LMFDB - Embedded newform 350.2.m.b.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.5
Character	$\chi$	$=$	350.169
Dual form			350.2.m.b.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(1.95978 + 2.69740i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.12074 - 0.708831i) q^{5} +(-2.69740 - 1.95978i) q^{6} +1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.50820 + 7.71945i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(1.95978 + 2.69740i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.12074 - 0.708831i) q^{5} +(-2.69740 - 1.95978i) q^{6} +1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.50820 + 7.71945i) q^{9} +(-1.79791 + 1.32948i) q^{10} +(-0.532081 - 1.63758i) q^{11} +(3.17099 + 1.03032i) q^{12} +(-0.812450 - 0.263981i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(6.06819 + 4.33135i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.75397 - 2.41413i) q^{17} -8.11671i q^{18} +(-1.65757 - 1.20430i) q^{19} +(1.29908 - 1.82000i) q^{20} +(-2.69740 + 1.95978i) q^{21} +(1.01208 + 1.39301i) q^{22} +(7.59821 - 2.46881i) q^{23} -3.33417 q^{24} +(3.99512 - 3.00650i) q^{25} +0.854261 q^{26} +(-16.2250 + 5.27183i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-7.36309 + 5.34960i) q^{29} +(-7.10965 - 2.24419i) q^{30} +(-3.44368 - 2.50198i) q^{31} +1.00000i q^{32} +(3.37444 - 4.64452i) q^{33} +(-0.922116 + 2.83798i) q^{34} +(0.708831 + 2.12074i) q^{35} +(2.50820 + 7.71945i) q^{36} +(-4.49584 - 1.46079i) q^{37} +(1.94860 + 0.633137i) q^{38} +(-0.880159 - 2.70885i) q^{39} +(-0.673087 + 2.13236i) q^{40} +(-1.92210 + 5.91560i) q^{41} +(1.95978 - 2.69740i) q^{42} -12.6427i q^{43} +(-1.39301 - 1.01208i) q^{44} +(0.152527 + 18.1489i) q^{45} +(-6.46343 + 4.69596i) q^{46} +(3.87292 + 5.33062i) q^{47} +(3.17099 - 1.03032i) q^{48} -1.00000 q^{49} +(-2.87052 + 4.09391i) q^{50} +9.94927 q^{51} +(-0.812450 + 0.263981i) q^{52} +(3.30648 + 4.55097i) q^{53} +(13.8018 - 10.0276i) q^{54} +(-2.28917 - 3.09573i) q^{55} +(-0.809017 - 0.587785i) q^{56} -6.83131i q^{57} +(5.34960 - 7.36309i) q^{58} +(3.93424 - 12.1083i) q^{59} +(7.45518 - 0.0626547i) q^{60} +(0.847938 + 2.60969i) q^{61} +(4.04829 + 1.31537i) q^{62} +(-7.71945 - 2.50820i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.91012 + 0.0160530i) q^{65} +(-1.77405 + 5.45996i) q^{66} +(1.84771 - 2.54315i) q^{67} -2.98403i q^{68} +(21.5502 + 15.6571i) q^{69} +(-1.32948 - 1.79791i) q^{70} +(5.91973 - 4.30094i) q^{71} +(-4.77088 - 6.56656i) q^{72} +(-8.91143 + 2.89550i) q^{73} +4.72721 q^{74} +(15.9393 + 4.88438i) q^{75} -2.04888 q^{76} +(1.63758 - 0.532081i) q^{77} +(1.67416 + 2.30429i) q^{78} +(-1.31410 + 0.954749i) q^{79} +(-0.0187917 - 2.23599i) q^{80} +(-26.3180 - 19.1212i) q^{81} -6.22003i q^{82} +(0.850507 - 1.17062i) q^{83} +(-1.03032 + 3.17099i) q^{84} +(2.00851 - 6.36302i) q^{85} +(3.90681 + 12.0239i) q^{86} +(-28.8601 - 9.37720i) q^{87} +(1.63758 + 0.532081i) q^{88} +(-0.620824 - 1.91070i) q^{89} +(-5.75337 - 17.2135i) q^{90} +(0.263981 - 0.812450i) q^{91} +(4.69596 - 6.46343i) q^{92} -14.1923i q^{93} +(-5.33062 - 3.87292i) q^{94} +(-4.36894 - 1.37907i) q^{95} +(-2.69740 + 1.95978i) q^{96} +(-3.60322 - 4.95940i) q^{97} +(0.951057 - 0.309017i) q^{98} +13.9758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	1.95978	+	2.69740i	1.13148	+	1.55735i	0.785231	+	0.619203i	$0.212544\pi$
$3$	1.95978	+	2.69740i	1.13148	+	1.55735i	0.346248	+	0.938143i	$0.387456\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	2.12074	−	0.708831i	0.948426	−	0.316999i
$5$	2.12074	−	0.708831i	0.948426	−	0.316999i
$6$	−2.69740	−	1.95978i	−1.10121	−	0.800076i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.50820	+	7.71945i	−0.836067	+	2.57315i
$10$	−1.79791	+	1.32948i	−0.568548	+	0.420420i
$11$	−0.532081	−	1.63758i	−0.160428	−	0.493748i	0.838242	−	0.545298i	$-0.183584\pi$
$11$	−0.532081	−	1.63758i	−0.160428	−	0.493748i	−0.998670	+	0.0515506i	$0.983584\pi$
$12$	3.17099	+	1.03032i	0.915385	+	0.297427i
$13$	−0.812450	−	0.263981i	−0.225333	−	0.0732152i	0.194174	−	0.980967i	$-0.437797\pi$
$13$	−0.812450	−	0.263981i	−0.225333	−	0.0732152i	−0.419508	+	0.907752i	$0.637797\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	6.06819	+	4.33135i	1.56680	+	1.11835i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.75397	−	2.41413i	0.425400	−	0.585513i	−0.541490	−	0.840707i	$-0.682140\pi$
$17$	1.75397	−	2.41413i	0.425400	−	0.585513i	0.966890	+	0.255195i	$0.0821395\pi$
$18$		−	8.11671i		−	1.91313i
$19$	−1.65757	−	1.20430i	−0.380274	−	0.276285i	0.381185	−	0.924499i	$-0.375516\pi$
$19$	−1.65757	−	1.20430i	−0.380274	−	0.276285i	−0.761458	+	0.648214i	$0.775516\pi$
$20$	1.29908	−	1.82000i	0.290483	−	0.406964i
$21$	−2.69740	+	1.95978i	−0.588622	+	0.427659i
$22$	1.01208	+	1.39301i	0.215776	+	0.296990i
$23$	7.59821	−	2.46881i	1.58434	−	0.514782i	0.621168	−	0.783678i	$-0.286659\pi$
$23$	7.59821	−	2.46881i	1.58434	−	0.514782i	0.963169	+	0.268895i	$0.0866585\pi$
$24$	−3.33417			−0.680585
$25$	3.99512	−	3.00650i	0.799024	−	0.601300i
$26$	0.854261			0.167534
$27$	−16.2250	+	5.27183i	−3.12251	+	1.01456i
$28$	0.587785	+	0.809017i	0.111081	+	0.152890i
$29$	−7.36309	+	5.34960i	−1.36729	+	0.993396i	−0.369349	+	0.929291i	$0.620419\pi$
$29$	−7.36309	+	5.34960i	−1.36729	+	0.993396i	−0.997943	+	0.0641054i	$0.979581\pi$
$30$	−7.10965	−	2.24419i	−1.29804	−	0.409731i
$31$	−3.44368	−	2.50198i	−0.618503	−	0.449369i	0.233895	−	0.972262i	$-0.424853\pi$
$31$	−3.44368	−	2.50198i	−0.618503	−	0.449369i	−0.852398	+	0.522893i	$0.824853\pi$
$32$			1.00000i			0.176777i
$33$	3.37444	−	4.64452i	0.587415	−	0.808508i
$34$	−0.922116	+	2.83798i	−0.158142	+	0.486710i
$35$	0.708831	+	2.12074i	0.119814	+	0.358471i
$36$	2.50820	+	7.71945i	0.418034	+	1.28658i
$37$	−4.49584	−	1.46079i	−0.739112	−	0.240152i	−0.0848224	−	0.996396i	$-0.527032\pi$
$37$	−4.49584	−	1.46079i	−0.739112	−	0.240152i	−0.654290	+	0.756244i	$0.727032\pi$
$38$	1.94860	+	0.633137i	0.316104	+	0.102708i
$39$	−0.880159	−	2.70885i	−0.140938	−	0.433763i
$40$	−0.673087	+	2.13236i	−0.106424	+	0.337156i
$41$	−1.92210	+	5.91560i	−0.300181	+	0.923862i	0.681251	+	0.732050i	$0.261436\pi$
$41$	−1.92210	+	5.91560i	−0.300181	+	0.923862i	−0.981432	+	0.191812i	$0.938564\pi$
$42$	1.95978	−	2.69740i	0.302400	−	0.416218i
$43$		−	12.6427i		−	1.92799i	−0.265912	−	0.963997i	$-0.585673\pi$
$43$		−	12.6427i		−	1.92799i	0.265912	−	0.963997i	$-0.414327\pi$
$44$	−1.39301	−	1.01208i	−0.210004	−	0.152576i
$45$	0.152527	+	18.1489i	0.0227373	+	2.70548i
$46$	−6.46343	+	4.69596i	−0.952980	+	0.692381i
$47$	3.87292	+	5.33062i	0.564924	+	0.777551i	0.991942	−	0.126692i	$-0.0404360\pi$
$47$	3.87292	+	5.33062i	0.564924	+	0.777551i	−0.427018	+	0.904243i	$0.640436\pi$
$48$	3.17099	−	1.03032i	0.457693	−	0.148713i
$49$	−1.00000			−0.142857
$50$	−2.87052	+	4.09391i	−0.405953	+	0.578966i
$51$	9.94927			1.39318
$52$	−0.812450	+	0.263981i	−0.112667	+	0.0366076i
$53$	3.30648	+	4.55097i	0.454180	+	0.625124i	0.973289	−	0.229583i	$-0.0737363\pi$
$53$	3.30648	+	4.55097i	0.454180	+	0.625124i	−0.519110	+	0.854708i	$0.673736\pi$
$54$	13.8018	−	10.0276i	1.87819	−	1.36459i
$55$	−2.28917	−	3.09573i	−0.308672	−	0.417428i
$56$	−0.809017	−	0.587785i	−0.108109	−	0.0785461i
$57$		−	6.83131i		−	0.904829i
$58$	5.34960	−	7.36309i	0.702437	−	0.966822i
$59$	3.93424	−	12.1083i	0.512194	−	1.57637i	−0.276135	−	0.961119i	$-0.589054\pi$
$59$	3.93424	−	12.1083i	0.512194	−	1.57637i	0.788330	−	0.615253i	$-0.210946\pi$
$60$	7.45518	−	0.0626547i	0.962459	−	0.00808868i
$61$	0.847938	+	2.60969i	0.108567	+	0.334136i	0.990551	−	0.137144i	$-0.0437922\pi$
$61$	0.847938	+	2.60969i	0.108567	+	0.334136i	−0.881984	+	0.471280i	$0.843792\pi$
$62$	4.04829	+	1.31537i	0.514133	+	0.167052i
$63$	−7.71945	−	2.50820i	−0.972560	−	0.316004i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.91012	+	0.0160530i	−0.236921	+	0.00199113i
$66$	−1.77405	+	5.45996i	−0.218370	+	0.672075i
$67$	1.84771	−	2.54315i	0.225734	−	0.310696i	−0.681095	−	0.732195i	$-0.738496\pi$
$67$	1.84771	−	2.54315i	0.225734	−	0.310696i	0.906829	+	0.421499i	$0.138496\pi$
$68$		−	2.98403i		−	0.361867i
$69$	21.5502	+	15.6571i	2.59434	+	1.88490i
$70$	−1.32948	−	1.79791i	−0.158904	−	0.214891i
$71$	5.91973	−	4.30094i	0.702543	−	0.510427i	−0.178217	−	0.983991i	$-0.557033\pi$
$71$	5.91973	−	4.30094i	0.702543	−	0.510427i	0.880759	+	0.473564i	$0.157033\pi$
$72$	−4.77088	−	6.56656i	−0.562254	−	0.773876i
$73$	−8.91143	+	2.89550i	−1.04300	+	0.338893i	−0.779919	−	0.625880i	$-0.784740\pi$
$73$	−8.91143	+	2.89550i	−1.04300	+	0.338893i	−0.263085	+	0.964773i	$0.584740\pi$
$74$	4.72721			0.549527
$75$	15.9393	+	4.88438i	1.84051	+	0.563999i
$76$	−2.04888			−0.235022
$77$	1.63758	−	0.532081i	0.186619	−	0.0606362i
$78$	1.67416	+	2.30429i	0.189562	+	0.260909i
$79$	−1.31410	+	0.954749i	−0.147848	+	0.107418i	−0.659250	−	0.751924i	$-0.729126\pi$
$79$	−1.31410	+	0.954749i	−0.147848	+	0.107418i	0.511402	+	0.859341i	$0.329126\pi$
$80$	−0.0187917	−	2.23599i	−0.00210097	−	0.249991i
$81$	−26.3180	−	19.1212i	−2.92423	−	2.12458i
$82$		−	6.22003i		−	0.686888i
$83$	0.850507	−	1.17062i	0.0933553	−	0.128492i	−0.759784	−	0.650175i	$-0.774695\pi$
$83$	0.850507	−	1.17062i	0.0933553	−	0.128492i	0.853140	+	0.521683i	$0.174695\pi$
$84$	−1.03032	+	3.17099i	−0.112417	+	0.345983i
$85$	2.00851	−	6.36302i	0.217854	−	0.690167i
$86$	3.90681	+	12.0239i	0.421282	+	1.29657i
$87$	−28.8601	−	9.37720i	−3.09412	−	1.00534i
$88$	1.63758	+	0.532081i	0.174566	+	0.0567200i
$89$	−0.620824	−	1.91070i	−0.0658072	−	0.202534i	0.912746	−	0.408527i	$-0.133957\pi$
$89$	−0.620824	−	1.91070i	−0.0658072	−	0.202534i	−0.978553	+	0.205993i	$0.933957\pi$
$90$	−5.75337	−	17.2135i	−0.606459	−	1.81446i
$91$	0.263981	−	0.812450i	0.0276727	−	0.0851680i
$92$	4.69596	−	6.46343i	0.489587	−	0.673859i
$93$		−	14.1923i		−	1.47167i
$94$	−5.33062	−	3.87292i	−0.549812	−	0.399462i
$95$	−4.36894	−	1.37907i	−0.448244	−	0.141490i
$96$	−2.69740	+	1.95978i	−0.275303	+	0.200019i
$97$	−3.60322	−	4.95940i	−0.365851	−	0.503551i	0.585916	−	0.810372i	$-0.300735\pi$
$97$	−3.60322	−	4.95940i	−0.365851	−	0.503551i	−0.951767	+	0.306821i	$0.900735\pi$
$98$	0.951057	−	0.309017i	0.0960712	−	0.0312154i
$99$	13.9758			1.40462
$100$	1.46494	−	4.78058i	0.146494	−	0.478058i
$101$	−0.0950491			−0.00945774			−0.00472887	−	0.999989i	$-0.501505\pi$
$101$	−0.0950491			−0.00945774			−0.00472887	+	0.999989i	$0.501505\pi$
$102$	−9.46232	+	3.07449i	−0.936909	+	0.304420i
$103$	5.27493	+	7.26032i	0.519755	+	0.715381i	0.985526	−	0.169524i	$-0.0542231\pi$
$103$	5.27493	+	7.26032i	0.519755	+	0.715381i	−0.465771	+	0.884905i	$0.654223\pi$
$104$	0.691112	−	0.502122i	0.0677691	−	0.0492371i
$105$	−4.33135	+	6.06819i	−0.422697	+	0.592195i
$106$	−4.55097	−	3.30648i	−0.442030	−	0.321153i
$107$		−	1.23517i		−	0.119409i	−0.998216	−	0.0597044i	$-0.980984\pi$
$107$		−	1.23517i		−	0.119409i	0.998216	−	0.0597044i	$-0.0190158\pi$
$108$	−10.0276	+	13.8018i	−0.964908	+	1.32808i
$109$	−2.34721	+	7.22397i	−0.224822	+	0.691931i	0.773488	+	0.633811i	$0.218510\pi$
$109$	−2.34721	+	7.22397i	−0.224822	+	0.691931i	−0.998310	+	0.0581196i	$0.981490\pi$
$110$	3.13376	+	2.23682i	0.298793	+	0.213272i
$111$	−4.87052	−	14.9899i	−0.462289	−	1.42278i
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	11.3516	+	3.68835i	1.06787	+	0.346971i	0.789657	−	0.613549i	$-0.210259\pi$
$113$	11.3516	+	3.68835i	1.06787	+	0.346971i	0.278211	+	0.960520i	$0.410259\pi$
$114$	2.11099	+	6.49696i	0.197712	+	0.608496i
$115$	14.3639	−	10.6216i	1.33944	−	0.990466i
$116$	−2.81245	+	8.65584i	−0.261130	+	0.803674i
$117$	4.07558	−	5.60955i	0.376788	−	0.518604i
$118$			12.7315i			1.17203i
$119$	2.41413	+	1.75397i	0.221303	+	0.160786i
$120$	−7.07093	+	2.36336i	−0.645485	+	0.215745i
$121$	6.50064	−	4.72299i	0.590967	−	0.429363i
$122$	−1.61287	−	2.21993i	−0.146023	−	0.200983i
$123$	−19.7236	+	6.40860i	−1.77842	+	0.577844i
$124$	−4.25662			−0.382256
$125$	6.34153	−	9.20788i	0.567204	−	0.823578i
$126$	8.11671			0.723094
$127$	3.05430	−	0.992403i	0.271026	−	0.0880615i	−0.170351	−	0.985383i	$-0.554490\pi$
$127$	3.05430	−	0.992403i	0.271026	−	0.0880615i	0.441377	+	0.897322i	$0.354490\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	34.1025	−	24.7769i	3.00256	−	2.18148i
$130$	1.81167	−	0.605526i	0.158894	−	0.0531082i
$131$	17.5751	+	12.7691i	1.53555	+	1.11564i	0.953052	+	0.302806i	$0.0979234\pi$
$131$	17.5751	+	12.7691i	1.53555	+	1.11564i	0.582495	+	0.812834i	$0.302077\pi$
$132$		−	5.74095i		−	0.499685i
$133$	1.20430	−	1.65757i	0.104426	−	0.143730i
$134$	−0.971398	+	2.98966i	−0.0839160	+	0.258267i
$135$	−30.6723	+	22.6810i	−2.63985	+	1.95207i
$136$	0.922116	+	2.83798i	0.0790708	+	0.243355i
$137$	7.79292	+	2.53207i	0.665794	+	0.216330i	0.622365	−	0.782727i	$-0.286172\pi$
$137$	7.79292	+	2.53207i	0.665794	+	0.216330i	0.0434289	+	0.999057i	$0.486172\pi$
$138$	−25.3338	−	8.23144i	−2.15655	−	0.700707i
$139$	−4.58761	−	14.1192i	−0.389116	−	1.19757i	−0.933450	−	0.358707i	$-0.883218\pi$
$139$	−4.58761	−	14.1192i	−0.389116	−	1.19757i	0.544335	−	0.838868i	$-0.316782\pi$
$140$	1.82000	+	1.29908i	0.153818	+	0.109792i
$141$	−6.78877	+	20.8937i	−0.571717	+	1.75956i
$142$	−4.30094	+	5.91973i	−0.360926	+	0.496773i
$143$			1.47091i			0.123004i
$144$	6.56656	+	4.77088i	0.547213	+	0.397574i
$145$	−11.8233	+	16.5643i	−0.981870	+	1.37559i
$146$	7.58051	−	5.50757i	0.627368	−	0.455809i
$147$	−1.95978	−	2.69740i	−0.161640	−	0.222478i
$148$	−4.49584	+	1.46079i	−0.369556	+	0.120076i
$149$	−11.0215			−0.902920			−0.451460	−	0.892291i	$-0.649097\pi$
$149$	−11.0215			−0.902920			−0.451460	+	0.892291i	$0.649097\pi$
$150$	−16.6685	+	0.280190i	−1.36098	+	0.0228774i
$151$	−11.8540			−0.964662			−0.482331	−	0.875989i	$-0.660210\pi$
$151$	−11.8540			−0.964662			−0.482331	+	0.875989i	$0.660210\pi$
$152$	1.94860	−	0.633137i	0.158052	−	0.0513542i
$153$	14.2365	+	19.5948i	1.15095	+	1.58415i
$154$	−1.39301	+	1.01208i	−0.112252	+	0.0815556i
$155$	−9.07665	−	2.86508i	−0.729054	−	0.230128i
$156$	−2.30429	−	1.67416i	−0.184491	−	0.134040i
$157$			7.32271i			0.584416i	0.956355	+	0.292208i	$0.0943899\pi$
$157$			7.32271i			0.584416i	−0.956355	+	0.292208i	$0.905610\pi$
$158$	0.954749	−	1.31410i	0.0759557	−	0.104544i
$159$	−5.79585	+	17.8378i	−0.459641	+	1.41463i
$160$	0.708831	+	2.12074i	0.0560380	+	0.167660i
$161$	2.46881	+	7.59821i	0.194569	+	0.598823i
$162$	30.9387	+	10.0526i	2.43077	+	0.789807i
$163$	−4.95644	−	1.61045i	−0.388219	−	0.126140i	0.108403	−	0.994107i	$-0.465426\pi$
$163$	−4.95644	−	1.61045i	−0.388219	−	0.126140i	−0.496622	+	0.867967i	$0.665426\pi$
$164$	1.92210	+	5.91560i	0.150090	+	0.461931i
$165$	3.86415	−	12.2418i	0.300824	−	0.953019i
$166$	−0.447138	+	1.37615i	−0.0347046	+	0.106810i
$167$	−3.34358	+	4.60205i	−0.258734	+	0.356117i	−0.918546	−	0.395314i	$-0.870636\pi$
$167$	−3.34358	+	4.60205i	−0.258734	+	0.356117i	0.659812	+	0.751431i	$0.270636\pi$
$168$		−	3.33417i		−	0.257237i
$169$	−9.92683	−	7.21227i	−0.763602	−	0.554790i
$170$	0.0560749	+	6.67226i	0.00430075	+	0.511739i
$171$	13.4541	−	9.77495i	1.02886	−	0.747509i
$172$	−7.43120	−	10.2282i	−0.566623	−	0.779890i
$173$	18.5850	−	6.03863i	1.41299	−	0.459108i	0.499622	−	0.866243i	$-0.333472\pi$
$173$	18.5850	−	6.03863i	1.41299	−	0.459108i	0.913368	+	0.407135i	$0.133472\pi$
$174$	30.3453			2.30047
$175$	3.00650	+	3.99512i	0.227270	+	0.302003i
$176$	−1.72185			−0.129789
$177$	40.3713	−	13.1174i	3.03449	−	0.985967i
$178$	1.18088	+	1.62534i	0.0885105	+	0.121824i
$179$	−13.8723	+	10.0788i	−1.03686	+	0.753324i	−0.969670	−	0.244417i	$-0.921404\pi$
$179$	−13.8723	+	10.0788i	−1.03686	+	0.753324i	−0.0671906	+	0.997740i	$0.521404\pi$
$180$	10.7910	+	14.5931i	0.804317	+	1.08771i
$181$	−1.41609	−	1.02885i	−0.105257	−	0.0764735i	0.533912	−	0.845540i	$-0.320721\pi$
$181$	−1.41609	−	1.02885i	−0.105257	−	0.0764735i	−0.639169	+	0.769067i	$0.720721\pi$
$182$			0.854261i			0.0633220i
$183$	−5.37760	+	7.40164i	−0.397524	+	0.547145i
$184$	−2.46881	+	7.59821i	−0.182003	+	0.560148i
$185$	−10.5700	+	0.0888321i	−0.777121	+	0.00653107i
$186$	4.38567	+	13.4977i	0.321573	+	0.989699i
$187$	−4.88658	−	1.58774i	−0.357342	−	0.116107i
$188$	6.26652	+	2.03612i	0.457033	+	0.148499i
$189$	−5.27183	−	16.2250i	−0.383469	−	1.18020i
$190$	4.58126	−	0.0385018i	0.332360	−	0.00279321i
$191$	−7.27437	+	22.3882i	−0.526355	+	1.61995i	0.235265	+	0.971931i	$0.424404\pi$
$191$	−7.27437	+	22.3882i	−0.526355	+	1.61995i	−0.761621	+	0.648023i	$0.775596\pi$
$192$	1.95978	−	2.69740i	0.141435	−	0.194668i
$193$		−	5.63399i		−	0.405543i	−0.979226	−	0.202772i	$-0.935005\pi$
$193$		−	5.63399i		−	0.405543i	0.979226	−	0.202772i	$-0.0649949\pi$
$194$	4.95940	+	3.60322i	0.356064	+	0.258696i
$195$	−3.78671	−	5.12090i	−0.271172	−	0.366715i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−11.8103	−	16.2555i	−0.841452	−	1.15816i	−0.985682	−	0.168615i	$-0.946071\pi$
$197$	−11.8103	−	16.2555i	−0.841452	−	1.15816i	0.144230	−	0.989544i	$-0.453929\pi$
$198$	−13.2917	+	4.31875i	−0.944603	+	0.306920i
$199$	−12.6727			−0.898346			−0.449173	−	0.893445i	$-0.648281\pi$
$199$	−12.6727			−0.898346			−0.449173	+	0.893445i	$0.648281\pi$
$200$	0.0840359	+	4.99929i	0.00594224	+	0.353503i
$201$	10.4810			0.739273
$202$	0.0903970	−	0.0293718i	0.00636031	−	0.00206659i
$203$	−5.34960	−	7.36309i	−0.375468	−	0.516788i
$204$	8.04913	−	5.84804i	0.563552	−	0.409444i
$205$	0.116885	+	13.9079i	0.00816359	+	0.971372i
$206$	−7.26032	−	5.27493i	−0.505851	−	0.367522i
$207$			64.8463i			4.50713i
$208$	−0.502122	+	0.691112i	−0.0348159	+	0.0479200i
$209$	−1.09017	+	3.35519i	−0.0754084	+	0.232083i
$210$	2.24419	−	7.10965i	0.154864	−	0.490613i
$211$	1.52895	+	4.70563i	0.105257	+	0.323949i	0.989791	−	0.142528i	$-0.0455230\pi$
$211$	1.52895	+	4.70563i	0.105257	+	0.323949i	−0.884533	+	0.466477i	$0.845523\pi$
$212$	5.34999	+	1.73832i	0.367439	+	0.119388i
$213$	23.2027	+	7.53902i	1.58982	+	0.516565i
$214$	0.381690	+	1.17472i	0.0260918	+	0.0803023i
$215$	−8.96154	−	26.8120i	−0.611172	−	1.82856i
$216$	5.27183	−	16.2250i	0.358703	−	1.10397i
$217$	2.50198	−	3.44368i	0.169845	−	0.233772i
$218$		−	7.59573i		−	0.514448i
$219$	−25.2748	−	18.3632i	−1.70791	−	1.24087i
$220$	−3.67160	−	1.15895i	−0.247539	−	0.0781367i
$221$	−2.06230	+	1.49835i	−0.138725	+	0.100790i
$222$	9.26428	+	12.7512i	0.621778	+	0.855804i
$223$	4.52075	−	1.46888i	0.302732	−	0.0983635i	−0.153712	−	0.988116i	$-0.549123\pi$
$223$	4.52075	−	1.46888i	0.302732	−	0.0983635i	0.456444	+	0.889752i	$0.349123\pi$
$224$	−1.00000			−0.0668153
$225$	13.1880	+	38.3810i	0.879197	+	2.55874i
$226$	−11.9358			−0.793955
$227$	12.8504	−	4.17535i	0.852912	−	0.277128i	0.150246	−	0.988649i	$-0.451993\pi$
$227$	12.8504	−	4.17535i	0.852912	−	0.277128i	0.702665	+	0.711521i	$0.251993\pi$
$228$	−4.01534	−	5.52664i	−0.265922	−	0.366011i
$229$	−14.8025	+	10.7547i	−0.978178	+	0.710688i	−0.957301	−	0.289094i	$-0.906646\pi$
$229$	−14.8025	+	10.7547i	−0.978178	+	0.710688i	−0.0208772	+	0.999782i	$0.506646\pi$
$230$	−10.3786	+	14.5404i	−0.684348	+	0.958765i
$231$	4.64452	+	3.37444i	0.305587	+	0.222022i
$232$		−	9.10129i		−	0.597529i
$233$	−14.5759	+	20.0620i	−0.954899	+	1.31431i	−0.00558279	+	0.999984i	$0.501777\pi$
$233$	−14.5759	+	20.0620i	−0.954899	+	1.31431i	−0.949317	+	0.314322i	$0.898223\pi$
$234$	−2.14266	+	6.59443i	−0.140070	+	0.431091i
$235$	11.9920	+	8.55964i	0.782271	+	0.558370i
$236$	−3.93424	−	12.1083i	−0.256097	−	0.788186i
$237$	−5.15068	−	1.67356i	−0.334573	−	0.108709i
$238$	−2.83798	−	0.922116i	−0.183959	−	0.0597719i
$239$	−8.60170	−	26.4733i	−0.556398	−	1.71242i	−0.692224	−	0.721683i	$-0.743369\pi$
$239$	−8.60170	−	26.4733i	−0.556398	−	1.71242i	0.135826	−	0.990733i	$-0.456631\pi$
$240$	5.99454	−	4.43273i	0.386946	−	0.286132i
$241$	−2.33129	+	7.17498i	−0.150172	+	0.462181i	−0.997640	−	0.0686653i	$-0.978126\pi$
$241$	−2.33129	+	7.17498i	−0.150172	+	0.462181i	0.847468	+	0.530847i	$0.178126\pi$
$242$	−4.72299	+	6.50064i	−0.303605	+	0.417877i
$243$		−	57.2836i		−	3.67474i
$244$	2.21993	+	1.61287i	0.142117	+	0.103254i
$245$	−2.12074	+	0.708831i	−0.135489	+	0.0452855i
$246$	16.7779	−	12.1899i	1.06972	−	0.777199i
$247$	1.02879	+	1.41600i	0.0654600	+	0.0900980i
$248$	4.04829	−	1.31537i	0.257067	−	0.0835260i
$249$	4.82444			0.305737
$250$	−3.18576	+	10.7169i	−0.201485	+	0.677793i
$251$	−19.9421			−1.25874			−0.629368	−	0.777108i	$-0.716686\pi$
$251$	−19.9421			−1.25874			−0.629368	+	0.777108i	$0.716686\pi$
$252$	−7.71945	+	2.50820i	−0.486280	+	0.158002i
$253$	−8.08573	−	11.1291i	−0.508345	−	0.699677i
$254$	−2.59814	+	1.88766i	−0.163022	+	0.118442i
$255$	21.0999	−	7.05235i	1.32133	−	0.441635i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			2.83618i			0.176916i	0.996080	+	0.0884581i	$0.0281939\pi$
$257$			2.83618i			0.176916i	−0.996080	+	0.0884581i	$0.971806\pi$
$258$	−24.7769	+	34.1025i	−1.54254	+	2.12313i
$259$	1.46079	−	4.49584i	0.0907690	−	0.279358i
$260$	−1.53588	+	1.13573i	−0.0952514	+	0.0704348i
$261$	−22.8279	−	70.2569i	−1.41301	−	4.34880i
$262$	−20.6608	−	6.71311i	−1.27643	−	0.414737i
$263$	−6.94702	−	2.25722i	−0.428371	−	0.139186i	0.0868928	−	0.996218i	$-0.472306\pi$
$263$	−6.94702	−	2.25722i	−0.428371	−	0.139186i	−0.515264	+	0.857031i	$0.672306\pi$
$264$	1.77405	+	5.45996i	0.109185	+	0.336038i
$265$	10.2381	+	7.30773i	0.628919	+	0.448910i
$266$	−0.633137	+	1.94860i	−0.0388201	+	0.119476i
$267$	3.93725	−	5.41916i	0.240956	−	0.331647i
$268$		−	3.14351i		−	0.192020i
$269$	−3.17999	−	2.31040i	−0.193887	−	0.140867i	0.486606	−	0.873621i	$-0.338235\pi$
$269$	−3.17999	−	2.31040i	−0.193887	−	0.140867i	−0.680494	+	0.732754i	$0.738235\pi$
$270$	22.1623	−	31.0492i	1.34875	−	1.88959i
$271$	−0.538324	+	0.391116i	−0.0327009	+	0.0237586i	−0.604016	−	0.796972i	$-0.706434\pi$
$271$	−0.538324	+	0.391116i	−0.0327009	+	0.0237586i	0.571315	+	0.820731i	$0.306434\pi$
$272$	−1.75397	−	2.41413i	−0.106350	−	0.146378i
$273$	2.70885	−	0.880159i	0.163947	−	0.0532696i
$274$	−8.19396			−0.495015
$275$	−7.04910	−	4.94261i	−0.425076	−	0.298051i
$276$	26.6375			1.60339
$277$	−17.0219	+	5.53076i	−1.02275	+	0.332311i	−0.771920	−	0.635720i	$-0.780703\pi$
$277$	−17.0219	+	5.53076i	−1.02275	+	0.332311i	−0.250829	+	0.968031i	$0.580703\pi$
$278$	8.72614	+	12.0105i	0.523359	+	0.720342i
$279$	27.9514	−	20.3079i	1.67340	−	1.21580i
$280$	−2.13236	−	0.673087i	−0.127433	−	0.0402246i
$281$	−6.85371	−	4.97951i	−0.408858	−	0.297053i	0.364281	−	0.931289i	$-0.381315\pi$
$281$	−6.85371	−	4.97951i	−0.408858	−	0.297053i	−0.773139	+	0.634236i	$0.781315\pi$
$282$		−	21.9689i		−	1.30823i
$283$	2.11876	−	2.91622i	0.125947	−	0.173351i	−0.741387	−	0.671078i	$-0.765832\pi$
$283$	2.11876	−	2.91622i	0.125947	−	0.173351i	0.867334	+	0.497726i	$0.165832\pi$
$284$	2.26114	−	6.95906i	0.134174	−	0.412944i
$285$	−4.84224	−	14.4875i	−0.286829	−	0.858163i
$286$	−0.454536	−	1.39892i	−0.0268773	−	0.0827197i
$287$	−5.91560	−	1.92210i	−0.349187	−	0.113458i
$288$	−7.71945	−	2.50820i	−0.454873	−	0.147797i
$289$	2.50167	+	7.69934i	0.147157	+	0.452902i
$290$	6.12595	−	19.4072i	0.359728	−	1.13963i
$291$	6.31600	−	19.4387i	0.370251	−	1.13951i
$292$	−5.50757	+	7.58051i	−0.322306	+	0.443616i
$293$			21.0780i			1.23139i	0.787985	+	0.615694i	$0.211124\pi$
$293$			21.0780i			1.23139i	−0.787985	+	0.615694i	$0.788876\pi$
$294$	2.69740	+	1.95978i	0.157316	+	0.114297i
$295$	−0.239245	−	28.4674i	−0.0139294	−	1.65744i
$296$	3.82439	−	2.77858i	0.222288	−	0.161502i
$297$	17.2661	+	23.7647i	1.00188	+	1.37897i
$298$	10.4821	−	3.40585i	0.607213	−	0.197295i
$299$	−6.82489			−0.394694
$300$	15.7661	−	5.41733i	0.910257	−	0.312770i
$301$	12.6427			0.728713
$302$	11.2738	−	3.66308i	0.648734	−	0.210786i
$303$	−0.186275	−	0.256386i	−0.0107012	−	0.0147290i
$304$	−1.65757	+	1.20430i	−0.0950684	+	0.0690713i
$305$	3.64809	+	4.93343i	0.208889	+	0.282488i
$306$	−19.5948	−	14.2365i	−1.12016	−	0.813844i
$307$			14.0304i			0.800758i	0.916350	+	0.400379i	$0.131121\pi$
$307$			14.0304i			0.800758i	−0.916350	+	0.400379i	$0.868879\pi$
$308$	1.01208	−	1.39301i	0.0576685	−	0.0793739i
$309$	−9.24632	+	28.4572i	−0.526005	+	1.61888i
$310$	9.51776	−	0.0799890i	0.540573	−	0.00454307i
$311$	4.69975	+	14.4643i	0.266498	+	0.820197i	0.991344	+	0.131287i	$0.0419108\pi$
$311$	4.69975	+	14.4643i	0.266498	+	0.820197i	−0.724846	+	0.688911i	$0.758089\pi$
$312$	2.70885	+	0.880159i	0.153358	+	0.0498292i
$313$	26.5288	+	8.61974i	1.49950	+	0.487216i	0.939871	−	0.341528i	$-0.110945\pi$
$313$	26.5288	+	8.61974i	1.49950	+	0.487216i	0.559627	+	0.828745i	$0.310945\pi$
$314$	−2.26284	−	6.96431i	−0.127700	−	0.393019i
$315$	−18.1489	+	0.152527i	−1.02257	+	0.00859390i
$316$	−0.501941	+	1.54482i	−0.0282364	+	0.0869027i
$317$	−5.80662	+	7.99213i	−0.326132	+	0.448883i	−0.940327	−	0.340272i	$-0.889481\pi$
$317$	−5.80662	+	7.99213i	−0.326132	+	0.448883i	0.614195	+	0.789155i	$0.289481\pi$
$318$		−	18.7558i		−	1.05177i
$319$	12.6781	+	9.21121i	0.709840	+	0.515729i
$320$	−1.32948	−	1.79791i	−0.0743204	−	0.100506i
$321$	3.33176	−	2.42067i	0.185961	−	0.135109i
$322$	−4.69596	−	6.46343i	−0.261695	−	0.360193i
$323$	−5.81467	+	1.88930i	−0.323537	+	0.105123i
$324$	−32.5309			−1.80727
$325$	−4.03949	+	1.38799i	−0.224071	+	0.0769921i
$326$	5.21151			0.288639
$327$	−24.0860	+	7.82601i	−1.33196	+	0.432779i
$328$	−3.65604	−	5.03211i	−0.201871	−	0.277852i
$329$	−5.33062	+	3.87292i	−0.293887	+	0.213521i
$330$	0.107882	+	12.8367i	0.00593870	+	0.706637i
$331$	11.8437	+	8.60493i	0.650987	+	0.472970i	0.863607	−	0.504165i	$-0.168200\pi$
$331$	11.8437	+	8.60493i	0.650987	+	0.472970i	−0.212620	+	0.977135i	$0.568200\pi$
$332$		−	1.44697i		−	0.0794127i
$333$	22.5530	−	31.0415i	1.23590	−	1.70106i
$334$	1.75783	−	5.41003i	0.0961840	−	0.296024i
$335$	2.11586	−	6.70309i	0.115602	−	0.366229i
$336$	1.03032	+	3.17099i	0.0562084	+	0.172992i
$337$	2.13834	+	0.694787i	0.116483	+	0.0378475i	0.366678	−	0.930348i	$-0.380495\pi$
$337$	2.13834	+	0.694787i	0.116483	+	0.0378475i	−0.250196	+	0.968195i	$0.580495\pi$
$338$	11.6697	+	3.79171i	0.634747	+	0.206242i
$339$	12.2976	+	37.8482i	0.667915	+	2.05563i
$340$	−2.11517	−	6.32837i	−0.114711	−	0.343204i
$341$	−2.26487	+	6.97055i	−0.122649	+	0.377476i
$342$	−9.77495	+	13.4541i	−0.528569	+	0.727512i
$343$		−	1.00000i		−	0.0539949i
$344$	10.2282	+	7.43120i	0.551466	+	0.400663i
$345$	56.8007	+	17.9293i	3.05805	+	0.965283i
$346$	−15.8093	+	11.4862i	−0.849915	+	0.617499i
$347$	5.26101	+	7.24116i	0.282426	+	0.388726i	0.926535	−	0.376207i	$-0.122772\pi$
$347$	5.26101	+	7.24116i	0.282426	+	0.388726i	−0.644110	+	0.764933i	$0.722772\pi$
$348$	−28.8601	+	9.37720i	−1.54706	+	0.502671i
$349$	−5.08467			−0.272176			−0.136088	−	0.990697i	$-0.543453\pi$
$349$	−5.08467			−0.272176			−0.136088	+	0.990697i	$0.543453\pi$
$350$	−4.09391	−	2.87052i	−0.218829	−	0.153436i
$351$	14.5737			0.777887
$352$	1.63758	−	0.532081i	0.0872831	−	0.0283600i
$353$	−8.62692	−	11.8739i	−0.459165	−	0.631986i	0.515171	−	0.857088i	$-0.327729\pi$
$353$	−8.62692	−	11.8739i	−0.459165	−	0.631986i	−0.974335	+	0.225102i	$0.927729\pi$
$354$	−34.3419	+	24.9508i	−1.82525	+	1.32612i
$355$	9.50560	−	13.3173i	0.504505	−	0.706807i
$356$	−1.62534	−	1.18088i	−0.0861427	−	0.0625864i
$357$			9.94927i			0.526571i
$358$	10.0788	−	13.8723i	0.532680	−	0.733171i
$359$	6.60818	−	20.3379i	0.348767	−	1.07339i	−0.610770	−	0.791808i	$-0.709140\pi$
$359$	6.60818	−	20.3379i	0.348767	−	1.07339i	0.959536	−	0.281585i	$-0.0908601\pi$
$360$	−14.7724	−	10.5442i	−0.778574	−	0.555731i
$361$	−4.57410	−	14.0776i	−0.240742	−	0.740929i
$362$	1.66471	+	0.540896i	0.0874951	+	0.0284289i
$363$	25.4796	+	8.27883i	1.33733	+	0.434526i
$364$	−0.263981	−	0.812450i	−0.0138364	−	0.0425840i
$365$	−16.8465	+	12.4573i	−0.881784	+	0.652045i
$366$	2.82717	−	8.70115i	0.147779	−	0.454816i
$367$	−14.2331	+	19.5901i	−0.742960	+	1.02260i	0.255483	+	0.966814i	$0.417765\pi$
$367$	−14.2331	+	19.5901i	−0.742960	+	1.02260i	−0.998443	+	0.0557830i	$0.982235\pi$
$368$		−	7.98924i		−	0.416468i
$369$	−40.8442	−	29.6751i	−2.12626	−	1.54482i
$370$	10.0252	−	3.35079i	0.521186	−	0.174199i
$371$	−4.55097	+	3.30648i	−0.236275	+	0.171664i
$372$	−8.34204	−	11.4818i	−0.432514	−	0.595305i
$373$	3.12177	−	1.01432i	0.161639	−	0.0525197i	−0.227080	−	0.973876i	$-0.572918\pi$
$373$	3.12177	−	1.01432i	0.161639	−	0.0525197i	0.388719	+	0.921356i	$0.372918\pi$
$374$	5.13805			0.265682
$375$	37.2653	−	0.939731i	1.92437	−	0.0485275i
$376$	−6.58901			−0.339802
$377$	7.39434	−	2.40257i	0.380828	−	0.123739i
$378$	10.0276	+	13.8018i	0.515765	+	0.709890i
$379$	−26.3665	+	19.1564i	−1.35436	+	0.983998i	−0.355575	+	0.934648i	$0.615715\pi$
$379$	−26.3665	+	19.1564i	−1.35436	+	0.983998i	−0.998782	+	0.0493501i	$0.984285\pi$
$380$	−4.34514	+	1.45231i	−0.222901	+	0.0745017i
$381$	8.66267	+	6.29380i	0.443802	+	0.322441i
$382$		−	23.5404i		−	1.20443i
$383$	−1.63701	+	2.25315i	−0.0836473	+	0.115131i	−0.848790	−	0.528730i	$-0.822668\pi$
$383$	−1.63701	+	2.25315i	−0.0836473	+	0.115131i	0.765143	+	0.643861i	$0.222668\pi$
$384$	−1.03032	+	3.17099i	−0.0525781	+	0.161819i
$385$	3.09573	−	2.28917i	0.157773	−	0.116667i
$386$	1.74100	+	5.35824i	0.0886145	+	0.272727i
$387$	97.5948	+	31.7105i	4.96102	+	1.61193i
$388$	−5.83013	−	1.89432i	−0.295980	−	0.0961697i
$389$	−11.2468	−	34.6141i	−0.570235	−	1.75500i	−0.651860	−	0.758339i	$-0.726011\pi$
$389$	−11.2468	−	34.6141i	−0.570235	−	1.75500i	0.0816250	−	0.996663i	$-0.473989\pi$
$390$	5.18382	+	3.70011i	0.262493	+	0.187362i
$391$	7.36700	−	22.6733i	0.372565	−	1.14664i
$392$	0.587785	−	0.809017i	0.0296876	−	0.0408615i
$393$			72.4318i			3.65370i
$394$	16.2555	+	11.8103i	0.818942	+	0.594996i
$395$	−2.11011	+	2.95625i	−0.106171	+	0.148745i
$396$	11.3066	−	8.21475i	0.568179	−	0.412807i
$397$	16.5176	+	22.7345i	0.828995	+	1.14101i	0.988109	+	0.153753i	$0.0491361\pi$
$397$	16.5176	+	22.7345i	0.828995	+	1.14101i	−0.159115	+	0.987260i	$0.550864\pi$
$398$	12.0525	−	3.91609i	0.604136	−	0.196296i
$399$	6.83131			0.341993
$400$	−1.62479	−	4.72864i	−0.0812395	−	0.236432i
$401$	−11.4620			−0.572385			−0.286192	−	0.958172i	$-0.592390\pi$
$401$	−11.4620			−0.572385			−0.286192	+	0.958172i	$0.592390\pi$
$402$	−9.96803	+	3.23881i	−0.497160	+	0.161537i
$403$	2.13734	+	2.94180i	0.106469	+	0.146542i
$404$	−0.0768963	+	0.0558684i	−0.00382573	+	0.00277956i
$405$	−69.3675	−	21.8961i	−3.44690	−	1.08803i
$406$	7.36309	+	5.34960i	0.365424	+	0.265496i
$407$			8.13954i			0.403462i
$408$	−5.84804	+	8.04913i	−0.289521	+	0.398491i
$409$	1.21570	−	3.74155i	0.0601127	−	0.185008i	−0.916491	−	0.400056i	$-0.868991\pi$
$409$	1.21570	−	3.74155i	0.0601127	−	0.185008i	0.976604	+	0.215048i	$0.0689907\pi$
$410$	−4.40895	−	13.1911i	−0.217742	−	0.651462i
$411$	8.44237	+	25.9830i	0.416432	+	1.28164i
$412$	8.53502	+	2.77320i	0.420490	+	0.136626i
$413$	12.1083	+	3.93424i	0.595813	+	0.193591i
$414$	−20.0386	−	61.6725i	−0.984844	−	3.03104i
$415$	0.973935	−	3.08546i	0.0478086	−	0.151459i
$416$	0.263981	−	0.812450i	0.0129427	−	0.0398337i
$417$	29.0945	−	40.0451i	1.42476	−	1.96102i
$418$		−	3.52786i		−	0.172553i
$419$	−15.2915	−	11.1100i	−0.747041	−	0.542757i	0.147868	−	0.989007i	$-0.452759\pi$
$419$	−15.2915	−	11.1100i	−0.747041	−	0.542757i	−0.894908	+	0.446250i	$0.852759\pi$
$420$	0.0626547	+	7.45518i	0.00305723	+	0.363775i
$421$	25.0071	−	18.1687i	1.21877	−	0.885488i	0.222772	−	0.974871i	$-0.428490\pi$
$421$	25.0071	−	18.1687i	1.21877	−	0.885488i	0.995997	+	0.0893830i	$0.0284895\pi$
$422$	−2.90824	−	4.00285i	−0.141571	−	0.194856i
$423$	−50.8636	+	16.5266i	−2.47307	+	0.803549i
$424$	−5.62531			−0.273189
$425$	−0.250766	−	14.9180i	−0.0121639	−	0.723631i
$426$	−24.3968			−1.18203
$427$	−2.60969	+	0.847938i	−0.126292	+	0.0410346i
$428$	−0.726018	−	0.999277i	−0.0350934	−	0.0483019i
$429$	−3.96763	+	2.88266i	−0.191559	+	0.139176i
$430$	16.8083	+	22.7304i	0.810567	+	1.09616i
$431$	4.25310	+	3.09006i	0.204865	+	0.148843i	0.685487	−	0.728085i	$-0.259589\pi$
$431$	4.25310	+	3.09006i	0.204865	+	0.148843i	−0.480623	+	0.876928i	$0.659589\pi$
$432$			17.0600i			0.820800i
$433$	−9.56496	+	13.1650i	−0.459662	+	0.632671i	−0.974439	−	0.224653i	$-0.927875\pi$
$433$	−9.56496	+	13.1650i	−0.459662	+	0.632671i	0.514776	+	0.857325i	$0.327875\pi$
$434$	−1.31537	+	4.04829i	−0.0631397	+	0.194324i
$435$	−67.8517	+	0.570238i	−3.25324	+	0.0273408i
$436$	2.34721	+	7.22397i	0.112411	+	0.345965i
$437$	−15.5678	−	5.05828i	−0.744709	−	0.241970i
$438$	29.7123	+	9.65410i	1.41971	+	0.461291i
$439$	8.64876	+	26.6181i	0.412783	+	1.27041i	0.914219	+	0.405220i	$0.132805\pi$
$439$	8.64876	+	26.6181i	0.412783	+	1.27041i	−0.501436	+	0.865195i	$0.667195\pi$
$440$	3.85004	−	0.0323564i	0.183543	−	0.00154253i
$441$	2.50820	−	7.71945i	0.119438	−	0.367593i
$442$	1.49835	−	2.06230i	0.0712691	−	0.0980935i
$443$		−	26.0620i		−	1.23824i	−0.785296	−	0.619121i	$-0.787489\pi$
$443$		−	26.0620i		−	1.23824i	0.785296	−	0.619121i	$-0.212511\pi$
$444$	−12.7512	−	9.26428i	−0.605145	−	0.439663i
$445$	−2.67097	−	3.61205i	−0.126616	−	0.171227i
$446$	−3.84558	+	2.79398i	−0.182093	+	0.132299i
$447$	−21.5998	−	29.7296i	−1.02163	−	1.40616i
$448$	0.951057	−	0.309017i	0.0449332	−	0.0145997i
$449$	−13.3501			−0.630032			−0.315016	−	0.949086i	$-0.602010\pi$
$449$	−13.3501			−0.630032			−0.315016	+	0.949086i	$0.602010\pi$
$450$	−24.4029	−	32.4272i	−1.15036	−	1.52863i
$451$	10.7100			0.504312
$452$	11.3516	−	3.68835i	0.533934	−	0.173486i
$453$	−23.2312	−	31.9749i	−1.09149	−	1.50231i
$454$	−10.9312	+	7.94199i	−0.513027	+	0.372736i
$455$	−0.0160530	−	1.91012i	−0.000752576	−	0.0895477i
$456$	5.52664	+	4.01534i	0.258809	+	0.188036i
$457$		−	20.8195i		−	0.973897i	−0.873431	−	0.486948i	$-0.838110\pi$
$457$		−	20.8195i		−	0.973897i	0.873431	−	0.486948i	$-0.161890\pi$
$458$	10.7547	−	14.8025i	0.502532	−	0.691676i
$459$	−15.7313	+	48.4160i	−0.734274	+	2.25986i
$460$	5.37745	−	17.0359i	0.250725	−	0.794304i
$461$	4.64230	+	14.2875i	0.216214	+	0.665437i	0.999065	+	0.0432286i	$0.0137644\pi$
$461$	4.64230	+	14.2875i	0.216214	+	0.665437i	−0.782852	+	0.622208i	$0.786236\pi$
$462$	−5.45996	−	1.77405i	−0.254021	−	0.0825363i
$463$	2.75812	+	0.896167i	0.128181	+	0.0416484i	0.372405	−	0.928070i	$-0.378533\pi$
$463$	2.75812	+	0.896167i	0.128181	+	0.0416484i	−0.244224	+	0.969719i	$0.578533\pi$
$464$	2.81245	+	8.65584i	0.130565	+	0.401837i
$465$	−10.0599	−	30.0983i	−0.466519	−	1.39577i
$466$	7.66301	−	23.5843i	0.354982	−	1.09252i
$467$	11.8687	−	16.3358i	0.549217	−	0.755933i	−0.440688	−	0.897660i	$-0.645266\pi$
$467$	11.8687	−	16.3358i	0.549217	−	0.755933i	0.989906	+	0.141727i	$0.0452656\pi$
$468$		−	6.93379i		−	0.320515i
$469$	2.54315	+	1.84771i	0.117432	+	0.0853193i
$470$	−14.0501	−	4.43498i	−0.648084	−	0.204570i
$471$	−19.7523	+	14.3509i	−0.910138	+	0.661254i
$472$	7.48337	+	10.3000i	0.344450	+	0.474095i
$473$	−20.7034	+	6.72694i	−0.951943	+	0.309305i
$474$	5.41575			0.248754
$475$	−10.2429	+	0.172179i	−0.469978	+	0.00790012i
$476$	2.98403			0.136773
$477$	−43.4243	+	14.1094i	−1.98826	+	0.646026i
$478$	16.3614	+	22.5195i	0.748353	+	1.03002i
$479$	13.6630	−	9.92676i	0.624279	−	0.453565i	−0.230135	−	0.973159i	$-0.573917\pi$
$479$	13.6630	−	9.92676i	0.624279	−	0.453565i	0.854413	+	0.519594i	$0.173917\pi$
$480$	−4.33135	+	6.06819i	−0.197698	+	0.276974i
$481$	3.26703	+	2.37364i	0.148964	+	0.108228i
$482$		−	7.54422i		−	0.343630i
$483$	−15.6571	+	21.5502i	−0.712424	+	0.980568i
$484$	2.48302	−	7.64196i	0.112865	−	0.347362i
$485$	−11.1569	−	7.96356i	−0.506608	−	0.361607i
$486$	17.7016	+	54.4799i	0.802961	+	2.47126i
$487$	−10.4308	−	3.38916i	−0.472662	−	0.153577i	0.0629930	−	0.998014i	$-0.479935\pi$
$487$	−10.4308	−	3.38916i	−0.472662	−	0.153577i	−0.535655	+	0.844437i	$0.679935\pi$
$488$	−2.60969	−	0.847938i	−0.118135	−	0.0383844i
$489$	−5.36951	−	16.5256i	−0.242818	−	0.747315i
$490$	1.79791	−	1.32948i	0.0812212	−	0.0600600i
$491$	1.65606	−	5.09682i	0.0747368	−	0.230016i	−0.906709	−	0.421757i	$-0.861413\pi$
$491$	1.65606	−	5.09682i	0.0747368	−	0.230016i	0.981446	+	0.191741i	$0.0614134\pi$
$492$	−12.1899	+	16.7779i	−0.549562	+	0.756408i
$493$			27.1585i			1.22316i
$494$	−1.41600	−	1.02879i	−0.0637089	−	0.0462872i
$495$	29.6390	−	9.90645i	1.33218	−	0.445262i
$496$	−3.44368	+	2.50198i	−0.154626	+	0.112342i
$497$	4.30094	+	5.91973i	0.192923	+	0.265536i
$498$	−4.58832	+	1.49084i	−0.205608	+	0.0668059i
$499$	13.9256			0.623397			0.311699	−	0.950181i	$-0.399102\pi$
$499$	13.9256			0.623397			0.311699	+	0.950181i	$0.399102\pi$
$500$	−0.281848	−	11.1768i	−0.0126046	−	0.499841i
$501$	−18.9663			−0.847350
$502$	18.9661	−	6.16246i	0.846498	−	0.275044i
$503$	24.7070	+	34.0063i	1.10163	+	1.51627i	0.833203	+	0.552967i	$0.186504\pi$
$503$	24.7070	+	34.0063i	1.10163	+	1.51627i	0.268429	+	0.963300i	$0.413496\pi$
$504$	6.56656	−	4.77088i	0.292498	−	0.212512i
$505$	−0.201575	+	0.0673737i	−0.00896996	+	0.00299809i
$506$	11.1291	+	8.08573i	0.494747	+	0.359455i
$507$		−	40.9111i		−	1.81693i
$508$	1.88766	−	2.59814i	0.0837515	−	0.115274i
$509$	−7.36808	+	22.6766i	−0.326584	+	1.00512i	0.644136	+	0.764911i	$0.277217\pi$
$509$	−7.36808	+	22.6766i	−0.326584	+	1.00512i	−0.970720	+	0.240212i	$0.922783\pi$
$510$	−17.8879	+	13.2274i	−0.792088	+	0.585719i
$511$	−2.89550	−	8.91143i	−0.128089	−	0.394218i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	33.2431	+	10.8013i	1.46772	+	0.476890i
$514$	−0.876428	−	2.69737i	−0.0386576	−	0.118976i
$515$	16.3331	+	11.6583i	0.719724	+	0.513724i
$516$	13.0260	−	40.0899i	0.573437	−	1.76486i
$517$	6.66859	−	9.17853i	0.293284	−	0.403671i
$518$			4.72721i			0.207702i
$519$	52.7110	+	38.2968i	2.31376	+	1.68104i
$520$	1.10975	−	1.55475i	0.0486659	−	0.0681805i
$521$	−14.0520	+	10.2094i	−0.615631	+	0.447282i	−0.851393	−	0.524529i	$-0.824242\pi$
$521$	−14.0520	+	10.2094i	−0.615631	+	0.447282i	0.235762	+	0.971811i	$0.424242\pi$
$522$	43.4212	+	59.7641i	1.90049	+	2.61580i
$523$	−24.6668	+	8.01472i	−1.07860	+	0.350459i	−0.793833	−	0.608136i	$-0.791917\pi$
$523$	−24.6668	+	8.01472i	−1.07860	+	0.350459i	−0.284771	+	0.958596i	$0.591917\pi$
$524$	21.7241			0.949020
$525$	−4.88438	+	15.9393i	−0.213172	+	0.695647i
$526$	7.30453			0.318493
$527$	−12.0802	+	3.92510i	−0.526222	+	0.170980i
$528$	−3.37444	−	4.64452i	−0.146854	−	0.202127i
$529$	33.0305	−	23.9980i	1.43611	−	1.04339i
$530$	−11.9952	−	3.78632i	−0.521038	−	0.164467i
$531$	83.6019	+	60.7403i	3.62801	+	2.63591i
$532$		−	2.04888i		−	0.0888300i
$533$	3.12322	−	4.29874i	0.135281	−	0.186199i
$534$	−2.06993	+	6.37060i	−0.0895748	+	0.275683i
$535$	−0.875530	−	2.61949i	−0.0378524	−	0.113250i
$536$	0.971398	+	2.98966i	0.0419580	+	0.129133i
$537$	−54.3731	−	17.6669i	−2.34637	−	0.762382i
$538$	3.73830	+	1.21465i	0.161170	+	0.0523672i
$539$	0.532081	+	1.63758i	0.0229183	+	0.0705354i
$540$	−11.4829	+	36.3781i	−0.494144	+	1.56546i
$541$	0.515504	−	1.58656i	0.0221632	−	0.0682114i	−0.939363	−	0.342924i	$-0.888583\pi$
$541$	0.515504	−	1.58656i	0.0221632	−	0.0682114i	0.961526	+	0.274713i	$0.0885827\pi$
$542$	0.391116	−	0.538324i	0.0167999	−	0.0231230i
$543$		−	5.83606i		−	0.250449i
$544$	2.41413	+	1.75397i	0.103505	+	0.0752008i
$545$	0.142736	+	16.9840i	0.00611416	+	0.727514i
$546$	−2.30429	+	1.67416i	−0.0986143	+	0.0716475i
$547$	−17.5150	−	24.1073i	−0.748886	−	1.03075i	−0.998058	−	0.0622944i	$-0.980158\pi$
$547$	−17.5150	−	24.1073i	−0.748886	−	1.03075i	0.249171	−	0.968459i	$-0.419842\pi$
$548$	7.79292	−	2.53207i	0.332897	−	0.108165i
$549$	−22.2722			−0.950552
$550$	8.23144	+	2.52241i	0.350990	+	0.107556i
$551$	18.6474			0.794406
$552$	−25.3338	+	8.23144i	−1.07828	+	0.350353i
$553$	−0.954749	−	1.31410i	−0.0406000	−	0.0558812i
$554$	14.4797	−	10.5201i	0.615184	−	0.446958i
$555$	−20.9544	−	28.3374i	−0.889467	−	1.20286i
$556$	−12.0105	−	8.72614i	−0.509359	−	0.370071i
$557$			3.20180i			0.135665i	0.997697	+	0.0678324i	$0.0216083\pi$
$557$			3.20180i			0.135665i	−0.997697	+	0.0678324i	$0.978392\pi$
$558$	−20.3079	+	27.9514i	−0.859700	+	1.18328i
$559$	−3.33744	+	10.2716i	−0.141159	+	0.434441i
$560$	2.23599	−	0.0187917i	0.0944878	−	0.000794093i
$561$	−5.29382	−	16.2927i	−0.223505	−	0.687878i
$562$	8.05702	+	2.61789i	0.339865	+	0.110429i
$563$	12.2126	+	3.96812i	0.514700	+	0.167236i	0.554839	−	0.831958i	$-0.312780\pi$
$563$	12.2126	+	3.96812i	0.514700	+	0.167236i	−0.0401388	+	0.999194i	$0.512780\pi$
$564$	6.78877	+	20.8937i	0.285859	+	0.879782i
$565$	26.6882	−	0.224293i	1.12278	−	0.00943607i
$566$	−1.11390	+	3.42823i	−0.0468206	+	0.144099i
$567$	19.1212	−	26.3180i	0.803014	−	1.10525i
$568$			7.31719i			0.307022i
$569$	20.5339	+	14.9187i	0.860824	+	0.625425i	0.928109	−	0.372308i	$-0.121434\pi$
$569$	20.5339	+	14.9187i	0.860824	+	0.625425i	−0.0672848	+	0.997734i	$0.521434\pi$
$570$	9.08211	+	12.2821i	0.380408	+	0.514439i
$571$	0.834820	−	0.606532i	0.0349361	−	0.0253826i	−0.570180	−	0.821520i	$-0.693127\pi$
$571$	0.834820	−	0.606532i	0.0349361	−	0.0253826i	0.605116	+	0.796137i	$0.293127\pi$
$572$	0.864579	+	1.18999i	0.0361499	+	0.0497560i
$573$	−74.6462	+	24.2540i	−3.11839	+	1.01323i
$574$	6.22003			0.259619
$575$	22.9333	−	32.7072i	0.956385	−	1.36398i
$576$	8.11671			0.338196
$577$	13.7418	−	4.46497i	0.572077	−	0.185879i	−0.00867107	−	0.999962i	$-0.502760\pi$
$577$	13.7418	−	4.46497i	0.572077	−	0.185879i	0.580748	+	0.814083i	$0.302760\pi$
$578$	−4.75846	−	6.54945i	−0.197926	−	0.272421i
$579$	15.1971	−	11.0414i	0.631572	−	0.458864i
$580$	0.171028	+	20.3504i	0.00710156	+	0.845003i
$581$	1.17062	+	0.850507i	0.0485656	+	0.0352850i
$582$			20.4390i			0.847224i
$583$	5.69326	−	7.83610i	0.235791	−	0.324538i
$584$	2.89550	−	8.91143i	0.119817	−	0.368758i
$585$	4.66704	−	14.7853i	0.192958	−	0.611298i
$586$	−6.51345	−	20.0463i	−0.269068	−	0.828107i
$587$	13.4421	+	4.36760i	0.554814	+	0.180270i	0.572987	−	0.819565i	$-0.305785\pi$
$587$	13.4421	+	4.36760i	0.554814	+	0.180270i	−0.0181721	+	0.999835i	$0.505785\pi$
$588$	−3.17099	−	1.03032i	−0.130769	−	0.0424895i
$589$	2.69503	+	8.29444i	0.111047	+	0.341766i
$590$	9.02445	+	27.0002i	0.371531	+	1.11158i
$591$	20.7021	−	63.7145i	0.851570	−	2.62086i
$592$	−2.77858	+	3.82439i	−0.114199	+	0.157182i
$593$		−	13.7863i		−	0.566136i	−0.959100	−	0.283068i	$-0.908648\pi$
$593$		−	13.7863i		−	0.566136i	0.959100	−	0.283068i	$-0.0913523\pi$
$594$	−23.7647	−	17.2661i	−0.975077	−	0.708435i
$595$	6.36302	+	2.00851i	0.260858	+	0.0823409i
$596$	−8.91662	+	6.47830i	−0.365239	+	0.265362i
$597$	−24.8357	−	34.1835i	−1.01646	−	1.39904i
$598$	6.49086	−	2.10901i	0.265431	−	0.0862437i
$599$	12.3944			0.506423			0.253211	−	0.967411i	$-0.418513\pi$
$599$	12.3944			0.506423			0.253211	+	0.967411i	$0.418513\pi$
$600$	−13.3204	+	10.0242i	−0.543804	+	0.409236i
$601$	9.96529			0.406492			0.203246	−	0.979128i	$-0.434851\pi$
$601$	9.96529			0.406492			0.203246	+	0.979128i	$0.434851\pi$
$602$	−12.0239	+	3.90681i	−0.490059	+	0.159230i
$603$	14.9973	+	20.6420i	0.610738	+	0.840609i
$604$	−9.59006	+	6.96759i	−0.390214	+	0.283507i
$605$	10.4384	−	14.6241i	0.424381	−	0.594555i
$606$	0.256386	+	0.186275i	0.0104150	+	0.00756691i
$607$		−	0.0880037i		−	0.00357196i	−0.999998	−	0.00178598i	$-0.999432\pi$
$607$		−	0.0880037i		−	0.00357196i	0.999998	−	0.00178598i	$-0.000568496\pi$
$608$	1.20430	−	1.65757i	0.0488408	−	0.0672235i
$609$	9.37720	−	28.8601i	0.379983	−	1.16947i
$610$	−4.99405	−	3.56465i	−0.202203	−	0.144329i
$611$	−1.73937	−	5.35325i	−0.0703676	−	0.216569i
$612$	23.0351	+	7.48455i	0.931138	+	0.302545i
$613$	−17.2668	−	5.61033i	−0.697401	−	0.226599i	−0.0612031	−	0.998125i	$-0.519494\pi$
$613$	−17.2668	−	5.61033i	−0.697401	−	0.226599i	−0.636198	+	0.771526i	$0.719494\pi$
$614$	−4.33564	−	13.3437i	−0.174972	−	0.538508i
$615$	−37.2862	+	27.5717i	−1.50353	+	1.11180i
$616$	−0.532081	+	1.63758i	−0.0214381	+	0.0659798i
$617$	−18.6611	+	25.6849i	−0.751270	+	1.03403i	0.246621	+	0.969112i	$0.420680\pi$
$617$	−18.6611	+	25.6849i	−0.751270	+	1.03403i	−0.997890	+	0.0649218i	$0.979320\pi$
$618$		−	29.9217i		−	1.20363i
$619$	26.2797	+	19.0933i	1.05627	+	0.767424i	0.973395	−	0.229136i	$-0.0735899\pi$
$619$	26.2797	+	19.0933i	1.05627	+	0.767424i	0.0828745	+	0.996560i	$0.473590\pi$
$620$	−9.02721	+	3.01722i	−0.362542	+	0.121175i
$621$	−110.266	+	80.1130i	−4.42483	+	3.21483i
$622$	−8.93945	−	12.3041i	−0.358439	−	0.493350i
$623$	1.91070	−	0.620824i	0.0765506	−	0.0248728i
$624$	−2.84825			−0.114021
$625$	6.92194	−	24.0226i	0.276878	−	0.960905i
$626$	−27.8941			−1.11487
$627$	−11.1868	+	3.63481i	−0.446757	+	0.145160i
$628$	4.30418	+	5.92420i	0.171755	+	0.236401i
$629$	−11.4121	+	8.29138i	−0.455030	+	0.330599i
$630$	17.2135	−	5.75337i	0.685801	−	0.229220i
$631$	14.1799	+	10.3023i	0.564495	+	0.410130i	0.833101	−	0.553121i	$-0.186563\pi$
$631$	14.1799	+	10.3023i	0.564495	+	0.410130i	−0.268606	+	0.963250i	$0.586563\pi$
$632$		−	1.62432i		−	0.0646118i
$633$	−9.69658	+	13.3462i	−0.385405	+	0.530464i
$634$	3.05272	−	9.39531i	0.121239	−	0.373136i
$635$	5.77395	−	4.26962i	0.229132	−	0.169435i
$636$	5.79585	+	17.8378i	0.229821	+	0.707315i
$637$	0.812450	+	0.263981i	0.0321905	+	0.0104593i
$638$	−14.9041	−	4.84262i	−0.590057	−	0.191721i
$639$	18.3530	+	56.4847i	0.726033	+	2.23450i
$640$	1.82000	+	1.29908i	0.0719418	+	0.0513506i
$641$	−13.8528	+	42.6346i	−0.547153	+	1.68396i	0.168661	+	0.985674i	$0.446056\pi$
$641$	−13.8528	+	42.6346i	−0.547153	+	1.68396i	−0.715815	+	0.698290i	$0.753944\pi$
$642$	−2.42067	+	3.33176i	−0.0955362	+	0.131494i
$643$		−	29.1987i		−	1.15149i	−0.817631	−	0.575743i	$-0.804713\pi$
$643$		−	29.1987i		−	1.15149i	0.817631	−	0.575743i	$-0.195287\pi$
$644$	6.46343	+	4.69596i	0.254695	+	0.185047i
$645$	54.7600	−	76.7184i	2.15617	−	3.02078i
$646$	4.94625	−	3.59366i	0.194608	−	0.141391i
$647$	15.4111	+	21.2116i	0.605873	+	0.833912i	0.996230	−	0.0867512i	$-0.0276485\pi$
$647$	15.4111	+	21.2116i	0.605873	+	0.833912i	−0.390357	+	0.920663i	$0.627649\pi$
$648$	30.9387	−	10.0526i	1.21539	−	0.394903i
$649$	−21.9217			−0.860501
$650$	3.41287	−	2.56833i	0.133864	−	0.100738i
$651$	14.1923			0.556241
$652$	−4.95644	+	1.61045i	−0.194109	+	0.0630699i
$653$	−8.37468	−	11.5268i	−0.327727	−	0.451077i	0.613080	−	0.790021i	$-0.289930\pi$
$653$	−8.37468	−	11.5268i	−0.327727	−	0.451077i	−0.940807	+	0.338944i	$0.889930\pi$
$654$	20.4888	−	14.8860i	0.801174	−	0.582087i
$655$	46.3235	+	14.6222i	1.81001	+	0.571336i
$656$	5.03211	+	3.65604i	0.196471	+	0.142745i
$657$		−	76.0539i		−	2.96714i
$658$	3.87292	−	5.33062i	0.150982	−	0.207809i
$659$	8.06201	−	24.8123i	0.314051	−	0.966551i	−0.662092	−	0.749423i	$-0.730331\pi$
$659$	8.06201	−	24.8123i	0.314051	−	0.966551i	0.976143	−	0.217128i	$-0.0696689\pi$
$660$	−4.06936	−	12.1751i	−0.158400	−	0.473914i
$661$	2.25363	+	6.93597i	0.0876562	+	0.269778i	0.985270	−	0.171004i	$-0.0547011\pi$
$661$	2.25363	+	6.93597i	0.0876562	+	0.269778i	−0.897614	+	0.440782i	$0.854701\pi$
$662$	−13.9231	−	4.52388i	−0.541135	−	0.175826i
$663$	−8.08329	−	2.62642i	−0.313929	−	0.102002i
$664$	0.447138	+	1.37615i	0.0173523	+	0.0534049i
$665$	1.37907	−	4.36894i	0.0534781	−	0.169420i
$666$	−11.8568	+	36.4915i	−0.459442	+	1.41402i
$667$	−42.7392	+	58.8255i	−1.65487	+	2.27773i
$668$			5.68845i			0.220093i
$669$	12.8218	+	9.31560i	0.495721	+	0.360162i
$670$	0.0590718	+	7.02885i	0.00228214	+	0.271548i
$671$	3.82239	−	2.77713i	0.147562	−	0.107210i
$672$	−1.95978	−	2.69740i	−0.0756001	−	0.104055i
$673$	−1.00804	+	0.327532i	−0.0388571	+	0.0126254i	−0.328381	−	0.944545i	$-0.606503\pi$
$673$	−1.00804	+	0.327532i	−0.0388571	+	0.0126254i	0.289524	+	0.957171i	$0.406503\pi$
$674$	−2.24838			−0.0866043
$675$	−48.9712	+	69.8421i	−1.88490	+	2.68822i
$676$	−12.2702			−0.471932
$677$	41.0211	−	13.3286i	1.57657	−	0.512258i	0.615398	−	0.788216i	$-0.288995\pi$
$677$	41.0211	−	13.3286i	1.57657	−	0.512258i	0.961170	+	0.275958i	$0.0889951\pi$
$678$	−23.3914	−	32.1956i	−0.898343	−	1.23646i
$679$	4.95940	−	3.60322i	0.190324	−	0.138279i
$680$	3.96722	+	5.36501i	0.152136	+	0.205739i
$681$	36.4465	+	26.4800i	1.39663	+	1.01471i
$682$		−	7.32927i		−	0.280652i
$683$	22.9140	−	31.5384i	0.876780	−	1.20678i	−0.100522	−	0.994935i	$-0.532051\pi$
$683$	22.9140	−	31.5384i	0.876780	−	1.20678i	0.977302	−	0.211850i	$-0.0679487\pi$
$684$	5.13899	−	15.8162i	0.196494	−	0.604747i
$685$	18.3216	−	0.153978i	0.700033	−	0.00588320i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−58.0193	−	18.8516i	−2.21357	−	0.719234i
$688$	−12.0239	−	3.90681i	−0.458408	−	0.148946i
$689$	−1.48498	−	4.57029i	−0.0565731	−	0.174114i
$690$	−59.5612	+	0.500563i	−2.26745	+	0.0190561i
$691$	11.1865	−	34.4284i	0.425554	−	1.30972i	−0.476909	−	0.878952i	$-0.658243\pi$
$691$	11.1865	−	34.4284i	0.425554	−	1.30972i	0.902463	−	0.430767i	$-0.141757\pi$
$692$	11.4862	−	15.8093i	0.436638	−	0.600981i
$693$			13.9758i			0.530895i
$694$	−7.24116	−	5.26101i	−0.274871	−	0.199705i
$695$	−19.7373	−	26.6914i	−0.748677	−	1.01246i
$696$	24.5498	−	17.8365i	0.930559	−	0.676091i
$697$	10.9097	+	15.0160i	0.413236	+	0.568770i
$698$	4.83581	−	1.57125i	0.183038	−	0.0594727i
$699$	−82.6809			−3.12728
$700$	4.78058	+	1.46494i	0.180689	+	0.0553697i
$701$	4.10776			0.155148			0.0775741	−	0.996987i	$-0.475283\pi$
$701$	4.10776			0.155148			0.0775741	+	0.996987i	$0.475283\pi$
$702$	−13.8604	+	4.50352i	−0.523128	+	0.169974i
$703$	5.69297	+	7.83570i	0.214715	+	0.295529i
$704$	−1.39301	+	1.01208i	−0.0525009	+	0.0381441i
$705$	0.412832	+	49.1222i	0.0155482	+	1.85005i
$706$	11.8739	+	8.62692i	0.446881	+	0.324678i
$707$		−	0.0950491i		−	0.00357469i
$708$	24.9508	−	34.3419i	0.937710	−	1.29065i
$709$	−4.88921	+	15.0475i	−0.183618	+	0.565119i	−0.999922	−	0.0125043i	$-0.996020\pi$
$709$	−4.88921	+	15.0475i	−0.183618	+	0.565119i	0.816304	+	0.577623i	$0.196020\pi$
$710$	−4.92510	+	15.6029i	−0.184836	+	0.585565i
$711$	−4.07411	−	12.5388i	−0.152791	−	0.470243i
$712$	1.91070	+	0.620824i	0.0716065	+	0.0232664i
$713$	−32.3427	−	10.5088i	−1.21124	−	0.393557i
$714$	−3.07449	−	9.46232i	−0.115060	−	0.354118i
$715$	1.04263	+	3.11942i	0.0389920	+	0.116660i
$716$	−5.29873	+	16.3078i	−0.198023	+	0.609452i
$717$	54.5517	−	75.0840i	2.03727	−	2.80406i
$718$			21.3845i			0.798064i
$719$	−7.18528	−	5.22041i	−0.267966	−	0.194689i	0.445686	−	0.895190i	$-0.352960\pi$
$719$	−7.18528	−	5.22041i	−0.267966	−	0.194689i	−0.713651	+	0.700501i	$0.752960\pi$
$720$	17.3077	+	5.46325i	0.645022	+	0.203603i
$721$	−7.26032	+	5.27493i	−0.270389	+	0.196449i
$722$	8.70046	+	11.9752i	0.323798	+	0.445669i
$723$	−23.9226	+	7.77294i	−0.889692	+	0.289079i
$724$	−1.75038			−0.0650523
$725$	−13.3329	+	43.5094i	−0.495170	+	1.61590i
$726$	−26.7909			−0.994302
$727$	47.2553	−	15.3542i	1.75260	−	0.569455i	0.756210	−	0.654329i	$-0.227049\pi$
$727$	47.2553	−	15.3542i	1.75260	−	0.569455i	0.996392	+	0.0848740i	$0.0270488\pi$
$728$	0.502122	+	0.691112i	0.0186099	+	0.0256143i
$729$	75.5628	−	54.8996i	2.79862	−	2.03332i
$730$	12.1724	−	17.0534i	0.450521	−	0.631176i
$731$	−30.5211	−	22.1749i	−1.12887	−	0.820169i
$732$			9.14893i			0.338154i
$733$	−15.0854	+	20.7633i	−0.557192	+	0.766909i	−0.990966	−	0.134113i	$-0.957182\pi$
$733$	−15.0854	+	20.7633i	−0.557192	+	0.766909i	0.433774	+	0.901022i	$0.357182\pi$
$734$	7.48276	−	23.0296i	0.276194	−	0.850037i
$735$	−6.06819	−	4.33135i	−0.223829	−	0.159764i
$736$	2.46881	+	7.59821i	0.0910015	+	0.280074i
$737$	−5.14774	−	1.67260i	−0.189619	−	0.0616111i
$738$	48.0152	+	15.6011i	1.76747	+	0.574284i
$739$	−13.2174	−	40.6791i	−0.486212	−	1.49641i	−0.830218	−	0.557439i	$-0.811784\pi$
$739$	−13.2174	−	40.6791i	−0.486212	−	1.49641i	0.344006	−	0.938967i	$-0.388216\pi$
$740$	−8.49909	+	6.28475i	−0.312433	+	0.231032i
$741$	−1.80334	+	5.55010i	−0.0662472	+	0.203888i
$742$	3.30648	−	4.55097i	0.121385	−	0.167072i
$743$			9.91998i			0.363929i	0.983305	+	0.181964i	$0.0582456\pi$
$743$			9.91998i			0.363929i	−0.983305	+	0.181964i	$0.941754\pi$
$744$	11.4818	+	8.34204i	0.420944	+	0.305834i
$745$	−23.3739	+	7.81241i	−0.856353	+	0.286225i
$746$	−2.65554	+	1.92936i	−0.0972261	+	0.0706389i
$747$	6.90332	+	9.50161i	0.252579	+	0.347646i
$748$	−4.88658	+	1.58774i	−0.178671	+	0.0580537i
$749$	1.23517			0.0451323
$750$	−35.1511	+	12.4094i	−1.28354	+	0.453126i
$751$	−33.7245			−1.23062			−0.615312	−	0.788284i	$-0.710970\pi$
$751$	−33.7245			−1.23062			−0.615312	+	0.788284i	$0.710970\pi$
$752$	6.26652	−	2.03612i	0.228517	−	0.0742495i
$753$	−39.0821	−	53.7919i	−1.42423	−	1.96029i
$754$	−6.29000	+	4.56996i	−0.229068	+	0.166428i
$755$	−25.1392	+	8.40246i	−0.914911	+	0.305797i
$756$	−13.8018	−	10.0276i	−0.501968	−	0.364701i
$757$			12.2698i			0.445952i	0.974824	+	0.222976i	$0.0715772\pi$
$757$			12.2698i			0.445952i	−0.974824	+	0.222976i	$0.928423\pi$
$758$	19.1564	−	26.3665i	0.695792	−	0.957675i
$759$	14.1733	−	43.6209i	0.514458	−	1.58334i
$760$	3.68369	−	2.72395i	0.133621	−	0.0988080i
$761$	−9.91370	−	30.5112i	−0.359371	−	1.10603i	−0.953431	−	0.301610i	$-0.902476\pi$
$761$	−9.91370	−	30.5112i	−0.359371	−	1.10603i	0.594060	−	0.804421i	$-0.297524\pi$
$762$	−10.1836	−	3.30884i	−0.368912	−	0.119867i
$763$	−7.22397	−	2.34721i	−0.261525	−	0.0849747i
$764$	7.27437	+	22.3882i	0.263178	+	0.809977i
$765$	44.0813	+	31.4643i	1.59376	+	1.13760i
$766$	0.860627	−	2.64874i	0.0310957	−	0.0957028i
$767$	−6.39275	+	8.79886i	−0.230829	+	0.317709i
$768$		−	3.33417i		−	0.120312i
$769$	24.6444	+	17.9052i	0.888700	+	0.645679i	0.935539	−	0.353224i	$-0.114915\pi$
$769$	24.6444	+	17.9052i	0.888700	+	0.645679i	−0.0468384	+	0.998902i	$0.514915\pi$
$770$	−2.23682	+	3.13376i	−0.0806093	+	0.112933i
$771$	−7.65032	+	5.55829i	−0.275520	+	0.200177i
$772$	−3.31158	−	4.55799i	−0.119186	−	0.164046i
$773$	−13.9875	+	4.54481i	−0.503094	+	0.163465i	−0.549559	−	0.835455i	$-0.685204\pi$
$773$	−13.9875	+	4.54481i	−0.503094	+	0.163465i	0.0464650	+	0.998920i	$0.485204\pi$
$774$	−102.617			−3.68850
$775$	−21.2801	+	0.357709i	−0.764404	+	0.0128493i
$776$	6.13016			0.220060
$777$	14.9899	−	4.87052i	0.537760	−	0.174729i
$778$	21.3927	+	29.4445i	0.766964	+	1.05564i
$779$	10.3102	−	7.49078i	0.369400	−	0.268385i
$780$	−6.07350	−	1.91712i	−0.217466	−	0.0686440i
$781$	−10.1929	−	7.40557i	−0.364730	−	0.264992i
$782$			23.8401i			0.852521i
$783$	91.2642	−	125.614i	3.26152	−	4.48909i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	5.19056	+	15.5296i	0.185259	+	0.554275i
$786$	−22.3827	−	68.8867i	−0.798363	−	2.45711i
$787$	−3.59995	−	1.16969i	−0.128324	−	0.0416951i	0.244151	−	0.969737i	$-0.421491\pi$
$787$	−3.59995	−	1.16969i	−0.128324	−	0.0416951i	−0.372475	+	0.928042i	$0.621491\pi$
$788$	−19.1095	−	6.20906i	−0.680749	−	0.221189i
$789$	−7.52597	−	23.1626i	−0.267932	−	0.824609i
$790$	1.09331	−	3.46362i	0.0388981	−	0.123230i
$791$	−3.68835	+	11.3516i	−0.131143	+	0.403616i
$792$	−8.21475	+	11.3066i	−0.291898	+	0.401764i
$793$		−	2.34408i		−	0.0832407i
$794$	−22.7345	−	16.5176i	−0.806818	−	0.586188i
$795$	0.352452	+	41.9377i	0.0125002	+	1.48738i
$796$	−10.2525	+	7.44884i	−0.363389	+	0.264017i
$797$	13.1552	+	18.1066i	0.465983	+	0.641370i	0.975736	−	0.218951i	$-0.0702634\pi$
$797$	13.1552	+	18.1066i	0.465983	+	0.641370i	−0.509753	+	0.860321i	$0.670263\pi$
$798$	−6.49696	+	2.11099i	−0.229990	+	0.0747282i
$799$	19.6618			0.695585
$800$	3.00650	+	3.99512i	0.106296	+	0.141249i
$801$	16.3067			0.576169
$802$	10.9010	−	3.54195i	0.384928	−	0.125071i
$803$	9.48320	+	13.0525i	0.334655	+	0.460613i
$804$	8.47931	−	6.16058i	0.299042	−	0.217267i
$805$	10.6216	+	14.3639i	0.374361	+	0.506261i
$806$	−2.94180	−	2.13734i	−0.103621	−	0.0752847i
$807$		−	13.1056i		−	0.461338i
$808$	0.0558684	−	0.0768963i	0.00196544	−	0.00270520i
$809$	−7.10559	+	21.8687i	−0.249819	+	0.768864i	0.744987	+	0.667079i	$0.232456\pi$
$809$	−7.10559	+	21.8687i	−0.249819	+	0.768864i	−0.994806	+	0.101786i	$0.967544\pi$
$810$	72.7387	−	0.611309i	2.55578	−	0.0214792i
$811$	−5.74765	−	17.6894i	−0.201827	−	0.621160i	−0.999829	−	0.0185048i	$-0.994109\pi$
$811$	−5.74765	−	17.6894i	−0.201827	−	0.621160i	0.798002	−	0.602655i	$-0.205891\pi$
$812$	−8.65584	−	2.81245i	−0.303760	−	0.0986977i
$813$	−2.10999	−	0.685578i	−0.0740007	−	0.0240443i
$814$	−2.51526	−	7.74117i	−0.0881597	−	0.271328i
$815$	−11.6529	+	0.0979330i	−0.408183	+	0.00343044i
$816$	3.07449	−	9.46232i	0.107629	−	0.331247i
$817$	−15.2256	+	20.9562i	−0.532676	+	0.733166i
$818$			3.93410i			0.137553i
$819$	5.60955	+	4.07558i	0.196014	+	0.142412i
$820$	8.26943	+	11.1830i	0.288781	+	0.390529i
$821$	32.2259	−	23.4135i	1.12469	−	0.817137i	0.139778	−	0.990183i	$-0.455361\pi$
$821$	32.2259	−	23.4135i	1.12469	−	0.817137i	0.984914	+	0.173046i	$0.0553610\pi$
$822$	−16.0584	−	22.1024i	−0.560099	−	0.770911i
$823$	−18.5400	+	6.02401i	−0.646264	+	0.209984i	−0.613766	−	0.789488i	$-0.710346\pi$
$823$	−18.5400	+	6.02401i	−0.646264	+	0.209984i	−0.0324976	+	0.999472i	$0.510346\pi$
$824$	−8.97425			−0.312633
$825$	−0.482446	−	28.7007i	−0.0167966	−	0.999229i
$826$	−12.7315			−0.442984
$827$	42.5130	−	13.8133i	1.47832	−	0.480336i	0.544712	−	0.838623i	$-0.316639\pi$
$827$	42.5130	−	13.8133i	1.47832	−	0.480336i	0.933611	+	0.358287i	$0.116639\pi$
$828$	38.1157	+	52.4618i	1.32461	+	1.82317i
$829$	−7.18205	+	5.21807i	−0.249443	+	0.181231i	−0.705480	−	0.708730i	$-0.749268\pi$
$829$	−7.18205	+	5.21807i	−0.249443	+	0.181231i	0.456037	+	0.889961i	$0.349268\pi$
$830$	0.0271909	+	3.23541i	0.000943812	+	0.112303i
$831$	−48.2779	−	35.0759i	−1.67474	−	1.21677i
$832$			0.854261i			0.0296162i
$833$	−1.75397	+	2.41413i	−0.0607714	+	0.0836447i
$834$	−15.2959	+	47.0759i	−0.529653	+	1.63010i
$835$	−3.82882	+	12.1298i	−0.132502	+	0.419769i
$836$	1.09017	+	3.35519i	0.0377042	+	0.116042i
$837$	69.0638	+	22.4402i	2.38720	+	0.775647i
$838$	17.9763	+	5.84085i	0.620980	+	0.201769i
$839$	−3.62077	−	11.1436i	−0.125003	−	0.384719i	0.868899	−	0.494990i	$-0.164828\pi$
$839$	−3.62077	−	11.1436i	−0.125003	−	0.384719i	−0.993902	+	0.110271i	$0.964828\pi$
$840$	−2.36336	−	7.07093i	−0.0815438	−	0.243970i
$841$	16.6354	−	51.1986i	0.573636	−	1.76547i
$842$	−18.1687	+	25.0071i	−0.626134	+	0.861800i
$843$		−	28.2460i		−	0.972843i
$844$	4.00285	+	2.90824i	0.137784	+	0.100106i
$845$	−26.1646	−	8.25893i	−0.900088	−	0.284116i
$846$	43.2671	−	31.4354i	1.48755	−	1.08077i
$847$	4.72299	+	6.50064i	0.162284	+	0.223365i
$848$	5.34999	−	1.73832i	0.183719	−	0.0596941i
$849$	12.0185			0.412475
$850$	4.84842	+	14.1104i	0.166299	+	0.483983i
$851$	−37.7668			−1.29463
$852$	23.2027	−	7.53902i	0.794912	−	0.258283i
$853$	−28.9619	−	39.8626i	−0.991636	−	1.36487i	−0.930319	−	0.366752i	$-0.880470\pi$
$853$	−28.9619	−	39.8626i	−0.991636	−	1.36487i	−0.0613171	−	0.998118i	$-0.519530\pi$
$854$	2.21993	−	1.61287i	0.0759645	−	0.0551914i
$855$	21.6038	−	30.2668i	0.738836	−	1.03510i
$856$	0.999277	+	0.726018i	0.0341546	+	0.0248148i
$857$			15.3667i			0.524915i	0.964944	+	0.262457i	$0.0845329\pi$
$857$			15.3667i			0.524915i	−0.964944	+	0.262457i	$0.915467\pi$
$858$	2.88266	−	3.96763i	0.0984122	−	0.135453i
$859$	−0.713964	+	2.19736i	−0.0243602	+	0.0749728i	−0.962498	−	0.271290i	$-0.912550\pi$
$859$	−0.713964	+	2.19736i	−0.0243602	+	0.0749728i	0.938137	+	0.346263i	$0.112550\pi$
$860$	−23.0097	−	16.4239i	−0.784625	−	0.560049i
$861$	−6.40860	−	19.7236i	−0.218405	−	0.672180i
$862$	−4.99982	−	1.62454i	−0.170294	−	0.0553320i
$863$	30.7956	+	10.0061i	1.04829	+	0.340611i	0.781999	−	0.623280i	$-0.214200\pi$
$863$	30.7956	+	10.0061i	1.04829	+	0.340611i	0.266295	+	0.963891i	$0.414200\pi$
$864$	−5.27183	−	16.2250i	−0.179351	−	0.551987i
$865$	35.1336	−	25.9800i	1.19458	−	0.883346i
$866$	5.02859	−	15.4764i	0.170879	−	0.525910i
$867$	−15.8655	+	21.8370i	−0.538821	+	0.741624i
$868$		−	4.25662i		−	0.144479i
$869$	2.26268	+	1.64393i	0.0767562	+	0.0557666i
$870$	64.3546	−	21.5097i	2.18182	−	0.729245i
$871$	−2.17252	+	1.57843i	−0.0736129	+	0.0534829i
$872$	−4.46466	−	6.14508i	−0.151192	−	0.208099i
$873$	47.3215	−	15.3757i	1.60159	−	0.520388i
$874$	16.3689			0.553688
$875$	9.20788	+	6.34153i	0.311283	+	0.214383i
$876$	−31.2413			−1.05555
$877$	−40.0677	+	13.0188i	−1.35299	+	0.439613i	−0.893697	−	0.448671i	$-0.851897\pi$
$877$	−40.0677	+	13.0188i	−1.35299	+	0.439613i	−0.459294	+	0.888284i	$0.651897\pi$
$878$	−16.4509	−	22.6427i	−0.555192	−	0.764156i
$879$	−56.8558	+	41.3082i	−1.91770	+	1.39329i
$880$	−3.65160	+	1.22050i	−0.123096	+	0.0411430i
$881$	35.9273	+	26.1027i	1.21042	+	0.879423i	0.995269	−	0.0971572i	$-0.0309749\pi$
$881$	35.9273	+	26.1027i	1.21042	+	0.879423i	0.215153	+	0.976580i	$0.430975\pi$
$882$			8.11671i			0.273304i
$883$	2.28617	−	3.14665i	0.0769359	−	0.105893i	−0.768815	−	0.639472i	$-0.779153\pi$
$883$	2.28617	−	3.14665i	0.0769359	−	0.105893i	0.845751	+	0.533579i	$0.179153\pi$
$884$	−0.787728	+	2.42438i	−0.0264941	+	0.0815406i
$885$	76.3192	−	56.4352i	2.56544	−	1.89705i
$886$	8.05359	+	24.7864i	0.270566	+	0.832716i
$887$	−13.9971	−	4.54792i	−0.469975	−	0.152704i	0.0644484	−	0.997921i	$-0.479471\pi$
$887$	−13.9971	−	4.54792i	−0.469975	−	0.152704i	−0.534423	+	0.845217i	$0.679471\pi$
$888$	14.9899	+	4.87052i	0.503029	+	0.163444i
$889$	0.992403	+	3.05430i	0.0332841	+	0.102438i
$890$	3.65643	+	2.60989i	0.122564	+	0.0874836i
$891$	−17.3091	+	53.2718i	−0.579875	+	1.78467i
$892$	2.79398	−	3.84558i	0.0935493	−	0.128760i
$893$		−	13.5001i		−	0.451762i
$894$	29.7296	+	21.5998i	0.994305	+	0.722405i
$895$	−22.2754	+	31.2076i	−0.744583	+	1.04316i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−13.3753	−	18.4095i	−0.446587	−	0.614675i
$898$	12.6967	−	4.12542i	0.423695	−	0.137667i
$899$	38.7407			1.29208
$900$	33.2291	+	23.2992i	1.10764	+	0.776641i
$901$	16.7861			0.559226
$902$	−10.1858	+	3.30956i	−0.339149	+	0.110196i
$903$	24.7769	+	34.1025i	0.824524	+	1.13486i
$904$	−9.65624	+	7.01567i	−0.321162	+	0.233338i
$905$	−3.73243	−	1.17816i	−0.124070	−	0.0391632i
$906$	31.9749	+	23.2312i	1.06230	+	0.771803i
$907$			24.4326i			0.811271i	0.914035	+	0.405636i	$0.132950\pi$
$907$			24.4326i			0.811271i	−0.914035	+	0.405636i	$0.867050\pi$
$908$	7.94199	−	10.9312i	0.263564	−	0.362765i
$909$	0.238402	−	0.733727i	0.00790730	−	0.0243362i
$910$	0.605526	+	1.81167i	0.0200730	+	0.0600563i
$911$	−9.66733	−	29.7530i	−0.320293	−	0.985761i	−0.973521	−	0.228599i	$-0.926586\pi$
$911$	−9.66733	−	29.7530i	−0.320293	−	0.985761i	0.653228	−	0.757162i	$-0.273414\pi$
$912$	−6.49696	−	2.11099i	−0.215136	−	0.0699018i
$913$	−2.36952	−	0.769904i	−0.0784197	−	0.0254801i
$914$	6.43359	+	19.8006i	0.212804	+	0.654944i
$915$	−6.15802	+	19.5088i	−0.203578	+	0.644941i
$916$	−5.65406	+	17.4014i	−0.186815	+	0.574959i
$917$	−12.7691	+	17.5751i	−0.421672	+	0.580382i
$918$		−	50.9076i		−	1.68020i
$919$	32.3649	+	23.5145i	1.06762	+	0.775671i	0.975483	−	0.220076i	$-0.0706305\pi$
$919$	32.3649	+	23.5145i	1.06762	+	0.775671i	0.0921363	+	0.995746i	$0.470630\pi$
$920$	0.150131	+	17.8638i	0.00494967	+	0.588953i
$921$	−37.8457	+	27.4965i	−1.24706	+	0.906040i
$922$	−8.83019	−	12.1537i	−0.290807	−	0.400261i
$923$	−5.94485	+	1.93160i	−0.195677	+	0.0635794i
$924$	5.74095			0.188863
$925$	−22.3533	+	7.68072i	−0.734971	+	0.252541i
$926$	−2.90006			−0.0953018
$927$	−69.2763	+	22.5092i	−2.27533	+	0.739300i
$928$	−5.34960	−	7.36309i	−0.175609	−	0.241705i
$929$	−12.0524	+	8.75661i	−0.395428	+	0.287295i	−0.767676	−	0.640838i	$-0.778587\pi$
$929$	−12.0524	+	8.75661i	−0.395428	+	0.287295i	0.372248	+	0.928133i	$0.378587\pi$
$930$	18.8685	+	25.5165i	0.618721	+	0.836718i
$931$	1.65757	+	1.20430i	0.0543248	+	0.0394693i
$932$			24.7980i			0.812286i
$933$	−29.8057	+	41.0240i	−0.975794	+	1.34307i
$934$	−6.23974	+	19.2039i	−0.204170	+	0.628372i
$935$	−11.4886	+	0.0965525i	−0.375718	+	0.00315760i
$936$	2.14266	+	6.59443i	0.0700350	+	0.215546i
$937$	35.1091	+	11.4076i	1.14696	+	0.372671i	0.819999	−	0.572365i	$-0.193974\pi$
$937$	35.1091	+	11.4076i	1.14696	+	0.372671i	0.326965	+	0.945036i	$0.393974\pi$
$938$	−2.98966	−	0.971398i	−0.0976157	−	0.0317173i
$939$	28.7397	+	88.4517i	0.937885	+	2.88651i
$940$	14.7330	−	0.123818i	0.480536	−	0.00403851i
$941$	−10.1691	+	31.2972i	−0.331502	+	1.02026i	0.636917	+	0.770932i	$0.280209\pi$
$941$	−10.1691	+	31.2972i	−0.331502	+	1.02026i	−0.968419	+	0.249327i	$0.919791\pi$
$942$	14.3509	−	19.7523i	0.467577	−	0.643565i
$943$			49.6933i			1.61824i
$944$	−10.3000	−	7.48337i	−0.335236	−	0.243563i
$945$	−22.6810	−	30.6723i	−0.737813	−	0.997771i
$946$	17.6114	−	12.7954i	0.572595	−	0.416014i
$947$	−32.6371	−	44.9212i	−1.06056	−	1.45974i	−0.879277	−	0.476311i	$-0.841974\pi$
$947$	−32.6371	−	44.9212i	−1.06056	−	1.45974i	−0.181287	−	0.983430i	$-0.558026\pi$
$948$	−5.15068	+	1.67356i	−0.167286	+	0.0543547i
$949$	8.00445			0.259836
$950$	9.68840	−	3.32899i	0.314333	−	0.108007i
$951$	−32.9377			−1.06808
$952$	−2.83798	+	0.922116i	−0.0919795	+	0.0298859i
$953$	−11.3687	−	15.6476i	−0.368267	−	0.506876i	0.584162	−	0.811637i	$-0.301423\pi$
$953$	−11.3687	−	15.6476i	−0.368267	−	0.506876i	−0.952429	+	0.304761i	$0.901423\pi$
$954$	36.9390	−	26.8377i	1.19594	−	0.868903i
$955$	0.442363	+	52.6360i	0.0143145	+	1.70326i
$956$	−22.5195	−	16.3614i	−0.728334	−	0.529166i
$957$			52.2500i			1.68900i
$958$	−9.92676	+	13.6630i	−0.320719	+	0.441432i
$959$	−2.53207	+	7.79292i	−0.0817649	+	0.251647i
$960$	2.24419	−	7.10965i	0.0724308	−	0.229463i
$961$	−3.98050	−	12.2507i	−0.128403	−	0.395184i
$962$	−3.84062	−	1.24789i	−0.123827	−	0.0402337i
$963$	9.53487	+	3.09807i	0.307257	+	0.0998339i
$964$	2.33129	+	7.17498i	0.0750859	+	0.231091i
$965$	−3.99354	−	11.9483i	−0.128557	−	0.384628i
$966$	8.23144	−	25.3338i	0.264842	−	0.815101i
$967$	−9.64462	+	13.2747i	−0.310150	+	0.426885i	−0.935428	−	0.353517i	$-0.884986\pi$
$967$	−9.64462	+	13.2747i	−0.310150	+	0.426885i	0.625278	+	0.780402i	$0.284986\pi$
$968$			8.03523i			0.258262i
$969$	−16.4917	−	11.9819i	−0.529789	−	0.384914i
$970$	13.0717	+	4.12613i	0.419707	+	0.132482i
$971$	−7.41136	+	5.38467i	−0.237842	+	0.172802i	−0.700321	−	0.713828i	$-0.746960\pi$
$971$	−7.41136	+	5.38467i	−0.237842	+	0.172802i	0.462479	+	0.886630i	$0.346960\pi$
$972$	−33.6705	−	46.3434i	−1.07998	−	1.48647i
$973$	14.1192	−	4.58761i	0.452641	−	0.147072i
$974$	10.9675			0.351423
$975$	−11.6605	−	8.17598i	−0.373435	−	0.261841i
$976$	2.74399			0.0878329
$977$	40.8630	−	13.2772i	1.30732	−	0.424775i	0.429199	−	0.903210i	$-0.358796\pi$
$977$	40.8630	−	13.2772i	1.30732	−	0.424775i	0.878123	+	0.478435i	$0.158796\pi$
$978$	10.2134	+	14.0576i	0.326589	+	0.449511i
$979$	−2.79859	+	2.03329i	−0.0894433	+	0.0649843i
$980$	−1.29908	+	1.82000i	−0.0414975	+	0.0581377i
$981$	−49.8778	−	36.2384i	−1.59248	−	1.15700i
$982$			5.35912i			0.171016i
$983$	−16.6457	+	22.9108i	−0.530915	+	0.730741i	−0.987269	−	0.159057i	$-0.949155\pi$
$983$	−16.6457	+	22.9108i	−0.530915	+	0.730741i	0.456355	+	0.889798i	$0.349155\pi$
$984$	6.40860	−	19.7236i	0.204299	−	0.628767i
$985$	−36.5691	−	26.1023i	−1.16519	−	0.831689i
$986$	−8.39244	−	25.8293i	−0.267270	−	0.822572i
$987$	−20.8937	−	6.78877i	−0.665053	−	0.216089i
$988$	1.66461	+	0.540864i	0.0529583	+	0.0172072i
$989$	−31.2124	−	96.0620i	−0.992498	−	3.05459i
$990$	−25.1271	+	18.5806i	−0.798592	+	0.590529i
$991$	15.6470	−	48.1567i	0.497045	−	1.52975i	−0.316701	−	0.948525i	$-0.602575\pi$
$991$	15.6470	−	48.1567i	0.497045	−	1.52975i	0.813746	−	0.581221i	$-0.197425\pi$
$992$	2.50198	−	3.44368i	0.0794379	−	0.109337i
$993$			48.8109i			1.54897i
$994$	−5.91973	−	4.30094i	−0.187762	−	0.136417i
$995$	−26.8756	+	8.98282i	−0.852015	+	0.284774i
$996$	3.90306	−	2.83574i	0.123673	−	0.0898538i
$997$	−10.6109	−	14.6046i	−0.336050	−	0.462534i	0.607232	−	0.794524i	$-0.292280\pi$
$997$	−10.6109	−	14.6046i	−0.336050	−	0.462534i	−0.943283	+	0.331991i	$0.892280\pi$
$998$	−13.2441	+	4.30326i	−0.419234	+	0.136217i
$999$	80.6462			2.55153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.169.5	yes	40
25.2	odd	20		8750.2.a.be.1.1		20
25.4	even	10	inner	350.2.m.b.29.5	✓	40
25.23	odd	20		8750.2.a.bf.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.5	✓	40	25.4	even	10	inner
350.2.m.b.169.5	yes	40	1.1	even	1	trivial
8750.2.a.be.1.1		20	25.2	odd	20
8750.2.a.bf.1.20		20	25.23	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.95978 + 2.69740i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.12074 - 0.708831i) q^{5} +(-2.69740 - 1.95978i) q^{6} +1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.50820 + 7.71945i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.95978 + 2.69740i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.12074 - 0.708831i) q^{5} +(-2.69740 - 1.95978i) q^{6} +1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.50820 + 7.71945i) q^{9} +(-1.79791 + 1.32948i) q^{10} +(-0.532081 - 1.63758i) q^{11} +(3.17099 + 1.03032i) q^{12} +(-0.812450 - 0.263981i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(6.06819 + 4.33135i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.75397 - 2.41413i) q^{17} -8.11671i q^{18} +(-1.65757 - 1.20430i) q^{19} +(1.29908 - 1.82000i) q^{20} +(-2.69740 + 1.95978i) q^{21} +(1.01208 + 1.39301i) q^{22} +(7.59821 - 2.46881i) q^{23} -3.33417 q^{24} +(3.99512 - 3.00650i) q^{25} +0.854261 q^{26} +(-16.2250 + 5.27183i) q^{27} +(0.587785 + 0.809017i) q^{28} +(-7.36309 + 5.34960i) q^{29} +(-7.10965 - 2.24419i) q^{30} +(-3.44368 - 2.50198i) q^{31} +1.00000i q^{32} +(3.37444 - 4.64452i) q^{33} +(-0.922116 + 2.83798i) q^{34} +(0.708831 + 2.12074i) q^{35} +(2.50820 + 7.71945i) q^{36} +(-4.49584 - 1.46079i) q^{37} +(1.94860 + 0.633137i) q^{38} +(-0.880159 - 2.70885i) q^{39} +(-0.673087 + 2.13236i) q^{40} +(-1.92210 + 5.91560i) q^{41} +(1.95978 - 2.69740i) q^{42} -12.6427i q^{43} +(-1.39301 - 1.01208i) q^{44} +(0.152527 + 18.1489i) q^{45} +(-6.46343 + 4.69596i) q^{46} +(3.87292 + 5.33062i) q^{47} +(3.17099 - 1.03032i) q^{48} -1.00000 q^{49} +(-2.87052 + 4.09391i) q^{50} +9.94927 q^{51} +(-0.812450 + 0.263981i) q^{52} +(3.30648 + 4.55097i) q^{53} +(13.8018 - 10.0276i) q^{54} +(-2.28917 - 3.09573i) q^{55} +(-0.809017 - 0.587785i) q^{56} -6.83131i q^{57} +(5.34960 - 7.36309i) q^{58} +(3.93424 - 12.1083i) q^{59} +(7.45518 - 0.0626547i) q^{60} +(0.847938 + 2.60969i) q^{61} +(4.04829 + 1.31537i) q^{62} +(-7.71945 - 2.50820i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.91012 + 0.0160530i) q^{65} +(-1.77405 + 5.45996i) q^{66} +(1.84771 - 2.54315i) q^{67} -2.98403i q^{68} +(21.5502 + 15.6571i) q^{69} +(-1.32948 - 1.79791i) q^{70} +(5.91973 - 4.30094i) q^{71} +(-4.77088 - 6.56656i) q^{72} +(-8.91143 + 2.89550i) q^{73} +4.72721 q^{74} +(15.9393 + 4.88438i) q^{75} -2.04888 q^{76} +(1.63758 - 0.532081i) q^{77} +(1.67416 + 2.30429i) q^{78} +(-1.31410 + 0.954749i) q^{79} +(-0.0187917 - 2.23599i) q^{80} +(-26.3180 - 19.1212i) q^{81} -6.22003i q^{82} +(0.850507 - 1.17062i) q^{83} +(-1.03032 + 3.17099i) q^{84} +(2.00851 - 6.36302i) q^{85} +(3.90681 + 12.0239i) q^{86} +(-28.8601 - 9.37720i) q^{87} +(1.63758 + 0.532081i) q^{88} +(-0.620824 - 1.91070i) q^{89} +(-5.75337 - 17.2135i) q^{90} +(0.263981 - 0.812450i) q^{91} +(4.69596 - 6.46343i) q^{92} -14.1923i q^{93} +(-5.33062 - 3.87292i) q^{94} +(-4.36894 - 1.37907i) q^{95} +(-2.69740 + 1.95978i) q^{96} +(-3.60322 - 4.95940i) q^{97} +(0.951057 - 0.309017i) q^{98} +13.9758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

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