LMFDB - Embedded newform 224.2.u.c.29.2

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			29.2
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.2

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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	0.910749	−	0.412960i	$-0.135505\pi$
$3$	2.18713	+	0.905938i	1.26274	+	0.523044i	0.351990	+	0.936004i	$0.385505\pi$
$4$	1.11244	+	1.66207i	0.556220	+	0.831035i
$5$	0.797931	+	1.92638i	0.356846	+	0.861502i	0.995740	+	0.0922070i	$0.0293922\pi$
$5$	0.797931	+	1.92638i	0.356846	+	0.861502i	−0.638894	+	0.769295i	$0.720608\pi$
$6$	−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	−0.561789	−	0.827280i	$-0.689887\pi$
$11$	−1.24061	+	0.513879i	−0.374059	+	0.154940i	0.187731	+	0.982221i	$0.439887\pi$
$12$	0.927318	+	4.64296i	0.267694	+	1.34031i
$13$	−1.97504	+	4.76818i	−0.547779	+	1.32245i	0.371348	+	0.928494i	$0.378896\pi$
$13$	−1.97504	+	4.76818i	−0.547779	+	1.32245i	−0.919127	+	0.393961i	$0.871104\pi$
$14$	−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	$-0.706807\pi$
$17$		−	6.56615i		−	1.59253i	0.604951	−	0.796263i	$-0.293193\pi$
$18$	−1.07049	−	3.52397i	−0.252317	−	0.830607i
$19$	0.246004	−	0.593907i	0.0564373	−	0.136252i	−0.893146	−	0.449767i	$-0.851507\pi$
$19$	0.246004	−	0.593907i	0.0564373	−	0.136252i	0.949583	+	0.313516i	$0.101507\pi$
$20$	−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	0.832669	−	0.553772i	$-0.186812\pi$
$23$	1.33754	+	1.33754i	0.278897	+	0.278897i	−0.553772	+	0.832669i	$0.686812\pi$
$24$	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	0.00463850	−	0.999989i	$-0.498524\pi$
$29$	−3.76520	−	1.55960i	−0.699181	−	0.289610i	−0.703819	+	0.710379i	$0.748524\pi$
$30$	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	0.967350	−	0.253443i	$-0.0815630\pi$
$37$	0.633332	+	1.52900i	0.104119	+	0.251366i	−0.863231	+	0.504809i	$0.831563\pi$
$38$	−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	0.457555	−	0.889181i	$-0.348725\pi$
$41$	−2.76376	−	2.76376i	−0.431627	−	0.431627i	−0.889181	+	0.457555i	$0.848725\pi$
$42$	−3.33192	−	0.326850i	−0.514126	−	0.0504340i
$43$	0.855100	−	0.354194i	0.130402	−	0.0540141i	−0.316528	−	0.948583i	$-0.602517\pi$
$43$	0.855100	−	0.354194i	0.130402	−	0.0540141i	0.446930	+	0.894569i	$0.352517\pi$
$44$	−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	$-0.717535\pi$
$47$		−	10.6321i		−	1.55085i	0.631438	−	0.775427i	$-0.282465\pi$
$48$	−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	−0.979297	−	0.202428i	$-0.935117\pi$
$53$	−11.1286	+	4.60960i	−1.52863	+	0.633178i	−0.549329	+	0.835606i	$0.685117\pi$
$54$	−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	0.977058	−	0.212972i	$-0.0683144\pi$
$59$	1.04141	+	2.51418i	0.135579	+	0.327318i	−0.841479	+	0.540290i	$0.818314\pi$
$60$	−8.20416	+	5.49113i	−1.05915	+	0.708902i
$61$	−9.47718	−	3.92558i	−1.21343	−	0.502619i	−0.318114	−	0.948052i	$-0.603050\pi$
$61$	−9.47718	−	3.92558i	−1.21343	−	0.502619i	−0.895315	+	0.445434i	$0.853050\pi$
$62$	−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	0.892137	−	0.451766i	$-0.149206\pi$
$67$	9.85128	+	4.08053i	1.20353	+	0.498517i	0.311389	+	0.950282i	$0.399206\pi$
$68$	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	−0.983508	−	0.180865i	$-0.942110\pi$
$71$	−6.76319	+	6.76319i	−0.802643	+	0.802643i	0.180865	+	0.983508i	$0.442110\pi$
$72$	4.66622	−	5.69943i	0.549920	−	0.671685i
$73$	0.141933	+	0.141933i	0.0166120	+	0.0166120i	0.715364	−	0.698752i	$-0.246261\pi$
$73$	0.141933	+	0.141933i	0.0166120	+	0.0166120i	−0.698752	+	0.715364i	$0.746261\pi$
$74$	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	$0.0296602\pi$
$79$			1.65401i			0.186091i	−0.995662	+	0.0930454i	$0.970340\pi$
$80$	−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	−0.521907	−	0.853002i	$-0.674779\pi$
$83$	4.10243	−	9.90415i	0.450301	−	1.08712i	0.972208	−	0.234120i	$-0.0752207\pi$
$84$	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	−0.963045	−	0.269342i	$-0.913194\pi$
$89$	−6.54438	+	6.54438i	−0.693702	+	0.693702i	0.269342	+	0.963045i	$0.413194\pi$
$90$	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	0.999596	+	0.0284369i	$0.00905297\pi$
$101$	3.14443	+	7.59133i	0.312883	+	0.755366i	−0.686713	+	0.726929i	$0.740947\pi$
$102$	−16.9876	+	13.9524i	−1.68202	+	1.38150i
$103$	−1.16285	+	1.16285i	−0.114579	+	0.114579i	−0.762072	−	0.647493i	$-0.775818\pi$
$103$	−1.16285	+	1.16285i	−0.114579	+	0.114579i	0.647493	+	0.762072i	$0.275818\pi$
$104$	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	0.301832	−	0.953361i	$-0.402402\pi$
$107$	12.3031	−	5.09612i	1.18939	−	0.492660i	0.887556	+	0.460701i	$0.152402\pi$
$108$	1.03976	−	1.55875i	0.100051	−	0.149991i
$109$	5.89338	−	14.2279i	0.564484	−	1.36278i	−0.341664	−	0.939822i	$-0.610990\pi$
$109$	5.89338	−	14.2279i	0.564484	−	1.36278i	0.906147	−	0.422962i	$-0.139010\pi$
$110$	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	$-0.757352\pi$
$113$		−	14.6821i		−	1.38117i	0.723250	−	0.690586i	$-0.242648\pi$
$114$	−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	0.397661	−	0.917533i	$-0.369822\pi$
$131$	0.344003	+	0.142491i	0.0300556	+	0.0124495i	−0.367605	+	0.929982i	$0.619822\pi$
$132$	−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	0.974486	+	0.224447i	$0.0720576\pi$
$137$	14.0332	+	14.0332i	1.19893	+	1.19893i	0.224447	+	0.974486i	$0.427942\pi$
$138$	0.618260	−	6.30256i	0.0526298	−	0.536510i
$139$	−21.0352	+	8.71308i	−1.78419	+	0.739034i	−0.792576	+	0.609774i	$0.791260\pi$
$139$	−21.0352	+	8.71308i	−1.78419	+	0.739034i	−0.991611	+	0.129260i	$0.958740\pi$
$140$	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	−0.319645	−	0.947537i	$-0.603564\pi$
$149$	1.51778	−	0.628685i	0.124341	−	0.0515038i	0.443987	+	0.896033i	$0.353564\pi$
$150$	−2.17368	−	0.213230i	−0.177480	−	0.0174102i
$151$	2.52338	+	2.52338i	0.205350	+	0.205350i	0.802288	−	0.596938i	$-0.203616\pi$
$151$	2.52338	+	2.52338i	0.205350	+	0.205350i	−0.596938	+	0.802288i	$0.703616\pi$
$152$	−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	0.134612	−	0.990898i	$-0.457021\pi$
$157$	−5.90004	−	2.44388i	−0.470875	−	0.195043i	−0.605486	+	0.795856i	$0.707021\pi$
$158$	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	0.497944	−	0.867209i	$-0.334089\pi$
$163$	3.02368	+	1.25245i	0.236833	+	0.0980995i	−0.261110	+	0.965309i	$0.584089\pi$
$164$	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	−0.956357	−	0.292201i	$-0.905612\pi$
$167$	−8.58278	+	8.58278i	−0.664156	+	0.664156i	0.292201	+	0.956357i	$0.405612\pi$
$168$	−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	−0.940328	−	0.340268i	$-0.889482\pi$
$173$	−0.457854	+	1.10536i	−0.0348100	+	0.0840388i	0.905518	+	0.424307i	$0.139482\pi$
$174$	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	0.219462	+	0.975621i	$0.429570\pi$
$179$	−8.36981	+	20.2065i	−0.625589	+	1.51031i	−0.845051	+	0.534685i	$0.820430\pi$
$180$	−10.6499	+	2.12706i	−0.793797	+	0.158541i
$181$	−4.05792	+	1.68084i	−0.301622	+	0.124936i	−0.528362	−	0.849019i	$-0.677193\pi$
$181$	−4.05792	+	1.68084i	−0.301622	+	0.124936i	0.226739	+	0.973956i	$0.427193\pi$
$182$	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	0.990257	+	0.139253i	$0.0444702\pi$
$197$	5.45295	+	13.1646i	0.388506	+	0.937937i	−0.601751	+	0.798684i	$0.705530\pi$
$198$	3.13895	+	3.82178i	0.223076	+	0.271602i
$199$	2.51502	−	2.51502i	0.178285	−	0.178285i	−0.612323	−	0.790608i	$-0.709765\pi$
$199$	2.51502	−	2.51502i	0.178285	−	0.178285i	0.790608	+	0.612323i	$0.209765\pi$
$200$	−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	−0.978025	−	0.208489i	$-0.933145\pi$
$211$	−2.01957	+	4.87567i	−0.139033	+	0.335655i	0.838992	+	0.544144i	$0.183145\pi$
$212$	−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	0.382210	−	0.924076i	$-0.375163\pi$
$227$	−0.0142692	−	0.00591051i	−0.000947082	−	0.000392294i	−0.383157	+	0.923683i	$0.625163\pi$
$228$	2.98561	+	0.591448i	0.197727	+	0.0391696i
$229$	−2.97206	−	7.17519i	−0.196399	−	0.474150i	0.794744	−	0.606945i	$-0.207605\pi$
$229$	−2.97206	−	7.17519i	−0.196399	−	0.474150i	−0.991144	+	0.132794i	$0.957605\pi$
$230$	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	0.875053	−	0.484027i	$-0.160826\pi$
$233$	5.96875	+	5.96875i	0.391026	+	0.391026i	−0.484027	+	0.875053i	$0.660826\pi$
$234$	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	$0.194396\pi$
$239$			17.7307i			1.14690i	−0.819239	+	0.573452i	$0.805604\pi$
$240$	−18.2533	−	7.52733i	−1.17824	−	0.485887i
$241$			26.5591i			1.71082i	0.517951	+	0.855410i	$0.326695\pi$
$241$			26.5591i			1.71082i	−0.517951	+	0.855410i	$0.673305\pi$
$242$	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	0.955294	−	0.295659i	$-0.0955391\pi$
$251$	1.12068	+	2.70556i	0.0707367	+	0.170773i	−0.884557	+	0.466432i	$0.845539\pi$
$252$	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	0.165555	−	0.986201i	$-0.447058\pi$
$263$	18.6783	−	18.6783i	1.15176	−	1.15176i	0.986201	−	0.165555i	$-0.0529415\pi$
$264$	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	−0.993024	−	0.117911i	$-0.962380\pi$
$269$	−3.40283	+	8.21516i	−0.207474	+	0.500887i	0.785550	+	0.618798i	$0.212380\pi$
$270$	−2.64331	+	0.802968i	−0.160867	+	0.0488670i
$271$		−	2.34539i		−	0.142472i	−0.997459	−	0.0712361i	$-0.977306\pi$
$271$		−	2.34539i		−	0.142472i	0.997459	−	0.0712361i	$-0.0226944\pi$
$272$	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	−0.648037	−	0.761609i	$-0.724410\pi$
$277$	−9.44890	+	3.91386i	−0.567729	+	0.235161i	0.0803076	+	0.996770i	$0.474410\pi$
$278$	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	−0.182315	+	0.983240i	$0.558359\pi$
$281$	−19.5383	+	19.5383i	−1.16555	+	1.16555i	−0.983240	+	0.182315i	$0.941641\pi$
$282$	−27.5068	+	22.5922i	−1.63800	+	1.34535i
$283$	1.95857	+	4.72840i	0.116425	+	0.281074i	0.971340	−	0.237693i	$-0.0763912\pi$
$283$	1.95857	+	4.72840i	0.116425	+	0.281074i	−0.854916	+	0.518767i	$0.826391\pi$
$284$	−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	0.974216	−	0.225619i	$-0.0724405\pi$
$293$	2.15342	+	5.19882i	0.125804	+	0.303718i	−0.848411	+	0.529337i	$0.822441\pi$
$294$	−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	−0.496208	−	0.868204i	$-0.665275\pi$
$307$	8.21013	−	19.8210i	0.468577	−	1.13124i	0.964785	−	0.263041i	$-0.0847254\pi$
$308$	−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	−0.991728	−	0.128354i	$-0.959031\pi$
$311$	−19.7529	−	19.7529i	−1.12008	−	1.12008i	−0.128354	−	0.991728i	$-0.540969\pi$
$312$	26.7389	+	21.8916i	1.51379	+	1.23937i
$313$	−7.28724	+	7.28724i	−0.411899	+	0.411899i	−0.882400	−	0.470501i	$-0.844073\pi$
$313$	−7.28724	+	7.28724i	−0.411899	+	0.411899i	0.470501	+	0.882400i	$0.344073\pi$
$314$	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	0.0239934	−	0.999712i	$-0.492362\pi$
$317$	−11.8568	−	4.91125i	−0.665944	−	0.275843i	−0.689937	+	0.723869i	$0.742362\pi$
$318$	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	0.138441	−	0.990371i	$-0.455791\pi$
$331$	17.0405	−	7.05841i	0.936631	−	0.387965i	0.798190	+	0.602406i	$0.205791\pi$
$332$	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	$0.228410\pi$
$337$			24.1423i			1.31511i	−0.753405	+	0.657556i	$0.771590\pi$
$338$	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	0.900800	−	0.434235i	$-0.142981\pi$
$347$	−0.804952	−	1.94333i	−0.0432121	−	0.104323i	−0.944012	+	0.329911i	$0.892981\pi$
$348$	3.74962	−	18.9279i	0.201000	−	1.01464i
$349$	−19.6991	−	8.15963i	−1.05447	−	0.436775i	−0.212983	−	0.977056i	$-0.568318\pi$
$349$	−19.6991	−	8.15963i	−1.05447	−	0.436775i	−0.841485	+	0.540281i	$0.818318\pi$
$350$	−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	−0.108349	+	0.994113i	$0.534556\pi$
$359$	−20.8887	+	20.8887i	−1.10246	+	1.10246i	−0.994113	+	0.108349i	$0.965444\pi$
$360$	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	$-0.895536\pi$
$367$		−	12.3497i		−	0.644650i	0.946629	−	0.322325i	$-0.104464\pi$
$368$	−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	−0.252512	−	0.967594i	$-0.581257\pi$
$373$	4.88869	−	2.02496i	0.253127	−	0.104848i	0.505639	+	0.862745i	$0.331257\pi$
$374$	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	−0.988174	−	0.153336i	$-0.950998\pi$
$379$	−7.74540	−	18.6990i	−0.397854	−	0.960505i	0.590320	−	0.807169i	$-0.299002\pi$
$380$	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	0.947078	−	0.321002i	$-0.104020\pi$
$389$	0.994237	+	2.40030i	0.0504098	+	0.121700i	−0.896669	+	0.442703i	$0.854020\pi$
$390$	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	0.0172845	−	0.999851i	$-0.494498\pi$
$397$	14.1878	−	34.2523i	0.712064	−	1.71907i	0.694779	−	0.719223i	$-0.255502\pi$
$398$	−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	$0.0937127\pi$
$401$			11.6214i			0.580345i	−0.956974	+	0.290173i	$0.906287\pi$
$402$	−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	−0.194102	−	0.980981i	$-0.562179\pi$
$409$	15.9136	−	15.9136i	0.786879	−	0.786879i	0.980981	+	0.194102i	$0.0621794\pi$
$410$	−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	0.753112	−	0.657892i	$-0.228552\pi$
$419$	16.7940	+	6.95632i	0.820442	+	0.339838i	0.0673304	+	0.997731i	$0.478552\pi$
$420$	−1.91840	+	9.68403i	−0.0936084	+	0.472532i
$421$	−3.70195	−	8.93730i	−0.180422	−	0.435577i	0.807632	−	0.589687i	$-0.200749\pi$
$421$	−3.70195	−	8.93730i	−0.180422	−	0.435577i	−0.988054	+	0.154110i	$0.950749\pi$
$422$	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	$-0.840318\pi$
$431$		−	19.9665i		−	0.961754i	0.876788	−	0.480877i	$-0.159682\pi$
$432$	3.74743	−	0.00586171i	0.180298	−	0.000282022i
$433$		−	33.2683i		−	1.59877i	−0.600816	−	0.799387i	$-0.705158\pi$
$433$		−	33.2683i		−	1.59877i	0.600816	−	0.799387i	$-0.294842\pi$
$434$	−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	0.831817	−	0.555051i	$-0.187301\pi$
$439$	5.79889	+	5.79889i	0.276766	+	0.276766i	−0.555051	+	0.831817i	$0.687301\pi$
$440$	−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	−0.937466	−	0.348078i	$-0.886835\pi$
$443$	−10.9596	−	26.4588i	−0.520706	−	1.25709i	0.416760	−	0.909016i	$-0.363165\pi$
$444$	−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	0.741083	−	0.671413i	$-0.234312\pi$
$457$	1.48938	+	1.48938i	0.0696702	+	0.0696702i	−0.671413	+	0.741083i	$0.734312\pi$
$458$	−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	−0.989884	−	0.141879i	$-0.954686\pi$
$461$	−4.07104	+	9.82835i	−0.189607	+	0.457752i	0.800277	+	0.599630i	$0.204686\pi$
$462$	4.30158	−	1.30671i	0.200128	−	0.0607935i
$463$		−	21.5685i		−	1.00237i	−0.865340	−	0.501186i	$-0.832897\pi$
$463$		−	21.5685i		−	1.00237i	0.865340	−	0.501186i	$-0.167103\pi$
$464$	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	−0.958451	−	0.285259i	$-0.907921\pi$
$467$	−1.70754	+	4.12236i	−0.0790154	+	0.190760i	0.879435	+	0.476019i	$0.157921\pi$
$468$	−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	−0.887653	−	0.460513i	$-0.847665\pi$
$487$	−9.42615	+	9.42615i	−0.427139	+	0.427139i	0.460513	+	0.887653i	$0.347665\pi$
$488$	−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	0.230343	−	0.973109i	$-0.426015\pi$
$491$	23.9603	−	9.92468i	1.08131	−	0.447895i	0.850970	+	0.525215i	$0.176015\pi$
$492$	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	0.0666215	+	0.997778i	$0.478778\pi$
$499$	−15.3246	+	36.9968i	−0.686023	+	1.65621i	−0.752644	+	0.658427i	$0.771222\pi$
$500$	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	0.484561	−	0.874757i	$-0.338979\pi$
$503$	−8.75118	−	8.75118i	−0.390196	−	0.390196i	−0.874757	+	0.484561i	$0.838979\pi$
$504$	−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	0.521822	−	0.853054i	$-0.325252\pi$
$509$	6.48869	+	2.68770i	0.287606	+	0.119130i	−0.234216	+	0.972185i	$0.575252\pi$
$510$	−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	0.251646	−	0.967819i	$-0.419028\pi$
$521$	−16.3470	−	16.3470i	−0.716173	−	0.716173i	−0.967819	+	0.251646i	$0.919028\pi$
$522$	−1.46537	+	14.9380i	−0.0641373	+	0.653818i
$523$	−10.2334	+	4.23880i	−0.447474	+	0.185350i	−0.595029	−	0.803704i	$-0.702860\pi$
$523$	−10.2334	+	4.23880i	−0.447474	+	0.185350i	0.147555	+	0.989054i	$0.452860\pi$
$524$	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	0.248297	−	0.968684i	$-0.420129\pi$
$541$	−6.07288	−	2.51547i	−0.261093	−	0.108148i	−0.509390	+	0.860536i	$0.670129\pi$
$542$	−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	0.907981	−	0.419011i	$-0.137623\pi$
$547$	29.3224	+	12.1457i	1.25374	+	0.519314i	0.345755	+	0.938325i	$0.387623\pi$
$548$	−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	0.572404	+	0.819972i	$0.306011\pi$
$557$	−9.72719	+	23.4835i	−0.412154	+	0.995028i	−0.984558	+	0.175057i	$0.943989\pi$
$558$	−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	−0.971373	−	0.237560i	$-0.923652\pi$
$563$	−2.76493	+	6.67513i	−0.116528	+	0.281323i	0.854845	+	0.518884i	$0.173652\pi$
$564$	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	−0.867955	−	0.496642i	$-0.834566\pi$
$569$	−8.85720	+	8.85720i	−0.371313	+	0.371313i	0.496642	+	0.867955i	$0.334566\pi$
$570$	−2.84819	−	3.46776i	−0.119297	−	0.145248i
$571$	−15.5860	−	37.6279i	−0.652253	−	1.57468i	−0.809501	−	0.587118i	$-0.800262\pi$
$571$	−15.5860	−	37.6279i	−0.652253	−	1.57468i	0.157249	−	0.987559i	$-0.449738\pi$
$572$	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	−0.677610	−	0.735421i	$-0.736984\pi$
$587$	−15.4268	+	6.38998i	−0.636731	+	0.263743i	0.0408789	+	0.999164i	$0.486984\pi$
$588$	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	$-0.945255\pi$
$593$		−	8.33506i		−	0.342280i	0.985247	−	0.171140i	$-0.0547450\pi$
$594$	−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	0.596271	−	0.802783i	$-0.296648\pi$
$599$	−5.05427	−	5.05427i	−0.206512	−	0.206512i	−0.802783	+	0.596271i	$0.796648\pi$
$600$	−2.06369	−	3.85001i	−0.0842496	−	0.157176i
$601$	−3.80362	+	3.80362i	−0.155153	+	0.155153i	−0.780415	−	0.625262i	$-0.784992\pi$
$601$	−3.80362	+	3.80362i	−0.155153	+	0.155153i	0.625262	+	0.780415i	$0.284992\pi$
$602$	−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	0.725609	−	0.688107i	$-0.241558\pi$
$613$	−6.78488	−	16.3802i	−0.274039	−	0.661588i	−0.999648	+	0.0265184i	$0.991558\pi$
$614$	−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	0.998161	−	0.0606166i	$-0.0193067\pi$
$617$	23.2881	+	23.2881i	0.937545	+	0.937545i	−0.0606166	+	0.998161i	$0.519307\pi$
$618$	5.47938	+	0.537509i	0.220413	+	0.0216218i
$619$	29.5955	−	12.2588i	1.18954	−	0.492724i	0.301936	−	0.953328i	$-0.402367\pi$
$619$	29.5955	−	12.2588i	1.18954	−	0.492724i	0.887606	+	0.460604i	$0.152367\pi$
$620$	−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	0.884652	−	0.466253i	$-0.154396\pi$
$631$	10.5101	+	10.5101i	0.418399	+	0.418399i	−0.466253	+	0.884652i	$0.654396\pi$
$632$	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	−0.274664	−	0.961540i	$-0.588567\pi$
$643$	−29.1304	−	12.0662i	−1.14879	−	0.475845i	−0.874128	+	0.485695i	$0.838567\pi$
$644$	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	−0.920114	−	0.391651i	$-0.871904\pi$
$647$	−13.4421	+	13.4421i	−0.528463	+	0.528463i	0.391651	+	0.920114i	$0.371904\pi$
$648$	−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	0.513310	+	0.858203i	$0.328419\pi$
$653$	−11.6652	+	28.1624i	−0.456496	+	1.10208i	−0.969806	+	0.243876i	$0.921581\pi$
$654$	−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	−0.743495	−	0.668742i	$-0.766833\pi$
$659$	6.54885	−	15.8103i	0.255107	−	0.615883i	0.998602	+	0.0528586i	$0.0168333\pi$
$660$	7.35641	−	11.0283i	0.286348	−	0.429276i
$661$	37.6737	−	15.6050i	1.46534	−	0.606963i	0.499547	−	0.866287i	$-0.333500\pi$
$661$	37.6737	−	15.6050i	1.46534	−	0.606963i	0.965790	+	0.259324i	$0.0834997\pi$
$662$	−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	0.999819	+	0.0190084i	$0.00605092\pi$
$677$	7.96920	+	19.2394i	0.306281	+	0.739428i	−0.693538	+	0.720420i	$0.743949\pi$
$678$	−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	−0.519794	−	0.854292i	$-0.673991\pi$
$683$	−7.40302	+	3.06643i	−0.283269	+	0.117334i	0.236525	+	0.971625i	$0.423991\pi$
$684$	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	−0.993556	−	0.113342i	$-0.963845\pi$
$691$	−5.54288	+	13.3817i	−0.210861	+	0.509064i	0.782695	+	0.622406i	$0.213845\pi$
$692$	−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	0.618306	−	0.785938i	$-0.287819\pi$
$701$	13.2322	+	5.48095i	0.499772	+	0.207012i	−0.118534	+	0.992950i	$0.537819\pi$
$702$	−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	0.997242	+	0.0742201i	$0.0236467\pi$
$709$	9.17480	+	22.1499i	0.344567	+	0.831858i	−0.652675	+	0.757638i	$0.726353\pi$
$710$	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	$0.00805543\pi$
$719$			1.35702i			0.0506084i	−0.999680	+	0.0253042i	$0.991945\pi$
$720$	−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	0.957761	+	0.287566i	$0.0928460\pi$
$727$	33.5777	+	33.5777i	1.24533	+	1.24533i	0.287566	+	0.957761i	$0.407154\pi$
$728$	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	−0.351749	−	0.936095i	$-0.614413\pi$
$733$	−34.1779	−	14.1570i	−1.26239	−	0.522900i	−0.910643	+	0.413195i	$0.864413\pi$
$734$	−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	0.362723	−	0.931897i	$-0.381847\pi$
$739$	−1.08042	−	0.447523i	−0.0397438	−	0.0164624i	−0.402467	+	0.915435i	$0.631847\pi$
$740$	−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	−0.128243	−	0.991743i	$-0.540934\pi$
$743$	23.5373	−	23.5373i	0.863500	−	0.863500i	0.991743	+	0.128243i	$0.0409338\pi$
$744$	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	$0.0439899\pi$
$751$			7.55039i			0.275517i	−0.990466	+	0.137759i	$0.956010\pi$
$752$	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	0.0612272	−	0.998124i	$-0.480499\pi$
$757$	22.2943	−	9.23462i	0.810302	−	0.335638i	0.749074	+	0.662486i	$0.230499\pi$
$758$	−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	−0.289788	−	0.957091i	$-0.593585\pi$
$761$	18.4084	−	18.4084i	0.667303	−	0.667303i	0.957091	+	0.289788i	$0.0935847\pi$
$762$	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	0.984567	+	0.175008i	$0.0559950\pi$
$773$	11.4582	+	27.6625i	0.412122	+	0.994951i	−0.572445	+	0.819943i	$0.694005\pi$
$774$	−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	−0.941238	−	0.337744i	$-0.890336\pi$
$787$	−1.03408	+	2.49649i	−0.0368609	+	0.0889901i	0.904377	+	0.426734i	$0.140336\pi$
$788$	−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	−0.569819	−	0.821770i	$-0.692987\pi$
$797$	−43.8662	−	18.1700i	−1.55382	−	0.643614i	−0.984002	+	0.178156i	$0.942987\pi$
$798$	−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	0.568094	−	0.822964i	$-0.307681\pi$
$809$	−7.24925	−	7.24925i	−0.254870	−	0.254870i	−0.822964	+	0.568094i	$0.807681\pi$
$810$	−29.4367	−	2.88764i	−1.03430	−	0.101461i
$811$	29.0585	−	12.0364i	1.02038	−	0.422656i	0.191150	−	0.981561i	$-0.438778\pi$
$811$	29.0585	−	12.0364i	1.02038	−	0.422656i	0.829232	+	0.558905i	$0.188778\pi$
$812$	−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	−0.994653	−	0.103271i	$-0.967069\pi$
$821$	−46.5600	+	19.2858i	−1.62496	+	0.673079i	−0.630303	+	0.776350i	$0.717069\pi$
$822$	6.48662	−	66.1249i	0.226247	−	2.30637i
$823$	22.0571	+	22.0571i	0.768863	+	0.768863i	0.977906	−	0.209043i	$-0.0670349\pi$
$823$	22.0571	+	22.0571i	0.768863	+	0.768863i	−0.209043	+	0.977906i	$0.567035\pi$
$824$	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	0.997483	−	0.0709000i	$-0.0225871\pi$
$827$	6.95998	+	16.8029i	0.242022	+	0.584293i	−0.755461	+	0.655193i	$0.772587\pi$
$828$	−8.18758	+	5.48004i	−0.284538	+	0.190444i
$829$	27.1969	+	11.2653i	0.944587	+	0.391261i	0.801194	−	0.598405i	$-0.204199\pi$
$829$	27.1969	+	11.2653i	0.944587	+	0.391261i	0.143393	+	0.989666i	$0.454199\pi$
$830$	−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	−0.749786	−	0.661680i	$-0.769844\pi$
$839$	−2.55203	+	2.55203i	−0.0881060	+	0.0881060i	0.661680	+	0.749786i	$0.269844\pi$
$840$	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	−0.483669	−	0.875251i	$-0.660696\pi$
$853$	−6.03922	+	2.50153i	−0.206779	+	0.0856506i	0.276890	+	0.960902i	$0.410696\pi$
$854$	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	−0.436030	−	0.899932i	$-0.643616\pi$
$857$	13.5805	−	13.5805i	0.463902	−	0.463902i	0.899932	+	0.436030i	$0.143616\pi$
$858$	−17.9299	+	14.7264i	−0.612117	+	0.502752i
$859$	−15.4573	−	37.3171i	−0.527395	−	1.27324i	−0.933224	−	0.359295i	$-0.883017\pi$
$859$	−15.4573	−	37.3171i	−0.527395	−	1.27324i	0.405829	−	0.913949i	$-0.366983\pi$
$860$	−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	−0.968618	−	0.248554i	$-0.920045\pi$
$877$	−3.19678	+	7.71771i	−0.107948	+	0.260608i	0.860671	+	0.509162i	$0.170045\pi$
$878$	−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	$-0.853773\pi$
$881$		−	26.3216i		−	0.886796i	0.896325	−	0.443398i	$-0.146227\pi$
$882$	−3.52397	+	1.07049i	−0.118658	+	0.0360452i
$883$	−0.0669901	+	0.161729i	−0.00225440	+	0.00544260i	−0.925003	−	0.379960i	$-0.875938\pi$
$883$	−0.0669901	+	0.161729i	−0.00225440	+	0.00544260i	0.922748	+	0.385403i	$0.125938\pi$
$884$	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	0.718550	−	0.695475i	$-0.244806\pi$
$887$	0.687235	+	0.687235i	0.0230751	+	0.0230751i	−0.695475	+	0.718550i	$0.744806\pi$
$888$	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	−0.476112	−	0.879384i	$-0.657954\pi$
$907$	−5.75091	+	2.38211i	−0.190956	+	0.0790966i	0.285156	+	0.958481i	$0.407954\pi$
$908$	−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	$-0.992997\pi$
$911$		−	1.32801i		−	0.0439989i	0.999758	−	0.0219995i	$-0.00700321\pi$
$912$	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	0.485038	−	0.874493i	$-0.338806\pi$
$919$	−11.8063	−	11.8063i	−0.389455	−	0.389455i	−0.874493	+	0.485038i	$0.838806\pi$
$920$	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	−0.998130	−	0.0611275i	$-0.980530\pi$
$937$	−32.4244	−	32.4244i	−1.05926	−	1.05926i	−0.0611275	−	0.998130i	$-0.519470\pi$
$938$	−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	0.242287	−	0.970205i	$-0.422102\pi$
$941$	23.2216	−	56.0619i	0.757002	−	1.82757i	0.514716	−	0.857361i	$-0.327898\pi$
$942$	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	−0.268934	−	0.963159i	$-0.586671\pi$
$947$	18.5344	−	44.7460i	0.602287	−	1.45405i	0.871221	−	0.490891i	$-0.163329\pi$
$948$	−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	−0.508942	−	0.860801i	$-0.669963\pi$
$953$	10.8621	−	10.8621i	0.351858	−	0.351858i	0.860801	+	0.508942i	$0.169963\pi$
$954$	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	−0.943381	−	0.331710i	$-0.892374\pi$
$967$	−19.0209	+	19.0209i	−0.611671	+	0.611671i	0.331710	+	0.943381i	$0.392374\pi$
$968$	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	0.399503	−	0.916732i	$-0.369183\pi$
$971$	41.4509	−	17.1695i	1.33022	−	0.550996i	0.930719	+	0.365736i	$0.119183\pi$
$972$	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	$0.0983636\pi$
$977$			19.0120i			0.608247i	−0.952633	+	0.304123i	$0.901636\pi$
$978$	−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	0.327932	−	0.944701i	$-0.393648\pi$
$983$	−19.3375	−	19.3375i	−0.616769	−	0.616769i	−0.944701	+	0.327932i	$0.893648\pi$
$984$	−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	−0.961920	−	0.273333i	$-0.911874\pi$
$997$	−14.9987	−	36.2102i	−0.475015	−	1.14679i	0.486905	−	0.873455i	$-0.338126\pi$
$998$	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.29.2	✓	52
4.3	odd	2		896.2.u.c.337.3		52
32.11	odd	8		896.2.u.c.561.3		52
32.21	even	8	inner	224.2.u.c.85.2	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.2	✓	52	1.1	even	1	trivial
224.2.u.c.85.2	yes	52	32.21	even	8	inner
896.2.u.c.337.3		52	4.3	odd	2
896.2.u.c.561.3		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
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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