LMFDB - Embedded newform 950.2.l.g.351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 $ x^12 - 24x^10 + 264x^8 - 1511x^6 + 4812x^4 - 7788*x^2 + 5329
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.1
Root			$-2.79086 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.g.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-2.00490 + 1.68231i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.00490 + 1.68231i) q^{6} +(0.485218 - 0.840422i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.668514 - 3.79133i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.00490 + 1.68231i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.00490 + 1.68231i) q^{6} +(0.485218 - 0.840422i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.668514 - 3.79133i) q^{9} +(0.280827 + 0.486406i) q^{11} +(1.30861 - 2.26658i) q^{12} +(0.350258 + 0.293901i) q^{13} +(-0.911911 - 0.331909i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.0682527 - 0.387080i) q^{17} -3.84982 q^{18} +(-1.58943 - 4.05878i) q^{19} +(0.441039 + 2.50125i) q^{21} +(0.430251 - 0.361024i) q^{22} +(4.92432 - 1.79231i) q^{23} +(-2.45938 - 0.895141i) q^{24} +(0.228615 - 0.395972i) q^{26} +(1.11208 + 1.92618i) q^{27} +(-0.168514 + 0.955692i) q^{28} +(-0.411474 + 2.33359i) q^{29} +(-5.44104 + 9.42416i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.38132 - 0.502759i) q^{33} +(-0.369347 + 0.134431i) q^{34} +(0.668514 + 3.79133i) q^{36} +5.14885 q^{37} +(-3.72112 + 2.27009i) q^{38} -1.19667 q^{39} +(6.14611 - 5.15720i) q^{41} +(2.38667 - 0.868676i) q^{42} +(9.61359 + 3.49906i) q^{43} +(-0.430251 - 0.361024i) q^{44} +(-2.62018 - 4.53828i) q^{46} +(-2.13139 + 12.0877i) q^{47} +(-0.454475 + 2.57745i) q^{48} +(3.02913 + 5.24660i) q^{49} +(0.788030 + 0.661236i) q^{51} +(-0.429655 - 0.156382i) q^{52} +(-4.26309 + 1.55164i) q^{53} +(1.70381 - 1.42967i) q^{54} +0.970436 q^{56} +(10.0148 + 5.46354i) q^{57} +2.36959 q^{58} +(0.759597 + 4.30789i) q^{59} +(4.02481 - 1.46491i) q^{61} +(10.2258 + 3.72189i) q^{62} +(-2.86194 - 2.40146i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.255257 + 1.44764i) q^{66} +(-2.11595 + 12.0001i) q^{67} +(0.196526 + 0.340392i) q^{68} +(-6.85757 + 11.8777i) q^{69} +(6.85757 + 2.49595i) q^{71} +(3.61765 - 1.31672i) q^{72} +(10.6787 - 8.96047i) q^{73} +(-0.894088 - 5.07062i) q^{74} +(2.88176 + 3.27039i) q^{76} +0.545048 q^{77} +(0.207799 + 1.17849i) q^{78} +(-0.730080 + 0.612610i) q^{79} +(5.38288 + 1.95921i) q^{81} +(-6.14611 - 5.15720i) q^{82} +(-5.63540 + 9.76080i) q^{83} +(-1.26992 - 2.19957i) q^{84} +(1.77652 - 10.0751i) q^{86} +(-3.10086 - 5.37084i) q^{87} +(-0.280827 + 0.486406i) q^{88} +(2.69822 + 2.26408i) q^{89} +(0.416952 - 0.151758i) q^{91} +(-4.01435 + 3.36844i) q^{92} +(-4.94563 - 28.0481i) q^{93} +12.2742 q^{94} +2.61722 q^{96} +(-1.25364 - 7.10973i) q^{97} +(4.64089 - 3.89417i) q^{98} +(2.03186 - 0.739538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−2.00490	+	1.68231i	−1.15753	+	0.971285i	−0.999869	−	0.0162084i	$-0.994840\pi$
$3$	−2.00490	+	1.68231i	−1.15753	+	0.971285i	−0.157663	+	0.987493i	$0.550396\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	2.00490	+	1.68231i	0.818499	+	0.686802i
$7$	0.485218	−	0.840422i	0.183395	−	0.317650i	−0.759639	−	0.650344i	$-0.774625\pi$
$7$	0.485218	−	0.840422i	0.183395	−	0.317650i	0.943035	+	0.332695i	$0.107958\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.668514	−	3.79133i	0.222838	−	1.26378i
$10$		0			0
$11$	0.280827	+	0.486406i	0.0846724	+	0.146657i	0.905252	−	0.424876i	$-0.139682\pi$
$11$	0.280827	+	0.486406i	0.0846724	+	0.146657i	−0.820579	+	0.571533i	$0.806349\pi$
$12$	1.30861	−	2.26658i	0.377763	−	0.654304i
$13$	0.350258	+	0.293901i	0.0971440	+	0.0815135i	0.690066	−	0.723746i	$-0.257581\pi$
$13$	0.350258	+	0.293901i	0.0971440	+	0.0815135i	−0.592922	+	0.805260i	$0.702026\pi$
$14$	−0.911911	−	0.331909i	−0.243719	−	0.0887063i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.0682527	−	0.387080i	−0.0165537	−	0.0938807i	0.975412	−	0.220391i	$-0.0707334\pi$
$17$	−0.0682527	−	0.387080i	−0.0165537	−	0.0938807i	−0.991965	+	0.126510i	$0.959622\pi$
$18$	−3.84982			−0.907411
$19$	−1.58943	−	4.05878i	−0.364641	−	0.931148i
$19$	−1.58943	−	4.05878i	−0.364641	−	0.931148i
$20$		0			0
$21$	0.441039	+	2.50125i	0.0962425	+	0.545818i
$22$	0.430251	−	0.361024i	0.0917299	−	0.0769705i
$23$	4.92432	−	1.79231i	1.02679	−	0.373722i	0.226934	−	0.973910i	$-0.427130\pi$
$23$	4.92432	−	1.79231i	1.02679	−	0.373722i	0.799859	+	0.600188i	$0.204908\pi$
$24$	−2.45938	−	0.895141i	−0.502019	−	0.182720i
$25$		0			0
$26$	0.228615	−	0.395972i	0.0448350	−	0.0776565i
$27$	1.11208	+	1.92618i	0.214020	+	0.370694i
$28$	−0.168514	+	0.955692i	−0.0318462	+	0.180609i
$29$	−0.411474	+	2.33359i	−0.0764088	+	0.433336i	0.922473	+	0.386061i	$0.126165\pi$
$29$	−0.411474	+	2.33359i	−0.0764088	+	0.433336i	−0.998882	+	0.0472746i	$0.984946\pi$
$30$		0			0
$31$	−5.44104	+	9.42416i	−0.977239	+	1.69263i	−0.304901	+	0.952384i	$0.598624\pi$
$31$	−5.44104	+	9.42416i	−0.977239	+	1.69263i	−0.672338	+	0.740244i	$0.734710\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.38132	−	0.502759i	−0.240457	−	0.0875191i
$34$	−0.369347	+	0.134431i	−0.0633426	+	0.0230548i
$35$		0			0
$36$	0.668514	+	3.79133i	0.111419	+	0.631889i
$37$	5.14885			0.846465			0.423232	−	0.906021i	$-0.360895\pi$
$37$	5.14885			0.846465			0.423232	+	0.906021i	$0.360895\pi$
$38$	−3.72112	+	2.27009i	−0.603645	+	0.368257i
$39$	−1.19667			−0.191620
$40$		0			0
$41$	6.14611	−	5.15720i	0.959862	−	0.805420i	−0.0210689	−	0.999778i	$-0.506707\pi$
$41$	6.14611	−	5.15720i	0.959862	−	0.805420i	0.980931	+	0.194358i	$0.0622625\pi$
$42$	2.38667	−	0.868676i	0.368271	−	0.134040i
$43$	9.61359	+	3.49906i	1.46606	+	0.533602i	0.947027	−	0.321154i	$-0.104071\pi$
$43$	9.61359	+	3.49906i	1.46606	+	0.533602i	0.519031	+	0.854755i	$0.326293\pi$
$44$	−0.430251	−	0.361024i	−0.0648628	−	0.0544264i
$45$		0			0
$46$	−2.62018	−	4.53828i	−0.386324	−	0.669133i
$47$	−2.13139	+	12.0877i	−0.310896	+	1.76318i	0.283468	+	0.958982i	$0.408515\pi$
$47$	−2.13139	+	12.0877i	−0.310896	+	1.76318i	−0.594364	+	0.804196i	$0.702596\pi$
$48$	−0.454475	+	2.57745i	−0.0655978	+	0.372024i
$49$	3.02913	+	5.24660i	0.432732	+	0.749515i
$50$		0			0
$51$	0.788030	+	0.661236i	0.110346	+	0.0925915i
$52$	−0.429655	−	0.156382i	−0.0595824	−	0.0216862i
$53$	−4.26309	+	1.55164i	−0.585581	+	0.213134i	−0.617785	−	0.786347i	$-0.711970\pi$
$53$	−4.26309	+	1.55164i	−0.585581	+	0.213134i	0.0322038	+	0.999481i	$0.489747\pi$
$54$	1.70381	−	1.42967i	0.231859	−	0.194553i
$55$		0			0
$56$	0.970436			0.129680
$57$	10.0148	+	5.46354i	1.32649	+	0.723663i
$58$	2.36959			0.311142
$59$	0.759597	+	4.30789i	0.0988911	+	0.560839i	0.993485	+	0.113960i	$0.0363536\pi$
$59$	0.759597	+	4.30789i	0.0988911	+	0.560839i	−0.894594	+	0.446879i	$0.852535\pi$
$60$		0			0
$61$	4.02481	−	1.46491i	0.515324	−	0.187562i	−0.0712499	−	0.997458i	$-0.522699\pi$
$61$	4.02481	−	1.46491i	0.515324	−	0.187562i	0.586573	+	0.809896i	$0.300477\pi$
$62$	10.2258	+	3.72189i	1.29868	+	0.472680i
$63$	−2.86194	−	2.40146i	−0.360571	−	0.302555i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−0.255257	+	1.44764i	−0.0314200	+	0.178192i
$67$	−2.11595	+	12.0001i	−0.258504	+	1.46605i	0.528411	+	0.848989i	$0.322788\pi$
$67$	−2.11595	+	12.0001i	−0.258504	+	1.46605i	−0.786915	+	0.617061i	$0.788323\pi$
$68$	0.196526	+	0.340392i	0.0238322	+	0.0412787i
$69$	−6.85757	+	11.8777i	−0.825555	+	1.42990i
$70$		0			0
$71$	6.85757	+	2.49595i	0.813844	+	0.296215i	0.715211	−	0.698909i	$-0.246331\pi$
$71$	6.85757	+	2.49595i	0.813844	+	0.296215i	0.0986333	+	0.995124i	$0.468553\pi$
$72$	3.61765	−	1.31672i	0.426344	−	0.155177i
$73$	10.6787	−	8.96047i	1.24984	−	1.04874i	0.253156	−	0.967426i	$-0.418531\pi$
$73$	10.6787	−	8.96047i	1.24984	−	1.04874i	0.996688	−	0.0813181i	$-0.0259130\pi$
$74$	−0.894088	−	5.07062i	−0.103936	−	0.589448i
$75$		0			0
$76$	2.88176	+	3.27039i	0.330561	+	0.375139i
$77$	0.545048			0.0621140
$78$	0.207799	+	1.17849i	0.0235286	+	0.133437i
$79$	−0.730080	+	0.612610i	−0.0821404	+	0.0689240i	−0.682933	−	0.730481i	$-0.739296\pi$
$79$	−0.730080	+	0.612610i	−0.0821404	+	0.0689240i	0.600793	+	0.799405i	$0.294852\pi$
$80$		0			0
$81$	5.38288	+	1.95921i	0.598098	+	0.217690i
$82$	−6.14611	−	5.15720i	−0.678725	−	0.569518i
$83$	−5.63540	+	9.76080i	−0.618566	+	1.07139i	0.371182	+	0.928560i	$0.378953\pi$
$83$	−5.63540	+	9.76080i	−0.618566	+	1.07139i	−0.989748	+	0.142827i	$0.954381\pi$
$84$	−1.26992	−	2.19957i	−0.138560	−	0.239992i
$85$		0			0
$86$	1.77652	−	10.0751i	0.191567	−	1.08643i
$87$	−3.10086	−	5.37084i	−0.332447	−	0.575815i
$88$	−0.280827	+	0.486406i	−0.0299362	+	0.0518511i
$89$	2.69822	+	2.26408i	0.286011	+	0.239992i	0.774493	−	0.632582i	$-0.218005\pi$
$89$	2.69822	+	2.26408i	0.286011	+	0.239992i	−0.488482	+	0.872574i	$0.662449\pi$
$90$		0			0
$91$	0.416952	−	0.151758i	0.0437085	−	0.0159086i
$92$	−4.01435	+	3.36844i	−0.418524	+	0.351184i
$93$	−4.94563	−	28.0481i	−0.512838	−	2.90845i
$94$	12.2742			1.26599
$95$		0			0
$96$	2.61722			0.267119
$97$	−1.25364	−	7.10973i	−0.127288	−	0.721883i	−0.979923	−	0.199377i	$-0.936108\pi$
$97$	−1.25364	−	7.10973i	−0.127288	−	0.721883i	0.852635	−	0.522506i	$-0.175003\pi$
$98$	4.64089	−	3.89417i	0.468801	−	0.393371i
$99$	2.03186	−	0.739538i	0.204210	−	0.0743264i
$100$		0			0
$101$	9.72875	+	8.16339i	0.968046	+	0.812287i	0.982243	−	0.187612i	$-0.0600747\pi$
$101$	9.72875	+	8.16339i	0.968046	+	0.812287i	−0.0141968	+	0.999899i	$0.504519\pi$
$102$	0.514350	−	0.890881i	0.0509283	−	0.0882103i
$103$	−5.73554	−	9.93425i	−0.565140	−	0.978851i	−0.997037	−	0.0769276i	$-0.975489\pi$
$103$	−5.73554	−	9.93425i	−0.565140	−	0.978851i	0.431897	−	0.901923i	$-0.357844\pi$
$104$	−0.0793970	+	0.450283i	−0.00778552	+	0.0441539i
$105$		0			0
$106$	2.26834	+	3.92889i	0.220321	+	0.381607i
$107$	−6.26711	+	10.8549i	−0.605864	+	1.04939i	0.386050	+	0.922478i	$0.373839\pi$
$107$	−6.26711	+	10.8549i	−0.605864	+	1.04939i	−0.991914	+	0.126909i	$0.959494\pi$
$108$	−1.70381	−	1.42967i	−0.163949	−	0.137570i
$109$	5.34478	+	1.94534i	0.511937	+	0.186330i	0.585055	−	0.810993i	$-0.301073\pi$
$109$	5.34478	+	1.94534i	0.511937	+	0.186330i	−0.0731182	+	0.997323i	$0.523295\pi$
$110$		0			0
$111$	−10.3229	+	8.66198i	−0.979810	+	0.822158i
$112$	−0.168514	−	0.955692i	−0.0159231	−	0.0903045i
$113$	4.13698			0.389174			0.194587	−	0.980885i	$-0.437663\pi$
$113$	4.13698			0.389174			0.194587	+	0.980885i	$0.437663\pi$
$114$	3.64148	−	10.8114i	0.341056	−	1.01258i
$115$		0			0
$116$	−0.411474	−	2.33359i	−0.0382044	−	0.216668i
$117$	1.34843	−	1.13147i	0.124662	−	0.104604i
$118$	4.11054	−	1.49611i	0.378406	−	0.137728i
$119$	−0.358428	−	0.130457i	−0.0328570	−	0.0119590i
$120$		0			0
$121$	5.34227	−	9.25309i	0.485661	−	0.841190i
$122$	−2.14155	−	3.70928i	−0.193887	−	0.335823i
$123$	−3.64633	+	20.6794i	−0.328779	+	1.86460i
$124$	1.88965	−	10.7168i	0.169696	−	0.962393i
$125$		0			0
$126$	−1.86800	+	3.23547i	−0.166415	+	0.288239i
$127$	−1.55236	−	1.30258i	−0.137749	−	0.115585i	0.571310	−	0.820735i	$-0.306436\pi$
$127$	−1.55236	−	1.30258i	−0.137749	−	0.115585i	−0.709059	+	0.705149i	$0.750880\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−25.1608	+	9.15780i	−2.21529	+	0.806299i
$130$		0			0
$131$	−1.26179	−	7.15598i	−0.110243	−	0.625221i	−0.988996	−	0.147943i	$-0.952735\pi$
$131$	−1.26179	−	7.15598i	−0.110243	−	0.625221i	0.878753	−	0.477278i	$-0.158376\pi$
$132$	1.46997			0.127944
$133$	−4.18231	−	0.633597i	−0.362652	−	0.0549398i
$134$	12.1853			1.05265
$135$		0			0
$136$	0.301095	−	0.252649i	0.0258187	−	0.0216644i
$137$	−7.12159	+	2.59205i	−0.608439	+	0.221454i	−0.627820	−	0.778359i	$-0.716053\pi$
$137$	−7.12159	+	2.59205i	−0.608439	+	0.221454i	0.0193814	+	0.999812i	$0.493830\pi$
$138$	12.8880	+	4.69086i	1.09710	+	0.399312i
$139$	−8.72724	−	7.32303i	−0.740235	−	0.621131i	0.192666	−	0.981264i	$-0.438287\pi$
$139$	−8.72724	−	7.32303i	−0.740235	−	0.621131i	−0.932901	+	0.360133i	$0.882731\pi$
$140$		0			0
$141$	−16.0621	−	27.8204i	−1.35268	−	2.34290i
$142$	1.26723	−	7.18681i	0.106343	−	0.603103i
$143$	−0.0445936	+	0.252903i	−0.00372910	+	0.0211488i
$144$	−1.92491	−	3.33404i	−0.160409	−	0.277837i
$145$		0			0
$146$	−10.6787	−	8.96047i	−0.883773	−	0.741574i
$147$	−14.8995	−	5.42299i	−1.22889	−	0.447281i
$148$	−4.83833	+	1.76101i	−0.397708	+	0.144754i
$149$	−0.00665635	+	0.00558534i	−0.000545309	+	0.000457569i	−0.643060	−	0.765816i	$-0.722336\pi$
$149$	−0.00665635	+	0.00558534i	−0.000545309	+	0.000457569i	0.642515	+	0.766273i	$0.277891\pi$
$150$		0			0
$151$	−15.3824			−1.25180			−0.625901	−	0.779902i	$-0.715269\pi$
$151$	−15.3824			−1.25180			−0.625901	+	0.779902i	$0.715269\pi$
$152$	2.72029	−	3.40588i	0.220645	−	0.276253i
$153$	−1.51318			−0.122333
$154$	−0.0946467	−	0.536768i	−0.00762684	−	0.0432540i
$155$		0			0
$156$	1.12450	−	0.409284i	0.0900320	−	0.0327690i
$157$	−16.9620	−	6.17365i	−1.35371	−	0.492711i	−0.439607	−	0.898190i	$-0.644882\pi$
$157$	−16.9620	−	6.17365i	−1.35371	−	0.492711i	−0.914104	+	0.405479i	$0.867105\pi$
$158$	0.730080	+	0.612610i	0.0580821	+	0.0487366i
$159$	5.93675	−	10.2827i	0.470815	−	0.815475i
$160$		0			0
$161$	0.883075	−	5.00817i	0.0695961	−	0.394699i
$162$	0.994716	−	5.64132i	0.0781523	−	0.443224i
$163$	2.45522	+	4.25257i	0.192308	+	0.333087i	0.946015	−	0.324124i	$-0.105069\pi$
$163$	2.45522	+	4.25257i	0.192308	+	0.333087i	−0.753707	+	0.657211i	$0.771736\pi$
$164$	−4.01159	+	6.94828i	−0.313253	+	0.542569i
$165$		0			0
$166$	10.5911	+	3.85484i	0.822028	+	0.299194i
$167$	15.6472	−	5.69511i	1.21082	−	0.440701i	0.343829	−	0.939032i	$-0.388276\pi$
$167$	15.6472	−	5.69511i	1.21082	−	0.440701i	0.866987	+	0.498331i	$0.166054\pi$
$168$	−1.94563	+	1.63258i	−0.150109	+	0.125956i
$169$	−2.22112	−	12.5966i	−0.170856	−	0.968971i
$170$		0			0
$171$	−16.4507	+	3.31272i	−1.25802	+	0.253330i
$172$	−10.2306			−0.780073
$173$	2.04745	+	11.6116i	0.155664	+	0.882817i	0.958176	+	0.286180i	$0.0923855\pi$
$173$	2.04745	+	11.6116i	0.155664	+	0.882817i	−0.802512	+	0.596637i	$0.796503\pi$
$174$	−4.75079	+	3.98639i	−0.360156	+	0.302207i
$175$		0			0
$176$	0.527781	+	0.192097i	0.0397830	+	0.0144798i
$177$	−8.77014	−	7.35902i	−0.659204	−	0.553138i
$178$	1.76114	−	3.05038i	0.132003	−	0.228636i
$179$	7.87873	+	13.6464i	0.588884	+	1.01998i	0.994379	+	0.105879i	$0.0337658\pi$
$179$	7.87873	+	13.6464i	0.588884	+	1.01998i	−0.405495	+	0.914097i	$0.632901\pi$
$180$		0			0
$181$	−2.58243	+	14.6457i	−0.191951	+	1.08861i	0.724744	+	0.689018i	$0.241958\pi$
$181$	−2.58243	+	14.6457i	−0.191951	+	1.08861i	−0.916695	+	0.399588i	$0.869153\pi$
$182$	−0.221856	−	0.384265i	−0.0164450	−	0.0284836i
$183$	−5.60491	+	9.70799i	−0.414327	+	0.717635i
$184$	4.01435	+	3.36844i	0.295941	+	0.248324i
$185$		0			0
$186$	−26.7631	+	9.74099i	−1.96237	+	0.714244i
$187$	0.169111	−	0.141901i	0.0123666	−	0.0103768i
$188$	−2.13139	−	12.0877i	−0.155448	−	0.881589i
$189$	2.15841			0.157001
$190$		0			0
$191$	26.1567			1.89263			0.946315	−	0.323247i	$-0.104774\pi$
$191$	26.1567			1.89263			0.946315	+	0.323247i	$0.104774\pi$
$192$	−0.454475	−	2.57745i	−0.0327989	−	0.186012i
$193$	9.37557	−	7.86704i	0.674868	−	0.566282i	−0.239634	−	0.970863i	$-0.577027\pi$
$193$	9.37557	−	7.86704i	0.674868	−	0.566282i	0.914502	+	0.404582i	$0.132583\pi$
$194$	−6.78402	+	2.46918i	−0.487064	+	0.177277i
$195$		0			0
$196$	−4.64089	−	3.89417i	−0.331492	−	0.278155i
$197$	0.156773	−	0.271540i	0.0111696	−	0.0193464i	−0.860387	−	0.509642i	$-0.829778\pi$
$197$	0.156773	−	0.271540i	0.0111696	−	0.0193464i	0.871556	+	0.490296i	$0.163111\pi$
$198$	−1.08113	−	1.87258i	−0.0768327	−	0.133078i
$199$	3.72685	−	21.1360i	0.264189	−	1.49829i	−0.507145	−	0.861861i	$-0.669299\pi$
$199$	3.72685	−	21.1360i	0.264189	−	1.49829i	0.771334	−	0.636430i	$-0.219590\pi$
$200$		0			0
$201$	−15.9457	−	27.6188i	−1.12473	−	1.94808i
$202$	6.34999	−	10.9985i	0.446784	−	0.773852i
$203$	1.76154	+	1.47811i	0.123636	+	0.103743i
$204$	−0.966662	−	0.351836i	−0.0676799	−	0.0246335i
$205$		0			0
$206$	−8.78736	+	7.37347i	−0.612244	+	0.513734i
$207$	−3.50325	−	19.8679i	−0.243493	−	1.38092i
$208$	0.457229			0.0317031
$209$	1.52786	−	1.91292i	0.105684	−	0.132320i
$210$		0			0
$211$	2.27645	+	12.9104i	0.156717	+	0.888788i	0.957199	+	0.289431i	$0.0934660\pi$
$211$	2.27645	+	12.9104i	0.156717	+	0.888788i	−0.800482	+	0.599357i	$0.795423\pi$
$212$	3.47530	−	2.91613i	0.238685	−	0.200280i
$213$	−17.9477	+	6.53245i	−1.22976	+	0.447596i
$214$	11.7783	+	4.28695i	0.805148	+	0.293050i
$215$		0			0
$216$	−1.11208	+	1.92618i	−0.0756676	+	0.131060i
$217$	5.28018	+	9.14554i	0.358442	+	0.620839i
$218$	0.987675	−	5.60139i	0.0668938	−	0.379374i
$219$	−6.33539	+	35.9298i	−0.428106	+	2.42791i
$220$		0			0
$221$	0.0898573	−	0.155637i	0.00604445	−	0.0104693i
$222$	10.3229	+	8.66198i	0.692830	+	0.581354i
$223$	20.6069	+	7.50031i	1.37994	+	0.502258i	0.922161	−	0.386806i	$-0.126422\pi$
$223$	20.6069	+	7.50031i	1.37994	+	0.502258i	0.457782	+	0.889065i	$0.348644\pi$
$224$	−0.911911	+	0.331909i	−0.0609296	+	0.0221766i
$225$		0			0
$226$	−0.718379	−	4.07413i	−0.0477859	−	0.271007i
$227$	3.93628			0.261260			0.130630	−	0.991431i	$-0.458300\pi$
$227$	3.93628			0.261260			0.130630	+	0.991431i	$0.458300\pi$
$228$	−11.2795	−	1.70878i	−0.747002	−	0.113167i
$229$	12.4712			0.824122			0.412061	−	0.911156i	$-0.364809\pi$
$229$	12.4712			0.824122			0.412061	+	0.911156i	$0.364809\pi$
$230$		0			0
$231$	−1.09277	+	0.916943i	−0.0718990	+	0.0603304i
$232$	−2.22668	+	0.810446i	−0.146189	+	0.0532084i
$233$	12.6103	+	4.58978i	0.826130	+	0.300687i	0.720270	−	0.693694i	$-0.244018\pi$
$233$	12.6103	+	4.58978i	0.826130	+	0.300687i	0.105860	+	0.994381i	$0.466240\pi$
$234$	−1.34843	−	1.13147i	−0.0881496	−	0.0739663i
$235$		0			0
$236$	−2.18717	−	3.78829i	−0.142373	−	0.246597i
$237$	0.433138	−	2.45645i	0.0281353	−	0.159563i
$238$	−0.0662348	+	0.375636i	−0.00429336	+	0.0243489i
$239$	−0.766043	−	1.32682i	−0.0495512	−	0.0858252i	0.840186	−	0.542298i	$-0.182446\pi$
$239$	−0.766043	−	1.32682i	−0.0495512	−	0.0858252i	−0.889737	+	0.456473i	$0.849112\pi$
$240$		0			0
$241$	−10.7084	−	8.98543i	−0.689790	−	0.578802i	0.229059	−	0.973413i	$-0.426435\pi$
$241$	−10.7084	−	8.98543i	−0.689790	−	0.578802i	−0.918849	+	0.394610i	$0.870880\pi$
$242$	−10.0402	−	3.65433i	−0.645408	−	0.234909i
$243$	−20.3583	+	7.40980i	−1.30598	+	0.475339i
$244$	−3.28105	+	2.75313i	−0.210048	+	0.176251i
$245$		0			0
$246$	20.9984			1.33881
$247$	0.636169	−	1.88876i	0.0404784	−	0.120179i
$248$	−10.8821			−0.691013
$249$	−5.12230	−	29.0500i	−0.324612	−	1.84097i
$250$		0			0
$251$	−15.7226	+	5.72255i	−0.992400	+	0.361204i	−0.786649	−	0.617400i	$-0.788186\pi$
$251$	−15.7226	+	5.72255i	−0.992400	+	0.361204i	−0.205751	+	0.978604i	$0.565964\pi$
$252$	3.51069	+	1.27779i	0.221153	+	0.0804931i
$253$	2.25467	+	1.89189i	0.141750	+	0.118942i
$254$	−1.01323	+	1.75496i	−0.0635756	+	0.110116i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.04270	+	5.91343i	−0.0650417	+	0.368870i	0.934862	+	0.355011i	$0.115523\pi$
$257$	−1.04270	+	5.91343i	−0.0650417	+	0.368870i	−0.999904	+	0.0138590i	$0.995588\pi$
$258$	13.3878	+	23.1884i	0.833488	+	1.44364i
$259$	2.49831	−	4.32720i	0.155238	−	0.268879i
$260$		0			0
$261$	8.57233	+	3.12007i	0.530614	+	0.193128i
$262$	−6.82816	+	2.48525i	−0.421845	+	0.153539i
$263$	4.83259	−	4.05502i	0.297990	−	0.250043i	−0.481517	−	0.876437i	$-0.659914\pi$
$263$	4.83259	−	4.05502i	0.297990	−	0.250043i	0.779507	+	0.626393i	$0.215470\pi$
$264$	−0.255257	−	1.44764i	−0.0157100	−	0.0890958i
$265$		0			0
$266$	0.102280	+	4.22879i	0.00627116	+	0.259284i
$267$	−9.21857			−0.564167
$268$	−2.11595	−	12.0001i	−0.129252	−	0.733025i
$269$	−16.7593	+	14.0627i	−1.02183	+	0.857418i	−0.989856	−	0.142071i	$-0.954624\pi$
$269$	−16.7593	+	14.0627i	−1.02183	+	0.857418i	−0.0319740	+	0.999489i	$0.510179\pi$
$270$		0			0
$271$	−9.43077	−	3.43252i	−0.572879	−	0.208511i	0.0393039	−	0.999227i	$-0.487486\pi$
$271$	−9.43077	−	3.43252i	−0.572879	−	0.208511i	−0.612182	+	0.790717i	$0.709708\pi$
$272$	−0.301095	−	0.252649i	−0.0182566	−	0.0153191i
$273$	−0.580644	+	1.00571i	−0.0351422	+	0.0608681i
$274$	3.78932	+	6.56329i	0.228921	+	0.396503i
$275$		0			0
$276$	2.38161	−	13.5068i	0.143356	−	0.813013i
$277$	8.50328	+	14.7281i	0.510913	+	0.884927i	0.999920	+	0.0126472i	$0.00402583\pi$
$277$	8.50328	+	14.7281i	0.510913	+	0.884927i	−0.489007	+	0.872280i	$0.662641\pi$
$278$	−5.69630	+	9.86629i	−0.341642	+	0.591741i
$279$	32.0927	+	26.9290i	1.92134	+	1.61220i
$280$		0			0
$281$	0.993565	−	0.361628i	0.0592711	−	0.0215729i	−0.312214	−	0.950012i	$-0.601071\pi$
$281$	0.993565	−	0.361628i	0.0592711	−	0.0215729i	0.371486	+	0.928439i	$0.378849\pi$
$282$	−24.6086	+	20.6491i	−1.46542	+	1.22963i
$283$	−4.09746	−	23.2379i	−0.243569	−	1.38135i	−0.823793	−	0.566891i	$-0.808146\pi$
$283$	−4.09746	−	23.2379i	−0.243569	−	1.38135i	0.580224	−	0.814457i	$-0.302965\pi$
$284$	−7.29768			−0.433037
$285$		0			0
$286$	0.256804			0.0151852
$287$	−1.35202	−	7.66769i	−0.0798073	−	0.452610i
$288$	−2.94913	+	2.47462i	−0.173779	+	0.145818i
$289$	15.8296	−	5.76150i	0.931153	−	0.338912i
$290$		0			0
$291$	14.4742	+	12.1453i	0.848494	+	0.711971i
$292$	−6.97001	+	12.0724i	−0.407889	+	0.706484i
$293$	−11.1409	−	19.2967i	−0.650860	−	1.12732i	−0.982915	−	0.184063i	$-0.941075\pi$
$293$	−11.1409	−	19.2967i	−0.650860	−	1.12732i	0.332054	−	0.943260i	$-0.392258\pi$
$294$	−2.75332	+	15.6149i	−0.160577	+	0.910678i
$295$		0			0
$296$	2.57442	+	4.45903i	0.149635	+	0.259176i
$297$	−0.624605	+	1.08185i	−0.0362432	+	0.0627751i
$298$	0.00665635	+	0.00558534i	0.000385592	+	0.000323550i
$299$	2.25154	+	0.819495i	0.130210	+	0.0473926i
$300$		0			0
$301$	7.60537	−	6.38166i	0.438366	−	0.367833i
$302$	2.67113	+	15.1487i	0.153706	+	0.871710i
$303$	−33.2386			−1.90951
$304$	−3.82651	−	2.08754i	−0.219465	−	0.119728i
$305$		0			0
$306$	0.262760	+	1.49019i	0.0150210	+	0.0851884i
$307$	20.9406	−	17.5713i	1.19514	−	1.00284i	0.195388	−	0.980726i	$-0.437403\pi$
$307$	20.9406	−	17.5713i	1.19514	−	1.00284i	0.999755	−	0.0221182i	$-0.00704102\pi$
$308$	−0.512178	+	0.186418i	−0.0291840	+	0.0106221i
$309$	28.2117	+	10.2682i	1.60491	+	0.584139i
$310$		0			0
$311$	−15.6908	+	27.1772i	−0.889743	+	1.54108i	−0.0495638	+	0.998771i	$0.515783\pi$
$311$	−15.6908	+	27.1772i	−0.889743	+	1.54108i	−0.840179	+	0.542309i	$0.817550\pi$
$312$	−0.598334	−	1.03634i	−0.0338740	−	0.0586715i
$313$	0.199842	−	1.13336i	0.0112957	−	0.0640613i	−0.978639	−	0.205587i	$-0.934090\pi$
$313$	0.199842	−	1.13336i	0.0112957	−	0.0640613i	0.989935	+	0.141526i	$0.0452008\pi$
$314$	−3.13444	+	17.7763i	−0.176887	+	1.00318i
$315$		0			0
$316$	0.476526	−	0.825367i	0.0268067	−	0.0464305i
$317$	15.8245	+	13.2783i	0.888791	+	0.745784i	0.967967	−	0.251077i	$-0.0807847\pi$
$317$	15.8245	+	13.2783i	0.888791	+	0.745784i	−0.0791766	+	0.996861i	$0.525229\pi$
$318$	−11.1574	−	4.06097i	−0.625678	−	0.227728i
$319$	−1.25062	+	0.455190i	−0.0700214	+	0.0254857i
$320$		0			0
$321$	−5.69648	−	32.3064i	−0.317947	−	1.80317i
$322$	−5.08543			−0.283400
$323$	−1.46259	+	0.892261i	−0.0813807	+	0.0496467i
$324$	−5.72834			−0.318241
$325$		0			0
$326$	3.76162	−	3.15637i	0.208337	−	0.174815i
$327$	−13.9884	+	5.09138i	−0.773563	+	0.281554i
$328$	7.53932	+	2.74409i	0.416290	+	0.151517i
$329$	9.12461	+	7.65645i	0.503056	+	0.422114i
$330$		0			0
$331$	5.97822	+	10.3546i	0.328593	+	0.569139i	0.982233	−	0.187666i	$-0.0600923\pi$
$331$	5.97822	+	10.3546i	0.328593	+	0.569139i	−0.653640	+	0.756806i	$0.726759\pi$
$332$	1.95715	−	11.0996i	0.107413	−	0.609168i
$333$	3.44208	−	19.5210i	0.188625	−	1.06974i
$334$	−8.32569	−	14.4205i	−0.455562	−	0.789056i
$335$		0			0
$336$	1.94563	+	1.63258i	0.106143	+	0.0890644i
$337$	−15.5291	−	5.65212i	−0.845923	−	0.307891i	−0.117546	−	0.993067i	$-0.537503\pi$
$337$	−15.5291	−	5.65212i	−0.845923	−	0.307891i	−0.728377	+	0.685177i	$0.759725\pi$
$338$	−12.0196	+	4.37476i	−0.653778	+	0.237956i
$339$	−8.29425	+	6.95970i	−0.450482	+	0.377999i
$340$		0			0
$341$	−6.11195			−0.330981
$342$	6.11904	+	15.6256i	0.330880	+	0.844934i
$343$	12.6722			0.684234
$344$	1.77652	+	10.0751i	0.0957835	+	0.543215i
$345$		0			0
$346$	11.0797	−	4.03268i	0.595648	−	0.216798i
$347$	−3.42558	−	1.24681i	−0.183895	−	0.0669321i	0.248432	−	0.968649i	$-0.420085\pi$
$347$	−3.42558	−	1.24681i	−0.183895	−	0.0669321i	−0.432326	+	0.901717i	$0.642307\pi$
$348$	4.75079	+	3.98639i	0.254669	+	0.213693i
$349$	9.09715	−	15.7567i	0.486959	−	0.843438i	−0.512928	−	0.858431i	$-0.671439\pi$
$349$	9.09715	−	15.7567i	0.486959	−	0.843438i	0.999888	+	0.0149933i	$0.00477270\pi$
$350$		0			0
$351$	−0.176592	+	1.00150i	−0.00942579	+	0.0534563i
$352$	0.0975301	−	0.553121i	0.00519837	−	0.0294814i
$353$	3.23461	+	5.60251i	0.172161	+	0.298191i	0.939175	−	0.343439i	$-0.111592\pi$
$353$	3.23461	+	5.60251i	0.172161	+	0.298191i	−0.767014	+	0.641630i	$0.778258\pi$
$354$	−5.72430	+	9.91478i	−0.304243	+	0.526965i
$355$		0			0
$356$	−3.30986	−	1.20469i	−0.175422	−	0.0638485i
$357$	0.938083	−	0.341434i	0.0496486	−	0.0180706i
$358$	12.0709	−	10.1287i	0.637968	−	0.535318i
$359$	−3.90895	−	22.1687i	−0.206306	−	1.17002i	−0.895371	−	0.445321i	$-0.853090\pi$
$359$	−3.90895	−	22.1687i	−0.206306	−	1.17002i	0.689065	−	0.724700i	$-0.258022\pi$
$360$		0			0
$361$	−13.9474	+	12.9023i	−0.734073	+	0.679070i
$362$	14.8716			0.781636
$363$	4.85586	+	27.5389i	0.254866	+	1.44542i
$364$	−0.339903	+	0.285212i	−0.0178157	+	0.0149492i
$365$		0			0
$366$	10.5338	+	3.83398i	0.550610	+	0.200406i
$367$	2.07282	+	1.73931i	0.108200	+	0.0907910i	0.695283	−	0.718736i	$-0.255279\pi$
$367$	2.07282	+	1.73931i	0.108200	+	0.0907910i	−0.587082	+	0.809527i	$0.699724\pi$
$368$	2.62018	−	4.53828i	0.136586	−	0.236574i
$369$	−15.4439	−	26.7496i	−0.803978	−	1.39253i
$370$		0			0
$371$	−0.764497	+	4.33568i	−0.0396907	+	0.225097i
$372$	14.2404	+	24.6651i	0.738329	+	1.27882i
$373$	9.82107	−	17.0106i	0.508516	−	0.880775i	−0.491436	−	0.870914i	$-0.663528\pi$
$373$	9.82107	−	17.0106i	0.508516	−	0.880775i	0.999951	−	0.00986133i	$-0.00313901\pi$
$374$	−0.169111	−	0.141901i	−0.00874452	−	0.00733752i
$375$		0			0
$376$	−11.5340	+	4.19803i	−0.594820	+	0.216497i
$377$	−0.829966	+	0.696424i	−0.0427454	+	0.0358677i
$378$	−0.374804	−	2.12562i	−0.0192778	−	0.109330i
$379$	−29.6893			−1.52504			−0.762519	−	0.646966i	$-0.776038\pi$
$379$	−29.6893			−1.52504			−0.762519	+	0.646966i	$0.776038\pi$
$380$		0			0
$381$	5.30368			0.271716
$382$	−4.54206	−	25.7593i	−0.232392	−	1.31796i
$383$	13.1589	−	11.0417i	0.672391	−	0.564203i	−0.241381	−	0.970430i	$-0.577600\pi$
$383$	13.1589	−	11.0417i	0.672391	−	0.564203i	0.913772	+	0.406228i	$0.133156\pi$
$384$	−2.45938	+	0.895141i	−0.125505	+	0.0456800i
$385$		0			0
$386$	−9.37557	−	7.86704i	−0.477204	−	0.400422i
$387$	19.6929	−	34.1091i	1.00105	−	1.73387i
$388$	3.60970	+	6.25219i	0.183255	+	0.317407i
$389$	−1.09317	+	6.19966i	−0.0554258	+	0.314335i	−0.999898	−	0.0142548i	$-0.995462\pi$
$389$	−1.09317	+	6.19966i	−0.0554258	+	0.314335i	0.944473	+	0.328590i	$0.106574\pi$
$390$		0			0
$391$	−1.02986	−	1.78378i	−0.0520825	−	0.0902095i
$392$	−3.02913	+	5.24660i	−0.152994	+	0.264993i
$393$	14.5684	+	12.2243i	0.734878	+	0.616635i
$394$	−0.294638	−	0.107239i	−0.0148436	−	0.00540264i
$395$		0			0
$396$	−1.65639	+	1.38988i	−0.0832368	+	0.0698439i
$397$	1.71645	+	9.73449i	0.0861463	+	0.488560i	0.997103	+	0.0760588i	$0.0242337\pi$
$397$	1.71645	+	9.73449i	0.0861463	+	0.488560i	−0.910957	+	0.412501i	$0.864655\pi$
$398$	−21.4620			−1.07580
$399$	9.45104	−	5.76566i	0.473144	−	0.288644i
$400$		0			0
$401$	5.40131	+	30.6323i	0.269728	+	1.52971i	0.755224	+	0.655467i	$0.227528\pi$
$401$	5.40131	+	30.6323i	0.269728	+	1.52971i	−0.485496	+	0.874239i	$0.661361\pi$
$402$	−24.4303	+	20.4994i	−1.21847	+	1.02242i
$403$	−4.67554	+	1.70176i	−0.232905	+	0.0847705i
$404$	−11.9341	−	4.34365i	−0.593742	−	0.216105i
$405$		0			0
$406$	1.14976	−	1.99145i	0.0570619	−	0.0988341i
$407$	1.44593	+	2.50443i	0.0716722	+	0.124140i
$408$	−0.178632	+	1.01307i	−0.00884360	+	0.0501545i
$409$	5.49089	−	31.1404i	0.271507	−	1.53979i	−0.478336	−	0.878177i	$-0.658760\pi$
$409$	5.49089	−	31.1404i	0.271507	−	1.53979i	0.749843	−	0.661616i	$-0.230129\pi$
$410$		0			0
$411$	9.91747	−	17.1776i	0.489193	−	0.847306i
$412$	8.78736	+	7.37347i	0.432922	+	0.363265i
$413$	3.98901	+	1.45188i	0.196287	+	0.0714424i
$414$	−18.9578	+	6.90006i	−0.931723	+	0.339120i
$415$		0			0
$416$	−0.0793970	−	0.450283i	−0.00389276	−	0.0220769i
$417$	29.8169			1.46014
$418$	−2.14917	−	1.17247i	−0.105119	−	0.0573475i
$419$	4.66623			0.227960			0.113980	−	0.993483i	$-0.463640\pi$
$419$	4.66623			0.227960			0.113980	+	0.993483i	$0.463640\pi$
$420$		0			0
$421$	7.29791	−	6.12367i	0.355678	−	0.298449i	−0.447387	−	0.894340i	$-0.647645\pi$
$421$	7.29791	−	6.12367i	0.355678	−	0.298449i	0.803065	+	0.595891i	$0.203201\pi$
$422$	12.3190	−	4.48373i	0.599677	−	0.218265i
$423$	44.4038	+	16.1617i	2.15899	+	0.785806i
$424$	−3.47530	−	2.91613i	−0.168776	−	0.141620i
$425$		0			0
$426$	9.54980	+	16.5407i	0.462689	+	0.801401i
$427$	0.721765	−	4.09333i	0.0349287	−	0.198090i
$428$	2.17654	−	12.3438i	0.105207	−	0.596659i
$429$	−0.336056	−	0.582066i	−0.0162249	−	0.0281024i
$430$		0			0
$431$	12.6794	+	10.6393i	0.610746	+	0.512477i	0.894880	−	0.446308i	$-0.147261\pi$
$431$	12.6794	+	10.6393i	0.610746	+	0.512477i	−0.284133	+	0.958785i	$0.591706\pi$
$432$	2.09003	+	0.760709i	0.100557	+	0.0365996i
$433$	−36.3423	+	13.2275i	−1.74650	+	0.635674i	−0.999573	−	0.0292319i	$-0.990694\pi$
$433$	−36.3423	+	13.2275i	−1.74650	+	0.635674i	−0.746927	+	0.664906i	$0.768472\pi$
$434$	8.08970	−	6.78807i	0.388318	−	0.325838i
$435$		0			0
$436$	−5.68780			−0.272396
$437$	−15.1015	−	17.1380i	−0.722401	−	0.819821i
$438$	36.4840			1.74327
$439$	−4.93804	−	28.0050i	−0.235680	−	1.33661i	−0.841177	−	0.540760i	$-0.818137\pi$
$439$	−4.93804	−	28.0050i	−0.235680	−	1.33661i	0.605497	−	0.795848i	$-0.292974\pi$
$440$		0			0
$441$	21.9166	−	7.97700i	1.04365	−	0.379857i
$442$	−0.168876	−	0.0614660i	−0.00803263	−	0.00292364i
$443$	−14.0691	−	11.8053i	−0.668442	−	0.560889i	0.244162	−	0.969734i	$-0.421487\pi$
$443$	−14.0691	−	11.8053i	−0.668442	−	0.560889i	−0.912604	+	0.408845i	$0.865932\pi$
$444$	6.73782	−	11.6702i	0.319763	−	0.553845i
$445$		0			0
$446$	3.80801	−	21.5963i	0.180314	−	1.02261i
$447$	0.00394904	−	0.0223961i	0.000186783	−	0.00105930i
$448$	0.485218	+	0.840422i	0.0229244	+	0.0397062i
$449$	−1.25413	+	2.17222i	−0.0591861	+	0.102513i	−0.894100	−	0.447867i	$-0.852184\pi$
$449$	−1.25413	+	2.17222i	−0.0591861	+	0.102513i	0.834914	+	0.550380i	$0.185517\pi$
$450$		0			0
$451$	4.23449	+	1.54123i	0.199394	+	0.0725735i
$452$	−3.88749	+	1.41493i	−0.182852	+	0.0665527i
$453$	30.8402	−	25.8780i	1.44900	−	1.21586i
$454$	−0.683528	−	3.87648i	−0.0320796	−	0.181932i
$455$		0			0
$456$	0.275843	+	11.4048i	0.0129175	+	0.534081i
$457$	32.8737			1.53777			0.768884	−	0.639389i	$-0.220813\pi$
$457$	32.8737			1.53777			0.768884	+	0.639389i	$0.220813\pi$
$458$	−2.16561	−	12.2818i	−0.101192	−	0.573889i
$459$	0.669685	−	0.561932i	0.0312582	−	0.0262287i
$460$		0			0
$461$	−1.13291	−	0.412346i	−0.0527649	−	0.0192049i	0.315503	−	0.948925i	$-0.397827\pi$
$461$	−1.13291	−	0.412346i	−0.0527649	−	0.0192049i	−0.368268	+	0.929720i	$0.620049\pi$
$462$	1.09277	+	0.916943i	0.0508402	+	0.0426600i
$463$	6.39390	−	11.0746i	0.297150	−	0.514678i	−0.678333	−	0.734755i	$-0.737297\pi$
$463$	6.39390	−	11.0746i	0.297150	−	0.514678i	0.975483	+	0.220076i	$0.0706306\pi$
$464$	1.18479	+	2.05212i	0.0550026	+	0.0952673i
$465$		0			0
$466$	2.33029	−	13.2158i	0.107949	−	0.612208i
$467$	−16.2360	−	28.1216i	−0.751313	−	1.30131i	−0.947187	−	0.320683i	$-0.896088\pi$
$467$	−16.2360	−	28.1216i	−0.751313	−	1.30131i	0.195873	−	0.980629i	$-0.437246\pi$
$468$	−0.880125	+	1.52442i	−0.0406838	+	0.0704664i
$469$	9.05848	+	7.60097i	0.418282	+	0.350980i
$470$		0			0
$471$	44.3931	−	16.1578i	2.04553	−	0.744511i
$472$	−3.35094	+	2.81177i	−0.154240	+	0.129422i
$473$	0.997788	+	5.65874i	0.0458783	+	0.260189i
$474$	−2.49434			−0.114569
$475$		0			0
$476$	0.381431			0.0174829
$477$	3.03284	+	17.2001i	0.138864	+	0.787538i
$478$	−1.17365	+	0.984806i	−0.0536813	+	0.0450440i
$479$	−16.3221	+	5.94076i	−0.745775	+	0.271440i	−0.686827	−	0.726821i	$-0.740997\pi$
$479$	−16.3221	+	5.94076i	−0.745775	+	0.271440i	−0.0589485	+	0.998261i	$0.518775\pi$
$480$		0			0
$481$	1.80342	+	1.51325i	0.0822290	+	0.0689984i
$482$	−6.98942	+	12.1060i	−0.318359	+	0.551415i
$483$	6.65483	+	11.5265i	0.302805	+	0.524474i
$484$	−1.85535	+	10.5222i	−0.0843342	+	0.478283i
$485$		0			0
$486$	10.8324	+	18.7623i	0.491368	+	0.851074i
$487$	3.83400	−	6.64068i	0.173735	−	0.300918i	−0.765988	−	0.642855i	$-0.777750\pi$
$487$	3.83400	−	6.64068i	0.173735	−	0.300918i	0.939723	+	0.341937i	$0.111083\pi$
$488$	3.28105	+	2.75313i	0.148526	+	0.124628i
$489$	−12.0766	−	4.39554i	−0.546124	−	0.198773i
$490$		0			0
$491$	25.9882	−	21.8067i	1.17283	−	0.984124i	0.172833	−	0.984951i	$-0.444708\pi$
$491$	25.9882	−	21.8067i	1.17283	−	0.984124i	1.00000		0.000827334i	$0.000263349\pi$
$492$	−3.64633	−	20.6794i	−0.164389	−	0.932299i
$493$	0.931369			0.0419467
$494$	−1.97053	−	0.298525i	−0.0886584	−	0.0134313i
$495$		0			0
$496$	1.88965	+	10.7168i	0.0848479	+	0.481196i
$497$	5.42507	−	4.55217i	0.243348	−	0.204193i
$498$	−27.7192	+	10.0890i	−1.24213	+	0.452097i
$499$	5.54507	+	2.01824i	0.248231	+	0.0903488i	0.463139	−	0.886285i	$-0.346723\pi$
$499$	5.54507	+	2.01824i	0.248231	+	0.0903488i	−0.214908	+	0.976634i	$0.568945\pi$
$500$		0			0
$501$	−21.7901	+	37.7416i	−0.973512	+	1.68617i
$502$	8.36580	+	14.4900i	0.373384	+	0.646720i
$503$	−6.95876	+	39.4651i	−0.310276	+	1.75966i	0.287292	+	0.957843i	$0.407245\pi$
$503$	−6.95876	+	39.4651i	−0.310276	+	1.75966i	−0.597567	+	0.801819i	$0.703866\pi$
$504$	0.648750	−	3.67924i	0.0288976	−	0.163887i
$505$		0			0
$506$	1.47163	−	2.54894i	0.0654220	−	0.113314i
$507$	25.6446	+	21.5184i	1.13892	+	0.955665i
$508$	1.90425	+	0.693090i	0.0844873	+	0.0307509i
$509$	−15.8140	+	5.75583i	−0.700944	+	0.255123i	−0.667814	−	0.744328i	$-0.732770\pi$
$509$	−15.8140	+	5.75583i	−0.700944	+	0.255123i	−0.0331303	+	0.999451i	$0.510548\pi$
$510$		0			0
$511$	−2.34909	−	13.3224i	−0.103918	−	0.589347i
$512$	−1.00000			−0.0441942
$513$	6.05037	−	7.57524i	0.267130	−	0.334455i
$514$	6.00465			0.264854
$515$		0			0
$516$	20.5113	−	17.2110i	0.902960	−	0.757673i
$517$	−6.47810	+	2.35784i	−0.284907	+	0.103697i
$518$	−4.69529	−	1.70895i	−0.206299	−	0.0750868i
$519$	−23.6394	−	19.8358i	−1.03765	−	0.870694i
$520$		0			0
$521$	−1.40131	−	2.42714i	−0.0613926	−	0.106335i	0.833696	−	0.552224i	$-0.186221\pi$
$521$	−1.40131	−	2.42714i	−0.0613926	−	0.106335i	−0.895088	+	0.445889i	$0.852887\pi$
$522$	1.58410	−	8.98389i	0.0693342	−	0.393214i
$523$	−1.69166	+	9.59389i	−0.0739712	+	0.419512i	0.925225	+	0.379419i	$0.123876\pi$
$523$	−1.69166	+	9.59389i	−0.0739712	+	0.419512i	−0.999196	+	0.0400921i	$0.987235\pi$
$524$	3.63319	+	6.29286i	0.158716	+	0.274905i
$525$		0			0
$526$	−4.83259	−	4.05502i	−0.210711	−	0.176807i
$527$	4.01927	+	1.46289i	0.175082	+	0.0637247i
$528$	−1.38132	+	0.502759i	−0.0601142	+	0.0218798i
$529$	3.41757	−	2.86768i	0.148590	−	0.124682i
$530$		0			0
$531$	16.8404			0.730813
$532$	4.14679	−	0.835048i	0.179786	−	0.0362039i
$533$	3.66843			0.158897
$534$	1.60079	+	9.07852i	0.0692729	+	0.392866i
$535$		0			0
$536$	−11.4504	+	4.16760i	−0.494582	+	0.180013i
$537$	−38.7536	−	14.1051i	−1.67234	−	0.608682i
$538$	16.7593	+	14.0627i	0.722543	+	0.606286i
$539$	−1.70132	+	2.94677i	−0.0732810	+	0.126926i
$540$		0			0
$541$	4.09756	−	23.2384i	0.176168	−	0.999097i	−0.760620	−	0.649198i	$-0.775105\pi$
$541$	4.09756	−	23.2384i	0.176168	−	0.999097i	0.936787	−	0.349899i	$-0.113784\pi$
$542$	−1.74274	+	9.88355i	−0.0748569	+	0.424535i
$543$	−19.4611	−	33.7077i	−0.835158	−	1.44654i
$544$	−0.196526	+	0.340392i	−0.00842597	+	0.0145942i
$545$		0			0
$546$	1.09125	+	0.397184i	0.0467014	+	0.0169979i
$547$	−3.95356	+	1.43898i	−0.169042	+	0.0615263i	−0.425155	−	0.905121i	$-0.639780\pi$
$547$	−3.95356	+	1.43898i	−0.169042	+	0.0615263i	0.256113	+	0.966647i	$0.417558\pi$
$548$	5.80557	−	4.87145i	0.248002	−	0.208098i
$549$	−2.86332	−	16.2387i	−0.122204	−	0.693050i
$550$		0			0
$551$	10.1255	−	2.03900i	0.431362	−	0.0868643i
$552$	−13.7151			−0.583755
$553$	0.160603	+	0.910825i	0.00682953	+	0.0387322i
$554$	13.0278	−	10.9316i	0.553498	−	0.464440i
$555$		0			0
$556$	10.7055	+	3.89650i	0.454016	+	0.165248i
$557$	−1.36125	−	1.14222i	−0.0576779	−	0.0483975i	0.613493	−	0.789700i	$-0.289764\pi$
$557$	−1.36125	−	1.14222i	−0.0576779	−	0.0483975i	−0.671171	+	0.741303i	$0.734208\pi$
$558$	20.9470	−	36.2813i	0.886758	−	1.53591i
$559$	2.33886	+	4.05102i	0.0989231	+	0.171340i
$560$		0			0
$561$	−0.100329	+	0.568995i	−0.00423590	+	0.0240230i
$562$	−0.528665	−	0.915675i	−0.0223004	−	0.0386254i
$563$	−18.2234	+	31.5639i	−0.768025	+	1.33026i	0.170607	+	0.985339i	$0.445427\pi$
$563$	−18.2234	+	31.5639i	−0.768025	+	1.33026i	−0.938632	+	0.344919i	$0.887906\pi$
$564$	24.6086	+	20.6491i	1.03621	+	0.869483i
$565$		0			0
$566$	−22.1733	+	8.07043i	−0.932014	+	0.339225i
$567$	4.25843	−	3.57325i	0.178837	−	0.150062i
$568$	1.26723	+	7.18681i	0.0531717	+	0.301552i
$569$	−22.6982			−0.951556			−0.475778	−	0.879565i	$-0.657833\pi$
$569$	−22.6982			−0.951556			−0.475778	+	0.879565i	$0.657833\pi$
$570$		0			0
$571$	9.60500			0.401957			0.200978	−	0.979596i	$-0.435588\pi$
$571$	9.60500			0.401957			0.200978	+	0.979596i	$0.435588\pi$
$572$	−0.0445936	−	0.252903i	−0.00186455	−	0.0105744i
$573$	−52.4416	+	44.0037i	−2.19078	+	1.83828i
$574$	−7.31643	+	2.66296i	−0.305382	+	0.111150i
$575$		0			0
$576$	2.94913	+	2.47462i	0.122881	+	0.103109i
$577$	−0.800539	+	1.38657i	−0.0333269	+	0.0577238i	−0.882208	−	0.470860i	$-0.843944\pi$
$577$	−0.800539	+	1.38657i	−0.0333269	+	0.0577238i	0.848881	+	0.528584i	$0.177277\pi$
$578$	−8.42276	−	14.5886i	−0.350340	−	0.606807i
$579$	−5.56229	+	31.5453i	−0.231161	+	1.31098i
$580$		0			0
$581$	5.46879	+	9.47223i	0.226884	+	0.392974i
$582$	9.44737	−	16.3633i	0.391606	−	0.678282i
$583$	−1.95192	−	1.63785i	−0.0808401	−	0.0678329i
$584$	13.0993	+	4.76777i	0.542054	+	0.197292i
$585$		0			0
$586$	−17.0689	+	14.3225i	−0.705110	+	0.591657i
$587$	−2.29493	−	13.0152i	−0.0947221	−	0.537196i	−0.994832	−	0.101533i	$-0.967625\pi$
$587$	−2.29493	−	13.0152i	−0.0947221	−	0.537196i	0.900110	−	0.435663i	$-0.143486\pi$
$588$	15.8558			0.653881
$589$	46.8988	+	7.10490i	1.93243	+	0.292752i
$590$		0			0
$591$	0.142499	+	0.808153i	0.00586163	+	0.0332430i
$592$	3.94424	−	3.30961i	0.162107	−	0.136024i
$593$	8.48936	−	3.08987i	0.348616	−	0.126886i	−0.161776	−	0.986827i	$-0.551722\pi$
$593$	8.48936	−	3.08987i	0.348616	−	0.126886i	0.510393	+	0.859942i	$0.329500\pi$
$594$	1.17387	+	0.427255i	0.0481646	+	0.0175305i
$595$		0			0
$596$	0.00434462	−	0.00752511i	0.000177963	−	0.000308240i
$597$	28.0854	+	48.6454i	1.14946	+	1.99092i
$598$	0.416069	−	2.35964i	0.0170143	−	0.0964929i
$599$	4.00135	−	22.6928i	0.163491	−	0.927203i	−0.787116	−	0.616805i	$-0.788427\pi$
$599$	4.00135	−	22.6928i	0.163491	−	0.927203i	0.950607	−	0.310398i	$-0.100462\pi$
$600$		0			0
$601$	−16.0194	+	27.7465i	−0.653447	+	1.13180i	0.328834	+	0.944388i	$0.393344\pi$
$601$	−16.0194	+	27.7465i	−0.653447	+	1.13180i	−0.982281	+	0.187415i	$0.939989\pi$
$602$	−7.60537	−	6.38166i	−0.309972	−	0.260097i
$603$	44.0820	+	16.0445i	1.79516	+	0.653384i
$604$	14.4547	−	5.26109i	0.588155	−	0.214071i
$605$		0			0
$606$	5.77182	+	32.7336i	0.234464	+	1.32971i
$607$	7.01008			0.284530			0.142265	−	0.989829i	$-0.454561\pi$
$607$	7.01008			0.284530			0.142265	+	0.989829i	$0.454561\pi$
$608$	−1.39136	+	4.13088i	−0.0564269	+	0.167529i
$609$	−6.01837			−0.243877
$610$		0			0
$611$	−4.29914	+	3.60741i	−0.173925	+	0.145940i
$612$	1.42192	−	0.517537i	0.0574778	−	0.0209202i
$613$	−34.6655	−	12.6172i	−1.40013	−	0.509604i	−0.471911	−	0.881646i	$-0.656436\pi$
$613$	−34.6655	−	12.6172i	−1.40013	−	0.509604i	−0.928216	+	0.372042i	$0.878658\pi$
$614$	−20.9406	−	17.5713i	−0.845094	−	0.709118i
$615$		0			0
$616$	0.272524	+	0.472026i	0.0109803	+	0.0190185i
$617$	−4.70336	+	26.6741i	−0.189350	+	1.07386i	0.730887	+	0.682498i	$0.239107\pi$
$617$	−4.70336	+	26.6741i	−0.189350	+	1.07386i	−0.920237	+	0.391360i	$0.872005\pi$
$618$	5.21332	−	29.5662i	0.209710	−	1.18933i
$619$	11.3313	+	19.6265i	0.455445	+	0.788855i	0.998714	−	0.0507046i	$-0.0161467\pi$
$619$	11.3313	+	19.6265i	0.455445	+	0.788855i	−0.543268	+	0.839559i	$0.682813\pi$
$620$		0			0
$621$	8.92857	+	7.49196i	0.358291	+	0.300642i
$622$	29.4890	+	10.7331i	1.18240	+	0.430359i
$623$	3.21201	−	1.16908i	0.128686	−	0.0468380i
$624$	−0.916701	+	0.769203i	−0.0366974	+	0.0307928i
$625$		0			0
$626$	−1.15084			−0.0459970
$627$	0.154928	+	6.40557i	0.00618723	+	0.255814i
$628$	18.0505			0.720295
$629$	−0.351422	−	1.99302i	−0.0140121	−	0.0794667i
$630$		0			0
$631$	−12.4587	+	4.53461i	−0.495974	+	0.180520i	−0.577882	−	0.816120i	$-0.696121\pi$
$631$	−12.4587	+	4.53461i	−0.495974	+	0.180520i	0.0819082	+	0.996640i	$0.473899\pi$
$632$	−0.895576	−	0.325963i	−0.0356241	−	0.0129661i
$633$	−26.2834	−	22.0544i	−1.04467	−	0.876583i
$634$	10.3287	−	17.8898i	0.410205	−	0.710495i
$635$		0			0
$636$	−2.06181	+	11.6931i	−0.0817561	+	0.463662i
$637$	−0.481007	+	2.72793i	−0.0190582	+	0.108084i
$638$	0.665443	+	1.15258i	0.0263451	+	0.0456311i
$639$	14.0474	−	24.3308i	0.555705	−	0.962510i
$640$		0			0
$641$	−2.21754	−	0.807120i	−0.0875877	−	0.0318793i	0.297855	−	0.954611i	$-0.403729\pi$
$641$	−2.21754	−	0.807120i	−0.0875877	−	0.0318793i	−0.385442	+	0.922732i	$0.625951\pi$
$642$	−30.8264	+	11.2199i	−1.21662	+	0.442813i
$643$	−21.4227	+	17.9758i	−0.844828	+	0.708895i	−0.958644	−	0.284607i	$-0.908137\pi$
$643$	−21.4227	+	17.9758i	−0.844828	+	0.708895i	0.113816	+	0.993502i	$0.463693\pi$
$644$	0.883075	+	5.00817i	0.0347980	+	0.197349i
$645$		0			0
$646$	1.13268	+	1.28543i	0.0445648	+	0.0505746i
$647$	26.0773			1.02520			0.512602	−	0.858626i	$-0.328682\pi$
$647$	26.0773			1.02520			0.512602	+	0.858626i	$0.328682\pi$
$648$	0.994716	+	5.64132i	0.0390761	+	0.221612i
$649$	−1.88207	+	1.57924i	−0.0738776	+	0.0619907i
$650$		0			0
$651$	−25.9719	−	9.45300i	−1.01792	−	0.370492i
$652$	−3.76162	−	3.15637i	−0.147316	−	0.123613i
$653$	18.7859	−	32.5381i	0.735149	−	1.27332i	−0.219509	−	0.975611i	$-0.570445\pi$
$653$	18.7859	−	32.5381i	0.735149	−	1.27332i	0.954658	−	0.297705i	$-0.0962212\pi$
$654$	7.44310	+	12.8918i	0.291048	+	0.504110i
$655$		0			0
$656$	1.39321	−	7.90129i	0.0543957	−	0.308494i
$657$	−26.8333	−	46.4766i	−1.04687	−	1.81323i
$658$	5.95566	−	10.3155i	0.232176	−	0.402141i
$659$	34.5955	+	29.0291i	1.34765	+	1.13081i	0.979589	+	0.201010i	$0.0644224\pi$
$659$	34.5955	+	29.0291i	1.34765	+	1.13081i	0.368060	+	0.929802i	$0.380022\pi$
$660$		0			0
$661$	19.6153	−	7.13939i	0.762947	−	0.277690i	0.0689038	−	0.997623i	$-0.478050\pi$
$661$	19.6153	−	7.13939i	0.762947	−	0.277690i	0.694043	+	0.719933i	$0.255828\pi$
$662$	9.15917	−	7.68545i	0.355981	−	0.298704i
$663$	0.0816757	+	0.463206i	0.00317202	+	0.0179894i
$664$	−11.2708			−0.437392
$665$		0			0
$666$	−19.8221			−0.768092
$667$	2.15627	+	12.2288i	0.0834911	+	0.473502i
$668$	−12.7557	+	10.7033i	−0.493533	+	0.414123i
$669$	−53.9328	+	19.6299i	−2.08516	+	0.758937i
$670$		0			0
$671$	1.84281	+	1.54630i	0.0711410	+	0.0596944i
$672$	1.26992	−	2.19957i	0.0489882	−	0.0848501i
$673$	−3.80693	−	6.59380i	−0.146747	−	0.254172i	0.783277	−	0.621673i	$-0.213547\pi$
$673$	−3.80693	−	6.59380i	−0.146747	−	0.254172i	−0.930023	+	0.367501i	$0.880214\pi$
$674$	−2.86966	+	16.2746i	−0.110535	+	0.626876i
$675$		0			0
$676$	6.39547	+	11.0773i	0.245980	+	0.426049i
$677$	−12.7420	+	22.0697i	−0.489714	+	0.848209i	−0.999930	−	0.0118369i	$-0.996232\pi$
$677$	−12.7420	+	22.0697i	−0.489714	+	0.848209i	0.510216	+	0.860046i	$0.329565\pi$
$678$	8.29425	+	6.95970i	0.318539	+	0.267286i
$679$	−6.58346	−	2.39618i	−0.252650	−	0.0919570i
$680$		0			0
$681$	−7.89187	+	6.62206i	−0.302417	+	0.253758i
$682$	1.06133	+	6.01910i	0.0406404	+	0.230483i
$683$	−46.2882			−1.77117			−0.885585	−	0.464478i	$-0.846242\pi$
$683$	−46.2882			−1.77117			−0.885585	+	0.464478i	$0.846242\pi$
$684$	14.3256	−	8.73943i	0.547754	−	0.334160i
$685$		0			0
$686$	−2.20050	−	12.4797i	−0.0840156	−	0.476476i
$687$	−25.0036	+	20.9805i	−0.953948	+	0.800457i
$688$	9.61359	−	3.49906i	0.366515	−	0.133400i
$689$	−1.94921	−	0.709454i	−0.0742590	−	0.0270281i
$690$		0			0
$691$	−10.4011	+	18.0153i	−0.395677	+	0.685333i	−0.993187	−	0.116528i	$-0.962823\pi$
$691$	−10.4011	+	18.0153i	−0.395677	+	0.685333i	0.597510	+	0.801861i	$0.296157\pi$
$692$	−5.89538	−	10.2111i	−0.224109	−	0.388168i
$693$	0.364373	−	2.06646i	0.0138414	−	0.0784983i
$694$	−0.633021	+	3.59004i	−0.0240291	+	0.136276i
$695$		0			0
$696$	3.10086	−	5.37084i	0.117538	−	0.203581i
$697$	−2.41574	−	2.02705i	−0.0915026	−	0.0767798i
$698$	−17.0970	−	6.22282i	−0.647133	−	0.235537i
$699$	−33.0040	+	12.0125i	−1.24832	+	0.454353i
$700$		0			0
$701$	−4.88207	−	27.6876i	−0.184393	−	1.04575i	−0.926732	−	0.375722i	$-0.877395\pi$
$701$	−4.88207	−	27.6876i	−0.184393	−	1.04575i	0.742339	−	0.670025i	$-0.233716\pi$
$702$	1.01695			0.0383824
$703$	−8.18375	−	20.8980i	−0.308656	−	0.788184i
$704$	−0.561653			−0.0211681
$705$		0			0
$706$	4.95571	−	4.15833i	0.186511	−	0.156501i
$707$	11.5813	−	4.21523i	0.435558	−	0.158530i
$708$	10.7582	+	3.91565i	0.404317	+	0.147159i
$709$	3.40036	+	2.85324i	0.127703	+	0.107156i	0.704402	−	0.709801i	$-0.251215\pi$
$709$	3.40036	+	2.85324i	0.127703	+	0.107156i	−0.576699	+	0.816957i	$0.695660\pi$
$710$		0			0
$711$	1.83454	+	3.17752i	0.0688006	+	0.119166i
$712$	−0.611638	+	3.46877i	−0.0229221	+	0.129998i
$713$	−9.90245	+	56.1596i	−0.370850	+	2.10319i
$714$	−0.499144	−	0.864542i	−0.0186800	−	0.0323547i
$715$		0			0
$716$	−12.0709	−	10.1287i	−0.451111	−	0.378527i
$717$	3.76798	+	1.37143i	0.140718	+	0.0512171i
$718$	−21.1532	+	7.69912i	−0.789429	+	0.287329i
$719$	−14.7672	+	12.3912i	−0.550725	+	0.462113i	−0.875186	−	0.483786i	$-0.839261\pi$
$719$	−14.7672	+	12.3912i	−0.550725	+	0.462113i	0.324461	+	0.945899i	$0.394817\pi$
$720$		0			0
$721$	−11.1319			−0.414575
$722$	15.1283	+	11.4950i	0.563015	+	0.427801i
$723$	36.5857			1.36064
$724$	−2.58243	−	14.6457i	−0.0959754	−	0.544303i
$725$		0			0
$726$	26.2773	−	9.56417i	0.975244	−	0.354960i
$727$	40.1199	+	14.6024i	1.48796	+	0.541575i	0.952913	−	0.303244i	$-0.0980699\pi$
$727$	40.1199	+	14.6024i	1.48796	+	0.541575i	0.535052	+	0.844819i	$0.320292\pi$
$728$	0.339903	+	0.285212i	0.0125976	+	0.0105707i
$729$	19.7582	−	34.2223i	0.731786	−	1.26749i
$730$		0			0
$731$	0.698263	−	3.96005i	0.0258262	−	0.146468i
$732$	1.94657	−	11.0395i	0.0719471	−	0.408032i
$733$	−3.23120	−	5.59661i	−0.119347	−	0.206715i	0.800162	−	0.599784i	$-0.204747\pi$
$733$	−3.23120	−	5.59661i	−0.119347	−	0.206715i	−0.919509	+	0.393069i	$0.871414\pi$
$734$	1.35294	−	2.34336i	0.0499379	−	0.0864950i
$735$		0			0
$736$	−4.92432	−	1.79231i	−0.181513	−	0.0660653i
$737$	−6.43115	+	2.34075i	−0.236895	+	0.0862226i
$738$	−23.6614	+	19.8543i	−0.870990	+	0.730847i
$739$	3.08387	+	17.4895i	0.113442	+	0.643361i	0.987510	+	0.157557i	$0.0503619\pi$
$739$	3.08387	+	17.4895i	0.113442	+	0.643361i	−0.874068	+	0.485804i	$0.838527\pi$
$740$		0			0
$741$	1.90203	+	4.85701i	0.0698726	+	0.178427i
$742$	4.40256			0.161623
$743$	−2.36266	−	13.3993i	−0.0866774	−	0.491572i	−0.996982	−	0.0776330i	$-0.975264\pi$
$743$	−2.36266	−	13.3993i	−0.0866774	−	0.491572i	0.910305	−	0.413939i	$-0.135847\pi$
$744$	21.8175	−	18.3071i	0.799869	−	0.671170i
$745$		0			0
$746$	−18.4576	−	6.71801i	−0.675780	−	0.245964i
$747$	33.2391	+	27.8909i	1.21616	+	1.02048i
$748$	−0.110379	+	0.191183i	−0.00403587	+	0.00699033i
$749$	6.08182	+	10.5340i	0.222225	+	0.384905i
$750$		0			0
$751$	−5.02602	+	28.5040i	−0.183402	+	1.04013i	0.744589	+	0.667523i	$0.232646\pi$
$751$	−5.02602	+	28.5040i	−0.183402	+	1.04013i	−0.927991	+	0.372602i	$0.878466\pi$
$752$	6.13710	+	10.6298i	0.223797	+	0.387628i
$753$	21.8951	−	37.9235i	0.797902	−	1.38201i
$754$	0.829966	+	0.696424i	0.0302256	+	0.0253623i
$755$		0			0
$756$	−2.02824	+	0.738219i	−0.0737664	+	0.0268488i
$757$	−25.9594	+	21.7825i	−0.943509	+	0.791698i	−0.978193	−	0.207700i	$-0.933402\pi$
$757$	−25.9594	+	21.7825i	−0.943509	+	0.791698i	0.0346833	+	0.999398i	$0.488958\pi$
$758$	5.15550	+	29.2383i	0.187256	+	1.06198i
$759$	−7.70316			−0.279607
$760$		0			0
$761$	−45.0675			−1.63370			−0.816848	−	0.576853i	$-0.804281\pi$
$761$	−45.0675			−1.63370			−0.816848	+	0.576853i	$0.804281\pi$
$762$	−0.920974	−	5.22310i	−0.0333634	−	0.189213i
$763$	4.22829	−	3.54796i	0.153074	−	0.128445i
$764$	−24.5792	+	8.94610i	−0.889245	+	0.323659i
$765$		0			0
$766$	−13.1589	−	11.0417i	−0.475452	−	0.398952i
$767$	−1.00004	+	1.73212i	−0.0361093	+	0.0625432i
$768$	1.30861	+	2.26658i	0.0472203	+	0.0817880i
$769$	−8.12888	+	46.1012i	−0.293135	+	1.66245i	0.381552	+	0.924347i	$0.375390\pi$
$769$	−8.12888	+	46.1012i	−0.293135	+	1.66245i	−0.674687	+	0.738104i	$0.735721\pi$
$770$		0			0
$771$	−7.85774	−	13.6100i	−0.282990	−	0.490152i
$772$	−6.11947	+	10.5992i	−0.220244	+	0.381475i
$773$	36.6869	+	30.7840i	1.31954	+	1.10722i	0.986403	+	0.164343i	$0.0525505\pi$
$773$	36.6869	+	30.7840i	1.31954	+	1.10722i	0.333134	+	0.942880i	$0.391894\pi$
$774$	−37.0106	−	13.4708i	−1.33032	−	0.484196i
$775$		0			0
$776$	5.53039	−	4.64054i	0.198529	−	0.166586i
$777$	2.27084	+	12.8786i	0.0814659	+	0.462016i
$778$	6.29530			0.225698
$779$	−30.7008	−	16.7487i	−1.09997	−	0.600084i
$780$		0			0
$781$	0.711743	+	4.03649i	0.0254682	+	0.144437i
$782$	−1.57784	+	1.32397i	−0.0564236	+	0.0473450i
$783$	−4.95251	+	1.80257i	−0.176988	+	0.0644184i
$784$	5.69290	+	2.07205i	0.203318	+	0.0740016i
$785$		0			0
$786$	9.50883	−	16.4698i	0.339169	−	0.587458i
$787$	−15.5552	−	26.9425i	−0.554485	−	0.960396i	−0.997943	−	0.0641009i	$-0.979582\pi$
$787$	−15.5552	−	26.9425i	−0.554485	−	0.960396i	0.443459	−	0.896295i	$-0.353751\pi$
$788$	−0.0544469	+	0.308783i	−0.00193959	+	0.0110000i
$789$	−2.86705	+	16.2599i	−0.102070	+	0.578866i
$790$		0			0
$791$	2.00734	−	3.47681i	0.0713727	−	0.123621i
$792$	1.65639	+	1.38988i	0.0588573	+	0.0493871i
$793$	1.84026	+	0.669799i	0.0653495	+	0.0237853i
$794$	9.28854	−	3.38075i	0.329638	−	0.119978i
$795$		0			0
$796$	3.72685	+	21.1360i	0.132095	+	0.749145i
$797$	−3.73434			−0.132277			−0.0661385	−	0.997810i	$-0.521068\pi$
$797$	−3.73434			−0.132277			−0.0661385	+	0.997810i	$0.521068\pi$
$798$	−7.31922	−	8.30626i	−0.259098	−	0.294038i
$799$	4.82439			0.170675
$800$		0			0
$801$	10.3877	−	8.71630i	0.367031	−	0.307975i
$802$	29.2290	−	10.6385i	1.03211	−	0.375658i
$803$	7.35728	+	2.67783i	0.259633	+	0.0944986i
$804$	24.4303	+	20.4994i	0.861589	+	0.722959i
$805$		0			0
$806$	2.48780	+	4.30900i	0.0876291	+	0.151778i
$807$	9.94285	−	56.3887i	0.350005	−	1.98498i
$808$	−2.20533	+	12.5070i	−0.0775832	+	0.439996i
$809$	1.59342	+	2.75989i	0.0560217	+	0.0970325i	0.892676	−	0.450699i	$-0.148825\pi$
$809$	1.59342	+	2.75989i	0.0560217	+	0.0970325i	−0.836654	+	0.547731i	$0.815492\pi$
$810$		0			0
$811$	−18.9972	−	15.9405i	−0.667081	−	0.559748i	0.245119	−	0.969493i	$-0.421173\pi$
$811$	−18.9972	−	15.9405i	−0.667081	−	0.559748i	−0.912200	+	0.409745i	$0.865618\pi$
$812$	−2.16085	−	0.786485i	−0.0758310	−	0.0276002i
$813$	24.6824	−	8.98365i	0.865648	−	0.315070i
$814$	2.21530	−	1.85886i	0.0776462	−	0.0651529i
$815$		0			0
$816$	1.02870			0.0360117
$817$	−1.07826	−	44.5810i	−0.0377234	−	1.55969i
$818$	−31.6208			−1.10559
$819$	−0.296627	−	1.68226i	−0.0103650	−	0.0587829i
$820$		0			0
$821$	−29.4494	+	10.7187i	−1.02779	+	0.374085i	−0.800239	−	0.599681i	$-0.795294\pi$
$821$	−29.4494	+	10.7187i	−1.02779	+	0.374085i	−0.227551	+	0.973766i	$0.573072\pi$
$822$	−18.6387	−	6.78395i	−0.650101	−	0.236617i
$823$	−16.5841	−	13.9157i	−0.578085	−	0.485071i	0.306233	−	0.951957i	$-0.400931\pi$
$823$	−16.5841	−	13.9157i	−0.578085	−	0.485071i	−0.884318	+	0.466886i	$0.845376\pi$
$824$	5.73554	−	9.93425i	0.199807	−	0.346076i
$825$		0			0
$826$	0.737140	−	4.18053i	0.0256484	−	0.145459i
$827$	1.31666	−	7.46717i	0.0457849	−	0.259659i	−0.953320	−	0.301962i	$-0.902358\pi$
$827$	1.31666	−	7.46717i	0.0457849	−	0.259659i	0.999105	+	0.0423030i	$0.0134695\pi$
$828$	10.0872	+	17.4716i	0.350555	+	0.607179i
$829$	−14.1716	+	24.5460i	−0.492200	+	0.852516i	−0.999960	−	0.00898284i	$-0.997141\pi$
$829$	−14.1716	+	24.5460i	−0.492200	+	0.852516i	0.507759	+	0.861499i	$0.330474\pi$
$830$		0			0
$831$	−41.8256	−	15.2233i	−1.45091	−	0.528089i
$832$	−0.429655	+	0.156382i	−0.0148956	+	0.00542156i
$833$	1.82411	−	1.53061i	0.0632016	−	0.0530325i
$834$	−5.17765	−	29.3639i	−0.179287	−	1.01679i
$835$		0			0
$836$	−0.781460	+	2.32012i	−0.0270273	+	0.0802430i
$837$	−24.2035			−0.836597
$838$	−0.810282	−	4.59534i	−0.0279907	−	0.158743i
$839$	12.0688	−	10.1269i	0.416661	−	0.349620i	−0.410230	−	0.911982i	$-0.634552\pi$
$839$	12.0688	−	10.1269i	0.416661	−	0.349620i	0.826891	+	0.562362i	$0.190107\pi$
$840$		0			0
$841$	21.9748	+	7.99816i	0.757751	+	0.275799i
$842$	−7.29791	−	6.12367i	−0.251502	−	0.211036i
$843$	−1.38363	+	2.39652i	−0.0476548	+	0.0825405i
$844$	−6.55478	−	11.3532i	−0.225625	−	0.390793i
$845$		0			0
$846$	8.20549	−	46.5356i	0.282110	−	1.59993i
$847$	−5.18433	−	8.97953i	−0.178136	−	0.308540i
$848$	−2.26834	+	3.92889i	−0.0778953	+	0.134919i
$849$	47.3084	+	39.6965i	1.62362	+	1.36238i
$850$		0			0
$851$	25.3546	−	9.22831i	0.869144	−	0.316342i
$852$	14.6311	−	12.2770i	0.501255	−	0.420602i
$853$	1.26427	+	7.17004i	0.0432878	+	0.245497i	0.998772	−	0.0495453i	$-0.0157772\pi$
$853$	1.26427	+	7.17004i	0.0432878	+	0.245497i	−0.955484	+	0.295043i	$0.904666\pi$
$854$	−4.15648			−0.142232
$855$		0			0
$856$	−12.5342			−0.428410
$857$	−3.93570	−	22.3205i	−0.134441	−	0.762452i	−0.975247	−	0.221117i	$-0.929030\pi$
$857$	−3.93570	−	22.3205i	−0.134441	−	0.762452i	0.840806	−	0.541336i	$-0.182081\pi$
$858$	−0.514868	+	0.432025i	−0.0175773	+	0.0147491i
$859$	13.0461	−	4.74841i	0.445129	−	0.162014i	−0.109724	−	0.993962i	$-0.534997\pi$
$859$	13.0461	−	4.74841i	0.445129	−	0.162014i	0.554853	+	0.831948i	$0.312775\pi$
$860$		0			0
$861$	15.6101	+	13.0985i	0.531992	+	0.446395i
$862$	8.27591	−	14.3343i	0.281879	−	0.488228i
$863$	−2.33964	−	4.05238i	−0.0796424	−	0.137945i	0.823453	−	0.567384i	$-0.192044\pi$
$863$	−2.33964	−	4.05238i	−0.0796424	−	0.137945i	−0.903096	+	0.429439i	$0.858711\pi$
$864$	0.386222	−	2.19037i	0.0131395	−	0.0745181i
$865$		0			0
$866$	19.3373	+	33.4933i	0.657109	+	1.13815i
$867$	−22.0442	+	38.1816i	−0.748659	+	1.29672i
$868$	−8.08970	−	6.78807i	−0.274582	−	0.230402i
$869$	−0.503003	−	0.183078i	−0.0170632	−	0.00621050i
$870$		0			0
$871$	−4.26798	+	3.58126i	−0.144615	+	0.121346i
$872$	0.987675	+	5.60139i	0.0334469	+	0.189687i
$873$	−27.7934			−0.940665
$874$	−14.2553	+	17.8480i	−0.482192	+	0.603719i
$875$		0			0
$876$	−6.33539	−	35.9298i	−0.214053	−	1.21395i
$877$	−0.177794	+	0.149187i	−0.00600369	+	0.00503770i	−0.645785	−	0.763520i	$-0.723470\pi$
$877$	−0.177794	+	0.149187i	−0.00600369	+	0.00503770i	0.639781	+	0.768557i	$0.279025\pi$
$878$	−26.7221	+	9.72605i	−0.901827	+	0.328238i
$879$	54.7995	+	19.9454i	1.84834	+	0.672742i
$880$		0			0
$881$	13.0872	−	22.6677i	0.440920	−	0.763695i	−0.556838	−	0.830621i	$-0.687986\pi$
$881$	13.0872	−	22.6677i	0.440920	−	0.763695i	0.997758	+	0.0669258i	$0.0213191\pi$
$882$	−11.6616	−	20.1985i	−0.392666	−	0.680118i
$883$	3.62098	−	20.5356i	0.121856	−	0.691079i	−0.861270	−	0.508148i	$-0.830330\pi$
$883$	3.62098	−	20.5356i	0.121856	−	0.691079i	0.983126	−	0.182931i	$-0.0585585\pi$
$884$	−0.0312071	+	0.176984i	−0.00104961	+	0.00595263i
$885$		0			0
$886$	−9.18293	+	15.9053i	−0.308507	+	0.534349i
$887$	−33.5482	−	28.1503i	−1.12644	−	0.945195i	−0.127528	−	0.991835i	$-0.540704\pi$
$887$	−33.5482	−	28.1503i	−1.12644	−	0.945195i	−0.998912	+	0.0466399i	$0.985149\pi$
$888$	−12.6630	−	4.60894i	−0.424941	−	0.154666i
$889$	−1.84795	+	0.672599i	−0.0619782	+	0.0225582i
$890$		0			0
$891$	0.558686	+	3.16846i	0.0187167	+	0.106148i
$892$	−21.9294			−0.734252
$893$	52.4492	−	10.5618i	1.75514	−	0.353437i
$894$	−0.0227416			−0.000760594
$895$		0			0
$896$	0.743397	−	0.623784i	0.0248351	−	0.0208392i
$897$	−5.89278	+	2.14480i	−0.196754	+	0.0716126i
$898$	2.35700	+	0.857876i	0.0786539	+	0.0286277i
$899$	−19.7532	−	16.5749i	−0.658807	−	0.552805i
$900$		0			0
$901$	0.891576	+	1.54425i	0.0297027	+	0.0514466i
$902$	0.782501	−	4.43779i	0.0260544	−	0.147762i
$903$	−4.51207	+	25.5892i	−0.150152	+	0.851557i
$904$	2.06849	+	3.58273i	0.0687970	+	0.119160i
$905$		0			0
$906$	−30.8402	−	25.8780i	−1.02460	−	0.859740i
$907$	−10.0831	−	3.66995i	−0.334804	−	0.121859i	0.169147	−	0.985591i	$-0.445899\pi$
$907$	−10.0831	−	3.66995i	−0.334804	−	0.121859i	−0.503951	+	0.863732i	$0.668121\pi$
$908$	−3.69890	+	1.34629i	−0.122752	+	0.0446781i
$909$	37.4539	−	31.4276i	1.24227	−	1.04239i
$910$		0			0
$911$	9.16696			0.303715			0.151858	−	0.988402i	$-0.451475\pi$
$911$	9.16696			0.303715			0.151858	+	0.988402i	$0.451475\pi$
$912$	11.1837	−	2.25208i	0.370329	−	0.0745739i
$913$	−6.33028			−0.209502
$914$	−5.70846	−	32.3743i	−0.188819	−	1.07085i
$915$		0			0
$916$	−11.7191	+	4.26541i	−0.387211	+	0.140933i
$917$	−6.62629	−	2.41177i	−0.218819	−	0.0796437i
$918$	−0.669685	−	0.561932i	−0.0221029	−	0.0185465i
$919$	12.1439	−	21.0339i	0.400592	−	0.693845i	−0.593206	−	0.805051i	$-0.702138\pi$
$919$	12.1439	−	21.0339i	0.400592	−	0.693845i	0.993797	+	0.111206i	$0.0354713\pi$
$920$		0			0
$921$	−12.4235	+	70.4573i	−0.409369	+	2.32165i
$922$	−0.209353	+	1.18730i	−0.00689469	+	0.0391017i
$923$	1.66835	+	2.88968i	0.0549146	+	0.0951148i
$924$	0.713255	−	1.23539i	0.0234644	−	0.0406415i
$925$		0			0
$926$	−12.0166	−	4.37368i	−0.394890	−	0.143728i
$927$	−41.4983	+	15.1042i	−1.36298	+	0.496086i
$928$	1.81521	−	1.52314i	0.0595871	−	0.0499995i
$929$	−8.78099	−	49.7995i	−0.288095	−	1.63387i	−0.694016	−	0.719960i	$-0.744160\pi$
$929$	−8.78099	−	49.7995i	−0.288095	−	1.63387i	0.405921	−	0.913908i	$-0.366951\pi$
$930$		0			0
$931$	16.4802	−	20.6337i	0.540117	−	0.676242i
$932$	−13.4196			−0.439575
$933$	−14.2621	−	80.8846i	−0.466921	−	2.64804i
$934$	−24.8750	+	20.8726i	−0.813935	+	0.682973i
$935$		0			0
$936$	1.65409	+	0.602041i	0.0540658	+	0.0196783i
$937$	−19.7492	−	16.5715i	−0.645177	−	0.541367i	0.260426	−	0.965494i	$-0.416137\pi$
$937$	−19.7492	−	16.5715i	−0.645177	−	0.541367i	−0.905603	+	0.424126i	$0.860581\pi$
$938$	5.91251	−	10.2408i	0.193050	−	0.334373i
$939$	1.50600	+	2.60847i	0.0491466	+	0.0851243i
$940$		0			0
$941$	−3.67924	+	20.8660i	−0.119940	+	0.680212i	0.864246	+	0.503070i	$0.167796\pi$
$941$	−3.67924	+	20.8660i	−0.119940	+	0.680212i	−0.984185	+	0.177142i	$0.943315\pi$
$942$	−23.6211	−	40.9129i	−0.769616	−	1.33301i
$943$	21.0222	−	36.4115i	0.684576	−	1.18572i
$944$	3.35094	+	2.81177i	0.109064	+	0.0915155i
$945$		0			0
$946$	5.39950	−	1.96526i	0.175553	−	0.0638961i
$947$	−20.1288	+	16.8901i	−0.654099	+	0.548855i	−0.908312	−	0.418294i	$-0.862628\pi$
$947$	−20.1288	+	16.8901i	−0.654099	+	0.548855i	0.254212	+	0.967148i	$0.418184\pi$
$948$	0.433138	+	2.45645i	0.0140677	+	0.0797817i
$949$	6.37378			0.206902
$950$		0			0
$951$	−54.0648			−1.75317
$952$	−0.0662348	−	0.375636i	−0.00214668	−	0.0121744i
$953$	−29.6414	+	24.8721i	−0.960179	+	0.805686i	−0.980982	−	0.194097i	$-0.937822\pi$
$953$	−29.6414	+	24.8721i	−0.960179	+	0.805686i	0.0208029	+	0.999784i	$0.493378\pi$
$954$	16.4121	−	5.97353i	0.531363	−	0.193400i
$955$		0			0
$956$	1.17365	+	0.984806i	0.0379584	+	0.0318509i
$957$	1.74161	−	3.01655i	0.0562982	−	0.0975113i
$958$	8.68480	+	15.0425i	0.280593	+	0.486002i
$959$	−1.27711	+	7.24285i	−0.0412400	+	0.233884i
$960$		0			0
$961$	−43.7098	−	75.7076i	−1.40999	−	2.44218i
$962$	1.17710	−	2.03880i	0.0379513	−	0.0657335i
$963$	36.9651	+	31.0174i	1.19118	+	0.999521i
$964$	13.1358	+	4.78105i	0.423076	+	0.153987i
$965$		0			0
$966$	10.1958	−	8.55529i	0.328044	−	0.275262i
$967$	−0.479982	−	2.72211i	−0.0154352	−	0.0875373i	0.976117	−	0.217245i	$-0.0697071\pi$
$967$	−0.479982	−	2.72211i	−0.0154352	−	0.0875373i	−0.991552	+	0.129708i	$0.958596\pi$
$968$	10.6845			0.343414
$969$	1.43129	−	4.24943i	0.0459796	−	0.136511i
$970$		0			0
$971$	−8.07923	−	45.8196i	−0.259275	−	1.47042i	−0.784857	−	0.619677i	$-0.787263\pi$
$971$	−8.07923	−	45.8196i	−0.259275	−	1.47042i	0.525582	−	0.850743i	$-0.323848\pi$
$972$	16.5962	−	13.9259i	0.532323	−	0.446672i
$973$	−10.3890	+	3.78130i	−0.333058	+	0.121223i
$974$	−7.20556	−	2.62261i	−0.230881	−	0.0840338i
$975$		0			0
$976$	2.14155	−	3.70928i	0.0685495	−	0.118731i
$977$	−26.3653	−	45.6660i	−0.843500	−	1.46099i	−0.886917	−	0.461928i	$-0.847158\pi$
$977$	−26.3653	−	45.6660i	−0.843500	−	1.46099i	0.0434169	−	0.999057i	$-0.486176\pi$
$978$	−2.23167	+	12.6564i	−0.0713610	+	0.404708i
$979$	−0.343528	+	1.94825i	−0.0109792	+	0.0622662i
$980$		0			0
$981$	10.9485	−	18.9634i	0.349559	−	0.605453i
$982$	−25.9882	−	21.8067i	−0.829318	−	0.695881i
$983$	24.3988	+	8.88043i	0.778200	+	0.283242i	0.700422	−	0.713729i	$-0.252995\pi$
$983$	24.3988	+	8.88043i	0.778200	+	0.283242i	0.0777783	+	0.996971i	$0.475217\pi$
$984$	−19.7320	+	7.18188i	−0.629035	+	0.228950i
$985$		0			0
$986$	−0.161730	−	0.917219i	−0.00515055	−	0.0292102i
$987$	−31.1745			−0.992296
$988$	0.0481899	+	1.99243i	0.00153313	+	0.0633877i
$989$	53.6118			1.70476
$990$		0			0
$991$	−7.40666	+	6.21493i	−0.235280	+	0.197424i	−0.752803	−	0.658246i	$-0.771299\pi$
$991$	−7.40666	+	6.21493i	−0.235280	+	0.197424i	0.517523	+	0.855669i	$0.326854\pi$
$992$	10.2258	−	3.72189i	0.324670	−	0.118170i
$993$	−29.4054	−	10.7027i	−0.933153	−	0.339640i
$994$	−5.42507	−	4.55217i	−0.172073	−	0.144386i
$995$		0			0
$996$	14.7491	+	25.5461i	0.467342	+	0.809460i
$997$	−5.68526	+	32.2427i	−0.180054	+	1.02114i	0.752093	+	0.659057i	$0.229044\pi$
$997$	−5.68526	+	32.2427i	−0.180054	+	1.02114i	−0.932147	+	0.362080i	$0.882067\pi$
$998$	1.02469	−	5.81129i	0.0324359	−	0.183953i
$999$	5.72594	+	9.91762i	0.181161	+	0.313780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.g.351.1		12
5.2	odd	4		950.2.u.f.199.4		24
5.3	odd	4		950.2.u.f.199.1		24
5.4	even	2		190.2.k.c.161.2	yes	12
19.17	even	9	inner	950.2.l.g.701.1		12
95.17	odd	36		950.2.u.f.549.1		24
95.44	even	18		3610.2.a.bf.1.6		6
95.74	even	18		190.2.k.c.131.2	✓	12
95.89	odd	18		3610.2.a.bd.1.1		6
95.93	odd	36		950.2.u.f.549.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.131.2	✓	12	95.74	even	18
190.2.k.c.161.2	yes	12	5.4	even	2
950.2.l.g.351.1		12	1.1	even	1	trivial
950.2.l.g.701.1		12	19.17	even	9	inner
950.2.u.f.199.1		24	5.3	odd	4
950.2.u.f.199.4		24	5.2	odd	4
950.2.u.f.549.1		24	95.17	odd	36
950.2.u.f.549.4		24	95.93	odd	36
3610.2.a.bd.1.1		6	95.89	odd	18
3610.2.a.bf.1.6		6	95.44	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.00490 + 1.68231i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.00490 + 1.68231i) q^{6} +(0.485218 - 0.840422i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.668514 - 3.79133i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-2.00490 + 1.68231i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.00490 + 1.68231i) q^{6} +(0.485218 - 0.840422i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.668514 - 3.79133i) q^{9} +(0.280827 + 0.486406i) q^{11} +(1.30861 - 2.26658i) q^{12} +(0.350258 + 0.293901i) q^{13} +(-0.911911 - 0.331909i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.0682527 - 0.387080i) q^{17} -3.84982 q^{18} +(-1.58943 - 4.05878i) q^{19} +(0.441039 + 2.50125i) q^{21} +(0.430251 - 0.361024i) q^{22} +(4.92432 - 1.79231i) q^{23} +(-2.45938 - 0.895141i) q^{24} +(0.228615 - 0.395972i) q^{26} +(1.11208 + 1.92618i) q^{27} +(-0.168514 + 0.955692i) q^{28} +(-0.411474 + 2.33359i) q^{29} +(-5.44104 + 9.42416i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.38132 - 0.502759i) q^{33} +(-0.369347 + 0.134431i) q^{34} +(0.668514 + 3.79133i) q^{36} +5.14885 q^{37} +(-3.72112 + 2.27009i) q^{38} -1.19667 q^{39} +(6.14611 - 5.15720i) q^{41} +(2.38667 - 0.868676i) q^{42} +(9.61359 + 3.49906i) q^{43} +(-0.430251 - 0.361024i) q^{44} +(-2.62018 - 4.53828i) q^{46} +(-2.13139 + 12.0877i) q^{47} +(-0.454475 + 2.57745i) q^{48} +(3.02913 + 5.24660i) q^{49} +(0.788030 + 0.661236i) q^{51} +(-0.429655 - 0.156382i) q^{52} +(-4.26309 + 1.55164i) q^{53} +(1.70381 - 1.42967i) q^{54} +0.970436 q^{56} +(10.0148 + 5.46354i) q^{57} +2.36959 q^{58} +(0.759597 + 4.30789i) q^{59} +(4.02481 - 1.46491i) q^{61} +(10.2258 + 3.72189i) q^{62} +(-2.86194 - 2.40146i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.255257 + 1.44764i) q^{66} +(-2.11595 + 12.0001i) q^{67} +(0.196526 + 0.340392i) q^{68} +(-6.85757 + 11.8777i) q^{69} +(6.85757 + 2.49595i) q^{71} +(3.61765 - 1.31672i) q^{72} +(10.6787 - 8.96047i) q^{73} +(-0.894088 - 5.07062i) q^{74} +(2.88176 + 3.27039i) q^{76} +0.545048 q^{77} +(0.207799 + 1.17849i) q^{78} +(-0.730080 + 0.612610i) q^{79} +(5.38288 + 1.95921i) q^{81} +(-6.14611 - 5.15720i) q^{82} +(-5.63540 + 9.76080i) q^{83} +(-1.26992 - 2.19957i) q^{84} +(1.77652 - 10.0751i) q^{86} +(-3.10086 - 5.37084i) q^{87} +(-0.280827 + 0.486406i) q^{88} +(2.69822 + 2.26408i) q^{89} +(0.416952 - 0.151758i) q^{91} +(-4.01435 + 3.36844i) q^{92} +(-4.94563 - 28.0481i) q^{93} +12.2742 q^{94} +2.61722 q^{96} +(-1.25364 - 7.10973i) q^{97} +(4.64089 - 3.89417i) q^{98} +(2.03186 - 0.739538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Introduction

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