LMFDB - Embedded newform 150.2.h.a.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (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:	$1.19775603032$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			79.2
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	150.79
Dual form			150.2.h.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.809017 - 0.587785i) q^{6} +2.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.809017 - 0.587785i) q^{6} +2.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.530249 - 2.17229i) q^{10} +(0.160734 - 0.494689i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-2.07919 + 0.675571i) q^{13} +(-0.642040 + 1.97599i) q^{14} +(-1.90211 - 1.17557i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58450 + 2.18088i) q^{17} -1.00000i q^{18} +(-5.55899 + 4.03884i) q^{19} +(1.17557 - 1.90211i) q^{20} +(1.68088 + 1.22123i) q^{21} +(0.305735 - 0.420808i) q^{22} +(3.67171 + 1.19301i) q^{23} +1.00000 q^{24} +(-4.94424 + 0.744661i) q^{25} -2.18619 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-1.22123 + 1.68088i) q^{28} +(-7.30844 - 5.30989i) q^{29} +(-1.44575 - 1.70582i) q^{30} +(5.99083 - 4.35259i) q^{31} +1.00000i q^{32} +(-0.305735 - 0.420808i) q^{33} +(0.833023 + 2.56378i) q^{34} +(4.63287 - 0.346926i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-5.04743 + 1.64001i) q^{37} +(-6.53498 + 2.12334i) q^{38} +(-0.675571 + 2.07919i) q^{39} +(1.70582 - 1.44575i) q^{40} +(-0.996141 - 3.06581i) q^{41} +(1.22123 + 1.68088i) q^{42} +9.53920i q^{43} +(0.420808 - 0.305735i) q^{44} +(-2.06909 + 0.847859i) q^{45} +(3.12334 + 2.26924i) q^{46} +(5.44627 - 7.49614i) q^{47} +(0.951057 + 0.309017i) q^{48} +2.68323 q^{49} +(-4.93236 - 0.819639i) q^{50} +2.69572 q^{51} +(-2.07919 - 0.675571i) q^{52} +(-1.43326 + 1.97271i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.12991 - 0.275807i) q^{55} +(-1.68088 + 1.22123i) q^{56} +6.87129i q^{57} +(-5.30989 - 7.30844i) q^{58} +(-2.67261 - 8.22545i) q^{59} +(-0.847859 - 2.06909i) q^{60} +(3.88998 - 11.9721i) q^{61} +(7.04264 - 2.28829i) q^{62} +(1.97599 - 0.642040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.85358 + 4.52343i) q^{65} +(-0.160734 - 0.494689i) q^{66} +(3.93455 + 5.41544i) q^{67} +2.69572i q^{68} +(3.12334 - 2.26924i) q^{69} +(4.51333 + 1.10169i) q^{70} +(6.60886 + 4.80162i) q^{71} +(0.587785 - 0.809017i) q^{72} +(3.65537 + 1.18770i) q^{73} -5.30719 q^{74} +(-2.30371 + 4.43767i) q^{75} -6.87129 q^{76} +(1.02781 + 0.333955i) q^{77} +(-1.28501 + 1.76867i) q^{78} +(2.84162 + 2.06455i) q^{79} +(2.06909 - 0.847859i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.22358i q^{82} +(7.71827 + 10.6233i) q^{83} +(0.642040 + 1.97599i) q^{84} +(4.59841 - 3.89732i) q^{85} +(-2.94777 + 9.07232i) q^{86} +(-8.59159 + 2.79158i) q^{87} +(0.494689 - 0.160734i) q^{88} +(3.04654 - 9.37628i) q^{89} +(-2.22982 + 0.166977i) q^{90} +(-1.40362 - 4.31990i) q^{91} +(2.26924 + 3.12334i) q^{92} -7.40507i q^{93} +(7.49614 - 5.44627i) q^{94} +(9.93414 + 11.7212i) q^{95} +(0.809017 + 0.587785i) q^{96} +(6.32443 - 8.70483i) q^{97} +(2.55190 + 0.829164i) q^{98} -0.520147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.166977	−	2.22982i	−0.0746746	−	0.997208i
$5$	−0.166977	−	2.22982i	−0.0746746	−	0.997208i
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$			2.07768i			0.785291i	0.919690	+	0.392645i	$0.128440\pi$
$7$			2.07768i			0.785291i	−0.919690	+	0.392645i	$0.871560\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	0.530249	−	2.17229i	0.167679	−	0.686938i
$11$	0.160734	−	0.494689i	0.0484632	−	0.149154i	−0.923896	−	0.382643i	$-0.875014\pi$
$11$	0.160734	−	0.494689i	0.0484632	−	0.149154i	0.972360	+	0.233488i	$0.0750140\pi$
$12$	0.951057	−	0.309017i	0.274546	−	0.0892055i
$13$	−2.07919	+	0.675571i	−0.576664	+	0.187370i	−0.582806	−	0.812612i	$-0.698045\pi$
$13$	−2.07919	+	0.675571i	−0.576664	+	0.187370i	0.00614146	+	0.999981i	$0.498045\pi$
$14$	−0.642040	+	1.97599i	−0.171592	+	0.528107i
$15$	−1.90211	−	1.17557i	−0.491123	−	0.303531i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.58450	+	2.18088i	0.384298	+	0.528941i	0.956717	−	0.291020i	$-0.0939947\pi$
$17$	1.58450	+	2.18088i	0.384298	+	0.528941i	−0.572418	+	0.819962i	$0.693995\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.55899	+	4.03884i	−1.27532	+	0.926574i	−0.999401	−	0.0346072i	$-0.988982\pi$
$19$	−5.55899	+	4.03884i	−1.27532	+	0.926574i	−0.275919	+	0.961181i	$0.588982\pi$
$20$	1.17557	−	1.90211i	0.262866	−	0.425325i
$21$	1.68088	+	1.22123i	0.366798	+	0.266495i
$22$	0.305735	−	0.420808i	0.0651829	−	0.0897165i
$23$	3.67171	+	1.19301i	0.765605	+	0.248760i	0.665682	−	0.746235i	$-0.268141\pi$
$23$	3.67171	+	1.19301i	0.765605	+	0.248760i	0.0999224	+	0.994995i	$0.468141\pi$
$24$	1.00000			0.204124
$25$	−4.94424	+	0.744661i	−0.988847	+	0.148932i
$26$	−2.18619			−0.428748
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−1.22123	+	1.68088i	−0.230791	+	0.317657i
$29$	−7.30844	−	5.30989i	−1.35714	−	0.986022i	−0.998621	−	0.0525013i	$-0.983281\pi$
$29$	−7.30844	−	5.30989i	−1.35714	−	0.986022i	−0.358523	−	0.933521i	$-0.616719\pi$
$30$	−1.44575	−	1.70582i	−0.263956	−	0.311439i
$31$	5.99083	−	4.35259i	1.07598	−	0.781749i	0.0990065	−	0.995087i	$-0.468434\pi$
$31$	5.99083	−	4.35259i	1.07598	−	0.781749i	0.976978	+	0.213338i	$0.0684335\pi$
$32$			1.00000i			0.176777i
$33$	−0.305735	−	0.420808i	−0.0532216	−	0.0732532i
$34$	0.833023	+	2.56378i	0.142862	+	0.439685i
$35$	4.63287	−	0.346926i	0.783098	−	0.0586413i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−5.04743	+	1.64001i	−0.829793	+	0.269616i	−0.692958	−	0.720978i	$-0.743693\pi$
$37$	−5.04743	+	1.64001i	−0.829793	+	0.269616i	−0.136835	+	0.990594i	$0.543693\pi$
$38$	−6.53498	+	2.12334i	−1.06011	+	0.344452i
$39$	−0.675571	+	2.07919i	−0.108178	+	0.332937i
$40$	1.70582	−	1.44575i	0.269714	−	0.228592i
$41$	−0.996141	−	3.06581i	−0.155571	−	0.478799i	0.842647	−	0.538466i	$-0.180996\pi$
$41$	−0.996141	−	3.06581i	−0.155571	−	0.478799i	−0.998218	+	0.0596673i	$0.980996\pi$
$42$	1.22123	+	1.68088i	0.188440	+	0.259366i
$43$			9.53920i			1.45471i	0.686259	+	0.727357i	$0.259252\pi$
$43$			9.53920i			1.45471i	−0.686259	+	0.727357i	$0.740748\pi$
$44$	0.420808	−	0.305735i	0.0634392	−	0.0460912i
$45$	−2.06909	+	0.847859i	−0.308442	+	0.126391i
$46$	3.12334	+	2.26924i	0.460512	+	0.334582i
$47$	5.44627	−	7.49614i	0.794419	−	1.09342i	−0.199124	−	0.979974i	$-0.563810\pi$
$47$	5.44627	−	7.49614i	0.794419	−	1.09342i	0.993544	−	0.113450i	$-0.0361903\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	2.68323			0.383319
$50$	−4.93236	−	0.819639i	−0.697541	−	0.115914i
$51$	2.69572			0.377476
$52$	−2.07919	−	0.675571i	−0.288332	−	0.0936848i
$53$	−1.43326	+	1.97271i	−0.196873	+	0.270973i	−0.896028	−	0.443998i	$-0.853560\pi$
$53$	−1.43326	+	1.97271i	−0.196873	+	0.270973i	0.699155	+	0.714970i	$0.253560\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−1.12991	−	0.275807i	−0.152357	−	0.0371898i
$56$	−1.68088	+	1.22123i	−0.224617	+	0.163194i
$57$			6.87129i			0.910124i
$58$	−5.30989	−	7.30844i	−0.697223	−	0.959645i
$59$	−2.67261	−	8.22545i	−0.347944	−	1.07086i	−0.959989	−	0.280039i	$-0.909653\pi$
$59$	−2.67261	−	8.22545i	−0.347944	−	1.07086i	0.612045	−	0.790823i	$-0.290347\pi$
$60$	−0.847859	−	2.06909i	−0.109458	−	0.267118i
$61$	3.88998	−	11.9721i	0.498061	−	1.53287i	−0.314070	−	0.949400i	$-0.601693\pi$
$61$	3.88998	−	11.9721i	0.498061	−	1.53287i	0.812131	−	0.583475i	$-0.198307\pi$
$62$	7.04264	−	2.28829i	0.894417	−	0.290614i
$63$	1.97599	−	0.642040i	0.248952	−	0.0808894i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.85358	+	4.52343i	0.229909	+	0.561062i
$66$	−0.160734	−	0.494689i	−0.0197850	−	0.0608920i
$67$	3.93455	+	5.41544i	0.480682	+	0.661601i	0.978636	−	0.205602i	$-0.0659152\pi$
$67$	3.93455	+	5.41544i	0.480682	+	0.661601i	−0.497954	+	0.867203i	$0.665915\pi$
$68$			2.69572i			0.326904i
$69$	3.12334	−	2.26924i	0.376007	−	0.273185i
$70$	4.51333	+	1.10169i	0.539446	+	0.131677i
$71$	6.60886	+	4.80162i	0.784328	+	0.569848i	0.906275	−	0.422689i	$-0.138914\pi$
$71$	6.60886	+	4.80162i	0.784328	+	0.569848i	−0.121947	+	0.992537i	$0.538914\pi$
$72$	0.587785	−	0.809017i	0.0692712	−	0.0953436i
$73$	3.65537	+	1.18770i	0.427828	+	0.139010i	0.515013	−	0.857182i	$-0.327787\pi$
$73$	3.65537	+	1.18770i	0.427828	+	0.139010i	−0.0871848	+	0.996192i	$0.527787\pi$
$74$	−5.30719			−0.616948
$75$	−2.30371	+	4.43767i	−0.266009	+	0.512418i
$76$	−6.87129			−0.788191
$77$	1.02781	+	0.333955i	0.117130	+	0.0380577i
$78$	−1.28501	+	1.76867i	−0.145499	+	0.200262i
$79$	2.84162	+	2.06455i	0.319707	+	0.232281i	0.736050	−	0.676927i	$-0.236689\pi$
$79$	2.84162	+	2.06455i	0.319707	+	0.232281i	−0.416344	+	0.909207i	$0.636689\pi$
$80$	2.06909	−	0.847859i	0.231331	−	0.0947935i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		−	3.22358i		−	0.355985i
$83$	7.71827	+	10.6233i	0.847190	+	1.16606i	0.984475	+	0.175526i	$0.0561625\pi$
$83$	7.71827	+	10.6233i	0.847190	+	1.16606i	−0.137285	+	0.990532i	$0.543837\pi$
$84$	0.642040	+	1.97599i	0.0700523	+	0.215599i
$85$	4.59841	−	3.89732i	0.498767	−	0.422724i
$86$	−2.94777	+	9.07232i	−0.317867	+	0.978293i
$87$	−8.59159	+	2.79158i	−0.921115	+	0.299288i
$88$	0.494689	−	0.160734i	0.0527340	−	0.0171343i
$89$	3.04654	−	9.37628i	0.322932	−	0.993883i	−0.649433	−	0.760419i	$-0.724994\pi$
$89$	3.04654	−	9.37628i	0.322932	−	0.993883i	0.972365	−	0.233465i	$-0.0750063\pi$
$90$	−2.22982	+	0.166977i	−0.235044	+	0.0176010i
$91$	−1.40362	−	4.31990i	−0.147140	−	0.452849i
$92$	2.26924	+	3.12334i	0.236585	+	0.325631i
$93$		−	7.40507i		−	0.767870i
$94$	7.49614	−	5.44627i	0.773168	−	0.561739i
$95$	9.93414	+	11.7212i	1.01922	+	1.20257i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	6.32443	−	8.70483i	0.642149	−	0.883842i	−0.356579	−	0.934265i	$-0.616057\pi$
$97$	6.32443	−	8.70483i	0.642149	−	0.883842i	0.998728	+	0.0504234i	$0.0160571\pi$
$98$	2.55190	+	0.829164i	0.257781	+	0.0837582i
$99$	−0.520147			−0.0522767
$100$	−4.43767	−	2.30371i	−0.443767	−	0.230371i
$101$	−17.6400			−1.75524			−0.877622	−	0.479353i	$-0.840871\pi$
$101$	−17.6400			−1.75524			−0.877622	+	0.479353i	$0.840871\pi$
$102$	2.56378	+	0.833023i	0.253852	+	0.0824815i
$103$	5.11231	−	7.03649i	0.503731	−	0.693326i	−0.479116	−	0.877752i	$-0.659043\pi$
$103$	5.11231	−	7.03649i	0.503731	−	0.693326i	0.982846	+	0.184426i	$0.0590425\pi$
$104$	−1.76867	−	1.28501i	−0.173432	−	0.126006i
$105$	2.44246	−	3.95199i	0.238360	−	0.385675i
$106$	−1.97271	+	1.43326i	−0.191607	+	0.139210i
$107$		−	5.40977i		−	0.522983i	−0.965206	−	0.261491i	$-0.915786\pi$
$107$		−	5.40977i		−	0.522983i	0.965206	−	0.261491i	$-0.0842143\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	−0.891135	−	2.74263i	−0.0853553	−	0.262697i	0.899265	−	0.437404i	$-0.144102\pi$
$109$	−0.891135	−	2.74263i	−0.0853553	−	0.262697i	−0.984620	+	0.174707i	$0.944102\pi$
$110$	−0.989378	−	0.611469i	−0.0943335	−	0.0583013i
$111$	−1.64001	+	5.04743i	−0.155663	+	0.479081i
$112$	−1.97599	+	0.642040i	−0.186714	+	0.0606670i
$113$	−6.05780	+	1.96830i	−0.569870	+	0.185162i	−0.579757	−	0.814789i	$-0.696853\pi$
$113$	−6.05780	+	1.96830i	−0.569870	+	0.185162i	0.00988741	+	0.999951i	$0.496853\pi$
$114$	−2.12334	+	6.53498i	−0.198869	+	0.612057i
$115$	2.04711	−	8.38648i	0.190894	−	0.782043i
$116$	−2.79158	−	8.59159i	−0.259191	−	0.797709i
$117$	1.28501	+	1.76867i	0.118799	+	0.163513i
$118$		−	8.64875i		−	0.796182i
$119$	−4.53118	+	3.29210i	−0.415373	+	0.301786i
$120$	−0.166977	−	2.22982i	−0.0152429	−	0.203554i
$121$	8.68031	+	6.30661i	0.789119	+	0.573328i
$122$	7.39919	−	10.1841i	0.669891	−	0.922026i
$123$	−3.06581	−	0.996141i	−0.276435	−	0.0898191i
$124$	7.40507			0.664995
$125$	2.48604	+	10.9004i	0.222358	+	0.974965i
$126$	2.07768			0.185095
$127$	−14.2348	−	4.62515i	−1.26313	−	0.410416i	−0.400522	−	0.916287i	$-0.631171\pi$
$127$	−14.2348	−	4.62515i	−1.26313	−	0.410416i	−0.862609	+	0.505871i	$0.831171\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	7.71737	+	5.60700i	0.679477	+	0.493669i
$130$	0.365045	+	4.87483i	0.0320165	+	0.427550i
$131$	−11.2090	+	8.14385i	−0.979339	+	0.711531i	−0.957561	−	0.288232i	$-0.906933\pi$
$131$	−11.2090	+	8.14385i	−0.979339	+	0.711531i	−0.0217781	+	0.999763i	$0.506933\pi$
$132$		−	0.520147i		−	0.0452730i
$133$	−8.39144	−	11.5498i	−0.727630	−	1.00150i
$134$	2.06851	+	6.36623i	0.178692	+	0.549959i
$135$	−0.530249	+	2.17229i	−0.0456365	+	0.186961i
$136$	−0.833023	+	2.56378i	−0.0714311	+	0.219842i
$137$	−18.9202	+	6.14755i	−1.61646	+	0.525221i	−0.971103	−	0.238659i	$-0.923292\pi$
$137$	−18.9202	+	6.14755i	−1.61646	+	0.525221i	−0.645359	+	0.763879i	$0.723292\pi$
$138$	3.67171	−	1.19301i	0.312557	−	0.101556i
$139$	−1.74398	+	5.36743i	−0.147923	+	0.455259i	−0.997375	−	0.0724056i	$-0.976932\pi$
$139$	−1.74398	+	5.36743i	−0.147923	+	0.455259i	0.849453	+	0.527665i	$0.176932\pi$
$140$	3.95199	+	2.44246i	0.334004	+	0.206426i
$141$	−2.86327	−	8.81224i	−0.241131	−	0.742125i
$142$	4.80162	+	6.60886i	0.402943	+	0.554604i
$143$			1.13714i			0.0950925i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$	−10.6198	+	17.1832i	−0.881925	+	1.42698i
$146$	3.10944	+	2.25914i	0.257339	+	0.186968i
$147$	1.57716	−	2.17078i	0.130082	−	0.179043i
$148$	−5.04743	−	1.64001i	−0.414897	−	0.134808i
$149$	15.0956			1.23668			0.618339	−	0.785911i	$-0.287806\pi$
$149$	15.0956			1.23668			0.618339	+	0.785911i	$0.287806\pi$
$150$	−3.56227	+	3.50859i	−0.290858	+	0.286475i
$151$	−20.9353			−1.70369			−0.851847	−	0.523791i	$-0.824517\pi$
$151$	−20.9353			−1.70369			−0.851847	+	0.523791i	$0.824517\pi$
$152$	−6.53498	−	2.12334i	−0.530057	−	0.172226i
$153$	1.58450	−	2.18088i	0.128099	−	0.176314i
$154$	0.874305	+	0.635220i	0.0704535	+	0.0511875i
$155$	−10.7059	−	12.6317i	−0.859915	−	1.01460i
$156$	−1.76867	+	1.28501i	−0.141607	+	0.102883i
$157$			5.71998i			0.456504i	0.973602	+	0.228252i	$0.0733010\pi$
$157$			5.71998i			0.456504i	−0.973602	+	0.228252i	$0.926699\pi$
$158$	2.06455	+	2.84162i	0.164247	+	0.226067i
$159$	0.753509	+	2.31906i	0.0597572	+	0.183914i
$160$	2.22982	−	0.166977i	0.176283	−	0.0132007i
$161$	−2.47870	+	7.62866i	−0.195349	+	0.601222i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	11.3129	−	3.67577i	0.886091	−	0.287908i	0.169607	−	0.985512i	$-0.445750\pi$
$163$	11.3129	−	3.67577i	0.886091	−	0.287908i	0.716484	+	0.697603i	$0.245750\pi$
$164$	0.996141	−	3.06581i	0.0777856	−	0.239399i
$165$	−0.887277	+	0.752000i	−0.0690744	+	0.0585431i
$166$	4.05774	+	12.4884i	0.314941	+	0.969290i
$167$	−5.25731	−	7.23607i	−0.406823	−	0.559944i	0.555617	−	0.831438i	$-0.312482\pi$
$167$	−5.25731	−	7.23607i	−0.406823	−	0.559944i	−0.962440	+	0.271495i	$0.912482\pi$
$168$			2.07768i			0.160297i
$169$	−6.65058	+	4.83193i	−0.511583	+	0.371687i
$170$	5.57768	−	2.28559i	0.427789	−	0.175297i
$171$	5.55899	+	4.03884i	0.425106	+	0.308858i
$172$	−5.60700	+	7.71737i	−0.427530	+	0.588444i
$173$	−15.5394	−	5.04904i	−1.18144	−	0.383872i	−0.348536	−	0.937295i	$-0.613321\pi$
$173$	−15.5394	−	5.04904i	−1.18144	−	0.383872i	−0.832900	+	0.553424i	$0.813321\pi$
$174$	−9.03373			−0.684845
$175$	−1.54717	−	10.2726i	−0.116955	−	0.776533i
$176$	0.520147			0.0392076
$177$	−8.22545	−	2.67261i	−0.618262	−	0.200886i
$178$	5.79486	−	7.97594i	0.434343	−	0.597822i
$179$	2.97599	+	2.16219i	0.222436	+	0.161609i	0.693423	−	0.720531i	$-0.256102\pi$
$179$	2.97599	+	2.16219i	0.222436	+	0.161609i	−0.470986	+	0.882140i	$0.656102\pi$
$180$	−2.17229	−	0.530249i	−0.161913	−	0.0395224i
$181$	18.6472	−	13.5480i	1.38604	−	1.00702i	0.389751	−	0.920920i	$-0.372561\pi$
$181$	18.6472	−	13.5480i	1.38604	−	1.00702i	0.996287	−	0.0860956i	$-0.0274391\pi$
$182$		−	4.54222i		−	0.336691i
$183$	−7.39919	−	10.1841i	−0.546964	−	0.752831i
$184$	1.19301	+	3.67171i	0.0879500	+	0.270682i
$185$	4.49975	+	10.9811i	0.330828	+	0.807343i
$186$	2.28829	−	7.04264i	0.167786	−	0.516392i
$187$	1.33354	−	0.433294i	0.0975183	−	0.0316856i
$188$	8.81224	−	2.86327i	0.642699	−	0.208826i
$189$	0.642040	−	1.97599i	0.0467015	−	0.143732i
$190$	5.82588	+	14.2173i	0.422654	+	1.03143i
$191$	−0.552424	−	1.70019i	−0.0399720	−	0.123021i	0.929079	−	0.369881i	$-0.120601\pi$
$191$	−0.552424	−	1.70019i	−0.0399720	−	0.123021i	−0.969051	+	0.246859i	$0.920601\pi$
$192$	0.587785	+	0.809017i	0.0424197	+	0.0583858i
$193$			6.60138i			0.475178i	0.971366	+	0.237589i	$0.0763571\pi$
$193$			6.60138i			0.475178i	−0.971366	+	0.237589i	$0.923643\pi$
$194$	8.70483	−	6.32443i	0.624970	−	0.454068i
$195$	4.74904	+	1.15923i	0.340086	+	0.0830139i
$196$	2.17078	+	1.57716i	0.155056	+	0.112655i
$197$	7.43989	−	10.2401i	0.530070	−	0.729579i	−0.457071	−	0.889430i	$-0.651101\pi$
$197$	7.43989	−	10.2401i	0.530070	−	0.729579i	0.987141	+	0.159851i	$0.0511014\pi$
$198$	−0.494689	−	0.160734i	−0.0351560	−	0.0114229i
$199$	−6.24148			−0.442447			−0.221223	−	0.975223i	$-0.571005\pi$
$199$	−6.24148			−0.442447			−0.221223	+	0.975223i	$0.571005\pi$
$200$	−3.50859	−	3.56227i	−0.248095	−	0.251891i
$201$	6.69385			0.472148
$202$	−16.7766	−	5.45106i	−1.18040	−	0.383535i
$203$	11.0323	−	15.1846i	0.774314	−	1.06575i
$204$	2.18088	+	1.58450i	0.152692	+	0.110937i
$205$	−6.66988	+	2.73314i	−0.465845	+	0.190891i
$206$	7.03649	−	5.11231i	0.490256	−	0.356192i
$207$		−	3.86067i		−	0.268335i
$208$	−1.28501	−	1.76867i	−0.0890995	−	0.122635i
$209$	1.10445	+	3.39915i	0.0763965	+	0.235124i
$210$	3.54415	−	3.00380i	0.244570	−	0.207282i
$211$	−6.94607	+	21.3778i	−0.478187	+	1.47171i	0.363424	+	0.931624i	$0.381608\pi$
$211$	−6.94607	+	21.3778i	−0.478187	+	1.47171i	−0.841611	+	0.540084i	$0.818392\pi$
$212$	−2.31906	+	0.753509i	−0.159274	+	0.0517512i
$213$	7.76919	−	2.52436i	0.532336	−	0.172966i
$214$	1.67171	−	5.14500i	0.114276	−	0.351705i
$215$	21.2707	−	1.59283i	1.45065	−	0.108630i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	9.04331	+	12.4471i	0.613900	+	0.844961i
$218$		−	2.88377i		−	0.195314i
$219$	3.10944	−	2.25914i	0.210117	−	0.152659i
$220$	−0.752000	−	0.887277i	−0.0506999	−	0.0598202i
$221$	−4.76783	−	3.46403i	−0.320719	−	0.233016i
$222$	−3.11949	+	4.29360i	−0.209366	+	0.288168i
$223$	17.0524	+	5.54065i	1.14191	+	0.371029i	0.818091	−	0.575089i	$-0.195033\pi$
$223$	17.0524	+	5.54065i	1.14191	+	0.371029i	0.323820	+	0.946119i	$0.395033\pi$
$224$	−2.07768			−0.138821
$225$	2.23607	+	4.47214i	0.149071	+	0.298142i
$226$	−6.36955			−0.423696
$227$	−8.42412	−	2.73716i	−0.559129	−	0.181672i	0.0158003	−	0.999875i	$-0.494970\pi$
$227$	−8.42412	−	2.73716i	−0.559129	−	0.181672i	−0.574929	+	0.818203i	$0.694970\pi$
$228$	−4.03884	+	5.55899i	−0.267479	+	0.368153i
$229$	17.8490	+	12.9681i	1.17950	+	0.856953i	0.992115	−	0.125334i	$-0.0400003\pi$
$229$	17.8490	+	12.9681i	1.17950	+	0.856953i	0.187380	+	0.982287i	$0.440000\pi$
$230$	4.53849	−	7.34342i	0.299259	−	0.484211i
$231$	0.874305	−	0.635220i	0.0575251	−	0.0417944i
$232$		−	9.03373i		−	0.593093i
$233$	6.78466	+	9.33828i	0.444478	+	0.611771i	0.971200	−	0.238267i	$-0.0765792\pi$
$233$	6.78466	+	9.33828i	0.444478	+	0.611771i	−0.526722	+	0.850037i	$0.676579\pi$
$234$	0.675571	+	2.07919i	0.0441634	+	0.135921i
$235$	−17.6245	−	10.8925i	−1.14969	−	0.710550i
$236$	2.67261	−	8.22545i	0.173972	−	0.535431i
$237$	3.34052	−	1.08540i	0.216990	−	0.0705043i
$238$	−5.32672	+	1.73076i	−0.345280	+	0.112188i
$239$	0.273457	−	0.841616i	0.0176885	−	0.0544396i	−0.941823	−	0.336110i	$-0.890889\pi$
$239$	0.273457	−	0.841616i	0.0176885	−	0.0544396i	0.959511	+	0.281671i	$0.0908885\pi$
$240$	0.530249	−	2.17229i	0.0342274	−	0.140221i
$241$	3.91637	+	12.0534i	0.252276	+	0.776425i	0.994354	+	0.106112i	$0.0338402\pi$
$241$	3.91637	+	12.0534i	0.252276	+	0.776425i	−0.742078	+	0.670313i	$0.766160\pi$
$242$	6.30661	+	8.68031i	0.405404	+	0.557991i
$243$			1.00000i			0.0641500i
$244$	10.1841	−	7.39919i	0.651971	−	0.473684i
$245$	−0.448039	−	5.98314i	−0.0286242	−	0.382248i
$246$	−2.60793	−	1.89477i	−0.166276	−	0.120806i
$247$	8.82968	−	12.1530i	0.561819	−	0.773278i
$248$	7.04264	+	2.28829i	0.447208	+	0.145307i
$249$	13.1311			0.832150
$250$	−1.00406	+	11.1352i	−0.0635021	+	0.704250i
$251$	18.0966			1.14225			0.571124	−	0.820864i	$-0.306507\pi$
$251$	18.0966			1.14225			0.571124	+	0.820864i	$0.306507\pi$
$252$	1.97599	+	0.642040i	0.124476	+	0.0404447i
$253$	1.18034	−	1.62460i	0.0742073	−	0.102138i
$254$	−12.1088	−	8.79756i	−0.759774	−	0.552008i
$255$	−0.450124	−	6.01098i	−0.0281879	−	0.376422i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			1.28053i			0.0798774i	0.999202	+	0.0399387i	$0.0127163\pi$
$257$			1.28053i			0.0798774i	−0.999202	+	0.0399387i	$0.987284\pi$
$258$	5.60700	+	7.71737i	0.349077	+	0.480463i
$259$	−3.40742	−	10.4870i	−0.211727	−	0.651629i
$260$	−1.15923	+	4.74904i	−0.0718921	+	0.294523i
$261$	−2.79158	+	8.59159i	−0.172794	+	0.531806i
$262$	−13.1770	+	4.28147i	−0.814079	+	0.264510i
$263$	−6.76605	+	2.19842i	−0.417213	+	0.135561i	−0.510098	−	0.860116i	$-0.670391\pi$
$263$	−6.76605	+	2.19842i	−0.417213	+	0.135561i	0.0928855	+	0.995677i	$0.470391\pi$
$264$	0.160734	−	0.494689i	0.00989251	−	0.0304460i
$265$	4.63812	+	2.86652i	0.284918	+	0.176089i
$266$	−4.41164	−	13.5776i	−0.270495	−	0.832498i
$267$	−5.79486	−	7.97594i	−0.354640	−	0.488119i
$268$			6.69385i			0.408892i
$269$	−7.62892	+	5.54274i	−0.465143	+	0.337947i	−0.795546	−	0.605894i	$-0.792816\pi$
$269$	−7.62892	+	5.54274i	−0.465143	+	0.337947i	0.330402	+	0.943840i	$0.392816\pi$
$270$	−1.17557	+	1.90211i	−0.0715429	+	0.115759i
$271$	−1.11231	−	0.808141i	−0.0675681	−	0.0490911i	0.553488	−	0.832857i	$-0.313296\pi$
$271$	−1.11231	−	0.808141i	−0.0675681	−	0.0490911i	−0.621057	+	0.783766i	$0.713296\pi$
$272$	−1.58450	+	2.18088i	−0.0960746	+	0.132235i
$273$	−4.31990	−	1.40362i	−0.261452	−	0.0849511i
$274$	−19.8939			−1.20183
$275$	−0.426333	+	2.56555i	−0.0257088	+	0.154709i
$276$	3.86067			0.232385
$277$	18.6375	+	6.05571i	1.11982	+	0.363852i	0.809700	−	0.586845i	$-0.199630\pi$
$277$	18.6375	+	6.05571i	1.11982	+	0.363852i	0.310122	+	0.950697i	$0.399630\pi$
$278$	−3.31725	+	4.56581i	−0.198956	+	0.273839i
$279$	−5.99083	−	4.35259i	−0.358662	−	0.260583i
$280$	3.00380	+	3.54415i	0.179512	+	0.211804i
$281$	2.29605	−	1.66817i	0.136971	−	0.0995150i	−0.517190	−	0.855871i	$-0.673022\pi$
$281$	2.29605	−	1.66817i	0.136971	−	0.0995150i	0.654161	+	0.756356i	$0.273022\pi$
$282$		−	9.26574i		−	0.551767i
$283$	−1.31285	−	1.80699i	−0.0780411	−	0.107414i	0.768212	−	0.640196i	$-0.221147\pi$
$283$	−1.31285	−	1.80699i	−0.0780411	−	0.107414i	−0.846253	+	0.532781i	$0.821147\pi$
$284$	2.52436	+	7.76919i	0.149793	+	0.461016i
$285$	15.3218	−	1.14735i	0.907583	−	0.0679632i
$286$	−0.351396	+	1.08149i	−0.0207785	+	0.0639496i
$287$	6.36978	−	2.06967i	0.375996	−	0.122169i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	3.00770	−	9.25673i	0.176923	−	0.544514i
$290$	−15.4099	+	13.0605i	−0.904901	+	0.766938i
$291$	−3.32495	−	10.2331i	−0.194912	−	0.599877i
$292$	2.25914	+	3.10944i	0.132206	+	0.181966i
$293$		−	24.0260i		−	1.40361i	−0.712367	−	0.701807i	$-0.752377\pi$
$293$		−	24.0260i		−	1.40361i	0.712367	−	0.701807i	$-0.247623\pi$
$294$	2.17078	−	1.57716i	0.126602	−	0.0919821i
$295$	−17.8950	+	7.33292i	−1.04189	+	0.426939i
$296$	−4.29360	−	3.11949i	−0.249561	−	0.181316i
$297$	−0.305735	+	0.420808i	−0.0177405	+	0.0244177i
$298$	14.3568	+	4.66479i	0.831664	+	0.270224i
$299$	−8.44016			−0.488107
$300$	−4.47214	+	2.23607i	−0.258199	+	0.129099i
$301$	−19.8194			−1.14237
$302$	−19.9107	−	6.46937i	−1.14573	−	0.372271i
$303$	−10.3685	+	14.2711i	−0.595656	+	0.819850i
$304$	−5.55899	−	4.03884i	−0.318830	−	0.231643i
$305$	−27.3453	−	6.67490i	−1.56579	−	0.382204i
$306$	2.18088	−	1.58450i	0.124673	−	0.0905800i
$307$			17.1204i			0.977111i	0.872533	+	0.488556i	$0.162476\pi$
$307$			17.1204i			0.977111i	−0.872533	+	0.488556i	$0.837524\pi$
$308$	0.635220	+	0.874305i	0.0361950	+	0.0498182i
$309$	−2.68770	−	8.27189i	−0.152898	−	0.470572i
$310$	−6.27846	−	15.3218i	−0.356592	−	0.870218i
$311$	−6.22754	+	19.1664i	−0.353131	+	1.08683i	0.603954	+	0.797020i	$0.293591\pi$
$311$	−6.22754	+	19.1664i	−0.353131	+	1.08683i	−0.957085	+	0.289807i	$0.906409\pi$
$312$	−2.07919	+	0.675571i	−0.117711	+	0.0382466i
$313$	−24.2560	+	7.88127i	−1.37103	+	0.445476i	−0.899711	−	0.436486i	$-0.856223\pi$
$313$	−24.2560	+	7.88127i	−1.37103	+	0.445476i	−0.471322	+	0.881961i	$0.656223\pi$
$314$	−1.76757	+	5.44002i	−0.0997498	+	0.306998i
$315$	−1.76158	−	4.29892i	−0.0992539	−	0.242216i
$316$	1.08540	+	3.34052i	0.0610586	+	0.187919i
$317$	18.5260	+	25.4988i	1.04052	+	1.43215i	0.896747	+	0.442544i	$0.145924\pi$
$317$	18.5260	+	25.4988i	1.04052	+	1.43215i	0.143775	+	0.989610i	$0.454076\pi$
$318$			2.43841i			0.136739i
$319$	−3.80146	+	2.76193i	−0.212841	+	0.154638i
$320$	2.17229	+	0.530249i	0.121435	+	0.0296418i
$321$	−4.37660	−	3.17979i	−0.244278	−	0.177478i
$322$	−4.71477	+	6.48932i	−0.262744	+	0.361636i
$323$	−17.6165	−	5.72394i	−0.980207	−	0.318488i
$324$	−1.00000			−0.0555556
$325$	9.77695	−	4.88847i	0.542328	−	0.271164i
$326$	11.8950			0.658805
$327$	−2.74263	−	0.891135i	−0.151668	−	0.0492799i
$328$	1.89477	−	2.60793i	0.104621	−	0.143999i
$329$	15.5746	+	11.3156i	0.858656	+	0.623850i
$330$	−1.07623	+	0.441011i	−0.0592446	+	0.0242769i
$331$	5.90633	−	4.29120i	0.324641	−	0.235866i	−0.413512	−	0.910499i	$-0.635698\pi$
$331$	5.90633	−	4.29120i	0.324641	−	0.235866i	0.738153	+	0.674633i	$0.235698\pi$
$332$			13.1311i			0.720663i
$333$	3.11949	+	4.29360i	0.170947	+	0.235288i
$334$	−2.76393	−	8.50651i	−0.151236	−	0.465455i
$335$	11.4185	−	9.67761i	0.623859	−	0.528744i
$336$	−0.642040	+	1.97599i	−0.0350261	+	0.107799i
$337$	25.4358	−	8.26459i	1.38558	−	0.450201i	0.481077	−	0.876678i	$-0.340246\pi$
$337$	25.4358	−	8.26459i	1.38558	−	0.450201i	0.904498	+	0.426477i	$0.140246\pi$
$338$	−7.81822	+	2.54029i	−0.425255	+	0.138174i
$339$	−1.96830	+	6.05780i	−0.106903	+	0.329015i
$340$	6.01098	−	0.450124i	0.325991	−	0.0244114i
$341$	−1.19025	−	3.66321i	−0.0644556	−	0.198374i
$342$	4.03884	+	5.55899i	0.218396	+	0.300596i
$343$			20.1187i			1.08631i
$344$	−7.71737	+	5.60700i	−0.416093	+	0.302309i
$345$	−5.58154	−	6.58560i	−0.300500	−	0.354557i
$346$	−13.2186	−	9.60385i	−0.710635	−	0.516306i
$347$	−2.86327	+	3.94095i	−0.153708	+	0.211562i	−0.878926	−	0.476958i	$-0.841739\pi$
$347$	−2.86327	+	3.94095i	−0.153708	+	0.211562i	0.725217	+	0.688520i	$0.241739\pi$
$348$	−8.59159	−	2.79158i	−0.460557	−	0.149644i
$349$	−16.7173			−0.894855			−0.447428	−	0.894320i	$-0.647660\pi$
$349$	−16.7173			−0.894855			−0.447428	+	0.894320i	$0.647660\pi$
$350$	1.70295	−	10.2479i	0.0910265	−	0.547773i
$351$	2.18619			0.116690
$352$	0.494689	+	0.160734i	0.0263670	+	0.00856717i
$353$	−15.9175	+	21.9086i	−0.847203	+	1.16608i	0.137269	+	0.990534i	$0.456168\pi$
$353$	−15.9175	+	21.9086i	−0.847203	+	1.16608i	−0.984472	+	0.175541i	$0.943832\pi$
$354$	−6.99698	−	5.08361i	−0.371885	−	0.270191i
$355$	9.60324	−	15.5384i	0.509687	−	0.824691i
$356$	7.97594	−	5.79486i	0.422724	−	0.307127i
$357$			5.60085i			0.296428i
$358$	2.16219	+	2.97599i	0.114275	+	0.157286i
$359$	2.62299	+	8.07273i	0.138436	+	0.426062i	0.996109	−	0.0881339i	$-0.0280903\pi$
$359$	2.62299	+	8.07273i	0.138436	+	0.426062i	−0.857673	+	0.514196i	$0.828090\pi$
$360$	−1.90211	−	1.17557i	−0.100250	−	0.0619580i
$361$	8.71879	−	26.8337i	0.458884	−	1.41230i
$362$	21.9211	−	7.12261i	1.15215	−	0.374356i
$363$	10.2043	−	3.31558i	0.535587	−	0.174023i
$364$	1.40362	−	4.31990i	0.0735698	−	0.226424i
$365$	2.03800	−	8.34915i	0.106674	−	0.437014i
$366$	−3.88998	−	11.9721i	−0.203333	−	0.625794i
$367$	−7.49289	−	10.3131i	−0.391126	−	0.538339i	0.567363	−	0.823468i	$-0.307964\pi$
$367$	−7.49289	−	10.3131i	−0.391126	−	0.538339i	−0.958489	+	0.285129i	$0.907964\pi$
$368$			3.86067i			0.201251i
$369$	−2.60793	+	1.89477i	−0.135764	+	0.0986380i
$370$	0.886181	+	11.8341i	0.0460703	+	0.615225i
$371$	−4.09867	−	2.97786i	−0.212792	−	0.154603i
$372$	4.35259	−	5.99083i	0.225671	−	0.310610i
$373$	−10.4051	−	3.38081i	−0.538754	−	0.175052i	0.0269853	−	0.999636i	$-0.491409\pi$
$373$	−10.4051	−	3.38081i	−0.538754	−	0.175052i	−0.565740	+	0.824584i	$0.691409\pi$
$374$	1.40217			0.0725045
$375$	10.2799	+	4.39587i	0.530852	+	0.227002i
$376$	9.26574			0.477844
$377$	18.7829	+	6.10292i	0.967367	+	0.314316i
$378$	1.22123	−	1.68088i	0.0628134	−	0.0864552i
$379$	−11.5124	−	8.36427i	−0.591354	−	0.429644i	0.251446	−	0.967871i	$-0.419094\pi$
$379$	−11.5124	−	8.36427i	−0.591354	−	0.429644i	−0.842799	+	0.538228i	$0.819094\pi$
$380$	1.14735	+	15.3218i	0.0588578	+	0.785990i
$381$	−12.1088	+	8.79756i	−0.620353	+	0.450713i
$382$		−	1.78768i		−	0.0914658i
$383$	−4.21101	−	5.79595i	−0.215172	−	0.296159i	0.687763	−	0.725935i	$-0.258593\pi$
$383$	−4.21101	−	5.79595i	−0.215172	−	0.296159i	−0.902936	+	0.429776i	$0.858593\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	0.573040	−	2.34759i	0.0292048	−	0.119644i
$386$	−2.03994	+	6.27828i	−0.103830	+	0.319556i
$387$	9.07232	−	2.94777i	0.461172	−	0.149844i
$388$	10.2331	−	3.32495i	0.519509	−	0.168799i
$389$	0.283978	−	0.873994i	0.0143982	−	0.0443133i	−0.943599	−	0.331090i	$-0.892584\pi$
$389$	0.283978	−	0.873994i	0.0143982	−	0.0443133i	0.957998	+	0.286776i	$0.0925837\pi$
$390$	4.15838	+	2.57002i	0.210568	+	0.130138i
$391$	3.21602	+	9.89790i	0.162641	+	0.500558i
$392$	1.57716	+	2.17078i	0.0796588	+	0.109641i
$393$			13.8551i			0.698899i
$394$	10.2401	−	7.43989i	0.515891	−	0.374816i
$395$	4.12911	−	6.68104i	0.207758	−	0.336160i
$396$	−0.420808	−	0.305735i	−0.0211464	−	0.0153637i
$397$	12.8148	−	17.6381i	0.643159	−	0.885232i	−0.355620	−	0.934630i	$-0.615730\pi$
$397$	12.8148	−	17.6381i	0.643159	−	0.885232i	0.998779	+	0.0493984i	$0.0157304\pi$
$398$	−5.93600	−	1.92872i	−0.297545	−	0.0966782i
$399$	−14.2764			−0.714712
$400$	−2.23607	−	4.47214i	−0.111803	−	0.223607i
$401$	22.8035			1.13875			0.569375	−	0.822078i	$-0.307185\pi$
$401$	22.8035			1.13875			0.569375	+	0.822078i	$0.307185\pi$
$402$	6.36623	+	2.06851i	0.317519	+	0.103168i
$403$	−9.51560	+	13.0971i	−0.474006	+	0.652413i
$404$	−14.2711	−	10.3685i	−0.710011	−	0.515853i
$405$	1.44575	+	1.70582i	0.0718397	+	0.0847628i
$406$	15.1846	−	11.0323i	0.753600	−	0.547523i
$407$			2.76052i			0.136834i
$408$	1.58450	+	2.18088i	0.0784446	+	0.107970i
$409$	−1.54554	−	4.75668i	−0.0764220	−	0.235203i	0.905547	−	0.424247i	$-0.139461\pi$
$409$	−1.54554	−	4.75668i	−0.0764220	−	0.235203i	−0.981969	+	0.189044i	$0.939461\pi$
$410$	−7.18802	+	0.538266i	−0.354991	+	0.0265830i
$411$	−6.14755	+	18.9202i	−0.303236	+	0.933265i
$412$	8.27189	−	2.68770i	0.407527	−	0.132414i
$413$	17.0899	−	5.55284i	0.840938	−	0.273237i
$414$	1.19301	−	3.67171i	0.0586333	−	0.180455i
$415$	22.3993	−	18.9842i	1.09954	−	0.931900i
$416$	−0.675571	−	2.07919i	−0.0331226	−	0.101941i
$417$	3.31725	+	4.56581i	0.162447	+	0.223589i
$418$			3.57408i			0.174814i
$419$	−18.4661	+	13.4164i	−0.902128	+	0.655434i	−0.939012	−	0.343885i	$-0.888257\pi$
$419$	−18.4661	+	13.4164i	−0.902128	+	0.655434i	0.0368836	+	0.999320i	$0.488257\pi$
$420$	4.29892	−	1.76158i	0.209766	−	0.0859564i
$421$	−12.7124	−	9.23612i	−0.619566	−	0.450141i	0.233204	−	0.972428i	$-0.425079\pi$
$421$	−12.7124	−	9.23612i	−0.619566	−	0.450141i	−0.852770	+	0.522287i	$0.825079\pi$
$422$	−13.2122	+	18.1850i	−0.643160	+	0.885234i
$423$	−8.81224	−	2.86327i	−0.428466	−	0.139217i
$424$	−2.43841			−0.118419
$425$	−9.45818	−	9.60288i	−0.458789	−	0.465808i
$426$	8.16901			0.395790
$427$	24.8743	+	8.08215i	1.20375	+	0.391123i
$428$	3.17979	−	4.37660i	0.153701	−	0.211551i
$429$	0.919967	+	0.668395i	0.0444164	+	0.0322704i
$430$	20.7219	+	5.05815i	0.999298	+	0.243926i
$431$	7.73154	−	5.61729i	0.372415	−	0.270576i	−0.385796	−	0.922584i	$-0.626073\pi$
$431$	7.73154	−	5.61729i	0.372415	−	0.270576i	0.758212	+	0.652008i	$0.226073\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	4.77408	+	6.57096i	0.229428	+	0.315780i	0.908174	−	0.418593i	$-0.137476\pi$
$433$	4.77408	+	6.57096i	0.229428	+	0.315780i	−0.678747	+	0.734373i	$0.737476\pi$
$434$	4.75435	+	14.6324i	0.228216	+	0.702377i
$435$	7.65933	+	18.6916i	0.367237	+	0.896194i
$436$	0.891135	−	2.74263i	0.0426776	−	0.131348i
$437$	−25.2294	+	8.19753i	−1.20689	+	0.392141i
$438$	3.65537	−	1.18770i	0.174660	−	0.0567505i
$439$	−2.84899	+	8.76829i	−0.135975	+	0.418488i	−0.995740	−	0.0922014i	$-0.970610\pi$
$439$	−2.84899	+	8.76829i	−0.135975	+	0.418488i	0.859766	+	0.510689i	$0.170610\pi$
$440$	−0.441011	−	1.07623i	−0.0210244	−	0.0513073i
$441$	−0.829164	−	2.55190i	−0.0394840	−	0.121519i
$442$	−3.46403	−	4.76783i	−0.164767	−	0.226782i
$443$		−	9.63232i		−	0.457645i	−0.973468	−	0.228823i	$-0.926512\pi$
$443$		−	9.63232i		−	0.457645i	0.973468	−	0.228823i	$-0.0734876\pi$
$444$	−4.29360	+	3.11949i	−0.203765	+	0.148044i
$445$	−21.4162	−	5.22762i	−1.01522	−	0.247813i
$446$	14.5056	+	10.5389i	0.686861	+	0.499033i
$447$	8.87296	−	12.2126i	0.419677	−	0.577635i
$448$	−1.97599	−	0.642040i	−0.0933570	−	0.0303335i
$449$	21.3096			1.00566			0.502831	−	0.864385i	$-0.332292\pi$
$449$	21.3096			1.00566			0.502831	+	0.864385i	$0.332292\pi$
$450$	0.744661	+	4.94424i	0.0351037	+	0.233074i
$451$	−1.67674			−0.0789544
$452$	−6.05780	−	1.96830i	−0.284935	−	0.0925810i
$453$	−12.3055	+	16.9370i	−0.578162	+	0.795772i
$454$	−7.16599	−	5.20640i	−0.336317	−	0.244348i
$455$	−9.39825	+	3.85116i	−0.440597	+	0.180545i
$456$	−5.55899	+	4.03884i	−0.260324	+	0.189136i
$457$		−	13.4662i		−	0.629923i	−0.949104	−	0.314961i	$-0.898008\pi$
$457$		−	13.4662i		−	0.629923i	0.949104	−	0.314961i	$-0.101992\pi$
$458$	12.9681	+	17.8490i	0.605958	+	0.834029i
$459$	−0.833023	−	2.56378i	−0.0388822	−	0.119667i
$460$	6.58560	−	5.58154i	0.307055	−	0.260241i
$461$	10.1468	−	31.2286i	0.472582	−	1.45446i	−0.376608	−	0.926373i	$-0.622910\pi$
$461$	10.1468	−	31.2286i	0.472582	−	1.45446i	0.849191	−	0.528086i	$-0.177090\pi$
$462$	1.02781	−	0.333955i	0.0478179	−	0.0155370i
$463$	−21.8083	+	7.08596i	−1.01352	+	0.329312i	−0.768255	−	0.640144i	$-0.778875\pi$
$463$	−21.8083	+	7.08596i	−1.01352	+	0.329312i	−0.245264	+	0.969456i	$0.578875\pi$
$464$	2.79158	−	8.59159i	0.129596	−	0.398854i
$465$	−16.5120	+	1.23648i	−0.765726	+	0.0573404i
$466$	3.56690	+	10.9778i	0.165234	+	0.508537i
$467$	−12.2459	−	16.8551i	−0.566674	−	0.779960i	0.425482	−	0.904967i	$-0.360105\pi$
$467$	−12.2459	−	16.8551i	−0.566674	−	0.779960i	−0.992156	+	0.125007i	$0.960105\pi$
$468$			2.18619i			0.101057i
$469$	−11.2516	+	8.17475i	−0.519549	+	0.377475i
$470$	−13.3959	−	15.8057i	−0.617907	−	0.729062i
$471$	4.62756	+	3.36212i	0.213227	+	0.154918i
$472$	5.08361	−	6.99698i	0.233992	−	0.322062i
$473$	4.71894	+	1.53328i	0.216977	+	0.0705001i
$474$	3.51243			0.161331
$475$	24.4774	−	24.1086i	1.12310	−	1.10618i
$476$	−5.60085			−0.256714
$477$	2.31906	+	0.753509i	0.106183	+	0.0345008i
$478$	0.520147	−	0.715921i	0.0237910	−	0.0327455i
$479$	10.9401	+	7.94842i	0.499864	+	0.363172i	0.808965	−	0.587857i	$-0.200028\pi$
$479$	10.9401	+	7.94842i	0.499864	+	0.363172i	−0.309101	+	0.951029i	$0.600028\pi$
$480$	1.17557	−	1.90211i	0.0536572	−	0.0868192i
$481$	9.38664	−	6.81980i	0.427994	−	0.310956i
$482$			12.6736i			0.577269i
$483$	4.71477	+	6.48932i	0.214529	+	0.295274i
$484$	3.31558	+	10.2043i	0.150708	+	0.463832i
$485$	−20.4663	−	12.6489i	−0.929326	−	0.574355i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−25.3198	+	8.22690i	−1.14735	+	0.372796i	−0.820144	−	0.572157i	$-0.806107\pi$
$487$	−25.3198	+	8.22690i	−1.14735	+	0.372796i	−0.327205	+	0.944953i	$0.606107\pi$
$488$	11.9721	−	3.88998i	0.541953	−	0.176091i
$489$	3.67577	−	11.3129i	0.166224	−	0.511585i
$490$	1.42278	−	5.82875i	0.0642746	−	0.263316i
$491$	−3.71521	−	11.4342i	−0.167665	−	0.516020i	0.831558	−	0.555438i	$-0.187449\pi$
$491$	−3.71521	−	11.4342i	−0.167665	−	0.516020i	−0.999223	+	0.0394184i	$0.987449\pi$
$492$	−1.89477	−	2.60793i	−0.0854230	−	0.117575i
$493$		−	24.3524i		−	1.09678i
$494$	12.1530	−	8.82968i	0.546790	−	0.397266i
$495$	0.0868528	+	1.15984i	0.00390374	+	0.0521308i
$496$	5.99083	+	4.35259i	0.268996	+	0.195437i
$497$	−9.97625	+	13.7311i	−0.447496	+	0.615925i
$498$	12.4884	+	4.05774i	0.559620	+	0.181831i
$499$	27.3600			1.22480			0.612400	−	0.790548i	$-0.290204\pi$
$499$	27.3600			1.22480			0.612400	+	0.790548i	$0.290204\pi$
$500$	−4.39587	+	10.2799i	−0.196589	+	0.459731i
$501$	−8.94427			−0.399601
$502$	17.2109	+	5.59216i	0.768161	+	0.249590i
$503$	5.38563	−	7.41268i	0.240133	−	0.330515i	−0.671892	−	0.740649i	$-0.734518\pi$
$503$	5.38563	−	7.41268i	0.240133	−	0.330515i	0.912025	+	0.410134i	$0.134518\pi$
$504$	1.68088	+	1.22123i	0.0748724	+	0.0543980i
$505$	2.94548	+	39.3341i	0.131072	+	1.75034i
$506$	1.62460	−	1.18034i	0.0722222	−	0.0524725i
$507$			8.22056i			0.365088i
$508$	−8.79756	−	12.1088i	−0.390329	−	0.537241i
$509$	0.725667	+	2.23337i	0.0321646	+	0.0989925i	0.965850	−	0.259102i	$-0.0834266\pi$
$509$	0.725667	+	2.23337i	0.0321646	+	0.0989925i	−0.933685	+	0.358094i	$0.883427\pi$
$510$	1.42940	−	5.85588i	0.0632949	−	0.259303i
$511$	−2.46767	+	7.59470i	−0.109163	+	0.335970i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	6.53498	−	2.12334i	0.288527	−	0.0937480i
$514$	−0.395706	+	1.21786i	−0.0174538	+	0.0537174i
$515$	−16.5438	−	10.2246i	−0.729006	−	0.450551i
$516$	2.94777	+	9.07232i	0.129769	+	0.399386i
$517$	−2.83286	−	3.89910i	−0.124589	−	0.171482i
$518$		−	11.0267i		−	0.484483i
$519$	−13.2186	+	9.60385i	−0.580231	+	0.421562i
$520$	−2.57002	+	4.15838i	−0.112703	+	0.182357i
$521$	1.24129	+	0.901848i	0.0543818	+	0.0395107i	0.614644	−	0.788805i	$-0.289300\pi$
$521$	1.24129	+	0.901848i	0.0543818	+	0.0395107i	−0.560262	+	0.828315i	$0.689300\pi$
$522$	−5.30989	+	7.30844i	−0.232408	+	0.319882i
$523$	39.5506	+	12.8508i	1.72943	+	0.561926i	0.993367	−	0.114988i	$-0.0366830\pi$
$523$	39.5506	+	12.8508i	1.72943	+	0.561926i	0.736062	+	0.676914i	$0.236683\pi$
$524$	−13.8551			−0.605265
$525$	−9.22008	−	4.78637i	−0.402397	−	0.208894i
$526$	−7.11425			−0.310196
$527$	18.9850	+	6.16859i	0.826999	+	0.268708i
$528$	0.305735	−	0.420808i	0.0133054	−	0.0183133i
$529$	−6.54920	−	4.75827i	−0.284748	−	0.206881i
$530$	3.52532	+	4.15948i	0.153130	+	0.180676i
$531$	−6.99698	+	5.08361i	−0.303643	+	0.220610i
$532$		−	14.2764i		−	0.618959i
$533$	4.14234	+	5.70144i	0.179425	+	0.246957i
$534$	−3.04654	−	9.37628i	−0.131837	−	0.405751i
$535$	−12.0628	+	0.903310i	−0.521522	+	0.0390535i
$536$	−2.06851	+	6.36623i	−0.0893462	+	0.274979i
$537$	3.49849	−	1.13673i	0.150971	−	0.0490535i
$538$	−8.96833	+	2.91399i	−0.386652	+	0.125631i
$539$	0.431287	−	1.32737i	0.0185769	−	0.0571737i
$540$	−1.70582	+	1.44575i	−0.0734068	+	0.0622150i
$541$	5.88428	+	18.1100i	0.252985	+	0.778608i	0.994220	+	0.107362i	$0.0342404\pi$
$541$	5.88428	+	18.1100i	0.252985	+	0.778608i	−0.741235	+	0.671246i	$0.765760\pi$
$542$	−0.808141	−	1.11231i	−0.0347126	−	0.0477778i
$543$		−	23.0493i		−	0.989138i
$544$	−2.18088	+	1.58450i	−0.0935045	+	0.0679350i
$545$	−5.96679	+	2.44503i	−0.255589	+	0.104734i
$546$	−3.67473	−	2.66985i	−0.157264	−	0.114259i
$547$	−16.0588	+	22.1030i	−0.686624	+	0.945057i	−0.999990	−	0.00457542i	$-0.998544\pi$
$547$	−16.0588	+	22.1030i	−0.686624	+	0.945057i	0.313365	+	0.949633i	$0.398544\pi$
$548$	−18.9202	−	6.14755i	−0.808231	−	0.262610i
$549$	−12.5882			−0.537253
$550$	−1.19827	+	2.30824i	−0.0510942	+	0.0984238i
$551$	62.0734			2.64441
$552$	3.67171	+	1.19301i	0.156278	+	0.0507779i
$553$	−4.28949	+	5.90398i	−0.182408	+	0.251063i
$554$	15.8540	+	11.5186i	0.673574	+	0.489380i
$555$	11.5287	+	2.81413i	0.489368	+	0.119453i
$556$	−4.56581	+	3.31725i	−0.193633	+	0.140683i
$557$			9.89921i			0.419443i	0.977761	+	0.209721i	$0.0672557\pi$
$557$			9.89921i			0.419443i	−0.977761	+	0.209721i	$0.932744\pi$
$558$	−4.35259	−	5.99083i	−0.184260	−	0.253612i
$559$	−6.44440	−	19.8338i	−0.272569	−	0.838881i
$560$	1.76158	+	4.29892i	0.0744404	+	0.181662i
$561$	0.433294	−	1.33354i	0.0182937	−	0.0563022i
$562$	2.69916	−	0.877011i	0.113857	−	0.0369945i
$563$	−1.91338	+	0.621694i	−0.0806392	+	0.0262013i	−0.349059	−	0.937101i	$-0.613499\pi$
$563$	−1.91338	+	0.621694i	−0.0806392	+	0.0262013i	0.268420	+	0.963302i	$0.413499\pi$
$564$	2.86327	−	8.81224i	0.120565	−	0.371062i
$565$	5.40048	+	13.1792i	0.227200	+	0.554452i
$566$	−0.690208	−	2.12424i	−0.0290116	−	0.0892886i
$567$	−1.22123	−	1.68088i	−0.0512869	−	0.0705904i
$568$			8.16901i			0.342764i
$569$	19.0969	−	13.8747i	0.800585	−	0.581659i	−0.110501	−	0.993876i	$-0.535245\pi$
$569$	19.0969	−	13.8747i	0.800585	−	0.581659i	0.911086	+	0.412217i	$0.135245\pi$
$570$	14.9264	+	3.64349i	0.625199	+	0.152609i
$571$	−17.1782	−	12.4807i	−0.718886	−	0.522301i	0.167142	−	0.985933i	$-0.446546\pi$
$571$	−17.1782	−	12.4807i	−0.718886	−	0.522301i	−0.886028	+	0.463631i	$0.846546\pi$
$572$	−0.668395	+	0.919967i	−0.0279470	+	0.0384657i
$573$	−1.70019	−	0.552424i	−0.0710263	−	0.0230779i
$574$	6.69758			0.279552
$575$	−19.0422	−	3.16435i	−0.794115	−	0.131963i
$576$	1.00000			0.0416667
$577$	−43.1167	−	14.0095i	−1.79497	−	0.583222i	−0.795238	−	0.606297i	$-0.792654\pi$
$577$	−43.1167	−	14.0095i	−1.79497	−	0.583222i	−0.999734	+	0.0230749i	$0.992654\pi$
$578$	5.72098	−	7.87425i	0.237961	−	0.327526i
$579$	5.34063	+	3.88019i	0.221949	+	0.161255i
$580$	−18.6916	+	7.65933i	−0.776127	+	0.318036i
$581$	−22.0718	+	16.0361i	−0.915694	+	0.665291i
$582$		−	10.7598i		−	0.446006i
$583$	0.745506	+	1.02610i	0.0308757	+	0.0424967i
$584$	1.18770	+	3.65537i	0.0491474	+	0.151260i
$585$	3.72925	−	3.16068i	0.154185	−	0.130678i
$586$	7.42445	−	22.8501i	0.306701	−	0.943929i
$587$	−15.5245	+	5.04421i	−0.640764	+	0.208197i	−0.611337	−	0.791370i	$-0.709368\pi$
$587$	−15.5245	+	5.04421i	−0.640764	+	0.208197i	−0.0294265	+	0.999567i	$0.509368\pi$
$588$	2.55190	−	0.829164i	0.105239	−	0.0341941i
$589$	−15.7235	+	48.3920i	−0.647877	+	1.99396i
$590$	−19.2852	+	1.44415i	−0.793959	+	0.0594545i
$591$	−3.91138	−	12.0380i	−0.160893	−	0.495177i
$592$	−3.11949	−	4.29360i	−0.128210	−	0.176466i
$593$		−	32.8357i		−	1.34840i	−0.738549	−	0.674199i	$-0.764489\pi$
$593$		−	32.8357i		−	1.34840i	0.738549	−	0.674199i	$-0.235511\pi$
$594$	−0.420808	+	0.305735i	−0.0172660	+	0.0125444i
$595$	8.09740	+	9.55403i	0.331961	+	0.391677i
$596$	12.2126	+	8.87296i	0.500247	+	0.363451i
$597$	−3.66865	+	5.04946i	−0.150148	+	0.206661i
$598$	−8.02707	−	2.60815i	−0.328251	−	0.106655i
$599$	13.1905			0.538947			0.269474	−	0.963008i	$-0.413150\pi$
$599$	13.1905			0.538947			0.269474	+	0.963008i	$0.413150\pi$
$600$	−4.94424	+	0.744661i	−0.201848	+	0.0304007i
$601$	−19.1992			−0.783152			−0.391576	−	0.920146i	$-0.628070\pi$
$601$	−19.1992			−0.783152			−0.391576	+	0.920146i	$0.628070\pi$
$602$	−18.8494	−	6.12454i	−0.768244	−	0.249618i
$603$	3.93455	−	5.41544i	0.160227	−	0.220534i
$604$	−16.9370	−	12.3055i	−0.689158	−	0.500703i
$605$	12.6132	−	20.4086i	0.512800	−	0.829728i
$606$	−14.2711	+	10.3685i	−0.579722	+	0.421193i
$607$		−	6.54268i		−	0.265559i	−0.991146	−	0.132779i	$-0.957610\pi$
$607$		−	6.54268i		−	0.265559i	0.991146	−	0.132779i	$-0.0423902\pi$
$608$	−4.03884	−	5.55899i	−0.163797	−	0.225447i
$609$	−5.80001	−	17.8506i	−0.235028	−	0.723343i
$610$	−23.9443	−	14.7984i	−0.969475	−	0.599169i
$611$	−6.25966	+	19.2653i	−0.253239	+	0.779389i
$612$	2.56378	−	0.833023i	0.103635	−	0.0336729i
$613$	8.87528	−	2.88375i	0.358469	−	0.116474i	−0.124245	−	0.992252i	$-0.539651\pi$
$613$	8.87528	−	2.88375i	0.358469	−	0.116474i	0.482714	+	0.875778i	$0.339651\pi$
$614$	−5.29049	+	16.2824i	−0.213507	+	0.657106i
$615$	−1.70930	+	7.00255i	−0.0689256	+	0.282370i
$616$	0.333955	+	1.02781i	0.0134554	+	0.0414115i
$617$	−19.3979	−	26.6989i	−0.780929	−	1.07486i	−0.995179	−	0.0980778i	$-0.968731\pi$
$617$	−19.3979	−	26.6989i	−0.780929	−	1.07486i	0.214250	−	0.976779i	$-0.431269\pi$
$618$		−	8.69758i		−	0.349868i
$619$	22.7569	−	16.5339i	0.914678	−	0.664553i	−0.0275155	−	0.999621i	$-0.508760\pi$
$619$	22.7569	−	16.5339i	0.914678	−	0.664553i	0.942194	+	0.335069i	$0.108760\pi$
$620$	−1.23648	−	16.5120i	−0.0496583	−	0.663139i
$621$	−3.12334	−	2.26924i	−0.125336	−	0.0910616i
$622$	−11.8455	+	16.3039i	−0.474961	+	0.653727i
$623$	19.4809	+	6.32974i	0.780487	+	0.253596i
$624$	−2.18619			−0.0875177
$625$	23.8910	−	7.36356i	0.955638	−	0.294542i
$626$	−25.5043			−1.01936
$627$	3.39915	+	1.10445i	0.135749	+	0.0441075i
$628$	−3.36212	+	4.62756i	−0.134163	+	0.184660i
$629$	−11.5743	−	8.40925i	−0.461499	−	0.335299i
$630$	−0.346926	−	4.63287i	−0.0138219	−	0.184578i
$631$	1.93909	−	1.40883i	0.0771940	−	0.0560847i	−0.548519	−	0.836138i	$-0.684808\pi$
$631$	1.93909	−	1.40883i	0.0771940	−	0.0560847i	0.625713	+	0.780053i	$0.284808\pi$
$632$			3.51243i			0.139717i
$633$	13.2122	+	18.1850i	0.525138	+	0.722790i
$634$	9.73967	+	29.9756i	0.386812	+	1.19048i
$635$	−7.93640	+	32.5133i	−0.314946	+	1.29025i
$636$	−0.753509	+	2.31906i	−0.0298786	+	0.0919568i
$637$	−5.57895	+	1.81271i	−0.221046	+	0.0718223i
$638$	−4.46889	+	1.45203i	−0.176925	+	0.0574864i
$639$	2.52436	−	7.76919i	0.0998622	−	0.307344i
$640$	1.90211	+	1.17557i	0.0751876	+	0.0464685i
$641$	3.76246	+	11.5797i	0.148608	+	0.457370i	0.997457	−	0.0712658i	$-0.0227039\pi$
$641$	3.76246	+	11.5797i	0.148608	+	0.457370i	−0.848849	+	0.528635i	$0.822704\pi$
$642$	−3.17979	−	4.37660i	−0.125496	−	0.172731i
$643$			27.0249i			1.06576i	0.846192	+	0.532878i	$0.178890\pi$
$643$			27.0249i			1.06576i	−0.846192	+	0.532878i	$0.821110\pi$
$644$	−6.48932	+	4.71477i	−0.255715	+	0.185788i
$645$	11.2140	−	18.1446i	0.441551	−	0.714444i
$646$	−14.9855	−	10.8876i	−0.589595	−	0.428366i
$647$	−19.9375	+	27.4417i	−0.783826	+	1.07884i	0.211024	+	0.977481i	$0.432320\pi$
$647$	−19.9375	+	27.4417i	−0.783826	+	1.07884i	−0.994850	+	0.101363i	$0.967680\pi$
$648$	−0.951057	−	0.309017i	−0.0373610	−	0.0121393i
$649$	−4.49862			−0.176586
$650$	10.8091	−	1.62797i	0.423966	−	0.0638543i
$651$	15.3854			0.603001
$652$	11.3129	+	3.67577i	0.443046	+	0.143954i
$653$	8.73039	−	12.0163i	0.341646	−	0.470236i	−0.603275	−	0.797533i	$-0.706138\pi$
$653$	8.73039	−	12.0163i	0.341646	−	0.470236i	0.944921	+	0.327297i	$0.106138\pi$
$654$	−2.33302	−	1.69504i	−0.0912284	−	0.0662813i
$655$	20.0310	+	23.6344i	0.782676	+	0.923471i
$656$	2.60793	−	1.89477i	0.101823	−	0.0739785i
$657$		−	3.84348i		−	0.149948i
$658$	11.3156	+	15.5746i	0.441129	+	0.607162i
$659$	−1.45835	−	4.48835i	−0.0568094	−	0.174841i	0.918625	−	0.395129i	$-0.129300\pi$
$659$	−1.45835	−	4.48835i	−0.0568094	−	0.174841i	−0.975435	+	0.220288i	$0.929300\pi$
$660$	−1.15984	+	0.0868528i	−0.0451466	+	0.00338074i
$661$	1.08059	−	3.32571i	0.0420300	−	0.129355i	−0.927840	−	0.372979i	$-0.878336\pi$
$661$	1.08059	−	3.32571i	0.0420300	−	0.129355i	0.969870	+	0.243624i	$0.0783363\pi$
$662$	6.94330	−	2.25602i	0.269859	−	0.0876826i
$663$	−5.60491	+	1.82115i	−0.217677	+	0.0707275i
$664$	−4.05774	+	12.4884i	−0.157471	+	0.484645i
$665$	−24.3529	+	20.6400i	−0.944365	+	0.800384i
$666$	1.64001	+	5.04743i	0.0635491	+	0.195584i
$667$	−20.4997	−	28.2155i	−0.793753	−	1.09251i
$668$		−	8.94427i		−	0.346064i
$669$	14.5056	−	10.5389i	0.560819	−	0.407459i
$670$	13.8502	−	5.67544i	0.535079	−	0.219261i
$671$	−5.29723	−	3.84867i	−0.204497	−	0.148576i
$672$	−1.22123	+	1.68088i	−0.0471100	+	0.0648414i
$673$	−23.4287	−	7.61244i	−0.903110	−	0.293438i	−0.179590	−	0.983742i	$-0.557477\pi$
$673$	−23.4287	−	7.61244i	−0.903110	−	0.293438i	−0.723520	+	0.690303i	$0.757477\pi$
$674$	26.7448			1.03017
$675$	4.93236	+	0.819639i	0.189847	+	0.0315479i
$676$	−8.22056			−0.316176
$677$	28.3655	+	9.21651i	1.09017	+	0.354219i	0.798314	−	0.602242i	$-0.205726\pi$
$677$	28.3655	+	9.21651i	1.09017	+	0.354219i	0.291861	+	0.956461i	$0.405726\pi$
$678$	−3.74393	+	5.15307i	−0.143785	+	0.197903i
$679$	18.0859	+	13.1402i	0.694072	+	0.504273i
$680$	5.85588	+	1.42940i	0.224563	+	0.0548150i
$681$	−7.16599	+	5.20640i	−0.274601	+	0.199510i
$682$		−	3.85173i		−	0.147490i
$683$	−15.3138	−	21.0776i	−0.585964	−	0.806511i	0.408369	−	0.912817i	$-0.366098\pi$
$683$	−15.3138	−	21.0776i	−0.585964	−	0.806511i	−0.994333	+	0.106306i	$0.966098\pi$
$684$	2.12334	+	6.53498i	0.0811881	+	0.249871i
$685$	16.8672	+	41.1623i	0.644463	+	1.57273i
$686$	−6.21702	+	19.1340i	−0.237367	+	0.730540i
$687$	20.9828	−	6.81771i	0.800542	−	0.260112i
$688$	−9.07232	+	2.94777i	−0.345879	+	0.112383i
$689$	1.64732	−	5.06992i	0.0627577	−	0.193148i
$690$	−3.27330	−	7.98807i	−0.124612	−	0.304101i
$691$	10.6313	+	32.7197i	0.404432	+	1.24471i	0.921368	+	0.388690i	$0.127072\pi$
$691$	10.6313	+	32.7197i	0.404432	+	1.24471i	−0.516936	+	0.856024i	$0.672928\pi$
$692$	−9.60385	−	13.2186i	−0.365084	−	0.502495i
$693$		−	1.08070i		−	0.0410524i
$694$	−3.94095	+	2.86327i	−0.149597	+	0.108688i
$695$	12.2596	+	2.99254i	0.465034	+	0.113513i
$696$	−7.30844	−	5.30989i	−0.277026	−	0.201271i
$697$	5.10777	−	7.03025i	0.193471	−	0.266290i
$698$	−15.8991	−	5.16592i	−0.601789	−	0.195533i
$699$	11.5427			0.436587
$700$	4.78637	−	9.22008i	0.180908	−	0.348486i
$701$	13.2937			0.502095			0.251047	−	0.967975i	$-0.419225\pi$
$701$	13.2937			0.502095			0.251047	+	0.967975i	$0.419225\pi$
$702$	2.07919	+	0.675571i	0.0784741	+	0.0254978i
$703$	21.4349	−	29.5026i	0.808432	−	1.11271i
$704$	0.420808	+	0.305735i	0.0158598	+	0.0115228i
$705$	−19.1717	+	7.85604i	−0.722046	+	0.295876i
$706$	−21.9086	+	15.9175i	−0.824540	+	0.599063i
$707$		−	36.6503i		−	1.37838i
$708$	−5.08361	−	6.99698i	−0.191054	−	0.262963i
$709$	2.24820	+	6.91924i	0.0844329	+	0.259858i	0.984356	−	0.176191i	$-0.0563776\pi$
$709$	2.24820	+	6.91924i	0.0844329	+	0.259858i	−0.899923	+	0.436049i	$0.856378\pi$
$710$	13.9348	−	11.8103i	0.522966	−	0.443233i
$711$	1.08540	−	3.34052i	0.0407057	−	0.125279i
$712$	9.37628	−	3.04654i	0.351391	−	0.114174i
$713$	27.1893	−	8.83434i	1.01825	−	0.330849i
$714$	−1.73076	+	5.32672i	−0.0647720	+	0.199348i
$715$	2.53563	−	0.189877i	0.0948270	−	0.00710100i
$716$	1.13673	+	3.49849i	0.0424815	+	0.130745i
$717$	−0.520147	−	0.715921i	−0.0194252	−	0.0267366i
$718$			8.48817i			0.316776i
$719$	−26.0071	+	18.8953i	−0.969902	+	0.704675i	−0.955429	−	0.295220i	$-0.904607\pi$
$719$	−26.0071	+	18.8953i	−0.969902	+	0.704675i	−0.0144727	+	0.999895i	$0.504607\pi$
$720$	−1.44575	−	1.70582i	−0.0538798	−	0.0635721i
$721$	14.6196	+	10.6218i	0.544462	+	0.395575i
$722$	16.5841	−	22.8261i	0.617197	−	0.849499i
$723$	12.0534	+	3.91637i	0.448269	+	0.145651i
$724$	23.0493			0.856619
$725$	40.0887	+	20.8111i	1.48886	+	0.772903i
$726$	10.7294			0.398207
$727$	2.97260	+	0.965858i	0.110248	+	0.0358217i	0.363621	−	0.931547i	$-0.381540\pi$
$727$	2.97260	+	0.965858i	0.110248	+	0.0358217i	−0.253374	+	0.967369i	$0.581540\pi$
$728$	2.66985	−	3.67473i	0.0989511	−	0.136195i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	4.51828	−	7.31073i	0.167229	−	0.270582i
$731$	−20.8039	+	15.1149i	−0.769458	+	0.559044i
$732$		−	12.5882i		−	0.465275i
$733$	−27.2488	−	37.5047i	−1.00646	−	1.38527i	−0.921279	−	0.388902i	$-0.872854\pi$
$733$	−27.2488	−	37.5047i	−1.00646	−	1.38527i	−0.0851773	−	0.996366i	$-0.527146\pi$
$734$	−3.93925	−	12.1238i	−0.145400	−	0.447496i
$735$	−5.10381	−	3.15433i	−0.188257	−	0.116349i
$736$	−1.19301	+	3.67171i	−0.0439750	+	0.135341i
$737$	3.31138	−	1.07593i	0.121976	−	0.0396324i
$738$	−3.06581	+	0.996141i	−0.112854	+	0.0366685i
$739$	14.8417	−	45.6779i	0.545959	−	1.68029i	−0.172739	−	0.984968i	$-0.555262\pi$
$739$	14.8417	−	45.6779i	0.545959	−	1.68029i	0.718698	−	0.695322i	$-0.244738\pi$
$740$	−2.81413	+	11.5287i	−0.103449	+	0.423805i
$741$	−4.64204	−	14.2867i	−0.170530	−	0.524836i
$742$	−2.97786	−	4.09867i	−0.109321	−	0.150467i
$743$			2.88963i			0.106010i	0.998594	+	0.0530051i	$0.0168799\pi$
$743$			2.88963i			0.106010i	−0.998594	+	0.0530051i	$0.983120\pi$
$744$	5.99083	−	4.35259i	0.219635	−	0.159574i
$745$	−2.52062	−	33.6605i	−0.0923484	−	1.23323i
$746$	−8.85108	−	6.43069i	−0.324061	−	0.235444i
$747$	7.71827	−	10.6233i	0.282397	−	0.388686i
$748$	1.33354	+	0.433294i	0.0487591	+	0.0158428i
$749$	11.2398			0.410693
$750$	8.41837	+	7.35738i	0.307395	+	0.268654i
$751$	−39.4965			−1.44125			−0.720624	−	0.693326i	$-0.756144\pi$
$751$	−39.4965			−1.44125			−0.720624	+	0.693326i	$0.756144\pi$
$752$	8.81224	+	2.86327i	0.321349	+	0.104413i
$753$	10.6369	−	14.6405i	0.387631	−	0.533529i
$754$	15.9777	+	11.6084i	0.581872	+	0.422755i
$755$	3.49573	+	46.6821i	0.127223	+	1.69894i
$756$	1.68088	−	1.22123i	0.0611331	−	0.0444158i
$757$			25.4654i			0.925555i	0.886475	+	0.462777i	$0.153147\pi$
$757$			25.4654i			0.925555i	−0.886475	+	0.462777i	$0.846853\pi$
$758$	−8.36427	−	11.5124i	−0.303804	−	0.418150i
$759$	−0.620541	−	1.90983i	−0.0225242	−	0.0693224i
$760$	−3.64349	+	14.9264i	−0.132163	+	0.541438i
$761$	12.8769	−	39.6310i	0.466787	−	1.43662i	−0.389934	−	0.920843i	$-0.627502\pi$
$761$	12.8769	−	39.6310i	0.466787	−	1.43662i	0.856721	−	0.515780i	$-0.172498\pi$
$762$	−14.2348	+	4.62515i	−0.515671	+	0.167552i
$763$	5.69832	−	1.85150i	0.206293	−	0.0670287i
$764$	0.552424	−	1.70019i	0.0199860	−	0.0615106i
$765$	−5.12756	−	3.16901i	−0.185387	−	0.114576i
$766$	−2.21386	−	6.81355i	−0.0799899	−	0.246184i
$767$	11.1137	+	15.2967i	0.401294	+	0.552334i
$768$			1.00000i			0.0360844i
$769$	1.67667	−	1.21817i	0.0604621	−	0.0439283i	−0.557144	−	0.830416i	$-0.688103\pi$
$769$	1.67667	−	1.21817i	0.0604621	−	0.0439283i	0.617606	+	0.786488i	$0.288103\pi$
$770$	1.27044	−	2.05562i	0.0457835	−	0.0740792i
$771$	1.03597	+	0.752678i	0.0373096	+	0.0271070i
$772$	−3.88019	+	5.34063i	−0.139651	+	0.192213i
$773$	7.59855	+	2.46892i	0.273301	+	0.0888009i	0.442461	−	0.896788i	$-0.354105\pi$
$773$	7.59855	+	2.46892i	0.273301	+	0.0888009i	−0.169160	+	0.985589i	$0.554105\pi$
$774$	9.53920			0.342879
$775$	−26.3789	+	25.9814i	−0.947557	+	0.933279i
$776$	10.7598			0.386253
$777$	−10.4870	−	3.40742i	−0.376218	−	0.122241i
$778$	0.540158	−	0.743464i	0.0193656	−	0.0266545i
$779$	17.9199	+	13.0195i	0.642045	+	0.466473i
$780$	3.16068	+	3.72925i	0.113170	+	0.133529i
$781$	3.43758	−	2.49755i	0.123006	−	0.0893693i
$782$			10.4073i			0.372163i
$783$	5.30989	+	7.30844i	0.189760	+	0.261182i
$784$	0.829164	+	2.55190i	0.0296130	+	0.0911394i
$785$	12.7545	−	0.955107i	0.455229	−	0.0340892i
$786$	−4.28147	+	13.1770i	−0.152715	+	0.470009i
$787$	17.0337	−	5.53459i	0.607186	−	0.197287i	0.0107432	−	0.999942i	$-0.496580\pi$
$787$	17.0337	−	5.53459i	0.607186	−	0.197287i	0.596443	+	0.802656i	$0.296580\pi$
$788$	12.0380	−	3.91138i	0.428836	−	0.139337i
$789$	−2.19842	+	6.76605i	−0.0782659	+	0.240878i
$790$	5.99157	−	5.07808i	0.213171	−	0.180670i
$791$	−4.08950	−	12.5862i	−0.145406	−	0.447514i
$792$	−0.305735	−	0.420808i	−0.0108638	−	0.0149528i
$793$			27.5203i			0.977276i
$794$	17.6381	−	12.8148i	0.625954	−	0.454782i
$795$	5.04528	−	2.06742i	0.178938	−	0.0733240i
$796$	−5.04946	−	3.66865i	−0.178973	−	0.130032i
$797$	−15.4319	+	21.2401i	−0.546625	+	0.752364i	−0.989549	−	0.144195i	$-0.953941\pi$
$797$	−15.4319	+	21.2401i	−0.546625	+	0.752364i	0.442925	+	0.896559i	$0.353941\pi$
$798$	−13.5776	−	4.41164i	−0.480643	−	0.156170i
$799$	24.9778			0.883652
$800$	−0.744661	−	4.94424i	−0.0263277	−	0.174805i
$801$	−9.85880			−0.348344
$802$	21.6874	+	7.04666i	0.765808	+	0.248826i
$803$	1.17509	−	1.61737i	0.0414679	−	0.0570756i
$804$	5.41544	+	3.93455i	0.190988	+	0.138761i
$805$	17.4245	+	4.25325i	0.614131	+	0.149908i
$806$	−13.0971	+	9.51560i	−0.461326	+	0.335173i
$807$			9.42986i			0.331947i
$808$	−10.3685	−	14.2711i	−0.364763	−	0.502054i
$809$	−9.12577	−	28.0862i	−0.320845	−	0.987459i	−0.973281	−	0.229616i	$-0.926253\pi$
$809$	−9.12577	−	28.0862i	−0.320845	−	0.987459i	0.652436	−	0.757844i	$-0.273747\pi$
$810$	0.847859	+	2.06909i	0.0297907	+	0.0727004i
$811$	9.10810	−	28.0318i	0.319829	−	0.984331i	−0.653893	−	0.756587i	$-0.726865\pi$
$811$	9.10810	−	28.0318i	0.319829	−	0.984331i	0.973721	−	0.227744i	$-0.0731348\pi$
$812$	17.8506	−	5.80001i	0.626433	−	0.203540i
$813$	−1.30760	+	0.424865i	−0.0458595	+	0.0149007i
$814$	−0.853047	+	2.62541i	−0.0298993	+	0.0920205i
$815$	−10.0853	−	24.6119i	−0.353273	−	0.862118i
$816$	0.833023	+	2.56378i	0.0291616	+	0.0897502i
$817$	−38.5273	−	53.0283i	−1.34790	−	1.85523i
$818$		−	5.00147i		−	0.174872i
$819$	−3.67473	+	2.66985i	−0.128405	+	0.0932920i
$820$	−7.00255	−	1.70930i	−0.244540	−	0.0596913i
$821$	−36.2580	−	26.3430i	−1.26541	−	0.919377i	−0.266404	−	0.963862i	$-0.585835\pi$
$821$	−36.2580	−	26.3430i	−1.26541	−	0.919377i	−0.999010	+	0.0444846i	$0.985835\pi$
$822$	−11.6933	+	16.0945i	−0.407852	+	0.561360i
$823$	20.6983	+	6.72529i	0.721498	+	0.234429i	0.646673	−	0.762768i	$-0.276160\pi$
$823$	20.6983	+	6.72529i	0.721498	+	0.234429i	0.0748255	+	0.997197i	$0.476160\pi$
$824$	8.69758			0.302995
$825$	1.82498	+	1.85290i	0.0635378	+	0.0645099i
$826$	17.9694			0.625234
$827$	18.1721	+	5.90446i	0.631905	+	0.205318i	0.607419	−	0.794382i	$-0.292205\pi$
$827$	18.1721	+	5.90446i	0.631905	+	0.205318i	0.0244861	+	0.999700i	$0.492205\pi$
$828$	2.26924	−	3.12334i	0.0788616	−	0.108544i
$829$	−29.3862	−	21.3503i	−1.02063	−	0.741528i	−0.0542146	−	0.998529i	$-0.517265\pi$
$829$	−29.3862	−	21.3503i	−1.02063	−	0.741528i	−0.966411	+	0.257001i	$0.917265\pi$
$830$	27.1694	−	11.1333i	0.943065	−	0.386443i
$831$	15.8540	−	11.5186i	0.549971	−	0.399577i
$832$		−	2.18619i		−	0.0757926i
$833$	4.25159	+	5.85181i	0.147309	+	0.202753i
$834$	1.74398	+	5.36743i	0.0603892	+	0.185859i
$835$	−15.2573	+	12.9311i	−0.528001	+	0.447501i
$836$	−1.10445	+	3.39915i	−0.0381983	+	0.117562i
$837$	−7.04264	+	2.28829i	−0.243429	+	0.0790950i
$838$	−21.7082	+	7.05342i	−0.749897	+	0.243656i
$839$	−6.13673	+	18.8869i	−0.211863	+	0.652049i	0.787498	+	0.616317i	$0.211376\pi$
$839$	−6.13673	+	18.8869i	−0.211863	+	0.652049i	−0.999361	+	0.0357313i	$0.988624\pi$
$840$	4.63287	−	0.346926i	0.159849	−	0.0119701i
$841$	16.2568	+	50.0334i	0.560581	+	1.72529i
$842$	−9.23612	−	12.7124i	−0.318298	−	0.438099i
$843$		−	2.83807i		−	0.0977483i
$844$	−18.1850	+	13.2122i	−0.625955	+	0.454783i
$845$	11.8848	+	14.0228i	0.408851	+	0.482399i
$846$	−7.49614	−	5.44627i	−0.257723	−	0.187246i
$847$	−13.1031	+	18.0349i	−0.450229	+	0.619687i
$848$	−2.31906	−	0.753509i	−0.0796369	−	0.0258756i
$849$	−2.23356			−0.0766556
$850$	−6.02781	−	12.0556i	−0.206752	−	0.413504i
$851$	−20.4893			−0.702363
$852$	7.76919	+	2.52436i	0.266168	+	0.0864832i
$853$	15.3025	−	21.0621i	0.523948	−	0.721153i	−0.462245	−	0.886752i	$-0.652956\pi$
$853$	15.3025	−	21.0621i	0.523948	−	0.721153i	0.986193	+	0.165600i	$0.0529559\pi$
$854$	21.1594	+	15.3732i	0.724058	+	0.526059i
$855$	8.07768	−	13.0700i	0.276251	−	0.446983i
$856$	4.37660	−	3.17979i	0.149589	−	0.108683i
$857$		−	34.8614i		−	1.19084i	−0.803414	−	0.595421i	$-0.796985\pi$
$857$		−	34.8614i		−	1.19084i	0.803414	−	0.595421i	$-0.203015\pi$
$858$	0.668395	+	0.919967i	0.0228186	+	0.0314071i
$859$	4.67229	+	14.3798i	0.159417	+	0.490634i	0.998582	−	0.0532431i	$-0.0169558\pi$
$859$	4.67229	+	14.3798i	0.159417	+	0.490634i	−0.839165	+	0.543877i	$0.816956\pi$
$860$	18.1446	+	11.2140i	0.618727	+	0.382394i
$861$	2.06967	−	6.36978i	0.0705341	−	0.217081i
$862$	9.08897	−	2.95319i	0.309572	−	0.100586i
$863$	−21.7819	+	7.07738i	−0.741466	+	0.240917i	−0.655305	−	0.755364i	$-0.727460\pi$
$863$	−21.7819	+	7.07738i	−0.741466	+	0.240917i	−0.0861610	+	0.996281i	$0.527460\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−8.66376	+	35.4931i	−0.294577	+	1.20680i
$866$	2.50988	+	7.72462i	0.0852892	+	0.262493i
$867$	−5.72098	−	7.87425i	−0.194295	−	0.267424i
$868$			15.3854i			0.522215i
$869$	1.47806	−	1.07387i	0.0501397	−	0.0364286i
$870$	1.50843	+	20.1436i	0.0511405	+	0.682933i
$871$	−11.8392	−	8.60168i	−0.401156	−	0.291457i
$872$	1.69504	−	2.33302i	0.0574013	−	0.0790061i
$873$	−10.2331	−	3.32495i	−0.346339	−	0.112532i
$874$	−26.5278			−0.897315
$875$	−22.6477	+	5.16520i	−0.765631	+	0.174616i
$876$	3.84348			0.129859
$877$	15.6806	+	5.09493i	0.529495	+	0.172043i	0.561550	−	0.827443i	$-0.310205\pi$
$877$	15.6806	+	5.09493i	0.529495	+	0.172043i	−0.0320550	+	0.999486i	$0.510205\pi$
$878$	−5.41910	+	7.45875i	−0.182886	+	0.251721i
$879$	−19.4375	−	14.1221i	−0.655609	−	0.476328i
$880$	−0.0868528	−	1.15984i	−0.00292781	−	0.0390981i
$881$	−18.7621	+	13.6315i	−0.632112	+	0.459257i	−0.857131	−	0.515098i	$-0.827756\pi$
$881$	−18.7621	+	13.6315i	−0.632112	+	0.459257i	0.225019	+	0.974354i	$0.427756\pi$
$882$		−	2.68323i		−	0.0903491i
$883$	−14.3841	−	19.7980i	−0.484062	−	0.666254i	0.495217	−	0.868769i	$-0.335089\pi$
$883$	−14.3841	−	19.7980i	−0.484062	−	0.666254i	−0.979279	+	0.202515i	$0.935089\pi$
$884$	−1.82115	−	5.60491i	−0.0612518	−	0.188514i
$885$	−4.58599	+	18.7876i	−0.154156	+	0.631537i
$886$	2.97655	−	9.16088i	0.0999991	−	0.307766i
$887$	3.75624	−	1.22048i	0.126122	−	0.0409796i	−0.245276	−	0.969453i	$-0.578879\pi$
$887$	3.75624	−	1.22048i	0.126122	−	0.0409796i	0.371398	+	0.928474i	$0.378879\pi$
$888$	−5.04743	+	1.64001i	−0.169381	+	0.0550352i
$889$	9.60960	−	29.5753i	0.322296	−	0.991924i
$890$	−18.7526	−	11.5897i	−0.628587	−	0.388488i
$891$	0.160734	+	0.494689i	0.00538480	+	0.0165727i
$892$	10.5389	+	14.5056i	0.352870	+	0.485684i
$893$			63.6676i			2.13055i
$894$	12.2126	−	8.87296i	0.408450	−	0.296756i
$895$	4.32437	−	6.99698i	0.144548	−	0.233883i
$896$	−1.68088	−	1.22123i	−0.0561543	−	0.0407985i
$897$	−4.96100	+	6.82823i	−0.165643	+	0.227988i
$898$	20.2666	+	6.58502i	0.676306	+	0.219745i
$899$	−66.8954			−2.23109
$900$	−0.819639	+	4.93236i	−0.0273213	+	0.164412i
$901$	−6.57325			−0.218987
$902$	−1.59467	−	0.518140i	−0.0530967	−	0.0172522i
$903$	−11.6496	+	16.0343i	−0.387673	+	0.533587i
$904$	−5.15307	−	3.74393i	−0.171389	−	0.124521i
$905$	−33.3234	−	39.3179i	−1.10771	−	1.30697i
$906$	−16.9370	+	12.3055i	−0.562695	+	0.408822i
$907$			52.8637i			1.75531i	0.479291	+	0.877656i	$0.340894\pi$
$907$			52.8637i			1.75531i	−0.479291	+	0.877656i	$0.659106\pi$
$908$	−5.20640	−	7.16599i	−0.172780	−	0.237812i
$909$	5.45106	+	16.7766i	0.180800	+	0.556446i
$910$	−10.1283	+	0.758448i	−0.335751	+	0.0251423i
$911$	3.55654	−	10.9459i	0.117833	−	0.362654i	−0.874694	−	0.484676i	$-0.838938\pi$
$911$	3.55654	−	10.9459i	0.117833	−	0.362654i	0.992527	+	0.122021i	$0.0389377\pi$
$912$	−6.53498	+	2.12334i	−0.216395	+	0.0703110i
$913$	6.49582	−	2.11062i	0.214980	−	0.0698513i
$914$	4.16129	−	12.8071i	0.137643	−	0.423622i
$915$	−21.4733	+	18.1994i	−0.709885	+	0.601654i
$916$	6.81771	+	20.9828i	0.225264	+	0.693290i
$917$	−16.9203	−	23.2888i	−0.558759	−	0.769066i
$918$		−	2.69572i		−	0.0889719i
$919$	25.1008	−	18.2368i	0.828000	−	0.601577i	−0.0909927	−	0.995852i	$-0.529004\pi$
$919$	25.1008	−	18.2368i	0.828000	−	0.601577i	0.918993	+	0.394274i	$0.129004\pi$
$920$	7.98807	−	3.27330i	0.263359	−	0.107918i
$921$	13.8507	+	10.0631i	0.456395	+	0.331590i
$922$	19.3003	−	26.5646i	0.635622	−	0.874858i
$923$	−16.9849	−	5.51874i	−0.559066	−	0.181652i
$924$	1.08070			0.0355524
$925$	23.7345	−	11.8672i	0.780384	−	0.390192i
$926$	−22.9306			−0.753547
$927$	−8.27189	−	2.68770i	−0.271685	−	0.0882757i
$928$	5.30989	−	7.30844i	0.174306	−	0.239911i
$929$	−9.67177	−	7.02695i	−0.317320	−	0.230547i	0.417711	−	0.908580i	$-0.362833\pi$
$929$	−9.67177	−	7.02695i	−0.317320	−	0.230547i	−0.735031	+	0.678033i	$0.762833\pi$
$930$	−16.0860	−	3.92653i	−0.527479	−	0.128756i
$931$	−14.9161	+	10.8371i	−0.488854	+	0.355173i
$932$			11.5427i			0.378095i
$933$	11.8455	+	16.3039i	0.387804	+	0.533766i
$934$	−6.43806	−	19.8143i	−0.210660	−	0.648344i
$935$	−1.18884	−	2.90122i	−0.0388793	−	0.0948799i
$936$	−0.675571	+	2.07919i	−0.0220817	+	0.0679605i
$937$	−13.9740	+	4.54042i	−0.456510	+	0.148329i	−0.528240	−	0.849095i	$-0.677148\pi$
$937$	−13.9740	+	4.54042i	−0.456510	+	0.148329i	0.0717304	+	0.997424i	$0.477148\pi$
$938$	−13.2270	+	4.29772i	−0.431877	+	0.140325i
$939$	−7.88127	+	24.2560i	−0.257195	+	0.791566i
$940$	−7.85604	−	19.1717i	−0.256236	−	0.625310i
$941$	15.6185	+	48.0688i	0.509149	+	1.56700i	0.793682	+	0.608333i	$0.208162\pi$
$941$	15.6185	+	48.0688i	0.509149	+	1.56700i	−0.284533	+	0.958666i	$0.591838\pi$
$942$	3.36212	+	4.62756i	0.109544	+	0.150774i
$943$		−	12.4452i		−	0.405271i
$944$	6.99698	−	5.08361i	0.227732	−	0.165457i
$945$	−4.51333	−	1.10169i	−0.146819	−	0.0358379i
$946$	4.01417	+	2.91646i	0.130512	+	0.0948224i
$947$	−23.3247	+	32.1037i	−0.757952	+	1.04323i	0.239430	+	0.970914i	$0.423040\pi$
$947$	−23.3247	+	32.1037i	−0.757952	+	1.04323i	−0.997382	+	0.0723177i	$0.976960\pi$
$948$	3.34052	+	1.08540i	0.108495	+	0.0352522i
$949$	−8.40259			−0.272759
$950$	30.7293	−	15.3647i	0.996991	−	0.498496i
$951$	31.5182			1.02205
$952$	−5.32672	−	1.73076i	−0.172640	−	0.0560942i
$953$	−29.7563	+	40.9560i	−0.963901	+	1.32670i	−0.0188330	+	0.999823i	$0.505995\pi$
$953$	−29.7563	+	40.9560i	−0.963901	+	1.32670i	−0.945068	+	0.326873i	$0.894005\pi$
$954$	1.97271	+	1.43326i	0.0638689	+	0.0464035i
$955$	−3.69888	+	1.51570i	−0.119693	+	0.0490470i
$956$	0.715921	−	0.520147i	0.0231545	−	0.0168228i
$957$			4.69887i			0.151893i
$958$	7.94842	+	10.9401i	0.256802	+	0.353457i
$959$	−12.7727	−	39.3102i	−0.412451	−	1.26939i
$960$	1.70582	−	1.44575i	0.0550551	−	0.0466612i
$961$	7.36546	−	22.6685i	0.237595	−	0.731243i
$962$	11.0347	−	3.58538i	0.355772	−	0.115597i
$963$	−5.14500	+	1.67171i	−0.165795	+	0.0538702i
$964$	−3.91637	+	12.0534i	−0.126138	+	0.388212i
$965$	14.7199	−	1.10228i	0.473851	−	0.0354837i
$966$	2.47870	+	7.62866i	0.0797509	+	0.245448i
$967$	6.49628	+	8.94137i	0.208906	+	0.287535i	0.900594	−	0.434662i	$-0.143132\pi$
$967$	6.49628	+	8.94137i	0.208906	+	0.287535i	−0.691687	+	0.722197i	$0.743132\pi$
$968$			10.7294i			0.344857i
$969$	−14.9855	+	10.8876i	−0.481402	+	0.349759i
$970$	−15.5559	−	18.3542i	−0.499469	−	0.589318i
$971$	−19.9495	−	14.4942i	−0.640211	−	0.465140i	0.219712	−	0.975565i	$-0.429488\pi$
$971$	−19.9495	−	14.4942i	−0.640211	−	0.465140i	−0.859923	+	0.510424i	$0.829488\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	−11.1518	−	3.62345i	−0.357511	−	0.116162i
$974$	−26.6228			−0.853050
$975$	1.79189	−	10.7831i	0.0573863	−	0.345335i
$976$	12.5882			0.402940
$977$	7.71967	+	2.50827i	0.246974	+	0.0802467i	0.429888	−	0.902882i	$-0.358553\pi$
$977$	7.71967	+	2.50827i	0.246974	+	0.0802467i	−0.182914	+	0.983129i	$0.558553\pi$
$978$	6.99173	−	9.62329i	0.223571	−	0.307719i
$979$	−4.14866	−	3.01418i	−0.132592	−	0.0963336i
$980$	3.15433	−	5.10381i	0.100761	−	0.163035i
$981$	−2.33302	+	1.69504i	−0.0744877	+	0.0541185i
$982$		−	12.0227i		−	0.383659i
$983$	15.6954	+	21.6028i	0.500605	+	0.689023i	0.982300	−	0.187316i	$-0.0599787\pi$
$983$	15.6954	+	21.6028i	0.500605	+	0.689023i	−0.481695	+	0.876339i	$0.659979\pi$
$984$	−0.996141	−	3.06581i	−0.0317558	−	0.0977344i
$985$	−24.0760	−	14.8798i	−0.767125	−	0.474109i
$986$	7.52530	−	23.1605i	0.239654	−	0.737580i
$987$	18.3091	−	5.94897i	0.582784	−	0.189358i
$988$	14.2867	−	4.64204i	0.454521	−	0.147683i
$989$	−11.3804	+	35.0252i	−0.361875	+	1.11374i
$990$	−0.275807	+	1.12991i	−0.00876573	+	0.0359109i
$991$	−16.3515	−	50.3248i	−0.519423	−	1.59862i	−0.775088	−	0.631854i	$-0.782294\pi$
$991$	−16.3515	−	50.3248i	−0.519423	−	1.59862i	0.255665	−	0.966765i	$-0.417706\pi$
$992$	4.35259	+	5.99083i	0.138195	+	0.190209i
$993$		−	7.30062i		−	0.231678i
$994$	−13.7311	+	9.97625i	−0.435525	+	0.316427i
$995$	1.04219	+	13.9174i	0.0330395	+	0.441211i
$996$	10.6233	+	7.71827i	0.336612	+	0.244563i
$997$	−16.6169	+	22.8712i	−0.526262	+	0.724337i	−0.986555	−	0.163430i	$-0.947744\pi$
$997$	−16.6169	+	22.8712i	−0.526262	+	0.724337i	0.460293	+	0.887767i	$0.347744\pi$
$998$	26.0209	+	8.45469i	0.823676	+	0.267629i
$999$	5.30719			0.167912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.a.79.2	yes	8
3.2	odd	2		450.2.l.a.379.1		8
5.2	odd	4		750.2.g.e.601.1		8
5.3	odd	4		750.2.g.c.601.2		8
5.4	even	2		750.2.h.c.649.1		8
25.6	even	5		750.2.h.c.349.1		8
25.8	odd	20		750.2.g.c.151.2		8
25.9	even	10		3750.2.c.e.1249.1		8
25.12	odd	20		3750.2.a.m.1.1		4
25.13	odd	20		3750.2.a.o.1.4		4
25.16	even	5		3750.2.c.e.1249.8		8
25.17	odd	20		750.2.g.e.151.1		8
25.19	even	10	inner	150.2.h.a.19.2	✓	8
75.44	odd	10		450.2.l.a.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.2	✓	8	25.19	even	10	inner
150.2.h.a.79.2	yes	8	1.1	even	1	trivial
450.2.l.a.19.1		8	75.44	odd	10
450.2.l.a.379.1		8	3.2	odd	2
750.2.g.c.151.2		8	25.8	odd	20
750.2.g.c.601.2		8	5.3	odd	4
750.2.g.e.151.1		8	25.17	odd	20
750.2.g.e.601.1		8	5.2	odd	4
750.2.h.c.349.1		8	25.6	even	5
750.2.h.c.649.1		8	5.4	even	2
3750.2.a.m.1.1		4	25.12	odd	20
3750.2.a.o.1.4		4	25.13	odd	20
3750.2.c.e.1249.1		8	25.9	even	10
3750.2.c.e.1249.8		8	25.16	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.809017 - 0.587785i) q^{6} +2.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.166977 - 2.22982i) q^{5} +(0.809017 - 0.587785i) q^{6} +2.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.530249 - 2.17229i) q^{10} +(0.160734 - 0.494689i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-2.07919 + 0.675571i) q^{13} +(-0.642040 + 1.97599i) q^{14} +(-1.90211 - 1.17557i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58450 + 2.18088i) q^{17} -1.00000i q^{18} +(-5.55899 + 4.03884i) q^{19} +(1.17557 - 1.90211i) q^{20} +(1.68088 + 1.22123i) q^{21} +(0.305735 - 0.420808i) q^{22} +(3.67171 + 1.19301i) q^{23} +1.00000 q^{24} +(-4.94424 + 0.744661i) q^{25} -2.18619 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-1.22123 + 1.68088i) q^{28} +(-7.30844 - 5.30989i) q^{29} +(-1.44575 - 1.70582i) q^{30} +(5.99083 - 4.35259i) q^{31} +1.00000i q^{32} +(-0.305735 - 0.420808i) q^{33} +(0.833023 + 2.56378i) q^{34} +(4.63287 - 0.346926i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-5.04743 + 1.64001i) q^{37} +(-6.53498 + 2.12334i) q^{38} +(-0.675571 + 2.07919i) q^{39} +(1.70582 - 1.44575i) q^{40} +(-0.996141 - 3.06581i) q^{41} +(1.22123 + 1.68088i) q^{42} +9.53920i q^{43} +(0.420808 - 0.305735i) q^{44} +(-2.06909 + 0.847859i) q^{45} +(3.12334 + 2.26924i) q^{46} +(5.44627 - 7.49614i) q^{47} +(0.951057 + 0.309017i) q^{48} +2.68323 q^{49} +(-4.93236 - 0.819639i) q^{50} +2.69572 q^{51} +(-2.07919 - 0.675571i) q^{52} +(-1.43326 + 1.97271i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.12991 - 0.275807i) q^{55} +(-1.68088 + 1.22123i) q^{56} +6.87129i q^{57} +(-5.30989 - 7.30844i) q^{58} +(-2.67261 - 8.22545i) q^{59} +(-0.847859 - 2.06909i) q^{60} +(3.88998 - 11.9721i) q^{61} +(7.04264 - 2.28829i) q^{62} +(1.97599 - 0.642040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.85358 + 4.52343i) q^{65} +(-0.160734 - 0.494689i) q^{66} +(3.93455 + 5.41544i) q^{67} +2.69572i q^{68} +(3.12334 - 2.26924i) q^{69} +(4.51333 + 1.10169i) q^{70} +(6.60886 + 4.80162i) q^{71} +(0.587785 - 0.809017i) q^{72} +(3.65537 + 1.18770i) q^{73} -5.30719 q^{74} +(-2.30371 + 4.43767i) q^{75} -6.87129 q^{76} +(1.02781 + 0.333955i) q^{77} +(-1.28501 + 1.76867i) q^{78} +(2.84162 + 2.06455i) q^{79} +(2.06909 - 0.847859i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.22358i q^{82} +(7.71827 + 10.6233i) q^{83} +(0.642040 + 1.97599i) q^{84} +(4.59841 - 3.89732i) q^{85} +(-2.94777 + 9.07232i) q^{86} +(-8.59159 + 2.79158i) q^{87} +(0.494689 - 0.160734i) q^{88} +(3.04654 - 9.37628i) q^{89} +(-2.22982 + 0.166977i) q^{90} +(-1.40362 - 4.31990i) q^{91} +(2.26924 + 3.12334i) q^{92} -7.40507i q^{93} +(7.49614 - 5.44627i) q^{94} +(9.93414 + 11.7212i) q^{95} +(0.809017 + 0.587785i) q^{96} +(6.32443 - 8.70483i) q^{97} +(2.55190 + 0.829164i) q^{98} -0.520147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more