LMFDB - Embedded newform 170.2.k.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.1
Root			$-1.33738i$ of defining polynomial
Character	$\chi$	$=$	170.151
Dual form			170.2.k.b.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.894478 - 2.15946i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{5} +(-0.894478 + 2.15946i) q^{6} +(-3.32333 - 1.37657i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74186 + 1.74186i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.894478 - 2.15946i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{5} +(-0.894478 + 2.15946i) q^{6} +(-3.32333 - 1.37657i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74186 + 1.74186i) q^{9} +(0.923880 + 0.382683i) q^{10} +(-0.760686 + 1.83646i) q^{11} +(2.15946 - 0.894478i) q^{12} -0.678817i q^{13} +(1.37657 + 3.32333i) q^{14} +(1.65278 + 1.65278i) q^{15} -1.00000 q^{16} +(-2.74368 + 3.07770i) q^{17} +2.46336 q^{18} +(-3.09055 - 3.09055i) q^{19} +(-0.382683 - 0.923880i) q^{20} +8.40790i q^{21} +(1.83646 - 0.760686i) q^{22} +(1.51321 - 3.65322i) q^{23} +(-2.15946 - 0.894478i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-0.479996 + 0.479996i) q^{26} +(-1.15885 - 0.480010i) q^{27} +(1.37657 - 3.32333i) q^{28} +(5.47189 - 2.26653i) q^{29} -2.33738i q^{30} +(-3.63256 - 8.76978i) q^{31} +(0.707107 + 0.707107i) q^{32} +4.64617 q^{33} +(4.11634 - 0.236183i) q^{34} +3.59714 q^{35} +(-1.74186 - 1.74186i) q^{36} +(-1.64894 - 3.98089i) q^{37} +4.37069i q^{38} +(-1.46588 + 0.607187i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(-1.70896 - 0.707874i) q^{41} +(5.94529 - 5.94529i) q^{42} +(8.51063 - 8.51063i) q^{43} +(-1.83646 - 0.760686i) q^{44} +(0.942688 - 2.27585i) q^{45} +(-3.65322 + 1.51321i) q^{46} +13.6499i q^{47} +(0.894478 + 2.15946i) q^{48} +(4.19982 + 4.19982i) q^{49} -1.00000 q^{50} +(9.10033 + 3.17194i) q^{51} +0.678817 q^{52} +(-4.30196 - 4.30196i) q^{53} +(0.480010 + 1.15885i) q^{54} -1.98777i q^{55} +(-3.32333 + 1.37657i) q^{56} +(-3.90949 + 9.43834i) q^{57} +(-5.47189 - 2.26653i) q^{58} +(-0.760963 + 0.760963i) q^{59} +(-1.65278 + 1.65278i) q^{60} +(1.68551 + 0.698163i) q^{61} +(-3.63256 + 8.76978i) q^{62} +(8.18656 - 3.39098i) q^{63} -1.00000i q^{64} +(0.259772 + 0.627145i) q^{65} +(-3.28534 - 3.28534i) q^{66} +5.62131 q^{67} +(-3.07770 - 2.74368i) q^{68} -9.24253 q^{69} +(-2.54356 - 2.54356i) q^{70} +(-4.51734 - 10.9058i) q^{71} +2.46336i q^{72} +(-5.67041 + 2.34876i) q^{73} +(-1.64894 + 3.98089i) q^{74} +(-2.15946 - 0.894478i) q^{75} +(3.09055 - 3.09055i) q^{76} +(5.05601 - 5.05601i) q^{77} +(1.46588 + 0.607187i) q^{78} +(-1.60739 + 3.88059i) q^{79} +(0.923880 - 0.382683i) q^{80} +10.3219i q^{81} +(0.707874 + 1.70896i) q^{82} +(11.8182 + 11.8182i) q^{83} -8.40790 q^{84} +(1.35705 - 3.89338i) q^{85} -12.0359 q^{86} +(-9.78898 - 9.78898i) q^{87} +(0.760686 + 1.83646i) q^{88} -0.600698i q^{89} +(-2.27585 + 0.942688i) q^{90} +(-0.934438 + 2.25593i) q^{91} +(3.65322 + 1.51321i) q^{92} +(-15.6887 + 15.6887i) q^{93} +(9.65190 - 9.65190i) q^{94} +(4.03799 + 1.67259i) q^{95} +(0.894478 - 2.15946i) q^{96} +(0.119918 - 0.0496715i) q^{97} -5.93944i q^{98} +(-1.87384 - 4.52386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.894478	−	2.15946i	−0.516427	−	1.24677i	−0.940084	−	0.340943i	$-0.889254\pi$
$3$	−0.894478	−	2.15946i	−0.516427	−	1.24677i	0.423657	−	0.905823i	$-0.360746\pi$
$4$			1.00000i			0.500000i
$5$	−0.923880	+	0.382683i	−0.413171	+	0.171141i
$5$	−0.923880	+	0.382683i	−0.413171	+	0.171141i
$6$	−0.894478	+	2.15946i	−0.365169	+	0.881596i
$7$	−3.32333	−	1.37657i	−1.25610	−	0.520293i	−0.347389	−	0.937721i	$-0.612932\pi$
$7$	−3.32333	−	1.37657i	−1.25610	−	0.520293i	−0.908710	+	0.417428i	$0.862932\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.74186	+	1.74186i	−0.580620	+	0.580620i
$10$	0.923880	+	0.382683i	0.292156	+	0.121015i
$11$	−0.760686	+	1.83646i	−0.229355	+	0.553713i	−0.996099	−	0.0882404i	$-0.971876\pi$
$11$	−0.760686	+	1.83646i	−0.229355	+	0.553713i	0.766744	+	0.641953i	$0.221876\pi$
$12$	2.15946	−	0.894478i	0.623383	−	0.258214i
$13$		−	0.678817i		−	0.188270i	−0.995559	−	0.0941350i	$-0.969991\pi$
$13$		−	0.678817i		−	0.188270i	0.995559	−	0.0941350i	$-0.0300085\pi$
$14$	1.37657	+	3.32333i	0.367903	+	0.888196i
$15$	1.65278	+	1.65278i	0.426746	+	0.426746i
$16$	−1.00000			−0.250000
$17$	−2.74368	+	3.07770i	−0.665441	+	0.746451i
$17$	−2.74368	+	3.07770i	−0.665441	+	0.746451i
$18$	2.46336			0.580620
$19$	−3.09055	−	3.09055i	−0.709020	−	0.709020i	0.257309	−	0.966329i	$-0.417164\pi$
$19$	−3.09055	−	3.09055i	−0.709020	−	0.709020i	−0.966329	+	0.257309i	$0.917164\pi$
$20$	−0.382683	−	0.923880i	−0.0855706	−	0.206586i
$21$			8.40790i			1.83475i
$22$	1.83646	−	0.760686i	0.391534	−	0.162179i
$23$	1.51321	−	3.65322i	0.315527	−	0.761749i	−0.683954	−	0.729525i	$-0.739741\pi$
$23$	1.51321	−	3.65322i	0.315527	−	0.761749i	0.999481	−	0.0322241i	$-0.0102590\pi$
$24$	−2.15946	−	0.894478i	−0.440798	−	0.182585i
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	−0.479996	+	0.479996i	−0.0941350	+	0.0941350i
$27$	−1.15885	−	0.480010i	−0.223020	−	0.0923779i
$28$	1.37657	−	3.32333i	0.260147	−	0.628050i
$29$	5.47189	−	2.26653i	1.01611	−	0.420885i	0.188427	−	0.982087i	$-0.439661\pi$
$29$	5.47189	−	2.26653i	1.01611	−	0.420885i	0.827678	+	0.561203i	$0.189661\pi$
$30$		−	2.33738i		−	0.426746i
$31$	−3.63256	−	8.76978i	−0.652427	−	1.57510i	−0.809245	−	0.587471i	$-0.800124\pi$
$31$	−3.63256	−	8.76978i	−0.652427	−	1.57510i	0.156818	−	0.987628i	$-0.449876\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.64617			0.808795
$34$	4.11634	−	0.236183i	0.705946	−	0.0405050i
$35$	3.59714			0.608028
$36$	−1.74186	−	1.74186i	−0.290310	−	0.290310i
$37$	−1.64894	−	3.98089i	−0.271084	−	0.654454i	0.728446	−	0.685103i	$-0.240243\pi$
$37$	−1.64894	−	3.98089i	−0.271084	−	0.654454i	−0.999530	+	0.0306487i	$0.990243\pi$
$38$			4.37069i			0.709020i
$39$	−1.46588	+	0.607187i	−0.234729	+	0.0972278i
$40$	−0.382683	+	0.923880i	−0.0605076	+	0.146078i
$41$	−1.70896	−	0.707874i	−0.266895	−	0.110551i	0.245223	−	0.969467i	$-0.421139\pi$
$41$	−1.70896	−	0.707874i	−0.266895	−	0.110551i	−0.512118	+	0.858915i	$0.671139\pi$
$42$	5.94529	−	5.94529i	0.917377	−	0.917377i
$43$	8.51063	−	8.51063i	1.29786	−	1.29786i	0.368055	−	0.929804i	$-0.380024\pi$
$43$	8.51063	−	8.51063i	1.29786	−	1.29786i	0.929804	−	0.368055i	$-0.119976\pi$
$44$	−1.83646	−	0.760686i	−0.276856	−	0.114678i
$45$	0.942688	−	2.27585i	0.140528	−	0.339264i
$46$	−3.65322	+	1.51321i	−0.538638	+	0.223111i
$47$			13.6499i			1.99104i	0.0945758	+	0.995518i	$0.469851\pi$
$47$			13.6499i			1.99104i	−0.0945758	+	0.995518i	$0.530149\pi$
$48$	0.894478	+	2.15946i	0.129107	+	0.311691i
$49$	4.19982	+	4.19982i	0.599974	+	0.599974i
$50$	−1.00000			−0.141421
$51$	9.10033	+	3.17194i	1.27430	+	0.444161i
$52$	0.678817			0.0941350
$53$	−4.30196	−	4.30196i	−0.590920	−	0.590920i	0.346960	−	0.937880i	$-0.387214\pi$
$53$	−4.30196	−	4.30196i	−0.590920	−	0.590920i	−0.937880	+	0.346960i	$0.887214\pi$
$54$	0.480010	+	1.15885i	0.0653210	+	0.157699i
$55$		−	1.98777i		−	0.268030i
$56$	−3.32333	+	1.37657i	−0.444098	+	0.183951i
$57$	−3.90949	+	9.43834i	−0.517824	+	1.25014i
$58$	−5.47189	−	2.26653i	−0.718495	−	0.297610i
$59$	−0.760963	+	0.760963i	−0.0990689	+	0.0990689i	−0.754904	−	0.655835i	$-0.772317\pi$
$59$	−0.760963	+	0.760963i	−0.0990689	+	0.0990689i	0.655835	+	0.754904i	$0.272317\pi$
$60$	−1.65278	+	1.65278i	−0.213373	+	0.213373i
$61$	1.68551	+	0.698163i	0.215808	+	0.0893906i	0.487968	−	0.872861i	$-0.337738\pi$
$61$	1.68551	+	0.698163i	0.215808	+	0.0893906i	−0.272160	+	0.962252i	$0.587738\pi$
$62$	−3.63256	+	8.76978i	−0.461336	+	1.11376i
$63$	8.18656	−	3.39098i	1.03141	−	0.427224i
$64$		−	1.00000i		−	0.125000i
$65$	0.259772	+	0.627145i	0.0322208	+	0.0777878i
$66$	−3.28534	−	3.28534i	−0.404398	−	0.404398i
$67$	5.62131			0.686752			0.343376	−	0.939198i	$-0.388429\pi$
$67$	5.62131			0.686752			0.343376	+	0.939198i	$0.388429\pi$
$68$	−3.07770	−	2.74368i	−0.373225	−	0.332720i
$69$	−9.24253			−1.11267
$70$	−2.54356	−	2.54356i	−0.304014	−	0.304014i
$71$	−4.51734	−	10.9058i	−0.536110	−	1.29428i	−0.927419	−	0.374024i	$-0.877978\pi$
$71$	−4.51734	−	10.9058i	−0.536110	−	1.29428i	0.391309	−	0.920259i	$-0.372022\pi$
$72$			2.46336i			0.290310i
$73$	−5.67041	+	2.34876i	−0.663671	+	0.274902i	−0.688982	−	0.724778i	$-0.741942\pi$
$73$	−5.67041	+	2.34876i	−0.663671	+	0.274902i	0.0253113	+	0.999680i	$0.491942\pi$
$74$	−1.64894	+	3.98089i	−0.191685	+	0.462769i
$75$	−2.15946	−	0.894478i	−0.249353	−	0.103285i
$76$	3.09055	−	3.09055i	0.354510	−	0.354510i
$77$	5.05601	−	5.05601i	0.576186	−	0.576186i
$78$	1.46588	+	0.607187i	0.165978	+	0.0687504i
$79$	−1.60739	+	3.88059i	−0.180846	+	0.436600i	−0.988141	−	0.153547i	$-0.950930\pi$
$79$	−1.60739	+	3.88059i	−0.180846	+	0.436600i	0.807296	+	0.590147i	$0.200930\pi$
$80$	0.923880	−	0.382683i	0.103293	−	0.0427853i
$81$			10.3219i			1.14688i
$82$	0.707874	+	1.70896i	0.0781717	+	0.188723i
$83$	11.8182	+	11.8182i	1.29722	+	1.29722i	0.930224	+	0.366991i	$0.119612\pi$
$83$	11.8182	+	11.8182i	1.29722	+	1.29722i	0.366991	+	0.930224i	$0.380388\pi$
$84$	−8.40790			−0.917377
$85$	1.35705	−	3.89338i	0.147193	−	0.422296i
$86$	−12.0359			−1.29786
$87$	−9.78898	−	9.78898i	−1.04949	−	1.04949i
$88$	0.760686	+	1.83646i	0.0810893	+	0.195767i
$89$		−	0.600698i		−	0.0636738i	−0.999493	−	0.0318369i	$-0.989864\pi$
$89$		−	0.600698i		−	0.0636738i	0.999493	−	0.0318369i	$-0.0101357\pi$
$90$	−2.27585	+	0.942688i	−0.239896	+	0.0993681i
$91$	−0.934438	+	2.25593i	−0.0979557	+	0.236486i
$92$	3.65322	+	1.51321i	0.380875	+	0.157763i
$93$	−15.6887	+	15.6887i	−1.62685	+	1.62685i
$94$	9.65190	−	9.65190i	0.995518	−	0.995518i
$95$	4.03799	+	1.67259i	0.414289	+	0.171604i
$96$	0.894478	−	2.15946i	0.0912923	−	0.220399i
$97$	0.119918	−	0.0496715i	0.0121758	−	0.00504338i	−0.376587	−	0.926381i	$-0.622902\pi$
$97$	0.119918	−	0.0496715i	0.0121758	−	0.00504338i	0.388763	+	0.921338i	$0.372902\pi$
$98$		−	5.93944i		−	0.599974i
$99$	−1.87384	−	4.52386i	−0.188328	−	0.454665i
$100$	0.707107	+	0.707107i	0.0707107	+	0.0707107i
$101$	9.29167			0.924556			0.462278	−	0.886735i	$-0.347032\pi$
$101$	9.29167			0.924556			0.462278	+	0.886735i	$0.347032\pi$
$102$	−4.19200	−	8.67781i	−0.415070	−	0.859231i
$103$	−14.7834			−1.45665			−0.728326	−	0.685231i	$-0.759701\pi$
$103$	−14.7834			−1.45665			−0.728326	+	0.685231i	$0.759701\pi$
$104$	−0.479996	−	0.479996i	−0.0470675	−	0.0470675i
$105$	−3.21757	−	7.76789i	−0.314002	−	0.758068i
$106$			6.08390i			0.590920i
$107$	−8.64919	+	3.58261i	−0.836149	+	0.346344i	−0.759334	−	0.650701i	$-0.774475\pi$
$107$	−8.64919	+	3.58261i	−0.836149	+	0.346344i	−0.0768148	+	0.997045i	$0.524475\pi$
$108$	0.480010	−	1.15885i	0.0461889	−	0.111510i
$109$	4.10558	+	1.70059i	0.393243	+	0.162887i	0.570538	−	0.821271i	$-0.306735\pi$
$109$	4.10558	+	1.70059i	0.393243	+	0.162887i	−0.177295	+	0.984158i	$0.556735\pi$
$110$	−1.40556	+	1.40556i	−0.134015	+	0.134015i
$111$	−7.12164	+	7.12164i	−0.675956	+	0.675956i
$112$	3.32333	+	1.37657i	0.314025	+	0.130073i
$113$	−0.934775	+	2.25675i	−0.0879362	+	0.212297i	−0.961729	−	0.274001i	$-0.911653\pi$
$113$	−0.934775	+	2.25675i	−0.0879362	+	0.212297i	0.873793	+	0.486298i	$0.161653\pi$
$114$	9.43834	−	3.90949i	0.883982	−	0.366157i
$115$			3.95422i			0.368733i
$116$	2.26653	+	5.47189i	0.210442	+	0.508053i
$117$	1.18241	+	1.18241i	0.109313	+	0.109313i
$118$	1.07616			0.0990689
$119$	13.3548	−	6.45132i	1.22423	−	0.591392i
$120$	2.33738			0.213373
$121$	4.98424	+	4.98424i	0.453113	+	0.453113i
$122$	−0.698163	−	1.68551i	−0.0632087	−	0.152599i
$123$			4.32361i			0.389847i
$124$	8.76978	−	3.63256i	0.787549	−	0.326214i
$125$	−0.382683	+	0.923880i	−0.0342282	+	0.0826343i
$126$	−8.18656	−	3.39098i	−0.729317	−	0.302093i
$127$	11.1826	−	11.1826i	0.992295	−	0.992295i	−0.00767572	−	0.999971i	$-0.502443\pi$
$127$	11.1826	−	11.1826i	0.992295	−	0.992295i	0.999971	+	0.00767572i	$0.00244328\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−25.9910	−	10.7658i	−2.28838	−	0.947876i
$130$	0.259772	−	0.627145i	0.0227835	−	0.0550043i
$131$	9.02792	−	3.73949i	0.788773	−	0.326721i	0.0483231	−	0.998832i	$-0.484612\pi$
$131$	9.02792	−	3.73949i	0.788773	−	0.326721i	0.740450	+	0.672111i	$0.234612\pi$
$132$			4.64617i			0.404398i
$133$	6.01655	+	14.5252i	0.521701	+	1.25950i
$134$	−3.97487	−	3.97487i	−0.343376	−	0.343376i
$135$	1.25433			0.107955
$136$	0.236183	+	4.11634i	0.0202525	+	0.352973i
$137$	−10.3127			−0.881072			−0.440536	−	0.897735i	$-0.645212\pi$
$137$	−10.3127			−0.881072			−0.440536	+	0.897735i	$0.645212\pi$
$138$	6.53545	+	6.53545i	0.556335	+	0.556335i
$139$	7.34028	+	17.7210i	0.622594	+	1.50307i	0.848647	+	0.528960i	$0.177418\pi$
$139$	7.34028	+	17.7210i	0.622594	+	1.50307i	−0.226053	+	0.974115i	$0.572582\pi$
$140$			3.59714i			0.304014i
$141$	29.4763	−	12.2095i	2.48235	−	1.02822i
$142$	−4.51734	+	10.9058i	−0.379087	+	0.915196i
$143$	1.24662	+	0.516367i	0.104248	+	0.0431807i
$144$	1.74186	−	1.74186i	0.145155	−	0.145155i
$145$	−4.18801	+	4.18801i	−0.347795	+	0.347795i
$146$	5.67041	+	2.34876i	0.469286	+	0.194385i
$147$	5.31270	−	12.8260i	0.438184	−	1.05787i
$148$	3.98089	−	1.64894i	0.327227	−	0.135542i
$149$		−	18.0124i		−	1.47563i	−0.675002	−	0.737816i	$-0.735857\pi$
$149$		−	18.0124i		−	1.47563i	0.675002	−	0.737816i	$-0.264143\pi$
$150$	0.894478	+	2.15946i	0.0730338	+	0.176319i
$151$	−6.77035	−	6.77035i	−0.550963	−	0.550963i	0.375755	−	0.926719i	$-0.377383\pi$
$151$	−6.77035	−	6.77035i	−0.550963	−	0.550963i	−0.926719	+	0.375755i	$0.877383\pi$
$152$	−4.37069			−0.354510
$153$	−0.581804	−	10.1400i	−0.0470361	−	0.819773i
$154$	−7.15028			−0.576186
$155$	6.71210	+	6.71210i	0.539129	+	0.539129i
$156$	−0.607187	−	1.46588i	−0.0486139	−	0.117364i
$157$		−	20.2328i		−	1.61476i	−0.590034	−	0.807378i	$-0.700886\pi$
$157$		−	20.2328i		−	1.61476i	0.590034	−	0.807378i	$-0.299114\pi$
$158$	3.88059	−	1.60739i	0.308723	−	0.127877i
$159$	−5.44191	+	13.1379i	−0.431572	+	1.04191i
$160$	−0.923880	−	0.382683i	−0.0730391	−	0.0302538i
$161$	−10.0578	+	10.0578i	−0.792666	+	0.792666i
$162$	7.29871	−	7.29871i	0.573441	−	0.573441i
$163$	−2.74437	−	1.13675i	−0.214955	−	0.0890375i	0.272607	−	0.962125i	$-0.412114\pi$
$163$	−2.74437	−	1.13675i	−0.214955	−	0.0890375i	−0.487563	+	0.873088i	$0.662114\pi$
$164$	0.707874	−	1.70896i	0.0552757	−	0.133447i
$165$	−4.29251	+	1.77801i	−0.334171	+	0.138418i
$166$		−	16.7135i		−	1.29722i
$167$	−7.25928	−	17.5255i	−0.561740	−	1.35616i	−0.908374	−	0.418160i	$-0.862675\pi$
$167$	−7.25928	−	17.5255i	−0.561740	−	1.35616i	0.346634	−	0.938001i	$-0.387325\pi$
$168$	5.94529	+	5.94529i	0.458689	+	0.458689i
$169$	12.5392			0.964554
$170$	−3.71261	+	1.79346i	−0.284745	+	0.137552i
$171$	10.7666			0.823343
$172$	8.51063	+	8.51063i	0.648930	+	0.648930i
$173$	−7.32175	−	17.6763i	−0.556663	−	1.34390i	−0.912394	−	0.409314i	$-0.865768\pi$
$173$	−7.32175	−	17.6763i	−0.556663	−	1.34390i	0.355731	−	0.934588i	$-0.384232\pi$
$174$			13.8437i			1.04949i
$175$	−3.32333	+	1.37657i	−0.251220	+	0.104059i
$176$	0.760686	−	1.83646i	0.0573388	−	0.138428i
$177$	2.32393	+	0.962605i	0.174678	+	0.0723538i
$178$	−0.424758	+	0.424758i	−0.0318369	+	0.0318369i
$179$	0.328338	−	0.328338i	0.0245411	−	0.0245411i	−0.694730	−	0.719271i	$-0.744476\pi$
$179$	0.328338	−	0.328338i	0.0245411	−	0.0245411i	0.719271	+	0.694730i	$0.244476\pi$
$180$	2.27585	+	0.942688i	0.169632	+	0.0702638i
$181$	5.16863	−	12.4782i	0.384181	−	0.927495i	−0.606966	−	0.794728i	$-0.707614\pi$
$181$	5.16863	−	12.4782i	0.384181	−	0.927495i	0.991147	−	0.132767i	$-0.0423863\pi$
$182$	2.25593	−	0.934438i	0.167221	−	0.0692651i
$183$		−	4.26429i		−	0.315226i
$184$	−1.51321	−	3.65322i	−0.111556	−	0.269319i
$185$	3.04684	+	3.04684i	0.224008	+	0.224008i
$186$	22.1872			1.62685
$187$	−3.56498	−	7.37981i	−0.260697	−	0.539665i
$188$	−13.6499			−0.995518
$189$	3.19046	+	3.19046i	0.232072	+	0.232072i
$190$	−1.67259	−	4.03799i	−0.121343	−	0.292947i
$191$			11.3006i			0.817683i	0.912605	+	0.408841i	$0.134067\pi$
$191$			11.3006i			0.817683i	−0.912605	+	0.408841i	$0.865933\pi$
$192$	−2.15946	+	0.894478i	−0.155846	+	0.0645534i
$193$	−1.88421	+	4.54889i	−0.135629	+	0.327437i	−0.977072	−	0.212909i	$-0.931706\pi$
$193$	−1.88421	+	4.54889i	−0.135629	+	0.327437i	0.841443	+	0.540345i	$0.181706\pi$
$194$	−0.119918	−	0.0496715i	−0.00860958	−	0.00356621i
$195$	1.12194	−	1.12194i	0.0803435	−	0.0803435i
$196$	−4.19982	+	4.19982i	−0.299987	+	0.299987i
$197$	24.9022	+	10.3148i	1.77421	+	0.734901i	0.994000	+	0.109380i	$0.0348866\pi$
$197$	24.9022	+	10.3148i	1.77421	+	0.734901i	0.780208	+	0.625521i	$0.215113\pi$
$198$	−1.87384	+	4.52386i	−0.133168	+	0.321497i
$199$	−17.3722	+	7.19579i	−1.23148	+	0.510096i	−0.901042	−	0.433731i	$-0.857197\pi$
$199$	−17.3722	+	7.19579i	−1.23148	+	0.510096i	−0.330439	+	0.943827i	$0.607197\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−5.02814	−	12.1390i	−0.354658	−	0.856219i
$202$	−6.57020	−	6.57020i	−0.462278	−	0.462278i
$203$	−21.3049			−1.49531
$204$	−3.17194	+	9.10033i	−0.222081	+	0.637150i
$205$	1.84976			0.129193
$206$	10.4534	+	10.4534i	0.728326	+	0.728326i
$207$	3.72760	+	8.99921i	0.259086	+	0.625489i
$208$			0.678817i			0.0470675i
$209$	8.02659	−	3.32472i	0.555211	−	0.229976i
$210$	−3.21757	+	7.76789i	−0.222033	+	0.536035i
$211$	−5.87001	−	2.43144i	−0.404108	−	0.167387i	0.171365	−	0.985208i	$-0.445182\pi$
$211$	−5.87001	−	2.43144i	−0.404108	−	0.167387i	−0.575473	+	0.817820i	$0.695182\pi$
$212$	4.30196	−	4.30196i	0.295460	−	0.295460i
$213$	−19.5100	+	19.5100i	−1.33681	+	1.33681i
$214$	8.64919	+	3.58261i	0.591246	+	0.244902i
$215$	−4.60592	+	11.1197i	−0.314121	+	0.758356i
$216$	−1.15885	+	0.480010i	−0.0788495	+	0.0326605i
$217$			34.1453i			2.31793i
$218$	−1.70059	−	4.10558i	−0.115178	−	0.278065i
$219$	10.1441	+	10.1441i	0.685476	+	0.685476i
$220$	1.98777			0.134015
$221$	2.08919	+	1.86246i	0.140534	+	0.125283i
$222$	10.0715			0.675956
$223$	−2.94156	−	2.94156i	−0.196981	−	0.196981i	0.601723	−	0.798705i	$-0.294481\pi$
$223$	−2.94156	−	2.94156i	−0.196981	−	0.196981i	−0.798705	+	0.601723i	$0.794481\pi$
$224$	−1.37657	−	3.32333i	−0.0919757	−	0.222049i
$225$			2.46336i			0.164224i
$226$	2.25675	−	0.934775i	0.150116	−	0.0621803i
$227$	−6.57804	+	15.8808i	−0.436600	+	1.05405i	0.540515	+	0.841334i	$0.318229\pi$
$227$	−6.57804	+	15.8808i	−0.436600	+	1.05405i	−0.977115	+	0.212711i	$0.931771\pi$
$228$	−9.43834	−	3.90949i	−0.625069	−	0.258912i
$229$	−12.5242	+	12.5242i	−0.827620	+	0.827620i	−0.987187	−	0.159567i	$-0.948990\pi$
$229$	−12.5242	+	12.5242i	−0.827620	+	0.827620i	0.159567	+	0.987187i	$0.448990\pi$
$230$	2.79606	−	2.79606i	0.184366	−	0.184366i
$231$	−15.4408	−	6.39577i	−1.01593	−	0.420811i
$232$	2.26653	−	5.47189i	0.148805	−	0.359247i
$233$	10.0887	−	4.17890i	0.660936	−	0.273769i	−0.0268965	−	0.999638i	$-0.508562\pi$
$233$	10.0887	−	4.17890i	0.660936	−	0.273769i	0.687832	+	0.725870i	$0.258562\pi$
$234$		−	1.67217i		−	0.109313i
$235$	−5.22357	−	12.6108i	−0.340748	−	0.822639i
$236$	−0.760963	−	0.760963i	−0.0495344	−	0.0495344i
$237$	9.81775			0.637732
$238$	−14.0050	−	4.88150i	−0.907812	−	0.316421i
$239$	−15.8397			−1.02459			−0.512293	−	0.858811i	$-0.671204\pi$
$239$	−15.8397			−1.02459			−0.512293	+	0.858811i	$0.671204\pi$
$240$	−1.65278	−	1.65278i	−0.106686	−	0.106686i
$241$	−8.11947	−	19.6021i	−0.523021	−	1.26268i	−0.936018	−	0.351952i	$-0.885518\pi$
$241$	−8.11947	−	19.6021i	−0.523021	−	1.26268i	0.412997	−	0.910732i	$-0.364482\pi$
$242$		−	7.04878i		−	0.453113i
$243$	18.8133	−	7.79271i	1.20687	−	0.499903i
$244$	−0.698163	+	1.68551i	−0.0446953	+	0.107904i
$245$	−5.48732	−	2.27292i	−0.350572	−	0.145212i
$246$	3.05725	−	3.05725i	0.194923	−	0.194923i
$247$	−2.09792	+	2.09792i	−0.133487	+	0.133487i
$248$	−8.76978	−	3.63256i	−0.556881	−	0.230668i
$249$	14.9498	−	36.0921i	0.947406	−	2.28724i
$250$	0.923880	−	0.382683i	0.0584313	−	0.0242030i
$251$		−	23.5061i		−	1.48369i	−0.670571	−	0.741845i	$-0.733951\pi$
$251$		−	23.5061i		−	1.48369i	0.670571	−	0.741845i	$-0.266049\pi$
$252$	3.39098	+	8.18656i	0.213612	+	0.515705i
$253$	5.55791	+	5.55791i	0.349423	+	0.349423i
$254$	−15.8146			−0.992295
$255$	−9.62146	+	0.552050i	−0.602519	+	0.0345707i
$256$	1.00000			0.0625000
$257$	−4.43685	−	4.43685i	−0.276763	−	0.276763i	0.555052	−	0.831815i	$-0.312698\pi$
$257$	−4.43685	−	4.43685i	−0.276763	−	0.276763i	−0.831815	+	0.555052i	$0.812698\pi$
$258$	10.7658	+	25.9910i	0.670250	+	1.61813i
$259$			15.4997i			0.963102i
$260$	−0.627145	+	0.259772i	−0.0388939	+	0.0161104i
$261$	−5.58329	+	13.4793i	−0.345597	+	0.834346i
$262$	−9.02792	−	3.73949i	−0.557747	−	0.231026i
$263$	−4.60829	+	4.60829i	−0.284159	+	0.284159i	−0.834765	−	0.550606i	$-0.814397\pi$
$263$	−4.60829	+	4.60829i	−0.284159	+	0.284159i	0.550606	+	0.834765i	$0.314397\pi$
$264$	3.28534	−	3.28534i	0.202199	−	0.202199i
$265$	5.62079	+	2.32821i	0.345282	+	0.143021i
$266$	6.01655	−	14.5252i	0.368898	−	0.890600i
$267$	−1.29718	+	0.537311i	−0.0793864	+	0.0328829i
$268$			5.62131i			0.343376i
$269$	−2.19244	−	5.29301i	−0.133675	−	0.322721i	0.842842	−	0.538162i	$-0.180881\pi$
$269$	−2.19244	−	5.29301i	−0.133675	−	0.322721i	−0.976517	+	0.215441i	$0.930881\pi$
$270$	−0.886942	−	0.886942i	−0.0539776	−	0.0539776i
$271$	−5.59061			−0.339605			−0.169803	−	0.985478i	$-0.554313\pi$
$271$	−5.59061			−0.339605			−0.169803	+	0.985478i	$0.554313\pi$
$272$	2.74368	−	3.07770i	0.166360	−	0.186613i
$273$	5.70743			0.345429
$274$	7.29217	+	7.29217i	0.440536	+	0.440536i
$275$	0.760686	+	1.83646i	0.0458711	+	0.110743i
$276$		−	9.24253i		−	0.556335i
$277$	−7.48335	+	3.09970i	−0.449631	+	0.186243i	−0.595996	−	0.802987i	$-0.703243\pi$
$277$	−7.48335	+	3.09970i	−0.449631	+	0.186243i	0.146365	+	0.989231i	$0.453243\pi$
$278$	7.34028	−	17.7210i	0.440240	−	1.06283i
$279$	21.6032	+	8.94832i	1.29335	+	0.535722i
$280$	2.54356	−	2.54356i	0.152007	−	0.152007i
$281$	1.73443	−	1.73443i	0.103467	−	0.103467i	−0.653478	−	0.756945i	$-0.726691\pi$
$281$	1.73443	−	1.73443i	0.103467	−	0.103467i	0.756945	+	0.653478i	$0.226691\pi$
$282$	−29.4763	−	12.2095i	−1.75529	−	0.727065i
$283$	−4.13832	+	9.99078i	−0.245997	+	0.593890i	−0.997857	−	0.0654331i	$-0.979157\pi$
$283$	−4.13832	+	9.99078i	−0.245997	+	0.593890i	0.751860	+	0.659323i	$0.229157\pi$
$284$	10.9058	−	4.51734i	0.647142	−	0.268055i
$285$		−	10.2160i		−	0.605143i
$286$	−0.516367	−	1.24662i	−0.0305334	−	0.0737141i
$287$	4.70500	+	4.70500i	0.277727	+	0.277727i
$288$	−2.46336			−0.145155
$289$	−1.94442	−	16.8884i	−0.114377	−	0.993437i
$290$	5.92274			0.347795
$291$	−0.214527	−	0.214527i	−0.0125758	−	0.0125758i
$292$	−2.34876	−	5.67041i	−0.137451	−	0.331836i
$293$			0.449251i			0.0262455i	0.999914	+	0.0131228i	$0.00417722\pi$
$293$			0.449251i			0.0262455i	−0.999914	+	0.0131228i	$0.995823\pi$
$294$	−12.8260	+	5.31270i	−0.748026	+	0.309843i
$295$	0.411830	−	0.994245i	0.0239777	−	0.0578872i
$296$	−3.98089	−	1.64894i	−0.231384	−	0.0958426i
$297$	1.76303	−	1.76303i	0.102302	−	0.102302i
$298$	−12.7367	+	12.7367i	−0.737816	+	0.737816i
$299$	−2.47987	−	1.02720i	−0.143415	−	0.0594043i
$300$	0.894478	−	2.15946i	0.0516427	−	0.124677i
$301$	−39.9991	+	16.5682i	−2.30551	+	0.954973i
$302$			9.57472i			0.550963i
$303$	−8.31120	−	20.0650i	−0.477466	−	1.15270i
$304$	3.09055	+	3.09055i	0.177255	+	0.177255i
$305$	−1.82439			−0.104464
$306$	−6.75869	+	7.58148i	−0.386368	+	0.433404i
$307$	−4.96740			−0.283504			−0.141752	−	0.989902i	$-0.545274\pi$
$307$	−4.96740			−0.283504			−0.141752	+	0.989902i	$0.545274\pi$
$308$	5.05601	+	5.05601i	0.288093	+	0.288093i
$309$	13.2234	+	31.9242i	0.752255	+	1.81610i
$310$		−	9.49234i		−	0.539129i
$311$	−0.632482	+	0.261982i	−0.0358647	+	0.0148557i	−0.400544	−	0.916278i	$-0.631179\pi$
$311$	−0.632482	+	0.261982i	−0.0358647	+	0.0148557i	0.364679	+	0.931133i	$0.381179\pi$
$312$	−0.607187	+	1.46588i	−0.0343752	+	0.0829891i
$313$	21.7219	+	8.99751i	1.22779	+	0.508569i	0.899880	−	0.436138i	$-0.143654\pi$
$313$	21.7219	+	8.99751i	1.22779	+	0.508569i	0.327915	+	0.944707i	$0.393654\pi$
$314$	−14.3068	+	14.3068i	−0.807378	+	0.807378i
$315$	−6.26572	+	6.26572i	−0.353033	+	0.353033i
$316$	−3.88059	−	1.60739i	−0.218300	−	0.0904229i
$317$	0.878646	−	2.12124i	0.0493496	−	0.119141i	−0.897282	−	0.441457i	$-0.854462\pi$
$317$	0.878646	−	2.12124i	0.0493496	−	0.119141i	0.946632	+	0.322317i	$0.104462\pi$
$318$	13.1379	−	5.44191i	0.736739	−	0.305167i
$319$			11.7730i			0.659162i
$320$	0.382683	+	0.923880i	0.0213927	+	0.0516464i
$321$	15.4730	+	15.4730i	0.863620	+	0.863620i
$322$	14.2239			0.792666
$323$	17.9912	−	1.03228i	1.00106	−	0.0574377i
$324$	−10.3219			−0.573441
$325$	−0.479996	−	0.479996i	−0.0266254	−	0.0266254i
$326$	1.13675	+	2.74437i	0.0629590	+	0.151996i
$327$		−	10.3870i		−	0.574401i
$328$	−1.70896	+	0.707874i	−0.0943615	+	0.0390858i
$329$	18.7899	−	45.3629i	1.03592	−	2.50094i
$330$	4.29251	+	1.77801i	0.236295	+	0.0978765i
$331$	12.4241	−	12.4241i	0.682890	−	0.682890i	−0.277761	−	0.960650i	$-0.589592\pi$
$331$	12.4241	−	12.4241i	0.682890	−	0.682890i	0.960650	+	0.277761i	$0.0895922\pi$
$332$	−11.8182	+	11.8182i	−0.648608	+	0.648608i
$333$	9.80638	+	4.06193i	0.537386	+	0.222593i
$334$	−7.25928	+	17.5255i	−0.397210	+	0.958950i
$335$	−5.19341	+	2.15118i	−0.283747	+	0.117532i
$336$		−	8.40790i		−	0.458689i
$337$	11.2475	+	27.1538i	0.612690	+	1.47916i	0.860034	+	0.510236i	$0.170442\pi$
$337$	11.2475	+	27.1538i	0.612690	+	1.47916i	−0.247345	+	0.968927i	$0.579558\pi$
$338$	−8.86656	−	8.86656i	−0.482277	−	0.482277i
$339$	5.70949			0.310097
$340$	3.89338	+	1.35705i	0.211148	+	0.0735963i
$341$	18.8686			1.02179
$342$	−7.61314	−	7.61314i	−0.411671	−	0.411671i
$343$	1.45994	+	3.52460i	0.0788292	+	0.190310i
$344$		−	12.0359i		−	0.648930i
$345$	8.53898	−	3.53696i	0.459723	−	0.190424i
$346$	−7.32175	+	17.6763i	−0.393620	+	0.950282i
$347$	23.7989	+	9.85783i	1.27759	+	0.529196i	0.915264	−	0.402855i	$-0.131982\pi$
$347$	23.7989	+	9.85783i	1.27759	+	0.529196i	0.362328	+	0.932051i	$0.381982\pi$
$348$	9.78898	−	9.78898i	0.524744	−	0.524744i
$349$	−0.680727	+	0.680727i	−0.0364385	+	0.0364385i	−0.725091	−	0.688653i	$-0.758202\pi$
$349$	−0.680727	+	0.680727i	−0.0364385	+	0.0364385i	0.688653	+	0.725091i	$0.258202\pi$
$350$	3.32333	+	1.37657i	0.177639	+	0.0735806i
$351$	−0.325839	+	0.786645i	−0.0173920	+	0.0419880i
$352$	−1.83646	+	0.760686i	−0.0978835	+	0.0405447i
$353$			3.98398i			0.212046i	0.994364	+	0.106023i	$0.0338117\pi$
$353$			3.98398i			0.212046i	−0.994364	+	0.106023i	$0.966188\pi$
$354$	−0.962605	−	2.32393i	−0.0511619	−	0.123516i
$355$	8.34696	+	8.34696i	0.443010	+	0.443010i
$356$	0.600698			0.0318369
$357$	−25.8770	−	23.0686i	−1.36955	−	1.22092i
$358$	−0.464340			−0.0245411
$359$	1.54650	+	1.54650i	0.0816214	+	0.0816214i	0.746739	−	0.665117i	$-0.231619\pi$
$359$	1.54650	+	1.54650i	0.0816214	+	0.0816214i	−0.665117	+	0.746739i	$0.731619\pi$
$360$	−0.942688	−	2.27585i	−0.0496840	−	0.119948i
$361$			0.102958i			0.00541883i
$362$	−12.4782	+	5.16863i	−0.655838	+	0.271657i
$363$	6.30498	−	15.2216i	0.330926	−	0.798925i
$364$	−2.25593	−	0.934438i	−0.118243	−	0.0489778i
$365$	4.33994	−	4.33994i	0.227163	−	0.227163i
$366$	−3.01531	+	3.01531i	−0.157613	+	0.157613i
$367$	25.1079	+	10.4000i	1.31062	+	0.542878i	0.925066	−	0.379806i	$-0.124009\pi$
$367$	25.1079	+	10.4000i	1.31062	+	0.542878i	0.385558	+	0.922684i	$0.374009\pi$
$368$	−1.51321	+	3.65322i	−0.0788817	+	0.190437i
$369$	4.20979	−	1.74375i	0.219153	−	0.0907761i
$370$		−	4.30888i		−	0.224008i
$371$	8.37489	+	20.2188i	0.434803	+	1.04971i
$372$	−15.6887	−	15.6887i	−0.813424	−	0.813424i
$373$	15.4149			0.798152			0.399076	−	0.916918i	$-0.369331\pi$
$373$	15.4149			0.798152			0.399076	+	0.916918i	$0.369331\pi$
$374$	−2.69750	+	7.73914i	−0.139484	+	0.400181i
$375$	2.33738			0.120702
$376$	9.65190	+	9.65190i	0.497759	+	0.497759i
$377$	−1.53856	−	3.71442i	−0.0792400	−	0.191302i
$378$		−	4.51199i		−	0.232072i
$379$	−23.3819	+	9.68511i	−1.20105	+	0.497491i	−0.891338	−	0.453340i	$-0.850232\pi$
$379$	−23.3819	+	9.68511i	−1.20105	+	0.497491i	−0.309711	+	0.950831i	$0.600232\pi$
$380$	−1.67259	+	4.03799i	−0.0858021	+	0.207145i
$381$	−34.1510	−	14.1458i	−1.74961	−	0.724711i
$382$	7.99073	−	7.99073i	0.408841	−	0.408841i
$383$	4.18478	−	4.18478i	0.213832	−	0.213832i	−0.592061	−	0.805893i	$-0.701686\pi$
$383$	4.18478	−	4.18478i	0.213832	−	0.213832i	0.805893	+	0.592061i	$0.201686\pi$
$384$	2.15946	+	0.894478i	0.110200	+	0.0456461i
$385$	−2.73629	+	6.60600i	−0.139454	+	0.336673i
$386$	4.54889	−	1.88421i	0.231533	−	0.0959039i
$387$			29.6487i			1.50713i
$388$	0.0496715	+	0.119918i	0.00252169	+	0.00608789i
$389$	−13.0626	−	13.0626i	−0.662298	−	0.662298i	0.293623	−	0.955921i	$-0.405139\pi$
$389$	−13.0626	−	13.0626i	−0.662298	−	0.662298i	−0.955921	+	0.293623i	$0.905139\pi$
$390$	−1.58666			−0.0803435
$391$	7.09173	+	14.6805i	0.358644	+	0.742424i
$392$	5.93944			0.299987
$393$	−16.1506	−	16.1506i	−0.814688	−	0.814688i
$394$	−10.3148	−	24.9022i	−0.519653	−	1.25455i
$395$		−	4.20032i		−	0.211341i
$396$	4.52386	−	1.87384i	0.227333	−	0.0941642i
$397$	15.2231	−	36.7519i	0.764026	−	1.84452i	0.327355	−	0.944901i	$-0.393843\pi$
$397$	15.2231	−	36.7519i	0.764026	−	1.84452i	0.436671	−	0.899621i	$-0.356157\pi$
$398$	17.3722	+	7.19579i	0.870789	+	0.360693i
$399$	25.9850	−	25.9850i	1.30088	−	1.30088i
$400$	−0.707107	+	0.707107i	−0.0353553	+	0.0353553i
$401$	−9.52077	−	3.94363i	−0.475445	−	0.196936i	0.132076	−	0.991240i	$-0.457836\pi$
$401$	−9.52077	−	3.94363i	−0.475445	−	0.196936i	−0.607521	+	0.794304i	$0.707836\pi$
$402$	−5.02814	+	12.1390i	−0.250781	+	0.605438i
$403$	−5.95308	+	2.46585i	−0.296544	+	0.122833i
$404$			9.29167i			0.462278i
$405$	−3.95003	−	9.53622i	−0.196279	−	0.473859i
$406$	15.0649	+	15.0649i	0.747656	+	0.747656i
$407$	8.56506			0.424554
$408$	8.67781	−	4.19200i	0.429615	−	0.207535i
$409$	−0.975603			−0.0482404			−0.0241202	−	0.999709i	$-0.507678\pi$
$409$	−0.975603			−0.0482404			−0.0241202	+	0.999709i	$0.507678\pi$
$410$	−1.30798	−	1.30798i	−0.0645966	−	0.0645966i
$411$	9.22447	+	22.2698i	0.455010	+	1.09849i
$412$		−	14.7834i		−	0.728326i
$413$	3.57644	−	1.48141i	0.175985	−	0.0728955i
$414$	3.72760	−	8.99921i	0.183201	−	0.442287i
$415$	−15.4412	−	6.39596i	−0.757980	−	0.313965i
$416$	0.479996	−	0.479996i	0.0235338	−	0.0235338i
$417$	31.7021	−	31.7021i	1.55246	−	1.55246i
$418$	−8.02659	−	3.32472i	−0.392593	−	0.162618i
$419$	−2.75705	+	6.65610i	−0.134691	+	0.325172i	−0.976806	−	0.214125i	$-0.931310\pi$
$419$	−2.75705	+	6.65610i	−0.134691	+	0.325172i	0.842116	+	0.539297i	$0.181310\pi$
$420$	7.76789	−	3.21757i	0.379034	−	0.157001i
$421$			18.0144i			0.877966i	0.898495	+	0.438983i	$0.144661\pi$
$421$			18.0144i			0.877966i	−0.898495	+	0.438983i	$0.855339\pi$
$422$	2.43144	+	5.87001i	0.118361	+	0.285748i
$423$	−23.7761	−	23.7761i	−1.15604	−	1.15604i
$424$	−6.08390			−0.295460
$425$	0.236183	+	4.11634i	0.0114566	+	0.199672i
$426$	27.5914			1.33681
$427$	−4.64044	−	4.64044i	−0.224567	−	0.224567i
$428$	−3.58261	−	8.64919i	−0.173172	−	0.418074i
$429$		−	3.15390i		−	0.152272i
$430$	11.1197	−	4.60592i	0.536238	−	0.222117i
$431$	−7.08715	+	17.1099i	−0.341376	+	0.824154i	0.656201	+	0.754586i	$0.272162\pi$
$431$	−7.08715	+	17.1099i	−0.341376	+	0.824154i	−0.997577	+	0.0695684i	$0.977838\pi$
$432$	1.15885	+	0.480010i	0.0557550	+	0.0230945i
$433$	25.3511	−	25.3511i	1.21829	−	1.21829i	0.250065	−	0.968229i	$-0.419548\pi$
$433$	25.3511	−	25.3511i	1.21829	−	1.21829i	0.968229	−	0.250065i	$-0.0804521\pi$
$434$	24.1444	−	24.1444i	1.15897	−	1.15897i
$435$	12.7899	+	5.29776i	0.613230	+	0.254008i
$436$	−1.70059	+	4.10558i	−0.0814433	+	0.196621i
$437$	−15.9671	+	6.61379i	−0.763811	+	0.316381i
$438$		−	14.3459i		−	0.685476i
$439$	3.63408	+	8.77346i	0.173445	+	0.418734i	0.986566	−	0.163360i	$-0.0522333\pi$
$439$	3.63408	+	8.77346i	0.173445	+	0.418734i	−0.813121	+	0.582095i	$0.802233\pi$
$440$	−1.40556	−	1.40556i	−0.0670076	−	0.0670076i
$441$	−14.6310			−0.696714
$442$	−0.160325	−	2.79424i	−0.00762588	−	0.132908i
$443$	−20.5704			−0.977330			−0.488665	−	0.872471i	$-0.662516\pi$
$443$	−20.5704			−0.977330			−0.488665	+	0.872471i	$0.662516\pi$
$444$	−7.12164	−	7.12164i	−0.337978	−	0.337978i
$445$	0.229877	+	0.554972i	0.0108972	+	0.0263082i
$446$			4.15999i			0.196981i
$447$	−38.8970	+	16.1117i	−1.83977	+	0.762056i
$448$	−1.37657	+	3.32333i	−0.0650367	+	0.157012i
$449$	−6.37569	−	2.64090i	−0.300887	−	0.124632i	0.227132	−	0.973864i	$-0.427065\pi$
$449$	−6.37569	−	2.64090i	−0.300887	−	0.124632i	−0.528019	+	0.849232i	$0.677065\pi$
$450$	1.74186	−	1.74186i	0.0821121	−	0.0821121i
$451$	2.59996	−	2.59996i	0.122427	−	0.122427i
$452$	−2.25675	−	0.934775i	−0.106148	−	0.0439681i
$453$	−8.56438	+	20.6762i	−0.402390	+	0.971455i
$454$	15.8808	−	6.57804i	0.745322	−	0.308723i
$455$		−	2.44180i		−	0.114473i
$456$	3.90949	+	9.43834i	0.183079	+	0.441991i
$457$	−24.2230	−	24.2230i	−1.13310	−	1.13310i	−0.989658	−	0.143446i	$-0.954182\pi$
$457$	−24.2230	−	24.2230i	−1.13310	−	1.13310i	−0.143446	−	0.989658i	$-0.545818\pi$
$458$	17.7118			0.827620
$459$	4.65683	−	2.24958i	0.217362	−	0.105001i
$460$	−3.95422			−0.184366
$461$	−3.65770	−	3.65770i	−0.170356	−	0.170356i	0.616780	−	0.787136i	$-0.288437\pi$
$461$	−3.65770	−	3.65770i	−0.170356	−	0.170356i	−0.787136	+	0.616780i	$0.788437\pi$
$462$	6.39577	+	15.4408i	0.297558	+	0.718369i
$463$		−	10.0414i		−	0.466663i	−0.972397	−	0.233332i	$-0.925037\pi$
$463$		−	10.0414i		−	0.466663i	0.972397	−	0.233332i	$-0.0749628\pi$
$464$	−5.47189	+	2.26653i	−0.254026	+	0.105221i
$465$	8.49069	−	20.4983i	0.393746	−	0.950588i
$466$	−10.0887	−	4.17890i	−0.467352	−	0.193584i
$467$	−16.3691	+	16.3691i	−0.757471	+	0.757471i	−0.975862	−	0.218390i	$-0.929919\pi$
$467$	−16.3691	+	16.3691i	−0.757471	+	0.757471i	0.218390	+	0.975862i	$0.429919\pi$
$468$	−1.18241	+	1.18241i	−0.0546567	+	0.0546567i
$469$	−18.6815	−	7.73811i	−0.862629	−	0.357313i
$470$	−5.22357	+	12.6108i	−0.240945	+	0.581694i
$471$	−43.6920	+	18.0978i	−2.01322	+	0.833904i
$472$			1.07616i			0.0495344i
$473$	9.15550	+	22.1033i	0.420970	+	1.01631i
$474$	−6.94220	−	6.94220i	−0.318866	−	0.318866i
$475$	−4.37069			−0.200541
$476$	6.45132	+	13.3548i	0.295696	+	0.612117i
$477$	14.9868			0.686201
$478$	11.2004	+	11.2004i	0.512293	+	0.512293i
$479$	0.0451472	+	0.108995i	0.00206283	+	0.00498011i	0.924908	−	0.380192i	$-0.124142\pi$
$479$	0.0451472	+	0.108995i	0.00206283	+	0.00498011i	−0.922845	+	0.385172i	$0.874142\pi$
$480$			2.33738i			0.106686i
$481$	−2.70230	+	1.11933i	−0.123214	+	0.0510370i
$482$	−8.11947	+	19.6021i	−0.369832	+	0.892852i
$483$	30.7159	+	12.7230i	1.39762	+	0.578915i
$484$	−4.98424	+	4.98424i	−0.226556	+	0.226556i
$485$	−0.0917809	+	0.0917809i	−0.00416756	+	0.00416756i
$486$	−18.8133	−	7.79271i	−0.853387	−	0.353485i
$487$	1.36158	−	3.28715i	0.0616992	−	0.148955i	−0.890023	−	0.455915i	$-0.849312\pi$
$487$	1.36158	−	3.28715i	0.0616992	−	0.148955i	0.951722	+	0.306960i	$0.0993119\pi$
$488$	1.68551	−	0.698163i	0.0762996	−	0.0316043i
$489$			6.94316i			0.313980i
$490$	2.27292	+	5.48732i	0.102680	+	0.247892i
$491$	−4.13702	−	4.13702i	−0.186701	−	0.186701i	0.607567	−	0.794268i	$-0.292146\pi$
$491$	−4.13702	−	4.13702i	−0.186701	−	0.186701i	−0.794268	+	0.607567i	$0.792146\pi$
$492$	−4.32361			−0.194923
$493$	−8.03744	+	23.0595i	−0.361988	+	1.03855i
$494$	2.96690			0.133487
$495$	3.46241	+	3.46241i	0.155624	+	0.155624i
$496$	3.63256	+	8.76978i	0.163107	+	0.393775i
$497$			42.4620i			1.90468i
$498$	−36.0921	+	14.9498i	−1.61732	+	0.669917i
$499$	5.43085	−	13.1112i	0.243118	−	0.586939i	−0.754471	−	0.656333i	$-0.772107\pi$
$499$	5.43085	−	13.1112i	0.243118	−	0.586939i	0.997589	+	0.0693939i	$0.0221065\pi$
$500$	−0.923880	−	0.382683i	−0.0413171	−	0.0171141i
$501$	−31.3523	+	31.3523i	−1.40072	+	1.40072i
$502$	−16.6213	+	16.6213i	−0.741845	+	0.741845i
$503$	18.9662	+	7.85604i	0.845659	+	0.350283i	0.763082	−	0.646301i	$-0.223685\pi$
$503$	18.9662	+	7.85604i	0.845659	+	0.350283i	0.0825766	+	0.996585i	$0.473685\pi$
$504$	3.39098	−	8.18656i	0.151046	−	0.364658i
$505$	−8.58439	+	3.55577i	−0.382000	+	0.158230i
$506$		−	7.86007i		−	0.349423i
$507$	−11.2160	−	27.0779i	−0.498122	−	1.20257i
$508$	11.1826	+	11.1826i	0.496147	+	0.496147i
$509$	−11.3992			−0.505259			−0.252629	−	0.967563i	$-0.581295\pi$
$509$	−11.3992			−0.505259			−0.252629	+	0.967563i	$0.581295\pi$
$510$	7.19376	+	6.41304i	0.318545	+	0.283974i
$511$	22.0778			0.976666
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.09797	+	5.06496i	0.0926278	+	0.223623i
$514$			6.27466i			0.276763i
$515$	13.6581	−	5.65736i	0.601847	−	0.249293i
$516$	10.7658	−	25.9910i	0.473938	−	1.14419i
$517$	−25.0674	−	10.3832i	−1.10246	−	0.456655i
$518$	10.9599	−	10.9599i	0.481551	−	0.481551i
$519$	−31.6221	+	31.6221i	−1.38806	+	1.38806i
$520$	0.627145	+	0.259772i	0.0275021	+	0.0113918i
$521$	−3.74292	+	9.03621i	−0.163980	+	0.395884i	−0.984416	−	0.175855i	$-0.943731\pi$
$521$	−3.74292	+	9.03621i	−0.163980	+	0.395884i	0.820436	+	0.571739i	$0.193731\pi$
$522$	13.4793	−	5.58329i	0.589971	−	0.244374i
$523$		−	33.9176i		−	1.48311i	−0.670889	−	0.741557i	$-0.734087\pi$
$523$		−	33.9176i		−	1.48311i	0.670889	−	0.741557i	$-0.265913\pi$
$524$	3.73949	+	9.02792i	0.163360	+	0.394387i
$525$	5.94529	+	5.94529i	0.259474	+	0.259474i
$526$	6.51710			0.284159
$527$	36.9573	+	12.8816i	1.60989	+	0.561130i
$528$	−4.64617			−0.202199
$529$	5.20724	+	5.20724i	0.226402	+	0.226402i
$530$	−2.32821	−	5.62079i	−0.101131	−	0.244151i
$531$		−	2.65098i		−	0.115043i
$532$	−14.5252	+	6.01655i	−0.629749	+	0.260851i
$533$	−0.480517	+	1.16007i	−0.0208135	+	0.0502483i
$534$	1.29718	+	0.537311i	0.0561346	+	0.0232517i
$535$	6.61980	−	6.61980i	0.286199	−	0.286199i
$536$	3.97487	−	3.97487i	0.171688	−	0.171688i
$537$	−1.00272	−	0.415342i	−0.0432707	−	0.0179233i
$538$	−2.19244	+	5.29301i	−0.0945227	+	0.228198i
$539$	−10.9075	+	4.51804i	−0.469820	+	0.194606i
$540$			1.25433i			0.0539776i
$541$	5.48166	+	13.2339i	0.235675	+	0.568969i	0.996827	−	0.0796046i	$-0.0253658\pi$
$541$	5.48166	+	13.2339i	0.235675	+	0.568969i	−0.761152	+	0.648574i	$0.775366\pi$
$542$	3.95316	+	3.95316i	0.169803	+	0.169803i
$543$	−31.5693			−1.35477
$544$	−4.11634	+	0.236183i	−0.176486	+	0.0101263i
$545$	−4.44384			−0.190353
$546$	−4.03576	−	4.03576i	−0.172715	−	0.172715i
$547$	8.51205	+	20.5499i	0.363949	+	0.878651i	0.994715	+	0.102677i	$0.0327409\pi$
$547$	8.51205	+	20.5499i	0.363949	+	0.878651i	−0.630766	+	0.775973i	$0.717259\pi$
$548$		−	10.3127i		−	0.440536i
$549$	−4.15203	+	1.71983i	−0.177204	+	0.0734005i
$550$	0.760686	−	1.83646i	0.0324357	−	0.0783068i
$551$	−23.9160	−	9.90632i	−1.01885	−	0.422023i
$552$	−6.53545	+	6.53545i	−0.278167	+	0.278167i
$553$	10.6838	−	10.6838i	0.454320	−	0.454320i
$554$	7.48335	+	3.09970i	0.317937	+	0.131694i
$555$	3.85420	−	9.30486i	0.163602	−	0.394970i
$556$	−17.7210	+	7.34028i	−0.751537	+	0.311297i
$557$		−	9.48459i		−	0.401875i	−0.979604	−	0.200938i	$-0.935601\pi$
$557$		−	9.48459i		−	0.401875i	0.979604	−	0.200938i	$-0.0643988\pi$
$558$	−8.94832	−	21.6032i	−0.378813	−	0.914534i
$559$	−5.77716	−	5.77716i	−0.244348	−	0.244348i
$560$	−3.59714			−0.152007
$561$	−12.7476	+	14.2995i	−0.538205	+	0.603726i
$562$	−2.45286			−0.103467
$563$	−30.1199	−	30.1199i	−1.26940	−	1.26940i	−0.946397	−	0.323006i	$-0.895307\pi$
$563$	−30.1199	−	30.1199i	−1.26940	−	1.26940i	−0.323006	−	0.946397i	$-0.604693\pi$
$564$	12.2095	+	29.4763i	0.514112	+	1.24118i
$565$		−	2.44268i		−	0.102764i
$566$	9.99078	−	4.13832i	0.419944	−	0.173946i
$567$	14.2088	−	34.3031i	0.596715	−	1.44060i
$568$	−10.9058	−	4.51734i	−0.457598	−	0.189543i
$569$	−1.69239	+	1.69239i	−0.0709488	+	0.0709488i	−0.741691	−	0.670742i	$-0.765976\pi$
$569$	−1.69239	+	1.69239i	−0.0709488	+	0.0709488i	0.670742	+	0.741691i	$0.265976\pi$
$570$	−7.22379	+	7.22379i	−0.302571	+	0.302571i
$571$	7.70661	+	3.19218i	0.322512	+	0.133589i	0.538065	−	0.842903i	$-0.319155\pi$
$571$	7.70661	+	3.19218i	0.322512	+	0.133589i	−0.215553	+	0.976492i	$0.569155\pi$
$572$	−0.516367	+	1.24662i	−0.0215904	+	0.0521238i
$573$	24.4032	−	10.1081i	1.01946	−	0.422274i
$574$		−	6.65387i		−	0.277727i
$575$	−1.51321	−	3.65322i	−0.0631054	−	0.152350i
$576$	1.74186	+	1.74186i	0.0725775	+	0.0725775i
$577$	−32.9029			−1.36977			−0.684883	−	0.728653i	$-0.740147\pi$
$577$	−32.9029			−1.36977			−0.684883	+	0.728653i	$0.740147\pi$
$578$	−10.5670	+	13.3168i	−0.439530	+	0.553907i
$579$	11.5085			0.478279
$580$	−4.18801	−	4.18801i	−0.173898	−	0.173898i
$581$	−23.0072	−	55.5443i	−0.954499	−	2.30436i
$582$			0.303387i			0.0125758i
$583$	11.1728	−	4.62793i	0.462731	−	0.191669i
$584$	−2.34876	+	5.67041i	−0.0971924	+	0.234643i
$585$	−1.54489	−	0.639913i	−0.0638732	−	0.0264572i
$586$	0.317668	−	0.317668i	0.0131228	−	0.0131228i
$587$	22.2379	−	22.2379i	0.917858	−	0.917858i	−0.0790152	−	0.996873i	$-0.525178\pi$
$587$	22.2379	−	22.2379i	0.917858	−	0.917858i	0.996873	+	0.0790152i	$0.0251776\pi$
$588$	12.8260	+	5.31270i	0.528935	+	0.219092i
$589$	−15.8768	+	38.3300i	−0.654193	+	1.57936i
$590$	−0.994245	+	0.411830i	−0.0409324	+	0.0169548i
$591$		−	63.0017i		−	2.59154i
$592$	1.64894	+	3.98089i	0.0677709	+	0.163614i
$593$	11.1052	+	11.1052i	0.456035	+	0.456035i	0.897352	−	0.441316i	$-0.145488\pi$
$593$	11.1052	+	11.1052i	0.456035	+	0.456035i	−0.441316	+	0.897352i	$0.645488\pi$
$594$	−2.49331			−0.102302
$595$	−9.86942	+	11.0709i	−0.404607	+	0.453863i
$596$	18.0124			0.737816
$597$	31.0781	+	31.0781i	1.27194	+	1.27194i
$598$	1.02720	+	2.47987i	0.0420052	+	0.101409i
$599$		−	33.0366i		−	1.34984i	−0.737892	−	0.674919i	$-0.764179\pi$
$599$		−	33.0366i		−	1.34984i	0.737892	−	0.674919i	$-0.235821\pi$
$600$	−2.15946	+	0.894478i	−0.0881596	+	0.0365169i
$601$	14.6688	−	35.4137i	0.598355	−	1.44456i	−0.276903	−	0.960898i	$-0.589308\pi$
$601$	14.6688	−	35.4137i	0.598355	−	1.44456i	0.875257	−	0.483658i	$-0.160692\pi$
$602$	39.9991	+	16.5682i	1.63024	+	0.675268i
$603$	−9.79154	+	9.79154i	−0.398742	+	0.398742i
$604$	6.77035	−	6.77035i	0.275482	−	0.275482i
$605$	−6.51223	−	2.69745i	−0.264760	−	0.109667i
$606$	−8.31120	+	20.0650i	−0.337619	+	0.815085i
$607$	15.7868	−	6.53911i	0.640767	−	0.265414i	−0.0385530	−	0.999257i	$-0.512275\pi$
$607$	15.7868	−	6.53911i	0.640767	−	0.265414i	0.679320	+	0.733842i	$0.262275\pi$
$608$		−	4.37069i		−	0.177255i
$609$	19.0568	+	46.0072i	0.772220	+	1.86430i
$610$	1.29004	+	1.29004i	0.0522320	+	0.0522320i
$611$	9.26576			0.374852
$612$	10.1400	−	0.581804i	0.409886	−	0.0235180i
$613$	45.5895			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$613$	45.5895			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$614$	3.51248	+	3.51248i	0.141752	+	0.141752i
$615$	−1.65457	−	3.99450i	−0.0667189	−	0.161074i
$616$		−	7.15028i		−	0.288093i
$617$	−35.1732	+	14.5692i	−1.41602	+	0.586535i	−0.953858	−	0.300259i	$-0.902927\pi$
$617$	−35.1732	+	14.5692i	−1.41602	+	0.586535i	−0.462164	+	0.886795i	$0.652927\pi$
$618$	13.2234	−	31.9242i	0.531924	−	1.28418i
$619$	5.06952	+	2.09986i	0.203761	+	0.0844006i	0.482230	−	0.876045i	$-0.339827\pi$
$619$	5.06952	+	2.09986i	0.203761	+	0.0844006i	−0.278469	+	0.960445i	$0.589827\pi$
$620$	−6.71210	+	6.71210i	−0.269564	+	0.269564i
$621$	−3.50716	+	3.50716i	−0.140738	+	0.140738i
$622$	0.632482	+	0.261982i	0.0253602	+	0.0105045i
$623$	−0.826901	+	1.99632i	−0.0331291	+	0.0799807i
$624$	1.46588	−	0.607187i	0.0586822	−	0.0243069i
$625$		−	1.00000i		−	0.0400000i
$626$	−8.99751	−	21.7219i	−0.359613	−	0.868182i
$627$	−14.3592	−	14.3592i	−0.573452	−	0.573452i
$628$	20.2328			0.807378
$629$	16.7761	+	5.84736i	0.668908	+	0.233150i
$630$	8.86107			0.353033
$631$	−3.72742	−	3.72742i	−0.148386	−	0.148386i	0.629011	−	0.777397i	$-0.283460\pi$
$631$	−3.72742	−	3.72742i	−0.148386	−	0.148386i	−0.777397	+	0.629011i	$0.783460\pi$
$632$	1.60739	+	3.88059i	0.0639386	+	0.154361i
$633$			14.8509i			0.590271i
$634$	−2.12124	+	0.878646i	−0.0842451	+	0.0348955i
$635$	−6.05198	+	14.6108i	−0.240165	+	0.579810i
$636$	−13.1379	−	5.44191i	−0.520953	−	0.215786i
$637$	2.85091	−	2.85091i	0.112957	−	0.112957i
$638$	8.32478	−	8.32478i	0.329581	−	0.329581i
$639$	26.8650	+	11.1279i	1.06276	+	0.440211i
$640$	0.382683	−	0.923880i	0.0151269	−	0.0365195i
$641$	−11.6663	+	4.83232i	−0.460789	+	0.190865i	−0.600988	−	0.799258i	$-0.705226\pi$
$641$	−11.6663	+	4.83232i	−0.460789	+	0.190865i	0.140198	+	0.990123i	$0.455226\pi$
$642$		−	21.8822i		−	0.863620i
$643$	−11.5597	−	27.9076i	−0.455870	−	1.10057i	−0.970054	−	0.242888i	$-0.921905\pi$
$643$	−11.5597	−	27.9076i	−0.455870	−	1.10057i	0.514184	−	0.857680i	$-0.328095\pi$
$644$	−10.0578	−	10.0578i	−0.396333	−	0.396333i
$645$	28.1324			1.10771
$646$	−13.4517	−	11.9918i	−0.529249	−	0.471811i
$647$	−1.13719			−0.0447075			−0.0223538	−	0.999750i	$-0.507116\pi$
$647$	−1.13719			−0.0447075			−0.0223538	+	0.999750i	$0.507116\pi$
$648$	7.29871	+	7.29871i	0.286720	+	0.286720i
$649$	−0.818622	−	1.97633i	−0.0321337	−	0.0775777i
$650$			0.678817i			0.0266254i
$651$	73.7354	−	30.5422i	2.88992	−	1.19704i
$652$	1.13675	−	2.74437i	0.0445187	−	0.107478i
$653$	−17.3246	−	7.17610i	−0.677965	−	0.280822i	0.0170107	−	0.999855i	$-0.494585\pi$
$653$	−17.3246	−	7.17610i	−0.677965	−	0.280822i	−0.694976	+	0.719033i	$0.744585\pi$
$654$	−7.34470	+	7.34470i	−0.287200	+	0.287200i
$655$	−6.90967	+	6.90967i	−0.269983	+	0.269983i
$656$	1.70896	+	0.707874i	0.0667237	+	0.0276379i
$657$	5.78585	−	13.9683i	0.225728	−	0.544954i
$658$	−45.3629	+	18.7899i	−1.76843	+	0.732508i
$659$			38.0451i			1.48202i	0.671491	+	0.741012i	$0.265654\pi$
$659$			38.0451i			1.48202i	−0.671491	+	0.741012i	$0.734346\pi$
$660$	−1.77801	−	4.29251i	−0.0692091	−	0.167086i
$661$	14.8582	+	14.8582i	0.577915	+	0.577915i	0.934328	−	0.356413i	$-0.116000\pi$
$661$	14.8582	+	14.8582i	0.577915	+	0.577915i	−0.356413	+	0.934328i	$0.616000\pi$
$662$	−17.5703			−0.682890
$663$	2.15317	−	6.17746i	0.0836222	−	0.239913i
$664$	16.7135			0.648608
$665$	−11.1171	−	11.1171i	−0.431104	−	0.431104i
$666$	−4.06193	−	9.80638i	−0.157397	−	0.379989i
$667$		−	23.4198i		−	0.906818i
$668$	17.5255	−	7.25928i	0.678080	−	0.280870i
$669$	−3.72102	+	8.98335i	−0.143863	+	0.347316i
$670$	5.19341	+	2.15118i	0.200639	+	0.0831074i
$671$	−2.56429	+	2.56429i	−0.0989934	+	0.0989934i
$672$	−5.94529	+	5.94529i	−0.229344	+	0.229344i
$673$	7.72784	+	3.20098i	0.297886	+	0.123389i	0.526621	−	0.850100i	$-0.323459\pi$
$673$	7.72784	+	3.20098i	0.297886	+	0.123389i	−0.228734	+	0.973489i	$0.573459\pi$
$674$	11.2475	−	27.1538i	0.433237	−	1.04593i
$675$	−1.15885	+	0.480010i	−0.0446040	+	0.0184756i
$676$			12.5392i			0.482277i
$677$	8.35739	+	20.1765i	0.321201	+	0.775447i	0.999185	+	0.0403706i	$0.0128538\pi$
$677$	8.35739	+	20.1765i	0.321201	+	0.775447i	−0.677984	+	0.735077i	$0.737146\pi$
$678$	−4.03722	−	4.03722i	−0.155048	−	0.155048i
$679$	−0.466901			−0.0179180
$680$	−1.79346	−	3.71261i	−0.0687760	−	0.142372i
$681$	40.1779			1.53962
$682$	−13.3421	−	13.3421i	−0.510895	−	0.510895i
$683$	6.63241	+	16.0120i	0.253782	+	0.612684i	0.998503	−	0.0546917i	$-0.0174176\pi$
$683$	6.63241	+	16.0120i	0.253782	+	0.612684i	−0.744721	+	0.667376i	$0.767418\pi$
$684$			10.7666i			0.411671i
$685$	9.52768	−	3.94649i	0.364034	−	0.150788i
$686$	1.45994	−	3.52460i	0.0557407	−	0.134570i
$687$	38.2480	+	15.8429i	1.45925	+	0.604443i
$688$	−8.51063	+	8.51063i	−0.324465	+	0.324465i
$689$	−2.92025	+	2.92025i	−0.111253	+	0.111253i
$690$	−8.53898	−	3.53696i	−0.325074	−	0.134650i
$691$	−1.21447	+	2.93200i	−0.0462007	+	0.111538i	−0.945295	−	0.326216i	$-0.894226\pi$
$691$	−1.21447	+	2.93200i	−0.0462007	+	0.111538i	0.899094	+	0.437755i	$0.144226\pi$
$692$	17.6763	−	7.32175i	0.671951	−	0.278331i
$693$			17.6137i			0.669091i
$694$	−9.85783	−	23.7989i	−0.374198	−	0.903394i
$695$	−13.5631	−	13.5631i	−0.514476	−	0.514476i
$696$	−13.8437			−0.524744
$697$	6.86746	−	3.31748i	0.260124	−	0.125658i
$698$	0.962694			0.0364385
$699$	−18.0483	−	18.0483i	−0.682650	−	0.682650i
$700$	−1.37657	−	3.32333i	−0.0520293	−	0.125610i
$701$		−	11.9472i		−	0.451239i	−0.974216	−	0.225619i	$-0.927559\pi$
$701$		−	11.9472i		−	0.451239i	0.974216	−	0.225619i	$-0.0724406\pi$
$702$	0.786645	−	0.325839i	0.0296900	−	0.0122980i
$703$	−7.20700	+	17.3992i	−0.271817	+	0.656225i
$704$	1.83646	+	0.760686i	0.0692141	+	0.0286694i
$705$	−22.5602	+	22.5602i	−0.849666	+	0.849666i
$706$	2.81710	−	2.81710i	0.106023	−	0.106023i
$707$	−30.8793	−	12.7906i	−1.16133	−	0.481040i
$708$	−0.962605	+	2.32393i	−0.0361769	+	0.0873388i
$709$	8.57474	−	3.55177i	0.322031	−	0.133390i	−0.215811	−	0.976435i	$-0.569240\pi$
$709$	8.57474	−	3.55177i	0.322031	−	0.133390i	0.537842	+	0.843046i	$0.319240\pi$
$710$		−	11.8044i		−	0.443010i
$711$	−3.95959	−	9.55930i	−0.148496	−	0.358502i
$712$	−0.424758	−	0.424758i	−0.0159185	−	0.0159185i
$713$	−37.5348			−1.40569
$714$	1.98580	+	34.6098i	0.0743168	+	1.29524i
$715$	−1.34933			−0.0504621
$716$	0.328338	+	0.328338i	0.0122706	+	0.0122706i
$717$	14.1683	+	34.2052i	0.529124	+	1.27742i
$718$		−	2.18709i		−	0.0816214i
$719$	16.9034	−	7.00162i	0.630391	−	0.261116i	−0.0445285	−	0.999008i	$-0.514179\pi$
$719$	16.9034	−	7.00162i	0.630391	−	0.261116i	0.674919	+	0.737892i	$0.264179\pi$
$720$	−0.942688	+	2.27585i	−0.0351319	+	0.0848160i
$721$	49.1301	+	20.3503i	1.82970	+	0.757887i
$722$	0.0728021	−	0.0728021i	0.00270941	−	0.00270941i
$723$	−35.0673	+	35.0673i	−1.30417	+	1.30417i
$724$	12.4782	+	5.16863i	0.463747	+	0.192090i
$725$	2.26653	−	5.47189i	0.0841769	−	0.203221i
$726$	−15.2216	+	6.30498i	−0.564925	+	0.234000i
$727$			19.9196i			0.738777i	0.929275	+	0.369389i	$0.120433\pi$
$727$			19.9196i			0.738777i	−0.929275	+	0.369389i	$0.879567\pi$
$728$	0.934438	+	2.25593i	0.0346326	+	0.0836104i
$729$	−11.7600	−	11.7600i	−0.435555	−	0.435555i
$730$	−6.13761			−0.227163
$731$	2.84266	+	49.5436i	0.105140	+	1.83244i
$732$	4.26429			0.157613
$733$	−11.0973	−	11.0973i	−0.409886	−	0.409886i	0.471812	−	0.881699i	$-0.343600\pi$
$733$	−11.0973	−	11.0973i	−0.409886	−	0.409886i	−0.881699	+	0.471812i	$0.843600\pi$
$734$	−10.4000	−	25.1079i	−0.383873	−	0.926751i
$735$			13.8827i			0.512073i
$736$	3.65322	−	1.51321i	0.134660	−	0.0557778i
$737$	−4.27605	+	10.3233i	−0.157510	+	0.380264i
$738$	−4.20979	−	1.74375i	−0.154964	−	0.0641884i
$739$	23.3949	−	23.3949i	0.860597	−	0.860597i	−0.130810	−	0.991407i	$-0.541758\pi$
$739$	23.3949	−	23.3949i	0.860597	−	0.860597i	0.991407	+	0.130810i	$0.0417579\pi$
$740$	−3.04684	+	3.04684i	−0.112004	+	0.112004i
$741$	6.40691	+	2.65383i	0.235364	+	0.0974908i
$742$	8.37489	−	20.2188i	0.307452	−	0.742254i
$743$	23.3771	−	9.68311i	0.857622	−	0.355239i	0.0898450	−	0.995956i	$-0.471363\pi$
$743$	23.3771	−	9.68311i	0.857622	−	0.355239i	0.767777	+	0.640717i	$0.221363\pi$
$744$			22.1872i			0.813424i
$745$	6.89304	+	16.6413i	0.252541	+	0.609689i
$746$	−10.9000	−	10.9000i	−0.399076	−	0.399076i
$747$	−41.1713			−1.50638
$748$	7.37981	−	3.56498i	0.269833	−	0.130348i
$749$	33.6758			1.23049
$750$	−1.65278	−	1.65278i	−0.0603510	−	0.0603510i
$751$	−6.15246	−	14.8533i	−0.224506	−	0.542006i	0.770986	−	0.636853i	$-0.219764\pi$
$751$	−6.15246	−	14.8533i	−0.224506	−	0.542006i	−0.995492	+	0.0948462i	$0.969764\pi$
$752$		−	13.6499i		−	0.497759i
$753$	−50.7605	+	21.0257i	−1.84981	+	0.766218i
$754$	−1.53856	+	3.71442i	−0.0560311	+	0.135271i
$755$	8.84589	+	3.66409i	0.321935	+	0.133350i
$756$	−3.19046	+	3.19046i	−0.116036	+	0.116036i
$757$	6.95586	−	6.95586i	0.252815	−	0.252815i	−0.569309	−	0.822124i	$-0.692789\pi$
$757$	6.95586	−	6.95586i	0.252815	−	0.252815i	0.822124	+	0.569309i	$0.192789\pi$
$758$	23.3819	+	9.68511i	0.849270	+	0.351779i
$759$	7.03066	−	16.9735i	0.255197	−	0.616099i
$760$	4.03799	−	1.67259i	0.146473	−	0.0606713i
$761$		−	16.8816i		−	0.611959i	−0.952038	−	0.305979i	$-0.901016\pi$
$761$		−	16.8816i		−	0.611959i	0.952038	−	0.305979i	$-0.0989838\pi$
$762$	14.1458	+	34.1510i	0.512448	+	1.23716i
$763$	−11.3032	−	11.3032i	−0.409203	−	0.409203i
$764$	−11.3006			−0.408841
$765$	4.41794	+	9.14552i	0.159731	+	0.330657i
$766$	−5.91817			−0.213832
$767$	0.516555	+	0.516555i	0.0186517	+	0.0186517i
$768$	−0.894478	−	2.15946i	−0.0322767	−	0.0779228i
$769$		−	25.4079i		−	0.916234i	−0.888892	−	0.458117i	$-0.848524\pi$
$769$		−	25.4079i		−	0.916234i	0.888892	−	0.458117i	$-0.151476\pi$
$770$	6.60600	−	2.73629i	0.238064	−	0.0986092i
$771$	−5.61254	+	13.5499i	−0.202131	+	0.487987i
$772$	−4.54889	−	1.88421i	−0.163718	−	0.0678143i
$773$	−26.1347	+	26.1347i	−0.940000	+	0.940000i	−0.998299	−	0.0582992i	$-0.981432\pi$
$773$	−26.1347	+	26.1347i	−0.940000	+	0.940000i	0.0582992	+	0.998299i	$0.481432\pi$
$774$	20.9648	−	20.9648i	0.753563	−	0.753563i
$775$	−8.76978	−	3.63256i	−0.315020	−	0.130485i
$776$	0.0496715	−	0.119918i	0.00178310	−	0.00430479i
$777$	33.4709	−	13.8641i	1.20076	−	0.497372i
$778$			18.4733i			0.662298i
$779$	3.09390	+	7.46934i	0.110851	+	0.267617i
$780$	1.12194	+	1.12194i	0.0401717	+	0.0401717i
$781$	23.4644			0.839621
$782$	5.36607	−	15.3953i	0.191890	−	0.550534i
$783$	−7.42904			−0.265492
$784$	−4.19982	−	4.19982i	−0.149993	−	0.149993i
$785$	7.74277	+	18.6927i	0.276351	+	0.667171i
$786$			22.8403i			0.814688i
$787$	31.1138	−	12.8878i	1.10909	−	0.459399i	0.248464	−	0.968641i	$-0.420074\pi$
$787$	31.1138	−	12.8878i	1.10909	−	0.459399i	0.860623	+	0.509242i	$0.170074\pi$
$788$	−10.3148	+	24.9022i	−0.367450	+	0.887104i
$789$	14.0734	+	5.82940i	0.501027	+	0.207532i
$790$	−2.97007	+	2.97007i	−0.105670	+	0.105670i
$791$	6.21312	−	6.21312i	0.220913	−	0.220913i
$792$	−4.52386	−	1.87384i	−0.160748	−	0.0665842i
$793$	0.473925	−	1.14416i	0.0168296	−	0.0406302i
$794$	−36.7519	+	15.2231i	−1.30427	+	0.540248i
$795$		−	14.2204i		−	0.504346i
$796$	−7.19579	−	17.3722i	−0.255048	−	0.615741i
$797$	−26.8204	−	26.8204i	−0.950029	−	0.950029i	0.0487805	−	0.998810i	$-0.484467\pi$
$797$	−26.8204	−	26.8204i	−0.950029	−	0.950029i	−0.998810	+	0.0487805i	$0.984467\pi$
$798$	−36.7484			−1.30088
$799$	−42.0101	−	37.4509i	−1.48621	−	1.32492i
$800$	1.00000			0.0353553
$801$	1.04633	+	1.04633i	0.0369703	+	0.0369703i
$802$	3.94363	+	9.52077i	0.139255	+	0.336190i
$803$		−	12.2001i		−	0.430533i
$804$	12.1390	−	5.02814i	0.428110	−	0.177329i
$805$	5.44325	−	13.1412i	0.191849	−	0.463165i
$806$	5.95308	+	2.46585i	0.209688	+	0.0868557i
$807$	−9.46896	+	9.46896i	−0.333323	+	0.333323i
$808$	6.57020	−	6.57020i	0.231139	−	0.231139i
$809$	−34.3715	−	14.2371i	−1.20844	−	0.500551i	−0.314721	−	0.949184i	$-0.601911\pi$
$809$	−34.3715	−	14.2371i	−1.20844	−	0.500551i	−0.893716	+	0.448633i	$0.851911\pi$
$810$	−3.95003	+	9.53622i	−0.138790	+	0.335069i
$811$	26.2281	−	10.8640i	0.920994	−	0.381488i	0.128739	−	0.991678i	$-0.458907\pi$
$811$	26.2281	−	10.8640i	0.920994	−	0.381488i	0.792255	+	0.610190i	$0.208907\pi$
$812$		−	21.3049i		−	0.747656i
$813$	5.00067	+	12.0727i	0.175381	+	0.423408i
$814$	−6.05641	−	6.05641i	−0.212277	−	0.212277i
$815$	2.97048			0.104051
$816$	−9.10033	−	3.17194i	−0.318575	−	0.111040i
$817$	−52.6050			−1.84042
$818$	0.689855	+	0.689855i	0.0241202	+	0.0241202i
$819$	−2.30186	−	5.55718i	−0.0804335	−	0.194184i
$820$			1.84976i			0.0645966i
$821$	12.4788	−	5.16887i	0.435511	−	0.180395i	−0.154146	−	0.988048i	$-0.549263\pi$
$821$	12.4788	−	5.16887i	0.435511	−	0.180395i	0.589658	+	0.807653i	$0.299263\pi$
$822$	9.22447	−	22.2698i	0.321740	−	0.776750i
$823$	32.7544	+	13.5673i	1.14175	+	0.472928i	0.871759	−	0.489936i	$-0.162980\pi$
$823$	32.7544	+	13.5673i	1.14175	+	0.472928i	0.269990	+	0.962863i	$0.412980\pi$
$824$	−10.4534	+	10.4534i	−0.364163	+	0.364163i
$825$	3.28534	−	3.28534i	0.114381	−	0.114381i
$826$	−3.57644	−	1.48141i	−0.124440	−	0.0515449i
$827$	−5.48875	+	13.2510i	−0.190863	+	0.460783i	−0.990123	−	0.140202i	$-0.955225\pi$
$827$	−5.48875	+	13.2510i	−0.190863	+	0.460783i	0.799260	+	0.600985i	$0.205225\pi$
$828$	−8.99921	+	3.72760i	−0.312744	+	0.129543i
$829$		−	38.8842i		−	1.35050i	−0.737587	−	0.675252i	$-0.764035\pi$
$829$		−	38.8842i		−	1.35050i	0.737587	−	0.675252i	$-0.235965\pi$
$830$	6.39596	+	15.4412i	0.222007	+	0.535973i
$831$	13.3874	+	13.3874i	0.464403	+	0.464403i
$832$	−0.678817			−0.0235338
$833$	−24.4487	+	1.40279i	−0.847098	+	0.0486039i
$834$	−44.8335			−1.55246
$835$	13.4134	+	13.4134i	0.464190	+	0.464190i
$836$	3.32472	+	8.02659i	0.114988	+	0.277605i
$837$			11.9065i			0.411548i
$838$	6.65610	−	2.75705i	0.229931	−	0.0952406i
$839$	−14.0553	+	33.9325i	−0.485244	+	1.17148i	0.471844	+	0.881682i	$0.343589\pi$
$839$	−14.0553	+	33.9325i	−0.485244	+	1.17148i	−0.957087	+	0.289799i	$0.906411\pi$
$840$	−7.76789	−	3.21757i	−0.268018	−	0.111017i
$841$	4.29836	−	4.29836i	0.148219	−	0.148219i
$842$	12.7381	−	12.7381i	0.438983	−	0.438983i
$843$	−5.29685	−	2.19403i	−0.182433	−	0.0755663i
$844$	2.43144	−	5.87001i	0.0836936	−	0.202054i
$845$	−11.5847	+	4.79855i	−0.398526	+	0.165075i
$846$			33.6245i			1.15604i
$847$	−9.70312	−	23.4254i	−0.333403	−	0.804906i
$848$	4.30196	+	4.30196i	0.147730	+	0.147730i
$849$	25.2763			0.867481
$850$	2.74368	−	3.07770i	0.0941075	−	0.105564i
$851$	−17.0383			−0.584064
$852$	−19.5100	−	19.5100i	−0.668403	−	0.668403i
$853$	−0.660999	−	1.59579i	−0.0226322	−	0.0546389i	0.912159	−	0.409836i	$-0.134414\pi$
$853$	−0.660999	−	1.59579i	−0.0226322	−	0.0546389i	−0.934792	+	0.355197i	$0.884414\pi$
$854$			6.56258i			0.224567i
$855$	−9.94705	+	4.12020i	−0.340182	+	0.140908i
$856$	−3.58261	+	8.64919i	−0.122451	+	0.295623i
$857$	24.6090	+	10.1934i	0.840628	+	0.348200i	0.761101	−	0.648633i	$-0.224659\pi$
$857$	24.6090	+	10.1934i	0.840628	+	0.348200i	0.0795271	+	0.996833i	$0.474659\pi$
$858$	−2.23015	+	2.23015i	−0.0761360	+	0.0761360i
$859$	−16.2328	+	16.2328i	−0.553857	+	0.553857i	−0.927552	−	0.373695i	$-0.878091\pi$
$859$	−16.2328	+	16.2328i	−0.553857	+	0.553857i	0.373695	+	0.927552i	$0.378091\pi$
$860$	−11.1197	−	4.60592i	−0.379178	−	0.157061i
$861$	5.95174	−	14.3688i	0.202835	−	0.489686i
$862$	17.1099	−	7.08715i	0.582765	−	0.241389i
$863$			5.20543i			0.177195i	0.996068	+	0.0885974i	$0.0282385\pi$
$863$			5.20543i			0.177195i	−0.996068	+	0.0885974i	$0.971762\pi$
$864$	−0.480010	−	1.15885i	−0.0163303	−	0.0394247i
$865$	13.5288	+	13.5288i	0.459994	+	0.459994i
$866$	−35.8518			−1.21829
$867$	−34.7307	+	19.3052i	−1.17952	+	0.655640i
$868$	−34.1453			−1.15897
$869$	−5.90381	−	5.90381i	−0.200273	−	0.200273i
$870$	−5.29776	−	12.7899i	−0.179611	−	0.433619i
$871$		−	3.81584i		−	0.129295i
$872$	4.10558	−	1.70059i	0.139032	−	0.0575891i
$873$	−0.122359	+	0.295401i	−0.00414122	+	0.00999780i
$874$	15.9671	+	6.61379i	0.540096	+	0.223715i
$875$	2.54356	−	2.54356i	0.0859882	−	0.0859882i
$876$	−10.1441	+	10.1441i	−0.342738	+	0.342738i
$877$	−23.8639	−	9.88474i	−0.805826	−	0.333784i	−0.0585387	−	0.998285i	$-0.518644\pi$
$877$	−23.8639	−	9.88474i	−0.805826	−	0.333784i	−0.747287	+	0.664501i	$0.768644\pi$
$878$	3.63408	−	8.77346i	0.122644	−	0.296090i
$879$	0.970139	−	0.401845i	0.0327220	−	0.0135539i
$880$			1.98777i			0.0670076i
$881$	−4.17405	−	10.0770i	−0.140627	−	0.339504i	0.837837	−	0.545920i	$-0.183820\pi$
$881$	−4.17405	−	10.0770i	−0.140627	−	0.339504i	−0.978464	+	0.206416i	$0.933820\pi$
$882$	10.3457	+	10.3457i	0.348357	+	0.348357i
$883$	−10.7160			−0.360621			−0.180310	−	0.983610i	$-0.557710\pi$
$883$	−10.7160			−0.360621			−0.180310	+	0.983610i	$0.557710\pi$
$884$	−1.86246	+	2.08919i	−0.0626413	+	0.0702672i
$885$	−2.51541			−0.0845545
$886$	14.5455	+	14.5455i	0.488665	+	0.488665i
$887$	0.217360	+	0.524754i	0.00729824	+	0.0176195i	0.927487	−	0.373856i	$-0.121965\pi$
$887$	0.217360	+	0.524754i	0.00729824	+	0.0176195i	−0.920188	+	0.391476i	$0.871965\pi$
$888$			10.0715i			0.337978i
$889$	−52.5570	+	21.7698i	−1.76271	+	0.730136i
$890$	0.229877	−	0.554972i	0.00770550	−	0.0186027i
$891$	−18.9558	−	7.85174i	−0.635043	−	0.263043i
$892$	2.94156	−	2.94156i	0.0984907	−	0.0984907i
$893$	42.1855	−	42.1855i	1.41168	−	1.41168i
$894$	38.8970	+	16.1117i	1.30091	+	0.538855i
$895$	−0.177695	+	0.428994i	−0.00593970	+	0.0143397i
$896$	3.32333	−	1.37657i	0.111025	−	0.0459879i
$897$			6.27399i			0.209482i
$898$	2.64090	+	6.37569i	0.0881279	+	0.212759i
$899$	−39.7540	−	39.7540i	−1.32587	−	1.32587i
$900$	−2.46336			−0.0821121
$901$	25.0434	−	1.43691i	0.834315	−	0.0478705i
$902$	−3.67690			−0.122427
$903$	71.5566	+	71.5566i	2.38125	+	2.38125i
$904$	0.934775	+	2.25675i	0.0310901	+	0.0750582i
$905$			13.5063i			0.448964i
$906$	20.6762	−	8.56438i	0.686922	−	0.284532i
$907$	12.1778	−	29.3998i	0.404357	−	0.976203i	−0.582239	−	0.813018i	$-0.697823\pi$
$907$	12.1778	−	29.3998i	0.404357	−	0.976203i	0.986595	−	0.163185i	$-0.0521769\pi$
$908$	−15.8808	−	6.57804i	−0.527023	−	0.218300i
$909$	−16.1848	+	16.1848i	−0.536816	+	0.536816i
$910$	−1.72662	+	1.72662i	−0.0572367	+	0.0572367i
$911$	42.9258	+	17.7804i	1.42220	+	0.589093i	0.955411	−	0.295279i	$-0.0954125\pi$
$911$	42.9258	+	17.7804i	1.42220	+	0.589093i	0.466784	+	0.884371i	$0.345413\pi$
$912$	3.90949	−	9.43834i	0.129456	−	0.312535i
$913$	−30.6935	+	12.7137i	−1.01581	+	0.420762i
$914$			34.2565i			1.13310i
$915$	1.63187	+	3.93969i	0.0539481	+	0.130242i
$916$	−12.5242	−	12.5242i	−0.413810	−	0.413810i
$917$	−35.1504			−1.16077
$918$	−4.88357	−	1.70218i	−0.161182	−	0.0561803i
$919$	50.5300			1.66683			0.833415	−	0.552648i	$-0.186383\pi$
$919$	50.5300			1.66683			0.833415	+	0.552648i	$0.186383\pi$
$920$	2.79606	+	2.79606i	0.0921832	+	0.0921832i
$921$	4.44323	+	10.7269i	0.146409	+	0.353463i
$922$			5.17277i			0.170356i
$923$	−7.40306	+	3.06645i	−0.243675	+	0.100933i
$924$	6.39577	−	15.4408i	0.210405	−	0.507964i
$925$	−3.98089	−	1.64894i	−0.130891	−	0.0542167i
$926$	−7.10034	+	7.10034i	−0.233332	+	0.233332i
$927$	25.7506	−	25.7506i	0.845762	−	0.845762i
$928$	5.47189	+	2.26653i	0.179624	+	0.0744026i
$929$	−4.58276	+	11.0638i	−0.150355	+	0.362990i	−0.981055	−	0.193731i	$-0.937941\pi$
$929$	−4.58276	+	11.0638i	−0.150355	+	0.362990i	0.830699	+	0.556722i	$0.187941\pi$
$930$	−20.4983	+	8.49069i	−0.672167	+	0.278421i
$931$		−	25.9595i		−	0.850787i
$932$	4.17890	+	10.0887i	0.136884	+	0.330468i
$933$	1.13148	+	1.13148i	0.0370431	+	0.0370431i
$934$	23.1494			0.757471
$935$	6.11774	+	5.45380i	0.200072	+	0.178358i
$936$	1.67217			0.0546567
$937$	23.5697	+	23.5697i	0.769987	+	0.769987i	0.978104	−	0.208117i	$-0.0667335\pi$
$937$	23.5697	+	23.5697i	0.769987	+	0.769987i	−0.208117	+	0.978104i	$0.566733\pi$
$938$	7.73811	+	18.6815i	0.252658	+	0.609971i
$939$		−	54.9557i		−	1.79341i
$940$	12.6108	−	5.22357i	0.411320	−	0.170374i
$941$	−15.3730	+	37.1136i	−0.501145	+	1.20987i	0.447716	+	0.894176i	$0.352237\pi$
$941$	−15.3730	+	37.1136i	−0.501145	+	1.20987i	−0.948861	+	0.315694i	$0.897763\pi$
$942$	43.6920	+	18.0978i	1.42356	+	0.589659i
$943$	−5.17204	+	5.17204i	−0.168425	+	0.168425i
$944$	0.760963	−	0.760963i	0.0247672	−	0.0247672i
$945$	−4.16853	−	1.72666i	−0.135602	−	0.0561684i
$946$	9.15550	−	22.1033i	0.297671	−	0.718641i
$947$	−2.25442	+	0.933811i	−0.0732588	+	0.0303448i	−0.419012	−	0.907981i	$-0.637623\pi$
$947$	−2.25442	+	0.933811i	−0.0732588	+	0.0303448i	0.345753	+	0.938326i	$0.387623\pi$
$948$			9.81775i			0.318866i
$949$	1.59438	+	3.84917i	0.0517557	+	0.124949i
$950$	3.09055	+	3.09055i	0.100271	+	0.100271i
$951$	−5.36666			−0.174026
$952$	4.88150	−	14.0050i	0.158210	−	0.453906i
$953$	7.17854			0.232536			0.116268	−	0.993218i	$-0.462907\pi$
$953$	7.17854			0.232536			0.116268	+	0.993218i	$0.462907\pi$
$954$	−10.5973	−	10.5973i	−0.343100	−	0.343100i
$955$	−4.32455	−	10.4404i	−0.139939	−	0.337843i
$956$		−	15.8397i		−	0.512293i
$957$	25.4234	−	10.5307i	0.821821	−	0.340409i
$958$	0.0451472	−	0.108995i	0.00145864	−	0.00352147i
$959$	34.2724	+	14.1961i	1.10671	+	0.458416i
$960$	1.65278	−	1.65278i	0.0533432	−	0.0533432i
$961$	−41.7932	+	41.7932i	−1.34817	+	1.34817i
$962$	2.70230	+	1.11933i	0.0871255	+	0.0360886i
$963$	8.82527	−	21.3061i	0.284390	−	0.686579i
$964$	19.6021	−	8.11947i	0.631342	−	0.261510i
$965$		−	4.92369i		−	0.158499i
$966$	−12.7230	−	30.7159i	−0.409354	−	0.988269i
$967$	0.0928418	+	0.0928418i	0.00298559	+	0.00298559i	0.708598	−	0.705612i	$-0.249328\pi$
$967$	0.0928418	+	0.0928418i	0.00298559	+	0.00298559i	−0.705612	+	0.708598i	$0.749328\pi$
$968$	7.04878			0.226556
$969$	−18.3219	−	37.9280i	−0.588586	−	1.21842i
$970$	0.129798			0.00416756
$971$	16.9368	+	16.9368i	0.543528	+	0.543528i	0.924561	−	0.381034i	$-0.124432\pi$
$971$	16.9368	+	16.9368i	0.543528	+	0.543528i	−0.381034	+	0.924561i	$0.624432\pi$
$972$	7.79271	+	18.8133i	0.249951	+	0.603436i
$973$		−	68.9970i		−	2.21194i
$974$	−3.28715	+	1.36158i	−0.105327	+	0.0436279i
$975$	−0.607187	+	1.46588i	−0.0194456	+	0.0469457i
$976$	−1.68551	−	0.698163i	−0.0539520	−	0.0223476i
$977$	−6.70509	+	6.70509i	−0.214515	+	0.214515i	−0.806182	−	0.591667i	$-0.798470\pi$
$977$	−6.70509	+	6.70509i	−0.214515	+	0.214515i	0.591667	+	0.806182i	$0.298470\pi$
$978$	4.90955	−	4.90955i	0.156990	−	0.156990i
$979$	1.10316	+	0.456942i	0.0352570	+	0.0146039i
$980$	2.27292	−	5.48732i	0.0726059	−	0.175286i
$981$	−10.1135	+	4.18916i	−0.322900	+	0.133750i
$982$			5.85062i			0.186701i
$983$	21.3232	+	51.4787i	0.680104	+	1.64192i	0.763822	+	0.645427i	$0.223320\pi$
$983$	21.3232	+	51.4787i	0.680104	+	1.64192i	−0.0837184	+	0.996489i	$0.526680\pi$
$984$	3.05725	+	3.05725i	0.0974617	+	0.0974617i
$985$	−26.9539			−0.858824
$986$	21.9888	−	10.6222i	0.700267	−	0.338279i
$987$	−114.767			−3.65306
$988$	−2.09792	−	2.09792i	−0.0667436	−	0.0667436i
$989$	−18.2128	−	43.9696i	−0.579134	−	1.39815i
$990$		−	4.89659i		−	0.155624i
$991$	−44.5554	+	18.4554i	−1.41535	+	0.586256i	−0.953687	−	0.300801i	$-0.902746\pi$
$991$	−44.5554	+	18.4554i	−1.41535	+	0.586256i	−0.461660	+	0.887057i	$0.652746\pi$
$992$	3.63256	−	8.76978i	0.115334	−	0.278441i
$993$	−37.9424	−	15.7163i	−1.20407	−	0.498740i
$994$	30.0252	−	30.0252i	0.952341	−	0.952341i
$995$	13.2961	−	13.2961i	0.421515	−	0.421515i
$996$	36.0921	+	14.9498i	1.14362	+	0.473703i
$997$	−2.25904	+	5.45380i	−0.0715445	+	0.172724i	−0.955606	−	0.294646i	$-0.904798\pi$
$997$	−2.25904	+	5.45380i	−0.0715445	+	0.172724i	0.884062	+	0.467370i	$0.154798\pi$
$998$	−13.1112	+	5.43085i	−0.415029	+	0.171911i
$999$			5.40474i			0.170998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.151.1	✓	16
5.2	odd	4		850.2.o.g.49.1		16
5.3	odd	4		850.2.o.j.49.4		16
5.4	even	2		850.2.l.e.151.4		16
17.3	odd	16		2890.2.b.r.2311.3		16
17.5	odd	16		2890.2.a.bj.1.7		8
17.8	even	8	inner	170.2.k.b.161.1	yes	16
17.12	odd	16		2890.2.a.bi.1.2		8
17.14	odd	16		2890.2.b.r.2311.14		16
85.8	odd	8		850.2.o.g.399.1		16
85.42	odd	8		850.2.o.j.399.4		16
85.59	even	8		850.2.l.e.501.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.151.1	✓	16	1.1	even	1	trivial
170.2.k.b.161.1	yes	16	17.8	even	8	inner
850.2.l.e.151.4		16	5.4	even	2
850.2.l.e.501.4		16	85.59	even	8
850.2.o.g.49.1		16	5.2	odd	4
850.2.o.g.399.1		16	85.8	odd	8
850.2.o.j.49.4		16	5.3	odd	4
850.2.o.j.399.4		16	85.42	odd	8
2890.2.a.bi.1.2		8	17.12	odd	16
2890.2.a.bj.1.7		8	17.5	odd	16
2890.2.b.r.2311.3		16	17.3	odd	16
2890.2.b.r.2311.14		16	17.14	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.894478 - 2.15946i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{5} +(-0.894478 + 2.15946i) q^{6} +(-3.32333 - 1.37657i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74186 + 1.74186i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.894478 - 2.15946i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{5} +(-0.894478 + 2.15946i) q^{6} +(-3.32333 - 1.37657i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74186 + 1.74186i) q^{9} +(0.923880 + 0.382683i) q^{10} +(-0.760686 + 1.83646i) q^{11} +(2.15946 - 0.894478i) q^{12} -0.678817i q^{13} +(1.37657 + 3.32333i) q^{14} +(1.65278 + 1.65278i) q^{15} -1.00000 q^{16} +(-2.74368 + 3.07770i) q^{17} +2.46336 q^{18} +(-3.09055 - 3.09055i) q^{19} +(-0.382683 - 0.923880i) q^{20} +8.40790i q^{21} +(1.83646 - 0.760686i) q^{22} +(1.51321 - 3.65322i) q^{23} +(-2.15946 - 0.894478i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-0.479996 + 0.479996i) q^{26} +(-1.15885 - 0.480010i) q^{27} +(1.37657 - 3.32333i) q^{28} +(5.47189 - 2.26653i) q^{29} -2.33738i q^{30} +(-3.63256 - 8.76978i) q^{31} +(0.707107 + 0.707107i) q^{32} +4.64617 q^{33} +(4.11634 - 0.236183i) q^{34} +3.59714 q^{35} +(-1.74186 - 1.74186i) q^{36} +(-1.64894 - 3.98089i) q^{37} +4.37069i q^{38} +(-1.46588 + 0.607187i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(-1.70896 - 0.707874i) q^{41} +(5.94529 - 5.94529i) q^{42} +(8.51063 - 8.51063i) q^{43} +(-1.83646 - 0.760686i) q^{44} +(0.942688 - 2.27585i) q^{45} +(-3.65322 + 1.51321i) q^{46} +13.6499i q^{47} +(0.894478 + 2.15946i) q^{48} +(4.19982 + 4.19982i) q^{49} -1.00000 q^{50} +(9.10033 + 3.17194i) q^{51} +0.678817 q^{52} +(-4.30196 - 4.30196i) q^{53} +(0.480010 + 1.15885i) q^{54} -1.98777i q^{55} +(-3.32333 + 1.37657i) q^{56} +(-3.90949 + 9.43834i) q^{57} +(-5.47189 - 2.26653i) q^{58} +(-0.760963 + 0.760963i) q^{59} +(-1.65278 + 1.65278i) q^{60} +(1.68551 + 0.698163i) q^{61} +(-3.63256 + 8.76978i) q^{62} +(8.18656 - 3.39098i) q^{63} -1.00000i q^{64} +(0.259772 + 0.627145i) q^{65} +(-3.28534 - 3.28534i) q^{66} +5.62131 q^{67} +(-3.07770 - 2.74368i) q^{68} -9.24253 q^{69} +(-2.54356 - 2.54356i) q^{70} +(-4.51734 - 10.9058i) q^{71} +2.46336i q^{72} +(-5.67041 + 2.34876i) q^{73} +(-1.64894 + 3.98089i) q^{74} +(-2.15946 - 0.894478i) q^{75} +(3.09055 - 3.09055i) q^{76} +(5.05601 - 5.05601i) q^{77} +(1.46588 + 0.607187i) q^{78} +(-1.60739 + 3.88059i) q^{79} +(0.923880 - 0.382683i) q^{80} +10.3219i q^{81} +(0.707874 + 1.70896i) q^{82} +(11.8182 + 11.8182i) q^{83} -8.40790 q^{84} +(1.35705 - 3.89338i) q^{85} -12.0359 q^{86} +(-9.78898 - 9.78898i) q^{87} +(0.760686 + 1.83646i) q^{88} -0.600698i q^{89} +(-2.27585 + 0.942688i) q^{90} +(-0.934438 + 2.25593i) q^{91} +(3.65322 + 1.51321i) q^{92} +(-15.6887 + 15.6887i) q^{93} +(9.65190 - 9.65190i) q^{94} +(4.03799 + 1.67259i) q^{95} +(0.894478 - 2.15946i) q^{96} +(0.119918 - 0.0496715i) q^{97} -5.93944i q^{98} +(-1.87384 - 4.52386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Introduction

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