LMFDB - Embedded newform 124.2.j.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(15,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("124.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.j (of order $10$, 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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	124.27
Dual form			124.2.j.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642040 + 1.26007i) q^{2} +(0.224514 - 0.690983i) q^{3} +(-1.17557 - 1.61803i) q^{4} +0.618034 q^{5} +(0.726543 + 0.726543i) q^{6} +(2.48990 + 3.42705i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.00000 + 1.45309i) q^{9} +O(q^{10})$	\(q+(-0.642040 + 1.26007i) q^{2} +(0.224514 - 0.690983i) q^{3} +(-1.17557 - 1.61803i) q^{4} +0.618034 q^{5} +(0.726543 + 0.726543i) q^{6} +(2.48990 + 3.42705i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.00000 + 1.45309i) q^{9} +(-0.396802 + 0.778768i) q^{10} +(1.17557 - 0.854102i) q^{11} +(-1.38197 + 0.449028i) q^{12} +(-4.73607 - 1.53884i) q^{13} +(-5.91695 + 0.937153i) q^{14} +(0.138757 - 0.427051i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(4.04508 - 5.56758i) q^{17} +(-3.11507 + 1.58721i) q^{18} +(-4.75528 + 1.54508i) q^{19} +(-0.726543 - 1.00000i) q^{20} +(2.92705 - 0.951057i) q^{21} +(0.321469 + 2.02967i) q^{22} +(2.48990 + 1.80902i) q^{23} +(0.321469 - 2.02967i) q^{24} -4.61803 q^{25} +(4.97980 - 4.97980i) q^{26} +(3.21644 - 2.33688i) q^{27} +(2.61803 - 8.05748i) q^{28} +(-3.19098 + 1.03681i) q^{29} +(0.449028 + 0.449028i) q^{30} +(-2.85317 - 4.78115i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.326238 - 1.00406i) q^{33} +(4.41846 + 8.67171i) q^{34} +(1.53884 + 2.11803i) q^{35} -4.94427i q^{36} +2.17963i q^{37} +(1.10616 - 6.98401i) q^{38} +(-2.12663 + 2.92705i) q^{39} +(1.72654 - 0.273457i) q^{40} +(-0.236068 - 0.726543i) q^{41} +(-0.680881 + 4.29892i) q^{42} +(-1.31433 - 4.04508i) q^{43} +(-2.76393 - 0.898056i) q^{44} +(1.23607 + 0.898056i) q^{45} +(-3.87811 + 1.97599i) q^{46} +(-3.21644 - 1.04508i) q^{47} +(2.35114 + 1.70820i) q^{48} +(-3.38197 + 10.4086i) q^{49} +(2.96496 - 5.81906i) q^{50} +(-2.93893 - 4.04508i) q^{51} +(3.07768 + 9.47214i) q^{52} +(1.28115 - 1.76336i) q^{53} +(0.879560 + 5.55332i) q^{54} +(0.726543 - 0.527864i) q^{55} +(8.47214 + 8.47214i) q^{56} +3.63271i q^{57} +(0.742276 - 4.68655i) q^{58} +(-3.30220 - 1.07295i) q^{59} +(-0.854102 + 0.277515i) q^{60} +9.95959i q^{61} +(7.85645 - 0.525514i) q^{62} +10.4721i q^{63} +(7.60845 - 2.47214i) q^{64} +(-2.92705 - 0.951057i) q^{65} +(1.47464 + 0.233561i) q^{66} -10.2361i q^{67} -13.7638 q^{68} +(1.80902 - 1.31433i) q^{69} +(-3.65688 + 0.579192i) q^{70} +(-2.57565 + 3.54508i) q^{71} +(6.23015 + 3.17442i) q^{72} +(-0.690983 - 0.951057i) q^{73} +(-2.74649 - 1.39941i) q^{74} +(-1.03681 + 3.19098i) q^{75} +(8.09017 + 5.87785i) q^{76} +(5.85410 + 1.90211i) q^{77} +(-2.32292 - 4.55899i) q^{78} +(11.8617 + 8.61803i) q^{79} +(-0.763932 + 2.35114i) q^{80} +(1.39919 + 4.30625i) q^{81} +(1.06706 + 0.169006i) q^{82} +(-1.98787 - 6.11803i) q^{83} +(-4.97980 - 3.61803i) q^{84} +(2.50000 - 3.44095i) q^{85} +(5.94095 + 0.940955i) q^{86} +2.43769i q^{87} +(2.90617 - 2.90617i) q^{88} +(-10.1631 - 13.9883i) q^{89} +(-1.92522 + 0.980949i) q^{90} +(-6.51864 - 20.0623i) q^{91} -6.15537i q^{92} +(-3.94427 + 0.898056i) q^{93} +(3.38197 - 3.38197i) q^{94} +(-2.93893 + 0.954915i) q^{95} +(-3.66199 + 1.86588i) q^{96} +(6.04508 - 4.39201i) q^{97} +(-10.9443 - 10.9443i) q^{98} +3.59222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9	$ 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9 + 6 * q^10 - 20 * q^12 - 20 * q^13 - 14 * q^14 + 8 * q^16 + 10 * q^17 - 24 * q^18 + 10 * q^21 + 20 * q^22 + 20 * q^24 - 28 * q^25 + 12 * q^28 - 30 * q^29 - 32 * q^32 + 60 * q^33 + 30 * q^34 + 10 * q^38 + 8 * q^40 + 16 * q^41 + 10 * q^42 - 40 * q^44 - 8 * q^45 - 10 * q^46 - 36 * q^49 + 2 * q^50 - 30 * q^53 - 50 * q^54 + 32 * q^56 + 20 * q^58 + 20 * q^60 + 38 * q^62 - 10 * q^65 - 20 * q^66 + 10 * q^69 - 8 * q^70 + 48 * q^72 - 10 * q^73 - 30 * q^74 + 20 * q^76 + 20 * q^77 - 24 * q^80 - 38 * q^81 - 4 * q^82 + 20 * q^85 + 20 * q^86 - 50 * q^89 + 32 * q^90 + 40 * q^93 + 36 * q^94 - 40 * q^96 + 26 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.642040	+	1.26007i	−0.453990	+	0.891007i
$2$	−0.642040	+	1.26007i	−0.453990	+	0.891007i
$3$	0.224514	−	0.690983i	0.129623	−	0.398939i	−0.865092	−	0.501614i	$-0.832740\pi$
$3$	0.224514	−	0.690983i	0.129623	−	0.398939i	0.994715	+	0.102674i	$0.0327399\pi$
$4$	−1.17557	−	1.61803i	−0.587785	−	0.809017i
$5$	0.618034			0.276393			0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034			0.276393			0.138197	+	0.990405i	$0.455869\pi$
$6$	0.726543	+	0.726543i	0.296610	+	0.296610i
$7$	2.48990	+	3.42705i	0.941093	+	1.29530i	0.955372	+	0.295405i	$0.0954547\pi$
$7$	2.48990	+	3.42705i	0.941093	+	1.29530i	−0.0142789	+	0.999898i	$0.504545\pi$
$8$	2.79360	−	0.442463i	0.987688	−	0.156434i
$9$	2.00000	+	1.45309i	0.666667	+	0.484362i
$10$	−0.396802	+	0.778768i	−0.125480	+	0.246268i
$11$	1.17557	−	0.854102i	0.354448	−	0.257521i	−0.396285	−	0.918128i	$-0.629701\pi$
$11$	1.17557	−	0.854102i	0.354448	−	0.257521i	0.750733	+	0.660606i	$0.229701\pi$
$12$	−1.38197	+	0.449028i	−0.398939	+	0.129623i
$13$	−4.73607	−	1.53884i	−1.31355	−	0.426798i	−0.433274	−	0.901262i	$-0.642642\pi$
$13$	−4.73607	−	1.53884i	−1.31355	−	0.426798i	−0.880275	+	0.474464i	$0.842642\pi$
$14$	−5.91695	+	0.937153i	−1.58137	+	0.250465i
$15$	0.138757	−	0.427051i	0.0358270	−	0.110264i
$16$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$17$	4.04508	−	5.56758i	0.981077	−	1.35034i	0.0448301	−	0.998995i	$-0.485725\pi$
$17$	4.04508	−	5.56758i	0.981077	−	1.35034i	0.936247	−	0.351342i	$-0.114275\pi$
$18$	−3.11507	+	1.58721i	−0.734230	+	0.374109i
$19$	−4.75528	+	1.54508i	−1.09094	+	0.354467i	−0.798608	−	0.601851i	$-0.794430\pi$
$19$	−4.75528	+	1.54508i	−1.09094	+	0.354467i	−0.292328	+	0.956318i	$0.594430\pi$
$20$	−0.726543	−	1.00000i	−0.162460	−	0.223607i
$21$	2.92705	−	0.951057i	0.638735	−	0.207538i
$22$	0.321469	+	2.02967i	0.0685373	+	0.432728i
$23$	2.48990	+	1.80902i	0.519180	+	0.377206i	0.816295	−	0.577636i	$-0.196025\pi$
$23$	2.48990	+	1.80902i	0.519180	+	0.377206i	−0.297115	+	0.954842i	$0.596025\pi$
$24$	0.321469	−	2.02967i	0.0656195	−	0.414305i
$25$	−4.61803			−0.923607
$26$	4.97980	−	4.97980i	0.976618	−	0.976618i
$27$	3.21644	−	2.33688i	0.619004	−	0.449733i
$28$	2.61803	−	8.05748i	0.494762	−	1.52272i
$29$	−3.19098	+	1.03681i	−0.592551	+	0.192531i	−0.589915	−	0.807465i	$-0.700839\pi$
$29$	−3.19098	+	1.03681i	−0.592551	+	0.192531i	−0.00263539	+	0.999997i	$0.500839\pi$
$30$	0.449028	+	0.449028i	0.0819809	+	0.0819809i
$31$	−2.85317	−	4.78115i	−0.512444	−	0.858720i
$31$	−2.85317	−	4.78115i	−0.512444	−	0.858720i
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−0.326238	−	1.00406i	−0.0567907	−	0.174784i
$34$	4.41846	+	8.67171i	0.757759	+	1.48719i
$35$	1.53884	+	2.11803i	0.260112	+	0.358013i
$36$		−	4.94427i		−	0.824045i
$37$			2.17963i			0.358329i	0.983819	+	0.179164i	$0.0573394\pi$
$37$			2.17963i			0.358329i	−0.983819	+	0.179164i	$0.942661\pi$
$38$	1.10616	−	6.98401i	0.179443	−	1.13296i
$39$	−2.12663	+	2.92705i	−0.340533	+	0.468703i
$40$	1.72654	−	0.273457i	0.272990	−	0.0432374i
$41$	−0.236068	−	0.726543i	−0.0368676	−	0.113467i	0.930929	−	0.365200i	$-0.118999\pi$
$41$	−0.236068	−	0.726543i	−0.0368676	−	0.113467i	−0.967797	+	0.251733i	$0.918999\pi$
$42$	−0.680881	+	4.29892i	−0.105062	+	0.663337i
$43$	−1.31433	−	4.04508i	−0.200433	−	0.616870i	−0.999870	−	0.0161197i	$-0.994869\pi$
$43$	−1.31433	−	4.04508i	−0.200433	−	0.616870i	0.799437	−	0.600750i	$-0.205131\pi$
$44$	−2.76393	−	0.898056i	−0.416678	−	0.135387i
$45$	1.23607	+	0.898056i	0.184262	+	0.133874i
$46$	−3.87811	+	1.97599i	−0.571796	+	0.291344i
$47$	−3.21644	−	1.04508i	−0.469166	−	0.152441i	0.0648863	−	0.997893i	$-0.479332\pi$
$47$	−3.21644	−	1.04508i	−0.469166	−	0.152441i	−0.534052	+	0.845451i	$0.679332\pi$
$48$	2.35114	+	1.70820i	0.339358	+	0.246558i
$49$	−3.38197	+	10.4086i	−0.483138	+	1.48695i
$50$	2.96496	−	5.81906i	0.419309	−	0.822940i
$51$	−2.93893	−	4.04508i	−0.411532	−	0.566425i
$52$	3.07768	+	9.47214i	0.426798	+	1.31355i
$53$	1.28115	−	1.76336i	0.175980	−	0.242216i	−0.711911	−	0.702270i	$-0.752170\pi$
$53$	1.28115	−	1.76336i	0.175980	−	0.242216i	0.887891	+	0.460054i	$0.152170\pi$
$54$	0.879560	+	5.55332i	0.119693	+	0.755711i
$55$	0.726543	−	0.527864i	0.0979670	−	0.0711772i
$56$	8.47214	+	8.47214i	1.13214	+	1.13214i
$57$			3.63271i			0.481165i
$58$	0.742276	−	4.68655i	0.0974657	−	0.615374i
$59$	−3.30220	−	1.07295i	−0.429909	−	0.139686i	0.0860659	−	0.996289i	$-0.472570\pi$
$59$	−3.30220	−	1.07295i	−0.429909	−	0.139686i	−0.515975	+	0.856603i	$0.672570\pi$
$60$	−0.854102	+	0.277515i	−0.110264	+	0.0358270i
$61$			9.95959i			1.27520i	0.770370	+	0.637598i	$0.220072\pi$
$61$			9.95959i			1.27520i	−0.770370	+	0.637598i	$0.779928\pi$
$62$	7.85645	−	0.525514i	0.997770	−	0.0667404i
$63$			10.4721i			1.31937i
$64$	7.60845	−	2.47214i	0.951057	−	0.309017i
$65$	−2.92705	−	0.951057i	−0.363056	−	0.117964i
$66$	1.47464	+	0.233561i	0.181516	+	0.0287493i
$67$		−	10.2361i		−	1.25053i	−0.780411	−	0.625267i	$-0.784990\pi$
$67$		−	10.2361i		−	1.25053i	0.780411	−	0.625267i	$-0.215010\pi$
$68$	−13.7638			−1.66911
$69$	1.80902	−	1.31433i	0.217780	−	0.158226i
$70$	−3.65688	+	0.579192i	−0.437080	+	0.0692267i
$71$	−2.57565	+	3.54508i	−0.305674	+	0.420724i	−0.934026	−	0.357205i	$-0.883730\pi$
$71$	−2.57565	+	3.54508i	−0.305674	+	0.420724i	0.628352	+	0.777929i	$0.283730\pi$
$72$	6.23015	+	3.17442i	0.734230	+	0.374109i
$73$	−0.690983	−	0.951057i	−0.0808734	−	0.111313i	0.766664	−	0.642049i	$-0.221915\pi$
$73$	−0.690983	−	0.951057i	−0.0808734	−	0.111313i	−0.847537	+	0.530736i	$0.821915\pi$
$74$	−2.74649	−	1.39941i	−0.319273	−	0.162678i
$75$	−1.03681	+	3.19098i	−0.119721	+	0.368463i
$76$	8.09017	+	5.87785i	0.928006	+	0.674236i
$77$	5.85410	+	1.90211i	0.667137	+	0.216766i
$78$	−2.32292	−	4.55899i	−0.263019	−	0.516204i
$79$	11.8617	+	8.61803i	1.33455	+	0.969605i	0.999626	+	0.0273582i	$0.00870947\pi$
$79$	11.8617	+	8.61803i	1.33455	+	0.969605i	0.334921	+	0.942246i	$0.391291\pi$
$80$	−0.763932	+	2.35114i	−0.0854102	+	0.262866i
$81$	1.39919	+	4.30625i	0.155465	+	0.478473i
$82$	1.06706	+	0.169006i	0.117837	+	0.0186636i
$83$	−1.98787	−	6.11803i	−0.218197	−	0.671541i	−0.998911	−	0.0466531i	$-0.985144\pi$
$83$	−1.98787	−	6.11803i	−0.218197	−	0.671541i	0.780714	−	0.624888i	$-0.214856\pi$
$84$	−4.97980	−	3.61803i	−0.543340	−	0.394760i
$85$	2.50000	−	3.44095i	0.271163	−	0.373224i
$86$	5.94095	+	0.940955i	0.640630	+	0.101466i
$87$			2.43769i			0.261348i
$88$	2.90617	−	2.90617i	0.309799	−	0.309799i
$89$	−10.1631	−	13.9883i	−1.07729	−	1.48276i	−0.862471	−	0.506106i	$-0.831084\pi$
$89$	−10.1631	−	13.9883i	−1.07729	−	1.48276i	−0.214817	−	0.976654i	$-0.568916\pi$
$90$	−1.92522	+	0.980949i	−0.202936	+	0.103401i
$91$	−6.51864	−	20.0623i	−0.683339	−	2.10310i
$92$		−	6.15537i		−	0.641741i
$93$	−3.94427	+	0.898056i	−0.409002	+	0.0931241i
$94$	3.38197	−	3.38197i	0.348823	−	0.348823i
$95$	−2.93893	+	0.954915i	−0.301527	+	0.0979722i
$96$	−3.66199	+	1.86588i	−0.373750	+	0.190435i
$97$	6.04508	−	4.39201i	0.613785	−	0.445941i	−0.236960	−	0.971519i	$-0.576151\pi$
$97$	6.04508	−	4.39201i	0.613785	−	0.445941i	0.850745	+	0.525578i	$0.176151\pi$
$98$	−10.9443	−	10.9443i	−1.10554	−	1.10554i
$99$	3.59222			0.361032
$100$	5.42882	+	7.47214i	0.542882	+	0.747214i
$101$	7.23607	+	5.25731i	0.720016	+	0.523122i	0.886389	−	0.462941i	$-0.153206\pi$
$101$	7.23607	+	5.25731i	0.720016	+	0.523122i	−0.166374	+	0.986063i	$0.553206\pi$
$102$	6.98401	−	1.10616i	0.691520	−	0.109526i
$103$	−0.865300	+	0.281153i	−0.0852605	+	0.0277028i	−0.351337	−	0.936249i	$-0.614273\pi$
$103$	−0.865300	+	0.281153i	−0.0852605	+	0.0277028i	0.266076	+	0.963952i	$0.414273\pi$
$104$	−13.9116	−	2.20338i	−1.36414	−	0.216059i
$105$	1.80902	−	0.587785i	0.176542	−	0.0573620i
$106$	1.39941	+	2.74649i	0.135922	+	0.266763i
$107$	−8.14324	+	11.2082i	−0.787236	+	1.08354i	0.207210	+	0.978296i	$0.433562\pi$
$107$	−8.14324	+	11.2082i	−0.787236	+	1.08354i	−0.994447	+	0.105242i	$0.966438\pi$
$108$	−7.56231	−	2.45714i	−0.727683	−	0.236439i
$109$	2.21885	−	6.82891i	0.212527	−	0.654091i	−0.786793	−	0.617217i	$-0.788260\pi$
$109$	2.21885	−	6.82891i	0.212527	−	0.654091i	0.999320	−	0.0368738i	$-0.0117400\pi$
$110$	0.198678	+	1.25441i	0.0189433	+	0.119603i
$111$	1.50609	+	0.489357i	0.142951	+	0.0464477i
$112$	−16.1150	+	5.23607i	−1.52272	+	0.494762i
$113$	9.35410	−	6.79615i	0.879960	−	0.639328i	−0.0532810	−	0.998580i	$-0.516968\pi$
$113$	9.35410	−	6.79615i	0.879960	−	0.639328i	0.933241	+	0.359251i	$0.116968\pi$
$114$	−4.57748	−	2.33235i	−0.428721	−	0.218444i
$115$	1.53884	+	1.11803i	0.143498	+	0.104257i
$116$	5.42882	+	3.94427i	0.504054	+	0.366216i
$117$	−7.23607	−	9.95959i	−0.668975	−	0.920765i
$118$	3.47214	−	3.47214i	0.319636	−	0.319636i
$119$	29.1522			2.67238
$120$	0.198678	−	1.25441i	0.0181368	−	0.114511i
$121$	−2.74671	+	8.45351i	−0.249701	+	0.768501i
$122$	−12.5498	−	6.39445i	−1.13621	−	0.578927i
$123$	−0.555029			−0.0500453
$124$	−4.38197	+	10.2371i	−0.393512	+	0.919319i
$125$	−5.94427			−0.531672
$126$	−13.1957	−	6.72353i	−1.17556	−	0.598979i
$127$	−1.22857	+	3.78115i	−0.109018	+	0.335523i	−0.990652	−	0.136410i	$-0.956444\pi$
$127$	−1.22857	+	3.78115i	−0.109018	+	0.335523i	0.881634	+	0.471933i	$0.156444\pi$
$128$	−1.76985	+	11.1744i	−0.156434	+	0.987688i
$129$	−3.09017			−0.272074
$130$	3.07768	−	3.07768i	0.269931	−	0.269931i
$131$	11.0822	+	15.2533i	0.968253	+	1.33269i	0.942924	+	0.333007i	$0.108063\pi$
$131$	11.0822	+	15.2533i	0.968253	+	1.33269i	0.0253287	+	0.999679i	$0.491937\pi$
$132$	−1.24108	+	1.70820i	−0.108022	+	0.148680i
$133$	−17.1353	−	12.4495i	−1.48582	−	1.07951i
$134$	12.8982	+	6.57196i	1.11423	+	0.567731i
$135$	1.98787	−	1.44427i	0.171089	−	0.124303i
$136$	8.83692	−	17.3434i	0.757759	−	1.48719i
$137$	0.854102	+	0.277515i	0.0729709	+	0.0237097i	0.345275	−	0.938502i	$-0.387786\pi$
$137$	0.854102	+	0.277515i	0.0729709	+	0.0237097i	−0.272304	+	0.962211i	$0.587786\pi$
$138$	0.494689	+	3.12334i	0.0421107	+	0.265877i
$139$	0.138757	−	0.427051i	0.0117692	−	0.0362220i	−0.944999	−	0.327072i	$-0.893938\pi$
$139$	0.138757	−	0.427051i	0.0117692	−	0.0362220i	0.956769	+	0.290850i	$0.0939380\pi$
$140$	1.61803	−	4.97980i	0.136749	−	0.420870i
$141$	−1.44427	+	1.98787i	−0.121630	+	0.167409i
$142$	−2.81340	−	5.52160i	−0.236095	−	0.463362i
$143$	−6.88191	+	2.23607i	−0.575494	+	0.186989i
$144$	−8.00000	+	5.81234i	−0.666667	+	0.484362i
$145$	−1.97214	+	0.640786i	−0.163777	+	0.0532144i
$146$	1.64204	−	0.260074i	0.135896	−	0.0215238i
$147$	6.43288	+	4.67376i	0.530575	+	0.385485i
$148$	3.52671	−	2.56231i	0.289894	−	0.210620i
$149$	10.8541			0.889203			0.444601	−	0.895729i	$-0.353345\pi$
$149$	10.8541			0.889203			0.444601	+	0.895729i	$0.353345\pi$
$150$	−3.35520	−	3.35520i	−0.273951	−	0.273951i
$151$	−12.8128	+	9.30902i	−1.04269	+	0.757557i	−0.970808	−	0.239856i	$-0.922900\pi$
$151$	−12.8128	+	9.30902i	−1.04269	+	0.757557i	−0.0718794	+	0.997413i	$0.522900\pi$
$152$	−12.6007	+	6.42040i	−1.02205	+	0.520763i
$153$	16.1803	−	5.25731i	1.30810	−	0.425028i
$154$	−6.15537	+	6.15537i	−0.496014	+	0.496014i
$155$	−1.76336	−	2.95492i	−0.141636	−	0.237344i
$156$	7.23607			0.579349
$157$	−0.291796	−	0.898056i	−0.0232879	−	0.0716727i	0.938737	−	0.344634i	$-0.111997\pi$
$157$	−0.291796	−	0.898056i	−0.0232879	−	0.0716727i	−0.962025	+	0.272961i	$0.911997\pi$
$158$	−18.4750	+	9.41350i	−1.46980	+	0.748898i
$159$	−0.930812	−	1.28115i	−0.0738182	−	0.101602i
$160$	−2.47214	−	2.47214i	−0.195440	−	0.195440i
$161$			13.0373i			1.02748i
$162$	−6.32453	−	1.00171i	−0.496902	−	0.0787016i
$163$	11.7229	−	16.1353i	0.918212	−	1.26381i	−0.0460712	−	0.998938i	$-0.514670\pi$
$163$	11.7229	−	16.1353i	0.918212	−	1.26381i	0.964283	−	0.264873i	$-0.0853299\pi$
$164$	−0.898056	+	1.23607i	−0.0701264	+	0.0965207i
$165$	−0.201626	−	0.620541i	−0.0156966	−	0.0483091i
$166$	8.98546	+	1.42316i	0.697407	+	0.110458i
$167$	2.52265	+	7.76393i	0.195209	+	0.600791i	0.999974	+	0.00719787i	$0.00229117\pi$
$167$	2.52265	+	7.76393i	0.195209	+	0.600791i	−0.804765	+	0.593593i	$0.797709\pi$
$168$	7.75621	−	3.95199i	0.598405	−	0.304903i
$169$	9.54508	+	6.93491i	0.734237	+	0.533455i
$170$	2.73076	+	5.35941i	0.209440	+	0.411048i
$171$	−11.7557	−	3.81966i	−0.898981	−	0.292097i
$172$	−5.00000	+	6.88191i	−0.381246	+	0.524741i
$173$	4.95492	−	15.2497i	0.376715	−	1.15941i	−0.565599	−	0.824680i	$-0.691355\pi$
$173$	4.95492	−	15.2497i	0.376715	−	1.15941i	0.942314	−	0.334730i	$-0.108645\pi$
$174$	−3.07167	−	1.56510i	−0.232863	−	0.118650i
$175$	−11.4984	−	15.8262i	−0.869200	−	1.19635i
$176$	1.79611	+	5.52786i	0.135387	+	0.416678i
$177$	−1.48278	+	2.04087i	−0.111453	+	0.153401i
$178$	24.1515	−	3.82521i	1.81023	−	0.286712i
$179$	2.12663	−	1.54508i	0.158952	−	0.115485i	−0.505466	−	0.862846i	$-0.668680\pi$
$179$	2.12663	−	1.54508i	0.158952	−	0.115485i	0.664418	+	0.747361i	$0.268680\pi$
$180$		−	3.05573i		−	0.227761i
$181$			3.07768i			0.228762i	0.993437	+	0.114381i	$0.0364885\pi$
$181$			3.07768i			0.228762i	−0.993437	+	0.114381i	$0.963511\pi$
$182$	29.4652	+	4.66683i	2.18411	+	0.345928i
$183$	6.88191	+	2.23607i	0.508725	+	0.165295i
$184$	7.75621	+	3.95199i	0.571796	+	0.291344i
$185$			1.34708i			0.0990396i
$186$	1.40076	−	5.54666i	0.102709	−	0.406701i
$187$		−	10.0000i		−	0.731272i
$188$	2.09017	+	6.43288i	0.152441	+	0.469166i
$189$	16.0172	+	5.20431i	1.16508	+	0.378558i
$190$	0.683644	−	4.31636i	0.0495967	−	0.313141i
$191$		−	15.3262i		−	1.10897i	−0.832194	−	0.554484i	$-0.812916\pi$
$191$		−	15.3262i		−	1.10897i	0.832194	−	0.554484i	$-0.187084\pi$
$192$		−	5.81234i		−	0.419470i
$193$	−12.0172	+	8.73102i	−0.865018	+	0.628473i	−0.929246	−	0.369463i	$-0.879542\pi$
$193$	−12.0172	+	8.73102i	−0.865018	+	0.628473i	0.0642271	+	0.997935i	$0.479542\pi$
$194$	1.65307	+	10.4371i	0.118684	+	0.749340i
$195$	−1.31433	+	1.80902i	−0.0941210	+	0.129546i
$196$	20.8172	−	6.76393i	1.48695	−	0.483138i
$197$	10.9549	+	15.0781i	0.780505	+	1.07427i	0.995226	+	0.0975980i	$0.0311159\pi$
$197$	10.9549	+	15.0781i	0.780505	+	1.07427i	−0.214721	+	0.976676i	$0.568884\pi$
$198$	−2.30635	+	4.52647i	−0.163905	+	0.321682i
$199$	−4.75528	+	14.6353i	−0.337093	+	1.03747i	0.628589	+	0.777738i	$0.283633\pi$
$199$	−4.75528	+	14.6353i	−0.337093	+	1.03747i	−0.965682	+	0.259728i	$0.916367\pi$
$200$	−12.9010	+	2.04331i	−0.912236	+	0.144484i
$201$	−7.07295	−	2.29814i	−0.498887	−	0.162098i
$202$	−11.2704	+	5.74258i	−0.792985	+	0.404046i
$203$	−11.4984	−	8.35410i	−0.807032	−	0.586343i
$204$	−3.09017	+	9.51057i	−0.216355	+	0.665873i
$205$	−0.145898	−	0.449028i	−0.0101900	−	0.0313615i
$206$	0.201283	−	1.27085i	0.0140241	−	0.0885445i
$207$	2.35114	+	7.23607i	0.163416	+	0.502941i
$208$	11.7082	−	16.1150i	0.811818	−	1.11737i
$209$	−4.27051	+	5.87785i	−0.295397	+	0.406580i
$210$	−0.420808	+	2.65688i	−0.0290385	+	0.183342i
$211$			21.4164i			1.47437i	0.675693	+	0.737183i	$0.263845\pi$
$211$			21.4164i			1.47437i	−0.675693	+	0.737183i	$0.736155\pi$
$212$	−4.35926			−0.299395
$213$	1.87132	+	2.57565i	0.128221	+	0.176481i
$214$	−8.89488	−	17.4572i	−0.608042	−	1.19335i
$215$	−0.812299	−	2.50000i	−0.0553983	−	0.170499i
$216$	7.95148	−	7.95148i	0.541030	−	0.541030i
$217$	9.28115	−	21.6825i	0.630046	−	1.47191i
$218$	7.18034	+	7.18034i	0.486314	+	0.486314i
$219$	−0.812299	+	0.263932i	−0.0548901	+	0.0178349i
$220$	−1.70820	−	0.555029i	−0.115167	−	0.0374201i
$221$	−27.7254	+	20.1437i	−1.86501	+	1.35501i
$222$	−1.58359	+	1.58359i	−0.106284	+	0.106284i
$223$	−9.23305			−0.618291			−0.309145	−	0.951015i	$-0.600043\pi$
$223$	−9.23305			−0.618291			−0.309145	+	0.951015i	$0.600043\pi$
$224$	3.74861	−	23.6678i	0.250465	−	1.58137i
$225$	−9.23607	−	6.71040i	−0.615738	−	0.447360i
$226$	2.55795	+	16.1503i	0.170152	+	1.07430i
$227$	−1.71036	+	0.555728i	−0.113520	+	0.0368850i	−0.365226	−	0.930919i	$-0.619008\pi$
$227$	−1.71036	+	0.555728i	−0.113520	+	0.0368850i	0.251706	+	0.967804i	$0.419008\pi$
$228$	5.87785	−	4.27051i	0.389270	−	0.282821i
$229$	−18.0902	+	5.87785i	−1.19543	+	0.388419i	−0.838078	−	0.545550i	$-0.816321\pi$
$229$	−18.0902	+	5.87785i	−1.19543	+	0.388419i	−0.357354	+	0.933969i	$0.616321\pi$
$230$	−2.39680	+	1.22123i	−0.158040	+	0.0805256i
$231$	2.62866	−	3.61803i	0.172953	−	0.238049i
$232$	−8.45559	+	4.30834i	−0.555137	+	0.282856i
$233$	−4.42705	+	13.6251i	−0.290026	+	0.892607i	0.694821	+	0.719182i	$0.255483\pi$
$233$	−4.42705	+	13.6251i	−0.290026	+	0.892607i	−0.984847	+	0.173425i	$0.944517\pi$
$234$	17.1957	−	2.72353i	1.12412	−	0.178042i
$235$	−1.98787	−	0.645898i	−0.129674	−	0.0421337i
$236$	2.14590	+	6.60440i	0.139686	+	0.429909i
$237$	8.61803	−	6.26137i	0.559801	−	0.406720i
$238$	−18.7169	+	36.7340i	−1.21324	+	2.38111i
$239$	−21.3723	−	15.5279i	−1.38246	−	1.00441i	−0.996646	−	0.0818364i	$-0.973921\pi$
$239$	−21.3723	−	15.5279i	−1.38246	−	1.00441i	−0.385812	−	0.922578i	$-0.626079\pi$
$240$	1.45309	+	1.05573i	0.0937962	+	0.0681470i
$241$	1.80902	+	2.48990i	0.116529	+	0.160388i	0.863297	−	0.504696i	$-0.168395\pi$
$241$	1.80902	+	2.48990i	0.116529	+	0.160388i	−0.746768	+	0.665085i	$0.768395\pi$
$242$	−8.88854	−	8.88854i	−0.571377	−	0.571377i
$243$	15.2169			0.976165
$244$	16.1150	−	11.7082i	1.03165	−	0.749541i
$245$	−2.09017	+	6.43288i	−0.133536	+	0.410982i
$246$	0.356351	−	0.699377i	0.0227201	−	0.0445907i
$247$	24.8990			1.58428
$248$	−10.0861	−	12.0942i	−0.640469	−	0.767984i
$249$	−4.67376			−0.296188
$250$	3.81646	−	7.49022i	0.241374	−	0.473723i
$251$	−0.726543	+	2.23607i	−0.0458590	+	0.141139i	−0.971364	−	0.237595i	$-0.923641\pi$
$251$	−0.726543	+	2.23607i	−0.0458590	+	0.141139i	0.925505	+	0.378735i	$0.123641\pi$
$252$	16.9443	−	12.3107i	1.06739	−	0.775503i
$253$	4.47214			0.281161
$254$	−3.97574	−	3.97574i	−0.249460	−	0.249460i
$255$	−1.81636	−	2.50000i	−0.113745	−	0.156556i
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	−5.61803	−	4.08174i	−0.350443	−	0.254612i	0.398612	−	0.917120i	$-0.369492\pi$
$257$	−5.61803	−	4.08174i	−0.350443	−	0.254612i	−0.749055	+	0.662508i	$0.769492\pi$
$258$	1.98401	−	3.89384i	0.123519	−	0.242420i
$259$	−7.46969	+	5.42705i	−0.464144	+	0.337221i
$260$	1.90211	+	5.85410i	0.117964	+	0.363056i
$261$	−7.88854	−	2.56314i	−0.488289	−	0.158655i
$262$	−26.3355	+	4.17113i	−1.62701	+	0.257693i
$263$	2.59590	−	7.98936i	0.160070	−	0.492645i	−0.838569	−	0.544795i	$-0.816607\pi$
$263$	2.59590	−	7.98936i	0.160070	−	0.492645i	0.998639	+	0.0521502i	$0.0166075\pi$
$264$	−1.35564	−	2.66059i	−0.0834338	−	0.163748i
$265$	0.791796	−	1.08981i	0.0486396	−	0.0669467i
$266$	26.6888	−	13.5986i	1.63639	−	0.833785i
$267$	−11.9475	+	3.88197i	−0.731173	+	0.237572i
$268$	−16.5623	+	12.0332i	−1.01170	+	0.735046i
$269$	26.9336	−	8.75127i	1.64217	−	0.533574i	0.665150	−	0.746710i	$-0.268368\pi$
$269$	26.9336	−	8.75127i	1.64217	−	0.533574i	0.977023	+	0.213136i	$0.0683677\pi$
$270$	0.543598	+	3.43214i	0.0330823	+	0.208873i
$271$	−7.69421	−	5.59017i	−0.467390	−	0.339579i	0.329033	−	0.944318i	$-0.393277\pi$
$271$	−7.69421	−	5.59017i	−0.467390	−	0.339579i	−0.796423	+	0.604740i	$0.793277\pi$
$272$	16.1803	+	22.2703i	0.981077	+	1.35034i
$273$	−15.3262			−0.927586
$274$	−0.898056	+	0.898056i	−0.0542535	+	0.0542535i
$275$	−5.42882	+	3.94427i	−0.327370	+	0.237849i
$276$	−4.25325	−	1.38197i	−0.256016	−	0.0831846i
$277$	−4.73607	+	1.53884i	−0.284563	+	0.0924600i	−0.447821	−	0.894123i	$-0.647800\pi$
$277$	−4.73607	+	1.53884i	−0.284563	+	0.0924600i	0.163258	+	0.986583i	$0.447800\pi$
$278$	0.449028	+	0.449028i	0.0269309	+	0.0269309i
$279$	1.24108	−	13.7082i	0.0743017	−	0.820689i
$280$	5.23607	+	5.23607i	0.312915	+	0.312915i
$281$	2.82624	+	8.69827i	0.168599	+	0.518895i	0.999283	−	0.0378488i	$-0.0120505\pi$
$281$	2.82624	+	8.69827i	0.168599	+	0.518895i	−0.830684	+	0.556744i	$0.812051\pi$
$282$	−1.57758	−	3.09618i	−0.0939437	−	0.184375i
$283$	8.28199	+	11.3992i	0.492313	+	0.677611i	0.980813	−	0.194953i	$-0.0624555\pi$
$283$	8.28199	+	11.3992i	0.492313	+	0.677611i	−0.488499	+	0.872564i	$0.662455\pi$
$284$	8.76393			0.520044
$285$			2.24514i			0.132991i
$286$	1.60085	−	10.1074i	0.0946601	−	0.597660i
$287$	1.90211	−	2.61803i	0.112278	−	0.154538i
$288$	−2.18766	−	13.8123i	−0.128909	−	0.813900i
$289$	−9.38197	−	28.8747i	−0.551880	−	1.69851i
$290$	0.458752	−	2.89645i	0.0269388	−	0.170085i
$291$	−1.67760	−	5.16312i	−0.0983426	−	0.302667i
$292$	−0.726543	+	2.23607i	−0.0425177	+	0.130856i
$293$	−9.51722	−	6.91467i	−0.556002	−	0.403959i	0.273992	−	0.961732i	$-0.411656\pi$
$293$	−9.51722	−	6.91467i	−0.556002	−	0.403959i	−0.829994	+	0.557773i	$0.811656\pi$
$294$	−10.0194	+	5.10516i	−0.584346	+	0.297739i
$295$	−2.04087	−	0.663119i	−0.118824	−	0.0386083i
$296$	0.964406	+	6.08902i	0.0560549	+	0.353917i
$297$	1.78522	−	5.49434i	0.103589	−	0.318814i
$298$	−6.96876	+	13.6770i	−0.403690	+	0.792285i
$299$	−9.00854	−	12.3992i	−0.520977	−	0.717063i
$300$	6.38197	−	2.07363i	0.368463	−	0.119721i
$301$	10.5902	−	14.5761i	0.610407	−	0.840153i
$302$	−3.50375	−	22.1218i	−0.201618	−	1.27297i
$303$	5.25731	−	3.81966i	0.302025	−	0.219434i
$304$		−	20.0000i		−	1.14708i
$305$			6.15537i			0.352455i
$306$	−3.76382	+	23.7638i	−0.215163	+	1.35849i
$307$	29.6870	+	9.64590i	1.69433	+	0.550520i	0.987604	−	0.156969i	$-0.0501722\pi$
$307$	29.6870	+	9.64590i	1.69433	+	0.550520i	0.706724	+	0.707489i	$0.250172\pi$
$308$	−3.80423	−	11.7082i	−0.216766	−	0.667137i
$309$			0.661030i			0.0376047i
$310$	4.85555	−	0.324786i	0.275777	−	0.0184466i
$311$			12.7639i			0.723776i	0.932222	+	0.361888i	$0.117868\pi$
$311$			12.7639i			0.723776i	−0.932222	+	0.361888i	$0.882132\pi$
$312$	−4.64584	+	9.11798i	−0.263019	+	0.516204i
$313$	7.76393	+	2.52265i	0.438843	+	0.142589i	0.520102	−	0.854104i	$-0.325894\pi$
$313$	7.76393	+	2.52265i	0.438843	+	0.142589i	−0.0812585	+	0.996693i	$0.525894\pi$
$314$	1.31896	+	0.208903i	0.0744333	+	0.0117891i
$315$			6.47214i			0.364664i
$316$		−	29.3238i		−	1.64959i
$317$	−10.2361	+	7.43694i	−0.574915	+	0.417700i	−0.836887	−	0.547375i	$-0.815627\pi$
$317$	−10.2361	+	7.43694i	−0.574915	+	0.417700i	0.261972	+	0.965075i	$0.415627\pi$
$318$	2.21197	−	0.350341i	0.124041	−	0.0196461i
$319$	−2.86568	+	3.94427i	−0.160447	+	0.220837i
$320$	4.70228	−	1.52786i	0.262866	−	0.0854102i
$321$	5.91641	+	8.14324i	0.330222	+	0.454511i
$322$	−16.4279	−	8.37045i	−0.915493	−	0.466467i
$323$	−10.6331	+	32.7254i	−0.591643	+	1.82089i
$324$	5.32282	−	7.32624i	0.295712	−	0.407013i
$325$	21.8713	+	7.10642i	1.21320	+	0.394193i
$326$	12.8050	+	25.1312i	0.709204	+	1.39189i
$327$	−4.22050	−	3.06637i	−0.233394	−	0.169571i
$328$	−0.980949	−	1.92522i	−0.0541639	−	0.106303i
$329$	−4.42705	−	13.6251i	−0.244071	−	0.751174i
$330$	0.911380	+	0.144348i	0.0501698	+	0.00794612i
$331$	−8.92278	−	27.4615i	−0.490440	−	1.50942i	−0.823944	−	0.566671i	$-0.808231\pi$
$331$	−8.92278	−	27.4615i	−0.490440	−	1.50942i	0.333504	−	0.942749i	$-0.391769\pi$
$332$	−7.56231	+	10.4086i	−0.415035	+	0.571247i
$333$	−3.16718	+	4.35926i	−0.173561	+	0.238886i
$334$	−11.4028	−	1.80602i	−0.623932	−	0.0988211i
$335$		−	6.32624i		−	0.345639i
$336$			12.3107i			0.671606i
$337$	9.40983	+	12.9515i	0.512586	+	0.705514i	0.984353	−	0.176209i	$-0.0563835\pi$
$337$	9.40983	+	12.9515i	0.512586	+	0.705514i	−0.471767	+	0.881723i	$0.656384\pi$
$338$	−14.8668	+	7.57502i	−0.808648	+	0.412027i
$339$	−2.59590	−	7.98936i	−0.140990	−	0.433922i
$340$	−8.50651			−0.461330
$341$	−7.43769	−	3.18368i	−0.402774	−	0.172406i
$342$	12.3607	−	12.3607i	0.668389	−	0.668389i
$343$	−15.8904	+	5.16312i	−0.858003	+	0.278782i
$344$	−5.46151	−	10.7188i	−0.294465	−	0.577920i
$345$	1.11803	−	0.812299i	0.0601929	−	0.0437327i
$346$	16.0344	+	16.0344i	0.862017	+	0.862017i
$347$	30.0503			1.61318			0.806592	−	0.591108i	$-0.201309\pi$
$347$	30.0503			1.61318			0.806592	+	0.591108i	$0.201309\pi$
$348$	3.94427	−	2.86568i	0.211435	−	0.153617i
$349$	11.2812	+	8.19624i	0.603866	+	0.438735i	0.847249	−	0.531196i	$-0.178257\pi$
$349$	11.2812	+	8.19624i	0.603866	+	0.438735i	−0.243383	+	0.969930i	$0.578257\pi$
$350$	27.3247	−	4.32780i	1.46057	−	0.231331i
$351$	−18.8294	+	6.11803i	−1.00504	+	0.326556i
$352$	−8.11869	−	1.28587i	−0.432728	−	0.0685373i
$353$	13.3541	−	4.33901i	0.710767	−	0.230942i	0.0687515	−	0.997634i	$-0.478098\pi$
$353$	13.3541	−	4.33901i	0.710767	−	0.230942i	0.642016	+	0.766692i	$0.278098\pi$
$354$	−1.61964	−	3.17873i	−0.0860831	−	0.168948i
$355$	−1.59184	+	2.19098i	−0.0844862	+	0.116285i
$356$	−10.6861	+	32.8885i	−0.566364	+	1.74309i
$357$	6.54508	−	20.1437i	0.346403	−	1.06612i
$358$	0.581542	+	3.67171i	0.0307355	+	0.194056i
$359$	18.8294	+	6.11803i	0.993776	+	0.322897i	0.760376	−	0.649483i	$-0.225015\pi$
$359$	18.8294	+	6.11803i	0.993776	+	0.322897i	0.233400	+	0.972381i	$0.425015\pi$
$360$	3.85044	+	1.96190i	0.202936	+	0.103401i
$361$	4.85410	−	3.52671i	0.255479	−	0.185616i
$362$	−3.87811	−	1.97599i	−0.203829	−	0.103856i
$363$	5.22455	+	3.79586i	0.274218	+	0.199231i
$364$	−24.7984	+	34.1320i	−1.29979	+	1.78900i
$365$	−0.427051	−	0.587785i	−0.0223529	−	0.0307661i
$366$	−7.23607	+	7.23607i	−0.378235	+	0.378235i
$367$	4.08174			0.213065			0.106533	−	0.994309i	$-0.466025\pi$
$367$	4.08174			0.213065			0.106533	+	0.994309i	$0.466025\pi$
$368$	−9.95959	+	7.23607i	−0.519180	+	0.377206i
$369$	0.583592	−	1.79611i	0.0303806	−	0.0935019i
$370$	−1.69742	−	0.864881i	−0.0882449	−	0.0449630i
$371$	9.23305			0.479356
$372$	6.08985	+	5.32624i	0.315744	+	0.276153i
$373$	−12.4164			−0.642897			−0.321449	−	0.946927i	$-0.604170\pi$
$373$	−12.4164			−0.642897			−0.321449	+	0.946927i	$0.604170\pi$
$374$	12.6007	+	6.42040i	0.651569	+	0.331991i
$375$	−1.33457	+	4.10739i	−0.0689170	+	0.212105i
$376$	−9.44788	−	1.49640i	−0.487237	−	0.0771708i
$377$	16.7082			0.860516
$378$	−16.8415	+	16.8415i	−0.866233	+	0.866233i
$379$	16.3597	+	22.5172i	0.840342	+	1.15663i	0.985909	+	0.167283i	$0.0534995\pi$
$379$	16.3597	+	22.5172i	0.840342	+	1.15663i	−0.145567	+	0.989348i	$0.546500\pi$
$380$	5.00000	+	3.63271i	0.256495	+	0.186354i
$381$	2.33688	+	1.69784i	0.119722	+	0.0869832i
$382$	19.3122	+	9.84005i	0.988097	+	0.503461i
$383$	28.2012	−	20.4894i	1.44101	−	1.04696i	0.453183	−	0.891417i	$-0.350288\pi$
$383$	28.2012	−	20.4894i	1.44101	−	1.04696i	0.987830	−	0.155540i	$-0.0497117\pi$
$384$	7.32398	+	3.73175i	0.373750	+	0.190435i
$385$	3.61803	+	1.17557i	0.184392	+	0.0599126i
$386$	−3.28620	−	20.7482i	−0.167263	−	1.05606i
$387$	3.24920	−	10.0000i	0.165166	−	0.508329i
$388$	−14.2128	−	4.61803i	−0.721548	−	0.234445i
$389$	−5.62868	+	7.74721i	−0.285385	+	0.392799i	−0.927508	−	0.373802i	$-0.878054\pi$
$389$	−5.62868	+	7.74721i	−0.285385	+	0.392799i	0.642123	+	0.766602i	$0.278054\pi$
$390$	−1.43564	−	2.81761i	−0.0726967	−	0.142675i
$391$	20.1437	−	6.54508i	1.01871	−	0.330999i
$392$	−4.84244	+	30.5740i	−0.244580	+	1.54422i
$393$	13.0279	−	4.23301i	0.657169	−	0.213527i
$394$	−26.0331	+	4.12323i	−1.31153	+	0.207725i
$395$	7.33094	+	5.32624i	0.368860	+	0.267992i
$396$	−4.22291	−	5.81234i	−0.212209	−	0.292081i
$397$	−12.0000			−0.602263			−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000			−0.602263			−0.301131	+	0.953583i	$0.597364\pi$
$398$	−15.3884	−	15.3884i	−0.771352	−	0.771352i
$399$	−12.4495	+	9.04508i	−0.623254	+	0.452821i
$400$	5.70820	−	17.5680i	0.285410	−	0.878402i
$401$	13.2533	−	4.30625i	0.661838	−	0.215044i	0.0412112	−	0.999150i	$-0.486878\pi$
$401$	13.2533	−	4.30625i	0.661838	−	0.215044i	0.620626	+	0.784106i	$0.286878\pi$
$402$	7.43694	−	7.43694i	0.370921	−	0.370921i
$403$	6.15537	+	27.0344i	0.306621	+	1.34668i
$404$		−	17.8885i		−	0.889988i
$405$	0.864745	+	2.66141i	0.0429695	+	0.132247i
$406$	17.9092	−	9.12521i	0.888820	−	0.452877i
$407$	1.86162	+	2.56231i	0.0922773	+	0.127009i
$408$	−10.0000	−	10.0000i	−0.495074	−	0.495074i
$409$			1.24108i			0.0613676i	0.999529	+	0.0306838i	$0.00976849\pi$
$409$			1.24108i			0.0613676i	−0.999529	+	0.0306838i	$0.990232\pi$
$410$	0.659481	+	0.104451i	0.0325694	+	0.00515849i
$411$	0.383516	−	0.527864i	0.0189174	−	0.0260376i
$412$	1.47214	+	1.06957i	0.0725269	+	0.0526939i
$413$	−4.54508	−	13.9883i	−0.223649	−	0.688321i
$414$	−10.6275	−	1.68323i	−0.522313	−	0.0827263i
$415$	−1.22857	−	3.78115i	−0.0603082	−	0.185609i
$416$	12.7889	+	25.0996i	0.627028	+	1.23061i
$417$	−0.263932	−	0.191758i	−0.0129248	−	0.00939042i
$418$	−4.66469	−	9.15497i	−0.228157	−	0.447784i
$419$	−2.07363	−	0.673762i	−0.101303	−	0.0329154i	0.257927	−	0.966164i	$-0.416961\pi$
$419$	−2.07363	−	0.673762i	−0.101303	−	0.0329154i	−0.359230	+	0.933249i	$0.616961\pi$
$420$	−3.07768	−	2.23607i	−0.150176	−	0.109109i
$421$	−6.67376	+	20.5397i	−0.325259	+	1.00105i	0.646064	+	0.763283i	$0.276414\pi$
$421$	−6.67376	+	20.5397i	−0.325259	+	1.00105i	−0.971323	+	0.237762i	$0.923586\pi$
$422$	−26.9862	−	13.7502i	−1.31367	−	0.669348i
$423$	−4.91428	−	6.76393i	−0.238941	−	0.328874i
$424$	2.79881	−	5.49298i	0.135922	−	0.266763i
$425$	−18.6803	+	25.7113i	−0.906130	+	1.24718i
$426$	−4.44698	+	0.704332i	−0.215457	+	0.0341250i
$427$	−34.1320	+	24.7984i	−1.65176	+	1.20008i
$428$	27.7082			1.33933
$429$			5.25731i			0.253825i
$430$	3.67171	+	0.581542i	0.177066	+	0.0280444i
$431$	−25.7970	−	8.38197i	−1.24260	−	0.403745i	−0.387336	−	0.921939i	$-0.626605\pi$
$431$	−25.7970	−	8.38197i	−1.24260	−	0.403745i	−0.855263	+	0.518193i	$0.826605\pi$
$432$	4.91428	+	15.1246i	0.236439	+	0.727683i
$433$		−	22.6134i		−	1.08673i	−0.839497	−	0.543364i	$-0.817150\pi$
$433$		−	22.6134i		−	1.08673i	0.839497	−	0.543364i	$-0.182850\pi$
$434$	21.3627	+	25.6160i	1.02544	+	1.22961i
$435$			1.50658i			0.0722349i
$436$	−13.6578	+	4.43769i	−0.654091	+	0.212527i
$437$	−14.6353	−	4.75528i	−0.700099	−	0.227476i
$438$	0.188954	−	1.19301i	0.00902859	−	0.0570043i
$439$		−	13.4721i		−	0.642990i	−0.946911	−	0.321495i	$-0.895815\pi$
$439$		−	13.4721i		−	0.642990i	0.946911	−	0.321495i	$-0.104185\pi$
$440$	1.79611	−	1.79611i	0.0856263	−	0.0856263i
$441$	−21.8885	+	15.9030i	−1.04231	+	0.757284i
$442$	−7.58172	−	47.8691i	−0.360626	−	2.27690i
$443$	−18.2946	+	25.1803i	−0.869202	+	1.19635i	0.110094	+	0.993921i	$0.464885\pi$
$443$	−18.2946	+	25.1803i	−0.869202	+	1.19635i	−0.979296	+	0.202433i	$0.935115\pi$
$444$	−0.978714	−	3.01217i	−0.0464477	−	0.142951i
$445$	−6.28115	−	8.64527i	−0.297755	−	0.409825i
$446$	5.92798	−	11.6343i	0.280698	−	0.550901i
$447$	2.43690	−	7.50000i	0.115261	−	0.354738i
$448$	27.4164	+	19.9192i	1.29530	+	0.941093i
$449$	34.5967	+	11.2412i	1.63272	+	0.530503i	0.974895	−	0.222666i	$-0.0714759\pi$
$449$	34.5967	+	11.2412i	1.63272	+	0.530503i	0.657827	+	0.753169i	$0.271476\pi$
$450$	14.3855	−	7.32979i	0.678140	−	0.345529i
$451$	−0.898056	−	0.652476i	−0.0422878	−	0.0307239i
$452$	−21.9928	−	7.14590i	−1.03445	−	0.336115i
$453$	3.55573	+	10.9434i	0.167063	+	0.514166i
$454$	0.397857	−	2.51197i	0.0186724	−	0.117893i
$455$	−4.02874	−	12.3992i	−0.188870	−	0.581283i
$456$	1.60734	+	10.1484i	0.0752707	+	0.475241i
$457$	7.17376	−	9.87384i	0.335574	−	0.461879i	−0.607568	−	0.794268i	$-0.707855\pi$
$457$	7.17376	−	9.87384i	0.335574	−	0.461879i	0.943142	+	0.332389i	$0.107855\pi$
$458$	4.20808	−	26.5688i	0.196631	−	1.24148i
$459$		−	27.3607i		−	1.27709i
$460$		−	3.80423i		−	0.177373i
$461$	−23.9058	−	32.9035i	−1.11340	−	1.53247i	−0.816306	−	0.577620i	$-0.803982\pi$
$461$	−23.9058	−	32.9035i	−1.11340	−	1.53247i	−0.297096	−	0.954848i	$-0.596018\pi$
$462$	2.87129	+	5.63522i	0.133584	+	0.262174i
$463$	1.79611	+	5.52786i	0.0834724	+	0.256902i	0.984078	−	0.177735i	$-0.0568769\pi$
$463$	1.79611	+	5.52786i	0.0834724	+	0.256902i	−0.900606	+	0.434636i	$0.856877\pi$
$464$		−	13.4208i		−	0.623045i
$465$	−2.43769	+	0.555029i	−0.113045	+	0.0257389i
$466$	−14.3262	−	14.3262i	−0.663650	−	0.663650i
$467$	24.1194	−	7.83688i	1.11611	−	0.362648i	0.307831	−	0.951441i	$-0.400397\pi$
$467$	24.1194	−	7.83688i	1.11611	−	0.362648i	0.808284	+	0.588793i	$0.200397\pi$
$468$	−7.60845	+	23.4164i	−0.351701	+	1.08242i
$469$	35.0795	−	25.4868i	1.61982	−	1.17687i
$470$	2.09017	−	2.09017i	0.0964124	−	0.0964124i
$471$	−0.686054			−0.0316117
$472$	−9.69977	−	1.53629i	−0.446468	−	0.0707136i
$473$	−5.00000	−	3.63271i	−0.229900	−	0.167032i
$474$	2.35667	+	14.8794i	0.108245	+	0.683434i
$475$	21.9601	−	7.13525i	1.00760	−	0.327388i
$476$	−34.2705	−	47.1693i	−1.57079	−	2.16200i
$477$	5.12461	−	1.66509i	0.234640	−	0.0762391i
$478$	33.2881	−	16.9611i	1.52256	−	0.775784i
$479$	10.4741	−	14.4164i	0.478575	−	0.658702i	−0.499655	−	0.866225i	$-0.666540\pi$
$479$	10.4741	−	14.4164i	0.478575	−	0.658702i	0.978230	+	0.207522i	$0.0665399\pi$
$480$	−2.26323	+	1.15317i	−0.103302	+	0.0526350i
$481$	3.35410	−	10.3229i	0.152934	−	0.470682i
$482$	−4.29892	+	0.680881i	−0.195810	+	0.0310133i
$483$	9.00854	+	2.92705i	0.409903	+	0.133185i
$484$	16.9070	−	5.49342i	0.768501	−	0.249701i
$485$	3.73607	−	2.71441i	0.169646	−	0.123255i
$486$	−9.76985	+	19.1744i	−0.443170	+	0.869769i
$487$	5.48183	+	3.98278i	0.248405	+	0.180477i	0.705020	−	0.709188i	$-0.250938\pi$
$487$	5.48183	+	3.98278i	0.248405	+	0.180477i	−0.456615	+	0.889665i	$0.650938\pi$
$488$	4.40676	+	27.8232i	0.199484	+	1.25950i
$489$	−8.51722	−	11.7229i	−0.385162	−	0.530130i
$490$	−6.76393	−	6.76393i	−0.305563	−	0.305563i
$491$	−33.1280			−1.49504			−0.747522	−	0.664237i	$-0.768757\pi$
$491$	−33.1280			−1.49504			−0.747522	+	0.664237i	$0.768757\pi$
$492$	0.652476	+	0.898056i	0.0294159	+	0.0404875i
$493$	−7.13525	+	21.9601i	−0.321356	+	0.989031i
$494$	−15.9861	+	31.3745i	−0.719250	+	1.41161i
$495$	2.22012			0.0997868
$496$	21.7153	−	4.94427i	0.975046	−	0.222004i
$497$	−18.5623			−0.832633
$498$	3.00074	−	5.88928i	0.134466	−	0.263905i
$499$	−0.930812	+	2.86475i	−0.0416689	+	0.128244i	−0.969727	−	0.244192i	$-0.921477\pi$
$499$	−0.930812	+	2.86475i	−0.0416689	+	0.128244i	0.928058	+	0.372436i	$0.121477\pi$
$500$	6.98791	+	9.61803i	0.312509	+	0.430132i
$501$	5.93112			0.264983
$502$	−2.35114	−	2.35114i	−0.104937	−	0.104937i
$503$	−18.4131	−	25.3435i	−0.821000	−	1.13001i	−0.989532	−	0.144313i	$-0.953903\pi$
$503$	−18.4131	−	25.3435i	−0.821000	−	1.13001i	0.168533	−	0.985696i	$-0.446097\pi$
$504$	4.63354	+	29.2550i	0.206394	+	1.30312i
$505$	4.47214	+	3.24920i	0.199007	+	0.144587i
$506$	−2.87129	+	5.63522i	−0.127644	+	0.250516i
$507$	6.93491	−	5.03851i	0.307990	−	0.223768i
$508$	7.56231	−	2.45714i	0.335523	−	0.109018i
$509$	−13.8820	−	4.51052i	−0.615307	−	0.199925i	−0.0152516	−	0.999884i	$-0.504855\pi$
$509$	−13.8820	−	4.51052i	−0.615307	−	0.199925i	−0.600056	+	0.799958i	$0.704855\pi$
$510$	4.31636	−	0.683644i	0.191131	−	0.0302723i
$511$	1.53884	−	4.73607i	0.0680744	−	0.209511i
$512$	20.1612	−	10.2726i	0.891007	−	0.453990i
$513$	−11.6844	+	16.0822i	−0.515879	+	0.710047i
$514$	8.75029	−	4.45850i	0.385959	−	0.196656i
$515$	−0.534785	+	0.173762i	−0.0235654	+	0.00765687i
$516$	3.63271	+	5.00000i	0.159921	+	0.220113i
$517$	−4.67376	+	1.51860i	−0.205552	+	0.0667878i
$518$	−2.04264	−	12.8967i	−0.0897486	−	0.566650i
$519$	−9.42481	−	6.84752i	−0.413703	−	0.300573i
$520$	−8.59783	−	1.36176i	−0.377040	−	0.0597172i
$521$	−4.34752			−0.190468			−0.0952342	−	0.995455i	$-0.530360\pi$
$521$	−4.34752			−0.190468			−0.0952342	+	0.995455i	$0.530360\pi$
$522$	8.29451	−	8.29451i	0.363041	−	0.363041i
$523$	−17.7068	+	12.8647i	−0.774264	+	0.562536i	−0.903252	−	0.429110i	$-0.858827\pi$
$523$	−17.7068	+	12.8647i	−0.774264	+	0.562536i	0.128988	+	0.991646i	$0.458827\pi$
$524$	11.6525	−	35.8626i	0.509041	−	1.56667i
$525$	−13.5172	+	4.39201i	−0.589940	+	0.191683i
$526$	8.40051	+	8.40051i	0.366280	+	0.366280i
$527$	−38.1608	−	3.45492i	−1.66231	−	0.150498i
$528$	4.22291			0.183779
$529$	−4.18034	−	12.8658i	−0.181754	−	0.559381i
$530$	0.864881	+	1.69742i	0.0375680	+	0.0737314i
$531$	−5.04531	−	6.94427i	−0.218948	−	0.301356i
$532$			42.3607i			1.83657i
$533$			3.80423i			0.164779i
$534$	2.77918	−	17.5471i	0.120267	−	0.759335i
$535$	−5.03280	+	6.92705i	−0.217587	+	0.299483i
$536$	−4.52909	−	28.5955i	−0.195627	−	1.23514i
$537$	−0.590170	−	1.81636i	−0.0254677	−	0.0783816i
$538$	−6.26522	+	39.5570i	−0.270113	+	1.70542i
$539$	4.91428	+	15.1246i	0.211673	+	0.651463i
$540$	−4.67376	−	1.51860i	−0.201127	−	0.0653500i
$541$	8.61803	+	6.26137i	0.370518	+	0.269197i	0.757426	−	0.652921i	$-0.226457\pi$
$541$	8.61803	+	6.26137i	0.370518	+	0.269197i	−0.386908	+	0.922119i	$0.626457\pi$
$542$	11.9840	−	6.10616i	0.514757	−	0.262282i
$543$	2.12663	+	0.690983i	0.0912623	+	0.0296529i
$544$	−38.4507	+	6.08999i	−1.64856	+	0.261106i
$545$	1.37132	−	4.22050i	0.0587410	−	0.180786i
$546$	9.84005	−	19.3122i	0.421115	−	0.826485i
$547$	−0.171513	−	0.236068i	−0.00733338	−	0.0100935i	0.805335	−	0.592821i	$-0.201986\pi$
$547$	−0.171513	−	0.236068i	−0.00733338	−	0.0100935i	−0.812668	+	0.582727i	$0.801986\pi$
$548$	−0.555029	−	1.70820i	−0.0237097	−	0.0729709i
$549$	−14.4721	+	19.9192i	−0.617656	+	0.850130i
$550$	−1.48455	−	9.37310i	−0.0633015	−	0.399670i
$551$	13.5721	−	9.86068i	0.578189	−	0.420079i
$552$	4.47214	−	4.47214i	0.190347	−	0.190347i
$553$			62.1087i			2.64113i
$554$	1.10169	−	6.95579i	0.0468063	−	0.295523i
$555$	0.930812	+	0.302439i	0.0395108	+	0.0128378i
$556$	−0.854102	+	0.277515i	−0.0362220	+	0.0117692i
$557$			24.9645i			1.05778i	0.848691	+	0.528890i	$0.177392\pi$
$557$			24.9645i			1.05778i	−0.848691	+	0.528890i	$0.822608\pi$
$558$	16.4765	+	10.3651i	0.697507	+	0.438788i
$559$			21.1803i			0.895833i
$560$	−9.95959	+	3.23607i	−0.420870	+	0.136749i
$561$	−6.90983	−	2.24514i	−0.291733	−	0.0947899i
$562$	−12.7750	−	2.02336i	−0.538881	−	0.0853504i
$563$			33.6869i			1.41973i	0.704336	+	0.709867i	$0.251245\pi$
$563$			33.6869i			1.41973i	−0.704336	+	0.709867i	$0.748755\pi$
$564$	4.91428			0.206929
$565$	5.78115	−	4.20025i	0.243215	−	0.176706i
$566$	−19.6812	+	3.11719i	−0.827262	+	0.131025i
$567$	−11.2739	+	15.5172i	−0.473460	+	0.651662i
$568$	−5.62679	+	11.0432i	−0.236095	+	0.463362i
$569$	−21.3820	−	29.4298i	−0.896379	−	1.23376i	−0.971609	−	0.236593i	$-0.923969\pi$
$569$	−21.3820	−	29.4298i	−0.896379	−	1.23376i	0.0752302	−	0.997166i	$-0.476031\pi$
$570$	−2.82904	−	1.44147i	−0.118496	−	0.0603765i
$571$	7.44945	−	22.9271i	0.311750	−	0.959467i	−0.665322	−	0.746557i	$-0.731706\pi$
$571$	7.44945	−	22.9271i	0.311750	−	0.959467i	0.977072	−	0.212911i	$-0.0682943\pi$
$572$	11.7082	+	8.50651i	0.489545	+	0.355675i
$573$	−10.5902	−	3.44095i	−0.442411	−	0.143748i
$574$	2.07768	+	4.07768i	0.0867208	+	0.170199i
$575$	−11.4984	−	8.35410i	−0.479518	−	0.348390i
$576$	18.8091	+	6.11146i	0.783714	+	0.254644i
$577$	3.10081	+	9.54332i	0.129089	+	0.397294i	0.994624	−	0.103554i	$-0.0330216\pi$
$577$	3.10081	+	9.54332i	0.129089	+	0.397294i	−0.865535	+	0.500848i	$0.833022\pi$
$578$	42.4079	+	6.71675i	1.76393	+	0.279380i
$579$	3.33495	+	10.2639i	0.138596	+	0.426554i
$580$	3.35520	+	2.43769i	0.139317	+	0.101220i
$581$	16.0172	−	22.0458i	0.664506	−	0.914614i
$582$	7.58299	+	1.20103i	0.314325	+	0.0497842i
$583$		−	3.16718i		−	0.131171i
$584$	−2.35114	−	2.35114i	−0.0972909	−	0.0972909i
$585$	−4.47214	−	6.15537i	−0.184900	−	0.254493i
$586$	14.8234	−	7.55291i	0.612350	−	0.312008i
$587$	0.0530006	+	0.163119i	0.00218757	+	0.00673264i	0.952144	−	0.305649i	$-0.0988733\pi$
$587$	0.0530006	+	0.163119i	0.00218757	+	0.00673264i	−0.949957	+	0.312381i	$0.898873\pi$
$588$		−	15.9030i		−	0.655827i
$589$	20.9549	+	18.3273i	0.863432	+	0.755165i
$590$	2.14590	−	2.14590i	0.0883452	−	0.0883452i
$591$	12.8783	−	4.18441i	0.529741	−	0.172123i
$592$	−8.29180	−	2.69417i	−0.340791	−	0.110730i
$593$	4.85410	−	3.52671i	0.199334	−	0.144825i	−0.483641	−	0.875267i	$-0.660686\pi$
$593$	4.85410	−	3.52671i	0.199334	−	0.144825i	0.682975	+	0.730442i	$0.260686\pi$
$594$	5.77709	+	5.77709i	0.237037	+	0.237037i
$595$	18.0171			0.738628
$596$	−12.7598	−	17.5623i	−0.522660	−	0.719380i
$597$	9.04508	+	6.57164i	0.370191	+	0.268959i
$598$	21.4077	−	3.39065i	0.875427	−	0.138654i
$599$	−30.5851	+	9.93769i	−1.24967	+	0.406043i	−0.857803	−	0.513978i	$-0.828171\pi$
$599$	−30.5851	+	9.93769i	−1.24967	+	0.406043i	−0.391869	+	0.920021i	$0.628171\pi$
$600$	−1.48455	+	9.37310i	−0.0606066	+	0.382655i
$601$	−30.8541	+	10.0251i	−1.25857	+	0.408933i	−0.860983	−	0.508634i	$-0.830151\pi$
$601$	−30.8541	+	10.0251i	−1.25857	+	0.408933i	−0.397582	+	0.917567i	$0.630151\pi$
$602$	11.5677	+	22.7028i	0.471463	+	0.925299i
$603$	14.8739	−	20.4721i	0.605711	−	0.833690i
$604$	30.1246	+	9.78808i	1.22575	+	0.398271i
$605$	−1.69756	+	5.22455i	−0.0690157	+	0.212408i
$606$	1.43765	+	9.07697i	0.0584006	+	0.368727i
$607$	−6.15537	−	2.00000i	−0.249839	−	0.0811775i	0.181420	−	0.983406i	$-0.441931\pi$
$607$	−6.15537	−	2.00000i	−0.249839	−	0.0811775i	−0.431259	+	0.902228i	$0.641931\pi$
$608$	25.2015	+	12.8408i	1.02205	+	0.520763i
$609$	−8.35410	+	6.06961i	−0.338525	+	0.245953i
$610$	−7.75621	−	3.95199i	−0.314040	−	0.160011i
$611$	13.6251	+	9.89919i	0.551211	+	0.400478i
$612$	−27.5276	−	20.0000i	−1.11274	−	0.808452i
$613$	23.2918	+	32.0584i	0.940747	+	1.29483i	0.955517	+	0.294936i	$0.0952983\pi$
$613$	23.2918	+	32.0584i	0.940747	+	1.29483i	−0.0147702	+	0.999891i	$0.504702\pi$
$614$	−31.2148	+	31.2148i	−1.25973	+	1.25973i
$615$	−0.343027			−0.0138322
$616$	17.1957	+	2.72353i	0.692833	+	0.109734i
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	−0.999723	−	0.0235215i	$-0.992512\pi$
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	0.822619	+	0.568593i	$0.192512\pi$
$618$	−0.832947	−	0.424408i	−0.0335060	−	0.0170722i
$619$	−10.1716			−0.408831			−0.204415	−	0.978884i	$-0.565529\pi$
$619$	−10.1716			−0.408831			−0.204415	+	0.978884i	$0.565529\pi$
$620$	−2.70820	+	6.32688i	−0.108764	+	0.254094i
$621$	12.2361			0.491016
$622$	−16.0835	−	8.19495i	−0.644889	−	0.328588i
$623$	22.6336	−	69.6591i	0.906796	−	2.79083i
$624$	−8.50651	−	11.7082i	−0.340533	−	0.468703i
$625$	19.4164			0.776656
$626$	−8.16348	+	8.16348i	−0.326278	+	0.326278i
$627$	3.10271	+	4.27051i	0.123910	+	0.170548i
$628$	−1.11006	+	1.52786i	−0.0442961	+	0.0609684i
$629$	12.1353	+	8.81678i	0.483864	+	0.351548i
$630$	−8.15537	−	4.15537i	−0.324918	−	0.165554i
$631$	−2.26538	+	1.64590i	−0.0901835	+	0.0655222i	−0.631963	−	0.774998i	$-0.717751\pi$
$631$	−2.26538	+	1.64590i	−0.0901835	+	0.0655222i	0.541780	+	0.840520i	$0.317751\pi$
$632$	36.9501	+	18.8270i	1.46980	+	0.748898i
$633$	14.7984	+	4.80828i	0.588183	+	0.191112i
$634$	−2.79913	−	17.6730i	−0.111168	−	0.701885i
$635$	−0.759299	+	2.33688i	−0.0301318	+	0.0927363i
$636$	−0.978714	+	3.01217i	−0.0388085	+	0.119440i
$637$	32.0344	−	44.0916i	1.26925	−	1.74697i
$638$	−3.13019	−	6.14335i	−0.123925	−	0.243217i
$639$	−10.3026	+	3.34752i	−0.407565	+	0.132426i
$640$	−1.09383	+	6.90617i	−0.0432374	+	0.272990i
$641$	9.57295	−	3.11044i	0.378109	−	0.122855i	−0.113796	−	0.993504i	$-0.536301\pi$
$641$	9.57295	−	3.11044i	0.378109	−	0.122855i	0.491904	+	0.870649i	$0.336301\pi$
$642$	−14.0596	+	2.22683i	−0.554890	+	0.0878859i
$643$	−18.8294	−	13.6803i	−0.742558	−	0.539500i	0.150953	−	0.988541i	$-0.451766\pi$
$643$	−18.8294	−	13.6803i	−0.742558	−	0.539500i	−0.893511	+	0.449041i	$0.851766\pi$
$644$	21.0948	−	15.3262i	0.831250	−	0.603938i
$645$	−1.90983			−0.0751995
$646$	−34.4095	−	34.4095i	−1.35383	−	1.35383i
$647$	14.9394	−	10.8541i	0.587328	−	0.426719i	−0.254031	−	0.967196i	$-0.581756\pi$
$647$	14.9394	−	10.8541i	0.587328	−	0.426719i	0.841359	+	0.540477i	$0.181756\pi$
$648$	5.81414	+	11.4109i	0.228401	+	0.448262i
$649$	−4.79837	+	1.55909i	−0.188353	+	0.0611995i
$650$	−22.9969	+	22.9969i	−0.902011	+	0.902011i
$651$	−12.8985	−	11.2812i	−0.505533	−	0.442143i
$652$	−39.8885			−1.56216
$653$	−1.27458	−	3.92274i	−0.0498780	−	0.153509i	0.923015	−	0.384763i	$-0.125717\pi$
$653$	−1.27458	−	3.92274i	−0.0498780	−	0.153509i	−0.972893	+	0.231255i	$0.925717\pi$
$654$	6.57358	−	3.34941i	0.257047	−	0.130972i
$655$	6.84915	+	9.42705i	0.267619	+	0.368345i
$656$	3.05573			0.119306
$657$		−	2.90617i		−	0.113380i
$658$	20.0109	+	3.16942i	0.780107	+	0.123557i
$659$	5.06555	−	6.97214i	0.197326	−	0.271596i	−0.698875	−	0.715243i	$-0.746316\pi$
$659$	5.06555	−	6.97214i	0.197326	−	0.271596i	0.896201	+	0.443648i	$0.146316\pi$
$660$	−0.767031	+	1.05573i	−0.0298567	+	0.0410942i
$661$	0.628677	+	1.93487i	0.0244527	+	0.0752577i	0.962538	−	0.271146i	$-0.0874027\pi$
$661$	0.628677	+	1.93487i	0.0244527	+	0.0752577i	−0.938085	+	0.346404i	$0.887403\pi$
$662$	40.3323	+	6.38801i	1.56756	+	0.248277i
$663$	7.69421	+	23.6803i	0.298818	+	0.919668i
$664$	−8.26033	−	16.2118i	−0.320563	−	0.629140i
$665$	−10.5902	−	7.69421i	−0.410669	−	0.298369i
$666$	−3.45952	−	6.78970i	−0.134054	−	0.263095i
$667$	−9.82084	−	3.19098i	−0.380264	−	0.123555i
$668$	9.59675	−	13.2088i	0.371309	−	0.511063i
$669$	−2.07295	+	6.37988i	−0.0801448	+	0.246660i
$670$	7.97152	+	4.06169i	0.307967	+	0.156917i
$671$	8.50651	+	11.7082i	0.328390	+	0.451990i
$672$	−15.5124	−	7.90398i	−0.598405	−	0.304903i
$673$	16.0795	−	22.1316i	0.619820	−	0.853109i	−0.377520	−	0.926002i	$-0.623223\pi$
$673$	16.0795	−	22.1316i	0.619820	−	0.853109i	0.997340	+	0.0728923i	$0.0232229\pi$
$674$	−22.3614	+	3.54169i	−0.861327	+	0.136421i
$675$	−14.8536	+	10.7918i	−0.571717	+	0.415376i
$676$		−	23.5967i		−	0.907567i
$677$		−	21.3723i		−	0.821403i	−0.911770	−	0.410702i	$-0.865284\pi$
$677$		−	21.3723i		−	0.821403i	0.911770	−	0.410702i	$-0.134716\pi$
$678$	11.7338	+	1.85846i	0.450636	+	0.0713737i
$679$	30.1033	+	9.78115i	1.15526	+	0.375366i
$680$	5.46151	−	10.7188i	0.209440	−	0.411048i
$681$			1.30660i			0.0500688i
$682$	8.78697	−	7.32799i	0.336470	−	0.280603i
$683$			14.1246i			0.540463i	0.962795	+	0.270232i	$0.0871003\pi$
$683$			14.1246i			0.540463i	−0.962795	+	0.270232i	$0.912900\pi$
$684$	7.63932	+	23.5114i	0.292097	+	0.898981i
$685$	0.527864	+	0.171513i	0.0201686	+	0.00655319i
$686$	3.69639	−	23.3381i	0.141129	−	0.891051i
$687$			13.8197i			0.527253i
$688$	17.0130			0.648615
$689$	−8.78115	+	6.37988i	−0.334535	+	0.243054i
$690$	0.305735	+	1.93033i	0.0116391	+	0.0734865i
$691$	13.6906	−	18.8435i	0.520814	−	0.716839i	−0.464882	−	0.885373i	$-0.653903\pi$
$691$	13.6906	−	18.8435i	0.520814	−	0.716839i	0.985696	+	0.168534i	$0.0539032\pi$
$692$	−30.4993	+	9.90983i	−1.15941	+	0.376715i
$693$	8.94427	+	12.3107i	0.339765	+	0.467646i
$694$	−19.2935	+	37.8656i	−0.732370	+	1.43736i
$695$	0.0857567	−	0.263932i	0.00325294	−	0.0100115i
$696$	1.07859	+	6.80995i	0.0408839	+	0.258131i
$697$	−5.00000	−	1.62460i	−0.189389	−	0.0615361i
$698$	−17.5708	+	8.95277i	−0.665065	+	0.338867i
$699$	8.42075	+	6.11803i	0.318502	+	0.231405i
$700$	−12.0902	+	37.2097i	−0.456965	+	1.40640i
$701$	−2.24671	−	6.91467i	−0.0848571	−	0.261163i	0.899621	−	0.436672i	$-0.143843\pi$
$701$	−2.24671	−	6.91467i	−0.0848571	−	0.261163i	−0.984478	+	0.175509i	$0.943843\pi$
$702$	4.38003	−	27.6544i	0.165314	−	1.04375i
$703$	−3.36771	−	10.3647i	−0.127016	−	0.390914i
$704$	6.83282	−	9.40456i	0.257521	−	0.354448i
$705$	−0.892609	+	1.22857i	−0.0336176	+	0.0462707i
$706$	−3.10639	+	19.6130i	−0.116910	+	0.738144i
$707$			37.8885i			1.42495i
$708$	5.04531			0.189614
$709$	−23.8050	−	32.7647i	−0.894014	−	1.23050i	−0.972338	−	0.233576i	$-0.924957\pi$
$709$	−23.8050	−	32.7647i	−0.894014	−	1.23050i	0.0783247	−	0.996928i	$-0.475043\pi$
$710$	−1.73877	−	3.41254i	−0.0652550	−	0.128070i
$711$	11.2007	+	34.4721i	0.420058	+	1.29281i
$712$	−34.5811	−	34.5811i	−1.29598	−	1.29598i
$713$	1.54508	−	17.0660i	0.0578639	−	0.639127i
$714$	21.1803	+	21.1803i	0.792654	+	0.792654i
$715$	−4.25325	+	1.38197i	−0.159063	+	0.0516826i
$716$	−5.00000	−	1.62460i	−0.186859	−	0.0607141i
$717$	−15.5279	+	11.2817i	−0.579899	+	0.421321i
$718$	−19.7984	+	19.7984i	−0.738869	+	0.738869i
$719$	5.15131			0.192111			0.0960557	−	0.995376i	$-0.469377\pi$
$719$	5.15131			0.192111			0.0960557	+	0.995376i	$0.469377\pi$
$720$	−4.94427	+	3.59222i	−0.184262	+	0.133874i
$721$	−3.11803	−	2.26538i	−0.116122	−	0.0843673i
$722$	1.32739	+	8.38081i	0.0494004	+	0.311902i
$723$	2.12663	−	0.690983i	0.0790901	−	0.0256979i
$724$	4.97980	−	3.61803i	0.185073	−	0.134463i
$725$	14.7361	−	4.78804i	0.547284	−	0.177823i
$726$	−8.13744	+	4.14623i	−0.302009	+	0.153881i
$727$	4.49801	−	6.19098i	0.166822	−	0.229611i	−0.717419	−	0.696642i	$-0.754677\pi$
$727$	4.49801	−	6.19098i	0.166822	−	0.229611i	0.884241	+	0.467031i	$0.154677\pi$
$728$	−27.0873	−	53.1619i	−1.00392	−	1.97031i
$729$	−0.781153	+	2.40414i	−0.0289316	+	0.0890423i
$730$	1.01484	−	0.160734i	0.0375608	−	0.00594904i
$731$	−27.8379	−	9.04508i	−1.02962	−	0.334545i
$732$	−4.47214	−	13.7638i	−0.165295	−	0.508725i
$733$	16.9894	−	12.3435i	0.627516	−	0.455917i	−0.228023	−	0.973656i	$-0.573226\pi$
$733$	16.9894	−	12.3435i	0.627516	−	0.455917i	0.855539	+	0.517739i	$0.173226\pi$
$734$	−2.62064	+	5.14329i	−0.0967295	+	0.189842i
$735$	3.97574	+	2.88854i	0.146647	+	0.106546i
$736$	−2.72353	−	17.1957i	−0.100390	−	0.633840i
$737$	−8.74265	−	12.0332i	−0.322039	−	0.443249i
$738$	1.88854	+	1.88854i	0.0695183	+	0.0695183i
$739$	−0.343027			−0.0126184			−0.00630922	−	0.999980i	$-0.502008\pi$
$739$	−0.343027			−0.0126184			−0.00630922	+	0.999980i	$0.502008\pi$
$740$	2.17963	−	1.58359i	0.0801247	−	0.0582140i
$741$	5.59017	−	17.2048i	0.205360	−	0.632033i
$742$	−5.92798	+	11.6343i	−0.217623	+	0.427109i
$743$	−6.43288			−0.236000			−0.118000	−	0.993014i	$-0.537648\pi$
$743$	−6.43288			−0.236000			−0.118000	+	0.993014i	$0.537648\pi$
$744$	−10.6214	+	4.25401i	−0.389399	+	0.155960i
$745$	6.70820			0.245770
$746$	7.97182	−	15.6456i	0.291869	−	0.572826i
$747$	4.91428	−	15.1246i	0.179804	−	0.553381i
$748$	−16.1803	+	11.7557i	−0.591612	+	0.429831i
$749$	−58.6869			−2.14437
$750$	−4.31877	−	4.31877i	−0.157699	−	0.157699i
$751$	9.75532	+	13.4271i	0.355977	+	0.489960i	0.949022	−	0.315209i	$-0.102075\pi$
$751$	9.75532	+	13.4271i	0.355977	+	0.489960i	−0.593046	+	0.805169i	$0.702075\pi$
$752$	7.95148	−	10.9443i	0.289961	−	0.399097i
$753$	1.38197	+	1.00406i	0.0503616	+	0.0365899i
$754$	−10.7273	+	21.0536i	−0.390666	+	0.766726i
$755$	−7.91872	+	5.75329i	−0.288192	+	0.209384i
$756$	−10.4086	−	32.0344i	−0.378558	−	1.16508i
$757$	−24.4721	−	7.95148i	−0.889455	−	0.289001i	−0.171577	−	0.985171i	$-0.554886\pi$
$757$	−24.4721	−	7.95148i	−0.889455	−	0.289001i	−0.717878	+	0.696169i	$0.754886\pi$
$758$	−38.8769	+	6.15750i	−1.41207	+	0.223651i
$759$	1.00406	−	3.09017i	0.0364450	−	0.112166i
$760$	−7.78768	+	3.96802i	−0.282489	+	0.143935i
$761$	−2.72542	+	3.75123i	−0.0987966	+	0.135982i	−0.855553	−	0.517715i	$-0.826783\pi$
$761$	−2.72542	+	3.75123i	−0.0987966	+	0.135982i	0.756757	+	0.653697i	$0.226783\pi$
$762$	−3.63978	+	1.85456i	−0.131855	+	0.0671836i
$763$	28.9277	−	9.39919i	1.04725	−	0.340273i
$764$	−24.7984	+	18.0171i	−0.897174	+	0.651835i
$765$	10.0000	−	3.24920i	0.361551	−	0.117475i
$766$	7.71182	+	48.6905i	0.278640	+	1.75926i
$767$	13.9883	+	10.1631i	0.505089	+	0.366969i
$768$	−9.40456	+	6.83282i	−0.339358	+	0.246558i
$769$	−23.0902			−0.832653			−0.416326	−	0.909215i	$-0.636683\pi$
$769$	−23.0902			−0.832653			−0.416326	+	0.909215i	$0.636683\pi$
$770$	−3.80423	+	3.80423i	−0.137095	+	0.137095i
$771$	−4.08174	+	2.96556i	−0.147000	+	0.106802i
$772$	28.2542	+	9.18034i	1.01689	+	0.330408i
$773$	41.7320	−	13.5595i	1.50100	−	0.487703i	0.560688	−	0.828027i	$-0.310537\pi$
$773$	41.7320	−	13.5595i	1.50100	−	0.487703i	0.940308	+	0.340324i	$0.110537\pi$
$774$	10.5146	+	10.5146i	0.377940	+	0.377940i
$775$	13.1760	+	22.0795i	0.473297	+	0.793120i
$776$	14.9443	−	14.9443i	0.536468	−	0.536468i
$777$	2.07295	+	6.37988i	0.0743666	+	0.228877i
$778$	−6.14822	−	12.0666i	−0.220424	−	0.432607i
$779$	2.24514	+	3.09017i	0.0804405	+	0.110717i
$780$	4.47214			0.160128
$781$			6.36737i			0.227842i
$782$	−4.68576	+	29.5847i	−0.167563	+	1.05795i
$783$	−7.84070	+	10.7918i	−0.280204	+	0.385667i
$784$	−35.4164	−	25.7315i	−1.26487	−	0.918983i
$785$	−0.180340	−	0.555029i	−0.00643661	−	0.0198098i
$786$	−3.03050	+	19.1338i	−0.108094	+	0.682481i
$787$	−6.76340	−	20.8156i	−0.241089	−	0.741996i	−0.996255	−	0.0864623i	$-0.972444\pi$
$787$	−6.76340	−	20.8156i	−0.241089	−	0.741996i	0.755166	−	0.655534i	$-0.227556\pi$
$788$	11.5187	−	35.4508i	0.410336	−	1.26288i
$789$	−4.93769	−	3.58744i	−0.175787	−	0.127716i
$790$	−11.4182	+	5.81787i	−0.406241	+	0.206990i
$791$	46.5815	+	15.1353i	1.65625	+	0.538148i
$792$	10.0353	−	1.58943i	0.356587	−	0.0564779i
$793$	15.3262	−	47.1693i	0.544251	−	1.67503i
$794$	7.70447	−	15.1209i	0.273422	−	0.536620i
$795$	−0.575274	−	0.791796i	−0.0204028	−	0.0280821i
$796$	29.2705	−	9.51057i	1.03747	−	0.337093i
$797$	20.0000	−	27.5276i	0.708436	−	0.975079i	−0.291393	−	0.956603i	$-0.594119\pi$
$797$	20.0000	−	27.5276i	0.708436	−	0.975079i	0.999829	−	0.0184755i	$-0.00588128\pi$
$798$	−3.40441	−	21.4946i	−0.120515	−	0.760900i
$799$	−18.8294	+	13.6803i	−0.666135	+	0.483976i
$800$	18.4721	+	18.4721i	0.653089	+	0.653089i
$801$		−	42.7445i		−	1.51030i
$802$	−3.08294	+	19.4649i	−0.108862	+	0.687330i
$803$	−1.62460	−	0.527864i	−0.0573308	−	0.0186279i
$804$	4.59628	+	14.1459i	0.162098	+	0.498887i
$805$			8.05748i			0.283989i
$806$	−38.0174	−	9.60097i	−1.33910	−	0.338180i
$807$		−	20.5755i		−	0.724291i
$808$	22.5409	+	11.4852i	0.792985	+	0.404046i
$809$	45.8779	+	14.9066i	1.61298	+	0.524089i	0.970271	−	0.242020i	$-0.0778101\pi$
$809$	45.8779	+	14.9066i	1.61298	+	0.524089i	0.642710	+	0.766110i	$0.277810\pi$
$810$	−3.90877	−	0.619089i	−0.137340	−	0.0217526i
$811$			7.36068i			0.258468i	0.991614	+	0.129234i	$0.0412519\pi$
$811$			7.36068i			0.258468i	−0.991614	+	0.129234i	$0.958748\pi$
$812$			28.4257i			0.997546i
$813$	−5.59017	+	4.06150i	−0.196056	+	0.142443i
$814$	−4.42393	+	0.700682i	−0.155059	+	0.0245589i
$815$	7.24518	−	9.97214i	0.253788	−	0.349309i
$816$	19.0211	−	6.18034i	0.665873	−	0.216355i
$817$	12.5000	+	17.2048i	0.437320	+	0.601919i
$818$	−1.56386	−	0.796824i	−0.0546789	−	0.0278603i
$819$	16.1150	−	49.5967i	0.563102	−	1.73305i
$820$	−0.555029	+	0.763932i	−0.0193825	+	0.0266777i
$821$	−45.4508	−	14.7679i	−1.58625	−	0.515402i	−0.622590	−	0.782549i	$-0.713919\pi$
$821$	−45.4508	−	14.7679i	−1.58625	−	0.515402i	−0.963656	+	0.267146i	$0.913919\pi$
$822$	0.418915	+	0.822168i	0.0146113	+	0.0286764i
$823$	−25.7643	−	18.7188i	−0.898086	−	0.652498i	0.0398873	−	0.999204i	$-0.487300\pi$
$823$	−25.7643	−	18.7188i	−0.898086	−	0.652498i	−0.937974	+	0.346706i	$0.887300\pi$
$824$	−2.29291	+	1.16829i	−0.0798771	+	0.0406994i
$825$	1.50658	+	4.63677i	0.0524523	+	0.161432i
$826$	20.5445	+	3.25392i	0.714833	+	0.113218i
$827$	−6.69015	−	20.5902i	−0.232639	−	0.715990i	−0.997426	−	0.0717065i	$-0.977156\pi$
$827$	−6.69015	−	20.5902i	−0.232639	−	0.715990i	0.764786	−	0.644284i	$-0.222844\pi$
$828$	8.94427	−	12.3107i	0.310835	−	0.427828i
$829$	−16.8328	+	23.1684i	−0.584628	+	0.804671i	−0.994193	−	0.107610i	$-0.965680\pi$
$829$	−16.8328	+	23.1684i	−0.584628	+	0.804671i	0.409565	+	0.912281i	$0.365680\pi$
$830$	5.55332	+	0.879560i	0.192759	+	0.0305300i
$831$			3.61803i			0.125508i
$832$	−39.8384			−1.38115
$833$	44.2705	+	60.9331i	1.53388	+	2.11121i
$834$	0.411084	−	0.209458i	0.0142347	−	0.00725292i
$835$	1.55909	+	4.79837i	0.0539544	+	0.166055i
$836$	14.5309			0.502560
$837$	−20.3500	−	8.71078i	−0.703400	−	0.301089i
$838$	2.18034	−	2.18034i	0.0753186	−	0.0753186i
$839$	−4.75528	+	1.54508i	−0.164171	+	0.0533423i	−0.389949	−	0.920836i	$-0.627507\pi$
$839$	−4.75528	+	1.54508i	−0.164171	+	0.0533423i	0.225779	+	0.974179i	$0.427507\pi$
$840$	4.79360	−	2.44246i	0.165395	−	0.0842730i
$841$	−14.3541	+	10.4289i	−0.494969	+	0.359616i
$842$	−21.5967	−	21.5967i	−0.744273	−	0.744273i
$843$	6.64488			0.228862
$844$	34.6525	−	25.1765i	1.19279	−	0.866611i
$845$	5.89919	+	4.28601i	0.202938	+	0.147443i
$846$	11.6782	−	1.84965i	0.401505	−	0.0635922i
$847$	−35.8096	+	11.6353i	−1.23043	+	0.399792i
$848$	5.12461	+	7.05342i	0.175980	+	0.242216i
$849$	9.73607	−	3.16344i	0.334141	−	0.108569i
$850$	−20.4046	−	40.0463i	−0.699872	−	1.37358i
$851$	−3.94298	+	5.42705i	−0.135164	+	0.186037i
$852$	1.96763	−	6.05573i	0.0674097	−	0.207466i
$853$	−13.4377	+	41.3570i	−0.460098	+	1.41604i	0.404947	+	0.914340i	$0.367290\pi$
$853$	−13.4377	+	41.3570i	−0.460098	+	1.41604i	−0.865044	+	0.501695i	$0.832710\pi$
$854$	−9.33366	−	58.9304i	−0.319391	−	2.01656i
$855$	−7.26543	−	2.36068i	−0.248472	−	0.0807335i
$856$	−17.7898	+	34.9144i	−0.608042	+	1.19335i
$857$	−15.0344	+	10.9232i	−0.513567	+	0.373128i	−0.814175	−	0.580620i	$-0.802810\pi$
$857$	−15.0344	+	10.9232i	−0.513567	+	0.373128i	0.300608	+	0.953748i	$0.402810\pi$
$858$	−6.62460	−	3.37540i	−0.226160	−	0.115234i
$859$	24.3112	+	17.6631i	0.829487	+	0.602658i	0.919414	−	0.393291i	$-0.128663\pi$
$859$	24.3112	+	17.6631i	0.829487	+	0.602658i	−0.0899269	+	0.995948i	$0.528663\pi$
$860$	−3.09017	+	4.25325i	−0.105374	+	0.145035i
$861$	−1.38197	−	1.90211i	−0.0470973	−	0.0648238i
$862$	27.1246	−	27.1246i	0.923868	−	0.923868i
$863$	−32.7194			−1.11378			−0.556891	−	0.830585i	$-0.688006\pi$
$863$	−32.7194			−1.11378			−0.556891	+	0.830585i	$0.688006\pi$
$864$	−22.2133	−	3.51824i	−0.755711	−	0.119693i
$865$	3.06231	−	9.42481i	0.104122	−	0.320453i
$866$	28.4945	+	14.5187i	0.968282	+	0.493364i
$867$	−22.0583			−0.749140
$868$	−45.9937	+	10.4721i	−1.56113	+	0.355447i
$869$	21.3050			0.722721
$870$	−1.89840	−	0.967282i	−0.0643617	−	0.0327939i
$871$	−15.7517	+	48.4787i	−0.533726	+	1.64264i
$872$	3.17704	−	20.0590i	0.107588	−	0.679284i
$873$	18.4721			0.625187
$874$	15.3884	−	15.3884i	0.520521	−	0.520521i
$875$	−14.8006	−	20.3713i	−0.500353	−	0.688676i
$876$	1.38197	+	1.00406i	0.0466923	+	0.0339239i
$877$	−17.4721	−	12.6942i	−0.589992	−	0.428654i	0.252320	−	0.967644i	$-0.418806\pi$
$877$	−17.4721	−	12.6942i	−0.589992	−	0.428654i	−0.842313	+	0.538989i	$0.818806\pi$
$878$	16.9759	+	8.64964i	0.572908	+	0.291911i
$879$	−6.91467	+	5.02380i	−0.233226	+	0.169449i
$880$	1.11006	+	3.41641i	0.0374201	+	0.115167i
$881$	4.30902	+	1.40008i	0.145174	+	0.0471700i	0.380703	−	0.924697i	$-0.375682\pi$
$881$	4.30902	+	1.40008i	0.145174	+	0.0471700i	−0.235528	+	0.971867i	$0.575682\pi$
$882$	−5.98559	−	37.7915i	−0.201545	−	1.27251i
$883$	11.1477	−	34.3090i	0.375149	−	1.15459i	−0.568229	−	0.822871i	$-0.692371\pi$
$883$	11.1477	−	34.3090i	0.375149	−	1.15459i	0.943378	−	0.331720i	$-0.107629\pi$
$884$	65.1864	+	21.1803i	2.19246	+	0.712372i
$885$	−0.916408	+	1.26133i	−0.0308047	+	0.0423991i
$886$	−19.9832	−	39.2193i	−0.671350	−	1.31760i
$887$	53.3449	−	17.3328i	1.79115	−	0.581979i	0.791571	−	0.611078i	$-0.209264\pi$
$887$	53.3449	−	17.3328i	1.79115	−	0.581979i	0.999577	+	0.0290987i	$0.00926371\pi$
$888$	4.42393	+	0.700682i	0.148457	+	0.0235133i
$889$	−16.0172	+	5.20431i	−0.537200	+	0.174547i
$890$	14.9264	−	2.36411i	0.500335	−	0.0792452i
$891$	5.32282	+	3.86726i	0.178321	+	0.129558i
$892$	10.8541	+	14.9394i	0.363422	+	0.500208i
$893$	16.9098			0.565866
$894$	7.88597	+	7.88597i	0.263746	+	0.263746i
$895$	1.31433	−	0.954915i	0.0439331	−	0.0319193i
$896$	−42.7021	+	21.7578i	−1.42658	+	0.726877i
$897$	−10.5902	+	3.44095i	−0.353595	+	0.114890i
$898$	−36.3772	+	36.3772i	−1.21392	+	1.21392i
$899$	14.0616	+	12.2984i	0.468980	+	0.410174i
$900$			22.8328i			0.761094i
$901$	−4.63525	−	14.2658i	−0.154423	−	0.475264i
$902$	1.39875	−	0.712701i	0.0465734	−	0.0237304i
$903$	−7.69421	−	10.5902i	−0.256047	−	0.352419i
$904$	23.1246	−	23.1246i	0.769113	−	0.769113i
$905$			1.90211i			0.0632284i
$906$	−16.0724	−	2.54562i	−0.533970	−	0.0845726i
$907$	−15.0579	+	20.7254i	−0.499989	+	0.688176i	−0.982191	−	0.187884i	$-0.939837\pi$
$907$	−15.0579	+	20.7254i	−0.499989	+	0.688176i	0.482202	+	0.876060i	$0.339837\pi$
$908$	2.90983	+	2.11412i	0.0965661	+	0.0701594i
$909$	6.83282	+	21.0292i	0.226630	+	0.697496i
$910$	18.2105	+	2.88426i	0.603672	+	0.0956123i
$911$	4.14725	+	12.7639i	0.137405	+	0.422888i	0.995956	−	0.0898391i	$-0.0286353\pi$
$911$	4.14725	+	12.7639i	0.137405	+	0.422888i	−0.858552	+	0.512727i	$0.828635\pi$
$912$	−13.8197	−	4.49028i	−0.457615	−	0.148688i
$913$	−7.56231	−	5.49434i	−0.250276	−	0.181836i
$914$	7.83592	+	15.3789i	0.259189	+	0.508688i
$915$	4.25325	+	1.38197i	0.140608	+	0.0456864i
$916$	30.7768	+	22.3607i	1.01690	+	0.738818i
$917$	−24.6803	+	75.9583i	−0.815017	+	2.50836i
$918$	34.4765	+	17.5666i	1.13789	+	0.579785i
$919$	17.3233	+	23.8435i	0.571443	+	0.786523i	0.992725	−	0.120406i	$-0.0384198\pi$
$919$	17.3233	+	23.8435i	0.571443	+	0.786523i	−0.421282	+	0.906930i	$0.638420\pi$
$920$	4.79360	+	2.44246i	0.158040	+	0.0805256i
$921$	13.3303	−	18.3476i	0.439248	−	0.604574i
$922$	56.8092	−	8.99770i	1.87091	−	0.296323i
$923$	17.6538	−	12.8262i	0.581082	−	0.422181i
$924$	−8.94427			−0.294245
$925$		−	10.0656i		−	0.330955i
$926$	−8.11869	−	1.28587i	−0.266797	−	0.0422564i
$927$	−2.13914	−	0.695048i	−0.0702585	−	0.0228284i
$928$	16.9112	+	8.61668i	0.555137	+	0.282856i
$929$		−	6.11488i		−	0.200623i	−0.994956	−	0.100311i	$-0.968016\pi$
$929$		−	6.11488i		−	0.200623i	0.994956	−	0.100311i	$-0.0319839\pi$
$930$	0.865718	−	3.42802i	0.0283880	−	0.112409i
$931$		−	54.7214i		−	1.79342i
$932$	27.2501	−	8.85410i	0.892607	−	0.290026i
$933$	8.81966	+	2.86568i	0.288743	+	0.0938182i
$934$	−5.61059	+	35.4239i	−0.183584	+	1.15910i
$935$		−	6.18034i		−	0.202119i
$936$	−24.6215	−	24.6215i	−0.804778	−	0.804778i
$937$	15.8435	−	11.5109i	0.517583	−	0.376046i	−0.298109	−	0.954532i	$-0.596356\pi$
$937$	15.8435	−	11.5109i	0.517583	−	0.376046i	0.815693	+	0.578485i	$0.196356\pi$
$938$	9.59276	+	60.5663i	0.313215	+	1.97756i
$939$	3.48622	−	4.79837i	0.113769	−	0.156589i
$940$	1.29180	+	3.97574i	0.0421337	+	0.129674i
$941$	15.8541	+	21.8213i	0.516829	+	0.711354i	0.985052	−	0.172256i	$-0.0551057\pi$
$941$	15.8541	+	21.8213i	0.516829	+	0.711354i	−0.468223	+	0.883610i	$0.655106\pi$
$942$	0.440474	−	0.864478i	0.0143514	−	0.0281662i
$943$	0.726543	−	2.23607i	0.0236595	−	0.0728164i
$944$	8.16348	−	11.2361i	0.265699	−	0.365703i
$945$	9.89919	+	3.21644i	0.322021	+	0.104631i
$946$	7.78768	−	3.96802i	0.253199	−	0.129012i
$947$	−9.40456	−	6.83282i	−0.305607	−	0.222037i	0.424402	−	0.905474i	$-0.360484\pi$
$947$	−9.40456	−	6.83282i	−0.305607	−	0.222037i	−0.730009	+	0.683437i	$0.760484\pi$
$948$	−20.2622	−	6.58359i	−0.658086	−	0.213825i
$949$	1.80902	+	5.56758i	0.0587232	+	0.180731i
$950$	−5.10828	+	32.2524i	−0.165734	+	1.04641i
$951$	2.84066	+	8.74265i	0.0921146	+	0.283500i
$952$	81.4398	−	12.8988i	2.63948	−	0.418053i
$953$	−9.73607	+	13.4005i	−0.315382	+	0.434086i	−0.937050	−	0.349194i	$-0.886455\pi$
$953$	−9.73607	+	13.4005i	−0.315382	+	0.434086i	0.621668	+	0.783281i	$0.286455\pi$
$954$	−1.19207	+	7.52644i	−0.0385947	+	0.243677i
$955$		−	9.47214i		−	0.306511i
$956$			52.8352i			1.70881i
$957$	2.08204	+	2.86568i	0.0673028	+	0.0926343i
$958$	11.4409	+	22.4541i	0.369640	+	0.725458i
$959$	1.17557	+	3.61803i	0.0379612	+	0.116832i
$960$		−	3.59222i		−	0.115939i
$961$	−14.7188	+	27.2829i	−0.474802	+	0.880093i
$962$	10.8541	+	10.8541i	0.349950	+	0.349950i
$963$	−32.5729	+	10.5836i	−1.04965	+	0.341051i
$964$	1.90211	−	5.85410i	0.0612629	−	0.188548i
$965$	−7.42705	+	5.39607i	−0.239085	+	0.173706i
$966$	−9.47214	+	9.47214i	−0.304761	+	0.304761i
$967$	−18.0826			−0.581497			−0.290748	−	0.956800i	$-0.593904\pi$
$967$	−18.0826			−0.581497			−0.290748	+	0.956800i	$0.593904\pi$
$968$	−3.93286	+	24.8311i	−0.126407	+	0.798101i
$969$	20.2254	+	14.6946i	0.649734	+	0.472060i
$970$	1.02166	+	6.45048i	0.0328034	+	0.207112i
$971$	−40.4792	+	13.1525i	−1.29904	+	0.422083i	−0.875247	−	0.483677i	$-0.839301\pi$
$971$	−40.4792	+	13.1525i	−1.29904	+	0.422083i	−0.423791	+	0.905760i	$0.639301\pi$
$972$	−17.8885	−	24.6215i	−0.573775	−	0.789734i
$973$	1.80902	−	0.587785i	0.0579944	−	0.0188435i
$974$	−8.53814	+	4.35040i	−0.273580	+	0.139396i
$975$	9.82084	−	13.5172i	0.314518	−	0.432898i
$976$	−37.8885	−	12.3107i	−1.21278	−	0.394057i
$977$	2.47214	−	7.60845i	0.0790906	−	0.243416i	−0.903691	−	0.428184i	$-0.859153\pi$
$977$	2.47214	−	7.60845i	0.0790906	−	0.243416i	0.982782	+	0.184768i	$0.0591534\pi$
$978$	20.2402	−	3.20573i	0.647209	−	0.102508i
$979$	−23.8949	−	7.76393i	−0.763685	−	0.248136i
$980$	12.8658	−	4.18034i	0.410982	−	0.133536i
$981$	14.3607	−	10.4336i	0.458501	−	0.333121i
$982$	21.2695	−	41.7437i	0.678736	−	1.33209i
$983$	−25.1235	−	18.2533i	−0.801315	−	0.582190i	0.109985	−	0.993933i	$-0.464920\pi$
$983$	−25.1235	−	18.2533i	−0.801315	−	0.582190i	−0.911300	+	0.411744i	$0.864920\pi$
$984$	−1.55053	+	0.245580i	−0.0494291	+	0.00782881i
$985$	6.77051	+	9.31881i	0.215726	+	0.296922i
$986$	−23.0902	−	23.0902i	−0.735341	−	0.735341i
$987$	−10.4086			−0.331310
$988$	−29.2705	−	40.2874i	−0.931219	−	1.28171i
$989$	4.04508	−	12.4495i	0.128626	−	0.395871i
$990$	−1.42540	+	2.79751i	−0.0453023	+	0.0889107i
$991$	−20.9232			−0.664649			−0.332324	−	0.943165i	$-0.607833\pi$
$991$	−20.9232			−0.664649			−0.332324	+	0.943165i	$0.607833\pi$
$992$	−7.71193	+	30.5373i	−0.244854	+	0.969560i
$993$	−20.9787			−0.665739
$994$	11.9177	−	23.3899i	0.378008	−	0.741882i
$995$	−2.93893	+	9.04508i	−0.0931702	+	0.286748i
$996$	5.49434	+	7.56231i	0.174095	+	0.239621i
$997$	−48.5279			−1.53689			−0.768446	−	0.639914i	$-0.778970\pi$
$997$	−48.5279			−1.53689			−0.768446	+	0.639914i	$0.778970\pi$
$998$	−3.01217	−	3.01217i	−0.0953486	−	0.0953486i
$999$	5.09353	+	7.01064i	0.161152	+	0.221807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.j.a.27.1	yes	8
4.3	odd	2	inner	124.2.j.a.27.2	yes	8
31.23	odd	10	inner	124.2.j.a.23.2	yes	8
124.23	even	10	inner	124.2.j.a.23.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.j.a.23.1	✓	8	124.23	even	10	inner
124.2.j.a.23.2	yes	8	31.23	odd	10	inner
124.2.j.a.27.1	yes	8	1.1	even	1	trivial
124.2.j.a.27.2	yes	8	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 + 1.26007i) q^{2} +(0.224514 - 0.690983i) q^{3} +(-1.17557 - 1.61803i) q^{4} +0.618034 q^{5} +(0.726543 + 0.726543i) q^{6} +(2.48990 + 3.42705i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.00000 + 1.45309i) q^{9} +O(q^{10})\)	\(q+(-0.642040 + 1.26007i) q^{2} +(0.224514 - 0.690983i) q^{3} +(-1.17557 - 1.61803i) q^{4} +0.618034 q^{5} +(0.726543 + 0.726543i) q^{6} +(2.48990 + 3.42705i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.00000 + 1.45309i) q^{9} +(-0.396802 + 0.778768i) q^{10} +(1.17557 - 0.854102i) q^{11} +(-1.38197 + 0.449028i) q^{12} +(-4.73607 - 1.53884i) q^{13} +(-5.91695 + 0.937153i) q^{14} +(0.138757 - 0.427051i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(4.04508 - 5.56758i) q^{17} +(-3.11507 + 1.58721i) q^{18} +(-4.75528 + 1.54508i) q^{19} +(-0.726543 - 1.00000i) q^{20} +(2.92705 - 0.951057i) q^{21} +(0.321469 + 2.02967i) q^{22} +(2.48990 + 1.80902i) q^{23} +(0.321469 - 2.02967i) q^{24} -4.61803 q^{25} +(4.97980 - 4.97980i) q^{26} +(3.21644 - 2.33688i) q^{27} +(2.61803 - 8.05748i) q^{28} +(-3.19098 + 1.03681i) q^{29} +(0.449028 + 0.449028i) q^{30} +(-2.85317 - 4.78115i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.326238 - 1.00406i) q^{33} +(4.41846 + 8.67171i) q^{34} +(1.53884 + 2.11803i) q^{35} -4.94427i q^{36} +2.17963i q^{37} +(1.10616 - 6.98401i) q^{38} +(-2.12663 + 2.92705i) q^{39} +(1.72654 - 0.273457i) q^{40} +(-0.236068 - 0.726543i) q^{41} +(-0.680881 + 4.29892i) q^{42} +(-1.31433 - 4.04508i) q^{43} +(-2.76393 - 0.898056i) q^{44} +(1.23607 + 0.898056i) q^{45} +(-3.87811 + 1.97599i) q^{46} +(-3.21644 - 1.04508i) q^{47} +(2.35114 + 1.70820i) q^{48} +(-3.38197 + 10.4086i) q^{49} +(2.96496 - 5.81906i) q^{50} +(-2.93893 - 4.04508i) q^{51} +(3.07768 + 9.47214i) q^{52} +(1.28115 - 1.76336i) q^{53} +(0.879560 + 5.55332i) q^{54} +(0.726543 - 0.527864i) q^{55} +(8.47214 + 8.47214i) q^{56} +3.63271i q^{57} +(0.742276 - 4.68655i) q^{58} +(-3.30220 - 1.07295i) q^{59} +(-0.854102 + 0.277515i) q^{60} +9.95959i q^{61} +(7.85645 - 0.525514i) q^{62} +10.4721i q^{63} +(7.60845 - 2.47214i) q^{64} +(-2.92705 - 0.951057i) q^{65} +(1.47464 + 0.233561i) q^{66} -10.2361i q^{67} -13.7638 q^{68} +(1.80902 - 1.31433i) q^{69} +(-3.65688 + 0.579192i) q^{70} +(-2.57565 + 3.54508i) q^{71} +(6.23015 + 3.17442i) q^{72} +(-0.690983 - 0.951057i) q^{73} +(-2.74649 - 1.39941i) q^{74} +(-1.03681 + 3.19098i) q^{75} +(8.09017 + 5.87785i) q^{76} +(5.85410 + 1.90211i) q^{77} +(-2.32292 - 4.55899i) q^{78} +(11.8617 + 8.61803i) q^{79} +(-0.763932 + 2.35114i) q^{80} +(1.39919 + 4.30625i) q^{81} +(1.06706 + 0.169006i) q^{82} +(-1.98787 - 6.11803i) q^{83} +(-4.97980 - 3.61803i) q^{84} +(2.50000 - 3.44095i) q^{85} +(5.94095 + 0.940955i) q^{86} +2.43769i q^{87} +(2.90617 - 2.90617i) q^{88} +(-10.1631 - 13.9883i) q^{89} +(-1.92522 + 0.980949i) q^{90} +(-6.51864 - 20.0623i) q^{91} -6.15537i q^{92} +(-3.94427 + 0.898056i) q^{93} +(3.38197 - 3.38197i) q^{94} +(-2.93893 + 0.954915i) q^{95} +(-3.66199 + 1.86588i) q^{96} +(6.04508 - 4.39201i) q^{97} +(-10.9443 - 10.9443i) q^{98} +3.59222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9	\( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9 + 6 * q^10 - 20 * q^12 - 20 * q^13 - 14 * q^14 + 8 * q^16 + 10 * q^17 - 24 * q^18 + 10 * q^21 + 20 * q^22 + 20 * q^24 - 28 * q^25 + 12 * q^28 - 30 * q^29 - 32 * q^32 + 60 * q^33 + 30 * q^34 + 10 * q^38 + 8 * q^40 + 16 * q^41 + 10 * q^42 - 40 * q^44 - 8 * q^45 - 10 * q^46 - 36 * q^49 + 2 * q^50 - 30 * q^53 - 50 * q^54 + 32 * q^56 + 20 * q^58 + 20 * q^60 + 38 * q^62 - 10 * q^65 - 20 * q^66 + 10 * q^69 - 8 * q^70 + 48 * q^72 - 10 * q^73 - 30 * q^74 + 20 * q^76 + 20 * q^77 - 24 * q^80 - 38 * q^81 - 4 * q^82 + 20 * q^85 + 20 * q^86 - 50 * q^89 + 32 * q^90 + 40 * q^93 + 36 * q^94 - 40 * q^96 + 26 * q^97 - 16 * q^98

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