LMFDB - Embedded newform 770.2.n.g.141.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 10 x^{10} - 9 x^{9} + 27 x^{8} - 26 x^{7} + 47 x^{6} + 46 x^{5} + 137 x^{4} + \cdots + 1 $ x^12 - 2x^11 + 10x^10 - 9x^9 + 27x^8 - 26x^7 + 47x^6 + 46x^5 + 137x^4 - 57x^3 + 113x^2 - 17*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.3
Root			$-1.06852 + 0.776327i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.g.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(1.06852 - 0.776327i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.408139 - 1.25612i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.387995 + 1.19412i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(1.06852 - 0.776327i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.408139 - 1.25612i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.387995 + 1.19412i) q^{9} +1.00000 q^{10} +(2.07142 + 2.59021i) q^{11} -1.32077 q^{12} +(1.65186 - 5.08391i) q^{13} +(0.809017 - 0.587785i) q^{14} +(1.06852 + 0.776327i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.99267 - 6.13282i) q^{17} +(1.01578 + 0.738009i) q^{18} +(5.19997 - 3.77800i) q^{19} +(0.309017 - 0.951057i) q^{20} +1.32077 q^{21} +(3.10354 - 1.16962i) q^{22} +5.51016 q^{23} +(-0.408139 + 1.25612i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.32463 - 3.14203i) q^{26} +(1.73687 + 5.34553i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(6.63005 + 4.81701i) q^{29} +(1.06852 - 0.776327i) q^{30} +(0.548378 - 1.68773i) q^{31} +1.00000 q^{32} +(4.22421 + 1.15960i) q^{33} -6.44843 q^{34} +(-0.309017 + 0.951057i) q^{35} +(1.01578 - 0.738009i) q^{36} +(-8.88469 - 6.45511i) q^{37} +(-1.98621 - 6.11293i) q^{38} +(-2.18172 - 6.71465i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-1.68559 + 1.22465i) q^{41} +(0.408139 - 1.25612i) q^{42} -2.71912 q^{43} +(-0.153326 - 3.31308i) q^{44} -1.25558 q^{45} +(1.70273 - 5.24047i) q^{46} +(-3.52527 + 2.56126i) q^{47} +(1.06852 + 0.776327i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-6.89029 - 5.00609i) q^{51} +(-4.32463 + 3.14203i) q^{52} +(-2.65485 + 8.17078i) q^{53} +5.62062 q^{54} +(-1.82334 + 2.77046i) q^{55} -1.00000 q^{56} +(2.62332 - 8.07375i) q^{57} +(6.63005 - 4.81701i) q^{58} +(4.40637 + 3.20141i) q^{59} +(-0.408139 - 1.25612i) q^{60} +(4.14044 + 12.7430i) q^{61} +(-1.43567 - 1.04308i) q^{62} +(-1.01578 + 0.738009i) q^{63} +(0.309017 - 0.951057i) q^{64} +5.34554 q^{65} +(2.40820 - 3.65913i) q^{66} -10.8106 q^{67} +(-1.99267 + 6.13282i) q^{68} +(5.88773 - 4.27768i) q^{69} +(0.809017 + 0.587785i) q^{70} +(-3.65122 - 11.2373i) q^{71} +(-0.387995 - 1.19412i) q^{72} +(4.48885 + 3.26134i) q^{73} +(-8.88469 + 6.45511i) q^{74} +(-0.408139 + 1.25612i) q^{75} -6.42752 q^{76} +(0.153326 + 3.31308i) q^{77} -7.06020 q^{78} +(-2.27393 + 6.99843i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.95841 + 2.14941i) q^{81} +(0.643838 + 1.98153i) q^{82} +(-2.22246 - 6.84003i) q^{83} +(-1.06852 - 0.776327i) q^{84} +(5.21689 - 3.79029i) q^{85} +(-0.840253 + 2.58603i) q^{86} +10.8239 q^{87} +(-3.19831 - 0.877976i) q^{88} -5.39995 q^{89} +(-0.387995 + 1.19412i) q^{90} +(4.32463 - 3.14203i) q^{91} +(-4.45781 - 3.23879i) q^{92} +(-0.724279 - 2.22910i) q^{93} +(1.34653 + 4.14420i) q^{94} +(5.19997 + 3.77800i) q^{95} +(1.06852 - 0.776327i) q^{96} +(-0.169453 + 0.521523i) q^{97} +1.00000 q^{98} +(-3.89674 + 1.46855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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
$3$	1.06852	−	0.776327i	0.616912	−	0.448213i	−0.234930	−	0.972012i	$-0.575486\pi$
$3$	1.06852	−	0.776327i	0.616912	−	0.448213i	0.851841	+	0.523800i	$0.175486\pi$
$4$	−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
$6$	−0.408139	−	1.25612i	−0.166622	−	0.512810i
$7$	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
$9$	−0.387995	+	1.19412i	−0.129332	+	0.398041i
$10$	1.00000			0.316228
$11$	2.07142	+	2.59021i	0.624557	+	0.780979i
$11$	2.07142	+	2.59021i	0.624557	+	0.780979i
$12$	−1.32077			−0.381272
$13$	1.65186	−	5.08391i	0.458144	−	1.41002i	−0.409260	−	0.912418i	$-0.634213\pi$
$13$	1.65186	−	5.08391i	0.458144	−	1.41002i	0.867404	−	0.497604i	$-0.165787\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	1.06852	+	0.776327i	0.275891	+	0.200447i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.99267	−	6.13282i	−0.483294	−	1.48743i	−0.834436	−	0.551105i	$-0.814206\pi$
$17$	−1.99267	−	6.13282i	−0.483294	−	1.48743i	0.351142	−	0.936322i	$-0.385794\pi$
$18$	1.01578	+	0.738009i	0.239422	+	0.173951i
$19$	5.19997	−	3.77800i	1.19295	−	0.866733i	0.199382	−	0.979922i	$-0.436107\pi$
$19$	5.19997	−	3.77800i	1.19295	−	0.866733i	0.993573	+	0.113189i	$0.0361067\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	1.32077			0.288215
$22$	3.10354	−	1.16962i	0.661678	−	0.249364i
$23$	5.51016			1.14895			0.574474	−	0.818523i	$-0.305207\pi$
$23$	5.51016			1.14895			0.574474	+	0.818523i	$0.305207\pi$
$24$	−0.408139	+	1.25612i	−0.0833111	+	0.256405i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−4.32463	−	3.14203i	−0.848130	−	0.616202i
$27$	1.73687	+	5.34553i	0.334260	+	1.02875i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	6.63005	+	4.81701i	1.23117	+	0.894497i	0.996977	−	0.0776938i	$-0.0247556\pi$
$29$	6.63005	+	4.81701i	1.23117	+	0.894497i	0.234192	+	0.972190i	$0.424756\pi$
$30$	1.06852	−	0.776327i	0.195085	−	0.141737i
$31$	0.548378	−	1.68773i	0.0984915	−	0.303126i	−0.889656	−	0.456631i	$-0.849056\pi$
$31$	0.548378	−	1.68773i	0.0984915	−	0.303126i	0.988148	+	0.153505i	$0.0490561\pi$
$32$	1.00000			0.176777
$33$	4.22421	+	1.15960i	0.735341	+	0.201861i
$34$	−6.44843			−1.10590
$35$	−0.309017	+	0.951057i	−0.0522334	+	0.160758i
$36$	1.01578	−	0.738009i	0.169297	−	0.123002i
$37$	−8.88469	−	6.45511i	−1.46063	−	1.06121i	−0.983197	−	0.182547i	$-0.941566\pi$
$37$	−8.88469	−	6.45511i	−1.46063	−	1.06121i	−0.477437	−	0.878666i	$-0.658434\pi$
$38$	−1.98621	−	6.11293i	−0.322206	−	0.991648i
$39$	−2.18172	−	6.71465i	−0.349355	−	1.07520i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	−1.68559	+	1.22465i	−0.263245	+	0.191259i	−0.711576	−	0.702609i	$-0.752018\pi$
$41$	−1.68559	+	1.22465i	−0.263245	+	0.191259i	0.448331	+	0.893867i	$0.352018\pi$
$42$	0.408139	−	1.25612i	0.0629772	−	0.193824i
$43$	−2.71912			−0.414661			−0.207331	−	0.978271i	$-0.566478\pi$
$43$	−2.71912			−0.414661			−0.207331	+	0.978271i	$0.566478\pi$
$44$	−0.153326	−	3.31308i	−0.0231147	−	0.499465i
$45$	−1.25558			−0.187170
$46$	1.70273	−	5.24047i	0.251054	−	0.772665i
$47$	−3.52527	+	2.56126i	−0.514213	+	0.373598i	−0.814420	−	0.580277i	$-0.802944\pi$
$47$	−3.52527	+	2.56126i	−0.514213	+	0.373598i	0.300206	+	0.953874i	$0.402944\pi$
$48$	1.06852	+	0.776327i	0.154228	+	0.112053i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−6.89029	−	5.00609i	−0.964833	−	0.700992i
$52$	−4.32463	+	3.14203i	−0.599718	+	0.435721i
$53$	−2.65485	+	8.17078i	−0.364672	+	1.12234i	0.585515	+	0.810662i	$0.300892\pi$
$53$	−2.65485	+	8.17078i	−0.364672	+	1.12234i	−0.950186	+	0.311682i	$0.899108\pi$
$54$	5.62062			0.764870
$55$	−1.82334	+	2.77046i	−0.245859	+	0.373569i
$56$	−1.00000			−0.133631
$57$	2.62332	−	8.07375i	0.347467	−	1.06939i
$58$	6.63005	−	4.81701i	0.870568	−	0.632505i
$59$	4.40637	+	3.20141i	0.573660	+	0.416788i	0.836433	−	0.548069i	$-0.184637\pi$
$59$	4.40637	+	3.20141i	0.573660	+	0.416788i	−0.262773	+	0.964858i	$0.584637\pi$
$60$	−0.408139	−	1.25612i	−0.0526905	−	0.162165i
$61$	4.14044	+	12.7430i	0.530129	+	1.63157i	0.753945	+	0.656937i	$0.228148\pi$
$61$	4.14044	+	12.7430i	0.530129	+	1.63157i	−0.223817	+	0.974631i	$0.571852\pi$
$62$	−1.43567	−	1.04308i	−0.182330	−	0.132471i
$63$	−1.01578	+	0.738009i	−0.127977	+	0.0929805i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	5.34554			0.663032
$66$	2.40820	−	3.65913i	0.296429	−	0.450408i
$67$	−10.8106			−1.32073			−0.660363	−	0.750947i	$-0.729597\pi$
$67$	−10.8106			−1.32073			−0.660363	+	0.750947i	$0.729597\pi$
$68$	−1.99267	+	6.13282i	−0.241647	+	0.743714i
$69$	5.88773	−	4.27768i	0.708799	−	0.514973i
$70$	0.809017	+	0.587785i	0.0966960	+	0.0702538i
$71$	−3.65122	−	11.2373i	−0.433320	−	1.33362i	−0.894798	−	0.446471i	$-0.852681\pi$
$71$	−3.65122	−	11.2373i	−0.433320	−	1.33362i	0.461478	−	0.887152i	$-0.347319\pi$
$72$	−0.387995	−	1.19412i	−0.0457256	−	0.140729i
$73$	4.48885	+	3.26134i	0.525380	+	0.381711i	0.818627	−	0.574326i	$-0.194736\pi$
$73$	4.48885	+	3.26134i	0.525380	+	0.381711i	−0.293247	+	0.956037i	$0.594736\pi$
$74$	−8.88469	+	6.45511i	−1.03282	+	0.750391i
$75$	−0.408139	+	1.25612i	−0.0471279	+	0.145045i
$76$	−6.42752			−0.737287
$77$	0.153326	+	3.31308i	0.0174731	+	0.377560i
$78$	−7.06020			−0.799411
$79$	−2.27393	+	6.99843i	−0.255837	+	0.787385i	0.737827	+	0.674990i	$0.235852\pi$
$79$	−2.27393	+	6.99843i	−0.255837	+	0.787385i	−0.993664	+	0.112395i	$0.964148\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	2.95841	+	2.14941i	0.328712	+	0.238823i
$82$	0.643838	+	1.98153i	0.0711000	+	0.218823i
$83$	−2.22246	−	6.84003i	−0.243947	−	0.750791i	−0.995808	−	0.0914696i	$-0.970844\pi$
$83$	−2.22246	−	6.84003i	−0.243947	−	0.750791i	0.751861	−	0.659322i	$-0.229156\pi$
$84$	−1.06852	−	0.776327i	−0.116585	−	0.0847042i
$85$	5.21689	−	3.79029i	0.565851	−	0.411115i
$86$	−0.840253	+	2.58603i	−0.0906068	+	0.278859i
$87$	10.8239			1.16045
$88$	−3.19831	−	0.877976i	−0.340941	−	0.0935926i
$89$	−5.39995			−0.572393			−0.286197	−	0.958171i	$-0.592391\pi$
$89$	−5.39995			−0.572393			−0.286197	+	0.958171i	$0.592391\pi$
$90$	−0.387995	+	1.19412i	−0.0408982	+	0.125872i
$91$	4.32463	−	3.14203i	0.453344	−	0.329374i
$92$	−4.45781	−	3.23879i	−0.464759	−	0.337667i
$93$	−0.724279	−	2.22910i	−0.0751042	−	0.231147i
$94$	1.34653	+	4.14420i	0.138884	+	0.427442i
$95$	5.19997	+	3.77800i	0.533506	+	0.387615i
$96$	1.06852	−	0.776327i	0.109056	−	0.0792335i
$97$	−0.169453	+	0.521523i	−0.0172053	+	0.0529526i	−0.959291	−	0.282421i	$-0.908863\pi$
$97$	−0.169453	+	0.521523i	−0.0172053	+	0.0529526i	0.942085	+	0.335374i	$0.108863\pi$
$98$	1.00000			0.101015
$99$	−3.89674	+	1.46855i	−0.391637	+	0.147594i
$100$	1.00000			0.100000
$101$	0.754710	−	2.32276i	0.0750964	−	0.231123i	−0.906461	−	0.422289i	$-0.861227\pi$
$101$	0.754710	−	2.32276i	0.0750964	−	0.231123i	0.981558	+	0.191166i	$0.0612268\pi$
$102$	−6.89029	+	5.00609i	−0.682240	+	0.495677i
$103$	−0.509914	−	0.370474i	−0.0502433	−	0.0365039i	0.562380	−	0.826879i	$-0.309886\pi$
$103$	−0.509914	−	0.370474i	−0.0502433	−	0.0365039i	−0.612623	+	0.790375i	$0.709886\pi$
$104$	1.65186	+	5.08391i	0.161978	+	0.498518i
$105$	0.408139	+	1.25612i	0.0398303	+	0.122585i
$106$	6.95048	+	5.04982i	0.675091	+	0.490482i
$107$	−9.25131	+	6.72147i	−0.894358	+	0.649789i	−0.937011	−	0.349301i	$-0.886419\pi$
$107$	−9.25131	+	6.72147i	−0.894358	+	0.649789i	0.0426530	+	0.999090i	$0.486419\pi$
$108$	1.73687	−	5.34553i	0.167130	−	0.514374i
$109$	−8.31582			−0.796512			−0.398256	−	0.917274i	$-0.630384\pi$
$109$	−8.31582			−0.796512			−0.398256	+	0.917274i	$0.630384\pi$
$110$	2.07142	+	2.59021i	0.197502	+	0.246967i
$111$	−14.5048			−1.37673
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	16.2996	−	11.8424i	1.53334	−	1.11404i	0.578993	−	0.815332i	$-0.303446\pi$
$113$	16.2996	−	11.8424i	1.53334	−	1.11404i	0.954346	−	0.298704i	$-0.0965543\pi$
$114$	−6.86794	−	4.98985i	−0.643242	−	0.467343i
$115$	1.70273	+	5.24047i	0.158781	+	0.488676i
$116$	−2.53245	−	7.79409i	−0.235132	−	0.723663i
$117$	5.42990	+	3.94506i	0.501995	+	0.364721i
$118$	4.40637	−	3.20141i	0.405639	−	0.294714i
$119$	1.99267	−	6.13282i	0.182668	−	0.562195i
$120$	−1.32077			−0.120569
$121$	−2.41842	+	10.7309i	−0.219857	+	0.975532i
$122$	13.3987			1.21306
$123$	−0.850360	+	2.61714i	−0.0766744	+	0.235979i
$124$	−1.43567	+	1.04308i	−0.128927	+	0.0936710i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	0.387995	+	1.19412i	0.0345653	+	0.106381i
$127$	−3.39949	−	10.4626i	−0.301656	−	0.928402i	−0.980904	−	0.194493i	$-0.937694\pi$
$127$	−3.39949	−	10.4626i	−0.301656	−	0.928402i	0.679248	−	0.733909i	$-0.262306\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−2.90544	+	2.11092i	−0.255809	+	0.185856i
$130$	1.65186	−	5.08391i	0.144878	−	0.445888i
$131$	−18.2978			−1.59868			−0.799342	−	0.600876i	$-0.794818\pi$
$131$	−18.2978			−1.59868			−0.799342	+	0.600876i	$0.794818\pi$
$132$	−2.73586	−	3.42107i	−0.238126	−	0.297766i
$133$	6.42752			0.557336
$134$	−3.34066	+	10.2815i	−0.288589	+	0.888186i
$135$	−4.54718	+	3.30372i	−0.391359	+	0.284339i
$136$	5.21689	+	3.79029i	0.447344	+	0.325015i
$137$	1.68750	+	5.19358i	0.144173	+	0.443718i	0.996904	−	0.0786325i	$-0.0250554\pi$
$137$	1.68750	+	5.19358i	0.144173	+	0.443718i	−0.852731	+	0.522350i	$0.825055\pi$
$138$	−2.24891	−	6.92144i	−0.191440	−	0.589192i
$139$	4.25131	+	3.08876i	0.360592	+	0.261985i	0.753299	−	0.657678i	$-0.228461\pi$
$139$	4.25131	+	3.08876i	0.360592	+	0.261985i	−0.392707	+	0.919664i	$0.628461\pi$
$140$	0.809017	−	0.587785i	0.0683744	−	0.0496769i
$141$	−1.77845	+	5.47352i	−0.149773	+	0.460954i
$142$	−11.8156			−0.991543
$143$	16.5901	−	6.25224i	1.38733	−	0.522839i
$144$	−1.25558			−0.104631
$145$	−2.53245	+	7.79409i	−0.210309	+	0.647264i
$146$	4.48885	−	3.26134i	0.371500	−	0.269910i
$147$	1.06852	+	0.776327i	0.0881302	+	0.0640304i
$148$	3.39365	+	10.4446i	0.278956	+	0.858539i
$149$	2.84682	+	8.76161i	0.233221	+	0.717779i	0.997352	+	0.0727192i	$0.0231677\pi$
$149$	2.84682	+	8.76161i	0.233221	+	0.717779i	−0.764132	+	0.645060i	$0.776832\pi$
$150$	1.06852	+	0.776327i	0.0872445	+	0.0633868i
$151$	−11.5506	+	8.39201i	−0.939975	+	0.682932i	−0.948415	−	0.317033i	$-0.897314\pi$
$151$	−11.5506	+	8.39201i	−0.939975	+	0.682932i	0.00843973	+	0.999964i	$0.497314\pi$
$152$	−1.98621	+	6.11293i	−0.161103	+	0.495824i
$153$	8.09650			0.654563
$154$	3.19831	+	0.877976i	0.257727	+	0.0707493i
$155$	1.77459			0.142538
$156$	−2.18172	+	6.71465i	−0.174678	+	0.537602i
$157$	−12.0898	+	8.78378i	−0.964874	+	0.701022i	−0.954278	−	0.298922i	$-0.903373\pi$
$157$	−12.0898	+	8.78378i	−0.964874	+	0.701022i	−0.0105966	+	0.999944i	$0.503373\pi$
$158$	5.95322	+	4.32527i	0.473613	+	0.344100i
$159$	3.50643	+	10.7917i	0.278078	+	0.855837i
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	4.45781	+	3.23879i	0.351325	+	0.255252i
$162$	2.95841	−	2.14941i	0.232435	−	0.168874i
$163$	5.18167	−	15.9475i	0.405860	−	1.24911i	−0.514316	−	0.857601i	$-0.671954\pi$
$163$	5.18167	−	15.9475i	0.405860	−	1.24911i	0.920175	−	0.391507i	$-0.128046\pi$
$164$	2.08350			0.162694
$165$	0.202507	+	4.37580i	0.0157652	+	0.340656i
$166$	−7.19204			−0.558210
$167$	1.91685	−	5.89944i	0.148330	−	0.456513i	−0.849094	−	0.528241i	$-0.822852\pi$
$167$	1.91685	−	5.89944i	0.148330	−	0.456513i	0.997424	+	0.0717287i	$0.0228516\pi$
$168$	−1.06852	+	0.776327i	−0.0824383	+	0.0598949i
$169$	−12.6002	−	9.15461i	−0.969250	−	0.704201i
$170$	−1.99267	−	6.13282i	−0.152831	−	0.470366i
$171$	2.49384	+	7.67525i	0.190709	+	0.586941i
$172$	2.19981	+	1.59826i	0.167734	+	0.121866i
$173$	5.94632	−	4.32026i	0.452091	−	0.328463i	−0.338330	−	0.941028i	$-0.609862\pi$
$173$	5.94632	−	4.32026i	0.452091	−	0.328463i	0.790421	+	0.612564i	$0.209862\pi$
$174$	3.34478	−	10.2942i	0.253567	−	0.780399i
$175$	−1.00000			−0.0755929
$176$	−1.82334	+	2.77046i	−0.137439	+	0.208831i
$177$	7.19364			0.540707
$178$	−1.66868	+	5.13565i	−0.125073	+	0.384934i
$179$	3.56317	−	2.58879i	0.266323	−	0.193495i	−0.446607	−	0.894730i	$-0.647368\pi$
$179$	3.56317	−	2.58879i	0.266323	−	0.193495i	0.712930	+	0.701235i	$0.247368\pi$
$180$	1.01578	+	0.738009i	0.0757120	+	0.0550080i
$181$	−3.42731	−	10.5482i	−0.254750	−	0.784039i	−0.993879	−	0.110475i	$-0.964763\pi$
$181$	−3.42731	−	10.5482i	−0.254750	−	0.784039i	0.739129	−	0.673564i	$-0.235237\pi$
$182$	−1.65186	−	5.08391i	−0.122444	−	0.376844i
$183$	14.3168	+	10.4018i	1.05833	+	0.768923i
$184$	−4.45781	+	3.23879i	−0.328634	+	0.238767i
$185$	3.39365	−	10.4446i	0.249506	−	0.767901i
$186$	−2.34381			−0.171857
$187$	11.7576	−	17.8651i	0.859804	−	1.30643i
$188$	4.35747			0.317801
$189$	−1.73687	+	5.34553i	−0.126339	+	0.388830i
$190$	5.19997	−	3.77800i	0.377245	−	0.274085i
$191$	11.6144	+	8.43835i	0.840388	+	0.610578i	0.922479	−	0.386047i	$-0.126160\pi$
$191$	11.6144	+	8.43835i	0.840388	+	0.610578i	−0.0820911	+	0.996625i	$0.526160\pi$
$192$	−0.408139	−	1.25612i	−0.0294549	−	0.0906529i
$193$	2.62104	+	8.06674i	0.188667	+	0.580656i	0.999992	−	0.00393825i	$-0.00125359\pi$
$193$	2.62104	+	8.06674i	0.188667	+	0.580656i	−0.811326	+	0.584595i	$0.801254\pi$
$194$	0.443634	+	0.322319i	0.0318510	+	0.0231411i
$195$	5.71182	−	4.14988i	0.409032	−	0.297179i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−4.97357			−0.354352			−0.177176	−	0.984179i	$-0.556696\pi$
$197$	−4.97357			−0.354352			−0.177176	+	0.984179i	$0.556696\pi$
$198$	0.192512	+	4.15982i	0.0136812	+	0.295626i
$199$	−22.6336			−1.60445			−0.802227	−	0.597018i	$-0.796352\pi$
$199$	−22.6336			−1.60445			−0.802227	+	0.597018i	$0.796352\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	−11.5514	+	8.39256i	−0.814771	+	0.591966i
$202$	−1.97586	−	1.43554i	−0.139021	−	0.101004i
$203$	2.53245	+	7.79409i	0.177743	+	0.547038i
$204$	2.63186	+	8.10002i	0.184267	+	0.567115i
$205$	−1.68559	−	1.22465i	−0.117727	−	0.0855335i
$206$	−0.509914	+	0.370474i	−0.0355274	+	0.0258122i
$207$	−2.13791	+	6.57981i	−0.148595	+	0.457329i
$208$	5.34554			0.370646
$209$	20.5572	+	5.64321i	1.42197	+	0.390349i
$210$	1.32077			0.0911415
$211$	−1.16940	+	3.59904i	−0.0805046	+	0.247768i	−0.983206	−	0.182500i	$-0.941581\pi$
$211$	−1.16940	+	3.59904i	−0.0805046	+	0.247768i	0.902701	+	0.430268i	$0.141581\pi$
$212$	6.95048	−	5.04982i	0.477361	−	0.346823i
$213$	−12.6252	−	9.17277i	−0.865067	−	0.628508i
$214$	3.53368	+	10.8756i	0.241558	+	0.743438i
$215$	−0.840253	−	2.58603i	−0.0573048	−	0.176366i
$216$	−4.54718	−	3.30372i	−0.309396	−	0.224790i
$217$	1.43567	−	1.04308i	0.0974597	−	0.0708086i
$218$	−2.56973	+	7.90882i	−0.174044	+	0.535653i
$219$	7.32830			0.495200
$220$	3.10354	−	1.16962i	0.209241	−	0.0788557i
$221$	−34.4703			−2.31872
$222$	−4.48222	+	13.7948i	−0.300827	+	0.925850i
$223$	−18.2142	+	13.2334i	−1.21971	+	0.886173i	−0.996076	−	0.0884996i	$-0.971793\pi$
$223$	−18.2142	+	13.2334i	−1.21971	+	0.886173i	−0.223636	+	0.974673i	$0.571793\pi$
$224$	0.809017	+	0.587785i	0.0540547	+	0.0392731i
$225$	−0.387995	−	1.19412i	−0.0258663	−	0.0796083i
$226$	−6.22590	−	19.1614i	−0.414141	−	1.27459i
$227$	8.81804	+	6.40668i	0.585274	+	0.425227i	0.840622	−	0.541623i	$-0.182190\pi$
$227$	8.81804	+	6.40668i	0.585274	+	0.425227i	−0.255348	+	0.966849i	$0.582190\pi$
$228$	−6.86794	+	4.98985i	−0.454841	+	0.330461i
$229$	−0.980958	+	3.01908i	−0.0648235	+	0.199506i	−0.978222	−	0.207559i	$-0.933448\pi$
$229$	−0.980958	+	3.01908i	−0.0648235	+	0.199506i	0.913399	+	0.407066i	$0.133448\pi$
$230$	5.51016			0.363329
$231$	2.73586	+	3.42107i	0.180007	+	0.225090i
$232$	−8.19519			−0.538041
$233$	−7.92082	+	24.3778i	−0.518910	+	1.59704i	0.257143	+	0.966373i	$0.417219\pi$
$233$	−7.92082	+	24.3778i	−0.518910	+	1.59704i	−0.776053	+	0.630667i	$0.782781\pi$
$234$	5.42990	−	3.94506i	0.354964	−	0.257896i
$235$	−3.52527	−	2.56126i	−0.229963	−	0.167078i
$236$	−1.68308	−	5.17999i	−0.109559	−	0.337189i
$237$	3.00333	+	9.24329i	0.195087	+	0.600416i
$238$	−5.21689	−	3.79029i	−0.338161	−	0.245688i
$239$	14.2116	−	10.3253i	0.919269	−	0.667888i	−0.0240731	−	0.999710i	$-0.507663\pi$
$239$	14.2116	−	10.3253i	0.919269	−	0.667888i	0.943342	+	0.331822i	$0.107663\pi$
$240$	−0.408139	+	1.25612i	−0.0263453	+	0.0810824i
$241$	5.63187			0.362781			0.181390	−	0.983411i	$-0.441940\pi$
$241$	5.63187			0.362781			0.181390	+	0.983411i	$0.441940\pi$
$242$	9.45832	+	5.61607i	0.608004	+	0.361015i
$243$	−12.0321			−0.771859
$244$	4.14044	−	12.7430i	0.265064	−	0.815784i
$245$	−0.809017	+	0.587785i	−0.0516862	+	0.0375522i
$246$	2.22627	+	1.61748i	0.141942	+	0.103127i
$247$	−10.6174	−	32.6769i	−0.675567	−	2.07918i
$248$	0.548378	+	1.68773i	0.0348220	+	0.107171i
$249$	−7.68485	−	5.58337i	−0.487008	−	0.353832i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	4.42150	−	13.6080i	0.279083	−	0.858928i	−0.709028	−	0.705181i	$-0.750866\pi$
$251$	4.42150	−	13.6080i	0.279083	−	0.858928i	0.988110	−	0.153747i	$-0.0491342\pi$
$252$	1.25558			0.0790939
$253$	11.4139	+	14.2725i	0.717583	+	0.897304i
$254$	−11.0010			−0.690263
$255$	2.63186	−	8.10002i	0.164813	−	0.507243i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.22372	+	4.52179i	0.388225	+	0.282062i	0.764728	−	0.644354i	$-0.222874\pi$
$257$	6.22372	+	4.52179i	0.388225	+	0.282062i	−0.376503	+	0.926415i	$0.622874\pi$
$258$	1.10978	+	3.41554i	0.0690917	+	0.212642i
$259$	−3.39365	−	10.4446i	−0.210871	−	0.648995i
$260$	−4.32463	−	3.14203i	−0.268202	−	0.194860i
$261$	−8.32453	+	6.04813i	−0.515276	+	0.374370i
$262$	−5.65432	+	17.4022i	−0.349325	+	1.07511i
$263$	−6.81613			−0.420300			−0.210150	−	0.977669i	$-0.567395\pi$
$263$	−6.81613			−0.420300			−0.210150	+	0.977669i	$0.567395\pi$
$264$	−4.09906	+	1.54479i	−0.252280	+	0.0950755i
$265$	−8.59127			−0.527758
$266$	1.98621	−	6.11293i	0.121782	−	0.374808i
$267$	−5.76996	+	4.19212i	−0.353116	+	0.256554i
$268$	8.74596	+	6.35431i	0.534245	+	0.388151i
$269$	1.17371	+	3.61232i	0.0715626	+	0.220247i	0.980441	−	0.196815i	$-0.0630598\pi$
$269$	1.17371	+	3.61232i	0.0715626	+	0.220247i	−0.908878	+	0.417062i	$0.863060\pi$
$270$	1.73687	+	5.34553i	0.105702	+	0.325319i
$271$	−1.90448	−	1.38368i	−0.115689	−	0.0840528i	0.528437	−	0.848973i	$-0.322778\pi$
$271$	−1.90448	−	1.38368i	−0.115689	−	0.0840528i	−0.644125	+	0.764920i	$0.722778\pi$
$272$	5.21689	−	3.79029i	0.316320	−	0.229820i
$273$	2.18172	−	6.71465i	0.132044	−	0.406389i
$274$	5.46086			0.329902
$275$	−3.19831	−	0.877976i	−0.192865	−	0.0529440i
$276$	−7.27763			−0.438062
$277$	−5.38954	+	16.5873i	−0.323826	+	0.996635i	0.648141	+	0.761520i	$0.275547\pi$
$277$	−5.38954	+	16.5873i	−0.323826	+	0.996635i	−0.971968	+	0.235115i	$0.924453\pi$
$278$	4.25131	−	3.08876i	0.254977	−	0.185252i
$279$	1.80260	+	1.30966i	0.107919	+	0.0784074i
$280$	−0.309017	−	0.951057i	−0.0184673	−	0.0568365i
$281$	−6.99337	−	21.5234i	−0.417190	−	1.28398i	−0.910278	−	0.413998i	$-0.864132\pi$
$281$	−6.99337	−	21.5234i	−0.417190	−	1.28398i	0.493088	−	0.869979i	$-0.335868\pi$
$282$	4.65606	+	3.38282i	0.277264	+	0.201444i
$283$	21.8917	−	15.9052i	1.30132	−	0.945467i	0.301356	−	0.953512i	$-0.402561\pi$
$283$	21.8917	−	15.9052i	1.30132	−	0.945467i	0.999968	+	0.00804445i	$0.00256065\pi$
$284$	−3.65122	+	11.2373i	−0.216660	+	0.666811i
$285$	8.48925			0.502860
$286$	−0.819608	−	17.7102i	−0.0484644	−	1.04723i
$287$	−2.08350			−0.122985
$288$	−0.387995	+	1.19412i	−0.0228628	+	0.0703645i
$289$	−19.8874	+	14.4491i	−1.16985	+	0.849945i
$290$	6.63005	+	4.81701i	0.389330	+	0.282865i
$291$	0.223808	+	0.688809i	0.0131198	+	0.0403787i
$292$	−1.71459	−	5.27695i	−0.100339	−	0.308810i
$293$	16.3387	+	11.8708i	0.954520	+	0.693499i	0.951872	−	0.306497i	$-0.0991570\pi$
$293$	16.3387	+	11.8708i	0.954520	+	0.693499i	0.00264825	+	0.999996i	$0.499157\pi$
$294$	1.06852	−	0.776327i	0.0623175	−	0.0452763i
$295$	−1.68308	+	5.17999i	−0.0979928	+	0.301591i
$296$	10.9821			0.638321
$297$	−10.2483	+	15.5717i	−0.594666	+	0.903562i
$298$	9.21250			0.533666
$299$	9.10202	−	28.0131i	0.526383	−	1.62004i
$300$	1.06852	−	0.776327i	0.0616912	−	0.0448213i
$301$	−2.19981	−	1.59826i	−0.126795	−	0.0921219i
$302$	4.41194	+	13.5786i	0.253879	+	0.781358i
$303$	−0.996795	−	3.06782i	−0.0572644	−	0.176242i
$304$	5.19997	+	3.77800i	0.298239	+	0.216683i
$305$	−10.8398	+	7.87558i	−0.620685	+	0.450954i
$306$	2.50195	−	7.70022i	0.143027	−	0.440193i
$307$	24.4128			1.39331			0.696656	−	0.717405i	$-0.254670\pi$
$307$	24.4128			1.39331			0.696656	+	0.717405i	$0.254670\pi$
$308$	1.82334	−	2.77046i	0.103894	−	0.157862i
$309$	−0.832464			−0.0473572
$310$	0.548378	−	1.68773i	0.0311458	−	0.0958568i
$311$	−20.4412	+	14.8514i	−1.15911	+	0.842144i	−0.989666	−	0.143395i	$-0.954198\pi$
$311$	−20.4412	+	14.8514i	−1.15911	+	0.842144i	−0.169447	+	0.985539i	$0.554198\pi$
$312$	5.71182	+	4.14988i	0.323368	+	0.234941i
$313$	−5.61629	−	17.2852i	−0.317451	−	0.977015i	−0.974734	−	0.223370i	$-0.928294\pi$
$313$	−5.61629	−	17.2852i	−0.317451	−	0.977015i	0.657282	−	0.753644i	$-0.271706\pi$
$314$	4.61791	+	14.2125i	0.260604	+	0.802055i
$315$	−1.01578	−	0.738009i	−0.0572329	−	0.0415821i
$316$	5.95322	−	4.32527i	0.334895	−	0.243315i
$317$	3.29842	−	10.1515i	0.185258	−	0.570164i	−0.814695	−	0.579890i	$-0.803096\pi$
$317$	3.29842	−	10.1515i	0.185258	−	0.570164i	0.999953	+	0.00972518i	$0.00309567\pi$
$318$	11.3471			0.636312
$319$	1.25653	+	27.1513i	0.0703523	+	1.52018i
$320$	1.00000			0.0559017
$321$	−4.66717	+	14.3641i	−0.260496	+	0.801725i
$322$	4.45781	−	3.23879i	0.248424	−	0.180491i
$323$	−33.5316	−	24.3622i	−1.86575	−	1.35555i
$324$	−1.13001	−	3.47782i	−0.0627785	−	0.193212i
$325$	1.65186	+	5.08391i	0.0916288	+	0.282004i
$326$	−13.5658	−	9.85612i	−0.751339	−	0.545880i
$327$	−8.88564	+	6.45580i	−0.491377	+	0.357006i
$328$	0.643838	−	1.98153i	0.0355500	−	0.109412i
$329$	−4.35747			−0.240235
$330$	4.22421	+	1.15960i	0.232535	+	0.0638340i
$331$	−9.75660			−0.536271			−0.268136	−	0.963381i	$-0.586408\pi$
$331$	−9.75660			−0.536271			−0.268136	+	0.963381i	$0.586408\pi$
$332$	−2.22246	+	6.84003i	−0.121973	+	0.375396i
$333$	11.1554	−	8.10488i	0.611313	−	0.444145i
$334$	−5.01837	−	3.64606i	−0.274593	−	0.199503i
$335$	−3.34066	−	10.2815i	−0.182520	−	0.561738i
$336$	0.408139	+	1.25612i	0.0222658	+	0.0685271i
$337$	−8.20845	−	5.96379i	−0.447143	−	0.324868i	0.341324	−	0.939946i	$-0.389125\pi$
$337$	−8.20845	−	5.96379i	−0.447143	−	0.324868i	−0.788467	+	0.615077i	$0.789125\pi$
$338$	−12.6002	+	9.15461i	−0.685363	+	0.497945i
$339$	8.22296	−	25.3077i	0.446610	−	1.37452i
$340$	−6.44843			−0.349715
$341$	5.50751	−	2.07559i	0.298248	−	0.112400i
$342$	8.07024			0.436389
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	2.19981	−	1.59826i	0.118606	−	0.0861722i
$345$	5.88773	+	4.27768i	0.316984	+	0.230303i
$346$	−2.27129	−	6.99032i	−0.122105	−	0.375802i
$347$	−6.54362	−	20.1392i	−0.351280	−	1.08113i	−0.958135	−	0.286316i	$-0.907569\pi$
$347$	−6.54362	−	20.1392i	−0.351280	−	1.08113i	0.606855	−	0.794813i	$-0.292431\pi$
$348$	−8.75674	−	6.36215i	−0.469411	−	0.341047i
$349$	3.71293	−	2.69760i	0.198749	−	0.144399i	−0.483960	−	0.875090i	$-0.660802\pi$
$349$	3.71293	−	2.69760i	0.198749	−	0.144399i	0.682708	+	0.730691i	$0.260802\pi$
$350$	−0.309017	+	0.951057i	−0.0165177	+	0.0508361i
$351$	30.0452			1.60370
$352$	2.07142	+	2.59021i	0.110407	+	0.138059i
$353$	32.2094			1.71433			0.857166	−	0.515040i	$-0.172223\pi$
$353$	32.2094			1.71433			0.857166	+	0.515040i	$0.172223\pi$
$354$	2.22296	−	6.84156i	0.118149	−	0.363625i
$355$	9.55902	−	6.94504i	0.507340	−	0.368604i
$356$	4.36865	+	3.17401i	0.231538	+	0.168222i
$357$	−2.63186	−	8.10002i	−0.139293	−	0.428698i
$358$	−1.36101	−	4.18875i	−0.0719315	−	0.221382i
$359$	5.29122	+	3.84430i	0.279260	+	0.202894i	0.718595	−	0.695429i	$-0.244786\pi$
$359$	5.29122	+	3.84430i	0.279260	+	0.202894i	−0.439335	+	0.898323i	$0.644786\pi$
$360$	1.01578	−	0.738009i	0.0535365	−	0.0388965i
$361$	6.89509	−	21.2209i	0.362899	−	1.11689i
$362$	−11.0910			−0.582930
$363$	5.74651	+	13.3436i	0.301614	+	0.700360i
$364$	−5.34554			−0.280182
$365$	−1.71459	+	5.27695i	−0.0897456	+	0.276208i
$366$	14.3168	−	10.4018i	0.748354	−	0.543711i
$367$	2.41537	+	1.75487i	0.126081	+	0.0916033i	0.649039	−	0.760755i	$-0.275171\pi$
$367$	2.41537	+	1.75487i	0.126081	+	0.0916033i	−0.522957	+	0.852359i	$0.675171\pi$
$368$	1.70273	+	5.24047i	0.0887611	+	0.273178i
$369$	−0.808388	−	2.48796i	−0.0420830	−	0.129518i
$370$	−8.88469	−	6.45511i	−0.461893	−	0.335585i
$371$	−6.95048	+	5.04982i	−0.360851	+	0.262174i
$372$	−0.724279	+	2.22910i	−0.0375521	+	0.115573i
$373$	−16.8471			−0.872311			−0.436155	−	0.899871i	$-0.643660\pi$
$373$	−16.8471			−0.872311			−0.436155	+	0.899871i	$0.643660\pi$
$374$	−13.3574	−	16.7028i	−0.690695	−	0.863682i
$375$	−1.32077			−0.0682041
$376$	1.34653	−	4.14420i	0.0694421	−	0.213721i
$377$	35.4412	−	25.7495i	1.82531	−	1.32617i
$378$	4.54718	+	3.30372i	0.233882	+	0.169925i
$379$	−8.49120	−	26.1332i	−0.436163	−	1.34237i	−0.891890	−	0.452253i	$-0.850620\pi$
$379$	−8.49120	−	26.1332i	−0.436163	−	1.34237i	0.455726	−	0.890120i	$-0.349380\pi$
$380$	−1.98621	−	6.11293i	−0.101891	−	0.313587i
$381$	−11.7548	−	8.54036i	−0.602217	−	0.437536i
$382$	11.6144	−	8.43835i	0.594244	−	0.431744i
$383$	−9.70098	+	29.8566i	−0.495697	+	1.52560i	0.320171	+	0.947360i	$0.396260\pi$
$383$	−9.70098	+	29.8566i	−0.495697	+	1.52560i	−0.815868	+	0.578239i	$0.803740\pi$
$384$	−1.32077			−0.0674001
$385$	−3.10354	+	1.16962i	−0.158171	+	0.0596093i
$386$	8.48187			0.431716
$387$	1.05500	−	3.24696i	0.0536288	−	0.165052i
$388$	0.443634	−	0.322319i	0.0225221	−	0.0163633i
$389$	0.0931976	+	0.0677120i	0.00472531	+	0.00343314i	0.590145	−	0.807297i	$-0.299070\pi$
$389$	0.0931976	+	0.0677120i	0.00472531	+	0.00343314i	−0.585420	+	0.810730i	$0.699070\pi$
$390$	−2.18172	−	6.71465i	−0.110476	−	0.340010i
$391$	−10.9799	−	33.7928i	−0.555280	−	1.70898i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	−19.5516	+	14.2051i	−0.986247	+	0.716550i
$394$	−1.53692	+	4.73015i	−0.0774288	+	0.238301i
$395$	−7.35859			−0.370251
$396$	4.01572	+	1.10237i	0.201797	+	0.0553960i
$397$	−18.2744			−0.917165			−0.458583	−	0.888652i	$-0.651643\pi$
$397$	−18.2744			−0.917165			−0.458583	+	0.888652i	$0.651643\pi$
$398$	−6.99417	+	21.5259i	−0.350586	+	1.07899i
$399$	6.86794	−	4.98985i	0.343827	−	0.249805i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	9.29049	+	28.5932i	0.463945	+	1.42788i	0.860305	+	0.509780i	$0.170273\pi$
$401$	9.29049	+	28.5932i	0.463945	+	1.42788i	−0.396360	+	0.918095i	$0.629727\pi$
$402$	4.41223	+	13.5794i	0.220062	+	0.677281i
$403$	−7.67443	−	5.57580i	−0.382291	−	0.277750i
$404$	−1.97586	+	1.43554i	−0.0983025	+	0.0714209i
$405$	−1.13001	+	3.47782i	−0.0561508	+	0.172814i
$406$	8.19519			0.406720
$407$	−1.68384	−	36.3845i	−0.0834646	−	1.80351i
$408$	8.51686			0.421648
$409$	9.04298	−	27.8314i	0.447147	−	1.37618i	−0.432966	−	0.901410i	$-0.642533\pi$
$409$	9.04298	−	27.8314i	0.447147	−	1.37618i	0.880112	−	0.474766i	$-0.157467\pi$
$410$	−1.68559	+	1.22465i	−0.0832454	+	0.0604813i
$411$	5.83505	+	4.23941i	0.287822	+	0.209115i
$412$	0.194770	+	0.599440i	0.00959562	+	0.0295323i
$413$	1.68308	+	5.17999i	0.0828190	+	0.254891i
$414$	5.59712	+	4.06655i	0.275084	+	0.199860i
$415$	5.81848	−	4.22737i	0.285618	−	0.207514i
$416$	1.65186	−	5.08391i	0.0809892	−	0.249259i
$417$	6.94051			0.339878
$418$	11.7195	−	17.8072i	0.573221	−	0.870977i
$419$	−17.3655			−0.848362			−0.424181	−	0.905577i	$-0.639438\pi$
$419$	−17.3655			−0.848362			−0.424181	+	0.905577i	$0.639438\pi$
$420$	0.408139	−	1.25612i	0.0199152	−	0.0612925i
$421$	−6.70920	+	4.87452i	−0.326986	+	0.237570i	−0.739151	−	0.673540i	$-0.764773\pi$
$421$	−6.70920	+	4.87452i	−0.326986	+	0.237570i	0.412164	+	0.911109i	$0.364773\pi$
$422$	3.06152	+	2.22433i	0.149033	+	0.108279i
$423$	−1.69068	−	5.20336i	−0.0822034	−	0.252996i
$424$	−2.65485	−	8.17078i	−0.128931	−	0.396808i
$425$	5.21689	+	3.79029i	0.253056	+	0.183856i
$426$	−12.6252	+	9.17277i	−0.611695	+	0.444422i
$427$	−4.14044	+	12.7430i	−0.200370	+	0.616675i
$428$	11.4352			0.552743
$429$	12.8731	−	19.5600i	0.621520	−	0.944366i
$430$	−2.71912			−0.131127
$431$	4.12206	−	12.6864i	0.198553	−	0.611083i	−0.801364	−	0.598177i	$-0.795892\pi$
$431$	4.12206	−	12.6864i	0.198553	−	0.611083i	0.999917	−	0.0129056i	$-0.00410808\pi$
$432$	−4.54718	+	3.30372i	−0.218776	+	0.158950i
$433$	11.9977	+	8.71686i	0.576574	+	0.418906i	0.837487	−	0.546457i	$-0.184024\pi$
$433$	11.9977	+	8.71686i	0.576574	+	0.418906i	−0.260913	+	0.965362i	$0.584024\pi$
$434$	−0.548378	−	1.68773i	−0.0263230	−	0.0810138i
$435$	3.34478	+	10.2942i	0.160370	+	0.493568i
$436$	6.72764	+	4.88792i	0.322196	+	0.234089i
$437$	28.6527	−	20.8174i	1.37064	−	0.995830i
$438$	2.26457	−	6.96962i	0.108205	−	0.333021i
$439$	−6.08156			−0.290257			−0.145128	−	0.989413i	$-0.546360\pi$
$439$	−6.08156			−0.290257			−0.145128	+	0.989413i	$0.546360\pi$
$440$	−0.153326	−	3.31308i	−0.00730951	−	0.157945i
$441$	−1.25558			−0.0597894
$442$	−10.6519	+	32.7832i	−0.506660	+	1.55934i
$443$	16.0663	−	11.6728i	0.763331	−	0.554593i	−0.136599	−	0.990626i	$-0.543617\pi$
$443$	16.0663	−	11.6728i	0.763331	−	0.554593i	0.899930	+	0.436034i	$0.143617\pi$
$444$	11.7346	+	8.52569i	0.556899	+	0.404611i
$445$	−1.66868	−	5.13565i	−0.0791028	−	0.243453i
$446$	6.95720	+	21.4121i	0.329433	+	1.01389i
$447$	9.84377	+	7.15191i	0.465594	+	0.338274i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	0.249234	−	0.767064i	0.0117621	−	0.0362000i	−0.945003	−	0.327061i	$-0.893942\pi$
$449$	0.249234	−	0.767064i	0.0117621	−	0.0362000i	0.956765	+	0.290861i	$0.0939417\pi$
$450$	−1.25558			−0.0591885
$451$	−6.66368	−	1.82927i	−0.313781	−	0.0861368i
$452$	−20.1474			−0.947656
$453$	−5.82714	+	17.9341i	−0.273783	+	0.842617i
$454$	8.81804	−	6.40668i	0.413851	−	0.300681i
$455$	4.32463	+	3.14203i	0.202742	+	0.147301i
$456$	2.62332	+	8.07375i	0.122848	+	0.378088i
$457$	−9.25040	−	28.4698i	−0.432716	−	1.33176i	−0.895409	−	0.445244i	$-0.853117\pi$
$457$	−9.25040	−	28.4698i	−0.432716	−	1.33176i	0.462694	−	0.886518i	$-0.346883\pi$
$458$	2.56818	+	1.86589i	0.120003	+	0.0871875i
$459$	29.3221	−	21.3038i	1.36864	−	0.994376i
$460$	1.70273	−	5.24047i	0.0793903	−	0.244338i
$461$	33.4831			1.55946			0.779732	−	0.626114i	$-0.215355\pi$
$461$	33.4831			1.55946			0.779732	+	0.626114i	$0.215355\pi$
$462$	4.09906	−	1.54479i	0.190705	−	0.0718703i
$463$	−29.7511			−1.38265			−0.691324	−	0.722545i	$-0.742972\pi$
$463$	−29.7511			−1.38265			−0.691324	+	0.722545i	$0.742972\pi$
$464$	−2.53245	+	7.79409i	−0.117566	+	0.361832i
$465$	1.89619	−	1.37766i	0.0879335	−	0.0638874i
$466$	20.7370	+	15.0663i	0.960621	+	0.697932i
$467$	−2.05513	−	6.32503i	−0.0950999	−	0.292688i	0.892180	−	0.451680i	$-0.149175\pi$
$467$	−2.05513	−	6.32503i	−0.0950999	−	0.292688i	−0.987280	+	0.158993i	$0.949175\pi$
$468$	−2.07404	−	6.38324i	−0.0958725	−	0.295065i
$469$	−8.74596	−	6.35431i	−0.403851	−	0.293415i
$470$	−3.52527	+	2.56126i	−0.162609	+	0.118142i
$471$	−6.09918	+	18.7713i	−0.281035	+	0.864937i
$472$	−5.44657			−0.250699
$473$	−5.63243	−	7.04309i	−0.258980	−	0.323842i
$474$	9.71897			0.446407
$475$	−1.98621	+	6.11293i	−0.0911337	+	0.280481i
$476$	−5.21689	+	3.79029i	−0.239116	+	0.173728i
$477$	−8.72687	−	6.34044i	−0.399576	−	0.290309i
$478$	−5.42833	−	16.7067i	−0.248286	−	0.764146i
$479$	−5.53996	−	17.0502i	−0.253127	−	0.779046i	−0.994193	−	0.107613i	$-0.965679\pi$
$479$	−5.53996	−	17.0502i	−0.253127	−	0.779046i	0.741066	−	0.671433i	$-0.234321\pi$
$480$	1.06852	+	0.776327i	0.0487711	+	0.0354343i
$481$	−47.4934	+	34.5060i	−2.16551	+	1.57334i
$482$	1.74034	−	5.35623i	0.0792705	−	0.243970i
$483$	7.27763			0.331144
$484$	8.26398	−	7.25993i	0.375636	−	0.329997i
$485$	−0.548361			−0.0248998
$486$	−3.71812	+	11.4432i	−0.168657	+	0.519074i
$487$	−30.1147	+	21.8796i	−1.36463	+	0.991461i	−0.366493	+	0.930421i	$0.619442\pi$
$487$	−30.1147	+	21.8796i	−1.36463	+	0.991461i	−0.998135	+	0.0610402i	$0.980558\pi$
$488$	−10.8398	−	7.87558i	−0.490695	−	0.356511i
$489$	−6.84377	−	21.0630i	−0.309486	−	0.952500i
$490$	0.309017	+	0.951057i	0.0139600	+	0.0429644i
$491$	17.5690	+	12.7646i	0.792878	+	0.576060i	0.908816	−	0.417197i	$-0.136987\pi$
$491$	17.5690	+	12.7646i	0.792878	+	0.576060i	−0.115938	+	0.993256i	$0.536987\pi$
$492$	2.22627	−	1.61748i	0.100368	−	0.0729216i
$493$	16.3303	−	50.2596i	0.735481	−	2.26358i
$494$	−34.3585			−1.54586
$495$	−2.60083	−	3.25221i	−0.116899	−	0.146176i
$496$	1.77459			0.0796813
$497$	3.65122	−	11.2373i	0.163780	−	0.504062i
$498$	−7.68485	+	5.58337i	−0.344366	+	0.250197i
$499$	12.7682	+	9.27663i	0.571583	+	0.415279i	0.835680	−	0.549217i	$-0.185074\pi$
$499$	12.7682	+	9.27663i	0.571583	+	0.415279i	−0.264097	+	0.964496i	$0.585074\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−2.53171	−	7.79179i	−0.113108	−	0.348111i
$502$	−11.5756	−	8.41019i	−0.516646	−	0.375365i
$503$	7.24898	−	5.26670i	0.323216	−	0.234830i	−0.414330	−	0.910127i	$-0.635984\pi$
$503$	7.24898	−	5.26670i	0.323216	−	0.234830i	0.737547	+	0.675296i	$0.235984\pi$
$504$	0.387995	−	1.19412i	0.0172827	−	0.0531905i
$505$	2.44229			0.108681
$506$	17.1010	−	6.44478i	0.760233	−	0.286506i
$507$	−20.5706			−0.913573
$508$	−3.39949	+	10.4626i	−0.150828	+	0.464201i
$509$	−35.2424	+	25.6051i	−1.56209	+	1.13493i	−0.627823	+	0.778356i	$0.716054\pi$
$509$	−35.2424	+	25.6051i	−1.56209	+	1.13493i	−0.934269	+	0.356570i	$0.883946\pi$
$510$	−6.89029	−	5.00609i	−0.305107	−	0.221673i
$511$	1.71459	+	5.27695i	0.0758488	+	0.233439i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	29.2271	+	21.2347i	1.29041	+	0.937535i
$514$	6.22372	−	4.52179i	0.274516	−	0.199448i
$515$	0.194770	−	0.599440i	0.00858259	−	0.0264145i
$516$	3.59132			0.158099
$517$	−13.9365	−	3.82576i	−0.612928	−	0.168257i
$518$	−10.9821			−0.482525
$519$	2.99985	−	9.23258i	0.131679	−	0.405265i
$520$	−4.32463	+	3.14203i	−0.189648	+	0.137787i
$521$	−0.705975	−	0.512921i	−0.0309293	−	0.0224715i	0.572213	−	0.820105i	$-0.306085\pi$
$521$	−0.705975	−	0.512921i	−0.0309293	−	0.0224715i	−0.603143	+	0.797633i	$0.706085\pi$
$522$	3.17969	+	9.78608i	0.139171	+	0.428325i
$523$	−6.93170	−	21.3336i	−0.303102	−	0.932853i	−0.980379	−	0.197124i	$-0.936840\pi$
$523$	−6.93170	−	21.3336i	−0.303102	−	0.932853i	0.677276	−	0.735729i	$-0.263160\pi$
$524$	14.8032	+	10.7552i	0.646681	+	0.469841i
$525$	−1.06852	+	0.776327i	−0.0466341	+	0.0338817i
$526$	−2.10630	+	6.48252i	−0.0918390	+	0.282651i
$527$	−11.4433			−0.498478
$528$	0.202507	+	4.37580i	0.00881300	+	0.190432i
$529$	7.36183			0.320080
$530$	−2.65485	+	8.17078i	−0.115319	+	0.354916i
$531$	−5.53253	+	4.01962i	−0.240091	+	0.174437i
$532$	−5.19997	−	3.77800i	−0.225447	−	0.163797i
$533$	3.44166	+	10.5923i	0.149075	+	0.458805i
$534$	2.20393	+	6.78300i	0.0953734	+	0.293529i
$535$	−9.25131	−	6.72147i	−0.399969	−	0.290594i
$536$	8.74596	−	6.35431i	0.377768	−	0.274464i
$537$	1.79757	−	5.53236i	0.0775710	−	0.238739i
$538$	3.79822			0.163753
$539$	−1.82334	+	2.77046i	−0.0785366	+	0.119332i
$540$	5.62062			0.241873
$541$	−3.10353	+	9.55170i	−0.133431	+	0.410660i	−0.995343	−	0.0963994i	$-0.969267\pi$
$541$	−3.10353	+	9.55170i	−0.133431	+	0.410660i	0.861911	+	0.507059i	$0.169267\pi$
$542$	−1.90448	+	1.38368i	−0.0818043	+	0.0594343i
$543$	−11.8510	−	8.61024i	−0.508574	−	0.369501i
$544$	−1.99267	−	6.13282i	−0.0854352	−	0.262942i
$545$	−2.56973	−	7.90882i	−0.110075	−	0.338777i
$546$	−5.71182	−	4.14988i	−0.244444	−	0.177599i
$547$	12.4301	−	9.03101i	0.531473	−	0.386138i	−0.289435	−	0.957198i	$-0.593467\pi$
$547$	12.4301	−	9.03101i	0.531473	−	0.386138i	0.820909	+	0.571060i	$0.193467\pi$
$548$	1.68750	−	5.19358i	0.0720863	−	0.221859i
$549$	−16.8231			−0.717994
$550$	−1.82334	+	2.77046i	−0.0777473	+	0.118133i
$551$	52.6747			2.24402
$552$	−2.24891	+	6.92144i	−0.0957200	+	0.294596i
$553$	−5.95322	+	4.32527i	−0.253157	+	0.183929i
$554$	14.1100	+	10.2515i	0.599477	+	0.435545i
$555$	−4.48222	−	13.7948i	−0.190260	−	0.585559i
$556$	−1.62386	−	4.99772i	−0.0688669	−	0.211951i
$557$	37.0667	+	26.9306i	1.57057	+	1.14108i	0.926610	+	0.376025i	$0.122709\pi$
$557$	37.0667	+	26.9306i	1.57057	+	1.14108i	0.643959	+	0.765060i	$0.277291\pi$
$558$	1.80260	−	1.30966i	0.0763100	−	0.0554424i
$559$	−4.49160	+	13.8237i	−0.189975	+	0.584681i
$560$	−1.00000			−0.0422577
$561$	−1.30585	−	28.2170i	−0.0551332	−	1.19132i
$562$	−22.6310			−0.954632
$563$	−5.28969	+	16.2800i	−0.222934	+	0.686120i	0.775561	+	0.631273i	$0.217467\pi$
$563$	−5.28969	+	16.2800i	−0.222934	+	0.686120i	−0.998495	+	0.0548469i	$0.982533\pi$
$564$	4.65606	−	3.38282i	0.196055	−	0.142443i
$565$	16.2996	+	11.8424i	0.685730	+	0.498212i
$566$	−8.36187	−	25.7352i	−0.351476	−	1.08173i
$567$	1.13001	+	3.47782i	0.0474561	+	0.146055i
$568$	9.55902	+	6.94504i	0.401088	+	0.291407i
$569$	−14.6161	+	10.6193i	−0.612741	+	0.445182i	−0.850378	−	0.526172i	$-0.823627\pi$
$569$	−14.6161	+	10.6193i	−0.612741	+	0.445182i	0.237638	+	0.971354i	$0.423627\pi$
$570$	2.62332	−	8.07375i	0.109879	−	0.338172i
$571$	13.8533			0.579743			0.289872	−	0.957066i	$-0.406387\pi$
$571$	13.8533			0.579743			0.289872	+	0.957066i	$0.406387\pi$
$572$	−17.0967	−	4.69325i	−0.714847	−	0.196235i
$573$	18.9612			0.792114
$574$	−0.643838	+	1.98153i	−0.0268733	+	0.0827075i
$575$	−4.45781	+	3.23879i	−0.185904	+	0.135067i
$576$	1.01578	+	0.738009i	0.0423243	+	0.0307504i
$577$	12.0971	+	37.2309i	0.503607	+	1.54994i	0.803099	+	0.595845i	$0.203183\pi$
$577$	12.0971	+	37.2309i	0.503607	+	1.54994i	−0.299492	+	0.954099i	$0.596817\pi$
$578$	7.59632	+	23.3791i	0.315965	+	0.972441i
$579$	9.06306	+	6.58470i	0.376648	+	0.273651i
$580$	6.63005	−	4.81701i	0.275298	−	0.200016i
$581$	2.22246	−	6.84003i	0.0922032	−	0.283772i
$582$	0.724257			0.0300214
$583$	−26.6634	+	10.0485i	−1.10429	+	0.416167i
$584$	−5.54852			−0.229599
$585$	−2.07404	+	6.38324i	−0.0857510	+	0.263914i
$586$	16.3387	−	11.8708i	0.674947	−	0.490378i
$587$	20.5275	+	14.9141i	0.847262	+	0.615572i	0.924390	−	0.381450i	$-0.124575\pi$
$587$	20.5275	+	14.9141i	0.847262	+	0.615572i	−0.0771280	+	0.997021i	$0.524575\pi$
$588$	−0.408139	−	1.25612i	−0.0168314	−	0.0518017i
$589$	−3.52471	−	10.8479i	−0.145233	−	0.446981i
$590$	4.40637	+	3.20141i	0.181407	+	0.131800i
$591$	−5.31437	+	3.86112i	−0.218604	+	0.158825i
$592$	3.39365	−	10.4446i	0.139478	−	0.429270i
$593$	24.5601			1.00856			0.504280	−	0.863540i	$-0.331758\pi$
$593$	24.5601			1.00856			0.504280	+	0.863540i	$0.331758\pi$
$594$	11.6427	+	14.5586i	0.477705	+	0.597347i
$595$	6.44843			0.264360
$596$	2.84682	−	8.76161i	0.116610	−	0.358890i
$597$	−24.1845	+	17.5711i	−0.989807	+	0.719137i
$598$	−23.8294	−	17.3131i	−0.974456	−	0.707984i
$599$	−10.9614	−	33.7358i	−0.447872	−	1.37841i	−0.879303	−	0.476262i	$-0.841991\pi$
$599$	−10.9614	−	33.7358i	−0.447872	−	1.37841i	0.431432	−	0.902146i	$-0.358009\pi$
$600$	−0.408139	−	1.25612i	−0.0166622	−	0.0512810i
$601$	11.9242	+	8.66346i	0.486399	+	0.353390i	0.803798	−	0.594902i	$-0.202809\pi$
$601$	11.9242	+	8.66346i	0.486399	+	0.353390i	−0.317399	+	0.948292i	$0.602809\pi$
$602$	−2.19981	+	1.59826i	−0.0896576	+	0.0651400i
$603$	4.19445	−	12.9092i	0.170811	−	0.525703i
$604$	14.2773			0.580936
$605$	−10.9530	+	1.01596i	−0.445302	+	0.0413046i
$606$	−3.22570			−0.131035
$607$	1.88477	−	5.80072i	0.0765003	−	0.235444i	−0.905492	−	0.424362i	$-0.860498\pi$
$607$	1.88477	−	5.80072i	0.0765003	−	0.235444i	0.981993	+	0.188919i	$0.0604982\pi$
$608$	5.19997	−	3.77800i	0.210887	−	0.153218i
$609$	8.75674	+	6.36215i	0.354841	+	0.257807i
$610$	4.14044	+	12.7430i	0.167641	+	0.515947i
$611$	7.19794	+	22.1530i	0.291197	+	0.896214i
$612$	−6.55020	−	4.75900i	−0.264776	−	0.192371i
$613$	−14.6342	+	10.6324i	−0.591071	+	0.429438i	−0.842698	−	0.538386i	$-0.819034\pi$
$613$	−14.6342	+	10.6324i	−0.591071	+	0.429438i	0.251627	+	0.967824i	$0.419034\pi$
$614$	7.54397	−	23.2180i	0.304450	−	0.937001i
$615$	−2.75182			−0.110964
$616$	−2.07142	−	2.59021i	−0.0834600	−	0.104363i
$617$	15.9814			0.643386			0.321693	−	0.946844i	$-0.395748\pi$
$617$	15.9814			0.643386			0.321693	+	0.946844i	$0.395748\pi$
$618$	−0.257245	+	0.791720i	−0.0103479	+	0.0318477i
$619$	−4.21055	+	3.05914i	−0.169236	+	0.122957i	−0.669179	−	0.743101i	$-0.733354\pi$
$619$	−4.21055	+	3.05914i	−0.169236	+	0.122957i	0.499943	+	0.866058i	$0.333354\pi$
$620$	−1.43567	−	1.04308i	−0.0576579	−	0.0418909i
$621$	9.57041	+	29.4547i	0.384047	+	1.18198i
$622$	7.80783	+	24.0300i	0.313065	+	0.963516i
$623$	−4.36865	−	3.17401i	−0.175026	−	0.127164i
$624$	5.71182	−	4.14988i	0.228656	−	0.166128i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−18.1747			−0.726407
$627$	26.3468	−	9.92918i	1.05219	−	0.396533i
$628$	14.9439			0.596325
$629$	−21.8837	+	67.3511i	−0.872561	+	2.68547i
$630$	−1.01578	+	0.738009i	−0.0404698	+	0.0294030i
$631$	27.7260	+	20.1441i	1.10376	+	0.801925i	0.981669	−	0.190594i	$-0.0610415\pi$
$631$	27.7260	+	20.1441i	1.10376	+	0.801925i	0.122086	+	0.992519i	$0.461041\pi$
$632$	−2.27393	−	6.99843i	−0.0904520	−	0.278383i
$633$	1.54450	+	4.75348i	0.0613884	+	0.188934i
$634$	−8.63537	−	6.27397i	−0.342954	−	0.249171i
$635$	8.89999	−	6.46622i	0.353185	−	0.256604i
$636$	3.50643	−	10.7917i	0.139039	−	0.427919i
$637$	5.34554			0.211798
$638$	26.2107	+	7.19518i	1.03769	+	0.284860i
$639$	14.8354			0.586879
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	−31.0577	+	22.5647i	−1.22670	+	0.891252i	−0.996639	−	0.0819228i	$-0.973894\pi$
$641$	−31.0577	+	22.5647i	−1.22670	+	0.891252i	−0.230065	+	0.973175i	$0.573894\pi$
$642$	12.2188	+	8.87749i	0.482238	+	0.350366i
$643$	1.50320	+	4.62637i	0.0592804	+	0.182446i	0.976312	−	0.216369i	$-0.0694214\pi$
$643$	1.50320	+	4.62637i	0.0592804	+	0.182446i	−0.917031	+	0.398815i	$0.869421\pi$
$644$	−1.70273	−	5.24047i	−0.0670970	−	0.206503i
$645$	−2.90544	−	2.11092i	−0.114401	−	0.0831175i
$646$	−33.5316	+	24.3622i	−1.31928	+	0.958516i
$647$	4.21546	−	12.9738i	0.165727	−	0.510054i	−0.833362	−	0.552727i	$-0.813587\pi$
$647$	4.21546	−	12.9738i	0.165727	−	0.510054i	0.999089	+	0.0426727i	$0.0135873\pi$
$648$	−3.65680			−0.143653
$649$	0.835099	+	18.0449i	0.0327805	+	0.708325i
$650$	5.34554			0.209669
$651$	0.724279	−	2.22910i	0.0283867	−	0.0873653i
$652$	−13.5658	+	9.85612i	−0.531277	+	0.385995i
$653$	−17.2511	−	12.5336i	−0.675086	−	0.490479i	0.196638	−	0.980476i	$-0.436998\pi$
$653$	−17.2511	−	12.5336i	−0.675086	−	0.490479i	−0.871724	+	0.489997i	$0.836998\pi$
$654$	3.39401	+	10.4457i	0.132716	+	0.408459i
$655$	−5.65432	−	17.4022i	−0.220933	−	0.679961i
$656$	−1.68559	−	1.22465i	−0.0658112	−	0.0478147i
$657$	−5.63609	+	4.09486i	−0.219885	+	0.159756i
$658$	−1.34653	+	4.14420i	−0.0524933	+	0.161558i
$659$	−12.6150			−0.491409			−0.245704	−	0.969345i	$-0.579019\pi$
$659$	−12.6150			−0.491409			−0.245704	+	0.969345i	$0.579019\pi$
$660$	2.40820	−	3.65913i	0.0937391	−	0.142431i
$661$	32.2901			1.25594			0.627969	−	0.778238i	$-0.283886\pi$
$661$	32.2901			1.25594			0.627969	+	0.778238i	$0.283886\pi$
$662$	−3.01496	+	9.27908i	−0.117180	+	0.360642i
$663$	−36.8323	+	26.7602i	−1.43045	+	1.03928i
$664$	5.81848	+	4.22737i	0.225801	+	0.164054i
$665$	1.98621	+	6.11293i	0.0770220	+	0.237049i
$666$	−4.26099	−	13.1140i	−0.165110	−	0.508156i
$667$	36.5326	+	26.5425i	1.41455	+	1.02773i
$668$	−5.01837	+	3.64606i	−0.194166	+	0.141070i
$669$	−9.18884	+	28.2803i	−0.355261	+	1.09338i
$670$	−10.8106			−0.417650
$671$	−24.4304	+	37.1207i	−0.943125	+	1.43303i
$672$	1.32077			0.0509497
$673$	2.40256	−	7.39433i	0.0926120	−	0.285030i	−0.894012	−	0.448043i	$-0.852121\pi$
$673$	2.40256	−	7.39433i	0.0926120	−	0.285030i	0.986624	+	0.163013i	$0.0521211\pi$
$674$	−8.20845	+	5.96379i	−0.316178	+	0.229717i
$675$	−4.54718	−	3.30372i	−0.175021	−	0.127160i
$676$	4.81286	+	14.8125i	0.185110	+	0.569711i
$677$	3.43893	+	10.5839i	0.132169	+	0.406774i	0.995139	−	0.0984810i	$-0.0313984\pi$
$677$	3.43893	+	10.5839i	0.132169	+	0.406774i	−0.862970	+	0.505255i	$0.831398\pi$
$678$	−21.5280	−	15.6410i	−0.826777	−	0.600689i
$679$	−0.443634	+	0.322319i	−0.0170251	+	0.0123695i
$680$	−1.99267	+	6.13282i	−0.0764155	+	0.235183i
$681$	14.3960			0.551654
$682$	−0.272090	−	5.87935i	−0.0104189	−	0.225132i
$683$	−6.91240			−0.264496			−0.132248	−	0.991217i	$-0.542219\pi$
$683$	−6.91240			−0.264496			−0.132248	+	0.991217i	$0.542219\pi$
$684$	2.49384	−	7.67525i	0.0953544	−	0.293471i
$685$	−4.41793	+	3.20981i	−0.168800	+	0.122641i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	1.29562	+	3.98750i	0.0494308	+	0.152133i
$688$	−0.840253	−	2.58603i	−0.0320343	−	0.0985916i
$689$	37.1541	+	26.9940i	1.41546	+	1.02839i
$690$	5.88773	−	4.27768i	0.224142	−	0.162849i
$691$	9.67837	−	29.7870i	0.368183	−	1.13315i	−0.579781	−	0.814772i	$-0.696862\pi$
$691$	9.67837	−	29.7870i	0.368183	−	1.13315i	0.947964	−	0.318377i	$-0.103138\pi$
$692$	−7.35006			−0.279407
$693$	−4.01572	−	1.10237i	−0.152545	−	0.0418754i
$694$	−21.1756			−0.803815
$695$	−1.62386	+	4.99772i	−0.0615964	+	0.189574i
$696$	−8.75674	+	6.36215i	−0.331923	+	0.241157i
$697$	10.8694	+	7.89709i	0.411708	+	0.299123i
$698$	−1.41821	−	4.36481i	−0.0536801	−	0.165210i
$699$	10.4615	+	32.1973i	0.395692	+	1.21781i
$700$	0.809017	+	0.587785i	0.0305780	+	0.0222162i
$701$	9.83296	−	7.14407i	0.371386	−	0.269828i	−0.386399	−	0.922332i	$-0.626281\pi$
$701$	9.83296	−	7.14407i	0.371386	−	0.269828i	0.757785	+	0.652504i	$0.226281\pi$
$702$	9.28449	−	28.5747i	0.350420	−	1.07848i
$703$	−70.5875			−2.66226
$704$	3.10354	−	1.16962i	0.116969	−	0.0440817i
$705$	−5.75520			−0.216753
$706$	9.95325	−	30.6330i	0.374595	−	1.15289i
$707$	1.97586	−	1.43554i	0.0743097	−	0.0539891i
$708$	−5.81978	−	4.22832i	−0.218721	−	0.158910i
$709$	−10.0112	−	30.8114i	−0.375979	−	1.15714i	−0.942816	−	0.333315i	$-0.891833\pi$
$709$	−10.0112	−	30.8114i	−0.375979	−	1.15714i	0.566837	−	0.823830i	$-0.308167\pi$
$710$	−3.65122	−	11.2373i	−0.137028	−	0.421729i
$711$	−7.47473	−	5.43071i	−0.280324	−	0.203667i
$712$	4.36865	−	3.17401i	0.163722	−	0.118951i
$713$	3.02165	−	9.29967i	0.113162	−	0.348275i
$714$	−8.51686			−0.318736
$715$	11.0729	+	13.8461i	0.414102	+	0.517814i
$716$	−4.40431			−0.164597
$717$	7.16955	−	22.0656i	0.267752	−	0.824056i
$718$	5.29122	−	3.84430i	0.197467	−	0.143468i
$719$	−9.97153	−	7.24474i	−0.371875	−	0.270183i	0.386113	−	0.922452i	$-0.373818\pi$
$719$	−9.97153	−	7.24474i	−0.371875	−	0.270183i	−0.757988	+	0.652268i	$0.773818\pi$
$720$	−0.387995	−	1.19412i	−0.0144597	−	0.0445024i
$721$	−0.194770	−	0.599440i	−0.00725361	−	0.0223243i
$722$	−18.0516	−	13.1152i	−0.671810	−	0.488098i
$723$	6.01778	−	4.37218i	0.223804	−	0.162603i
$724$	−3.42731	+	10.5482i	−0.127375	+	0.392019i
$725$	−8.19519			−0.304362
$726$	14.4663	−	1.34185i	0.536896	−	0.0498006i
$727$	2.42914			0.0900918			0.0450459	−	0.998985i	$-0.485657\pi$
$727$	2.42914			0.0900918			0.0450459	+	0.998985i	$0.485657\pi$
$728$	−1.65186	+	5.08391i	−0.0612221	+	0.188422i
$729$	−21.7318	+	15.7891i	−0.804881	+	0.584780i
$730$	4.48885	+	3.26134i	0.166140	+	0.120708i
$731$	5.41831	+	16.6758i	0.200403	+	0.616778i
$732$	−5.46855	−	16.8305i	−0.202123	−	0.622072i
$733$	−37.3546	−	27.1397i	−1.37972	−	1.00243i	−0.996906	−	0.0786056i	$-0.974953\pi$
$733$	−37.3546	−	27.1397i	−1.37972	−	1.00243i	−0.382819	−	0.923823i	$-0.625047\pi$
$734$	2.41537	−	1.75487i	0.0891529	−	0.0647733i
$735$	−0.408139	+	1.25612i	−0.0150544	+	0.0463328i
$736$	5.51016			0.203107
$737$	−22.3933	−	28.0018i	−0.824868	−	1.03146i
$738$	−2.61600			−0.0962963
$739$	15.1017	−	46.4781i	0.555524	−	1.70973i	−0.139033	−	0.990288i	$-0.544399\pi$
$739$	15.1017	−	46.4781i	0.555524	−	1.70973i	0.694557	−	0.719438i	$-0.255601\pi$
$740$	−8.88469	+	6.45511i	−0.326608	+	0.237294i
$741$	−36.7128	−	26.6734i	−1.34868	−	0.979873i
$742$	2.65485	+	8.17078i	0.0974626	+	0.299959i
$743$	6.09116	+	18.7467i	0.223463	+	0.687748i	0.998444	+	0.0557637i	$0.0177593\pi$
$743$	6.09116	+	18.7467i	0.223463	+	0.687748i	−0.774981	+	0.631984i	$0.782241\pi$
$744$	1.89619	+	1.37766i	0.0695176	+	0.0505075i
$745$	−7.45307	+	5.41497i	−0.273059	+	0.198389i
$746$	−5.20605	+	16.0226i	−0.190607	+	0.586628i
$747$	9.03015			0.330396
$748$	−20.0130	+	7.54220i	−0.731747	+	0.275770i
$749$	−11.4352			−0.417835
$750$	−0.408139	+	1.25612i	−0.0149031	+	0.0458671i
$751$	42.2037	−	30.6628i	1.54004	−	1.11890i	0.589724	−	0.807605i	$-0.299237\pi$
$751$	42.2037	−	30.6628i	1.54004	−	1.11890i	0.950313	−	0.311297i	$-0.100763\pi$
$752$	−3.52527	−	2.56126i	−0.128553	−	0.0933994i
$753$	−5.83977	−	17.9730i	−0.212813	−	0.654971i
$754$	−13.5373	−	41.6636i	−0.493000	−	1.51730i
$755$	−11.5506	−	8.39201i	−0.420370	−	0.305416i
$756$	4.54718	−	3.30372i	0.165379	−	0.120155i
$757$	−10.1054	+	31.1011i	−0.367285	+	1.13039i	0.581252	+	0.813724i	$0.302563\pi$
$757$	−10.1054	+	31.1011i	−0.367285	+	1.13039i	−0.948537	+	0.316665i	$0.897437\pi$
$758$	−27.4781			−0.998049
$759$	23.2761	+	6.38959i	0.844868	+	0.231927i
$760$	−6.42752			−0.233151
$761$	7.50933	−	23.1113i	0.272213	−	0.837785i	−0.717730	−	0.696321i	$-0.754819\pi$
$761$	7.50933	−	23.1113i	0.272213	−	0.837785i	0.989943	−	0.141464i	$-0.0451810\pi$
$762$	−11.7548	+	8.54036i	−0.425832	+	0.309385i
$763$	−6.72764	−	4.88792i	−0.243557	−	0.176955i
$764$	−4.43630	−	13.6535i	−0.160500	−	0.493968i
$765$	2.50195	+	7.70022i	0.0904584	+	0.278402i
$766$	25.3975	+	18.4524i	0.917649	+	0.666711i
$767$	23.5544	−	17.1133i	0.850500	−	0.617924i
$768$	−0.408139	+	1.25612i	−0.0147275	+	0.0453264i
$769$	34.3945			1.24030			0.620148	−	0.784485i	$-0.287073\pi$
$769$	34.3945			1.24030			0.620148	+	0.784485i	$0.287073\pi$
$770$	0.153326	+	3.31308i	0.00552547	+	0.119395i
$771$	10.1606			0.365924
$772$	2.62104	−	8.06674i	0.0943333	−	0.290328i
$773$	−9.48558	+	6.89167i	−0.341172	+	0.247876i	−0.745156	−	0.666890i	$-0.767625\pi$
$773$	−9.48558	+	6.89167i	−0.341172	+	0.247876i	0.403984	+	0.914766i	$0.367625\pi$
$774$	−2.76203	−	2.00673i	−0.0992791	−	0.0721305i
$775$	0.548378	+	1.68773i	0.0196983	+	0.0606252i
$776$	−0.169453	−	0.521523i	−0.00608301	−	0.0187216i
$777$	−11.7346	−	8.52569i	−0.420976	−	0.305857i
$778$	0.0931976	−	0.0677120i	0.00334130	−	0.00242759i
$779$	−4.13828	+	12.7363i	−0.148269	+	0.456326i
$780$	−7.06020			−0.252796
$781$	21.5438	−	32.7346i	0.770898	−	1.17134i
$782$	−35.5318			−1.27062
$783$	−14.2340	+	43.8076i	−0.508680	+	1.56556i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−12.0898	−	8.78378i	−0.431505	−	0.313507i
$786$	7.46804	+	22.9843i	0.266376	+	0.819822i
$787$	3.44643	+	10.6070i	0.122852	+	0.378100i	0.993504	−	0.113800i	$-0.0363024\pi$
$787$	3.44643	+	10.6070i	0.122852	+	0.378100i	−0.870652	+	0.491900i	$0.836302\pi$
$788$	4.02370	+	2.92339i	0.143338	+	0.104141i
$789$	−7.28318	+	5.29154i	−0.259288	+	0.188384i
$790$	−2.27393	+	6.99843i	−0.0809027	+	0.248993i
$791$	20.1474			0.716360
$792$	2.28934	−	3.47852i	0.0813481	−	0.123604i
$793$	71.6234			2.54342
$794$	−5.64710	+	17.3800i	−0.200408	+	0.616792i
$795$	−9.17996	+	6.66963i	−0.325580	+	0.236548i
$796$	18.3110	+	13.3037i	0.649016	+	0.471537i
$797$	−4.35682	−	13.4089i	−0.154327	−	0.474969i	0.843765	−	0.536712i	$-0.180334\pi$
$797$	−4.35682	−	13.4089i	−0.154327	−	0.474969i	−0.998092	+	0.0617436i	$0.980334\pi$
$798$	−2.62332	−	8.07375i	−0.0928646	−	0.285808i
$799$	22.7324	+	16.5161i	0.804216	+	0.584297i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	2.09515	−	6.44821i	0.0740285	−	0.227836i
$802$	30.0646			1.06162
$803$	0.850730	+	18.3827i	0.0300216	+	0.648711i
$804$	14.2783			0.503556
$805$	−1.70273	+	5.24047i	−0.0600134	+	0.184702i
$806$	−7.67443	+	5.57580i	−0.270320	+	0.196399i
$807$	4.05848	+	2.94866i	0.142865	+	0.103798i
$808$	0.754710	+	2.32276i	0.0265506	+	0.0817143i
$809$	13.8360	+	42.5828i	0.486447	+	1.49713i	0.829874	+	0.557951i	$0.188412\pi$
$809$	13.8360	+	42.5828i	0.486447	+	1.49713i	−0.343426	+	0.939180i	$0.611588\pi$
$810$	2.95841	+	2.14941i	0.103948	+	0.0755226i
$811$	−27.0771	+	19.6727i	−0.950807	+	0.690802i	−0.950998	−	0.309198i	$-0.899939\pi$
$811$	−27.0771	+	19.6727i	−0.950807	+	0.690802i	0.000190568		1.00000i	$0.499939\pi$
$812$	2.53245	−	7.79409i	0.0888717	−	0.273519i
$813$	−3.10917			−0.109043
$814$	−35.1241	−	9.64201i	−1.23110	−	0.337952i
$815$	16.7682			0.587366
$816$	2.63186	−	8.10002i	0.0921334	−	0.283557i
$817$	−14.1393	+	10.2728i	−0.494672	+	0.359400i
$818$	−23.6748	−	17.2008i	−0.827771	−	0.601411i
$819$	2.07404	+	6.38324i	0.0724728	+	0.223048i
$820$	0.643838	+	1.98153i	0.0224838	+	0.0691980i
$821$	36.0727	+	26.2084i	1.25895	+	0.914678i	0.998706	−	0.0508653i	$-0.0161979\pi$
$821$	36.0727	+	26.2084i	1.25895	+	0.914678i	0.260241	+	0.965544i	$0.416198\pi$
$822$	5.83505	−	4.23941i	0.203521	−	0.147866i
$823$	−12.6842	+	39.0380i	−0.442144	+	1.36078i	0.443441	+	0.896304i	$0.353758\pi$
$823$	−12.6842	+	39.0380i	−0.442144	+	1.36078i	−0.885585	+	0.464477i	$0.846242\pi$
$824$	0.630289			0.0219571
$825$	−4.09906	+	1.54479i	−0.142711	+	0.0537828i
$826$	5.44657			0.189510
$827$	10.5947	−	32.6071i	0.368413	−	1.13386i	−0.579403	−	0.815041i	$-0.696714\pi$
$827$	10.5947	−	32.6071i	0.368413	−	1.13386i	0.947816	−	0.318818i	$-0.103286\pi$
$828$	5.59712	−	4.06655i	0.194513	−	0.141322i
$829$	−12.5590	−	9.12463i	−0.436191	−	0.316912i	0.347928	−	0.937521i	$-0.386885\pi$
$829$	−12.5590	−	9.12463i	−0.436191	−	0.316912i	−0.784120	+	0.620610i	$0.786885\pi$
$830$	−2.22246	−	6.84003i	−0.0771428	−	0.237421i
$831$	7.11833	+	21.9080i	0.246932	+	0.759979i
$832$	−4.32463	−	3.14203i	−0.149930	−	0.108930i
$833$	5.21689	−	3.79029i	0.180754	−	0.131326i
$834$	2.14474	−	6.60082i	0.0742661	−	0.228568i
$835$	6.20304			0.214665
$836$	−13.3141	−	16.6486i	−0.460478	−	0.575805i
$837$	9.97428			0.344762
$838$	−5.36625	+	16.5156i	−0.185374	+	0.570522i
$839$	−9.73205	+	7.07075i	−0.335988	+	0.244109i	−0.742967	−	0.669328i	$-0.766582\pi$
$839$	−9.73205	+	7.07075i	−0.335988	+	0.244109i	0.406979	+	0.913437i	$0.366582\pi$
$840$	−1.06852	−	0.776327i	−0.0368675	−	0.0267858i
$841$	11.7924	+	36.2934i	0.406636	+	1.25150i
$842$	2.56269	+	7.88714i	0.0883160	+	0.271809i
$843$	−24.1818	−	17.5691i	−0.832864	−	0.605111i
$844$	3.06152	−	2.22433i	0.105382	−	0.0765645i
$845$	4.81286	−	14.8125i	0.165568	−	0.509565i
$846$	−5.47114			−0.188102
$847$	−8.26398	+	7.25993i	−0.283954	+	0.249454i
$848$	−8.59127			−0.295025
$849$	11.0441	−	33.9902i	0.379032	−	1.16654i
$850$	5.21689	−	3.79029i	0.178938	−	0.130006i
$851$	−48.9560	−	35.5686i	−1.67819	−	1.21928i
$852$	4.82241	+	14.8419i	0.165213	+	0.508473i
$853$	−10.9771	−	33.7839i	−0.375848	−	1.15674i	−0.942905	−	0.333062i	$-0.891918\pi$
$853$	−10.9771	−	33.7839i	−0.375848	−	1.15674i	0.567057	−	0.823678i	$-0.308082\pi$
$854$	10.8398	+	7.87558i	0.370930	+	0.269497i
$855$	−6.52896	+	4.74357i	−0.223286	+	0.162227i
$856$	3.53368	−	10.8756i	0.120779	−	0.371719i
$857$	−48.4891			−1.65636			−0.828178	−	0.560465i	$-0.810622\pi$
$857$	−48.4891			−1.65636			−0.828178	+	0.560465i	$0.810622\pi$
$858$	−14.6247	−	18.2874i	−0.499278	−	0.624323i
$859$	−1.93679			−0.0660823			−0.0330411	−	0.999454i	$-0.510519\pi$
$859$	−1.93679			−0.0660823			−0.0330411	+	0.999454i	$0.510519\pi$
$860$	−0.840253	+	2.58603i	−0.0286524	+	0.0881830i
$861$	−2.22627	+	1.61748i	−0.0758711	+	0.0551236i
$862$	−10.7917	−	7.84063i	−0.367567	−	0.267053i
$863$	6.57611	+	20.2392i	0.223853	+	0.688950i	0.998406	+	0.0564403i	$0.0179751\pi$
$863$	6.57611	+	20.2392i	0.223853	+	0.688950i	−0.774553	+	0.632509i	$0.782025\pi$
$864$	1.73687	+	5.34553i	0.0590894	+	0.181859i
$865$	5.94632	+	4.32026i	0.202181	+	0.146893i
$866$	11.9977	−	8.71686i	0.407700	−	0.296211i
$867$	−10.0330	+	30.8783i	−0.340737	+	1.04868i
$868$	−1.77459			−0.0602334
$869$	−22.8377	+	8.60674i	−0.774716	+	0.291964i
$870$	10.8239			0.366966
$871$	−17.8576	+	54.9601i	−0.605082	+	1.86225i
$872$	6.72764	−	4.88792i	0.227827	−	0.165526i
$873$	−0.557016	−	0.404696i	−0.0188521	−	0.0136969i
$874$	−10.9443	−	33.6832i	−0.370198	−	1.13935i
$875$	−0.309017	−	0.951057i	−0.0104467	−	0.0321516i
$876$	−5.92872	−	4.30746i	−0.200313	−	0.145536i
$877$	−23.0148	+	16.7212i	−0.777153	+	0.564635i	−0.904123	−	0.427272i	$-0.859475\pi$
$877$	−23.0148	+	16.7212i	−0.777153	+	0.564635i	0.126970	+	0.991907i	$0.459475\pi$
$878$	−1.87930	+	5.78390i	−0.0634234	+	0.195197i
$879$	26.6739			0.899689
$880$	−3.19831	−	0.877976i	−0.107815	−	0.0295966i
$881$	−19.2969			−0.650127			−0.325064	−	0.945692i	$-0.605386\pi$
$881$	−19.2969			−0.650127			−0.325064	+	0.945692i	$0.605386\pi$
$882$	−0.387995	+	1.19412i	−0.0130645	+	0.0402083i
$883$	−0.563801	+	0.409626i	−0.0189734	+	0.0137850i	−0.597232	−	0.802069i	$-0.703733\pi$
$883$	−0.563801	+	0.409626i	−0.0189734	+	0.0137850i	0.578258	+	0.815854i	$0.303733\pi$
$884$	27.8871	+	20.2611i	0.937943	+	0.681456i
$885$	2.22296	+	6.84156i	0.0747239	+	0.229977i
$886$	−6.13677	−	18.8870i	−0.206169	−	0.634522i
$887$	−8.18559	−	5.94718i	−0.274845	−	0.199687i	0.441821	−	0.897103i	$-0.354333\pi$
$887$	−8.18559	−	5.94718i	−0.274845	−	0.199687i	−0.716666	+	0.697417i	$0.754333\pi$
$888$	11.7346	−	8.52569i	0.393787	−	0.286103i
$889$	3.39949	−	10.4626i	0.114015	−	0.350903i
$890$	−5.39995			−0.181007
$891$	0.560681	+	12.1153i	0.0187835	+	0.405876i
$892$	22.5140			0.753824
$893$	−8.65486	+	26.6369i	−0.289624	+	0.891371i
$894$	9.84377	−	7.15191i	0.329225	−	0.239196i
$895$	3.56317	+	2.58879i	0.119103	+	0.0865337i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	−12.0216	−	36.9988i	−0.401391	−	1.23535i
$898$	−0.652503	−	0.474072i	−0.0217743	−	0.0158200i
$899$	11.7656	−	8.54821i	0.392405	−	0.285099i
$900$	−0.387995	+	1.19412i	−0.0129332	+	0.0398041i
$901$	55.4002			1.84565
$902$	−3.79893	+	5.77226i	−0.126490	+	0.192195i
$903$	−3.59132			−0.119511
$904$	−6.22590	+	19.1614i	−0.207070	+	0.637297i
$905$	8.97280	−	6.51912i	0.298266	−	0.216703i
$906$	15.2556	+	11.0839i	0.506835	+	0.368237i
$907$	−8.09051	−	24.9000i	−0.268641	−	0.826792i	−0.990832	−	0.135099i	$-0.956865\pi$
$907$	−8.09051	−	24.9000i	−0.268641	−	0.826792i	0.722191	−	0.691694i	$-0.243135\pi$
$908$	−3.36819	−	10.3662i	−0.111777	−	0.344015i
$909$	2.48084	+	1.80243i	0.0822842	+	0.0597830i
$910$	4.32463	−	3.14203i	0.143360	−	0.104157i
$911$	−10.5241	+	32.3899i	−0.348679	+	1.07312i	0.610905	+	0.791704i	$0.290806\pi$
$911$	−10.5241	+	32.3899i	−0.348679	+	1.07312i	−0.959585	+	0.281421i	$0.909194\pi$
$912$	8.48925			0.281107
$913$	13.1135	−	19.9252i	0.433993	−	0.659429i
$914$	−29.9349			−0.990160
$915$	−5.46855	+	16.8305i	−0.180785	+	0.556398i
$916$	2.56818	−	1.86589i	0.0848551	−	0.0616509i
$917$	−14.8032	−	10.7552i	−0.488845	−	0.355167i
$918$	−11.2001	−	34.4703i	−0.369657	−	1.13769i
$919$	11.6466	+	35.8444i	0.384184	+	1.18240i	0.937070	+	0.349141i	$0.113527\pi$
$919$	11.6466	+	35.8444i	0.384184	+	1.18240i	−0.552886	+	0.833257i	$0.686473\pi$
$920$	−4.45781	−	3.23879i	−0.146970	−	0.106780i
$921$	26.0856	−	18.9523i	0.859551	−	0.624500i
$922$	10.3468	−	31.8443i	0.340755	−	1.04874i
$923$	−63.1607			−2.07896
$924$	−0.202507	−	4.37580i	−0.00666200	−	0.143953i
$925$	10.9821			0.361089
$926$	−9.19358	+	28.2949i	−0.302120	+	0.929829i
$927$	0.640236	−	0.465159i	0.0210281	−	0.0152778i
$928$	6.63005	+	4.81701i	0.217642	+	0.158126i
$929$	7.58090	+	23.3316i	0.248721	+	0.765486i	0.995002	+	0.0998544i	$0.0318377\pi$
$929$	7.58090	+	23.3316i	0.248721	+	0.765486i	−0.746281	+	0.665631i	$0.768162\pi$
$930$	−0.724279	−	2.22910i	−0.0237500	−	0.0730951i
$931$	5.19997	+	3.77800i	0.170422	+	0.123819i
$932$	20.7370	−	15.0663i	0.679262	−	0.493513i
$933$	−10.3123	+	31.7381i	−0.337610	+	1.03906i
$934$	−6.65053			−0.217612
$935$	20.6240	+	5.66157i	0.674478	+	0.185153i
$936$	−6.71173			−0.219380
$937$	9.54071	−	29.3633i	0.311681	−	0.959257i	−0.665418	−	0.746471i	$-0.731746\pi$
$937$	9.54071	−	29.3633i	0.311681	−	0.959257i	0.977099	−	0.212785i	$-0.0682535\pi$
$938$	−8.74596	+	6.35431i	−0.285566	+	0.207476i
$939$	−19.4201	−	14.1095i	−0.633750	−	0.460446i
$940$	1.34653	+	4.14420i	0.0439191	+	0.135169i
$941$	−14.3402	−	44.1347i	−0.467478	−	1.43875i	−0.855839	−	0.517243i	$-0.826958\pi$
$941$	−14.3402	−	44.1347i	−0.467478	−	1.43875i	0.388360	−	0.921508i	$-0.373042\pi$
$942$	15.9679	+	11.6013i	0.520261	+	0.377992i
$943$	−9.28787	+	6.74803i	−0.302455	+	0.219746i
$944$	−1.68308	+	5.17999i	−0.0547796	+	0.168594i
$945$	−5.62062			−0.182839
$946$	−8.43890	+	3.18033i	−0.274372	+	0.103401i
$947$	8.46285			0.275006			0.137503	−	0.990501i	$-0.456092\pi$
$947$	8.46285			0.275006			0.137503	+	0.990501i	$0.456092\pi$
$948$	3.00333	−	9.24329i	0.0975435	−	0.300208i
$949$	23.9953	−	17.4336i	0.778920	−	0.565919i
$950$	5.19997	+	3.77800i	0.168709	+	0.122574i
$951$	−4.35644	−	13.4077i	−0.141267	−	0.434776i
$952$	1.99267	+	6.13282i	0.0645829	+	0.198766i
$953$	−17.0901	−	12.4167i	−0.553602	−	0.402215i	0.275510	−	0.961298i	$-0.411153\pi$
$953$	−17.0901	−	12.4167i	−0.553602	−	0.402215i	−0.829112	+	0.559083i	$0.811153\pi$
$954$	−8.72687	+	6.34044i	−0.282543	+	0.205279i
$955$	−4.43630	+	13.6535i	−0.143555	+	0.441818i
$956$	−17.5664			−0.568139
$957$	22.4209	+	28.0363i	0.724766	+	0.906285i
$958$	−17.9277			−0.579217
$959$	−1.68750	+	5.19358i	−0.0544921	+	0.167710i
$960$	1.06852	−	0.776327i	0.0344864	−	0.0250558i
$961$	22.5318	+	16.3703i	0.726832	+	0.528075i
$962$	18.1409	+	55.8319i	0.584885	+	1.80009i
$963$	−4.43681	−	13.6551i	−0.142974	−	0.440030i
$964$	−4.55628	−	3.31033i	−0.146748	−	0.106619i
$965$	−6.86198	+	4.98552i	−0.220895	+	0.160489i
$966$	2.24891	−	6.92144i	0.0723575	−	0.222694i
$967$	−5.05793			−0.162652			−0.0813260	−	0.996688i	$-0.525915\pi$
$967$	−5.05793			−0.162652			−0.0813260	+	0.996688i	$0.525915\pi$
$968$	−4.35089	−	10.1030i	−0.139843	−	0.324721i
$969$	−54.7423			−1.75858
$970$	−0.169453	+	0.521523i	−0.00544081	+	0.0167451i
$971$	−11.9743	+	8.69983i	−0.384273	+	0.279191i	−0.763105	−	0.646275i	$-0.776326\pi$
$971$	−11.9743	+	8.69983i	−0.384273	+	0.279191i	0.378831	+	0.925466i	$0.376326\pi$
$972$	9.73417	+	7.07229i	0.312224	+	0.226844i
$973$	1.62386	+	4.99772i	0.0520585	+	0.160220i
$974$	11.5028	+	35.4020i	0.368574	+	1.13435i
$975$	5.71182	+	4.14988i	0.182925	+	0.132903i
$976$	−10.8398	+	7.87558i	−0.346974	+	0.252091i
$977$	−2.28100	+	7.02019i	−0.0729756	+	0.224596i	−0.980891	−	0.194557i	$-0.937673\pi$
$977$	−2.28100	+	7.02019i	−0.0729756	+	0.224596i	0.907916	+	0.419153i	$0.137673\pi$
$978$	−22.1469			−0.708180
$979$	−11.1856	−	13.9870i	−0.357492	−	0.447027i
$980$	1.00000			0.0319438
$981$	3.22649	−	9.93013i	0.103014	−	0.317045i
$982$	17.5690	−	12.7646i	0.560649	−	0.407336i
$983$	−1.17870	−	0.856373i	−0.0375946	−	0.0273140i	0.568829	−	0.822456i	$-0.307397\pi$
$983$	−1.17870	−	0.856373i	−0.0375946	−	0.0273140i	−0.606424	+	0.795142i	$0.707397\pi$
$984$	−0.850360	−	2.61714i	−0.0271085	−	0.0834313i
$985$	−1.53692	−	4.73015i	−0.0489703	−	0.150715i
$986$	−42.7534	−	31.0622i	−1.36155	−	0.989220i
$987$	−4.65606	+	3.38282i	−0.148204	+	0.107676i
$988$	−10.6174	+	32.6769i	−0.337783	+	1.03959i
$989$	−14.9828			−0.476424
$990$	−3.89674	+	1.46855i	−0.123846	+	0.0466735i
$991$	34.1561			1.08501			0.542503	−	0.840054i	$-0.317477\pi$
$991$	34.1561			1.08501			0.542503	+	0.840054i	$0.317477\pi$
$992$	0.548378	−	1.68773i	0.0174110	−	0.0535856i
$993$	−10.4251	+	7.57431i	−0.330832	+	0.240364i
$994$	−9.55902	−	6.94504i	−0.303194	−	0.220283i
$995$	−6.99417	−	21.5259i	−0.221730	−	0.682415i
$996$	2.93535	+	9.03409i	0.0930102	+	0.286256i
$997$	46.0723	+	33.4735i	1.45912	+	1.06012i	0.983590	+	0.180420i	$0.0577455\pi$
$997$	46.0723	+	33.4735i	1.45912	+	1.06012i	0.475535	+	0.879697i	$0.342254\pi$
$998$	12.7682	−	9.27663i	0.404170	−	0.293647i
$999$	19.0744	−	58.7050i	0.603488	−	1.85735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.g.141.3	yes	12
11.4	even	5		8470.2.a.db.1.2		6
11.5	even	5	inner	770.2.n.g.71.3	✓	12
11.7	odd	10		8470.2.a.cv.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.71.3	✓	12	11.5	even	5	inner
770.2.n.g.141.3	yes	12	1.1	even	1	trivial
8470.2.a.cv.1.2		6	11.7	odd	10
8470.2.a.db.1.2		6	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.06852 - 0.776327i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.408139 - 1.25612i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.387995 + 1.19412i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.06852 - 0.776327i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.408139 - 1.25612i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.387995 + 1.19412i) q^{9} +1.00000 q^{10} +(2.07142 + 2.59021i) q^{11} -1.32077 q^{12} +(1.65186 - 5.08391i) q^{13} +(0.809017 - 0.587785i) q^{14} +(1.06852 + 0.776327i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.99267 - 6.13282i) q^{17} +(1.01578 + 0.738009i) q^{18} +(5.19997 - 3.77800i) q^{19} +(0.309017 - 0.951057i) q^{20} +1.32077 q^{21} +(3.10354 - 1.16962i) q^{22} +5.51016 q^{23} +(-0.408139 + 1.25612i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.32463 - 3.14203i) q^{26} +(1.73687 + 5.34553i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(6.63005 + 4.81701i) q^{29} +(1.06852 - 0.776327i) q^{30} +(0.548378 - 1.68773i) q^{31} +1.00000 q^{32} +(4.22421 + 1.15960i) q^{33} -6.44843 q^{34} +(-0.309017 + 0.951057i) q^{35} +(1.01578 - 0.738009i) q^{36} +(-8.88469 - 6.45511i) q^{37} +(-1.98621 - 6.11293i) q^{38} +(-2.18172 - 6.71465i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-1.68559 + 1.22465i) q^{41} +(0.408139 - 1.25612i) q^{42} -2.71912 q^{43} +(-0.153326 - 3.31308i) q^{44} -1.25558 q^{45} +(1.70273 - 5.24047i) q^{46} +(-3.52527 + 2.56126i) q^{47} +(1.06852 + 0.776327i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-6.89029 - 5.00609i) q^{51} +(-4.32463 + 3.14203i) q^{52} +(-2.65485 + 8.17078i) q^{53} +5.62062 q^{54} +(-1.82334 + 2.77046i) q^{55} -1.00000 q^{56} +(2.62332 - 8.07375i) q^{57} +(6.63005 - 4.81701i) q^{58} +(4.40637 + 3.20141i) q^{59} +(-0.408139 - 1.25612i) q^{60} +(4.14044 + 12.7430i) q^{61} +(-1.43567 - 1.04308i) q^{62} +(-1.01578 + 0.738009i) q^{63} +(0.309017 - 0.951057i) q^{64} +5.34554 q^{65} +(2.40820 - 3.65913i) q^{66} -10.8106 q^{67} +(-1.99267 + 6.13282i) q^{68} +(5.88773 - 4.27768i) q^{69} +(0.809017 + 0.587785i) q^{70} +(-3.65122 - 11.2373i) q^{71} +(-0.387995 - 1.19412i) q^{72} +(4.48885 + 3.26134i) q^{73} +(-8.88469 + 6.45511i) q^{74} +(-0.408139 + 1.25612i) q^{75} -6.42752 q^{76} +(0.153326 + 3.31308i) q^{77} -7.06020 q^{78} +(-2.27393 + 6.99843i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.95841 + 2.14941i) q^{81} +(0.643838 + 1.98153i) q^{82} +(-2.22246 - 6.84003i) q^{83} +(-1.06852 - 0.776327i) q^{84} +(5.21689 - 3.79029i) q^{85} +(-0.840253 + 2.58603i) q^{86} +10.8239 q^{87} +(-3.19831 - 0.877976i) q^{88} -5.39995 q^{89} +(-0.387995 + 1.19412i) q^{90} +(4.32463 - 3.14203i) q^{91} +(-4.45781 - 3.23879i) q^{92} +(-0.724279 - 2.22910i) q^{93} +(1.34653 + 4.14420i) q^{94} +(5.19997 + 3.77800i) q^{95} +(1.06852 - 0.776327i) q^{96} +(-0.169453 + 0.521523i) q^{97} +1.00000 q^{98} +(-3.89674 + 1.46855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

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