LMFDB - Embedded newform 403.2.f.c.94.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.10
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0496225 - 0.0859486i) q^{2} +(0.816280 + 1.41384i) q^{3} +(0.995075 - 1.72352i) q^{4} -0.352370 q^{5} +(0.0810117 - 0.140316i) q^{6} +(2.05703 - 3.56288i) q^{7} -0.396002 q^{8} +(0.167373 - 0.289899i) q^{9} +O(q^{10})$	\(q+(-0.0496225 - 0.0859486i) q^{2} +(0.816280 + 1.41384i) q^{3} +(0.995075 - 1.72352i) q^{4} -0.352370 q^{5} +(0.0810117 - 0.140316i) q^{6} +(2.05703 - 3.56288i) q^{7} -0.396002 q^{8} +(0.167373 - 0.289899i) q^{9} +(0.0174854 + 0.0302857i) q^{10} +(-2.45188 - 4.24678i) q^{11} +3.24904 q^{12} +(-1.56626 + 3.24759i) q^{13} -0.408299 q^{14} +(-0.287632 - 0.498194i) q^{15} +(-1.97050 - 3.41301i) q^{16} +(-1.84743 + 3.19985i) q^{17} -0.0332218 q^{18} +(2.16903 - 3.75686i) q^{19} +(-0.350634 + 0.607316i) q^{20} +6.71644 q^{21} +(-0.243337 + 0.421472i) q^{22} +(2.83246 + 4.90596i) q^{23} +(-0.323249 - 0.559883i) q^{24} -4.87584 q^{25} +(0.356847 - 0.0265360i) q^{26} +5.44417 q^{27} +(-4.09379 - 7.09066i) q^{28} +(3.66951 + 6.35578i) q^{29} +(-0.0285460 + 0.0494432i) q^{30} +1.00000 q^{31} +(-0.591564 + 1.02462i) q^{32} +(4.00285 - 6.93313i) q^{33} +0.366697 q^{34} +(-0.724834 + 1.25545i) q^{35} +(-0.333097 - 0.576942i) q^{36} +(4.65608 + 8.06456i) q^{37} -0.430529 q^{38} +(-5.87007 + 0.436512i) q^{39} +0.139539 q^{40} +(3.57804 + 6.19735i) q^{41} +(-0.333286 - 0.577269i) q^{42} +(0.204002 - 0.353341i) q^{43} -9.75923 q^{44} +(-0.0589771 + 0.102151i) q^{45} +(0.281107 - 0.486892i) q^{46} +5.39075 q^{47} +(3.21696 - 5.57194i) q^{48} +(-4.96272 - 8.59569i) q^{49} +(0.241951 + 0.419071i) q^{50} -6.03209 q^{51} +(4.03875 + 5.93107i) q^{52} -7.56811 q^{53} +(-0.270153 - 0.467919i) q^{54} +(0.863968 + 1.49644i) q^{55} +(-0.814587 + 1.41091i) q^{56} +7.08213 q^{57} +(0.364180 - 0.630779i) q^{58} +(0.912475 - 1.58045i) q^{59} -1.14486 q^{60} +(4.33875 - 7.51494i) q^{61} +(-0.0496225 - 0.0859486i) q^{62} +(-0.688582 - 1.19266i) q^{63} -7.76458 q^{64} +(0.551901 - 1.14435i) q^{65} -0.794524 q^{66} +(5.65194 + 9.78945i) q^{67} +(3.67667 + 6.36818i) q^{68} +(-4.62416 + 8.00928i) q^{69} +0.143872 q^{70} +(-1.13977 + 1.97414i) q^{71} +(-0.0662801 + 0.114800i) q^{72} -2.21345 q^{73} +(0.462092 - 0.800367i) q^{74} +(-3.98005 - 6.89365i) q^{75} +(-4.31669 - 7.47672i) q^{76} -20.1743 q^{77} +(0.328805 + 0.482864i) q^{78} +2.80577 q^{79} +(0.694344 + 1.20264i) q^{80} +(3.94185 + 6.82749i) q^{81} +(0.355103 - 0.615056i) q^{82} -10.5846 q^{83} +(6.68337 - 11.5759i) q^{84} +(0.650979 - 1.12753i) q^{85} -0.0404923 q^{86} +(-5.99070 + 10.3762i) q^{87} +(0.970950 + 1.68174i) q^{88} +(-6.24828 - 10.8223i) q^{89} +0.0117064 q^{90} +(8.34893 + 12.2608i) q^{91} +11.2740 q^{92} +(0.816280 + 1.41384i) q^{93} +(-0.267502 - 0.463327i) q^{94} +(-0.764298 + 1.32380i) q^{95} -1.93153 q^{96} +(6.37242 - 11.0374i) q^{97} +(-0.492525 + 0.853078i) q^{98} -1.64151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.0496225	−	0.0859486i	−0.0350884	−	0.0607748i	0.847948	−	0.530080i	$-0.177838\pi$
$2$	−0.0496225	−	0.0859486i	−0.0350884	−	0.0607748i	−0.883036	+	0.469305i	$0.844505\pi$
$3$	0.816280	+	1.41384i	0.471280	+	0.816280i	0.999460	−	0.0328518i	$-0.0104589\pi$
$3$	0.816280	+	1.41384i	0.471280	+	0.816280i	−0.528181	+	0.849132i	$0.677126\pi$
$4$	0.995075	−	1.72352i	0.497538	−	0.861760i
$5$	−0.352370			−0.157584			−0.0787922	−	0.996891i	$-0.525106\pi$
$5$	−0.352370			−0.157584			−0.0787922	+	0.996891i	$0.525106\pi$
$6$	0.0810117	−	0.140316i	0.0330729	−	0.0572839i
$7$	2.05703	−	3.56288i	0.777483	−	1.34664i	−0.155905	−	0.987772i	$-0.549829\pi$
$7$	2.05703	−	3.56288i	0.777483	−	1.34664i	0.933388	−	0.358868i	$-0.116837\pi$
$8$	−0.396002			−0.140008
$9$	0.167373	−	0.289899i	0.0557910	−	0.0966328i
$10$	0.0174854	+	0.0302857i	0.00552938	+	0.00957717i
$11$	−2.45188	−	4.24678i	−0.739270	−	1.28045i	−0.952824	−	0.303522i	$-0.901837\pi$
$11$	−2.45188	−	4.24678i	−0.739270	−	1.28045i	0.213554	−	0.976931i	$-0.431496\pi$
$12$	3.24904			0.937917
$13$	−1.56626	+	3.24759i	−0.434401	+	0.900720i
$13$	−1.56626	+	3.24759i	−0.434401	+	0.900720i
$14$	−0.408299			−0.109122
$15$	−0.287632	−	0.498194i	−0.0742663	−	0.128633i
$16$	−1.97050	−	3.41301i	−0.492625	−	0.853251i
$17$	−1.84743	+	3.19985i	−0.448068	+	0.776077i	−0.998260	−	0.0589610i	$-0.981221\pi$
$17$	−1.84743	+	3.19985i	−0.448068	+	0.776077i	0.550192	+	0.835038i	$0.314555\pi$
$18$	−0.0332218			−0.00783046
$19$	2.16903	−	3.75686i	0.497609	−	0.861883i	−0.502388	−	0.864642i	$-0.667545\pi$
$19$	2.16903	−	3.75686i	0.497609	−	0.861883i	0.999996	+	0.00275925i	$0.000878298\pi$
$20$	−0.350634	+	0.607316i	−0.0784042	+	0.135800i
$21$	6.71644			1.46565
$22$	−0.243337	+	0.421472i	−0.0518796	+	0.0898580i
$23$	2.83246	+	4.90596i	0.590609	+	1.02296i	0.994151	+	0.108003i	$0.0344457\pi$
$23$	2.83246	+	4.90596i	0.590609	+	1.02296i	−0.403542	+	0.914961i	$0.632221\pi$
$24$	−0.323249	−	0.559883i	−0.0659829	−	0.114286i
$25$	−4.87584			−0.975167
$26$	0.356847	−	0.0265360i	0.0699835	−	0.00520413i
$27$	5.44417			1.04773
$28$	−4.09379	−	7.09066i	−0.773654	−	1.34001i
$29$	3.66951	+	6.35578i	0.681411	+	1.18024i	0.974550	+	0.224169i	$0.0719668\pi$
$29$	3.66951	+	6.35578i	0.681411	+	1.18024i	−0.293139	+	0.956070i	$0.594700\pi$
$30$	−0.0285460	+	0.0494432i	−0.00521177	+	0.00902705i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.591564	+	1.02462i	−0.104575	+	0.181129i
$33$	4.00285	−	6.93313i	0.696806	−	1.20690i
$34$	0.366697			0.0628880
$35$	−0.724834	+	1.25545i	−0.122519	+	0.212210i
$36$	−0.333097	−	0.576942i	−0.0555162	−	0.0961569i
$37$	4.65608	+	8.06456i	0.765454	+	1.32581i	0.940006	+	0.341158i	$0.110819\pi$
$37$	4.65608	+	8.06456i	0.765454	+	1.32581i	−0.174552	+	0.984648i	$0.555848\pi$
$38$	−0.430529			−0.0698411
$39$	−5.87007	+	0.436512i	−0.939964	+	0.0698978i
$40$	0.139539			0.0220631
$41$	3.57804	+	6.19735i	0.558796	+	0.967864i	0.997597	+	0.0692795i	$0.0220700\pi$
$41$	3.57804	+	6.19735i	0.558796	+	0.967864i	−0.438801	+	0.898584i	$0.644597\pi$
$42$	−0.333286	−	0.577269i	−0.0514272	−	0.0890745i
$43$	0.204002	−	0.353341i	0.0311100	−	0.0538841i	−0.850051	−	0.526700i	$-0.823429\pi$
$43$	0.204002	−	0.353341i	0.0311100	−	0.0538841i	0.881161	+	0.472816i	$0.156762\pi$
$44$	−9.75923			−1.47126
$45$	−0.0589771	+	0.102151i	−0.00879179	+	0.0152278i
$46$	0.281107	−	0.486892i	0.0414470	−	0.0717883i
$47$	5.39075			0.786321			0.393161	−	0.919470i	$-0.371382\pi$
$47$	5.39075			0.786321			0.393161	+	0.919470i	$0.371382\pi$
$48$	3.21696	−	5.57194i	0.464328	−	0.804240i
$49$	−4.96272	−	8.59569i	−0.708960	−	1.22796i
$50$	0.241951	+	0.419071i	0.0342170	+	0.0592656i
$51$	−6.03209			−0.844662
$52$	4.03875	+	5.93107i	0.560074	+	0.822491i
$53$	−7.56811			−1.03956			−0.519780	−	0.854300i	$-0.673986\pi$
$53$	−7.56811			−1.03956			−0.519780	+	0.854300i	$0.673986\pi$
$54$	−0.270153	−	0.467919i	−0.0367632	−	0.0636757i
$55$	0.863968	+	1.49644i	0.116497	+	0.201780i
$56$	−0.814587	+	1.41091i	−0.108854	+	0.188540i
$57$	7.08213			0.938051
$58$	0.364180	−	0.630779i	0.0478192	−	0.0828253i
$59$	0.912475	−	1.58045i	0.118794	−	0.205757i	−0.800496	−	0.599338i	$-0.795430\pi$
$59$	0.912475	−	1.58045i	0.118794	−	0.205757i	0.919290	+	0.393581i	$0.128764\pi$
$60$	−1.14486			−0.147801
$61$	4.33875	−	7.51494i	0.555520	−	0.962189i	−0.442343	−	0.896846i	$-0.645853\pi$
$61$	4.33875	−	7.51494i	0.555520	−	0.962189i	0.997863	−	0.0653429i	$-0.0208141\pi$
$62$	−0.0496225	−	0.0859486i	−0.00630206	−	0.0109155i
$63$	−0.688582	−	1.19266i	−0.0867531	−	0.150261i
$64$	−7.76458			−0.970572
$65$	0.551901	−	1.14435i	0.0684548	−	0.141939i
$66$	−0.794524			−0.0977991
$67$	5.65194	+	9.78945i	0.690495	+	1.19597i	0.971676	+	0.236317i	$0.0759404\pi$
$67$	5.65194	+	9.78945i	0.690495	+	1.19597i	−0.281181	+	0.959655i	$0.590726\pi$
$68$	3.67667	+	6.36818i	0.445862	+	0.772255i
$69$	−4.62416	+	8.00928i	−0.556684	+	0.964205i
$70$	0.143872			0.0171960
$71$	−1.13977	+	1.97414i	−0.135266	+	0.234288i	−0.925699	−	0.378261i	$-0.876522\pi$
$71$	−1.13977	+	1.97414i	−0.135266	+	0.234288i	0.790433	+	0.612548i	$0.209856\pi$
$72$	−0.0662801	+	0.114800i	−0.00781118	+	0.0135294i
$73$	−2.21345			−0.259065			−0.129532	−	0.991575i	$-0.541348\pi$
$73$	−2.21345			−0.259065			−0.129532	+	0.991575i	$0.541348\pi$
$74$	0.462092	−	0.800367i	0.0537171	−	0.0930407i
$75$	−3.98005	−	6.89365i	−0.459576	−	0.796010i
$76$	−4.31669	−	7.47672i	−0.495158	−	0.857639i
$77$	−20.1743			−2.29908
$78$	0.328805	+	0.482864i	0.0372298	+	0.0546736i
$79$	2.80577			0.315674			0.157837	−	0.987465i	$-0.449548\pi$
$79$	2.80577			0.315674			0.157837	+	0.987465i	$0.449548\pi$
$80$	0.694344	+	1.20264i	0.0776300	+	0.134459i
$81$	3.94185	+	6.82749i	0.437984	+	0.758610i
$82$	0.355103	−	0.615056i	0.0392145	−	0.0679215i
$83$	−10.5846			−1.16181			−0.580905	−	0.813971i	$-0.697301\pi$
$83$	−10.5846			−1.16181			−0.580905	+	0.813971i	$0.697301\pi$
$84$	6.68337	−	11.5759i	0.729215	−	1.26304i
$85$	0.650979	−	1.12753i	0.0706086	−	0.122298i
$86$	−0.0404923			−0.00436639
$87$	−5.99070	+	10.3762i	−0.642270	+	1.11245i
$88$	0.970950	+	1.68174i	0.103504	+	0.179274i
$89$	−6.24828	−	10.8223i	−0.662317	−	1.14717i	−0.980005	−	0.198971i	$-0.936240\pi$
$89$	−6.24828	−	10.8223i	−0.662317	−	1.14717i	0.317689	−	0.948195i	$-0.397093\pi$
$90$	0.0117064			0.00123396
$91$	8.34893	+	12.2608i	0.875206	+	1.28528i
$92$	11.2740			1.17540
$93$	0.816280	+	1.41384i	0.0846443	+	0.146608i
$94$	−0.267502	−	0.463327i	−0.0275907	−	0.0477885i
$95$	−0.764298	+	1.32380i	−0.0784154	+	0.135819i
$96$	−1.93153			−0.197136
$97$	6.37242	−	11.0374i	0.647021	−	1.12067i	−0.336810	−	0.941573i	$-0.609348\pi$
$97$	6.37242	−	11.0374i	0.647021	−	1.12067i	0.983831	−	0.179101i	$-0.0573187\pi$
$98$	−0.492525	+	0.853078i	−0.0497525	+	0.0861739i
$99$	−1.64151			−0.164978
$100$	−4.85182	+	8.40360i	−0.485182	+	0.840360i
$101$	−4.18621	−	7.25074i	−0.416544	−	0.721475i	0.579045	−	0.815295i	$-0.303425\pi$
$101$	−4.18621	−	7.25074i	−0.416544	−	0.721475i	−0.995589	+	0.0938202i	$0.970092\pi$
$102$	0.299327	+	0.518450i	0.0296378	+	0.0513342i
$103$	−13.6121			−1.34124			−0.670620	−	0.741801i	$-0.733972\pi$
$103$	−13.6121			−1.34124			−0.670620	+	0.741801i	$0.733972\pi$
$104$	0.620240	−	1.28605i	0.0608196	−	0.126108i
$105$	−2.36667			−0.230963
$106$	0.375548	+	0.650468i	0.0364765	+	0.0631791i
$107$	6.88234	+	11.9206i	0.665341	+	1.15240i	0.979193	+	0.202932i	$0.0650472\pi$
$107$	6.88234	+	11.9206i	0.665341	+	1.15240i	−0.313852	+	0.949472i	$0.601619\pi$
$108$	5.41736	−	9.38315i	0.521286	−	0.902894i
$109$	5.02812			0.481606			0.240803	−	0.970574i	$-0.422589\pi$
$109$	5.02812			0.481606			0.240803	+	0.970574i	$0.422589\pi$
$110$	0.0857445	−	0.148514i	0.00817541	−	0.0141602i
$111$	−7.60133	+	13.1659i	−0.721486	+	1.24965i
$112$	−16.2135			−1.53203
$113$	−8.27244	+	14.3283i	−0.778206	+	1.34789i	0.154769	+	0.987951i	$0.450537\pi$
$113$	−8.27244	+	14.3283i	−0.778206	+	1.34789i	−0.932975	+	0.359941i	$0.882797\pi$
$114$	−0.351433	−	0.608699i	−0.0329147	−	0.0570099i
$115$	−0.998073	−	1.72871i	−0.0930708	−	0.161203i
$116$	14.6058			1.35611
$117$	0.679323	+	0.997614i	0.0628034	+	0.0922294i
$118$	−0.181117			−0.0166732
$119$	7.60044	+	13.1644i	0.696731	+	1.20677i
$120$	0.113903	+	0.197286i	0.0103979	+	0.0180096i
$121$	−6.52345	+	11.2989i	−0.593041	+	1.02718i
$122$	−0.861198			−0.0779692
$123$	−5.84137	+	10.1176i	−0.526699	+	0.912269i
$124$	0.995075	−	1.72352i	0.0893604	−	0.154777i
$125$	3.47994			0.311256
$126$	−0.0683382	+	0.118365i	−0.00608805	+	0.0105448i
$127$	−6.05023	−	10.4793i	−0.536871	−	0.929888i	−0.999070	−	0.0431118i	$-0.986273\pi$
$127$	−6.05023	−	10.4793i	−0.536871	−	0.929888i	0.462199	−	0.886776i	$-0.347060\pi$
$128$	1.56843	+	2.71659i	0.138631	+	0.240115i
$129$	0.666090			0.0586460
$130$	−0.125742	+	0.00935047i	−0.0110283	+	0.000820090i
$131$	1.16464			0.101755			0.0508777	−	0.998705i	$-0.483798\pi$
$131$	1.16464			0.101755			0.0508777	+	0.998705i	$0.483798\pi$
$132$	−7.96626	−	13.7980i	−0.693374	−	1.20096i
$133$	−8.92349	−	15.4559i	−0.773765	−	1.34020i
$134$	0.560926	−	0.971553i	0.0484567	−	0.0839294i
$135$	−1.91836			−0.165106
$136$	0.731588	−	1.26715i	0.0627331	−	0.108657i
$137$	−2.64756	+	4.58571i	−0.226197	+	0.391784i	−0.956678	−	0.291149i	$-0.905963\pi$
$137$	−2.64756	+	4.58571i	−0.226197	+	0.391784i	0.730481	+	0.682933i	$0.239296\pi$
$138$	0.917849			0.0781325
$139$	−5.76270	+	9.98130i	−0.488786	+	0.846603i	−0.999917	−	0.0129005i	$-0.995894\pi$
$139$	−5.76270	+	9.98130i	−0.488786	+	0.846603i	0.511131	+	0.859503i	$0.329227\pi$
$140$	1.44253	+	2.49853i	0.121916	+	0.211165i
$141$	4.40036	+	7.62165i	0.370577	+	0.641858i
$142$	0.226233			0.0189851
$143$	17.6321	−	1.31116i	1.47447	−	0.109645i
$144$	−1.31923			−0.109936
$145$	−1.29302	−	2.23958i	−0.107380	−	0.185987i
$146$	0.109837	+	0.190243i	0.00909016	+	0.0157446i
$147$	8.10195	−	14.0330i	0.668237	−	1.15742i
$148$	18.5326			1.52337
$149$	7.26840	−	12.5892i	0.595450	−	1.03135i	−0.398033	−	0.917371i	$-0.630307\pi$
$149$	7.26840	−	12.5892i	0.595450	−	1.03135i	0.993483	−	0.113979i	$-0.0363597\pi$
$150$	−0.395000	+	0.684159i	−0.0322516	+	0.0558614i
$151$	−5.58426			−0.454441			−0.227221	−	0.973843i	$-0.572964\pi$
$151$	−5.58426			−0.454441			−0.227221	+	0.973843i	$0.572964\pi$
$152$	−0.858939	+	1.48773i	−0.0696691	+	0.120670i
$153$	0.618421	+	1.07114i	0.0499964	+	0.0865963i
$154$	1.00110	+	1.73396i	0.0806710	+	0.139726i
$155$	−0.352370			−0.0283030
$156$	−5.08883	+	10.5516i	−0.407432	+	0.844801i
$157$	13.1500			1.04949			0.524743	−	0.851261i	$-0.324162\pi$
$157$	13.1500			1.04949			0.524743	+	0.851261i	$0.324162\pi$
$158$	−0.139229	−	0.241152i	−0.0110765	−	0.0191850i
$159$	−6.17770	−	10.7001i	−0.489923	−	0.848572i
$160$	0.208449	−	0.361045i	0.0164794	−	0.0285431i
$161$	23.3058			1.83675
$162$	0.391209	−	0.677594i	0.0307363	−	0.0532368i
$163$	−2.02292	+	3.50380i	−0.158447	+	0.274439i	−0.934309	−	0.356464i	$-0.883982\pi$
$163$	−2.02292	+	3.50380i	−0.158447	+	0.274439i	0.775862	+	0.630903i	$0.217316\pi$
$164$	14.2417			1.11209
$165$	−1.41048	+	2.44302i	−0.109806	+	0.190189i
$166$	0.525234	+	0.909732i	0.0407661	+	0.0706089i
$167$	−3.16904	−	5.48894i	−0.245228	−	0.424747i	0.716968	−	0.697106i	$-0.245529\pi$
$167$	−3.16904	−	5.48894i	−0.245228	−	0.424747i	−0.962196	+	0.272359i	$0.912196\pi$
$168$	−2.65973			−0.205202
$169$	−8.09369	−	10.1731i	−0.622592	−	0.782547i
$170$	−0.129213			−0.00991017
$171$	−0.726072	−	1.25759i	−0.0555241	−	0.0961706i
$172$	−0.405994	−	0.703203i	−0.0309568	−	0.0536187i
$173$	9.95946	−	17.2503i	0.757204	−	1.31152i	−0.187067	−	0.982347i	$-0.559898\pi$
$173$	9.95946	−	17.2503i	0.757204	−	1.31152i	0.944271	−	0.329169i	$-0.106768\pi$
$174$	1.18909			0.0901449
$175$	−10.0297	+	17.3720i	−0.758176	+	1.31320i
$176$	−9.66286	+	16.7366i	−0.728366	+	1.26157i
$177$	2.97934			0.223941
$178$	−0.620110	+	1.07406i	−0.0464792	+	0.0805044i
$179$	8.97483	+	15.5449i	0.670810	+	1.16188i	0.977675	+	0.210124i	$0.0673868\pi$
$179$	8.97483	+	15.5449i	0.670810	+	1.16188i	−0.306865	+	0.951753i	$0.599280\pi$
$180$	0.117373	+	0.203297i	0.00874850	+	0.0151528i
$181$	0.619124			0.0460191			0.0230095	−	0.999735i	$-0.492675\pi$
$181$	0.619124			0.0460191			0.0230095	+	0.999735i	$0.492675\pi$
$182$	0.639500	−	1.32599i	0.0474029	−	0.0982888i
$183$	14.1665			1.04722
$184$	−1.12166	−	1.94277i	−0.0826899	−	0.143223i
$185$	−1.64066	−	2.84171i	−0.120624	−	0.208926i
$186$	0.0810117	−	0.140316i	0.00594006	−	0.0102885i
$187$	18.1188			1.32497
$188$	5.36420	−	9.29106i	0.391224	−	0.677620i
$189$	11.1988	−	19.3969i	0.814594	−	1.41092i
$190$	0.151705			0.0110059
$191$	3.40627	−	5.89983i	0.246469	−	0.426897i	−0.716075	−	0.698024i	$-0.754063\pi$
$191$	3.40627	−	5.89983i	0.246469	−	0.426897i	0.962544	+	0.271127i	$0.0873963\pi$
$192$	−6.33807	−	10.9779i	−0.457411	−	0.792259i
$193$	−7.18157	−	12.4389i	−0.516941	−	0.895368i	−0.999806	−	0.0196735i	$-0.993737\pi$
$193$	−7.18157	−	12.4389i	−0.516941	−	0.895368i	0.482865	−	0.875695i	$-0.339596\pi$
$194$	−1.26486			−0.0908117
$195$	2.06844	−	0.153813i	0.148124	−	0.0110148i
$196$	−19.7531			−1.41094
$197$	−10.5955	−	18.3520i	−0.754902	−	1.30753i	−0.945423	−	0.325845i	$-0.894351\pi$
$197$	−10.5955	−	18.3520i	−0.754902	−	1.30753i	0.190522	−	0.981683i	$-0.438982\pi$
$198$	0.0814560	+	0.141086i	0.00578883	+	0.0100265i
$199$	6.63839	−	11.4980i	0.470583	−	0.815074i	−0.528851	−	0.848715i	$-0.677377\pi$
$199$	6.63839	−	11.4980i	0.470583	−	0.815074i	0.999434	+	0.0336411i	$0.0107103\pi$
$200$	1.93084			0.136531
$201$	−9.22714	+	15.9819i	−0.650832	+	1.12727i
$202$	−0.415460	+	0.719599i	−0.0292317	+	0.0506308i
$203$	30.1931			2.11914
$204$	−6.00239	+	10.3964i	−0.420251	+	0.727896i
$205$	−1.26079	−	2.18376i	−0.0880576	−	0.152520i
$206$	0.675466	+	1.16994i	0.0470619	+	0.0815137i
$207$	1.89631			0.131803
$208$	14.1704	−	1.05374i	0.982537	−	0.0730637i
$209$	−21.2728			−1.47147
$210$	0.117440	+	0.203412i	0.00810413	+	0.0140368i
$211$	−4.12132	−	7.13833i	−0.283723	−	0.491423i	0.688575	−	0.725165i	$-0.258236\pi$
$211$	−4.12132	−	7.13833i	−0.283723	−	0.491423i	−0.972299	+	0.233741i	$0.924903\pi$
$212$	−7.53084	+	13.0438i	−0.517220	+	0.895851i
$213$	−3.72149			−0.254992
$214$	0.683037	−	1.18306i	0.0466915	−	0.0808720i
$215$	−0.0718840	+	0.124507i	−0.00490245	+	0.00849129i
$216$	−2.15590			−0.146691
$217$	2.05703	−	3.56288i	0.139640	−	0.241864i
$218$	−0.249508	−	0.432160i	−0.0168988	−	0.0292695i
$219$	−1.80679	−	3.12946i	−0.122092	−	0.211469i
$220$	3.43885			0.231848
$221$	−7.49825	−	11.0115i	−0.504387	−	0.740713i
$222$	1.50879			0.101263
$223$	−10.5719	−	18.3112i	−0.707950	−	1.22621i	−0.965616	−	0.259971i	$-0.916287\pi$
$223$	−10.5719	−	18.3112i	−0.707950	−	1.22621i	0.257666	−	0.966234i	$-0.417047\pi$
$224$	2.43373	+	4.21534i	0.162610	+	0.281649i
$225$	−0.816083	+	1.41350i	−0.0544055	+	0.0942332i
$226$	1.64199			0.109224
$227$	5.50941	−	9.54257i	0.365672	−	0.633363i	−0.623212	−	0.782053i	$-0.714172\pi$
$227$	5.50941	−	9.54257i	0.365672	−	0.633363i	0.988884	+	0.148690i	$0.0475058\pi$
$228$	7.04725	−	12.2062i	0.466716	−	0.808375i
$229$	16.6985			1.10347			0.551735	−	0.834020i	$-0.313966\pi$
$229$	16.6985			1.10347			0.551735	+	0.834020i	$0.313966\pi$
$230$	−0.0990536	+	0.171566i	−0.00653140	+	0.0113127i
$231$	−16.4679	−	28.5233i	−1.08351	−	1.87669i
$232$	−1.45313	−	2.51690i	−0.0954029	−	0.165243i
$233$	−24.5734			−1.60986			−0.804930	−	0.593370i	$-0.797797\pi$
$233$	−24.5734			−1.60986			−0.804930	+	0.593370i	$0.797797\pi$
$234$	0.0520339	−	0.107891i	0.00340156	−	0.00705305i
$235$	−1.89953			−0.123912
$236$	−1.81596	−	3.14534i	−0.118209	−	0.204744i
$237$	2.29030	+	3.96691i	0.148771	+	0.257678i
$238$	0.754305	−	1.30649i	0.0488943	−	0.0846875i
$239$	−14.5666			−0.942236			−0.471118	−	0.882070i	$-0.656149\pi$
$239$	−14.5666			−0.942236			−0.471118	+	0.882070i	$0.656149\pi$
$240$	−1.13356	+	1.96338i	−0.0731709	+	0.126736i
$241$	−14.7466	+	25.5418i	−0.949911	+	1.64529i	−0.204305	+	0.978907i	$0.565494\pi$
$241$	−14.7466	+	25.5418i	−0.949911	+	1.64529i	−0.745606	+	0.666387i	$0.767840\pi$
$242$	1.29484			0.0832353
$243$	1.73095	−	2.99809i	0.111040	−	0.192327i
$244$	−8.63477	−	14.9559i	−0.552784	−	0.957450i
$245$	1.74871	+	3.02886i	0.111721	+	0.193507i
$246$	1.15945			0.0739240
$247$	8.80350	+	12.9283i	0.560153	+	0.822609i
$248$	−0.396002			−0.0251462
$249$	−8.64000	−	14.9649i	−0.547538	−	0.948363i
$250$	−0.172683	−	0.299096i	−0.0109215	−	0.0189165i
$251$	−2.79829	+	4.84678i	−0.176627	+	0.305926i	−0.940723	−	0.339176i	$-0.889852\pi$
$251$	−2.79829	+	4.84678i	−0.176627	+	0.305926i	0.764096	+	0.645102i	$0.223185\pi$
$252$	−2.74076			−0.172652
$253$	13.8897	−	24.0577i	0.873239	−	1.51249i
$254$	−0.600454	+	1.04002i	−0.0376759	+	0.0652565i
$255$	2.12553			0.133106
$256$	−7.60892	+	13.1790i	−0.475558	+	0.823690i
$257$	9.86636	+	17.0890i	0.615446	+	1.06598i	0.990306	+	0.138903i	$0.0443576\pi$
$257$	9.86636	+	17.0890i	0.615446	+	1.06598i	−0.374860	+	0.927082i	$0.622309\pi$
$258$	−0.0330530	−	0.0572496i	−0.00205779	−	0.00356420i
$259$	38.3107			2.38051
$260$	−1.42313	−	2.08993i	−0.0882589	−	0.129612i
$261$	2.45671			0.152066
$262$	−0.0577925	−	0.100100i	−0.00357043	−	0.00618417i
$263$	11.4419	+	19.8179i	0.705536	+	1.22202i	0.966498	+	0.256676i	$0.0826272\pi$
$263$	11.4419	+	19.8179i	0.705536	+	1.22202i	−0.260961	+	0.965349i	$0.584039\pi$
$264$	−1.58514	+	2.74553i	−0.0975583	+	0.168976i
$265$	2.66677			0.163818
$266$	−0.885611	+	1.53392i	−0.0543003	+	0.0940508i
$267$	10.2007	−	17.6681i	0.624273	−	1.08127i
$268$	22.4964			1.37419
$269$	−6.35221	+	11.0024i	−0.387301	+	0.670825i	−0.992086	−	0.125564i	$-0.959926\pi$
$269$	−6.35221	+	11.0024i	−0.387301	+	0.670825i	0.604784	+	0.796389i	$0.293259\pi$
$270$	0.0951938	+	0.164881i	0.00579331	+	0.0100343i
$271$	−4.72337	−	8.18111i	−0.286924	−	0.496967i	0.686150	−	0.727460i	$-0.259299\pi$
$271$	−4.72337	−	8.18111i	−0.286924	−	0.496967i	−0.973074	+	0.230493i	$0.925966\pi$
$272$	14.5615			0.882919
$273$	−10.5197	+	21.8123i	−0.636679	+	1.32014i
$274$	0.525514			0.0317475
$275$	11.9550	+	20.7066i	0.720912	+	1.24866i
$276$	9.20278	+	15.9397i	0.553942	+	0.959456i
$277$	−11.4413	+	19.8169i	−0.687441	+	1.19068i	0.285222	+	0.958461i	$0.407933\pi$
$277$	−11.4413	+	19.8169i	−0.687441	+	1.19068i	−0.972663	+	0.232221i	$0.925401\pi$
$278$	1.14384			0.0686029
$279$	0.167373	−	0.289899i	0.0100204	−	0.0173558i
$280$	0.287036	−	0.497160i	0.0171537	−	0.0297110i
$281$	3.84201			0.229195			0.114597	−	0.993412i	$-0.463442\pi$
$281$	3.84201			0.229195			0.114597	+	0.993412i	$0.463442\pi$
$282$	0.436713	−	0.756410i	0.0260059	−	0.0450435i
$283$	12.6961	+	21.9903i	0.754706	+	1.30719i	0.945520	+	0.325564i	$0.105554\pi$
$283$	12.6961	+	21.9903i	0.754706	+	1.30719i	−0.190814	+	0.981626i	$0.561113\pi$
$284$	2.26832	+	3.92884i	0.134600	+	0.233134i
$285$	−2.49553			−0.147822
$286$	−0.987640	−	1.45039i	−0.0584004	−	0.0857634i
$287$	29.4405			1.73782
$288$	0.198024	+	0.342987i	0.0116687	+	0.0202107i
$289$	1.67398	+	2.89942i	0.0984693	+	0.170554i
$290$	−0.128326	+	0.222267i	−0.00753557	+	0.0130520i
$291$	20.8067			1.21971
$292$	−2.20255	+	3.81493i	−0.128894	+	0.223252i
$293$	−9.13112	+	15.8156i	−0.533446	+	0.923955i	0.465791	+	0.884895i	$0.345770\pi$
$293$	−9.13112	+	15.8156i	−0.533446	+	0.923955i	−0.999237	+	0.0390606i	$0.987563\pi$
$294$	−1.60815			−0.0937894
$295$	−0.321528	+	0.556904i	−0.0187201	+	0.0324242i
$296$	−1.84382	−	3.19358i	−0.107170	−	0.185623i
$297$	−13.3485	−	23.1202i	−0.774557	−	1.34157i
$298$	−1.44270			−0.0835735
$299$	−20.3689	+	1.51468i	−1.17797	+	0.0875961i
$300$	−15.8418			−0.914626
$301$	−0.839274	−	1.45367i	−0.0483750	−	0.0837879i
$302$	0.277105	+	0.479960i	0.0159456	+	0.0276186i
$303$	6.83425	−	11.8373i	0.392617	−	0.680033i
$304$	−17.0963			−0.980538
$305$	−1.52884	+	2.64803i	−0.0875413	+	0.151626i
$306$	0.0613751	−	0.106305i	0.00350858	−	0.00607704i
$307$	10.0238			0.572091			0.286046	−	0.958216i	$-0.407659\pi$
$307$	10.0238			0.572091			0.286046	+	0.958216i	$0.407659\pi$
$308$	−20.0750	+	34.7709i	−1.14388	+	1.98126i
$309$	−11.1113	−	19.2453i	−0.632099	−	1.09483i
$310$	0.0174854	+	0.0302857i	0.000993106	+	0.00172011i
$311$	−17.2019			−0.975430			−0.487715	−	0.873003i	$-0.662169\pi$
$311$	−17.2019			−0.975430			−0.487715	+	0.873003i	$0.662169\pi$
$312$	2.32456	−	0.172860i	0.131602	−	0.00978625i
$313$	15.1598			0.856884			0.428442	−	0.903569i	$-0.359063\pi$
$313$	15.1598			0.856884			0.428442	+	0.903569i	$0.359063\pi$
$314$	−0.652536	−	1.13023i	−0.0368247	−	0.0637823i
$315$	0.242635	+	0.420257i	0.0136709	+	0.0236788i
$316$	2.79195	−	4.83580i	0.157060	−	0.272035i
$317$	1.96316			0.110262			0.0551311	−	0.998479i	$-0.482442\pi$
$317$	1.96316			0.110262			0.0551311	+	0.998479i	$0.482442\pi$
$318$	−0.613105	+	1.06193i	−0.0343812	+	0.0595500i
$319$	17.9944	−	31.1672i	1.00749	−	1.74503i
$320$	2.73600			0.152947
$321$	−11.2358	+	19.4610i	−0.627123	+	1.08621i
$322$	−1.15649	−	2.00310i	−0.0644487	−	0.111628i
$323$	8.01426	+	13.8811i	0.445925	+	0.772365i
$324$	15.6898			0.871654
$325$	7.63680	−	15.8347i	0.423614	−	0.878352i
$326$	0.401529			0.0222387
$327$	4.10435	+	7.10895i	0.226971	+	0.393126i
$328$	−1.41691	−	2.45416i	−0.0782359	−	0.135509i
$329$	11.0889	−	19.2066i	0.611352	−	1.05889i
$330$	0.279966			0.0154116
$331$	−8.23538	+	14.2641i	−0.452658	+	0.784026i	−0.998550	−	0.0538291i	$-0.982857\pi$
$331$	−8.23538	+	14.2641i	−0.452658	+	0.784026i	0.545892	+	0.837855i	$0.316191\pi$
$332$	−10.5325	+	18.2428i	−0.578045	+	1.00120i
$333$	3.11721			0.170822
$334$	−0.314511	+	0.544749i	−0.0172093	+	0.0298074i
$335$	−1.99157	−	3.44950i	−0.108811	−	0.188467i
$336$	−13.2348	−	22.9233i	−0.722015	−	1.25057i
$337$	−16.6551			−0.907261			−0.453631	−	0.891190i	$-0.649871\pi$
$337$	−16.6551			−0.907261			−0.453631	+	0.891190i	$0.649871\pi$
$338$	−0.472736	+	1.20046i	−0.0257134	+	0.0652962i
$339$	−27.0105			−1.46701
$340$	−1.29555	−	2.24395i	−0.0702609	−	0.121695i
$341$	−2.45188	−	4.24678i	−0.132777	−	0.229976i
$342$	−0.0720590	+	0.124810i	−0.00389650	+	0.00674894i
$343$	−12.0354			−0.649853
$344$	−0.0807851	+	0.139924i	−0.00435564	+	0.00754419i
$345$	1.62941	−	2.82223i	0.0877247	−	0.151944i
$346$	−1.97685			−0.106276
$347$	10.0623	−	17.4284i	0.540172	−	0.935605i	−0.458722	−	0.888580i	$-0.651693\pi$
$347$	10.0623	−	17.4284i	0.540172	−	0.935605i	0.998894	−	0.0470250i	$-0.0149740\pi$
$348$	11.9224	+	20.6502i	0.639107	+	1.10697i
$349$	3.14554	+	5.44824i	0.168377	+	0.291638i	0.937849	−	0.347042i	$-0.112814\pi$
$349$	3.14554	+	5.44824i	0.168377	+	0.291638i	−0.769472	+	0.638680i	$0.779481\pi$
$350$	1.99080			0.106413
$351$	−8.52697	+	17.6805i	−0.455136	+	0.943713i
$352$	5.80178			0.309236
$353$	−6.91104	−	11.9703i	−0.367838	−	0.637113i	0.621390	−	0.783502i	$-0.286568\pi$
$353$	−6.91104	−	11.9703i	−0.367838	−	0.637113i	−0.989227	+	0.146388i	$0.953235\pi$
$354$	−0.147842	−	0.256070i	−0.00785773	−	0.0136100i
$355$	0.401621	−	0.695628i	0.0213158	−	0.0369201i
$356$	−24.8701			−1.31811
$357$	−12.4082	+	21.4916i	−0.656711	+	1.13746i
$358$	0.890706	−	1.54275i	0.0470753	−	0.0815368i
$359$	−26.4579			−1.39640			−0.698198	−	0.715905i	$-0.746014\pi$
$359$	−26.4579			−1.39640			−0.698198	+	0.715905i	$0.746014\pi$
$360$	0.0233551	−	0.0404522i	0.00123092	−	0.00213202i
$361$	0.0906591	+	0.157026i	0.00477153	+	0.00826454i
$362$	−0.0307224	−	0.0532128i	−0.00161473	−	0.00279680i
$363$	−21.2998			−1.11795
$364$	29.4395	−	2.18919i	1.54305	−	0.114745i
$365$	0.779952			0.0408246
$366$	−0.702979	−	1.21759i	−0.0367453	−	0.0636447i
$367$	−1.32802	−	2.30020i	−0.0693222	−	0.120070i	0.829281	−	0.558832i	$-0.188750\pi$
$367$	−1.32802	−	2.30020i	−0.0693222	−	0.120070i	−0.898603	+	0.438762i	$0.855417\pi$
$368$	11.1627	−	19.3344i	0.581897	−	1.00788i
$369$	2.39547			0.124703
$370$	−0.162827	+	0.282025i	−0.00846498	+	0.0146618i
$371$	−15.5678	+	26.9642i	−0.808240	+	1.39991i
$372$	3.24904			0.168455
$373$	−4.42392	+	7.66245i	−0.229062	+	0.396747i	−0.957530	−	0.288332i	$-0.906899\pi$
$373$	−4.42392	+	7.66245i	−0.229062	+	0.396747i	0.728468	+	0.685079i	$0.240232\pi$
$374$	−0.899097	−	1.55728i	−0.0464912	−	0.0805251i
$375$	2.84061	+	4.92008i	0.146688	+	0.254072i
$376$	−2.13475			−0.110091
$377$	−26.3884	+	1.96230i	−1.35907	+	0.101063i
$378$	−2.22285			−0.114331
$379$	15.2744	+	26.4561i	0.784594	+	1.35896i	0.929241	+	0.369473i	$0.120462\pi$
$379$	15.2744	+	26.4561i	0.784594	+	1.35896i	−0.144647	+	0.989483i	$0.546205\pi$
$380$	1.52107	+	2.63457i	0.0780292	+	0.135151i
$381$	9.87737	−	17.1081i	0.506033	−	0.876474i
$382$	−0.676110			−0.0345928
$383$	4.01794	−	6.95927i	0.205307	−	0.355602i	−0.744923	−	0.667150i	$-0.767514\pi$
$383$	4.01794	−	6.95927i	0.205307	−	0.355602i	0.950231	+	0.311548i	$0.100847\pi$
$384$	−2.56055	+	4.43500i	−0.130668	+	0.226323i
$385$	7.10883			0.362299
$386$	−0.712735	+	1.23449i	−0.0362772	+	0.0628340i
$387$	−0.0682888	−	0.118280i	−0.00347131	−	0.00601249i
$388$	−12.6821	−	21.9660i	−0.643835	−	1.11515i
$389$	−4.97958			−0.252475			−0.126237	−	0.992000i	$-0.540290\pi$
$389$	−4.97958			−0.252475			−0.126237	+	0.992000i	$0.540290\pi$
$390$	−0.115861	−	0.170147i	−0.00586684	−	0.00861570i
$391$	−20.9311			−1.05853
$392$	1.96525	+	3.40391i	0.0992600	+	0.171923i
$393$	0.950676	+	1.64662i	0.0479553	+	0.0830609i
$394$	−1.05155	+	1.82135i	−0.0529765	+	0.0917581i
$395$	−0.988668			−0.0497453
$396$	−1.63343	+	2.82919i	−0.0820830	+	0.142172i
$397$	−12.8080	+	22.1841i	−0.642815	+	1.11339i	0.341986	+	0.939705i	$0.388900\pi$
$397$	−12.8080	+	22.1841i	−0.642815	+	1.11339i	−0.984802	+	0.173684i	$0.944433\pi$
$398$	−1.31765			−0.0660480
$399$	14.5681	−	25.2327i	0.729319	−	1.26322i
$400$	9.60783	+	16.6413i	0.480392	+	0.832063i
$401$	−2.37139	−	4.10737i	−0.118422	−	0.205112i	0.800721	−	0.599038i	$-0.204450\pi$
$401$	−2.37139	−	4.10737i	−0.118422	−	0.205112i	−0.919142	+	0.393926i	$0.871117\pi$
$402$	1.83149			0.0913465
$403$	−1.56626	+	3.24759i	−0.0780207	+	0.161774i
$404$	−16.6624			−0.828985
$405$	−1.38899	−	2.40580i	−0.0690194	−	0.119545i
$406$	−1.49826	−	2.59506i	−0.0743573	−	0.128791i
$407$	22.8323	−	39.5467i	1.13176	−	1.96026i
$408$	2.38872			0.118259
$409$	−13.6325	+	23.6121i	−0.674082	+	1.16754i	0.302655	+	0.953100i	$0.402127\pi$
$409$	−13.6325	+	23.6121i	−0.674082	+	1.16754i	−0.976736	+	0.214443i	$0.931206\pi$
$410$	−0.125127	+	0.216727i	−0.00617960	+	0.0107034i
$411$	−8.64461			−0.426407
$412$	−13.5451	+	23.4607i	−0.667317	+	1.15583i
$413$	−3.75397	−	6.50207i	−0.184721	−	0.319946i
$414$	−0.0940995	−	0.162985i	−0.00462474	−	0.00801028i
$415$	3.72969			0.183083
$416$	−2.40100	−	3.52597i	−0.117719	−	0.172875i
$417$	−18.8159			−0.921420
$418$	1.05561	+	1.82837i	0.0516314	+	0.0894283i
$419$	0.725822	+	1.25716i	0.0354587	+	0.0614163i	0.883210	−	0.468977i	$-0.155377\pi$
$419$	0.725822	+	1.25716i	0.0354587	+	0.0614163i	−0.847751	+	0.530394i	$0.822044\pi$
$420$	−2.35501	+	4.07901i	−0.114913	+	0.199035i
$421$	−25.1206			−1.22430			−0.612151	−	0.790741i	$-0.709696\pi$
$421$	−25.1206			−1.22430			−0.612151	+	0.790741i	$0.709696\pi$
$422$	−0.409020	+	0.708443i	−0.0199108	+	0.0344865i
$423$	0.902265	−	1.56277i	0.0438696	−	0.0759844i
$424$	2.99699			0.145547
$425$	9.00778	−	15.6019i	0.436942	−	0.756805i
$426$	0.184670	+	0.319857i	0.00894727	+	0.0154971i
$427$	−17.8499	−	30.9169i	−0.863815	−	1.49617i
$428$	27.3938			1.32413
$429$	16.2465	+	23.8587i	0.784388	+	1.15191i
$430$	0.0142682			0.000688076
$431$	−13.4969	−	23.3773i	−0.650122	−	1.12605i	−0.983093	−	0.183108i	$-0.941384\pi$
$431$	−13.4969	−	23.3773i	−0.650122	−	1.12605i	0.332970	−	0.942937i	$-0.391949\pi$
$432$	−10.7277	−	18.5810i	−0.516139	−	0.893979i
$433$	7.86090	−	13.6155i	0.377771	−	0.654318i	−0.612967	−	0.790109i	$-0.710024\pi$
$433$	7.86090	−	13.6155i	0.377771	−	0.654318i	0.990738	+	0.135791i	$0.0433574\pi$
$434$	−0.408299			−0.0195990
$435$	2.11094	−	3.65626i	0.101212	−	0.175304i
$436$	5.00336	−	8.66607i	0.239617	−	0.415029i
$437$	24.5747			1.17557
$438$	−0.179315	+	0.310583i	−0.00856801	+	0.0148402i
$439$	0.868774	+	1.50476i	0.0414643	+	0.0718183i	0.886013	−	0.463661i	$-0.153464\pi$
$439$	0.868774	+	1.50476i	0.0414643	+	0.0718183i	−0.844548	+	0.535479i	$0.820131\pi$
$440$	−0.342133	−	0.592592i	−0.0163106	−	0.0282507i
$441$	−3.32250			−0.158214
$442$	−0.574341	+	1.19088i	−0.0273186	+	0.0566444i
$443$	−32.5863			−1.54822			−0.774110	−	0.633051i	$-0.781802\pi$
$443$	−32.5863			−1.54822			−0.774110	+	0.633051i	$0.781802\pi$
$444$	15.1278	+	26.2021i	0.717933	+	1.24350i
$445$	2.20171	+	3.81347i	0.104371	+	0.180776i
$446$	−1.04921	+	1.81729i	−0.0496816	+	0.0860511i
$447$	23.7322			1.12249
$448$	−15.9720	+	27.6642i	−0.754604	+	1.30701i
$449$	−12.4043	+	21.4850i	−0.585397	+	1.01394i	0.409429	+	0.912342i	$0.365728\pi$
$449$	−12.4043	+	21.4850i	−0.585397	+	1.01394i	−0.994826	+	0.101595i	$0.967605\pi$
$450$	0.161984			0.00763601
$451$	17.5459	−	30.3903i	0.826203	−	1.43103i
$452$	16.4634	+	28.5154i	0.774373	+	1.34125i
$453$	−4.55833	−	7.89525i	−0.214169	−	0.370951i
$454$	−1.09356			−0.0513234
$455$	−2.94191	−	4.32032i	−0.137919	−	0.202540i
$456$	−2.80454			−0.131335
$457$	−15.5717	−	26.9710i	−0.728414	−	1.26165i	−0.957553	−	0.288257i	$-0.906924\pi$
$457$	−15.5717	−	26.9710i	−0.728414	−	1.26165i	0.229139	−	0.973394i	$-0.426409\pi$
$458$	−0.828622	−	1.43522i	−0.0387190	−	0.0670632i
$459$	−10.0578	+	17.4205i	−0.469456	+	0.813121i
$460$	−3.97263			−0.185225
$461$	7.49383	−	12.9797i	0.349022	−	0.604525i	−0.637054	−	0.770819i	$-0.719847\pi$
$461$	7.49383	−	12.9797i	0.349022	−	0.604525i	0.986076	+	0.166295i	$0.0531804\pi$
$462$	−1.63436	+	2.83079i	−0.0760372	+	0.131700i
$463$	−19.3711			−0.900250			−0.450125	−	0.892965i	$-0.648621\pi$
$463$	−19.3711			−0.900250			−0.450125	+	0.892965i	$0.648621\pi$
$464$	14.4615	−	25.0481i	0.671360	−	1.16283i
$465$	−0.287632	−	0.498194i	−0.0133386	−	0.0231032i
$466$	1.21939	+	2.11205i	0.0564874	+	0.0978390i
$467$	34.8122			1.61091			0.805457	−	0.592654i	$-0.201920\pi$
$467$	34.8122			1.61091			0.805457	+	0.592654i	$0.201920\pi$
$468$	2.39539	−	0.178126i	0.110727	−	0.00823389i
$469$	46.5048			2.14739
$470$	0.0942596	+	0.163262i	0.00434787	+	0.00753073i
$471$	10.7341	+	18.5920i	0.494601	+	0.856674i
$472$	−0.361342	+	0.625863i	−0.0166321	+	0.0288077i
$473$	−2.00075			−0.0919947
$474$	0.227300	−	0.393695i	0.0104402	−	0.0180830i
$475$	−10.5758	+	18.3178i	−0.485251	+	0.840480i
$476$	30.2520			1.38660
$477$	−1.26670	+	2.19398i	−0.0579981	+	0.100456i
$478$	0.722831	+	1.25198i	0.0330615	+	0.0572642i
$479$	4.02171	+	6.96581i	0.183757	+	0.318276i	0.943157	−	0.332348i	$-0.107841\pi$
$479$	4.02171	+	6.96581i	0.183757	+	0.318276i	−0.759400	+	0.650624i	$0.774507\pi$
$480$	0.680612			0.0310655
$481$	−33.4830	+	2.48987i	−1.52669	+	0.113528i
$482$	2.92705			0.133323
$483$	19.0241	+	32.9506i	0.865625	+	1.49931i
$484$	12.9826	+	22.4866i	0.590120	+	1.02212i
$485$	−2.24545	+	3.88923i	−0.101960	+	0.176601i
$486$	−0.343575			−0.0155849
$487$	12.6859	−	21.9727i	0.574854	−	0.995677i	−0.421203	−	0.906966i	$-0.638392\pi$
$487$	12.6859	−	21.9727i	0.574854	−	0.995677i	0.996057	−	0.0887106i	$-0.0282746\pi$
$488$	−1.71815	+	2.97593i	−0.0777772	+	0.134714i
$489$	−6.60509			−0.298692
$490$	0.173551	−	0.300599i	0.00784023	−	0.0135797i
$491$	−13.7249	−	23.7723i	−0.619398	−	1.07283i	−0.989596	−	0.143875i	$-0.954044\pi$
$491$	−13.7249	−	23.7723i	−0.619398	−	1.07283i	0.370198	−	0.928953i	$-0.379290\pi$
$492$	11.6252	+	20.1355i	0.524105	+	0.907776i
$493$	−27.1167			−1.22128
$494$	0.674319	−	1.39818i	0.0303390	−	0.0629072i
$495$	0.578420			0.0259980
$496$	−1.97050	−	3.41301i	−0.0884781	−	0.153248i
$497$	4.68908	+	8.12173i	0.210334	+	0.364309i
$498$	−0.857476	+	1.48519i	−0.0384244	+	0.0665531i
$499$	20.8686			0.934207			0.467103	−	0.884203i	$-0.345298\pi$
$499$	20.8686			0.934207			0.467103	+	0.884203i	$0.345298\pi$
$500$	3.46281	−	5.99776i	0.154861	−	0.268228i
$501$	5.17365	−	8.96103i	0.231142	−	0.400349i
$502$	0.555433			0.0247902
$503$	0.230372	−	0.399016i	0.0102718	−	0.0177912i	−0.860844	−	0.508869i	$-0.830064\pi$
$503$	0.230372	−	0.399016i	0.0102718	−	0.0177912i	0.871116	+	0.491078i	$0.163397\pi$
$504$	0.272680	+	0.472295i	0.0121461	+	0.0210377i
$505$	1.47509	+	2.55494i	0.0656409	+	0.113693i
$506$	−2.75697			−0.122562
$507$	7.77642	−	19.7473i	0.345363	−	0.877008i
$508$	−24.0817			−1.06845
$509$	8.64425	+	14.9723i	0.383150	+	0.663635i	0.991511	−	0.130026i	$-0.0415060\pi$
$509$	8.64425	+	14.9723i	0.383150	+	0.663635i	−0.608361	+	0.793660i	$0.708173\pi$
$510$	−0.105474	−	0.182686i	−0.00467046	−	0.00808947i
$511$	−4.55313	+	7.88624i	−0.201418	+	0.348867i
$512$	7.78400			0.344007
$513$	11.8086	−	20.4530i	0.521360	−	0.903023i
$514$	0.979186	−	1.69600i	0.0431900	−	0.0748073i
$515$	4.79649			0.211359
$516$	0.662810	−	1.14802i	0.0291786	−	0.0505388i
$517$	−13.2175	−	22.8933i	−0.581304	−	1.00685i
$518$	−1.90107	−	3.29275i	−0.0835283	−	0.144675i
$519$	32.5189			1.42742
$520$	−0.218554	+	0.453166i	−0.00958422	+	0.0198726i
$521$	27.3044			1.19623			0.598114	−	0.801411i	$-0.295917\pi$
$521$	27.3044			1.19623			0.598114	+	0.801411i	$0.295917\pi$
$522$	−0.121908	−	0.211151i	−0.00533576	−	0.00924181i
$523$	3.98893	+	6.90903i	0.174424	+	0.302111i	0.939962	−	0.341280i	$-0.110860\pi$
$523$	3.98893	+	6.90903i	0.174424	+	0.302111i	−0.765538	+	0.643391i	$0.777527\pi$
$524$	1.15891	−	2.00729i	0.0506271	−	0.0876888i
$525$	−32.7483			−1.42925
$526$	1.13555	−	1.96683i	0.0495122	−	0.0857577i
$527$	−1.84743	+	3.19985i	−0.0804755	+	0.139388i
$528$	−31.5504			−1.37306
$529$	−4.54566	+	7.87332i	−0.197637	+	0.342318i
$530$	−0.132332	−	0.229205i	−0.00574812	−	0.00995604i
$531$	−0.305447	−	0.529050i	−0.0132553	−	0.0229588i
$532$	−35.5182			−1.53991
$533$	−25.7306	+	1.91338i	−1.11452	+	0.0828779i
$534$	−2.02474			−0.0876189
$535$	−2.42513	−	4.20044i	−0.104847	−	0.181601i
$536$	−2.23818	−	3.87664i	−0.0966747	−	0.167445i
$537$	−14.6520	+	25.3779i	−0.632278	+	1.09514i
$538$	1.26085			0.0543591
$539$	−24.3360	+	42.1512i	−1.04823	+	1.81558i
$540$	−1.90891	+	3.30634i	−0.0821466	+	0.142282i
$541$	22.0724			0.948964			0.474482	−	0.880265i	$-0.342635\pi$
$541$	22.0724			0.948964			0.474482	+	0.880265i	$0.342635\pi$
$542$	−0.468770	+	0.811934i	−0.0201354	+	0.0348756i
$543$	0.505378	+	0.875341i	0.0216879	+	0.0375645i
$544$	−2.18575	−	3.78583i	−0.0937133	−	0.162316i
$545$	−1.77176			−0.0758937
$546$	2.39674	−	0.178227i	0.102571	−	0.00762742i
$547$	4.24489			0.181498			0.0907492	−	0.995874i	$-0.471074\pi$
$547$	4.24489			0.181498			0.0907492	+	0.995874i	$0.471074\pi$
$548$	5.26905	+	9.12626i	0.225083	+	0.389855i
$549$	−1.45238	−	2.51559i	−0.0619860	−	0.107363i
$550$	1.18647	−	2.05503i	0.0505913	−	0.0876266i
$551$	31.8371			1.35630
$552$	1.83118	−	3.17169i	0.0779401	−	0.134996i
$553$	5.77155	−	9.99661i	0.245431	−	0.425099i
$554$	2.27098			0.0964847
$555$	2.67848	−	4.63926i	0.113695	−	0.196926i
$556$	11.4686	+	19.8643i	0.486379	+	0.842433i
$557$	−8.42548	−	14.5934i	−0.356999	−	0.618340i	0.630459	−	0.776223i	$-0.282867\pi$
$557$	−8.42548	−	14.5934i	−0.356999	−	0.618340i	−0.987458	+	0.157882i	$0.949533\pi$
$558$	−0.0332218			−0.00140639
$559$	0.827989	+	1.21594i	0.0350202	+	0.0514287i
$560$	5.71314			0.241424
$561$	14.7900	+	25.6170i	0.624433	+	1.08155i
$562$	−0.190650	−	0.330215i	−0.00804208	−	0.0139293i
$563$	5.36648	−	9.29502i	0.226170	−	0.391738i	−0.730500	−	0.682913i	$-0.760713\pi$
$563$	5.36648	−	9.29502i	0.226170	−	0.391738i	0.956670	+	0.291175i	$0.0940461\pi$
$564$	17.5148			0.737504
$565$	2.91496	−	5.04885i	0.122633	−	0.212407i
$566$	1.26003	−	2.18243i	0.0529628	−	0.0917343i
$567$	32.4340			1.36210
$568$	0.451352	−	0.781765i	0.0189383	−	0.0328021i
$569$	−16.7833	−	29.0695i	−0.703591	−	1.21866i	−0.967197	−	0.254026i	$-0.918245\pi$
$569$	−16.7833	−	29.0695i	−0.703591	−	1.21866i	0.263606	−	0.964630i	$-0.415088\pi$
$570$	0.123834	+	0.214487i	0.00518684	+	0.00898388i
$571$	−2.06125			−0.0862605			−0.0431302	−	0.999069i	$-0.513733\pi$
$571$	−2.06125			−0.0862605			−0.0431302	+	0.999069i	$0.513733\pi$
$572$	15.2854	−	31.6940i	0.639116	−	1.32519i
$573$	11.1219			0.464623
$574$	−1.46091	−	2.53037i	−0.0609773	−	0.105616i
$575$	−13.8106	−	23.9207i	−0.575942	−	0.997561i
$576$	−1.29958	+	2.25094i	−0.0541492	+	0.0937892i
$577$	22.8295			0.950402			0.475201	−	0.879877i	$-0.342375\pi$
$577$	22.8295			0.950402			0.475201	+	0.879877i	$0.342375\pi$
$578$	0.166134	−	0.287752i	0.00691026	−	0.0119689i
$579$	11.7244	−	20.3072i	0.487248	−	0.843937i
$580$	−5.14663			−0.213702
$581$	−21.7728	+	37.7116i	−0.903289	+	1.56454i
$582$	−1.03248	−	1.78831i	−0.0427977	−	0.0741278i
$583$	18.5561	+	32.1401i	0.768515	+	1.33111i
$584$	0.876531			0.0362711
$585$	−0.239373	−	0.351529i	−0.00989684	−	0.0145339i
$586$	1.81243			0.0748710
$587$	−11.9457	−	20.6905i	−0.493050	−	0.853988i	0.506918	−	0.861994i	$-0.330785\pi$
$587$	−11.9457	−	20.6905i	−0.493050	−	0.853988i	−0.999968	+	0.00800654i	$0.997451\pi$
$588$	−16.1241	−	27.9277i	−0.664946	−	1.15172i
$589$	2.16903	−	3.75686i	0.0893731	−	0.154799i
$590$	0.0638201			0.00262743
$591$	17.2979	−	29.9608i	0.711540	−	1.23242i
$592$	18.3496	−	31.7824i	0.754164	−	1.30625i
$593$	15.9683			0.655739			0.327870	−	0.944723i	$-0.393669\pi$
$593$	15.9683			0.655739			0.327870	+	0.944723i	$0.393669\pi$
$594$	−1.32477	+	2.29457i	−0.0543559	+	0.0941471i
$595$	−2.67816	−	4.63872i	−0.109794	−	0.190169i
$596$	−14.4652	−	25.0545i	−0.592518	−	1.02627i
$597$	21.6751			0.887105
$598$	1.14094	+	1.67552i	0.0466565	+	0.0685170i
$599$	−20.0246			−0.818185			−0.409092	−	0.912493i	$-0.634155\pi$
$599$	−20.0246			−0.818185			−0.409092	+	0.912493i	$0.634155\pi$
$600$	1.57611	+	2.72990i	0.0643443	+	0.111448i
$601$	4.12228	+	7.14000i	0.168151	+	0.291247i	0.937770	−	0.347257i	$-0.112887\pi$
$601$	4.12228	+	7.14000i	0.168151	+	0.291247i	−0.769619	+	0.638504i	$0.779554\pi$
$602$	−0.0832937	+	0.144269i	−0.00339480	+	0.00587996i
$603$	3.78393			0.154094
$604$	−5.55676	+	9.62460i	−0.226101	+	0.391619i
$605$	2.29866	−	3.98140i	0.0934540	−	0.161867i
$606$	−1.35653			−0.0551052
$607$	6.15849	−	10.6668i	0.249966	−	0.432953i	−0.713550	−	0.700604i	$-0.752914\pi$
$607$	6.15849	−	10.6668i	0.249966	−	0.432953i	0.963516	+	0.267651i	$0.0862474\pi$
$608$	2.56624	+	4.44485i	0.104075	+	0.180262i
$609$	24.6461	+	42.6882i	0.998709	+	1.72981i
$610$	0.303460			0.0122867
$611$	−8.44328	+	17.5069i	−0.341579	+	0.708255i
$612$	2.46150			0.0995003
$613$	−16.2823	−	28.2018i	−0.657636	−	1.13906i	−0.981226	−	0.192861i	$-0.938223\pi$
$613$	−16.2823	−	28.2018i	−0.657636	−	1.13906i	0.323590	−	0.946197i	$-0.395110\pi$
$614$	−0.497408	−	0.861536i	−0.0200738	−	0.0347688i
$615$	2.05832	−	3.56512i	0.0829995	−	0.143759i
$616$	7.98908			0.321889
$617$	10.8282	−	18.7551i	0.435929	−	0.755051i	−0.561442	−	0.827516i	$-0.689753\pi$
$617$	10.8282	−	18.7551i	0.435929	−	0.755051i	0.997371	+	0.0724651i	$0.0230866\pi$
$618$	−1.10274	+	1.91000i	−0.0443587	+	0.0768315i
$619$	15.6516			0.629093			0.314546	−	0.949242i	$-0.398148\pi$
$619$	15.6516			0.629093			0.314546	+	0.949242i	$0.398148\pi$
$620$	−0.350634	+	0.607316i	−0.0140818	+	0.0243904i
$621$	15.4204	+	26.7089i	0.618800	+	1.07179i
$622$	0.853600	+	1.47848i	0.0342262	+	0.0592816i
$623$	−51.4116			−2.05976
$624$	13.0568	+	19.1744i	0.522690	+	0.767592i
$625$	23.1530			0.926118
$626$	−0.752268	−	1.30297i	−0.0300667	−	0.0520770i
$627$	−17.3645	−	30.0763i	−0.693473	−	1.20113i
$628$	13.0852	−	22.6643i	0.522158	−	0.904405i
$629$	−34.4072			−1.37190
$630$	0.0240803	−	0.0417083i	0.000959382	−	0.00166170i
$631$	−12.5414	+	21.7223i	−0.499264	+	0.864750i	−1.00000		0.000849998i	$-0.999729\pi$
$631$	−12.5414	+	21.7223i	−0.499264	+	0.864750i	0.500736	+	0.865600i	$0.333063\pi$
$632$	−1.11109			−0.0441968
$633$	6.72830	−	11.6538i	0.267426	−	0.463196i
$634$	−0.0974170	−	0.168731i	−0.00386892	−	0.00670117i
$635$	2.13192	+	3.69259i	0.0846025	+	0.146536i
$636$	−24.5891			−0.975021
$637$	35.6882	−	2.65385i	1.41402	−	0.105149i
$638$	−3.57171			−0.141405
$639$	0.381534	+	0.660836i	0.0150933	+	0.0261423i
$640$	−0.552666	−	0.957245i	−0.0218460	−	0.0378384i
$641$	−24.1012	+	41.7446i	−0.951942	+	1.64881i	−0.210725	+	0.977545i	$0.567582\pi$
$641$	−24.1012	+	41.7446i	−0.951942	+	1.64881i	−0.741217	+	0.671266i	$0.765751\pi$
$642$	2.23020			0.0880190
$643$	13.7958	−	23.8951i	0.544055	−	0.942331i	−0.454611	−	0.890690i	$-0.650222\pi$
$643$	13.7958	−	23.8951i	0.544055	−	0.942331i	0.998666	−	0.0516405i	$-0.0164450\pi$
$644$	23.1910	−	40.1680i	0.913854	−	1.58284i
$645$	−0.234710			−0.00924170
$646$	0.795374	−	1.37763i	0.0312936	−	0.0542021i
$647$	5.66913	+	9.81922i	0.222876	+	0.386033i	0.955680	−	0.294407i	$-0.0951220\pi$
$647$	5.66913	+	9.81922i	0.222876	+	0.386033i	−0.732804	+	0.680440i	$0.761789\pi$
$648$	−1.56098	−	2.70370i	−0.0613212	−	0.106211i
$649$	−8.94912			−0.351284
$650$	−1.73993	+	0.129385i	−0.0682456	+	0.00507490i
$651$	6.71644			0.263238
$652$	4.02592	+	6.97310i	0.157667	+	0.273088i
$653$	−9.90531	−	17.1565i	−0.387625	−	0.671386i	0.604505	−	0.796602i	$-0.293371\pi$
$653$	−9.90531	−	17.1565i	−0.387625	−	0.671386i	−0.992130	+	0.125216i	$0.960038\pi$
$654$	0.407336	−	0.705527i	0.0159281	−	0.0275883i
$655$	−0.410385			−0.0160351
$656$	14.1011	−	24.4238i	0.550554	−	0.953588i
$657$	−0.370472	+	0.641676i	−0.0144535	+	0.0250342i
$658$	−2.20104			−0.0858053
$659$	0.701085	−	1.21431i	0.0273104	−	0.0473030i	−0.852047	−	0.523465i	$-0.824639\pi$
$659$	0.701085	−	1.21431i	0.0273104	−	0.0473030i	0.879358	+	0.476162i	$0.157972\pi$
$660$	2.80707	+	4.86199i	0.109265	+	0.189253i
$661$	−4.43240	−	7.67714i	−0.172400	−	0.298606i	0.766858	−	0.641816i	$-0.221819\pi$
$661$	−4.43240	−	7.67714i	−0.172400	−	0.298606i	−0.939259	+	0.343210i	$0.888486\pi$
$662$	1.63464			0.0635321
$663$	9.44780	−	19.5898i	0.366922	−	0.760804i
$664$	4.19152			0.162663
$665$	3.14437	+	5.44620i	0.121933	+	0.211195i
$666$	−0.154683	−	0.267920i	−0.00599386	−	0.0103817i
$667$	−20.7875	+	36.0050i	−0.804895	+	1.39412i
$668$	−12.6137			−0.488040
$669$	17.2593	−	29.8941i	0.667285	−	1.15577i
$670$	−0.197653	+	0.342346i	−0.00763602	+	0.0132260i
$671$	−42.5524			−1.64272
$672$	−3.97321	+	6.88180i	−0.153270	+	0.265471i
$673$	13.4149	+	23.2352i	0.517105	+	0.895653i	0.999803	+	0.0198656i	$0.00632384\pi$
$673$	13.4149	+	23.2352i	0.517105	+	0.895653i	−0.482697	+	0.875787i	$0.660343\pi$
$674$	0.826467	+	1.43148i	0.0318343	+	0.0551387i
$675$	−26.5449			−1.02171
$676$	−25.5874	+	3.82663i	−0.984131	+	0.147178i
$677$	−18.9373			−0.727821			−0.363910	−	0.931434i	$-0.618559\pi$
$677$	−18.9373			−0.727821			−0.363910	+	0.931434i	$0.618559\pi$
$678$	1.34033	+	2.32152i	0.0514750	+	0.0891573i
$679$	−26.2165	−	45.4083i	−1.00610	−	1.74261i
$680$	−0.257789	+	0.446504i	−0.00988576	+	0.0171226i
$681$	17.9889			0.689336
$682$	−0.243337	+	0.421472i	−0.00931785	+	0.0161390i
$683$	−7.41159	+	12.8373i	−0.283597	+	0.491204i	−0.972268	−	0.233870i	$-0.924861\pi$
$683$	−7.41159	+	12.8373i	−0.283597	+	0.491204i	0.688671	+	0.725074i	$0.258194\pi$
$684$	−2.88999			−0.110501
$685$	0.932921	−	1.61587i	0.0356451	−	0.0617391i
$686$	0.597228	+	1.03443i	0.0228023	+	0.0394947i
$687$	13.6307	+	23.6090i	0.520043	+	0.900741i
$688$	−1.60794			−0.0613022
$689$	11.8536	−	24.5781i	0.451586	−	0.936352i
$690$	−0.323422			−0.0123125
$691$	8.79400	+	15.2317i	0.334540	+	0.579440i	0.983396	−	0.181471i	$-0.0580858\pi$
$691$	8.79400	+	15.2317i	0.334540	+	0.579440i	−0.648857	+	0.760911i	$0.724752\pi$
$692$	−19.8208	−	34.3307i	−0.753475	−	1.30506i
$693$	−3.37664	+	5.84851i	−0.128268	+	0.222167i
$694$	−1.99726			−0.0758150
$695$	2.03060	−	3.51711i	0.0770251	−	0.133411i
$696$	2.37233	−	4.10900i	0.0899229	−	0.155751i
$697$	−26.4408			−1.00152
$698$	0.312179	−	0.540710i	0.0118162	−	0.0204662i
$699$	−20.0588	−	34.7429i	−0.758694	−	1.31410i
$700$	19.9607	+	34.5729i	0.754442	+	1.30673i
$701$	28.9940			1.09509			0.547543	−	0.836777i	$-0.315563\pi$
$701$	28.9940			1.09509			0.547543	+	0.836777i	$0.315563\pi$
$702$	1.94274	−	0.144466i	0.0733240	−	0.00545253i
$703$	40.3966			1.52359
$704$	19.0378	+	32.9745i	0.717515	+	1.24277i
$705$	−1.55055	−	2.68564i	−0.0583972	−	0.101147i
$706$	−0.685886	+	1.18799i	−0.0258136	+	0.0447105i
$707$	−34.4446			−1.29542
$708$	2.96467	−	5.13496i	0.111419	−	0.192984i
$709$	−0.313029	+	0.542183i	−0.0117561	+	0.0203621i	−0.871844	−	0.489784i	$-0.837075\pi$
$709$	−0.313029	+	0.542183i	−0.0117561	+	0.0203621i	0.860088	+	0.510146i	$0.170409\pi$
$710$	−0.0797177			−0.00299175
$711$	0.469610	−	0.813389i	0.0176118	−	0.0305045i
$712$	2.47433	+	4.28567i	0.0927296	+	0.160612i
$713$	2.83246	+	4.90596i	0.106076	+	0.183730i
$714$	2.46290			0.0921716
$715$	−6.21301	+	0.462013i	−0.232353	+	0.0172783i
$716$	35.7225			1.33501
$717$	−11.8904	−	20.5948i	−0.444056	−	0.769128i
$718$	1.31291	+	2.27402i	0.0489972	+	0.0848657i
$719$	3.86964	−	6.70241i	0.144313	−	0.249958i	−0.784803	−	0.619745i	$-0.787236\pi$
$719$	3.86964	−	6.70241i	0.144313	−	0.249958i	0.929116	+	0.369787i	$0.120569\pi$
$720$	0.464858			0.0173242
$721$	−28.0005	+	48.4982i	−1.04279	+	1.80617i
$722$	0.00899745	−	0.0155840i	0.000334851	−	0.000579978i
$723$	−48.1494			−1.79070
$724$	0.616074	−	1.06707i	0.0228962	−	0.0396574i
$725$	−17.8919	−	30.9897i	−0.664490	−	1.15093i
$726$	1.05695	+	1.83069i	0.0392271	+	0.0679433i
$727$	29.9506			1.11081			0.555404	−	0.831581i	$-0.312564\pi$
$727$	29.9506			1.11081			0.555404	+	0.831581i	$0.312564\pi$
$728$	−3.30619	−	4.85528i	−0.122536	−	0.179949i
$729$	29.3029			1.08529
$730$	−0.0387031	−	0.0670358i	−0.00143247	−	0.00248111i
$731$	0.753759	+	1.30555i	0.0278788	+	0.0482875i
$732$	14.0968	−	24.4163i	0.521032	−	0.902454i
$733$	−12.4258			−0.458957			−0.229478	−	0.973314i	$-0.573702\pi$
$733$	−12.4258			−0.458957			−0.229478	+	0.973314i	$0.573702\pi$
$734$	−0.131800	+	0.228283i	−0.00486481	+	0.00842610i
$735$	−2.85488	+	4.94480i	−0.105304	+	0.182392i
$736$	−6.70233			−0.247051
$737$	27.7158	−	48.0051i	1.02092	−	1.76829i
$738$	−0.118869	−	0.205887i	−0.00437563	−	0.00757882i
$739$	4.61257	+	7.98921i	0.169676	+	0.293888i	0.938306	−	0.345806i	$-0.112394\pi$
$739$	4.61257	+	7.98921i	0.169676	+	0.293888i	−0.768630	+	0.639694i	$0.779061\pi$
$740$	−6.53032			−0.240059
$741$	−11.0924	+	22.9999i	−0.407490	+	0.844921i
$742$	3.09005			0.113439
$743$	6.27332	+	10.8657i	0.230146	+	0.398624i	0.957851	−	0.287266i	$-0.0927464\pi$
$743$	6.27332	+	10.8657i	0.230146	+	0.398624i	−0.727705	+	0.685890i	$0.759413\pi$
$744$	−0.323249	−	0.559883i	−0.0118509	−	0.0205263i
$745$	−2.56116	+	4.43606i	−0.0938337	+	0.162525i
$746$	0.878103			0.0321496
$747$	−1.77158	+	3.06846i	−0.0648186	+	0.112269i
$748$	18.0295	−	31.2280i	0.659225	−	1.14181i
$749$	56.6287			2.06917
$750$	0.281916	−	0.488293i	0.0102941	−	0.0178299i
$751$	0.617465	+	1.06948i	0.0225316	+	0.0390259i	0.877071	−	0.480360i	$-0.159494\pi$
$751$	0.617465	+	1.06948i	0.0225316	+	0.0390259i	−0.854540	+	0.519386i	$0.826161\pi$
$752$	−10.6225	−	18.3986i	−0.387361	−	0.670930i
$753$	−9.13676			−0.332962
$754$	1.47811	+	2.17067i	0.0538297	+	0.0790511i
$755$	1.96772			0.0716128
$756$	−22.2873	−	38.6028i	−0.810582	−	1.40397i
$757$	22.8900	+	39.6466i	0.831951	+	1.44098i	0.896489	+	0.443065i	$0.146109\pi$
$757$	22.8900	+	39.6466i	0.831951	+	1.44098i	−0.0645387	+	0.997915i	$0.520558\pi$
$758$	1.51591	−	2.62563i	0.0550603	−	0.0953672i
$759$	45.3516			1.64616
$760$	0.302664	−	0.524229i	0.0109788	−	0.0190158i
$761$	2.33625	−	4.04650i	0.0846889	−	0.146686i	−0.820570	−	0.571546i	$-0.806344\pi$
$761$	2.33625	−	4.04650i	0.0846889	−	0.146686i	0.905259	+	0.424861i	$0.139677\pi$
$762$	−1.96056			−0.0710235
$763$	10.3430	−	17.9146i	0.374441	−	0.648551i
$764$	−6.77899	−	11.7415i	−0.245255	−	0.424794i
$765$	−0.217913	−	0.377436i	−0.00787865	−	0.0136462i
$766$	−0.797520			−0.0288156
$767$	3.70350	+	5.43874i	0.133725	+	0.196381i
$768$	−24.8441			−0.896482
$769$	−10.4078	−	18.0268i	−0.375314	−	0.650062i	0.615060	−	0.788480i	$-0.289132\pi$
$769$	−10.4078	−	18.0268i	−0.375314	−	0.650062i	−0.990374	+	0.138418i	$0.955798\pi$
$770$	−0.352757	−	0.610994i	−0.0127125	−	0.0220187i
$771$	−16.1074	+	27.8989i	−0.580095	+	1.00475i
$772$	−28.5848			−1.02879
$773$	−17.2805	+	29.9307i	−0.621537	+	1.07653i	0.367663	+	0.929959i	$0.380158\pi$
$773$	−17.2805	+	29.9307i	−0.621537	+	1.07653i	−0.989200	+	0.146574i	$0.953175\pi$
$774$	−0.00677731	+	0.0117387i	−0.000243605	+	0.000421937i
$775$	−4.87584			−0.175145
$776$	−2.52349	+	4.37081i	−0.0905880	+	0.156903i
$777$	31.2723	+	54.1652i	1.12189	+	1.94316i
$778$	0.247099	+	0.427988i	0.00885893	+	0.0153441i
$779$	31.0435			1.11225
$780$	1.79315	−	3.71805i	0.0642050	−	0.133127i
$781$	11.1783			0.399993
$782$	1.03865	+	1.79900i	0.0371422	+	0.0643322i
$783$	19.9775	+	34.6020i	0.713936	+	1.23657i
$784$	−19.5581	+	33.8756i	−0.698503	+	1.20984i
$785$	−4.63366			−0.165383
$786$	0.0943497	−	0.163419i	0.00336534	−	0.00582895i
$787$	−2.81953	+	4.88357i	−0.100505	+	0.174081i	−0.911893	−	0.410428i	$-0.865379\pi$
$787$	−2.81953	+	4.88357i	−0.100505	+	0.174081i	0.811388	+	0.584509i	$0.198713\pi$
$788$	−42.1735			−1.50237
$789$	−18.6796	+	32.3539i	−0.665010	+	1.15183i
$790$	0.0490601	+	0.0849747i	0.00174548	+	0.00302326i
$791$	34.0333	+	58.9473i	1.21008	+	2.09593i
$792$	0.650043			0.0230983
$793$	17.6098	+	25.8608i	0.625344	+	0.918344i
$794$	2.54226			0.0902213
$795$	2.17683	+	3.77038i	0.0772043	+	0.133722i
$796$	−13.2114	−	22.8828i	−0.468265	−	0.811059i
$797$	5.04659	−	8.74095i	0.178759	−	0.309621i	−0.762696	−	0.646757i	$-0.776125\pi$
$797$	5.04659	−	8.74095i	0.178759	−	0.309621i	0.941456	+	0.337136i	$0.109458\pi$
$798$	−2.89163			−0.102362
$799$	−9.95905	+	17.2496i	−0.352326	+	0.610246i
$800$	2.88437	−	4.99587i	0.101978	−	0.176631i
$801$	−4.18318			−0.147805
$802$	−0.235349	+	0.407636i	−0.00831045	+	0.0143941i
$803$	5.42711	+	9.40004i	0.191519	+	0.331720i
$804$	18.3634	+	31.8063i	0.647627	+	1.12172i
$805$	−8.21225			−0.289444
$806$	0.356847	−	0.0265360i	0.0125694	−	0.000934689i
$807$	−20.7407			−0.730109
$808$	1.65775	+	2.87131i	0.0583194	+	0.101012i
$809$	−27.2857	−	47.2601i	−0.959312	−	1.66158i	−0.724176	−	0.689616i	$-0.757780\pi$
$809$	−27.2857	−	47.2601i	−0.959312	−	1.66158i	−0.235137	−	0.971962i	$-0.575554\pi$
$810$	−0.137850	+	0.238763i	−0.00484356	+	0.00838929i
$811$	21.9872			0.772075			0.386037	−	0.922483i	$-0.373844\pi$
$811$	21.9872			0.772075			0.386037	+	0.922483i	$0.373844\pi$
$812$	30.0444	−	52.0385i	1.05435	−	1.82619i
$813$	7.71119	−	13.3562i	0.270443	−	0.468421i
$814$	−4.53198			−0.158846
$815$	0.712816	−	1.23463i	0.0249689	−	0.0432473i
$816$	11.8862	+	20.5876i	0.416102	+	0.720709i
$817$	−0.884970	−	1.53281i	−0.0309612	−	0.0536263i
$818$	2.70590			0.0946097
$819$	4.95176	−	0.368224i	0.173029	−	0.0128668i
$820$	−5.01834			−0.175248
$821$	−14.7549	−	25.5562i	−0.514949	−	0.891917i	−0.999850	−	0.0173481i	$-0.994478\pi$
$821$	−14.7549	−	25.5562i	−0.514949	−	0.891917i	0.484901	−	0.874569i	$-0.338856\pi$
$822$	0.428967	+	0.742993i	0.0149619	+	0.0259148i
$823$	−7.46508	+	12.9299i	−0.260216	+	0.450708i	−0.966299	−	0.257421i	$-0.917127\pi$
$823$	−7.46508	+	12.9299i	−0.260216	+	0.450708i	0.706083	+	0.708129i	$0.250461\pi$
$824$	5.39042			0.187784
$825$	−19.5172	+	33.8048i	−0.679502	+	1.17693i
$826$	−0.372563	+	0.645297i	−0.0129631	+	0.0224528i
$827$	−15.6346			−0.543667			−0.271834	−	0.962344i	$-0.587630\pi$
$827$	−15.6346			−0.543667			−0.271834	+	0.962344i	$0.587630\pi$
$828$	1.88697	−	3.26833i	0.0655768	−	0.113582i
$829$	2.97538	+	5.15350i	0.103339	+	0.178989i	0.913058	−	0.407829i	$-0.133714\pi$
$829$	2.97538	+	5.15350i	0.103339	+	0.178989i	−0.809719	+	0.586817i	$0.800381\pi$
$830$	−0.185076	−	0.320562i	−0.00642410	−	0.0111269i
$831$	−37.3572			−1.29591
$832$	12.1613	−	25.2162i	0.421618	−	0.874214i
$833$	36.6732			1.27065
$834$	0.933693	+	1.61720i	0.0323311	+	0.0559992i
$835$	1.11667	+	1.93414i	0.0386441	+	0.0669335i
$836$	−21.1680	+	36.6641i	−0.732111	+	1.26805i
$837$	5.44417			0.188178
$838$	0.0720341	−	0.124767i	0.00248838	−	0.00431000i
$839$	3.18266	−	5.51253i	0.109878	−	0.190314i	−0.805843	−	0.592129i	$-0.798287\pi$
$839$	3.18266	−	5.51253i	0.109878	−	0.190314i	0.915721	+	0.401816i	$0.131621\pi$
$840$	0.937206			0.0323367
$841$	−12.4306	+	21.5305i	−0.428642	+	0.742430i
$842$	1.24654	+	2.15908i	0.0429588	+	0.0744068i
$843$	3.13615	+	5.43198i	0.108015	+	0.187087i
$844$	−16.4041			−0.564652
$845$	2.85197	+	3.58469i	0.0981108	+	0.123317i
$846$	−0.179090			−0.00615726
$847$	26.8378	+	46.4845i	0.922158	+	1.59722i
$848$	14.9130	+	25.8300i	0.512113	+	0.887006i
$849$	−20.7272	+	35.9006i	−0.711356	+	1.23210i
$850$	−1.78795			−0.0613263
$851$	−26.3763	+	45.6851i	−0.904168	+	1.56607i
$852$	−3.70317	+	6.41407i	−0.126868	+	0.219742i
$853$	−29.2437			−1.00129			−0.500643	−	0.865654i	$-0.666903\pi$
$853$	−29.2437			−1.00129			−0.500643	+	0.865654i	$0.666903\pi$
$854$	−1.77151	+	3.06834i	−0.0606197	+	0.104996i
$855$	0.255846	+	0.443138i	0.00874974	+	0.0151550i
$856$	−2.72542	−	4.72057i	−0.0931530	−	0.161346i
$857$	−48.7381			−1.66486			−0.832431	−	0.554129i	$-0.813051\pi$
$857$	−48.7381			−1.66486			−0.832431	+	0.554129i	$0.813051\pi$
$858$	1.24443	−	2.58029i	0.0424840	−	0.0880896i
$859$	−15.1469			−0.516807			−0.258403	−	0.966037i	$-0.583196\pi$
$859$	−15.1469			−0.516807			−0.258403	+	0.966037i	$0.583196\pi$
$860$	0.143060	+	0.247787i	0.00487831	+	0.00844947i
$861$	24.0317	+	41.6242i	0.818999	+	1.41855i
$862$	−1.33950	+	2.32008i	−0.0456235	+	0.0790222i
$863$	3.19596			0.108792			0.0543958	−	0.998519i	$-0.482677\pi$
$863$	3.19596			0.108792			0.0543958	+	0.998519i	$0.482677\pi$
$864$	−3.22058	+	5.57821i	−0.109566	+	0.189774i
$865$	−3.50941	+	6.07848i	−0.119324	+	0.206675i
$866$	−1.56031			−0.0530214
$867$	−2.73287	+	4.73347i	−0.0928132	+	0.160757i
$868$	−4.09379	−	7.09066i	−0.138952	−	0.240673i
$869$	−6.87942	−	11.9155i	−0.233368	−	0.404206i
$870$	−0.419000			−0.0142054
$871$	−40.6445	+	3.02242i	−1.37719	+	0.102411i
$872$	−1.99115			−0.0674287
$873$	−2.13314	−	3.69471i	−0.0721959	−	0.125047i
$874$	−1.21946	−	2.11216i	−0.0412488	−	0.0714450i
$875$	7.15834	−	12.3986i	0.241996	−	0.419149i
$876$	−7.19159			−0.242981
$877$	20.1247	−	34.8571i	0.679564	−	1.17704i	−0.295548	−	0.955328i	$-0.595502\pi$
$877$	20.1247	−	34.8571i	0.679564	−	1.17704i	0.975112	−	0.221712i	$-0.0711645\pi$
$878$	0.0862214	−	0.149340i	0.00290983	−	0.00503998i
$879$	−29.8142			−1.00561
$880$	3.40490	−	5.89746i	0.114779	−	0.198803i
$881$	−20.5998	−	35.6798i	−0.694024	−	1.20208i	−0.970509	−	0.241066i	$-0.922503\pi$
$881$	−20.5998	−	35.6798i	−0.694024	−	1.20208i	0.276485	−	0.961018i	$-0.410830\pi$
$882$	0.164871	+	0.285564i	0.00555149	+	0.00961546i
$883$	42.3740			1.42600			0.713000	−	0.701164i	$-0.247336\pi$
$883$	42.3740			1.42600			0.713000	+	0.701164i	$0.247336\pi$
$884$	−26.4398	+	1.96613i	−0.889268	+	0.0661280i
$885$	−1.04983			−0.0352896
$886$	1.61701	+	2.80074i	0.0543245	+	0.0940928i
$887$	−9.53047	−	16.5073i	−0.320002	−	0.554259i	0.660486	−	0.750838i	$-0.270350\pi$
$887$	−9.53047	−	16.5073i	−0.320002	−	0.554259i	−0.980488	+	0.196579i	$0.937017\pi$
$888$	3.01014	−	5.21372i	0.101014	−	0.174961i
$889$	−49.7819			−1.66963
$890$	0.218508	−	0.378467i	0.00732441	−	0.0126862i
$891$	19.3299	−	33.4804i	0.647577	−	1.12164i
$892$	−42.0795			−1.40893
$893$	11.6927	−	20.2523i	0.391280	−	0.677717i
$894$	−1.17765	−	2.03975i	−0.0393865	−	0.0682194i
$895$	−3.16246	−	5.47754i	−0.105709	−	0.183094i
$896$	12.9052			0.431132
$897$	−18.7683	−	27.5620i	−0.626654	−	0.920267i
$898$	2.46214			0.0821625
$899$	3.66951	+	6.35578i	0.122385	+	0.211977i
$900$	1.62413	+	2.81307i	0.0541376	+	0.0937691i
$901$	13.9816	−	24.2168i	0.465794	−	0.806779i
$902$	−3.48268			−0.115960
$903$	1.37017	−	2.37320i	0.0455963	−	0.0789751i
$904$	3.27590	−	5.67403i	0.108955	−	0.188715i
$905$	−0.218160			−0.00725189
$906$	−0.452391	+	0.783563i	−0.0150297	+	0.0260322i
$907$	−7.18342	−	12.4420i	−0.238521	−	0.413131i	0.721769	−	0.692134i	$-0.243329\pi$
$907$	−7.18342	−	12.4420i	−0.238521	−	0.413131i	−0.960290	+	0.279003i	$0.909996\pi$
$908$	−10.9646	−	18.9912i	−0.363871	−	0.630244i
$909$	−2.80264			−0.0929576
$910$	−0.225340	+	0.467238i	−0.00746996	+	0.0154888i
$911$	33.8934			1.12294			0.561469	−	0.827498i	$-0.310236\pi$
$911$	33.8934			1.12294			0.561469	+	0.827498i	$0.310236\pi$
$912$	−13.9553	−	24.1714i	−0.462107	−	0.800393i
$913$	25.9522	+	44.9505i	0.858892	+	1.48764i
$914$	−1.54541	+	2.67673i	−0.0511177	+	0.0885385i
$915$	−4.99186			−0.165026
$916$	16.6163	−	28.7803i	0.549018	−	0.950927i
$917$	2.39570	−	4.14948i	0.0791131	−	0.137028i
$918$	1.99636			0.0658897
$919$	18.9818	−	32.8775i	0.626153	−	1.08453i	−0.362163	−	0.932115i	$-0.617962\pi$
$919$	18.9818	−	32.8775i	0.626153	−	1.08453i	0.988317	−	0.152415i	$-0.0487049\pi$
$920$	0.395239	+	0.684574i	0.0130306	+	0.0225697i
$921$	8.18227	+	14.1721i	0.269615	+	0.466987i
$922$	−1.48745			−0.0489865
$923$	−4.62603	−	6.79352i	−0.152268	−	0.223612i
$924$	−65.5473			−2.15635
$925$	−22.7023	−	39.3215i	−0.746446	−	1.29288i
$926$	0.961241	+	1.66492i	0.0315883	+	0.0547126i
$927$	−2.27830	+	3.94613i	−0.0748291	+	0.129608i
$928$	−8.68301			−0.285034
$929$	−0.689800	+	1.19477i	−0.0226316	+	0.0391991i	−0.877119	−	0.480272i	$-0.840538\pi$
$929$	−0.689800	+	1.19477i	−0.0226316	+	0.0391991i	0.854488	+	0.519471i	$0.173871\pi$
$930$	−0.0285460	+	0.0494432i	−0.000936062	+	0.00162131i
$931$	−43.0571			−1.41114
$932$	−24.4524	+	42.3528i	−0.800966	+	1.38731i
$933$	−14.0416	−	24.3207i	−0.459700	−	0.796224i
$934$	−1.72747	−	2.99206i	−0.0565244	−	0.0979031i
$935$	−6.38450			−0.208795
$936$	−0.269013	−	0.395057i	−0.00879298	−	0.0129129i
$937$	−37.5518			−1.22676			−0.613382	−	0.789786i	$-0.710191\pi$
$937$	−37.5518			−1.22676			−0.613382	+	0.789786i	$0.710191\pi$
$938$	−2.30768	−	3.99702i	−0.0753485	−	0.130507i
$939$	12.3747	+	21.4336i	0.403832	+	0.699458i
$940$	−1.89018	+	3.27389i	−0.0616509	+	0.106782i
$941$	31.3839			1.02309			0.511543	−	0.859258i	$-0.329074\pi$
$941$	31.3839			1.02309			0.511543	+	0.859258i	$0.329074\pi$
$942$	1.06530	−	1.84516i	0.0347095	−	0.0601186i
$943$	−20.2693	+	35.1075i	−0.660060	+	1.14326i
$944$	−7.19213			−0.234084
$945$	−3.94612	+	6.83488i	−0.128367	+	0.222339i
$946$	0.0992823	+	0.171962i	0.00322794	+	0.00559096i
$947$	−9.56989	−	16.5755i	−0.310979	−	0.538632i	0.667595	−	0.744524i	$-0.267324\pi$
$947$	−9.56989	−	16.5755i	−0.310979	−	0.538632i	−0.978575	+	0.205892i	$0.933990\pi$
$948$	9.11607			0.296076
$949$	3.46683	−	7.18838i	0.112538	−	0.233345i
$950$	2.09919			0.0681067
$951$	1.60249	+	2.77560i	0.0519643	+	0.0900049i
$952$	−3.00979	−	5.21311i	−0.0975479	−	0.168958i
$953$	23.6829	−	41.0200i	0.767165	−	1.32877i	−0.171929	−	0.985109i	$-0.555000\pi$
$953$	23.6829	−	41.0200i	0.767165	−	1.32877i	0.939094	−	0.343660i	$-0.111667\pi$
$954$	0.251426			0.00814023
$955$	−1.20027	+	2.07892i	−0.0388397	+	0.0672723i
$956$	−14.4949	+	25.1059i	−0.468798	+	0.811981i
$957$	58.7539			1.89925
$958$	0.399134	−	0.691321i	0.0128954	−	0.0223356i
$959$	10.8922	+	18.8659i	0.351728	+	0.609211i
$960$	2.23334	+	3.86827i	0.0720809	+	0.124848i
$961$	1.00000			0.0322581
$962$	1.87551	+	2.75426i	0.0604689	+	0.0888010i
$963$	4.60767			0.148480
$964$	29.3479	+	50.8321i	0.945233	+	1.63719i
$965$	2.53057	+	4.38307i	0.0814619	+	0.141096i
$966$	1.88804	−	3.27018i	0.0607467	−	0.105216i
$967$	−30.6565			−0.985846			−0.492923	−	0.870073i	$-0.664072\pi$
$967$	−30.6565			−0.985846			−0.492923	+	0.870073i	$0.664072\pi$
$968$	2.58330	−	4.47440i	0.0830303	−	0.143813i
$969$	−13.0838	+	22.6617i	−0.420311	+	0.728000i
$970$	0.445698			0.0143105
$971$	12.9507	−	22.4313i	0.415608	−	0.719855i	−0.579884	−	0.814699i	$-0.696902\pi$
$971$	12.9507	−	22.4313i	0.415608	−	0.719855i	0.995492	+	0.0948445i	$0.0302354\pi$
$972$	−3.44485	−	5.96665i	−0.110493	−	0.191380i
$973$	23.7081	+	41.0636i	0.760046	+	1.31644i
$974$	−2.51803			−0.0806828
$975$	28.6215	−	2.12836i	0.916622	−	0.0681621i
$976$	−34.1980			−1.09465
$977$	11.4514	+	19.8345i	0.366364	+	0.634561i	0.988994	−	0.147956i	$-0.0472693\pi$
$977$	11.4514	+	19.8345i	0.366364	+	0.634561i	−0.622630	+	0.782516i	$0.713936\pi$
$978$	0.327761	+	0.567698i	0.0104806	+	0.0181530i
$979$	−30.6401	+	53.0702i	−0.979262	+	1.69613i
$980$	6.96040			0.222342
$981$	0.841571	−	1.45764i	0.0268693	−	0.0465390i
$982$	−1.36213	+	2.35928i	−0.0434673	+	0.0752876i
$983$	−18.5203			−0.590707			−0.295354	−	0.955388i	$-0.595437\pi$
$983$	−18.5203			−0.590707			−0.295354	+	0.955388i	$0.595437\pi$
$984$	2.31320	−	4.00657i	0.0737420	−	0.127725i
$985$	3.73355	+	6.46670i	0.118961	+	0.206046i
$986$	1.34560	+	2.33064i	0.0428526	+	0.0742228i
$987$	36.2066			1.15247
$988$	31.0424	−	2.30838i	0.987589	−	0.0734393i
$989$	2.31131			0.0734953
$990$	−0.0287026	−	0.0497144i	−0.000912229	−	0.00158003i
$991$	14.4680	+	25.0592i	0.459590	+	0.796033i	0.998939	−	0.0460494i	$-0.0146632\pi$
$991$	14.4680	+	25.0592i	0.459590	+	0.796033i	−0.539350	+	0.842082i	$0.681330\pi$
$992$	−0.591564	+	1.02462i	−0.0187822	+	0.0325317i
$993$	−26.8895			−0.853313
$994$	0.465368	−	0.806040i	0.0147606	−	0.0255660i
$995$	−2.33917	+	4.05155i	−0.0741566	+	0.128443i
$996$	−34.3898			−1.08968
$997$	16.8047	−	29.1066i	0.532210	−	0.921814i	−0.467083	−	0.884213i	$-0.654695\pi$
$997$	16.8047	−	29.1066i	0.532210	−	0.921814i	0.999293	−	0.0376009i	$-0.0119716\pi$
$998$	−1.03555	−	1.79363i	−0.0327798	−	0.0567763i
$999$	25.3485	+	43.9049i	0.801991	+	1.38909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.10	✓	36
13.3	even	3		5239.2.a.p.1.9		18
13.9	even	3	inner	403.2.f.c.373.10	yes	36
13.10	even	6		5239.2.a.o.1.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.10	✓	36	1.1	even	1	trivial
403.2.f.c.373.10	yes	36	13.9	even	3	inner
5239.2.a.o.1.10		18	13.10	even	6
5239.2.a.p.1.9		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0496225 - 0.0859486i) q^{2} +(0.816280 + 1.41384i) q^{3} +(0.995075 - 1.72352i) q^{4} -0.352370 q^{5} +(0.0810117 - 0.140316i) q^{6} +(2.05703 - 3.56288i) q^{7} -0.396002 q^{8} +(0.167373 - 0.289899i) q^{9} +O(q^{10})\)	\(q+(-0.0496225 - 0.0859486i) q^{2} +(0.816280 + 1.41384i) q^{3} +(0.995075 - 1.72352i) q^{4} -0.352370 q^{5} +(0.0810117 - 0.140316i) q^{6} +(2.05703 - 3.56288i) q^{7} -0.396002 q^{8} +(0.167373 - 0.289899i) q^{9} +(0.0174854 + 0.0302857i) q^{10} +(-2.45188 - 4.24678i) q^{11} +3.24904 q^{12} +(-1.56626 + 3.24759i) q^{13} -0.408299 q^{14} +(-0.287632 - 0.498194i) q^{15} +(-1.97050 - 3.41301i) q^{16} +(-1.84743 + 3.19985i) q^{17} -0.0332218 q^{18} +(2.16903 - 3.75686i) q^{19} +(-0.350634 + 0.607316i) q^{20} +6.71644 q^{21} +(-0.243337 + 0.421472i) q^{22} +(2.83246 + 4.90596i) q^{23} +(-0.323249 - 0.559883i) q^{24} -4.87584 q^{25} +(0.356847 - 0.0265360i) q^{26} +5.44417 q^{27} +(-4.09379 - 7.09066i) q^{28} +(3.66951 + 6.35578i) q^{29} +(-0.0285460 + 0.0494432i) q^{30} +1.00000 q^{31} +(-0.591564 + 1.02462i) q^{32} +(4.00285 - 6.93313i) q^{33} +0.366697 q^{34} +(-0.724834 + 1.25545i) q^{35} +(-0.333097 - 0.576942i) q^{36} +(4.65608 + 8.06456i) q^{37} -0.430529 q^{38} +(-5.87007 + 0.436512i) q^{39} +0.139539 q^{40} +(3.57804 + 6.19735i) q^{41} +(-0.333286 - 0.577269i) q^{42} +(0.204002 - 0.353341i) q^{43} -9.75923 q^{44} +(-0.0589771 + 0.102151i) q^{45} +(0.281107 - 0.486892i) q^{46} +5.39075 q^{47} +(3.21696 - 5.57194i) q^{48} +(-4.96272 - 8.59569i) q^{49} +(0.241951 + 0.419071i) q^{50} -6.03209 q^{51} +(4.03875 + 5.93107i) q^{52} -7.56811 q^{53} +(-0.270153 - 0.467919i) q^{54} +(0.863968 + 1.49644i) q^{55} +(-0.814587 + 1.41091i) q^{56} +7.08213 q^{57} +(0.364180 - 0.630779i) q^{58} +(0.912475 - 1.58045i) q^{59} -1.14486 q^{60} +(4.33875 - 7.51494i) q^{61} +(-0.0496225 - 0.0859486i) q^{62} +(-0.688582 - 1.19266i) q^{63} -7.76458 q^{64} +(0.551901 - 1.14435i) q^{65} -0.794524 q^{66} +(5.65194 + 9.78945i) q^{67} +(3.67667 + 6.36818i) q^{68} +(-4.62416 + 8.00928i) q^{69} +0.143872 q^{70} +(-1.13977 + 1.97414i) q^{71} +(-0.0662801 + 0.114800i) q^{72} -2.21345 q^{73} +(0.462092 - 0.800367i) q^{74} +(-3.98005 - 6.89365i) q^{75} +(-4.31669 - 7.47672i) q^{76} -20.1743 q^{77} +(0.328805 + 0.482864i) q^{78} +2.80577 q^{79} +(0.694344 + 1.20264i) q^{80} +(3.94185 + 6.82749i) q^{81} +(0.355103 - 0.615056i) q^{82} -10.5846 q^{83} +(6.68337 - 11.5759i) q^{84} +(0.650979 - 1.12753i) q^{85} -0.0404923 q^{86} +(-5.99070 + 10.3762i) q^{87} +(0.970950 + 1.68174i) q^{88} +(-6.24828 - 10.8223i) q^{89} +0.0117064 q^{90} +(8.34893 + 12.2608i) q^{91} +11.2740 q^{92} +(0.816280 + 1.41384i) q^{93} +(-0.267502 - 0.463327i) q^{94} +(-0.764298 + 1.32380i) q^{95} -1.93153 q^{96} +(6.37242 - 11.0374i) q^{97} +(-0.492525 + 0.853078i) q^{98} -1.64151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

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