LMFDB - Embedded newform 252.2.ba.a.155.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.9
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16483 - 0.801973i) q^{2} +(1.63407 + 0.574282i) q^{3} +(0.713677 + 1.86833i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(-1.44287 - 1.97943i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +O(q^{10})$	\(q+(-1.16483 - 0.801973i) q^{2} +(1.63407 + 0.574282i) q^{3} +(0.713677 + 1.86833i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(-1.44287 - 1.97943i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +(5.41092 + 0.430306i) q^{10} +(-2.92354 + 5.06371i) q^{11} +(0.0932525 + 3.46285i) q^{12} +(-0.515084 - 0.892151i) q^{13} +(0.607789 + 1.27695i) q^{14} +(-6.53369 + 1.22704i) q^{15} +(-2.98133 + 2.66677i) q^{16} +0.189865i q^{17} +(-1.22100 - 4.06315i) q^{18} +4.14257i q^{19} +(-5.95773 - 4.84065i) q^{20} +(-1.12801 - 1.31438i) q^{21} +(7.46640 - 3.55379i) q^{22} +(-0.717351 - 1.24249i) q^{23} +(2.66849 - 4.10843i) q^{24} +(4.86580 - 8.42781i) q^{25} +(-0.115494 + 1.45229i) q^{26} +(2.74655 + 4.41095i) q^{27} +(0.316103 - 1.97486i) q^{28} +(3.21880 + 1.85838i) q^{29} +(8.59473 + 3.81055i) q^{30} +(-6.05438 + 3.49550i) q^{31} +(5.61143 - 0.715402i) q^{32} +(-7.68528 + 6.59555i) q^{33} +(0.152266 - 0.221161i) q^{34} +3.83818 q^{35} +(-1.83627 + 5.71210i) q^{36} +4.78395 q^{37} +(3.32223 - 4.82541i) q^{38} +(-0.329339 - 1.75365i) q^{39} +(3.05770 + 10.4165i) q^{40} +(8.15688 - 4.70938i) q^{41} +(0.259846 + 2.43567i) q^{42} +(5.25147 + 3.03194i) q^{43} +(-11.5472 - 1.84828i) q^{44} +(-11.3812 - 1.74710i) q^{45} +(-0.160848 + 2.02259i) q^{46} +(1.78283 - 3.08795i) q^{47} +(-6.40319 + 2.64558i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-12.4267 + 5.91476i) q^{50} +(-0.109036 + 0.310253i) q^{51} +(1.29923 - 1.59906i) q^{52} -4.68954i q^{53} +(0.338183 - 7.34068i) q^{54} -22.4421i q^{55} +(-1.95199 + 2.04688i) q^{56} +(-2.37901 + 6.76927i) q^{57} +(-2.25900 - 4.74610i) q^{58} +(-4.24070 - 7.34512i) q^{59} +(-6.95548 - 11.3314i) q^{60} +(-0.477327 + 0.826755i) q^{61} +(9.85564 + 0.783775i) q^{62} +(-1.08843 - 2.79559i) q^{63} +(-7.11012 - 3.66690i) q^{64} +(3.42423 + 1.97698i) q^{65} +(14.2415 - 1.51934i) q^{66} +(-0.704892 + 0.406970i) q^{67} +(-0.354730 + 0.135502i) q^{68} +(-0.458666 - 2.44228i) q^{69} +(-4.47084 - 3.07812i) q^{70} +5.09132 q^{71} +(6.71990 - 5.18101i) q^{72} -8.12043 q^{73} +(-5.57251 - 3.83660i) q^{74} +(12.7910 - 10.9773i) q^{75} +(-7.73970 + 2.95646i) q^{76} +(5.06371 - 2.92354i) q^{77} +(-1.02275 + 2.30683i) q^{78} +(6.10558 + 3.52506i) q^{79} +(4.79204 - 14.5857i) q^{80} +(1.95494 + 8.78511i) q^{81} +(-13.2782 - 1.05596i) q^{82} +(-7.57956 + 13.1282i) q^{83} +(1.65066 - 3.04554i) q^{84} +(-0.364367 - 0.631102i) q^{85} +(-3.68556 - 7.74325i) q^{86} +(4.19253 + 4.88523i) q^{87} +(11.9683 + 11.4135i) q^{88} +2.51704i q^{89} +(11.8561 + 11.1625i) q^{90} +1.03017i q^{91} +(1.80942 - 2.22699i) q^{92} +(-11.9007 + 2.23498i) q^{93} +(-4.55315 + 2.16717i) q^{94} +(-7.94997 - 13.7697i) q^{95} +(9.58035 + 2.05353i) q^{96} +(1.26529 - 2.19154i) q^{97} +(0.112112 - 1.40976i) q^{98} +(-16.3460 + 6.36410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.16483	−	0.801973i	−0.823662	−	0.567081i
$2$	−1.16483	−	0.801973i	−0.823662	−	0.567081i
$3$	1.63407	+	0.574282i	0.943433	+	0.331562i
$3$	1.63407	+	0.574282i	0.943433	+	0.331562i
$4$	0.713677	+	1.86833i	0.356839	+	0.934166i
$5$	−3.32396	+	1.91909i	−1.48652	+	0.858242i	−0.999882	−	0.0153615i	$-0.995110\pi$
$5$	−3.32396	+	1.91909i	−1.48652	+	0.858242i	−0.486638	+	0.873604i	$0.661777\pi$
$6$	−1.44287	−	1.97943i	−0.589048	−	0.808098i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	0.667037	−	2.74865i	0.235833	−	0.971794i
$9$	2.34040	+	1.87684i	0.780133	+	0.625613i
$10$	5.41092	+	0.430306i	1.71108	+	0.136075i
$11$	−2.92354	+	5.06371i	−0.881479	+	1.52677i	−0.0317829	+	0.999495i	$0.510119\pi$
$11$	−2.92354	+	5.06371i	−0.881479	+	1.52677i	−0.849696	+	0.527272i	$0.823215\pi$
$12$	0.0932525	+	3.46285i	0.0269197	+	0.999638i
$13$	−0.515084	−	0.892151i	−0.142859	−	0.247438i	0.785713	−	0.618591i	$-0.212296\pi$
$13$	−0.515084	−	0.892151i	−0.142859	−	0.247438i	−0.928572	+	0.371152i	$0.878963\pi$
$14$	0.607789	+	1.27695i	0.162439	+	0.341278i
$15$	−6.53369	+	1.22704i	−1.68699	+	0.316821i
$16$	−2.98133	+	2.66677i	−0.745332	+	0.666693i
$17$			0.189865i			0.0460489i	0.999735	+	0.0230245i	$0.00732956\pi$
$17$			0.189865i			0.0460489i	−0.999735	+	0.0230245i	$0.992670\pi$
$18$	−1.22100	−	4.06315i	−0.287793	−	0.957693i
$19$			4.14257i			0.950372i	0.879885	+	0.475186i	$0.157619\pi$
$19$			4.14257i			0.950372i	−0.879885	+	0.475186i	$0.842381\pi$
$20$	−5.95773	−	4.84065i	−1.33219	−	1.08240i
$21$	−1.12801	−	1.31438i	−0.246152	−	0.286821i
$22$	7.46640	−	3.55379i	1.59184	−	0.757670i
$23$	−0.717351	−	1.24249i	−0.149578	−	0.259077i	0.781493	−	0.623913i	$-0.214458\pi$
$23$	−0.717351	−	1.24249i	−0.149578	−	0.259077i	−0.931072	+	0.364837i	$0.881125\pi$
$24$	2.66849	−	4.10843i	0.544703	−	0.838629i
$25$	4.86580	−	8.42781i	0.973160	−	1.68556i
$26$	−0.115494	+	1.45229i	−0.0226503	+	0.284818i
$27$	2.74655	+	4.41095i	0.528574	+	0.848887i
$28$	0.316103	−	1.97486i	0.0597379	−	0.373214i
$29$	3.21880	+	1.85838i	0.597717	+	0.345092i	0.768143	−	0.640278i	$-0.221181\pi$
$29$	3.21880	+	1.85838i	0.597717	+	0.345092i	−0.170426	+	0.985370i	$0.554514\pi$
$30$	8.59473	+	3.81055i	1.56918	+	0.695708i
$31$	−6.05438	+	3.49550i	−1.08740	+	0.627810i	−0.932883	−	0.360181i	$-0.882715\pi$
$31$	−6.05438	+	3.49550i	−1.08740	+	0.627810i	−0.154515	+	0.987990i	$0.549382\pi$
$32$	5.61143	−	0.715402i	0.991971	−	0.126466i
$33$	−7.68528	+	6.59555i	−1.33783	+	1.14814i
$34$	0.152266	−	0.221161i	0.0261134	−	0.0379287i
$35$	3.83818			0.648770
$36$	−1.83627	+	5.71210i	−0.306045	+	0.952017i
$37$	4.78395			0.786476			0.393238	−	0.919437i	$-0.371355\pi$
$37$	4.78395			0.786476			0.393238	+	0.919437i	$0.371355\pi$
$38$	3.32223	−	4.82541i	0.538937	−	0.782785i
$39$	−0.329339	−	1.75365i	−0.0527364	−	0.280808i
$40$	3.05770	+	10.4165i	0.483464	+	1.64699i
$41$	8.15688	−	4.70938i	1.27389	−	0.735481i	0.298172	−	0.954512i	$-0.403623\pi$
$41$	8.15688	−	4.70938i	1.27389	−	0.735481i	0.975718	+	0.219031i	$0.0702896\pi$
$42$	0.259846	+	2.43567i	0.0400950	+	0.375832i
$43$	5.25147	+	3.03194i	0.800842	+	0.462366i	0.843765	−	0.536712i	$-0.180334\pi$
$43$	5.25147	+	3.03194i	0.800842	+	0.462366i	−0.0429236	+	0.999078i	$0.513667\pi$
$44$	−11.5472	−	1.84828i	−1.74080	−	0.278638i
$45$	−11.3812	−	1.74710i	−1.69661	−	0.260443i
$46$	−0.160848	+	2.02259i	−0.0237157	+	0.298215i
$47$	1.78283	−	3.08795i	0.260052	−	0.450423i	−0.706204	−	0.708009i	$-0.749594\pi$
$47$	1.78283	−	3.08795i	0.260052	−	0.450423i	0.966255	+	0.257586i	$0.0829270\pi$
$48$	−6.40319	+	2.64558i	−0.924221	+	0.381857i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−12.4267	+	5.91476i	−1.75741	+	0.836474i
$51$	−0.109036	+	0.310253i	−0.0152681	+	0.0434441i
$52$	1.29923	−	1.59906i	0.180171	−	0.221749i
$53$		−	4.68954i		−	0.644158i	−0.946713	−	0.322079i	$-0.895618\pi$
$53$		−	4.68954i		−	0.644158i	0.946713	−	0.322079i	$-0.104382\pi$
$54$	0.338183	−	7.34068i	0.0460209	−	0.998940i
$55$		−	22.4421i		−	3.02609i
$56$	−1.95199	+	2.04688i	−0.260846	+	0.273526i
$57$	−2.37901	+	6.76927i	−0.315107	+	0.896612i
$58$	−2.25900	−	4.74610i	−0.296622	−	0.623193i
$59$	−4.24070	−	7.34512i	−0.552093	−	0.956253i	−0.998123	−	0.0612350i	$-0.980496\pi$
$59$	−4.24070	−	7.34512i	−0.552093	−	0.956253i	0.446031	−	0.895018i	$-0.352837\pi$
$60$	−6.95548	−	11.3314i	−0.897948	−	1.46288i
$61$	−0.477327	+	0.826755i	−0.0611155	+	0.105855i	−0.894964	−	0.446138i	$-0.852799\pi$
$61$	−0.477327	+	0.826755i	−0.0611155	+	0.105855i	0.833849	+	0.551993i	$0.186132\pi$
$62$	9.85564	+	0.783775i	1.25167	+	0.0995396i
$63$	−1.08843	−	2.79559i	−0.137129	−	0.352211i
$64$	−7.11012	−	3.66690i	−0.888766	−	0.458362i
$65$	3.42423	+	1.97698i	0.424724	+	0.245214i
$66$	14.2415	−	1.51934i	1.75301	−	0.187017i
$67$	−0.704892	+	0.406970i	−0.0861163	+	0.0497192i	−0.542440	−	0.840095i	$-0.682499\pi$
$67$	−0.704892	+	0.406970i	−0.0861163	+	0.0497192i	0.456323	+	0.889814i	$0.349166\pi$
$68$	−0.354730	+	0.135502i	−0.0430173	+	0.0164320i
$69$	−0.458666	−	2.44228i	−0.0552169	−	0.294016i
$70$	−4.47084	−	3.07812i	−0.534368	−	0.367905i
$71$	5.09132			0.604229			0.302114	−	0.953272i	$-0.402308\pi$
$71$	5.09132			0.604229			0.302114	+	0.953272i	$0.402308\pi$
$72$	6.71990	−	5.18101i	0.791948	−	0.610588i
$73$	−8.12043			−0.950424			−0.475212	−	0.879871i	$-0.657629\pi$
$73$	−8.12043			−0.950424			−0.475212	+	0.879871i	$0.657629\pi$
$74$	−5.57251	−	3.83660i	−0.647791	−	0.445996i
$75$	12.7910	−	10.9773i	1.47698	−	1.26755i
$76$	−7.73970	+	2.95646i	−0.887805	+	0.339129i
$77$	5.06371	−	2.92354i	0.577064	−	0.333168i
$78$	−1.02275	+	2.30683i	−0.115804	+	0.261197i
$79$	6.10558	+	3.52506i	0.686931	+	0.396600i	0.802461	−	0.596704i	$-0.203523\pi$
$79$	6.10558	+	3.52506i	0.686931	+	0.396600i	−0.115530	+	0.993304i	$0.536857\pi$
$80$	4.79204	−	14.5857i	0.535766	−	1.63073i
$81$	1.95494	+	8.78511i	0.217216	+	0.976124i
$82$	−13.2782	−	1.05596i	−1.46633	−	0.116611i
$83$	−7.57956	+	13.1282i	−0.831965	+	1.44101i	0.0645125	+	0.997917i	$0.479451\pi$
$83$	−7.57956	+	13.1282i	−0.831965	+	1.44101i	−0.896478	+	0.443089i	$0.853883\pi$
$84$	1.65066	−	3.04554i	0.180102	−	0.332296i
$85$	−0.364367	−	0.631102i	−0.0395211	−	0.0684526i
$86$	−3.68556	−	7.74325i	−0.397424	−	0.834976i
$87$	4.19253	+	4.88523i	0.449487	+	0.523751i
$88$	11.9683	+	11.4135i	1.27582	+	1.21668i
$89$			2.51704i			0.266806i	0.991062	+	0.133403i	$0.0425905\pi$
$89$			2.51704i			0.266806i	−0.991062	+	0.133403i	$0.957410\pi$
$90$	11.8561	+	11.1625i	1.24974	+	1.17663i
$91$			1.03017i			0.107991i
$92$	1.80942	−	2.22699i	0.188646	−	0.232179i
$93$	−11.9007	+	2.23498i	−1.23405	+	0.231757i
$94$	−4.55315	+	2.16717i	−0.469621	+	0.223526i
$95$	−7.94997	−	13.7697i	−0.815649	−	1.41275i
$96$	9.58035	+	2.05353i	0.977790	+	0.209587i
$97$	1.26529	−	2.19154i	0.128471	−	0.222517i	−0.794614	−	0.607115i	$-0.792327\pi$
$97$	1.26529	−	2.19154i	0.128471	−	0.222517i	0.923084	+	0.384598i	$0.125660\pi$
$98$	0.112112	−	1.40976i	0.0113250	−	0.142408i
$99$	−16.3460	+	6.36410i	−1.64284	+	0.639617i
$100$	19.2186	+	3.07619i	1.92186	+	0.307619i
$101$	−2.49788	−	1.44215i	−0.248549	−	0.143500i	0.370551	−	0.928812i	$-0.379169\pi$
$101$	−2.49788	−	1.44215i	−0.248549	−	0.143500i	−0.619099	+	0.785313i	$0.712502\pi$
$102$	0.375823	−	0.273949i	0.0372120	−	0.0271250i
$103$	−9.45187	+	5.45704i	−0.931321	+	0.537698i	−0.887229	−	0.461329i	$-0.847373\pi$
$103$	−9.45187	+	5.45704i	−0.931321	+	0.537698i	−0.0440916	+	0.999027i	$0.514039\pi$
$104$	−2.79579	+	0.820686i	−0.274150	+	0.0804749i
$105$	6.27187	+	2.20420i	0.612072	+	0.215108i
$106$	−3.76088	+	5.46253i	−0.365289	+	0.530568i
$107$	13.4510			1.30036			0.650179	−	0.759781i	$-0.274694\pi$
$107$	13.4510			1.30036			0.650179	+	0.759781i	$0.274694\pi$
$108$	−6.28096	+	8.27947i	−0.604386	+	0.796692i
$109$	5.00998			0.479869			0.239934	−	0.970789i	$-0.422874\pi$
$109$	5.00998			0.479869			0.239934	+	0.970789i	$0.422874\pi$
$110$	−17.9980	+	26.1413i	−1.71604	+	2.49248i
$111$	7.81733	+	2.74734i	0.741988	+	0.260766i
$112$	3.91529	−	0.818829i	0.369960	−	0.0773720i
$113$	3.70388	−	2.13843i	0.348431	−	0.201167i	−0.315563	−	0.948905i	$-0.602193\pi$
$113$	3.70388	−	2.13843i	0.348431	−	0.201167i	0.663994	+	0.747738i	$0.268860\pi$
$114$	8.19993	−	5.97718i	0.767993	−	0.559814i
$115$	4.76889	+	2.75332i	0.444702	+	0.256749i
$116$	−1.17488	+	7.34008i	−0.109085	+	0.681509i
$117$	0.468923	−	3.05472i	0.0433519	−	0.282409i
$118$	−0.950869	+	11.9568i	−0.0875346	+	1.10071i
$119$	0.0949323	−	0.164427i	0.00870243	−	0.0150730i
$120$	−0.985503	+	18.7773i	−0.0899637	+	1.71413i
$121$	−11.5941	−	20.0816i	−1.05401	−	1.82560i
$122$	1.21904	−	0.580229i	0.110367	−	0.0525315i
$123$	16.0335	−	3.01112i	1.44569	−	0.271504i
$124$	−10.8516	−	8.81693i	−0.974504	−	0.791783i
$125$			18.1607i			1.62434i
$126$	−0.974154	+	4.12929i	−0.0867845	+	0.367866i
$127$			5.78278i			0.513139i	0.966526	+	0.256569i	$0.0825922\pi$
$127$			5.78278i			0.513139i	−0.966526	+	0.256569i	$0.917408\pi$
$128$	5.34136	+	9.97346i	0.472114	+	0.881537i
$129$	6.84011	+	7.97024i	0.602238	+	0.701740i
$130$	−2.40318	−	5.04900i	−0.210773	−	0.442827i
$131$	4.22134	+	7.31158i	0.368820	+	0.638815i	0.989381	−	0.145343i	$-0.0464284\pi$
$131$	4.22134	+	7.31158i	0.368820	+	0.638815i	−0.620561	+	0.784158i	$0.713095\pi$
$132$	−17.8075	−	9.65155i	−1.54994	−	0.840060i
$133$	2.07129	−	3.58757i	0.179603	−	0.311082i
$134$	1.14746	+	0.0912525i	0.0991255	+	0.00788302i
$135$	−17.5944	−	9.39093i	−1.51429	−	0.808242i
$136$	0.521871	+	0.126647i	0.0447500	+	0.0108599i
$137$	17.5423	+	10.1280i	1.49874	+	0.865297i	0.999999	−	0.00145585i	$-0.000463412\pi$
$137$	17.5423	+	10.1280i	1.49874	+	0.865297i	0.498739	+	0.866752i	$0.333797\pi$
$138$	−1.42437	+	3.21269i	−0.121251	+	0.273482i
$139$	1.85791	−	1.07266i	0.157586	−	0.0909822i	−0.419133	−	0.907925i	$-0.637666\pi$
$139$	1.85791	−	1.07266i	0.157586	−	0.0909822i	0.576719	+	0.816942i	$0.304333\pi$
$140$	2.73922	+	7.17099i	0.231506	+	0.606059i
$141$	4.68662	−	4.02209i	0.394685	−	0.338721i
$142$	−5.93054	−	4.08310i	−0.497680	−	0.342646i
$143$	6.02346			0.503707
$144$	−11.9826	+	0.645838i	−0.998551	+	0.0538198i
$145$	−14.2656			−1.18469
$146$	9.45895	+	6.51237i	0.782828	+	0.538967i
$147$	0.319694	+	1.70229i	0.0263679	+	0.140403i
$148$	3.41420	+	8.93800i	0.280645	+	0.734699i
$149$	−10.2202	+	5.90065i	−0.837274	+	0.483400i	−0.856337	−	0.516418i	$-0.827265\pi$
$149$	−10.2202	+	5.90065i	−0.837274	+	0.483400i	0.0190630	+	0.999818i	$0.493932\pi$
$150$	−23.7030	+	2.52871i	−1.93534	+	0.206469i
$151$	11.5465	+	6.66639i	0.939643	+	0.542503i	0.889848	−	0.456256i	$-0.150810\pi$
$151$	11.5465	+	6.66639i	0.939643	+	0.542503i	0.0497946	+	0.998759i	$0.484143\pi$
$152$	11.3865	+	2.76325i	0.923565	+	0.224129i
$153$	−0.356345	+	0.444359i	−0.0288088	+	0.0359243i
$154$	−8.24298	−	0.655528i	−0.664239	−	0.0528240i
$155$	13.4163	−	23.2378i	1.07763	−	1.86650i
$156$	3.04135	−	1.86685i	0.243503	−	0.149468i
$157$	−0.586019	−	1.01501i	−0.0467694	−	0.0810069i	0.841693	−	0.539956i	$-0.181559\pi$
$157$	−0.586019	−	1.01501i	−0.0467694	−	0.0810069i	−0.888462	+	0.458949i	$0.848226\pi$
$158$	−4.28498	−	9.00261i	−0.340895	−	0.716210i
$159$	2.69312	−	7.66306i	0.213578	−	0.607720i
$160$	−17.2793	+	13.1468i	−1.36605	+	1.03935i
$161$			1.43470i			0.113070i
$162$	4.76824	−	11.8010i	0.374628	−	0.927175i
$163$		−	15.6643i		−	1.22693i	−0.789723	−	0.613463i	$-0.789776\pi$
$163$		−	15.6643i		−	1.22693i	0.789723	−	0.613463i	$-0.210224\pi$
$164$	14.6201	+	11.8788i	1.14163	+	0.927577i
$165$	12.8881	−	36.6721i	1.00334	−	2.85492i
$166$	19.3574	−	9.21356i	1.50242	−	0.715111i
$167$	7.87953	+	13.6477i	0.609736	+	1.05609i	0.991284	+	0.131745i	$0.0420579\pi$
$167$	7.87953	+	13.6477i	0.609736	+	1.05609i	−0.381548	+	0.924349i	$0.624609\pi$
$168$	−4.36519	+	2.22376i	−0.336782	+	0.171567i
$169$	5.96938	−	10.3393i	0.459183	−	0.795328i
$170$	−0.0816999	+	1.02734i	−0.00626610	+	0.0787935i
$171$	−7.77495	+	9.69528i	−0.594565	+	0.741417i
$172$	−1.91681	+	11.9753i	−0.146155	+	0.913109i
$173$	10.7242	+	6.19161i	0.815344	+	0.470739i	0.848808	−	0.528701i	$-0.177321\pi$
$173$	10.7242	+	6.19161i	0.815344	+	0.470739i	−0.0334641	+	0.999440i	$0.510654\pi$
$174$	−0.965782	−	9.05278i	−0.0732158	−	0.686290i
$175$	−8.42781	+	4.86580i	−0.637083	+	0.367820i
$176$	−4.78775	−	22.8930i	−0.360890	−	1.72562i
$177$	−2.71146	−	14.4378i	−0.203806	−	1.08521i
$178$	2.01860	−	2.93194i	0.151301	−	0.219758i
$179$	−14.6038			−1.09154			−0.545769	−	0.837936i	$-0.683762\pi$
$179$	−14.6038			−1.09154			−0.545769	+	0.837936i	$0.683762\pi$
$180$	−4.85835	−	22.5108i	−0.362120	−	1.67785i
$181$	−6.78702			−0.504476			−0.252238	−	0.967665i	$-0.581167\pi$
$181$	−6.78702			−0.504476			−0.252238	+	0.967665i	$0.581167\pi$
$182$	0.826167	−	1.19997i	0.0612396	−	0.0889480i
$183$	−1.25478	+	1.07686i	−0.0927560	+	0.0796037i
$184$	−3.89366	+	1.14296i	−0.287045	+	0.0842601i
$185$	−15.9016	+	9.18082i	−1.16911	+	0.674987i
$186$	15.6547	+	6.94066i	1.14786	+	0.508914i
$187$	−0.961419	−	0.555076i	−0.0703059	−	0.0405912i
$188$	7.04167	+	1.12711i	0.513567	+	0.0822032i
$189$	−0.173111	−	5.19327i	−0.0125920	−	0.377755i
$190$	−1.78258	+	22.4151i	−0.129322	+	1.62616i
$191$	−11.0178	+	19.0834i	−0.797219	+	1.38082i	0.124202	+	0.992257i	$0.460363\pi$
$191$	−11.0178	+	19.0834i	−0.797219	+	1.38082i	−0.921421	+	0.388567i	$0.872970\pi$
$192$	−9.51264	−	10.0752i	−0.686516	−	0.727115i
$193$	2.98789	+	5.17517i	0.215073	+	0.372517i	0.953295	−	0.302041i	$-0.0976678\pi$
$193$	2.98789	+	5.17517i	0.215073	+	0.372517i	−0.738222	+	0.674557i	$0.764334\pi$
$194$	−3.23141	+	1.53806i	−0.232002	+	0.110426i
$195$	4.46011	+	5.19701i	0.319395	+	0.372166i
$196$	−1.26118	+	1.55223i	−0.0900846	+	0.110873i
$197$			1.32760i			0.0945878i	0.998881	+	0.0472939i	$0.0150597\pi$
$197$			1.32760i			0.0945878i	−0.998881	+	0.0472939i	$0.984940\pi$
$198$	24.1442	+	5.69595i	1.71586	+	0.404793i
$199$		−	4.06971i		−	0.288494i	−0.989542	−	0.144247i	$-0.953924\pi$
$199$		−	4.06971i		−	0.288494i	0.989542	−	0.144247i	$-0.0460760\pi$
$200$	−19.9194	−	18.9960i	−1.40852	−	1.34322i
$201$	−1.38556	+	0.260212i	−0.0977300	+	0.0183539i
$202$	1.75305	+	3.68310i	0.123344	+	0.259142i
$203$	−1.85838	−	3.21880i	−0.130433	−	0.225916i
$204$	−0.657472	+	0.0177053i	−0.0460322	+	0.00123962i
$205$	−18.0754	+	31.3075i	−1.26244	+	2.18661i
$206$	15.3863	+	1.22360i	1.07201	+	0.0852524i
$207$	0.653064	−	4.25427i	0.0453911	−	0.295693i
$208$	3.91480	+	1.28618i	0.271442	+	0.0891809i
$209$	−20.9768	−	12.1110i	−1.45100	−	0.837733i
$210$	−5.53798	−	7.59739i	−0.382157	−	0.524270i
$211$	5.65597	−	3.26548i	0.389373	−	0.224805i	−0.292515	−	0.956261i	$-0.594492\pi$
$211$	5.65597	−	3.26548i	0.389373	−	0.224805i	0.681889	+	0.731456i	$0.261159\pi$
$212$	8.76161	−	3.34682i	0.601750	−	0.229860i
$213$	8.31960	+	2.92385i	0.570049	+	0.200339i
$214$	−15.6682	−	10.7874i	−1.07106	−	0.737408i
$215$	−23.2742			−1.58729
$216$	13.9562	−	4.60704i	0.949598	−	0.313469i
$217$	6.99099			0.474579
$218$	−5.83579	−	4.01787i	−0.395250	−	0.272124i
$219$	−13.2694	−	4.66342i	−0.896662	−	0.315124i
$220$	41.9293	−	16.0164i	2.82687	−	1.07983i
$221$	0.169388	−	0.0977961i	0.0113943	−	0.00657848i
$222$	−6.90260	−	9.46948i	−0.463272	−	0.635550i
$223$	−21.6090	−	12.4760i	−1.44705	−	0.835452i	−0.448741	−	0.893662i	$-0.648128\pi$
$223$	−21.6090	−	12.4760i	−1.44705	−	0.835452i	−0.998304	+	0.0582095i	$0.981461\pi$
$224$	−5.21735	−	2.18616i	−0.348599	−	0.146069i
$225$	27.2056	−	10.5921i	1.81371	−	0.706142i
$226$	−6.02937	−	0.479489i	−0.401068	−	0.0318951i
$227$	5.18442	−	8.97967i	0.344102	−	0.596002i	−0.641088	−	0.767467i	$-0.721517\pi$
$227$	5.18442	−	8.97967i	0.344102	−	0.596002i	0.985190	+	0.171465i	$0.0548501\pi$
$228$	−14.3451	+	0.386305i	−0.950027	+	0.0255837i
$229$	11.0340	+	19.1115i	0.729150	+	1.26293i	0.957243	+	0.289286i	$0.0934179\pi$
$229$	11.0340	+	19.1115i	0.729150	+	1.26293i	−0.228092	+	0.973640i	$0.573249\pi$
$230$	−3.34688	−	7.03169i	−0.220687	−	0.463656i
$231$	9.95342	−	1.86928i	0.654887	−	0.122989i
$232$	7.25508	−	7.60775i	0.476320	−	0.499473i
$233$		−	22.9418i		−	1.50297i	−0.659751	−	0.751485i	$-0.729338\pi$
$233$		−	22.9418i		−	1.50297i	0.659751	−	0.751485i	$-0.270662\pi$
$234$	−2.99602	+	3.18218i	−0.195856	+	0.208026i
$235$			13.6856i			0.892750i
$236$	10.6966	−	13.1651i	0.696291	−	0.856974i
$237$	7.95259	+	9.26653i	0.516576	+	0.601926i
$238$	−0.242447	+	0.115398i	−0.0157155	+	0.00748012i
$239$	−7.15276	−	12.3890i	−0.462674	−	0.801375i	0.536419	−	0.843952i	$-0.319777\pi$
$239$	−7.15276	−	12.3890i	−0.462674	−	0.801375i	−0.999093	+	0.0425770i	$0.986443\pi$
$240$	16.2068	−	21.0821i	1.04615	−	1.36084i
$241$	−4.03440	+	6.98778i	−0.259878	+	0.450123i	−0.966209	−	0.257759i	$-0.917016\pi$
$241$	−4.03440	+	6.98778i	−0.259878	+	0.450123i	0.706331	+	0.707882i	$0.250349\pi$
$242$	−2.59969	+	32.6899i	−0.167114	+	2.10139i
$243$	−1.85061	+	15.4782i	−0.118717	+	0.992928i
$244$	−1.88531	−	0.301769i	−0.120695	−	0.0193188i
$245$	−3.32396	−	1.91909i	−0.212360	−	0.122606i
$246$	−21.0912	−	9.35095i	−1.34472	−	0.596195i
$247$	3.69580	−	2.13377i	0.235158	−	0.135769i
$248$	5.56939	+	18.9730i	0.353657	+	1.20478i
$249$	−19.9249	+	17.0996i	−1.26269	+	1.08365i
$250$	14.5644	−	21.1542i	0.921135	−	1.33791i
$251$	6.31087			0.398338			0.199169	−	0.979965i	$-0.436176\pi$
$251$	6.31087			0.398338			0.199169	+	0.979965i	$0.436176\pi$
$252$	4.44631	−	4.02869i	0.280091	−	0.253784i
$253$	8.38881			0.527400
$254$	4.63764	−	6.73598i	0.290991	−	0.422653i
$255$	−0.232972	−	1.24052i	−0.0145893	−	0.0776842i
$256$	1.77664	−	15.9011i	0.111040	−	0.993816i
$257$	−12.4534	+	7.18998i	−0.776822	+	0.448499i	−0.835303	−	0.549790i	$-0.814708\pi$
$257$	−12.4534	+	7.18998i	−0.776822	+	0.448499i	0.0584805	+	0.998289i	$0.481374\pi$
$258$	−1.57567	−	14.7696i	−0.0980970	−	0.919515i
$259$	−4.14302	−	2.39197i	−0.257435	−	0.148630i
$260$	−1.24986	+	7.80853i	−0.0775131	+	0.484265i
$261$	4.04541	+	10.3905i	0.250405	+	0.643157i
$262$	0.946528	−	11.9022i	0.0584767	−	0.735319i
$263$	3.95944	−	6.85794i	0.244149	−	0.422879i	−0.717743	−	0.696308i	$-0.754825\pi$
$263$	3.95944	−	6.85794i	0.244149	−	0.422879i	0.961892	+	0.273429i	$0.0881580\pi$
$264$	13.0025	+	25.5236i	0.800247	+	1.57087i
$265$	8.99964	+	15.5878i	0.552843	+	0.957553i
$266$	−5.28984	+	2.51781i	−0.324341	+	0.154377i
$267$	−1.44549	+	4.11304i	−0.0884628	+	0.251714i
$268$	−1.26342	−	1.02653i	−0.0771756	−	0.0627051i
$269$			8.59237i			0.523886i	0.965083	+	0.261943i	$0.0843632\pi$
$269$			8.59237i			0.523886i	−0.965083	+	0.261943i	$0.915637\pi$
$270$	12.9633	+	25.0491i	0.788922	+	1.52444i
$271$			2.69257i			0.163562i	0.996650	+	0.0817811i	$0.0260608\pi$
$271$			2.69257i			0.163562i	−0.996650	+	0.0817811i	$0.973939\pi$
$272$	−0.506326	−	0.566049i	−0.0307005	−	0.0343217i
$273$	−0.591607	+	1.68337i	−0.0358057	+	0.101882i
$274$	−12.3114	−	25.8659i	−0.743760	−	1.56262i
$275$	28.4507	+	49.2780i	1.71564	+	2.97158i
$276$	4.23565	−	2.59994i	0.254956	−	0.156498i
$277$	−10.2042	+	17.6742i	−0.613112	+	1.06194i	0.377601	+	0.925969i	$0.376749\pi$
$277$	−10.2042	+	17.6742i	−0.613112	+	1.06194i	−0.990713	+	0.135973i	$0.956584\pi$
$278$	−3.02440	−	0.240517i	−0.181392	−	0.0144253i
$279$	−20.7301	−	3.18224i	−1.24108	−	0.190516i
$280$	2.56020	−	10.5498i	0.153001	−	0.630471i
$281$	−23.5939	−	13.6219i	−1.40749	−	0.812616i	−0.412347	−	0.911027i	$-0.635291\pi$
$281$	−23.5939	−	13.6219i	−1.40749	−	0.812616i	−0.995146	+	0.0984104i	$0.968624\pi$
$282$	−8.68475	+	0.926519i	−0.517169	+	0.0551734i
$283$	6.95732	−	4.01681i	0.413570	−	0.238775i	−0.278753	−	0.960363i	$-0.589921\pi$
$283$	6.95732	−	4.01681i	0.413570	−	0.238775i	0.692322	+	0.721588i	$0.256588\pi$
$284$	3.63356	+	9.51228i	0.215612	+	0.564450i
$285$	−5.08312	−	27.0663i	−0.301098	−	1.60327i
$286$	−7.01634	−	4.83066i	−0.414885	−	0.285643i
$287$	−9.41875			−0.555971
$288$	14.4757	+	8.85744i	0.852989	+	0.521930i
$289$	16.9640			0.997879
$290$	16.6170	+	11.4406i	0.975785	+	0.671815i
$291$	3.32614	−	2.85451i	0.194982	−	0.167334i
$292$	−5.79537	−	15.1717i	−0.339148	−	0.887854i
$293$	25.8214	−	14.9080i	1.50850	−	0.870933i	0.508549	−	0.861033i	$-0.330182\pi$
$293$	25.8214	−	14.9080i	1.50850	−	0.870933i	0.999951	−	0.00989946i	$-0.00315115\pi$
$294$	0.992801	−	2.23927i	0.0579013	−	0.130597i
$295$	28.1919	+	16.2766i	1.64139	+	0.947659i
$296$	3.19107	−	13.1494i	0.185477	−	0.764293i
$297$	−30.3654	+	1.01219i	−1.76198	+	0.0587334i
$298$	16.6370	+	1.32307i	0.963757	+	0.0766434i
$299$	−0.738992	+	1.27997i	−0.0427370	+	0.0740227i
$300$	29.6380	+	16.0636i	1.71115	+	0.927433i
$301$	−3.03194	−	5.25147i	−0.174758	−	0.302690i
$302$	−8.10352	−	17.0252i	−0.466305	−	0.979693i
$303$	−3.25352	−	3.79108i	−0.186910	−	0.217792i
$304$	−11.0473	−	12.3504i	−0.633606	−	0.708343i
$305$		−	3.66413i		−	0.209808i
$306$	0.771447	−	0.231825i	0.0441007	−	0.0132526i
$307$			19.7274i			1.12590i	0.826490	+	0.562951i	$0.190334\pi$
$307$			19.7274i			1.12590i	−0.826490	+	0.562951i	$0.809666\pi$
$308$	9.07599	+	7.37424i	0.517153	+	0.420186i
$309$	−18.5789	+	3.48917i	−1.05692	+	0.198492i
$310$	−34.2639	+	16.3086i	−1.94606	+	0.926267i
$311$	−7.44017	−	12.8868i	−0.421893	−	0.730741i	0.574231	−	0.818693i	$-0.305301\pi$
$311$	−7.44017	−	12.8868i	−0.421893	−	0.730741i	−0.996125	+	0.0879525i	$0.971968\pi$
$312$	−5.03983	−	0.264509i	−0.285324	−	0.0149749i
$313$	12.3404	−	21.3741i	0.697518	−	1.20814i	−0.271807	−	0.962352i	$-0.587621\pi$
$313$	12.3404	−	21.3741i	0.697518	−	1.20814i	0.969324	−	0.245785i	$-0.0790456\pi$
$314$	−0.131400	+	1.65229i	−0.00741531	+	0.0932444i
$315$	8.98287	+	7.20364i	0.506127	+	0.405879i
$316$	−2.22856	+	13.9230i	−0.125366	+	0.783230i
$317$	16.1561	+	9.32772i	0.907416	+	0.523897i	0.879599	−	0.475716i	$-0.157811\pi$
$317$	16.1561	+	9.32772i	0.907416	+	0.523897i	0.0278171	+	0.999613i	$0.491144\pi$
$318$	−9.28260	+	6.76638i	−0.520542	+	0.379440i
$319$	−18.8206	+	10.8661i	−1.05375	+	0.608383i
$320$	30.6709	−	1.45635i	1.71455	−	0.0814122i
$321$	21.9800	+	7.72468i	1.22680	+	0.431149i
$322$	1.15059	−	1.67119i	0.0641201	−	0.0931318i
$323$	−0.786528			−0.0437636
$324$	−15.0183	+	9.92222i	−0.834350	+	0.551234i
$325$	−10.0252			−0.556097
$326$	−12.5624	+	18.2464i	−0.695766	+	1.01057i
$327$	8.18668	+	2.87714i	0.452724	+	0.159106i
$328$	−7.50348	−	25.5617i	−0.414310	−	1.41141i
$329$	−3.08795	+	1.78283i	−0.170244	+	0.0982904i
$330$	−44.4225	+	32.3810i	−2.44538	+	1.78251i
$331$	−14.3672	−	8.29491i	−0.789693	−	0.455930i	0.0501612	−	0.998741i	$-0.484027\pi$
$331$	−14.3672	−	8.29491i	−0.789693	−	0.455930i	−0.839855	+	0.542811i	$0.817360\pi$
$332$	−29.9372	−	4.79185i	−1.64302	−	0.262987i
$333$	11.1964	+	8.97870i	0.613556	+	0.492030i
$334$	1.76678	−	22.2165i	0.0966740	−	1.21563i
$335$	1.56202	−	2.70550i	0.0853423	−	0.147817i
$336$	6.86812	+	0.910456i	0.374687	+	0.0496694i
$337$	2.97884	+	5.15950i	0.162268	+	0.281056i	0.935682	−	0.352846i	$-0.114786\pi$
$337$	2.97884	+	5.15950i	0.162268	+	0.281056i	−0.773414	+	0.633901i	$0.781453\pi$
$338$	−15.2452	+	7.25625i	−0.829227	+	0.394688i
$339$	7.28047	−	1.36729i	0.395421	−	0.0742610i
$340$	0.919067	−	1.13116i	0.0498434	−	0.0613458i
$341$		−	40.8768i		−	2.21360i
$342$	16.8319	−	5.05809i	0.910164	−	0.273510i
$343$		−	1.00000i		−	0.0539949i
$344$	11.8367	−	12.4120i	0.638189	−	0.669212i
$345$	6.21154	+	7.23782i	0.334418	+	0.389671i
$346$	−7.52639	−	15.8127i	−0.404621	−	0.850096i
$347$	−6.43730	−	11.1497i	−0.345572	−	0.598549i	0.639885	−	0.768470i	$-0.278982\pi$
$347$	−6.43730	−	11.1497i	−0.345572	−	0.598549i	−0.985458	+	0.169922i	$0.945648\pi$
$348$	−6.13511	+	11.3195i	−0.328877	+	0.606790i
$349$	8.33062	−	14.4291i	0.445928	−	0.772370i	−0.552188	−	0.833719i	$-0.686207\pi$
$349$	8.33062	−	14.4291i	0.445928	−	0.772370i	0.998116	+	0.0613493i	$0.0195404\pi$
$350$	13.7192	+	1.09103i	0.733325	+	0.0583181i
$351$	2.52053	−	4.72235i	0.134536	−	0.252060i
$352$	−12.7826	+	30.5062i	−0.681317	+	1.62599i
$353$	−25.3982	−	14.6636i	−1.35181	−	0.780467i	−0.363306	−	0.931670i	$-0.618352\pi$
$353$	−25.3982	−	14.6636i	−1.35181	−	0.780467i	−0.988503	+	0.151203i	$0.951685\pi$
$354$	−8.42035	+	18.9922i	−0.447537	+	1.00942i
$355$	−16.9233	+	9.77069i	−0.898198	+	0.518575i
$356$	−4.70267	+	1.79636i	−0.249241	+	0.0952068i
$357$	0.249554	−	0.214169i	0.0132078	−	0.0113350i
$358$	17.0110	+	11.7118i	0.899058	+	0.618990i
$359$	−2.39895			−0.126612			−0.0633060	−	0.997994i	$-0.520164\pi$
$359$	−2.39895			−0.126612			−0.0633060	+	0.997994i	$0.520164\pi$
$360$	−12.3939	+	30.1176i	−0.653214	+	1.58733i
$361$	1.83908			0.0967938
$362$	7.90576	+	5.44301i	0.415517	+	0.286078i
$363$	−7.41315	−	39.4732i	−0.389090	−	2.07180i
$364$	−1.92469	+	0.735207i	−0.100881	+	0.0385353i
$365$	26.9920	−	15.5838i	1.41282	−	0.815694i
$366$	2.32522	−	0.248063i	0.121541	−	0.0129665i
$367$	17.1124	+	9.87986i	0.893261	+	0.515724i	0.875008	−	0.484109i	$-0.160856\pi$
$367$	17.1124	+	9.87986i	0.893261	+	0.515724i	0.0182530	+	0.999833i	$0.494190\pi$
$368$	5.45210	+	1.79126i	0.284210	+	0.0933756i
$369$	27.9291	+	4.28733i	1.45393	+	0.223190i
$370$	25.8856	+	2.05856i	1.34573	+	0.107020i
$371$	−2.34477	+	4.06126i	−0.121734	+	0.210850i
$372$	−12.6689	−	20.6394i	−0.656854	−	1.07010i
$373$	8.62492	+	14.9388i	0.446582	+	0.773502i	0.998161	−	0.0606204i	$-0.0193079\pi$
$373$	8.62492	+	14.9388i	0.446582	+	0.773502i	−0.551579	+	0.834122i	$0.685975\pi$
$374$	0.674738	+	1.41760i	0.0348899	+	0.0733026i
$375$	−10.4294	+	29.6760i	−0.538571	+	1.53246i
$376$	−7.29846	−	6.96013i	−0.376390	−	0.358941i
$377$		−	3.82888i		−	0.197197i
$378$	−3.96322	+	6.18813i	−0.203846	+	0.318283i
$379$		−	26.3144i		−	1.35168i	−0.737049	−	0.675840i	$-0.763781\pi$
$379$		−	26.3144i		−	1.35168i	0.737049	−	0.675840i	$-0.236219\pi$
$380$	20.0527	−	24.6803i	1.02868	−	1.26607i
$381$	−3.32095	+	9.44949i	−0.170137	+	0.484112i
$382$	28.1382	−	13.3930i	1.43968	−	0.685245i
$383$	−9.11566	−	15.7888i	−0.465788	−	0.806769i	0.533448	−	0.845833i	$-0.320896\pi$
$383$	−9.11566	−	15.7888i	−0.465788	−	0.806769i	−0.999237	+	0.0390634i	$0.987563\pi$
$384$	3.00061	+	19.3648i	0.153124	+	0.988207i
$385$	−11.2210	+	19.4354i	−0.571878	+	0.990521i
$386$	0.669957	−	8.42442i	0.0340999	−	0.428792i
$387$	6.60008	+	16.9521i	0.335501	+	0.861725i
$388$	4.99754	+	0.799923i	0.253711	+	0.0406099i
$389$	−28.6977	−	16.5687i	−1.45503	−	0.840064i	−0.456273	−	0.889840i	$-0.650816\pi$
$389$	−28.6977	−	16.5687i	−1.45503	−	0.840064i	−0.998760	+	0.0497759i	$0.984149\pi$
$390$	−1.02742	−	9.63055i	−0.0520254	−	0.487662i
$391$	0.235905	−	0.136200i	0.0119302	−	0.00688791i
$392$	2.71392	−	0.796653i	0.137073	−	0.0402371i
$393$	2.69908	+	14.3719i	0.136150	+	0.724967i
$394$	1.06470	−	1.54644i	0.0536389	−	0.0779084i
$395$	−27.0596			−1.36151
$396$	−23.5560	−	25.9979i	−1.18374	−	1.30644i
$397$	−7.24602			−0.363667			−0.181834	−	0.983329i	$-0.558203\pi$
$397$	−7.24602			−0.363667			−0.181834	+	0.983329i	$0.558203\pi$
$398$	−3.26380	+	4.74054i	−0.163600	+	0.237622i
$399$	5.44492	−	4.67286i	0.272587	−	0.233936i
$400$	7.96851	+	38.1021i	0.398426	+	1.90510i
$401$	−18.5998	+	10.7386i	−0.928831	+	0.536261i	−0.886442	−	0.462841i	$-0.846830\pi$
$401$	−18.5998	+	10.7386i	−0.928831	+	0.536261i	−0.0423890	+	0.999101i	$0.513497\pi$
$402$	1.82263	+	0.808080i	0.0909046	+	0.0403034i
$403$	6.23702	+	3.60095i	0.310688	+	0.179376i
$404$	0.911738	−	5.69611i	0.0453607	−	0.283392i
$405$	−23.3576	−	25.4496i	−1.16065	−	1.26460i
$406$	−0.416693	+	5.23974i	−0.0206802	+	0.260044i
$407$	−13.9860	+	24.2245i	−0.693263	+	1.20077i
$408$	0.780045	+	0.506651i	0.0386180	+	0.0250830i
$409$	2.23549	+	3.87198i	0.110538	+	0.191457i	0.915987	−	0.401207i	$-0.131409\pi$
$409$	2.23549	+	3.87198i	0.110538	+	0.191457i	−0.805449	+	0.592664i	$0.798076\pi$
$410$	46.1627	−	21.9721i	2.27981	−	1.08512i
$411$	22.8490	+	26.6242i	1.12706	+	1.31327i
$412$	−16.9412	−	13.7647i	−0.834631	−	0.678137i
$413$			8.48141i			0.417343i
$414$	−4.17253	+	4.43178i	−0.205068	+	0.217810i
$415$		−	58.1834i		−	2.85611i
$416$	−3.52861	−	4.63776i	−0.173004	−	0.227385i
$417$	3.65197	−	0.685849i	0.178838	−	0.0335862i
$418$	14.7218	+	30.9301i	0.720068	+	1.51284i
$419$	7.21795	+	12.5019i	0.352620	+	0.610756i	0.986708	−	0.162505i	$-0.0519575\pi$
$419$	7.21795	+	12.5019i	0.352620	+	0.610756i	−0.634088	+	0.773261i	$0.718624\pi$
$420$	0.357920	+	13.2910i	0.0174647	+	0.648535i
$421$	−6.17131	+	10.6890i	−0.300771	+	0.520951i	−0.976311	−	0.216372i	$-0.930577\pi$
$421$	−6.17131	+	10.6890i	−0.300771	+	0.520951i	0.675539	+	0.737324i	$0.263911\pi$
$422$	−9.20710	−	0.732200i	−0.448195	−	0.0356429i
$423$	9.96811	−	3.88095i	0.484666	−	0.188698i
$424$	−12.8899	−	3.12809i	−0.625988	−	0.151914i
$425$	1.60014	+	0.923843i	0.0776183	+	0.0448130i
$426$	−7.34610	−	10.0779i	−0.355920	−	0.488276i
$427$	0.826755	−	0.477327i	0.0400095	−	0.0230995i
$428$	9.59968	+	25.1310i	0.464018	+	1.21475i
$429$	9.84279	+	3.45917i	0.475214	+	0.167010i
$430$	27.1106	+	18.6653i	1.30739	+	0.900121i
$431$	33.1403			1.59631			0.798155	−	0.602452i	$-0.205810\pi$
$431$	33.1403			1.59631			0.798155	+	0.602452i	$0.205810\pi$
$432$	−19.9514	−	5.82605i	−0.959911	−	0.280306i
$433$	−2.62906			−0.126345			−0.0631723	−	0.998003i	$-0.520122\pi$
$433$	−2.62906			−0.126345			−0.0631723	+	0.998003i	$0.520122\pi$
$434$	−8.14335	−	5.60659i	−0.390893	−	0.269125i
$435$	−23.3110	−	8.19246i	−1.11768	−	0.392798i
$436$	3.57551	+	9.36030i	0.171236	+	0.448277i
$437$	5.14710	−	2.97168i	0.246219	−	0.142155i
$438$	11.7167	+	16.0738i	0.559845	+	0.768036i
$439$	−21.0031	−	12.1261i	−1.00242	−	0.578749i	−0.0934587	−	0.995623i	$-0.529792\pi$
$439$	−21.0031	−	12.1261i	−1.00242	−	0.578749i	−0.908964	+	0.416874i	$0.863126\pi$
$440$	−61.6854	−	14.9697i	−2.94074	−	0.713652i
$441$	−0.455191	+	2.96527i	−0.0216758	+	0.141203i
$442$	−0.275739	−	0.0219283i	−0.0131155	−	0.00104302i
$443$	−2.13519	+	3.69826i	−0.101446	+	0.175710i	−0.912281	−	0.409566i	$-0.865680\pi$
$443$	−2.13519	+	3.69826i	−0.101446	+	0.175710i	0.810835	+	0.585275i	$0.199014\pi$
$444$	0.446115	+	16.5661i	0.0211717	+	0.786191i
$445$	−4.83043	−	8.36655i	−0.228984	−	0.396613i
$446$	15.1655	+	31.8623i	0.718108	+	1.50872i
$447$	−20.0893	+	3.77281i	−0.950189	+	0.178448i
$448$	4.32410	+	6.73069i	0.204295	+	0.317995i
$449$			32.8830i			1.55184i	0.630829	+	0.775922i	$0.282715\pi$
$449$			32.8830i			1.55184i	−0.630829	+	0.775922i	$0.717285\pi$
$450$	−40.1846	−	9.48008i	−1.89432	−	0.446895i
$451$			55.0721i			2.59324i
$452$	6.63868	+	5.39392i	0.312257	+	0.253709i
$453$	15.0395	+	17.5243i	0.706617	+	0.823365i
$454$	−13.2404	+	6.30207i	−0.621405	+	0.295771i
$455$	−1.97698	−	3.42423i	−0.0926824	−	0.160531i
$456$	17.0195	+	11.0544i	0.797009	+	0.517670i
$457$	7.47452	−	12.9463i	0.349643	−	0.605600i	−0.636543	−	0.771241i	$-0.719636\pi$
$457$	7.47452	−	12.9463i	0.349643	−	0.605600i	0.986186	+	0.165641i	$0.0529694\pi$
$458$	2.47410	−	31.1108i	0.115607	−	1.45371i
$459$	−0.837482	+	0.521473i	−0.0390903	+	0.0243403i
$460$	−1.74067	+	10.8749i	−0.0811590	+	0.507043i
$461$	2.46420	+	1.42270i	0.114769	+	0.0662620i	0.556286	−	0.830991i	$-0.312226\pi$
$461$	2.46420	+	1.42270i	0.114769	+	0.0662620i	−0.441517	+	0.897253i	$0.645559\pi$
$462$	−13.0932	−	5.80498i	−0.609151	−	0.270072i
$463$	21.5768	−	12.4574i	1.00276	−	0.578943i	0.0936949	−	0.995601i	$-0.470132\pi$
$463$	21.5768	−	12.4574i	1.00276	−	0.578943i	0.909063	+	0.416658i	$0.136799\pi$
$464$	−14.5522	+	3.04338i	−0.675568	+	0.141286i
$465$	35.2683	−	30.2675i	1.63553	−	1.40362i
$466$	−18.3987	+	26.7234i	−0.852305	+	1.23794i
$467$	6.16661			0.285356			0.142678	−	0.989769i	$-0.454429\pi$
$467$	6.16661			0.285356			0.142678	+	0.989769i	$0.454429\pi$
$468$	6.04189	−	1.30398i	0.279287	−	0.0602765i
$469$	0.813939			0.0375842
$470$	10.9755	−	15.9415i	0.506262	−	0.735325i
$471$	−0.374694	−	1.99515i	−0.0172650	−	0.0919316i
$472$	−23.0178	+	6.75674i	−1.05948	+	0.311004i
$473$	−30.7057	+	17.7280i	−1.41185	+	0.815133i
$474$	−1.83194	−	17.1717i	−0.0841438	−	0.788724i
$475$	34.9128	+	20.1569i	1.60191	+	0.924864i
$476$	0.374956	+	0.0600168i	0.0171861	+	0.00275086i
$477$	8.80151	−	10.9754i	0.402994	−	0.502529i
$478$	−1.60382	+	20.1674i	−0.0733572	+	0.922435i
$479$	15.1497	−	26.2401i	0.692209	−	1.19894i	−0.278904	−	0.960319i	$-0.589971\pi$
$479$	15.1497	−	26.2401i	0.692209	−	1.19894i	0.971113	−	0.238622i	$-0.0766956\pi$
$480$	−35.7856	+	11.5597i	−1.63338	+	0.527625i
$481$	−2.46413	−	4.26801i	−0.112355	−	0.194604i
$482$	10.3034	−	4.90413i	0.469308	−	0.223377i
$483$	−0.823924	+	2.34441i	−0.0374898	+	0.106674i
$484$	29.2447	−	35.9935i	1.32930	−	1.63607i
$485$			9.71280i			0.441035i
$486$	14.5688	−	16.5454i	0.660853	−	0.750515i
$487$		−	17.9066i		−	0.811425i	−0.914001	−	0.405713i	$-0.867023\pi$
$487$		−	17.9066i		−	0.811425i	0.914001	−	0.405713i	$-0.132977\pi$
$488$	1.95406	+	1.86348i	0.0884563	+	0.0843558i
$489$	8.99576	−	25.5967i	0.406802	−	1.15752i
$490$	2.33280	+	4.90115i	0.105385	+	0.221411i
$491$	3.95405	+	6.84862i	0.178444	+	0.309074i	0.941348	−	0.337438i	$-0.109560\pi$
$491$	3.95405	+	6.84862i	0.178444	+	0.309074i	−0.762904	+	0.646512i	$0.776227\pi$
$492$	17.0685	+	27.8069i	0.769507	+	1.25363i
$493$	−0.352840	+	0.611137i	−0.0158911	+	0.0275242i
$494$	−6.01623	−	0.478444i	−0.270683	−	0.0215262i
$495$	42.1202	−	52.5235i	1.89316	−	2.36076i
$496$	8.72839	−	26.5669i	0.391916	−	1.19289i
$497$	−4.40921	−	2.54566i	−0.197780	−	0.114188i
$498$	36.9226	−	3.93903i	1.65454	−	0.176512i
$499$	28.2925	−	16.3347i	1.26654	−	0.731240i	0.292212	−	0.956353i	$-0.405609\pi$
$499$	28.2925	−	16.3347i	1.26654	−	0.731240i	0.974333	+	0.225113i	$0.0722753\pi$
$500$	−33.9303	+	12.9609i	−1.51741	+	0.579629i
$501$	5.03808	+	26.8265i	0.225085	+	1.19852i
$502$	−7.35111	−	5.06115i	−0.328096	−	0.225890i
$503$	37.5962			1.67633			0.838166	−	0.545415i	$-0.183628\pi$
$503$	37.5962			1.67633			0.838166	+	0.545415i	$0.183628\pi$
$504$	−8.41011	+	1.12694i	−0.374616	+	0.0501978i
$505$	11.0705			0.492630
$506$	−9.77157	−	6.72760i	−0.434399	−	0.299078i
$507$	15.6921	−	13.4670i	0.696909	−	0.598092i
$508$	−10.8042	+	4.12704i	−0.479357	+	0.183108i
$509$	−8.47297	+	4.89187i	−0.375558	+	0.216828i	−0.675884	−	0.737008i	$-0.736238\pi$
$509$	−8.47297	+	4.89187i	−0.375558	+	0.216828i	0.300326	+	0.953837i	$0.402905\pi$
$510$	−0.723488	+	1.63183i	−0.0320366	+	0.0722588i
$511$	7.03250	+	4.06021i	0.311099	+	0.179613i
$512$	−14.8217	+	17.0973i	−0.655034	+	0.755600i
$513$	−18.2727	+	11.3778i	−0.806758	+	0.502342i
$514$	20.2723	+	1.61217i	0.894174	+	0.0711097i
$515$	20.9451	−	36.2780i	0.922951	−	1.59860i
$516$	−10.0094	+	18.4678i	−0.440640	+	0.812998i
$517$	10.4243	+	18.0554i	0.458461	+	0.794077i
$518$	2.90763	+	6.10885i	0.127754	+	0.268407i
$519$	13.9684	+	16.2763i	0.613144	+	0.714448i
$520$	7.71812	−	8.09329i	0.338462	−	0.354914i
$521$		−	28.3001i		−	1.23985i	−0.784662	−	0.619924i	$-0.787163\pi$
$521$		−	28.3001i		−	1.23985i	0.784662	−	0.619924i	$-0.212837\pi$
$522$	3.62069	−	15.3476i	0.158473	−	0.671744i
$523$		−	20.8387i		−	0.911213i	−0.890181	−	0.455607i	$-0.849422\pi$
$523$		−	20.8387i		−	0.911213i	0.890181	−	0.455607i	$-0.150578\pi$
$524$	−10.6478	+	13.1050i	−0.465150	+	0.572493i
$525$	−16.5660	+	3.11114i	−0.723000	+	0.135781i
$526$	−10.1120	+	4.81301i	−0.440903	+	0.209857i
$527$	−0.663671	−	1.14951i	−0.0289099	−	0.0500735i
$528$	5.32350	−	40.1584i	0.231676	−	1.74767i
$529$	10.4708	−	18.1360i	0.455253	−	0.788521i
$530$	2.01794	−	25.3747i	0.0876536	−	1.10221i
$531$	3.86066	−	25.1496i	0.167538	−	1.09140i
$532$	8.18101	+	1.30948i	0.354692	+	0.0567732i
$533$	−8.40295	−	4.85145i	−0.363972	−	0.210139i
$534$	4.98231	−	3.63176i	0.215606	−	0.157162i
$535$	−44.7106	+	25.8137i	−1.93301	+	1.11602i
$536$	0.648427	+	2.20896i	0.0280078	+	0.0954127i
$537$	−23.8637	−	8.38669i	−1.02979	−	0.361912i
$538$	6.89085	−	10.0087i	0.297086	−	0.431505i
$539$	−5.84707			−0.251851
$540$	4.98863	−	39.5743i	0.214676	−	1.70301i
$541$	−20.0201			−0.860732			−0.430366	−	0.902655i	$-0.641615\pi$
$541$	−20.0201			−0.860732			−0.430366	+	0.902655i	$0.641615\pi$
$542$	2.15937	−	3.13640i	0.0927530	−	0.134720i
$543$	−11.0905	−	3.89767i	−0.475939	−	0.167265i
$544$	0.135829	+	1.06541i	0.00582364	+	0.0456792i
$545$	−16.6530	+	9.61459i	−0.713334	+	0.411844i
$546$	2.03914	−	1.48639i	0.0872672	−	0.0636118i
$547$	−29.8020	−	17.2062i	−1.27424	−	0.735684i	−0.298458	−	0.954423i	$-0.596472\pi$
$547$	−29.8020	−	17.2062i	−1.27424	−	0.735684i	−0.975783	+	0.218739i	$0.929806\pi$
$548$	−6.40301	+	40.0029i	−0.273523	+	1.70884i
$549$	−2.66882	+	1.03907i	−0.113903	+	0.0443465i
$550$	6.37934	−	80.2174i	0.272016	−	3.42048i
$551$	−7.69846	+	13.3341i	−0.327966	+	0.568053i
$552$	−7.01892	−	0.368379i	−0.298745	−	0.0156793i
$553$	−3.52506	−	6.10558i	−0.149901	−	0.259635i
$554$	26.0605	−	12.4040i	1.10720	−	0.526997i
$555$	−31.2569	+	5.87011i	−1.32678	+	0.249172i
$556$	3.33004	+	2.70565i	0.141225	+	0.114745i
$557$		−	9.89200i		−	0.419137i	−0.977794	−	0.209569i	$-0.932794\pi$
$557$		−	9.89200i		−	0.419137i	0.977794	−	0.209569i	$-0.0672060\pi$
$558$	21.5951	+	20.3318i	0.914194	+	0.860714i
$559$		−	6.24681i		−	0.264212i
$560$	−11.4429	+	10.2355i	−0.483549	+	0.432531i
$561$	−1.25226	−	1.45916i	−0.0528705	−	0.0616058i
$562$	16.5585	+	34.7890i	0.698480	+	1.46748i
$563$	−18.6487	−	32.3004i	−0.785947	−	1.36130i	−0.928432	−	0.371503i	$-0.878842\pi$
$563$	−18.6487	−	32.3004i	−0.785947	−	1.36130i	0.142485	−	0.989797i	$-0.454491\pi$
$564$	10.8593	+	5.88569i	0.457260	+	0.247832i
$565$	−8.20769	+	14.2161i	−0.345300	+	0.598077i
$566$	−11.3255	−	0.900667i	−0.476046	−	0.0378579i
$567$	2.69953	−	8.58560i	0.113369	−	0.360561i
$568$	3.39610	−	13.9942i	0.142497	−	0.587185i
$569$	−9.96571	−	5.75371i	−0.417784	−	0.241208i	0.276345	−	0.961059i	$-0.410877\pi$
$569$	−9.96571	−	5.75371i	−0.417784	−	0.241208i	−0.694129	+	0.719851i	$0.744210\pi$
$570$	−15.7855	+	35.6043i	−0.661181	+	1.49130i
$571$	6.13735	−	3.54340i	0.256840	−	0.148287i	−0.366052	−	0.930594i	$-0.619291\pi$
$571$	6.13735	−	3.54340i	0.256840	−	0.148287i	0.622892	+	0.782308i	$0.285958\pi$
$572$	4.29881	+	11.2538i	0.179742	+	0.470546i
$573$	−28.9631	+	24.8563i	−1.20995	+	1.03839i
$574$	10.9713	+	7.55359i	0.457933	+	0.315281i
$575$	−13.9620			−0.582254
$576$	−9.75836	−	21.9266i	−0.406598	−	0.913607i
$577$	35.9128			1.49507			0.747534	−	0.664223i	$-0.231238\pi$
$577$	35.9128			1.49507			0.747534	+	0.664223i	$0.231238\pi$
$578$	−19.7602	−	13.6046i	−0.821916	−	0.565878i
$579$	1.91042	+	10.1725i	0.0793944	+	0.422755i
$580$	−10.1810	−	26.6528i	−0.422743	−	1.10670i
$581$	13.1282	−	7.57956i	0.544649	−	0.314453i
$582$	−6.16364	+	0.657559i	−0.255491	+	0.0272567i
$583$	23.7465	+	13.7100i	0.983479	+	0.567812i
$584$	−5.41662	+	22.3202i	−0.224141	+	0.923616i
$585$	4.30360	+	11.0537i	0.177932	+	0.457013i
$586$	−42.0334	−	3.34273i	−1.73638	−	0.138087i
$587$	0.675757	−	1.17045i	0.0278915	−	0.0483095i	−0.851743	−	0.523960i	$-0.824454\pi$
$587$	0.675757	−	1.17045i	0.0278915	−	0.0483095i	0.879634	+	0.475651i	$0.157787\pi$
$588$	−2.95229	+	1.81218i	−0.121750	+	0.0747331i
$589$	−14.4803	−	25.0807i	−0.596652	−	1.03343i
$590$	−19.7855	−	41.5686i	−0.814554	−	1.71135i
$591$	−0.762418	+	2.16940i	−0.0313617	+	0.0892372i
$592$	−14.2625	+	12.7577i	−0.586186	+	0.524338i
$593$			14.2740i			0.586162i	0.956088	+	0.293081i	$0.0946805\pi$
$593$			14.2740i			0.586162i	−0.956088	+	0.293081i	$0.905319\pi$
$594$	36.1824	+	23.1732i	1.48458	+	0.950809i
$595$			0.728734i			0.0298752i
$596$	−18.3183	−	14.8836i	−0.750348	−	0.609657i
$597$	2.33716	−	6.65021i	0.0956537	−	0.272175i
$598$	1.88731	−	0.898303i	0.0771777	−	0.0367343i
$599$	22.8918	+	39.6498i	0.935335	+	1.62005i	0.774035	+	0.633143i	$0.218236\pi$
$599$	22.8918	+	39.6498i	0.935335	+	1.62005i	0.161301	+	0.986905i	$0.448431\pi$
$600$	−21.6407	−	42.4803i	−0.883480	−	1.73425i
$601$	9.37297	−	16.2345i	0.382331	−	0.662218i	−0.609064	−	0.793121i	$-0.708455\pi$
$601$	9.37297	−	16.2345i	0.382331	−	0.662218i	0.991395	+	0.130904i	$0.0417879\pi$
$602$	−0.679834	+	8.54863i	−0.0277080	+	0.348416i
$603$	−2.41355	−	0.370498i	−0.0982872	−	0.0150878i
$604$	−4.21453	+	26.3304i	−0.171487	+	1.07137i
$605$	77.0768	+	44.5003i	3.13362	+	1.80920i
$606$	0.749474	+	7.02521i	0.0304453	+	0.285380i
$607$	8.08350	−	4.66701i	0.328099	−	0.189428i	−0.326898	−	0.945060i	$-0.606003\pi$
$607$	8.08350	−	4.66701i	0.328099	−	0.189428i	0.654997	+	0.755632i	$0.272670\pi$
$608$	2.96361	+	23.2458i	0.120190	+	0.942741i
$609$	−1.18823	−	6.32700i	−0.0481493	−	0.256383i
$610$	−2.93854	+	4.26811i	−0.118978	+	0.172811i
$611$	−3.67322			−0.148603
$612$	−1.08453	−	0.348642i	−0.0438393	−	0.0140930i
$613$	−5.11320			−0.206520			−0.103260	−	0.994654i	$-0.532927\pi$
$613$	−5.11320			−0.206520			−0.103260	+	0.994654i	$0.532927\pi$
$614$	15.8208	−	22.9791i	0.638477	−	0.927362i
$615$	−47.5159	+	40.7785i	−1.91603	+	1.64435i
$616$	−4.65809	−	15.8685i	−0.187680	−	0.639359i
$617$	−4.20354	+	2.42691i	−0.169228	+	0.0977038i	−0.582222	−	0.813030i	$-0.697816\pi$
$617$	−4.20354	+	2.42691i	−0.169228	+	0.0977038i	0.412994	+	0.910734i	$0.364483\pi$
$618$	24.4396	+	10.8355i	0.983105	+	0.435868i
$619$	−18.5748	−	10.7241i	−0.746582	−	0.431040i	0.0778753	−	0.996963i	$-0.475186\pi$
$619$	−18.5748	−	10.7241i	−0.746582	−	0.431040i	−0.824458	+	0.565924i	$0.808520\pi$
$620$	52.9908	+	8.48189i	2.12816	+	0.340641i
$621$	3.51031	−	6.57676i	0.140864	−	0.263916i
$622$	−1.66827	+	20.9777i	−0.0668914	+	0.841131i
$623$	1.25852	−	2.17982i	0.0504216	−	0.0873328i
$624$	5.65844	+	4.34992i	0.226519	+	0.174136i
$625$	−10.5230	−	18.2264i	−0.420921	−	0.729057i
$626$	−31.5159	+	15.0007i	−1.25963	+	0.599547i
$627$	−27.3226	−	31.8368i	−1.09116	−	1.27144i
$628$	1.47815	−	1.81927i	0.0589848	−	0.0725968i
$629$			0.908302i			0.0362164i
$630$	−4.68642	−	15.5951i	−0.186712	−	0.621323i
$631$			19.1254i			0.761369i	0.924705	+	0.380684i	$0.124312\pi$
$631$			19.1254i			0.761369i	−0.924705	+	0.380684i	$0.875688\pi$
$632$	13.7618	−	14.4307i	0.547414	−	0.574024i
$633$	11.1176	−	2.08791i	0.441885	−	0.0829870i
$634$	−11.3386	−	23.8220i	−0.450312	−	0.946092i
$635$	−11.0977	−	19.2217i	−0.440397	−	0.762791i
$636$	16.2391	−	0.437311i	0.643924	−	0.0173405i
$637$	0.515084	−	0.892151i	0.0204084	−	0.0353483i
$638$	30.6371	+	2.43644i	1.21294	+	0.0964595i
$639$	11.9157	+	9.55559i	0.471379	+	0.378013i
$640$	−36.8944	−	22.9008i	−1.45838	−	0.905234i
$641$	12.4751	+	7.20251i	0.492737	+	0.284482i	0.725709	−	0.688001i	$-0.241512\pi$
$641$	12.4751	+	7.20251i	0.492737	+	0.284482i	−0.232972	+	0.972483i	$0.574845\pi$
$642$	−19.4080	−	26.6253i	−0.765973	−	1.05082i
$643$	7.01273	−	4.04880i	0.276555	−	0.159669i	−0.355308	−	0.934749i	$-0.615624\pi$
$643$	7.01273	−	4.04880i	0.276555	−	0.159669i	0.631863	+	0.775080i	$0.282291\pi$
$644$	−2.68050	+	1.02391i	−0.105627	+	0.0403479i
$645$	−38.0318	−	13.3660i	−1.49750	−	0.526285i
$646$	0.916174	+	0.630774i	0.0360464	+	0.0248175i
$647$	−16.2684			−0.639576			−0.319788	−	0.947489i	$-0.603612\pi$
$647$	−16.2684			−0.639576			−0.319788	+	0.947489i	$0.603612\pi$
$648$	25.4512	+	0.486540i	0.999817	+	0.0191131i
$649$	49.5914			1.94663
$650$	11.6777	+	8.03993i	0.458036	+	0.315352i
$651$	11.4238	+	4.01480i	0.447734	+	0.157352i
$652$	29.2662	−	11.1793i	1.14615	−	0.437815i
$653$	26.4229	−	15.2553i	1.03401	−	0.596985i	0.115878	−	0.993263i	$-0.463032\pi$
$653$	26.4229	−	15.2553i	1.03401	−	0.596985i	0.918131	+	0.396278i	$0.129698\pi$
$654$	−7.22873	−	9.91689i	−0.282666	−	0.387781i
$655$	−28.0631	−	16.2023i	−1.09652	−	0.633074i
$656$	−11.7595	+	35.7927i	−0.459131	+	1.39747i
$657$	−19.0050	−	15.2407i	−0.741457	−	0.594598i
$658$	5.02672	+	0.399753i	0.195962	+	0.0155840i
$659$	−16.4657	+	28.5194i	−0.641413	+	1.11096i	0.343705	+	0.939078i	$0.388318\pi$
$659$	−16.4657	+	28.5194i	−0.641413	+	1.11096i	−0.985118	+	0.171882i	$0.945015\pi$
$660$	77.7135	−	2.09278i	3.02500	−	0.0814614i
$661$	14.0288	+	24.2985i	0.545655	+	0.945103i	0.998565	+	0.0535464i	$0.0170525\pi$
$661$	14.0288	+	24.2985i	0.545655	+	0.945103i	−0.452910	+	0.891556i	$0.649614\pi$
$662$	10.0831	+	21.1843i	0.391892	+	0.823352i
$663$	0.332955	−	0.0625297i	0.0129309	−	0.00242845i
$664$	31.0289	+	29.5905i	1.20416	+	1.14834i
$665$			15.8999i			0.616573i
$666$	−5.84121	−	19.4379i	−0.226342	−	0.753202i
$667$		−	5.33244i		−	0.206473i
$668$	−19.8751	+	24.4617i	−0.768989	+	0.946450i
$669$	−28.1460	−	32.7963i	−1.08819	−	1.26798i
$670$	−3.98923	+	1.89876i	−0.154118	+	0.0733555i
$671$	−2.79097	−	4.83410i	−0.107744	−	0.186618i
$672$	−7.27006	−	6.56858i	−0.280449	−	0.253388i
$673$	−19.1422	+	33.1553i	−0.737877	+	1.27804i	0.215572	+	0.976488i	$0.430838\pi$
$673$	−19.1422	+	33.1553i	−0.737877	+	1.27804i	−0.953449	+	0.301553i	$0.902495\pi$
$674$	0.667928	−	8.39891i	0.0257276	−	0.323514i
$675$	50.5388	−	1.68465i	1.94524	−	0.0648421i
$676$	23.5774	+	3.77388i	0.906823	+	0.145149i
$677$	20.7627	+	11.9873i	0.797973	+	0.460710i	0.842762	−	0.538286i	$-0.180928\pi$
$677$	20.7627	+	11.9873i	0.797973	+	0.460710i	−0.0447886	+	0.998996i	$0.514261\pi$
$678$	−9.57707	−	4.24608i	−0.367805	−	0.163070i
$679$	−2.19154	+	1.26529i	−0.0841037	+	0.0485573i
$680$	−1.97772	+	0.580548i	−0.0758422	+	0.0222630i
$681$	13.6286	−	11.6961i	0.522249	−	0.448197i
$682$	−32.7821	+	47.6147i	−1.25529	+	1.82326i
$683$	−29.2758			−1.12021			−0.560104	−	0.828422i	$-0.689239\pi$
$683$	−29.2758			−1.12021			−0.560104	+	0.828422i	$0.689239\pi$
$684$	−23.6628	−	7.60688i	−0.904770	−	0.290856i
$685$	−77.7464			−2.97054
$686$	−0.801973	+	1.16483i	−0.0306195	+	0.0444736i
$687$	7.05505	+	37.5663i	0.269167	+	1.43324i
$688$	−23.7419	+	4.96528i	−0.905150	+	0.189299i
$689$	−4.18378	+	2.41550i	−0.159389	+	0.0920234i
$690$	−1.43088	−	13.4124i	−0.0544725	−	0.510600i
$691$	12.8452	+	7.41617i	0.488654	+	0.282125i	0.724016	−	0.689783i	$-0.242294\pi$
$691$	12.8452	+	7.41617i	0.488654	+	0.282125i	−0.235362	+	0.971908i	$0.575628\pi$
$692$	−3.91437	+	24.4551i	−0.148802	+	0.929645i
$693$	17.3381	+	2.66154i	0.658621	+	0.101103i
$694$	−1.44340	+	18.1501i	−0.0547907	+	0.688969i
$695$	−4.11707	+	7.13098i	−0.156170	+	0.270494i
$696$	16.2243	−	8.26517i	0.614982	−	0.313290i
$697$	0.894143	+	1.54870i	0.0338681	+	0.0586613i
$698$	−21.2755	+	10.1265i	−0.805290	+	0.383295i
$699$	13.1751	−	37.4887i	0.498328	−	1.41795i
$700$	−15.1057	−	12.2733i	−0.570941	−	0.463889i
$701$		−	2.86753i		−	0.108305i	−0.998533	−	0.0541525i	$-0.982754\pi$
$701$		−	2.86753i		−	0.108305i	0.998533	−	0.0541525i	$-0.0172457\pi$
$702$	−6.72319	+	3.47936i	−0.253751	+	0.131320i
$703$			19.8179i			0.747445i
$704$	39.3548	−	25.2833i	1.48324	−	0.952901i
$705$	−7.85940	+	22.3633i	−0.296002	+	0.842251i
$706$	17.8248	+	37.4494i	0.670846	+	1.40943i
$707$	1.44215	+	2.49788i	0.0542378	+	0.0939425i
$708$	25.0396	−	15.3699i	0.941044	−	0.577635i
$709$	6.21193	−	10.7594i	0.233294	−	0.404077i	−0.725482	−	0.688241i	$-0.758383\pi$
$709$	6.21193	−	10.7594i	0.233294	−	0.404077i	0.958775	+	0.284165i	$0.0917163\pi$
$710$	27.5487	+	2.19083i	1.03389	+	0.0822203i
$711$	7.67352	+	19.7092i	0.287780	+	0.739154i
$712$	6.91847	+	1.67896i	0.259281	+	0.0629217i
$713$	8.68623	+	5.01500i	0.325302	+	0.187813i
$714$	−0.462447	+	0.0493355i	−0.0173066	+	0.00184633i
$715$	−20.0217	+	11.5596i	−0.748771	+	0.432303i
$716$	−10.4224	−	27.2847i	−0.389503	−	1.01968i
$717$	−4.57340	−	24.3522i	−0.170797	−	0.909449i
$718$	2.79438	+	1.92390i	0.104285	+	0.0717992i
$719$	37.0087			1.38019			0.690095	−	0.723719i	$-0.257569\pi$
$719$	37.0087			1.38019			0.690095	+	0.723719i	$0.257569\pi$
$720$	38.5903	−	25.1424i	1.43817	−	0.937003i
$721$	10.9141			0.406462
$722$	−2.14223	−	1.47490i	−0.0797254	−	0.0548899i
$723$	−10.6055	+	9.10168i	−0.394422	+	0.338495i
$724$	−4.84375	−	12.6804i	−0.180016	−	0.471264i
$725$	31.3241	−	18.0850i	1.16335	−	0.671660i
$726$	−23.0213	+	51.9248i	−0.854402	+	1.92711i
$727$	3.21382	+	1.85550i	0.119194	+	0.0688167i	0.558412	−	0.829564i	$-0.311411\pi$
$727$	3.21382	+	1.85550i	0.119194	+	0.0688167i	−0.439218	+	0.898381i	$0.644744\pi$
$728$	2.83157	+	0.687159i	0.104945	+	0.0254678i
$729$	−11.9129	+	24.2298i	−0.441218	+	0.897400i
$730$	−43.9390	−	3.49427i	−1.62625	−	0.129329i
$731$	−0.575657	+	0.997068i	−0.0212915	+	0.0368779i
$732$	−2.90744	−	1.57581i	−0.107462	−	0.0582438i
$733$	−21.5278	−	37.2872i	−0.795147	−	1.37723i	−0.922746	−	0.385409i	$-0.874060\pi$
$733$	−21.5278	−	37.2872i	−0.795147	−	1.37723i	0.127599	−	0.991826i	$-0.459273\pi$
$734$	−12.0097	−	25.2321i	−0.443288	−	0.931334i
$735$	−4.32950	−	5.04482i	−0.159696	−	0.186081i
$736$	−4.91425	−	6.45895i	−0.181142	−	0.238080i
$737$		−	4.75916i		−	0.175306i
$738$	−29.0944	−	27.3924i	−1.07098	−	1.00833i
$739$			23.8378i			0.876886i	0.898759	+	0.438443i	$0.144470\pi$
$739$			23.8378i			0.876886i	−0.898759	+	0.438443i	$0.855530\pi$
$740$	−28.5015	−	23.1574i	−1.04773	−	0.851283i
$741$	7.26460	−	1.36431i	0.266872	−	0.0501192i
$742$	5.98829	−	2.85025i	0.219837	−	0.104636i
$743$	4.54659	+	7.87492i	0.166798	+	0.288903i	0.937292	−	0.348544i	$-0.113324\pi$
$743$	4.54659	+	7.87492i	0.166798	+	0.288903i	−0.770494	+	0.637447i	$0.779991\pi$
$744$	−1.79503	+	34.2016i	−0.0658090	+	1.25389i
$745$	22.6477	−	39.2270i	0.829749	−	1.43717i
$746$	1.93392	−	24.3182i	0.0708058	−	0.890352i
$747$	−42.3787	+	16.4996i	−1.55056	+	0.603688i
$748$	0.350922	−	2.19240i	0.0128310	−	0.0801619i
$749$	−11.6489	−	6.72550i	−0.425642	−	0.245745i
$750$	35.9478	−	26.2035i	1.31263	−	0.956817i
$751$	39.4261	−	22.7626i	1.43868	−	0.830621i	0.440920	−	0.897547i	$-0.354652\pi$
$751$	39.4261	−	22.7626i	1.43868	−	0.830621i	0.997758	+	0.0669258i	$0.0213191\pi$
$752$	2.91966	+	13.9606i	0.106469	+	0.509090i
$753$	10.3124	+	3.62422i	0.375806	+	0.132074i
$754$	−3.07066	+	4.46001i	−0.111827	+	0.162424i
$755$	−51.1736			−1.86240
$756$	9.57920	−	4.02975i	0.348392	−	0.146560i
$757$	−45.3678			−1.64892			−0.824461	−	0.565919i	$-0.808521\pi$
$757$	−45.3678			−1.64892			−0.824461	+	0.565919i	$0.808521\pi$
$758$	−21.1034	+	30.6519i	−0.766511	+	1.11333i
$759$	13.7079	+	4.81754i	0.497567	+	0.174866i
$760$	−43.1511	+	12.6667i	−1.56525	+	0.459471i
$761$	36.3207	−	20.9698i	1.31662	−	0.760153i	0.333440	−	0.942771i	$-0.391791\pi$
$761$	36.3207	−	20.9698i	1.31662	−	0.760153i	0.983184	+	0.182618i	$0.0584573\pi$
$762$	11.4466	−	8.34378i	0.414666	−	0.302263i
$763$	−4.33877	−	2.50499i	−0.157074	−	0.0906867i
$764$	−43.5172	−	6.96551i	−1.57440	−	0.252003i
$765$	0.331713	−	2.16089i	0.0119931	−	0.0781271i
$766$	−2.04395	+	25.7018i	−0.0738510	+	0.928645i
$767$	−4.36864	+	7.56670i	−0.157742	+	0.273218i
$768$	12.0349	−	24.9632i	0.434271	−	0.900782i
$769$	4.76432	+	8.25204i	0.171806	+	0.297576i	0.939051	−	0.343777i	$-0.111707\pi$
$769$	4.76432	+	8.25204i	0.171806	+	0.297576i	−0.767246	+	0.641353i	$0.778373\pi$
$770$	28.6574	−	13.6401i	1.03274	−	0.491554i
$771$	−24.4789	+	4.59719i	−0.881585	+	0.165564i
$772$	−7.53655	+	9.27576i	−0.271246	+	0.333842i
$773$		−	4.15447i		−	0.149426i	−0.997205	−	0.0747129i	$-0.976196\pi$
$773$		−	4.15447i		−	0.149426i	0.997205	−	0.0747129i	$-0.0238041\pi$
$774$	5.90715	−	25.0395i	0.212328	−	0.900026i
$775$			68.0335i			2.44384i
$776$	−5.17978	−	4.93967i	−0.185943	−	0.177324i
$777$	−5.39634	−	6.28793i	−0.193593	−	0.225578i
$778$	20.1405	+	42.3146i	0.722072	+	1.51705i
$779$	19.5089	+	33.7905i	0.698980	+	1.21067i
$780$	−6.52667	+	12.0420i	−0.233692	+	0.431171i
$781$	−14.8847	+	25.7810i	−0.532615	+	0.922516i
$782$	−0.384018	−	0.0305393i	−0.0137325	−	0.00109208i
$783$	0.643411	+	19.3021i	0.0229936	+	0.689801i
$784$	−3.80016	−	1.24852i	−0.135720	−	0.0445900i
$785$	3.89580	+	2.24924i	0.139047	+	0.0802789i
$786$	8.38191	−	18.9055i	0.298973	−	0.674336i
$787$	−5.57632	+	3.21949i	−0.198774	+	0.114762i	−0.596084	−	0.802922i	$-0.703277\pi$
$787$	−5.57632	+	3.21949i	−0.198774	+	0.114762i	0.397309	+	0.917685i	$0.369944\pi$
$788$	−2.48040	+	0.947480i	−0.0883607	+	0.0337526i
$789$	10.4084	−	8.93256i	0.370549	−	0.318008i
$790$	31.5199	+	21.7011i	1.12143	+	0.772089i
$791$	−4.27687			−0.152068
$792$	6.58928	+	49.1745i	0.234140	+	1.74734i
$793$	0.983454			0.0349235
$794$	8.44041	+	5.81111i	0.299539	+	0.206229i
$795$	5.75427	+	30.6400i	0.204083	+	1.08669i
$796$	7.60357	−	2.90446i	0.269501	−	0.102946i
$797$	−0.509800	+	0.294333i	−0.0180580	+	0.0104258i	−0.509002	−	0.860765i	$-0.669985\pi$
$797$	−0.509800	+	0.294333i	−0.0180580	+	0.0104258i	0.490944	+	0.871191i	$0.336652\pi$
$798$	−10.0899	+	1.07643i	−0.357180	+	0.0381052i
$799$	0.586291	+	0.338495i	0.0207415	+	0.0119751i
$800$	21.2748	−	50.7731i	0.752180	−	1.79510i
$801$	−4.72409	+	5.89089i	−0.166917	+	0.208144i
$802$	30.2778	+	2.40786i	1.06915	+	0.0850244i
$803$	23.7404	−	41.1195i	0.837779	−	1.45108i
$804$	−1.47501	−	2.40298i	−0.0520195	−	0.0847466i
$805$	−2.75332	−	4.76889i	−0.0970418	−	0.168081i
$806$	−4.37723	−	9.19643i	−0.154181	−	0.323930i
$807$	−4.93444	+	14.0406i	−0.173701	+	0.494252i
$808$	−5.63015	+	5.90383i	−0.198068	+	0.207696i
$809$			39.3028i			1.38181i	0.722944	+	0.690907i	$0.242789\pi$
$809$			39.3028i			1.38181i	−0.722944	+	0.690907i	$0.757211\pi$
$810$	6.79775	+	48.3768i	0.238849	+	1.69979i
$811$			8.97336i			0.315097i	0.987511	+	0.157549i	$0.0503591\pi$
$811$			8.97336i			0.315097i	−0.987511	+	0.157549i	$0.949641\pi$
$812$	4.68751	−	5.76925i	0.164499	−	0.202461i
$813$	−1.54630	+	4.39987i	−0.0542310	+	0.154310i
$814$	35.7189	−	17.0011i	1.25195	−	0.595890i
$815$	30.0613	+	52.0677i	1.05300	+	1.82385i
$816$	−0.502302	−	1.21574i	−0.0175841	−	0.0425594i
$817$	−12.5600	+	21.7546i	−0.439420	+	0.761097i
$818$	0.501251	−	6.30302i	0.0175258	−	0.220380i
$819$	−1.93346	+	2.41100i	−0.0675605	+	0.0842473i
$820$	−71.3929	−	11.4274i	−2.49315	−	0.399062i
$821$	20.5858	+	11.8852i	0.718449	+	0.414797i	0.814182	−	0.580610i	$-0.197186\pi$
$821$	20.5858	+	11.8852i	0.718449	+	0.414797i	−0.0957326	+	0.995407i	$0.530519\pi$
$822$	−5.26345	−	49.3371i	−0.183584	−	1.72083i
$823$	−29.7775	+	17.1921i	−1.03798	+	0.599278i	−0.919260	−	0.393650i	$-0.871212\pi$
$823$	−29.7775	+	17.1921i	−1.03798	+	0.599278i	−0.118719	+	0.992928i	$0.537879\pi$
$824$	8.69474	+	29.6199i	0.302896	+	1.03186i
$825$	18.1911	+	96.8627i	0.633331	+	3.37233i
$826$	6.80186	−	9.87944i	0.236667	−	0.343750i
$827$	19.5161			0.678640			0.339320	−	0.940671i	$-0.389803\pi$
$827$	19.5161			0.678640			0.339320	+	0.940671i	$0.389803\pi$
$828$	8.41447	−	1.81604i	0.292423	−	0.0631117i
$829$	27.1294			0.942244			0.471122	−	0.882068i	$-0.343849\pi$
$829$	27.1294			0.942244			0.471122	+	0.882068i	$0.343849\pi$
$830$	−46.6615	+	67.7740i	−1.61965	+	2.35247i
$831$	−26.8244	+	23.0209i	−0.930530	+	0.798586i
$832$	0.390883	+	8.23206i	0.0135514	+	0.285395i
$833$	−0.164427	+	0.0949323i	−0.00569707	+	0.00328921i
$834$	−4.80398	−	2.12988i	−0.166348	−	0.0737519i
$835$	−52.3824	−	30.2430i	−1.81277	−	1.04660i
$836$	7.65663	−	47.8350i	0.264810	−	1.65441i
$837$	−32.0471	−	17.1050i	−1.10771	−	0.591234i
$838$	1.61844	−	20.3512i	0.0559081	−	0.703021i
$839$	3.29790	−	5.71213i	0.113856	−	0.197205i	−0.803466	−	0.595351i	$-0.797013\pi$
$839$	3.29790	−	5.71213i	0.113856	−	0.197205i	0.917322	+	0.398146i	$0.130346\pi$
$840$	10.2421	−	15.7689i	0.353387	−	0.544078i
$841$	−7.59287	−	13.1512i	−0.261823	−	0.453491i
$842$	15.7609	−	7.50172i	0.543156	−	0.258526i
$843$	−30.7313	−	35.8088i	−1.05844	−	1.23332i
$844$	10.1375	+	8.23674i	0.348949	+	0.283520i
$845$			45.8231i			1.57636i
$846$	−14.7236	−	3.47349i	−0.506208	−	0.119421i
$847$			23.1883i			0.796758i
$848$	12.5059	+	13.9811i	0.429456	+	0.480111i
$849$	13.6756	−	2.56830i	0.469344	−	0.0881439i
$850$	−1.12300	−	2.35940i	−0.0385187	−	0.0809266i
$851$	−3.43177	−	5.94400i	−0.117640	−	0.203758i
$852$	0.474778	+	17.6305i	0.0162656	+	0.604010i
$853$	26.3454	−	45.6316i	0.902051	−	1.56240i	0.0772227	−	0.997014i	$-0.475395\pi$
$853$	26.3454	−	45.6316i	0.902051	−	1.56240i	0.824828	−	0.565384i	$-0.191272\pi$
$854$	−1.34584	−	0.107028i	−0.0460536	−	0.00366244i
$855$	7.23751	−	47.1475i	0.247518	−	1.61241i
$856$	8.97232	−	36.9721i	0.306667	−	1.26368i
$857$	22.9985	+	13.2782i	0.785615	+	0.453575i	0.838417	−	0.545030i	$-0.183482\pi$
$857$	22.9985	+	13.2782i	0.785615	+	0.453575i	−0.0528014	+	0.998605i	$0.516815\pi$
$858$	−8.69106	−	11.9230i	−0.296708	−	0.407045i
$859$	−1.60435	+	0.926272i	−0.0547398	+	0.0316040i	−0.527120	−	0.849791i	$-0.676728\pi$
$859$	−1.60435	+	0.926272i	−0.0547398	+	0.0316040i	0.472380	+	0.881395i	$0.343395\pi$
$860$	−16.6103	−	43.4840i	−0.566406	−	1.48279i
$861$	−15.3909	−	5.40902i	−0.524522	−	0.184339i
$862$	−38.6029	−	26.5776i	−1.31482	−	0.905237i
$863$	−14.3763			−0.489376			−0.244688	−	0.969602i	$-0.578685\pi$
$863$	−14.3763			−0.489376			−0.244688	+	0.969602i	$0.578685\pi$
$864$	18.5677	+	22.7868i	0.631686	+	0.775224i
$865$	−47.5290			−1.61603
$866$	3.06242	+	2.10844i	0.104065	+	0.0716476i
$867$	27.7204	+	9.74210i	0.941433	+	0.330859i
$868$	4.98931	+	13.0615i	0.169348	+	0.443336i
$869$	−35.6997	+	20.6113i	−1.21103	+	0.699189i
$870$	20.5833	+	28.2376i	0.697839	+	0.957346i
$871$	0.726157	+	0.419247i	0.0246049	+	0.0142056i
$872$	3.34184	−	13.7707i	0.113169	−	0.466333i
$873$	7.07445	−	2.75434i	0.239434	−	0.0932204i
$874$	−8.37873	−	0.666323i	−0.283415	−	0.0225387i
$875$	9.08036	−	15.7276i	0.306972	−	0.531692i
$876$	−0.757250	−	28.1198i	−0.0255851	−	0.950080i
$877$	−12.7181	−	22.0285i	−0.429461	−	0.743849i	0.567364	−	0.823467i	$-0.307963\pi$
$877$	−12.7181	−	22.0285i	−0.429461	−	0.743849i	−0.996825	+	0.0796183i	$0.974630\pi$
$878$	14.7403	+	30.9689i	0.497460	+	1.04515i
$879$	50.7554	−	9.53199i	1.71194	−	0.321506i
$880$	59.8480	+	66.9073i	2.01747	+	2.25544i
$881$			48.0956i			1.62038i	0.586166	+	0.810191i	$0.300637\pi$
$881$			48.0956i			1.62038i	−0.586166	+	0.810191i	$0.699363\pi$
$882$	2.90829	−	3.08899i	0.0979271	−	0.104012i
$883$		−	12.3742i		−	0.416423i	−0.978084	−	0.208212i	$-0.933236\pi$
$883$		−	12.3742i		−	0.416423i	0.978084	−	0.208212i	$-0.0667643\pi$
$884$	0.303604	+	0.246678i	0.0102113	+	0.00829667i
$885$	36.7202	+	42.7872i	1.23434	+	1.43828i
$886$	5.45306	−	2.59550i	0.183199	−	0.0871974i
$887$	−10.9124	−	18.9008i	−0.366401	−	0.634625i	0.622599	−	0.782541i	$-0.286077\pi$
$887$	−10.9124	−	18.9008i	−0.366401	−	0.634625i	−0.989000	+	0.147916i	$0.952743\pi$
$888$	12.7659	−	19.6545i	0.428396	−	0.659562i
$889$	2.89139	−	5.00803i	0.0969741	−	0.167964i
$890$	−1.08310	+	13.6195i	−0.0363056	+	0.456527i
$891$	−50.2006	−	15.7843i	−1.68178	−	0.528795i
$892$	7.88738	−	49.2766i	0.264089	−	1.64990i
$893$	12.7920	+	7.38549i	0.428069	+	0.247146i
$894$	26.4263	+	11.7163i	0.883829	+	0.391853i
$895$	48.5423	−	28.0259i	1.62259	−	0.936804i
$896$	0.360972	−	11.3079i	0.0120592	−	0.377772i
$897$	−1.94263	+	1.66718i	−0.0648626	+	0.0556655i
$898$	26.3713	−	38.3032i	0.880020	−	1.27819i
$899$	−25.9838			−0.866608
$900$	39.2056	+	43.2697i	1.30685	+	1.44232i
$901$	0.890377			0.0296628
$902$	44.1664	−	64.1499i	1.47058	−	2.13596i
$903$	−1.93859	−	10.3225i	−0.0645121	−	0.343511i
$904$	−3.40718	−	11.6071i	−0.113321	−	0.386045i
$905$	22.5598	−	13.0249i	0.749913	−	0.432962i
$906$	−3.46446	−	32.4742i	−0.115099	−	1.07888i
$907$	−14.3578	−	8.28950i	−0.476744	−	0.275248i	0.242315	−	0.970198i	$-0.422093\pi$
$907$	−14.3578	−	8.28950i	−0.476744	−	0.275248i	−0.719059	+	0.694949i	$0.755427\pi$
$908$	20.4770	+	3.27762i	0.679553	+	0.108772i
$909$	−3.13935	−	8.06334i	−0.104126	−	0.267444i
$910$	−0.443288	+	5.57415i	−0.0146948	+	0.184781i
$911$	5.19404	−	8.99634i	0.172086	−	0.298062i	−0.767063	−	0.641572i	$-0.778283\pi$
$911$	5.19404	−	8.99634i	0.172086	−	0.298062i	0.939149	+	0.343510i	$0.111616\pi$
$912$	−10.9595	−	26.5257i	−0.362906	−	0.878354i
$913$	−44.3183	−	76.7615i	−1.46672	−	2.54043i
$914$	−19.0891	+	9.08587i	−0.631412	+	0.300534i
$915$	2.10425	−	5.98747i	0.0695643	−	0.197940i
$916$	−27.8319	+	34.2547i	−0.919593	+	1.13181i
$917$		−	8.44268i		−	0.278802i
$918$	1.39374	+	0.0642090i	0.0460001	+	0.00211921i
$919$			47.3884i			1.56320i	0.623780	+	0.781600i	$0.285596\pi$
$919$			47.3884i			1.56320i	−0.623780	+	0.781600i	$0.714404\pi$
$920$	10.7489	−	11.2714i	0.354382	−	0.371608i
$921$	−11.3291	+	32.2360i	−0.373306	+	1.06221i
$922$	−1.72941	−	3.63344i	−0.0569551	−	0.119661i
$923$	−2.62246	−	4.54223i	−0.0863192	−	0.149509i
$924$	10.5960	+	17.2622i	0.348581	+	0.567886i
$925$	23.2777	−	40.3182i	0.765367	−	1.32566i
$926$	−35.1238	−	2.79324i	−1.15424	−	0.0917917i
$927$	−32.3632	−	4.96799i	−1.06295	−	0.163170i
$928$	19.3916	+	8.12542i	0.636560	+	0.266730i
$929$	−37.3688	−	21.5749i	−1.22603	−	0.707849i	−0.259833	−	0.965654i	$-0.583668\pi$
$929$	−37.3688	−	21.5749i	−1.22603	−	0.707849i	−0.966197	+	0.257805i	$0.917001\pi$
$930$	−65.3555	+	6.97235i	−2.14309	+	0.228632i
$931$	−3.58757	+	2.07129i	−0.117578	+	0.0678837i
$932$	42.8630	−	16.3731i	1.40402	−	0.536318i
$933$	−4.75716	−	25.3307i	−0.155742	−	0.829289i
$934$	−7.18307	−	4.94545i	−0.235037	−	0.161820i
$935$	4.26096			0.139348
$936$	−8.08356	−	3.32651i	−0.264219	−	0.108731i
$937$	−14.1414			−0.461978			−0.230989	−	0.972956i	$-0.574196\pi$
$937$	−14.1414			−0.461978			−0.230989	+	0.972956i	$0.574196\pi$
$938$	−0.948104	−	0.652758i	−0.0309567	−	0.0213133i
$939$	32.4398	−	27.8401i	1.05863	−	0.908526i
$940$	−25.5693	+	9.76711i	−0.833977	+	0.318568i
$941$	−7.29412	+	4.21126i	−0.237781	+	0.137283i	−0.614157	−	0.789184i	$-0.710504\pi$
$941$	−7.29412	+	4.21126i	−0.237781	+	0.137283i	0.376375	+	0.926467i	$0.377170\pi$
$942$	−1.16360	+	2.62451i	−0.0379121	+	0.0855112i
$943$	−11.7027	−	6.75655i	−0.381092	−	0.220024i
$944$	32.2307	+	10.5892i	1.04902	+	0.344649i
$945$	10.5418	+	16.9300i	0.342923	+	0.550733i
$946$	49.9844	+	3.97504i	1.62513	+	0.129240i
$947$	23.2734	−	40.3107i	0.756284	−	1.30992i	−0.188450	−	0.982083i	$-0.560346\pi$
$947$	23.2734	−	40.3107i	0.756284	−	1.30992i	0.944733	−	0.327839i	$-0.106320\pi$
$948$	−11.6374	+	21.4714i	−0.377964	+	0.697358i
$949$	4.18270	+	7.24465i	0.135776	+	0.235171i
$950$	−24.5023	−	51.4787i	−0.794961	−	1.67019i
$951$	21.0435	+	24.5203i	0.682382	+	0.795126i
$952$	−0.388630	−	0.370614i	−0.0125956	−	0.0120117i
$953$			21.4063i			0.693419i	0.937973	+	0.346710i	$0.112701\pi$
$953$			21.4063i			0.693419i	−0.937973	+	0.346710i	$0.887299\pi$
$954$	−19.0543	+	5.72594i	−0.616905	+	0.185384i
$955$		−	84.5764i		−	2.73683i
$956$	18.0419	−	22.2055i	0.583517	−	0.718176i
$957$	−36.9944	+	6.94764i	−1.19586	+	0.224585i
$958$	−38.6908	+	18.4157i	−1.25004	+	0.594984i
$959$	−10.1280	−	17.5423i	−0.327051	−	0.566470i
$960$	50.9548	+	15.2340i	1.64456	+	0.491674i
$961$	8.93698	−	15.4793i	0.288290	−	0.499332i
$962$	−0.552519	+	6.94769i	−0.0178139	+	0.224002i
$963$	31.4807	+	25.2454i	1.01445	+	0.813521i
$964$	−15.9348	−	2.55057i	−0.513224	−	0.0821484i
$965$	−19.8632	−	11.4680i	−0.639420	−	0.369169i
$966$	2.83989	−	2.07009i	0.0913720	−	0.0666039i
$967$	7.92319	−	4.57446i	0.254793	−	0.147105i	−0.367164	−	0.930156i	$-0.619671\pi$
$967$	7.92319	−	4.57446i	0.254793	−	0.147105i	0.621957	+	0.783052i	$0.286338\pi$
$968$	−62.9310	+	18.4730i	−2.02268	+	0.593745i
$969$	−1.28524	−	0.451689i	−0.0412880	−	0.0145103i
$970$	7.78940	−	11.3138i	0.250103	−	0.363264i
$971$	−22.8058			−0.731872			−0.365936	−	0.930640i	$-0.619251\pi$
$971$	−22.8058			−0.731872			−0.365936	+	0.930640i	$0.619251\pi$
$972$	−30.2392	+	7.58890i	−0.969922	+	0.243414i
$973$	−2.14533			−0.0687761
$974$	−14.3606	+	20.8582i	−0.460144	+	0.668340i
$975$	−16.3819	−	5.75728i	−0.524640	−	0.184381i
$976$	−0.781699	−	3.73775i	−0.0250216	−	0.119643i
$977$	34.1902	−	19.7397i	1.09384	−	0.631529i	0.159244	−	0.987239i	$-0.449094\pi$
$977$	34.1902	−	19.7397i	1.09384	−	0.631529i	0.934596	+	0.355710i	$0.115761\pi$
$978$	−31.0065	+	22.6016i	−0.991477	+	0.722719i
$979$	−12.7456	−	7.35867i	−0.407351	−	0.235184i
$980$	1.21326	−	7.57987i	0.0387562	−	0.242130i
$981$	11.7254	+	9.40293i	0.374362	+	0.300212i
$982$	0.886595	−	11.1485i	0.0282924	−	0.355765i
$983$	−9.06226	+	15.6963i	−0.289041	+	0.500634i	−0.973581	−	0.228341i	$-0.926670\pi$
$983$	−9.06226	+	15.6963i	−0.289041	+	0.500634i	0.684540	+	0.728975i	$0.260003\pi$
$984$	2.41839	−	46.0789i	0.0770955	−	1.46894i
$985$	−2.54779	−	4.41290i	−0.0811792	−	0.140607i
$986$	0.901115	−	0.428905i	0.0286974	−	0.0136591i
$987$	−6.06978	+	1.13992i	−0.193203	+	0.0362840i
$988$	6.62421	+	5.38216i	0.210744	+	0.171229i
$989$		−	8.69986i		−	0.276639i
$990$	−91.1855	+	27.4019i	−2.89807	+	0.870888i
$991$		−	2.44943i		−	0.0778088i	−0.999243	−	0.0389044i	$-0.987613\pi$
$991$		−	2.44943i		−	0.0778088i	0.999243	−	0.0389044i	$-0.0123868\pi$
$992$	−31.4731	+	23.9461i	−0.999270	+	0.760288i
$993$	−18.7135	−	21.8053i	−0.593854	−	0.691972i
$994$	3.09445	+	6.50134i	0.0981500	+	0.206210i
$995$	7.81014	+	13.5276i	0.247598	+	0.428852i
$996$	−46.1677	−	25.0226i	−1.46288	−	0.792872i
$997$	−7.06115	+	12.2303i	−0.223629	+	0.387336i	−0.955907	−	0.293669i	$-0.905124\pi$
$997$	−7.06115	+	12.2303i	−0.223629	+	0.387336i	0.732278	+	0.681005i	$0.238457\pi$
$998$	−46.0560	−	3.66263i	−1.45788	−	0.115939i
$999$	13.1394	+	21.1017i	0.415711	+	0.667629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.9	yes	72
3.2	odd	2		756.2.ba.a.575.28		72
4.3	odd	2	inner	252.2.ba.a.155.4	✓	72
9.4	even	3		756.2.ba.a.71.33		72
9.5	odd	6	inner	252.2.ba.a.239.4	yes	72
12.11	even	2		756.2.ba.a.575.33		72
36.23	even	6	inner	252.2.ba.a.239.9	yes	72
36.31	odd	6		756.2.ba.a.71.28		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.4	✓	72	4.3	odd	2	inner
252.2.ba.a.155.9	yes	72	1.1	even	1	trivial
252.2.ba.a.239.4	yes	72	9.5	odd	6	inner
252.2.ba.a.239.9	yes	72	36.23	even	6	inner
756.2.ba.a.71.28		72	36.31	odd	6
756.2.ba.a.71.33		72	9.4	even	3
756.2.ba.a.575.28		72	3.2	odd	2
756.2.ba.a.575.33		72	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16483 - 0.801973i) q^{2} +(1.63407 + 0.574282i) q^{3} +(0.713677 + 1.86833i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(-1.44287 - 1.97943i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +O(q^{10})\)	\(q+(-1.16483 - 0.801973i) q^{2} +(1.63407 + 0.574282i) q^{3} +(0.713677 + 1.86833i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(-1.44287 - 1.97943i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +(5.41092 + 0.430306i) q^{10} +(-2.92354 + 5.06371i) q^{11} +(0.0932525 + 3.46285i) q^{12} +(-0.515084 - 0.892151i) q^{13} +(0.607789 + 1.27695i) q^{14} +(-6.53369 + 1.22704i) q^{15} +(-2.98133 + 2.66677i) q^{16} +0.189865i q^{17} +(-1.22100 - 4.06315i) q^{18} +4.14257i q^{19} +(-5.95773 - 4.84065i) q^{20} +(-1.12801 - 1.31438i) q^{21} +(7.46640 - 3.55379i) q^{22} +(-0.717351 - 1.24249i) q^{23} +(2.66849 - 4.10843i) q^{24} +(4.86580 - 8.42781i) q^{25} +(-0.115494 + 1.45229i) q^{26} +(2.74655 + 4.41095i) q^{27} +(0.316103 - 1.97486i) q^{28} +(3.21880 + 1.85838i) q^{29} +(8.59473 + 3.81055i) q^{30} +(-6.05438 + 3.49550i) q^{31} +(5.61143 - 0.715402i) q^{32} +(-7.68528 + 6.59555i) q^{33} +(0.152266 - 0.221161i) q^{34} +3.83818 q^{35} +(-1.83627 + 5.71210i) q^{36} +4.78395 q^{37} +(3.32223 - 4.82541i) q^{38} +(-0.329339 - 1.75365i) q^{39} +(3.05770 + 10.4165i) q^{40} +(8.15688 - 4.70938i) q^{41} +(0.259846 + 2.43567i) q^{42} +(5.25147 + 3.03194i) q^{43} +(-11.5472 - 1.84828i) q^{44} +(-11.3812 - 1.74710i) q^{45} +(-0.160848 + 2.02259i) q^{46} +(1.78283 - 3.08795i) q^{47} +(-6.40319 + 2.64558i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-12.4267 + 5.91476i) q^{50} +(-0.109036 + 0.310253i) q^{51} +(1.29923 - 1.59906i) q^{52} -4.68954i q^{53} +(0.338183 - 7.34068i) q^{54} -22.4421i q^{55} +(-1.95199 + 2.04688i) q^{56} +(-2.37901 + 6.76927i) q^{57} +(-2.25900 - 4.74610i) q^{58} +(-4.24070 - 7.34512i) q^{59} +(-6.95548 - 11.3314i) q^{60} +(-0.477327 + 0.826755i) q^{61} +(9.85564 + 0.783775i) q^{62} +(-1.08843 - 2.79559i) q^{63} +(-7.11012 - 3.66690i) q^{64} +(3.42423 + 1.97698i) q^{65} +(14.2415 - 1.51934i) q^{66} +(-0.704892 + 0.406970i) q^{67} +(-0.354730 + 0.135502i) q^{68} +(-0.458666 - 2.44228i) q^{69} +(-4.47084 - 3.07812i) q^{70} +5.09132 q^{71} +(6.71990 - 5.18101i) q^{72} -8.12043 q^{73} +(-5.57251 - 3.83660i) q^{74} +(12.7910 - 10.9773i) q^{75} +(-7.73970 + 2.95646i) q^{76} +(5.06371 - 2.92354i) q^{77} +(-1.02275 + 2.30683i) q^{78} +(6.10558 + 3.52506i) q^{79} +(4.79204 - 14.5857i) q^{80} +(1.95494 + 8.78511i) q^{81} +(-13.2782 - 1.05596i) q^{82} +(-7.57956 + 13.1282i) q^{83} +(1.65066 - 3.04554i) q^{84} +(-0.364367 - 0.631102i) q^{85} +(-3.68556 - 7.74325i) q^{86} +(4.19253 + 4.88523i) q^{87} +(11.9683 + 11.4135i) q^{88} +2.51704i q^{89} +(11.8561 + 11.1625i) q^{90} +1.03017i q^{91} +(1.80942 - 2.22699i) q^{92} +(-11.9007 + 2.23498i) q^{93} +(-4.55315 + 2.16717i) q^{94} +(-7.94997 - 13.7697i) q^{95} +(9.58035 + 2.05353i) q^{96} +(1.26529 - 2.19154i) q^{97} +(0.112112 - 1.40976i) q^{98} +(-16.3460 + 6.36410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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