LMFDB - Embedded newform 418.2.f.d.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.d.267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.618034 + 1.90211i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.363271i) q^{5} +(1.61803 - 1.17557i) q^{6} +(0.572949 + 1.76336i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.618034 q^{10} +(0.309017 - 3.30220i) q^{11} -2.00000 q^{12} +(5.23607 + 3.80423i) q^{13} +(0.572949 - 1.76336i) q^{14} +(0.381966 + 1.17557i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.54508 + 3.30220i) q^{17} +(0.309017 + 0.951057i) q^{18} +(0.309017 - 0.951057i) q^{19} +(0.500000 + 0.363271i) q^{20} -3.70820 q^{21} +(-2.19098 + 2.48990i) q^{22} -1.14590 q^{23} +(1.61803 + 1.17557i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(-3.23607 + 2.35114i) q^{27} +(-1.50000 + 1.08981i) q^{28} +(0.472136 + 1.45309i) q^{29} +(0.381966 - 1.17557i) q^{30} +(-1.61803 - 1.17557i) q^{31} +1.00000 q^{32} +(6.09017 + 2.62866i) q^{33} +5.61803 q^{34} +(0.927051 + 0.673542i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.23607 + 3.80423i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.4721 + 7.60845i) q^{39} +(-0.190983 - 0.587785i) q^{40} +(-2.85410 + 8.78402i) q^{41} +(3.00000 + 2.17963i) q^{42} +2.09017 q^{43} +(3.23607 - 0.726543i) q^{44} -0.618034 q^{45} +(0.927051 + 0.673542i) q^{46} +(1.11803 - 3.44095i) q^{47} +(-0.618034 - 1.90211i) q^{48} +(2.88197 - 2.09387i) q^{49} +(3.73607 - 2.71441i) q^{50} +(-3.47214 - 10.6861i) q^{51} +(-2.00000 + 6.15537i) q^{52} +(7.47214 + 5.42882i) q^{53} +4.00000 q^{54} +(-1.04508 - 1.76336i) q^{55} +1.85410 q^{56} +(1.61803 + 1.17557i) q^{57} +(0.472136 - 1.45309i) q^{58} +(-3.85410 - 11.8617i) q^{59} +(-1.00000 + 0.726543i) q^{60} +(-8.54508 + 6.20837i) q^{61} +(0.618034 + 1.90211i) q^{62} +(0.572949 - 1.76336i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-3.38197 - 5.70634i) q^{66} +7.23607 q^{67} +(-4.54508 - 3.30220i) q^{68} +(0.708204 - 2.17963i) q^{69} +(-0.354102 - 1.08981i) q^{70} +(10.4721 - 7.60845i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-4.32624 - 13.3148i) q^{73} +(1.23607 - 3.80423i) q^{74} +(-7.47214 - 5.42882i) q^{75} +1.00000 q^{76} +(6.00000 - 1.34708i) q^{77} +12.9443 q^{78} +(7.85410 + 5.70634i) q^{79} +(-0.190983 + 0.587785i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(7.47214 - 5.42882i) q^{82} +(-8.73607 + 6.34712i) q^{83} +(-1.14590 - 3.52671i) q^{84} +(-1.07295 + 3.30220i) q^{85} +(-1.69098 - 1.22857i) q^{86} -3.05573 q^{87} +(-3.04508 - 1.31433i) q^{88} +6.76393 q^{89} +(0.500000 + 0.363271i) q^{90} +(-3.70820 + 11.4127i) q^{91} +(-0.354102 - 1.08981i) q^{92} +(3.23607 - 2.35114i) q^{93} +(-2.92705 + 2.12663i) q^{94} +(-0.190983 - 0.587785i) q^{95} +(-0.618034 + 1.90211i) q^{96} +(3.85410 + 2.80017i) q^{97} -3.56231 q^{98} +(-2.19098 + 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9} + 2 q^{10} - q^{11} - 8 q^{12} + 12 q^{13} + 9 q^{14} + 6 q^{15} - q^{16} - 7 q^{17} - q^{18} - q^{19} + 2 q^{20} + 12 q^{21}+ \cdots - 11 q^{99}+O(q^{100}) $ 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9 + 2 * q^10 - q^11 - 8 * q^12 + 12 * q^13 + 9 * q^14 + 6 * q^15 - q^16 - 7 * q^17 - q^18 - q^19 + 2 * q^20 + 12 * q^21 - 11 * q^22 - 18 * q^23 + 2 * q^24 + q^25 - 8 * q^26 - 4 * q^27 - 6 * q^28 - 16 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^33 + 18 * q^34 - 3 * q^35 - q^36 - 4 * q^37 - q^38 - 24 * q^39 - 3 * q^40 + 2 * q^41 + 12 * q^42 - 14 * q^43 + 4 * q^44 + 2 * q^45 - 3 * q^46 + 2 * q^48 + 16 * q^49 + 6 * q^50 + 4 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 7 * q^55 - 6 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^59 - 4 * q^60 - 23 * q^61 - 2 * q^62 + 9 * q^63 - q^64 + 16 * q^65 - 18 * q^66 + 20 * q^67 - 7 * q^68 - 24 * q^69 + 12 * q^70 + 24 * q^71 - q^72 + 14 * q^73 - 4 * q^74 - 12 * q^75 + 4 * q^76 + 24 * q^77 + 16 * q^78 + 18 * q^79 - 3 * q^80 + 11 * q^81 + 12 * q^82 - 26 * q^83 - 18 * q^84 - 11 * q^85 - 9 * q^86 - 48 * q^87 - q^88 + 36 * q^89 + 2 * q^90 + 12 * q^91 + 12 * q^92 + 4 * q^93 - 5 * q^94 - 3 * q^95 + 2 * q^96 + 2 * q^97 + 26 * q^98 - 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.618034	+	1.90211i	−0.356822	+	1.09819i	0.598123	+	0.801404i	$0.295913\pi$
$3$	−0.618034	+	1.90211i	−0.356822	+	1.09819i	−0.954945	+	0.296781i	$0.904087\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	−0.470342	−	0.882484i	$-0.655869\pi$
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	0.693949	+	0.720024i	$0.255869\pi$
$6$	1.61803	−	1.17557i	0.660560	−	0.479925i
$7$	0.572949	+	1.76336i	0.216554	+	0.666486i	0.999040	+	0.0438167i	$0.0139517\pi$
$7$	0.572949	+	1.76336i	0.216554	+	0.666486i	−0.782485	+	0.622669i	$0.786048\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.618034			−0.195440
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−2.00000			−0.577350
$13$	5.23607	+	3.80423i	1.45222	+	1.05510i	0.985305	+	0.170802i	$0.0546359\pi$
$13$	5.23607	+	3.80423i	1.45222	+	1.05510i	0.466919	+	0.884300i	$0.345364\pi$
$14$	0.572949	−	1.76336i	0.153127	−	0.471277i
$15$	0.381966	+	1.17557i	0.0986232	+	0.303531i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.981441	−	0.191764i	$-0.938579\pi$
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.120904	+	0.992664i	$0.538579\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	0.500000	+	0.363271i	0.111803	+	0.0812299i
$21$	−3.70820			−0.809196
$22$	−2.19098	+	2.48990i	−0.467119	+	0.530848i
$23$	−1.14590			−0.238936			−0.119468	−	0.992838i	$-0.538119\pi$
$23$	−1.14590			−0.238936			−0.119468	+	0.992838i	$0.538119\pi$
$24$	1.61803	+	1.17557i	0.330280	+	0.239962i
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$	−2.00000	−	6.15537i	−0.392232	−	1.20717i
$27$	−3.23607	+	2.35114i	−0.622782	+	0.452477i
$28$	−1.50000	+	1.08981i	−0.283473	+	0.205955i
$29$	0.472136	+	1.45309i	0.0876734	+	0.269831i	0.985275	−	0.170976i	$-0.0546922\pi$
$29$	0.472136	+	1.45309i	0.0876734	+	0.269831i	−0.897602	+	0.440807i	$0.854692\pi$
$30$	0.381966	−	1.17557i	0.0697371	−	0.214629i
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$	1.00000			0.176777
$33$	6.09017	+	2.62866i	1.06016	+	0.457590i
$34$	5.61803			0.963485
$35$	0.927051	+	0.673542i	0.156700	+	0.113849i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	1.23607	+	3.80423i	0.203208	+	0.625411i	0.999782	+	0.0208697i	$0.00664352\pi$
$37$	1.23607	+	3.80423i	0.203208	+	0.625411i	−0.796574	+	0.604541i	$0.793356\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	−10.4721	+	7.60845i	−1.67688	+	1.21833i
$40$	−0.190983	−	0.587785i	−0.0301971	−	0.0929370i
$41$	−2.85410	+	8.78402i	−0.445736	+	1.37183i	0.435939	+	0.899976i	$0.356416\pi$
$41$	−2.85410	+	8.78402i	−0.445736	+	1.37183i	−0.881675	+	0.471858i	$0.843584\pi$
$42$	3.00000	+	2.17963i	0.462910	+	0.336324i
$43$	2.09017			0.318748			0.159374	−	0.987218i	$-0.449052\pi$
$43$	2.09017			0.318748			0.159374	+	0.987218i	$0.449052\pi$
$44$	3.23607	−	0.726543i	0.487856	−	0.109530i
$45$	−0.618034			−0.0921311
$46$	0.927051	+	0.673542i	0.136686	+	0.0993083i
$47$	1.11803	−	3.44095i	0.163082	−	0.501915i	−0.835808	−	0.549022i	$-0.815000\pi$
$47$	1.11803	−	3.44095i	0.163082	−	0.501915i	0.998890	+	0.0471073i	$0.0150003\pi$
$48$	−0.618034	−	1.90211i	−0.0892055	−	0.274546i
$49$	2.88197	−	2.09387i	0.411709	−	0.299124i
$50$	3.73607	−	2.71441i	0.528360	−	0.383876i
$51$	−3.47214	−	10.6861i	−0.486196	−	1.49636i
$52$	−2.00000	+	6.15537i	−0.277350	+	0.853596i
$53$	7.47214	+	5.42882i	1.02638	+	0.745706i	0.967580	−	0.252564i	$-0.0812737\pi$
$53$	7.47214	+	5.42882i	1.02638	+	0.745706i	0.0587965	+	0.998270i	$0.481274\pi$
$54$	4.00000			0.544331
$55$	−1.04508	−	1.76336i	−0.140919	−	0.237771i
$56$	1.85410			0.247765
$57$	1.61803	+	1.17557i	0.214314	+	0.155708i
$58$	0.472136	−	1.45309i	0.0619945	−	0.190799i
$59$	−3.85410	−	11.8617i	−0.501761	−	1.54426i	−0.806148	−	0.591714i	$-0.798451\pi$
$59$	−3.85410	−	11.8617i	−0.501761	−	1.54426i	0.304387	−	0.952549i	$-0.401549\pi$
$60$	−1.00000	+	0.726543i	−0.129099	+	0.0937962i
$61$	−8.54508	+	6.20837i	−1.09409	+	0.794900i	−0.980085	−	0.198581i	$-0.936367\pi$
$61$	−8.54508	+	6.20837i	−1.09409	+	0.794900i	−0.114001	+	0.993481i	$0.536367\pi$
$62$	0.618034	+	1.90211i	0.0784904	+	0.241569i
$63$	0.572949	−	1.76336i	0.0721848	−	0.222162i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.00000			0.496139
$66$	−3.38197	−	5.70634i	−0.416291	−	0.702402i
$67$	7.23607			0.884026			0.442013	−	0.897009i	$-0.354264\pi$
$67$	7.23607			0.884026			0.442013	+	0.897009i	$0.354264\pi$
$68$	−4.54508	−	3.30220i	−0.551173	−	0.400450i
$69$	0.708204	−	2.17963i	0.0852577	−	0.262396i
$70$	−0.354102	−	1.08981i	−0.0423233	−	0.130258i
$71$	10.4721	−	7.60845i	1.24281	−	0.902957i	0.245031	−	0.969515i	$-0.421202\pi$
$71$	10.4721	−	7.60845i	1.24281	−	0.902957i	0.997783	+	0.0665580i	$0.0212017\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	−4.32624	−	13.3148i	−0.506348	−	1.55838i	−0.798493	−	0.602004i	$-0.794369\pi$
$73$	−4.32624	−	13.3148i	−0.506348	−	1.55838i	0.292145	−	0.956374i	$-0.405631\pi$
$74$	1.23607	−	3.80423i	0.143690	−	0.442232i
$75$	−7.47214	−	5.42882i	−0.862808	−	0.626867i
$76$	1.00000			0.114708
$77$	6.00000	−	1.34708i	0.683763	−	0.153514i
$78$	12.9443			1.46565
$79$	7.85410	+	5.70634i	0.883656	+	0.642013i	0.934216	−	0.356708i	$-0.116101\pi$
$79$	7.85410	+	5.70634i	0.883656	+	0.642013i	−0.0505605	+	0.998721i	$0.516101\pi$
$80$	−0.190983	+	0.587785i	−0.0213525	+	0.0657164i
$81$	−3.39919	−	10.4616i	−0.377687	−	1.16240i
$82$	7.47214	−	5.42882i	0.825159	−	0.599513i
$83$	−8.73607	+	6.34712i	−0.958908	+	0.696687i	−0.952897	−	0.303294i	$-0.901913\pi$
$83$	−8.73607	+	6.34712i	−0.958908	+	0.696687i	−0.00601115	+	0.999982i	$0.501913\pi$
$84$	−1.14590	−	3.52671i	−0.125028	−	0.384796i
$85$	−1.07295	+	3.30220i	−0.116378	+	0.358174i
$86$	−1.69098	−	1.22857i	−0.182343	−	0.132480i
$87$	−3.05573			−0.327608
$88$	−3.04508	−	1.31433i	−0.324607	−	0.140108i
$89$	6.76393			0.716975			0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393			0.716975			0.358488	+	0.933534i	$0.383293\pi$
$90$	0.500000	+	0.363271i	0.0527046	+	0.0382922i
$91$	−3.70820	+	11.4127i	−0.388725	+	1.19637i
$92$	−0.354102	−	1.08981i	−0.0369177	−	0.113621i
$93$	3.23607	−	2.35114i	0.335565	−	0.243802i
$94$	−2.92705	+	2.12663i	−0.301902	+	0.219345i
$95$	−0.190983	−	0.587785i	−0.0195944	−	0.0603055i
$96$	−0.618034	+	1.90211i	−0.0630778	+	0.194134i
$97$	3.85410	+	2.80017i	0.391325	+	0.284314i	0.765998	−	0.642843i	$-0.222245\pi$
$97$	3.85410	+	2.80017i	0.391325	+	0.284314i	−0.374673	+	0.927157i	$0.622245\pi$
$98$	−3.56231			−0.359847
$99$	−2.19098	+	2.48990i	−0.220202	+	0.250244i
$100$	−4.61803			−0.461803
$101$	−4.50000	−	3.26944i	−0.447767	−	0.325322i	0.340947	−	0.940083i	$-0.389252\pi$
$101$	−4.50000	−	3.26944i	−0.447767	−	0.325322i	−0.788713	+	0.614761i	$0.789252\pi$
$102$	−3.47214	+	10.6861i	−0.343793	+	1.05809i
$103$	−2.85410	−	8.78402i	−0.281223	−	0.865515i	−0.987505	−	0.157585i	$-0.949629\pi$
$103$	−2.85410	−	8.78402i	−0.281223	−	0.865515i	0.706282	−	0.707930i	$-0.250371\pi$
$104$	5.23607	−	3.80423i	0.513439	−	0.373035i
$105$	−1.85410	+	1.34708i	−0.180942	+	0.131462i
$106$	−2.85410	−	8.78402i	−0.277215	−	0.853180i
$107$	1.85410	−	5.70634i	0.179243	−	0.551653i	−0.820559	−	0.571562i	$-0.806338\pi$
$107$	1.85410	−	5.70634i	0.179243	−	0.551653i	0.999802	+	0.0199092i	$0.00633772\pi$
$108$	−3.23607	−	2.35114i	−0.311391	−	0.226239i
$109$	−1.23607			−0.118394			−0.0591969	−	0.998246i	$-0.518854\pi$
$109$	−1.23607			−0.118394			−0.0591969	+	0.998246i	$0.518854\pi$
$110$	−0.190983	+	2.04087i	−0.0182095	+	0.194589i
$111$	−8.00000			−0.759326
$112$	−1.50000	−	1.08981i	−0.141737	−	0.102978i
$113$	4.47214	−	13.7638i	0.420703	−	1.29479i	−0.486346	−	0.873766i	$-0.661671\pi$
$113$	4.47214	−	13.7638i	0.420703	−	1.29479i	0.907049	−	0.421025i	$-0.138329\pi$
$114$	−0.618034	−	1.90211i	−0.0578842	−	0.178149i
$115$	−0.572949	+	0.416272i	−0.0534278	+	0.0388175i
$116$	−1.23607	+	0.898056i	−0.114766	+	0.0833824i
$117$	−2.00000	−	6.15537i	−0.184900	−	0.569064i
$118$	−3.85410	+	11.8617i	−0.354799	+	1.09196i
$119$	−8.42705	−	6.12261i	−0.772506	−	0.561259i
$120$	1.23607			0.112837
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	10.5623			0.956266
$123$	−14.9443	−	10.8576i	−1.34748	−	0.979001i
$124$	0.618034	−	1.90211i	0.0555011	−	0.170815i
$125$	1.83688	+	5.65334i	0.164296	+	0.505650i
$126$	−1.50000	+	1.08981i	−0.133631	+	0.0970883i
$127$	−6.00000	+	4.35926i	−0.532414	+	0.386821i	−0.821260	−	0.570554i	$-0.806728\pi$
$127$	−6.00000	+	4.35926i	−0.532414	+	0.386821i	0.288846	+	0.957376i	$0.406728\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−1.29180	+	3.97574i	−0.113736	+	0.350044i
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	−0.909830			−0.0794922			−0.0397461	−	0.999210i	$-0.512655\pi$
$131$	−0.909830			−0.0794922			−0.0397461	+	0.999210i	$0.512655\pi$
$132$	−0.618034	+	6.60440i	−0.0537930	+	0.574839i
$133$	1.85410			0.160771
$134$	−5.85410	−	4.25325i	−0.505717	−	0.367425i
$135$	−0.763932	+	2.35114i	−0.0657488	+	0.202354i
$136$	1.73607	+	5.34307i	0.148867	+	0.458164i
$137$	12.2082	−	8.86978i	1.04302	−	0.757796i	0.0721450	−	0.997394i	$-0.477016\pi$
$137$	12.2082	−	8.86978i	1.04302	−	0.757796i	0.970872	+	0.239598i	$0.0770156\pi$
$138$	−1.85410	+	1.34708i	−0.157832	+	0.114671i
$139$	1.64590	+	5.06555i	0.139603	+	0.429655i	0.996278	−	0.0862030i	$-0.0274734\pi$
$139$	1.64590	+	5.06555i	0.139603	+	0.429655i	−0.856674	+	0.515858i	$0.827473\pi$
$140$	−0.354102	+	1.08981i	−0.0299271	+	0.0921061i
$141$	5.85410	+	4.25325i	0.493004	+	0.358189i
$142$	−12.9443			−1.08626
$143$	14.1803	−	16.1150i	1.18582	−	1.34760i
$144$	1.00000			0.0833333
$145$	0.763932	+	0.555029i	0.0634411	+	0.0460927i
$146$	−4.32624	+	13.3148i	−0.358042	+	1.10194i
$147$	2.20163	+	6.77591i	0.181587	+	0.558868i
$148$	−3.23607	+	2.35114i	−0.266003	+	0.193263i
$149$	16.5623	−	12.0332i	1.35684	−	0.985800i	0.358198	−	0.933646i	$-0.383391\pi$
$149$	16.5623	−	12.0332i	1.35684	−	0.985800i	0.998639	−	0.0521541i	$-0.0166087\pi$
$150$	2.85410	+	8.78402i	0.233036	+	0.717212i
$151$	−0.0901699	+	0.277515i	−0.00733793	+	0.0225838i	−0.954658	−	0.297703i	$-0.903779\pi$
$151$	−0.0901699	+	0.277515i	−0.00733793	+	0.0225838i	0.947321	+	0.320287i	$0.103779\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	5.61803			0.454191
$154$	−5.64590	−	2.43690i	−0.454959	−	0.196371i
$155$	−1.23607			−0.0992834
$156$	−10.4721	−	7.60845i	−0.838442	−	0.609164i
$157$	2.37132	−	7.29818i	0.189252	−	0.582458i	−0.810743	−	0.585402i	$-0.800937\pi$
$157$	2.37132	−	7.29818i	0.189252	−	0.582458i	0.999996	+	0.00294327i	$0.000936872\pi$
$158$	−3.00000	−	9.23305i	−0.238667	−	0.734542i
$159$	−14.9443	+	10.8576i	−1.18516	+	0.861068i
$160$	0.500000	−	0.363271i	0.0395285	−	0.0287191i
$161$	−0.656541	−	2.02063i	−0.0517427	−	0.159248i
$162$	−3.39919	+	10.4616i	−0.267065	+	0.821943i
$163$	13.2082	+	9.59632i	1.03455	+	0.751642i	0.969214	−	0.246222i	$-0.0791891\pi$
$163$	13.2082	+	9.59632i	1.03455	+	0.751642i	0.0653328	+	0.997864i	$0.479189\pi$
$164$	−9.23607			−0.721216
$165$	4.00000	−	0.898056i	0.311400	−	0.0699136i
$166$	10.7984			0.838116
$167$	20.5623	+	14.9394i	1.59116	+	1.15604i	0.902264	+	0.431183i	$0.141904\pi$
$167$	20.5623	+	14.9394i	1.59116	+	1.15604i	0.688895	+	0.724862i	$0.258096\pi$
$168$	−1.14590	+	3.52671i	−0.0884080	+	0.272092i
$169$	8.92705	+	27.4746i	0.686696	+	2.11343i
$170$	2.80902	−	2.04087i	0.215442	−	0.156528i
$171$	−0.809017	+	0.587785i	−0.0618671	+	0.0449491i
$172$	0.645898	+	1.98787i	0.0492493	+	0.151574i
$173$	−0.944272	+	2.90617i	−0.0717917	+	0.220952i	−0.980514	−	0.196449i	$-0.937059\pi$
$173$	−0.944272	+	2.90617i	−0.0717917	+	0.220952i	0.908722	+	0.417401i	$0.137059\pi$
$174$	2.47214	+	1.79611i	0.187412	+	0.136163i
$175$	−8.56231			−0.647249
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$	24.9443			1.87493
$178$	−5.47214	−	3.97574i	−0.410154	−	0.297994i
$179$	−6.23607	+	19.1926i	−0.466106	+	1.43453i	0.391481	+	0.920186i	$0.371963\pi$
$179$	−6.23607	+	19.1926i	−0.466106	+	1.43453i	−0.857587	+	0.514339i	$0.828037\pi$
$180$	−0.190983	−	0.587785i	−0.0142350	−	0.0438109i
$181$	11.0902	−	8.05748i	0.824326	−	0.598908i	−0.0936225	−	0.995608i	$-0.529845\pi$
$181$	11.0902	−	8.05748i	0.824326	−	0.598908i	0.917948	+	0.396700i	$0.129845\pi$
$182$	9.70820	−	7.05342i	0.719620	−	0.522834i
$183$	−6.52786	−	20.0907i	−0.482554	−	1.48515i
$184$	−0.354102	+	1.08981i	−0.0261047	+	0.0803421i
$185$	2.00000	+	1.45309i	0.147043	+	0.106833i
$186$	−4.00000			−0.293294
$187$	9.50000	+	16.0292i	0.694709	+	1.17217i
$188$	3.61803			0.263872
$189$	−6.00000	−	4.35926i	−0.436436	−	0.317089i
$190$	−0.190983	+	0.587785i	−0.0138554	+	0.0426424i
$191$	−7.42705	−	22.8581i	−0.537403	−	1.65395i	−0.738400	−	0.674363i	$-0.764418\pi$
$191$	−7.42705	−	22.8581i	−0.537403	−	1.65395i	0.200997	−	0.979592i	$-0.435582\pi$
$192$	1.61803	−	1.17557i	0.116772	−	0.0848395i
$193$	17.0902	−	12.4167i	1.23018	−	0.893776i	0.233274	−	0.972411i	$-0.425056\pi$
$193$	17.0902	−	12.4167i	1.23018	−	0.893776i	0.996903	+	0.0786349i	$0.0250561\pi$
$194$	−1.47214	−	4.53077i	−0.105693	−	0.325290i
$195$	−2.47214	+	7.60845i	−0.177033	+	0.544853i
$196$	2.88197	+	2.09387i	0.205855	+	0.149562i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	3.23607	−	0.726543i	0.229977	−	0.0516331i
$199$	−5.56231			−0.394301			−0.197151	−	0.980373i	$-0.563169\pi$
$199$	−5.56231			−0.394301			−0.197151	+	0.980373i	$0.563169\pi$
$200$	3.73607	+	2.71441i	0.264180	+	0.191938i
$201$	−4.47214	+	13.7638i	−0.315440	+	0.970825i
$202$	1.71885	+	5.29007i	0.120938	+	0.372208i
$203$	−2.29180	+	1.66509i	−0.160853	+	0.116866i
$204$	9.09017	−	6.60440i	0.636439	−	0.462400i
$205$	1.76393	+	5.42882i	0.123198	+	0.379166i
$206$	−2.85410	+	8.78402i	−0.198855	+	0.612012i
$207$	0.927051	+	0.673542i	0.0644345	+	0.0468144i
$208$	−6.47214			−0.448762
$209$	−3.04508	−	1.31433i	−0.210633	−	0.0909140i
$210$	2.29180			0.158149
$211$	9.23607	+	6.71040i	0.635837	+	0.461963i	0.858418	−	0.512952i	$-0.171448\pi$
$211$	9.23607	+	6.71040i	0.635837	+	0.461963i	−0.222580	+	0.974914i	$0.571448\pi$
$212$	−2.85410	+	8.78402i	−0.196021	+	0.603289i
$213$	8.00000	+	24.6215i	0.548151	+	1.68704i
$214$	−4.85410	+	3.52671i	−0.331820	+	0.241081i
$215$	1.04508	−	0.759299i	0.0712742	−	0.0517837i
$216$	1.23607	+	3.80423i	0.0841038	+	0.258845i
$217$	1.14590	−	3.52671i	0.0777886	−	0.239409i
$218$	1.00000	+	0.726543i	0.0677285	+	0.0492077i
$219$	28.0000			1.89206
$220$	1.35410	−	1.53884i	0.0912935	−	0.103749i
$221$	−36.3607			−2.44588
$222$	6.47214	+	4.70228i	0.434381	+	0.315597i
$223$	1.14590	−	3.52671i	0.0767350	−	0.236166i	−0.905330	−	0.424709i	$-0.860376\pi$
$223$	1.14590	−	3.52671i	0.0767350	−	0.236166i	0.982065	+	0.188543i	$0.0603764\pi$
$224$	0.572949	+	1.76336i	0.0382818	+	0.117819i
$225$	3.73607	−	2.71441i	0.249071	−	0.180961i
$226$	−11.7082	+	8.50651i	−0.778818	+	0.565845i
$227$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$227$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$228$	−0.618034	+	1.90211i	−0.0409303	+	0.125971i
$229$	−19.6353	−	14.2658i	−1.29753	−	0.942714i	−0.297606	−	0.954689i	$-0.596188\pi$
$229$	−19.6353	−	14.2658i	−1.29753	−	0.942714i	−0.999928	+	0.0119751i	$0.996188\pi$
$230$	0.708204			0.0466976
$231$	−1.14590	+	12.2452i	−0.0753946	+	0.805676i
$232$	1.52786			0.100309
$233$	15.2082	+	11.0494i	0.996323	+	0.723871i	0.961297	−	0.275516i	$-0.0888486\pi$
$233$	15.2082	+	11.0494i	0.996323	+	0.723871i	0.0350260	+	0.999386i	$0.488849\pi$
$234$	−2.00000	+	6.15537i	−0.130744	+	0.402389i
$235$	−0.690983	−	2.12663i	−0.0450748	−	0.138726i
$236$	10.0902	−	7.33094i	0.656814	−	0.477203i
$237$	−15.7082	+	11.4127i	−1.02036	+	0.741333i
$238$	3.21885	+	9.90659i	0.208647	+	0.642149i
$239$	0.826238	−	2.54290i	0.0534449	−	0.164486i	−0.920771	−	0.390103i	$-0.872440\pi$
$239$	0.826238	−	2.54290i	0.0534449	−	0.164486i	0.974216	+	0.225616i	$0.0724395\pi$
$240$	−1.00000	−	0.726543i	−0.0645497	−	0.0468981i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	7.54508	+	8.00448i	0.485016	+	0.514547i
$243$	10.0000			0.641500
$244$	−8.54508	−	6.20837i	−0.547043	−	0.397450i
$245$	0.680340	−	2.09387i	0.0434653	−	0.133773i
$246$	5.70820	+	17.5680i	0.363942	+	1.12010i
$247$	5.23607	−	3.80423i	0.333163	−	0.242057i
$248$	−1.61803	+	1.17557i	−0.102745	+	0.0746488i
$249$	−6.67376	−	20.5397i	−0.422932	−	1.30165i
$250$	1.83688	−	5.65334i	0.116175	−	0.357549i
$251$	−8.78115	−	6.37988i	−0.554261	−	0.402695i	0.275093	−	0.961418i	$-0.411291\pi$
$251$	−8.78115	−	6.37988i	−0.554261	−	0.402695i	−0.829354	+	0.558723i	$0.811291\pi$
$252$	1.85410			0.116797
$253$	−0.354102	+	3.78398i	−0.0222622	+	0.237897i
$254$	7.41641			0.465347
$255$	−5.61803	−	4.08174i	−0.351815	−	0.255609i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.38197	−	10.4086i	−0.210961	−	0.649272i	−0.999416	−	0.0341788i	$-0.989118\pi$
$257$	−3.38197	−	10.4086i	−0.210961	−	0.649272i	0.788454	−	0.615093i	$-0.210882\pi$
$258$	3.38197	−	2.45714i	0.210552	−	0.152975i
$259$	−6.00000	+	4.35926i	−0.372822	+	0.270871i
$260$	1.23607	+	3.80423i	0.0766577	+	0.235928i
$261$	0.472136	−	1.45309i	0.0292245	−	0.0899437i
$262$	0.736068	+	0.534785i	0.0454744	+	0.0330391i
$263$	6.47214			0.399089			0.199544	−	0.979889i	$-0.436054\pi$
$263$	6.47214			0.399089			0.199544	+	0.979889i	$0.436054\pi$
$264$	4.38197	−	4.97980i	0.269691	−	0.306485i
$265$	5.70820			0.350652
$266$	−1.50000	−	1.08981i	−0.0919709	−	0.0668208i
$267$	−4.18034	+	12.8658i	−0.255833	+	0.787372i
$268$	2.23607	+	6.88191i	0.136590	+	0.420380i
$269$	−15.0902	+	10.9637i	−0.920064	+	0.668466i	−0.943540	−	0.331259i	$-0.892527\pi$
$269$	−15.0902	+	10.9637i	−0.920064	+	0.668466i	0.0234760	+	0.999724i	$0.492527\pi$
$270$	2.00000	−	1.45309i	0.121716	−	0.0884319i
$271$	−9.64590	−	29.6870i	−0.585947	−	1.80336i	−0.595435	−	0.803403i	$-0.703020\pi$
$271$	−9.64590	−	29.6870i	−0.585947	−	1.80336i	0.00948887	−	0.999955i	$-0.496980\pi$
$272$	1.73607	−	5.34307i	0.105265	−	0.323971i
$273$	−19.4164	−	14.1068i	−1.17513	−	0.853785i
$274$	−15.0902			−0.911631
$275$	14.0623	+	6.06961i	0.847989	+	0.366011i
$276$	2.29180			0.137950
$277$	2.85410	+	2.07363i	0.171486	+	0.124592i	0.670218	−	0.742164i	$-0.266201\pi$
$277$	2.85410	+	2.07363i	0.171486	+	0.124592i	−0.498732	+	0.866757i	$0.666201\pi$
$278$	1.64590	−	5.06555i	0.0987144	−	0.303812i
$279$	0.618034	+	1.90211i	0.0370007	+	0.113877i
$280$	0.927051	−	0.673542i	0.0554019	−	0.0402518i
$281$	−3.76393	+	2.73466i	−0.224537	+	0.163136i	−0.694367	−	0.719621i	$-0.744315\pi$
$281$	−3.76393	+	2.73466i	−0.224537	+	0.163136i	0.469829	+	0.882757i	$0.344315\pi$
$282$	−2.23607	−	6.88191i	−0.133156	−	0.409812i
$283$	−2.95492	+	9.09429i	−0.175651	+	0.540600i	−0.999663	−	0.0259740i	$-0.991731\pi$
$283$	−2.95492	+	9.09429i	−0.175651	+	0.540600i	0.824011	+	0.566574i	$0.191731\pi$
$284$	10.4721	+	7.60845i	0.621407	+	0.451479i
$285$	1.23607			0.0732183
$286$	−20.9443	+	4.70228i	−1.23846	+	0.278052i
$287$	−17.1246			−1.01083
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	4.50000	−	13.8496i	0.264706	−	0.814681i
$290$	−0.291796	−	0.898056i	−0.0171349	−	0.0527357i
$291$	−7.70820	+	5.60034i	−0.451863	+	0.328298i
$292$	11.3262	−	8.22899i	0.662818	−	0.481565i
$293$	0.201626	+	0.620541i	0.0117791	+	0.0362524i	0.956773	−	0.290835i	$-0.0939330\pi$
$293$	0.201626	+	0.620541i	0.0117791	+	0.0362524i	−0.944994	+	0.327087i	$0.893933\pi$
$294$	2.20163	−	6.77591i	0.128401	−	0.395179i
$295$	−6.23607	−	4.53077i	−0.363078	−	0.263792i
$296$	4.00000			0.232495
$297$	6.76393	+	11.4127i	0.392483	+	0.662231i
$298$	−20.4721			−1.18592
$299$	−6.00000	−	4.35926i	−0.346989	−	0.252102i
$300$	2.85410	−	8.78402i	0.164782	−	0.507146i
$301$	1.19756	+	3.68571i	0.0690263	+	0.212441i
$302$	0.236068	−	0.171513i	0.0135842	−	0.00986949i
$303$	9.00000	−	6.53888i	0.517036	−	0.375649i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	−2.01722	+	6.20837i	−0.115506	+	0.355490i
$306$	−4.54508	−	3.30220i	−0.259825	−	0.188774i
$307$	−27.4164			−1.56474			−0.782369	−	0.622816i	$-0.785989\pi$
$307$	−27.4164			−1.56474			−0.782369	+	0.622816i	$0.785989\pi$
$308$	3.13525	+	5.29007i	0.178648	+	0.301430i
$309$	18.4721			1.05084
$310$	1.00000	+	0.726543i	0.0567962	+	0.0412648i
$311$	−1.29837	+	3.99598i	−0.0736240	+	0.226591i	−0.981096	−	0.193521i	$-0.938009\pi$
$311$	−1.29837	+	3.99598i	−0.0736240	+	0.226591i	0.907472	+	0.420112i	$0.138009\pi$
$312$	4.00000	+	12.3107i	0.226455	+	0.696958i
$313$	0.0729490	−	0.0530006i	0.00412332	−	0.00299577i	−0.585722	−	0.810512i	$-0.699189\pi$
$313$	0.0729490	−	0.0530006i	0.00412332	−	0.00299577i	0.589845	+	0.807516i	$0.299189\pi$
$314$	−6.20820	+	4.51052i	−0.350349	+	0.254544i
$315$	−0.354102	−	1.08981i	−0.0199514	−	0.0614041i
$316$	−3.00000	+	9.23305i	−0.168763	+	0.519400i
$317$	−1.76393	−	1.28157i	−0.0990723	−	0.0719802i	0.537146	−	0.843489i	$-0.319502\pi$
$317$	−1.76393	−	1.28157i	−0.0990723	−	0.0719802i	−0.636219	+	0.771509i	$0.719502\pi$
$318$	18.4721			1.03587
$319$	4.94427	−	1.11006i	0.276826	−	0.0621513i
$320$	−0.618034			−0.0345492
$321$	9.70820	+	7.05342i	0.541859	+	0.393684i
$322$	−0.656541	+	2.02063i	−0.0365876	+	0.112605i
$323$	1.73607	+	5.34307i	0.0965974	+	0.297296i
$324$	8.89919	−	6.46564i	0.494399	−	0.359202i
$325$	−24.1803	+	17.5680i	−1.34128	+	0.974500i
$326$	−5.04508	−	15.5272i	−0.279421	−	0.859971i
$327$	0.763932	−	2.35114i	0.0422455	−	0.130018i
$328$	7.47214	+	5.42882i	0.412580	+	0.299757i
$329$	6.70820			0.369835
$330$	−3.76393	−	1.62460i	−0.207198	−	0.0894312i
$331$	−9.70820			−0.533611			−0.266806	−	0.963750i	$-0.585968\pi$
$331$	−9.70820			−0.533611			−0.266806	+	0.963750i	$0.585968\pi$
$332$	−8.73607	−	6.34712i	−0.479454	−	0.348344i
$333$	1.23607	−	3.80423i	0.0677361	−	0.208470i
$334$	−7.85410	−	24.1724i	−0.429757	−	1.32266i
$335$	3.61803	−	2.62866i	0.197674	−	0.143619i
$336$	3.00000	−	2.17963i	0.163663	−	0.118908i
$337$	−5.27051	−	16.2210i	−0.287103	−	0.883612i	−0.985760	−	0.168156i	$-0.946219\pi$
$337$	−5.27051	−	16.2210i	−0.287103	−	0.883612i	0.698657	−	0.715456i	$-0.253781\pi$
$338$	8.92705	−	27.4746i	0.485568	−	1.49442i
$339$	23.4164	+	17.0130i	1.27180	+	0.924020i
$340$	−3.47214			−0.188303
$341$	−4.38197	+	4.97980i	−0.237297	+	0.269671i
$342$	1.00000			0.0540738
$343$	15.8435	+	11.5109i	0.855466	+	0.621533i
$344$	0.645898	−	1.98787i	0.0348245	−	0.107179i
$345$	−0.437694	−	1.34708i	−0.0235647	−	0.0725246i
$346$	2.47214	−	1.79611i	0.132903	−	0.0965596i
$347$	−6.92705	+	5.03280i	−0.371864	+	0.270175i	−0.757983	−	0.652274i	$-0.773815\pi$
$347$	−6.92705	+	5.03280i	−0.371864	+	0.270175i	0.386120	+	0.922449i	$0.373815\pi$
$348$	−0.944272	−	2.90617i	−0.0506183	−	0.155787i
$349$	6.48278	−	19.9519i	0.347015	−	1.06800i	−0.613481	−	0.789710i	$-0.710231\pi$
$349$	6.48278	−	19.9519i	0.347015	−	1.06800i	0.960496	−	0.278293i	$-0.0897688\pi$
$350$	6.92705	+	5.03280i	0.370266	+	0.269014i
$351$	−25.8885			−1.38183
$352$	0.309017	−	3.30220i	0.0164707	−	0.176008i
$353$	15.3820			0.818699			0.409350	−	0.912378i	$-0.365756\pi$
$353$	15.3820			0.818699			0.409350	+	0.912378i	$0.365756\pi$
$354$	−20.1803	−	14.6619i	−1.07257	−	0.779270i
$355$	2.47214	−	7.60845i	0.131207	−	0.403815i
$356$	2.09017	+	6.43288i	0.110779	+	0.340942i
$357$	16.8541	−	12.2452i	0.892014	−	0.648086i
$358$	16.3262	−	11.8617i	0.862868	−	0.626911i
$359$	−1.88197	−	5.79210i	−0.0993264	−	0.305695i	0.889031	−	0.457848i	$-0.151379\pi$
$359$	−1.88197	−	5.79210i	−0.0993264	−	0.305695i	−0.988357	+	0.152153i	$0.951379\pi$
$360$	−0.190983	+	0.587785i	−0.0100657	+	0.0309790i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−13.7082			−0.720487
$363$	10.5623	−	19.2986i	0.554377	−	1.01292i
$364$	−12.0000			−0.628971
$365$	−7.00000	−	5.08580i	−0.366397	−	0.266203i
$366$	−6.52786	+	20.0907i	−0.341217	+	1.05016i
$367$	−6.66312	−	20.5070i	−0.347812	−	1.07046i	−0.960061	−	0.279790i	$-0.909735\pi$
$367$	−6.66312	−	20.5070i	−0.347812	−	1.07046i	0.612249	−	0.790665i	$-0.290265\pi$
$368$	0.927051	−	0.673542i	0.0483259	−	0.0351108i
$369$	7.47214	−	5.42882i	0.388984	−	0.282613i
$370$	−0.763932	−	2.35114i	−0.0397149	−	0.122230i
$371$	−5.29180	+	16.2865i	−0.274736	+	0.845552i
$372$	3.23607	+	2.35114i	0.167782	+	0.121901i
$373$	−30.3607			−1.57202			−0.786008	−	0.618216i	$-0.787856\pi$
$373$	−30.3607			−1.57202			−0.786008	+	0.618216i	$0.787856\pi$
$374$	1.73607	−	18.5519i	0.0897699	−	0.959294i
$375$	−11.8885			−0.613922
$376$	−2.92705	−	2.12663i	−0.150951	−	0.109672i
$377$	−3.05573	+	9.40456i	−0.157378	+	0.484360i
$378$	2.29180	+	7.05342i	0.117877	+	0.362789i
$379$	−1.00000	+	0.726543i	−0.0513665	+	0.0373200i	−0.613172	−	0.789949i	$-0.710107\pi$
$379$	−1.00000	+	0.726543i	−0.0513665	+	0.0373200i	0.561806	+	0.827269i	$0.310107\pi$
$380$	0.500000	−	0.363271i	0.0256495	−	0.0186354i
$381$	−4.58359	−	14.1068i	−0.234825	−	0.722716i
$382$	−7.42705	+	22.8581i	−0.380001	+	1.16952i
$383$	−12.0902	−	8.78402i	−0.617779	−	0.448843i	0.234366	−	0.972148i	$-0.424699\pi$
$383$	−12.0902	−	8.78402i	−0.617779	−	0.448843i	−0.852145	+	0.523306i	$0.824699\pi$
$384$	−2.00000			−0.102062
$385$	2.51064	−	2.85317i	0.127954	−	0.145411i
$386$	−21.1246			−1.07521
$387$	−1.69098	−	1.22857i	−0.0859575	−	0.0624518i
$388$	−1.47214	+	4.53077i	−0.0747364	+	0.230015i
$389$	4.02786	+	12.3965i	0.204221	+	0.628527i	0.999744	+	0.0226045i	$0.00719586\pi$
$389$	4.02786	+	12.3965i	0.204221	+	0.628527i	−0.795524	+	0.605923i	$0.792804\pi$
$390$	6.47214	−	4.70228i	0.327729	−	0.238109i
$391$	5.20820	−	3.78398i	0.263390	−	0.191364i
$392$	−1.10081	−	3.38795i	−0.0555995	−	0.171118i
$393$	0.562306	−	1.73060i	0.0283646	−	0.0872972i
$394$	14.5623	+	10.5801i	0.733638	+	0.533019i
$395$	6.00000			0.301893
$396$	−3.04508	−	1.31433i	−0.153021	−	0.0660475i
$397$	20.8541			1.04664			0.523319	−	0.852137i	$-0.324694\pi$
$397$	20.8541			1.04664			0.523319	+	0.852137i	$0.324694\pi$
$398$	4.50000	+	3.26944i	0.225565	+	0.163882i
$399$	−1.14590	+	3.52671i	−0.0573667	+	0.176556i
$400$	−1.42705	−	4.39201i	−0.0713525	−	0.219601i
$401$	−10.0902	+	7.33094i	−0.503879	+	0.366090i	−0.810497	−	0.585743i	$-0.800803\pi$
$401$	−10.0902	+	7.33094i	−0.503879	+	0.366090i	0.306618	+	0.951833i	$0.400803\pi$
$402$	11.7082	−	8.50651i	0.583952	−	0.424266i
$403$	−4.00000	−	12.3107i	−0.199254	−	0.613241i
$404$	1.71885	−	5.29007i	0.0855158	−	0.263191i
$405$	−5.50000	−	3.99598i	−0.273297	−	0.198562i
$406$	2.83282			0.140590
$407$	12.9443	−	2.90617i	0.641624	−	0.144054i
$408$	−11.2361			−0.556268
$409$	18.5623	+	13.4863i	0.917847	+	0.666855i	0.942987	−	0.332829i	$-0.108003\pi$
$409$	18.5623	+	13.4863i	0.917847	+	0.666855i	−0.0251402	+	0.999684i	$0.508003\pi$
$410$	1.76393	−	5.42882i	0.0871144	−	0.268111i
$411$	9.32624	+	28.7032i	0.460029	+	1.41582i
$412$	7.47214	−	5.42882i	0.368126	−	0.267459i
$413$	18.7082	−	13.5923i	0.920571	−	0.668834i
$414$	−0.354102	−	1.08981i	−0.0174032	−	0.0535614i
$415$	−2.06231	+	6.34712i	−0.101235	+	0.311568i
$416$	5.23607	+	3.80423i	0.256719	+	0.186518i
$417$	−10.6525			−0.521654
$418$	1.69098	+	2.85317i	0.0827087	+	0.139553i
$419$	9.32624			0.455617			0.227808	−	0.973706i	$-0.426844\pi$
$419$	9.32624			0.455617			0.227808	+	0.973706i	$0.426844\pi$
$420$	−1.85410	−	1.34708i	−0.0904709	−	0.0657310i
$421$	8.65248	−	26.6296i	0.421696	−	1.29785i	−0.484427	−	0.874832i	$-0.660972\pi$
$421$	8.65248	−	26.6296i	0.421696	−	1.29785i	0.906123	−	0.423015i	$-0.139028\pi$
$422$	−3.52786	−	10.8576i	−0.171734	−	0.528542i
$423$	−2.92705	+	2.12663i	−0.142318	+	0.103400i
$424$	7.47214	−	5.42882i	0.362879	−	0.263647i
$425$	−8.01722	−	24.6745i	−0.388892	−	1.19689i
$426$	8.00000	−	24.6215i	0.387601	−	1.19291i
$427$	−15.8435	−	11.5109i	−0.766719	−	0.557054i
$428$	6.00000			0.290021
$429$	21.8885	+	36.9322i	1.05679	+	1.78310i
$430$	−1.29180			−0.0622959
$431$	−29.0344	−	21.0948i	−1.39854	−	1.01610i	−0.994867	−	0.101195i	$-0.967733\pi$
$431$	−29.0344	−	21.0948i	−1.39854	−	1.01610i	−0.403673	−	0.914903i	$-0.632267\pi$
$432$	1.23607	−	3.80423i	0.0594703	−	0.183031i
$433$	1.70820	+	5.25731i	0.0820910	+	0.252650i	0.983675	−	0.179954i	$-0.0575948\pi$
$433$	1.70820	+	5.25731i	0.0820910	+	0.252650i	−0.901584	+	0.432604i	$0.857595\pi$
$434$	−3.00000	+	2.17963i	−0.144005	+	0.104625i
$435$	−1.52786	+	1.11006i	−0.0732555	+	0.0532232i
$436$	−0.381966	−	1.17557i	−0.0182929	−	0.0562996i
$437$	−0.354102	+	1.08981i	−0.0169390	+	0.0521329i
$438$	−22.6525	−	16.4580i	−1.08238	−	0.786393i
$439$	23.1246			1.10368			0.551839	−	0.833951i	$-0.313926\pi$
$439$	23.1246			1.10368			0.551839	+	0.833951i	$0.313926\pi$
$440$	−2.00000	+	0.449028i	−0.0953463	+	0.0214066i
$441$	−3.56231			−0.169634
$442$	29.4164	+	21.3723i	1.39920	+	1.01658i
$443$	4.39261	−	13.5191i	0.208699	−	0.642310i	−0.790842	−	0.612020i	$-0.790357\pi$
$443$	4.39261	−	13.5191i	0.208699	−	0.642310i	0.999541	−	0.0302896i	$-0.00964296\pi$
$444$	−2.47214	−	7.60845i	−0.117322	−	0.361081i
$445$	3.38197	−	2.45714i	0.160321	−	0.116480i
$446$	−3.00000	+	2.17963i	−0.142054	+	0.103208i
$447$	12.6525	+	38.9403i	0.598442	+	1.84181i
$448$	0.572949	−	1.76336i	0.0270693	−	0.0833107i
$449$	6.61803	+	4.80828i	0.312324	+	0.226917i	0.732893	−	0.680344i	$-0.238169\pi$
$449$	6.61803	+	4.80828i	0.312324	+	0.226917i	−0.420569	+	0.907261i	$0.638169\pi$
$450$	−4.61803			−0.217696
$451$	28.1246	+	12.1392i	1.32434	+	0.571614i
$452$	14.4721			0.680712
$453$	−0.472136	−	0.343027i	−0.0221829	−	0.0161168i
$454$		0			0
$455$	2.29180	+	7.05342i	0.107441	+	0.330670i
$456$	1.61803	−	1.17557i	0.0757714	−	0.0550511i
$457$	18.9164	−	13.7436i	0.884872	−	0.642897i	−0.0496637	−	0.998766i	$-0.515815\pi$
$457$	18.9164	−	13.7436i	0.884872	−	0.642897i	0.934536	+	0.355869i	$0.115815\pi$
$458$	7.50000	+	23.0826i	0.350452	+	1.07858i
$459$	6.94427	−	21.3723i	0.324131	−	0.997572i
$460$	−0.572949	−	0.416272i	−0.0267139	−	0.0194088i
$461$	5.20163			0.242264			0.121132	−	0.992636i	$-0.461348\pi$
$461$	5.20163			0.242264			0.121132	+	0.992636i	$0.461348\pi$
$462$	8.12461	−	9.23305i	0.377991	−	0.429560i
$463$	2.79837			0.130051			0.0650257	−	0.997884i	$-0.479287\pi$
$463$	2.79837			0.130051			0.0650257	+	0.997884i	$0.479287\pi$
$464$	−1.23607	−	0.898056i	−0.0573830	−	0.0416912i
$465$	0.763932	−	2.35114i	0.0354265	−	0.109032i
$466$	−5.80902	−	17.8783i	−0.269098	−	0.828197i
$467$	−25.1525	+	18.2743i	−1.16392	+	0.845636i	−0.990268	−	0.139172i	$-0.955556\pi$
$467$	−25.1525	+	18.2743i	−1.16392	+	0.845636i	−0.173650	+	0.984808i	$0.555556\pi$
$468$	5.23607	−	3.80423i	0.242037	−	0.175850i
$469$	4.14590	+	12.7598i	0.191440	+	0.589191i
$470$	−0.690983	+	2.12663i	−0.0318727	+	0.0980940i
$471$	12.4164	+	9.02105i	0.572118	+	0.415668i
$472$	−12.4721			−0.574077
$473$	0.645898	−	6.90215i	0.0296984	−	0.317361i
$474$	19.4164			0.891825
$475$	3.73607	+	2.71441i	0.171423	+	0.124546i
$476$	3.21885	−	9.90659i	0.147536	−	0.454068i
$477$	−2.85410	−	8.78402i	−0.130680	−	0.402193i
$478$	−2.16312	+	1.57160i	−0.0989388	+	0.0718832i
$479$	8.16312	−	5.93085i	0.372982	−	0.270988i	−0.385464	−	0.922723i	$-0.625959\pi$
$479$	8.16312	−	5.93085i	0.372982	−	0.270988i	0.758447	+	0.651735i	$0.225959\pi$
$480$	0.381966	+	1.17557i	0.0174343	+	0.0536572i
$481$	−8.00000	+	24.6215i	−0.364769	+	1.12264i
$482$	−8.09017	−	5.87785i	−0.368497	−	0.267729i
$483$	4.24922			0.193346
$484$	−1.39919	−	10.9106i	−0.0635994	−	0.495939i
$485$	2.94427			0.133693
$486$	−8.09017	−	5.87785i	−0.366978	−	0.266625i
$487$	3.09017	−	9.51057i	0.140029	−	0.430965i	−0.856309	−	0.516463i	$-0.827248\pi$
$487$	3.09017	−	9.51057i	0.140029	−	0.430965i	0.996338	+	0.0854984i	$0.0272483\pi$
$488$	3.26393	+	10.0453i	0.147751	+	0.454732i
$489$	−26.4164	+	19.1926i	−1.19459	+	0.867921i
$490$	−1.78115	+	1.29408i	−0.0804643	+	0.0584607i
$491$	−3.13525	−	9.64932i	−0.141492	−	0.435468i	0.855051	−	0.518544i	$-0.173526\pi$
$491$	−3.13525	−	9.64932i	−0.141492	−	0.435468i	−0.996543	+	0.0830758i	$0.973526\pi$
$492$	5.70820	−	17.5680i	0.257346	−	0.792029i
$493$	−6.94427	−	5.04531i	−0.312754	−	0.227229i
$494$	−6.47214			−0.291195
$495$	−0.190983	+	2.04087i	−0.00858405	+	0.0917303i
$496$	2.00000			0.0898027
$497$	19.4164	+	14.1068i	0.870945	+	0.632779i
$498$	−6.67376	+	20.5397i	−0.299058	+	0.920407i
$499$	5.42705	+	16.7027i	0.242948	+	0.747718i	0.995967	+	0.0897188i	$0.0285968\pi$
$499$	5.42705	+	16.7027i	0.242948	+	0.747718i	−0.753019	+	0.657999i	$0.771403\pi$
$500$	−4.80902	+	3.49396i	−0.215066	+	0.156254i
$501$	−41.1246	+	29.8788i	−1.83731	+	1.33489i
$502$	3.35410	+	10.3229i	0.149701	+	0.460732i
$503$	−9.05573	+	27.8707i	−0.403775	+	1.24269i	0.518139	+	0.855297i	$0.326625\pi$
$503$	−9.05573	+	27.8707i	−0.403775	+	1.24269i	−0.921914	+	0.387395i	$0.873375\pi$
$504$	−1.50000	−	1.08981i	−0.0668153	−	0.0485442i
$505$	−3.43769			−0.152975
$506$	2.51064	−	2.85317i	0.111612	−	0.126839i
$507$	−57.7771			−2.56597
$508$	−6.00000	−	4.35926i	−0.266207	−	0.193411i
$509$	6.27051	−	19.2986i	0.277935	−	0.855397i	−0.710492	−	0.703705i	$-0.751528\pi$
$509$	6.27051	−	19.2986i	0.277935	−	0.855397i	0.988428	−	0.151692i	$-0.0484723\pi$
$510$	2.14590	+	6.60440i	0.0950220	+	0.292448i
$511$	21.0000	−	15.2574i	0.928985	−	0.674947i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.23607	+	3.80423i	0.0545737	+	0.167961i
$514$	−3.38197	+	10.4086i	−0.149172	+	0.459105i
$515$	−4.61803	−	3.35520i	−0.203495	−	0.147848i
$516$	−4.18034			−0.184029
$517$	−11.0172	−	4.75528i	−0.484537	−	0.209137i
$518$	7.41641			0.325858
$519$	−4.94427	−	3.59222i	−0.217029	−	0.157681i
$520$	1.23607	−	3.80423i	0.0542052	−	0.166826i
$521$	0.673762	+	2.07363i	0.0295181	+	0.0908472i	0.964730	−	0.263241i	$-0.0847913\pi$
$521$	0.673762	+	2.07363i	0.0295181	+	0.0908472i	−0.935212	+	0.354088i	$0.884791\pi$
$522$	−1.23607	+	0.898056i	−0.0541012	+	0.0393068i
$523$	23.5623	−	17.1190i	1.03031	−	0.748562i	0.0619375	−	0.998080i	$-0.480272\pi$
$523$	23.5623	−	17.1190i	1.03031	−	0.748562i	0.968370	+	0.249518i	$0.0802721\pi$
$524$	−0.281153	−	0.865300i	−0.0122822	−	0.0378008i
$525$	5.29180	−	16.2865i	0.230953	−	0.710800i
$526$	−5.23607	−	3.80423i	−0.228303	−	0.165872i
$527$	11.2361			0.489451
$528$	−6.47214	+	1.45309i	−0.281664	+	0.0632374i
$529$	−21.6869			−0.942909
$530$	−4.61803	−	3.35520i	−0.200595	−	0.145740i
$531$	−3.85410	+	11.8617i	−0.167254	+	0.514754i
$532$	0.572949	+	1.76336i	0.0248405	+	0.0764512i
$533$	−48.3607	+	35.1361i	−2.09473	+	1.52191i
$534$	10.9443	−	7.95148i	0.473605	−	0.344094i
$535$	−1.14590	−	3.52671i	−0.0495415	−	0.152473i
$536$	2.23607	−	6.88191i	0.0965834	−	0.297253i
$537$	−32.6525	−	23.7234i	−1.40906	−	1.02374i
$538$	18.6525			0.804165
$539$	−6.02380	−	10.1639i	−0.259463	−	0.437789i
$540$	−2.47214			−0.106384
$541$	−21.9615	−	15.9560i	−0.944198	−	0.686000i	0.00522926	−	0.999986i	$-0.498335\pi$
$541$	−21.9615	−	15.9560i	−0.944198	−	0.686000i	−0.949428	+	0.313986i	$0.898335\pi$
$542$	−9.64590	+	29.6870i	−0.414327	+	1.27517i
$543$	8.47214	+	26.0746i	0.363574	+	1.11897i
$544$	−4.54508	+	3.30220i	−0.194869	+	0.141581i
$545$	−0.618034	+	0.449028i	−0.0264737	+	0.0192342i
$546$	7.41641	+	22.8254i	0.317393	+	0.976835i
$547$	1.94427	−	5.98385i	0.0831311	−	0.255851i	−0.900848	−	0.434134i	$-0.857054\pi$
$547$	1.94427	−	5.98385i	0.0831311	−	0.255851i	0.983979	+	0.178283i	$0.0570543\pi$
$548$	12.2082	+	8.86978i	0.521509	+	0.378898i
$549$	10.5623			0.450788
$550$	−7.80902	−	13.1760i	−0.332978	−	0.561828i
$551$	1.52786			0.0650892
$552$	−1.85410	−	1.34708i	−0.0789158	−	0.0573357i
$553$	−5.56231	+	17.1190i	−0.236533	+	0.727975i
$554$	−1.09017	−	3.35520i	−0.0463169	−	0.142549i
$555$	−4.00000	+	2.90617i	−0.169791	+	0.123360i
$556$	−4.30902	+	3.13068i	−0.182743	+	0.132771i
$557$	10.9549	+	33.7158i	0.464175	+	1.42858i	0.860018	+	0.510264i	$0.170452\pi$
$557$	10.9549	+	33.7158i	0.464175	+	1.42858i	−0.395843	+	0.918318i	$0.629548\pi$
$558$	0.618034	−	1.90211i	0.0261635	−	0.0805229i
$559$	10.9443	+	7.95148i	0.462893	+	0.336312i
$560$	−1.14590			−0.0484230
$561$	−36.3607	+	8.16348i	−1.53515	+	0.344662i
$562$	4.65248			0.196253
$563$	7.85410	+	5.70634i	0.331011	+	0.240494i	0.740859	−	0.671660i	$-0.234418\pi$
$563$	7.85410	+	5.70634i	0.331011	+	0.240494i	−0.409849	+	0.912154i	$0.634418\pi$
$564$	−2.23607	+	6.88191i	−0.0941554	+	0.289781i
$565$	−2.76393	−	8.50651i	−0.116279	−	0.357871i
$566$	7.73607	−	5.62058i	0.325171	−	0.236251i
$567$	16.5000	−	11.9880i	0.692935	−	0.503447i
$568$	−4.00000	−	12.3107i	−0.167836	−	0.516547i
$569$	−5.14590	+	15.8374i	−0.215727	+	0.663940i	0.783374	+	0.621551i	$0.213497\pi$
$569$	−5.14590	+	15.8374i	−0.215727	+	0.663940i	−0.999101	+	0.0423895i	$0.986503\pi$
$570$	−1.00000	−	0.726543i	−0.0418854	−	0.0304315i
$571$	6.14590			0.257198			0.128599	−	0.991697i	$-0.458952\pi$
$571$	6.14590			0.257198			0.128599	+	0.991697i	$0.458952\pi$
$572$	19.7082	+	8.50651i	0.824041	+	0.355675i
$573$	48.0689			2.00811
$574$	13.8541	+	10.0656i	0.578259	+	0.420130i
$575$	1.63525	−	5.03280i	0.0681948	−	0.209882i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−10.0902	+	7.33094i	−0.420059	+	0.305191i	−0.777662	−	0.628683i	$-0.783594\pi$
$577$	−10.0902	+	7.33094i	−0.420059	+	0.305191i	0.357602	+	0.933874i	$0.383594\pi$
$578$	−11.7812	+	8.55951i	−0.490031	+	0.356029i
$579$	13.0557	+	40.1814i	0.542578	+	1.66988i
$580$	−0.291796	+	0.898056i	−0.0121162	+	0.0372897i
$581$	−16.1976	−	11.7682i	−0.671988	−	0.488228i
$582$	9.52786			0.394943
$583$	20.2361	−	22.9969i	0.838092	−	0.952433i
$584$	−14.0000			−0.579324
$585$	−3.23607	−	2.35114i	−0.133795	−	0.0972077i
$586$	0.201626	−	0.620541i	0.00832910	−	0.0256343i
$587$	8.94427	+	27.5276i	0.369170	+	1.13619i	0.947329	+	0.320263i	$0.103771\pi$
$587$	8.94427	+	27.5276i	0.369170	+	1.13619i	−0.578159	+	0.815924i	$0.696229\pi$
$588$	−5.76393	+	4.18774i	−0.237701	+	0.172700i
$589$	−1.61803	+	1.17557i	−0.0666699	+	0.0484385i
$590$	2.38197	+	7.33094i	0.0980640	+	0.301810i
$591$	11.1246	−	34.2380i	0.457605	−	1.40836i
$592$	−3.23607	−	2.35114i	−0.133002	−	0.0966313i
$593$	−44.4508			−1.82538			−0.912689	−	0.408655i	$-0.865998\pi$
$593$	−44.4508			−1.82538			−0.912689	+	0.408655i	$0.865998\pi$
$594$	1.23607	−	13.2088i	0.0507165	−	0.541963i
$595$	−6.43769			−0.263920
$596$	16.5623	+	12.0332i	0.678418	+	0.492900i
$597$	3.43769	−	10.5801i	0.140695	−	0.433016i
$598$	2.29180	+	7.05342i	0.0937185	+	0.288436i
$599$	−12.6180	+	9.16754i	−0.515559	+	0.374575i	−0.814928	−	0.579562i	$-0.803224\pi$
$599$	−12.6180	+	9.16754i	−0.515559	+	0.374575i	0.299369	+	0.954137i	$0.403224\pi$
$600$	−7.47214	+	5.42882i	−0.305049	+	0.221631i
$601$	9.79837	+	30.1563i	0.399684	+	1.23010i	0.925253	+	0.379350i	$0.123852\pi$
$601$	9.79837	+	30.1563i	0.399684	+	1.23010i	−0.525569	+	0.850751i	$0.676148\pi$
$602$	1.19756	−	3.68571i	0.0488089	−	0.150218i
$603$	−5.85410	−	4.25325i	−0.238397	−	0.173206i
$604$	−0.291796			−0.0118730
$605$	−6.14590	+	2.90617i	−0.249866	+	0.118153i
$606$	−11.1246			−0.451906
$607$	−20.1803	−	14.6619i	−0.819095	−	0.595107i	0.0973583	−	0.995249i	$-0.468961\pi$
$607$	−20.1803	−	14.6619i	−0.819095	−	0.595107i	−0.916453	+	0.400142i	$0.868961\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	−1.75078	−	5.38834i	−0.0709450	−	0.218346i
$610$	5.28115	−	3.83698i	0.213828	−	0.155355i
$611$	18.9443	−	13.7638i	0.766403	−	0.556825i
$612$	1.73607	+	5.34307i	0.0701764	+	0.215981i
$613$	−2.38854	+	7.35118i	−0.0964724	+	0.296911i	−0.987635	−	0.156773i	$-0.949891\pi$
$613$	−2.38854	+	7.35118i	−0.0964724	+	0.296911i	0.891162	+	0.453685i	$0.149891\pi$
$614$	22.1803	+	16.1150i	0.895126	+	0.650347i
$615$	−11.4164			−0.460354
$616$	0.572949	−	6.12261i	0.0230848	−	0.246687i
$617$	42.7214			1.71990			0.859949	−	0.510381i	$-0.170495\pi$
$617$	42.7214			1.71990			0.859949	+	0.510381i	$0.170495\pi$
$618$	−14.9443	−	10.8576i	−0.601147	−	0.436759i
$619$	3.88197	−	11.9475i	0.156029	−	0.480209i	−0.842234	−	0.539112i	$-0.818760\pi$
$619$	3.88197	−	11.9475i	0.156029	−	0.480209i	0.998264	+	0.0589025i	$0.0187601\pi$
$620$	−0.381966	−	1.17557i	−0.0153401	−	0.0472120i
$621$	3.70820	−	2.69417i	0.148805	−	0.108113i
$622$	3.39919	−	2.46965i	0.136295	−	0.0990241i
$623$	3.87539	+	11.9272i	0.155264	+	0.477854i
$624$	4.00000	−	12.3107i	0.160128	−	0.492824i
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$	−0.0901699			−0.00360392
$627$	4.38197	−	4.97980i	0.174999	−	0.198874i
$628$	7.67376			0.306216
$629$	−18.1803	−	13.2088i	−0.724898	−	0.526669i
$630$	−0.354102	+	1.08981i	−0.0141078	+	0.0434192i
$631$	−7.52786	−	23.1684i	−0.299680	−	0.922319i	−0.981609	−	0.190901i	$-0.938859\pi$
$631$	−7.52786	−	23.1684i	−0.299680	−	0.922319i	0.681930	−	0.731418i	$-0.261141\pi$
$632$	7.85410	−	5.70634i	0.312419	−	0.226986i
$633$	−18.4721	+	13.4208i	−0.734201	+	0.533429i
$634$	0.673762	+	2.07363i	0.0267585	+	0.0823542i
$635$	−1.41641	+	4.35926i	−0.0562084	+	0.172992i
$636$	−14.9443	−	10.8576i	−0.592579	−	0.430534i
$637$	23.0557			0.913501
$638$	−4.65248	−	2.00811i	−0.184193	−	0.0795020i
$639$	−12.9443			−0.512067
$640$	0.500000	+	0.363271i	0.0197642	+	0.0143596i
$641$	6.58359	−	20.2622i	0.260036	−	0.800309i	−0.732759	−	0.680488i	$-0.761768\pi$
$641$	6.58359	−	20.2622i	0.260036	−	0.800309i	0.992795	−	0.119821i	$-0.0382322\pi$
$642$	−3.70820	−	11.4127i	−0.146351	−	0.450422i
$643$	−16.9271	+	12.2982i	−0.667538	+	0.484995i	−0.869200	−	0.494461i	$-0.835366\pi$
$643$	−16.9271	+	12.2982i	−0.667538	+	0.484995i	0.201662	+	0.979455i	$0.435366\pi$
$644$	1.71885	−	1.24882i	0.0677321	−	0.0492102i
$645$	0.798374	+	2.45714i	0.0314359	+	0.0967499i
$646$	1.73607	−	5.34307i	0.0683047	−	0.210220i
$647$	9.70820	+	7.05342i	0.381669	+	0.277299i	0.762033	−	0.647538i	$-0.224201\pi$
$647$	9.70820	+	7.05342i	0.381669	+	0.277299i	−0.380364	+	0.924837i	$0.624201\pi$
$648$	−11.0000			−0.432121
$649$	−40.3607	+	9.06154i	−1.58430	+	0.355696i
$650$	29.8885			1.17233
$651$	6.00000	+	4.35926i	0.235159	+	0.170853i
$652$	−5.04508	+	15.5272i	−0.197581	+	0.608091i
$653$	−0.500000	−	1.53884i	−0.0195665	−	0.0602195i	0.940797	−	0.338972i	$-0.110079\pi$
$653$	−0.500000	−	1.53884i	−0.0195665	−	0.0602195i	−0.960363	+	0.278752i	$0.910079\pi$
$654$	−2.00000	+	1.45309i	−0.0782062	+	0.0568201i
$655$	−0.454915	+	0.330515i	−0.0177750	+	0.0129143i
$656$	−2.85410	−	8.78402i	−0.111434	−	0.342958i
$657$	−4.32624	+	13.3148i	−0.168783	+	0.519459i
$658$	−5.42705	−	3.94298i	−0.211568	−	0.153713i
$659$	20.2918			0.790456			0.395228	−	0.918583i	$-0.370666\pi$
$659$	20.2918			0.790456			0.395228	+	0.918583i	$0.370666\pi$
$660$	2.09017	+	3.52671i	0.0813598	+	0.137277i
$661$	19.5967			0.762225			0.381113	−	0.924529i	$-0.375541\pi$
$661$	19.5967			0.762225			0.381113	+	0.924529i	$0.375541\pi$
$662$	7.85410	+	5.70634i	0.305258	+	0.221783i
$663$	22.4721	−	69.1621i	0.872745	−	2.68603i
$664$	3.33688	+	10.2699i	0.129496	+	0.398548i
$665$	0.927051	−	0.673542i	0.0359495	−	0.0261188i
$666$	−3.23607	+	2.35114i	−0.125395	+	0.0911049i
$667$	−0.541020	−	1.66509i	−0.0209484	−	0.0644724i
$668$	−7.85410	+	24.1724i	−0.303884	+	0.935260i
$669$	6.00000	+	4.35926i	0.231973	+	0.168539i
$670$	−4.47214			−0.172774
$671$	17.8607	+	30.1360i	0.689504	+	1.16339i
$672$	−3.70820			−0.143047
$673$	36.4164	+	26.4581i	1.40375	+	1.01988i	0.994194	+	0.107598i	$0.0343160\pi$
$673$	36.4164	+	26.4581i	1.40375	+	1.01988i	0.409555	+	0.912285i	$0.365684\pi$
$674$	−5.27051	+	16.2210i	−0.203012	+	0.624808i
$675$	−5.70820	−	17.5680i	−0.219709	−	0.676194i
$676$	−23.3713	+	16.9803i	−0.898897	+	0.653087i
$677$	−27.2705	+	19.8132i	−1.04809	+	0.761483i	−0.971848	−	0.235607i	$-0.924292\pi$
$677$	−27.2705	+	19.8132i	−1.04809	+	0.761483i	−0.0762424	+	0.997089i	$0.524292\pi$
$678$	−8.94427	−	27.5276i	−0.343503	−	1.05719i
$679$	−2.72949	+	8.40051i	−0.104748	+	0.322382i
$680$	2.80902	+	2.04087i	0.107721	+	0.0782638i
$681$		0			0
$682$	6.47214	−	1.45309i	0.247831	−	0.0556415i
$683$	−20.0689			−0.767914			−0.383957	−	0.923351i	$-0.625439\pi$
$683$	−20.0689			−0.767914			−0.383957	+	0.923351i	$0.625439\pi$
$684$	−0.809017	−	0.587785i	−0.0309335	−	0.0224745i
$685$	2.88197	−	8.86978i	0.110114	−	0.338897i
$686$	−6.05166	−	18.6251i	−0.231054	−	0.711110i
$687$	39.2705	−	28.5317i	1.49826	−	1.08855i
$688$	−1.69098	+	1.22857i	−0.0644681	+	0.0468388i
$689$	18.4721	+	56.8514i	0.703732	+	2.16587i
$690$	−0.437694	+	1.34708i	−0.0166627	+	0.0512826i
$691$	16.4443	+	11.9475i	0.625570	+	0.454503i	0.854863	−	0.518855i	$-0.173641\pi$
$691$	16.4443	+	11.9475i	0.625570	+	0.454503i	−0.229293	+	0.973357i	$0.573641\pi$
$692$	−3.05573			−0.116161
$693$	−5.64590	−	2.43690i	−0.214470	−	0.0925701i
$694$	8.56231			0.325021
$695$	2.66312	+	1.93487i	0.101018	+	0.0733938i
$696$	−0.944272	+	2.90617i	−0.0357925	+	0.110158i
$697$	−16.0344	−	49.3489i	−0.607348	−	1.86922i
$698$	−16.9721	+	12.3310i	−0.642405	+	0.466734i
$699$	−30.4164	+	22.0988i	−1.15045	+	0.835854i
$700$	−2.64590	−	8.14324i	−0.100006	−	0.307785i
$701$	4.55573	−	14.0211i	0.172067	−	0.529569i	−0.827420	−	0.561584i	$-0.810192\pi$
$701$	4.55573	−	14.0211i	0.172067	−	0.529569i	0.999487	+	0.0320145i	$0.0101923\pi$
$702$	20.9443	+	15.2169i	0.790491	+	0.574325i
$703$	4.00000			0.150863
$704$	−2.19098	+	2.48990i	−0.0825758	+	0.0938416i
$705$	4.47214			0.168430
$706$	−12.4443	−	9.04129i	−0.468346	−	0.340274i
$707$	3.18692	−	9.80832i	0.119856	−	0.368880i
$708$	7.70820	+	23.7234i	0.289692	+	0.891580i
$709$	−4.20820	+	3.05744i	−0.158042	+	0.114825i	−0.663996	−	0.747736i	$-0.731141\pi$
$709$	−4.20820	+	3.05744i	−0.158042	+	0.114825i	0.505953	+	0.862561i	$0.331141\pi$
$710$	−6.47214	+	4.70228i	−0.242895	+	0.176473i
$711$	−3.00000	−	9.23305i	−0.112509	−	0.346266i
$712$	2.09017	−	6.43288i	0.0783324	−	0.241082i
$713$	1.85410	+	1.34708i	0.0694367	+	0.0504487i
$714$	−20.8328			−0.779649
$715$	1.23607	−	13.2088i	0.0462263	−	0.493981i
$716$	−20.1803			−0.754175
$717$	4.32624	+	3.14320i	0.161566	+	0.117385i
$718$	−1.88197	+	5.79210i	−0.0702343	+	0.216159i
$719$	−6.28115	−	19.3314i	−0.234247	−	0.720940i	−0.997220	−	0.0745091i	$-0.976261\pi$
$719$	−6.28115	−	19.3314i	−0.234247	−	0.720940i	0.762973	−	0.646431i	$-0.223739\pi$
$720$	0.500000	−	0.363271i	0.0186339	−	0.0135383i
$721$	13.8541	−	10.0656i	0.515954	−	0.374862i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	−6.18034	+	19.0211i	−0.229849	+	0.707403i
$724$	11.0902	+	8.05748i	0.412163	+	0.299454i
$725$	−7.05573			−0.262043
$726$	−19.8885	+	9.40456i	−0.738133	+	0.349036i
$727$	18.8541			0.699260			0.349630	−	0.936888i	$-0.386307\pi$
$727$	18.8541			0.699260			0.349630	+	0.936888i	$0.386307\pi$
$728$	9.70820	+	7.05342i	0.359810	+	0.261417i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	2.67376	+	8.22899i	0.0989604	+	0.304569i
$731$	−9.50000	+	6.90215i	−0.351370	+	0.255285i
$732$	17.0902	−	12.4167i	0.631671	−	0.458936i
$733$	13.6976	+	42.1568i	0.505931	+	1.55710i	0.799200	+	0.601065i	$0.205257\pi$
$733$	13.6976	+	42.1568i	0.505931	+	1.55710i	−0.293269	+	0.956030i	$0.594743\pi$
$734$	−6.66312	+	20.5070i	−0.245940	+	0.756926i
$735$	3.56231	+	2.58817i	0.131398	+	0.0954660i
$736$	−1.14590			−0.0422384
$737$	2.23607	−	23.8949i	0.0823666	−	0.880181i
$738$	−9.23607			−0.339984
$739$	35.1525	+	25.5398i	1.29310	+	0.939496i	0.999863	−	0.0165428i	$-0.00526598\pi$
$739$	35.1525	+	25.5398i	1.29310	+	0.939496i	0.293242	+	0.956038i	$0.405266\pi$
$740$	−0.763932	+	2.35114i	−0.0280827	+	0.0864297i
$741$	4.00000	+	12.3107i	0.146944	+	0.452246i
$742$	13.8541	−	10.0656i	0.508600	−	0.369520i
$743$	−23.1803	+	16.8415i	−0.850404	+	0.617855i	−0.925257	−	0.379340i	$-0.876151\pi$
$743$	−23.1803	+	16.8415i	−0.850404	+	0.617855i	0.0748533	+	0.997195i	$0.476151\pi$
$744$	−1.23607	−	3.80423i	−0.0453165	−	0.139470i
$745$	3.90983	−	12.0332i	0.143245	−	0.440863i
$746$	24.5623	+	17.8456i	0.899290	+	0.653372i
$747$	10.7984			0.395092
$748$	−12.3090	+	13.9883i	−0.450062	+	0.511464i
$749$	11.1246			0.406484
$750$	9.61803	+	6.98791i	0.351201	+	0.255162i
$751$	−11.5623	+	35.5851i	−0.421915	+	1.29852i	0.484003	+	0.875066i	$0.339182\pi$
$751$	−11.5623	+	35.5851i	−0.421915	+	1.29852i	−0.905918	+	0.423453i	$0.860818\pi$
$752$	1.11803	+	3.44095i	0.0407705	+	0.125479i
$753$	17.5623	−	12.7598i	0.640006	−	0.464992i
$754$	8.00000	−	5.81234i	0.291343	−	0.211673i
$755$	0.0557281	+	0.171513i	0.00202815	+	0.00624201i
$756$	2.29180	−	7.05342i	0.0833518	−	0.256531i
$757$	−1.14590	−	0.832544i	−0.0416484	−	0.0302593i	0.566766	−	0.823879i	$-0.308194\pi$
$757$	−1.14590	−	0.832544i	−0.0416484	−	0.0302593i	−0.608415	+	0.793619i	$0.708194\pi$
$758$	1.23607			0.0448960
$759$	−6.97871	−	3.01217i	−0.253311	−	0.109335i
$760$	−0.618034			−0.0224184
$761$	−41.5066	−	30.1563i	−1.50461	−	1.09316i	−0.968499	−	0.249019i	$-0.919892\pi$
$761$	−41.5066	−	30.1563i	−1.50461	−	1.09316i	−0.536114	−	0.844146i	$-0.680108\pi$
$762$	−4.58359	+	14.1068i	−0.166046	+	0.511037i
$763$	−0.708204	−	2.17963i	−0.0256387	−	0.0789078i
$764$	19.4443	−	14.1271i	0.703469	−	0.511100i
$765$	2.80902	−	2.04087i	0.101560	−	0.0737878i
$766$	4.61803	+	14.2128i	0.166856	+	0.513531i
$767$	24.9443	−	76.7706i	0.900685	−	2.77202i
$768$	1.61803	+	1.17557i	0.0583858	+	0.0424197i
$769$	34.5066			1.24434			0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066			1.24434			0.622170	+	0.782883i	$0.286251\pi$
$770$	−3.70820	+	0.832544i	−0.133634	+	0.0300028i
$771$	21.8885			0.788297
$772$	17.0902	+	12.4167i	0.615089	+	0.446888i
$773$	−10.3820	+	31.9524i	−0.373413	+	1.14925i	0.571129	+	0.820860i	$0.306505\pi$
$773$	−10.3820	+	31.9524i	−0.373413	+	1.14925i	−0.944543	+	0.328388i	$0.893495\pi$
$774$	0.645898	+	1.98787i	0.0232163	+	0.0714525i
$775$	7.47214	−	5.42882i	0.268407	−	0.195009i
$776$	3.85410	−	2.80017i	0.138354	−	0.100520i
$777$	−4.58359	−	14.1068i	−0.164435	−	0.506080i
$778$	4.02786	−	12.3965i	0.144406	−	0.444436i
$779$	7.47214	+	5.42882i	0.267717	+	0.194508i
$780$	−8.00000			−0.286446
$781$	−21.8885	−	36.9322i	−0.783234	−	1.32154i
$782$	−6.43769			−0.230211
$783$	−4.94427	−	3.59222i	−0.176694	−	0.128376i
$784$	−1.10081	+	3.38795i	−0.0393148	+	0.120998i
$785$	−1.46556	−	4.51052i	−0.0523080	−	0.160988i
$786$	−1.47214	+	1.06957i	−0.0525094	+	0.0381503i
$787$	34.7426	−	25.2420i	1.23844	−	0.899780i	0.240948	−	0.970538i	$-0.422542\pi$
$787$	34.7426	−	25.2420i	1.23844	−	0.899780i	0.997494	+	0.0707575i	$0.0225417\pi$
$788$	−5.56231	−	17.1190i	−0.198149	−	0.609840i
$789$	−4.00000	+	12.3107i	−0.142404	+	0.438274i
$790$	−4.85410	−	3.52671i	−0.172701	−	0.125475i
$791$	26.8328			0.954065
$792$	1.69098	+	2.85317i	0.0600865	+	0.101383i
$793$	−68.3607			−2.42756
$794$	−16.8713	−	12.2577i	−0.598741	−	0.435011i
$795$	−3.52786	+	10.8576i	−0.125120	+	0.385081i
$796$	−1.71885	−	5.29007i	−0.0609229	−	0.187501i
$797$	43.5066	−	31.6094i	1.54108	−	1.11966i	0.591429	−	0.806357i	$-0.298564\pi$
$797$	43.5066	−	31.6094i	1.54108	−	1.11966i	0.949653	−	0.313305i	$-0.101436\pi$
$798$	3.00000	−	2.17963i	0.106199	−	0.0771580i
$799$	6.28115	+	19.3314i	0.222211	+	0.683896i
$800$	−1.42705	+	4.39201i	−0.0504539	+	0.155281i
$801$	−5.47214	−	3.97574i	−0.193348	−	0.140476i
$802$	12.4721			0.440406
$803$	−45.3050	+	10.1716i	−1.59878	+	0.358948i
$804$	−14.4721			−0.510393
$805$	−1.06231	−	0.771810i	−0.0374414	−	0.0272027i
$806$	−4.00000	+	12.3107i	−0.140894	+	0.433627i
$807$	−11.5279	−	35.4791i	−0.405800	−	1.24892i
$808$	−4.50000	+	3.26944i	−0.158309	+	0.115019i
$809$	−4.50000	+	3.26944i	−0.158212	+	0.114947i	−0.664074	−	0.747666i	$-0.731174\pi$
$809$	−4.50000	+	3.26944i	−0.158212	+	0.114947i	0.505863	+	0.862614i	$0.331174\pi$
$810$	2.10081	+	6.46564i	0.0738150	+	0.227179i
$811$	−12.4377	+	38.2793i	−0.436747	+	1.34417i	0.454540	+	0.890726i	$0.349804\pi$
$811$	−12.4377	+	38.2793i	−0.436747	+	1.34417i	−0.891286	+	0.453441i	$0.850196\pi$
$812$	−2.29180	−	1.66509i	−0.0804263	−	0.0584331i
$813$	62.4296			2.18950
$814$	−12.1803	−	5.25731i	−0.426921	−	0.184269i
$815$	10.0902			0.353443
$816$	9.09017	+	6.60440i	0.318220	+	0.231200i
$817$	0.645898	−	1.98787i	0.0225971	−	0.0695468i
$818$	−7.09017	−	21.8213i	−0.247902	−	0.762964i
$819$	9.70820	−	7.05342i	0.339232	−	0.246467i
$820$	−4.61803	+	3.35520i	−0.161269	+	0.117169i
$821$	1.20820	+	3.71847i	0.0421666	+	0.129775i	0.969924	−	0.243409i	$-0.0782658\pi$
$821$	1.20820	+	3.71847i	0.0421666	+	0.129775i	−0.927757	+	0.373185i	$0.878266\pi$
$822$	9.32624	−	28.7032i	0.325290	−	1.00114i
$823$	−11.2082	−	8.14324i	−0.390693	−	0.283855i	0.375046	−	0.927006i	$-0.377627\pi$
$823$	−11.2082	−	8.14324i	−0.390693	−	0.283855i	−0.765740	+	0.643151i	$0.777627\pi$
$824$	−9.23607			−0.321754
$825$	−20.2361	+	22.9969i	−0.704529	+	0.800648i
$826$	−23.1246			−0.804608
$827$	−22.8541	−	16.6045i	−0.794715	−	0.577394i	0.114644	−	0.993407i	$-0.463427\pi$
$827$	−22.8541	−	16.6045i	−0.794715	−	0.577394i	−0.909359	+	0.416012i	$0.863427\pi$
$828$	−0.354102	+	1.08981i	−0.0123059	+	0.0378736i
$829$	−5.81966	−	17.9111i	−0.202125	−	0.622077i	−0.999819	−	0.0190149i	$-0.993947\pi$
$829$	−5.81966	−	17.9111i	−0.202125	−	0.622077i	0.797694	−	0.603062i	$-0.206053\pi$
$830$	5.39919	−	3.92274i	0.187409	−	0.136160i
$831$	−5.70820	+	4.14725i	−0.198015	+	0.143867i
$832$	−2.00000	−	6.15537i	−0.0693375	−	0.213399i
$833$	−6.18441	+	19.0336i	−0.214277	+	0.659477i
$834$	8.61803	+	6.26137i	0.298418	+	0.216813i
$835$	15.7082			0.543605
$836$	0.309017	−	3.30220i	0.0106876	−	0.114209i
$837$	8.00000			0.276520
$838$	−7.54508	−	5.48183i	−0.260641	−	0.189367i
$839$	−7.47214	+	22.9969i	−0.257967	+	0.793940i	0.735264	+	0.677781i	$0.237058\pi$
$839$	−7.47214	+	22.9969i	−0.257967	+	0.793940i	−0.993231	+	0.116159i	$0.962942\pi$
$840$	0.708204	+	2.17963i	0.0244354	+	0.0752043i
$841$	21.5729	−	15.6737i	0.743895	−	0.540471i
$842$	−22.6525	+	16.4580i	−0.780656	+	0.567180i
$843$	−2.87539	−	8.84953i	−0.0990336	−	0.304794i
$844$	−3.52786	+	10.8576i	−0.121434	+	0.373736i
$845$	14.4443	+	10.4944i	0.496898	+	0.361018i
$846$	3.61803			0.124391
$847$	−2.59424	−	20.2295i	−0.0891390	−	0.695092i
$848$	−9.23607			−0.317168
$849$	−15.4721	−	11.2412i	−0.531002	−	0.385796i
$850$	−8.01722	+	24.6745i	−0.274988	+	0.846327i
$851$	−1.41641	−	4.35926i	−0.0485538	−	0.149433i
$852$	−20.9443	+	15.2169i	−0.717539	+	0.521323i
$853$	3.45492	−	2.51014i	0.118294	−	0.0859456i	−0.527065	−	0.849825i	$-0.676708\pi$
$853$	3.45492	−	2.51014i	0.118294	−	0.0859456i	0.645359	+	0.763879i	$0.276708\pi$
$854$	6.05166	+	18.6251i	0.207084	+	0.637338i
$855$	−0.190983	+	0.587785i	−0.00653148	+	0.0201018i
$856$	−4.85410	−	3.52671i	−0.165910	−	0.120541i
$857$	−19.0132			−0.649477			−0.324739	−	0.945804i	$-0.605276\pi$
$857$	−19.0132			−0.649477			−0.324739	+	0.945804i	$0.605276\pi$
$858$	4.00000	−	42.7445i	0.136558	−	1.45927i
$859$	33.6869			1.14938			0.574691	−	0.818370i	$-0.305122\pi$
$859$	33.6869			1.14938			0.574691	+	0.818370i	$0.305122\pi$
$860$	1.04508	+	0.759299i	0.0356371	+	0.0258919i
$861$	10.5836	−	32.5729i	0.360688	−	1.11008i
$862$	11.0902	+	34.1320i	0.377733	+	1.16254i
$863$	−38.9787	+	28.3197i	−1.32685	+	0.964014i	−0.327031	+	0.945013i	$0.606048\pi$
$863$	−38.9787	+	28.3197i	−1.32685	+	0.964014i	−0.999819	+	0.0190001i	$0.993952\pi$
$864$	−3.23607	+	2.35114i	−0.110093	+	0.0799874i
$865$	0.583592	+	1.79611i	0.0198427	+	0.0610696i
$866$	1.70820	−	5.25731i	0.0580471	−	0.178651i
$867$	23.5623	+	17.1190i	0.800218	+	0.581392i
$868$	3.70820			0.125865
$869$	21.2705	−	24.1724i	0.721553	−	0.819994i
$870$	1.88854			0.0640276
$871$	37.8885	+	27.5276i	1.28380	+	0.932738i
$872$	−0.381966	+	1.17557i	−0.0129350	+	0.0398098i
$873$	−1.47214	−	4.53077i	−0.0498243	−	0.153343i
$874$	0.927051	−	0.673542i	0.0313580	−	0.0227829i
$875$	−8.91641	+	6.47815i	−0.301430	+	0.219001i
$876$	8.65248	+	26.6296i	0.292340	+	0.899730i
$877$	−4.50658	+	13.8698i	−0.152176	+	0.468351i	−0.997864	−	0.0653278i	$-0.979191\pi$
$877$	−4.50658	+	13.8698i	−0.152176	+	0.468351i	0.845688	+	0.533678i	$0.179191\pi$
$878$	−18.7082	−	13.5923i	−0.631371	−	0.458718i
$879$	−1.30495			−0.0440149
$880$	1.88197	+	0.812299i	0.0634411	+	0.0273826i
$881$	25.4164			0.856301			0.428150	−	0.903708i	$-0.359165\pi$
$881$	25.4164			0.856301			0.428150	+	0.903708i	$0.359165\pi$
$882$	2.88197	+	2.09387i	0.0970408	+	0.0705043i
$883$	−7.53851	+	23.2011i	−0.253691	+	0.780781i	0.740394	+	0.672173i	$0.234639\pi$
$883$	−7.53851	+	23.2011i	−0.253691	+	0.780781i	−0.994085	+	0.108607i	$0.965361\pi$
$884$	−11.2361	−	34.5811i	−0.377910	−	1.16309i
$885$	12.4721	−	9.06154i	0.419246	−	0.304600i
$886$	−11.5000	+	8.35524i	−0.386350	+	0.280700i
$887$	3.74265	+	11.5187i	0.125666	+	0.386759i	0.994022	−	0.109182i	$-0.0348231\pi$
$887$	3.74265	+	11.5187i	0.125666	+	0.386759i	−0.868356	+	0.495941i	$0.834823\pi$
$888$	−2.47214	+	7.60845i	−0.0829595	+	0.255323i
$889$	−11.1246	−	8.08250i	−0.373108	−	0.271078i
$890$	−4.18034			−0.140125
$891$	−35.5967	+	7.99197i	−1.19254	+	0.267741i
$892$	3.70820			0.124160
$893$	−2.92705	−	2.12663i	−0.0979500	−	0.0711649i
$894$	12.6525	−	38.9403i	0.423162	−	1.30236i
$895$	3.85410	+	11.8617i	0.128828	+	0.396493i
$896$	−1.50000	+	1.08981i	−0.0501115	+	0.0364081i
$897$	12.0000	−	8.71851i	0.400668	−	0.291103i
$898$	−2.52786	−	7.77997i	−0.0843559	−	0.259621i
$899$	0.944272	−	2.90617i	0.0314932	−	0.0969262i
$900$	3.73607	+	2.71441i	0.124536	+	0.0904804i
$901$	−51.8885			−1.72866
$902$	−15.6180	−	26.3521i	−0.520024	−	0.877428i
$903$	−7.75078			−0.257930
$904$	−11.7082	−	8.50651i	−0.389409	−	0.282922i
$905$	2.61803	−	8.05748i	0.0870264	−	0.267840i
$906$	0.180340	+	0.555029i	0.00599139	+	0.0184396i
$907$	24.9443	−	18.1231i	0.828261	−	0.601767i	−0.0908058	−	0.995869i	$-0.528944\pi$
$907$	24.9443	−	18.1231i	0.828261	−	0.601767i	0.919067	+	0.394102i	$0.128944\pi$
$908$		0			0
$909$	1.71885	+	5.29007i	0.0570106	+	0.175460i
$910$	2.29180	−	7.05342i	0.0759723	−	0.233819i
$911$	−10.8541	−	7.88597i	−0.359612	−	0.261274i	0.393278	−	0.919420i	$-0.371341\pi$
$911$	−10.8541	−	7.88597i	−0.359612	−	0.261274i	−0.752890	+	0.658146i	$0.771341\pi$
$912$	−2.00000			−0.0662266
$913$	18.2599	+	30.8096i	0.604313	+	1.01965i
$914$	−23.3820			−0.773407
$915$	−10.5623	−	7.67396i	−0.349179	−	0.253693i
$916$	7.50000	−	23.0826i	0.247807	−	0.762671i
$917$	−0.521286	−	1.60435i	−0.0172144	−	0.0529804i
$918$	−18.1803	+	13.2088i	−0.600041	+	0.435955i
$919$	23.2082	−	16.8617i	0.765568	−	0.556218i	−0.135045	−	0.990839i	$-0.543118\pi$
$919$	23.2082	−	16.8617i	0.765568	−	0.556218i	0.900613	+	0.434622i	$0.143118\pi$
$920$	0.218847	+	0.673542i	0.00721517	+	0.0222060i
$921$	16.9443	−	52.1491i	0.558333	−	1.71837i
$922$	−4.20820	−	3.05744i	−0.138590	−	0.100691i
$923$	83.7771			2.75756
$924$	−12.0000	+	2.69417i	−0.394771	+	0.0886316i
$925$	−18.4721			−0.607360
$926$	−2.26393	−	1.64484i	−0.0743974	−	0.0540529i
$927$	−2.85410	+	8.78402i	−0.0937410	+	0.288505i
$928$	0.472136	+	1.45309i	0.0154986	+	0.0476999i
$929$	−39.0517	+	28.3727i	−1.28124	+	0.930878i	−0.999590	−	0.0286383i	$-0.990883\pi$
$929$	−39.0517	+	28.3727i	−1.28124	+	0.930878i	−0.281654	+	0.959516i	$0.590883\pi$
$930$	−2.00000	+	1.45309i	−0.0655826	+	0.0476485i
$931$	−1.10081	−	3.38795i	−0.0360777	−	0.111036i
$932$	−5.80902	+	17.8783i	−0.190281	+	0.585624i
$933$	−6.79837	−	4.93931i	−0.222569	−	0.161706i
$934$	31.0902			1.01730
$935$	10.5729	+	4.56352i	0.345772	+	0.149243i
$936$	−6.47214			−0.211548
$937$	−45.9615	−	33.3930i	−1.50150	−	1.09090i	−0.969781	−	0.243978i	$-0.921547\pi$
$937$	−45.9615	−	33.3930i	−1.50150	−	1.09090i	−0.531716	−	0.846923i	$-0.678453\pi$
$938$	4.14590	−	12.7598i	0.135368	−	0.416621i
$939$	0.0557281	+	0.171513i	0.00181862	+	0.00559713i
$940$	1.80902	−	1.31433i	0.0590036	−	0.0428686i
$941$	−7.23607	+	5.25731i	−0.235889	+	0.171383i	−0.699450	−	0.714682i	$-0.746572\pi$
$941$	−7.23607	+	5.25731i	−0.235889	+	0.171383i	0.463561	+	0.886065i	$0.346572\pi$
$942$	−4.74265	−	14.5964i	−0.154524	−	0.475575i
$943$	3.27051	−	10.0656i	0.106502	−	0.327781i
$944$	10.0902	+	7.33094i	0.328407	+	0.238602i
$945$	−4.58359			−0.149104
$946$	−4.57953	+	5.20431i	−0.148893	+	0.169207i
$947$	−37.9230			−1.23233			−0.616166	−	0.787617i	$-0.711315\pi$
$947$	−37.9230			−1.23233			−0.616166	+	0.787617i	$0.711315\pi$
$948$	−15.7082	−	11.4127i	−0.510179	−	0.370667i
$949$	28.0000	−	86.1751i	0.908918	−	2.79736i
$950$	−1.42705	−	4.39201i	−0.0462996	−	0.142496i
$951$	3.52786	−	2.56314i	0.114399	−	0.0831156i
$952$	−8.42705	+	6.12261i	−0.273122	+	0.198435i
$953$	15.3820	+	47.3408i	0.498271	+	1.53352i	0.811797	+	0.583940i	$0.198490\pi$
$953$	15.3820	+	47.3408i	0.498271	+	1.53352i	−0.313526	+	0.949580i	$0.601510\pi$
$954$	−2.85410	+	8.78402i	−0.0924050	+	0.284393i
$955$	−12.0172	−	8.73102i	−0.388868	−	0.282529i
$956$	2.67376			0.0864756
$957$	−0.944272	+	10.0906i	−0.0305240	+	0.326183i
$958$	−10.0902			−0.325999
$959$	22.6353	+	16.4455i	0.730931	+	0.531052i
$960$	0.381966	−	1.17557i	0.0123279	−	0.0379414i
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	20.9443	−	15.2169i	0.675270	−	0.490613i
$963$	−4.85410	+	3.52671i	−0.156421	+	0.113647i
$964$	3.09017	+	9.51057i	0.0995277	+	0.306315i
$965$	4.03444	−	12.4167i	0.129873	−	0.399709i
$966$	−3.43769	−	2.49763i	−0.110606	−	0.0803600i
$967$	−58.2705			−1.87385			−0.936927	−	0.349526i	$-0.886343\pi$
$967$	−58.2705			−1.87385			−0.936927	+	0.349526i	$0.886343\pi$
$968$	−5.28115	+	9.64932i	−0.169743	+	0.310141i
$969$	−11.2361			−0.360955
$970$	−2.38197	−	1.73060i	−0.0764803	−	0.0555662i
$971$	−10.6180	+	32.6789i	−0.340749	+	1.04872i	0.623071	+	0.782165i	$0.285885\pi$
$971$	−10.6180	+	32.6789i	−0.340749	+	1.04872i	−0.963820	+	0.266552i	$0.914115\pi$
$972$	3.09017	+	9.51057i	0.0991172	+	0.305052i
$973$	−7.98936	+	5.80461i	−0.256127	+	0.186087i
$974$	−8.09017	+	5.87785i	−0.259226	+	0.188339i
$975$	−18.4721	−	56.8514i	−0.591582	−	1.82070i
$976$	3.26393	−	10.0453i	0.104476	−	0.321544i
$977$	−7.14590	−	5.19180i	−0.228618	−	0.166100i	0.467580	−	0.883951i	$-0.345126\pi$
$977$	−7.14590	−	5.19180i	−0.228618	−	0.166100i	−0.696197	+	0.717851i	$0.745126\pi$
$978$	32.6525			1.04411
$979$	2.09017	−	22.3358i	0.0668021	−	0.713857i
$980$	2.20163			0.0703284
$981$	1.00000	+	0.726543i	0.0319275	+	0.0231967i
$982$	−3.13525	+	9.64932i	−0.100050	+	0.307922i
$983$	−17.9656	−	55.2923i	−0.573012	−	1.76355i	−0.642850	−	0.765992i	$-0.722248\pi$
$983$	−17.9656	−	55.2923i	−0.573012	−	1.76355i	0.0698376	−	0.997558i	$-0.477752\pi$
$984$	−14.9443	+	10.8576i	−0.476406	+	0.346129i
$985$	−9.00000	+	6.53888i	−0.286764	+	0.208346i
$986$	2.65248	+	8.16348i	0.0844720	+	0.259978i
$987$	−4.14590	+	12.7598i	−0.131965	+	0.406148i
$988$	5.23607	+	3.80423i	0.166582	+	0.121029i
$989$	−2.39512			−0.0761604
$990$	1.35410	−	1.53884i	0.0430362	−	0.0489076i
$991$	−26.3607			−0.837375			−0.418687	−	0.908130i	$-0.637510\pi$
$991$	−26.3607			−0.837375			−0.418687	+	0.908130i	$0.637510\pi$
$992$	−1.61803	−	1.17557i	−0.0513726	−	0.0373244i
$993$	6.00000	−	18.4661i	0.190404	−	0.586004i
$994$	−7.41641	−	22.8254i	−0.235234	−	0.723976i
$995$	−2.78115	+	2.02063i	−0.0881685	+	0.0640581i
$996$	17.4721	−	12.6942i	0.553626	−	0.402233i
$997$	−6.57295	−	20.2295i	−0.208167	−	0.640673i	−0.999568	−	0.0293760i	$-0.990648\pi$
$997$	−6.57295	−	20.2295i	−0.208167	−	0.640673i	0.791401	−	0.611297i	$-0.209352\pi$
$998$	5.42705	−	16.7027i	0.171790	−	0.528716i
$999$	−12.9443	−	9.40456i	−0.409539	−	0.297547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.d.191.1	✓	4
11.3	even	5	inner	418.2.f.d.267.1	yes	4
11.5	even	5		4598.2.a.bb.1.1		2
11.6	odd	10		4598.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.d.191.1	✓	4	1.1	even	1	trivial
418.2.f.d.267.1	yes	4	11.3	even	5	inner
4598.2.a.t.1.1		2	11.6	odd	10
4598.2.a.bb.1.1		2	11.5	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.618034 + 1.90211i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.363271i) q^{5} +(1.61803 - 1.17557i) q^{6} +(0.572949 + 1.76336i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.618034 q^{10} +(0.309017 - 3.30220i) q^{11} -2.00000 q^{12} +(5.23607 + 3.80423i) q^{13} +(0.572949 - 1.76336i) q^{14} +(0.381966 + 1.17557i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.54508 + 3.30220i) q^{17} +(0.309017 + 0.951057i) q^{18} +(0.309017 - 0.951057i) q^{19} +(0.500000 + 0.363271i) q^{20} -3.70820 q^{21} +(-2.19098 + 2.48990i) q^{22} -1.14590 q^{23} +(1.61803 + 1.17557i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(-3.23607 + 2.35114i) q^{27} +(-1.50000 + 1.08981i) q^{28} +(0.472136 + 1.45309i) q^{29} +(0.381966 - 1.17557i) q^{30} +(-1.61803 - 1.17557i) q^{31} +1.00000 q^{32} +(6.09017 + 2.62866i) q^{33} +5.61803 q^{34} +(0.927051 + 0.673542i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.23607 + 3.80423i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-10.4721 + 7.60845i) q^{39} +(-0.190983 - 0.587785i) q^{40} +(-2.85410 + 8.78402i) q^{41} +(3.00000 + 2.17963i) q^{42} +2.09017 q^{43} +(3.23607 - 0.726543i) q^{44} -0.618034 q^{45} +(0.927051 + 0.673542i) q^{46} +(1.11803 - 3.44095i) q^{47} +(-0.618034 - 1.90211i) q^{48} +(2.88197 - 2.09387i) q^{49} +(3.73607 - 2.71441i) q^{50} +(-3.47214 - 10.6861i) q^{51} +(-2.00000 + 6.15537i) q^{52} +(7.47214 + 5.42882i) q^{53} +4.00000 q^{54} +(-1.04508 - 1.76336i) q^{55} +1.85410 q^{56} +(1.61803 + 1.17557i) q^{57} +(0.472136 - 1.45309i) q^{58} +(-3.85410 - 11.8617i) q^{59} +(-1.00000 + 0.726543i) q^{60} +(-8.54508 + 6.20837i) q^{61} +(0.618034 + 1.90211i) q^{62} +(0.572949 - 1.76336i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-3.38197 - 5.70634i) q^{66} +7.23607 q^{67} +(-4.54508 - 3.30220i) q^{68} +(0.708204 - 2.17963i) q^{69} +(-0.354102 - 1.08981i) q^{70} +(10.4721 - 7.60845i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-4.32624 - 13.3148i) q^{73} +(1.23607 - 3.80423i) q^{74} +(-7.47214 - 5.42882i) q^{75} +1.00000 q^{76} +(6.00000 - 1.34708i) q^{77} +12.9443 q^{78} +(7.85410 + 5.70634i) q^{79} +(-0.190983 + 0.587785i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(7.47214 - 5.42882i) q^{82} +(-8.73607 + 6.34712i) q^{83} +(-1.14590 - 3.52671i) q^{84} +(-1.07295 + 3.30220i) q^{85} +(-1.69098 - 1.22857i) q^{86} -3.05573 q^{87} +(-3.04508 - 1.31433i) q^{88} +6.76393 q^{89} +(0.500000 + 0.363271i) q^{90} +(-3.70820 + 11.4127i) q^{91} +(-0.354102 - 1.08981i) q^{92} +(3.23607 - 2.35114i) q^{93} +(-2.92705 + 2.12663i) q^{94} +(-0.190983 - 0.587785i) q^{95} +(-0.618034 + 1.90211i) q^{96} +(3.85410 + 2.80017i) q^{97} -3.56231 q^{98} +(-2.19098 + 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9} + 2 q^{10} - q^{11} - 8 q^{12} + 12 q^{13} + 9 q^{14} + 6 q^{15} - q^{16} - 7 q^{17} - q^{18} - q^{19} + 2 q^{20} + 12 q^{21}+ \cdots - 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9 + 2 * q^10 - q^11 - 8 * q^12 + 12 * q^13 + 9 * q^14 + 6 * q^15 - q^16 - 7 * q^17 - q^18 - q^19 + 2 * q^20 + 12 * q^21 - 11 * q^22 - 18 * q^23 + 2 * q^24 + q^25 - 8 * q^26 - 4 * q^27 - 6 * q^28 - 16 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^33 + 18 * q^34 - 3 * q^35 - q^36 - 4 * q^37 - q^38 - 24 * q^39 - 3 * q^40 + 2 * q^41 + 12 * q^42 - 14 * q^43 + 4 * q^44 + 2 * q^45 - 3 * q^46 + 2 * q^48 + 16 * q^49 + 6 * q^50 + 4 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 7 * q^55 - 6 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^59 - 4 * q^60 - 23 * q^61 - 2 * q^62 + 9 * q^63 - q^64 + 16 * q^65 - 18 * q^66 + 20 * q^67 - 7 * q^68 - 24 * q^69 + 12 * q^70 + 24 * q^71 - q^72 + 14 * q^73 - 4 * q^74 - 12 * q^75 + 4 * q^76 + 24 * q^77 + 16 * q^78 + 18 * q^79 - 3 * q^80 + 11 * q^81 + 12 * q^82 - 26 * q^83 - 18 * q^84 - 11 * q^85 - 9 * q^86 - 48 * q^87 - q^88 + 36 * q^89 + 2 * q^90 + 12 * q^91 + 12 * q^92 + 4 * q^93 - 5 * q^94 - 3 * q^95 + 2 * q^96 + 2 * q^97 + 26 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more