LMFDB - Embedded newform 342.2.f.g.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(7,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("342.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.f (of order $3$, degree $2$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.2
Root			$-0.238928 - 1.71549i$ of defining polynomial
Character	$\chi$	$=$	342.49
Dual form			342.2.f.g.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.60512 - 0.650828i) q^{3} +1.00000 q^{4} +(-0.706161 - 1.22311i) q^{5} +(1.60512 + 0.650828i) q^{6} +(1.53389 + 2.65678i) q^{7} -1.00000 q^{8} +(2.15285 + 2.08932i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.60512 - 0.650828i) q^{3} +1.00000 q^{4} +(-0.706161 - 1.22311i) q^{5} +(1.60512 + 0.650828i) q^{6} +(1.53389 + 2.65678i) q^{7} -1.00000 q^{8} +(2.15285 + 2.08932i) q^{9} +(0.706161 + 1.22311i) q^{10} +(-0.769616 - 1.33301i) q^{11} +(-1.60512 - 0.650828i) q^{12} +1.33016 q^{13} +(-1.53389 - 2.65678i) q^{14} +(0.337444 + 2.42283i) q^{15} +1.00000 q^{16} +(1.80351 - 3.12377i) q^{17} +(-2.15285 - 2.08932i) q^{18} +(-2.00583 - 3.86997i) q^{19} +(-0.706161 - 1.22311i) q^{20} +(-0.732981 - 5.26276i) q^{21} +(0.769616 + 1.33301i) q^{22} +4.98816 q^{23} +(1.60512 + 0.650828i) q^{24} +(1.50267 - 2.60271i) q^{25} -1.33016 q^{26} +(-2.09580 - 4.75475i) q^{27} +(1.53389 + 2.65678i) q^{28} +(3.48033 - 6.02810i) q^{29} +(-0.337444 - 2.42283i) q^{30} +(-1.06849 + 1.85068i) q^{31} -1.00000 q^{32} +(0.367766 + 2.64054i) q^{33} +(-1.80351 + 3.12377i) q^{34} +(2.16635 - 3.75222i) q^{35} +(2.15285 + 2.08932i) q^{36} +3.07968 q^{37} +(2.00583 + 3.86997i) q^{38} +(-2.13507 - 0.865705i) q^{39} +(0.706161 + 1.22311i) q^{40} +(-2.94049 - 5.09307i) q^{41} +(0.732981 + 5.26276i) q^{42} +11.0494 q^{43} +(-0.769616 - 1.33301i) q^{44} +(1.03520 - 4.10855i) q^{45} -4.98816 q^{46} +(-3.75078 + 6.49654i) q^{47} +(-1.60512 - 0.650828i) q^{48} +(-1.20565 + 2.08824i) q^{49} +(-1.50267 + 2.60271i) q^{50} +(-4.92789 + 3.84026i) q^{51} +1.33016 q^{52} +(2.17631 + 3.76947i) q^{53} +(2.09580 + 4.75475i) q^{54} +(-1.08695 + 1.88264i) q^{55} +(-1.53389 - 2.65678i) q^{56} +(0.700921 + 7.51723i) q^{57} +(-3.48033 + 6.02810i) q^{58} +(-4.28487 - 7.42161i) q^{59} +(0.337444 + 2.42283i) q^{60} +(4.68857 - 8.12084i) q^{61} +(1.06849 - 1.85068i) q^{62} +(-2.24863 + 8.92442i) q^{63} +1.00000 q^{64} +(-0.939306 - 1.62693i) q^{65} +(-0.367766 - 2.64054i) q^{66} -9.98175 q^{67} +(1.80351 - 3.12377i) q^{68} +(-8.00661 - 3.24643i) q^{69} +(-2.16635 + 3.75222i) q^{70} +(-4.48160 + 7.76235i) q^{71} +(-2.15285 - 2.08932i) q^{72} +(-1.51369 + 2.62179i) q^{73} -3.07968 q^{74} +(-4.10589 + 3.19969i) q^{75} +(-2.00583 - 3.86997i) q^{76} +(2.36102 - 4.08940i) q^{77} +(2.13507 + 0.865705i) q^{78} +8.70478 q^{79} +(-0.706161 - 1.22311i) q^{80} +(0.269490 + 8.99596i) q^{81} +(2.94049 + 5.09307i) q^{82} +(7.47039 + 12.9391i) q^{83} +(-0.732981 - 5.26276i) q^{84} -5.09426 q^{85} -11.0494 q^{86} +(-9.50961 + 7.41076i) q^{87} +(0.769616 + 1.33301i) q^{88} +(3.40283 + 5.89387i) q^{89} +(-1.03520 + 4.10855i) q^{90} +(2.04032 + 3.53394i) q^{91} +4.98816 q^{92} +(2.91953 - 2.27516i) q^{93} +(3.75078 - 6.49654i) q^{94} +(-3.31694 + 5.18616i) q^{95} +(1.60512 + 0.650828i) q^{96} +1.08724 q^{97} +(1.20565 - 2.08824i) q^{98} +(1.12823 - 4.47775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.60512	−	0.650828i	−0.926719	−	0.375756i
$3$	−1.60512	−	0.650828i	−0.926719	−	0.375756i
$4$	1.00000			0.500000
$5$	−0.706161	−	1.22311i	−0.315805	−	0.546990i	0.663804	−	0.747907i	$-0.268941\pi$
$5$	−0.706161	−	1.22311i	−0.315805	−	0.546990i	−0.979608	+	0.200917i	$0.935608\pi$
$6$	1.60512	+	0.650828i	0.655289	+	0.265699i
$7$	1.53389	+	2.65678i	0.579757	+	1.00417i	0.995507	+	0.0946891i	$0.0301857\pi$
$7$	1.53389	+	2.65678i	0.579757	+	1.00417i	−0.415750	+	0.909479i	$0.636481\pi$
$8$	−1.00000			−0.353553
$9$	2.15285	+	2.08932i	0.717615	+	0.696440i
$10$	0.706161	+	1.22311i	0.223308	+	0.386780i
$11$	−0.769616	−	1.33301i	−0.232048	−	0.401919i	0.726363	−	0.687312i	$-0.241209\pi$
$11$	−0.769616	−	1.33301i	−0.232048	−	0.401919i	−0.958411	+	0.285393i	$0.907876\pi$
$12$	−1.60512	−	0.650828i	−0.463359	−	0.187878i
$13$	1.33016			0.368920			0.184460	−	0.982840i	$-0.440946\pi$
$13$	1.33016			0.368920			0.184460	+	0.982840i	$0.440946\pi$
$14$	−1.53389	−	2.65678i	−0.409950	−	0.710054i
$15$	0.337444	+	2.42283i	0.0871276	+	0.625571i
$16$	1.00000			0.250000
$17$	1.80351	−	3.12377i	0.437415	−	0.757625i	−0.560074	−	0.828442i	$-0.689227\pi$
$17$	1.80351	−	3.12377i	0.437415	−	0.757625i	0.997489	+	0.0708174i	$0.0225608\pi$
$18$	−2.15285	−	2.08932i	−0.507431	−	0.492457i
$19$	−2.00583	−	3.86997i	−0.460169	−	0.887831i
$19$	−2.00583	−	3.86997i	−0.460169	−	0.887831i
$20$	−0.706161	−	1.22311i	−0.157902	−	0.273495i
$21$	−0.732981	−	5.26276i	−0.159949	−	1.14843i
$22$	0.769616	+	1.33301i	0.164083	+	0.284200i
$23$	4.98816			1.04010			0.520051	−	0.854135i	$-0.325913\pi$
$23$	4.98816			1.04010			0.520051	+	0.854135i	$0.325913\pi$
$24$	1.60512	+	0.650828i	0.327645	+	0.132850i
$25$	1.50267	−	2.60271i	0.300535	−	0.520542i
$26$	−1.33016			−0.260866
$27$	−2.09580	−	4.75475i	−0.403336	−	0.915052i
$28$	1.53389	+	2.65678i	0.289878	+	0.502084i
$29$	3.48033	−	6.02810i	0.646281	−	1.11939i	−0.337724	−	0.941245i	$-0.609657\pi$
$29$	3.48033	−	6.02810i	0.646281	−	1.11939i	0.984004	−	0.178145i	$-0.0570097\pi$
$30$	−0.337444	−	2.42283i	−0.0616085	−	0.442345i
$31$	−1.06849	+	1.85068i	−0.191906	+	0.332391i	−0.945882	−	0.324511i	$-0.894800\pi$
$31$	−1.06849	+	1.85068i	−0.191906	+	0.332391i	0.753976	+	0.656902i	$0.228134\pi$
$32$	−1.00000			−0.176777
$33$	0.367766	+	2.64054i	0.0640199	+	0.459659i
$34$	−1.80351	+	3.12377i	−0.309299	+	0.535722i
$35$	2.16635	−	3.75222i	0.366180	−	0.634242i
$36$	2.15285	+	2.08932i	0.358808	+	0.348220i
$37$	3.07968			0.506296			0.253148	−	0.967428i	$-0.418534\pi$
$37$	3.07968			0.506296			0.253148	+	0.967428i	$0.418534\pi$
$38$	2.00583	+	3.86997i	0.325388	+	0.627792i
$39$	−2.13507	−	0.865705i	−0.341885	−	0.138624i
$40$	0.706161	+	1.22311i	0.111654	+	0.193390i
$41$	−2.94049	−	5.09307i	−0.459227	−	0.795404i	0.539693	−	0.841862i	$-0.318540\pi$
$41$	−2.94049	−	5.09307i	−0.459227	−	0.795404i	−0.998920	+	0.0464572i	$0.985207\pi$
$42$	0.732981	+	5.26276i	0.113101	+	0.812061i
$43$	11.0494			1.68502			0.842509	−	0.538683i	$-0.181078\pi$
$43$	11.0494			1.68502			0.842509	+	0.538683i	$0.181078\pi$
$44$	−0.769616	−	1.33301i	−0.116024	−	0.200959i
$45$	1.03520	−	4.10855i	0.154319	−	0.612467i
$46$	−4.98816			−0.735464
$47$	−3.75078	+	6.49654i	−0.547108	+	0.947618i	0.451363	+	0.892340i	$0.350938\pi$
$47$	−3.75078	+	6.49654i	−0.547108	+	0.947618i	−0.998471	+	0.0552779i	$0.982396\pi$
$48$	−1.60512	−	0.650828i	−0.231680	−	0.0939389i
$49$	−1.20565	+	2.08824i	−0.172236	+	0.298321i
$50$	−1.50267	+	2.60271i	−0.212510	+	0.368079i
$51$	−4.92789	+	3.84026i	−0.690043	+	0.537744i
$52$	1.33016			0.184460
$53$	2.17631	+	3.76947i	0.298939	+	0.517777i	0.975893	−	0.218248i	$-0.0700340\pi$
$53$	2.17631	+	3.76947i	0.298939	+	0.517777i	−0.676955	+	0.736025i	$0.736701\pi$
$54$	2.09580	+	4.75475i	0.285202	+	0.647039i
$55$	−1.08695	+	1.88264i	−0.146564	+	0.253856i
$56$	−1.53389	−	2.65678i	−0.204975	−	0.355027i
$57$	0.700921	+	7.51723i	0.0928392	+	0.995681i
$58$	−3.48033	+	6.02810i	−0.456989	+	0.791529i
$59$	−4.28487	−	7.42161i	−0.557842	−	0.966211i	−0.997676	−	0.0681321i	$-0.978296\pi$
$59$	−4.28487	−	7.42161i	−0.557842	−	0.966211i	0.439834	−	0.898079i	$-0.355037\pi$
$60$	0.337444	+	2.42283i	0.0435638	+	0.312785i
$61$	4.68857	−	8.12084i	0.600309	−	1.03977i	−0.392465	−	0.919767i	$-0.628377\pi$
$61$	4.68857	−	8.12084i	0.600309	−	1.03977i	0.992774	−	0.119999i	$-0.0382892\pi$
$62$	1.06849	−	1.85068i	0.135698	−	0.235036i
$63$	−2.24863	+	8.92442i	−0.283300	+	1.12437i
$64$	1.00000			0.125000
$65$	−0.939306	−	1.62693i	−0.116507	−	0.201795i
$66$	−0.367766	−	2.64054i	−0.0452689	−	0.325028i
$67$	−9.98175			−1.21947			−0.609733	−	0.792607i	$-0.708723\pi$
$67$	−9.98175			−1.21947			−0.609733	+	0.792607i	$0.708723\pi$
$68$	1.80351	−	3.12377i	0.218707	−	0.378812i
$69$	−8.00661	−	3.24643i	−0.963883	−	0.390825i
$70$	−2.16635	+	3.75222i	−0.258928	+	0.448477i
$71$	−4.48160	+	7.76235i	−0.531868	+	0.921222i	0.467440	+	0.884025i	$0.345176\pi$
$71$	−4.48160	+	7.76235i	−0.531868	+	0.921222i	−0.999308	+	0.0371970i	$0.988157\pi$
$72$	−2.15285	−	2.08932i	−0.253715	−	0.246229i
$73$	−1.51369	+	2.62179i	−0.177164	+	0.306858i	−0.940908	−	0.338662i	$-0.890026\pi$
$73$	−1.51369	+	2.62179i	−0.177164	+	0.306858i	0.763744	+	0.645519i	$0.223359\pi$
$74$	−3.07968			−0.358005
$75$	−4.10589	+	3.19969i	−0.474108	+	0.369468i
$76$	−2.00583	−	3.86997i	−0.230084	−	0.443916i
$77$	2.36102	−	4.08940i	0.269063	−	0.466030i
$78$	2.13507	+	0.865705i	0.241749	+	0.0980217i
$79$	8.70478			0.979365			0.489682	−	0.871901i	$-0.337113\pi$
$79$	8.70478			0.979365			0.489682	+	0.871901i	$0.337113\pi$
$80$	−0.706161	−	1.22311i	−0.0789511	−	0.136747i
$81$	0.269490	+	8.99596i	0.0299434	+	0.999552i
$82$	2.94049	+	5.09307i	0.324723	+	0.562436i
$83$	7.47039	+	12.9391i	0.819982	+	1.42025i	0.905695	+	0.423930i	$0.139350\pi$
$83$	7.47039	+	12.9391i	0.819982	+	1.42025i	−0.0857129	+	0.996320i	$0.527317\pi$
$84$	−0.732981	−	5.26276i	−0.0799747	−	0.574214i
$85$	−5.09426			−0.552551
$86$	−11.0494			−1.19149
$87$	−9.50961	+	7.41076i	−1.01954	+	0.794517i
$88$	0.769616	+	1.33301i	0.0820414	+	0.142100i
$89$	3.40283	+	5.89387i	0.360699	+	0.624749i	0.988076	−	0.153967i	$-0.0492048\pi$
$89$	3.40283	+	5.89387i	0.360699	+	0.624749i	−0.627377	+	0.778716i	$0.715871\pi$
$90$	−1.03520	+	4.10855i	−0.109120	+	0.433080i
$91$	2.04032	+	3.53394i	0.213884	+	0.370457i
$92$	4.98816			0.520051
$93$	2.91953	−	2.27516i	0.302741	−	0.235923i
$94$	3.75078	−	6.49654i	0.386863	−	0.670067i
$95$	−3.31694	+	5.18616i	−0.340311	+	0.532089i
$96$	1.60512	+	0.650828i	0.163822	+	0.0664249i
$97$	1.08724			0.110393			0.0551963	−	0.998476i	$-0.482422\pi$
$97$	1.08724			0.110393			0.0551963	+	0.998476i	$0.482422\pi$
$98$	1.20565	−	2.08824i	0.121789	−	0.210945i
$99$	1.12823	−	4.47775i	0.113391	−	0.450031i
$100$	1.50267	−	2.60271i	0.150267	−	0.260271i
$101$	−1.47900	+	2.56170i	−0.147166	+	0.254899i	−0.930179	−	0.367106i	$-0.880348\pi$
$101$	−1.47900	+	2.56170i	−0.147166	+	0.254899i	0.783013	+	0.622005i	$0.213682\pi$
$102$	4.92789	−	3.84026i	0.487934	−	0.380242i
$103$	−1.08452	+	1.87845i	−0.106861	+	0.185089i	−0.914497	−	0.404593i	$-0.867413\pi$
$103$	−1.08452	+	1.87845i	−0.106861	+	0.185089i	0.807636	+	0.589681i	$0.200747\pi$
$104$	−1.33016			−0.130433
$105$	−5.91931	+	4.61287i	−0.577665	+	0.450170i
$106$	−2.17631	−	3.76947i	−0.211382	−	0.366124i
$107$	−5.44381			−0.526273			−0.263136	−	0.964759i	$-0.584757\pi$
$107$	−5.44381			−0.526273			−0.263136	+	0.964759i	$0.584757\pi$
$108$	−2.09580	−	4.75475i	−0.201668	−	0.457526i
$109$	1.17697	−	2.03858i	0.112734	−	0.195260i	−0.804138	−	0.594443i	$-0.797373\pi$
$109$	1.17697	−	2.03858i	0.112734	−	0.195260i	0.916871	+	0.399183i	$0.130706\pi$
$110$	1.08695	−	1.88264i	0.103636	−	0.179503i
$111$	−4.94327	−	2.00434i	−0.469194	−	0.190244i
$112$	1.53389	+	2.65678i	0.144939	+	0.251042i
$113$	6.52086	−	11.2945i	0.613431	−	1.06249i	−0.377227	−	0.926121i	$-0.623122\pi$
$113$	6.52086	−	11.2945i	0.613431	−	1.06249i	0.990658	−	0.136372i	$-0.0435444\pi$
$114$	−0.700921	−	7.51723i	−0.0656473	−	0.704053i
$115$	−3.52244	−	6.10105i	−0.328469	−	0.568925i
$116$	3.48033	−	6.02810i	0.323140	−	0.559695i
$117$	2.86363	+	2.77913i	0.264742	+	0.256930i
$118$	4.28487	+	7.42161i	0.394454	+	0.683214i
$119$	11.0655			1.01438
$120$	−0.337444	−	2.42283i	−0.0308042	−	0.221173i
$121$	4.31538	−	7.47446i	0.392307	−	0.679496i
$122$	−4.68857	+	8.12084i	−0.424483	+	0.735226i
$123$	1.40513	+	10.0888i	0.126696	+	0.909673i
$124$	−1.06849	+	1.85068i	−0.0959531	+	0.166196i
$125$	−11.3061			−1.01125
$126$	2.24863	−	8.92442i	0.200324	−	0.795051i
$127$	5.20044	+	9.00742i	0.461464	+	0.799280i	0.999034	−	0.0439396i	$-0.0139909\pi$
$127$	5.20044	+	9.00742i	0.461464	+	0.799280i	−0.537570	+	0.843219i	$0.680658\pi$
$128$	−1.00000			−0.0883883
$129$	−17.7356	−	7.19126i	−1.56154	−	0.633155i
$130$	0.939306	+	1.62693i	0.0823826	+	0.142691i
$131$	8.46661	+	14.6646i	0.739731	+	1.28125i	0.952616	+	0.304175i	$0.0983806\pi$
$131$	8.46661	+	14.6646i	0.739731	+	1.28125i	−0.212885	+	0.977077i	$0.568286\pi$
$132$	0.367766	+	2.64054i	0.0320099	+	0.229830i
$133$	7.20492	−	11.2652i	0.624746	−	0.976813i
$134$	9.98175			0.862292
$135$	−4.33559	+	5.92100i	−0.373148	+	0.509598i
$136$	−1.80351	+	3.12377i	−0.154650	+	0.267861i
$137$	5.36678	−	9.29554i	0.458515	−	0.794171i	−0.540368	−	0.841429i	$-0.681715\pi$
$137$	5.36678	−	9.29554i	0.458515	−	0.794171i	0.998883	+	0.0472577i	$0.0150482\pi$
$138$	8.00661	+	3.24643i	0.681568	+	0.276355i
$139$	−17.0861			−1.44923			−0.724613	−	0.689156i	$-0.757981\pi$
$139$	−17.0861			−1.44923			−0.724613	+	0.689156i	$0.757981\pi$
$140$	2.16635	−	3.75222i	0.183090	−	0.317121i
$141$	10.2486	−	7.98664i	0.863088	−	0.672597i
$142$	4.48160	−	7.76235i	0.376087	−	0.651402i
$143$	−1.02371	−	1.77312i	−0.0856071	−	0.148276i
$144$	2.15285	+	2.08932i	0.179404	+	0.174110i
$145$	−9.83068			−0.816393
$146$	1.51369	−	2.62179i	0.125274	−	0.216981i
$147$	3.29430	−	2.56722i	0.271710	−	0.211741i
$148$	3.07968			0.253148
$149$	−0.651536	−	1.12849i	−0.0533759	−	0.0924498i	0.838103	−	0.545512i	$-0.183665\pi$
$149$	−0.651536	−	1.12849i	−0.0533759	−	0.0924498i	−0.891479	+	0.453062i	$0.850332\pi$
$150$	4.10589	−	3.19969i	0.335245	−	0.261253i
$151$	−11.8441	−	20.5145i	−0.963857	−	1.66945i	−0.712655	−	0.701514i	$-0.752508\pi$
$151$	−11.8441	−	20.5145i	−0.963857	−	1.66945i	−0.251202	−	0.967935i	$-0.580826\pi$
$152$	2.00583	+	3.86997i	0.162694	+	0.313896i
$153$	10.4092	−	2.95689i	0.841536	−	0.239050i
$154$	−2.36102	+	4.08940i	−0.190256	+	0.329533i
$155$	3.01810			0.242419
$156$	−2.13507	−	0.865705i	−0.170942	−	0.0693118i
$157$	−2.02780	−	3.51225i	−0.161836	−	0.280308i	0.773691	−	0.633563i	$-0.218408\pi$
$157$	−2.02780	−	3.51225i	−0.161836	−	0.280308i	−0.935527	+	0.353255i	$0.885075\pi$
$158$	−8.70478			−0.692515
$159$	−1.03996	−	7.46688i	−0.0824744	−	0.592162i
$160$	0.706161	+	1.22311i	0.0558269	+	0.0966950i
$161$	7.65130	+	13.2524i	0.603007	+	1.04444i
$162$	−0.269490	−	8.99596i	−0.0211731	−	0.706790i
$163$	5.44799			0.426720			0.213360	−	0.976974i	$-0.431559\pi$
$163$	5.44799			0.426720			0.213360	+	0.976974i	$0.431559\pi$
$164$	−2.94049	−	5.09307i	−0.229613	−	0.397702i
$165$	2.96996	−	2.31446i	0.231211	−	0.180181i
$166$	−7.47039	−	12.9391i	−0.579815	−	1.00427i
$167$	16.7477			1.29597			0.647987	−	0.761651i	$-0.275611\pi$
$167$	16.7477			1.29597			0.647987	+	0.761651i	$0.275611\pi$
$168$	0.732981	+	5.26276i	0.0565507	+	0.406031i
$169$	−11.2307			−0.863898
$170$	5.09426			0.390712
$171$	3.76736	−	12.5223i	0.288097	−	0.957601i
$172$	11.0494			0.842509
$173$	−11.8441			−0.900492			−0.450246	−	0.892904i	$-0.648664\pi$
$173$	−11.8441			−0.900492			−0.450246	+	0.892904i	$0.648664\pi$
$174$	9.50961	−	7.41076i	0.720922	−	0.561808i
$175$	9.21976			0.696948
$176$	−0.769616	−	1.33301i	−0.0580120	−	0.100480i
$177$	2.04755	+	14.7013i	0.153904	+	1.10502i
$178$	−3.40283	−	5.89387i	−0.255053	−	0.441764i
$179$	−3.30259			−0.246847			−0.123424	−	0.992354i	$-0.539387\pi$
$179$	−3.30259			−0.246847			−0.123424	+	0.992354i	$0.539387\pi$
$180$	1.03520	−	4.10855i	0.0771596	−	0.306233i
$181$	13.0051	+	22.5255i	0.966662	+	1.67431i	0.705083	+	0.709125i	$0.250910\pi$
$181$	13.0051	+	22.5255i	0.966662	+	1.67431i	0.261579	+	0.965182i	$0.415757\pi$
$182$	−2.04032	−	3.53394i	−0.151239	−	0.261953i
$183$	−12.8110	+	9.98350i	−0.947016	+	0.738001i
$184$	−4.98816			−0.367732
$185$	−2.17475	−	3.76677i	−0.159891	−	0.276939i
$186$	−2.91953	+	2.27516i	−0.214070	+	0.166823i
$187$	−5.55204			−0.406005
$188$	−3.75078	+	6.49654i	−0.273554	+	0.473809i
$189$	9.41759	−	12.8613i	0.685029	−	0.935525i
$190$	3.31694	−	5.18616i	0.240636	−	0.376244i
$191$	6.40837	+	11.0996i	0.463693	+	0.803141i	0.999142	−	0.0414276i	$-0.0131906\pi$
$191$	6.40837	+	11.0996i	0.463693	+	0.803141i	−0.535448	+	0.844568i	$0.679857\pi$
$192$	−1.60512	−	0.650828i	−0.115840	−	0.0469695i
$193$	6.68326	+	11.5757i	0.481072	+	0.833241i	0.999764	−	0.0217203i	$-0.00691432\pi$
$193$	6.68326	+	11.5757i	0.481072	+	0.833241i	−0.518692	+	0.854961i	$0.673581\pi$
$194$	−1.08724			−0.0780593
$195$	0.448854	+	3.22274i	0.0321431	+	0.230785i
$196$	−1.20565	+	2.08824i	−0.0861178	+	0.149160i
$197$	−7.77217			−0.553744			−0.276872	−	0.960907i	$-0.589298\pi$
$197$	−7.77217			−0.553744			−0.276872	+	0.960907i	$0.589298\pi$
$198$	−1.12823	+	4.47775i	−0.0801796	+	0.318220i
$199$	−13.4519	−	23.2994i	−0.953582	−	1.65165i	−0.737580	−	0.675259i	$-0.764032\pi$
$199$	−13.4519	−	23.2994i	−0.953582	−	1.65165i	−0.216001	−	0.976393i	$-0.569302\pi$
$200$	−1.50267	+	2.60271i	−0.106255	+	0.184039i
$201$	16.0220	+	6.49640i	1.13010	+	0.458221i
$202$	1.47900	−	2.56170i	0.104062	−	0.180241i
$203$	21.3538			1.49874
$204$	−4.92789	+	3.84026i	−0.345021	+	0.268872i
$205$	−4.15291	+	7.19306i	−0.290052	+	0.502385i
$206$	1.08452	−	1.87845i	0.0755622	−	0.130878i
$207$	10.7387	+	10.4219i	0.746394	+	0.724369i
$208$	1.33016			0.0922299
$209$	−3.61500	+	5.65219i	−0.250055	+	0.390970i
$210$	5.91931	−	4.61287i	0.408471	−	0.318318i
$211$	−8.95097	−	15.5035i	−0.616210	−	1.06731i	−0.990171	−	0.139863i	$-0.955334\pi$
$211$	−8.95097	−	15.5035i	−0.616210	−	1.06731i	0.373961	−	0.927445i	$-0.377999\pi$
$212$	2.17631	+	3.76947i	0.149469	+	0.258889i
$213$	12.2455	−	9.54279i	0.839046	−	0.653861i
$214$	5.44381			0.372131
$215$	−7.80265	−	13.5146i	−0.532136	−	0.921687i
$216$	2.09580	+	4.75475i	0.142601	+	0.323520i
$217$	−6.55578			−0.445036
$218$	−1.17697	+	2.03858i	−0.0797146	+	0.138070i
$219$	4.13600	−	3.22315i	0.279485	−	0.217800i
$220$	−1.08695	+	1.88264i	−0.0732818	+	0.126928i
$221$	2.39895	−	4.15511i	0.161371	−	0.279503i
$222$	4.94327	+	2.00434i	0.331770	+	0.134523i
$223$	−9.09509			−0.609053			−0.304526	−	0.952504i	$-0.598498\pi$
$223$	−9.09509			−0.609053			−0.304526	+	0.952504i	$0.598498\pi$
$224$	−1.53389	−	2.65678i	−0.102487	−	0.177513i
$225$	8.67292	−	2.46366i	0.578194	−	0.164244i
$226$	−6.52086	+	11.2945i	−0.433761	+	0.751296i
$227$	−4.50967	−	7.81097i	−0.299317	−	0.518432i	0.676663	−	0.736293i	$-0.263425\pi$
$227$	−4.50967	−	7.81097i	−0.299317	−	0.518432i	−0.975980	+	0.217861i	$0.930092\pi$
$228$	0.700921	+	7.51723i	0.0464196	+	0.497841i
$229$	−0.209905	+	0.363565i	−0.0138709	+	0.0240251i	−0.872878	−	0.487939i	$-0.837749\pi$
$229$	−0.209905	+	0.363565i	−0.0138709	+	0.0240251i	0.859007	+	0.511964i	$0.171082\pi$
$230$	3.52244	+	6.10105i	0.232263	+	0.402291i
$231$	−6.45122	+	5.02738i	−0.424459	+	0.330777i
$232$	−3.48033	+	6.02810i	−0.228495	+	0.395764i
$233$	−14.5187	+	25.1471i	−0.951150	+	1.64744i	−0.208209	+	0.978084i	$0.566763\pi$
$233$	−14.5187	+	25.1471i	−0.951150	+	1.64744i	−0.742942	+	0.669356i	$0.766570\pi$
$234$	−2.86363	−	2.77913i	−0.187201	−	0.181677i
$235$	10.5946			0.691116
$236$	−4.28487	−	7.42161i	−0.278921	−	0.483106i
$237$	−13.9723	−	5.66532i	−0.907595	−	0.368002i
$238$	−11.0655			−0.717273
$239$	−7.93433	+	13.7427i	−0.513229	+	0.888939i	0.486653	+	0.873595i	$0.338218\pi$
$239$	−7.93433	+	13.7427i	−0.513229	+	0.888939i	−0.999882	+	0.0153436i	$0.995116\pi$
$240$	0.337444	+	2.42283i	0.0217819	+	0.156393i
$241$	−0.738688	+	1.27945i	−0.0475831	+	0.0824164i	−0.888836	−	0.458225i	$-0.848485\pi$
$241$	−0.738688	+	1.27945i	−0.0475831	+	0.0824164i	0.841253	+	0.540642i	$0.181819\pi$
$242$	−4.31538	+	7.47446i	−0.277403	+	0.480477i
$243$	5.42226	−	14.6150i	0.347838	−	0.937555i
$244$	4.68857	−	8.12084i	0.300155	−	0.519883i
$245$	3.40553			0.217571
$246$	−1.40513	−	10.0888i	−0.0895879	−	0.643236i
$247$	−2.66807	−	5.14767i	−0.169765	−	0.327539i
$248$	1.06849	−	1.85068i	0.0678491	−	0.117518i
$249$	−3.56978	−	25.6308i	−0.226225	−	1.62429i
$250$	11.3061			0.715062
$251$	−4.56139	−	7.90056i	−0.287912	−	0.498679i	0.685399	−	0.728168i	$-0.259628\pi$
$251$	−4.56139	−	7.90056i	−0.287912	−	0.498679i	−0.973311	+	0.229489i	$0.926295\pi$
$252$	−2.24863	+	8.92442i	−0.141650	+	0.562186i
$253$	−3.83897	−	6.64929i	−0.241354	−	0.418037i
$254$	−5.20044	−	9.00742i	−0.326305	−	0.565176i
$255$	8.17693	+	3.31549i	0.512059	+	0.207624i
$256$	1.00000			0.0625000
$257$	4.95952			0.309366			0.154683	−	0.987964i	$-0.450564\pi$
$257$	4.95952			0.309366			0.154683	+	0.987964i	$0.450564\pi$
$258$	17.7356	+	7.19126i	1.10417	+	0.447708i
$259$	4.72390	+	8.18203i	0.293529	+	0.508406i
$260$	−0.939306	−	1.62693i	−0.0582533	−	0.100898i
$261$	20.0872	−	5.70606i	1.24337	−	0.353196i
$262$	−8.46661	−	14.6646i	−0.523069	−	0.905982i
$263$	−6.22031			−0.383561			−0.191780	−	0.981438i	$-0.561426\pi$
$263$	−6.22031			−0.383561			−0.191780	+	0.981438i	$0.561426\pi$
$264$	−0.367766	−	2.64054i	−0.0226344	−	0.162514i
$265$	3.07364	−	5.32371i	0.188812	−	0.327033i
$266$	−7.20492	+	11.2652i	−0.441762	+	0.690711i
$267$	−1.62606	−	11.6751i	−0.0995135	−	0.714502i
$268$	−9.98175			−0.609733
$269$	2.01130	−	3.48367i	0.122631	−	0.212403i	−0.798173	−	0.602428i	$-0.794200\pi$
$269$	2.01130	−	3.48367i	0.122631	−	0.212403i	0.920804	+	0.390025i	$0.127533\pi$
$270$	4.33559	−	5.92100i	0.263856	−	0.360340i
$271$	−6.53300	+	11.3155i	−0.396852	+	0.687367i	−0.993336	−	0.115258i	$-0.963231\pi$
$271$	−6.53300	+	11.3155i	−0.396852	+	0.687367i	0.596484	+	0.802625i	$0.296564\pi$
$272$	1.80351	−	3.12377i	0.109354	−	0.189406i
$273$	−0.974981	−	7.00031i	−0.0590085	−	0.423678i
$274$	−5.36678	+	9.29554i	−0.324219	+	0.561564i
$275$	−4.62593			−0.278954
$276$	−8.00661	−	3.24643i	−0.481941	−	0.195412i
$277$	5.20162	+	9.00947i	0.312535	+	0.541326i	0.978910	−	0.204290i	$-0.0654885\pi$
$277$	5.20162	+	9.00947i	0.312535	+	0.541326i	−0.666375	+	0.745616i	$0.732155\pi$
$278$	17.0861			1.02476
$279$	−6.16694	+	1.75181i	−0.369205	+	0.104878i
$280$	−2.16635	+	3.75222i	−0.129464	+	0.224238i
$281$	−10.4052	+	18.0223i	−0.620721	+	1.07512i	0.368630	+	0.929576i	$0.379827\pi$
$281$	−10.4052	+	18.0223i	−0.620721	+	1.07512i	−0.989352	+	0.145545i	$0.953506\pi$
$282$	−10.2486	+	7.98664i	−0.610295	+	0.475598i
$283$	−16.7470	−	29.0066i	−0.995505	−	1.72427i	−0.579772	−	0.814778i	$-0.696859\pi$
$283$	−16.7470	−	29.0066i	−0.995505	−	1.72427i	−0.415733	−	0.909487i	$-0.636475\pi$
$284$	−4.48160	+	7.76235i	−0.265934	+	0.460611i
$285$	8.69940	−	6.16567i	0.515308	−	0.365223i
$286$	1.02371	+	1.77312i	0.0605333	+	0.104847i
$287$	9.02078	−	15.6244i	0.532480	−	0.922282i
$288$	−2.15285	−	2.08932i	−0.126858	−	0.123114i
$289$	1.99472	+	3.45495i	0.117336	+	0.203233i
$290$	9.83068			0.577277
$291$	−1.74516	−	0.707607i	−0.102303	−	0.0414806i
$292$	−1.51369	+	2.62179i	−0.0885821	+	0.153429i
$293$	−8.17191	+	14.1542i	−0.477408	+	0.826896i	−0.999665	−	0.0258930i	$-0.991757\pi$
$293$	−8.17191	+	14.1542i	−0.477408	+	0.826896i	0.522256	+	0.852789i	$0.325090\pi$
$294$	−3.29430	+	2.56722i	−0.192128	+	0.149723i
$295$	−6.05161	+	10.4817i	−0.352338	+	0.610268i
$296$	−3.07968			−0.179003
$297$	−4.72519	+	6.45306i	−0.274183	+	0.374444i
$298$	0.651536	+	1.12849i	0.0377425	+	0.0653719i
$299$	6.63504			0.383714
$300$	−4.10589	+	3.19969i	−0.237054	+	0.184734i
$301$	16.9486	+	29.3558i	0.976900	+	1.69204i
$302$	11.8441	+	20.5145i	0.681550	+	1.18048i
$303$	4.04121	−	3.14928i	0.232161	−	0.180921i
$304$	−2.00583	−	3.86997i	−0.115042	−	0.221958i
$305$	−13.2435			−0.758322
$306$	−10.4092	+	2.95689i	−0.595056	+	0.169034i
$307$	−5.08101	+	8.80056i	−0.289988	+	0.502275i	−0.973807	−	0.227378i	$-0.926985\pi$
$307$	−5.08101	+	8.80056i	−0.289988	+	0.502275i	0.683818	+	0.729652i	$0.260318\pi$
$308$	2.36102	−	4.08940i	0.134531	−	0.233015i
$309$	2.96334	−	2.30930i	0.168578	−	0.131372i
$310$	−3.01810			−0.171416
$311$	−7.35458	+	12.7385i	−0.417040	+	0.722335i	−0.995640	−	0.0932767i	$-0.970266\pi$
$311$	−7.35458	+	12.7385i	−0.417040	+	0.722335i	0.578600	+	0.815611i	$0.303599\pi$
$312$	2.13507	+	0.865705i	0.120875	+	0.0490109i
$313$	−9.63983	+	16.6967i	−0.544875	+	0.943752i	0.453740	+	0.891134i	$0.350090\pi$
$313$	−9.63983	+	16.6967i	−0.544875	+	0.943752i	−0.998615	+	0.0526172i	$0.983244\pi$
$314$	2.02780	+	3.51225i	0.114435	+	0.198208i
$315$	12.5034	−	3.55177i	0.704487	−	0.200119i
$316$	8.70478			0.489682
$317$	−0.961061	+	1.66461i	−0.0539786	+	0.0934936i	−0.891752	−	0.452524i	$-0.850524\pi$
$317$	−0.961061	+	1.66461i	−0.0539786	+	0.0934936i	0.837774	+	0.546018i	$0.183857\pi$
$318$	1.03996	+	7.46688i	0.0583182	+	0.418722i
$319$	−10.7141			−0.599872
$320$	−0.706161	−	1.22311i	−0.0394756	−	0.0683737i
$321$	8.73798	+	3.54298i	0.487707	+	0.197750i
$322$	−7.65130	−	13.2524i	−0.426390	−	0.738529i
$323$	−15.7064	−	0.713774i	−0.873928	−	0.0397155i
$324$	0.269490	+	8.99596i	0.0149717	+	0.499776i
$325$	1.99880	−	3.46202i	0.110873	−	0.192038i
$326$	−5.44799			−0.301736
$327$	−3.21595	+	2.50616i	−0.177842	+	0.138591i
$328$	2.94049	+	5.09307i	0.162361	+	0.281218i
$329$	−23.0132			−1.26876
$330$	−2.96996	+	2.31446i	−0.163491	+	0.127407i
$331$	14.3888	+	24.9221i	0.790878	+	1.36984i	0.925424	+	0.378933i	$0.123709\pi$
$331$	14.3888	+	24.9221i	0.790878	+	1.36984i	−0.134546	+	0.990907i	$0.542958\pi$
$332$	7.47039	+	12.9391i	0.409991	+	0.710125i
$333$	6.63007	+	6.43443i	0.363326	+	0.352605i
$334$	−16.7477			−0.916392
$335$	7.04872	+	12.2087i	0.385113	+	0.667035i
$336$	−0.732981	−	5.26276i	−0.0399874	−	0.287107i
$337$	3.78100	+	6.54889i	0.205964	+	0.356741i	0.950440	−	0.310909i	$-0.100634\pi$
$337$	3.78100	+	6.54889i	0.205964	+	0.356741i	−0.744475	+	0.667650i	$0.767300\pi$
$338$	11.2307			0.610868
$339$	−17.8175	+	13.8850i	−0.967716	+	0.754132i
$340$	−5.09426			−0.276275
$341$	3.28930			0.178126
$342$	−3.76736	+	12.5223i	−0.203715	+	0.677126i
$343$	14.0771			0.760095
$344$	−11.0494			−0.595743
$345$	1.68322	+	12.0854i	0.0906216	+	0.650658i
$346$	11.8441			0.636744
$347$	14.8609	+	25.7398i	0.797774	+	1.38179i	0.921063	+	0.389414i	$0.127323\pi$
$347$	14.8609	+	25.7398i	0.797774	+	1.38179i	−0.123289	+	0.992371i	$0.539344\pi$
$348$	−9.50961	+	7.41076i	−0.509769	+	0.397258i
$349$	−7.74593	−	13.4163i	−0.414630	−	0.718160i	0.580759	−	0.814075i	$-0.302756\pi$
$349$	−7.74593	−	13.4163i	−0.414630	−	0.718160i	−0.995390	+	0.0959149i	$0.969422\pi$
$350$	−9.21976			−0.492817
$351$	−2.78774	−	6.32457i	−0.148799	−	0.337581i
$352$	0.769616	+	1.33301i	0.0410207	+	0.0710499i
$353$	−8.64592	−	14.9752i	−0.460176	−	0.797048i	0.538793	−	0.842438i	$-0.318880\pi$
$353$	−8.64592	−	14.9752i	−0.460176	−	0.797048i	−0.998969	+	0.0453897i	$0.985547\pi$
$354$	−2.04755	−	14.7013i	−0.108826	−	0.781366i
$355$	12.6589			0.671865
$356$	3.40283	+	5.89387i	0.180350	+	0.312375i
$357$	−17.7616	−	7.20177i	−0.940042	−	0.381158i
$358$	3.30259			0.174547
$359$	17.6705	−	30.6061i	0.932612	−	1.61533i	0.153773	−	0.988106i	$-0.450858\pi$
$359$	17.6705	−	30.6061i	0.932612	−	1.61533i	0.778839	−	0.627224i	$-0.215809\pi$
$360$	−1.03520	+	4.10855i	−0.0545600	+	0.216540i
$361$	−10.9533	+	15.5250i	−0.576489	+	0.817105i
$362$	−13.0051	−	22.5255i	−0.683533	−	1.18391i
$363$	−11.7913	+	9.18886i	−0.618883	+	0.482290i
$364$	2.04032	+	3.53394i	0.106942	+	0.185229i
$365$	4.27564			0.223797
$366$	12.8110	−	9.98350i	0.669642	−	0.521846i
$367$	12.5735	−	21.7780i	0.656333	−	1.13680i	−0.325225	−	0.945637i	$-0.605440\pi$
$367$	12.5735	−	21.7780i	0.656333	−	1.13680i	0.981558	−	0.191165i	$-0.0612265\pi$
$368$	4.98816			0.260026
$369$	4.31064	−	17.1082i	0.224403	−	0.890618i
$370$	2.17475	+	3.76677i	0.113060	+	0.195825i
$371$	−6.67644	+	11.5639i	−0.346623	+	0.600369i
$372$	2.91953	−	2.27516i	0.151370	−	0.117962i
$373$	−17.4889	+	30.2917i	−0.905543	+	1.56845i	−0.0853570	+	0.996350i	$0.527203\pi$
$373$	−17.4889	+	30.2917i	−0.905543	+	1.56845i	−0.820186	+	0.572097i	$0.806130\pi$
$374$	5.55204			0.287089
$375$	18.1477	+	7.35834i	0.937145	+	0.379983i
$376$	3.75078	−	6.49654i	0.193432	−	0.335034i
$377$	4.62939	−	8.01833i	0.238426	−	0.412965i
$378$	−9.41759	+	12.8613i	−0.484389	+	0.661516i
$379$	9.07430			0.466115			0.233058	−	0.972463i	$-0.425127\pi$
$379$	9.07430			0.466115			0.233058	+	0.972463i	$0.425127\pi$
$380$	−3.31694	+	5.18616i	−0.170156	+	0.266044i
$381$	−2.48506	−	17.8426i	−0.127314	−	0.914105i
$382$	−6.40837	−	11.0996i	−0.327881	−	0.567906i
$383$	−7.35390	−	12.7373i	−0.375767	−	0.650847i	0.614675	−	0.788781i	$-0.289287\pi$
$383$	−7.35390	−	12.7373i	−0.375767	−	0.650847i	−0.990441	+	0.137934i	$0.955954\pi$
$384$	1.60512	+	0.650828i	0.0819111	+	0.0332124i
$385$	−6.66902			−0.339885
$386$	−6.68326	−	11.5757i	−0.340169	−	0.589190i
$387$	23.7876	+	23.0857i	1.20919	+	1.17351i
$388$	1.08724			0.0551963
$389$	6.44691	−	11.1664i	0.326871	−	0.566158i	−0.655018	−	0.755613i	$-0.727339\pi$
$389$	6.44691	−	11.1664i	0.326871	−	0.566158i	0.981889	+	0.189456i	$0.0606723\pi$
$390$	−0.448854	−	3.22274i	−0.0227286	−	0.163190i
$391$	8.99618	−	15.5818i	0.454957	−	0.788008i
$392$	1.20565	−	2.08824i	0.0608945	−	0.105472i
$393$	−4.04583	−	29.0488i	−0.204085	−	1.46532i
$394$	7.77217			0.391556
$395$	−6.14697	−	10.6469i	−0.309288	−	0.535702i
$396$	1.12823	−	4.47775i	0.0566956	−	0.225015i
$397$	4.69327	−	8.12899i	0.235549	−	0.407982i	−0.723883	−	0.689922i	$-0.757645\pi$
$397$	4.69327	−	8.12899i	0.235549	−	0.407982i	0.959432	+	0.281940i	$0.0909780\pi$
$398$	13.4519	+	23.2994i	0.674284	+	1.16789i
$399$	−18.8965	+	13.3928i	−0.946007	+	0.670479i
$400$	1.50267	−	2.60271i	0.0751337	−	0.130135i
$401$	−12.0674	−	20.9014i	−0.602618	−	1.04376i	−0.992423	−	0.122867i	$-0.960791\pi$
$401$	−12.0674	−	20.9014i	−0.602618	−	1.04376i	0.389806	−	0.920897i	$-0.372542\pi$
$402$	−16.0220	−	6.49640i	−0.799102	−	0.324011i
$403$	−1.42126	+	2.46169i	−0.0707980	+	0.122626i
$404$	−1.47900	+	2.56170i	−0.0735830	+	0.127449i
$405$	10.8127	−	6.68221i	0.537288	−	0.332042i
$406$	−21.3538			−1.05977
$407$	−2.37017	−	4.10526i	−0.117485	−	0.203490i
$408$	4.92789	−	3.84026i	0.243967	−	0.190121i
$409$	−23.2135			−1.14783			−0.573916	−	0.818914i	$-0.694577\pi$
$409$	−23.2135			−1.14783			−0.573916	+	0.818914i	$0.694577\pi$
$410$	4.15291	−	7.19306i	0.205098	−	0.355240i
$411$	−14.6641	+	11.4276i	−0.723329	+	0.563684i
$412$	−1.08452	+	1.87845i	−0.0534306	+	0.0925445i
$413$	13.1450	−	22.7679i	0.646826	−	1.12033i
$414$	−10.7387	−	10.4219i	−0.527780	−	0.512206i
$415$	10.5506	−	18.2742i	0.517908	−	0.897043i
$416$	−1.33016			−0.0652164
$417$	27.4253	+	11.1201i	1.34302	+	0.544555i
$418$	3.61500	−	5.65219i	0.176816	−	0.276458i
$419$	9.92625	−	17.1928i	0.484929	−	0.839922i	−0.514921	−	0.857238i	$-0.672179\pi$
$419$	9.92625	−	17.1928i	0.484929	−	0.839922i	0.999850	+	0.0173157i	$0.00551205\pi$
$420$	−5.91931	+	4.61287i	−0.288833	+	0.225085i
$421$	33.1954			1.61784			0.808921	−	0.587917i	$-0.200052\pi$
$421$	33.1954			1.61784			0.808921	+	0.587917i	$0.200052\pi$
$422$	8.95097	+	15.5035i	0.435726	+	0.754700i
$423$	−21.6482	+	6.14948i	−1.05257	+	0.298998i
$424$	−2.17631	−	3.76947i	−0.105691	−	0.183062i
$425$	−5.42017	−	9.38801i	−0.262917	−	0.455385i
$426$	−12.2455	+	9.54279i	−0.593295	+	0.462350i
$427$	28.7670			1.39213
$428$	−5.44381			−0.263136
$429$	0.489188	+	3.51234i	0.0236182	+	0.169577i
$430$	7.80265	+	13.5146i	0.376277	+	0.651731i
$431$	12.0807	+	20.9243i	0.581905	+	1.00789i	0.995253	+	0.0973165i	$0.0310259\pi$
$431$	12.0807	+	20.9243i	0.581905	+	1.00789i	−0.413348	+	0.910573i	$0.635641\pi$
$432$	−2.09580	−	4.75475i	−0.100834	−	0.228763i
$433$	−0.219374	−	0.379967i	−0.0105424	−	0.0182601i	0.860706	−	0.509102i	$-0.170022\pi$
$433$	−0.219374	−	0.379967i	−0.0105424	−	0.0182601i	−0.871248	+	0.490842i	$0.836689\pi$
$434$	6.55578			0.314688
$435$	15.7795	+	6.39808i	0.756567	+	0.306764i
$436$	1.17697	−	2.03858i	0.0563668	−	0.0976301i
$437$	−10.0054	−	19.3040i	−0.478623	−	0.923436i
$438$	−4.13600	+	3.22315i	−0.197626	+	0.154008i
$439$	4.94462			0.235994			0.117997	−	0.993014i	$-0.462353\pi$
$439$	4.94462			0.235994			0.117997	+	0.993014i	$0.462353\pi$
$440$	1.08695	−	1.88264i	0.0518181	−	0.0897515i
$441$	−6.95859	+	1.97668i	−0.331361	+	0.0941278i
$442$	−2.39895	+	4.15511i	−0.114107	+	0.197638i
$443$	−1.08240	+	1.87477i	−0.0514262	+	0.0890729i	−0.890593	−	0.454802i	$-0.849710\pi$
$443$	−1.08240	+	1.87477i	−0.0514262	+	0.0890729i	0.839166	+	0.543875i	$0.183043\pi$
$444$	−4.94327	−	2.00434i	−0.234597	−	0.0951218i
$445$	4.80589	−	8.32404i	0.227821	−	0.394597i
$446$	9.09509			0.430665
$447$	0.311341	+	2.23541i	0.0147259	+	0.105731i
$448$	1.53389	+	2.65678i	0.0724696	+	0.125521i
$449$	20.6697			0.975465			0.487732	−	0.872993i	$-0.337824\pi$
$449$	20.6697			0.975465			0.487732	+	0.872993i	$0.337824\pi$
$450$	−8.67292	+	2.46366i	−0.408845	+	0.116138i
$451$	−4.52609	+	7.83942i	−0.213125	+	0.369144i
$452$	6.52086	−	11.2945i	0.306715	−	0.531247i
$453$	5.65977	+	40.6368i	0.265919	+	1.90928i
$454$	4.50967	+	7.81097i	0.211649	+	0.366587i
$455$	2.88159	−	4.99105i	0.135091	−	0.233984i
$456$	−0.700921	−	7.51723i	−0.0328236	−	0.352026i
$457$	4.14925	+	7.18672i	0.194094	+	0.336181i	0.946603	−	0.322401i	$-0.104490\pi$
$457$	4.14925	+	7.18672i	0.194094	+	0.336181i	−0.752509	+	0.658582i	$0.771157\pi$
$458$	0.209905	−	0.363565i	0.00980819	−	0.0169883i
$459$	−18.6325	−	2.02845i	−0.869691	−	0.0946797i
$460$	−3.52244	−	6.10105i	−0.164235	−	0.284463i
$461$	20.0208			0.932462			0.466231	−	0.884663i	$-0.345612\pi$
$461$	20.0208			0.932462			0.466231	+	0.884663i	$0.345612\pi$
$462$	6.45122	−	5.02738i	0.300138	−	0.233895i
$463$	18.4367	−	31.9332i	0.856824	−	1.48406i	−0.0181188	−	0.999836i	$-0.505768\pi$
$463$	18.4367	−	31.9332i	0.856824	−	1.48406i	0.874943	−	0.484227i	$-0.160899\pi$
$464$	3.48033	−	6.02810i	0.161570	−	0.279848i
$465$	−4.84442	−	1.96426i	−0.224655	−	0.0910905i
$466$	14.5187	−	25.1471i	0.672565	−	1.16492i
$467$	−11.5109			−0.532659			−0.266330	−	0.963882i	$-0.585811\pi$
$467$	−11.5109			−0.532659			−0.266330	+	0.963882i	$0.585811\pi$
$468$	2.86363	+	2.77913i	0.132371	+	0.128465i
$469$	−15.3109	−	26.5193i	−0.706993	−	1.22455i
$470$	−10.5946			−0.488693
$471$	0.968997	+	6.95734i	0.0446490	+	0.320577i
$472$	4.28487	+	7.42161i	0.197227	+	0.341607i
$473$	−8.50379	−	14.7290i	−0.391005	−	0.677240i
$474$	13.9723	+	5.66532i	0.641767	+	0.260217i
$475$	−13.0865	−	0.594713i	−0.600450	−	0.0272873i
$476$	11.0655			0.507188
$477$	−3.19038	+	12.6621i	−0.146078	+	0.579758i
$478$	7.93433	−	13.7427i	0.362908	−	0.628575i
$479$	0.780105	−	1.35118i	0.0356439	−	0.0617370i	−0.847653	−	0.530551i	$-0.821985\pi$
$479$	0.780105	−	1.35118i	0.0356439	−	0.0617370i	0.883297	+	0.468814i	$0.155318\pi$
$480$	−0.337444	−	2.42283i	−0.0154021	−	0.110586i
$481$	4.09646			0.186783
$482$	0.738688	−	1.27945i	0.0336463	−	0.0582772i
$483$	−3.65622	−	26.2515i	−0.166364	−	1.19448i
$484$	4.31538	−	7.47446i	0.196154	−	0.339748i
$485$	−0.767767	−	1.32981i	−0.0348625	−	0.0603836i
$486$	−5.42226	+	14.6150i	−0.245959	+	0.662951i
$487$	−1.21510			−0.0550612			−0.0275306	−	0.999621i	$-0.508764\pi$
$487$	−1.21510			−0.0550612			−0.0275306	+	0.999621i	$0.508764\pi$
$488$	−4.68857	+	8.12084i	−0.212241	+	0.367613i
$489$	−8.74471	−	3.54571i	−0.395449	−	0.160342i
$490$	−3.40553			−0.153846
$491$	−16.1839	−	28.0313i	−0.730368	−	1.26504i	−0.956726	−	0.290991i	$-0.906015\pi$
$491$	−16.1839	−	28.0313i	−0.730368	−	1.26504i	0.226357	−	0.974044i	$-0.427318\pi$
$492$	1.40513	+	10.0888i	0.0633482	+	0.454837i
$493$	−12.5536	−	21.7435i	−0.565386	−	0.979276i
$494$	2.66807	+	5.14767i	0.120042	+	0.231605i
$495$	−6.27347	+	1.78207i	−0.281971	+	0.0800980i
$496$	−1.06849	+	1.85068i	−0.0479765	+	0.0830978i
$497$	−27.4971			−1.23341
$498$	3.56978	+	25.6308i	0.159966	+	1.14854i
$499$	6.55498	+	11.3536i	0.293441	+	0.508255i	0.974621	−	0.223861i	$-0.0718661\pi$
$499$	6.55498	+	11.3536i	0.293441	+	0.508255i	−0.681180	+	0.732116i	$0.738533\pi$
$500$	−11.3061			−0.505625
$501$	−26.8821	−	10.8999i	−1.20100	−	0.486970i
$502$	4.56139	+	7.90056i	0.203585	+	0.352619i
$503$	11.9204	+	20.6468i	0.531506	+	0.920595i	0.999324	+	0.0367703i	$0.0117070\pi$
$503$	11.9204	+	20.6468i	0.531506	+	0.920595i	−0.467818	+	0.883825i	$0.654960\pi$
$504$	2.24863	−	8.92442i	0.100162	−	0.397525i
$505$	4.17764			0.185903
$506$	3.83897	+	6.64929i	0.170663	+	0.295597i
$507$	18.0266	+	7.30924i	0.800591	+	0.324615i
$508$	5.20044	+	9.00742i	0.230732	+	0.399640i
$509$	16.9796			0.752606			0.376303	−	0.926497i	$-0.377195\pi$
$509$	16.9796			0.752606			0.376303	+	0.926497i	$0.377195\pi$
$510$	−8.17693	−	3.31549i	−0.362080	−	0.146812i
$511$	−9.28736			−0.410849
$512$	−1.00000			−0.0441942
$513$	−14.1969	+	17.6479i	−0.626809	+	0.779173i
$514$	−4.95952			−0.218755
$515$	3.06339			0.134989
$516$	−17.7356	−	7.19126i	−0.780768	−	0.316577i
$517$	11.5466			0.507821
$518$	−4.72390	−	8.18203i	−0.207556	−	0.359498i
$519$	19.0113	+	7.70849i	0.834503	+	0.338365i
$520$	0.939306	+	1.62693i	0.0411913	+	0.0713454i
$521$	14.1380			0.619396			0.309698	−	0.950835i	$-0.399772\pi$
$521$	14.1380			0.619396			0.309698	+	0.950835i	$0.399772\pi$
$522$	−20.0872	+	5.70606i	−0.879195	+	0.249748i
$523$	2.54862	+	4.41434i	0.111443	+	0.193026i	0.916352	−	0.400373i	$-0.131119\pi$
$523$	2.54862	+	4.41434i	0.111443	+	0.193026i	−0.804909	+	0.593398i	$0.797786\pi$
$524$	8.46661	+	14.6646i	0.369866	+	0.640626i
$525$	−14.7989	−	6.00048i	−0.645875	−	0.261882i
$526$	6.22031			0.271218
$527$	3.85406	+	6.67542i	0.167885	+	0.290786i
$528$	0.367766	+	2.64054i	0.0160050	+	0.114915i
$529$	1.88172			0.0818141
$530$	−3.07364	+	5.32371i	−0.133511	+	0.231247i
$531$	6.28145	−	24.9300i	0.272592	−	1.08187i
$532$	7.20492	−	11.2652i	0.312373	−	0.488406i
$533$	−3.91132	−	6.77460i	−0.169418	−	0.293440i
$534$	1.62606	+	11.6751i	0.0703667	+	0.505229i
$535$	3.84420	+	6.65835i	0.166199	+	0.287866i
$536$	9.98175			0.431146
$537$	5.30107	+	2.14942i	0.228758	+	0.0927543i
$538$	−2.01130	+	3.48367i	−0.0867132	+	0.150192i
$539$	3.71155			0.159868
$540$	−4.33559	+	5.92100i	−0.186574	+	0.254799i
$541$	16.6051	+	28.7609i	0.713910	+	1.23653i	0.963378	+	0.268145i	$0.0864108\pi$
$541$	16.6051	+	28.7609i	0.713910	+	1.23653i	−0.249469	+	0.968383i	$0.580256\pi$
$542$	6.53300	−	11.3155i	0.280616	−	0.486042i
$543$	−6.21458	−	44.6203i	−0.266693	−	1.91484i
$544$	−1.80351	+	3.12377i	−0.0773248	+	0.133930i
$545$	−3.32453			−0.142407
$546$	0.974981	+	7.00031i	0.0417253	+	0.299585i
$547$	−20.8006	+	36.0277i	−0.889370	+	1.54043i	−0.0487491	+	0.998811i	$0.515523\pi$
$547$	−20.8006	+	36.0277i	−0.889370	+	1.54043i	−0.840621	+	0.541623i	$0.817810\pi$
$548$	5.36678	−	9.29554i	0.229257	−	0.397086i
$549$	27.0608	−	7.68699i	1.15493	−	0.328073i
$550$	4.62593			0.197250
$551$	−30.3095	−	1.37741i	−1.29123	−	0.0586796i
$552$	8.00661	+	3.24643i	0.340784	+	0.138177i
$553$	13.3522	+	23.1267i	0.567793	+	0.983446i
$554$	−5.20162	−	9.00947i	−0.220996	−	0.382776i
$555$	1.03922	+	7.46153i	0.0441123	+	0.316724i
$556$	−17.0861			−0.724613
$557$	−16.8601	−	29.2026i	−0.714387	−	1.23735i	−0.963196	−	0.268801i	$-0.913372\pi$
$557$	−16.8601	−	29.2026i	−0.714387	−	1.23735i	0.248809	−	0.968553i	$-0.419961\pi$
$558$	6.16694	−	1.75181i	0.261068	−	0.0741599i
$559$	14.6975			0.621636
$560$	2.16635	−	3.75222i	0.0915449	−	0.158560i
$561$	8.91170	+	3.61342i	0.376252	+	0.152559i
$562$	10.4052	−	18.0223i	0.438916	−	0.760225i
$563$	9.80936	−	16.9903i	0.413415	−	0.716056i	−0.581845	−	0.813299i	$-0.697669\pi$
$563$	9.80936	−	16.9903i	0.413415	−	0.716056i	0.995261	+	0.0972431i	$0.0310024\pi$
$564$	10.2486	−	7.98664i	0.431544	−	0.336298i
$565$	−18.4191			−0.774897
$566$	16.7470	+	29.0066i	0.703928	+	1.21924i
$567$	−23.4869	+	14.5148i	−0.986358	+	0.609565i
$568$	4.48160	−	7.76235i	0.188044	−	0.325701i
$569$	22.2984	+	38.6220i	0.934798	+	1.61912i	0.774995	+	0.631968i	$0.217753\pi$
$569$	22.2984	+	38.6220i	0.934798	+	1.61912i	0.159803	+	0.987149i	$0.448914\pi$
$570$	−8.69940	+	6.16567i	−0.364378	+	0.258251i
$571$	−14.4627	+	25.0501i	−0.605245	+	1.04832i	0.386767	+	0.922177i	$0.373592\pi$
$571$	−14.4627	+	25.0501i	−0.605245	+	1.04832i	−0.992013	+	0.126138i	$0.959742\pi$
$572$	−1.02371	−	1.77312i	−0.0428035	−	0.0741379i
$573$	−3.06228	−	21.9870i	−0.127929	−	0.918521i
$574$	−9.02078	+	15.6244i	−0.376520	+	0.652152i
$575$	7.49558	−	12.9827i	0.312587	−	0.541417i
$576$	2.15285	+	2.08932i	0.0897019	+	0.0870550i
$577$	−17.0827			−0.711163			−0.355581	−	0.934645i	$-0.615717\pi$
$577$	−17.0827			−0.711163			−0.355581	+	0.934645i	$0.615717\pi$
$578$	−1.99472	−	3.45495i	−0.0829693	−	0.143707i
$579$	−3.19364	−	22.9302i	−0.132723	−	0.952945i
$580$	−9.83068			−0.408197
$581$	−22.9175	+	39.6943i	−0.950780	+	1.64680i
$582$	1.74516	+	0.707607i	0.0723391	+	0.0293312i
$583$	3.34984	−	5.80210i	0.138736	−	0.240298i
$584$	1.51369	−	2.62179i	0.0626370	−	0.108491i
$585$	1.37699	−	5.46503i	0.0569314	−	0.225951i
$586$	8.17191	−	14.1542i	0.337579	−	0.584703i
$587$	31.9211			1.31753			0.658763	−	0.752350i	$-0.271080\pi$
$587$	31.9211			1.31753			0.658763	+	0.752350i	$0.271080\pi$
$588$	3.29430	−	2.56722i	0.135855	−	0.105870i
$589$	9.30526	+	0.422876i	0.383417	+	0.0174243i
$590$	6.05161	−	10.4817i	0.249141	−	0.431525i
$591$	12.4753	+	5.05835i	0.513165	+	0.208073i
$592$	3.07968			0.126574
$593$	7.61429	+	13.1883i	0.312681	+	0.541580i	0.978942	−	0.204139i	$-0.0654395\pi$
$593$	7.61429	+	13.1883i	0.312681	+	0.541580i	−0.666261	+	0.745719i	$0.732106\pi$
$594$	4.72519	−	6.45306i	0.193877	−	0.264772i
$595$	−7.81405	−	13.5343i	−0.320345	−	0.554854i
$596$	−0.651536	−	1.12849i	−0.0266880	−	0.0462249i
$597$	6.42810	+	46.1534i	0.263084	+	1.88893i
$598$	−6.63504			−0.271327
$599$	27.5484			1.12560			0.562798	−	0.826594i	$-0.309725\pi$
$599$	27.5484			1.12560			0.562798	+	0.826594i	$0.309725\pi$
$600$	4.10589	−	3.19969i	0.167622	−	0.130627i
$601$	19.8432	+	34.3695i	0.809423	+	1.40196i	0.913264	+	0.407367i	$0.133553\pi$
$601$	19.8432	+	34.3695i	0.809423	+	1.40196i	−0.103842	+	0.994594i	$0.533114\pi$
$602$	−16.9486	−	29.3558i	−0.690772	−	1.19645i
$603$	−21.4892	−	20.8551i	−0.875107	−	0.849284i
$604$	−11.8441	−	20.5145i	−0.481928	−	0.834725i
$605$	−12.1894			−0.495570
$606$	−4.04121	+	3.14928i	−0.164163	+	0.127931i
$607$	14.1225	−	24.4610i	0.573217	−	0.992840i	−0.423016	−	0.906122i	$-0.639029\pi$
$607$	14.1225	−	24.4610i	0.573217	−	0.992840i	0.996233	−	0.0867181i	$-0.0276379\pi$
$608$	2.00583	+	3.86997i	0.0813471	+	0.156948i
$609$	−34.2755	−	13.8976i	−1.38891	−	0.563161i
$610$	13.2435			0.536215
$611$	−4.98913	+	8.64143i	−0.201839	+	0.349595i
$612$	10.4092	−	2.95689i	0.420768	−	0.119525i
$613$	−10.1956	+	17.6593i	−0.411798	+	0.713254i	−0.995086	−	0.0990105i	$-0.968432\pi$
$613$	−10.1956	+	17.6593i	−0.411798	+	0.713254i	0.583289	+	0.812265i	$0.301766\pi$
$614$	5.08101	−	8.80056i	0.205053	−	0.355162i
$615$	11.3474	−	8.84291i	0.457571	−	0.356581i
$616$	−2.36102	+	4.08940i	−0.0951280	+	0.164767i
$617$	−36.5717			−1.47232			−0.736160	−	0.676808i	$-0.763363\pi$
$617$	−36.5717			−1.47232			−0.736160	+	0.676808i	$0.763363\pi$
$618$	−2.96334	+	2.30930i	−0.119203	+	0.0928938i
$619$	−10.8139	−	18.7303i	−0.434648	−	0.752833i	0.562618	−	0.826717i	$-0.309794\pi$
$619$	−10.8139	−	18.7303i	−0.434648	−	0.752833i	−0.997267	+	0.0738835i	$0.976461\pi$
$620$	3.01810			0.121210
$621$	−10.4542	−	23.7174i	−0.419511	−	0.951748i
$622$	7.35458	−	12.7385i	0.294892	−	0.510768i
$623$	−10.4391	+	18.0811i	−0.418235	+	0.724405i
$624$	−2.13507	−	0.865705i	−0.0854712	−	0.0346559i
$625$	0.470565	+	0.815043i	0.0188226	+	0.0326017i
$626$	9.63983	−	16.6967i	0.385285	−	0.667333i
$627$	9.48113	−	6.71972i	0.378640	−	0.268360i
$628$	−2.02780	−	3.51225i	−0.0809179	−	0.140154i
$629$	5.55423	−	9.62020i	0.221462	−	0.383583i
$630$	−12.5034	+	3.55177i	−0.498148	+	0.141506i
$631$	−8.43111	−	14.6031i	−0.335637	−	0.581341i	0.647970	−	0.761666i	$-0.275618\pi$
$631$	−8.43111	−	14.6031i	−0.335637	−	0.581341i	−0.983607	+	0.180325i	$0.942285\pi$
$632$	−8.70478			−0.346258
$633$	4.27728	+	30.7106i	0.170007	+	1.22064i
$634$	0.961061	−	1.66461i	0.0381686	−	0.0661100i
$635$	7.34469	−	12.7214i	0.291465	−	0.504832i
$636$	−1.03996	−	7.46688i	−0.0412372	−	0.296081i
$637$	−1.60370	+	2.77770i	−0.0635411	+	0.110056i
$638$	10.7141			0.424174
$639$	−25.8662	+	7.34766i	−1.02325	+	0.290669i
$640$	0.706161	+	1.22311i	0.0279134	+	0.0483475i
$641$	27.6367			1.09158			0.545791	−	0.837921i	$-0.316229\pi$
$641$	27.6367			1.09158			0.545791	+	0.837921i	$0.316229\pi$
$642$	−8.73798	−	3.54298i	−0.344861	−	0.139830i
$643$	24.3772	+	42.2225i	0.961342	+	1.66509i	0.719138	+	0.694867i	$0.244537\pi$
$643$	24.3772	+	42.2225i	0.961342	+	1.66509i	0.242203	+	0.970226i	$0.422130\pi$
$644$	7.65130	+	13.2524i	0.301503	+	0.522219i
$645$	3.72855	+	26.7708i	0.146811	+	1.05410i
$646$	15.7064	+	0.713774i	0.617960	+	0.0280831i
$647$	−23.7074			−0.932035			−0.466018	−	0.884775i	$-0.654312\pi$
$647$	−23.7074			−0.932035			−0.466018	+	0.884775i	$0.654312\pi$
$648$	−0.269490	−	8.99596i	−0.0105866	−	0.353395i
$649$	−6.59541	+	11.4236i	−0.258892	+	0.448415i
$650$	−1.99880	+	3.46202i	−0.0783992	+	0.135791i
$651$	10.5228	+	4.26669i	0.412423	+	0.167225i
$652$	5.44799			0.213360
$653$	12.3141	−	21.3286i	0.481887	−	0.834653i	−0.517897	−	0.855443i	$-0.673285\pi$
$653$	12.3141	−	21.3286i	0.481887	−	0.834653i	0.999784	+	0.0207902i	$0.00661820\pi$
$654$	3.21595	−	2.50616i	0.125754	−	0.0979986i
$655$	11.9576	−	20.7111i	0.467221	−	0.809250i
$656$	−2.94049	−	5.09307i	−0.114807	−	0.198851i
$657$	−8.73651	+	2.48173i	−0.340844	+	0.0968214i
$658$	23.0132			0.897147
$659$	−4.37112	+	7.57101i	−0.170275	+	0.294925i	−0.938516	−	0.345236i	$-0.887799\pi$
$659$	−4.37112	+	7.57101i	−0.170275	+	0.294925i	0.768241	+	0.640161i	$0.221132\pi$
$660$	2.96996	−	2.31446i	0.115605	−	0.0900903i
$661$	23.0730			0.897437			0.448718	−	0.893673i	$-0.351881\pi$
$661$	23.0730			0.897437			0.448718	+	0.893673i	$0.351881\pi$
$662$	−14.3888	−	24.9221i	−0.559235	−	0.968624i
$663$	−6.55488	+	5.10816i	−0.254570	+	0.198384i
$664$	−7.47039	−	12.9391i	−0.289907	−	0.502134i
$665$	−18.8663	−	0.857375i	−0.731604	−	0.0332476i
$666$	−6.63007	−	6.43443i	−0.256910	−	0.249329i
$667$	17.3604	−	30.0691i	0.672198	−	1.16428i
$668$	16.7477			0.647987
$669$	14.5988	+	5.91934i	0.564420	+	0.228855i
$670$	−7.04872	−	12.2087i	−0.272316	−	0.471665i
$671$	−14.4336			−0.557202
$672$	0.732981	+	5.26276i	0.0282753	+	0.203015i
$673$	16.1641	+	27.9970i	0.623080	+	1.07921i	0.988909	+	0.148524i	$0.0474522\pi$
$673$	16.1641	+	27.9970i	0.623080	+	1.07921i	−0.365829	+	0.930682i	$0.619214\pi$
$674$	−3.78100	−	6.54889i	−0.145639	−	0.252254i
$675$	−15.5245	−	1.69009i	−0.597539	−	0.0650516i
$676$	−11.2307			−0.431949
$677$	−19.2764	−	33.3877i	−0.740852	−	1.28319i	−0.952108	−	0.305762i	$-0.901089\pi$
$677$	−19.2764	−	33.3877i	−0.740852	−	1.28319i	0.211256	−	0.977431i	$-0.432245\pi$
$678$	17.8175	−	13.8850i	0.684278	−	0.533252i
$679$	1.66771	+	2.88856i	0.0640008	+	0.110853i
$680$	5.09426			0.195356
$681$	2.15497	+	15.4726i	0.0825788	+	0.592911i
$682$	−3.28930			−0.125954
$683$	−45.5130			−1.74151			−0.870753	−	0.491720i	$-0.836368\pi$
$683$	−45.5130			−1.74151			−0.870753	+	0.491720i	$0.836368\pi$
$684$	3.76736	−	12.5223i	0.144049	−	0.478801i
$685$	−15.1592			−0.579205
$686$	−14.0771			−0.537468
$687$	0.573541	−	0.446956i	0.0218820	−	0.0170524i
$688$	11.0494			0.421254
$689$	2.89483	+	5.01400i	0.110284	+	0.191018i
$690$	−1.68322	−	12.0854i	−0.0640792	−	0.460085i
$691$	22.9860	+	39.8129i	0.874429	+	1.51456i	0.857370	+	0.514701i	$0.172097\pi$
$691$	22.9860	+	39.8129i	0.874429	+	1.51456i	0.0170592	+	0.999854i	$0.494570\pi$
$692$	−11.8441			−0.450246
$693$	13.6270	−	3.87093i	0.517646	−	0.147044i
$694$	−14.8609	−	25.7398i	−0.564111	−	0.977070i
$695$	12.0655	+	20.8981i	0.457672	+	0.792711i
$696$	9.50961	−	7.41076i	0.360461	−	0.280904i
$697$	−21.2128			−0.803491
$698$	7.74593	+	13.4163i	0.293188	+	0.507816i
$699$	39.6707	−	30.9150i	1.50048	−	1.16931i
$700$	9.21976			0.348474
$701$	−18.5068	+	32.0546i	−0.698990	+	1.21069i	0.269827	+	0.962909i	$0.413034\pi$
$701$	−18.5068	+	32.0546i	−0.698990	+	1.21069i	−0.968817	+	0.247778i	$0.920300\pi$
$702$	2.78774	+	6.32457i	0.105217	+	0.238706i
$703$	−6.17731	−	11.9183i	−0.232982	−	0.449506i
$704$	−0.769616	−	1.33301i	−0.0290060	−	0.0502399i
$705$	−17.0057	−	6.89527i	−0.640470	−	0.259691i
$706$	8.64592	+	14.9752i	0.325394	+	0.563598i
$707$	−9.07450			−0.341282
$708$	2.04755	+	14.7013i	0.0769518	+	0.552509i
$709$	−3.00550	+	5.20568i	−0.112874	+	0.195503i	−0.916928	−	0.399053i	$-0.869339\pi$
$709$	−3.00550	+	5.20568i	−0.112874	+	0.195503i	0.804054	+	0.594556i	$0.202672\pi$
$710$	−12.6589			−0.475080
$711$	18.7401	+	18.1871i	0.702807	+	0.682068i
$712$	−3.40283	−	5.89387i	−0.127526	−	0.220882i
$713$	−5.32979	+	9.23147i	−0.199602	+	0.345721i
$714$	17.7616	+	7.20177i	0.664710	+	0.269519i
$715$	−1.44581	+	2.50422i	−0.0540702	+	0.0936524i
$716$	−3.30259			−0.123424
$717$	21.6797	−	16.8948i	0.809643	−	0.630948i
$718$	−17.6705	+	30.6061i	−0.659456	+	1.14221i
$719$	20.3061	−	35.1712i	0.757290	−	1.31166i	−0.186938	−	0.982372i	$-0.559856\pi$
$719$	20.3061	−	35.1712i	0.757290	−	1.31166i	0.944228	−	0.329293i	$-0.106810\pi$
$720$	1.03520	−	4.10855i	0.0385798	−	0.153117i
$721$	−6.65416			−0.247814
$722$	10.9533	−	15.5250i	0.407640	−	0.577780i
$723$	2.01839	−	1.57291i	0.0750646	−	0.0584972i
$724$	13.0051	+	22.5255i	0.483331	+	0.837153i
$725$	−10.4596	−	18.1166i	−0.388460	−	0.672832i
$726$	11.7913	−	9.18886i	0.437617	−	0.341031i
$727$	−40.3960			−1.49821			−0.749103	−	0.662453i	$-0.769515\pi$
$727$	−40.3960			−1.49821			−0.749103	+	0.662453i	$0.769515\pi$
$728$	−2.04032	−	3.53394i	−0.0756193	−	0.130976i
$729$	−18.2153	+	19.9300i	−0.674640	+	0.738147i
$730$	−4.27564			−0.158249
$731$	19.9277	−	34.5157i	0.737052	−	1.27661i
$732$	−12.8110	+	9.98350i	−0.473508	+	0.369001i
$733$	−14.9471	+	25.8892i	−0.552085	+	0.956239i	0.446039	+	0.895013i	$0.352834\pi$
$733$	−14.9471	+	25.8892i	−0.552085	+	0.956239i	−0.998124	+	0.0612255i	$0.980499\pi$
$734$	−12.5735	+	21.7780i	−0.464097	+	0.803840i
$735$	−5.46629	−	2.21641i	−0.201627	−	0.0817536i
$736$	−4.98816			−0.183866
$737$	7.68212	+	13.3058i	0.282974	+	0.490126i
$738$	−4.31064	+	17.1082i	−0.158677	+	0.629762i
$739$	−11.3895	+	19.7272i	−0.418969	+	0.725675i	−0.995836	−	0.0911627i	$-0.970942\pi$
$739$	−11.3895	+	19.7272i	−0.418969	+	0.725675i	0.576867	+	0.816838i	$0.304275\pi$
$740$	−2.17475	−	3.76677i	−0.0799453	−	0.138469i
$741$	0.932336	+	9.99911i	0.0342502	+	0.367326i
$742$	6.67644	−	11.5639i	0.245100	−	0.424525i
$743$	8.10439	+	14.0372i	0.297321	+	0.514975i	0.975522	−	0.219901i	$-0.0705734\pi$
$743$	8.10439	+	14.0372i	0.297321	+	0.514975i	−0.678201	+	0.734876i	$0.737240\pi$
$744$	−2.91953	+	2.27516i	−0.107035	+	0.0834115i
$745$	−0.920179	+	1.59380i	−0.0337127	+	0.0583922i
$746$	17.4889	−	30.2917i	0.640316	−	1.10906i
$747$	−10.9513	+	43.4639i	−0.400687	+	1.59026i
$748$	−5.55204			−0.203003
$749$	−8.35021	−	14.4630i	−0.305110	−	0.528466i
$750$	−18.1477	−	7.35834i	−0.662661	−	0.268689i
$751$	−7.39712			−0.269925			−0.134962	−	0.990851i	$-0.543091\pi$
$751$	−7.39712			−0.269925			−0.134962	+	0.990851i	$0.543091\pi$
$752$	−3.75078	+	6.49654i	−0.136777	+	0.236905i
$753$	2.17969	+	15.6501i	0.0794324	+	0.570320i
$754$	−4.62939	+	8.01833i	−0.168592	+	0.292011i
$755$	−16.7276	+	28.9731i	−0.608781	+	1.05444i
$756$	9.41759	−	12.8613i	0.342514	−	0.467762i
$757$	19.3191	−	33.4616i	0.702164	−	1.21618i	−0.265542	−	0.964099i	$-0.585551\pi$
$757$	19.3191	−	33.4616i	0.702164	−	1.21618i	0.967705	−	0.252084i	$-0.0811159\pi$
$758$	−9.07430			−0.329593
$759$	1.83448	+	13.1714i	0.0665873	+	0.478093i
$760$	3.31694	−	5.18616i	0.120318	−	0.188122i
$761$	−3.80635	+	6.59279i	−0.137980	+	0.238988i	−0.926732	−	0.375723i	$-0.877394\pi$
$761$	−3.80635	+	6.59279i	−0.137980	+	0.238988i	0.788752	+	0.614712i	$0.210728\pi$
$762$	2.48506	+	17.8426i	0.0900244	+	0.646370i
$763$	7.22139			0.261432
$764$	6.40837	+	11.0996i	0.231847	+	0.401570i
$765$	−10.9672	−	10.6435i	−0.396519	−	0.384818i
$766$	7.35390	+	12.7373i	0.265707	+	0.460218i
$767$	−5.69955	−	9.87192i	−0.205799	−	0.356454i
$768$	−1.60512	−	0.650828i	−0.0579199	−	0.0234847i
$769$	−3.83350			−0.138240			−0.0691198	−	0.997608i	$-0.522019\pi$
$769$	−3.83350			−0.138240			−0.0691198	+	0.997608i	$0.522019\pi$
$770$	6.66902			0.240335
$771$	−7.96065	−	3.22780i	−0.286696	−	0.116246i
$772$	6.68326	+	11.5757i	0.240536	+	0.416620i
$773$	10.2883	+	17.8199i	0.370044	+	0.640936i	0.989572	−	0.144039i	$-0.0460091\pi$
$773$	10.2883	+	17.8199i	0.370044	+	0.640936i	−0.619528	+	0.784975i	$0.712676\pi$
$774$	−23.7876	−	23.0857i	−0.855029	−	0.829799i
$775$	3.21118	+	5.56193i	0.115349	+	0.199790i
$776$	−1.08724			−0.0390297
$777$	−2.25735	−	16.2076i	−0.0809818	−	0.581445i
$778$	−6.44691	+	11.1664i	−0.231133	+	0.400334i
$779$	−13.8119	+	21.5954i	−0.494863	+	0.773736i
$780$	0.448854	+	3.22274i	0.0160715	+	0.115393i
$781$	13.7964			0.493675
$782$	−8.99618	+	15.5818i	−0.321703	+	0.557206i
$783$	−35.9562	−	3.91440i	−1.28497	−	0.139889i
$784$	−1.20565	+	2.08824i	−0.0430589	+	0.0745802i
$785$	−2.86390	+	4.96042i	−0.102217	+	0.177045i
$786$	4.04583	+	29.0488i	0.144310	+	1.03614i
$787$	−1.39148	+	2.41011i	−0.0496008	+	0.0859111i	−0.889760	−	0.456429i	$-0.849128\pi$
$787$	−1.39148	+	2.41011i	−0.0496008	+	0.0859111i	0.840159	+	0.542340i	$0.182462\pi$
$788$	−7.77217			−0.276872
$789$	9.98437	+	4.04835i	0.355453	+	0.144125i
$790$	6.14697	+	10.6469i	0.218700	+	0.378799i
$791$	40.0092			1.42256
$792$	−1.12823	+	4.47775i	−0.0400898	+	0.159110i
$793$	6.23654	−	10.8020i	0.221466	−	0.383590i
$794$	−4.69327	+	8.12899i	−0.166558	+	0.288487i
$795$	−8.39840	+	6.54480i	−0.297861	+	0.232120i
$796$	−13.4519	−	23.2994i	−0.476791	−	0.825826i
$797$	−20.0446	+	34.7182i	−0.710016	+	1.22978i	0.254835	+	0.966985i	$0.417979\pi$
$797$	−20.0446	+	34.7182i	−0.710016	+	1.22978i	−0.964851	+	0.262799i	$0.915355\pi$
$798$	18.8965	−	13.3928i	0.668928	−	0.474100i
$799$	13.5291	+	23.4331i	0.478626	+	0.829005i
$800$	−1.50267	+	2.60271i	−0.0531276	+	0.0920197i
$801$	−4.98841	+	19.7982i	−0.176257	+	0.699535i
$802$	12.0674	+	20.9014i	0.426115	+	0.738053i
$803$	4.65985			0.164442
$804$	16.0220	+	6.49640i	0.565051	+	0.229111i
$805$	10.8061	−	18.7167i	0.380864	−	0.659677i
$806$	1.42126	−	2.46169i	0.0500617	−	0.0867095i
$807$	−5.49565	+	4.28272i	−0.193456	+	0.150759i
$808$	1.47900	−	2.56170i	0.0520310	−	0.0901204i
$809$	−49.1404			−1.72769			−0.863843	−	0.503761i	$-0.831949\pi$
$809$	−49.1404			−1.72769			−0.863843	+	0.503761i	$0.831949\pi$
$810$	−10.8127	+	6.68221i	−0.379920	+	0.234789i
$811$	−11.8736	−	20.5658i	−0.416940	−	0.722161i	0.578690	−	0.815548i	$-0.303564\pi$
$811$	−11.8736	−	20.5658i	−0.416940	−	0.722161i	−0.995630	+	0.0933862i	$0.970231\pi$
$812$	21.3538			0.749371
$813$	17.8507	−	13.9109i	0.626052	−	0.487877i
$814$	2.37017	+	4.10526i	0.0830744	+	0.143889i
$815$	−3.84716	−	6.66347i	−0.134760	−	0.233411i
$816$	−4.92789	+	3.84026i	−0.172511	+	0.134436i
$817$	−22.1632	−	42.7608i	−0.775392	−	1.49601i
$818$	23.2135			0.811640
$819$	−2.99103	+	11.8709i	−0.104515	+	0.414803i
$820$	−4.15291	+	7.19306i	−0.145026	+	0.251192i
$821$	−6.10013	+	10.5657i	−0.212896	+	0.368747i	−0.952620	−	0.304164i	$-0.901623\pi$
$821$	−6.10013	+	10.5657i	−0.212896	+	0.368747i	0.739724	+	0.672911i	$0.234956\pi$
$822$	14.6641	−	11.4276i	0.511471	−	0.398585i
$823$	17.6317			0.614602			0.307301	−	0.951612i	$-0.400574\pi$
$823$	17.6317			0.614602			0.307301	+	0.951612i	$0.400574\pi$
$824$	1.08452	−	1.87845i	0.0377811	−	0.0654388i
$825$	7.42519	+	3.01069i	0.258512	+	0.104819i
$826$	−13.1450	+	22.7679i	−0.457375	+	0.792196i
$827$	−9.97998	−	17.2858i	−0.347038	−	0.601087i	0.638684	−	0.769469i	$-0.279479\pi$
$827$	−9.97998	−	17.2858i	−0.347038	−	0.601087i	−0.985722	+	0.168382i	$0.946146\pi$
$828$	10.7387	+	10.4219i	0.373197	+	0.362185i
$829$	−36.5421			−1.26916			−0.634579	−	0.772858i	$-0.718827\pi$
$829$	−36.5421			−1.26916			−0.634579	+	0.772858i	$0.718827\pi$
$830$	−10.5506	+	18.2742i	−0.366216	+	0.634305i
$831$	−2.48563	−	17.8467i	−0.0862255	−	0.619094i
$832$	1.33016			0.0461150
$833$	4.34879	+	7.53233i	0.150677	+	0.260980i
$834$	−27.4253	−	11.1201i	−0.949661	−	0.385058i
$835$	−11.8266	−	20.4842i	−0.409275	−	0.708885i
$836$	−3.61500	+	5.65219i	−0.125028	+	0.195485i
$837$	11.0388	+	1.20175i	0.381558	+	0.0415386i
$838$	−9.92625	+	17.1928i	−0.342897	+	0.593915i
$839$	21.5561			0.744200			0.372100	−	0.928193i	$-0.378638\pi$
$839$	21.5561			0.744200			0.372100	+	0.928193i	$0.378638\pi$
$840$	5.91931	−	4.61287i	0.204236	−	0.159159i
$841$	−9.72535	−	16.8448i	−0.335357	−	0.580855i
$842$	−33.1954			−1.14399
$843$	28.4310	−	22.1561i	0.979217	−	0.763095i
$844$	−8.95097	−	15.5035i	−0.308105	−	0.533654i
$845$	7.93066	+	13.7363i	0.272823	+	0.472543i
$846$	21.6482	−	6.14948i	0.744281	−	0.211423i
$847$	26.4773			0.909771
$848$	2.17631	+	3.76947i	0.0747347	+	0.129444i
$849$	8.00266	+	57.4586i	0.274651	+	1.97198i
$850$	5.42017	+	9.38801i	0.185910	+	0.322006i
$851$	15.3619			0.526600
$852$	12.2455	−	9.54279i	0.419523	−	0.326931i
$853$	−39.8741			−1.36526			−0.682632	−	0.730762i	$-0.739165\pi$
$853$	−39.8741			−1.36526			−0.682632	+	0.730762i	$0.739165\pi$
$854$	−28.7670			−0.984387
$855$	−17.9764	+	4.23485i	−0.614780	+	0.144829i
$856$	5.44381			0.186065
$857$	31.4895			1.07566			0.537831	−	0.843053i	$-0.319244\pi$
$857$	31.4895			1.07566			0.537831	+	0.843053i	$0.319244\pi$
$858$	−0.489188	−	3.51234i	−0.0167006	−	0.119909i
$859$	−47.5261			−1.62157			−0.810784	−	0.585345i	$-0.800959\pi$
$859$	−47.5261			−1.62157			−0.810784	+	0.585345i	$0.800959\pi$
$860$	−7.80265	−	13.5146i	−0.266068	−	0.460843i
$861$	−24.6483	+	19.2082i	−0.840012	+	0.654614i
$862$	−12.0807	−	20.9243i	−0.411469	−	0.712686i
$863$	8.64843			0.294396			0.147198	−	0.989107i	$-0.452975\pi$
$863$	8.64843			0.294396			0.147198	+	0.989107i	$0.452975\pi$
$864$	2.09580	+	4.75475i	0.0713005	+	0.161760i
$865$	8.36386	+	14.4866i	0.284380	+	0.492560i
$866$	0.219374	+	0.379967i	0.00745464	+	0.0129118i
$867$	−0.953189	−	6.84385i	−0.0323720	−	0.232429i
$868$	−6.55578			−0.222518
$869$	−6.69934	−	11.6036i	−0.227260	−	0.393625i
$870$	−15.7795	−	6.39808i	−0.534974	−	0.216915i
$871$	−13.2773			−0.449885
$872$	−1.17697	+	2.03858i	−0.0398573	+	0.0690349i
$873$	2.34066	+	2.27159i	0.0792194	+	0.0768818i
$874$	10.0054	+	19.3040i	0.338437	+	0.652968i
$875$	−17.3424	−	30.0379i	−0.586279	−	1.01547i
$876$	4.13600	−	3.22315i	0.139742	−	0.108900i
$877$	−6.33290	−	10.9689i	−0.213847	−	0.370394i	0.739068	−	0.673630i	$-0.235266\pi$
$877$	−6.33290	−	10.9689i	−0.213847	−	0.370394i	−0.952915	+	0.303237i	$0.901933\pi$
$878$	−4.94462			−0.166873
$879$	22.3289	−	17.4007i	0.753134	−	0.586911i
$880$	−1.08695	+	1.88264i	−0.0366409	+	0.0634639i
$881$	−1.11692			−0.0376301			−0.0188151	−	0.999823i	$-0.505989\pi$
$881$	−1.11692			−0.0376301			−0.0188151	+	0.999823i	$0.505989\pi$
$882$	6.95859	−	1.97668i	0.234308	−	0.0665584i
$883$	4.90542	+	8.49643i	0.165080	+	0.285928i	0.936684	−	0.350176i	$-0.113878\pi$
$883$	4.90542	+	8.49643i	0.165080	+	0.285928i	−0.771603	+	0.636104i	$0.780545\pi$
$884$	2.39895	−	4.15511i	0.0806855	−	0.139751i
$885$	16.5354	−	12.8859i	0.555830	−	0.433154i
$886$	1.08240	−	1.87477i	0.0363638	−	0.0629840i
$887$	55.3048			1.85695			0.928476	−	0.371392i	$-0.121119\pi$
$887$	55.3048			1.85695			0.928476	+	0.371392i	$0.121119\pi$
$888$	4.94327	+	2.00434i	0.165885	+	0.0672613i
$889$	−15.9538	+	27.6328i	−0.535074	+	0.926775i
$890$	−4.80589	+	8.32404i	−0.161094	+	0.279022i
$891$	11.7843	−	7.28267i	0.394790	−	0.243979i
$892$	−9.09509			−0.304526
$893$	32.6648	+	1.48445i	1.09309	+	0.0496751i
$894$	−0.311341	−	2.23541i	−0.0104128	−	0.0747633i
$895$	2.33216	+	4.03942i	0.0779555	+	0.135023i
$896$	−1.53389	−	2.65678i	−0.0512437	−	0.0887567i
$897$	−10.6501	−	4.31827i	−0.355595	−	0.144183i
$898$	−20.6697			−0.689758
$899$	7.43738	+	12.8819i	0.248050	+	0.429636i
$900$	8.67292	−	2.46366i	0.289097	−	0.0821221i
$901$	15.6999			0.523041
$902$	4.52609	−	7.83942i	0.150702	−	0.261024i
$903$	−8.09899	−	58.1503i	−0.269518	−	1.93512i
$904$	−6.52086	+	11.2945i	−0.216881	+	0.375648i
$905$	18.3674	−	31.8132i	0.610552	−	1.05751i
$906$	−5.65977	−	40.6368i	−0.188033	−	1.35007i
$907$	1.08534			0.0360381			0.0180191	−	0.999838i	$-0.494264\pi$
$907$	1.08534			0.0360381			0.0180191	+	0.999838i	$0.494264\pi$
$908$	−4.50967	−	7.81097i	−0.149659	−	0.259216i
$909$	−8.53627	+	2.42485i	−0.283130	+	0.0804271i
$910$	−2.88159	+	4.99105i	−0.0955237	+	0.165452i
$911$	12.5344	+	21.7102i	0.415282	+	0.719289i	0.995458	−	0.0952016i	$-0.0303496\pi$
$911$	12.5344	+	21.7102i	0.415282	+	0.719289i	−0.580176	+	0.814491i	$0.697016\pi$
$912$	0.700921	+	7.51723i	0.0232098	+	0.248920i
$913$	11.4987	−	19.9163i	0.380550	−	0.659132i
$914$	−4.14925	−	7.18672i	−0.137245	−	0.237716i
$915$	21.2575	+	8.61926i	0.702751	+	0.284944i
$916$	−0.209905	+	0.363565i	−0.00693544	+	0.0120125i
$917$	−25.9737	+	44.9878i	−0.857728	+	1.48563i
$918$	18.6325	+	2.02845i	0.614965	+	0.0669487i
$919$	−42.9217			−1.41586			−0.707928	−	0.706284i	$-0.750370\pi$
$919$	−42.9217			−1.41586			−0.707928	+	0.706284i	$0.750370\pi$
$920$	3.52244	+	6.10105i	0.116131	+	0.201146i
$921$	13.8833	−	10.8191i	0.457470	−	0.356502i
$922$	−20.0208			−0.659350
$923$	−5.96123	+	10.3252i	−0.196216	+	0.339857i
$924$	−6.45122	+	5.02738i	−0.212230	+	0.165389i
$925$	4.62776	−	8.01551i	0.152160	−	0.263548i
$926$	−18.4367	+	31.9332i	−0.605866	+	1.04939i
$927$	−6.25949	+	1.77809i	−0.205588	+	0.0584003i
$928$	−3.48033	+	6.02810i	−0.114247	+	0.197882i
$929$	−17.7657			−0.582872			−0.291436	−	0.956590i	$-0.594133\pi$
$929$	−17.7657			−0.582872			−0.291436	+	0.956590i	$0.594133\pi$
$930$	4.84442	+	1.96426i	0.158855	+	0.0644107i
$931$	10.4998	+	0.477159i	0.344116	+	0.0156383i
$932$	−14.5187	+	25.1471i	−0.475575	+	0.823720i
$933$	20.0956	−	15.6603i	0.657900	−	0.512696i
$934$	11.5109			0.376647
$935$	3.92063	+	6.79073i	0.128218	+	0.222081i
$936$	−2.86363	−	2.77913i	−0.0936006	−	0.0908386i
$937$	16.9140	+	29.2958i	0.552555	+	0.957053i	0.998089	+	0.0617884i	$0.0196804\pi$
$937$	16.9140	+	29.2958i	0.552555	+	0.957053i	−0.445534	+	0.895265i	$0.646986\pi$
$938$	15.3109	+	26.5193i	0.499920	+	0.865886i
$939$	26.3398	−	20.5264i	0.859566	−	0.669852i
$940$	10.5946			0.345558
$941$	54.4276			1.77429			0.887145	−	0.461491i	$-0.152685\pi$
$941$	54.4276			1.77429			0.887145	+	0.461491i	$0.152685\pi$
$942$	−0.968997	−	6.95734i	−0.0315716	−	0.226682i
$943$	−14.6676	−	25.4051i	−0.477643	−	0.827303i
$944$	−4.28487	−	7.42161i	−0.139461	−	0.241553i
$945$	−22.3811	−	2.43654i	−0.728058	−	0.0792606i
$946$	8.50379	+	14.7290i	0.276482	+	0.478881i
$947$	−29.4987			−0.958580			−0.479290	−	0.877657i	$-0.659106\pi$
$947$	−29.4987			−0.958580			−0.479290	+	0.877657i	$0.659106\pi$
$948$	−13.9723	−	5.66532i	−0.453798	−	0.184001i
$949$	−2.01345	+	3.48740i	−0.0653594	+	0.113206i
$950$	13.0865	+	0.594713i	0.424582	+	0.0192951i
$951$	2.62599	−	2.04641i	0.0851537	−	0.0663595i
$952$	−11.0655			−0.358636
$953$	−4.72289	+	8.18029i	−0.152989	+	0.264985i	−0.932325	−	0.361621i	$-0.882223\pi$
$953$	−4.72289	+	8.18029i	−0.152989	+	0.264985i	0.779336	+	0.626607i	$0.215557\pi$
$954$	3.19038	−	12.6621i	0.103292	−	0.409951i
$955$	9.05068	−	15.6762i	0.292873	−	0.507271i
$956$	−7.93433	+	13.7427i	−0.256615	+	0.444469i
$957$	17.1974	+	6.97301i	0.555913	+	0.225405i
$958$	−0.780105	+	1.35118i	−0.0252040	+	0.0436547i
$959$	32.9282			1.06331
$960$	0.337444	+	2.42283i	0.0108909	+	0.0781964i
$961$	13.2167	+	22.8919i	0.426344	+	0.738450i
$962$	−4.09646			−0.132075
$963$	−11.7197	−	11.3738i	−0.377661	−	0.366517i
$964$	−0.738688	+	1.27945i	−0.0237916	+	0.0412082i
$965$	9.43891	−	16.3487i	0.303849	−	0.526282i
$966$	3.65622	+	26.2515i	0.117637	+	0.844627i
$967$	−10.6501	−	18.4464i	−0.342483	−	0.593198i	0.642410	−	0.766361i	$-0.277935\pi$
$967$	−10.6501	−	18.4464i	−0.342483	−	0.593198i	−0.984893	+	0.173163i	$0.944601\pi$
$968$	−4.31538	+	7.47446i	−0.138702	+	0.240238i
$969$	24.7462	+	11.3679i	0.794962	+	0.365188i
$970$	0.767767	+	1.32981i	0.0246515	+	0.0426976i
$971$	−4.19426	+	7.26467i	−0.134600	+	0.233134i	−0.925445	−	0.378883i	$-0.876308\pi$
$971$	−4.19426	+	7.26467i	−0.134600	+	0.233134i	0.790844	+	0.612017i	$0.209642\pi$
$972$	5.42226	−	14.6150i	0.173919	−	0.468777i
$973$	−26.2083	−	45.3940i	−0.840198	−	1.45527i
$974$	1.21510			0.0389342
$975$	−5.46149	+	4.25609i	−0.174908	+	0.136304i
$976$	4.68857	−	8.12084i	0.150077	−	0.259942i
$977$	−10.8321	+	18.7617i	−0.346549	+	0.600241i	−0.985634	−	0.168895i	$-0.945980\pi$
$977$	−10.8321	+	18.7617i	−0.346549	+	0.600241i	0.639085	+	0.769136i	$0.279313\pi$
$978$	8.74471	+	3.54571i	0.279625	+	0.113379i
$979$	5.23774	−	9.07204i	0.167399	−	0.289944i
$980$	3.40553			0.108786
$981$	6.79308	−	1.92967i	0.216886	−	0.0616096i
$982$	16.1839	+	28.0313i	0.516448	+	0.894515i
$983$	−6.00745			−0.191608			−0.0958040	−	0.995400i	$-0.530542\pi$
$983$	−6.00745			−0.191608			−0.0958040	+	0.995400i	$0.530542\pi$
$984$	−1.40513	−	10.0888i	−0.0447940	−	0.321618i
$985$	5.48840	+	9.50619i	0.174875	+	0.302892i
$986$	12.5536	+	21.7435i	0.399788	+	0.692453i
$987$	36.9390	+	14.9776i	1.17578	+	0.476743i
$988$	−2.66807	−	5.14767i	−0.0848827	−	0.163769i
$989$	55.1161			1.75259
$990$	6.27347	−	1.78207i	0.199384	−	0.0566378i
$991$	9.56536	−	16.5677i	0.303854	−	0.526290i	−0.673152	−	0.739504i	$-0.735060\pi$
$991$	9.56536	−	16.5677i	0.303854	−	0.526290i	0.977005	+	0.213214i	$0.0683933\pi$
$992$	1.06849	−	1.85068i	0.0339245	−	0.0587590i
$993$	−6.87577	−	49.3676i	−0.218196	−	1.56663i
$994$	27.4971			0.872156
$995$	−18.9984	+	32.9063i	−0.602291	+	1.04320i
$996$	−3.56978	−	25.6308i	−0.113113	−	0.812143i
$997$	11.4223	−	19.7840i	0.361747	−	0.626564i	−0.626501	−	0.779420i	$-0.715514\pi$
$997$	11.4223	−	19.7840i	0.361747	−	0.626564i	0.988248	+	0.152856i	$0.0488470\pi$
$998$	−6.55498	−	11.3536i	−0.207494	−	0.359391i
$999$	−6.45438	−	14.6431i	−0.204208	−	0.463287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.f.g.49.2	yes	18
3.2	odd	2		1026.2.f.g.847.7		18
9.2	odd	6		1026.2.h.g.505.3		18
9.7	even	3		342.2.h.g.277.8	yes	18
19.7	even	3		342.2.h.g.121.8	yes	18
57.26	odd	6		1026.2.h.g.577.3		18
171.7	even	3	inner	342.2.f.g.7.2	✓	18
171.83	odd	6		1026.2.f.g.235.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.2	✓	18	171.7	even	3	inner
342.2.f.g.49.2	yes	18	1.1	even	1	trivial
342.2.h.g.121.8	yes	18	19.7	even	3
342.2.h.g.277.8	yes	18	9.7	even	3
1026.2.f.g.235.7		18	171.83	odd	6
1026.2.f.g.847.7		18	3.2	odd	2
1026.2.h.g.505.3		18	9.2	odd	6
1026.2.h.g.577.3		18	57.26	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.60512 - 0.650828i) q^{3} +1.00000 q^{4} +(-0.706161 - 1.22311i) q^{5} +(1.60512 + 0.650828i) q^{6} +(1.53389 + 2.65678i) q^{7} -1.00000 q^{8} +(2.15285 + 2.08932i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.60512 - 0.650828i) q^{3} +1.00000 q^{4} +(-0.706161 - 1.22311i) q^{5} +(1.60512 + 0.650828i) q^{6} +(1.53389 + 2.65678i) q^{7} -1.00000 q^{8} +(2.15285 + 2.08932i) q^{9} +(0.706161 + 1.22311i) q^{10} +(-0.769616 - 1.33301i) q^{11} +(-1.60512 - 0.650828i) q^{12} +1.33016 q^{13} +(-1.53389 - 2.65678i) q^{14} +(0.337444 + 2.42283i) q^{15} +1.00000 q^{16} +(1.80351 - 3.12377i) q^{17} +(-2.15285 - 2.08932i) q^{18} +(-2.00583 - 3.86997i) q^{19} +(-0.706161 - 1.22311i) q^{20} +(-0.732981 - 5.26276i) q^{21} +(0.769616 + 1.33301i) q^{22} +4.98816 q^{23} +(1.60512 + 0.650828i) q^{24} +(1.50267 - 2.60271i) q^{25} -1.33016 q^{26} +(-2.09580 - 4.75475i) q^{27} +(1.53389 + 2.65678i) q^{28} +(3.48033 - 6.02810i) q^{29} +(-0.337444 - 2.42283i) q^{30} +(-1.06849 + 1.85068i) q^{31} -1.00000 q^{32} +(0.367766 + 2.64054i) q^{33} +(-1.80351 + 3.12377i) q^{34} +(2.16635 - 3.75222i) q^{35} +(2.15285 + 2.08932i) q^{36} +3.07968 q^{37} +(2.00583 + 3.86997i) q^{38} +(-2.13507 - 0.865705i) q^{39} +(0.706161 + 1.22311i) q^{40} +(-2.94049 - 5.09307i) q^{41} +(0.732981 + 5.26276i) q^{42} +11.0494 q^{43} +(-0.769616 - 1.33301i) q^{44} +(1.03520 - 4.10855i) q^{45} -4.98816 q^{46} +(-3.75078 + 6.49654i) q^{47} +(-1.60512 - 0.650828i) q^{48} +(-1.20565 + 2.08824i) q^{49} +(-1.50267 + 2.60271i) q^{50} +(-4.92789 + 3.84026i) q^{51} +1.33016 q^{52} +(2.17631 + 3.76947i) q^{53} +(2.09580 + 4.75475i) q^{54} +(-1.08695 + 1.88264i) q^{55} +(-1.53389 - 2.65678i) q^{56} +(0.700921 + 7.51723i) q^{57} +(-3.48033 + 6.02810i) q^{58} +(-4.28487 - 7.42161i) q^{59} +(0.337444 + 2.42283i) q^{60} +(4.68857 - 8.12084i) q^{61} +(1.06849 - 1.85068i) q^{62} +(-2.24863 + 8.92442i) q^{63} +1.00000 q^{64} +(-0.939306 - 1.62693i) q^{65} +(-0.367766 - 2.64054i) q^{66} -9.98175 q^{67} +(1.80351 - 3.12377i) q^{68} +(-8.00661 - 3.24643i) q^{69} +(-2.16635 + 3.75222i) q^{70} +(-4.48160 + 7.76235i) q^{71} +(-2.15285 - 2.08932i) q^{72} +(-1.51369 + 2.62179i) q^{73} -3.07968 q^{74} +(-4.10589 + 3.19969i) q^{75} +(-2.00583 - 3.86997i) q^{76} +(2.36102 - 4.08940i) q^{77} +(2.13507 + 0.865705i) q^{78} +8.70478 q^{79} +(-0.706161 - 1.22311i) q^{80} +(0.269490 + 8.99596i) q^{81} +(2.94049 + 5.09307i) q^{82} +(7.47039 + 12.9391i) q^{83} +(-0.732981 - 5.26276i) q^{84} -5.09426 q^{85} -11.0494 q^{86} +(-9.50961 + 7.41076i) q^{87} +(0.769616 + 1.33301i) q^{88} +(3.40283 + 5.89387i) q^{89} +(-1.03520 + 4.10855i) q^{90} +(2.04032 + 3.53394i) q^{91} +4.98816 q^{92} +(2.91953 - 2.27516i) q^{93} +(3.75078 - 6.49654i) q^{94} +(-3.31694 + 5.18616i) q^{95} +(1.60512 + 0.650828i) q^{96} +1.08724 q^{97} +(1.20565 - 2.08824i) q^{98} +(1.12823 - 4.47775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

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