LMFDB - Embedded newform 825.2.r.a.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(31,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 6]))

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

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

chi := DirichletCharacter("825.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.r (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.136
Dual form			825.2.r.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} +(-0.809017 - 0.587785i) q^{3} +3.00000 q^{4} +(0.690983 + 2.12663i) q^{5} +(1.80902 + 1.31433i) q^{6} +(0.809017 + 2.48990i) q^{7} -2.23607 q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q-2.23607 q^{2} +(-0.809017 - 0.587785i) q^{3} +3.00000 q^{4} +(0.690983 + 2.12663i) q^{5} +(1.80902 + 1.31433i) q^{6} +(0.809017 + 2.48990i) q^{7} -2.23607 q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.54508 - 4.75528i) q^{10} +(-2.80902 - 1.76336i) q^{11} +(-2.42705 - 1.76336i) q^{12} +(-1.85410 - 5.70634i) q^{13} +(-1.80902 - 5.56758i) q^{14} +(0.690983 - 2.12663i) q^{15} -1.00000 q^{16} +(-5.04508 - 3.66547i) q^{17} +(-0.690983 - 2.12663i) q^{18} +6.61803 q^{19} +(2.07295 + 6.37988i) q^{20} +(0.809017 - 2.48990i) q^{21} +(6.28115 + 3.94298i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 + 1.31433i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(4.14590 + 12.7598i) q^{26} +(0.309017 - 0.951057i) q^{27} +(2.42705 + 7.46969i) q^{28} +7.09017 q^{29} +(-1.54508 + 4.75528i) q^{30} +(2.30902 - 7.10642i) q^{31} +6.70820 q^{32} +(1.23607 + 3.07768i) q^{33} +(11.2812 + 8.19624i) q^{34} +(-4.73607 + 3.44095i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.354102 - 1.08981i) q^{37} -14.7984 q^{38} +(-1.85410 + 5.70634i) q^{39} +(-1.54508 - 4.75528i) q^{40} +(-1.42705 + 1.03681i) q^{41} +(-1.80902 + 5.56758i) q^{42} +7.94427 q^{43} +(-8.42705 - 5.29007i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(9.89919 - 7.19218i) q^{46} +(-6.54508 - 4.75528i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(9.04508 - 6.57164i) q^{50} +(1.92705 + 5.93085i) q^{51} +(-5.56231 - 17.1190i) q^{52} +(0.809017 - 0.587785i) q^{53} +(-0.690983 + 2.12663i) q^{54} +(1.80902 - 7.19218i) q^{55} +(-1.80902 - 5.56758i) q^{56} +(-5.35410 - 3.88998i) q^{57} -15.8541 q^{58} +(3.61803 - 11.1352i) q^{59} +(2.07295 - 6.37988i) q^{60} +(-1.64590 + 5.06555i) q^{61} +(-5.16312 + 15.8904i) q^{62} +(-2.11803 + 1.53884i) q^{63} -13.0000 q^{64} +(10.8541 - 7.88597i) q^{65} +(-2.76393 - 6.88191i) q^{66} +(-1.80902 - 5.56758i) q^{67} +(-15.1353 - 10.9964i) q^{68} +5.47214 q^{69} +(10.5902 - 7.69421i) q^{70} +(2.30902 + 7.10642i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(2.61803 + 1.90211i) q^{73} +(-0.791796 + 2.43690i) q^{74} +5.00000 q^{75} +19.8541 q^{76} +(2.11803 - 8.42075i) q^{77} +(4.14590 - 12.7598i) q^{78} +(10.4721 - 7.60845i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.19098 - 2.31838i) q^{82} +(6.92705 + 5.03280i) q^{83} +(2.42705 - 7.46969i) q^{84} +(4.30902 - 13.2618i) q^{85} -17.7639 q^{86} +(-5.73607 - 4.16750i) q^{87} +(6.28115 + 3.94298i) q^{88} +(-2.88197 + 2.09387i) q^{89} +(4.04508 - 2.93893i) q^{90} +(12.7082 - 9.23305i) q^{91} +(-13.2812 + 9.64932i) q^{92} +(-6.04508 + 4.39201i) q^{93} +(14.6353 + 10.6331i) q^{94} +(4.57295 + 14.0741i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(-2.04508 + 1.48584i) q^{97} +(-0.263932 + 0.191758i) q^{98} +(0.809017 - 3.21644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9} + 5 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} - 5 q^{14} + 5 q^{15} - 4 q^{16} - 9 q^{17} - 5 q^{18} + 22 q^{19} + 15 q^{20} + q^{21} + 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} - q^{27} + 3 q^{28} + 6 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{33} + 25 q^{34} - 10 q^{35} - 3 q^{36} - 12 q^{37} - 10 q^{38} + 6 q^{39} + 5 q^{40} + q^{41} - 5 q^{42} - 4 q^{43} - 27 q^{44} - 5 q^{45} + 15 q^{46} - 15 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} + 5 q^{55} - 5 q^{56} - 8 q^{57} - 50 q^{58} + 10 q^{59} + 15 q^{60} - 20 q^{61} - 5 q^{62} - 4 q^{63} - 52 q^{64} + 30 q^{65} - 20 q^{66} - 5 q^{67} - 27 q^{68} + 4 q^{69} + 20 q^{70} + 7 q^{71} - 5 q^{72} + 6 q^{73} - 30 q^{74} + 20 q^{75} + 66 q^{76} + 4 q^{77} + 30 q^{78} + 24 q^{79} - 5 q^{80} - q^{81} + 15 q^{82} + 21 q^{83} + 3 q^{84} + 15 q^{85} - 80 q^{86} - 14 q^{87} + 5 q^{88} - 16 q^{89} + 5 q^{90} + 24 q^{91} - 33 q^{92} - 13 q^{93} + 25 q^{94} + 25 q^{95} - 15 q^{96} + 3 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9 + 5 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 - 5 * q^14 + 5 * q^15 - 4 * q^16 - 9 * q^17 - 5 * q^18 + 22 * q^19 + 15 * q^20 + q^21 + 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 - q^27 + 3 * q^28 + 6 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^33 + 25 * q^34 - 10 * q^35 - 3 * q^36 - 12 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 + q^41 - 5 * q^42 - 4 * q^43 - 27 * q^44 - 5 * q^45 + 15 * q^46 - 15 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 + 5 * q^55 - 5 * q^56 - 8 * q^57 - 50 * q^58 + 10 * q^59 + 15 * q^60 - 20 * q^61 - 5 * q^62 - 4 * q^63 - 52 * q^64 + 30 * q^65 - 20 * q^66 - 5 * q^67 - 27 * q^68 + 4 * q^69 + 20 * q^70 + 7 * q^71 - 5 * q^72 + 6 * q^73 - 30 * q^74 + 20 * q^75 + 66 * q^76 + 4 * q^77 + 30 * q^78 + 24 * q^79 - 5 * q^80 - q^81 + 15 * q^82 + 21 * q^83 + 3 * q^84 + 15 * q^85 - 80 * q^86 - 14 * q^87 + 5 * q^88 - 16 * q^89 + 5 * q^90 + 24 * q^91 - 33 * q^92 - 13 * q^93 + 25 * q^94 + 25 * q^95 - 15 * q^96 + 3 * q^97 - 10 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.23607			−1.58114			−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607			−1.58114			−0.790569	+	0.612372i	$0.790215\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	3.00000			1.50000
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$	1.80902	+	1.31433i	0.738528	+	0.536572i
$7$	0.809017	+	2.48990i	0.305780	+	0.941093i	0.979385	+	0.202002i	$0.0647447\pi$
$7$	0.809017	+	2.48990i	0.305780	+	0.941093i	−0.673605	+	0.739091i	$0.735255\pi$
$8$	−2.23607			−0.790569
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.54508	−	4.75528i	−0.488599	−	1.50375i
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$12$	−2.42705	−	1.76336i	−0.700629	−	0.509037i
$13$	−1.85410	−	5.70634i	−0.514235	−	1.58265i	−0.784669	−	0.619915i	$-0.787167\pi$
$13$	−1.85410	−	5.70634i	−0.514235	−	1.58265i	0.270434	−	0.962739i	$-0.412833\pi$
$14$	−1.80902	−	5.56758i	−0.483480	−	1.48800i
$15$	0.690983	−	2.12663i	0.178411	−	0.549093i
$16$	−1.00000			−0.250000
$17$	−5.04508	−	3.66547i	−1.22361	−	0.889007i	−0.227218	−	0.973844i	$-0.572963\pi$
$17$	−5.04508	−	3.66547i	−1.22361	−	0.889007i	−0.996395	+	0.0848372i	$0.972963\pi$
$18$	−0.690983	−	2.12663i	−0.162866	−	0.501251i
$19$	6.61803			1.51828			0.759141	−	0.650927i	$-0.225619\pi$
$19$	6.61803			1.51828			0.759141	+	0.650927i	$0.225619\pi$
$20$	2.07295	+	6.37988i	0.463525	+	1.42658i
$21$	0.809017	−	2.48990i	0.176542	−	0.543340i
$22$	6.28115	+	3.94298i	1.33915	+	0.840647i
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	−0.944295	−	0.329101i	$-0.893254\pi$
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	0.0211907	+	0.999775i	$0.493254\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	4.14590	+	12.7598i	0.813077	+	2.50240i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	2.42705	+	7.46969i	0.458670	+	1.41164i
$29$	7.09017			1.31661			0.658306	−	0.752751i	$-0.271273\pi$
$29$	7.09017			1.31661			0.658306	+	0.752751i	$0.271273\pi$
$30$	−1.54508	+	4.75528i	−0.282093	+	0.868192i
$31$	2.30902	−	7.10642i	0.414712	−	1.27635i	−0.497797	−	0.867294i	$-0.665857\pi$
$31$	2.30902	−	7.10642i	0.414712	−	1.27635i	0.912509	−	0.409058i	$-0.134143\pi$
$32$	6.70820			1.18585
$33$	1.23607	+	3.07768i	0.215172	+	0.535756i
$34$	11.2812	+	8.19624i	1.93470	+	1.40564i
$35$	−4.73607	+	3.44095i	−0.800542	+	0.581628i
$36$	0.927051	+	2.85317i	0.154508	+	0.475528i
$37$	0.354102	−	1.08981i	0.0582140	−	0.179164i	−0.917721	−	0.397225i	$-0.869973\pi$
$37$	0.354102	−	1.08981i	0.0582140	−	0.179164i	0.975935	+	0.218061i	$0.0699732\pi$
$38$	−14.7984			−2.40061
$39$	−1.85410	+	5.70634i	−0.296894	+	0.913746i
$40$	−1.54508	−	4.75528i	−0.244299	−	0.751876i
$41$	−1.42705	+	1.03681i	−0.222868	+	0.161923i	−0.693617	−	0.720344i	$-0.743984\pi$
$41$	−1.42705	+	1.03681i	−0.222868	+	0.161923i	0.470749	+	0.882267i	$0.343984\pi$
$42$	−1.80902	+	5.56758i	−0.279137	+	0.859097i
$43$	7.94427			1.21149			0.605745	−	0.795659i	$-0.292875\pi$
$43$	7.94427			1.21149			0.605745	+	0.795659i	$0.292875\pi$
$44$	−8.42705	−	5.29007i	−1.27043	−	0.797508i
$45$	−1.80902	+	1.31433i	−0.269672	+	0.195928i
$46$	9.89919	−	7.19218i	1.45956	−	1.06043i
$47$	−6.54508	−	4.75528i	−0.954699	−	0.693629i	−0.00278525	−	0.999996i	$-0.500887\pi$
$47$	−6.54508	−	4.75528i	−0.954699	−	0.693629i	−0.951914	+	0.306367i	$0.900887\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.118034	−	0.0857567i	0.0168620	−	0.0122510i
$50$	9.04508	−	6.57164i	1.27917	−	0.929370i
$51$	1.92705	+	5.93085i	0.269841	+	0.830486i
$52$	−5.56231	−	17.1190i	−0.771353	−	2.37398i
$53$	0.809017	−	0.587785i	0.111127	−	0.0807385i	−0.530834	−	0.847476i	$-0.678121\pi$
$53$	0.809017	−	0.587785i	0.111127	−	0.0807385i	0.641961	+	0.766737i	$0.278121\pi$
$54$	−0.690983	+	2.12663i	−0.0940309	+	0.289397i
$55$	1.80902	−	7.19218i	0.243928	−	0.969793i
$56$	−1.80902	−	5.56758i	−0.241740	−	0.743999i
$57$	−5.35410	−	3.88998i	−0.709168	−	0.515241i
$58$	−15.8541			−2.08175
$59$	3.61803	−	11.1352i	0.471028	−	1.44967i	−0.380213	−	0.924899i	$-0.624149\pi$
$59$	3.61803	−	11.1352i	0.471028	−	1.44967i	0.851241	−	0.524776i	$-0.175851\pi$
$60$	2.07295	−	6.37988i	0.267617	−	0.823639i
$61$	−1.64590	+	5.06555i	−0.210736	+	0.648578i	0.788693	+	0.614787i	$0.210758\pi$
$61$	−1.64590	+	5.06555i	−0.210736	+	0.648578i	−0.999429	+	0.0337908i	$0.989242\pi$
$62$	−5.16312	+	15.8904i	−0.655717	+	2.01809i
$63$	−2.11803	+	1.53884i	−0.266847	+	0.193876i
$64$	−13.0000			−1.62500
$65$	10.8541	−	7.88597i	1.34629	−	0.978134i
$66$	−2.76393	−	6.88191i	−0.340217	−	0.847105i
$67$	−1.80902	−	5.56758i	−0.221007	−	0.680188i	−0.998672	−	0.0515105i	$-0.983596\pi$
$67$	−1.80902	−	5.56758i	−0.221007	−	0.680188i	0.777666	−	0.628678i	$-0.216404\pi$
$68$	−15.1353	−	10.9964i	−1.83542	−	1.33351i
$69$	5.47214			0.658768
$70$	10.5902	−	7.69421i	1.26577	−	0.919634i
$71$	2.30902	+	7.10642i	0.274030	+	0.843377i	0.989474	+	0.144708i	$0.0462242\pi$
$71$	2.30902	+	7.10642i	0.274030	+	0.843377i	−0.715445	+	0.698670i	$0.753776\pi$
$72$	−0.690983	−	2.12663i	−0.0814331	−	0.250625i
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	0.730358	−	0.683065i	$-0.239353\pi$
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	−0.423940	+	0.905690i	$0.639353\pi$
$74$	−0.791796	+	2.43690i	−0.0920444	+	0.283284i
$75$	5.00000			0.577350
$76$	19.8541			2.27742
$77$	2.11803	−	8.42075i	0.241372	−	0.959634i
$78$	4.14590	−	12.7598i	0.469431	−	1.44476i
$79$	10.4721	−	7.60845i	1.17821	−	0.856018i	0.186239	−	0.982504i	$-0.440370\pi$
$79$	10.4721	−	7.60845i	1.17821	−	0.856018i	0.991968	+	0.126487i	$0.0403701\pi$
$80$	−0.690983	−	2.12663i	−0.0772542	−	0.237764i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	3.19098	−	2.31838i	0.352385	−	0.256023i
$83$	6.92705	+	5.03280i	0.760343	+	0.552421i	0.899015	−	0.437917i	$-0.144284\pi$
$83$	6.92705	+	5.03280i	0.760343	+	0.552421i	−0.138673	+	0.990338i	$0.544284\pi$
$84$	2.42705	−	7.46969i	0.264813	−	0.815011i
$85$	4.30902	−	13.2618i	0.467379	−	1.43844i
$86$	−17.7639			−1.91553
$87$	−5.73607	−	4.16750i	−0.614971	−	0.446803i
$88$	6.28115	+	3.94298i	0.669573	+	0.420323i
$89$	−2.88197	+	2.09387i	−0.305488	+	0.221950i	−0.729958	−	0.683492i	$-0.760460\pi$
$89$	−2.88197	+	2.09387i	−0.305488	+	0.221950i	0.424470	+	0.905442i	$0.360460\pi$
$90$	4.04508	−	2.93893i	0.426389	−	0.309790i
$91$	12.7082	−	9.23305i	1.33218	−	0.967887i
$92$	−13.2812	+	9.64932i	−1.38466	+	1.00601i
$93$	−6.04508	+	4.39201i	−0.626846	+	0.455430i
$94$	14.6353	+	10.6331i	1.50951	+	1.09672i
$95$	4.57295	+	14.0741i	0.469175	+	1.44397i
$96$	−5.42705	−	3.94298i	−0.553896	−	0.402429i
$97$	−2.04508	+	1.48584i	−0.207647	+	0.150864i	−0.686748	−	0.726895i	$-0.740963\pi$
$97$	−2.04508	+	1.48584i	−0.207647	+	0.150864i	0.479101	+	0.877760i	$0.340963\pi$
$98$	−0.263932	+	0.191758i	−0.0266612	+	0.0193705i
$99$	0.809017	−	3.21644i	0.0813093	−	0.323264i
$100$	−12.1353	+	8.81678i	−1.21353	+	0.881678i
$101$	2.66312	+	1.93487i	0.264990	+	0.192527i	0.712344	−	0.701830i	$-0.247634\pi$
$101$	2.66312	+	1.93487i	0.264990	+	0.192527i	−0.447354	+	0.894357i	$0.647634\pi$
$102$	−4.30902	−	13.2618i	−0.426656	−	1.31311i
$103$	−8.70820			−0.858045			−0.429022	−	0.903294i	$-0.641142\pi$
$103$	−8.70820			−0.858045			−0.429022	+	0.903294i	$0.641142\pi$
$104$	4.14590	+	12.7598i	0.406539	+	1.25120i
$105$	5.85410			0.571302
$106$	−1.80902	+	1.31433i	−0.175707	+	0.127659i
$107$	3.83688	−	11.8087i	0.370925	−	1.14159i	−0.575261	−	0.817970i	$-0.695100\pi$
$107$	3.83688	−	11.8087i	0.370925	−	1.14159i	0.946187	−	0.323621i	$-0.104900\pi$
$108$	0.927051	−	2.85317i	0.0892055	−	0.274546i
$109$	−3.47214	−	2.52265i	−0.332570	−	0.241626i	0.408950	−	0.912557i	$-0.365895\pi$
$109$	−3.47214	−	2.52265i	−0.332570	−	0.241626i	−0.741520	+	0.670930i	$0.765895\pi$
$110$	−4.04508	+	16.0822i	−0.385684	+	1.53338i
$111$	−0.927051	+	0.673542i	−0.0879918	+	0.0639298i
$112$	−0.809017	−	2.48990i	−0.0764449	−	0.235273i
$113$	6.04508	−	4.39201i	0.568674	−	0.413166i	−0.265949	−	0.963987i	$-0.585685\pi$
$113$	6.04508	−	4.39201i	0.568674	−	0.413166i	0.834623	+	0.550821i	$0.185685\pi$
$114$	11.9721	+	8.69827i	1.12129	+	0.814667i
$115$	−9.89919	−	7.19218i	−0.923104	−	0.670674i
$116$	21.2705			1.97492
$117$	4.85410	−	3.52671i	0.448762	−	0.326045i
$118$	−8.09017	+	24.8990i	−0.744761	+	2.29214i
$119$	5.04508	−	15.5272i	0.462482	−	1.42337i
$120$	−1.54508	+	4.75528i	−0.141046	+	0.434096i
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	3.68034	−	11.3269i	0.333202	−	1.02549i
$123$	1.76393			0.159048
$124$	6.92705	−	21.3193i	0.622068	−	1.91453i
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$	4.73607	−	3.44095i	0.421922	−	0.306545i
$127$	2.20820	−	6.79615i	0.195946	−	0.603061i	−0.804018	−	0.594605i	$-0.797308\pi$
$127$	2.20820	−	6.79615i	0.195946	−	0.603061i	0.999964	−	0.00845587i	$-0.00269162\pi$
$128$	15.6525			1.38350
$129$	−6.42705	−	4.66953i	−0.565870	−	0.411129i
$130$	−24.2705	+	17.6336i	−2.12866	+	1.54657i
$131$	−5.35410	−	16.4782i	−0.467790	−	1.43971i	−0.855439	−	0.517903i	$-0.826713\pi$
$131$	−5.35410	−	16.4782i	−0.467790	−	1.43971i	0.387649	−	0.921807i	$-0.373287\pi$
$132$	3.70820	+	9.23305i	0.322758	+	0.803634i
$133$	5.35410	+	16.4782i	0.464260	+	1.42884i
$134$	4.04508	+	12.4495i	0.349442	+	1.07547i
$135$	2.23607			0.192450
$136$	11.2812	+	8.19624i	0.967351	+	0.702822i
$137$	21.7082			1.85466			0.927329	−	0.374248i	$-0.122099\pi$
$137$	21.7082			1.85466			0.927329	+	0.374248i	$0.122099\pi$
$138$	−12.2361			−1.04160
$139$	−4.16312	−	3.02468i	−0.353111	−	0.256550i	0.397062	−	0.917792i	$-0.370030\pi$
$139$	−4.16312	−	3.02468i	−0.353111	−	0.256550i	−0.750173	+	0.661242i	$0.770030\pi$
$140$	−14.2082	+	10.3229i	−1.20081	+	0.872441i
$141$	2.50000	+	7.69421i	0.210538	+	0.647969i
$142$	−5.16312	−	15.8904i	−0.433279	−	1.33350i
$143$	−4.85410	+	19.2986i	−0.405920	+	1.61383i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	4.89919	+	15.0781i	0.406855	+	1.25217i
$146$	−5.85410	−	4.25325i	−0.484489	−	0.352002i
$147$	−0.145898			−0.0120335
$148$	1.06231	−	3.26944i	0.0873210	−	0.268746i
$149$	0.545085	−	0.396027i	0.0446551	−	0.0324438i	−0.565234	−	0.824931i	$-0.691214\pi$
$149$	0.545085	−	0.396027i	0.0446551	−	0.0324438i	0.609889	+	0.792487i	$0.291214\pi$
$150$	−11.1803			−0.912871
$151$	0.500000	−	1.53884i	0.0406894	−	0.125229i	−0.928648	−	0.370961i	$-0.879028\pi$
$151$	0.500000	−	1.53884i	0.0406894	−	0.125229i	0.969338	+	0.245732i	$0.0790283\pi$
$152$	−14.7984			−1.20031
$153$	1.92705	−	5.93085i	0.155793	−	0.479481i
$154$	−4.73607	+	18.8294i	−0.381643	+	1.51731i
$155$	16.7082			1.34204
$156$	−5.56231	+	17.1190i	−0.445341	+	1.37062i
$157$	−2.69098	+	8.28199i	−0.214764	+	0.660975i	0.784406	+	0.620247i	$0.212968\pi$
$157$	−2.69098	+	8.28199i	−0.214764	+	0.660975i	−0.999170	+	0.0407279i	$0.987032\pi$
$158$	−23.4164	+	17.0130i	−1.86291	+	1.35348i
$159$	−1.00000			−0.0793052
$160$	4.63525	+	14.2658i	0.366449	+	1.12781i
$161$	−11.5902	−	8.42075i	−0.913433	−	0.663648i
$162$	1.80902	−	1.31433i	0.142130	−	0.103263i
$163$	−4.01722	−	12.3637i	−0.314653	−	0.968402i	−0.975897	−	0.218232i	$-0.929971\pi$
$163$	−4.01722	−	12.3637i	−0.314653	−	0.968402i	0.661244	−	0.750171i	$-0.270029\pi$
$164$	−4.28115	+	3.11044i	−0.334302	+	0.242885i
$165$	−5.69098	+	4.75528i	−0.443042	+	0.370198i
$166$	−15.4894	−	11.2537i	−1.20221	−	0.873455i
$167$	7.82624	−	24.0867i	0.605612	−	1.86388i	0.113088	−	0.993585i	$-0.463926\pi$
$167$	7.82624	−	24.0867i	0.605612	−	1.86388i	0.492525	−	0.870299i	$-0.336074\pi$
$168$	−1.80902	+	5.56758i	−0.139569	+	0.429548i
$169$	−18.6074	+	13.5191i	−1.43134	+	1.03993i
$170$	−9.63525	+	29.6543i	−0.738990	+	2.27438i
$171$	2.04508	+	6.29412i	0.156392	+	0.481324i
$172$	23.8328			1.81724
$173$	6.26393	+	19.2784i	0.476238	+	1.46571i	0.844281	+	0.535901i	$0.180028\pi$
$173$	6.26393	+	19.2784i	0.476238	+	1.46571i	−0.368043	+	0.929809i	$0.619972\pi$
$174$	12.8262	+	9.31881i	0.972355	+	0.706457i
$175$	−10.5902	−	7.69421i	−0.800542	−	0.581628i
$176$	2.80902	+	1.76336i	0.211738	+	0.132918i
$177$	−9.47214	+	6.88191i	−0.711969	+	0.517276i
$178$	6.44427	−	4.68204i	0.483019	−	0.350934i
$179$	−7.00000	−	5.08580i	−0.523205	−	0.380130i	0.294605	−	0.955619i	$-0.404812\pi$
$179$	−7.00000	−	5.08580i	−0.523205	−	0.380130i	−0.817810	+	0.575489i	$0.804812\pi$
$180$	−5.42705	+	3.94298i	−0.404508	+	0.293893i
$181$	9.20820	+	6.69015i	0.684440	+	0.497275i	0.874828	−	0.484434i	$-0.160974\pi$
$181$	9.20820	+	6.69015i	0.684440	+	0.497275i	−0.190387	+	0.981709i	$0.560974\pi$
$182$	−28.4164	+	20.6457i	−2.10636	+	1.53036i
$183$	4.30902	−	3.13068i	0.318532	−	0.231427i
$184$	9.89919	−	7.19218i	0.729778	−	0.530215i
$185$	2.56231			0.188384
$186$	13.5172	−	9.82084i	0.991131	−	0.720099i
$187$	7.70820	+	19.1926i	0.563680	+	1.40351i
$188$	−19.6353	−	14.2658i	−1.43205	−	1.04044i
$189$	2.61803			0.190434
$190$	−10.2254	−	31.4706i	−0.741830	−	2.28312i
$191$	4.44427	−	13.6781i	0.321576	−	0.989710i	−0.651386	−	0.758746i	$-0.725812\pi$
$191$	4.44427	−	13.6781i	0.321576	−	0.989710i	0.972962	−	0.230964i	$-0.0741878\pi$
$192$	10.5172	+	7.64121i	0.759015	+	0.551457i
$193$	2.73607	−	1.98787i	0.196946	−	0.143090i	−0.484942	−	0.874547i	$-0.661159\pi$
$193$	2.73607	−	1.98787i	0.196946	−	0.143090i	0.681888	+	0.731457i	$0.261159\pi$
$194$	4.57295	−	3.32244i	0.328319	−	0.238537i
$195$	−13.4164			−0.960769
$196$	0.354102	−	0.257270i	0.0252930	−	0.0183764i
$197$	−2.01722	+	6.20837i	−0.143721	+	0.442328i	−0.996844	−	0.0793815i	$-0.974705\pi$
$197$	−2.01722	+	6.20837i	−0.143721	+	0.442328i	0.853123	+	0.521709i	$0.174705\pi$
$198$	−1.80902	+	7.19218i	−0.128561	+	0.511126i
$199$	−13.7984			−0.978141			−0.489070	−	0.872244i	$-0.662664\pi$
$199$	−13.7984			−0.978141			−0.489070	+	0.872244i	$0.662664\pi$
$200$	9.04508	−	6.57164i	0.639584	−	0.464685i
$201$	−1.80902	+	5.56758i	−0.127598	+	0.392707i
$202$	−5.95492	−	4.32650i	−0.418986	−	0.304411i
$203$	5.73607	+	17.6538i	0.402593	+	1.23905i
$204$	5.78115	+	17.7926i	0.404762	+	1.24573i
$205$	−3.19098	−	2.31838i	−0.222868	−	0.161923i
$206$	19.4721			1.35669
$207$	−4.42705	−	3.21644i	−0.307701	−	0.223558i
$208$	1.85410	+	5.70634i	0.128559	+	0.395663i
$209$	−18.5902	−	11.6699i	−1.28591	−	0.807227i
$210$	−13.0902			−0.903308
$211$	−11.7082			−0.806026			−0.403013	−	0.915194i	$-0.632037\pi$
$211$	−11.7082			−0.806026			−0.403013	+	0.915194i	$0.632037\pi$
$212$	2.42705	−	1.76336i	0.166691	−	0.121108i
$213$	2.30902	−	7.10642i	0.158211	−	0.486924i
$214$	−8.57953	+	26.4051i	−0.586484	+	1.80501i
$215$	5.48936	+	16.8945i	0.374371	+	1.15220i
$216$	−0.690983	+	2.12663i	−0.0470154	+	0.144699i
$217$	19.5623			1.32798
$218$	7.76393	+	5.64083i	0.525840	+	0.382045i
$219$	−1.00000	−	3.07768i	−0.0675737	−	0.207971i
$220$	5.42705	−	21.5765i	0.365892	−	1.45469i
$221$	−11.5623	+	35.5851i	−0.777765	+	2.39371i
$222$	2.07295	−	1.50609i	0.139127	−	0.101082i
$223$	1.11803	+	3.44095i	0.0748691	+	0.230423i	0.981487	−	0.191530i	$-0.0613448\pi$
$223$	1.11803	+	3.44095i	0.0748691	+	0.230423i	−0.906618	+	0.421953i	$0.861345\pi$
$224$	5.42705	+	16.7027i	0.362610	+	1.11600i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	−13.5172	+	9.82084i	−0.899152	+	0.653272i
$227$	−7.51722	−	5.46158i	−0.498935	−	0.362498i	0.309675	−	0.950843i	$-0.399780\pi$
$227$	−7.51722	−	5.46158i	−0.498935	−	0.362498i	−0.808610	+	0.588345i	$0.799780\pi$
$228$	−16.0623	−	11.6699i	−1.06375	−	0.772861i
$229$	−13.7533	+	9.99235i	−0.908843	+	0.660313i	−0.940722	−	0.339179i	$-0.889851\pi$
$229$	−13.7533	+	9.99235i	−0.908843	+	0.660313i	0.0318790	+	0.999492i	$0.489851\pi$
$230$	22.1353	+	16.0822i	1.45956	+	1.06043i
$231$	−6.66312	+	5.56758i	−0.438401	+	0.366320i
$232$	−15.8541			−1.04087
$233$	7.52786	−	23.1684i	0.493167	−	1.51781i	−0.326628	−	0.945153i	$-0.605912\pi$
$233$	7.52786	−	23.1684i	0.493167	−	1.51781i	0.819794	−	0.572658i	$-0.194088\pi$
$234$	−10.8541	+	7.88597i	−0.709555	+	0.515522i
$235$	5.59017	−	17.2048i	0.364662	−	1.12232i
$236$	10.8541	−	33.4055i	0.706542	−	2.17451i
$237$	−12.9443			−0.840821
$238$	−11.2812	+	34.7198i	−0.731249	+	2.25055i
$239$	−4.04508	−	12.4495i	−0.261655	−	0.805291i	−0.992445	−	0.122689i	$-0.960848\pi$
$239$	−4.04508	−	12.4495i	−0.261655	−	0.805291i	0.730790	−	0.682602i	$-0.239152\pi$
$240$	−0.690983	+	2.12663i	−0.0446028	+	0.137273i
$241$	−14.4443	−	10.4944i	−0.930437	−	0.676002i	0.0156625	−	0.999877i	$-0.495014\pi$
$241$	−14.4443	−	10.4944i	−0.930437	−	0.676002i	−0.946100	+	0.323875i	$0.895014\pi$
$242$	−10.6910	−	22.1518i	−0.687242	−	1.42397i
$243$	1.00000			0.0641500
$244$	−4.93769	+	15.1967i	−0.316103	+	0.972866i
$245$	0.263932	+	0.191758i	0.0168620	+	0.0122510i
$246$	−3.94427			−0.251478
$247$	−12.2705	−	37.7647i	−0.780754	−	2.40291i
$248$	−5.16312	+	15.8904i	−0.327858	+	1.00904i
$249$	−2.64590	−	8.14324i	−0.167677	−	0.516057i
$250$	20.2254	+	14.6946i	1.27917	+	0.929370i
$251$	0.0278640	+	0.0202444i	0.00175876	+	0.00127782i	0.588664	−	0.808378i	$-0.299654\pi$
$251$	0.0278640	+	0.0202444i	0.00175876	+	0.00127782i	−0.586906	+	0.809655i	$0.699654\pi$
$252$	−6.35410	+	4.61653i	−0.400271	+	0.290814i
$253$	18.1074	−	1.22857i	1.13840	−	0.0772396i
$254$	−4.93769	+	15.1967i	−0.309818	+	0.953523i
$255$	−11.2812	+	8.19624i	−0.706453	+	0.513268i
$256$	−9.00000			−0.562500
$257$	5.01722	+	15.4414i	0.312966	+	0.963209i	0.976584	+	0.215138i	$0.0690200\pi$
$257$	5.01722	+	15.4414i	0.312966	+	0.963209i	−0.663618	+	0.748072i	$0.730980\pi$
$258$	14.3713	+	10.4414i	0.894719	+	0.650052i
$259$	3.00000			0.186411
$260$	32.5623	−	23.6579i	2.01943	−	1.46720i
$261$	2.19098	+	6.74315i	0.135618	+	0.417391i
$262$	11.9721	+	36.8464i	0.739641	+	2.27638i
$263$	18.7082	+	13.5923i	1.15360	+	0.838137i	0.988955	−	0.148216i	$-0.0473530\pi$
$263$	18.7082	+	13.5923i	1.15360	+	0.838137i	0.164642	+	0.986353i	$0.447353\pi$
$264$	−2.76393	−	6.88191i	−0.170108	−	0.423552i
$265$	1.80902	+	1.31433i	0.111127	+	0.0807385i
$266$	−11.9721	−	36.8464i	−0.734059	−	2.25920i
$267$	3.56231			0.218010
$268$	−5.42705	−	16.7027i	−0.331510	−	1.02028i
$269$	14.2812	+	10.3759i	0.870737	+	0.632628i	0.930785	−	0.365568i	$-0.119125\pi$
$269$	14.2812	+	10.3759i	0.870737	+	0.632628i	−0.0600474	+	0.998196i	$0.519125\pi$
$270$	−5.00000			−0.304290
$271$	3.79837			0.230735			0.115367	−	0.993323i	$-0.463195\pi$
$271$	3.79837			0.230735			0.115367	+	0.993323i	$0.463195\pi$
$272$	5.04508	+	3.66547i	0.305903	+	0.222252i
$273$	−15.7082			−0.950704
$274$	−48.5410			−2.93247
$275$	16.5451	−	1.12257i	0.997706	−	0.0676935i
$276$	16.4164			0.988152
$277$	20.6180			1.23882			0.619409	−	0.785069i	$-0.287372\pi$
$277$	20.6180			1.23882			0.619409	+	0.785069i	$0.287372\pi$
$278$	9.30902	+	6.76340i	0.558318	+	0.405642i
$279$	7.47214			0.447345
$280$	10.5902	−	7.69421i	0.632884	−	0.459817i
$281$	−11.5172	−	8.36775i	−0.687060	−	0.499178i	0.188632	−	0.982048i	$-0.439595\pi$
$281$	−11.5172	−	8.36775i	−0.687060	−	0.499178i	−0.875692	+	0.482870i	$0.839595\pi$
$282$	−5.59017	−	17.2048i	−0.332890	−	1.02453i
$283$	−18.8885			−1.12281			−0.561404	−	0.827542i	$-0.689738\pi$
$283$	−18.8885			−1.12281			−0.561404	+	0.827542i	$0.689738\pi$
$284$	6.92705	+	21.3193i	0.411045	+	1.26507i
$285$	4.57295	−	14.0741i	0.270878	−	0.833677i
$286$	10.8541	−	43.1531i	0.641817	−	2.55170i
$287$	−3.73607	−	2.71441i	−0.220533	−	0.160227i
$288$	2.07295	+	6.37988i	0.122150	+	0.375938i
$289$	6.76393	+	20.8172i	0.397878	+	1.22454i
$290$	−10.9549	−	33.7158i	−0.643295	−	1.97986i
$291$	2.52786			0.148186
$292$	7.85410	+	5.70634i	0.459627	+	0.333938i
$293$	−9.03444	−	27.8052i	−0.527798	−	1.62439i	−0.758716	−	0.651421i	$-0.774173\pi$
$293$	−9.03444	−	27.8052i	−0.527798	−	1.62439i	0.230918	−	0.972973i	$-0.425827\pi$
$294$	0.326238			0.0190266
$295$	26.1803			1.52428
$296$	−0.791796	+	2.43690i	−0.0460222	+	0.141642i
$297$	−2.54508	+	2.12663i	−0.147681	+	0.123399i
$298$	−1.21885	+	0.885544i	−0.0706059	+	0.0512982i
$299$	26.5623	+	19.2986i	1.53614	+	1.11607i
$300$	15.0000			0.866025
$301$	6.42705	+	19.7804i	0.370449	+	1.14012i
$302$	−1.11803	+	3.44095i	−0.0643356	+	0.198005i
$303$	−1.01722	−	3.13068i	−0.0584378	−	0.179853i
$304$	−6.61803			−0.379570
$305$	−11.9098			−0.681955
$306$	−4.30902	+	13.2618i	−0.246330	+	0.758126i
$307$	1.58359			0.0903804			0.0451902	−	0.998978i	$-0.485611\pi$
$307$	1.58359			0.0903804			0.0451902	+	0.998978i	$0.485611\pi$
$308$	6.35410	−	25.2623i	0.362059	−	1.43945i
$309$	7.04508	+	5.11855i	0.400781	+	0.291184i
$310$	−37.3607			−2.12194
$311$	−8.54508	−	26.2991i	−0.484547	−	1.49128i	−0.832635	−	0.553821i	$-0.813169\pi$
$311$	−8.54508	−	26.2991i	−0.484547	−	1.49128i	0.348088	−	0.937462i	$-0.386831\pi$
$312$	4.14590	−	12.7598i	0.234715	−	0.722379i
$313$	−26.4164			−1.49314			−0.746572	−	0.665305i	$-0.768302\pi$
$313$	−26.4164			−1.49314			−0.746572	+	0.665305i	$0.768302\pi$
$314$	6.01722	−	18.5191i	0.339571	−	1.04509i
$315$	−4.73607	−	3.44095i	−0.266847	−	0.193876i
$316$	31.4164	−	22.8254i	1.76731	−	1.28403i
$317$	−3.09017	+	9.51057i	−0.173561	+	0.534167i	−0.999565	−	0.0294983i	$-0.990609\pi$
$317$	−3.09017	+	9.51057i	−0.173561	+	0.534167i	0.826004	+	0.563665i	$0.190609\pi$
$318$	2.23607			0.125392
$319$	−19.9164	−	12.5025i	−1.11510	−	0.700005i
$320$	−8.98278	−	27.6462i	−0.502153	−	1.54547i
$321$	−10.0451	+	7.29818i	−0.560662	+	0.407345i
$322$	25.9164	+	18.8294i	1.44426	+	1.04932i
$323$	−33.3885	−	24.2582i	−1.85779	−	1.34976i
$324$	−2.42705	+	1.76336i	−0.134836	+	0.0979642i
$325$	24.2705	+	17.6336i	1.34629	+	0.978134i
$326$	8.98278	+	27.6462i	0.497510	+	1.53118i
$327$	1.32624	+	4.08174i	0.0733411	+	0.225721i
$328$	3.19098	−	2.31838i	0.176193	−	0.128011i
$329$	6.54508	−	20.1437i	0.360842	−	1.11056i
$330$	12.7254	−	10.6331i	0.700512	−	0.585335i
$331$	2.18034	+	6.71040i	0.119842	+	0.368837i	0.992926	−	0.118733i	$-0.0378834\pi$
$331$	2.18034	+	6.71040i	0.119842	+	0.368837i	−0.873084	+	0.487570i	$0.837883\pi$
$332$	20.7812	+	15.0984i	1.14051	+	0.828632i
$333$	1.14590			0.0627948
$334$	−17.5000	+	53.8595i	−0.957557	+	2.94706i
$335$	10.5902	−	7.69421i	0.578603	−	0.420380i
$336$	−0.809017	+	2.48990i	−0.0441355	+	0.135835i
$337$	3.74671	−	11.5312i	0.204096	−	0.628144i	−0.795653	−	0.605753i	$-0.792872\pi$
$337$	3.74671	−	11.5312i	0.204096	−	0.628144i	0.999749	−	0.0223912i	$-0.00712795\pi$
$338$	41.6074	−	30.2295i	2.26314	−	1.64427i
$339$	−7.47214			−0.405831
$340$	12.9271	−	39.7854i	0.701068	−	2.15766i
$341$	−19.0172	+	15.8904i	−1.02984	+	0.860516i
$342$	−4.57295	−	14.0741i	−0.247277	−	0.761040i
$343$	15.1353	+	10.9964i	0.817227	+	0.593750i
$344$	−17.7639			−0.957767
$345$	3.78115	+	11.6372i	0.203570	+	0.626525i
$346$	−14.0066	−	43.1078i	−0.752998	−	2.31749i
$347$	5.54508	+	17.0660i	0.297676	+	0.916152i	0.982310	+	0.187265i	$0.0599622\pi$
$347$	5.54508	+	17.0660i	0.297676	+	0.916152i	−0.684634	+	0.728887i	$0.740038\pi$
$348$	−17.2082	−	12.5025i	−0.922457	−	0.670204i
$349$	−0.100813	+	0.310271i	−0.00539640	+	0.0166084i	−0.953718	−	0.300701i	$-0.902779\pi$
$349$	−0.100813	+	0.310271i	−0.00539640	+	0.0166084i	0.948322	+	0.317309i	$0.102779\pi$
$350$	23.6803	+	17.2048i	1.26577	+	0.919634i
$351$	−6.00000			−0.320256
$352$	−18.8435	−	11.8290i	−1.00436	−	0.630485i
$353$	4.50000	−	13.8496i	0.239511	−	0.737139i	−0.756980	−	0.653438i	$-0.773326\pi$
$353$	4.50000	−	13.8496i	0.239511	−	0.737139i	0.996491	−	0.0837006i	$-0.0266739\pi$
$354$	21.1803	−	15.3884i	1.12572	−	0.817885i
$355$	−13.5172	+	9.82084i	−0.717420	+	0.521236i
$356$	−8.64590	+	6.28161i	−0.458232	+	0.332925i
$357$	−13.2082	+	9.59632i	−0.699052	+	0.507891i
$358$	15.6525	+	11.3722i	0.827259	+	0.601039i
$359$	−3.27051	+	10.0656i	−0.172611	+	0.531242i	−0.999516	−	0.0310993i	$-0.990099\pi$
$359$	−3.27051	+	10.0656i	−0.172611	+	0.531242i	0.826905	+	0.562341i	$0.190099\pi$
$360$	4.04508	−	2.93893i	0.213195	−	0.154895i
$361$	24.7984			1.30518
$362$	−20.5902	−	14.9596i	−1.08220	−	0.786261i
$363$	1.95492	−	10.8249i	0.102606	−	0.568160i
$364$	38.1246	−	27.6992i	1.99827	−	1.45183i
$365$	−2.23607	+	6.88191i	−0.117041	+	0.360216i
$366$	−9.63525	+	7.00042i	−0.503643	+	0.365918i
$367$	8.69098	−	6.31437i	0.453666	−	0.329607i	−0.337376	−	0.941370i	$-0.609539\pi$
$367$	8.69098	−	6.31437i	0.453666	−	0.329607i	0.791041	+	0.611763i	$0.209539\pi$
$368$	4.42705	−	3.21644i	0.230776	−	0.167669i
$369$	−1.42705	−	1.03681i	−0.0742893	−	0.0539743i
$370$	−5.72949			−0.297862
$371$	2.11803	+	1.53884i	0.109963	+	0.0798927i
$372$	−18.1353	+	13.1760i	−0.940269	+	0.683146i
$373$	3.20820	−	2.33090i	0.166115	−	0.120689i	−0.501622	−	0.865087i	$-0.667263\pi$
$373$	3.20820	−	2.33090i	0.166115	−	0.120689i	0.667737	+	0.744398i	$0.267263\pi$
$374$	−17.2361	−	42.9161i	−0.891256	−	2.21914i
$375$	3.45492	+	10.6331i	0.178411	+	0.549093i
$376$	14.6353	+	10.6331i	0.754756	+	0.548362i
$377$	−13.1459	−	40.4589i	−0.677048	−	2.08374i
$378$	−5.85410			−0.301103
$379$	8.29837	+	25.5398i	0.426259	+	1.31189i	0.901784	+	0.432188i	$0.142258\pi$
$379$	8.29837	+	25.5398i	0.426259	+	1.31189i	−0.475525	+	0.879702i	$0.657742\pi$
$380$	13.7188	+	42.2223i	0.703762	+	2.16596i
$381$	−5.78115	+	4.20025i	−0.296177	+	0.215186i
$382$	−9.93769	+	30.5851i	−0.508457	+	1.56487i
$383$	−6.20163	+	19.0866i	−0.316888	+	0.975282i	0.658082	+	0.752946i	$0.271368\pi$
$383$	−6.20163	+	19.0866i	−0.316888	+	0.975282i	−0.974970	+	0.222336i	$0.928632\pi$
$384$	−12.6631	−	9.20029i	−0.646212	−	0.469501i
$385$	19.3713	−	1.31433i	0.987254	−	0.0669843i
$386$	−6.11803	+	4.44501i	−0.311400	+	0.226245i
$387$	2.45492	+	7.55545i	0.124790	+	0.384065i
$388$	−6.13525	+	4.45752i	−0.311470	+	0.226296i
$389$	−3.88197	−	2.82041i	−0.196823	−	0.143001i	0.485009	−	0.874509i	$-0.338816\pi$
$389$	−3.88197	−	2.82041i	−0.196823	−	0.143001i	−0.681832	+	0.731509i	$0.738816\pi$
$390$	30.0000			1.51911
$391$	34.1246			1.72576
$392$	−0.263932	+	0.191758i	−0.0133306	+	0.00968523i
$393$	−5.35410	+	16.4782i	−0.270079	+	0.831217i
$394$	4.51064	−	13.8823i	0.227243	−	0.699382i
$395$	23.4164	+	17.0130i	1.17821	+	0.856018i
$396$	2.42705	−	9.64932i	0.121964	−	0.484897i
$397$	6.60739	−	20.3355i	0.331615	−	1.02061i	−0.636750	−	0.771070i	$-0.719722\pi$
$397$	6.60739	−	20.3355i	0.331615	−	1.02061i	0.968365	−	0.249537i	$-0.0802784\pi$
$398$	30.8541			1.54658
$399$	5.35410	−	16.4782i	0.268040	−	0.824943i
$400$	4.04508	−	2.93893i	0.202254	−	0.146946i
$401$	13.2812	−	9.64932i	0.663229	−	0.481864i	−0.204523	−	0.978862i	$-0.565564\pi$
$401$	13.2812	−	9.64932i	0.663229	−	0.481864i	0.867752	+	0.496998i	$0.165564\pi$
$402$	4.04508	−	12.4495i	0.201751	−	0.620924i
$403$	−44.8328			−2.23328
$404$	7.98936	+	5.80461i	0.397485	+	0.288790i
$405$	−1.80902	−	1.31433i	−0.0898908	−	0.0653095i
$406$	−12.8262	−	39.4751i	−0.636555	−	1.95912i
$407$	−2.91641	+	2.43690i	−0.144561	+	0.120793i
$408$	−4.30902	−	13.2618i	−0.213328	−	0.656556i
$409$	−0.600813	−	1.84911i	−0.0297083	−	0.0914327i	0.935103	−	0.354376i	$-0.115307\pi$
$409$	−0.600813	−	1.84911i	−0.0297083	−	0.0914327i	−0.964811	+	0.262943i	$0.915307\pi$
$410$	7.13525	+	5.18407i	0.352385	+	0.256023i
$411$	−17.5623	−	12.7598i	−0.866285	−	0.629393i
$412$	−26.1246			−1.28707
$413$	30.6525			1.50831
$414$	9.89919	+	7.19218i	0.486518	+	0.353476i
$415$	−5.91641	+	18.2088i	−0.290425	+	0.893836i
$416$	−12.4377	−	38.2793i	−0.609808	−	1.87680i
$417$	1.59017	+	4.89404i	0.0778710	+	0.239662i
$418$	41.5689	+	26.0948i	2.03320	+	1.27634i
$419$	−7.05573	−	21.7153i	−0.344695	−	1.06086i	−0.961747	−	0.273939i	$-0.911673\pi$
$419$	−7.05573	−	21.7153i	−0.344695	−	1.06086i	0.617052	−	0.786922i	$-0.288327\pi$
$420$	17.5623			0.856953
$421$	−21.0172	−	15.2699i	−1.02432	−	0.744210i	−0.0571534	−	0.998365i	$-0.518202\pi$
$421$	−21.0172	−	15.2699i	−1.02432	−	0.744210i	−0.967163	+	0.254156i	$0.918202\pi$
$422$	26.1803			1.27444
$423$	2.50000	−	7.69421i	0.121554	−	0.374105i
$424$	−1.80902	+	1.31433i	−0.0878536	+	0.0638294i
$425$	31.1803			1.51247
$426$	−5.16312	+	15.8904i	−0.250154	+	0.769895i
$427$	−13.9443			−0.674811
$428$	11.5106	−	35.4261i	0.556388	−	1.71239i
$429$	15.2705	−	12.7598i	0.737267	−	0.616047i
$430$	−12.2746	−	37.7773i	−0.591933	−	1.82178i
$431$	1.54508	−	4.75528i	0.0744241	−	0.229054i	−0.906924	−	0.421295i	$-0.861576\pi$
$431$	1.54508	−	4.75528i	0.0744241	−	0.229054i	0.981348	+	0.192241i	$0.0615756\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−20.1803	+	14.6619i	−0.969805	+	0.704605i	−0.955407	−	0.295292i	$-0.904583\pi$
$433$	−20.1803	+	14.6619i	−0.969805	+	0.704605i	−0.0143981	+	0.999896i	$0.504583\pi$
$434$	−43.7426			−2.09971
$435$	4.89919	−	15.0781i	0.234898	−	0.722942i
$436$	−10.4164	−	7.56796i	−0.498855	−	0.362440i
$437$	−29.2984	+	21.2865i	−1.40153	+	1.01827i
$438$	2.23607	+	6.88191i	0.106843	+	0.328830i
$439$	3.88197	−	2.82041i	0.185276	−	0.134611i	−0.491281	−	0.871001i	$-0.663471\pi$
$439$	3.88197	−	2.82041i	0.185276	−	0.134611i	0.676557	+	0.736390i	$0.263471\pi$
$440$	−4.04508	+	16.0822i	−0.192842	+	0.766689i
$441$	0.118034	+	0.0857567i	0.00562067	+	0.00408365i
$442$	25.8541	−	79.5707i	1.22975	−	3.78479i
$443$	−11.8713	+	36.5362i	−0.564024	+	1.73589i	0.106811	+	0.994279i	$0.465936\pi$
$443$	−11.8713	+	36.5362i	−0.564024	+	1.73589i	−0.670835	+	0.741607i	$0.734064\pi$
$444$	−2.78115	+	2.02063i	−0.131988	+	0.0958947i
$445$	−6.44427	−	4.68204i	−0.305488	−	0.221950i
$446$	−2.50000	−	7.69421i	−0.118378	−	0.364331i
$447$	−0.673762			−0.0318679
$448$	−10.5172	−	32.3687i	−0.496892	−	1.52928i
$449$	−9.78115	−	7.10642i	−0.461601	−	0.335373i	0.332558	−	0.943083i	$-0.392088\pi$
$449$	−9.78115	−	7.10642i	−0.461601	−	0.335373i	−0.794159	+	0.607710i	$0.792088\pi$
$450$	9.04508	+	6.57164i	0.426389	+	0.309790i
$451$	5.83688	−	0.396027i	0.274848	−	0.0186482i
$452$	18.1353	−	13.1760i	0.853011	−	0.619749i
$453$	−1.30902	+	0.951057i	−0.0615030	+	0.0446845i
$454$	16.8090	+	12.2125i	0.788886	+	0.573159i
$455$	28.4164	+	20.6457i	1.33218	+	0.967887i
$456$	11.9721	+	8.69827i	0.560647	+	0.407334i
$457$	−7.94427	+	5.77185i	−0.371617	+	0.269996i	−0.757881	−	0.652392i	$-0.773765\pi$
$457$	−7.94427	+	5.77185i	−0.371617	+	0.269996i	0.386264	+	0.922388i	$0.373765\pi$
$458$	30.7533	−	22.3436i	1.43701	−	1.04405i
$459$	−5.04508	+	3.66547i	−0.235484	+	0.171089i
$460$	−29.6976	−	21.5765i	−1.38466	−	1.00601i
$461$	−25.8713	+	18.7966i	−1.20495	+	0.875446i	−0.994762	−	0.102216i	$-0.967407\pi$
$461$	−25.8713	+	18.7966i	−1.20495	+	0.875446i	−0.210185	+	0.977662i	$0.567407\pi$
$462$	14.8992	−	12.4495i	0.693173	−	0.579203i
$463$	27.6074	+	20.0579i	1.28302	+	0.932172i	0.999640	−	0.0268347i	$-0.00854278\pi$
$463$	27.6074	+	20.0579i	1.28302	+	0.932172i	0.283384	+	0.959006i	$0.408543\pi$
$464$	−7.09017			−0.329153
$465$	−13.5172	−	9.82084i	−0.626846	−	0.455430i
$466$	−16.8328	+	51.8061i	−0.779765	+	2.39987i
$467$	12.5902	+	9.14729i	0.582604	+	0.423286i	0.839662	−	0.543110i	$-0.182753\pi$
$467$	12.5902	+	9.14729i	0.582604	+	0.423286i	−0.257058	+	0.966396i	$0.582753\pi$
$468$	14.5623	−	10.5801i	0.673143	−	0.489067i
$469$	12.3992	−	9.00854i	0.572541	−	0.415976i
$470$	−12.5000	+	38.4710i	−0.576582	+	1.77454i
$471$	7.04508	−	5.11855i	0.324620	−	0.235851i
$472$	−8.09017	+	24.8990i	−0.372380	+	1.14607i
$473$	−22.3156	−	14.0086i	−1.02607	−	0.644115i
$474$	28.9443			1.32945
$475$	−26.7705	+	19.4499i	−1.22832	+	0.892423i
$476$	15.1353	−	46.5815i	0.693723	−	2.13506i
$477$	0.809017	+	0.587785i	0.0370423	+	0.0269128i
$478$	9.04508	+	27.8379i	0.413713	+	1.27328i
$479$	4.36475	+	13.4333i	0.199430	+	0.613783i	0.999896	+	0.0144051i	$0.00458544\pi$
$479$	4.36475	+	13.4333i	0.199430	+	0.613783i	−0.800466	+	0.599378i	$0.795415\pi$
$480$	4.63525	−	14.2658i	0.211569	−	0.651144i
$481$	−6.87539			−0.313491
$482$	32.2984	+	23.4661i	1.47115	+	1.06885i
$483$	4.42705	+	13.6251i	0.201438	+	0.619962i
$484$	14.3435	+	29.7198i	0.651975	+	1.35090i
$485$	−4.57295	−	3.32244i	−0.207647	−	0.150864i
$486$	−2.23607			−0.101430
$487$	−12.2082	+	8.86978i	−0.553207	+	0.401928i	−0.828966	−	0.559299i	$-0.811071\pi$
$487$	−12.2082	+	8.86978i	−0.553207	+	0.401928i	0.275760	+	0.961227i	$0.411071\pi$
$488$	3.68034	−	11.3269i	0.166601	−	0.512746i
$489$	−4.01722	+	12.3637i	−0.181665	+	0.559107i
$490$	−0.590170	−	0.428784i	−0.0266612	−	0.0193705i
$491$	−7.89261	+	24.2910i	−0.356188	+	1.09624i	0.599129	+	0.800653i	$0.295514\pi$
$491$	−7.89261	+	24.2910i	−0.356188	+	1.09624i	−0.955317	+	0.295583i	$0.904486\pi$
$492$	5.29180			0.238573
$493$	−35.7705	−	25.9888i	−1.61102	−	1.17048i
$494$	27.4377	+	84.4445i	1.23448	+	3.79934i
$495$	7.39919	−	0.502029i	0.332569	−	0.0225645i
$496$	−2.30902	+	7.10642i	−0.103678	+	0.319088i
$497$	−15.8262	+	11.4984i	−0.709904	+	0.515775i
$498$	5.91641	+	18.2088i	0.265121	+	0.815957i
$499$	−2.83688	−	8.73102i	−0.126996	−	0.390854i	0.867263	−	0.497850i	$-0.165877\pi$
$499$	−2.83688	−	8.73102i	−0.126996	−	0.390854i	−0.994259	+	0.106996i	$0.965877\pi$
$500$	−27.1353	−	19.7149i	−1.21353	−	0.881678i
$501$	−20.4894	+	14.8864i	−0.915397	+	0.665075i
$502$	−0.0623059	−	0.0452679i	−0.00278085	−	0.00202040i
$503$	−4.85410	−	3.52671i	−0.216434	−	0.157248i	0.474286	−	0.880371i	$-0.342706\pi$
$503$	−4.85410	−	3.52671i	−0.216434	−	0.157248i	−0.690720	+	0.723122i	$0.742706\pi$
$504$	4.73607	−	3.44095i	0.210961	−	0.153272i
$505$	−2.27458	+	7.00042i	−0.101217	+	0.311515i
$506$	−40.4894	+	2.74717i	−1.79997	+	0.122127i
$507$	23.0000			1.02147
$508$	6.62461	−	20.3885i	0.293920	−	0.904592i
$509$	−7.61803	+	5.53483i	−0.337663	+	0.245327i	−0.743675	−	0.668541i	$-0.766919\pi$
$509$	−7.61803	+	5.53483i	−0.337663	+	0.245327i	0.406012	+	0.913868i	$0.366919\pi$
$510$	25.2254	−	18.3273i	1.11700	−	0.811548i
$511$	−2.61803	+	8.05748i	−0.115815	+	0.356442i
$512$	−11.1803			−0.494106
$513$	2.04508	−	6.29412i	0.0902927	−	0.277892i
$514$	−11.2188	−	34.5281i	−0.494842	−	1.52297i
$515$	−6.01722	−	18.5191i	−0.265150	−	0.816049i
$516$	−19.2812	−	14.0086i	−0.848805	−	0.616693i
$517$	10.0000	+	24.8990i	0.439799	+	1.09506i
$518$	−6.70820			−0.294742
$519$	6.26393	−	19.2784i	0.274956	−	0.846228i
$520$	−24.2705	+	17.6336i	−1.06433	+	0.773283i
$521$	−6.47214			−0.283549			−0.141775	−	0.989899i	$-0.545281\pi$
$521$	−6.47214			−0.283549			−0.141775	+	0.989899i	$0.545281\pi$
$522$	−4.89919	−	15.0781i	−0.214432	−	0.659953i
$523$	9.82624	−	30.2421i	0.429671	−	1.32239i	−0.468778	−	0.883316i	$-0.655306\pi$
$523$	9.82624	−	30.2421i	0.429671	−	1.32239i	0.898450	−	0.439077i	$-0.144694\pi$
$524$	−16.0623	−	49.4347i	−0.701685	−	2.15956i
$525$	4.04508	+	12.4495i	0.176542	+	0.543340i
$526$	−41.8328	−	30.3933i	−1.82400	−	1.32521i
$527$	−37.6976	+	27.3889i	−1.64213	+	1.19308i
$528$	−1.23607	−	3.07768i	−0.0537930	−	0.133939i
$529$	2.14590	−	6.60440i	0.0932999	−	0.287148i
$530$	−4.04508	−	2.93893i	−0.175707	−	0.127659i
$531$	11.7082			0.508093
$532$	16.0623	+	49.4347i	0.696389	+	2.14327i
$533$	8.56231	+	6.22088i	0.370875	+	0.269456i
$534$	−7.96556			−0.344703
$535$	27.7639			1.20034
$536$	4.04508	+	12.4495i	0.174721	+	0.537736i
$537$	2.67376	+	8.22899i	0.115381	+	0.355107i
$538$	−31.9336	−	23.2011i	−1.37676	−	1.00027i
$539$	−0.482779	+	0.0327561i	−0.0207948	+	0.00141091i
$540$	6.70820			0.288675
$541$	−0.618034	−	1.90211i	−0.0265714	−	0.0817782i	0.936891	−	0.349620i	$-0.113689\pi$
$541$	−0.618034	−	1.90211i	−0.0265714	−	0.0817782i	−0.963463	+	0.267842i	$0.913689\pi$
$542$	−8.49342			−0.364824
$543$	−3.51722	−	10.8249i	−0.150938	−	0.464541i
$544$	−33.8435	−	24.5887i	−1.45103	−	1.05423i
$545$	2.96556	−	9.12705i	0.127031	−	0.390960i
$546$	35.1246			1.50319
$547$	−32.1697	−	23.3727i	−1.37548	−	0.999342i	−0.997287	−	0.0736145i	$-0.976547\pi$
$547$	−32.1697	−	23.3727i	−1.37548	−	0.999342i	−0.378190	−	0.925728i	$-0.623453\pi$
$548$	65.1246			2.78199
$549$	−5.32624			−0.227318
$550$	−36.9959	+	2.51014i	−1.57751	+	0.107033i
$551$	46.9230			1.99899
$552$	−12.2361			−0.520802
$553$	27.4164	+	19.9192i	1.16586	+	0.847050i
$554$	−46.1033			−1.95874
$555$	−2.07295	−	1.50609i	−0.0879918	−	0.0639298i
$556$	−12.4894	−	9.07405i	−0.529667	−	0.384825i
$557$	13.2254	+	40.7037i	0.560379	+	1.72467i	0.681297	+	0.732007i	$0.261416\pi$
$557$	13.2254	+	40.7037i	0.560379	+	1.72467i	−0.120917	+	0.992663i	$0.538584\pi$
$558$	−16.7082			−0.707315
$559$	−14.7295	−	45.3327i	−0.622991	−	1.91737i
$560$	4.73607	−	3.44095i	0.200135	−	0.145407i
$561$	5.04508	−	20.0579i	0.213004	−	0.846847i
$562$	25.7533	+	18.7109i	1.08634	+	0.789270i
$563$	−6.93363	−	21.3395i	−0.292218	−	0.899353i	−0.984142	−	0.177383i	$-0.943237\pi$
$563$	−6.93363	−	21.3395i	−0.292218	−	0.899353i	0.691924	−	0.721970i	$-0.256763\pi$
$564$	7.50000	+	23.0826i	0.315807	+	0.971954i
$565$	13.5172	+	9.82084i	0.568674	+	0.413166i
$566$	42.2361			1.77531
$567$	−2.11803	−	1.53884i	−0.0889491	−	0.0646253i
$568$	−5.16312	−	15.8904i	−0.216640	−	0.666748i
$569$	8.74265			0.366511			0.183255	−	0.983065i	$-0.441336\pi$
$569$	8.74265			0.366511			0.183255	+	0.983065i	$0.441336\pi$
$570$	−10.2254	+	31.4706i	−0.428296	+	1.31816i
$571$	6.13525	−	18.8824i	0.256752	−	0.790203i	−0.736727	−	0.676190i	$-0.763630\pi$
$571$	6.13525	−	18.8824i	0.256752	−	0.790203i	0.993479	−	0.114012i	$-0.0363703\pi$
$572$	−14.5623	+	57.8959i	−0.608881	+	2.42075i
$573$	−11.6353	+	8.45351i	−0.486070	+	0.353150i
$574$	8.35410	+	6.06961i	0.348693	+	0.253341i
$575$	8.45492	−	26.0216i	0.352594	−	1.08517i
$576$	−4.01722	−	12.3637i	−0.167384	−	0.515156i
$577$	−2.70820	+	8.33499i	−0.112744	+	0.346990i	−0.991470	−	0.130337i	$-0.958394\pi$
$577$	−2.70820	+	8.33499i	−0.112744	+	0.346990i	0.878726	+	0.477327i	$0.158394\pi$
$578$	−15.1246	−	46.5488i	−0.629101	−	1.93617i
$579$	−3.38197			−0.140550
$580$	14.6976	+	45.2344i	0.610283	+	1.87826i
$581$	−6.92705	+	21.3193i	−0.287382	+	0.884472i
$582$	−5.65248			−0.234303
$583$	−3.30902	+	0.224514i	−0.137045	+	0.00929842i
$584$	−5.85410	−	4.25325i	−0.242244	−	0.176001i
$585$	10.8541	+	7.88597i	0.448762	+	0.326045i
$586$	20.2016	+	62.1742i	0.834521	+	2.56839i
$587$	0.190983	−	0.587785i	0.00788271	−	0.0242605i	−0.947038	−	0.321122i	$-0.895940\pi$
$587$	0.190983	−	0.587785i	0.00788271	−	0.0242605i	0.954921	+	0.296862i	$0.0959400\pi$
$588$	−0.437694			−0.0180502
$589$	15.2812	−	47.0306i	0.629649	−	1.93786i
$590$	−58.5410			−2.41010
$591$	5.28115	−	3.83698i	0.217238	−	0.157832i
$592$	−0.354102	+	1.08981i	−0.0145535	+	0.0447911i
$593$	−20.7082			−0.850384			−0.425192	−	0.905103i	$-0.639793\pi$
$593$	−20.7082			−0.850384			−0.425192	+	0.905103i	$0.639793\pi$
$594$	5.69098	−	4.75528i	0.233504	−	0.195112i
$595$	36.5066			1.49662
$596$	1.63525	−	1.18808i	0.0669827	−	0.0486657i
$597$	11.1631	+	8.11048i	0.456876	+	0.331940i
$598$	−59.3951	−	43.1531i	−2.42885	−	1.76466i
$599$	2.32624	−	1.69011i	0.0950475	−	0.0690561i	−0.539246	−	0.842148i	$-0.681291\pi$
$599$	2.32624	−	1.69011i	0.0950475	−	0.0690561i	0.634294	+	0.773092i	$0.281291\pi$
$600$	−11.1803			−0.456435
$601$	−1.35410	−	4.16750i	−0.0552350	−	0.169996i	0.919633	−	0.392778i	$-0.128486\pi$
$601$	−1.35410	−	4.16750i	−0.0552350	−	0.169996i	−0.974868	+	0.222783i	$0.928486\pi$
$602$	−14.3713	−	44.2304i	−0.585731	−	1.80270i
$603$	4.73607	−	3.44095i	0.192868	−	0.140127i
$604$	1.50000	−	4.61653i	0.0610341	−	0.187844i
$605$	−17.7639	+	17.0130i	−0.722207	+	0.691677i
$606$	2.27458	+	7.00042i	0.0923983	+	0.284373i
$607$	0.954915	+	0.693786i	0.0387588	+	0.0281599i	0.606996	−	0.794705i	$-0.292374\pi$
$607$	0.954915	+	0.693786i	0.0387588	+	0.0281599i	−0.568237	+	0.822865i	$0.692374\pi$
$608$	44.3951			1.80046
$609$	5.73607	−	17.6538i	0.232437	−	0.715368i
$610$	26.6312			1.07827
$611$	−15.0000	+	46.1653i	−0.606835	+	1.86765i
$612$	5.78115	−	17.7926i	0.233689	−	0.719222i
$613$	−11.4894	+	8.34751i	−0.464051	+	0.337153i	−0.795118	−	0.606454i	$-0.792591\pi$
$613$	−11.4894	+	8.34751i	−0.464051	+	0.337153i	0.331067	+	0.943607i	$0.392591\pi$
$614$	−3.54102			−0.142904
$615$	1.21885	+	3.75123i	0.0491487	+	0.151264i
$616$	−4.73607	+	18.8294i	−0.190822	+	0.758657i
$617$	2.03851	+	6.27388i	0.0820672	+	0.252577i	0.983668	−	0.179992i	$-0.0576072\pi$
$617$	2.03851	+	6.27388i	0.0820672	+	0.252577i	−0.901601	+	0.432569i	$0.857607\pi$
$618$	−15.7533	−	11.4454i	−0.633690	−	0.460403i
$619$	0.819660			0.0329449			0.0164725	−	0.999864i	$-0.494756\pi$
$619$	0.819660			0.0329449			0.0164725	+	0.999864i	$0.494756\pi$
$620$	50.1246			2.01305
$621$	1.69098	+	5.20431i	0.0678568	+	0.208842i
$622$	19.1074	+	58.8065i	0.766137	+	2.35793i
$623$	−7.54508	−	5.48183i	−0.302287	−	0.219625i
$624$	1.85410	−	5.70634i	0.0742235	−	0.228436i
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	59.0689			2.36087
$627$	8.18034	+	20.3682i	0.326691	+	0.813428i
$628$	−8.07295	+	24.8460i	−0.322146	+	0.991463i
$629$	−5.78115	+	4.20025i	−0.230510	+	0.167475i
$630$	10.5902	+	7.69421i	0.421922	+	0.306545i
$631$	−11.5623	+	8.40051i	−0.460288	+	0.334419i	−0.793644	−	0.608382i	$-0.791819\pi$
$631$	−11.5623	+	8.40051i	−0.460288	+	0.334419i	0.333356	+	0.942801i	$0.391819\pi$
$632$	−23.4164	+	17.0130i	−0.931455	+	0.676741i
$633$	9.47214	+	6.88191i	0.376484	+	0.273531i
$634$	6.90983	−	21.2663i	0.274424	−	0.844591i
$635$	15.9787			0.634096
$636$	−3.00000			−0.118958
$637$	−0.708204	−	0.514540i	−0.0280601	−	0.0203868i
$638$	44.5344	+	27.9564i	1.76314	+	1.10681i
$639$	−6.04508	+	4.39201i	−0.239140	+	0.173745i
$640$	10.8156	+	33.2870i	0.427524	+	1.31578i
$641$	2.42705	−	1.76336i	0.0958628	−	0.0696484i	−0.538821	−	0.842420i	$-0.681130\pi$
$641$	2.42705	−	1.76336i	0.0958628	−	0.0696484i	0.634684	+	0.772772i	$0.281130\pi$
$642$	22.4615	−	16.3192i	0.886484	−	0.644069i
$643$	−6.61803	+	4.80828i	−0.260990	+	0.189620i	−0.710583	−	0.703613i	$-0.751569\pi$
$643$	−6.61803	+	4.80828i	−0.260990	+	0.189620i	0.449594	+	0.893233i	$0.351569\pi$
$644$	−34.7705	−	25.2623i	−1.37015	−	0.995472i
$645$	5.48936	−	16.8945i	0.216143	−	0.665220i
$646$	74.6591	+	54.2430i	2.93742	+	2.13416i
$647$	20.4721	−	14.8739i	0.804843	−	0.584752i	−0.107488	−	0.994206i	$-0.534281\pi$
$647$	20.4721	−	14.8739i	0.804843	−	0.584752i	0.912331	+	0.409454i	$0.134281\pi$
$648$	1.80902	−	1.31433i	0.0710649	−	0.0516317i
$649$	−29.7984	+	24.8990i	−1.16969	+	0.977371i
$650$	−54.2705	−	39.4298i	−2.12866	−	1.54657i
$651$	−15.8262	−	11.4984i	−0.620279	−	0.450659i
$652$	−12.0517	−	37.0912i	−0.471980	−	1.45260i
$653$	8.03444			0.314412			0.157206	−	0.987566i	$-0.449751\pi$
$653$	8.03444			0.314412			0.157206	+	0.987566i	$0.449751\pi$
$654$	−2.96556	−	9.12705i	−0.115962	−	0.356896i
$655$	31.3435	−	22.7724i	1.22469	−	0.889790i
$656$	1.42705	−	1.03681i	0.0557170	−	0.0404808i
$657$	−1.00000	+	3.07768i	−0.0390137	+	0.120072i
$658$	−14.6353	+	45.0427i	−0.570542	+	1.75595i
$659$	−19.5902	−	14.2331i	−0.763125	−	0.554443i	0.136742	−	0.990607i	$-0.456337\pi$
$659$	−19.5902	−	14.2331i	−0.763125	−	0.554443i	−0.899867	+	0.436164i	$0.856337\pi$
$660$	−17.0729	+	14.2658i	−0.664564	+	0.555297i
$661$	−12.9443	+	9.40456i	−0.503474	+	0.365795i	−0.810342	−	0.585957i	$-0.800719\pi$
$661$	−12.9443	+	9.40456i	−0.503474	+	0.365795i	0.306868	+	0.951752i	$0.400719\pi$
$662$	−4.87539	−	15.0049i	−0.189487	−	0.583182i
$663$	30.2705	−	21.9928i	1.17561	−	0.854130i
$664$	−15.4894	−	11.2537i	−0.601104	−	0.436727i
$665$	−31.3435	+	22.7724i	−1.21545	+	0.883074i
$666$	−2.56231			−0.0992873
$667$	−31.3885	+	22.8051i	−1.21537	+	0.883017i
$668$	23.4787	−	72.2601i	0.908419	−	2.79583i
$669$	1.11803	−	3.44095i	0.0432257	−	0.133035i
$670$	−23.6803	+	17.2048i	−0.914851	+	0.664678i
$671$	13.5557	−	11.3269i	0.523313	−	0.437271i
$672$	5.42705	−	16.7027i	0.209353	−	0.644322i
$673$	−25.0902			−0.967155			−0.483577	−	0.875302i	$-0.660663\pi$
$673$	−25.0902			−0.967155			−0.483577	+	0.875302i	$0.660663\pi$
$674$	−8.37790	+	25.7845i	−0.322705	+	0.993183i
$675$	1.54508	+	4.75528i	0.0594703	+	0.183031i
$676$	−55.8222	+	40.5572i	−2.14701	+	1.55989i
$677$	1.54508	−	4.75528i	0.0593824	−	0.182760i	−0.916965	−	0.398967i	$-0.869369\pi$
$677$	1.54508	−	4.75528i	0.0593824	−	0.182760i	0.976348	+	0.216207i	$0.0693686\pi$
$678$	16.7082			0.641675
$679$	−5.35410	−	3.88998i	−0.205472	−	0.149284i
$680$	−9.63525	+	29.6543i	−0.369495	+	1.13719i
$681$	2.87132	+	8.83702i	0.110029	+	0.338635i
$682$	42.5238	−	35.5321i	1.62832	−	1.36060i
$683$	−5.75329	−	17.7068i	−0.220143	−	0.677532i	−0.998748	−	0.0500175i	$-0.984072\pi$
$683$	−5.75329	−	17.7068i	−0.220143	−	0.677532i	0.778605	−	0.627515i	$-0.215928\pi$
$684$	6.13525	+	18.8824i	0.234587	+	0.721986i
$685$	15.0000	+	46.1653i	0.573121	+	1.76388i
$686$	−33.8435	−	24.5887i	−1.29215	−	0.938801i
$687$	17.0000			0.648590
$688$	−7.94427			−0.302873
$689$	−4.85410	−	3.52671i	−0.184927	−	0.134357i
$690$	−8.45492	−	26.0216i	−0.321873	−	0.990624i
$691$	3.88854	+	11.9677i	0.147927	+	0.455273i	0.997376	−	0.0723983i	$-0.0230653\pi$
$691$	3.88854	+	11.9677i	0.147927	+	0.455273i	−0.849449	+	0.527671i	$0.823065\pi$
$692$	18.7918	+	57.8352i	0.714357	+	2.19856i
$693$	8.66312	−	0.587785i	0.329085	−	0.0223281i
$694$	−12.3992	−	38.1608i	−0.470667	−	1.44856i
$695$	3.55573	−	10.9434i	0.134876	−	0.415107i
$696$	12.8262	+	9.31881i	0.486177	+	0.353228i
$697$	11.0000			0.416655
$698$	0.225425	−	0.693786i	0.00853246	−	0.0262602i
$699$	−19.7082	+	14.3188i	−0.745433	+	0.541589i
$700$	−31.7705	−	23.0826i	−1.20081	−	0.872441i
$701$	−5.40983	+	16.6497i	−0.204326	+	0.628852i	0.795414	+	0.606067i	$0.207254\pi$
$701$	−5.40983	+	16.6497i	−0.204326	+	0.628852i	−0.999740	+	0.0227856i	$0.992746\pi$
$702$	13.4164			0.506370
$703$	2.34346	−	7.21242i	0.0883852	−	0.272022i
$704$	36.5172	+	22.9236i	1.37629	+	0.863967i
$705$	−14.6353	+	10.6331i	−0.551196	+	0.400467i
$706$	−10.0623	+	30.9686i	−0.378700	+	1.16552i
$707$	−2.66312	+	8.19624i	−0.100157	+	0.308251i
$708$	−28.4164	+	20.6457i	−1.06795	+	0.775914i
$709$	−18.5279			−0.695829			−0.347914	−	0.937526i	$-0.613110\pi$
$709$	−18.5279			−0.695829			−0.347914	+	0.937526i	$0.613110\pi$
$710$	30.2254	−	21.9601i	1.13434	−	0.824146i
$711$	10.4721	+	7.60845i	0.392736	+	0.285339i
$712$	6.44427	−	4.68204i	0.241509	−	0.175467i
$713$	12.6353	+	38.8873i	0.473194	+	1.45634i
$714$	29.5344	−	21.4580i	1.10530	−	0.803047i
$715$	−44.3951	+	3.01217i	−1.66028	+	0.112649i
$716$	−21.0000	−	15.2574i	−0.784807	−	0.570196i
$717$	−4.04508	+	12.4495i	−0.151066	+	0.464935i
$718$	7.31308	−	22.5074i	0.272922	−	0.839967i
$719$	13.6353	−	9.90659i	0.508509	−	0.369454i	−0.303749	−	0.952752i	$-0.598238\pi$
$719$	13.6353	−	9.90659i	0.508509	−	0.369454i	0.812258	+	0.583299i	$0.198238\pi$
$720$	1.80902	−	1.31433i	0.0674181	−	0.0489821i
$721$	−7.04508	−	21.6825i	−0.262373	−	0.807500i
$722$	−55.4508			−2.06367
$723$	5.51722	+	16.9803i	0.205188	+	0.631503i
$724$	27.6246	+	20.0705i	1.02666	+	0.745913i
$725$	−28.6803	+	20.8375i	−1.06516	+	0.773885i
$726$	−4.37132	+	24.2052i	−0.162235	+	0.898339i
$727$	23.6803	−	17.2048i	0.878255	−	0.638090i	−0.0545341	−	0.998512i	$-0.517367\pi$
$727$	23.6803	−	17.2048i	0.878255	−	0.638090i	0.932789	+	0.360422i	$0.117367\pi$
$728$	−28.4164	+	20.6457i	−1.05318	+	0.765182i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	5.00000	−	15.3884i	0.185058	−	0.569551i
$731$	−40.0795	−	29.1195i	−1.48239	−	1.07702i
$732$	12.9271	−	9.39205i	0.477798	−	0.347140i
$733$	10.8713	−	7.89848i	0.401541	−	0.291737i	−0.368627	−	0.929577i	$-0.620172\pi$
$733$	10.8713	−	7.89848i	0.401541	−	0.291737i	0.770169	+	0.637840i	$0.220172\pi$
$734$	−19.4336	+	14.1194i	−0.717308	+	0.521155i
$735$	−0.100813	−	0.310271i	−0.00371855	−	0.0114445i
$736$	−29.6976	+	21.5765i	−1.09467	+	0.795322i
$737$	−4.73607	+	18.8294i	−0.174455	+	0.693589i
$738$	3.19098	+	2.31838i	0.117462	+	0.0853409i
$739$	27.6525			1.01721			0.508606	−	0.860999i	$-0.330161\pi$
$739$	27.6525			1.01721			0.508606	+	0.860999i	$0.330161\pi$
$740$	7.68692			0.282577
$741$	−12.2705	+	37.7647i	−0.450768	+	1.38732i
$742$	−4.73607	−	3.44095i	−0.173867	−	0.126321i
$743$	−26.4894	+	19.2456i	−0.971800	+	0.706054i	−0.955861	−	0.293819i	$-0.905074\pi$
$743$	−26.4894	+	19.2456i	−0.971800	+	0.706054i	−0.0159391	+	0.999873i	$0.505074\pi$
$744$	13.5172	−	9.82084i	0.495565	−	0.360049i
$745$	1.21885	+	0.885544i	0.0446551	+	0.0324438i
$746$	−7.17376	+	5.21204i	−0.262650	+	0.190826i
$747$	−2.64590	+	8.14324i	−0.0968083	+	0.297945i
$748$	23.1246	+	57.5779i	0.845520	+	2.10526i
$749$	32.5066			1.18776
$750$	−7.72542	−	23.7764i	−0.282093	−	0.868192i
$751$	−6.78115	+	20.8702i	−0.247448	+	0.761566i	0.747776	+	0.663951i	$0.231121\pi$
$751$	−6.78115	+	20.8702i	−0.247448	+	0.761566i	−0.995224	+	0.0976154i	$0.968879\pi$
$752$	6.54508	+	4.75528i	0.238675	+	0.173407i
$753$	−0.0106431	−	0.0327561i	−0.000387857	−	0.00119370i
$754$	29.3951	+	90.4689i	1.07051	+	3.29468i
$755$	3.61803			0.131674
$756$	7.85410			0.285651
$757$	−36.4894	−	26.5111i	−1.32623	−	0.963561i	−0.999832	−	0.0183282i	$-0.994166\pi$
$757$	−36.4894	−	26.5111i	−1.32623	−	0.963561i	−0.326396	−	0.945233i	$-0.605834\pi$
$758$	−18.5557	−	57.1087i	−0.673974	−	2.07428i
$759$	−15.3713	−	9.64932i	−0.557944	−	0.350248i
$760$	−10.2254	−	31.4706i	−0.370915	−	1.14156i
$761$	31.3820			1.13760			0.568798	−	0.822477i	$-0.307409\pi$
$761$	31.3820			1.13760			0.568798	+	0.822477i	$0.307409\pi$
$762$	12.9271	−	9.39205i	0.468298	−	0.340238i
$763$	3.47214	−	10.6861i	0.125700	−	0.386864i
$764$	13.3328	−	41.0342i	0.482364	−	1.48456i
$765$	13.9443			0.504156
$766$	13.8673	−	42.6790i	0.501044	−	1.54206i
$767$	−70.2492			−2.53655
$768$	7.28115	+	5.29007i	0.262736	+	0.190889i
$769$	−4.81966	−	14.8334i	−0.173801	−	0.534906i	0.825775	−	0.563999i	$-0.190738\pi$
$769$	−4.81966	−	14.8334i	−0.173801	−	0.534906i	−0.999577	+	0.0290936i	$0.990738\pi$
$770$	−43.3156	+	2.93893i	−1.56099	+	0.105912i
$771$	5.01722	−	15.4414i	0.180691	−	0.556109i
$772$	8.20820	−	5.96361i	0.295420	−	0.214635i
$773$	12.3885	+	38.1280i	0.445585	+	1.37137i	0.881841	+	0.471547i	$0.156304\pi$
$773$	12.3885	+	38.1280i	0.445585	+	1.37137i	−0.436256	+	0.899823i	$0.643696\pi$
$774$	−5.48936	−	16.8945i	−0.197311	−	0.607260i
$775$	11.5451	+	35.5321i	0.414712	+	1.27635i
$776$	4.57295	−	3.32244i	0.164159	−	0.119269i
$777$	−2.42705	−	1.76336i	−0.0870700	−	0.0632600i
$778$	8.68034	+	6.30664i	0.311205	+	0.226104i
$779$	−9.44427	+	6.86167i	−0.338376	+	0.245845i
$780$	−40.2492			−1.44115
$781$	6.04508	−	24.0337i	0.216310	−	0.859993i
$782$	−76.3050			−2.72866
$783$	2.19098	−	6.74315i	0.0782993	−	0.240981i
$784$	−0.118034	+	0.0857567i	−0.00421550	+	0.00306274i
$785$	−19.4721			−0.694990
$786$	11.9721	−	36.8464i	0.427032	−	1.31427i
$787$	−0.854102			−0.0304454			−0.0152227	−	0.999884i	$-0.504846\pi$
$787$	−0.854102			−0.0304454			−0.0152227	+	0.999884i	$0.504846\pi$
$788$	−6.05166	+	18.6251i	−0.215582	+	0.663492i
$789$	−7.14590	−	21.9928i	−0.254401	−	0.782965i
$790$	−52.3607	−	38.0423i	−1.86291	−	1.35348i
$791$	15.8262	+	11.4984i	0.562716	+	0.408837i
$792$	−1.80902	+	7.19218i	−0.0642806	+	0.255563i
$793$	31.9574			1.13484
$794$	−14.7746	+	45.4715i	−0.524330	+	1.61372i
$795$	−0.690983	−	2.12663i	−0.0245066	−	0.0754237i
$796$	−41.3951			−1.46721
$797$	5.65248	+	17.3965i	0.200221	+	0.616217i	0.999876	+	0.0157569i	$0.00501578\pi$
$797$	5.65248	+	17.3965i	0.200221	+	0.616217i	−0.799655	+	0.600460i	$0.794984\pi$
$798$	−11.9721	+	36.8464i	−0.423809	+	1.30435i
$799$	15.5902	+	47.9816i	0.551541	+	1.69747i
$800$	−27.1353	+	19.7149i	−0.959376	+	0.697028i
$801$	−2.88197	−	2.09387i	−0.101829	−	0.0739833i
$802$	−29.6976	+	21.5765i	−1.04866	+	0.761894i
$803$	−4.00000	−	9.95959i	−0.141157	−	0.351466i
$804$	−5.42705	+	16.7027i	−0.191397	+	0.589060i
$805$	9.89919	−	30.4666i	0.348900	−	1.07381i
$806$	100.249			3.53113
$807$	−5.45492	−	16.7885i	−0.192022	−	0.590983i
$808$	−5.95492	−	4.32650i	−0.209493	−	0.152206i
$809$	25.2918			0.889212			0.444606	−	0.895726i	$-0.353344\pi$
$809$	25.2918			0.889212			0.444606	+	0.895726i	$0.353344\pi$
$810$	4.04508	+	2.93893i	0.142130	+	0.103263i
$811$	8.69098	+	26.7481i	0.305182	+	0.939253i	0.979609	+	0.200912i	$0.0643904\pi$
$811$	8.69098	+	26.7481i	0.305182	+	0.939253i	−0.674428	+	0.738341i	$0.735610\pi$
$812$	17.2082	+	52.9614i	0.603890	+	1.85858i
$813$	−3.07295	−	2.23263i	−0.107773	−	0.0783017i
$814$	6.52129	−	5.44907i	0.228571	−	0.190990i
$815$	23.5172	−	17.0863i	0.823772	−	0.598506i
$816$	−1.92705	−	5.93085i	−0.0674603	−	0.207621i
$817$	52.5755			1.83938
$818$	1.34346	+	4.13474i	0.0469729	+	0.144568i
$819$	12.7082	+	9.23305i	0.444061	+	0.322629i
$820$	−9.57295	−	6.95515i	−0.334302	−	0.242885i
$821$	26.3050			0.918049			0.459025	−	0.888424i	$-0.348199\pi$
$821$	26.3050			0.918049			0.459025	+	0.888424i	$0.348199\pi$
$822$	39.2705	+	28.5317i	1.36972	+	0.995157i
$823$	47.9443			1.67123			0.835616	−	0.549314i	$-0.185111\pi$
$823$	47.9443			1.67123			0.835616	+	0.549314i	$0.185111\pi$
$824$	19.4721			0.678344
$825$	−14.0451	−	8.81678i	−0.488987	−	0.306961i
$826$	−68.5410			−2.38485
$827$	15.9443			0.554437			0.277218	−	0.960807i	$-0.410587\pi$
$827$	15.9443			0.554437			0.277218	+	0.960807i	$0.410587\pi$
$828$	−13.2812	−	9.64932i	−0.461552	−	0.335337i
$829$	27.2918			0.947883			0.473942	−	0.880556i	$-0.342831\pi$
$829$	27.2918			0.947883			0.473942	+	0.880556i	$0.342831\pi$
$830$	13.2295	−	40.7162i	0.459202	−	1.41328i
$831$	−16.6803	−	12.1190i	−0.578635	−	0.420403i
$832$	24.1033	+	74.1824i	0.835632	+	2.57181i
$833$	−0.909830			−0.0315237
$834$	−3.55573	−	10.9434i	−0.123125	−	0.378939i
$835$	56.6312			1.95980
$836$	−55.7705	−	35.0098i	−1.92886	−	1.21084i
$837$	−6.04508	−	4.39201i	−0.208949	−	0.151810i
$838$	15.7771	+	48.5569i	0.545010	+	1.67737i
$839$	−5.62868	−	17.3233i	−0.194324	−	0.598066i	−0.999984	−	0.00568847i	$-0.998189\pi$
$839$	−5.62868	−	17.3233i	−0.194324	−	0.598066i	0.805660	−	0.592378i	$-0.201811\pi$
$840$	−13.0902			−0.451654
$841$	21.2705			0.733466
$842$	46.9959	+	34.1445i	1.61959	+	1.17670i
$843$	4.39919	+	13.5393i	0.151516	+	0.466318i
$844$	−35.1246			−1.20904
$845$	−41.6074	−	30.2295i	−1.43134	−	1.03993i
$846$	−5.59017	+	17.2048i	−0.192194	+	0.591512i
$847$	−20.7984	+	19.9192i	−0.714641	+	0.684431i
$848$	−0.809017	+	0.587785i	−0.0277818	+	0.0201846i
$849$	15.2812	+	11.1024i	0.524448	+	0.381034i
$850$	−69.7214			−2.39142
$851$	1.93769	+	5.96361i	0.0664233	+	0.204430i
$852$	6.92705	−	21.3193i	0.237317	−	0.730386i
$853$	−7.09017	−	21.8213i	−0.242763	−	0.747147i	−0.995996	−	0.0893939i	$-0.971507\pi$
$853$	−7.09017	−	21.8213i	−0.242763	−	0.747147i	0.753234	−	0.657753i	$-0.228493\pi$
$854$	31.1803			1.06697
$855$	−11.9721	+	8.69827i	−0.409438	+	0.297474i
$856$	−8.57953	+	26.4051i	−0.293242	+	0.902507i
$857$	−0.729490			−0.0249189			−0.0124595	−	0.999922i	$-0.503966\pi$
$857$	−0.729490			−0.0249189			−0.0124595	+	0.999922i	$0.503966\pi$
$858$	−34.1459	+	28.5317i	−1.16572	+	0.974056i
$859$	2.28115	+	1.65735i	0.0778319	+	0.0565482i	0.626021	−	0.779806i	$-0.284682\pi$
$859$	2.28115	+	1.65735i	0.0778319	+	0.0565482i	−0.548189	+	0.836355i	$0.684682\pi$
$860$	16.4681	+	50.6835i	0.561557	+	1.72829i
$861$	1.42705	+	4.39201i	0.0486338	+	0.149679i
$862$	−3.45492	+	10.6331i	−0.117675	+	0.362166i
$863$	−7.20163			−0.245146			−0.122573	−	0.992459i	$-0.539115\pi$
$863$	−7.20163			−0.245146			−0.122573	+	0.992459i	$0.539115\pi$
$864$	2.07295	−	6.37988i	0.0705232	−	0.217048i
$865$	−36.6697	+	26.6421i	−1.24681	+	0.905858i
$866$	45.1246	−	32.7849i	1.53340	−	1.11408i
$867$	6.76393	−	20.8172i	0.229715	−	0.706991i
$868$	58.6869			1.99196
$869$	−42.8328	+	2.90617i	−1.45300	+	0.0985851i
$870$	−10.9549	+	33.7158i	−0.371406	+	1.14307i
$871$	−28.4164	+	20.6457i	−0.962853	+	0.699554i
$872$	7.76393	+	5.64083i	0.262920	+	0.191022i
$873$	−2.04508	−	1.48584i	−0.0692156	−	0.0502881i
$874$	65.5132	−	47.5981i	2.21602	−	1.61003i
$875$	9.04508	−	27.8379i	0.305780	−	0.941093i
$876$	−3.00000	−	9.23305i	−0.101361	−	0.311956i
$877$	−3.15654	−	9.71483i	−0.106589	−	0.328047i	0.883511	−	0.468410i	$-0.155173\pi$
$877$	−3.15654	−	9.71483i	−0.106589	−	0.328047i	−0.990100	+	0.140363i	$0.955173\pi$
$878$	−8.68034	+	6.30664i	−0.292947	+	0.212839i
$879$	−9.03444	+	27.8052i	−0.304724	+	0.937845i
$880$	−1.80902	+	7.19218i	−0.0609820	+	0.242448i
$881$	0.263932	+	0.812299i	0.00889210	+	0.0273671i	0.955404	−	0.295301i	$-0.0954201\pi$
$881$	0.263932	+	0.812299i	0.00889210	+	0.0273671i	−0.946512	+	0.322669i	$0.895420\pi$
$882$	−0.263932	−	0.191758i	−0.00888705	−	0.00645682i
$883$	14.8328			0.499164			0.249582	−	0.968354i	$-0.419707\pi$
$883$	14.8328			0.499164			0.249582	+	0.968354i	$0.419707\pi$
$884$	−34.6869	+	106.755i	−1.16665	+	3.59057i
$885$	−21.1803	−	15.3884i	−0.711969	−	0.517276i
$886$	26.5451	−	81.6974i	0.891800	−	2.74468i
$887$	15.6697	−	48.2264i	0.526137	−	1.61928i	−0.235920	−	0.971773i	$-0.575810\pi$
$887$	15.6697	−	48.2264i	0.526137	−	1.61928i	0.762057	−	0.647510i	$-0.224190\pi$
$888$	2.07295	−	1.50609i	0.0695636	−	0.0505409i
$889$	18.7082			0.627453
$890$	14.4098	+	10.4694i	0.483019	+	0.350934i
$891$	3.30902	−	0.224514i	0.110856	−	0.00752150i
$892$	3.35410	+	10.3229i	0.112304	+	0.345635i
$893$	−43.3156	−	31.4706i	−1.44950	−	1.05312i
$894$	1.50658			0.0503875
$895$	5.97871	−	18.4006i	0.199846	−	0.615064i
$896$	12.6631	+	38.9731i	0.423045	+	1.30200i
$897$	−10.1459	−	31.2259i	−0.338762	−	1.04260i
$898$	21.8713	+	15.8904i	0.729855	+	0.530271i
$899$	16.3713	−	50.3858i	0.546014	−	1.68046i
$900$	−12.1353	−	8.81678i	−0.404508	−	0.293893i
$901$	−6.23607			−0.207754
$902$	−13.0517	+	0.885544i	−0.434573	+	0.0294854i
$903$	6.42705	−	19.7804i	0.213879	−	0.658251i
$904$	−13.5172	+	9.82084i	−0.449576	+	0.326636i
$905$	−7.86475	+	24.2052i	−0.261433	+	0.804608i
$906$	2.92705	−	2.12663i	0.0972448	−	0.0706525i
$907$	33.2533	−	24.1599i	1.10416	−	0.802217i	0.122424	−	0.992478i	$-0.460933\pi$
$907$	33.2533	−	24.1599i	1.10416	−	0.802217i	0.981734	+	0.190261i	$0.0609333\pi$
$908$	−22.5517	−	16.3847i	−0.748403	−	0.543747i
$909$	−1.01722	+	3.13068i	−0.0337391	+	0.103838i
$910$	−63.5410	−	46.1653i	−2.10636	−	1.53036i
$911$	−39.0689			−1.29441			−0.647205	−	0.762316i	$-0.724062\pi$
$911$	−39.0689			−1.29441			−0.647205	+	0.762316i	$0.724062\pi$
$912$	5.35410	+	3.88998i	0.177292	+	0.128810i
$913$	−10.5836	−	26.3521i	−0.350266	−	0.872126i
$914$	17.7639	−	12.9063i	0.587579	−	0.426901i
$915$	9.63525	+	7.00042i	0.318532	+	0.231427i
$916$	−41.2599	+	29.9770i	−1.36326	+	0.990470i
$917$	36.6976	−	26.6623i	1.21186	−	0.880468i
$918$	11.2812	−	8.19624i	0.372334	−	0.270516i
$919$	11.0451	+	8.02472i	0.364344	+	0.264711i	0.754862	−	0.655884i	$-0.227704\pi$
$919$	11.0451	+	8.02472i	0.364344	+	0.264711i	−0.390518	+	0.920595i	$0.627704\pi$
$920$	22.1353	+	16.0822i	0.729778	+	0.530215i
$921$	−1.28115	−	0.930812i	−0.0422154	−	0.0306713i
$922$	57.8500	−	42.0305i	1.90519	−	1.38420i
$923$	36.2705	−	26.3521i	1.19386	−	0.867389i
$924$	−19.9894	+	16.7027i	−0.657602	+	0.549480i
$925$	1.77051	+	5.44907i	0.0582140	+	0.179164i
$926$	−61.7320	−	44.8509i	−2.02864	−	1.47389i
$927$	−2.69098	−	8.28199i	−0.0883835	−	0.272016i
$928$	47.5623			1.56131
$929$	−8.59675	−	26.4581i	−0.282050	−	0.868061i	−0.987267	−	0.159070i	$-0.949151\pi$
$929$	−8.59675	−	26.4581i	−0.282050	−	0.868061i	0.705217	−	0.708991i	$-0.250849\pi$
$930$	30.2254	+	21.9601i	0.991131	+	0.720099i
$931$	0.781153	−	0.567541i	0.0256013	−	0.0186004i
$932$	22.5836	−	69.5051i	0.739750	−	2.27672i
$933$	−8.54508	+	26.2991i	−0.279754	+	0.860993i
$934$	−28.1525	−	20.4540i	−0.921177	−	0.669274i
$935$	−35.4894	+	29.6543i	−1.16063	+	0.969798i
$936$	−10.8541	+	7.88597i	−0.354777	+	0.257761i
$937$	−11.5729	−	35.6179i	−0.378072	−	1.16359i	−0.941383	−	0.337340i	$-0.890473\pi$
$937$	−11.5729	−	35.6179i	−0.378072	−	1.16359i	0.563311	−	0.826245i	$-0.309527\pi$
$938$	−27.7254	+	20.1437i	−0.905267	+	0.657715i
$939$	21.3713	+	15.5272i	0.697427	+	0.506710i
$940$	16.7705	−	51.6143i	0.546994	−	1.68347i
$941$	−1.76393			−0.0575025			−0.0287513	−	0.999587i	$-0.509153\pi$
$941$	−1.76393			−0.0575025			−0.0287513	+	0.999587i	$0.509153\pi$
$942$	−15.7533	+	11.4454i	−0.513270	+	0.372912i
$943$	2.98278	−	9.18005i	0.0971327	−	0.298944i
$944$	−3.61803	+	11.1352i	−0.117757	+	0.362419i
$945$	1.80902	+	5.56758i	0.0588473	+	0.181113i
$946$	49.8992	+	31.3241i	1.62236	+	1.01844i
$947$	−11.9549	+	36.7934i	−0.388483	+	1.19563i	0.545440	+	0.838150i	$0.316363\pi$
$947$	−11.9549	+	36.7934i	−0.388483	+	1.19563i	−0.933922	+	0.357476i	$0.883637\pi$
$948$	−38.8328			−1.26123
$949$	6.00000	−	18.4661i	0.194768	−	0.599435i
$950$	59.8607	−	43.4913i	1.94214	−	1.41105i
$951$	8.09017	−	5.87785i	0.262342	−	0.190602i
$952$	−11.2812	+	34.7198i	−0.365624	+	1.12528i
$953$	−17.2705			−0.559447			−0.279723	−	0.960081i	$-0.590243\pi$
$953$	−17.2705			−0.559447			−0.279723	+	0.960081i	$0.590243\pi$
$954$	−1.80902	−	1.31433i	−0.0585691	−	0.0425529i
$955$	32.1591			1.04064
$956$	−12.1353	−	37.3485i	−0.392482	−	1.20794i
$957$	8.76393	+	21.8213i	0.283298	+	0.705382i
$958$	−9.75987	−	30.0378i	−0.315327	−	0.970477i
$959$	17.5623	+	54.0512i	0.567116	+	1.74540i
$960$	−8.98278	+	27.6462i	−0.289918	+	0.892276i
$961$	−20.0902	−	14.5964i	−0.648070	−	0.470850i
$962$	15.3738			0.495672
$963$	12.4164			0.400113
$964$	−43.3328	−	31.4831i	−1.39566	−	1.01400i
$965$	6.11803	+	4.44501i	0.196946	+	0.143090i
$966$	−9.89919	−	30.4666i	−0.318501	−	0.980246i
$967$	−9.92705	−	30.5523i	−0.319232	−	0.982496i	−0.973977	−	0.226646i	$-0.927224\pi$
$967$	−9.92705	−	30.5523i	−0.319232	−	0.982496i	0.654745	−	0.755850i	$-0.272776\pi$
$968$	−10.6910	−	22.1518i	−0.343621	−	0.711986i
$969$	12.7533	+	39.2506i	0.409695	+	1.26091i
$970$	10.2254	+	7.42921i	0.328319	+	0.238537i
$971$	−3.33688	−	2.42439i	−0.107086	−	0.0778022i	0.532954	−	0.846144i	$-0.321082\pi$
$971$	−3.33688	−	2.42439i	−0.107086	−	0.0778022i	−0.640039	+	0.768342i	$0.721082\pi$
$972$	3.00000			0.0962250
$973$	4.16312	−	12.8128i	0.133463	−	0.410758i
$974$	27.2984	−	19.8334i	0.874696	−	0.635504i
$975$	−9.27051	−	28.5317i	−0.296894	−	0.913746i
$976$	1.64590	−	5.06555i	0.0526839	−	0.162144i
$977$	−1.34752			−0.0431111			−0.0215556	−	0.999768i	$-0.506862\pi$
$977$	−1.34752			−0.0431111			−0.0215556	+	0.999768i	$0.506862\pi$
$978$	8.98278	−	27.6462i	0.287238	−	0.884026i
$979$	11.7877	−	0.799788i	0.376738	−	0.0255613i
$980$	0.791796	+	0.575274i	0.0252930	+	0.0183764i
$981$	1.32624	−	4.08174i	0.0423435	−	0.130320i
$982$	17.6484	−	54.3162i	0.563183	−	1.73330i
$983$	7.23607	−	5.25731i	0.230795	−	0.167682i	−0.466378	−	0.884586i	$-0.654441\pi$
$983$	7.23607	−	5.25731i	0.230795	−	0.167682i	0.697172	+	0.716904i	$0.254441\pi$
$984$	−3.94427			−0.125739
$985$	−14.5967			−0.465091
$986$	79.9853	+	58.1127i	2.54725	+	1.85069i
$987$	−17.1353	+	12.4495i	−0.545421	+	0.396272i
$988$	−36.8115	−	113.294i	−1.17113	−	3.60437i
$989$	−35.1697	+	25.5523i	−1.11833	+	0.812515i
$990$	−16.5451	+	1.12257i	−0.525837	+	0.0356776i
$991$	36.9336	+	26.8339i	1.17324	+	0.852405i	0.991393	−	0.130922i	$-0.0417938\pi$
$991$	36.9336	+	26.8339i	1.17324	+	0.852405i	0.181843	+	0.983328i	$0.441794\pi$
$992$	15.4894	−	47.6713i	0.491788	−	1.51357i
$993$	2.18034	−	6.71040i	0.0691910	−	0.212948i
$994$	35.3885	−	25.7113i	1.12246	−	0.815512i
$995$	−9.53444	−	29.3440i	−0.302262	−	0.930267i
$996$	−7.93769	−	24.4297i	−0.251515	−	0.774085i
$997$	28.6180			0.906342			0.453171	−	0.891424i	$-0.350293\pi$
$997$	28.6180			0.906342			0.453171	+	0.891424i	$0.350293\pi$
$998$	6.34346	+	19.5232i	0.200799	+	0.617995i
$999$	−0.927051	−	0.673542i	−0.0293306	−	0.0213099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.r.a.136.1	yes	4
11.3	even	5		825.2.p.a.586.1	yes	4
25.16	even	5		825.2.p.a.466.1	✓	4
275.91	even	5	inner	825.2.r.a.91.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.p.a.466.1	✓	4	25.16	even	5
825.2.p.a.586.1	yes	4	11.3	even	5
825.2.r.a.91.1	yes	4	275.91	even	5	inner
825.2.r.a.136.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +(-0.809017 - 0.587785i) q^{3} +3.00000 q^{4} +(0.690983 + 2.12663i) q^{5} +(1.80902 + 1.31433i) q^{6} +(0.809017 + 2.48990i) q^{7} -2.23607 q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} +(-0.809017 - 0.587785i) q^{3} +3.00000 q^{4} +(0.690983 + 2.12663i) q^{5} +(1.80902 + 1.31433i) q^{6} +(0.809017 + 2.48990i) q^{7} -2.23607 q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.54508 - 4.75528i) q^{10} +(-2.80902 - 1.76336i) q^{11} +(-2.42705 - 1.76336i) q^{12} +(-1.85410 - 5.70634i) q^{13} +(-1.80902 - 5.56758i) q^{14} +(0.690983 - 2.12663i) q^{15} -1.00000 q^{16} +(-5.04508 - 3.66547i) q^{17} +(-0.690983 - 2.12663i) q^{18} +6.61803 q^{19} +(2.07295 + 6.37988i) q^{20} +(0.809017 - 2.48990i) q^{21} +(6.28115 + 3.94298i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 + 1.31433i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(4.14590 + 12.7598i) q^{26} +(0.309017 - 0.951057i) q^{27} +(2.42705 + 7.46969i) q^{28} +7.09017 q^{29} +(-1.54508 + 4.75528i) q^{30} +(2.30902 - 7.10642i) q^{31} +6.70820 q^{32} +(1.23607 + 3.07768i) q^{33} +(11.2812 + 8.19624i) q^{34} +(-4.73607 + 3.44095i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.354102 - 1.08981i) q^{37} -14.7984 q^{38} +(-1.85410 + 5.70634i) q^{39} +(-1.54508 - 4.75528i) q^{40} +(-1.42705 + 1.03681i) q^{41} +(-1.80902 + 5.56758i) q^{42} +7.94427 q^{43} +(-8.42705 - 5.29007i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(9.89919 - 7.19218i) q^{46} +(-6.54508 - 4.75528i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(9.04508 - 6.57164i) q^{50} +(1.92705 + 5.93085i) q^{51} +(-5.56231 - 17.1190i) q^{52} +(0.809017 - 0.587785i) q^{53} +(-0.690983 + 2.12663i) q^{54} +(1.80902 - 7.19218i) q^{55} +(-1.80902 - 5.56758i) q^{56} +(-5.35410 - 3.88998i) q^{57} -15.8541 q^{58} +(3.61803 - 11.1352i) q^{59} +(2.07295 - 6.37988i) q^{60} +(-1.64590 + 5.06555i) q^{61} +(-5.16312 + 15.8904i) q^{62} +(-2.11803 + 1.53884i) q^{63} -13.0000 q^{64} +(10.8541 - 7.88597i) q^{65} +(-2.76393 - 6.88191i) q^{66} +(-1.80902 - 5.56758i) q^{67} +(-15.1353 - 10.9964i) q^{68} +5.47214 q^{69} +(10.5902 - 7.69421i) q^{70} +(2.30902 + 7.10642i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(2.61803 + 1.90211i) q^{73} +(-0.791796 + 2.43690i) q^{74} +5.00000 q^{75} +19.8541 q^{76} +(2.11803 - 8.42075i) q^{77} +(4.14590 - 12.7598i) q^{78} +(10.4721 - 7.60845i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(3.19098 - 2.31838i) q^{82} +(6.92705 + 5.03280i) q^{83} +(2.42705 - 7.46969i) q^{84} +(4.30902 - 13.2618i) q^{85} -17.7639 q^{86} +(-5.73607 - 4.16750i) q^{87} +(6.28115 + 3.94298i) q^{88} +(-2.88197 + 2.09387i) q^{89} +(4.04508 - 2.93893i) q^{90} +(12.7082 - 9.23305i) q^{91} +(-13.2812 + 9.64932i) q^{92} +(-6.04508 + 4.39201i) q^{93} +(14.6353 + 10.6331i) q^{94} +(4.57295 + 14.0741i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(-2.04508 + 1.48584i) q^{97} +(-0.263932 + 0.191758i) q^{98} +(0.809017 - 3.21644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9} + 5 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} - 5 q^{14} + 5 q^{15} - 4 q^{16} - 9 q^{17} - 5 q^{18} + 22 q^{19} + 15 q^{20} + q^{21} + 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} - q^{27} + 3 q^{28} + 6 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{33} + 25 q^{34} - 10 q^{35} - 3 q^{36} - 12 q^{37} - 10 q^{38} + 6 q^{39} + 5 q^{40} + q^{41} - 5 q^{42} - 4 q^{43} - 27 q^{44} - 5 q^{45} + 15 q^{46} - 15 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} + 5 q^{55} - 5 q^{56} - 8 q^{57} - 50 q^{58} + 10 q^{59} + 15 q^{60} - 20 q^{61} - 5 q^{62} - 4 q^{63} - 52 q^{64} + 30 q^{65} - 20 q^{66} - 5 q^{67} - 27 q^{68} + 4 q^{69} + 20 q^{70} + 7 q^{71} - 5 q^{72} + 6 q^{73} - 30 q^{74} + 20 q^{75} + 66 q^{76} + 4 q^{77} + 30 q^{78} + 24 q^{79} - 5 q^{80} - q^{81} + 15 q^{82} + 21 q^{83} + 3 q^{84} + 15 q^{85} - 80 q^{86} - 14 q^{87} + 5 q^{88} - 16 q^{89} + 5 q^{90} + 24 q^{91} - 33 q^{92} - 13 q^{93} + 25 q^{94} + 25 q^{95} - 15 q^{96} + 3 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9 + 5 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 - 5 * q^14 + 5 * q^15 - 4 * q^16 - 9 * q^17 - 5 * q^18 + 22 * q^19 + 15 * q^20 + q^21 + 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 - q^27 + 3 * q^28 + 6 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^33 + 25 * q^34 - 10 * q^35 - 3 * q^36 - 12 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 + q^41 - 5 * q^42 - 4 * q^43 - 27 * q^44 - 5 * q^45 + 15 * q^46 - 15 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 + 5 * q^55 - 5 * q^56 - 8 * q^57 - 50 * q^58 + 10 * q^59 + 15 * q^60 - 20 * q^61 - 5 * q^62 - 4 * q^63 - 52 * q^64 + 30 * q^65 - 20 * q^66 - 5 * q^67 - 27 * q^68 + 4 * q^69 + 20 * q^70 + 7 * q^71 - 5 * q^72 + 6 * q^73 - 30 * q^74 + 20 * q^75 + 66 * q^76 + 4 * q^77 + 30 * q^78 + 24 * q^79 - 5 * q^80 - q^81 + 15 * q^82 + 21 * q^83 + 3 * q^84 + 15 * q^85 - 80 * q^86 - 14 * q^87 + 5 * q^88 - 16 * q^89 + 5 * q^90 + 24 * q^91 - 33 * q^92 - 13 * q^93 + 25 * q^94 + 25 * q^95 - 15 * q^96 + 3 * q^97 - 10 * q^98 + q^99

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