LMFDB - Embedded newform 770.2.n.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.b.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-2.11803 - 1.53884i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.809017 + 2.48990i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.19098 + 3.66547i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.11803 - 1.53884i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.809017 + 2.48990i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.19098 + 3.66547i) q^{9} +1.00000 q^{10} +(-0.809017 + 3.21644i) q^{11} +2.61803 q^{12} +(-0.618034 - 1.90211i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(2.11803 - 1.53884i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.500000 - 1.53884i) q^{17} +(3.11803 - 2.26538i) q^{18} +(5.54508 + 4.02874i) q^{19} +(-0.309017 - 0.951057i) q^{20} -2.61803 q^{21} +(3.30902 - 0.224514i) q^{22} +6.00000 q^{23} +(-0.809017 - 2.48990i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-1.61803 + 1.17557i) q^{26} +(0.690983 - 2.12663i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.61803 - 1.90211i) q^{29} +(-2.11803 - 1.53884i) q^{30} +(-0.381966 - 1.17557i) q^{31} -1.00000 q^{32} +(6.66312 - 5.56758i) q^{33} -1.61803 q^{34} +(0.309017 + 0.951057i) q^{35} +(-3.11803 - 2.26538i) q^{36} +(5.23607 - 3.80423i) q^{37} +(2.11803 - 6.51864i) q^{38} +(-1.61803 + 4.97980i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-8.35410 - 6.06961i) q^{41} +(0.809017 + 2.48990i) q^{42} -1.85410 q^{43} +(-1.23607 - 3.07768i) q^{44} -3.85410 q^{45} +(-1.85410 - 5.70634i) q^{46} +(-7.47214 - 5.42882i) q^{47} +(-2.11803 + 1.53884i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-3.42705 + 2.48990i) q^{51} +(1.61803 + 1.17557i) q^{52} +(0.381966 + 1.17557i) q^{53} -2.23607 q^{54} +(-2.80902 - 1.76336i) q^{55} +1.00000 q^{56} +(-5.54508 - 17.0660i) q^{57} +(-2.61803 - 1.90211i) q^{58} +(6.16312 - 4.47777i) q^{59} +(-0.809017 + 2.48990i) q^{60} +(1.09017 - 3.35520i) q^{61} +(-1.00000 + 0.726543i) q^{62} +(3.11803 + 2.26538i) q^{63} +(0.309017 + 0.951057i) q^{64} +2.00000 q^{65} +(-7.35410 - 4.61653i) q^{66} +6.09017 q^{67} +(0.500000 + 1.53884i) q^{68} +(-12.7082 - 9.23305i) q^{69} +(0.809017 - 0.587785i) q^{70} +(-3.00000 + 9.23305i) q^{71} +(-1.19098 + 3.66547i) q^{72} +(11.2082 - 8.14324i) q^{73} +(-5.23607 - 3.80423i) q^{74} +(0.809017 + 2.48990i) q^{75} -6.85410 q^{76} +(1.23607 + 3.07768i) q^{77} +5.23607 q^{78} +(2.61803 + 8.05748i) q^{79} +(0.809017 + 0.587785i) q^{80} +(4.61803 - 3.35520i) q^{81} +(-3.19098 + 9.82084i) q^{82} +(-3.19098 + 9.82084i) q^{83} +(2.11803 - 1.53884i) q^{84} +(1.30902 + 0.951057i) q^{85} +(0.572949 + 1.76336i) q^{86} -8.47214 q^{87} +(-2.54508 + 2.12663i) q^{88} +13.0902 q^{89} +(1.19098 + 3.66547i) q^{90} +(-1.61803 - 1.17557i) q^{91} +(-4.85410 + 3.52671i) q^{92} +(-1.00000 + 3.07768i) q^{93} +(-2.85410 + 8.78402i) q^{94} +(-5.54508 + 4.02874i) q^{95} +(2.11803 + 1.53884i) q^{96} +(-2.95492 - 9.09429i) q^{97} -1.00000 q^{98} +(-12.7533 + 0.865300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 - q^4 + q^5 - q^6 + q^7 + q^8 + 7 * q^9	\( 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} + 2 q^{13} - q^{14} + 4 q^{15} - q^{16} + 2 q^{17} + 8 q^{18} + 11 q^{19} + q^{20} - 6 q^{21} + 11 q^{22} + 24 q^{23} - q^{24} - q^{25} - 2 q^{26} + 5 q^{27} + q^{28} + 6 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} + 11 q^{33} - 2 q^{34} - q^{35} - 8 q^{36} + 12 q^{37} + 4 q^{38} - 2 q^{39} - q^{40} - 20 q^{41} + q^{42} + 6 q^{43} + 4 q^{44} - 2 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - q^{49} + q^{50} - 7 q^{51} + 2 q^{52} + 6 q^{53} - 9 q^{55} + 4 q^{56} - 11 q^{57} - 6 q^{58} + 9 q^{59} - q^{60} - 18 q^{61} - 4 q^{62} + 8 q^{63} - q^{64} + 8 q^{65} - 16 q^{66} + 2 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 12 q^{71} - 7 q^{72} + 18 q^{73} - 12 q^{74} + q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 6 q^{79} + q^{80} + 14 q^{81} - 15 q^{82} - 15 q^{83} + 4 q^{84} + 3 q^{85} + 9 q^{86} - 16 q^{87} + q^{88} + 30 q^{89} + 7 q^{90} - 2 q^{91} - 6 q^{92} - 4 q^{93} + 2 q^{94} - 11 q^{95} + 4 q^{96} - 23 q^{97} - 4 q^{98} - 13 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 - q^4 + q^5 - q^6 + q^7 + q^8 + 7 * q^9 + 4 * q^10 - q^11 + 6 * q^12 + 2 * q^13 - q^14 + 4 * q^15 - q^16 + 2 * q^17 + 8 * q^18 + 11 * q^19 + q^20 - 6 * q^21 + 11 * q^22 + 24 * q^23 - q^24 - q^25 - 2 * q^26 + 5 * q^27 + q^28 + 6 * q^29 - 4 * q^30 - 6 * q^31 - 4 * q^32 + 11 * q^33 - 2 * q^34 - q^35 - 8 * q^36 + 12 * q^37 + 4 * q^38 - 2 * q^39 - q^40 - 20 * q^41 + q^42 + 6 * q^43 + 4 * q^44 - 2 * q^45 + 6 * q^46 - 12 * q^47 - 4 * q^48 - q^49 + q^50 - 7 * q^51 + 2 * q^52 + 6 * q^53 - 9 * q^55 + 4 * q^56 - 11 * q^57 - 6 * q^58 + 9 * q^59 - q^60 - 18 * q^61 - 4 * q^62 + 8 * q^63 - q^64 + 8 * q^65 - 16 * q^66 + 2 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 12 * q^71 - 7 * q^72 + 18 * q^73 - 12 * q^74 + q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 6 * q^79 + q^80 + 14 * q^81 - 15 * q^82 - 15 * q^83 + 4 * q^84 + 3 * q^85 + 9 * q^86 - 16 * q^87 + q^88 + 30 * q^89 + 7 * q^90 - 2 * q^91 - 6 * q^92 - 4 * q^93 + 2 * q^94 - 11 * q^95 + 4 * q^96 - 23 * q^97 - 4 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−2.11803	−	1.53884i	−1.22285	−	0.888451i	−0.226514	−	0.974008i	$-0.572733\pi$
$3$	−2.11803	−	1.53884i	−1.22285	−	0.888451i	−0.996333	+	0.0855571i	$0.972733\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	−0.809017	+	2.48990i	−0.330280	+	1.01650i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.19098	+	3.66547i	0.396994	+	1.22182i
$10$	1.00000			0.316228
$11$	−0.809017	+	3.21644i	−0.243928	+	0.969793i
$11$	−0.809017	+	3.21644i	−0.243928	+	0.969793i
$12$	2.61803			0.755761
$13$	−0.618034	−	1.90211i	−0.171412	−	0.527551i	0.828040	−	0.560670i	$-0.189456\pi$
$13$	−0.618034	−	1.90211i	−0.171412	−	0.527551i	−0.999451	+	0.0331183i	$0.989456\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	2.11803	−	1.53884i	0.546874	−	0.397327i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	−0.871935	−	0.489622i	$-0.837135\pi$
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	0.993203	+	0.116398i	$0.0371348\pi$
$18$	3.11803	−	2.26538i	0.734928	−	0.533956i
$19$	5.54508	+	4.02874i	1.27213	+	0.924256i	0.999285	−	0.0378018i	$-0.0120356\pi$
$19$	5.54508	+	4.02874i	1.27213	+	0.924256i	0.272844	+	0.962058i	$0.412036\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−2.61803			−0.571302
$22$	3.30902	−	0.224514i	0.705485	−	0.0478665i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	−0.809017	−	2.48990i	−0.165140	−	0.508248i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−1.61803	+	1.17557i	−0.317323	+	0.230548i
$27$	0.690983	−	2.12663i	0.132980	−	0.409270i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	2.61803	−	1.90211i	0.486157	−	0.353214i	−0.317548	−	0.948242i	$-0.602859\pi$
$29$	2.61803	−	1.90211i	0.486157	−	0.353214i	0.803704	+	0.595029i	$0.202859\pi$
$30$	−2.11803	−	1.53884i	−0.386698	−	0.280953i
$31$	−0.381966	−	1.17557i	−0.0686031	−	0.211139i	0.910878	−	0.412677i	$-0.135406\pi$
$31$	−0.381966	−	1.17557i	−0.0686031	−	0.211139i	−0.979481	+	0.201538i	$0.935406\pi$
$32$	−1.00000			−0.176777
$33$	6.66312	−	5.56758i	1.15990	−	0.969192i
$34$	−1.61803			−0.277491
$35$	0.309017	+	0.951057i	0.0522334	+	0.160758i
$36$	−3.11803	−	2.26538i	−0.519672	−	0.377564i
$37$	5.23607	−	3.80423i	0.860804	−	0.625411i	−0.0672994	−	0.997733i	$-0.521438\pi$
$37$	5.23607	−	3.80423i	0.860804	−	0.625411i	0.928104	+	0.372322i	$0.121438\pi$
$38$	2.11803	−	6.51864i	0.343590	−	1.05746i
$39$	−1.61803	+	4.97980i	−0.259093	+	0.797406i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−8.35410	−	6.06961i	−1.30469	−	0.947914i	−0.304702	−	0.952448i	$-0.598557\pi$
$41$	−8.35410	−	6.06961i	−1.30469	−	0.947914i	−0.999990	+	0.00453391i	$0.998557\pi$
$42$	0.809017	+	2.48990i	0.124834	+	0.384200i
$43$	−1.85410			−0.282748			−0.141374	−	0.989956i	$-0.545152\pi$
$43$	−1.85410			−0.282748			−0.141374	+	0.989956i	$0.545152\pi$
$44$	−1.23607	−	3.07768i	−0.186344	−	0.463978i
$45$	−3.85410			−0.574536
$46$	−1.85410	−	5.70634i	−0.273372	−	0.841354i
$47$	−7.47214	−	5.42882i	−1.08992	−	0.791875i	−0.110537	−	0.993872i	$-0.535257\pi$
$47$	−7.47214	−	5.42882i	−1.08992	−	0.791875i	−0.979386	+	0.201997i	$0.935257\pi$
$48$	−2.11803	+	1.53884i	−0.305712	+	0.222113i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−3.42705	+	2.48990i	−0.479883	+	0.348655i
$52$	1.61803	+	1.17557i	0.224381	+	0.163022i
$53$	0.381966	+	1.17557i	0.0524671	+	0.161477i	0.973857	−	0.227163i	$-0.0729450\pi$
$53$	0.381966	+	1.17557i	0.0524671	+	0.161477i	−0.921390	+	0.388640i	$0.872945\pi$
$54$	−2.23607			−0.304290
$55$	−2.80902	−	1.76336i	−0.378768	−	0.237771i
$56$	1.00000			0.133631
$57$	−5.54508	−	17.0660i	−0.734464	−	2.26045i
$58$	−2.61803	−	1.90211i	−0.343765	−	0.249760i
$59$	6.16312	−	4.47777i	0.802370	−	0.582956i	−0.109239	−	0.994016i	$-0.534841\pi$
$59$	6.16312	−	4.47777i	0.802370	−	0.582956i	0.911608	+	0.411060i	$0.134841\pi$
$60$	−0.809017	+	2.48990i	−0.104444	+	0.321444i
$61$	1.09017	−	3.35520i	0.139582	−	0.429589i	−0.856693	−	0.515827i	$-0.827485\pi$
$61$	1.09017	−	3.35520i	0.139582	−	0.429589i	0.996275	+	0.0862382i	$0.0274846\pi$
$62$	−1.00000	+	0.726543i	−0.127000	+	0.0922710i
$63$	3.11803	+	2.26538i	0.392835	+	0.285412i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.00000			0.248069
$66$	−7.35410	−	4.61653i	−0.905227	−	0.568255i
$67$	6.09017			0.744033			0.372016	−	0.928226i	$-0.378667\pi$
$67$	6.09017			0.744033			0.372016	+	0.928226i	$0.378667\pi$
$68$	0.500000	+	1.53884i	0.0606339	+	0.186612i
$69$	−12.7082	−	9.23305i	−1.52989	−	1.11153i
$70$	0.809017	−	0.587785i	0.0966960	−	0.0702538i
$71$	−3.00000	+	9.23305i	−0.356034	+	1.09576i	0.599373	+	0.800470i	$0.295417\pi$
$71$	−3.00000	+	9.23305i	−0.356034	+	1.09576i	−0.955407	+	0.295291i	$0.904583\pi$
$72$	−1.19098	+	3.66547i	−0.140359	+	0.431980i
$73$	11.2082	−	8.14324i	1.31182	−	0.953094i	0.311825	−	0.950139i	$-0.399060\pi$
$73$	11.2082	−	8.14324i	1.31182	−	0.953094i	0.999996	−	0.00295436i	$-0.000940404\pi$
$74$	−5.23607	−	3.80423i	−0.608681	−	0.442232i
$75$	0.809017	+	2.48990i	0.0934172	+	0.287509i
$76$	−6.85410			−0.786219
$77$	1.23607	+	3.07768i	0.140863	+	0.350735i
$78$	5.23607			0.592868
$79$	2.61803	+	8.05748i	0.294552	+	0.906537i	0.983372	+	0.181605i	$0.0581291\pi$
$79$	2.61803	+	8.05748i	0.294552	+	0.906537i	−0.688820	+	0.724933i	$0.741871\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	4.61803	−	3.35520i	0.513115	−	0.372800i
$82$	−3.19098	+	9.82084i	−0.352385	+	1.08453i
$83$	−3.19098	+	9.82084i	−0.350256	+	1.07798i	0.608454	+	0.793589i	$0.291790\pi$
$83$	−3.19098	+	9.82084i	−0.350256	+	1.07798i	−0.958709	+	0.284387i	$0.908210\pi$
$84$	2.11803	−	1.53884i	0.231096	−	0.167901i
$85$	1.30902	+	0.951057i	0.141983	+	0.103157i
$86$	0.572949	+	1.76336i	0.0617827	+	0.190148i
$87$	−8.47214			−0.908308
$88$	−2.54508	+	2.12663i	−0.271307	+	0.226699i
$89$	13.0902			1.38756			0.693778	−	0.720189i	$-0.255945\pi$
$89$	13.0902			1.38756			0.693778	+	0.720189i	$0.255945\pi$
$90$	1.19098	+	3.66547i	0.125541	+	0.386374i
$91$	−1.61803	−	1.17557i	−0.169616	−	0.123233i
$92$	−4.85410	+	3.52671i	−0.506075	+	0.367685i
$93$	−1.00000	+	3.07768i	−0.103695	+	0.319141i
$94$	−2.85410	+	8.78402i	−0.294378	+	0.906003i
$95$	−5.54508	+	4.02874i	−0.568914	+	0.413340i
$96$	2.11803	+	1.53884i	0.216171	+	0.157057i
$97$	−2.95492	−	9.09429i	−0.300026	−	0.923386i	−0.981487	−	0.191531i	$-0.938655\pi$
$97$	−2.95492	−	9.09429i	−0.300026	−	0.923386i	0.681460	−	0.731855i	$-0.261345\pi$
$98$	−1.00000			−0.101015
$99$	−12.7533	+	0.865300i	−1.28175	+	0.0869659i
$100$	1.00000			0.100000
$101$	−2.76393	−	8.50651i	−0.275022	−	0.846429i	−0.989214	−	0.146480i	$-0.953206\pi$
$101$	−2.76393	−	8.50651i	−0.275022	−	0.846429i	0.714192	−	0.699950i	$-0.246794\pi$
$102$	3.42705	+	2.48990i	0.339329	+	0.246537i
$103$	13.7082	−	9.95959i	1.35071	−	0.981348i	0.351734	−	0.936100i	$-0.385592\pi$
$103$	13.7082	−	9.95959i	1.35071	−	0.981348i	0.998976	−	0.0452478i	$-0.0144077\pi$
$104$	0.618034	−	1.90211i	0.0606032	−	0.186518i
$105$	0.809017	−	2.48990i	0.0789520	−	0.242989i
$106$	1.00000	−	0.726543i	0.0971286	−	0.0705680i
$107$	12.4443	+	9.04129i	1.20303	+	0.874055i	0.994580	−	0.103978i	$-0.0331570\pi$
$107$	12.4443	+	9.04129i	1.20303	+	0.874055i	0.208454	+	0.978032i	$0.433157\pi$
$108$	0.690983	+	2.12663i	0.0664899	+	0.204635i
$109$	0.472136			0.0452224			0.0226112	−	0.999744i	$-0.492802\pi$
$109$	0.472136			0.0452224			0.0226112	+	0.999744i	$0.492802\pi$
$110$	−0.809017	+	3.21644i	−0.0771367	+	0.306676i
$111$	−16.9443			−1.60828
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	7.54508	+	5.48183i	0.709782	+	0.515687i	0.883103	−	0.469179i	$-0.155450\pi$
$113$	7.54508	+	5.48183i	0.709782	+	0.515687i	−0.173321	+	0.984865i	$0.555450\pi$
$114$	−14.5172	+	10.5474i	−1.35966	+	0.987852i
$115$	−1.85410	+	5.70634i	−0.172896	+	0.532119i
$116$	−1.00000	+	3.07768i	−0.0928477	+	0.285756i
$117$	6.23607	−	4.53077i	0.576525	−	0.418870i
$118$	−6.16312	−	4.47777i	−0.567361	−	0.412212i
$119$	−0.500000	−	1.53884i	−0.0458349	−	0.141065i
$120$	2.61803			0.238993
$121$	−9.69098	−	5.20431i	−0.880998	−	0.473119i
$122$	−3.52786			−0.319398
$123$	8.35410	+	25.7113i	0.753264	+	2.31831i
$124$	1.00000	+	0.726543i	0.0898027	+	0.0652454i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	1.19098	−	3.66547i	0.106101	−	0.326546i
$127$	3.52786	−	10.8576i	0.313047	−	0.963461i	−0.663503	−	0.748173i	$-0.730931\pi$
$127$	3.52786	−	10.8576i	0.313047	−	0.963461i	0.976551	−	0.215287i	$-0.0690688\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	3.92705	+	2.85317i	0.345758	+	0.251208i
$130$	−0.618034	−	1.90211i	−0.0542052	−	0.166826i
$131$	7.79837			0.681347			0.340674	−	0.940182i	$-0.389345\pi$
$131$	7.79837			0.681347			0.340674	+	0.940182i	$0.389345\pi$
$132$	−2.11803	+	8.42075i	−0.184351	+	0.732932i
$133$	6.85410			0.594326
$134$	−1.88197	−	5.79210i	−0.162577	−	0.500361i
$135$	1.80902	+	1.31433i	0.155695	+	0.113119i
$136$	1.30902	−	0.951057i	0.112247	−	0.0815524i
$137$	−0.336881	+	1.03681i	−0.0287817	+	0.0885809i	−0.964416	−	0.264391i	$-0.914829\pi$
$137$	−0.336881	+	1.03681i	−0.0287817	+	0.0885809i	0.935634	+	0.352972i	$0.114829\pi$
$138$	−4.85410	+	14.9394i	−0.413209	+	1.27173i
$139$	14.9443	−	10.8576i	1.26756	−	0.920934i	0.268454	−	0.963292i	$-0.413487\pi$
$139$	14.9443	−	10.8576i	1.26756	−	0.920934i	0.999102	+	0.0423587i	$0.0134872\pi$
$140$	−0.809017	−	0.587785i	−0.0683744	−	0.0496769i
$141$	7.47214	+	22.9969i	0.629267	+	1.93669i
$142$	9.70820			0.814694
$143$	6.61803	−	0.449028i	0.553428	−	0.0375496i
$144$	3.85410			0.321175
$145$	1.00000	+	3.07768i	0.0830455	+	0.255588i
$146$	−11.2082	−	8.14324i	−0.927598	−	0.673939i
$147$	−2.11803	+	1.53884i	−0.174692	+	0.126922i
$148$	−2.00000	+	6.15537i	−0.164399	+	0.505968i
$149$	−7.47214	+	22.9969i	−0.612141	+	1.88398i	−0.175051	+	0.984559i	$0.556009\pi$
$149$	−7.47214	+	22.9969i	−0.612141	+	1.88398i	−0.437090	+	0.899418i	$0.643991\pi$
$150$	2.11803	−	1.53884i	0.172937	−	0.125646i
$151$	1.85410	+	1.34708i	0.150885	+	0.109624i	0.660666	−	0.750680i	$-0.270274\pi$
$151$	1.85410	+	1.34708i	0.150885	+	0.109624i	−0.509782	+	0.860304i	$0.670274\pi$
$152$	2.11803	+	6.51864i	0.171795	+	0.528731i
$153$	6.23607			0.504156
$154$	2.54508	−	2.12663i	0.205089	−	0.171368i
$155$	1.23607			0.0992834
$156$	−1.61803	−	4.97980i	−0.129546	−	0.398703i
$157$	−0.236068	−	0.171513i	−0.0188403	−	0.0136883i	0.578325	−	0.815806i	$-0.303706\pi$
$157$	−0.236068	−	0.171513i	−0.0188403	−	0.0136883i	−0.597166	+	0.802118i	$0.703706\pi$
$158$	6.85410	−	4.97980i	0.545283	−	0.396171i
$159$	1.00000	−	3.07768i	0.0793052	−	0.244076i
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	4.85410	−	3.52671i	0.382557	−	0.277944i
$162$	−4.61803	−	3.35520i	−0.362827	−	0.263609i
$163$	0.881966	+	2.71441i	0.0690809	+	0.212609i	0.979637	−	0.200776i	$-0.0643463\pi$
$163$	0.881966	+	2.71441i	0.0690809	+	0.212609i	−0.910556	+	0.413385i	$0.864346\pi$
$164$	10.3262			0.806344
$165$	3.23607	+	8.05748i	0.251928	+	0.627274i
$166$	10.3262			0.801471
$167$	−2.00000	−	6.15537i	−0.154765	−	0.476317i	0.843372	−	0.537330i	$-0.180567\pi$
$167$	−2.00000	−	6.15537i	−0.154765	−	0.476317i	−0.998137	+	0.0610130i	$0.980567\pi$
$168$	−2.11803	−	1.53884i	−0.163410	−	0.118724i
$169$	7.28115	−	5.29007i	0.560089	−	0.406928i
$170$	0.500000	−	1.53884i	0.0383482	−	0.118024i
$171$	−8.16312	+	25.1235i	−0.624249	+	1.92124i
$172$	1.50000	−	1.08981i	0.114374	−	0.0830975i
$173$	9.70820	+	7.05342i	0.738101	+	0.536262i	0.892116	−	0.451807i	$-0.149220\pi$
$173$	9.70820	+	7.05342i	0.738101	+	0.536262i	−0.154015	+	0.988069i	$0.549220\pi$
$174$	2.61803	+	8.05748i	0.198473	+	0.610836i
$175$	−1.00000			−0.0755929
$176$	2.80902	+	1.76336i	0.211738	+	0.132918i
$177$	−19.9443			−1.49910
$178$	−4.04508	−	12.4495i	−0.303192	−	0.933129i
$179$	5.16312	+	3.75123i	0.385910	+	0.280380i	0.763777	−	0.645480i	$-0.223343\pi$
$179$	5.16312	+	3.75123i	0.385910	+	0.280380i	−0.377868	+	0.925860i	$0.623343\pi$
$180$	3.11803	−	2.26538i	0.232405	−	0.168852i
$181$	1.09017	−	3.35520i	0.0810317	−	0.249390i	−0.902331	−	0.431044i	$-0.858145\pi$
$181$	1.09017	−	3.35520i	0.0810317	−	0.249390i	0.983362	+	0.181654i	$0.0581452\pi$
$182$	−0.618034	+	1.90211i	−0.0458117	+	0.140994i
$183$	−7.47214	+	5.42882i	−0.552356	+	0.401310i
$184$	4.85410	+	3.52671i	0.357849	+	0.259993i
$185$	2.00000	+	6.15537i	0.147043	+	0.452552i
$186$	3.23607			0.237280
$187$	4.54508	+	2.85317i	0.332370	+	0.208644i
$188$	9.23607			0.673609
$189$	−0.690983	−	2.12663i	−0.0502616	−	0.154689i
$190$	5.54508	+	4.02874i	0.402283	+	0.292276i
$191$	1.23607	−	0.898056i	0.0894387	−	0.0649810i	−0.542167	−	0.840271i	$-0.682396\pi$
$191$	1.23607	−	0.898056i	0.0894387	−	0.0649810i	0.631606	+	0.775290i	$0.282396\pi$
$192$	0.809017	−	2.48990i	0.0583858	−	0.179693i
$193$	0.618034	−	1.90211i	0.0444871	−	0.136917i	−0.926346	−	0.376674i	$-0.877068\pi$
$193$	0.618034	−	1.90211i	0.0444871	−	0.136917i	0.970833	+	0.239757i	$0.0770677\pi$
$194$	−7.73607	+	5.62058i	−0.555417	+	0.403534i
$195$	−4.23607	−	3.07768i	−0.303351	−	0.220397i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	4.76393	+	11.8617i	0.338558	+	0.842975i
$199$	−19.4164			−1.37639			−0.688196	−	0.725525i	$-0.741597\pi$
$199$	−19.4164			−1.37639			−0.688196	+	0.725525i	$0.741597\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	−12.8992	−	9.37181i	−0.909838	−	0.661036i
$202$	−7.23607	+	5.25731i	−0.509128	+	0.369903i
$203$	1.00000	−	3.07768i	0.0701862	−	0.216011i
$204$	1.30902	−	4.02874i	0.0916495	−	0.282068i
$205$	8.35410	−	6.06961i	0.583476	−	0.423920i
$206$	−13.7082	−	9.95959i	−0.955096	−	0.693918i
$207$	7.14590	+	21.9928i	0.496674	+	1.52861i
$208$	−2.00000			−0.138675
$209$	−17.4443	+	14.5761i	−1.20665	+	1.00825i
$210$	−2.61803			−0.180662
$211$	−3.48278	−	10.7189i	−0.239764	−	0.737919i	−0.996454	−	0.0841442i	$-0.973184\pi$
$211$	−3.48278	−	10.7189i	−0.239764	−	0.737919i	0.756689	−	0.653775i	$-0.226816\pi$
$212$	−1.00000	−	0.726543i	−0.0686803	−	0.0498991i
$213$	20.5623	−	14.9394i	1.40891	−	1.02363i
$214$	4.75329	−	14.6291i	0.324928	−	1.00003i
$215$	0.572949	−	1.76336i	0.0390748	−	0.120260i
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	−1.00000	−	0.726543i	−0.0678844	−	0.0493209i
$218$	−0.145898	−	0.449028i	−0.00988146	−	0.0304120i
$219$	−36.2705			−2.45093
$220$	3.30902	−	0.224514i	0.223094	−	0.0151367i
$221$	−3.23607			−0.217681
$222$	5.23607	+	16.1150i	0.351422	+	1.08157i
$223$	−5.09017	−	3.69822i	−0.340863	−	0.247651i	0.404163	−	0.914687i	$-0.367563\pi$
$223$	−5.09017	−	3.69822i	−0.340863	−	0.247651i	−0.745026	+	0.667036i	$0.767563\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	1.19098	−	3.66547i	0.0793989	−	0.244365i
$226$	2.88197	−	8.86978i	0.191706	−	0.590009i
$227$	−19.6353	+	14.2658i	−1.30324	+	0.946858i	−0.999982	−	0.00605157i	$-0.998074\pi$
$227$	−19.6353	+	14.2658i	−1.30324	+	0.946858i	−0.303256	+	0.952909i	$0.598074\pi$
$228$	14.5172	+	10.5474i	0.961426	+	0.698517i
$229$	3.43769	+	10.5801i	0.227169	+	0.699155i	0.998064	+	0.0621927i	$0.0198093\pi$
$229$	3.43769	+	10.5801i	0.227169	+	0.699155i	−0.770895	+	0.636962i	$0.780191\pi$
$230$	6.00000			0.395628
$231$	2.11803	−	8.42075i	0.139356	−	0.554045i
$232$	3.23607			0.212458
$233$	−3.37132	−	10.3759i	−0.220863	−	0.679746i	−0.998685	−	0.0512616i	$-0.983676\pi$
$233$	−3.37132	−	10.3759i	−0.220863	−	0.679746i	0.777823	−	0.628484i	$-0.216324\pi$
$234$	−6.23607	−	4.53077i	−0.407665	−	0.296186i
$235$	7.47214	−	5.42882i	0.487428	−	0.354137i
$236$	−2.35410	+	7.24518i	−0.153239	+	0.471621i
$237$	6.85410	−	21.0948i	0.445222	−	1.37025i
$238$	−1.30902	+	0.951057i	−0.0848510	+	0.0616478i
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$	−0.809017	−	2.48990i	−0.0522218	−	0.160722i
$241$	6.27051			0.403919			0.201960	−	0.979394i	$-0.435269\pi$
$241$	6.27051			0.403919			0.201960	+	0.979394i	$0.435269\pi$
$242$	−1.95492	+	10.8249i	−0.125667	+	0.695850i
$243$	−21.6525			−1.38901
$244$	1.09017	+	3.35520i	0.0697910	+	0.214795i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	21.8713	−	15.8904i	1.39446	−	1.01314i
$247$	4.23607	−	13.0373i	0.269535	−	0.829542i
$248$	0.381966	−	1.17557i	0.0242549	−	0.0746488i
$249$	21.8713	−	15.8904i	1.38604	−	1.00702i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	8.29180	+	25.5195i	0.523374	+	1.61078i	0.767510	+	0.641037i	$0.221496\pi$
$251$	8.29180	+	25.5195i	0.523374	+	1.61078i	−0.244136	+	0.969741i	$0.578504\pi$
$252$	−3.85410			−0.242786
$253$	−4.85410	+	19.2986i	−0.305175	+	1.21330i
$254$	−11.4164			−0.716329
$255$	−1.30902	−	4.02874i	−0.0819738	−	0.252289i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−23.9164	+	17.3763i	−1.49186	+	1.08390i	−0.518380	+	0.855150i	$0.673465\pi$
$257$	−23.9164	+	17.3763i	−1.49186	+	1.08390i	−0.973485	+	0.228753i	$0.926535\pi$
$258$	1.50000	−	4.61653i	0.0933859	−	0.287412i
$259$	2.00000	−	6.15537i	0.124274	−	0.382476i
$260$	−1.61803	+	1.17557i	−0.100346	+	0.0729058i
$261$	10.0902	+	7.33094i	0.624566	+	0.453774i
$262$	−2.40983	−	7.41669i	−0.148880	−	0.458205i
$263$	−20.1803			−1.24437			−0.622187	−	0.782869i	$-0.713755\pi$
$263$	−20.1803			−1.24437			−0.622187	+	0.782869i	$0.713755\pi$
$264$	8.66312	−	0.587785i	0.533178	−	0.0361757i
$265$	−1.23607			−0.0759311
$266$	−2.11803	−	6.51864i	−0.129865	−	0.399683i
$267$	−27.7254	−	20.1437i	−1.69677	−	1.23277i
$268$	−4.92705	+	3.57971i	−0.300968	+	0.218666i
$269$	−3.76393	+	11.5842i	−0.229491	+	0.706301i	0.768314	+	0.640074i	$0.221096\pi$
$269$	−3.76393	+	11.5842i	−0.229491	+	0.706301i	−0.997805	+	0.0662270i	$0.978904\pi$
$270$	0.690983	−	2.12663i	0.0420519	−	0.129422i
$271$	−7.61803	+	5.53483i	−0.462763	+	0.336217i	−0.794614	−	0.607115i	$-0.792327\pi$
$271$	−7.61803	+	5.53483i	−0.462763	+	0.336217i	0.331851	+	0.943332i	$0.392327\pi$
$272$	−1.30902	−	0.951057i	−0.0793708	−	0.0576663i
$273$	1.61803	+	4.97980i	0.0979279	+	0.301391i
$274$	1.09017			0.0658596
$275$	2.54508	−	2.12663i	0.153474	−	0.128240i
$276$	15.7082			0.945523
$277$	−1.94427	−	5.98385i	−0.116820	−	0.359535i	0.875502	−	0.483214i	$-0.160531\pi$
$277$	−1.94427	−	5.98385i	−0.116820	−	0.359535i	−0.992322	+	0.123679i	$0.960531\pi$
$278$	−14.9443	−	10.8576i	−0.896298	−	0.651199i
$279$	3.85410	−	2.80017i	0.230739	−	0.167642i
$280$	−0.309017	+	0.951057i	−0.0184673	+	0.0568365i
$281$	7.42705	−	22.8581i	0.443061	−	1.36360i	−0.441536	−	0.897244i	$-0.645566\pi$
$281$	7.42705	−	22.8581i	0.443061	−	1.36360i	0.884597	−	0.466357i	$-0.154434\pi$
$282$	19.5623	−	14.2128i	1.16492	−	0.846363i
$283$	−9.70820	−	7.05342i	−0.577093	−	0.419282i	0.260582	−	0.965452i	$-0.416086\pi$
$283$	−9.70820	−	7.05342i	−0.577093	−	0.419282i	−0.837675	+	0.546169i	$0.816086\pi$
$284$	−3.00000	−	9.23305i	−0.178017	−	0.547881i
$285$	17.9443			1.06293
$286$	−2.47214	−	6.15537i	−0.146180	−	0.363974i
$287$	−10.3262			−0.609539
$288$	−1.19098	−	3.66547i	−0.0701793	−	0.215990i
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$	2.61803	−	1.90211i	0.153736	−	0.111696i
$291$	−7.73607	+	23.8092i	−0.453496	+	1.39572i
$292$	−4.28115	+	13.1760i	−0.250536	+	0.771069i
$293$	13.3262	−	9.68208i	0.778527	−	0.565633i	−0.126009	−	0.992029i	$-0.540217\pi$
$293$	13.3262	−	9.68208i	0.778527	−	0.565633i	0.904537	+	0.426396i	$0.140217\pi$
$294$	2.11803	+	1.53884i	0.123526	+	0.0897471i
$295$	2.35410	+	7.24518i	0.137061	+	0.421831i
$296$	6.47214			0.376185
$297$	6.28115	+	3.94298i	0.364469	+	0.228795i
$298$	24.1803			1.40073
$299$	−3.70820	−	11.4127i	−0.214451	−	0.660012i
$300$	−2.11803	−	1.53884i	−0.122285	−	0.0888451i
$301$	−1.50000	+	1.08981i	−0.0864586	+	0.0628158i
$302$	0.708204	−	2.17963i	0.0407526	−	0.125423i
$303$	−7.23607	+	22.2703i	−0.415701	+	1.27940i
$304$	5.54508	−	4.02874i	0.318032	−	0.231064i
$305$	2.85410	+	2.07363i	0.163425	+	0.118736i
$306$	−1.92705	−	5.93085i	−0.110162	−	0.339044i
$307$	27.5623			1.57306			0.786532	−	0.617550i	$-0.211875\pi$
$307$	27.5623			1.57306			0.786532	+	0.617550i	$0.211875\pi$
$308$	−2.80902	−	1.76336i	−0.160059	−	0.100477i
$309$	−44.3607			−2.52359
$310$	−0.381966	−	1.17557i	−0.0216942	−	0.0667679i
$311$	23.5623	+	17.1190i	1.33610	+	0.970730i	0.999578	+	0.0290534i	$0.00924927\pi$
$311$	23.5623	+	17.1190i	1.33610	+	0.970730i	0.336518	+	0.941677i	$0.390751\pi$
$312$	−4.23607	+	3.07768i	−0.239820	+	0.174240i
$313$	−0.263932	+	0.812299i	−0.0149183	+	0.0459139i	−0.958239	−	0.285970i	$-0.907684\pi$
$313$	−0.263932	+	0.812299i	−0.0149183	+	0.0459139i	0.943320	+	0.331884i	$0.107684\pi$
$314$	−0.0901699	+	0.277515i	−0.00508858	+	0.0156611i
$315$	−3.11803	+	2.26538i	−0.175681	+	0.127640i
$316$	−6.85410	−	4.97980i	−0.385573	−	0.280135i
$317$	−6.41641	−	19.7477i	−0.360381	−	1.10914i	−0.952823	−	0.303526i	$-0.901836\pi$
$317$	−6.41641	−	19.7477i	−0.360381	−	1.10914i	0.592442	−	0.805613i	$-0.298164\pi$
$318$	−3.23607			−0.181470
$319$	4.00000	+	9.95959i	0.223957	+	0.557630i
$320$	−1.00000			−0.0559017
$321$	−12.4443	−	38.2995i	−0.694572	−	2.13767i
$322$	−4.85410	−	3.52671i	−0.270509	−	0.196536i
$323$	8.97214	−	6.51864i	0.499223	−	0.362707i
$324$	−1.76393	+	5.42882i	−0.0979962	+	0.301601i
$325$	−0.618034	+	1.90211i	−0.0342824	+	0.105510i
$326$	2.30902	−	1.67760i	0.127885	−	0.0929136i
$327$	−1.00000	−	0.726543i	−0.0553001	−	0.0401779i
$328$	−3.19098	−	9.82084i	−0.176193	−	0.542265i
$329$	−9.23607			−0.509201
$330$	6.66312	−	5.56758i	0.366793	−	0.306485i
$331$	6.03444			0.331683			0.165841	−	0.986152i	$-0.446966\pi$
$331$	6.03444			0.331683			0.165841	+	0.986152i	$0.446966\pi$
$332$	−3.19098	−	9.82084i	−0.175128	−	0.538988i
$333$	20.1803	+	14.6619i	1.10588	+	0.803466i
$334$	−5.23607	+	3.80423i	−0.286505	+	0.208158i
$335$	−1.88197	+	5.79210i	−0.102823	+	0.316456i
$336$	−0.809017	+	2.48990i	−0.0441355	+	0.135835i
$337$	−12.6353	+	9.18005i	−0.688286	+	0.500069i	−0.876096	−	0.482136i	$-0.839861\pi$
$337$	−12.6353	+	9.18005i	−0.688286	+	0.500069i	0.187810	+	0.982205i	$0.439861\pi$
$338$	−7.28115	−	5.29007i	−0.396043	−	0.287742i
$339$	−7.54508	−	23.2214i	−0.409793	−	1.26121i
$340$	−1.61803			−0.0877502
$341$	4.09017	−	0.277515i	0.221495	−	0.0150283i
$342$	26.4164			1.42844
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−1.50000	−	1.08981i	−0.0808746	−	0.0587588i
$345$	12.7082	−	9.23305i	0.684187	−	0.497091i
$346$	3.70820	−	11.4127i	0.199354	−	0.613549i
$347$	−1.64590	+	5.06555i	−0.0883564	+	0.271933i	−0.985465	−	0.169876i	$-0.945663\pi$
$347$	−1.64590	+	5.06555i	−0.0883564	+	0.271933i	0.897109	+	0.441809i	$0.145663\pi$
$348$	6.85410	−	4.97980i	0.367418	−	0.266945i
$349$	4.47214	+	3.24920i	0.239388	+	0.173926i	0.701011	−	0.713151i	$-0.252733\pi$
$349$	4.47214	+	3.24920i	0.239388	+	0.173926i	−0.461623	+	0.887076i	$0.652733\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	−4.47214			−0.238705
$352$	0.809017	−	3.21644i	0.0431208	−	0.171437i
$353$	−28.4508			−1.51429			−0.757143	−	0.653249i	$-0.773405\pi$
$353$	−28.4508			−1.51429			−0.757143	+	0.653249i	$0.773405\pi$
$354$	6.16312	+	18.9681i	0.327566	+	1.00814i
$355$	−7.85410	−	5.70634i	−0.416852	−	0.302861i
$356$	−10.5902	+	7.69421i	−0.561278	+	0.407792i
$357$	−1.30902	+	4.02874i	−0.0692805	+	0.213224i
$358$	1.97214	−	6.06961i	0.104231	−	0.320789i
$359$	15.0902	−	10.9637i	0.796429	−	0.578639i	−0.113436	−	0.993545i	$-0.536186\pi$
$359$	15.0902	−	10.9637i	0.796429	−	0.578639i	0.909864	+	0.414906i	$0.136186\pi$
$360$	−3.11803	−	2.26538i	−0.164335	−	0.119396i
$361$	8.64590	+	26.6093i	0.455047	+	1.40049i
$362$	−3.52786			−0.185420
$363$	12.5172	+	25.9358i	0.656984	+	1.36128i
$364$	2.00000			0.104828
$365$	4.28115	+	13.1760i	0.224086	+	0.689665i
$366$	7.47214	+	5.42882i	0.390575	+	0.283769i
$367$	−22.7984	+	16.5640i	−1.19007	+	0.864633i	−0.993271	−	0.115812i	$-0.963053\pi$
$367$	−22.7984	+	16.5640i	−1.19007	+	0.864633i	−0.196794	+	0.980445i	$0.563053\pi$
$368$	1.85410	−	5.70634i	0.0966517	−	0.297463i
$369$	12.2984	−	37.8505i	0.640228	−	1.97042i
$370$	5.23607	−	3.80423i	0.272210	−	0.197772i
$371$	1.00000	+	0.726543i	0.0519174	+	0.0377202i
$372$	−1.00000	−	3.07768i	−0.0518476	−	0.159570i
$373$	24.4721			1.26712			0.633560	−	0.773694i	$-0.281593\pi$
$373$	24.4721			1.26712			0.633560	+	0.773694i	$0.281593\pi$
$374$	1.30902	−	5.20431i	0.0676877	−	0.269108i
$375$	−2.61803			−0.135195
$376$	−2.85410	−	8.78402i	−0.147189	−	0.453001i
$377$	−5.23607	−	3.80423i	−0.269671	−	0.195928i
$378$	−1.80902	+	1.31433i	−0.0930458	+	0.0676017i
$379$	−8.60739	+	26.4908i	−0.442132	+	1.36074i	0.443467	+	0.896291i	$0.353748\pi$
$379$	−8.60739	+	26.4908i	−0.442132	+	1.36074i	−0.885599	+	0.464451i	$0.846252\pi$
$380$	2.11803	−	6.51864i	0.108653	−	0.334399i
$381$	−24.1803	+	17.5680i	−1.23880	+	0.900038i
$382$	−1.23607	−	0.898056i	−0.0632427	−	0.0459485i
$383$	−7.41641	−	22.8254i	−0.378961	−	1.16632i	−0.940767	−	0.339053i	$-0.889894\pi$
$383$	−7.41641	−	22.8254i	−0.378961	−	1.16632i	0.561807	−	0.827269i	$-0.310106\pi$
$384$	−2.61803			−0.133601
$385$	−3.30902	+	0.224514i	−0.168643	+	0.0114423i
$386$	−2.00000			−0.101797
$387$	−2.20820	−	6.79615i	−0.112249	−	0.345468i
$388$	7.73607	+	5.62058i	0.392739	+	0.285342i
$389$	26.5623	−	19.2986i	1.34676	−	0.978480i	0.347597	−	0.937644i	$-0.386998\pi$
$389$	26.5623	−	19.2986i	1.34676	−	0.978480i	0.999166	−	0.0408359i	$-0.0130021\pi$
$390$	−1.61803	+	4.97980i	−0.0819323	+	0.252162i
$391$	3.00000	−	9.23305i	0.151717	−	0.466935i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−16.5172	−	12.0005i	−0.833184	−	0.605343i
$394$	1.85410	+	5.70634i	0.0934083	+	0.287481i
$395$	−8.47214			−0.426279
$396$	9.80902	−	8.19624i	0.492922	−	0.411876i
$397$	−16.9443			−0.850409			−0.425204	−	0.905097i	$-0.639798\pi$
$397$	−16.9443			−0.850409			−0.425204	+	0.905097i	$0.639798\pi$
$398$	6.00000	+	18.4661i	0.300753	+	0.925622i
$399$	−14.5172	−	10.5474i	−0.726770	−	0.528029i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−8.19098	+	25.2093i	−0.409038	+	1.25889i	0.508438	+	0.861099i	$0.330223\pi$
$401$	−8.19098	+	25.2093i	−0.409038	+	1.25889i	−0.917476	+	0.397791i	$0.869777\pi$
$402$	−4.92705	+	15.1639i	−0.245739	+	0.756307i
$403$	−2.00000	+	1.45309i	−0.0996271	+	0.0723833i
$404$	7.23607	+	5.25731i	0.360008	+	0.261561i
$405$	1.76393	+	5.42882i	0.0876505	+	0.269760i
$406$	−3.23607			−0.160603
$407$	8.00000	+	19.9192i	0.396545	+	0.987357i
$408$	−4.23607			−0.209717
$409$	−8.61803	−	26.5236i	−0.426134	−	1.31151i	−0.901904	−	0.431937i	$-0.857830\pi$
$409$	−8.61803	−	26.5236i	−0.426134	−	1.31151i	0.475770	−	0.879570i	$-0.342170\pi$
$410$	−8.35410	−	6.06961i	−0.412580	−	0.299757i
$411$	2.30902	−	1.67760i	0.113895	−	0.0827499i
$412$	−5.23607	+	16.1150i	−0.257963	+	0.793927i
$413$	2.35410	−	7.24518i	0.115838	−	0.356512i
$414$	18.7082	−	13.5923i	0.919458	−	0.668025i
$415$	−8.35410	−	6.06961i	−0.410087	−	0.297945i
$416$	0.618034	+	1.90211i	0.0303016	+	0.0932588i
$417$	−48.3607			−2.36823
$418$	19.2533	+	12.0862i	0.941709	+	0.591156i
$419$	12.3262			0.602176			0.301088	−	0.953596i	$-0.402650\pi$
$419$	12.3262			0.602176			0.301088	+	0.953596i	$0.402650\pi$
$420$	0.809017	+	2.48990i	0.0394760	+	0.121495i
$421$	5.14590	+	3.73871i	0.250796	+	0.182214i	0.706079	−	0.708133i	$-0.250462\pi$
$421$	5.14590	+	3.73871i	0.250796	+	0.182214i	−0.455284	+	0.890346i	$0.650462\pi$
$422$	−9.11803	+	6.62464i	−0.443859	+	0.322482i
$423$	11.0000	−	33.8545i	0.534838	−	1.64606i
$424$	−0.381966	+	1.17557i	−0.0185499	+	0.0570908i
$425$	−1.30902	+	0.951057i	−0.0634967	+	0.0461330i
$426$	−20.5623	−	14.9394i	−0.996247	−	0.723816i
$427$	−1.09017	−	3.35520i	−0.0527570	−	0.162369i
$428$	−15.3820			−0.743515
$429$	−14.7082	−	9.23305i	−0.710119	−	0.445776i
$430$	−1.85410			−0.0894127
$431$	−9.65248	−	29.7073i	−0.464943	−	1.43095i	−0.859054	−	0.511885i	$-0.828947\pi$
$431$	−9.65248	−	29.7073i	−0.464943	−	1.43095i	0.394110	−	0.919063i	$-0.371053\pi$
$432$	−1.80902	−	1.31433i	−0.0870364	−	0.0632356i
$433$	−13.3090	+	9.66957i	−0.639591	+	0.464690i	−0.859709	−	0.510783i	$-0.829355\pi$
$433$	−13.3090	+	9.66957i	−0.639591	+	0.464690i	0.220119	+	0.975473i	$0.429355\pi$
$434$	−0.381966	+	1.17557i	−0.0183350	+	0.0564292i
$435$	2.61803	−	8.05748i	0.125525	−	0.386327i
$436$	−0.381966	+	0.277515i	−0.0182929	+	0.0132905i
$437$	33.2705	+	24.1724i	1.59154	+	1.15632i
$438$	11.2082	+	34.4953i	0.535549	+	1.64825i
$439$	28.6525			1.36751			0.683754	−	0.729713i	$-0.260346\pi$
$439$	28.6525			1.36751			0.683754	+	0.729713i	$0.260346\pi$
$440$	−1.23607	−	3.07768i	−0.0589272	−	0.146723i
$441$	3.85410			0.183529
$442$	1.00000	+	3.07768i	0.0475651	+	0.146390i
$443$	−22.6803	−	16.4782i	−1.07758	−	0.782904i	−0.100317	−	0.994956i	$-0.531986\pi$
$443$	−22.6803	−	16.4782i	−1.07758	−	0.782904i	−0.977259	+	0.212051i	$0.931986\pi$
$444$	13.7082	−	9.95959i	0.650563	−	0.472661i
$445$	−4.04508	+	12.4495i	−0.191755	+	0.590162i
$446$	−1.94427	+	5.98385i	−0.0920639	+	0.283344i
$447$	51.2148	−	37.2097i	2.42238	−	1.75996i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	7.55573	+	23.2541i	0.356577	+	1.09743i	0.955090	+	0.296317i	$0.0957586\pi$
$449$	7.55573	+	23.2541i	0.356577	+	1.09743i	−0.598513	+	0.801113i	$0.704241\pi$
$450$	−3.85410			−0.181684
$451$	26.2812	−	21.9601i	1.23753	−	1.03406i
$452$	−9.32624			−0.438669
$453$	−1.85410	−	5.70634i	−0.0871133	−	0.268107i
$454$	19.6353	+	14.2658i	0.921528	+	0.669529i
$455$	1.61803	−	1.17557i	0.0758546	−	0.0551116i
$456$	5.54508	−	17.0660i	0.259672	−	0.799189i
$457$	9.66312	−	29.7400i	0.452022	−	1.39118i	−0.422575	−	0.906328i	$-0.638874\pi$
$457$	9.66312	−	29.7400i	0.452022	−	1.39118i	0.874596	−	0.484852i	$-0.161126\pi$
$458$	9.00000	−	6.53888i	0.420542	−	0.305542i
$459$	−2.92705	−	2.12663i	−0.136623	−	0.0992624i
$460$	−1.85410	−	5.70634i	−0.0864479	−	0.266059i
$461$	−6.94427			−0.323427			−0.161713	−	0.986838i	$-0.551702\pi$
$461$	−6.94427			−0.323427			−0.161713	+	0.986838i	$0.551702\pi$
$462$	−8.66312	+	0.587785i	−0.403045	+	0.0273462i
$463$	−7.41641			−0.344670			−0.172335	−	0.985038i	$-0.555131\pi$
$463$	−7.41641			−0.344670			−0.172335	+	0.985038i	$0.555131\pi$
$464$	−1.00000	−	3.07768i	−0.0464238	−	0.142878i
$465$	−2.61803	−	1.90211i	−0.121408	−	0.0882084i
$466$	−8.82624	+	6.41264i	−0.408868	+	0.297060i
$467$	−5.52786	+	17.0130i	−0.255799	+	0.787268i	0.737872	+	0.674941i	$0.235831\pi$
$467$	−5.52786	+	17.0130i	−0.255799	+	0.787268i	−0.993671	+	0.112328i	$0.964169\pi$
$468$	−2.38197	+	7.33094i	−0.110106	+	0.338873i
$469$	4.92705	−	3.57971i	0.227510	−	0.165296i
$470$	−7.47214	−	5.42882i	−0.344664	−	0.250413i
$471$	0.236068	+	0.726543i	0.0108774	+	0.0334773i
$472$	7.61803			0.350648
$473$	1.50000	−	5.96361i	0.0689701	−	0.274207i
$474$	−22.1803			−1.01878
$475$	−2.11803	−	6.51864i	−0.0971821	−	0.299096i
$476$	1.30902	+	0.951057i	0.0599987	+	0.0435916i
$477$	−3.85410	+	2.80017i	−0.176467	+	0.128211i
$478$		0			0
$479$	11.7082	−	36.0341i	0.534961	−	1.64644i	−0.208771	−	0.977965i	$-0.566946\pi$
$479$	11.7082	−	36.0341i	0.534961	−	1.64644i	0.743732	−	0.668478i	$-0.233054\pi$
$480$	−2.11803	+	1.53884i	−0.0966746	+	0.0702382i
$481$	−10.4721	−	7.60845i	−0.477488	−	0.346916i
$482$	−1.93769	−	5.96361i	−0.0882595	−	0.271635i
$483$	−15.7082			−0.714748
$484$	10.8992	−	1.48584i	0.495418	−	0.0675382i
$485$	9.56231			0.434202
$486$	6.69098	+	20.5927i	0.303509	+	0.934105i
$487$	21.7082	+	15.7719i	0.983693	+	0.714695i	0.958531	−	0.284989i	$-0.0919899\pi$
$487$	21.7082	+	15.7719i	0.983693	+	0.714695i	0.0251618	+	0.999683i	$0.491990\pi$
$488$	2.85410	−	2.07363i	0.129199	−	0.0938687i
$489$	2.30902	−	7.10642i	0.104417	−	0.321364i
$490$	0.309017	−	0.951057i	0.0139600	−	0.0429644i
$491$	−26.2984	+	19.1069i	−1.18683	+	0.862282i	−0.992926	−	0.118739i	$-0.962115\pi$
$491$	−26.2984	+	19.1069i	−1.18683	+	0.862282i	−0.193903	+	0.981021i	$0.562115\pi$
$492$	−21.8713	−	15.8904i	−0.986035	−	0.716397i
$493$	−1.61803	−	4.97980i	−0.0728726	−	0.224279i
$494$	−13.7082			−0.616761
$495$	3.11803	−	12.3965i	0.140145	−	0.557181i
$496$	−1.23607			−0.0555011
$497$	3.00000	+	9.23305i	0.134568	+	0.414159i
$498$	−21.8713	−	15.8904i	−0.980077	−	0.712068i
$499$	12.2984	−	8.93529i	0.550551	−	0.399999i	−0.277438	−	0.960744i	$-0.589485\pi$
$499$	12.2984	−	8.93529i	0.550551	−	0.399999i	0.827989	+	0.560745i	$0.189485\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−5.23607	+	16.1150i	−0.233930	+	0.719963i
$502$	21.7082	−	15.7719i	0.968885	−	0.703936i
$503$	−13.8541	−	10.0656i	−0.617724	−	0.448803i	0.234402	−	0.972140i	$-0.424687\pi$
$503$	−13.8541	−	10.0656i	−0.617724	−	0.448803i	−0.852126	+	0.523337i	$0.824687\pi$
$504$	1.19098	+	3.66547i	0.0530506	+	0.163273i
$505$	8.94427			0.398015
$506$	19.8541	−	1.34708i	0.882622	−	0.0598852i
$507$	−23.5623			−1.04644
$508$	3.52786	+	10.8576i	0.156524	+	0.481730i
$509$	20.6525	+	15.0049i	0.915405	+	0.665081i	0.942376	−	0.334556i	$-0.108586\pi$
$509$	20.6525	+	15.0049i	0.915405	+	0.665081i	−0.0269711	+	0.999636i	$0.508586\pi$
$510$	−3.42705	+	2.48990i	−0.151752	+	0.110255i
$511$	4.28115	−	13.1760i	0.189387	−	0.582873i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	12.3992	−	9.00854i	0.547437	−	0.397737i
$514$	23.9164	+	17.3763i	1.05491	+	0.766435i
$515$	5.23607	+	16.1150i	0.230729	+	0.710110i
$516$	−4.85410			−0.213690
$517$	23.5066	−	19.6417i	1.03382	−	0.863840i
$518$	−6.47214			−0.284369
$519$	−9.70820	−	29.8788i	−0.426143	−	1.31153i
$520$	1.61803	+	1.17557i	0.0709555	+	0.0515522i
$521$	−28.9615	+	21.0418i	−1.26883	+	0.921856i	−0.999155	−	0.0410965i	$-0.986915\pi$
$521$	−28.9615	+	21.0418i	−1.26883	+	0.921856i	−0.269671	+	0.962953i	$0.586915\pi$
$522$	3.85410	−	11.8617i	0.168689	−	0.519173i
$523$	−1.84752	+	5.68609i	−0.0807866	+	0.248636i	−0.983290	−	0.182048i	$-0.941727\pi$
$523$	−1.84752	+	5.68609i	−0.0807866	+	0.248636i	0.902503	+	0.430683i	$0.141727\pi$
$524$	−6.30902	+	4.58377i	−0.275611	+	0.200243i
$525$	2.11803	+	1.53884i	0.0924386	+	0.0671606i
$526$	6.23607	+	19.1926i	0.271905	+	0.836839i
$527$	−2.00000			−0.0871214
$528$	−3.23607	−	8.05748i	−0.140832	−	0.350657i
$529$	13.0000			0.565217
$530$	0.381966	+	1.17557i	0.0165915	+	0.0510635i
$531$	23.7533	+	17.2578i	1.03080	+	0.748924i
$532$	−5.54508	+	4.02874i	−0.240410	+	0.174668i
$533$	−6.38197	+	19.6417i	−0.276434	+	0.850775i
$534$	−10.5902	+	32.5932i	−0.458281	+	1.41045i
$535$	−12.4443	+	9.04129i	−0.538013	+	0.390889i
$536$	4.92705	+	3.57971i	0.212816	+	0.154620i
$537$	−5.16312	−	15.8904i	−0.222805	−	0.685723i
$538$	12.1803			0.525132
$539$	2.80902	+	1.76336i	0.120993	+	0.0759531i
$540$	−2.23607			−0.0962250
$541$	−4.58359	−	14.1068i	−0.197064	−	0.606501i	−0.999946	−	0.0103631i	$-0.996701\pi$
$541$	−4.58359	−	14.1068i	−0.197064	−	0.606501i	0.802882	−	0.596138i	$-0.203299\pi$
$542$	7.61803	+	5.53483i	0.327223	+	0.237741i
$543$	−7.47214	+	5.42882i	−0.320660	+	0.232973i
$544$	−0.500000	+	1.53884i	−0.0214373	+	0.0659773i
$545$	−0.145898	+	0.449028i	−0.00624959	+	0.0192342i
$546$	4.23607	−	3.07768i	0.181287	−	0.131713i
$547$	−14.4894	−	10.5271i	−0.619520	−	0.450108i	0.233234	−	0.972421i	$-0.425069\pi$
$547$	−14.4894	−	10.5271i	−0.619520	−	0.450108i	−0.852754	+	0.522313i	$0.825069\pi$
$548$	−0.336881	−	1.03681i	−0.0143908	−	0.0442905i
$549$	13.5967			0.580295
$550$	−2.80902	−	1.76336i	−0.119777	−	0.0751897i
$551$	22.1803			0.944914
$552$	−4.85410	−	14.9394i	−0.206604	−	0.635863i
$553$	6.85410	+	4.97980i	0.291466	+	0.211762i
$554$	−5.09017	+	3.69822i	−0.216261	+	0.157123i
$555$	5.23607	−	16.1150i	0.222259	−	0.684042i
$556$	−5.70820	+	17.5680i	−0.242082	+	0.745051i
$557$	30.8885	−	22.4418i	1.30879	−	0.950891i	0.308790	−	0.951130i	$-0.400076\pi$
$557$	30.8885	−	22.4418i	1.30879	−	0.950891i	1.00000		0.000239051i	$7.60924e-5\pi$
$558$	−3.85410	−	2.80017i	−0.163157	−	0.118541i
$559$	1.14590	+	3.52671i	0.0484663	+	0.149164i
$560$	1.00000			0.0422577
$561$	−5.23607	−	13.0373i	−0.221067	−	0.550434i
$562$	−24.0344			−1.01383
$563$	−1.07953	−	3.32244i	−0.0454966	−	0.140024i	0.925728	−	0.378191i	$-0.123454\pi$
$563$	−1.07953	−	3.32244i	−0.0454966	−	0.140024i	−0.971224	+	0.238166i	$0.923454\pi$
$564$	−19.5623	−	14.2128i	−0.823722	−	0.598469i
$565$	−7.54508	+	5.48183i	−0.317424	+	0.230622i
$566$	−3.70820	+	11.4127i	−0.155867	+	0.479711i
$567$	1.76393	−	5.42882i	0.0740782	−	0.227989i
$568$	−7.85410	+	5.70634i	−0.329551	+	0.239433i
$569$	−6.54508	−	4.75528i	−0.274384	−	0.199352i	0.442080	−	0.896976i	$-0.354241\pi$
$569$	−6.54508	−	4.75528i	−0.274384	−	0.199352i	−0.716464	+	0.697624i	$0.754241\pi$
$570$	−5.54508	−	17.0660i	−0.232258	−	0.714817i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−5.09017	+	4.25325i	−0.212831	+	0.177837i
$573$	−4.00000			−0.167102
$574$	3.19098	+	9.82084i	0.133189	+	0.409914i
$575$	−4.85410	−	3.52671i	−0.202430	−	0.147074i
$576$	−3.11803	+	2.26538i	−0.129918	+	0.0943910i
$577$	7.79180	−	23.9807i	0.324377	−	0.998329i	−0.647344	−	0.762198i	$-0.724120\pi$
$577$	7.79180	−	23.9807i	0.324377	−	0.998329i	0.971721	−	0.236131i	$-0.0758795\pi$
$578$	4.44427	−	13.6781i	0.184857	−	0.568932i
$579$	−4.23607	+	3.07768i	−0.176045	+	0.127904i
$580$	−2.61803	−	1.90211i	−0.108708	−	0.0789809i
$581$	3.19098	+	9.82084i	0.132384	+	0.407437i
$582$	25.0344			1.03771
$583$	−4.09017	+	0.277515i	−0.169398	+	0.0114935i
$584$	13.8541			0.573287
$585$	2.38197	+	7.33094i	0.0984822	+	0.303097i
$586$	−13.3262	−	9.68208i	−0.550502	−	0.399963i
$587$	−2.21885	+	1.61209i	−0.0915816	+	0.0665379i	−0.632634	−	0.774451i	$-0.718026\pi$
$587$	−2.21885	+	1.61209i	−0.0915816	+	0.0665379i	0.541052	+	0.840989i	$0.318026\pi$
$588$	0.809017	−	2.48990i	0.0333633	−	0.102682i
$589$	2.61803	−	8.05748i	0.107874	−	0.332003i
$590$	6.16312	−	4.47777i	0.253732	−	0.184347i
$591$	12.7082	+	9.23305i	0.522746	+	0.379797i
$592$	−2.00000	−	6.15537i	−0.0821995	−	0.252984i
$593$	−12.0902			−0.496484			−0.248242	−	0.968698i	$-0.579853\pi$
$593$	−12.0902			−0.496484			−0.248242	+	0.968698i	$0.579853\pi$
$594$	1.80902	−	7.19218i	0.0742249	−	0.295099i
$595$	1.61803			0.0663329
$596$	−7.47214	−	22.9969i	−0.306071	−	0.941988i
$597$	41.1246	+	29.8788i	1.68312	+	1.22286i
$598$	−9.70820	+	7.05342i	−0.396998	+	0.288436i
$599$	−7.79837	+	24.0009i	−0.318633	+	0.980651i	0.655600	+	0.755108i	$0.272416\pi$
$599$	−7.79837	+	24.0009i	−0.318633	+	0.980651i	−0.974233	+	0.225543i	$0.927584\pi$
$600$	−0.809017	+	2.48990i	−0.0330280	+	0.101650i
$601$	−23.5344	+	17.0988i	−0.959990	+	0.697473i	−0.953148	−	0.302503i	$-0.902178\pi$
$601$	−23.5344	+	17.0988i	−0.959990	+	0.697473i	−0.00684151	+	0.999977i	$0.502178\pi$
$602$	1.50000	+	1.08981i	0.0611354	+	0.0444175i
$603$	7.25329	+	22.3233i	0.295377	+	0.909076i
$604$	−2.29180			−0.0932519
$605$	7.94427	−	7.60845i	0.322981	−	0.309328i
$606$	23.4164			0.951227
$607$	9.14590	+	28.1482i	0.371221	+	1.14250i	0.945993	+	0.324186i	$0.105090\pi$
$607$	9.14590	+	28.1482i	0.371221	+	1.14250i	−0.574773	+	0.818313i	$0.694910\pi$
$608$	−5.54508	−	4.02874i	−0.224883	−	0.163387i
$609$	−6.85410	+	4.97980i	−0.277742	+	0.201792i
$610$	1.09017	−	3.35520i	0.0441397	−	0.135848i
$611$	−5.70820	+	17.5680i	−0.230929	+	0.710727i
$612$	−5.04508	+	3.66547i	−0.203935	+	0.148168i
$613$	−30.2705	−	21.9928i	−1.22261	−	0.888281i	−0.226300	−	0.974058i	$-0.572663\pi$
$613$	−30.2705	−	21.9928i	−1.22261	−	0.888281i	−0.996314	+	0.0857763i	$0.972663\pi$
$614$	−8.51722	−	26.2133i	−0.343727	−	1.05788i
$615$	−27.0344			−1.09013
$616$	−0.809017	+	3.21644i	−0.0325962	+	0.129594i
$617$	23.0344			0.927332			0.463666	−	0.886010i	$-0.346534\pi$
$617$	23.0344			0.927332			0.463666	+	0.886010i	$0.346534\pi$
$618$	13.7082	+	42.1895i	0.551425	+	1.69711i
$619$	−15.1074	−	10.9762i	−0.607217	−	0.441169i	0.241216	−	0.970471i	$-0.422454\pi$
$619$	−15.1074	−	10.9762i	−0.607217	−	0.441169i	−0.848433	+	0.529302i	$0.822454\pi$
$620$	−1.00000	+	0.726543i	−0.0401610	+	0.0291787i
$621$	4.14590	−	12.7598i	0.166369	−	0.512032i
$622$	9.00000	−	27.6992i	0.360867	−	1.11063i
$623$	10.5902	−	7.69421i	0.424286	−	0.308262i
$624$	4.23607	+	3.07768i	0.169578	+	0.123206i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	0.854102			0.0341368
$627$	59.3779	−	4.02874i	2.37132	−	0.160892i
$628$	0.291796			0.0116439
$629$	−3.23607	−	9.95959i	−0.129030	−	0.397115i
$630$	3.11803	+	2.26538i	0.124225	+	0.0902551i
$631$	19.1803	−	13.9353i	0.763557	−	0.554757i	−0.136442	−	0.990648i	$-0.543567\pi$
$631$	19.1803	−	13.9353i	0.763557	−	0.554757i	0.899999	+	0.435891i	$0.143567\pi$
$632$	−2.61803	+	8.05748i	−0.104140	+	0.320509i
$633$	−9.11803	+	28.0624i	−0.362409	+	1.11538i
$634$	−16.7984	+	12.2047i	−0.667149	+	0.484712i
$635$	9.23607	+	6.71040i	0.366522	+	0.266294i
$636$	1.00000	+	3.07768i	0.0396526	+	0.122038i
$637$	−2.00000			−0.0792429
$638$	8.23607	−	6.88191i	0.326069	−	0.272457i
$639$	−37.4164			−1.48017
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−32.6246	−	23.7032i	−1.28859	−	0.936219i	−0.288819	−	0.957384i	$-0.593262\pi$
$641$	−32.6246	−	23.7032i	−1.28859	−	0.936219i	−0.999776	+	0.0211650i	$0.993262\pi$
$642$	−32.5795	+	23.6704i	−1.28581	+	0.934197i
$643$	−4.62868	+	14.2456i	−0.182537	+	0.561792i	−0.999897	−	0.0143355i	$-0.995437\pi$
$643$	−4.62868	+	14.2456i	−0.182537	+	0.561792i	0.817360	+	0.576127i	$0.195437\pi$
$644$	−1.85410	+	5.70634i	−0.0730619	+	0.224861i
$645$	−3.92705	+	2.85317i	−0.154627	+	0.112343i
$646$	−8.97214	−	6.51864i	−0.353004	−	0.256472i
$647$	0.0557281	+	0.171513i	0.00219090	+	0.00674289i	0.952146	−	0.305644i	$-0.0988716\pi$
$647$	0.0557281	+	0.171513i	0.00219090	+	0.00674289i	−0.949955	+	0.312386i	$0.898872\pi$
$648$	5.70820			0.224239
$649$	9.41641	+	23.4459i	0.369626	+	0.920332i
$650$	2.00000			0.0784465
$651$	1.00000	+	3.07768i	0.0391931	+	0.120624i
$652$	−2.30902	−	1.67760i	−0.0904281	−	0.0656998i
$653$	−21.7082	+	15.7719i	−0.849508	+	0.617203i	−0.925010	−	0.379942i	$-0.875944\pi$
$653$	−21.7082	+	15.7719i	−0.849508	+	0.617203i	0.0755026	+	0.997146i	$0.475944\pi$
$654$	−0.381966	+	1.17557i	−0.0149361	+	0.0459684i
$655$	−2.40983	+	7.41669i	−0.0941599	+	0.289794i
$656$	−8.35410	+	6.06961i	−0.326173	+	0.236978i
$657$	43.1976	+	31.3849i	1.68530	+	1.22444i
$658$	2.85410	+	8.78402i	0.111264	+	0.342437i
$659$	−4.09017			−0.159330			−0.0796652	−	0.996822i	$-0.525385\pi$
$659$	−4.09017			−0.159330			−0.0796652	+	0.996822i	$0.525385\pi$
$660$	−7.35410	−	4.61653i	−0.286258	−	0.179698i
$661$	−45.8885			−1.78486			−0.892429	−	0.451188i	$-0.851000\pi$
$661$	−45.8885			−1.78486			−0.892429	+	0.451188i	$0.851000\pi$
$662$	−1.86475	−	5.73910i	−0.0724754	−	0.223056i
$663$	6.85410	+	4.97980i	0.266191	+	0.193399i
$664$	−8.35410	+	6.06961i	−0.324202	+	0.235547i
$665$	−2.11803	+	6.51864i	−0.0821338	+	0.252782i
$666$	7.70820	−	23.7234i	0.298687	−	0.919264i
$667$	15.7082	−	11.4127i	0.608224	−	0.441901i
$668$	5.23607	+	3.80423i	0.202590	+	0.147190i
$669$	5.09017	+	15.6659i	0.196797	+	0.605680i
$670$	6.09017			0.235284
$671$	9.90983	+	6.22088i	0.382565	+	0.240154i
$672$	2.61803			0.100993
$673$	12.0066	+	36.9524i	0.462820	+	1.42441i	0.861704	+	0.507411i	$0.169397\pi$
$673$	12.0066	+	36.9524i	0.462820	+	1.42441i	−0.398885	+	0.917001i	$0.630603\pi$
$674$	12.6353	+	9.18005i	0.486692	+	0.353602i
$675$	−1.80902	+	1.31433i	−0.0696291	+	0.0505885i
$676$	−2.78115	+	8.55951i	−0.106967	+	0.329212i
$677$	4.20163	−	12.9313i	0.161482	−	0.496989i	−0.837278	−	0.546777i	$-0.815855\pi$
$677$	4.20163	−	12.9313i	0.161482	−	0.496989i	0.998760	+	0.0497878i	$0.0158545\pi$
$678$	−19.7533	+	14.3516i	−0.758620	+	0.551170i
$679$	−7.73607	−	5.62058i	−0.296883	−	0.215698i
$680$	0.500000	+	1.53884i	0.0191741	+	0.0590119i
$681$	63.5410			2.43490
$682$	−1.52786	−	3.80423i	−0.0585049	−	0.145671i
$683$	−31.0557			−1.18831			−0.594157	−	0.804349i	$-0.702514\pi$
$683$	−31.0557			−1.18831			−0.594157	+	0.804349i	$0.702514\pi$
$684$	−8.16312	−	25.1235i	−0.312125	−	0.960621i
$685$	−0.881966	−	0.640786i	−0.0336982	−	0.0244832i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	9.00000	−	27.6992i	0.343371	−	1.05679i
$688$	−0.572949	+	1.76336i	−0.0218435	+	0.0672273i
$689$	2.00000	−	1.45309i	0.0761939	−	0.0553581i
$690$	−12.7082	−	9.23305i	−0.483793	−	0.351496i
$691$	6.53444	+	20.1109i	0.248582	+	0.765056i	0.995027	+	0.0996090i	$0.0317592\pi$
$691$	6.53444	+	20.1109i	0.248582	+	0.765056i	−0.746445	+	0.665447i	$0.768241\pi$
$692$	−12.0000			−0.456172
$693$	−9.80902	+	8.19624i	−0.372614	+	0.311349i
$694$	5.32624			0.202181
$695$	5.70820	+	17.5680i	0.216525	+	0.666394i
$696$	−6.85410	−	4.97980i	−0.259804	−	0.188759i
$697$	−13.5172	+	9.82084i	−0.512001	+	0.371991i
$698$	1.70820	−	5.25731i	0.0646565	−	0.198992i
$699$	−8.82624	+	27.1644i	−0.333839	+	1.02745i
$700$	0.809017	−	0.587785i	0.0305780	−	0.0222162i
$701$	−9.85410	−	7.15942i	−0.372184	−	0.270408i	0.385932	−	0.922527i	$-0.373880\pi$
$701$	−9.85410	−	7.15942i	−0.372184	−	0.270408i	−0.758116	+	0.652120i	$0.773880\pi$
$702$	1.38197	+	4.25325i	0.0521589	+	0.160529i
$703$	44.3607			1.67309
$704$	−3.30902	+	0.224514i	−0.124713	+	0.00846169i
$705$	−24.1803			−0.910684
$706$	8.79180	+	27.0584i	0.330884	+	1.01836i
$707$	−7.23607	−	5.25731i	−0.272140	−	0.197722i
$708$	16.1353	−	11.7229i	0.606400	−	0.440575i
$709$	−7.70820	+	23.7234i	−0.289488	+	0.890951i	0.695530	+	0.718497i	$0.255170\pi$
$709$	−7.70820	+	23.7234i	−0.289488	+	0.890951i	−0.985018	+	0.172454i	$0.944830\pi$
$710$	−3.00000	+	9.23305i	−0.112588	+	0.346510i
$711$	−26.4164	+	19.1926i	−0.990693	+	0.719780i
$712$	10.5902	+	7.69421i	0.396883	+	0.288353i
$713$	−2.29180	−	7.05342i	−0.0858284	−	0.264153i
$714$	4.23607			0.158531
$715$	−1.61803	+	6.43288i	−0.0605110	+	0.240576i
$716$	−6.38197			−0.238505
$717$		0			0
$718$	−15.0902	−	10.9637i	−0.563160	−	0.409160i
$719$	−26.1803	+	19.0211i	−0.976362	+	0.709368i	−0.956893	−	0.290442i	$-0.906198\pi$
$719$	−26.1803	+	19.0211i	−0.976362	+	0.709368i	−0.0194693	+	0.999810i	$0.506198\pi$
$720$	−1.19098	+	3.66547i	−0.0443853	+	0.136604i
$721$	5.23607	−	16.1150i	0.195001	−	0.600152i
$722$	22.6353	−	16.4455i	0.842397	−	0.612037i
$723$	−13.2812	−	9.64932i	−0.493931	−	0.358862i
$724$	1.09017	+	3.35520i	0.0405158	+	0.124695i
$725$	−3.23607			−0.120185
$726$	20.7984	−	19.9192i	0.771900	−	0.739270i
$727$	38.8328			1.44023			0.720115	−	0.693855i	$-0.244089\pi$
$727$	38.8328			1.44023			0.720115	+	0.693855i	$0.244089\pi$
$728$	−0.618034	−	1.90211i	−0.0229059	−	0.0704970i
$729$	32.0066	+	23.2541i	1.18543	+	0.861264i
$730$	11.2082	−	8.14324i	0.414834	−	0.301395i
$731$	−0.927051	+	2.85317i	−0.0342882	+	0.105528i
$732$	2.85410	−	8.78402i	0.105491	−	0.324667i
$733$	−10.7082	+	7.77997i	−0.395517	+	0.287360i	−0.767712	−	0.640795i	$-0.778605\pi$
$733$	−10.7082	+	7.77997i	−0.395517	+	0.287360i	0.372196	+	0.928154i	$0.378605\pi$
$734$	22.7984	+	16.5640i	0.841503	+	0.611388i
$735$	−0.809017	−	2.48990i	−0.0298410	−	0.0918413i
$736$	−6.00000			−0.221163
$737$	−4.92705	+	19.5887i	−0.181490	+	0.721558i
$738$	−39.7984			−1.46500
$739$	7.62461	+	23.4661i	0.280476	+	0.863216i	0.987718	+	0.156245i	$0.0499389\pi$
$739$	7.62461	+	23.4661i	0.280476	+	0.863216i	−0.707242	+	0.706971i	$0.750061\pi$
$740$	−5.23607	−	3.80423i	−0.192482	−	0.139846i
$741$	−29.0344	+	21.0948i	−1.06661	+	0.774935i
$742$	0.381966	−	1.17557i	0.0140224	−	0.0431566i
$743$	3.74265	−	11.5187i	0.137304	−	0.422579i	−0.858637	−	0.512584i	$-0.828688\pi$
$743$	3.74265	−	11.5187i	0.137304	−	0.422579i	0.995941	+	0.0900048i	$0.0286882\pi$
$744$	−2.61803	+	1.90211i	−0.0959818	+	0.0697348i
$745$	−19.5623	−	14.2128i	−0.716707	−	0.520718i
$746$	−7.56231	−	23.2744i	−0.276876	−	0.852136i
$747$	−39.7984			−1.45615
$748$	−5.35410	+	0.363271i	−0.195765	+	0.0132825i
$749$	15.3820			0.562045
$750$	0.809017	+	2.48990i	0.0295411	+	0.0909182i
$751$	26.4164	+	19.1926i	0.963948	+	0.700350i	0.954064	−	0.299602i	$-0.0968538\pi$
$751$	26.4164	+	19.1926i	0.963948	+	0.700350i	0.00988402	+	0.999951i	$0.496854\pi$
$752$	−7.47214	+	5.42882i	−0.272481	+	0.197969i
$753$	21.7082	−	66.8110i	0.791091	−	2.43473i
$754$	−2.00000	+	6.15537i	−0.0728357	+	0.224165i
$755$	−1.85410	+	1.34708i	−0.0674777	+	0.0490254i
$756$	1.80902	+	1.31433i	0.0657933	+	0.0478016i
$757$	6.14590	+	18.9151i	0.223376	+	0.687482i	0.998452	+	0.0556139i	$0.0177116\pi$
$757$	6.14590	+	18.9151i	0.223376	+	0.687482i	−0.775076	+	0.631868i	$0.782288\pi$
$758$	27.8541			1.01171
$759$	39.9787	−	33.4055i	1.45114	−	1.21254i
$760$	−6.85410			−0.248624
$761$	9.82624	+	30.2421i	0.356201	+	1.09627i	0.955310	+	0.295606i	$0.0955216\pi$
$761$	9.82624	+	30.2421i	0.356201	+	1.09627i	−0.599109	+	0.800667i	$0.704478\pi$
$762$	24.1803	+	17.5680i	0.875961	+	0.636423i
$763$	0.381966	−	0.277515i	0.0138281	−	0.0100467i
$764$	−0.472136	+	1.45309i	−0.0170813	+	0.0525708i
$765$	−1.92705	+	5.93085i	−0.0696727	+	0.214430i
$766$	−19.4164	+	14.1068i	−0.701543	+	0.509701i
$767$	−12.3262	−	8.95554i	−0.445075	−	0.323366i
$768$	0.809017	+	2.48990i	0.0291929	+	0.0898465i
$769$	7.88854			0.284468			0.142234	−	0.989833i	$-0.454571\pi$
$769$	7.88854			0.284468			0.142234	+	0.989833i	$0.454571\pi$
$770$	1.23607	+	3.07768i	0.0445448	+	0.110912i
$771$	77.3951			2.78732
$772$	0.618034	+	1.90211i	0.0222435	+	0.0684585i
$773$	19.9443	+	14.4904i	0.717346	+	0.521182i	0.885535	−	0.464573i	$-0.153792\pi$
$773$	19.9443	+	14.4904i	0.717346	+	0.521182i	−0.168189	+	0.985755i	$0.553792\pi$
$774$	−5.78115	+	4.20025i	−0.207799	+	0.150975i
$775$	−0.381966	+	1.17557i	−0.0137206	+	0.0422277i
$776$	2.95492	−	9.09429i	0.106075	−	0.326466i
$777$	−13.7082	+	9.95959i	−0.491779	+	0.357298i
$778$	−26.5623	−	19.2986i	−0.952305	−	0.691890i
$779$	−21.8713	−	67.3130i	−0.783621	−	2.41174i
$780$	5.23607			0.187481
$781$	−27.2705	−	17.1190i	−0.975816	−	0.612567i
$782$	−9.70820			−0.347165
$783$	−2.23607	−	6.88191i	−0.0799106	−	0.245939i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	0.236068	−	0.171513i	0.00842563	−	0.00612158i
$786$	−6.30902	+	19.4172i	−0.225035	+	0.692587i
$787$	−15.7918	+	48.6022i	−0.562917	+	1.73248i	0.111145	+	0.993804i	$0.464548\pi$
$787$	−15.7918	+	48.6022i	−0.562917	+	1.73248i	−0.674061	+	0.738675i	$0.735452\pi$
$788$	4.85410	−	3.52671i	0.172920	−	0.125634i
$789$	42.7426	+	31.0543i	1.52168	+	1.10556i
$790$	2.61803	+	8.05748i	0.0931455	+	0.286672i
$791$	9.32624			0.331603
$792$	−10.8262	−	6.79615i	−0.384694	−	0.241491i
$793$	−7.05573			−0.250556
$794$	5.23607	+	16.1150i	0.185821	+	0.571899i
$795$	2.61803	+	1.90211i	0.0928521	+	0.0674610i
$796$	15.7082	−	11.4127i	0.556763	−	0.404512i
$797$	−1.96556	+	6.04937i	−0.0696236	+	0.214280i	−0.979814	−	0.199910i	$-0.935935\pi$
$797$	−1.96556	+	6.04937i	−0.0696236	+	0.214280i	0.910191	+	0.414190i	$0.135935\pi$
$798$	−5.54508	+	17.0660i	−0.196294	+	0.604130i
$799$	−12.0902	+	8.78402i	−0.427719	+	0.310756i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	15.5902	+	47.9816i	0.550852	+	1.69535i
$802$	26.5066			0.935980
$803$	17.1246	+	42.6385i	0.604314	+	1.50468i
$804$	15.9443			0.562311
$805$	1.85410	+	5.70634i	0.0653485	+	0.201122i
$806$	2.00000	+	1.45309i	0.0704470	+	0.0511827i
$807$	25.7984	−	18.7436i	0.908146	−	0.659807i
$808$	2.76393	−	8.50651i	0.0972348	−	0.299258i
$809$	15.0836	−	46.4225i	0.530311	−	1.63213i	−0.223258	−	0.974759i	$-0.571669\pi$
$809$	15.0836	−	46.4225i	0.530311	−	1.63213i	0.753568	−	0.657370i	$-0.228331\pi$
$810$	4.61803	−	3.35520i	0.162261	−	0.117890i
$811$	−24.2082	−	17.5883i	−0.850065	−	0.617608i	0.0750989	−	0.997176i	$-0.476073\pi$
$811$	−24.2082	−	17.5883i	−0.850065	−	0.617608i	−0.925164	+	0.379568i	$0.876073\pi$
$812$	1.00000	+	3.07768i	0.0350931	+	0.108006i
$813$	24.6525			0.864600
$814$	16.4721	−	13.7638i	0.577348	−	0.482422i
$815$	−2.85410			−0.0999748
$816$	1.30902	+	4.02874i	0.0458248	+	0.141034i
$817$	−10.2812	−	7.46969i	−0.359692	−	0.261332i
$818$	−22.5623	+	16.3925i	−0.788873	+	0.573149i
$819$	2.38197	−	7.33094i	0.0832326	−	0.256164i
$820$	−3.19098	+	9.82084i	−0.111434	+	0.342958i
$821$	25.1246	−	18.2541i	0.876855	−	0.637072i	−0.0555626	−	0.998455i	$-0.517695\pi$
$821$	25.1246	−	18.2541i	0.876855	−	0.637072i	0.932418	+	0.361383i	$0.117695\pi$
$822$	−2.30902	−	1.67760i	−0.0805362	−	0.0585130i
$823$	−0.875388	−	2.69417i	−0.0305141	−	0.0939128i	0.934640	−	0.355597i	$-0.115722\pi$
$823$	−0.875388	−	2.69417i	−0.0305141	−	0.0939128i	−0.965154	+	0.261684i	$0.915722\pi$
$824$	16.9443			0.590282
$825$	−8.66312	+	0.587785i	−0.301611	+	0.0204641i
$826$	−7.61803			−0.265065
$827$	12.5902	+	38.7486i	0.437803	+	1.34742i	0.890187	+	0.455596i	$0.150574\pi$
$827$	12.5902	+	38.7486i	0.437803	+	1.34742i	−0.452384	+	0.891823i	$0.649426\pi$
$828$	−18.7082	−	13.5923i	−0.650155	−	0.472365i
$829$	−27.6525	+	20.0907i	−0.960410	+	0.697779i	−0.953246	−	0.302195i	$-0.902280\pi$
$829$	−27.6525	+	20.0907i	−0.960410	+	0.697779i	−0.00716421	+	0.999974i	$0.502280\pi$
$830$	−3.19098	+	9.82084i	−0.110761	+	0.340886i
$831$	−5.09017	+	15.6659i	−0.176576	+	0.543445i
$832$	1.61803	−	1.17557i	0.0560952	−	0.0407556i
$833$	−1.30902	−	0.951057i	−0.0453548	−	0.0329522i
$834$	14.9443	+	45.9937i	0.517478	+	1.59263i
$835$	6.47214			0.223978
$836$	5.54508	−	22.0458i	0.191781	−	0.762470i
$837$	−2.76393			−0.0955355
$838$	−3.80902	−	11.7229i	−0.131580	−	0.404963i
$839$	−3.61803	−	2.62866i	−0.124908	−	0.0907513i	0.523577	−	0.851978i	$-0.324597\pi$
$839$	−3.61803	−	2.62866i	−0.124908	−	0.0907513i	−0.648485	+	0.761227i	$0.724597\pi$
$840$	2.11803	−	1.53884i	0.0730791	−	0.0530951i
$841$	−5.72542	+	17.6210i	−0.197428	+	0.607622i
$842$	1.96556	−	6.04937i	0.0677376	−	0.208475i
$843$	−50.9058	+	36.9852i	−1.75329	+	1.27384i
$844$	9.11803	+	6.62464i	0.313856	+	0.228029i
$845$	2.78115	+	8.55951i	0.0956746	+	0.294456i
$846$	−35.5967			−1.22384
$847$	−10.8992	+	1.48584i	−0.374500	+	0.0510541i
$848$	1.23607			0.0424467
$849$	9.70820	+	29.8788i	0.333185	+	1.02544i
$850$	1.30902	+	0.951057i	0.0448989	+	0.0326210i
$851$	31.4164	−	22.8254i	1.07694	−	0.782443i
$852$	−7.85410	+	24.1724i	−0.269077	+	0.828134i
$853$	1.32624	−	4.08174i	0.0454095	−	0.139756i	−0.925781	−	0.378060i	$-0.876591\pi$
$853$	1.32624	−	4.08174i	0.0454095	−	0.139756i	0.971191	+	0.238304i	$0.0765914\pi$
$854$	−2.85410	+	2.07363i	−0.0976654	+	0.0709580i
$855$	−21.3713	−	15.5272i	−0.730884	−	0.531018i
$856$	4.75329	+	14.6291i	0.162464	+	0.500013i
$857$	9.27051			0.316675			0.158337	−	0.987385i	$-0.449387\pi$
$857$	9.27051			0.316675			0.158337	+	0.987385i	$0.449387\pi$
$858$	−4.23607	+	16.8415i	−0.144617	+	0.574959i
$859$	−7.43769			−0.253771			−0.126885	−	0.991917i	$-0.540498\pi$
$859$	−7.43769			−0.253771			−0.126885	+	0.991917i	$0.540498\pi$
$860$	0.572949	+	1.76336i	0.0195374	+	0.0601299i
$861$	21.8713	+	15.8904i	0.745373	+	0.541545i
$862$	−25.2705	+	18.3601i	−0.860717	+	0.625347i
$863$	2.09017	−	6.43288i	0.0711502	−	0.218978i	−0.909158	−	0.416451i	$-0.863274\pi$
$863$	2.09017	−	6.43288i	0.0711502	−	0.218978i	0.980308	+	0.197473i	$0.0632736\pi$
$864$	−0.690983	+	2.12663i	−0.0235077	+	0.0723493i
$865$	−9.70820	+	7.05342i	−0.330089	+	0.239824i
$866$	13.3090	+	9.66957i	0.452259	+	0.328585i
$867$	−11.6353	−	35.8096i	−0.395154	−	1.21616i
$868$	1.23607			0.0419549
$869$	−28.0344	+	1.90211i	−0.951003	+	0.0645248i
$870$	−8.47214			−0.287232
$871$	−3.76393	−	11.5842i	−0.127536	−	0.392515i
$872$	0.381966	+	0.277515i	0.0129350	+	0.00939783i
$873$	29.8156	−	21.6623i	1.00910	−	0.733158i
$874$	12.7082	−	39.1118i	0.429861	−	1.32298i
$875$	0.309017	−	0.951057i	0.0104467	−	0.0321516i
$876$	29.3435	−	21.3193i	0.991424	−	0.720311i
$877$	14.5623	+	10.5801i	0.491734	+	0.357266i	0.805851	−	0.592119i	$-0.201708\pi$
$877$	14.5623	+	10.5801i	0.491734	+	0.357266i	−0.314117	+	0.949384i	$0.601708\pi$
$878$	−8.85410	−	27.2501i	−0.298811	−	0.919647i
$879$	−43.1246			−1.45456
$880$	−2.54508	+	2.12663i	−0.0857948	+	0.0716886i
$881$	4.14590			0.139679			0.0698394	−	0.997558i	$-0.477751\pi$
$881$	4.14590			0.139679			0.0698394	+	0.997558i	$0.477751\pi$
$882$	−1.19098	−	3.66547i	−0.0401025	−	0.123423i
$883$	−1.97214	−	1.43284i	−0.0663677	−	0.0482189i	0.554107	−	0.832446i	$-0.313060\pi$
$883$	−1.97214	−	1.43284i	−0.0663677	−	0.0482189i	−0.620474	+	0.784227i	$0.713060\pi$
$884$	2.61803	−	1.90211i	0.0880540	−	0.0639750i
$885$	6.16312	−	18.9681i	0.207171	−	0.637607i
$886$	−8.66312	+	26.6623i	−0.291043	+	0.895739i
$887$	−3.52786	+	2.56314i	−0.118454	+	0.0860619i	−0.645435	−	0.763815i	$-0.723324\pi$
$887$	−3.52786	+	2.56314i	−0.118454	+	0.0860619i	0.526981	+	0.849877i	$0.323324\pi$
$888$	−13.7082	−	9.95959i	−0.460017	−	0.334222i
$889$	−3.52786	−	10.8576i	−0.118321	−	0.364154i
$890$	13.0902			0.438783
$891$	7.05573	+	17.5680i	0.236376	+	0.588552i
$892$	6.29180			0.210665
$893$	−19.5623	−	60.2066i	−0.654628	−	2.01474i
$894$	−51.2148	−	37.2097i	−1.71288	−	1.24448i
$895$	−5.16312	+	3.75123i	−0.172584	+	0.125390i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	−9.70820	+	29.8788i	−0.324147	+	0.997623i
$898$	19.7812	−	14.3718i	0.660106	−	0.479595i
$899$	−3.23607	−	2.35114i	−0.107929	−	0.0784149i
$900$	1.19098	+	3.66547i	0.0396994	+	0.122182i
$901$	2.00000			0.0666297
$902$	−29.0066	−	18.2088i	−0.965813	−	0.606288i
$903$	4.85410			0.161534
$904$	2.88197	+	8.86978i	0.0958528	+	0.295004i
$905$	2.85410	+	2.07363i	0.0948736	+	0.0689297i
$906$	−4.85410	+	3.52671i	−0.161267	+	0.117167i
$907$	6.88197	−	21.1805i	0.228512	−	0.703287i	−0.769404	−	0.638762i	$-0.779447\pi$
$907$	6.88197	−	21.1805i	0.228512	−	0.703287i	0.997916	−	0.0645251i	$-0.0205533\pi$
$908$	7.50000	−	23.0826i	0.248896	−	0.766024i
$909$	27.8885	−	20.2622i	0.925005	−	0.672055i
$910$	−1.61803	−	1.17557i	−0.0536373	−	0.0389698i
$911$	−15.9443	−	49.0714i	−0.528257	−	1.62581i	−0.757783	−	0.652506i	$-0.773718\pi$
$911$	−15.9443	−	49.0714i	−0.528257	−	1.62581i	0.229526	−	0.973303i	$-0.426282\pi$
$912$	−17.9443			−0.594194
$913$	−29.0066	−	18.2088i	−0.959978	−	0.602624i
$914$	−31.2705			−1.03434
$915$	−2.85410	−	8.78402i	−0.0943537	−	0.290391i
$916$	−9.00000	−	6.53888i	−0.297368	−	0.216051i
$917$	6.30902	−	4.58377i	0.208342	−	0.151369i
$918$	−1.11803	+	3.44095i	−0.0369006	+	0.113568i
$919$	2.72949	−	8.40051i	0.0900376	−	0.277107i	−0.895891	−	0.444274i	$-0.853462\pi$
$919$	2.72949	−	8.40051i	0.0900376	−	0.277107i	0.985929	+	0.167167i	$0.0534618\pi$
$920$	−4.85410	+	3.52671i	−0.160035	+	0.116272i
$921$	−58.3779	−	42.4140i	−1.92362	−	1.39759i
$922$	2.14590	+	6.60440i	0.0706714	+	0.217504i
$923$	19.4164			0.639099
$924$	3.23607	+	8.05748i	0.106459	+	0.265072i
$925$	−6.47214			−0.212803
$926$	2.29180	+	7.05342i	0.0753131	+	0.231790i
$927$	52.8328	+	38.3853i	1.73526	+	1.26074i
$928$	−2.61803	+	1.90211i	−0.0859412	+	0.0624399i
$929$	−1.00658	+	3.09793i	−0.0330247	+	0.101640i	−0.966210	−	0.257756i	$-0.917017\pi$
$929$	−1.00658	+	3.09793i	−0.0330247	+	0.101640i	0.933185	+	0.359395i	$0.117017\pi$
$930$	−1.00000	+	3.07768i	−0.0327913	+	0.100921i
$931$	5.54508	−	4.02874i	0.181733	−	0.132037i
$932$	8.82624	+	6.41264i	0.289113	+	0.210053i
$933$	−23.5623	−	72.5173i	−0.771395	−	2.37411i
$934$	17.8885			0.585331
$935$	−4.11803	+	3.44095i	−0.134674	+	0.112531i
$936$	7.70820			0.251951
$937$	−10.3197	−	31.7606i	−0.337129	−	1.03758i	−0.965664	−	0.259794i	$-0.916345\pi$
$937$	−10.3197	−	31.7606i	−0.337129	−	1.03758i	0.628535	−	0.777781i	$-0.283655\pi$
$938$	−4.92705	−	3.57971i	−0.160874	−	0.116882i
$939$	1.80902	−	1.31433i	0.0590350	−	0.0428915i
$940$	−2.85410	+	8.78402i	−0.0930905	+	0.286503i
$941$	−10.5623	+	32.5074i	−0.344321	+	1.05971i	0.617625	+	0.786473i	$0.288095\pi$
$941$	−10.5623	+	32.5074i	−0.344321	+	1.05971i	−0.961946	+	0.273239i	$0.911905\pi$
$942$	0.618034	−	0.449028i	0.0201366	−	0.0146301i
$943$	−50.1246	−	36.4177i	−1.63228	−	1.18592i
$944$	−2.35410	−	7.24518i	−0.0766195	−	0.235811i
$945$	2.23607			0.0727393
$946$	−6.13525	+	0.416272i	−0.199474	+	0.0135342i
$947$	−41.9098			−1.36189			−0.680943	−	0.732336i	$-0.738430\pi$
$947$	−41.9098			−1.36189			−0.680943	+	0.732336i	$0.738430\pi$
$948$	6.85410	+	21.0948i	0.222611	+	0.685126i
$949$	−22.4164	−	16.2865i	−0.727667	−	0.528681i
$950$	−5.54508	+	4.02874i	−0.179906	+	0.130710i
$951$	−16.7984	+	51.7001i	−0.544725	+	1.67649i
$952$	0.500000	−	1.53884i	0.0162051	−	0.0498741i
$953$	23.8262	−	17.3108i	0.771808	−	0.560751i	−0.130702	−	0.991422i	$-0.541723\pi$
$953$	23.8262	−	17.3108i	0.771808	−	0.560751i	0.902509	+	0.430671i	$0.141723\pi$
$954$	3.85410	+	2.80017i	0.124781	+	0.0906588i
$955$	0.472136	+	1.45309i	0.0152780	+	0.0470207i
$956$		0			0
$957$	6.85410	−	27.2501i	0.221562	−	0.880871i
$958$	−37.8885			−1.22412
$959$	0.336881	+	1.03681i	0.0108785	+	0.0334804i
$960$	2.11803	+	1.53884i	0.0683593	+	0.0496659i
$961$	23.8435	−	17.3233i	0.769144	−	0.558816i
$962$	−4.00000	+	12.3107i	−0.128965	+	0.396914i
$963$	−18.3197	+	56.3821i	−0.590343	+	1.81689i
$964$	−5.07295	+	3.68571i	−0.163389	+	0.118709i
$965$	1.61803	+	1.17557i	0.0520864	+	0.0378430i
$966$	4.85410	+	14.9394i	0.156178	+	0.480667i
$967$	−27.0132			−0.868685			−0.434342	−	0.900748i	$-0.643019\pi$
$967$	−27.0132			−0.868685			−0.434342	+	0.900748i	$0.643019\pi$
$968$	−4.78115	−	9.90659i	−0.153672	−	0.318410i
$969$	−29.0344			−0.932721
$970$	−2.95492	−	9.09429i	−0.0948766	−	0.292000i
$971$	21.7082	+	15.7719i	0.696649	+	0.506145i	0.878839	−	0.477118i	$-0.158319\pi$
$971$	21.7082	+	15.7719i	0.696649	+	0.506145i	−0.182190	+	0.983263i	$0.558319\pi$
$972$	17.5172	−	12.7270i	0.561865	−	0.408219i
$973$	5.70820	−	17.5680i	0.182997	−	0.563206i
$974$	8.29180	−	25.5195i	0.265686	−	0.817698i
$975$	4.23607	−	3.07768i	0.135663	−	0.0985648i
$976$	−2.85410	−	2.07363i	−0.0913576	−	0.0663752i
$977$	13.3820	+	41.1855i	0.428127	+	1.31764i	0.899968	+	0.435956i	$0.143590\pi$
$977$	13.3820	+	41.1855i	0.428127	+	1.31764i	−0.471841	+	0.881684i	$0.656410\pi$
$978$	−7.47214			−0.238933
$979$	−10.5902	+	42.1038i	−0.338463	+	1.34564i
$980$	−1.00000			−0.0319438
$981$	0.562306	+	1.73060i	0.0179530	+	0.0552538i
$982$	26.2984	+	19.1069i	0.839215	+	0.609725i
$983$	11.8541	−	8.61251i	0.378087	−	0.274696i	−0.382469	−	0.923968i	$-0.624926\pi$
$983$	11.8541	−	8.61251i	0.378087	−	0.274696i	0.760556	+	0.649272i	$0.224926\pi$
$984$	−8.35410	+	25.7113i	−0.266319	+	0.819646i
$985$	1.85410	−	5.70634i	0.0590766	−	0.181819i
$986$	−4.23607	+	3.07768i	−0.134904	+	0.0980134i
$987$	19.5623	+	14.2128i	0.622675	+	0.452400i
$988$	4.23607	+	13.0373i	0.134767	+	0.414771i
$989$	−11.1246			−0.353742
$990$	−12.7533	+	0.865300i	−0.405326	+	0.0275010i
$991$	20.6525			0.656048			0.328024	−	0.944669i	$-0.393617\pi$
$991$	20.6525			0.656048			0.328024	+	0.944669i	$0.393617\pi$
$992$	0.381966	+	1.17557i	0.0121274	+	0.0373244i
$993$	−12.7812	−	9.28605i	−0.405598	−	0.294684i
$994$	7.85410	−	5.70634i	0.249117	−	0.180994i
$995$	6.00000	−	18.4661i	0.190213	−	0.585415i
$996$	−8.35410	+	25.7113i	−0.264710	+	0.814693i
$997$	−18.7082	+	13.5923i	−0.592495	+	0.430473i	−0.843207	−	0.537589i	$-0.819335\pi$
$997$	−18.7082	+	13.5923i	−0.592495	+	0.430473i	0.250712	+	0.968062i	$0.419335\pi$
$998$	−12.2984	−	8.93529i	−0.389298	−	0.282842i
$999$	−4.47214	−	13.7638i	−0.141492	−	0.435468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.b.71.1	✓	4
11.3	even	5		8470.2.a.bt.1.2		2
11.8	odd	10		8470.2.a.cf.1.2		2
11.9	even	5	inner	770.2.n.b.141.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.b.71.1	✓	4	1.1	even	1	trivial
770.2.n.b.141.1	yes	4	11.9	even	5	inner
8470.2.a.bt.1.2		2	11.3	even	5
8470.2.a.cf.1.2		2	11.8	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.11803 - 1.53884i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.809017 + 2.48990i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.19098 + 3.66547i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.11803 - 1.53884i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.809017 + 2.48990i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.19098 + 3.66547i) q^{9} +1.00000 q^{10} +(-0.809017 + 3.21644i) q^{11} +2.61803 q^{12} +(-0.618034 - 1.90211i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(2.11803 - 1.53884i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.500000 - 1.53884i) q^{17} +(3.11803 - 2.26538i) q^{18} +(5.54508 + 4.02874i) q^{19} +(-0.309017 - 0.951057i) q^{20} -2.61803 q^{21} +(3.30902 - 0.224514i) q^{22} +6.00000 q^{23} +(-0.809017 - 2.48990i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-1.61803 + 1.17557i) q^{26} +(0.690983 - 2.12663i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.61803 - 1.90211i) q^{29} +(-2.11803 - 1.53884i) q^{30} +(-0.381966 - 1.17557i) q^{31} -1.00000 q^{32} +(6.66312 - 5.56758i) q^{33} -1.61803 q^{34} +(0.309017 + 0.951057i) q^{35} +(-3.11803 - 2.26538i) q^{36} +(5.23607 - 3.80423i) q^{37} +(2.11803 - 6.51864i) q^{38} +(-1.61803 + 4.97980i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-8.35410 - 6.06961i) q^{41} +(0.809017 + 2.48990i) q^{42} -1.85410 q^{43} +(-1.23607 - 3.07768i) q^{44} -3.85410 q^{45} +(-1.85410 - 5.70634i) q^{46} +(-7.47214 - 5.42882i) q^{47} +(-2.11803 + 1.53884i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-3.42705 + 2.48990i) q^{51} +(1.61803 + 1.17557i) q^{52} +(0.381966 + 1.17557i) q^{53} -2.23607 q^{54} +(-2.80902 - 1.76336i) q^{55} +1.00000 q^{56} +(-5.54508 - 17.0660i) q^{57} +(-2.61803 - 1.90211i) q^{58} +(6.16312 - 4.47777i) q^{59} +(-0.809017 + 2.48990i) q^{60} +(1.09017 - 3.35520i) q^{61} +(-1.00000 + 0.726543i) q^{62} +(3.11803 + 2.26538i) q^{63} +(0.309017 + 0.951057i) q^{64} +2.00000 q^{65} +(-7.35410 - 4.61653i) q^{66} +6.09017 q^{67} +(0.500000 + 1.53884i) q^{68} +(-12.7082 - 9.23305i) q^{69} +(0.809017 - 0.587785i) q^{70} +(-3.00000 + 9.23305i) q^{71} +(-1.19098 + 3.66547i) q^{72} +(11.2082 - 8.14324i) q^{73} +(-5.23607 - 3.80423i) q^{74} +(0.809017 + 2.48990i) q^{75} -6.85410 q^{76} +(1.23607 + 3.07768i) q^{77} +5.23607 q^{78} +(2.61803 + 8.05748i) q^{79} +(0.809017 + 0.587785i) q^{80} +(4.61803 - 3.35520i) q^{81} +(-3.19098 + 9.82084i) q^{82} +(-3.19098 + 9.82084i) q^{83} +(2.11803 - 1.53884i) q^{84} +(1.30902 + 0.951057i) q^{85} +(0.572949 + 1.76336i) q^{86} -8.47214 q^{87} +(-2.54508 + 2.12663i) q^{88} +13.0902 q^{89} +(1.19098 + 3.66547i) q^{90} +(-1.61803 - 1.17557i) q^{91} +(-4.85410 + 3.52671i) q^{92} +(-1.00000 + 3.07768i) q^{93} +(-2.85410 + 8.78402i) q^{94} +(-5.54508 + 4.02874i) q^{95} +(2.11803 + 1.53884i) q^{96} +(-2.95492 - 9.09429i) q^{97} -1.00000 q^{98} +(-12.7533 + 0.865300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 - q^4 + q^5 - q^6 + q^7 + q^8 + 7 * q^9	\( 4 q + q^{2} - 4 q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} + 2 q^{13} - q^{14} + 4 q^{15} - q^{16} + 2 q^{17} + 8 q^{18} + 11 q^{19} + q^{20} - 6 q^{21} + 11 q^{22} + 24 q^{23} - q^{24} - q^{25} - 2 q^{26} + 5 q^{27} + q^{28} + 6 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} + 11 q^{33} - 2 q^{34} - q^{35} - 8 q^{36} + 12 q^{37} + 4 q^{38} - 2 q^{39} - q^{40} - 20 q^{41} + q^{42} + 6 q^{43} + 4 q^{44} - 2 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - q^{49} + q^{50} - 7 q^{51} + 2 q^{52} + 6 q^{53} - 9 q^{55} + 4 q^{56} - 11 q^{57} - 6 q^{58} + 9 q^{59} - q^{60} - 18 q^{61} - 4 q^{62} + 8 q^{63} - q^{64} + 8 q^{65} - 16 q^{66} + 2 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 12 q^{71} - 7 q^{72} + 18 q^{73} - 12 q^{74} + q^{75} - 14 q^{76} - 4 q^{77} + 12 q^{78} + 6 q^{79} + q^{80} + 14 q^{81} - 15 q^{82} - 15 q^{83} + 4 q^{84} + 3 q^{85} + 9 q^{86} - 16 q^{87} + q^{88} + 30 q^{89} + 7 q^{90} - 2 q^{91} - 6 q^{92} - 4 q^{93} + 2 q^{94} - 11 q^{95} + 4 q^{96} - 23 q^{97} - 4 q^{98} - 13 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 - q^4 + q^5 - q^6 + q^7 + q^8 + 7 * q^9 + 4 * q^10 - q^11 + 6 * q^12 + 2 * q^13 - q^14 + 4 * q^15 - q^16 + 2 * q^17 + 8 * q^18 + 11 * q^19 + q^20 - 6 * q^21 + 11 * q^22 + 24 * q^23 - q^24 - q^25 - 2 * q^26 + 5 * q^27 + q^28 + 6 * q^29 - 4 * q^30 - 6 * q^31 - 4 * q^32 + 11 * q^33 - 2 * q^34 - q^35 - 8 * q^36 + 12 * q^37 + 4 * q^38 - 2 * q^39 - q^40 - 20 * q^41 + q^42 + 6 * q^43 + 4 * q^44 - 2 * q^45 + 6 * q^46 - 12 * q^47 - 4 * q^48 - q^49 + q^50 - 7 * q^51 + 2 * q^52 + 6 * q^53 - 9 * q^55 + 4 * q^56 - 11 * q^57 - 6 * q^58 + 9 * q^59 - q^60 - 18 * q^61 - 4 * q^62 + 8 * q^63 - q^64 + 8 * q^65 - 16 * q^66 + 2 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 12 * q^71 - 7 * q^72 + 18 * q^73 - 12 * q^74 + q^75 - 14 * q^76 - 4 * q^77 + 12 * q^78 + 6 * q^79 + q^80 + 14 * q^81 - 15 * q^82 - 15 * q^83 + 4 * q^84 + 3 * q^85 + 9 * q^86 - 16 * q^87 + q^88 + 30 * q^89 + 7 * q^90 - 2 * q^91 - 6 * q^92 - 4 * q^93 + 2 * q^94 - 11 * q^95 + 4 * q^96 - 23 * q^97 - 4 * q^98 - 13 * q^99

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