LMFDB - Embedded newform 819.2.fy.a.50.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.5
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.676409 - 2.52439i) q^{2} +(1.29284 - 1.15263i) q^{3} +(-4.18297 + 2.41504i) q^{4} +(-0.237212 - 0.885285i) q^{5} +(-3.78419 - 2.48398i) q^{6} +(0.707107 - 0.707107i) q^{7} +(5.22994 + 5.22994i) q^{8} +(0.342872 - 2.98034i) q^{9} +O(q^{10})$	\(q+(-0.676409 - 2.52439i) q^{2} +(1.29284 - 1.15263i) q^{3} +(-4.18297 + 2.41504i) q^{4} +(-0.237212 - 0.885285i) q^{5} +(-3.78419 - 2.48398i) q^{6} +(0.707107 - 0.707107i) q^{7} +(5.22994 + 5.22994i) q^{8} +(0.342872 - 2.98034i) q^{9} +(-2.07435 + 1.19763i) q^{10} +(-4.48282 + 1.20117i) q^{11} +(-2.62426 + 7.94369i) q^{12} +(1.92171 - 3.05074i) q^{13} +(-2.26331 - 1.30672i) q^{14} +(-1.32709 - 0.871115i) q^{15} +(4.83475 - 8.37403i) q^{16} +(-1.79245 + 3.10462i) q^{17} +(-7.75547 + 1.15039i) q^{18} +(-5.83481 + 1.56343i) q^{19} +(3.13025 + 3.13025i) q^{20} +(0.0991412 - 1.72921i) q^{21} +(6.06444 + 10.5039i) q^{22} -8.61675 q^{23} +(12.7897 + 0.733273i) q^{24} +(3.60267 - 2.08000i) q^{25} +(-9.00113 - 2.78761i) q^{26} +(-2.99196 - 4.24831i) q^{27} +(-1.25012 + 4.66550i) q^{28} +(-2.94524 - 1.70044i) q^{29} +(-1.30138 + 3.93931i) q^{30} +(0.515850 - 0.138221i) q^{31} +(-10.1212 - 2.71195i) q^{32} +(-4.41107 + 6.71997i) q^{33} +(9.04969 + 2.42486i) q^{34} +(-0.793725 - 0.458257i) q^{35} +(5.76342 + 13.2947i) q^{36} +(2.89405 + 0.775458i) q^{37} +(7.89343 + 13.6718i) q^{38} +(-1.03192 - 6.15915i) q^{39} +(3.38938 - 5.87059i) q^{40} +(1.10671 - 1.10671i) q^{41} +(-4.43226 + 0.919382i) q^{42} -1.72852i q^{43} +(15.8506 - 15.8506i) q^{44} +(-2.71979 + 0.403432i) q^{45} +(5.82845 + 21.7521i) q^{46} +(2.06096 - 7.69162i) q^{47} +(-3.40163 - 16.3990i) q^{48} -1.00000i q^{49} +(-7.68761 - 7.68761i) q^{50} +(1.26113 + 6.07981i) q^{51} +(-0.670809 + 17.4022i) q^{52} +14.0127i q^{53} +(-8.70061 + 10.4265i) q^{54} +(2.12675 + 3.68365i) q^{55} +7.39625 q^{56} +(-5.74141 + 8.74667i) q^{57} +(-2.30038 + 8.58513i) q^{58} +(1.95236 - 7.28631i) q^{59} +(7.65494 + 0.438882i) q^{60} +13.4093 q^{61} +(-0.697850 - 1.20871i) q^{62} +(-1.86497 - 2.34987i) q^{63} +8.04513i q^{64} +(-3.15663 - 0.977594i) q^{65} +(19.9475 + 6.58981i) q^{66} +(-9.24196 - 9.24196i) q^{67} -17.3154i q^{68} +(-11.1401 + 9.93196i) q^{69} +(-0.619939 + 2.31364i) q^{70} +(0.0984490 + 0.367417i) q^{71} +(17.3802 - 13.7938i) q^{72} +(0.807556 - 0.807556i) q^{73} -7.83023i q^{74} +(2.26019 - 6.84166i) q^{75} +(20.6311 - 20.6311i) q^{76} +(-2.32048 + 4.01919i) q^{77} +(-14.8501 + 6.77107i) q^{78} +(1.94902 + 3.37579i) q^{79} +(-8.56027 - 2.29372i) q^{80} +(-8.76488 - 2.04375i) q^{81} +(-3.54234 - 2.04517i) q^{82} +(-5.13815 - 1.37676i) q^{83} +(3.76141 + 7.47267i) q^{84} +(3.17366 + 0.850380i) q^{85} +(-4.36346 + 1.16918i) q^{86} +(-5.76771 + 1.19639i) q^{87} +(-29.7269 - 17.1628i) q^{88} +(2.00933 - 7.49892i) q^{89} +(2.85811 + 6.59292i) q^{90} +(-0.798343 - 3.51606i) q^{91} +(36.0436 - 20.8098i) q^{92} +(0.507592 - 0.773284i) q^{93} -20.8107 q^{94} +(2.76817 + 4.79461i) q^{95} +(-16.2109 + 8.15986i) q^{96} +(-9.89722 - 9.89722i) q^{97} +(-2.52439 + 0.676409i) q^{98} +(2.04286 + 13.7722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.676409	−	2.52439i	−0.478293	−	1.78501i	−0.608530	−	0.793531i	$-0.708240\pi$
$2$	−0.676409	−	2.52439i	−0.478293	−	1.78501i	0.130237	−	0.991483i	$-0.458426\pi$
$3$	1.29284	−	1.15263i	0.746422	−	0.665473i
$3$	1.29284	−	1.15263i	0.746422	−	0.665473i
$4$	−4.18297	+	2.41504i	−2.09149	+	1.20752i
$5$	−0.237212	−	0.885285i	−0.106084	−	0.395912i	0.892382	−	0.451281i	$-0.149033\pi$
$5$	−0.237212	−	0.885285i	−0.106084	−	0.395912i	−0.998466	+	0.0553697i	$0.982366\pi$
$6$	−3.78419	−	2.48398i	−1.54489	−	1.01408i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	5.22994	+	5.22994i	1.84906	+	1.84906i
$9$	0.342872	−	2.98034i	0.114291	−	0.993447i
$10$	−2.07435	+	1.19763i	−0.655969	+	0.378724i
$11$	−4.48282	+	1.20117i	−1.35162	+	0.362166i	−0.860733	−	0.509056i	$-0.829994\pi$
$11$	−4.48282	+	1.20117i	−1.35162	+	0.362166i	−0.490889	+	0.871222i	$0.663328\pi$
$12$	−2.62426	+	7.94369i	−0.757558	+	2.29315i
$13$	1.92171	−	3.05074i	0.532987	−	0.846123i
$13$	1.92171	−	3.05074i	0.532987	−	0.846123i
$14$	−2.26331	−	1.30672i	−0.604894	−	0.349236i
$15$	−1.32709	−	0.871115i	−0.342652	−	0.224921i
$16$	4.83475	−	8.37403i	1.20869	−	2.09351i
$17$	−1.79245	+	3.10462i	−0.434733	+	0.752980i	−0.997274	−	0.0737898i	$-0.976491\pi$
$17$	−1.79245	+	3.10462i	−0.434733	+	0.752980i	0.562541	+	0.826770i	$0.309824\pi$
$18$	−7.75547	+	1.15039i	−1.82798	+	0.271148i
$19$	−5.83481	+	1.56343i	−1.33860	+	0.358676i	−0.855914	−	0.517119i	$-0.827005\pi$
$19$	−5.83481	+	1.56343i	−1.33860	+	0.358676i	−0.482684	+	0.875795i	$0.660338\pi$
$20$	3.13025	+	3.13025i	0.699945	+	0.699945i
$21$	0.0991412	−	1.72921i	0.0216344	−	0.377345i
$22$	6.06444	+	10.5039i	1.29294	+	2.23944i
$23$	−8.61675			−1.79672			−0.898359	−	0.439263i	$-0.855240\pi$
$23$	−8.61675			−1.79672			−0.898359	+	0.439263i	$0.855240\pi$
$24$	12.7897	+	0.733273i	2.61068	+	0.149679i
$25$	3.60267	−	2.08000i	0.720533	−	0.416000i
$26$	−9.00113	−	2.78761i	−1.76527	−	0.546695i
$27$	−2.99196	−	4.24831i	−0.575804	−	0.817588i
$28$	−1.25012	+	4.66550i	−0.236250	+	0.881696i
$29$	−2.94524	−	1.70044i	−0.546918	−	0.315763i	0.200960	−	0.979599i	$-0.435594\pi$
$29$	−2.94524	−	1.70044i	−0.546918	−	0.315763i	−0.747878	+	0.663836i	$0.768927\pi$
$30$	−1.30138	+	3.93931i	−0.237599	+	0.719217i
$31$	0.515850	−	0.138221i	0.0926493	−	0.0248253i	−0.212197	−	0.977227i	$-0.568062\pi$
$31$	0.515850	−	0.138221i	0.0926493	−	0.0248253i	0.304846	+	0.952402i	$0.401395\pi$
$32$	−10.1212	−	2.71195i	−1.78918	−	0.479410i
$33$	−4.41107	+	6.71997i	−0.767868	+	1.16980i
$34$	9.04969	+	2.42486i	1.55201	+	0.415860i
$35$	−0.793725	−	0.458257i	−0.134164	−	0.0774597i
$36$	5.76342	+	13.2947i	0.960570	+	2.21579i
$37$	2.89405	+	0.775458i	0.475778	+	0.127484i	0.488736	−	0.872432i	$-0.337458\pi$
$37$	2.89405	+	0.775458i	0.475778	+	0.127484i	−0.0129578	+	0.999916i	$0.504125\pi$
$38$	7.89343	+	13.6718i	1.28048	+	2.21786i
$39$	−1.03192	−	6.15915i	−0.165239	−	0.986254i
$40$	3.38938	−	5.87059i	0.535909	−	0.928221i
$41$	1.10671	−	1.10671i	0.172838	−	0.172838i	−0.615387	−	0.788225i	$-0.711000\pi$
$41$	1.10671	−	1.10671i	0.172838	−	0.172838i	0.788225	+	0.615387i	$0.211000\pi$
$42$	−4.43226	+	0.919382i	−0.683913	+	0.141864i
$43$		−	1.72852i		−	0.263597i	−0.991277	−	0.131798i	$-0.957925\pi$
$43$		−	1.72852i		−	0.263597i	0.991277	−	0.131798i	$-0.0420751\pi$
$44$	15.8506	−	15.8506i	2.38957	−	2.38957i
$45$	−2.71979	+	0.403432i	−0.405442	+	0.0601401i
$46$	5.82845	+	21.7521i	0.859357	+	3.20717i
$47$	2.06096	−	7.69162i	0.300623	−	1.12194i	−0.636026	−	0.771668i	$-0.719423\pi$
$47$	2.06096	−	7.69162i	0.300623	−	1.12194i	0.936648	−	0.350271i	$-0.113910\pi$
$48$	−3.40163	−	16.3990i	−0.490983	−	2.36699i
$49$		−	1.00000i		−	0.142857i
$50$	−7.68761	−	7.68761i	−1.08719	−	1.08719i
$51$	1.26113	+	6.07981i	0.176594	+	0.851344i
$52$	−0.670809	+	17.4022i	−0.0930245	+	2.41325i
$53$			14.0127i			1.92479i	0.271657	+	0.962394i	$0.412428\pi$
$53$			14.0127i			1.92479i	−0.271657	+	0.962394i	$0.587572\pi$
$54$	−8.70061	+	10.4265i	−1.18400	+	1.41886i
$55$	2.12675	+	3.68365i	0.286771	+	0.496703i
$56$	7.39625			0.988365
$57$	−5.74141	+	8.74667i	−0.760469	+	1.15852i
$58$	−2.30038	+	8.58513i	−0.302055	+	1.12728i
$59$	1.95236	−	7.28631i	0.254176	−	0.948596i	−0.714372	−	0.699767i	$-0.753287\pi$
$59$	1.95236	−	7.28631i	0.254176	−	0.948596i	0.968547	−	0.248830i	$-0.0800460\pi$
$60$	7.65494	+	0.438882i	0.988248	+	0.0566594i
$61$	13.4093			1.71688			0.858441	−	0.512913i	$-0.171434\pi$
$61$	13.4093			1.71688			0.858441	+	0.512913i	$0.171434\pi$
$62$	−0.697850	−	1.20871i	−0.0886271	−	0.153507i
$63$	−1.86497	−	2.34987i	−0.234964	−	0.296055i
$64$			8.04513i			1.00564i
$65$	−3.15663	−	0.977594i	−0.391532	−	0.121256i
$66$	19.9475	+	6.58981i	2.45537	+	0.811150i
$67$	−9.24196	−	9.24196i	−1.12908	−	1.12908i	−0.990326	−	0.138759i	$-0.955689\pi$
$67$	−9.24196	−	9.24196i	−1.12908	−	1.12908i	−0.138759	−	0.990326i	$-0.544311\pi$
$68$		−	17.3154i		−	2.09979i
$69$	−11.1401	+	9.93196i	−1.34111	+	1.19567i
$70$	−0.619939	+	2.31364i	−0.0740968	+	0.276533i
$71$	0.0984490	+	0.367417i	0.0116837	+	0.0436043i	0.971522	−	0.236951i	$-0.0761481\pi$
$71$	0.0984490	+	0.367417i	0.0116837	+	0.0436043i	−0.959838	+	0.280555i	$0.909481\pi$
$72$	17.3802	−	13.7938i	2.04828	−	1.62561i
$73$	0.807556	−	0.807556i	0.0945172	−	0.0945172i	−0.658267	−	0.752784i	$-0.728710\pi$
$73$	0.807556	−	0.807556i	0.0945172	−	0.0945172i	0.752784	+	0.658267i	$0.228710\pi$
$74$		−	7.83023i		−	0.910246i
$75$	2.26019	−	6.84166i	0.260985	−	0.790007i
$76$	20.6311	−	20.6311i	2.36655	−	2.36655i
$77$	−2.32048	+	4.01919i	−0.264443	+	0.458029i
$78$	−14.8501	+	6.77107i	−1.68144	+	0.766672i
$79$	1.94902	+	3.37579i	0.219281	+	0.379806i	0.954588	−	0.297928i	$-0.0962954\pi$
$79$	1.94902	+	3.37579i	0.219281	+	0.379806i	−0.735307	+	0.677734i	$0.762962\pi$
$80$	−8.56027	−	2.29372i	−0.957067	−	0.256445i
$81$	−8.76488	−	2.04375i	−0.973875	−	0.227084i
$82$	−3.54234	−	2.04517i	−0.391186	−	0.225851i
$83$	−5.13815	−	1.37676i	−0.563985	−	0.151119i	−0.0344484	−	0.999406i	$-0.510967\pi$
$83$	−5.13815	−	1.37676i	−0.563985	−	0.151119i	−0.529536	+	0.848287i	$0.677634\pi$
$84$	3.76141	+	7.47267i	0.410403	+	0.815335i
$85$	3.17366	+	0.850380i	0.344232	+	0.0922366i
$86$	−4.36346	+	1.16918i	−0.470523	+	0.126076i
$87$	−5.76771	+	1.19639i	−0.618363	+	0.128267i
$88$	−29.7269	−	17.1628i	−3.16890	−	1.82956i
$89$	2.00933	−	7.49892i	0.212989	−	0.794884i	−0.773876	−	0.633337i	$-0.781685\pi$
$89$	2.00933	−	7.49892i	0.212989	−	0.794884i	0.986865	−	0.161548i	$-0.0516485\pi$
$90$	2.85811	+	6.59292i	0.301271	+	0.694955i
$91$	−0.798343	−	3.51606i	−0.0836891	−	0.368583i
$92$	36.0436	−	20.8098i	3.75781	−	2.16957i
$93$	0.507592	−	0.773284i	0.0526349	−	0.0801858i
$94$	−20.8107			−2.14646
$95$	2.76817	+	4.79461i	0.284008	+	0.491916i
$96$	−16.2109	+	8.15986i	−1.65452	+	0.832812i
$97$	−9.89722	−	9.89722i	−1.00491	−	1.00491i	−0.999988	−	0.00492304i	$-0.998433\pi$
$97$	−9.89722	−	9.89722i	−1.00491	−	1.00491i	−0.00492304	−	0.999988i	$-0.501567\pi$
$98$	−2.52439	+	0.676409i	−0.255002	+	0.0683276i
$99$	2.04286	+	13.7722i	0.205315	+	1.38416i
$100$	−10.0466	+	17.4012i	−1.00466	+	1.74012i
$101$	6.65779	−	11.5316i	0.662475	−	1.14744i	−0.317489	−	0.948262i	$-0.602840\pi$
$101$	6.65779	−	11.5316i	0.662475	−	1.14744i	0.979963	−	0.199178i	$-0.0638271\pi$
$102$	14.4948	−	7.29602i	1.43520	−	0.722414i
$103$	5.09168	+	2.93969i	0.501699	+	0.289656i	0.729415	−	0.684072i	$-0.239793\pi$
$103$	5.09168	+	2.93969i	0.501699	+	0.289656i	−0.227716	+	0.973728i	$0.573126\pi$
$104$	26.0056	−	5.90474i	2.55006	−	0.579008i
$105$	−1.55436	+	0.322421i	−0.151690	+	0.0314650i
$106$	35.3735	−	9.47829i	3.43577	−	0.920613i
$107$	−2.76836	+	1.59831i	−0.267627	+	0.154515i	−0.627809	−	0.778367i	$-0.716048\pi$
$107$	−2.76836	+	1.59831i	−0.267627	+	0.154515i	0.360182	+	0.932882i	$0.382715\pi$
$108$	22.7751	+	10.5449i	2.19154	+	1.01468i
$109$	−3.14000	−	3.14000i	−0.300757	−	0.300757i	0.540553	−	0.841310i	$-0.318215\pi$
$109$	−3.14000	−	3.14000i	−0.300757	−	0.300757i	−0.841310	+	0.540553i	$0.818215\pi$
$110$	7.86041	−	7.86041i	0.749461	−	0.749461i
$111$	4.63536	−	2.33323i	0.439969	−	0.221461i
$112$	−2.50265	−	9.34002i	−0.236478	−	0.882549i
$113$	7.21615	−	4.16624i	0.678838	−	0.391927i	−0.120579	−	0.992704i	$-0.538475\pi$
$113$	7.21615	−	4.16624i	0.678838	−	0.391927i	0.799417	+	0.600776i	$0.205142\pi$
$114$	25.9635	+	8.57725i	2.43171	+	0.803333i
$115$	2.04399	+	7.62829i	0.190603	+	0.711341i
$116$	16.4265			1.52516
$117$	−8.43335	−	6.77338i	−0.779663	−	0.626199i
$118$	−19.7141			−1.81483
$119$	0.927841	+	3.46275i	0.0850550	+	0.317430i
$120$	−2.38470	−	11.4964i	−0.217692	−	1.04948i
$121$	9.12661	−	5.26925i	0.829692	−	0.479023i
$122$	−9.07015	−	33.8502i	−0.821172	−	3.06466i
$123$	0.155168	−	2.70642i	0.0139910	−	0.244030i
$124$	−1.82397	+	1.82397i	−0.163798	+	0.163798i
$125$	−5.93636	−	5.93636i	−0.530964	−	0.530964i
$126$	−4.67050	+	6.29739i	−0.416081	+	0.561016i
$127$	9.22540	−	5.32629i	0.818622	−	0.472632i	−0.0313190	−	0.999509i	$-0.509971\pi$
$127$	9.22540	−	5.32629i	0.818622	−	0.472632i	0.849941	+	0.526878i	$0.176637\pi$
$128$	0.0667591	−	0.0178881i	0.00590073	−	0.00158110i
$129$	−1.99235	−	2.23470i	−0.175416	−	0.196754i
$130$	−0.332658	+	8.62982i	−0.0291760	+	0.756885i
$131$	3.60980	+	2.08412i	0.315390	+	0.182091i	0.649336	−	0.760502i	$-0.275047\pi$
$131$	3.60980	+	2.08412i	0.315390	+	0.182091i	−0.333946	+	0.942592i	$0.608380\pi$
$132$	2.22237	−	38.7623i	0.193432	−	3.37383i
$133$	−3.02032	+	5.23135i	−0.261895	+	0.453615i
$134$	−17.0790	+	29.5817i	−1.47540	+	2.55547i
$135$	−3.05124	+	3.65649i	−0.262609	+	0.314701i
$136$	−25.6113	+	6.86254i	−2.19615	+	0.588458i
$137$	2.84860	+	2.84860i	0.243372	+	0.243372i	0.818244	−	0.574871i	$-0.194948\pi$
$137$	2.84860	+	2.84860i	0.243372	+	0.243372i	−0.574871	+	0.818244i	$0.694948\pi$
$138$	32.6074	+	21.4039i	2.77573	+	1.82202i
$139$	7.02948	+	12.1754i	0.596233	+	1.03271i	0.993372	+	0.114947i	$0.0366697\pi$
$139$	7.02948	+	12.1754i	0.596233	+	1.03271i	−0.397139	+	0.917758i	$0.629997\pi$
$140$	4.42684			0.374136
$141$	−6.20113	−	12.3196i	−0.522229	−	1.03750i
$142$	0.860912	−	0.497048i	0.0722461	−	0.0417113i
$143$	−4.95024	+	15.9842i	−0.413960	+	1.33667i
$144$	−23.2998	−	17.2804i	−1.94165	−	1.44004i
$145$	−0.806726	+	3.01074i	−0.0669950	+	0.250029i
$146$	−2.58482	−	1.49235i	−0.213921	−	0.123508i
$147$	−1.15263	−	1.29284i	−0.0950676	−	0.106632i
$148$	−13.9785	+	3.74552i	−1.14902	+	0.307880i
$149$	11.3350	+	3.03720i	0.928598	+	0.248817i	0.691257	−	0.722609i	$-0.257057\pi$
$149$	11.3350	+	3.03720i	0.928598	+	0.248817i	0.237341	+	0.971426i	$0.423724\pi$
$150$	−18.7998	−	1.07786i	−1.53500	−	0.0880065i
$151$	−20.4143	−	5.46998i	−1.66129	−	0.445141i	−0.698547	−	0.715564i	$-0.746170\pi$
$151$	−20.4143	−	5.46998i	−1.66129	−	0.445141i	−0.962742	+	0.270423i	$0.912836\pi$
$152$	−38.6923	−	22.3390i	−3.13836	−	1.81193i
$153$	8.63823	+	6.40660i	0.698360	+	0.517943i
$154$	11.7156	+	3.13918i	0.944070	+	0.252963i
$155$	−0.244731	−	0.423886i	−0.0196573	−	0.0340474i
$156$	19.1911	+	23.2714i	1.53652	+	1.86321i
$157$	−11.4639	+	19.8560i	−0.914916	+	1.58468i	−0.107892	+	0.994163i	$0.534410\pi$
$157$	−11.4639	+	19.8560i	−0.914916	+	1.58468i	−0.807024	+	0.590519i	$0.798923\pi$
$158$	7.20349	−	7.20349i	0.573079	−	0.573079i
$159$	16.1515	+	18.1161i	1.28090	+	1.43670i
$160$			9.60342i			0.759217i
$161$	−6.09296	+	6.09296i	−0.480193	+	0.480193i
$162$	0.769407	+	23.5084i	0.0604503	+	1.84699i
$163$	−3.98125	−	14.8582i	−0.311836	−	1.16379i	−0.926900	−	0.375309i	$-0.877536\pi$
$163$	−3.98125	−	14.8582i	−0.311836	−	1.16379i	0.615064	−	0.788477i	$-0.289130\pi$
$164$	−1.95658	+	7.30205i	−0.152783	+	0.570195i
$165$	6.99545	+	2.31100i	0.544595	+	0.179911i
$166$			13.9019i			1.07900i
$167$	−0.919693	−	0.919693i	−0.0711680	−	0.0711680i	0.670627	−	0.741795i	$-0.266025\pi$
$167$	−0.919693	−	0.919693i	−0.0711680	−	0.0711680i	−0.741795	+	0.670627i	$0.766025\pi$
$168$	9.56216	−	8.52516i	0.737737	−	0.657730i
$169$	−5.61404	−	11.7253i	−0.431849	−	0.901946i
$170$		−	8.58676i		−	0.658575i
$171$	2.65897	+	17.9258i	0.203337	+	1.37082i
$172$	4.17444	+	7.23034i	0.318298	+	0.551308i
$173$	−13.7185			−1.04300			−0.521500	−	0.853251i	$-0.674627\pi$
$173$	−13.7185			−1.04300			−0.521500	+	0.853251i	$0.674627\pi$
$174$	6.92149	+	13.7507i	0.524717	+	1.04244i
$175$	1.07669	−	4.01825i	0.0813899	−	0.303751i
$176$	−11.6147	+	43.3467i	−0.875491	+	3.26738i
$177$	−5.87435	−	11.6704i	−0.441543	−	0.877200i
$178$	−20.2893			−1.52075
$179$	−0.846580	−	1.46632i	−0.0632764	−	0.109598i	0.832652	−	0.553797i	$-0.186822\pi$
$179$	−0.846580	−	1.46632i	−0.0632764	−	0.109598i	−0.895928	+	0.444199i	$0.853488\pi$
$180$	10.4025	−	8.25593i	0.775355	−	0.615361i
$181$			9.46664i			0.703650i	0.936066	+	0.351825i	$0.114439\pi$
$181$			9.46664i			0.703650i	−0.936066	+	0.351825i	$0.885561\pi$
$182$	−8.33589	+	4.39362i	−0.617898	+	0.325677i
$183$	17.3360	−	15.4560i	1.28152	−	1.14254i
$184$	−45.0651	−	45.0651i	−3.32224	−	3.32224i
$185$		−	2.74601i		−	0.201890i
$186$	−2.29541	−	0.758306i	−0.168308	−	0.0556017i
$187$	4.30607	−	16.0705i	0.314891	−	1.17519i
$188$	9.95462	+	37.1511i	0.726015	+	2.70953i
$189$	−5.11965	−	0.888373i	−0.372400	−	0.0646196i
$190$	10.2311	−	10.2311i	0.742239	−	0.742239i
$191$		−	9.85540i		−	0.713112i	−0.934274	−	0.356556i	$-0.883951\pi$
$191$		−	9.85540i		−	0.713112i	0.934274	−	0.356556i	$-0.116049\pi$
$192$	9.27309	+	10.4011i	0.669228	+	0.750633i
$193$	6.57769	−	6.57769i	0.473473	−	0.473473i	−0.429564	−	0.903036i	$-0.641333\pi$
$193$	6.57769	−	6.57769i	0.473473	−	0.473473i	0.903036	+	0.429564i	$0.141333\pi$
$194$	−18.2899	+	31.6790i	−1.31314	+	2.27442i
$195$	−5.20782	+	2.37456i	−0.372940	+	0.170046i
$196$	2.41504	+	4.18297i	0.172503	+	0.298784i
$197$	−20.7434	−	5.55817i	−1.47790	−	0.396003i	−0.572270	−	0.820065i	$-0.693937\pi$
$197$	−20.7434	−	5.55817i	−1.47790	−	0.396003i	−0.905633	+	0.424062i	$0.860604\pi$
$198$	33.3846	−	14.4726i	2.37254	−	1.02852i
$199$	−9.94014	−	5.73894i	−0.704638	−	0.406823i	0.104435	−	0.994532i	$-0.466697\pi$
$199$	−9.94014	−	5.73894i	−0.704638	−	0.406823i	−0.809072	+	0.587709i	$0.800030\pi$
$200$	29.7200	+	7.96344i	2.10152	+	0.563101i
$201$	−22.6010	−	1.29579i	−1.59415	−	0.0913977i
$202$	−33.6137	−	9.00677i	−2.36505	−	0.633714i
$203$	−3.28499	+	0.880211i	−0.230561	+	0.0617787i
$204$	−19.9583	−	22.3860i	−1.39736	−	1.56733i
$205$	−1.24227	−	0.717227i	−0.0867641	−	0.0500933i
$206$	3.97686	−	14.8418i	0.277081	−	1.03408i
$207$	−2.95444	+	25.6809i	−0.205348	+	1.78494i
$208$	−16.2560	−	30.8421i	−1.12715	−	2.13851i
$209$	24.2785	−	14.0172i	1.67938	−	0.969589i
$210$	1.86530	+	3.70573i	0.128718	+	0.255720i
$211$	20.8968			1.43859			0.719296	−	0.694704i	$-0.244464\pi$
$211$	20.8968			1.43859			0.719296	+	0.694704i	$0.244464\pi$
$212$	−33.8412	−	58.6146i	−2.32422	−	4.02567i
$213$	0.550776	+	0.361535i	0.0377385	+	0.0247720i
$214$	5.90731	+	5.90731i	0.403815	+	0.403815i
$215$	−1.53023	+	0.410024i	−0.104361	+	0.0279634i
$216$	6.57063	−	37.8662i	0.447074	−	2.57647i
$217$	0.267023	−	0.462498i	0.0181267	−	0.0313964i
$218$	−5.80266	+	10.0505i	−0.393005	+	0.680705i
$219$	0.113225	−	1.97486i	0.00765102	−	0.133448i
$220$	−17.7923	−	10.2724i	−1.19956	−	0.692564i
$221$	6.02680	+	11.4345i	0.405407	+	0.769166i
$222$	−9.02539	−	10.1232i	−0.605744	−	0.679427i
$223$	−2.75407	+	0.737950i	−0.184426	+	0.0494168i	−0.349850	−	0.936806i	$-0.613767\pi$
$223$	−2.75407	+	0.737950i	−0.184426	+	0.0494168i	0.165424	+	0.986223i	$0.447101\pi$
$224$	−9.07438	+	5.23909i	−0.606307	+	0.350052i
$225$	−4.96386	−	11.4504i	−0.330924	−	0.763357i
$226$	−15.3983	−	15.3983i	−1.02428	−	1.02428i
$227$	5.48148	−	5.48148i	0.363819	−	0.363819i	−0.501398	−	0.865217i	$-0.667181\pi$
$227$	5.48148	−	5.48148i	0.363819	−	0.363819i	0.865217	+	0.501398i	$0.167181\pi$
$228$	2.89262	−	50.4528i	0.191568	−	3.34132i
$229$	1.06220	+	3.96418i	0.0701921	+	0.261960i	0.992100	−	0.125448i	$-0.0400369\pi$
$229$	1.06220	+	3.96418i	0.0701921	+	0.261960i	−0.921908	+	0.387409i	$0.873370\pi$
$230$	17.8742	−	10.3197i	1.17859	−	0.680459i
$231$	1.63264	+	7.87083i	0.107420	+	0.517863i
$232$	−6.51025	−	24.2966i	−0.427419	−	1.59515i
$233$	24.2863			1.59105			0.795525	−	0.605921i	$-0.207195\pi$
$233$	24.2863			1.59105			0.795525	+	0.605921i	$0.207195\pi$
$234$	−11.3943	+	25.8706i	−0.744866	+	1.69122i
$235$	−7.29817			−0.476080
$236$	9.43005	+	35.1934i	0.613844	+	2.29090i
$237$	6.41082	+	2.11786i	0.416427	+	0.137570i
$238$	8.11373	−	4.68447i	0.525935	−	0.303649i
$239$	−3.78086	−	14.1104i	−0.244563	−	0.912723i	−0.973602	−	0.228251i	$-0.926699\pi$
$239$	−3.78086	−	14.1104i	−0.244563	−	0.912723i	0.729039	−	0.684472i	$-0.239967\pi$
$240$	−13.7109	+	6.90144i	−0.885033	+	0.445486i
$241$	−3.92680	+	3.92680i	−0.252947	+	0.252947i	−0.822178	−	0.569231i	$-0.807241\pi$
$241$	−3.92680	+	3.92680i	−0.252947	+	0.252947i	0.569231	+	0.822178i	$0.307241\pi$
$242$	−19.4750	−	19.4750i	−1.25190	−	1.25190i
$243$	−13.6873	+	7.46045i	−0.878040	+	0.478588i
$244$	−56.0906	+	32.3839i	−3.59083	+	2.07317i
$245$	−0.885285	+	0.237212i	−0.0565588	+	0.0151549i
$246$	−6.93702	+	1.43894i	−0.442288	+	0.0917435i
$247$	−6.44320	+	20.8050i	−0.409971	+	1.32379i
$248$	3.42075	+	1.97497i	0.217218	+	0.125411i
$249$	−8.22971	+	4.14247i	−0.521536	+	0.262518i
$250$	−10.9703	+	19.0011i	−0.693822	+	1.20173i
$251$	−4.88928	+	8.46847i	−0.308608	+	0.534525i	−0.978058	−	0.208332i	$-0.933197\pi$
$251$	−4.88928	+	8.46847i	−0.308608	+	0.534525i	0.669450	+	0.742857i	$0.266530\pi$
$252$	13.4761	+	5.32544i	0.848918	+	0.335471i
$253$	38.6274	−	10.3502i	2.42848	−	0.650710i
$254$	−19.6858	−	19.6858i	−1.23520	−	1.23520i
$255$	5.08321	−	2.55866i	0.318323	−	0.160230i
$256$	7.95482	+	13.7782i	0.497176	+	0.861135i
$257$	−8.18966			−0.510857			−0.255428	−	0.966828i	$-0.582216\pi$
$257$	−8.18966			−0.510857			−0.255428	+	0.966828i	$0.582216\pi$
$258$	−4.29361	+	6.54103i	−0.267308	+	0.407227i
$259$	2.59473	−	1.49807i	0.161229	−	0.0930855i
$260$	15.5650	−	3.53414i	0.965301	−	0.219178i
$261$	−6.07772	+	8.19480i	−0.376202	+	0.507245i
$262$	2.81944	−	10.5223i	0.174185	−	0.650068i
$263$	−12.8141	−	7.39823i	−0.790152	−	0.456194i	0.0498641	−	0.998756i	$-0.484121\pi$
$263$	−12.8141	−	7.39823i	−0.790152	−	0.456194i	−0.840016	+	0.542562i	$0.817455\pi$
$264$	−58.2146	+	12.0754i	−3.58286	+	0.743191i
$265$	12.4052	−	3.32397i	0.762046	−	0.204190i
$266$	15.2489	+	4.08594i	0.934972	+	0.250525i
$267$	−6.04577	−	12.0109i	−0.369995	−	0.735057i
$268$	60.9785	+	16.3391i	3.72486	+	0.998072i
$269$	−22.2758	−	12.8609i	−1.35818	−	0.784145i	−0.368801	−	0.929508i	$-0.620232\pi$
$269$	−22.2758	−	12.8609i	−1.35818	−	0.784145i	−0.989378	+	0.145363i	$0.953565\pi$
$270$	11.2943	+	5.22924i	0.687349	+	0.318242i
$271$	27.0677	+	7.25276i	1.64424	+	0.440574i	0.957993	−	0.286792i	$-0.0925889\pi$
$271$	27.0677	+	7.25276i	1.64424	+	0.440574i	0.686250	+	0.727366i	$0.259256\pi$
$272$	17.3321	+	30.0201i	1.05091	+	1.82023i
$273$	−5.08485	−	3.62550i	−0.307749	−	0.219425i
$274$	5.26416	−	9.11780i	0.318020	−	0.550826i
$275$	−13.6517	+	13.6517i	−0.823227	+	0.823227i
$276$	22.6126	−	68.4488i	1.36112	−	4.12014i
$277$		−	16.9171i		−	1.01645i	−0.861224	−	0.508225i	$-0.830302\pi$
$277$		−	16.9171i		−	1.01645i	0.861224	−	0.508225i	$-0.169698\pi$
$278$	25.9807	−	25.9807i	1.55822	−	1.55822i
$279$	−0.235077	−	1.58480i	−0.0140737	−	0.0948795i
$280$	−1.75447	−	6.54779i	−0.104850	−	0.391305i
$281$	2.72300	−	10.1624i	0.162441	−	0.606236i	−0.835912	−	0.548863i	$-0.815061\pi$
$281$	2.72300	−	10.1624i	0.162441	−	0.606236i	0.998353	−	0.0573733i	$-0.0182725\pi$
$282$	−26.9049	+	23.9871i	−1.60217	+	1.42841i
$283$			1.22417i			0.0727694i	0.999338	+	0.0363847i	$0.0115842\pi$
$283$			1.22417i			0.0727694i	−0.999338	+	0.0363847i	$0.988416\pi$
$284$	−1.29913	−	1.29913i	−0.0770895	−	0.0770895i
$285$	9.10523	+	3.00798i	0.539347	+	0.178177i
$286$	43.6988	+	1.68448i	2.58397	+	0.0996053i
$287$		−	1.56512i		−	0.0923860i
$288$	−11.5528	+	29.2346i	−0.680756	+	1.72267i
$289$	2.07424	+	3.59269i	0.122014	+	0.211335i
$290$	8.14597			0.478348
$291$	−24.2034	−	1.38766i	−1.41883	−	0.0813460i
$292$	−1.42770	+	5.32826i	−0.0835500	+	0.311813i
$293$	−1.37477	+	5.13071i	−0.0803149	+	0.299739i	−0.994386	−	0.105815i	$-0.966255\pi$
$293$	−1.37477	+	5.13071i	−0.0803149	+	0.299739i	0.914071	+	0.405554i	$0.132922\pi$
$294$	−2.48398	+	3.78419i	−0.144869	+	0.220698i
$295$	−6.91358			−0.402524
$296$	11.0801	+	19.1913i	0.644017	+	1.11547i
$297$	18.5154	+	15.4506i	1.07437	+	0.896533i
$298$		−	30.6683i		−	1.77657i
$299$	−16.5589	+	26.2875i	−0.957627	+	1.52024i
$300$	7.06856	+	34.0769i	0.408103	+	1.96743i
$301$	−1.22225	−	1.22225i	−0.0704491	−	0.0704491i
$302$			55.2335i			3.17833i
$303$	−4.68428	−	22.5825i	−0.269105	−	1.29733i
$304$	−15.1176	+	56.4197i	−0.867055	+	3.23589i
$305$	−3.18083	−	11.8710i	−0.182134	−	0.679733i
$306$	10.3298	−	26.1398i	0.590515	−	1.49431i
$307$	−9.29517	+	9.29517i	−0.530503	+	0.530503i	−0.920722	−	0.390219i	$-0.872399\pi$
$307$	−9.29517	+	9.29517i	−0.530503	+	0.530503i	0.390219	+	0.920722i	$0.372399\pi$
$308$		−	22.4162i		−	1.27728i
$309$	9.97111	−	2.06830i	0.567237	−	0.117662i
$310$	−0.904517	+	0.904517i	−0.0513731	+	0.0513731i
$311$	6.75475	−	11.6996i	0.383026	−	0.663421i	−0.608467	−	0.793579i	$-0.708215\pi$
$311$	6.75475	−	11.6996i	0.383026	−	0.663421i	0.991493	+	0.130158i	$0.0415485\pi$
$312$	26.8151	−	37.6088i	1.51811	−	2.12918i
$313$	7.05641	+	12.2221i	0.398852	+	0.690831i	0.993585	−	0.113092i	$-0.0360755\pi$
$313$	7.05641	+	12.2221i	0.398852	+	0.690831i	−0.594733	+	0.803923i	$0.702742\pi$
$314$	57.8786	+	15.5085i	3.26628	+	0.875196i
$315$	−1.63791	+	2.20845i	−0.0922858	+	0.124432i
$316$	−16.3053	−	9.41390i	−0.917248	−	0.529573i
$317$	17.0133	+	4.55869i	0.955561	+	0.256042i	0.702720	−	0.711466i	$-0.251969\pi$
$317$	17.0133	+	4.55869i	0.955561	+	0.256042i	0.252840	+	0.967508i	$0.418635\pi$
$318$	34.8072	−	53.0266i	1.95189	−	2.97358i
$319$	15.2455	+	4.08502i	0.853585	+	0.228717i
$320$	7.12224	−	1.90840i	0.398145	−	0.106683i
$321$	−1.73678	+	5.25727i	−0.0969375	+	0.293432i
$322$	19.5024	+	11.2597i	1.08682	+	0.627478i
$323$	5.60475	−	20.9172i	0.311857	−	1.16387i
$324$	41.5990	−	12.6186i	2.31105	−	0.701031i
$325$	0.577748	−	14.9880i	0.0320477	−	0.831383i
$326$	−34.8150	+	20.1005i	−1.92823	+	1.11326i
$327$	−7.67878	−	0.440249i	−0.424637	−	0.0243458i
$328$	11.5760			0.639177
$329$	−3.98148	−	6.89612i	−0.219506	−	0.380195i
$330$	1.10208	−	19.2224i	0.0606677	−	1.05816i
$331$	18.2315	+	18.2315i	1.00209	+	1.00209i	0.999998	+	0.00209635i	$0.000667289\pi$
$331$	18.2315	+	18.2315i	1.00209	+	1.00209i	0.00209635	+	0.999998i	$0.499333\pi$
$332$	24.8177	−	6.64987i	1.36205	−	0.364959i
$333$	3.30342	−	8.35937i	0.181026	−	0.458090i
$334$	−1.69958	+	2.94375i	−0.0929967	+	0.161075i
$335$	−5.98947	+	10.3741i	−0.327240	+	0.566796i
$336$	−14.0011	−	9.19052i	−0.763825	−	0.501384i
$337$	−22.0287	−	12.7183i	−1.19998	−	0.692809i	−0.239430	−	0.970914i	$-0.576961\pi$
$337$	−22.0287	−	12.7183i	−1.19998	−	0.692809i	−0.960551	+	0.278104i	$0.910294\pi$
$338$	−25.8018	+	22.1031i	−1.40344	+	1.20225i
$339$	4.52717	−	13.7039i	0.245882	−	0.744292i
$340$	−15.3290	+	4.10740i	−0.831333	+	0.222755i
$341$	−2.14644	+	1.23924i	−0.116236	+	0.0671089i
$342$	43.4531	−	18.8374i	2.34968	−	1.01861i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	9.04004	−	9.04004i	0.487406	−	0.487406i
$345$	11.4352	+	7.50618i	0.615649	+	0.404119i
$346$	9.27933	+	34.6309i	0.498860	+	1.86177i
$347$	3.92097	−	2.26377i	0.210489	−	0.121526i	−0.391050	−	0.920370i	$-0.627888\pi$
$347$	3.92097	−	2.26377i	0.210489	−	0.121526i	0.601538	+	0.798844i	$0.294555\pi$
$348$	21.2368	−	18.9337i	1.13841	−	1.01495i
$349$	−4.53175	−	16.9127i	−0.242579	−	0.905317i	−0.974585	−	0.224019i	$-0.928082\pi$
$349$	−4.53175	−	16.9127i	−0.242579	−	0.905317i	0.732006	−	0.681299i	$-0.238584\pi$
$350$	−10.8719			−0.581129
$351$	−18.7102	+	0.963668i	−0.998676	+	0.0514368i
$352$	48.6288			2.59193
$353$	6.14343	+	22.9276i	0.326982	+	1.22031i	0.912304	+	0.409513i	$0.134301\pi$
$353$	6.14343	+	22.9276i	0.326982	+	1.22031i	−0.585322	+	0.810801i	$0.699032\pi$
$354$	−25.4872	+	22.7231i	−1.35463	+	1.20772i
$355$	0.301915	−	0.174311i	0.0160240	−	0.00925146i
$356$	9.70523	+	36.2204i	0.514376	+	1.91968i
$357$	5.19083	+	3.40732i	0.274728	+	0.180335i
$358$	−3.12893	+	3.12893i	−0.165369	+	0.165369i
$359$	−12.7928	−	12.7928i	−0.675181	−	0.675181i	0.283725	−	0.958906i	$-0.408430\pi$
$359$	−12.7928	−	12.7928i	−0.675181	−	0.675181i	−0.958906	+	0.283725i	$0.908430\pi$
$360$	−16.3342	−	12.1144i	−0.860890	−	0.638484i
$361$	15.1462	−	8.74467i	0.797169	−	0.460246i
$362$	23.8975	−	6.40331i	1.25602	−	0.336551i
$363$	5.72574	−	17.3319i	0.300523	−	0.909691i
$364$	11.8309	+	12.7795i	0.620106	+	0.669829i
$365$	−0.906479	−	0.523356i	−0.0474473	−	0.0273937i
$366$	−50.7432	−	33.3084i	−2.65239	−	1.74106i
$367$	9.24233	−	16.0082i	0.482446	−	0.835620i	−0.517351	−	0.855773i	$-0.673082\pi$
$367$	9.24233	−	16.0082i	0.482446	−	0.835620i	0.999797	+	0.0201528i	$0.00641526\pi$
$368$	−41.6599	+	72.1570i	−2.17167	+	3.76144i
$369$	−2.91890	−	3.67782i	−0.151952	−	0.191460i
$370$	−6.93199	+	1.85742i	−0.360377	+	0.0965627i
$371$	9.90845	+	9.90845i	0.514421	+	0.514421i
$372$	−0.255734	+	4.46048i	−0.0132592	+	0.231265i
$373$	2.78239	+	4.81924i	0.144067	+	0.249531i	0.929024	−	0.370019i	$-0.120649\pi$
$373$	2.78239	+	4.81924i	0.144067	+	0.249531i	−0.784958	+	0.619549i	$0.787315\pi$
$374$	−43.4808			−2.24834
$375$	−14.5172	−	0.832318i	−0.749665	−	0.0429807i
$376$	51.0054	−	29.4480i	2.63040	−	1.51866i
$377$	−10.8475	+	5.71742i	−0.558675	+	0.294462i
$378$	1.22037	+	13.5249i	0.0627692	+	0.695646i
$379$	−2.35205	+	8.77796i	−0.120817	+	0.450893i	−0.999656	−	0.0262240i	$-0.991652\pi$
$379$	−2.35205	+	8.77796i	−0.120817	+	0.450893i	0.878840	+	0.477117i	$0.158318\pi$
$380$	−23.1583	−	13.3705i	−1.18800	−	0.685891i
$381$	5.78771	−	17.5195i	0.296514	−	0.897554i
$382$	−24.8789	+	6.66628i	−1.27291	+	0.341076i
$383$	25.3644	+	6.79637i	1.29606	+	0.347278i	0.839959	−	0.542649i	$-0.182579\pi$
$383$	25.3644	+	6.79637i	1.29606	+	0.347278i	0.456102	+	0.889928i	$0.349245\pi$
$384$	0.0656905	−	0.100075i	0.00335226	−	0.00510694i
$385$	4.10857	+	1.10089i	0.209392	+	0.0561065i
$386$	−21.0539	−	12.1555i	−1.07161	−	0.618697i
$387$	−5.15157	−	0.592661i	−0.261869	−	0.0301266i
$388$	65.3020	+	17.4976i	3.31521	+	0.888307i
$389$	−4.66374	−	8.07784i	−0.236461	−	0.409563i	0.723235	−	0.690602i	$-0.242654\pi$
$389$	−4.66374	−	8.07784i	−0.236461	−	0.409563i	−0.959696	+	0.281039i	$0.909321\pi$
$390$	9.51694	+	11.5404i	0.481909	+	0.584371i
$391$	15.4451	−	26.7517i	0.781092	−	1.35289i
$392$	5.22994	−	5.22994i	0.264152	−	0.264152i
$393$	7.06913	−	1.46635i	0.356590	−	0.0739673i
$394$			56.1239i			2.82748i
$395$	2.52621	−	2.52621i	0.127108	−	0.127108i
$396$	−41.8056	−	52.6751i	−2.10081	−	2.64702i
$397$	−2.55465	−	9.53410i	−0.128214	−	0.478503i	0.871719	−	0.490005i	$-0.163005\pi$
$397$	−2.55465	−	9.53410i	−0.128214	−	0.478503i	−0.999934	+	0.0115027i	$0.996338\pi$
$398$	−7.76374	+	28.9747i	−0.389161	+	1.45237i
$399$	2.12504	+	10.2446i	0.106385	+	0.512872i
$400$		−	40.2251i		−	2.01126i
$401$	24.8946	+	24.8946i	1.24318	+	1.24318i	0.958676	+	0.284500i	$0.0918277\pi$
$401$	24.8946	+	24.8946i	1.24318	+	1.24318i	0.284500	+	0.958676i	$0.408172\pi$
$402$	12.0164	+	57.9302i	0.599324	+	2.88929i
$403$	0.569637	−	1.83935i	0.0283756	−	0.0916243i
$404$			64.3153i			3.19980i
$405$	0.269825	+	8.24422i	0.0134077	+	0.409659i
$406$	4.44399	+	7.69722i	0.220552	+	0.382007i
$407$	−13.9050			−0.689243
$408$	−25.2014	+	38.3927i	−1.24765	+	1.90072i
$409$	−0.754191	+	2.81468i	−0.0372923	+	0.139177i	−0.982062	−	0.188558i	$-0.939619\pi$
$409$	−0.754191	+	2.81468i	−0.0372923	+	0.139177i	0.944770	+	0.327735i	$0.106285\pi$
$410$	−0.970277	+	3.62112i	−0.0479186	+	0.178834i
$411$	6.96618	+	0.399393i	0.343616	+	0.0197006i
$412$	−28.3978			−1.39906
$413$	−3.77167	−	6.53272i	−0.185592	−	0.321454i
$414$	66.8270	−	9.91259i	3.28437	−	0.487177i
$415$			4.87531i			0.239320i
$416$	−27.7234	+	25.6654i	−1.35925	+	1.25835i
$417$	23.1218	+	7.63845i	1.13228	+	0.374057i
$418$	−51.8070	−	51.8070i	−2.53396	−	2.53396i
$419$			1.18244i			0.0577661i	0.999583	+	0.0288830i	$0.00919504\pi$
$419$			1.18244i			0.0577661i	−0.999583	+	0.0288830i	$0.990805\pi$
$420$	5.72320	−	5.10252i	0.279263	−	0.248978i
$421$	7.27964	−	27.1680i	0.354788	−	1.32409i	−0.525964	−	0.850507i	$-0.676295\pi$
$421$	7.27964	−	27.1680i	0.354788	−	1.32409i	0.880751	−	0.473579i	$-0.157038\pi$
$422$	−14.1347	−	52.7516i	−0.688069	−	2.56791i
$423$	−22.2170	−	8.77962i	−1.08023	−	0.426880i
$424$	−73.2854	+	73.2854i	−3.55905	+	3.55905i
$425$			14.9132i			0.723396i
$426$	0.540108	−	1.63492i	0.0261683	−	0.0792121i
$427$	9.48179	−	9.48179i	0.458856	−	0.458856i
$428$	7.71998	−	13.3714i	0.373159	−	0.646331i
$429$	12.0241	+	26.3709i	0.580528	+	1.27320i
$430$	2.07012	+	3.58556i	0.0998302	+	0.172911i
$431$	−11.5341	−	3.09055i	−0.555578	−	0.148867i	−0.0299042	−	0.999553i	$-0.509520\pi$
$431$	−11.5341	−	3.09055i	−0.555578	−	0.148867i	−0.525674	+	0.850686i	$0.676187\pi$
$432$	−50.0409	+	4.51527i	−2.40759	+	0.217241i
$433$	25.1119	+	14.4984i	1.20680	+	0.696748i	0.962059	−	0.272840i	$-0.0879631\pi$
$433$	25.1119	+	14.4984i	1.20680	+	0.696748i	0.244743	+	0.969588i	$0.421296\pi$
$434$	−1.34814	−	0.361234i	−0.0647129	−	0.0173398i
$435$	2.42732	+	4.82227i	0.116381	+	0.231210i
$436$	20.7177	+	5.55130i	0.992199	+	0.265859i
$437$	50.2771	−	13.4717i	2.40508	−	0.644439i
$438$	−5.06189	+	1.04999i	−0.241867	+	0.0501703i
$439$	−33.5193	−	19.3524i	−1.59979	−	0.923640i	−0.991526	−	0.129906i	$-0.958533\pi$
$439$	−33.5193	−	19.3524i	−1.59979	−	0.923640i	−0.608265	−	0.793734i	$-0.708134\pi$
$440$	−8.14245	+	30.3880i	−0.388176	+	1.44869i
$441$	−2.98034	−	0.342872i	−0.141921	−	0.0163272i
$442$	24.7885	−	22.9484i	1.17907	−	1.09154i
$443$	−0.609461	+	0.351873i	−0.0289564	+	0.0167180i	−0.514408	−	0.857545i	$-0.671988\pi$
$443$	−0.609461	+	0.351873i	−0.0289564	+	0.0167180i	0.485452	+	0.874263i	$0.338655\pi$
$444$	−13.7547	+	20.9544i	−0.652770	+	0.994453i
$445$	−7.11533			−0.337299
$446$	3.72575	+	6.45319i	0.176419	+	0.305567i
$447$	18.1551	−	9.13847i	0.858707	−	0.432235i
$448$	5.68877	+	5.68877i	0.268769	+	0.268769i
$449$	9.03388	−	2.42062i	0.426335	−	0.114236i	−0.0392702	−	0.999229i	$-0.512503\pi$
$449$	9.03388	−	2.42062i	0.426335	−	0.114236i	0.465605	+	0.884992i	$0.345837\pi$
$450$	−25.5476	+	20.2758i	−1.20432	+	0.955812i
$451$	−3.63182	+	6.29050i	−0.171016	+	0.296208i
$452$	−20.1233	+	34.8546i	−0.946520	+	1.63942i
$453$	−32.6973	+	16.4583i	−1.53625	+	0.773280i
$454$	−17.5451	−	10.1297i	−0.823434	−	0.475410i
$455$	−2.92334	+	1.54081i	−0.137048	+	0.0722343i
$456$	−75.7717	+	15.7173i	−3.54834	+	0.736029i
$457$	−3.83391	+	1.02729i	−0.179343	+	0.0480547i	−0.347373	−	0.937727i	$-0.612926\pi$
$457$	−3.83391	+	1.02729i	−0.179343	+	0.0480547i	0.168030	+	0.985782i	$0.446259\pi$
$458$	9.28866	−	5.36281i	0.434030	−	0.250588i
$459$	18.5523	−	1.67400i	0.865948	−	0.0781359i
$460$	−26.9726	−	26.9726i	−1.25760	−	1.25760i
$461$	−7.23536	+	7.23536i	−0.336984	+	0.336984i	−0.855231	−	0.518247i	$-0.826585\pi$
$461$	−7.23536	+	7.23536i	−0.336984	+	0.336984i	0.518247	+	0.855231i	$0.326585\pi$
$462$	18.7647	−	9.44532i	0.873014	−	0.439436i
$463$	−4.34694	−	16.2230i	−0.202019	−	0.753946i	−0.990337	−	0.138678i	$-0.955715\pi$
$463$	−4.34694	−	16.2230i	−0.202019	−	0.753946i	0.788318	−	0.615268i	$-0.210952\pi$
$464$	−28.4790	+	16.4424i	−1.32211	+	0.763318i
$465$	−0.804984	−	0.265932i	−0.0373302	−	0.0123323i
$466$	−16.4275	−	61.3082i	−0.760988	−	2.84005i
$467$	0.317382			0.0146867			0.00734335	−	0.999973i	$-0.497663\pi$
$467$	0.317382			0.0146867			0.00734335	+	0.999973i	$0.497663\pi$
$468$	51.6344	+	7.96596i	2.38680	+	0.368227i
$469$	−13.0701			−0.603521
$470$	4.93654	+	18.4234i	0.227706	+	0.849809i
$471$	8.06574	+	38.8843i	0.371650	+	1.79169i
$472$	48.3176	−	27.8962i	2.22400	−	1.28403i
$473$	2.07624	+	7.74864i	0.0954657	+	0.356283i
$474$	1.00998	−	17.6160i	0.0463899	−	0.809127i
$475$	−17.7689	+	17.7689i	−0.815295	+	0.815295i
$476$	−12.2438	−	12.2438i	−0.561194	−	0.561194i
$477$	41.7626	+	4.80455i	1.91218	+	0.219985i
$478$	−33.0627	+	19.0887i	−1.51225	+	0.873098i
$479$	−6.88654	+	1.84524i	−0.314654	+	0.0843113i	−0.412690	−	0.910872i	$-0.635411\pi$
$479$	−6.88654	+	1.84524i	−0.314654	+	0.0843113i	0.0980358	+	0.995183i	$0.468744\pi$
$480$	11.0692	+	12.4157i	0.505238	+	0.566696i
$481$	7.92725	−	7.33878i	0.361451	−	0.334620i
$482$	12.5689	+	7.25665i	0.572497	+	0.330531i
$483$	−0.854275	+	14.9002i	−0.0388709	+	0.677982i
$484$	−25.4509	+	44.0823i	−1.15686	+	2.00374i
$485$	−6.41413	+	11.1096i	−0.291251	+	0.504461i
$486$	28.0913	+	29.5057i	1.27425	+	1.33841i
$487$	35.4779	−	9.50628i	1.60766	−	0.430771i	0.660315	−	0.750989i	$-0.270423\pi$
$487$	35.4779	−	9.50628i	1.60766	−	0.430771i	0.947344	+	0.320218i	$0.103756\pi$
$488$	70.1296	+	70.1296i	3.17462	+	3.17462i
$489$	−22.2732	−	14.6204i	−1.00723	−	0.661157i
$490$	1.19763	+	2.07435i	0.0541034	+	0.0937098i
$491$	23.1645			1.04540			0.522701	−	0.852516i	$-0.324925\pi$
$491$	23.1645			1.04540			0.522701	+	0.852516i	$0.324925\pi$
$492$	5.88705	+	11.6956i	0.265409	+	0.527279i
$493$	10.5584	−	6.09590i	0.475526	−	0.274545i
$494$	56.8781	+	2.19251i	2.55907	+	0.0986455i
$495$	11.7077	−	5.07544i	0.526223	−	0.228124i
$496$	1.33653	−	4.98801i	0.0600121	−	0.223968i
$497$	0.329417	+	0.190189i	0.0147764	+	0.00853114i
$498$	16.0238	+	17.9730i	0.718046	+	0.805389i
$499$	19.1775	−	5.13859i	0.858501	−	0.230035i	0.197392	−	0.980325i	$-0.436753\pi$
$499$	19.1775	−	5.13859i	0.858501	−	0.230035i	0.661109	+	0.750290i	$0.270086\pi$
$500$	39.1681	+	10.4951i	1.75165	+	0.469354i
$501$	−2.24909	−	0.128947i	−0.100482	−	0.00576094i
$502$	24.6849	+	6.61430i	1.10174	+	0.295210i
$503$	36.0121	+	20.7916i	1.60570	+	0.927051i	0.990317	+	0.138823i	$0.0443320\pi$
$503$	36.0121	+	20.7916i	1.60570	+	0.927051i	0.615383	+	0.788228i	$0.289001\pi$
$504$	2.53597	−	22.0433i	0.112961	−	0.981889i
$505$	−11.7881	−	3.15861i	−0.524563	−	0.140556i
$506$	−52.2558	−	90.5097i	−2.32305	−	4.02364i
$507$	−20.7730	−	8.68800i	−0.922562	−	0.385848i
$508$	−25.7264	+	44.5594i	−1.14142	+	1.97700i
$509$	19.4166	−	19.4166i	0.860626	−	0.860626i	−0.130785	−	0.991411i	$-0.541750\pi$
$509$	19.4166	−	19.4166i	0.860626	−	0.860626i	0.991411	+	0.130785i	$0.0417498\pi$
$510$	−9.89739	−	11.1013i	−0.438264	−	0.491575i
$511$		−	1.14206i		−	0.0505216i
$512$	29.4985	−	29.4985i	1.30366	−	1.30366i
$513$	24.0995	+	20.1104i	1.06402	+	0.887894i
$514$	5.53955	+	20.6739i	0.244339	+	0.911886i
$515$	1.39465	−	5.20492i	0.0614558	−	0.229356i
$516$	13.7308	+	4.53608i	0.604465	+	0.199690i
$517$			36.9557i			1.62531i
$518$	−5.53681	−	5.53681i	−0.243273	−	0.243273i
$519$	−17.7359	+	15.8124i	−0.778518	+	0.694089i
$520$	−11.3962	−	21.6217i	−0.499757	−	0.948175i
$521$			30.5264i			1.33739i	0.743538	+	0.668693i	$0.233146\pi$
$521$			30.5264i			1.33739i	−0.743538	+	0.668693i	$0.766854\pi$
$522$	24.7979	+	9.79952i	1.08537	+	0.428913i
$523$	2.04772	+	3.54676i	0.0895407	+	0.155089i	0.907317	−	0.420447i	$-0.138127\pi$
$523$	2.04772	+	3.54676i	0.0895407	+	0.155089i	−0.817776	+	0.575536i	$0.804793\pi$
$524$	−20.1329			−0.879512
$525$	−3.23959	−	6.43598i	−0.141387	−	0.280889i
$526$	−10.0085	+	37.3521i	−0.436389	+	1.62863i
$527$	−0.495510	+	1.84927i	−0.0215848	+	0.0805555i
$528$	34.9469	+	69.4278i	1.52087	+	3.02146i
$529$	51.2484			2.22819
$530$	−16.7820	−	29.0673i	−0.728963	−	1.26260i
$531$	−21.0463	−	8.31697i	−0.913331	−	0.360926i
$532$		−	29.1768i		−	1.26497i
$533$	−1.24950	−	5.50304i	−0.0541219	−	0.238363i
$534$	−26.2309	+	23.3862i	−1.13512	+	1.01202i
$535$	2.07165	+	2.07165i	0.0895653	+	0.0895653i
$536$		−	96.6697i		−	4.17549i
$537$	−2.78462	−	0.919921i	−0.120165	−	0.0396975i
$538$	−17.3985	+	64.9321i	−0.750103	+	2.79942i
$539$	1.20117	+	4.48282i	0.0517380	+	0.193089i
$540$	3.93268	−	22.6639i	0.169236	−	0.975297i
$541$	−13.1548	+	13.1548i	−0.565571	+	0.565571i	−0.930884	−	0.365314i	$-0.880962\pi$
$541$	−13.1548	+	13.1548i	−0.565571	+	0.565571i	0.365314	+	0.930884i	$0.380962\pi$
$542$		−	73.2352i		−	3.14572i
$543$	10.9116	+	12.2389i	0.468260	+	0.525219i
$544$	26.5612	−	26.5612i	1.13880	−	1.13880i
$545$	−2.03495	+	3.52464i	−0.0871676	+	0.150979i
$546$	−5.71274	+	15.2885i	−0.244483	+	0.654287i
$547$	7.35471	+	12.7387i	0.314465	+	0.544669i	0.979324	−	0.202300i	$-0.0648417\pi$
$547$	7.35471	+	12.7387i	0.314465	+	0.544669i	−0.664859	+	0.746969i	$0.731508\pi$
$548$	−18.7951	−	5.03613i	−0.802887	−	0.215133i
$549$	4.59767	−	39.9642i	0.196224	−	1.70563i
$550$	43.6963	+	25.2281i	1.86322	+	1.07573i
$551$	19.8434	+	5.31704i	0.845359	+	0.226513i
$552$	−110.205	−	6.31843i	−4.69065	−	0.268930i
$553$	3.76521	+	1.00888i	0.160113	+	0.0429021i
$554$	−42.7054	+	11.4429i	−1.81438	+	0.486161i
$555$	−3.16514	−	3.55015i	−0.134353	−	0.150695i
$556$	−58.8082	−	33.9529i	−2.49402	−	1.43993i
$557$	−0.558580	+	2.08465i	−0.0236678	+	0.0883294i	−0.976750	−	0.214384i	$-0.931226\pi$
$557$	−0.558580	+	2.08465i	−0.0236678	+	0.0883294i	0.953082	+	0.302713i	$0.0978924\pi$
$558$	−3.84165	+	1.66540i	−0.162630	+	0.0705019i
$559$	−5.27326	−	3.32172i	−0.223035	−	0.140494i
$560$	−7.67493	+	4.43112i	−0.324325	+	0.187249i
$561$	−12.9563	−	25.7399i	−0.547016	−	1.08674i
$562$	−27.4957			−1.15983
$563$	−13.4745	−	23.3385i	−0.567882	−	0.983600i	−0.996775	−	0.0802449i	$-0.974430\pi$
$563$	−13.4745	−	23.3385i	−0.567882	−	0.983600i	0.428893	−	0.903355i	$-0.358904\pi$
$564$	55.6914	+	36.5565i	2.34503	+	1.53931i
$565$	−5.40007	−	5.40007i	−0.227183	−	0.227183i
$566$	3.09028	−	0.828039i	0.129894	−	0.0348051i
$567$	−7.64286	+	4.75255i	−0.320970	+	0.199588i
$568$	−1.40668	+	2.43645i	−0.0590231	+	0.102231i
$569$	18.9762	−	32.8678i	0.795525	−	1.37789i	−0.126981	−	0.991905i	$-0.540529\pi$
$569$	18.9762	−	32.8678i	0.795525	−	1.37789i	0.922506	−	0.385984i	$-0.126138\pi$
$570$	1.43446	−	25.0198i	0.0600831	−	1.04796i
$571$	6.52130	+	3.76508i	0.272908	+	0.157564i	0.630208	−	0.776426i	$-0.282969\pi$
$571$	6.52130	+	3.76508i	0.272908	+	0.157564i	−0.357300	+	0.933990i	$0.616303\pi$
$572$	−17.8958	−	78.8166i	−0.748262	−	3.29549i
$573$	−11.3597	−	12.7415i	−0.474557	−	0.532282i
$574$	−3.95097	+	1.05866i	−0.164910	+	0.0441876i
$575$	−31.0433	+	17.9228i	−1.29459	+	0.747434i
$576$	23.9773	+	2.75845i	0.999052	+	0.114936i
$577$	−6.03650	−	6.03650i	−0.251303	−	0.251303i	0.570202	−	0.821505i	$-0.306865\pi$
$577$	−6.03650	−	6.03650i	−0.251303	−	0.251303i	−0.821505	+	0.570202i	$0.806865\pi$
$578$	7.66633	−	7.66633i	0.318877	−	0.318877i
$579$	0.922237	−	16.0856i	0.0383269	−	0.668494i
$580$	−3.89655	−	14.5421i	−0.161795	−	0.603829i
$581$	−4.60674	+	2.65970i	−0.191120	+	0.110343i
$582$	12.8684	+	62.0375i	0.533412	+	2.57154i
$583$	−16.8316	−	62.8163i	−0.697093	−	2.60159i
$584$	8.44693			0.349536
$585$	−3.99588	+	9.07264i	−0.165209	+	0.375108i
$586$	13.8818			0.573453
$587$	−0.0538632	−	0.201020i	−0.00222317	−	0.00829699i	0.964805	−	0.262965i	$-0.0847004\pi$
$587$	−0.0538632	−	0.201020i	−0.00222317	−	0.00829699i	−0.967029	+	0.254668i	$0.918034\pi$
$588$	7.94369	+	2.62426i	0.327592	+	0.108223i
$589$	−2.79378	+	1.61299i	−0.115116	+	0.0664622i
$590$	4.67641	+	17.4526i	0.192525	+	0.718512i
$591$	−33.2244	+	16.7237i	−1.36667	+	0.687920i
$592$	20.4857	−	20.4857i	0.841957	−	0.841957i
$593$	−1.88246	−	1.88246i	−0.0773032	−	0.0773032i	0.667398	−	0.744701i	$-0.267408\pi$
$593$	−1.88246	−	1.88246i	−0.0773032	−	0.0773032i	−0.744701	+	0.667398i	$0.767408\pi$
$594$	26.4793	−	57.1910i	1.08646	−	2.34657i
$595$	2.84543	−	1.64281i	0.116651	−	0.0673485i
$596$	−54.7488	+	14.6699i	−2.24260	+	0.600903i
$597$	−19.4659	+	4.03780i	−0.796686	+	0.165256i
$598$	77.5605	+	24.0201i	3.17168	+	0.982256i
$599$	−36.7841	−	21.2373i	−1.50296	−	0.867732i	−0.999994	−	0.00342314i	$-0.998910\pi$
$599$	−36.7841	−	21.2373i	−1.50296	−	0.867732i	−0.502962	−	0.864309i	$-0.667756\pi$
$600$	47.6021	−	23.9608i	1.94335	−	0.978195i
$601$	5.97791	−	10.3540i	0.243844	−	0.422350i	−0.717962	−	0.696082i	$-0.754925\pi$
$601$	5.97791	−	10.3540i	0.243844	−	0.422350i	0.961806	+	0.273732i	$0.0882582\pi$
$602$	−2.25869	+	3.91217i	−0.0920574	+	0.159448i
$603$	−30.7130	+	24.3754i	−1.25073	+	0.992642i
$604$	98.6025	−	26.4205i	4.01208	−	1.07503i
$605$	−6.82973	−	6.82973i	−0.277668	−	0.277668i
$606$	−53.8387	+	27.1000i	−2.18705	+	1.10086i
$607$	5.95823	+	10.3200i	0.241837	+	0.418874i	0.961238	−	0.275721i	$-0.0889167\pi$
$607$	5.95823	+	10.3200i	0.241837	+	0.418874i	−0.719401	+	0.694595i	$0.755583\pi$
$608$	63.2950			2.56695
$609$	−3.23241	+	4.92436i	−0.130984	+	0.199545i
$610$	−27.8156	+	16.0593i	−1.12622	+	0.650224i
$611$	−19.5046	−	21.0686i	−0.789070	−	0.852343i
$612$	−51.6057	−	5.93695i	−2.08604	−	0.239987i
$613$	−4.51918	+	16.8658i	−0.182528	+	0.681204i	0.812618	+	0.582797i	$0.198042\pi$
$613$	−4.51918	+	16.8658i	−0.182528	+	0.681204i	−0.995146	+	0.0984077i	$0.968625\pi$
$614$	29.7520	+	17.1773i	1.20069	+	0.693220i
$615$	−2.43276	+	0.504626i	−0.0980984	+	0.0203485i
$616$	−33.1561	+	8.88414i	−1.33590	+	0.357952i
$617$	−20.5519	−	5.50686i	−0.827387	−	0.221698i	−0.179814	−	0.983701i	$-0.557549\pi$
$617$	−20.5519	−	5.50686i	−0.827387	−	0.221698i	−0.647573	+	0.762003i	$0.724216\pi$
$618$	−11.9657	−	23.7720i	−0.481333	−	0.956249i
$619$	11.8636	+	3.17883i	0.476836	+	0.127768i	0.489229	−	0.872155i	$-0.337278\pi$
$619$	11.8636	+	3.17883i	0.476836	+	0.127768i	−0.0123927	+	0.999923i	$0.503945\pi$
$620$	2.04740	+	1.18207i	0.0822258	+	0.0474731i
$621$	25.7810	+	36.6067i	1.03456	+	1.46897i
$622$	−34.1032	−	9.13793i	−1.36742	−	0.366398i
$623$	−3.88173	−	6.72335i	−0.155518	−	0.269365i
$624$	−56.5660	−	21.1366i	−2.26445	−	0.846143i
$625$	6.55280	−	11.3498i	0.262112	−	0.453991i
$626$	26.0802	−	26.0802i	1.04238	−	1.04238i
$627$	15.2315	−	46.1062i	0.608288	−	1.84130i
$628$		−	110.743i		−	4.41912i
$629$	−7.59493	+	7.59493i	−0.302830	+	0.302830i
$630$	6.68289	+	2.64091i	0.266253	+	0.105216i
$631$	−7.89172	−	29.4523i	−0.314164	−	1.17248i	−0.924765	−	0.380539i	$-0.875739\pi$
$631$	−7.89172	−	29.4523i	−0.314164	−	1.17248i	0.610601	−	0.791939i	$-0.290928\pi$
$632$	−7.46196	+	27.8484i	−0.296821	+	1.10775i
$633$	27.0162	−	24.0863i	1.07380	−	0.957345i
$634$		−	46.0317i		−	1.82815i
$635$	−6.90366	−	6.90366i	−0.273963	−	0.273963i
$636$	−111.312	−	36.7729i	−4.41382	−	1.45814i
$637$	−3.05074	−	1.92171i	−0.120875	−	0.0761410i
$638$		−	41.2488i		−	1.63305i
$639$	1.12878	−	0.167435i	0.0446540	−	0.00662362i
$640$	−0.0316721	−	0.0548576i	−0.00125195	−	0.00216844i
$641$	4.48938			0.177320			0.0886600	−	0.996062i	$-0.471742\pi$
$641$	4.48938			0.177320			0.0886600	+	0.996062i	$0.471742\pi$
$642$	14.4462	+	0.828245i	0.570145	+	0.0326882i
$643$	−2.99106	+	11.1628i	−0.117956	+	0.440218i	−0.999491	−	0.0319008i	$-0.989844\pi$
$643$	−2.99106	+	11.1628i	−0.117956	+	0.440218i	0.881535	+	0.472119i	$0.156511\pi$
$644$	10.7719	−	40.2014i	0.424474	−	1.58416i
$645$	−1.50574	+	2.29389i	−0.0592884	+	0.0903219i
$646$	−56.5943			−2.22667
$647$	10.2507	+	17.7548i	0.402998	+	0.698012i	0.994086	−	0.108594i	$-0.0346349\pi$
$647$	10.2507	+	17.7548i	0.402998	+	0.698012i	−0.591088	+	0.806607i	$0.701302\pi$
$648$	−35.1510	−	56.5284i	−1.38086	−	2.22065i
$649$			35.0083i			1.37420i
$650$	−38.2263	+	8.67952i	−1.49936	+	0.340439i
$651$	−0.187872	−	0.905716i	−0.00736329	−	0.0354978i
$652$	52.5367	+	52.5367i	2.05749	+	2.05749i
$653$			15.3643i			0.601251i	0.953742	+	0.300625i	$0.0971954\pi$
$653$			15.3643i			0.601251i	−0.953742	+	0.300625i	$0.902805\pi$
$654$	4.08263	+	19.6820i	0.159643	+	0.769628i
$655$	0.988755	−	3.69009i	0.0386339	−	0.144184i
$656$	−3.91694	−	14.6182i	−0.152931	−	0.570746i
$657$	−2.12990	−	2.68368i	−0.0830954	−	0.104700i
$658$	−14.7154	+	14.7154i	−0.573666	+	0.573666i
$659$		−	21.3849i		−	0.833038i	−0.909127	−	0.416519i	$-0.863250\pi$
$659$		−	21.3849i		−	0.833038i	0.909127	−	0.416519i	$-0.136750\pi$
$660$	−34.8429	+	7.22744i	−1.35626	+	0.281328i
$661$	−23.3384	+	23.3384i	−0.907760	+	0.907760i	−0.996091	−	0.0883314i	$-0.971847\pi$
$661$	−23.3384	+	23.3384i	−0.907760	+	0.907760i	0.0883314	+	0.996091i	$0.471847\pi$
$662$	33.6915	−	58.3554i	1.30946	−	2.26805i
$663$	20.9715	+	7.83626i	0.814464	+	0.304335i
$664$	−19.6718	−	34.0726i	−0.763414	−	1.32227i
$665$	5.34769	+	1.43291i	0.207375	+	0.0555658i
$666$	−23.3368	−	2.68477i	−0.904281	−	0.104033i
$667$	25.3784	+	14.6522i	0.982656	+	0.567337i
$668$	6.06814	+	1.62595i	0.234784	+	0.0629101i
$669$	−2.70998	+	4.12848i	−0.104774	+	0.159616i
$670$	30.2395	+	8.10266i	1.16826	+	0.313033i
$671$	−60.1114	+	16.1068i	−2.32057	+	0.621796i
$672$	−5.69297	+	17.2327i	−0.219611	+	0.664768i
$673$	−4.75984	−	2.74809i	−0.183478	−	0.105931i	0.405448	−	0.914118i	$-0.367116\pi$
$673$	−4.75984	−	2.74809i	−0.183478	−	0.105931i	−0.588926	+	0.808187i	$0.700449\pi$
$674$	−17.2055	+	64.2119i	−0.662732	+	2.47335i
$675$	−19.6155	−	9.08197i	−0.755002	−	0.349565i
$676$	51.8004	+	35.4884i	1.99232	+	1.36494i
$677$	16.0192	−	9.24869i	0.615668	−	0.355456i	−0.159513	−	0.987196i	$-0.550992\pi$
$677$	16.0192	−	9.24869i	0.615668	−	0.355456i	0.775180	+	0.631740i	$0.217659\pi$
$678$	−37.6561	−	2.15895i	−1.44617	−	0.0829138i
$679$	−13.9968			−0.537147
$680$	12.1506	+	21.0455i	0.465955	+	0.807057i
$681$	0.768541	−	13.4048i	0.0294506	−	0.513674i
$682$	4.58021	+	4.58021i	0.175385	+	0.175385i
$683$	6.23228	−	1.66994i	0.238472	−	0.0638983i	−0.137604	−	0.990487i	$-0.543940\pi$
$683$	6.23228	−	1.66994i	0.238472	−	0.0638983i	0.376075	+	0.926589i	$0.377273\pi$
$684$	−54.4139	−	68.5615i	−2.08057	−	2.62152i
$685$	1.84610	−	3.19755i	0.0705360	−	0.122172i
$686$	−1.30672	+	2.26331i	−0.0498908	+	0.0864135i
$687$	5.94250	+	3.90072i	0.226720	+	0.148822i
$688$	−14.4747	−	8.35695i	−0.551842	−	0.318606i
$689$	42.7490	+	26.9283i	1.62861	+	1.02589i
$690$	11.2137	−	33.9441i	0.426898	−	1.29223i
$691$	−20.3142	+	5.44317i	−0.772789	+	0.207068i	−0.623603	−	0.781741i	$-0.714332\pi$
$691$	−20.3142	+	5.44317i	−0.772789	+	0.207068i	−0.149186	+	0.988809i	$0.547665\pi$
$692$	57.3842	−	33.1308i	2.18142	−	1.25944i
$693$	11.1829	+	8.29389i	0.424804	+	0.315059i
$694$	−8.36682	−	8.36682i	−0.317600	−	0.317600i
$695$	9.11124	−	9.11124i	0.345609	−	0.345609i
$696$	−36.4218	−	23.9077i	−1.38056	−	0.906218i
$697$	1.45218	+	5.41961i	0.0550052	+	0.205282i
$698$	−39.6290	+	22.8798i	−1.49998	+	0.866014i
$699$	31.3983	−	27.9932i	1.18759	−	1.05880i
$700$	5.20048	+	19.4085i	0.196560	+	0.733571i
$701$	30.6562			1.15787			0.578934	−	0.815375i	$-0.303469\pi$
$701$	30.6562			1.15787			0.578934	+	0.815375i	$0.303469\pi$
$702$	15.0884	+	46.5800i	0.569475	+	1.75805i
$703$	−18.0986			−0.682601
$704$	−9.66356	−	36.0649i	−0.364209	−	1.35925i
$705$	−9.43536	+	8.41211i	−0.355356	+	0.316818i
$706$	53.7228	−	31.0169i	2.02188	−	1.16733i
$707$	−3.44632	−	12.8619i	−0.129612	−	0.483720i
$708$	52.7567	+	34.6301i	1.98272	+	1.30148i
$709$	−23.2926	+	23.2926i	−0.874771	+	0.874771i	−0.992988	−	0.118216i	$-0.962282\pi$
$709$	−23.2926	+	23.2926i	−0.874771	+	0.874771i	0.118216	+	0.992988i	$0.462282\pi$
$710$	−0.644247	−	0.644247i	−0.0241782	−	0.0241782i
$711$	10.7293	−	4.65127i	0.402380	−	0.174436i
$712$	49.7276	−	28.7102i	1.86362	−	1.07596i
$713$	−4.44495	+	1.19102i	−0.166465	+	0.0446041i
$714$	5.09029	−	15.4084i	0.190499	−	0.576646i
$715$	15.3249	+	0.590734i	0.573117	+	0.0220922i
$716$	7.08244	+	4.08905i	0.264683	+	0.152815i
$717$	−21.1521	−	13.8845i	−0.789940	−	0.518526i
$718$	−23.6410	+	40.9473i	−0.882273	+	1.52814i
$719$	−2.84283	+	4.92392i	−0.106020	+	0.183631i	−0.914154	−	0.405366i	$-0.867144\pi$
$719$	−2.84283	+	4.92392i	−0.106020	+	0.183631i	0.808135	+	0.588998i	$0.200477\pi$
$720$	−9.77114	+	24.7261i	−0.364149	+	0.921487i
$721$	5.67904	−	1.52169i	0.211498	−	0.0566708i
$722$	−32.3200	−	32.3200i	−1.20283	−	1.20283i
$723$	−0.550564	+	9.60288i	−0.0204757	+	0.357135i
$724$	−22.8623	−	39.5987i	−0.849671	−	1.47167i
$725$	−14.1476			−0.525430
$726$	−47.6255	−	2.73052i	−1.76755	−	0.101339i
$727$	−44.1949	+	25.5159i	−1.63910	+	0.946333i	−0.657953	+	0.753059i	$0.728577\pi$
$727$	−44.1949	+	25.5159i	−1.63910	+	0.946333i	−0.981145	+	0.193274i	$0.938089\pi$
$728$	14.2135	−	22.5640i	0.526786	−	0.836279i
$729$	−9.09631	+	25.4216i	−0.336901	+	0.941540i
$730$	−0.708004	+	2.64231i	−0.0262044	+	0.0977962i
$731$	5.36638	+	3.09828i	0.198483	+	0.114594i
$732$	−35.1894	+	106.519i	−1.30064	+	3.93706i
$733$	−42.4858	+	11.3840i	−1.56925	+	0.420479i	−0.935577	−	0.353123i	$-0.885120\pi$
$733$	−42.4858	+	11.3840i	−1.56925	+	0.420479i	−0.633672	+	0.773602i	$0.718453\pi$
$734$	−46.6625	−	12.5032i	−1.72234	−	0.461501i
$735$	−0.871115	+	1.32709i	−0.0321316	+	0.0489503i
$736$	87.2115	+	23.3682i	3.21466	+	0.861365i
$737$	52.5312	+	30.3289i	1.93501	+	1.11718i
$738$	−7.30988	+	9.85616i	−0.269081	+	0.362810i
$739$	28.1774	+	7.55010i	1.03652	+	0.277735i	0.736671	−	0.676251i	$-0.236397\pi$
$739$	28.1774	+	7.55010i	1.03652	+	0.277735i	0.299850	+	0.953986i	$0.403063\pi$
$740$	6.63171	+	11.4865i	0.243787	+	0.422251i
$741$	15.6505	+	34.3241i	0.574934	+	1.26093i
$742$	18.3107	−	31.7150i	0.672205	−	1.16429i
$743$	9.28567	−	9.28567i	0.340658	−	0.340658i	−0.515957	−	0.856615i	$-0.672563\pi$
$743$	9.28567	−	9.28567i	0.340658	−	0.340658i	0.856615	+	0.515957i	$0.172563\pi$
$744$	6.69890	−	1.38955i	0.245594	−	0.0509433i
$745$		−	10.7552i		−	0.394038i
$746$	10.2836	−	10.2836i	0.376510	−	0.376510i
$747$	−5.86495	+	14.8414i	−0.214587	+	0.543018i
$748$	20.7987	+	77.6217i	0.760474	+	2.83813i
$749$	−0.827348	+	3.08770i	−0.0302306	+	0.112822i
$750$	7.71847	+	37.2101i	0.281839	+	1.35872i
$751$			27.8879i			1.01765i	0.860871	+	0.508823i	$0.169919\pi$
$751$			27.8879i			1.01765i	−0.860871	+	0.508823i	$0.830081\pi$
$752$	−54.4457	−	54.4457i	−1.98543	−	1.98543i
$753$	3.43999	+	16.5839i	0.125360	+	0.604352i
$754$	21.7703	+	23.5160i	0.792829	+	0.856403i
$755$			19.3700i			0.704946i
$756$	23.5608	−	8.64811i	0.856898	−	0.314529i
$757$	−0.374558	−	0.648754i	−0.0136135	−	0.0235794i	0.859138	−	0.511743i	$-0.171000\pi$
$757$	−0.374558	−	0.648754i	−0.0136135	−	0.0235794i	−0.872752	+	0.488164i	$0.837667\pi$
$758$	23.7499			0.862637
$759$	38.0091	−	57.9043i	1.37964	−	2.10179i
$760$	−10.5982	+	39.5528i	−0.384435	+	1.43473i
$761$	−3.22212	+	12.0251i	−0.116802	+	0.435911i	−0.999415	−	0.0341887i	$-0.989115\pi$
$761$	−3.22212	+	12.0251i	−0.116802	+	0.435911i	0.882613	+	0.470099i	$0.155782\pi$
$762$	−48.1410	−	2.76008i	−1.74397	−	0.0999872i
$763$	−4.44062			−0.160761
$764$	23.8012	+	41.2248i	0.861096	+	1.49146i
$765$	3.62258	−	9.16702i	0.130975	−	0.331434i
$766$		−	68.6268i		−	2.47959i
$767$	−18.4768	−	19.9583i	−0.667157	−	0.720654i
$768$	26.1655	+	8.64396i	0.944165	+	0.311912i
$769$	−3.66383	−	3.66383i	−0.132121	−	0.132121i	0.637954	−	0.770075i	$-0.279781\pi$
$769$	−3.66383	−	3.66383i	−0.132121	−	0.132121i	−0.770075	+	0.637954i	$0.779781\pi$
$770$		−	11.1163i		−	0.400604i
$771$	−10.5879	+	9.43967i	−0.381315	+	0.339961i
$772$	−11.6289	+	43.3997i	−0.418534	+	1.56199i
$773$	4.24875	+	15.8566i	0.152817	+	0.570321i	0.999282	+	0.0378771i	$0.0120595\pi$
$773$	4.24875	+	15.8566i	0.152817	+	0.570321i	−0.846465	+	0.532444i	$0.821274\pi$
$774$	1.98846	+	13.4055i	0.0714738	+	0.481850i
$775$	1.57093	−	1.57093i	0.0564296	−	0.0564296i
$776$		−	103.524i		−	3.71628i
$777$	1.62785	−	4.92754i	0.0583988	−	0.176774i
$778$	−17.2370	+	17.2370i	−0.617977	+	0.617977i
$779$	−4.72716	+	8.18768i	−0.169368	+	0.293354i
$780$	16.0495	−	22.5098i	0.574665	−	0.805981i
$781$	−0.882659	−	1.52881i	−0.0315840	−	0.0547051i
$782$	−77.9790	−	20.8944i	−2.78852	−	0.747182i
$783$	1.58807	+	17.6000i	0.0567530	+	0.628971i
$784$	−8.37403	−	4.83475i	−0.299073	−	0.172670i
$785$	20.2976	+	5.43872i	0.724452	+	0.194116i
$786$	−8.48325	−	16.8534i	−0.302587	−	0.601141i
$787$	−20.3092	−	5.44184i	−0.723946	−	0.193981i	−0.122014	−	0.992528i	$-0.538935\pi$
$787$	−20.3092	−	5.44184i	−0.723946	−	0.193981i	−0.601932	+	0.798548i	$0.705602\pi$
$788$	100.192	−	26.8464i	3.56919	−	0.956363i
$789$	−25.0940	+	5.20524i	−0.893372	+	0.185312i
$790$	−8.08590	−	4.66840i	−0.287683	−	0.166094i
$791$	2.15661	−	8.04857i	0.0766801	−	0.286174i
$792$	−61.3437	+	82.7117i	−2.17975	+	2.93903i
$793$	25.7688	−	40.9082i	0.915076	−	1.45269i
$794$	−22.3398	+	12.8979i	−0.792810	+	0.457729i
$795$	12.2066	−	18.5960i	0.432925	−	0.659533i
$796$	55.4391			1.96499
$797$	4.20995	+	7.29185i	0.149124	+	0.258290i	0.930904	−	0.365264i	$-0.119021\pi$
$797$	4.20995	+	7.29185i	0.149124	+	0.258290i	−0.781780	+	0.623554i	$0.785688\pi$
$798$	24.4240	−	12.2940i	0.864601	−	0.435202i
$799$	20.1854	+	20.1854i	0.714107	+	0.714107i
$800$	−42.1040	+	11.2817i	−1.48860	+	0.398869i
$801$	−21.6604	−	8.55967i	−0.765333	−	0.302441i
$802$	46.0048	−	79.6826i	1.62448	−	2.81369i
$803$	−2.65012	+	4.59014i	−0.0935206	+	0.161982i
$804$	97.6685	−	49.1620i	3.44450	−	1.73381i
$805$	6.83933	+	3.94869i	0.241055	+	0.139173i
$806$	−5.02853	−	0.193837i	−0.177123	−	0.00682762i
$807$	−43.6230	+	9.04869i	−1.53560	+	0.318529i
$808$	95.1295	−	25.4899i	3.34664	−	0.896730i
$809$	−11.7642	+	6.79208i	−0.413608	+	0.238797i	−0.692339	−	0.721572i	$-0.743420\pi$
$809$	−11.7642	+	6.79208i	−0.413608	+	0.238797i	0.278731	+	0.960369i	$0.410086\pi$
$810$	20.6291	−	6.25761i	0.724833	−	0.219870i
$811$	−6.48562	−	6.48562i	−0.227741	−	0.227741i	0.584007	−	0.811748i	$-0.301484\pi$
$811$	−6.48562	−	6.48562i	−0.227741	−	0.227741i	−0.811748	+	0.584007i	$0.801484\pi$
$812$	11.6153	−	11.6153i	0.407616	−	0.407616i
$813$	43.3539	−	21.8224i	1.52049	−	0.765346i
$814$	9.40543	+	35.1015i	0.329660	+	1.23031i
$815$	−12.2094	+	7.04909i	−0.427676	+	0.246919i
$816$	57.0098	+	18.8336i	1.99574	+	0.659308i
$817$	2.70242	+	10.0856i	0.0945458	+	0.352850i
$818$	7.61549			0.266269
$819$	−10.7528	+	1.17378i	−0.375732	+	0.0410151i
$820$	6.92852			0.241955
$821$	13.6487	+	50.9375i	0.476341	+	1.77773i	0.616234	+	0.787563i	$0.288657\pi$
$821$	13.6487	+	50.9375i	0.476341	+	1.77773i	−0.139893	+	0.990167i	$0.544676\pi$
$822$	−3.70376	−	17.8555i	−0.129183	−	0.622783i
$823$	−30.2534	+	17.4668i	−1.05457	+	0.608854i	−0.923924	−	0.382576i	$-0.875037\pi$
$823$	−30.2534	+	17.4668i	−1.05457	+	0.608854i	−0.130642	+	0.991430i	$0.541704\pi$
$824$	11.2548	+	42.0035i	0.392080	+	1.46326i
$825$	−1.91406	+	33.3848i	−0.0666390	+	1.16231i
$826$	−13.9400	+	13.9400i	−0.485033	+	0.485033i
$827$	27.1366	+	27.1366i	0.943632	+	0.943632i	0.998494	−	0.0548615i	$-0.0174717\pi$
$827$	27.1366	+	27.1366i	0.943632	+	0.943632i	−0.0548615	+	0.998494i	$0.517472\pi$
$828$	−49.6620	−	114.557i	−1.72587	−	3.98115i
$829$	−9.85809	+	5.69157i	−0.342385	+	0.197676i	−0.661326	−	0.750098i	$-0.730006\pi$
$829$	−9.85809	+	5.69157i	−0.342385	+	0.197676i	0.318941	+	0.947775i	$0.396673\pi$
$830$	12.3072	−	3.29770i	0.427189	−	0.114465i
$831$	−19.4992	−	21.8711i	−0.676420	−	0.758700i
$832$	24.5436	+	15.4604i	0.850897	+	0.535994i
$833$	3.10462	+	1.79245i	0.107569	+	0.0621047i
$834$	3.64267	−	63.5351i	0.126135	−	2.20004i
$835$	−0.596029	+	1.03235i	−0.0206264	+	0.0357260i
$836$	−67.7041	+	117.267i	−2.34160	+	4.05576i
$837$	−2.13061	−	1.77794i	−0.0736447	−	0.0614545i
$838$	2.98495	−	0.799814i	0.103113	−	0.0276291i
$839$	7.93089	+	7.93089i	0.273805	+	0.273805i	0.830630	−	0.556825i	$-0.187981\pi$
$839$	7.93089	+	7.93089i	0.273805	+	0.273805i	−0.556825	+	0.830630i	$0.687981\pi$
$840$	−9.81546	−	6.44298i	−0.338665	−	0.222304i
$841$	−8.71703	−	15.0983i	−0.300587	−	0.520633i
$842$	−73.5066			−2.53320
$843$	−8.19309	−	16.2770i	−0.282185	−	0.560608i
$844$	−87.4105	+	50.4665i	−3.00879	+	1.73713i
$845$	−9.04852	+	7.75140i	−0.311279	+	0.266656i
$846$	−7.13542	+	62.0231i	−0.245321	+	2.13240i
$847$	2.72757	−	10.1794i	0.0937203	−	0.349769i
$848$	117.343	+	67.7478i	4.02956	+	2.32647i
$849$	1.41102	+	1.58266i	0.0484261	+	0.0543166i
$850$	37.6467	−	10.0874i	1.29127	−	0.345995i
$851$	−24.9373	−	6.68193i	−0.854839	−	0.229053i
$852$	−3.17700	−	0.182148i	−0.108842	−	0.00624027i
$853$	−3.10097	−	0.830904i	−0.106175	−	0.0284496i	0.205340	−	0.978691i	$-0.434170\pi$
$853$	−3.10097	−	0.830904i	−0.106175	−	0.0284496i	−0.311516	+	0.950241i	$0.600837\pi$
$854$	−30.3493	−	17.5222i	−1.03853	−	0.599597i
$855$	15.2387	−	6.60615i	0.521153	−	0.225926i
$856$	−22.8374	−	6.11927i	−0.780567	−	0.209152i
$857$	5.51659	+	9.55501i	0.188443	+	0.326393i	0.944731	−	0.327846i	$-0.106323\pi$
$857$	5.51659	+	9.55501i	0.188443	+	0.326393i	−0.756288	+	0.654239i	$0.772989\pi$
$858$	58.4372	−	48.1910i	1.99501	−	1.64521i
$859$	−11.4188	+	19.7780i	−0.389605	+	0.674815i	−0.992396	−	0.123084i	$-0.960722\pi$
$859$	−11.4188	+	19.7780i	−0.389605	+	0.674815i	0.602792	+	0.797899i	$0.294055\pi$
$860$	5.41069	−	5.41069i	0.184503	−	0.184503i
$861$	−1.80401	−	2.02345i	−0.0614804	−	0.0689589i
$862$			31.2071i			1.06292i
$863$	1.07490	−	1.07490i	0.0365901	−	0.0365901i	−0.688575	−	0.725165i	$-0.741763\pi$
$863$	1.07490	−	1.07490i	0.0365901	−	0.0365901i	0.725165	+	0.688575i	$0.241763\pi$
$864$	18.7609	+	51.1119i	0.638258	+	1.73886i
$865$	3.25419	+	12.1448i	0.110646	+	0.412936i
$866$	19.6137	−	73.1992i	0.666499	−	2.48741i
$867$	6.82272	+	2.25394i	0.231712	+	0.0765477i
$868$			2.57949i			0.0875535i
$869$	−12.7920	−	12.7920i	−0.433938	−	0.433938i
$870$	10.5314	−	9.38932i	0.357049	−	0.318328i
$871$	−45.9552	+	10.4344i	−1.55713	+	0.353557i
$872$		−	32.8439i		−	1.11224i
$873$	−32.8906	+	26.1036i	−1.11318	+	0.883474i
$874$	−68.0157	−	117.807i	−2.30067	−	3.98487i
$875$	−8.39528			−0.283812
$876$	4.29574	+	8.53421i	0.145140	+	0.288344i
$877$	2.56998	−	9.59130i	0.0867821	−	0.323875i	−0.908864	−	0.417093i	$-0.863049\pi$
$877$	2.56998	−	9.59130i	0.0867821	−	0.323875i	0.995646	+	0.0932183i	$0.0297155\pi$
$878$	−26.1803	+	97.7061i	−0.883541	+	3.29742i
$879$	4.13647	+	8.21779i	0.139520	+	0.277179i
$880$	41.1293			1.38647
$881$	−3.18690	−	5.51988i	−0.107369	−	0.185969i	0.807334	−	0.590094i	$-0.200909\pi$
$881$	−3.18690	−	5.51988i	−0.107369	−	0.185969i	−0.914704	+	0.404125i	$0.867576\pi$
$882$	1.15039	+	7.75547i	0.0387355	+	0.261140i
$883$		−	8.21985i		−	0.276620i	−0.990389	−	0.138310i	$-0.955833\pi$
$883$		−	8.21985i		−	0.276620i	0.990389	−	0.138310i	$-0.0441670\pi$
$884$	−52.8247	−	33.2751i	−1.77669	−	1.11916i
$885$	−8.93816	+	7.96883i	−0.300453	+	0.267869i
$886$	1.30051	+	1.30051i	0.0436915	+	0.0436915i
$887$		−	29.2379i		−	0.981712i	−0.871241	−	0.490856i	$-0.836684\pi$
$887$		−	29.2379i		−	0.981712i	0.871241	−	0.490856i	$-0.163316\pi$
$888$	36.4453	+	12.0400i	1.22302	+	0.404035i
$889$	2.75709	−	10.2896i	0.0924698	−	0.345102i
$890$	4.81287	+	17.9619i	0.161328	+	0.602083i
$891$	41.7463	−	1.36632i	1.39855	−	0.0457733i
$892$	9.73800	−	9.73800i	0.326053	−	0.326053i
$893$			48.1013i			1.60965i
$894$	−35.3493	−	39.6492i	−1.18226	−	1.32607i
$895$	−1.09729	+	1.09729i	−0.0366785	+	0.0366785i
$896$	0.0345571	−	0.0598546i	0.00115447	−	0.00199960i
$897$	8.89178	+	53.0719i	0.296888	+	1.77202i
$898$	−12.2212	−	21.1677i	−0.407826	−	0.706376i
$899$	−1.75434	−	0.470074i	−0.0585105	−	0.0156778i
$900$	48.4167	+	35.9086i	1.61389	+	1.19695i
$901$	−43.5040	−	25.1170i	−1.44933	−	0.836769i
$902$	18.3363	+	4.91319i	0.610532	+	0.163591i
$903$	−2.98897	−	0.171367i	−0.0994668	−	0.00570275i
$904$	59.5292	+	15.9508i	1.97991	+	0.530515i
$905$	8.38068	−	2.24560i	0.278583	−	0.0746461i
$906$	63.6640	+	71.4081i	2.11509	+	2.37238i
$907$	−24.4427	−	14.1120i	−0.811607	−	0.468581i	0.0359069	−	0.999355i	$-0.488568\pi$
$907$	−24.4427	−	14.1120i	−0.811607	−	0.468581i	−0.847513	+	0.530774i	$0.821901\pi$
$908$	−9.69089	+	36.1669i	−0.321603	+	1.20024i
$909$	−32.0854	−	23.7964i	−1.06421	−	0.789275i
$910$	5.86698	+	6.33743i	0.194488	+	0.210084i
$911$	−7.91974	+	4.57247i	−0.262393	+	0.151493i	−0.625426	−	0.780284i	$-0.715075\pi$
$911$	−7.91974	+	4.57247i	−0.262393	+	0.151493i	0.363033	+	0.931776i	$0.381741\pi$
$912$	45.4866	+	90.3667i	1.50621	+	2.99234i
$913$	24.6871			0.817025
$914$	5.18657	+	8.98341i	0.171557	+	0.297145i
$915$	−17.7953	−	11.6810i	−0.588293	−	0.386162i
$916$	−14.0168	−	14.0168i	−0.463128	−	0.463128i
$917$	4.02621	−	1.07882i	0.132957	−	0.0356258i
$918$	−16.7748	−	45.7010i	−0.553651	−	1.50836i
$919$	−1.57521	+	2.72834i	−0.0519613	+	0.0899996i	−0.890836	−	0.454325i	$-0.849881\pi$
$919$	−1.57521	+	2.72834i	−0.0519613	+	0.0899996i	0.838875	+	0.544324i	$0.183214\pi$
$920$	−29.2055	+	50.5854i	−0.962877	+	1.66775i
$921$	−1.30325	+	22.7311i	−0.0429434	+	0.749015i
$922$	23.1589	+	13.3708i	0.762699	+	0.440344i
$923$	1.31008	+	0.405727i	0.0431219	+	0.0133547i
$924$	−25.8377	−	28.9806i	−0.849997	−	0.953391i
$925$	12.0392	−	3.22590i	0.395848	−	0.106067i
$926$	−38.0128	+	21.9467i	−1.24918	+	0.721214i
$927$	10.5071	−	14.1670i	0.345097	−	0.465306i
$928$	25.1977	+	25.1977i	0.827156	+	0.827156i
$929$	−21.1198	+	21.1198i	−0.692919	+	0.692919i	−0.962873	−	0.269954i	$-0.912992\pi$
$929$	−21.1198	+	21.1198i	−0.692919	+	0.692919i	0.269954	+	0.962873i	$0.412992\pi$
$930$	−0.126819	+	2.21197i	−0.00415857	+	0.0725334i
$931$	1.56343	+	5.83481i	0.0512394	+	0.191228i
$932$	−101.589	+	58.6524i	−3.32766	+	1.92122i
$933$	−4.75250	−	22.9114i	−0.155590	−	0.750086i
$934$	−0.214680	−	0.801197i	−0.00702455	−	0.0262160i
$935$	−15.2484			−0.498676
$936$	−8.68156	−	79.5302i	−0.283766	−	2.59953i
$937$	22.6120			0.738701			0.369350	−	0.929290i	$-0.379580\pi$
$937$	22.6120			0.738701			0.369350	+	0.929290i	$0.379580\pi$
$938$	8.84073	+	32.9940i	0.288660	+	1.07729i
$939$	23.2104	+	7.66772i	0.757441	+	0.250226i
$940$	30.5280	−	17.6254i	0.995714	−	0.574876i
$941$	6.94255	+	25.9100i	0.226321	+	0.844641i	0.981871	+	0.189550i	$0.0607029\pi$
$941$	6.94255	+	25.9100i	0.226321	+	0.844641i	−0.755550	+	0.655091i	$0.772630\pi$
$942$	92.7034	−	46.6627i	3.02044	−	1.52035i
$943$	−9.53621	+	9.53621i	−0.310542	+	0.310542i
$944$	−51.5766	−	51.5766i	−1.67868	−	1.67868i
$945$	0.427976	+	4.74308i	0.0139221	+	0.154292i
$946$	18.1562	−	10.4825i	0.590309	−	0.340815i
$947$	−8.04553	+	2.15579i	−0.261445	+	0.0700539i	−0.387160	−	0.922012i	$-0.626544\pi$
$947$	−8.04553	+	2.15579i	−0.261445	+	0.0700539i	0.125716	+	0.992066i	$0.459877\pi$
$948$	−31.9310	+	6.62342i	−1.03707	+	0.215119i
$949$	−0.911753	−	4.01553i	−0.0295967	−	0.130350i
$950$	56.8748	+	32.8367i	1.84526	+	1.06536i
$951$	27.2499	−	13.7164i	0.883640	−	0.444785i
$952$	−13.2574	+	22.9625i	−0.429675	+	0.744219i
$953$	27.6786	−	47.9408i	0.896598	−	1.55295i	0.0647847	−	0.997899i	$-0.479364\pi$
$953$	27.6786	−	47.9408i	0.896598	−	1.55295i	0.831814	−	0.555055i	$-0.187303\pi$
$954$	−16.1200	−	108.675i	−0.521903	−	3.51848i
$955$	−8.72484	+	2.33781i	−0.282329	+	0.0756499i
$956$	49.8923	+	49.8923i	1.61363	+	1.61363i
$957$	24.4185	−	12.2912i	0.789339	−	0.397318i
$958$	9.31623	+	16.1362i	0.300994	+	0.521337i
$959$	4.02853			0.130088
$960$	7.00824	−	10.6766i	0.226190	−	0.344585i
$961$	−26.5998	+	15.3574i	−0.858058	+	0.495400i
$962$	−23.8880	−	15.0475i	−0.770180	−	0.485150i
$963$	3.81433	+	8.79868i	0.122915	+	0.283533i
$964$	6.94231	−	25.9090i	0.223597	−	0.834474i
$965$	−7.38344	−	4.26283i	−0.237681	−	0.137225i
$966$	38.1917	−	7.92209i	1.22880	−	0.254889i
$967$	−44.9679	+	12.0491i	−1.44607	+	0.387473i	−0.894655	−	0.446758i	$-0.852578\pi$
$967$	−44.9679	+	12.0491i	−1.44607	+	0.387473i	−0.551415	+	0.834231i	$0.685912\pi$
$968$	75.2894	+	20.1737i	2.41989	+	0.648409i
$969$	−16.8638	−	33.5028i	−0.541744	−	1.07627i
$970$	32.3836	+	8.67715i	1.03977	+	0.278606i
$971$	−20.3734	−	11.7626i	−0.653813	−	0.377479i	0.136103	−	0.990695i	$-0.456542\pi$
$971$	−20.3734	−	11.7626i	−0.653813	−	0.377479i	−0.789915	+	0.613216i	$0.789876\pi$
$972$	39.2362	−	64.2622i	1.25850	−	2.06121i
$973$	13.5799	+	3.63873i	0.435352	+	0.116652i
$974$	−47.9952	−	83.1300i	−1.53786	−	2.66366i
$975$	−16.5287	−	20.0430i	−0.529342	−	0.641889i
$976$	64.8305	−	112.290i	2.07517	−	3.59431i
$977$	39.1508	−	39.1508i	1.25254	−	1.25254i	0.297968	−	0.954576i	$-0.403691\pi$
$977$	39.1508	−	39.1508i	1.25254	−	1.25254i	0.954576	−	0.297968i	$-0.0963088\pi$
$978$	−21.8418	+	66.1157i	−0.698424	+	2.11415i
$979$			36.0299i			1.15152i
$980$	3.13025	−	3.13025i	0.0999921	−	0.0999921i
$981$	−10.4349	+	8.28164i	−0.333160	+	0.264413i
$982$	−15.6687	−	58.4764i	−0.500008	−	1.86606i
$983$	−4.83592	+	18.0479i	−0.154242	+	0.575638i	0.844927	+	0.534881i	$0.179644\pi$
$983$	−4.83592	+	18.0479i	−0.154242	+	0.575638i	−0.999169	+	0.0407572i	$0.987023\pi$
$984$	14.9659	−	13.3429i	0.477096	−	0.425355i
$985$			19.6823i			0.627129i
$986$	−22.5302	−	22.5302i	−0.717508	−	0.717508i
$987$	−13.0961	−	4.32640i	−0.416854	−	0.137711i
$988$	−23.2931	−	102.587i	−0.741052	−	3.26373i
$989$			14.8942i			0.473608i
$990$	−20.7316	−	26.1218i	−0.658893	−	0.830206i
$991$	−11.0885	−	19.2058i	−0.352237	−	0.610092i	0.634404	−	0.773001i	$-0.281245\pi$
$991$	−11.0885	−	19.2058i	−0.352237	−	0.610092i	−0.986641	+	0.162910i	$0.947912\pi$
$992$	−5.59584			−0.177668
$993$	44.5847	+	2.55618i	1.41485	+	0.0811180i
$994$	0.257291	−	0.960222i	0.00816077	−	0.0304564i
$995$	−2.72269	+	10.1612i	−0.0863149	+	0.322132i
$996$	24.4204	−	37.2029i	0.773790	−	1.17882i
$997$	54.7717			1.73464			0.867319	−	0.497753i	$-0.165841\pi$
$997$	54.7717			1.73464			0.867319	+	0.497753i	$0.165841\pi$
$998$	−25.9436	−	44.9356i	−0.821230	−	1.42241i
$999$	−5.36450	−	14.6150i	−0.169725	−	0.462397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.5	yes	336
9.2	odd	6		819.2.ew.a.596.80	✓	336
13.6	odd	12		819.2.ew.a.617.80	yes	336
117.110	even	12	inner	819.2.fy.a.344.5	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.80	✓	336	9.2	odd	6
819.2.ew.a.617.80	yes	336	13.6	odd	12
819.2.fy.a.50.5	yes	336	1.1	even	1	trivial
819.2.fy.a.344.5	yes	336	117.110	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.676409 - 2.52439i) q^{2} +(1.29284 - 1.15263i) q^{3} +(-4.18297 + 2.41504i) q^{4} +(-0.237212 - 0.885285i) q^{5} +(-3.78419 - 2.48398i) q^{6} +(0.707107 - 0.707107i) q^{7} +(5.22994 + 5.22994i) q^{8} +(0.342872 - 2.98034i) q^{9} +O(q^{10})\)	\(q+(-0.676409 - 2.52439i) q^{2} +(1.29284 - 1.15263i) q^{3} +(-4.18297 + 2.41504i) q^{4} +(-0.237212 - 0.885285i) q^{5} +(-3.78419 - 2.48398i) q^{6} +(0.707107 - 0.707107i) q^{7} +(5.22994 + 5.22994i) q^{8} +(0.342872 - 2.98034i) q^{9} +(-2.07435 + 1.19763i) q^{10} +(-4.48282 + 1.20117i) q^{11} +(-2.62426 + 7.94369i) q^{12} +(1.92171 - 3.05074i) q^{13} +(-2.26331 - 1.30672i) q^{14} +(-1.32709 - 0.871115i) q^{15} +(4.83475 - 8.37403i) q^{16} +(-1.79245 + 3.10462i) q^{17} +(-7.75547 + 1.15039i) q^{18} +(-5.83481 + 1.56343i) q^{19} +(3.13025 + 3.13025i) q^{20} +(0.0991412 - 1.72921i) q^{21} +(6.06444 + 10.5039i) q^{22} -8.61675 q^{23} +(12.7897 + 0.733273i) q^{24} +(3.60267 - 2.08000i) q^{25} +(-9.00113 - 2.78761i) q^{26} +(-2.99196 - 4.24831i) q^{27} +(-1.25012 + 4.66550i) q^{28} +(-2.94524 - 1.70044i) q^{29} +(-1.30138 + 3.93931i) q^{30} +(0.515850 - 0.138221i) q^{31} +(-10.1212 - 2.71195i) q^{32} +(-4.41107 + 6.71997i) q^{33} +(9.04969 + 2.42486i) q^{34} +(-0.793725 - 0.458257i) q^{35} +(5.76342 + 13.2947i) q^{36} +(2.89405 + 0.775458i) q^{37} +(7.89343 + 13.6718i) q^{38} +(-1.03192 - 6.15915i) q^{39} +(3.38938 - 5.87059i) q^{40} +(1.10671 - 1.10671i) q^{41} +(-4.43226 + 0.919382i) q^{42} -1.72852i q^{43} +(15.8506 - 15.8506i) q^{44} +(-2.71979 + 0.403432i) q^{45} +(5.82845 + 21.7521i) q^{46} +(2.06096 - 7.69162i) q^{47} +(-3.40163 - 16.3990i) q^{48} -1.00000i q^{49} +(-7.68761 - 7.68761i) q^{50} +(1.26113 + 6.07981i) q^{51} +(-0.670809 + 17.4022i) q^{52} +14.0127i q^{53} +(-8.70061 + 10.4265i) q^{54} +(2.12675 + 3.68365i) q^{55} +7.39625 q^{56} +(-5.74141 + 8.74667i) q^{57} +(-2.30038 + 8.58513i) q^{58} +(1.95236 - 7.28631i) q^{59} +(7.65494 + 0.438882i) q^{60} +13.4093 q^{61} +(-0.697850 - 1.20871i) q^{62} +(-1.86497 - 2.34987i) q^{63} +8.04513i q^{64} +(-3.15663 - 0.977594i) q^{65} +(19.9475 + 6.58981i) q^{66} +(-9.24196 - 9.24196i) q^{67} -17.3154i q^{68} +(-11.1401 + 9.93196i) q^{69} +(-0.619939 + 2.31364i) q^{70} +(0.0984490 + 0.367417i) q^{71} +(17.3802 - 13.7938i) q^{72} +(0.807556 - 0.807556i) q^{73} -7.83023i q^{74} +(2.26019 - 6.84166i) q^{75} +(20.6311 - 20.6311i) q^{76} +(-2.32048 + 4.01919i) q^{77} +(-14.8501 + 6.77107i) q^{78} +(1.94902 + 3.37579i) q^{79} +(-8.56027 - 2.29372i) q^{80} +(-8.76488 - 2.04375i) q^{81} +(-3.54234 - 2.04517i) q^{82} +(-5.13815 - 1.37676i) q^{83} +(3.76141 + 7.47267i) q^{84} +(3.17366 + 0.850380i) q^{85} +(-4.36346 + 1.16918i) q^{86} +(-5.76771 + 1.19639i) q^{87} +(-29.7269 - 17.1628i) q^{88} +(2.00933 - 7.49892i) q^{89} +(2.85811 + 6.59292i) q^{90} +(-0.798343 - 3.51606i) q^{91} +(36.0436 - 20.8098i) q^{92} +(0.507592 - 0.773284i) q^{93} -20.8107 q^{94} +(2.76817 + 4.79461i) q^{95} +(-16.2109 + 8.15986i) q^{96} +(-9.89722 - 9.89722i) q^{97} +(-2.52439 + 0.676409i) q^{98} +(2.04286 + 13.7722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

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