LMFDB - Embedded newform 975.2.v.c.781.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(196,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("975.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.v (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			781.13
Character	$\chi$	$=$	975.781
Dual form			975.2.v.c.196.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.491587 + 1.51295i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.429324 + 0.311922i) q^{4} +(-2.15278 - 0.604601i) q^{5} +(1.28699 + 0.935054i) q^{6} +0.787992 q^{7} +(1.89101 + 1.37390i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.491587 + 1.51295i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.429324 + 0.311922i) q^{4} +(-2.15278 - 0.604601i) q^{5} +(1.28699 + 0.935054i) q^{6} +0.787992 q^{7} +(1.89101 + 1.37390i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.143548 - 3.55426i) q^{10} +(-1.28573 - 3.95708i) q^{11} +(-0.163987 + 0.504700i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.387367 + 1.19219i) q^{14} +(-2.09701 + 0.776239i) q^{15} +(-1.47702 + 4.54580i) q^{16} +(3.47376 + 2.52383i) q^{17} +1.59081 q^{18} +(5.49597 + 3.99306i) q^{19} +(1.11283 - 0.411930i) q^{20} +(0.637499 - 0.463170i) q^{21} +(5.35482 - 3.89050i) q^{22} +(-2.40052 - 7.38804i) q^{23} +2.33742 q^{24} +(4.26892 + 2.60314i) q^{25} +1.59081 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.338304 + 0.245792i) q^{28} +(8.50219 - 6.17721i) q^{29} +(-2.20527 - 2.79108i) q^{30} +(6.11421 + 4.44223i) q^{31} -2.92881 q^{32} +(-3.36610 - 2.44561i) q^{33} +(-2.11078 + 6.49630i) q^{34} +(-1.69637 - 0.476421i) q^{35} +(0.163987 + 0.504700i) q^{36} +(0.312755 - 0.962562i) q^{37} +(-3.33955 + 10.2781i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-3.24027 - 4.10101i) q^{40} +(2.86903 - 8.82997i) q^{41} +(1.01414 + 0.736816i) q^{42} -6.73639 q^{43} +(1.78630 + 1.29782i) q^{44} +(-1.24026 + 1.86058i) q^{45} +(9.99766 - 7.26372i) q^{46} +(3.38656 - 2.46048i) q^{47} +(1.47702 + 4.54580i) q^{48} -6.37907 q^{49} +(-1.83988 + 7.73832i) q^{50} +4.29380 q^{51} +(0.163987 + 0.504700i) q^{52} +(-8.13177 + 5.90807i) q^{53} +(1.28699 - 0.935054i) q^{54} +(0.375445 + 9.29609i) q^{55} +(1.49010 + 1.08262i) q^{56} +6.79340 q^{57} +(13.5254 + 9.82676i) q^{58} +(-1.50018 + 4.61708i) q^{59} +(0.658170 - 0.987362i) q^{60} +(-1.01523 - 3.12456i) q^{61} +(-3.71521 + 11.4342i) q^{62} +(0.243503 - 0.749425i) q^{63} +(1.51427 + 4.66046i) q^{64} +(-1.24026 + 1.86058i) q^{65} +(2.04536 - 6.29497i) q^{66} +(3.96603 + 2.88149i) q^{67} -2.27861 q^{68} +(-6.28464 - 4.56606i) q^{69} +(-0.113114 - 2.80073i) q^{70} +(-2.87672 + 2.09006i) q^{71} +(1.89101 - 1.37390i) q^{72} +(-0.438671 - 1.35009i) q^{73} +1.61005 q^{74} +(4.98372 - 0.403217i) q^{75} -3.60507 q^{76} +(-1.01315 - 3.11815i) q^{77} +(1.28699 - 0.935054i) q^{78} +(-1.26087 + 0.916074i) q^{79} +(5.92809 - 8.89309i) q^{80} +(-0.809017 - 0.587785i) q^{81} +14.7697 q^{82} +(0.857284 + 0.622853i) q^{83} +(-0.129221 + 0.397700i) q^{84} +(-5.95232 - 7.53349i) q^{85} +(-3.31152 - 10.1918i) q^{86} +(3.24755 - 9.99493i) q^{87} +(3.00530 - 9.24936i) q^{88} +(1.77846 + 5.47354i) q^{89} +(-3.42466 - 0.961805i) q^{90} +(0.243503 - 0.749425i) q^{91} +(3.33509 + 2.42309i) q^{92} +7.55758 q^{93} +(5.38736 + 3.91415i) q^{94} +(-9.41741 - 11.9190i) q^{95} +(-2.36945 + 1.72151i) q^{96} +(-9.85384 + 7.15923i) q^{97} +(-3.13587 - 9.65121i) q^{98} -4.16072 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 17 q^{13} - 26 q^{14} - q^{15} - 19 q^{16} - 7 q^{17} + 4 q^{18} - 8 q^{19} + 55 q^{20} - q^{21} - 26 q^{22} - 15 q^{23} - 18 q^{24} + 3 q^{25} + 4 q^{26} + 17 q^{27} + 9 q^{28} - 25 q^{29} - 28 q^{30} - 26 q^{31} + 180 q^{32} + 8 q^{33} + 26 q^{34} - 46 q^{35} - 19 q^{36} - 8 q^{37} + 8 q^{38} + 17 q^{39} + 82 q^{40} - 9 q^{41} - 4 q^{42} - 100 q^{43} - 5 q^{44} + 6 q^{45} + 32 q^{46} + 2 q^{47} + 19 q^{48} + 204 q^{49} - 29 q^{50} + 2 q^{51} - 19 q^{52} - 31 q^{53} + q^{54} - 37 q^{55} - 17 q^{56} + 8 q^{57} + 11 q^{58} - 13 q^{59} - 25 q^{60} + 14 q^{61} - 46 q^{62} + q^{63} - 56 q^{64} + 6 q^{65} - 39 q^{66} - 12 q^{67} + 26 q^{68} - 10 q^{69} + 117 q^{70} + 7 q^{71} - 12 q^{72} - 10 q^{73} + 76 q^{74} + 2 q^{75} + 6 q^{76} - 5 q^{77} + q^{78} - 46 q^{79} + 128 q^{80} - 17 q^{81} + 102 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{85} - 60 q^{86} + 64 q^{88} - 38 q^{89} - 17 q^{90} + q^{91} - 42 q^{92} - 64 q^{93} + 39 q^{94} - 49 q^{95} + 60 q^{96} - 34 q^{97} + 53 q^{98} + 12 q^{99}+O(q^{100}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 17 * q^13 - 26 * q^14 - q^15 - 19 * q^16 - 7 * q^17 + 4 * q^18 - 8 * q^19 + 55 * q^20 - q^21 - 26 * q^22 - 15 * q^23 - 18 * q^24 + 3 * q^25 + 4 * q^26 + 17 * q^27 + 9 * q^28 - 25 * q^29 - 28 * q^30 - 26 * q^31 + 180 * q^32 + 8 * q^33 + 26 * q^34 - 46 * q^35 - 19 * q^36 - 8 * q^37 + 8 * q^38 + 17 * q^39 + 82 * q^40 - 9 * q^41 - 4 * q^42 - 100 * q^43 - 5 * q^44 + 6 * q^45 + 32 * q^46 + 2 * q^47 + 19 * q^48 + 204 * q^49 - 29 * q^50 + 2 * q^51 - 19 * q^52 - 31 * q^53 + q^54 - 37 * q^55 - 17 * q^56 + 8 * q^57 + 11 * q^58 - 13 * q^59 - 25 * q^60 + 14 * q^61 - 46 * q^62 + q^63 - 56 * q^64 + 6 * q^65 - 39 * q^66 - 12 * q^67 + 26 * q^68 - 10 * q^69 + 117 * q^70 + 7 * q^71 - 12 * q^72 - 10 * q^73 + 76 * q^74 + 2 * q^75 + 6 * q^76 - 5 * q^77 + q^78 - 46 * q^79 + 128 * q^80 - 17 * q^81 + 102 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^85 - 60 * q^86 + 64 * q^88 - 38 * q^89 - 17 * q^90 + q^91 - 42 * q^92 - 64 * q^93 + 39 * q^94 - 49 * q^95 + 60 * q^96 - 34 * q^97 + 53 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.491587	+	1.51295i	0.347605	+	1.06982i	0.960175	+	0.279400i	$0.0901357\pi$
$2$	0.491587	+	1.51295i	0.347605	+	1.06982i	−0.612570	+	0.790416i	$0.709864\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.429324	+	0.311922i	−0.214662	+	0.155961i
$5$	−2.15278	−	0.604601i	−0.962752	−	0.270386i
$5$	−2.15278	−	0.604601i	−0.962752	−	0.270386i
$6$	1.28699	+	0.935054i	0.525412	+	0.381734i
$7$	0.787992			0.297833			0.148917	−	0.988850i	$-0.452421\pi$
$7$	0.787992			0.297833			0.148917	+	0.988850i	$0.452421\pi$
$8$	1.89101	+	1.37390i	0.668573	+	0.485747i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.143548	−	3.55426i	−0.0453937	−	1.12396i
$11$	−1.28573	−	3.95708i	−0.387664	−	1.19311i	−0.934530	−	0.355886i	$-0.884179\pi$
$11$	−1.28573	−	3.95708i	−0.387664	−	1.19311i	0.546866	−	0.837220i	$-0.315821\pi$
$12$	−0.163987	+	0.504700i	−0.0473390	+	0.145694i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	0.387367	+	1.19219i	0.103528	+	0.318627i
$15$	−2.09701	+	0.776239i	−0.541446	+	0.200424i
$16$	−1.47702	+	4.54580i	−0.369255	+	1.13645i
$17$	3.47376	+	2.52383i	0.842510	+	0.612119i	0.923071	−	0.384630i	$-0.125671\pi$
$17$	3.47376	+	2.52383i	0.842510	+	0.612119i	−0.0805605	+	0.996750i	$0.525671\pi$
$18$	1.59081			0.374957
$19$	5.49597	+	3.99306i	1.26086	+	0.916070i	0.998800	−	0.0489804i	$-0.0155972\pi$
$19$	5.49597	+	3.99306i	1.26086	+	0.916070i	0.262063	+	0.965051i	$0.415597\pi$
$20$	1.11283	−	0.411930i	0.248836	−	0.0921102i
$21$	0.637499	−	0.463170i	0.139114	−	0.101072i
$22$	5.35482	−	3.89050i	1.14165	−	0.829458i
$23$	−2.40052	−	7.38804i	−0.500543	−	1.54051i	−0.808137	−	0.588994i	$-0.799524\pi$
$23$	−2.40052	−	7.38804i	−0.500543	−	1.54051i	0.307594	−	0.951518i	$-0.400476\pi$
$24$	2.33742			0.477123
$25$	4.26892	+	2.60314i	0.853783	+	0.520629i
$26$	1.59081			0.311983
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.338304	+	0.245792i	−0.0639334	+	0.0464504i
$29$	8.50219	−	6.17721i	1.57882	−	1.14708i	0.660784	−	0.750576i	$-0.270224\pi$
$29$	8.50219	−	6.17721i	1.57882	−	1.14708i	0.918034	−	0.396503i	$-0.129776\pi$
$30$	−2.20527	−	2.79108i	−0.402626	−	0.509579i
$31$	6.11421	+	4.44223i	1.09814	+	0.797849i	0.980756	−	0.195237i	$-0.0625478\pi$
$31$	6.11421	+	4.44223i	1.09814	+	0.797849i	0.117388	+	0.993086i	$0.462548\pi$
$32$	−2.92881			−0.517745
$33$	−3.36610	−	2.44561i	−0.585962	−	0.425727i
$34$	−2.11078	+	6.49630i	−0.361995	+	1.11411i
$35$	−1.69637	−	0.476421i	−0.286739	−	0.0805298i
$36$	0.163987	+	0.504700i	0.0273312	+	0.0841167i
$37$	0.312755	−	0.962562i	0.0514167	−	0.158244i	−0.922051	−	0.387068i	$-0.873488\pi$
$37$	0.312755	−	0.962562i	0.0514167	−	0.158244i	0.973468	+	0.228824i	$0.0734879\pi$
$38$	−3.33955	+	10.2781i	−0.541746	+	1.66732i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−3.24027	−	4.10101i	−0.512331	−	0.648427i
$41$	2.86903	−	8.82997i	0.448067	−	1.37901i	−0.431017	−	0.902344i	$-0.641845\pi$
$41$	2.86903	−	8.82997i	0.448067	−	1.37901i	0.879085	−	0.476666i	$-0.158155\pi$
$42$	1.01414	+	0.736816i	0.156485	+	0.113693i
$43$	−6.73639			−1.02729			−0.513645	−	0.858003i	$-0.671705\pi$
$43$	−6.73639			−1.02729			−0.513645	+	0.858003i	$0.671705\pi$
$44$	1.78630	+	1.29782i	0.269295	+	0.195654i
$45$	−1.24026	+	1.86058i	−0.184886	+	0.277359i
$46$	9.99766	−	7.26372i	1.47407	−	1.07098i
$47$	3.38656	−	2.46048i	0.493980	−	0.358897i	−0.312733	−	0.949841i	$-0.601244\pi$
$47$	3.38656	−	2.46048i	0.493980	−	0.358897i	0.806713	+	0.590944i	$0.201244\pi$
$48$	1.47702	+	4.54580i	0.213189	+	0.656129i
$49$	−6.37907			−0.911295
$50$	−1.83988	+	7.73832i	−0.260199	+	1.09436i
$51$	4.29380			0.601253
$52$	0.163987	+	0.504700i	0.0227409	+	0.0699894i
$53$	−8.13177	+	5.90807i	−1.11698	+	0.811536i	−0.983749	−	0.179548i	$-0.942536\pi$
$53$	−8.13177	+	5.90807i	−1.11698	+	0.811536i	−0.133235	+	0.991084i	$0.542536\pi$
$54$	1.28699	−	0.935054i	0.175137	−	0.127245i
$55$	0.375445	+	9.29609i	0.0506251	+	1.25348i
$56$	1.49010	+	1.08262i	0.199123	+	0.144672i
$57$	6.79340			0.899807
$58$	13.5254	+	9.82676i	1.77597	+	1.29032i
$59$	−1.50018	+	4.61708i	−0.195307	+	0.601093i	0.804666	+	0.593728i	$0.202344\pi$
$59$	−1.50018	+	4.61708i	−0.195307	+	0.601093i	−0.999973	+	0.00736530i	$0.997656\pi$
$60$	0.658170	−	0.987362i	0.0849694	−	0.127468i
$61$	−1.01523	−	3.12456i	−0.129987	−	0.400059i	0.864790	−	0.502134i	$-0.167452\pi$
$61$	−1.01523	−	3.12456i	−0.129987	−	0.400059i	−0.994777	+	0.102076i	$0.967452\pi$
$62$	−3.71521	+	11.4342i	−0.471832	+	1.45215i
$63$	0.243503	−	0.749425i	0.0306785	−	0.0944187i
$64$	1.51427	+	4.66046i	0.189284	+	0.582557i
$65$	−1.24026	+	1.86058i	−0.153835	+	0.230777i
$66$	2.04536	−	6.29497i	0.251766	−	0.774857i
$67$	3.96603	+	2.88149i	0.484527	+	0.352030i	0.803076	−	0.595877i	$-0.203195\pi$
$67$	3.96603	+	2.88149i	0.484527	+	0.352030i	−0.318549	+	0.947907i	$0.603195\pi$
$68$	−2.27861			−0.276322
$69$	−6.28464	−	4.56606i	−0.756582	−	0.549689i
$70$	−0.113114	−	2.80073i	−0.0135198	−	0.334751i
$71$	−2.87672	+	2.09006i	−0.341404	+	0.248045i	−0.745254	−	0.666781i	$-0.767672\pi$
$71$	−2.87672	+	2.09006i	−0.341404	+	0.248045i	0.403850	+	0.914825i	$0.367672\pi$
$72$	1.89101	−	1.37390i	0.222858	−	0.161916i
$73$	−0.438671	−	1.35009i	−0.0513425	−	0.158016i	0.922098	−	0.386957i	$-0.126474\pi$
$73$	−0.438671	−	1.35009i	−0.0513425	−	0.158016i	−0.973440	+	0.228941i	$0.926474\pi$
$74$	1.61005			0.187165
$75$	4.98372	−	0.403217i	0.575470	−	0.0465595i
$76$	−3.60507			−0.413530
$77$	−1.01315	−	3.11815i	−0.115459	−	0.355346i
$78$	1.28699	−	0.935054i	0.145723	−	0.105874i
$79$	−1.26087	+	0.916074i	−0.141859	+	0.103066i	−0.656451	−	0.754369i	$-0.727943\pi$
$79$	−1.26087	+	0.916074i	−0.141859	+	0.103066i	0.514593	+	0.857435i	$0.327943\pi$
$80$	5.92809	−	8.89309i	0.662780	−	0.994277i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	14.7697			1.63104
$83$	0.857284	+	0.622853i	0.0940991	+	0.0683670i	0.633840	−	0.773464i	$-0.281478\pi$
$83$	0.857284	+	0.622853i	0.0940991	+	0.0683670i	−0.539741	+	0.841831i	$0.681478\pi$
$84$	−0.129221	+	0.397700i	−0.0140991	+	0.0433926i
$85$	−5.95232	−	7.53349i	−0.645620	−	0.817122i
$86$	−3.31152	−	10.1918i	−0.357091	−	1.09901i
$87$	3.24755	−	9.99493i	0.348174	−	1.07157i
$88$	3.00530	−	9.24936i	0.320366	−	0.985985i
$89$	1.77846	+	5.47354i	0.188516	+	0.580194i	0.999991	−	0.00419354i	$-0.00133485\pi$
$89$	1.77846	+	5.47354i	0.188516	+	0.580194i	−0.811475	+	0.584387i	$0.801335\pi$
$90$	−3.42466	−	0.961805i	−0.360991	−	0.101383i
$91$	0.243503	−	0.749425i	0.0255261	−	0.0785611i
$92$	3.33509	+	2.42309i	0.347707	+	0.252624i
$93$	7.55758			0.783684
$94$	5.38736	+	3.91415i	0.555664	+	0.403714i
$95$	−9.41741	−	11.9190i	−0.966206	−	1.22287i
$96$	−2.36945	+	1.72151i	−0.241831	+	0.175701i
$97$	−9.85384	+	7.15923i	−1.00051	+	0.726910i	−0.962197	−	0.272356i	$-0.912197\pi$
$97$	−9.85384	+	7.15923i	−1.00051	+	0.726910i	−0.0383090	+	0.999266i	$0.512197\pi$
$98$	−3.13587	−	9.65121i	−0.316770	−	0.974919i
$99$	−4.16072			−0.418169
$100$	−2.64472	+	0.213977i	−0.264472	+	0.0213977i
$101$	−4.34616			−0.432459			−0.216230	−	0.976343i	$-0.569376\pi$
$101$	−4.34616			−0.432459			−0.216230	+	0.976343i	$0.569376\pi$
$102$	2.11078	+	6.49630i	0.208998	+	0.643230i
$103$	−7.15893	+	5.20127i	−0.705390	+	0.512496i	−0.881683	−	0.471842i	$-0.843589\pi$
$103$	−7.15893	+	5.20127i	−0.705390	+	0.512496i	0.176293	+	0.984338i	$0.443589\pi$
$104$	1.89101	−	1.37390i	0.185429	−	0.134722i
$105$	−1.65243	+	0.611671i	−0.161260	+	0.0596929i
$106$	−12.9361	−	9.39862i	−1.25646	−	0.912875i
$107$	2.56968			0.248420			0.124210	−	0.992256i	$-0.460360\pi$
$107$	2.56968			0.248420			0.124210	+	0.992256i	$0.460360\pi$
$108$	0.429324	+	0.311922i	0.0413117	+	0.0300147i
$109$	−3.35662	+	10.3306i	−0.321506	+	0.989494i	0.651487	+	0.758660i	$0.274145\pi$
$109$	−3.35662	+	10.3306i	−0.321506	+	0.989494i	−0.972993	+	0.230834i	$0.925855\pi$
$110$	−13.8799	+	5.13786i	−1.32340	+	0.489876i
$111$	−0.312755	−	0.962562i	−0.0296854	−	0.0913623i
$112$	−1.16388	+	3.58205i	−0.109976	+	0.338472i
$113$	−0.0985361	+	0.303263i	−0.00926949	+	0.0285286i	−0.955584	−	0.294718i	$-0.904774\pi$
$113$	−0.0985361	+	0.303263i	−0.00926949	+	0.0285286i	0.946315	+	0.323247i	$0.104774\pi$
$114$	3.33955	+	10.2781i	0.312777	+	0.962629i
$115$	0.700972	+	17.3562i	0.0653660	+	1.61847i
$116$	−1.72339	+	5.30404i	−0.160013	+	0.492468i
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$	−7.72289			−0.710949
$119$	2.73730	+	1.98876i	0.250927	+	0.182309i
$120$	−5.03194	−	1.41321i	−0.459352	−	0.129007i
$121$	−5.10622	+	3.70988i	−0.464202	+	0.337262i
$122$	4.22822	−	3.07198i	0.382805	−	0.278124i
$123$	−2.86903	−	8.82997i	−0.258692	−	0.796172i
$124$	−4.01061			−0.360163
$125$	−7.61617	−	8.18499i	−0.681211	−	0.732087i
$126$	1.25355			0.111675
$127$	0.196541	+	0.604892i	0.0174402	+	0.0536755i	0.959398	−	0.282056i	$-0.0910165\pi$
$127$	0.196541	+	0.604892i	0.0174402	+	0.0536755i	−0.941958	+	0.335732i	$0.891016\pi$
$128$	−11.0455	+	8.02506i	−0.976297	+	0.709322i
$129$	−5.44986	+	3.95955i	−0.479833	+	0.348619i
$130$	−3.42466	−	0.961805i	−0.300363	−	0.0843559i
$131$	−2.72677	−	1.98111i	−0.238239	−	0.173090i	0.462260	−	0.886745i	$-0.347039\pi$
$131$	−2.72677	−	1.98111i	−0.238239	−	0.173090i	−0.700498	+	0.713654i	$0.747039\pi$
$132$	2.20799			0.192181
$133$	4.33079	+	3.14650i	0.375527	+	0.272836i
$134$	−2.40990	+	7.41690i	−0.208183	+	0.640722i
$135$	0.0902356	+	2.23425i	0.00776624	+	0.192293i
$136$	3.10142	+	9.54519i	0.265945	+	0.818494i
$137$	−5.95641	+	18.3320i	−0.508891	+	1.56620i	0.285239	+	0.958456i	$0.407927\pi$
$137$	−5.95641	+	18.3320i	−0.508891	+	1.56620i	−0.794130	+	0.607748i	$0.792073\pi$
$138$	3.81877	−	11.7530i	0.325075	−	1.00048i
$139$	−6.80052	−	20.9299i	−0.576813	−	1.77525i	−0.629922	−	0.776658i	$-0.716913\pi$
$139$	−6.80052	−	20.9299i	−0.576813	−	1.77525i	0.0531091	−	0.998589i	$-0.483087\pi$
$140$	0.876900	−	0.324597i	0.0741116	−	0.0274335i
$141$	1.29355	−	3.98114i	0.108937	−	0.335272i
$142$	−4.57631	−	3.32489i	−0.384036	−	0.279018i
$143$	−4.16072			−0.347937
$144$	3.86688	+	2.80946i	0.322240	+	0.234121i
$145$	−22.0381	+	8.15772i	−1.83016	+	0.677462i
$146$	1.82697	−	1.32737i	0.151201	−	0.109854i
$147$	−5.16077	+	3.74952i	−0.425653	+	0.309255i
$148$	0.165971	+	0.510806i	0.0136427	+	0.0419880i
$149$	−8.33737			−0.683024			−0.341512	−	0.939877i	$-0.610939\pi$
$149$	−8.33737			−0.683024			−0.341512	+	0.939877i	$0.610939\pi$
$150$	3.05998	+	7.34189i	0.249846	+	0.599463i
$151$	19.5063			1.58740			0.793700	−	0.608310i	$-0.208152\pi$
$151$	19.5063			1.58740			0.793700	+	0.608310i	$0.208152\pi$
$152$	4.90688	+	15.1018i	0.398001	+	1.22492i
$153$	3.47376	−	2.52383i	0.280837	−	0.204040i
$154$	4.21956	−	3.06569i	0.340021	−	0.247040i
$155$	−10.4768	−	13.2598i	−0.841514	−	1.06505i
$156$	0.429324	+	0.311922i	0.0343734	+	0.0249737i
$157$	20.2711			1.61781			0.808903	−	0.587942i	$-0.200062\pi$
$157$	20.2711			1.61781			0.808903	+	0.587942i	$0.200062\pi$
$158$	−2.00580	−	1.45730i	−0.159573	−	0.115936i
$159$	−3.10606	+	9.55947i	−0.246326	+	0.758115i
$160$	6.30507	+	1.77076i	0.498460	+	0.139991i
$161$	−1.89159	−	5.82172i	−0.149078	−	0.458815i
$162$	0.491587	−	1.51295i	0.0386227	−	0.118869i
$163$	−3.22466	+	9.92448i	−0.252575	+	0.777345i	0.741723	+	0.670706i	$0.234009\pi$
$163$	−3.22466	+	9.92448i	−0.252575	+	0.777345i	−0.994298	+	0.106639i	$0.965991\pi$
$164$	1.52252	+	4.68583i	0.118889	+	0.365902i
$165$	5.76784	+	7.30001i	0.449026	+	0.568305i
$166$	−0.520916	+	1.60321i	−0.0404309	+	0.124433i
$167$	−7.69442	−	5.59032i	−0.595412	−	0.432592i	0.248835	−	0.968546i	$-0.419952\pi$
$167$	−7.69442	−	5.59032i	−0.595412	−	0.432592i	−0.844248	+	0.535953i	$0.819952\pi$
$168$	1.84187			0.142103
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	8.47171	−	12.7089i	0.649750	−	0.974730i
$171$	5.49597	−	3.99306i	0.420288	−	0.305357i
$172$	2.89209	−	2.10123i	0.220520	−	0.160217i
$173$	−2.18038	−	6.71052i	−0.165771	−	0.510191i	0.833321	−	0.552789i	$-0.186437\pi$
$173$	−2.18038	−	6.71052i	−0.165771	−	0.510191i	−0.999092	+	0.0425980i	$0.986437\pi$
$174$	16.7183			1.26741
$175$	3.36387	+	2.05126i	0.254285	+	0.155061i
$176$	19.8872			1.49905
$177$	1.50018	+	4.61708i	0.112761	+	0.347041i
$178$	−7.40692	+	5.38144i	−0.555172	+	0.403356i
$179$	−11.2289	+	8.15830i	−0.839290	+	0.609780i	−0.922172	−	0.386780i	$-0.873587\pi$
$179$	−11.2289	+	8.15830i	−0.839290	+	0.609780i	0.0828823	+	0.996559i	$0.473587\pi$
$180$	−0.0478856	−	1.18566i	−0.00356918	−	0.0883735i
$181$	−19.5769	−	14.2235i	−1.45514	−	1.05722i	−0.984596	−	0.174845i	$-0.944058\pi$
$181$	−19.5769	−	14.2235i	−1.45514	−	1.05722i	−0.470544	−	0.882376i	$-0.655942\pi$
$182$	1.25355			0.0929190
$183$	−2.65791	−	1.93108i	−0.196478	−	0.142750i
$184$	5.61101	−	17.2689i	0.413649	−	1.27308i
$185$	−1.25526	+	1.88309i	−0.0922885	+	0.138448i
$186$	3.71521	+	11.4342i	0.272412	+	0.838399i
$187$	5.52069	−	16.9909i	0.403713	−	1.24250i
$188$	−0.686452	+	2.11268i	−0.0500647	+	0.154083i
$189$	−0.243503	−	0.749425i	−0.0177122	−	0.0545127i
$190$	13.4034	−	20.1073i	0.972387	−	1.45874i
$191$	7.05102	−	21.7008i	0.510194	−	1.57021i	−0.281666	−	0.959512i	$-0.590887\pi$
$191$	7.05102	−	21.7008i	0.510194	−	1.57021i	0.791860	−	0.610703i	$-0.209113\pi$
$192$	3.96442	+	2.88032i	0.286107	+	0.207869i
$193$	9.46993			0.681660			0.340830	−	0.940125i	$-0.389292\pi$
$193$	9.46993			0.681660			0.340830	+	0.940125i	$0.389292\pi$
$194$	−15.6756	−	11.3890i	−1.12544	−	0.817680i
$195$	0.0902356	+	2.23425i	0.00646191	+	0.159998i
$196$	2.73869	−	1.98977i	0.195620	−	0.142127i
$197$	−13.2850	+	9.65212i	−0.946518	+	0.687685i	−0.949981	−	0.312309i	$-0.898898\pi$
$197$	−13.2850	+	9.65212i	−0.946518	+	0.687685i	0.00346299	+	0.999994i	$0.498898\pi$
$198$	−2.04536	−	6.29497i	−0.145357	−	0.447364i
$199$	−6.54247			−0.463783			−0.231892	−	0.972742i	$-0.574492\pi$
$199$	−6.54247			−0.463783			−0.231892	+	0.972742i	$0.574492\pi$
$200$	4.49611	+	10.7876i	0.317923	+	0.762801i
$201$	4.90228			0.345780
$202$	−2.13652	−	6.57552i	−0.150325	−	0.462652i
$203$	6.69966	−	4.86759i	0.470224	−	0.341638i
$204$	−1.84343	+	1.33933i	−0.129066	+	0.0937719i
$205$	−11.5150	+	17.2744i	−0.804242	+	1.20649i
$206$	−11.3885	−	8.27422i	−0.793474	−	0.576492i
$207$	−7.76824			−0.539930
$208$	3.86688	+	2.80946i	0.268120	+	0.194801i
$209$	8.73451	−	26.8820i	0.604178	−	1.85947i
$210$	−1.73774	−	2.19935i	−0.119915	−	0.151770i
$211$	1.74686	+	5.37627i	0.120259	+	0.370118i	0.993007	−	0.118052i	$-0.0376648\pi$
$211$	1.74686	+	5.37627i	0.120259	+	0.370118i	−0.872749	+	0.488169i	$0.837665\pi$
$212$	1.64830	−	5.07295i	0.113206	−	0.348412i
$213$	−1.09881	+	3.38179i	−0.0752892	+	0.231716i
$214$	1.26322	+	3.88779i	0.0863520	+	0.265764i
$215$	14.5020	+	4.07283i	0.989026	+	0.277765i
$216$	0.722302	−	2.22302i	0.0491464	−	0.151257i
$217$	4.81795	+	3.50045i	0.327064	+	0.237626i
$218$	−17.2798			−1.17033
$219$	−1.14846	−	0.834401i	−0.0776054	−	0.0563836i
$220$	−3.06084	−	3.87392i	−0.206362	−	0.261180i
$221$	3.47376	−	2.52383i	0.233670	−	0.169771i
$222$	1.30256	−	0.946366i	0.0874222	−	0.0635159i
$223$	−0.121069	−	0.372611i	−0.00810735	−	0.0249519i	0.946921	−	0.321466i	$-0.104176\pi$
$223$	−0.121069	−	0.372611i	−0.00810735	−	0.0249519i	−0.955028	+	0.296514i	$0.904176\pi$
$224$	−2.30788			−0.154201
$225$	3.79491	−	3.25556i	0.252994	−	0.217038i
$226$	−0.507260			−0.0337425
$227$	4.35357	+	13.3989i	0.288956	+	0.889317i	0.985185	+	0.171496i	$0.0548601\pi$
$227$	4.35357	+	13.3989i	0.288956	+	0.889317i	−0.696228	+	0.717820i	$0.745140\pi$
$228$	−2.91657	+	2.11901i	−0.193154	+	0.140335i
$229$	16.1869	−	11.7605i	1.06966	−	0.777156i	0.0938112	−	0.995590i	$-0.470095\pi$
$229$	16.1869	−	11.7605i	1.06966	−	0.777156i	0.975852	+	0.218434i	$0.0700950\pi$
$230$	−25.9144	+	9.59260i	−1.70875	+	0.632517i
$231$	−2.65246	−	1.92712i	−0.174519	−	0.126795i
$232$	24.5646			1.61275
$233$	10.0239	+	7.28276i	0.656685	+	0.477109i	0.865542	−	0.500837i	$-0.166974\pi$
$233$	10.0239	+	7.28276i	0.656685	+	0.477109i	−0.208857	+	0.977946i	$0.566974\pi$
$234$	0.491587	−	1.51295i	0.0321360	−	0.0989046i
$235$	−8.77811	+	3.24935i	−0.572621	+	0.211964i
$236$	−0.796107	−	2.45016i	−0.0518221	−	0.159492i
$237$	−0.481609	+	1.48224i	−0.0312838	+	0.0962818i
$238$	−1.66328	+	5.11904i	−0.107814	+	0.331818i
$239$	4.62164	+	14.2239i	0.298949	+	0.920071i	0.981866	+	0.189575i	$0.0607109\pi$
$239$	4.62164	+	14.2239i	0.298949	+	0.920071i	−0.682917	+	0.730496i	$0.739289\pi$
$240$	−0.431302	−	10.6791i	−0.0278404	−	0.689333i
$241$	0.313790	−	0.965747i	0.0202130	−	0.0622092i	−0.940441	−	0.339956i	$-0.889588\pi$
$241$	0.313790	−	0.965747i	0.0202130	−	0.0622092i	0.960654	+	0.277747i	$0.0895877\pi$
$242$	−8.12302	−	5.90172i	−0.522167	−	0.379377i
$243$	−1.00000			−0.0641500
$244$	1.41048	+	1.02477i	0.0902968	+	0.0656044i
$245$	13.7327	+	3.85679i	0.877352	+	0.246401i
$246$	11.9489	−	8.68140i	0.761835	−	0.553506i
$247$	5.49597	−	3.99306i	0.349700	−	0.254072i
$248$	5.45885	+	16.8006i	0.346638	+	1.06684i
$249$	1.05966			0.0671533
$250$	8.63946	−	15.5465i	0.546407	−	0.983248i
$251$	−24.4607			−1.54395			−0.771973	−	0.635656i	$-0.780730\pi$
$251$	−24.4607			−1.54395			−0.771973	+	0.635656i	$0.780730\pi$
$252$	0.129221	+	0.397700i	0.00814013	+	0.0250527i
$253$	−26.1487	+	18.9981i	−1.64395	+	1.19440i
$254$	−0.818554	+	0.594714i	−0.0513606	+	0.0373157i
$255$	−9.24361	−	2.59604i	−0.578857	−	0.162570i
$256$	−9.64251	−	7.00569i	−0.602657	−	0.437856i
$257$	−7.54665			−0.470747			−0.235374	−	0.971905i	$-0.575631\pi$
$257$	−7.54665			−0.470747			−0.235374	+	0.971905i	$0.575631\pi$
$258$	−8.66968	−	6.29889i	−0.539751	−	0.392152i
$259$	0.246449	−	0.758492i	0.0153136	−	0.0471304i
$260$	−0.0478856	−	1.18566i	−0.00296974	−	0.0735312i
$261$	−3.24755	−	9.99493i	−0.201018	−	0.618671i
$262$	1.65688	−	5.09935i	0.102362	−	0.315039i
$263$	−7.37917	+	22.7107i	−0.455019	+	1.40040i	0.416094	+	0.909322i	$0.363399\pi$
$263$	−7.37917	+	22.7107i	−0.455019	+	1.40040i	−0.871113	+	0.491083i	$0.836601\pi$
$264$	−3.00530	−	9.24936i	−0.184963	−	0.569259i
$265$	21.0779	−	7.80230i	1.29481	−	0.479292i
$266$	−2.63154	+	8.09904i	−0.161350	+	0.496584i
$267$	4.65607	+	3.38283i	0.284947	+	0.207026i
$268$	−2.60151			−0.158912
$269$	2.99009	+	2.17242i	0.182309	+	0.132455i	0.675197	−	0.737638i	$-0.264059\pi$
$269$	2.99009	+	2.17242i	0.182309	+	0.132455i	−0.492888	+	0.870093i	$0.664059\pi$
$270$	−3.33594	+	1.23485i	−0.203019	+	0.0751505i
$271$	15.3894	−	11.1811i	0.934840	−	0.679201i	−0.0123334	−	0.999924i	$-0.503926\pi$
$271$	15.3894	−	11.1811i	0.934840	−	0.679201i	0.947173	+	0.320723i	$0.103926\pi$
$272$	−16.6036	+	12.0632i	−1.00674	+	0.731442i
$273$	−0.243503	−	0.749425i	−0.0147375	−	0.0453573i
$274$	−30.6634			−1.85244
$275$	4.81217	−	20.2394i	0.290185	−	1.22048i
$276$	4.12240			0.248139
$277$	−8.51197	−	26.1971i	−0.511434	−	1.57403i	−0.789677	−	0.613523i	$-0.789752\pi$
$277$	−8.51197	−	26.1971i	−0.511434	−	1.57403i	0.278243	−	0.960511i	$-0.410248\pi$
$278$	28.3228	−	20.5777i	1.69869	−	1.23417i
$279$	6.11421	−	4.44223i	0.366048	−	0.265950i
$280$	−2.55331	−	3.23156i	−0.152589	−	0.193123i
$281$	6.94375	+	5.04493i	0.414229	+	0.300955i	0.775312	−	0.631579i	$-0.217593\pi$
$281$	6.94375	+	5.04493i	0.414229	+	0.300955i	−0.361082	+	0.932534i	$0.617593\pi$
$282$	6.65915			0.396547
$283$	13.8592	+	10.0693i	0.823847	+	0.598560i	0.917812	−	0.397016i	$-0.129954\pi$
$283$	13.8592	+	10.0693i	0.823847	+	0.598560i	−0.0939649	+	0.995576i	$0.529954\pi$
$284$	0.583109	−	1.79463i	0.0346012	−	0.106491i
$285$	−14.6247	−	4.10729i	−0.866291	−	0.243295i
$286$	−2.04536	−	6.29497i	−0.120945	−	0.372229i
$287$	2.26077	−	6.95795i	0.133449	−	0.410715i
$288$	−0.905051	+	2.78546i	−0.0533306	+	0.164135i
$289$	0.443975	+	1.36641i	0.0261162	+	0.0803773i
$290$	−23.1759	−	29.3323i	−1.36093	−	1.72245i
$291$	−3.76383	+	11.5839i	−0.220640	+	0.679059i
$292$	0.609455	+	0.442795i	0.0356656	+	0.0259126i
$293$	22.4851			1.31360			0.656798	−	0.754067i	$-0.271911\pi$
$293$	22.4851			1.31360			0.656798	+	0.754067i	$0.271911\pi$
$294$	−8.20981	−	5.96477i	−0.478806	−	0.347873i
$295$	6.02105	−	9.03255i	0.350559	−	0.525896i
$296$	1.91389	−	1.39052i	0.111242	−	0.0808224i
$297$	−3.36610	+	2.44561i	−0.195321	+	0.141909i
$298$	−4.09854	−	12.6140i	−0.237422	−	0.730710i
$299$	−7.76824			−0.449249
$300$	−2.01386	+	1.72764i	−0.116270	+	0.0997454i
$301$	−5.30823			−0.305961
$302$	9.58904	+	29.5120i	0.551787	+	1.69823i
$303$	−3.51612	+	2.55461i	−0.201996	+	0.146758i
$304$	−26.2693	+	19.0858i	−1.50665	+	1.09464i
$305$	0.296456	+	7.34029i	0.0169750	+	0.420304i
$306$	5.52609	+	4.01494i	0.315905	+	0.229519i
$307$	−27.4151			−1.56466			−0.782332	−	0.622862i	$-0.785970\pi$
$307$	−27.4151			−1.56466			−0.782332	+	0.622862i	$0.785970\pi$
$308$	1.40759	+	1.02267i	0.0802048	+	0.0582722i
$309$	−2.73447	+	8.41583i	−0.155558	+	0.478760i
$310$	14.9112	−	22.3692i	0.846897	−	1.27048i
$311$	−1.41132	−	4.34359i	−0.0800285	−	0.246302i	0.903035	−	0.429566i	$-0.141334\pi$
$311$	−1.41132	−	4.34359i	−0.0800285	−	0.246302i	−0.983064	+	0.183264i	$0.941334\pi$
$312$	0.722302	−	2.22302i	0.0408923	−	0.125854i
$313$	−2.11462	+	6.50814i	−0.119526	+	0.367862i	−0.992864	−	0.119252i	$-0.961950\pi$
$313$	−2.11462	+	6.50814i	−0.119526	+	0.367862i	0.873338	+	0.487114i	$0.161950\pi$
$314$	9.96499	+	30.6691i	0.562357	+	1.73076i
$315$	−0.977312	+	1.46612i	−0.0550653	+	0.0826068i
$316$	0.255577	−	0.786585i	0.0143773	−	0.0442488i
$317$	−24.7209	−	17.9608i	−1.38847	−	1.00878i	−0.996032	−	0.0889986i	$-0.971633\pi$
$317$	−24.7209	−	17.9608i	−1.38847	−	1.00878i	−0.392433	−	0.919780i	$-0.628367\pi$
$318$	−15.9899			−0.896668
$319$	−35.3753	−	25.7017i	−1.98064	−	1.43902i
$320$	−0.442181	−	10.9485i	−0.0247187	−	0.612038i
$321$	2.07891	−	1.51042i	0.116034	−	0.0843033i
$322$	7.87808	−	5.72376i	0.439028	−	0.318973i
$323$	9.01387	+	27.7418i	0.501545	+	1.54360i
$324$	0.530673			0.0294819
$325$	3.79491	−	3.25556i	0.210503	−	0.180586i
$326$	−16.6004			−0.919413
$327$	3.35662	+	10.3306i	0.185622	+	0.571285i
$328$	17.5569	−	12.7558i	0.969416	−	0.704322i
$329$	2.66858	−	1.93884i	0.147124	−	0.106892i
$330$	−8.20915	+	12.3150i	−0.451899	+	0.677921i
$331$	12.0572	+	8.76007i	0.662723	+	0.481497i	0.867582	−	0.497295i	$-0.165673\pi$
$331$	12.0572	+	8.76007i	0.662723	+	0.481497i	−0.204858	+	0.978792i	$0.565673\pi$
$332$	−0.562334			−0.0308621
$333$	−0.818804	−	0.594896i	−0.0448702	−	0.0326001i
$334$	4.67540	−	14.3894i	0.255827	−	0.787353i
$335$	−6.79583	−	8.60107i	−0.371296	−	0.469927i
$336$	1.16388	+	3.58205i	0.0634948	+	0.195417i
$337$	−0.951550	+	2.92857i	−0.0518342	+	0.159529i	−0.973623	−	0.228164i	$-0.926728\pi$
$337$	−0.951550	+	2.92857i	−0.0518342	+	0.159529i	0.921789	+	0.387693i	$0.126728\pi$
$338$	0.491587	−	1.51295i	0.0267388	−	0.0822936i
$339$	0.0985361	+	0.303263i	0.00535174	+	0.0164710i
$340$	4.90534	+	1.37765i	0.266029	+	0.0747134i
$341$	9.71704	−	29.9060i	0.526207	−	1.61950i
$342$	8.74304	+	6.35219i	0.472770	+	0.343487i
$343$	−10.5426			−0.569247
$344$	−12.7386	−	9.25513i	−0.686819	−	0.499003i
$345$	10.7688	+	13.6294i	0.579772	+	0.733783i
$346$	9.08083	−	6.59761i	0.488188	−	0.354690i
$347$	−14.8111	+	10.7609i	−0.795102	+	0.577675i	−0.909473	−	0.415763i	$-0.863515\pi$
$347$	−14.8111	+	10.7609i	−0.795102	+	0.577675i	0.114371	+	0.993438i	$0.463515\pi$
$348$	1.72339	+	5.30404i	0.0923833	+	0.284327i
$349$	8.31201			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$349$	8.31201			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$350$	−1.44981	+	6.09774i	−0.0774958	+	0.325938i
$351$	−1.00000			−0.0533761
$352$	3.76567	+	11.5895i	0.200711	+	0.617724i
$353$	−3.53676	+	2.56961i	−0.188243	+	0.136766i	−0.677915	−	0.735140i	$-0.737116\pi$
$353$	−3.53676	+	2.56961i	−0.188243	+	0.136766i	0.489672	+	0.871906i	$0.337116\pi$
$354$	−6.24795	+	4.53940i	−0.332075	+	0.241266i
$355$	7.45660	−	2.76017i	0.395755	−	0.146495i
$356$	−2.47085	−	1.79518i	−0.130955	−	0.0951443i
$357$	3.38348			0.179073
$358$	−17.8631	−	12.9783i	−0.944094	−	0.685924i
$359$	−4.44454	+	13.6789i	−0.234574	+	0.721943i	0.762604	+	0.646866i	$0.223921\pi$
$359$	−4.44454	+	13.6789i	−0.234574	+	0.721943i	−0.997178	+	0.0750778i	$0.976079\pi$
$360$	−4.90159	+	1.81440i	−0.258336	+	0.0956271i
$361$	8.38988	+	25.8214i	0.441573	+	1.35902i
$362$	11.8956	−	36.6109i	0.625220	−	1.92423i
$363$	−1.95040	+	6.00272i	−0.102370	+	0.315061i
$364$	0.129221	+	0.397700i	0.00677300	+	0.0208451i
$365$	0.128096	+	3.17167i	0.00670483	+	0.166013i
$366$	1.61504	−	4.97057i	0.0844193	−	0.259816i
$367$	9.61211	+	6.98361i	0.501748	+	0.364541i	0.809684	−	0.586866i	$-0.199638\pi$
$367$	9.61211	+	6.98361i	0.501748	+	0.364541i	−0.307936	+	0.951407i	$0.599638\pi$
$368$	37.1301			1.93554
$369$	−7.51122	−	5.45722i	−0.391019	−	0.284092i
$370$	−3.46609	−	0.973440i	−0.180193	−	0.0506068i
$371$	−6.40777	+	4.65552i	−0.332675	+	0.241702i
$372$	−3.24465	+	2.35737i	−0.168227	+	0.122224i
$373$	−2.02655	−	6.23708i	−0.104931	−	0.322944i	0.884783	−	0.466002i	$-0.154306\pi$
$373$	−2.02655	−	6.23708i	−0.104931	−	0.322944i	−0.989714	+	0.143059i	$0.954306\pi$
$374$	28.4203			1.46958
$375$	−10.9726	−	2.14512i	−0.566624	−	0.110774i
$376$	9.78446			0.504595
$377$	−3.24755	−	9.99493i	−0.167257	−	0.514765i
$378$	1.01414	−	0.736816i	0.0521617	−	0.0378977i
$379$	23.9637	−	17.4107i	1.23093	−	0.894325i	0.233973	−	0.972243i	$-0.424827\pi$
$379$	23.9637	−	17.4107i	1.23093	−	0.894325i	0.996960	+	0.0779178i	$0.0248272\pi$
$380$	7.76093	+	2.17963i	0.398127	+	0.111813i
$381$	0.514552	+	0.373844i	0.0263613	+	0.0191526i
$382$	36.2984			1.85719
$383$	27.3820	+	19.8942i	1.39915	+	1.01654i	0.994790	+	0.101946i	$0.0325069\pi$
$383$	27.3820	+	19.8942i	1.39915	+	1.01654i	0.404364	+	0.914598i	$0.367493\pi$
$384$	−4.21902	+	12.9848i	−0.215301	+	0.662629i
$385$	0.295848	+	7.32524i	0.0150778	+	0.373329i
$386$	4.65529	+	14.3275i	0.236948	+	0.729252i
$387$	−2.08166	+	6.40669i	−0.105817	+	0.325670i
$388$	1.99736	−	6.14726i	0.101401	−	0.312080i
$389$	6.83771	+	21.0443i	0.346685	+	1.06699i	0.960675	+	0.277674i	$0.0895635\pi$
$389$	6.83771	+	21.0443i	0.346685	+	1.06699i	−0.613990	+	0.789314i	$0.710436\pi$
$390$	−3.33594	+	1.23485i	−0.168922	+	0.0625290i
$391$	10.3073	−	31.7228i	0.521265	−	1.60429i
$392$	−12.0629	−	8.76420i	−0.609268	−	0.442659i
$393$	−3.37047			−0.170018
$394$	−21.1339	−	15.3547i	−1.06471	−	0.773558i
$395$	3.26823	−	1.20978i	0.164442	−	0.0608708i
$396$	1.78630	−	1.29782i	0.0897649	−	0.0652180i
$397$	21.9154	−	15.9225i	1.09990	−	0.799126i	0.118859	−	0.992911i	$-0.462076\pi$
$397$	21.9154	−	15.9225i	1.09990	−	0.799126i	0.981044	+	0.193785i	$0.0620764\pi$
$398$	−3.21619	−	9.89843i	−0.161213	−	0.496163i
$399$	5.35314			0.267992
$400$	−18.1386	+	15.5607i	−0.906932	+	0.778036i
$401$	−17.5844			−0.878125			−0.439063	−	0.898456i	$-0.644689\pi$
$401$	−17.5844			−0.878125			−0.439063	+	0.898456i	$0.644689\pi$
$402$	2.40990	+	7.41690i	0.120195	+	0.369921i
$403$	6.11421	−	4.44223i	0.304570	−	0.221283i
$404$	1.86591	−	1.35566i	0.0928325	−	0.0674468i
$405$	1.38626	+	1.75450i	0.0688838	+	0.0871820i
$406$	10.6579	+	7.74341i	0.528942	+	0.384299i
$407$	−4.21106			−0.208734
$408$	8.11963	+	5.89925i	0.401981	+	0.292057i
$409$	−3.28557	+	10.1120i	−0.162461	+	0.500004i	−0.998840	−	0.0481475i	$-0.984668\pi$
$409$	−3.28557	+	10.1120i	−0.162461	+	0.500004i	0.836379	+	0.548151i	$0.184668\pi$
$410$	−31.7958	−	8.92976i	−1.57028	−	0.441009i
$411$	5.95641	+	18.3320i	0.293808	+	0.904249i
$412$	1.45111	−	4.46606i	0.0714910	−	0.220027i
$413$	−1.18213	+	3.63823i	−0.0581689	+	0.179025i
$414$	−3.81877	−	11.7530i	−0.187682	−	0.577626i
$415$	−1.46896	−	1.85918i	−0.0721086	−	0.0912635i
$416$	−0.905051	+	2.78546i	−0.0443738	+	0.136568i
$417$	−17.8040	−	12.9354i	−0.871866	−	0.633447i
$418$	44.9649			2.19931
$419$	5.98319	+	4.34704i	0.292298	+	0.212367i	0.724264	−	0.689523i	$-0.242180\pi$
$419$	5.98319	+	4.34704i	0.292298	+	0.212367i	−0.431966	+	0.901890i	$0.642180\pi$
$420$	0.518633	−	0.778033i	0.0253067	−	0.0379641i
$421$	−15.3634	+	11.1621i	−0.748764	+	0.544009i	−0.895444	−	0.445175i	$-0.853141\pi$
$421$	−15.3634	+	11.1621i	−0.748764	+	0.544009i	0.146679	+	0.989184i	$0.453141\pi$
$422$	−7.27529	+	5.28581i	−0.354156	+	0.257309i
$423$	−1.29355	−	3.98114i	−0.0628945	−	0.193569i
$424$	−23.4944			−1.14099
$425$	8.25928	+	19.8167i	0.400634	+	0.961252i
$426$	−5.65664			−0.274065
$427$	−0.799994	−	2.46213i	−0.0387144	−	0.119151i
$428$	−1.10322	+	0.801539i	−0.0533263	+	0.0387438i
$429$	−3.36610	+	2.44561i	−0.162517	+	0.118075i
$430$	0.966993	+	23.9429i	0.0466326	+	1.15463i
$431$	29.7999	+	21.6509i	1.43541	+	1.04289i	0.988977	+	0.148069i	$0.0473057\pi$
$431$	29.7999	+	21.6509i	1.43541	+	1.04289i	0.446433	+	0.894817i	$0.352694\pi$
$432$	4.77973			0.229965
$433$	24.0650	+	17.4842i	1.15649	+	0.840238i	0.989330	−	0.145692i	$-0.0465409\pi$
$433$	24.0650	+	17.4842i	1.15649	+	0.840238i	0.167158	+	0.985930i	$0.446541\pi$
$434$	−2.92756	+	9.01009i	−0.140527	+	0.432498i
$435$	−13.0342	+	19.5534i	−0.624942	+	0.937514i
$436$	−1.78127	−	5.48218i	−0.0853074	−	0.262549i
$437$	16.3077	−	50.1899i	0.780102	−	2.40091i
$438$	0.697841	−	2.14774i	0.0333442	−	0.102623i
$439$	4.67822	+	14.3981i	0.223279	+	0.687183i	0.998462	+	0.0554457i	$0.0176580\pi$
$439$	4.67822	+	14.3981i	0.223279	+	0.687183i	−0.775182	+	0.631738i	$0.782342\pi$
$440$	−12.0619	+	18.0948i	−0.575029	+	0.862637i
$441$	−1.97124	+	6.06685i	−0.0938686	+	0.288898i
$442$	5.52609	+	4.01494i	0.262849	+	0.190971i
$443$	−28.0187			−1.33121			−0.665605	−	0.746304i	$-0.731826\pi$
$443$	−28.0187			−1.33121			−0.665605	+	0.746304i	$0.731826\pi$
$444$	0.434518	+	0.315696i	0.0206213	+	0.0149822i
$445$	−0.519326	−	12.8586i	−0.0246184	−	0.609555i
$446$	0.504225	−	0.366341i	0.0238758	−	0.0173468i
$447$	−6.74507	+	4.90058i	−0.319031	+	0.231790i
$448$	1.19324	+	3.67240i	0.0563751	+	0.173505i
$449$	17.8405			0.841947			0.420973	−	0.907073i	$-0.361689\pi$
$449$	17.8405			0.841947			0.420973	+	0.907073i	$0.361689\pi$
$450$	6.79103	+	4.14111i	0.320132	+	0.195214i
$451$	−38.6297			−1.81900
$452$	−0.0522905	−	0.160934i	−0.00245954	−	0.00756968i
$453$	15.7809	−	11.4655i	0.741452	−	0.538697i
$454$	−18.1317	+	13.1735i	−0.850963	+	0.618261i
$455$	−0.977312	+	1.46612i	−0.0458171	+	0.0687330i
$456$	12.8464	+	9.33345i	0.601587	+	0.437079i
$457$	−18.0977			−0.846574			−0.423287	−	0.905996i	$-0.639124\pi$
$457$	−18.0977			−0.846574			−0.423287	+	0.905996i	$0.639124\pi$
$458$	25.7503	+	18.7087i	1.20323	+	0.874200i
$459$	1.32686	−	4.08365i	0.0619324	−	0.190608i
$460$	−5.71471	−	7.23277i	−0.266450	−	0.337229i
$461$	−8.05528	−	24.7916i	−0.375172	−	1.15466i	−0.943363	−	0.331763i	$-0.892357\pi$
$461$	−8.05528	−	24.7916i	−0.375172	−	1.15466i	0.568191	−	0.822897i	$-0.307643\pi$
$462$	1.61173	−	4.96039i	0.0749843	−	0.230778i
$463$	−6.14938	+	18.9258i	−0.285786	+	0.879559i	0.700376	+	0.713774i	$0.253016\pi$
$463$	−6.14938	+	18.9258i	−0.285786	+	0.879559i	−0.986162	+	0.165785i	$0.946984\pi$
$464$	15.5224	+	47.7731i	0.720610	+	2.21781i
$465$	−16.2698	−	4.56932i	−0.754494	−	0.211897i
$466$	−6.09085	+	18.7457i	−0.282153	+	0.868378i
$467$	25.9689	+	18.8675i	1.20170	+	0.873084i	0.994451	−	0.105204i	$-0.0335496\pi$
$467$	25.9689	+	18.8675i	1.20170	+	0.873084i	0.207247	+	0.978289i	$0.433550\pi$
$468$	0.530673			0.0245304
$469$	3.12520	+	2.27059i	0.144308	+	0.104846i
$470$	−9.23131	−	11.6835i	−0.425808	−	0.538920i
$471$	16.3996	−	11.9150i	0.755655	−	0.549016i
$472$	−9.18027	+	6.66986i	−0.422556	+	0.307005i
$473$	8.66122	+	26.6565i	0.398243	+	1.22567i
$474$	−2.47930			−0.113878
$475$	13.0673	+	31.3528i	0.599570	+	1.43857i
$476$	−1.79552			−0.0822977
$477$	3.10606	+	9.55947i	0.142217	+	0.437698i
$478$	−19.2482	+	13.9846i	−0.880391	+	0.639641i
$479$	−3.45725	+	2.51184i	−0.157966	+	0.114769i	−0.663960	−	0.747768i	$-0.731126\pi$
$479$	−3.45725	+	2.51184i	−0.157966	+	0.114769i	0.505994	+	0.862537i	$0.331126\pi$
$480$	6.14174	−	2.27345i	0.280331	−	0.103769i
$481$	−0.818804	−	0.594896i	−0.0373343	−	0.0271249i
$482$	1.61538			0.0735786
$483$	−4.95225	−	3.59802i	−0.225335	−	0.163715i
$484$	1.03503	−	3.18548i	0.0470466	−	0.144795i
$485$	25.5416	−	9.45460i	1.15978	−	0.429311i
$486$	−0.491587	−	1.51295i	−0.0222988	−	0.0686288i
$487$	1.14232	−	3.51570i	0.0517634	−	0.159311i	−0.921833	−	0.387587i	$-0.873309\pi$
$487$	1.14232	−	3.51570i	0.0517634	−	0.159311i	0.973597	+	0.228276i	$0.0733087\pi$
$488$	2.37302	−	7.30340i	0.107421	−	0.330609i
$489$	3.22466	+	9.92448i	0.145824	+	0.448800i
$490$	0.915700	+	22.6729i	0.0413671	+	1.02426i
$491$	5.16872	−	15.9077i	0.233261	−	0.717904i	−0.764086	−	0.645114i	$-0.776810\pi$
$491$	5.16872	−	15.9077i	0.233261	−	0.717904i	0.997347	−	0.0727899i	$-0.0231903\pi$
$492$	3.98600	+	2.89600i	0.179703	+	0.130562i
$493$	45.1248			2.03232
$494$	8.74304	+	6.35219i	0.393368	+	0.285799i
$495$	8.95712	+	2.51558i	0.402593	+	0.113067i
$496$	−29.2243	+	21.2327i	−1.31221	+	0.953376i
$497$	−2.26683	+	1.64695i	−0.101681	+	0.0738759i
$498$	0.520916	+	1.60321i	0.0233428	+	0.0718417i
$499$	−34.9395			−1.56411			−0.782053	−	0.623212i	$-0.785827\pi$
$499$	−34.9395			−1.56411			−0.782053	+	0.623212i	$0.785827\pi$
$500$	5.82288	+	1.13836i	0.260407	+	0.0509090i
$501$	−9.51083			−0.424912
$502$	−12.0246	−	37.0078i	−0.536682	−	1.65174i
$503$	−25.4898	+	18.5194i	−1.13653	+	0.825739i	−0.986632	−	0.162962i	$-0.947895\pi$
$503$	−25.4898	+	18.5194i	−1.13653	+	0.825739i	−0.149900	+	0.988701i	$0.547895\pi$
$504$	1.49010	−	1.08262i	0.0663744	−	0.0482238i
$505$	9.35633	+	2.62769i	0.416351	+	0.116931i
$506$	−41.5975	−	30.2224i	−1.84923	−	1.34355i
$507$	−1.00000			−0.0444116
$508$	−0.273059	−	0.198389i	−0.0121150	−	0.00880209i
$509$	10.4145	−	32.0526i	0.461615	−	1.42070i	−0.401576	−	0.915826i	$-0.631537\pi$
$509$	10.4145	−	32.0526i	0.461615	−	1.42070i	0.863190	−	0.504879i	$-0.168463\pi$
$510$	−0.616365	−	15.2613i	−0.0272931	−	0.675781i
$511$	−0.345669	−	1.06386i	−0.0152915	−	0.0470624i
$512$	−2.57892	+	7.93710i	−0.113973	+	0.350773i
$513$	2.09927	−	6.46090i	0.0926853	−	0.285256i
$514$	−3.70984	−	11.4177i	−0.163634	−	0.503613i
$515$	18.5563	−	6.86888i	0.817688	−	0.302679i
$516$	1.10468	−	3.39986i	0.0486309	−	0.149671i
$517$	−14.0905	−	10.2374i	−0.619701	−	0.450239i
$518$	1.26871			0.0557439
$519$	−5.70831	−	4.14733i	−0.250567	−	0.182047i
$520$	−4.90159	+	1.81440i	−0.214949	+	0.0795665i
$521$	20.7918	−	15.1062i	0.910907	−	0.661813i	−0.0303369	−	0.999540i	$-0.509658\pi$
$521$	20.7918	−	15.1062i	0.910907	−	0.661813i	0.941244	+	0.337727i	$0.109658\pi$
$522$	13.5254	−	9.82676i	0.591989	−	0.430105i
$523$	3.56739	+	10.9793i	0.155991	+	0.480091i	0.998260	−	0.0589664i	$-0.0187805\pi$
$523$	3.56739	+	10.9793i	0.155991	+	0.480091i	−0.842269	+	0.539058i	$0.818780\pi$
$524$	1.78862			0.0781361
$525$	3.92713	−	0.317732i	0.171394	−	0.0138670i
$526$	−37.9877			−1.65634
$527$	10.0278	+	30.8625i	0.436819	+	1.34439i
$528$	16.0890	−	11.6894i	0.700186	−	0.508715i
$529$	−30.2132	+	21.9512i	−1.31362	+	0.954399i
$530$	22.1661	+	28.0543i	0.962835	+	1.21860i
$531$	3.92753	+	2.85352i	0.170440	+	0.123832i
$532$	−2.84077			−0.123163
$533$	−7.51122	−	5.45722i	−0.325347	−	0.236378i
$534$	−2.82919	+	8.70735i	−0.122431	+	0.376804i
$535$	−5.53195	−	1.55363i	−0.239167	−	0.0671693i
$536$	3.54092	+	10.8978i	0.152945	+	0.470715i
$537$	−4.28907	+	13.2004i	−0.185087	+	0.569639i
$538$	−1.81688	+	5.59178i	−0.0783313	+	0.241079i
$539$	8.20179	+	25.2425i	0.353276	+	1.08727i
$540$	−0.735651	−	0.931069i	−0.0316574	−	0.0400668i
$541$	−5.55678	+	17.1020i	−0.238905	+	0.735273i	0.757675	+	0.652632i	$0.226335\pi$
$541$	−5.55678	+	17.1020i	−0.238905	+	0.735273i	−0.996579	+	0.0826405i	$0.973665\pi$
$542$	24.4816	+	17.7869i	1.05157	+	0.764014i
$543$	−24.1984			−1.03845
$544$	−10.1740	−	7.39182i	−0.436205	−	0.316922i
$545$	13.4720	−	20.2101i	0.577076	−	0.865707i
$546$	1.01414	−	0.736816i	0.0434012	−	0.0315328i
$547$	13.9656	−	10.1466i	0.597125	−	0.433836i	−0.247732	−	0.968828i	$-0.579685\pi$
$547$	13.9656	−	10.1466i	0.597125	−	0.433836i	0.844857	+	0.534992i	$0.179685\pi$
$548$	−3.16091	−	9.72828i	−0.135027	−	0.415572i
$549$	−3.28535			−0.140215
$550$	32.9868	−	2.66886i	1.40656	−	0.113801i
$551$	71.3938			3.04148
$552$	−5.61101	−	17.2689i	−0.238821	−	0.735014i
$553$	−0.993554	+	0.721859i	−0.0422502	+	0.0306966i
$554$	35.4506	−	25.7563i	1.50615	−	1.09428i
$555$	0.0913272	+	2.26128i	0.00387663	+	0.0959858i
$556$	9.44811	+	6.86445i	0.400689	+	0.291118i
$557$	27.1617			1.15088			0.575439	−	0.817845i	$-0.304831\pi$
$557$	27.1617			1.15088			0.575439	+	0.817845i	$0.304831\pi$
$558$	9.72654	+	7.06674i	0.411757	+	0.299159i
$559$	−2.08166	+	6.40669i	−0.0880448	+	0.270974i
$560$	4.67129	−	7.00768i	0.197398	−	0.296129i
$561$	−5.52069	−	16.9909i	−0.233084	−	0.717358i
$562$	−4.21927	+	12.9856i	−0.177979	+	0.547763i
$563$	−2.73269	+	8.41034i	−0.115169	+	0.354454i	−0.991982	−	0.126377i	$-0.959665\pi$
$563$	−2.73269	+	8.41034i	−0.115169	+	0.354454i	0.876813	+	0.480831i	$0.159665\pi$
$564$	0.686452	+	2.11268i	0.0289049	+	0.0889600i
$565$	0.395479	−	0.593283i	0.0166379	−	0.0249596i
$566$	−8.42137	+	25.9183i	−0.353976	+	1.08943i
$567$	−0.637499	−	0.463170i	−0.0267725	−	0.0194513i
$568$	−8.31145			−0.348741
$569$	−28.1105	−	20.4235i	−1.17845	−	0.856196i	−0.186456	−	0.982463i	$-0.559700\pi$
$569$	−28.1105	−	20.4235i	−1.17845	−	0.856196i	−0.991996	+	0.126267i	$0.959700\pi$
$570$	−0.975176	−	24.1455i	−0.0408456	−	1.01134i
$571$	−22.0583	+	16.0263i	−0.923111	+	0.670679i	−0.944296	−	0.329096i	$-0.893256\pi$
$571$	−22.0583	+	16.0263i	−0.923111	+	0.670679i	0.0211853	+	0.999776i	$0.493256\pi$
$572$	1.78630	−	1.29782i	0.0746889	−	0.0542646i
$573$	−7.05102	−	21.7008i	−0.294561	−	0.906564i
$574$	11.6384			0.485777
$575$	8.98452	−	37.7878i	0.374680	−	1.57586i
$576$	4.90029			0.204179
$577$	4.99642	+	15.3774i	0.208004	+	0.640169i	0.999577	+	0.0290947i	$0.00926245\pi$
$577$	4.99642	+	15.3774i	0.208004	+	0.640169i	−0.791573	+	0.611075i	$0.790738\pi$
$578$	−1.84906	+	1.34342i	−0.0769109	+	0.0558790i
$579$	7.66133	−	5.56629i	0.318394	−	0.231327i
$580$	6.91690	−	10.3765i	0.287209	−	0.430860i
$581$	0.675533	+	0.490803i	0.0280258	+	0.0203620i
$582$	−19.3761			−0.803164
$583$	33.8340	+	24.5819i	1.40126	+	1.01808i
$584$	1.02536	−	3.15572i	0.0424296	−	0.130585i
$585$	1.38626	+	1.75450i	0.0573148	+	0.0725398i
$586$	11.0534	+	34.0189i	0.456612	+	1.40531i
$587$	−4.10684	+	12.6396i	−0.169508	+	0.521691i	−0.999340	−	0.0363217i	$-0.988436\pi$
$587$	−4.10684	+	12.6396i	−0.169508	+	0.521691i	0.829833	+	0.558013i	$0.188436\pi$
$588$	1.04608	−	3.21952i	0.0431398	−	0.132771i
$589$	15.8654	+	48.8288i	0.653724	+	2.01196i
$590$	16.6257	+	4.66926i	0.684468	+	0.192231i
$591$	−5.07442	+	15.6175i	−0.208734	+	0.642417i
$592$	3.91367	+	2.84344i	0.160851	+	0.116865i
$593$	−28.9936			−1.19063			−0.595313	−	0.803494i	$-0.702972\pi$
$593$	−28.9936			−1.19063			−0.595313	+	0.803494i	$0.702972\pi$
$594$	−5.35482	−	3.89050i	−0.219711	−	0.159629i
$595$	−4.69038	−	5.93634i	−0.192287	−	0.243366i
$596$	3.57943	−	2.60061i	0.146619	−	0.106525i
$597$	−5.29297	+	3.84557i	−0.216627	+	0.157389i
$598$	−3.81877	−	11.7530i	−0.156161	−	0.480614i
$599$	−34.5402			−1.41127			−0.705637	−	0.708573i	$-0.749339\pi$
$599$	−34.5402			−1.41127			−0.705637	+	0.708573i	$0.749339\pi$
$600$	9.97824	+	6.08464i	0.407360	+	0.248404i
$601$	25.7660			1.05102			0.525508	−	0.850789i	$-0.323875\pi$
$601$	25.7660			1.05102			0.525508	+	0.850789i	$0.323875\pi$
$602$	−2.60946	−	8.03108i	−0.106353	−	0.327322i
$603$	3.96603	−	2.88149i	0.161509	−	0.117343i
$604$	−8.37452	+	6.08444i	−0.340754	+	0.247572i
$605$	13.2356	−	4.89934i	0.538102	−	0.199186i
$606$	−5.59347	−	4.06390i	−0.227219	−	0.165085i
$607$	−29.5779			−1.20053			−0.600265	−	0.799801i	$-0.704938\pi$
$607$	−29.5779			−1.20053			−0.600265	+	0.799801i	$0.704938\pi$
$608$	−16.0966	−	11.6949i	−0.652805	−	0.474290i
$609$	2.55904	−	7.87593i	0.103698	−	0.319149i
$610$	−10.9598	+	4.05691i	−0.443747	+	0.164260i
$611$	−1.29355	−	3.98114i	−0.0523314	−	0.161060i
$612$	−0.704128	+	2.16708i	−0.0284627	+	0.0875992i
$613$	4.22649	−	13.0078i	0.170706	−	0.525380i	−0.828705	−	0.559685i	$-0.810922\pi$
$613$	4.22649	−	13.0078i	0.170706	−	0.525380i	0.999411	+	0.0343057i	$0.0109220\pi$
$614$	−13.4769	−	41.4777i	−0.543884	−	1.67390i
$615$	0.837781	+	20.7436i	0.0337826	+	0.836462i
$616$	2.36815	−	7.28843i	0.0954156	−	0.293659i
$617$	0.863020	+	0.627021i	0.0347439	+	0.0252429i	0.605022	−	0.796209i	$-0.293164\pi$
$617$	0.863020	+	0.627021i	0.0347439	+	0.0252429i	−0.570278	+	0.821452i	$0.693164\pi$
$618$	−14.0769			−0.566258
$619$	−34.9805	−	25.4148i	−1.40599	−	1.02151i	−0.993891	−	0.110367i	$-0.964797\pi$
$619$	−34.9805	−	25.4148i	−1.40599	−	1.02151i	−0.412094	−	0.911141i	$-0.635203\pi$
$620$	8.63395	+	2.42482i	0.346748	+	0.0973830i
$621$	−6.28464	+	4.56606i	−0.252194	+	0.183230i
$622$	5.87784	−	4.27050i	0.235680	−	0.171232i
$623$	1.40141	+	4.31311i	0.0561464	+	0.172801i
$624$	4.77973			0.191342
$625$	11.4473	+	22.2252i	0.457891	+	0.889008i
$626$	−10.8860			−0.435092
$627$	−8.73451	−	26.8820i	−0.348823	−	1.07357i
$628$	−8.70285	+	6.32299i	−0.347281	+	0.252315i
$629$	3.51578	−	2.55437i	0.140183	−	0.101849i
$630$	−2.69861	−	0.757895i	−0.107515	−	0.0301953i
$631$	14.0810	+	10.2305i	0.560556	+	0.407268i	0.831662	−	0.555282i	$-0.187390\pi$
$631$	14.0810	+	10.2305i	0.560556	+	0.407268i	−0.271106	+	0.962549i	$0.587390\pi$
$632$	−3.64291			−0.144907
$633$	4.57333	+	3.32272i	0.181773	+	0.132066i
$634$	15.0213	−	46.2308i	0.596572	−	1.83606i
$635$	−0.0573917	−	1.42103i	−0.00227752	−	0.0563918i
$636$	−1.64830	−	5.07295i	−0.0653595	−	0.201156i
$637$	−1.97124	+	6.06685i	−0.0781034	+	0.240378i
$638$	21.4953	−	66.1556i	0.851006	−	2.61913i
$639$	1.09881	+	3.38179i	0.0434682	+	0.133782i
$640$	28.6306	−	10.5980i	1.13172	−	0.418924i
$641$	−2.12842	+	6.55061i	−0.0840677	+	0.258734i	−0.984251	−	0.176778i	$-0.943433\pi$
$641$	−2.12842	+	6.55061i	−0.0840677	+	0.258734i	0.900183	+	0.435512i	$0.143433\pi$
$642$	3.30715	+	2.40279i	0.130523	+	0.0948305i
$643$	−38.9186			−1.53480			−0.767400	−	0.641169i	$-0.778450\pi$
$643$	−38.9186			−1.53480			−0.767400	+	0.641169i	$0.778450\pi$
$644$	2.62803	+	1.90937i	0.103559	+	0.0752398i
$645$	14.1263	−	5.22905i	0.556222	−	0.205894i
$646$	−37.5409	+	27.2751i	−1.47703	+	1.07312i
$647$	−14.3546	+	10.4292i	−0.564337	+	0.410015i	−0.833044	−	0.553207i	$-0.813404\pi$
$647$	−14.3546	+	10.4292i	−0.564337	+	0.410015i	0.268707	+	0.963222i	$0.413404\pi$
$648$	−0.722302	−	2.22302i	−0.0283747	−	0.0873283i
$649$	20.1990			0.792881
$650$	6.79103	+	4.14111i	0.266366	+	0.162428i
$651$	5.95531			0.233407
$652$	−1.71124	−	5.26666i	−0.0670174	−	0.206258i
$653$	−13.0732	+	9.49827i	−0.511596	+	0.371696i	−0.813429	−	0.581665i	$-0.802402\pi$
$653$	−13.0732	+	9.49827i	−0.511596	+	0.371696i	0.301833	+	0.953361i	$0.402402\pi$
$654$	−13.9796	+	10.1568i	−0.546647	+	0.397162i
$655$	4.67234	+	5.91350i	0.182564	+	0.231060i
$656$	35.9016	+	26.0841i	1.40172	+	1.01841i
$657$	−1.41957			−0.0553826
$658$	4.24520	+	3.08432i	0.165495	+	0.120239i
$659$	1.00739	−	3.10042i	0.0392422	−	0.120775i	−0.929516	−	0.368781i	$-0.879775\pi$
$659$	1.00739	−	3.10042i	0.0392422	−	0.120775i	0.968759	+	0.248006i	$0.0797752\pi$
$660$	−4.75331	−	1.33495i	−0.185022	−	0.0519629i
$661$	−1.91164	−	5.88342i	−0.0743541	−	0.228838i	0.906972	−	0.421192i	$-0.138388\pi$
$661$	−1.91164	−	5.88342i	−0.0743541	−	0.228838i	−0.981326	+	0.192353i	$0.938388\pi$
$662$	−7.32637	+	22.5483i	−0.284748	+	0.876363i
$663$	1.32686	−	4.08365i	0.0515309	−	0.158596i
$664$	0.765395	+	2.35564i	0.0297031	+	0.0914167i
$665$	−7.42085	−	9.39212i	−0.287768	−	0.364211i
$666$	0.497534	−	1.53125i	0.0192791	−	0.0593348i
$667$	−66.0471	−	47.9860i	−2.55735	−	1.85803i
$668$	5.04714			0.195280
$669$	−0.316962	−	0.230286i	−0.0122544	−	0.00890338i
$670$	9.67224	−	14.5099i	0.373671	−	0.560567i
$671$	−11.0588	+	8.03470i	−0.426921	+	0.310176i
$672$	−1.86711	+	1.35654i	−0.0720254	+	0.0523295i
$673$	6.18894	+	19.0476i	0.238566	+	0.734231i	0.996628	+	0.0820486i	$0.0261463\pi$
$673$	6.18894	+	19.0476i	0.238566	+	0.734231i	−0.758062	+	0.652182i	$0.773854\pi$
$674$	−4.89855			−0.188685
$675$	1.15657	−	4.86440i	0.0445164	−	0.187231i
$676$	0.530673			0.0204105
$677$	−13.2847	−	40.8862i	−0.510574	−	1.57139i	−0.791193	−	0.611567i	$-0.790540\pi$
$677$	−13.2847	−	40.8862i	−0.510574	−	1.57139i	0.280619	−	0.959819i	$-0.409460\pi$
$678$	−0.410382	+	0.298160i	−0.0157606	+	0.0114508i
$679$	−7.76475	+	5.64142i	−0.297984	+	0.216498i
$680$	−0.905641	−	22.4238i	−0.0347298	−	0.859914i
$681$	11.3978	+	8.28098i	0.436764	+	0.317328i
$682$	50.0230			1.91548
$683$	−9.09507	−	6.60795i	−0.348013	−	0.252846i	0.400022	−	0.916506i	$-0.369002\pi$
$683$	−9.09507	−	6.60795i	−0.348013	−	0.252846i	−0.748035	+	0.663659i	$0.769002\pi$
$684$	−1.11403	+	3.42863i	−0.0425960	+	0.131097i
$685$	23.9064	−	35.8634i	0.913415	−	1.37027i
$686$	−5.18261	−	15.9504i	−0.197873	−	0.608990i
$687$	6.18286	−	19.0289i	0.235891	−	0.725997i
$688$	9.94978	−	30.6223i	0.379332	−	1.16746i
$689$	3.10606	+	9.55947i	0.118331	+	0.364187i
$690$	−15.3268	+	22.9927i	−0.583482	+	0.875316i
$691$	−5.25411	+	16.1705i	−0.199876	+	0.615154i	0.800009	+	0.599988i	$0.204828\pi$
$691$	−5.25411	+	16.1705i	−0.199876	+	0.615154i	−0.999885	+	0.0151664i	$0.995172\pi$
$692$	3.02925	+	2.20088i	0.115155	+	0.0836648i
$693$	−3.27862			−0.124544
$694$	−23.5616	−	17.1185i	−0.894388	−	0.649811i
$695$	1.98581	+	49.1690i	0.0753261	+	1.86508i
$696$	19.8732	−	14.4387i	0.753291	−	0.547298i
$697$	32.2517	−	23.4322i	1.22162	−	0.887559i
$698$	4.08608	+	12.5757i	0.154660	+	0.475995i
$699$	12.3902			0.468639
$700$	−2.08402	+	0.168612i	−0.0787687	+	0.00637293i
$701$	1.21708			0.0459684			0.0229842	−	0.999736i	$-0.492683\pi$
$701$	1.21708			0.0459684			0.0229842	+	0.999736i	$0.492683\pi$
$702$	−0.491587	−	1.51295i	−0.0185538	−	0.0571026i
$703$	5.56246	−	4.04136i	0.209792	−	0.152423i
$704$	16.4949	−	11.9842i	0.621674	−	0.451672i
$705$	−5.19172	+	7.78842i	−0.195532	+	0.293329i
$706$	−5.62631	−	4.08776i	−0.211749	−	0.153845i
$707$	−3.42474			−0.128801
$708$	−2.08423	−	1.51428i	−0.0783303	−	0.0569103i
$709$	−3.20288	+	9.85747i	−0.120287	+	0.370205i	−0.993013	−	0.118005i	$-0.962350\pi$
$709$	−3.20288	+	9.85747i	−0.120287	+	0.370205i	0.872726	+	0.488210i	$0.162350\pi$
$710$	7.84156	+	9.92459i	0.294289	+	0.372463i
$711$	0.481609	+	1.48224i	0.0180617	+	0.0555883i
$712$	−4.15701	+	12.7939i	−0.155790	+	0.479473i
$713$	18.1421	−	55.8357i	0.679427	−	2.09106i
$714$	1.66328	+	5.11904i	0.0622466	+	0.191575i
$715$	8.95712	+	2.51558i	0.334977	+	0.0940773i
$716$	2.27610	−	7.00510i	0.0850617	−	0.261793i
$717$	12.0996	+	8.79088i	0.451868	+	0.328301i
$718$	−22.8803			−0.853886
$719$	−15.0378	−	10.9256i	−0.560816	−	0.407457i	0.270942	−	0.962596i	$-0.412665\pi$
$719$	−15.0378	−	10.9256i	−0.560816	−	0.407457i	−0.831757	+	0.555139i	$0.812665\pi$
$720$	−6.62595	−	8.38606i	−0.246935	−	0.312530i
$721$	−5.64118	+	4.09856i	−0.210089	+	0.152638i
$722$	−34.9421	+	25.3869i	−1.30041	+	0.944804i
$723$	−0.313790	−	0.965747i	−0.0116700	−	0.0359165i
$724$	12.8414			0.477248
$725$	52.3753	−	4.23753i	1.94517	−	0.157378i
$726$	−10.0406			−0.372642
$727$	8.18963	+	25.2051i	0.303736	+	0.934804i	0.980146	+	0.198279i	$0.0635351\pi$
$727$	8.18963	+	25.2051i	0.303736	+	0.934804i	−0.676409	+	0.736526i	$0.736465\pi$
$728$	1.49010	−	1.08262i	0.0552269	−	0.0401247i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−4.73560	+	1.75295i	−0.175272	+	0.0648797i
$731$	−23.4006	−	17.0015i	−0.865503	−	0.628825i
$732$	1.74345			0.0644398
$733$	9.58690	+	6.96529i	0.354100	+	0.257269i	0.750587	−	0.660771i	$-0.229771\pi$
$733$	9.58690	+	6.96529i	0.354100	+	0.257269i	−0.396487	+	0.918040i	$0.629771\pi$
$734$	−5.84066	+	17.9757i	−0.215583	+	0.663495i
$735$	13.3770	−	4.95168i	0.493417	−	0.182646i
$736$	7.03065	+	21.6381i	0.259153	+	0.797592i
$737$	6.30303	−	19.3987i	0.232175	−	0.714561i
$738$	4.56408	−	14.0468i	0.168006	−	0.517070i
$739$	−11.3003	−	34.7789i	−0.415690	−	1.27936i	−0.911633	−	0.411006i	$-0.865177\pi$
$739$	−11.3003	−	34.7789i	−0.415690	−	1.27936i	0.495943	−	0.868355i	$-0.334823\pi$
$740$	−0.0484649	−	1.20000i	−0.00178161	−	0.0441128i
$741$	2.09927	−	6.46090i	0.0771188	−	0.237347i
$742$	−10.1935	−	7.40604i	−0.374217	−	0.271884i
$743$	−6.28668			−0.230636			−0.115318	−	0.993329i	$-0.536789\pi$
$743$	−6.28668			−0.230636			−0.115318	+	0.993329i	$0.536789\pi$
$744$	14.2915	+	10.3834i	0.523950	+	0.380672i
$745$	17.9485	+	5.04078i	0.657583	+	0.184680i
$746$	8.44016	−	6.13214i	0.309016	−	0.224513i
$747$	0.857284	−	0.622853i	0.0313664	−	0.0227890i
$748$	2.92968	+	9.01664i	0.107120	+	0.329681i
$749$	2.02489			0.0739877
$750$	−2.14854	−	17.6555i	−0.0784535	−	0.644689i
$751$	−5.22576			−0.190691			−0.0953454	−	0.995444i	$-0.530396\pi$
$751$	−5.22576			−0.190691			−0.0953454	+	0.995444i	$0.530396\pi$
$752$	6.18282	+	19.0288i	0.225464	+	0.693908i
$753$	−19.7891	+	14.3776i	−0.721155	+	0.523950i
$754$	13.5254	−	9.82676i	0.492565	−	0.357869i
$755$	−41.9927	−	11.7935i	−1.52827	−	0.429210i
$756$	0.338304	+	0.245792i	0.0123040	+	0.00893937i
$757$	8.77818			0.319048			0.159524	−	0.987194i	$-0.449004\pi$
$757$	8.77818			0.319048			0.159524	+	0.987194i	$0.449004\pi$
$758$	38.1217	+	27.6970i	1.38464	+	1.00600i
$759$	−9.98790	+	30.7396i	−0.362538	+	1.11578i
$760$	−1.43285	−	35.4776i	−0.0519750	−	1.28691i
$761$	5.98815	+	18.4296i	0.217070	+	0.668074i	0.999000	+	0.0447073i	$0.0142355\pi$
$761$	5.98815	+	18.4296i	0.217070	+	0.668074i	−0.781930	+	0.623367i	$0.785764\pi$
$762$	−0.312660	+	0.962267i	−0.0113265	+	0.0348593i
$763$	−2.64499	+	8.14045i	−0.0957551	+	0.294704i
$764$	3.74179	+	11.5160i	0.135373	+	0.416636i
$765$	−9.00415	+	3.33302i	−0.325546	+	0.120506i
$766$	−16.6382	+	51.2073i	−0.601164	+	1.85019i
$767$	3.92753	+	2.85352i	0.141815	+	0.103034i
$768$	−11.9188			−0.430083
$769$	−25.1389	−	18.2645i	−0.906533	−	0.658634i	0.0336030	−	0.999435i	$-0.489302\pi$
$769$	−25.1389	−	18.2645i	−0.906533	−	0.658634i	−0.940136	+	0.340801i	$0.889302\pi$
$770$	−10.9373	+	4.04860i	−0.394153	+	0.145901i
$771$	−6.10537	+	4.43581i	−0.219880	+	0.159752i
$772$	−4.06567	+	2.95388i	−0.146327	+	0.106312i
$773$	−6.69044	−	20.5911i	−0.240638	−	0.740609i	−0.996323	−	0.0856736i	$-0.972696\pi$
$773$	−6.69044	−	20.5911i	−0.240638	−	0.740609i	0.755685	−	0.654936i	$-0.227304\pi$
$774$	−10.7163			−0.385190
$775$	14.5373	+	34.8797i	0.522194	+	1.25292i
$776$	−28.4698			−1.02201
$777$	−0.246449	−	0.758492i	−0.00884130	−	0.0272107i
$778$	−28.4776	+	20.6902i	−1.02097	+	0.741780i
$779$	51.0267	−	37.0731i	1.82822	−	1.32828i
$780$	−0.735651	−	0.931069i	−0.0263405	−	0.0333376i
$781$	11.9692	+	8.69617i	0.428293	+	0.311173i
$782$	53.0619			1.89749
$783$	−8.50219	−	6.17721i	−0.303844	−	0.220755i
$784$	9.42200	−	28.9979i	0.336500	−	1.03564i
$785$	−43.6391	−	12.2559i	−1.55755	−	0.437432i
$786$	−1.65688	−	5.09935i	−0.0590989	−	0.181888i
$787$	0.761310	−	2.34307i	0.0271378	−	0.0835215i	−0.936570	−	0.350480i	$-0.886019\pi$
$787$	0.761310	−	2.34307i	0.0271378	−	0.0835215i	0.963708	+	0.266958i	$0.0860186\pi$
$788$	2.69286	−	8.28777i	0.0959292	−	0.295240i
$789$	7.37917	+	22.7107i	0.262705	+	0.808524i
$790$	3.43696	+	4.34995i	0.122282	+	0.154764i
$791$	−0.0776457	+	0.238969i	−0.00276076	+	0.00849675i
$792$	−7.86798	−	5.71642i	−0.279576	−	0.203124i
$793$	−3.28535			−0.116666
$794$	34.8632	+	25.3296i	1.23725	+	0.898915i
$795$	12.4663	−	18.7015i	0.442135	−	0.663274i
$796$	2.80884	−	2.04074i	0.0995566	−	0.0723321i
$797$	13.1779	−	9.57430i	0.466785	−	0.339139i	−0.329402	−	0.944190i	$-0.606847\pi$
$797$	13.1779	−	9.57430i	0.466785	−	0.339139i	0.796187	+	0.605051i	$0.206847\pi$
$798$	2.63154	+	8.09904i	0.0931554	+	0.286703i
$799$	17.9739			0.635871
$800$	−12.5028	−	7.62410i	−0.442042	−	0.269553i
$801$	5.75522			0.203351
$802$	−8.64429	−	26.6044i	−0.305240	−	0.939433i
$803$	−4.77841	+	3.47171i	−0.168626	+	0.122514i
$804$	−2.10466	+	1.52913i	−0.0742258	+	0.0539282i
$805$	0.552360	+	13.6765i	0.0194681	+	0.482034i
$806$	9.72654	+	7.06674i	0.342603	+	0.248915i
$807$	3.69595			0.130104
$808$	−8.21864	−	5.97119i	−0.289131	−	0.210066i
$809$	11.8492	−	36.4680i	0.416595	−	1.28215i	−0.494222	−	0.869336i	$-0.664547\pi$
$809$	11.8492	−	36.4680i	0.416595	−	1.28215i	0.910817	−	0.412811i	$-0.135453\pi$
$810$	−1.97301	+	2.95983i	−0.0693245	+	0.103998i
$811$	8.40784	+	25.8767i	0.295239	+	0.908653i	0.983141	+	0.182849i	$0.0585320\pi$
$811$	8.40784	+	25.8767i	0.295239	+	0.908653i	−0.687902	+	0.725804i	$0.741468\pi$
$812$	−1.35802	+	4.17955i	−0.0476570	+	0.146673i
$813$	5.87823	−	18.0913i	0.206158	−	0.634491i
$814$	−2.07010	−	6.37112i	−0.0725571	−	0.223308i
$815$	12.9423	−	19.4156i	0.453350	−	0.680098i
$816$	−6.34202	+	19.5187i	−0.222015	+	0.683293i
$817$	−37.0230	−	26.8988i	−1.29527	−	0.941070i
$818$	−16.9140			−0.591385
$819$	−0.637499	−	0.463170i	−0.0222760	−	0.0161845i
$820$	−0.444588	−	11.0081i	−0.0155257	−	0.384419i
$821$	34.3829	−	24.9807i	1.19997	−	0.871831i	0.205690	−	0.978617i	$-0.434056\pi$
$821$	34.3829	−	24.9807i	1.19997	−	0.871831i	0.994282	+	0.106786i	$0.0340561\pi$
$822$	−24.8072	+	18.0235i	−0.865251	+	0.628642i
$823$	1.37523	+	4.23252i	0.0479375	+	0.147536i	0.972160	−	0.234318i	$-0.0752856\pi$
$823$	1.37523	+	4.23252i	0.0479375	+	0.147536i	−0.924223	+	0.381854i	$0.875286\pi$
$824$	−20.6836			−0.720549
$825$	−8.00330	−	19.2026i	−0.278639	−	0.668547i
$826$	−6.08557			−0.211744
$827$	8.41439	+	25.8968i	0.292597	+	0.900521i	0.984018	+	0.178069i	$0.0569850\pi$
$827$	8.41439	+	25.8968i	0.292597	+	0.900521i	−0.691421	+	0.722452i	$0.743015\pi$
$828$	3.33509	−	2.42309i	0.115902	−	0.0842080i
$829$	28.1424	−	20.4466i	0.977425	−	0.710141i	0.0202933	−	0.999794i	$-0.493540\pi$
$829$	28.1424	−	20.4466i	0.977425	−	0.710141i	0.957132	+	0.289653i	$0.0935400\pi$
$830$	2.09072	−	3.13642i	0.0725700	−	0.108867i
$831$	−22.2846	−	16.1907i	−0.773045	−	0.561650i
$832$	4.90029			0.169887
$833$	−22.1593	−	16.0997i	−0.767776	−	0.557822i
$834$	10.8183	−	33.2954i	0.374608	−	1.15293i
$835$	13.1845	+	16.6868i	0.456268	+	0.577470i
$836$	4.63517	+	14.2656i	0.160311	+	0.493386i
$837$	2.33542	−	7.18768i	0.0807239	−	0.248443i
$838$	−3.63559	+	11.1892i	−0.125590	+	0.386525i
$839$	−0.444077	−	1.36673i	−0.0153312	−	0.0471847i	0.943098	−	0.332514i	$-0.107897\pi$
$839$	−0.444077	−	1.36673i	−0.0153312	−	0.0471847i	−0.958429	+	0.285330i	$0.907897\pi$
$840$	−3.96513	−	1.11359i	−0.136810	−	0.0384227i
$841$	25.1679	−	77.4590i	0.867860	−	2.67100i
$842$	−24.4402	−	17.7568i	−0.842264	−	0.611941i
$843$	8.58295			0.295612
$844$	−2.42694	−	1.76328i	−0.0835388	−	0.0606945i
$845$	1.38626	+	1.75450i	0.0476888	+	0.0603568i
$846$	5.38736	−	3.91415i	0.185221	−	0.134571i
$847$	−4.02366	+	2.92336i	−0.138255	+	0.100448i
$848$	−14.8461	−	45.6917i	−0.509818	−	1.56906i
$849$	17.1310			0.587934
$850$	−25.9215	+	22.2375i	−0.889102	+	0.762740i
$851$	−7.86222			−0.269513
$852$	−0.583109	−	1.79463i	−0.0199770	−	0.0614829i
$853$	11.8682	−	8.62272i	0.406358	−	0.295236i	−0.365768	−	0.930706i	$-0.619194\pi$
$853$	11.8682	−	8.62272i	0.406358	−	0.295236i	0.772126	+	0.635470i	$0.219194\pi$
$854$	3.33181	−	2.42070i	0.114012	−	0.0828346i
$855$	−14.2458	+	5.27330i	−0.487197	+	0.180343i
$856$	4.85929	+	3.53048i	0.166087	+	0.120669i
$857$	−10.7784			−0.368183			−0.184091	−	0.982909i	$-0.558934\pi$
$857$	−10.7784			−0.368183			−0.184091	+	0.982909i	$0.558934\pi$
$858$	−5.35482	−	3.89050i	−0.182810	−	0.132820i
$859$	0.771435	−	2.37423i	0.0263210	−	0.0810078i	−0.937033	−	0.349241i	$-0.886440\pi$
$859$	0.771435	−	2.37423i	0.0263210	−	0.0810078i	0.963354	+	0.268233i	$0.0864396\pi$
$860$	−7.49645	+	2.77492i	−0.255627	+	0.0946240i
$861$	−2.26077	−	6.95795i	−0.0770470	−	0.237126i
$862$	−18.1074	+	55.7290i	−0.616742	+	1.89814i
$863$	11.9255	−	36.7028i	0.405948	−	1.24938i	−0.514153	−	0.857698i	$-0.671894\pi$
$863$	11.9255	−	36.7028i	0.405948	−	1.24938i	0.920101	−	0.391681i	$-0.128106\pi$
$864$	0.905051	+	2.78546i	0.0307905	+	0.0947633i
$865$	0.636689	+	15.7645i	0.0216481	+	0.536010i
$866$	−14.6227	+	45.0041i	−0.496900	+	1.52930i
$867$	1.16234	+	0.844491i	0.0394752	+	0.0286804i
$868$	−3.16033			−0.107268
$869$	5.24612	+	3.81153i	0.177963	+	0.129297i
$870$	−35.9908	−	10.1079i	−1.22020	−	0.342689i
$871$	3.96603	−	2.88149i	0.134384	−	0.0976355i
$872$	−20.5406	+	14.9237i	−0.695594	+	0.505379i
$873$	3.76383	+	11.5839i	0.127386	+	0.392055i
$874$	83.9513			2.83970
$875$	−6.00148	−	6.44971i	−0.202887	−	0.218040i
$876$	0.753327			0.0254526
$877$	−13.0918	−	40.2925i	−0.442079	−	1.36058i	−0.885655	−	0.464344i	$-0.846290\pi$
$877$	−13.0918	−	40.2925i	−0.442079	−	1.36058i	0.443576	−	0.896237i	$-0.353710\pi$
$878$	−19.4838	+	14.1558i	−0.657547	+	0.477736i
$879$	18.1909	−	13.2164i	0.613562	−	0.445779i
$880$	−42.8126	−	12.0238i	−1.44321	−	0.405322i
$881$	−17.2376	−	12.5238i	−0.580749	−	0.421939i	0.258245	−	0.966079i	$-0.416856\pi$
$881$	−17.2376	−	12.5238i	−0.580749	−	0.421939i	−0.838994	+	0.544141i	$0.816856\pi$
$882$	−10.1479			−0.341697
$883$	37.8283	+	27.4839i	1.27302	+	0.924906i	0.999319	−	0.0369077i	$-0.0117507\pi$
$883$	37.8283	+	27.4839i	1.27302	+	0.924906i	0.273705	+	0.961814i	$0.411751\pi$
$884$	−0.704128	+	2.16708i	−0.0236824	+	0.0728869i
$885$	−0.438066	−	10.8466i	−0.0147254	−	0.364604i
$886$	−13.7736	−	42.3909i	−0.462735	−	1.42415i
$887$	12.7779	−	39.3262i	0.429038	−	1.32044i	−0.470036	−	0.882647i	$-0.655759\pi$
$887$	12.7779	−	39.3262i	0.429038	−	1.32044i	0.899074	−	0.437797i	$-0.144241\pi$
$888$	0.731040	−	2.24991i	0.0245321	−	0.0755020i
$889$	0.154873	+	0.476650i	0.00519427	+	0.0159863i
$890$	19.1991	−	7.10682i	0.643555	−	0.238221i
$891$	−1.28573	+	3.95708i	−0.0430737	+	0.132567i
$892$	0.168203	+	0.122207i	0.00563186	+	0.00409178i
$893$	28.4373			0.951616
$894$	−10.7301	−	7.79589i	−0.358869	−	0.260734i
$895$	29.1059	−	10.7740i	0.972904	−	0.360135i
$896$	−8.70381	+	6.32368i	−0.290774	+	0.211259i
$897$	−6.28464	+	4.56606i	−0.209838	+	0.152456i
$898$	8.77017	+	26.9918i	0.292664	+	0.900728i
$899$	79.4248			2.64897
$900$	−0.613761	+	2.58141i	−0.0204587	+	0.0860468i
$901$	−43.1588			−1.43783
$902$	−18.9899	−	58.4448i	−0.632294	−	1.94600i
$903$	−4.29445	+	3.12010i	−0.142910	+	0.103830i
$904$	−0.602986	+	0.438095i	−0.0200550	+	0.0145708i
$905$	33.5452	+	42.4562i	1.11508	+	1.41129i
$906$	25.1044	+	18.2394i	0.834039	+	0.605965i
$907$	−24.9772			−0.829356			−0.414678	−	0.909968i	$-0.636106\pi$
$907$	−24.9772			−0.829356			−0.414678	+	0.909968i	$0.636106\pi$
$908$	−6.04850	−	4.39450i	−0.200727	−	0.145836i
$909$	−1.34304	+	4.13345i	−0.0445458	+	0.137098i
$910$	−2.69861	−	0.757895i	−0.0894579	−	0.0251240i
$911$	15.3523	+	47.2495i	0.508644	+	1.56545i	0.794557	+	0.607189i	$0.207703\pi$
$911$	15.3523	+	47.2495i	0.508644	+	1.56545i	−0.285913	+	0.958256i	$0.592297\pi$
$912$	−10.0340	+	30.8814i	−0.332258	+	1.02259i
$913$	1.36244	−	4.19317i	0.0450903	−	0.138774i
$914$	−8.89659	−	27.3809i	−0.294273	−	0.905679i
$915$	4.55435	+	5.76417i	0.150562	+	0.190557i
$916$	−3.28108	+	10.0981i	−0.108410	+	0.333651i
$917$	−2.14867	−	1.56110i	−0.0709554	−	0.0515521i
$918$	6.83062			0.225444
$919$	6.77001	+	4.91870i	0.223322	+	0.162253i	0.693821	−	0.720148i	$-0.255926\pi$
$919$	6.77001	+	4.91870i	0.223322	+	0.162253i	−0.470499	+	0.882401i	$0.655926\pi$
$920$	−22.5201	+	33.7838i	−0.742465	+	1.11382i
$921$	−22.1793	+	16.1142i	−0.730833	+	0.530981i
$922$	33.5486	−	24.3745i	1.10486	−	0.802730i
$923$	1.09881	+	3.38179i	0.0361678	+	0.111313i
$924$	1.73988			0.0572377
$925$	3.84081	−	3.29495i	0.126285	−	0.108337i
$926$	−31.6568			−1.04031
$927$	2.73447	+	8.41583i	0.0898117	+	0.276412i
$928$	−24.9013	+	18.0918i	−0.817424	+	0.593894i
$929$	−43.3097	+	31.4664i	−1.42095	+	1.03238i	−0.429332	+	0.903147i	$0.641251\pi$
$929$	−43.3097	+	31.4664i	−1.42095	+	1.03238i	−0.991615	+	0.129231i	$0.958749\pi$
$930$	−1.08487	−	26.8616i	−0.0355744	−	0.880826i
$931$	−35.0592	−	25.4720i	−1.14902	−	0.834811i
$932$	−6.57513			−0.215376
$933$	−3.69488	−	2.68448i	−0.120965	−	0.0878861i
$934$	−15.7796	+	48.5647i	−0.516325	+	1.58908i
$935$	−22.1576	+	33.2399i	−0.724630	+	1.08706i
$936$	−0.722302	−	2.22302i	−0.0236092	−	0.0726616i
$937$	6.74456	−	20.7576i	0.220335	−	0.678122i	−0.778397	−	0.627773i	$-0.783967\pi$
$937$	6.74456	−	20.7576i	0.220335	−	0.678122i	0.998732	−	0.0503488i	$-0.0160333\pi$
$938$	−1.89898	+	5.84446i	−0.0620039	+	0.190828i
$939$	2.11462	+	6.50814i	0.0690081	+	0.212385i
$940$	2.75511	−	4.13311i	0.0898618	−	0.134807i
$941$	10.5449	−	32.4537i	0.343752	−	1.05796i	−0.618496	−	0.785788i	$-0.712258\pi$
$941$	10.5449	−	32.4537i	0.343752	−	1.05796i	0.962248	−	0.272173i	$-0.0877423\pi$
$942$	26.0887	+	18.9545i	0.850015	+	0.617572i
$943$	−72.1233			−2.34866
$944$	−18.7725	−	13.6390i	−0.610994	−	0.443913i
$945$	0.0711050	+	1.76057i	0.00231304	+	0.0572713i
$946$	−36.0722	+	26.2080i	−1.17281	+	0.852094i
$947$	−40.5513	+	29.4622i	−1.31774	+	0.957393i	−0.317781	+	0.948164i	$0.602938\pi$
$947$	−40.5513	+	29.4622i	−1.31774	+	0.957393i	−0.999957	+	0.00922903i	$0.997062\pi$
$948$	−0.255577	−	0.786585i	−0.00830075	−	0.0255471i
$949$	−1.41957			−0.0460811
$950$	−41.0115	+	35.1829i	−1.33059	+	1.14148i
$951$	−30.5567			−0.990870
$952$	2.44390	+	7.52154i	0.0792071	+	0.243774i
$953$	17.2614	−	12.5411i	0.559151	−	0.406247i	−0.271997	−	0.962298i	$-0.587684\pi$
$953$	17.2614	−	12.5411i	0.559151	−	0.406247i	0.831148	+	0.556051i	$0.187684\pi$
$954$	−12.9361	+	9.39862i	−0.418821	+	0.304292i
$955$	−28.2996	+	42.4540i	−0.915754	+	1.37378i
$956$	−6.42094	−	4.66509i	−0.207668	−	0.150880i
$957$	−43.7263			−1.41347
$958$	−5.49983	−	3.99586i	−0.177691	−	0.129100i
$959$	−4.69361	+	14.4454i	−0.151565	+	0.466468i
$960$	−6.79308	−	8.59759i	−0.219246	−	0.277486i
$961$	8.07059	+	24.8387i	0.260342	+	0.801249i
$962$	0.497534	−	1.53125i	0.0160411	−	0.0493696i
$963$	0.794074	−	2.44391i	0.0255887	−	0.0787539i
$964$	0.166520	+	0.512496i	0.00536325	+	0.0165064i
$965$	−20.3867	−	5.72553i	−0.656270	−	0.184311i
$966$	3.00916	−	9.26124i	0.0968181	−	0.297975i
$967$	−42.1743	−	30.6414i	−1.35623	−	0.985361i	−0.998675	−	0.0514699i	$-0.983609\pi$
$967$	−42.1743	−	30.6414i	−1.35623	−	0.985361i	−0.357558	−	0.933891i	$-0.616391\pi$
$968$	−14.7529			−0.474177
$969$	23.5986	+	17.1454i	0.758097	+	0.550790i
$970$	26.8603	+	33.9954i	0.862431	+	1.09153i
$971$	24.6429	−	17.9041i	0.790828	−	0.574570i	−0.117381	−	0.993087i	$-0.537450\pi$
$971$	24.6429	−	17.9041i	0.790828	−	0.574570i	0.908209	+	0.418517i	$0.137450\pi$
$972$	0.429324	−	0.311922i	0.0137706	−	0.0100049i
$973$	−5.35876	−	16.4926i	−0.171794	−	0.528727i
$974$	5.88062			0.188427
$975$	1.15657	−	4.86440i	0.0370399	−	0.155785i
$976$	15.7031			0.502644
$977$	9.49546	+	29.2240i	0.303787	+	0.934960i	0.980127	+	0.198370i	$0.0635649\pi$
$977$	9.49546	+	29.2240i	0.303787	+	0.934960i	−0.676340	+	0.736589i	$0.736435\pi$
$978$	−13.4300	+	9.75749i	−0.429445	+	0.312010i
$979$	19.3726	−	14.0750i	0.619152	−	0.449840i
$980$	−7.09880	+	2.62773i	−0.226763	+	0.0839396i
$981$	8.78775	+	6.38467i	0.280571	+	0.203847i
$982$	26.6084			0.849109
$983$	−3.31209	−	2.40638i	−0.105639	−	0.0767515i	0.533711	−	0.845667i	$-0.320797\pi$
$983$	−3.31209	−	2.40638i	−0.105639	−	0.0767515i	−0.639351	+	0.768915i	$0.720797\pi$
$984$	6.70612	−	20.6393i	0.213783	−	0.657958i
$985$	34.4354	−	12.7468i	1.09720	−	0.406146i
$986$	22.1828	+	68.2716i	0.706443	+	2.17421i
$987$	1.01931	−	3.13710i	0.0324449	−	0.0998551i
$988$	−1.11403	+	3.42863i	−0.0354420	+	0.109079i
$989$	16.1708	+	49.7687i	0.514203	+	1.58255i
$990$	0.597262	+	14.7883i	0.0189822	+	0.470003i
$991$	5.70433	−	17.5561i	0.181204	−	0.557689i	−0.818658	−	0.574281i	$-0.805282\pi$
$991$	5.70433	−	17.5561i	0.181204	−	0.557689i	0.999862	+	0.0165922i	$0.00528169\pi$
$992$	−17.9073	−	13.0104i	−0.568558	−	0.413082i
$993$	14.9035			0.472949
$994$	−3.60610	−	2.61999i	−0.114379	−	0.0831009i
$995$	14.0845	+	3.95558i	0.446509	+	0.125400i
$996$	−0.454938	+	0.330532i	−0.0144153	+	0.0104733i
$997$	−20.5997	+	14.9666i	−0.652400	+	0.473996i	−0.864088	−	0.503341i	$-0.832104\pi$
$997$	−20.5997	+	14.9666i	−0.652400	+	0.473996i	0.211688	+	0.977337i	$0.432104\pi$
$998$	−17.1758	−	52.8617i	−0.543690	−	1.67331i
$999$	−1.01210			−0.0320214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.v.c.781.13	yes	68
25.21	even	5	inner	975.2.v.c.196.13	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.v.c.196.13	✓	68	25.21	even	5	inner
975.2.v.c.781.13	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.v (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.491587 + 1.51295i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.429324 + 0.311922i) q^{4} +(-2.15278 - 0.604601i) q^{5} +(1.28699 + 0.935054i) q^{6} +0.787992 q^{7} +(1.89101 + 1.37390i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.491587 + 1.51295i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.429324 + 0.311922i) q^{4} +(-2.15278 - 0.604601i) q^{5} +(1.28699 + 0.935054i) q^{6} +0.787992 q^{7} +(1.89101 + 1.37390i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.143548 - 3.55426i) q^{10} +(-1.28573 - 3.95708i) q^{11} +(-0.163987 + 0.504700i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.387367 + 1.19219i) q^{14} +(-2.09701 + 0.776239i) q^{15} +(-1.47702 + 4.54580i) q^{16} +(3.47376 + 2.52383i) q^{17} +1.59081 q^{18} +(5.49597 + 3.99306i) q^{19} +(1.11283 - 0.411930i) q^{20} +(0.637499 - 0.463170i) q^{21} +(5.35482 - 3.89050i) q^{22} +(-2.40052 - 7.38804i) q^{23} +2.33742 q^{24} +(4.26892 + 2.60314i) q^{25} +1.59081 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.338304 + 0.245792i) q^{28} +(8.50219 - 6.17721i) q^{29} +(-2.20527 - 2.79108i) q^{30} +(6.11421 + 4.44223i) q^{31} -2.92881 q^{32} +(-3.36610 - 2.44561i) q^{33} +(-2.11078 + 6.49630i) q^{34} +(-1.69637 - 0.476421i) q^{35} +(0.163987 + 0.504700i) q^{36} +(0.312755 - 0.962562i) q^{37} +(-3.33955 + 10.2781i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-3.24027 - 4.10101i) q^{40} +(2.86903 - 8.82997i) q^{41} +(1.01414 + 0.736816i) q^{42} -6.73639 q^{43} +(1.78630 + 1.29782i) q^{44} +(-1.24026 + 1.86058i) q^{45} +(9.99766 - 7.26372i) q^{46} +(3.38656 - 2.46048i) q^{47} +(1.47702 + 4.54580i) q^{48} -6.37907 q^{49} +(-1.83988 + 7.73832i) q^{50} +4.29380 q^{51} +(0.163987 + 0.504700i) q^{52} +(-8.13177 + 5.90807i) q^{53} +(1.28699 - 0.935054i) q^{54} +(0.375445 + 9.29609i) q^{55} +(1.49010 + 1.08262i) q^{56} +6.79340 q^{57} +(13.5254 + 9.82676i) q^{58} +(-1.50018 + 4.61708i) q^{59} +(0.658170 - 0.987362i) q^{60} +(-1.01523 - 3.12456i) q^{61} +(-3.71521 + 11.4342i) q^{62} +(0.243503 - 0.749425i) q^{63} +(1.51427 + 4.66046i) q^{64} +(-1.24026 + 1.86058i) q^{65} +(2.04536 - 6.29497i) q^{66} +(3.96603 + 2.88149i) q^{67} -2.27861 q^{68} +(-6.28464 - 4.56606i) q^{69} +(-0.113114 - 2.80073i) q^{70} +(-2.87672 + 2.09006i) q^{71} +(1.89101 - 1.37390i) q^{72} +(-0.438671 - 1.35009i) q^{73} +1.61005 q^{74} +(4.98372 - 0.403217i) q^{75} -3.60507 q^{76} +(-1.01315 - 3.11815i) q^{77} +(1.28699 - 0.935054i) q^{78} +(-1.26087 + 0.916074i) q^{79} +(5.92809 - 8.89309i) q^{80} +(-0.809017 - 0.587785i) q^{81} +14.7697 q^{82} +(0.857284 + 0.622853i) q^{83} +(-0.129221 + 0.397700i) q^{84} +(-5.95232 - 7.53349i) q^{85} +(-3.31152 - 10.1918i) q^{86} +(3.24755 - 9.99493i) q^{87} +(3.00530 - 9.24936i) q^{88} +(1.77846 + 5.47354i) q^{89} +(-3.42466 - 0.961805i) q^{90} +(0.243503 - 0.749425i) q^{91} +(3.33509 + 2.42309i) q^{92} +7.55758 q^{93} +(5.38736 + 3.91415i) q^{94} +(-9.41741 - 11.9190i) q^{95} +(-2.36945 + 1.72151i) q^{96} +(-9.85384 + 7.15923i) q^{97} +(-3.13587 - 9.65121i) q^{98} -4.16072 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9	\( 68 q - q^{2} + 17 q^{3} - 19 q^{4} + q^{5} + q^{6} - 4 q^{7} - 12 q^{8} - 17 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 17 q^{13} - 26 q^{14} - q^{15} - 19 q^{16} - 7 q^{17} + 4 q^{18} - 8 q^{19} + 55 q^{20} - q^{21} - 26 q^{22} - 15 q^{23} - 18 q^{24} + 3 q^{25} + 4 q^{26} + 17 q^{27} + 9 q^{28} - 25 q^{29} - 28 q^{30} - 26 q^{31} + 180 q^{32} + 8 q^{33} + 26 q^{34} - 46 q^{35} - 19 q^{36} - 8 q^{37} + 8 q^{38} + 17 q^{39} + 82 q^{40} - 9 q^{41} - 4 q^{42} - 100 q^{43} - 5 q^{44} + 6 q^{45} + 32 q^{46} + 2 q^{47} + 19 q^{48} + 204 q^{49} - 29 q^{50} + 2 q^{51} - 19 q^{52} - 31 q^{53} + q^{54} - 37 q^{55} - 17 q^{56} + 8 q^{57} + 11 q^{58} - 13 q^{59} - 25 q^{60} + 14 q^{61} - 46 q^{62} + q^{63} - 56 q^{64} + 6 q^{65} - 39 q^{66} - 12 q^{67} + 26 q^{68} - 10 q^{69} + 117 q^{70} + 7 q^{71} - 12 q^{72} - 10 q^{73} + 76 q^{74} + 2 q^{75} + 6 q^{76} - 5 q^{77} + q^{78} - 46 q^{79} + 128 q^{80} - 17 q^{81} + 102 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{85} - 60 q^{86} + 64 q^{88} - 38 q^{89} - 17 q^{90} + q^{91} - 42 q^{92} - 64 q^{93} + 39 q^{94} - 49 q^{95} + 60 q^{96} - 34 q^{97} + 53 q^{98} + 12 q^{99}+O(q^{100}) \) 68 * q - q^2 + 17 * q^3 - 19 * q^4 + q^5 + q^6 - 4 * q^7 - 12 * q^8 - 17 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 17 * q^13 - 26 * q^14 - q^15 - 19 * q^16 - 7 * q^17 + 4 * q^18 - 8 * q^19 + 55 * q^20 - q^21 - 26 * q^22 - 15 * q^23 - 18 * q^24 + 3 * q^25 + 4 * q^26 + 17 * q^27 + 9 * q^28 - 25 * q^29 - 28 * q^30 - 26 * q^31 + 180 * q^32 + 8 * q^33 + 26 * q^34 - 46 * q^35 - 19 * q^36 - 8 * q^37 + 8 * q^38 + 17 * q^39 + 82 * q^40 - 9 * q^41 - 4 * q^42 - 100 * q^43 - 5 * q^44 + 6 * q^45 + 32 * q^46 + 2 * q^47 + 19 * q^48 + 204 * q^49 - 29 * q^50 + 2 * q^51 - 19 * q^52 - 31 * q^53 + q^54 - 37 * q^55 - 17 * q^56 + 8 * q^57 + 11 * q^58 - 13 * q^59 - 25 * q^60 + 14 * q^61 - 46 * q^62 + q^63 - 56 * q^64 + 6 * q^65 - 39 * q^66 - 12 * q^67 + 26 * q^68 - 10 * q^69 + 117 * q^70 + 7 * q^71 - 12 * q^72 - 10 * q^73 + 76 * q^74 + 2 * q^75 + 6 * q^76 - 5 * q^77 + q^78 - 46 * q^79 + 128 * q^80 - 17 * q^81 + 102 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^85 - 60 * q^86 + 64 * q^88 - 38 * q^89 - 17 * q^90 + q^91 - 42 * q^92 - 64 * q^93 + 39 * q^94 - 49 * q^95 + 60 * q^96 - 34 * q^97 + 53 * q^98 + 12 * q^99

Introduction

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