LMFDB - Embedded newform 475.2.l.c.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.2
Root			$0.154946 - 0.268374i$ of defining polynomial
Character	$\chi$	$=$	475.101
Dual form			475.2.l.c.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528654 + 0.443593i) q^{2} +(-0.652945 - 0.237653i) q^{3} +(-0.264596 + 1.50060i) q^{4} +(0.450603 - 0.164006i) q^{6} +(-1.16732 + 2.02186i) q^{7} +(-1.21589 - 2.10598i) q^{8} +(-1.92827 - 1.61801i) q^{9} +O(q^{10})$	\(q+(-0.528654 + 0.443593i) q^{2} +(-0.652945 - 0.237653i) q^{3} +(-0.264596 + 1.50060i) q^{4} +(0.450603 - 0.164006i) q^{6} +(-1.16732 + 2.02186i) q^{7} +(-1.21589 - 2.10598i) q^{8} +(-1.92827 - 1.61801i) q^{9} +(-2.28929 - 3.96516i) q^{11} +(0.529389 - 0.916928i) q^{12} +(1.20379 - 0.438145i) q^{13} +(-0.279774 - 1.58668i) q^{14} +(-1.28673 - 0.468333i) q^{16} +(0.501495 - 0.420805i) q^{17} +1.73713 q^{18} +(3.67523 + 2.34365i) q^{19} +(1.24270 - 1.04275i) q^{21} +(2.96916 + 1.08069i) q^{22} +(0.966645 - 5.48212i) q^{23} +(0.293416 + 1.66404i) q^{24} +(-0.442032 + 0.765622i) q^{26} +(1.91681 + 3.32001i) q^{27} +(-2.72513 - 2.28666i) q^{28} +(-3.62387 - 3.04079i) q^{29} +(2.24045 - 3.88057i) q^{31} +(5.45822 - 1.98663i) q^{32} +(0.552448 + 3.13309i) q^{33} +(-0.0784514 + 0.444920i) q^{34} +(2.93821 - 2.46545i) q^{36} -7.79252 q^{37} +(-2.98255 + 0.391324i) q^{38} -0.890138 q^{39} +(-8.17440 - 2.97524i) q^{41} +(-0.194401 + 1.10250i) q^{42} +(-1.66494 - 9.44233i) q^{43} +(6.55586 - 2.38614i) q^{44} +(1.92081 + 3.32694i) q^{46} +(-4.84673 - 4.06689i) q^{47} +(0.728866 + 0.611591i) q^{48} +(0.774723 + 1.34186i) q^{49} +(-0.427454 + 0.155581i) q^{51} +(0.338961 + 1.92235i) q^{52} +(-1.14634 + 6.50124i) q^{53} +(-2.48606 - 0.904852i) q^{54} +5.67731 q^{56} +(-1.84275 - 2.40370i) q^{57} +3.26464 q^{58} +(4.51420 - 3.78786i) q^{59} +(-1.30132 + 7.38016i) q^{61} +(0.536973 + 3.04533i) q^{62} +(5.52231 - 2.00996i) q^{63} +(-0.634941 + 1.09975i) q^{64} +(-1.68187 - 1.41126i) q^{66} +(-10.0048 - 8.39500i) q^{67} +(0.498766 + 0.863888i) q^{68} +(-1.93401 + 3.34980i) q^{69} +(0.651454 + 3.69458i) q^{71} +(-1.06294 + 6.02822i) q^{72} +(7.48353 + 2.72378i) q^{73} +(4.11955 - 3.45671i) q^{74} +(-4.48934 + 4.89493i) q^{76} +10.6893 q^{77} +(0.470575 - 0.394859i) q^{78} +(-5.92896 - 2.15796i) q^{79} +(0.848752 + 4.81351i) q^{81} +(5.64122 - 2.05324i) q^{82} +(-4.91848 + 8.51905i) q^{83} +(1.23593 + 2.14070i) q^{84} +(5.06873 + 4.25317i) q^{86} +(1.64354 + 2.84669i) q^{87} +(-5.56702 + 9.64236i) q^{88} +(-11.4439 + 4.16525i) q^{89} +(-0.519346 + 2.94536i) q^{91} +(7.97070 + 2.90110i) q^{92} +(-2.38512 + 2.00135i) q^{93} +4.36629 q^{94} -4.03605 q^{96} +(-3.22485 + 2.70597i) q^{97} +(-1.00480 - 0.365717i) q^{98} +(-2.00131 + 11.3500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.528654	+	0.443593i	−0.373815	+	0.313668i	−0.810268	−	0.586059i	$-0.800679\pi$
$2$	−0.528654	+	0.443593i	−0.373815	+	0.313668i	0.436454	+	0.899727i	$0.356234\pi$
$3$	−0.652945	−	0.237653i	−0.376978	−	0.137209i	0.146580	−	0.989199i	$-0.453173\pi$
$3$	−0.652945	−	0.237653i	−0.376978	−	0.137209i	−0.523558	+	0.851990i	$0.675396\pi$
$4$	−0.264596	+	1.50060i	−0.132298	+	0.750300i
$5$		0			0
$5$		0			0
$6$	0.450603	−	0.164006i	0.183958	−	0.0669552i
$7$	−1.16732	+	2.02186i	−0.441206	+	0.764191i	−0.997779	−	0.0666074i	$-0.978782\pi$
$7$	−1.16732	+	2.02186i	−0.441206	+	0.764191i	0.556573	+	0.830798i	$0.312116\pi$
$8$	−1.21589	−	2.10598i	−0.429880	−	0.744575i
$9$	−1.92827	−	1.61801i	−0.642758	−	0.539338i
$10$		0			0
$11$	−2.28929	−	3.96516i	−0.690246	−	1.19554i	−0.971757	−	0.235983i	$-0.924169\pi$
$11$	−2.28929	−	3.96516i	−0.690246	−	1.19554i	0.281511	−	0.959558i	$-0.409164\pi$
$12$	0.529389	−	0.916928i	0.152821	−	0.264694i
$13$	1.20379	−	0.438145i	0.333872	−	0.121520i	−0.169644	−	0.985505i	$-0.554262\pi$
$13$	1.20379	−	0.438145i	0.333872	−	0.121520i	0.503516	+	0.863986i	$0.332039\pi$
$14$	−0.279774	−	1.58668i	−0.0747729	−	0.424058i
$15$		0			0
$16$	−1.28673	−	0.468333i	−0.321683	−	0.117083i
$17$	0.501495	−	0.420805i	0.121631	−	0.102060i	−0.579944	−	0.814657i	$-0.696925\pi$
$17$	0.501495	−	0.420805i	0.121631	−	0.102060i	0.701574	+	0.712597i	$0.252481\pi$
$18$	1.73713			0.409446
$19$	3.67523	+	2.34365i	0.843155	+	0.537671i
$19$	3.67523	+	2.34365i	0.843155	+	0.537671i
$20$		0			0
$21$	1.24270	−	1.04275i	0.271179	−	0.227546i
$22$	2.96916	+	1.08069i	0.633027	+	0.230403i
$23$	0.966645	−	5.48212i	0.201559	−	1.14310i	−0.701203	−	0.712961i	$-0.747353\pi$
$23$	0.966645	−	5.48212i	0.201559	−	1.14310i	0.902763	−	0.430139i	$-0.141535\pi$
$24$	0.293416	+	1.66404i	0.0598933	+	0.339672i
$25$		0			0
$26$	−0.442032	+	0.765622i	−0.0866897	+	0.150151i
$27$	1.91681	+	3.32001i	0.368890	+	0.638936i
$28$	−2.72513	−	2.28666i	−0.515002	−	0.432138i
$29$	−3.62387	−	3.04079i	−0.672935	−	0.564660i	0.240997	−	0.970526i	$-0.422526\pi$
$29$	−3.62387	−	3.04079i	−0.672935	−	0.564660i	−0.913933	+	0.405866i	$0.866970\pi$
$30$		0			0
$31$	2.24045	−	3.88057i	0.402396	−	0.696971i	−0.591618	−	0.806218i	$-0.701511\pi$
$31$	2.24045	−	3.88057i	0.402396	−	0.696971i	0.994015	+	0.109248i	$0.0348441\pi$
$32$	5.45822	−	1.98663i	0.964886	−	0.351190i
$33$	0.552448	+	3.13309i	0.0961688	+	0.545400i
$34$	−0.0784514	+	0.444920i	−0.0134543	+	0.0763032i
$35$		0			0
$36$	2.93821	−	2.46545i	0.489701	−	0.410908i
$37$	−7.79252			−1.28108			−0.640541	−	0.767924i	$-0.721290\pi$
$37$	−7.79252			−1.28108			−0.640541	+	0.767924i	$0.721290\pi$
$38$	−2.98255	+	0.391324i	−0.483834	+	0.0634812i
$39$	−0.890138			−0.142536
$40$		0			0
$41$	−8.17440	−	2.97524i	−1.27663	−	0.464654i	−0.387311	−	0.921949i	$-0.626596\pi$
$41$	−8.17440	−	2.97524i	−1.27663	−	0.464654i	−0.889315	+	0.457295i	$0.848818\pi$
$42$	−0.194401	+	1.10250i	−0.0299968	+	0.170120i
$43$	−1.66494	−	9.44233i	−0.253901	−	1.43994i	−0.798879	−	0.601491i	$-0.794573\pi$
$43$	−1.66494	−	9.44233i	−0.253901	−	1.43994i	0.544979	−	0.838450i	$-0.316538\pi$
$44$	6.55586	−	2.38614i	0.988333	−	0.359724i
$45$		0			0
$46$	1.92081	+	3.32694i	0.283208	+	0.490531i
$47$	−4.84673	−	4.06689i	−0.706968	−	0.593217i	0.216779	−	0.976221i	$-0.430445\pi$
$47$	−4.84673	−	4.06689i	−0.706968	−	0.593217i	−0.923747	+	0.383004i	$0.874889\pi$
$48$	0.728866	+	0.611591i	0.105203	+	0.0882756i
$49$	0.774723	+	1.34186i	0.110675	+	0.191694i
$50$		0			0
$51$	−0.427454	+	0.155581i	−0.0598556	+	0.0217856i
$52$	0.338961	+	1.92235i	0.0470055	+	0.266581i
$53$	−1.14634	+	6.50124i	−0.157462	+	0.893013i	0.799038	+	0.601281i	$0.205343\pi$
$53$	−1.14634	+	6.50124i	−0.157462	+	0.893013i	−0.956500	+	0.291732i	$0.905768\pi$
$54$	−2.48606	−	0.904852i	−0.338310	−	0.123135i
$55$		0			0
$56$	5.67731			0.758663
$57$	−1.84275	−	2.40370i	−0.244078	−	0.318378i
$58$	3.26464			0.428669
$59$	4.51420	−	3.78786i	0.587699	−	0.493138i	−0.299766	−	0.954013i	$-0.596909\pi$
$59$	4.51420	−	3.78786i	0.587699	−	0.493138i	0.887465	+	0.460875i	$0.152464\pi$
$60$		0			0
$61$	−1.30132	+	7.38016i	−0.166617	+	0.944932i	0.780764	+	0.624826i	$0.214830\pi$
$61$	−1.30132	+	7.38016i	−0.166617	+	0.944932i	−0.947381	+	0.320107i	$0.896281\pi$
$62$	0.536973	+	3.04533i	0.0681956	+	0.386757i
$63$	5.52231	−	2.00996i	0.695746	−	0.253231i
$64$	−0.634941	+	1.09975i	−0.0793676	+	0.137469i
$65$		0			0
$66$	−1.68187	−	1.41126i	−0.207024	−	0.173714i
$67$	−10.0048	−	8.39500i	−1.22228	−	1.02561i	−0.998702	−	0.0509251i	$-0.983783\pi$
$67$	−10.0048	−	8.39500i	−1.22228	−	1.02561i	−0.223574	−	0.974687i	$-0.571773\pi$
$68$	0.498766	+	0.863888i	0.0604842	+	0.104762i
$69$	−1.93401	+	3.34980i	−0.232827	+	0.403268i
$70$		0			0
$71$	0.651454	+	3.69458i	0.0773134	+	0.438466i	0.998752	+	0.0499424i	$0.0159038\pi$
$71$	0.651454	+	3.69458i	0.0773134	+	0.438466i	−0.921439	+	0.388524i	$0.872985\pi$
$72$	−1.06294	+	6.02822i	−0.125268	+	0.710432i
$73$	7.48353	+	2.72378i	0.875881	+	0.318795i	0.740546	−	0.672005i	$-0.234567\pi$
$73$	7.48353	+	2.72378i	0.875881	+	0.318795i	0.135335	+	0.990800i	$0.456789\pi$
$74$	4.11955	−	3.45671i	0.478888	−	0.401834i
$75$		0			0
$76$	−4.48934	+	4.89493i	−0.514963	+	0.561486i
$77$	10.6893			1.21816
$78$	0.470575	−	0.394859i	0.0532821	−	0.0447090i
$79$	−5.92896	−	2.15796i	−0.667060	−	0.242790i	−0.0137784	−	0.999905i	$-0.504386\pi$
$79$	−5.92896	−	2.15796i	−0.667060	−	0.242790i	−0.653281	+	0.757115i	$0.726608\pi$
$80$		0			0
$81$	0.848752	+	4.81351i	0.0943058	+	0.534835i
$82$	5.64122	−	2.05324i	0.622969	−	0.226742i
$83$	−4.91848	+	8.51905i	−0.539873	+	0.935088i	0.459037	+	0.888417i	$0.348194\pi$
$83$	−4.91848	+	8.51905i	−0.539873	+	0.935088i	−0.998910	+	0.0466706i	$0.985139\pi$
$84$	1.23593	+	2.14070i	0.134851	+	0.233569i
$85$		0			0
$86$	5.06873	+	4.25317i	0.546575	+	0.458631i
$87$	1.64354	+	2.84669i	0.176206	+	0.305197i
$88$	−5.56702	+	9.64236i	−0.593446	+	1.02788i
$89$	−11.4439	+	4.16525i	−1.21305	+	0.441516i	−0.867762	−	0.496979i	$-0.834442\pi$
$89$	−11.4439	+	4.16525i	−1.21305	+	0.441516i	−0.345292	+	0.938495i	$0.612220\pi$
$90$		0			0
$91$	−0.519346	+	2.94536i	−0.0544423	+	0.308758i
$92$	7.97070	+	2.90110i	0.831003	+	0.302460i
$93$	−2.38512	+	2.00135i	−0.247325	+	0.207530i
$94$	4.36629			0.450348
$95$		0			0
$96$	−4.03605			−0.411927
$97$	−3.22485	+	2.70597i	−0.327434	+	0.274750i	−0.791653	−	0.610971i	$-0.790779\pi$
$97$	−3.22485	+	2.70597i	−0.327434	+	0.274750i	0.464219	+	0.885720i	$0.346335\pi$
$98$	−1.00480	−	0.365717i	−0.101500	−	0.0369430i
$99$	−2.00131	+	11.3500i	−0.201140	+	1.14072i
$100$		0			0
$101$	0.0536285	−	0.0195192i	0.00533623	−	0.00194223i	−0.339351	−	0.940660i	$-0.610207\pi$
$101$	0.0536285	−	0.0195192i	0.00533623	−	0.00194223i	0.344687	+	0.938718i	$0.387985\pi$
$102$	0.156961	−	0.271864i	0.0155414	−	0.0269186i
$103$	3.62170	+	6.27298i	0.356857	+	0.618095i	0.987434	−	0.158032i	$-0.0505150\pi$
$103$	3.62170	+	6.27298i	0.356857	+	0.618095i	−0.630577	+	0.776127i	$0.717182\pi$
$104$	−2.38640	−	2.00243i	−0.234006	−	0.196354i
$105$		0			0
$106$	−2.27789	−	3.94541i	−0.221248	−	0.383213i
$107$	7.42998	−	12.8691i	0.718283	−	1.24410i	−0.243396	−	0.969927i	$-0.578262\pi$
$107$	7.42998	−	12.8691i	0.718283	−	1.24410i	0.961680	−	0.274176i	$-0.0884050\pi$
$108$	−5.48918	+	1.99790i	−0.528197	+	0.192248i
$109$	−2.33021	−	13.2153i	−0.223193	−	1.26579i	−0.866109	−	0.499855i	$-0.833387\pi$
$109$	−2.33021	−	13.2153i	−0.223193	−	1.26579i	0.642916	−	0.765937i	$-0.277724\pi$
$110$		0			0
$111$	5.08809	+	1.85191i	0.482940	+	0.175776i
$112$	2.44893	−	2.05490i	0.231403	−	0.194170i
$113$	4.23499			0.398395			0.199197	−	0.979959i	$-0.436167\pi$
$113$	4.23499			0.398395			0.199197	+	0.979959i	$0.436167\pi$
$114$	2.04044	+	0.453298i	0.191105	+	0.0424552i
$115$		0			0
$116$	5.52187	−	4.63340i	0.512693	−	0.430200i
$117$	−3.03017	−	1.10289i	−0.280139	−	0.101962i
$118$	−0.706178	+	4.00494i	−0.0650090	+	0.368684i
$119$	0.265402	+	1.50517i	0.0243293	+	0.137978i
$120$		0			0
$121$	−4.98166	+	8.62850i	−0.452879	+	0.784409i
$122$	−2.58584	−	4.47881i	−0.234111	−	0.405492i
$123$	4.63036	+	3.88533i	0.417505	+	0.350329i
$124$	5.23037	+	4.38880i	0.469701	+	0.394126i
$125$		0			0
$126$	−2.02779	+	3.51223i	−0.180650	+	0.312895i
$127$	−17.1659	+	6.24787i	−1.52323	+	0.554409i	−0.961951	−	0.273221i	$-0.911911\pi$
$127$	−17.1659	+	6.24787i	−1.52323	+	0.554409i	−0.561274	+	0.827630i	$0.689689\pi$
$128$	1.86510	+	10.5775i	0.164853	+	0.934928i
$129$	−1.15688	+	6.56100i	−0.101858	+	0.577664i
$130$		0			0
$131$	6.43888	−	5.40286i	0.562568	−	0.472050i	−0.316602	−	0.948558i	$-0.602542\pi$
$131$	6.43888	−	5.40286i	0.562568	−	0.472050i	0.879170	+	0.476508i	$0.158098\pi$
$132$	−4.84769			−0.421937
$133$	−9.02871	+	4.69500i	−0.782888	+	0.407108i
$134$	9.01302			0.778607
$135$		0			0
$136$	−1.49596	−	0.544487i	−0.128278	−	0.0466894i
$137$	2.05932	−	11.6790i	0.175940	−	0.997804i	−0.761114	−	0.648618i	$-0.775347\pi$
$137$	2.05932	−	11.6790i	0.175940	−	0.997804i	0.937054	−	0.349186i	$-0.113542\pi$
$138$	−0.463527	−	2.62879i	−0.0394581	−	0.223778i
$139$	−0.0351557	+	0.0127956i	−0.00298187	+	0.00108531i	−0.343511	−	0.939149i	$-0.611616\pi$
$139$	−0.0351557	+	0.0127956i	−0.00298187	+	0.00108531i	0.340529	+	0.940234i	$0.389394\pi$
$140$		0			0
$141$	2.19814	+	3.80729i	0.185117	+	0.320632i
$142$	−1.98329	−	1.66417i	−0.166434	−	0.139654i
$143$	−4.49315	−	3.77020i	−0.375736	−	0.315280i
$144$	1.72341	+	2.98503i	0.143617	+	0.248752i
$145$		0			0
$146$	−5.16445	+	1.87971i	−0.427413	+	0.155566i
$147$	−0.186955	−	1.06028i	−0.0154198	−	0.0874500i
$148$	2.06187	−	11.6935i	0.169485	−	0.961197i
$149$	9.11593	+	3.31793i	0.746806	+	0.271815i	0.687261	−	0.726410i	$-0.258813\pi$
$149$	9.11593	+	3.31793i	0.746806	+	0.271815i	0.0595451	+	0.998226i	$0.481035\pi$
$150$		0			0
$151$	4.60766			0.374966			0.187483	−	0.982268i	$-0.439967\pi$
$151$	4.60766			0.374966			0.187483	+	0.982268i	$0.439967\pi$
$152$	0.467022	−	10.5895i	0.0378805	−	0.858926i
$153$	−1.64789			−0.133224
$154$	−5.65096	+	4.74172i	−0.455367	+	0.382098i
$155$		0			0
$156$	0.235527	−	1.33574i	0.0188573	−	0.106945i
$157$	3.54300	+	20.0934i	0.282762	+	1.60362i	0.713171	+	0.700990i	$0.247258\pi$
$157$	3.54300	+	20.0934i	0.282762	+	1.60362i	−0.430409	+	0.902634i	$0.641631\pi$
$158$	4.09163	−	1.48923i	0.325512	−	0.118477i
$159$	2.29353	−	3.97252i	0.181889	−	0.315041i
$160$		0			0
$161$	9.95568	+	8.35381i	0.784618	+	0.658373i
$162$	−2.58394	−	2.16818i	−0.203013	−	0.170348i
$163$	−1.89681	−	3.28537i	−0.148569	−	0.257330i	0.782130	−	0.623116i	$-0.214134\pi$
$163$	−1.89681	−	3.28537i	−0.148569	−	0.257330i	−0.930699	+	0.365786i	$0.880800\pi$
$164$	6.62756	−	11.4793i	0.517525	−	0.896380i
$165$		0			0
$166$	−1.17882	−	6.68544i	−0.0914944	−	0.518890i
$167$	−2.69126	+	15.2629i	−0.208256	+	1.18108i	0.683977	+	0.729504i	$0.260249\pi$
$167$	−2.69126	+	15.2629i	−0.208256	+	1.18108i	−0.892233	+	0.451576i	$0.850862\pi$
$168$	−3.70697	−	1.34923i	−0.285999	−	0.104095i
$169$	−8.70143	+	7.30137i	−0.669341	+	0.561643i
$170$		0			0
$171$	−3.29478	−	10.4658i	−0.251958	−	0.800338i
$172$	14.6097			1.11398
$173$	−12.9585	+	10.8734i	−0.985214	+	0.826693i	−0.984868	−	0.173307i	$-0.944555\pi$
$173$	−12.9585	+	10.8734i	−0.985214	+	0.826693i	−0.000346094		1.00000i	$0.500110\pi$
$174$	−2.13163	−	0.775851i	−0.161599	−	0.0588171i
$175$		0			0
$176$	1.08869	+	6.17425i	0.0820629	+	0.465402i
$177$	−3.84772	+	1.40046i	−0.289212	+	0.105265i
$178$	4.20220	−	7.27843i	0.314968	−	0.545541i
$179$	−1.52632	−	2.64366i	−0.114082	−	0.197597i	0.803330	−	0.595534i	$-0.203059\pi$
$179$	−1.52632	−	2.64366i	−0.114082	−	0.197597i	−0.917413	+	0.397937i	$0.869726\pi$
$180$		0			0
$181$	−18.7574	−	15.7394i	−1.39423	−	1.16990i	−0.963594	−	0.267371i	$-0.913845\pi$
$181$	−18.7574	−	15.7394i	−1.39423	−	1.16990i	−0.430636	−	0.902526i	$-0.641711\pi$
$182$	−1.03199	−	1.78745i	−0.0764960	−	0.132495i
$183$	2.60361	−	4.50958i	0.192464	−	0.333357i
$184$	−12.7205	+	4.62989i	−0.937770	+	0.341320i
$185$		0			0
$186$	0.373115	−	2.11604i	0.0273582	−	0.155156i
$187$	−2.81662	−	1.02517i	−0.205972	−	0.0749677i
$188$	7.38520	−	6.19692i	0.538621	−	0.451957i
$189$	−8.95012			−0.651025
$190$		0			0
$191$	−1.69095			−0.122353			−0.0611765	−	0.998127i	$-0.519485\pi$
$191$	−1.69095			−0.122353			−0.0611765	+	0.998127i	$0.519485\pi$
$192$	0.675940	−	0.567181i	0.0487817	−	0.0409327i
$193$	16.7180	+	6.08486i	1.20339	+	0.437997i	0.864406	−	0.502795i	$-0.167695\pi$
$193$	16.7180	+	6.08486i	1.20339	+	0.437997i	0.338983	+	0.940793i	$0.389917\pi$
$194$	0.504479	−	2.86104i	0.0362195	−	0.205411i
$195$		0			0
$196$	−2.21858	+	0.807498i	−0.158470	+	0.0576785i
$197$	7.25076	−	12.5587i	0.516595	−	0.894769i	−0.483219	−	0.875499i	$-0.660533\pi$
$197$	7.25076	−	12.5587i	0.516595	−	0.894769i	0.999814	−	0.0192697i	$-0.00613411\pi$
$198$	−3.97679	−	6.88800i	−0.282618	−	0.489509i
$199$	−9.21831	−	7.73508i	−0.653469	−	0.548325i	0.254652	−	0.967033i	$-0.418039\pi$
$199$	−9.21831	−	7.73508i	−0.653469	−	0.548325i	−0.908121	+	0.418707i	$0.862483\pi$
$200$		0			0
$201$	4.53747	+	7.85913i	0.320049	+	0.554340i
$202$	−0.0196923	+	0.0341081i	−0.00138555	+	0.00239984i
$203$	10.3783	−	3.77738i	0.728411	−	0.265120i
$204$	−0.120362	−	0.682604i	−0.00842699	−	0.0477919i
$205$		0			0
$206$	−4.69728	−	1.70967i	−0.327275	−	0.119118i
$207$	−10.7341	+	9.00698i	−0.746072	+	0.626028i
$208$	−1.75416			−0.121629
$209$	0.879316	−	19.9382i	0.0608235	−	1.37915i
$210$		0			0
$211$	6.18615	−	5.19079i	0.425872	−	0.357349i	−0.404520	−	0.914529i	$-0.632561\pi$
$211$	6.18615	−	5.19079i	0.425872	−	0.357349i	0.830391	+	0.557180i	$0.188117\pi$
$212$	−9.45244	−	3.44041i	−0.649196	−	0.236288i
$213$	0.452663	−	2.56718i	0.0310160	−	0.175900i
$214$	1.78076	+	10.0992i	0.121730	+	0.690366i
$215$		0			0
$216$	4.66123	−	8.07349i	0.317157	−	0.549332i
$217$	5.23064	+	9.05974i	0.355079	+	0.615015i
$218$	7.09407	+	5.95263i	0.480471	+	0.403163i
$219$	−4.23902	−	3.55696i	−0.286446	−	0.240357i
$220$		0			0
$221$	0.419324	−	0.726290i	0.0282068	−	0.0488556i
$222$	−3.51133	+	1.27802i	−0.235665	+	0.0857752i
$223$	−2.63587	−	14.9488i	−0.176511	−	1.00104i	−0.936385	−	0.350974i	$-0.885851\pi$
$223$	−2.63587	−	14.9488i	−0.176511	−	1.00104i	0.759874	−	0.650070i	$-0.225261\pi$
$224$	−2.35481	+	13.3548i	−0.157337	+	0.892304i
$225$		0			0
$226$	−2.23885	+	1.87862i	−0.148926	+	0.124964i
$227$	20.9433			1.39005			0.695026	−	0.718984i	$-0.255393\pi$
$227$	20.9433			1.39005			0.695026	+	0.718984i	$0.255393\pi$
$228$	4.09458	−	2.12921i	0.271170	−	0.141011i
$229$	28.1530			1.86040			0.930200	−	0.367054i	$-0.119633\pi$
$229$	28.1530			1.86040			0.930200	+	0.367054i	$0.119633\pi$
$230$		0			0
$231$	−6.97955	−	2.54035i	−0.459220	−	0.167143i
$232$	−1.99761	+	11.3290i	−0.131150	+	0.743787i
$233$	−3.62673	−	20.5682i	−0.237595	−	1.34747i	−0.837079	−	0.547083i	$-0.815738\pi$
$233$	−3.62673	−	20.5682i	−0.237595	−	1.34747i	0.599483	−	0.800387i	$-0.295373\pi$
$234$	2.09115	−	0.761116i	0.136703	−	0.0497557i
$235$		0			0
$236$	4.48963	+	7.77626i	0.292250	+	0.506192i
$237$	3.35844	+	2.81806i	0.218154	+	0.183053i
$238$	−0.807988	−	0.677982i	−0.0523741	−	0.0439471i
$239$	0.619806	+	1.07353i	0.0400919	+	0.0694412i	0.885375	−	0.464877i	$-0.153902\pi$
$239$	0.619806	+	1.07353i	0.0400919	+	0.0694412i	−0.845283	+	0.534319i	$0.820568\pi$
$240$		0			0
$241$	−1.10023	+	0.400452i	−0.0708723	+	0.0257954i	−0.377213	−	0.926127i	$-0.623118\pi$
$241$	−1.10023	+	0.400452i	−0.0708723	+	0.0257954i	0.306341	+	0.951922i	$0.400895\pi$
$242$	−1.19397	−	6.77132i	−0.0767511	−	0.435277i
$243$	2.58685	−	14.6708i	0.165947	−	0.941131i
$244$	−10.7303	−	3.90553i	−0.686940	−	0.250026i
$245$		0			0
$246$	−4.17137			−0.265957
$247$	5.45108	+	1.21099i	0.346844	+	0.0770537i
$248$	−10.8965			−0.691929
$249$	5.23607	−	4.39359i	0.331823	−	0.278432i
$250$		0			0
$251$	3.81928	−	21.6602i	0.241071	−	1.36718i	−0.588373	−	0.808589i	$-0.700231\pi$
$251$	3.81928	−	21.6602i	0.241071	−	1.36718i	0.829444	−	0.558590i	$-0.188657\pi$
$252$	1.55496	+	8.81862i	0.0979533	+	0.555521i
$253$	−23.9504	+	8.71723i	−1.50575	+	0.548048i
$254$	6.30330	−	10.9176i	0.395504	−	0.685033i
$255$		0			0
$256$	−7.62367	−	6.39702i	−0.476480	−	0.399814i
$257$	−12.7665	−	10.7123i	−0.796350	−	0.668217i	0.150959	−	0.988540i	$-0.451764\pi$
$257$	−12.7665	−	10.7123i	−0.796350	−	0.668217i	−0.947308	+	0.320323i	$0.896208\pi$
$258$	−2.29883	−	3.98168i	−0.143119	−	0.247889i
$259$	9.09637	−	15.7554i	0.565221	−	0.978992i
$260$		0			0
$261$	2.06778	+	11.7269i	0.127992	+	0.725879i
$262$	−1.00727	+	5.71249i	−0.0622291	+	0.352919i
$263$	−4.06239	−	1.47859i	−0.250498	−	0.0911737i	0.213720	−	0.976895i	$-0.431442\pi$
$263$	−4.06239	−	1.47859i	−0.250498	−	0.0911737i	−0.464217	+	0.885721i	$0.653664\pi$
$264$	5.92649	−	4.97292i	0.364750	−	0.306062i
$265$		0			0
$266$	2.69039	−	6.48710i	0.164959	−	0.397750i
$267$	8.46214			0.517875
$268$	15.2448	−	12.7919i	0.931222	−	0.781388i
$269$	22.8324	+	8.31030i	1.39211	+	0.506688i	0.925828	−	0.377946i	$-0.123369\pi$
$269$	22.8324	+	8.31030i	1.39211	+	0.506688i	0.466286	+	0.884634i	$0.345592\pi$
$270$		0			0
$271$	−1.42694	−	8.09260i	−0.0866807	−	0.491591i	−0.996981	−	0.0776427i	$-0.975261\pi$
$271$	−1.42694	−	8.09260i	−0.0866807	−	0.491591i	0.910301	−	0.413948i	$-0.135850\pi$
$272$	−0.842368	+	0.306597i	−0.0510760	+	0.0185902i
$273$	1.03908	−	1.79973i	0.0628878	−	0.108925i
$274$	4.09206	+	7.08765i	0.247210	+	0.428181i
$275$		0			0
$276$	−4.51497	−	3.78851i	−0.271770	−	0.228042i
$277$	9.66010	+	16.7318i	0.580419	+	1.00532i	0.995430	+	0.0954986i	$0.0304446\pi$
$277$	9.66010	+	16.7318i	0.580419	+	1.00532i	−0.415011	+	0.909817i	$0.636222\pi$
$278$	0.0129091	−	0.0223593i	0.000774239	−	0.00134102i
$279$	−10.5990	+	3.85773i	−0.634546	+	0.230956i
$280$		0			0
$281$	1.37960	−	7.82413i	0.0823003	−	0.466748i	−0.915606	−	0.402076i	$-0.868289\pi$
$281$	1.37960	−	7.82413i	0.0823003	−	0.466748i	0.997907	−	0.0646721i	$-0.0206002\pi$
$282$	−2.85095	−	1.03766i	−0.169771	−	0.0617917i
$283$	12.9560	−	10.8714i	0.770154	−	0.646236i	−0.170594	−	0.985341i	$-0.554569\pi$
$283$	12.9560	−	10.8714i	0.770154	−	0.646236i	0.940748	+	0.339105i	$0.110124\pi$
$284$	−5.71646			−0.339210
$285$		0			0
$286$	4.04775			0.239349
$287$	15.5577	−	13.0544i	0.918339	−	0.770578i
$288$	−13.7393	−	5.00071i	−0.809599	−	0.294670i
$289$	−2.87760	+	16.3197i	−0.169270	+	0.959981i
$290$		0			0
$291$	2.74873	−	1.00046i	0.161133	−	0.0586478i
$292$	−6.06742	+	10.5091i	−0.355069	+	0.614998i
$293$	−2.41533	−	4.18348i	−0.141105	−	0.244402i	0.786808	−	0.617198i	$-0.211732\pi$
$293$	−2.41533	−	4.18348i	−0.141105	−	0.244402i	−0.927913	+	0.372797i	$0.878399\pi$
$294$	0.569166	+	0.477587i	0.0331944	+	0.0278534i
$295$		0			0
$296$	9.47481	+	16.4109i	0.550712	+	0.953861i
$297$	8.77624	−	15.2009i	0.509249	−	0.882045i
$298$	−6.29099	+	2.28973i	−0.364427	+	0.132641i
$299$	−1.23832	−	7.02287i	−0.0716140	−	0.406143i
$300$		0			0
$301$	21.0346	+	7.65596i	1.21241	+	0.441282i
$302$	−2.43586	+	2.04393i	−0.140168	+	0.117615i
$303$	−0.0396552			−0.00227813
$304$	−3.63143	−	4.73689i	−0.208277	−	0.271679i
$305$		0			0
$306$	0.871163	−	0.730993i	0.0498011	−	0.0417881i
$307$	−5.78211	−	2.10452i	−0.330003	−	0.120111i	0.171705	−	0.985148i	$-0.445072\pi$
$307$	−5.78211	−	2.10452i	−0.330003	−	0.120111i	−0.501708	+	0.865037i	$0.667295\pi$
$308$	−2.82836	+	16.0404i	−0.161161	+	0.913988i
$309$	−0.873985	−	4.95662i	−0.0497193	−	0.281972i
$310$		0			0
$311$	−1.43076	+	2.47815i	−0.0811311	+	0.140523i	−0.903736	−	0.428090i	$-0.859187\pi$
$311$	−1.43076	+	2.47815i	−0.0811311	+	0.140523i	0.822605	+	0.568613i	$0.192520\pi$
$312$	1.08231	+	1.87461i	0.0612735	+	0.106129i
$313$	4.96486	+	4.16601i	0.280630	+	0.235477i	0.772228	−	0.635346i	$-0.219142\pi$
$313$	4.96486	+	4.16601i	0.280630	+	0.235477i	−0.491597	+	0.870823i	$0.663587\pi$
$314$	−10.7863	−	9.05078i	−0.608706	−	0.510765i
$315$		0			0
$316$	4.80702	−	8.32601i	0.270416	−	0.468375i
$317$	−29.1565	+	10.6121i	−1.63759	+	0.596034i	−0.986615	−	0.163065i	$-0.947862\pi$
$317$	−29.1565	+	10.6121i	−1.63759	+	0.596034i	−0.650975	+	0.759099i	$0.725640\pi$
$318$	0.549697	+	3.11748i	0.0308255	+	0.174820i
$319$	−3.76113	+	21.3304i	−0.210583	+	1.19428i
$320$		0			0
$321$	−7.90974	+	6.63706i	−0.441479	+	0.370445i
$322$	−8.96881			−0.499812
$323$	2.82933	−	0.371221i	0.157428	−	0.0206553i
$324$	−7.44773			−0.413763
$325$		0			0
$326$	2.46012	+	0.895411i	0.136254	+	0.0495922i
$327$	−1.61914	+	9.18261i	−0.0895388	+	0.507800i
$328$	3.67335	+	20.8326i	0.202827	+	1.15029i
$329$	13.8804	−	5.05204i	0.765249	−	0.278528i
$330$		0			0
$331$	−8.80238	−	15.2462i	−0.483823	−	0.838005i	0.516005	−	0.856586i	$-0.327419\pi$
$331$	−8.80238	−	15.2462i	−0.483823	−	0.838005i	−0.999827	+	0.0185804i	$0.994085\pi$
$332$	−11.4823	−	9.63478i	−0.630172	−	0.528777i
$333$	15.0261	+	12.6084i	0.823426	+	0.690937i
$334$	−5.34778	−	9.26262i	−0.292617	−	0.506828i
$335$		0			0
$336$	−2.08737	+	0.759741i	−0.113876	+	0.0414473i
$337$	−4.80448	−	27.2476i	−0.261717	−	1.48427i	−0.778224	−	0.627987i	$-0.783879\pi$
$337$	−4.80448	−	27.2476i	−0.261717	−	1.48427i	0.516507	−	0.856283i	$-0.327232\pi$
$338$	1.36121	−	7.71979i	0.0740399	−	0.419901i
$339$	−2.76522	−	1.00646i	−0.150186	−	0.0546633i
$340$		0			0
$341$	−20.5161			−1.11101
$342$	6.38435	+	4.07123i	0.345226	+	0.220147i
$343$	−19.9599			−1.07773
$344$	−17.8609	+	14.9871i	−0.962997	+	0.808050i
$345$		0			0
$346$	2.02716	−	11.4966i	0.108981	−	0.618060i
$347$	3.69547	+	20.9581i	0.198383	+	1.12509i	0.907517	+	0.420014i	$0.137975\pi$
$347$	3.69547	+	20.9581i	0.198383	+	1.12509i	−0.709134	+	0.705074i	$0.750914\pi$
$348$	−4.70662	+	1.71307i	−0.252301	+	0.0918301i
$349$	−9.82495	+	17.0173i	−0.525917	+	0.910916i	0.473627	+	0.880726i	$0.342945\pi$
$349$	−9.82495	+	17.0173i	−0.525917	+	0.910916i	−0.999544	+	0.0301899i	$0.990389\pi$
$350$		0			0
$351$	3.76209	+	3.15677i	0.200805	+	0.168496i
$352$	−20.3727	−	17.0948i	−1.08587	−	0.911153i
$353$	3.23301	+	5.59974i	0.172076	+	0.298044i	0.939145	−	0.343520i	$-0.111619\pi$
$353$	3.23301	+	5.59974i	0.172076	+	0.298044i	−0.767070	+	0.641564i	$0.778286\pi$
$354$	1.41288	−	2.44718i	0.0750937	−	0.130066i
$355$		0			0
$356$	−3.22236	−	18.2749i	−0.170784	−	0.968567i
$357$	0.184414	−	1.04587i	0.00976024	−	0.0553530i
$358$	1.97960	+	0.720517i	0.104625	+	0.0380805i
$359$	−14.8577	+	12.4671i	−0.784159	+	0.657988i	−0.944292	−	0.329108i	$-0.893252\pi$
$359$	−14.8577	+	12.4671i	−0.784159	+	0.657988i	0.160133	+	0.987095i	$0.448808\pi$
$360$		0			0
$361$	8.01458	+	17.2269i	0.421820	+	0.906680i
$362$	16.8981			0.888143
$363$	5.30334	−	4.45003i	0.278353	−	0.233566i
$364$	−4.28239	−	1.55866i	−0.224458	−	0.0816961i
$365$		0			0
$366$	0.624012	+	3.53895i	0.0326176	+	0.184984i
$367$	28.2213	−	10.2717i	1.47314	−	0.536179i	0.524189	−	0.851602i	$-0.324368\pi$
$367$	28.2213	−	10.2717i	1.47314	−	0.536179i	0.948951	+	0.315423i	$0.102146\pi$
$368$	−3.81127	+	6.60131i	−0.198676	+	0.344117i
$369$	10.9485	+	18.9634i	0.569956	+	0.987193i
$370$		0			0
$371$	−11.8064	−	9.90678i	−0.612960	−	0.514334i
$372$	−2.37213	−	4.10866i	−0.122989	−	0.213024i
$373$	−2.47898	+	4.29372i	−0.128357	+	0.222320i	−0.923040	−	0.384704i	$-0.874304\pi$
$373$	−2.47898	+	4.29372i	−0.128357	+	0.222320i	0.794683	+	0.607024i	$0.207637\pi$
$374$	1.94378	−	0.707477i	0.100510	−	0.0365828i
$375$		0			0
$376$	−2.67170	+	15.1520i	−0.137782	+	0.781403i
$377$	−5.69470	−	2.07270i	−0.293292	−	0.106749i
$378$	4.73151	−	3.97021i	0.243363	−	0.204206i
$379$	−4.05839			−0.208465			−0.104233	−	0.994553i	$-0.533239\pi$
$379$	−4.05839			−0.208465			−0.104233	+	0.994553i	$0.533239\pi$
$380$		0			0
$381$	12.6932			0.650292
$382$	0.893928	−	0.750095i	0.0457374	−	0.0383782i
$383$	−2.26407	−	0.824054i	−0.115689	−	0.0421072i	0.283527	−	0.958964i	$-0.408495\pi$
$383$	−2.26407	−	0.824054i	−0.115689	−	0.0421072i	−0.399216	+	0.916857i	$0.630718\pi$
$384$	1.29596	−	7.34977i	0.0661344	−	0.375067i
$385$		0			0
$386$	−11.5372	+	4.19921i	−0.587230	+	0.213734i
$387$	−12.0674	+	20.9013i	−0.613419	+	1.06247i
$388$	−3.20730	−	5.55520i	−0.162826	−	0.282023i
$389$	−4.57546	−	3.83927i	−0.231985	−	0.194659i	0.519384	−	0.854541i	$-0.326162\pi$
$389$	−4.57546	−	3.83927i	−0.231985	−	0.194659i	−0.751369	+	0.659883i	$0.770606\pi$
$390$		0			0
$391$	−1.82213	−	3.15602i	−0.0921492	−	0.159607i
$392$	1.88395	−	3.26309i	0.0951537	−	0.164811i
$393$	−5.48824	+	1.99756i	−0.276845	+	0.100763i
$394$	1.73781	+	9.85559i	0.0875494	+	0.496517i
$395$		0			0
$396$	−16.5023	−	6.00635i	−0.829272	−	0.301830i
$397$	21.7311	−	18.2346i	1.09065	−	0.915168i	0.0938929	−	0.995582i	$-0.470069\pi$
$397$	21.7311	−	18.2346i	1.09065	−	0.915168i	0.996762	+	0.0804146i	$0.0256244\pi$
$398$	8.30453			0.416268
$399$	7.01103	−	0.919879i	0.350990	−	0.0460515i
$400$		0			0
$401$	−24.0310	+	20.1644i	−1.20005	+	1.00696i	−0.200421	+	0.979710i	$0.564231\pi$
$401$	−24.0310	+	20.1644i	−1.20005	+	1.00696i	−0.999629	+	0.0272515i	$0.991325\pi$
$402$	−5.88501	−	2.14197i	−0.293518	−	0.106832i
$403$	0.996785	−	5.65305i	0.0496534	−	0.281598i
$404$	0.0151006	+	0.0856396i	0.000751282	+	0.00426073i
$405$		0			0
$406$	−3.81089	+	6.60065i	−0.189131	+	0.327585i
$407$	17.8393	+	30.8986i	0.884262	+	1.53159i
$408$	0.847384	+	0.711040i	0.0419518	+	0.0352017i
$409$	−22.8163	−	19.1452i	−1.12820	−	0.946669i	−0.129207	−	0.991618i	$-0.541243\pi$
$409$	−22.8163	−	19.1452i	−1.12820	−	0.946669i	−0.998989	+	0.0449489i	$0.985687\pi$
$410$		0			0
$411$	−4.12017	+	7.13634i	−0.203233	+	0.352010i
$412$	−10.3715	+	3.77493i	−0.510968	+	0.185977i
$413$	2.38901	+	13.5487i	0.117555	+	0.666689i
$414$	1.67919	−	9.52315i	0.0825276	−	0.468037i
$415$		0			0
$416$	5.70014	−	4.78299i	0.279472	−	0.234505i
$417$	0.0259957			0.00127301
$418$	8.37958	+	10.9304i	0.409859	+	0.534626i
$419$	35.7692			1.74744			0.873719	−	0.486431i	$-0.161702\pi$
$419$	35.7692			1.74744			0.873719	+	0.486431i	$0.161702\pi$
$420$		0			0
$421$	35.7451	+	13.0102i	1.74211	+	0.634077i	0.999370	−	0.0355017i	$-0.0113029\pi$
$421$	35.7451	+	13.0102i	1.74211	+	0.634077i	0.742741	+	0.669578i	$0.233525\pi$
$422$	−0.967730	+	5.48827i	−0.0471083	+	0.267165i
$423$	2.76554	+	15.6842i	0.134465	+	0.762590i
$424$	15.0853	−	5.49059i	0.732605	−	0.266646i
$425$		0			0
$426$	0.899482	+	1.55795i	0.0435800	+	0.0754828i
$427$	−13.4026	−	11.2461i	−0.648597	−	0.544237i
$428$	17.3454	+	14.5545i	0.838423	+	0.703521i
$429$	2.03778	+	3.52954i	0.0983850	+	0.170408i
$430$		0			0
$431$	7.88210	−	2.86885i	0.379667	−	0.138188i	−0.145135	−	0.989412i	$-0.546362\pi$
$431$	7.88210	−	2.86885i	0.379667	−	0.138188i	0.524802	+	0.851224i	$0.324139\pi$
$432$	−0.911552	−	5.16967i	−0.0438571	−	0.248726i
$433$	−4.03137	+	22.8630i	−0.193735	+	1.09873i	0.720474	+	0.693482i	$0.243924\pi$
$433$	−4.03137	+	22.8630i	−0.193735	+	1.09873i	−0.914209	+	0.405244i	$0.867187\pi$
$434$	−6.78404	−	2.46919i	−0.325644	−	0.118525i
$435$		0			0
$436$	20.4474			0.979252
$437$	16.4008	−	17.8825i	0.784558	−	0.855438i
$438$	3.81882			0.182470
$439$	13.5703	−	11.3869i	0.647677	−	0.543465i	−0.258688	−	0.965961i	$-0.583290\pi$
$439$	13.5703	−	11.3869i	0.647677	−	0.543465i	0.906365	+	0.422495i	$0.138846\pi$
$440$		0			0
$441$	0.677269	−	3.84099i	0.0322509	−	0.182904i
$442$	0.100500	+	0.569965i	0.00478031	+	0.0271105i
$443$	1.67598	−	0.610008i	0.0796283	−	0.0289823i	−0.301899	−	0.953340i	$-0.597620\pi$
$443$	1.67598	−	0.610008i	0.0796283	−	0.0289823i	0.381527	+	0.924358i	$0.375398\pi$
$444$	−4.12527	+	7.14518i	−0.195777	+	0.339095i
$445$		0			0
$446$	8.02464	+	6.73348i	0.379978	+	0.318839i
$447$	−5.16369	−	4.33285i	−0.244234	−	0.204937i
$448$	−1.48236	−	2.56752i	−0.0700349	−	0.121304i
$449$	−4.42844	+	7.67028i	−0.208991	+	0.361983i	−0.951397	−	0.307967i	$-0.900351\pi$
$449$	−4.42844	+	7.67028i	−0.208991	+	0.361983i	0.742406	+	0.669950i	$0.233685\pi$
$450$		0			0
$451$	6.91624	+	39.2240i	0.325673	+	1.84698i
$452$	−1.12056	+	6.35504i	−0.0527069	+	0.298916i
$453$	−3.00855	−	1.09502i	−0.141354	−	0.0514486i
$454$	−11.0717	+	9.29029i	−0.519622	+	0.436015i
$455$		0			0
$456$	−2.82157	+	6.80341i	−0.132132	+	0.318599i
$457$	−3.00530			−0.140582			−0.0702909	−	0.997527i	$-0.522393\pi$
$457$	−3.00530			−0.140582			−0.0702909	+	0.997527i	$0.522393\pi$
$458$	−14.8832	+	12.4885i	−0.695445	+	0.583548i
$459$	2.35834	+	0.858367i	0.110078	+	0.0400651i
$460$		0			0
$461$	3.49320	+	19.8109i	0.162695	+	0.922686i	0.951410	+	0.307928i	$0.0996355\pi$
$461$	3.49320	+	19.8109i	0.162695	+	0.922686i	−0.788715	+	0.614759i	$0.789253\pi$
$462$	4.81665	−	1.75312i	0.224091	−	0.0815623i
$463$	4.07718	−	7.06188i	0.189483	−	0.328194i	−0.755595	−	0.655039i	$-0.772652\pi$
$463$	4.07718	−	7.06188i	0.189483	−	0.328194i	0.945078	+	0.326845i	$0.105986\pi$
$464$	3.23885	+	5.60986i	0.150360	+	0.260431i
$465$		0			0
$466$	11.0412	+	9.26468i	0.511475	+	0.429178i
$467$	−3.07873	−	5.33252i	−0.142467	−	0.246759i	0.785958	−	0.618280i	$-0.212170\pi$
$467$	−3.07873	−	5.33252i	−0.142467	−	0.246759i	−0.928425	+	0.371520i	$0.878837\pi$
$468$	2.45677	−	4.25526i	0.113564	−	0.196699i
$469$	28.6523	−	10.4286i	1.32304	−	0.481547i
$470$		0			0
$471$	2.46185	−	13.9619i	0.113436	−	0.643328i
$472$	−13.4659	−	4.90118i	−0.619818	−	0.225595i
$473$	−33.6288	+	28.2179i	−1.54625	+	1.29746i
$474$	−3.02553			−0.138967
$475$		0			0
$476$	−2.32888			−0.106744
$477$	12.7296	−	10.6814i	0.582846	−	0.489066i
$478$	−0.803876	−	0.292587i	−0.0367684	−	0.0133826i
$479$	5.91976	−	33.5726i	0.270481	−	1.53397i	−0.482479	−	0.875907i	$-0.660264\pi$
$479$	5.91976	−	33.5726i	0.270481	−	1.53397i	0.752960	−	0.658066i	$-0.228625\pi$
$480$		0			0
$481$	−9.38059	+	3.41426i	−0.427718	+	0.155677i
$482$	0.404005	−	0.699757i	0.0184019	−	0.0318731i
$483$	−4.51521	−	7.82057i	−0.205449	−	0.355848i
$484$	−11.6298	−	9.75856i	−0.528627	−	0.443571i
$485$		0			0
$486$	5.14031	+	8.90328i	0.233169	+	0.403861i
$487$	14.2860	−	24.7441i	0.647360	−	1.12126i	−0.336391	−	0.941723i	$-0.609206\pi$
$487$	14.2860	−	24.7441i	0.647360	−	1.12126i	0.983751	−	0.179538i	$-0.0574604\pi$
$488$	17.1247	−	6.23288i	0.775198	−	0.282149i
$489$	0.457735	+	2.59595i	0.0206995	+	0.117393i
$490$		0			0
$491$	4.92500	+	1.79255i	0.222262	+	0.0808968i	0.450751	−	0.892650i	$-0.351156\pi$
$491$	4.92500	+	1.79255i	0.222262	+	0.0808968i	−0.228489	+	0.973547i	$0.573378\pi$
$492$	−7.05551	+	5.92028i	−0.318087	+	0.266907i
$493$	−3.09693			−0.139479
$494$	−3.41892	+	1.77787i	−0.153825	+	0.0799899i
$495$		0			0
$496$	−4.70026	+	3.94398i	−0.211048	+	0.177090i
$497$	−8.23038	−	2.99561i	−0.369183	−	0.134372i
$498$	−0.819105	+	4.64537i	−0.0367050	+	0.208164i
$499$	6.57832	+	37.3075i	0.294486	+	1.67011i	0.669284	+	0.743007i	$0.266601\pi$
$499$	6.57832	+	37.3075i	0.294486	+	1.67011i	−0.374798	+	0.927107i	$0.622288\pi$
$500$		0			0
$501$	5.38452	−	9.32626i	0.240562	−	0.416666i
$502$	7.58924	+	13.1450i	0.338725	+	0.586688i
$503$	−11.4325	−	9.59297i	−0.509748	−	0.427729i	0.351292	−	0.936266i	$-0.385742\pi$
$503$	−11.4325	−	9.59297i	−0.509748	−	0.427729i	−0.861040	+	0.508536i	$0.830187\pi$
$504$	−10.9474	−	9.18598i	−0.487637	−	0.409176i
$505$		0			0
$506$	8.79457	−	15.2326i	0.390966	−	0.677173i
$507$	7.41674	−	2.69947i	0.329389	−	0.119888i
$508$	−4.83353	−	27.4123i	−0.214453	−	1.21622i
$509$	−2.27541	+	12.9045i	−0.100856	+	0.571982i	0.891939	+	0.452156i	$0.149345\pi$
$509$	−2.27541	+	12.9045i	−0.100856	+	0.571982i	−0.992795	+	0.119826i	$0.961766\pi$
$510$		0			0
$511$	−14.2428	+	11.9511i	−0.630064	+	0.528686i
$512$	−14.6134			−0.645827
$513$	−0.736246	+	16.6941i	−0.0325061	+	0.737063i
$514$	11.5010			0.507285
$515$		0			0
$516$	−9.53933	−	3.47203i	−0.419946	−	0.152848i
$517$	−5.03031	+	28.5283i	−0.221233	+	1.25467i
$518$	2.18015	+	12.3642i	0.0957902	+	0.543253i
$519$	11.0453	−	4.02015i	0.484833	−	0.176465i
$520$		0			0
$521$	−2.05831	−	3.56509i	−0.0901761	−	0.156190i	0.817409	−	0.576058i	$-0.195410\pi$
$521$	−2.05831	−	3.56509i	−0.0901761	−	0.156190i	−0.907585	+	0.419868i	$0.862076\pi$
$522$	−6.29513	−	5.28224i	−0.275530	−	0.231197i
$523$	6.37125	+	5.34611i	0.278595	+	0.233769i	0.771369	−	0.636388i	$-0.219572\pi$
$523$	6.37125	+	5.34611i	0.278595	+	0.233769i	−0.492774	+	0.870158i	$0.664017\pi$
$524$	6.40384	+	11.0918i	0.279753	+	0.484546i
$525$		0			0
$526$	2.80349	−	1.02039i	0.122238	−	0.0444910i
$527$	−0.509387	−	2.88888i	−0.0221892	−	0.125841i
$528$	0.756474	−	4.29018i	0.0329213	−	0.186706i
$529$	−7.50627	−	2.73206i	−0.326360	−	0.118785i
$530$		0			0
$531$	−14.8334			−0.643716
$532$	−4.65635	−	14.7908i	−0.201878	−	0.641261i
$533$	−11.1439			−0.482695
$534$	−4.47355	+	3.75375i	−0.193589	+	0.162441i
$535$		0			0
$536$	−5.51500	+	31.2771i	−0.238212	+	1.35097i
$537$	0.368329	+	2.08890i	0.0158946	+	0.0901427i
$538$	−15.7568	+	5.73501i	−0.679325	+	0.247254i
$539$	3.54712	−	6.14380i	0.152785	−	0.264632i
$540$		0			0
$541$	−30.7437	−	25.7970i	−1.32177	−	1.10910i	−0.985926	−	0.167184i	$-0.946533\pi$
$541$	−30.7437	−	25.7970i	−1.32177	−	1.10910i	−0.335848	−	0.941916i	$-0.609023\pi$
$542$	4.34418	+	3.64520i	0.186599	+	0.156575i
$543$	8.50708	+	14.7347i	0.365074	+	0.632326i
$544$	1.90129	−	3.29313i	0.0815171	−	0.141192i
$545$		0			0
$546$	0.249038	+	1.41236i	0.0106578	+	0.0604436i
$547$	−4.40095	+	24.9590i	−0.188171	+	1.06717i	0.733642	+	0.679536i	$0.237819\pi$
$547$	−4.40095	+	24.9590i	−0.188171	+	1.06717i	−0.921813	+	0.387635i	$0.873292\pi$
$548$	16.9806	+	6.18044i	0.725376	+	0.264015i
$549$	14.4505	−	12.1254i	0.616733	−	0.517500i
$550$		0			0
$551$	−6.19199	−	19.6687i	−0.263787	−	0.837913i
$552$	9.40612			0.400351
$553$	11.2841	−	9.46848i	0.479849	−	0.402641i
$554$	−12.5290	−	4.56017i	−0.532304	−	0.193743i
$555$		0			0
$556$	−0.00989906	−	0.0561403i	−0.000419814	−	0.00238088i
$557$	10.9782	−	3.99573i	0.465160	−	0.169304i	−0.0987986	−	0.995107i	$-0.531500\pi$
$557$	10.9782	−	3.99573i	0.465160	−	0.169304i	0.563959	+	0.825803i	$0.309278\pi$
$558$	3.89195	−	6.74105i	0.164759	−	0.285372i
$559$	−6.14135	−	10.6371i	−0.259752	−	0.449903i
$560$		0			0
$561$	1.59547	+	1.33876i	0.0673607	+	0.0565223i
$562$	2.74140	+	4.74824i	0.115639	+	0.200292i
$563$	8.40055	−	14.5502i	0.354041	−	0.613217i	−0.632912	−	0.774223i	$-0.718141\pi$
$563$	8.40055	−	14.5502i	0.354041	−	0.613217i	0.986953	+	0.161007i	$0.0514741\pi$
$564$	−6.29485	+	2.29114i	−0.265061	+	0.0964742i
$565$		0			0
$566$	−2.02677	+	11.4944i	−0.0851916	+	0.483145i
$567$	−10.7230	−	3.90286i	−0.450324	−	0.163905i
$568$	6.98860	−	5.86414i	0.293235	−	0.246054i
$569$	−36.3784			−1.52506			−0.762530	−	0.646953i	$-0.776043\pi$
$569$	−36.3784			−1.52506			−0.762530	+	0.646953i	$0.776043\pi$
$570$		0			0
$571$	33.6369			1.40766			0.703831	−	0.710368i	$-0.251471\pi$
$571$	33.6369			1.40766			0.703831	+	0.710368i	$0.251471\pi$
$572$	6.84643	−	5.74484i	0.286264	−	0.240204i
$573$	1.10410	+	0.401859i	0.0461244	+	0.0167879i
$574$	−2.43376	+	13.8025i	−0.101583	+	0.576107i
$575$		0			0
$576$	3.00375	−	1.09328i	0.125156	−	0.0455532i
$577$	13.4247	−	23.2522i	0.558876	−	0.968002i	−0.438715	−	0.898626i	$-0.644566\pi$
$577$	13.4247	−	23.2522i	0.558876	−	0.968002i	0.997591	−	0.0693753i	$-0.0221006\pi$
$578$	−5.71804	−	9.90394i	−0.237839	−	0.411950i
$579$	−9.46986	−	7.94615i	−0.393554	−	0.330231i
$580$		0			0
$581$	−11.4829	−	19.8889i	−0.476390	−	0.825132i
$582$	−1.00933	+	1.74821i	−0.0418381	+	0.0724658i
$583$	28.4028	−	10.3378i	1.17632	−	0.428146i
$584$	−3.36290	−	19.0719i	−0.139158	−	0.789202i
$585$		0			0
$586$	3.13264	+	1.14019i	0.129408	+	0.0471007i
$587$	−13.1076	+	10.9986i	−0.541010	+	0.453962i	−0.871883	−	0.489714i	$-0.837101\pi$
$587$	−13.1076	+	10.9986i	−0.541010	+	0.453962i	0.330873	+	0.943675i	$0.392657\pi$
$588$	1.64052			0.0676538
$589$	17.3289	−	9.01113i	0.714023	−	0.371297i
$590$		0			0
$591$	−7.71895	+	6.47697i	−0.317515	+	0.266427i
$592$	10.0269	+	3.64949i	0.412103	+	0.149993i
$593$	7.07542	−	40.1267i	0.290553	−	1.64781i	−0.394196	−	0.919026i	$-0.628977\pi$
$593$	7.07542	−	40.1267i	0.290553	−	1.64781i	0.684749	−	0.728779i	$-0.259912\pi$
$594$	2.10342	+	11.9291i	0.0863044	+	0.489457i
$595$		0			0
$596$	−7.39093	+	12.8015i	−0.302744	+	0.524368i
$597$	4.18079	+	7.24134i	0.171108	+	0.296368i
$598$	3.76994	+	3.16336i	0.154164	+	0.129359i
$599$	9.21441	+	7.73181i	0.376490	+	0.315913i	0.811323	−	0.584598i	$-0.198748\pi$
$599$	9.21441	+	7.73181i	0.376490	+	0.315913i	−0.434832	+	0.900511i	$0.643192\pi$
$600$		0			0
$601$	6.29815	−	10.9087i	0.256907	−	0.444976i	−0.708505	−	0.705706i	$-0.750630\pi$
$601$	6.29815	−	10.9087i	0.256907	−	0.444976i	0.965412	+	0.260730i	$0.0839632\pi$
$602$	−14.5161	+	5.28344i	−0.591634	+	0.215337i
$603$	5.70871	+	32.3757i	0.232477	+	1.31844i
$604$	−1.21917	+	6.91426i	−0.0496073	+	0.281337i
$605$		0			0
$606$	0.0209639	−	0.0175908i	0.000851600	−	0.000714577i
$607$	−5.16663			−0.209707			−0.104854	−	0.994488i	$-0.533437\pi$
$607$	−5.16663			−0.209707			−0.104854	+	0.994488i	$0.533437\pi$
$608$	24.7162	+	5.49086i	1.00237	+	0.222684i
$609$	−7.67414			−0.310972
$610$		0			0
$611$	−7.61635	−	2.77213i	−0.308125	−	0.112148i
$612$	0.436025	−	2.47282i	0.0176253	−	0.0999580i
$613$	0.0704640	+	0.399621i	0.00284601	+	0.0161405i	0.986198	−	0.165572i	$-0.0529471\pi$
$613$	0.0704640	+	0.399621i	0.00284601	+	0.0161405i	−0.983352	+	0.181713i	$0.941836\pi$
$614$	3.99029	−	1.45235i	0.161035	−	0.0586119i
$615$		0			0
$616$	−12.9970	−	22.5115i	−0.523664	−	0.907013i
$617$	−7.69345	−	6.45557i	−0.309727	−	0.259892i	0.474652	−	0.880173i	$-0.342574\pi$
$617$	−7.69345	−	6.45557i	−0.309727	−	0.259892i	−0.784379	+	0.620282i	$0.787018\pi$
$618$	2.66076	+	2.23264i	0.107031	+	0.0898100i
$619$	8.16582	+	14.1436i	0.328212	+	0.568480i	0.982157	−	0.188062i	$-0.0602206\pi$
$619$	8.16582	+	14.1436i	0.328212	+	0.568480i	−0.653945	+	0.756542i	$0.726887\pi$
$620$		0			0
$621$	20.0535	−	7.29889i	0.804721	−	0.292894i
$622$	−0.342914	−	1.94476i	−0.0137496	−	0.0779779i
$623$	4.93719	−	28.0002i	0.197804	−	1.12180i
$624$	1.14537	+	0.416881i	0.0458515	+	0.0166886i
$625$		0			0
$626$	−4.47271			−0.178765
$627$	−5.31250	+	12.8095i	−0.212161	+	0.511564i
$628$	−31.0896			−1.24061
$629$	−3.90791	+	3.27913i	−0.155819	+	0.130747i
$630$		0			0
$631$	0.803192	−	4.55513i	0.0319746	−	0.181337i	−0.964638	−	0.263579i	$-0.915097\pi$
$631$	0.803192	−	4.55513i	0.0319746	−	0.181337i	0.996612	+	0.0822422i	$0.0262081\pi$
$632$	2.66431	+	15.1101i	0.105981	+	0.601046i
$633$	−5.27282	+	1.91915i	−0.209576	+	0.0762793i
$634$	10.7062	−	18.5437i	0.425199	−	0.736466i
$635$		0			0
$636$	5.35430	+	4.49279i	0.212312	+	0.178151i
$637$	1.52054	+	1.27588i	0.0602458	+	0.0505523i
$638$	−7.47371	−	12.9448i	−0.295887	−	0.512491i
$639$	4.72170	−	8.17823i	0.186788	−	0.323526i
$640$		0			0
$641$	−4.67772	−	26.5287i	−0.184759	−	1.04782i	−0.926265	−	0.376873i	$-0.876999\pi$
$641$	−4.67772	−	26.5287i	−0.184759	−	1.04782i	0.741506	−	0.670946i	$-0.234112\pi$
$642$	1.23736	−	7.01742i	0.0488347	−	0.276955i
$643$	−5.70932	−	2.07802i	−0.225154	−	0.0819492i	0.226980	−	0.973899i	$-0.427115\pi$
$643$	−5.70932	−	2.07802i	−0.225154	−	0.0819492i	−0.452134	+	0.891950i	$0.649337\pi$
$644$	−15.1700	+	12.7291i	−0.597781	+	0.501598i
$645$		0			0
$646$	−1.33107	+	1.45132i	−0.0523701	+	0.0571014i
$647$	14.8936			0.585529			0.292765	−	0.956185i	$-0.405425\pi$
$647$	14.8936			0.585529			0.292765	+	0.956185i	$0.405425\pi$
$648$	9.10515	−	7.64013i	0.357684	−	0.300133i
$649$	−25.3538	−	9.22802i	−0.995223	−	0.362231i
$650$		0			0
$651$	−1.26225	−	7.15859i	−0.0494716	−	0.280567i
$652$	5.43191	−	1.97705i	0.212730	−	0.0774274i
$653$	2.52297	−	4.36991i	0.0987315	−	0.171008i	−0.812428	−	0.583061i	$-0.801855\pi$
$653$	2.52297	−	4.36991i	0.0987315	−	0.171008i	0.911160	+	0.412053i	$0.135188\pi$
$654$	−3.21738	−	5.57267i	−0.125810	−	0.217908i
$655$		0			0
$656$	9.12487	+	7.65668i	0.356266	+	0.298943i
$657$	−10.0232	−	17.3607i	−0.391042	−	0.677304i
$658$	−5.09686	+	8.82802i	−0.198696	+	0.344152i
$659$	−29.7179	+	10.8164i	−1.15764	+	0.421348i	−0.848256	−	0.529587i	$-0.822347\pi$
$659$	−29.7179	+	10.8164i	−1.15764	+	0.421348i	−0.309389	+	0.950935i	$0.600125\pi$
$660$		0			0
$661$	−1.97045	+	11.1750i	−0.0766418	+	0.434657i	0.922207	+	0.386696i	$0.126384\pi$
$661$	−1.97045	+	11.1750i	−0.0766418	+	0.434657i	−0.998849	+	0.0479615i	$0.984728\pi$
$662$	11.4165	+	4.15527i	0.443715	+	0.161499i
$663$	−0.446400	+	0.374574i	−0.0173367	+	0.0145473i
$664$	23.9212			0.928323
$665$		0			0
$666$	−13.5366			−0.524534
$667$	−20.1729	+	16.9271i	−0.781099	+	0.655420i
$668$	−22.1914	−	8.07702i	−0.858612	−	0.312509i
$669$	−1.83154	+	10.3872i	−0.0708113	+	0.401591i
$670$		0			0
$671$	32.2426	−	11.7354i	1.24471	−	0.453038i
$672$	4.71136	−	8.16032i	0.181745	−	0.314791i
$673$	3.76192	+	6.51584i	0.145011	+	0.251167i	0.929377	−	0.369131i	$-0.120345\pi$
$673$	3.76192	+	6.51584i	0.145011	+	0.251167i	−0.784366	+	0.620299i	$0.787011\pi$
$674$	14.6268	+	12.2733i	0.563402	+	0.472750i
$675$		0			0
$676$	−8.65407	−	14.9893i	−0.332849	−	0.576511i
$677$	−9.11850	+	15.7937i	−0.350453	+	0.607002i	−0.986329	−	0.164789i	$-0.947306\pi$
$677$	−9.11850	+	15.7937i	−0.350453	+	0.607002i	0.635876	+	0.771791i	$0.280639\pi$
$678$	1.90830	−	0.694565i	0.0732879	−	0.0266746i
$679$	−1.70666	−	9.67893i	−0.0654954	−	0.371443i
$680$		0			0
$681$	−13.6748	−	4.97722i	−0.524019	−	0.190727i
$682$	10.8459	−	9.10081i	0.415312	−	0.348488i
$683$	−28.9640			−1.10828			−0.554139	−	0.832424i	$-0.686952\pi$
$683$	−28.9640			−1.10828			−0.554139	+	0.832424i	$0.686952\pi$
$684$	16.5767	−	2.17494i	0.633828	−	0.0831610i
$685$		0			0
$686$	10.5519	−	8.85408i	0.402873	−	0.338050i
$687$	−18.3823	−	6.69062i	−0.701330	−	0.255263i
$688$	−2.27982	+	12.9295i	−0.0869174	+	0.492933i
$689$	1.46852	+	8.32842i	0.0559463	+	0.317287i
$690$		0			0
$691$	16.3005	−	28.2333i	0.620100	−	1.07404i	−0.369367	−	0.929284i	$-0.620425\pi$
$691$	16.3005	−	28.2333i	0.620100	−	1.07404i	0.989467	−	0.144761i	$-0.0462413\pi$
$692$	−12.8879	−	22.3226i	−0.489926	−	0.848576i
$693$	−20.6120	−	17.2955i	−0.782984	−	0.657001i
$694$	−11.2505	−	9.44028i	−0.427063	−	0.358348i
$695$		0			0
$696$	3.99670	−	6.92249i	0.151495	−	0.262396i
$697$	−5.35142	+	1.94776i	−0.202699	+	0.0737765i
$698$	−2.35477	−	13.3545i	−0.0891292	−	0.505477i
$699$	−2.52004	+	14.2918i	−0.0953165	+	0.540567i
$700$		0			0
$701$	−0.701156	+	0.588339i	−0.0264823	+	0.0222213i	−0.655933	−	0.754819i	$-0.727725\pi$
$701$	−0.701156	+	0.588339i	−0.0264823	+	0.0222213i	0.629450	+	0.777041i	$0.283280\pi$
$702$	−3.38916			−0.127916
$703$	−28.6393	−	18.2630i	−1.08015	−	0.688801i
$704$	5.81424			0.219133
$705$		0			0
$706$	−4.19315	−	1.52618i	−0.157811	−	0.0574386i
$707$	−0.0231366	+	0.131214i	−0.000870142	+	0.00493482i
$708$	−1.08343	−	6.14445i	−0.0407179	−	0.230922i
$709$	−15.0820	+	5.48939i	−0.566415	+	0.206158i	−0.609325	−	0.792921i	$-0.708559\pi$
$709$	−15.0820	+	5.48939i	−0.566415	+	0.206158i	0.0429098	+	0.999079i	$0.486337\pi$
$710$		0			0
$711$	7.94104	+	13.7543i	0.297812	+	0.515826i
$712$	22.6864	+	19.0362i	0.850210	+	0.713411i
$713$	−19.1080	−	16.0335i	−0.715601	−	0.600460i
$714$	0.366447	+	0.634706i	0.0137140	+	0.0237533i
$715$		0			0
$716$	4.37094	−	1.59089i	0.163350	−	0.0594544i
$717$	−0.149571	−	0.848258i	−0.00558582	−	0.0316788i
$718$	2.32426	−	13.1815i	0.0867407	−	0.491931i
$719$	30.9864	+	11.2781i	1.15560	+	0.420603i	0.847523	−	0.530759i	$-0.178093\pi$
$719$	30.9864	+	11.2781i	1.15560	+	0.420603i	0.308075	+	0.951362i	$0.400315\pi$
$720$		0			0
$721$	−16.9108			−0.629790
$722$	−11.8787	−	5.55186i	−0.442079	−	0.206619i
$723$	0.813561			0.0302567
$724$	28.5816	−	23.9828i	1.06223	−	0.891315i
$725$		0			0
$726$	−0.829627	+	4.70505i	−0.0307904	+	0.174621i
$727$	−1.64266	−	9.31601i	−0.0609230	−	0.345512i	−0.999998	−	0.00180034i	$-0.999427\pi$
$727$	−1.64266	−	9.31601i	−0.0609230	−	0.345512i	0.939075	−	0.343711i	$-0.111684\pi$
$728$	6.83432	−	2.48749i	0.253297	−	0.0921925i
$729$	2.15603	−	3.73435i	0.0798528	−	0.138309i
$730$		0			0
$731$	−4.80833	−	4.03467i	−0.177843	−	0.149228i
$732$	6.07817	+	5.10019i	0.224656	+	0.188508i
$733$	5.22951	+	9.05778i	0.193156	+	0.334557i	0.946295	−	0.323306i	$-0.104794\pi$
$733$	5.22951	+	9.05778i	0.193156	+	0.334557i	−0.753138	+	0.657862i	$0.771461\pi$
$734$	−10.3628	+	17.9490i	−0.382500	+	0.662509i
$735$		0			0
$736$	−5.61477	−	31.8430i	−0.206963	−	1.17375i
$737$	−10.3837	+	58.8891i	−0.382490	+	2.16921i
$738$	−14.2000	−	5.16838i	−0.522709	−	0.190251i
$739$	−5.97281	+	5.01178i	−0.219713	+	0.184361i	−0.746000	−	0.665946i	$-0.768028\pi$
$739$	−5.97281	+	5.01178i	−0.219713	+	0.184361i	0.526287	+	0.850307i	$0.323584\pi$
$740$		0			0
$741$	−3.27146	−	2.08617i	−0.120180	−	0.0766375i
$742$	10.6361			0.390463
$743$	−15.6403	+	13.1238i	−0.573787	+	0.481464i	−0.882900	−	0.469561i	$-0.844412\pi$
$743$	−15.6403	+	13.1238i	−0.573787	+	0.481464i	0.309113	+	0.951025i	$0.399968\pi$
$744$	7.11482	+	2.58958i	0.260842	+	0.0949387i
$745$		0			0
$746$	−0.594143	−	3.36955i	−0.0217531	−	0.123368i
$747$	23.2681	−	8.46891i	0.851336	−	0.309861i
$748$	2.28364	−	3.95537i	0.0834980	−	0.144623i
$749$	17.3463	+	30.0447i	0.633821	+	1.09781i
$750$		0			0
$751$	26.8265	+	22.5101i	0.978914	+	0.821407i	0.983925	−	0.178581i	$-0.0571506\pi$
$751$	26.8265	+	22.5101i	0.978914	+	0.821407i	−0.00501107	+	0.999987i	$0.501595\pi$
$752$	4.33179	+	7.50288i	0.157964	+	0.273602i
$753$	−7.64138	+	13.2353i	−0.278467	+	0.482320i
$754$	3.92996	−	1.43039i	0.143121	−	0.0520917i
$755$		0			0
$756$	2.36817	−	13.4306i	0.0861295	−	0.488464i
$757$	33.3503	+	12.1385i	1.21214	+	0.441182i	0.867444	−	0.497534i	$-0.165761\pi$
$757$	33.3503	+	12.1385i	1.21214	+	0.441182i	0.344692	+	0.938716i	$0.387983\pi$
$758$	2.14548	−	1.80027i	0.0779275	−	0.0653889i
$759$	17.7100			0.642831
$760$		0			0
$761$	−24.2563			−0.879290			−0.439645	−	0.898172i	$-0.644896\pi$
$761$	−24.2563			−0.879290			−0.439645	+	0.898172i	$0.644896\pi$
$762$	−6.71031	+	5.63062i	−0.243089	+	0.203976i
$763$	29.4395	+	10.7151i	1.06578	+	0.387912i
$764$	0.447420	−	2.53744i	0.0161871	−	0.0918015i
$765$		0			0
$766$	1.56245	−	0.568687i	0.0564538	−	0.0205475i
$767$	3.77453	−	6.53768i	0.136290	−	0.236062i
$768$	3.45757	+	5.98869i	0.124764	+	0.216098i
$769$	−19.7393	−	16.5633i	−0.711819	−	0.597287i	0.213290	−	0.976989i	$-0.431582\pi$
$769$	−19.7393	−	16.5633i	−0.711819	−	0.597287i	−0.925109	+	0.379702i	$0.876027\pi$
$770$		0			0
$771$	5.78998	+	10.0285i	0.208521	+	0.361169i
$772$	−13.5545	+	23.4770i	−0.487836	+	0.844956i
$773$	35.6601	−	12.9792i	1.28260	−	0.466829i	0.391311	−	0.920259i	$-0.372022\pi$
$773$	35.6601	−	12.9792i	1.28260	−	0.466829i	0.891292	+	0.453429i	$0.149800\pi$
$774$	−2.89221	−	16.4026i	−0.103958	−	0.589578i
$775$		0			0
$776$	9.61975	+	3.50130i	0.345329	+	0.125689i
$777$	−9.68374	+	8.12562i	−0.347402	+	0.291505i
$778$	4.12191			0.147778
$779$	−23.0698	−	30.0926i	−0.826562	−	1.07818i
$780$		0			0
$781$	13.1582	−	11.0411i	0.470839	−	0.395081i
$782$	2.36327	+	0.860160i	0.0845103	+	0.0307592i
$783$	3.14918	−	17.8599i	0.112542	−	0.638259i
$784$	−0.368425	−	2.08944i	−0.0131580	−	0.0746230i
$785$		0			0
$786$	2.01528	−	3.49056i	0.0718826	−	0.124504i
$787$	−3.32256	−	5.75484i	−0.118437	−	0.205138i	0.800712	−	0.599050i	$-0.204455\pi$
$787$	−3.32256	−	5.75484i	−0.118437	−	0.205138i	−0.919148	+	0.393912i	$0.871122\pi$
$788$	16.9270	+	14.2035i	0.603001	+	0.505978i
$789$	2.30113	+	1.93087i	0.0819223	+	0.0687409i
$790$		0			0
$791$	−4.94360	+	8.56256i	−0.175774	+	0.304450i
$792$	26.3362	−	9.58560i	0.935817	−	0.340610i
$793$	1.66706	+	9.45436i	0.0591990	+	0.335734i
$794$	−3.39951	+	19.2796i	−0.120644	+	0.684206i
$795$		0			0
$796$	14.0464	−	11.7863i	0.497862	−	0.417755i
$797$	−15.3836			−0.544916			−0.272458	−	0.962168i	$-0.587837\pi$
$797$	−15.3836			−0.544916			−0.272458	+	0.962168i	$0.587837\pi$
$798$	−3.29836	+	3.59634i	−0.116761	+	0.127309i
$799$	−4.14198			−0.146533
$800$		0			0
$801$	28.8065	+	10.4847i	1.01783	+	0.370459i
$802$	3.75928	−	21.3200i	0.132745	−	0.752834i
$803$	−6.33171	−	35.9089i	−0.223441	−	1.26720i
$804$	−12.9940	+	4.72943i	−0.458264	+	0.166794i
$805$		0			0
$806$	1.98070	+	3.43067i	0.0697672	+	0.120840i
$807$	−12.9333	−	10.8523i	−0.455274	−	0.382021i
$808$	−0.106313	−	0.0892071i	−0.00374008	−	0.00313830i
$809$	−6.12735	−	10.6129i	−0.215426	−	0.373129i	0.737978	−	0.674825i	$-0.235781\pi$
$809$	−6.12735	−	10.6129i	−0.215426	−	0.373129i	−0.953404	+	0.301695i	$0.902447\pi$
$810$		0			0
$811$	−47.3559	+	17.2361i	−1.66289	+	0.605243i	−0.990813	−	0.135238i	$-0.956820\pi$
$811$	−47.3559	+	17.2361i	−1.66289	+	0.605243i	−0.672078	+	0.740481i	$0.734598\pi$
$812$	2.92229	+	16.5731i	0.102552	+	0.581602i
$813$	−0.991512	+	5.62314i	−0.0347738	+	0.197212i
$814$	−23.1372	−	8.42126i	−0.810960	−	0.295165i
$815$		0			0
$816$	0.622883			0.0218053
$817$	16.0105	−	38.6047i	0.560137	−	1.35061i
$818$	20.5546			0.718676
$819$	5.76708	−	4.83915i	0.201518	−	0.169094i
$820$		0			0
$821$	−1.07376	+	6.08959i	−0.0374745	+	0.212528i	−0.997795	−	0.0663702i	$-0.978858\pi$
$821$	−1.07376	+	6.08959i	−0.0374745	+	0.212528i	0.960321	+	0.278898i	$0.0899693\pi$
$822$	−0.987490	−	5.60033i	−0.0344427	−	0.195334i
$823$	27.0925	−	9.86085i	0.944384	−	0.343728i	0.176488	−	0.984303i	$-0.443526\pi$
$823$	27.0925	−	9.86085i	0.944384	−	0.343728i	0.767896	+	0.640575i	$0.221304\pi$
$824$	8.80715	−	15.2544i	0.306812	−	0.531414i
$825$		0			0
$826$	−7.27308	−	6.10284i	−0.253063	−	0.212345i
$827$	15.7181	+	13.1891i	0.546572	+	0.458629i	0.873778	−	0.486324i	$-0.161663\pi$
$827$	15.7181	+	13.1891i	0.546572	+	0.458629i	−0.327206	+	0.944953i	$0.606107\pi$
$828$	−10.6757	−	18.4908i	−0.371005	−	0.642600i
$829$	4.29107	−	7.43236i	0.149035	−	0.258136i	−0.781836	−	0.623484i	$-0.785717\pi$
$829$	4.29107	−	7.43236i	0.149035	−	0.258136i	0.930871	+	0.365348i	$0.119050\pi$
$830$		0			0
$831$	−2.33116	−	13.2207i	−0.0808671	−	0.458620i
$832$	−0.282488	+	1.60207i	−0.00979350	+	0.0555417i
$833$	0.953180	+	0.346929i	0.0330257	+	0.0120204i
$834$	−0.0137427	+	0.0115315i	−0.000475871	+	0.000399303i
$835$		0			0
$836$	29.6865	+	6.59507i	1.02673	+	0.228095i
$837$	17.1780			0.593759
$838$	−18.9095	+	15.8670i	−0.653218	+	0.548115i
$839$	−39.4563	−	14.3609i	−1.36218	−	0.495794i	−0.445455	−	0.895305i	$-0.646958\pi$
$839$	−39.4563	−	14.3609i	−1.36218	−	0.495794i	−0.916729	+	0.399510i	$0.869180\pi$
$840$		0			0
$841$	−1.14976	−	6.52061i	−0.0396469	−	0.224849i
$842$	−24.6680	+	8.97843i	−0.850116	+	0.309417i
$843$	−2.76023	+	4.78086i	−0.0950674	+	0.164661i
$844$	6.15248	+	10.6564i	0.211777	+	0.366808i
$845$		0			0
$846$	−8.41940	−	7.06472i	−0.289465	−	0.242890i
$847$	−11.6304	−	20.1445i	−0.399625	−	0.692172i
$848$	4.51978	−	7.82849i	0.155210	−	0.268831i
$849$	−11.0432	+	4.01939i	−0.379001	+	0.137945i
$850$		0			0
$851$	−7.53260	+	42.7195i	−0.258214	+	1.46441i
$852$	3.73254	+	1.35853i	0.127875	+	0.0465426i
$853$	11.8447	−	9.93891i	0.405556	−	0.340302i	−0.417081	−	0.908869i	$-0.636947\pi$
$853$	11.8447	−	9.93891i	0.405556	−	0.340302i	0.822636	+	0.568568i	$0.192502\pi$
$854$	12.0740			0.413165
$855$		0			0
$856$	−36.1360			−1.23510
$857$	−20.3501	+	17.0757i	−0.695144	+	0.583295i	−0.920388	−	0.391007i	$-0.872127\pi$
$857$	−20.3501	+	17.0757i	−0.695144	+	0.583295i	0.225243	+	0.974303i	$0.427682\pi$
$858$	−2.64296	−	0.961959i	−0.0902292	−	0.0328407i
$859$	4.03858	−	22.9039i	0.137795	−	0.781471i	−0.835078	−	0.550131i	$-0.814578\pi$
$859$	4.03858	−	22.9039i	0.137795	−	0.781471i	0.972873	−	0.231340i	$-0.0743111\pi$
$860$		0			0
$861$	−13.2607	+	4.82650i	−0.451924	+	0.164487i
$862$	−2.89430	+	5.01307i	−0.0985802	+	0.170746i
$863$	−0.0573750	−	0.0993764i	−0.00195307	−	0.00338281i	0.865047	−	0.501690i	$-0.167288\pi$
$863$	−0.0573750	−	0.0993764i	−0.00195307	−	0.00338281i	−0.867000	+	0.498308i	$0.833955\pi$
$864$	17.0580	+	14.3133i	0.580324	+	0.486950i
$865$		0			0
$866$	−8.01068	−	13.8749i	−0.272214	−	0.471489i
$867$	5.75732	−	9.97198i	0.195529	−	0.338666i
$868$	−14.9791	+	5.45193i	−0.508422	+	0.185051i
$869$	5.01641	+	28.4495i	0.170170	+	0.965082i
$870$		0			0
$871$	−15.7219	−	5.72231i	−0.532717	−	0.193893i
$872$	−24.9977	+	20.9756i	−0.846530	+	0.710323i
$873$	10.5967			0.358644
$874$	−0.737784	+	16.7290i	−0.0249559	+	0.565866i
$875$		0			0
$876$	6.45921	−	5.41992i	0.218236	−	0.183122i
$877$	21.7949	+	7.93269i	0.735961	+	0.267868i	0.682686	−	0.730712i	$-0.260812\pi$
$877$	21.7949	+	7.93269i	0.735961	+	0.267868i	0.0532749	+	0.998580i	$0.483034\pi$
$878$	−2.12288	+	12.0394i	−0.0716436	+	0.406311i
$879$	0.582865	+	3.30559i	0.0196596	+	0.111495i
$880$		0			0
$881$	−4.15319	+	7.19353i	−0.139924	+	0.242356i	−0.927468	−	0.373903i	$-0.878019\pi$
$881$	−4.15319	+	7.19353i	−0.139924	+	0.242356i	0.787543	+	0.616259i	$0.211353\pi$
$882$	1.34579	+	2.33098i	0.0453153	+	0.0784883i
$883$	22.7800	+	19.1147i	0.766609	+	0.643261i	0.939838	−	0.341620i	$-0.110976\pi$
$883$	22.7800	+	19.1147i	0.766609	+	0.643261i	−0.173229	+	0.984882i	$0.555420\pi$
$884$	0.978920	+	0.821411i	0.0329246	+	0.0276270i
$885$		0			0
$886$	−0.615419	+	1.06594i	−0.0206754	+	0.0358109i
$887$	−10.7996	+	3.93072i	−0.362614	+	0.131981i	−0.516901	−	0.856045i	$-0.672914\pi$
$887$	−10.7996	+	3.93072i	−0.362614	+	0.131981i	0.154287	+	0.988026i	$0.450692\pi$
$888$	−2.28645	−	12.9671i	−0.0767282	−	0.435147i
$889$	7.40578	−	42.0003i	0.248382	−	1.40864i
$890$		0			0
$891$	17.1433	−	14.3849i	0.574322	−	0.481914i
$892$	23.1296			0.774436
$893$	−8.28145	−	26.3058i	−0.277128	−	0.880290i
$894$	4.65183			0.155580
$895$		0			0
$896$	−23.5634	−	8.57637i	−0.787198	−	0.286517i
$897$	−0.860447	+	4.87984i	−0.0287295	+	0.162933i
$898$	−1.06137	−	6.01935i	−0.0354185	−	0.200868i
$899$	−19.9191	+	7.24994i	−0.664338	+	0.241799i
$900$		0			0
$901$	2.16086	+	3.74273i	0.0719888	+	0.124688i
$902$	−21.0558	−	17.6679i	−0.701081	−	0.588277i
$903$	−11.9150	−	9.99784i	−0.396505	−	0.332707i
$904$	−5.14927	−	8.91879i	−0.171262	−	0.296635i
$905$		0			0
$906$	2.07623	−	0.755684i	0.0689780	−	0.0251059i
$907$	−4.13253	−	23.4367i	−0.137218	−	0.778204i	−0.973289	−	0.229582i	$-0.926264\pi$
$907$	−4.13253	−	23.4367i	−0.137218	−	0.778204i	0.836071	−	0.548621i	$-0.184847\pi$
$908$	−5.54151	+	31.4275i	−0.183901	+	1.04296i
$909$	−0.134993	−	0.0491333i	−0.00447742	−	0.00162965i
$910$		0			0
$911$	23.2831			0.771405			0.385702	−	0.922623i	$-0.373959\pi$
$911$	23.2831			0.771405			0.385702	+	0.922623i	$0.373959\pi$
$912$	1.24539	+	3.95595i	0.0412390	+	0.130994i
$913$	45.0392			1.49058
$914$	1.58876	−	1.33313i	0.0525515	−	0.0440960i
$915$		0			0
$916$	−7.44917	+	42.2463i	−0.246128	+	1.39586i
$917$	3.40759	+	19.3254i	0.112528	+	0.638181i
$918$	−1.62751	+	0.592367i	−0.0537160	+	0.0195510i
$919$	−18.5406	+	32.1133i	−0.611599	+	1.05932i	0.379372	+	0.925244i	$0.376140\pi$
$919$	−18.5406	+	32.1133i	−0.611599	+	1.05932i	−0.990971	+	0.134077i	$0.957193\pi$
$920$		0			0
$921$	3.27526	+	2.74827i	0.107923	+	0.0905585i
$922$	−10.6347	−	8.92356i	−0.350235	−	0.293882i
$923$	2.40298	+	4.16208i	0.0790951	+	0.136997i
$924$	5.65881	−	9.80134i	0.186161	−	0.322441i
$925$		0			0
$926$	0.977187	+	5.54190i	0.0321124	+	0.182118i
$927$	3.16613	−	17.9560i	0.103989	−	0.589752i
$928$	−25.8208	−	9.39800i	−0.847609	−	0.308504i
$929$	15.3901	−	12.9139i	0.504934	−	0.423690i	−0.354408	−	0.935091i	$-0.615318\pi$
$929$	15.3901	−	12.9139i	0.504934	−	0.423690i	0.859342	+	0.511401i	$0.170873\pi$
$930$		0			0
$931$	−0.297571	+	6.74732i	−0.00975250	+	0.221134i
$932$	31.8243			1.04244
$933$	1.52315	−	1.27807i	0.0498657	−	0.0418423i
$934$	3.99305	+	1.45335i	0.130657	+	0.0475551i
$935$		0			0
$936$	1.36168	+	7.72246i	0.0445078	+	0.252416i
$937$	−18.8820	+	6.87247i	−0.616847	+	0.224514i	−0.631496	−	0.775379i	$-0.717559\pi$
$937$	−18.8820	+	6.87247i	−0.616847	+	0.224514i	0.0146495	+	0.999893i	$0.495337\pi$
$938$	−10.5211	+	18.2231i	−0.343526	+	0.595004i
$939$	−2.25172	−	3.90009i	−0.0734820	−	0.127275i
$940$		0			0
$941$	3.26137	+	2.73661i	0.106318	+	0.0892111i	0.694397	−	0.719592i	$-0.255671\pi$
$941$	3.26137	+	2.73661i	0.106318	+	0.0892111i	−0.588079	+	0.808803i	$0.700116\pi$
$942$	4.89192	+	8.47305i	0.159387	+	0.276067i
$943$	−24.2123	+	41.9370i	−0.788462	+	1.36566i
$944$	−7.58255	+	2.75982i	−0.246791	+	0.0898246i
$945$		0			0
$946$	5.26072	−	29.8350i	0.171041	−	0.970021i
$947$	−41.1890	−	14.9916i	−1.33846	−	0.487160i	−0.429134	−	0.903241i	$-0.641181\pi$
$947$	−41.1890	−	14.9916i	−1.33846	−	0.487160i	−0.909328	+	0.416080i	$0.863404\pi$
$948$	−5.11742	+	4.29402i	−0.166206	+	0.139463i
$949$	10.2020			0.331172
$950$		0			0
$951$	21.5596			0.699117
$952$	2.84715	−	2.38904i	0.0922766	−	0.0774292i
$953$	28.3499	+	10.3185i	0.918343	+	0.334250i	0.757579	−	0.652743i	$-0.226382\pi$
$953$	28.3499	+	10.3185i	0.918343	+	0.334250i	0.160764	+	0.986993i	$0.448604\pi$
$954$	−1.99135	+	11.2935i	−0.0644723	+	0.365640i
$955$		0			0
$956$	−1.77495	+	0.646027i	−0.0574058	+	0.0208940i
$957$	7.52505	−	13.0338i	0.243250	−	0.421322i
$958$	11.7631	+	20.3743i	0.380048	+	0.658263i
$959$	21.2094	+	17.7968i	0.684887	+	0.574689i
$960$		0			0
$961$	5.46080	+	9.45838i	0.176155	+	0.305109i
$962$	3.44455	−	5.96613i	0.111057	−	0.192356i
$963$	−35.1494	+	12.7933i	−1.13267	+	0.412260i
$964$	−0.309801	−	1.75697i	−0.00997803	−	0.0565882i
$965$		0			0
$966$	5.85614	+	2.13146i	0.188418	+	0.0685786i
$967$	−9.52967	+	7.99635i	−0.306454	+	0.257145i	−0.783024	−	0.621991i	$-0.786324\pi$
$967$	−9.52967	+	7.99635i	−0.306454	+	0.257145i	0.476571	+	0.879136i	$0.341880\pi$
$968$	24.2285			0.778735
$969$	−1.93562	−	0.430011i	−0.0621810	−	0.0138139i
$970$		0			0
$971$	−22.6566	+	19.0111i	−0.727084	+	0.610096i	−0.929335	−	0.369238i	$-0.879619\pi$
$971$	−22.6566	+	19.0111i	−0.727084	+	0.610096i	0.202251	+	0.979334i	$0.435174\pi$
$972$	21.3305	+	7.76367i	0.684177	+	0.249020i
$973$	0.0151670	−	0.0860165i	0.000486233	−	0.00275756i
$974$	3.42396	+	19.4182i	0.109711	+	0.622200i
$975$		0			0
$976$	5.13082	−	8.88685i	0.164234	−	0.284461i
$977$	−19.6892	−	34.1028i	−0.629915	−	1.09104i	−0.987568	−	0.157190i	$-0.949757\pi$
$977$	−19.6892	−	34.1028i	−0.629915	−	1.09104i	0.357654	−	0.933854i	$-0.383577\pi$
$978$	−1.39353	−	1.16931i	−0.0445601	−	0.0373904i
$979$	42.7143	+	35.8416i	1.36516	+	1.14550i
$980$		0			0
$981$	−16.8892	+	29.2529i	−0.539230	+	0.933975i
$982$	−3.39879	+	1.23706i	−0.108460	+	0.0394761i
$983$	6.67169	+	37.8370i	0.212794	+	1.20681i	0.884694	+	0.466172i	$0.154367\pi$
$983$	6.67169	+	37.8370i	0.212794	+	1.20681i	−0.671900	+	0.740642i	$0.734522\pi$
$984$	2.55243	−	14.4755i	0.0813684	−	0.461463i
$985$		0			0
$986$	1.63720	−	1.37378i	0.0521392	−	0.0437500i
$987$	−10.2637			−0.326699
$988$	−3.25955	+	7.85947i	−0.103700	+	0.250043i
$989$	−53.3733			−1.69717
$990$		0			0
$991$	−9.83853	−	3.58093i	−0.312531	−	0.113752i	0.180992	−	0.983485i	$-0.442069\pi$
$991$	−9.83853	−	3.58093i	−0.312531	−	0.113752i	−0.493524	+	0.869732i	$0.664291\pi$
$992$	4.51960	−	25.6319i	0.143497	−	0.813815i
$993$	2.12418	+	12.0468i	0.0674088	+	0.382294i
$994$	5.67986	−	2.06730i	0.180154	−	0.0655708i
$995$		0			0
$996$	5.20757	+	9.01978i	0.165008	+	0.285803i
$997$	2.76477	+	2.31992i	0.0875612	+	0.0734725i	0.685518	−	0.728056i	$-0.259576\pi$
$997$	2.76477	+	2.31992i	0.0875612	+	0.0734725i	−0.597956	+	0.801529i	$0.704020\pi$
$998$	−20.0270	−	16.8047i	−0.633944	−	0.531942i
$999$	−14.9368	−	25.8712i	−0.472578	−	0.818529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.101.2		18
5.2	odd	4		475.2.u.b.424.2		36
5.3	odd	4		475.2.u.b.424.5		36
5.4	even	2		95.2.k.a.6.2	✓	18
15.14	odd	2		855.2.bs.c.766.2		18
19.4	even	9		9025.2.a.cc.1.5		9
19.15	odd	18		9025.2.a.cf.1.5		9
19.16	even	9	inner	475.2.l.c.301.2		18
95.4	even	18		1805.2.a.v.1.5		9
95.34	odd	18		1805.2.a.s.1.5		9
95.54	even	18		95.2.k.a.16.2	yes	18
95.73	odd	36		475.2.u.b.149.2		36
95.92	odd	36		475.2.u.b.149.5		36
285.149	odd	18		855.2.bs.c.586.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.2	✓	18	5.4	even	2
95.2.k.a.16.2	yes	18	95.54	even	18
475.2.l.c.101.2		18	1.1	even	1	trivial
475.2.l.c.301.2		18	19.16	even	9	inner
475.2.u.b.149.2		36	95.73	odd	36
475.2.u.b.149.5		36	95.92	odd	36
475.2.u.b.424.2		36	5.2	odd	4
475.2.u.b.424.5		36	5.3	odd	4
855.2.bs.c.586.2		18	285.149	odd	18
855.2.bs.c.766.2		18	15.14	odd	2
1805.2.a.s.1.5		9	95.34	odd	18
1805.2.a.v.1.5		9	95.4	even	18
9025.2.a.cc.1.5		9	19.4	even	9
9025.2.a.cf.1.5		9	19.15	odd	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.528654 + 0.443593i) q^{2} +(-0.652945 - 0.237653i) q^{3} +(-0.264596 + 1.50060i) q^{4} +(0.450603 - 0.164006i) q^{6} +(-1.16732 + 2.02186i) q^{7} +(-1.21589 - 2.10598i) q^{8} +(-1.92827 - 1.61801i) q^{9} +O(q^{10})\)	\(q+(-0.528654 + 0.443593i) q^{2} +(-0.652945 - 0.237653i) q^{3} +(-0.264596 + 1.50060i) q^{4} +(0.450603 - 0.164006i) q^{6} +(-1.16732 + 2.02186i) q^{7} +(-1.21589 - 2.10598i) q^{8} +(-1.92827 - 1.61801i) q^{9} +(-2.28929 - 3.96516i) q^{11} +(0.529389 - 0.916928i) q^{12} +(1.20379 - 0.438145i) q^{13} +(-0.279774 - 1.58668i) q^{14} +(-1.28673 - 0.468333i) q^{16} +(0.501495 - 0.420805i) q^{17} +1.73713 q^{18} +(3.67523 + 2.34365i) q^{19} +(1.24270 - 1.04275i) q^{21} +(2.96916 + 1.08069i) q^{22} +(0.966645 - 5.48212i) q^{23} +(0.293416 + 1.66404i) q^{24} +(-0.442032 + 0.765622i) q^{26} +(1.91681 + 3.32001i) q^{27} +(-2.72513 - 2.28666i) q^{28} +(-3.62387 - 3.04079i) q^{29} +(2.24045 - 3.88057i) q^{31} +(5.45822 - 1.98663i) q^{32} +(0.552448 + 3.13309i) q^{33} +(-0.0784514 + 0.444920i) q^{34} +(2.93821 - 2.46545i) q^{36} -7.79252 q^{37} +(-2.98255 + 0.391324i) q^{38} -0.890138 q^{39} +(-8.17440 - 2.97524i) q^{41} +(-0.194401 + 1.10250i) q^{42} +(-1.66494 - 9.44233i) q^{43} +(6.55586 - 2.38614i) q^{44} +(1.92081 + 3.32694i) q^{46} +(-4.84673 - 4.06689i) q^{47} +(0.728866 + 0.611591i) q^{48} +(0.774723 + 1.34186i) q^{49} +(-0.427454 + 0.155581i) q^{51} +(0.338961 + 1.92235i) q^{52} +(-1.14634 + 6.50124i) q^{53} +(-2.48606 - 0.904852i) q^{54} +5.67731 q^{56} +(-1.84275 - 2.40370i) q^{57} +3.26464 q^{58} +(4.51420 - 3.78786i) q^{59} +(-1.30132 + 7.38016i) q^{61} +(0.536973 + 3.04533i) q^{62} +(5.52231 - 2.00996i) q^{63} +(-0.634941 + 1.09975i) q^{64} +(-1.68187 - 1.41126i) q^{66} +(-10.0048 - 8.39500i) q^{67} +(0.498766 + 0.863888i) q^{68} +(-1.93401 + 3.34980i) q^{69} +(0.651454 + 3.69458i) q^{71} +(-1.06294 + 6.02822i) q^{72} +(7.48353 + 2.72378i) q^{73} +(4.11955 - 3.45671i) q^{74} +(-4.48934 + 4.89493i) q^{76} +10.6893 q^{77} +(0.470575 - 0.394859i) q^{78} +(-5.92896 - 2.15796i) q^{79} +(0.848752 + 4.81351i) q^{81} +(5.64122 - 2.05324i) q^{82} +(-4.91848 + 8.51905i) q^{83} +(1.23593 + 2.14070i) q^{84} +(5.06873 + 4.25317i) q^{86} +(1.64354 + 2.84669i) q^{87} +(-5.56702 + 9.64236i) q^{88} +(-11.4439 + 4.16525i) q^{89} +(-0.519346 + 2.94536i) q^{91} +(7.97070 + 2.90110i) q^{92} +(-2.38512 + 2.00135i) q^{93} +4.36629 q^{94} -4.03605 q^{96} +(-3.22485 + 2.70597i) q^{97} +(-1.00480 - 0.365717i) q^{98} +(-2.00131 + 11.3500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

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