LMFDB - Embedded newform 350.2.m.b.169.6

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			169.6
Character	$\chi$	$=$	350.169
Dual form			350.2.m.b.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-1.58093 - 2.17596i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.479579 - 2.18403i) q^{5} +(-2.17596 - 1.58093i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.30843 + 4.02693i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.58093 - 2.17596i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.479579 - 2.18403i) q^{5} +(-2.17596 - 1.58093i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.30843 + 4.02693i) q^{9} +(-0.218797 - 2.22534i) q^{10} +(0.920434 + 2.83281i) q^{11} +(-2.55800 - 0.831144i) q^{12} +(-3.71772 - 1.20796i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-5.51056 + 2.40926i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.04614 - 2.81627i) q^{17} +4.23416i q^{18} +(4.04349 + 2.93777i) q^{19} +(-0.895756 - 2.04881i) q^{20} +(-2.17596 + 1.58093i) q^{21} +(1.75077 + 2.40973i) q^{22} +(-5.97630 + 1.94182i) q^{23} -2.68964 q^{24} +(-4.54001 - 2.09483i) q^{25} -3.90904 q^{26} +(3.15699 - 1.02577i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(5.40499 - 3.92696i) q^{29} +(-4.49635 + 3.99420i) q^{30} +(-1.39255 - 1.01175i) q^{31} -1.00000i q^{32} +(4.70894 - 6.48130i) q^{33} +(1.07572 - 3.31072i) q^{34} +(-2.18403 - 0.479579i) q^{35} +(1.30843 + 4.02693i) q^{36} +(8.43813 + 2.74171i) q^{37} +(4.75341 + 1.54448i) q^{38} +(3.24898 + 9.99933i) q^{39} +(-1.48503 - 1.67173i) q^{40} +(3.32178 - 10.2234i) q^{41} +(-1.58093 + 2.17596i) q^{42} -9.22078i q^{43} +(2.40973 + 1.75077i) q^{44} +(8.16745 + 4.78888i) q^{45} +(-5.08375 + 3.69356i) q^{46} +(4.13527 + 5.69172i) q^{47} +(-2.55800 + 0.831144i) q^{48} -1.00000 q^{49} +(-4.96514 - 0.589364i) q^{50} -9.36289 q^{51} +(-3.71772 + 1.20796i) q^{52} +(4.70581 + 6.47699i) q^{53} +(2.68549 - 1.95113i) q^{54} +(6.62836 - 0.651707i) q^{55} +(-0.809017 - 0.587785i) q^{56} -13.4429i q^{57} +(3.92696 - 5.40499i) q^{58} +(-3.12245 + 9.60993i) q^{59} +(-3.04201 + 5.18816i) q^{60} +(0.513705 + 1.58102i) q^{61} +(-1.63704 - 0.531906i) q^{62} +(4.02693 + 1.30843i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.42117 + 7.54031i) q^{65} +(2.47564 - 7.61923i) q^{66} +(5.51246 - 7.58725i) q^{67} -3.48110i q^{68} +(13.6735 + 9.93434i) q^{69} +(-2.22534 + 0.218797i) q^{70} +(-4.51235 + 3.27841i) q^{71} +(2.48878 + 3.42551i) q^{72} +(7.11902 - 2.31311i) q^{73} +8.87238 q^{74} +(2.61916 + 13.1907i) q^{75} +4.99803 q^{76} +(2.83281 - 0.920434i) q^{77} +(6.17992 + 8.50594i) q^{78} +(2.25804 - 1.64056i) q^{79} +(-1.92894 - 1.13101i) q^{80} +(3.05352 + 2.21851i) q^{81} -10.7495i q^{82} +(1.92269 - 2.64635i) q^{83} +(-0.831144 + 2.55800i) q^{84} +(-5.16954 - 5.81945i) q^{85} +(-2.84938 - 8.76948i) q^{86} +(-17.0898 - 5.55283i) q^{87} +(2.83281 + 0.920434i) q^{88} +(-0.829521 - 2.55300i) q^{89} +(9.24755 + 2.03061i) q^{90} +(-1.20796 + 3.71772i) q^{91} +(-3.69356 + 5.08375i) q^{92} +4.62963i q^{93} +(5.69172 + 4.13527i) q^{94} +(8.35536 - 7.42224i) q^{95} +(-2.17596 + 1.58093i) q^{96} +(-5.86421 - 8.07139i) q^{97} +(-0.951057 + 0.309017i) q^{98} -12.6118 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
$3$	−1.58093	−	2.17596i	−0.912751	−	1.25629i	−0.966219	−	0.257724i	$-0.917027\pi$
$3$	−1.58093	−	2.17596i	−0.912751	−	1.25629i	0.0534678	−	0.998570i	$-0.482973\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.479579	−	2.18403i	0.214474	−	0.976730i
$5$	0.479579	−	2.18403i	0.214474	−	0.976730i
$6$	−2.17596	−	1.58093i	−0.888334	−	0.645412i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.30843	+	4.02693i	−0.436143	+	1.34231i
$10$	−0.218797	−	2.22534i	−0.0691898	−	0.703714i
$11$	0.920434	+	2.83281i	0.277521	+	0.854123i	0.988541	+	0.150951i	$0.0482336\pi$
$11$	0.920434	+	2.83281i	0.277521	+	0.854123i	−0.711020	+	0.703172i	$0.751766\pi$
$12$	−2.55800	−	0.831144i	−0.738431	−	0.239931i
$13$	−3.71772	−	1.20796i	−1.03111	−	0.335028i	−0.255881	−	0.966708i	$-0.582366\pi$
$13$	−3.71772	−	1.20796i	−1.03111	−	0.335028i	−0.775229	+	0.631680i	$0.782366\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−5.51056	+	2.40926i	−1.42282	+	0.622068i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.04614	−	2.81627i	0.496261	−	0.683045i	−0.485266	−	0.874366i	$-0.661277\pi$
$17$	2.04614	−	2.81627i	0.496261	−	0.683045i	0.981527	+	0.191322i	$0.0612773\pi$
$18$			4.23416i			0.998002i
$19$	4.04349	+	2.93777i	0.927641	+	0.673971i	0.945414	−	0.325871i	$-0.105658\pi$
$19$	4.04349	+	2.93777i	0.927641	+	0.673971i	−0.0177731	+	0.999842i	$0.505658\pi$
$20$	−0.895756	−	2.04881i	−0.200297	−	0.458128i
$21$	−2.17596	+	1.58093i	−0.474834	+	0.344987i
$22$	1.75077	+	2.40973i	0.373265	+	0.513756i
$23$	−5.97630	+	1.94182i	−1.24615	+	0.404897i	−0.856538	−	0.516084i	$-0.827389\pi$
$23$	−5.97630	+	1.94182i	−1.24615	+	0.404897i	−0.389608	+	0.920981i	$0.627389\pi$
$24$	−2.68964			−0.549020
$25$	−4.54001	−	2.09483i	−0.908002	−	0.418966i
$26$	−3.90904			−0.766626
$27$	3.15699	−	1.02577i	0.607562	−	0.197409i
$28$	−0.587785	−	0.809017i	−0.111081	−	0.152890i
$29$	5.40499	−	3.92696i	1.00368	−	0.729218i	0.0408076	−	0.999167i	$-0.487007\pi$
$29$	5.40499	−	3.92696i	1.00368	−	0.729218i	0.962875	+	0.269949i	$0.0870069\pi$
$30$	−4.49635	+	3.99420i	−0.820918	+	0.729238i
$31$	−1.39255	−	1.01175i	−0.250109	−	0.181715i	0.455666	−	0.890151i	$-0.349401\pi$
$31$	−1.39255	−	1.01175i	−0.250109	−	0.181715i	−0.705775	+	0.708436i	$0.749401\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.70894	−	6.48130i	0.819721	−	1.12825i
$34$	1.07572	−	3.31072i	0.184484	−	0.567784i
$35$	−2.18403	−	0.479579i	−0.369169	−	0.0810636i
$36$	1.30843	+	4.02693i	0.218071	+	0.671155i
$37$	8.43813	+	2.74171i	1.38722	+	0.450735i	0.905036	−	0.425335i	$-0.139844\pi$
$37$	8.43813	+	2.74171i	1.38722	+	0.450735i	0.482184	+	0.876070i	$0.339844\pi$
$38$	4.75341	+	1.54448i	0.771105	+	0.250547i
$39$	3.24898	+	9.99933i	0.520253	+	1.60117i
$40$	−1.48503	−	1.67173i	−0.234804	−	0.264324i
$41$	3.32178	−	10.2234i	0.518775	−	1.59662i	−0.257533	−	0.966270i	$-0.582910\pi$
$41$	3.32178	−	10.2234i	0.518775	−	1.59662i	0.776308	−	0.630354i	$-0.217090\pi$
$42$	−1.58093	+	2.17596i	−0.243943	+	0.335759i
$43$		−	9.22078i		−	1.40616i	−0.711113	−	0.703078i	$-0.751808\pi$
$43$		−	9.22078i		−	1.40616i	0.711113	−	0.703078i	$-0.248192\pi$
$44$	2.40973	+	1.75077i	0.363280	+	0.263938i
$45$	8.16745	+	4.78888i	1.21753	+	0.713884i
$46$	−5.08375	+	3.69356i	−0.749558	+	0.544586i
$47$	4.13527	+	5.69172i	0.603192	+	0.830222i	0.995996	−	0.0894001i	$-0.0284950\pi$
$47$	4.13527	+	5.69172i	0.603192	+	0.830222i	−0.392804	+	0.919622i	$0.628495\pi$
$48$	−2.55800	+	0.831144i	−0.369215	+	0.119965i
$49$	−1.00000			−0.142857
$50$	−4.96514	−	0.589364i	−0.702177	−	0.0833486i
$51$	−9.36289			−1.31107
$52$	−3.71772	+	1.20796i	−0.515555	+	0.167514i
$53$	4.70581	+	6.47699i	0.646393	+	0.889683i	0.998936	−	0.0461123i	$-0.0146832\pi$
$53$	4.70581	+	6.47699i	0.646393	+	0.889683i	−0.352544	+	0.935795i	$0.614683\pi$
$54$	2.68549	−	1.95113i	0.365449	−	0.265515i
$55$	6.62836	−	0.651707i	0.893768	−	0.0878761i
$56$	−0.809017	−	0.587785i	−0.108109	−	0.0785461i
$57$		−	13.4429i		−	1.78056i
$58$	3.92696	−	5.40499i	0.515635	−	0.709710i
$59$	−3.12245	+	9.60993i	−0.406509	+	1.25111i	0.513120	+	0.858317i	$0.328490\pi$
$59$	−3.12245	+	9.60993i	−0.406509	+	1.25111i	−0.919629	+	0.392789i	$0.871510\pi$
$60$	−3.04201	+	5.18816i	−0.392722	+	0.669788i
$61$	0.513705	+	1.58102i	0.0657732	+	0.202429i	0.978542	−	0.206047i	$-0.0660601\pi$
$61$	0.513705	+	1.58102i	0.0657732	+	0.202429i	−0.912769	+	0.408477i	$0.866060\pi$
$62$	−1.63704	−	0.531906i	−0.207904	−	0.0675521i
$63$	4.02693	+	1.30843i	0.507345	+	0.164846i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−4.42117	+	7.54031i	−0.548378	+	0.935261i
$66$	2.47564	−	7.61923i	0.304730	−	0.937862i
$67$	5.51246	−	7.58725i	0.673454	−	0.926931i	−0.326378	−	0.945239i	$-0.605828\pi$
$67$	5.51246	−	7.58725i	0.673454	−	0.926931i	0.999832	+	0.0183088i	$0.00582821\pi$
$68$		−	3.48110i		−	0.422145i
$69$	13.6735	+	9.93434i	1.64609	+	1.19595i
$70$	−2.22534	+	0.218797i	−0.265979	+	0.0261513i
$71$	−4.51235	+	3.27841i	−0.535517	+	0.389076i	−0.822417	−	0.568884i	$-0.807375\pi$
$71$	−4.51235	+	3.27841i	−0.535517	+	0.389076i	0.286900	+	0.957960i	$0.407375\pi$
$72$	2.48878	+	3.42551i	0.293305	+	0.403700i
$73$	7.11902	−	2.31311i	0.833218	−	0.270729i	0.138818	−	0.990318i	$-0.455670\pi$
$73$	7.11902	−	2.31311i	0.833218	−	0.270729i	0.694400	+	0.719589i	$0.255670\pi$
$74$	8.87238			1.03139
$75$	2.61916	+	13.1907i	0.302434	+	1.52313i
$76$	4.99803			0.573314
$77$	2.83281	−	0.920434i	0.322828	−	0.104893i
$78$	6.17992	+	8.50594i	0.699739	+	0.963108i
$79$	2.25804	−	1.64056i	0.254050	−	0.184578i	−0.453470	−	0.891271i	$-0.649814\pi$
$79$	2.25804	−	1.64056i	0.254050	−	0.184578i	0.707520	+	0.706694i	$0.249814\pi$
$80$	−1.92894	−	1.13101i	−0.215662	−	0.126451i
$81$	3.05352	+	2.21851i	0.339280	+	0.246501i
$82$		−	10.7495i		−	1.18708i
$83$	1.92269	−	2.64635i	0.211042	−	0.290475i	−0.690352	−	0.723473i	$-0.742545\pi$
$83$	1.92269	−	2.64635i	0.211042	−	0.290475i	0.901395	+	0.432999i	$0.142545\pi$
$84$	−0.831144	+	2.55800i	−0.0906853	+	0.279101i
$85$	−5.16954	−	5.81945i	−0.560715	−	0.631208i
$86$	−2.84938	−	8.76948i	−0.307256	−	0.945638i
$87$	−17.0898	−	5.55283i	−1.83222	−	0.595325i
$88$	2.83281	+	0.920434i	0.301978	+	0.0981186i
$89$	−0.829521	−	2.55300i	−0.0879290	−	0.270618i	0.897417	−	0.441182i	$-0.145441\pi$
$89$	−0.829521	−	2.55300i	−0.0879290	−	0.270618i	−0.985346	+	0.170565i	$0.945441\pi$
$90$	9.24755	+	2.03061i	0.974778	+	0.214045i
$91$	−1.20796	+	3.71772i	−0.126629	+	0.389723i
$92$	−3.69356	+	5.08375i	−0.385080	+	0.530017i
$93$			4.62963i			0.480071i
$94$	5.69172	+	4.13527i	0.587056	+	0.426521i
$95$	8.35536	−	7.42224i	0.857242	−	0.761505i
$96$	−2.17596	+	1.58093i	−0.222083	+	0.161353i
$97$	−5.86421	−	8.07139i	−0.595420	−	0.819526i	0.399859	−	0.916577i	$-0.369059\pi$
$97$	−5.86421	−	8.07139i	−0.595420	−	0.819526i	−0.995279	+	0.0970507i	$0.969059\pi$
$98$	−0.951057	+	0.309017i	−0.0960712	+	0.0312154i
$99$	−12.6118			−1.26754
$100$	−4.90426	+	0.973796i	−0.490426	+	0.0973796i
$101$	−5.94728			−0.591776			−0.295888	−	0.955223i	$-0.595616\pi$
$101$	−5.94728			−0.591776			−0.295888	+	0.955223i	$0.595616\pi$
$102$	−8.90464	+	2.89329i	−0.881691	+	0.286479i
$103$	−4.03708	−	5.55656i	−0.397785	−	0.547504i	0.562401	−	0.826864i	$-0.309878\pi$
$103$	−4.03708	−	5.55656i	−0.397785	−	0.547504i	−0.960186	+	0.279360i	$0.909878\pi$
$104$	−3.16248	+	2.29768i	−0.310107	+	0.225306i
$105$	2.40926	+	5.51056i	0.235120	+	0.537776i
$106$	6.47699	+	4.70581i	0.629101	+	0.457069i
$107$			17.4179i			1.68385i	0.539595	+	0.841925i	$0.318577\pi$
$107$			17.4179i			1.68385i	−0.539595	+	0.841925i	$0.681423\pi$
$108$	1.95113	−	2.68549i	0.187747	−	0.258412i
$109$	−0.986913	+	3.03741i	−0.0945291	+	0.290931i	−0.987131	−	0.159916i	$-0.948878\pi$
$109$	−0.986913	+	3.03741i	−0.0945291	+	0.290931i	0.892602	+	0.450846i	$0.148878\pi$
$110$	6.10256	−	2.66809i	0.581856	−	0.254392i
$111$	−7.37423	−	22.6955i	−0.699930	−	2.15416i
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	9.09902	+	2.95645i	0.855963	+	0.278119i	0.703942	−	0.710258i	$-0.251422\pi$
$113$	9.09902	+	2.95645i	0.855963	+	0.278119i	0.152022	+	0.988377i	$0.451422\pi$
$114$	−4.15409	−	12.7850i	−0.389066	−	1.19742i
$115$	1.37489	+	13.9837i	0.128209	+	1.30399i
$116$	2.06452	−	6.35395i	0.191686	−	0.589950i
$117$	9.72874	−	13.3905i	0.899422	−	1.23795i
$118$			10.1045i			0.930192i
$119$	−2.81627	−	2.04614i	−0.258167	−	0.187569i
$120$	−1.28989	+	5.87426i	−0.117751	+	0.536245i
$121$	1.72160	−	1.25082i	0.156509	−	0.113711i
$122$	0.977126	+	1.34490i	0.0884648	+	0.121761i
$123$	−27.4972	+	8.93439i	−2.47934	+	0.805586i
$124$	−1.72128			−0.154576
$125$	−6.75247	+	8.91090i	−0.603960	+	0.797015i
$126$	4.23416			0.377209
$127$	0.757834	−	0.246235i	0.0672469	−	0.0218499i	−0.275200	−	0.961387i	$-0.588744\pi$
$127$	0.757834	−	0.246235i	0.0672469	−	0.0218499i	0.342447	+	0.939537i	$0.388744\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−20.0641	+	14.5774i	−1.76654	+	1.28347i
$130$	−1.87469	+	8.53748i	−0.164421	+	0.748787i
$131$	5.38537	+	3.91270i	0.470522	+	0.341854i	0.797645	−	0.603128i	$-0.206079\pi$
$131$	5.38537	+	3.91270i	0.470522	+	0.341854i	−0.327123	+	0.944982i	$0.606079\pi$
$132$		−	8.01133i		−	0.697297i
$133$	2.93777	−	4.04349i	0.254737	−	0.350615i
$134$	2.89807	−	8.91935i	0.250355	−	0.770515i
$135$	−0.726287	−	7.38690i	−0.0625088	−	0.635763i
$136$	−1.07572	−	3.31072i	−0.0922420	−	0.283892i
$137$	−21.5840	−	7.01305i	−1.84404	−	0.599166i	−0.997795	−	0.0663761i	$-0.978856\pi$
$137$	−21.5840	−	7.01305i	−1.84404	−	0.599166i	−0.846248	−	0.532790i	$-0.821144\pi$
$138$	16.0741	+	5.22279i	1.36832	+	0.444594i
$139$	0.856644	+	2.63648i	0.0726596	+	0.223623i	0.980791	−	0.195062i	$-0.0624909\pi$
$139$	0.856644	+	2.63648i	0.0726596	+	0.223623i	−0.908131	+	0.418686i	$0.862491\pi$
$140$	−2.04881	+	0.895756i	−0.173156	+	0.0757052i
$141$	5.84739	−	17.9964i	0.492439	−	1.51557i
$142$	−3.27841	+	4.51235i	−0.275118	+	0.378668i
$143$		−	11.6434i		−	0.973672i
$144$	3.42551	+	2.48878i	0.285459	+	0.207398i
$145$	−5.98449	−	13.6880i	−0.496985	−	1.13672i
$146$	6.05580	−	4.39980i	0.501182	−	0.364130i
$147$	1.58093	+	2.17596i	0.130393	+	0.179471i
$148$	8.43813	−	2.74171i	0.693610	−	0.225368i
$149$	−17.9721			−1.47233			−0.736165	−	0.676802i	$-0.763365\pi$
$149$	−17.9721			−1.47233			−0.736165	+	0.676802i	$0.763365\pi$
$150$	6.56711	+	11.7357i	0.536203	+	0.958217i
$151$	1.83769			0.149549			0.0747747	−	0.997200i	$-0.476176\pi$
$151$	1.83769			0.149549			0.0747747	+	0.997200i	$0.476176\pi$
$152$	4.75341	−	1.54448i	0.385553	−	0.125274i
$153$	8.66368	+	11.9245i	0.700417	+	0.964041i
$154$	2.40973	−	1.75077i	0.194181	−	0.141081i
$155$	−2.87752	+	2.55616i	−0.231128	+	0.205316i
$156$	8.50594	+	6.17992i	0.681020	+	0.494790i
$157$			21.5048i			1.71627i	0.513423	+	0.858136i	$0.328377\pi$
$157$			21.5048i			1.71627i	−0.513423	+	0.858136i	$0.671623\pi$
$158$	1.64056	−	2.25804i	0.130516	−	0.179640i
$159$	6.65414	−	20.4793i	0.527708	−	1.62412i
$160$	−2.18403	−	0.479579i	−0.172663	−	0.0379140i
$161$	1.94182	+	5.97630i	0.153037	+	0.470999i
$162$	3.58963	+	1.16634i	0.282028	+	0.0916363i
$163$	19.5827	+	6.36281i	1.53384	+	0.498374i	0.949668	−	0.313258i	$-0.101420\pi$
$163$	19.5827	+	6.36281i	1.53384	+	0.498374i	0.584169	+	0.811632i	$0.301420\pi$
$164$	−3.32178	−	10.2234i	−0.259387	−	0.798312i
$165$	−11.8971	−	13.3928i	−0.926186	−	1.04263i
$166$	1.01082	−	3.11097i	0.0784545	−	0.241458i
$167$	−8.34676	+	11.4883i	−0.645891	+	0.888993i	−0.998913	−	0.0466220i	$-0.985154\pi$
$167$	−8.34676	+	11.4883i	−0.645891	+	0.888993i	0.353021	+	0.935615i	$0.385154\pi$
$168$			2.68964i			0.207510i
$169$	1.84505	+	1.34051i	0.141927	+	0.103116i
$170$	−6.71483	−	3.93715i	−0.515004	−	0.301966i
$171$	−17.1208	+	12.4390i	−1.30926	+	0.951234i
$172$	−5.41984	−	7.45977i	−0.413259	−	0.568802i
$173$	−2.61664	+	0.850197i	−0.198939	+	0.0646393i	−0.406792	−	0.913521i	$-0.633353\pi$
$173$	−2.61664	+	0.850197i	−0.198939	+	0.0646393i	0.207853	+	0.978160i	$0.433353\pi$
$174$	−17.9693			−1.36225
$175$	−2.09483	+	4.54001i	−0.158354	+	0.343192i
$176$	2.97859			0.224519
$177$	25.8472	−	8.39828i	1.94280	−	0.631253i
$178$	−1.57784	−	2.17171i	−0.118264	−	0.162777i
$179$	15.3119	−	11.1247i	1.14446	−	0.831501i	0.156728	−	0.987642i	$-0.449905\pi$
$179$	15.3119	−	11.1247i	1.14446	−	0.831501i	0.987735	+	0.156141i	$0.0499053\pi$
$180$	9.42244	−	0.926423i	0.702307	−	0.0690515i
$181$	5.21015	+	3.78540i	0.387268	+	0.281366i	0.764335	−	0.644819i	$-0.223067\pi$
$181$	5.21015	+	3.78540i	0.387268	+	0.281366i	−0.377067	+	0.926186i	$0.623067\pi$
$182$			3.90904i			0.289757i
$183$	2.62812	−	3.61729i	0.194276	−	0.267398i
$184$	−1.94182	+	5.97630i	−0.143153	+	0.440579i
$185$	10.0347	−	17.1143i	0.737769	−	1.25827i
$186$	1.43064	+	4.40304i	0.104899	+	0.322847i
$187$	9.86127	+	3.20412i	0.721127	+	0.234308i
$188$	6.69101	+	2.17404i	0.487992	+	0.158558i
$189$	−1.02577	−	3.15699i	−0.0746136	−	0.229637i
$190$	5.65282	−	9.64091i	0.410099	−	0.699425i
$191$	−5.92838	+	18.2457i	−0.428962	+	1.32021i	0.470186	+	0.882567i	$0.344187\pi$
$191$	−5.92838	+	18.2457i	−0.428962	+	1.32021i	−0.899149	+	0.437643i	$0.855813\pi$
$192$	−1.58093	+	2.17596i	−0.114094	+	0.157037i
$193$		−	6.94363i		−	0.499813i	−0.968270	−	0.249907i	$-0.919600\pi$
$193$		−	6.94363i		−	0.499813i	0.968270	−	0.249907i	$-0.0803999\pi$
$194$	−8.07139	−	5.86421i	−0.579492	−	0.421026i
$195$	23.3970	−	2.30042i	1.67549	−	0.164736i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	11.2258	+	15.4510i	0.799807	+	1.10084i	0.992817	+	0.119643i	$0.0381749\pi$
$197$	11.2258	+	15.4510i	0.799807	+	1.10084i	−0.193010	+	0.981197i	$0.561825\pi$
$198$	−11.9946	+	3.89727i	−0.852416	+	0.276967i
$199$	12.4222			0.880588			0.440294	−	0.897854i	$-0.354874\pi$
$199$	12.4222			0.880588			0.440294	+	0.897854i	$0.354874\pi$
$200$	−4.36330	+	2.44163i	−0.308532	+	0.172650i
$201$	−25.2244			−1.77919
$202$	−5.65620	+	1.83781i	−0.397969	+	0.129308i
$203$	−3.92696	−	5.40499i	−0.275618	−	0.379356i
$204$	−7.57474	+	5.50337i	−0.530338	+	0.385313i
$205$	−20.7352	−	12.1578i	−1.44821	−	0.849137i
$206$	−5.55656	−	4.03708i	−0.387144	−	0.281276i
$207$		−	26.6069i		−	1.84931i
$208$	−2.29768	+	3.16248i	−0.159315	+	0.219279i
$209$	−4.60036	+	14.1585i	−0.318214	+	0.979361i
$210$	3.99420	+	4.49635i	0.275626	+	0.310278i
$211$	−1.22758	−	3.77811i	−0.0845102	−	0.260096i	0.899868	−	0.436162i	$-0.143663\pi$
$211$	−1.22758	−	3.77811i	−0.0845102	−	0.260096i	−0.984378	+	0.176067i	$0.943663\pi$
$212$	7.61416	+	2.47399i	0.522943	+	0.169914i
$213$	14.2674	+	4.63577i	0.977587	+	0.317637i
$214$	5.38242	+	16.5654i	0.367935	+	1.13239i
$215$	−20.1385	−	4.42209i	−1.37343	−	0.301584i
$216$	1.02577	−	3.15699i	0.0697946	−	0.214806i
$217$	−1.01175	+	1.39255i	−0.0686818	+	0.0945323i
$218$			3.19372i			0.216306i
$219$	−16.2879	−	11.8339i	−1.10064	−	0.799659i
$220$	4.97939	−	4.42330i	0.335711	−	0.298219i
$221$	−11.0089	+	7.99844i	−0.740539	+	0.538033i
$222$	−14.0266	−	19.3060i	−0.941404	−	1.29573i
$223$	−18.5068	+	6.01321i	−1.23930	+	0.402674i	−0.854077	−	0.520147i	$-0.825877\pi$
$223$	−18.5068	+	6.01321i	−1.23930	+	0.402674i	−0.385228	+	0.922822i	$0.625877\pi$
$224$	−1.00000			−0.0668153
$225$	14.3760	−	15.5414i	0.958401	−	1.03609i
$226$	9.56727			0.636405
$227$	−8.44684	+	2.74455i	−0.560637	+	0.182162i	−0.575608	−	0.817726i	$-0.695234\pi$
$227$	−8.44684	+	2.74455i	−0.560637	+	0.182162i	0.0149709	+	0.999888i	$0.495234\pi$
$228$	−7.90154	−	10.8755i	−0.523292	−	0.720250i
$229$	6.96575	−	5.06092i	0.460310	−	0.334435i	−0.333343	−	0.942806i	$-0.608177\pi$
$229$	6.96575	−	5.06092i	0.460310	−	0.334435i	0.793653	+	0.608371i	$0.208177\pi$
$230$	5.62880	+	12.8744i	0.371152	+	0.848915i
$231$	−6.48130	−	4.70894i	−0.426438	−	0.309826i
$232$		−	6.68094i		−	0.438625i
$233$	0.749393	−	1.03145i	0.0490944	−	0.0675726i	−0.783764	−	0.621059i	$-0.786703\pi$
$233$	0.749393	−	1.03145i	0.0490944	−	0.0675726i	0.832858	+	0.553486i	$0.186703\pi$
$234$	5.11470	−	15.7414i	0.334358	−	1.02905i
$235$	14.4141	−	6.30195i	0.940271	−	0.411094i
$236$	3.12245	+	9.60993i	0.203255	+	0.625553i
$237$	−7.13961	−	2.31980i	−0.463768	−	0.150687i
$238$	−3.31072	−	1.07572i	−0.214602	−	0.0697284i
$239$	1.01174	+	3.11381i	0.0654439	+	0.201416i	0.978431	−	0.206572i	$-0.0662307\pi$
$239$	1.01174	+	3.11381i	0.0654439	+	0.201416i	−0.912988	+	0.407987i	$0.866231\pi$
$240$	0.588486	+	5.98536i	0.0379866	+	0.386353i
$241$	0.331702	−	1.02087i	0.0213668	−	0.0657602i	−0.939805	−	0.341712i	$-0.888993\pi$
$241$	0.331702	−	1.02087i	0.0213668	−	0.0657602i	0.961171	+	0.275952i	$0.0889931\pi$
$242$	1.25082	−	1.72160i	0.0804055	−	0.110669i
$243$		−	20.1100i		−	1.29006i
$244$	1.34490	+	0.977126i	0.0860983	+	0.0625541i
$245$	−0.479579	+	2.18403i	−0.0306392	+	0.139533i
$246$	−23.3905	+	16.9942i	−1.49133	+	1.08351i
$247$	−11.4839	−	15.8062i	−0.730701	−	1.00572i
$248$	−1.63704	+	0.531906i	−0.103952	+	0.0337761i
$249$	−8.79799			−0.557550
$250$	−3.66837	+	10.5614i	−0.232008	+	0.667961i
$251$	−21.6066			−1.36379			−0.681897	−	0.731448i	$-0.738845\pi$
$251$	−21.6066			−1.36379			−0.681897	+	0.731448i	$0.738845\pi$
$252$	4.02693	−	1.30843i	0.253673	−	0.0824232i
$253$	−11.0016	−	15.1424i	−0.691664	−	0.951994i
$254$	0.644652	−	0.468367i	0.0404491	−	0.0293880i
$255$	−4.49024	+	20.4489i	−0.281190	+	1.28056i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			28.0746i			1.75125i	0.482996	+	0.875623i	$0.339549\pi$
$257$			28.0746i			1.75125i	−0.482996	+	0.875623i	$0.660451\pi$
$258$	−14.5774	+	20.0641i	−0.907550	+	1.24914i
$259$	2.74171	−	8.43813i	0.170362	−	0.524320i
$260$	0.855288	+	8.69894i	0.0530427	+	0.539485i
$261$	8.74153	+	26.9037i	0.541087	+	1.66529i
$262$	6.33088	+	2.05703i	0.391123	+	0.127084i
$263$	−10.1875	−	3.31011i	−0.628186	−	0.204110i	−0.0224148	−	0.999749i	$-0.507135\pi$
$263$	−10.1875	−	3.31011i	−0.628186	−	0.204110i	−0.605772	+	0.795639i	$0.707135\pi$
$264$	−2.47564	−	7.61923i	−0.152365	−	0.468931i
$265$	16.4028	−	7.17142i	1.00761	−	0.440537i
$266$	1.54448	−	4.75341i	0.0946980	−	0.291450i
$267$	−4.24383	+	5.84113i	−0.259718	+	0.357471i
$268$		−	9.37836i		−	0.572875i
$269$	14.9645	+	10.8723i	0.912400	+	0.662897i	0.941621	−	0.336676i	$-0.109303\pi$
$269$	14.9645	+	10.8723i	0.912400	+	0.662897i	−0.0292211	+	0.999573i	$0.509303\pi$
$270$	−2.97342	−	6.80093i	−0.180957	−	0.413891i
$271$	11.4466	−	8.31648i	0.695334	−	0.505190i	−0.183075	−	0.983099i	$-0.558605\pi$
$271$	11.4466	−	8.31648i	0.695334	−	0.505190i	0.878409	+	0.477909i	$0.158605\pi$
$272$	−2.04614	−	2.81627i	−0.124065	−	0.170761i
$273$	9.99933	−	3.24898i	0.605187	−	0.196637i
$274$	−22.6947			−1.37104
$275$	1.75547	−	14.7891i	0.105859	−	0.891817i
$276$	16.9013			1.01734
$277$	22.6615	−	7.36317i	1.36160	−	0.442410i	0.465022	−	0.885299i	$-0.346046\pi$
$277$	22.6615	−	7.36317i	1.36160	−	0.442410i	0.896576	+	0.442889i	$0.146046\pi$
$278$	1.62943	+	2.24272i	0.0977269	+	0.134510i
$279$	5.89628	−	4.28389i	0.353001	−	0.256470i
$280$	−1.67173	+	1.48503i	−0.0999050	+	0.0887476i
$281$	24.8086	+	18.0245i	1.47996	+	1.07525i	0.977570	+	0.210609i	$0.0675446\pi$
$281$	24.8086	+	18.0245i	1.47996	+	1.07525i	0.502387	+	0.864643i	$0.332455\pi$
$282$		−	18.9225i		−	1.12682i
$283$	−11.3265	+	15.5896i	−0.673291	+	0.926706i	−0.999829	−	0.0184784i	$-0.994118\pi$
$283$	−11.3265	+	15.5896i	−0.673291	+	0.926706i	0.326538	+	0.945184i	$0.394118\pi$
$284$	−1.72356	+	5.30458i	−0.102275	+	0.314769i
$285$	−29.3598	−	6.44693i	−1.73912	−	0.381883i
$286$	−3.59802	−	11.0736i	−0.212755	−	0.654793i
$287$	−10.2234	−	3.32178i	−0.603467	−	0.196078i
$288$	4.02693	+	1.30843i	0.237289	+	0.0770999i
$289$	1.50861	+	4.64303i	0.0887419	+	0.273119i
$290$	−9.92141	−	11.1687i	−0.582605	−	0.655850i
$291$	−8.29216	+	25.5206i	−0.486095	+	1.49605i
$292$	4.39980	−	6.05580i	0.257479	−	0.354389i
$293$			2.62443i			0.153321i	0.997057	+	0.0766603i	$0.0244257\pi$
$293$			2.62443i			0.153321i	−0.997057	+	0.0766603i	$0.975574\pi$
$294$	2.17596	+	1.58093i	0.126905	+	0.0922017i
$295$	19.4909	+	11.4283i	1.13481	+	0.665379i
$296$	7.17790	−	5.21505i	0.417207	−	0.303119i
$297$	5.81160	+	7.99898i	0.337223	+	0.464148i
$298$	−17.0925	+	5.55368i	−0.990139	+	0.321716i
$299$	24.5639			1.42057
$300$	9.87223	+	9.13198i	0.569974	+	0.527235i
$301$	−9.22078			−0.531477
$302$	1.74775	−	0.567879i	0.100572	−	0.0326778i
$303$	9.40223	+	12.9411i	0.540144	+	0.743445i
$304$	4.04349	−	2.93777i	0.231910	−	0.168493i
$305$	3.69937	−	0.363725i	0.211825	−	0.0208269i
$306$	11.9245	+	8.66368i	0.681680	+	0.495269i
$307$			1.23961i			0.0707483i	0.999374	+	0.0353741i	$0.0112623\pi$
$307$			1.23961i			0.0707483i	−0.999374	+	0.0353741i	$0.988738\pi$
$308$	1.75077	−	2.40973i	0.0997594	−	0.137307i
$309$	−5.70854	+	17.5691i	−0.324747	+	0.999469i
$310$	−1.94679	+	3.32026i	−0.110570	+	0.188578i
$311$	−3.09855	−	9.53636i	−0.175703	−	0.540757i	0.823962	−	0.566645i	$-0.191759\pi$
$311$	−3.09855	−	9.53636i	−0.175703	−	0.540757i	−0.999665	+	0.0258875i	$0.991759\pi$
$312$	9.99933	+	3.24898i	0.566100	+	0.183937i
$313$	−16.9176	−	5.49686i	−0.956240	−	0.310701i	−0.210991	−	0.977488i	$-0.567669\pi$
$313$	−16.9176	−	5.49686i	−0.956240	−	0.310701i	−0.745249	+	0.666787i	$0.767669\pi$
$314$	6.64535	+	20.4523i	0.375019	+	1.15419i
$315$	4.78888	−	8.16745i	0.269823	−	0.460184i
$316$	0.862495	−	2.65449i	0.0485191	−	0.149327i
$317$	−8.42308	+	11.5934i	−0.473088	+	0.651149i	−0.977158	−	0.212513i	$-0.931835\pi$
$317$	−8.42308	+	11.5934i	−0.473088	+	0.651149i	0.504071	+	0.863662i	$0.331835\pi$
$318$		−	21.5333i		−	1.20753i
$319$	16.0992	+	11.6968i	0.901385	+	0.654894i
$320$	−2.22534	+	0.218797i	−0.124400	+	0.0122311i
$321$	37.9007	−	27.5365i	2.11541	−	1.53693i
$322$	3.69356	+	5.08375i	0.205834	+	0.283306i
$323$	16.5471	−	5.37647i	0.920704	−	0.299155i
$324$	3.77436			0.209686
$325$	14.3480	+	13.2721i	0.795884	+	0.736206i
$326$	20.5905			1.14040
$327$	8.16953	−	2.65444i	0.451776	−	0.146791i
$328$	−6.31840	−	8.69653i	−0.348875	−	0.480185i
$329$	5.69172	−	4.13527i	0.313794	−	0.227985i
$330$	−15.4534	−	9.06089i	−0.850681	−	0.498786i
$331$	9.55117	+	6.93933i	0.524980	+	0.381420i	0.818477	−	0.574540i	$-0.194819\pi$
$331$	9.55117	+	6.93933i	0.524980	+	0.381420i	−0.293497	+	0.955960i	$0.594819\pi$
$332$		−	3.27107i		−	0.179523i
$333$	−22.0814	+	30.3924i	−1.21005	+	1.66549i
$334$	−4.38815	+	13.5053i	−0.240109	+	0.738979i
$335$	−13.9272	−	15.6781i	−0.760922	−	0.856585i
$336$	0.831144	+	2.55800i	0.0453426	+	0.139550i
$337$	18.3676	+	5.96800i	1.00055	+	0.325097i	0.763084	−	0.646299i	$-0.223684\pi$
$337$	18.3676	+	5.96800i	1.00055	+	0.325097i	0.237463	+	0.971397i	$0.423684\pi$
$338$	2.16899	+	0.704747i	0.117977	+	0.0383332i
$339$	−7.95178	−	24.4731i	−0.431882	−	1.32920i
$340$	−7.60283	−	1.66946i	−0.412321	−	0.0905391i
$341$	1.58433	−	4.87606i	0.0857962	−	0.264054i
$342$	−12.4390	+	17.1208i	−0.672624	+	0.925787i
$343$			1.00000i			0.0539949i
$344$	−7.45977	−	5.41984i	−0.402204	−	0.292218i
$345$	28.2544	−	25.0990i	1.52117	−	1.35128i
$346$	−2.22584	+	1.61717i	−0.119662	+	0.0869396i
$347$	9.55804	+	13.1555i	0.513103	+	0.706225i	0.984439	−	0.175728i	$-0.0562281\pi$
$347$	9.55804	+	13.1555i	0.513103	+	0.706225i	−0.471336	+	0.881954i	$0.656228\pi$
$348$	−17.0898	+	5.55283i	−0.916112	+	0.297663i
$349$	−29.2030			−1.56320			−0.781600	−	0.623780i	$-0.785596\pi$
$349$	−29.2030			−1.56320			−0.781600	+	0.623780i	$0.785596\pi$
$350$	−0.589364	+	4.96514i	−0.0315028	+	0.265398i
$351$	−12.9759			−0.692601
$352$	2.83281	−	0.920434i	0.150989	−	0.0490593i
$353$	5.86879	+	8.07770i	0.312364	+	0.429932i	0.936117	−	0.351689i	$-0.114393\pi$
$353$	5.86879	+	8.07770i	0.312364	+	0.429932i	−0.623753	+	0.781622i	$0.714393\pi$
$354$	21.9870	−	15.9745i	1.16859	−	0.849034i
$355$	4.99614	+	11.4274i	0.265168	+	0.606502i
$356$	−2.17171	−	1.57784i	−0.115101	−	0.0836255i
$357$			9.36289i			0.495537i
$358$	11.1247	−	15.3119i	0.587960	−	0.809258i
$359$	8.93793	−	27.5081i	0.471726	−	1.45182i	−0.378596	−	0.925562i	$-0.623593\pi$
$359$	8.93793	−	27.5081i	0.471726	−	1.45182i	0.850323	−	0.526262i	$-0.176407\pi$
$360$	8.67499	−	3.79278i	0.457212	−	0.199897i
$361$	1.84802	+	5.68763i	0.0972644	+	0.299349i
$362$	6.12490	+	1.99010i	0.321918	+	0.104597i
$363$	−5.44347	−	1.76869i	−0.285708	−	0.0928321i
$364$	1.20796	+	3.71772i	0.0633143	+	0.194861i
$365$	−1.63778	−	16.6575i	−0.0857254	−	0.871893i
$366$	1.38168	−	4.25238i	0.0722217	−	0.222276i
$367$	12.6587	−	17.4233i	0.660781	−	0.909487i	−0.338726	−	0.940885i	$-0.609996\pi$
$367$	12.6587	−	17.4233i	0.660781	−	0.909487i	0.999507	+	0.0313984i	$0.00999606\pi$
$368$			6.28386i			0.327569i
$369$	36.8225	+	26.7531i	1.91690	+	1.39271i
$370$	4.25500	−	19.3776i	0.221207	−	1.00739i
$371$	6.47699	−	4.70581i	0.336269	−	0.244313i
$372$	2.72123	+	3.74545i	0.141089	+	0.194193i
$373$	−16.8477	+	5.47415i	−0.872341	+	0.283441i	−0.710773	−	0.703421i	$-0.751655\pi$
$373$	−16.8477	+	5.47415i	−0.872341	+	0.283441i	−0.161567	+	0.986862i	$0.551655\pi$
$374$	10.3687			0.536155
$375$	30.0650	+	0.605635i	1.55255	+	0.0312748i
$376$	7.03535			0.362820
$377$	−24.8379	+	8.07031i	−1.27921	+	0.415642i
$378$	−1.95113	−	2.68549i	−0.100355	−	0.138127i
$379$	13.8574	−	10.0680i	0.711807	−	0.517158i	−0.171949	−	0.985106i	$-0.555007\pi$
$379$	13.8574	−	10.0680i	0.711807	−	0.517158i	0.883756	+	0.467948i	$0.155007\pi$
$380$	2.39695	−	10.9159i	0.122961	−	0.559972i
$381$	−1.73388	−	1.25974i	−0.0888295	−	0.0645384i
$382$			19.1846i			0.981571i
$383$	−13.6584	+	18.7992i	−0.697913	+	0.960595i	0.302060	+	0.953289i	$0.402326\pi$
$383$	−13.6584	+	18.7992i	−0.697913	+	0.960595i	−0.999973	+	0.00730594i	$0.997674\pi$
$384$	−0.831144	+	2.55800i	−0.0424142	+	0.130537i
$385$	−0.651707	−	6.62836i	−0.0332141	−	0.337813i
$386$	−2.14570	−	6.60378i	−0.109213	−	0.336124i
$387$	37.1314	+	12.0647i	1.88750	+	0.613285i
$388$	−9.48849	−	3.08300i	−0.481705	−	0.156516i
$389$	2.80894	+	8.64502i	0.142419	+	0.438320i	0.996670	−	0.0815404i	$-0.0259840\pi$
$389$	2.80894	+	8.64502i	0.142419	+	0.438320i	−0.854251	+	0.519860i	$0.825984\pi$
$390$	21.5410	−	9.41790i	1.09077	−	0.476894i
$391$	−6.75966	+	20.8041i	−0.341851	+	1.05211i
$392$	−0.587785	+	0.809017i	−0.0296876	+	0.0408615i
$393$		−	17.9041i		−	0.903141i
$394$	15.4510	+	11.2258i	0.778411	+	0.565549i
$395$	−2.50014	−	5.71842i	−0.125796	−	0.287725i
$396$	−10.2032	+	7.41304i	−0.512729	+	0.372519i
$397$	7.06753	+	9.72763i	0.354709	+	0.488216i	0.948665	−	0.316282i	$-0.102435\pi$
$397$	7.06753	+	9.72763i	0.354709	+	0.488216i	−0.593956	+	0.804498i	$0.702435\pi$
$398$	11.8142	−	3.83868i	0.592194	−	0.192415i
$399$	−13.4429			−0.672987
$400$	−3.39524	+	3.67047i	−0.169762	+	0.183523i
$401$	−14.1278			−0.705507			−0.352753	−	0.935716i	$-0.614754\pi$
$401$	−14.1278			−0.705507			−0.352753	+	0.935716i	$0.614754\pi$
$402$	−23.9898	+	7.79477i	−1.19650	+	0.388768i
$403$	3.95496	+	5.44353i	0.197010	+	0.271162i
$404$	−4.81145	+	3.49572i	−0.239379	+	0.173919i
$405$	6.30970	−	5.60504i	0.313532	−	0.278516i
$406$	−5.40499	−	3.92696i	−0.268245	−	0.194892i
$407$			26.4271i			1.30994i
$408$	−5.50337	+	7.57474i	−0.272457	+	0.375006i
$409$	1.21761	−	3.74741i	0.0602068	−	0.185297i	−0.916430	−	0.400196i	$-0.868942\pi$
$409$	1.21761	−	3.74741i	0.0602068	−	0.185297i	0.976636	+	0.214899i	$0.0689421\pi$
$410$	−23.4773	−	5.15523i	−1.15946	−	0.254599i
$411$	18.8626	+	58.0531i	0.930423	+	2.86355i
$412$	−6.53213	−	2.12242i	−0.321815	−	0.104564i
$413$	9.60993	+	3.12245i	0.472874	+	0.153646i
$414$	−8.22198	−	25.3046i	−0.404088	−	1.24366i
$415$	−4.85764	−	5.46834i	−0.238452	−	0.268430i
$416$	−1.20796	+	3.71772i	−0.0592251	+	0.182276i
$417$	4.38259	−	6.03212i	0.214616	−	0.295394i
$418$			14.8871i			0.728151i
$419$	−26.7875	−	19.4622i	−1.30865	−	0.950793i	−0.308654	−	0.951174i	$-0.599879\pi$
$419$	−26.7875	−	19.4622i	−1.30865	−	0.950793i	−1.00000		0.000381417i	$0.999879\pi$
$420$	5.18816	+	3.04201i	0.253156	+	0.148435i
$421$	13.3895	−	9.72806i	0.652565	−	0.474117i	−0.211579	−	0.977361i	$-0.567860\pi$
$421$	13.3895	−	9.72806i	0.652565	−	0.474117i	0.864144	+	0.503244i	$0.167860\pi$
$422$	−2.33500	−	3.21385i	−0.113666	−	0.156448i
$423$	−28.3308	+	9.20525i	−1.37749	+	0.447574i
$424$	8.00600			0.388806
$425$	−15.1891	+	8.49956i	−0.736779	+	0.412289i
$426$	15.0017			0.726832
$427$	1.58102	−	0.513705i	0.0765111	−	0.0248599i
$428$	10.2380	+	14.0914i	0.494871	+	0.681131i
$429$	−25.3357	+	18.4074i	−1.22322	+	0.888720i
$430$	−20.5194	+	2.01748i	−0.989531	+	0.0972916i
$431$	0.807698	+	0.586827i	0.0389055	+	0.0282665i	0.607068	−	0.794650i	$-0.292346\pi$
$431$	0.807698	+	0.586827i	0.0389055	+	0.0282665i	−0.568163	+	0.822916i	$0.692346\pi$
$432$		−	3.31945i		−	0.159707i
$433$	10.9109	−	15.0175i	0.524342	−	0.721695i	−0.461913	−	0.886925i	$-0.652837\pi$
$433$	10.9109	−	15.0175i	0.524342	−	0.721695i	0.986255	+	0.165230i	$0.0528366\pi$
$434$	−0.531906	+	1.63704i	−0.0255323	+	0.0785804i
$435$	−20.3235	+	34.6618i	−0.974436	+	1.66190i
$436$	0.986913	+	3.03741i	0.0472646	+	0.145465i
$437$	−29.8698	−	9.70527i	−1.42886	−	0.464266i
$438$	−19.1476	−	6.22143i	−0.914908	−	0.297271i
$439$	1.53052	+	4.71044i	0.0730476	+	0.224817i	0.980914	−	0.194442i	$-0.0622897\pi$
$439$	1.53052	+	4.71044i	0.0730476	+	0.224817i	−0.907866	+	0.419260i	$0.862290\pi$
$440$	3.36881	−	5.74552i	0.160602	−	0.273907i
$441$	1.30843	−	4.02693i	0.0623061	−	0.191758i
$442$	−7.99844	+	11.0089i	−0.380447	+	0.523640i
$443$		−	5.41373i		−	0.257214i	−0.991696	−	0.128607i	$-0.958949\pi$
$443$		−	5.41373i		−	0.257214i	0.991696	−	0.128607i	$-0.0410506\pi$
$444$	−19.3060	−	14.0266i	−0.916221	−	0.665673i
$445$	−5.97366	+	0.587336i	−0.283179	+	0.0278424i
$446$	−15.7428	+	11.4378i	−0.745443	+	0.541596i
$447$	28.4126	+	39.1066i	1.34387	+	1.84968i
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−31.6366			−1.49302			−0.746512	−	0.665372i	$-0.768273\pi$
$449$	−31.6366			−1.49302			−0.746512	+	0.665372i	$0.768273\pi$
$450$	8.86986	−	19.2231i	0.418129	−	0.906187i
$451$	32.0183			1.50768
$452$	9.09902	−	2.95645i	0.427982	−	0.139060i
$453$	−2.90527	−	3.99876i	−0.136501	−	0.187878i
$454$	−7.18532	+	5.22044i	−0.337224	+	0.245007i
$455$	7.54031	+	4.42117i	0.353495	+	0.207267i
$456$	−10.8755	−	7.90154i	−0.509294	−	0.370024i
$457$		−	31.0450i		−	1.45222i	−0.687576	−	0.726112i	$-0.741325\pi$
$457$		−	31.0450i		−	1.45222i	0.687576	−	0.726112i	$-0.258675\pi$
$458$	5.06092	−	6.96575i	0.236481	−	0.325488i
$459$	3.57079	−	10.9898i	0.166670	−	0.512959i
$460$	9.33173	+	10.5049i	0.435094	+	0.489794i
$461$	−5.04532	−	15.5279i	−0.234984	−	0.723206i	−0.997124	−	0.0757935i	$-0.975851\pi$
$461$	−5.04532	−	15.5279i	−0.234984	−	0.723206i	0.762140	−	0.647413i	$-0.224149\pi$
$462$	−7.61923	−	2.47564i	−0.354478	−	0.115177i
$463$	−36.8833	−	11.9841i	−1.71411	−	0.556949i	−0.723103	−	0.690741i	$-0.757285\pi$
$463$	−36.8833	−	11.9841i	−1.71411	−	0.556949i	−0.991009	+	0.133792i	$0.957285\pi$
$464$	−2.06452	−	6.35395i	−0.0958431	−	0.294975i
$465$	10.1113	+	2.22027i	0.468899	+	0.102963i
$466$	0.393979	−	1.21254i	0.0182507	−	0.0561700i
$467$	−9.36493	+	12.8897i	−0.433358	+	0.596465i	−0.968720	−	0.248157i	$-0.920175\pi$
$467$	−9.36493	+	12.8897i	−0.433358	+	0.596465i	0.535362	+	0.844623i	$0.320175\pi$
$468$		−	16.5515i		−	0.765094i
$469$	−7.58725	−	5.51246i	−0.350347	−	0.254542i
$470$	11.7612	−	10.4477i	0.542504	−	0.481917i
$471$	46.7937	−	33.9976i	2.15614	−	1.56653i
$472$	5.93926	+	8.17469i	0.273377	+	0.376271i
$473$	26.1207	−	8.48712i	1.20103	−	0.390238i
$474$	−7.50703			−0.344810
$475$	−12.2034	−	21.8079i	−0.559929	−	1.00062i
$476$	−3.48110			−0.159556
$477$	−32.2396	+	10.4753i	−1.47615	+	0.479630i
$478$	1.92444	+	2.64877i	0.0880219	+	0.121152i
$479$	0.386524	−	0.280826i	0.0176607	−	0.0128313i	−0.578920	−	0.815384i	$-0.696526\pi$
$479$	0.386524	−	0.280826i	0.0176607	−	0.0128313i	0.596581	+	0.802553i	$0.296526\pi$
$480$	2.40926	+	5.51056i	0.109967	+	0.251522i
$481$	−28.0587	−	20.3859i	−1.27937	−	0.929515i
$482$		−	1.07341i		−	0.0488925i
$483$	9.93434	−	13.6735i	0.452028	−	0.622164i
$484$	0.657593	−	2.02386i	0.0298906	−	0.0919938i
$485$	−20.4406	+	8.93677i	−0.928158	+	0.405798i
$486$	−6.21434	−	19.1258i	−0.281888	−	0.867562i
$487$	−26.9222	−	8.74754i	−1.21996	−	0.396389i	−0.372892	−	0.927875i	$-0.621634\pi$
$487$	−26.9222	−	8.74754i	−1.21996	−	0.396389i	−0.847067	+	0.531486i	$0.821634\pi$
$488$	1.58102	+	0.513705i	0.0715695	+	0.0232544i
$489$	−17.1137	−	52.6705i	−0.773907	−	2.38184i
$490$	0.218797	+	2.22534i	0.00988425	+	0.100531i
$491$	10.0986	−	31.0802i	0.455743	−	1.40263i	−0.414518	−	0.910041i	$-0.636050\pi$
$491$	10.0986	−	31.0802i	0.455743	−	1.40263i	0.870261	−	0.492591i	$-0.163950\pi$
$492$	−16.9942	+	23.3905i	−0.766158	+	1.05453i
$493$		−	23.2570i		−	1.04744i
$494$	−15.8062	−	11.4839i	−0.711154	−	0.516684i
$495$	−6.04836	+	27.5447i	−0.271854	+	1.23804i
$496$	−1.39255	+	1.01175i	−0.0625273	+	0.0454287i
$497$	3.27841	+	4.51235i	0.147057	+	0.202406i
$498$	−8.36739	+	2.71873i	−0.374952	+	0.121829i
$499$	18.1560			0.812773			0.406387	−	0.913701i	$-0.366789\pi$
$499$	18.1560			0.812773			0.406387	+	0.913701i	$0.366789\pi$
$500$	−0.225173	+	11.1781i	−0.0100700	+	0.499899i
$501$	38.1938			1.70637
$502$	−20.5491	+	6.67680i	−0.917150	+	0.298000i
$503$	9.85851	+	13.5691i	0.439569	+	0.605015i	0.970116	−	0.242640i	$-0.0780135\pi$
$503$	9.85851	+	13.5691i	0.439569	+	0.605015i	−0.530547	+	0.847655i	$0.678013\pi$
$504$	3.42551	−	2.48878i	0.152584	−	0.110859i
$505$	−2.85219	+	12.9891i	−0.126921	+	0.578005i
$506$	−15.1424	−	11.0016i	−0.673161	−	0.489080i
$507$		−	6.13402i		−	0.272421i
$508$	0.468367	−	0.644652i	0.0207804	−	0.0286018i
$509$	6.95713	−	21.4118i	0.308369	−	0.949063i	−0.670029	−	0.742335i	$-0.733718\pi$
$509$	6.95713	−	21.4118i	0.308369	−	0.949063i	0.978398	−	0.206728i	$-0.0662816\pi$
$510$	2.04858	+	20.8356i	0.0907125	+	0.922616i
$511$	−2.31311	−	7.11902i	−0.102326	−	0.314927i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	15.7787	+	5.12682i	0.696648	+	0.226355i
$514$	8.67553	+	26.7005i	0.382661	+	1.17771i
$515$	−14.0718	+	6.15230i	−0.620078	+	0.271103i
$516$	−7.66380	+	23.5868i	−0.337380	+	1.03835i
$517$	−12.3173	+	16.9533i	−0.541713	+	0.745604i
$518$		−	8.87238i		−	0.389830i
$519$	5.98672	+	4.34961i	0.262788	+	0.190927i
$520$	3.50155	+	8.00888i	0.153553	+	0.351213i
$521$	14.9902	−	10.8910i	0.656734	−	0.477145i	−0.208824	−	0.977953i	$-0.566964\pi$
$521$	14.9902	−	10.8910i	0.656734	−	0.477145i	0.865558	+	0.500808i	$0.166964\pi$
$522$	16.6274	+	22.8856i	0.727761	+	1.00168i
$523$	−38.1354	+	12.3909i	−1.66754	+	0.541818i	−0.982432	−	0.186621i	$-0.940247\pi$
$523$	−38.1354	+	12.3909i	−1.66754	+	0.541818i	−0.685111	+	0.728438i	$0.740247\pi$
$524$	6.65668			0.290799
$525$	13.1907	−	2.61916i	0.575689	−	0.114309i
$526$	−10.7117			−0.467054
$527$	−5.69869	+	1.85162i	−0.248239	+	0.0806577i
$528$	−4.70894	−	6.48130i	−0.204930	−	0.282062i
$529$	13.3382	−	9.69074i	0.579920	−	0.421337i
$530$	13.3839	−	11.8892i	0.581358	−	0.516432i
$531$	−34.6130	−	25.1478i	−1.50208	−	1.09132i
$532$		−	4.99803i		−	0.216692i
$533$	−24.6989	+	33.9951i	−1.06983	+	1.47249i
$534$	−2.23111	+	6.86666i	−0.0965496	+	0.297149i
$535$	38.0412	+	8.35324i	1.64467	+	0.361142i
$536$	−2.89807	−	8.91935i	−0.125178	−	0.385257i
$537$	−48.4140	−	15.7307i	−2.08922	−	0.678828i
$538$	17.5918	+	5.71592i	0.758436	+	0.246431i
$539$	−0.920434	−	2.83281i	−0.0396459	−	0.122018i
$540$	−4.92949	−	5.54923i	−0.212132	−	0.238801i
$541$	−7.48062	+	23.0230i	−0.321617	+	0.989835i	0.651328	+	0.758796i	$0.274212\pi$
$541$	−7.48062	+	23.0230i	−0.321617	+	0.989835i	−0.972945	+	0.231038i	$0.925788\pi$
$542$	8.31648	−	11.4466i	0.357223	−	0.491676i
$543$		−	17.3216i		−	0.743339i
$544$	−2.81627	−	2.04614i	−0.120746	−	0.0877274i
$545$	6.16049	+	3.61213i	0.263887	+	0.154726i
$546$	8.50594	−	6.17992i	0.364020	−	0.264476i
$547$	−12.6467	−	17.4066i	−0.540733	−	0.744255i	0.447986	−	0.894041i	$-0.352141\pi$
$547$	−12.6467	−	17.4066i	−0.540733	−	0.744255i	−0.988718	+	0.149786i	$0.952141\pi$
$548$	−21.5840	+	7.01305i	−0.922021	+	0.299583i
$549$	−7.03881			−0.300409
$550$	−2.90054	−	14.6078i	−0.123679	−	0.622877i
$551$	33.3916			1.42253
$552$	16.0741	−	5.22279i	0.684159	−	0.222297i
$553$	−1.64056	−	2.25804i	−0.0697638	−	0.0960217i
$554$	19.2770	−	14.0056i	0.819003	−	0.595040i
$555$	−53.1043	+	5.22127i	−2.25415	+	0.221630i
$556$	2.24272	+	1.62943i	0.0951127	+	0.0691034i
$557$		−	37.9571i		−	1.60829i	−0.594430	−	0.804147i	$-0.702622\pi$
$557$		−	37.9571i		−	1.60829i	0.594430	−	0.804147i	$-0.297378\pi$
$558$	4.28389	−	5.89628i	0.181352	−	0.249609i
$559$	−11.1383	+	34.2803i	−0.471102	+	1.44990i
$560$	−1.13101	+	1.92894i	−0.0477939	+	0.0815127i
$561$	−8.61793	−	26.5233i	−0.363849	−	1.11981i
$562$	29.1643	+	9.47604i	1.23022	+	0.399723i
$563$	16.0410	+	5.21205i	0.676050	+	0.219662i	0.626865	−	0.779128i	$-0.284338\pi$
$563$	16.0410	+	5.21205i	0.676050	+	0.219662i	0.0491845	+	0.998790i	$0.484338\pi$
$564$	−5.84739	−	17.9964i	−0.246220	−	0.757786i
$565$	10.8207	−	18.4547i	0.455229	−	0.776396i
$566$	−5.95470	+	18.3267i	−0.250295	+	0.770328i
$567$	2.21851	−	3.05352i	0.0931687	−	0.128236i
$568$			5.57757i			0.234030i
$569$	6.42865	+	4.67069i	0.269503	+	0.195805i	0.714326	−	0.699813i	$-0.246733\pi$
$569$	6.42865	+	4.67069i	0.269503	+	0.195805i	−0.444823	+	0.895619i	$0.646733\pi$
$570$	−29.9150	+	2.94127i	−1.25300	+	0.123196i
$571$	1.60546	−	1.16643i	0.0671863	−	0.0488137i	−0.553685	−	0.832726i	$-0.686779\pi$
$571$	1.60546	−	1.16643i	0.0671863	−	0.0488137i	0.620871	+	0.783912i	$0.286779\pi$
$572$	−6.84383	−	9.41973i	−0.286155	−	0.393859i
$573$	49.0743	−	15.9452i	2.05011	−	0.666120i
$574$	−10.7495			−0.448675
$575$	31.2003	+	3.70348i	1.30114	+	0.154446i
$576$	4.23416			0.176423
$577$	−18.7050	+	6.07761i	−0.778698	+	0.253014i	−0.671284	−	0.741200i	$-0.734257\pi$
$577$	−18.7050	+	6.07761i	−0.778698	+	0.253014i	−0.107414	+	0.994214i	$0.534257\pi$
$578$	2.86955	+	3.94960i	0.119358	+	0.164282i
$579$	−15.1091	+	10.9774i	−0.627912	+	0.456205i
$580$	−12.8871	−	7.55621i	−0.535110	−	0.313755i
$581$	−2.64635	−	1.92269i	−0.109789	−	0.0797664i
$582$			26.8340i			1.11230i
$583$	−14.0167	+	19.2923i	−0.580511	+	0.799005i
$584$	2.31311	−	7.11902i	0.0957172	−	0.294587i
$585$	−24.5795	−	27.6697i	−1.01624	−	1.14400i
$586$	0.810992	+	2.49598i	0.0335018	+	0.103108i
$587$	40.0365	+	13.0086i	1.65248	+	0.536924i	0.979276	−	0.202532i	$-0.0649169\pi$
$587$	40.0365	+	13.0086i	1.65248	+	0.536924i	0.673206	+	0.739455i	$0.264917\pi$
$588$	2.55800	+	0.831144i	0.105490	+	0.0342758i
$589$	−2.65848	−	8.18197i	−0.109541	−	0.337132i
$590$	22.0685	+	4.84589i	0.908547	+	0.199502i
$591$	15.8736	−	48.8540i	0.652953	−	2.00958i
$592$	5.21505	−	7.17790i	0.214337	−	0.295010i
$593$		−	23.6004i		−	0.969153i	−0.874749	−	0.484576i	$-0.838974\pi$
$593$		−	23.6004i		−	0.969153i	0.874749	−	0.484576i	$-0.161026\pi$
$594$	7.99898	+	5.81160i	0.328202	+	0.238453i
$595$	−5.81945	+	5.16954i	−0.238574	+	0.211930i
$596$	−14.5397	+	10.5637i	−0.595570	+	0.432707i
$597$	−19.6387	−	27.0303i	−0.803757	−	1.10628i
$598$	23.3616	−	7.59065i	0.955328	−	0.310405i
$599$	6.94170			0.283630			0.141815	−	0.989893i	$-0.454706\pi$
$599$	6.94170			0.283630			0.141815	+	0.989893i	$0.454706\pi$
$600$	12.2110	+	5.63434i	0.498512	+	0.230021i
$601$	22.3315			0.910923			0.455461	−	0.890256i	$-0.349474\pi$
$601$	22.3315			0.910923			0.455461	+	0.890256i	$0.349474\pi$
$602$	−8.76948	+	2.84938i	−0.357417	+	0.116132i
$603$	23.3407	+	32.1257i	0.950505	+	1.30826i
$604$	1.48673	−	1.08017i	0.0604940	−	0.0439515i
$605$	−1.90618	−	4.35990i	−0.0774974	−	0.177255i
$606$	12.9411	+	9.40223i	0.525695	+	0.381940i
$607$			8.80192i			0.357259i	0.983916	+	0.178629i	$0.0571663\pi$
$607$			8.80192i			0.357259i	−0.983916	+	0.178629i	$0.942834\pi$
$608$	2.93777	−	4.04349i	0.119142	−	0.163985i
$609$	−5.55283	+	17.0898i	−0.225012	+	0.692515i
$610$	3.40591	−	1.48909i	0.137901	−	0.0602916i
$611$	−8.49842	−	26.1554i	−0.343809	−	1.05814i
$612$	14.0181	+	4.55476i	0.566649	+	0.184115i
$613$	−26.3663	−	8.56694i	−1.06493	−	0.346016i	−0.276417	−	0.961038i	$-0.589147\pi$
$613$	−26.3663	−	8.56694i	−1.06493	−	0.346016i	−0.788510	+	0.615022i	$0.789147\pi$
$614$	0.383061	+	1.17894i	0.0154591	+	0.0475781i
$615$	6.32593	+	64.3396i	0.255086	+	2.59442i
$616$	0.920434	−	2.83281i	0.0370853	−	0.114137i
$617$	−2.23619	+	3.07785i	−0.0900255	+	0.123909i	−0.851654	−	0.524104i	$-0.824400\pi$
$617$	−2.23619	+	3.07785i	−0.0900255	+	0.123909i	0.761629	+	0.648014i	$0.224400\pi$
$618$			18.4732i			0.743102i
$619$	−27.3780	−	19.8913i	−1.10042	−	0.799499i	−0.119288	−	0.992860i	$-0.538061\pi$
$619$	−27.3780	−	19.8913i	−1.10042	−	0.799499i	−0.981128	+	0.193361i	$0.938061\pi$
$620$	−0.825491	+	3.75934i	−0.0331525	+	0.150979i
$621$	−16.8753	+	12.2606i	−0.677181	+	0.492001i
$622$	−5.89379	−	8.11211i	−0.236320	−	0.325266i
$623$	−2.55300	+	0.829521i	−0.102284	+	0.0332340i
$624$	10.5139			0.420893
$625$	16.2234	+	19.0211i	0.648934	+	0.760844i
$626$	−17.7882			−0.710960
$627$	38.0811	−	12.3733i	1.52081	−	0.494142i
$628$	12.6402	+	17.3978i	0.504400	+	0.694246i
$629$	24.9870	−	18.1541i	0.996296	−	0.723851i
$630$	2.03061	−	9.24755i	0.0809016	−	0.368431i
$631$	−10.5992	−	7.70078i	−0.421948	−	0.306563i	0.356473	−	0.934306i	$-0.383979\pi$
$631$	−10.5992	−	7.70078i	−0.421948	−	0.306563i	−0.778421	+	0.627742i	$0.783979\pi$
$632$		−	2.79109i		−	0.111024i
$633$	−6.28031	+	8.64410i	−0.249620	+	0.343572i
$634$	−4.42828	+	13.6288i	−0.175869	+	0.541270i
$635$	−0.174345	−	1.77323i	−0.00691868	−	0.0703683i
$636$	−6.65414	−	20.4793i	−0.263854	−	0.812059i
$637$	3.71772	+	1.20796i	0.147301	+	0.0478611i
$638$	18.9258	+	6.14937i	0.749280	+	0.243456i
$639$	−7.29785	−	22.4605i	−0.288698	−	0.888522i
$640$	−2.04881	+	0.895756i	−0.0809863	+	0.0354079i
$641$	−13.3911	+	41.2137i	−0.528918	+	1.62784i	0.227518	+	0.973774i	$0.426939\pi$
$641$	−13.3911	+	41.2137i	−0.528918	+	1.62784i	−0.756436	+	0.654068i	$0.773061\pi$
$642$	27.5365	−	37.9007i	1.08678	−	1.49582i
$643$		−	44.8320i		−	1.76800i	−0.467484	−	0.884001i	$-0.654839\pi$
$643$		−	44.8320i		−	1.76800i	0.467484	−	0.884001i	$-0.345161\pi$
$644$	5.08375	+	3.69356i	0.200328	+	0.145547i
$645$	22.2153	+	50.8117i	0.874725	+	2.00071i
$646$	14.0758	−	10.2267i	0.553804	−	0.402363i
$647$	−18.3043	−	25.1937i	−0.719616	−	0.990466i	−0.999536	−	0.0304432i	$-0.990308\pi$
$647$	−18.3043	−	25.1937i	−0.719616	−	0.990466i	0.279921	−	0.960023i	$-0.409692\pi$
$648$	3.58963	−	1.16634i	0.141014	−	0.0458182i
$649$	−30.0971			−1.18141
$650$	17.7471	+	8.18879i	0.696098	+	0.321191i
$651$	4.62963			0.181450
$652$	19.5827	−	6.36281i	0.766919	−	0.249187i
$653$	−23.1900	−	31.9184i	−0.907497	−	1.24906i	−0.968014	−	0.250895i	$-0.919275\pi$
$653$	−23.1900	−	31.9184i	−0.907497	−	1.24906i	0.0605176	−	0.998167i	$-0.480725\pi$
$654$	6.94941	−	5.04905i	0.271744	−	0.197433i
$655$	11.1282	−	9.88538i	0.434814	−	0.386254i
$656$	−8.69653	−	6.31840i	−0.339542	−	0.246692i
$657$			31.6943i			1.23651i
$658$	4.13527	−	5.69172i	0.161210	−	0.221886i
$659$	−2.80993	+	8.64807i	−0.109459	+	0.336881i	−0.990751	−	0.135691i	$-0.956674\pi$
$659$	−2.80993	+	8.64807i	−0.109459	+	0.336881i	0.881292	+	0.472572i	$0.156674\pi$
$660$	−17.4970	−	3.84206i	−0.681070	−	0.149552i
$661$	14.1026	+	43.4034i	0.548528	+	1.68819i	0.712451	+	0.701722i	$0.247585\pi$
$661$	14.1026	+	43.4034i	0.548528	+	1.68819i	−0.163923	+	0.986473i	$0.552415\pi$
$662$	11.2281	+	3.64822i	0.436391	+	0.141792i
$663$	34.8086	+	11.3100i	1.35185	+	0.439244i
$664$	−1.01082	−	3.11097i	−0.0392272	−	0.120729i
$665$	−7.42224	−	8.35536i	−0.287822	−	0.324007i
$666$	−11.6089	+	35.7284i	−0.449834	+	1.38445i
$667$	−24.6764	+	33.9642i	−0.955476	+	1.31510i
$668$			14.2004i			0.549428i
$669$	42.3424	+	30.7636i	1.63705	+	1.18939i
$670$	−18.0903	−	10.6070i	−0.698890	−	0.409785i
$671$	−4.00590	+	2.91045i	−0.154646	+	0.112357i
$672$	1.58093	+	2.17596i	0.0609857	+	0.0839396i
$673$	−12.4131	+	4.03326i	−0.478490	+	0.155471i	−0.538325	−	0.842737i	$-0.680943\pi$
$673$	−12.4131	+	4.03326i	−0.478490	+	0.155471i	0.0598347	+	0.998208i	$0.480943\pi$
$674$	19.3128			0.743903
$675$	−16.4816	−	1.95636i	−0.634375	−	0.0753005i
$676$	2.28061			0.0877157
$677$	−19.5168	+	6.34140i	−0.750092	+	0.243720i	−0.659021	−	0.752125i	$-0.729029\pi$
$677$	−19.5168	+	6.34140i	−0.750092	+	0.243720i	−0.0910714	+	0.995844i	$0.529029\pi$
$678$	−15.1252	−	20.8180i	−0.580880	−	0.799512i
$679$	−8.07139	+	5.86421i	−0.309752	+	0.225048i
$680$	−7.74661	+	0.761654i	−0.297069	+	0.0292081i
$681$	19.3259	+	14.0411i	0.740570	+	0.538056i
$682$		−	5.12700i		−	0.196323i
$683$	21.0616	−	28.9888i	0.805901	−	1.10923i	−0.186042	−	0.982542i	$-0.559566\pi$
$683$	21.0616	−	28.9888i	0.805901	−	1.10923i	0.991943	−	0.126686i	$-0.0404339\pi$
$684$	−6.53957	+	20.1267i	−0.250047	+	0.769564i
$685$	−25.6680	+	43.7768i	−0.980722	+	1.67263i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−22.0247	−	7.15627i	−0.840296	−	0.273029i
$688$	−8.76948	−	2.84938i	−0.334333	−	0.108632i
$689$	−9.67093	−	29.7641i	−0.368433	−	1.13392i
$690$	19.1156	−	32.6017i	0.727717	−	1.24112i
$691$	−2.68626	+	8.26745i	−0.102190	+	0.314509i	−0.989061	−	0.147509i	$-0.952874\pi$
$691$	−2.68626	+	8.26745i	−0.102190	+	0.314509i	0.886871	+	0.462018i	$0.152874\pi$
$692$	−1.61717	+	2.22584i	−0.0614756	+	0.0846139i
$693$			12.6118i			0.479084i
$694$	13.1555	+	9.55804i	0.499377	+	0.362818i
$695$	6.16899	−	0.606541i	0.234003	−	0.0230074i
$696$	−14.5375	+	10.5621i	−0.551042	+	0.400355i
$697$	−21.9949	−	30.2734i	−0.833118	−	1.14669i
$698$	−27.7737	+	9.02422i	−1.05125	+	0.341572i
$699$	−3.42914			−0.129702
$700$	0.973796	+	4.90426i	0.0368060	+	0.185363i
$701$	−11.0566			−0.417603			−0.208802	−	0.977958i	$-0.566956\pi$
$701$	−11.0566			−0.417603			−0.208802	+	0.977958i	$0.566956\pi$
$702$	−12.3408	+	4.00977i	−0.465773	+	0.151339i
$703$	26.0650	+	35.8754i	0.983060	+	1.35307i
$704$	2.40973	−	1.75077i	0.0908200	−	0.0659846i
$705$	−36.5005	−	21.4016i	−1.37469	−	0.806031i
$706$	8.07770	+	5.86879i	0.304008	+	0.220875i
$707$			5.94728i			0.223670i
$708$	15.9745	−	21.9870i	0.600358	−	0.826321i
$709$	−14.2090	+	43.7309i	−0.533631	+	1.64235i	0.212958	+	0.977061i	$0.431690\pi$
$709$	−14.2090	+	43.7309i	−0.533631	+	1.64235i	−0.746589	+	0.665286i	$0.768310\pi$
$710$	8.28286	+	9.32419i	0.310850	+	0.349931i
$711$	3.65194	+	11.2395i	0.136959	+	0.421515i
$712$	−2.55300	−	0.829521i	−0.0956778	−	0.0310876i
$713$	10.2869	+	3.34242i	0.385248	+	0.125175i
$714$	2.89329	+	8.90464i	0.108279	+	0.333248i
$715$	−25.4296	−	5.58394i	−0.951014	−	0.208827i
$716$	5.84861	−	18.0002i	0.218573	−	0.672698i
$717$	5.17605	−	7.12422i	0.193303	−	0.266059i
$718$		−	28.9238i		−	1.07943i
$719$	12.9692	+	9.42266i	0.483669	+	0.351406i	0.802744	−	0.596323i	$-0.203372\pi$
$719$	12.9692	+	9.42266i	0.483669	+	0.351406i	−0.319075	+	0.947729i	$0.603372\pi$
$720$	7.07838	−	6.28786i	0.263796	−	0.234335i
$721$	−5.55656	+	4.03708i	−0.206937	+	0.150349i
$722$	3.51515	+	4.83819i	0.130820	+	0.180059i
$723$	−2.74578	+	0.892158i	−0.102117	+	0.0331797i
$724$	6.44010			0.239345
$725$	−32.7650	+	6.50587i	−1.21686	+	0.241622i
$726$	−5.72360			−0.212423
$727$	21.7430	−	7.06474i	0.806404	−	0.262017i	0.123330	−	0.992366i	$-0.460643\pi$
$727$	21.7430	−	7.06474i	0.806404	−	0.262017i	0.683074	+	0.730349i	$0.260643\pi$
$728$	2.29768	+	3.16248i	0.0851576	+	0.117209i
$729$	−34.5981	+	25.1370i	−1.28141	+	0.931000i
$730$	−6.70507	−	15.3361i	−0.248166	−	0.567615i
$731$	−25.9682	−	18.8670i	−0.960467	−	0.697820i
$732$		−	4.47122i		−	0.165261i
$733$	1.79131	−	2.46553i	0.0661636	−	0.0910664i	−0.774653	−	0.632387i	$-0.782075\pi$
$733$	1.79131	−	2.46553i	0.0661636	−	0.0910664i	0.840816	+	0.541320i	$0.182075\pi$
$734$	6.65509	−	20.4823i	0.245644	−	0.756014i
$735$	5.51056	−	2.40926i	0.203260	−	0.0888669i
$736$	1.94182	+	5.97630i	0.0715764	+	0.220290i
$737$	26.5671	+	8.63216i	0.978611	+	0.317970i
$738$	43.2875	+	14.0649i	1.59343	+	0.517738i
$739$	−10.3479	−	31.8477i	−0.380655	−	1.17154i	−0.939583	−	0.342320i	$-0.888787\pi$
$739$	−10.3479	−	31.8477i	−0.380655	−	1.17154i	0.558928	−	0.829216i	$-0.311213\pi$
$740$	−1.94125	−	19.7440i	−0.0713618	−	0.725805i
$741$	−16.2385	+	49.9770i	−0.596536	+	1.83595i
$742$	4.70581	−	6.47699i	0.172756	−	0.237778i
$743$			25.6139i			0.939682i	0.882751	+	0.469841i	$0.155689\pi$
$743$			25.6139i			0.939682i	−0.882751	+	0.469841i	$0.844311\pi$
$744$	3.74545	+	2.72123i	0.137315	+	0.0997652i
$745$	−8.61902	+	39.2516i	−0.315776	+	1.43807i
$746$	−14.3315	+	10.4124i	−0.524714	+	0.381227i
$747$	8.14096	+	11.2051i	0.297862	+	0.409972i
$748$	9.86127	−	3.20412i	0.360564	−	0.117154i
$749$	17.4179			0.636435
$750$	28.7807	−	8.71460i	1.05092	−	0.318212i
$751$	−47.4140			−1.73016			−0.865081	−	0.501632i	$-0.832733\pi$
$751$	−47.4140			−1.73016			−0.865081	+	0.501632i	$0.832733\pi$
$752$	6.69101	−	2.17404i	0.243996	−	0.0792791i
$753$	34.1585	+	47.0151i	1.24480	+	1.71333i
$754$	−21.1283	+	15.3506i	−0.769449	+	0.559037i
$755$	0.881319	−	4.01359i	0.0320745	−	0.146069i
$756$	−2.68549	−	1.95113i	−0.0976705	−	0.0709617i
$757$		−	12.3294i		−	0.448120i	−0.974575	−	0.224060i	$-0.928069\pi$
$757$		−	12.3294i		−	0.448120i	0.974575	−	0.224060i	$-0.0719312\pi$
$758$	10.0680	−	13.8574i	0.365686	−	0.503323i
$759$	−15.5565	+	47.8781i	−0.564667	+	1.73787i
$760$	−1.09356	−	11.1223i	−0.0396674	−	0.403449i
$761$	10.7287	+	33.0197i	0.388917	+	1.19696i	0.933599	+	0.358320i	$0.116650\pi$
$761$	10.7287	+	33.0197i	0.388917	+	1.19696i	−0.544682	+	0.838643i	$0.683350\pi$
$762$	−2.03830	−	0.662284i	−0.0738399	−	0.0239920i
$763$	3.03741	+	0.986913i	0.109961	+	0.0357286i
$764$	5.92838	+	18.2457i	0.214481	+	0.660105i
$765$	30.1985	−	13.2030i	1.09183	−	0.477356i
$766$	−7.18066	+	22.0998i	−0.259448	+	0.798498i
$767$	23.2168	−	31.9552i	0.838311	−	1.15384i
$768$			2.68964i			0.0970540i
$769$	−37.0750	−	26.9365i	−1.33696	−	0.971356i	−0.999550	−	0.0299974i	$-0.990450\pi$
$769$	−37.0750	−	26.9365i	−1.33696	−	0.971356i	−0.337407	−	0.941359i	$-0.609550\pi$
$770$	−2.66809	−	6.10256i	−0.0961512	−	0.219921i
$771$	61.0893	−	44.3840i	2.20008	−	1.59845i
$772$	−4.08136	−	5.61751i	−0.146891	−	0.202179i
$773$	17.6298	−	5.72827i	0.634099	−	0.206031i	0.0257093	−	0.999669i	$-0.491816\pi$
$773$	17.6298	−	5.72827i	0.634099	−	0.206031i	0.608390	+	0.793638i	$0.291816\pi$
$774$	39.0423			1.40335
$775$	4.20274	+	7.51049i	0.150967	+	0.269785i
$776$	−9.97679			−0.358146
$777$	−22.6955	+	7.37423i	−0.814198	+	0.264549i
$778$	5.34292	+	7.35390i	0.191553	+	0.263650i
$779$	43.4655	−	31.5796i	1.55731	−	1.13145i
$780$	17.5764	−	15.6135i	0.629337	−	0.559053i
$781$	−13.4404	−	9.76504i	−0.480936	−	0.349421i
$782$			21.8747i			0.782238i
$783$	13.0354	−	17.9416i	0.465845	−	0.641181i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	46.9673	+	10.3133i	1.67633	+	0.368096i
$786$	−5.53266	−	17.0278i	−0.197344	−	0.607361i
$787$	35.0639	+	11.3929i	1.24989	+	0.406114i	0.857882	−	0.513847i	$-0.171780\pi$
$787$	35.0639	+	11.3929i	1.24989	+	0.406114i	0.392010	+	0.919961i	$0.371780\pi$
$788$	18.1638	+	5.90176i	0.647057	+	0.210242i
$789$	8.90300	+	27.4006i	0.316955	+	0.975488i
$790$	−4.14486	−	4.66595i	−0.147468	−	0.166007i
$791$	2.95645	−	9.09902i	0.105119	−	0.323524i
$792$	−7.41304	+	10.2032i	−0.263411	+	0.362554i
$793$		−	6.49834i		−	0.230763i
$794$	9.72763	+	7.06753i	0.345221	+	0.250817i
$795$	−41.5364	−	24.3543i	−1.47314	−	0.863759i
$796$	10.0498	−	7.30160i	0.356205	−	0.258798i
$797$	−22.7663	−	31.3351i	−0.806424	−	1.10995i	−0.991865	−	0.127292i	$-0.959372\pi$
$797$	−22.7663	−	31.3351i	−0.806424	−	1.10995i	0.185441	−	0.982655i	$-0.440628\pi$
$798$	−12.7850	+	4.15409i	−0.452583	+	0.147053i
$799$	24.4907			0.866419
$800$	−2.09483	+	4.54001i	−0.0740635	+	0.160514i
$801$	11.3661			0.401602
$802$	−13.4363	+	4.36572i	−0.474452	+	0.154159i
$803$	13.1052	+	18.0377i	0.462472	+	0.636538i
$804$	−20.4070	+	14.8265i	−0.719699	+	0.522892i
$805$	13.9837	−	1.37489i	0.492861	−	0.0484585i
$806$	5.44353	+	3.95496i	0.191740	+	0.139307i
$807$		−	49.7505i		−	1.75130i
$808$	−3.49572	+	4.81145i	−0.122979	+	0.169266i
$809$	−0.0676763	+	0.208286i	−0.00237937	+	0.00732296i	−0.952239	−	0.305353i	$-0.901225\pi$
$809$	−0.0676763	+	0.208286i	−0.00237937	+	0.00732296i	0.949860	+	0.312676i	$0.101225\pi$
$810$	4.26883	−	7.28051i	0.149992	−	0.255811i
$811$	6.69275	+	20.5982i	0.235014	+	0.723300i	0.997120	+	0.0758464i	$0.0241659\pi$
$811$	6.69275	+	20.5982i	0.235014	+	0.723300i	−0.762105	+	0.647453i	$0.775834\pi$
$812$	−6.35395	−	2.06452i	−0.222980	−	0.0724506i
$813$	−36.1927	−	11.7597i	−1.26933	−	0.412432i
$814$	8.16644	+	25.1337i	0.286233	+	0.880936i
$815$	23.2881	−	39.7179i	0.815745	−	1.39126i
$816$	−2.89329	+	8.90464i	−0.101286	+	0.311725i
$817$	27.0885	−	37.2842i	0.947708	−	1.30441i
$818$		−	3.94026i		−	0.137768i
$819$	−13.3905	−	9.72874i	−0.467901	−	0.339950i
$820$	−23.9213	+	2.35196i	−0.835367	+	0.0821340i
$821$	11.7937	−	8.56861i	0.411602	−	0.299047i	−0.362648	−	0.931926i	$-0.618127\pi$
$821$	11.7937	−	8.56861i	0.411602	−	0.299047i	0.774250	+	0.632880i	$0.218127\pi$
$822$	35.8788	+	49.3829i	1.25142	+	1.72243i
$823$	−24.0274	+	7.80696i	−0.837541	+	0.272134i	−0.696219	−	0.717830i	$-0.745136\pi$
$823$	−24.0274	+	7.80696i	−0.837541	+	0.272134i	−0.141323	+	0.989964i	$0.545136\pi$
$824$	−6.86828			−0.239268
$825$	−34.9559	+	19.5607i	−1.21701	+	0.681017i
$826$	10.1045			0.351580
$827$	26.0947	−	8.47868i	0.907401	−	0.294833i	0.182113	−	0.983278i	$-0.441706\pi$
$827$	26.0947	−	8.47868i	0.907401	−	0.294833i	0.725288	+	0.688445i	$0.241706\pi$
$828$	−15.6391	−	21.5254i	−0.543497	−	0.748060i
$829$	9.72344	−	7.06450i	0.337709	−	0.245360i	−0.405985	−	0.913880i	$-0.633072\pi$
$829$	9.72344	−	7.06450i	0.337709	−	0.245360i	0.743695	+	0.668519i	$0.233072\pi$
$830$	−6.30970	−	3.69961i	−0.219013	−	0.128415i
$831$	−51.8483	−	37.6700i	−1.79860	−	1.30676i
$832$			3.90904i			0.135522i
$833$	−2.04614	+	2.81627i	−0.0708944	+	0.0975778i
$834$	2.30406	−	7.09118i	0.0797832	−	0.245547i
$835$	21.0880	+	23.7392i	0.729779	+	0.821527i
$836$	4.60036	+	14.1585i	0.159107	+	0.489680i
$837$	−5.43407	−	1.76564i	−0.187829	−	0.0610293i
$838$	−31.4906	−	10.2319i	−1.08782	−	0.353455i
$839$	5.90120	+	18.1620i	0.203732	+	0.627023i	0.999763	+	0.0217669i	$0.00692917\pi$
$839$	5.90120	+	18.1620i	0.203732	+	0.627023i	−0.796031	+	0.605256i	$0.793071\pi$
$840$	5.87426	+	1.28989i	0.202681	+	0.0445056i
$841$	4.83147	−	14.8697i	0.166602	−	0.512749i
$842$	9.72806	−	13.3895i	0.335251	−	0.461433i
$843$		−	82.4781i		−	2.84070i
$844$	−3.21385	−	2.33500i	−0.110625	−	0.0803740i
$845$	3.81256	−	3.38678i	0.131156	−	0.116509i
$846$	−24.0996	+	17.5094i	−0.828563	+	0.601986i
$847$	−1.25082	−	1.72160i	−0.0429786	−	0.0591549i
$848$	7.61416	−	2.47399i	0.261471	−	0.0849572i
$849$	51.8288			1.77876
$850$	−11.8192	+	12.7772i	−0.405394	+	0.438256i
$851$	−55.7528			−1.91118
$852$	14.2674	−	4.63577i	0.488794	−	0.158819i
$853$	24.1077	+	33.1814i	0.825432	+	1.13611i	0.988756	+	0.149538i	$0.0477786\pi$
$853$	24.1077	+	33.1814i	0.825432	+	1.13611i	−0.163324	+	0.986573i	$0.552221\pi$
$854$	1.34490	−	0.977126i	0.0460215	−	0.0334366i
$855$	18.9564	+	43.3579i	0.648296	+	1.48281i
$856$	14.0914	+	10.2380i	0.481633	+	0.349927i
$857$			50.7840i			1.73475i	0.497657	+	0.867374i	$0.334194\pi$
$857$			50.7840i			1.73475i	−0.497657	+	0.867374i	$0.665806\pi$
$858$	−18.4074	+	25.3357i	−0.628420	+	0.864946i
$859$	2.08051	−	6.40316i	0.0709862	−	0.218473i	−0.909269	−	0.416208i	$-0.863359\pi$
$859$	2.08051	−	6.40316i	0.0709862	−	0.218473i	0.980255	+	0.197735i	$0.0633587\pi$
$860$	−18.8916	+	8.25957i	−0.644199	+	0.281649i
$861$	8.93439	+	27.4972i	0.304483	+	0.937103i
$862$	0.949506	+	0.308513i	0.0323403	+	0.0105080i
$863$	9.43193	+	3.06462i	0.321067	+	0.104321i	0.465116	−	0.885250i	$-0.346012\pi$
$863$	9.43193	+	3.06462i	0.321067	+	0.104321i	−0.144050	+	0.989570i	$0.546012\pi$
$864$	−1.02577	−	3.15699i	−0.0348973	−	0.107403i
$865$	0.601976	+	6.12256i	0.0204678	+	0.208173i
$866$	5.73618	−	17.6541i	0.194923	−	0.599912i
$867$	7.71806	−	10.6230i	0.262119	−	0.360776i
$868$			1.72128i			0.0584242i
$869$	6.72577	+	4.88656i	0.228156	+	0.165765i
$870$	−8.61770	+	39.2456i	−0.292167	+	1.33055i
$871$	−29.6589	+	21.5484i	−1.00495	+	0.730141i
$872$	1.87722	+	2.58377i	0.0635707	+	0.0874975i
$873$	40.1758	−	13.0539i	1.35975	−	0.441808i
$874$	−31.4069			−1.06236
$875$	8.91090	+	6.75247i	0.301243	+	0.228275i
$876$	−20.1330			−0.680230
$877$	2.80899	−	0.912696i	0.0948528	−	0.0308195i	−0.261206	−	0.965283i	$-0.584120\pi$
$877$	2.80899	−	0.912696i	0.0948528	−	0.0308195i	0.356059	+	0.934463i	$0.384120\pi$
$878$	2.91121	+	4.00694i	0.0982487	+	0.135228i
$879$	5.71066	−	4.14904i	0.192616	−	0.139943i
$880$	1.42847	−	6.50534i	0.0481536	−	0.219295i
$881$	27.3519	+	19.8724i	0.921510	+	0.669517i	0.943900	−	0.330233i	$-0.107127\pi$
$881$	27.3519	+	19.8724i	0.921510	+	0.669517i	−0.0223891	+	0.999749i	$0.507127\pi$
$882$		−	4.23416i		−	0.142572i
$883$	−17.3504	+	23.8808i	−0.583888	+	0.803653i	−0.994115	−	0.108330i	$-0.965450\pi$
$883$	−17.3504	+	23.8808i	−0.583888	+	0.803653i	0.410227	+	0.911984i	$0.365450\pi$
$884$	−4.20503	+	12.9417i	−0.141430	+	0.435278i
$885$	−5.94634	−	60.4789i	−0.199884	−	2.03298i
$886$	−1.67293	−	5.14876i	−0.0562033	−	0.172976i
$887$	−3.65105	−	1.18630i	−0.122590	−	0.0398320i	0.247079	−	0.968995i	$-0.420529\pi$
$887$	−3.65105	−	1.18630i	−0.122590	−	0.0398320i	−0.369670	+	0.929163i	$0.620529\pi$
$888$	−22.6955	−	7.37423i	−0.761612	−	0.247463i
$889$	−0.246235	−	0.757834i	−0.00825847	−	0.0254169i
$890$	−5.49979	+	2.40455i	−0.184354	+	0.0806008i
$891$	−3.47405	+	10.6920i	−0.116385	+	0.358196i
$892$	−11.4378	+	15.7428i	−0.382966	+	0.527108i
$893$			35.1629i			1.17668i
$894$	39.1066	+	28.4126i	1.30792	+	0.950259i
$895$	−16.9535	−	38.7768i	−0.566694	−	1.29617i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−38.8338	−	53.4501i	−1.29662	−	1.78465i
$898$	−30.0882	+	9.77624i	−1.00406	+	0.326238i
$899$	−11.4998			−0.383540
$900$	2.49546	−	21.0232i	0.0831820	−	0.700774i
$901$	27.8697			0.928473
$902$	30.4512	−	9.89421i	1.01392	−	0.329441i
$903$	14.5774	+	20.0641i	0.485106	+	0.667691i
$904$	7.74009	−	5.62350i	0.257431	−	0.187035i
$905$	10.7661	−	9.56376i	0.357878	−	0.317910i
$906$	−3.99876	−	2.90527i	−0.132850	−	0.0965211i
$907$		−	22.8313i		−	0.758100i	−0.925376	−	0.379050i	$-0.876251\pi$
$907$		−	22.8313i		−	0.758100i	0.925376	−	0.379050i	$-0.123749\pi$
$908$	−5.22044	+	7.18532i	−0.173246	+	0.238453i
$909$	7.78159	−	23.9493i	0.258099	−	0.794347i
$910$	8.53748	+	1.87469i	0.283015	+	0.0621455i
$911$	−4.03394	−	12.4152i	−0.133650	−	0.411333i	0.861727	−	0.507372i	$-0.169383\pi$
$911$	−4.03394	−	12.4152i	−0.133650	−	0.411333i	−0.995378	+	0.0960384i	$0.969383\pi$
$912$	−12.7850	−	4.15409i	−0.423352	−	0.137556i
$913$	9.26630	+	3.01080i	0.306670	+	0.0996430i
$914$	−9.59343	−	29.5256i	−0.317323	−	0.976619i
$915$	−6.63990	−	7.47467i	−0.219508	−	0.247105i
$916$	2.66068	−	8.18873i	0.0879114	−	0.270563i
$917$	3.91270	−	5.38537i	0.129209	−	0.177841i
$918$		−	11.5553i		−	0.381383i
$919$	−19.0303	−	13.8263i	−0.627752	−	0.456088i	0.227869	−	0.973692i	$-0.426824\pi$
$919$	−19.0303	−	13.8263i	−0.627752	−	0.456088i	−0.855621	+	0.517603i	$0.826824\pi$
$920$	12.1212	+	7.10711i	0.399624	+	0.234314i
$921$	2.69735	−	1.95974i	0.0888806	−	0.0645756i
$922$	−9.59677	−	13.2088i	−0.316053	−	0.435009i
$923$	20.7358	−	6.73748i	0.682528	−	0.221767i
$924$	−8.01133			−0.263553
$925$	−32.5658	−	30.1239i	−1.07076	−	0.990467i
$926$	−38.7814			−1.27444
$927$	27.6581	−	8.98666i	0.908411	−	0.295161i
$928$	−3.92696	−	5.40499i	−0.128909	−	0.177428i
$929$	17.4617	−	12.6867i	0.572900	−	0.416236i	−0.263258	−	0.964726i	$-0.584797\pi$
$929$	17.4617	−	12.6867i	0.572900	−	0.416236i	0.836157	+	0.548490i	$0.184797\pi$
$930$	10.3025	−	1.01295i	0.337832	−	0.0332160i
$931$	−4.04349	−	2.93777i	−0.132520	−	0.0962815i
$932$		−	1.27494i		−	0.0417622i
$933$	−15.8522	+	21.8187i	−0.518977	+	0.714311i
$934$	−4.92344	+	15.1528i	−0.161100	+	0.495814i
$935$	11.7272	−	20.0007i	0.383519	−	0.654093i
$936$	−5.11470	−	15.7414i	−0.167179	−	0.514525i
$937$	54.4182	+	17.6815i	1.77776	+	0.577630i	0.998778	−	0.0494120i	$-0.0157347\pi$
$937$	54.4182	+	17.6815i	1.77776	+	0.577630i	0.778985	+	0.627042i	$0.215735\pi$
$938$	−8.91935	−	2.89807i	−0.291227	−	0.0946254i
$939$	14.7846	+	45.5023i	0.482477	+	1.48491i
$940$	7.95705	−	13.5708i	0.259530	−	0.442630i
$941$	−3.11449	+	9.58540i	−0.101529	+	0.312475i	−0.988900	−	0.148581i	$-0.952529\pi$
$941$	−3.11449	+	9.58540i	−0.101529	+	0.312475i	0.887371	+	0.461056i	$0.152529\pi$
$942$	33.9976	−	46.7937i	1.10770	−	1.52462i
$943$			67.5483i			2.19968i
$944$	8.17469	+	5.93926i	0.266064	+	0.193307i
$945$	−7.38690	+	0.726287i	−0.240296	+	0.0236261i
$946$	22.2196	−	16.1435i	0.722421	−	0.524869i
$947$	−22.4055	−	30.8385i	−0.728081	−	1.00212i	−0.999217	−	0.0395759i	$-0.987399\pi$
$947$	−22.4055	−	30.8385i	−0.728081	−	1.00212i	0.271136	−	0.962541i	$-0.412601\pi$
$948$	−7.13961	+	2.31980i	−0.231884	+	0.0753436i
$949$	−29.2607			−0.949841
$950$	−18.3451	−	16.9695i	−0.595194	−	0.550564i
$951$	38.5431			1.24985
$952$	−3.31072	+	1.07572i	−0.107301	+	0.0348642i
$953$	−17.1798	−	23.6459i	−0.556507	−	0.765967i	0.434370	−	0.900735i	$-0.356971\pi$
$953$	−17.1798	−	23.6459i	−0.556507	−	0.765967i	−0.990877	+	0.134768i	$0.956971\pi$
$954$	−27.4246	+	19.9252i	−0.887905	+	0.645101i
$955$	37.0060	+	21.6980i	1.19749	+	0.702131i
$956$	2.64877	+	1.92444i	0.0856672	+	0.0622409i
$957$		−	53.5232i		−	1.73016i
$958$	0.280826	−	0.386524i	0.00907308	−	0.0124880i
$959$	−7.01305	+	21.5840i	−0.226463	+	0.696983i
$960$	3.99420	+	4.49635i	0.128912	+	0.145119i
$961$	−8.66397	−	26.6649i	−0.279483	−	0.860159i
$962$	−32.9850	−	10.7175i	−1.06348	−	0.345545i
$963$	−70.1405	−	22.7900i	−2.26025	−	0.734399i
$964$	−0.331702	−	1.02087i	−0.0106834	−	0.0328801i
$965$	−15.1651	−	3.33002i	−0.488183	−	0.107197i
$966$	5.22279	−	16.0741i	0.168041	−	0.517176i
$967$	−1.79216	+	2.46669i	−0.0576319	+	0.0793235i	−0.836860	−	0.547417i	$-0.815611\pi$
$967$	−1.79216	+	2.46669i	−0.0576319	+	0.0793235i	0.779228	+	0.626740i	$0.215611\pi$
$968$		−	2.12802i		−	0.0683970i
$969$	−37.8588	−	27.5060i	−1.21620	−	0.883621i
$970$	−16.6785	+	14.8159i	−0.535515	+	0.475708i
$971$	−4.00003	+	2.90619i	−0.128367	+	0.0932641i	−0.650116	−	0.759835i	$-0.725280\pi$
$971$	−4.00003	+	2.90619i	−0.128367	+	0.0932641i	0.521749	+	0.853099i	$0.325280\pi$
$972$	−11.8204	−	16.2693i	−0.379139	−	0.521839i
$973$	2.63648	−	0.856644i	0.0845216	−	0.0274627i
$974$	−28.3076			−0.907035
$975$	6.19652	−	52.2031i	0.198447	−	1.67184i
$976$	1.66239			0.0532117
$977$	−8.66078	+	2.81406i	−0.277083	+	0.0900297i	−0.444262	−	0.895897i	$-0.646534\pi$
$977$	−8.66078	+	2.81406i	−0.277083	+	0.0900297i	0.167179	+	0.985927i	$0.446534\pi$
$978$	−32.5522	−	44.8042i	−1.04090	−	1.43268i
$979$	6.46864	−	4.69974i	0.206739	−	0.150204i
$980$	0.895756	+	2.04881i	0.0286139	+	0.0654468i
$981$	−10.9401	−	7.94845i	−0.349291	−	0.253775i
$982$		−	32.6797i		−	1.04285i
$983$	9.32581	−	12.8359i	0.297447	−	0.409401i	−0.633968	−	0.773359i	$-0.718575\pi$
$983$	9.32581	−	12.8359i	0.297447	−	0.409401i	0.931415	+	0.363958i	$0.118575\pi$
$984$	−8.93439	+	27.4972i	−0.284818	+	0.876579i
$985$	39.1292	−	17.1076i	1.24676	−	0.545093i
$986$	−7.18681	−	22.1187i	−0.228875	−	0.704403i
$987$	−17.9964	−	5.84739i	−0.572832	−	0.186124i
$988$	−18.5813	−	6.03743i	−0.591149	−	0.192076i
$989$	17.9051	+	55.1062i	0.569349	+	1.75228i
$990$	2.75943	+	28.0656i	0.0877005	+	0.891982i
$991$	0.454026	−	1.39735i	0.0144226	−	0.0443882i	−0.943586	−	0.331127i	$-0.892571\pi$
$991$	0.454026	−	1.39735i	0.0144226	−	0.0443882i	0.958009	+	0.286739i	$0.0925712\pi$
$992$	−1.01175	+	1.39255i	−0.0321230	+	0.0442134i
$993$		−	31.7536i		−	1.00767i
$994$	4.51235	+	3.27841i	0.143123	+	0.103985i
$995$	5.95743	−	27.1305i	0.188863	−	0.860096i
$996$	−7.11773	+	5.17133i	−0.225534	+	0.163860i
$997$	0.0116125	+	0.0159832i	0.000367772	+	0.000506194i	0.809201	−	0.587532i	$-0.199900\pi$
$997$	0.0116125	+	0.0159832i	0.000367772	+	0.000506194i	−0.808833	+	0.588038i	$0.799900\pi$
$998$	17.2674	−	5.61050i	0.546589	−	0.177597i
$999$	29.4514			0.931802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.169.6	yes	40
25.2	odd	20		8750.2.a.bf.1.17		20
25.4	even	10	inner	350.2.m.b.29.6	✓	40
25.23	odd	20		8750.2.a.be.1.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.6	✓	40	25.4	even	10	inner
350.2.m.b.169.6	yes	40	1.1	even	1	trivial
8750.2.a.be.1.4		20	25.23	odd	20
8750.2.a.bf.1.17		20	25.2	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.58093 - 2.17596i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.479579 - 2.18403i) q^{5} +(-2.17596 - 1.58093i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.30843 + 4.02693i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.58093 - 2.17596i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.479579 - 2.18403i) q^{5} +(-2.17596 - 1.58093i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.30843 + 4.02693i) q^{9} +(-0.218797 - 2.22534i) q^{10} +(0.920434 + 2.83281i) q^{11} +(-2.55800 - 0.831144i) q^{12} +(-3.71772 - 1.20796i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-5.51056 + 2.40926i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.04614 - 2.81627i) q^{17} +4.23416i q^{18} +(4.04349 + 2.93777i) q^{19} +(-0.895756 - 2.04881i) q^{20} +(-2.17596 + 1.58093i) q^{21} +(1.75077 + 2.40973i) q^{22} +(-5.97630 + 1.94182i) q^{23} -2.68964 q^{24} +(-4.54001 - 2.09483i) q^{25} -3.90904 q^{26} +(3.15699 - 1.02577i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(5.40499 - 3.92696i) q^{29} +(-4.49635 + 3.99420i) q^{30} +(-1.39255 - 1.01175i) q^{31} -1.00000i q^{32} +(4.70894 - 6.48130i) q^{33} +(1.07572 - 3.31072i) q^{34} +(-2.18403 - 0.479579i) q^{35} +(1.30843 + 4.02693i) q^{36} +(8.43813 + 2.74171i) q^{37} +(4.75341 + 1.54448i) q^{38} +(3.24898 + 9.99933i) q^{39} +(-1.48503 - 1.67173i) q^{40} +(3.32178 - 10.2234i) q^{41} +(-1.58093 + 2.17596i) q^{42} -9.22078i q^{43} +(2.40973 + 1.75077i) q^{44} +(8.16745 + 4.78888i) q^{45} +(-5.08375 + 3.69356i) q^{46} +(4.13527 + 5.69172i) q^{47} +(-2.55800 + 0.831144i) q^{48} -1.00000 q^{49} +(-4.96514 - 0.589364i) q^{50} -9.36289 q^{51} +(-3.71772 + 1.20796i) q^{52} +(4.70581 + 6.47699i) q^{53} +(2.68549 - 1.95113i) q^{54} +(6.62836 - 0.651707i) q^{55} +(-0.809017 - 0.587785i) q^{56} -13.4429i q^{57} +(3.92696 - 5.40499i) q^{58} +(-3.12245 + 9.60993i) q^{59} +(-3.04201 + 5.18816i) q^{60} +(0.513705 + 1.58102i) q^{61} +(-1.63704 - 0.531906i) q^{62} +(4.02693 + 1.30843i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.42117 + 7.54031i) q^{65} +(2.47564 - 7.61923i) q^{66} +(5.51246 - 7.58725i) q^{67} -3.48110i q^{68} +(13.6735 + 9.93434i) q^{69} +(-2.22534 + 0.218797i) q^{70} +(-4.51235 + 3.27841i) q^{71} +(2.48878 + 3.42551i) q^{72} +(7.11902 - 2.31311i) q^{73} +8.87238 q^{74} +(2.61916 + 13.1907i) q^{75} +4.99803 q^{76} +(2.83281 - 0.920434i) q^{77} +(6.17992 + 8.50594i) q^{78} +(2.25804 - 1.64056i) q^{79} +(-1.92894 - 1.13101i) q^{80} +(3.05352 + 2.21851i) q^{81} -10.7495i q^{82} +(1.92269 - 2.64635i) q^{83} +(-0.831144 + 2.55800i) q^{84} +(-5.16954 - 5.81945i) q^{85} +(-2.84938 - 8.76948i) q^{86} +(-17.0898 - 5.55283i) q^{87} +(2.83281 + 0.920434i) q^{88} +(-0.829521 - 2.55300i) q^{89} +(9.24755 + 2.03061i) q^{90} +(-1.20796 + 3.71772i) q^{91} +(-3.69356 + 5.08375i) q^{92} +4.62963i q^{93} +(5.69172 + 4.13527i) q^{94} +(8.35536 - 7.42224i) q^{95} +(-2.17596 + 1.58093i) q^{96} +(-5.86421 - 8.07139i) q^{97} +(-0.951057 + 0.309017i) q^{98} -12.6118 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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