LMFDB - Embedded newform 310.2.h.e.221.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(101,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("310.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.h (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
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			221.2
Root			$-1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	310.221
Dual form			310.2.h.e.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.0389262 + 0.119803i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +0.125968 q^{6} +(0.664894 - 0.483074i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41421 + 1.75403i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.0389262 + 0.119803i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +0.125968 q^{6} +(0.664894 - 0.483074i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41421 + 1.75403i) q^{9} +(0.309017 + 0.951057i) q^{10} +(3.09726 - 2.25029i) q^{11} +(-0.0389262 - 0.119803i) q^{12} +(1.77828 - 5.47298i) q^{13} +(-0.664894 - 0.483074i) q^{14} +(0.0389262 - 0.119803i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.24932 - 1.63423i) q^{17} +(0.922148 - 2.83808i) q^{18} +(-0.796180 - 2.45039i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.0319917 + 0.0984603i) q^{21} +(-3.09726 - 2.25029i) q^{22} +(3.49003 + 2.53566i) q^{23} +(-0.101910 + 0.0740421i) q^{24} +1.00000 q^{25} -5.75464 q^{26} +(-0.609844 + 0.443078i) q^{27} +(-0.253967 + 0.781630i) q^{28} +(2.14615 + 6.60518i) q^{29} -0.125968 q^{30} +(2.71242 - 4.86238i) q^{31} -1.00000 q^{32} +(0.149026 + 0.458656i) q^{33} +(-0.859164 + 2.64423i) q^{34} +(-0.664894 + 0.483074i) q^{35} -2.98413 q^{36} -0.990705 q^{37} +(-2.08443 + 1.51442i) q^{38} +(0.586456 + 0.426085i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(1.01200 + 3.11460i) q^{41} +(0.0837554 - 0.0608518i) q^{42} +(-0.874032 - 2.68999i) q^{43} +(-1.18305 + 3.64105i) q^{44} +(-2.41421 - 1.75403i) q^{45} +(1.33307 - 4.10278i) q^{46} +(1.12800 - 3.47162i) q^{47} +(0.101910 + 0.0740421i) q^{48} +(-1.95440 + 6.01501i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(0.283342 - 0.205860i) q^{51} +(1.77828 + 5.47298i) q^{52} +(-7.90628 - 5.74425i) q^{53} +(0.609844 + 0.443078i) q^{54} +(-3.09726 + 2.25029i) q^{55} +0.821854 q^{56} +0.324555 q^{57} +(5.61870 - 4.08223i) q^{58} +(-3.88635 + 11.9610i) q^{59} +(0.0389262 + 0.119803i) q^{60} -3.67678 q^{61} +(-5.46258 - 1.07711i) q^{62} +2.45252 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.77828 + 5.47298i) q^{65} +(0.390156 - 0.283465i) q^{66} +7.89041 q^{67} +2.78031 q^{68} +(-0.439633 + 0.319412i) q^{69} +(0.664894 + 0.483074i) q^{70} +(10.9969 + 7.98969i) q^{71} +(0.922148 + 2.83808i) q^{72} +(0.863397 - 0.627295i) q^{73} +(0.306145 + 0.942216i) q^{74} +(-0.0389262 + 0.119803i) q^{75} +(2.08443 + 1.51442i) q^{76} +(0.972294 - 2.99241i) q^{77} +(0.224006 - 0.689421i) q^{78} +(-3.76013 - 2.73189i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.73710 + 8.42393i) q^{81} +(2.64944 - 1.92493i) q^{82} +(1.78544 + 5.49502i) q^{83} +(-0.0837554 - 0.0608518i) q^{84} +(2.24932 + 1.63423i) q^{85} +(-2.28825 + 1.66251i) q^{86} -0.874860 q^{87} +3.82843 q^{88} +(-9.96420 + 7.23942i) q^{89} +(-0.922148 + 2.83808i) q^{90} +(-1.46149 - 4.49800i) q^{91} -4.31392 q^{92} +(0.476942 + 0.514230i) q^{93} -3.65028 q^{94} +(0.796180 + 2.45039i) q^{95} +(0.0389262 - 0.119803i) q^{96} +(-4.61803 + 3.35520i) q^{97} +6.32456 q^{98} +11.4245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} - 14 q^{13} - 10 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{18} - 4 q^{19} + 2 q^{20} + 22 q^{21} - 2 q^{22} + 18 q^{23} - 2 q^{24} + 8 q^{25} - 16 q^{26} - 22 q^{27} - 10 q^{28} + 2 q^{29} - 8 q^{30} + 2 q^{31} - 8 q^{32} - 26 q^{33} - 8 q^{34} - 10 q^{35} + 8 q^{36} + 40 q^{37} + 4 q^{38} - 22 q^{39} - 2 q^{40} + 12 q^{41} + 18 q^{42} + 2 q^{44} - 8 q^{45} + 12 q^{46} + 10 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 14 q^{52} - 36 q^{53} + 22 q^{54} - 2 q^{55} - 48 q^{57} - 2 q^{58} + 16 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{62} + 56 q^{63} - 2 q^{64} + 14 q^{65} - 14 q^{66} + 4 q^{67} - 12 q^{68} - 30 q^{69} + 10 q^{70} + 20 q^{71} + 12 q^{72} + 28 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 18 q^{77} - 18 q^{78} - 18 q^{79} + 2 q^{80} - 42 q^{81} - 2 q^{82} + 6 q^{83} - 18 q^{84} + 2 q^{85} - 8 q^{87} + 8 q^{88} - 28 q^{89} - 12 q^{90} - 18 q^{91} - 12 q^{92} + 38 q^{93} + 4 q^{95} - 2 q^{96} - 28 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 - 14 * q^13 - 10 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^18 - 4 * q^19 + 2 * q^20 + 22 * q^21 - 2 * q^22 + 18 * q^23 - 2 * q^24 + 8 * q^25 - 16 * q^26 - 22 * q^27 - 10 * q^28 + 2 * q^29 - 8 * q^30 + 2 * q^31 - 8 * q^32 - 26 * q^33 - 8 * q^34 - 10 * q^35 + 8 * q^36 + 40 * q^37 + 4 * q^38 - 22 * q^39 - 2 * q^40 + 12 * q^41 + 18 * q^42 + 2 * q^44 - 8 * q^45 + 12 * q^46 + 10 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 14 * q^52 - 36 * q^53 + 22 * q^54 - 2 * q^55 - 48 * q^57 - 2 * q^58 + 16 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^62 + 56 * q^63 - 2 * q^64 + 14 * q^65 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 30 * q^69 + 10 * q^70 + 20 * q^71 + 12 * q^72 + 28 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 18 * q^77 - 18 * q^78 - 18 * q^79 + 2 * q^80 - 42 * q^81 - 2 * q^82 + 6 * q^83 - 18 * q^84 + 2 * q^85 - 8 * q^87 + 8 * q^88 - 28 * q^89 - 12 * q^90 - 18 * q^91 - 12 * q^92 + 38 * q^93 + 4 * q^95 - 2 * q^96 - 28 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.0389262	+	0.119803i	−0.0224741	+	0.0691681i	−0.961665	−	0.274229i	$-0.911578\pi$
$3$	−0.0389262	+	0.119803i	−0.0224741	+	0.0691681i	0.939190	+	0.343397i	$0.111578\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.125968			0.0514262
$7$	0.664894	−	0.483074i	0.251306	−	0.182585i	−0.454999	−	0.890492i	$-0.650360\pi$
$7$	0.664894	−	0.483074i	0.251306	−	0.182585i	0.706306	+	0.707907i	$0.250360\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.41421	+	1.75403i	0.804738	+	0.584676i
$10$	0.309017	+	0.951057i	0.0977198	+	0.300750i
$11$	3.09726	−	2.25029i	0.933860	−	0.678489i	−0.0130750	−	0.999915i	$-0.504162\pi$
$11$	3.09726	−	2.25029i	0.933860	−	0.678489i	0.946935	+	0.321426i	$0.104162\pi$
$12$	−0.0389262	−	0.119803i	−0.0112370	−	0.0345840i
$13$	1.77828	−	5.47298i	0.493206	−	1.51793i	−0.326527	−	0.945188i	$-0.605878\pi$
$13$	1.77828	−	5.47298i	0.493206	−	1.51793i	0.819734	−	0.572745i	$-0.194122\pi$
$14$	−0.664894	−	0.483074i	−0.177700	−	0.129107i
$15$	0.0389262	−	0.119803i	0.0100507	−	0.0309329i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.24932	−	1.63423i	−0.545540	−	0.396358i	0.280598	−	0.959825i	$-0.409467\pi$
$17$	−2.24932	−	1.63423i	−0.545540	−	0.396358i	−0.826138	+	0.563467i	$0.809467\pi$
$18$	0.922148	−	2.83808i	0.217352	−	0.668941i
$19$	−0.796180	−	2.45039i	−0.182656	−	0.562158i	0.817244	−	0.576292i	$-0.195501\pi$
$19$	−0.796180	−	2.45039i	−0.182656	−	0.562158i	−0.999900	+	0.0141341i	$0.995501\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	0.0319917	+	0.0984603i	0.00698116	+	0.0214858i
$22$	−3.09726	−	2.25029i	−0.660339	−	0.479764i
$23$	3.49003	+	2.53566i	0.727723	+	0.528721i	0.888842	−	0.458213i	$-0.151510\pi$
$23$	3.49003	+	2.53566i	0.727723	+	0.528721i	−0.161120	+	0.986935i	$0.551510\pi$
$24$	−0.101910	+	0.0740421i	−0.0208023	+	0.0151138i
$25$	1.00000			0.200000
$26$	−5.75464			−1.12858
$27$	−0.609844	+	0.443078i	−0.117365	+	0.0852703i
$28$	−0.253967	+	0.781630i	−0.0479952	+	0.147714i
$29$	2.14615	+	6.60518i	0.398531	+	1.22655i	0.926178	+	0.377088i	$0.123074\pi$
$29$	2.14615	+	6.60518i	0.398531	+	1.22655i	−0.527647	+	0.849464i	$0.676926\pi$
$30$	−0.125968			−0.0229985
$31$	2.71242	−	4.86238i	0.487166	−	0.873310i
$31$	2.71242	−	4.86238i	0.487166	−	0.873310i
$32$	−1.00000			−0.176777
$33$	0.149026	+	0.458656i	0.0259421	+	0.0798417i
$34$	−0.859164	+	2.64423i	−0.147345	+	0.453482i
$35$	−0.664894	+	0.483074i	−0.112388	+	0.0816544i
$36$	−2.98413			−0.497355
$37$	−0.990705			−0.162871			−0.0814354	−	0.996679i	$-0.525950\pi$
$37$	−0.990705			−0.162871			−0.0814354	+	0.996679i	$0.525950\pi$
$38$	−2.08443	+	1.51442i	−0.338138	+	0.245672i
$39$	0.586456	+	0.426085i	0.0939082	+	0.0682283i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	1.01200	+	3.11460i	0.158047	+	0.486419i	0.998457	−	0.0555323i	$-0.0176856\pi$
$41$	1.01200	+	3.11460i	0.158047	+	0.486419i	−0.840410	+	0.541952i	$0.817686\pi$
$42$	0.0837554	−	0.0608518i	0.0129237	−	0.00938964i
$43$	−0.874032	−	2.68999i	−0.133289	−	0.410220i	0.862031	−	0.506855i	$-0.169192\pi$
$43$	−0.874032	−	2.68999i	−0.133289	−	0.410220i	−0.995320	+	0.0966349i	$0.969192\pi$
$44$	−1.18305	+	3.64105i	−0.178351	+	0.548909i
$45$	−2.41421	−	1.75403i	−0.359890	−	0.261475i
$46$	1.33307	−	4.10278i	0.196551	−	0.604922i
$47$	1.12800	−	3.47162i	0.164536	−	0.506388i	−0.834466	−	0.551059i	$-0.814224\pi$
$47$	1.12800	−	3.47162i	0.164536	−	0.506388i	0.999002	+	0.0446707i	$0.0142239\pi$
$48$	0.101910	+	0.0740421i	0.0147095	+	0.0106871i
$49$	−1.95440	+	6.01501i	−0.279199	+	0.859287i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	0.283342	−	0.205860i	0.0396758	−	0.0288262i
$52$	1.77828	+	5.47298i	0.246603	+	0.758966i
$53$	−7.90628	−	5.74425i	−1.08601	−	0.789033i	−0.107290	−	0.994228i	$-0.534217\pi$
$53$	−7.90628	−	5.74425i	−1.08601	−	0.789033i	−0.978721	+	0.205195i	$0.934217\pi$
$54$	0.609844	+	0.443078i	0.0829893	+	0.0602952i
$55$	−3.09726	+	2.25029i	−0.417635	+	0.303429i
$56$	0.821854			0.109825
$57$	0.324555			0.0429884
$58$	5.61870	−	4.08223i	0.737772	−	0.536023i
$59$	−3.88635	+	11.9610i	−0.505960	+	1.55718i	0.293192	+	0.956054i	$0.405283\pi$
$59$	−3.88635	+	11.9610i	−0.505960	+	1.55718i	−0.799151	+	0.601130i	$0.794717\pi$
$60$	0.0389262	+	0.119803i	0.00502536	+	0.0154665i
$61$	−3.67678			−0.470764			−0.235382	−	0.971903i	$-0.575634\pi$
$61$	−3.67678			−0.470764			−0.235382	+	0.971903i	$0.575634\pi$
$62$	−5.46258	−	1.07711i	−0.693749	−	0.136793i
$63$	2.45252			0.308989
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.77828	+	5.47298i	−0.220569	+	0.678840i
$66$	0.390156	−	0.283465i	0.0480249	−	0.0348921i
$67$	7.89041			0.963967			0.481984	−	0.876180i	$-0.339916\pi$
$67$	7.89041			0.963967			0.481984	+	0.876180i	$0.339916\pi$
$68$	2.78031			0.337162
$69$	−0.439633	+	0.319412i	−0.0529255	+	0.0384527i
$70$	0.664894	+	0.483074i	0.0794701	+	0.0577384i
$71$	10.9969	+	7.98969i	1.30509	+	0.948202i	0.999992	−	0.00411994i	$-0.00131142\pi$
$71$	10.9969	+	7.98969i	1.30509	+	0.948202i	0.305096	+	0.952322i	$0.401311\pi$
$72$	0.922148	+	2.83808i	0.108676	+	0.334471i
$73$	0.863397	−	0.627295i	0.101053	−	0.0734193i	−0.536111	−	0.844147i	$-0.680107\pi$
$73$	0.863397	−	0.627295i	0.101053	−	0.0734193i	0.637164	+	0.770728i	$0.280107\pi$
$74$	0.306145	+	0.942216i	0.0355886	+	0.109530i
$75$	−0.0389262	+	0.119803i	−0.00449481	+	0.0138336i
$76$	2.08443	+	1.51442i	0.239100	+	0.173716i
$77$	0.972294	−	2.99241i	0.110803	−	0.341017i
$78$	0.224006	−	0.689421i	0.0253637	−	0.0780615i
$79$	−3.76013	−	2.73189i	−0.423047	−	0.307362i	0.355816	−	0.934556i	$-0.384203\pi$
$79$	−3.76013	−	2.73189i	−0.423047	−	0.307362i	−0.778863	+	0.627194i	$0.784203\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	2.73710	+	8.42393i	0.304122	+	0.935992i
$82$	2.64944	−	1.92493i	0.292582	−	0.212573i
$83$	1.78544	+	5.49502i	0.195977	+	0.603156i	0.999964	+	0.00850867i	$0.00270843\pi$
$83$	1.78544	+	5.49502i	0.195977	+	0.603156i	−0.803986	+	0.594648i	$0.797292\pi$
$84$	−0.0837554	−	0.0608518i	−0.00913846	−	0.00663948i
$85$	2.24932	+	1.63423i	0.243973	+	0.177257i
$86$	−2.28825	+	1.66251i	−0.246748	+	0.179273i
$87$	−0.874860			−0.0937948
$88$	3.82843			0.408112
$89$	−9.96420	+	7.23942i	−1.05620	+	0.767377i	−0.973382	−	0.229188i	$-0.926393\pi$
$89$	−9.96420	+	7.23942i	−1.05620	+	0.767377i	−0.0828211	+	0.996564i	$0.526393\pi$
$90$	−0.922148	+	2.83808i	−0.0972029	+	0.299160i
$91$	−1.46149	−	4.49800i	−0.153206	−	0.471518i
$92$	−4.31392			−0.449757
$93$	0.476942	+	0.514230i	0.0494565	+	0.0533231i
$94$	−3.65028			−0.376498
$95$	0.796180	+	2.45039i	0.0816863	+	0.251405i
$96$	0.0389262	−	0.119803i	0.00397289	−	0.0122273i
$97$	−4.61803	+	3.35520i	−0.468890	+	0.340669i	−0.797009	−	0.603968i	$-0.793586\pi$
$97$	−4.61803	+	3.35520i	−0.468890	+	0.340669i	0.328118	+	0.944637i	$0.393586\pi$
$98$	6.32456			0.638877
$99$	11.4245			1.14821
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	−14.8283	−	10.7734i	−1.47547	−	1.07199i	−0.978982	−	0.203945i	$-0.934624\pi$
$101$	−14.8283	−	10.7734i	−1.47547	−	1.07199i	−0.496486	−	0.868045i	$-0.665376\pi$
$102$	−0.283342	−	0.205860i	−0.0280551	−	0.0203832i
$103$	−4.06450	−	12.5092i	−0.400487	−	1.23257i	−0.924606	−	0.380926i	$-0.875605\pi$
$103$	−4.06450	−	12.5092i	−0.400487	−	1.23257i	0.524119	−	0.851645i	$-0.324395\pi$
$104$	4.65560	−	3.38249i	0.456519	−	0.331680i
$105$	−0.0319917	−	0.0984603i	−0.00312207	−	0.00960874i
$106$	−3.01993	+	9.29439i	−0.293322	+	0.902751i
$107$	−1.73743	−	1.26232i	−0.167964	−	0.122033i	0.500628	−	0.865663i	$-0.333103\pi$
$107$	−1.73743	−	1.26232i	−0.167964	−	0.122033i	−0.668592	+	0.743630i	$0.733103\pi$
$108$	0.232940	−	0.716915i	0.0224146	−	0.0689852i
$109$	−0.470039	+	1.44663i	−0.0450216	+	0.138562i	−0.971041	−	0.238915i	$-0.923208\pi$
$109$	−0.470039	+	1.44663i	−0.0450216	+	0.138562i	0.926019	+	0.377477i	$0.123208\pi$
$110$	3.09726	+	2.25029i	0.295312	+	0.214557i
$111$	0.0385644	−	0.118689i	0.00366037	−	0.0112655i
$112$	−0.253967	−	0.781630i	−0.0239976	−	0.0738571i
$113$	−12.0055	+	8.72248i	−1.12938	+	0.820542i	−0.985604	−	0.169068i	$-0.945924\pi$
$113$	−12.0055	+	8.72248i	−1.12938	+	0.820542i	−0.143775	+	0.989610i	$0.545924\pi$
$114$	−0.100293	−	0.308670i	−0.00939331	−	0.0289096i
$115$	−3.49003	−	2.53566i	−0.325447	−	0.236451i
$116$	−5.61870	−	4.08223i	−0.521684	−	0.379025i
$117$	13.8929	−	10.0938i	1.28440	−	0.933172i
$118$	12.5765			1.15776
$119$	−2.28501			−0.209467
$120$	0.101910	−	0.0740421i	0.00930309	−	0.00675909i
$121$	1.13003	−	3.47788i	0.102730	−	0.316170i
$122$	1.13619	+	3.49683i	0.102866	+	0.316588i
$123$	−0.412531			−0.0371967
$124$	0.663639	+	5.52807i	0.0595965	+	0.496436i
$125$	−1.00000			−0.0894427
$126$	−0.757871	−	2.33249i	−0.0675165	−	0.207794i
$127$	−0.364067	+	1.12048i	−0.0323057	+	0.0994268i	−0.965909	−	0.258881i	$-0.916646\pi$
$127$	−0.364067	+	1.12048i	−0.0323057	+	0.0994268i	0.933603	+	0.358308i	$0.116646\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	0.356291			0.0313697
$130$	5.75464			0.504715
$131$	11.3448	−	8.24248i	0.991200	−	0.720149i	0.0310167	−	0.999519i	$-0.490125\pi$
$131$	11.3448	−	8.24248i	0.991200	−	0.720149i	0.960184	+	0.279370i	$0.0901255\pi$
$132$	−0.390156	−	0.283465i	−0.0339587	−	0.0246724i
$133$	−1.71309	−	1.24464i	−0.148544	−	0.107924i
$134$	−2.43827	−	7.50423i	−0.210635	−	0.648267i
$135$	0.609844	−	0.443078i	0.0524870	−	0.0381341i
$136$	−0.859164	−	2.64423i	−0.0736727	−	0.226741i
$137$	−5.56073	+	17.1142i	−0.475085	+	1.46216i	0.370758	+	0.928730i	$0.379098\pi$
$137$	−5.56073	+	17.1142i	−0.475085	+	1.46216i	−0.845843	+	0.533432i	$0.820902\pi$
$138$	0.439633	+	0.319412i	0.0374240	+	0.0271901i
$139$	2.80850	−	8.64367i	0.238214	−	0.733146i	−0.758465	−	0.651713i	$-0.774050\pi$
$139$	2.80850	−	8.64367i	0.238214	−	0.733146i	0.996679	−	0.0814326i	$-0.0259495\pi$
$140$	0.253967	−	0.781630i	0.0214641	−	0.0660598i
$141$	0.372001	+	0.270275i	0.0313281	+	0.0227612i
$142$	4.20043	−	12.9276i	0.352492	−	1.08486i
$143$	−6.80802	−	20.9529i	−0.569315	−	1.75217i
$144$	2.41421	−	1.75403i	0.201184	−	0.146169i
$145$	−2.14615	−	6.60518i	−0.178228	−	0.548531i
$146$	−0.863397	−	0.627295i	−0.0714553	−	0.0519153i
$147$	−0.644537	−	0.468283i	−0.0531605	−	0.0386234i
$148$	0.801497	−	0.582322i	0.0658826	−	0.0478665i
$149$	−7.33364			−0.600795			−0.300398	−	0.953814i	$-0.597119\pi$
$149$	−7.33364			−0.600795			−0.300398	+	0.953814i	$0.597119\pi$
$150$	0.125968			0.0102852
$151$	−0.172243	+	0.125142i	−0.0140169	+	0.0101839i	−0.594772	−	0.803895i	$-0.702758\pi$
$151$	−0.172243	+	0.125142i	−0.0140169	+	0.0101839i	0.580755	+	0.814079i	$0.302758\pi$
$152$	0.796180	−	2.45039i	0.0645787	−	0.198753i
$153$	−2.56386	−	7.89074i	−0.207276	−	0.637929i
$154$	−3.14641			−0.253545
$155$	−2.71242	+	4.86238i	−0.217867	+	0.390556i
$156$	−0.724900			−0.0580384
$157$	3.44724	+	10.6095i	0.275119	+	0.846731i	0.989188	+	0.146655i	$0.0468506\pi$
$157$	3.44724	+	10.6095i	0.275119	+	0.846731i	−0.714068	+	0.700076i	$0.753149\pi$
$158$	−1.43624	+	4.42029i	−0.114261	+	0.351660i
$159$	0.995938	−	0.723591i	0.0789830	−	0.0573845i
$160$	1.00000			0.0790569
$161$	3.54541			0.279418
$162$	7.16582	−	5.20627i	0.563000	−	0.409043i
$163$	−9.40247	−	6.83130i	−0.736459	−	0.535068i	0.155141	−	0.987892i	$-0.450417\pi$
$163$	−9.40247	−	6.83130i	−0.736459	−	0.535068i	−0.891600	+	0.452824i	$0.850417\pi$
$164$	−2.64944	−	1.92493i	−0.206887	−	0.150312i
$165$	−0.149026	−	0.458656i	−0.0116017	−	0.0357063i
$166$	4.67434	−	3.39611i	0.362799	−	0.263589i
$167$	1.90983	+	5.87785i	0.147787	+	0.454842i	0.997359	−	0.0726311i	$-0.0231396\pi$
$167$	1.90983	+	5.87785i	0.147787	+	0.454842i	−0.849572	+	0.527473i	$0.823140\pi$
$168$	−0.0319917	+	0.0984603i	−0.00246821	+	0.00759638i
$169$	−16.2741	−	11.8238i	−1.25185	−	0.909523i
$170$	0.859164	−	2.64423i	0.0658948	−	0.202803i
$171$	2.37591	−	7.31228i	0.181690	−	0.559184i
$172$	2.28825	+	1.66251i	0.174477	+	0.126765i
$173$	−0.403927	+	1.24316i	−0.0307100	+	0.0945157i	−0.965237	−	0.261377i	$-0.915823\pi$
$173$	−0.403927	+	1.24316i	−0.0307100	+	0.0945157i	0.934527	+	0.355893i	$0.115823\pi$
$174$	0.270347	+	0.832041i	0.0204949	+	0.0630769i
$175$	0.664894	−	0.483074i	0.0502613	−	0.0365170i
$176$	−1.18305	−	3.64105i	−0.0891757	−	0.274455i
$177$	−1.28167	−	0.931190i	−0.0963364	−	0.0699925i
$178$	9.96420	+	7.23942i	0.746849	+	0.542617i
$179$	15.9964	−	11.6221i	1.19563	−	0.868677i	0.201783	−	0.979430i	$-0.435326\pi$
$179$	15.9964	−	11.6221i	1.19563	−	0.868677i	0.993848	+	0.110754i	$0.0353265\pi$
$180$	2.98413			0.222424
$181$	25.5017			1.89552			0.947762	−	0.318979i	$-0.103340\pi$
$181$	25.5017			1.89552			0.947762	+	0.318979i	$0.103340\pi$
$182$	−3.82622	+	2.77991i	−0.283619	+	0.206061i
$183$	0.143123	−	0.440488i	0.0105800	−	0.0325618i
$184$	1.33307	+	4.10278i	0.0982756	+	0.302461i
$185$	0.990705			0.0728381
$186$	0.341679	−	0.612504i	0.0250531	−	0.0449110i
$187$	−10.6442			−0.778382
$188$	1.12800	+	3.47162i	0.0822678	+	0.253194i
$189$	−0.191443	+	0.589200i	−0.0139254	+	0.0428580i
$190$	2.08443	−	1.51442i	0.151220	−	0.109868i
$191$	−18.6025			−1.34603			−0.673014	−	0.739630i	$-0.735000\pi$
$191$	−18.6025			−1.34603			−0.673014	+	0.739630i	$0.735000\pi$
$192$	−0.125968			−0.00909095
$193$	−16.6600	+	12.1042i	−1.19921	+	0.871278i	−0.994207	−	0.107483i	$-0.965721\pi$
$193$	−16.6600	+	12.1042i	−1.19921	+	0.871278i	−0.205005	+	0.978761i	$0.565721\pi$
$194$	4.61803	+	3.35520i	0.331556	+	0.240889i
$195$	−0.586456	−	0.426085i	−0.0419970	−	0.0305126i
$196$	−1.95440	−	6.01501i	−0.139600	−	0.429644i
$197$	22.4067	−	16.2794i	1.59641	−	1.15986i	0.702431	−	0.711752i	$-0.252098\pi$
$197$	22.4067	−	16.2794i	1.59641	−	1.15986i	0.893980	−	0.448108i	$-0.147902\pi$
$198$	−3.53037	−	10.8654i	−0.250893	−	0.772169i
$199$	−0.563918	+	1.73556i	−0.0399751	+	0.123031i	−0.969053	−	0.246855i	$-0.920603\pi$
$199$	−0.563918	+	1.73556i	−0.0399751	+	0.123031i	0.929077	+	0.369885i	$0.120603\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	−0.307144	+	0.945292i	−0.0216643	+	0.0666758i
$202$	−5.66389	+	17.4317i	−0.398510	+	1.22649i
$203$	4.61776	+	3.35500i	0.324103	+	0.235475i
$204$	−0.108227	+	0.333089i	−0.00757741	+	0.0233209i
$205$	−1.01200	−	3.11460i	−0.0706809	−	0.217533i
$206$	−10.6410	+	7.73113i	−0.741393	+	0.538653i
$207$	3.97807	+	12.2432i	0.276495	+	0.850964i
$208$	−4.65560	−	3.38249i	−0.322808	−	0.234534i
$209$	−7.98007	−	5.79786i	−0.551993	−	0.401046i
$210$	−0.0837554	+	0.0608518i	−0.00577967	+	0.00419918i
$211$	16.2918			1.12157			0.560786	−	0.827961i	$-0.310499\pi$
$211$	16.2918			1.12157			0.560786	+	0.827961i	$0.310499\pi$
$212$	9.77270			0.671192
$213$	−1.38525	+	1.00644i	−0.0949159	+	0.0689605i
$214$	−0.663639	+	2.04247i	−0.0453654	+	0.139620i
$215$	0.874032	+	2.68999i	0.0596085	+	0.183456i
$216$	−0.753809			−0.0512902
$217$	−0.545415	−	4.54327i	−0.0370252	−	0.308417i
$218$	1.52108			0.103020
$219$	0.0415428	+	0.127855i	0.00280720	+	0.00863967i
$220$	1.18305	−	3.64105i	0.0797612	−	0.245480i
$221$	−12.9440	+	9.40438i	−0.870709	+	0.632607i
$222$	−0.124797			−0.00837583
$223$	22.5140			1.50765			0.753824	−	0.657077i	$-0.228207\pi$
$223$	22.5140			1.50765			0.753824	+	0.657077i	$0.228207\pi$
$224$	−0.664894	+	0.483074i	−0.0444251	+	0.0322767i
$225$	2.41421	+	1.75403i	0.160948	+	0.116935i
$226$	12.0055	+	8.72248i	0.798592	+	0.580211i
$227$	−2.10755	−	6.48637i	−0.139883	−	0.430515i	0.856435	−	0.516256i	$-0.172675\pi$
$227$	−2.10755	−	6.48637i	−0.139883	−	0.430515i	−0.996318	+	0.0857401i	$0.972675\pi$
$228$	−0.262571	+	0.190769i	−0.0173892	+	0.0126340i
$229$	3.40174	+	10.4695i	0.224793	+	0.691842i	0.998313	+	0.0580696i	$0.0184945\pi$
$229$	3.40174	+	10.4695i	0.224793	+	0.691842i	−0.773519	+	0.633773i	$0.781505\pi$
$230$	−1.33307	+	4.10278i	−0.0879003	+	0.270529i
$231$	0.320651	+	0.232967i	0.0210973	+	0.0153281i
$232$	−2.14615	+	6.60518i	−0.140902	+	0.433651i
$233$	−4.05369	+	12.4760i	−0.265566	+	0.817328i	0.725997	+	0.687698i	$0.241379\pi$
$233$	−4.05369	+	12.4760i	−0.265566	+	0.817328i	−0.991562	+	0.129630i	$0.958621\pi$
$234$	−13.8929	−	10.0938i	−0.908209	−	0.659852i
$235$	−1.12800	+	3.47162i	−0.0735825	+	0.226464i
$236$	−3.88635	−	11.9610i	−0.252980	−	0.778592i
$237$	0.473655	−	0.344131i	0.0307672	−	0.0223537i
$238$	0.706107	+	2.17317i	0.0457701	+	0.140866i
$239$	−0.664723	−	0.482949i	−0.0429973	−	0.0312394i	0.566079	−	0.824351i	$-0.308460\pi$
$239$	−0.664723	−	0.482949i	−0.0429973	−	0.0312394i	−0.609076	+	0.793112i	$0.708460\pi$
$240$	−0.101910	−	0.0740421i	−0.00657828	−	0.00477940i
$241$	9.20987	−	6.69136i	0.593260	−	0.431029i	−0.250220	−	0.968189i	$-0.580503\pi$
$241$	9.20987	−	6.69136i	0.593260	−	0.431029i	0.843480	+	0.537160i	$0.180503\pi$
$242$	−3.65685			−0.235071
$243$	−3.37718			−0.216646
$244$	2.97458	−	2.16116i	0.190428	−	0.138354i
$245$	1.95440	−	6.01501i	0.124862	−	0.384285i
$246$	0.127479	+	0.392340i	0.00812777	+	0.0250147i
$247$	−14.8268			−0.943405
$248$	5.05243	−	2.33943i	0.320830	−	0.148554i
$249$	−0.727818			−0.0461236
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−7.37048	+	22.6840i	−0.465221	+	1.43180i	0.393484	+	0.919331i	$0.371270\pi$
$251$	−7.37048	+	22.6840i	−0.465221	+	1.43180i	−0.858705	+	0.512471i	$0.828730\pi$
$252$	−1.98413	+	1.44156i	−0.124989	+	0.0908095i
$253$	16.5155			1.03832
$254$	1.17815			0.0739234
$255$	−0.283342	+	0.205860i	−0.0177436	+	0.0128915i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.4158	+	8.29409i	0.712100	+	0.517371i	0.883850	−	0.467770i	$-0.154942\pi$
$257$	11.4158	+	8.29409i	0.712100	+	0.517371i	−0.171750	+	0.985140i	$0.554942\pi$
$258$	−0.110100	−	0.338853i	−0.00685453	−	0.0210961i
$259$	−0.658714	+	0.478584i	−0.0409305	+	0.0297377i
$260$	−1.77828	−	5.47298i	−0.110284	−	0.339420i
$261$	−6.40441	+	19.7107i	−0.396423	+	1.22006i
$262$	−11.3448	−	8.24248i	−0.700885	−	0.509222i
$263$	−9.60187	+	29.5515i	−0.592077	+	1.82222i	−0.0233060	+	0.999728i	$0.507419\pi$
$263$	−9.60187	+	29.5515i	−0.592077	+	1.82222i	−0.568771	+	0.822496i	$0.692581\pi$
$264$	−0.149026	+	0.458656i	−0.00917193	+	0.0282283i
$265$	7.90628	+	5.74425i	0.485679	+	0.352866i
$266$	−0.654344	+	2.01386i	−0.0401204	+	0.123478i
$267$	−0.479432	−	1.47554i	−0.0293408	−	0.0903016i
$268$	−6.38348	+	4.63787i	−0.389933	+	0.283303i
$269$	−4.22391	−	12.9999i	−0.257536	−	0.792615i	−0.993319	−	0.115398i	$-0.963186\pi$
$269$	−4.22391	−	12.9999i	−0.257536	−	0.792615i	0.735783	−	0.677217i	$-0.236814\pi$
$270$	−0.609844	−	0.443078i	−0.0371139	−	0.0269649i
$271$	8.40831	+	6.10900i	0.510768	+	0.371095i	0.813115	−	0.582103i	$-0.197770\pi$
$271$	8.40831	+	6.10900i	0.510768	+	0.371095i	−0.302347	+	0.953198i	$0.597770\pi$
$272$	−2.24932	+	1.63423i	−0.136385	+	0.0990895i
$273$	0.595762			0.0360572
$274$	17.9949			1.08711
$275$	3.09726	−	2.25029i	0.186772	−	0.135698i
$276$	0.167925	−	0.516819i	0.0101079	−	0.0311089i
$277$	−5.19375	−	15.9847i	−0.312062	−	0.960429i	−0.976947	−	0.213483i	$-0.931519\pi$
$277$	−5.19375	−	15.9847i	−0.312062	−	0.960429i	0.664885	−	0.746946i	$-0.268481\pi$
$278$	−9.08849			−0.545091
$279$	15.0771	−	6.98116i	0.902644	−	0.417951i
$280$	−0.821854			−0.0491152
$281$	−0.656664	−	2.02100i	−0.0391733	−	0.120563i	0.929558	−	0.368677i	$-0.120189\pi$
$281$	−0.656664	−	2.02100i	−0.0391733	−	0.120563i	−0.968731	+	0.248114i	$0.920189\pi$
$282$	0.142092	−	0.437313i	0.00846144	−	0.0260416i
$283$	−11.3221	+	8.22599i	−0.673030	+	0.488985i	−0.871038	−	0.491216i	$-0.836553\pi$
$283$	−11.3221	+	8.22599i	−0.673030	+	0.488985i	0.198008	+	0.980200i	$0.436553\pi$
$284$	−13.5929			−0.806588
$285$	−0.324555			−0.0192250
$286$	−17.8236	+	12.9496i	−1.05393	+	0.765727i
$287$	2.17745	+	1.58201i	0.128531	+	0.0933833i
$288$	−2.41421	−	1.75403i	−0.142259	−	0.103357i
$289$	−2.86455	−	8.81617i	−0.168503	−	0.518598i
$290$	−5.61870	+	4.08223i	−0.329942	+	0.239717i
$291$	−0.222199	−	0.683858i	−0.0130255	−	0.0400885i
$292$	−0.329788	+	1.01498i	−0.0192994	+	0.0593975i
$293$	−1.20508	−	0.875539i	−0.0704013	−	0.0511495i	0.552028	−	0.833826i	$-0.313854\pi$
$293$	−1.20508	−	0.875539i	−0.0704013	−	0.0511495i	−0.622429	+	0.782676i	$0.713854\pi$
$294$	−0.246191	+	0.757698i	−0.0143582	+	0.0441899i
$295$	3.88635	−	11.9610i	0.226272	−	0.696394i
$296$	−0.801497	−	0.582322i	−0.0465861	−	0.0338468i
$297$	−0.891793	+	2.74466i	−0.0517471	+	0.159261i
$298$	2.26622	+	6.97470i	0.131279	+	0.404034i
$299$	20.0839	−	14.5918i	1.16148	−	0.843865i
$300$	−0.0389262	−	0.119803i	−0.00224741	−	0.00691681i
$301$	−1.88060	−	1.36634i	−0.108396	−	0.0787545i
$302$	0.172243	+	0.125142i	0.00991145	+	0.00720109i
$303$	1.86789	−	1.35710i	0.107307	−	0.0779633i
$304$	−2.57649			−0.147772
$305$	3.67678			0.210532
$306$	−6.71227	+	4.87675i	−0.383715	+	0.278785i
$307$	−9.52734	+	29.3221i	−0.543754	+	1.67350i	0.180181	+	0.983633i	$0.442332\pi$
$307$	−9.52734	+	29.3221i	−0.543754	+	1.67350i	−0.723935	+	0.689869i	$0.757668\pi$
$308$	0.972294	+	2.99241i	0.0554016	+	0.170509i
$309$	1.65685			0.0942551
$310$	5.46258	+	1.07711i	0.310254	+	0.0611757i
$311$	−19.6946			−1.11678			−0.558390	−	0.829578i	$-0.688581\pi$
$311$	−19.6946			−1.11678			−0.558390	+	0.829578i	$0.688581\pi$
$312$	0.224006	+	0.689421i	0.0126819	+	0.0390308i
$313$	−7.02302	+	21.6146i	−0.396964	+	1.22173i	0.530457	+	0.847712i	$0.322020\pi$
$313$	−7.02302	+	21.6146i	−0.396964	+	1.22173i	−0.927421	+	0.374019i	$0.877980\pi$
$314$	9.02498	−	6.55703i	0.509309	−	0.370035i
$315$	−2.45252			−0.138184
$316$	4.64777			0.261458
$317$	2.13171	−	1.54878i	0.119729	−	0.0869881i	−0.526309	−	0.850293i	$-0.676425\pi$
$317$	2.13171	−	1.54878i	0.119729	−	0.0869881i	0.646038	+	0.763305i	$0.276425\pi$
$318$	−0.995938	−	0.723591i	−0.0558494	−	0.0405770i
$319$	21.5108	+	15.6285i	1.20437	+	0.875029i
$320$	−0.309017	−	0.951057i	−0.0172746	−	0.0531657i
$321$	0.218860	−	0.159011i	0.0122156	−	0.00887515i
$322$	−1.09559	−	3.37189i	−0.0610550	−	0.187908i
$323$	−2.21363	+	6.81284i	−0.123170	+	0.379077i
$324$	−7.16582	−	5.20627i	−0.398101	−	0.289237i
$325$	1.77828	−	5.47298i	0.0986413	−	0.303587i
$326$	−3.59143	+	11.0533i	−0.198911	+	0.612184i
$327$	−0.155014	−	0.112624i	−0.00857227	−	0.00622812i
$328$	−1.01200	+	3.11460i	−0.0558781	+	0.171975i
$329$	−0.927051	−	2.85317i	−0.0511100	−	0.157300i
$330$	−0.390156	+	0.283465i	−0.0214774	+	0.0156042i
$331$	1.60280	+	4.93292i	0.0880981	+	0.271138i	0.985394	−	0.170292i	$-0.0544712\pi$
$331$	1.60280	+	4.93292i	0.0880981	+	0.271138i	−0.897296	+	0.441430i	$0.854471\pi$
$332$	−4.67434	−	3.39611i	−0.256538	−	0.186386i
$333$	−2.39177	−	1.73772i	−0.131068	−	0.0952267i
$334$	5.00000	−	3.63271i	0.273588	−	0.198773i
$335$	−7.89041			−0.431099
$336$	0.103527			0.00564788
$337$	9.88390	−	7.18108i	0.538411	−	0.391178i	−0.285084	−	0.958503i	$-0.592021\pi$
$337$	9.88390	−	7.18108i	0.538411	−	0.391178i	0.823494	+	0.567324i	$0.192021\pi$
$338$	−6.21614	+	19.1313i	−0.338113	+	1.04061i
$339$	−0.577649	−	1.77782i	−0.0313736	−	0.0965579i
$340$	−2.78031			−0.150784
$341$	−2.54069	−	21.1638i	−0.137586	−	1.14609i
$342$	−7.68859			−0.415751
$343$	3.38400	+	10.4149i	0.182719	+	0.562350i
$344$	0.874032	−	2.68999i	0.0471246	−	0.145035i
$345$	0.439633	−	0.319412i	0.0236690	−	0.0171966i
$346$	1.30714			0.0702721
$347$	−5.44189			−0.292136			−0.146068	−	0.989275i	$-0.546662\pi$
$347$	−5.44189			−0.292136			−0.146068	+	0.989275i	$0.546662\pi$
$348$	0.707777	−	0.514230i	0.0379408	−	0.0275656i
$349$	−4.62210	−	3.35815i	−0.247415	−	0.179758i	0.457165	−	0.889382i	$-0.348865\pi$
$349$	−4.62210	−	3.35815i	−0.247415	−	0.179758i	−0.704580	+	0.709624i	$0.748865\pi$
$350$	−0.664894	−	0.483074i	−0.0355401	−	0.0258214i
$351$	1.34048	+	4.12558i	0.0715497	+	0.220207i
$352$	−3.09726	+	2.25029i	−0.165085	+	0.119941i
$353$	1.54937	+	4.76847i	0.0824647	+	0.253800i	0.983785	−	0.179354i	$-0.0574007\pi$
$353$	1.54937	+	4.76847i	0.0824647	+	0.253800i	−0.901320	+	0.433154i	$0.857401\pi$
$354$	−0.489555	+	1.50670i	−0.0260196	+	0.0800800i
$355$	−10.9969	−	7.98969i	−0.583653	−	0.424049i
$356$	3.80599	−	11.7136i	0.201717	−	0.620821i
$357$	0.0889469	−	0.273750i	0.00470757	−	0.0144884i
$358$	−15.9964	−	11.6221i	−0.845439	−	0.614247i
$359$	8.90418	−	27.4043i	0.469945	−	1.44634i	−0.382711	−	0.923868i	$-0.625009\pi$
$359$	8.90418	−	27.4043i	0.469945	−	1.44634i	0.852656	−	0.522473i	$-0.174991\pi$
$360$	−0.922148	−	2.83808i	−0.0486014	−	0.149580i
$361$	10.0008	−	7.26602i	0.526359	−	0.382422i
$362$	−7.88045	−	24.2535i	−0.414187	−	1.27474i
$363$	0.372671	+	0.270761i	0.0195601	+	0.0142113i
$364$	3.82622	+	2.77991i	0.200549	+	0.145707i
$365$	−0.863397	+	0.627295i	−0.0451923	+	0.0328341i
$366$	−0.463157			−0.0242096
$367$	−31.1672			−1.62691			−0.813456	−	0.581626i	$-0.802417\pi$
$367$	−31.1672			−1.62691			−0.813456	+	0.581626i	$0.802417\pi$
$368$	3.49003	−	2.53566i	0.181931	−	0.132180i
$369$	−3.01993	+	9.29439i	−0.157211	+	0.483847i
$370$	−0.306145	−	0.942216i	−0.0159157	−	0.0489835i
$371$	−8.03174			−0.416987
$372$	−0.688111	−	0.135681i	−0.0356769	−	0.00703475i
$373$	−17.1923			−0.890184			−0.445092	−	0.895485i	$-0.646829\pi$
$373$	−17.1923			−0.890184			−0.445092	+	0.895485i	$0.646829\pi$
$374$	3.28925	+	10.1233i	0.170083	+	0.523461i
$375$	0.0389262	−	0.119803i	0.00201014	−	0.00618658i
$376$	2.95314	−	2.14558i	0.152297	−	0.110650i
$377$	39.9665			2.05838
$378$	0.619521			0.0318647
$379$	−23.9620	+	17.4094i	−1.23085	+	0.894262i	−0.996953	−	0.0780005i	$-0.975146\pi$
$379$	−23.9620	+	17.4094i	−1.23085	+	0.894262i	−0.233893	+	0.972262i	$0.575146\pi$
$380$	−2.08443	−	1.51442i	−0.106929	−	0.0776883i
$381$	−0.120065	−	0.0872324i	−0.00615112	−	0.00446905i
$382$	5.74848	+	17.6920i	0.294118	+	0.905201i
$383$	24.4977	−	17.7986i	1.25177	−	0.909466i	0.253450	−	0.967349i	$-0.418435\pi$
$383$	24.4977	−	17.7986i	1.25177	−	0.909466i	0.998323	+	0.0578821i	$0.0184348\pi$
$384$	0.0389262	+	0.119803i	0.00198645	+	0.00611365i
$385$	−0.972294	+	2.99241i	−0.0495527	+	0.152508i
$386$	16.6600	+	12.1042i	0.847971	+	0.616087i
$387$	2.60823	−	8.02730i	0.132584	−	0.408050i
$388$	1.76393	−	5.42882i	0.0895501	−	0.275607i
$389$	23.1611	+	16.8275i	1.17431	+	0.853189i	0.991519	−	0.129963i	$-0.0414857\pi$
$389$	23.1611	+	16.8275i	1.17431	+	0.853189i	0.182794	+	0.983151i	$0.441486\pi$
$390$	−0.224006	+	0.689421i	−0.0113430	+	0.0349102i
$391$	−3.70636	−	11.4070i	−0.187439	−	0.576877i
$392$	−5.11667	+	3.71748i	−0.258431	+	0.187761i
$393$	0.545861	+	1.67999i	0.0275350	+	0.0847441i
$394$	−22.4067	−	16.2794i	−1.12883	−	0.820145i
$395$	3.76013	+	2.73189i	0.189192	+	0.137456i
$396$	−9.24264	+	6.71517i	−0.464460	+	0.337450i
$397$	2.74128			0.137581			0.0687904	−	0.997631i	$-0.478086\pi$
$397$	2.74128			0.137581			0.0687904	+	0.997631i	$0.478086\pi$
$398$	1.82488			0.0914728
$399$	0.215795	−	0.156784i	0.0108033	−	0.00784903i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	3.52012	+	10.8338i	0.175786	+	0.541015i	0.999669	−	0.0257463i	$-0.00819619\pi$
$401$	3.52012	+	10.8338i	0.175786	+	0.541015i	−0.823882	+	0.566761i	$0.808196\pi$
$402$	0.993939			0.0495732
$403$	−21.7883	−	23.4917i	−1.08535	−	1.17021i
$404$	18.3287			0.911889
$405$	−2.73710	−	8.42393i	−0.136008	−	0.418588i
$406$	1.76383	−	5.42850i	0.0875372	−	0.269412i
$407$	−3.06847	+	2.22938i	−0.152099	+	0.110506i
$408$	0.350230			0.0173390
$409$	13.2219			0.653780			0.326890	−	0.945062i	$-0.393999\pi$
$409$	13.2219			0.653780			0.326890	+	0.945062i	$0.393999\pi$
$410$	−2.64944	+	1.92493i	−0.130847	+	0.0950656i
$411$	−1.83386	−	1.33238i	−0.0904578	−	0.0657215i
$412$	10.6410	+	7.73113i	0.524244	+	0.380885i
$413$	3.19401	+	9.83016i	0.157167	+	0.483711i
$414$	10.4147	−	7.56674i	0.511856	−	0.371885i
$415$	−1.78544	−	5.49502i	−0.0876437	−	0.269740i
$416$	−1.77828	+	5.47298i	−0.0871874	+	0.268335i
$417$	0.926210	+	0.672931i	0.0453567	+	0.0329536i
$418$	−3.04812	+	9.38113i	−0.149088	+	0.458846i
$419$	8.26070	−	25.4238i	0.403562	−	1.24204i	−0.518528	−	0.855060i	$-0.673520\pi$
$419$	8.26070	−	25.4238i	0.403562	−	1.24204i	0.922090	−	0.386975i	$-0.126480\pi$
$420$	0.0837554	+	0.0608518i	0.00408684	+	0.00296927i
$421$	−4.99400	+	15.3699i	−0.243393	+	0.749086i	0.752504	+	0.658588i	$0.228846\pi$
$421$	−4.99400	+	15.3699i	−0.243393	+	0.749086i	−0.995897	+	0.0904979i	$0.971154\pi$
$422$	−5.03444	−	15.4944i	−0.245073	−	0.754256i
$423$	8.81256	−	6.40270i	0.428481	−	0.311310i
$424$	−3.01993	−	9.29439i	−0.146661	−	0.451375i
$425$	−2.24932	−	1.63423i	−0.109108	−	0.0792716i
$426$	1.38525	+	1.00644i	0.0671157	+	0.0487624i
$427$	−2.44467	+	1.77616i	−0.118306	+	0.0859543i
$428$	2.14758			0.103807
$429$	2.77523			0.133989
$430$	2.28825	−	1.66251i	0.110349	−	0.0801732i
$431$	−0.803122	+	2.47176i	−0.0386850	+	0.119060i	−0.968534	−	0.248881i	$-0.919937\pi$
$431$	−0.803122	+	2.47176i	−0.0386850	+	0.119060i	0.929849	+	0.367941i	$0.119937\pi$
$432$	0.232940	+	0.716915i	0.0112073	+	0.0344926i
$433$	9.53399			0.458174			0.229087	−	0.973406i	$-0.426426\pi$
$433$	9.53399			0.458174			0.229087	+	0.973406i	$0.426426\pi$
$434$	−4.15236	+	1.92267i	−0.199320	+	0.0922910i
$435$	0.874860			0.0419463
$436$	−0.470039	−	1.44663i	−0.0225108	−	0.0692811i
$437$	3.43466	−	10.5708i	0.164302	−	0.505669i
$438$	0.108760	−	0.0790190i	0.00519677	−	0.00377568i
$439$	3.86944			0.184678			0.0923392	−	0.995728i	$-0.470566\pi$
$439$	3.86944			0.184678			0.0923392	+	0.995728i	$0.470566\pi$
$440$	−3.82843			−0.182513
$441$	−15.2688	+	11.0935i	−0.727087	+	0.528260i
$442$	12.9440	+	9.40438i	0.615684	+	0.447321i
$443$	29.5545	+	21.4726i	1.40417	+	1.02019i	0.994137	+	0.108124i	$0.0344843\pi$
$443$	29.5545	+	21.4726i	1.40417	+	1.02019i	0.410037	+	0.912069i	$0.365516\pi$
$444$	0.0385644	+	0.118689i	0.00183019	+	0.00563273i
$445$	9.96420	−	7.23942i	0.472348	−	0.343181i
$446$	−6.95720	−	21.4121i	−0.329433	−	1.01389i
$447$	0.285471	−	0.878589i	0.0135023	−	0.0415558i
$448$	0.664894	+	0.483074i	0.0314133	+	0.0228231i
$449$	−3.20840	+	9.87445i	−0.151414	+	0.466004i	−0.997780	−	0.0665977i	$-0.978786\pi$
$449$	−3.20840	+	9.87445i	−0.151414	+	0.466004i	0.846366	+	0.532602i	$0.178786\pi$
$450$	0.922148	−	2.83808i	0.0434705	−	0.133788i
$451$	10.1432	+	7.36946i	0.477624	+	0.347014i
$452$	4.58568	−	14.1133i	0.215692	−	0.663833i
$453$	−0.00828754	−	0.0255064i	−0.000389383	−	0.00119840i
$454$	−5.51763	+	4.00880i	−0.258955	+	0.188142i
$455$	1.46149	+	4.49800i	0.0685156	+	0.210869i
$456$	0.262571	+	0.190769i	0.0122960	+	0.00893357i
$457$	−22.8132	−	16.5748i	−1.06716	−	0.775336i	−0.0917591	−	0.995781i	$-0.529249\pi$
$457$	−22.8132	−	16.5748i	−1.06716	−	0.775336i	−0.975399	+	0.220445i	$0.929249\pi$
$458$	8.90587	−	6.47049i	0.416144	−	0.302346i
$459$	2.09582			0.0978247
$460$	4.31392			0.201138
$461$	19.3657	−	14.0700i	0.901952	−	0.655306i	−0.0370147	−	0.999315i	$-0.511785\pi$
$461$	19.3657	−	14.0700i	0.901952	−	0.655306i	0.938967	+	0.344008i	$0.111785\pi$
$462$	0.122478	−	0.376948i	0.00569819	−	0.0175372i
$463$	4.60096	+	14.1603i	0.213825	+	0.658085i	0.999235	+	0.0391095i	$0.0124521\pi$
$463$	4.60096	+	14.1603i	0.213825	+	0.658085i	−0.785410	+	0.618976i	$0.787548\pi$
$464$	6.94510			0.322418
$465$	−0.476942	−	0.514230i	−0.0221176	−	0.0238468i
$466$	13.1180			0.607680
$467$	2.76493	+	8.50958i	0.127946	+	0.393777i	0.994426	−	0.105434i	$-0.0336233\pi$
$467$	2.76493	+	8.50958i	0.127946	+	0.393777i	−0.866480	+	0.499211i	$0.833623\pi$
$468$	−5.30662	+	16.3321i	−0.245299	+	0.754952i
$469$	5.24629	−	3.81165i	0.242251	−	0.176006i
$470$	3.65028			0.168375
$471$	−1.40523			−0.0647498
$472$	−10.1746	+	7.39228i	−0.468324	+	0.340257i
$473$	−8.76038	−	6.36479i	−0.402803	−	0.292653i
$474$	−0.473655	−	0.344131i	−0.0217557	−	0.0158064i
$475$	−0.796180	−	2.45039i	−0.0365312	−	0.112432i
$476$	1.84861	−	1.34310i	0.0847310	−	0.0615607i
$477$	−9.01187	−	27.7357i	−0.412625	−	1.26993i
$478$	−0.253901	+	0.781428i	−0.0116132	+	0.0357417i
$479$	−15.5734	−	11.3147i	−0.711565	−	0.516982i	0.172113	−	0.985077i	$-0.444940\pi$
$479$	−15.5734	−	11.3147i	−0.711565	−	0.516982i	−0.883678	+	0.468095i	$0.844940\pi$
$480$	−0.0389262	+	0.119803i	−0.00177673	+	0.00546822i
$481$	−1.76175	+	5.42211i	−0.0803289	+	0.247227i
$482$	−9.20987	−	6.69136i	−0.419498	−	0.304783i
$483$	−0.138010	+	0.424750i	−0.00627966	+	0.0193268i
$484$	1.13003	+	3.47788i	0.0513650	+	0.158085i
$485$	4.61803	−	3.35520i	0.209694	−	0.152352i
$486$	1.04361	+	3.21189i	0.0473389	+	0.145694i
$487$	−7.59439	−	5.51765i	−0.344135	−	0.250028i	0.402270	−	0.915521i	$-0.368221\pi$
$487$	−7.59439	−	5.51765i	−0.344135	−	0.250028i	−0.746404	+	0.665493i	$0.768221\pi$
$488$	−2.97458	−	2.16116i	−0.134653	−	0.0978311i
$489$	1.18441	−	0.860524i	0.0535609	−	0.0389143i
$490$	−6.32456			−0.285714
$491$	8.77270			0.395906			0.197953	−	0.980211i	$-0.436571\pi$
$491$	8.77270			0.395906			0.197953	+	0.980211i	$0.436571\pi$
$492$	0.333745	−	0.242480i	0.0150464	−	0.0109318i
$493$	5.96698	−	18.3645i	0.268739	−	0.827094i
$494$	4.58172	+	14.1011i	0.206142	+	0.634438i
$495$	−11.4245			−0.513495
$496$	−3.78621	−	4.08223i	−0.170006	−	0.183297i
$497$	11.1714			0.501104
$498$	0.224908	+	0.692196i	0.0100784	+	0.0310180i
$499$	1.37758	−	4.23976i	0.0616691	−	0.189798i	−0.915476	−	0.402374i	$-0.868185\pi$
$499$	1.37758	−	4.23976i	0.0616691	−	0.189798i	0.977145	+	0.212576i	$0.0681853\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−0.778525			−0.0347819
$502$	23.8514			1.06454
$503$	15.1404	−	11.0001i	0.675077	−	0.490472i	−0.196644	−	0.980475i	$-0.563004\pi$
$503$	15.1404	−	11.0001i	0.675077	−	0.490472i	0.871721	+	0.490003i	$0.163004\pi$
$504$	1.98413	+	1.44156i	0.0883803	+	0.0642120i
$505$	14.8283	+	10.7734i	0.659849	+	0.479409i
$506$	−5.10358	−	15.7072i	−0.226882	−	0.698270i
$507$	2.05001	−	1.48942i	0.0910441	−	0.0661474i
$508$	−0.364067	−	1.12048i	−0.0161529	−	0.0497134i
$509$	6.51774	−	20.0595i	0.288894	−	0.889124i	−0.696311	−	0.717741i	$-0.745176\pi$
$509$	6.51774	−	20.0595i	0.288894	−	0.889124i	0.985204	−	0.171383i	$-0.0548236\pi$
$510$	0.283342	+	0.205860i	0.0125466	+	0.00911564i
$511$	0.271038	−	0.834169i	0.0119900	−	0.0369015i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	1.57126	+	1.14159i	0.0693727	+	0.0504022i
$514$	4.36046	−	13.4201i	0.192332	−	0.591936i
$515$	4.06450	+	12.5092i	0.179103	+	0.551223i
$516$	−0.288246	+	0.209423i	−0.0126893	+	0.00921932i
$517$	−4.31846	−	13.2909i	−0.189926	−	0.584531i
$518$	0.658714	+	0.478584i	0.0289422	+	0.0210278i
$519$	−0.133210	−	0.0967831i	−0.00584729	−	0.00424831i
$520$	−4.65560	+	3.38249i	−0.204162	+	0.148332i
$521$	−8.56875			−0.375404			−0.187702	−	0.982226i	$-0.560104\pi$
$521$	−8.56875			−0.375404			−0.187702	+	0.982226i	$0.560104\pi$
$522$	20.7251			0.907113
$523$	0.972158	−	0.706314i	0.0425095	−	0.0308849i	−0.566328	−	0.824180i	$-0.691636\pi$
$523$	0.972158	−	0.706314i	0.0425095	−	0.0308849i	0.608837	+	0.793295i	$0.291636\pi$
$524$	−4.33333	+	13.3366i	−0.189302	+	0.582613i
$525$	0.0319917	+	0.0984603i	0.00139623	+	0.00429716i
$526$	31.0723			1.35482
$527$	−14.0473	+	6.50433i	−0.611912	+	0.283333i
$528$	0.482259			0.0209876
$529$	−1.35661	−	4.17522i	−0.0589832	−	0.181531i
$530$	3.01993	−	9.29439i	0.131177	−	0.403722i
$531$	−30.3623	+	22.0595i	−1.31761	+	0.957302i
$532$	2.11750			0.0918053
$533$	18.8458			0.816302
$534$	−1.25517	+	0.911934i	−0.0543165	+	0.0394633i
$535$	1.73743	+	1.26232i	0.0751156	+	0.0545747i
$536$	6.38348	+	4.63787i	0.275724	+	0.200325i
$537$	0.769677	+	2.36882i	0.0332140	+	0.102222i
$538$	−11.0583	+	8.03435i	−0.476759	+	0.346385i
$539$	7.48226	+	23.0280i	0.322284	+	0.991887i
$540$	−0.232940	+	0.716915i	−0.0100241	+	0.0308511i
$541$	−14.7114	−	10.6884i	−0.632492	−	0.459532i	0.224771	−	0.974412i	$-0.427837\pi$
$541$	−14.7114	−	10.6884i	−0.632492	−	0.459532i	−0.857263	+	0.514879i	$0.827837\pi$
$542$	3.21169	−	9.88456i	0.137954	−	0.424578i
$543$	−0.992684	+	3.05517i	−0.0426001	+	0.131110i
$544$	2.24932	+	1.63423i	0.0964388	+	0.0700669i
$545$	0.470039	−	1.44663i	0.0201343	−	0.0619669i
$546$	−0.184101	−	0.566603i	−0.00787878	−	0.0242484i
$547$	−13.9813	+	10.1580i	−0.597797	+	0.434325i	−0.845096	−	0.534614i	$-0.820457\pi$
$547$	−13.9813	+	10.1580i	−0.597797	+	0.434325i	0.247299	+	0.968939i	$0.420457\pi$
$548$	−5.56073	−	17.1142i	−0.237543	−	0.731081i
$549$	−8.87654	−	6.44919i	−0.378842	−	0.275245i
$550$	−3.09726	−	2.25029i	−0.132068	−	0.0959528i
$551$	14.4765	−	10.5178i	0.616721	−	0.448074i
$552$	−0.543416			−0.0231293
$553$	−3.81979			−0.162434
$554$	−13.5974	+	9.87910i	−0.577699	+	0.419723i
$555$	−0.0385644	+	0.118689i	−0.00163697	+	0.00503807i
$556$	2.80850	+	8.64367i	0.119107	+	0.366573i
$557$	−38.9338			−1.64968			−0.824839	−	0.565367i	$-0.808734\pi$
$557$	−38.9338			−1.64968			−0.824839	+	0.565367i	$0.808734\pi$
$558$	−11.2986	−	12.1819i	−0.478306	−	0.515701i
$559$	−16.2766			−0.688426
$560$	0.253967	+	0.781630i	0.0107321	+	0.0330299i
$561$	0.414339	−	1.27521i	0.0174934	−	0.0538392i
$562$	−1.71917	+	1.24905i	−0.0725187	+	0.0526880i
$563$	−25.3842			−1.06982			−0.534909	−	0.844910i	$-0.679654\pi$
$563$	−25.3842			−1.06982			−0.534909	+	0.844910i	$0.679654\pi$
$564$	−0.459818			−0.0193619
$565$	12.0055	−	8.72248i	0.505074	−	0.366958i
$566$	11.3221	+	8.22599i	0.475904	+	0.345764i
$567$	5.88926	+	4.27880i	0.247326	+	0.179693i
$568$	4.20043	+	12.9276i	0.176246	+	0.542430i
$569$	12.6317	−	9.17746i	0.529548	−	0.384739i	−0.290641	−	0.956832i	$-0.593868\pi$
$569$	12.6317	−	9.17746i	0.529548	−	0.384739i	0.820189	+	0.572093i	$0.193868\pi$
$570$	0.100293	+	0.308670i	0.00420082	+	0.0129288i
$571$	3.51702	−	10.8243i	0.147183	−	0.452981i	−0.850103	−	0.526617i	$-0.823460\pi$
$571$	3.51702	−	10.8243i	0.147183	−	0.452981i	0.997285	+	0.0736356i	$0.0234602\pi$
$572$	17.8236	+	12.9496i	0.745243	+	0.541451i
$573$	0.724124	−	2.22862i	0.0302507	−	0.0931021i
$574$	0.831713	−	2.55975i	0.0347150	−	0.106842i
$575$	3.49003	+	2.53566i	0.145545	+	0.105744i
$576$	−0.922148	+	2.83808i	−0.0384228	+	0.118253i
$577$	−0.745935	−	2.29575i	−0.0310537	−	0.0955734i	0.934328	−	0.356413i	$-0.116001\pi$
$577$	−0.745935	−	2.29575i	−0.0310537	−	0.0955734i	−0.965382	+	0.260840i	$0.916001\pi$
$578$	−7.49948	+	5.44869i	−0.311937	+	0.226636i
$579$	−0.801603	−	2.46708i	−0.0333135	−	0.102528i
$580$	5.61870	+	4.08223i	0.233304	+	0.169505i
$581$	3.84163	+	2.79110i	0.159378	+	0.115795i
$582$	−0.581724	+	0.422647i	−0.0241132	+	0.0175193i
$583$	−37.4141			−1.54953
$584$	1.06722			0.0441618
$585$	−13.8929	+	10.0938i	−0.574402	+	0.417327i
$586$	−0.460298	+	1.41665i	−0.0190147	+	0.0585213i
$587$	−6.00564	−	18.4835i	−0.247879	−	0.762894i	−0.995150	−	0.0983737i	$-0.968636\pi$
$587$	−6.00564	−	18.4835i	−0.247879	−	0.762894i	0.747270	−	0.664520i	$-0.231364\pi$
$588$	0.796691			0.0328550
$589$	−14.0743	−	2.77516i	−0.579922	−	0.114349i
$590$	−12.5765			−0.517766
$591$	1.07811	+	3.31808i	0.0443475	+	0.136487i
$592$	−0.306145	+	0.942216i	−0.0125825	+	0.0387248i
$593$	−26.2739	+	19.0891i	−1.07894	+	0.783895i	−0.977498	−	0.210946i	$-0.932346\pi$
$593$	−26.2739	+	19.0891i	−1.07894	+	0.783895i	−0.101442	+	0.994841i	$0.532346\pi$
$594$	2.88590			0.118410
$595$	2.28501			0.0936763
$596$	5.93304	−	4.31060i	0.243027	−	0.176569i
$597$	−0.185974	−	0.135118i	−0.00761139	−	0.00553000i
$598$	−20.0839	−	14.5918i	−0.821291	−	0.596703i
$599$	−3.44093	−	10.5901i	−0.140593	−	0.432699i	0.855825	−	0.517265i	$-0.173050\pi$
$599$	−3.44093	−	10.5901i	−0.140593	−	0.432699i	−0.996418	+	0.0845655i	$0.973050\pi$
$600$	−0.101910	+	0.0740421i	−0.00416047	+	0.00302276i
$601$	−4.49852	−	13.8450i	−0.183499	−	0.564750i	0.816421	−	0.577457i	$-0.195955\pi$
$601$	−4.49852	−	13.8450i	−0.183499	−	0.564750i	−0.999919	+	0.0127072i	$0.995955\pi$
$602$	−0.718327	+	2.21078i	−0.0292768	+	0.0901048i
$603$	19.0491	+	13.8400i	0.775741	+	0.563609i
$604$	0.0657909	−	0.202483i	0.00267699	−	0.00823893i
$605$	−1.13003	+	3.47788i	−0.0459423	+	0.141396i
$606$	−1.86789	−	1.35710i	−0.0758777	−	0.0551284i
$607$	−10.8880	+	33.5097i	−0.441928	+	1.36012i	0.443889	+	0.896082i	$0.353598\pi$
$607$	−10.8880	+	33.5097i	−0.441928	+	1.36012i	−0.885817	+	0.464034i	$0.846402\pi$
$608$	0.796180	+	2.45039i	0.0322893	+	0.0993764i
$609$	−0.581689	+	0.422622i	−0.0235712	+	0.0171255i
$610$	−1.13619	−	3.49683i	−0.0460029	−	0.141582i
$611$	−16.9942	−	12.3470i	−0.687514	−	0.499508i
$612$	6.71227	+	4.87675i	0.271327	+	0.197131i
$613$	31.1178	−	22.6084i	1.25684	−	0.913146i	0.258239	−	0.966081i	$-0.416858\pi$
$613$	31.1178	−	22.6084i	1.25684	−	0.913146i	0.998598	+	0.0529351i	$0.0168576\pi$
$614$	30.8311			1.24424
$615$	0.412531			0.0166349
$616$	2.54550	−	1.84941i	0.102561	−	0.0745150i
$617$	−6.75064	+	20.7763i	−0.271771	+	0.836424i	0.718285	+	0.695749i	$0.244927\pi$
$617$	−6.75064	+	20.7763i	−0.271771	+	0.836424i	−0.990056	+	0.140675i	$0.955073\pi$
$618$	−0.511996	−	1.57576i	−0.0205955	−	0.0633864i
$619$	−40.4268			−1.62489			−0.812446	−	0.583037i	$-0.801864\pi$
$619$	−40.4268			−1.62489			−0.812446	+	0.583037i	$0.801864\pi$
$620$	−0.663639	−	5.52807i	−0.0266524	−	0.222013i
$621$	−3.25187			−0.130493
$622$	6.08598	+	18.7307i	0.244025	+	0.751033i
$623$	−3.12797	+	9.62689i	−0.125319	+	0.385693i
$624$	0.586456	−	0.426085i	0.0234770	−	0.0170571i
$625$	1.00000			0.0400000
$626$	22.7270			0.908352
$627$	1.00523	−	0.730345i	0.0401451	−	0.0291672i
$628$	−9.02498	−	6.55703i	−0.360136	−	0.261654i
$629$	2.22841	+	1.61904i	0.0888526	+	0.0645552i
$630$	0.757871	+	2.33249i	0.0301943	+	0.0929285i
$631$	−8.59661	+	6.24580i	−0.342225	+	0.248641i	−0.745600	−	0.666394i	$-0.767837\pi$
$631$	−8.59661	+	6.24580i	−0.342225	+	0.248641i	0.403375	+	0.915035i	$0.367837\pi$
$632$	−1.43624	−	4.42029i	−0.0571306	−	0.175830i
$633$	−0.634178	+	1.95180i	−0.0252063	+	0.0775770i
$634$	−2.13171	−	1.54878i	−0.0846611	−	0.0615099i
$635$	0.364067	−	1.12048i	0.0144476	−	0.0444650i
$636$	−0.380414	+	1.17080i	−0.0150844	+	0.0464250i
$637$	29.4446	+	21.3927i	1.16664	+	0.847612i
$638$	8.21639	−	25.2875i	0.325290	−	1.00114i
$639$	12.5346	+	38.5776i	0.495862	+	1.52611i
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−7.61313	−	23.4308i	−0.300701	−	0.925461i	−0.981247	−	0.192756i	$-0.938257\pi$
$641$	−7.61313	−	23.4308i	−0.300701	−	0.925461i	0.680546	−	0.732705i	$-0.261743\pi$
$642$	−0.218860	−	0.159011i	−0.00863773	−	0.00627568i
$643$	−12.5165	−	9.09374i	−0.493601	−	0.358622i	0.312966	−	0.949764i	$-0.398677\pi$
$643$	−12.5165	−	9.09374i	−0.493601	−	0.358622i	−0.806568	+	0.591142i	$0.798677\pi$
$644$	−2.86830	+	2.08394i	−0.113027	+	0.0821188i
$645$	−0.356291			−0.0140290
$646$	7.16345			0.281842
$647$	11.9369	−	8.67268i	0.469289	−	0.340958i	−0.327875	−	0.944721i	$-0.606333\pi$
$647$	11.9369	−	8.67268i	0.469289	−	0.340958i	0.797164	+	0.603763i	$0.206333\pi$
$648$	−2.73710	+	8.42393i	−0.107523	+	0.330923i
$649$	14.8786	+	45.7916i	0.584036	+	1.79748i
$650$	−5.75464			−0.225715
$651$	0.565527	+	0.111510i	0.0221647	+	0.00437043i
$652$	11.6221			0.455156
$653$	−6.45787	−	19.8753i	−0.252716	−	0.777780i	−0.994271	−	0.106888i	$-0.965911\pi$
$653$	−6.45787	−	19.8753i	−0.252716	−	0.777780i	0.741555	−	0.670892i	$-0.234089\pi$
$654$	−0.0592099	+	0.182229i	−0.00231529	+	0.00712573i
$655$	−11.3448	+	8.24248i	−0.443278	+	0.322061i
$656$	3.27489			0.127863
$657$	3.18472			0.124248
$658$	−2.42705	+	1.76336i	−0.0946163	+	0.0687428i
$659$	−31.2978	−	22.7392i	−1.21919	−	0.885794i	−0.223158	−	0.974782i	$-0.571637\pi$
$659$	−31.2978	−	22.7392i	−1.21919	−	0.885794i	−0.996033	+	0.0889886i	$0.971637\pi$
$660$	0.390156	+	0.283465i	0.0151868	+	0.0110339i
$661$	0.208199	+	0.640770i	0.00809800	+	0.0249231i	0.955024	−	0.296529i	$-0.0958291\pi$
$661$	0.208199	+	0.640770i	0.00809800	+	0.0249231i	−0.946926	+	0.321452i	$0.895829\pi$
$662$	4.19619	−	3.04871i	0.163090	−	0.118492i
$663$	−0.622807	−	1.91680i	−0.0241878	−	0.0744425i
$664$	−1.78544	+	5.49502i	−0.0692885	+	0.213248i
$665$	1.71309	+	1.24464i	0.0664309	+	0.0482649i
$666$	−0.913576	+	2.81170i	−0.0354003	+	0.108951i
$667$	−9.25834	+	28.4942i	−0.358484	+	1.10330i
$668$	−5.00000	−	3.63271i	−0.193456	−	0.140554i
$669$	−0.876384	+	2.69723i	−0.0338830	+	0.104281i
$670$	2.43827	+	7.50423i	0.0941986	+	0.289914i
$671$	−11.3880	+	8.27384i	−0.439628	+	0.319408i
$672$	−0.0319917	−	0.0984603i	−0.00123411	−	0.00379819i
$673$	27.5553	+	20.0201i	1.06218	+	0.771718i	0.974490	−	0.224430i	$-0.0720521\pi$
$673$	27.5553	+	20.0201i	1.06218	+	0.771718i	0.0876880	+	0.996148i	$0.472052\pi$
$674$	−9.88390	−	7.18108i	−0.380714	−	0.276605i
$675$	−0.609844	+	0.443078i	−0.0234729	+	0.0170541i
$676$	20.1158			0.773686
$677$	17.5943			0.676205			0.338103	−	0.941109i	$-0.390215\pi$
$677$	17.5943			0.676205			0.338103	+	0.941109i	$0.390215\pi$
$678$	−1.51230	+	1.09875i	−0.0580797	+	0.0421974i
$679$	−1.44970	+	4.46170i	−0.0556342	+	0.171224i
$680$	0.859164	+	2.64423i	0.0329474	+	0.101402i
$681$	0.859123			0.0329217
$682$	−19.3429	+	8.95632i	−0.740677	+	0.342955i
$683$	43.9669			1.68235			0.841173	−	0.540767i	$-0.181866\pi$
$683$	43.9669			1.68235			0.841173	+	0.540767i	$0.181866\pi$
$684$	2.37591	+	7.31228i	0.0908450	+	0.279592i
$685$	5.56073	−	17.1142i	0.212465	−	0.653899i
$686$	8.85942	−	6.43674i	0.338254	−	0.245756i
$687$	−1.38669			−0.0529054
$688$	−2.82843			−0.107833
$689$	−45.4978	+	33.0561i	−1.73333	+	1.25934i
$690$	−0.439633	−	0.319412i	−0.0167365	−	0.0121598i
$691$	−31.1842	−	22.6566i	−1.18630	−	0.861899i	−0.193433	−	0.981113i	$-0.561962\pi$
$691$	−31.1842	−	22.6566i	−1.18630	−	0.861899i	−0.992868	+	0.119215i	$0.961962\pi$
$692$	−0.403927	−	1.24316i	−0.0153550	−	0.0472579i
$693$	7.59611	−	5.51889i	0.288552	−	0.209645i
$694$	1.68164	+	5.17554i	0.0638340	+	0.196461i
$695$	−2.80850	+	8.64367i	−0.106532	+	0.327873i
$696$	−0.707777	−	0.514230i	−0.0268282	−	0.0194918i
$697$	2.81366	−	8.65957i	0.106575	−	0.328005i
$698$	−1.76548	+	5.43360i	−0.0668245	+	0.205665i
$699$	−1.33686	−	0.971285i	−0.0505647	−	0.0367374i
$700$	−0.253967	+	0.781630i	−0.00959905	+	0.0295428i
$701$	3.68989	+	11.3563i	0.139365	+	0.428922i	0.996243	−	0.0865971i	$-0.0275993\pi$
$701$	3.68989	+	11.3563i	0.139365	+	0.428922i	−0.856878	+	0.515519i	$0.827599\pi$
$702$	3.50943	−	2.54975i	0.132455	−	0.0962342i
$703$	0.788779	+	2.42761i	0.0297494	+	0.0915591i
$704$	3.09726	+	2.25029i	0.116732	+	0.0848111i
$705$	−0.372001	−	0.270275i	−0.0140104	−	0.0101791i
$706$	4.05631	−	2.94708i	0.152661	−	0.110915i
$707$	−15.0636			−0.566524
$708$	1.58423			0.0595392
$709$	−30.7959	+	22.3745i	−1.15656	+	0.840293i	−0.989340	−	0.145625i	$-0.953481\pi$
$709$	−30.7959	+	22.3745i	−1.15656	+	0.840293i	−0.167225	+	0.985919i	$0.553481\pi$
$710$	−4.20043	+	12.9276i	−0.157639	+	0.485164i
$711$	−4.28593	−	13.1907i	−0.160735	−	0.494691i
$712$	−12.3164			−0.461578
$713$	21.7958	−	10.0921i	0.816259	−	0.377952i
$714$	−0.287838			−0.0107721
$715$	6.80802	+	20.9529i	0.254605	+	0.783595i
$716$	−6.11010	+	18.8050i	−0.228345	+	0.702774i
$717$	0.0837338	−	0.0608361i	0.00312709	−	0.00227197i
$718$	−28.8145			−1.07535
$719$	−28.5608			−1.06514			−0.532568	−	0.846387i	$-0.678773\pi$
$719$	−28.5608			−1.06514			−0.532568	+	0.846387i	$0.678773\pi$
$720$	−2.41421	+	1.75403i	−0.0899724	+	0.0653688i
$721$	−8.74534	−	6.35386i	−0.325694	−	0.236630i
$722$	−10.0008	−	7.26602i	−0.372192	−	0.270413i
$723$	0.443137	+	1.36384i	0.0164805	+	0.0507216i
$724$	−20.6313	+	14.9895i	−0.766755	+	0.557080i
$725$	2.14615	+	6.60518i	0.0797062	+	0.245310i
$726$	0.142348	−	0.438101i	0.00528301	−	0.0162594i
$727$	−26.7980	−	19.4699i	−0.993884	−	0.722099i	−0.0331157	−	0.999452i	$-0.510543\pi$
$727$	−26.7980	−	19.4699i	−0.993884	−	0.722099i	−0.960768	+	0.277353i	$0.910543\pi$
$728$	1.46149	−	4.49800i	0.0541663	−	0.166707i
$729$	−8.07984	+	24.8672i	−0.299253	+	0.921007i
$730$	0.863397	+	0.627295i	0.0319558	+	0.0232172i
$731$	−2.43008	+	7.47902i	−0.0898798	+	0.276622i
$732$	0.143123	+	0.440488i	0.00528999	+	0.0162809i
$733$	38.5384	−	27.9998i	1.42345	−	1.03420i	0.432258	−	0.901750i	$-0.357717\pi$
$733$	38.5384	−	27.9998i	1.42345	−	1.03420i	0.991190	−	0.132446i	$-0.0422830\pi$
$734$	9.63118	+	29.6417i	0.355493	+	1.09410i
$735$	0.644537	+	0.468283i	0.0237741	+	0.0172729i
$736$	−3.49003	−	2.53566i	−0.128644	−	0.0934656i
$737$	24.4387	−	17.7557i	0.900210	−	0.654041i
$738$	9.77270			0.359738
$739$	44.5005			1.63698			0.818488	−	0.574524i	$-0.194813\pi$
$739$	44.5005			1.63698			0.818488	+	0.574524i	$0.194813\pi$
$740$	−0.801497	+	0.582322i	−0.0294636	+	0.0214066i
$741$	0.577150	−	1.77629i	0.0212022	−	0.0652535i
$742$	2.48194	+	7.63863i	0.0911150	+	0.280423i
$743$	27.7385			1.01763			0.508813	−	0.860877i	$-0.330085\pi$
$743$	27.7385			1.01763			0.508813	+	0.860877i	$0.330085\pi$
$744$	0.0835972	+	0.696360i	0.00306482	+	0.0255298i
$745$	7.33364			0.268684
$746$	5.31272	+	16.3509i	0.194512	+	0.598648i
$747$	−5.32798	+	16.3979i	−0.194941	+	0.599966i
$748$	8.61136	−	6.25652i	0.314862	−	0.228761i
$749$	−1.76500			−0.0644916
$750$	−0.125968			−0.00459970
$751$	10.0049	−	7.26900i	0.365085	−	0.265249i	−0.390085	−	0.920779i	$-0.627554\pi$
$751$	10.0049	−	7.26900i	0.365085	−	0.265249i	0.755170	+	0.655529i	$0.227554\pi$
$752$	−2.95314	−	2.14558i	−0.107690	−	0.0782413i
$753$	−2.43070	−	1.76601i	−0.0885796	−	0.0643568i
$754$	−12.3503	−	38.0104i	−0.449773	−	1.38426i
$755$	0.172243	−	0.125142i	0.00626855	−	0.00455437i
$756$	−0.191443	−	0.589200i	−0.00696270	−	0.0214290i
$757$	−1.42669	+	4.39091i	−0.0518541	+	0.159590i	−0.973630	−	0.228132i	$-0.926738\pi$
$757$	−1.42669	+	4.39091i	−0.0518541	+	0.159590i	0.921776	+	0.387723i	$0.126738\pi$
$758$	23.9620	+	17.4094i	0.870339	+	0.632339i
$759$	−0.642887	+	1.97860i	−0.0233353	+	0.0718188i
$760$	−0.796180	+	2.45039i	−0.0288805	+	0.0888849i
$761$	6.79922	+	4.93992i	0.246472	+	0.179072i	0.704162	−	0.710040i	$-0.251323\pi$
$761$	6.79922	+	4.93992i	0.246472	+	0.179072i	−0.457690	+	0.889112i	$0.651323\pi$
$762$	−0.0458608	+	0.141145i	−0.00166136	+	0.00511314i
$763$	0.386304	+	1.18892i	0.0139851	+	0.0430418i
$764$	15.0497	−	10.9343i	0.544479	−	0.395587i
$765$	2.56386	+	7.89074i	0.0926965	+	0.285290i
$766$	−24.4977	−	17.7986i	−0.885137	−	0.643090i
$767$	58.5511	+	42.5399i	2.11416	+	1.53603i
$768$	0.101910	−	0.0740421i	0.00367737	−	0.00267176i
$769$	−1.38093			−0.0497975			−0.0248987	−	0.999690i	$-0.507926\pi$
$769$	−1.38093			−0.0497975			−0.0248987	+	0.999690i	$0.507926\pi$
$770$	3.14641			0.113389
$771$	−1.43803	+	1.04479i	−0.0517893	+	0.0376272i
$772$	6.36355	−	19.5850i	0.229029	−	0.704879i
$773$	−16.8025	−	51.7128i	−0.604345	−	1.85998i	−0.501234	−	0.865312i	$-0.667120\pi$
$773$	−16.8025	−	51.7128i	−0.604345	−	1.85998i	−0.103110	−	0.994670i	$-0.532880\pi$
$774$	−8.44040			−0.303384
$775$	2.71242	−	4.86238i	0.0974332	−	0.174662i
$776$	−5.70820			−0.204913
$777$	−0.0316943	−	0.0975451i	−0.00113703	−	0.00349941i
$778$	8.84675	−	27.2275i	0.317171	−	0.976153i
$779$	6.82626	−	4.95957i	0.244576	−	0.177695i
$780$	0.724900			0.0259556
$781$	52.0393			1.86211
$782$	−9.70338	+	7.04992i	−0.346992	+	0.252105i
$783$	−4.23543	−	3.07722i	−0.151362	−	0.109971i
$784$	5.11667	+	3.71748i	0.182738	+	0.132767i
$785$	−3.44724	−	10.6095i	−0.123037	−	0.378669i
$786$	1.42908	−	1.03829i	0.0509737	−	0.0370345i
$787$	−9.96740	−	30.6765i	−0.355299	−	1.09350i	−0.955836	−	0.293901i	$-0.905046\pi$
$787$	−9.96740	−	30.6765i	−0.355299	−	1.09350i	0.600536	−	0.799597i	$-0.294954\pi$
$788$	−8.55859	+	26.3406i	−0.304887	+	0.938346i
$789$	−3.16659	−	2.30066i	−0.112733	−	0.0819056i
$790$	1.43624	−	4.42029i	0.0510991	−	0.157267i
$791$	−3.76876	+	11.5991i	−0.134002	+	0.412415i
$792$	9.24264	+	6.71517i	0.328423	+	0.238613i
$793$	−6.53835	+	20.1230i	−0.232184	+	0.714588i
$794$	−0.847102	−	2.60711i	−0.0300625	−	0.0925229i
$795$	−0.995938	+	0.723591i	−0.0353223	+	0.0256631i
$796$	−0.563918	−	1.73556i	−0.0199875	−	0.0615153i
$797$	29.6347	+	21.5309i	1.04972	+	0.762663i	0.972158	−	0.234325i	$-0.0752880\pi$
$797$	29.6347	+	21.5309i	1.04972	+	0.762663i	0.0775571	+	0.996988i	$0.475288\pi$
$798$	−0.215795	−	0.156784i	−0.00763906	−	0.00555010i
$799$	−8.21065	+	5.96539i	−0.290472	+	0.211040i
$800$	−1.00000			−0.0353553
$801$	−36.7539			−1.29863
$802$	9.21579	−	6.69567i	0.325421	−	0.236432i
$803$	1.26257	−	3.88579i	0.0445552	−	0.137127i
$804$	−0.307144	−	0.945292i	−0.0108321	−	0.0333379i
$805$	−3.54541			−0.124959
$806$	−15.6090	+	27.9812i	−0.549804	+	0.985597i
$807$	1.72184			0.0606116
$808$	−5.66389	−	17.4317i	−0.199255	−	0.613244i
$809$	1.94299	−	5.97991i	0.0683119	−	0.210243i	−0.911073	−	0.412245i	$-0.864745\pi$
$809$	1.94299	−	5.97991i	0.0683119	−	0.210243i	0.979385	+	0.202002i	$0.0647448\pi$
$810$	−7.16582	+	5.20627i	−0.251781	+	0.182930i
$811$	2.23709			0.0785549			0.0392775	−	0.999228i	$-0.487494\pi$
$811$	2.23709			0.0785549			0.0392775	+	0.999228i	$0.487494\pi$
$812$	−5.70786			−0.200307
$813$	−1.05918	+	0.769538i	−0.0371470	+	0.0269889i
$814$	3.06847	+	2.22938i	0.107550	+	0.0781396i
$815$	9.40247	+	6.83130i	0.329354	+	0.239290i
$816$	−0.108227	−	0.333089i	−0.00378871	−	0.0116604i
$817$	−5.89564	+	4.28344i	−0.206262	+	0.149858i
$818$	−4.08579	−	12.5748i	−0.142856	−	0.439666i
$819$	4.36127	−	13.4226i	0.152395	−	0.469024i
$820$	2.64944	+	1.92493i	0.0925225	+	0.0672215i
$821$	−8.75918	+	26.9580i	−0.305698	+	0.940841i	0.673718	+	0.738988i	$0.264696\pi$
$821$	−8.75918	+	26.9580i	−0.305698	+	0.940841i	−0.979416	+	0.201852i	$0.935304\pi$
$822$	−0.700474	+	2.15584i	−0.0244318	+	0.0751934i
$823$	−25.0680	−	18.2129i	−0.873814	−	0.634863i	0.0577938	−	0.998329i	$-0.481593\pi$
$823$	−25.0680	−	18.2129i	−0.873814	−	0.634863i	−0.931608	+	0.363466i	$0.881593\pi$
$824$	4.06450	−	12.5092i	0.141593	−	0.435780i
$825$	0.149026	+	0.458656i	0.00518843	+	0.0159683i
$826$	8.36204	−	6.07537i	0.290952	−	0.211389i
$827$	0.664638	+	2.04555i	0.0231117	+	0.0711306i	0.961947	−	0.273236i	$-0.0880938\pi$
$827$	0.664638	+	2.04555i	0.0231117	+	0.0711306i	−0.938835	+	0.344366i	$0.888094\pi$
$828$	−10.4147	−	7.56674i	−0.361937	−	0.262962i
$829$	−9.96521	−	7.24015i	−0.346106	−	0.251461i	0.401127	−	0.916022i	$-0.368618\pi$
$829$	−9.96521	−	7.24015i	−0.346106	−	0.251461i	−0.747234	+	0.664561i	$0.768618\pi$
$830$	−4.67434	+	3.39611i	−0.162249	+	0.117881i
$831$	2.11718			0.0734443
$832$	5.75464			0.199506
$833$	14.2259	−	10.3358i	0.492900	−	0.358113i
$834$	0.353781	−	1.08882i	0.0122504	−	0.0377029i
$835$	−1.90983	−	5.87785i	−0.0660924	−	0.203411i
$836$	9.86391			0.341150
$837$	0.500257	+	4.16711i	0.0172914	+	0.144036i
$838$	−26.7322			−0.923448
$839$	10.8102	+	33.2704i	0.373210	+	1.14862i	0.944678	+	0.327999i	$0.106374\pi$
$839$	10.8102	+	33.2704i	0.373210	+	1.14862i	−0.571468	+	0.820625i	$0.693626\pi$
$840$	0.0319917	−	0.0984603i	0.00110382	−	0.00339720i
$841$	−15.5610	+	11.3057i	−0.536585	+	0.389852i
$842$	16.1609			0.556942
$843$	0.267683			0.00921949
$844$	−13.1803	+	9.57607i	−0.453686	+	0.329622i
$845$	16.2741	+	11.8238i	0.559845	+	0.406751i
$846$	−8.81256	−	6.40270i	−0.302982	−	0.220129i
$847$	−0.928720	−	2.85831i	−0.0319112	−	0.0982126i
$848$	−7.90628	+	5.74425i	−0.271503	+	0.197258i
$849$	−0.544769	−	1.67663i	−0.0186964	−	0.0575416i
$850$	−0.859164	+	2.64423i	−0.0294691	+	0.0906965i
$851$	−3.45759	−	2.51209i	−0.118525	−	0.0861133i
$852$	0.529119	−	1.62846i	0.0181273	−	0.0557902i
$853$	−8.09073	+	24.9007i	−0.277021	+	0.852584i	0.711656	+	0.702528i	$0.247945\pi$
$853$	−8.09073	+	24.9007i	−0.277021	+	0.852584i	−0.988677	+	0.150056i	$0.952055\pi$
$854$	2.44467	+	1.77616i	0.0836550	+	0.0607789i
$855$	−2.37591	+	7.31228i	−0.0812542	+	0.250075i
$856$	−0.663639	−	2.04247i	−0.0226827	−	0.0698102i
$857$	12.5978	−	9.15286i	0.430334	−	0.312656i	−0.351449	−	0.936207i	$-0.614311\pi$
$857$	12.5978	−	9.15286i	0.430334	−	0.312656i	0.781782	+	0.623552i	$0.214311\pi$
$858$	−0.857592	−	2.63940i	−0.0292777	−	0.0901075i
$859$	24.8787	+	18.0754i	0.848850	+	0.616726i	0.924829	−	0.380384i	$-0.124208\pi$
$859$	24.8787	+	18.0754i	0.848850	+	0.616726i	−0.0759785	+	0.997109i	$0.524208\pi$
$860$	−2.28825	−	1.66251i	−0.0780285	−	0.0566910i
$861$	−0.274289	+	0.199283i	−0.00934776	+	0.00679154i
$862$	2.59896			0.0885209
$863$	−33.3740			−1.13607			−0.568033	−	0.823006i	$-0.692295\pi$
$863$	−33.3740			−1.13607			−0.568033	+	0.823006i	$0.692295\pi$
$864$	0.609844	−	0.443078i	0.0207473	−	0.0150738i
$865$	0.403927	−	1.24316i	0.0137339	−	0.0422687i
$866$	−2.94616	−	9.06736i	−0.100115	−	0.308122i
$867$	1.16771			0.0396574
$868$	3.11172	+	3.35500i	0.105619	+	0.113876i
$869$	−17.7937			−0.603608
$870$	−0.270347	−	0.832041i	−0.00916561	−	0.0282088i
$871$	14.0314	−	43.1841i	0.475435	−	1.46324i
$872$	−1.23058	+	0.894068i	−0.0416727	+	0.0302770i
$873$	−17.0340			−0.576515
$874$	−11.1148			−0.375963
$875$	−0.664894	+	0.483074i	−0.0224775	+	0.0163309i
$876$	−0.108760	−	0.0790190i	−0.00367467	−	0.00266981i
$877$	13.6919	+	9.94775i	0.462343	+	0.335912i	0.794450	−	0.607330i	$-0.207759\pi$
$877$	13.6919	+	9.94775i	0.462343	+	0.335912i	−0.332107	+	0.943242i	$0.607759\pi$
$878$	−1.19572	−	3.68006i	−0.0403537	−	0.124196i
$879$	0.151801	−	0.110290i	0.00512012	−	0.00371998i
$880$	1.18305	+	3.64105i	0.0398806	+	0.122740i
$881$	8.55668	−	26.3347i	0.288282	−	0.887240i	−0.697114	−	0.716960i	$-0.745533\pi$
$881$	8.55668	−	26.3347i	0.288282	−	0.887240i	0.985396	−	0.170280i	$-0.0544672\pi$
$882$	15.2688	+	11.0935i	0.514128	+	0.373536i
$883$	13.0105	−	40.0423i	0.437839	−	1.34753i	−0.452310	−	0.891861i	$-0.649400\pi$
$883$	13.0105	−	40.0423i	0.437839	−	1.34753i	0.890149	−	0.455670i	$-0.150600\pi$
$884$	4.94417	−	15.2166i	0.166291	−	0.511790i
$885$	1.28167	+	0.931190i	0.0430830	+	0.0313016i
$886$	11.2888	−	34.7433i	0.379255	−	1.16723i
$887$	−18.0195	−	55.4582i	−0.605034	−	1.86210i	−0.496556	−	0.868004i	$-0.665402\pi$
$887$	−18.0195	−	55.4582i	−0.605034	−	1.86210i	−0.108478	−	0.994099i	$-0.534598\pi$
$888$	0.100963	−	0.0733539i	0.00338809	−	0.00246159i
$889$	0.299210	+	0.920874i	0.0100352	+	0.0308851i
$890$	−9.96420	−	7.23942i	−0.334001	−	0.242666i
$891$	27.4338	+	19.9318i	0.919068	+	0.667742i
$892$	−18.2142	+	13.2334i	−0.609856	+	0.443086i
$893$	−9.40492			−0.314724
$894$	−0.923803			−0.0308966
$895$	−15.9964	+	11.6221i	−0.534702	+	0.388484i
$896$	0.253967	−	0.781630i	0.00848444	−	0.0261124i
$897$	0.966346	+	2.97411i	0.0322653	+	0.0993025i
$898$	10.3826			0.346472
$899$	37.9382	+	7.48064i	1.26531	+	0.249493i
$900$	−2.98413			−0.0994711
$901$	8.39635	+	25.8413i	0.279723	+	0.860898i
$902$	3.87435	−	11.9240i	0.129002	−	0.397027i
$903$	0.236896	−	0.172115i	0.00788340	−	0.00572763i
$904$	−14.8396			−0.493557
$905$	−25.5017			−0.847704
$906$	−0.0216971	+	0.0157638i	−0.000720837	+	0.000523718i
$907$	−10.5028	−	7.63071i	−0.348739	−	0.253373i	0.399601	−	0.916689i	$-0.369149\pi$
$907$	−10.5028	−	7.63071i	−0.348739	−	0.253373i	−0.748340	+	0.663316i	$0.769149\pi$
$908$	5.51763	+	4.00880i	0.183109	+	0.133037i
$909$	−16.9018	−	52.0184i	−0.560598	−	1.72534i
$910$	3.82622	−	2.77991i	0.126838	−	0.0921533i
$911$	1.22065	+	3.75677i	0.0404418	+	0.124467i	0.969239	−	0.246121i	$-0.0791561\pi$
$911$	1.22065	+	3.75677i	0.0404418	+	0.124467i	−0.928797	+	0.370588i	$0.879156\pi$
$912$	0.100293	−	0.308670i	0.00332104	−	0.0102211i
$913$	17.8954	+	13.0017i	0.592250	+	0.430295i
$914$	−8.71388	+	26.8186i	−0.288230	+	0.887080i
$915$	−0.143123	+	0.440488i	−0.00473151	+	0.0145621i
$916$	−8.90587	−	6.47049i	−0.294258	−	0.213791i
$917$	3.56137	−	10.9608i	0.117607	−	0.361956i
$918$	−0.647645	−	1.99325i	−0.0213755	−	0.0657869i
$919$	44.2254	−	32.1316i	1.45886	−	1.05993i	0.475204	−	0.879875i	$-0.342374\pi$
$919$	44.2254	−	32.1316i	1.45886	−	1.05993i	0.983658	−	0.180050i	$-0.0576259\pi$
$920$	−1.33307	−	4.10278i	−0.0439502	−	0.135265i
$921$	−3.14200	−	2.28280i	−0.103533	−	0.0752208i
$922$	−19.3657	−	14.0700i	−0.637776	−	0.463372i
$923$	63.2830	−	45.9778i	2.08298	−	1.51338i
$924$	−0.396347			−0.0130389
$925$	−0.990705			−0.0325742
$926$	12.0455	−	8.75155i	0.395839	−	0.287594i
$927$	12.1290	−	37.3292i	0.398368	−	1.22605i
$928$	−2.14615	−	6.60518i	−0.0704510	−	0.216826i
$929$	−25.0499			−0.821862			−0.410931	−	0.911667i	$-0.634796\pi$
$929$	−25.0499			−0.821862			−0.410931	+	0.911667i	$0.634796\pi$
$930$	−0.341679	+	0.612504i	−0.0112041	+	0.0200848i
$931$	16.2952			0.534052
$932$	−4.05369	−	12.4760i	−0.132783	−	0.408664i
$933$	0.766638	−	2.35947i	0.0250986	−	0.0772456i
$934$	7.23868	−	5.25921i	0.236857	−	0.172087i
$935$	10.6442			0.348103
$936$	17.1726			0.561304
$937$	48.1962	−	35.0166i	1.57450	−	1.14394i	0.651821	−	0.758373i	$-0.274005\pi$
$937$	48.1962	−	35.0166i	1.57450	−	1.14394i	0.922679	−	0.385568i	$-0.125995\pi$
$938$	−5.24629	−	3.81165i	−0.171297	−	0.124455i
$939$	−2.31611	−	1.68275i	−0.0755834	−	0.0549145i
$940$	−1.12800	−	3.47162i	−0.0367913	−	0.113232i
$941$	−9.77733	+	7.10365i	−0.318732	+	0.231572i	−0.735634	−	0.677379i	$-0.763116\pi$
$941$	−9.77733	+	7.10365i	−0.318732	+	0.231572i	0.416902	+	0.908951i	$0.363116\pi$
$942$	0.434241	+	1.33646i	0.0141483	+	0.0435441i
$943$	−4.36567	+	13.4362i	−0.142166	+	0.437541i
$944$	10.1746	+	7.39228i	0.331155	+	0.240598i
$945$	0.191443	−	0.589200i	0.00622763	−	0.0191667i
$946$	−3.34617	+	10.2984i	−0.108793	+	0.334831i
$947$	15.4107	+	11.1965i	0.500779	+	0.363837i	0.809315	−	0.587375i	$-0.199839\pi$
$947$	15.4107	+	11.1965i	0.500779	+	0.363837i	−0.308535	+	0.951213i	$0.599839\pi$
$948$	−0.180920	+	0.556815i	−0.00587602	+	0.0180845i
$949$	−1.89781	−	5.84087i	−0.0616056	−	0.189603i
$950$	−2.08443	+	1.51442i	−0.0676277	+	0.0491344i
$951$	0.102568	+	0.315673i	0.00332601	+	0.0102364i
$952$	−1.84861	−	1.34310i	−0.0599139	−	0.0435300i
$953$	−9.61965	−	6.98909i	−0.311611	−	0.226399i	0.420976	−	0.907072i	$-0.361688\pi$
$953$	−9.61965	−	6.98909i	−0.311611	−	0.226399i	−0.732587	+	0.680673i	$0.761688\pi$
$954$	−23.5934	+	17.1416i	−0.763864	+	0.554980i
$955$	18.6025			0.601962
$956$	0.821642			0.0265738
$957$	−2.70967	+	1.96869i	−0.0875912	+	0.0636388i
$958$	−5.94849	+	18.3076i	−0.192187	+	0.591491i
$959$	4.57011	+	14.0654i	0.147577	+	0.454194i
$960$	0.125968			0.00406560
$961$	−16.2855	−	26.3777i	−0.525339	−	0.850893i
$962$	5.70115			0.183812
$963$	−1.98039	−	6.09500i	−0.0638171	−	0.196409i
$964$	−3.51786	+	10.8269i	−0.113303	+	0.348710i
$965$	16.6600	−	12.1042i	0.536304	−	0.389648i
$966$	0.446609			0.0143694
$967$	−39.6198			−1.27409			−0.637044	−	0.770827i	$-0.719843\pi$
$967$	−39.6198			−1.27409			−0.637044	+	0.770827i	$0.719843\pi$
$968$	2.95846	−	2.14944i	0.0950884	−	0.0690858i
$969$	−0.730029	−	0.530397i	−0.0234519	−	0.0170388i
$970$	−4.61803	−	3.35520i	−0.148276	−	0.107729i
$971$	−8.41681	−	25.9043i	−0.270108	−	0.831307i	−0.990472	−	0.137711i	$-0.956025\pi$
$971$	−8.41681	−	25.9043i	−0.270108	−	0.831307i	0.720364	−	0.693596i	$-0.243975\pi$
$972$	2.73220	−	1.98506i	0.0876352	−	0.0636707i
$973$	−2.30818	−	7.10383i	−0.0739967	−	0.227738i
$974$	−2.90080	+	8.92774i	−0.0929476	+	0.286063i
$975$	0.586456	+	0.426085i	0.0187816	+	0.0136457i
$976$	−1.13619	+	3.49683i	−0.0363685	+	0.111931i
$977$	15.5155	−	47.7519i	0.496386	−	1.52772i	−0.318400	−	0.947956i	$-0.603146\pi$
$977$	15.5155	−	47.7519i	0.496386	−	1.52772i	0.814786	−	0.579762i	$-0.196854\pi$
$978$	−1.18441	−	0.860524i	−0.0378733	−	0.0275165i
$979$	−14.5709	+	44.8447i	−0.465689	+	1.43324i
$980$	1.95440	+	6.01501i	0.0624309	+	0.192142i
$981$	−3.67221	+	2.66802i	−0.117245	+	0.0851832i
$982$	−2.71091	−	8.34333i	−0.0865087	−	0.266246i
$983$	−5.36995	−	3.90150i	−0.171275	−	0.124438i	0.498846	−	0.866691i	$-0.333757\pi$
$983$	−5.36995	−	3.90150i	−0.171275	−	0.124438i	−0.670120	+	0.742253i	$0.733757\pi$
$984$	−0.333745	−	0.242480i	−0.0106394	−	0.00772997i
$985$	−22.4067	+	16.2794i	−0.713936	+	0.518705i
$986$	−19.3095			−0.614941
$987$	0.377904			0.0120288
$988$	11.9951	−	8.71496i	0.381615	−	0.277260i
$989$	3.77050	−	11.6044i	0.119895	−	0.368999i
$990$	3.53037	+	10.8654i	0.112203	+	0.345324i
$991$	55.2367			1.75465			0.877325	−	0.479896i	$-0.159326\pi$
$991$	55.2367			1.75465			0.877325	+	0.479896i	$0.159326\pi$
$992$	−2.71242	+	4.86238i	−0.0861196	+	0.154381i
$993$	−0.653368			−0.0207340
$994$	−3.45214	−	10.6246i	−0.109495	−	0.336992i
$995$	0.563918	−	1.73556i	0.0178774	−	0.0550210i
$996$	0.588817	−	0.427801i	0.0186574	−	0.0135554i
$997$	−44.4529			−1.40784			−0.703918	−	0.710281i	$-0.748568\pi$
$997$	−44.4529			−1.40784			−0.703918	+	0.710281i	$0.748568\pi$
$998$	−4.45795			−0.141114
$999$	0.604176	−	0.438959i	0.0191153	−	0.0138881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.h.e.221.2	yes	8
31.8	even	5	inner	310.2.h.e.101.2	✓	8
31.15	odd	10		9610.2.a.bh.1.2		4
31.16	even	5		9610.2.a.ba.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.h.e.101.2	✓	8	31.8	even	5	inner
310.2.h.e.221.2	yes	8	1.1	even	1	trivial
9610.2.a.ba.1.3		4	31.16	even	5
9610.2.a.bh.1.2		4	31.15	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.0389262 + 0.119803i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +0.125968 q^{6} +(0.664894 - 0.483074i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41421 + 1.75403i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.0389262 + 0.119803i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +0.125968 q^{6} +(0.664894 - 0.483074i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41421 + 1.75403i) q^{9} +(0.309017 + 0.951057i) q^{10} +(3.09726 - 2.25029i) q^{11} +(-0.0389262 - 0.119803i) q^{12} +(1.77828 - 5.47298i) q^{13} +(-0.664894 - 0.483074i) q^{14} +(0.0389262 - 0.119803i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.24932 - 1.63423i) q^{17} +(0.922148 - 2.83808i) q^{18} +(-0.796180 - 2.45039i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.0319917 + 0.0984603i) q^{21} +(-3.09726 - 2.25029i) q^{22} +(3.49003 + 2.53566i) q^{23} +(-0.101910 + 0.0740421i) q^{24} +1.00000 q^{25} -5.75464 q^{26} +(-0.609844 + 0.443078i) q^{27} +(-0.253967 + 0.781630i) q^{28} +(2.14615 + 6.60518i) q^{29} -0.125968 q^{30} +(2.71242 - 4.86238i) q^{31} -1.00000 q^{32} +(0.149026 + 0.458656i) q^{33} +(-0.859164 + 2.64423i) q^{34} +(-0.664894 + 0.483074i) q^{35} -2.98413 q^{36} -0.990705 q^{37} +(-2.08443 + 1.51442i) q^{38} +(0.586456 + 0.426085i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(1.01200 + 3.11460i) q^{41} +(0.0837554 - 0.0608518i) q^{42} +(-0.874032 - 2.68999i) q^{43} +(-1.18305 + 3.64105i) q^{44} +(-2.41421 - 1.75403i) q^{45} +(1.33307 - 4.10278i) q^{46} +(1.12800 - 3.47162i) q^{47} +(0.101910 + 0.0740421i) q^{48} +(-1.95440 + 6.01501i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(0.283342 - 0.205860i) q^{51} +(1.77828 + 5.47298i) q^{52} +(-7.90628 - 5.74425i) q^{53} +(0.609844 + 0.443078i) q^{54} +(-3.09726 + 2.25029i) q^{55} +0.821854 q^{56} +0.324555 q^{57} +(5.61870 - 4.08223i) q^{58} +(-3.88635 + 11.9610i) q^{59} +(0.0389262 + 0.119803i) q^{60} -3.67678 q^{61} +(-5.46258 - 1.07711i) q^{62} +2.45252 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.77828 + 5.47298i) q^{65} +(0.390156 - 0.283465i) q^{66} +7.89041 q^{67} +2.78031 q^{68} +(-0.439633 + 0.319412i) q^{69} +(0.664894 + 0.483074i) q^{70} +(10.9969 + 7.98969i) q^{71} +(0.922148 + 2.83808i) q^{72} +(0.863397 - 0.627295i) q^{73} +(0.306145 + 0.942216i) q^{74} +(-0.0389262 + 0.119803i) q^{75} +(2.08443 + 1.51442i) q^{76} +(0.972294 - 2.99241i) q^{77} +(0.224006 - 0.689421i) q^{78} +(-3.76013 - 2.73189i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.73710 + 8.42393i) q^{81} +(2.64944 - 1.92493i) q^{82} +(1.78544 + 5.49502i) q^{83} +(-0.0837554 - 0.0608518i) q^{84} +(2.24932 + 1.63423i) q^{85} +(-2.28825 + 1.66251i) q^{86} -0.874860 q^{87} +3.82843 q^{88} +(-9.96420 + 7.23942i) q^{89} +(-0.922148 + 2.83808i) q^{90} +(-1.46149 - 4.49800i) q^{91} -4.31392 q^{92} +(0.476942 + 0.514230i) q^{93} -3.65028 q^{94} +(0.796180 + 2.45039i) q^{95} +(0.0389262 - 0.119803i) q^{96} +(-4.61803 + 3.35520i) q^{97} +6.32456 q^{98} +11.4245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} + 10 q^{7} + 2 q^{8} + 8 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} - 14 q^{13} - 10 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{18} - 4 q^{19} + 2 q^{20} + 22 q^{21} - 2 q^{22} + 18 q^{23} - 2 q^{24} + 8 q^{25} - 16 q^{26} - 22 q^{27} - 10 q^{28} + 2 q^{29} - 8 q^{30} + 2 q^{31} - 8 q^{32} - 26 q^{33} - 8 q^{34} - 10 q^{35} + 8 q^{36} + 40 q^{37} + 4 q^{38} - 22 q^{39} - 2 q^{40} + 12 q^{41} + 18 q^{42} + 2 q^{44} - 8 q^{45} + 12 q^{46} + 10 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 14 q^{52} - 36 q^{53} + 22 q^{54} - 2 q^{55} - 48 q^{57} - 2 q^{58} + 16 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{62} + 56 q^{63} - 2 q^{64} + 14 q^{65} - 14 q^{66} + 4 q^{67} - 12 q^{68} - 30 q^{69} + 10 q^{70} + 20 q^{71} + 12 q^{72} + 28 q^{73} + 10 q^{74} + 2 q^{75} - 4 q^{76} + 18 q^{77} - 18 q^{78} - 18 q^{79} + 2 q^{80} - 42 q^{81} - 2 q^{82} + 6 q^{83} - 18 q^{84} + 2 q^{85} - 8 q^{87} + 8 q^{88} - 28 q^{89} - 12 q^{90} - 18 q^{91} - 12 q^{92} + 38 q^{93} + 4 q^{95} - 2 q^{96} - 28 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 + 10 * q^7 + 2 * q^8 + 8 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 - 14 * q^13 - 10 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 12 * q^18 - 4 * q^19 + 2 * q^20 + 22 * q^21 - 2 * q^22 + 18 * q^23 - 2 * q^24 + 8 * q^25 - 16 * q^26 - 22 * q^27 - 10 * q^28 + 2 * q^29 - 8 * q^30 + 2 * q^31 - 8 * q^32 - 26 * q^33 - 8 * q^34 - 10 * q^35 + 8 * q^36 + 40 * q^37 + 4 * q^38 - 22 * q^39 - 2 * q^40 + 12 * q^41 + 18 * q^42 + 2 * q^44 - 8 * q^45 + 12 * q^46 + 10 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 14 * q^52 - 36 * q^53 + 22 * q^54 - 2 * q^55 - 48 * q^57 - 2 * q^58 + 16 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^62 + 56 * q^63 - 2 * q^64 + 14 * q^65 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 30 * q^69 + 10 * q^70 + 20 * q^71 + 12 * q^72 + 28 * q^73 + 10 * q^74 + 2 * q^75 - 4 * q^76 + 18 * q^77 - 18 * q^78 - 18 * q^79 + 2 * q^80 - 42 * q^81 - 2 * q^82 + 6 * q^83 - 18 * q^84 + 2 * q^85 - 8 * q^87 + 8 * q^88 - 28 * q^89 - 12 * q^90 - 18 * q^91 - 12 * q^92 + 38 * q^93 + 4 * q^95 - 2 * q^96 - 28 * q^97 - 40 * q^99

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