LMFDB - Embedded newform 225.2.p.b.68.4

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			68.4
Root			$0.601150 + 2.24352i$ of defining polynomial
Character	$\chi$	$=$	225.68
Dual form			225.2.p.b.182.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.601150 - 2.24352i) q^{2} +(1.72336 - 0.173261i) q^{3} +(-2.93996 - 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(-0.751454 - 0.201351i) q^{7} +(-2.29074 + 2.29074i) q^{8} +(2.93996 - 0.597183i) q^{9} +O(q^{10})$	\(q+(0.601150 - 2.24352i) q^{2} +(1.72336 - 0.173261i) q^{3} +(-2.93996 - 1.69739i) q^{4} +(0.647285 - 3.97056i) q^{6} +(-0.751454 - 0.201351i) q^{7} +(-2.29074 + 2.29074i) q^{8} +(2.93996 - 0.597183i) q^{9} +(-0.220188 + 0.127126i) q^{11} +(-5.36071 - 2.41583i) q^{12} +(-3.70486 + 0.992714i) q^{13} +(-0.903473 + 1.56486i) q^{14} +(0.367473 + 0.636483i) q^{16} +(3.93311 + 3.93311i) q^{17} +(0.427565 - 6.95487i) q^{18} -0.440377i q^{19} +(-1.32991 - 0.216804i) q^{21} +(0.152843 + 0.570419i) q^{22} +(0.917076 + 3.42258i) q^{23} +(-3.55088 + 4.34467i) q^{24} +8.90871i q^{26} +(4.96315 - 1.53854i) q^{27} +(1.86747 + 1.86747i) q^{28} +(2.76265 + 4.78505i) q^{29} +(-0.0971829 + 0.168326i) q^{31} +(-4.60955 + 1.23512i) q^{32} +(-0.357439 + 0.257234i) q^{33} +(11.1884 - 6.45964i) q^{34} +(-9.65702 - 3.23456i) q^{36} +(0.123005 - 0.123005i) q^{37} +(-0.987995 - 0.264732i) q^{38} +(-6.21282 + 2.35271i) q^{39} +(-3.88223 - 2.24141i) q^{41} +(-1.28588 + 2.85336i) q^{42} +(0.357680 - 1.33488i) q^{43} +0.863127 q^{44} +8.22993 q^{46} +(-1.11828 + 4.17348i) q^{47} +(0.743568 + 1.03322i) q^{48} +(-5.53804 - 3.19739i) q^{49} +(7.45964 + 6.09673i) q^{51} +(12.5772 + 3.37004i) q^{52} +(0.938022 - 0.938022i) q^{53} +(-0.468157 - 12.0598i) q^{54} +(2.18263 - 1.26014i) q^{56} +(-0.0763000 - 0.758929i) q^{57} +(12.3961 - 3.32153i) q^{58} +(4.02279 - 6.96768i) q^{59} +(-1.44186 - 2.49737i) q^{61} +(0.319221 + 0.319221i) q^{62} +(-2.32949 - 0.143210i) q^{63} +12.5540i q^{64} +(0.362236 + 0.956558i) q^{66} +(-3.47438 - 12.9666i) q^{67} +(-4.88718 - 18.2392i) q^{68} +(2.17345 + 5.73945i) q^{69} -2.15986i q^{71} +(-5.36670 + 8.10268i) q^{72} +(9.18432 + 9.18432i) q^{73} +(-0.202021 - 0.349910i) q^{74} +(-0.747490 + 1.29469i) q^{76} +(0.191058 - 0.0511939i) q^{77} +(1.54353 + 15.3529i) q^{78} +(-11.9729 + 6.91256i) q^{79} +(8.28675 - 3.51139i) q^{81} +(-7.36245 + 7.36245i) q^{82} +(5.20187 + 1.39384i) q^{83} +(3.54190 + 2.89477i) q^{84} +(-2.77981 - 1.60493i) q^{86} +(5.59011 + 7.76772i) q^{87} +(0.213182 - 0.795606i) q^{88} -0.285526 q^{89} +2.98392 q^{91} +(3.11327 - 11.6189i) q^{92} +(-0.138317 + 0.306924i) q^{93} +(8.69105 + 5.01778i) q^{94} +(-7.72993 + 2.92722i) q^{96} +(-8.73543 - 2.34065i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.601150	−	2.24352i	0.425077	−	1.58641i	−0.338677	−	0.940903i	$-0.609979\pi$
$2$	0.601150	−	2.24352i	0.425077	−	1.58641i	0.763754	−	0.645507i	$-0.223354\pi$
$3$	1.72336	−	0.173261i	0.994984	−	0.100032i
$3$	1.72336	−	0.173261i	0.994984	−	0.100032i
$4$	−2.93996	−	1.69739i	−1.46998	−	0.848694i
$5$		0			0
$5$		0			0
$6$	0.647285	−	3.97056i	0.264253	−	1.62097i
$7$	−0.751454	−	0.201351i	−0.284023	−	0.0761037i	0.113995	−	0.993481i	$-0.463635\pi$
$7$	−0.751454	−	0.201351i	−0.284023	−	0.0761037i	−0.398018	+	0.917378i	$0.630302\pi$
$8$	−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	$0.345537\pi$
$12$	−5.36071	−	2.41583i	−1.54750	−	0.697391i
$13$	−3.70486	+	0.992714i	−1.02754	+	0.275329i	−0.732942	−	0.680291i	$-0.761853\pi$
$13$	−3.70486	+	0.992714i	−1.02754	+	0.275329i	−0.294601	+	0.955620i	$0.595187\pi$
$14$	−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	$-0.0143492\pi$
$17$	3.93311	+	3.93311i	0.953920	+	0.953920i	−0.0450642	+	0.998984i	$0.514349\pi$
$18$	0.427565	−	6.95487i	0.100778	−	1.63928i
$19$		−	0.440377i		−	0.101029i	−0.998723	−	0.0505147i	$-0.983914\pi$
$19$		−	0.440377i		−	0.101029i	0.998723	−	0.0505147i	$-0.0160862\pi$
$20$		0			0
$21$	−1.32991	−	0.216804i	−0.290211	−	0.0473105i
$22$	0.152843	+	0.570419i	0.0325863	+	0.121614i
$23$	0.917076	+	3.42258i	0.191224	+	0.713656i	0.993212	+	0.116317i	$0.0371088\pi$
$23$	0.917076	+	3.42258i	0.191224	+	0.713656i	−0.801989	+	0.597339i	$0.796225\pi$
$24$	−3.55088	+	4.34467i	−0.724821	+	0.886853i
$25$		0			0
$26$			8.90871i			1.74714i
$27$	4.96315	−	1.53854i	0.955159	−	0.296093i
$28$	1.86747	+	1.86747i	0.352919	+	0.352919i
$29$	2.76265	+	4.78505i	0.513011	+	0.888561i	0.999886	+	0.0150897i	$0.00480338\pi$
$29$	2.76265	+	4.78505i	0.513011	+	0.888561i	−0.486875	+	0.873472i	$0.661863\pi$
$30$		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	$0.172223\pi$
$32$	−4.60955	+	1.23512i	−0.814861	+	0.218341i
$33$	−0.357439	+	0.257234i	−0.0622221	+	0.0447787i
$34$	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	−0.696924	−	0.717145i	$-0.745448\pi$
$37$	0.123005	−	0.123005i	0.0202220	−	0.0202220i	0.717145	+	0.696924i	$0.245448\pi$
$38$	−0.987995	−	0.264732i	−0.160274	−	0.0429453i
$39$	−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	$0.780502\pi$
$42$	−1.28588	+	2.85336i	−0.198416	+	0.440283i
$43$	0.357680	−	1.33488i	0.0545456	−	0.203567i	−0.933275	−	0.359162i	$-0.883063\pi$
$43$	0.357680	−	1.33488i	0.0545456	−	0.203567i	0.987821	+	0.155595i	$0.0497293\pi$
$44$	0.863127			0.130121
$45$		0			0
$46$	8.22993			1.21344
$47$	−1.11828	+	4.17348i	−0.163118	+	0.608765i	0.835155	+	0.550015i	$0.185378\pi$
$47$	−1.11828	+	4.17348i	−0.163118	+	0.608765i	−0.998273	+	0.0587499i	$0.981289\pi$
$48$	0.743568	+	1.03322i	0.107325	+	0.149133i
$49$	−5.53804	−	3.19739i	−0.791148	−	0.456770i
$50$		0			0
$51$	7.45964	+	6.09673i	1.04456	+	0.853713i
$52$	12.5772	+	3.37004i	1.74414	+	0.467341i
$53$	0.938022	−	0.938022i	0.128847	−	0.128847i	−0.639742	−	0.768589i	$-0.720959\pi$
$53$	0.938022	−	0.938022i	0.128847	−	0.128847i	0.768589	+	0.639742i	$0.220959\pi$
$54$	−0.468157	−	12.0598i	−0.0637081	−	1.64114i
$55$		0			0
$56$	2.18263	−	1.26014i	0.291666	−	0.168393i
$57$	−0.0763000	−	0.758929i	−0.0101062	−	0.100523i
$58$	12.3961	−	3.32153i	1.62769	−	0.436139i
$59$	4.02279	−	6.96768i	0.523723	−	0.907114i	−0.475896	−	0.879502i	$-0.657876\pi$
$59$	4.02279	−	6.96768i	0.523723	−	0.907114i	0.999619	−	0.0276128i	$-0.00879055\pi$
$60$		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
$63$	−2.32949	−	0.143210i	−0.293488	−	0.0180428i
$64$			12.5540i			1.56925i
$65$		0			0
$66$	0.362236	+	0.956558i	0.0445882	+	0.117744i
$67$	−3.47438	−	12.9666i	−0.424463	−	1.58412i	−0.765093	−	0.643919i	$-0.777307\pi$
$67$	−3.47438	−	12.9666i	−0.424463	−	1.58412i	0.340631	−	0.940197i	$-0.389359\pi$
$68$	−4.88718	−	18.2392i	−0.592658	−	2.21183i
$69$	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	$-0.0409085\pi$
$72$	−5.36670	+	8.10268i	−0.632471	+	0.954910i
$73$	9.18432	+	9.18432i	1.07494	+	1.07494i	0.996954	+	0.0779897i	$0.0248501\pi$
$73$	9.18432	+	9.18432i	1.07494	+	1.07494i	0.0779897	+	0.996954i	$0.475150\pi$
$74$	−0.202021	−	0.349910i	−0.0234844	−	0.0406762i
$75$		0			0
$76$	−0.747490	+	1.29469i	−0.0857430	+	0.148511i
$77$	0.191058	−	0.0511939i	0.0217731	−	0.00583409i
$78$	1.54353	+	15.3529i	0.174770	+	1.73838i
$79$	−11.9729	+	6.91256i	−1.34706	+	0.777723i	−0.987832	−	0.155528i	$-0.950292\pi$
$79$	−11.9729	+	6.91256i	−1.34706	+	0.777723i	−0.359225	+	0.933251i	$0.616959\pi$
$80$		0			0
$81$	8.28675	−	3.51139i	0.920749	−	0.390154i
$82$	−7.36245	+	7.36245i	−0.813047	+	0.813047i
$83$	5.20187	+	1.39384i	0.570979	+	0.152993i	0.532746	−	0.846275i	$-0.321160\pi$
$83$	5.20187	+	1.39384i	0.570979	+	0.152993i	0.0382335	+	0.999269i	$0.487827\pi$
$84$	3.54190	+	2.89477i	0.386452	+	0.315846i
$85$		0			0
$86$	−2.77981	−	1.60493i	−0.299755	−	0.173064i
$87$	5.59011	+	7.76772i	0.599323	+	0.832787i
$88$	0.213182	−	0.795606i	0.0227253	−	0.0848119i
$89$	−0.285526			−0.0302657			−0.0151328	−	0.999885i	$-0.504817\pi$
$89$	−0.285526			−0.0302657			−0.0151328	+	0.999885i	$0.504817\pi$
$90$		0			0
$91$	2.98392			0.312799
$92$	3.11327	−	11.6189i	0.324581	−	1.21135i
$93$	−0.138317	+	0.306924i	−0.0143428	+	0.0318266i
$94$	8.69105	+	5.01778i	0.896413	+	0.517545i
$95$		0			0
$96$	−7.72993	+	2.92722i	−0.788932	+	0.298758i
$97$	−8.73543	−	2.34065i	−0.886948	−	0.237657i	−0.213546	−	0.976933i	$-0.568501\pi$
$97$	−8.73543	−	2.34065i	−0.886948	−	0.237657i	−0.673402	+	0.739276i	$0.735168\pi$
$98$	−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	$0.560489\pi$
$102$	18.1625	−	13.0708i	1.79836	−	1.29420i
$103$	−15.8082	+	4.23579i	−1.55763	+	0.417364i	−0.931911	−	0.362688i	$-0.881859\pi$
$103$	−15.8082	+	4.23579i	−1.55763	+	0.417364i	−0.625714	+	0.780052i	$0.715192\pi$
$104$	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	$-0.380101\pi$
$107$	−5.81401	−	5.81401i	−0.562062	−	0.562062i	−0.929893	+	0.367831i	$0.880101\pi$
$108$	−17.2030	−	3.90114i	−1.65536	−	0.375387i
$109$		−	8.81907i		−	0.844713i	−0.906430	−	0.422357i	$-0.861203\pi$
$109$		−	8.81907i		−	0.844713i	0.906430	−	0.422357i	$-0.138797\pi$
$110$		0			0
$111$	0.190671	−	0.233295i	0.0180977	−	0.0221434i
$112$	−0.147983	−	0.552279i	−0.0139830	−	0.0521854i
$113$	−3.48580	−	13.0092i	−0.327916	−	1.22380i	−0.911347	−	0.411638i	$-0.864957\pi$
$113$	−3.48580	−	13.0092i	−0.327916	−	1.22380i	0.583431	−	0.812163i	$-0.301710\pi$
$114$	−1.74854	−	0.285049i	−0.163766	−	0.0266973i
$115$		0			0
$116$		−	18.7571i		−	1.74156i
$117$	−10.2993	+	5.13102i	−0.952172	+	0.474363i
$118$	−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
$122$	−6.46967	+	1.73354i	−0.585736	+	0.156948i
$123$	−7.07884	−	3.19012i	−0.638278	−	0.287643i
$124$	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	−0.342915	−	0.939366i	$-0.611414\pi$
$127$	6.72167	−	6.72167i	0.596452	−	0.596452i	0.939366	+	0.342915i	$0.111414\pi$
$128$	18.9461	+	5.07660i	1.67462	+	0.448712i
$129$	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	$0.466750\pi$
$132$	1.48748	−	0.149546i	0.129469	−	0.0130163i
$133$	−0.0886705	+	0.330923i	−0.00768870	+	0.0286946i
$134$	−31.1794			−2.69349
$135$		0			0
$136$	−18.0195			−1.54516
$137$	−2.53378	+	9.45618i	−0.216475	+	0.807896i	0.769167	+	0.639048i	$0.220671\pi$
$137$	−2.53378	+	9.45618i	−0.216475	+	0.807896i	−0.985642	+	0.168848i	$0.945995\pi$
$138$	14.1832	−	1.42592i	1.20735	−	0.121383i
$139$	6.84922	+	3.95440i	0.580943	+	0.335408i	0.761508	−	0.648155i	$-0.224459\pi$
$139$	6.84922	+	3.95440i	0.580943	+	0.335408i	−0.180565	+	0.983563i	$0.557793\pi$
$140$		0			0
$141$	−1.20410	+	7.38618i	−0.101404	+	0.622029i
$142$	−4.84570	−	1.29840i	−0.406642	−	0.108959i
$143$	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
$147$	−10.0980	−	4.55073i	−0.832872	−	0.375338i
$148$	−0.570419	+	0.152843i	−0.0468882	+	0.0125636i
$149$	−4.56755	+	7.91123i	−0.374188	+	0.648113i	−0.990205	−	0.139620i	$-0.955412\pi$
$149$	−4.56755	+	7.91123i	−0.374188	+	0.648113i	0.616017	+	0.787733i	$0.288745\pi$
$150$		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
$153$	13.9120	+	9.21441i	1.12472	+	0.744941i
$154$		−	0.459419i		−	0.0370210i
$155$		0			0
$156$	22.2589	+	3.62867i	1.78214	+	0.290527i
$157$	4.38274	+	16.3566i	0.349781	+	1.30540i	0.886926	+	0.461911i	$0.152836\pi$
$157$	4.38274	+	16.3566i	0.349781	+	1.30540i	−0.537146	+	0.843490i	$0.680497\pi$
$158$	8.31097	+	31.0169i	0.661185	+	2.46758i
$159$	1.45403	−	1.77907i	0.115312	−	0.141090i
$160$		0			0
$161$		−	2.75656i		−	0.217248i
$162$	−2.89630	−	20.7024i	−0.227555	−	1.62653i
$163$	−9.74771	−	9.74771i	−0.763499	−	0.763499i	0.213454	−	0.976953i	$-0.431529\pi$
$163$	−9.74771	−	9.74771i	−0.763499	−	0.763499i	−0.976953	+	0.213454i	$0.931529\pi$
$164$	7.60907	+	13.1793i	0.594169	+	1.02913i
$165$		0			0
$166$	6.25421	−	10.8326i	0.485421	−	0.840773i
$167$	19.0563	−	5.10613i	1.47462	−	0.395124i	0.570110	−	0.821568i	$-0.306900\pi$
$167$	19.0563	−	5.10613i	1.47462	−	0.395124i	0.904514	+	0.426444i	$0.140234\pi$
$168$	3.54313	−	2.54985i	0.273358	−	0.196725i
$169$	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
$173$	10.0263	+	2.68653i	0.762284	+	0.204253i	0.618960	−	0.785422i	$-0.287554\pi$
$173$	10.0263	+	2.68653i	0.762284	+	0.204253i	0.143324	+	0.989676i	$0.454221\pi$
$174$	20.7875	−	7.87197i	1.57590	−	0.596773i
$175$		0			0
$176$	−0.161827	−	0.0934307i	−0.0121981	−	0.00704260i
$177$	5.72550	−	12.7048i	0.430355	−	0.954954i
$178$	−0.171644	+	0.640584i	−0.0128653	+	0.0480138i
$179$	15.1015			1.12874			0.564370	−	0.825522i	$-0.309119\pi$
$179$	15.1015			1.12874			0.564370	+	0.825522i	$0.309119\pi$
$180$		0			0
$181$	−7.82954			−0.581965			−0.290983	−	0.956728i	$-0.593982\pi$
$181$	−7.82954			−0.581965			−0.290983	+	0.956728i	$0.593982\pi$
$182$	1.79378	−	6.69448i	0.132964	−	0.496228i
$183$	−2.91754	−	4.05405i	−0.215671	−	0.299684i
$184$	−9.94101	−	5.73945i	−0.732861	−	0.423118i
$185$		0			0
$186$	0.605442	+	0.494825i	0.0443932	+	0.0362823i
$187$	−1.36603	−	0.366025i	−0.0998937	−	0.0267664i
$188$	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	$0.197092\pi$
$192$	2.17512	+	21.6351i	0.156976	+	1.56138i
$193$	5.33034	−	1.42826i	0.383686	−	0.102808i	−0.0618198	−	0.998087i	$-0.519690\pi$
$193$	5.33034	−	1.42826i	0.383686	−	0.102808i	0.445506	+	0.895279i	$0.353024\pi$
$194$	−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	$-0.287337\pi$
$197$	−2.32295	−	2.32295i	−0.165504	−	0.165504i	−0.785000	+	0.619496i	$0.787337\pi$
$198$	0.789998	+	1.58573i	0.0561427	+	0.112693i
$199$		−	17.1978i		−	1.21912i	−0.792741	−	0.609558i	$-0.791347\pi$
$199$		−	17.1978i		−	1.21912i	0.792741	−	0.609558i	$-0.208653\pi$
$200$		0			0
$201$	−8.23421	−	21.7441i	−0.580796	−	1.53371i
$202$	7.90930	+	29.5179i	0.556497	+	2.07687i
$203$	−1.11253	−	4.15201i	−0.0780841	−	0.291414i
$204$	−11.5825	−	30.5860i	−0.810940	−	2.14145i
$205$		0			0
$206$			38.0123i			2.64844i
$207$	4.74007	+	9.51458i	0.329458	+	0.661309i
$208$	−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	$0.216721\pi$
$212$	−4.34993	+	1.16556i	−0.298755	+	0.0800511i
$213$	−0.374220	−	3.72223i	−0.0256411	−	0.255043i
$214$	−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
$218$	−19.7858	−	5.30158i	−1.34006	−	0.359068i
$219$	17.4192	+	14.2366i	1.17708	+	0.962023i
$220$		0			0
$221$	−18.4761	−	10.6672i	−1.24284	−	0.717552i
$222$	−0.408781	−	0.568020i	−0.0274356	−	0.0381230i
$223$	4.74061	−	17.6922i	0.317455	−	1.18476i	−0.604227	−	0.796812i	$-0.706518\pi$
$223$	4.74061	−	17.6922i	0.317455	−	1.18476i	0.921682	−	0.387946i	$-0.126815\pi$
$224$	3.71256			0.248056
$225$		0			0
$226$	−31.2819			−2.08084
$227$	2.91961	−	10.8961i	0.193781	−	0.723202i	−0.798798	−	0.601600i	$-0.794530\pi$
$227$	2.91961	−	10.8961i	0.193781	−	0.723202i	0.992579	−	0.121602i	$-0.0388031\pi$
$228$	−1.06388	+	2.36073i	−0.0704570	+	0.156343i
$229$	4.22418	+	2.43883i	0.279142	+	0.161163i	0.633035	−	0.774123i	$-0.281809\pi$
$229$	4.22418	+	2.43883i	0.279142	+	0.161163i	−0.353893	+	0.935286i	$0.615142\pi$
$230$		0			0
$231$	0.320393	−	0.121329i	0.0210803	−	0.00798284i
$232$	−17.2898	−	4.63279i	−1.13513	−	0.304158i
$233$	−7.90742	+	7.90742i	−0.518033	+	0.518033i	−0.916976	−	0.398943i	$-0.869377\pi$
$233$	−7.90742	+	7.90742i	−0.518033	+	0.518033i	0.398943	+	0.916976i	$0.369377\pi$
$234$	5.32013	+	26.1913i	0.347788	+	1.71218i
$235$		0			0
$236$	−23.6537	+	13.6565i	−1.53972	+	0.888960i
$237$	−19.4360	+	13.9873i	−1.26250	+	0.908571i
$238$	−9.70823	+	2.60131i	−0.629291	+	0.168618i
$239$	11.1362	−	19.2884i	0.720340	−	1.24767i	−0.240523	−	0.970643i	$-0.577319\pi$
$239$	11.1362	−	19.2884i	0.720340	−	1.24767i	0.960864	−	0.277022i	$-0.0893476\pi$
$240$		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
$243$	13.6727	−	7.48717i	0.877103	−	0.480302i
$244$			9.78955i			0.626712i
$245$		0			0
$246$	−11.4126	+	13.9638i	−0.727638	+	0.890300i
$247$	0.437168	+	1.63153i	0.0278163	+	0.103812i
$248$	−0.162970	−	0.608211i	−0.0103486	−	0.0386214i
$249$	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	$-0.222937\pi$
$252$	6.60552	+	4.37508i	0.416109	+	0.275604i
$253$	−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
$257$	−7.09249	+	1.90043i	−0.442417	+	0.118545i	−0.473149	−	0.880982i	$-0.656883\pi$
$257$	−7.09249	+	1.90043i	−0.442417	+	0.118545i	0.0307319	+	0.999528i	$0.490216\pi$
$258$	−5.06870	−	2.28424i	−0.315563	−	0.142210i
$259$	−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
$263$	−14.1097	−	3.78069i	−0.870044	−	0.233127i	−0.203937	−	0.978984i	$-0.565374\pi$
$263$	−14.1097	−	3.78069i	−0.870044	−	0.233127i	−0.666107	+	0.745857i	$0.732040\pi$
$264$	0.229543	−	1.40805i	0.0141274	−	0.0866598i
$265$		0			0
$266$	0.689128	+	0.397868i	0.0422532	+	0.0243949i
$267$	−0.492065	+	0.0494705i	−0.0301139	+	0.00302754i
$268$	−11.7947	+	44.0185i	−0.720478	+	2.68886i
$269$	3.76010			0.229257			0.114629	−	0.993408i	$-0.463432\pi$
$269$	3.76010			0.229257			0.114629	+	0.993408i	$0.463432\pi$
$270$		0			0
$271$	14.0785			0.855209			0.427604	−	0.903966i	$-0.359358\pi$
$271$	14.0785			0.855209			0.427604	+	0.903966i	$0.359358\pi$
$272$	−1.05804	+	3.94867i	−0.0641533	+	0.239423i
$273$	5.14237	−	0.516996i	0.311230	−	0.0312900i
$274$	19.6920	+	11.3692i	1.18964	+	0.686837i
$275$		0			0
$276$	3.35219	−	20.5629i	0.201778	−	1.23774i
$277$	2.02071	+	0.541447i	0.121413	+	0.0325324i	0.319014	−	0.947750i	$-0.396648\pi$
$277$	2.02071	+	0.541447i	0.121413	+	0.0325324i	−0.197601	+	0.980283i	$0.563315\pi$
$278$	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	$0.244174\pi$
$282$	15.8472	+	7.14164i	0.943688	+	0.425278i
$283$	31.1104	−	8.33602i	1.84932	−	0.495525i	0.849821	−	0.527071i	$-0.176710\pi$
$283$	31.1104	−	8.33602i	1.84932	−	0.495525i	0.999502	+	0.0315464i	$0.0100432\pi$
$284$	−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
$288$	−12.8143	+	6.38396i	−0.755090	+	0.376179i
$289$			13.9387i			0.819926i
$290$		0			0
$291$	−15.4599	−	2.52028i	−0.906273	−	0.147742i
$292$	−11.4122	−	42.5909i	−0.667849	−	2.49244i
$293$	−1.70948	−	6.37987i	−0.0998690	−	0.372716i	0.897844	−	0.440314i	$-0.145133\pi$
$293$	−1.70948	−	6.37987i	−0.0998690	−	0.372716i	−0.997713	+	0.0675984i	$0.978466\pi$
$294$	−16.2801	+	19.9195i	−0.949475	+	1.16173i
$295$		0			0
$296$			0.563547i			0.0327555i
$297$	−0.897240	+	0.969714i	−0.0520631	+	0.0562685i
$298$	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
$302$	−32.9794	+	8.83680i	−1.89775	+	0.508501i
$303$	−18.4966	+	13.3113i	−1.06260	+	0.764713i
$304$	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	−0.853434	−	0.521201i	$-0.825484\pi$
$307$	−5.82120	+	5.82120i	−0.332233	+	0.332233i	0.521201	+	0.853434i	$0.325484\pi$
$308$	−0.648600	−	0.173792i	−0.0369574	−	0.00990271i
$309$	−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	$0.560645\pi$
$312$	8.84250	−	19.6214i	0.500608	−	1.11084i
$313$	−1.72368	+	6.43287i	−0.0974283	+	0.363607i	−0.997376	−	0.0723896i	$-0.976937\pi$
$313$	−1.72368	+	6.43287i	−0.0974283	+	0.363607i	0.899948	+	0.435997i	$0.143604\pi$
$314$	39.3311			2.21958
$315$		0			0
$316$	46.9331			2.64020
$317$	−0.519254	+	1.93788i	−0.0291642	+	0.108842i	−0.978974	−	0.203987i	$-0.934610\pi$
$317$	−0.519254	+	1.93788i	−0.0291642	+	0.108842i	0.949809	+	0.312829i	$0.101277\pi$
$318$	−3.11730	−	4.33164i	−0.174810	−	0.242906i
$319$	−1.21661	−	0.702408i	−0.0681169	−	0.0393273i
$320$		0			0
$321$	−11.0270	−	9.01232i	−0.615467	−	0.503018i
$322$	−6.18441	−	1.65711i	−0.344644	−	0.0923470i
$323$	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
$327$	−1.52800	−	15.1985i	−0.0844986	−	0.840477i
$328$	14.0277	−	3.75870i	0.774548	−	0.207540i
$329$	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
$333$	0.288174	−	0.435088i	0.0157919	−	0.0238427i
$334$		−	45.8229i		−	2.50732i
$335$		0			0
$336$	−0.350716	−	0.926137i	−0.0191331	−	0.0505249i
$337$	2.94873	+	11.0048i	0.160627	+	0.599470i	0.998558	+	0.0536923i	$0.0170990\pi$
$337$	2.94873	+	11.0048i	0.160627	+	0.599470i	−0.837930	+	0.545778i	$0.816234\pi$
$338$	−1.02885	−	3.83973i	−0.0559622	−	0.208854i
$339$	−8.26128	−	21.8156i	−0.448691	−	1.18486i
$340$		0			0
$341$		−	0.0494178i		−	0.00267612i
$342$	−3.06276	−	0.188289i	−0.165615	−	0.0101815i
$343$	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
$347$	13.8028	−	3.69845i	0.740974	−	0.198543i	0.131463	−	0.991321i	$-0.458033\pi$
$347$	13.8028	−	3.69845i	0.740974	−	0.198543i	0.609511	+	0.792778i	$0.291366\pi$
$348$	−3.24988	−	32.3254i	−0.174212	−	1.73282i
$349$	15.2113	−	8.78224i	0.814242	−	0.470103i	−0.0341849	−	0.999416i	$-0.510884\pi$
$349$	15.2113	−	8.78224i	0.814242	−	0.470103i	0.848427	+	0.529313i	$0.177550\pi$
$350$		0			0
$351$	−16.8605	+	10.6271i	−0.899944	+	0.567232i
$352$	0.857952	−	0.857952i	0.0457290	−	0.0457290i
$353$	−16.8366	−	4.51136i	−0.896124	−	0.240116i	−0.218773	−	0.975776i	$-0.570205\pi$
$353$	−16.8366	−	4.51136i	−0.896124	−	0.240116i	−0.677351	+	0.735660i	$0.736872\pi$
$354$	−25.0617	−	20.4828i	−1.33201	−	1.08865i
$355$		0			0
$356$	0.839435	+	0.484648i	0.0444900	+	0.0256863i
$357$	−4.37799	−	6.08342i	−0.231708	−	0.321969i
$358$	9.07828	−	33.8806i	0.479802	−	1.79064i
$359$	−34.0577			−1.79750			−0.898748	−	0.438465i	$-0.855522\pi$
$359$	−34.0577			−1.79750			−0.898748	+	0.438465i	$0.855522\pi$
$360$		0			0
$361$	18.8061			0.989793
$362$	−4.70673	+	17.5658i	−0.247380	+	0.923236i
$363$	−7.78196	+	17.2681i	−0.408447	+	0.906340i
$364$	−8.77260	−	5.06486i	−0.459809	−	0.265471i
$365$		0			0
$366$	−10.8492	+	4.10847i	−0.567099	+	0.214753i
$367$	13.6337	+	3.65315i	0.711675	+	0.190693i	0.596454	−	0.802647i	$-0.296576\pi$
$367$	13.6337	+	3.65315i	0.711675	+	0.190693i	0.115221	+	0.993340i	$0.463242\pi$
$368$	−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
$372$	0.927616	−	0.667568i	0.0480947	−	0.0346118i
$373$	−20.7962	+	5.57233i	−1.07679	+	0.288524i	−0.753279	−	0.657701i	$-0.771529\pi$
$373$	−20.7962	+	5.57233i	−1.07679	+	0.288524i	−0.323508	+	0.946225i	$0.604862\pi$
$374$	−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
$378$	−2.07647	+	9.15668i	−0.106802	+	0.470969i
$379$			9.52893i			0.489468i	0.969590	+	0.244734i	$0.0787007\pi$
$379$			9.52893i			0.489468i	−0.969590	+	0.244734i	$0.921299\pi$
$380$		0			0
$381$	10.4193	−	12.7485i	0.533795	−	0.653124i
$382$	−6.89676	−	25.7391i	−0.352869	−	1.31693i
$383$	2.57714	+	9.61802i	0.131686	+	0.491458i	0.999990	−	0.00457478i	$-0.00145620\pi$
$383$	2.57714	+	9.61802i	0.131686	+	0.491458i	−0.868304	+	0.496033i	$0.834790\pi$
$384$	33.5306	+	5.46620i	1.71110	+	0.278946i
$385$		0			0
$386$		−	12.8173i		−	0.652385i
$387$	0.254398	−	4.13809i	0.0129318	−	0.210351i
$388$	21.7088	+	21.7088i	1.10210	+	1.10210i
$389$	14.5672	+	25.2312i	0.738587	+	1.27927i	0.953131	+	0.302557i	$0.0978401\pi$
$389$	14.5672	+	25.2312i	0.738587	+	1.27927i	−0.214544	+	0.976714i	$0.568827\pi$
$390$		0			0
$391$	−9.85441	+	17.0683i	−0.498359	+	0.863183i
$392$	20.0106	−	5.36182i	1.01069	−	0.270813i
$393$	21.2392	+	9.57158i	1.07138	+	0.482822i
$394$	−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	−0.0484856	−	0.998824i	$-0.515439\pi$
$397$	18.9354	−	18.9354i	0.950338	−	0.950338i	0.998824	+	0.0484856i	$0.0154395\pi$
$398$	−38.5836	−	10.3384i	−1.93402	−	0.518219i
$399$	−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	$0.457232\pi$
$402$	−53.7334	+	5.40217i	−2.67998	+	0.269436i
$403$	0.192950	−	0.720098i	0.00961151	−	0.0358706i
$404$	44.6649			2.22216
$405$		0			0
$406$	−9.98392			−0.495493
$407$	−0.0114472	+	0.0427215i	−0.000567417	+	0.00211763i
$408$	−31.0541	+	3.12207i	−1.53741	+	0.154566i
$409$	12.2649	+	7.08116i	0.606462	+	0.350141i	0.771579	−	0.636133i	$-0.219467\pi$
$409$	12.2649	+	7.08116i	0.606462	+	0.350141i	−0.165118	+	0.986274i	$0.552800\pi$
$410$		0			0
$411$	−2.72823	+	16.7354i	−0.134574	+	0.825498i
$412$	53.6652	+	14.3795i	2.64389	+	0.708429i
$413$	−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
$417$	12.4888	+	5.62816i	0.611581	+	0.275612i
$418$	0.251199	−	0.0673086i	0.0122866	−	0.00329217i
$419$	−13.8808	+	24.0422i	−0.678120	+	1.17454i	0.297426	+	0.954745i	$0.403872\pi$
$419$	−13.8808	+	24.0422i	−0.678120	+	1.17454i	−0.975546	+	0.219794i	$0.929461\pi$
$420$		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
$423$	−0.795372	+	12.9377i	−0.0386723	+	0.629053i
$424$			4.29753i			0.208706i
$425$		0			0
$426$	−8.57586	−	1.39805i	−0.415502	−	0.0677356i
$427$	0.580639	+	2.16698i	0.0280991	+	0.104867i
$428$	7.22434	+	26.9616i	0.349202	+	1.30324i
$429$	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	$0.788752\pi$
$432$	2.80308	+	2.59359i	0.134863	+	0.124784i
$433$	−6.30733	−	6.30733i	−0.303111	−	0.303111i	0.539119	−	0.842230i	$-0.318757\pi$
$433$	−6.30733	−	6.30733i	−0.303111	−	0.303111i	−0.842230	+	0.539119i	$0.818757\pi$
$434$	−0.175604	−	0.304155i	−0.00842927	−	0.0145999i
$435$		0			0
$436$	−14.9694	+	25.9277i	−0.716903	+	1.24171i
$437$	1.50722	−	0.403859i	0.0721002	−	0.0193192i
$438$	42.4118	−	30.5220i	2.02651	−	1.45840i
$439$	−12.4666	+	7.19760i	−0.594999	+	0.343523i	−0.767072	−	0.641561i	$-0.778287\pi$
$439$	−12.4666	+	7.19760i	−0.594999	+	0.343523i	0.172073	+	0.985084i	$0.444954\pi$
$440$		0			0
$441$	−18.1910	−	6.09297i	−0.866240	−	0.290142i
$442$	−35.0390	+	35.0390i	−1.66663	+	1.66663i
$443$	21.1741	+	5.67359i	1.00601	+	0.269560i	0.723962	−	0.689839i	$-0.242319\pi$
$443$	21.1741	+	5.67359i	1.00601	+	0.269560i	0.282050	+	0.959400i	$0.408986\pi$
$444$	−0.956558	+	0.362236i	−0.0453962	+	0.0171910i
$445$		0			0
$446$	−36.8430	−	21.2713i	−1.74457	−	1.00723i
$447$	−6.50084	+	14.4253i	−0.307479	+	0.682293i
$448$	2.52777	−	9.43376i	0.119426	−	0.445703i
$449$	−23.6447			−1.11586			−0.557931	−	0.829888i	$-0.688404\pi$
$449$	−23.6447			−1.11586			−0.557931	+	0.829888i	$0.688404\pi$
$450$		0			0
$451$	1.13976			0.0536693
$452$	−11.8335	+	44.1632i	−0.556601	+	2.07726i
$453$	−14.8722	−	20.6657i	−0.698759	−	0.970958i
$454$	−22.6906	−	13.1004i	−1.06492	−	0.614833i
$455$		0			0
$456$	1.91329	+	1.56373i	0.0895981	+	0.0732281i
$457$	−5.50956	−	1.47628i	−0.257726	−	0.0690575i	0.127642	−	0.991820i	$-0.459259\pi$
$457$	−5.50956	−	1.47628i	−0.257726	−	0.0690575i	−0.385369	+	0.922763i	$0.625926\pi$
$458$	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	$0.603315\pi$
$462$	−0.0795993	−	0.791745i	−0.00370329	−	0.0368353i
$463$	−6.17544	+	1.65471i	−0.286997	+	0.0769007i	−0.399446	−	0.916757i	$-0.630797\pi$
$463$	−6.17544	+	1.65471i	−0.286997	+	0.0769007i	0.112448	+	0.993658i	$0.464131\pi$
$464$	−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	$-0.387539\pi$
$467$	−12.7982	−	12.7982i	−0.592230	−	0.592230i	−0.938233	+	0.346003i	$0.887539\pi$
$468$	38.9889	+	2.39692i	1.80226	+	0.110798i
$469$			10.4433i			0.482228i
$470$		0			0
$471$	10.3870	+	27.4290i	0.478609	+	1.26386i
$472$	6.74597	+	25.1763i	0.310508	+	1.15883i
$473$	0.0909406	+	0.339395i	0.00418145	+	0.0156054i
$474$	19.6968	+	52.0135i	0.904706	+	2.38906i
$475$		0			0
$476$			14.6900i			0.673314i
$477$	2.19758	−	3.31792i	0.100620	−	0.151917i
$478$	−36.5795	−	36.5795i	−1.67311	−	1.67311i
$479$	1.76166	+	3.05128i	0.0804921	+	0.139416i	0.903461	−	0.428669i	$-0.141017\pi$
$479$	1.76166	+	3.05128i	0.0804921	+	0.139416i	−0.822969	+	0.568086i	$0.807684\pi$
$480$		0			0
$481$	−0.333609	+	0.577827i	−0.0152112	+	0.0263467i
$482$	64.9482	−	17.4028i	2.95831	−	0.792677i
$483$	−0.477604	−	4.75056i	−0.0217318	−	0.216158i
$484$	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	−0.424098	+	0.905616i	$0.639409\pi$
$487$	−29.3442	+	29.3442i	−1.32971	+	1.32971i	−0.905616	+	0.424098i	$0.860591\pi$
$488$	9.02373	+	2.41790i	0.408485	+	0.109453i
$489$	−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	$0.512219\pi$
$492$	15.3967	+	21.3944i	0.694135	+	0.964533i
$493$	−7.95433	+	29.6859i	−0.358245	+	1.33699i
$494$	3.92319			0.176513
$495$		0			0
$496$	−0.142849			−0.00641409
$497$	−0.434891	+	1.62304i	−0.0195075	+	0.0728031i
$498$	8.90140	−	19.7521i	0.398881	−	0.885114i
$499$	−22.6691	−	13.0880i	−1.01481	−	0.585901i	−0.102214	−	0.994762i	$-0.532593\pi$
$499$	−22.6691	−	13.0880i	−1.01481	−	0.585901i	−0.912596	+	0.408862i	$0.865926\pi$
$500$		0			0
$501$	31.9563	−	12.1014i	1.42770	−	0.540652i
$502$	−45.8168	−	12.2766i	−2.04490	−	0.547930i
$503$	−6.72022	+	6.72022i	−0.299640	+	0.299640i	−0.840873	−	0.541233i	$-0.817958\pi$
$503$	−6.72022	+	6.72022i	−0.299640	+	0.299640i	0.541233	+	0.840873i	$0.317958\pi$
$504$	5.66431	−	5.00820i	0.252308	−	0.223083i
$505$		0			0
$506$	−1.81213	+	1.04624i	−0.0805592	+	0.0465109i
$507$	2.40607	−	1.73155i	0.106857	−	0.0769008i
$508$	−31.1707	+	8.35217i	−1.38298	+	0.370568i
$509$	11.9676	−	20.7285i	0.530454	−	0.918773i	−0.468915	−	0.883243i	$-0.655355\pi$
$509$	11.9676	−	20.7285i	0.530454	−	0.918773i	0.999369	−	0.0355293i	$-0.0113117\pi$
$510$		0			0
$511$	−5.05232	−	8.75087i	−0.223501	−	0.387116i
$512$	−5.84717	−	5.84717i	−0.258411	−	0.258411i
$513$	−0.677538	−	2.18566i	−0.0299141	−	0.0964991i
$514$			17.0546i			0.752246i
$515$		0			0
$516$	−5.14226	+	6.29181i	−0.226376	+	0.276981i
$517$	−0.284325	−	1.06111i	−0.0125046	−	0.0466678i
$518$	0.0813543	+	0.303618i	0.00357450	+	0.0133402i
$519$	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	$-0.0225505\pi$
$522$	34.4606	−	17.1679i	1.50830	−	0.751420i
$523$	8.67002	+	8.67002i	0.379114	+	0.379114i	0.870782	−	0.491669i	$-0.163613\pi$
$523$	8.67002	+	8.67002i	0.379114	+	0.379114i	−0.491669	+	0.870782i	$0.663613\pi$
$524$	−22.8301	−	39.5429i	−0.997339	−	1.72744i
$525$		0			0
$526$	−16.9641	+	29.3827i	−0.739672	+	1.28115i
$527$	−1.04427	+	0.279813i	−0.0454893	+	0.0121888i
$528$	−0.295074	−	0.132977i	−0.0128415	−	0.00578707i
$529$	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
$533$	16.6082	+	4.45016i	0.719381	+	0.192758i
$534$	−0.184817	+	1.13370i	−0.00799780	+	0.0490599i
$535$		0			0
$536$	37.6619	+	21.7441i	1.62675	+	0.939202i
$537$	26.0254	−	2.61650i	1.12308	−	0.112910i
$538$	2.26038	−	8.43586i	0.0974520	−	0.363696i
$539$	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	$0.577047\pi$
$542$	8.46330	−	31.5855i	0.363530	−	1.35671i
$543$	−13.4931	+	1.35655i	−0.579046	+	0.0582153i
$544$	−22.9878	−	13.2720i	−0.985592	−	0.569032i
$545$		0			0
$546$	1.93144	−	11.8478i	0.0826582	−	0.507040i
$547$	13.2305	+	3.54511i	0.565697	+	0.151578i	0.530323	−	0.847796i	$-0.322071\pi$
$547$	13.2305	+	3.54511i	0.565697	+	0.151578i	0.0353748	+	0.999374i	$0.488737\pi$
$548$	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
$552$	−18.1264	−	8.16876i	−0.771511	−	0.347686i
$553$	10.3889	−	2.78371i	0.441782	−	0.118375i
$554$	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	$-0.134025\pi$
$557$	11.8934	+	11.8934i	0.503938	+	0.503938i	−0.408721	+	0.912659i	$0.634025\pi$
$558$	1.12913	+	0.747864i	0.0477999	+	0.0316596i
$559$			5.30061i			0.224192i
$560$		0			0
$561$	−2.41758	−	0.394116i	−0.102070	−	0.0166396i
$562$	−5.57173	−	20.7940i	−0.235029	−	0.877141i
$563$	6.37683	+	23.7986i	0.268751	+	1.00299i	0.959914	+	0.280294i	$0.0904321\pi$
$563$	6.37683	+	23.7986i	0.268751	+	1.00299i	−0.691163	+	0.722699i	$0.742901\pi$
$564$	16.0772	−	19.6713i	0.676974	−	0.828310i
$565$		0			0
$566$		−	74.8082i		−	3.14442i
$567$	−6.93413	+	0.970098i	−0.291206	+	0.0407403i
$568$	4.94768	+	4.94768i	0.207600	+	0.207600i
$569$	−6.24856	−	10.8228i	−0.261953	−	0.453716i	0.704808	−	0.709399i	$-0.251033\pi$
$569$	−6.24856	−	10.8228i	−0.261953	−	0.453716i	−0.966761	+	0.255682i	$0.917700\pi$
$570$		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	$-0.0277872\pi$
$572$	−3.19776	+	0.856838i	−0.133705	+	0.0358262i
$573$	16.1287	−	11.6072i	0.673787	−	0.484897i
$574$	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	−0.435455	−	0.900210i	$-0.643413\pi$
$577$	11.1638	−	11.1638i	0.464755	−	0.464755i	0.900210	+	0.435455i	$0.143413\pi$
$578$	31.2719	+	8.37928i	1.30074	+	0.348532i
$579$	8.93865	−	3.38495i	0.371478	−	0.140674i
$580$		0			0
$581$	−3.62831	−	2.09481i	−0.150528	−	0.0869072i
$582$	−14.9480	+	33.1695i	−0.619615	+	1.37492i
$583$	−0.0872947	+	0.325788i	−0.00361538	+	0.0134928i
$584$	−42.0778			−1.74119
$585$		0			0
$586$	−15.3410			−0.633733
$587$	−4.76574	+	17.7860i	−0.196703	+	0.734106i	0.795116	+	0.606457i	$0.207410\pi$
$587$	−4.76574	+	17.7860i	−0.196703	+	0.734106i	−0.991819	+	0.127649i	$0.959257\pi$
$588$	21.9635	+	30.5193i	0.905758	+	1.25859i
$589$	0.0741267	+	0.0427971i	0.00305434	+	0.00176342i
$590$		0			0
$591$	−4.40577	−	3.60082i	−0.181229	−	0.148118i
$592$	0.123492	+	0.0330896i	0.00507549	+	0.00135997i
$593$	−14.5424	+	14.5424i	−0.597186	+	0.597186i	−0.939563	−	0.342377i	$-0.888768\pi$
$593$	−14.5424	+	14.5424i	−0.597186	+	0.597186i	0.342377	+	0.939563i	$0.388768\pi$
$594$	1.63620	+	2.59592i	0.0671341	+	0.106512i
$595$		0			0
$596$	26.8568	−	15.5058i	1.10010	−	0.635143i
$597$	−2.97970	−	29.6380i	−0.121951	−	1.21300i
$598$	−30.4907	+	8.16997i	−1.24686	+	0.334095i
$599$	−17.6972	+	30.6525i	−0.723089	+	1.25243i	0.236666	+	0.971591i	$0.423945\pi$
$599$	−17.6972	+	30.6525i	−0.723089	+	1.25243i	−0.959756	+	0.280836i	$0.909388\pi$
$600$		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
$603$	−17.9579	−	36.0463i	−0.731304	−	1.46792i
$604$			49.9026i			2.03051i
$605$		0			0
$606$	18.7449	+	49.4997i	0.761460	+	2.01079i
$607$	−2.02270	−	7.54883i	−0.0820989	−	0.306397i	0.912650	−	0.408742i	$-0.134032\pi$
$607$	−2.02270	−	7.54883i	−0.0820989	−	0.306397i	−0.994749	+	0.102344i	$0.967366\pi$
$608$	0.543920	+	2.02994i	0.0220589	+	0.0823248i
$609$	−2.63667	−	6.96266i	−0.106843	−	0.282141i
$610$		0			0
$611$		−	16.5723i		−	0.670444i
$612$	−25.2603	−	50.7040i	−1.02109	−	2.04959i
$613$	−3.49830	−	3.49830i	−0.141295	−	0.141295i	0.632921	−	0.774216i	$-0.281856\pi$
$613$	−3.49830	−	3.49830i	−0.141295	−	0.141295i	−0.774216	+	0.632921i	$0.781856\pi$
$614$	9.56058	+	16.5594i	0.385833	+	0.668283i
$615$		0			0
$616$	−0.320393	+	0.554937i	−0.0129090	+	0.0223590i
$617$	−23.9061	+	6.40561i	−0.962421	+	0.257880i	−0.705625	−	0.708585i	$-0.749334\pi$
$617$	−23.9061	+	6.40561i	−0.962421	+	0.257880i	−0.256796	+	0.966466i	$0.582667\pi$
$618$	6.58605	+	65.5090i	0.264930	+	2.63516i
$619$	15.4357	−	8.91182i	0.620414	−	0.358196i	−0.156616	−	0.987660i	$-0.550059\pi$
$619$	15.4357	−	8.91182i	0.620414	−	0.358196i	0.777030	+	0.629463i	$0.216725\pi$
$620$		0			0
$621$	9.81737	+	15.5758i	0.393958	+	0.625035i
$622$	18.9394	−	18.9394i	0.759402	−	0.759402i
$623$	0.214559	+	0.0574910i	0.00859614	+	0.00230333i
$624$	−3.78051	−	3.08979i	−0.151342	−	0.123691i
$625$		0			0
$626$	13.3961	+	7.73424i	0.535416	+	0.309122i
$627$	0.113280	+	0.157408i	0.00452396	+	0.00628625i
$628$	14.8784	−	55.5270i	0.593714	−	2.21577i
$629$	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	$0.703028\pi$
$632$	11.5919	−	43.2617i	0.461102	−	1.72086i
$633$	−3.23763	+	7.18428i	−0.128684	+	0.285549i
$634$	4.03553	+	2.32991i	0.160271	+	0.0925327i
$635$		0			0
$636$	−7.29457	+	2.76236i	−0.289249	+	0.109535i
$637$	23.6917	+	6.34819i	0.938701	+	0.251524i
$638$	−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	$0.434779\pi$
$642$	−26.8482	+	19.3216i	−1.05961	+	0.762561i
$643$	22.4568	−	6.01727i	0.885608	−	0.237298i	0.212783	−	0.977099i	$-0.431747\pi$
$643$	22.4568	−	6.01727i	0.885608	−	0.237298i	0.672825	+	0.739801i	$0.265081\pi$
$644$	−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	$-0.329669\pi$
$647$	−8.90965	−	8.90965i	−0.350274	−	0.350274i	−0.860212	+	0.509937i	$0.829669\pi$
$648$	−10.9391	+	27.0265i	−0.429728	+	1.06170i
$649$			2.04560i			0.0802969i
$650$		0			0
$651$	0.165739	−	0.202789i	0.00649581	−	0.00794793i
$652$	12.1122	+	45.2035i	0.474352	+	1.77031i
$653$	−3.76260	−	14.0422i	−0.147242	−	0.549515i	−0.999645	−	0.0266300i	$-0.991522\pi$
$653$	−3.76260	−	14.0422i	−0.147242	−	0.549515i	0.852403	−	0.522885i	$-0.175144\pi$
$654$	−35.0166	−	5.70845i	−1.36926	−	0.223218i
$655$		0			0
$656$		−	3.29463i		−	0.128634i
$657$	32.4863	+	21.5168i	1.26741	+	0.839452i
$658$	−5.52058	−	5.52058i	−0.215215	−	0.215215i
$659$	4.50735	+	7.80696i	0.175582	+	0.304116i	0.940362	−	0.340174i	$-0.110486\pi$
$659$	4.50735	+	7.80696i	0.175582	+	0.304116i	−0.764781	+	0.644291i	$0.777153\pi$
$660$		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	$-0.0316757\pi$
$662$	−52.8125	+	14.1511i	−2.05261	+	0.549996i
$663$	−33.6892	−	15.1822i	−1.30838	−	0.589629i
$664$	−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
$668$	−64.6920	−	17.3342i	−2.50301	−	0.670679i
$669$	5.10443	−	31.3115i	0.197349	−	1.21057i
$670$		0			0
$671$	0.634959	+	0.366594i	0.0245123	+	0.0141522i
$672$	6.39808	−	0.643241i	0.246811	−	0.0248136i
$673$	7.04218	−	26.2818i	0.271456	−	1.01309i	−0.686723	−	0.726919i	$-0.740951\pi$
$673$	7.04218	−	26.2818i	0.271456	−	1.01309i	0.958179	−	0.286169i	$-0.0923819\pi$
$674$	26.4622			1.01928
$675$		0			0
$676$	−5.81007			−0.223464
$677$	−4.49141	+	16.7622i	−0.172619	+	0.644223i	0.824326	+	0.566116i	$0.191554\pi$
$677$	−4.49141	+	16.7622i	−0.172619	+	0.644223i	−0.996945	+	0.0781075i	$0.975112\pi$
$678$	−53.9100	+	5.41993i	−2.07040	+	0.208151i
$679$	6.09297	+	3.51778i	0.233827	+	0.135000i
$680$		0			0
$681$	3.14367	−	19.2838i	0.120466	−	0.738959i
$682$	−0.110870	−	0.0297075i	−0.00424543	−	0.00113756i
$683$	27.4945	−	27.4945i	1.05205	−	1.05205i	0.0534806	−	0.998569i	$-0.482968\pi$
$683$	27.4945	−	27.4945i	1.05205	−	1.05205i	0.998569	−	0.0534806i	$-0.0170315\pi$
$684$	−1.42442	+	4.25273i	−0.0544642	+	0.162607i
$685$		0			0
$686$	20.9610	−	12.1018i	0.800293	−	0.462049i
$687$	7.70236	+	3.47111i	0.293863	+	0.132431i
$688$	0.981065	−	0.262876i	0.0374028	−	0.0100220i
$689$	−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
$693$	0.531132	−	0.264605i	0.0201760	−	0.0100515i
$694$		−	33.1902i		−	1.25988i
$695$		0			0
$696$	−30.5993	−	4.98833i	−1.15986	−	0.189082i
$697$	−6.45355	−	24.0850i	−0.244446	−	0.912283i
$698$	−10.5589	−	39.4063i	−0.399660	−	1.49155i
$699$	−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	$0.968479\pi$
$702$	13.7064	+	44.2153i	0.517316	+	1.66880i
$703$	−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
$707$	9.88684	−	2.64917i	0.371833	−	0.0996323i
$708$	−38.3978	+	27.6333i	−1.44308	+	1.03852i
$709$	14.7176	−	8.49720i	0.552730	−	0.319119i	−0.197492	−	0.980304i	$-0.563280\pi$
$709$	14.7176	−	8.49720i	0.552730	−	0.319119i	0.750222	+	0.661186i	$0.229946\pi$
$710$		0			0
$711$	−31.0718	+	27.4727i	−1.16528	+	1.03031i
$712$	0.654066	−	0.654066i	0.0245121	−	0.0245121i
$713$	−0.665231	−	0.178248i	−0.0249131	−	0.00667545i
$714$	−16.2801	+	6.16507i	−0.609268	+	0.230722i
$715$		0			0
$716$	−44.3979	−	25.6331i	−1.65923	−	0.957955i
$717$	15.8498	−	35.1705i	0.591920	−	1.31346i
$718$	−20.4738	+	76.4092i	−0.764075	+	2.85157i
$719$	49.3502			1.84045			0.920225	−	0.391389i	$-0.128005\pi$
$719$	49.3502			1.84045			0.920225	+	0.391389i	$0.128005\pi$
$720$		0			0
$721$	12.7320			0.474164
$722$	11.3053	−	42.1918i	0.420739	−	1.57022i
$723$	29.2888	+	40.6981i	1.08926	+	1.51358i
$724$	23.0186	+	13.2898i	0.855478	+	0.493910i
$725$		0			0
$726$	34.0632	+	27.8397i	1.26421	+	1.03323i
$727$	−37.8991	−	10.1550i	−1.40560	−	0.376630i	−0.525249	−	0.850949i	$-0.676028\pi$
$727$	−37.8991	−	10.1550i	−1.40560	−	0.376630i	−0.880353	+	0.474319i	$0.842694\pi$
$728$	−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
$732$	1.69615	+	16.8709i	0.0626914	+	0.623568i
$733$	−7.32362	+	1.96236i	−0.270504	+	0.0724813i	−0.391521	−	0.920169i	$-0.628051\pi$
$733$	−7.32362	+	1.96236i	−0.270504	+	0.0724813i	0.121017	+	0.992650i	$0.461384\pi$
$734$	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
$738$	−17.2486	+	26.0421i	−0.634930	+	0.958621i
$739$			43.8329i			1.61242i	0.591629	+	0.806210i	$0.298485\pi$
$739$			43.8329i			1.61242i	−0.591629	+	0.806210i	$0.701515\pi$
$740$		0			0
$741$	1.03608	+	2.73598i	0.0380614	+	0.100509i
$742$	0.620396	+	2.31535i	0.0227755	+	0.0849992i
$743$	2.41659	+	9.01884i	0.0886561	+	0.330869i	0.995981	−	0.0895603i	$-0.0285462\pi$
$743$	2.41659	+	9.01884i	0.0886561	+	0.330869i	−0.907325	+	0.420429i	$0.861879\pi$
$744$	−0.386235	−	1.01993i	−0.0141601	−	0.0373925i
$745$		0			0
$746$			50.0066i			1.83087i
$747$	16.1257	+	0.991358i	0.590007	+	0.0362719i
$748$	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	$-0.165818\pi$
$752$	−3.06729	+	0.821878i	−0.111853	+	0.0299708i
$753$	−3.53830	−	35.1942i	−0.128943	−	1.28255i
$754$	−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	−0.731724	−	0.681601i	$-0.761284\pi$
$757$	−1.37906	+	1.37906i	−0.0501227	+	0.0501227i	0.681601	+	0.731724i	$0.261284\pi$
$758$	21.3784	+	5.72832i	0.776497	+	0.208062i
$759$	−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	$-0.673103\pi$
$762$	−22.3379	−	31.0396i	−0.809218	−	1.12445i
$763$	−1.77573	+	6.62712i	−0.0642858	+	0.239918i
$764$	−38.9469			−1.40905
$765$		0			0
$766$	23.1275			0.835631
$767$	−7.98696	+	29.8078i	−0.288393	+	1.07630i
$768$	14.5528	−	32.2924i	0.525128	−	1.16525i
$769$	25.7542	+	14.8692i	0.928719	+	0.536196i	0.886406	−	0.462908i	$-0.153194\pi$
$769$	25.7542	+	14.8692i	0.928719	+	0.536196i	0.0423126	+	0.999104i	$0.486527\pi$
$770$		0			0
$771$	−11.8937	+	4.50398i	−0.428340	+	0.162207i
$772$	−18.0953	−	4.84862i	−0.651264	−	0.174506i
$773$	14.1444	−	14.1444i	0.508738	−	0.508738i	−0.405401	−	0.914139i	$-0.632868\pi$
$773$	14.1444	−	14.1444i	0.508738	−	0.508738i	0.914139	+	0.405401i	$0.132868\pi$
$774$	−9.13097	−	3.05836i	−0.328206	−	0.109931i
$775$		0			0
$776$	25.3724	−	14.6488i	0.910816	−	0.525860i
$777$	−0.190255	+	0.136919i	−0.00682535	+	0.00491193i
$778$	65.3638	−	17.5142i	2.34340	−	0.627913i
$779$	−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
$783$	21.0735	+	19.4985i	0.753104	+	0.696819i
$784$		−	4.69982i		−	0.167851i
$785$		0			0
$786$	34.2420	−	41.8967i	1.22137	−	1.49441i
$787$	−0.466583	−	1.74131i	−0.0166319	−	0.0620710i	0.957111	−	0.289721i	$-0.0935625\pi$
$787$	−0.466583	−	1.74131i	−0.0166319	−	0.0620710i	−0.973743	+	0.227650i	$0.926896\pi$
$788$	2.88644	+	10.7723i	0.102825	+	0.383749i
$789$	−24.9712	−	4.07084i	−0.889000	−	0.144926i
$790$		0			0
$791$			10.4777i			0.372543i
$792$	0.151625	−	2.46636i	0.00538774	−	0.0876383i
$793$	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
$797$	−6.85000	+	1.83545i	−0.242639	+	0.0650150i	−0.378089	−	0.925769i	$-0.623419\pi$
$797$	−6.85000	+	1.83545i	−0.242639	+	0.0650150i	0.135450	+	0.990784i	$0.456752\pi$
$798$	1.25655	+	0.566273i	0.0444815	+	0.0200458i
$799$	−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
$803$	−3.18985	−	0.854717i	−0.112567	−	0.0301623i
$804$	−12.6999	+	77.9035i	−0.447891	+	2.74744i
$805$		0			0
$806$	−1.49956	−	0.865774i	−0.0528199	−	0.0304956i
$807$	6.48001	−	0.651477i	0.228107	−	0.0229331i
$808$	11.0317	−	41.1709i	0.388094	−	1.44839i
$809$	−24.7868			−0.871457			−0.435728	−	0.900078i	$-0.643509\pi$
$809$	−24.7868			−0.871457			−0.435728	+	0.900078i	$0.643509\pi$
$810$		0			0
$811$	−5.24853			−0.184301			−0.0921505	−	0.995745i	$-0.529374\pi$
$811$	−5.24853			−0.184301			−0.0921505	+	0.995745i	$0.529374\pi$
$812$	−3.77678	+	14.0951i	−0.132539	+	0.494642i
$813$	24.2624	−	2.43926i	0.850919	−	0.0855484i
$814$	0.0889652	+	0.0513641i	0.00311823	+	0.00180031i
$815$		0			0
$816$	−1.13924	+	6.98831i	−0.0398815	+	0.244640i
$817$	−0.587849	−	0.157514i	−0.0205662	−	0.00551071i
$818$	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	$0.175872\pi$
$822$	35.9063	+	16.1814i	1.25237	+	0.564390i
$823$	−32.5062	+	8.71001i	−1.13309	+	0.303612i	−0.776171	−	0.630522i	$-0.782841\pi$
$823$	−32.5062	+	8.71001i	−1.13309	+	0.303612i	−0.356923	+	0.934134i	$0.616174\pi$
$824$	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	$-0.177941\pi$
$827$	9.12836	+	9.12836i	0.317424	+	0.317424i	−0.530353	+	0.847777i	$0.677941\pi$
$828$	2.21429	−	36.0182i	0.0769521	−	1.25172i
$829$		−	44.3456i		−	1.54019i	−0.637931	−	0.770093i	$-0.720210\pi$
$829$		−	44.3456i		−	1.54019i	0.637931	−	0.770093i	$-0.279790\pi$
$830$		0			0
$831$	3.57623	+	0.583001i	0.124058	+	0.0202241i
$832$	−12.4626	−	46.5109i	−0.432061	−	1.61247i
$833$	−9.20604	−	34.3574i	−0.318970	−	1.19041i
$834$	20.1346	−	24.6356i	0.697203	−	0.853061i
$835$		0			0
$836$		−	0.380101i		−	0.0131461i
$837$	−0.223357	+	0.984946i	−0.00772035	+	0.0340447i
$838$	45.5948	+	45.5948i	1.57505	+	1.57505i
$839$	−23.9660	−	41.5104i	−0.827399	−	1.43310i	−0.900072	−	0.435742i	$-0.856486\pi$
$839$	−23.9660	−	41.5104i	−0.827399	−	1.43310i	0.0726721	−	0.997356i	$-0.476847\pi$
$840$		0			0
$841$	−0.764464	+	1.32409i	−0.0263608	+	0.0456583i
$842$	−1.92899	+	0.516871i	−0.0664773	+	0.0178125i
$843$	13.0300	−	9.37717i	0.448778	−	0.322967i
$844$	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
$848$	0.941733	+	0.252337i	0.0323392	+	0.00866527i
$849$	52.1703	−	19.7562i	1.79048	−	0.678031i
$850$		0			0
$851$	0.533801	+	0.308190i	0.0182985	+	0.0105646i
$852$	−5.21787	+	11.5784i	−0.178761	+	0.396669i
$853$	−1.50103	+	5.60190i	−0.0513941	+	0.191806i	−0.986850	−	0.161637i	$-0.948322\pi$
$853$	−1.50103	+	5.60190i	−0.0513941	+	0.191806i	0.935456	+	0.353443i	$0.114989\pi$
$854$	5.21071			0.178307
$855$		0			0
$856$	26.6368			0.910427
$857$	8.23598	−	30.7371i	0.281336	−	1.04996i	−0.670140	−	0.742235i	$-0.733766\pi$
$857$	8.23598	−	30.7371i	0.281336	−	1.04996i	0.951476	−	0.307724i	$-0.0995674\pi$
$858$	−2.29162	−	3.18432i	−0.0782347	−	0.108711i
$859$	10.3188	+	5.95757i	0.352074	+	0.203270i	0.665598	−	0.746310i	$-0.268176\pi$
$859$	10.3188	+	5.95757i	0.352074	+	0.203270i	−0.313525	+	0.949580i	$0.601510\pi$
$860$		0			0
$861$	4.67709	+	3.82256i	0.159395	+	0.130273i
$862$	57.3825	+	15.3756i	1.95446	+	0.523695i
$863$	−13.3552	+	13.3552i	−0.454617	+	0.454617i	−0.896884	−	0.442267i	$-0.854174\pi$
$863$	−13.3552	+	13.3552i	−0.454617	+	0.454617i	0.442267	+	0.896884i	$0.354174\pi$
$864$	−20.9776	+	13.2221i	−0.713672	+	0.449825i
$865$		0			0
$866$	−17.9423	+	10.3590i	−0.609704	+	0.352013i
$867$	2.41504	+	24.0215i	0.0820191	+	0.815814i
$868$	−0.495830	+	0.132857i	−0.0168296	+	0.00450947i
$869$	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
$873$	−27.0796	−	1.66477i	−0.916506	−	0.0563441i
$874$		−	3.62427i		−	0.122593i
$875$		0			0
$876$	−27.0467	−	71.4223i	−0.913824	−	2.41314i
$877$	−1.73140	−	6.46168i	−0.0584653	−	0.218195i	0.930512	−	0.366261i	$-0.119362\pi$
$877$	−1.73140	−	6.46168i	−0.0584653	−	0.218195i	−0.988978	+	0.148065i	$0.952695\pi$
$878$	8.65368	+	32.2960i	0.292048	+	1.08994i
$879$	−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	$0.927251\pi$
$882$	−24.6053	+	37.1492i	−0.828503	+	1.25088i
$883$	−32.5618	−	32.5618i	−1.09579	−	1.09579i	−0.994897	−	0.100896i	$-0.967829\pi$
$883$	−32.5618	−	32.5618i	−1.09579	−	1.09579i	−0.100896	−	0.994897i	$-0.532171\pi$
$884$	36.2127	+	62.7222i	1.21796	+	2.10957i
$885$		0			0
$886$	25.4576	−	44.0939i	0.855266	−	1.48136i
$887$	−25.4475	+	6.81864i	−0.854444	+	0.228948i	−0.659349	−	0.751837i	$-0.729168\pi$
$887$	−25.4475	+	6.81864i	−0.854444	+	0.228948i	−0.195095	+	0.980784i	$0.562501\pi$
$888$	0.0976406	+	0.971196i	0.00327661	+	0.0325912i
$889$	−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
$893$	1.83790	+	0.492465i	0.0615031	+	0.0164797i
$894$	28.4555	+	23.2566i	0.951694	+	0.777816i
$895$		0			0
$896$	−13.2150	−	7.62966i	−0.441481	−	0.254889i
$897$	−13.7500	−	19.1062i	−0.459098	−	0.637939i
$898$	−14.2140	+	53.0474i	−0.474327	+	1.77021i
$899$	−1.07393			−0.0358175
$900$		0			0
$901$	7.37869			0.245820
$902$	0.685169	−	2.55708i	0.0228136	−	0.0851416i
$903$	−0.765090	+	1.69773i	−0.0254606	+	0.0564968i
$904$	37.7857	+	21.8156i	1.25673	+	0.725576i
$905$		0			0
$906$	−55.3044	+	20.9430i	−1.83736	+	0.695786i
$907$	−45.4294	−	12.1728i	−1.50846	−	0.404190i	−0.592536	−	0.805544i	$-0.701873\pi$
$907$	−45.4294	−	12.1728i	−1.50846	−	0.404190i	−0.915923	+	0.401354i	$0.868540\pi$
$908$	−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	$0.452165\pi$
$912$	0.455007	−	0.327450i	0.0150668	−	0.0108429i
$913$	−1.32258	+	0.354385i	−0.0437711	+	0.0117284i
$914$	−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
$918$	45.5914	−	49.2740i	1.50474	−	1.62629i
$919$		−	28.3896i		−	0.936486i	−0.883600	−	0.468243i	$-0.844887\pi$
$919$		−	28.3896i		−	0.936486i	0.883600	−	0.468243i	$-0.155113\pi$
$920$		0			0
$921$	−9.02345	+	11.0406i	−0.297333	+	0.363801i
$922$	19.3627	+	72.2628i	0.637678	+	2.37985i
$923$	2.14413	+	8.00199i	0.0705748	+	0.263389i
$924$	−1.14788	−	0.187129i	−0.0377626	−	0.00615611i
$925$		0			0
$926$			14.8495i			0.487984i
$927$	−43.9459	+	21.8934i	−1.44337	+	0.719074i
$928$	−18.6447	−	18.6447i	−0.612042	−	0.612042i
$929$	18.9202	+	32.7708i	0.620753	+	1.07518i	0.989346	+	0.145585i	$0.0465063\pi$
$929$	18.9202	+	32.7708i	0.620753	+	1.07518i	−0.368593	+	0.929591i	$0.620160\pi$
$930$		0			0
$931$	−1.40805	+	2.43882i	−0.0461471	+	0.0799292i
$932$	36.6695	−	9.82556i	1.20115	−	0.321847i
$933$	18.2099	+	8.20637i	0.596164	+	0.268665i
$934$	−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	−0.213379	+	0.976969i	$0.568447\pi$
$937$	−36.4371	+	36.4371i	−1.19035	+	1.19035i	−0.976969	+	0.213379i	$0.931553\pi$
$938$	23.4299	+	6.27801i	0.765012	+	0.204984i
$939$	−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	$0.496509\pi$
$942$	67.7818	−	6.81455i	2.20845	−	0.222030i
$943$	4.11108	−	15.3428i	0.133875	−	0.499630i
$944$	5.91308			0.192454
$945$		0			0
$946$	0.816109			0.0265340
$947$	−3.89239	+	14.5266i	−0.126486	+	0.472050i	−0.999888	−	0.0149482i	$-0.995242\pi$
$947$	−3.89239	+	14.5266i	−0.126486	+	0.472050i	0.873403	+	0.486999i	$0.161908\pi$
$948$	80.8828	−	8.13168i	2.62695	−	0.264105i
$949$	−43.1441	−	24.9092i	−1.40052	−	0.808588i
$950$		0			0
$951$	−0.559103	+	3.42964i	−0.0181302	+	0.111214i
$952$	13.5408	+	3.62825i	0.438860	+	0.117592i
$953$	−37.2073	+	37.2073i	−1.20526	+	1.20526i	−0.232720	+	0.972544i	$0.574763\pi$
$953$	−37.2073	+	37.2073i	−1.20526	+	1.20526i	−0.972544	+	0.232720i	$0.925237\pi$
$954$	−6.12275	−	6.92488i	−0.198231	−	0.224201i
$955$		0			0
$956$	−65.4799	+	37.8048i	−2.11777	+	1.22270i
$957$	−2.21835	−	0.999714i	−0.0717092	−	0.0323162i
$958$	7.90463	−	2.11804i	0.255387	−	0.0684308i
$959$	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
$963$	−20.5650	−	13.6209i	−0.662698	−	0.438929i
$964$		−	98.2761i		−	3.16526i
$965$		0			0
$966$	−10.9451	−	1.78428i	−0.352153	−	0.0574083i
$967$	5.09683	+	19.0216i	0.163903	+	0.611694i	0.998178	+	0.0603451i	$0.0192201\pi$
$967$	5.09683	+	19.0216i	0.163903	+	0.611694i	−0.834275	+	0.551349i	$0.814113\pi$
$968$	−9.16896	−	34.2190i	−0.294701	−	1.09984i
$969$	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	$0.965441\pi$
$972$	−52.9058	−	1.19586i	−1.69695	−	0.0383573i
$973$	−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
$977$	28.6341	−	7.67249i	0.916086	−	0.245465i	0.230175	−	0.973149i	$-0.426070\pi$
$977$	28.6341	−	7.67249i	0.916086	−	0.245465i	0.685912	+	0.727685i	$0.259404\pi$
$978$	−45.0134	+	32.3943i	−1.43937	+	1.03586i
$979$	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
$983$	17.0781	+	4.57606i	0.544706	+	0.145954i	0.520671	−	0.853758i	$-0.325682\pi$
$983$	17.0781	+	4.57606i	0.544706	+	0.145954i	0.0240353	+	0.999711i	$0.492349\pi$
$984$	23.5235	−	8.90805i	0.749903	−	0.283978i
$985$		0			0
$986$	61.8194	+	35.6914i	1.96873	+	1.13665i
$987$	2.39205	−	5.30793i	0.0761397	−	0.168953i
$988$	1.48409	−	5.53869i	0.0472151	−	0.176209i
$989$	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	$0.942279\pi$
$992$	0.240066	−	0.895938i	0.00762210	−	0.0284461i
$993$	−23.8161	−	33.0936i	−0.755781	−	1.05019i
$994$	3.37988	+	1.95138i	0.107203	+	0.0618939i
$995$		0			0
$996$	−24.5184	−	20.0388i	−0.776896	−	0.634954i
$997$	24.2734	+	6.50403i	0.768745	+	0.205985i	0.621817	−	0.783163i	$-0.286395\pi$
$997$	24.2734	+	6.50403i	0.768745	+	0.205985i	0.146928	+	0.989147i	$0.453061\pi$
$998$	−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.68.4		16
3.2	odd	2		675.2.q.a.368.1		16
5.2	odd	4	inner	225.2.p.b.32.4		16
5.3	odd	4		45.2.l.a.32.1	yes	16
5.4	even	2		45.2.l.a.23.1	yes	16
9.2	odd	6	inner	225.2.p.b.218.4		16
9.7	even	3		675.2.q.a.143.1		16
15.2	even	4		675.2.q.a.557.1		16
15.8	even	4		135.2.m.a.17.4		16
15.14	odd	2		135.2.m.a.98.4		16
20.3	even	4		720.2.cu.c.257.2		16
20.19	odd	2		720.2.cu.c.113.4		16
45.2	even	12	inner	225.2.p.b.182.4		16
45.4	even	6		405.2.f.a.323.1		16
45.7	odd	12		675.2.q.a.332.1		16
45.13	odd	12		405.2.f.a.242.8		16
45.14	odd	6		405.2.f.a.323.8		16
45.23	even	12		405.2.f.a.242.1		16
45.29	odd	6		45.2.l.a.38.1	yes	16
45.34	even	6		135.2.m.a.8.4		16
45.38	even	12		45.2.l.a.2.1	✓	16
45.43	odd	12		135.2.m.a.62.4		16
180.83	odd	12		720.2.cu.c.497.4		16
180.119	even	6		720.2.cu.c.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.1	✓	16	45.38	even	12
45.2.l.a.23.1	yes	16	5.4	even	2
45.2.l.a.32.1	yes	16	5.3	odd	4
45.2.l.a.38.1	yes	16	45.29	odd	6
135.2.m.a.8.4		16	45.34	even	6
135.2.m.a.17.4		16	15.8	even	4
135.2.m.a.62.4		16	45.43	odd	12
135.2.m.a.98.4		16	15.14	odd	2
225.2.p.b.32.4		16	5.2	odd	4	inner
225.2.p.b.68.4		16	1.1	even	1	trivial
225.2.p.b.182.4		16	45.2	even	12	inner
225.2.p.b.218.4		16	9.2	odd	6	inner
405.2.f.a.242.1		16	45.23	even	12
405.2.f.a.242.8		16	45.13	odd	12
405.2.f.a.323.1		16	45.4	even	6
405.2.f.a.323.8		16	45.14	odd	6
675.2.q.a.143.1		16	9.7	even	3
675.2.q.a.332.1		16	45.7	odd	12
675.2.q.a.368.1		16	3.2	odd	2
675.2.q.a.557.1		16	15.2	even	4
720.2.cu.c.113.4		16	20.19	odd	2
720.2.cu.c.257.2		16	20.3	even	4
720.2.cu.c.353.2		16	180.119	even	6
720.2.cu.c.497.4		16	180.83	odd	12

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)

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