964i	−1.91880	+	1.10782i
$35$		0			0
$36$	−9.65702	−	3.23456i	−1.60950	−	0.539093i
$37$	0.123005	+	0.123005i	0.0202220	+	0.0202220i	0.717145	−	0.696924i	$-0.245448\pi$
$37$	0.123005	+	0.123005i	0.0202220	+	0.0202220i	−0.696924	+	0.717145i	$0.745448\pi$
$38$	−0.264732	+	0.987995i	−0.0429453	+	0.160274i
$39$	6.21282	−	2.35271i	0.994848	−	0.376736i
$40$		0			0
$41$	−3.88223	−	2.24141i	−0.606303	−	0.350049i	0.165214	−	0.986258i	$-0.447168\pi$
$41$	−3.88223	−	2.24141i	−0.606303	−	0.350049i	−0.771517	+	0.636209i	$0.780502\pi$
$42$	−2.85336	−	1.28588i	−0.440283	−	0.198416i
$43$	−1.33488	−	0.357680i	−0.203567	−	0.0545456i	0.155595	−	0.987821i	$-0.450271\pi$
$43$	−1.33488	−	0.357680i	−0.203567	−	0.0545456i	−0.359162	+	0.933275i	$0.616937\pi$
$44$	−0.863127			−0.130121
$45$		0			0
$46$	8.22993			1.21344
$47$	−4.17348	−	1.11828i	−0.608765	−	0.163118i	−0.0587499	−	0.998273i	$-0.518711\pi$
$47$	−4.17348	−	1.11828i	−0.608765	−	0.163118i	−0.550015	+	0.835155i	$0.685378\pi$
$48$	1.03322	−	0.743568i	0.149133	−	0.107325i
$49$	5.53804	+	3.19739i	0.791148	+	0.456770i
$50$		0			0
$51$	7.45964	+	6.09673i	1.04456	+	0.853713i
$52$	−3.37004	+	12.5772i	−0.467341	+	1.74414i
$53$	−0.938022	−	0.938022i	−0.128847	−	0.128847i	0.639742	−	0.768589i	$-0.279041\pi$
$53$	−0.938022	−	0.938022i	−0.128847	−	0.128847i	−0.768589	+	0.639742i	$0.779041\pi$
$54$	0.468157	+	12.0598i	0.0637081	+	1.64114i
$55$		0			0
$56$	2.18263	−	1.26014i	0.291666	−	0.168393i
$57$	0.758929	−	0.0763000i	0.100523	−	0.0101062i
$58$	−3.32153	−	12.3961i	−0.436139	−	1.62769i
$59$	−4.02279	+	6.96768i	−0.523723	+	0.907114i	0.475896	+	0.879502i	$0.342124\pi$
$59$	−4.02279	+	6.96768i	−0.523723	+	0.907114i	−0.999619	+	0.0276128i	$0.991209\pi$
$60$		0			0
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	0.758835	−	0.651283i	$-0.225769\pi$
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	−0.943445	+	0.331528i	$0.892436\pi$
$62$	−0.319221	+	0.319221i	−0.0405411	+	0.0405411i
$63$	−0.143210	+	2.32949i	−0.0180428	+	0.293488i
$64$		−	12.5540i		−	1.56925i
$65$		0			0
$66$	0.362236	+	0.956558i	0.0445882	+	0.117744i
$67$	12.9666	−	3.47438i	1.58412	−	0.424463i	0.643919	−	0.765093i	$-0.277307\pi$
$67$	12.9666	−	3.47438i	1.58412	−	0.424463i	0.940197	+	0.340631i	$0.110641\pi$
$68$	−18.2392	+	4.88718i	−2.21183	+	0.592658i
$69$	−2.17345	−	5.73945i	−0.261653	−	0.690948i
$70$		0			0
$71$		−	2.15986i		−	0.256328i	−0.991753	−	0.128164i	$-0.959092\pi$
$71$		−	2.15986i		−	0.256328i	0.991753	−	0.128164i	$-0.0409085\pi$
$72$	−8.10268	−	5.36670i	−0.954910	−	0.632471i
$73$	9.18432	−	9.18432i	1.07494	−	1.07494i	0.0779897	−	0.996954i	$-0.475150\pi$
$73$	9.18432	−	9.18432i	1.07494	−	1.07494i	0.996954	−	0.0779897i	$-0.0248501\pi$
$74$	0.202021	+	0.349910i	0.0234844	+	0.0406762i
$75$		0			0
$76$	−0.747490	+	1.29469i	−0.0857430	+	0.148511i
$77$	0.0511939	+	0.191058i	0.00583409	+	0.0217731i
$78$	15.3529	−	1.54353i	1.73838	−	0.174770i
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.359225	−	0.933251i	$-0.383041\pi$
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.987832	+	0.155528i	$0.0497079\pi$
$80$		0			0
$81$	8.28675	−	3.51139i	0.920749	−	0.390154i
$82$	−7.36245	−	7.36245i	−0.813047	−	0.813047i
$83$	1.39384	−	5.20187i	0.152993	−	0.570979i	−0.846275	−	0.532746i	$-0.821160\pi$
$83$	1.39384	−	5.20187i	0.152993	−	0.570979i	0.999269	−	0.0382335i	$-0.0121731\pi$
$84$	−3.54190	−	2.89477i	−0.386452	−	0.315846i
$85$		0			0
$86$	−2.77981	−	1.60493i	−0.299755	−	0.173064i
$87$	−7.76772	+	5.59011i	−0.832787	+	0.599323i
$88$	−0.795606	−	0.213182i	−0.0848119	−	0.0227253i
$89$	0.285526			0.0302657			0.0151328	−	0.999885i	$-0.495183\pi$
$89$	0.285526			0.0302657			0.0151328	+	0.999885i	$0.495183\pi$
$90$		0			0
$91$	2.98392			0.312799
$92$	11.6189	+	3.11327i	1.21135	+	0.324581i
$93$	0.306924	+	0.138317i	0.0318266	+	0.0143428i
$94$	−8.69105	−	5.01778i	−0.896413	−	0.517545i
$95$		0			0
$96$	−7.72993	+	2.92722i	−0.788932	+	0.298758i
$97$	2.34065	−	8.73543i	0.237657	−	0.886948i	−0.739276	−	0.673402i	$-0.764832\pi$
$97$	2.34065	−	8.73543i	0.237657	−	0.886948i	0.976933	−	0.213546i	$-0.0685012\pi$
$98$	10.5026	+	10.5026i	1.06092	+	1.06092i
$99$	0.571428	−	0.505238i	0.0574307	−	0.0507783i
$100$		0			0
$101$	−11.3943	+	6.57848i	−1.13377	+	0.654583i	−0.944881	−	0.327415i	$-0.893822\pi$
$101$	−11.3943	+	6.57848i	−1.13377	+	0.654583i	−0.188890	+	0.981998i	$0.560489\pi$
$102$	13.0708	+	18.1625i	1.29420	+	1.79836i
$103$	4.23579	+	15.8082i	0.417364	+	1.55763i	0.780052	+	0.625714i	$0.215192\pi$
$103$	4.23579	+	15.8082i	0.417364	+	1.55763i	−0.362688	+	0.931911i	$0.618141\pi$
$104$	−6.21282	+	10.7609i	−0.609217	+	1.05520i
$105$		0			0
$106$	−1.54058	−	2.66836i	−0.149634	−	0.259175i
$107$	5.81401	−	5.81401i	0.562062	−	0.562062i	−0.367831	−	0.929893i	$-0.619899\pi$
$107$	5.81401	−	5.81401i	0.562062	−	0.562062i	0.929893	+	0.367831i	$0.119899\pi$
$108$	−3.90114	+	17.2030i	−0.375387	+	1.65536i
$109$			8.81907i			0.844713i	0.906430	+	0.422357i	$0.138797\pi$
$109$			8.81907i			0.844713i	−0.906430	+	0.422357i	$0.861203\pi$
$110$		0			0
$111$	0.190671	−	0.233295i	0.0180977	−	0.0221434i
$112$	0.552279	−	0.147983i	0.0521854	−	0.0139830i
$113$	−13.0092	+	3.48580i	−1.22380	+	0.327916i	−0.812163	−	0.583431i	$-0.801710\pi$
$113$	−13.0092	+	3.48580i	−1.22380	+	0.327916i	−0.411638	+	0.911347i	$0.635043\pi$
$114$	1.74854	+	0.285049i	0.163766	+	0.0266973i
$115$		0			0
$116$		−	18.7571i		−	1.74156i
$117$	−5.13102	−	10.2993i	−0.474363	−	0.952172i
$118$	−13.2138	+	13.2138i	−1.21643	+	1.21643i
$119$	2.16361	+	3.74749i	0.198338	+	0.343532i
$120$		0			0
$121$	−5.46768	+	9.47030i	−0.497062	+	0.860936i
$122$	−1.73354	−	6.46967i	−0.156948	−	0.585736i
$123$	−3.19012	+	7.07884i	−0.287643	+	0.638278i
$124$	−0.571428	+	0.329914i	−0.0513157	+	0.0296272i
$125$		0			0
$126$	−1.72167	+	5.14017i	−0.153378	+	0.457923i
$127$	6.72167	+	6.72167i	0.596452	+	0.596452i	0.939366	−	0.342915i	$-0.111414\pi$
$127$	6.72167	+	6.72167i	0.596452	+	0.596452i	−0.342915	+	0.939366i	$0.611414\pi$
$128$	5.07660	−	18.9461i	0.448712	−	1.67462i
$129$	−0.385130	+	2.36245i	−0.0339088	+	0.208002i
$130$		0			0
$131$	11.6482	+	6.72508i	1.01771	+	0.587573i	0.913439	−	0.406977i	$-0.133417\pi$
$131$	11.6482	+	6.72508i	1.01771	+	0.587573i	0.104267	+	0.994549i	$0.466750\pi$
$132$	0.149546	+	1.48748i	0.0130163	+	0.129469i
$133$	0.330923	+	0.0886705i	0.0286946	+	0.00768870i
$134$	31.1794			2.69349
$135$		0			0
$136$	−18.0195			−1.54516
$137$	−9.45618	−	2.53378i	−0.807896	−	0.216475i	−0.168848	−	0.985642i	$-0.554005\pi$
$137$	−9.45618	−	2.53378i	−0.807896	−	0.216475i	−0.639048	+	0.769167i	$0.720671\pi$
$138$	−1.42592	−	14.1832i	−0.121383	−	1.20735i
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	0.180565	−	0.983563i	$-0.442207\pi$
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	−0.761508	+	0.648155i	$0.775541\pi$
$140$		0			0
$141$	−1.20410	+	7.38618i	−0.101404	+	0.622029i
$142$	1.29840	−	4.84570i	0.108959	−	0.406642i
$143$	−0.689567	−	0.689567i	−0.0576645	−	0.0576645i
$144$	−1.46045	−	1.65179i	−0.121705	−	0.137649i
$145$		0			0
$146$	26.1264	−	15.0841i	2.16224	−	1.24837i
$147$	4.55073	−	10.0980i	0.375338	−	0.832872i
$148$	0.152843	+	0.570419i	0.0125636	+	0.0468882i
$149$	4.56755	−	7.91123i	0.374188	−	0.648113i	−0.616017	−	0.787733i	$-0.711255\pi$
$149$	4.56755	−	7.91123i	0.374188	−	0.648113i	0.990205	+	0.139620i	$0.0445880\pi$
$150$		0			0
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	−0.993097	−	0.117293i	$-0.962578\pi$
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	0.394970	−	0.918694i	$-0.370755\pi$
$152$	−1.00879	+	1.00879i	−0.0818235	+	0.0818235i
$153$	9.21441	−	13.9120i	0.744941	−	1.12472i
$154$			0.459419i			0.0370210i
$155$		0			0
$156$	22.2589	+	3.62867i	1.78214	+	0.290527i
$157$	−16.3566	+	4.38274i	−1.30540	+	0.349781i	−0.843490	−	0.537146i	$-0.819503\pi$
$157$	−16.3566	+	4.38274i	−1.30540	+	0.349781i	−0.461911	+	0.886926i	$0.652836\pi$
$158$	31.0169	−	8.31097i	2.46758	−	0.661185i
$159$	−1.45403	+	1.77907i	−0.115312	+	0.141090i
$160$		0			0
$161$		−	2.75656i		−	0.217248i
$162$	20.7024	−	2.89630i	1.62653	−	0.227555i
$163$	−9.74771	+	9.74771i	−0.763499	+	0.763499i	−0.976953	−	0.213454i	$-0.931529\pi$
$163$	−9.74771	+	9.74771i	−0.763499	+	0.763499i	0.213454	+	0.976953i	$0.431529\pi$
$164$	−7.60907	−	13.1793i	−0.594169	−	1.02913i
$165$		0			0
$166$	6.25421	−	10.8326i	0.485421	−	0.840773i
$167$	5.10613	+	19.0563i	0.395124	+	1.47462i	0.821568	+	0.570110i	$0.193100\pi$
$167$	5.10613	+	19.0563i	0.395124	+	1.47462i	−0.426444	+	0.904514i	$0.640234\pi$
$168$	−2.54985	−	3.54313i	−0.196725	−	0.273358i
$169$	−1.48218	+	0.855737i	−0.114014	+	0.0658259i
$170$		0			0
$171$	−0.262985	−	1.29469i	−0.0201110	−	0.0990074i
$172$	−3.31737	−	3.31737i	−0.252947	−	0.252947i
$173$	2.68653	−	10.0263i	0.204253	−	0.762284i	−0.785422	−	0.618960i	$-0.787554\pi$
$173$	2.68653	−	10.0263i	0.204253	−	0.762284i	0.989676	−	0.143324i	$-0.0457791\pi$
$174$	−20.7875	+	7.87197i	−1.57590	+	0.596773i
$175$		0			0
$176$	−0.161827	−	0.0934307i	−0.0121981	−	0.00704260i
$177$	12.7048	+	5.72550i	0.954954	+	0.430355i
$178$	0.640584	+	0.171644i	0.0480138	+	0.0128653i
$179$	−15.1015			−1.12874			−0.564370	−	0.825522i	$-0.690881\pi$
$179$	−15.1015			−1.12874			−0.564370	+	0.825522i	$0.690881\pi$
$180$		0			0
$181$	−7.82954			−0.581965			−0.290983	−	0.956728i	$-0.593982\pi$
$181$	−7.82954			−0.581965			−0.290983	+	0.956728i	$0.593982\pi$
$182$	6.69448	+	1.79378i	0.496228	+	0.132964i
$183$	−4.05405	+	2.91754i	−0.299684	+	0.215671i
$184$	9.94101	+	5.73945i	0.732861	+	0.423118i
$185$		0			0
$186$	0.605442	+	0.494825i	0.0443932	+	0.0362823i
$187$	0.366025	−	1.36603i	0.0267664	−	0.0998937i
$188$	−10.3717	−	10.3717i	−0.756436	−	0.756436i
$189$	4.03937	−	0.156806i	0.293821	−	0.0114060i
$190$		0			0
$191$	9.93557	−	5.73631i	0.718913	−	0.415065i	−0.0954396	−	0.995435i	$-0.530426\pi$
$191$	9.93557	−	5.73631i	0.718913	−	0.415065i	0.814352	+	0.580371i	$0.197092\pi$
$192$	−21.6351	+	2.17512i	−1.56138	+	0.156976i
$193$	−1.42826	−	5.33034i	−0.102808	−	0.383686i	0.895279	−	0.445506i	$-0.146976\pi$
$193$	−1.42826	−	5.33034i	−0.102808	−	0.383686i	−0.998087	+	0.0618198i	$0.980310\pi$
$194$	10.5026	−	18.1910i	0.754043	−	1.30604i
$195$		0			0
$196$	10.8544	+	18.8004i	0.775315	+	1.34289i
$197$	2.32295	−	2.32295i	0.165504	−	0.165504i	−0.619496	−	0.785000i	$-0.712663\pi$
$197$	2.32295	−	2.32295i	0.165504	−	0.165504i	0.785000	+	0.619496i	$0.212663\pi$
$198$	1.58573	−	0.789998i	0.112693	−	0.0561427i
$199$			17.1978i			1.21912i	0.792741	+	0.609558i	$0.208653\pi$
$199$			17.1978i			1.21912i	−0.792741	+	0.609558i	$0.791347\pi$
$200$		0			0
$201$	−8.23421	−	21.7441i	−0.580796	−	1.53371i
$202$	−29.5179	+	7.90930i	−2.07687	+	0.556497i
$203$	−4.15201	+	1.11253i	−0.291414	+	0.0780841i
$204$	11.5825	+	30.5860i	0.810940	+	2.14145i
$205$		0			0
$206$			38.0123i			2.64844i
$207$	−9.51458	+	4.74007i	−0.661309	+	0.329458i
$208$	−1.99328	+	1.99328i	−0.138209	+	0.138209i
$209$	−0.0559832	−	0.0969658i	−0.00387244	−	0.00670726i
$210$		0			0
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	−0.933642	−	0.358209i	$-0.883388\pi$
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	0.777039	+	0.629453i	$0.216721\pi$
$212$	−1.16556	−	4.34993i	−0.0800511	−	0.298755i
$213$	−3.72223	+	0.374220i	−0.255043	+	0.0256411i
$214$	16.5390	−	9.54878i	1.13058	−	0.652741i
$215$		0			0
$216$	−7.84489	+	14.8937i	−0.533777	+	1.01339i
$217$	0.106921	+	0.106921i	0.00725827	+	0.00725827i
$218$	−5.30158	+	19.7858i	−0.359068	+	1.34006i
$219$	−17.4192	−	14.2366i	−1.17708	−	0.962023i
$220$		0			0
$221$	−18.4761	−	10.6672i	−1.24284	−	0.717552i
$222$	0.568020	−	0.408781i	0.0381230	−	0.0274356i
$223$	−17.6922	−	4.74061i	−1.18476	−	0.317455i	−0.387946	−	0.921682i	$-0.626815\pi$
$223$	−17.6922	−	4.74061i	−1.18476	−	0.317455i	−0.796812	+	0.604227i	$0.793482\pi$
$224$	−3.71256			−0.248056
$225$		0			0
$226$	−31.2819			−2.08084
$227$	10.8961	+	2.91961i	0.723202	+	0.193781i	0.601600	−	0.798798i	$-0.294530\pi$
$227$	10.8961	+	2.91961i	0.723202	+	0.193781i	0.121602	+	0.992579i	$0.461197\pi$
$228$	2.36073	+	1.06388i	0.156343	+	0.0704570i
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	0.353893	−	0.935286i	$-0.384858\pi$
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	−0.633035	+	0.774123i	$0.718191\pi$
$230$		0			0
$231$	0.320393	−	0.121329i	0.0210803	−	0.00798284i
$232$	4.63279	−	17.2898i	0.304158	−	1.13513i
$233$	7.90742	+	7.90742i	0.518033	+	0.518033i	0.916976	−	0.398943i	$-0.130623\pi$
$233$	7.90742	+	7.90742i	0.518033	+	0.518033i	−0.398943	+	0.916976i	$0.630623\pi$
$234$	−5.32013	−	26.1913i	−0.347788	−	1.71218i
$235$		0			0
$236$	−23.6537	+	13.6565i	−1.53972	+	0.888960i
$237$	−13.9873	−	19.4360i	−0.908571	−	1.26250i
$238$	2.60131	+	9.70823i	0.168618	+	0.629291i
$239$	−11.1362	+	19.2884i	−0.720340	+	1.24767i	0.240523	+	0.970643i	$0.422681\pi$
$239$	−11.1362	+	19.2884i	−0.720340	+	1.24767i	−0.960864	+	0.277022i	$0.910652\pi$
$240$		0			0
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.779220	+	0.626750i	$0.215615\pi$
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.153171	+	0.988200i	$0.451051\pi$
$242$	−17.9599	+	17.9599i	−1.15451	+	1.15451i
$243$	−7.48717	−	13.6727i	−0.480302	−	0.877103i
$244$		−	9.78955i		−	0.626712i
$245$		0			0
$246$	−11.4126	+	13.9638i	−0.727638	+	0.890300i
$247$	−1.63153	+	0.437168i	−0.103812	+	0.0278163i
$248$	−0.608211	+	0.162970i	−0.0386214	+	0.0103486i
$249$	−9.20620	−	1.50081i	−0.583420	−	0.0951097i
$250$		0			0
$251$		−	20.4218i		−	1.28901i	−0.764599	−	0.644507i	$-0.777063\pi$
$251$		−	20.4218i		−	1.28901i	0.764599	−	0.644507i	$-0.222937\pi$
$252$	−4.37508	+	6.60552i	−0.275604	+	0.416109i
$253$	−0.637027	+	0.637027i	−0.0400496	+	0.0400496i
$254$	11.0395	+	19.1209i	0.692679	+	1.19975i
$255$		0			0
$256$	10.2249	−	17.7101i	0.639057	−	1.10688i
$257$	−1.90043	−	7.09249i	−0.118545	−	0.442417i	0.880982	−	0.473149i	$-0.156883\pi$
$257$	−1.90043	−	7.09249i	−0.118545	−	0.442417i	−0.999528	+	0.0307319i	$0.990216\pi$
$258$	−2.28424	+	5.06870i	−0.142210	+	0.315563i
$259$	0.117200	−	0.0676656i	0.00728247	−	0.00420453i
$260$		0			0
$261$	10.9796	+	12.4181i	0.679622	+	0.768658i
$262$	22.0902	+	22.0902i	1.36473	+	1.36473i
$263$	−3.78069	+	14.1097i	−0.233127	+	0.870044i	0.745857	+	0.666107i	$0.232040\pi$
$263$	−3.78069	+	14.1097i	−0.233127	+	0.870044i	−0.978984	+	0.203937i	$0.934626\pi$
$264$	−0.229543	+	1.40805i	−0.0141274	+	0.0866598i
$265$		0			0
$266$	0.689128	+	0.397868i	0.0422532	+	0.0243949i
$267$	−0.0494705	−	0.492065i	−0.00302754	−	0.0301139i
$268$	44.0185	+	11.7947i	2.68886	+	0.720478i
$269$	−3.76010			−0.229257			−0.114629	−	0.993408i	$-0.536568\pi$
$269$	−3.76010			−0.229257			−0.114629	+	0.993408i	$0.536568\pi$
$270$		0			0
$271$	14.0785			0.855209			0.427604	−	0.903966i	$-0.359358\pi$
$271$	14.0785			0.855209			0.427604	+	0.903966i	$0.359358\pi$
$272$	−3.94867	−	1.05804i	−0.239423	−	0.0641533i
$273$	−0.516996	−	5.14237i	−0.0312900	−	0.311230i
$274$	−19.6920	−	11.3692i	−1.18964	−	0.686837i
$275$		0			0
$276$	3.35219	−	20.5629i	0.201778	−	1.23774i
$277$	−0.541447	+	2.02071i	−0.0325324	+	0.121413i	−0.980283	−	0.197601i	$-0.936685\pi$
$277$	−0.541447	+	2.02071i	−0.0325324	+	0.121413i	0.947750	+	0.319014i	$0.103352\pi$
$278$	−12.9892	−	12.9892i	−0.779040	−	0.779040i
$279$	0.185193	−	0.552907i	0.0110872	−	0.0331017i
$280$		0			0
$281$	8.02672	−	4.63423i	0.478834	−	0.276455i	−0.241097	−	0.970501i	$-0.577507\pi$
$281$	8.02672	−	4.63423i	0.478834	−	0.276455i	0.719930	+	0.694046i	$0.244174\pi$
$282$	−7.14164	+	15.8472i	−0.425278	+	0.943688i
$283$	−8.33602	−	31.1104i	−0.495525	−	1.84932i	−0.527071	−	0.849821i	$-0.676710\pi$
$283$	−8.33602	−	31.1104i	−0.495525	−	1.84932i	0.0315464	−	0.999502i	$-0.489957\pi$
$284$	3.66612	−	6.34991i	0.217544	−	0.376798i
$285$		0			0
$286$	−1.13253	−	1.96159i	−0.0669677	−	0.115991i
$287$	−2.46601	+	2.46601i	−0.145564	+	0.145564i
$288$	6.38396	+	12.8143i	0.376179	+	0.755090i
$289$		−	13.9387i		−	0.819926i
$290$		0			0
$291$	−15.4599	−	2.52028i	−0.906273	−	0.147742i
$292$	42.5909	−	11.4122i	2.49244	−	0.667849i
$293$	−6.37987	+	1.70948i	−0.372716	+	0.0998690i	−0.440314	−	0.897844i	$-0.645133\pi$
$293$	−6.37987	+	1.70948i	−0.372716	+	0.0998690i	0.0675984	+	0.997713i	$0.478466\pi$
$294$	16.2801	−	19.9195i	0.949475	−	1.16173i
$295$		0			0
$296$			0.563547i			0.0327555i
$297$	−0.969714	−	0.897240i	−0.0562685	−	0.0520631i
$298$	15.0032	−	15.0032i	0.869114	−	0.869114i
$299$	6.79528	+	11.7698i	0.392981	+	0.680663i
$300$		0			0
$301$	−0.537559	+	0.931080i	−0.0309844	+	0.0536666i
$302$	−8.83680	−	32.9794i	−0.508501	−	1.89775i
$303$	13.3113	+	18.4966i	0.764713	+	1.06260i
$304$	−0.280292	+	0.161827i	−0.0160759	+	0.00928140i
$305$		0			0
$306$	29.0359	−	25.6726i	1.65987	−	1.46761i
$307$	−5.82120	−	5.82120i	−0.332233	−	0.332233i	0.521201	−	0.853434i	$-0.325484\pi$
$307$	−5.82120	−	5.82120i	−0.332233	−	0.332233i	−0.853434	+	0.521201i	$0.825484\pi$
$308$	−0.173792	+	0.648600i	−0.00990271	+	0.0369574i
$309$	26.5093	−	10.0387i	1.50806	−	0.571084i
$310$		0			0
$311$	9.98678	+	5.76587i	0.566299	+	0.326953i	0.755670	−	0.654953i	$-0.227312\pi$
$311$	9.98678	+	5.76587i	0.566299	+	0.326953i	−0.189371	+	0.981906i	$0.560645\pi$
$312$	19.6214	+	8.84250i	1.11084	+	0.500608i
$313$	6.43287	+	1.72368i	0.363607	+	0.0974283i	0.435997	−	0.899948i	$-0.356396\pi$
$313$	6.43287	+	1.72368i	0.363607	+	0.0974283i	−0.0723896	+	0.997376i	$0.523063\pi$
$314$	−39.3311			−2.21958
$315$		0			0
$316$	46.9331			2.64020
$317$	−1.93788	−	0.519254i	−0.108842	−	0.0291642i	0.203987	−	0.978974i	$-0.434610\pi$
$317$	−1.93788	−	0.519254i	−0.108842	−	0.0291642i	−0.312829	+	0.949809i	$0.601277\pi$
$318$	−4.33164	+	3.11730i	−0.242906	+	0.174810i
$319$	1.21661	+	0.702408i	0.0681169	+	0.0393273i
$320$		0			0
$321$	−11.0270	−	9.01232i	−0.615467	−	0.503018i
$322$	1.65711	−	6.18441i	0.0923470	−	0.344644i
$323$	−1.73205	−	1.73205i	−0.0963739	−	0.0963739i
$324$	30.3229	+	3.74247i	1.68461	+	0.207915i
$325$		0			0
$326$	−27.7290	+	16.0094i	−1.53577	+	0.886677i
$327$	15.1985	−	1.52800i	0.840477	−	0.0844986i
$328$	−3.75870	−	14.0277i	−0.207540	−	0.774548i
$329$	−1.68067	+	2.91101i	−0.0926585	+	0.160489i
$330$		0			0
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	−0.983850	−	0.178992i	$-0.942716\pi$
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	0.336913	−	0.941536i	$-0.390617\pi$
$332$	12.9274	−	12.9274i	0.709484	−	0.709484i
$333$	−0.435088	−	0.288174i	−0.0238427	−	0.0157919i
$334$			45.8229i			2.50732i
$335$		0			0
$336$	−0.350716	−	0.926137i	−0.0191331	−	0.0505249i
$337$	−11.0048	+	2.94873i	−0.599470	+	0.160627i	−0.545778	−	0.837930i	$-0.683766\pi$
$337$	−11.0048	+	2.94873i	−0.599470	+	0.160627i	−0.0536923	+	0.998558i	$0.517099\pi$
$338$	−3.83973	+	1.02885i	−0.208854	+	0.0559622i
$339$	8.26128	+	21.8156i	0.448691	+	1.18486i
$340$		0			0
$341$		−	0.0494178i		−	0.00267612i
$342$	0.188289	−	3.06276i	0.0101815	−	0.165615i
$343$	7.36850	−	7.36850i	0.397861	−	0.397861i
$344$	−2.23851	−	3.87721i	−0.120692	−	0.209045i
$345$		0			0
$346$	12.0546	−	20.8792i	0.648059	−	1.12247i
$347$	3.69845	+	13.8028i	0.198543	+	0.740974i	0.991321	+	0.131463i	$0.0419674\pi$
$347$	3.69845	+	13.8028i	0.198543	+	0.740974i	−0.792778	+	0.609511i	$0.791366\pi$
$348$	−32.3254	+	3.24988i	−1.73282	+	0.174212i
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	−0.848427	−	0.529313i	$-0.822450\pi$
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	0.0341849	+	0.999416i	$0.489116\pi$
$350$		0			0
$351$	−16.8605	+	10.6271i	−0.899944	+	0.567232i
$352$	0.857952	+	0.857952i	0.0457290	+	0.0457290i
$353$	−4.51136	+	16.8366i	−0.240116	+	0.896124i	0.735660	+	0.677351i	$0.236872\pi$
$353$	−4.51136	+	16.8366i	−0.240116	+	0.896124i	−0.975776	+	0.218773i	$0.929795\pi$
$354$	25.0617	+	20.4828i	1.33201	+	1.08865i
$355$		0			0
$356$	0.839435	+	0.484648i	0.0444900	+	0.0256863i
$357$	6.08342	−	4.37799i	0.321969	−	0.231708i
$358$	−33.8806	−	9.07828i	−1.79064	−	0.479802i
$359$	34.0577			1.79750			0.898748	−	0.438465i	$-0.144478\pi$
$359$	34.0577			1.79750			0.898748	+	0.438465i	$0.144478\pi$
$360$		0			0
$361$	18.8061			0.989793
$362$	−17.5658	−	4.70673i	−0.923236	−	0.247380i
$363$	17.2681	+	7.78196i	0.906340	+	0.408447i
$364$	8.77260	+	5.06486i	0.459809	+	0.265471i
$365$		0			0
$366$	−10.8492	+	4.10847i	−0.567099	+	0.214753i
$367$	−3.65315	+	13.6337i	−0.190693	+	0.711675i	0.802647	+	0.596454i	$0.203424\pi$
$367$	−3.65315	+	13.6337i	−0.190693	+	0.711675i	−0.993340	+	0.115221i	$0.963242\pi$
$368$	1.84141	+	1.84141i	0.0959901	+	0.0959901i
$369$	12.7521	+	4.27125i	0.663850	+	0.222352i
$370$		0			0
$371$	−0.893752	+	0.516008i	−0.0464013	+	0.0267898i
$372$	0.667568	+	0.927616i	0.0346118	+	0.0480947i
$373$	5.57233	+	20.7962i	0.288524	+	1.07679i	0.946225	+	0.323508i	$0.104862\pi$
$373$	5.57233	+	20.7962i	0.288524	+	1.07679i	−0.657701	+	0.753279i	$0.728471\pi$
$374$	1.64237	−	2.84467i	0.0849251	−	0.147095i
$375$		0			0
$376$	−6.99867	−	12.1221i	−0.360929	−	0.625147i
$377$	14.9854	−	14.9854i	0.771788	−	0.771788i
$378$	9.15668	+	2.07647i	0.470969	+	0.106802i
$379$		−	9.52893i		−	0.489468i	−0.969590	−	0.244734i	$-0.921299\pi$
$379$		−	9.52893i		−	0.489468i	0.969590	−	0.244734i	$-0.0787007\pi$
$380$		0			0
$381$	10.4193	−	12.7485i	0.533795	−	0.653124i
$382$	25.7391	−	6.89676i	1.31693	−	0.352869i
$383$	9.61802	−	2.57714i	0.491458	−	0.131686i	−0.00457478	−	0.999990i	$-0.501456\pi$
$383$	9.61802	−	2.57714i	0.491458	−	0.131686i	0.496033	+	0.868304i	$0.334790\pi$
$384$	−33.5306	−	5.46620i	−1.71110	−	0.278946i
$385$		0			0
$386$		−	12.8173i		−	0.652385i
$387$	4.13809	+	0.254398i	0.210351	+	0.0129318i
$388$	21.7088	−	21.7088i	1.10210	−	1.10210i
$389$	−14.5672	−	25.2312i	−0.738587	−	1.27927i	−0.953131	−	0.302557i	$-0.902160\pi$
$389$	−14.5672	−	25.2312i	−0.738587	−	1.27927i	0.214544	−	0.976714i	$-0.431173\pi$
$390$		0			0
$391$	−9.85441	+	17.0683i	−0.498359	+	0.863183i
$392$	5.36182	+	20.0106i	0.270813	+	1.01069i
$393$	9.57158	−	21.2392i	0.482822	−	1.07138i
$394$	6.60804	−	3.81516i	0.332908	−	0.192205i
$395$		0			0
$396$	2.53756	−	0.515445i	0.127517	−	0.0259021i
$397$	18.9354	+	18.9354i	0.950338	+	0.950338i	0.998824	−	0.0484856i	$-0.0154395\pi$
$397$	18.9354	+	18.9354i	0.950338	+	0.950338i	−0.0484856	+	0.998824i	$0.515439\pi$
$398$	−10.3384	+	38.5836i	−0.518219	+	1.93402i
$399$	0.0954754	−	0.585663i	0.00477975	−	0.0293198i
$400$		0			0
$401$	21.2096	+	12.2453i	1.05916	+	0.611503i	0.925198	−	0.379484i	$-0.123898\pi$
$401$	21.2096	+	12.2453i	1.05916	+	0.611503i	0.133957	+	0.990987i	$0.457232\pi$
$402$	−5.40217	−	53.7334i	−0.269436	−	2.67998i
$403$	−0.720098	−	0.192950i	−0.0358706	−	0.00961151i
$404$	−44.6649			−2.22216
$405$		0			0
$406$	−9.98392			−0.495493
$407$	−0.0427215	−	0.0114472i	−0.00211763	−	0.000567417i
$408$	3.12207	+	31.0541i	0.154566	+	1.53741i
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	0.165118	−	0.986274i	$-0.447200\pi$
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	−0.771579	+	0.636133i	$0.780533\pi$
$410$		0			0
$411$	−2.72823	+	16.7354i	−0.134574	+	0.825498i
$412$	−14.3795	+	53.6652i	−0.708429	+	2.64389i
$413$	4.42589	+	4.42589i	0.217784	+	0.217784i
$414$	−24.1957	+	4.91477i	−1.18915	+	0.241548i
$415$		0			0
$416$	15.8516	−	9.15193i	0.777189	−	0.448710i
$417$	−5.62816	+	12.4888i	−0.275612	+	0.611581i
$418$	−0.0673086	−	0.251199i	−0.00329217	−	0.0122866i
$419$	13.8808	−	24.0422i	0.678120	−	1.17454i	−0.297426	−	0.954745i	$-0.596128\pi$
$419$	13.8808	−	24.0422i	0.678120	−	1.17454i	0.975546	−	0.219794i	$-0.0705385\pi$
$420$		0			0
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	0.855359	−	0.518035i	$-0.173336\pi$
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	−0.876311	+	0.481745i	$0.840003\pi$
$422$	−7.47211	+	7.47211i	−0.363737	+	0.363737i
$423$	12.9377	+	0.795372i	0.629053	+	0.0386723i
$424$		−	4.29753i		−	0.208706i
$425$		0			0
$426$	−8.57586	−	1.39805i	−0.415502	−	0.0677356i
$427$	−2.16698	+	0.580639i	−0.104867	+	0.0280991i
$428$	26.9616	−	7.22434i	1.30324	−	0.349202i
$429$	−1.06890	+	1.30785i	−0.0516070	+	0.0631436i
$430$		0			0
$431$			25.5770i			1.23200i	0.787746	+	0.616000i	$0.211248\pi$
$431$			25.5770i			1.23200i	−0.787746	+	0.616000i	$0.788752\pi$
$432$	−2.59359	+	2.80308i	−0.124784	+	0.134863i
$433$	−6.30733	+	6.30733i	−0.303111	+	0.303111i	−0.842230	−	0.539119i	$-0.818757\pi$
$433$	−6.30733	+	6.30733i	−0.303111	+	0.303111i	0.539119	+	0.842230i	$0.318757\pi$
$434$	0.175604	+	0.304155i	0.00842927	+	0.0145999i
$435$		0			0
$436$	−14.9694	+	25.9277i	−0.716903	+	1.24171i
$437$	0.403859	+	1.50722i	0.0193192	+	0.0721002i
$438$	−30.5220	−	42.4118i	−1.45840	−	2.02651i
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	−0.172073	−	0.985084i	$-0.555046\pi$
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	0.767072	+	0.641561i	$0.221713\pi$
$440$		0			0
$441$	−18.1910	−	6.09297i	−0.866240	−	0.290142i
$442$	−35.0390	−	35.0390i	−1.66663	−	1.66663i
$443$	5.67359	−	21.1741i	0.269560	−	1.00601i	−0.689839	−	0.723962i	$-0.742319\pi$
$443$	5.67359	−	21.1741i	0.269560	−	1.00601i	0.959400	−	0.282050i	$-0.0910144\pi$
$444$	0.956558	−	0.362236i	0.0453962	−	0.0171910i
$445$		0			0
$446$	−36.8430	−	21.2713i	−1.74457	−	1.00723i
$447$	−14.4253	−	6.50084i	−0.682293	−	0.307479i
$448$	−9.43376	−	2.52777i	−0.445703	−	0.119426i
$449$	23.6447			1.11586			0.557931	−	0.829888i	$-0.311596\pi$
$449$	23.6447			1.11586			0.557931	+	0.829888i	$0.311596\pi$
$450$		0			0
$451$	1.13976			0.0536693
$452$	−44.1632	−	11.8335i	−2.07726	−	0.556601i
$453$	−20.6657	+	14.8722i	−0.970958	+	0.698759i
$454$	22.6906	+	13.1004i	1.06492	+	0.614833i
$455$		0			0
$456$	1.91329	+	1.56373i	0.0895981	+	0.0732281i
$457$	1.47628	−	5.50956i	0.0690575	−	0.257726i	−0.922763	−	0.385369i	$-0.874074\pi$
$457$	1.47628	−	5.50956i	0.0690575	−	0.257726i	0.991820	+	0.127642i	$0.0407410\pi$
$458$	−8.01095	−	8.01095i	−0.374327	−	0.374327i
$459$	−25.5719	−	13.4694i	−1.19359	−	0.628697i
$460$		0			0
$461$	−27.8943	+	16.1048i	−1.29916	+	0.750073i	−0.980260	−	0.197713i	$-0.936648\pi$
$461$	−27.8943	+	16.1048i	−1.29916	+	0.750073i	−0.318905	+	0.947787i	$0.603315\pi$
$462$	0.791745	−	0.0795993i	0.0368353	−	0.00370329i
$463$	1.65471	+	6.17544i	0.0769007	+	0.286997i	0.993658	−	0.112448i	$-0.0358693\pi$
$463$	1.65471	+	6.17544i	0.0769007	+	0.286997i	−0.916757	+	0.399446i	$0.869203\pi$
$464$	2.03040	−	3.51676i	0.0942590	−	0.163261i
$465$		0			0
$466$	12.9869	+	22.4940i	0.601608	+	1.04202i
$467$	12.7982	−	12.7982i	0.592230	−	0.592230i	−0.346003	−	0.938233i	$-0.612461\pi$
$467$	12.7982	−	12.7982i	0.592230	−	0.592230i	0.938233	+	0.346003i	$0.112461\pi$
$468$	2.39692	−	38.9889i	0.110798	−	1.80226i
$469$		−	10.4433i		−	0.482228i
$470$		0			0
$471$	10.3870	+	27.4290i	0.478609	+	1.26386i
$472$	−25.1763	+	6.74597i	−1.15883	+	0.310508i
$473$	0.339395	−	0.0909406i	0.0156054	−	0.00418145i
$474$	−19.6968	−	52.0135i	−0.904706	−	2.38906i
$475$		0			0
$476$			14.6900i			0.673314i
$477$	3.31792	+	2.19758i	0.151917	+	0.100620i
$478$	−36.5795	+	36.5795i	−1.67311	+	1.67311i
$479$	−1.76166	−	3.05128i	−0.0804921	−	0.139416i	0.822969	−	0.568086i	$-0.192316\pi$
$479$	−1.76166	−	3.05128i	−0.0804921	−	0.139416i	−0.903461	+	0.428669i	$0.858983\pi$
$480$		0			0
$481$	−0.333609	+	0.577827i	−0.0152112	+	0.0263467i
$482$	17.4028	+	64.9482i	0.792677	+	2.95831i
$483$	−4.75056	+	0.477604i	−0.216158	+	0.0217318i
$484$	−32.1495	+	18.5615i	−1.46134	+	0.843706i
$485$		0			0
$486$	−8.57829	−	35.1759i	−0.389119	−	1.59561i
$487$	−29.3442	−	29.3442i	−1.32971	−	1.32971i	−0.905616	−	0.424098i	$-0.860591\pi$
$487$	−29.3442	−	29.3442i	−1.32971	−	1.32971i	−0.424098	−	0.905616i	$-0.639409\pi$
$488$	2.41790	−	9.02373i	0.109453	−	0.408485i
$489$	18.4877	+	15.1099i	0.836044	+	0.683295i
$490$		0			0
$491$	17.9001	+	10.3346i	0.807819	+	0.466395i	0.846198	−	0.532869i	$-0.178886\pi$
$491$	17.9001	+	10.3346i	0.807819	+	0.466395i	−0.0383788	+	0.999263i	$0.512219\pi$
$492$	−21.3944	+	15.3967i	−0.964533	+	0.694135i
$493$	29.6859	+	7.95433i	1.33699	+	0.358245i
$494$	−3.92319			−0.176513
$495$		0			0
$496$	−0.142849			−0.00641409
$497$	−1.62304	−	0.434891i	−0.0728031	−	0.0195075i
$498$	−19.7521	−	8.90140i	−0.885114	−	0.398881i
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.912596	−	0.408862i	$-0.134074\pi$
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.102214	+	0.994762i	$0.467407\pi$
$500$		0			0
$501$	31.9563	−	12.1014i	1.42770	−	0.540652i
$502$	12.2766	−	45.8168i	0.547930	−	2.04490i
$503$	6.72022	+	6.72022i	0.299640	+	0.299640i	0.840873	−	0.541233i	$-0.182042\pi$
$503$	6.72022	+	6.72022i	0.299640	+	0.299640i	−0.541233	+	0.840873i	$0.682042\pi$
$504$	−5.66431	+	5.00820i	−0.252308	+	0.223083i
$505$		0			0
$506$	−1.81213	+	1.04624i	−0.0805592	+	0.0465109i
$507$	1.73155	+	2.40607i	0.0769008	+	0.106857i
$508$	8.35217	+	31.1707i	0.370568	+	1.38298i
$509$	−11.9676	+	20.7285i	−0.530454	+	0.918773i	0.468915	+	0.883243i	$0.344645\pi$
$509$	−11.9676	+	20.7285i	−0.530454	+	0.918773i	−0.999369	+	0.0355293i	$0.988688\pi$
$510$		0			0
$511$	−5.05232	−	8.75087i	−0.223501	−	0.387116i
$512$	5.84717	−	5.84717i	0.258411	−	0.258411i
$513$	−2.18566	+	0.677538i	−0.0964991	+	0.0299141i
$514$		−	17.0546i		−	0.752246i
$515$		0			0
$516$	−5.14226	+	6.29181i	−0.226376	+	0.276981i
$517$	1.06111	−	0.284325i	0.0466678	−	0.0125046i
$518$	0.303618	−	0.0813543i	0.0133402	−	0.00357450i
$519$	−17.7444	−	2.89271i	−0.778893	−	0.126976i
$520$		0			0
$521$		−	3.23141i		−	0.141571i	−0.997492	−	0.0707853i	$-0.977449\pi$
$521$		−	3.23141i		−	0.141571i	0.997492	−	0.0707853i	$-0.0225505\pi$
$522$	17.1679	+	34.4606i	0.751420	+	1.50830i
$523$	8.67002	−	8.67002i	0.379114	−	0.379114i	−0.491669	−	0.870782i	$-0.663613\pi$
$523$	8.67002	−	8.67002i	0.379114	−	0.379114i	0.870782	+	0.491669i	$0.163613\pi$
$524$	22.8301	+	39.5429i	0.997339	+	1.72744i
$525$		0			0
$526$	−16.9641	+	29.3827i	−0.739672	+	1.28115i
$527$	−0.279813	−	1.04427i	−0.0121888	−	0.0454893i
$528$	−0.132977	+	0.295074i	−0.00578707	+	0.0128415i
$529$	−9.04559	+	5.22247i	−0.393286	+	0.227064i
$530$		0			0
$531$	7.66587	−	22.8870i	0.332670	−	0.993213i
$532$	0.822392	+	0.822392i	0.0356552	+	0.0356552i
$533$	4.45016	−	16.6082i	0.192758	−	0.719381i
$534$	0.184817	−	1.13370i	0.00799780	−	0.0490599i
$535$		0			0
$536$	37.6619	+	21.7441i	1.62675	+	0.939202i
$537$	2.61650	+	26.0254i	0.112910	+	1.12308i
$538$	−8.43586	−	2.26038i	−0.363696	−	0.0974520i
$539$	−1.62588			−0.0700317
$540$		0			0
$541$	−11.1502			−0.479386			−0.239693	−	0.970849i	$-0.577047\pi$
$541$	−11.1502			−0.479386			−0.239693	+	0.970849i	$0.577047\pi$
$542$	31.5855	+	8.46330i	1.35671	+	0.363530i
$543$	1.35655	+	13.4931i	0.0582153	+	0.579046i
$544$	22.9878	+	13.2720i	0.985592	+	0.569032i
$545$		0			0
$546$	1.93144	−	11.8478i	0.0826582	−	0.507040i
$547$	−3.54511	+	13.2305i	−0.151578	+	0.565697i	0.847796	+	0.530323i	$0.177929\pi$
$547$	−3.54511	+	13.2305i	−0.151578	+	0.565697i	−0.999374	+	0.0353748i	$0.988737\pi$
$548$	−23.5000	−	23.5000i	−1.00387	−	1.00387i
$549$	5.73038	+	6.48111i	0.244567	+	0.276607i
$550$		0			0
$551$	2.10722	−	1.21661i	0.0897708	−	0.0518292i
$552$	8.16876	−	18.1264i	0.347686	−	0.771511i
$553$	−2.78371	−	10.3889i	−0.118375	−	0.441782i
$554$	−2.42950	+	4.20802i	−0.103220	+	0.178781i
$555$		0			0
$556$	−13.4243	−	23.2516i	−0.569317	−	0.986086i
$557$	−11.8934	+	11.8934i	−0.503938	+	0.503938i	−0.912659	−	0.408721i	$-0.865975\pi$
$557$	−11.8934	+	11.8934i	−0.503938	+	0.503938i	0.408721	+	0.912659i	$0.365975\pi$
$558$	0.747864	−	1.12913i	0.0316596	−	0.0477999i
$559$		−	5.30061i		−	0.224192i
$560$		0			0
$561$	−2.41758	−	0.394116i	−0.102070	−	0.0166396i
$562$	20.7940	−	5.57173i	0.877141	−	0.235029i
$563$	23.7986	−	6.37683i	1.00299	−	0.268751i	0.280294	−	0.959914i	$-0.409568\pi$
$563$	23.7986	−	6.37683i	1.00299	−	0.268751i	0.722699	+	0.691163i	$0.242901\pi$
$564$	−16.0772	+	19.6713i	−0.676974	+	0.828310i
$565$		0			0
$566$		−	74.8082i		−	3.14442i
$567$	−0.970098	−	6.93413i	−0.0407403	−	0.291206i
$568$	4.94768	−	4.94768i	0.207600	−	0.207600i
$569$	6.24856	+	10.8228i	0.261953	+	0.453716i	0.966761	−	0.255682i	$-0.0823000\pi$
$569$	6.24856	+	10.8228i	0.261953	+	0.453716i	−0.704808	+	0.709399i	$0.748967\pi$
$570$		0			0
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	−0.422591	−	0.906320i	$-0.638879\pi$
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	0.996192	−	0.0871853i	$-0.0277872\pi$
$572$	−0.856838	−	3.19776i	−0.0358262	−	0.133705i
$573$	−11.6072	−	16.1287i	−0.484897	−	0.673787i
$574$	−7.01498	+	4.05010i	−0.292800	+	0.169048i
$575$		0			0
$576$	7.49704	+	36.9083i	0.312377	+	1.53785i
$577$	11.1638	+	11.1638i	0.464755	+	0.464755i	0.900210	−	0.435455i	$-0.143413\pi$
$577$	11.1638	+	11.1638i	0.464755	+	0.464755i	−0.435455	+	0.900210i	$0.643413\pi$
$578$	8.37928	−	31.2719i	0.348532	−	1.30074i
$579$	−8.93865	+	3.38495i	−0.371478	+	0.140674i
$580$		0			0
$581$	−3.62831	−	2.09481i	−0.150528	−	0.0869072i
$582$	−33.1695	−	14.9480i	−1.37492	−	0.619615i
$583$	0.325788	+	0.0872947i	0.0134928	+	0.00361538i
$584$	42.0778			1.74119
$585$		0			0
$586$	−15.3410			−0.633733
$587$	−17.7860	−	4.76574i	−0.734106	−	0.196703i	−0.127649	−	0.991819i	$-0.540743\pi$
$587$	−17.7860	−	4.76574i	−0.734106	−	0.196703i	−0.606457	+	0.795116i	$0.707410\pi$
$588$	30.5193	−	21.9635i	1.25859	−	0.905758i
$589$	−0.0741267	−	0.0427971i	−0.00305434	−	0.00176342i
$590$		0			0
$591$	−4.40577	−	3.60082i	−0.181229	−	0.148118i
$592$	−0.0330896	+	0.123492i	−0.00135997	+	0.00507549i
$593$	14.5424	+	14.5424i	0.597186	+	0.597186i	0.939563	−	0.342377i	$-0.111232\pi$
$593$	14.5424	+	14.5424i	0.597186	+	0.597186i	−0.342377	+	0.939563i	$0.611232\pi$
$594$	−1.63620	−	2.59592i	−0.0671341	−	0.106512i
$595$		0			0
$596$	26.8568	−	15.5058i	1.10010	−	0.635143i
$597$	29.6380	−	2.97970i	1.21300	−	0.121951i
$598$	8.16997	+	30.4907i	0.334095	+	1.24686i
$599$	17.6972	−	30.6525i	0.723089	−	1.25243i	−0.236666	−	0.971591i	$-0.576055\pi$
$599$	17.6972	−	30.6525i	0.723089	−	1.25243i	0.959756	−	0.280836i	$-0.0906118\pi$
$600$		0			0
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	0.975789	−	0.218715i	$-0.0701864\pi$
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	−0.677307	+	0.735700i	$0.736853\pi$
$602$	−1.76575	+	1.76575i	−0.0719664	+	0.0719664i
$603$	−36.0463	+	17.9579i	−1.46792	+	0.731304i
$604$		−	49.9026i		−	2.03051i
$605$		0			0
$606$	18.7449	+	49.4997i	0.761460	+	2.01079i
$607$	7.54883	−	2.02270i	0.306397	−	0.0820989i	−0.102344	−	0.994749i	$-0.532634\pi$
$607$	7.54883	−	2.02270i	0.306397	−	0.0820989i	0.408742	+	0.912650i	$0.365968\pi$
$608$	2.02994	−	0.543920i	0.0823248	−	0.0220589i
$609$	2.63667	+	6.96266i	0.106843	+	0.282141i
$610$		0			0
$611$		−	16.5723i		−	0.670444i
$612$	50.7040	−	25.2603i	2.04959	−	1.02109i
$613$	−3.49830	+	3.49830i	−0.141295	+	0.141295i	−0.774216	−	0.632921i	$-0.781856\pi$
$613$	−3.49830	+	3.49830i	−0.141295	+	0.141295i	0.632921	+	0.774216i	$0.281856\pi$
$614$	−9.56058	−	16.5594i	−0.385833	−	0.668283i
$615$		0			0
$616$	−0.320393	+	0.554937i	−0.0129090	+	0.0223590i
$617$	−6.40561	−	23.9061i	−0.257880	−	0.962421i	−0.966466	−	0.256796i	$-0.917333\pi$
$617$	−6.40561	−	23.9061i	−0.257880	−	0.962421i	0.708585	−	0.705625i	$-0.249334\pi$
$618$	65.5090	−	6.58605i	2.63516	−	0.264930i
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	−0.777030	−	0.629463i	$-0.783275\pi$
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	0.156616	+	0.987660i	$0.449941\pi$
$620$		0			0
$621$	9.81737	+	15.5758i	0.393958	+	0.625035i
$622$	18.9394	+	18.9394i	0.759402	+	0.759402i
$623$	0.0574910	−	0.214559i	0.00230333	−	0.00859614i
$624$	3.78051	+	3.08979i	0.151342	+	0.123691i
$625$		0			0
$626$	13.3961	+	7.73424i	0.535416	+	0.309122i
$627$	−0.157408	+	0.113280i	−0.00628625	+	0.00452396i
$628$	−55.5270	−	14.8784i	−2.21577	−	0.593714i
$629$	−0.967588			−0.0385803
$630$		0			0
$631$	−29.9153			−1.19091			−0.595454	−	0.803389i	$-0.703028\pi$
$631$	−29.9153			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$632$	43.2617	+	11.5919i	1.72086	+	0.461102i
$633$	7.18428	+	3.23763i	0.285549	+	0.128684i
$634$	−4.03553	−	2.32991i	−0.160271	−	0.0925327i
$635$		0			0
$636$	−7.29457	+	2.76236i	−0.289249	+	0.109535i
$637$	−6.34819	+	23.6917i	−0.251524	+	0.938701i
$638$	2.30723	+	2.30723i	0.0913441	+	0.0913441i
$639$	1.28983	+	6.34991i	0.0510250	+	0.251199i
$640$		0			0
$641$	−13.7403	+	7.93299i	−0.542711	+	0.313334i	−0.746177	−	0.665748i	$-0.768113\pi$
$641$	−13.7403	+	7.93299i	−0.542711	+	0.313334i	0.203466	+	0.979082i	$0.434779\pi$
$642$	−19.3216	−	26.8482i	−0.762561	−	1.05961i
$643$	−6.01727	−	22.4568i	−0.237298	−	0.885608i	−0.977099	−	0.212783i	$-0.931747\pi$
$643$	−6.01727	−	22.4568i	−0.237298	−	0.885608i	0.739801	−	0.672825i	$-0.234919\pi$
$644$	4.67895	−	8.10419i	0.184377	−	0.319350i
$645$		0			0
$646$	−2.84467	−	4.92712i	−0.111922	−	0.193855i
$647$	8.90965	−	8.90965i	0.350274	−	0.350274i	−0.509937	−	0.860212i	$-0.670331\pi$
$647$	8.90965	−	8.90965i	0.350274	−	0.350274i	0.860212	+	0.509937i	$0.170331\pi$
$648$	27.0265	+	10.9391i	1.06170	+	0.429728i
$649$		−	2.04560i		−	0.0802969i
$650$		0			0
$651$	0.165739	−	0.202789i	0.00649581	−	0.00794793i
$652$	−45.2035	+	12.1122i	−1.77031	+	0.474352i
$653$	−14.0422	+	3.76260i	−0.549515	+	0.147242i	−0.522885	−	0.852403i	$-0.675144\pi$
$653$	−14.0422	+	3.76260i	−0.549515	+	0.147242i	−0.0266300	+	0.999645i	$0.508478\pi$
$654$	35.0166	+	5.70845i	1.36926	+	0.223218i
$655$		0			0
$656$		−	3.29463i		−	0.128634i
$657$	−21.5168	+	32.4863i	−0.839452	+	1.26741i
$658$	−5.52058	+	5.52058i	−0.215215	+	0.215215i
$659$	−4.50735	−	7.80696i	−0.175582	−	0.304116i	0.764781	−	0.644291i	$-0.222847\pi$
$659$	−4.50735	−	7.80696i	−0.175582	−	0.304116i	−0.940362	+	0.340174i	$0.889514\pi$
$660$		0			0
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	−0.411488	−	0.911415i	$-0.634991\pi$
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	0.995053	−	0.0993481i	$-0.0316757\pi$
$662$	−14.1511	−	52.8125i	−0.549996	−	2.05261i
$663$	−15.1822	+	33.6892i	−0.589629	+	1.30838i
$664$	15.1090	−	8.72321i	0.586345	−	0.338526i
$665$		0			0
$666$	−0.802894	−	0.908079i	−0.0311115	−	0.0351874i
$667$	−13.8436	−	13.8436i	−0.536028	−	0.536028i
$668$	−17.3342	+	64.6920i	−0.670679	+	2.50301i
$669$	−5.10443	+	31.3115i	−0.197349	+	1.21057i
$670$		0			0
$671$	0.634959	+	0.366594i	0.0245123	+	0.0141522i
$672$	0.643241	+	6.39808i	0.0248136	+	0.246811i
$673$	−26.2818	−	7.04218i	−1.01309	−	0.271456i	−0.286169	−	0.958179i	$-0.592382\pi$
$673$	−26.2818	−	7.04218i	−1.01309	−	0.271456i	−0.726919	+	0.686723i	$0.759049\pi$
$674$	−26.4622			−1.01928
$675$		0			0
$676$	−5.81007			−0.223464
$677$	−16.7622	−	4.49141i	−0.644223	−	0.172619i	−0.0781075	−	0.996945i	$-0.524888\pi$
$677$	−16.7622	−	4.49141i	−0.644223	−	0.172619i	−0.566116	+	0.824326i	$0.691554\pi$
$678$	5.41993	+	53.9100i	0.208151	+	2.07040i
$679$	−6.09297	−	3.51778i	−0.233827	−	0.135000i
$680$		0			0
$681$	3.14367	−	19.2838i	0.120466	−	0.738959i
$682$	0.0297075	−	0.110870i	0.00113756	−	0.00424543i
$683$	−27.4945	−	27.4945i	−1.05205	−	1.05205i	−0.998569	−	0.0534806i	$-0.982968\pi$
$683$	−27.4945	−	27.4945i	−1.05205	−	1.05205i	−0.0534806	−	0.998569i	$-0.517032\pi$
$684$	1.42442	−	4.25273i	0.0544642	−	0.162607i
$685$		0			0
$686$	20.9610	−	12.1018i	0.800293	−	0.462049i
$687$	−3.47111	+	7.70236i	−0.132431	+	0.293863i
$688$	−0.262876	−	0.981065i	−0.0100220	−	0.0374028i
$689$	2.54405	−	4.40643i	0.0969207	−	0.167872i
$690$		0			0
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	0.640162	−	0.768240i	$-0.278867\pi$
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	−0.985396	+	0.170277i	$0.945534\pi$
$692$	24.9168	−	24.9168i	0.947195	−	0.947195i
$693$	−0.264605	−	0.531132i	−0.0100515	−	0.0201760i
$694$			33.1902i			1.25988i
$695$		0			0
$696$	−30.5993	−	4.98833i	−1.15986	−	0.189082i
$697$	24.0850	−	6.45355i	0.912283	−	0.244446i
$698$	−39.4063	+	10.5589i	−1.49155	+	0.399660i
$699$	12.2573	−	14.9974i	0.463614	−	0.567254i
$700$		0			0
$701$			5.23510i			0.197727i	0.995101	+	0.0988635i	$0.0315207\pi$
$701$			5.23510i			0.197727i	−0.995101	+	0.0988635i	$0.968479\pi$
$702$	−44.2153	+	13.7064i	−1.66880	+	0.517316i
$703$	−0.0541687	+	0.0541687i	−0.00204301	+	0.00204301i
$704$	1.59594	+	2.76425i	0.0601492	+	0.104181i
$705$		0			0
$706$	−20.2427	+	35.0614i	−0.761844	+	1.31955i
$707$	2.64917	+	9.88684i	0.0996323	+	0.371833i
$708$	27.6333	+	38.3978i	1.03852	+	1.44308i
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	−0.750222	−	0.661186i	$-0.770054\pi$
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	0.197492	+	0.980304i	$0.436720\pi$
$710$		0			0
$711$	−31.0718	+	27.4727i	−1.16528	+	1.03031i
$712$	0.654066	+	0.654066i	0.0245121	+	0.0245121i
$713$	−0.178248	+	0.665231i	−0.00667545	+	0.0249131i
$714$	16.2801	−	6.16507i	0.609268	−	0.230722i
$715$		0			0
$716$	−44.3979	−	25.6331i	−1.65923	−	0.957955i
$717$	35.1705	+	15.8498i	1.31346	+	0.591920i
$718$	76.4092	+	20.4738i	2.85157	+	0.764075i
$719$	−49.3502			−1.84045			−0.920225	−	0.391389i	$-0.871995\pi$
$719$	−49.3502			−1.84045			−0.920225	+	0.391389i	$0.871995\pi$
$720$		0			0
$721$	12.7320			0.474164
$722$	42.1918	+	11.3053i	1.57022	+	0.420739i
$723$	40.6981	−	29.2888i	1.51358	−	1.08926i
$724$	−23.0186	−	13.2898i	−0.855478	−	0.493910i
$725$		0			0
$726$	34.0632	+	27.8397i	1.26421	+	1.03323i
$727$	10.1550	−	37.8991i	0.376630	−	1.40560i	−0.474319	−	0.880353i	$-0.657306\pi$
$727$	10.1550	−	37.8991i	0.376630	−	1.40560i	0.850949	−	0.525249i	$-0.176028\pi$
$728$	6.83537	+	6.83537i	0.253336	+	0.253336i
$729$	−22.2658	+	15.2721i	−0.824658	+	0.565632i
$730$		0			0
$731$	6.65702	−	3.84343i	0.246219	−	0.142155i
$732$	−16.8709	+	1.69615i	−0.623568	+	0.0626914i
$733$	1.96236	+	7.32362i	0.0724813	+	0.270504i	0.992650	−	0.121017i	$-0.0386156\pi$
$733$	1.96236	+	7.32362i	0.0724813	+	0.270504i	−0.920169	+	0.391521i	$0.871949\pi$
$734$	−16.3918	+	28.3915i	−0.605034	+	1.04795i
$735$		0			0
$736$	−8.45462	−	14.6438i	−0.311641	−	0.539778i
$737$	−2.41340	+	2.41340i	−0.0888987	+	0.0888987i
$738$	26.0421	+	17.2486i	0.958621	+	0.634930i
$739$		−	43.8329i		−	1.61242i	−0.591629	−	0.806210i	$-0.701515\pi$
$739$		−	43.8329i		−	1.61242i	0.591629	−	0.806210i	$-0.298485\pi$
$740$		0			0
$741$	1.03608	+	2.73598i	0.0380614	+	0.100509i
$742$	−2.31535	+	0.620396i	−0.0849992	+	0.0227755i
$743$	9.01884	−	2.41659i	0.330869	−	0.0886561i	−0.0895603	−	0.995981i	$-0.528546\pi$
$743$	9.01884	−	2.41659i	0.330869	−	0.0886561i	0.420429	+	0.907325i	$0.361879\pi$
$744$	0.386235	+	1.01993i	0.0141601	+	0.0373925i
$745$		0			0
$746$			50.0066i			1.83087i
$747$	−0.991358	+	16.1257i	−0.0362719	+	0.590007i
$748$	3.39477	−	3.39477i	0.124125	−	0.124125i
$749$	−3.19830	−	5.53962i	−0.116863	−	0.202413i
$750$		0			0
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	−0.00266566	−	0.999996i	$-0.500849\pi$
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	0.867355	−	0.497690i	$-0.165818\pi$
$752$	−0.821878	−	3.06729i	−0.0299708	−	0.111853i
$753$	−35.1942	+	3.53830i	−1.28255	+	0.128943i
$754$	42.6286	−	24.6116i	1.55244	−	0.896303i
$755$		0			0
$756$	12.1417	+	6.39537i	0.441591	+	0.232597i
$757$	−1.37906	−	1.37906i	−0.0501227	−	0.0501227i	0.681601	−	0.731724i	$-0.261284\pi$
$757$	−1.37906	−	1.37906i	−0.0501227	−	0.0501227i	−0.731724	+	0.681601i	$0.761284\pi$
$758$	5.72832	−	21.3784i	0.208062	−	0.776497i
$759$	1.20820	+	0.987457i	0.0438549	+	0.0358424i
$760$		0			0
$761$	−41.8540	−	24.1644i	−1.51720	−	0.875958i	−0.999796	−	0.0202203i	$-0.993563\pi$
$761$	−41.8540	−	24.1644i	−1.51720	−	0.875958i	−0.517409	−	0.855738i	$-0.673103\pi$
$762$	31.0396	−	22.3379i	1.12445	−	0.809218i
$763$	6.62712	+	1.77573i	0.239918	+	0.0642858i
$764$	38.9469			1.40905
$765$		0			0
$766$	23.1275			0.835631
$767$	−29.8078	−	7.98696i	−1.07630	−	0.288393i
$768$	−32.2924	−	14.5528i	−1.16525	−	0.525128i
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.0423126	−	0.999104i	$-0.513473\pi$
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.886406	+	0.462908i	$0.846806\pi$
$770$		0			0
$771$	−11.8937	+	4.50398i	−0.428340	+	0.162207i
$772$	4.84862	−	18.0953i	0.174506	−	0.651264i
$773$	−14.1444	−	14.1444i	−0.508738	−	0.508738i	0.405401	−	0.914139i	$-0.367132\pi$
$773$	−14.1444	−	14.1444i	−0.508738	−	0.508738i	−0.914139	+	0.405401i	$0.867132\pi$
$774$	9.13097	+	3.05836i	0.328206	+	0.109931i
$775$		0			0
$776$	25.3724	−	14.6488i	0.910816	−	0.525860i
$777$	−0.136919	−	0.190255i	−0.00491193	−	0.00682535i
$778$	−17.5142	−	65.3638i	−0.627913	−	2.34340i
$779$	0.987064	−	1.70964i	0.0353652	−	0.0612544i
$780$		0			0
$781$	0.274574	+	0.475576i	0.00982503	+	0.0170175i
$782$	−32.3692	+	32.3692i	−1.15752	+	1.15752i
$783$	19.4985	−	21.0735i	0.696819	−	0.753104i
$784$			4.69982i			0.167851i
$785$		0			0
$786$	34.2420	−	41.8967i	1.22137	−	1.49441i
$787$	1.74131	−	0.466583i	0.0620710	−	0.0166319i	−0.227650	−	0.973743i	$-0.573104\pi$
$787$	1.74131	−	0.466583i	0.0620710	−	0.0166319i	0.289721	+	0.957111i	$0.406438\pi$
$788$	10.7723	−	2.88644i	0.383749	−	0.102825i
$789$	24.9712	+	4.07084i	0.889000	+	0.144926i
$790$		0			0
$791$			10.4777i			0.372543i
$792$	2.46636	+	0.151625i	0.0876383	+	0.00538774i
$793$	7.82105	−	7.82105i	0.277733	−	0.277733i
$794$	31.0989	+	53.8649i	1.10366	+	1.91159i
$795$		0			0
$796$	−29.1913	+	50.5607i	−1.03466	+	1.79208i
$797$	−1.83545	−	6.85000i	−0.0650150	−	0.242639i	0.925769	−	0.378089i	$-0.123419\pi$
$797$	−1.83545	−	6.85000i	−0.0650150	−	0.242639i	−0.990784	+	0.135450i	$0.956752\pi$
$798$	0.566273	−	1.25655i	0.0200458	−	0.0444815i
$799$	20.8131	−	12.0165i	0.736315	−	0.425112i
$800$		0			0
$801$	−0.839435	+	0.170511i	−0.0296600	+	0.00602472i
$802$	40.2228	+	40.2228i	1.42032	+	1.42032i
$803$	−0.854717	+	3.18985i	−0.0301623	+	0.112567i
$804$	12.6999	−	77.9035i	0.447891	−	2.74744i
$805$		0			0
$806$	−1.49956	−	0.865774i	−0.0528199	−	0.0304956i
$807$	0.651477	+	6.48001i	0.0229331	+	0.228107i
$808$	−41.1709	−	11.0317i	−1.44839	−	0.388094i
$809$	24.7868			0.871457			0.435728	−	0.900078i	$-0.356491\pi$
$809$	24.7868			0.871457			0.435728	+	0.900078i	$0.356491\pi$
$810$		0			0
$811$	−5.24853			−0.184301			−0.0921505	−	0.995745i	$-0.529374\pi$
$811$	−5.24853			−0.184301			−0.0921505	+	0.995745i	$0.529374\pi$
$812$	−14.0951	−	3.77678i	−0.494642	−	0.132539i
$813$	−2.43926	−	24.2624i	−0.0855484	−	0.850919i
$814$	−0.0889652	−	0.0513641i	−0.00311823	−	0.00180031i
$815$		0			0
$816$	−1.13924	+	6.98831i	−0.0398815	+	0.244640i
$817$	0.157514	−	0.587849i	0.00551071	−	0.0205662i
$818$	−23.2598	−	23.2598i	−0.813260	−	0.813260i
$819$	−8.77260	+	1.78194i	−0.306539	+	0.0622661i
$820$		0			0
$821$	23.5611	−	13.6030i	0.822288	−	0.474748i	−0.0289167	−	0.999582i	$-0.509206\pi$
$821$	23.5611	−	13.6030i	0.822288	−	0.474748i	0.851205	+	0.524834i	$0.175872\pi$
$822$	−16.1814	+	35.9063i	−0.564390	+	1.25237i
$823$	8.71001	+	32.5062i	0.303612	+	1.13309i	0.934134	+	0.356923i	$0.116174\pi$
$823$	8.71001	+	32.5062i	0.303612	+	1.13309i	−0.630522	+	0.776171i	$0.717159\pi$
$824$	−26.5093	+	45.9155i	−0.923496	+	1.59954i
$825$		0			0
$826$	7.26896	+	12.5902i	0.252920	+	0.438070i
$827$	−9.12836	+	9.12836i	−0.317424	+	0.317424i	−0.847777	−	0.530353i	$-0.822059\pi$
$827$	−9.12836	+	9.12836i	−0.317424	+	0.317424i	0.530353	+	0.847777i	$0.322059\pi$
$828$	−36.0182	−	2.21429i	−1.25172	−	0.0769521i
$829$			44.3456i			1.54019i	0.637931	+	0.770093i	$0.279790\pi$
$829$			44.3456i			1.54019i	−0.637931	+	0.770093i	$0.720210\pi$
$830$		0			0
$831$	3.57623	+	0.583001i	0.124058	+	0.0202241i
$832$	46.5109	−	12.4626i	1.61247	−	0.432061i
$833$	−34.3574	+	9.20604i	−1.19041	+	0.318970i
$834$	−20.1346	+	24.6356i	−0.697203	+	0.853061i
$835$		0			0
$836$		−	0.380101i		−	0.0131461i
$837$	−0.984946	−	0.223357i	−0.0340447	−	0.00772035i
$838$	45.5948	−	45.5948i	1.57505	−	1.57505i
$839$	23.9660	+	41.5104i	0.827399	+	1.43310i	0.900072	+	0.435742i	$0.143514\pi$
$839$	23.9660	+	41.5104i	0.827399	+	1.43310i	−0.0726721	+	0.997356i	$0.523153\pi$
$840$		0			0
$841$	−0.764464	+	1.32409i	−0.0263608	+	0.0456583i
$842$	−0.516871	−	1.92899i	−0.0178125	−	0.0664773i
$843$	−9.37717	−	13.0300i	−0.322967	−	0.448778i
$844$	−13.3756	+	7.72240i	−0.460407	+	0.265816i
$845$		0			0
$846$	28.5479	+	9.56193i	0.981497	+	0.328746i
$847$	6.01556	+	6.01556i	0.206697	+	0.206697i
$848$	0.252337	−	0.941733i	0.00866527	−	0.0323392i
$849$	−52.1703	+	19.7562i	−1.79048	+	0.678031i
$850$		0			0
$851$	0.533801	+	0.308190i	0.0182985	+	0.0105646i
$852$	−11.5784	−	5.21787i	−0.396669	−	0.178761i
$853$	5.60190	+	1.50103i	0.191806	+	0.0513941i	0.353443	−	0.935456i	$-0.385011\pi$
$853$	5.60190	+	1.50103i	0.191806	+	0.0513941i	−0.161637	+	0.986850i	$0.551678\pi$
$854$	−5.21071			−0.178307
$855$		0			0
$856$	26.6368			0.910427
$857$	30.7371	+	8.23598i	1.04996	+	0.281336i	0.742235	−	0.670140i	$-0.233766\pi$
$857$	30.7371	+	8.23598i	1.04996	+	0.281336i	0.307724	+	0.951476i	$0.400433\pi$
$858$	−3.18432	+	2.29162i	−0.108711	+	0.0782347i
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	0.313525	−	0.949580i	$-0.398490\pi$
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	−0.665598	+	0.746310i	$0.731824\pi$
$860$		0			0
$861$	4.67709	+	3.82256i	0.159395	+	0.130273i
$862$	−15.3756	+	57.3825i	−0.523695	+	1.95446i
$863$	13.3552	+	13.3552i	0.454617	+	0.454617i	0.896884	−	0.442267i	$-0.145826\pi$
$863$	13.3552	+	13.3552i	0.454617	+	0.454617i	−0.442267	+	0.896884i	$0.645826\pi$
$864$	20.9776	−	13.2221i	0.713672	−	0.449825i
$865$		0			0
$866$	−17.9423	+	10.3590i	−0.609704	+	0.352013i
$867$	−24.0215	+	2.41504i	−0.815814	+	0.0820191i
$868$	0.132857	+	0.495830i	0.00450947	+	0.0168296i
$869$	−1.75753	+	3.04413i	−0.0596201	+	0.103265i
$870$		0			0
$871$	25.7442	+	44.5902i	0.872308	+	1.51088i
$872$	−20.2022	+	20.2022i	−0.684132	+	0.684132i
$873$	−1.66477	+	27.0796i	−0.0563441	+	0.916506i
$874$			3.62427i			0.122593i
$875$		0			0
$876$	−27.0467	−	71.4223i	−0.913824	−	2.41314i
$877$	6.46168	−	1.73140i	0.218195	−	0.0584653i	−0.148065	−	0.988978i	$-0.547305\pi$
$877$	6.46168	−	1.73140i	0.218195	−	0.0584653i	0.366261	+	0.930512i	$0.380638\pi$
$878$	32.2960	−	8.65368i	1.08994	−	0.292048i
$879$	4.05144	+	10.6986i	0.136652	+	0.360856i
$880$		0			0
$881$			13.4495i			0.453126i	0.973996	+	0.226563i	$0.0727490\pi$
$881$			13.4495i			0.453126i	−0.973996	+	0.226563i	$0.927251\pi$
$882$	−37.1492	−	24.6053i	−1.25088	−	0.828503i
$883$	−32.5618	+	32.5618i	−1.09579	+	1.09579i	−0.100896	+	0.994897i	$0.532171\pi$
$883$	−32.5618	+	32.5618i	−1.09579	+	1.09579i	−0.994897	+	0.100896i	$0.967829\pi$
$884$	−36.2127	−	62.7222i	−1.21796	−	2.10957i
$885$		0			0
$886$	25.4576	−	44.0939i	0.855266	−	1.48136i
$887$	−6.81864	−	25.4475i	−0.228948	−	0.854444i	−0.980784	−	0.195095i	$-0.937499\pi$
$887$	−6.81864	−	25.4475i	−0.228948	−	0.854444i	0.751837	−	0.659349i	$-0.229168\pi$
$888$	0.971196	−	0.0976406i	0.0325912	−	0.00327661i
$889$	6.40444	−	3.69760i	0.214798	−	0.124014i
$890$		0			0
$891$	−1.37826	+	1.82663i	−0.0461733	+	0.0611943i
$892$	−43.9677	−	43.9677i	−1.47215	−	1.47215i
$893$	0.492465	−	1.83790i	0.0164797	−	0.0615031i
$894$	−28.4555	−	23.2566i	−0.951694	−	0.777816i
$895$		0			0
$896$	−13.2150	−	7.62966i	−0.441481	−	0.254889i
$897$	19.1062	−	13.7500i	0.637939	−	0.459098i
$898$	53.0474	+	14.2140i	1.77021	+	0.474327i
$899$	1.07393			0.0358175
$900$		0			0
$901$	7.37869			0.245820
$902$	2.55708	+	0.685169i	0.0851416	+	0.0228136i
$903$	1.69773	+	0.765090i	0.0564968	+	0.0254606i
$904$	−37.7857	−	21.8156i	−1.25673	−	0.725576i
$905$		0			0
$906$	−55.3044	+	20.9430i	−1.83736	+	0.695786i
$907$	12.1728	−	45.4294i	0.404190	−	1.50846i	−0.401354	−	0.915923i	$-0.631460\pi$
$907$	12.1728	−	45.4294i	0.404190	−	1.50846i	0.805544	−	0.592536i	$-0.201873\pi$
$908$	27.0785	+	27.0785i	0.898632	+	0.898632i
$909$	29.5701	−	26.1449i	0.980779	−	0.867172i
$910$		0			0
$911$	−19.0663	+	11.0079i	−0.631694	+	0.364709i	−0.781408	−	0.624021i	$-0.785498\pi$
$911$	−19.0663	+	11.0079i	−0.631694	+	0.364709i	0.149714	+	0.988729i	$0.452165\pi$
$912$	0.327450	+	0.455007i	0.0108429	+	0.0150668i
$913$	0.354385	+	1.32258i	0.0117284	+	0.0437711i
$914$	6.62414	−	11.4733i	0.219107	−	0.379505i
$915$		0			0
$916$	−8.27929	−	14.3402i	−0.273556	−	0.473812i
$917$	7.39896	−	7.39896i	0.244335	−	0.244335i
$918$	−49.2740	−	45.5914i	−1.62629	−	1.50474i
$919$			28.3896i			0.936486i	0.883600	+	0.468243i	$0.155113\pi$
$919$			28.3896i			0.936486i	−0.883600	+	0.468243i	$0.844887\pi$
$920$		0			0
$921$	−9.02345	+	11.0406i	−0.297333	+	0.363801i
$922$	−72.2628	+	19.3627i	−2.37985	+	0.637678i
$923$	8.00199	−	2.14413i	0.263389	−	0.0705748i
$924$	1.14788	+	0.187129i	0.0377626	+	0.00615611i
$925$		0			0
$926$			14.8495i			0.487984i
$927$	−21.8934	−	43.9459i	−0.719074	−	1.44337i
$928$	−18.6447	+	18.6447i	−0.612042	+	0.612042i
$929$	−18.9202	−	32.7708i	−0.620753	−	1.07518i	−0.989346	−	0.145585i	$-0.953494\pi$
$929$	−18.9202	−	32.7708i	−0.620753	−	1.07518i	0.368593	−	0.929591i	$-0.379840\pi$
$930$		0			0
$931$	−1.40805	+	2.43882i	−0.0461471	+	0.0799292i
$932$	9.82556	+	36.6695i	0.321847	+	1.20115i
$933$	8.20637	−	18.2099i	0.268665	−	0.596164i
$934$	36.4067	−	21.0194i	1.19126	−	0.687776i
$935$		0			0
$936$	11.8392	−	35.3469i	0.386977	−	1.15535i
$937$	−36.4371	−	36.4371i	−1.19035	−	1.19035i	−0.976969	−	0.213379i	$-0.931553\pi$
$937$	−36.4371	−	36.4371i	−1.19035	−	1.19035i	−0.213379	−	0.976969i	$-0.568447\pi$
$938$	6.27801	−	23.4299i	0.204984	−	0.765012i
$939$	1.85597	−	11.3848i	0.0605672	−	0.371530i
$940$		0			0
$941$	27.0690	+	15.6283i	0.882423	+	0.509467i	0.871457	−	0.490473i	$-0.163176\pi$
$941$	27.0690	+	15.6283i	0.882423	+	0.509467i	0.0109667	+	0.999940i	$0.496509\pi$
$942$	6.81455	+	67.7818i	0.222030	+	2.20845i
$943$	−15.3428	−	4.11108i	−0.499630	−	0.133875i
$944$	−5.91308			−0.192454
$945$		0			0
$946$	0.816109			0.0265340
$947$	−14.5266	−	3.89239i	−0.472050	−	0.126486i	0.0149482	−	0.999888i	$-0.495242\pi$
$947$	−14.5266	−	3.89239i	−0.472050	−	0.126486i	−0.486999	+	0.873403i	$0.661908\pi$
$948$	−8.13168	−	80.8828i	−0.264105	−	2.62695i
$949$	43.1441	+	24.9092i	1.40052	+	0.808588i
$950$		0			0
$951$	−0.559103	+	3.42964i	−0.0181302	+	0.111214i
$952$	−3.62825	+	13.5408i	−0.117592	+	0.438860i
$953$	37.2073	+	37.2073i	1.20526	+	1.20526i	0.972544	+	0.232720i	$0.0747627\pi$
$953$	37.2073	+	37.2073i	1.20526	+	1.20526i	0.232720	+	0.972544i	$0.425237\pi$
$954$	6.12275	+	6.92488i	0.198231	+	0.224201i
$955$		0			0
$956$	−65.4799	+	37.8048i	−2.11777	+	1.22270i
$957$	0.999714	−	2.21835i	0.0323162	−	0.0717092i
$958$	−2.11804	−	7.90463i	−0.0684308	−	0.255387i
$959$	−3.80803	+	6.59570i	−0.122968	+	0.212986i
$960$		0			0
$961$	15.4811	+	26.8141i	0.499391	+	0.864970i
$962$	−1.09582	+	1.09582i	−0.0353306	+	0.0353306i
$963$	−13.6209	+	20.5650i	−0.438929	+	0.662698i
$964$			98.2761i			3.16526i
$965$		0			0
$966$	−10.9451	−	1.78428i	−0.352153	−	0.0574083i
$967$	−19.0216	+	5.09683i	−0.611694	+	0.163903i	−0.551349	−	0.834275i	$-0.685887\pi$
$967$	−19.0216	+	5.09683i	−0.611694	+	0.163903i	−0.0603451	+	0.998178i	$0.519220\pi$
$968$	−34.2190	+	9.16896i	−1.09984	+	0.294701i
$969$	−2.68486	+	3.28505i	−0.0862500	+	0.105531i
$970$		0			0
$971$			6.75294i			0.216712i	0.994112	+	0.108356i	$0.0345586\pi$
$971$			6.75294i			0.216712i	−0.994112	+	0.108356i	$0.965441\pi$
$972$	1.19586	−	52.9058i	0.0383573	−	1.69695i
$973$	−4.35065	+	4.35065i	−0.139475	+	0.139475i
$974$	−48.1942	−	83.4747i	−1.54424	−	2.67470i
$975$		0			0
$976$	1.05969	−	1.83543i	0.0339198	−	0.0587508i
$977$	7.67249	+	28.6341i	0.245465	+	0.916086i	0.973149	+	0.230175i	$0.0739297\pi$
$977$	7.67249	+	28.6341i	0.245465	+	0.916086i	−0.727685	+	0.685912i	$0.759404\pi$
$978$	32.3943	+	45.0134i	1.03586	+	1.43937i
$979$	−0.0628695	+	0.0362977i	−0.00200932	+	0.00116008i
$980$		0			0
$981$	−5.26660	−	25.9277i	−0.168149	−	0.827808i
$982$	33.9466	+	33.9466i	1.08328	+	1.08328i
$983$	4.57606	−	17.0781i	0.145954	−	0.544706i	−0.853758	−	0.520671i	$-0.825682\pi$
$983$	4.57606	−	17.0781i	0.145954	−	0.544706i	0.999711	−	0.0240353i	$-0.00765141\pi$
$984$	−23.5235	+	8.90805i	−0.749903	+	0.283978i
$985$		0			0
$986$	61.8194	+	35.6914i	1.96873	+	1.13665i
$987$	5.30793	+	2.39205i	0.168953	+	0.0761397i
$988$	−5.53869	−	1.48409i	−0.176209	−	0.0472151i
$989$	−4.89674			−0.155707
$990$		0			0
$991$	−61.9280			−1.96721			−0.983603	−	0.180345i	$-0.942279\pi$
$991$	−61.9280			−1.96721			−0.983603	+	0.180345i	$0.942279\pi$
$992$	0.895938	+	0.240066i	0.0284461	+	0.00762210i
$993$	−33.0936	+	23.8161i	−1.05019	+	0.755781i
$994$	−3.37988	−	1.95138i	−0.107203	−	0.0618939i
$995$		0			0
$996$	−24.5184	−	20.0388i	−0.776896	−	0.634954i
$997$	−6.50403	+	24.2734i	−0.205985	+	0.768745i	0.783163	+	0.621817i	$0.213605\pi$
$997$	−6.50403	+	24.2734i	−0.205985	+	0.768745i	−0.989147	+	0.146928i	$0.953061\pi$
$998$	42.9908	+	42.9908i	1.36085	+	1.36085i
$999$	−0.421246	+	0.799744i	−0.0133276	+	0.0253028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.p.b.32.4		16
3.2	odd	2		675.2.q.a.557.1		16
5.2	odd	4		45.2.l.a.23.1	yes	16
5.3	odd	4	inner	225.2.p.b.68.4		16
5.4	even	2		45.2.l.a.32.1	yes	16
9.2	odd	6	inner	225.2.p.b.182.4		16
9.7	even	3		675.2.q.a.332.1		16
15.2	even	4		135.2.m.a.98.4		16
15.8	even	4		675.2.q.a.368.1		16
15.14	odd	2		135.2.m.a.17.4		16
20.7	even	4		720.2.cu.c.113.4		16
20.19	odd	2		720.2.cu.c.257.2		16
45.2	even	12		45.2.l.a.38.1	yes	16
45.4	even	6		405.2.f.a.242.8		16
45.7	odd	12		135.2.m.a.8.4		16
45.14	odd	6		405.2.f.a.242.1		16
45.22	odd	12		405.2.f.a.323.1		16
45.29	odd	6		45.2.l.a.2.1	✓	16
45.32	even	12		405.2.f.a.323.8		16
45.34	even	6		135.2.m.a.62.4		16
45.38	even	12	inner	225.2.p.b.218.4		16
45.43	odd	12		675.2.q.a.143.1		16
180.47	odd	12		720.2.cu.c.353.2		16
180.119	even	6		720.2.cu.c.497.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.1	✓	16	45.29	odd	6
45.2.l.a.23.1	yes	16	5.2	odd	4
45.2.l.a.32.1	yes	16	5.4	even	2
45.2.l.a.38.1	yes	16	45.2	even	12
135.2.m.a.8.4		16	45.7	odd	12
135.2.m.a.17.4		16	15.14	odd	2
135.2.m.a.62.4		16	45.34	even	6
135.2.m.a.98.4		16	15.2	even	4
225.2.p.b.32.4		16	1.1	even	1	trivial
225.2.p.b.68.4		16	5.3	odd	4	inner
225.2.p.b.182.4		16	9.2	odd	6	inner
225.2.p.b.218.4		16	45.38	even	12	inner
405.2.f.a.242.1		16	45.14	odd	6
405.2.f.a.242.8		16	45.4	even	6
405.2.f.a.323.1		16	45.22	odd	12
405.2.f.a.323.8		16	45.32	even	12
675.2.q.a.143.1		16	45.43	odd	12
675.2.q.a.332.1		16	9.7	even	3
675.2.q.a.368.1		16	15.8	even	4
675.2.q.a.557.1		16	3.2	odd	2
720.2.cu.c.113.4		16	20.7	even	4
720.2.cu.c.257.2		16	20.19	odd	2
720.2.cu.c.353.2		16	180.47	odd	12
720.2.cu.c.497.4		16	180.119	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24352 + 0.601150i) q^{2} +(-0.173261 - 1.72336i) q^{3} +(2.93996 + 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(0.201351 - 0.751454i) q^{7} +(2.29074 + 2.29074i) q^{8} +(-2.93996 + 0.597183i) q^{9} +O(q^{10})\)	\(q+(2.24352 + 0.601150i) q^{2} +(-0.173261 - 1.72336i) q^{3} +(2.93996 + 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(0.201351 - 0.751454i) q^{7} +(2.29074 + 2.29074i) q^{8} +(-2.93996 + 0.597183i) q^{9} +(-0.220188 + 0.127126i) q^{11} +(2.41583 - 5.36071i) q^{12} +(0.992714 + 3.70486i) q^{13} +(0.903473 - 1.56486i) q^{14} +(0.367473 + 0.636483i) q^{16} +(-3.93311 + 3.93311i) q^{17} +(-6.95487 - 0.427565i) q^{18} +0.440377i q^{19} +(-1.32991 - 0.216804i) q^{21} +(-0.570419 + 0.152843i) q^{22} +(3.42258 - 0.917076i) q^{23} +(3.55088 - 4.34467i) q^{24} +8.90871i q^{26} +(1.53854 + 4.96315i) q^{27} +(1.86747 - 1.86747i) q^{28} +(-2.76265 - 4.78505i) q^{29} +(-0.0971829 + 0.168326i) q^{31} +(-1.23512 - 4.60955i) q^{32} +(0.257234 + 0.357439i) q^{33} +(-11.1884 + 6.45964i) q^{34} +(-9.65702 - 3.23456i) q^{36} +(0.123005 + 0.123005i) q^{37} +(-0.264732 + 0.987995i) q^{38} +(6.21282 - 2.35271i) q^{39} +(-3.88223 - 2.24141i) q^{41} +(-2.85336 - 1.28588i) q^{42} +(-1.33488 - 0.357680i) q^{43} -0.863127 q^{44} +8.22993 q^{46} +(-4.17348 - 1.11828i) q^{47} +(1.03322 - 0.743568i) q^{48} +(5.53804 + 3.19739i) q^{49} +(7.45964 + 6.09673i) q^{51} +(-3.37004 + 12.5772i) q^{52} +(-0.938022 - 0.938022i) q^{53} +(0.468157 + 12.0598i) q^{54} +(2.18263 - 1.26014i) q^{56} +(0.758929 - 0.0763000i) q^{57} +(-3.32153 - 12.3961i) q^{58} +(-4.02279 + 6.96768i) q^{59} +(-1.44186 - 2.49737i) q^{61} +(-0.319221 + 0.319221i) q^{62} +(-0.143210 + 2.32949i) q^{63} -12.5540i q^{64} +(0.362236 + 0.956558i) q^{66} +(12.9666 - 3.47438i) q^{67} +(-18.2392 + 4.88718i) q^{68} +(-2.17345 - 5.73945i) q^{69} -2.15986i q^{71} +(-8.10268 - 5.36670i) q^{72} +(9.18432 - 9.18432i) q^{73} +(0.202021 + 0.349910i) q^{74} +(-0.747490 + 1.29469i) q^{76} +(0.0511939 + 0.191058i) q^{77} +(15.3529 - 1.54353i) q^{78} +(11.9729 - 6.91256i) q^{79} +(8.28675 - 3.51139i) q^{81} +(-7.36245 - 7.36245i) q^{82} +(1.39384 - 5.20187i) q^{83} +(-3.54190 - 2.89477i) q^{84} +(-2.77981 - 1.60493i) q^{86} +(-7.76772 + 5.59011i) q^{87} +(-0.795606 - 0.213182i) q^{88} +0.285526 q^{89} +2.98392 q^{91} +(11.6189 + 3.11327i) q^{92} +(0.306924 + 0.138317i) q^{93} +(-8.69105 - 5.01778i) q^{94} +(-7.72993 + 2.92722i) q^{96} +(2.34065 - 8.73543i) q^{97} +(10.5026 + 10.5026i) q^{98} +(0.571428 - 0.505238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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