LMFDB - Embedded newform 252.2.ba.a.155.12

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			155.12
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687522 + 1.23585i) q^{2} +(-1.67512 - 0.440428i) q^{3} +(-1.05463 - 1.69934i) q^{4} +(0.256612 - 0.148155i) q^{5} +(1.69598 - 1.76738i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +(2.61205 + 1.47554i) q^{9} +O(q^{10})$	\(q+(-0.687522 + 1.23585i) q^{2} +(-1.67512 - 0.440428i) q^{3} +(-1.05463 - 1.69934i) q^{4} +(0.256612 - 0.148155i) q^{5} +(1.69598 - 1.76738i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +(2.61205 + 1.47554i) q^{9} +(0.00667042 + 0.418992i) q^{10} +(-2.21618 + 3.83853i) q^{11} +(1.01819 + 3.31109i) q^{12} +(-0.227431 - 0.393922i) q^{13} +(-1.21333 + 0.726513i) q^{14} +(-0.495107 + 0.135158i) q^{15} +(-1.77552 + 3.58435i) q^{16} +6.53822i q^{17} +(-3.61938 + 2.21362i) q^{18} -1.47447i q^{19} +(-0.522396 - 0.279823i) q^{20} +(-1.23048 - 1.21898i) q^{21} +(-3.22016 - 5.37793i) q^{22} +(2.09235 + 3.62406i) q^{23} +(-4.79202 - 1.01812i) q^{24} +(-2.45610 + 4.25409i) q^{25} +(0.643190 - 0.0102397i) q^{26} +(-3.72562 - 3.62212i) q^{27} +(-0.0636644 - 1.99899i) q^{28} +(5.71624 + 3.30027i) q^{29} +(0.173362 - 0.704800i) q^{30} +(5.73985 - 3.31390i) q^{31} +(-3.20899 - 4.65858i) q^{32} +(5.40296 - 5.45393i) q^{33} +(-8.08023 - 4.49517i) q^{34} +0.296310 q^{35} +(-0.247295 - 5.99490i) q^{36} -7.53908 q^{37} +(1.82221 + 1.01373i) q^{38} +(0.207480 + 0.760033i) q^{39} +(0.704976 - 0.453216i) q^{40} +(1.57065 - 0.906813i) q^{41} +(2.35246 - 0.682609i) q^{42} +(8.80511 + 5.08363i) q^{43} +(8.86022 - 0.282183i) q^{44} +(0.888890 - 0.00834685i) q^{45} +(-5.91731 + 0.0942044i) q^{46} +(-3.32792 + 5.76413i) q^{47} +(4.55285 - 5.22222i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-3.56878 - 5.96014i) q^{50} +(2.87961 - 10.9523i) q^{51} +(-0.429553 + 0.801924i) q^{52} -1.22675i q^{53} +(7.03783 - 2.11400i) q^{54} +1.31335i q^{55} +(2.51421 + 1.29567i) q^{56} +(-0.649396 + 2.46991i) q^{57} +(-8.00866 + 4.79538i) q^{58} +(-6.57365 - 11.3859i) q^{59} +(0.751833 + 0.698814i) q^{60} +(1.86594 - 3.23190i) q^{61} +(0.149203 + 9.37195i) q^{62} +(1.52433 + 2.58388i) q^{63} +(7.96354 - 0.762941i) q^{64} +(-0.116723 - 0.0673900i) q^{65} +(3.02557 + 10.4269i) q^{66} +(-0.941252 + 0.543432i) q^{67} +(11.1107 - 6.89539i) q^{68} +(-1.90880 - 6.99226i) q^{69} +(-0.203719 + 0.366193i) q^{70} +1.66151 q^{71} +(7.57879 + 3.81601i) q^{72} +3.76397 q^{73} +(5.18328 - 9.31713i) q^{74} +(5.98788 - 6.04437i) q^{75} +(-2.50562 + 1.55501i) q^{76} +(-3.83853 + 2.21618i) q^{77} +(-1.08193 - 0.266126i) q^{78} +(-4.13444 - 2.38702i) q^{79} +(0.0754193 + 1.18284i) q^{80} +(4.64557 + 7.70835i) q^{81} +(0.0408277 + 2.56453i) q^{82} +(-4.93471 + 8.54717i) q^{83} +(-0.773764 + 3.37658i) q^{84} +(0.968669 + 1.67778i) q^{85} +(-12.3363 + 7.38665i) q^{86} +(-8.12185 - 8.04594i) q^{87} +(-5.74286 + 11.1439i) q^{88} -11.2455i q^{89} +(-0.600816 + 1.10427i) q^{90} -0.454862i q^{91} +(3.95186 - 7.37765i) q^{92} +(-11.0745 + 3.02319i) q^{93} +(-4.83555 - 8.07576i) q^{94} +(-0.218449 - 0.378366i) q^{95} +(3.32367 + 9.21701i) q^{96} +(5.52923 - 9.57690i) q^{97} +(-1.41403 + 0.0225116i) q^{98} +(-11.4527 + 6.75637i) 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 $

$2$	−0.687522	+	1.23585i	−0.486151	+	0.873875i
$2$	−0.687522	+	1.23585i	−0.486151	+	0.873875i
$3$	−1.67512	−	0.440428i	−0.967130	−	0.254281i
$3$	−1.67512	−	0.440428i	−0.967130	−	0.254281i
$4$	−1.05463	−	1.69934i	−0.527314	−	0.849670i
$5$	0.256612	−	0.148155i	0.114760	−	0.0662569i	−0.441521	−	0.897251i	$-0.645561\pi$
$5$	0.256612	−	0.148155i	0.114760	−	0.0662569i	0.556281	+	0.830994i	$0.312228\pi$
$6$	1.69598	−	1.76738i	0.692381	−	0.721532i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	2.82520	−	0.135024i	0.998860	−	0.0477382i
$9$	2.61205	+	1.47554i	0.870682	+	0.491846i
$10$	0.00667042	+	0.418992i	0.00210937	+	0.132497i
$11$	−2.21618	+	3.83853i	−0.668203	+	1.15736i	0.310203	+	0.950670i	$0.399603\pi$
$11$	−2.21618	+	3.83853i	−0.668203	+	1.15736i	−0.978406	+	0.206691i	$0.933730\pi$
$12$	1.01819	+	3.31109i	0.293926	+	0.955828i
$13$	−0.227431	−	0.393922i	−0.0630780	−	0.109254i	0.832762	−	0.553631i	$-0.186758\pi$
$13$	−0.227431	−	0.393922i	−0.0630780	−	0.109254i	−0.895840	+	0.444377i	$0.853425\pi$
$14$	−1.21333	+	0.726513i	−0.324277	+	0.194169i
$15$	−0.495107	+	0.135158i	−0.127836	+	0.0348977i
$16$	−1.77552	+	3.58435i	−0.443880	+	0.896086i
$17$			6.53822i			1.58575i	0.609384	+	0.792875i	$0.291417\pi$
$17$			6.53822i			1.58575i	−0.609384	+	0.792875i	$0.708583\pi$
$18$	−3.61938	+	2.21362i	−0.853095	+	0.521756i
$19$		−	1.47447i		−	0.338266i	−0.985593	−	0.169133i	$-0.945903\pi$
$19$		−	1.47447i		−	0.338266i	0.985593	−	0.169133i	$-0.0540967\pi$
$20$	−0.522396	−	0.279823i	−0.116811	−	0.0625702i
$21$	−1.23048	−	1.21898i	−0.268513	−	0.266004i
$22$	−3.22016	−	5.37793i	−0.686541	−	1.14658i
$23$	2.09235	+	3.62406i	0.436285	+	0.755669i	0.997400	−	0.0720699i	$-0.0229605\pi$
$23$	2.09235	+	3.62406i	0.436285	+	0.755669i	−0.561114	+	0.827738i	$0.689627\pi$
$24$	−4.79202	−	1.01812i	−0.978167	−	0.207822i
$25$	−2.45610	+	4.25409i	−0.491220	+	0.850818i
$26$	0.643190	−	0.0102397i	0.126140	−	0.00200817i
$27$	−3.72562	−	3.62212i	−0.716996	−	0.697077i
$28$	−0.0636644	−	1.99899i	−0.0120314	−	0.377773i
$29$	5.71624	+	3.30027i	1.06148	+	0.612845i	0.925841	−	0.377913i	$-0.123358\pi$
$29$	5.71624	+	3.30027i	1.06148	+	0.612845i	0.135638	+	0.990758i	$0.456692\pi$
$30$	0.173362	−	0.704800i	0.0316515	−	0.128678i
$31$	5.73985	−	3.31390i	1.03091	−	0.595195i	0.113663	−	0.993519i	$-0.463742\pi$
$31$	5.73985	−	3.31390i	1.03091	−	0.595195i	0.917244	+	0.398325i	$0.130408\pi$
$32$	−3.20899	−	4.65858i	−0.567275	−	0.823529i
$33$	5.40296	−	5.45393i	0.940535	−	0.949408i
$34$	−8.08023	−	4.49517i	−1.38575	−	0.770914i
$35$	0.296310			0.0500855
$36$	−0.247295	−	5.99490i	−0.0412158	−	0.999150i
$37$	−7.53908			−1.23942			−0.619708	−	0.784832i	$-0.712749\pi$
$37$	−7.53908			−1.23942			−0.619708	+	0.784832i	$0.712749\pi$
$38$	1.82221	+	1.01373i	0.295602	+	0.164448i
$39$	0.207480	+	0.760033i	0.0332233	+	0.121703i
$40$	0.704976	−	0.453216i	0.111466	−	0.0716598i
$41$	1.57065	−	0.906813i	0.245294	−	0.141620i	−0.372314	−	0.928107i	$-0.621435\pi$
$41$	1.57065	−	0.906813i	0.245294	−	0.141620i	0.617607	+	0.786487i	$0.288102\pi$
$42$	2.35246	−	0.682609i	0.362992	−	0.105329i
$43$	8.80511	+	5.08363i	1.34277	+	0.775247i	0.987213	−	0.159409i	$-0.0509588\pi$
$43$	8.80511	+	5.08363i	1.34277	+	0.775247i	0.355554	+	0.934656i	$0.384292\pi$
$44$	8.86022	−	0.282183i	1.33573	−	0.0425407i
$45$	0.888890	−	0.00834685i	0.132508	−	0.00124428i
$46$	−5.91731	+	0.0942044i	−0.872460	+	0.0138897i
$47$	−3.32792	+	5.76413i	−0.485427	+	0.840785i	−0.999860	−	0.0167463i	$-0.994669\pi$
$47$	−3.32792	+	5.76413i	−0.485427	+	0.840785i	0.514433	+	0.857531i	$0.328003\pi$
$48$	4.55285	−	5.22222i	0.657147	−	0.753762i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−3.56878	−	5.96014i	−0.504701	−	0.842891i
$51$	2.87961	−	10.9523i	0.403227	−	1.53363i
$52$	−0.429553	+	0.801924i	−0.0595682	+	0.111207i
$53$		−	1.22675i		−	0.168508i	−0.996444	−	0.0842538i	$-0.973149\pi$
$53$		−	1.22675i		−	0.168508i	0.996444	−	0.0842538i	$-0.0268506\pi$
$54$	7.03783	−	2.11400i	0.957727	−	0.287680i
$55$			1.31335i			0.177092i
$56$	2.51421	+	1.29567i	0.335975	+	0.173141i
$57$	−0.649396	+	2.46991i	−0.0860146	+	0.327147i
$58$	−8.00866	+	4.79538i	−1.05159	+	0.629664i
$59$	−6.57365	−	11.3859i	−0.855817	−	1.48232i	−0.875885	−	0.482520i	$-0.839722\pi$
$59$	−6.57365	−	11.3859i	−0.855817	−	1.48232i	0.0200684	−	0.999799i	$-0.493612\pi$
$60$	0.751833	+	0.698814i	0.0970613	+	0.0902165i
$61$	1.86594	−	3.23190i	0.238909	−	0.413802i	−0.721493	−	0.692422i	$-0.756544\pi$
$61$	1.86594	−	3.23190i	0.238909	−	0.413802i	0.960401	+	0.278620i	$0.0898770\pi$
$62$	0.149203	+	9.37195i	0.0189488	+	1.19024i
$63$	1.52433	+	2.58388i	0.192047	+	0.325538i
$64$	7.96354	−	0.762941i	0.995442	−	0.0953676i
$65$	−0.116723	−	0.0673900i	−0.0144777	−	0.00835871i
$66$	3.02557	+	10.4269i	0.372422	+	1.28347i
$67$	−0.941252	+	0.543432i	−0.114992	+	0.0663908i	−0.556393	−	0.830919i	$-0.687815\pi$
$67$	−0.941252	+	0.543432i	−0.114992	+	0.0663908i	0.441401	+	0.897310i	$0.354482\pi$
$68$	11.1107	−	6.89539i	1.34737	−	0.836189i
$69$	−1.90880	−	6.99226i	−0.229793	−	0.841769i
$70$	−0.203719	+	0.366193i	−0.0243491	+	0.0437685i
$71$	1.66151			0.197185			0.0985926	−	0.995128i	$-0.468566\pi$
$71$	1.66151			0.197185			0.0985926	+	0.995128i	$0.468566\pi$
$72$	7.57879	+	3.81601i	0.893169	+	0.449721i
$73$	3.76397			0.440539			0.220270	−	0.975439i	$-0.429306\pi$
$73$	3.76397			0.440539			0.220270	+	0.975439i	$0.429306\pi$
$74$	5.18328	−	9.31713i	0.602544	−	1.08309i
$75$	5.98788	−	6.04437i	0.691421	−	0.697944i
$76$	−2.50562	+	1.55501i	−0.287414	+	0.178372i
$77$	−3.83853	+	2.21618i	−0.437442	+	0.252557i
$78$	−1.08193	−	0.266126i	−0.122504	−	0.0301329i
$79$	−4.13444	−	2.38702i	−0.465160	−	0.268560i	0.249051	−	0.968490i	$-0.419881\pi$
$79$	−4.13444	−	2.38702i	−0.465160	−	0.268560i	−0.714212	+	0.699930i	$0.753215\pi$
$80$	0.0754193	+	1.18284i	0.00843214	+	0.132245i
$81$	4.64557	+	7.70835i	0.516175	+	0.856483i
$82$	0.0408277	+	2.56453i	0.00450866	+	0.283205i
$83$	−4.93471	+	8.54717i	−0.541655	+	0.938174i	0.457154	+	0.889387i	$0.348869\pi$
$83$	−4.93471	+	8.54717i	−0.541655	+	0.938174i	−0.998809	+	0.0487865i	$0.984465\pi$
$84$	−0.773764	+	3.37658i	−0.0844246	+	0.368415i
$85$	0.968669	+	1.67778i	0.105067	+	0.181981i
$86$	−12.3363	+	7.38665i	−1.33026	+	0.796523i
$87$	−8.12185	−	8.04594i	−0.870754	−	0.862615i
$88$	−5.74286	+	11.1439i	−0.612191	+	1.18794i
$89$		−	11.2455i		−	1.19202i	−0.802976	−	0.596011i	$-0.796751\pi$
$89$		−	11.2455i		−	1.19202i	0.802976	−	0.596011i	$-0.203249\pi$
$90$	−0.600816	+	1.10427i	−0.0633316	+	0.116400i
$91$		−	0.454862i		−	0.0476825i
$92$	3.95186	−	7.37765i	0.412010	−	0.769173i
$93$	−11.0745	+	3.02319i	−1.14837	+	0.313490i
$94$	−4.83555	−	8.07576i	−0.498749	−	0.832951i
$95$	−0.218449	−	0.378366i	−0.0224124	−	0.0388195i
$96$	3.32367	+	9.21701i	0.339221	+	0.940707i
$97$	5.52923	−	9.57690i	0.561408	−	0.972387i	−0.435966	−	0.899963i	$-0.643593\pi$
$97$	5.52923	−	9.57690i	0.561408	−	0.972387i	0.997374	−	0.0724238i	$-0.0230734\pi$
$98$	−1.41403	+	0.0225116i	−0.142839	+	0.00227402i
$99$	−11.4527	+	6.75637i	−1.15104	+	0.679041i
$100$	9.81942	−	0.312732i	0.981942	−	0.0312732i
$101$	−8.89923	−	5.13797i	−0.885506	−	0.511247i	−0.0130363	−	0.999915i	$-0.504150\pi$
$101$	−8.89923	−	5.13797i	−0.885506	−	0.511247i	−0.872470	+	0.488668i	$0.837483\pi$
$102$	11.5555	+	11.0887i	1.14417	+	1.09794i
$103$	6.75540	−	3.90023i	0.665629	−	0.384301i	−0.128789	−	0.991672i	$-0.541109\pi$
$103$	6.75540	−	3.90023i	0.665629	−	0.384301i	0.794418	+	0.607371i	$0.207776\pi$
$104$	−0.695728	−	1.08220i	−0.0682217	−	0.106119i
$105$	−0.496354	−	0.130503i	−0.0484392	−	0.0127358i
$106$	1.51608	+	0.843420i	0.147255	+	0.0819201i
$107$	−3.24508			−0.313714			−0.156857	−	0.987621i	$-0.550136\pi$
$107$	−3.24508			−0.313714			−0.156857	+	0.987621i	$0.550136\pi$
$108$	−2.22607	+	10.1511i	−0.214204	+	0.976789i
$109$	−9.77063			−0.935857			−0.467928	−	0.883766i	$-0.654999\pi$
$109$	−9.77063			−0.935857			−0.467928	+	0.883766i	$0.654999\pi$
$110$	−1.62310	−	0.902957i	−0.154756	−	0.0860936i
$111$	12.6288	+	3.32042i	1.19868	+	0.315160i
$112$	−3.32982	+	2.21638i	−0.314638	+	0.209428i
$113$	−5.85142	+	3.37832i	−0.550455	+	0.317805i	−0.749306	−	0.662224i	$-0.769613\pi$
$113$	−5.85142	+	3.37832i	−0.550455	+	0.317805i	0.198850	+	0.980030i	$0.436279\pi$
$114$	−2.60595	−	2.50067i	−0.244069	−	0.234209i
$115$	1.07384	+	0.619984i	0.100137	+	0.0578138i
$116$	−0.420220	−	13.1944i	−0.0390164	−	1.22507i
$117$	−0.0128132	−	1.36453i	−0.00118458	−	0.126150i
$118$	18.5907	−	0.295967i	1.71142	−	0.0272460i
$119$	−3.26911	+	5.66226i	−0.299679	+	0.519059i
$120$	−1.38053	+	0.448700i	−0.126024	+	0.0409605i
$121$	−4.32289	−	7.48747i	−0.392990	−	0.680679i
$122$	2.71126	+	4.52801i	0.245466	+	0.409947i
$123$	−3.03041	+	0.827263i	−0.273243	+	0.0745918i
$124$	−11.6849	−	6.25902i	−1.04933	−	0.562077i
$125$			2.93708i			0.262701i
$126$	−4.24128	+	0.107364i	−0.377843	+	0.00956477i
$127$			17.2613i			1.53169i	0.643026	+	0.765844i	$0.277679\pi$
$127$			17.2613i			1.53169i	−0.643026	+	0.765844i	$0.722321\pi$
$128$	−4.53223	+	10.3662i	−0.400596	+	0.916255i
$129$	−12.5106	−	12.3937i	−1.10150	−	1.09121i
$130$	0.163533	−	0.0979195i	0.0143428	−	0.00858810i
$131$	−0.624945	−	1.08244i	−0.0546017	−	0.0945730i	0.837433	−	0.546541i	$-0.184056\pi$
$131$	−0.624945	−	1.08244i	−0.0546017	−	0.0945730i	−0.892034	+	0.451968i	$0.850722\pi$
$132$	−14.9662	−	3.42960i	−1.30264	−	0.298508i
$133$	0.737233	−	1.27693i	0.0639262	−	0.110723i
$134$	−0.0244671	−	1.53686i	−0.00211363	−	0.132765i
$135$	−1.49267	−	0.377510i	−0.128469	−	0.0324909i
$136$	0.882817	+	18.4718i	0.0757009	+	1.58394i
$137$	−12.7469	−	7.35942i	−1.08904	−	0.628758i	−0.155720	−	0.987801i	$-0.549770\pi$
$137$	−12.7469	−	7.35942i	−1.08904	−	0.628758i	−0.933321	+	0.359043i	$0.883103\pi$
$138$	9.95369	+	2.44835i	0.847315	+	0.208417i
$139$	−4.89178	+	2.82427i	−0.414915	+	0.239551i	−0.692899	−	0.721034i	$-0.743667\pi$
$139$	−4.89178	+	2.82427i	−0.414915	+	0.239551i	0.277984	+	0.960586i	$0.410334\pi$
$140$	−0.312497	−	0.503531i	−0.0264108	−	0.0425562i
$141$	8.11335	−	8.18989i	0.683267	−	0.689713i
$142$	−1.14233	+	2.05337i	−0.0958618	+	0.172315i
$143$	2.01611			0.168596
$144$	−9.92658	+	6.74263i	−0.827215	+	0.561886i
$145$	1.95581			0.162421
$146$	−2.58781	+	4.65168i	−0.214169	+	0.384976i
$147$	−0.456138	−	1.67091i	−0.0376216	−	0.137814i
$148$	7.95092	+	12.8115i	0.653562	+	1.05310i
$149$	16.2394	−	9.37583i	1.33038	−	0.768098i	0.345026	−	0.938593i	$-0.387870\pi$
$149$	16.2394	−	9.37583i	1.33038	−	0.768098i	0.985358	+	0.170496i	$0.0545369\pi$
$150$	3.35311	+	11.5557i	0.273781	+	0.943521i
$151$	18.6131	+	10.7463i	1.51471	+	0.874519i	0.999851	+	0.0172443i	$0.00548930\pi$
$151$	18.6131	+	10.7463i	1.51471	+	0.874519i	0.514860	+	0.857274i	$0.327844\pi$
$152$	−0.199089	−	4.16567i	−0.0161482	−	0.337880i
$153$	−9.64739	+	17.0781i	−0.779945	+	1.38068i
$154$	−0.0997795	−	6.26751i	−0.00804046	−	0.505050i
$155$	0.981942	−	1.70077i	0.0788715	−	0.136609i
$156$	1.07274	−	1.15413i	0.0858881	−	0.0924044i
$157$	10.4124	+	18.0347i	0.830996	+	1.43933i	0.897249	+	0.441525i	$0.145562\pi$
$157$	10.4124	+	18.0347i	0.830996	+	1.43933i	−0.0662526	+	0.997803i	$0.521104\pi$
$158$	5.79250	−	3.46840i	0.460826	−	0.275931i
$159$	−0.540297	+	2.05496i	−0.0428483	+	0.162969i
$160$	−1.51366	−	0.720020i	−0.119665	−	0.0569225i
$161$			4.18470i			0.329801i
$162$	−12.7203	+	0.441553i	−0.999398	+	0.0346917i
$163$		−	11.1576i		−	0.873930i	−0.899478	−	0.436965i	$-0.856053\pi$
$163$		−	11.1576i		−	0.873930i	0.899478	−	0.436965i	$-0.143947\pi$
$164$	−3.19743	−	1.71271i	−0.249678	−	0.133740i
$165$	0.578437	−	2.20002i	0.0450312	−	0.171271i
$166$	−7.17026	−	11.9749i	−0.556520	−	0.929433i
$167$	8.54592	+	14.8020i	0.661303	+	1.14541i	0.980274	+	0.197646i	$0.0633295\pi$
$167$	8.54592	+	14.8020i	0.661303	+	1.14541i	−0.318971	+	0.947765i	$0.603337\pi$
$168$	−3.64095	−	3.27772i	−0.280905	−	0.252882i
$169$	6.39655	−	11.0792i	0.492042	−	0.852242i
$170$	−2.73946	+	0.0436126i	−0.210107	+	0.00334494i
$171$	2.17563	−	3.85137i	0.166375	−	0.294522i
$172$	−0.647293	−	20.3242i	−0.0493556	−	1.54971i
$173$	4.04776	+	2.33697i	0.307745	+	0.177677i	0.645917	−	0.763408i	$-0.276475\pi$
$173$	4.04776	+	2.33697i	0.307745	+	0.177677i	−0.338172	+	0.941084i	$0.609808\pi$
$174$	15.5275	−	4.50559i	1.17714	−	0.341568i
$175$	−4.25409	+	2.45610i	−0.321579	+	0.185664i
$176$	−9.82377	−	14.7589i	−0.740494	−	1.11250i
$177$	5.99698	+	21.9680i	0.450761	+	1.65121i
$178$	13.8977	+	7.73153i	1.04168	+	0.579503i
$179$	6.17066			0.461217			0.230608	−	0.973047i	$-0.425928\pi$
$179$	6.17066			0.461217			0.230608	+	0.973047i	$0.425928\pi$
$180$	−0.951633	−	1.50172i	−0.0709305	−	0.111932i
$181$	−3.95246			−0.293784			−0.146892	−	0.989153i	$-0.546927\pi$
$181$	−3.95246			−0.293784			−0.146892	+	0.989153i	$0.546927\pi$
$182$	0.562139	+	0.312727i	0.0416685	+	0.0231809i
$183$	−4.54909	+	4.59200i	−0.336278	+	0.339451i
$184$	6.40065	+	9.95618i	0.471862	+	0.733979i
$185$	−1.93462	+	1.11695i	−0.142236	+	0.0821199i
$186$	3.87774	−	15.7648i	0.284329	−	1.15593i
$187$	−25.0972	−	14.4899i	−1.83529	−	1.05960i
$188$	13.3049	−	0.423740i	0.970362	−	0.0309044i
$189$	−1.41542	−	4.99966i	−0.102957	−	0.363672i
$190$	0.617790	−	0.00983530i	0.0448192	−	0.000713528i
$191$	−0.422858	+	0.732412i	−0.0305970	+	0.0529955i	−0.880918	−	0.473268i	$-0.843074\pi$
$191$	−0.422858	+	0.732412i	−0.0305970	+	0.0529955i	0.850321	+	0.526264i	$0.176408\pi$
$192$	−13.6759	−	2.22935i	−0.986972	−	0.160889i
$193$	8.03323	+	13.9140i	0.578244	+	1.00155i	0.995681	+	0.0928426i	$0.0295953\pi$
$193$	8.03323	+	13.9140i	0.578244	+	1.00155i	−0.417436	+	0.908706i	$0.637071\pi$
$194$	8.03411	+	13.4176i	0.576815	+	0.963327i
$195$	0.165844	+	0.164294i	0.0118764	+	0.0117654i
$196$	0.944358	−	1.76301i	0.0674542	−	0.125929i
$197$		−	18.1135i		−	1.29053i	−0.763959	−	0.645265i	$-0.776747\pi$
$197$		−	18.1135i		−	1.29053i	0.763959	−	0.645265i	$-0.223253\pi$
$198$	−0.475877	−	18.7989i	−0.0338191	−	1.33598i
$199$		−	17.5844i		−	1.24652i	−0.782013	−	0.623262i	$-0.785807\pi$
$199$		−	17.5844i		−	1.24652i	0.782013	−	0.623262i	$-0.214193\pi$
$200$	−6.36458	+	12.3503i	−0.450043	+	0.873298i
$201$	1.81605	−	0.495760i	0.128094	−	0.0349682i
$202$	12.4682	−	7.46560i	0.877256	−	0.525278i
$203$	3.30027	+	5.71624i	0.231634	+	0.401201i
$204$	−21.6486	+	6.65715i	−1.51571	+	0.466094i
$205$	0.268698	−	0.465398i	0.0187667	−	0.0325048i
$206$	0.175601	+	11.0301i	0.0122347	+	0.768505i
$207$	0.117880	+	12.5536i	0.00819325	+	0.872532i
$208$	1.81576	−	0.115775i	0.125900	−	0.00802758i
$209$	5.65979	+	3.26768i	0.391496	+	0.226030i
$210$	0.502536	−	0.523693i	0.0346783	−	0.0361383i
$211$	13.2587	−	7.65494i	0.912770	−	0.526988i	0.0314486	−	0.999505i	$-0.489988\pi$
$211$	13.2587	−	7.65494i	0.912770	−	0.526988i	0.881321	+	0.472517i	$0.156655\pi$
$212$	−2.08467	+	1.29377i	−0.143176	+	0.0888564i
$213$	−2.78323	−	0.731776i	−0.190704	−	0.0501405i
$214$	2.23106	−	4.01042i	0.152512	−	0.274146i
$215$	3.01266			0.205462
$216$	−11.0147	−	9.73018i	−0.749456	−	0.662055i
$217$	6.62781			0.449925
$218$	6.71752	−	12.0750i	0.454968	−	0.817822i
$219$	−6.30509	−	1.65776i	−0.426059	−	0.112021i
$220$	2.23183	−	1.38510i	0.150470	−	0.0933832i
$221$	2.57555	−	1.48699i	0.173250	−	0.100026i
$222$	−12.7861	+	13.3244i	−0.858149	+	0.894278i
$223$	−0.724566	−	0.418329i	−0.0485206	−	0.0280134i	0.475543	−	0.879692i	$-0.342251\pi$
$223$	−0.724566	−	0.418329i	−0.0485206	−	0.0280134i	−0.524064	+	0.851679i	$0.675585\pi$
$224$	−0.449776	−	5.63895i	−0.0300519	−	0.376768i
$225$	−12.6925	+	7.48781i	−0.846168	+	0.499187i
$226$	−0.152103	−	9.55411i	−0.0101177	−	0.635530i
$227$	9.95185	−	17.2371i	0.660527	−	1.14407i	−0.319950	−	0.947435i	$-0.603666\pi$
$227$	9.95185	−	17.2371i	0.660527	−	1.14407i	0.980477	−	0.196633i	$-0.0630006\pi$
$228$	4.88209	−	1.50129i	0.323324	−	0.0994252i
$229$	12.8198	+	22.2046i	0.847158	+	1.46732i	0.883734	+	0.467990i	$0.155022\pi$
$229$	12.8198	+	22.2046i	0.847158	+	1.46732i	−0.0365756	+	0.999331i	$0.511645\pi$
$230$	−1.50450	+	0.900853i	−0.0992035	+	0.0594005i
$231$	7.40607	−	2.02176i	0.487283	−	0.133022i
$232$	16.5951	+	8.55211i	1.08952	+	0.561473i
$233$		−	9.73332i		−	0.637651i	−0.947813	−	0.318825i	$-0.896712\pi$
$233$		−	9.73332i		−	0.637651i	0.947813	−	0.318825i	$-0.103288\pi$
$234$	1.69515	+	0.922306i	0.110816	+	0.0602930i
$235$			1.97219i			0.128652i
$236$	−12.4158	+	23.1788i	−0.808198	+	1.50881i
$237$	5.87436	+	5.81946i	0.381581	+	0.378014i
$238$	−4.75010	−	7.93304i	−0.307903	−	0.514223i
$239$	−8.89438	−	15.4055i	−0.575330	−	0.996500i	−0.996006	−	0.0892892i	$-0.971540\pi$
$239$	−8.89438	−	15.4055i	−0.575330	−	0.996500i	0.420676	−	0.907211i	$-0.361793\pi$
$240$	0.394618	−	2.01461i	0.0254725	−	0.130043i
$241$	10.0336	−	17.3787i	0.646319	−	1.11946i	−0.337676	−	0.941262i	$-0.609641\pi$
$241$	10.0336	−	17.3787i	0.646319	−	1.11946i	0.983995	−	0.178195i	$-0.0570259\pi$
$242$	12.2254	−	0.194631i	0.785881	−	0.0125113i
$243$	−4.38691	−	14.9584i	−0.281421	−	0.959585i
$244$	−7.45997	+	0.237588i	−0.477576	+	0.0152100i
$245$	0.256612	+	0.148155i	0.0163943	+	0.00946527i
$246$	1.06110	−	4.31388i	0.0676533	−	0.275043i
$247$	−0.580825	+	0.335339i	−0.0369570	+	0.0213371i
$248$	15.7688	−	10.1375i	1.00132	−	0.643730i
$249$	12.0306	−	12.1441i	0.762411	−	0.769604i
$250$	−3.62978	−	2.01931i	−0.229567	−	0.127712i
$251$	1.79971			0.113597			0.0567984	−	0.998386i	$-0.481911\pi$
$251$	1.79971			0.113597			0.0567984	+	0.998386i	$0.481911\pi$
$252$	2.78329	−	5.31538i	0.175331	−	0.334838i
$253$	−18.5481			−1.16611
$254$	−21.3322	−	11.8675i	−1.33850	−	0.744632i
$255$	−0.883693	−	3.23712i	−0.0553390	−	0.202716i
$256$	−9.69507	−	12.7281i	−0.605942	−	0.795509i
$257$	−25.2755	+	14.5928i	−1.57664	+	0.910274i	−0.581317	+	0.813677i	$0.697462\pi$
$257$	−25.2755	+	14.5928i	−1.57664	+	0.910274i	−0.995324	+	0.0965969i	$0.969204\pi$
$258$	23.9180	−	6.94027i	1.48907	−	0.432082i
$259$	−6.52903	−	3.76954i	−0.405694	−	0.234228i
$260$	0.00858069	+	0.269424i	0.000532152	+	0.0167089i
$261$	10.0614	+	17.0550i	0.622785	+	1.05568i
$262$	1.76739	−	0.0281371i	0.109190	−	0.00173831i
$263$	6.96390	−	12.0618i	0.429413	−	0.743764i	−0.567409	−	0.823436i	$-0.692054\pi$
$263$	6.96390	−	12.0618i	0.429413	−	0.743764i	0.996821	+	0.0796720i	$0.0253873\pi$
$264$	14.5280	−	16.1380i	0.894139	−	0.993225i
$265$	−0.181750	−	0.314800i	−0.0111648	−	0.0193380i
$266$	1.07122	+	1.78902i	0.0656806	+	0.109692i
$267$	−4.95284	+	18.8376i	−0.303109	+	1.15284i
$268$	1.91615	+	1.02639i	0.117047	+	0.0626967i
$269$			25.9733i			1.58362i	0.610766	+	0.791811i	$0.290862\pi$
$269$			25.9733i			1.58362i	−0.610766	+	0.791811i	$0.709138\pi$
$270$	1.49279	−	1.58517i	0.0908483	−	0.0964702i
$271$			16.7706i			1.01874i	0.860547	+	0.509371i	$0.170122\pi$
$271$			16.7706i			1.01874i	−0.860547	+	0.509371i	$0.829878\pi$
$272$	−23.4352	−	11.6087i	−1.42097	−	0.703882i
$273$	−0.200334	+	0.761948i	−0.0121248	+	0.0461152i
$274$	17.8589	−	10.6934i	1.07889	−	0.646014i
$275$	−10.8863	−	18.8556i	−0.656469	−	1.13704i
$276$	−9.86916	+	10.6179i	−0.594053	+	0.639125i
$277$	6.69523	−	11.5965i	0.402278	−	0.696765i	−0.591723	−	0.806142i	$-0.701552\pi$
$277$	6.69523	−	11.5965i	0.402278	−	0.696765i	0.994000	+	0.109376i	$0.0348853\pi$
$278$	−0.127158	−	7.98723i	−0.00762642	−	0.479042i
$279$	19.8825	−	0.186701i	1.19034	−	0.0111775i
$280$	0.837135	−	0.0400090i	0.0500284	−	0.00239099i
$281$	11.2366	+	6.48745i	0.670319	+	0.387009i	0.796198	−	0.605037i	$-0.206842\pi$
$281$	11.2366	+	6.48745i	0.670319	+	0.387009i	−0.125878	+	0.992046i	$0.540175\pi$
$282$	4.54334	+	15.6576i	0.270552	+	0.932395i
$283$	−17.6067	+	10.1652i	−1.04661	+	0.604260i	−0.921698	−	0.387908i	$-0.873198\pi$
$283$	−17.6067	+	10.1652i	−1.04661	+	0.604260i	−0.124911	+	0.992168i	$0.539864\pi$
$284$	−1.75228	−	2.82348i	−0.103979	−	0.167542i
$285$	0.199286	+	0.730019i	0.0118047	+	0.0432426i
$286$	−1.38612	+	2.49160i	−0.0819630	+	0.147331i
$287$	1.81363			0.107055
$288$	−1.50811	−	16.9034i	−0.0888665	−	0.996044i
$289$	−25.7483			−1.51461
$290$	−1.34466	+	2.41707i	−0.0789611	+	0.141936i
$291$	−13.4800	+	13.6072i	−0.790214	+	0.797669i
$292$	−3.96959	−	6.39626i	−0.232302	−	0.374313i
$293$	13.3803	−	7.72510i	0.781684	−	0.451305i	−0.0553431	−	0.998467i	$-0.517625\pi$
$293$	13.3803	−	7.72510i	0.781684	−	0.451305i	0.837027	+	0.547162i	$0.184292\pi$
$294$	2.37859	+	0.585071i	0.138722	+	0.0341220i
$295$	−3.37376	−	1.94784i	−0.196428	−	0.113408i
$296$	−21.2994	+	1.01796i	−1.23800	+	0.0591675i
$297$	22.1603	−	6.27365i	1.28587	−	0.364034i
$298$	0.422130	+	26.5155i	0.0244533	+	1.53600i
$299$	0.951731	−	1.64845i	0.0550400	−	0.0953321i
$300$	−16.5864	−	3.80088i	−0.957618	−	0.219444i
$301$	5.08363	+	8.80511i	0.293016	+	0.507518i
$302$	−26.0776	+	15.6146i	−1.50060	+	0.898519i
$303$	12.6444	+	12.5262i	0.726399	+	0.719610i
$304$	5.28500	+	2.61794i	0.303115	+	0.150149i
$305$		−	1.10579i		−	0.0633174i
$306$	−14.4731	−	23.6643i	−0.827374	−	1.35280i
$307$		−	25.1623i		−	1.43609i	−0.695999	−	0.718043i	$-0.745038\pi$
$307$		−	25.1623i		−	1.43609i	0.695999	−	0.718043i	$-0.254962\pi$
$308$	7.81427	+	4.18573i	0.445259	+	0.238504i
$309$	−13.0339	+	3.55808i	−0.741471	+	0.202412i
$310$	1.42679	+	2.38285i	0.0810361	+	0.135337i
$311$	−2.95532	−	5.11876i	−0.167581	−	0.290258i	0.769988	−	0.638058i	$-0.220262\pi$
$311$	−2.95532	−	5.11876i	−0.167581	−	0.290258i	−0.937569	+	0.347800i	$0.886929\pi$
$312$	0.688795	+	2.11923i	0.0389953	+	0.119978i
$313$	−1.83498	+	3.17828i	−0.103719	+	0.179647i	−0.913214	−	0.407480i	$-0.866408\pi$
$313$	−1.83498	+	3.17828i	−0.103719	+	0.179647i	0.809495	+	0.587127i	$0.199741\pi$
$314$	−29.4469	+	0.468798i	−1.66178	+	0.0264558i
$315$	0.773975	+	0.437217i	0.0436086	+	0.0246344i
$316$	0.303936	+	9.54323i	0.0170977	+	0.536849i
$317$	21.2356	+	12.2604i	1.19271	+	0.688611i	0.958920	−	0.283676i	$-0.0915541\pi$
$317$	21.2356	+	12.2604i	1.19271	+	0.688611i	0.233789	+	0.972287i	$0.424887\pi$
$318$	−2.16815	−	2.08055i	−0.121584	−	0.116672i
$319$	−25.3364	+	14.6280i	−1.41857	+	0.819010i
$320$	1.93050	−	1.37562i	0.107918	−	0.0768993i
$321$	5.43589	+	1.42922i	0.303402	+	0.0797715i
$322$	−5.17165	−	2.87707i	−0.288205	−	0.160333i
$323$	9.64038			0.536405
$324$	8.19976	−	16.0239i	0.455542	−	0.890214i
$325$	2.23437			0.123941
$326$	13.7891	+	7.67109i	0.763706	+	0.424862i
$327$	16.3670	+	4.30326i	0.905095	+	0.237971i
$328$	4.31495	−	2.77401i	0.238253	−	0.153169i
$329$	−5.76413	+	3.32792i	−0.317787	+	0.183474i
$330$	2.32120	+	2.22742i	0.127778	+	0.122615i
$331$	−9.40387	−	5.42933i	−0.516884	−	0.298423i	0.218775	−	0.975775i	$-0.429794\pi$
$331$	−9.40387	−	5.42933i	−0.516884	−	0.298423i	−0.735659	+	0.677352i	$0.763127\pi$
$332$	19.7288	−	0.628331i	1.08276	−	0.0344841i
$333$	−19.6924	−	11.1242i	−1.07914	−	0.609602i
$334$	−24.1684	+	0.384765i	−1.32244	+	0.0210534i
$335$	−0.161024	+	0.278902i	−0.00879770	+	0.0152381i
$336$	6.55399	−	2.24615i	0.357550	−	0.122537i
$337$	−2.58303	−	4.47395i	−0.140707	−	0.243711i	0.787056	−	0.616881i	$-0.211604\pi$
$337$	−2.58303	−	4.47395i	−0.140707	−	0.243711i	−0.927763	+	0.373170i	$0.878271\pi$
$338$	9.29435	+	15.5223i	0.505546	+	0.844302i
$339$	11.2897	−	3.08196i	0.613174	−	0.167389i
$340$	1.82954	−	3.41554i	0.0992208	−	0.185234i
$341$			29.3768i			1.59084i
$342$	3.26391	+	5.33665i	0.176492	+	0.288573i
$343$			1.00000i			0.0539949i
$344$	25.5626	+	13.1734i	1.37824	+	0.710262i
$345$	−1.52576	−	1.51150i	−0.0821441	−	0.0813763i
$346$	−5.67106	+	3.39568i	−0.304878	+	0.182553i
$347$	4.05959	+	7.03141i	0.217930	+	0.377466i	0.954175	−	0.299249i	$-0.0967362\pi$
$347$	4.05959	+	7.03141i	0.217930	+	0.377466i	−0.736245	+	0.676715i	$0.763403\pi$
$348$	−5.10726	+	22.2873i	−0.273778	+	1.19472i
$349$	−7.98580	+	13.8318i	−0.427470	+	0.740400i	−0.996648	−	0.0818146i	$-0.973928\pi$
$349$	−7.98580	+	13.8318i	−0.427470	+	0.740400i	0.569177	+	0.822215i	$0.307262\pi$
$350$	−0.110582	−	6.94602i	−0.00591083	−	0.371280i
$351$	−0.579512	+	2.29139i	−0.0309321	+	0.122305i
$352$	24.9938	−	1.99357i	1.33217	−	0.106258i
$353$	−23.8711	−	13.7820i	−1.27053	−	0.733541i	−0.295442	−	0.955361i	$-0.595467\pi$
$353$	−23.8711	−	13.7820i	−1.27053	−	0.733541i	−0.975088	+	0.221820i	$0.928800\pi$
$354$	−31.2721	−	7.69210i	−1.66209	−	0.408831i
$355$	0.426364	−	0.246161i	0.0226290	−	0.0130649i
$356$	−19.1100	+	11.8598i	−1.01283	+	0.628570i
$357$	7.96996	−	8.04516i	0.421815	−	0.425795i
$358$	−4.24246	+	7.62598i	−0.224221	+	0.403046i
$359$	7.06180			0.372708			0.186354	−	0.982483i	$-0.440333\pi$
$359$	7.06180			0.372708			0.186354	+	0.982483i	$0.440333\pi$
$360$	2.51017	−	0.143603i	0.132297	−	0.00756855i
$361$	16.8259			0.885576
$362$	2.71740	−	4.88463i	0.142823	−	0.256730i
$363$	3.94367	+	14.4463i	0.206989	+	0.758236i
$364$	−0.772966	+	0.479710i	−0.0405144	+	0.0251436i
$365$	0.965879	−	0.557650i	0.0505564	−	0.0291888i
$366$	−2.54741	−	8.77907i	−0.133155	−	0.458889i
$367$	10.9395	+	6.31591i	0.571036	+	0.329688i	0.757563	−	0.652762i	$-0.226390\pi$
$367$	10.9395	+	6.31591i	0.571036	+	0.329688i	−0.186527	+	0.982450i	$0.559723\pi$
$368$	−16.7049	+	1.06513i	−0.870803	+	0.0555236i
$369$	5.44064	−	0.0510887i	0.283228	−	0.00265957i
$370$	−0.0502888	−	3.15881i	−0.00261439	−	0.164219i
$371$	0.613377	−	1.06240i	0.0318449	−	0.0551570i
$372$	16.8169	+	15.6309i	0.871915	+	0.810427i
$373$	−10.8851	−	18.8535i	−0.563609	−	0.976199i	−0.997178	−	0.0750788i	$-0.976079\pi$
$373$	−10.8851	−	18.8535i	−0.563609	−	0.976199i	0.433569	−	0.901121i	$-0.357254\pi$
$374$	35.1621	−	21.0541i	1.81819	−	1.08868i
$375$	1.29357	−	4.91996i	0.0667998	−	0.254066i
$376$	−8.62375	+	16.7342i	−0.444736	+	0.862999i
$377$		−	3.00234i		−	0.154628i
$378$	7.15194	+	1.68813i	0.367856	+	0.0868281i
$379$			31.0746i			1.59620i	0.602527	+	0.798098i	$0.294160\pi$
$379$			31.0746i			1.59620i	−0.602527	+	0.798098i	$0.705840\pi$
$380$	−0.412589	+	0.770255i	−0.0211654	+	0.0395133i
$381$	7.60234	−	28.9147i	0.389480	−	1.48134i
$382$	−0.614424	−	1.02614i	−0.0314367	−	0.0525017i
$383$	11.0121	+	19.0735i	0.562692	+	0.974612i	0.997260	+	0.0739726i	$0.0235677\pi$
$383$	11.0121	+	19.0735i	0.562692	+	0.974612i	−0.434568	+	0.900639i	$0.643099\pi$
$384$	12.1576	−	15.3686i	0.620415	−	0.784274i
$385$	−0.656676	+	1.13740i	−0.0334673	+	0.0579670i
$386$	−22.7185	+	0.361682i	−1.15634	+	0.0184091i
$387$	15.4983	+	26.2710i	0.787821	+	1.33543i
$388$	−22.1057	+	0.704030i	−1.12225	+	0.0357417i
$389$	23.3935	+	13.5062i	1.18610	+	0.684794i	0.957417	−	0.288708i	$-0.0932255\pi$
$389$	23.3935	+	13.5062i	1.18610	+	0.684794i	0.228681	+	0.973502i	$0.426559\pi$
$390$	−0.317064	+	0.0920021i	−0.0160552	+	0.00465871i
$391$	−23.6949	+	13.6802i	−1.19830	+	0.691840i
$392$	1.52954	+	2.37918i	0.0772532	+	0.120167i
$393$	0.570122	+	2.08845i	0.0287589	+	0.105349i
$394$	22.3854	+	12.4534i	1.12776	+	0.627393i
$395$	−1.41459			−0.0711759
$396$	23.5597	+	12.3365i	1.18392	+	0.619934i
$397$	−8.14977			−0.409025			−0.204513	−	0.978864i	$-0.565561\pi$
$397$	−8.14977			−0.409025			−0.204513	+	0.978864i	$0.565561\pi$
$398$	21.7316	+	12.0896i	1.08930	+	0.605999i
$399$	−1.79735	+	1.81430i	−0.0899799	+	0.0908288i
$400$	−10.8873	−	16.3567i	−0.544364	−	0.817836i
$401$	29.9154	−	17.2717i	1.49391	−	0.862507i	0.493930	−	0.869501i	$-0.335560\pi$
$401$	29.9154	−	17.2717i	1.49391	−	0.862507i	0.999976	+	0.00699448i	$0.00222643\pi$
$402$	−0.635893	+	2.58521i	−0.0317154	+	0.128938i
$403$	−2.61084	−	1.50737i	−0.130055	−	0.0750874i
$404$	0.654212	+	20.5415i	0.0325483	+	1.02198i
$405$	2.33414	+	1.28979i	0.115984	+	0.0640902i
$406$	−9.33340	+	0.148589i	−0.463209	+	0.00737435i
$407$	16.7079	−	28.9390i	0.828182	−	1.43445i
$408$	6.65667	−	31.3313i	0.329554	−	1.55113i
$409$	−4.75787	−	8.24087i	−0.235261	−	0.407485i	0.724087	−	0.689708i	$-0.242261\pi$
$409$	−4.75787	−	8.24087i	−0.235261	−	0.407485i	−0.959349	+	0.282224i	$0.908928\pi$
$410$	0.390425	+	0.652040i	0.0192817	+	0.0322020i
$411$	18.1113	+	17.9420i	0.893363	+	0.885014i
$412$	−13.7523	−	7.36643i	−0.677525	−	0.362918i
$413$		−	13.1473i		−	0.646937i
$414$	−15.5953	−	8.48516i	−0.766467	−	0.417023i
$415$			2.92441i			0.143554i
$416$	−1.10529	+	2.32360i	−0.0541915	+	0.113924i
$417$	9.43820	−	2.57651i	0.462190	−	0.126172i
$418$	−7.92958	+	4.74802i	−0.387848	+	0.232233i
$419$	−12.4203	−	21.5126i	−0.606771	−	1.05096i	−0.991769	−	0.128040i	$-0.959131\pi$
$419$	−12.4203	−	21.5126i	−0.606771	−	1.05096i	0.384998	−	0.922917i	$-0.374202\pi$
$420$	0.301700	+	0.981107i	0.0147214	+	0.0478731i
$421$	−6.76981	+	11.7257i	−0.329940	+	0.571473i	−0.982500	−	0.186264i	$-0.940362\pi$
$421$	−6.76981	+	11.7257i	−0.329940	+	0.571473i	0.652559	+	0.757738i	$0.273695\pi$
$422$	0.344650	+	21.6487i	0.0167773	+	1.05384i
$423$	−17.1979	+	10.1457i	−0.836189	+	0.493301i
$424$	−0.165641	−	3.46583i	−0.00804425	−	0.168315i
$425$	−27.8142	−	16.0585i	−1.34919	−	0.778952i
$426$	2.81789	−	2.93653i	0.136527	−	0.142275i
$427$	3.23190	−	1.86594i	0.156403	−	0.0902991i
$428$	3.42235	+	5.51449i	0.165426	+	0.266553i
$429$	−3.37722	−	0.887952i	−0.163054	−	0.0428707i
$430$	−2.07127	+	3.72318i	−0.0998855	+	0.179548i
$431$	−17.3938			−0.837829			−0.418914	−	0.908026i	$-0.637589\pi$
$431$	−17.3938			−0.837829			−0.418914	+	0.908026i	$0.637589\pi$
$432$	19.5978	−	6.92277i	0.942901	−	0.333072i
$433$	−32.1442			−1.54475			−0.772377	−	0.635165i	$-0.780932\pi$
$433$	−32.1442			−1.54475			−0.772377	+	0.635165i	$0.780932\pi$
$434$	−4.55676	+	8.19095i	−0.218732	+	0.393178i
$435$	−3.27621	−	0.861392i	−0.157082	−	0.0413006i
$436$	10.3044	+	16.6036i	0.493490	+	0.795170i
$437$	5.34355	−	3.08510i	0.255617	−	0.147580i
$438$	6.38362	−	6.65238i	0.305021	−	0.317863i
$439$	−25.0879	−	14.4845i	−1.19738	−	0.691309i	−0.237411	−	0.971409i	$-0.576299\pi$
$439$	−25.0879	−	14.4845i	−1.19738	−	0.691309i	−0.959971	+	0.280100i	$0.909632\pi$
$440$	0.177334	+	3.71048i	0.00845407	+	0.176890i
$441$	0.0281693	+	2.99987i	0.00134140	+	0.142851i
$442$	0.0669493	+	4.20532i	0.00318445	+	0.200027i
$443$	−3.31751	+	5.74609i	−0.157619	+	0.273005i	−0.934010	−	0.357248i	$-0.883715\pi$
$443$	−3.31751	+	5.74609i	−0.157619	+	0.273005i	0.776390	+	0.630252i	$0.217049\pi$
$444$	−7.67621	−	24.9625i	−0.364297	−	1.18467i
$445$	−1.66608	−	2.88573i	−0.0789797	−	0.136797i
$446$	1.01514	−	0.607842i	0.0480685	−	0.0287822i
$447$	−31.3323	+	8.55333i	−1.48197	+	0.404559i
$448$	7.27810	+	3.32104i	0.343858	+	0.156905i
$449$			5.68888i			0.268475i	0.990949	+	0.134237i	$0.0428585\pi$
$449$			5.68888i			0.268475i	−0.990949	+	0.134237i	$0.957142\pi$
$450$	−0.527395	−	20.8340i	−0.0248616	−	0.982125i
$451$			8.03864i			0.378525i
$452$	11.9120	+	6.38068i	0.560293	+	0.300122i
$453$	−26.4462	−	26.1990i	−1.24255	−	1.23094i
$454$	14.4603	+	24.1498i	0.678655	+	1.13341i
$455$	−0.0673900	−	0.116723i	−0.00315929	−	0.00547206i
$456$	−1.50118	+	7.06567i	−0.0702992	+	0.330880i
$457$	16.5673	−	28.6953i	0.774984	−	1.34231i	−0.159819	−	0.987146i	$-0.551091\pi$
$457$	16.5673	−	28.6953i	0.774984	−	1.34231i	0.934803	−	0.355165i	$-0.115575\pi$
$458$	−36.2554	+	0.577190i	−1.69410	+	0.0269703i
$459$	23.6822	−	24.3589i	1.10539	−	1.13698i
$460$	−0.0789419	−	2.47868i	−0.00368068	−	0.115569i
$461$	3.69384	+	2.13264i	0.172039	+	0.0993270i	0.583547	−	0.812079i	$-0.301664\pi$
$461$	3.69384	+	2.13264i	0.172039	+	0.0993270i	−0.411508	+	0.911406i	$0.634998\pi$
$462$	−2.59324	+	10.5428i	−0.120649	+	0.490494i
$463$	20.3913	−	11.7729i	0.947665	−	0.547134i	0.0553099	−	0.998469i	$-0.482385\pi$
$463$	20.3913	−	11.7729i	0.947665	−	0.547134i	0.892355	+	0.451335i	$0.149052\pi$
$464$	−21.9786	+	14.6293i	−1.02033	+	0.679147i
$465$	−2.39394	+	2.41652i	−0.111016	+	0.112064i
$466$	12.0289	+	6.69186i	0.557227	+	0.309995i
$467$	−9.98701			−0.462144			−0.231072	−	0.972937i	$-0.574223\pi$
$467$	−9.98701			−0.462144			−0.231072	+	0.972937i	$0.574223\pi$
$468$	−2.30528	+	1.46084i	−0.106562	+	0.0675274i
$469$	−1.08686			−0.0501867
$470$	−2.43732	−	1.35592i	−0.112425	−	0.0625441i
$471$	−9.49893	−	34.7962i	−0.437688	−	1.60332i
$472$	−20.1093	−	31.2799i	−0.925604	−	1.43977i
$473$	−39.0274	+	22.5325i	−1.79448	+	1.03604i
$474$	−11.2307	+	3.25880i	−0.515843	+	0.149682i
$475$	6.27251	+	3.62144i	0.287803	+	0.166163i
$476$	13.0698	−	0.416252i	0.599054	−	0.0190789i
$477$	1.81012	−	3.20434i	0.0828798	−	0.146717i
$478$	25.1539	−	0.400454i	1.15051	−	0.0183163i
$479$	7.07341	−	12.2515i	0.323192	−	0.559785i	−0.657953	−	0.753059i	$-0.728577\pi$
$479$	7.07341	−	12.2515i	0.323192	−	0.559785i	0.981145	+	0.193274i	$0.0619106\pi$
$480$	2.21844	+	1.87278i	0.101257	+	0.0854801i
$481$	1.71462	+	2.96981i	0.0781799	+	0.135412i
$482$	14.5790	+	24.3481i	0.664057	+	1.10903i
$483$	1.84306	−	7.00987i	0.0838621	−	0.318960i
$484$	−8.16472	+	15.2426i	−0.371124	+	0.692844i
$485$		−	3.27673i		−	0.148789i
$486$	21.5024	+	4.86271i	0.975370	+	0.220577i
$487$		−	37.5888i		−	1.70331i	−0.524102	−	0.851656i	$-0.675599\pi$
$487$		−	37.5888i		−	1.70331i	0.524102	−	0.851656i	$-0.324401\pi$
$488$	4.83527	−	9.38272i	0.218882	−	0.424736i
$489$	−4.91412	+	18.6903i	−0.222224	+	0.845204i
$490$	−0.359523	+	0.215273i	−0.0162416	+	0.00972504i
$491$	1.91801	+	3.32210i	0.0865588	+	0.149924i	0.906054	−	0.423161i	$-0.139080\pi$
$491$	1.91801	+	3.32210i	0.0865588	+	0.149924i	−0.819496	+	0.573085i	$0.805746\pi$
$492$	4.60175	+	4.27724i	0.207463	+	0.192833i
$493$	−21.5779	+	37.3740i	−0.971820	+	1.68324i
$494$	−0.0150981	−	0.948363i	−0.000679294	−	0.0426689i
$495$	−1.93790	+	3.43053i	−0.0871021	+	0.154191i
$496$	1.68697	+	26.4575i	0.0757470	+	1.18798i
$497$	1.43891	+	0.830756i	0.0645440	+	0.0372645i
$498$	6.73696	+	23.2174i	0.301890	+	1.04040i
$499$	8.09253	−	4.67223i	0.362272	−	0.209158i	−0.307805	−	0.951449i	$-0.599595\pi$
$499$	8.09253	−	4.67223i	0.362272	−	0.209158i	0.670077	+	0.742292i	$0.266261\pi$
$500$	4.99110	−	3.09753i	0.223209	−	0.138526i
$501$	−7.79623	−	28.5589i	−0.348310	−	1.27592i
$502$	−1.23734	+	2.22416i	−0.0552252	+	0.0992693i
$503$	−3.43652			−0.153227			−0.0766134	−	0.997061i	$-0.524411\pi$
$503$	−3.43652			−0.153227			−0.0766134	+	0.997061i	$0.524411\pi$
$504$	4.65542	+	7.09415i	0.207369	+	0.315999i
$505$	−3.04486			−0.135495
$506$	12.7522	−	22.9226i	0.566905	−	1.01903i
$507$	−15.5945	+	15.7417i	−0.692578	+	0.699112i
$508$	29.3328	−	18.2042i	1.30143	−	0.807681i
$509$	6.05939	−	3.49839i	0.268578	−	0.155063i	−0.359663	−	0.933082i	$-0.617108\pi$
$509$	6.05939	−	3.49839i	0.268578	−	0.155063i	0.628241	+	0.778019i	$0.283775\pi$
$510$	4.60813	+	1.13348i	0.204052	+	0.0501913i
$511$	3.25969	+	1.88198i	0.144200	+	0.0832541i
$512$	22.3956	−	3.23073i	0.989755	−	0.142780i
$513$	−5.34070	+	5.49330i	−0.235797	+	0.242535i
$514$	−0.657015	−	41.2694i	−0.0289797	−	1.82032i
$515$	1.15568	−	2.00169i	0.0509252	−	0.0882050i
$516$	−7.86707	+	34.3306i	−0.346328	+	1.51132i
$517$	−14.7505	−	25.5487i	−0.648728	−	1.12363i
$518$	9.14742	−	5.47723i	0.401914	−	0.240656i
$519$	−5.75121	−	5.69746i	−0.252450	−	0.250091i
$520$	−0.338865	−	0.174630i	−0.0148602	−	0.00765804i
$521$		−	14.3013i		−	0.626553i	−0.949662	−	0.313276i	$-0.898573\pi$
$521$		−	14.3013i		−	0.626553i	0.949662	−	0.313276i	$-0.101427\pi$
$522$	−27.9948	+	0.708663i	−1.22530	+	0.0310173i
$523$		−	0.431887i		−	0.0188851i	−0.999955	−	0.00944254i	$-0.996994\pi$
$523$		−	0.431887i		−	0.0188851i	0.999955	−	0.00944254i	$-0.00300570\pi$
$524$	−1.18034	+	2.20356i	−0.0515636	+	0.0962632i
$525$	8.20784	−	2.24064i	0.358220	−	0.0977895i
$526$	10.1187	+	16.8991i	0.441197	+	0.736835i
$527$	21.6670	+	37.5284i	0.943830	+	1.63476i
$528$	9.95573	+	29.0496i	0.433267	+	1.26422i
$529$	2.74413	−	4.75297i	0.119310	−	0.206651i
$530$	0.514000	−	0.00818296i	0.0223267	−	0.000355445i
$531$	−0.370351	−	39.4402i	−0.0160719	−	1.71156i
$532$	−2.94744	+	0.0938710i	−0.127788	+	0.00406983i
$533$	−0.714428	−	0.412475i	−0.0309453	−	0.0178663i
$534$	−19.8751	−	19.0722i	−0.860082	−	0.825334i
$535$	−0.832726	+	0.480774i	−0.0360019	+	0.0207857i
$536$	−2.58585	+	1.66240i	−0.111692	+	0.0718046i
$537$	−10.3366	−	2.71773i	−0.446057	−	0.117279i
$538$	−32.0990	−	17.8572i	−1.38389	−	0.769880i
$539$	−4.43236			−0.190915
$540$	0.932697	+	2.93469i	0.0401369	+	0.126289i
$541$	−10.1004			−0.434251			−0.217125	−	0.976144i	$-0.569668\pi$
$541$	−10.1004			−0.434251			−0.217125	+	0.976144i	$0.569668\pi$
$542$	−20.7259	−	11.5302i	−0.890253	−	0.495263i
$543$	6.62084	+	1.74077i	0.284127	+	0.0747038i
$544$	30.4588	−	20.9811i	1.30591	−	0.899556i
$545$	−2.50726	+	1.44757i	−0.107399	+	0.0620070i
$546$	−0.803916	−	0.771437i	−0.0344044	−	0.0330145i
$547$	−12.6249	−	7.28900i	−0.539803	−	0.311655i	0.205196	−	0.978721i	$-0.434217\pi$
$547$	−12.6249	−	7.28900i	−0.539803	−	0.311655i	−0.744999	+	0.667066i	$0.767550\pi$
$548$	0.937067	+	29.4228i	0.0400295	+	1.25688i
$549$	9.64271	−	5.68861i	0.411541	−	0.242784i
$550$	30.7872	−	0.490137i	1.31277	−	0.0208995i
$551$	4.86614	−	8.42840i	0.207305	−	0.359062i
$552$	−6.33687	−	19.4968i	−0.269715	−	0.829840i
$553$	−2.38702	−	4.13444i	−0.101506	−	0.175814i
$554$	9.72835	+	16.2471i	0.413318	+	0.690274i
$555$	3.73265	−	1.01897i	0.158442	−	0.0432527i
$556$	9.95840	+	5.33424i	0.422330	+	0.226222i
$557$		−	0.720867i		−	0.0305441i	−0.999883	−	0.0152720i	$-0.995139\pi$
$557$		−	0.720867i		−	0.0305441i	0.999883	−	0.0152720i	$-0.00486143\pi$
$558$	−13.4389	+	24.7001i	−0.568916	+	1.04564i
$559$		−	4.62470i		−	0.195604i
$560$	−0.526104	+	1.06208i	−0.0222319	+	0.0448809i
$561$	35.6590	+	35.3257i	1.50552	+	1.49145i
$562$	−15.7429	+	9.42643i	−0.664074	+	0.397630i
$563$	17.1195	+	29.6518i	0.721499	+	1.24967i	0.960399	+	0.278628i	$0.0898798\pi$
$563$	17.1195	+	29.6518i	0.721499	+	1.24967i	−0.238900	+	0.971044i	$0.576787\pi$
$564$	−22.4740	−	5.15005i	−0.946325	−	0.216856i
$565$	−1.00103	+	1.73383i	−0.0421136	+	0.0729429i
$566$	−0.457671	−	28.7479i	−0.0192374	−	1.20837i
$567$	0.169009	+	8.99841i	0.00709769	+	0.377898i
$568$	4.69411	−	0.224344i	0.196960	−	0.00941327i
$569$	−9.54066	−	5.50830i	−0.399965	−	0.230920i	0.286504	−	0.958079i	$-0.407507\pi$
$569$	−9.54066	−	5.50830i	−0.399965	−	0.230920i	−0.686469	+	0.727159i	$0.740840\pi$
$570$	−1.03920	−	0.255617i	−0.0435275	−	0.0107066i
$571$	8.18899	−	4.72792i	0.342699	−	0.197857i	−0.318766	−	0.947833i	$-0.603268\pi$
$571$	8.18899	−	4.72792i	0.342699	−	0.197857i	0.661465	+	0.749976i	$0.269935\pi$
$572$	−2.12625	−	3.42606i	−0.0889029	−	0.143251i
$573$	1.03091	−	1.04064i	0.0430670	−	0.0434733i
$574$	−1.24691	+	2.24136i	−0.0520449	+	0.0935527i
$575$	−20.5561			−0.857249
$576$	21.9269	+	9.75767i	0.913620	+	0.406570i
$577$	34.2938			1.42767			0.713835	−	0.700314i	$-0.246957\pi$
$577$	34.2938			1.42767			0.713835	+	0.700314i	$0.246957\pi$
$578$	17.7025	−	31.8209i	0.736327	−	1.32358i
$579$	−7.32852	−	26.8456i	−0.304563	−	1.11566i
$580$	−2.06265	−	3.32358i	−0.0856468	−	0.138004i
$581$	−8.54717	+	4.93471i	−0.354596	+	0.204726i
$582$	−7.54860	−	26.0145i	−0.312900	−	1.07834i
$583$	4.70894	+	2.71870i	0.195024	+	0.112597i
$584$	10.6340	−	0.508226i	0.440037	−	0.0210306i
$585$	−0.205449	−	0.348255i	−0.00849428	−	0.0143986i
$586$	0.347809	+	21.8471i	0.0143679	+	0.902496i
$587$	1.53425	−	2.65739i	0.0633251	−	0.109682i	−0.832625	−	0.553838i	$-0.813163\pi$
$587$	1.53425	−	2.65739i	0.0633251	−	0.109682i	0.895950	+	0.444155i	$0.146496\pi$
$588$	−2.35839	+	2.53732i	−0.0972583	+	0.104637i
$589$	−4.88624	−	8.46322i	−0.201334	−	0.348721i
$590$	4.72676	−	2.83026i	0.194597	−	0.116520i
$591$	−7.97768	+	30.3422i	−0.328158	+	1.24811i
$592$	13.3858	−	27.0227i	0.550152	−	1.11062i
$593$			29.4946i			1.21120i	0.795770	+	0.605598i	$0.207066\pi$
$593$			29.4946i			1.21120i	−0.795770	+	0.605598i	$0.792934\pi$
$594$	−7.48240	+	31.6999i	−0.307007	+	1.30066i
$595$			1.93734i			0.0794231i
$596$	−33.0593	−	17.7083i	−1.35416	−	0.725359i
$597$	−7.74465	+	29.4559i	−0.316967	+	1.20555i
$598$	1.38289	+	2.30954i	0.0565506	+	0.0944439i
$599$	−2.77278	−	4.80259i	−0.113293	−	0.196228i	0.803803	−	0.594895i	$-0.202806\pi$
$599$	−2.77278	−	4.80259i	−0.113293	−	0.196228i	−0.917096	+	0.398667i	$0.869473\pi$
$600$	16.1008	−	17.8851i	0.657314	−	0.730155i
$601$	9.01719	−	15.6182i	0.367819	−	0.637081i	−0.621405	−	0.783489i	$-0.713438\pi$
$601$	9.01719	−	15.6182i	0.367819	−	0.637081i	0.989224	+	0.146408i	$0.0467713\pi$
$602$	−14.3769	+	0.228882i	−0.585957	+	0.00932852i
$603$	−3.26045	+	0.0306162i	−0.132776	+	0.00124679i
$604$	−1.36831	−	42.9633i	−0.0556757	−	1.74815i
$605$	−2.21861	−	1.28092i	−0.0901994	−	0.0520767i
$606$	−24.1737	+	7.01445i	−0.981989	+	0.284943i
$607$	28.7368	−	16.5912i	1.16639	−	0.673417i	0.213564	−	0.976929i	$-0.431493\pi$
$607$	28.7368	−	16.5912i	1.16639	−	0.673417i	0.952827	+	0.303512i	$0.0981594\pi$
$608$	−6.86892	+	4.73155i	−0.278572	+	0.191890i
$609$	−3.01076	−	11.0289i	−0.122002	−	0.446914i
$610$	1.36659	+	0.760255i	0.0553315	+	0.0307818i
$611$	3.02749			0.122479
$612$	39.1960	−	1.61687i	1.58440	−	0.0653580i
$613$	40.1767			1.62272			0.811361	−	0.584545i	$-0.198727\pi$
$613$	40.1767			1.62272			0.811361	+	0.584545i	$0.198727\pi$
$614$	31.0967	+	17.2996i	1.25496	+	0.698155i
$615$	−0.655075	+	0.661255i	−0.0264152	+	0.0266644i
$616$	−10.5454	+	6.77945i	−0.424886	+	0.273152i
$617$	1.00311	−	0.579145i	0.0403836	−	0.0233155i	−0.479672	−	0.877448i	$-0.659244\pi$
$617$	1.00311	−	0.579145i	0.0403836	−	0.0233155i	0.520056	+	0.854132i	$0.325911\pi$
$618$	4.56382	−	18.5541i	0.183584	−	0.746355i
$619$	26.7639	+	15.4521i	1.07573	+	0.621074i	0.929742	−	0.368213i	$-0.120030\pi$
$619$	26.7639	+	15.4521i	1.07573	+	0.621074i	0.145989	+	0.989286i	$0.453363\pi$
$620$	−3.92578	+	0.125030i	−0.157663	+	0.00502131i
$621$	5.33147	−	21.0806i	0.213945	−	0.845936i
$622$	8.35784	−	0.133058i	0.335119	−	0.00533514i
$623$	5.62276	−	9.73890i	0.225271	−	0.390181i
$624$	−3.09261	−	0.605774i	−0.123803	−	0.0242504i
$625$	−11.8454	−	20.5168i	−0.473814	−	0.820670i
$626$	−2.66628	−	4.45289i	−0.106566	−	0.177973i
$627$	−8.04164	−	7.96648i	−0.321152	−	0.318151i
$628$	19.6660	−	36.7141i	0.784758	−	1.46505i
$629$		−	49.2921i		−	1.96541i
$630$	−1.07246	+	0.655918i	−0.0427277	+	0.0261324i
$631$		−	20.8271i		−	0.829113i	−0.910023	−	0.414557i	$-0.863937\pi$
$631$		−	20.8271i		−	0.829113i	0.910023	−	0.414557i	$-0.136063\pi$
$632$	−12.0029	−	6.18556i	−0.477451	−	0.246048i
$633$	−25.5814	+	6.98341i	−1.01677	+	0.277566i
$634$	−29.7518	+	17.8146i	−1.18160	+	0.707509i
$635$	2.55734	+	4.42944i	0.101485	+	0.175777i
$636$	4.06189	−	1.24907i	0.161064	−	0.0495288i
$637$	0.227431	−	0.393922i	0.00901114	−	0.0156078i
$638$	−0.658599	−	41.3689i	−0.0260742	−	1.63781i
$639$	4.33995	+	2.45163i	0.171686	+	0.0969848i
$640$	0.372786	+	3.33157i	0.0147357	+	0.131692i
$641$	9.86746	+	5.69698i	0.389741	+	0.225017i	0.682048	−	0.731307i	$-0.261090\pi$
$641$	9.86746	+	5.69698i	0.389741	+	0.225017i	−0.292307	+	0.956325i	$0.594423\pi$
$642$	−5.50359	+	5.73530i	−0.217209	+	0.226354i
$643$	3.84437	−	2.21955i	0.151607	−	0.0875305i	−0.422277	−	0.906467i	$-0.638769\pi$
$643$	3.84437	−	2.21955i	0.151607	−	0.0875305i	0.573885	+	0.818936i	$0.305436\pi$
$644$	7.11124	−	4.41331i	0.280222	−	0.173909i
$645$	−5.04657	−	1.32686i	−0.198708	−	0.0522451i
$646$	−6.62797	+	11.9140i	−0.260774	+	0.468751i
$647$	−23.4155			−0.920558			−0.460279	−	0.887774i	$-0.652251\pi$
$647$	−23.4155			−0.920558			−0.460279	+	0.887774i	$0.652251\pi$
$648$	14.1655	+	21.1504i	0.556473	+	0.830866i
$649$	58.2736			2.28744
$650$	−1.53618	+	2.76134i	−0.0602539	+	0.108309i
$651$	−11.1024	−	2.91907i	−0.435136	−	0.114407i
$652$	−18.9606	+	11.7671i	−0.742553	+	0.460836i
$653$	24.8536	−	14.3492i	0.972596	−	0.561528i	0.0725691	−	0.997363i	$-0.476880\pi$
$653$	24.8536	−	14.3492i	0.972596	−	0.561528i	0.900027	+	0.435835i	$0.143547\pi$
$654$	−16.5708	+	17.2685i	−0.647970	+	0.675250i
$655$	−0.320737	−	0.185178i	−0.0125322	−	0.00723548i
$656$	0.461620	+	7.23981i	0.0180232	+	0.282667i
$657$	9.83166	+	5.55388i	0.383569	+	0.216677i
$658$	−0.149834	−	9.41159i	−0.00584113	−	0.366902i
$659$	−9.63833	+	16.6941i	−0.375456	+	0.650309i	−0.990395	−	0.138266i	$-0.955847\pi$
$659$	−9.63833	+	16.6941i	−0.375456	+	0.650309i	0.614939	+	0.788574i	$0.289181\pi$
$660$	−4.34862	+	1.33724i	−0.169270	+	0.0520521i
$661$	23.0539	+	39.9305i	0.896692	+	1.55312i	0.831696	+	0.555231i	$0.187370\pi$
$661$	23.0539	+	39.9305i	0.896692	+	1.55312i	0.0649955	+	0.997886i	$0.479297\pi$
$662$	13.1752	−	7.88895i	0.512068	−	0.306613i
$663$	−4.96926	+	1.35655i	−0.192990	+	0.0526839i
$664$	−12.7875	+	24.8138i	−0.496251	+	0.962962i
$665$		−	0.436899i		−	0.0169422i
$666$	27.2867	−	16.6887i	1.05734	−	0.646672i
$667$			27.6213i			1.06950i
$668$	16.1408	−	30.1330i	0.624507	−	1.16588i
$669$	1.02949	+	1.01987i	0.0398024	+	0.0394304i
$670$	−0.233972	−	0.390753i	−0.00903915	−	0.0150961i
$671$	8.27050	+	14.3249i	0.319279	+	0.553008i
$672$	−1.73012	+	9.64400i	−0.0667409	+	0.372025i
$673$	−11.8145	+	20.4632i	−0.455414	+	0.788800i	−0.998712	−	0.0507398i	$-0.983842\pi$
$673$	−11.8145	+	20.4632i	−0.455414	+	0.788800i	0.543298	+	0.839540i	$0.317175\pi$
$674$	7.30500	−	0.116297i	0.281378	−	0.00447958i
$675$	24.5593	−	6.95283i	0.945289	−	0.267615i
$676$	−25.5732	+	0.814465i	−0.983586	+	0.0313256i
$677$	−22.2416	−	12.8412i	−0.854814	−	0.493527i	0.00745832	−	0.999972i	$-0.497626\pi$
$677$	−22.2416	−	12.8412i	−0.854814	−	0.493527i	−0.862272	+	0.506445i	$0.830959\pi$
$678$	−3.95311	+	16.0713i	−0.151818	+	0.617213i
$679$	9.57690	−	5.52923i	0.367528	−	0.212192i
$680$	2.96323	+	4.60929i	0.113635	+	0.176758i
$681$	−24.2622	+	24.4911i	−0.929731	+	0.938502i
$682$	−36.3052	−	20.1972i	−1.39020	−	0.773390i
$683$	5.57791			0.213433			0.106716	−	0.994290i	$-0.465966\pi$
$683$	5.57791			0.213433			0.106716	+	0.994290i	$0.465966\pi$
$684$	−8.83928	+	0.364628i	−0.337978	+	0.0139419i
$685$	−4.36134			−0.166638
$686$	−1.23585	−	0.687522i	−0.0471848	−	0.0262497i
$687$	−11.6952	−	42.8415i	−0.446200	−	1.63451i
$688$	−33.8551	+	22.5345i	−1.29072	+	0.859119i
$689$	−0.483245	+	0.279002i	−0.0184102	+	0.0106291i
$690$	2.91697	−	0.846414i	0.111047	−	0.0322224i
$691$	38.5847	+	22.2769i	1.46783	+	0.847453i	0.999351	−	0.0360214i	$-0.0114684\pi$
$691$	38.5847	+	22.2769i	1.46783	+	0.847453i	0.468480	+	0.883474i	$0.344802\pi$
$692$	−0.297564	−	9.34316i	−0.0113117	−	0.355174i
$693$	−13.2965	+	0.124857i	−0.505092	+	0.00474291i
$694$	−11.4808	+	0.182776i	−0.435805	+	0.00693808i
$695$	−0.836859	+	1.44948i	−0.0317439	+	0.0549820i
$696$	−24.0323	−	21.6348i	−0.910940	−	0.820064i
$697$	5.92894	+	10.2692i	0.224575	+	0.388975i
$698$	−11.6036	−	19.3789i	−0.439202	−	0.733502i
$699$	−4.28683	+	16.3045i	−0.162143	+	0.616691i
$700$	8.66024	+	4.63888i	0.327326	+	0.175333i
$701$		−	16.8238i		−	0.635428i	−0.948187	−	0.317714i	$-0.897085\pi$
$701$		−	16.8238i		−	0.635428i	0.948187	−	0.317714i	$-0.102915\pi$
$702$	−2.43337	−	2.29156i	−0.0918417	−	0.0864895i
$703$			11.1161i			0.419252i
$704$	−14.7200	+	32.2591i	−0.554783	+	1.21581i
$705$	0.868608	−	3.30366i	0.0327137	−	0.124423i
$706$	33.4443	−	20.0256i	1.25869	−	0.753672i
$707$	−5.13797	−	8.89923i	−0.193233	−	0.334690i
$708$	31.0065	−	33.3589i	1.16529	−	1.25371i
$709$	−21.8146	+	37.7841i	−0.819266	+	1.41901i	0.0869576	+	0.996212i	$0.472286\pi$
$709$	−21.8146	+	37.7841i	−0.819266	+	1.41901i	−0.906224	+	0.422798i	$0.861048\pi$
$710$	0.0110830	+	0.696161i	0.000415937	+	0.0261265i
$711$	−7.27720	−	12.3355i	−0.272916	−	0.462618i
$712$	−1.51842	−	31.7708i	−0.0569050	−	1.19066i
$713$	24.0196	+	13.8677i	0.899540	+	0.519350i
$714$	4.46305	+	15.3809i	0.167025	+	0.575614i
$715$	0.517358	−	0.298697i	0.0193481	−	0.0111706i
$716$	−6.50775	−	10.4861i	−0.243206	−	0.391882i
$717$	8.11412	+	29.7234i	0.303027	+	1.11004i
$718$	−4.85514	+	8.72730i	−0.181192	+	0.325700i
$719$	−22.2951			−0.831469			−0.415734	−	0.909486i	$-0.636475\pi$
$719$	−22.2951			−0.831469			−0.415734	+	0.909486i	$0.636475\pi$
$720$	−1.54832	+	3.20091i	−0.0577026	+	0.119291i
$721$	7.80046			0.290504
$722$	−11.5682	+	20.7943i	−0.430524	+	0.773883i
$723$	−24.4615	+	24.6923i	−0.909732	+	0.918315i
$724$	4.16838	+	6.71658i	0.154916	+	0.249620i
$725$	−28.0793	+	16.2116i	−1.04284	+	0.602084i
$726$	−20.5648	−	5.05840i	−0.763231	−	0.187735i
$727$	20.6516	+	11.9232i	0.765925	+	0.442207i	0.831419	−	0.555646i	$-0.187529\pi$
$727$	20.6516	+	11.9232i	0.765925	+	0.442207i	−0.0654939	+	0.997853i	$0.520862\pi$
$728$	−0.0614173	−	1.28508i	−0.00227628	−	0.0476281i
$729$	0.760483	+	26.9893i	0.0281660	+	0.999603i
$730$	0.0251072	+	1.57707i	0.000929260	+	0.0583701i
$731$	−33.2379	+	57.5697i	−1.22935	+	2.12929i
$732$	12.6010	+	2.88759i	0.465745	+	0.106728i
$733$	−3.96590	−	6.86914i	−0.146484	−	0.253717i	0.783442	−	0.621465i	$-0.213462\pi$
$733$	−3.96590	−	6.86914i	−0.146484	−	0.253717i	−0.929926	+	0.367748i	$0.880129\pi$
$734$	−15.3266	+	9.17718i	−0.565716	+	0.338736i
$735$	−0.364604	−	0.361196i	−0.0134486	−	0.0133229i
$736$	10.1686	−	21.3770i	0.374821	−	0.787965i
$737$		−	4.81737i		−	0.177450i
$738$	−3.67742	+	6.75892i	−0.135368	+	0.248799i
$739$			11.4276i			0.420372i	0.977661	+	0.210186i	$0.0674070\pi$
$739$			11.4276i			0.420372i	−0.977661	+	0.210186i	$0.932593\pi$
$740$	3.93838	+	2.10960i	0.144778	+	0.0775506i
$741$	1.12064	−	0.305922i	0.0411679	−	0.0112383i
$742$	0.891252	+	1.48846i	0.0327189	+	0.0546431i
$743$	4.19883	+	7.27258i	0.154040	+	0.266805i	0.932709	−	0.360630i	$-0.117438\pi$
$743$	4.19883	+	7.27258i	0.154040	+	0.266805i	−0.778669	+	0.627435i	$0.784105\pi$
$744$	−30.8794	+	10.0364i	−1.13209	+	0.367954i
$745$	2.77815	−	4.81190i	0.101784	−	0.176294i
$746$	30.7838	−	0.490082i	1.12708	−	0.0179432i
$747$	−25.5014	+	15.0443i	−0.933047	+	0.550440i
$748$	1.84498	+	57.9301i	0.0674590	+	2.11813i
$749$	−2.81032	−	1.62254i	−0.102687	−	0.0592863i
$750$	5.19095	+	4.98124i	0.189547	+	0.181889i
$751$	−23.7769	+	13.7276i	−0.867632	+	0.500928i	−0.866561	−	0.499072i	$-0.833674\pi$
$751$	−23.7769	+	13.7276i	−0.867632	+	0.500928i	−0.00107134	+	0.999999i	$0.500341\pi$
$752$	−14.7518	−	22.1627i	−0.537944	−	0.808192i
$753$	−3.01473	−	0.792643i	−0.109863	−	0.0288855i
$754$	3.71042	+	2.06417i	0.135126	+	0.0751727i
$755$	6.36845			0.231772
$756$	−7.00338	+	7.67806i	−0.254711	+	0.279248i
$757$	21.3239			0.775032			0.387516	−	0.921863i	$-0.373333\pi$
$757$	21.3239			0.775032			0.387516	+	0.921863i	$0.373333\pi$
$758$	−38.4034	−	21.3645i	−1.39488	−	0.775993i
$759$	31.0703	+	8.16910i	1.12778	+	0.296520i
$760$	−0.668252	−	1.03946i	−0.0242401	−	0.0377053i
$761$	20.3381	−	11.7422i	0.737254	−	0.425654i	−0.0838162	−	0.996481i	$-0.526711\pi$
$761$	20.3381	−	11.7422i	0.737254	−	0.425654i	0.821070	+	0.570828i	$0.193378\pi$
$762$	30.5073	+	29.2748i	1.10516	+	1.06051i
$763$	−8.46162	−	4.88532i	−0.306331	−	0.176860i
$764$	1.69058	−	0.0538421i	0.0611629	−	0.00194794i
$765$	0.0545735	+	5.81176i	0.00197311	+	0.210125i
$766$	−31.1430	+	0.495801i	−1.12524	+	0.0179140i
$767$	−2.99010	+	5.17901i	−0.107966	+	0.187003i
$768$	10.6346	+	25.5911i	0.383742	+	0.923441i
$769$	0.126197	+	0.218580i	0.00455079	+	0.00788219i	0.868292	−	0.496054i	$-0.165218\pi$
$769$	0.126197	+	0.218580i	0.00455079	+	0.00788219i	−0.863741	+	0.503936i	$0.831885\pi$
$770$	−0.954166	−	1.59353i	−0.0343858	−	0.0574270i
$771$	48.7665	−	13.3127i	1.75628	−	0.479443i
$772$	15.1725	−	28.3252i	0.546070	−	1.01945i
$773$			44.8216i			1.61212i	0.591833	+	0.806061i	$0.298405\pi$
$773$			44.8216i			1.61212i	−0.591833	+	0.806061i	$0.701595\pi$
$774$	−43.1222	+	1.09160i	−1.55000	+	0.0392368i
$775$			32.5571i			1.16949i
$776$	14.3281	−	27.8033i	0.514348	−	0.998079i
$777$	9.27669	+	9.18999i	0.332799	+	0.329689i
$778$	−32.7752	+	19.6249i	−1.17505	+	0.703588i
$779$	−1.33707	−	2.31587i	−0.0479054	−	0.0829745i
$780$	0.104288	−	0.455096i	0.00373411	−	0.0162950i
$781$	−3.68221	+	6.37777i	−0.131760	+	0.228215i
$782$	−0.615929	−	38.6887i	−0.0220256	−	1.38350i
$783$	−9.34255	−	33.0005i	−0.333875	−	1.17934i
$784$	−3.99189	+	0.254529i	−0.142568	+	0.00909031i
$785$	5.34387	+	3.08528i	0.190731	+	0.110118i
$786$	−2.97298	−	0.731275i	−0.106043	−	0.0260837i
$787$	1.97648	−	1.14112i	0.0704538	−	0.0406765i	−0.464359	−	0.885647i	$-0.653715\pi$
$787$	1.97648	−	1.14112i	0.0704538	−	0.0406765i	0.534813	+	0.844970i	$0.320382\pi$
$788$	−30.7809	+	19.1030i	−1.09653	+	0.680515i
$789$	−16.9777	+	17.1379i	−0.604423	+	0.610126i
$790$	0.972564	−	1.74822i	0.0346023	−	0.0621988i
$791$	−6.75664			−0.240238
$792$	−31.4438	+	20.6345i	−1.11731	+	0.733215i
$793$	−1.69749			−0.0602796
$794$	5.60314	−	10.0719i	0.198848	−	0.357437i
$795$	0.165806	+	0.607374i	0.00588052	+	0.0215413i
$796$	−29.8818	+	18.5450i	−1.05913	+	0.657309i
$797$	7.57149	−	4.37140i	0.268196	−	0.154843i	−0.359872	−	0.933002i	$-0.617180\pi$
$797$	7.57149	−	4.37140i	0.268196	−	0.154843i	0.628067	+	0.778159i	$0.283846\pi$
$798$	−1.00648	−	3.46862i	−0.0356292	−	0.122788i
$799$	−37.6871	−	21.7587i	−1.33327	−	0.769766i
$800$	27.6996	−	2.20939i	0.979330	−	0.0781138i
$801$	16.5932	−	29.3738i	0.586291	−	1.03787i
$802$	0.777627	+	48.8455i	0.0274590	+	1.72480i
$803$	−8.34162	+	14.4481i	−0.294369	+	0.509863i
$804$	−2.75772	−	2.56325i	−0.0972574	−	0.0903988i
$805$	0.619984	+	1.07384i	0.0218516	+	0.0378480i
$806$	3.65788	−	2.19025i	0.128843	−	0.0771481i
$807$	11.4394	−	43.5084i	0.402686	−	1.53157i
$808$	−25.8359	−	13.3142i	−0.908903	−	0.468392i
$809$			6.30809i			0.221781i	0.993833	+	0.110890i	$0.0353702\pi$
$809$			6.30809i			0.221781i	−0.993833	+	0.110890i	$0.964630\pi$
$810$	−3.19875	+	1.99788i	−0.112393	+	0.0701982i
$811$		−	14.2487i		−	0.500338i	−0.968202	−	0.250169i	$-0.919514\pi$
$811$		−	14.2487i		−	0.500338i	0.968202	−	0.250169i	$-0.0804862\pi$
$812$	6.23328	−	11.6368i	0.218745	−	0.408371i
$813$	7.38625	−	28.0928i	0.259047	−	0.985256i
$814$	24.2771	+	40.5446i	0.850911	+	1.42109i
$815$	−1.65305	−	2.86317i	−0.0579039	−	0.100293i
$816$	34.1440	+	29.7675i	1.19528	+	1.04207i
$817$	7.49565	−	12.9828i	0.262240	−	0.454212i
$818$	13.4556	−	0.214215i	0.470463	−	0.00748984i
$819$	0.671166	−	1.18812i	0.0234525	−	0.0415163i
$820$	−1.07425	+	0.0342130i	−0.0375143	+	0.00119477i
$821$	14.8959	+	8.60014i	0.519870	+	0.300147i	0.736881	−	0.676022i	$-0.236298\pi$
$821$	14.8959	+	8.60014i	0.519870	+	0.300147i	−0.217012	+	0.976169i	$0.569631\pi$
$822$	−34.6254	+	10.0472i	−1.20770	+	0.350437i
$823$	19.1570	−	11.0603i	0.667769	−	0.385537i	−0.127461	−	0.991844i	$-0.540683\pi$
$823$	19.1570	−	11.0603i	0.667769	−	0.385537i	0.795231	+	0.606307i	$0.207350\pi$
$824$	18.5587	−	11.9311i	0.646524	−	0.415639i
$825$	9.93131	+	36.3801i	0.345764	+	1.26659i
$826$	16.2480	+	9.03906i	0.565342	+	0.314509i
$827$	3.45796			0.120245			0.0601224	−	0.998191i	$-0.480851\pi$
$827$	3.45796			0.120245			0.0601224	+	0.998191i	$0.480851\pi$
$828$	21.2084	−	13.4397i	0.737045	−	0.467060i
$829$	−12.1136			−0.420722			−0.210361	−	0.977624i	$-0.567464\pi$
$829$	−12.1136			−0.420722			−0.210361	+	0.977624i	$0.567464\pi$
$830$	−3.61412	−	2.01059i	−0.125448	−	0.0697887i
$831$	−16.3227	+	16.4767i	−0.566229	+	0.571571i
$832$	−2.11169	−	2.96350i	−0.0732098	−	0.102741i
$833$	−5.66226	+	3.26911i	−0.196186	+	0.113268i
$834$	−3.30479	+	13.4356i	−0.114436	+	0.465235i
$835$	4.38597	+	2.53224i	0.151783	+	0.0876318i
$836$	−0.416070	−	13.0641i	−0.0143901	−	0.451831i
$837$	−33.3879	−	8.44408i	−1.15405	−	0.291870i
$838$	35.1254	−	0.559202i	1.21339	−	0.0193173i
$839$	5.59414	−	9.68934i	0.193131	−	0.334513i	−0.753155	−	0.657843i	$-0.771469\pi$
$839$	5.59414	−	9.68934i	0.193131	−	0.334513i	0.946286	+	0.323330i	$0.104802\pi$
$840$	−1.41992	−	0.301678i	−0.0489920	−	0.0104089i
$841$	7.28360	+	12.6156i	0.251158	+	0.435019i
$842$	−9.83670	−	16.4281i	−0.338995	−	0.566149i
$843$	−15.9654	−	15.8162i	−0.549877	−	0.544738i
$844$	−26.9914	−	14.4580i	−0.929083	−	0.497665i
$845$		−	3.79072i		−	0.130405i
$846$	−0.714600	−	28.2293i	−0.0245684	−	0.970543i
$847$		−	8.64579i		−	0.297073i
$848$	4.39711	+	2.17812i	0.150997	+	0.0747971i
$849$	33.9703	−	9.27348i	1.16586	−	0.318265i
$850$	38.9687	−	23.3334i	1.33661	−	0.800330i
$851$	−15.7744	−	27.3221i	−0.540739	−	0.936588i
$852$	1.69174	+	5.50141i	0.0579579	+	0.188475i
$853$	−18.5045	+	32.0507i	−0.633581	+	1.09739i	0.353233	+	0.935535i	$0.385082\pi$
$853$	−18.5045	+	32.0507i	−0.633581	+	1.09739i	−0.986814	+	0.161858i	$0.948251\pi$
$854$	0.0840106	+	5.27700i	0.00287478	+	0.180575i
$855$	−0.0123072	−	1.31064i	−0.000420896	−	0.0448229i
$856$	−9.16800	+	0.438164i	−0.313356	+	0.0149761i
$857$	−47.7999	−	27.5973i	−1.63281	−	0.942706i	−0.983220	−	0.182425i	$-0.941605\pi$
$857$	−47.7999	−	27.5973i	−1.63281	−	0.942706i	−0.649595	−	0.760281i	$-0.725061\pi$
$858$	3.41929	−	3.56324i	0.116732	−	0.121647i
$859$	−13.8649	+	8.00490i	−0.473064	+	0.273124i	−0.717521	−	0.696536i	$-0.754723\pi$
$859$	−13.8649	+	8.00490i	−0.473064	+	0.273124i	0.244458	+	0.969660i	$0.421390\pi$
$860$	−3.17724	−	5.11954i	−0.108343	−	0.174575i
$861$	−3.03804	−	0.798772i	−0.103536	−	0.0272221i
$862$	11.9586	−	21.4960i	0.407311	−	0.732157i
$863$	−21.2743			−0.724185			−0.362092	−	0.932142i	$-0.617937\pi$
$863$	−21.2743			−0.724185			−0.362092	+	0.932142i	$0.617937\pi$
$864$	−4.91847	+	28.9795i	−0.167330	+	0.985901i
$865$	1.38494			0.0470893
$866$	22.0999	−	39.7253i	0.750984	−	1.34992i
$867$	43.1314	+	11.3403i	1.46482	+	0.385136i
$868$	−6.98987	−	11.2629i	−0.237252	−	0.382288i
$869$	18.3253	−	10.5801i	0.621643	−	0.358906i
$870$	3.31701	−	3.45666i	0.112457	−	0.117192i
$871$	0.428140	+	0.247187i	0.0145070	+	0.00837560i
$872$	−27.6040	+	1.31927i	−0.934790	+	0.0446761i
$873$	28.5737	−	16.8567i	0.967073	−	0.570514i
$874$	0.138901	+	8.72488i	0.00469841	+	0.295123i
$875$	−1.46854	+	2.54359i	−0.0496458	+	0.0859890i
$876$	3.83244	+	12.4628i	0.129486	+	0.421080i
$877$	−11.8291	−	20.4886i	−0.399441	−	0.691852i	0.594216	−	0.804306i	$-0.297462\pi$
$877$	−11.8291	−	20.4886i	−0.399441	−	0.691852i	−0.993657	+	0.112453i	$0.964129\pi$
$878$	35.1491	−	21.0464i	1.18623	−	0.710281i
$879$	−25.8159	+	7.04742i	−0.870748	+	0.237703i
$880$	−4.70750	−	2.33188i	−0.158690	−	0.0786076i
$881$		−	15.8924i		−	0.535428i	−0.963498	−	0.267714i	$-0.913732\pi$
$881$		−	15.8924i		−	0.535428i	0.963498	−	0.267714i	$-0.0862683\pi$
$882$	−3.72674	−	2.02766i	−0.125486	−	0.0682749i
$883$		−	22.0899i		−	0.743386i	−0.928356	−	0.371693i	$-0.878777\pi$
$883$		−	22.0899i		−	0.743386i	0.928356	−	0.371693i	$-0.121223\pi$
$884$	−5.24315	−	2.80851i	−0.176346	−	0.0944604i
$885$	4.79356	+	4.74876i	0.161134	+	0.159628i
$886$	−4.82042	−	8.05048i	−0.161945	−	0.270461i
$887$	−22.9637	−	39.7744i	−0.771047	−	1.33549i	−0.936990	−	0.349357i	$-0.886400\pi$
$887$	−22.9637	−	39.7744i	−0.771047	−	1.33549i	0.165942	−	0.986135i	$-0.446933\pi$
$888$	36.1274	+	7.67566i	1.21236	+	0.257578i
$889$	−8.63063	+	14.9487i	−0.289462	+	0.501363i
$890$	4.71178	−	0.0750122i	0.157939	−	0.00251442i
$891$	−39.8842	+	0.749106i	−1.33617	+	0.0250960i
$892$	0.0532653	+	1.67247i	0.00178345	+	0.0559983i
$893$	8.49901	+	4.90691i	0.284409	+	0.164203i
$894$	10.9710	−	44.6025i	0.366927	−	1.49173i
$895$	1.58346	−	0.914214i	0.0529294	−	0.0305588i
$896$	−9.10814	+	6.71131i	−0.304282	+	0.224209i
$897$	−2.32028	+	2.34217i	−0.0774721	+	0.0782029i
$898$	−7.03058	−	3.91123i	−0.234613	−	0.130519i
$899$	43.7471			1.45905
$900$	26.1102	+	13.6721i	0.870341	+	0.455735i
$901$	8.02078			0.267211
$902$	−9.93452	−	5.52674i	−0.330783	−	0.184020i
$903$	−4.63767	−	16.9886i	−0.154332	−	0.565345i
$904$	−16.0753	+	10.3345i	−0.534656	+	0.343721i
$905$	−1.01425	+	0.585576i	−0.0337148	+	0.0194652i
$906$	50.5602	−	14.6710i	1.67975	−	0.487411i
$907$	29.5720	+	17.0734i	0.981922	+	0.566913i	0.902850	−	0.429956i	$-0.141471\pi$
$907$	29.5720	+	17.0734i	0.981922	+	0.566913i	0.0790723	+	0.996869i	$0.474804\pi$
$908$	−39.7872	+	1.26716i	−1.32039	+	0.0420521i
$909$	−15.6639	−	26.5518i	−0.519539	−	0.880667i
$910$	0.190584	−	0.00303412i	0.00631779	−	0.000100580i
$911$	−18.4144	+	31.8947i	−0.610097	+	1.05672i	0.381127	+	0.924523i	$0.375536\pi$
$911$	−18.4144	+	31.8947i	−0.610097	+	1.05672i	−0.991224	+	0.132196i	$0.957797\pi$
$912$	−7.69998	−	6.71303i	−0.254972	−	0.222291i
$913$	−21.8724	−	37.8841i	−0.723871	−	1.25378i
$914$	24.0727	+	40.2032i	0.796253	+	1.32981i
$915$	−0.487022	+	1.85233i	−0.0161004	+	0.0612362i
$916$	24.2130	−	45.2029i	0.800021	−	1.49354i
$917$		−	1.24989i		−	0.0412750i
$918$	13.8218	+	46.0148i	0.456188	+	1.51872i
$919$			33.7648i			1.11380i	0.830581	+	0.556898i	$0.188009\pi$
$919$			33.7648i			1.11380i	−0.830581	+	0.556898i	$0.811991\pi$
$920$	3.11754	+	1.60659i	0.102782	+	0.0529676i
$921$	−11.0822	+	42.1498i	−0.365170	+	1.38888i
$922$	−5.17521	+	3.09878i	−0.170437	+	0.102053i
$923$	−0.377879	−	0.654506i	−0.0124380	−	0.0215433i
$924$	−11.2463	−	10.4532i	−0.369977	−	0.343886i
$925$	18.5167	−	32.0719i	0.608826	−	1.05452i
$926$	0.530055	+	33.2947i	0.0174187	+	1.09413i
$927$	23.4004	−	0.219734i	0.768568	−	0.00721700i
$928$	−2.96877	−	37.2201i	−0.0974546	−	1.22181i
$929$	6.66528	+	3.84820i	0.218681	+	0.126255i	0.605339	−	0.795968i	$-0.293037\pi$
$929$	6.66528	+	3.84820i	0.218681	+	0.126255i	−0.386659	+	0.922223i	$0.626371\pi$
$930$	−1.34057	−	4.61995i	−0.0439589	−	0.151494i
$931$	1.27693	−	0.737233i	0.0418495	−	0.0241618i
$932$	−16.5402	+	10.2650i	−0.541793	+	0.336242i
$933$	2.69606	+	9.87614i	0.0882651	+	0.323330i
$934$	6.86629	−	12.3424i	0.224672	−	0.403856i
$935$	−8.58697			−0.280824
$936$	−0.220444	−	3.85333i	−0.00720543	−	0.125950i
$937$	35.6979			1.16620			0.583100	−	0.812400i	$-0.301839\pi$
$937$	35.6979			1.16620			0.583100	+	0.812400i	$0.301839\pi$
$938$	0.747243	−	1.34320i	0.0243983	−	0.0438569i
$939$	4.47362	−	4.51582i	0.145991	−	0.147368i
$940$	3.35143	−	2.07993i	0.109311	−	0.0678398i
$941$	−3.86824	+	2.23333i	−0.126101	+	0.0728045i	−0.561724	−	0.827325i	$-0.689862\pi$
$941$	−3.86824	+	2.23333i	−0.126101	+	0.0728045i	0.435623	+	0.900129i	$0.356528\pi$
$942$	49.5335	+	12.1839i	1.61389	+	0.396974i
$943$	6.57269	+	3.79474i	0.214036	+	0.123574i
$944$	52.4827	−	3.34637i	1.70816	−	0.108915i
$945$	−1.10394	−	1.07327i	−0.0359111	−	0.0349135i
$946$	−1.01449	−	63.7234i	−0.0329838	−	2.07183i
$947$	−1.84265	+	3.19156i	−0.0598780	+	0.103712i	−0.894411	−	0.447247i	$-0.852405\pi$
$947$	−1.84265	+	3.19156i	−0.0598780	+	0.103712i	0.834532	+	0.550959i	$0.185738\pi$
$948$	3.69398	−	16.1199i	0.119975	−	0.523550i
$949$	−0.856043	−	1.48271i	−0.0277883	−	0.0481308i
$950$	−8.78803	+	5.26204i	−0.285121	+	0.170723i
$951$	−30.1723	−	29.8903i	−0.978404	−	0.969260i
$952$	−8.47135	+	16.4384i	−0.274558	+	0.532773i
$953$		−	12.8618i		−	0.416636i	−0.978061	−	0.208318i	$-0.933201\pi$
$953$		−	12.8618i		−	0.416636i	0.978061	−	0.208318i	$-0.0667988\pi$
$954$	2.71557	+	4.44008i	0.0879198	+	0.143753i
$955$			0.250594i			0.00810904i
$956$	−16.7990	+	31.3617i	−0.543317	+	1.01431i
$957$	48.8841	−	13.3447i	1.58020	−	0.431374i
$958$	10.2778	+	17.1648i	0.332062	+	0.554570i
$959$	−7.35942	−	12.7469i	−0.237648	−	0.411619i
$960$	−3.83968	+	1.45407i	−0.123925	+	0.0469300i
$961$	6.46392	−	11.1958i	0.208513	−	0.361156i
$962$	−4.84906	+	0.0771977i	−0.156340	+	0.00248895i
$963$	−8.47630	−	4.78824i	−0.273145	−	0.154299i
$964$	−40.1140	+	1.27756i	−1.29198	+	0.0411475i
$965$	4.12284	+	2.38032i	0.132719	+	0.0766254i
$966$	7.39598	+	7.09718i	0.237962	+	0.228348i
$967$	−5.51188	+	3.18228i	−0.177250	+	0.102335i	−0.586000	−	0.810311i	$-0.699298\pi$
$967$	−5.51188	+	3.18228i	−0.177250	+	0.102335i	0.408750	+	0.912646i	$0.365965\pi$
$968$	−13.2240	−	20.5699i	−0.425037	−	0.661143i
$969$	−16.1488	−	4.24589i	−0.518774	−	0.136398i
$970$	4.04953	+	2.25282i	0.130023	+	0.0723337i
$971$	50.7663			1.62917			0.814583	−	0.580046i	$-0.196966\pi$
$971$	50.7663			1.62917			0.814583	+	0.580046i	$0.196966\pi$
$972$	−20.7929	+	23.2305i	−0.666934	+	0.745117i
$973$	−5.64854			−0.181084
$974$	46.4539	+	25.8431i	1.48848	+	0.828067i
$975$	−3.74284	−	0.984081i	−0.119867	−	0.0315158i
$976$	8.27124	+	12.4265i	0.264756	+	0.397761i
$977$	−8.03866	+	4.64112i	−0.257179	+	0.148483i	−0.623047	−	0.782184i	$-0.714106\pi$
$977$	−8.03866	+	4.64112i	−0.257179	+	0.148483i	0.365868	+	0.930667i	$0.380772\pi$
$978$	−19.7198	−	18.9231i	−0.630568	−	0.605093i
$979$	43.1663	+	24.9221i	1.37960	+	0.796513i
$980$	−0.0188644	−	0.592319i	−0.000602601	−	0.0189209i
$981$	−25.5213	−	14.4169i	−0.814834	−	0.460298i
$982$	−5.42428	+	0.0863552i	−0.173096	+	0.00275571i
$983$	−9.75429	+	16.8949i	−0.311113	+	0.538864i	−0.978604	−	0.205754i	$-0.934035\pi$
$983$	−9.75429	+	16.8949i	−0.311113	+	0.538864i	0.667490	+	0.744619i	$0.267369\pi$
$984$	−8.44981	+	2.74636i	−0.269370	+	0.0875509i
$985$	−2.68360	−	4.64813i	−0.0855066	−	0.148102i
$986$	−31.3532	−	52.3624i	−0.998491	−	1.66756i
$987$	11.1213	−	3.03598i	0.353995	−	0.0966363i
$988$	1.18241	+	0.633361i	0.0376175	+	0.0201499i
$989$			42.5470i			1.35292i
$990$	−2.90726	−	4.75351i	−0.0923988	−	0.151077i
$991$		−	29.1799i		−	0.926932i	−0.886115	−	0.463466i	$-0.846606\pi$
$991$		−	29.1799i		−	0.926932i	0.886115	−	0.463466i	$-0.153394\pi$
$992$	−33.8572	−	16.1053i	−1.07497	−	0.511343i
$993$	13.3614	+	13.2365i	0.424010	+	0.420048i
$994$	−2.01597	+	1.20711i	−0.0639427	+	0.0382872i
$995$	−2.60521	−	4.51236i	−0.0825908	−	0.143051i
$996$	−33.3249	−	7.63661i	−1.05594	−	0.241975i
$997$	7.57302	−	13.1169i	0.239840	−	0.415415i	−0.720828	−	0.693114i	$-0.756238\pi$
$997$	7.57302	−	13.1169i	0.239840	−	0.415415i	0.960668	+	0.277699i	$0.0895717\pi$
$998$	0.210359	+	13.2134i	0.00665879	+	0.418262i
$999$	28.0877	+	27.3074i	0.888656	+	0.863969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.12	✓	72
3.2	odd	2		756.2.ba.a.575.25		72
4.3	odd	2	inner	252.2.ba.a.155.24	yes	72
9.4	even	3		756.2.ba.a.71.13		72
9.5	odd	6	inner	252.2.ba.a.239.24	yes	72
12.11	even	2		756.2.ba.a.575.13		72
36.23	even	6	inner	252.2.ba.a.239.12	yes	72
36.31	odd	6		756.2.ba.a.71.25		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.12	✓	72	1.1	even	1	trivial
252.2.ba.a.155.24	yes	72	4.3	odd	2	inner
252.2.ba.a.239.12	yes	72	36.23	even	6	inner
252.2.ba.a.239.24	yes	72	9.5	odd	6	inner
756.2.ba.a.71.13		72	9.4	even	3
756.2.ba.a.71.25		72	36.31	odd	6
756.2.ba.a.575.13		72	12.11	even	2
756.2.ba.a.575.25		72	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.687522 + 1.23585i) q^{2} +(-1.67512 - 0.440428i) q^{3} +(-1.05463 - 1.69934i) q^{4} +(0.256612 - 0.148155i) q^{5} +(1.69598 - 1.76738i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +(2.61205 + 1.47554i) q^{9} +O(q^{10})\)	\(q+(-0.687522 + 1.23585i) q^{2} +(-1.67512 - 0.440428i) q^{3} +(-1.05463 - 1.69934i) q^{4} +(0.256612 - 0.148155i) q^{5} +(1.69598 - 1.76738i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.82520 - 0.135024i) q^{8} +(2.61205 + 1.47554i) q^{9} +(0.00667042 + 0.418992i) q^{10} +(-2.21618 + 3.83853i) q^{11} +(1.01819 + 3.31109i) q^{12} +(-0.227431 - 0.393922i) q^{13} +(-1.21333 + 0.726513i) q^{14} +(-0.495107 + 0.135158i) q^{15} +(-1.77552 + 3.58435i) q^{16} +6.53822i q^{17} +(-3.61938 + 2.21362i) q^{18} -1.47447i q^{19} +(-0.522396 - 0.279823i) q^{20} +(-1.23048 - 1.21898i) q^{21} +(-3.22016 - 5.37793i) q^{22} +(2.09235 + 3.62406i) q^{23} +(-4.79202 - 1.01812i) q^{24} +(-2.45610 + 4.25409i) q^{25} +(0.643190 - 0.0102397i) q^{26} +(-3.72562 - 3.62212i) q^{27} +(-0.0636644 - 1.99899i) q^{28} +(5.71624 + 3.30027i) q^{29} +(0.173362 - 0.704800i) q^{30} +(5.73985 - 3.31390i) q^{31} +(-3.20899 - 4.65858i) q^{32} +(5.40296 - 5.45393i) q^{33} +(-8.08023 - 4.49517i) q^{34} +0.296310 q^{35} +(-0.247295 - 5.99490i) q^{36} -7.53908 q^{37} +(1.82221 + 1.01373i) q^{38} +(0.207480 + 0.760033i) q^{39} +(0.704976 - 0.453216i) q^{40} +(1.57065 - 0.906813i) q^{41} +(2.35246 - 0.682609i) q^{42} +(8.80511 + 5.08363i) q^{43} +(8.86022 - 0.282183i) q^{44} +(0.888890 - 0.00834685i) q^{45} +(-5.91731 + 0.0942044i) q^{46} +(-3.32792 + 5.76413i) q^{47} +(4.55285 - 5.22222i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-3.56878 - 5.96014i) q^{50} +(2.87961 - 10.9523i) q^{51} +(-0.429553 + 0.801924i) q^{52} -1.22675i q^{53} +(7.03783 - 2.11400i) q^{54} +1.31335i q^{55} +(2.51421 + 1.29567i) q^{56} +(-0.649396 + 2.46991i) q^{57} +(-8.00866 + 4.79538i) q^{58} +(-6.57365 - 11.3859i) q^{59} +(0.751833 + 0.698814i) q^{60} +(1.86594 - 3.23190i) q^{61} +(0.149203 + 9.37195i) q^{62} +(1.52433 + 2.58388i) q^{63} +(7.96354 - 0.762941i) q^{64} +(-0.116723 - 0.0673900i) q^{65} +(3.02557 + 10.4269i) q^{66} +(-0.941252 + 0.543432i) q^{67} +(11.1107 - 6.89539i) q^{68} +(-1.90880 - 6.99226i) q^{69} +(-0.203719 + 0.366193i) q^{70} +1.66151 q^{71} +(7.57879 + 3.81601i) q^{72} +3.76397 q^{73} +(5.18328 - 9.31713i) q^{74} +(5.98788 - 6.04437i) q^{75} +(-2.50562 + 1.55501i) q^{76} +(-3.83853 + 2.21618i) q^{77} +(-1.08193 - 0.266126i) q^{78} +(-4.13444 - 2.38702i) q^{79} +(0.0754193 + 1.18284i) q^{80} +(4.64557 + 7.70835i) q^{81} +(0.0408277 + 2.56453i) q^{82} +(-4.93471 + 8.54717i) q^{83} +(-0.773764 + 3.37658i) q^{84} +(0.968669 + 1.67778i) q^{85} +(-12.3363 + 7.38665i) q^{86} +(-8.12185 - 8.04594i) q^{87} +(-5.74286 + 11.1439i) q^{88} -11.2455i q^{89} +(-0.600816 + 1.10427i) q^{90} -0.454862i q^{91} +(3.95186 - 7.37765i) q^{92} +(-11.0745 + 3.02319i) q^{93} +(-4.83555 - 8.07576i) q^{94} +(-0.218449 - 0.378366i) q^{95} +(3.32367 + 9.21701i) q^{96} +(5.52923 - 9.57690i) q^{97} +(-1.41403 + 0.0225116i) q^{98} +(-11.4527 + 6.75637i) 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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