LMFDB - Embedded newform 418.2.f.e.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			229.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.e.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(1.80902 - 1.31433i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-0.690983 - 2.12663i) q^{6} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(1.80902 - 1.31433i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-0.690983 - 2.12663i) q^{6} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.618034 - 1.90211i) q^{9} +0.618034 q^{10} +(2.54508 - 2.12663i) q^{11} -2.23607 q^{12} +(0.500000 - 1.53884i) q^{13} +(-2.30902 + 1.67760i) q^{14} +(1.11803 + 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.92705 - 5.93085i) q^{17} +(-1.61803 - 1.17557i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.190983 - 0.587785i) q^{20} -6.38197 q^{21} +(-1.23607 - 3.07768i) q^{22} -0.236068 q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.73607 - 2.71441i) q^{25} +(-1.30902 - 0.951057i) q^{26} +(0.690983 + 2.12663i) q^{27} +(0.881966 + 2.71441i) q^{28} +(8.47214 + 6.15537i) q^{29} +(1.11803 - 0.812299i) q^{30} +(-3.30902 + 10.1841i) q^{31} +1.00000 q^{32} +(1.80902 - 7.19218i) q^{33} -6.23607 q^{34} +(0.545085 - 1.67760i) q^{35} +(-1.61803 + 1.17557i) q^{36} +(6.35410 + 4.61653i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.11803 - 3.44095i) q^{39} +(-0.500000 - 0.363271i) q^{40} +(-3.30902 + 2.40414i) q^{41} +(-1.97214 + 6.06961i) q^{42} +3.70820 q^{43} +(-3.30902 + 0.224514i) q^{44} +1.23607 q^{45} +(-0.0729490 + 0.224514i) q^{46} +(-9.28115 + 6.74315i) q^{47} +(1.80902 + 1.31433i) q^{48} +(0.354102 + 1.08981i) q^{49} +(-1.42705 - 4.39201i) q^{50} +(-11.2812 - 8.19624i) q^{51} +(-1.30902 + 0.951057i) q^{52} +(1.83688 - 5.65334i) q^{53} +2.23607 q^{54} +(1.73607 + 1.08981i) q^{55} +2.85410 q^{56} +(-0.690983 + 2.12663i) q^{57} +(8.47214 - 6.15537i) q^{58} +(10.5902 + 7.69421i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-1.35410 - 4.16750i) q^{61} +(8.66312 + 6.29412i) q^{62} +(-4.61803 + 3.35520i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.00000 q^{65} +(-6.28115 - 3.94298i) q^{66} -6.09017 q^{67} +(-1.92705 + 5.93085i) q^{68} +(-0.427051 + 0.310271i) q^{69} +(-1.42705 - 1.03681i) q^{70} +(-1.16312 - 3.57971i) q^{71} +(0.618034 + 1.90211i) q^{72} +(-1.07295 - 0.779543i) q^{73} +(6.35410 - 4.61653i) q^{74} +(3.19098 - 9.82084i) q^{75} +1.00000 q^{76} +(-9.44427 + 0.640786i) q^{77} -3.61803 q^{78} +(0.927051 - 2.85317i) q^{79} +(-0.500000 + 0.363271i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.26393 + 3.88998i) q^{82} +(0.336881 + 1.03681i) q^{83} +(5.16312 + 3.75123i) q^{84} +(3.11803 - 2.26538i) q^{85} +(1.14590 - 3.52671i) q^{86} +23.4164 q^{87} +(-0.809017 + 3.21644i) q^{88} -9.18034 q^{89} +(0.381966 - 1.17557i) q^{90} +(-3.73607 + 2.71441i) q^{91} +(0.190983 + 0.138757i) q^{92} +(7.39919 + 22.7724i) q^{93} +(3.54508 + 10.9106i) q^{94} +(-0.500000 - 0.363271i) q^{95} +(1.80902 - 1.31433i) q^{96} +(5.07295 - 15.6129i) q^{97} +1.14590 q^{98} +(-2.47214 - 6.15537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{13} - 7 q^{14} - q^{16} - q^{17} - 2 q^{18} - q^{19} + 3 q^{20} - 30 q^{21} + 4 q^{22} + 8 q^{23} - 5 q^{24} + 6 q^{25} - 3 q^{26} + 5 q^{27} + 8 q^{28} + 16 q^{29} - 11 q^{31} + 4 q^{32} + 5 q^{33} - 16 q^{34} - 9 q^{35} - 2 q^{36} + 12 q^{37} - q^{38} - 2 q^{40} - 11 q^{41} + 10 q^{42} - 12 q^{43} - 11 q^{44} - 4 q^{45} - 7 q^{46} - 17 q^{47} + 5 q^{48} - 12 q^{49} + q^{50} - 25 q^{51} - 3 q^{52} + 23 q^{53} - 2 q^{55} - 2 q^{56} - 5 q^{57} + 16 q^{58} + 20 q^{59} + 5 q^{60} + 8 q^{61} + 19 q^{62} - 14 q^{63} - q^{64} + 4 q^{65} - 5 q^{66} - 2 q^{67} - q^{68} + 5 q^{69} + q^{70} + 11 q^{71} - 2 q^{72} - 11 q^{73} + 12 q^{74} + 15 q^{75} + 4 q^{76} - 2 q^{77} - 10 q^{78} - 3 q^{79} - 2 q^{80} + 11 q^{81} + 14 q^{82} + 17 q^{83} + 5 q^{84} + 8 q^{85} + 18 q^{86} + 40 q^{87} - q^{88} + 8 q^{89} + 6 q^{90} - 6 q^{91} + 3 q^{92} + 5 q^{93} + 3 q^{94} - 2 q^{95} + 5 q^{96} + 27 q^{97} + 18 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^13 - 7 * q^14 - q^16 - q^17 - 2 * q^18 - q^19 + 3 * q^20 - 30 * q^21 + 4 * q^22 + 8 * q^23 - 5 * q^24 + 6 * q^25 - 3 * q^26 + 5 * q^27 + 8 * q^28 + 16 * q^29 - 11 * q^31 + 4 * q^32 + 5 * q^33 - 16 * q^34 - 9 * q^35 - 2 * q^36 + 12 * q^37 - q^38 - 2 * q^40 - 11 * q^41 + 10 * q^42 - 12 * q^43 - 11 * q^44 - 4 * q^45 - 7 * q^46 - 17 * q^47 + 5 * q^48 - 12 * q^49 + q^50 - 25 * q^51 - 3 * q^52 + 23 * q^53 - 2 * q^55 - 2 * q^56 - 5 * q^57 + 16 * q^58 + 20 * q^59 + 5 * q^60 + 8 * q^61 + 19 * q^62 - 14 * q^63 - q^64 + 4 * q^65 - 5 * q^66 - 2 * q^67 - q^68 + 5 * q^69 + q^70 + 11 * q^71 - 2 * q^72 - 11 * q^73 + 12 * q^74 + 15 * q^75 + 4 * q^76 - 2 * q^77 - 10 * q^78 - 3 * q^79 - 2 * q^80 + 11 * q^81 + 14 * q^82 + 17 * q^83 + 5 * q^84 + 8 * q^85 + 18 * q^86 + 40 * q^87 - q^88 + 8 * q^89 + 6 * q^90 - 6 * q^91 + 3 * q^92 + 5 * q^93 + 3 * q^94 - 2 * q^95 + 5 * q^96 + 27 * q^97 + 18 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	1.80902	−	1.31433i	1.04444	−	0.758827i	0.0732898	−	0.997311i	$-0.476650\pi$
$3$	1.80902	−	1.31433i	1.04444	−	0.758827i	0.971147	+	0.238483i	$0.0766502\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.190983	+	0.587785i	0.0854102	+	0.262866i	0.984636	−	0.174619i	$-0.0558694\pi$
$5$	0.190983	+	0.587785i	0.0854102	+	0.262866i	−0.899226	+	0.437485i	$0.855869\pi$
$6$	−0.690983	−	2.12663i	−0.282093	−	0.868192i
$7$	−2.30902	−	1.67760i	−0.872726	−	0.634073i	0.0585908	−	0.998282i	$-0.481339\pi$
$7$	−2.30902	−	1.67760i	−0.872726	−	0.634073i	−0.931317	+	0.364209i	$0.881339\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.618034	−	1.90211i	0.206011	−	0.634038i
$10$	0.618034			0.195440
$11$	2.54508	−	2.12663i	0.767372	−	0.641202i
$11$	2.54508	−	2.12663i	0.767372	−	0.641202i
$12$	−2.23607			−0.645497
$13$	0.500000	−	1.53884i	0.138675	−	0.426798i	−0.857468	−	0.514536i	$-0.827964\pi$
$13$	0.500000	−	1.53884i	0.138675	−	0.426798i	0.996144	+	0.0877386i	$0.0279640\pi$
$14$	−2.30902	+	1.67760i	−0.617111	+	0.448357i
$15$	1.11803	+	0.812299i	0.288675	+	0.209735i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.92705	−	5.93085i	−0.467379	−	1.43844i	−0.855966	−	0.517031i	$-0.827037\pi$
$17$	−1.92705	−	5.93085i	−0.467379	−	1.43844i	0.388588	−	0.921412i	$-0.372963\pi$
$18$	−1.61803	−	1.17557i	−0.381374	−	0.277085i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$20$	0.190983	−	0.587785i	0.0427051	−	0.131433i
$21$	−6.38197			−1.39266
$22$	−1.23607	−	3.07768i	−0.263531	−	0.656164i
$23$	−0.236068			−0.0492236			−0.0246118	−	0.999697i	$-0.507835\pi$
$23$	−0.236068			−0.0492236			−0.0246118	+	0.999697i	$0.507835\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	3.73607	−	2.71441i	0.747214	−	0.542882i
$26$	−1.30902	−	0.951057i	−0.256719	−	0.186518i
$27$	0.690983	+	2.12663i	0.132980	+	0.409270i
$28$	0.881966	+	2.71441i	0.166676	+	0.512976i
$29$	8.47214	+	6.15537i	1.57324	+	1.14302i	0.923972	+	0.382460i	$0.124923\pi$
$29$	8.47214	+	6.15537i	1.57324	+	1.14302i	0.649264	+	0.760563i	$0.275077\pi$
$30$	1.11803	−	0.812299i	0.204124	−	0.148305i
$31$	−3.30902	+	10.1841i	−0.594317	+	1.82912i	−0.0362201	+	0.999344i	$0.511532\pi$
$31$	−3.30902	+	10.1841i	−0.594317	+	1.82912i	−0.558097	+	0.829776i	$0.688468\pi$
$32$	1.00000			0.176777
$33$	1.80902	−	7.19218i	0.314909	−	1.25200i
$34$	−6.23607			−1.06948
$35$	0.545085	−	1.67760i	0.0921362	−	0.283566i
$36$	−1.61803	+	1.17557i	−0.269672	+	0.195928i
$37$	6.35410	+	4.61653i	1.04461	+	0.758952i	0.971180	−	0.238348i	$-0.0766060\pi$
$37$	6.35410	+	4.61653i	1.04461	+	0.758952i	0.0734282	+	0.997301i	$0.476606\pi$
$38$	0.309017	+	0.951057i	0.0501292	+	0.154282i
$39$	−1.11803	−	3.44095i	−0.179029	−	0.550994i
$40$	−0.500000	−	0.363271i	−0.0790569	−	0.0574382i
$41$	−3.30902	+	2.40414i	−0.516782	+	0.375464i	−0.815390	−	0.578912i	$-0.803478\pi$
$41$	−3.30902	+	2.40414i	−0.516782	+	0.375464i	0.298608	+	0.954376i	$0.403478\pi$
$42$	−1.97214	+	6.06961i	−0.304307	+	0.936561i
$43$	3.70820			0.565496			0.282748	−	0.959194i	$-0.408754\pi$
$43$	3.70820			0.565496			0.282748	+	0.959194i	$0.408754\pi$
$44$	−3.30902	+	0.224514i	−0.498853	+	0.0338468i
$45$	1.23607			0.184262
$46$	−0.0729490	+	0.224514i	−0.0107557	+	0.0331028i
$47$	−9.28115	+	6.74315i	−1.35380	+	0.983590i	−0.354983	+	0.934873i	$0.615513\pi$
$47$	−9.28115	+	6.74315i	−1.35380	+	0.983590i	−0.998813	+	0.0487170i	$0.984487\pi$
$48$	1.80902	+	1.31433i	0.261109	+	0.189707i
$49$	0.354102	+	1.08981i	0.0505860	+	0.155688i
$50$	−1.42705	−	4.39201i	−0.201815	−	0.621124i
$51$	−11.2812	−	8.19624i	−1.57968	−	1.14770i
$52$	−1.30902	+	0.951057i	−0.181528	+	0.131888i
$53$	1.83688	−	5.65334i	0.252315	−	0.776546i	−0.742032	−	0.670365i	$-0.766138\pi$
$53$	1.83688	−	5.65334i	0.252315	−	0.776546i	0.994347	−	0.106181i	$-0.0338623\pi$
$54$	2.23607			0.304290
$55$	1.73607	+	1.08981i	0.234091	+	0.146950i
$56$	2.85410			0.381395
$57$	−0.690983	+	2.12663i	−0.0915229	+	0.281679i
$58$	8.47214	−	6.15537i	1.11245	−	0.808239i
$59$	10.5902	+	7.69421i	1.37872	+	1.00170i	0.996998	+	0.0774245i	$0.0246697\pi$
$59$	10.5902	+	7.69421i	1.37872	+	1.00170i	0.381724	+	0.924276i	$0.375330\pi$
$60$	−0.427051	−	1.31433i	−0.0551320	−	0.169679i
$61$	−1.35410	−	4.16750i	−0.173375	−	0.533593i	0.826181	−	0.563405i	$-0.190509\pi$
$61$	−1.35410	−	4.16750i	−0.173375	−	0.533593i	−0.999556	+	0.0298121i	$0.990509\pi$
$62$	8.66312	+	6.29412i	1.10022	+	0.799355i
$63$	−4.61803	+	3.35520i	−0.581818	+	0.422715i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.00000			0.124035
$66$	−6.28115	−	3.94298i	−0.773156	−	0.485348i
$67$	−6.09017			−0.744033			−0.372016	−	0.928226i	$-0.621333\pi$
$67$	−6.09017			−0.744033			−0.372016	+	0.928226i	$0.621333\pi$
$68$	−1.92705	+	5.93085i	−0.233689	+	0.719222i
$69$	−0.427051	+	0.310271i	−0.0514109	+	0.0373522i
$70$	−1.42705	−	1.03681i	−0.170565	−	0.123923i
$71$	−1.16312	−	3.57971i	−0.138037	−	0.424834i	0.858013	−	0.513628i	$-0.171699\pi$
$71$	−1.16312	−	3.57971i	−0.138037	−	0.424834i	−0.996050	+	0.0887940i	$0.971699\pi$
$72$	0.618034	+	1.90211i	0.0728360	+	0.224166i
$73$	−1.07295	−	0.779543i	−0.125579	−	0.0912386i	0.523223	−	0.852196i	$-0.324730\pi$
$73$	−1.07295	−	0.779543i	−0.125579	−	0.0912386i	−0.648802	+	0.760957i	$0.724730\pi$
$74$	6.35410	−	4.61653i	0.738649	−	0.536660i
$75$	3.19098	−	9.82084i	0.368463	−	1.13401i
$76$	1.00000			0.114708
$77$	−9.44427	+	0.640786i	−1.07627	+	0.0730243i
$78$	−3.61803			−0.409662
$79$	0.927051	−	2.85317i	0.104301	−	0.321007i	−0.885264	−	0.465088i	$-0.846023\pi$
$79$	0.927051	−	2.85317i	0.104301	−	0.321007i	0.989566	+	0.144081i	$0.0460227\pi$
$80$	−0.500000	+	0.363271i	−0.0559017	+	0.0406150i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$	1.26393	+	3.88998i	0.139578	+	0.429577i
$83$	0.336881	+	1.03681i	0.0369775	+	0.113805i	0.967841	−	0.251561i	$-0.0809439\pi$
$83$	0.336881	+	1.03681i	0.0369775	+	0.113805i	−0.930864	+	0.365366i	$0.880944\pi$
$84$	5.16312	+	3.75123i	0.563342	+	0.409292i
$85$	3.11803	−	2.26538i	0.338198	−	0.245715i
$86$	1.14590	−	3.52671i	0.123565	−	0.380295i
$87$	23.4164			2.51050
$88$	−0.809017	+	3.21644i	−0.0862415	+	0.342874i
$89$	−9.18034			−0.973114			−0.486557	−	0.873649i	$-0.661747\pi$
$89$	−9.18034			−0.973114			−0.486557	+	0.873649i	$0.661747\pi$
$90$	0.381966	−	1.17557i	0.0402628	−	0.123916i
$91$	−3.73607	+	2.71441i	−0.391646	+	0.284548i
$92$	0.190983	+	0.138757i	0.0199114	+	0.0144664i
$93$	7.39919	+	22.7724i	0.767260	+	2.36138i
$94$	3.54508	+	10.9106i	0.365648	+	1.12535i
$95$	−0.500000	−	0.363271i	−0.0512989	−	0.0372708i
$96$	1.80902	−	1.31433i	0.184632	−	0.134143i
$97$	5.07295	−	15.6129i	0.515080	−	1.58525i	−0.268057	−	0.963403i	$-0.586381\pi$
$97$	5.07295	−	15.6129i	0.515080	−	1.58525i	0.783136	−	0.621850i	$-0.213619\pi$
$98$	1.14590			0.115753
$99$	−2.47214	−	6.15537i	−0.248459	−	0.618638i
$100$	−4.61803			−0.461803
$101$	−0.163119	+	0.502029i	−0.0162309	+	0.0499537i	−0.958844	−	0.283934i	$-0.908360\pi$
$101$	−0.163119	+	0.502029i	−0.0162309	+	0.0499537i	0.942613	+	0.333887i	$0.108360\pi$
$102$	−11.2812	+	8.19624i	−1.11700	+	0.811548i
$103$	6.92705	+	5.03280i	0.682543	+	0.495896i	0.874200	−	0.485566i	$-0.161386\pi$
$103$	6.92705	+	5.03280i	0.682543	+	0.495896i	−0.191658	+	0.981462i	$0.561386\pi$
$104$	0.500000	+	1.53884i	0.0490290	+	0.150896i
$105$	−1.21885	−	3.75123i	−0.118947	−	0.366082i
$106$	−4.80902	−	3.49396i	−0.467093	−	0.339363i
$107$	−2.42705	+	1.76336i	−0.234632	+	0.170470i	−0.698888	−	0.715231i	$-0.746322\pi$
$107$	−2.42705	+	1.76336i	−0.234632	+	0.170470i	0.464256	+	0.885701i	$0.346322\pi$
$108$	0.690983	−	2.12663i	0.0664899	−	0.204635i
$109$	10.3262			0.989074			0.494537	−	0.869157i	$-0.335338\pi$
$109$	10.3262			0.989074			0.494537	+	0.869157i	$0.335338\pi$
$110$	1.57295	−	1.31433i	0.149975	−	0.125316i
$111$	17.5623			1.66694
$112$	0.881966	−	2.71441i	0.0833380	−	0.256488i
$113$	−13.2812	+	9.64932i	−1.24939	+	0.907732i	−0.998186	−	0.0602034i	$-0.980825\pi$
$113$	−13.2812	+	9.64932i	−1.24939	+	0.907732i	−0.251200	+	0.967935i	$0.580825\pi$
$114$	1.80902	+	1.31433i	0.169430	+	0.123098i
$115$	−0.0450850	−	0.138757i	−0.00420420	−	0.0129392i
$116$	−3.23607	−	9.95959i	−0.300461	−	0.924725i
$117$	−2.61803	−	1.90211i	−0.242037	−	0.175850i
$118$	10.5902	−	7.69421i	0.974904	−	0.708309i
$119$	−5.50000	+	16.9273i	−0.504184	+	1.55172i
$120$	−1.38197			−0.126156
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	−4.38197			−0.396725
$123$	−2.82624	+	8.69827i	−0.254833	+	0.784296i
$124$	8.66312	−	6.29412i	0.777971	−	0.565229i
$125$	4.80902	+	3.49396i	0.430132	+	0.312509i
$126$	1.76393	+	5.42882i	0.157144	+	0.483638i
$127$	−5.92705	−	18.2416i	−0.525941	−	1.61868i	−0.762448	−	0.647049i	$-0.776003\pi$
$127$	−5.92705	−	18.2416i	−0.525941	−	1.61868i	0.236507	−	0.971630i	$-0.423997\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	6.70820	−	4.87380i	0.590624	−	0.429114i
$130$	0.309017	−	0.951057i	0.0271026	−	0.0834132i
$131$	−16.6525			−1.45493			−0.727467	−	0.686143i	$-0.759302\pi$
$131$	−16.6525			−1.45493			−0.727467	+	0.686143i	$0.759302\pi$
$132$	−5.69098	+	4.75528i	−0.495336	+	0.413894i
$133$	2.85410			0.247482
$134$	−1.88197	+	5.79210i	−0.162577	+	0.500361i
$135$	−1.11803	+	0.812299i	−0.0962250	+	0.0699116i
$136$	5.04508	+	3.66547i	0.432612	+	0.314311i
$137$	0.454915	+	1.40008i	0.0388660	+	0.119617i	0.968607	−	0.248597i	$-0.0799694\pi$
$137$	0.454915	+	1.40008i	0.0388660	+	0.119617i	−0.929741	+	0.368214i	$0.879969\pi$
$138$	0.163119	+	0.502029i	0.0138856	+	0.0427355i
$139$	3.92705	+	2.85317i	0.333088	+	0.242003i	0.741740	−	0.670688i	$-0.234001\pi$
$139$	3.92705	+	2.85317i	0.333088	+	0.242003i	−0.408652	+	0.912690i	$0.634001\pi$
$140$	−1.42705	+	1.03681i	−0.120608	+	0.0876267i
$141$	−7.92705	+	24.3970i	−0.667578	+	2.05459i
$142$	−3.76393			−0.315862
$143$	−2.00000	−	4.97980i	−0.167248	−	0.416432i
$144$	2.00000			0.166667
$145$	−2.00000	+	6.15537i	−0.166091	+	0.511175i
$146$	−1.07295	+	0.779543i	−0.0887979	+	0.0645154i
$147$	2.07295	+	1.50609i	0.170974	+	0.124220i
$148$	−2.42705	−	7.46969i	−0.199502	−	0.614005i
$149$	5.48936	+	16.8945i	0.449706	+	1.38405i	0.877240	+	0.480052i	$0.159382\pi$
$149$	5.48936	+	16.8945i	0.449706	+	1.38405i	−0.427534	+	0.903999i	$0.640618\pi$
$150$	−8.35410	−	6.06961i	−0.682110	−	0.495582i
$151$	−0.236068	+	0.171513i	−0.0192109	+	0.0139576i	−0.597349	−	0.801981i	$-0.703779\pi$
$151$	−0.236068	+	0.171513i	−0.0192109	+	0.0139576i	0.578138	+	0.815939i	$0.303779\pi$
$152$	0.309017	−	0.951057i	0.0250646	−	0.0771409i
$153$	−12.4721			−1.00831
$154$	−2.30902	+	9.18005i	−0.186066	+	0.739750i
$155$	−6.61803			−0.531573
$156$	−1.11803	+	3.44095i	−0.0895144	+	0.275497i
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	−2.42705	−	1.76336i	−0.193086	−	0.140285i
$159$	−4.10739	−	12.6412i	−0.325737	−	1.00252i
$160$	0.190983	+	0.587785i	0.0150985	+	0.0464685i
$161$	0.545085	+	0.396027i	0.0429587	+	0.0312113i
$162$	8.89919	−	6.46564i	0.699186	−	0.507988i
$163$	−1.55573	+	4.78804i	−0.121854	+	0.375028i	−0.993315	−	0.115437i	$-0.963173\pi$
$163$	−1.55573	+	4.78804i	−0.121854	+	0.375028i	0.871461	+	0.490465i	$0.163173\pi$
$164$	4.09017			0.319389
$165$	4.57295	−	0.310271i	0.356004	−	0.0241545i
$166$	1.09017			0.0846136
$167$	−2.59017	+	7.97172i	−0.200433	+	0.616870i	0.799437	+	0.600750i	$0.205131\pi$
$167$	−2.59017	+	7.97172i	−0.200433	+	0.616870i	−0.999870	+	0.0161201i	$0.994869\pi$
$168$	5.16312	−	3.75123i	0.398343	−	0.289413i
$169$	8.39919	+	6.10237i	0.646091	+	0.469413i
$170$	−1.19098	−	3.66547i	−0.0913442	−	0.281129i
$171$	0.618034	+	1.90211i	0.0472622	+	0.145458i
$172$	−3.00000	−	2.17963i	−0.228748	−	0.166195i
$173$	−7.11803	+	5.17155i	−0.541174	+	0.393186i	−0.824521	−	0.565832i	$-0.808555\pi$
$173$	−7.11803	+	5.17155i	−0.541174	+	0.393186i	0.283347	+	0.959018i	$0.408555\pi$
$174$	7.23607	−	22.2703i	0.548565	−	1.68831i
$175$	−13.1803			−0.996340
$176$	2.80902	+	1.76336i	0.211738	+	0.132918i
$177$	29.2705			2.20011
$178$	−2.83688	+	8.73102i	−0.212633	+	0.654418i
$179$	13.9443	−	10.1311i	1.04224	−	0.757234i	0.0715215	−	0.997439i	$-0.477215\pi$
$179$	13.9443	−	10.1311i	1.04224	−	0.757234i	0.970722	+	0.240205i	$0.0772145\pi$
$180$	−1.00000	−	0.726543i	−0.0745356	−	0.0541533i
$181$	1.25329	+	3.85723i	0.0931562	+	0.286705i	0.986769	−	0.162134i	$-0.0518376\pi$
$181$	1.25329	+	3.85723i	0.0931562	+	0.286705i	−0.893613	+	0.448839i	$0.851838\pi$
$182$	1.42705	+	4.39201i	0.105780	+	0.325558i
$183$	−7.92705	−	5.75934i	−0.585984	−	0.425743i
$184$	0.190983	−	0.138757i	0.0140795	−	0.0102293i
$185$	−1.50000	+	4.61653i	−0.110282	+	0.339414i
$186$	23.9443			1.75568
$187$	−17.5172	−	10.9964i	−1.28099	−	0.804137i
$188$	11.4721			0.836692
$189$	1.97214	−	6.06961i	0.143452	−	0.441499i
$190$	−0.500000	+	0.363271i	−0.0362738	+	0.0263545i
$191$	−12.8992	−	9.37181i	−0.933352	−	0.678120i	0.0134589	−	0.999909i	$-0.495716\pi$
$191$	−12.8992	−	9.37181i	−0.933352	−	0.678120i	−0.946811	+	0.321789i	$0.895716\pi$
$192$	−0.690983	−	2.12663i	−0.0498674	−	0.153476i
$193$	−7.89919	−	24.3112i	−0.568596	−	1.74996i	−0.657018	−	0.753875i	$-0.728182\pi$
$193$	−7.89919	−	24.3112i	−0.568596	−	1.74996i	0.0884218	−	0.996083i	$-0.471818\pi$
$194$	−13.2812	−	9.64932i	−0.953531	−	0.692781i
$195$	1.80902	−	1.31433i	0.129546	−	0.0941210i
$196$	0.354102	−	1.08981i	0.0252930	−	0.0778438i
$197$	0.819660			0.0583984			0.0291992	−	0.999574i	$-0.490704\pi$
$197$	0.819660			0.0583984			0.0291992	+	0.999574i	$0.490704\pi$
$198$	−6.61803	+	0.449028i	−0.470323	+	0.0319110i
$199$	−21.8885			−1.55164			−0.775819	−	0.630956i	$-0.782663\pi$
$199$	−21.8885			−1.55164			−0.775819	+	0.630956i	$0.782663\pi$
$200$	−1.42705	+	4.39201i	−0.100908	+	0.310562i
$201$	−11.0172	+	8.00448i	−0.777095	+	0.564592i
$202$	0.427051	+	0.310271i	0.0300472	+	0.0218306i
$203$	−9.23607	−	28.4257i	−0.648245	−	1.99509i
$204$	4.30902	+	13.2618i	0.301692	+	0.928511i
$205$	−2.04508	−	1.48584i	−0.142835	−	0.103776i
$206$	6.92705	−	5.03280i	0.482631	−	0.350652i
$207$	−0.145898	+	0.449028i	−0.0101406	+	0.0312096i
$208$	1.61803			0.112190
$209$	−0.809017	+	3.21644i	−0.0559609	+	0.222486i
$210$	−3.94427			−0.272181
$211$	−2.48936	+	7.66145i	−0.171374	+	0.527436i	−0.999449	−	0.0331812i	$-0.989436\pi$
$211$	−2.48936	+	7.66145i	−0.171374	+	0.527436i	0.828075	+	0.560617i	$0.189436\pi$
$212$	−4.80902	+	3.49396i	−0.330285	+	0.239966i
$213$	−6.80902	−	4.94704i	−0.466546	−	0.338966i
$214$	0.927051	+	2.85317i	0.0633719	+	0.195039i
$215$	0.708204	+	2.17963i	0.0482991	+	0.148649i
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$	24.7254	−	17.9641i	1.67847	−	1.21948i
$218$	3.19098	−	9.82084i	0.216121	−	0.665151i
$219$	−2.96556			−0.200394
$220$	−0.763932	−	1.90211i	−0.0515043	−	0.128240i
$221$	−10.0902			−0.678738
$222$	5.42705	−	16.7027i	0.364240	−	1.12101i
$223$	16.1803	−	11.7557i	1.08352	−	0.787220i	0.105223	−	0.994449i	$-0.466444\pi$
$223$	16.1803	−	11.7557i	1.08352	−	0.787220i	0.978293	+	0.207228i	$0.0664443\pi$
$224$	−2.30902	−	1.67760i	−0.154278	−	0.112089i
$225$	−2.85410	−	8.78402i	−0.190273	−	0.585602i
$226$	5.07295	+	15.6129i	0.337448	+	1.03856i
$227$	−10.5451	−	7.66145i	−0.699902	−	0.508508i	0.179998	−	0.983667i	$-0.442391\pi$
$227$	−10.5451	−	7.66145i	−0.699902	−	0.508508i	−0.879900	+	0.475158i	$0.842391\pi$
$228$	1.80902	−	1.31433i	0.119805	−	0.0870435i
$229$	1.37132	−	4.22050i	0.0906196	−	0.278898i	−0.895468	−	0.445126i	$-0.853159\pi$
$229$	1.37132	−	4.22050i	0.0906196	−	0.278898i	0.986087	+	0.166228i	$0.0531588\pi$
$230$	−0.145898			−0.00962023
$231$	−16.2426	+	13.5721i	−1.06869	+	0.892976i
$232$	−10.4721			−0.687529
$233$	−2.36475	+	7.27794i	−0.154920	+	0.476794i	−0.998153	−	0.0607545i	$-0.980649\pi$
$233$	−2.36475	+	7.27794i	−0.154920	+	0.476794i	0.843233	+	0.537548i	$0.180649\pi$
$234$	−2.61803	+	1.90211i	−0.171146	+	0.124345i
$235$	−5.73607	−	4.16750i	−0.374180	−	0.271858i
$236$	−4.04508	−	12.4495i	−0.263313	−	0.810393i
$237$	−2.07295	−	6.37988i	−0.134653	−	0.414418i
$238$	14.3992	+	10.4616i	0.933361	+	0.678126i
$239$	−17.7812	+	12.9188i	−1.15017	+	0.835645i	−0.988503	−	0.151200i	$-0.951686\pi$
$239$	−17.7812	+	12.9188i	−1.15017	+	0.835645i	−0.161664	+	0.986846i	$0.551686\pi$
$240$	−0.427051	+	1.31433i	−0.0275660	+	0.0848395i
$241$	−7.32624			−0.471924			−0.235962	−	0.971762i	$-0.575824\pi$
$241$	−7.32624			−0.471924			−0.235962	+	0.971762i	$0.575824\pi$
$242$	−9.69098	−	5.20431i	−0.622960	−	0.334546i
$243$	17.8885			1.14755
$244$	−1.35410	+	4.16750i	−0.0866875	+	0.266797i
$245$	−0.572949	+	0.416272i	−0.0366044	+	0.0265946i
$246$	7.39919	+	5.37582i	0.471755	+	0.342750i
$247$	0.500000	+	1.53884i	0.0318142	+	0.0979142i
$248$	−3.30902	−	10.1841i	−0.210123	−	0.646691i
$249$	1.97214	+	1.43284i	0.124979	+	0.0908026i
$250$	4.80902	−	3.49396i	0.304149	−	0.220977i
$251$	0.944272	−	2.90617i	0.0596019	−	0.183436i	−0.916823	−	0.399295i	$-0.869255\pi$
$251$	0.944272	−	2.90617i	0.0596019	−	0.183436i	0.976425	+	0.215859i	$0.0692551\pi$
$252$	5.70820			0.359583
$253$	−0.600813	+	0.502029i	−0.0377728	+	0.0315623i
$254$	−19.1803			−1.20348
$255$	2.66312	−	8.19624i	0.166771	−	0.513268i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.11803	−	3.71847i	−0.319254	−	0.231952i	0.416603	−	0.909089i	$-0.363221\pi$
$257$	−5.11803	−	3.71847i	−0.319254	−	0.231952i	−0.735857	+	0.677137i	$0.763221\pi$
$258$	−2.56231	−	7.88597i	−0.159522	−	0.490959i
$259$	−6.92705	−	21.3193i	−0.430426	−	1.32472i
$260$	−0.809017	−	0.587785i	−0.0501731	−	0.0364529i
$261$	16.9443	−	12.3107i	1.04882	−	0.762015i
$262$	−5.14590	+	15.8374i	−0.317915	+	0.978441i
$263$	−13.0344			−0.803738			−0.401869	−	0.915697i	$-0.631639\pi$
$263$	−13.0344			−0.803738			−0.401869	+	0.915697i	$0.631639\pi$
$264$	2.76393	+	6.88191i	0.170108	+	0.423552i
$265$	3.67376			0.225677
$266$	0.881966	−	2.71441i	0.0540768	−	0.166431i
$267$	−16.6074	+	12.0660i	−1.01636	+	0.738426i
$268$	4.92705	+	3.57971i	0.300968	+	0.218666i
$269$	8.63525	+	26.5766i	0.526501	+	1.62040i	0.761329	+	0.648366i	$0.224547\pi$
$269$	8.63525	+	26.5766i	0.526501	+	1.62040i	−0.234828	+	0.972037i	$0.575453\pi$
$270$	0.427051	+	1.31433i	0.0259895	+	0.0799874i
$271$	6.23607	+	4.53077i	0.378814	+	0.275225i	0.760856	−	0.648920i	$-0.224779\pi$
$271$	6.23607	+	4.53077i	0.378814	+	0.275225i	−0.382042	+	0.924145i	$0.624779\pi$
$272$	5.04508	−	3.66547i	0.305903	−	0.222252i
$273$	−3.19098	+	9.82084i	−0.193127	+	0.594384i
$274$	1.47214			0.0889350
$275$	3.73607	−	14.8536i	0.225293	−	0.895708i
$276$	0.527864			0.0317737
$277$	−3.97214	+	12.2250i	−0.238663	+	0.734528i	0.757952	+	0.652310i	$0.226200\pi$
$277$	−3.97214	+	12.2250i	−0.238663	+	0.734528i	−0.996614	+	0.0822173i	$0.973800\pi$
$278$	3.92705	−	2.85317i	0.235529	−	0.171122i
$279$	17.3262	+	12.5882i	1.03729	+	0.753639i
$280$	0.545085	+	1.67760i	0.0325751	+	0.100256i
$281$	−0.319660	−	0.983813i	−0.0190693	−	0.0586893i	0.941069	−	0.338215i	$-0.109823\pi$
$281$	−0.319660	−	0.983813i	−0.0190693	−	0.0586893i	−0.960138	+	0.279525i	$0.909823\pi$
$282$	20.7533	+	15.0781i	1.23584	+	0.897891i
$283$	4.28115	−	3.11044i	0.254488	−	0.184896i	−0.453225	−	0.891396i	$-0.649727\pi$
$283$	4.28115	−	3.11044i	0.254488	−	0.184896i	0.707714	+	0.706499i	$0.249727\pi$
$284$	−1.16312	+	3.57971i	−0.0690184	+	0.212417i
$285$	−1.38197			−0.0818606
$286$	−5.35410	+	0.363271i	−0.316595	+	0.0214807i
$287$	11.6738			0.689080
$288$	0.618034	−	1.90211i	0.0364180	−	0.112083i
$289$	−17.7082	+	12.8658i	−1.04166	+	0.756810i
$290$	5.23607	+	3.80423i	0.307472	+	0.223392i
$291$	−11.3435	−	34.9116i	−0.664965	−	2.04655i
$292$	0.409830	+	1.26133i	0.0239835	+	0.0738136i
$293$	−8.51722	−	6.18812i	−0.497581	−	0.361514i	0.310511	−	0.950570i	$-0.399500\pi$
$293$	−8.51722	−	6.18812i	−0.497581	−	0.361514i	−0.808092	+	0.589056i	$0.799500\pi$
$294$	2.07295	−	1.50609i	0.120897	−	0.0878367i
$295$	−2.50000	+	7.69421i	−0.145556	+	0.447974i
$296$	−7.85410			−0.456510
$297$	6.28115	+	3.94298i	0.364469	+	0.228795i
$298$	17.7639			1.02904
$299$	−0.118034	+	0.363271i	−0.00682608	+	0.0210085i
$300$	−8.35410	+	6.06961i	−0.482324	+	0.350429i
$301$	−8.56231	−	6.22088i	−0.493523	−	0.358566i
$302$	0.0901699	+	0.277515i	0.00518870	+	0.0159692i
$303$	0.364745	+	1.12257i	0.0209541	+	0.0644900i
$304$	−0.809017	−	0.587785i	−0.0464003	−	0.0337118i
$305$	2.19098	−	1.59184i	0.125455	−	0.0911486i
$306$	−3.85410	+	11.8617i	−0.220324	+	0.678089i
$307$	−18.2361			−1.04079			−0.520394	−	0.853926i	$-0.674215\pi$
$307$	−18.2361			−1.04079			−0.520394	+	0.853926i	$0.674215\pi$
$308$	8.01722	+	5.03280i	0.456824	+	0.286770i
$309$	19.1459			1.08917
$310$	−2.04508	+	6.29412i	−0.116153	+	0.357482i
$311$	−13.3262	+	9.68208i	−0.755662	+	0.549020i	−0.897577	−	0.440859i	$-0.854674\pi$
$311$	−13.3262	+	9.68208i	−0.755662	+	0.549020i	0.141915	+	0.989879i	$0.454674\pi$
$312$	2.92705	+	2.12663i	0.165712	+	0.120397i
$313$	3.07295	+	9.45756i	0.173693	+	0.534573i	0.999571	−	0.0292757i	$-0.00932006\pi$
$313$	3.07295	+	9.45756i	0.173693	+	0.534573i	−0.825878	+	0.563849i	$0.809320\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$	−2.85410	−	2.07363i	−0.160810	−	0.116836i
$316$	−2.42705	+	1.76336i	−0.136532	+	0.0991965i
$317$	−0.927051	+	2.85317i	−0.0520684	+	0.160250i	−0.973709	−	0.227793i	$-0.926849\pi$
$317$	−0.927051	+	2.85317i	−0.0520684	+	0.160250i	0.921641	+	0.388043i	$0.126849\pi$
$318$	−13.2918			−0.745367
$319$	34.6525	−	2.35114i	1.94017	−	0.131639i
$320$	0.618034			0.0345492
$321$	−2.07295	+	6.37988i	−0.115701	+	0.356090i
$322$	0.545085	−	0.396027i	0.0303764	−	0.0220697i
$323$	5.04508	+	3.66547i	0.280716	+	0.203952i
$324$	−3.39919	−	10.4616i	−0.188844	−	0.581201i
$325$	−2.30902	−	7.10642i	−0.128081	−	0.394193i
$326$	4.07295	+	2.95917i	0.225580	+	0.163893i
$327$	18.6803	−	13.5721i	1.03303	−	0.750537i
$328$	1.26393	−	3.88998i	0.0697890	−	0.214788i
$329$	32.7426			1.80516
$330$	1.11803	−	4.44501i	0.0615457	−	0.244690i
$331$	9.70820			0.533611			0.266806	−	0.963750i	$-0.414032\pi$
$331$	9.70820			0.533611			0.266806	+	0.963750i	$0.414032\pi$
$332$	0.336881	−	1.03681i	0.0184887	−	0.0569025i
$333$	12.7082	−	9.23305i	0.696405	−	0.505968i
$334$	6.78115	+	4.92680i	0.371048	+	0.269582i
$335$	−1.16312	−	3.57971i	−0.0635480	−	0.195581i
$336$	−1.97214	−	6.06961i	−0.107589	−	0.331124i
$337$	12.2812	+	8.92278i	0.668997	+	0.486055i	0.869689	−	0.493600i	$-0.164319\pi$
$337$	12.2812	+	8.92278i	0.668997	+	0.486055i	−0.200692	+	0.979654i	$0.564319\pi$
$338$	8.39919	−	6.10237i	0.456856	−	0.331925i
$339$	−11.3435	+	34.9116i	−0.616092	+	1.89614i
$340$	−3.85410			−0.209018
$341$	13.2361	+	32.9565i	0.716773	+	1.78469i
$342$	2.00000			0.108148
$343$	−5.16312	+	15.8904i	−0.278782	+	0.858003i
$344$	−3.00000	+	2.17963i	−0.161749	+	0.117518i
$345$	−0.263932	−	0.191758i	−0.0142096	−	0.0103239i
$346$	2.71885	+	8.36775i	0.146166	+	0.449853i
$347$	−7.90983	−	24.3440i	−0.424622	−	1.30685i	−0.903356	−	0.428892i	$-0.858904\pi$
$347$	−7.90983	−	24.3440i	−0.424622	−	1.30685i	0.478734	−	0.877960i	$-0.341096\pi$
$348$	−18.9443	−	13.7638i	−1.01552	−	0.737818i
$349$	10.2533	−	7.44945i	0.548846	−	0.398760i	−0.278514	−	0.960432i	$-0.589842\pi$
$349$	10.2533	−	7.44945i	0.548846	−	0.398760i	0.827360	+	0.561672i	$0.189842\pi$
$350$	−4.07295	+	12.5352i	−0.217708	+	0.670037i
$351$	3.61803			0.193116
$352$	2.54508	−	2.12663i	0.135653	−	0.113350i
$353$	26.9443			1.43410			0.717049	−	0.697022i	$-0.245492\pi$
$353$	26.9443			1.43410			0.717049	+	0.697022i	$0.245492\pi$
$354$	9.04508	−	27.8379i	0.480741	−	1.47957i
$355$	1.88197	−	1.36733i	0.0998844	−	0.0725703i
$356$	7.42705	+	5.39607i	0.393633	+	0.285991i
$357$	12.2984	+	37.8505i	0.650899	+	2.00326i
$358$	−5.32624	−	16.3925i	−0.281500	−	0.866369i
$359$	16.0623	+	11.6699i	0.847736	+	0.615916i	0.924521	−	0.381131i	$-0.124465\pi$
$359$	16.0623	+	11.6699i	0.847736	+	0.615916i	−0.0767848	+	0.997048i	$0.524465\pi$
$360$	−1.00000	+	0.726543i	−0.0527046	+	0.0382922i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	4.05573			0.213164
$363$	−10.6910	−	22.1518i	−0.561131	−	1.16267i
$364$	4.61803			0.242051
$365$	0.253289	−	0.779543i	0.0132577	−	0.0408032i
$366$	−7.92705	+	5.75934i	−0.414354	+	0.301046i
$367$	−10.8713	−	7.89848i	−0.567478	−	0.412297i	0.266710	−	0.963777i	$-0.414063\pi$
$367$	−10.8713	−	7.89848i	−0.567478	−	0.412297i	−0.834188	+	0.551480i	$0.814063\pi$
$368$	−0.0729490	−	0.224514i	−0.00380273	−	0.0117036i
$369$	2.52786	+	7.77997i	0.131595	+	0.405009i
$370$	3.92705	+	2.85317i	0.204158	+	0.148329i
$371$	−13.7254	+	9.97210i	−0.712589	+	0.517726i
$372$	7.39919	−	22.7724i	0.383630	−	1.18069i
$373$	−19.1246			−0.990235			−0.495117	−	0.868826i	$-0.664875\pi$
$373$	−19.1246			−0.990235			−0.495117	+	0.868826i	$0.664875\pi$
$374$	−15.8713	+	13.2618i	−0.820687	+	0.685751i
$375$	13.2918			0.686385
$376$	3.54508	−	10.9106i	0.182824	−	0.562674i
$377$	13.7082	−	9.95959i	0.706008	−	0.512945i
$378$	−5.16312	−	3.75123i	−0.265562	−	0.192942i
$379$	6.75329	+	20.7845i	0.346893	+	1.06763i	0.960562	+	0.278064i	$0.0896928\pi$
$379$	6.75329	+	20.7845i	0.346893	+	1.06763i	−0.613669	+	0.789563i	$0.710307\pi$
$380$	0.190983	+	0.587785i	0.00979722	+	0.0301527i
$381$	−34.6976	−	25.2093i	−1.77761	−	1.29151i
$382$	−12.8992	+	9.37181i	−0.659980	+	0.479503i
$383$	−4.51722	+	13.9026i	−0.230819	+	0.710388i	0.766829	+	0.641851i	$0.221833\pi$
$383$	−4.51722	+	13.9026i	−0.230819	+	0.710388i	−0.997649	+	0.0685374i	$0.978167\pi$
$384$	−2.23607			−0.114109
$385$	−2.18034	−	5.42882i	−0.111120	−	0.276679i
$386$	−25.5623			−1.30109
$387$	2.29180	−	7.05342i	0.116499	−	0.358546i
$388$	−13.2812	+	9.64932i	−0.674248	+	0.489870i
$389$	−22.7082	−	16.4985i	−1.15135	−	0.836506i	−0.162692	−	0.986677i	$-0.552018\pi$
$389$	−22.7082	−	16.4985i	−1.15135	−	0.836506i	−0.988660	+	0.150171i	$0.952018\pi$
$390$	−0.690983	−	2.12663i	−0.0349893	−	0.107686i
$391$	0.454915	+	1.40008i	0.0230060	+	0.0708053i
$392$	−0.927051	−	0.673542i	−0.0468231	−	0.0340190i
$393$	−30.1246	+	21.8868i	−1.51959	+	1.10404i
$394$	0.253289	−	0.779543i	0.0127605	−	0.0392728i
$395$	1.85410			0.0932900
$396$	−1.61803	+	6.43288i	−0.0813093	+	0.323264i
$397$	29.8328			1.49727			0.748633	−	0.662985i	$-0.230711\pi$
$397$	29.8328			1.49727			0.748633	+	0.662985i	$0.230711\pi$
$398$	−6.76393	+	20.8172i	−0.339045	+	1.04347i
$399$	5.16312	−	3.75123i	0.258479	−	0.187796i
$400$	3.73607	+	2.71441i	0.186803	+	0.135721i
$401$	−9.10739	−	28.0297i	−0.454801	−	1.39973i	−0.871368	−	0.490630i	$-0.836767\pi$
$401$	−9.10739	−	28.0297i	−0.454801	−	1.39973i	0.416567	−	0.909105i	$-0.363233\pi$
$402$	4.20820	+	12.9515i	0.209886	+	0.645963i
$403$	14.0172	+	10.1841i	0.698248	+	0.507307i
$404$	0.427051	−	0.310271i	0.0212466	−	0.0154365i
$405$	−2.10081	+	6.46564i	−0.104390	+	0.321280i
$406$	−29.8885			−1.48334
$407$	25.9894	−	1.76336i	1.28824	−	0.0874063i
$408$	13.9443			0.690344
$409$	−0.927051	+	2.85317i	−0.0458397	+	0.141080i	−0.971357	−	0.237626i	$-0.923631\pi$
$409$	−0.927051	+	2.85317i	−0.0458397	+	0.141080i	0.925517	+	0.378706i	$0.123631\pi$
$410$	−2.04508	+	1.48584i	−0.101000	+	0.0733805i
$411$	2.66312	+	1.93487i	0.131362	+	0.0954401i
$412$	−2.64590	−	8.14324i	−0.130354	−	0.401188i
$413$	−11.5451	−	35.5321i	−0.568096	−	1.74842i
$414$	0.381966	+	0.277515i	0.0187726	+	0.0136391i
$415$	−0.545085	+	0.396027i	−0.0267572	+	0.0194402i
$416$	0.500000	−	1.53884i	0.0245145	−	0.0754479i
$417$	10.8541			0.531528
$418$	2.80902	+	1.76336i	0.137394	+	0.0862485i
$419$	31.4164			1.53479			0.767396	−	0.641173i	$-0.221552\pi$
$419$	31.4164			1.53479			0.767396	+	0.641173i	$0.221552\pi$
$420$	−1.21885	+	3.75123i	−0.0594736	+	0.183041i
$421$	8.42705	−	6.12261i	0.410709	−	0.298398i	−0.363180	−	0.931719i	$-0.618309\pi$
$421$	8.42705	−	6.12261i	0.410709	−	0.298398i	0.773889	+	0.633321i	$0.218309\pi$
$422$	6.51722	+	4.73504i	0.317253	+	0.230498i
$423$	7.09017	+	21.8213i	0.344736	+	1.06099i
$424$	1.83688	+	5.65334i	0.0892068	+	0.274550i
$425$	−23.2984	−	16.9273i	−1.13014	−	0.821093i
$426$	−6.80902	+	4.94704i	−0.329898	+	0.239685i
$427$	−3.86475	+	11.8945i	−0.187028	+	0.575613i
$428$	3.00000			0.145010
$429$	−10.1631	−	6.37988i	−0.490680	−	0.308024i
$430$	2.29180			0.110520
$431$	−8.35410	+	25.7113i	−0.402403	+	1.23847i	0.520641	+	0.853775i	$0.325693\pi$
$431$	−8.35410	+	25.7113i	−0.402403	+	1.23847i	−0.923044	+	0.384693i	$0.874307\pi$
$432$	−1.80902	+	1.31433i	−0.0870364	+	0.0632356i
$433$	26.2705	+	19.0866i	1.26248	+	0.917246i	0.998877	−	0.0473856i	$-0.0150890\pi$
$433$	26.2705	+	19.0866i	1.26248	+	0.917246i	0.263603	+	0.964631i	$0.415089\pi$
$434$	−9.44427	−	29.0665i	−0.453340	−	1.39524i
$435$	4.47214	+	13.7638i	0.214423	+	0.659925i
$436$	−8.35410	−	6.06961i	−0.400089	−	0.290682i
$437$	0.190983	−	0.138757i	0.00913596	−	0.00663766i
$438$	−0.916408	+	2.82041i	−0.0437877	+	0.134765i
$439$	26.8541			1.28168			0.640838	−	0.767676i	$-0.278587\pi$
$439$	26.8541			1.28168			0.640838	+	0.767676i	$0.278587\pi$
$440$	−2.04508	+	0.138757i	−0.0974956	+	0.00661499i
$441$	2.29180			0.109133
$442$	−3.11803	+	9.59632i	−0.148310	+	0.456450i
$443$	−1.50000	+	1.08981i	−0.0712672	+	0.0517786i	−0.622848	−	0.782343i	$-0.714025\pi$
$443$	−1.50000	+	1.08981i	−0.0712672	+	0.0517786i	0.551581	+	0.834121i	$0.314025\pi$
$444$	−14.2082	−	10.3229i	−0.674292	−	0.489901i
$445$	−1.75329	−	5.39607i	−0.0831139	−	0.255798i
$446$	−6.18034	−	19.0211i	−0.292648	−	0.900677i
$447$	32.1353	+	23.3476i	1.51995	+	1.10430i
$448$	−2.30902	+	1.67760i	−0.109091	+	0.0792591i
$449$	3.92705	−	12.0862i	0.185329	−	0.570384i	−0.814625	−	0.579988i	$-0.803057\pi$
$449$	3.92705	−	12.0862i	0.185329	−	0.570384i	0.999954	+	0.00960419i	$0.00305716\pi$
$450$	−9.23607			−0.435392
$451$	−3.30902	+	13.1558i	−0.155816	+	0.619482i
$452$	16.4164			0.772163
$453$	−0.201626	+	0.620541i	−0.00947322	+	0.0291556i
$454$	−10.5451	+	7.66145i	−0.494905	+	0.359570i
$455$	−2.30902	−	1.67760i	−0.108248	−	0.0786471i
$456$	−0.690983	−	2.12663i	−0.0323582	−	0.0995884i
$457$	2.78115	+	8.55951i	0.130097	+	0.400397i	0.994795	−	0.101895i	$-0.0324904\pi$
$457$	2.78115	+	8.55951i	0.130097	+	0.400397i	−0.864698	+	0.502292i	$0.832490\pi$
$458$	−3.59017	−	2.60841i	−0.167758	−	0.121883i
$459$	11.2812	−	8.19624i	0.526559	−	0.382568i
$460$	−0.0450850	+	0.138757i	−0.00210210	+	0.00646959i
$461$	−32.3050			−1.50459			−0.752296	−	0.658825i	$-0.771054\pi$
$461$	−32.3050			−1.50459			−0.752296	+	0.658825i	$0.771054\pi$
$462$	7.88854	+	19.6417i	0.367008	+	0.913813i
$463$	−16.1459			−0.750364			−0.375182	−	0.926951i	$-0.622420\pi$
$463$	−16.1459			−0.750364			−0.375182	+	0.926951i	$0.622420\pi$
$464$	−3.23607	+	9.95959i	−0.150231	+	0.462363i
$465$	−11.9721	+	8.69827i	−0.555195	+	0.403372i
$466$	6.19098	+	4.49801i	0.286792	+	0.208366i
$467$	−5.10081	−	15.6987i	−0.236037	−	0.726449i	−0.996982	−	0.0776318i	$-0.975264\pi$
$467$	−5.10081	−	15.6987i	−0.236037	−	0.726449i	0.760945	−	0.648817i	$-0.224736\pi$
$468$	1.00000	+	3.07768i	0.0462250	+	0.142266i
$469$	14.0623	+	10.2169i	0.649337	+	0.471771i
$470$	−5.73607	+	4.16750i	−0.264585	+	0.192232i
$471$	2.56231	−	7.88597i	0.118065	−	0.363366i
$472$	−13.0902			−0.602524
$473$	9.43769	−	7.88597i	0.433946	−	0.362597i
$474$	−6.70820			−0.308118
$475$	−1.42705	+	4.39201i	−0.0654776	+	0.201519i
$476$	14.3992	−	10.4616i	0.659986	−	0.479508i
$477$	−9.61803	−	6.98791i	−0.440380	−	0.319954i
$478$	6.79180	+	20.9030i	0.310650	+	0.956081i
$479$	−2.54508	−	7.83297i	−0.116288	−	0.357897i	0.875926	−	0.482446i	$-0.160252\pi$
$479$	−2.54508	−	7.83297i	−0.116288	−	0.357897i	−0.992213	+	0.124549i	$0.960252\pi$
$480$	1.11803	+	0.812299i	0.0510310	+	0.0370762i
$481$	10.2812	−	7.46969i	0.468780	−	0.340589i
$482$	−2.26393	+	6.96767i	−0.103119	+	0.317369i
$483$	1.50658			0.0685517
$484$	−7.94427	+	7.60845i	−0.361103	+	0.345839i
$485$	10.1459			0.460701
$486$	5.52786	−	17.0130i	0.250749	−	0.771726i
$487$	1.57295	−	1.14281i	0.0712771	−	0.0517859i	−0.551576	−	0.834125i	$-0.685973\pi$
$487$	1.57295	−	1.14281i	0.0712771	−	0.0517859i	0.622853	+	0.782339i	$0.285973\pi$
$488$	3.54508	+	2.57565i	0.160478	+	0.116594i
$489$	3.47871	+	10.7064i	0.157313	+	0.484159i
$490$	0.218847	+	0.673542i	0.00988650	+	0.0304275i
$491$	23.3435	+	16.9600i	1.05348	+	0.765395i	0.972870	−	0.231351i	$-0.0743147\pi$
$491$	23.3435	+	16.9600i	1.05348	+	0.765395i	0.0806053	+	0.996746i	$0.474315\pi$
$492$	7.39919	−	5.37582i	0.333581	−	0.242361i
$493$	20.1803	−	62.1087i	0.908877	−	2.79724i
$494$	1.61803			0.0727988
$495$	3.14590	−	2.62866i	0.141398	−	0.118149i
$496$	−10.7082			−0.480813
$497$	−3.31966	+	10.2169i	−0.148907	+	0.458289i
$498$	1.97214	−	1.43284i	0.0883735	−	0.0642071i
$499$	−25.0795	−	18.2213i	−1.12271	−	0.815699i	−0.138096	−	0.990419i	$-0.544098\pi$
$499$	−25.0795	−	18.2213i	−1.12271	−	0.815699i	−0.984618	+	0.174720i	$0.944098\pi$
$500$	−1.83688	−	5.65334i	−0.0821478	−	0.252825i
$501$	5.79180	+	17.8253i	0.258758	+	0.796376i
$502$	−2.47214	−	1.79611i	−0.110337	−	0.0801644i
$503$	−15.2082	+	11.0494i	−0.678100	+	0.492669i	−0.872727	−	0.488209i	$-0.837650\pi$
$503$	−15.2082	+	11.0494i	−0.678100	+	0.492669i	0.194627	+	0.980877i	$0.437650\pi$
$504$	1.76393	−	5.42882i	0.0785718	−	0.241819i
$505$	−0.326238			−0.0145174
$506$	0.291796	+	0.726543i	0.0129719	+	0.0322988i
$507$	23.2148			1.03100
$508$	−5.92705	+	18.2416i	−0.262970	+	0.809340i
$509$	−22.2812	+	16.1882i	−0.987595	+	0.717530i	−0.959393	−	0.282073i	$-0.908978\pi$
$509$	−22.2812	+	16.1882i	−0.987595	+	0.717530i	−0.0282017	+	0.999602i	$0.508978\pi$
$510$	−6.97214	−	5.06555i	−0.308731	−	0.224306i
$511$	1.16970	+	3.59996i	0.0517443	+	0.159253i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.80902	−	1.31433i	−0.0798701	−	0.0580290i
$514$	−5.11803	+	3.71847i	−0.225747	+	0.164015i
$515$	−1.63525	+	5.03280i	−0.0720579	+	0.221772i
$516$	−8.29180			−0.365026
$517$	−9.28115	+	36.8994i	−0.408185	+	1.62284i
$518$	−22.4164			−0.984920
$519$	−6.07953	+	18.7109i	−0.266862	+	0.821316i
$520$	−0.809017	+	0.587785i	−0.0354777	+	0.0257761i
$521$	−12.5172	−	9.09429i	−0.548389	−	0.398428i	0.278802	−	0.960349i	$-0.410063\pi$
$521$	−12.5172	−	9.09429i	−0.548389	−	0.398428i	−0.827191	+	0.561920i	$0.810063\pi$
$522$	−6.47214	−	19.9192i	−0.283278	−	0.871839i
$523$	−1.77458	−	5.46158i	−0.0775968	−	0.238818i	0.904732	−	0.425981i	$-0.140071\pi$
$523$	−1.77458	−	5.46158i	−0.0775968	−	0.238818i	−0.982329	+	0.187163i	$0.940071\pi$
$524$	13.4721	+	9.78808i	0.588533	+	0.427594i
$525$	−23.8435	+	17.3233i	−1.04061	+	0.756050i
$526$	−4.02786	+	12.3965i	−0.175623	+	0.540513i
$527$	66.7771			2.90886
$528$	7.39919	−	0.502029i	0.322008	−	0.0218480i
$529$	−22.9443			−0.997577
$530$	1.13525	−	3.49396i	0.0493123	−	0.151768i
$531$	21.1803	−	15.3884i	0.919148	−	0.667800i
$532$	−2.30902	−	1.67760i	−0.100109	−	0.0727331i
$533$	2.04508	+	6.29412i	0.0885825	+	0.272629i
$534$	6.34346	+	19.5232i	0.274508	+	0.844850i
$535$	−1.50000	−	1.08981i	−0.0648507	−	0.0471168i
$536$	4.92705	−	3.57971i	0.212816	−	0.154620i
$537$	11.9098	−	36.6547i	0.513947	−	1.58177i
$538$	27.9443			1.20476
$539$	3.21885	+	2.02063i	0.138646	+	0.0870345i
$540$	1.38197			0.0594703
$541$	7.62868	−	23.4787i	0.327982	−	1.00943i	−0.642094	−	0.766626i	$-0.721934\pi$
$541$	7.62868	−	23.4787i	0.327982	−	1.00943i	0.970076	−	0.242800i	$-0.0780659\pi$
$542$	6.23607	−	4.53077i	0.267862	−	0.194613i
$543$	7.33688	+	5.33056i	0.314856	+	0.228756i
$544$	−1.92705	−	5.93085i	−0.0826216	−	0.254283i
$545$	1.97214	+	6.06961i	0.0844770	+	0.259994i
$546$	8.35410	+	6.06961i	0.357523	+	0.259755i
$547$	−15.2082	+	11.0494i	−0.650256	+	0.472439i	−0.863358	−	0.504591i	$-0.831643\pi$
$547$	−15.2082	+	11.0494i	−0.650256	+	0.472439i	0.213102	+	0.977030i	$0.431643\pi$
$548$	0.454915	−	1.40008i	0.0194330	−	0.0598086i
$549$	−8.76393			−0.374036
$550$	−12.9721	−	8.14324i	−0.553134	−	0.347229i
$551$	−10.4721			−0.446128
$552$	0.163119	−	0.502029i	0.00694280	−	0.0213678i
$553$	−6.92705	+	5.03280i	−0.294568	+	0.214016i
$554$	10.3992	+	7.55545i	0.441819	+	0.321000i
$555$	3.35410	+	10.3229i	0.142374	+	0.438181i
$556$	−1.50000	−	4.61653i	−0.0636142	−	0.195784i
$557$	21.7984	+	15.8374i	0.923627	+	0.671054i	0.944424	−	0.328730i	$-0.106620\pi$
$557$	21.7984	+	15.8374i	0.923627	+	0.671054i	−0.0207973	+	0.999784i	$0.506620\pi$
$558$	17.3262	−	12.5882i	0.733478	−	0.532903i
$559$	1.85410	−	5.70634i	0.0784202	−	0.241352i
$560$	1.76393			0.0745397
$561$	−46.1418	+	3.13068i	−1.94811	+	0.132178i
$562$	−1.03444			−0.0436353
$563$	3.89261	−	11.9802i	0.164054	−	0.504906i	−0.834911	−	0.550384i	$-0.814481\pi$
$563$	3.89261	−	11.9802i	0.164054	−	0.504906i	0.998965	+	0.0454783i	$0.0144812\pi$
$564$	20.7533	−	15.0781i	0.873871	−	0.634905i
$565$	−8.20820	−	5.96361i	−0.345322	−	0.250891i
$566$	−1.63525	−	5.03280i	−0.0687349	−	0.211544i
$567$	−9.70163	−	29.8585i	−0.407430	−	1.25394i
$568$	3.04508	+	2.21238i	0.127769	+	0.0928296i
$569$	4.47214	−	3.24920i	0.187482	−	0.136213i	−0.490085	−	0.871674i	$-0.663034\pi$
$569$	4.47214	−	3.24920i	0.187482	−	0.136213i	0.677567	+	0.735461i	$0.263034\pi$
$570$	−0.427051	+	1.31433i	−0.0178872	+	0.0550511i
$571$	10.8885			0.455671			0.227836	−	0.973700i	$-0.426835\pi$
$571$	10.8885			0.455671			0.227836	+	0.973700i	$0.426835\pi$
$572$	−1.30902	+	5.20431i	−0.0547328	+	0.217603i
$573$	−35.6525			−1.48940
$574$	3.60739	−	11.1024i	0.150570	−	0.463406i
$575$	−0.881966	+	0.640786i	−0.0367805	+	0.0267226i
$576$	−1.61803	−	1.17557i	−0.0674181	−	0.0489821i
$577$	5.01064	+	15.4212i	0.208596	+	0.641992i	0.999547	+	0.0301120i	$0.00958640\pi$
$577$	5.01064	+	15.4212i	0.208596	+	0.641992i	−0.790951	+	0.611880i	$0.790414\pi$
$578$	6.76393	+	20.8172i	0.281342	+	0.865883i
$579$	−46.2426	−	33.5972i	−1.92178	−	1.39625i
$580$	5.23607	−	3.80423i	0.217416	−	0.157962i
$581$	0.961493	−	2.95917i	0.0398894	−	0.122767i
$582$	−36.7082			−1.52160
$583$	−7.34752	−	18.2946i	−0.304303	−	0.757684i
$584$	1.32624			0.0548801
$585$	0.618034	−	1.90211i	0.0255526	−	0.0786427i
$586$	−8.51722	+	6.18812i	−0.351843	+	0.255629i
$587$	6.13525	+	4.45752i	0.253229	+	0.183982i	0.707157	−	0.707057i	$-0.249978\pi$
$587$	6.13525	+	4.45752i	0.253229	+	0.183982i	−0.453928	+	0.891039i	$0.649978\pi$
$588$	−0.791796	−	2.43690i	−0.0326531	−	0.100496i
$589$	−3.30902	−	10.1841i	−0.136346	−	0.419629i
$590$	6.54508	+	4.75528i	0.269457	+	0.195772i
$591$	1.48278	−	1.07730i	0.0609934	−	0.0443143i
$592$	−2.42705	+	7.46969i	−0.0997512	+	0.307003i
$593$	28.4164			1.16692			0.583461	−	0.812141i	$-0.301698\pi$
$593$	28.4164			1.16692			0.583461	+	0.812141i	$0.301698\pi$
$594$	5.69098	−	4.75528i	0.233504	−	0.195112i
$595$	−11.0000			−0.450956
$596$	5.48936	−	16.8945i	0.224853	−	0.692026i
$597$	−39.5967	+	28.7687i	−1.62059	+	1.17743i
$598$	0.309017	+	0.224514i	0.0126366	+	0.00918106i
$599$	3.35410	+	10.3229i	0.137045	+	0.421781i	0.995902	−	0.0904336i	$-0.0288253\pi$
$599$	3.35410	+	10.3229i	0.137045	+	0.421781i	−0.858858	+	0.512214i	$0.828825\pi$
$600$	3.19098	+	9.82084i	0.130271	+	0.400934i
$601$	−30.1525	−	21.9071i	−1.22995	−	0.893607i	−0.233059	−	0.972463i	$-0.574874\pi$
$601$	−30.1525	−	21.9071i	−1.22995	−	0.893607i	−0.996886	+	0.0788551i	$0.974874\pi$
$602$	−8.56231	+	6.22088i	−0.348974	+	0.253544i
$603$	−3.76393	+	11.5842i	−0.153279	+	0.471745i
$604$	0.291796			0.0118730
$605$	6.73607	−	0.918300i	0.273860	−	0.0373342i
$606$	1.18034			0.0479480
$607$	0.927051	−	2.85317i	0.0376278	−	0.115807i	−0.930478	−	0.366347i	$-0.880608\pi$
$607$	0.927051	−	2.85317i	0.0376278	−	0.115807i	0.968106	+	0.250540i	$0.0806083\pi$
$608$	−0.809017	+	0.587785i	−0.0328100	+	0.0238378i
$609$	−54.0689	−	39.2833i	−2.19098	−	1.59184i
$610$	−0.836881	−	2.57565i	−0.0338843	−	0.104285i
$611$	5.73607	+	17.6538i	0.232056	+	0.714196i
$612$	10.0902	+	7.33094i	0.407871	+	0.296336i
$613$	17.0902	−	12.4167i	0.690265	−	0.501507i	−0.186482	−	0.982458i	$-0.559709\pi$
$613$	17.0902	−	12.4167i	0.690265	−	0.501507i	0.876747	+	0.480951i	$0.159709\pi$
$614$	−5.63525	+	17.3435i	−0.227420	+	0.699928i
$615$	−5.65248			−0.227930
$616$	7.26393	−	6.06961i	0.292672	−	0.244552i
$617$	−11.6180			−0.467724			−0.233862	−	0.972270i	$-0.575136\pi$
$617$	−11.6180			−0.467724			−0.233862	+	0.972270i	$0.575136\pi$
$618$	5.91641	−	18.2088i	0.237993	−	0.732467i
$619$	0.736068	−	0.534785i	0.0295851	−	0.0214948i	−0.572894	−	0.819629i	$-0.694180\pi$
$619$	0.736068	−	0.534785i	0.0295851	−	0.0214948i	0.602480	+	0.798134i	$0.294180\pi$
$620$	5.35410	+	3.88998i	0.215026	+	0.156225i
$621$	−0.163119	−	0.502029i	−0.00654574	−	0.0201457i
$622$	5.09017	+	15.6659i	0.204097	+	0.628147i
$623$	21.1976	+	15.4009i	0.849262	+	0.617025i
$624$	2.92705	−	2.12663i	0.117176	−	0.0851332i
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$	9.94427			0.397453
$627$	2.76393	+	6.88191i	0.110381	+	0.274837i
$628$	−3.70820			−0.147973
$629$	15.1353	−	46.5815i	0.603482	−	1.85733i
$630$	−2.85410	+	2.07363i	−0.113710	+	0.0826153i
$631$	1.73607	+	1.26133i	0.0691118	+	0.0502126i	0.621805	−	0.783172i	$-0.286400\pi$
$631$	1.73607	+	1.26133i	0.0691118	+	0.0502126i	−0.552693	+	0.833385i	$0.686400\pi$
$632$	0.927051	+	2.85317i	0.0368761	+	0.113493i
$633$	5.56637	+	17.1315i	0.221243	+	0.680917i
$634$	2.42705	+	1.76336i	0.0963905	+	0.0700318i
$635$	9.59017	−	6.96767i	0.380574	−	0.276503i
$636$	−4.10739	+	12.6412i	−0.162869	+	0.501258i
$637$	1.85410			0.0734622
$638$	8.47214	−	33.6830i	0.335415	−	1.33352i
$639$	−7.52786			−0.297798
$640$	0.190983	−	0.587785i	0.00754927	−	0.0232343i
$641$	30.3262	−	22.0333i	1.19781	−	0.870263i	0.203746	−	0.979024i	$-0.434688\pi$
$641$	30.3262	−	22.0333i	1.19781	−	0.870263i	0.994068	+	0.108761i	$0.0346882\pi$
$642$	5.42705	+	3.94298i	0.214189	+	0.155617i
$643$	7.85410	+	24.1724i	0.309736	+	0.953268i	0.977867	+	0.209225i	$0.0670942\pi$
$643$	7.85410	+	24.1724i	0.309736	+	0.953268i	−0.668132	+	0.744043i	$0.732906\pi$
$644$	−0.208204	−	0.640786i	−0.00820438	−	0.0252505i
$645$	4.14590	+	3.01217i	0.163245	+	0.118604i
$646$	5.04508	−	3.66547i	0.198496	−	0.144216i
$647$	−0.190983	+	0.587785i	−0.00750832	+	0.0231082i	−0.954740	−	0.297440i	$-0.903867\pi$
$647$	−0.190983	+	0.587785i	−0.00750832	+	0.0231082i	0.947232	+	0.320548i	$0.103867\pi$
$648$	−11.0000			−0.432121
$649$	43.3156	−	2.93893i	1.70029	−	0.115363i
$650$	−7.47214			−0.293081
$651$	21.1180	−	64.9946i	0.827681	−	2.54734i
$652$	4.07295	−	2.95917i	0.159509	−	0.115890i
$653$	−26.1525	−	19.0009i	−1.02343	−	0.743562i	−0.0564432	−	0.998406i	$-0.517976\pi$
$653$	−26.1525	−	19.0009i	−1.02343	−	0.743562i	−0.966982	+	0.254844i	$0.917976\pi$
$654$	−7.13525	−	21.9601i	−0.279011	−	0.858706i
$655$	−3.18034	−	9.78808i	−0.124266	−	0.382452i
$656$	−3.30902	−	2.40414i	−0.129195	−	0.0938660i
$657$	−2.14590	+	1.55909i	−0.0837195	+	0.0608257i
$658$	10.1180	−	31.1401i	0.394442	−	1.21397i
$659$	−40.5279			−1.57874			−0.789371	−	0.613917i	$-0.789593\pi$
$659$	−40.5279			−1.57874			−0.789371	+	0.613917i	$0.789593\pi$
$660$	−3.88197	−	2.43690i	−0.151105	−	0.0948561i
$661$	−46.6180			−1.81323			−0.906616	−	0.421957i	$-0.861343\pi$
$661$	−46.6180			−1.81323			−0.906616	+	0.421957i	$0.861343\pi$
$662$	3.00000	−	9.23305i	0.116598	−	0.358853i
$663$	−18.2533	+	13.2618i	−0.708899	+	0.515045i
$664$	−0.881966	−	0.640786i	−0.0342269	−	0.0248673i
$665$	0.545085	+	1.67760i	0.0211375	+	0.0650545i
$666$	−4.85410	−	14.9394i	−0.188093	−	0.578890i
$667$	−2.00000	−	1.45309i	−0.0774403	−	0.0562637i
$668$	6.78115	−	4.92680i	0.262371	−	0.190623i
$669$	13.8197	−	42.5325i	0.534299	−	1.64440i
$670$	−3.76393			−0.145413
$671$	−12.3090	−	7.72696i	−0.475184	−	0.298296i
$672$	−6.38197			−0.246190
$673$	−2.07953	+	6.40013i	−0.0801599	+	0.246707i	−0.983103	−	0.183053i	$-0.941402\pi$
$673$	−2.07953	+	6.40013i	−0.0801599	+	0.246707i	0.902943	+	0.429760i	$0.141402\pi$
$674$	12.2812	−	8.92278i	0.473052	−	0.343693i
$675$	8.35410	+	6.06961i	0.321550	+	0.233619i
$676$	−3.20820	−	9.87384i	−0.123392	−	0.379763i
$677$	−0.815595	−	2.51014i	−0.0313459	−	0.0964726i	0.934160	−	0.356856i	$-0.116151\pi$
$677$	−0.815595	−	2.51014i	−0.0313459	−	0.0964726i	−0.965505	+	0.260383i	$0.916151\pi$
$678$	29.6976	+	21.5765i	1.14053	+	0.828642i
$679$	−37.9058	+	27.5402i	−1.45469	+	1.05689i
$680$	−1.19098	+	3.66547i	−0.0456721	+	0.140564i
$681$	−29.1459			−1.11687
$682$	35.4336	−	2.40414i	1.35682	−	0.0920593i
$683$	23.2148			0.888289			0.444144	−	0.895955i	$-0.353508\pi$
$683$	23.2148			0.888289			0.444144	+	0.895955i	$0.353508\pi$
$684$	0.618034	−	1.90211i	0.0236311	−	0.0727291i
$685$	−0.736068	+	0.534785i	−0.0281237	+	0.0204331i
$686$	13.5172	+	9.82084i	0.516090	+	0.374961i
$687$	−3.06637	−	9.43732i	−0.116989	−	0.360056i
$688$	1.14590	+	3.52671i	0.0436870	+	0.134455i
$689$	−7.78115	−	5.65334i	−0.296438	−	0.215375i
$690$	−0.263932	+	0.191758i	−0.0100477	+	0.00730010i
$691$	8.41641	−	25.9030i	0.320175	−	0.985398i	−0.653396	−	0.757016i	$-0.726656\pi$
$691$	8.41641	−	25.9030i	0.320175	−	0.985398i	0.973572	−	0.228382i	$-0.0733435\pi$
$692$	8.79837			0.334464
$693$	−4.61803	+	18.3601i	−0.175425	+	0.697443i
$694$	−25.5967			−0.971639
$695$	−0.927051	+	2.85317i	−0.0351650	+	0.108227i
$696$	−18.9443	+	13.7638i	−0.718081	+	0.521716i
$697$	20.6353	+	14.9924i	0.781616	+	0.567877i
$698$	−3.91641	−	12.0535i	−0.148238	−	0.456230i
$699$	5.28773	+	16.2740i	0.200000	+	0.615538i
$700$	10.6631	+	7.74721i	0.403028	+	0.292817i
$701$	15.4894	−	11.2537i	0.585025	−	0.425045i	−0.255507	−	0.966807i	$-0.582242\pi$
$701$	15.4894	−	11.2537i	0.585025	−	0.425045i	0.840532	+	0.541762i	$0.182242\pi$
$702$	1.11803	−	3.44095i	0.0421975	−	0.129870i
$703$	−7.85410			−0.296223
$704$	−1.23607	−	3.07768i	−0.0465861	−	0.115995i
$705$	−15.8541			−0.597100
$706$	8.32624	−	25.6255i	0.313362	−	0.964429i
$707$	1.21885	−	0.885544i	0.0458395	−	0.0333043i
$708$	−23.6803	−	17.2048i	−0.889962	−	0.646595i
$709$	−9.81559	−	30.2093i	−0.368632	−	1.13453i	−0.947675	−	0.319237i	$-0.896574\pi$
$709$	−9.81559	−	30.2093i	−0.368632	−	1.13453i	0.579043	−	0.815297i	$-0.303426\pi$
$710$	−0.718847	−	2.21238i	−0.0269778	−	0.0830293i
$711$	−4.85410	−	3.52671i	−0.182043	−	0.132262i
$712$	7.42705	−	5.39607i	0.278341	−	0.202226i
$713$	0.781153	−	2.40414i	0.0292544	−	0.0900358i
$714$	39.7984			1.48942
$715$	2.54508	−	2.12663i	0.0951808	−	0.0795313i
$716$	−17.2361			−0.644142
$717$	−15.1869	+	46.7405i	−0.567166	+	1.74556i
$718$	16.0623	−	11.6699i	0.599440	−	0.435519i
$719$	−20.3435	−	14.7804i	−0.758683	−	0.551215i	0.139823	−	0.990176i	$-0.455347\pi$
$719$	−20.3435	−	14.7804i	−0.758683	−	0.551215i	−0.898506	+	0.438961i	$0.855347\pi$
$720$	0.381966	+	1.17557i	0.0142350	+	0.0438109i
$721$	−7.55166	−	23.2416i	−0.281239	−	0.865563i
$722$	−0.809017	−	0.587785i	−0.0301085	−	0.0218751i
$723$	−13.2533	+	9.62908i	−0.492895	+	0.358109i
$724$	1.25329	−	3.85723i	0.0465781	−	0.143353i
$725$	48.3607			1.79607
$726$	−24.3713	+	3.32244i	−0.904505	+	0.123307i
$727$	7.83282			0.290503			0.145252	−	0.989395i	$-0.453601\pi$
$727$	7.83282			0.290503			0.145252	+	0.989395i	$0.453601\pi$
$728$	1.42705	−	4.39201i	0.0528900	−	0.162779i
$729$	5.66312	−	4.11450i	0.209745	−	0.152389i
$730$	−0.663119	−	0.481784i	−0.0245431	−	0.0178316i
$731$	−7.14590	−	21.9928i	−0.264301	−	0.813434i
$732$	3.02786	+	9.31881i	0.111913	+	0.344433i
$733$	4.39919	+	3.19620i	0.162488	+	0.118054i	0.666058	−	0.745900i	$-0.267980\pi$
$733$	4.39919	+	3.19620i	0.162488	+	0.118054i	−0.503570	+	0.863954i	$0.667980\pi$
$734$	−10.8713	+	7.89848i	−0.401268	+	0.291538i
$735$	−0.489357	+	1.50609i	−0.0180502	+	0.0555528i
$736$	−0.236068			−0.00870158
$737$	−15.5000	+	12.9515i	−0.570950	+	0.477075i
$738$	8.18034			0.301122
$739$	4.67376	−	14.3844i	0.171927	−	0.529137i	−0.827553	−	0.561388i	$-0.810268\pi$
$739$	4.67376	−	14.3844i	0.171927	−	0.529137i	0.999480	+	0.0322508i	$0.0102675\pi$
$740$	3.92705	−	2.85317i	0.144361	−	0.104885i
$741$	2.92705	+	2.12663i	0.107528	+	0.0781236i
$742$	5.24265	+	16.1352i	0.192464	+	0.592342i
$743$	7.47214	+	22.9969i	0.274126	+	0.843673i	0.989449	+	0.144880i	$0.0462795\pi$
$743$	7.47214	+	22.9969i	0.274126	+	0.843673i	−0.715323	+	0.698794i	$0.753721\pi$
$744$	−19.3713	−	14.0741i	−0.710187	−	0.515981i
$745$	−8.88197	+	6.45313i	−0.325410	+	0.236424i
$746$	−5.90983	+	18.1886i	−0.216374	+	0.665931i
$747$	2.18034			0.0797745
$748$	7.70820	+	19.1926i	0.281840	+	0.701753i
$749$	8.56231			0.312860
$750$	4.10739	−	12.6412i	0.149981	−	0.461593i
$751$	39.5517	−	28.7360i	1.44326	−	1.04859i	0.455912	−	0.890025i	$-0.349313\pi$
$751$	39.5517	−	28.7360i	1.44326	−	1.04859i	0.987348	−	0.158566i	$-0.0506869\pi$
$752$	−9.28115	−	6.74315i	−0.338449	−	0.245897i
$753$	−2.11146	−	6.49839i	−0.0769457	−	0.236815i
$754$	−5.23607	−	16.1150i	−0.190686	−	0.586872i
$755$	−0.145898	−	0.106001i	−0.00530977	−	0.00385778i
$756$	−5.16312	+	3.75123i	−0.187781	+	0.136431i
$757$	4.30244	−	13.2415i	0.156375	−	0.481272i	−0.841923	−	0.539598i	$-0.818576\pi$
$757$	4.30244	−	13.2415i	0.156375	−	0.481272i	0.998298	+	0.0583258i	$0.0185762\pi$
$758$	21.8541			0.793777
$759$	−0.427051	+	1.69784i	−0.0155010	+	0.0616278i
$760$	0.618034			0.0224184
$761$	−15.7254	+	48.3979i	−0.570046	+	1.75442i	0.0824133	+	0.996598i	$0.473737\pi$
$761$	−15.7254	+	48.3979i	−0.570046	+	1.75442i	−0.652460	+	0.757824i	$0.726263\pi$
$762$	−34.6976	+	25.2093i	−1.25696	+	0.913235i
$763$	−23.8435	−	17.3233i	−0.863191	−	0.627145i
$764$	4.92705	+	15.1639i	0.178254	+	0.548611i
$765$	−2.38197	−	7.33094i	−0.0861202	−	0.265051i
$766$	11.8262	+	8.59226i	0.427299	+	0.310451i
$767$	17.1353	−	12.4495i	0.618718	−	0.449525i
$768$	−0.690983	+	2.12663i	−0.0249337	+	0.0767380i
$769$	35.2918			1.27265			0.636327	−	0.771419i	$-0.280453\pi$
$769$	35.2918			1.27265			0.636327	+	0.771419i	$0.280453\pi$
$770$	−5.83688	+	0.396027i	−0.210347	+	0.0142718i
$771$	−14.1459			−0.509452
$772$	−7.89919	+	24.3112i	−0.284298	+	0.874979i
$773$	−4.44427	+	3.22895i	−0.159849	+	0.116137i	−0.664835	−	0.746991i	$-0.731498\pi$
$773$	−4.44427	+	3.22895i	−0.159849	+	0.116137i	0.504985	+	0.863128i	$0.331498\pi$
$774$	−6.00000	−	4.35926i	−0.215666	−	0.156690i
$775$	15.2812	+	47.0306i	0.548915	+	1.68939i
$776$	5.07295	+	15.6129i	0.182108	+	0.560472i
$777$	−40.5517	−	29.4625i	−1.45478	−	1.05696i
$778$	−22.7082	+	16.4985i	−0.814129	+	0.591499i
$779$	1.26393	−	3.88998i	0.0452851	−	0.139373i
$780$	−2.23607			−0.0800641
$781$	−10.5729	−	6.63715i	−0.378330	−	0.237496i
$782$	1.47214			0.0526435
$783$	−7.23607	+	22.2703i	−0.258596	+	0.795877i
$784$	−0.927051	+	0.673542i	−0.0331090	+	0.0240551i
$785$	1.85410	+	1.34708i	0.0661757	+	0.0480795i
$786$	11.5066	+	35.4136i	0.410426	+	1.26316i
$787$	9.14590	+	28.1482i	0.326016	+	1.00337i	0.970980	+	0.239161i	$0.0768724\pi$
$787$	9.14590	+	28.1482i	0.326016	+	1.00337i	−0.644964	+	0.764213i	$0.723128\pi$
$788$	−0.663119	−	0.481784i	−0.0236226	−	0.0171628i
$789$	−23.5795	+	17.1315i	−0.839453	+	0.609899i
$790$	0.572949	−	1.76336i	0.0203846	−	0.0627374i
$791$	46.8541			1.66594
$792$	5.61803	+	3.52671i	0.199628	+	0.125316i
$793$	−7.09017			−0.251779
$794$	9.21885	−	28.3727i	0.327165	−	1.00691i
$795$	6.64590	−	4.82853i	0.235706	−	0.171250i
$796$	17.7082	+	12.8658i	0.627651	+	0.456015i
$797$	3.15248	+	9.70232i	0.111666	+	0.343674i	0.991237	−	0.132094i	$-0.0421701\pi$
$797$	3.15248	+	9.70232i	0.111666	+	0.343674i	−0.879571	+	0.475768i	$0.842170\pi$
$798$	−1.97214	−	6.06961i	−0.0698129	−	0.214862i
$799$	57.8779	+	42.0508i	2.04757	+	1.48765i
$800$	3.73607	−	2.71441i	0.132090	−	0.0959690i
$801$	−5.67376	+	17.4620i	−0.200473	+	0.616991i
$802$	−29.4721			−1.04070
$803$	−4.38854	+	0.297759i	−0.154868	+	0.0105077i
$804$	13.6180			0.480271
$805$	−0.128677	+	0.396027i	−0.00453527	+	0.0139581i
$806$	14.0172	−	10.1841i	0.493736	−	0.358720i
$807$	50.5517	+	36.7279i	1.77950	+	1.29288i
$808$	−0.163119	−	0.502029i	−0.00573851	−	0.0176613i
$809$	6.47214	+	19.9192i	0.227548	+	0.700321i	0.998023	+	0.0628508i	$0.0200192\pi$
$809$	6.47214	+	19.9192i	0.227548	+	0.700321i	−0.770475	+	0.637471i	$0.779981\pi$
$810$	5.50000	+	3.99598i	0.193250	+	0.140405i
$811$	−44.0689	+	32.0179i	−1.54747	+	1.12430i	−0.602042	+	0.798465i	$0.705646\pi$
$811$	−44.0689	+	32.0179i	−1.54747	+	1.12430i	−0.945426	+	0.325837i	$0.894354\pi$
$812$	−9.23607	+	28.4257i	−0.324122	+	0.997546i
$813$	17.2361			0.604495
$814$	6.35410	−	25.2623i	0.222711	−	0.885442i
$815$	−3.11146			−0.108990
$816$	4.30902	−	13.2618i	0.150846	−	0.464256i
$817$	−3.00000	+	2.17963i	−0.104957	+	0.0762555i
$818$	2.42705	+	1.76336i	0.0848598	+	0.0616543i
$819$	2.85410	+	8.78402i	0.0997304	+	0.306939i
$820$	0.781153	+	2.40414i	0.0272790	+	0.0839563i
$821$	−0.354102	−	0.257270i	−0.0123582	−	0.00897879i	0.581589	−	0.813483i	$-0.302431\pi$
$821$	−0.354102	−	0.257270i	−0.0123582	−	0.00897879i	−0.593947	+	0.804504i	$0.702431\pi$
$822$	2.66312	−	1.93487i	0.0928869	−	0.0674863i
$823$	−5.18034	+	15.9434i	−0.180575	+	0.555754i	−0.999844	−	0.0176560i	$-0.994380\pi$
$823$	−5.18034	+	15.9434i	−0.180575	+	0.555754i	0.819269	+	0.573410i	$0.194380\pi$
$824$	−8.56231			−0.298282
$825$	−12.7639	−	31.7809i	−0.444383	−	1.10647i
$826$	−37.3607			−1.29994
$827$	8.71478	−	26.8213i	0.303043	−	0.932669i	−0.677358	−	0.735654i	$-0.736875\pi$
$827$	8.71478	−	26.8213i	0.303043	−	0.932669i	0.980400	−	0.197016i	$-0.0631250\pi$
$828$	0.381966	−	0.277515i	0.0132742	−	0.00964430i
$829$	−26.1803	−	19.0211i	−0.909281	−	0.660631i	0.0315521	−	0.999502i	$-0.489955\pi$
$829$	−26.1803	−	19.0211i	−0.909281	−	0.660631i	−0.940833	+	0.338871i	$0.889955\pi$
$830$	0.208204	+	0.640786i	0.00722686	+	0.0222420i
$831$	8.88197	+	27.3359i	0.308112	+	0.948271i
$832$	−1.30902	−	0.951057i	−0.0453820	−	0.0329720i
$833$	5.78115	−	4.20025i	0.200305	−	0.145530i
$834$	3.35410	−	10.3229i	0.116143	−	0.357452i
$835$	−5.18034			−0.179273
$836$	2.54508	−	2.12663i	0.0880236	−	0.0735509i
$837$	−23.9443			−0.827635
$838$	9.70820	−	29.8788i	0.335364	−	1.03215i
$839$	−21.9721	+	15.9637i	−0.758562	+	0.551128i	−0.898469	−	0.439037i	$-0.855320\pi$
$839$	−21.9721	+	15.9637i	−0.758562	+	0.551128i	0.139907	+	0.990165i	$0.455320\pi$
$840$	3.19098	+	2.31838i	0.110099	+	0.0799919i
$841$	24.9271	+	76.7176i	0.859553	+	2.64543i
$842$	−3.21885	−	9.90659i	−0.110929	−	0.341404i
$843$	−1.87132	−	1.35960i	−0.0644518	−	0.0468270i
$844$	6.51722	−	4.73504i	0.224332	−	0.162987i
$845$	−1.98278	+	6.10237i	−0.0682097	+	0.209928i
$846$	22.9443			0.788840
$847$	−22.6738	+	21.7153i	−0.779080	+	0.746146i
$848$	5.94427			0.204127
$849$	3.65654	−	11.2537i	0.125492	−	0.386225i
$850$	−23.2984	+	16.9273i	−0.799128	+	0.580600i
$851$	−1.50000	−	1.08981i	−0.0514193	−	0.0373583i
$852$	2.60081	+	8.00448i	0.0891024	+	0.274229i
$853$	1.11803	+	3.44095i	0.0382808	+	0.117816i	0.968371	−	0.249516i	$-0.0802714\pi$
$853$	1.11803	+	3.44095i	0.0382808	+	0.117816i	−0.930090	+	0.367332i	$0.880271\pi$
$854$	10.1180	+	7.35118i	0.346232	+	0.251552i
$855$	−1.00000	+	0.726543i	−0.0341993	+	0.0248472i
$856$	0.927051	−	2.85317i	0.0316860	−	0.0975193i
$857$	22.9098			0.782585			0.391292	−	0.920266i	$-0.372028\pi$
$857$	22.9098			0.782585			0.391292	+	0.920266i	$0.372028\pi$
$858$	−9.20820	+	7.69421i	−0.314363	+	0.262676i
$859$	−2.52786			−0.0862496			−0.0431248	−	0.999070i	$-0.513731\pi$
$859$	−2.52786			−0.0862496			−0.0431248	+	0.999070i	$0.513731\pi$
$860$	0.708204	−	2.17963i	0.0241496	−	0.0743247i
$861$	21.1180	−	15.3431i	0.719701	−	0.522893i
$862$	21.8713	+	15.8904i	0.744940	+	0.541231i
$863$	−9.32624	−	28.7032i	−0.317469	−	0.977069i	−0.974726	−	0.223402i	$-0.928284\pi$
$863$	−9.32624	−	28.7032i	−0.317469	−	0.977069i	0.657257	−	0.753666i	$-0.271716\pi$
$864$	0.690983	+	2.12663i	0.0235077	+	0.0723493i
$865$	−4.39919	−	3.19620i	−0.149577	−	0.108674i
$866$	26.2705	−	19.0866i	0.892708	−	0.648591i
$867$	−15.1246	+	46.5488i	−0.513659	+	1.58088i
$868$	−30.5623			−1.03735
$869$	−3.70820	−	9.23305i	−0.125792	−	0.313210i
$870$	14.4721			0.490651
$871$	−3.04508	+	9.37181i	−0.103179	+	0.317552i
$872$	−8.35410	+	6.06961i	−0.282906	+	0.205543i
$873$	−26.5623	−	19.2986i	−0.898998	−	0.653160i
$874$	−0.0729490	−	0.224514i	−0.00246754	−	0.00759430i
$875$	−5.24265	−	16.1352i	−0.177234	−	0.545469i
$876$	2.39919	+	1.74311i	0.0810610	+	0.0588943i
$877$	27.9164	−	20.2825i	0.942670	−	0.684890i	−0.00639180	−	0.999980i	$-0.502035\pi$
$877$	27.9164	−	20.2825i	0.942670	−	0.684890i	0.949062	+	0.315090i	$0.102035\pi$
$878$	8.29837	−	25.5398i	0.280057	−	0.861925i
$879$	−23.5410			−0.794019
$880$	−0.500000	+	1.98787i	−0.0168550	+	0.0670111i
$881$	−23.0557			−0.776767			−0.388384	−	0.921498i	$-0.626966\pi$
$881$	−23.0557			−0.776767			−0.388384	+	0.921498i	$0.626966\pi$
$882$	0.708204	−	2.17963i	0.0238465	−	0.0733919i
$883$	−10.1459	+	7.37143i	−0.341437	+	0.248068i	−0.745268	−	0.666765i	$-0.767678\pi$
$883$	−10.1459	+	7.37143i	−0.341437	+	0.248068i	0.403831	+	0.914834i	$0.367678\pi$
$884$	8.16312	+	5.93085i	0.274555	+	0.199476i
$885$	5.59017	+	17.2048i	0.187912	+	0.578332i
$886$	0.572949	+	1.76336i	0.0192486	+	0.0592411i
$887$	36.0795	+	26.2133i	1.21143	+	0.880157i	0.995360	−	0.0962206i	$-0.0306754\pi$
$887$	36.0795	+	26.2133i	1.21143	+	0.880157i	0.216072	+	0.976377i	$0.430675\pi$
$888$	−14.2082	+	10.3229i	−0.476796	+	0.346413i
$889$	−16.9164	+	52.0633i	−0.567358	+	1.74615i
$890$	−5.67376			−0.190185
$891$	36.3992	−	2.46965i	1.21942	−	0.0827365i
$892$	−20.0000			−0.669650
$893$	3.54508	−	10.9106i	0.118632	−	0.365111i
$894$	32.1353	−	23.3476i	1.07476	−	0.780862i
$895$	8.61803	+	6.26137i	0.288069	+	0.209294i
$896$	0.881966	+	2.71441i	0.0294644	+	0.0906821i
$897$	0.263932	+	0.812299i	0.00881243	+	0.0271219i
$898$	−10.2812	−	7.46969i	−0.343087	−	0.249267i
$899$	−90.7214	+	65.9129i	−3.02573	+	2.19832i
$900$	−2.85410	+	8.78402i	−0.0951367	+	0.292801i
$901$	−37.0689			−1.23494
$902$	11.4894	+	7.21242i	0.382554	+	0.240147i
$903$	−23.6656			−0.787543
$904$	5.07295	−	15.6129i	0.168724	−	0.519278i
$905$	−2.02786	+	1.47333i	−0.0674085	+	0.0489751i
$906$	0.527864	+	0.383516i	0.0175371	+	0.0127415i
$907$	−15.8050	−	48.6426i	−0.524795	−	1.61515i	−0.764721	−	0.644361i	$-0.777123\pi$
$907$	−15.8050	−	48.6426i	−0.524795	−	1.61515i	0.239926	−	0.970791i	$-0.422877\pi$
$908$	4.02786	+	12.3965i	0.133669	+	0.411392i
$909$	0.854102	+	0.620541i	0.0283288	+	0.0205821i
$910$	−2.30902	+	1.67760i	−0.0765432	+	0.0556119i
$911$	6.29180	−	19.3642i	0.208457	−	0.641563i	−0.791097	−	0.611690i	$-0.790490\pi$
$911$	6.29180	−	19.3642i	0.208457	−	0.641563i	0.999554	−	0.0298727i	$-0.00951019\pi$
$912$	−2.23607			−0.0740436
$913$	3.06231	+	1.92236i	0.101348	+	0.0636207i
$914$	9.00000			0.297694
$915$	1.87132	−	5.75934i	0.0618640	−	0.190398i
$916$	−3.59017	+	2.60841i	−0.118623	+	0.0861843i
$917$	38.4508	+	27.9362i	1.26976	+	0.922534i
$918$	−4.30902	−	13.2618i	−0.142219	−	0.437704i
$919$	5.07295	+	15.6129i	0.167341	+	0.515023i	0.999201	−	0.0399624i	$-0.0127238\pi$
$919$	5.07295	+	15.6129i	0.167341	+	0.515023i	−0.831860	+	0.554985i	$0.812724\pi$
$920$	0.118034	+	0.0857567i	0.00389147	+	0.00282732i
$921$	−32.9894	+	23.9682i	−1.08704	+	0.789778i
$922$	−9.98278	+	30.7238i	−0.328765	+	1.01184i
$923$	−6.09017			−0.200460
$924$	21.1180	−	1.43284i	0.694732	−	0.0471370i
$925$	36.2705			1.19257
$926$	−4.98936	+	15.3557i	−0.163960	+	0.504618i
$927$	13.8541	−	10.0656i	0.455028	−	0.330597i
$928$	8.47214	+	6.15537i	0.278111	+	0.202060i
$929$	9.25329	+	28.4787i	0.303591	+	0.934356i	0.980199	+	0.198013i	$0.0634488\pi$
$929$	9.25329	+	28.4787i	0.303591	+	0.934356i	−0.676609	+	0.736343i	$0.736551\pi$
$930$	4.57295	+	14.0741i	0.149953	+	0.461508i
$931$	−0.927051	−	0.673542i	−0.0303829	−	0.0220744i
$932$	6.19098	−	4.49801i	0.202792	−	0.147337i
$933$	−11.3820	+	35.0301i	−0.372629	+	1.14683i
$934$	−16.5066			−0.540112
$935$	3.11803	−	12.3965i	0.101971	−	0.405409i
$936$	3.23607			0.105774
$937$	−1.14590	+	3.52671i	−0.0374349	+	0.115213i	−0.968028	−	0.250843i	$-0.919292\pi$
$937$	−1.14590	+	3.52671i	−0.0374349	+	0.115213i	0.930593	+	0.366056i	$0.119292\pi$
$938$	14.0623	−	10.2169i	0.459151	−	0.333592i
$939$	17.9894	+	13.0700i	0.587060	+	0.426524i
$940$	2.19098	+	6.74315i	0.0714620	+	0.219937i
$941$	12.3435	+	37.9893i	0.402385	+	1.23841i	0.923059	+	0.384659i	$0.125681\pi$
$941$	12.3435	+	37.9893i	0.402385	+	1.23841i	−0.520674	+	0.853756i	$0.674319\pi$
$942$	−6.70820	−	4.87380i	−0.218565	−	0.158797i
$943$	0.781153	−	0.567541i	0.0254378	−	0.0184817i
$944$	−4.04508	+	12.4495i	−0.131656	+	0.405196i
$945$	3.94427			0.128307
$946$	−4.58359	−	11.4127i	−0.149025	−	0.371058i
$947$	5.94427			0.193163			0.0965814	−	0.995325i	$-0.469209\pi$
$947$	5.94427			0.193163			0.0965814	+	0.995325i	$0.469209\pi$
$948$	−2.07295	+	6.37988i	−0.0673263	+	0.207209i
$949$	−1.73607	+	1.26133i	−0.0563552	+	0.0409444i
$950$	3.73607	+	2.71441i	0.121214	+	0.0880672i
$951$	2.07295	+	6.37988i	0.0672200	+	0.206882i
$952$	−5.50000	−	16.9273i	−0.178256	−	0.548616i
$953$	37.2705	+	27.0786i	1.20731	+	0.877162i	0.994984	−	0.100037i	$-0.0318960\pi$
$953$	37.2705	+	27.0786i	1.20731	+	0.877162i	0.212326	+	0.977199i	$0.431896\pi$
$954$	−9.61803	+	6.98791i	−0.311395	+	0.226242i
$955$	3.04508	−	9.37181i	0.0985366	−	0.303265i
$956$	21.9787			0.710842
$957$	59.5967	−	49.7980i	1.92649	−	1.60974i
$958$	−8.23607			−0.266095
$959$	1.29837	−	3.99598i	0.0419267	−	0.129037i
$960$	1.11803	−	0.812299i	0.0360844	−	0.0262168i
$961$	−67.6869	−	49.1774i	−2.18345	−	1.58637i
$962$	−3.92705	−	12.0862i	−0.126613	−	0.389675i
$963$	1.85410	+	5.70634i	0.0597476	+	0.183884i
$964$	5.92705	+	4.30625i	0.190897	+	0.138695i
$965$	12.7812	−	9.28605i	0.411440	−	0.298929i
$966$	0.465558	−	1.43284i	0.0149791	−	0.0461009i
$967$	−54.3951			−1.74923			−0.874615	−	0.484819i	$-0.838886\pi$
$967$	−54.3951			−1.74923			−0.874615	+	0.484819i	$0.838886\pi$
$968$	4.78115	+	9.90659i	0.153672	+	0.318410i
$969$	13.9443			0.447955
$970$	3.13525	−	9.64932i	0.100667	−	0.309821i
$971$	30.7705	−	22.3561i	0.987473	−	0.717441i	0.0281065	−	0.999605i	$-0.491052\pi$
$971$	30.7705	−	22.3561i	0.987473	−	0.717441i	0.959366	+	0.282164i	$0.0910522\pi$
$972$	−14.4721	−	10.5146i	−0.464194	−	0.337257i
$973$	−4.28115	−	13.1760i	−0.137247	−	0.422404i
$974$	−0.600813	−	1.84911i	−0.0192513	−	0.0592494i
$975$	−13.5172	−	9.82084i	−0.432898	−	0.314518i
$976$	3.54508	−	2.57565i	0.113475	−	0.0824447i
$977$	6.67376	−	20.5397i	0.213513	−	0.657124i	−0.785743	−	0.618553i	$-0.787719\pi$
$977$	6.67376	−	20.5397i	0.213513	−	0.657124i	0.999256	−	0.0385714i	$-0.0122807\pi$
$978$	11.2574			0.359970
$979$	−23.3647	+	19.5232i	−0.746740	+	0.623963i
$980$	0.708204			0.0226227
$981$	6.38197	−	19.6417i	0.203760	−	0.627110i
$982$	23.3435	−	16.9600i	0.744920	−	0.541216i
$983$	15.0000	+	10.8981i	0.478426	+	0.347597i	0.800716	−	0.599044i	$-0.204453\pi$
$983$	15.0000	+	10.8981i	0.478426	+	0.347597i	−0.322290	+	0.946641i	$0.604453\pi$
$984$	−2.82624	−	8.69827i	−0.0900972	−	0.277291i
$985$	0.156541	+	0.481784i	0.00498782	+	0.0153509i
$986$	−52.8328	−	38.3853i	−1.68254	−	1.22244i
$987$	59.2320	−	43.0346i	1.88538	−	1.36981i
$988$	0.500000	−	1.53884i	0.0159071	−	0.0489571i
$989$	−0.875388			−0.0278357
$990$	−1.52786	−	3.80423i	−0.0485587	−	0.120906i
$991$	0.167184			0.00531078			0.00265539	−	0.999996i	$-0.499155\pi$
$991$	0.167184			0.00531078			0.00265539	+	0.999996i	$0.499155\pi$
$992$	−3.30902	+	10.1841i	−0.105061	+	0.323346i
$993$	17.5623	−	12.7598i	0.557323	−	0.404919i
$994$	8.69098	+	6.31437i	0.275661	+	0.200280i
$995$	−4.18034	−	12.8658i	−0.132526	−	0.407872i
$996$	−0.753289	−	2.31838i	−0.0238689	−	0.0734608i
$997$	−22.2254	−	16.1477i	−0.703886	−	0.511403i	0.177309	−	0.984155i	$-0.443261\pi$
$997$	−22.2254	−	16.1477i	−0.703886	−	0.511403i	−0.881196	+	0.472752i	$0.843261\pi$
$998$	−25.0795	+	18.2213i	−0.793879	+	0.576787i
$999$	−5.42705	+	16.7027i	−0.171704	+	0.528451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.e.229.1	yes	4
11.4	even	5		4598.2.a.bi.1.1		2
11.5	even	5	inner	418.2.f.e.115.1	✓	4
11.7	odd	10		4598.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.e.115.1	✓	4	11.5	even	5	inner
418.2.f.e.229.1	yes	4	1.1	even	1	trivial
4598.2.a.ba.1.1		2	11.7	odd	10
4598.2.a.bi.1.1		2	11.4	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.80902 - 1.31433i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-0.690983 - 2.12663i) q^{6} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.80902 - 1.31433i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-0.690983 - 2.12663i) q^{6} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.618034 - 1.90211i) q^{9} +0.618034 q^{10} +(2.54508 - 2.12663i) q^{11} -2.23607 q^{12} +(0.500000 - 1.53884i) q^{13} +(-2.30902 + 1.67760i) q^{14} +(1.11803 + 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.92705 - 5.93085i) q^{17} +(-1.61803 - 1.17557i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.190983 - 0.587785i) q^{20} -6.38197 q^{21} +(-1.23607 - 3.07768i) q^{22} -0.236068 q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.73607 - 2.71441i) q^{25} +(-1.30902 - 0.951057i) q^{26} +(0.690983 + 2.12663i) q^{27} +(0.881966 + 2.71441i) q^{28} +(8.47214 + 6.15537i) q^{29} +(1.11803 - 0.812299i) q^{30} +(-3.30902 + 10.1841i) q^{31} +1.00000 q^{32} +(1.80902 - 7.19218i) q^{33} -6.23607 q^{34} +(0.545085 - 1.67760i) q^{35} +(-1.61803 + 1.17557i) q^{36} +(6.35410 + 4.61653i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.11803 - 3.44095i) q^{39} +(-0.500000 - 0.363271i) q^{40} +(-3.30902 + 2.40414i) q^{41} +(-1.97214 + 6.06961i) q^{42} +3.70820 q^{43} +(-3.30902 + 0.224514i) q^{44} +1.23607 q^{45} +(-0.0729490 + 0.224514i) q^{46} +(-9.28115 + 6.74315i) q^{47} +(1.80902 + 1.31433i) q^{48} +(0.354102 + 1.08981i) q^{49} +(-1.42705 - 4.39201i) q^{50} +(-11.2812 - 8.19624i) q^{51} +(-1.30902 + 0.951057i) q^{52} +(1.83688 - 5.65334i) q^{53} +2.23607 q^{54} +(1.73607 + 1.08981i) q^{55} +2.85410 q^{56} +(-0.690983 + 2.12663i) q^{57} +(8.47214 - 6.15537i) q^{58} +(10.5902 + 7.69421i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-1.35410 - 4.16750i) q^{61} +(8.66312 + 6.29412i) q^{62} +(-4.61803 + 3.35520i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.00000 q^{65} +(-6.28115 - 3.94298i) q^{66} -6.09017 q^{67} +(-1.92705 + 5.93085i) q^{68} +(-0.427051 + 0.310271i) q^{69} +(-1.42705 - 1.03681i) q^{70} +(-1.16312 - 3.57971i) q^{71} +(0.618034 + 1.90211i) q^{72} +(-1.07295 - 0.779543i) q^{73} +(6.35410 - 4.61653i) q^{74} +(3.19098 - 9.82084i) q^{75} +1.00000 q^{76} +(-9.44427 + 0.640786i) q^{77} -3.61803 q^{78} +(0.927051 - 2.85317i) q^{79} +(-0.500000 + 0.363271i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.26393 + 3.88998i) q^{82} +(0.336881 + 1.03681i) q^{83} +(5.16312 + 3.75123i) q^{84} +(3.11803 - 2.26538i) q^{85} +(1.14590 - 3.52671i) q^{86} +23.4164 q^{87} +(-0.809017 + 3.21644i) q^{88} -9.18034 q^{89} +(0.381966 - 1.17557i) q^{90} +(-3.73607 + 2.71441i) q^{91} +(0.190983 + 0.138757i) q^{92} +(7.39919 + 22.7724i) q^{93} +(3.54508 + 10.9106i) q^{94} +(-0.500000 - 0.363271i) q^{95} +(1.80902 - 1.31433i) q^{96} +(5.07295 - 15.6129i) q^{97} +1.14590 q^{98} +(-2.47214 - 6.15537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9	\( 4 q - q^{2} + 5 q^{3} - q^{4} + 3 q^{5} - 5 q^{6} - 7 q^{7} - q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{13} - 7 q^{14} - q^{16} - q^{17} - 2 q^{18} - q^{19} + 3 q^{20} - 30 q^{21} + 4 q^{22} + 8 q^{23} - 5 q^{24} + 6 q^{25} - 3 q^{26} + 5 q^{27} + 8 q^{28} + 16 q^{29} - 11 q^{31} + 4 q^{32} + 5 q^{33} - 16 q^{34} - 9 q^{35} - 2 q^{36} + 12 q^{37} - q^{38} - 2 q^{40} - 11 q^{41} + 10 q^{42} - 12 q^{43} - 11 q^{44} - 4 q^{45} - 7 q^{46} - 17 q^{47} + 5 q^{48} - 12 q^{49} + q^{50} - 25 q^{51} - 3 q^{52} + 23 q^{53} - 2 q^{55} - 2 q^{56} - 5 q^{57} + 16 q^{58} + 20 q^{59} + 5 q^{60} + 8 q^{61} + 19 q^{62} - 14 q^{63} - q^{64} + 4 q^{65} - 5 q^{66} - 2 q^{67} - q^{68} + 5 q^{69} + q^{70} + 11 q^{71} - 2 q^{72} - 11 q^{73} + 12 q^{74} + 15 q^{75} + 4 q^{76} - 2 q^{77} - 10 q^{78} - 3 q^{79} - 2 q^{80} + 11 q^{81} + 14 q^{82} + 17 q^{83} + 5 q^{84} + 8 q^{85} + 18 q^{86} + 40 q^{87} - q^{88} + 8 q^{89} + 6 q^{90} - 6 q^{91} + 3 q^{92} + 5 q^{93} + 3 q^{94} - 2 q^{95} + 5 q^{96} + 27 q^{97} + 18 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - q^2 + 5 * q^3 - q^4 + 3 * q^5 - 5 * q^6 - 7 * q^7 - q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^13 - 7 * q^14 - q^16 - q^17 - 2 * q^18 - q^19 + 3 * q^20 - 30 * q^21 + 4 * q^22 + 8 * q^23 - 5 * q^24 + 6 * q^25 - 3 * q^26 + 5 * q^27 + 8 * q^28 + 16 * q^29 - 11 * q^31 + 4 * q^32 + 5 * q^33 - 16 * q^34 - 9 * q^35 - 2 * q^36 + 12 * q^37 - q^38 - 2 * q^40 - 11 * q^41 + 10 * q^42 - 12 * q^43 - 11 * q^44 - 4 * q^45 - 7 * q^46 - 17 * q^47 + 5 * q^48 - 12 * q^49 + q^50 - 25 * q^51 - 3 * q^52 + 23 * q^53 - 2 * q^55 - 2 * q^56 - 5 * q^57 + 16 * q^58 + 20 * q^59 + 5 * q^60 + 8 * q^61 + 19 * q^62 - 14 * q^63 - q^64 + 4 * q^65 - 5 * q^66 - 2 * q^67 - q^68 + 5 * q^69 + q^70 + 11 * q^71 - 2 * q^72 - 11 * q^73 + 12 * q^74 + 15 * q^75 + 4 * q^76 - 2 * q^77 - 10 * q^78 - 3 * q^79 - 2 * q^80 + 11 * q^81 + 14 * q^82 + 17 * q^83 + 5 * q^84 + 8 * q^85 + 18 * q^86 + 40 * q^87 - q^88 + 8 * q^89 + 6 * q^90 - 6 * q^91 + 3 * q^92 + 5 * q^93 + 3 * q^94 - 2 * q^95 + 5 * q^96 + 27 * q^97 + 18 * q^98 + 8 * q^99

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