LMFDB - Embedded newform 224.2.u.c.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24749 + 0.666168i) q^{2} +(2.18713 - 0.905938i) q^{3} +(1.11244 - 1.66207i) q^{4} +(0.797931 - 1.92638i) q^{5} +(-2.12490 + 2.58714i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.280536 + 2.81448i) q^{8} +(1.84149 - 1.84149i) q^{9} +O(q^{10})$	\(q+(-1.24749 + 0.666168i) q^{2} +(2.18713 - 0.905938i) q^{3} +(1.11244 - 1.66207i) q^{4} +(0.797931 - 1.92638i) q^{5} +(-2.12490 + 2.58714i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.280536 + 2.81448i) q^{8} +(1.84149 - 1.84149i) q^{9} +(0.287882 + 2.93468i) q^{10} +(-1.24061 - 0.513879i) q^{11} +(0.927318 - 4.64296i) q^{12} +(-1.97504 - 4.76818i) q^{13} +(-1.35316 - 0.411054i) q^{14} -4.93611i q^{15} +(-1.52495 - 3.69791i) q^{16} +6.56615i q^{17} +(-1.07049 + 3.52397i) q^{18} +(0.246004 + 0.593907i) q^{19} +(-2.31412 - 3.46920i) q^{20} +(2.18713 + 0.905938i) q^{21} +(1.88998 - 0.185400i) q^{22} +(1.33754 - 1.33754i) q^{23} +(1.93618 + 6.40978i) q^{24} +(0.461303 + 0.461303i) q^{25} +(5.64025 + 4.63252i) q^{26} +(-0.358520 + 0.865544i) q^{27} +(1.96188 - 0.388646i) q^{28} +(-3.76520 + 1.55960i) q^{29} +(3.28828 + 6.15772i) q^{30} +10.2099 q^{31} +(4.36578 + 3.59721i) q^{32} -3.17892 q^{33} +(-4.37416 - 8.19118i) q^{34} +(1.92638 - 0.797931i) q^{35} +(-1.01213 - 5.10922i) q^{36} +(0.633332 - 1.52900i) q^{37} +(-0.702529 - 0.577010i) q^{38} +(-8.63935 - 8.63935i) q^{39} +(5.19790 + 2.78618i) q^{40} +(-2.76376 + 2.76376i) q^{41} +(-3.33192 + 0.326850i) q^{42} +(0.855100 + 0.354194i) q^{43} +(-2.23421 + 1.49033i) q^{44} +(-2.07802 - 5.01678i) q^{45} +(-0.777538 + 2.55959i) q^{46} +10.6321i q^{47} +(-6.68534 - 6.70629i) q^{48} +1.00000i q^{49} +(-0.882774 - 0.268164i) q^{50} +(5.94853 + 14.3610i) q^{51} +(-10.1222 - 2.02166i) q^{52} +(-11.1286 - 4.60960i) q^{53} +(-0.129349 - 1.31859i) q^{54} +(-1.97985 + 1.97985i) q^{55} +(-2.18851 + 1.79177i) q^{56} +(1.07609 + 1.07609i) q^{57} +(3.65808 - 4.45383i) q^{58} +(1.04141 - 2.51418i) q^{59} +(-8.20416 - 5.49113i) q^{60} +(-9.47718 + 3.92558i) q^{61} +(-12.7367 + 6.80151i) q^{62} +2.60426 q^{63} +(-7.84260 - 1.57913i) q^{64} -10.7613 q^{65} +(3.96566 - 2.11770i) q^{66} +(9.85128 - 4.08053i) q^{67} +(10.9134 + 7.30445i) q^{68} +(1.71365 - 4.13711i) q^{69} +(-1.87157 + 2.27870i) q^{70} +(-6.76319 - 6.76319i) q^{71} +(4.66622 + 5.69943i) q^{72} +(0.141933 - 0.141933i) q^{73} +(0.228497 + 2.32931i) q^{74} +(1.42684 + 0.591017i) q^{75} +(1.26078 + 0.251810i) q^{76} +(-0.513879 - 1.24061i) q^{77} +(16.5327 + 5.02221i) q^{78} -1.65401i q^{79} +(-8.34037 - 0.0130460i) q^{80} +10.0306i q^{81} +(1.60662 - 5.28888i) q^{82} +(4.10243 + 9.90415i) q^{83} +(3.93878 - 2.62736i) q^{84} +(12.6489 + 5.23934i) q^{85} +(-1.30268 + 0.127788i) q^{86} +(-6.82208 + 6.82208i) q^{87} +(1.79434 - 3.34752i) q^{88} +(-6.54438 - 6.54438i) q^{89} +(5.93431 + 4.87405i) q^{90} +(1.97504 - 4.76818i) q^{91} +(-0.735153 - 3.71103i) q^{92} +(22.3304 - 9.24954i) q^{93} +(-7.08277 - 13.2634i) q^{94} +1.34038 q^{95} +(12.8074 + 3.91244i) q^{96} -14.6079 q^{97} +(-0.666168 - 1.24749i) q^{98} +(-3.23087 + 1.33827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.24749	+	0.666168i	−0.882106	+	0.471052i
$2$	−1.24749	+	0.666168i	−0.882106	+	0.471052i
$3$	2.18713	−	0.905938i	1.26274	−	0.523044i	0.351990	−	0.936004i	$-0.385505\pi$
$3$	2.18713	−	0.905938i	1.26274	−	0.523044i	0.910749	+	0.412960i	$0.135505\pi$
$4$	1.11244	−	1.66207i	0.556220	−	0.831035i
$5$	0.797931	−	1.92638i	0.356846	−	0.861502i	−0.638894	−	0.769295i	$-0.720608\pi$
$5$	0.797931	−	1.92638i	0.356846	−	0.861502i	0.995740	−	0.0922070i	$-0.0293922\pi$
$6$	−2.12490	+	2.58714i	−0.867489	+	1.05620i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.280536	+	2.81448i	−0.0991846	+	0.995069i
$9$	1.84149	−	1.84149i	0.613829	−	0.613829i
$10$	0.287882	+	2.93468i	0.0910364	+	0.928028i
$11$	−1.24061	−	0.513879i	−0.374059	−	0.154940i	0.187731	−	0.982221i	$-0.439887\pi$
$11$	−1.24061	−	0.513879i	−0.374059	−	0.154940i	−0.561789	+	0.827280i	$0.689887\pi$
$12$	0.927318	−	4.64296i	0.267694	−	1.34031i
$13$	−1.97504	−	4.76818i	−0.547779	−	1.32245i	−0.919127	−	0.393961i	$-0.871104\pi$
$13$	−1.97504	−	4.76818i	−0.547779	−	1.32245i	0.371348	−	0.928494i	$-0.378896\pi$
$14$	−1.35316	−	0.411054i	−0.361647	−	0.109859i
$15$		−	4.93611i		−	1.27450i
$16$	−1.52495	−	3.69791i	−0.381238	−	0.924477i
$17$			6.56615i			1.59253i	0.604951	+	0.796263i	$0.293193\pi$
$17$			6.56615i			1.59253i	−0.604951	+	0.796263i	$0.706807\pi$
$18$	−1.07049	+	3.52397i	−0.252317	+	0.830607i
$19$	0.246004	+	0.593907i	0.0564373	+	0.136252i	0.949583	−	0.313516i	$-0.101507\pi$
$19$	0.246004	+	0.593907i	0.0564373	+	0.136252i	−0.893146	+	0.449767i	$0.851507\pi$
$20$	−2.31412	−	3.46920i	−0.517453	−	0.775736i
$21$	2.18713	+	0.905938i	0.477271	+	0.197692i
$22$	1.88998	−	0.185400i	0.402944	−	0.0395274i
$23$	1.33754	−	1.33754i	0.278897	−	0.278897i	−0.553772	−	0.832669i	$-0.686812\pi$
$23$	1.33754	−	1.33754i	0.278897	−	0.278897i	0.832669	+	0.553772i	$0.186812\pi$
$24$	1.93618	+	6.40978i	0.395220	+	1.30839i
$25$	0.461303	+	0.461303i	0.0922606	+	0.0922606i
$26$	5.64025	+	4.63252i	1.10614	+	0.908513i
$27$	−0.358520	+	0.865544i	−0.0689972	+	0.166574i
$28$	1.96188	−	0.388646i	0.370760	−	0.0734473i
$29$	−3.76520	+	1.55960i	−0.699181	+	0.289610i	−0.703819	−	0.710379i	$-0.748524\pi$
$29$	−3.76520	+	1.55960i	−0.699181	+	0.289610i	0.00463850	+	0.999989i	$0.498524\pi$
$30$	3.28828	+	6.15772i	0.600355	+	1.12424i
$31$	10.2099			1.83375			0.916876	−	0.399171i	$-0.130702\pi$
$31$	10.2099			1.83375			0.916876	+	0.399171i	$0.130702\pi$
$32$	4.36578	+	3.59721i	0.771769	+	0.635903i
$33$	−3.17892			−0.553379
$34$	−4.37416	−	8.19118i	−0.750162	−	1.40478i
$35$	1.92638	−	0.797931i	0.325617	−	0.134875i
$36$	−1.01213	−	5.10922i	−0.168689	−	0.851537i
$37$	0.633332	−	1.52900i	0.104119	−	0.251366i	−0.863231	−	0.504809i	$-0.831563\pi$
$37$	0.633332	−	1.52900i	0.104119	−	0.251366i	0.967350	+	0.253443i	$0.0815630\pi$
$38$	−0.702529	−	0.577010i	−0.113965	−	0.0936034i
$39$	−8.63935	−	8.63935i	−1.38340	−	1.38340i
$40$	5.19790	+	2.78618i	0.821860	+	0.440534i
$41$	−2.76376	+	2.76376i	−0.431627	+	0.431627i	−0.889181	−	0.457555i	$-0.848725\pi$
$41$	−2.76376	+	2.76376i	−0.431627	+	0.431627i	0.457555	+	0.889181i	$0.348725\pi$
$42$	−3.33192	+	0.326850i	−0.514126	+	0.0504340i
$43$	0.855100	+	0.354194i	0.130402	+	0.0540141i	0.446930	−	0.894569i	$-0.352517\pi$
$43$	0.855100	+	0.354194i	0.130402	+	0.0540141i	−0.316528	+	0.948583i	$0.602517\pi$
$44$	−2.23421	+	1.49033i	−0.336820	+	0.224675i
$45$	−2.07802	−	5.01678i	−0.309772	−	0.747857i
$46$	−0.777538	+	2.55959i	−0.114642	+	0.377392i
$47$			10.6321i			1.55085i	0.631438	+	0.775427i	$0.282465\pi$
$47$			10.6321i			1.55085i	−0.631438	+	0.775427i	$0.717535\pi$
$48$	−6.68534	−	6.70629i	−0.964946	−	0.967969i
$49$			1.00000i			0.142857i
$50$	−0.882774	−	0.268164i	−0.124843	−	0.0379240i
$51$	5.94853	+	14.3610i	0.832961	+	2.01094i
$52$	−10.1222	−	2.02166i	−1.40369	−	0.280353i
$53$	−11.1286	−	4.60960i	−1.52863	−	0.633178i	−0.549329	−	0.835606i	$-0.685117\pi$
$53$	−11.1286	−	4.60960i	−1.52863	−	0.633178i	−0.979297	+	0.202428i	$0.935117\pi$
$54$	−0.129349	−	1.31859i	−0.0176022	−	0.179437i
$55$	−1.97985	+	1.97985i	−0.266962	+	0.266962i
$56$	−2.18851	+	1.79177i	−0.292452	+	0.239435i
$57$	1.07609	+	1.07609i	0.142531	+	0.142531i
$58$	3.65808	−	4.45383i	0.480330	−	0.584817i
$59$	1.04141	−	2.51418i	0.135579	−	0.327318i	−0.841479	−	0.540290i	$-0.818314\pi$
$59$	1.04141	−	2.51418i	0.135579	−	0.327318i	0.977058	+	0.212972i	$0.0683144\pi$
$60$	−8.20416	−	5.49113i	−1.05915	−	0.708902i
$61$	−9.47718	+	3.92558i	−1.21343	+	0.502619i	−0.895315	−	0.445434i	$-0.853050\pi$
$61$	−9.47718	+	3.92558i	−1.21343	+	0.502619i	−0.318114	+	0.948052i	$0.603050\pi$
$62$	−12.7367	+	6.80151i	−1.61756	+	0.863793i
$63$	2.60426			0.328105
$64$	−7.84260	−	1.57913i	−0.980325	−	0.197391i
$65$	−10.7613			−1.33477
$66$	3.96566	−	2.11770i	0.488139	−	0.260670i
$67$	9.85128	−	4.08053i	1.20353	−	0.498517i	0.311389	−	0.950282i	$-0.399206\pi$
$67$	9.85128	−	4.08053i	1.20353	−	0.498517i	0.892137	+	0.451766i	$0.149206\pi$
$68$	10.9134	+	7.30445i	1.32344	+	0.885795i
$69$	1.71365	−	4.13711i	0.206299	−	0.498050i
$70$	−1.87157	+	2.27870i	−0.223695	+	0.272356i
$71$	−6.76319	−	6.76319i	−0.802643	−	0.802643i	0.180865	−	0.983508i	$-0.442110\pi$
$71$	−6.76319	−	6.76319i	−0.802643	−	0.802643i	−0.983508	+	0.180865i	$0.942110\pi$
$72$	4.66622	+	5.69943i	0.549920	+	0.671685i
$73$	0.141933	−	0.141933i	0.0166120	−	0.0166120i	−0.698752	−	0.715364i	$-0.746261\pi$
$73$	0.141933	−	0.141933i	0.0166120	−	0.0166120i	0.715364	+	0.698752i	$0.246261\pi$
$74$	0.228497	+	2.32931i	0.0265623	+	0.270777i
$75$	1.42684	+	0.591017i	0.164757	+	0.0682447i
$76$	1.26078	+	0.251810i	0.144621	+	0.0288846i
$77$	−0.513879	−	1.24061i	−0.0585619	−	0.141381i
$78$	16.5327	+	5.02221i	1.87196	+	0.568653i
$79$		−	1.65401i		−	0.186091i	−0.995662	−	0.0930454i	$-0.970340\pi$
$79$		−	1.65401i		−	0.186091i	0.995662	−	0.0930454i	$-0.0296602\pi$
$80$	−8.34037	−	0.0130460i	−0.932481	−	0.00145859i
$81$			10.0306i			1.11451i
$82$	1.60662	−	5.28888i	0.177422	−	0.584059i
$83$	4.10243	+	9.90415i	0.450301	+	1.08712i	0.972208	+	0.234120i	$0.0752207\pi$
$83$	4.10243	+	9.90415i	0.450301	+	1.08712i	−0.521907	+	0.853002i	$0.674779\pi$
$84$	3.93878	−	2.62736i	0.429757	−	0.286668i
$85$	12.6489	+	5.23934i	1.37196	+	0.568286i
$86$	−1.30268	+	0.127788i	−0.140471	+	0.0137798i
$87$	−6.82208	+	6.82208i	−0.731404	+	0.731404i
$88$	1.79434	−	3.34752i	0.191277	−	0.356847i
$89$	−6.54438	−	6.54438i	−0.693702	−	0.693702i	0.269342	−	0.963045i	$-0.413194\pi$
$89$	−6.54438	−	6.54438i	−0.693702	−	0.693702i	−0.963045	+	0.269342i	$0.913194\pi$
$90$	5.93431	+	4.87405i	0.625531	+	0.513770i
$91$	1.97504	−	4.76818i	0.207041	−	0.499841i
$92$	−0.735153	−	3.71103i	−0.0766450	−	0.386901i
$93$	22.3304	−	9.24954i	2.31555	−	0.959133i
$94$	−7.08277	−	13.2634i	−0.730532	−	1.36802i
$95$	1.34038			0.137520
$96$	12.8074	+	3.91244i	1.30715	+	0.399312i
$97$	−14.6079			−1.48320			−0.741601	−	0.670841i	$-0.765933\pi$
$97$	−14.6079			−1.48320			−0.741601	+	0.670841i	$0.765933\pi$
$98$	−0.666168	−	1.24749i	−0.0672931	−	0.126015i
$99$	−3.23087	+	1.33827i	−0.324715	+	0.134501i
$100$	1.27989	−	0.253545i	0.127989	−	0.0253545i
$101$	3.14443	−	7.59133i	0.312883	−	0.755366i	−0.686713	−	0.726929i	$-0.740947\pi$
$101$	3.14443	−	7.59133i	0.312883	−	0.755366i	0.999596	−	0.0284369i	$-0.00905297\pi$
$102$	−16.9876	−	13.9524i	−1.68202	−	1.38150i
$103$	−1.16285	−	1.16285i	−0.114579	−	0.114579i	0.647493	−	0.762072i	$-0.275818\pi$
$103$	−1.16285	−	1.16285i	−0.114579	−	0.114579i	−0.762072	+	0.647493i	$0.775818\pi$
$104$	13.9740	−	4.22108i	1.37027	−	0.413911i
$105$	3.49036	−	3.49036i	0.340624	−	0.340624i
$106$	16.9535	−	1.66308i	1.64667	−	0.161533i
$107$	12.3031	+	5.09612i	1.18939	+	0.492660i	0.887556	−	0.460701i	$-0.152402\pi$
$107$	12.3031	+	5.09612i	1.18939	+	0.492660i	0.301832	+	0.953361i	$0.402402\pi$
$108$	1.03976	+	1.55875i	0.100051	+	0.149991i
$109$	5.89338	+	14.2279i	0.564484	+	1.36278i	0.906147	+	0.422962i	$0.139010\pi$
$109$	5.89338	+	14.2279i	0.564484	+	1.36278i	−0.341664	+	0.939822i	$0.610990\pi$
$110$	1.15092	−	3.78874i	0.109736	−	0.361242i
$111$		−	3.91788i		−	0.371868i
$112$	1.53651	−	3.69312i	0.145187	−	0.348967i
$113$			14.6821i			1.38117i	0.723250	+	0.690586i	$0.242648\pi$
$113$			14.6821i			1.38117i	−0.723250	+	0.690586i	$0.757352\pi$
$114$	−2.05926	−	0.625548i	−0.192867	−	0.0585879i
$115$	−1.50934	−	3.64388i	−0.140747	−	0.339793i
$116$	−1.59640	+	7.99299i	−0.148222	+	0.742131i
$117$	−12.4176	−	5.14352i	−1.14800	−	0.475519i
$118$	0.375725	+	3.83015i	0.0345882	+	0.352594i
$119$	−4.64297	+	4.64297i	−0.425620	+	0.425620i
$120$	13.8926	+	1.38476i	1.26821	+	0.126411i
$121$	−6.50313	−	6.50313i	−0.591193	−	0.591193i
$122$	9.20756	−	11.2105i	0.833613	−	1.01495i
$123$	−3.54090	+	8.54850i	−0.319272	+	0.770792i
$124$	11.3579	−	16.9696i	1.01997	−	1.52391i
$125$	10.8886	−	4.51021i	0.973907	−	0.403405i
$126$	−3.24877	+	1.73487i	−0.289424	+	0.154555i
$127$	−3.75030			−0.332786			−0.166393	−	0.986060i	$-0.553212\pi$
$127$	−3.75030			−0.332786			−0.166393	+	0.986060i	$0.553212\pi$
$128$	10.8355	−	3.25455i	0.957731	−	0.287664i
$129$	2.19109			0.192915
$130$	13.4245	−	7.16880i	1.17741	−	0.628746i
$131$	0.344003	−	0.142491i	0.0300556	−	0.0124495i	−0.367605	−	0.929982i	$-0.619822\pi$
$131$	0.344003	−	0.142491i	0.0300556	−	0.0124495i	0.397661	+	0.917533i	$0.369822\pi$
$132$	−3.53636	+	5.28359i	−0.307801	+	0.459877i
$133$	−0.246004	+	0.593907i	−0.0213313	+	0.0514983i
$134$	−9.57101	+	11.6530i	−0.826809	+	1.00667i
$135$	1.38129	+	1.38129i	0.118882	+	0.118882i
$136$	−18.4803	−	1.84204i	−1.58467	−	0.157954i
$137$	14.0332	−	14.0332i	1.19893	−	1.19893i	0.224447	−	0.974486i	$-0.427942\pi$
$137$	14.0332	−	14.0332i	1.19893	−	1.19893i	0.974486	−	0.224447i	$-0.0720576\pi$
$138$	0.618260	+	6.30256i	0.0526298	+	0.536510i
$139$	−21.0352	−	8.71308i	−1.78419	−	0.739034i	−0.991611	−	0.129260i	$-0.958740\pi$
$139$	−21.0352	−	8.71308i	−1.78419	−	0.739034i	−0.792576	−	0.609774i	$-0.791260\pi$
$140$	0.816762	−	4.08942i	0.0690290	−	0.345619i
$141$	9.63204	+	23.2538i	0.811164	+	1.95832i
$142$	12.9424	+	3.93156i	1.08610	+	0.329929i
$143$			6.93040i			0.579549i
$144$	−9.61783	−	4.00147i	−0.801486	−	0.333456i
$145$			8.49765i			0.705691i
$146$	−0.0825083	+	0.271611i	−0.00682844	+	0.0224787i
$147$	0.905938	+	2.18713i	0.0747205	+	0.180391i
$148$	−1.83676	−	2.75356i	−0.150981	−	0.226341i
$149$	1.51778	+	0.628685i	0.124341	+	0.0515038i	0.443987	−	0.896033i	$-0.353564\pi$
$149$	1.51778	+	0.628685i	0.124341	+	0.0515038i	−0.319645	+	0.947537i	$0.603564\pi$
$150$	−2.17368	+	0.213230i	−0.177480	+	0.0174102i
$151$	2.52338	−	2.52338i	0.205350	−	0.205350i	−0.596938	−	0.802288i	$-0.703616\pi$
$151$	2.52338	−	2.52338i	0.205350	−	0.205350i	0.802288	+	0.596938i	$0.203616\pi$
$152$	−1.74055	+	0.525762i	−0.141177	+	0.0426449i
$153$	12.0915	+	12.0915i	0.977538	+	0.977538i
$154$	1.46751	+	1.20532i	0.118256	+	0.0971272i
$155$	8.14680	−	19.6681i	0.654367	−	1.57978i
$156$	−23.9700	+	4.74844i	−1.91913	+	0.380179i
$157$	−5.90004	+	2.44388i	−0.470875	+	0.195043i	−0.605486	−	0.795856i	$-0.707021\pi$
$157$	−5.90004	+	2.44388i	−0.470875	+	0.195043i	0.134612	+	0.990898i	$0.457021\pi$
$158$	1.10185	+	2.06335i	0.0876584	+	0.164152i
$159$	−28.5156			−2.26144
$160$	10.4132	−	5.53981i	0.823234	−	0.437960i
$161$	1.89157			0.149077
$162$	−6.68208	−	12.5131i	−0.524994	−	0.983118i
$163$	3.02368	−	1.25245i	0.236833	−	0.0980995i	−0.261110	−	0.965309i	$-0.584089\pi$
$163$	3.02368	−	1.25245i	0.236833	−	0.0980995i	0.497944	+	0.867209i	$0.334089\pi$
$164$	1.51904	+	7.66808i	0.118617	+	0.598777i
$165$	−2.53656	+	6.12380i	−0.197471	+	0.476737i
$166$	−11.7156	−	9.62238i	−0.909303	−	0.746841i
$167$	−8.58278	−	8.58278i	−0.664156	−	0.664156i	0.292201	−	0.956357i	$-0.405612\pi$
$167$	−8.58278	−	8.58278i	−0.664156	−	0.664156i	−0.956357	+	0.292201i	$0.905612\pi$
$168$	−3.16331	+	5.90148i	−0.244055	+	0.455309i
$169$	−9.64234	+	9.64234i	−0.741719	+	0.741719i
$170$	−19.2696	+	1.89028i	−1.47791	+	0.144978i
$171$	1.54669	+	0.640658i	0.118278	+	0.0489924i
$172$	1.53994	−	1.02722i	0.117420	−	0.0783245i
$173$	−0.457854	−	1.10536i	−0.0348100	−	0.0840388i	0.905518	−	0.424307i	$-0.139482\pi$
$173$	−0.457854	−	1.10536i	−0.0348100	−	0.0840388i	−0.940328	+	0.340268i	$0.889482\pi$
$174$	3.96580	−	13.0551i	0.300646	−	0.989705i
$175$			0.652381i			0.0493153i
$176$	−0.00840179	+	5.37131i	−0.000633309	+	0.404878i
$177$		−	6.44228i		−	0.484231i
$178$	12.5237	+	3.80436i	0.938689	+	0.285149i
$179$	−8.36981	−	20.2065i	−0.625589	−	1.51031i	−0.845051	−	0.534685i	$-0.820430\pi$
$179$	−8.36981	−	20.2065i	−0.625589	−	1.51031i	0.219462	−	0.975621i	$-0.429570\pi$
$180$	−10.6499	−	2.12706i	−0.793797	−	0.158541i
$181$	−4.05792	−	1.68084i	−0.301622	−	0.124936i	0.226739	−	0.973956i	$-0.427193\pi$
$181$	−4.05792	−	1.68084i	−0.301622	−	0.124936i	−0.528362	+	0.849019i	$0.677193\pi$
$182$	0.712568	+	7.26395i	0.0528191	+	0.538440i
$183$	−17.1715	+	17.1715i	−1.26935	+	1.26935i
$184$	3.38926	+	4.13972i	0.249860	+	0.305184i
$185$	−2.44007	−	2.44007i	−0.179398	−	0.179398i
$186$	−21.6951	+	26.4144i	−1.59076	+	1.93680i
$187$	3.37420	−	8.14605i	0.246746	−	0.595698i
$188$	17.6713	+	11.8276i	1.28881	+	0.862616i
$189$	−0.865544	+	0.358520i	−0.0629590	+	0.0260785i
$190$	−1.67211	+	0.892920i	−0.121307	+	0.0647792i
$191$	−6.12672			−0.443314			−0.221657	−	0.975125i	$-0.571147\pi$
$191$	−6.12672			−0.443314			−0.221657	+	0.975125i	$0.571147\pi$
$192$	−18.5834	+	3.65115i	−1.34114	+	0.263499i
$193$	19.3732			1.39451			0.697257	−	0.716822i	$-0.254404\pi$
$193$	19.3732			1.39451			0.697257	+	0.716822i	$0.254404\pi$
$194$	18.2231	−	9.73128i	1.30834	−	0.698665i
$195$	−23.5363	+	9.74903i	−1.68547	+	0.698143i
$196$	1.66207	+	1.11244i	0.118719	+	0.0794601i
$197$	5.45295	−	13.1646i	0.388506	−	0.937937i	−0.601751	−	0.798684i	$-0.705530\pi$
$197$	5.45295	−	13.1646i	0.388506	−	0.937937i	0.990257	−	0.139253i	$-0.0444702\pi$
$198$	3.13895	−	3.82178i	0.223076	−	0.271602i
$199$	2.51502	+	2.51502i	0.178285	+	0.178285i	0.790608	−	0.612323i	$-0.209765\pi$
$199$	2.51502	+	2.51502i	0.178285	+	0.178285i	−0.612323	+	0.790608i	$0.709765\pi$
$200$	−1.42774	+	1.16892i	−0.100956	+	0.0826548i
$201$	17.8493	−	17.8493i	1.25899	−	1.25899i
$202$	1.13447	+	11.5648i	0.0798208	+	0.813696i
$203$	−3.76520	−	1.55960i	−0.264265	−	0.109462i
$204$	30.4864	+	6.08891i	2.13447	+	0.426309i
$205$	3.11875	+	7.52933i	0.217823	+	0.525871i
$206$	2.22529	+	0.675983i	0.155043	+	0.0470980i
$207$		−	4.92614i		−	0.342390i
$208$	−14.6204	+	14.5748i	−1.01375	+	1.01058i
$209$		−	0.863225i		−	0.0597105i
$210$	−2.02901	+	6.67933i	−0.140015	+	0.460918i
$211$	−2.01957	−	4.87567i	−0.139033	−	0.335655i	0.838992	−	0.544144i	$-0.183145\pi$
$211$	−2.01957	−	4.87567i	−0.139033	−	0.335655i	−0.978025	+	0.208489i	$0.933145\pi$
$212$	−20.0414	+	13.3685i	−1.37645	+	0.918155i
$213$	−20.9190	−	8.66493i	−1.43335	−	0.593711i
$214$	−18.7428	+	1.83861i	−1.28123	+	0.125685i
$215$	1.36462	−	1.36462i	0.0930665	−	0.0930665i
$216$	−2.33548	−	1.25186i	−0.158909	−	0.0851785i
$217$	7.21949	+	7.21949i	0.490091	+	0.490091i
$218$	−16.8301	−	13.8231i	−1.13988	−	0.936218i
$219$	0.181844	−	0.439009i	0.0122878	−	0.0296655i
$220$	1.08818	+	5.49311i	0.0733652	+	0.370345i
$221$	31.3086	−	12.9684i	2.10604	−	0.872352i
$222$	2.60996	+	4.88749i	0.175169	+	0.328027i
$223$	26.5415			1.77735			0.888675	−	0.458537i	$-0.151626\pi$
$223$	26.5415			1.77735			0.888675	+	0.458537i	$0.151626\pi$
$224$	0.543460	+	5.63069i	0.0363115	+	0.376216i
$225$	1.69897			0.113264
$226$	−9.78072	−	18.3157i	−0.650604	−	1.21834i
$227$	−0.0142692	+	0.00591051i	−0.000947082	+	0.000392294i	−0.383157	−	0.923683i	$-0.625163\pi$
$227$	−0.0142692	+	0.00591051i	−0.000947082	+	0.000392294i	0.382210	+	0.924076i	$0.375163\pi$
$228$	2.98561	−	0.591448i	0.197727	−	0.0391696i
$229$	−2.97206	+	7.17519i	−0.196399	+	0.474150i	−0.991144	−	0.132794i	$-0.957605\pi$
$229$	−2.97206	+	7.17519i	−0.196399	+	0.474150i	0.794744	+	0.606945i	$0.207605\pi$
$230$	4.31032	+	3.54021i	0.284214	+	0.233435i
$231$	−2.24784	−	2.24784i	−0.147897	−	0.147897i
$232$	−3.33318	−	11.0346i	−0.218834	−	0.724458i
$233$	5.96875	−	5.96875i	0.391026	−	0.391026i	−0.484027	−	0.875053i	$-0.660826\pi$
$233$	5.96875	−	5.96875i	0.391026	−	0.391026i	0.875053	+	0.484027i	$0.160826\pi$
$234$	18.9172	−	1.85571i	1.23665	−	0.121312i
$235$	20.4814	+	8.48369i	1.33606	+	0.553415i
$236$	−3.02023	−	4.52776i	−0.196600	−	0.294732i
$237$	−1.49843	−	3.61753i	−0.0973336	−	0.234984i
$238$	2.69904	−	8.88504i	0.174953	−	0.575931i
$239$		−	17.7307i		−	1.14690i	−0.819239	−	0.573452i	$-0.805604\pi$
$239$		−	17.7307i		−	1.14690i	0.819239	−	0.573452i	$-0.194396\pi$
$240$	−18.2533	+	7.52733i	−1.17824	+	0.485887i
$241$		−	26.5591i		−	1.71082i	−0.517951	−	0.855410i	$-0.673305\pi$
$241$		−	26.5591i		−	1.71082i	0.517951	−	0.855410i	$-0.326695\pi$
$242$	12.4447	+	3.78038i	0.799978	+	0.243012i
$243$	8.01156	+	19.3416i	0.513942	+	1.24077i
$244$	−4.01822	+	20.1187i	−0.257240	+	1.28797i
$245$	1.92638	+	0.797931i	0.123072	+	0.0509780i
$246$	−1.27751	−	13.0230i	−0.0814509	−	0.830314i
$247$	2.34599	−	2.34599i	0.149271	−	0.149271i
$248$	−2.86425	+	28.7356i	−0.181880	+	1.82471i
$249$	17.9451	+	17.9451i	1.13722	+	1.13722i
$250$	−10.5788	+	12.8801i	−0.669064	+	0.814607i
$251$	1.12068	−	2.70556i	0.0707367	−	0.170773i	−0.884557	−	0.466432i	$-0.845539\pi$
$251$	1.12068	−	2.70556i	0.0707367	−	0.170773i	0.955294	+	0.295659i	$0.0955391\pi$
$252$	2.89708	−	4.32845i	0.182499	−	0.272667i
$253$	−2.34671	+	0.972038i	−0.147536	+	0.0611115i
$254$	4.67845	−	2.49833i	0.293552	−	0.156759i
$255$	32.4112			2.02967
$256$	−11.3490	+	11.2783i	−0.709315	+	0.704891i
$257$	4.51796			0.281823			0.140911	−	0.990022i	$-0.454997\pi$
$257$	4.51796			0.281823			0.140911	+	0.990022i	$0.454997\pi$
$258$	−2.73336	+	1.45964i	−0.170171	+	0.0908729i
$259$	1.52900	−	0.633332i	0.0950073	−	0.0393533i
$260$	−11.9713	+	17.8860i	−0.742426	+	1.10924i
$261$	−4.06159	+	9.80555i	−0.251406	+	0.606948i
$262$	−0.334216	+	0.406918i	−0.0206479	+	0.0251395i
$263$	18.6783	+	18.6783i	1.15176	+	1.15176i	0.986201	+	0.165555i	$0.0529415\pi$
$263$	18.6783	+	18.6783i	1.15176	+	1.15176i	0.165555	+	0.986201i	$0.447058\pi$
$264$	0.891803	−	8.94701i	0.0548867	−	0.550650i
$265$	−17.7597	+	17.7597i	−1.09097	+	1.09097i
$266$	−0.0887549	−	0.904771i	−0.00544191	−	0.0554750i
$267$	−20.2422	−	8.38459i	−1.23880	−	0.513129i
$268$	4.17683	−	20.9129i	0.255141	−	1.27746i
$269$	−3.40283	−	8.21516i	−0.207474	−	0.500887i	0.785550	−	0.618798i	$-0.212380\pi$
$269$	−3.40283	−	8.21516i	−0.207474	−	0.500887i	−0.993024	+	0.117911i	$0.962380\pi$
$270$	−2.64331	−	0.802968i	−0.160867	−	0.0488670i
$271$			2.34539i			0.142472i	0.997459	+	0.0712361i	$0.0226944\pi$
$271$			2.34539i			0.142472i	−0.997459	+	0.0712361i	$0.977306\pi$
$272$	24.2810	−	10.0131i	1.47225	−	0.607131i
$273$		−	12.2179i		−	0.739460i
$274$	−8.15772	+	26.8546i	−0.492826	+	1.62235i
$275$	−0.335244	−	0.809352i	−0.0202160	−	0.0488057i
$276$	−4.96984	−	7.45049i	−0.299149	−	0.448467i
$277$	−9.44890	−	3.91386i	−0.567729	−	0.235161i	0.0803076	−	0.996770i	$-0.474410\pi$
$277$	−9.44890	−	3.91386i	−0.567729	−	0.235161i	−0.648037	+	0.761609i	$0.724410\pi$
$278$	32.0455	−	3.14356i	1.92196	−	0.188538i
$279$	18.8014	−	18.8014i	1.12561	−	1.12561i
$280$	1.70534	+	5.64560i	0.101914	+	0.337389i
$281$	−19.5383	−	19.5383i	−1.16555	−	1.16555i	−0.983240	−	0.182315i	$-0.941641\pi$
$281$	−19.5383	−	19.5383i	−1.16555	−	1.16555i	−0.182315	−	0.983240i	$-0.558359\pi$
$282$	−27.5068	−	22.5922i	−1.63800	−	1.34535i
$283$	1.95857	−	4.72840i	0.116425	−	0.281074i	−0.854916	−	0.518767i	$-0.826391\pi$
$283$	1.95857	−	4.72840i	0.116425	−	0.281074i	0.971340	+	0.237693i	$0.0763912\pi$
$284$	−18.7645	+	3.71724i	−1.11347	+	0.220578i
$285$	2.93159	−	1.21430i	0.173652	−	0.0719292i
$286$	−4.61681	−	8.64557i	−0.272998	−	0.511223i
$287$	−3.90855			−0.230714
$288$	14.6638	−	1.41531i	0.864070	−	0.0833979i
$289$	−26.1143			−1.53614
$290$	−5.66086	−	10.6007i	−0.332417	−	0.622494i
$291$	−31.9493	+	13.2338i	−1.87290	+	0.775780i
$292$	−0.0780107	−	0.393795i	−0.00456523	−	0.0230451i
$293$	2.15342	−	5.19882i	0.125804	−	0.303718i	−0.848411	−	0.529337i	$-0.822441\pi$
$293$	2.15342	−	5.19882i	0.125804	−	0.303718i	0.974216	+	0.225619i	$0.0724405\pi$
$294$	−2.58714	−	2.12490i	−0.150885	−	0.123927i
$295$	−4.01228	−	4.01228i	−0.233604	−	0.233604i
$296$	4.12566	+	2.21144i	0.239799	+	0.128537i
$297$	0.889569	−	0.889569i	0.0516180	−	0.0516180i
$298$	−2.31222	+	0.226821i	−0.133943	+	0.0131394i
$299$	−9.01935	−	3.73594i	−0.521603	−	0.216055i
$300$	2.56959	−	1.71404i	0.148355	−	0.0989600i
$301$	0.354194	+	0.855100i	0.0204154	+	0.0492872i
$302$	−1.46689	+	4.82887i	−0.0844098	+	0.277871i
$303$		−	19.4519i		−	1.11748i
$304$	1.82107	−	1.81538i	0.104445	−	0.104119i
$305$			21.3890i			1.22473i
$306$	−23.1389	−	7.02899i	−1.32276	−	0.401821i
$307$	8.21013	+	19.8210i	0.468577	+	1.13124i	0.964785	+	0.263041i	$0.0847254\pi$
$307$	8.21013	+	19.8210i	0.468577	+	1.13124i	−0.496208	+	0.868204i	$0.665275\pi$
$308$	−2.63364	−	0.526006i	−0.150066	−	0.0299720i
$309$	−3.59676	−	1.48983i	−0.204613	−	0.0847533i
$310$	2.93925	+	29.9628i	0.166938	+	1.70177i
$311$	−19.7529	+	19.7529i	−1.12008	+	1.12008i	−0.128354	+	0.991728i	$0.540969\pi$
$311$	−19.7529	+	19.7529i	−1.12008	+	1.12008i	−0.991728	+	0.128354i	$0.959031\pi$
$312$	26.7389	−	21.8916i	1.51379	−	1.23937i
$313$	−7.28724	−	7.28724i	−0.411899	−	0.411899i	0.470501	−	0.882400i	$-0.344073\pi$
$313$	−7.28724	−	7.28724i	−0.411899	−	0.411899i	−0.882400	+	0.470501i	$0.844073\pi$
$314$	5.73218	−	6.97912i	0.323486	−	0.393855i
$315$	2.07802	−	5.01678i	0.117083	−	0.282663i
$316$	−2.74908	−	1.83999i	−0.154648	−	0.103507i
$317$	−11.8568	+	4.91125i	−0.665944	+	0.275843i	−0.689937	−	0.723869i	$-0.742362\pi$
$317$	−11.8568	+	4.91125i	−0.665944	+	0.275843i	0.0239934	+	0.999712i	$0.492362\pi$
$318$	35.5728	−	18.9962i	1.99483	−	1.06525i
$319$	5.47260			0.306407
$320$	−9.29985	+	13.8478i	−0.519877	+	0.774113i
$321$	31.5253			1.75957
$322$	−2.35971	+	1.26010i	−0.131501	+	0.0702229i
$323$	−3.89968	+	1.61530i	−0.216984	+	0.0898778i
$324$	16.6716	+	11.1585i	0.926199	+	0.619915i
$325$	1.28848	−	3.11067i	0.0714721	−	0.172549i
$326$	−2.93766	+	3.57669i	−0.162702	+	0.198095i
$327$	25.7792	+	25.7792i	1.42559	+	1.42559i
$328$	−7.00321	−	8.55388i	−0.386688	−	0.472309i
$329$	−7.51804	+	7.51804i	−0.414483	+	0.414483i
$330$	−0.915155	−	9.32913i	−0.0503776	−	0.513551i
$331$	17.0405	+	7.05841i	0.936631	+	0.387965i	0.798190	−	0.602406i	$-0.205791\pi$
$331$	17.0405	+	7.05841i	0.936631	+	0.387965i	0.138441	+	0.990371i	$0.455791\pi$
$332$	21.0251	+	4.19925i	1.15390	+	0.230464i
$333$	−1.64936	−	3.98190i	−0.0903843	−	0.218207i
$334$	16.4245	+	4.98932i	0.898707	+	0.273004i
$335$		−	22.2333i		−	1.21473i
$336$	0.0148119	−	9.46931i	0.000808054	−	0.516593i
$337$		−	24.1423i		−	1.31511i	−0.753405	−	0.657556i	$-0.771590\pi$
$337$		−	24.1423i		−	1.31511i	0.753405	−	0.657556i	$-0.228410\pi$
$338$	5.60527	−	18.4521i	0.304886	−	1.00366i
$339$	13.3010	+	32.1116i	0.722414	+	1.74406i
$340$	22.7793	−	15.1949i	1.23538	−	0.824057i
$341$	−12.6665	−	5.24665i	−0.685931	−	0.284122i
$342$	−2.35625	+	0.231140i	−0.127412	+	0.0124986i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−1.23676	+	2.30730i	−0.0666816	+	0.124401i
$345$	−6.60226	−	6.60226i	−0.355454	−	0.355454i
$346$	1.30752	+	1.07391i	0.0702927	+	0.0577338i
$347$	−0.804952	+	1.94333i	−0.0432121	+	0.104323i	−0.944012	−	0.329911i	$-0.892981\pi$
$347$	−0.804952	+	1.94333i	−0.0432121	+	0.104323i	0.900800	+	0.434235i	$0.142981\pi$
$348$	3.74962	+	18.9279i	0.201000	+	1.01464i
$349$	−19.6991	+	8.15963i	−1.05447	+	0.436775i	−0.841485	−	0.540281i	$-0.818318\pi$
$349$	−19.6991	+	8.15963i	−1.05447	+	0.436775i	−0.212983	+	0.977056i	$0.568318\pi$
$350$	−0.434595	−	0.813836i	−0.0232301	−	0.0435013i
$351$	4.83516			0.258082
$352$	−3.56771	−	6.70623i	−0.190160	−	0.357443i
$353$	6.41869			0.341633			0.170816	−	0.985303i	$-0.445360\pi$
$353$	6.41869			0.341633			0.170816	+	0.985303i	$0.445360\pi$
$354$	4.29164	+	8.03665i	0.228098	+	0.427143i
$355$	−18.4250	+	7.63189i	−0.977898	+	0.405059i
$356$	−18.1574	+	3.59698i	−0.962342	+	0.190640i
$357$	−5.94853	+	14.3610i	−0.314830	+	0.760066i
$358$	23.9022	+	19.6316i	1.26327	+	1.03756i
$359$	−20.8887	−	20.8887i	−1.10246	−	1.10246i	−0.994113	−	0.108349i	$-0.965444\pi$
$359$	−20.8887	−	20.8887i	−1.10246	−	1.10246i	−0.108349	−	0.994113i	$-0.534556\pi$
$360$	14.7026	−	4.44115i	0.774894	−	0.234069i
$361$	13.1428	−	13.1428i	0.691727	−	0.691727i
$362$	6.18192	−	0.606425i	0.324914	−	0.0318730i
$363$	−20.1146	−	8.33174i	−1.05574	−	0.437303i
$364$	−5.72793	−	8.58698i	−0.300225	−	0.450080i
$365$	−0.160164	−	0.386670i	−0.00838336	−	0.0202392i
$366$	9.98209	−	32.8603i	0.521772	−	1.71763i
$367$			12.3497i			0.644650i	0.946629	+	0.322325i	$0.104464\pi$
$367$			12.3497i			0.644650i	−0.946629	+	0.322325i	$0.895536\pi$
$368$	−6.98580	−	2.90642i	−0.364160	−	0.151508i
$369$			10.1789i			0.529890i
$370$	4.66945	+	1.41846i	0.242753	+	0.0737420i
$371$	−4.60960	−	11.1286i	−0.239319	−	0.577766i
$372$	9.46783	−	47.4042i	0.490884	−	2.45779i
$373$	4.88869	+	2.02496i	0.253127	+	0.104848i	0.505639	−	0.862745i	$-0.331257\pi$
$373$	4.88869	+	2.02496i	0.253127	+	0.104848i	−0.252512	+	0.967594i	$0.581257\pi$
$374$	1.21737	+	12.4099i	0.0629485	+	0.641699i
$375$	19.7288	−	19.7288i	1.01879	−	1.01879i
$376$	−29.9239	−	2.98269i	−1.54321	−	0.153821i
$377$	14.8729	+	14.8729i	0.765993	+	0.765993i
$378$	0.840919	−	1.02385i	0.0432522	−	0.0526610i
$379$	−7.74540	+	18.6990i	−0.397854	+	0.960505i	0.590320	+	0.807169i	$0.299002\pi$
$379$	−7.74540	+	18.6990i	−0.397854	+	0.960505i	−0.988174	+	0.153336i	$0.950998\pi$
$380$	1.49110	−	2.22781i	0.0764916	−	0.114284i
$381$	−8.20240	+	3.39754i	−0.420222	+	0.174061i
$382$	7.64299	−	4.08142i	0.391050	−	0.208824i
$383$	−7.18276			−0.367022			−0.183511	−	0.983018i	$-0.558746\pi$
$383$	−7.18276			−0.367022			−0.183511	+	0.983018i	$0.558746\pi$
$384$	20.7502	−	16.9344i	1.05890	−	0.864180i
$385$	−2.79993			−0.142697
$386$	−24.1678	+	12.9058i	−1.23011	+	0.656888i
$387$	2.22690	−	0.922412i	0.113200	−	0.0468888i
$388$	−16.2504	+	24.2793i	−0.824988	+	1.23259i
$389$	0.994237	−	2.40030i	0.0504098	−	0.121700i	−0.896669	−	0.442703i	$-0.854020\pi$
$389$	0.994237	−	2.40030i	0.0504098	−	0.121700i	0.947078	+	0.321002i	$0.104020\pi$
$390$	22.8666	−	27.8409i	1.15790	−	1.40978i
$391$	8.78251	+	8.78251i	0.444151	+	0.444151i
$392$	−2.81448	−	0.280536i	−0.142153	−	0.0141692i
$393$	0.623290	−	0.623290i	0.0314408	−	0.0314408i
$394$	1.96735	+	20.0552i	0.0991135	+	1.01037i
$395$	−3.18625	−	1.31979i	−0.160317	−	0.0664057i
$396$	−1.36985	+	6.85868i	−0.0688377	+	0.344662i
$397$	14.1878	+	34.2523i	0.712064	+	1.71907i	0.694779	+	0.719223i	$0.255502\pi$
$397$	14.1878	+	34.2523i	0.712064	+	1.71907i	0.0172845	+	0.999851i	$0.494498\pi$
$398$	−4.81287	−	1.46202i	−0.241248	−	0.0732847i
$399$			1.52182i			0.0761861i
$400$	1.00239	−	2.40932i	0.0501196	−	0.120466i
$401$		−	11.6214i		−	0.580345i	−0.956974	−	0.290173i	$-0.906287\pi$
$401$		−	11.6214i		−	0.580345i	0.956974	−	0.290173i	$-0.0937127\pi$
$402$	−10.3761	+	34.1574i	−0.517514	+	1.70362i
$403$	−20.1650	−	48.6827i	−1.00449	−	2.42506i
$404$	−9.11933	−	13.6712i	−0.453703	−	0.680166i
$405$	19.3227	+	8.00374i	0.960155	+	0.397709i
$406$	5.73599	−	0.562681i	0.284672	−	0.0279254i
$407$	−1.57144	+	1.57144i	−0.0778933	+	0.0778933i
$408$	−42.0876	+	12.7132i	−2.08365	+	0.629399i
$409$	15.9136	+	15.9136i	0.786879	+	0.786879i	0.980981	−	0.194102i	$-0.0621794\pi$
$409$	15.9136	+	15.9136i	0.786879	+	0.786879i	−0.194102	+	0.980981i	$0.562179\pi$
$410$	−8.90640	−	7.31512i	−0.439856	−	0.361268i
$411$	17.9791	−	43.4055i	0.886846	−	2.14103i
$412$	−3.22633	+	0.639134i	−0.158950	+	0.0314879i
$413$	2.51418	−	1.04141i	0.123715	−	0.0512442i
$414$	3.28163	+	6.14529i	0.161284	+	0.302024i
$415$	22.3526			1.09725
$416$	8.52954	−	27.9215i	0.418195	−	1.36896i
$417$	−53.9003			−2.63951
$418$	0.575053	+	1.07686i	0.0281267	+	0.0526710i
$419$	16.7940	−	6.95632i	0.820442	−	0.339838i	0.0673304	−	0.997731i	$-0.478552\pi$
$419$	16.7940	−	6.95632i	0.820442	−	0.339838i	0.753112	+	0.657892i	$0.228552\pi$
$420$	−1.91840	−	9.68403i	−0.0936084	−	0.472532i
$421$	−3.70195	+	8.93730i	−0.180422	+	0.435577i	−0.988054	−	0.154110i	$-0.950749\pi$
$421$	−3.70195	+	8.93730i	−0.180422	+	0.435577i	0.807632	+	0.589687i	$0.200749\pi$
$422$	5.76739	+	4.73695i	0.280752	+	0.230591i
$423$	19.5789	+	19.5789i	0.951959	+	0.951959i
$424$	16.0956	−	30.0280i	0.781672	−	1.45829i
$425$	−3.02898	+	3.02898i	−0.146927	+	0.146927i
$426$	31.8684	−	3.12619i	1.54403	−	0.151464i
$427$	−9.47718	−	3.92558i	−0.458633	−	0.189972i
$428$	22.1566	−	14.7795i	1.07098	−	0.714395i
$429$	6.27851	+	15.1577i	0.303129	+	0.731819i
$430$	−0.793279	+	2.61141i	−0.0382553	+	0.125934i
$431$			19.9665i			0.961754i	0.876788	+	0.480877i	$0.159682\pi$
$431$			19.9665i			0.961754i	−0.876788	+	0.480877i	$0.840318\pi$
$432$	3.74743	+	0.00586171i	0.180298	+	0.000282022i
$433$			33.2683i			1.59877i	0.600816	+	0.799387i	$0.294842\pi$
$433$			33.2683i			1.59877i	−0.600816	+	0.799387i	$0.705158\pi$
$434$	−13.8156	−	4.19682i	−0.663170	−	0.201454i
$435$	7.69835	+	18.5855i	0.369108	+	0.891104i
$436$	30.2038	+	6.03247i	1.44650	+	0.288903i
$437$	1.12342	+	0.465335i	0.0537404	+	0.0222600i
$438$	0.0656066	+	0.668796i	0.00313480	+	0.0319563i
$439$	5.79889	−	5.79889i	0.276766	−	0.276766i	−0.555051	−	0.831817i	$-0.687301\pi$
$439$	5.79889	−	5.79889i	0.276766	−	0.276766i	0.831817	+	0.555051i	$0.187301\pi$
$440$	−5.01682	−	6.12766i	−0.239168	−	0.292125i
$441$	1.84149	+	1.84149i	0.0876898	+	0.0876898i
$442$	−30.4179	+	37.0347i	−1.44683	+	1.76156i
$443$	−10.9596	+	26.4588i	−0.520706	+	1.25709i	0.416760	+	0.909016i	$0.363165\pi$
$443$	−10.9596	+	26.4588i	−0.520706	+	1.25709i	−0.937466	+	0.348078i	$0.886835\pi$
$444$	−6.51178	−	4.35840i	−0.309035	−	0.206841i
$445$	−17.8289	+	7.38497i	−0.845171	+	0.350081i
$446$	−33.1101	+	17.6811i	−1.56781	+	0.837224i
$447$	3.88913			0.183949
$448$	−4.42894	−	6.66217i	−0.209248	−	0.314758i
$449$	29.2072			1.37837			0.689186	−	0.724584i	$-0.257968\pi$
$449$	29.2072			1.37837			0.689186	+	0.724584i	$0.257968\pi$
$450$	−2.11944	+	1.13180i	−0.0999112	+	0.0533534i
$451$	4.84899	−	2.00852i	0.228330	−	0.0945774i
$452$	24.4026	+	16.3329i	1.14780	+	0.768237i
$453$	3.23293	−	7.80498i	0.151896	−	0.366710i
$454$	0.0138633	−	0.0168790i	0.000650636	−	0.000792170i
$455$	−7.60936	−	7.60936i	−0.356732	−	0.356732i
$456$	−3.33050	+	2.72674i	−0.155965	+	0.127691i
$457$	1.48938	−	1.48938i	0.0696702	−	0.0696702i	−0.671413	−	0.741083i	$-0.734312\pi$
$457$	1.48938	−	1.48938i	0.0696702	−	0.0696702i	0.741083	+	0.671413i	$0.234312\pi$
$458$	−1.07228	−	10.9308i	−0.0501043	−	0.510765i
$459$	−5.68329	−	2.35410i	−0.265273	−	0.109880i
$460$	−7.73544	−	1.54496i	−0.360667	−	0.0720343i
$461$	−4.07104	−	9.82835i	−0.189607	−	0.457752i	0.800277	−	0.599630i	$-0.204686\pi$
$461$	−4.07104	−	9.82835i	−0.189607	−	0.457752i	−0.989884	+	0.141879i	$0.954686\pi$
$462$	4.30158	+	1.30671i	0.200128	+	0.0607935i
$463$			21.5685i			1.00237i	0.865340	+	0.501186i	$0.167103\pi$
$463$			21.5685i			1.00237i	−0.865340	+	0.501186i	$0.832897\pi$
$464$	11.5090	+	11.5451i	0.534292	+	0.535966i
$465$		−	50.3972i		−	2.33711i
$466$	−3.46974	+	11.4221i	−0.160733	+	0.529119i
$467$	−1.70754	−	4.12236i	−0.0790154	−	0.190760i	0.879435	−	0.476019i	$-0.157921\pi$
$467$	−1.70754	−	4.12236i	−0.0790154	−	0.190760i	−0.958451	+	0.285259i	$0.907921\pi$
$468$	−22.3627	+	14.9170i	−1.03372	+	0.689538i
$469$	9.85128	+	4.08053i	0.454890	+	0.188422i
$470$	−31.2019	+	3.06080i	−1.43924	+	0.141184i
$471$	−10.6901	+	10.6901i	−0.492576	+	0.492576i
$472$	6.78395	+	3.63633i	0.312256	+	0.167376i
$473$	−0.878835	−	0.878835i	−0.0404089	−	0.0404089i
$474$	4.27916	+	3.51461i	0.196548	+	0.161432i
$475$	−0.160488	+	0.387453i	−0.00736372	+	0.0177776i
$476$	2.55191	+	12.8820i	0.116967	+	0.590444i
$477$	−28.9816	+	12.0046i	−1.32698	+	0.549652i
$478$	11.8116	+	22.1188i	0.540251	+	1.01169i
$479$	1.00696			0.0460092			0.0230046	−	0.999735i	$-0.492677\pi$
$479$	1.00696			0.0460092			0.0230046	+	0.999735i	$0.492677\pi$
$480$	17.7562	−	21.5500i	0.810458	−	0.983617i
$481$	−8.54140			−0.389454
$482$	17.6928	+	33.1321i	0.805885	+	1.50912i
$483$	4.13711	−	1.71365i	0.188245	−	0.0779737i
$484$	−18.0430	+	3.57431i	−0.820136	+	0.162468i
$485$	−11.6561	+	28.1402i	−0.529275	+	1.27778i
$486$	−22.8791	−	18.7914i	−1.03782	−	0.852393i
$487$	−9.42615	−	9.42615i	−0.427139	−	0.427139i	0.460513	−	0.887653i	$-0.347665\pi$
$487$	−9.42615	−	9.42615i	−0.427139	−	0.427139i	−0.887653	+	0.460513i	$0.847665\pi$
$488$	−8.38977	−	27.7746i	−0.379787	−	1.25730i
$489$	5.47854	−	5.47854i	0.247748	−	0.247748i
$490$	−2.93468	+	0.287882i	−0.132575	+	0.0130052i
$491$	23.9603	+	9.92468i	1.08131	+	0.447895i	0.850970	−	0.525215i	$-0.176015\pi$
$491$	23.9603	+	9.92468i	1.08131	+	0.447895i	0.230343	+	0.973109i	$0.426015\pi$
$492$	10.2692	+	15.3949i	0.462969	+	0.694057i
$493$	−10.2406	−	24.7229i	−0.461212	−	1.11346i
$494$	−1.36376	+	4.48940i	−0.0613586	+	0.201988i
$495$			7.29172i			0.327739i
$496$	−15.5696	−	37.7553i	−0.699096	−	1.69526i
$497$		−	9.56459i		−	0.429031i
$498$	−34.3407	−	10.4318i	−1.53884	−	0.467460i
$499$	−15.3246	−	36.9968i	−0.686023	−	1.65621i	−0.752644	−	0.658427i	$-0.771222\pi$
$499$	−15.3246	−	36.9968i	−0.686023	−	1.65621i	0.0666215	−	0.997778i	$-0.478778\pi$
$500$	4.61665	−	23.1150i	0.206463	−	1.03373i
$501$	−26.5471	−	10.9962i	−1.18604	−	0.491273i
$502$	0.404325	+	4.12171i	0.0180459	+	0.183961i
$503$	−8.75118	+	8.75118i	−0.390196	+	0.390196i	−0.874757	−	0.484561i	$-0.838979\pi$
$503$	−8.75118	+	8.75118i	−0.390196	+	0.390196i	0.484561	+	0.874757i	$0.338979\pi$
$504$	−0.730588	+	7.32963i	−0.0325430	+	0.326488i
$505$	−12.1147	−	12.1147i	−0.539098	−	0.539098i
$506$	2.27994	−	2.77591i	0.101356	−	0.123404i
$507$	−12.3537	+	29.8244i	−0.548646	+	1.32455i
$508$	−4.17199	+	6.23327i	−0.185102	+	0.276557i
$509$	6.48869	−	2.68770i	0.287606	−	0.119130i	−0.234216	−	0.972185i	$-0.575252\pi$
$509$	6.48869	−	2.68770i	0.287606	−	0.119130i	0.521822	+	0.853054i	$0.325252\pi$
$510$	−40.4326	+	21.5913i	−1.79038	+	0.956080i
$511$	0.200724			0.00887951
$512$	6.64456	−	21.6298i	0.293651	−	0.955913i
$513$	−0.602250			−0.0265900
$514$	−5.63609	+	3.00972i	−0.248597	+	0.132753i
$515$	−3.16795	+	1.31221i	−0.139597	+	0.0578228i
$516$	2.43746	−	3.64175i	0.107303	−	0.160319i
$517$	5.46361	−	13.1903i	0.240289	−	0.580110i
$518$	−1.48550	+	1.80864i	−0.0652690	+	0.0794672i
$519$	−2.00277	−	2.00277i	−0.0879119	−	0.0879119i
$520$	3.01892	−	30.2873i	0.132389	−	1.32819i
$521$	−16.3470	+	16.3470i	−0.716173	+	0.716173i	−0.967819	−	0.251646i	$-0.919028\pi$
$521$	−16.3470	+	16.3470i	−0.716173	+	0.716173i	0.251646	+	0.967819i	$0.419028\pi$
$522$	−1.46537	−	14.9380i	−0.0641373	−	0.653818i
$523$	−10.2334	−	4.23880i	−0.447474	−	0.185350i	0.147555	−	0.989054i	$-0.452860\pi$
$523$	−10.2334	−	4.23880i	−0.447474	−	0.185350i	−0.595029	+	0.803704i	$0.702860\pi$
$524$	0.145853	−	0.730268i	0.00637163	−	0.0319019i
$525$	0.591017	+	1.42684i	0.0257941	+	0.0622724i
$526$	−35.7439	−	10.8580i	−1.55851	−	0.473433i
$527$			67.0398i			2.92030i
$528$	4.84770	+	11.7554i	0.210969	+	0.511586i
$529$			19.4220i			0.844433i
$530$	10.3240	−	33.9858i	0.448446	−	1.47625i
$531$	−2.71209	−	6.54756i	−0.117695	−	0.284140i
$532$	0.713450	+	1.06956i	0.0309320	+	0.0463714i
$533$	18.6367	+	7.71955i	0.807243	+	0.334371i
$534$	30.8374	−	3.02504i	1.33446	−	0.130906i
$535$	19.6341	−	19.6341i	0.848855	−	0.848855i
$536$	8.72094	+	28.8710i	0.376687	+	1.24704i
$537$	−36.6117	−	36.6117i	−1.57991	−	1.57991i
$538$	9.71766	+	7.98144i	0.418958	+	0.344104i
$539$	0.513879	−	1.24061i	0.0221343	−	0.0534370i
$540$	3.83240	−	0.759196i	0.164920	−	0.0326706i
$541$	−6.07288	+	2.51547i	−0.261093	+	0.108148i	−0.509390	−	0.860536i	$-0.670129\pi$
$541$	−6.07288	+	2.51547i	−0.261093	+	0.108148i	0.248297	+	0.968684i	$0.420129\pi$
$542$	−1.56242	−	2.92584i	−0.0671118	−	0.125676i
$543$	−10.3979			−0.446218
$544$	−23.6198	+	28.6664i	−1.01269	+	1.22906i
$545$	32.1108			1.37547
$546$	8.13917	+	15.2416i	0.348324	+	0.652282i
$547$	29.3224	−	12.1457i	1.25374	−	0.519314i	0.345755	−	0.938325i	$-0.387623\pi$
$547$	29.3224	−	12.1457i	1.25374	−	0.519314i	0.907981	+	0.419011i	$0.137623\pi$
$548$	−7.71303	−	38.9351i	−0.329484	−	1.66323i
$549$	−10.2232	+	24.6810i	−0.436316	+	1.05336i
$550$	0.957377	+	0.786325i	0.0408227	+	0.0335290i
$551$	−1.85251	−	1.85251i	−0.0789197	−	0.0789197i
$552$	11.1631	+	5.98364i	0.475132	+	0.254681i
$553$	1.16956	−	1.16956i	0.0497348	−	0.0497348i
$554$	14.3947	−	1.41207i	0.611570	−	0.0599929i
$555$	−7.54730	−	3.12619i	−0.320365	−	0.132700i
$556$	−37.8822	+	25.2693i	−1.60656	+	1.07166i
$557$	−9.72719	−	23.4835i	−0.412154	−	0.995028i	−0.984558	−	0.175057i	$-0.943989\pi$
$557$	−9.72719	−	23.4835i	−0.412154	−	0.995028i	0.572404	−	0.819972i	$-0.306011\pi$
$558$	−10.9296	+	35.9794i	−0.462686	+	1.52313i
$559$		−	4.77682i		−	0.202038i
$560$	−5.88831	−	5.90676i	−0.248826	−	0.249606i
$561$		−	20.8733i		−	0.881271i
$562$	37.3895	+	11.3579i	1.57718	+	0.479106i
$563$	−2.76493	−	6.67513i	−0.116528	−	0.281323i	0.854845	−	0.518884i	$-0.173652\pi$
$563$	−2.76493	−	6.67513i	−0.116528	−	0.281323i	−0.971373	+	0.237560i	$0.923652\pi$
$564$	49.3645	+	9.85935i	2.07862	+	0.415154i
$565$	28.2832	+	11.7153i	1.18988	+	0.492866i
$566$	0.706624	+	7.20335i	0.0297016	+	0.302779i
$567$	−7.09272	+	7.09272i	−0.297866	+	0.297866i
$568$	20.9322	−	17.1375i	0.878295	−	0.719075i
$569$	−8.85720	−	8.85720i	−0.371313	−	0.371313i	0.496642	−	0.867955i	$-0.334566\pi$
$569$	−8.85720	−	8.85720i	−0.371313	−	0.371313i	−0.867955	+	0.496642i	$0.834566\pi$
$570$	−2.84819	+	3.46776i	−0.119297	+	0.145248i
$571$	−15.5860	+	37.6279i	−0.652253	+	1.57468i	0.157249	+	0.987559i	$0.449738\pi$
$571$	−15.5860	+	37.6279i	−0.652253	+	1.57468i	−0.809501	+	0.587118i	$0.800262\pi$
$572$	11.5188	+	7.70965i	0.481625	+	0.322357i
$573$	−13.3999	+	5.55043i	−0.559790	+	0.231873i
$574$	4.87586	−	2.60375i	0.203514	−	0.108678i
$575$	1.23403			0.0514624
$576$	−17.3500	+	11.5341i	−0.722916	+	0.480587i
$577$	−19.4322			−0.808973			−0.404487	−	0.914544i	$-0.632550\pi$
$577$	−19.4322			−0.808973			−0.404487	+	0.914544i	$0.632550\pi$
$578$	32.5773	−	17.3965i	1.35504	−	0.723601i
$579$	42.3717	−	17.5509i	1.76091	−	0.729391i
$580$	14.1237	+	9.45313i	0.586454	+	0.392520i
$581$	−4.10243	+	9.90415i	−0.170198	+	0.410893i
$582$	31.0403	−	37.7926i	1.28666	−	1.56655i
$583$	11.4375	+	11.4375i	0.473691	+	0.473691i
$584$	0.359651	+	0.439286i	0.0148825	+	0.0181778i
$585$	−19.8167	+	19.8167i	−0.819320	+	0.819320i
$586$	0.776924	+	7.91999i	0.0320944	+	0.327172i
$587$	−15.4268	−	6.38998i	−0.636731	−	0.263743i	0.0408789	−	0.999164i	$-0.486984\pi$
$587$	−15.4268	−	6.38998i	−0.636731	−	0.263743i	−0.677610	+	0.735421i	$0.736984\pi$
$588$	4.64296	+	0.927318i	0.191473	+	0.0382420i
$589$	2.51168	+	6.06373i	0.103492	+	0.249852i
$590$	7.67811	+	2.33241i	0.316103	+	0.0960238i
$591$		−	33.7327i		−	1.38758i
$592$	−6.61989	−	0.0103548i	−0.272076	−	0.000425581i
$593$			8.33506i			0.342280i	0.985247	+	0.171140i	$0.0547450\pi$
$593$			8.33506i			0.342280i	−0.985247	+	0.171140i	$0.945255\pi$
$594$	−0.517122	+	1.70233i	−0.0212178	+	0.0698473i
$595$	5.23934	+	12.6489i	0.214792	+	0.518553i
$596$	2.73336	−	1.82328i	0.111963	−	0.0746845i
$597$	7.77912	+	3.22222i	0.318378	+	0.131877i
$598$	13.7403	−	1.34787i	0.561882	−	0.0551187i
$599$	−5.05427	+	5.05427i	−0.206512	+	0.206512i	−0.802783	−	0.596271i	$-0.796648\pi$
$599$	−5.05427	+	5.05427i	−0.206512	+	0.206512i	0.596271	+	0.802783i	$0.296648\pi$
$600$	−2.06369	+	3.85001i	−0.0842496	+	0.157176i
$601$	−3.80362	−	3.80362i	−0.155153	−	0.155153i	0.625262	−	0.780415i	$-0.284992\pi$
$601$	−3.80362	−	3.80362i	−0.155153	−	0.155153i	−0.780415	+	0.625262i	$0.784992\pi$
$602$	−1.01149	−	0.830772i	−0.0412254	−	0.0338598i
$603$	10.6268	−	25.6553i	0.432755	−	1.04476i
$604$	−1.38692	−	7.00114i	−0.0564331	−	0.284872i
$605$	−17.7165	+	7.33842i	−0.720279	+	0.298349i
$606$	12.9582	+	24.2659i	0.526392	+	0.985736i
$607$	−30.9804			−1.25746			−0.628729	−	0.777625i	$-0.716424\pi$
$607$	−30.9804			−1.25746			−0.628729	+	0.777625i	$0.716424\pi$
$608$	−1.06241	+	3.47780i	−0.0430864	+	0.141043i
$609$	−9.64788			−0.390952
$610$	−14.2486	−	26.6824i	−0.576911	−	1.08034i
$611$	50.6958	−	20.9989i	2.05093	−	0.849524i
$612$	33.5479	−	6.64583i	1.35610	−	0.268642i
$613$	−6.78488	+	16.3802i	−0.274039	+	0.661588i	−0.999648	−	0.0265184i	$-0.991558\pi$
$613$	−6.78488	+	16.3802i	−0.274039	+	0.661588i	0.725609	+	0.688107i	$0.241558\pi$
$614$	−23.4461	−	19.2571i	−0.946209	−	0.777153i
$615$	13.6422	+	13.6422i	0.550107	+	0.550107i
$616$	3.63584	−	1.09826i	0.146492	−	0.0442503i
$617$	23.2881	−	23.2881i	0.937545	−	0.937545i	−0.0606166	−	0.998161i	$-0.519307\pi$
$617$	23.2881	−	23.2881i	0.937545	−	0.937545i	0.998161	+	0.0606166i	$0.0193067\pi$
$618$	5.47938	−	0.537509i	0.220413	−	0.0216218i
$619$	29.5955	+	12.2588i	1.18954	+	0.492724i	0.887606	−	0.460604i	$-0.152367\pi$
$619$	29.5955	+	12.2588i	1.18954	+	0.492724i	0.301936	+	0.953328i	$0.402367\pi$
$620$	−23.6269	−	35.4202i	−0.948881	−	1.42251i
$621$	0.678166	+	1.63724i	0.0272139	+	0.0657001i
$622$	11.4827	−	37.8002i	0.460414	−	1.51565i
$623$		−	9.25515i		−	0.370800i
$624$	−18.7729	+	45.1221i	−0.751519	+	1.80633i
$625$		−	21.3125i		−	0.852500i
$626$	13.9452	+	4.23620i	0.557364	+	0.169313i
$627$	−0.782028	−	1.88798i	−0.0312312	−	0.0753988i
$628$	−2.50155	+	12.5249i	−0.0998228	+	0.499800i
$629$	10.0396	+	4.15855i	0.400306	+	0.165812i
$630$	0.749719	+	7.64266i	0.0298695	+	0.304491i
$631$	10.5101	−	10.5101i	0.418399	−	0.418399i	−0.466253	−	0.884652i	$-0.654396\pi$
$631$	10.5101	−	10.5101i	0.418399	−	0.418399i	0.884652	+	0.466253i	$0.154396\pi$
$632$	4.65518	+	0.464010i	0.185173	+	0.0184573i
$633$	−8.83411	−	8.83411i	−0.351124	−	0.351124i
$634$	11.5195	−	14.0253i	0.457496	−	0.557017i
$635$	−2.99248	+	7.22450i	−0.118753	+	0.286695i
$636$	−31.7219	+	47.3950i	−1.25786	+	1.87933i
$637$	4.76818	−	1.97504i	0.188922	−	0.0782541i
$638$	−6.82699	+	3.64567i	−0.270283	+	0.144334i
$639$	−24.9086			−0.985371
$640$	2.37649	−	23.4701i	0.0939392	−	0.927739i
$641$	11.8514			0.468102			0.234051	−	0.972224i	$-0.424802\pi$
$641$	11.8514			0.468102			0.234051	+	0.972224i	$0.424802\pi$
$642$	−39.3273	+	21.0011i	−1.55213	+	0.828848i
$643$	−29.1304	+	12.0662i	−1.14879	+	0.475845i	−0.874128	−	0.485695i	$-0.838567\pi$
$643$	−29.1304	+	12.0662i	−1.14879	+	0.475845i	−0.274664	+	0.961540i	$0.588567\pi$
$644$	2.10426	−	3.14392i	0.0829195	−	0.123888i
$645$	1.74834	−	4.22087i	0.0688408	−	0.166197i
$646$	3.78874	−	4.61291i	0.149066	−	0.181492i
$647$	−13.4421	−	13.4421i	−0.528463	−	0.528463i	0.391651	−	0.920114i	$-0.371904\pi$
$647$	−13.4421	−	13.4421i	−0.528463	−	0.528463i	−0.920114	+	0.391651i	$0.871904\pi$
$648$	−28.2310	−	2.81395i	−1.10902	−	0.110543i
$649$	−2.58396	+	2.58396i	−0.101429	+	0.101429i
$650$	0.464866	+	4.73886i	0.0182335	+	0.185873i
$651$	22.3304	+	9.24954i	0.875196	+	0.362518i
$652$	1.28201	−	6.41885i	0.0502073	−	0.251381i
$653$	−11.6652	−	28.1624i	−0.456496	−	1.10208i	−0.969806	−	0.243876i	$-0.921581\pi$
$653$	−11.6652	−	28.1624i	−0.456496	−	1.10208i	0.513310	−	0.858203i	$-0.328419\pi$
$654$	−49.3324	−	14.9859i	−1.92905	−	0.585995i
$655$		−	0.776376i		−	0.0303355i
$656$	14.4347	+	6.00553i	0.563582	+	0.234477i
$657$		−	0.522737i		−	0.0203939i
$658$	4.37037	−	14.3869i	0.170375	−	0.560861i
$659$	6.54885	+	15.8103i	0.255107	+	0.615883i	0.998602	−	0.0528586i	$-0.0168333\pi$
$659$	6.54885	+	15.8103i	0.255107	+	0.615883i	−0.743495	+	0.668742i	$0.766833\pi$
$660$	7.35641	+	11.0283i	0.286348	+	0.429276i
$661$	37.6737	+	15.6050i	1.46534	+	0.606963i	0.965790	−	0.259324i	$-0.0834997\pi$
$661$	37.6737	+	15.6050i	1.46534	+	0.606963i	0.499547	+	0.866287i	$0.333500\pi$
$662$	−25.9599	+	2.54657i	−1.00896	+	0.0989754i
$663$	56.7273	−	56.7273i	2.20311	−	2.20311i
$664$	−29.0259	+	8.76775i	−1.12642	+	0.340255i
$665$	0.947794	+	0.947794i	0.0367539	+	0.0367539i
$666$	4.71017	+	3.86862i	0.182515	+	0.149906i
$667$	−2.95009	+	7.12215i	−0.114228	+	0.275771i
$668$	−23.8130	+	4.71735i	−0.921353	+	0.182520i
$669$	58.0497	−	24.0450i	2.24433	−	0.929632i
$670$	14.8111	+	27.7357i	0.572202	+	1.07152i
$671$	13.7748			0.531770
$672$	6.28967	+	11.8227i	0.242629	+	0.456070i
$673$	9.56376			0.368656			0.184328	−	0.982865i	$-0.440989\pi$
$673$	9.56376			0.368656			0.184328	+	0.982865i	$0.440989\pi$
$674$	16.0828	+	30.1171i	0.619486	+	1.16007i
$675$	−0.564664	+	0.233891i	−0.0217339	+	0.00900249i
$676$	5.29971	+	26.7528i	0.203835	+	1.02895i
$677$	7.96920	−	19.2394i	0.306281	−	0.739428i	−0.693538	−	0.720420i	$-0.743949\pi$
$677$	7.96920	−	19.2394i	0.306281	−	0.739428i	0.999819	−	0.0190084i	$-0.00605092\pi$
$678$	−37.9846	−	31.1980i	−1.45879	−	1.19815i
$679$	−10.3293	−	10.3293i	−0.396403	−	0.396403i
$680$	−18.2945	+	34.1302i	−0.701561	+	1.30883i
$681$	−0.0258541	+	0.0258541i	−0.000990731	+	0.000990731i
$682$	19.2965	−	1.89292i	0.738900	−	0.0724836i
$683$	−7.40302	−	3.06643i	−0.283269	−	0.117334i	0.236525	−	0.971625i	$-0.423991\pi$
$683$	−7.40302	−	3.06643i	−0.283269	−	0.117334i	−0.519794	+	0.854292i	$0.673991\pi$
$684$	2.78541	−	1.85801i	0.106503	−	0.0710426i
$685$	−15.8356	−	38.2306i	−0.605049	−	1.46072i
$686$	0.411054	−	1.35316i	0.0156941	−	0.0516638i
$687$			18.3856i			0.701453i
$688$	0.00579099	−	3.70221i	0.000220779	−	0.141145i
$689$			62.1672i			2.36838i
$690$	12.6344	+	3.83801i	0.480985	+	0.146111i
$691$	−5.54288	−	13.3817i	−0.210861	−	0.509064i	0.782695	−	0.622406i	$-0.213845\pi$
$691$	−5.54288	−	13.3817i	−0.210861	−	0.509064i	−0.993556	+	0.113342i	$0.963845\pi$
$692$	−2.34652	−	0.468659i	−0.0892012	−	0.0178158i
$693$	−3.23087	−	1.33827i	−0.122731	−	0.0508367i
$694$	−0.290415	−	2.96051i	−0.0110240	−	0.112379i
$695$	−33.5694	+	33.5694i	−1.27336	+	1.27336i
$696$	−17.2868	−	21.1145i	−0.655254	−	0.800342i
$697$	−18.1473	−	18.1473i	−0.687377	−	0.687377i
$698$	19.1386	−	23.3019i	0.724409	−	0.881991i
$699$	7.64710	−	18.4617i	0.289240	−	0.698287i
$700$	1.08430	+	0.725735i	0.0409828	+	0.0274302i
$701$	13.2322	−	5.48095i	0.499772	−	0.207012i	−0.118534	−	0.992950i	$-0.537819\pi$
$701$	13.2322	−	5.48095i	0.499772	−	0.207012i	0.618306	+	0.785938i	$0.287819\pi$
$702$	−6.03179	+	3.22103i	−0.227655	+	0.121570i
$703$	1.06389			0.0401252
$704$	8.91815	+	5.98923i	0.336115	+	0.225728i
$705$	52.4813			1.97656
$706$	−8.00723	+	4.27593i	−0.301356	+	0.160927i
$707$	7.59133	−	3.14443i	0.285501	−	0.118259i
$708$	−10.7075	−	7.16665i	−0.402413	−	0.269339i
$709$	9.17480	−	22.1499i	0.344567	−	0.831858i	−0.652675	−	0.757638i	$-0.726353\pi$
$709$	9.17480	−	22.1499i	0.344567	−	0.831858i	0.997242	−	0.0742201i	$-0.0236467\pi$
$710$	17.9008	−	21.7948i	0.671805	−	0.817945i
$711$	−3.04584	−	3.04584i	−0.114228	−	0.114228i
$712$	20.2550	−	16.5831i	0.759086	−	0.621477i
$713$	13.6562	−	13.6562i	0.511428	−	0.511428i
$714$	−2.14615	−	21.8779i	−0.0803175	−	0.818759i
$715$	13.3505	+	5.52998i	0.499282	+	0.206809i
$716$	−42.8956	−	8.56734i	−1.60308	−	0.320176i
$717$	−16.0629	−	38.7793i	−0.599881	−	1.44824i
$718$	39.9737	+	12.1430i	1.49180	+	0.453171i
$719$		−	1.35702i		−	0.0506084i	−0.999680	−	0.0253042i	$-0.991945\pi$
$719$		−	1.35702i		−	0.0506084i	0.999680	−	0.0253042i	$-0.00805543\pi$
$720$	−15.3827	+	15.3347i	−0.573279	+	0.571489i
$721$		−	1.64451i		−	0.0612449i
$722$	−7.64016	+	25.1508i	−0.284337	+	0.936016i
$723$	−24.0609	−	58.0881i	−0.894834	−	2.16032i
$724$	−7.30787	+	4.87470i	−0.271595	+	0.181167i
$725$	−2.45635	−	1.01745i	−0.0912264	−	0.0377872i
$726$	30.6430	−	3.00598i	1.13727	−	0.111562i
$727$	33.5777	−	33.5777i	1.24533	−	1.24533i	0.287566	−	0.957761i	$-0.407154\pi$
$727$	33.5777	−	33.5777i	1.24533	−	1.24533i	0.957761	−	0.287566i	$-0.0928460\pi$
$728$	12.8659	+	6.89637i	0.476841	+	0.255597i
$729$	13.7665	+	13.7665i	0.509870	+	0.509870i
$730$	0.457389	+	0.375669i	0.0169287	+	0.0139041i
$731$	−2.32569	+	5.61472i	−0.0860188	+	0.207668i
$732$	9.43795	+	47.6425i	0.348837	+	1.76092i
$733$	−34.1779	+	14.1570i	−1.26239	+	0.522900i	−0.910643	−	0.413195i	$-0.864413\pi$
$733$	−34.1779	+	14.1570i	−1.26239	+	0.522900i	−0.351749	+	0.936095i	$0.614413\pi$
$734$	−8.22699	−	15.4061i	−0.303664	−	0.568649i
$735$	4.93611			0.182071
$736$	10.6509	−	1.02799i	0.392596	−	0.0378924i
$737$	−14.3185			−0.527430
$738$	−6.78083	−	12.6980i	−0.249606	−	0.467419i
$739$	−1.08042	+	0.447523i	−0.0397438	+	0.0164624i	−0.402467	−	0.915435i	$-0.631847\pi$
$739$	−1.08042	+	0.447523i	−0.0397438	+	0.0164624i	0.362723	+	0.931897i	$0.381847\pi$
$740$	−6.77000	+	1.34113i	−0.248870	+	0.0493010i
$741$	3.00565	−	7.25629i	0.110415	−	0.266566i
$742$	13.1639	+	10.8120i	0.483262	+	0.396919i
$743$	23.5373	+	23.5373i	0.863500	+	0.863500i	0.991743	−	0.128243i	$-0.0409338\pi$
$743$	23.5373	+	23.5373i	0.863500	+	0.863500i	−0.128243	+	0.991743i	$0.540934\pi$
$744$	19.7682	+	65.4432i	0.724736	+	2.39927i
$745$	2.42217	−	2.42217i	0.0887413	−	0.0887413i
$746$	−7.44753	+	0.730577i	−0.272673	+	0.0267483i
$747$	25.7929	+	10.6838i	0.943715	+	0.390899i
$748$	−9.78570	−	14.6702i	−0.357801	−	0.536394i
$749$	5.09612	+	12.3031i	0.186208	+	0.449546i
$750$	−11.4687	+	37.7541i	−0.418778	+	1.37859i
$751$		−	7.55039i		−	0.275517i	−0.990466	−	0.137759i	$-0.956010\pi$
$751$		−	7.55039i		−	0.275517i	0.990466	−	0.137759i	$-0.0439899\pi$
$752$	39.3166	−	16.2135i	1.43373	−	0.591244i
$753$		−	6.93268i		−	0.252641i
$754$	−28.4616	−	8.64587i	−1.03651	−	0.314864i
$755$	−2.84750	−	6.87446i	−0.103631	−	0.250187i
$756$	−0.366981	+	1.83743i	−0.0133470	+	0.0668265i
$757$	22.2943	+	9.23462i	0.810302	+	0.335638i	0.749074	−	0.662486i	$-0.230499\pi$
$757$	22.2943	+	9.23462i	0.810302	+	0.335638i	0.0612272	+	0.998124i	$0.480499\pi$
$758$	−2.79443	−	28.4865i	−0.101498	−	1.03468i
$759$	−4.25195	+	4.25195i	−0.154336	+	0.154336i
$760$	−0.376026	+	3.77248i	−0.0136399	+	0.136842i
$761$	18.4084	+	18.4084i	0.667303	+	0.667303i	0.957091	−	0.289788i	$-0.0935847\pi$
$761$	18.4084	+	18.4084i	0.667303	+	0.667303i	−0.289788	+	0.957091i	$0.593585\pi$
$762$	7.96904	−	9.70256i	0.288688	−	0.351487i
$763$	−5.89338	+	14.2279i	−0.213355	+	0.515084i
$764$	−6.81561	+	10.1830i	−0.246580	+	0.368409i
$765$	32.9409	−	13.6446i	1.19098	−	0.493321i
$766$	8.96040	−	4.78493i	0.323752	−	0.172886i
$767$	−14.0449			−0.507131
$768$	−14.6044	+	34.9485i	−0.526992	+	1.26110i
$769$	−17.6323			−0.635835			−0.317918	−	0.948118i	$-0.602984\pi$
$769$	−17.6323			−0.635835			−0.317918	+	0.948118i	$0.602984\pi$
$770$	3.49287	−	1.86522i	0.125874	−	0.0672179i
$771$	9.88137	−	4.09300i	0.355869	−	0.147406i
$772$	21.5515	−	32.1996i	0.775657	−	1.15889i
$773$	11.4582	−	27.6625i	0.412122	−	0.994951i	−0.572445	−	0.819943i	$-0.694005\pi$
$773$	11.4582	−	27.6625i	0.412122	−	0.994951i	0.984567	−	0.175008i	$-0.0559950\pi$
$774$	−2.16354	+	2.63418i	−0.0777670	+	0.0946838i
$775$	4.70986	+	4.70986i	0.169183	+	0.169183i
$776$	4.09803	−	41.1135i	0.147111	−	1.47589i
$777$	2.77036	−	2.77036i	0.0993860	−	0.0993860i
$778$	0.358707	+	3.65667i	0.0128603	+	0.131098i
$779$	−2.32131	−	0.961520i	−0.0831697	−	0.0344500i
$780$	−9.97911	+	49.9641i	−0.357309	+	1.78900i
$781$	4.91504	+	11.8660i	0.175874	+	0.424597i
$782$	−16.8067	−	5.10543i	−0.601006	−	0.182570i
$783$		−	3.81810i		−	0.136448i
$784$	3.69791	−	1.52495i	0.132068	−	0.0544625i
$785$			13.3157i			0.475259i
$786$	−0.362330	+	1.19276i	−0.0129239	+	0.0425444i
$787$	−1.03408	−	2.49649i	−0.0368609	−	0.0889901i	0.904377	−	0.426734i	$-0.140336\pi$
$787$	−1.03408	−	2.49649i	−0.0368609	−	0.0889901i	−0.941238	+	0.337744i	$0.890336\pi$
$788$	−15.8144	−	23.7080i	−0.563363	−	0.844562i
$789$	57.7733	+	23.9305i	2.05679	+	0.851948i
$790$	4.85400	−	0.476160i	0.172697	−	0.0169410i
$791$	−10.3818	+	10.3818i	−0.369134	+	0.369134i
$792$	−2.86016	−	9.46866i	−0.101631	−	0.336454i
$793$	37.4357	+	37.4357i	1.32938	+	1.32938i
$794$	−40.5168	−	33.2778i	−1.43789	−	1.18099i
$795$	−22.7535	+	54.9318i	−0.806984	+	1.94823i
$796$	6.97795	−	1.38233i	0.247327	−	0.0489953i
$797$	−43.8662	+	18.1700i	−1.55382	+	0.643614i	−0.984002	−	0.178156i	$-0.942987\pi$
$797$	−43.8662	+	18.1700i	−1.55382	+	0.643614i	−0.569819	+	0.821770i	$0.692987\pi$
$798$	−1.01378	−	1.89844i	−0.0358876	−	0.0672042i
$799$	−69.8121			−2.46977
$800$	0.354543	+	3.67335i	0.0125350	+	0.129873i
$801$	−24.1028			−0.851629
$802$	7.74181	+	14.4975i	0.273373	+	0.511926i
$803$	−0.249021	+	0.103148i	−0.00878775	+	0.00364000i
$804$	−9.81050	−	49.5231i	−0.345990	−	1.74654i
$805$	1.50934	−	3.64388i	0.0531974	−	0.128430i
$806$	57.5864	+	47.2976i	2.02839	+	1.66599i
$807$	−14.8849	−	14.8849i	−0.523972	−	0.523972i
$808$	20.4835	+	10.9796i	0.720608	+	0.386261i
$809$	−7.24925	+	7.24925i	−0.254870	+	0.254870i	−0.822964	−	0.568094i	$-0.807681\pi$
$809$	−7.24925	+	7.24925i	−0.254870	+	0.254870i	0.568094	+	0.822964i	$0.307681\pi$
$810$	−29.4367	+	2.88764i	−1.03430	+	0.101461i
$811$	29.0585	+	12.0364i	1.02038	+	0.422656i	0.829232	−	0.558905i	$-0.188778\pi$
$811$	29.0585	+	12.0364i	1.02038	+	0.422656i	0.191150	+	0.981561i	$0.438778\pi$
$812$	−6.78073	+	4.52307i	−0.237957	+	0.158729i
$813$	2.12478	+	5.12967i	0.0745192	+	0.179905i
$814$	0.913505	−	3.00719i	0.0320183	−	0.105402i
$815$		−	6.82412i		−	0.239038i
$816$	44.0345	−	43.8970i	1.54152	−	1.53670i
$817$			0.594983i			0.0208158i
$818$	−30.4532	−	9.25088i	−1.06477	−	0.323449i
$819$	−5.14352	−	12.4176i	−0.179729	−	0.433905i
$820$	15.9837	+	3.19235i	0.558175	+	0.111482i
$821$	−46.5600	−	19.2858i	−1.62496	−	0.673079i	−0.630303	−	0.776350i	$-0.717069\pi$
$821$	−46.5600	−	19.2858i	−1.62496	−	0.673079i	−0.994653	+	0.103271i	$0.967069\pi$
$822$	6.48662	+	66.1249i	0.226247	+	2.30637i
$823$	22.0571	−	22.0571i	0.768863	−	0.768863i	−0.209043	−	0.977906i	$-0.567035\pi$
$823$	22.0571	−	22.0571i	0.768863	−	0.768863i	0.977906	+	0.209043i	$0.0670349\pi$
$824$	3.59903	−	2.94659i	0.125378	−	0.102649i
$825$	−1.46645	−	1.46645i	−0.0510551	−	0.0510551i
$826$	−2.44265	+	2.97400i	−0.0849906	+	0.103479i
$827$	6.95998	−	16.8029i	0.242022	−	0.584293i	−0.755461	−	0.655193i	$-0.772587\pi$
$827$	6.95998	−	16.8029i	0.242022	−	0.584293i	0.997483	+	0.0709000i	$0.0225871\pi$
$828$	−8.18758	−	5.48004i	−0.284538	−	0.190444i
$829$	27.1969	−	11.2653i	0.944587	−	0.391261i	0.143393	−	0.989666i	$-0.454199\pi$
$829$	27.1969	−	11.2653i	0.944587	−	0.391261i	0.801194	+	0.598405i	$0.204199\pi$
$830$	−27.8845	+	14.8906i	−0.967886	+	0.516859i
$831$	−24.2117			−0.839894
$832$	7.95992	+	40.5138i	0.275960	+	1.40456i
$833$	−6.56615			−0.227504
$834$	67.2399	−	35.9067i	2.32833	−	1.24335i
$835$	−23.3821	+	9.68520i	−0.809172	+	0.335170i
$836$	−1.43474	−	0.960286i	−0.0496215	−	0.0332122i
$837$	−3.66045	+	8.83712i	−0.126524	+	0.305455i
$838$	−16.3162	+	19.8656i	−0.563635	+	0.686244i
$839$	−2.55203	−	2.55203i	−0.0881060	−	0.0881060i	0.661680	−	0.749786i	$-0.269844\pi$
$839$	−2.55203	−	2.55203i	−0.0881060	−	0.0881060i	−0.749786	+	0.661680i	$0.769844\pi$
$840$	8.84437	+	10.8027i	0.305160	+	0.372729i
$841$	−8.76169	+	8.76169i	−0.302127	+	0.302127i
$842$	−1.33561	−	13.6153i	−0.0460282	−	0.469213i
$843$	−60.4332	−	25.0322i	−2.08143	−	0.862156i
$844$	−10.3503	−	2.06723i	−0.356274	−	0.0711569i
$845$	10.8809	+	26.2687i	0.374313	+	0.903671i
$846$	−37.4672	−	11.3816i	−1.28815	−	0.391306i
$847$		−	9.19681i		−	0.316006i
$848$	−0.0753659	+	48.1818i	−0.00258808	+	1.65457i
$849$		−	12.1160i		−	0.415819i
$850$	1.76080	−	5.79643i	0.0603950	−	0.198816i
$851$	−1.19799	−	2.89221i	−0.0410667	−	0.0991437i
$852$	−37.6729	+	25.1296i	−1.29065	+	0.860926i
$853$	−6.03922	−	2.50153i	−0.206779	−	0.0856506i	0.276890	−	0.960902i	$-0.410696\pi$
$853$	−6.03922	−	2.50153i	−0.206779	−	0.0856506i	−0.483669	+	0.875251i	$0.660696\pi$
$854$	14.4377	−	1.41629i	0.494049	−	0.0484646i
$855$	2.46830	−	2.46830i	0.0844140	−	0.0844140i
$856$	−17.7944	+	33.1972i	−0.608200	+	1.13466i
$857$	13.5805	+	13.5805i	0.463902	+	0.463902i	0.899932	−	0.436030i	$-0.143616\pi$
$857$	13.5805	+	13.5805i	0.463902	+	0.463902i	−0.436030	+	0.899932i	$0.643616\pi$
$858$	−17.9299	−	14.7264i	−0.612117	−	0.502752i
$859$	−15.4573	+	37.3171i	−0.527395	+	1.27324i	0.405829	+	0.913949i	$0.366983\pi$
$859$	−15.4573	+	37.3171i	−0.527395	+	1.27324i	−0.933224	+	0.359295i	$0.883017\pi$
$860$	−0.750036	−	3.78616i	−0.0255760	−	0.129107i
$861$	−8.54850	+	3.54090i	−0.291332	+	0.120674i
$862$	−13.3011	−	24.9080i	−0.453036	−	0.848368i
$863$	−10.1175			−0.344402			−0.172201	−	0.985062i	$-0.555088\pi$
$863$	−10.1175			−0.344402			−0.172201	+	0.985062i	$0.555088\pi$
$864$	−4.67877	+	2.48910i	−0.159175	+	0.0846810i
$865$	−2.49467			−0.0848213
$866$	−22.1623	−	41.5018i	−0.753106	−	1.41029i
$867$	−57.1154	+	23.6580i	−1.93974	+	0.803467i
$868$	20.0306	−	3.96804i	0.679881	−	0.134684i
$869$	−0.849960	+	2.05199i	−0.0288329	+	0.0696089i
$870$	−21.9846	−	18.0567i	−0.745348	−	0.612179i
$871$	−38.9134	−	38.9134i	−1.31853	−	1.31853i
$872$	−41.6974	+	12.5954i	−1.41205	+	0.426533i
$873$	−26.9002	+	26.9002i	−0.910433	+	0.910433i
$874$	−1.71144	+	0.167886i	−0.0578903	+	0.00567884i
$875$	10.8886	+	4.51021i	0.368102	+	0.152473i
$876$	−0.527374	−	0.790608i	−0.0178183	−	0.0267122i
$877$	−3.19678	−	7.71771i	−0.107948	−	0.260608i	0.860671	−	0.509162i	$-0.170045\pi$
$877$	−3.19678	−	7.71771i	−0.107948	−	0.260608i	−0.968618	+	0.248554i	$0.920045\pi$
$878$	−3.37100	+	11.0971i	−0.113766	+	0.374508i
$879$		−	13.3213i		−	0.449318i
$880$	10.3405	+	4.30212i	0.348577	+	0.145024i
$881$			26.3216i			0.886796i	0.896325	+	0.443398i	$0.146227\pi$
$881$			26.3216i			0.886796i	−0.896325	+	0.443398i	$0.853773\pi$
$882$	−3.52397	−	1.07049i	−0.118658	−	0.0360452i
$883$	−0.0669901	−	0.161729i	−0.00225440	−	0.00544260i	0.922748	−	0.385403i	$-0.125938\pi$
$883$	−0.0669901	−	0.161729i	−0.00225440	−	0.00544260i	−0.925003	+	0.379960i	$0.875938\pi$
$884$	13.2745	−	66.4637i	0.446470	−	2.23542i
$885$	−12.4102	−	5.14049i	−0.417166	−	0.172796i
$886$	−3.95406	−	40.3079i	−0.132839	−	1.35417i
$887$	0.687235	−	0.687235i	0.0230751	−	0.0230751i	−0.695475	−	0.718550i	$-0.744806\pi$
$887$	0.687235	−	0.687235i	0.0230751	−	0.0230751i	0.718550	+	0.695475i	$0.244806\pi$
$888$	11.0268	+	1.09911i	0.370035	+	0.0368836i
$889$	−2.65187	−	2.65187i	−0.0889407	−	0.0889407i
$890$	17.3217	−	21.0897i	0.580623	−	0.706928i
$891$	5.15452	−	12.4441i	0.172683	−	0.416893i
$892$	29.5258	−	44.1138i	0.988599	−	1.47704i
$893$	−6.31449	+	2.61555i	−0.211306	+	0.0875259i
$894$	−4.85163	+	2.59081i	−0.162263	+	0.0866497i
$895$	−45.6039			−1.52437
$896$	9.96316	+	5.36054i	0.332846	+	0.179083i
$897$	−23.1110			−0.771654
$898$	−36.4355	+	19.4569i	−1.21587	+	0.649285i
$899$	−38.4424	+	15.9233i	−1.28212	+	0.531073i
$900$	1.89000	−	2.82380i	0.0630000	−	0.0941267i
$901$	30.2674	−	73.0719i	1.00835	−	2.43438i
$902$	−4.71104	+	5.73584i	−0.156860	+	0.190983i
$903$	1.54934	+	1.54934i	0.0515587	+	0.0515587i
$904$	−41.3224	−	4.11885i	−1.37436	−	0.136991i
$905$	−6.47587	+	6.47587i	−0.215265	+	0.215265i
$906$	1.16640	+	11.8903i	0.0387509	+	0.395028i
$907$	−5.75091	−	2.38211i	−0.190956	−	0.0790966i	0.285156	−	0.958481i	$-0.407954\pi$
$907$	−5.75091	−	2.38211i	−0.190956	−	0.0790966i	−0.476112	+	0.879384i	$0.657954\pi$
$908$	−0.00605000	+	0.0302916i	−0.000200776	+	0.00100526i
$909$	−8.18891	−	19.7698i	−0.271609	−	0.655722i
$910$	14.5617	+	4.42345i	0.482715	+	0.146636i
$911$			1.32801i			0.0439989i	0.999758	+	0.0219995i	$0.00700321\pi$
$911$			1.32801i			0.0439989i	−0.999758	+	0.0219995i	$0.992997\pi$
$912$	2.33829	−	5.62025i	0.0774285	−	0.186105i
$913$		−	14.3954i		−	0.476417i
$914$	−0.865803	+	2.85016i	−0.0286382	+	0.0942748i
$915$	19.3771	+	46.7804i	0.640587	+	1.54651i
$916$	8.61943	+	12.9218i	0.284794	+	0.426947i
$917$	0.344003	+	0.142491i	0.0113600	+	0.00470545i
$918$	8.65805	−	0.849325i	0.285758	−	0.0280319i
$919$	−11.8063	+	11.8063i	−0.389455	+	0.389455i	−0.874493	−	0.485038i	$-0.838806\pi$
$919$	−11.8063	+	11.8063i	−0.389455	+	0.389455i	0.485038	+	0.874493i	$0.338806\pi$
$920$	10.6791	−	3.22578i	0.352078	−	0.106351i
$921$	35.9132	+	35.9132i	1.18338	+	1.18338i
$922$	11.6259	+	9.54873i	0.382878	+	0.314471i
$923$	−18.8905	+	45.6057i	−0.621788	+	1.50113i
$924$	−6.23665	+	1.23548i	−0.205171	+	0.0406442i
$925$	0.997489	−	0.413173i	0.0327972	−	0.0135851i
$926$	−14.3682	−	26.9064i	−0.472169	−	0.884198i
$927$	−4.28273			−0.140663
$928$	−22.0483	−	6.73537i	−0.723770	−	0.221099i
$929$	29.2700			0.960317			0.480158	−	0.877182i	$-0.340579\pi$
$929$	29.2700			0.960317			0.480158	+	0.877182i	$0.340579\pi$
$930$	33.5730	+	62.8698i	1.10090	+	2.06158i
$931$	−0.593907	+	0.246004i	−0.0194645	+	0.00806247i
$932$	−3.28060	−	16.5604i	−0.107460	−	0.542453i
$933$	−25.3072	+	61.0970i	−0.828520	+	2.00022i
$934$	4.87631	+	4.00508i	0.159558	+	0.131050i
$935$	−13.0000	−	13.0000i	−0.425145	−	0.425145i
$936$	17.9599	−	33.5060i	0.587038	−	1.09518i
$937$	−32.4244	+	32.4244i	−1.05926	+	1.05926i	−0.0611275	+	0.998130i	$0.519470\pi$
$937$	−32.4244	+	32.4244i	−1.05926	+	1.05926i	−0.998130	+	0.0611275i	$0.980530\pi$
$938$	−15.0077	+	1.47220i	−0.490017	+	0.0480690i
$939$	−22.5399	−	9.33634i	−0.735562	−	0.304680i
$940$	36.8849	−	24.6040i	1.20305	−	0.802494i
$941$	23.2216	+	56.0619i	0.757002	+	1.82757i	0.514716	+	0.857361i	$0.327898\pi$
$941$	23.2216	+	56.0619i	0.757002	+	1.82757i	0.242287	+	0.970205i	$0.422102\pi$
$942$	6.21437	−	20.4572i	0.202475	−	0.666533i
$943$			7.39330i			0.240759i
$944$	−10.8853	−	0.0170267i	−0.354286	−	0.000554173i
$945$			1.95344i			0.0635453i
$946$	1.68179	+	0.510883i	0.0546796	+	0.0166102i
$947$	18.5344	+	44.7460i	0.602287	+	1.45405i	0.871221	+	0.490891i	$0.163329\pi$
$947$	18.5344	+	44.7460i	0.602287	+	1.45405i	−0.268934	+	0.963159i	$0.586671\pi$
$948$	−7.67951	−	1.53379i	−0.249419	−	0.0498153i
$949$	−0.957088	−	0.396439i	−0.0310684	−	0.0128689i
$950$	−0.0579020	−	0.590255i	−0.00187859	−	0.0191504i
$951$	−21.4830	+	21.4830i	−0.696636	+	0.696636i
$952$	−11.7650	−	14.3701i	−0.381307	−	0.465737i
$953$	10.8621	+	10.8621i	0.351858	+	0.351858i	0.860801	−	0.508942i	$-0.169963\pi$
$953$	10.8621	+	10.8621i	0.351858	+	0.351858i	−0.508942	+	0.860801i	$0.669963\pi$
$954$	28.1571	−	34.2822i	0.911620	−	1.10993i
$955$	−4.88870	+	11.8024i	−0.158195	+	0.381916i
$956$	−29.4697	−	19.7243i	−0.953117	−	0.637931i
$957$	11.9693	−	4.95784i	0.386912	−	0.160264i
$958$	−1.25617	+	0.670804i	−0.0405849	+	0.0216727i
$959$	19.8459			0.640857
$960$	−7.79475	+	38.7119i	−0.251574	+	1.24942i
$961$	73.2421			2.36265
$962$	10.6553	−	5.69000i	0.343540	−	0.183453i
$963$	32.0405	−	13.2716i	1.03249	−	0.427671i
$964$	−44.1430	−	29.5454i	−1.42175	−	0.951593i
$965$	15.4585	−	37.3201i	0.497626	−	1.20138i
$966$	−4.01941	+	4.89376i	−0.129322	+	0.157454i
$967$	−19.0209	−	19.0209i	−0.611671	−	0.611671i	0.331710	−	0.943381i	$-0.392374\pi$
$967$	−19.0209	−	19.0209i	−0.611671	−	0.611671i	−0.943381	+	0.331710i	$0.892374\pi$
$968$	20.1273	−	16.4786i	0.646915	−	0.529641i
$969$	−7.06575	+	7.06575i	−0.226984	+	0.226984i
$970$	−4.20534	−	42.8694i	−0.135025	−	1.37645i
$971$	41.4509	+	17.1695i	1.33022	+	0.550996i	0.930719	−	0.365736i	$-0.119183\pi$
$971$	41.4509	+	17.1695i	1.33022	+	0.550996i	0.399503	+	0.916732i	$0.369183\pi$
$972$	41.0595	+	8.20063i	1.31698	+	0.263035i
$973$	−8.71308	−	21.0352i	−0.279329	−	0.674359i
$974$	18.0384	+	5.47959i	0.577987	+	0.175577i
$975$		−	7.97072i		−	0.255267i
$976$	28.9687	+	29.0594i	0.927265	+	0.930170i
$977$		−	19.0120i		−	0.608247i	−0.952633	−	0.304123i	$-0.901636\pi$
$977$		−	19.0120i		−	0.608247i	0.952633	−	0.304123i	$-0.0983636\pi$
$978$	−3.18477	+	10.4840i	−0.101838	+	0.335242i
$979$	4.75602	+	11.4820i	0.152003	+	0.366968i
$980$	3.46920	−	2.31412i	0.110819	−	0.0739219i
$981$	37.0531	+	15.3479i	1.18301	+	0.490020i
$982$	−36.5016	+	3.58068i	−1.16481	+	0.114264i
$983$	−19.3375	+	19.3375i	−0.616769	+	0.616769i	−0.944701	−	0.327932i	$-0.893648\pi$
$983$	−19.3375	+	19.3375i	−0.616769	+	0.616769i	0.327932	+	0.944701i	$0.393648\pi$
$984$	−23.0662	−	12.3640i	−0.735324	−	0.394149i
$985$	−21.0089	−	21.0089i	−0.669398	−	0.669398i
$986$	29.2446	+	24.0195i	0.931336	+	0.764938i
$987$	−9.63204	+	23.2538i	−0.306591	+	0.740177i
$988$	−1.28942	−	6.50896i	−0.0410220	−	0.207078i
$989$	1.61748	−	0.669984i	0.0514330	−	0.0213042i
$990$	−4.85751	−	9.09632i	−0.154382	−	0.289100i
$991$	48.9563			1.55515			0.777574	−	0.628792i	$-0.216450\pi$
$991$	48.9563			1.55515			0.777574	+	0.628792i	$0.216450\pi$
$992$	44.5742	+	36.7272i	1.41523	+	1.16609i
$993$	43.6642			1.38564
$994$	6.37162	+	11.9317i	0.202096	+	0.378450i
$995$	6.85168	−	2.83806i	0.217213	−	0.0899726i
$996$	49.7889	−	9.86315i	1.57762	−	0.312526i
$997$	−14.9987	+	36.2102i	−0.475015	+	1.14679i	0.486905	+	0.873455i	$0.338126\pi$
$997$	−14.9987	+	36.2102i	−0.475015	+	1.14679i	−0.961920	+	0.273333i	$0.911874\pi$
$998$	43.7633	+	35.9443i	1.38530	+	1.13780i
$999$	1.09635	+	1.09635i	0.0346871	+	0.0346871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.85.2	yes	52
4.3	odd	2		896.2.u.c.561.3		52
32.3	odd	8		896.2.u.c.337.3		52
32.29	even	8	inner	224.2.u.c.29.2	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.2	✓	52	32.29	even	8	inner
224.2.u.c.85.2	yes	52	1.1	even	1	trivial
896.2.u.c.337.3		52	32.3	odd	8
896.2.u.c.561.3		52	4.3	odd	2

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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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24749 + 0.666168i) q^{2} +(2.18713 - 0.905938i) q^{3} +(1.11244 - 1.66207i) q^{4} +(0.797931 - 1.92638i) q^{5} +(-2.12490 + 2.58714i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.280536 + 2.81448i) q^{8} +(1.84149 - 1.84149i) q^{9} +O(q^{10})\)	\(q+(-1.24749 + 0.666168i) q^{2} +(2.18713 - 0.905938i) q^{3} +(1.11244 - 1.66207i) q^{4} +(0.797931 - 1.92638i) q^{5} +(-2.12490 + 2.58714i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.280536 + 2.81448i) q^{8} +(1.84149 - 1.84149i) q^{9} +(0.287882 + 2.93468i) q^{10} +(-1.24061 - 0.513879i) q^{11} +(0.927318 - 4.64296i) q^{12} +(-1.97504 - 4.76818i) q^{13} +(-1.35316 - 0.411054i) q^{14} -4.93611i q^{15} +(-1.52495 - 3.69791i) q^{16} +6.56615i q^{17} +(-1.07049 + 3.52397i) q^{18} +(0.246004 + 0.593907i) q^{19} +(-2.31412 - 3.46920i) q^{20} +(2.18713 + 0.905938i) q^{21} +(1.88998 - 0.185400i) q^{22} +(1.33754 - 1.33754i) q^{23} +(1.93618 + 6.40978i) q^{24} +(0.461303 + 0.461303i) q^{25} +(5.64025 + 4.63252i) q^{26} +(-0.358520 + 0.865544i) q^{27} +(1.96188 - 0.388646i) q^{28} +(-3.76520 + 1.55960i) q^{29} +(3.28828 + 6.15772i) q^{30} +10.2099 q^{31} +(4.36578 + 3.59721i) q^{32} -3.17892 q^{33} +(-4.37416 - 8.19118i) q^{34} +(1.92638 - 0.797931i) q^{35} +(-1.01213 - 5.10922i) q^{36} +(0.633332 - 1.52900i) q^{37} +(-0.702529 - 0.577010i) q^{38} +(-8.63935 - 8.63935i) q^{39} +(5.19790 + 2.78618i) q^{40} +(-2.76376 + 2.76376i) q^{41} +(-3.33192 + 0.326850i) q^{42} +(0.855100 + 0.354194i) q^{43} +(-2.23421 + 1.49033i) q^{44} +(-2.07802 - 5.01678i) q^{45} +(-0.777538 + 2.55959i) q^{46} +10.6321i q^{47} +(-6.68534 - 6.70629i) q^{48} +1.00000i q^{49} +(-0.882774 - 0.268164i) q^{50} +(5.94853 + 14.3610i) q^{51} +(-10.1222 - 2.02166i) q^{52} +(-11.1286 - 4.60960i) q^{53} +(-0.129349 - 1.31859i) q^{54} +(-1.97985 + 1.97985i) q^{55} +(-2.18851 + 1.79177i) q^{56} +(1.07609 + 1.07609i) q^{57} +(3.65808 - 4.45383i) q^{58} +(1.04141 - 2.51418i) q^{59} +(-8.20416 - 5.49113i) q^{60} +(-9.47718 + 3.92558i) q^{61} +(-12.7367 + 6.80151i) q^{62} +2.60426 q^{63} +(-7.84260 - 1.57913i) q^{64} -10.7613 q^{65} +(3.96566 - 2.11770i) q^{66} +(9.85128 - 4.08053i) q^{67} +(10.9134 + 7.30445i) q^{68} +(1.71365 - 4.13711i) q^{69} +(-1.87157 + 2.27870i) q^{70} +(-6.76319 - 6.76319i) q^{71} +(4.66622 + 5.69943i) q^{72} +(0.141933 - 0.141933i) q^{73} +(0.228497 + 2.32931i) q^{74} +(1.42684 + 0.591017i) q^{75} +(1.26078 + 0.251810i) q^{76} +(-0.513879 - 1.24061i) q^{77} +(16.5327 + 5.02221i) q^{78} -1.65401i q^{79} +(-8.34037 - 0.0130460i) q^{80} +10.0306i q^{81} +(1.60662 - 5.28888i) q^{82} +(4.10243 + 9.90415i) q^{83} +(3.93878 - 2.62736i) q^{84} +(12.6489 + 5.23934i) q^{85} +(-1.30268 + 0.127788i) q^{86} +(-6.82208 + 6.82208i) q^{87} +(1.79434 - 3.34752i) q^{88} +(-6.54438 - 6.54438i) q^{89} +(5.93431 + 4.87405i) q^{90} +(1.97504 - 4.76818i) q^{91} +(-0.735153 - 3.71103i) q^{92} +(22.3304 - 9.24954i) q^{93} +(-7.08277 - 13.2634i) q^{94} +1.34038 q^{95} +(12.8074 + 3.91244i) q^{96} -14.6079 q^{97} +(-0.666168 - 1.24749i) q^{98} +(-3.23087 + 1.33827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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