LMFDB - Embedded newform 375.2.g.c.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			226.3
Root			$-2.17386 - 1.57940i$ of defining polynomial
Character	$\chi$	$=$	375.226
Dual form			375.2.g.c.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.830342 - 2.55553i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.22323 - 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.830342 - 2.55553i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.22323 - 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.333373 - 1.02602i) q^{11} +(1.61313 + 4.96470i) q^{12} +(-0.827310 - 2.54620i) q^{13} +(-1.40082 + 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(-3.18079 + 2.31098i) q^{17} +2.68704 q^{18} +(0.952655 - 0.692144i) q^{19} +(1.36485 + 0.991619i) q^{21} +(-2.34520 - 1.70389i) q^{22} +(1.25552 - 3.86409i) q^{23} +8.65280 q^{24} -7.19384 q^{26} +(0.309017 - 0.951057i) q^{27} +(7.12476 + 5.17644i) q^{28} +(-4.81846 - 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} +17.1155 q^{32} +(-0.872782 + 0.634113i) q^{33} +(3.26463 + 10.0475i) q^{34} +(1.61313 - 4.96470i) q^{36} +(1.41587 + 4.35761i) q^{37} +(-0.977766 - 3.00925i) q^{38} +(-0.827310 + 2.54620i) q^{39} +(-3.47998 - 10.7103i) q^{41} +(3.66740 - 2.66452i) q^{42} -2.58587 q^{43} +(-4.55609 + 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.55155 - 1.12727i) q^{47} +(3.95852 - 12.1831i) q^{48} -4.15389 q^{49} +3.93167 q^{51} +(-4.31872 + 13.2917i) q^{52} +(-2.06187 - 1.49803i) q^{53} +(-2.17386 - 1.57940i) q^{54} +(11.8097 - 8.58028i) q^{56} -1.17755 q^{57} +(-12.9474 + 9.40685i) q^{58} +(0.412843 + 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-5.89800 - 18.1522i) q^{62} +(-0.521325 - 1.60447i) q^{63} +(6.29470 - 19.3731i) q^{64} +(0.895787 + 2.75695i) q^{66} +(10.0683 - 7.31502i) q^{67} +20.5241 q^{68} +(-3.28699 + 2.38814i) q^{69} +(4.84181 + 3.51778i) q^{71} +(-7.00026 - 5.08599i) q^{72} +(1.01996 - 3.13911i) q^{73} +12.3117 q^{74} -6.14702 q^{76} +(-0.562414 + 1.73093i) q^{77} +(5.81994 + 4.22843i) q^{78} +(3.23934 + 2.35351i) q^{79} +(-0.809017 + 0.587785i) q^{81} -30.2600 q^{82} +(7.17988 - 5.21649i) q^{83} +(-2.72142 - 8.37566i) q^{84} +(-2.14716 + 6.60827i) q^{86} +(1.84049 + 5.66445i) q^{87} +(2.88461 + 8.87792i) q^{88} +(4.77234 - 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(-17.1587 + 12.4666i) q^{92} -7.10310 q^{93} +(-4.16908 + 3.02901i) q^{94} +(-13.8468 - 10.0603i) q^{96} +(8.71166 + 6.32939i) q^{97} +(-3.44915 + 10.6154i) q^{98} +1.07882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.830342	−	2.55553i	0.587140	−	1.80703i	−0.00335992	−	0.999994i	$-0.501069\pi$
$2$	0.830342	−	2.55553i	0.587140	−	1.80703i	0.590500	−	0.807038i	$-0.298931\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−4.22323	−	3.06835i	−2.11161	−	1.53418i
$5$		0			0
$5$		0			0
$6$	−2.17386	+	1.57940i	−0.887476	+	0.644789i
$7$	−1.68704			−0.637642			−0.318821	−	0.947815i	$-0.603287\pi$
$7$	−1.68704			−0.637642			−0.318821	+	0.947815i	$0.603287\pi$
$8$	−7.00026	+	5.08599i	−2.47497	+	1.79817i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	0.333373	−	1.02602i	0.100516	−	0.309356i	−0.888136	−	0.459581i	$-0.848000\pi$
$11$	0.333373	−	1.02602i	0.100516	−	0.309356i	0.988652	+	0.150225i	$0.0479998\pi$
$12$	1.61313	+	4.96470i	0.465670	+	1.43319i
$13$	−0.827310	−	2.54620i	−0.229455	−	0.706189i	−0.997809	−	0.0661638i	$-0.978924\pi$
$13$	−0.827310	−	2.54620i	−0.229455	−	0.706189i	0.768354	−	0.640025i	$-0.221076\pi$
$14$	−1.40082	+	4.31129i	−0.374385	+	1.15224i
$15$		0			0
$16$	3.95852	+	12.1831i	0.989631	+	3.04577i
$17$	−3.18079	+	2.31098i	−0.771454	+	0.560494i	−0.902402	−	0.430895i	$-0.858198\pi$
$17$	−3.18079	+	2.31098i	−0.771454	+	0.560494i	0.130948	+	0.991389i	$0.458198\pi$
$18$	2.68704			0.633342
$19$	0.952655	−	0.692144i	0.218554	−	0.158789i	−0.473121	−	0.880997i	$-0.656873\pi$
$19$	0.952655	−	0.692144i	0.218554	−	0.158789i	0.691676	+	0.722208i	$0.256873\pi$
$20$		0			0
$21$	1.36485	+	0.991619i	0.297834	+	0.216389i
$22$	−2.34520	−	1.70389i	−0.499999	−	0.363270i
$23$	1.25552	−	3.86409i	0.261794	−	0.805719i	−0.730621	−	0.682783i	$-0.760769\pi$
$23$	1.25552	−	3.86409i	0.261794	−	0.805719i	0.992415	−	0.122935i	$-0.0392307\pi$
$24$	8.65280			1.76625
$25$		0			0
$26$	−7.19384			−1.41083
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	7.12476	+	5.17644i	1.34645	+	0.978256i
$29$	−4.81846	−	3.50082i	−0.894766	−	0.650086i	0.0423500	−	0.999103i	$-0.486516\pi$
$29$	−4.81846	−	3.50082i	−0.894766	−	0.650086i	−0.937116	+	0.349017i	$0.886516\pi$
$30$		0			0
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.0633776	−	0.997990i	$-0.479813\pi$
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.968729	+	0.248120i	$0.0798128\pi$
$32$	17.1155			3.02563
$33$	−0.872782	+	0.634113i	−0.151932	+	0.110385i
$34$	3.26463	+	10.0475i	0.559879	+	1.72313i
$35$		0			0
$36$	1.61313	−	4.96470i	0.268855	−	0.827450i
$37$	1.41587	+	4.35761i	0.232768	+	0.716387i	0.997410	+	0.0719311i	$0.0229162\pi$
$37$	1.41587	+	4.35761i	0.232768	+	0.716387i	−0.764641	+	0.644456i	$0.777084\pi$
$38$	−0.977766	−	3.00925i	−0.158615	−	0.488165i
$39$	−0.827310	+	2.54620i	−0.132476	+	0.407718i
$40$		0			0
$41$	−3.47998	−	10.7103i	−0.543481	−	1.67266i	−0.724574	−	0.689197i	$-0.757963\pi$
$41$	−3.47998	−	10.7103i	−0.543481	−	1.67266i	0.181093	−	0.983466i	$-0.442037\pi$
$42$	3.66740	−	2.66452i	0.565892	−	0.411144i
$43$	−2.58587			−0.394342			−0.197171	−	0.980369i	$-0.563175\pi$
$43$	−2.58587			−0.394342			−0.197171	+	0.980369i	$0.563175\pi$
$44$	−4.55609	+	3.31019i	−0.686857	+	0.499031i
$45$		0			0
$46$	−8.83229	−	6.41703i	−1.30225	−	0.946140i
$47$	−1.55155	−	1.12727i	−0.226317	−	0.164429i	0.468849	−	0.883278i	$-0.344669\pi$
$47$	−1.55155	−	1.12727i	−0.226317	−	0.164429i	−0.695166	+	0.718850i	$0.744669\pi$
$48$	3.95852	−	12.1831i	0.571364	−	1.75848i
$49$	−4.15389			−0.593413
$50$		0			0
$51$	3.93167			0.550544
$52$	−4.31872	+	13.2917i	−0.598899	+	1.84322i
$53$	−2.06187	−	1.49803i	−0.283219	−	0.205771i	0.437101	−	0.899412i	$-0.356005\pi$
$53$	−2.06187	−	1.49803i	−0.283219	−	0.205771i	−0.720320	+	0.693642i	$0.756005\pi$
$54$	−2.17386	−	1.57940i	−0.295825	−	0.214930i
$55$		0			0
$56$	11.8097	−	8.58028i	1.57814	−	1.14659i
$57$	−1.17755			−0.155970
$58$	−12.9474	+	9.40685i	−1.70008	+	1.23518i
$59$	0.412843	+	1.27060i	0.0537476	+	0.165418i	0.974327	−	0.225137i	$-0.0722830\pi$
$59$	0.412843	+	1.27060i	0.0537476	+	0.165418i	−0.920579	+	0.390555i	$0.872283\pi$
$60$		0			0
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	0.697379	+	0.716702i	$0.254349\pi$
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	−0.985459	+	0.169915i	$0.945651\pi$
$62$	−5.89800	−	18.1522i	−0.749047	−	2.30533i
$63$	−0.521325	−	1.60447i	−0.0656807	−	0.202145i
$64$	6.29470	−	19.3731i	0.786838	−	2.42164i
$65$		0			0
$66$	0.895787	+	2.75695i	0.110264	+	0.339357i
$67$	10.0683	−	7.31502i	1.23003	−	0.893672i	0.233141	−	0.972443i	$-0.425100\pi$
$67$	10.0683	−	7.31502i	1.23003	−	0.893672i	0.996893	+	0.0787711i	$0.0250996\pi$
$68$	20.5241			2.48891
$69$	−3.28699	+	2.38814i	−0.395707	+	0.287498i
$70$		0			0
$71$	4.84181	+	3.51778i	0.574617	+	0.417484i	0.836779	−	0.547540i	$-0.184436\pi$
$71$	4.84181	+	3.51778i	0.574617	+	0.417484i	−0.262162	+	0.965024i	$0.584436\pi$
$72$	−7.00026	−	5.08599i	−0.824989	−	0.599390i
$73$	1.01996	−	3.13911i	0.119377	−	0.367405i	−0.873458	−	0.486900i	$-0.838128\pi$
$73$	1.01996	−	3.13911i	0.119377	−	0.367405i	0.992835	+	0.119495i	$0.0381276\pi$
$74$	12.3117			1.43120
$75$		0			0
$76$	−6.14702			−0.705112
$77$	−0.562414	+	1.73093i	−0.0640931	+	0.197258i
$78$	5.81994	+	4.22843i	0.658978	+	0.478776i
$79$	3.23934	+	2.35351i	0.364454	+	0.264791i	0.754907	−	0.655831i	$-0.227682\pi$
$79$	3.23934	+	2.35351i	0.364454	+	0.264791i	−0.390454	+	0.920623i	$0.627682\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−30.2600			−3.34166
$83$	7.17988	−	5.21649i	0.788094	−	0.572584i	−0.119303	−	0.992858i	$-0.538066\pi$
$83$	7.17988	−	5.21649i	0.788094	−	0.572584i	0.907397	+	0.420274i	$0.138066\pi$
$84$	−2.72142	−	8.37566i	−0.296931	−	0.913859i
$85$		0			0
$86$	−2.14716	+	6.60827i	−0.231534	+	0.712588i
$87$	1.84049	+	5.66445i	0.197321	+	0.607292i
$88$	2.88461	+	8.87792i	0.307501	+	0.946389i
$89$	4.77234	−	14.6877i	0.505867	−	1.55690i	−0.293442	−	0.955977i	$-0.594801\pi$
$89$	4.77234	−	14.6877i	0.505867	−	1.55690i	0.799309	−	0.600920i	$-0.205199\pi$
$90$		0			0
$91$	1.39571	+	4.29555i	0.146310	+	0.450296i
$92$	−17.1587	+	12.4666i	−1.78892	+	1.29973i
$93$	−7.10310			−0.736557
$94$	−4.16908	+	3.02901i	−0.430008	+	0.312419i
$95$		0			0
$96$	−13.8468	−	10.0603i	−1.41323	−	1.02677i
$97$	8.71166	+	6.32939i	0.884535	+	0.642652i	0.934447	−	0.356101i	$-0.115894\pi$
$97$	8.71166	+	6.32939i	0.884535	+	0.642652i	−0.0499122	+	0.998754i	$0.515894\pi$
$98$	−3.44915	+	10.6154i	−0.348416	+	1.07232i
$99$	1.07882			0.108425
$100$		0			0
$101$	−13.5654			−1.34981			−0.674905	−	0.737905i	$-0.735815\pi$
$101$	−13.5654			−1.34981			−0.674905	+	0.737905i	$0.735815\pi$
$102$	3.26463	−	10.0475i	0.323246	−	0.994850i
$103$	1.10757	+	0.804700i	0.109133	+	0.0792894i	0.641013	−	0.767530i	$-0.278514\pi$
$103$	1.10757	+	0.804700i	0.109133	+	0.0792894i	−0.531880	+	0.846819i	$0.678514\pi$
$104$	18.7413	+	13.6164i	1.83774	+	1.33520i
$105$		0			0
$106$	−5.54032	+	4.02528i	−0.538124	+	0.390970i
$107$	−11.0115			−1.06452			−0.532262	−	0.846579i	$-0.678658\pi$
$107$	−11.0115			−1.06452			−0.532262	+	0.846579i	$0.678658\pi$
$108$	−4.22323	+	3.06835i	−0.406380	+	0.295253i
$109$	1.06577	+	3.28010i	0.102082	+	0.314176i	0.989035	−	0.147684i	$-0.0471820\pi$
$109$	1.06577	+	3.28010i	0.102082	+	0.314176i	−0.886952	+	0.461861i	$0.847182\pi$
$110$		0			0
$111$	1.41587	−	4.35761i	0.134389	−	0.413606i
$112$	−6.67820	−	20.5534i	−0.631030	−	1.94211i
$113$	−1.87015	−	5.75574i	−0.175929	−	0.541455i	0.823745	−	0.566960i	$-0.191881\pi$
$113$	−1.87015	−	5.75574i	−0.175929	−	0.541455i	−0.999675	+	0.0255053i	$0.991881\pi$
$114$	−0.977766	+	3.00925i	−0.0915762	+	0.281842i
$115$		0			0
$116$	9.60772	+	29.5695i	0.892054	+	2.74546i
$117$	2.16593	−	1.57364i	0.200240	−	0.145483i
$118$	3.58986			0.330473
$119$	5.36612	−	3.89872i	0.491912	−	0.357395i
$120$		0			0
$121$	7.95761	+	5.78155i	0.723419	+	0.525595i
$122$	15.8280	+	11.4997i	1.43300	+	1.04114i
$123$	−3.47998	+	10.7103i	−0.313779	+	0.965713i
$124$	−37.0796			−3.32984
$125$		0			0
$126$	−4.53315			−0.403845
$127$	6.25332	−	19.2457i	0.554893	−	1.70778i	−0.141334	−	0.989962i	$-0.545139\pi$
$127$	6.25332	−	19.2457i	0.554893	−	1.70778i	0.696227	−	0.717822i	$-0.254861\pi$
$128$	−16.5882	−	12.0521i	−1.46621	−	1.06526i
$129$	2.09201	+	1.51994i	0.184192	+	0.133823i
$130$		0			0
$131$	2.46759	−	1.79281i	0.215595	−	0.156639i	−0.474747	−	0.880122i	$-0.657460\pi$
$131$	2.46759	−	1.79281i	0.215595	−	0.156639i	0.690341	+	0.723484i	$0.257460\pi$
$132$	5.63164			0.490171
$133$	−1.60717	+	1.16768i	−0.139359	+	0.101250i
$134$	−10.3336	−	31.8037i	−0.892691	−	2.74742i
$135$		0			0
$136$	10.5127	−	32.3549i	0.901460	−	2.77441i
$137$	6.33795	+	19.5062i	0.541487	+	1.66653i	0.729199	+	0.684302i	$0.239893\pi$
$137$	6.33795	+	19.5062i	0.541487	+	1.66653i	−0.187711	+	0.982224i	$0.560107\pi$
$138$	3.37363	+	10.3830i	0.287183	+	0.883858i
$139$	5.66068	−	17.4218i	0.480133	−	1.47770i	−0.358775	−	0.933424i	$-0.616806\pi$
$139$	5.66068	−	17.4218i	0.480133	−	1.47770i	0.838908	−	0.544273i	$-0.183194\pi$
$140$		0			0
$141$	0.592639	+	1.82396i	0.0499092	+	0.153605i
$142$	13.0101	−	9.45242i	1.09179	−	0.793230i
$143$	−2.88825			−0.241527
$144$	−10.3635	+	7.52956i	−0.863629	+	0.627463i
$145$		0			0
$146$	−7.17517	−	5.21306i	−0.593821	−	0.431436i
$147$	3.36057	+	2.44159i	0.277175	+	0.201379i
$148$	7.39114	−	22.7476i	0.607548	−	1.86984i
$149$	0.705938			0.0578327			0.0289163	−	0.999582i	$-0.490794\pi$
$149$	0.705938			0.0578327			0.0289163	+	0.999582i	$0.490794\pi$
$150$		0			0
$151$	7.04538			0.573345			0.286673	−	0.958029i	$-0.407451\pi$
$151$	7.04538			0.573345			0.286673	+	0.958029i	$0.407451\pi$
$152$	−3.14860	+	9.69039i	−0.255385	+	0.785994i
$153$	−3.18079	−	2.31098i	−0.257151	−	0.186831i
$154$	3.95645	+	2.87453i	0.318820	+	0.231636i
$155$		0			0
$156$	11.3066	−	8.21470i	0.905249	−	0.657702i
$157$	5.12880			0.409323			0.204662	−	0.978833i	$-0.434391\pi$
$157$	5.12880			0.409323			0.204662	+	0.978833i	$0.434391\pi$
$158$	8.70423	−	6.32399i	0.692471	−	0.503110i
$159$	0.787563	+	2.42387i	0.0624578	+	0.192225i
$160$		0			0
$161$	−2.11811	+	6.51888i	−0.166931	+	0.513760i
$162$	0.830342	+	2.55553i	0.0652378	+	0.200781i
$163$	7.49715	+	23.0739i	0.587222	+	1.80728i	0.590157	+	0.807289i	$0.299066\pi$
$163$	7.49715	+	23.0739i	0.587222	+	1.80728i	−0.00293441	+	0.999996i	$0.500934\pi$
$164$	−18.1662	+	55.9097i	−1.41854	+	4.36581i
$165$		0			0
$166$	−7.36913	−	22.6799i	−0.571955	−	1.76030i
$167$	3.68013	−	2.67377i	0.284777	−	0.206903i	−0.436221	−	0.899840i	$-0.643683\pi$
$167$	3.68013	−	2.67377i	0.284777	−	0.206903i	0.720998	+	0.692937i	$0.243683\pi$
$168$	−14.5976			−1.12623
$169$	4.71853	−	3.42821i	0.362964	−	0.263709i
$170$		0			0
$171$	0.952655	+	0.692144i	0.0728513	+	0.0529296i
$172$	10.9207	+	7.93437i	0.832697	+	0.604990i
$173$	0.827327	−	2.54625i	0.0629005	−	0.193588i	−0.914668	−	0.404206i	$-0.867548\pi$
$173$	0.827327	−	2.54625i	0.0629005	−	0.193588i	0.977568	+	0.210618i	$0.0675478\pi$
$174$	16.0039			1.21325
$175$		0			0
$176$	13.8197			1.04170
$177$	0.412843	−	1.27060i	0.0310312	−	0.0955042i
$178$	−33.5723	−	24.3917i	−2.51635	−	1.82823i
$179$	12.6422	+	9.18511i	0.944924	+	0.686528i	0.949601	−	0.313461i	$-0.101489\pi$
$179$	12.6422	+	9.18511i	0.944924	+	0.686528i	−0.00467674	+	0.999989i	$0.501489\pi$
$180$		0			0
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	−0.593867	−	0.804563i	$-0.702400\pi$
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	0.581670	+	0.813425i	$0.302400\pi$
$182$	12.1363			0.899603
$183$	5.89050	−	4.27970i	0.435439	−	0.316365i
$184$	10.8638	+	33.4352i	0.800887	+	2.46488i
$185$		0			0
$186$	−5.89800	+	18.1522i	−0.432462	+	1.33098i
$187$	1.31071	+	4.03396i	0.0958488	+	0.294992i
$188$	3.09369	+	9.52141i	0.225631	+	0.694420i
$189$	−0.521325	+	1.60447i	−0.0379208	+	0.116708i
$190$		0			0
$191$	−2.44734	−	7.53213i	−0.177083	−	0.545006i	0.822639	−	0.568563i	$-0.192501\pi$
$191$	−2.44734	−	7.53213i	−0.177083	−	0.545006i	−0.999722	+	0.0235578i	$0.992501\pi$
$192$	−16.4798	+	11.9732i	−1.18932	+	0.864094i
$193$	16.4269			1.18243			0.591216	−	0.806513i	$-0.298648\pi$
$193$	16.4269			1.18243			0.591216	+	0.806513i	$0.298648\pi$
$194$	23.4086	−	17.0073i	1.68064	−	1.22106i
$195$		0			0
$196$	17.5428	+	12.7456i	1.25306	+	0.910400i
$197$	−13.8640	−	10.0728i	−0.987770	−	0.717657i	−0.0283382	−	0.999598i	$-0.509022\pi$
$197$	−13.8640	−	10.0728i	−0.987770	−	0.717657i	−0.959432	+	0.281942i	$0.909022\pi$
$198$	0.895787	−	2.75695i	0.0636608	−	0.195928i
$199$	−2.01848			−0.143086			−0.0715430	−	0.997438i	$-0.522792\pi$
$199$	−2.01848			−0.143086			−0.0715430	+	0.997438i	$0.522792\pi$
$200$		0			0
$201$	−12.4451			−0.877806
$202$	−11.2639	+	34.6668i	−0.792528	+	2.43915i
$203$	8.12895	+	5.90603i	0.570541	+	0.414522i
$204$	−16.6043	−	12.0638i	−1.16254	−	0.844632i
$205$		0			0
$206$	2.97610	−	2.16226i	0.207355	−	0.150652i
$207$	4.06295			0.282394
$208$	27.7456	−	20.1584i	1.92381	−	1.39773i
$209$	−0.392562	−	1.20818i	−0.0271541	−	0.0835717i
$210$		0			0
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	0.291018	+	0.956718i	$0.406006\pi$
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	−0.797783	+	0.602945i	$0.793994\pi$
$212$	4.11123	+	12.6531i	0.282361	+	0.869017i
$213$	−1.84941	−	5.69189i	−0.126719	−	0.390002i
$214$	−9.14333	+	28.1403i	−0.625025	+	1.92363i
$215$		0			0
$216$	2.67386	+	8.22930i	0.181933	+	0.559933i
$217$	−9.69463	+	7.04356i	−0.658115	+	0.478148i
$218$	9.26733			0.627663
$219$	−2.67028	+	1.94007i	−0.180441	+	0.131098i
$220$		0			0
$221$	8.51571	+	6.18702i	0.572828	+	0.416184i
$222$	−9.96035	−	7.23662i	−0.668495	−	0.485690i
$223$	−4.05158	+	12.4695i	−0.271314	+	0.835017i	0.718858	+	0.695157i	$0.244665\pi$
$223$	−4.05158	+	12.4695i	−0.271314	+	0.835017i	−0.990171	+	0.139860i	$0.955335\pi$
$224$	−28.8746			−1.92927
$225$		0			0
$226$	−16.2618			−1.08172
$227$	8.12118	−	24.9944i	0.539022	−	1.65894i	−0.195774	−	0.980649i	$-0.562722\pi$
$227$	8.12118	−	24.9944i	0.539022	−	1.65894i	0.734795	−	0.678289i	$-0.237278\pi$
$228$	4.97305	+	3.61313i	0.329348	+	0.239285i
$229$	−1.61484	−	1.17325i	−0.106711	−	0.0775304i	0.533150	−	0.846021i	$-0.321008\pi$
$229$	−1.61484	−	1.17325i	−0.106711	−	0.0775304i	−0.639861	+	0.768490i	$0.721008\pi$
$230$		0			0
$231$	1.47242	−	1.06978i	0.0968781	−	0.0703861i
$232$	51.5357			3.38348
$233$	−0.425178	+	0.308910i	−0.0278543	+	0.0202373i	−0.601625	−	0.798778i	$-0.705480\pi$
$233$	−0.425178	+	0.308910i	−0.0278543	+	0.0202373i	0.573771	+	0.819016i	$0.305480\pi$
$234$	−2.22302	−	6.84175i	−0.145323	−	0.447259i
$235$		0			0
$236$	2.15512	−	6.63278i	0.140286	−	0.431757i
$237$	−1.23732	−	3.80807i	−0.0803723	−	0.247361i
$238$	−5.50757	−	16.9505i	−0.357002	−	1.09874i
$239$	−2.16612	+	6.66663i	−0.140115	+	0.431229i	−0.996350	−	0.0853565i	$-0.972797\pi$
$239$	−2.16612	+	6.66663i	−0.140115	+	0.431229i	0.856236	+	0.516585i	$0.172797\pi$
$240$		0			0
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	0.971454	−	0.237228i	$-0.0762388\pi$
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	−0.925362	+	0.379085i	$0.876239\pi$
$242$	21.3824	−	15.5353i	1.37452	−	0.998644i
$243$	1.00000			0.0641500
$244$	30.7496	−	22.3409i	1.96854	−	1.43023i
$245$		0			0
$246$	24.4808	+	17.7864i	1.56084	+	1.13402i
$247$	−2.55048	−	1.85303i	−0.162283	−	0.117906i
$248$	−18.9927	+	58.4536i	−1.20604	+	3.71180i
$249$	−8.87482			−0.562419
$250$		0			0
$251$	−6.17885			−0.390005			−0.195003	−	0.980803i	$-0.562472\pi$
$251$	−6.17885			−0.390005			−0.195003	+	0.980803i	$0.562472\pi$
$252$	−2.72142	+	8.37566i	−0.171433	+	0.527617i
$253$	−3.54607	−	2.57637i	−0.222939	−	0.161975i
$254$	−43.9907	−	31.9611i	−2.76022	−	2.00542i
$255$		0			0
$256$	−11.6138	+	8.43794i	−0.725864	+	0.527371i
$257$	−13.2239			−0.824882			−0.412441	−	0.910984i	$-0.635324\pi$
$257$	−13.2239			−0.824882			−0.412441	+	0.910984i	$0.635324\pi$
$258$	5.62133	−	4.08413i	0.349969	−	0.254267i
$259$	−2.38864	−	7.35148i	−0.148423	−	0.456799i
$260$		0			0
$261$	1.84049	−	5.66445i	0.113923	−	0.350620i
$262$	−2.53264	−	7.79465i	−0.156467	−	0.481555i
$263$	2.15583	+	6.63498i	0.132934	+	0.409130i	0.995263	−	0.0972190i	$-0.0309947\pi$
$263$	2.15583	+	6.63498i	0.132934	+	0.409130i	−0.862329	+	0.506349i	$0.830995\pi$
$264$	2.88461	−	8.87792i	0.177536	−	0.546398i
$265$		0			0
$266$	1.64953	+	5.07674i	0.101139	+	0.311275i
$267$	−12.4941	+	9.07752i	−0.764629	+	0.555535i
$268$	−64.9656			−3.96841
$269$	−19.1898	+	13.9422i	−1.17002	+	0.850070i	−0.991011	−	0.133777i	$-0.957289\pi$
$269$	−19.1898	+	13.9422i	−1.17002	+	0.850070i	−0.179010	+	0.983847i	$0.557289\pi$
$270$		0			0
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.990966	−	0.134114i	$-0.957181\pi$
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.433775	−	0.901021i	$-0.642819\pi$
$272$	−40.7460	−	29.6037i	−2.47059	−	1.79499i
$273$	1.39571	−	4.29555i	0.0844721	−	0.259978i
$274$	55.1113			3.32940
$275$		0			0
$276$	21.2094			1.27665
$277$	2.65343	−	8.16641i	0.159429	−	0.490672i	−0.839154	−	0.543894i	$-0.816949\pi$
$277$	2.65343	−	8.16641i	0.159429	−	0.490672i	0.998583	+	0.0532223i	$0.0169492\pi$
$278$	−39.8216	−	28.9321i	−2.38834	−	1.73523i
$279$	5.74653	+	4.17510i	0.344036	+	0.249957i
$280$		0			0
$281$	−13.8877	+	10.0900i	−0.828471	+	0.601919i	−0.919126	−	0.393963i	$-0.871104\pi$
$281$	−13.8877	+	10.0900i	−0.828471	+	0.601919i	0.0906557	+	0.995882i	$0.471104\pi$
$282$	5.15327			0.306872
$283$	−7.78278	+	5.65452i	−0.462638	+	0.336126i	−0.794565	−	0.607179i	$-0.792301\pi$
$283$	−7.78278	+	5.65452i	−0.462638	+	0.336126i	0.331927	+	0.943305i	$0.392301\pi$
$284$	−9.65426	−	29.7128i	−0.572875	−	1.76313i
$285$		0			0
$286$	−2.39823	+	7.38100i	−0.141810	+	0.436447i
$287$	5.87087	+	18.0687i	0.346546	+	1.06656i
$288$	5.28899	+	16.2779i	0.311657	+	0.959182i
$289$	−0.476498	+	1.46651i	−0.0280293	+	0.0862654i
$290$		0			0
$291$	−3.32756	−	10.2412i	−0.195065	−	0.600348i
$292$	−13.9394	+	10.1276i	−0.815742	+	0.592671i
$293$	−16.8202			−0.982649			−0.491324	−	0.870977i	$-0.663487\pi$
$293$	−16.8202			−0.982649			−0.491324	+	0.870977i	$0.663487\pi$
$294$	9.02998	−	6.56067i	0.526639	−	0.382626i
$295$		0			0
$296$	−32.0743	−	23.3033i	−1.86428	−	1.35448i
$297$	−0.872782	−	0.634113i	−0.0506439	−	0.0367950i
$298$	0.586170	−	1.80404i	0.0339559	−	0.104505i
$299$	−10.8775			−0.629059
$300$		0			0
$301$	4.36247			0.251449
$302$	5.85008	−	18.0047i	0.336634	−	1.03605i
$303$	10.9747	+	7.97356i	0.630478	+	0.458069i
$304$	12.2036	+	8.86641i	0.699922	+	0.508523i
$305$		0			0
$306$	−8.54691	+	6.20969i	−0.488594	+	0.354984i
$307$	−11.3212			−0.646134			−0.323067	−	0.946376i	$-0.604714\pi$
$307$	−11.3212			−0.646134			−0.323067	+	0.946376i	$0.604714\pi$
$308$	7.68632	−	5.58444i	0.437969	−	0.318203i
$309$	−0.423056	−	1.30203i	−0.0240668	−	0.0740700i
$310$		0			0
$311$	5.73642	−	17.6549i	0.325283	−	1.00112i	−0.646030	−	0.763312i	$-0.723572\pi$
$311$	5.73642	−	17.6549i	0.325283	−	1.00112i	0.971313	−	0.237805i	$-0.0764280\pi$
$312$	−7.15855	−	22.0318i	−0.405273	−	1.24730i
$313$	2.99731	+	9.22478i	0.169418	+	0.521416i	0.999335	−	0.0364720i	$-0.0116120\pi$
$313$	2.99731	+	9.22478i	0.169418	+	0.521416i	−0.829916	+	0.557888i	$0.811612\pi$
$314$	4.25866	−	13.1068i	0.240330	−	0.739660i
$315$		0			0
$316$	−6.45903	−	19.8789i	−0.363349	−	1.11827i
$317$	6.04859	−	4.39456i	0.339723	−	0.246823i	−0.404822	−	0.914395i	$-0.632667\pi$
$317$	6.04859	−	4.39456i	0.339723	−	0.246823i	0.744545	+	0.667573i	$0.232667\pi$
$318$	6.84822			0.384029
$319$	−5.19825	+	3.77675i	−0.291046	+	0.211457i
$320$		0			0
$321$	8.90851	+	6.47241i	0.497225	+	0.361255i
$322$	14.9004	+	10.8258i	0.830369	+	0.603298i
$323$	−1.43066	+	4.40313i	−0.0796042	+	0.244997i
$324$	5.22020			0.290011
$325$		0			0
$326$	65.1911			3.61060
$327$	1.06577	−	3.28010i	0.0589371	−	0.181390i
$328$	78.8331	+	57.2756i	4.35283	+	3.16252i
$329$	2.61753	+	1.90175i	0.144309	+	0.104847i
$330$		0			0
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.138439	−	0.990371i	$-0.455791\pi$
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.984679	+	0.174378i	$0.0557914\pi$
$332$	−46.3283			−2.54259
$333$	−3.70681	+	2.69315i	−0.203132	+	0.147584i
$334$	−3.77714	−	11.6248i	−0.206676	−	0.636083i
$335$		0			0
$336$	−6.67820	+	20.5534i	−0.364325	+	1.12128i
$337$	4.02464	+	12.3866i	0.219236	+	0.674739i	0.998826	+	0.0484485i	$0.0154277\pi$
$337$	4.02464	+	12.3866i	0.219236	+	0.674739i	−0.779590	+	0.626291i	$0.784572\pi$
$338$	−4.84291	−	14.9049i	−0.263419	−	0.810721i
$339$	−1.87015	+	5.75574i	−0.101573	+	0.312609i
$340$		0			0
$341$	−2.36798	−	7.28790i	−0.128233	−	0.394662i
$342$	2.55982	−	1.85982i	0.138419	−	0.100568i
$343$	18.8171			1.01603
$344$	18.1018	−	13.1517i	0.975983	−	0.709093i
$345$		0			0
$346$	−5.82005	−	4.22852i	−0.312888	−	0.227326i
$347$	−4.85531	−	3.52759i	−0.260647	−	0.189371i	0.449785	−	0.893137i	$-0.351500\pi$
$347$	−4.85531	−	3.52759i	−0.260647	−	0.189371i	−0.710432	+	0.703766i	$0.751500\pi$
$348$	9.60772	−	29.5695i	0.515028	−	1.58509i
$349$	−22.7183			−1.21608			−0.608042	−	0.793905i	$-0.708045\pi$
$349$	−22.7183			−1.21608			−0.608042	+	0.793905i	$0.708045\pi$
$350$		0			0
$351$	−2.67723			−0.142900
$352$	5.70586	−	17.5608i	0.304123	−	0.935996i
$353$	−3.92772	−	2.85366i	−0.209052	−	0.151885i	0.478333	−	0.878179i	$-0.341241\pi$
$353$	−3.92772	−	2.85366i	−0.209052	−	0.151885i	−0.687385	+	0.726294i	$0.741241\pi$
$354$	−2.90425	−	2.11006i	−0.154359	−	0.112149i
$355$		0			0
$356$	−65.2218	+	47.3864i	−3.45675	+	2.51148i
$357$	−6.63289			−0.351050
$358$	33.9702	−	24.6808i	1.79538	−	1.30442i
$359$	8.92780	+	27.4769i	0.471191	+	1.45018i	0.851026	+	0.525123i	$0.175981\pi$
$359$	8.92780	+	27.4769i	0.471191	+	1.45018i	−0.379835	+	0.925054i	$0.624019\pi$
$360$		0			0
$361$	−5.44284	+	16.7513i	−0.286465	+	0.881649i
$362$	0.168429	+	0.518371i	0.00885242	+	0.0272450i
$363$	−3.03954	−	9.35474i	−0.159534	−	0.490996i
$364$	7.28587	−	22.4236i	0.381883	−	1.17532i
$365$		0			0
$366$	−6.04577	−	18.6070i	−0.316018	−	0.972602i
$367$	−11.8998	+	8.64570i	−0.621163	+	0.451302i	−0.853328	−	0.521375i	$-0.825419\pi$
$367$	−11.8998	+	8.64570i	−0.621163	+	0.451302i	0.232164	+	0.972677i	$0.425419\pi$
$368$	52.0465			2.71311
$369$	9.11070	−	6.61931i	0.474284	−	0.344588i
$370$		0			0
$371$	3.47846	+	2.52725i	0.180592	+	0.131208i
$372$	29.9980	+	21.7948i	1.55532	+	1.13001i
$373$	10.2096	−	31.4220i	0.528635	−	1.62697i	−0.228378	−	0.973572i	$-0.573342\pi$
$373$	10.2096	−	31.4220i	0.528635	−	1.62697i	0.757013	−	0.653399i	$-0.226658\pi$
$374$	11.3972			0.589337
$375$		0			0
$376$	16.5945			0.855797
$377$	−4.92742	+	15.1650i	−0.253775	+	0.781039i
$378$	3.66740	+	2.66452i	0.188631	+	0.137048i
$379$	12.2612	+	8.90826i	0.629814	+	0.457587i	0.856336	−	0.516419i	$-0.172735\pi$
$379$	12.2612	+	8.90826i	0.629814	+	0.457587i	−0.226522	+	0.974006i	$0.572735\pi$
$380$		0			0
$381$	−16.3714	+	11.8945i	−0.838733	+	0.609375i
$382$	−21.2807			−1.08882
$383$	−6.47870	+	4.70705i	−0.331046	+	0.240519i	−0.740874	−	0.671644i	$-0.765589\pi$
$383$	−6.47870	+	4.70705i	−0.331046	+	0.240519i	0.409828	+	0.912163i	$0.365589\pi$
$384$	6.33615	+	19.5007i	0.323340	+	0.995139i
$385$		0			0
$386$	13.6399	−	41.9793i	0.694253	−	2.13669i
$387$	−0.799078	−	2.45931i	−0.0406194	−	0.125014i
$388$	−17.3705	−	53.4609i	−0.881854	−	2.71407i
$389$	0.332078	−	1.02203i	0.0168370	−	0.0518191i	−0.942285	−	0.334812i	$-0.891327\pi$
$389$	0.332078	−	1.02203i	0.0168370	−	0.0518191i	0.959122	+	0.282993i	$0.0913272\pi$
$390$		0			0
$391$	4.93629	+	15.1923i	0.249639	+	0.768309i
$392$	29.0783	−	21.1266i	1.46868	−	1.06706i
$393$	−3.05011			−0.153858
$394$	−37.2532	+	27.0660i	−1.87679	+	1.36357i
$395$		0			0
$396$	−4.55609	−	3.31019i	−0.228952	−	0.166344i
$397$	−19.5894	−	14.2326i	−0.983166	−	0.714312i	−0.0247517	−	0.999694i	$-0.507880\pi$
$397$	−19.5894	−	14.2326i	−0.983166	−	0.714312i	−0.958414	+	0.285382i	$0.907880\pi$
$398$	−1.67603	+	5.15828i	−0.0840116	+	0.258561i
$399$	1.98657			0.0994529
$400$		0			0
$401$	−1.99317			−0.0995340			−0.0497670	−	0.998761i	$-0.515848\pi$
$401$	−1.99317			−0.0995340			−0.0497670	+	0.998761i	$0.515848\pi$
$402$	−10.3336	+	31.8037i	−0.515395	+	1.58622i
$403$	−15.3848	−	11.1777i	−0.766371	−	0.556801i
$404$	57.2899	+	41.6235i	2.85028	+	2.07085i
$405$		0			0
$406$	21.8428	−	15.8698i	1.08404	−	0.787603i
$407$	4.94300			0.245015
$408$	−27.5227	+	19.9964i	−1.36258	+	0.989971i
$409$	2.05953	+	6.33858i	0.101837	+	0.313423i	0.988975	−	0.148082i	$-0.0473098\pi$
$409$	2.05953	+	6.33858i	0.101837	+	0.313423i	−0.887138	+	0.461504i	$0.847310\pi$
$410$		0			0
$411$	6.33795	−	19.5062i	0.312628	−	0.962169i
$412$	−2.20843	−	6.79686i	−0.108802	−	0.334857i
$413$	−0.696484	−	2.14356i	−0.0342717	−	0.105477i
$414$	3.37363	−	10.3830i	0.165805	−	0.510295i
$415$		0			0
$416$	−14.1599	−	43.5796i	−0.694245	−	2.13667i
$417$	−14.8199	+	10.7673i	−0.725732	+	0.527275i
$418$	−3.41351			−0.166960
$419$	−17.2758	+	12.5516i	−0.843977	+	0.613185i	−0.923479	−	0.383650i	$-0.874667\pi$
$419$	−17.2758	+	12.5516i	−0.843977	+	0.613185i	0.0795021	+	0.996835i	$0.474667\pi$
$420$		0			0
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	0.0527243	−	0.998609i	$-0.483210\pi$
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	−0.933441	+	0.358731i	$0.883210\pi$
$422$	51.7842	+	37.6235i	2.52082	+	1.83148i
$423$	0.592639	−	1.82396i	0.0288151	−	0.0886838i
$424$	22.0526			1.07097
$425$		0			0
$426$	−16.0814			−0.779147
$427$	3.79580	−	11.6823i	0.183692	−	0.565344i
$428$	46.5042	+	33.7873i	2.24786	+	1.63317i
$429$	2.33664	+	1.69767i	0.112814	+	0.0819642i
$430$		0			0
$431$	24.6046	−	17.8763i	1.18516	−	0.861070i	0.192416	−	0.981313i	$-0.438368\pi$
$431$	24.6046	−	17.8763i	1.18516	−	0.861070i	0.992744	+	0.120244i	$0.0383677\pi$
$432$	12.8101			0.616324
$433$	0.466511	−	0.338940i	0.0224191	−	0.0162884i	−0.576519	−	0.817084i	$-0.695589\pi$
$433$	0.466511	−	0.338940i	0.0224191	−	0.0162884i	0.598938	+	0.800795i	$0.295589\pi$
$434$	9.95017	+	30.6235i	0.477624	+	1.46997i
$435$		0			0
$436$	5.56352	−	17.1227i	0.266444	−	0.820031i
$437$	−1.47843	−	4.55015i	−0.0707230	−	0.217663i
$438$	2.74067	+	8.43491i	0.130954	+	0.403036i
$439$	3.95681	−	12.1778i	0.188848	−	0.581215i	−0.811145	−	0.584845i	$-0.801155\pi$
$439$	3.95681	−	12.1778i	0.188848	−	0.581215i	0.999993	+	0.00363006i	$0.00115549\pi$
$440$		0			0
$441$	−1.28362	−	3.95058i	−0.0611249	−	0.188123i
$442$	22.8821	−	16.6248i	1.08839	−	0.790761i
$443$	−14.3147			−0.680110			−0.340055	−	0.940405i	$-0.610446\pi$
$443$	−14.3147			−0.680110			−0.340055	+	0.940405i	$0.610446\pi$
$444$	−19.3503	+	14.0588i	−0.918323	+	0.667200i
$445$		0			0
$446$	28.5019	+	20.7078i	1.34960	+	0.980545i
$447$	−0.571116	−	0.414940i	−0.0270128	−	0.0196260i
$448$	−10.6194	+	32.6833i	−0.501721	+	1.54414i
$449$	−11.9663			−0.564724			−0.282362	−	0.959308i	$-0.591118\pi$
$449$	−11.9663			−0.564724			−0.282362	+	0.959308i	$0.591118\pi$
$450$		0			0
$451$	−12.1490			−0.572076
$452$	−9.76257	+	30.0461i	−0.459193	+	1.41325i
$453$	−5.69983	−	4.14117i	−0.267802	−	0.194569i
$454$	−57.1306	−	41.5078i	−2.68127	−	1.94806i
$455$		0			0
$456$	8.24313	−	5.98899i	0.386020	−	0.280460i
$457$	8.22154			0.384587			0.192294	−	0.981337i	$-0.438407\pi$
$457$	8.22154			0.384587			0.192294	+	0.981337i	$0.438407\pi$
$458$	−4.33913	+	3.15257i	−0.202754	+	0.147310i
$459$	1.21495	+	3.73924i	0.0567091	+	0.174533i
$460$		0			0
$461$	0.393120	−	1.20990i	0.0183094	−	0.0563506i	−0.941484	−	0.337057i	$-0.890569\pi$
$461$	0.393120	−	1.20990i	0.0183094	−	0.0563506i	0.959794	+	0.280706i	$0.0905686\pi$
$462$	−1.51123	−	4.65109i	−0.0703088	−	0.216388i
$463$	−10.0976	−	31.0771i	−0.469273	−	1.44428i	−0.853527	−	0.521048i	$-0.825541\pi$
$463$	−10.0976	−	31.0771i	−0.469273	−	1.44428i	0.384254	−	0.923227i	$-0.374459\pi$
$464$	23.5768	−	72.5618i	1.09452	−	3.36860i
$465$		0			0
$466$	0.436385	+	1.34305i	0.0202151	+	0.0622158i
$467$	11.6779	−	8.48450i	0.540389	−	0.392616i	−0.283840	−	0.958872i	$-0.591609\pi$
$467$	11.6779	−	8.48450i	0.540389	−	0.392616i	0.824230	+	0.566256i	$0.191609\pi$
$468$	−13.9757			−0.646026
$469$	−16.9856	+	12.3407i	−0.784321	+	0.569843i
$470$		0			0
$471$	−4.14929	−	3.01464i	−0.191189	−	0.138907i
$472$	−9.35227	−	6.79482i	−0.430473	−	0.312757i
$473$	−0.862060	+	2.65315i	−0.0396375	+	0.121992i
$474$	−10.7590			−0.494178
$475$		0			0
$476$	−34.6250			−1.58703
$477$	0.787563	−	2.42387i	0.0360600	−	0.110981i
$478$	15.2382	+	11.0712i	0.696977	+	0.506383i
$479$	13.6415	+	9.91113i	0.623296	+	0.452851i	0.854071	−	0.520156i	$-0.174126\pi$
$479$	13.6415	+	9.91113i	0.623296	+	0.452851i	−0.230775	+	0.973007i	$0.574126\pi$
$480$		0			0
$481$	9.92398	−	7.21020i	0.452495	−	0.328757i
$482$	6.22196			0.283403
$483$	5.54529	−	4.02889i	0.252320	−	0.183321i
$484$	−15.8670	−	48.8336i	−0.721227	−	2.21971i
$485$		0			0
$486$	0.830342	−	2.55553i	0.0376651	−	0.115921i
$487$	−12.3061	−	37.8744i	−0.557644	−	1.71625i	−0.688856	−	0.724898i	$-0.741887\pi$
$487$	−12.3061	−	37.8744i	−0.557644	−	1.71625i	0.131212	−	0.991354i	$-0.458113\pi$
$488$	−19.4686	−	59.9181i	−0.881301	−	2.71236i
$489$	7.49715	−	23.0739i	0.339033	−	1.04344i
$490$		0			0
$491$	4.33411	+	13.3390i	0.195596	+	0.601981i	0.999969	+	0.00785739i	$0.00250111\pi$
$491$	4.33411	+	13.3390i	0.195596	+	0.601981i	−0.804374	+	0.594124i	$0.797499\pi$
$492$	47.5596	−	34.5541i	2.14415	−	1.55782i
$493$	23.4168			1.05464
$494$	−6.85324	+	4.97917i	−0.308342	+	0.224024i
$495$		0			0
$496$	73.6133	+	53.4832i	3.30534	+	2.40147i
$497$	−8.16834	−	5.93464i	−0.366400	−	0.266205i
$498$	−7.36913	+	22.6799i	−0.330219	+	1.01631i
$499$	15.2315			0.681857			0.340929	−	0.940089i	$-0.389259\pi$
$499$	15.2315			0.681857			0.340929	+	0.940089i	$0.389259\pi$
$500$		0			0
$501$	−4.54890			−0.203230
$502$	−5.13055	+	15.7902i	−0.228988	+	0.704752i
$503$	19.2004	+	13.9499i	0.856104	+	0.621996i	0.926822	−	0.375501i	$-0.122529\pi$
$503$	19.2004	+	13.9499i	0.856104	+	0.621996i	−0.0707185	+	0.997496i	$0.522529\pi$
$504$	11.8097	+	8.58028i	0.526048	+	0.382196i
$505$		0			0
$506$	−9.52843	+	6.92281i	−0.423590	+	0.307756i
$507$	−5.83243			−0.259027
$508$	−85.4620	+	62.0918i	−3.79176	+	2.75488i
$509$	−3.86570	−	11.8974i	−0.171344	−	0.527343i	0.828103	−	0.560575i	$-0.189420\pi$
$509$	−3.86570	−	11.8974i	−0.171344	−	0.527343i	−0.999448	+	0.0332320i	$0.989420\pi$
$510$		0			0
$511$	−1.72071	+	5.29581i	−0.0761198	+	0.234273i
$512$	−0.752345	−	2.31548i	−0.0332493	−	0.102331i
$513$	−0.363882	−	1.11991i	−0.0160658	−	0.0494454i
$514$	−10.9803	+	33.7940i	−0.484321	+	1.49059i
$515$		0			0
$516$	−4.17134	−	12.8381i	−0.183633	−	0.565165i
$517$	−1.67384	+	1.21612i	−0.0736154	+	0.0534847i
$518$	−20.7703			−0.912595
$519$	−2.16597	+	1.57367i	−0.0950755	+	0.0690764i
$520$		0			0
$521$	22.6232	+	16.4367i	0.991141	+	0.720106i	0.960171	−	0.279414i	$-0.0901403\pi$
$521$	22.6232	+	16.4367i	0.991141	+	0.720106i	0.0309702	+	0.999520i	$0.490140\pi$
$522$	−12.9474	−	9.40685i	−0.566693	−	0.411727i
$523$	−4.85196	+	14.9328i	−0.212162	+	0.652966i	0.787181	+	0.616722i	$0.211540\pi$
$523$	−4.85196	+	14.9328i	−0.212162	+	0.652966i	−0.999343	+	0.0362446i	$0.988460\pi$
$524$	−15.9222			−0.695564
$525$		0			0
$526$	18.7460			0.817362
$527$	−8.62993	+	26.5602i	−0.375926	+	1.15698i
$528$	−11.1804	−	8.12302i	−0.486564	−	0.353509i
$529$	5.25252	+	3.81618i	0.228370	+	0.165921i
$530$		0			0
$531$	−1.08084	+	0.785274i	−0.0469043	+	0.0340780i
$532$	10.3703			0.449609
$533$	−24.3915	+	17.7214i	−1.05651	+	0.767601i
$534$	12.8235	+	39.4666i	0.554926	+	1.70789i
$535$		0			0
$536$	−33.2764	+	102.414i	−1.43732	+	4.42362i
$537$	−4.82890	−	14.8618i	−0.208382	−	0.641335i
$538$	19.6956	+	60.6168i	0.849137	+	2.61338i
$539$	−1.38479	+	4.26196i	−0.0596473	+	0.183576i
$540$		0			0
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	−0.974261	−	0.225425i	$-0.927623\pi$
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	0.655692	−	0.755028i	$-0.272377\pi$
$542$	−63.0224	+	45.7885i	−2.70705	+	1.96678i
$543$	0.202843			0.00870482
$544$	−54.4409	+	39.5536i	−2.33413	+	1.69585i
$545$		0			0
$546$	−9.81848	−	7.13354i	−0.420192	−	0.305287i
$547$	−4.55219	−	3.30736i	−0.194637	−	0.141412i	0.486198	−	0.873848i	$-0.338383\pi$
$547$	−4.55219	−	3.30736i	−0.194637	−	0.141412i	−0.680836	+	0.732436i	$0.738383\pi$
$548$	33.0853	−	101.826i	1.41333	−	4.34980i
$549$	−7.28106			−0.310748
$550$		0			0
$551$	−7.01341			−0.298781
$552$	10.8638	−	33.4352i	0.462392	−	1.42310i
$553$	−5.46490	−	3.97048i	−0.232391	−	0.168842i
$554$	−18.6663	−	13.5618i	−0.793053	−	0.576187i
$555$		0			0
$556$	−77.3626	+	56.2072i	−3.28090	+	2.38372i
$557$	42.4247			1.79759			0.898796	−	0.438366i	$-0.144443\pi$
$557$	42.4247			1.79759			0.898796	+	0.438366i	$0.144443\pi$
$558$	15.4412	−	11.2187i	0.653677	−	0.474924i
$559$	2.13932	+	6.58414i	0.0904835	+	0.278480i
$560$		0			0
$561$	1.31071	−	4.03396i	0.0553383	−	0.170314i
$562$	14.2538	+	43.8686i	0.601259	+	1.85048i
$563$	−1.78796	−	5.50279i	−0.0753537	−	0.231915i	0.906284	−	0.422669i	$-0.138907\pi$
$563$	−1.78796	−	5.50279i	−0.0753537	−	0.231915i	−0.981638	+	0.190754i	$0.938907\pi$
$564$	3.09369	−	9.52141i	0.130268	−	0.400924i
$565$		0			0
$566$	7.98793	+	24.5843i	0.335758	+	1.03336i
$567$	1.36485	−	0.991619i	0.0573181	−	0.0416441i
$568$	−51.7853			−2.17286
$569$	17.8029	−	12.9346i	0.746336	−	0.542245i	−0.148353	−	0.988934i	$-0.547397\pi$
$569$	17.8029	−	12.9346i	0.746336	−	0.542245i	0.894689	+	0.446690i	$0.147397\pi$
$570$		0			0
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.151210	−	0.988502i	$-0.548317\pi$
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.986847	+	0.161654i	$0.948317\pi$
$572$	12.1977	+	8.86216i	0.510012	+	0.370546i
$573$	−2.44734	+	7.53213i	−0.102239	+	0.314659i
$574$	51.0499			2.13078
$575$		0			0
$576$	20.3701			0.848754
$577$	−12.4333	+	38.2658i	−0.517605	+	1.59303i	0.260886	+	0.965370i	$0.415985\pi$
$577$	−12.4333	+	38.2658i	−0.517605	+	1.59303i	−0.778491	+	0.627656i	$0.784015\pi$
$578$	3.35205	+	2.43541i	0.139427	+	0.101300i
$579$	−13.2896	−	9.65547i	−0.552297	−	0.401268i
$580$		0			0
$581$	−12.1128	+	8.80043i	−0.502522	+	0.365103i
$582$	−28.9346			−1.19938
$583$	−2.22438	+	1.61611i	−0.0921243	+	0.0669323i
$584$	8.82549	+	27.1621i	0.365201	+	1.12397i
$585$		0			0
$586$	−13.9665	+	42.9846i	−0.576952	+	1.77568i
$587$	0.872353	+	2.68483i	0.0360059	+	0.110815i	0.967444	−	0.253085i	$-0.0814452\pi$
$587$	0.872353	+	2.68483i	0.0360059	+	0.110815i	−0.931438	+	0.363899i	$0.881445\pi$
$588$	−6.70076	−	20.6228i	−0.276335	−	0.850471i
$589$	2.58469	−	7.95485i	0.106500	−	0.327774i
$590$		0			0
$591$	5.29558	+	16.2981i	0.217831	+	0.670415i
$592$	−47.4844	+	34.4994i	−1.95160	+	1.41792i
$593$	24.6805			1.01351			0.506754	−	0.862091i	$-0.330845\pi$
$593$	24.6805			1.01351			0.506754	+	0.862091i	$0.330845\pi$
$594$	−2.34520	+	1.70389i	−0.0962248	+	0.0699114i
$595$		0			0
$596$	−2.98134	−	2.16607i	−0.122120	−	0.0887256i
$597$	1.63298	+	1.18643i	0.0668335	+	0.0485574i
$598$	−9.03200	+	27.7976i	−0.369346	+	1.13673i
$599$	−7.71547			−0.315245			−0.157623	−	0.987499i	$-0.550383\pi$
$599$	−7.71547			−0.315245			−0.157623	+	0.987499i	$0.550383\pi$
$600$		0			0
$601$	22.6506			0.923938			0.461969	−	0.886896i	$-0.347143\pi$
$601$	22.6506			0.923938			0.461969	+	0.886896i	$0.347143\pi$
$602$	3.62234	−	11.1484i	0.147636	−	0.454376i
$603$	10.0683	+	7.31502i	0.410011	+	0.297891i
$604$	−29.7543	−	21.6177i	−1.21068	−	0.879613i
$605$		0			0
$606$	29.4894	−	21.4253i	1.19792	−	0.870343i
$607$	24.6423			1.00020			0.500099	−	0.865968i	$-0.333297\pi$
$607$	24.6423			1.00020			0.500099	+	0.865968i	$0.333297\pi$
$608$	16.3052	−	11.8464i	0.661264	−	0.480436i
$609$	−3.10498	−	9.55616i	−0.125820	−	0.387235i
$610$		0			0
$611$	−1.58663	+	4.88315i	−0.0641883	+	0.197551i
$612$	6.34229	+	19.5196i	0.256372	+	0.789031i
$613$	12.9180	+	39.7574i	0.521751	+	1.60579i	0.770652	+	0.637256i	$0.219931\pi$
$613$	12.9180	+	39.7574i	0.521751	+	1.60579i	−0.248901	+	0.968529i	$0.580069\pi$
$614$	−9.40045	+	28.9316i	−0.379371	+	1.16758i
$615$		0			0
$616$	−4.86646	−	14.9774i	−0.196075	−	0.603458i
$617$	12.8949	−	9.36871i	0.519130	−	0.377170i	−0.297146	−	0.954832i	$-0.596035\pi$
$617$	12.8949	−	9.36871i	0.519130	−	0.377170i	0.816276	+	0.577662i	$0.196035\pi$
$618$	−3.67866			−0.147977
$619$	38.1613	−	27.7258i	1.53383	−	1.11440i	0.579775	−	0.814777i	$-0.303141\pi$
$619$	38.1613	−	27.7258i	1.53383	−	1.11440i	0.954059	−	0.299619i	$-0.0968595\pi$
$620$		0			0
$621$	−3.28699	−	2.38814i	−0.131902	−	0.0958327i
$622$	−40.3544	−	29.3192i	−1.61806	−	1.17559i
$623$	−8.05113	+	24.7788i	−0.322562	+	0.992743i
$624$	−34.2955			−1.37292
$625$		0			0
$626$	26.0630			1.04169
$627$	−0.392562	+	1.20818i	−0.0156774	+	0.0482501i
$628$	−21.6601	−	15.7370i	−0.864332	−	0.627974i
$629$	−14.5739	−	10.5886i	−0.581101	−	0.422195i
$630$		0			0
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.970735	−	0.240153i	$-0.922802\pi$
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.0715741	+	0.997435i	$0.522802\pi$
$632$	−34.6462			−1.37815
$633$	19.2718	−	14.0018i	0.765987	−	0.556522i
$634$	−6.20802	−	19.1063i	−0.246552	−	0.758809i
$635$		0			0
$636$	4.11123	−	12.6531i	0.163021	−	0.501727i
$637$	3.43656	+	10.5766i	0.136161	+	0.419061i
$638$	5.33526	+	16.4203i	0.211225	+	0.650084i
$639$	−1.84941	+	5.69189i	−0.0731614	+	0.225168i
$640$		0			0
$641$	5.56360	+	17.1230i	0.219749	+	0.676317i	0.998782	+	0.0493350i	$0.0157102\pi$
$641$	5.56360	+	17.1230i	0.219749	+	0.676317i	−0.779033	+	0.626982i	$0.784290\pi$
$642$	23.9376	−	17.3916i	0.944740	−	0.686394i
$643$	−21.8891			−0.863224			−0.431612	−	0.902059i	$-0.642055\pi$
$643$	−21.8891			−0.863224			−0.431612	+	0.902059i	$0.642055\pi$
$644$	28.9475	−	21.0316i	1.14069	−	0.828761i
$645$		0			0
$646$	10.0644	+	7.31220i	0.395978	+	0.287695i
$647$	15.3926	+	11.1834i	0.605147	+	0.439665i	0.847702	−	0.530473i	$-0.177985\pi$
$647$	15.3926	+	11.1834i	0.605147	+	0.439665i	−0.242555	+	0.970138i	$0.577985\pi$
$648$	2.67386	−	8.22930i	0.105039	−	0.323278i
$649$	1.44129			0.0565755
$650$		0			0
$651$	11.9832			0.469660
$652$	39.1366	−	120.450i	1.53271	−	4.71719i
$653$	−1.87669	−	1.36349i	−0.0734405	−	0.0533576i	0.550459	−	0.834862i	$-0.314453\pi$
$653$	−1.87669	−	1.36349i	−0.0734405	−	0.0533576i	−0.623900	+	0.781504i	$0.714453\pi$
$654$	−7.49743	−	5.44720i	−0.293173	−	0.213002i
$655$		0			0
$656$	116.709	−	84.7937i	4.55670	−	3.31064i
$657$	3.30065			0.128771
$658$	7.03341	−	5.11007i	0.274191	−	0.199211i
$659$	2.22239	+	6.83980i	0.0865719	+	0.266441i	0.984966	−	0.172750i	$-0.0552652\pi$
$659$	2.22239	+	6.83980i	0.0865719	+	0.266441i	−0.898394	+	0.439191i	$0.855265\pi$
$660$		0			0
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	−0.262358	−	0.964971i	$-0.584500\pi$
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	0.779447	−	0.626468i	$-0.215500\pi$
$662$	−20.9719	−	64.5450i	−0.815098	−	2.50861i
$663$	−3.25271	−	10.0108i	−0.126325	−	0.388788i
$664$	−23.7300	+	73.0336i	−0.920904	+	2.83425i
$665$		0			0
$666$	3.80451	+	11.7091i	0.147422	+	0.453718i
$667$	−19.5772	+	14.2236i	−0.758031	+	0.550742i
$668$	−23.7461			−0.918765
$669$	10.6072	−	7.70656i	0.410097	−	0.297953i
$670$		0			0
$671$	6.35478	+	4.61702i	0.245324	+	0.178238i
$672$	23.3601	+	16.9721i	0.901135	+	0.654713i
$673$	9.20966	−	28.3444i	0.355006	−	1.09260i	−0.600999	−	0.799250i	$-0.705231\pi$
$673$	9.20966	−	28.3444i	0.355006	−	1.09260i	0.956006	−	0.293348i	$-0.0947694\pi$
$674$	34.9961			1.34800
$675$		0			0
$676$	−30.4464			−1.17102
$677$	8.26144	−	25.4261i	0.317513	−	0.977204i	−0.657195	−	0.753721i	$-0.728257\pi$
$677$	8.26144	−	25.4261i	0.317513	−	0.977204i	0.974708	−	0.223483i	$-0.0717428\pi$
$678$	13.1561	+	9.55846i	0.505257	+	0.367091i
$679$	−14.6969	−	10.6780i	−0.564017	−	0.409782i
$680$		0			0
$681$	−21.2615	+	15.4474i	−0.814743	+	0.591946i
$682$	−20.5907			−0.788457
$683$	23.0529	−	16.7489i	0.882096	−	0.640880i	−0.0517093	−	0.998662i	$-0.516467\pi$
$683$	23.0529	−	16.7489i	0.882096	−	0.640880i	0.933805	+	0.357782i	$0.116467\pi$
$684$	−1.89953	−	5.84617i	−0.0726305	−	0.223534i
$685$		0			0
$686$	15.6246	−	48.0876i	0.596550	−	1.83599i
$687$	0.616813	+	1.89835i	0.0235329	+	0.0724267i
$688$	−10.2362	−	31.5039i	−0.390253	−	1.20107i
$689$	−2.10849	+	6.48926i	−0.0803270	+	0.247221i
$690$		0			0
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	0.918965	+	0.394340i	$0.129027\pi$
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	−0.511671	+	0.859182i	$0.670973\pi$
$692$	−11.3068	+	8.21486i	−0.429820	+	0.312282i
$693$	−1.82001			−0.0691365
$694$	−13.0464	+	9.47878i	−0.495235	+	0.359810i
$695$		0			0
$696$	−41.6932	−	30.2919i	−1.58038	−	1.14821i
$697$	35.8203	+	26.0249i	1.35679	+	0.985765i
$698$	−18.8640	+	58.0574i	−0.714012	+	2.19750i
$699$	0.525548			0.0198781
$700$		0			0
$701$	0.973305			0.0367612			0.0183806	−	0.999831i	$-0.494149\pi$
$701$	0.973305			0.0367612			0.0183806	+	0.999831i	$0.494149\pi$
$702$	−2.22302	+	6.84175i	−0.0839024	+	0.258225i
$703$	4.36494	+	3.17131i	0.164627	+	0.119608i
$704$	−17.7786	−	12.9169i	−0.670058	−	0.486826i
$705$		0			0
$706$	−10.5540	+	7.66790i	−0.397204	+	0.288585i
$707$	22.8854			0.860696
$708$	−5.64218	+	4.09928i	−0.212046	+	0.154061i
$709$	−3.49938	−	10.7700i	−0.131422	−	0.404475i	0.863594	−	0.504187i	$-0.168208\pi$
$709$	−3.49938	−	10.7700i	−0.131422	−	0.404475i	−0.995016	+	0.0997119i	$0.968208\pi$
$710$		0			0
$711$	−1.23732	+	3.80807i	−0.0464030	+	0.142814i
$712$	41.2941	+	127.090i	1.54756	+	4.76290i
$713$	−8.91808	−	27.4470i	−0.333985	−	1.02790i
$714$	−5.50757	+	16.9505i	−0.206115	+	0.634358i
$715$		0			0
$716$	−25.2078	−	77.5816i	−0.942060	−	2.89936i
$717$	5.67098	−	4.12021i	0.211787	−	0.153872i
$718$	77.6312			2.89717
$719$	24.8627	−	18.0638i	0.927224	−	0.673667i	−0.0180878	−	0.999836i	$-0.505758\pi$
$719$	24.8627	−	18.0638i	0.927224	−	0.673667i	0.945311	+	0.326169i	$0.105758\pi$
$720$		0			0
$721$	−1.86852	−	1.35756i	−0.0695875	−	0.0505583i
$722$	38.2891	+	27.8186i	1.42497	+	1.03530i
$723$	0.715542	−	2.20221i	0.0266113	−	0.0819011i
$724$	1.05888			0.0393529
$725$		0			0
$726$	−26.4302			−0.980915
$727$	2.02973	−	6.24688i	0.0752787	−	0.231684i	−0.906336	−	0.422558i	$-0.861132\pi$
$727$	2.02973	−	6.24688i	0.0752787	−	0.231684i	0.981615	+	0.190874i	$0.0611322\pi$
$728$	−31.6174	−	22.9714i	−1.17182	−	0.851377i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	8.22510	−	5.97589i	0.304216	−	0.221026i
$732$	−38.0086			−1.40484
$733$	−25.8300	+	18.7666i	−0.954051	+	0.693159i	−0.951762	−	0.306838i	$-0.900729\pi$
$733$	−25.8300	+	18.7666i	−0.954051	+	0.693159i	−0.00228977	+	0.999997i	$0.500729\pi$
$734$	12.2134	+	37.5891i	0.450806	+	1.38744i
$735$		0			0
$736$	21.4889	−	66.1360i	0.792091	−	2.43781i
$737$	−4.14885	−	12.7688i	−0.152825	−	0.470346i
$738$	−9.35085	−	28.7789i	−0.344209	−	1.05937i
$739$	−4.73017	+	14.5580i	−0.174002	+	0.535524i	−0.999586	−	0.0287550i	$-0.990846\pi$
$739$	−4.73017	+	14.5580i	−0.174002	+	0.535524i	0.825584	+	0.564279i	$0.190846\pi$
$740$		0			0
$741$	0.974196	+	2.99827i	0.0357880	+	0.110144i
$742$	9.34676	−	6.79082i	0.343130	−	0.249299i
$743$	−16.5455			−0.606995			−0.303498	−	0.952832i	$-0.598154\pi$
$743$	−16.5455			−0.606995			−0.303498	+	0.952832i	$0.598154\pi$
$744$	49.7236	−	36.1263i	1.82295	−	1.32445i
$745$		0			0
$746$	−71.8225	−	52.1821i	−2.62961	−	1.91052i
$747$	7.17988	+	5.21649i	0.262698	+	0.190861i
$748$	6.84217	−	21.0580i	0.250175	−	0.769959i
$749$	18.5769			0.678786
$750$		0			0
$751$	46.0279			1.67958			0.839791	−	0.542911i	$-0.182678\pi$
$751$	46.0279			1.67958			0.839791	+	0.542911i	$0.182678\pi$
$752$	7.59174	−	23.3650i	0.276842	−	0.852033i
$753$	4.99879	+	3.63184i	0.182166	+	0.132351i
$754$	34.6632	+	25.1843i	1.26236	+	0.917159i
$755$		0			0
$756$	7.12476	−	5.17644i	0.259125	−	0.188265i
$757$	26.5282			0.964184			0.482092	−	0.876121i	$-0.339877\pi$
$757$	26.5282			0.964184			0.482092	+	0.876121i	$0.339877\pi$
$758$	32.9463	−	23.9369i	1.19666	−	0.869427i
$759$	1.35448	+	4.16865i	0.0491644	+	0.151312i
$760$		0			0
$761$	−8.78353	+	27.0329i	−0.318403	+	0.979943i	0.655928	+	0.754823i	$0.272277\pi$
$761$	−8.78353	+	27.0329i	−0.318403	+	0.979943i	−0.974331	+	0.225120i	$0.927723\pi$
$762$	16.8029	+	51.7141i	0.608706	+	1.87341i
$763$	−1.79800	−	5.53366i	−0.0650918	−	0.200332i
$764$	−12.7756	+	39.3192i	−0.462204	+	1.42252i
$765$		0			0
$766$	6.64947	+	20.4650i	0.240255	+	0.739429i
$767$	2.89365	−	2.10236i	0.104484	−	0.0759119i
$768$	14.3555			0.518009
$769$	7.24841	−	5.26628i	0.261384	−	0.189907i	−0.449373	−	0.893344i	$-0.648353\pi$
$769$	7.24841	−	5.26628i	0.261384	−	0.189907i	0.710757	+	0.703438i	$0.248353\pi$
$770$		0			0
$771$	10.6983	+	7.77279i	0.385291	+	0.279930i
$772$	−69.3744	−	50.4034i	−2.49684	−	1.81406i
$773$	−7.13959	+	21.9734i	−0.256793	+	0.790329i	0.736678	+	0.676244i	$0.236393\pi$
$773$	−7.13959	+	21.9734i	−0.256793	+	0.790329i	−0.993471	+	0.114085i	$0.963607\pi$
$774$	−6.94834			−0.249753
$775$		0			0
$776$	−93.1752			−3.34479
$777$	−2.38864	+	7.35148i	−0.0856920	+	0.263733i
$778$	−2.33609	−	1.69727i	−0.0837530	−	0.0608501i
$779$	−10.7283	−	7.79455i	−0.384380	−	0.279269i
$780$		0			0
$781$	5.22343	−	3.79504i	0.186909	−	0.135797i
$782$	42.9232			1.53493
$783$	−4.81846	+	3.50082i	−0.172198	+	0.125109i
$784$	−16.4433	−	50.6072i	−0.587260	−	1.80740i
$785$		0			0
$786$	−2.53264	+	7.79465i	−0.0903361	+	0.278026i
$787$	0.628511	+	1.93436i	0.0224040	+	0.0689524i	0.961633	−	0.274338i	$-0.0884586\pi$
$787$	0.628511	+	1.93436i	0.0224040	+	0.0689524i	−0.939229	+	0.343290i	$0.888459\pi$
$788$	27.6440	+	85.0794i	0.984776	+	3.03083i
$789$	2.15583	−	6.63498i	0.0767497	−	0.236211i
$790$		0			0
$791$	3.15503	+	9.71018i	0.112180	+	0.345254i
$792$	−7.55201	+	5.48686i	−0.268349	+	0.194967i
$793$	19.4931			0.692220
$794$	−52.6376	+	38.2435i	−1.86804	+	1.35721i
$795$		0			0
$796$	8.52449	+	6.19340i	0.302142	+	0.219519i
$797$	−9.86379	−	7.16646i	−0.349393	−	0.253849i	0.399221	−	0.916855i	$-0.369281\pi$
$797$	−9.86379	−	7.16646i	−0.349393	−	0.253849i	−0.748614	+	0.663006i	$0.769281\pi$
$798$	1.64953	−	5.07674i	0.0583928	−	0.179715i
$799$	7.54024			0.266754
$800$		0			0
$801$	15.4436			0.545673
$802$	−1.65501	+	5.09359i	−0.0584404	+	0.179861i
$803$	−2.88075	−	2.09299i	−0.101659	−	0.0738599i
$804$	52.5583	+	38.1858i	1.85359	+	1.34671i
$805$		0			0
$806$	−41.3396	+	30.0350i	−1.45612	+	1.05794i
$807$	23.7199			0.834979
$808$	94.9616	−	68.9936i	3.34074	−	2.42719i
$809$	2.72972	+	8.40121i	0.0959718	+	0.295371i	0.987506	−	0.157583i	$-0.0503702\pi$
$809$	2.72972	+	8.40121i	0.0959718	+	0.295371i	−0.891534	+	0.452954i	$0.850370\pi$
$810$		0			0
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	−0.997737	−	0.0672381i	$-0.978581\pi$
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	0.846708	+	0.532058i	$0.178581\pi$
$812$	−16.2086	−	49.8850i	−0.568811	−	1.75062i
$813$	8.95871	+	27.5721i	0.314196	+	0.966995i
$814$	4.10438	−	12.6320i	0.143858	−	0.442750i
$815$		0			0
$816$	15.5636	+	47.8998i	0.544835	+	1.67683i
$817$	−2.46344	+	1.78980i	−0.0861850	+	0.0626170i
$818$	17.9085			0.626158
$819$	−3.65401	+	2.65479i	−0.127681	+	0.0927660i
$820$		0			0
$821$	23.8603	+	17.3355i	0.832731	+	0.605015i	0.920331	−	0.391141i	$-0.127920\pi$
$821$	23.8603	+	17.3355i	0.832731	+	0.605015i	−0.0875994	+	0.996156i	$0.527920\pi$
$822$	−44.5860	−	32.3936i	−1.55511	−	1.12986i
$823$	12.9682	−	39.9121i	0.452044	−	1.39125i	−0.422527	−	0.906350i	$-0.638857\pi$
$823$	12.9682	−	39.9121i	0.452044	−	1.39125i	0.874571	−	0.484898i	$-0.161143\pi$
$824$	−11.8460			−0.412675
$825$		0			0
$826$	−6.05624			−0.210724
$827$	−11.5781	+	35.6336i	−0.402609	+	1.23910i	0.520266	+	0.854004i	$0.325833\pi$
$827$	−11.5781	+	35.6336i	−0.402609	+	1.23910i	−0.922875	+	0.385099i	$0.874167\pi$
$828$	−17.1587	−	12.4666i	−0.596307	−	0.433243i
$829$	7.73108	+	5.61696i	0.268512	+	0.195085i	0.713891	−	0.700257i	$-0.246931\pi$
$829$	7.73108	+	5.61696i	0.268512	+	0.195085i	−0.445379	+	0.895342i	$0.646931\pi$
$830$		0			0
$831$	−6.94677	+	5.04712i	−0.240981	+	0.175083i
$832$	−54.5355			−1.89068
$833$	13.2126	−	9.59954i	0.457791	−	0.332604i
$834$	15.2105	+	46.8131i	0.526696	+	1.62100i
$835$		0			0
$836$	−2.04925	+	6.30695i	−0.0708748	+	0.218130i
$837$	−2.19498	−	6.75545i	−0.0758695	−	0.233502i
$838$	17.7311	+	54.5708i	0.612512	+	1.88512i
$839$	16.9128	−	52.0522i	0.583895	−	1.79704i	−0.0197702	−	0.999805i	$-0.506293\pi$
$839$	16.9128	−	52.0522i	0.583895	−	1.79704i	0.603665	−	0.797238i	$-0.293707\pi$
$840$		0			0
$841$	2.00037	+	6.15651i	0.0689783	+	0.212294i
$842$	−48.5570	+	35.2787i	−1.67338	+	1.21579i
$843$	17.1661			0.591233
$844$	100.603	−	73.0922i	3.46289	−	2.51594i
$845$		0			0
$846$	−4.16908	−	3.02901i	−0.143336	−	0.104140i
$847$	−13.4248	−	9.75371i	−0.461283	−	0.335141i
$848$	10.0887	−	31.0499i	0.346448	−	1.06626i
$849$	9.62005			0.330159
$850$		0			0
$851$	18.6159			0.638144
$852$	−9.65426	+	29.7128i	−0.330750	+	1.01794i
$853$	−12.3834	−	8.99706i	−0.423999	−	0.308053i	0.355246	−	0.934773i	$-0.384397\pi$
$853$	−12.3834	−	8.99706i	−0.423999	−	0.308053i	−0.779245	+	0.626720i	$0.784397\pi$
$854$	−26.7026	−	19.4005i	−0.913743	−	0.663873i
$855$		0			0
$856$	77.0836	−	56.0045i	2.63466	−	1.91419i
$857$	8.66910			0.296131			0.148065	−	0.988978i	$-0.452695\pi$
$857$	8.66910			0.296131			0.148065	+	0.988978i	$0.452695\pi$
$858$	6.27865	−	4.56171i	0.214350	−	0.155734i
$859$	−9.39653	−	28.9195i	−0.320605	−	0.986722i	−0.973385	−	0.229174i	$-0.926397\pi$
$859$	−9.39653	−	28.9195i	−0.320605	−	0.986722i	0.652780	−	0.757547i	$-0.273603\pi$
$860$		0			0
$861$	5.87087	−	18.0687i	0.200079	−	0.615779i
$862$	−25.2531	−	77.7211i	−0.860125	−	2.64719i
$863$	5.57545	+	17.1595i	0.189791	+	0.584115i	0.999998	−	0.00202803i	$-0.000645543\pi$
$863$	5.57545	+	17.1595i	0.189791	+	0.584115i	−0.810207	+	0.586143i	$0.800646\pi$
$864$	5.28899	−	16.2779i	0.179935	−	0.553784i
$865$		0			0
$866$	−0.478808	−	1.47362i	−0.0162706	−	0.0500756i
$867$	1.24749	−	0.906354i	0.0423669	−	0.0307814i
$868$	62.5548			2.12325
$869$	3.49465	−	2.53901i	0.118548	−	0.0861301i
$870$		0			0
$871$	−26.9551	−	19.5840i	−0.913338	−	0.663579i
$872$	−24.1432	−	17.5411i	−0.817591	−	0.594015i
$873$	−3.32756	+	10.2412i	−0.112621	+	0.346611i
$874$	−12.8556			−0.434848
$875$		0			0
$876$	17.2301			0.582149
$877$	−6.89285	+	21.2140i	−0.232755	+	0.716346i	0.764656	+	0.644438i	$0.222909\pi$
$877$	−6.89285	+	21.2140i	−0.232755	+	0.716346i	−0.997411	+	0.0719076i	$0.977091\pi$
$878$	−27.8352	−	20.2235i	−0.939393	−	0.682509i
$879$	13.6079	+	9.88669i	0.458982	+	0.333470i
$880$		0			0
$881$	−6.27761	+	4.56095i	−0.211498	+	0.153662i	−0.688491	−	0.725245i	$-0.741727\pi$
$881$	−6.27761	+	4.56095i	−0.211498	+	0.153662i	0.476993	+	0.878907i	$0.341727\pi$
$882$	−11.1617			−0.375833
$883$	−16.1421	+	11.7279i	−0.543224	+	0.394675i	−0.825281	−	0.564722i	$-0.808983\pi$
$883$	−16.1421	+	11.7279i	−0.543224	+	0.394675i	0.282057	+	0.959398i	$0.408983\pi$
$884$	−16.9798	−	52.2584i	−0.571092	−	1.75764i
$885$		0			0
$886$	−11.8861	+	36.5816i	−0.399320	+	1.22898i
$887$	−2.65844	−	8.18183i	−0.0892616	−	0.274719i	0.896454	−	0.443137i	$-0.146134\pi$
$887$	−2.65844	−	8.18183i	−0.0892616	−	0.274719i	−0.985716	+	0.168418i	$0.946134\pi$
$888$	12.2513	+	37.7056i	0.411126	+	1.26532i
$889$	−10.5496	+	32.4684i	−0.353823	+	1.08895i
$890$		0			0
$891$	0.333373	+	1.02602i	0.0111684	+	0.0343729i
$892$	55.3715	−	40.2297i	1.85397	−	1.34699i
$893$	−2.25832			−0.0755719
$894$	−1.53461	+	1.11496i	−0.0513251	+	0.0372899i
$895$		0			0
$896$	27.9851	+	20.3323i	0.934916	+	0.679256i
$897$	8.80004	+	6.39360i	0.293825	+	0.213476i
$898$	−9.93611	+	30.5802i	−0.331572	+	1.02047i
$899$	−42.3057			−1.41097
$900$		0			0
$901$	10.0203			0.333824
$902$	−10.0879	+	31.0472i	−0.335889	+	1.03376i
$903$	−3.52932	−	2.56420i	−0.117448	−	0.0853312i
$904$	42.3652	+	30.7801i	1.40905	+	1.02373i
$905$		0			0
$906$	−15.3157	+	11.1275i	−0.508830	+	0.369687i
$907$	−6.26125			−0.207902			−0.103951	−	0.994582i	$-0.533148\pi$
$907$	−6.26125			−0.207902			−0.103951	+	0.994582i	$0.533148\pi$
$908$	−110.989	+	80.6385i	−3.68331	+	2.67608i
$909$	−4.19195	−	12.9015i	−0.139038	−	0.427915i
$910$		0			0
$911$	0.279838	−	0.861253i	0.00927145	−	0.0285346i	−0.946314	−	0.323250i	$-0.895225\pi$
$911$	0.279838	−	0.861253i	0.00927145	−	0.0285346i	0.955585	+	0.294715i	$0.0952247\pi$
$912$	−4.66135	−	14.3461i	−0.154353	−	0.475048i
$913$	−2.95862	−	9.10571i	−0.0979162	−	0.301355i
$914$	6.82669	−	21.0104i	0.225807	−	0.694962i
$915$		0			0
$916$	3.21988	+	9.90978i	0.106388	+	0.327428i
$917$	−4.16293	+	3.02455i	−0.137472	+	0.0998794i
$918$	10.5646			0.348682
$919$	−35.5913	+	25.8586i	−1.17405	+	0.852997i	−0.991488	−	0.130198i	$-0.958439\pi$
$919$	−35.5913	+	25.8586i	−1.17405	+	0.852997i	−0.182561	+	0.983194i	$0.558439\pi$
$920$		0			0
$921$	9.15903	+	6.65443i	0.301800	+	0.219271i
$922$	−2.76551	−	2.00926i	−0.0910771	−	0.0661714i
$923$	4.95129	−	15.2385i	0.162974	−	0.501582i
$924$	−9.50081			−0.312554
$925$		0			0
$926$	−87.8029			−2.88538
$927$	−0.423056	+	1.30203i	−0.0138950	+	0.0427643i
$928$	−82.4707	−	59.9184i	−2.70723	−	1.96692i
$929$	29.7271	+	21.5980i	0.975313	+	0.708606i	0.956656	−	0.291220i	$-0.0940610\pi$
$929$	29.7271	+	21.5980i	0.975313	+	0.708606i	0.0186568	+	0.999826i	$0.494061\pi$
$930$		0			0
$931$	−3.95722	+	2.87509i	−0.129693	+	0.0942273i
$932$	2.74347			0.0898652
$933$	−15.0181	+	10.9113i	−0.491672	+	0.357221i
$934$	−11.9857	−	36.8883i	−0.392185	−	1.20702i
$935$		0			0
$936$	−7.15855	+	22.0318i	−0.233985	+	0.720131i
$937$	−7.61696	−	23.4426i	−0.248835	−	0.765836i	−0.994982	−	0.100055i	$-0.968098\pi$
$937$	−7.61696	−	23.4426i	−0.248835	−	0.765836i	0.746147	−	0.665782i	$-0.231902\pi$
$938$	17.4333	+	53.6542i	0.569217	+	1.75187i
$939$	2.99731	−	9.22478i	0.0978137	−	0.301039i
$940$		0			0
$941$	−18.2777	−	56.2530i	−0.595836	−	1.83379i	−0.550520	−	0.834822i	$-0.685571\pi$
$941$	−18.2777	−	56.2530i	−0.595836	−	1.83379i	−0.0453159	−	0.998973i	$-0.514429\pi$
$942$	−11.1493	+	8.10045i	−0.363264	+	0.263927i
$943$	−45.7546			−1.48998
$944$	−13.8456	+	10.0594i	−0.450635	+	0.327406i
$945$		0			0
$946$	6.06439	+	4.40604i	0.197170	+	0.143253i
$947$	−24.3482	−	17.6900i	−0.791210	−	0.574848i	0.117112	−	0.993119i	$-0.462636\pi$
$947$	−24.3482	−	17.6900i	−0.791210	−	0.574848i	−0.908322	+	0.418271i	$0.862636\pi$
$948$	−6.45903	+	19.8789i	−0.209780	+	0.645635i
$949$	−8.83661			−0.286849
$950$		0			0
$951$	−7.47647			−0.242441
$952$	−17.7354	+	54.5841i	−0.574809	+	1.76908i
$953$	−16.6975	−	12.1315i	−0.540886	−	0.392977i	0.283528	−	0.958964i	$-0.408495\pi$
$953$	−16.6975	−	12.1315i	−0.540886	−	0.392977i	−0.824414	+	0.565987i	$0.808495\pi$
$954$	−5.54032	−	4.02528i	−0.179375	−	0.130323i
$955$		0			0
$956$	29.6036	−	21.5083i	0.957449	−	0.695628i
$957$	6.42538			0.207703
$958$	36.6553	−	26.6316i	1.18428	−	0.860429i
$959$	−10.6924	−	32.9078i	−0.345275	−	1.06265i
$960$		0			0
$961$	6.01162	−	18.5019i	0.193923	−	0.596834i
$962$	−10.1856	−	31.3480i	−0.328396	−	1.01070i
$963$	−3.40275	−	10.4726i	−0.109652	−	0.337474i
$964$	3.73527	−	11.4960i	0.120305	−	0.370260i
$965$		0			0
$966$	−5.69146	−	17.5165i	−0.183120	−	0.563585i
$967$	−18.2850	+	13.2849i	−0.588007	+	0.427212i	−0.841602	−	0.540098i	$-0.818387\pi$
$967$	−18.2850	+	13.2849i	−0.588007	+	0.427212i	0.253595	+	0.967311i	$0.418387\pi$
$968$	−85.1103			−2.73555
$969$	3.74552	−	2.72128i	0.120324	−	0.0874202i
$970$		0			0
$971$	−19.5281	−	14.1880i	−0.626687	−	0.455315i	0.228564	−	0.973529i	$-0.426597\pi$
$971$	−19.5281	−	14.1880i	−0.626687	−	0.455315i	−0.855251	+	0.518214i	$0.826597\pi$
$972$	−4.22323	−	3.06835i	−0.135460	−	0.0984175i
$973$	−9.54981	+	29.3913i	−0.306153	+	0.942242i
$974$	−107.007			−3.42874
$975$		0			0
$976$	−93.2708			−2.98553
$977$	−7.12302	+	21.9224i	−0.227886	+	0.701360i	0.770100	+	0.637923i	$0.220206\pi$
$977$	−7.12302	+	21.9224i	−0.227886	+	0.701360i	−0.997986	+	0.0634371i	$0.979794\pi$
$978$	−52.7407	−	38.3184i	−1.68646	−	1.22529i
$979$	−13.4789	−	9.79299i	−0.430787	−	0.312985i
$980$		0			0
$981$	−2.79022	+	2.02721i	−0.0890847	+	0.0647239i
$982$	37.6870			1.20264
$983$	24.1664	−	17.5579i	0.770787	−	0.560010i	−0.131413	−	0.991328i	$-0.541951\pi$
$983$	24.1664	−	17.5579i	0.770787	−	0.560010i	0.902200	+	0.431318i	$0.141951\pi$
$984$	−30.1116	−	92.6738i	−0.959921	−	2.95433i
$985$		0			0
$986$	19.4440	−	59.8424i	0.619222	−	1.90577i
$987$	−0.999807	−	3.07709i	−0.0318242	−	0.0979449i
$988$	5.08550	+	15.6515i	0.161791	+	0.497942i
$989$	−3.24661	+	9.99204i	−0.103236	+	0.317728i
$990$		0			0
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	0.998923	−	0.0464072i	$-0.0147772\pi$
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	−0.835423	+	0.549608i	$0.814777\pi$
$992$	98.3550	−	71.4591i	3.12277	−	2.26883i
$993$	−25.2570			−0.801507
$994$	−21.9487	+	15.9466i	−0.696169	+	0.505797i
$995$		0			0
$996$	37.4804	+	27.2311i	1.18761	+	0.862850i
$997$	10.1074	+	7.34343i	0.320103	+	0.232569i	0.736220	−	0.676743i	$-0.236609\pi$
$997$	10.1074	+	7.34343i	0.320103	+	0.232569i	−0.416116	+	0.909311i	$0.636609\pi$
$998$	12.6474	−	38.9246i	0.400346	−	1.23214i
$999$	4.58187			0.144964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.226.3		12
5.2	odd	4		375.2.i.d.274.6		24
5.3	odd	4		375.2.i.d.274.1		24
5.4	even	2		75.2.g.c.46.1	yes	12
15.14	odd	2		225.2.h.d.46.3		12
25.6	even	5	inner	375.2.g.c.151.3		12
25.8	odd	20		375.2.i.d.349.6		24
25.9	even	10		1875.2.a.j.1.1		6
25.12	odd	20		1875.2.b.f.1249.12		12
25.13	odd	20		1875.2.b.f.1249.1		12
25.16	even	5		1875.2.a.k.1.6		6
25.17	odd	20		375.2.i.d.349.1		24
25.19	even	10		75.2.g.c.31.1	✓	12
75.41	odd	10		5625.2.a.q.1.1		6
75.44	odd	10		225.2.h.d.181.3		12
75.59	odd	10		5625.2.a.p.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.1	✓	12	25.19	even	10
75.2.g.c.46.1	yes	12	5.4	even	2
225.2.h.d.46.3		12	15.14	odd	2
225.2.h.d.181.3		12	75.44	odd	10
375.2.g.c.151.3		12	25.6	even	5	inner
375.2.g.c.226.3		12	1.1	even	1	trivial
375.2.i.d.274.1		24	5.3	odd	4
375.2.i.d.274.6		24	5.2	odd	4
375.2.i.d.349.1		24	25.17	odd	20
375.2.i.d.349.6		24	25.8	odd	20
1875.2.a.j.1.1		6	25.9	even	10
1875.2.a.k.1.6		6	25.16	even	5
1875.2.b.f.1249.1		12	25.13	odd	20
1875.2.b.f.1249.12		12	25.12	odd	20
5625.2.a.p.1.6		6	75.59	odd	10
5625.2.a.q.1.1		6	75.41	odd	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.830342 - 2.55553i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.22323 - 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.830342 - 2.55553i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.22323 - 3.06835i) q^{4} +(-2.17386 + 1.57940i) q^{6} -1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.333373 - 1.02602i) q^{11} +(1.61313 + 4.96470i) q^{12} +(-0.827310 - 2.54620i) q^{13} +(-1.40082 + 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(-3.18079 + 2.31098i) q^{17} +2.68704 q^{18} +(0.952655 - 0.692144i) q^{19} +(1.36485 + 0.991619i) q^{21} +(-2.34520 - 1.70389i) q^{22} +(1.25552 - 3.86409i) q^{23} +8.65280 q^{24} -7.19384 q^{26} +(0.309017 - 0.951057i) q^{27} +(7.12476 + 5.17644i) q^{28} +(-4.81846 - 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} +17.1155 q^{32} +(-0.872782 + 0.634113i) q^{33} +(3.26463 + 10.0475i) q^{34} +(1.61313 - 4.96470i) q^{36} +(1.41587 + 4.35761i) q^{37} +(-0.977766 - 3.00925i) q^{38} +(-0.827310 + 2.54620i) q^{39} +(-3.47998 - 10.7103i) q^{41} +(3.66740 - 2.66452i) q^{42} -2.58587 q^{43} +(-4.55609 + 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.55155 - 1.12727i) q^{47} +(3.95852 - 12.1831i) q^{48} -4.15389 q^{49} +3.93167 q^{51} +(-4.31872 + 13.2917i) q^{52} +(-2.06187 - 1.49803i) q^{53} +(-2.17386 - 1.57940i) q^{54} +(11.8097 - 8.58028i) q^{56} -1.17755 q^{57} +(-12.9474 + 9.40685i) q^{58} +(0.412843 + 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-5.89800 - 18.1522i) q^{62} +(-0.521325 - 1.60447i) q^{63} +(6.29470 - 19.3731i) q^{64} +(0.895787 + 2.75695i) q^{66} +(10.0683 - 7.31502i) q^{67} +20.5241 q^{68} +(-3.28699 + 2.38814i) q^{69} +(4.84181 + 3.51778i) q^{71} +(-7.00026 - 5.08599i) q^{72} +(1.01996 - 3.13911i) q^{73} +12.3117 q^{74} -6.14702 q^{76} +(-0.562414 + 1.73093i) q^{77} +(5.81994 + 4.22843i) q^{78} +(3.23934 + 2.35351i) q^{79} +(-0.809017 + 0.587785i) q^{81} -30.2600 q^{82} +(7.17988 - 5.21649i) q^{83} +(-2.72142 - 8.37566i) q^{84} +(-2.14716 + 6.60827i) q^{86} +(1.84049 + 5.66445i) q^{87} +(2.88461 + 8.87792i) q^{88} +(4.77234 - 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(-17.1587 + 12.4666i) q^{92} -7.10310 q^{93} +(-4.16908 + 3.02901i) q^{94} +(-13.8468 - 10.0603i) q^{96} +(8.71166 + 6.32939i) q^{97} +(-3.44915 + 10.6154i) q^{98} +1.07882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

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