LMFDB - Embedded newform 770.2.n.h.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} - 3 x^{11} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 $ x^12 - 3x^11 + 7x^10 - 9x^9 + 55x^8 - 32x^7 + 287x^6 - 302x^5 + 1175x^4 - 1639x^3 + 1692x^2 - 988*x + 361
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			$-1.85915 - 1.35075i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.h.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(2.66817 - 1.93854i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.01915 - 3.13662i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.43414 - 7.49150i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(2.66817 - 1.93854i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.01915 - 3.13662i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.43414 - 7.49150i) q^{9} -1.00000 q^{10} +(-2.43559 + 2.25120i) q^{11} -3.29803 q^{12} +(0.335621 - 1.03294i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-2.66817 - 1.93854i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.300214 + 0.923964i) q^{17} +(-6.37265 - 4.63000i) q^{18} +(0.845336 - 0.614173i) q^{19} +(-0.309017 + 0.951057i) q^{20} -3.29803 q^{21} +(1.38838 + 3.01204i) q^{22} +2.42388 q^{23} +(-1.01915 + 3.13662i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.878668 - 0.638390i) q^{26} +(-4.97042 - 15.2974i) q^{27} +(0.309017 + 0.951057i) q^{28} +(6.66252 + 4.84060i) q^{29} +(-2.66817 + 1.93854i) q^{30} +(-1.29164 + 3.97526i) q^{31} +1.00000 q^{32} +(-2.13451 + 10.7281i) q^{33} +0.971513 q^{34} +(-0.309017 + 0.951057i) q^{35} +(-6.37265 + 4.63000i) q^{36} +(-4.92134 - 3.57557i) q^{37} +(-0.322890 - 0.993753i) q^{38} +(-1.10689 - 3.40666i) q^{39} +(0.809017 + 0.587785i) q^{40} +(6.90716 - 5.01835i) q^{41} +(-1.01915 + 3.13662i) q^{42} -3.06122 q^{43} +(3.29366 - 0.389659i) q^{44} -7.87703 q^{45} +(0.749021 - 2.30525i) q^{46} +(10.0270 - 7.28505i) q^{47} +(2.66817 + 1.93854i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(2.59216 + 1.88331i) q^{51} +(-0.878668 + 0.638390i) q^{52} +(-0.0999804 + 0.307708i) q^{53} -16.0846 q^{54} +(2.89366 + 1.62072i) q^{55} +1.00000 q^{56} +(1.06490 - 3.27743i) q^{57} +(6.66252 - 4.84060i) q^{58} +(-9.61777 - 6.98772i) q^{59} +(1.01915 + 3.13662i) q^{60} +(4.06378 + 12.5070i) q^{61} +(3.38156 + 2.45685i) q^{62} +(-6.37265 + 4.63000i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.08609 q^{65} +(9.54339 + 5.34519i) q^{66} +8.03278 q^{67} +(0.300214 - 0.923964i) q^{68} +(6.46732 - 4.69878i) q^{69} +(0.809017 + 0.587785i) q^{70} +(1.29220 + 3.97699i) q^{71} +(2.43414 + 7.49150i) q^{72} +(8.04264 + 5.84332i) q^{73} +(-4.92134 + 3.57557i) q^{74} +(-1.01915 + 3.13662i) q^{75} -1.04489 q^{76} +(3.29366 - 0.389659i) q^{77} -3.58197 q^{78} +(-3.53522 + 10.8803i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-23.7985 - 17.2906i) q^{81} +(-2.63830 - 8.11985i) q^{82} +(-0.118057 - 0.363342i) q^{83} +(2.66817 + 1.93854i) q^{84} +(0.785971 - 0.571041i) q^{85} +(-0.945971 + 2.91140i) q^{86} +27.1604 q^{87} +(0.647208 - 3.25286i) q^{88} -11.2206 q^{89} +(-2.43414 + 7.49150i) q^{90} +(-0.878668 + 0.638390i) q^{91} +(-1.96096 - 1.42472i) q^{92} +(4.25987 + 13.1105i) q^{93} +(-3.82997 - 11.7875i) q^{94} +(-0.845336 - 0.614173i) q^{95} +(2.66817 - 1.93854i) q^{96} +(4.59114 - 14.1301i) q^{97} +1.00000 q^{98} +(10.9363 + 23.7259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * 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
$3$	2.66817	−	1.93854i	1.54047	−	1.11921i	0.590424	−	0.807093i	$-0.298961\pi$
$3$	2.66817	−	1.93854i	1.54047	−	1.11921i	0.950042	−	0.312121i	$-0.101039\pi$
$4$	−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
$6$	−1.01915	−	3.13662i	−0.416066	−	1.28052i
$7$	−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
$9$	2.43414	−	7.49150i	0.811379	−	2.49717i
$10$	−1.00000			−0.316228
$11$	−2.43559	+	2.25120i	−0.734357	+	0.678763i
$11$	−2.43559	+	2.25120i	−0.734357	+	0.678763i
$12$	−3.29803			−0.952060
$13$	0.335621	−	1.03294i	0.0930846	−	0.286485i	−0.893665	−	0.448734i	$-0.851875\pi$
$13$	0.335621	−	1.03294i	0.0930846	−	0.286485i	0.986750	+	0.162249i	$0.0518749\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	−2.66817	−	1.93854i	−0.688917	−	0.500528i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.300214	+	0.923964i	0.0728126	+	0.224094i	0.980839	−	0.194818i	$-0.0624116\pi$
$17$	0.300214	+	0.923964i	0.0728126	+	0.224094i	−0.908027	+	0.418912i	$0.862412\pi$
$18$	−6.37265	−	4.63000i	−1.50205	−	1.09130i
$19$	0.845336	−	0.614173i	0.193933	−	0.140901i	−0.486581	−	0.873635i	$-0.661756\pi$
$19$	0.845336	−	0.614173i	0.193933	−	0.140901i	0.680515	+	0.732734i	$0.261756\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	−3.29803			−0.719690
$22$	1.38838	+	3.01204i	0.296004	+	0.642169i
$23$	2.42388			0.505414			0.252707	−	0.967543i	$-0.418679\pi$
$23$	2.42388			0.505414			0.252707	+	0.967543i	$0.418679\pi$
$24$	−1.01915	+	3.13662i	−0.208033	+	0.640259i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−0.878668	−	0.638390i	−0.172321	−	0.125199i
$27$	−4.97042	−	15.2974i	−0.956557	−	2.94398i
$28$	0.309017	+	0.951057i	0.0583987	+	0.179733i
$29$	6.66252	+	4.84060i	1.23720	+	0.898878i	0.997408	−	0.0719472i	$-0.0229213\pi$
$29$	6.66252	+	4.84060i	1.23720	+	0.898878i	0.239790	+	0.970825i	$0.422921\pi$
$30$	−2.66817	+	1.93854i	−0.487138	+	0.353927i
$31$	−1.29164	+	3.97526i	−0.231985	+	0.713978i	0.765522	+	0.643410i	$0.222481\pi$
$31$	−1.29164	+	3.97526i	−0.231985	+	0.713978i	−0.997507	+	0.0705675i	$0.977519\pi$
$32$	1.00000			0.176777
$33$	−2.13451	+	10.7281i	−0.371571	+	1.86751i
$34$	0.971513			0.166613
$35$	−0.309017	+	0.951057i	−0.0522334	+	0.160758i
$36$	−6.37265	+	4.63000i	−1.06211	+	0.771667i
$37$	−4.92134	−	3.57557i	−0.809064	−	0.587819i	0.104495	−	0.994525i	$-0.466677\pi$
$37$	−4.92134	−	3.57557i	−0.809064	−	0.587819i	−0.913559	+	0.406706i	$0.866677\pi$
$38$	−0.322890	−	0.993753i	−0.0523796	−	0.161208i
$39$	−1.10689	−	3.40666i	−0.177244	−	0.545502i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	6.90716	−	5.01835i	1.07872	−	0.783734i	0.101259	−	0.994860i	$-0.467713\pi$
$41$	6.90716	−	5.01835i	1.07872	−	0.783734i	0.977459	+	0.211126i	$0.0677131\pi$
$42$	−1.01915	+	3.13662i	−0.157258	+	0.483991i
$43$	−3.06122			−0.466832			−0.233416	−	0.972377i	$-0.574990\pi$
$43$	−3.06122			−0.466832			−0.233416	+	0.972377i	$0.574990\pi$
$44$	3.29366	−	0.389659i	0.496537	−	0.0587433i
$45$	−7.87703			−1.17424
$46$	0.749021	−	2.30525i	0.110437	−	0.339890i
$47$	10.0270	−	7.28505i	1.46259	−	1.06263i	0.479910	−	0.877318i	$-0.340669\pi$
$47$	10.0270	−	7.28505i	1.46259	−	1.06263i	0.982679	−	0.185315i	$-0.0593306\pi$
$48$	2.66817	+	1.93854i	0.385117	+	0.279804i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	2.59216	+	1.88331i	0.362975	+	0.263717i
$52$	−0.878668	+	0.638390i	−0.121849	+	0.0885287i
$53$	−0.0999804	+	0.307708i	−0.0137334	+	0.0422670i	−0.957688	−	0.287807i	$-0.907074\pi$
$53$	−0.0999804	+	0.307708i	−0.0137334	+	0.0422670i	0.943955	+	0.330074i	$0.107074\pi$
$54$	−16.0846			−2.18884
$55$	2.89366	+	1.62072i	0.390181	+	0.218538i
$56$	1.00000			0.133631
$57$	1.06490	−	3.27743i	0.141050	−	0.434106i
$58$	6.66252	−	4.84060i	0.874832	−	0.635602i
$59$	−9.61777	−	6.98772i	−1.25213	−	0.909724i	−0.253784	−	0.967261i	$-0.581675\pi$
$59$	−9.61777	−	6.98772i	−1.25213	−	0.909724i	−0.998343	+	0.0575370i	$0.981675\pi$
$60$	1.01915	+	3.13662i	0.131572	+	0.404936i
$61$	4.06378	+	12.5070i	0.520313	+	1.60136i	0.773402	+	0.633916i	$0.218554\pi$
$61$	4.06378	+	12.5070i	0.520313	+	1.60136i	−0.253089	+	0.967443i	$0.581446\pi$
$62$	3.38156	+	2.45685i	0.429458	+	0.312020i
$63$	−6.37265	+	4.63000i	−0.802879	+	0.583325i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.08609			−0.134713
$66$	9.54339	+	5.34519i	1.17471	+	0.657948i
$67$	8.03278			0.981361			0.490680	−	0.871340i	$-0.336748\pi$
$67$	8.03278			0.981361			0.490680	+	0.871340i	$0.336748\pi$
$68$	0.300214	−	0.923964i	0.0364063	−	0.112047i
$69$	6.46732	−	4.69878i	0.778574	−	0.565667i
$70$	0.809017	+	0.587785i	0.0966960	+	0.0702538i
$71$	1.29220	+	3.97699i	0.153356	+	0.471982i	0.997991	−	0.0633613i	$-0.0201821\pi$
$71$	1.29220	+	3.97699i	0.153356	+	0.471982i	−0.844634	+	0.535344i	$0.820182\pi$
$72$	2.43414	+	7.49150i	0.286866	+	0.882882i
$73$	8.04264	+	5.84332i	0.941320	+	0.683909i	0.948738	−	0.316064i	$-0.102361\pi$
$73$	8.04264	+	5.84332i	0.941320	+	0.683909i	−0.00741831	+	0.999972i	$0.502361\pi$
$74$	−4.92134	+	3.57557i	−0.572095	+	0.415651i
$75$	−1.01915	+	3.13662i	−0.117681	+	0.362185i
$76$	−1.04489			−0.119857
$77$	3.29366	−	0.389659i	0.375347	−	0.0444058i
$78$	−3.58197			−0.405579
$79$	−3.53522	+	10.8803i	−0.397743	+	1.22413i	0.529061	+	0.848584i	$0.322544\pi$
$79$	−3.53522	+	10.8803i	−0.397743	+	1.22413i	−0.926804	+	0.375544i	$0.877456\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−23.7985	−	17.2906i	−2.64427	−	1.92118i
$82$	−2.63830	−	8.11985i	−0.291352	−	0.896688i
$83$	−0.118057	−	0.363342i	−0.0129584	−	0.0398820i	0.944368	−	0.328890i	$-0.106675\pi$
$83$	−0.118057	−	0.363342i	−0.0129584	−	0.0398820i	−0.957327	+	0.289008i	$0.906675\pi$
$84$	2.66817	+	1.93854i	0.291121	+	0.211512i
$85$	0.785971	−	0.571041i	0.0852505	−	0.0619381i
$86$	−0.945971	+	2.91140i	−0.102007	+	0.313944i
$87$	27.1604			2.91190
$88$	0.647208	−	3.25286i	0.0689926	−	0.346756i
$89$	−11.2206			−1.18938			−0.594692	−	0.803954i	$-0.702726\pi$
$89$	−11.2206			−1.18938			−0.594692	+	0.803954i	$0.702726\pi$
$90$	−2.43414	+	7.49150i	−0.256580	+	0.789673i
$91$	−0.878668	+	0.638390i	−0.0921094	+	0.0669214i
$92$	−1.96096	−	1.42472i	−0.204444	−	0.148538i
$93$	4.25987	+	13.1105i	0.441728	+	1.35950i
$94$	−3.82997	−	11.7875i	−0.395032	−	1.21578i
$95$	−0.845336	−	0.614173i	−0.0867297	−	0.0630128i
$96$	2.66817	−	1.93854i	0.272319	−	0.197851i
$97$	4.59114	−	14.1301i	0.466160	−	1.43469i	−0.391359	−	0.920238i	$-0.627995\pi$
$97$	4.59114	−	14.1301i	0.466160	−	1.43469i	0.857518	−	0.514454i	$-0.172005\pi$
$98$	1.00000			0.101015
$99$	10.9363	+	23.7259i	1.09914	+	2.38455i
$100$	1.00000			0.100000
$101$	1.80987	−	5.57020i	0.180089	−	0.554256i	−0.819741	−	0.572735i	$-0.805882\pi$
$101$	1.80987	−	5.57020i	0.180089	−	0.554256i	0.999829	+	0.0184791i	$0.00588241\pi$
$102$	2.59216	−	1.88331i	0.256662	−	0.186476i
$103$	8.98703	+	6.52946i	0.885518	+	0.643367i	0.934706	−	0.355423i	$-0.115663\pi$
$103$	8.98703	+	6.52946i	0.885518	+	0.643367i	−0.0491873	+	0.998790i	$0.515663\pi$
$104$	0.335621	+	1.03294i	0.0329104	+	0.101288i
$105$	1.01915	+	3.13662i	0.0994587	+	0.306102i
$106$	0.261752	+	0.190174i	0.0254236	+	0.0184713i
$107$	−5.95094	+	4.32361i	−0.575299	+	0.417979i	−0.837026	−	0.547163i	$-0.815708\pi$
$107$	−5.95094	+	4.32361i	−0.575299	+	0.417979i	0.261727	+	0.965142i	$0.415708\pi$
$108$	−4.97042	+	15.2974i	−0.478279	+	1.47199i
$109$	−1.17544			−0.112587			−0.0562933	−	0.998414i	$-0.517928\pi$
$109$	−1.17544			−0.112587			−0.0562933	+	0.998414i	$0.517928\pi$
$110$	2.43559	−	2.25120i	0.232224	−	0.214644i
$111$	−20.0623			−1.90423
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	−9.14556	+	6.64464i	−0.860342	+	0.625075i	−0.927978	−	0.372635i	$-0.878454\pi$
$113$	−9.14556	+	6.64464i	−0.860342	+	0.625075i	0.0676363	+	0.997710i	$0.478454\pi$
$114$	−2.78795	−	2.02556i	−0.261115	−	0.189711i
$115$	−0.749021	−	2.30525i	−0.0698465	−	0.214966i
$116$	−2.54486	−	7.83226i	−0.236284	−	0.727207i
$117$	−6.92129	−	5.02861i	−0.639874	−	0.464896i
$118$	−9.61777	+	6.98772i	−0.885388	+	0.643272i
$119$	0.300214	−	0.923964i	0.0275206	−	0.0846996i
$120$	3.29803			0.301068
$121$	0.864173	−	10.9660i	0.0785611	−	0.996909i
$122$	13.1507			1.19060
$123$	8.70121	−	26.7796i	0.784561	−	2.41463i
$124$	3.38156	−	2.45685i	0.303673	−	0.220631i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	2.43414	+	7.49150i	0.216850	+	0.667396i
$127$	2.14617	+	6.60523i	0.190442	+	0.586119i	1.00000		0.000920737i	$-0.000293080\pi$
$127$	2.14617	+	6.60523i	0.190442	+	0.586119i	−0.809558	+	0.587040i	$0.800293\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−8.16786	+	5.93429i	−0.719140	+	0.522485i
$130$	−0.335621	+	1.03294i	−0.0294359	+	0.0905945i
$131$	−4.83817			−0.422713			−0.211356	−	0.977409i	$-0.567788\pi$
$131$	−4.83817			−0.422713			−0.211356	+	0.977409i	$0.567788\pi$
$132$	8.03265	−	7.42454i	0.699153	−	0.646224i
$133$	−1.04489			−0.0906037
$134$	2.48227	−	7.63963i	0.214435	−	0.659964i
$135$	−13.0127	+	9.45430i	−1.11996	+	0.813696i
$136$	−0.785971	−	0.571041i	−0.0673964	−	0.0489664i
$137$	−5.23623	−	16.1155i	−0.447361	−	1.37684i	−0.879873	−	0.475208i	$-0.842373\pi$
$137$	−5.23623	−	16.1155i	−0.447361	−	1.37684i	0.432512	−	0.901628i	$-0.357627\pi$
$138$	−2.47030	−	7.60279i	−0.210286	−	0.647192i
$139$	7.93808	+	5.76736i	0.673299	+	0.489181i	0.871128	−	0.491056i	$-0.163389\pi$
$139$	7.93808	+	5.76736i	0.673299	+	0.489181i	−0.197829	+	0.980237i	$0.563389\pi$
$140$	0.809017	−	0.587785i	0.0683744	−	0.0496769i
$141$	12.6314	−	38.8754i	1.06375	−	3.27390i
$142$	4.18166			0.350917
$143$	1.50791	+	3.27136i	0.126098	+	0.273565i
$144$	7.87703			0.656419
$145$	2.54486	−	7.83226i	0.211339	−	0.650434i
$146$	8.04264	−	5.84332i	0.665614	−	0.483597i
$147$	2.66817	+	1.93854i	0.220067	+	0.159888i
$148$	1.87979	+	5.78539i	0.154517	+	0.475556i
$149$	−5.33279	−	16.4126i	−0.436879	−	1.34458i	−0.891149	−	0.453711i	$-0.850100\pi$
$149$	−5.33279	−	16.4126i	−0.436879	−	1.34458i	0.454270	−	0.890864i	$-0.349900\pi$
$150$	2.66817	+	1.93854i	0.217855	+	0.158281i
$151$	−12.6738	+	9.20804i	−1.03138	+	0.749340i	−0.968584	−	0.248687i	$-0.920001\pi$
$151$	−12.6738	+	9.20804i	−1.03138	+	0.749340i	−0.0627937	+	0.998027i	$0.520001\pi$
$152$	−0.322890	+	0.993753i	−0.0261898	+	0.0806040i
$153$	7.65264			0.618679
$154$	0.647208	−	3.25286i	0.0521535	−	0.262123i
$155$	4.17984			0.335732
$156$	−1.10689	+	3.40666i	−0.0886222	+	0.272751i
$157$	−7.48981	+	5.44167i	−0.597752	+	0.434292i	−0.845080	−	0.534639i	$-0.820447\pi$
$157$	−7.48981	+	5.44167i	−0.597752	+	0.434292i	0.247328	+	0.968932i	$0.420447\pi$
$158$	9.25533	+	6.72439i	0.736314	+	0.534964i
$159$	0.329739	+	1.01483i	0.0261500	+	0.0804814i
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	−1.96096	−	1.42472i	−0.154545	−	0.112284i
$162$	−23.7985	+	17.2906i	−1.86978	+	1.35848i
$163$	−2.26026	+	6.95638i	−0.177037	+	0.544865i	−0.999721	−	0.0236348i	$-0.992476\pi$
$163$	−2.26026	+	6.95638i	−0.177037	+	0.544865i	0.822683	+	0.568500i	$0.192476\pi$
$164$	−8.53772			−0.666684
$165$	10.8626	−	1.28511i	0.845651	−	0.100046i
$166$	−0.382041			−0.0296521
$167$	−3.90900	+	12.0307i	−0.302487	+	0.930960i	0.678116	+	0.734955i	$0.262797\pi$
$167$	−3.90900	+	12.0307i	−0.302487	+	0.930960i	−0.980603	+	0.196005i	$0.937203\pi$
$168$	2.66817	−	1.93854i	0.205853	−	0.149561i
$169$	9.56291	+	6.94786i	0.735608	+	0.534451i
$170$	−0.300214	−	0.923964i	−0.0230254	−	0.0708648i
$171$	−2.54341	−	7.82782i	−0.194500	−	0.598608i
$172$	2.47658	+	1.79934i	0.188838	+	0.137199i
$173$	−0.820754	+	0.596312i	−0.0624007	+	0.0453368i	−0.618548	−	0.785747i	$-0.712279\pi$
$173$	−0.820754	+	0.596312i	−0.0624007	+	0.0453368i	0.556148	+	0.831084i	$0.312279\pi$
$174$	8.39302	−	25.8311i	0.636273	−	1.95825i
$175$	1.00000			0.0755929
$176$	−2.89366	−	1.62072i	−0.218118	−	0.122166i
$177$	−39.2078			−2.94704
$178$	−3.46736	+	10.6714i	−0.259890	+	0.799859i
$179$	13.9118	−	10.1075i	1.03982	−	0.755470i	0.0695662	−	0.997577i	$-0.477838\pi$
$179$	13.9118	−	10.1075i	1.03982	−	0.755470i	0.970250	+	0.242107i	$0.0778385\pi$
$180$	6.37265	+	4.63000i	0.474989	+	0.345100i
$181$	6.29479	+	19.3734i	0.467888	+	1.44001i	0.855313	+	0.518111i	$0.173365\pi$
$181$	6.29479	+	19.3734i	0.467888	+	1.44001i	−0.387425	+	0.921901i	$0.626635\pi$
$182$	0.335621	+	1.03294i	0.0248779	+	0.0765663i
$183$	35.0881	+	25.4930i	2.59379	+	1.88450i
$184$	−1.96096	+	1.42472i	−0.144564	+	0.105032i
$185$	−1.87979	+	5.78539i	−0.138205	+	0.425350i
$186$	13.7852			1.01078
$187$	−2.81123	−	1.57455i	−0.205577	−	0.115143i
$188$	−12.3941			−0.903930
$189$	−4.97042	+	15.2974i	−0.361545	+	1.11272i
$190$	−0.845336	+	0.614173i	−0.0613272	+	0.0445568i
$191$	5.19886	+	3.77720i	0.376177	+	0.273308i	0.759768	−	0.650195i	$-0.225313\pi$
$191$	5.19886	+	3.77720i	0.376177	+	0.273308i	−0.383591	+	0.923503i	$0.625313\pi$
$192$	−1.01915	−	3.13662i	−0.0735507	−	0.226366i
$193$	4.33063	+	13.3283i	0.311725	+	0.959392i	0.977081	+	0.212866i	$0.0682798\pi$
$193$	4.33063	+	13.3283i	0.311725	+	0.959392i	−0.665356	+	0.746526i	$0.731720\pi$
$194$	−12.0198	−	8.73287i	−0.862969	−	0.626983i
$195$	−2.89788	+	2.10543i	−0.207521	+	0.150773i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	21.3383			1.52029			0.760147	−	0.649752i	$-0.225127\pi$
$197$	21.3383			1.52029			0.760147	+	0.649752i	$0.225127\pi$
$198$	25.9442	−	3.06935i	1.84378	−	0.218130i
$199$	−26.4689			−1.87633			−0.938166	−	0.346186i	$-0.887477\pi$
$199$	−26.4689			−1.87633			−0.938166	+	0.346186i	$0.887477\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	21.4328	−	15.5718i	1.51175	−	1.09835i
$202$	−4.73830	−	3.44257i	−0.333385	−	0.242219i
$203$	−2.54486	−	7.83226i	−0.178614	−	0.549717i
$204$	−0.990116	−	3.04726i	−0.0693220	−	0.213351i
$205$	−6.90716	−	5.01835i	−0.482417	−	0.350497i
$206$	8.98703	−	6.52946i	0.626156	−	0.454929i
$207$	5.90006	−	18.1585i	0.410082	−	1.26210i
$208$	1.08609			0.0753070
$209$	−0.676263	+	3.39890i	−0.0467781	+	0.235107i
$210$	3.29803			0.227586
$211$	3.90948	−	12.0322i	0.269140	−	0.828327i	−0.721571	−	0.692341i	$-0.756580\pi$
$211$	3.90948	−	12.0322i	0.269140	−	0.828327i	0.990711	−	0.135987i	$-0.0434204\pi$
$212$	0.261752	−	0.190174i	0.0179772	−	0.0130612i
$213$	11.1574	+	8.10630i	0.764490	+	0.555434i
$214$	2.27306	+	6.99575i	0.155383	+	0.478219i
$215$	0.945971	+	2.91140i	0.0645147	+	0.198556i
$216$	13.0127	+	9.45430i	0.885404	+	0.643283i
$217$	3.38156	−	2.45685i	0.229555	−	0.166782i
$218$	−0.363230	+	1.11791i	−0.0246011	+	0.0757143i
$219$	32.7866			2.21551
$220$	−1.38838	−	3.01204i	−0.0936048	−	0.203072i
$221$	1.05515			0.0709773
$222$	−6.19960	+	19.0804i	−0.416090	+	1.28059i
$223$	15.5334	−	11.2856i	1.04019	−	0.755743i	0.0698680	−	0.997556i	$-0.477742\pi$
$223$	15.5334	−	11.2856i	1.04019	−	0.755743i	0.970323	+	0.241813i	$0.0777422\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	2.43414	+	7.49150i	0.162276	+	0.499433i
$226$	3.49329	+	10.7512i	0.232370	+	0.715162i
$227$	−1.81759	−	1.32056i	−0.120638	−	0.0876484i	0.525830	−	0.850589i	$-0.323755\pi$
$227$	−1.81759	−	1.32056i	−0.120638	−	0.0876484i	−0.646468	+	0.762941i	$0.723755\pi$
$228$	−2.78795	+	2.02556i	−0.184636	+	0.134146i
$229$	−1.47964	+	4.55387i	−0.0977774	+	0.300928i	−0.987968	−	0.154661i	$-0.950571\pi$
$229$	−1.47964	+	4.55387i	−0.0977774	+	0.300928i	0.890190	+	0.455589i	$0.150571\pi$
$230$	−2.42388			−0.159826
$231$	8.03265	−	7.42454i	0.528510	−	0.488499i
$232$	−8.23533			−0.540676
$233$	3.93774	−	12.1191i	0.257970	−	0.793949i	−0.735260	−	0.677785i	$-0.762940\pi$
$233$	3.93774	−	12.1191i	0.257970	−	0.793949i	0.993230	−	0.116164i	$-0.0370599\pi$
$234$	−6.92129	+	5.02861i	−0.452459	+	0.328731i
$235$	−10.0270	−	7.28505i	−0.654090	−	0.475224i
$236$	3.67366	+	11.3064i	0.239135	+	0.735982i
$237$	11.6593	+	35.8836i	0.757351	+	2.33089i
$238$	−0.785971	−	0.571041i	−0.0509469	−	0.0370151i
$239$	1.82817	−	1.32824i	0.118254	−	0.0859167i	−0.527086	−	0.849812i	$-0.676716\pi$
$239$	1.82817	−	1.32824i	0.118254	−	0.0859167i	0.645340	+	0.763895i	$0.276716\pi$
$240$	1.01915	−	3.13662i	0.0657858	−	0.202468i
$241$	1.94631			0.125373			0.0626865	−	0.998033i	$-0.480033\pi$
$241$	1.94631			0.125373			0.0626865	+	0.998033i	$0.480033\pi$
$242$	−10.1622	−	4.21056i	−0.653254	−	0.270665i
$243$	−48.7628			−3.12814
$244$	4.06378	−	12.5070i	0.260157	−	0.800680i
$245$	0.809017	−	0.587785i	0.0516862	−	0.0375522i
$246$	−22.7801	−	16.5507i	−1.45240	−	1.05523i
$247$	−0.350688	−	1.07931i	−0.0223138	−	0.0686747i
$248$	−1.29164	−	3.97526i	−0.0820192	−	0.252429i
$249$	−1.01935	−	0.740600i	−0.0645986	−	0.0469336i
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−4.90677	+	15.1015i	−0.309712	+	0.953197i	0.668164	+	0.744014i	$0.267080\pi$
$251$	−4.90677	+	15.1015i	−0.309712	+	0.953197i	−0.977877	+	0.209183i	$0.932920\pi$
$252$	7.87703			0.496206
$253$	−5.90358	+	5.45665i	−0.371155	+	0.343057i
$254$	6.94515			0.435777
$255$	0.990116	−	3.04726i	0.0620035	−	0.190827i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	5.72416	+	4.15885i	0.357064	+	0.259422i	0.751826	−	0.659361i	$-0.229173\pi$
$257$	5.72416	+	4.15885i	0.357064	+	0.259422i	−0.394763	+	0.918783i	$0.629173\pi$
$258$	3.11984	+	9.60189i	0.194233	+	0.597788i
$259$	1.87979	+	5.78539i	0.116804	+	0.359486i
$260$	0.878668	+	0.638390i	0.0544927	+	0.0395912i
$261$	52.4809	−	38.1296i	3.24848	−	2.36016i
$262$	−1.49508	+	4.60137i	−0.0923661	+	0.284274i
$263$	−26.1468			−1.61228			−0.806139	−	0.591726i	$-0.798447\pi$
$263$	−26.1468			−1.61228			−0.806139	+	0.591726i	$0.798447\pi$
$264$	−4.57894	−	9.93382i	−0.281814	−	0.611384i
$265$	0.323543			0.0198751
$266$	−0.322890	+	0.993753i	−0.0197976	+	0.0609309i
$267$	−29.9385	+	21.7516i	−1.83221	+	1.33118i
$268$	−6.49866	−	4.72155i	−0.396969	−	0.288415i
$269$	5.42097	+	16.6840i	0.330522	+	1.01724i	0.968886	+	0.247508i	$0.0796117\pi$
$269$	5.42097	+	16.6840i	0.330522	+	1.01724i	−0.638363	+	0.769735i	$0.720388\pi$
$270$	4.97042	+	15.2974i	0.302490	+	0.930969i
$271$	22.1061	+	16.0610i	1.34285	+	0.975637i	0.999334	+	0.0364903i	$0.0116178\pi$
$271$	22.1061	+	16.0610i	1.34285	+	0.975637i	0.343516	+	0.939147i	$0.388382\pi$
$272$	−0.785971	+	0.571041i	−0.0476565	+	0.0346245i
$273$	−1.10689	+	3.40666i	−0.0669921	+	0.206180i
$274$	−16.9448			−1.02367
$275$	0.647208	−	3.25286i	0.0390281	−	0.196155i
$276$	−7.99404			−0.481185
$277$	−1.32772	+	4.08630i	−0.0797750	+	0.245522i	−0.982988	−	0.183671i	$-0.941202\pi$
$277$	−1.32772	+	4.08630i	−0.0797750	+	0.245522i	0.903213	+	0.429193i	$0.141202\pi$
$278$	7.93808	−	5.76736i	0.476095	−	0.345903i
$279$	26.6366	+	19.3526i	1.59469	+	1.15861i
$280$	−0.309017	−	0.951057i	−0.0184673	−	0.0568365i
$281$	−7.99374	−	24.6022i	−0.476866	−	1.46764i	−0.843424	−	0.537248i	$-0.819464\pi$
$281$	−7.99374	−	24.6022i	−0.476866	−	1.46764i	0.366558	−	0.930395i	$-0.380536\pi$
$282$	−33.0694	−	24.0263i	−1.96925	−	1.43075i
$283$	−21.9606	+	15.9553i	−1.30542	+	0.948445i	−0.999993	−	0.00376982i	$-0.998800\pi$
$283$	−21.9606	+	15.9553i	−1.30542	+	0.948445i	−0.305429	+	0.952215i	$0.598800\pi$
$284$	1.29220	−	3.97699i	0.0766782	−	0.235991i
$285$	−3.44609			−0.204129
$286$	3.57722	−	0.423206i	0.211525	−	0.0250247i
$287$	−8.53772			−0.503966
$288$	2.43414	−	7.49150i	0.143433	−	0.441441i
$289$	12.9897	−	9.43758i	0.764100	−	0.555151i
$290$	−6.66252	−	4.84060i	−0.391237	−	0.284250i
$291$	−15.1417	−	46.6015i	−0.887624	−	2.73183i
$292$	−3.07201	−	9.45469i	−0.179776	−	0.553294i
$293$	23.2733	+	16.9090i	1.35964	+	0.987837i	0.998468	+	0.0553378i	$0.0176236\pi$
$293$	23.2733	+	16.9090i	1.35964	+	0.987837i	0.361173	+	0.932499i	$0.382376\pi$
$294$	2.66817	−	1.93854i	0.155611	−	0.113058i
$295$	−3.67366	+	11.3064i	−0.213889	+	0.658282i
$296$	6.08312			0.353574
$297$	46.5434	+	26.0687i	2.70072	+	1.51266i
$298$	−17.2573			−0.999686
$299$	0.813506	−	2.50372i	0.0470463	−	0.144794i
$300$	2.66817	−	1.93854i	0.154047	−	0.111921i
$301$	2.47658	+	1.79934i	0.142748	+	0.103712i
$302$	4.84095	+	14.8989i	0.278566	+	0.857337i
$303$	−5.96901	−	18.3707i	−0.342911	−	1.05537i
$304$	0.845336	+	0.614173i	0.0484834	+	0.0352252i
$305$	10.6391	−	7.72976i	0.609193	−	0.442605i
$306$	2.36480	−	7.27809i	0.135186	−	0.416061i
$307$	−22.6960			−1.29533			−0.647666	−	0.761924i	$-0.724255\pi$
$307$	−22.6960			−1.29533			−0.647666	+	0.761924i	$0.724255\pi$
$308$	−2.89366	−	1.62072i	−0.164882	−	0.0923492i
$309$	36.6365			2.08418
$310$	1.29164	−	3.97526i	0.0733602	−	0.225780i
$311$	−0.614078	+	0.446154i	−0.0348212	+	0.0252991i	−0.605060	−	0.796180i	$-0.706851\pi$
$311$	−0.614078	+	0.446154i	−0.0348212	+	0.0252991i	0.570239	+	0.821479i	$0.306851\pi$
$312$	2.89788	+	2.10543i	0.164060	+	0.119197i
$313$	6.68302	+	20.5682i	0.377746	+	1.16258i	0.941607	+	0.336714i	$0.109316\pi$
$313$	6.68302	+	20.5682i	0.377746	+	1.16258i	−0.563860	+	0.825870i	$0.690684\pi$
$314$	2.86085	+	8.80480i	0.161447	+	0.496884i
$315$	6.37265	+	4.63000i	0.359058	+	0.260871i
$316$	9.25533	−	6.72439i	0.520653	−	0.378276i
$317$	0.0265098	−	0.0815889i	0.00148894	−	0.00458249i	−0.950309	−	0.311307i	$-0.899233\pi$
$317$	0.0265098	−	0.0815889i	0.00148894	−	0.00458249i	0.951798	+	0.306725i	$0.0992331\pi$
$318$	1.06706			0.0598376
$319$	−27.1243	+	3.20897i	−1.51867	+	0.179668i
$320$	−1.00000			−0.0559017
$321$	−7.49661	+	23.0722i	−0.418420	+	1.28777i
$322$	−1.96096	+	1.42472i	−0.109280	+	0.0793966i
$323$	0.821255	+	0.596677i	0.0456959	+	0.0332000i
$324$	9.09020	+	27.9768i	0.505011	+	1.55426i
$325$	0.335621	+	1.03294i	0.0186169	+	0.0572970i
$326$	5.91745	+	4.29928i	0.327737	+	0.238115i
$327$	−3.13626	+	2.27863i	−0.173436	+	0.126008i
$328$	−2.63830	+	8.11985i	−0.145676	+	0.448344i
$329$	−12.3941			−0.683307
$330$	2.13451	−	10.7281i	0.117501	−	0.590560i
$331$	−22.6026			−1.24235			−0.621177	−	0.783670i	$-0.713345\pi$
$331$	−22.6026			−1.24235			−0.621177	+	0.783670i	$0.713345\pi$
$332$	−0.118057	+	0.363342i	−0.00647922	+	0.0199410i
$333$	−38.7656	+	28.1648i	−2.12434	+	1.54342i
$334$	10.2339	+	7.43536i	0.559974	+	0.406845i
$335$	−2.48227	−	7.63963i	−0.135621	−	0.417398i
$336$	−1.01915	−	3.13662i	−0.0555991	−	0.171116i
$337$	−12.3528	−	8.97487i	−0.672902	−	0.488892i	0.198093	−	0.980183i	$-0.436525\pi$
$337$	−12.3528	−	8.97487i	−0.672902	−	0.488892i	−0.870995	+	0.491291i	$0.836525\pi$
$338$	9.56291	−	6.94786i	0.520153	−	0.377914i
$339$	−11.5210	+	35.4580i	−0.625735	+	1.92581i
$340$	−0.971513			−0.0526877
$341$	−5.80321	−	12.5898i	−0.314262	−	0.681778i
$342$	−8.23066			−0.445063
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	2.47658	−	1.79934i	0.133528	−	0.0970141i
$345$	−6.46732	−	4.69878i	−0.348189	−	0.252974i
$346$	0.313500	+	0.964854i	0.0168539	+	0.0518709i
$347$	1.82294	+	5.61043i	0.0978605	+	0.301184i	0.987989	−	0.154527i	$-0.0493853\pi$
$347$	1.82294	+	5.61043i	0.0978605	+	0.301184i	−0.890128	+	0.455710i	$0.849385\pi$
$348$	−21.9732	−	15.9645i	−1.17789	−	0.855786i
$349$	−13.6736	+	9.93447i	−0.731932	+	0.531780i	−0.890174	−	0.455620i	$-0.849417\pi$
$349$	−13.6736	+	9.93447i	−0.731932	+	0.531780i	0.158242	+	0.987400i	$0.449417\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	−17.4694			−0.932447
$352$	−2.43559	+	2.25120i	−0.129817	+	0.119990i
$353$	−17.3914			−0.925648			−0.462824	−	0.886450i	$-0.653164\pi$
$353$	−17.3914			−0.925648			−0.462824	+	0.886450i	$0.653164\pi$
$354$	−12.1159	+	37.2888i	−0.643951	+	1.98188i
$355$	3.38303	−	2.45792i	0.179553	−	0.130453i
$356$	9.07768	+	6.59532i	0.481116	+	0.349551i
$357$	−0.990116	−	3.04726i	−0.0524025	−	0.161278i
$358$	−5.31383	−	16.3543i	−0.280845	−	0.864351i
$359$	−18.1609	−	13.1946i	−0.958494	−	0.696387i	−0.00569348	−	0.999984i	$-0.501812\pi$
$359$	−18.1609	−	13.1946i	−0.958494	−	0.696387i	−0.952800	+	0.303597i	$0.901812\pi$
$360$	6.37265	−	4.63000i	0.335868	−	0.244023i
$361$	−5.53394	+	17.0317i	−0.291260	+	0.896406i
$362$	20.3704			1.07064
$363$	−18.9522	−	30.9343i	−0.994734	−	1.62363i
$364$	1.08609			0.0569268
$365$	3.07201	−	9.45469i	0.160797	−	0.494881i
$366$	35.0881	−	25.4930i	1.83409	−	1.33254i
$367$	3.89360	+	2.82886i	0.203244	+	0.147666i	0.684752	−	0.728776i	$-0.259911\pi$
$367$	3.89360	+	2.82886i	0.203244	+	0.147666i	−0.481508	+	0.876442i	$0.659911\pi$
$368$	0.749021	+	2.30525i	0.0390454	+	0.120169i
$369$	−20.7820	−	63.9603i	−1.08187	−	3.32964i
$370$	4.92134	+	3.57557i	0.255848	+	0.185885i
$371$	0.261752	−	0.190174i	0.0135895	−	0.00987335i
$372$	4.25987	−	13.1105i	0.220864	−	0.679750i
$373$	−6.77161			−0.350621			−0.175310	−	0.984513i	$-0.556093\pi$
$373$	−6.77161			−0.350621			−0.175310	+	0.984513i	$0.556093\pi$
$374$	−2.36621	+	2.18707i	−0.122354	+	0.113091i
$375$	3.29803			0.170310
$376$	−3.82997	+	11.7875i	−0.197516	+	0.607891i
$377$	7.23612	−	5.25735i	0.372679	−	0.270767i
$378$	13.0127	+	9.45430i	0.669302	+	0.486277i
$379$	−10.9826	−	33.8011i	−0.564140	−	1.73624i	−0.670494	−	0.741915i	$-0.733918\pi$
$379$	−10.9826	−	33.8011i	−0.564140	−	1.73624i	0.106354	−	0.994328i	$-0.466082\pi$
$380$	0.322890	+	0.993753i	0.0165639	+	0.0509784i
$381$	18.5308	+	13.4634i	0.949362	+	0.689752i
$382$	5.19886	−	3.77720i	0.265997	−	0.193258i
$383$	6.50367	−	20.0163i	0.332322	−	1.02278i	−0.635704	−	0.771933i	$-0.719290\pi$
$383$	6.50367	−	20.0163i	0.332322	−	1.02278i	0.968026	−	0.250850i	$-0.0807100\pi$
$384$	−3.29803			−0.168302
$385$	−1.38838	−	3.01204i	−0.0707586	−	0.153508i
$386$	14.0142			0.713304
$387$	−7.45144	+	22.9332i	−0.378778	+	1.16576i
$388$	−12.0198	+	8.73287i	−0.610211	+	0.443344i
$389$	−28.4096	−	20.6408i	−1.44042	−	1.04653i	−0.987954	−	0.154747i	$-0.950544\pi$
$389$	−28.4096	−	20.6408i	−1.44042	−	1.04653i	−0.452468	−	0.891781i	$-0.649456\pi$
$390$	1.10689	+	3.40666i	0.0560496	+	0.172503i
$391$	0.727683	+	2.23958i	0.0368005	+	0.113260i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	−12.9090	+	9.37896i	−0.651175	+	0.473106i
$394$	6.59391	−	20.2940i	0.332196	−	1.02239i
$395$	11.4402			0.575620
$396$	5.09808	−	25.6229i	0.256188	−	1.28760i
$397$	10.4987			0.526914			0.263457	−	0.964671i	$-0.415137\pi$
$397$	10.4987			0.526914			0.263457	+	0.964671i	$0.415137\pi$
$398$	−8.17935	+	25.1734i	−0.409994	+	1.26183i
$399$	−2.78795	+	2.02556i	−0.139572	+	0.101405i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−6.76831	−	20.8307i	−0.337993	−	1.04024i	−0.965229	−	0.261406i	$-0.915814\pi$
$401$	−6.76831	−	20.8307i	−0.337993	−	1.04024i	0.627236	−	0.778829i	$-0.284186\pi$
$402$	−8.18660	−	25.1958i	−0.408311	−	1.25665i
$403$	3.67269	+	2.66836i	0.182950	+	0.132921i
$404$	−4.73830	+	3.44257i	−0.235739	+	0.171275i
$405$	−9.09020	+	27.9768i	−0.451696	+	1.39018i
$406$	−8.23533			−0.408712
$407$	20.0357	−	2.37034i	0.993132	−	0.117493i
$408$	−3.20408			−0.158626
$409$	2.85769	−	8.79508i	0.141304	−	0.434889i	−0.855213	−	0.518276i	$-0.826574\pi$
$409$	2.85769	−	8.79508i	0.141304	−	0.434889i	0.996517	+	0.0833876i	$0.0265740\pi$
$410$	−6.90716	+	5.01835i	−0.341120	+	0.247838i
$411$	−45.2115	−	32.8481i	−2.23012	−	1.62028i
$412$	−3.43274	−	10.5649i	−0.169119	−	0.520495i
$413$	3.67366	+	11.3064i	0.180769	+	0.556350i
$414$	−15.4466	−	11.2226i	−0.759157	−	0.551560i
$415$	−0.309077	+	0.224558i	−0.0151720	+	0.0110231i
$416$	0.335621	−	1.03294i	0.0164552	−	0.0506439i
$417$	32.3603			1.58469
$418$	3.02356	+	1.69348i	0.147887	+	0.0828309i
$419$	2.02744			0.0990469			0.0495235	−	0.998773i	$-0.484230\pi$
$419$	2.02744			0.0990469			0.0495235	+	0.998773i	$0.484230\pi$
$420$	1.01915	−	3.13662i	0.0497294	−	0.153051i
$421$	−7.52251	+	5.46543i	−0.366625	+	0.266369i	−0.755810	−	0.654791i	$-0.772757\pi$
$421$	−7.52251	+	5.46543i	−0.366625	+	0.266369i	0.389185	+	0.921160i	$0.372757\pi$
$422$	−10.2352	−	7.43628i	−0.498240	−	0.361992i
$423$	−30.1688	−	92.8501i	−1.46686	−	4.51453i
$424$	−0.0999804	−	0.307708i	−0.00485548	−	0.0149436i
$425$	−0.785971	−	0.571041i	−0.0381252	−	0.0276996i
$426$	11.1574	−	8.10630i	0.540576	−	0.392751i
$427$	4.06378	−	12.5070i	0.196660	−	0.605257i
$428$	7.35576			0.355554
$429$	10.3650	+	5.80538i	0.500427	+	0.280286i
$430$	3.06122			0.147625
$431$	−5.60091	+	17.2378i	−0.269787	+	0.830318i	0.720765	+	0.693179i	$0.243791\pi$
$431$	−5.60091	+	17.2378i	−0.269787	+	0.830318i	−0.990552	+	0.137139i	$0.956209\pi$
$432$	13.0127	−	9.45430i	0.626075	−	0.454870i
$433$	27.0943	+	19.6852i	1.30207	+	0.946009i	0.999974	−	0.00726825i	$-0.00231357\pi$
$433$	27.0943	+	19.6852i	1.30207	+	0.946009i	0.302096	+	0.953277i	$0.402314\pi$
$434$	−1.29164	−	3.97526i	−0.0620007	−	0.190819i
$435$	−8.39302	−	25.8311i	−0.402415	−	1.23850i
$436$	0.950949	+	0.690905i	0.0455422	+	0.0330883i
$437$	2.04900	−	1.48868i	0.0980167	−	0.0712133i
$438$	10.1316	−	31.1819i	0.484107	−	1.48993i
$439$	−39.7487			−1.89710			−0.948551	−	0.316623i	$-0.897451\pi$
$439$	−39.7487			−1.89710			−0.948551	+	0.316623i	$0.897451\pi$
$440$	−3.29366	+	0.389659i	−0.157019	+	0.0185763i
$441$	7.87703			0.375097
$442$	0.326061	−	1.00351i	0.0155091	−	0.0477322i
$443$	−29.1375	+	21.1696i	−1.38436	+	1.00580i	−0.387906	+	0.921699i	$0.626802\pi$
$443$	−29.1375	+	21.1696i	−1.38436	+	1.00580i	−0.996457	+	0.0841001i	$0.973198\pi$
$444$	16.2308	+	11.7923i	0.770278	+	0.559640i
$445$	3.46736	+	10.6714i	0.164369	+	0.505875i
$446$	−5.93322	−	18.2606i	−0.280946	−	0.864663i
$447$	−46.0452	−	33.4538i	−2.17787	−	1.58231i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	1.74300	−	5.36441i	0.0822573	−	0.253162i	−0.901467	−	0.432849i	$-0.857508\pi$
$449$	1.74300	−	5.36441i	0.0822573	−	0.253162i	0.983724	+	0.179687i	$0.0575084\pi$
$450$	7.87703			0.371327
$451$	−5.52568	+	27.7720i	−0.260194	+	1.30773i
$452$	11.3045			0.531720
$453$	−15.9656	+	49.1372i	−0.750131	+	2.30867i
$454$	−1.81759	+	1.32056i	−0.0853038	+	0.0619768i
$455$	0.878668	+	0.638390i	0.0411926	+	0.0299282i
$456$	1.06490	+	3.27743i	0.0498686	+	0.153480i
$457$	−6.56207	−	20.1960i	−0.306961	−	0.944727i	−0.978938	−	0.204156i	$-0.934555\pi$
$457$	−6.56207	−	20.1960i	−0.306961	−	0.944727i	0.671978	−	0.740571i	$-0.265445\pi$
$458$	3.87375	+	2.81444i	0.181008	+	0.131510i
$459$	12.6420	−	9.18497i	0.590080	−	0.428718i
$460$	−0.749021	+	2.30525i	−0.0349233	+	0.107483i
$461$	−36.7740			−1.71273			−0.856367	−	0.516367i	$-0.827284\pi$
$461$	−36.7740			−1.71273			−0.856367	+	0.516367i	$0.827284\pi$
$462$	−4.57894	−	9.93382i	−0.213031	−	0.462163i
$463$	21.8388			1.01494			0.507469	−	0.861670i	$-0.330581\pi$
$463$	21.8388			1.01494			0.507469	+	0.861670i	$0.330581\pi$
$464$	−2.54486	+	7.83226i	−0.118142	+	0.363604i
$465$	11.1525	−	8.10276i	0.517185	−	0.375757i
$466$	−10.3091	−	7.49002i	−0.477561	−	0.346968i
$467$	10.6524	+	32.7847i	0.492934	+	1.51710i	0.820152	+	0.572146i	$0.193889\pi$
$467$	10.6524	+	32.7847i	0.492934	+	1.51710i	−0.327217	+	0.944949i	$0.606111\pi$
$468$	2.64370	+	8.13647i	0.122205	+	0.376108i
$469$	−6.49866	−	4.72155i	−0.300080	−	0.218021i
$470$	−10.0270	+	7.28505i	−0.462511	+	0.336034i
$471$	−9.43519	+	29.0385i	−0.434751	+	1.33803i
$472$	11.8882			0.547200
$473$	7.45588	−	6.89144i	0.342822	−	0.316869i
$474$	37.7302			1.73301
$475$	−0.322890	+	0.993753i	−0.0148152	+	0.0455965i
$476$	−0.785971	+	0.571041i	−0.0360249	+	0.0261736i
$477$	2.06183	+	1.49801i	0.0944047	+	0.0685890i
$478$	−0.698297	−	2.14914i	−0.0319394	−	0.0982993i
$479$	−1.77209	−	5.45394i	−0.0809689	−	0.249197i	0.902375	−	0.430952i	$-0.141822\pi$
$479$	−1.77209	−	5.45394i	−0.0809689	−	0.249197i	−0.983344	+	0.181755i	$0.941822\pi$
$480$	−2.66817	−	1.93854i	−0.121785	−	0.0884817i
$481$	−5.34504	+	3.88340i	−0.243713	+	0.177068i
$482$	0.601444	−	1.85105i	0.0273950	−	0.0843132i
$483$	−7.99404			−0.363742
$484$	−7.14478	+	8.36373i	−0.324763	+	0.380170i
$485$	−14.8572			−0.674633
$486$	−15.0685	+	46.3762i	−0.683523	+	2.10367i
$487$	−5.64968	+	4.10474i	−0.256012	+	0.186003i	−0.708387	−	0.705824i	$-0.750577\pi$
$487$	−5.64968	+	4.10474i	−0.256012	+	0.186003i	0.452375	+	0.891828i	$0.350577\pi$
$488$	−10.6391	−	7.72976i	−0.481610	−	0.349910i
$489$	7.45443	+	22.9424i	0.337101	+	1.03749i
$490$	−0.309017	−	0.951057i	−0.0139600	−	0.0429644i
$491$	34.0264	+	24.7216i	1.53559	+	1.11567i	0.953028	+	0.302882i	$0.0979487\pi$
$491$	34.0264	+	24.7216i	1.53559	+	1.11567i	0.582560	+	0.812788i	$0.302051\pi$
$492$	−22.7801	+	16.5507i	−1.02700	+	0.746162i
$493$	−2.47236	+	7.60914i	−0.111350	+	0.342699i
$494$	−1.13485			−0.0510594
$495$	19.1852	−	17.7328i	0.862310	−	0.797030i
$496$	−4.17984			−0.187680
$497$	1.29220	−	3.97699i	0.0579633	−	0.178393i
$498$	−1.01935	+	0.740600i	−0.0456781	+	0.0331871i
$499$	16.1168	+	11.7096i	0.721488	+	0.524191i	0.886859	−	0.462040i	$-0.152882\pi$
$499$	16.1168	+	11.7096i	0.721488	+	0.524191i	−0.165371	+	0.986231i	$0.552882\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	12.8920	+	39.6775i	0.575973	+	1.77266i
$502$	12.8461	+	9.33322i	0.573349	+	0.416562i
$503$	−6.81374	+	4.95047i	−0.303810	+	0.220731i	−0.729236	−	0.684262i	$-0.760124\pi$
$503$	−6.81374	+	4.95047i	−0.303810	+	0.220731i	0.425426	+	0.904993i	$0.360124\pi$
$504$	2.43414	−	7.49150i	0.108425	−	0.333698i
$505$	−5.85686			−0.260627
$506$	3.36528	+	7.30083i	0.149605	+	0.324562i
$507$	38.9841			1.73134
$508$	2.14617	−	6.60523i	0.0952209	−	0.293060i
$509$	6.36874	−	4.62716i	0.282290	−	0.205095i	−0.437626	−	0.899157i	$-0.644181\pi$
$509$	6.36874	−	4.62716i	0.282290	−	0.205095i	0.719915	+	0.694062i	$0.244181\pi$
$510$	−2.59216	−	1.88331i	−0.114783	−	0.0833945i
$511$	−3.07201	−	9.45469i	−0.135898	−	0.418251i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−13.5969	−	9.87873i	−0.600318	−	0.436157i
$514$	5.72416	−	4.15885i	0.252482	−	0.183439i
$515$	3.43274	−	10.5649i	0.151265	−	0.465545i
$516$	10.0960			0.444453
$517$	−8.02153	+	40.3162i	−0.352787	+	1.77310i
$518$	6.08312			0.267277
$519$	−1.03393	+	3.18212i	−0.0453847	+	0.139680i
$520$	0.878668	−	0.638390i	0.0385321	−	0.0279952i
$521$	−19.0115	−	13.8127i	−0.832911	−	0.605145i	0.0874707	−	0.996167i	$-0.472122\pi$
$521$	−19.0115	−	13.8127i	−0.832911	−	0.605145i	−0.920381	+	0.391022i	$0.872122\pi$
$522$	−20.0459	−	61.6950i	−0.877385	−	2.70031i
$523$	−2.65092	−	8.15871i	−0.115917	−	0.356755i	0.876220	−	0.481911i	$-0.160057\pi$
$523$	−2.65092	−	8.15871i	−0.115917	−	0.356755i	−0.992137	+	0.125155i	$0.960057\pi$
$524$	3.91416	+	2.84380i	0.170991	+	0.124232i
$525$	2.66817	−	1.93854i	0.116448	−	0.0846046i
$526$	−8.07980	+	24.8671i	−0.352296	+	1.08426i
$527$	−4.06077			−0.176890
$528$	−10.8626	+	1.28511i	−0.472733	+	0.0559272i
$529$	−17.1248			−0.744556
$530$	0.0999804	−	0.307708i	0.00434287	−	0.0133660i
$531$	−75.7595	+	55.0425i	−3.28768	+	2.38864i
$532$	0.845336	+	0.614173i	0.0366500	+	0.0266278i
$533$	−2.86544	−	8.81892i	−0.124116	−	0.381990i
$534$	11.4355	+	35.1948i	0.494862	+	1.52303i
$535$	5.95094	+	4.32361i	0.257281	+	0.186926i
$536$	−6.49866	+	4.72155i	−0.280699	+	0.203940i
$537$	17.5252	−	53.9370i	0.756268	−	2.32755i
$538$	17.5426			0.756316
$539$	−2.89366	−	1.62072i	−0.124639	−	0.0698094i
$540$	16.0846			0.692171
$541$	−5.82770	+	17.9358i	−0.250552	+	0.771120i	0.744121	+	0.668045i	$0.232868\pi$
$541$	−5.82770	+	17.9358i	−0.250552	+	0.771120i	−0.994673	+	0.103076i	$0.967132\pi$
$542$	22.1061	−	16.0610i	0.949538	−	0.689880i
$543$	54.3515	+	39.4887i	2.33245	+	1.69462i
$544$	0.300214	+	0.923964i	0.0128716	+	0.0396146i
$545$	0.363230	+	1.11791i	0.0155591	+	0.0478859i
$546$	2.89788	+	2.10543i	0.124018	+	0.0901041i
$547$	−25.9861	+	18.8800i	−1.11108	+	0.807250i	−0.982834	−	0.184492i	$-0.940936\pi$
$547$	−25.9861	+	18.8800i	−1.11108	+	0.807250i	−0.128250	+	0.991742i	$0.540936\pi$
$548$	−5.23623	+	16.1155i	−0.223681	+	0.688418i
$549$	103.588			4.42103
$550$	−2.89366	−	1.62072i	−0.123386	−	0.0691078i
$551$	8.60504			0.366587
$552$	−2.47030	+	7.60279i	−0.105143	+	0.323596i
$553$	9.25533	−	6.72439i	0.393577	−	0.285950i
$554$	3.47602	+	2.52547i	0.147682	+	0.107297i
$555$	6.19960	+	19.0804i	0.263158	+	0.809918i
$556$	−3.03208	−	9.33178i	−0.128589	−	0.395756i
$557$	20.0225	+	14.5472i	0.848382	+	0.616386i	0.924700	−	0.380698i	$-0.124316\pi$
$557$	20.0225	+	14.5472i	0.848382	+	0.616386i	−0.0763171	+	0.997084i	$0.524316\pi$
$558$	26.6366	−	19.3526i	1.12762	−	0.819263i
$559$	−1.02741	+	3.16205i	−0.0434549	+	0.133740i
$560$	−1.00000			−0.0422577
$561$	−10.5531	+	1.24850i	−0.445554	+	0.0527117i
$562$	−25.8683			−1.09119
$563$	1.39286	−	4.28679i	0.0587021	−	0.180667i	−0.917406	−	0.397953i	$-0.869721\pi$
$563$	1.39286	−	4.28679i	0.0587021	−	0.180667i	0.976108	+	0.217287i	$0.0697206\pi$
$564$	−33.0694	+	24.0263i	−1.39247	+	1.01169i
$565$	9.14556	+	6.64464i	0.384756	+	0.279542i
$566$	8.38820	+	25.8162i	0.352583	+	1.08514i
$567$	9.09020	+	27.9768i	0.381753	+	1.17491i
$568$	−3.38303	−	2.45792i	−0.141949	−	0.103132i
$569$	28.5722	−	20.7589i	1.19781	−	0.870260i	0.203743	−	0.979024i	$-0.434689\pi$
$569$	28.5722	−	20.7589i	1.19781	−	0.870260i	0.994068	+	0.108764i	$0.0346894\pi$
$570$	−1.06490	+	3.27743i	−0.0446038	+	0.137276i
$571$	−21.6537			−0.906179			−0.453089	−	0.891465i	$-0.649678\pi$
$571$	−21.6537			−0.906179			−0.453089	+	0.891465i	$0.649678\pi$
$572$	0.702928	−	3.53291i	0.0293909	−	0.147719i
$573$	21.1937			0.885378
$574$	−2.63830	+	8.11985i	−0.110121	+	0.338916i
$575$	−1.96096	+	1.42472i	−0.0817777	+	0.0594150i
$576$	−6.37265	−	4.63000i	−0.265527	−	0.192917i
$577$	−1.85591	−	5.71192i	−0.0772627	−	0.237790i	0.904964	−	0.425488i	$-0.139897\pi$
$577$	−1.85591	−	5.71192i	−0.0772627	−	0.237790i	−0.982227	+	0.187698i	$0.939897\pi$
$578$	−4.96163	−	15.2703i	−0.206376	−	0.635161i
$579$	37.3922	+	27.1670i	1.55397	+	1.12902i
$580$	−6.66252	+	4.84060i	−0.276646	+	0.200995i
$581$	−0.118057	+	0.363342i	−0.00489783	+	0.0150740i
$582$	−48.9997			−2.03110
$583$	−0.449202	−	0.974526i	−0.0186041	−	0.0403608i
$584$	−9.94125			−0.411372
$585$	−2.64370	+	8.13647i	−0.109304	+	0.336402i
$586$	23.2733	−	16.9090i	0.961411	−	0.698506i
$587$	−4.67053	−	3.39334i	−0.192773	−	0.140058i	0.487212	−	0.873284i	$-0.338014\pi$
$587$	−4.67053	−	3.39334i	−0.192773	−	0.140058i	−0.679985	+	0.733226i	$0.738014\pi$
$588$	−1.01915	−	3.13662i	−0.0420290	−	0.129352i
$589$	1.34963	+	4.15372i	0.0556104	+	0.171151i
$590$	9.61777	+	6.98772i	0.395957	+	0.287680i
$591$	56.9342	−	41.3651i	2.34196	−	1.70153i
$592$	1.87979	−	5.78539i	0.0772587	−	0.237778i
$593$	10.5859			0.434710			0.217355	−	0.976093i	$-0.430257\pi$
$593$	10.5859			0.434710			0.217355	+	0.976093i	$0.430257\pi$
$594$	39.1755	−	36.2097i	1.60739	−	1.48570i
$595$	−0.971513			−0.0398282
$596$	−5.33279	+	16.4126i	−0.218439	+	0.672288i
$597$	−70.6235	+	51.3110i	−2.89043	+	2.10002i
$598$	−2.12979	−	1.54738i	−0.0870935	−	0.0632771i
$599$	−6.63325	−	20.4150i	−0.271027	−	0.834136i	−0.990243	−	0.139349i	$-0.955499\pi$
$599$	−6.63325	−	20.4150i	−0.271027	−	0.834136i	0.719216	−	0.694786i	$-0.244501\pi$
$600$	−1.01915	−	3.13662i	−0.0416066	−	0.128052i
$601$	−17.5485	−	12.7497i	−0.715819	−	0.520073i	0.169227	−	0.985577i	$-0.445873\pi$
$601$	−17.5485	−	12.7497i	−0.715819	−	0.520073i	−0.885046	+	0.465504i	$0.845873\pi$
$602$	2.47658	−	1.79934i	0.100938	−	0.0733357i
$603$	19.5529	−	60.1776i	0.796255	−	2.45062i
$604$	15.6657			0.637426
$605$	−10.6963	+	2.56680i	−0.434868	+	0.104355i
$606$	−19.3161			−0.784664
$607$	1.12402	−	3.45937i	0.0456224	−	0.140411i	−0.925651	−	0.378380i	$-0.876481\pi$
$607$	1.12402	−	3.45937i	0.0456224	−	0.140411i	0.971273	+	0.237968i	$0.0764814\pi$
$608$	0.845336	−	0.614173i	0.0342829	−	0.0249080i
$609$	−21.9732	−	15.9645i	−0.890400	−	0.646913i
$610$	−4.06378	−	12.5070i	−0.164537	−	0.506394i
$611$	−4.15971	−	12.8023i	−0.168284	−	0.517924i
$612$	−6.19111	−	4.49811i	−0.250261	−	0.181825i
$613$	27.0880	−	19.6806i	1.09407	−	0.794890i	0.113990	−	0.993482i	$-0.463637\pi$
$613$	27.0880	−	19.6806i	1.09407	−	0.794890i	0.980082	+	0.198591i	$0.0636367\pi$
$614$	−7.01346	+	21.5852i	−0.283040	+	0.871109i
$615$	−28.1577			−1.13543
$616$	−2.43559	+	2.25120i	−0.0981326	+	0.0907035i
$617$	19.6244			0.790048			0.395024	−	0.918671i	$-0.370736\pi$
$617$	19.6244			0.790048			0.395024	+	0.918671i	$0.370736\pi$
$618$	11.3213	−	34.8434i	0.455409	−	1.40161i
$619$	−3.91044	+	2.84110i	−0.157174	+	0.114194i	−0.663593	−	0.748094i	$-0.730969\pi$
$619$	−3.91044	+	2.84110i	−0.157174	+	0.114194i	0.506419	+	0.862288i	$0.330969\pi$
$620$	−3.38156	−	2.45685i	−0.135807	−	0.0986693i
$621$	−12.0477	−	37.0790i	−0.483458	−	1.48793i
$622$	0.234557	+	0.721892i	0.00940488	+	0.0289452i
$623$	9.07768	+	6.59532i	0.363689	+	0.264236i
$624$	2.89788	−	2.10543i	0.116008	−	0.0842847i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	21.6267			0.864377
$627$	4.78450	+	10.3798i	0.191074	+	0.414528i
$628$	9.25792			0.369431
$629$	1.82624	−	5.62058i	0.0728168	−	0.224107i
$630$	6.37265	−	4.63000i	0.253892	−	0.184464i
$631$	−8.30221	−	6.03191i	−0.330506	−	0.240127i	0.410139	−	0.912023i	$-0.365480\pi$
$631$	−8.30221	−	6.03191i	−0.330506	−	0.240127i	−0.740645	+	0.671896i	$0.765480\pi$
$632$	−3.53522	−	10.8803i	−0.140624	−	0.432795i
$633$	−12.8936	−	39.6824i	−0.512475	−	1.57724i
$634$	−0.0694036	−	0.0504247i	−0.00275637	−	0.00200262i
$635$	5.61874	−	4.08226i	0.222973	−	0.161999i
$636$	0.329739	−	1.01483i	0.0130750	−	0.0402407i
$637$	1.08609			0.0430326
$638$	−5.32997	+	26.7884i	−0.211015	+	1.06056i
$639$	32.9391			1.30305
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	8.83796	−	6.42115i	0.349078	−	0.253620i	−0.399404	−	0.916775i	$-0.630783\pi$
$641$	8.83796	−	6.42115i	0.349078	−	0.253620i	0.748482	+	0.663155i	$0.230783\pi$
$642$	19.6264	+	14.2594i	0.774592	+	0.562774i
$643$	−1.11743	−	3.43909i	−0.0440671	−	0.135624i	0.926602	−	0.376043i	$-0.122715\pi$
$643$	−1.11743	−	3.43909i	−0.0440671	−	0.135624i	−0.970669	+	0.240418i	$0.922715\pi$
$644$	0.749021	+	2.30525i	0.0295155	+	0.0908395i
$645$	8.16786	+	5.93429i	0.321609	+	0.233663i
$646$	0.821255	−	0.596677i	0.0323119	−	0.0234759i
$647$	−4.68285	+	14.4123i	−0.184102	+	0.566607i	−0.999932	−	0.0116848i	$-0.996281\pi$
$647$	−4.68285	+	14.4123i	−0.184102	+	0.566607i	0.815830	+	0.578292i	$0.196281\pi$
$648$	29.4165			1.15559
$649$	39.1557	−	4.63235i	1.53700	−	0.181836i
$650$	1.08609			0.0426001
$651$	4.25987	−	13.1105i	0.166958	−	0.513843i
$652$	5.91745	−	4.29928i	0.231745	−	0.168373i
$653$	8.37912	+	6.08779i	0.327900	+	0.238234i	0.739539	−	0.673114i	$-0.235043\pi$
$653$	8.37912	+	6.08779i	0.327900	+	0.238234i	−0.411639	+	0.911347i	$0.635043\pi$
$654$	1.19795	+	3.68690i	0.0468434	+	0.144169i
$655$	1.49508	+	4.60137i	0.0584175	+	0.179790i
$656$	6.90716	+	5.01835i	0.269679	+	0.195934i
$657$	63.3521	−	46.0280i	2.47160	−	1.79572i
$658$	−3.82997	+	11.7875i	−0.149308	+	0.459523i
$659$	−36.6439			−1.42744			−0.713722	−	0.700429i	$-0.752992\pi$
$659$	−36.6439			−1.42744			−0.713722	+	0.700429i	$0.752992\pi$
$660$	−9.54339	−	5.34519i	−0.371476	−	0.208061i
$661$	−23.5064			−0.914292			−0.457146	−	0.889392i	$-0.651128\pi$
$661$	−23.5064			−0.914292			−0.457146	+	0.889392i	$0.651128\pi$
$662$	−6.98460	+	21.4964i	−0.271464	+	0.835481i
$663$	2.81533	−	2.04545i	0.109338	−	0.0794388i
$664$	0.309077	+	0.224558i	0.0119945	+	0.00871454i
$665$	0.322890	+	0.993753i	0.0125211	+	0.0385361i
$666$	14.8071	+	45.5717i	0.573765	+	1.76587i
$667$	16.1492	+	11.7331i	0.625298	+	0.454306i
$668$	10.2339	−	7.43536i	0.395961	−	0.287683i
$669$	19.5679	−	60.2240i	0.756541	−	2.32839i
$670$	−8.03278			−0.310334
$671$	−38.0535	−	21.3135i	−1.46904	−	0.822800i
$672$	−3.29803			−0.127224
$673$	0.784039	−	2.41302i	0.0302225	−	0.0930153i	−0.934807	−	0.355155i	$-0.884428\pi$
$673$	0.784039	−	2.41302i	0.0302225	−	0.0930153i	0.965030	+	0.262140i	$0.0844281\pi$
$674$	−12.3528	+	8.97487i	−0.475814	+	0.345699i
$675$	13.0127	+	9.45430i	0.500860	+	0.363896i
$676$	−3.65270	−	11.2419i	−0.140489	−	0.432380i
$677$	−8.93951	−	27.5130i	−0.343573	−	1.05741i	−0.962343	−	0.271838i	$-0.912369\pi$
$677$	−8.93951	−	27.5130i	−0.343573	−	1.05741i	0.618770	−	0.785572i	$-0.287631\pi$
$678$	30.1624	+	21.9142i	1.15838	+	0.841611i
$679$	−12.0198	+	8.73287i	−0.461276	+	0.335137i
$680$	−0.300214	+	0.923964i	−0.0115127	+	0.0354324i
$681$	−7.40958			−0.283936
$682$	−13.7669	+	1.62871i	−0.527163	+	0.0623665i
$683$	−5.90465			−0.225935			−0.112968	−	0.993599i	$-0.536036\pi$
$683$	−5.90465			−0.225935			−0.112968	+	0.993599i	$0.536036\pi$
$684$	−2.54341	+	7.82782i	−0.0972498	+	0.299304i
$685$	−13.7086	+	9.95990i	−0.523780	+	0.380548i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	4.87991	+	15.0188i	0.186180	+	0.573003i
$688$	−0.945971	−	2.91140i	−0.0360648	−	0.110996i
$689$	0.284287	+	0.206547i	0.0108305	+	0.00786881i
$690$	−6.46732	+	4.69878i	−0.246207	+	0.178880i
$691$	−14.8269	+	45.6325i	−0.564042	+	1.73594i	0.106738	+	0.994287i	$0.465959\pi$
$691$	−14.8269	+	45.6325i	−0.564042	+	1.73594i	−0.670780	+	0.741656i	$0.734041\pi$
$692$	1.01451			0.0385658
$693$	5.09808	−	25.6229i	0.193660	−	0.973334i
$694$	5.89915			0.223929
$695$	3.03208	−	9.33178i	0.115013	−	0.353974i
$696$	−21.9732	+	15.9645i	−0.832893	+	0.605132i
$697$	6.71040	+	4.87539i	0.254174	+	0.184669i
$698$	5.22286	+	16.0743i	0.197688	+	0.608422i
$699$	−12.9868	−	39.9692i	−0.491205	−	1.51178i
$700$	−0.809017	−	0.587785i	−0.0305780	−	0.0222162i
$701$	25.1602	−	18.2799i	0.950287	−	0.690424i	−0.000587861	−	1.00000i	$-0.500187\pi$
$701$	25.1602	−	18.2799i	0.950287	−	0.690424i	0.950875	+	0.309576i	$0.100187\pi$
$702$	−5.39834	+	16.6144i	−0.203747	+	0.627069i
$703$	−6.35621			−0.239729
$704$	1.38838	+	3.01204i	0.0523267	+	0.113521i
$705$	−40.8760			−1.53948
$706$	−5.37422	+	16.5402i	−0.202262	+	0.622497i
$707$	−4.73830	+	3.44257i	−0.178202	+	0.129471i
$708$	31.7197	+	23.0457i	1.19210	+	0.866112i
$709$	0.477131	+	1.46846i	0.0179190	+	0.0551491i	0.959616	−	0.281313i	$-0.0907698\pi$
$709$	0.477131	+	1.46846i	0.0179190	+	0.0551491i	−0.941697	+	0.336462i	$0.890770\pi$
$710$	−1.29220	−	3.97699i	−0.0484956	−	0.149254i
$711$	72.9045	+	52.9682i	2.73413	+	1.98646i
$712$	9.07768	−	6.59532i	0.340200	−	0.247170i
$713$	−3.13078	+	9.63556i	−0.117249	+	0.360855i
$714$	−3.20408			−0.119910
$715$	2.64528	−	2.44502i	0.0989277	−	0.0914384i
$716$	−17.1959			−0.642641
$717$	2.30301	−	7.08793i	0.0860074	−	0.264704i
$718$	−18.1609	+	13.1946i	−0.677758	+	0.492420i
$719$	22.5770	+	16.4031i	0.841979	+	0.611733i	0.922923	−	0.384985i	$-0.125793\pi$
$719$	22.5770	+	16.4031i	0.841979	+	0.611733i	−0.0809440	+	0.996719i	$0.525793\pi$
$720$	−2.43414	−	7.49150i	−0.0907149	−	0.279192i
$721$	−3.43274	−	10.5649i	−0.127842	−	0.393457i
$722$	14.4880	+	10.5262i	0.539189	+	0.391744i
$723$	5.19308	−	3.77300i	0.193133	−	0.140319i
$724$	6.29479	−	19.3734i	0.233944	−	0.720006i
$725$	−8.23533			−0.305852
$726$	−35.2769	+	8.46541i	−1.30925	+	0.314181i
$727$	19.3666			0.718267			0.359133	−	0.933286i	$-0.383072\pi$
$727$	19.3666			0.718267			0.359133	+	0.933286i	$0.383072\pi$
$728$	0.335621	−	1.03294i	0.0124390	−	0.0382832i
$729$	−58.7119	+	42.6567i	−2.17452	+	1.57988i
$730$	−8.04264	−	5.84332i	−0.297671	−	0.216271i
$731$	−0.919023	−	2.82846i	−0.0339913	−	0.104614i
$732$	−13.4025	−	41.2486i	−0.495370	−	1.52459i
$733$	4.23223	+	3.07489i	0.156321	+	0.113574i	0.663196	−	0.748446i	$-0.269200\pi$
$733$	4.23223	+	3.07489i	0.156321	+	0.113574i	−0.506875	+	0.862019i	$0.669200\pi$
$734$	3.89360	−	2.82886i	0.143715	−	0.104415i
$735$	1.01915	−	3.13662i	0.0375919	−	0.115696i
$736$	2.42388			0.0893455
$737$	−19.5645	+	18.0834i	−0.720669	+	0.666112i
$738$	−67.2519			−2.47558
$739$	3.38013	−	10.4030i	0.124340	−	0.382680i	−0.869440	−	0.494038i	$-0.835520\pi$
$739$	3.38013	−	10.4030i	0.124340	−	0.382680i	0.993780	+	0.111359i	$0.0355202\pi$
$740$	4.92134	−	3.57557i	0.180912	−	0.131440i
$741$	−3.02797	−	2.19995i	−0.111235	−	0.0808172i
$742$	−0.0999804	−	0.307708i	−0.00367040	−	0.0112963i
$743$	9.91163	+	30.5048i	0.363622	+	1.11911i	0.950839	+	0.309685i	$0.100224\pi$
$743$	9.91163	+	30.5048i	0.363622	+	1.11911i	−0.587217	+	0.809430i	$0.699776\pi$
$744$	−11.1525	−	8.10276i	−0.408870	−	0.297062i
$745$	−13.9614	+	10.1436i	−0.511507	+	0.371631i
$746$	−2.09254	+	6.44018i	−0.0766134	+	0.235792i
$747$	−3.00935			−0.110106
$748$	1.34883	+	2.92624i	0.0493182	+	0.106994i
$749$	7.35576			0.268774
$750$	1.01915	−	3.13662i	0.0372140	−	0.114533i
$751$	−1.85431	+	1.34724i	−0.0676648	+	0.0491614i	−0.621103	−	0.783729i	$-0.713315\pi$
$751$	−1.85431	+	1.34724i	−0.0676648	+	0.0491614i	0.553439	+	0.832890i	$0.313315\pi$
$752$	10.0270	+	7.28505i	0.365647	+	0.265658i
$753$	16.1827	+	49.8052i	0.589730	+	1.81500i
$754$	−2.76395	−	8.50657i	−0.100657	−	0.309791i
$755$	12.6738	+	9.20804i	0.461246	+	0.335115i
$756$	13.0127	−	9.45430i	0.473268	−	0.343849i
$757$	15.2012	−	46.7843i	0.552495	−	1.70041i	−0.149973	−	0.988690i	$-0.547919\pi$
$757$	15.2012	−	46.7843i	0.552495	−	1.70041i	0.702468	−	0.711715i	$-0.252081\pi$
$758$	−35.5405			−1.29089
$759$	−5.17381	+	26.0035i	−0.187797	+	0.943869i
$760$	1.04489			0.0379023
$761$	−9.96749	+	30.6768i	−0.361321	+	1.11203i	0.590932	+	0.806722i	$0.298760\pi$
$761$	−9.96749	+	30.6768i	−0.361321	+	1.11203i	−0.952253	+	0.305311i	$0.901240\pi$
$762$	18.5308	−	13.4634i	0.671300	−	0.487728i
$763$	0.950949	+	0.690905i	0.0344267	+	0.0250124i
$764$	−1.98579	−	6.11163i	−0.0718433	−	0.221111i
$765$	−2.36480	−	7.27809i	−0.0854994	−	0.263140i
$766$	−17.0268	−	12.3707i	−0.615205	−	0.446972i
$767$	−10.4458	+	7.58932i	−0.377176	+	0.274034i
$768$	−1.01915	+	3.13662i	−0.0367754	+	0.113183i
$769$	36.9722			1.33325			0.666625	−	0.745393i	$-0.267738\pi$
$769$	36.9722			1.33325			0.666625	+	0.745393i	$0.267738\pi$
$770$	−3.29366	+	0.389659i	−0.118695	+	0.0140423i
$771$	23.3351			0.840393
$772$	4.33063	−	13.3283i	0.155863	−	0.479696i
$773$	35.7016	−	25.9387i	1.28410	−	0.932951i	0.284429	−	0.958697i	$-0.408196\pi$
$773$	35.7016	−	25.9387i	1.28410	−	0.932951i	0.999669	+	0.0257458i	$0.00819605\pi$
$774$	19.5081	+	14.1735i	0.701205	+	0.509455i
$775$	−1.29164	−	3.97526i	−0.0463971	−	0.142796i
$776$	4.59114	+	14.1301i	0.164812	+	0.507240i
$777$	16.2308	+	11.7923i	0.582275	+	0.423048i
$778$	−28.4096	+	20.6408i	−1.01853	+	0.740007i
$779$	2.75674	−	8.48438i	0.0987706	−	0.303985i
$780$	3.58197			0.128255
$781$	−12.1003	−	6.77731i	−0.432983	−	0.242511i
$782$	2.35483			0.0842087
$783$	40.9330	−	125.979i	1.46283	−	4.50212i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	7.48981	+	5.44167i	0.267323	+	0.194221i
$786$	4.93081	+	15.1755i	0.175876	+	0.541292i
$787$	−8.47776	−	26.0919i	−0.302200	−	0.930075i	−0.980707	−	0.195481i	$-0.937373\pi$
$787$	−8.47776	−	26.0919i	−0.302200	−	0.930075i	0.678508	−	0.734593i	$-0.262627\pi$
$788$	−17.2631	−	12.5424i	−0.614971	−	0.446803i
$789$	−69.7639	+	50.6864i	−2.48366	+	1.80449i
$790$	3.53522	−	10.8803i	0.125777	−	0.387103i
$791$	11.3045			0.401943
$792$	−22.7934	−	12.7665i	−0.809930	−	0.453637i
$793$	14.2828			0.507198
$794$	3.24427	−	9.98484i	0.115135	−	0.354349i
$795$	0.863268	−	0.627201i	0.0306169	−	0.0222445i
$796$	21.4138	+	15.5580i	0.758992	+	0.551440i
$797$	−1.07916	−	3.32130i	−0.0382257	−	0.117647i	0.930123	−	0.367249i	$-0.119700\pi$
$797$	−1.07916	−	3.32130i	−0.0382257	−	0.117647i	−0.968348	+	0.249602i	$0.919700\pi$
$798$	1.06490	+	3.27743i	0.0376971	+	0.116020i
$799$	9.74137	+	7.07752i	0.344625	+	0.250385i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−27.3125	+	84.0593i	−0.965041	+	2.97009i
$802$	−21.9027			−0.773411
$803$	−32.7430	+	3.87370i	−1.15548	+	0.136700i
$804$	−26.4924			−0.934315
$805$	−0.749021	+	2.30525i	−0.0263995	+	0.0812493i
$806$	3.67269	−	2.66836i	0.129365	−	0.0939891i
$807$	46.8066	+	34.0070i	1.64767	+	1.19710i
$808$	1.80987	+	5.57020i	0.0636710	+	0.195959i
$809$	−7.09247	−	21.8284i	−0.249358	−	0.767444i	−0.994889	−	0.100974i	$-0.967804\pi$
$809$	−7.09247	−	21.8284i	−0.249358	−	0.767444i	0.745531	−	0.666471i	$-0.232196\pi$
$810$	23.7985	+	17.2906i	0.836192	+	0.607529i
$811$	20.5362	−	14.9204i	0.721122	−	0.523926i	−0.165620	−	0.986190i	$-0.552963\pi$
$811$	20.5362	−	14.9204i	0.721122	−	0.523926i	0.886743	+	0.462264i	$0.152963\pi$
$812$	−2.54486	+	7.83226i	−0.0893069	+	0.274858i
$813$	90.1176			3.16056
$814$	3.93704	−	19.7875i	0.137993	−	0.693553i
$815$	7.31437			0.256211
$816$	−0.990116	+	3.04726i	−0.0346610	+	0.106676i
$817$	−2.58776	+	1.88012i	−0.0905344	+	0.0657771i
$818$	−7.48154	−	5.43566i	−0.261586	−	0.190053i
$819$	2.64370	+	8.13647i	0.0923783	+	0.284311i
$820$	2.63830	+	8.11985i	0.0921335	+	0.283558i
$821$	0.126729	+	0.0920737i	0.00442286	+	0.00321339i	0.589994	−	0.807407i	$-0.299130\pi$
$821$	0.126729	+	0.0920737i	0.00442286	+	0.00321339i	−0.585572	+	0.810621i	$0.699130\pi$
$822$	−45.2115	+	32.8481i	−1.57693	+	1.14571i
$823$	6.25973	−	19.2655i	0.218201	−	0.671552i	−0.780710	−	0.624893i	$-0.785143\pi$
$823$	6.25973	−	19.2655i	0.218201	−	0.671552i	0.998911	−	0.0466591i	$-0.0148574\pi$
$824$	−11.1086			−0.386986
$825$	−4.57894	−	9.93382i	−0.159418	−	0.345851i
$826$	11.8882			0.413644
$827$	−1.60898	+	4.95192i	−0.0559496	+	0.172195i	−0.975126	−	0.221651i	$-0.928856\pi$
$827$	−1.60898	+	4.95192i	−0.0559496	+	0.172195i	0.919177	+	0.393846i	$0.128856\pi$
$828$	−15.4466	+	11.2226i	−0.536805	+	0.390012i
$829$	−31.5088	−	22.8925i	−1.09434	−	0.795088i	−0.114217	−	0.993456i	$-0.536436\pi$
$829$	−31.5088	−	22.8925i	−1.09434	−	0.795088i	−0.980128	+	0.198368i	$0.936436\pi$
$830$	0.118057	+	0.363342i	0.00409782	+	0.0126118i
$831$	4.37887	+	13.4768i	0.151901	+	0.467504i
$832$	−0.878668	−	0.638390i	−0.0304623	−	0.0221322i
$833$	−0.785971	+	0.571041i	−0.0272323	+	0.0197854i
$834$	9.99990	−	30.7765i	0.346268	−	1.06570i
$835$	12.6498			0.437764
$836$	2.54493	−	2.35227i	0.0880182	−	0.0813548i
$837$	67.2310			2.32384
$838$	0.626513	−	1.92821i	0.0216425	−	0.0666089i
$839$	−7.69034	+	5.58736i	−0.265500	+	0.192897i	−0.712568	−	0.701603i	$-0.752468\pi$
$839$	−7.69034	+	5.58736i	−0.265500	+	0.192897i	0.447068	+	0.894500i	$0.352468\pi$
$840$	−2.66817	−	1.93854i	−0.0920605	−	0.0668858i
$841$	11.9962	+	36.9206i	0.413663	+	1.27312i
$842$	2.87334	+	8.84325i	0.0990220	+	0.304758i
$843$	−69.0208	−	50.1466i	−2.37720	−	1.72714i
$844$	−10.2352	+	7.43628i	−0.352309	+	0.255967i
$845$	3.65270	−	11.2419i	0.125657	−	0.386732i
$846$	−97.6284			−3.35653
$847$	−7.14478	+	8.36373i	−0.245498	+	0.287381i
$848$	−0.323543			−0.0111105
$849$	−27.6646	+	85.1428i	−0.949446	+	2.92209i
$850$	−0.785971	+	0.571041i	−0.0269586	+	0.0195865i
$851$	−11.9288	−	8.66675i	−0.408912	−	0.297092i
$852$	−4.26173	−	13.1163i	−0.146005	−	0.449356i
$853$	−0.416716	−	1.28252i	−0.0142681	−	0.0439127i	0.943669	−	0.330891i	$-0.107349\pi$
$853$	−0.416716	−	1.28252i	−0.0142681	−	0.0439127i	−0.957937	+	0.286978i	$0.907349\pi$
$854$	−10.6391	−	7.72976i	−0.364063	−	0.264507i
$855$	−6.65874	+	4.83786i	−0.227724	+	0.165451i
$856$	2.27306	−	6.99575i	0.0776914	−	0.239110i
$857$	24.4121			0.833900			0.416950	−	0.908929i	$-0.363099\pi$
$857$	24.4121			0.833900			0.416950	+	0.908929i	$0.363099\pi$
$858$	8.72421	−	8.06375i	0.297840	−	0.275292i
$859$	4.39769			0.150047			0.0750236	−	0.997182i	$-0.476097\pi$
$859$	4.39769			0.150047			0.0750236	+	0.997182i	$0.476097\pi$
$860$	0.945971	−	2.91140i	0.0322573	−	0.0992778i
$861$	−22.7801	+	16.5507i	−0.776342	+	0.564046i
$862$	14.6634	+	10.6536i	0.499437	+	0.362862i
$863$	−6.38548	−	19.6525i	−0.217364	−	0.668978i	−0.998977	−	0.0452147i	$-0.985603\pi$
$863$	−6.38548	−	19.6525i	−0.217364	−	0.668978i	0.781613	−	0.623764i	$-0.214397\pi$
$864$	−4.97042	−	15.2974i	−0.169097	−	0.520427i
$865$	0.820754	+	0.596312i	0.0279065	+	0.0202752i
$866$	27.0943	−	19.6852i	0.920702	−	0.668929i
$867$	16.3636	−	50.3620i	0.555738	−	1.71038i
$868$	−4.17984			−0.141873
$869$	−15.8834	−	34.4584i	−0.538807	−	1.16892i
$870$	−27.1604			−0.920823
$871$	2.69597	−	8.29735i	0.0913496	−	0.281145i
$872$	0.950949	−	0.690905i	0.0322032	−	0.0233970i
$873$	−94.6800	−	68.7891i	−3.20443	−	2.32816i
$874$	−0.782647	−	2.40874i	−0.0264734	−	0.0814768i
$875$	−0.309017	−	0.951057i	−0.0104467	−	0.0321516i
$876$	−26.5249	−	19.2715i	−0.896193	−	0.651122i
$877$	−14.3461	+	10.4231i	−0.484434	+	0.351962i	−0.803040	−	0.595925i	$-0.796785\pi$
$877$	−14.3461	+	10.4231i	−0.484434	+	0.351962i	0.318606	+	0.947887i	$0.396785\pi$
$878$	−12.2830	+	37.8033i	−0.414532	+	1.27580i
$879$	94.8758			3.20008
$880$	−0.647208	+	3.25286i	−0.0218174	+	0.109654i
$881$	52.1966			1.75855			0.879274	−	0.476317i	$-0.158029\pi$
$881$	52.1966			1.75855			0.879274	+	0.476317i	$0.158029\pi$
$882$	2.43414	−	7.49150i	0.0819616	−	0.252252i
$883$	−2.64331	+	1.92048i	−0.0889544	+	0.0646291i	−0.631373	−	0.775479i	$-0.717508\pi$
$883$	−2.64331	+	1.92048i	−0.0889544	+	0.0646291i	0.542419	+	0.840108i	$0.317508\pi$
$884$	−0.853638	−	0.620204i	−0.0287109	−	0.0208597i
$885$	12.1159	+	37.2888i	0.407270	+	1.25345i
$886$	11.1295	+	34.2532i	0.373904	+	1.15076i
$887$	35.2055	+	25.5783i	1.18209	+	0.858836i	0.992405	−	0.123010i	$-0.0392548\pi$
$887$	35.2055	+	25.5783i	1.18209	+	0.858836i	0.189681	+	0.981846i	$0.439255\pi$
$888$	16.2308	−	11.7923i	0.544669	−	0.395725i
$889$	2.14617	−	6.60523i	0.0719802	−	0.221532i
$890$	11.2206			0.376116
$891$	96.8878	−	11.4624i	3.24586	−	0.384005i
$892$	−19.2003			−0.642873
$893$	4.00192	−	12.3166i	0.133919	−	0.412160i
$894$	−46.0452	+	33.4538i	−1.53998	+	1.11886i
$895$	−13.9118	−	10.1075i	−0.465020	−	0.337857i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	−2.68297	−	8.25734i	−0.0895818	−	0.275704i
$898$	−4.56324	−	3.31539i	−0.152277	−	0.110636i
$899$	−27.8482	+	20.2329i	−0.928791	+	0.674806i
$900$	2.43414	−	7.49150i	0.0811379	−	0.249717i
$901$	−0.314327			−0.0104717
$902$	24.7053	+	13.8373i	0.822595	+	0.460731i
$903$	10.0960			0.335975
$904$	3.49329	−	10.7512i	0.116185	−	0.357581i
$905$	16.4800	−	11.9734i	0.547813	−	0.398010i
$906$	41.7986	+	30.3684i	1.38866	+	1.00892i
$907$	5.88521	+	18.1128i	0.195415	+	0.601427i	0.999971	+	0.00755001i	$0.00240327\pi$
$907$	5.88521	+	18.1128i	0.195415	+	0.601427i	−0.804556	+	0.593877i	$0.797597\pi$
$908$	0.694258	+	2.13671i	0.0230398	+	0.0709091i
$909$	−37.3237	−	27.1173i	−1.23795	−	0.899423i
$910$	0.878668	−	0.638390i	0.0291276	−	0.0211624i
$911$	4.05935	−	12.4934i	0.134492	−	0.413925i	−0.861018	−	0.508574i	$-0.830173\pi$
$911$	4.05935	−	12.4934i	0.134492	−	0.413925i	0.995511	+	0.0946492i	$0.0301729\pi$
$912$	3.44609			0.114112
$913$	1.10550	+	0.619182i	0.0365866	+	0.0204919i
$914$	−21.2353			−0.702401
$915$	13.4025	−	41.2486i	0.443072	−	1.36364i
$916$	3.87375	−	2.81444i	0.127992	−	0.0929919i
$917$	3.91416	+	2.84380i	0.129257	+	0.0939107i
$918$	−4.82883	−	14.8616i	−0.159375	−	0.490506i
$919$	−6.24859	−	19.2312i	−0.206122	−	0.634378i	−0.999665	−	0.0258645i	$-0.991766\pi$
$919$	−6.24859	−	19.2312i	−0.206122	−	0.634378i	0.793544	−	0.608513i	$-0.208234\pi$
$920$	1.96096	+	1.42472i	0.0646510	+	0.0469717i
$921$	−60.5568	+	43.9971i	−1.99542	+	1.44975i
$922$	−11.3638	+	34.9741i	−0.374246	+	1.15181i
$923$	4.54167			0.149491
$924$	−10.8626	+	1.28511i	−0.357353	+	0.0422770i
$925$	6.08312			0.200012
$926$	6.74857	−	20.7700i	0.221772	−	0.682544i
$927$	70.7911	−	51.4327i	2.32508	−	1.68927i
$928$	6.66252	+	4.84060i	0.218708	+	0.158901i
$929$	−8.26981	−	25.4519i	−0.271324	−	0.835049i	−0.990169	−	0.139878i	$-0.955329\pi$
$929$	−8.26981	−	25.4519i	−0.271324	−	0.835049i	0.718845	−	0.695170i	$-0.244671\pi$
$930$	−4.25987	−	13.1105i	−0.139687	−	0.429912i
$931$	0.845336	+	0.614173i	0.0277048	+	0.0201287i
$932$	−10.3091	+	7.49002i	−0.337687	+	0.245344i
$933$	−0.773577	+	2.38083i	−0.0253258	+	0.0779447i
$934$	34.4719			1.12795
$935$	−0.628771	+	3.16020i	−0.0205630	+	0.103350i
$936$	8.55519			0.279635
$937$	12.0389	−	37.0518i	0.393293	−	1.21043i	−0.536990	−	0.843588i	$-0.680439\pi$
$937$	12.0389	−	37.0518i	0.393293	−	1.21043i	0.930283	−	0.366842i	$-0.119561\pi$
$938$	−6.49866	+	4.72155i	−0.212189	+	0.154164i
$939$	57.7036	+	41.9241i	1.88309	+	1.36814i
$940$	3.82997	+	11.7875i	0.124920	+	0.384464i
$941$	5.31931	+	16.3711i	0.173405	+	0.533684i	0.999557	−	0.0297624i	$-0.00947506\pi$
$941$	5.31931	+	16.3711i	0.173405	+	0.533684i	−0.826152	+	0.563447i	$0.809475\pi$
$942$	24.7017	+	17.9468i	0.804823	+	0.584738i
$943$	16.7421	−	12.1639i	0.545199	−	0.396110i
$944$	3.67366	−	11.3064i	0.119568	−	0.367991i
$945$	16.0846			0.523232
$946$	−4.25015	−	9.22054i	−0.138184	−	0.299785i
$947$	−9.19053			−0.298652			−0.149326	−	0.988788i	$-0.547710\pi$
$947$	−9.19053			−0.298652			−0.149326	+	0.988788i	$0.547710\pi$
$948$	11.6593	−	35.8836i	0.378676	−	1.16544i
$949$	8.73506	−	6.34639i	0.283552	−	0.206013i
$950$	0.845336	+	0.614173i	0.0274263	+	0.0199264i
$951$	−0.0874303	−	0.269083i	−0.00283512	−	0.00872561i
$952$	0.300214	+	0.923964i	0.00972999	+	0.0299458i
$953$	12.2428	+	8.89492i	0.396584	+	0.288135i	0.768148	−	0.640272i	$-0.221178\pi$
$953$	12.2428	+	8.89492i	0.396584	+	0.288135i	−0.371564	+	0.928407i	$0.621178\pi$
$954$	2.06183	−	1.49801i	0.0667542	−	0.0484998i
$955$	1.98579	−	6.11163i	0.0642586	−	0.197768i
$956$	−2.25974			−0.0730851
$957$	−66.1515	+	61.1435i	−2.13837	+	1.97649i
$958$	−5.73461			−0.185277
$959$	−5.23623	+	16.1155i	−0.169087	+	0.520395i
$960$	−2.66817	+	1.93854i	−0.0861147	+	0.0625660i
$961$	10.9452	+	7.95213i	0.353070	+	0.256520i
$962$	2.04162	+	6.28347i	0.0658246	+	0.202587i
$963$	17.9049	+	55.1057i	0.576978	+	1.77576i
$964$	−1.57460	−	1.14401i	−0.0507144	−	0.0368462i
$965$	11.3377	−	8.23734i	0.364975	−	0.265170i
$966$	−2.47030	+	7.60279i	−0.0794805	+	0.244616i
$967$	−34.7020			−1.11594			−0.557970	−	0.829861i	$-0.688420\pi$
$967$	−34.7020			−1.11594			−0.557970	+	0.829861i	$0.688420\pi$
$968$	5.74652	+	9.37963i	0.184700	+	0.301473i
$969$	3.34793			0.107551
$970$	−4.59114	+	14.1301i	−0.147413	+	0.453689i
$971$	6.57060	−	4.77382i	0.210860	−	0.153199i	−0.477342	−	0.878717i	$-0.658400\pi$
$971$	6.57060	−	4.77382i	0.210860	−	0.153199i	0.688203	+	0.725518i	$0.258400\pi$
$972$	39.4499	+	28.6621i	1.26536	+	0.919336i
$973$	−3.03208	−	9.33178i	−0.0972040	−	0.299163i
$974$	2.15799	+	6.64160i	0.0691464	+	0.212811i
$975$	2.89788	+	2.10543i	0.0928063	+	0.0674278i
$976$	−10.6391	+	7.72976i	−0.340549	+	0.247424i
$977$	7.35143	−	22.6254i	0.235193	−	0.723850i	−0.761903	−	0.647692i	$-0.775735\pi$
$977$	7.35143	−	22.6254i	0.235193	−	0.723850i	0.997096	−	0.0761583i	$-0.0242654\pi$
$978$	24.1230			0.771369
$979$	27.3288	−	25.2599i	0.873433	−	0.807310i
$980$	−1.00000			−0.0319438
$981$	−2.86118	+	8.80579i	−0.0913503	+	0.281147i
$982$	34.0264	−	24.7216i	1.08582	−	0.788898i
$983$	18.7929	+	13.6539i	0.599402	+	0.435491i	0.845666	−	0.533712i	$-0.179203\pi$
$983$	18.7929	+	13.6539i	0.599402	+	0.435491i	−0.246265	+	0.969203i	$0.579203\pi$
$984$	8.70121	+	26.7796i	0.277384	+	0.853701i
$985$	−6.59391	−	20.2940i	−0.210099	−	0.646619i
$986$	6.47273	+	4.70271i	0.206134	+	0.149765i
$987$	−33.0694	+	24.0263i	−1.05261	+	0.764766i
$988$	−0.350688	+	1.07931i	−0.0111569	+	0.0343374i
$989$	−7.42005			−0.235944
$990$	−10.9363	−	23.7259i	−0.347580	−	0.754060i
$991$	19.2128			0.610315			0.305157	−	0.952302i	$-0.401291\pi$
$991$	19.2128			0.610315			0.305157	+	0.952302i	$0.401291\pi$
$992$	−1.29164	+	3.97526i	−0.0410096	+	0.126215i
$993$	−60.3076	+	43.8160i	−1.91380	+	1.39046i
$994$	−3.38303	−	2.45792i	−0.107303	−	0.0779604i
$995$	8.17935	+	25.1734i	0.259303	+	0.798052i
$996$	0.389356	+	1.19832i	0.0123372	+	0.0379701i
$997$	−9.74504	−	7.08018i	−0.308628	−	0.224232i	0.422679	−	0.906279i	$-0.361090\pi$
$997$	−9.74504	−	7.08018i	−0.308628	−	0.224232i	−0.731308	+	0.682048i	$0.761090\pi$
$998$	16.1168	−	11.7096i	0.510169	−	0.370659i
$999$	−30.2356	+	93.0557i	−0.956613	+	2.94415i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.71.3	✓	12	11.5	even	5	inner
770.2.n.h.141.3	yes	12	1.1	even	1	trivial
8470.2.a.cu.1.1		6	11.7	odd	10
8470.2.a.da.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.66817 - 1.93854i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.01915 - 3.13662i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.43414 - 7.49150i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.66817 - 1.93854i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.01915 - 3.13662i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.43414 - 7.49150i) q^{9} -1.00000 q^{10} +(-2.43559 + 2.25120i) q^{11} -3.29803 q^{12} +(0.335621 - 1.03294i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-2.66817 - 1.93854i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.300214 + 0.923964i) q^{17} +(-6.37265 - 4.63000i) q^{18} +(0.845336 - 0.614173i) q^{19} +(-0.309017 + 0.951057i) q^{20} -3.29803 q^{21} +(1.38838 + 3.01204i) q^{22} +2.42388 q^{23} +(-1.01915 + 3.13662i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.878668 - 0.638390i) q^{26} +(-4.97042 - 15.2974i) q^{27} +(0.309017 + 0.951057i) q^{28} +(6.66252 + 4.84060i) q^{29} +(-2.66817 + 1.93854i) q^{30} +(-1.29164 + 3.97526i) q^{31} +1.00000 q^{32} +(-2.13451 + 10.7281i) q^{33} +0.971513 q^{34} +(-0.309017 + 0.951057i) q^{35} +(-6.37265 + 4.63000i) q^{36} +(-4.92134 - 3.57557i) q^{37} +(-0.322890 - 0.993753i) q^{38} +(-1.10689 - 3.40666i) q^{39} +(0.809017 + 0.587785i) q^{40} +(6.90716 - 5.01835i) q^{41} +(-1.01915 + 3.13662i) q^{42} -3.06122 q^{43} +(3.29366 - 0.389659i) q^{44} -7.87703 q^{45} +(0.749021 - 2.30525i) q^{46} +(10.0270 - 7.28505i) q^{47} +(2.66817 + 1.93854i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(2.59216 + 1.88331i) q^{51} +(-0.878668 + 0.638390i) q^{52} +(-0.0999804 + 0.307708i) q^{53} -16.0846 q^{54} +(2.89366 + 1.62072i) q^{55} +1.00000 q^{56} +(1.06490 - 3.27743i) q^{57} +(6.66252 - 4.84060i) q^{58} +(-9.61777 - 6.98772i) q^{59} +(1.01915 + 3.13662i) q^{60} +(4.06378 + 12.5070i) q^{61} +(3.38156 + 2.45685i) q^{62} +(-6.37265 + 4.63000i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.08609 q^{65} +(9.54339 + 5.34519i) q^{66} +8.03278 q^{67} +(0.300214 - 0.923964i) q^{68} +(6.46732 - 4.69878i) q^{69} +(0.809017 + 0.587785i) q^{70} +(1.29220 + 3.97699i) q^{71} +(2.43414 + 7.49150i) q^{72} +(8.04264 + 5.84332i) q^{73} +(-4.92134 + 3.57557i) q^{74} +(-1.01915 + 3.13662i) q^{75} -1.04489 q^{76} +(3.29366 - 0.389659i) q^{77} -3.58197 q^{78} +(-3.53522 + 10.8803i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-23.7985 - 17.2906i) q^{81} +(-2.63830 - 8.11985i) q^{82} +(-0.118057 - 0.363342i) q^{83} +(2.66817 + 1.93854i) q^{84} +(0.785971 - 0.571041i) q^{85} +(-0.945971 + 2.91140i) q^{86} +27.1604 q^{87} +(0.647208 - 3.25286i) q^{88} -11.2206 q^{89} +(-2.43414 + 7.49150i) q^{90} +(-0.878668 + 0.638390i) q^{91} +(-1.96096 - 1.42472i) q^{92} +(4.25987 + 13.1105i) q^{93} +(-3.82997 - 11.7875i) q^{94} +(-0.845336 - 0.614173i) q^{95} +(2.66817 - 1.93854i) q^{96} +(4.59114 - 14.1301i) q^{97} +1.00000 q^{98} +(10.9363 + 23.7259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

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