LMFDB - Embedded newform 429.2.s.b.166.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (of order $6$, degree $2$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.6
Character	$\chi$	$=$	429.166
Dual form			429.2.s.b.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.489701 + 0.282729i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.840128 + 1.45515i) q^{4} -1.14515i q^{5} +(0.489701 + 0.282729i) q^{6} +(2.75529 + 1.59077i) q^{7} -2.08103i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.489701 + 0.282729i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.840128 + 1.45515i) q^{4} -1.14515i q^{5} +(0.489701 + 0.282729i) q^{6} +(2.75529 + 1.59077i) q^{7} -2.08103i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.323767 + 0.560780i) q^{10} +(-0.866025 + 0.500000i) q^{11} +1.68026 q^{12} +(-2.18094 + 2.87115i) q^{13} -1.79902 q^{14} +(-0.991727 + 0.572574i) q^{15} +(-1.09189 - 1.89121i) q^{16} +(1.58351 - 2.74273i) q^{17} -0.565458i q^{18} +(4.59345 + 2.65203i) q^{19} +(1.66636 + 0.962071i) q^{20} -3.18153i q^{21} +(0.282729 - 0.489701i) q^{22} +(3.16876 + 5.48845i) q^{23} +(-1.80223 + 1.04052i) q^{24} +3.68864 q^{25} +(0.256254 - 2.02262i) q^{26} +1.00000 q^{27} +(-4.62959 + 2.67290i) q^{28} +(3.72041 + 6.44394i) q^{29} +(0.323767 - 0.560780i) q^{30} +7.39302i q^{31} +(4.67385 + 2.69845i) q^{32} +(0.866025 + 0.500000i) q^{33} +1.79082i q^{34} +(1.82166 - 3.15521i) q^{35} +(-0.840128 - 1.45515i) q^{36} +(-5.06907 + 2.92663i) q^{37} -2.99923 q^{38} +(3.57696 + 0.453179i) q^{39} -2.38309 q^{40} +(2.55277 - 1.47385i) q^{41} +(0.899512 + 1.55800i) q^{42} +(3.14032 - 5.43919i) q^{43} -1.68026i q^{44} +(0.991727 + 0.572574i) q^{45} +(-3.10349 - 1.79180i) q^{46} -5.76932i q^{47} +(-1.09189 + 1.89121i) q^{48} +(1.56108 + 2.70386i) q^{49} +(-1.80633 + 1.04289i) q^{50} -3.16703 q^{51} +(-2.34566 - 5.58572i) q^{52} -0.509048 q^{53} +(-0.489701 + 0.282729i) q^{54} +(0.572574 + 0.991727i) q^{55} +(3.31044 - 5.73384i) q^{56} -5.30406i q^{57} +(-3.64378 - 2.10374i) q^{58} +(-1.29318 - 0.746618i) q^{59} -1.92414i q^{60} +(-4.23333 + 7.33235i) q^{61} +(-2.09022 - 3.62037i) q^{62} +(-2.75529 + 1.59077i) q^{63} +1.31583 q^{64} +(3.28789 + 2.49750i) q^{65} -0.565458 q^{66} +(3.40283 - 1.96463i) q^{67} +(2.66071 + 4.60848i) q^{68} +(3.16876 - 5.48845i) q^{69} +2.06015i q^{70} +(-6.96332 - 4.02027i) q^{71} +(1.80223 + 1.04052i) q^{72} -0.446383i q^{73} +(1.65489 - 2.86635i) q^{74} +(-1.84432 - 3.19445i) q^{75} +(-7.71818 + 4.45609i) q^{76} -3.18153 q^{77} +(-1.87977 + 0.789388i) q^{78} -14.3374 q^{79} +(-2.16571 + 1.25037i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.833398 + 1.44349i) q^{82} -10.4452i q^{83} +(4.62959 + 2.67290i) q^{84} +(-3.14082 - 1.81336i) q^{85} +3.55144i q^{86} +(3.72041 - 6.44394i) q^{87} +(1.04052 + 1.80223i) q^{88} +(7.51085 - 4.33639i) q^{89} -0.647533 q^{90} +(-10.5765 + 4.44147i) q^{91} -10.6487 q^{92} +(6.40255 - 3.69651i) q^{93} +(1.63116 + 2.82525i) q^{94} +(3.03697 - 5.26018i) q^{95} -5.39690i q^{96} +(2.73813 + 1.58086i) q^{97} +(-1.52892 - 0.882723i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.489701	+	0.282729i	−0.346271	+	0.199920i	−0.663042	−	0.748582i	$-0.730735\pi$
$2$	−0.489701	+	0.282729i	−0.346271	+	0.199920i	0.316771	+	0.948502i	$0.397401\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.840128	+	1.45515i	−0.420064	+	0.727573i
$5$		−	1.14515i		−	0.512126i	−0.966660	−	0.256063i	$-0.917575\pi$
$5$		−	1.14515i		−	0.512126i	0.966660	−	0.256063i	$-0.0824254\pi$
$6$	0.489701	+	0.282729i	0.199920	+	0.115424i
$7$	2.75529	+	1.59077i	1.04140	+	0.601253i	0.920230	−	0.391378i	$-0.128002\pi$
$7$	2.75529	+	1.59077i	1.04140	+	0.601253i	0.121171	+	0.992632i	$0.461335\pi$
$8$		−	2.08103i		−	0.735756i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.323767	+	0.560780i	0.102384	+	0.177334i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	1.68026			0.485048
$13$	−2.18094	+	2.87115i	−0.604885	+	0.796313i
$13$	−2.18094	+	2.87115i	−0.604885	+	0.796313i
$14$	−1.79902			−0.480810
$15$	−0.991727	+	0.572574i	−0.256063	+	0.147838i
$16$	−1.09189	−	1.89121i	−0.272972	−	0.472801i
$17$	1.58351	−	2.74273i	0.384058	−	0.665209i	−0.607580	−	0.794259i	$-0.707859\pi$
$17$	1.58351	−	2.74273i	0.384058	−	0.665209i	0.991638	+	0.129050i	$0.0411928\pi$
$18$		−	0.565458i		−	0.133280i
$19$	4.59345	+	2.65203i	1.05381	+	0.608417i	0.923714	−	0.383084i	$-0.125138\pi$
$19$	4.59345	+	2.65203i	1.05381	+	0.608417i	0.130096	+	0.991501i	$0.458471\pi$
$20$	1.66636	+	0.962071i	0.372608	+	0.215126i
$21$		−	3.18153i		−	0.694267i
$22$	0.282729	−	0.489701i	0.0602781	−	0.104405i
$23$	3.16876	+	5.48845i	0.660731	+	1.14442i	0.980424	+	0.196899i	$0.0630871\pi$
$23$	3.16876	+	5.48845i	0.660731	+	1.14442i	−0.319692	+	0.947521i	$0.603580\pi$
$24$	−1.80223	+	1.04052i	−0.367878	+	0.212394i
$25$	3.68864			0.737727
$26$	0.256254	−	2.02262i	0.0502556	−	0.396669i
$27$	1.00000			0.192450
$28$	−4.62959	+	2.67290i	−0.874911	+	0.505130i
$29$	3.72041	+	6.44394i	0.690863	+	1.19661i	0.971555	+	0.236813i	$0.0761027\pi$
$29$	3.72041	+	6.44394i	0.690863	+	1.19661i	−0.280692	+	0.959798i	$0.590564\pi$
$30$	0.323767	−	0.560780i	0.0591114	−	0.102384i
$31$			7.39302i			1.32783i	0.747810	+	0.663913i	$0.231106\pi$
$31$			7.39302i			1.32783i	−0.747810	+	0.663913i	$0.768894\pi$
$32$	4.67385	+	2.69845i	0.826228	+	0.477023i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$			1.79082i			0.307123i
$35$	1.82166	−	3.15521i	0.307917	−	0.533328i
$36$	−0.840128	−	1.45515i	−0.140021	−	0.242524i
$37$	−5.06907	+	2.92663i	−0.833350	+	0.481135i	−0.854998	−	0.518631i	$-0.826442\pi$
$37$	−5.06907	+	2.92663i	−0.833350	+	0.481135i	0.0216481	+	0.999766i	$0.493109\pi$
$38$	−2.99923			−0.486539
$39$	3.57696	+	0.453179i	0.572772	+	0.0725668i
$40$	−2.38309			−0.376799
$41$	2.55277	−	1.47385i	0.398676	−	0.230176i	−0.287236	−	0.957860i	$-0.592736\pi$
$41$	2.55277	−	1.47385i	0.398676	−	0.230176i	0.685913	+	0.727684i	$0.259403\pi$
$42$	0.899512	+	1.55800i	0.138798	+	0.240405i
$43$	3.14032	−	5.43919i	0.478894	−	0.829468i	−0.520813	−	0.853671i	$-0.674371\pi$
$43$	3.14032	−	5.43919i	0.478894	−	0.829468i	0.999707	+	0.0242023i	$0.00770458\pi$
$44$		−	1.68026i		−	0.253308i
$45$	0.991727	+	0.572574i	0.147838	+	0.0853543i
$46$	−3.10349	−	1.79180i	−0.457585	−	0.264187i
$47$		−	5.76932i		−	0.841542i	−0.907167	−	0.420771i	$-0.861760\pi$
$47$		−	5.76932i		−	0.841542i	0.907167	−	0.420771i	$-0.138240\pi$
$48$	−1.09189	+	1.89121i	−0.157600	+	0.272972i
$49$	1.56108	+	2.70386i	0.223011	+	0.386266i
$50$	−1.80633	+	1.04289i	−0.255454	+	0.147486i
$51$	−3.16703			−0.443472
$52$	−2.34566	−	5.58572i	−0.325285	−	0.774600i
$53$	−0.509048			−0.0699231			−0.0349616	−	0.999389i	$-0.511131\pi$
$53$	−0.509048			−0.0699231			−0.0349616	+	0.999389i	$0.511131\pi$
$54$	−0.489701	+	0.282729i	−0.0666399	+	0.0384746i
$55$	0.572574	+	0.991727i	0.0772058	+	0.133724i
$56$	3.31044	−	5.73384i	0.442376	−	0.766217i
$57$		−	5.30406i		−	0.702540i
$58$	−3.64378	−	2.10374i	−0.478452	−	0.276234i
$59$	−1.29318	−	0.746618i	−0.168358	−	0.0972014i	0.413453	−	0.910525i	$-0.364322\pi$
$59$	−1.29318	−	0.746618i	−0.168358	−	0.0972014i	−0.581811	+	0.813324i	$0.697656\pi$
$60$		−	1.92414i		−	0.248406i
$61$	−4.23333	+	7.33235i	−0.542023	+	0.938811i	0.456765	+	0.889587i	$0.349008\pi$
$61$	−4.23333	+	7.33235i	−0.542023	+	0.938811i	−0.998788	+	0.0492237i	$0.984325\pi$
$62$	−2.09022	−	3.62037i	−0.265459	−	0.459788i
$63$	−2.75529	+	1.59077i	−0.347134	+	0.200418i
$64$	1.31583			0.164479
$65$	3.28789	+	2.49750i	0.407812	+	0.309777i
$66$	−0.565458			−0.0696031
$67$	3.40283	−	1.96463i	0.415722	−	0.240017i	−0.277523	−	0.960719i	$-0.589514\pi$
$67$	3.40283	−	1.96463i	0.415722	−	0.240017i	0.693245	+	0.720702i	$0.256180\pi$
$68$	2.66071	+	4.60848i	0.322658	+	0.558861i
$69$	3.16876	−	5.48845i	0.381474	−	0.660731i
$70$			2.06015i			0.246235i
$71$	−6.96332	−	4.02027i	−0.826393	−	0.477119i	0.0262227	−	0.999656i	$-0.491652\pi$
$71$	−6.96332	−	4.02027i	−0.826393	−	0.477119i	−0.852616	+	0.522538i	$0.824985\pi$
$72$	1.80223	+	1.04052i	0.212394	+	0.122626i
$73$		−	0.446383i		−	0.0522451i	−0.999659	−	0.0261226i	$-0.991684\pi$
$73$		−	0.446383i		−	0.0522451i	0.999659	−	0.0261226i	$-0.00831602\pi$
$74$	1.65489	−	2.86635i	0.192377	−	0.333206i
$75$	−1.84432	−	3.19445i	−0.212964	−	0.368864i
$76$	−7.71818	+	4.45609i	−0.885336	+	0.511149i
$77$	−3.18153			−0.362569
$78$	−1.87977	+	0.789388i	−0.212842	+	0.0893806i
$79$	−14.3374			−1.61308			−0.806539	−	0.591180i	$-0.798662\pi$
$79$	−14.3374			−1.61308			−0.806539	+	0.591180i	$0.798662\pi$
$80$	−2.16571	+	1.25037i	−0.242134	+	0.139796i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.833398	+	1.44349i	−0.0920334	+	0.159407i
$83$		−	10.4452i		−	1.14651i	−0.819377	−	0.573256i	$-0.805680\pi$
$83$		−	10.4452i		−	1.14651i	0.819377	−	0.573256i	$-0.194320\pi$
$84$	4.62959	+	2.67290i	0.505130	+	0.291637i
$85$	−3.14082	−	1.81336i	−0.340670	−	0.196686i
$86$			3.55144i			0.382961i
$87$	3.72041	−	6.44394i	0.398870	−	0.690863i
$88$	1.04052	+	1.80223i	0.110919	+	0.192118i
$89$	7.51085	−	4.33639i	0.796148	−	0.459656i	−0.0459744	−	0.998943i	$-0.514639\pi$
$89$	7.51085	−	4.33639i	0.796148	−	0.459656i	0.842122	+	0.539286i	$0.181306\pi$
$90$	−0.647533			−0.0682560
$91$	−10.5765	+	4.44147i	−1.10871	+	0.465592i
$92$	−10.6487			−1.11020
$93$	6.40255	−	3.69651i	0.663913	−	0.383310i
$94$	1.63116	+	2.82525i	0.168241	+	0.291402i
$95$	3.03697	−	5.26018i	0.311586	−	0.539683i
$96$		−	5.39690i		−	0.550819i
$97$	2.73813	+	1.58086i	0.278015	+	0.160512i	0.632524	−	0.774540i	$-0.282019\pi$
$97$	2.73813	+	1.58086i	0.278015	+	0.160512i	−0.354509	+	0.935052i	$0.615352\pi$
$98$	−1.52892	−	0.882723i	−0.154444	−	0.0891685i
$99$		−	1.00000i		−	0.100504i
$100$	−3.09893	+	5.36750i	−0.309893	+	0.536750i
$101$	−3.70783	−	6.42215i	−0.368943	−	0.639028i	0.620458	−	0.784240i	$-0.286947\pi$
$101$	−3.70783	−	6.42215i	−0.368943	−	0.639028i	−0.989401	+	0.145212i	$0.953613\pi$
$102$	1.55090	−	0.895411i	0.153562	−	0.0886589i
$103$	18.9322			1.86544			0.932721	−	0.360600i	$-0.117428\pi$
$103$	18.9322			1.86544			0.932721	+	0.360600i	$0.117428\pi$
$104$	5.97495	+	4.53861i	0.585892	+	0.445048i
$105$	−3.64332			−0.355552
$106$	0.249281	−	0.143923i	0.0242124	−	0.0139790i
$107$	−2.25105	−	3.89893i	−0.217617	−	0.376924i	0.736462	−	0.676479i	$-0.236495\pi$
$107$	−2.25105	−	3.89893i	−0.217617	−	0.376924i	−0.954079	+	0.299555i	$0.903162\pi$
$108$	−0.840128	+	1.45515i	−0.0808414	+	0.140021i
$109$			0.307611i			0.0294638i	0.999891	+	0.0147319i	$0.00468948\pi$
$109$			0.307611i			0.0294638i	−0.999891	+	0.0147319i	$0.995311\pi$
$110$	−0.560780	−	0.323767i	−0.0534683	−	0.0308699i
$111$	5.06907	+	2.92663i	0.481135	+	0.277783i
$112$		−	6.94776i		−	0.656501i
$113$	−8.84208	+	15.3149i	−0.831793	+	1.44071i	0.0648228	+	0.997897i	$0.479352\pi$
$113$	−8.84208	+	15.3149i	−0.831793	+	1.44071i	−0.896615	+	0.442810i	$0.853982\pi$
$114$	1.49961	+	2.59741i	0.140452	+	0.243269i
$115$	6.28508	−	3.62869i	0.586087	−	0.338377i
$116$	−12.5025			−1.16083
$117$	−1.39601	−	3.32433i	−0.129062	−	0.307334i
$118$	0.844363			0.0777299
$119$	8.72607	−	5.03800i	0.799918	−	0.461833i
$120$	1.19154	+	2.06382i	0.108773	+	0.188400i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	4.78755i		−	0.433444i
$123$	−2.55277	−	1.47385i	−0.230176	−	0.132892i
$124$	−10.7579	−	6.21109i	−0.966090	−	0.557772i
$125$		−	9.94977i		−	0.889935i
$126$	0.899512	−	1.55800i	0.0801349	−	0.138798i
$127$	−1.22740	−	2.12591i	−0.108914	−	0.188644i	0.806417	−	0.591348i	$-0.201404\pi$
$127$	−1.22740	−	2.12591i	−0.108914	−	0.188644i	−0.915331	+	0.402703i	$0.868071\pi$
$128$	−9.99207	+	5.76892i	−0.883182	+	0.509906i
$129$	−6.28063			−0.552979
$130$	−2.31620	−	0.293449i	−0.203144	−	0.0257372i
$131$	−10.5237			−0.919456			−0.459728	−	0.888060i	$-0.652053\pi$
$131$	−10.5237			−0.919456			−0.459728	+	0.888060i	$0.652053\pi$
$132$	−1.45515	+	0.840128i	−0.126654	+	0.0731238i
$133$	8.43752	+	14.6142i	0.731626	+	1.26721i
$134$	−1.11092	+	1.92416i	−0.0959684	+	0.166222i
$135$		−	1.14515i		−	0.0985586i
$136$	−5.70770	−	3.29534i	−0.489431	−	0.282573i
$137$	13.6067	+	7.85582i	1.16250	+	0.671168i	0.951901	−	0.306406i	$-0.0991264\pi$
$137$	13.6067	+	7.85582i	1.16250	+	0.671168i	0.210595	+	0.977573i	$0.432460\pi$
$138$			3.58360i			0.305056i
$139$	4.70234	−	8.14469i	0.398847	−	0.690823i	−0.594737	−	0.803920i	$-0.702744\pi$
$139$	4.70234	−	8.14469i	0.398847	−	0.690823i	0.993584	+	0.113097i	$0.0360771\pi$
$140$	3.06086	+	5.30157i	0.258690	+	0.448064i
$141$	−4.99638	+	2.88466i	−0.420771	+	0.242932i
$142$	4.54659			0.381542
$143$	0.453179	−	3.57696i	0.0378968	−	0.299120i
$144$	2.18378			0.181981
$145$	7.37927	−	4.26042i	0.612815	−	0.353809i
$146$	0.126205	+	0.218594i	0.0104448	+	0.0180910i
$147$	1.56108	−	2.70386i	0.128755	−	0.223011i
$148$		−	9.83498i		−	0.808430i
$149$	−17.2413	−	9.95429i	−1.41247	−	0.815487i	−0.416845	−	0.908978i	$-0.636864\pi$
$149$	−17.2413	−	9.95429i	−1.41247	−	0.815487i	−0.995620	+	0.0934903i	$0.970198\pi$
$150$	1.80633	+	1.04289i	0.147486	+	0.0851512i
$151$		−	19.5123i		−	1.58789i	−0.607993	−	0.793943i	$-0.708025\pi$
$151$		−	19.5123i		−	1.58789i	0.607993	−	0.793943i	$-0.291975\pi$
$152$	5.51896	−	9.55912i	0.447647	−	0.775347i
$153$	1.58351	+	2.74273i	0.128019	+	0.221736i
$154$	1.55800	−	0.899512i	0.125547	−	0.0724848i
$155$	8.46610			0.680014
$156$	−3.66455	+	4.82426i	−0.293398	+	0.386250i
$157$	−15.5653			−1.24224			−0.621121	−	0.783714i	$-0.713323\pi$
$157$	−15.5653			−1.24224			−0.621121	+	0.783714i	$0.713323\pi$
$158$	7.02102	−	4.05359i	0.558563	−	0.322486i
$159$	0.254524	+	0.440848i	0.0201851	+	0.0349616i
$160$	3.09012	−	5.35225i	0.244296	−	0.423132i
$161$			20.1630i			1.58907i
$162$	0.489701	+	0.282729i	0.0384746	+	0.0222133i
$163$	12.0514	+	6.95787i	0.943938	+	0.544983i	0.891192	−	0.453625i	$-0.149870\pi$
$163$	12.0514	+	6.95787i	0.943938	+	0.544983i	0.0527452	+	0.998608i	$0.483203\pi$
$164$			4.95288i			0.386755i
$165$	0.572574	−	0.991727i	0.0445748	−	0.0772058i
$166$	2.95317	+	5.11504i	0.229210	+	0.397004i
$167$	5.01232	−	2.89386i	0.387865	−	0.223934i	−0.293370	−	0.955999i	$-0.594777\pi$
$167$	5.01232	−	2.89386i	0.387865	−	0.223934i	0.681235	+	0.732065i	$0.261443\pi$
$168$	−6.62087			−0.510811
$169$	−3.48697	−	12.5236i	−0.268228	−	0.963355i
$170$	2.05075			0.157286
$171$	−4.59345	+	2.65203i	−0.351270	+	0.202806i
$172$	5.27654	+	9.13923i	0.402332	+	0.696860i
$173$	−10.5530	+	18.2783i	−0.802331	+	1.38968i	0.115748	+	0.993279i	$0.463073\pi$
$173$	−10.5530	+	18.2783i	−0.802331	+	1.38968i	−0.918079	+	0.396399i	$0.870260\pi$
$174$			4.20748i			0.318968i
$175$	10.1633	+	5.86776i	0.768270	+	0.443561i
$176$	1.89121	+	1.09189i	0.142555	+	0.0823042i
$177$			1.49324i			0.112239i
$178$	−2.45205	+	4.24707i	−0.183789	+	0.318331i
$179$	2.54838	+	4.41392i	0.190475	+	0.329912i	0.945408	−	0.325890i	$-0.105664\pi$
$179$	2.54838	+	4.41392i	0.190475	+	0.329912i	−0.754933	+	0.655802i	$0.772331\pi$
$180$	−1.66636	+	0.962071i	−0.124203	+	0.0717085i
$181$	12.8949			0.958469			0.479234	−	0.877687i	$-0.340914\pi$
$181$	12.8949			0.958469			0.479234	+	0.877687i	$0.340914\pi$
$182$	3.92357	−	5.16526i	0.290834	−	0.382875i
$183$	8.46667			0.625874
$184$	11.4216	−	6.59429i	0.842014	−	0.486137i
$185$	3.35142	+	5.80484i	0.246402	+	0.426780i
$186$	−2.09022	+	3.62037i	−0.153263	+	0.265459i
$187$			3.16703i			0.231596i
$188$	8.39520	+	4.84697i	0.612283	+	0.353502i
$189$	2.75529	+	1.59077i	0.200418	+	0.115711i
$190$			3.43456i			0.249169i
$191$	−3.54383	+	6.13809i	−0.256422	+	0.444137i	−0.965281	−	0.261214i	$-0.915877\pi$
$191$	−3.54383	+	6.13809i	−0.256422	+	0.444137i	0.708858	+	0.705351i	$0.249211\pi$
$192$	−0.657915	−	1.13954i	−0.0474810	−	0.0822394i
$193$	2.88342	−	1.66474i	0.207553	−	0.119831i	−0.392621	−	0.919701i	$-0.628431\pi$
$193$	2.88342	−	1.66474i	0.207553	−	0.119831i	0.600174	+	0.799870i	$0.295098\pi$
$194$	−1.78782			−0.128358
$195$	0.518957	−	4.09614i	0.0371633	−	0.293331i
$196$	−5.24602			−0.374715
$197$	10.9064	−	6.29681i	0.777049	−	0.448629i	−0.0583347	−	0.998297i	$-0.518579\pi$
$197$	10.9064	−	6.29681i	0.777049	−	0.448629i	0.835383	+	0.549668i	$0.185246\pi$
$198$	0.282729	+	0.489701i	0.0200927	+	0.0348016i
$199$	−3.03502	+	5.25681i	−0.215147	+	0.372645i	−0.953318	−	0.301968i	$-0.902356\pi$
$199$	−3.03502	+	5.25681i	−0.215147	+	0.372645i	0.738171	+	0.674613i	$0.235690\pi$
$200$		−	7.67617i		−	0.542787i
$201$	−3.40283	−	1.96463i	−0.240017	−	0.138574i
$202$	3.63146	+	2.09662i	0.255508	+	0.147518i
$203$			23.6732i			1.66154i
$204$	2.66071	−	4.60848i	0.186287	−	0.322658i
$205$	−1.68777	−	2.92330i	−0.117879	−	0.204172i
$206$	−9.27111	+	5.35268i	−0.645949	+	0.372939i
$207$	−6.33751			−0.440488
$208$	7.81128	+	0.989642i	0.541615	+	0.0686193i
$209$	−5.30406			−0.366890
$210$	1.78414	−	1.03007i	0.123117	−	0.0710819i
$211$	−6.55752	−	11.3580i	−0.451438	−	0.781914i	0.547037	−	0.837108i	$-0.315756\pi$
$211$	−6.55752	−	11.3580i	−0.451438	−	0.781914i	−0.998476	+	0.0551942i	$0.982422\pi$
$212$	0.427666	−	0.740739i	0.0293722	−	0.0508741i
$213$			8.04054i			0.550929i
$214$	2.20468	+	1.27287i	0.150709	+	0.0870119i
$215$	−6.22867	−	3.59613i	−0.424792	−	0.245254i
$216$		−	2.08103i		−	0.141596i
$217$	−11.7606	+	20.3699i	−0.798360	+	1.38280i
$218$	−0.0869707	−	0.150638i	−0.00589040	−	0.0102025i
$219$	−0.386579	+	0.223191i	−0.0261226	+	0.0150819i
$220$	−1.92414			−0.129726
$221$	4.42121	+	10.5282i	0.297403	+	0.708205i
$222$	−3.30978			−0.222138
$223$	8.75236	−	5.05318i	0.586101	−	0.338386i	−0.177453	−	0.984129i	$-0.556786\pi$
$223$	8.75236	−	5.05318i	0.586101	−	0.338386i	0.763554	+	0.645744i	$0.223452\pi$
$224$	8.58521	+	14.8700i	0.573623	+	0.993545i
$225$	−1.84432	+	3.19445i	−0.122955	+	0.212964i
$226$		−	9.99965i		−	0.665167i
$227$	−12.6683	−	7.31406i	−0.840826	−	0.485451i	0.0167187	−	0.999860i	$-0.494678\pi$
$227$	−12.6683	−	7.31406i	−0.840826	−	0.485451i	−0.857545	+	0.514409i	$0.828011\pi$
$228$	7.71818	+	4.45609i	0.511149	+	0.295112i
$229$			2.04428i			0.135090i	0.997716	+	0.0675450i	$0.0215166\pi$
$229$			2.04428i			0.135090i	−0.997716	+	0.0675450i	$0.978483\pi$
$230$	−2.05188	+	3.55395i	−0.135297	+	0.234341i
$231$	1.59077	+	2.75529i	0.104665	+	0.181285i
$232$	13.4101	−	7.74230i	0.880413	−	0.508307i
$233$	−23.3721			−1.53116			−0.765580	−	0.643341i	$-0.777548\pi$
$233$	−23.3721			−1.53116			−0.765580	+	0.643341i	$0.777548\pi$
$234$	1.62351	+	1.23323i	0.106132	+	0.0806190i
$235$	−6.60673			−0.430975
$236$	2.17288	−	1.25451i	0.141442	−	0.0816617i
$237$	7.16868	+	12.4165i	0.465656	+	0.806539i
$238$	−2.84878	+	4.93423i	−0.184659	+	0.319839i
$239$			5.19681i			0.336154i	0.985774	+	0.168077i	$0.0537557\pi$
$239$			5.19681i			0.336154i	−0.985774	+	0.168077i	$0.946244\pi$
$240$	2.16571	+	1.25037i	0.139796	+	0.0807112i
$241$	20.1134	+	11.6125i	1.29562	+	0.748027i	0.979644	−	0.200741i	$-0.0643348\pi$
$241$	20.1134	+	11.6125i	1.29562	+	0.748027i	0.315976	+	0.948767i	$0.397668\pi$
$242$			0.565458i			0.0363490i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.11309	−	12.3202i	−0.455369	−	0.788722i
$245$	3.09632	−	1.78766i	0.197817	−	0.114210i
$246$	1.66680			0.106271
$247$	−17.6324	+	7.40454i	−1.12192	+	0.471140i
$248$	15.3851			0.976956
$249$	−9.04582	+	5.22261i	−0.573256	+	0.330969i
$250$	2.81309	+	4.87242i	0.177915	+	0.308159i
$251$	14.1748	−	24.5514i	0.894704	−	1.54967i	0.0605342	−	0.998166i	$-0.480720\pi$
$251$	14.1748	−	24.5514i	0.894704	−	1.54967i	0.834170	−	0.551507i	$-0.185947\pi$
$252$		−	5.34579i		−	0.336753i
$253$	−5.48845	−	3.16876i	−0.345056	−	0.199218i
$254$	1.20212	+	0.694042i	0.0754275	+	0.0435481i
$255$			3.62671i			0.227114i
$256$	1.94626	−	3.37101i	0.121641	−	0.210688i
$257$	12.0636	+	20.8948i	0.752509	+	1.30338i	0.946603	+	0.322400i	$0.104490\pi$
$257$	12.0636	+	20.8948i	0.752509	+	1.30338i	−0.194095	+	0.980983i	$0.562177\pi$
$258$	3.07563	−	1.77572i	0.191481	−	0.110551i
$259$	−18.6223			−1.15714
$260$	−6.39648	+	2.68613i	−0.396693	+	0.166587i
$261$	−7.44083			−0.460576
$262$	5.15345	−	2.97535i	0.318381	−	0.183817i
$263$	0.0462103	+	0.0800386i	0.00284945	+	0.00493539i	0.867447	−	0.497530i	$-0.165760\pi$
$263$	0.0462103	+	0.0800386i	0.00284945	+	0.00493539i	−0.864597	+	0.502466i	$0.832426\pi$
$264$	1.04052	−	1.80223i	0.0640393	−	0.110919i
$265$			0.582935i			0.0358094i
$266$	−8.26373	−	4.77107i	−0.506682	−	0.292533i
$267$	−7.51085	−	4.33639i	−0.459656	−	0.265383i
$268$			6.60216i			0.403291i
$269$	−12.4233	+	21.5179i	−0.757465	+	1.31197i	0.186675	+	0.982422i	$0.440229\pi$
$269$	−12.4233	+	21.5179i	−0.757465	+	1.31197i	−0.944140	+	0.329546i	$0.893104\pi$
$270$	0.323767	+	0.560780i	0.0197038	+	0.0341280i
$271$	12.1204	−	6.99771i	0.736261	−	0.425081i	−0.0844470	−	0.996428i	$-0.526912\pi$
$271$	12.1204	−	6.99771i	0.736261	−	0.425081i	0.820708	+	0.571347i	$0.193579\pi$
$272$	−6.91608			−0.419349
$273$	9.13465	+	6.93874i	0.552854	+	0.419952i
$274$	−8.88428			−0.536719
$275$	−3.19445	+	1.84432i	−0.192633	+	0.111217i
$276$	5.32433	+	9.22200i	0.320487	+	0.555099i
$277$	−5.43400	+	9.41196i	−0.326497	+	0.565510i	−0.981814	−	0.189844i	$-0.939202\pi$
$277$	−5.43400	+	9.41196i	−0.326497	+	0.565510i	0.655317	+	0.755354i	$0.272535\pi$
$278$			5.31795i			0.318950i
$279$	−6.40255	−	3.69651i	−0.383310	−	0.221304i
$280$	−6.56610	−	3.79094i	−0.392399	−	0.226552i
$281$		−	31.3892i		−	1.87252i	−0.351305	−	0.936261i	$-0.614262\pi$
$281$		−	31.3892i		−	1.87252i	0.351305	−	0.936261i	$-0.385738\pi$
$282$	1.63116	−	2.82525i	0.0971340	−	0.168241i
$283$	1.07424	+	1.86063i	0.0638567	+	0.110603i	0.896186	−	0.443678i	$-0.146327\pi$
$283$	1.07424	+	1.86063i	0.0638567	+	0.110603i	−0.832330	+	0.554281i	$0.812993\pi$
$284$	11.7002	−	6.75509i	0.694277	−	0.400841i
$285$	−6.07393			−0.359789
$286$	0.789388	+	1.87977i	0.0466775	+	0.111153i
$287$	9.37817			0.553576
$288$	−4.67385	+	2.69845i	−0.275409	+	0.159008i
$289$	3.48497	+	6.03615i	0.204998	+	0.355068i
$290$	−2.40909	+	4.17267i	−0.141467	+	0.245028i
$291$		−	3.16172i		−	0.185343i
$292$	0.649551	+	0.375019i	0.0380121	+	0.0219463i
$293$	13.2618	+	7.65672i	0.774764	+	0.447310i	0.834572	−	0.550900i	$-0.185715\pi$
$293$	13.2618	+	7.65672i	0.774764	+	0.447310i	−0.0598072	+	0.998210i	$0.519049\pi$
$294$			1.76545i			0.102963i
$295$	−0.854988	+	1.48088i	−0.0497793	+	0.0862203i
$296$	6.09041	+	10.5489i	0.353998	+	0.613142i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	11.2575			0.652128
$299$	−22.6690	−	2.87203i	−1.31098	−	0.166094i
$300$	6.19786			0.357833
$301$	17.3050	−	9.99102i	0.997441	−	0.575873i
$302$	5.51669	+	9.55518i	0.317450	+	0.549839i
$303$	−3.70783	+	6.42215i	−0.213009	+	0.368943i
$304$		−	11.5829i		−	0.664324i
$305$	8.39662	+	4.84779i	0.480789	+	0.277584i
$306$	−1.55090	−	0.895411i	−0.0886589	−	0.0511872i
$307$		−	13.1885i		−	0.752710i	−0.926476	−	0.376355i	$-0.877177\pi$
$307$		−	13.1885i		−	0.752710i	0.926476	−	0.376355i	$-0.122823\pi$
$308$	2.67290	−	4.62959i	0.152302	−	0.263795i
$309$	−9.46608	−	16.3957i	−0.538507	−	0.932721i
$310$	−4.14586	+	2.39361i	−0.235469	+	0.135948i
$311$	21.7253			1.23193			0.615965	−	0.787773i	$-0.288766\pi$
$311$	21.7253			1.23193			0.615965	+	0.787773i	$0.288766\pi$
$312$	0.943081	−	7.44376i	0.0533914	−	0.421420i
$313$	24.2354			1.36987			0.684934	−	0.728605i	$-0.259831\pi$
$313$	24.2354			1.36987			0.684934	+	0.728605i	$0.259831\pi$
$314$	7.62233	−	4.40075i	0.430153	−	0.248349i
$315$	1.82166	+	3.15521i	0.102639	+	0.177776i
$316$	12.0452	−	20.8629i	0.677597	−	1.17363i
$317$		−	31.8516i		−	1.78897i	−0.447102	−	0.894483i	$-0.647544\pi$
$317$		−	31.8516i		−	1.78897i	0.447102	−	0.894483i	$-0.352456\pi$
$318$	−0.249281	−	0.143923i	−0.0139790	−	0.00807079i
$319$	−6.44394	−	3.72041i	−0.360792	−	0.208303i
$320$		−	1.50682i		−	0.0842338i
$321$	−2.25105	+	3.89893i	−0.125641	+	0.217617i
$322$	−5.70067	−	9.87385i	−0.317686	−	0.550248i
$323$	14.5476	−	8.39905i	0.809449	−	0.467336i
$324$	1.68026			0.0933476
$325$	−8.04471	+	10.5906i	−0.446240	+	0.587462i
$326$	−7.86878			−0.435811
$327$	0.266399	−	0.153806i	0.0147319	−	0.00850547i
$328$	−3.06712	−	5.31241i	−0.169353	−	0.293329i
$329$	9.17765	−	15.8962i	0.505980	−	0.876383i
$330$			0.647533i			0.0356455i
$331$	−18.6166	−	10.7483i	−1.02326	−	0.590780i	−0.108215	−	0.994128i	$-0.534513\pi$
$331$	−18.6166	−	10.7483i	−1.02326	−	0.590780i	−0.915047	+	0.403347i	$0.867847\pi$
$332$	15.1993	+	8.77532i	0.834170	+	0.481608i
$333$		−	5.85326i		−	0.320757i
$334$	−1.63636	+	2.83426i	−0.0895377	+	0.155084i
$335$	−2.24979	−	3.89675i	−0.122919	−	0.212902i
$336$	−6.01693	+	3.47388i	−0.328251	+	0.189516i
$337$	28.3426			1.54392			0.771959	−	0.635673i	$-0.219277\pi$
$337$	28.3426			1.54392			0.771959	+	0.635673i	$0.219277\pi$
$338$	5.24837	+	5.14697i	0.285473	+	0.279958i
$339$	17.6842			0.960471
$340$	5.27739	−	3.04690i	0.286207	−	0.165242i
$341$	−3.69651	−	6.40255i	−0.200177	−	0.346717i
$342$	1.49961	−	2.59741i	0.0810898	−	0.140452i
$343$		−	12.3375i		−	0.666163i
$344$	−11.3191	−	6.53510i	−0.610286	−	0.352349i
$345$	−6.28508	−	3.62869i	−0.338377	−	0.195362i
$346$		−	11.9346i		−	0.641607i
$347$	−2.20540	+	3.81987i	−0.118392	+	0.205061i	−0.919131	−	0.393953i	$-0.871107\pi$
$347$	−2.20540	+	3.81987i	−0.118392	+	0.205061i	0.800738	+	0.599014i	$0.204441\pi$
$348$	6.25125	+	10.8275i	0.335102	+	0.580414i
$349$	−18.5688	+	10.7207i	−0.993966	+	0.573867i	−0.906458	−	0.422297i	$-0.861224\pi$
$349$	−18.5688	+	10.7207i	−0.993966	+	0.573867i	−0.0875089	+	0.996164i	$0.527891\pi$
$350$	−6.63595			−0.354706
$351$	−2.18094	+	2.87115i	−0.116410	+	0.153250i
$352$	−5.39690			−0.287656
$353$	−20.3434	+	11.7453i	−1.08277	+	0.625139i	−0.931643	−	0.363375i	$-0.881624\pi$
$353$	−20.3434	+	11.7453i	−1.08277	+	0.625139i	−0.151129	+	0.988514i	$0.548291\pi$
$354$	−0.422182	−	0.731240i	−0.0224387	−	0.0388650i
$355$	−4.60380	+	7.97402i	−0.244345	+	0.423217i
$356$			14.5725i			0.772341i
$357$	−8.72607	−	5.03800i	−0.461833	−	0.266639i
$358$	−2.49589	−	1.44100i	−0.131912	−	0.0761594i
$359$		−	31.3374i		−	1.65393i	−0.562256	−	0.826963i	$-0.690067\pi$
$359$		−	31.3374i		−	1.65393i	0.562256	−	0.826963i	$-0.309933\pi$
$360$	1.19154	−	2.06382i	0.0627999	−	0.108773i
$361$	4.56653	+	7.90946i	0.240344	+	0.416288i
$362$	−6.31464	+	3.64576i	−0.331890	+	0.191617i
$363$	−1.00000			−0.0524864
$364$	2.42260	−	19.1217i	0.126979	−	1.00225i
$365$	−0.511174			−0.0267561
$366$	−4.14614	+	2.39377i	−0.216722	+	0.125125i
$367$	−15.8040	−	27.3734i	−0.824964	−	1.42888i	−0.901947	−	0.431848i	$-0.857862\pi$
$367$	−15.8040	−	27.3734i	−0.824964	−	1.42888i	0.0769823	−	0.997032i	$-0.475472\pi$
$368$	6.91986	−	11.9855i	0.360722	−	0.624790i
$369$			2.94769i			0.153451i
$370$	−3.28239	−	1.89509i	−0.170643	−	0.0985211i
$371$	−1.40257	−	0.809776i	−0.0728180	−	0.0420415i
$372$			12.4222i			0.644060i
$373$	−10.9569	+	18.9780i	−0.567329	+	0.982643i	0.429500	+	0.903067i	$0.358690\pi$
$373$	−10.9569	+	18.9780i	−0.567329	+	0.982643i	−0.996829	+	0.0795761i	$0.974643\pi$
$374$	−0.895411	−	1.55090i	−0.0463006	−	0.0801950i
$375$	−8.61675	+	4.97489i	−0.444967	+	0.256902i
$376$	−12.0061			−0.619170
$377$	−26.6155	−	3.37203i	−1.37077	−	0.173668i
$378$	−1.79902			−0.0925318
$379$	3.93282	−	2.27061i	0.202015	−	0.116634i	−0.395580	−	0.918432i	$-0.629456\pi$
$379$	3.93282	−	2.27061i	0.202015	−	0.116634i	0.597595	+	0.801798i	$0.296123\pi$
$380$	5.10288	+	8.83845i	0.261772	+	0.453403i
$381$	−1.22740	+	2.12591i	−0.0628815	+	0.108914i
$382$		−	4.00778i		−	0.205056i
$383$	−2.77735	−	1.60350i	−0.141916	−	0.0819352i	0.427361	−	0.904081i	$-0.359443\pi$
$383$	−2.77735	−	1.60350i	−0.141916	−	0.0819352i	−0.569277	+	0.822146i	$0.692777\pi$
$384$	9.99207	+	5.76892i	0.509906	+	0.294394i
$385$			3.64332i			0.185681i
$386$	−0.941343	+	1.63045i	−0.0479131	+	0.0829879i
$387$	3.14032	+	5.43919i	0.159631	+	0.276489i
$388$	−4.60076	+	2.65625i	−0.233568	+	0.134851i
$389$	−38.0952			−1.93151			−0.965753	−	0.259465i	$-0.916454\pi$
$389$	−38.0952			−1.93151			−0.965753	+	0.259465i	$0.916454\pi$
$390$	0.903966	+	2.15261i	0.0457741	+	0.109002i
$391$	20.0711			1.01504
$392$	5.62682	−	3.24865i	0.284198	−	0.164082i
$393$	5.26183	+	9.11375i	0.265424	+	0.459728i
$394$	−3.56059	+	6.16711i	−0.179380	+	0.310695i
$395$			16.4184i			0.826099i
$396$	1.45515	+	0.840128i	0.0731238	+	0.0422180i
$397$	−5.66354	−	3.26985i	−0.284245	−	0.164109i	0.351099	−	0.936338i	$-0.385808\pi$
$397$	−5.66354	−	3.26985i	−0.284245	−	0.164109i	−0.635344	+	0.772230i	$0.719141\pi$
$398$		−	3.43235i		−	0.172048i
$399$	8.43752	−	14.6142i	0.422404	−	0.731626i
$400$	−4.02758	−	6.97597i	−0.201379	−	0.348799i
$401$	−9.84558	+	5.68435i	−0.491665	+	0.283863i	−0.725265	−	0.688470i	$-0.758283\pi$
$401$	−9.84558	+	5.68435i	−0.491665	+	0.283863i	0.233600	+	0.972333i	$0.424949\pi$
$402$	2.22183			0.110815
$403$	−21.2265	−	16.1238i	−1.05737	−	0.803182i
$404$	12.4602			0.619919
$405$	−0.991727	+	0.572574i	−0.0492793	+	0.0284514i
$406$	−6.69311	−	11.5928i	−0.332174	−	0.575342i
$407$	2.92663	−	5.06907i	0.145068	−	0.251265i
$408$			6.59068i			0.326287i
$409$	16.3534	+	9.44164i	0.808623	+	0.466859i	0.846478	−	0.532424i	$-0.178719\pi$
$409$	16.3534	+	9.44164i	0.808623	+	0.466859i	−0.0378542	+	0.999283i	$0.512052\pi$
$410$	1.65301	+	0.954364i	0.0816362	+	0.0471327i
$411$		−	15.7116i		−	0.774998i
$412$	−15.9054	+	27.5490i	−0.783605	+	1.35724i
$413$	−2.37539	−	4.11430i	−0.116885	−	0.202451i
$414$	3.10349	−	1.79180i	0.152528	−	0.0880622i
$415$	−11.9613			−0.587158
$416$	−17.9411	+	7.53415i	−0.879632	+	0.369392i
$417$	−9.40468			−0.460549
$418$	2.59741	−	1.49961i	0.127043	−	0.0733485i
$419$	6.77220	+	11.7298i	0.330844	+	0.573038i	0.982678	−	0.185324i	$-0.0593333\pi$
$419$	6.77220	+	11.7298i	0.330844	+	0.573038i	−0.651834	+	0.758362i	$0.726000\pi$
$420$	3.06086	−	5.30157i	0.149355	−	0.258690i
$421$		−	34.5157i		−	1.68219i	−0.540886	−	0.841096i	$-0.681911\pi$
$421$		−	34.5157i		−	1.68219i	0.540886	−	0.841096i	$-0.318089\pi$
$422$	6.42245	+	3.70800i	0.312640	+	0.180503i
$423$	4.99638	+	2.88466i	0.242932	+	0.140257i
$424$			1.05935i			0.0514464i
$425$	5.84101	−	10.1169i	0.283330	−	0.490743i
$426$	−2.27330	−	3.93747i	−0.110142	−	0.190771i
$427$	−23.3281	+	13.4685i	−1.12893	+	0.651786i
$428$	7.56468			0.365653
$429$	−3.32433	+	1.39601i	−0.160500	+	0.0674002i
$430$	4.06692			0.196124
$431$	−21.4219	+	12.3680i	−1.03186	+	0.595744i	−0.917517	−	0.397697i	$-0.869809\pi$
$431$	−21.4219	+	12.3680i	−1.03186	+	0.595744i	−0.114342	+	0.993441i	$0.536476\pi$
$432$	−1.09189	−	1.89121i	−0.0525335	−	0.0909907i
$433$	4.98001	−	8.62562i	0.239324	−	0.414521i	−0.721197	−	0.692730i	$-0.756408\pi$
$433$	4.98001	−	8.62562i	0.239324	−	0.414521i	0.960520	+	0.278209i	$0.0897409\pi$
$434$		−	13.3002i		−	0.638432i
$435$	−7.37927	−	4.26042i	−0.353809	−	0.204272i
$436$	−0.447619	−	0.258433i	−0.0214371	−	0.0123767i
$437$			33.6146i			1.60800i
$438$	0.126205	−	0.218594i	0.00603033	−	0.0104448i
$439$	2.14962	+	3.72325i	0.102596	+	0.177701i	0.912753	−	0.408511i	$-0.133952\pi$
$439$	2.14962	+	3.72325i	0.102596	+	0.177701i	−0.810158	+	0.586212i	$0.800619\pi$
$440$	2.06382	−	1.19154i	0.0983885	−	0.0568047i
$441$	−3.12215			−0.148674
$442$	−5.14171	−	3.90568i	−0.244566	−	0.185774i
$443$	8.66562			0.411716			0.205858	−	0.978582i	$-0.434002\pi$
$443$	8.66562			0.411716			0.205858	+	0.978582i	$0.434002\pi$
$444$	−8.51734	+	4.91749i	−0.404215	+	0.233374i
$445$	−4.96581	−	8.60103i	−0.235402	−	0.407728i
$446$	−2.85736	+	4.94910i	−0.135300	+	0.234346i
$447$			19.9086i			0.941644i
$448$	3.62549	+	2.09318i	0.171288	+	0.0988934i
$449$	2.94890	+	1.70255i	0.139167	+	0.0803483i	0.567967	−	0.823051i	$-0.307730\pi$
$449$	2.94890	+	1.70255i	0.139167	+	0.0803483i	−0.428800	+	0.903400i	$0.641063\pi$
$450$		−	2.08577i		−	0.0983242i
$451$	−1.47385	+	2.55277i	−0.0694007	+	0.120205i
$452$	−14.8570	−	25.7330i	−0.698813	−	1.21038i
$453$	−16.8981	+	9.75613i	−0.793943	+	0.458383i
$454$	8.27160			0.388205
$455$	5.08613	+	12.1116i	0.238442	+	0.567801i
$456$	−11.0379			−0.516898
$457$	15.2201	−	8.78734i	0.711967	−	0.411054i	−0.0998219	−	0.995005i	$-0.531827\pi$
$457$	15.2201	−	8.78734i	0.711967	−	0.411054i	0.811789	+	0.583951i	$0.198494\pi$
$458$	−0.577978	−	1.00109i	−0.0270071	−	0.0467778i
$459$	1.58351	−	2.74273i	0.0739121	−	0.128019i
$460$			12.1943i			0.568561i
$461$	−14.3070	−	8.26015i	−0.666343	−	0.384713i	0.128346	−	0.991729i	$-0.459033\pi$
$461$	−14.3070	−	8.26015i	−0.666343	−	0.384713i	−0.794690	+	0.607016i	$0.792366\pi$
$462$	−1.55800	−	0.899512i	−0.0724848	−	0.0418491i
$463$			18.5503i			0.862108i	0.902326	+	0.431054i	$0.141858\pi$
$463$			18.5503i			0.862108i	−0.902326	+	0.431054i	$0.858142\pi$
$464$	8.12455	−	14.0721i	0.377173	−	0.653282i
$465$	−4.23305	−	7.33186i	−0.196303	−	0.340007i
$466$	11.4454	−	6.60798i	0.530196	−	0.306109i
$467$	−0.827179			−0.0382773			−0.0191387	−	0.999817i	$-0.506092\pi$
$467$	−0.827179			−0.0382773			−0.0191387	+	0.999817i	$0.506092\pi$
$468$	6.01021	+	0.761458i	0.277822	+	0.0351984i
$469$	12.5011			0.577245
$470$	3.23532	−	1.86791i	0.149234	−	0.0861605i
$471$	7.78263	+	13.4799i	0.358605	+	0.621121i
$472$	−1.55374	+	2.69115i	−0.0715165	+	0.123870i
$473$			6.28063i			0.288784i
$474$	−7.02102	−	4.05359i	−0.322486	−	0.186188i
$475$	16.9436	+	9.78238i	0.777425	+	0.448846i
$476$			16.9303i			0.775997i
$477$	0.254524	−	0.440848i	0.0116539	−	0.0201851i
$478$	−1.46929	−	2.54488i	−0.0672038	−	0.116400i
$479$	−10.2093	+	5.89433i	−0.466474	+	0.269319i	−0.714762	−	0.699367i	$-0.753465\pi$
$479$	−10.2093	+	5.89433i	−0.466474	+	0.269319i	0.248289	+	0.968686i	$0.420132\pi$
$480$	−6.18025			−0.282088
$481$	2.65258	−	20.9369i	0.120947	−	0.954639i
$482$	−13.1328			−0.598181
$483$	17.4617	−	10.0815i	0.794534	−	0.458724i
$484$	0.840128	+	1.45515i	0.0381877	+	0.0661430i
$485$	1.81032	−	3.13556i	0.0822023	−	0.142379i
$486$		−	0.565458i		−	0.0256497i
$487$	31.8482	+	18.3876i	1.44318	+	0.833220i	0.998061	−	0.0622514i	$-0.0198281\pi$
$487$	31.8482	+	18.3876i	1.44318	+	0.833220i	0.445119	+	0.895471i	$0.353161\pi$
$488$	15.2589	+	8.80970i	0.690736	+	0.398797i
$489$		−	13.9157i		−	0.629292i
$490$	−1.01085	+	1.75084i	−0.0456655	+	0.0790949i
$491$	−17.0822	−	29.5872i	−0.770908	−	1.33525i	−0.937066	−	0.349153i	$-0.886469\pi$
$491$	−17.0822	−	29.5872i	−0.770908	−	1.33525i	0.166157	−	0.986099i	$-0.446864\pi$
$492$	4.28932	−	2.47644i	0.193377	−	0.111646i
$493$	23.5653			1.06133
$494$	6.54114	−	8.61122i	0.294300	−	0.387437i
$495$	−1.14515			−0.0514706
$496$	13.9817	−	8.07236i	0.627798	−	0.362459i
$497$	−12.7906	−	22.1540i	−0.573738	−	0.993743i
$498$	2.95317	−	5.11504i	0.132335	−	0.229210i
$499$			18.1480i			0.812416i	0.913781	+	0.406208i	$0.133149\pi$
$499$			18.1480i			0.812416i	−0.913781	+	0.406208i	$0.866851\pi$
$500$	14.4784	+	8.35909i	0.647492	+	0.373830i
$501$	−5.01232	−	2.89386i	−0.223934	−	0.129288i
$502$			16.0305i			0.715476i
$503$	8.62544	−	14.9397i	0.384589	−	0.666128i	−0.607123	−	0.794608i	$-0.707676\pi$
$503$	8.62544	−	14.9397i	0.384589	−	0.666128i	0.991712	+	0.128480i	$0.0410098\pi$
$504$	3.31044	+	5.73384i	0.147459	+	0.255406i
$505$	−7.35431	+	4.24601i	−0.327262	+	0.188945i
$506$	3.58360			0.159310
$507$	−9.10229	+	9.28161i	−0.404247	+	0.412211i
$508$	4.12469			0.183003
$509$	−18.9375	+	10.9336i	−0.839392	+	0.484623i	−0.857057	−	0.515221i	$-0.827710\pi$
$509$	−18.9375	+	10.9336i	−0.839392	+	0.484623i	0.0176656	+	0.999844i	$0.494377\pi$
$510$	−1.02538	−	1.77601i	−0.0454045	−	0.0786429i
$511$	0.710090	−	1.22991i	0.0314126	−	0.0544081i
$512$		−	20.8746i		−	0.922537i
$513$	4.59345	+	2.65203i	0.202806	+	0.117090i
$514$	−11.8152	−	6.82148i	−0.521144	−	0.300883i
$515$		−	21.6801i		−	0.955340i
$516$	5.27654	−	9.13923i	0.232287	−	0.402332i
$517$	2.88466	+	4.99638i	0.126867	+	0.219741i
$518$	9.11938	−	5.26508i	0.400683	−	0.231334i
$519$	21.1060			0.926451
$520$	5.19738	−	6.84220i	0.227920	−	0.300050i
$521$	−2.76795			−0.121266			−0.0606331	−	0.998160i	$-0.519312\pi$
$521$	−2.76795			−0.121266			−0.0606331	+	0.998160i	$0.519312\pi$
$522$	3.64378	−	2.10374i	0.159484	−	0.0920782i
$523$	15.3489	+	26.5851i	0.671161	+	1.16248i	0.977575	+	0.210586i	$0.0675373\pi$
$523$	15.3489	+	26.5851i	0.671161	+	1.16248i	−0.306415	+	0.951898i	$0.599129\pi$
$524$	8.84122	−	15.3134i	0.386231	−	0.668971i
$525$		−	11.7355i		−	0.512180i
$526$	−0.0452585	−	0.0261300i	−0.00197336	−	0.00113932i
$527$	20.2770	+	11.7070i	0.883281	+	0.509963i
$528$		−	2.18378i		−	0.0950367i
$529$	−8.58204	+	14.8645i	−0.373132	+	0.646284i
$530$	−0.164813	−	0.285464i	−0.00715901	−	0.0123998i
$531$	1.29318	−	0.746618i	0.0561193	−	0.0324005i
$532$	−28.3544			−1.22932
$533$	−1.33583	+	10.5438i	−0.0578613	+	0.456701i
$534$	4.90410			0.212221
$535$	−4.46485	+	2.57778i	−0.193032	+	0.111447i
$536$	−4.08845	−	7.08141i	−0.176594	−	0.305870i
$537$	2.54838	−	4.41392i	0.109971	−	0.190475i
$538$		−	14.0498i		−	0.605729i
$539$	−2.70386	−	1.56108i	−0.116464	−	0.0672403i
$540$	1.66636	+	0.962071i	0.0717085	+	0.0414009i
$541$			19.8933i			0.855279i	0.903949	+	0.427639i	$0.140655\pi$
$541$			19.8933i			0.855279i	−0.903949	+	0.427639i	$0.859345\pi$
$542$	−3.95692	+	6.85358i	−0.169964	+	0.294386i
$543$	−6.44744	−	11.1673i	−0.276686	−	0.479234i
$544$	14.8022	−	8.54606i	0.634640	−	0.366409i
$545$	0.352260			0.0150892
$546$	−6.43504	−	0.815281i	−0.275394	−	0.0348908i
$547$	−16.9595			−0.725137			−0.362569	−	0.931957i	$-0.618100\pi$
$547$	−16.9595			−0.725137			−0.362569	+	0.931957i	$0.618100\pi$
$548$	−22.8627	+	13.1998i	−0.976646	+	0.563867i
$549$	−4.23333	−	7.33235i	−0.180674	−	0.312937i
$550$	1.04289	−	1.80633i	0.0444688	−	0.0770222i
$551$			39.4666i			1.68133i
$552$	−11.4216	−	6.59429i	−0.486137	−	0.280671i
$553$	−39.5036	−	22.8074i	−1.67986	−	0.969869i
$554$		−	6.14540i		−	0.261093i
$555$	3.35142	−	5.80484i	0.142260	−	0.246402i
$556$	7.90114	+	13.6852i	0.335083	+	0.580380i
$557$	3.46661	−	2.00145i	0.146885	−	0.0848041i	−0.424756	−	0.905308i	$-0.639640\pi$
$557$	3.46661	−	2.00145i	0.146885	−	0.0848041i	0.571641	+	0.820504i	$0.306307\pi$
$558$	4.18045			0.176972
$559$	8.76785	+	20.8789i	0.370841	+	0.883082i
$560$	−7.95621			−0.336211
$561$	2.74273	−	1.58351i	0.115798	−	0.0668560i
$562$	8.87464	+	15.3713i	0.374354	+	0.648400i
$563$	−0.319414	+	0.553241i	−0.0134617	+	0.0233163i	−0.872678	−	0.488297i	$-0.837618\pi$
$563$	−0.319414	+	0.553241i	−0.0134617	+	0.0233163i	0.859216	+	0.511613i	$0.170952\pi$
$564$		−	9.69395i		−	0.408189i
$565$	17.5378	+	10.1255i	0.737823	+	0.425982i
$566$	−1.05211	−	0.607436i	−0.0442235	−	0.0255324i
$567$		−	3.18153i		−	0.133612i
$568$	−8.36632	+	14.4909i	−0.351043	+	0.608024i
$569$	−1.41808	−	2.45618i	−0.0594488	−	0.102968i	0.834769	−	0.550600i	$-0.185601\pi$
$569$	−1.41808	−	2.45618i	−0.0594488	−	0.102968i	−0.894218	+	0.447631i	$0.852268\pi$
$570$	2.97441	−	1.71728i	0.124584	−	0.0719289i
$571$	−10.0407			−0.420190			−0.210095	−	0.977681i	$-0.567377\pi$
$571$	−10.0407			−0.420190			−0.210095	+	0.977681i	$0.567377\pi$
$572$	4.82426	+	3.66455i	0.201713	+	0.153222i
$573$	7.08766			0.296091
$574$	−4.59250	+	2.65148i	−0.191687	+	0.110671i
$575$	11.6884	+	20.2449i	0.487440	+	0.844270i
$576$	−0.657915	+	1.13954i	−0.0274131	+	0.0474810i
$577$		−	35.5503i		−	1.47998i	−0.672618	−	0.739990i	$-0.734830\pi$
$577$		−	35.5503i		−	1.47998i	0.672618	−	0.739990i	$-0.265170\pi$
$578$	−3.41319	−	1.97061i	−0.141970	−	0.0819665i
$579$	−2.88342	−	1.66474i	−0.119831	−	0.0691844i
$580$			14.3172i			0.594490i
$581$	16.6159	−	28.7796i	0.689344	−	1.19398i
$582$	0.893911	+	1.54830i	0.0370538	+	0.0641791i
$583$	0.440848	−	0.254524i	0.0182581	−	0.0105413i
$584$	−0.928937			−0.0384397
$585$	−3.80684	+	1.59864i	−0.157394	+	0.0660957i
$586$	−8.65911			−0.357705
$587$	30.7386	−	17.7469i	1.26872	−	0.732494i	0.293972	−	0.955814i	$-0.405023\pi$
$587$	30.7386	−	17.7469i	1.26872	−	0.732494i	0.974745	+	0.223320i	$0.0716896\pi$
$588$	2.62301	+	4.54318i	0.108171	+	0.187358i
$589$	−19.6065	+	33.9595i	−0.807873	+	1.39928i
$590$		−	0.966920i		−	0.0398075i
$591$	−10.9064	−	6.29681i	−0.448629	−	0.259016i
$592$	11.0697	+	6.39111i	0.454963	+	0.262673i
$593$			0.893536i			0.0366931i	0.999832	+	0.0183466i	$0.00584022\pi$
$593$			0.893536i			0.0366931i	−0.999832	+	0.0183466i	$0.994160\pi$
$594$	0.282729	−	0.489701i	0.0116005	−	0.0200927i
$595$	−5.76925	−	9.99264i	−0.236516	−	0.409658i
$596$	28.9699	−	16.7258i	1.18665	−	0.685114i
$597$	6.07004			0.248430
$598$	11.9131	−	5.00276i	0.487161	−	0.204578i
$599$	24.0472			0.982542			0.491271	−	0.871007i	$-0.336533\pi$
$599$	24.0472			0.982542			0.491271	+	0.871007i	$0.336533\pi$
$600$	−6.64776	+	3.83809i	−0.271394	+	0.156689i
$601$	−9.35265	−	16.1993i	−0.381503	−	0.660782i	0.609775	−	0.792575i	$-0.291260\pi$
$601$	−9.35265	−	16.1993i	−0.381503	−	0.660782i	−0.991277	+	0.131793i	$0.957927\pi$
$602$	−5.64951	+	9.78523i	−0.230257	+	0.398816i
$603$			3.92925i			0.160012i
$604$	28.3932	+	16.3928i	1.15530	+	0.667014i
$605$	−0.991727	−	0.572574i	−0.0403194	−	0.0232784i
$606$		−	4.19325i		−	0.170339i
$607$	3.60020	−	6.23573i	0.146128	−	0.253101i	−0.783665	−	0.621183i	$-0.786652\pi$
$607$	3.60020	−	6.23573i	0.146128	−	0.253101i	0.929793	+	0.368083i	$0.119986\pi$
$608$	14.3127	+	24.7904i	0.580458	+	1.00538i
$609$	20.5016	−	11.8366i	0.830768	−	0.479644i
$610$	−5.48245			−0.221978
$611$	16.5646	+	12.5826i	0.670131	+	0.509036i
$612$	−5.32142			−0.215106
$613$	17.2457	−	9.95683i	0.696549	−	0.402153i	−0.109512	−	0.993985i	$-0.534929\pi$
$613$	17.2457	−	9.95683i	0.696549	−	0.402153i	0.806061	+	0.591833i	$0.201595\pi$
$614$	3.72879	+	6.45845i	0.150482	+	0.260642i
$615$	−1.68777	+	2.92330i	−0.0680575	+	0.117879i
$616$			6.62087i			0.266763i
$617$	−13.7329	−	7.92871i	−0.552867	−	0.319198i	0.197411	−	0.980321i	$-0.436747\pi$
$617$	−13.7329	−	7.92871i	−0.552867	−	0.319198i	−0.750277	+	0.661123i	$0.770080\pi$
$618$	9.27111	+	5.35268i	0.372939	+	0.215316i
$619$			13.8796i			0.557869i	0.960310	+	0.278935i	$0.0899813\pi$
$619$			13.8796i			0.557869i	−0.960310	+	0.278935i	$0.910019\pi$
$620$	−7.11261	+	12.3194i	−0.285649	+	0.494759i
$621$	3.16876	+	5.48845i	0.127158	+	0.220244i
$622$	−10.6389	+	6.14239i	−0.426582	+	0.246287i
$623$	27.5927			1.10548
$624$	−3.04858	−	7.25958i	−0.122041	−	0.290616i
$625$	7.04923			0.281969
$626$	−11.8681	+	6.85206i	−0.474346	+	0.273864i
$627$	2.65203	+	4.59345i	0.105912	+	0.183445i
$628$	13.0768	−	22.6497i	0.521822	−	0.903822i
$629$			18.5374i			0.739136i
$630$	−1.78414	−	1.03007i	−0.0710819	−	0.0410391i
$631$	−35.0744	−	20.2502i	−1.39629	−	0.806148i	−0.402288	−	0.915513i	$-0.631785\pi$
$631$	−35.0744	−	20.2502i	−1.39629	−	0.806148i	−0.994002	+	0.109365i	$0.965118\pi$
$632$			29.8365i			1.18683i
$633$	−6.55752	+	11.3580i	−0.260638	+	0.451438i
$634$	9.00539	+	15.5978i	0.357650	+	0.619467i
$635$	−2.43449	+	1.40555i	−0.0966096	+	0.0557776i
$636$	−0.855331			−0.0339161
$637$	−11.1678	−	1.41489i	−0.442485	−	0.0560602i
$638$	4.20748			0.166576
$639$	6.96332	−	4.02027i	0.275464	−	0.159040i
$640$	6.60627	+	11.4424i	0.261136	+	0.452300i
$641$	1.17247	−	2.03078i	0.0463097	−	0.0802108i	−0.841941	−	0.539569i	$-0.818587\pi$
$641$	1.17247	−	2.03078i	0.0463097	−	0.0802108i	0.888251	+	0.459358i	$0.151921\pi$
$642$		−	2.54575i		−	0.100473i
$643$	1.90321	+	1.09882i	0.0750554	+	0.0433332i	0.537058	−	0.843545i	$-0.319536\pi$
$643$	1.90321	+	1.09882i	0.0750554	+	0.0433332i	−0.462003	+	0.886879i	$0.652869\pi$
$644$	−29.3401	−	16.9395i	−1.15616	−	0.667510i
$645$			7.19225i			0.283195i
$646$	−4.74931	+	8.22605i	−0.186859	+	0.323650i
$647$	5.95698	+	10.3178i	0.234193	+	0.405634i	0.959038	−	0.283278i	$-0.0914219\pi$
$647$	5.95698	+	10.3178i	0.234193	+	0.405634i	−0.724845	+	0.688912i	$0.758089\pi$
$648$	−1.80223	+	1.04052i	−0.0707982	+	0.0408753i
$649$	1.49324			0.0586147
$650$	0.945228	−	7.46071i	0.0370749	−	0.292633i
$651$	23.5212			0.921867
$652$	−20.2494	+	11.6910i	−0.793029	+	0.457855i
$653$	18.7227	+	32.4287i	0.732676	+	1.26903i	0.955736	+	0.294227i	$0.0950621\pi$
$653$	18.7227	+	32.4287i	0.732676	+	1.26903i	−0.223060	+	0.974805i	$0.571605\pi$
$654$	−0.0869707	+	0.150638i	−0.00340082	+	0.00589040i
$655$			12.0511i			0.470877i
$656$	−5.57469	−	3.21855i	−0.217655	−	0.125663i
$657$	0.386579	+	0.223191i	0.0150819	+	0.00870752i
$658$			10.3792i			0.404622i
$659$	12.4307	−	21.5305i	0.484230	−	0.838711i	−0.515606	−	0.856826i	$-0.672433\pi$
$659$	12.4307	−	21.5305i	0.484230	−	0.838711i	0.999836	+	0.0181150i	$0.00576651\pi$
$660$	0.962071	+	1.66636i	0.0374486	+	0.0648628i
$661$	−18.0448	+	10.4182i	−0.701862	+	0.405220i	−0.808040	−	0.589127i	$-0.799472\pi$
$661$	−18.0448	+	10.4182i	−0.701862	+	0.405220i	0.106179	+	0.994347i	$0.466138\pi$
$662$	12.1554			0.472435
$663$	6.90711	−	9.09300i	0.268250	−	0.353143i
$664$	−21.7368			−0.843552
$665$	16.7354	−	9.66221i	0.648972	−	0.374684i
$666$	1.65489	+	2.86635i	0.0641256	+	0.111069i
$667$	−23.5782	+	40.8386i	−0.912950	+	1.58128i
$668$			9.72487i			0.376267i
$669$	−8.75236	−	5.05318i	−0.338386	−	0.195367i
$670$	2.20345	+	1.27216i	0.0851266	+	0.0491479i
$671$		−	8.46667i		−	0.326852i
$672$	8.58521	−	14.8700i	0.331182	−	0.573623i
$673$	11.1197	+	19.2599i	0.428633	+	0.742414i	0.996752	−	0.0805324i	$-0.0256620\pi$
$673$	11.1197	+	19.2599i	0.428633	+	0.742414i	−0.568119	+	0.822946i	$0.692329\pi$
$674$	−13.8794	+	8.01327i	−0.534614	+	0.308660i
$675$	3.68864			0.141976
$676$	21.1532	+	5.44740i	0.813584	+	0.209516i
$677$	14.3251			0.550557			0.275279	−	0.961365i	$-0.411230\pi$
$677$	14.3251			0.550557			0.275279	+	0.961365i	$0.411230\pi$
$678$	−8.65995	+	4.99983i	−0.332584	+	0.192017i
$679$	5.02956	+	8.71145i	0.193017	+	0.334315i
$680$	−3.77365	+	6.53616i	−0.144713	+	0.250650i
$681$			14.6281i			0.560551i
$682$	3.62037	+	2.09022i	0.138631	+	0.0800388i
$683$	−34.6694	−	20.0164i	−1.32659	−	0.765906i	−0.341818	−	0.939766i	$-0.611043\pi$
$683$	−34.6694	−	20.0164i	−1.32659	−	0.765906i	−0.984770	+	0.173860i	$0.944376\pi$
$684$		−	8.91218i		−	0.340766i
$685$	8.99607	−	15.5816i	0.343722	−	0.595344i
$686$	3.48817	+	6.04169i	0.133179	+	0.230673i
$687$	1.77040	−	1.02214i	0.0675450	−	0.0389971i
$688$	−13.7155			−0.522898
$689$	1.11021	−	1.46155i	0.0422954	−	0.0556807i
$690$	4.10375			0.156227
$691$	−1.19982	+	0.692718i	−0.0456434	+	0.0263522i	−0.522648	−	0.852549i	$-0.675056\pi$
$691$	−1.19982	+	0.692718i	−0.0456434	+	0.0263522i	0.477005	+	0.878901i	$0.341722\pi$
$692$	−17.7318	−	30.7123i	−0.674061	−	1.16751i
$693$	1.59077	−	2.75529i	0.0604282	−	0.104665i
$694$		−	2.49413i		−	0.0946758i
$695$	−9.32687	−	5.38487i	−0.353788	−	0.204260i
$696$	−13.4101	−	7.74230i	−0.508307	−	0.293471i
$697$		−	9.33541i		−	0.353604i
$698$	6.06212	−	10.4999i	0.229455	−	0.397427i
$699$	11.6861	+	20.2409i	0.442008	+	0.765580i
$700$	−17.0769	+	9.85934i	−0.645446	+	0.372648i
$701$	0.173553			0.00655501			0.00327751	−	0.999995i	$-0.498957\pi$
$701$	0.173553			0.00655501			0.00327751	+	0.999995i	$0.498957\pi$
$702$	0.256254	−	2.02262i	0.00967169	−	0.0763389i
$703$	−31.0460			−1.17092
$704$	−1.13954	+	0.657915i	−0.0429481	+	0.0247961i
$705$	3.30336	+	5.72159i	0.124412	+	0.215488i
$706$	6.64147	−	11.5034i	0.249955	−	0.432935i
$707$		−	23.5932i		−	0.887312i
$708$	−2.17288	−	1.25451i	−0.0816617	−	0.0471474i
$709$	−16.2899	−	9.40495i	−0.611778	−	0.353210i	0.161883	−	0.986810i	$-0.448243\pi$
$709$	−16.2899	−	9.40495i	−0.611778	−	0.353210i	−0.773661	+	0.633600i	$0.781577\pi$
$710$		−	5.20652i		−	0.195397i
$711$	7.16868	−	12.4165i	0.268846	−	0.465656i
$712$	−9.02417	−	15.6303i	−0.338195	−	0.585771i
$713$	−40.5762	+	23.4267i	−1.51959	+	0.877337i
$714$	5.69756			0.213226
$715$	−4.09614	−	0.518957i	−0.153187	−	0.0194079i
$716$	−8.56387			−0.320047
$717$	4.50057	−	2.59841i	0.168077	−	0.0970392i
$718$	8.86000	+	15.3460i	0.330652	+	0.572707i
$719$	6.37701	−	11.0453i	0.237822	−	0.411920i	−0.722267	−	0.691614i	$-0.756900\pi$
$719$	6.37701	−	11.0453i	0.237822	−	0.411920i	0.960089	+	0.279694i	$0.0902331\pi$
$720$		−	2.50075i		−	0.0931973i
$721$	52.1636	+	30.1166i	1.94267	+	1.12160i
$722$	−4.47247	−	2.58218i	−0.166448	−	0.0960989i
$723$		−	23.2250i		−	0.863747i
$724$	−10.8334	+	18.7639i	−0.402618	+	0.697355i
$725$	13.7233	+	23.7694i	0.509669	+	0.882772i
$726$	0.489701	−	0.282729i	0.0181745	−	0.0104931i
$727$	13.7467			0.509836			0.254918	−	0.966963i	$-0.417952\pi$
$727$	13.7467			0.509836			0.254918	+	0.966963i	$0.417952\pi$
$728$	9.24283	+	22.0099i	0.342562	+	0.815743i
$729$	1.00000			0.0370370
$730$	0.250323	−	0.144524i	0.00926485	−	0.00534907i
$731$	−9.94546	−	17.2260i	−0.367846	−	0.637128i
$732$	−7.11309	+	12.3202i	−0.262907	+	0.455369i
$733$		−	15.4100i		−	0.569182i	−0.958649	−	0.284591i	$-0.908142\pi$
$733$		−	15.4100i		−	0.569182i	0.958649	−	0.284591i	$-0.0918578\pi$
$734$	15.4785	+	8.93653i	0.571323	+	0.329853i
$735$	−3.09632	−	1.78766i	−0.114210	−	0.0659389i
$736$			34.2029i			1.26074i
$737$	−1.96463	+	3.40283i	−0.0723680	+	0.125345i
$738$	−0.833398	−	1.44349i	−0.0306778	−	0.0531355i
$739$	34.8583	−	20.1254i	1.28228	−	0.740327i	0.305018	−	0.952347i	$-0.401338\pi$
$739$	34.8583	−	20.1254i	1.28228	−	0.740327i	0.977265	+	0.212020i	$0.0680042\pi$
$740$	−11.2625			−0.414018
$741$	15.2287	+	11.5679i	0.559442	+	0.424956i
$742$	0.915790			0.0336197
$743$	25.9276	−	14.9693i	0.951190	−	0.549170i	0.0577399	−	0.998332i	$-0.481611\pi$
$743$	25.9276	−	14.9693i	0.951190	−	0.549170i	0.893451	+	0.449162i	$0.148277\pi$
$744$	−7.69256	−	13.3239i	−0.282023	−	0.488478i
$745$	−11.3991	+	19.7439i	−0.417632	+	0.723360i
$746$		−	12.3914i		−	0.453681i
$747$	9.04582	+	5.22261i	0.330969	+	0.191085i
$748$	−4.60848	−	2.66071i	−0.168503	−	0.0972851i
$749$		−	14.3236i		−	0.523372i
$750$	2.81309	−	4.87242i	0.102720	−	0.177915i
$751$	−3.40689	−	5.90091i	−0.124319	−	0.215327i	0.797147	−	0.603785i	$-0.206341\pi$
$751$	−3.40689	−	5.90091i	−0.124319	−	0.215327i	−0.921467	+	0.388457i	$0.873008\pi$
$752$	−10.9110	+	6.29946i	−0.397882	+	0.229718i
$753$	−28.3496			−1.03312
$754$	13.9870	−	5.87370i	0.509378	−	0.213907i
$755$	−22.3444			−0.813197
$756$	−4.62959	+	2.67290i	−0.168377	+	0.0972123i
$757$	−21.6929	−	37.5733i	−0.788444	−	1.36562i	−0.926920	−	0.375259i	$-0.877554\pi$
$757$	−21.6929	−	37.5733i	−0.788444	−	1.36562i	0.138477	−	0.990366i	$-0.455779\pi$
$758$	−1.28394	+	2.22384i	−0.0466347	+	0.0807736i
$759$			6.33751i			0.230037i
$760$	−10.9466	−	6.32002i	−0.397075	−	0.229251i
$761$	−2.51046	−	1.44942i	−0.0910042	−	0.0525413i	0.453807	−	0.891100i	$-0.350065\pi$
$761$	−2.51046	−	1.44942i	−0.0910042	−	0.0525413i	−0.544811	+	0.838559i	$0.683399\pi$
$762$		−	1.38808i		−	0.0502850i
$763$	−0.489338	+	0.847557i	−0.0177152	+	0.0306836i
$764$	−5.95454	−	10.3136i	−0.215428	−	0.373132i
$765$	3.14082	−	1.81336i	0.113557	−	0.0655620i
$766$	1.81343			0.0655219
$767$	4.96401	−	2.08458i	0.179240	−	0.0752698i
$768$	−3.89251			−0.140459
$769$	−12.2829	+	7.09153i	−0.442932	+	0.255727i	−0.704841	−	0.709366i	$-0.748982\pi$
$769$	−12.2829	+	7.09153i	−0.442932	+	0.255727i	0.261908	+	0.965093i	$0.415648\pi$
$770$	−1.03007	−	1.78414i	−0.0371213	−	0.0642960i
$771$	12.0636	−	20.8948i	0.434461	−	0.752509i
$772$			5.59439i			0.201347i
$773$	25.7566	+	14.8706i	0.926401	+	0.534858i	0.885672	−	0.464312i	$-0.153698\pi$
$773$	25.7566	+	14.8706i	0.926401	+	0.534858i	0.0407297	+	0.999170i	$0.487032\pi$
$774$	−3.07563	−	1.77572i	−0.110551	−	0.0638269i
$775$			27.2702i			0.979574i
$776$	3.28982	−	5.69814i	0.118098	−	0.204551i
$777$	9.31117	+	16.1274i	0.334036	+	0.578568i
$778$	18.6553	−	10.7706i	0.668824	−	0.386146i
$779$	15.6347			0.560172
$780$	5.52449	+	4.19645i	0.197809	+	0.150257i
$781$	8.04054			0.287713
$782$	−9.82883	+	5.67468i	−0.351478	+	0.202926i
$783$	3.72041	+	6.44394i	0.132957	+	0.230288i
$784$	3.40904	−	5.90463i	0.121751	−	0.210880i
$785$			17.8245i			0.636184i
$786$	−5.15345	−	2.97535i	−0.183817	−	0.106127i
$787$	−19.4248	−	11.2149i	−0.692419	−	0.399768i	0.112098	−	0.993697i	$-0.464243\pi$
$787$	−19.4248	−	11.2149i	−0.692419	−	0.399768i	−0.804518	+	0.593929i	$0.797576\pi$
$788$			21.1605i			0.753812i
$789$	0.0462103	−	0.0800386i	0.00164513	−	0.00284945i
$790$	−4.64196	−	8.04011i	−0.165153	−	0.286054i
$791$	−48.7249	+	28.1314i	−1.73246	+	1.00024i
$792$	−2.08103			−0.0739463
$793$	−11.8196	−	28.1460i	−0.419726	−	0.999493i
$794$	3.69792			0.131234
$795$	0.504837	−	0.291468i	0.0179047	−	0.0103373i
$796$	−5.09961	−	8.83279i	−0.180751	−	0.313070i
$797$	−0.00383197	+	0.00663716i	−0.000135735	+	0.000235100i	−0.866093	−	0.499882i	$-0.833377\pi$
$797$	−0.00383197	+	0.00663716i	−0.000135735	+	0.000235100i	0.865958	+	0.500118i	$0.166710\pi$
$798$			9.54214i			0.337788i
$799$	−15.8237	−	9.13580i	−0.559801	−	0.323201i
$800$	17.2401	+	9.95360i	0.609531	+	0.351913i
$801$			8.67278i			0.306438i
$802$	3.21426	−	5.56727i	0.113500	−	0.196587i
$803$	0.223191	+	0.386579i	0.00787625	+	0.0136421i
$804$	5.71764	−	3.30108i	0.201645	−	0.116420i
$805$	23.0896			0.813802
$806$	14.9533	+	1.89449i	0.526707	+	0.0667307i
$807$	24.8467			0.874645
$808$	−13.3647	+	7.71611i	−0.470168	+	0.271452i
$809$	−21.6154	−	37.4390i	−0.759957	−	1.31628i	−0.942872	−	0.333156i	$-0.891887\pi$
$809$	−21.6154	−	37.4390i	−0.759957	−	1.31628i	0.182915	−	0.983129i	$-0.441447\pi$
$810$	0.323767	−	0.560780i	0.0113760	−	0.0197038i
$811$		−	21.5592i		−	0.757046i	−0.925592	−	0.378523i	$-0.876432\pi$
$811$		−	21.5592i		−	0.757046i	0.925592	−	0.378523i	$-0.123568\pi$
$812$	−34.4480	−	19.8886i	−1.20889	−	0.697951i
$813$	−12.1204	−	6.99771i	−0.425081	−	0.245420i
$814$			3.30978i			0.116008i
$815$	7.96779	−	13.8006i	0.279100	−	0.483415i
$816$	3.45804	+	5.98950i	0.121056	+	0.209674i
$817$	28.8498	−	16.6564i	1.00933	−	0.582735i
$818$	−10.6777			−0.373337
$819$	1.44180	−	11.3802i	0.0503807	−	0.397657i
$820$	5.67177			0.198067
$821$	35.2837	−	20.3711i	1.23141	−	0.710956i	0.264087	−	0.964499i	$-0.414929\pi$
$821$	35.2837	−	20.3711i	1.23141	−	0.710956i	0.967324	+	0.253543i	$0.0815960\pi$
$822$	4.44214	+	7.69401i	0.154937	+	0.268359i
$823$	−5.07887	+	8.79687i	−0.177038	+	0.306639i	−0.940865	−	0.338782i	$-0.889985\pi$
$823$	−5.07887	+	8.79687i	−0.177038	+	0.306639i	0.763826	+	0.645422i	$0.223318\pi$
$824$		−	39.3984i		−	1.37251i
$825$	3.19445	+	1.84432i	0.111217	+	0.0642109i
$826$	2.32646	+	1.34318i	0.0809480	+	0.0467354i
$827$			17.5998i			0.612005i	0.952031	+	0.306002i	$0.0989916\pi$
$827$			17.5998i			0.612005i	−0.952031	+	0.306002i	$0.901008\pi$
$828$	5.32433	−	9.22200i	0.185033	−	0.320487i
$829$	22.5937	+	39.1335i	0.784713	+	1.35916i	0.929171	+	0.369651i	$0.120523\pi$
$829$	22.5937	+	39.1335i	0.784713	+	1.35916i	−0.144458	+	0.989511i	$0.546144\pi$
$830$	5.85747	−	3.38181i	0.203316	−	0.117384i
$831$	10.8680			0.377006
$832$	−2.86975	+	3.77794i	−0.0994908	+	0.130977i
$833$	9.88794			0.342597
$834$	4.60548	−	2.65898i	0.159475	−	0.0920728i
$835$	−3.31390	−	5.73985i	−0.114682	−	0.198636i
$836$	4.45609	−	7.71818i	0.154117	−	0.266939i
$837$			7.39302i			0.255540i
$838$	−6.63271	−	3.82940i	−0.229123	−	0.132284i
$839$	37.8496	+	21.8524i	1.30671	+	0.754430i	0.981546	−	0.191227i	$-0.0612466\pi$
$839$	37.8496	+	21.8524i	1.30671	+	0.754430i	0.325166	+	0.945657i	$0.394580\pi$
$840$			7.58188i			0.261600i
$841$	−13.1829	+	22.8335i	−0.454584	+	0.787363i
$842$	9.75860	+	16.9024i	0.336303	+	0.582495i
$843$	−27.1838	+	15.6946i	−0.936261	+	0.540550i
$844$	22.0366			0.758532
$845$	−14.3414	+	3.99309i	−0.493359	+	0.137367i
$846$	−3.26231			−0.112161
$847$	2.75529	−	1.59077i	0.0946728	−	0.0546594i
$848$	0.555823	+	0.962714i	0.0190871	+	0.0330598i
$849$	1.07424	−	1.86063i	0.0368677	−	0.0638567i
$850$			6.60569i			0.226573i
$851$	−32.1253	−	18.5476i	−1.10124	−	0.635802i
$852$	−11.7002	−	6.75509i	−0.400841	−	0.231426i
$853$		−	12.1377i		−	0.415587i	−0.978173	−	0.207794i	$-0.933372\pi$
$853$		−	12.1377i		−	0.415587i	0.978173	−	0.207794i	$-0.0666282\pi$
$854$	7.61587	−	13.1911i	0.260610	−	0.451389i
$855$	3.03697	+	5.26018i	0.103862	+	0.179894i
$856$	−8.11380	+	4.68451i	−0.277324	+	0.160113i
$857$	10.5390			0.360005			0.180003	−	0.983666i	$-0.442389\pi$
$857$	10.5390			0.360005			0.180003	+	0.983666i	$0.442389\pi$
$858$	1.23323	−	1.62351i	0.0421019	−	0.0554259i
$859$	−50.1178			−1.71000			−0.854998	−	0.518631i	$-0.826442\pi$
$859$	−50.1178			−1.71000			−0.854998	+	0.518631i	$0.826442\pi$
$860$	10.4658	−	6.04241i	0.356880	−	0.206045i
$861$	−4.68909	−	8.12174i	−0.159804	−	0.276788i
$862$	6.99357	−	12.1132i	0.238202	−	0.412578i
$863$			41.1504i			1.40077i	0.713763	+	0.700387i	$0.246989\pi$
$863$			41.1504i			1.40077i	−0.713763	+	0.700387i	$0.753011\pi$
$864$	4.67385	+	2.69845i	0.159008	+	0.0918031i
$865$	20.9314	+	12.0848i	0.711689	+	0.410894i
$866$			5.63197i			0.191382i
$867$	3.48497	−	6.03615i	0.118356	−	0.204998i
$868$	−19.7608	−	34.2267i	−0.670725	−	1.16173i
$869$	12.4165	−	7.16868i	0.421201	−	0.243181i
$870$	4.81818			0.163352
$871$	−1.78066	+	14.0548i	−0.0603353	+	0.476228i
$872$	0.640149			0.0216782
$873$	−2.73813	+	1.58086i	−0.0926717	+	0.0535040i
$874$	−9.50382	−	16.4611i	−0.321471	−	0.556805i
$875$	15.8278	−	27.4145i	0.535076	−	0.926779i
$876$		−	0.750037i		−	0.0253414i
$877$	19.5251	+	11.2728i	0.659315	+	0.380656i	0.792016	−	0.610501i	$-0.209032\pi$
$877$	19.5251	+	11.2728i	0.659315	+	0.380656i	−0.132701	+	0.991156i	$0.542365\pi$
$878$	−2.10534	−	1.21552i	−0.0710519	−	0.0410218i
$879$		−	15.3134i		−	0.516510i
$880$	1.25037	−	2.16571i	0.0421501	−	0.0730061i
$881$	−14.5180	−	25.1458i	−0.489123	−	0.847185i	0.510799	−	0.859700i	$-0.329350\pi$
$881$	−14.5180	−	25.1458i	−0.489123	−	0.847185i	−0.999922	+	0.0125150i	$0.996016\pi$
$882$	1.52892	−	0.882723i	0.0514815	−	0.0297228i
$883$	17.9090			0.602685			0.301342	−	0.953516i	$-0.402565\pi$
$883$	17.9090			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$884$	−19.0345	−	2.41156i	−0.640199	−	0.0811094i
$885$	1.70998			0.0574802
$886$	−4.24356	+	2.45002i	−0.142565	+	0.0823101i
$887$	−0.0604606	−	0.104721i	−0.00203007	−	0.00351618i	0.865009	−	0.501757i	$-0.167313\pi$
$887$	−0.0604606	−	0.104721i	−0.00203007	−	0.00351618i	−0.867039	+	0.498241i	$0.833980\pi$
$888$	6.09041	−	10.5489i	0.204381	−	0.353998i
$889$		−	7.81001i		−	0.261939i
$890$	4.86352	+	2.80796i	0.163026	+	0.0941229i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$			16.9813i			0.568575i
$893$	15.3004	−	26.5011i	0.512009	−	0.886826i
$894$	−5.62874	−	9.74926i	−0.188253	−	0.326064i
$895$	5.05459	−	2.91827i	0.168956	−	0.0975471i
$896$	−36.7080			−1.22633
$897$	8.84726	+	21.0680i	0.295401	+	0.703439i
$898$	−1.92544			−0.0642528
$899$	−47.6402	+	27.5051i	−1.58889	+	0.917347i
$900$	−3.09893	−	5.36750i	−0.103298	−	0.178917i
$901$	−0.806084	+	1.39618i	−0.0268546	+	0.0465135i
$902$		−	1.66680i		−	0.0554982i
$903$	−17.3050	−	9.99102i	−0.575873	−	0.332480i
$904$	31.8709	+	18.4006i	1.06001	+	0.611996i
$905$		−	14.7665i		−	0.490856i
$906$	5.51669	−	9.55518i	0.183280	−	0.317450i
$907$	−7.04660	−	12.2051i	−0.233979	−	0.405263i	0.724997	−	0.688752i	$-0.241841\pi$
$907$	−7.04660	−	12.2051i	−0.233979	−	0.405263i	−0.958975	+	0.283490i	$0.908508\pi$
$908$	21.2860	−	12.2895i	0.706402	−	0.407841i
$909$	7.41566			0.245962
$910$	−5.91499	−	4.49307i	−0.196080	−	0.148944i
$911$	18.8741			0.625326			0.312663	−	0.949864i	$-0.398779\pi$
$911$	18.8741			0.625326			0.312663	+	0.949864i	$0.398779\pi$
$912$	−10.0311	+	5.79144i	−0.332162	+	0.191774i
$913$	5.22261	+	9.04582i	0.172843	+	0.299373i
$914$	−4.96887	+	8.60634i	−0.164356	+	0.284673i
$915$		−	9.69558i		−	0.320526i
$916$	−2.97473	−	1.71746i	−0.0982877	−	0.0567465i
$917$	−28.9957	−	16.7407i	−0.957523	−	0.552826i
$918$			1.79082i			0.0591059i
$919$	−16.9429	+	29.3460i	−0.558895	+	0.968035i	0.438694	+	0.898637i	$0.355441\pi$
$919$	−16.9429	+	29.3460i	−0.558895	+	0.968035i	−0.997589	+	0.0693986i	$0.977892\pi$
$920$	−7.55143	−	13.0795i	−0.248963	−	0.431217i
$921$	−11.4216	+	6.59427i	−0.376355	+	0.217289i
$922$	9.34154			0.307647
$923$	26.7294	−	11.2247i	0.879809	−	0.369466i
$924$	−5.34579			−0.175864
$925$	−18.6980	+	10.7953i	−0.614785	+	0.354946i
$926$	−5.24472	−	9.08413i	−0.172352	−	0.298523i
$927$	−9.46608	+	16.3957i	−0.310907	+	0.538507i
$928$			40.1574i			1.31823i
$929$	−22.9644	−	13.2585i	−0.753438	−	0.434998i	0.0734969	−	0.997295i	$-0.476584\pi$
$929$	−22.9644	−	13.2585i	−0.753438	−	0.434998i	−0.826935	+	0.562298i	$0.809917\pi$
$930$	4.14586	+	2.39361i	0.135948	+	0.0784897i
$931$			16.5601i			0.542735i
$932$	19.6356	−	34.0098i	0.643185	−	1.11403i
$933$	−10.8627	−	18.8147i	−0.355628	−	0.615965i
$934$	0.405071	−	0.233868i	0.0132543	−	0.00765239i
$935$	3.62671			0.118606
$936$	−6.91803	+	2.90515i	−0.226123	+	0.0949578i
$937$	−53.7826			−1.75700			−0.878500	−	0.477743i	$-0.841455\pi$
$937$	−53.7826			−1.75700			−0.878500	+	0.477743i	$0.841455\pi$
$938$	−6.12178	+	3.53441i	−0.199883	+	0.115403i
$939$	−12.1177	−	20.9885i	−0.395447	−	0.684934i
$940$	5.55050	−	9.61375i	0.181037	−	0.313566i
$941$		−	1.87615i		−	0.0611607i	−0.999532	−	0.0305803i	$-0.990264\pi$
$941$		−	1.87615i		−	0.0611607i	0.999532	−	0.0305803i	$-0.00973554\pi$
$942$	−7.62233	−	4.40075i	−0.248349	−	0.143384i
$943$	16.1782	+	9.34051i	0.526836	+	0.304169i
$944$			3.26089i			0.106133i
$945$	1.82166	−	3.15521i	0.0592587	−	0.102639i
$946$	−1.77572	−	3.07563i	−0.0577336	−	0.0999975i
$947$	10.0761	−	5.81742i	0.327428	−	0.189041i	−0.327271	−	0.944931i	$-0.606129\pi$
$947$	10.0761	−	5.81742i	0.327428	−	0.189041i	0.654699	+	0.755890i	$0.272796\pi$
$948$	−24.0904			−0.782421
$949$	1.28163	+	0.973535i	0.0416035	+	0.0316023i
$950$	−11.0631			−0.358933
$951$	−27.5843	+	15.9258i	−0.894483	+	0.516430i
$952$	−10.4842	−	18.1592i	−0.339796	−	0.588544i
$953$	−12.6265	+	21.8698i	−0.409014	+	0.708433i	−0.994779	−	0.102048i	$-0.967461\pi$
$953$	−12.6265	+	21.8698i	−0.409014	+	0.708433i	0.585766	+	0.810480i	$0.300794\pi$
$954$			0.287845i			0.00931934i
$955$	7.02902	+	4.05821i	0.227454	+	0.131321i
$956$	−7.56211	−	4.36599i	−0.244576	−	0.141206i
$957$			7.44083i			0.240528i
$958$	3.33300	−	5.77292i	0.107684	−	0.186515i
$959$	24.9935	+	43.2901i	0.807083	+	1.39791i
$960$	−1.30494	+	0.753410i	−0.0421169	+	0.0243162i
$961$	−23.6568			−0.763123
$962$	4.62049	+	11.0028i	0.148971	+	0.354744i
$963$	4.50210			0.145078
$964$	−33.7957	+	19.5120i	−1.08849	+	0.628438i
$965$	−1.90638	−	3.30194i	−0.0613684	−	0.106293i
$966$	−5.70067	+	9.87385i	−0.183416	+	0.317686i
$967$		−	28.4241i		−	0.914057i	−0.889452	−	0.457028i	$-0.848914\pi$
$967$		−	28.4241i		−	0.914057i	0.889452	−	0.457028i	$-0.151086\pi$
$968$	−1.80223	−	1.04052i	−0.0579258	−	0.0334435i
$969$	−14.5476	−	8.39905i	−0.467336	−	0.269816i
$970$			2.04732i			0.0657355i
$971$	4.10199	−	7.10486i	0.131639	−	0.228006i	−0.792669	−	0.609652i	$-0.791309\pi$
$971$	4.10199	−	7.10486i	0.131639	−	0.228006i	0.924309	+	0.381646i	$0.124643\pi$
$972$	−0.840128	−	1.45515i	−0.0269471	−	0.0466738i
$973$	25.9126	−	14.9606i	0.830720	−	0.479616i
$974$	−20.7948			−0.666309
$975$	13.1941	+	1.67161i	0.422549	+	0.0535345i
$976$	18.4893			0.591828
$977$	8.41350	−	4.85754i	0.269172	−	0.155406i	−0.359339	−	0.933207i	$-0.616998\pi$
$977$	8.41350	−	4.85754i	0.269172	−	0.155406i	0.628511	+	0.777801i	$0.283665\pi$
$978$	3.93439	+	6.81456i	0.125808	+	0.217906i
$979$	−4.33639	+	7.51085i	−0.138592	+	0.240048i
$980$			6.00746i			0.191901i
$981$	−0.266399	−	0.153806i	−0.00850547	−	0.00491063i
$982$	16.7303	+	9.65927i	0.533887	+	0.308240i
$983$		−	6.64254i		−	0.211864i	−0.994373	−	0.105932i	$-0.966217\pi$
$983$		−	6.64254i		−	0.211864i	0.994373	−	0.105932i	$-0.0337826\pi$
$984$	−3.06712	+	5.31241i	−0.0977762	+	0.169353i
$985$	−7.21078	−	12.4894i	−0.229754	−	0.397946i
$986$	−11.5400	+	6.66260i	−0.367507	+	0.212180i
$987$	−18.3553			−0.584255
$988$	4.03882	−	31.8785i	0.128492	−	1.01419i
$989$	39.8036			1.26568
$990$	0.560780	−	0.323767i	0.0178228	−	0.0102900i
$991$	−13.2337	−	22.9215i	−0.420383	−	0.728125i	0.575594	−	0.817736i	$-0.304771\pi$
$991$	−13.2337	−	22.9215i	−0.420383	−	0.728125i	−0.995977	+	0.0896111i	$0.971438\pi$
$992$	−19.9497	+	34.5539i	−0.633404	+	1.09709i
$993$			21.4966i			0.682174i
$994$	12.5272	+	7.23257i	0.397338	+	0.229403i
$995$	6.01982	+	3.47555i	0.190841	+	0.110182i
$996$		−	17.5506i		−	0.556113i
$997$	−4.06316	+	7.03760i	−0.128682	+	0.222883i	−0.923166	−	0.384401i	$-0.874408\pi$
$997$	−4.06316	+	7.03760i	−0.128682	+	0.222883i	0.794484	+	0.607284i	$0.207741\pi$
$998$	−5.13097	−	8.88711i	−0.162418	−	0.281316i
$999$	−5.06907	+	2.92663i	−0.160378	+	0.0925945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.b.166.6	✓	28
13.2	odd	12		5577.2.a.bg.1.5		14
13.4	even	6	inner	429.2.s.b.199.6	yes	28
13.11	odd	12		5577.2.a.bf.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.6	✓	28	1.1	even	1	trivial
429.2.s.b.199.6	yes	28	13.4	even	6	inner
5577.2.a.bf.1.10		14	13.11	odd	12
5577.2.a.bg.1.5		14	13.2	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.489701 + 0.282729i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.840128 + 1.45515i) q^{4} -1.14515i q^{5} +(0.489701 + 0.282729i) q^{6} +(2.75529 + 1.59077i) q^{7} -2.08103i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.489701 + 0.282729i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.840128 + 1.45515i) q^{4} -1.14515i q^{5} +(0.489701 + 0.282729i) q^{6} +(2.75529 + 1.59077i) q^{7} -2.08103i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.323767 + 0.560780i) q^{10} +(-0.866025 + 0.500000i) q^{11} +1.68026 q^{12} +(-2.18094 + 2.87115i) q^{13} -1.79902 q^{14} +(-0.991727 + 0.572574i) q^{15} +(-1.09189 - 1.89121i) q^{16} +(1.58351 - 2.74273i) q^{17} -0.565458i q^{18} +(4.59345 + 2.65203i) q^{19} +(1.66636 + 0.962071i) q^{20} -3.18153i q^{21} +(0.282729 - 0.489701i) q^{22} +(3.16876 + 5.48845i) q^{23} +(-1.80223 + 1.04052i) q^{24} +3.68864 q^{25} +(0.256254 - 2.02262i) q^{26} +1.00000 q^{27} +(-4.62959 + 2.67290i) q^{28} +(3.72041 + 6.44394i) q^{29} +(0.323767 - 0.560780i) q^{30} +7.39302i q^{31} +(4.67385 + 2.69845i) q^{32} +(0.866025 + 0.500000i) q^{33} +1.79082i q^{34} +(1.82166 - 3.15521i) q^{35} +(-0.840128 - 1.45515i) q^{36} +(-5.06907 + 2.92663i) q^{37} -2.99923 q^{38} +(3.57696 + 0.453179i) q^{39} -2.38309 q^{40} +(2.55277 - 1.47385i) q^{41} +(0.899512 + 1.55800i) q^{42} +(3.14032 - 5.43919i) q^{43} -1.68026i q^{44} +(0.991727 + 0.572574i) q^{45} +(-3.10349 - 1.79180i) q^{46} -5.76932i q^{47} +(-1.09189 + 1.89121i) q^{48} +(1.56108 + 2.70386i) q^{49} +(-1.80633 + 1.04289i) q^{50} -3.16703 q^{51} +(-2.34566 - 5.58572i) q^{52} -0.509048 q^{53} +(-0.489701 + 0.282729i) q^{54} +(0.572574 + 0.991727i) q^{55} +(3.31044 - 5.73384i) q^{56} -5.30406i q^{57} +(-3.64378 - 2.10374i) q^{58} +(-1.29318 - 0.746618i) q^{59} -1.92414i q^{60} +(-4.23333 + 7.33235i) q^{61} +(-2.09022 - 3.62037i) q^{62} +(-2.75529 + 1.59077i) q^{63} +1.31583 q^{64} +(3.28789 + 2.49750i) q^{65} -0.565458 q^{66} +(3.40283 - 1.96463i) q^{67} +(2.66071 + 4.60848i) q^{68} +(3.16876 - 5.48845i) q^{69} +2.06015i q^{70} +(-6.96332 - 4.02027i) q^{71} +(1.80223 + 1.04052i) q^{72} -0.446383i q^{73} +(1.65489 - 2.86635i) q^{74} +(-1.84432 - 3.19445i) q^{75} +(-7.71818 + 4.45609i) q^{76} -3.18153 q^{77} +(-1.87977 + 0.789388i) q^{78} -14.3374 q^{79} +(-2.16571 + 1.25037i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.833398 + 1.44349i) q^{82} -10.4452i q^{83} +(4.62959 + 2.67290i) q^{84} +(-3.14082 - 1.81336i) q^{85} +3.55144i q^{86} +(3.72041 - 6.44394i) q^{87} +(1.04052 + 1.80223i) q^{88} +(7.51085 - 4.33639i) q^{89} -0.647533 q^{90} +(-10.5765 + 4.44147i) q^{91} -10.6487 q^{92} +(6.40255 - 3.69651i) q^{93} +(1.63116 + 2.82525i) q^{94} +(3.03697 - 5.26018i) q^{95} -5.39690i q^{96} +(2.73813 + 1.58086i) q^{97} +(-1.52892 - 0.882723i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Introduction

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