LMFDB - Embedded newform 770.2.n.h.71.2

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			71.2
Root			$0.609000 - 0.442464i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.h.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.200017 + 0.145321i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.0763997 + 0.235134i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.908162 - 2.79504i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.200017 + 0.145321i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.0763997 + 0.235134i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.908162 - 2.79504i) q^{9} -1.00000 q^{10} +(-3.26734 + 0.569637i) q^{11} -0.247235 q^{12} +(0.875876 + 2.69567i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.200017 + 0.145321i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.78163 + 5.48331i) q^{17} +(2.37760 - 1.72743i) q^{18} +(-2.96862 - 2.15683i) q^{19} +(-0.309017 - 0.951057i) q^{20} -0.247235 q^{21} +(-1.55142 - 2.93140i) q^{22} -7.17432 q^{23} +(-0.0763997 - 0.235134i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.29307 + 1.66601i) q^{26} +(0.453728 - 1.39643i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-1.14498 + 0.831879i) q^{29} +(-0.200017 - 0.145321i) q^{30} +(-0.110144 - 0.338990i) q^{31} +1.00000 q^{32} +(-0.736304 - 0.360876i) q^{33} -5.76549 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.37760 + 1.72743i) q^{36} +(-2.38460 + 1.73251i) q^{37} +(1.13391 - 3.48982i) q^{38} +(-0.216547 + 0.666462i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.80069 - 1.30828i) q^{41} +(-0.0763997 - 0.235134i) q^{42} +9.64018 q^{43} +(2.30851 - 2.38134i) q^{44} +2.93888 q^{45} +(-2.21699 - 6.82318i) q^{46} +(-2.53720 - 1.84338i) q^{47} +(0.200017 - 0.145321i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-1.15320 + 0.837846i) q^{51} +(-2.29307 - 1.66601i) q^{52} +(0.270126 + 0.831363i) q^{53} +1.46830 q^{54} +(0.467907 - 3.28345i) q^{55} +1.00000 q^{56} +(-0.280342 - 0.862804i) q^{57} +(-1.14498 - 0.831879i) q^{58} +(8.49158 - 6.16949i) q^{59} +(0.0763997 - 0.235134i) q^{60} +(-2.84337 + 8.75101i) q^{61} +(0.288362 - 0.209507i) q^{62} +(2.37760 + 1.72743i) q^{63} +(0.309017 + 0.951057i) q^{64} -2.83439 q^{65} +(0.115683 - 0.811783i) q^{66} -13.5466 q^{67} +(-1.78163 - 5.48331i) q^{68} +(-1.43499 - 1.04258i) q^{69} +(0.809017 - 0.587785i) q^{70} +(-3.86699 + 11.9014i) q^{71} +(-0.908162 + 2.79504i) q^{72} +(5.82359 - 4.23109i) q^{73} +(-2.38460 - 1.73251i) q^{74} +(-0.0763997 - 0.235134i) q^{75} +3.66941 q^{76} +(2.30851 - 2.38134i) q^{77} -0.700760 q^{78} +(1.89893 + 5.84432i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-6.83912 + 4.96891i) q^{81} +(0.687804 - 2.11684i) q^{82} +(0.952443 - 2.93132i) q^{83} +(0.200017 - 0.145321i) q^{84} +(-4.66438 - 3.38887i) q^{85} +(2.97898 + 9.16835i) q^{86} -0.349905 q^{87} +(2.97816 + 1.45965i) q^{88} -5.75443 q^{89} +(0.908162 + 2.79504i) q^{90} +(-2.29307 - 1.66601i) q^{91} +(5.80414 - 4.21696i) q^{92} +(0.0272315 - 0.0838100i) q^{93} +(0.969124 - 2.98266i) q^{94} +(2.96862 - 2.15683i) q^{95} +(0.200017 + 0.145321i) q^{96} +(3.87129 + 11.9146i) q^{97} +1.00000 q^{98} +(4.55943 + 8.61501i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.200017	+	0.145321i	0.115480	+	0.0839011i	0.644026	−	0.765003i	$-0.277263\pi$
$3$	0.200017	+	0.145321i	0.115480	+	0.0839011i	−0.528546	+	0.848904i	$0.677263\pi$
$4$	−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
$6$	−0.0763997	+	0.235134i	−0.0311901	+	0.0959931i
$7$	−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
$9$	−0.908162	−	2.79504i	−0.302721	−	0.931679i
$10$	−1.00000			−0.316228
$11$	−3.26734	+	0.569637i	−0.985140	+	0.171752i
$11$	−3.26734	+	0.569637i	−0.985140	+	0.171752i
$12$	−0.247235			−0.0713705
$13$	0.875876	+	2.69567i	0.242924	+	0.747644i	0.995971	+	0.0896767i	$0.0285834\pi$
$13$	0.875876	+	2.69567i	0.242924	+	0.747644i	−0.753047	+	0.657967i	$0.771417\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−0.200017	+	0.145321i	−0.0516442	+	0.0375217i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.78163	+	5.48331i	−0.432110	+	1.32990i	0.463910	+	0.885882i	$0.346446\pi$
$17$	−1.78163	+	5.48331i	−0.432110	+	1.32990i	−0.896020	+	0.444015i	$0.853554\pi$
$18$	2.37760	−	1.72743i	0.560406	−	0.407159i
$19$	−2.96862	−	2.15683i	−0.681047	−	0.494810i	0.192658	−	0.981266i	$-0.438289\pi$
$19$	−2.96862	−	2.15683i	−0.681047	−	0.494810i	−0.873705	+	0.486456i	$0.838289\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−0.247235			−0.0539510
$22$	−1.55142	−	2.93140i	−0.330764	−	0.624976i
$23$	−7.17432			−1.49595			−0.747974	−	0.663728i	$-0.768973\pi$
$23$	−7.17432			−1.49595			−0.747974	+	0.663728i	$0.768973\pi$
$24$	−0.0763997	−	0.235134i	−0.0155950	−	0.0479966i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−2.29307	+	1.66601i	−0.449708	+	0.326732i
$27$	0.453728	−	1.39643i	0.0873201	−	0.268744i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−1.14498	+	0.831879i	−0.212618	+	0.154476i	−0.688997	−	0.724764i	$-0.741949\pi$
$29$	−1.14498	+	0.831879i	−0.212618	+	0.154476i	0.476379	+	0.879240i	$0.341949\pi$
$30$	−0.200017	−	0.145321i	−0.0365179	−	0.0265318i
$31$	−0.110144	−	0.338990i	−0.0197825	−	0.0608843i	0.940678	−	0.339301i	$-0.110190\pi$
$31$	−0.110144	−	0.338990i	−0.0197825	−	0.0608843i	−0.960460	+	0.278416i	$0.910190\pi$
$32$	1.00000			0.176777
$33$	−0.736304	−	0.360876i	−0.128174	−	0.0628204i
$34$	−5.76549			−0.988773
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	2.37760	+	1.72743i	0.396267	+	0.287905i
$37$	−2.38460	+	1.73251i	−0.392025	+	0.284823i	−0.766285	−	0.642501i	$-0.777897\pi$
$37$	−2.38460	+	1.73251i	−0.392025	+	0.284823i	0.374260	+	0.927324i	$0.377897\pi$
$38$	1.13391	−	3.48982i	0.183945	−	0.566123i
$39$	−0.216547	+	0.666462i	−0.0346752	+	0.106719i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−1.80069	−	1.30828i	−0.281221	−	0.204319i	0.438229	−	0.898863i	$-0.355606\pi$
$41$	−1.80069	−	1.30828i	−0.281221	−	0.204319i	−0.719450	+	0.694544i	$0.755606\pi$
$42$	−0.0763997	−	0.235134i	−0.0117887	−	0.0362820i
$43$	9.64018			1.47011			0.735057	−	0.678006i	$-0.237156\pi$
$43$	9.64018			1.47011			0.735057	+	0.678006i	$0.237156\pi$
$44$	2.30851	−	2.38134i	0.348021	−	0.359001i
$45$	2.93888			0.438102
$46$	−2.21699	−	6.82318i	−0.326877	−	1.00602i
$47$	−2.53720	−	1.84338i	−0.370089	−	0.268885i	0.387159	−	0.922013i	$-0.373456\pi$
$47$	−2.53720	−	1.84338i	−0.370089	−	0.268885i	−0.757248	+	0.653128i	$0.773456\pi$
$48$	0.200017	−	0.145321i	0.0288700	−	0.0209753i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	−1.15320	+	0.837846i	−0.161480	+	0.117322i
$52$	−2.29307	−	1.66601i	−0.317992	−	0.231035i
$53$	0.270126	+	0.831363i	0.0371047	+	0.114196i	0.967893	−	0.251361i	$-0.0808783\pi$
$53$	0.270126	+	0.831363i	0.0371047	+	0.114196i	−0.930789	+	0.365558i	$0.880878\pi$
$54$	1.46830			0.199810
$55$	0.467907	−	3.28345i	0.0630926	−	0.442741i
$56$	1.00000			0.133631
$57$	−0.280342	−	0.862804i	−0.0371322	−	0.114281i
$58$	−1.14498	−	0.831879i	−0.150344	−	0.109231i
$59$	8.49158	−	6.16949i	1.10551	−	0.803200i	0.123559	−	0.992337i	$-0.460569\pi$
$59$	8.49158	−	6.16949i	1.10551	−	0.803200i	0.981951	+	0.189137i	$0.0605692\pi$
$60$	0.0763997	−	0.235134i	0.00986316	−	0.0303557i
$61$	−2.84337	+	8.75101i	−0.364057	+	1.12045i	0.586513	+	0.809940i	$0.300500\pi$
$61$	−2.84337	+	8.75101i	−0.364057	+	1.12045i	−0.950570	+	0.310512i	$0.899500\pi$
$62$	0.288362	−	0.209507i	0.0366220	−	0.0266074i
$63$	2.37760	+	1.72743i	0.299549	+	0.217635i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.83439			−0.351563
$66$	0.115683	−	0.811783i	0.0142396	−	0.0999236i
$67$	−13.5466			−1.65498			−0.827492	−	0.561478i	$-0.810233\pi$
$67$	−13.5466			−1.65498			−0.827492	+	0.561478i	$0.810233\pi$
$68$	−1.78163	−	5.48331i	−0.216055	−	0.664948i
$69$	−1.43499	−	1.04258i	−0.172752	−	0.125512i
$70$	0.809017	−	0.587785i	0.0966960	−	0.0702538i
$71$	−3.86699	+	11.9014i	−0.458928	+	1.41243i	0.407534	+	0.913190i	$0.366389\pi$
$71$	−3.86699	+	11.9014i	−0.458928	+	1.41243i	−0.866461	+	0.499244i	$0.833611\pi$
$72$	−0.908162	+	2.79504i	−0.107028	+	0.329398i
$73$	5.82359	−	4.23109i	0.681600	−	0.495211i	−0.192288	−	0.981339i	$-0.561591\pi$
$73$	5.82359	−	4.23109i	0.681600	−	0.495211i	0.873888	+	0.486127i	$0.161591\pi$
$74$	−2.38460	−	1.73251i	−0.277204	−	0.201400i
$75$	−0.0763997	−	0.235134i	−0.00882188	−	0.0271510i
$76$	3.66941			0.420910
$77$	2.30851	−	2.38134i	0.263079	−	0.271379i
$78$	−0.700760			−0.0793455
$79$	1.89893	+	5.84432i	0.213647	+	0.657537i	0.999247	+	0.0388027i	$0.0123544\pi$
$79$	1.89893	+	5.84432i	0.213647	+	0.657537i	−0.785600	+	0.618735i	$0.787646\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−6.83912	+	4.96891i	−0.759902	+	0.552101i
$82$	0.687804	−	2.11684i	0.0759552	−	0.233766i
$83$	0.952443	−	2.93132i	0.104544	−	0.321754i	−0.885079	−	0.465441i	$-0.845896\pi$
$83$	0.952443	−	2.93132i	0.104544	−	0.321754i	0.989623	+	0.143687i	$0.0458958\pi$
$84$	0.200017	−	0.145321i	0.0218236	−	0.0158558i
$85$	−4.66438	−	3.38887i	−0.505923	−	0.367574i
$86$	2.97898	+	9.16835i	0.321232	+	0.988649i
$87$	−0.349905			−0.0375138
$88$	2.97816	+	1.45965i	0.317473	+	0.155599i
$89$	−5.75443			−0.609968			−0.304984	−	0.952357i	$-0.598651\pi$
$89$	−5.75443			−0.609968			−0.304984	+	0.952357i	$0.598651\pi$
$90$	0.908162	+	2.79504i	0.0957287	+	0.294623i
$91$	−2.29307	−	1.66601i	−0.240379	−	0.174646i
$92$	5.80414	−	4.21696i	0.605124	−	0.439648i
$93$	0.0272315	−	0.0838100i	0.00282378	−	0.00869069i
$94$	0.969124	−	2.98266i	0.0999575	−	0.307638i
$95$	2.96862	−	2.15683i	0.304574	−	0.221286i
$96$	0.200017	+	0.145321i	0.0204142	+	0.0148318i
$97$	3.87129	+	11.9146i	0.393070	+	1.20975i	0.930454	+	0.366408i	$0.119412\pi$
$97$	3.87129	+	11.9146i	0.393070	+	1.20975i	−0.537384	+	0.843337i	$0.680588\pi$
$98$	1.00000			0.101015
$99$	4.55943	+	8.61501i	0.458240	+	0.865841i
$100$	1.00000			0.100000
$101$	−1.82358	−	5.61241i	−0.181453	−	0.558455i	0.818416	−	0.574626i	$-0.194852\pi$
$101$	−1.82358	−	5.61241i	−0.181453	−	0.558455i	−0.999869	+	0.0161707i	$0.994852\pi$
$102$	−1.15320	−	0.837846i	−0.114183	−	0.0829591i
$103$	9.68158	−	7.03408i	0.953955	−	0.693089i	0.00221586	−	0.999998i	$-0.499295\pi$
$103$	9.68158	−	7.03408i	0.953955	−	0.693089i	0.951739	+	0.306909i	$0.0992947\pi$
$104$	0.875876	−	2.69567i	0.0858867	−	0.264332i
$105$	0.0763997	−	0.235134i	0.00745585	−	0.0229467i
$106$	−0.707199	+	0.513810i	−0.0686893	+	0.0499057i
$107$	5.08787	+	3.69655i	0.491863	+	0.357359i	0.805900	−	0.592051i	$-0.201682\pi$
$107$	5.08787	+	3.69655i	0.491863	+	0.357359i	−0.314037	+	0.949411i	$0.601682\pi$
$108$	0.453728	+	1.39643i	0.0436600	+	0.134372i
$109$	−3.42125			−0.327696			−0.163848	−	0.986486i	$-0.552391\pi$
$109$	−3.42125			−0.327696			−0.163848	+	0.986486i	$0.552391\pi$
$110$	3.26734	−	0.569637i	0.311529	−	0.0543127i
$111$	−0.728730			−0.0691680
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	13.6095	+	9.88788i	1.28027	+	0.930174i	0.999561	−	0.0296178i	$-0.00942903\pi$
$113$	13.6095	+	9.88788i	1.28027	+	0.930174i	0.280713	+	0.959792i	$0.409429\pi$
$114$	0.733945	−	0.533242i	0.0687402	−	0.0499427i
$115$	2.21699	−	6.82318i	0.206735	−	0.636265i
$116$	0.437344	−	1.34601i	0.0406064	−	0.124974i
$117$	6.73905	−	4.89621i	0.623026	−	0.452655i
$118$	8.49158	+	6.16949i	0.781713	+	0.567948i
$119$	−1.78163	−	5.48331i	−0.163322	−	0.502654i
$120$	0.247235			0.0225693
$121$	10.3510	−	3.72240i	0.941003	−	0.338400i
$122$	−9.20135			−0.833051
$123$	−0.170049	−	0.523357i	−0.0153328	−	0.0471895i
$124$	0.288362	+	0.209507i	0.0258957	+	0.0188143i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−0.908162	+	2.79504i	−0.0809055	+	0.249002i
$127$	0.0543127	−	0.167157i	0.00481947	−	0.0148328i	−0.948618	−	0.316424i	$-0.897518\pi$
$127$	0.0543127	−	0.167157i	0.00481947	−	0.0148328i	0.953437	+	0.301591i	$0.0975178\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	1.92820	+	1.40092i	0.169769	+	0.123344i
$130$	−0.875876	−	2.69567i	−0.0768194	−	0.236426i
$131$	−11.4391			−0.999438			−0.499719	−	0.866187i	$-0.666563\pi$
$131$	−11.4391			−0.999438			−0.499719	+	0.866187i	$0.666563\pi$
$132$	0.807800	−	0.140834i	0.0703100	−	0.0122580i
$133$	3.66941			0.318178
$134$	−4.18614	−	12.8836i	−0.361627	−	1.11297i
$135$	1.18788	+	0.863043i	0.102236	+	0.0742789i
$136$	4.66438	−	3.38887i	0.399967	−	0.290593i
$137$	−3.07577	+	9.46626i	−0.262781	+	0.808757i	0.729415	+	0.684071i	$0.239792\pi$
$137$	−3.07577	+	9.46626i	−0.262781	+	0.808757i	−0.992196	+	0.124686i	$0.960208\pi$
$138$	0.548116	−	1.68693i	0.0466587	−	0.143601i
$139$	0.507435	−	0.368673i	0.0430401	−	0.0312705i	−0.566057	−	0.824366i	$-0.691532\pi$
$139$	0.507435	−	0.368673i	0.0430401	−	0.0312705i	0.609097	+	0.793095i	$0.291532\pi$
$140$	0.809017	+	0.587785i	0.0683744	+	0.0496769i
$141$	−0.239601	−	0.737416i	−0.0201780	−	0.0621017i
$142$	−12.5139			−1.05014
$143$	−4.39734	−	8.30873i	−0.367724	−	0.694811i
$144$	−2.93888			−0.244906
$145$	−0.437344	−	1.34601i	−0.0363195	−	0.111780i
$146$	5.82359	+	4.23109i	0.481964	+	0.350167i
$147$	0.200017	−	0.145321i	0.0164971	−	0.0119859i
$148$	0.910835	−	2.80326i	0.0748701	−	0.230427i
$149$	−4.64498	+	14.2958i	−0.380532	+	1.17116i	0.559139	+	0.829074i	$0.311132\pi$
$149$	−4.64498	+	14.2958i	−0.380532	+	1.17116i	−0.939670	+	0.342082i	$0.888868\pi$
$150$	0.200017	−	0.145321i	0.0163313	−	0.0118654i
$151$	−0.417831	−	0.303572i	−0.0340026	−	0.0247043i	0.570654	−	0.821191i	$-0.306690\pi$
$151$	−0.417831	−	0.303572i	−0.0340026	−	0.0247043i	−0.604657	+	0.796486i	$0.706690\pi$
$152$	1.13391	+	3.48982i	0.0919723	+	0.283062i
$153$	16.9441			1.36985
$154$	2.97816	+	1.45965i	0.239987	+	0.117622i
$155$	0.356435			0.0286295
$156$	−0.216547	−	0.666462i	−0.0173376	−	0.0533597i
$157$	18.4280	+	13.3887i	1.47071	+	1.06853i	0.980407	+	0.196982i	$0.0631141\pi$
$157$	18.4280	+	13.3887i	1.47071	+	1.06853i	0.490304	+	0.871552i	$0.336886\pi$
$158$	−4.97148	+	3.61199i	−0.395509	+	0.287354i
$159$	−0.0667845	+	0.205542i	−0.00529636	+	0.0163005i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	5.80414	−	4.21696i	0.457431	−	0.332343i
$162$	−6.83912	−	4.96891i	−0.537332	−	0.390394i
$163$	1.15063	+	3.54129i	0.0901246	+	0.277375i	0.985952	−	0.167026i	$-0.0534164\pi$
$163$	1.15063	+	3.54129i	0.0901246	+	0.277375i	−0.895828	+	0.444401i	$0.853416\pi$
$164$	2.22578			0.173804
$165$	0.570744	−	0.588750i	0.0444323	−	0.0458341i
$166$	3.08217			0.239223
$167$	4.81526	+	14.8199i	0.372616	+	1.14680i	0.945073	+	0.326860i	$0.105991\pi$
$167$	4.81526	+	14.8199i	0.372616	+	1.14680i	−0.572456	+	0.819935i	$0.694009\pi$
$168$	0.200017	+	0.145321i	0.0154316	+	0.0112117i
$169$	4.01775	−	2.91907i	0.309058	−	0.224544i
$170$	1.78163	−	5.48331i	0.136645	−	0.420550i
$171$	−3.33242	+	10.2561i	−0.254837	+	0.784307i
$172$	−7.79907	+	5.66635i	−0.594673	+	0.432055i
$173$	−4.77281	−	3.46765i	−0.362870	−	0.263641i	0.391378	−	0.920230i	$-0.371998\pi$
$173$	−4.77281	−	3.46765i	−0.362870	−	0.263641i	−0.754248	+	0.656589i	$0.771998\pi$
$174$	−0.108127	−	0.332780i	−0.00819706	−	0.0252280i
$175$	1.00000			0.0755929
$176$	−0.467907	+	3.28345i	−0.0352698	+	0.247500i
$177$	2.59502			0.195053
$178$	−1.77822	−	5.47279i	−0.133283	−	0.410203i
$179$	−13.2131	−	9.59989i	−0.987595	−	0.717529i	−0.0282016	−	0.999602i	$-0.508978\pi$
$179$	−13.2131	−	9.59989i	−0.987595	−	0.717529i	−0.959393	+	0.282073i	$0.908978\pi$
$180$	−2.37760	+	1.72743i	−0.177216	+	0.128755i
$181$	−1.07727	+	3.31548i	−0.0800725	+	0.246438i	−0.983077	−	0.183194i	$-0.941356\pi$
$181$	−1.07727	+	3.31548i	−0.0800725	+	0.246438i	0.903004	+	0.429631i	$0.141356\pi$
$182$	0.875876	−	2.69567i	0.0649242	−	0.199816i
$183$	−1.84043	+	1.33715i	−0.136048	+	0.0988449i
$184$	5.80414	+	4.21696i	0.427887	+	0.310878i
$185$	−0.910835	−	2.80326i	−0.0669659	−	0.206100i
$186$	0.0881230			0.00646149
$187$	2.69771	−	18.9307i	0.197276	−	1.38435i
$188$	3.13615			0.228727
$189$	0.453728	+	1.39643i	0.0330039	+	0.101576i
$190$	2.96862	+	2.15683i	0.215366	+	0.156473i
$191$	−21.0104	+	15.2649i	−1.52026	+	1.10453i	−0.558900	+	0.829235i	$0.688777\pi$
$191$	−21.0104	+	15.2649i	−1.52026	+	1.10453i	−0.961359	+	0.275298i	$0.911223\pi$
$192$	−0.0763997	+	0.235134i	−0.00551367	+	0.0169693i
$193$	−0.209360	+	0.644343i	−0.0150700	+	0.0463808i	−0.958309	−	0.285735i	$-0.907762\pi$
$193$	−0.209360	+	0.644343i	−0.0150700	+	0.0463808i	0.943239	+	0.332116i	$0.107762\pi$
$194$	−10.1352	+	7.36363i	−0.727663	+	0.528678i
$195$	−0.566927	−	0.411896i	−0.0405985	−	0.0294965i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	5.80812			0.413811			0.206906	−	0.978361i	$-0.433661\pi$
$197$	5.80812			0.413811			0.206906	+	0.978361i	$0.433661\pi$
$198$	−6.78442	+	6.99846i	−0.482148	+	0.497359i
$199$	10.9475			0.776046			0.388023	−	0.921650i	$-0.373158\pi$
$199$	10.9475			0.776046			0.388023	+	0.921650i	$0.373158\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	−2.70955	−	1.96861i	−0.191117	−	0.138855i
$202$	4.77420	−	3.46866i	0.335911	−	0.244054i
$203$	0.437344	−	1.34601i	0.0306956	−	0.0944712i
$204$	0.440482	−	1.35566i	0.0308399	−	0.0949154i
$205$	1.80069	−	1.30828i	0.125766	−	0.0913742i
$206$	9.68158	+	7.03408i	0.674548	+	0.490088i
$207$	6.51544	+	20.0525i	0.452855	+	1.39374i
$208$	2.83439			0.196530
$209$	10.9281	+	5.35605i	0.755912	+	0.370486i
$210$	0.247235			0.0170608
$211$	−1.98632	−	6.11326i	−0.136744	−	0.420854i	0.859113	−	0.511785i	$-0.171016\pi$
$211$	−1.98632	−	6.11326i	−0.136744	−	0.420854i	−0.995857	+	0.0909311i	$0.971016\pi$
$212$	−0.707199	−	0.513810i	−0.0485706	−	0.0352886i
$213$	−2.50298	+	1.81852i	−0.171502	+	0.124603i
$214$	−1.94339	+	5.98115i	−0.132848	+	0.408863i
$215$	−2.97898	+	9.16835i	−0.203165	+	0.625277i
$216$	−1.18788	+	0.863043i	−0.0808247	+	0.0587226i
$217$	0.288362	+	0.209507i	0.0195753	+	0.0142223i
$218$	−1.05722	−	3.25380i	−0.0716042	−	0.220375i
$219$	1.77968			0.120260
$220$	1.55142	+	2.93140i	0.104597	+	0.197635i
$221$	−16.3417			−1.09926
$222$	−0.225190	−	0.693063i	−0.0151138	−	0.0465154i
$223$	−18.7731	−	13.6394i	−1.25714	−	0.913365i	−0.258525	−	0.966004i	$-0.583237\pi$
$223$	−18.7731	−	13.6394i	−1.25714	−	0.913365i	−0.998614	+	0.0526396i	$0.983237\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	−0.908162	+	2.79504i	−0.0605442	+	0.186336i
$226$	−5.19837	+	15.9989i	−0.345790	+	1.06423i
$227$	20.6878	−	15.0306i	1.37310	−	0.997614i	0.375610	−	0.926778i	$-0.377433\pi$
$227$	20.6878	−	15.0306i	1.37310	−	0.997614i	0.997488	−	0.0708363i	$-0.0225668\pi$
$228$	0.733945	+	0.533242i	0.0486067	+	0.0353148i
$229$	1.24380	+	3.82801i	0.0821923	+	0.252962i	0.983705	−	0.179791i	$-0.0575422\pi$
$229$	1.24380	+	3.82801i	0.0821923	+	0.252962i	−0.901512	+	0.432753i	$0.857542\pi$
$230$	7.17432			0.473060
$231$	0.807800	−	0.140834i	0.0531493	−	0.00926620i
$232$	1.41528			0.0929174
$233$	−1.13632	−	3.49724i	−0.0744428	−	0.229111i	0.906911	−	0.421323i	$-0.138434\pi$
$233$	−1.13632	−	3.49724i	−0.0744428	−	0.229111i	−0.981354	+	0.192211i	$0.938434\pi$
$234$	6.73905	+	4.89621i	0.440546	+	0.320075i
$235$	2.53720	−	1.84338i	0.165509	−	0.120249i
$236$	−3.24350	+	9.98245i	−0.211134	+	0.649802i
$237$	−0.469482	+	1.44492i	−0.0304962	+	0.0938575i
$238$	4.66438	−	3.38887i	0.302347	−	0.219668i
$239$	0.885417	+	0.643293i	0.0572728	+	0.0416112i	0.616053	−	0.787704i	$-0.288731\pi$
$239$	0.885417	+	0.643293i	0.0572728	+	0.0416112i	−0.558780	+	0.829316i	$0.688731\pi$
$240$	0.0763997	+	0.235134i	0.00493158	+	0.0151778i
$241$	6.24902			0.402535			0.201267	−	0.979536i	$-0.435494\pi$
$241$	6.24902			0.402535			0.201267	+	0.979536i	$0.435494\pi$
$242$	6.73885	+	8.69413i	0.433190	+	0.558880i
$243$	−6.49491			−0.416649
$244$	−2.84337	−	8.75101i	−0.182028	−	0.560226i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	0.445194	−	0.323452i	0.0283845	−	0.0206226i
$247$	3.21395	−	9.89152i	0.204499	−	0.629382i
$248$	−0.110144	+	0.338990i	−0.00699418	+	0.0215259i
$249$	0.616486	−	0.447904i	0.0390682	−	0.0283847i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−5.96142	−	18.3474i	−0.376281	−	1.15808i	−0.942610	−	0.333896i	$-0.891637\pi$
$251$	−5.96142	−	18.3474i	−0.376281	−	1.15808i	0.566329	−	0.824179i	$-0.308363\pi$
$252$	−2.93888			−0.185132
$253$	23.4409	−	4.08675i	1.47372	−	0.256932i
$254$	0.175760			0.0110281
$255$	−0.440482	−	1.35566i	−0.0275840	−	0.0848949i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−20.4409	+	14.8512i	−1.27507	+	0.926391i	−0.999392	−	0.0348601i	$-0.988901\pi$
$257$	−20.4409	+	14.8512i	−1.27507	+	0.926391i	−0.275675	+	0.961251i	$0.588901\pi$
$258$	−0.736507	+	2.26673i	−0.0458529	+	0.141121i
$259$	0.910835	−	2.80326i	0.0565965	−	0.174186i
$260$	2.29307	−	1.66601i	0.142210	−	0.103322i
$261$	3.36496	+	2.44479i	0.208286	+	0.151329i
$262$	−3.53487	−	10.8792i	−0.218385	−	0.672121i
$263$	2.99352			0.184589			0.0922943	−	0.995732i	$-0.470580\pi$
$263$	2.99352			0.184589			0.0922943	+	0.995732i	$0.470580\pi$
$264$	0.383565	+	0.724743i	0.0236068	+	0.0446049i
$265$	−0.874146			−0.0536984
$266$	1.13391	+	3.48982i	0.0695245	+	0.213975i
$267$	−1.15098	−	0.836239i	−0.0704390	−	0.0511770i
$268$	10.9594	−	7.96250i	0.669455	−	0.486387i
$269$	−6.95328	+	21.4000i	−0.423949	+	1.30478i	0.480048	+	0.877242i	$0.340619\pi$
$269$	−6.95328	+	21.4000i	−0.423949	+	1.30478i	−0.903997	+	0.427539i	$0.859381\pi$
$270$	−0.453728	+	1.39643i	−0.0276130	+	0.0849842i
$271$	11.0258	−	8.01071i	0.669770	−	0.486616i	−0.200178	−	0.979759i	$-0.564152\pi$
$271$	11.0258	−	8.01071i	0.669770	−	0.486616i	0.869948	+	0.493143i	$0.164152\pi$
$272$	4.66438	+	3.38887i	0.282819	+	0.205480i
$273$	−0.216547	−	0.666462i	−0.0131060	−	0.0403361i
$274$	−9.95341			−0.601307
$275$	2.97816	+	1.45965i	0.179590	+	0.0880201i
$276$	1.77374			0.106767
$277$	−7.27627	−	22.3941i	−0.437189	−	1.34553i	−0.890827	−	0.454343i	$-0.849874\pi$
$277$	−7.27627	−	22.3941i	−0.437189	−	1.34553i	0.453638	−	0.891186i	$-0.350126\pi$
$278$	0.507435	+	0.368673i	0.0304339	+	0.0221115i
$279$	−0.847459	+	0.615715i	−0.0507361	+	0.0368619i
$280$	−0.309017	+	0.951057i	−0.0184673	+	0.0568365i
$281$	−5.92808	+	18.2448i	−0.353640	+	1.08839i	0.603154	+	0.797625i	$0.293910\pi$
$281$	−5.92808	+	18.2448i	−0.353640	+	1.08839i	−0.956794	+	0.290767i	$0.906090\pi$
$282$	0.627284	−	0.455748i	0.0373542	−	0.0271394i
$283$	−13.9735	−	10.1523i	−0.830639	−	0.603494i	0.0891012	−	0.996023i	$-0.471601\pi$
$283$	−13.9735	−	10.1523i	−0.830639	−	0.603494i	−0.919740	+	0.392528i	$0.871601\pi$
$284$	−3.86699	−	11.9014i	−0.229464	−	0.706217i
$285$	0.907206			0.0537382
$286$	6.54322	−	6.74965i	0.386909	−	0.399115i
$287$	2.22578			0.131384
$288$	−0.908162	−	2.79504i	−0.0535140	−	0.164699i
$289$	−13.1391	−	9.54614i	−0.772890	−	0.561538i
$290$	1.14498	−	0.831879i	0.0672357	−	0.0488496i
$291$	−0.957117	+	2.94570i	−0.0561072	+	0.172680i
$292$	−2.22441	+	6.84604i	−0.130174	+	0.400634i
$293$	26.6424	−	19.3568i	1.55646	−	1.13084i	0.617628	−	0.786470i	$-0.288094\pi$
$293$	26.6424	−	19.3568i	1.55646	−	1.13084i	0.938835	−	0.344366i	$-0.111906\pi$
$294$	0.200017	+	0.145321i	0.0116652	+	0.00847529i
$295$	3.24350	+	9.98245i	0.188844	+	0.581201i
$296$	2.94752			0.171321
$297$	−0.687026	+	4.82108i	−0.0398653	+	0.279747i
$298$	−15.0315			−0.870750
$299$	−6.28381	−	19.3396i	−0.363402	−	1.11844i
$300$	0.200017	+	0.145321i	0.0115480	+	0.00839011i
$301$	−7.79907	+	5.66635i	−0.449531	+	0.326603i
$302$	0.159597	−	0.491190i	0.00918379	−	0.0282648i
$303$	0.450853	−	1.38758i	0.0259008	−	0.0797145i
$304$	−2.96862	+	2.15683i	−0.170262	+	0.123702i
$305$	−7.44405	−	5.40842i	−0.426245	−	0.309685i
$306$	5.23600	+	16.1147i	0.299322	+	0.921219i
$307$	−7.97195			−0.454983			−0.227492	−	0.973780i	$-0.573052\pi$
$307$	−7.97195			−0.454983			−0.227492	+	0.973780i	$0.573052\pi$
$308$	−0.467907	+	3.28345i	−0.0266615	+	0.187092i
$309$	2.95868			0.168313
$310$	0.110144	+	0.338990i	0.00625578	+	0.0192533i
$311$	3.24283	+	2.35606i	0.183884	+	0.133600i	0.675919	−	0.736976i	$-0.263747\pi$
$311$	3.24283	+	2.35606i	0.183884	+	0.133600i	−0.492035	+	0.870575i	$0.663747\pi$
$312$	0.566927	−	0.411896i	0.0320959	−	0.0233190i
$313$	1.62932	−	5.01454i	0.0920949	−	0.283439i	−0.894391	−	0.447286i	$-0.852390\pi$
$313$	1.62932	−	5.01454i	0.0920949	−	0.283439i	0.986486	+	0.163847i	$0.0523905\pi$
$314$	−7.03885	+	21.6634i	−0.397225	+	1.22253i
$315$	−2.37760	+	1.72743i	−0.133963	+	0.0973295i
$316$	−4.97148	−	3.61199i	−0.279667	−	0.203190i
$317$	−1.43995	−	4.43172i	−0.0808758	−	0.248910i	0.902440	−	0.430815i	$-0.141774\pi$
$317$	−1.43995	−	4.43172i	−0.0808758	−	0.248910i	−0.983316	+	0.181905i	$0.941774\pi$
$318$	−0.216119			−0.0121194
$319$	3.26718	−	3.37025i	0.182927	−	0.188698i
$320$	−1.00000			−0.0559017
$321$	0.480474	+	1.47875i	0.0268174	+	0.0825356i
$322$	5.80414	+	4.21696i	0.323452	+	0.235002i
$323$	17.1155	−	12.4352i	0.952333	−	0.691911i
$324$	2.61231	−	8.03986i	0.145128	−	0.446659i
$325$	0.875876	−	2.69567i	0.0485848	−	0.149529i
$326$	−3.01240	+	2.18864i	−0.166841	+	0.121217i
$327$	−0.684308	−	0.497179i	−0.0378423	−	0.0274940i
$328$	0.687804	+	2.11684i	0.0379776	+	0.116883i
$329$	3.13615			0.172902
$330$	0.736304	+	0.360876i	0.0405322	+	0.0198656i
$331$	−25.0199			−1.37522			−0.687608	−	0.726082i	$-0.741339\pi$
$331$	−25.0199			−1.37522			−0.687608	+	0.726082i	$0.741339\pi$
$332$	0.952443	+	2.93132i	0.0522721	+	0.160877i
$333$	7.00803	+	5.09163i	0.384038	+	0.279020i
$334$	−12.6065	+	9.15918i	−0.689798	+	0.501168i
$335$	4.18614	−	12.8836i	0.228713	−	0.703906i
$336$	−0.0763997	+	0.235134i	−0.00416795	+	0.0128276i
$337$	−12.8931	+	9.36738i	−0.702332	+	0.510274i	−0.880691	−	0.473692i	$-0.842921\pi$
$337$	−12.8931	+	9.36738i	−0.702332	+	0.510274i	0.178359	+	0.983965i	$0.442921\pi$
$338$	4.01775	+	2.91907i	0.218537	+	0.158776i
$339$	1.28522	+	3.95549i	0.0698034	+	0.214833i
$340$	5.76549			0.312678
$341$	0.552980	+	1.04485i	0.0299456	+	0.0565819i
$342$	−10.7839			−0.583129
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−7.79907	−	5.66635i	−0.420498	−	0.305509i
$345$	1.43499	−	1.04258i	0.0772570	−	0.0561305i
$346$	1.82305	−	5.61078i	0.0980079	−	0.301637i
$347$	−3.84030	+	11.8192i	−0.206158	+	0.634490i	0.793506	+	0.608563i	$0.208254\pi$
$347$	−3.84030	+	11.8192i	−0.206158	+	0.634490i	−0.999664	+	0.0259268i	$0.991746\pi$
$348$	0.283079	−	0.205669i	0.0151746	−	0.0110250i
$349$	13.1165	+	9.52968i	0.702109	+	0.510112i	0.880618	−	0.473826i	$-0.157128\pi$
$349$	13.1165	+	9.52968i	0.702109	+	0.510112i	−0.178510	+	0.983938i	$0.557128\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	4.16173			0.222137
$352$	−3.26734	+	0.569637i	−0.174150	+	0.0303617i
$353$	−21.8320			−1.16200			−0.580999	−	0.813904i	$-0.697338\pi$
$353$	−21.8320			−1.16200			−0.580999	+	0.813904i	$0.697338\pi$
$354$	0.801904	+	2.46801i	0.0426207	+	0.131173i
$355$	−10.1239	−	7.35546i	−0.537322	−	0.390387i
$356$	4.65543	−	3.38237i	0.246737	−	0.179265i
$357$	0.440482	−	1.35566i	0.0233128	−	0.0717493i
$358$	5.04696	−	15.5329i	0.266740	−	0.820942i
$359$	14.7326	−	10.7039i	0.777559	−	0.564930i	−0.126686	−	0.991943i	$-0.540434\pi$
$359$	14.7326	−	10.7039i	0.777559	−	0.564930i	0.904246	+	0.427013i	$0.140434\pi$
$360$	−2.37760	−	1.72743i	−0.125311	−	0.0910434i
$361$	−1.71054	−	5.26449i	−0.0900282	−	0.277078i
$362$	−3.48610			−0.183226
$363$	2.61132	+	0.759678i	0.137059	+	0.0398728i
$364$	2.83439			0.148563
$365$	2.22441	+	6.84604i	0.116431	+	0.358338i
$366$	−1.84043	−	1.33715i	−0.0962007	−	0.0698939i
$367$	4.27045	−	3.10266i	0.222916	−	0.161958i	−0.470722	−	0.882281i	$-0.656007\pi$
$367$	4.27045	−	3.10266i	0.222916	−	0.161958i	0.693638	+	0.720324i	$0.256007\pi$
$368$	−2.21699	+	6.82318i	−0.115568	+	0.355683i
$369$	−2.02137	+	6.22113i	−0.105228	+	0.323859i
$370$	2.38460	−	1.73251i	0.123969	−	0.0900689i
$371$	−0.707199	−	0.513810i	−0.0367160	−	0.0266757i
$372$	0.0272315	+	0.0838100i	0.00141189	+	0.00434535i
$373$	18.5799			0.962031			0.481016	−	0.876712i	$-0.340268\pi$
$373$	18.5799			0.962031			0.481016	+	0.876712i	$0.340268\pi$
$374$	18.8378	−	3.28423i	0.974080	−	0.169824i
$375$	0.247235			0.0127671
$376$	0.969124	+	2.98266i	0.0499788	+	0.153819i
$377$	−3.24533	−	2.35787i	−0.167143	−	0.121437i
$378$	−1.18788	+	0.863043i	−0.0610978	+	0.0443901i
$379$	7.05813	−	21.7227i	0.362552	−	1.11582i	−0.588948	−	0.808171i	$-0.700458\pi$
$379$	7.05813	−	21.7227i	0.362552	−	1.11582i	0.951500	−	0.307648i	$-0.0995421\pi$
$380$	−1.13391	+	3.48982i	−0.0581684	+	0.179024i
$381$	0.0351549	−	0.0255416i	0.00180104	−	0.00130853i
$382$	−21.0104	−	15.2649i	−1.07499	−	0.781023i
$383$	−6.94469	−	21.3735i	−0.354857	−	1.09214i	−0.956092	−	0.293065i	$-0.905325\pi$
$383$	−6.94469	−	21.3735i	−0.354857	−	1.09214i	0.601235	−	0.799072i	$-0.294675\pi$
$384$	−0.247235			−0.0126166
$385$	1.55142	+	2.93140i	0.0790677	+	0.149398i
$386$	−0.677502			−0.0344840
$387$	−8.75485	−	26.9446i	−0.445034	−	1.36967i
$388$	−10.1352	−	7.36363i	−0.514535	−	0.373832i
$389$	−29.3267	+	21.3071i	−1.48692	+	1.08031i	−0.511678	+	0.859178i	$0.670976\pi$
$389$	−29.3267	+	21.3071i	−1.48692	+	1.08031i	−0.975243	+	0.221134i	$0.929024\pi$
$390$	0.216547	−	0.666462i	0.0109653	−	0.0337476i
$391$	12.7820	−	39.3390i	0.646414	−	1.98946i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	−2.28801	−	1.66234i	−0.115415	−	0.0838539i
$394$	1.79481	+	5.52385i	0.0904211	+	0.278288i
$395$	−6.14508			−0.309193
$396$	−8.75243	−	4.28973i	−0.439826	−	0.215567i
$397$	−8.02992			−0.403010			−0.201505	−	0.979487i	$-0.564583\pi$
$397$	−8.02992			−0.403010			−0.201505	+	0.979487i	$0.564583\pi$
$398$	3.38296	+	10.4117i	0.169572	+	0.521890i
$399$	0.733945	+	0.533242i	0.0367432	+	0.0266955i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	0.207790	−	0.639511i	0.0103765	−	0.0319356i	−0.945734	−	0.324941i	$-0.894655\pi$
$401$	0.207790	−	0.639511i	0.0103765	−	0.0319356i	0.956111	+	0.293006i	$0.0946555\pi$
$402$	1.03496	−	3.18527i	0.0516190	−	0.158867i
$403$	0.817331	−	0.593825i	0.0407141	−	0.0295806i
$404$	4.77420	+	3.46866i	0.237525	+	0.172572i
$405$	−2.61231	−	8.03986i	−0.129807	−	0.399504i
$406$	1.41528			0.0702390
$407$	6.80439	−	7.01906i	0.337281	−	0.347922i
$408$	1.42543			0.0705692
$409$	−6.71756	−	20.6745i	−0.332162	−	1.02229i	−0.968103	−	0.250552i	$-0.919388\pi$
$409$	−6.71756	−	20.6745i	−0.332162	−	1.02229i	0.635941	−	0.771738i	$-0.280612\pi$
$410$	1.80069	+	1.30828i	0.0889299	+	0.0646113i
$411$	−1.99085	+	1.44644i	−0.0982015	+	0.0713475i
$412$	−3.69804	+	11.3814i	−0.182189	+	0.560721i
$413$	−3.24350	+	9.98245i	−0.159602	+	0.491204i
$414$	−17.0577	+	12.3931i	−0.838338	+	0.609088i
$415$	2.49353	+	1.81165i	0.122402	+	0.0889306i
$416$	0.875876	+	2.69567i	0.0429433	+	0.132166i
$417$	0.155072			0.00759389
$418$	−1.71694	+	12.0483i	−0.0839784	+	0.589304i
$419$	−7.38003			−0.360538			−0.180269	−	0.983617i	$-0.557697\pi$
$419$	−7.38003			−0.360538			−0.180269	+	0.983617i	$0.557697\pi$
$420$	0.0763997	+	0.235134i	0.00372792	+	0.0114734i
$421$	−23.8253	−	17.3101i	−1.16118	−	0.843643i	−0.171249	−	0.985228i	$-0.554780\pi$
$421$	−23.8253	−	17.3101i	−1.16118	−	0.843643i	−0.989926	+	0.141585i	$0.954780\pi$
$422$	5.20025	−	3.77820i	0.253144	−	0.183920i
$423$	−2.84813	+	8.76566i	−0.138481	+	0.426201i
$424$	0.270126	−	0.831363i	0.0131185	−	0.0403745i
$425$	4.66438	−	3.38887i	0.226256	−	0.164384i
$426$	−2.50298	−	1.81852i	−0.121270	−	0.0881078i
$427$	−2.84337	−	8.75101i	−0.137601	−	0.423491i
$428$	−6.28895			−0.303988
$429$	0.327891	−	2.30091i	0.0158307	−	0.111089i
$430$	−9.64018			−0.464891
$431$	−6.07841	−	18.7074i	−0.292787	−	0.901105i	−0.983956	−	0.178412i	$-0.942904\pi$
$431$	−6.07841	−	18.7074i	−0.292787	−	0.901105i	0.691169	−	0.722693i	$-0.257096\pi$
$432$	−1.18788	−	0.863043i	−0.0571517	−	0.0415232i
$433$	13.7941	−	10.0220i	0.662901	−	0.481626i	−0.204741	−	0.978816i	$-0.565635\pi$
$433$	13.7941	−	10.0220i	0.662901	−	0.481626i	0.867641	+	0.497191i	$0.165635\pi$
$434$	−0.110144	+	0.338990i	−0.00528710	+	0.0162720i
$435$	0.108127	−	0.332780i	0.00518428	−	0.0159556i
$436$	2.76785	−	2.01096i	0.132556	−	0.0963075i
$437$	21.2978	+	15.4738i	1.01881	+	0.740210i
$438$	0.549952	+	1.69258i	0.0262777	+	0.0808746i
$439$	29.9589			1.42986			0.714929	−	0.699197i	$-0.246459\pi$
$439$	29.9589			1.42986			0.714929	+	0.699197i	$0.246459\pi$
$440$	−2.30851	+	2.38134i	−0.110054	+	0.113526i
$441$	−2.93888			−0.139946
$442$	−5.04985	−	15.5418i	−0.240197	−	0.739250i
$443$	−33.4087	−	24.2728i	−1.58730	−	1.15324i	−0.907675	−	0.419675i	$-0.862144\pi$
$443$	−33.4087	−	24.2728i	−1.58730	−	1.15324i	−0.679621	−	0.733563i	$-0.737856\pi$
$444$	0.589555	−	0.428337i	0.0279790	−	0.0203280i
$445$	1.77822	−	5.47279i	0.0842955	−	0.259435i
$446$	7.17068	−	22.0691i	0.339542	−	1.04500i
$447$	−3.00655	+	2.18439i	−0.142205	+	0.103318i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	10.4838	+	32.2658i	0.494761	+	1.52272i	0.817328	+	0.576172i	$0.195454\pi$
$449$	10.4838	+	32.2658i	0.494761	+	1.52272i	−0.322567	+	0.946547i	$0.604546\pi$
$450$	−2.93888			−0.138540
$451$	6.62872	+	3.24886i	0.312134	+	0.152983i
$452$	−16.8223			−0.791253
$453$	−0.0394580	−	0.121439i	−0.00185390	−	0.00570571i
$454$	20.6878	+	15.0306i	0.970927	+	0.705420i
$455$	2.29307	−	1.66601i	0.107501	−	0.0781040i
$456$	−0.280342	+	0.862804i	−0.0131282	+	0.0404045i
$457$	6.17812	−	19.0143i	0.289000	−	0.889452i	−0.696171	−	0.717876i	$-0.745114\pi$
$457$	6.17812	−	19.0143i	0.289000	−	0.889452i	0.985171	−	0.171575i	$-0.0548857\pi$
$458$	−3.25630	+	2.36584i	−0.152157	+	0.110548i
$459$	6.84869	+	4.97586i	0.319669	+	0.232253i
$460$	2.21699	+	6.82318i	0.103367	+	0.318132i
$461$	−17.4739			−0.813840			−0.406920	−	0.913464i	$-0.633397\pi$
$461$	−17.4739			−0.813840			−0.406920	+	0.913464i	$0.633397\pi$
$462$	0.383565	+	0.724743i	0.0178451	+	0.0337181i
$463$	−41.7730			−1.94135			−0.970677	−	0.240386i	$-0.922726\pi$
$463$	−41.7730			−1.94135			−0.970677	+	0.240386i	$0.922726\pi$
$464$	0.437344	+	1.34601i	0.0203032	+	0.0624868i
$465$	0.0712930	+	0.0517974i	0.00330614	+	0.00240205i
$466$	2.97493	−	2.16141i	0.137811	−	0.100125i
$467$	−4.24825	+	13.0748i	−0.196586	+	0.605028i	0.803369	+	0.595482i	$0.203039\pi$
$467$	−4.24825	+	13.0748i	−0.196586	+	0.605028i	−0.999954	+	0.00954640i	$0.996961\pi$
$468$	−2.57409	+	7.92223i	−0.118987	+	0.366205i
$469$	10.9594	−	7.96250i	0.506060	−	0.367674i
$470$	2.53720	+	1.84338i	0.117032	+	0.0850289i
$471$	1.74025	+	5.35593i	0.0801864	+	0.246788i
$472$	−10.4962			−0.483125
$473$	−31.4977	+	5.49140i	−1.44827	+	0.252495i
$474$	−1.51928			−0.0697827
$475$	1.13391	+	3.48982i	0.0520274	+	0.160124i
$476$	4.66438	+	3.38887i	0.213791	+	0.155329i
$477$	2.07837	−	1.51002i	0.0951620	−	0.0691393i
$478$	−0.338199	+	1.04087i	−0.0154689	+	0.0476083i
$479$	−6.38541	+	19.6523i	−0.291757	+	0.897935i	0.692535	+	0.721385i	$0.256494\pi$
$479$	−6.38541	+	19.6523i	−0.291757	+	0.897935i	−0.984292	+	0.176551i	$0.943506\pi$
$480$	−0.200017	+	0.145321i	−0.00912949	+	0.00663296i
$481$	−6.75888	−	4.91062i	−0.308178	−	0.223905i
$482$	1.93105	+	5.94317i	0.0879571	+	0.270704i
$483$	1.77374			0.0807079
$484$	−6.18619	+	9.09566i	−0.281190	+	0.413439i
$485$	−12.5278			−0.568856
$486$	−2.00704	−	6.17703i	−0.0910411	−	0.280196i
$487$	17.8833	+	12.9929i	0.810368	+	0.588767i	0.913937	−	0.405856i	$-0.133026\pi$
$487$	17.8833	+	12.9929i	0.810368	+	0.588767i	−0.103570	+	0.994622i	$0.533026\pi$
$488$	7.44405	−	5.40842i	0.336976	−	0.244828i
$489$	−0.284477	+	0.875529i	−0.0128645	+	0.0395928i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	−8.65440	+	6.28779i	−0.390568	+	0.283764i	−0.765688	−	0.643212i	$-0.777601\pi$
$491$	−8.65440	+	6.28779i	−0.390568	+	0.283764i	0.375120	+	0.926976i	$0.377601\pi$
$492$	0.445194	+	0.323452i	0.0200709	+	0.0145824i
$493$	−2.52150	−	7.76039i	−0.113563	−	0.349510i
$494$	10.4006			0.467943
$495$	−9.60231	+	1.67409i	−0.431592	+	0.0752448i
$496$	−0.356435			−0.0160044
$497$	−3.86699	−	11.9014i	−0.173458	−	0.533850i
$498$	0.616486	+	0.447904i	0.0276254	+	0.0200710i
$499$	−1.50322	+	1.09216i	−0.0672935	+	0.0488916i	−0.620923	−	0.783871i	$-0.713242\pi$
$499$	−1.50322	+	1.09216i	−0.0672935	+	0.0488916i	0.553630	+	0.832763i	$0.313242\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−1.19050	+	3.66398i	−0.0531876	+	0.163695i
$502$	15.6072	−	11.3393i	0.696583	−	0.506097i
$503$	10.9612	+	7.96375i	0.488734	+	0.355086i	0.804697	−	0.593686i	$-0.202328\pi$
$503$	10.9612	+	7.96375i	0.488734	+	0.355086i	−0.315963	+	0.948771i	$0.602328\pi$
$504$	−0.908162	−	2.79504i	−0.0404528	−	0.124501i
$505$	5.90123			0.262601
$506$	11.1304	+	21.0308i	0.494806	+	0.934932i
$507$	1.22782			0.0545295
$508$	0.0543127	+	0.167157i	0.00240974	+	0.00741641i
$509$	5.15160	+	3.74285i	0.228341	+	0.165899i	0.696073	−	0.717971i	$-0.254929\pi$
$509$	5.15160	+	3.74285i	0.228341	+	0.165899i	−0.467733	+	0.883870i	$0.654929\pi$
$510$	1.15320	−	0.837846i	0.0510644	−	0.0371004i
$511$	−2.22441	+	6.84604i	−0.0984023	+	0.302851i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−4.35881	+	3.16686i	−0.192446	+	0.139820i
$514$	−20.4409	−	14.8512i	−0.901609	−	0.655057i
$515$	3.69804	+	11.3814i	0.162955	+	0.501524i
$516$	−2.38339			−0.104923
$517$	9.33995	+	4.57768i	0.410771	+	0.201326i
$518$	2.94752			0.129507
$519$	−0.450722	−	1.38718i	−0.0197845	−	0.0608904i
$520$	2.29307	+	1.66601i	0.100558	+	0.0730596i
$521$	19.5534	−	14.2064i	0.856650	−	0.622393i	−0.0703212	−	0.997524i	$-0.522402\pi$
$521$	19.5534	−	14.2064i	0.856650	−	0.622393i	0.926972	+	0.375131i	$0.122402\pi$
$522$	−1.28530	+	3.95575i	−0.0562561	+	0.173138i
$523$	−9.45125	+	29.0879i	−0.413274	+	1.27193i	0.500511	+	0.865730i	$0.333145\pi$
$523$	−9.45125	+	29.0879i	−0.413274	+	1.27193i	−0.913785	+	0.406197i	$0.866855\pi$
$524$	9.25442	−	6.72373i	0.404281	−	0.293728i
$525$	0.200017	+	0.145321i	0.00872946	+	0.00634232i
$526$	0.925049	+	2.84701i	0.0403341	+	0.124136i
$527$	2.05502			0.0895181
$528$	−0.570744	+	0.588750i	−0.0248384	+	0.0256221i
$529$	28.4708			1.23786
$530$	−0.270126	−	0.831363i	−0.0117335	−	0.0361121i
$531$	−24.9557	−	18.1314i	−1.08298	−	0.786835i
$532$	−2.96862	+	2.15683i	−0.128706	+	0.0935103i
$533$	1.94951	−	5.99996i	0.0844424	−	0.259887i
$534$	0.439637	−	1.35306i	0.0190249	−	0.0585527i
$535$	−5.08787	+	3.69655i	−0.219968	+	0.159816i
$536$	10.9594	+	7.96250i	0.473376	+	0.343928i
$537$	−1.24778	−	3.84028i	−0.0538458	−	0.165720i
$538$	−22.5013			−0.970100
$539$	−0.467907	+	3.28345i	−0.0201542	+	0.141428i
$540$	−1.46830			−0.0631854
$541$	6.85751	+	21.1053i	0.294828	+	0.907386i	0.983279	+	0.182104i	$0.0582907\pi$
$541$	6.85751	+	21.1053i	0.294828	+	0.907386i	−0.688452	+	0.725282i	$0.741709\pi$
$542$	11.0258	+	8.01071i	0.473599	+	0.344090i
$543$	−0.697280	+	0.506604i	−0.0299232	+	0.0217404i
$544$	−1.78163	+	5.48331i	−0.0763869	+	0.235095i
$545$	1.05722	−	3.25380i	0.0452865	−	0.139377i
$546$	0.566927	−	0.411896i	0.0242622	−	0.0176275i
$547$	−13.9053	−	10.1028i	−0.594549	−	0.431965i	0.249391	−	0.968403i	$-0.419770\pi$
$547$	−13.9053	−	10.1028i	−0.594549	−	0.431965i	−0.843940	+	0.536438i	$0.819770\pi$
$548$	−3.07577	−	9.46626i	−0.131391	−	0.404378i
$549$	27.0416			1.15411
$550$	−0.467907	+	3.28345i	−0.0199516	+	0.140007i
$551$	5.19323			0.221239
$552$	0.548116	+	1.68693i	0.0233294	+	0.0718004i
$553$	−4.97148	−	3.61199i	−0.211409	−	0.153597i
$554$	19.0495	−	13.8403i	0.809337	−	0.588018i
$555$	0.225190	−	0.693063i	0.00955878	−	0.0294189i
$556$	−0.193823	+	0.596526i	−0.00821992	+	0.0252983i
$557$	4.87829	−	3.54428i	0.206700	−	0.150176i	−0.479620	−	0.877477i	$-0.659225\pi$
$557$	4.87829	−	3.54428i	0.206700	−	0.150176i	0.686319	+	0.727300i	$0.259225\pi$
$558$	−0.847459	−	0.615715i	−0.0358758	−	0.0260653i
$559$	8.44360	+	25.9867i	0.357126	+	1.09912i
$560$	−1.00000			−0.0422577
$561$	3.29062	−	3.39443i	0.138930	−	0.143313i
$562$	−19.1837			−0.809215
$563$	8.40482	+	25.8674i	0.354221	+	1.09018i	0.956460	+	0.291864i	$0.0942755\pi$
$563$	8.40482	+	25.8674i	0.354221	+	1.09018i	−0.602239	+	0.798316i	$0.705724\pi$
$564$	0.627284	+	0.455748i	0.0264134	+	0.0191905i
$565$	−13.6095	+	9.88788i	−0.572556	+	0.415986i
$566$	5.33740	−	16.4268i	0.224348	−	0.690472i
$567$	2.61231	−	8.03986i	0.109707	−	0.337642i
$568$	10.1239	−	7.35546i	0.424790	−	0.308628i
$569$	−25.7900	−	18.7376i	−1.08117	−	0.785519i	−0.103287	−	0.994652i	$-0.532936\pi$
$569$	−25.7900	−	18.7376i	−1.08117	−	0.785519i	−0.977887	+	0.209132i	$0.932936\pi$
$570$	0.280342	+	0.862804i	0.0117422	+	0.0361389i
$571$	−26.4539			−1.10706			−0.553531	−	0.832829i	$-0.686720\pi$
$571$	−26.4539			−1.10706			−0.553531	+	0.832829i	$0.686720\pi$
$572$	8.44127	+	4.13722i	0.352947	+	0.172986i
$573$	−6.42075			−0.268231
$574$	0.687804	+	2.11684i	0.0287084	+	0.0883553i
$575$	5.80414	+	4.21696i	0.242050	+	0.175859i
$576$	2.37760	−	1.72743i	0.0990667	−	0.0719761i
$577$	−9.28678	+	28.5818i	−0.386614	+	1.18987i	0.548689	+	0.836026i	$0.315127\pi$
$577$	−9.28678	+	28.5818i	−0.386614	+	1.18987i	−0.935303	+	0.353848i	$0.884873\pi$
$578$	5.01870	−	15.4460i	0.208750	−	0.642468i
$579$	−0.135512	+	0.0984552i	−0.00563169	+	0.00409166i
$580$	1.14498	+	0.831879i	0.0475428	+	0.0345419i
$581$	0.952443	+	2.93132i	0.0395140	+	0.121612i
$582$	−3.09730			−0.128387
$583$	−1.35617	−	2.56247i	−0.0561668	−	0.106127i
$584$	−7.19836			−0.297870
$585$	2.57409	+	7.92223i	0.106425	+	0.327544i
$586$	26.6424	+	19.3568i	1.10059	+	0.799622i
$587$	−21.6472	+	15.7276i	−0.893475	+	0.649148i	−0.936782	−	0.349914i	$-0.886211\pi$
$587$	−21.6472	+	15.7276i	−0.893475	+	0.649148i	0.0433068	+	0.999062i	$0.486211\pi$
$588$	−0.0763997	+	0.235134i	−0.00315067	+	0.00969677i
$589$	−0.404165	+	1.24389i	−0.0166533	+	0.0512537i
$590$	−8.49158	+	6.16949i	−0.349593	+	0.253994i
$591$	1.16172	+	0.844041i	0.0477869	+	0.0347192i
$592$	0.910835	+	2.80326i	0.0374351	+	0.115213i
$593$	−3.33504			−0.136954			−0.0684768	−	0.997653i	$-0.521814\pi$
$593$	−3.33504			−0.136954			−0.0684768	+	0.997653i	$0.521814\pi$
$594$	−4.79742	+	0.836395i	−0.196841	+	0.0343177i
$595$	5.76549			0.236362
$596$	−4.64498	−	14.2958i	−0.190266	−	0.585578i
$597$	2.18968	+	1.59090i	0.0896177	+	0.0651111i
$598$	16.4512	−	11.9525i	0.672741	−	0.488775i
$599$	−1.02951	+	3.16849i	−0.0420645	+	0.129461i	−0.969883	−	0.243570i	$-0.921681\pi$
$599$	−1.02951	+	3.16849i	−0.0420645	+	0.129461i	0.927819	+	0.373031i	$0.121681\pi$
$600$	−0.0763997	+	0.235134i	−0.00311901	+	0.00959931i
$601$	33.6092	−	24.4185i	1.37095	−	0.996052i	0.373286	−	0.927716i	$-0.378231\pi$
$601$	33.6092	−	24.4185i	1.37095	−	0.996052i	0.997662	−	0.0683358i	$-0.0217689\pi$
$602$	−7.79907	−	5.66635i	−0.317866	−	0.230943i
$603$	12.3025	+	37.8633i	0.500998	+	1.54191i
$604$	0.516467			0.0210148
$605$	0.341565	+	10.9947i	0.0138866	+	0.446998i
$606$	1.45899			0.0592674
$607$	6.47935	+	19.9414i	0.262989	+	0.809396i	0.992150	+	0.125054i	$0.0399104\pi$
$607$	6.47935	+	19.9414i	0.262989	+	0.809396i	−0.729161	+	0.684342i	$0.760090\pi$
$608$	−2.96862	−	2.15683i	−0.120393	−	0.0874709i
$609$	0.283079	−	0.205669i	0.0114710	−	0.00833414i
$610$	2.84337	−	8.75101i	0.115125	−	0.354318i
$611$	2.74688	−	8.45402i	0.111127	−	0.342013i
$612$	−13.7080	+	9.95946i	−0.554114	+	0.402587i
$613$	2.24252	+	1.62929i	0.0905746	+	0.0658063i	0.632151	−	0.774845i	$-0.282172\pi$
$613$	2.24252	+	1.62929i	0.0905746	+	0.0658063i	−0.541576	+	0.840652i	$0.682172\pi$
$614$	−2.46347	−	7.58177i	−0.0994175	−	0.305976i
$615$	0.550290			0.0221898
$616$	−3.26734	+	0.569637i	−0.131645	+	0.0229513i
$617$	48.3567			1.94677			0.973384	−	0.229180i	$-0.0736043\pi$
$617$	48.3567			1.94677			0.973384	+	0.229180i	$0.0736043\pi$
$618$	0.914283	+	2.81387i	0.0367778	+	0.113191i
$619$	−37.9263	−	27.5551i	−1.52439	−	1.10753i	−0.959259	−	0.282528i	$-0.908827\pi$
$619$	−37.9263	−	27.5551i	−1.52439	−	1.10753i	−0.565128	−	0.825003i	$-0.691173\pi$
$620$	−0.288362	+	0.209507i	−0.0115809	+	0.00841401i
$621$	−3.25519	+	10.0184i	−0.130626	+	0.402026i
$622$	−1.23865	+	3.81218i	−0.0496654	+	0.152854i
$623$	4.65543	−	3.38237i	0.186516	−	0.135512i
$624$	0.566927	+	0.411896i	0.0226952	+	0.0164891i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	5.27260			0.210736
$627$	1.40746	+	2.65938i	0.0562085	+	0.106205i
$628$	−22.7782			−0.908949
$629$	−5.25141	−	16.1622i	−0.209387	−	0.644428i
$630$	−2.37760	−	1.72743i	−0.0947258	−	0.0688224i
$631$	17.4598	−	12.6853i	0.695063	−	0.504993i	−0.183258	−	0.983065i	$-0.558664\pi$
$631$	17.4598	−	12.6853i	0.695063	−	0.504993i	0.878321	+	0.478072i	$0.158664\pi$
$632$	1.89893	−	5.84432i	0.0755356	−	0.232475i
$633$	0.491087	−	1.51141i	0.0195190	−	0.0600732i
$634$	3.76984	−	2.73895i	0.149720	−	0.108778i
$635$	0.142193	+	0.103309i	0.00564274	+	0.00409969i
$636$	−0.0667845	−	0.205542i	−0.00264818	−	0.00815026i
$637$	2.83439			0.112303
$638$	4.21492	+	2.06581i	0.166870	+	0.0817860i
$639$	36.7766			1.45486
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−18.5952	−	13.5102i	−0.734466	−	0.533621i	0.156507	−	0.987677i	$-0.449977\pi$
$641$	−18.5952	−	13.5102i	−0.734466	−	0.533621i	−0.890973	+	0.454056i	$0.849977\pi$
$642$	−1.25790	+	0.913916i	−0.0496452	+	0.0360694i
$643$	−10.1692	+	31.2975i	−0.401034	+	1.23425i	0.523129	+	0.852254i	$0.324765\pi$
$643$	−10.1692	+	31.2975i	−0.401034	+	1.23425i	−0.924162	+	0.382001i	$0.875235\pi$
$644$	−2.21699	+	6.82318i	−0.0873615	+	0.268871i
$645$	−1.92820	+	1.40092i	−0.0759228	+	0.0551611i
$646$	17.1155	+	12.4352i	0.673401	+	0.489255i
$647$	6.15565	+	18.9451i	0.242004	+	0.744810i	0.996115	+	0.0880637i	$0.0280679\pi$
$647$	6.15565	+	18.9451i	0.242004	+	0.744810i	−0.754111	+	0.656747i	$0.771932\pi$
$648$	8.45361			0.332089
$649$	−24.2305	+	24.9950i	−0.951131	+	0.981138i
$650$	2.83439			0.111174
$651$	0.0272315	+	0.0838100i	0.00106729	+	0.00328477i
$652$	−3.01240	−	2.18864i	−0.117975	−	0.0857136i
$653$	−27.5761	+	20.0352i	−1.07914	+	0.784039i	−0.977532	−	0.210786i	$-0.932398\pi$
$653$	−27.5761	+	20.0352i	−1.07914	+	0.784039i	−0.101604	+	0.994825i	$0.532398\pi$
$654$	0.261382	−	0.804452i	0.0102209	−	0.0314566i
$655$	3.53487	−	10.8792i	0.138119	−	0.425087i
$656$	−1.80069	+	1.30828i	−0.0703052	+	0.0510798i
$657$	−17.1148	−	12.4346i	−0.667712	−	0.485121i
$658$	0.969124	+	2.98266i	0.0377804	+	0.116276i
$659$	7.54952			0.294088			0.147044	−	0.989130i	$-0.453024\pi$
$659$	7.54952			0.294088			0.147044	+	0.989130i	$0.453024\pi$
$660$	−0.115683	+	0.811783i	−0.00450295	+	0.0315986i
$661$	41.0094			1.59508			0.797541	−	0.603265i	$-0.206134\pi$
$661$	41.0094			1.59508			0.797541	+	0.603265i	$0.206134\pi$
$662$	−7.73156	−	23.7953i	−0.300496	−	0.924830i
$663$	−3.26861	−	2.37478i	−0.126942	−	0.0922290i
$664$	−2.49353	+	1.81165i	−0.0967676	+	0.0703058i
$665$	−1.13391	+	3.48982i	−0.0439712	+	0.135329i
$666$	−2.67683	+	8.23843i	−0.103725	+	0.319233i
$667$	8.21447	−	5.96816i	0.318065	−	0.231088i
$668$	−12.6065	−	9.15918i	−0.487761	−	0.354379i
$669$	−1.77284	−	5.45624i	−0.0685420	−	0.210951i
$670$	13.5466			0.523352
$671$	4.30538	−	30.2122i	0.166207	−	1.16633i
$672$	−0.247235			−0.00953728
$673$	14.9484	+	46.0065i	0.576220	+	1.77342i	0.631989	+	0.774978i	$0.282239\pi$
$673$	14.9484	+	46.0065i	0.576220	+	1.77342i	−0.0557690	+	0.998444i	$0.517761\pi$
$674$	−12.8931	−	9.36738i	−0.496624	−	0.360818i
$675$	−1.18788	+	0.863043i	−0.0457214	+	0.0332185i
$676$	−1.53465	+	4.72315i	−0.0590248	+	0.181660i
$677$	1.66363	−	5.12013i	0.0639386	−	0.196783i	−0.913984	−	0.405750i	$-0.867010\pi$
$677$	1.66363	−	5.12013i	0.0639386	−	0.196783i	0.977923	+	0.208967i	$0.0670103\pi$
$678$	−3.36474	+	2.44463i	−0.129222	+	0.0938854i
$679$	−10.1352	−	7.36363i	−0.388952	−	0.282590i
$680$	1.78163	+	5.48331i	0.0683225	+	0.210275i
$681$	6.32217			0.242266
$682$	−0.822833	+	0.848793i	−0.0315079	+	0.0325019i
$683$	12.5734			0.481106			0.240553	−	0.970636i	$-0.422671\pi$
$683$	12.5734			0.481106			0.240553	+	0.970636i	$0.422671\pi$
$684$	−3.33242	−	10.2561i	−0.127418	−	0.392153i
$685$	−8.05248	−	5.85047i	−0.307669	−	0.223535i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	−0.307509	+	0.946417i	−0.0117322	+	0.0361080i
$688$	2.97898	−	9.16835i	0.113572	−	0.349540i
$689$	−2.00448	+	1.45634i	−0.0763646	+	0.0554822i
$690$	1.43499	+	1.04258i	0.0546290	+	0.0396903i
$691$	−8.04764	−	24.7681i	−0.306147	−	0.942223i	−0.979247	−	0.202671i	$-0.935038\pi$
$691$	−8.04764	−	24.7681i	−0.306147	−	0.942223i	0.673100	−	0.739551i	$-0.264962\pi$
$692$	5.89952			0.224266
$693$	−8.75243	−	4.28973i	−0.332477	−	0.162953i
$694$	−12.4275			−0.471741
$695$	0.193823	+	0.596526i	0.00735212	+	0.0226275i
$696$	0.283079	+	0.205669i	0.0107301	+	0.00779587i
$697$	10.3819	−	7.54287i	0.393242	−	0.285707i
$698$	−5.01005	+	15.4193i	−0.189633	+	0.583631i
$699$	0.280938	−	0.864638i	0.0106260	−	0.0327036i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	37.3401	+	27.1292i	1.41032	+	1.02465i	0.993276	+	0.115767i	$0.0369326\pi$
$701$	37.3401	+	27.1292i	1.41032	+	1.02465i	0.417040	+	0.908888i	$0.363067\pi$
$702$	1.28604	+	3.95804i	0.0485386	+	0.149386i
$703$	10.8157			0.407921
$704$	−1.55142	−	2.93140i	−0.0584714	−	0.110481i
$705$	0.775365			0.0292019
$706$	−6.74645	−	20.7634i	−0.253906	−	0.781442i
$707$	4.77420	+	3.46866i	0.179552	+	0.130452i
$708$	−2.09941	+	1.52531i	−0.0789008	+	0.0573248i
$709$	13.7553	−	42.3346i	0.516593	−	1.58991i	−0.263772	−	0.964585i	$-0.584967\pi$
$709$	13.7553	−	42.3346i	0.516593	−	1.58991i	0.780365	−	0.625324i	$-0.215033\pi$
$710$	3.86699	−	11.9014i	0.145126	−	0.446651i
$711$	14.6105	−	10.6152i	0.547938	−	0.398100i
$712$	4.65543	+	3.38237i	0.174470	+	0.126760i
$713$	0.790211	+	2.43202i	0.0295936	+	0.0910798i
$714$	1.42543			0.0533453
$715$	9.26093	−	1.61457i	0.346339	−	0.0603817i
$716$	16.3323			0.610367
$717$	0.0836145	+	0.257339i	0.00312264	+	0.00961050i
$718$	14.7326	+	10.7039i	0.549817	+	0.399466i
$719$	−19.5788	+	14.2248i	−0.730167	+	0.530497i	−0.889616	−	0.456709i	$-0.849028\pi$
$719$	−19.5788	+	14.2248i	−0.730167	+	0.530497i	0.159449	+	0.987206i	$0.449028\pi$
$720$	0.908162	−	2.79504i	0.0338452	−	0.104165i
$721$	−3.69804	+	11.3814i	−0.137722	+	0.423865i
$722$	4.47824	−	3.25363i	0.166663	−	0.121088i
$723$	1.24991	+	0.908114i	0.0464847	+	0.0337731i
$724$	−1.07727	−	3.31548i	−0.0400362	−	0.123219i
$725$	1.41528			0.0525620
$726$	0.0844466	+	2.71827i	0.00313411	+	0.100884i
$727$	−5.25083			−0.194742			−0.0973712	−	0.995248i	$-0.531043\pi$
$727$	−5.25083			−0.194742			−0.0973712	+	0.995248i	$0.531043\pi$
$728$	0.875876	+	2.69567i	0.0324621	+	0.0999081i
$729$	19.2183	+	13.9629i	0.711787	+	0.517144i
$730$	−5.82359	+	4.23109i	−0.215541	+	0.156600i
$731$	−17.1753	+	52.8600i	−0.635250	+	1.95510i
$732$	0.702981	−	2.16355i	0.0259829	−	0.0799672i
$733$	38.5130	−	27.9814i	1.42251	−	1.03352i	0.431161	−	0.902275i	$-0.358104\pi$
$733$	38.5130	−	27.9814i	1.42251	−	1.03352i	0.991351	−	0.131240i	$-0.0418958\pi$
$734$	4.27045	+	3.10266i	0.157625	+	0.114521i
$735$	0.0763997	+	0.235134i	0.00281805	+	0.00867305i
$736$	−7.17432			−0.264449
$737$	44.2614	−	7.71665i	1.63039	−	0.284247i
$738$	−6.54129			−0.240788
$739$	8.40875	+	25.8795i	0.309321	+	0.951991i	0.978029	+	0.208467i	$0.0668473\pi$
$739$	8.40875	+	25.8795i	0.309321	+	0.951991i	−0.668709	+	0.743524i	$0.733153\pi$
$740$	2.38460	+	1.73251i	0.0876595	+	0.0636884i
$741$	2.08029	−	1.51142i	0.0764213	−	0.0555233i
$742$	0.270126	−	0.831363i	0.00991664	−	0.0305203i
$743$	−1.63727	+	5.03901i	−0.0600658	+	0.184863i	−0.976587	−	0.215122i	$-0.930985\pi$
$743$	−1.63727	+	5.03901i	−0.0600658	+	0.184863i	0.916521	+	0.399986i	$0.130985\pi$
$744$	−0.0712930	+	0.0517974i	−0.00261373	+	0.00189899i
$745$	−12.1607	−	8.83528i	−0.445534	−	0.323699i
$746$	5.74151	+	17.6705i	0.210212	+	0.646965i
$747$	−9.05811			−0.331419
$748$	8.94470	+	16.9009i	0.327051	+	0.617960i
$749$	−6.28895			−0.229793
$750$	0.0763997	+	0.235134i	0.00278972	+	0.00858588i
$751$	16.2309	+	11.7924i	0.592273	+	0.430311i	0.843128	−	0.537713i	$-0.180712\pi$
$751$	16.2309	+	11.7924i	0.592273	+	0.430311i	−0.250855	+	0.968025i	$0.580712\pi$
$752$	−2.53720	+	1.84338i	−0.0925222	+	0.0672213i
$753$	1.47387	−	4.53610i	0.0537108	−	0.165305i
$754$	1.23961	−	3.81511i	0.0451438	−	0.138938i
$755$	0.417831	−	0.303572i	0.0152064	−	0.0110481i
$756$	−1.18788	−	0.863043i	−0.0432026	−	0.0313886i
$757$	−1.34999	−	4.15484i	−0.0490662	−	0.151010i	0.923522	−	0.383547i	$-0.125297\pi$
$757$	−1.34999	−	4.15484i	−0.0490662	−	0.151010i	−0.972588	+	0.232537i	$0.925297\pi$
$758$	22.8406			0.829607
$759$	5.28248	+	2.58904i	0.191742	+	0.0939761i
$760$	−3.66941			−0.133104
$761$	0.668820	+	2.05842i	0.0242447	+	0.0746176i	0.962447	−	0.271470i	$-0.0875099\pi$
$761$	0.668820	+	2.05842i	0.0242447	+	0.0746176i	−0.938202	+	0.346088i	$0.887510\pi$
$762$	0.0351549	+	0.0255416i	0.00127353	+	0.000925273i
$763$	2.76785	−	2.01096i	0.100203	−	0.0728016i
$764$	8.02526	−	24.6992i	0.290344	−	0.893586i
$765$	−5.23600	+	16.1147i	−0.189308	+	0.582630i
$766$	18.1814	−	13.2096i	0.656922	−	0.477282i
$767$	24.0685	+	17.4868i	0.869062	+	0.631411i
$768$	−0.0763997	−	0.235134i	−0.00275684	−	0.00848467i
$769$	−32.7883			−1.18237			−0.591187	−	0.806534i	$-0.701341\pi$
$769$	−32.7883			−1.18237			−0.591187	+	0.806534i	$0.701341\pi$
$770$	−2.30851	+	2.38134i	−0.0831929	+	0.0858176i
$771$	−6.24671			−0.224970
$772$	−0.209360	−	0.644343i	−0.00753502	−	0.0231904i
$773$	5.90457	+	4.28992i	0.212373	+	0.154298i	0.688887	−	0.724869i	$-0.258100\pi$
$773$	5.90457	+	4.28992i	0.212373	+	0.154298i	−0.476514	+	0.879167i	$0.658100\pi$
$774$	22.9205	−	16.6527i	0.823860	−	0.598569i
$775$	−0.110144	+	0.338990i	−0.00395650	+	0.0121769i
$776$	3.87129	−	11.9146i	0.138971	−	0.427710i
$777$	0.589555	−	0.428337i	0.0211502	−	0.0153665i
$778$	−29.3267	−	21.3071i	−1.05141	−	0.763895i
$779$	2.52383	+	7.76756i	0.0904258	+	0.278302i
$780$	0.700760			0.0250912
$781$	5.85532	−	41.0886i	0.209520	−	1.47027i
$782$	41.3634			1.47915
$783$	0.642151	+	1.97634i	0.0229486	+	0.0706285i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−18.4280	+	13.3887i	−0.657722	+	0.477863i
$786$	0.873944	−	2.68972i	0.0311725	−	0.0959392i
$787$	−0.258450	+	0.795426i	−0.00921273	+	0.0283539i	−0.955557	−	0.294806i	$-0.904745\pi$
$787$	−0.258450	+	0.795426i	−0.00921273	+	0.0283539i	0.946344	+	0.323160i	$0.104745\pi$
$788$	−4.69887	+	3.41393i	−0.167390	+	0.121616i
$789$	0.598756	+	0.435021i	0.0213163	+	0.0154872i
$790$	−1.89893	−	5.84432i	−0.0675611	−	0.207932i
$791$	−16.8223			−0.598131
$792$	1.37512	−	9.64966i	0.0488628	−	0.342886i
$793$	−26.0802			−0.926137
$794$	−2.48138	−	7.63691i	−0.0880610	−	0.271024i
$795$	−0.174844	−	0.127032i	−0.00620108	−	0.00450535i
$796$	−8.85670	+	6.43477i	−0.313917	+	0.228074i
$797$	−0.628080	+	1.93303i	−0.0222477	+	0.0684715i	−0.961564	−	0.274581i	$-0.911461\pi$
$797$	−0.628080	+	1.93303i	−0.0222477	+	0.0684715i	0.939316	+	0.343052i	$0.111461\pi$
$798$	−0.280342	+	0.862804i	−0.00992400	+	0.0305429i
$799$	14.6282	−	10.6280i	0.517508	−	0.375992i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	5.22595	+	16.0838i	0.184650	+	0.568294i
$802$	0.672421			0.0237440
$803$	−16.6175	+	17.1417i	−0.586418	+	0.604919i
$804$	3.34919			0.118117
$805$	2.21699	+	6.82318i	0.0781385	+	0.240485i
$806$	0.817331	+	0.593825i	0.0287892	+	0.0209166i
$807$	−4.50064	+	3.26991i	−0.158430	+	0.115106i
$808$	−1.82358	+	5.61241i	−0.0641534	+	0.197444i
$809$	−13.0405	+	40.1344i	−0.458478	+	1.41105i	0.408525	+	0.912747i	$0.366043\pi$
$809$	−13.0405	+	40.1344i	−0.458478	+	1.41105i	−0.867003	+	0.498303i	$0.833957\pi$
$810$	6.83912	−	4.96891i	0.240302	−	0.174590i
$811$	2.45448	+	1.78328i	0.0861884	+	0.0626195i	0.630045	−	0.776559i	$-0.283036\pi$
$811$	2.45448	+	1.78328i	0.0861884	+	0.0626195i	−0.543857	+	0.839178i	$0.683036\pi$
$812$	0.437344	+	1.34601i	0.0153478	+	0.0472356i
$813$	3.36947			0.118173
$814$	8.77819	+	4.30235i	0.307675	+	0.150797i
$815$	−3.72353			−0.130430
$816$	0.440482	+	1.35566i	0.0154199	+	0.0474577i
$817$	−28.6180	−	20.7922i	−1.00122	−	0.727427i
$818$	17.5868	−	12.7776i	0.614908	−	0.446757i
$819$	−2.57409	+	7.92223i	−0.0899459	+	0.276825i
$820$	−0.687804	+	2.11684i	−0.0240191	+	0.0739233i
$821$	−27.9839	+	20.3315i	−0.976644	+	0.709574i	−0.956956	−	0.290233i	$-0.906267\pi$
$821$	−27.9839	+	20.3315i	−0.976644	+	0.709574i	−0.0196880	+	0.999806i	$0.506267\pi$
$822$	−1.99085	−	1.44644i	−0.0694389	−	0.0504503i
$823$	15.6787	+	48.2540i	0.546524	+	1.68203i	0.717337	+	0.696726i	$0.245361\pi$
$823$	15.6787	+	48.2540i	0.546524	+	1.68203i	−0.170813	+	0.985303i	$0.554639\pi$
$824$	−11.9671			−0.416894
$825$	0.383565	+	0.724743i	0.0133540	+	0.0252323i
$826$	−10.4962			−0.365209
$827$	−3.99220	−	12.2867i	−0.138822	−	0.427251i	0.857343	−	0.514746i	$-0.172114\pi$
$827$	−3.99220	−	12.2867i	−0.138822	−	0.427251i	−0.996165	+	0.0874949i	$0.972114\pi$
$828$	−17.0577	−	12.3931i	−0.592794	−	0.430690i
$829$	−10.3757	+	7.53841i	−0.360364	+	0.261820i	−0.753204	−	0.657787i	$-0.771493\pi$
$829$	−10.3757	+	7.53841i	−0.360364	+	0.261820i	0.392840	+	0.919607i	$0.371493\pi$
$830$	−0.952443	+	2.93132i	−0.0330598	+	0.101748i
$831$	1.79895	−	5.53659i	0.0624048	−	0.192062i
$832$	−2.29307	+	1.66601i	−0.0794980	+	0.0577587i
$833$	4.66438	+	3.38887i	0.161611	+	0.117417i
$834$	0.0479198	+	0.147482i	0.00165933	+	0.00510688i
$835$	−15.5825			−0.539255
$836$	−11.9892	+	2.09023i	−0.414656	+	0.0722922i
$837$	−0.523352			−0.0180897
$838$	−2.28056	−	7.01883i	−0.0787805	−	0.242461i
$839$	6.49497	+	4.71887i	0.224231	+	0.162914i	0.694229	−	0.719754i	$-0.255745\pi$
$839$	6.49497	+	4.71887i	0.224231	+	0.162914i	−0.469998	+	0.882668i	$0.655745\pi$
$840$	−0.200017	+	0.145321i	−0.00690124	+	0.00501405i
$841$	−8.34253	+	25.6757i	−0.287673	+	0.885368i
$842$	9.10046	−	28.0083i	0.313623	−	0.965231i
$843$	−3.83706	+	2.78779i	−0.132155	+	0.0960165i
$844$	5.20025	+	3.77820i	0.179000	+	0.130051i
$845$	1.53465	+	4.72315i	0.0527934	+	0.162481i
$846$	−9.21676			−0.316879
$847$	−6.18619	+	9.09566i	−0.212560	+	0.312531i
$848$	0.874146			0.0300183
$849$	−1.31959	−	4.06128i	−0.0452883	−	0.139383i
$850$	4.66438	+	3.38887i	0.159987	+	0.116237i
$851$	17.1078	−	12.4296i	0.586449	−	0.426080i
$852$	0.956055	−	2.94243i	0.0327539	−	0.100806i
$853$	−9.32113	+	28.6875i	−0.319150	+	0.982241i	0.654863	+	0.755748i	$0.272726\pi$
$853$	−9.32113	+	28.6875i	−0.319150	+	0.982241i	−0.974013	+	0.226494i	$0.927274\pi$
$854$	7.44405	−	5.40842i	0.254730	−	0.185072i
$855$	−8.72439	−	6.33864i	−0.298368	−	0.216777i
$856$	−1.94339	−	5.98115i	−0.0664238	−	0.204431i
$857$	32.8279			1.12138			0.560689	−	0.828026i	$-0.310536\pi$
$857$	32.8279			1.12138			0.560689	+	0.828026i	$0.310536\pi$
$858$	2.28962	−	0.399179i	0.0781664	−	0.0136277i
$859$	40.7882			1.39168			0.695838	−	0.718199i	$-0.255033\pi$
$859$	40.7882			1.39168			0.695838	+	0.718199i	$0.255033\pi$
$860$	−2.97898	−	9.16835i	−0.101582	−	0.312638i
$861$	0.445194	+	0.323452i	0.0151722	+	0.0110232i
$862$	15.9135	−	11.5618i	0.542015	−	0.393797i
$863$	12.9902	−	39.9796i	0.442190	−	1.36092i	−0.443345	−	0.896351i	$-0.646208\pi$
$863$	12.9902	−	39.9796i	0.442190	−	1.36092i	0.885536	−	0.464571i	$-0.153792\pi$
$864$	0.453728	−	1.39643i	0.0154362	−	0.0475076i
$865$	4.77281	−	3.46765i	0.162281	−	0.117904i
$866$	13.7941	+	10.0220i	0.468742	+	0.340561i
$867$	−1.24080	−	3.81878i	−0.0421397	−	0.129693i
$868$	−0.356435			−0.0120982
$869$	−9.53361	−	18.0137i	−0.323405	−	0.611072i
$870$	0.349905			0.0118629
$871$	−11.8652	−	36.5172i	−0.402035	−	1.23734i
$872$	2.76785	+	2.01096i	0.0937311	+	0.0680997i
$873$	29.7860	−	21.6408i	1.00810	−	0.732430i
$874$	−8.13503	+	25.0371i	−0.275172	+	0.846891i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	−1.43979	+	1.04607i	−0.0486461	+	0.0353435i
$877$	1.75054	+	1.27184i	0.0591116	+	0.0429471i	0.616949	−	0.787003i	$-0.288369\pi$
$877$	1.75054	+	1.27184i	0.0591116	+	0.0429471i	−0.557837	+	0.829950i	$0.688369\pi$
$878$	9.25780	+	28.4926i	0.312436	+	0.961578i
$879$	8.14187			0.274619
$880$	−2.97816	−	1.45965i	−0.100394	−	0.0492047i
$881$	9.74157			0.328202			0.164101	−	0.986444i	$-0.447528\pi$
$881$	9.74157			0.328202			0.164101	+	0.986444i	$0.447528\pi$
$882$	−0.908162	−	2.79504i	−0.0305794	−	0.0941138i
$883$	−20.4526	−	14.8597i	−0.688286	−	0.500069i	0.187810	−	0.982205i	$-0.439861\pi$
$883$	−20.4526	−	14.8597i	−0.688286	−	0.500069i	−0.876096	+	0.482137i	$0.839861\pi$
$884$	13.2207	−	9.60539i	0.444660	−	0.323064i
$885$	−0.801904	+	2.46801i	−0.0269557	+	0.0829612i
$886$	12.7610	−	39.2743i	0.428714	−	1.31945i
$887$	37.0819	−	26.9416i	1.24509	−	0.904610i	0.247163	−	0.968974i	$-0.420502\pi$
$887$	37.0819	−	26.9416i	1.24509	−	0.904610i	0.997927	+	0.0643637i	$0.0205018\pi$
$888$	0.589555	+	0.428337i	0.0197842	+	0.0143740i
$889$	0.0543127	+	0.167157i	0.00182159	+	0.00560628i
$890$	5.75443			0.192889
$891$	19.5152	−	20.1309i	0.653785	−	0.674411i
$892$	23.2048			0.776955
$893$	3.55612	+	10.9446i	0.119001	+	0.366247i
$894$	−3.00655	−	2.18439i	−0.100554	−	0.0730568i
$895$	13.2131	−	9.59989i	0.441666	−	0.320889i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	1.55358	−	4.78141i	0.0518724	−	0.159647i
$898$	−27.4470	+	19.9414i	−0.915917	+	0.665453i
$899$	0.408112	+	0.296510i	0.0136113	+	0.00988918i
$900$	−0.908162	−	2.79504i	−0.0302721	−	0.0931679i
$901$	−5.03988			−0.167903
$902$	−1.04146	+	7.30824i	−0.0346767	+	0.243338i
$903$	−2.38339			−0.0793141
$904$	−5.19837	−	15.9989i	−0.172895	−	0.532117i
$905$	−2.82032	−	2.04908i	−0.0937505	−	0.0681137i
$906$	0.103302	−	0.0750535i	0.00343199	−	0.00249349i
$907$	−4.67540	+	14.3894i	−0.155244	+	0.477792i	−0.998186	−	0.0602130i	$-0.980822\pi$
$907$	−4.67540	+	14.3894i	−0.155244	+	0.477792i	0.842941	+	0.538005i	$0.180822\pi$
$908$	−7.90204	+	24.3200i	−0.262238	+	0.807087i
$909$	−14.0308	+	10.1940i	−0.465371	+	0.338112i
$910$	2.29307	+	1.66601i	0.0760146	+	0.0552278i
$911$	4.54462	+	13.9869i	0.150570	+	0.463407i	0.997685	−	0.0680025i	$-0.0216626\pi$
$911$	4.54462	+	13.9869i	0.150570	+	0.463407i	−0.847115	+	0.531409i	$0.821663\pi$
$912$	−0.907206			−0.0300406
$913$	−1.44217	+	10.1202i	−0.0477288	+	0.334928i
$914$	19.9928			0.661304
$915$	−0.702981	−	2.16355i	−0.0232398	−	0.0715248i
$916$	−3.25630	−	2.36584i	−0.107591	−	0.0781695i
$917$	9.25442	−	6.72373i	0.305608	−	0.222037i
$918$	−2.61597	+	8.05111i	−0.0863397	+	0.265726i
$919$	0.552844	−	1.70148i	0.0182367	−	0.0561266i	−0.941524	−	0.336946i	$-0.890606\pi$
$919$	0.552844	−	1.70148i	0.0182367	−	0.0561266i	0.959761	+	0.280819i	$0.0906061\pi$
$920$	−5.80414	+	4.21696i	−0.191357	+	0.139029i
$921$	−1.59453	−	1.15849i	−0.0525414	−	0.0381736i
$922$	−5.39973	−	16.6187i	−0.177831	−	0.547306i
$923$	−35.4692			−1.16748
$924$	−0.570744	+	0.588750i	−0.0187761	+	0.0193684i
$925$	2.94752			0.0969140
$926$	−12.9086	−	39.7285i	−0.424202	−	1.30556i
$927$	−28.4530	−	20.6723i	−0.934518	−	0.678967i
$928$	−1.14498	+	0.831879i	−0.0375859	+	0.0273078i
$929$	15.6997	−	48.3187i	0.515090	−	1.58528i	−0.268028	−	0.963411i	$-0.586372\pi$
$929$	15.6997	−	48.3187i	0.515090	−	1.58528i	0.783118	−	0.621873i	$-0.213628\pi$
$930$	−0.0272315	+	0.0838100i	−0.000892957	+	0.00274824i
$931$	−2.96862	+	2.15683i	−0.0972925	+	0.0706871i
$932$	2.97493	+	2.16141i	0.0974469	+	0.0707993i
$933$	0.306238	+	0.942503i	0.0100258	+	0.0308562i
$934$	−13.7476			−0.449836
$935$	17.1705	+	8.41559i	0.561537	+	0.275219i
$936$	−8.32993			−0.272272
$937$	17.3204	+	53.3067i	0.565833	+	1.74146i	0.665463	+	0.746431i	$0.268234\pi$
$937$	17.3204	+	53.3067i	0.565833	+	1.74146i	−0.0996302	+	0.995025i	$0.531766\pi$
$938$	10.9594	+	7.96250i	0.357839	+	0.259985i
$939$	1.05461	−	0.766220i	0.0344159	−	0.0250046i
$940$	−0.969124	+	2.98266i	−0.0316093	+	0.0972836i
$941$	9.84310	−	30.2940i	0.320876	−	0.987555i	−0.652392	−	0.757882i	$-0.726234\pi$
$941$	9.84310	−	30.2940i	0.320876	−	0.987555i	0.973268	−	0.229673i	$-0.0737656\pi$
$942$	−4.55603	+	3.31015i	−0.148443	+	0.107850i
$943$	12.9187	+	9.38601i	0.420692	+	0.305651i
$944$	−3.24350	−	9.98245i	−0.105567	−	0.324901i
$945$	−1.46830			−0.0477637
$946$	−14.9560	−	28.2592i	−0.486261	−	0.918786i
$947$	16.7087			0.542959			0.271479	−	0.962444i	$-0.412487\pi$
$947$	16.7087			0.542959			0.271479	+	0.962444i	$0.412487\pi$
$948$	−0.469482	−	1.44492i	−0.0152481	−	0.0469288i
$949$	16.5063	+	11.9926i	0.535819	+	0.389295i
$950$	−2.96862	+	2.15683i	−0.0963147	+	0.0699767i
$951$	0.356006	−	1.09567i	0.0115443	−	0.0355297i
$952$	−1.78163	+	5.48331i	−0.0577431	+	0.177715i
$953$	−2.40268	+	1.74565i	−0.0778304	+	0.0565471i	−0.626020	−	0.779807i	$-0.715317\pi$
$953$	−2.40268	+	1.74565i	−0.0778304	+	0.0565471i	0.548190	+	0.836354i	$0.315317\pi$
$954$	2.07837	+	1.51002i	0.0672897	+	0.0488888i
$955$	−8.02526	−	24.6992i	−0.259691	−	0.799248i
$956$	−1.09444			−0.0353966
$957$	1.14326	−	0.199319i	0.0369563	−	0.00644307i
$958$	−20.6636			−0.667611
$959$	−3.07577	−	9.46626i	−0.0993219	−	0.305681i
$960$	−0.200017	−	0.145321i	−0.00645552	−	0.00469021i
$961$	24.9767	−	18.1467i	0.805701	−	0.585376i
$962$	2.58166	−	7.94554i	0.0832362	−	0.256175i
$963$	5.71139	−	17.5778i	0.184047	−	0.566438i
$964$	−5.05557	+	3.67308i	−0.162829	+	0.118302i
$965$	−0.548111	−	0.398226i	−0.0176443	−	0.0128193i
$966$	0.548116	+	1.68693i	0.0176353	+	0.0542760i
$967$	−20.4576			−0.657873			−0.328936	−	0.944352i	$-0.606690\pi$
$967$	−20.4576			−0.657873			−0.328936	+	0.944352i	$0.606690\pi$
$968$	−10.5621	−	3.07270i	−0.339480	−	0.0987603i
$969$	5.23049			0.168027
$970$	−3.87129	−	11.9146i	−0.124300	−	0.382555i
$971$	48.5583	+	35.2796i	1.55831	+	1.13218i	0.937379	+	0.348312i	$0.113245\pi$
$971$	48.5583	+	35.2796i	1.55831	+	1.13218i	0.620930	+	0.783866i	$0.286755\pi$
$972$	5.25450	−	3.81761i	0.168538	−	0.122450i
$973$	−0.193823	+	0.596526i	−0.00621368	+	0.0191237i
$974$	−6.83080	+	21.0230i	−0.218873	+	0.673621i
$975$	0.566927	−	0.411896i	0.0181562	−	0.0131912i
$976$	7.44405	+	5.40842i	0.238278	+	0.173119i
$977$	5.18500	+	15.9578i	0.165883	+	0.510535i	0.999100	−	0.0424105i	$-0.0135037\pi$
$977$	5.18500	+	15.9578i	0.165883	+	0.510535i	−0.833217	+	0.552946i	$0.813504\pi$
$978$	−0.920586			−0.0294371
$979$	18.8017	−	3.27793i	0.600904	−	0.104763i
$980$	−1.00000			−0.0319438
$981$	3.10705	+	9.56251i	0.0992004	+	0.305308i
$982$	−8.65440	−	6.28779i	−0.276173	−	0.200652i
$983$	−39.3229	+	28.5697i	−1.25421	+	0.911233i	−0.998458	−	0.0555104i	$-0.982321\pi$
$983$	−39.3229	+	28.5697i	−1.25421	+	0.911233i	−0.255747	+	0.966744i	$0.582321\pi$
$984$	−0.170049	+	0.523357i	−0.00542096	+	0.0166840i
$985$	−1.79481	+	5.52385i	−0.0571873	+	0.176005i
$986$	6.60138	−	4.79619i	0.210231	−	0.152742i
$987$	0.627284	+	0.455748i	0.0199667	+	0.0145066i
$988$	3.21395	+	9.89152i	0.102249	+	0.314691i
$989$	−69.1617			−2.19921
$990$	−4.55943	−	8.61501i	−0.144908	−	0.273803i
$991$	55.7217			1.77006			0.885028	−	0.465537i	$-0.154139\pi$
$991$	55.7217			1.77006			0.885028	+	0.465537i	$0.154139\pi$
$992$	−0.110144	−	0.338990i	−0.00349709	−	0.0107629i
$993$	−5.00440	−	3.63591i	−0.158810	−	0.115382i
$994$	10.1239	−	7.35546i	0.321111	−	0.233301i
$995$	−3.38296	+	10.4117i	−0.107247	+	0.330072i
$996$	−0.235477	+	0.724723i	−0.00746137	+	0.0229637i
$997$	−31.3954	+	22.8101i	−0.994303	+	0.722403i	−0.960859	−	0.277037i	$-0.910647\pi$
$997$	−31.3954	+	22.8101i	−0.994303	+	0.722403i	−0.0334436	+	0.999441i	$0.510647\pi$
$998$	−1.50322	−	1.09216i	−0.0475837	−	0.0345716i
$999$	1.33737	+	4.11602i	0.0423127	+	0.130225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.h.71.2	✓	12
11.3	even	5		8470.2.a.da.1.4		6
11.8	odd	10		8470.2.a.cu.1.4		6
11.9	even	5	inner	770.2.n.h.141.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.71.2	✓	12	1.1	even	1	trivial
770.2.n.h.141.2	yes	12	11.9	even	5	inner
8470.2.a.cu.1.4		6	11.8	odd	10
8470.2.a.da.1.4		6	11.3	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.200017 + 0.145321i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.0763997 + 0.235134i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.908162 - 2.79504i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.200017 + 0.145321i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.0763997 + 0.235134i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.908162 - 2.79504i) q^{9} -1.00000 q^{10} +(-3.26734 + 0.569637i) q^{11} -0.247235 q^{12} +(0.875876 + 2.69567i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.200017 + 0.145321i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.78163 + 5.48331i) q^{17} +(2.37760 - 1.72743i) q^{18} +(-2.96862 - 2.15683i) q^{19} +(-0.309017 - 0.951057i) q^{20} -0.247235 q^{21} +(-1.55142 - 2.93140i) q^{22} -7.17432 q^{23} +(-0.0763997 - 0.235134i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.29307 + 1.66601i) q^{26} +(0.453728 - 1.39643i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-1.14498 + 0.831879i) q^{29} +(-0.200017 - 0.145321i) q^{30} +(-0.110144 - 0.338990i) q^{31} +1.00000 q^{32} +(-0.736304 - 0.360876i) q^{33} -5.76549 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.37760 + 1.72743i) q^{36} +(-2.38460 + 1.73251i) q^{37} +(1.13391 - 3.48982i) q^{38} +(-0.216547 + 0.666462i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.80069 - 1.30828i) q^{41} +(-0.0763997 - 0.235134i) q^{42} +9.64018 q^{43} +(2.30851 - 2.38134i) q^{44} +2.93888 q^{45} +(-2.21699 - 6.82318i) q^{46} +(-2.53720 - 1.84338i) q^{47} +(0.200017 - 0.145321i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-1.15320 + 0.837846i) q^{51} +(-2.29307 - 1.66601i) q^{52} +(0.270126 + 0.831363i) q^{53} +1.46830 q^{54} +(0.467907 - 3.28345i) q^{55} +1.00000 q^{56} +(-0.280342 - 0.862804i) q^{57} +(-1.14498 - 0.831879i) q^{58} +(8.49158 - 6.16949i) q^{59} +(0.0763997 - 0.235134i) q^{60} +(-2.84337 + 8.75101i) q^{61} +(0.288362 - 0.209507i) q^{62} +(2.37760 + 1.72743i) q^{63} +(0.309017 + 0.951057i) q^{64} -2.83439 q^{65} +(0.115683 - 0.811783i) q^{66} -13.5466 q^{67} +(-1.78163 - 5.48331i) q^{68} +(-1.43499 - 1.04258i) q^{69} +(0.809017 - 0.587785i) q^{70} +(-3.86699 + 11.9014i) q^{71} +(-0.908162 + 2.79504i) q^{72} +(5.82359 - 4.23109i) q^{73} +(-2.38460 - 1.73251i) q^{74} +(-0.0763997 - 0.235134i) q^{75} +3.66941 q^{76} +(2.30851 - 2.38134i) q^{77} -0.700760 q^{78} +(1.89893 + 5.84432i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-6.83912 + 4.96891i) q^{81} +(0.687804 - 2.11684i) q^{82} +(0.952443 - 2.93132i) q^{83} +(0.200017 - 0.145321i) q^{84} +(-4.66438 - 3.38887i) q^{85} +(2.97898 + 9.16835i) q^{86} -0.349905 q^{87} +(2.97816 + 1.45965i) q^{88} -5.75443 q^{89} +(0.908162 + 2.79504i) q^{90} +(-2.29307 - 1.66601i) q^{91} +(5.80414 - 4.21696i) q^{92} +(0.0272315 - 0.0838100i) q^{93} +(0.969124 - 2.98266i) q^{94} +(2.96862 - 2.15683i) q^{95} +(0.200017 + 0.145321i) q^{96} +(3.87129 + 11.9146i) q^{97} +1.00000 q^{98} +(4.55943 + 8.61501i) 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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