LMFDB - Embedded newform 287.2.h.c.57.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.9
Character	$\chi$	$=$	287.57
Dual form			287.2.h.c.141.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.571535 - 1.75900i) q^{2} -3.10319 q^{3} +(-1.14941 - 0.835096i) q^{4} +(2.72110 + 1.97700i) q^{5} +(-1.77358 + 5.45852i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.866730 - 0.629716i) q^{8} +6.62977 q^{9} +O(q^{10})$	\(q+(0.571535 - 1.75900i) q^{2} -3.10319 q^{3} +(-1.14941 - 0.835096i) q^{4} +(2.72110 + 1.97700i) q^{5} +(-1.77358 + 5.45852i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.866730 - 0.629716i) q^{8} +6.62977 q^{9} +(5.03276 - 3.65651i) q^{10} +(-0.802857 + 0.583310i) q^{11} +(3.56684 + 2.59146i) q^{12} +(-0.132482 + 0.407738i) q^{13} +1.84953 q^{14} +(-8.44410 - 6.13500i) q^{15} +(-1.49038 - 4.58692i) q^{16} +(3.56217 - 2.58807i) q^{17} +(3.78915 - 11.6618i) q^{18} +(2.04986 + 6.30883i) q^{19} +(-1.47668 - 4.54477i) q^{20} +(-0.958938 - 2.95131i) q^{21} +(0.567184 + 1.74561i) q^{22} +(1.91298 - 5.88754i) q^{23} +(-2.68963 + 1.95413i) q^{24} +(1.95080 + 6.00395i) q^{25} +(0.641494 + 0.466073i) q^{26} -11.2639 q^{27} +(0.439036 - 1.35121i) q^{28} +(-1.05639 - 0.767514i) q^{29} +(-15.6176 + 11.3468i) q^{30} +(2.18353 - 1.58643i) q^{31} -6.77754 q^{32} +(2.49142 - 1.81012i) q^{33} +(-2.51652 - 7.74505i) q^{34} +(-1.03937 + 3.19885i) q^{35} +(-7.62034 - 5.53650i) q^{36} +(5.87259 + 4.26668i) q^{37} +12.2688 q^{38} +(0.411116 - 1.26529i) q^{39} +3.60341 q^{40} +(-3.43596 + 5.40316i) q^{41} -5.73943 q^{42} +(0.227782 - 0.701042i) q^{43} +1.40993 q^{44} +(18.0403 + 13.1070i) q^{45} +(-9.26288 - 6.72988i) q^{46} +(1.18165 - 3.63673i) q^{47} +(4.62493 + 14.2341i) q^{48} +(-0.809017 + 0.587785i) q^{49} +11.6759 q^{50} +(-11.0541 + 8.03126i) q^{51} +(0.492776 - 0.358023i) q^{52} +(7.29906 + 5.30308i) q^{53} +(-6.43770 + 19.8132i) q^{54} -3.33786 q^{55} +(0.866730 + 0.629716i) q^{56} +(-6.36111 - 19.5775i) q^{57} +(-1.95383 + 1.41954i) q^{58} +(-4.67949 + 14.4020i) q^{59} +(4.58243 + 14.1033i) q^{60} +(-4.32979 - 13.3257i) q^{61} +(-1.54257 - 4.74754i) q^{62} +(2.04871 + 6.30529i) q^{63} +(-0.892843 + 2.74789i) q^{64} +(-1.16659 + 0.847580i) q^{65} +(-1.76008 - 5.41696i) q^{66} +(-10.9806 - 7.97787i) q^{67} -6.25569 q^{68} +(-5.93633 + 18.2701i) q^{69} +(5.03276 + 3.65651i) q^{70} +(-3.48664 + 2.53319i) q^{71} +(5.74623 - 4.17488i) q^{72} -16.0362 q^{73} +(10.8615 - 7.89135i) q^{74} +(-6.05371 - 18.6314i) q^{75} +(2.91235 - 8.96328i) q^{76} +(-0.802857 - 0.583310i) q^{77} +(-1.99068 - 1.44631i) q^{78} -1.29056 q^{79} +(5.01285 - 15.4280i) q^{80} +15.0646 q^{81} +(7.54041 + 9.13197i) q^{82} +8.58168 q^{83} +(-1.36241 + 4.19307i) q^{84} +14.8096 q^{85} +(-1.10295 - 0.801341i) q^{86} +(3.27818 + 2.38174i) q^{87} +(-0.328541 + 1.01115i) q^{88} +(0.508155 + 1.56394i) q^{89} +(33.3660 - 24.2418i) q^{90} -0.428721 q^{91} +(-7.11546 + 5.16969i) q^{92} +(-6.77591 + 4.92298i) q^{93} +(-5.72168 - 4.15704i) q^{94} +(-6.89466 + 21.2196i) q^{95} +21.0320 q^{96} +(-11.2401 - 8.16641i) q^{97} +(0.571535 + 1.75900i) q^{98} +(-5.32276 + 3.86721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.571535	−	1.75900i	0.404136	−	1.24380i	−0.517478	−	0.855697i	$-0.673129\pi$
$2$	0.571535	−	1.75900i	0.404136	−	1.24380i	0.921614	−	0.388107i	$-0.126871\pi$
$3$	−3.10319			−1.79163			−0.895813	−	0.444431i	$-0.853406\pi$
$3$	−3.10319			−1.79163			−0.895813	+	0.444431i	$0.853406\pi$
$4$	−1.14941	−	0.835096i	−0.574706	−	0.417548i
$5$	2.72110	+	1.97700i	1.21691	+	0.884140i	0.995840	−	0.0911166i	$-0.0290436\pi$
$5$	2.72110	+	1.97700i	1.21691	+	0.884140i	0.221075	+	0.975257i	$0.429044\pi$
$6$	−1.77358	+	5.45852i	−0.724062	+	2.22843i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.866730	−	0.629716i	0.306435	−	0.222638i
$9$	6.62977			2.20992
$10$	5.03276	−	3.65651i	1.59150	−	1.15629i
$11$	−0.802857	+	0.583310i	−0.242071	+	0.175875i	−0.702205	−	0.711975i	$-0.747801\pi$
$11$	−0.802857	+	0.583310i	−0.242071	+	0.175875i	0.460135	+	0.887849i	$0.347801\pi$
$12$	3.56684	+	2.59146i	1.02966	+	0.748090i
$13$	−0.132482	+	0.407738i	−0.0367439	+	0.113086i	−0.967746	−	0.251927i	$-0.918936\pi$
$13$	−0.132482	+	0.407738i	−0.0367439	+	0.113086i	0.931002	+	0.365013i	$0.118936\pi$
$14$	1.84953			0.494307
$15$	−8.44410	−	6.13500i	−2.18026	−	1.58405i
$16$	−1.49038	−	4.58692i	−0.372595	−	1.14673i
$17$	3.56217	−	2.58807i	0.863953	−	0.627699i	−0.0650042	−	0.997885i	$-0.520706\pi$
$17$	3.56217	−	2.58807i	0.863953	−	0.627699i	0.928958	+	0.370186i	$0.120706\pi$
$18$	3.78915	−	11.6618i	0.893111	−	2.74871i
$19$	2.04986	+	6.30883i	0.470271	+	1.44735i	0.852230	+	0.523166i	$0.175249\pi$
$19$	2.04986	+	6.30883i	0.470271	+	1.44735i	−0.381959	+	0.924179i	$0.624751\pi$
$20$	−1.47668	−	4.54477i	−0.330197	−	1.01624i
$21$	−0.958938	−	2.95131i	−0.209257	−	0.644028i
$22$	0.567184	+	1.74561i	0.120924	+	0.372166i
$23$	1.91298	−	5.88754i	0.398884	−	1.22764i	−0.527012	−	0.849858i	$-0.676688\pi$
$23$	1.91298	−	5.88754i	0.398884	−	1.22764i	0.925896	−	0.377779i	$-0.123312\pi$
$24$	−2.68963	+	1.95413i	−0.549018	+	0.398885i
$25$	1.95080	+	6.00395i	0.390160	+	1.20079i
$26$	0.641494	+	0.466073i	0.125807	+	0.0914044i
$27$	−11.2639			−2.16773
$28$	0.439036	−	1.35121i	0.0829700	−	0.255355i
$29$	−1.05639	−	0.767514i	−0.196167	−	0.142524i	0.485366	−	0.874311i	$-0.338686\pi$
$29$	−1.05639	−	0.767514i	−0.196167	−	0.142524i	−0.681533	+	0.731787i	$0.738686\pi$
$30$	−15.6176	+	11.3468i	−2.85137	+	2.07164i
$31$	2.18353	−	1.58643i	0.392174	−	0.284931i	−0.374172	−	0.927359i	$-0.622073\pi$
$31$	2.18353	−	1.58643i	0.392174	−	0.284931i	0.766346	+	0.642428i	$0.222073\pi$
$32$	−6.77754			−1.19811
$33$	2.49142	−	1.81012i	0.433700	−	0.315102i
$34$	−2.51652	−	7.74505i	−0.431579	−	1.32827i
$35$	−1.03937	+	3.19885i	−0.175685	+	0.540704i
$36$	−7.62034	−	5.53650i	−1.27006	−	0.922750i
$37$	5.87259	+	4.26668i	0.965447	+	0.701439i	0.954409	−	0.298500i	$-0.0964865\pi$
$37$	5.87259	+	4.26668i	0.965447	+	0.701439i	0.0110379	+	0.999939i	$0.496486\pi$
$38$	12.2688			1.99027
$39$	0.411116	−	1.26529i	0.0658313	−	0.202608i
$40$	3.60341			0.569749
$41$	−3.43596	+	5.40316i	−0.536607	+	0.843832i
$41$	−3.43596	+	5.40316i	−0.536607	+	0.843832i
$42$	−5.73943			−0.885613
$43$	0.227782	−	0.701042i	0.0347365	−	0.106908i	−0.932185	−	0.361982i	$-0.882100\pi$
$43$	0.227782	−	0.701042i	0.0347365	−	0.106908i	0.966921	+	0.255075i	$0.0821000\pi$
$44$	1.40993			0.212555
$45$	18.0403	+	13.1070i	2.68929	+	1.95388i
$46$	−9.26288	−	6.72988i	−1.36574	−	0.992266i
$47$	1.18165	−	3.63673i	0.172361	−	0.530472i	−0.827142	−	0.561992i	$-0.810035\pi$
$47$	1.18165	−	3.63673i	0.172361	−	0.530472i	0.999503	+	0.0315206i	$0.0100350\pi$
$48$	4.62493	+	14.2341i	0.667551	+	2.05451i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	11.6759			1.65123
$51$	−11.0541	+	8.03126i	−1.54788	+	1.12460i
$52$	0.492776	−	0.358023i	0.0683358	−	0.0496489i
$53$	7.29906	+	5.30308i	1.00260	+	0.728434i	0.962645	−	0.270768i	$-0.0872776\pi$
$53$	7.29906	+	5.30308i	1.00260	+	0.728434i	0.0399581	+	0.999201i	$0.487278\pi$
$54$	−6.43770	+	19.8132i	−0.876060	+	2.69624i
$55$	−3.33786			−0.450077
$56$	0.866730	+	0.629716i	0.115822	+	0.0841494i
$57$	−6.36111	−	19.5775i	−0.842550	−	2.59310i
$58$	−1.95383	+	1.41954i	−0.256550	+	0.186395i
$59$	−4.67949	+	14.4020i	−0.609217	+	1.87498i	−0.144538	+	0.989499i	$0.546170\pi$
$59$	−4.67949	+	14.4020i	−0.609217	+	1.87498i	−0.464679	+	0.885479i	$0.653830\pi$
$60$	4.58243	+	14.1033i	0.591589	+	1.82072i
$61$	−4.32979	−	13.3257i	−0.554373	−	1.70618i	−0.697593	−	0.716494i	$-0.745746\pi$
$61$	−4.32979	−	13.3257i	−0.554373	−	1.70618i	0.143220	−	0.989691i	$-0.454254\pi$
$62$	−1.54257	−	4.74754i	−0.195907	−	0.602938i
$63$	2.04871	+	6.30529i	0.258114	+	0.794392i
$64$	−0.892843	+	2.74789i	−0.111605	+	0.343486i
$65$	−1.16659	+	0.847580i	−0.144698	+	0.105129i
$66$	−1.76008	−	5.41696i	−0.216651	−	0.666782i
$67$	−10.9806	−	7.97787i	−1.34149	−	0.974652i	−0.999388	−	0.0349909i	$-0.988860\pi$
$67$	−10.9806	−	7.97787i	−1.34149	−	0.974652i	−0.342106	−	0.939661i	$-0.611140\pi$
$68$	−6.25569			−0.758613
$69$	−5.93633	+	18.2701i	−0.714650	+	2.19947i
$70$	5.03276	+	3.65651i	0.601529	+	0.437037i
$71$	−3.48664	+	2.53319i	−0.413788	+	0.300634i	−0.775133	−	0.631798i	$-0.782317\pi$
$71$	−3.48664	+	2.53319i	−0.413788	+	0.300634i	0.361346	+	0.932432i	$0.382317\pi$
$72$	5.74623	−	4.17488i	0.677199	−	0.492014i
$73$	−16.0362			−1.87689			−0.938446	−	0.345427i	$-0.887734\pi$
$73$	−16.0362			−1.87689			−0.938446	+	0.345427i	$0.887734\pi$
$74$	10.8615	−	7.89135i	1.26262	−	0.917351i
$75$	−6.05371	−	18.6314i	−0.699022	−	2.15137i
$76$	2.91235	−	8.96328i	0.334069	−	1.02816i
$77$	−0.802857	−	0.583310i	−0.0914941	−	0.0664743i
$78$	−1.99068	−	1.44631i	−0.225400	−	0.163763i
$79$	−1.29056			−0.145199			−0.0725995	−	0.997361i	$-0.523129\pi$
$79$	−1.29056			−0.145199			−0.0725995	+	0.997361i	$0.523129\pi$
$80$	5.01285	−	15.4280i	0.560453	−	1.72490i
$81$	15.0646			1.67384
$82$	7.54041	+	9.13197i	0.832699	+	1.00846i
$83$	8.58168			0.941962			0.470981	−	0.882143i	$-0.343900\pi$
$83$	8.58168			0.941962			0.470981	+	0.882143i	$0.343900\pi$
$84$	−1.36241	+	4.19307i	−0.148651	+	0.457502i
$85$	14.8096			1.60633
$86$	−1.10295	−	0.801341i	−0.118934	−	0.0864108i
$87$	3.27818	+	2.38174i	0.351458	+	0.255349i
$88$	−0.328541	+	1.01115i	−0.0350226	+	0.107788i
$89$	0.508155	+	1.56394i	0.0538643	+	0.165777i	0.974370	−	0.224953i	$-0.0722227\pi$
$89$	0.508155	+	1.56394i	0.0538643	+	0.165777i	−0.920505	+	0.390730i	$0.872223\pi$
$90$	33.3660	−	24.2418i	3.51709	−	2.55531i
$91$	−0.428721			−0.0449421
$92$	−7.11546	+	5.16969i	−0.741838	+	0.538977i
$93$	−6.77591	+	4.92298i	−0.702629	+	0.510490i
$94$	−5.72168	−	4.15704i	−0.590146	−	0.428766i
$95$	−6.89466	+	21.2196i	−0.707377	+	2.17708i
$96$	21.0320			2.14657
$97$	−11.2401	−	8.16641i	−1.14126	−	0.829173i	−0.153965	−	0.988076i	$-0.549204\pi$
$97$	−11.2401	−	8.16641i	−1.14126	−	0.829173i	−0.987294	+	0.158903i	$0.949204\pi$
$98$	0.571535	+	1.75900i	0.0577338	+	0.177686i
$99$	−5.32276	+	3.86721i	−0.534958	+	0.388670i
$100$	2.77160	−	8.53012i	0.277160	−	0.853012i
$101$	−2.80249	−	8.62519i	−0.278859	−	0.858238i	−0.988173	−	0.153346i	$-0.950995\pi$
$101$	−2.80249	−	8.62519i	−0.278859	−	0.858238i	0.709314	−	0.704893i	$-0.249005\pi$
$102$	7.80923	+	24.0343i	0.773229	+	2.37975i
$103$	−2.03454	−	6.26166i	−0.200469	−	0.616980i	−0.999869	−	0.0161808i	$-0.994849\pi$
$103$	−2.03454	−	6.26166i	−0.200469	−	0.616980i	0.799400	−	0.600799i	$-0.205151\pi$
$104$	0.141933	+	0.436825i	0.0139177	+	0.0428342i
$105$	3.22536	−	9.92663i	0.314763	−	0.968740i
$106$	13.4998	−	9.80818i	1.31122	−	0.952655i
$107$	−0.161183	−	0.496071i	−0.0155822	−	0.0479570i	0.942963	−	0.332897i	$-0.108026\pi$
$107$	−0.161183	−	0.496071i	−0.0155822	−	0.0479570i	−0.958545	+	0.284940i	$0.908026\pi$
$108$	12.9468	+	9.40641i	1.24581	+	0.905133i
$109$	−5.57378			−0.533872			−0.266936	−	0.963714i	$-0.586011\pi$
$109$	−5.57378			−0.533872			−0.266936	+	0.963714i	$0.586011\pi$
$110$	−1.90771	+	5.87131i	−0.181893	+	0.559808i
$111$	−18.2237	−	13.2403i	−1.72972	−	1.25672i
$112$	3.90186	−	2.83487i	0.368691	−	0.267870i
$113$	−5.06069	+	3.67681i	−0.476070	+	0.345885i	−0.799802	−	0.600264i	$-0.795062\pi$
$113$	−5.06069	+	3.67681i	−0.476070	+	0.345885i	0.323732	+	0.946149i	$0.395062\pi$
$114$	−38.0725			−3.56582
$115$	16.8451	−	12.2387i	1.57081	−	1.14126i
$116$	0.573282	+	1.76438i	0.0532279	+	0.163818i
$117$	−0.878325	+	2.70321i	−0.0812012	+	0.249912i
$118$	22.6587	+	16.4625i	2.08590	+	1.51549i
$119$	3.56217	+	2.58807i	0.326544	+	0.237248i
$120$	−11.1821			−1.02078
$121$	−3.09486	+	9.52499i	−0.281351	+	0.865908i
$122$	−25.9147			−2.34620
$123$	10.6624	−	16.7670i	0.961400	−	1.51183i
$124$	−3.83460			−0.344357
$125$	−1.36462	+	4.19986i	−0.122055	+	0.375647i
$126$	12.2619			1.09238
$127$	2.97844	+	2.16396i	0.264293	+	0.192020i	0.712038	−	0.702141i	$-0.247772\pi$
$127$	2.97844	+	2.16396i	0.264293	+	0.192020i	−0.447744	+	0.894162i	$0.647772\pi$
$128$	−6.64303	−	4.82644i	−0.587166	−	0.426601i
$129$	−0.706852	+	2.17547i	−0.0622348	+	0.191539i
$130$	0.824148	+	2.53647i	0.0722825	+	0.222463i
$131$	−8.19696	+	5.95544i	−0.716172	+	0.520329i	−0.885159	−	0.465289i	$-0.845950\pi$
$131$	−8.19696	+	5.95544i	−0.716172	+	0.520329i	0.168987	+	0.985618i	$0.445950\pi$
$132$	−4.37529			−0.380820
$133$	−5.36661	+	3.89907i	−0.465344	+	0.338093i
$134$	−20.3089	+	14.7553i	−1.75442	+	1.27466i
$135$	−30.6502	−	22.2686i	−2.63795	−	1.91658i
$136$	1.45769	−	4.48632i	0.124996	−	0.384698i
$137$	3.41337			0.291624			0.145812	−	0.989312i	$-0.453421\pi$
$137$	3.41337			0.291624			0.145812	+	0.989312i	$0.453421\pi$
$138$	28.7445	+	20.8841i	2.44689	+	1.77777i
$139$	0.914697	+	2.81515i	0.0775836	+	0.238778i	0.982325	−	0.187184i	$-0.0599359\pi$
$139$	0.914697	+	2.81515i	0.0775836	+	0.238778i	−0.904741	+	0.425961i	$0.859936\pi$
$140$	3.86601	−	2.80882i	0.326737	−	0.237389i
$141$	−3.66687	+	11.2855i	−0.308806	+	0.950407i
$142$	2.46316	+	7.58082i	0.206704	+	0.636168i
$143$	−0.131473	−	0.404633i	−0.0109943	−	0.0338371i
$144$	−9.88088	−	30.4102i	−0.823407	−	2.53418i
$145$	−1.35718	−	4.17697i	−0.112708	−	0.346879i
$146$	−9.16523	+	28.2077i	−0.758520	+	2.33448i
$147$	2.51053	−	1.82401i	0.207065	−	0.150442i
$148$	−3.18693	−	9.80835i	−0.261964	−	0.806241i
$149$	13.9165	+	10.1109i	1.14008	+	0.828319i	0.987131	−	0.159914i	$-0.0511218\pi$
$149$	13.9165	+	10.1109i	1.14008	+	0.828319i	0.152953	+	0.988234i	$0.451122\pi$
$150$	−36.2326			−2.95838
$151$	1.99946	−	6.15369i	0.162713	−	0.500781i	−0.836147	−	0.548505i	$-0.815197\pi$
$151$	1.99946	−	6.15369i	0.162713	−	0.500781i	0.998861	+	0.0477248i	$0.0151970\pi$
$152$	5.74946	+	4.17722i	0.466342	+	0.338818i
$153$	23.6164	−	17.1583i	1.90927	−	1.38717i
$154$	−1.48491	+	1.07885i	−0.119657	+	0.0869360i
$155$	9.07798			0.729161
$156$	−1.52918	+	1.11101i	−0.122432	+	0.0889522i
$157$	−7.59669	−	23.3802i	−0.606281	−	1.86594i	−0.487730	−	0.872995i	$-0.662175\pi$
$157$	−7.59669	−	23.3802i	−0.606281	−	1.86594i	−0.118552	−	0.992948i	$-0.537825\pi$
$158$	−0.737599	+	2.27010i	−0.0586802	+	0.180599i
$159$	−22.6503	−	16.4564i	−1.79629	−	1.30508i
$160$	−18.4424	−	13.3992i	−1.45800	−	1.05930i
$161$	6.19053			0.487882
$162$	8.60994	−	26.4987i	0.676461	−	2.08193i
$163$	3.54535			0.277694			0.138847	−	0.990314i	$-0.455660\pi$
$163$	3.54535			0.277694			0.138847	+	0.990314i	$0.455660\pi$
$164$	8.46150	−	3.34109i	0.660732	−	0.260896i
$165$	10.3580			0.806370
$166$	4.90473	−	15.0952i	0.380681	−	1.17162i
$167$	7.72271			0.597602			0.298801	−	0.954316i	$-0.403413\pi$
$167$	7.72271			0.597602			0.298801	+	0.954316i	$0.403413\pi$
$168$	−2.68963	−	1.95413i	−0.207509	−	0.150764i
$169$	10.3685	+	7.53317i	0.797579	+	0.579475i
$170$	8.46424	−	26.0502i	0.649177	−	1.99796i
$171$	13.5901	+	41.8261i	1.03926	+	3.19852i
$172$	−0.847254	+	0.615566i	−0.0646025	+	0.0469364i
$173$	−4.74375			−0.360661			−0.180330	−	0.983606i	$-0.557717\pi$
$173$	−4.74375			−0.360661			−0.180330	+	0.983606i	$0.557717\pi$
$174$	6.06309	−	4.40509i	0.459642	−	0.333949i
$175$	−5.10727	+	3.71065i	−0.386073	+	0.280499i
$176$	3.87216	+	2.81329i	0.291875	+	0.212059i
$177$	14.5213	−	44.6921i	1.09149	−	3.35926i
$178$	3.04141			0.227963
$179$	−7.93752	−	5.76695i	−0.593278	−	0.431042i	0.250209	−	0.968192i	$-0.419501\pi$
$179$	−7.93752	−	5.76695i	−0.593278	−	0.431042i	−0.843487	+	0.537150i	$0.819501\pi$
$180$	−9.79008	−	30.1308i	−0.729710	−	2.24582i
$181$	−12.9843	+	9.43364i	−0.965115	+	0.701197i	−0.954333	−	0.298745i	$-0.903432\pi$
$181$	−12.9843	+	9.43364i	−0.965115	+	0.701197i	−0.0107816	+	0.999942i	$0.503432\pi$
$182$	−0.245029	+	0.754122i	−0.0181628	+	0.0558992i
$183$	13.4362	+	41.3522i	0.993229	+	3.05685i
$184$	−2.04945	−	6.30754i	−0.151087	−	0.464998i
$185$	7.54470	+	23.2202i	0.554697	+	1.70718i
$186$	4.78688	+	14.7325i	0.350991	+	1.08024i
$187$	−1.35027	+	4.15570i	−0.0987414	+	0.303895i
$188$	−4.39522	+	3.19331i	−0.320554	+	0.232896i
$189$	−3.48073	−	10.7126i	−0.253186	−	0.779225i
$190$	33.3848	+	24.2555i	2.42199	+	1.75968i
$191$	6.82957			0.494170			0.247085	−	0.968994i	$-0.420527\pi$
$191$	6.82957			0.494170			0.247085	+	0.968994i	$0.420527\pi$
$192$	2.77066	−	8.52721i	0.199955	−	0.615398i
$193$	2.72528	+	1.98004i	0.196170	+	0.142526i	0.681534	−	0.731786i	$-0.261313\pi$
$193$	2.72528	+	1.98004i	0.196170	+	0.142526i	−0.485364	+	0.874312i	$0.661313\pi$
$194$	−20.7889	+	15.1040i	−1.49255	+	1.08440i
$195$	3.62016	−	2.63020i	0.259245	−	0.188352i
$196$	1.42075			0.101482
$197$	−1.01820	+	0.739767i	−0.0725439	+	0.0527062i	−0.623466	−	0.781850i	$-0.714276\pi$
$197$	−1.01820	+	0.739767i	−0.0725439	+	0.0527062i	0.550922	+	0.834557i	$0.314276\pi$
$198$	3.76030	+	11.5730i	0.267233	+	0.822458i
$199$	0.117065	−	0.360291i	0.00829855	−	0.0255403i	−0.946822	−	0.321759i	$-0.895726\pi$
$199$	0.117065	−	0.360291i	0.00829855	−	0.0255403i	0.955120	+	0.296219i	$0.0957258\pi$
$200$	5.47161	+	3.97536i	0.386901	+	0.281100i
$201$	34.0749	+	24.7568i	2.40346	+	1.74621i
$202$	−16.7735			−1.18018
$203$	0.403506	−	1.24186i	0.0283206	−	0.0871618i
$204$	19.4126			1.35915
$205$	−20.0317	+	7.90967i	−1.39907	+	0.552435i
$206$	−12.1771			−0.848419
$207$	12.6826	−	39.0331i	0.881503	−	2.71299i
$208$	2.06771			0.143370
$209$	−5.32575	−	3.86939i	−0.368390	−	0.267651i
$210$	−15.6176	−	11.3468i	−1.07772	−	0.783006i
$211$	3.28294	−	10.1039i	0.226007	−	0.695578i	−0.772181	−	0.635403i	$-0.780834\pi$
$211$	3.28294	−	10.1039i	0.226007	−	0.695578i	0.998188	−	0.0601751i	$-0.0191659\pi$
$212$	−3.96104	−	12.1908i	−0.272045	−	0.837270i
$213$	10.8197	−	7.86096i	0.741353	−	0.538624i
$214$	−0.964712			−0.0659464
$215$	2.00578	−	1.45728i	0.136793	−	0.0993859i
$216$	−9.76274	+	7.09304i	−0.664270	+	0.482621i
$217$	2.18353	+	1.58643i	0.148228	+	0.107694i
$218$	−3.18561	+	9.80431i	−0.215757	+	0.664032i
$219$	49.7632			3.36269
$220$	3.83658	+	2.78744i	0.258662	+	0.187929i
$221$	0.583329	+	1.79530i	0.0392390	+	0.120765i
$222$	−33.7053	+	24.4883i	−2.26215	+	1.64355i
$223$	4.02136	−	12.3765i	0.269290	−	0.828791i	−0.721383	−	0.692536i	$-0.756493\pi$
$223$	4.02136	−	12.3765i	0.269290	−	0.828791i	0.990674	−	0.136255i	$-0.0435066\pi$
$224$	−2.09437	−	6.44582i	−0.139936	−	0.430679i
$225$	12.9334	+	39.8048i	0.862225	+	2.65366i
$226$	3.57516	+	11.0032i	0.237816	+	0.731922i
$227$	1.79235	+	5.51629i	0.118963	+	0.366129i	0.992753	−	0.120174i	$-0.0383452\pi$
$227$	1.79235	+	5.51629i	0.118963	+	0.366129i	−0.873790	+	0.486303i	$0.838345\pi$
$228$	−9.03755	+	27.8147i	−0.598527	+	1.84208i
$229$	17.8136	−	12.9424i	1.17716	−	0.855255i	0.185309	−	0.982680i	$-0.440671\pi$
$229$	17.8136	−	12.9424i	1.17716	−	0.855255i	0.991848	+	0.127425i	$0.0406713\pi$
$230$	−11.9003	−	36.6254i	−0.784683	−	2.41501i
$231$	2.49142	+	1.81012i	0.163923	+	0.119097i
$232$	−1.39892			−0.0918439
$233$	7.04283	−	21.6756i	0.461391	−	1.42002i	−0.402074	−	0.915607i	$-0.631710\pi$
$233$	7.04283	−	21.6756i	0.461391	−	1.42002i	0.863465	−	0.504409i	$-0.168290\pi$
$234$	4.25296	+	3.08996i	0.278025	+	0.201997i
$235$	10.4052	−	7.55982i	0.678760	−	0.493148i
$236$	17.4057	−	12.6460i	1.13301	−	0.823183i
$237$	4.00484			0.260142
$238$	6.58833	−	4.78670i	0.427058	−	0.310276i
$239$	−7.67951	−	23.6351i	−0.496746	−	1.52883i	−0.814218	−	0.580560i	$-0.802834\pi$
$239$	−7.67951	−	23.6351i	−0.496746	−	1.52883i	0.317472	−	0.948268i	$-0.397166\pi$
$240$	−15.5558	+	47.8758i	−1.00412	+	3.09037i
$241$	−8.10626	−	5.88954i	−0.522170	−	0.379379i	0.295251	−	0.955420i	$-0.404597\pi$
$241$	−8.10626	−	5.88954i	−0.522170	−	0.379379i	−0.817421	+	0.576041i	$0.804597\pi$
$242$	14.9857	+	10.8877i	0.963316	+	0.699890i
$243$	−12.9566			−0.831167
$244$	−6.15155	+	18.9325i	−0.393813	+	1.21203i
$245$	−3.36347			−0.214884
$246$	−23.3993	−	28.3382i	−1.49189	−	1.80678i
$247$	−2.84392			−0.180954
$248$	0.893533	−	2.75001i	0.0567394	−	0.174626i
$249$	−26.6306			−1.68764
$250$	6.60765	+	4.80074i	0.417905	+	0.303625i
$251$	−9.00668	−	6.54373i	−0.568496	−	0.413037i	0.266062	−	0.963956i	$-0.414277\pi$
$251$	−9.00668	−	6.54373i	−0.568496	−	0.413037i	−0.834559	+	0.550919i	$0.814277\pi$
$252$	2.91071	−	8.95824i	0.183357	−	0.564316i
$253$	1.89841	+	5.84272i	0.119352	+	0.367328i
$254$	5.50870	−	4.00230i	0.345646	−	0.251127i
$255$	−45.9571			−2.87795
$256$	−16.9614	+	12.3232i	−1.06009	+	0.770201i
$257$	−13.0635	+	9.49121i	−0.814881	+	0.592045i	−0.915241	−	0.402906i	$-0.868000\pi$
$257$	−13.0635	+	9.49121i	−0.814881	+	0.592045i	0.100361	+	0.994951i	$0.468000\pi$
$258$	3.42266	+	2.48671i	0.213086	+	0.154816i
$259$	−2.24313	+	6.90364i	−0.139381	+	0.428971i
$260$	2.04871			0.127055
$261$	−7.00364	−	5.08845i	−0.433515	−	0.314967i
$262$	5.79080	+	17.8222i	0.357757	+	1.10106i
$263$	5.21978	−	3.79239i	0.321865	−	0.233849i	−0.415106	−	0.909773i	$-0.636255\pi$
$263$	5.21978	−	3.79239i	0.321865	−	0.233849i	0.736971	+	0.675924i	$0.236255\pi$
$264$	1.01952	−	3.13777i	0.0627474	−	0.193117i
$265$	9.37733	+	28.8604i	0.576045	+	1.77288i
$266$	3.79128	+	11.6684i	0.232458	+	0.715433i
$267$	−1.57690	−	4.85320i	−0.0965047	−	0.297011i
$268$	5.95893	+	18.3397i	0.364000	+	1.12028i
$269$	−3.15461	+	9.70891i	−0.192340	+	0.591962i	0.807657	+	0.589652i	$0.200735\pi$
$269$	−3.15461	+	9.70891i	−0.192340	+	0.591962i	−0.999997	+	0.00230993i	$0.999265\pi$
$270$	−56.6883	+	41.1865i	−3.44994	+	2.50653i
$271$	−2.23726	−	6.88557i	−0.135904	−	0.418268i	0.859826	−	0.510587i	$-0.170572\pi$
$271$	−2.23726	−	6.88557i	−0.135904	−	0.418268i	−0.995729	+	0.0923191i	$0.970572\pi$
$272$	−17.1802	−	12.4822i	−1.04171	−	0.756843i
$273$	1.33040			0.0805195
$274$	1.95086	−	6.00413i	0.117856	−	0.362723i
$275$	−5.06838	−	3.68239i	−0.305635	−	0.222057i
$276$	22.0806	−	16.0425i	1.32910	−	0.965645i
$277$	−20.0676	+	14.5800i	−1.20574	+	0.876025i	−0.994837	−	0.101481i	$-0.967642\pi$
$277$	−20.0676	+	14.5800i	−1.20574	+	0.876025i	−0.210907	+	0.977506i	$0.567642\pi$
$278$	5.47464			0.328347
$279$	14.4763	−	10.5177i	0.866674	−	0.629676i
$280$	1.11352	+	3.42705i	0.0665453	+	0.204805i
$281$	−0.0823369	+	0.253407i	−0.00491181	+	0.0151170i	−0.953482	−	0.301449i	$-0.902530\pi$
$281$	−0.0823369	+	0.253407i	−0.00491181	+	0.0151170i	0.948571	+	0.316566i	$0.102530\pi$
$282$	17.7554	+	12.9001i	1.05732	+	0.768189i
$283$	21.2966	+	15.4729i	1.26595	+	0.919770i	0.999034	−	0.0439488i	$-0.0139939\pi$
$283$	21.2966	+	15.4729i	1.26595	+	0.919770i	0.266921	+	0.963719i	$0.413994\pi$
$284$	6.12304			0.363335
$285$	21.3954	−	65.8483i	1.26735	−	3.90052i
$286$	−0.786893			−0.0465300
$287$	−6.20048	−	1.59813i	−0.366003	−	0.0943345i
$288$	−44.9335			−2.64773
$289$	0.737675	−	2.27033i	0.0433926	−	0.133549i
$290$	−8.12299			−0.476998
$291$	34.8801	+	25.3419i	2.04471	+	1.48557i
$292$	18.4321	+	13.3917i	1.07866	+	0.783692i
$293$	−1.79142	+	5.51343i	−0.104656	+	0.322098i	−0.989650	−	0.143505i	$-0.954163\pi$
$293$	−1.79142	+	5.51343i	−0.104656	+	0.322098i	0.884994	+	0.465603i	$0.154163\pi$
$294$	−1.77358	−	5.45852i	−0.103437	−	0.318347i
$295$	−41.2061	+	29.9380i	−2.39911	+	1.74306i
$296$	7.77675			0.452014
$297$	9.04328	−	6.57033i	0.524744	−	0.381249i
$298$	25.7389	−	18.7004i	1.49102	−	1.08329i
$299$	2.14714	+	1.55999i	0.124172	+	0.0902163i
$300$	−8.60081	+	26.4706i	−0.496568	+	1.52828i
$301$	0.737120			0.0424869
$302$	−9.68162	−	7.03411i	−0.557115	−	0.404767i
$303$	8.69666	+	26.7656i	0.499610	+	1.53764i
$304$	25.8830	−	18.8051i	1.48449	−	1.07855i
$305$	14.5631	−	44.8207i	0.833882	−	2.56643i
$306$	−16.6840	−	51.3479i	−0.953758	−	2.93537i
$307$	0.590369	+	1.81697i	0.0336941	+	0.103700i	0.966489	−	0.256708i	$-0.0826377\pi$
$307$	0.590369	+	1.81697i	0.0336941	+	0.103700i	−0.932795	+	0.360407i	$0.882638\pi$
$308$	0.435693	+	1.34093i	0.0248259	+	0.0764064i
$309$	6.31355	+	19.4311i	0.359165	+	1.10540i
$310$	5.18839	−	15.9682i	0.294681	−	0.906933i
$311$	−23.2121	+	16.8645i	−1.31624	+	0.956301i	−0.316264	+	0.948671i	$0.602429\pi$
$311$	−23.2121	+	16.8645i	−1.31624	+	0.956301i	−0.999971	+	0.00762970i	$0.997571\pi$
$312$	−0.440444	−	1.35555i	−0.0249353	−	0.0767428i
$313$	−25.9935	−	18.8853i	−1.46924	−	1.06746i	−0.980834	−	0.194845i	$-0.937580\pi$
$313$	−25.9935	−	18.8853i	−1.46924	−	1.06746i	−0.488403	−	0.872618i	$-0.662420\pi$
$314$	−45.4676			−2.56589
$315$	−6.89078	+	21.2077i	−0.388252	+	1.19492i
$316$	1.48338	+	1.07774i	0.0834467	+	0.0606276i
$317$	−13.6800	+	9.93913i	−0.768347	+	0.558237i	−0.901459	−	0.432864i	$-0.857503\pi$
$317$	−13.6800	+	9.93913i	−0.768347	+	0.558237i	0.133112	+	0.991101i	$0.457503\pi$
$318$	−41.8924	+	30.4366i	−2.34921	+	1.70680i
$319$	1.29583			0.0725526
$320$	−7.86209	+	5.71214i	−0.439504	+	0.319318i
$321$	0.500181	+	1.53940i	0.0279174	+	0.0859209i
$322$	3.53810	−	10.8892i	0.197171	−	0.606830i
$323$	23.6297	+	17.1680i	1.31479	+	0.955251i
$324$	−17.3154	−	12.5804i	−0.961967	−	0.698910i
$325$	−2.70648			−0.150129
$326$	2.02629	−	6.23629i	0.112226	−	0.345396i
$327$	17.2965			0.956499
$328$	0.424406	+	6.84677i	0.0234339	+	0.378049i
$329$	3.82389			0.210818
$330$	5.91997	−	18.2198i	0.325884	−	1.00297i
$331$	−7.47391			−0.410803			−0.205402	−	0.978678i	$-0.565850\pi$
$331$	−7.47391			−0.410803			−0.205402	+	0.978678i	$0.565850\pi$
$332$	−9.86388	−	7.16653i	−0.541351	−	0.393314i
$333$	38.9339	+	28.2872i	2.13357	+	1.55013i
$334$	4.41380	−	13.5843i	0.241513	−	0.743299i
$335$	−14.1071	−	43.4172i	−0.770754	−	2.37214i
$336$	−12.1082	+	8.79713i	−0.660557	+	0.479923i
$337$	−18.4764			−1.00647			−0.503237	−	0.864148i	$-0.667858\pi$
$337$	−18.4764			−1.00647			−0.503237	+	0.864148i	$0.667858\pi$
$338$	19.1769	−	13.9328i	1.04308	−	0.757845i
$339$	15.7043	−	11.4098i	0.852939	−	0.619697i
$340$	−17.0224	−	12.3675i	−0.923168	−	0.670721i
$341$	−0.827685	+	2.54735i	−0.0448216	+	0.137947i
$342$	81.3396			4.39834
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−0.244032	−	0.751053i	−0.0131573	−	0.0404941i
$345$	−52.2734	+	37.9789i	−2.81431	+	2.04471i
$346$	−2.71122	+	8.34428i	−0.145756	+	0.448591i
$347$	8.78957	+	27.0515i	0.471849	+	1.45220i	0.850161	+	0.526523i	$0.176505\pi$
$347$	8.78957	+	27.0515i	0.471849	+	1.45220i	−0.378312	+	0.925678i	$0.623495\pi$
$348$	−1.77900	−	5.47520i	−0.0953644	−	0.293501i
$349$	9.88484	+	30.4224i	0.529123	+	1.62847i	0.756015	+	0.654554i	$0.227143\pi$
$349$	9.88484	+	30.4224i	0.529123	+	1.62847i	−0.226892	+	0.973920i	$0.572857\pi$
$350$	3.60806	+	11.1045i	0.192859	+	0.593559i
$351$	1.49226	−	4.59270i	0.0796509	−	0.245140i
$352$	5.44140	−	3.95341i	0.290027	−	0.210717i
$353$	0.751470	+	2.31279i	0.0399967	+	0.123097i	0.969061	−	0.246821i	$-0.0793858\pi$
$353$	0.751470	+	2.31279i	0.0399967	+	0.123097i	−0.929064	+	0.369918i	$0.879386\pi$
$354$	−70.3141	−	51.0862i	−3.73715	−	2.71520i
$355$	−14.4956			−0.769347
$356$	0.721961	−	2.22197i	0.0382639	−	0.117764i
$357$	−11.0541	−	8.03126i	−0.585044	−	0.425060i
$358$	−14.6807	+	10.6661i	−0.775897	+	0.563722i
$359$	0.239414	−	0.173944i	0.0126358	−	0.00918043i	−0.581449	−	0.813583i	$-0.697514\pi$
$359$	0.239414	−	0.173944i	0.0126358	−	0.00918043i	0.594085	+	0.804402i	$0.297514\pi$
$360$	23.8898			1.25910
$361$	−20.2281	+	14.6966i	−1.06464	+	0.773504i
$362$	9.17284	+	28.2311i	0.482114	+	1.48379i
$363$	9.60392	−	29.5578i	0.504075	−	1.55138i
$364$	0.492776	+	0.358023i	0.0258285	+	0.0187655i
$365$	−43.6361	−	31.7035i	−2.28402	−	1.65944i
$366$	80.4180			4.20352
$367$	2.04209	−	6.28492i	0.106596	−	0.328070i	−0.883505	−	0.468421i	$-0.844823\pi$
$367$	2.04209	−	6.28492i	0.106596	−	0.328070i	0.990102	+	0.140351i	$0.0448231\pi$
$368$	−29.8567			−1.55639
$369$	−22.7797	+	35.8217i	−1.18586	+	1.86481i
$370$	45.1565			2.34757
$371$	−2.78799	+	8.58056i	−0.144745	+	0.445480i
$372$	11.8995			0.616959
$373$	4.68228	+	3.40187i	0.242439	+	0.176142i	0.702369	−	0.711813i	$-0.252126\pi$
$373$	4.68228	+	3.40187i	0.242439	+	0.176142i	−0.459930	+	0.887955i	$0.652126\pi$
$374$	6.53817	+	4.75026i	0.338081	+	0.245630i
$375$	4.23467	−	13.0330i	0.218677	−	0.673019i
$376$	−1.26594	−	3.89617i	−0.0652860	−	0.200930i
$377$	0.452897	−	0.329049i	0.0233254	−	0.0169469i
$378$	−20.8328			−1.07153
$379$	7.39090	−	5.36981i	0.379645	−	0.275828i	−0.381554	−	0.924347i	$-0.624611\pi$
$379$	7.39090	−	5.36981i	0.379645	−	0.275828i	0.761199	+	0.648518i	$0.224611\pi$
$380$	25.6452	−	18.6323i	1.31557	−	0.955817i
$381$	−9.24265	−	6.71518i	−0.473515	−	0.344029i
$382$	3.90334	−	12.0132i	0.199712	−	0.614651i
$383$	6.39806			0.326926			0.163463	−	0.986549i	$-0.447734\pi$
$383$	6.39806			0.326926			0.163463	+	0.986549i	$0.447734\pi$
$384$	20.6146	+	14.9774i	1.05198	+	0.764310i
$385$	−1.03146	−	3.17449i	−0.0525679	−	0.161787i
$386$	5.04049	−	3.66213i	0.256554	−	0.186397i
$387$	1.51015	−	4.64775i	0.0767651	−	0.236259i
$388$	6.09976	+	18.7731i	0.309668	+	0.953061i
$389$	−4.30337	−	13.2444i	−0.218190	−	0.671519i	−0.998912	−	0.0466405i	$-0.985148\pi$
$389$	−4.30337	−	13.2444i	−0.218190	−	0.671519i	0.780722	−	0.624879i	$-0.214852\pi$
$390$	−2.55748	−	7.87113i	−0.129503	−	0.398570i
$391$	−8.42301	−	25.9234i	−0.425970	−	1.31100i
$392$	−0.331062	+	1.01890i	−0.0167211	+	0.0514624i
$393$	25.4367	−	18.4809i	1.28311	−	0.932236i
$394$	0.719316	+	2.21383i	0.0362386	+	0.111531i
$395$	−3.51174	−	2.55143i	−0.176695	−	0.128376i
$396$	9.34754			0.469732
$397$	−2.23028	+	6.86409i	−0.111934	+	0.344499i	−0.991295	−	0.131657i	$-0.957970\pi$
$397$	−2.23028	+	6.86409i	−0.111934	+	0.344499i	0.879361	+	0.476156i	$0.157970\pi$
$398$	−0.566846	−	0.411838i	−0.0284134	−	0.0206435i
$399$	16.6536	−	12.0996i	0.833723	−	0.605735i
$400$	24.6322	−	17.8963i	1.23161	−	0.894817i
$401$	21.8579			1.09153			0.545766	−	0.837937i	$-0.316239\pi$
$401$	21.8579			1.09153			0.545766	+	0.837937i	$0.316239\pi$
$402$	63.0224	−	45.7884i	3.14327	−	2.28372i
$403$	0.357568	+	1.10048i	0.0178117	+	0.0548188i
$404$	−3.98164	+	12.2542i	−0.198094	+	0.609671i
$405$	40.9923	+	29.7826i	2.03692	+	1.47991i
$406$	−1.95383	−	1.41954i	−0.0969668	−	0.0704505i
$407$	−7.20365			−0.357072
$408$	−4.52349	+	13.9219i	−0.223946	+	0.689236i
$409$	−18.0873			−0.894358			−0.447179	−	0.894444i	$-0.647571\pi$
$409$	−18.0873			−0.894358			−0.447179	+	0.894444i	$0.647571\pi$
$410$	2.46435	+	39.7564i	0.121706	+	1.96343i
$411$	−10.5923			−0.522481
$412$	−2.89057	+	8.89626i	−0.142408	+	0.438287i
$413$	−15.1431			−0.745145
$414$	−61.4108	−	44.6176i	−3.01818	−	2.19283i
$415$	23.3517	+	16.9660i	1.14629	+	0.832827i
$416$	0.897901	−	2.76346i	0.0440232	−	0.135490i
$417$	−2.83848	−	8.73594i	−0.139001	−	0.427801i
$418$	−9.85013	+	7.15654i	−0.481785	+	0.350038i
$419$	25.6257			1.25190			0.625949	−	0.779864i	$-0.284712\pi$
$419$	25.6257			1.25190			0.625949	+	0.779864i	$0.284712\pi$
$420$	−11.9970	+	8.71630i	−0.585391	+	0.425312i
$421$	15.7742	−	11.4606i	0.768788	−	0.558557i	−0.132805	−	0.991142i	$-0.542398\pi$
$421$	15.7742	−	11.4606i	0.768788	−	0.558557i	0.901593	+	0.432585i	$0.142398\pi$
$422$	−15.8964	−	11.5494i	−0.773825	−	0.562217i
$423$	7.83405	−	24.1107i	0.380904	−	1.17230i
$424$	9.66575			0.469410
$425$	22.4877	+	16.3383i	1.09082	+	0.792524i
$426$	−7.64364	−	23.5247i	−0.370335	−	1.13978i
$427$	11.3355	−	8.23575i	0.548565	−	0.398556i
$428$	−0.229001	+	0.704793i	−0.0110692	+	0.0340674i
$429$	0.407986	+	1.25565i	0.0196978	+	0.0606235i
$430$	−1.41700	−	4.36106i	−0.0683336	−	0.210309i
$431$	1.10244	+	3.39297i	0.0531028	+	0.163434i	0.974091	−	0.226157i	$-0.0726164\pi$
$431$	1.10244	+	3.39297i	0.0531028	+	0.163434i	−0.920988	+	0.389591i	$0.872616\pi$
$432$	16.7874	+	51.6664i	0.807686	+	2.48580i
$433$	10.5468	−	32.4598i	0.506848	−	1.55992i	−0.290795	−	0.956785i	$-0.593920\pi$
$433$	10.5468	−	32.4598i	0.506848	−	1.55992i	0.797642	−	0.603131i	$-0.206080\pi$
$434$	4.03850	−	2.93414i	0.193854	−	0.140843i
$435$	4.21159	+	12.9619i	0.201930	+	0.621477i
$436$	6.40657	+	4.65465i	0.306819	+	0.222917i
$437$	41.0649			1.96440
$438$	28.4414	−	87.5338i	1.35898	−	4.18252i
$439$	−0.0379678	−	0.0275853i	−0.00181211	−	0.00131657i	0.586879	−	0.809675i	$-0.300356\pi$
$439$	−0.0379678	−	0.0275853i	−0.00181211	−	0.00131657i	−0.588691	+	0.808358i	$0.700356\pi$
$440$	−2.89303	+	2.10191i	−0.137920	+	0.100204i
$441$	−5.36360	+	3.89688i	−0.255410	+	0.185566i
$442$	3.49134			0.166066
$443$	−16.7635	+	12.1794i	−0.796460	+	0.578662i	−0.909873	−	0.414886i	$-0.863821\pi$
$443$	−16.7635	+	12.1794i	−0.796460	+	0.578662i	0.113414	+	0.993548i	$0.463821\pi$
$444$	9.88963	+	30.4372i	0.469341	+	1.44448i
$445$	−1.70916	+	5.26026i	−0.0810221	+	0.249360i
$446$	−19.4719	−	14.1472i	−0.922023	−	0.669889i
$447$	−43.1855	−	31.3761i	−2.04260	−	1.48404i
$448$	−2.88930			−0.136507
$449$	6.70903	−	20.6483i	0.316619	−	0.974453i	−0.658464	−	0.752612i	$-0.728794\pi$
$449$	6.70903	−	20.6483i	0.316619	−	0.974453i	0.975083	−	0.221841i	$-0.0712065\pi$
$450$	77.4088			3.64909
$451$	−0.393129	−	6.34220i	−0.0185117	−	0.298643i
$452$	8.88730			0.418024
$453$	−6.20469	+	19.0961i	−0.291522	+	0.897212i
$454$	10.7276			0.503470
$455$	−1.16659	−	0.847580i	−0.0546907	−	0.0397352i
$456$	−17.8416	−	12.9627i	−0.835511	−	0.607035i
$457$	−0.745736	+	2.29514i	−0.0348841	+	0.107362i	−0.966982	−	0.254843i	$-0.917976\pi$
$457$	−0.745736	+	2.29514i	−0.0348841	+	0.107362i	0.932098	+	0.362205i	$0.117976\pi$
$458$	−12.5845	−	38.7313i	−0.588037	−	1.80979i
$459$	−40.1238	+	29.1517i	−1.87282	+	1.36068i
$460$	−29.5824			−1.37929
$461$	6.13821	−	4.45967i	0.285885	−	0.207708i	−0.435595	−	0.900143i	$-0.643462\pi$
$461$	6.13821	−	4.45967i	0.285885	−	0.207708i	0.721480	+	0.692435i	$0.243462\pi$
$462$	4.60794	−	3.34787i	0.214381	−	0.155757i
$463$	22.5500	+	16.3836i	1.04799	+	0.761409i	0.971829	−	0.235687i	$-0.0757339\pi$
$463$	22.5500	+	16.3836i	1.04799	+	0.761409i	0.0761604	+	0.997096i	$0.475734\pi$
$464$	−1.94610	+	5.98947i	−0.0903453	+	0.278054i
$465$	−28.1707			−1.30638
$466$	−34.1023	−	24.7768i	−1.57976	−	1.14776i
$467$	4.42246	+	13.6109i	0.204647	+	0.629839i	0.999728	+	0.0233352i	$0.00742851\pi$
$467$	4.42246	+	13.6109i	0.204647	+	0.629839i	−0.795081	+	0.606504i	$0.792571\pi$
$468$	3.26700	−	2.37361i	0.151017	−	0.109720i
$469$	4.19422	−	12.9085i	0.193671	−	0.596058i
$470$	−7.35082	−	22.6235i	−0.339068	−	1.04354i
$471$	23.5739	+	72.5531i	1.08623	+	3.34307i
$472$	5.01331	+	15.4294i	0.230756	+	0.710195i
$473$	0.226048	+	0.695705i	0.0103937	+	0.0319885i
$474$	2.28891	−	7.04453i	0.105133	−	0.323566i
$475$	−33.8791	+	24.6146i	−1.55448	+	1.12939i
$476$	−1.93311	−	5.94951i	−0.0886041	−	0.272695i
$477$	48.3911	+	35.1582i	2.21568	+	1.60978i
$478$	−45.9634			−2.10232
$479$	−5.04597	+	15.5299i	−0.230556	+	0.709579i	0.767124	+	0.641499i	$0.221687\pi$
$479$	−5.04597	+	15.5299i	−0.230556	+	0.709579i	−0.997680	+	0.0680796i	$0.978313\pi$
$480$	57.2302	+	41.5802i	2.61219	+	1.89787i
$481$	−2.51770	+	1.82922i	−0.114797	+	0.0834051i
$482$	−14.9927	+	10.8929i	−0.682901	+	0.496156i
$483$	−19.2104			−0.874102
$484$	11.5115	−	8.36363i	0.523252	−	0.380165i
$485$	−14.4405	−	44.4433i	−0.655709	−	2.01807i
$486$	−7.40516	+	22.7907i	−0.335905	+	1.03381i
$487$	−17.3751	−	12.6238i	−0.787343	−	0.572038i	0.119831	−	0.992794i	$-0.461765\pi$
$487$	−17.3751	−	12.6238i	−0.787343	−	0.572038i	−0.907174	+	0.420756i	$0.861765\pi$
$488$	−12.1442	−	8.82327i	−0.549742	−	0.399411i
$489$	−11.0019			−0.497523
$490$	−1.92234	+	5.91636i	−0.0868425	+	0.267274i
$491$	26.9193			1.21485			0.607426	−	0.794377i	$-0.292202\pi$
$491$	26.9193			1.21485			0.607426	+	0.794377i	$0.292202\pi$
$492$	−26.2576	+	10.3680i	−1.18378	+	0.467428i
$493$	−5.74943			−0.258941
$494$	−1.62540	+	5.00247i	−0.0731302	+	0.225072i
$495$	−22.1293			−0.994637
$496$	−10.5311	−	7.65129i	−0.472860	−	0.343553i
$497$	−3.48664	−	2.53319i	−0.156397	−	0.113629i
$498$	−15.2203	+	46.8433i	−0.682039	+	2.09910i
$499$	2.64145	+	8.12955i	0.118248	+	0.363929i	0.992611	−	0.121344i	$-0.0387204\pi$
$499$	2.64145	+	8.12955i	0.118248	+	0.363929i	−0.874363	+	0.485272i	$0.838720\pi$
$500$	5.07580	−	3.68778i	0.226997	−	0.164923i
$501$	−23.9650			−1.07068
$502$	−16.6581	+	12.1028i	−0.743487	+	0.540175i
$503$	−3.04720	+	2.21392i	−0.135868	+	0.0987140i	−0.653643	−	0.756803i	$-0.726760\pi$
$503$	−3.04720	+	2.21392i	−0.135868	+	0.0987140i	0.517775	+	0.855517i	$0.326760\pi$
$504$	5.74623	+	4.17488i	0.255957	+	0.185964i
$505$	9.42610	−	29.0106i	0.419456	−	1.29095i
$506$	11.3624			0.505119
$507$	−32.1755	−	23.3768i	−1.42896	−	1.03820i
$508$	−1.61633	−	4.97456i	−0.0717132	−	0.220710i
$509$	19.0434	−	13.8358i	0.844083	−	0.613262i	−0.0794256	−	0.996841i	$-0.525309\pi$
$509$	19.0434	−	13.8358i	0.844083	−	0.613262i	0.923508	+	0.383579i	$0.125309\pi$
$510$	−26.2661	+	80.8388i	−1.16308	+	3.57960i
$511$	−4.95545	−	15.2513i	−0.219216	−	0.674678i
$512$	6.90770	+	21.2597i	0.305280	+	0.939556i
$513$	−23.0894	−	71.0619i	−1.01942	−	3.13746i
$514$	9.22882	+	28.4034i	0.407066	+	1.25282i
$515$	6.84310	−	21.0609i	0.301543	−	0.928054i
$516$	2.62919	−	1.91022i	0.115743	−	0.0840926i
$517$	1.17265	+	3.60904i	0.0515731	+	0.158726i
$518$	10.8615	+	7.89135i	0.477227	+	0.346726i
$519$	14.7207			0.646169
$520$	−0.477387	+	1.46925i	−0.0209348	+	0.0644307i
$521$	25.4955	+	18.5236i	1.11698	+	0.811533i	0.983748	−	0.179552i	$-0.0574650\pi$
$521$	25.4955	+	18.5236i	1.11698	+	0.811533i	0.133230	+	0.991085i	$0.457465\pi$
$522$	−12.9534	+	9.41122i	−0.566956	+	0.411918i
$523$	−11.3430	+	8.24116i	−0.495994	+	0.360361i	−0.807485	−	0.589888i	$-0.799172\pi$
$523$	−11.3430	+	8.24116i	−0.495994	+	0.360361i	0.311491	+	0.950249i	$0.399172\pi$
$524$	14.3951			0.628851
$525$	15.8488	−	11.5148i	0.691699	−	0.502549i
$526$	−3.68755	−	11.3491i	−0.160785	−	0.494844i
$527$	3.67233	−	11.3023i	0.159969	−	0.492334i
$528$	−12.0160	−	8.73016i	−0.522930	−	0.379931i
$529$	−12.3963	−	9.00641i	−0.538968	−	0.391583i
$530$	56.1251			2.43792
$531$	−31.0239	+	95.4819i	−1.34632	+	4.14356i
$532$	9.42455			0.408606
$533$	−1.74787	−	2.11679i	−0.0757086	−	0.0916885i
$534$	−9.43805			−0.408424
$535$	0.542135	−	1.66852i	0.0234385	−	0.0721363i
$536$	−14.5410			−0.628076
$537$	24.6316	+	17.8959i	1.06293	+	0.772266i
$538$	15.2750	+	11.0980i	0.658554	+	0.478467i
$539$	0.306664	−	0.943815i	0.0132090	−	0.0406530i
$540$	16.6332	+	51.1917i	0.715778	+	2.20294i
$541$	8.36256	−	6.07576i	0.359535	−	0.261217i	−0.393323	−	0.919400i	$-0.628675\pi$
$541$	8.36256	−	6.07576i	0.359535	−	0.261217i	0.752858	+	0.658183i	$0.228675\pi$
$542$	−13.3904			−0.575167
$543$	40.2927	−	29.2743i	1.72912	−	1.25628i
$544$	−24.1427	+	17.5407i	−1.03511	+	0.752053i
$545$	−15.1668	−	11.0194i	−0.649676	−	0.472018i
$546$	0.760371	−	2.34018i	0.0325409	−	0.100151i
$547$	−6.20570			−0.265337			−0.132668	−	0.991160i	$-0.542354\pi$
$547$	−6.20570			−0.265337			−0.132668	+	0.991160i	$0.542354\pi$
$548$	−3.92336	−	2.85049i	−0.167598	−	0.121767i
$549$	−28.7055	−	88.3466i	−1.22512	−	3.77054i
$550$	−9.37411	+	6.81069i	−0.399713	+	0.290409i
$551$	2.67666	−	8.23791i	0.114029	−	0.350947i
$552$	6.35981	+	19.5735i	0.270692	+	0.833103i
$553$	−0.398804	−	1.22739i	−0.0169589	−	0.0521940i
$554$	14.1769	+	43.6320i	0.602318	+	1.85374i
$555$	−23.4126	−	72.0566i	−0.993810	−	3.05863i
$556$	1.29956	−	3.99962i	0.0551135	−	0.169622i
$557$	−20.6520	+	15.0046i	−0.875054	+	0.635764i	−0.931938	−	0.362617i	$-0.881883\pi$
$557$	−20.6520	+	15.0046i	−0.875054	+	0.635764i	0.0568844	+	0.998381i	$0.481883\pi$
$558$	−10.2269	−	31.4751i	−0.432939	−	1.33245i
$559$	0.255664	+	0.185751i	0.0108134	+	0.00785643i
$560$	16.2219			0.685501
$561$	4.19014	−	12.8959i	0.176908	−	0.544466i
$562$	0.398686	+	0.289662i	0.0168175	+	0.0122187i
$563$	24.1847	−	17.5712i	1.01927	−	0.740540i	0.0531334	−	0.998587i	$-0.483079\pi$
$563$	24.1847	−	17.5712i	1.01927	−	0.740540i	0.966132	+	0.258048i	$0.0830791\pi$
$564$	13.6392	−	9.90945i	0.574313	−	0.417263i
$565$	−21.0397			−0.885147
$566$	39.3887	−	28.6176i	1.65563	−	1.20289i
$567$	4.65521	+	14.3273i	0.195501	+	0.601689i
$568$	−1.42678	+	4.39118i	−0.0598665	+	0.184250i
$569$	10.7358	+	7.80002i	0.450068	+	0.326994i	0.789623	−	0.613593i	$-0.210276\pi$
$569$	10.7358	+	7.80002i	0.450068	+	0.326994i	−0.339554	+	0.940586i	$0.610276\pi$
$570$	−103.599	−	75.2693i	−4.33930	−	3.15268i
$571$	−26.0728			−1.09111			−0.545556	−	0.838074i	$-0.683681\pi$
$571$	−26.0728			−1.09111			−0.545556	+	0.838074i	$0.683681\pi$
$572$	−0.186791	+	0.574883i	−0.00781011	+	0.0240371i
$573$	−21.1934			−0.885369
$574$	−6.35491	+	9.99329i	−0.265249	+	0.417112i
$575$	39.0804			1.62976
$576$	−5.91935	+	18.2179i	−0.246639	+	0.759078i
$577$	−1.16688			−0.0485777			−0.0242889	−	0.999705i	$-0.507732\pi$
$577$	−1.16688			−0.0485777			−0.0242889	+	0.999705i	$0.507732\pi$
$578$	−3.57191	−	2.59515i	−0.148572	−	0.107944i
$579$	−8.45707	−	6.14442i	−0.351464	−	0.255353i
$580$	−1.92822	+	5.93444i	−0.0800648	+	0.246414i
$581$	2.65189	+	8.16167i	0.110019	+	0.338603i
$582$	64.5117	−	46.8705i	2.67410	−	1.94285i
$583$	−8.95344			−0.370814
$584$	−13.8990	+	10.0982i	−0.575146	+	0.417868i
$585$	−7.73425	+	5.61926i	−0.319772	+	0.232328i
$586$	8.67429	+	6.30224i	0.358332	+	0.260343i
$587$	0.181772	−	0.559438i	0.00750255	−	0.0230905i	−0.947235	−	0.320539i	$-0.896136\pi$
$587$	0.181772	−	0.559438i	0.00750255	−	0.0230905i	0.954738	+	0.297449i	$0.0961358\pi$
$588$	−4.40886			−0.181818
$589$	14.4845	+	10.5236i	0.596821	+	0.433616i
$590$	29.1103	+	89.5923i	1.19845	+	3.68845i
$591$	3.15967	−	2.29564i	0.129972	−	0.0944299i
$592$	10.8185	−	33.2960i	0.444639	−	1.36846i
$593$	1.36270	+	4.19396i	0.0559594	+	0.172225i	0.975130	−	0.221635i	$-0.0711394\pi$
$593$	1.36270	+	4.19396i	0.0559594	+	0.172225i	−0.919170	+	0.393860i	$0.871139\pi$
$594$	−6.38868	−	19.6623i	−0.262131	−	0.806756i
$595$	4.57643	+	14.0848i	0.187615	+	0.577421i
$596$	−7.55218	−	23.2432i	−0.309349	−	0.952080i
$597$	−0.363276	+	1.11805i	−0.0148679	+	0.0457587i
$598$	3.97119	−	2.88524i	0.162394	−	0.117986i
$599$	5.16681	+	15.9018i	0.211110	+	0.649730i	0.999407	+	0.0344347i	$0.0109631\pi$
$599$	5.16681	+	15.9018i	0.211110	+	0.649730i	−0.788297	+	0.615295i	$0.789037\pi$
$600$	−16.9794	−	12.3363i	−0.693182	−	0.503626i
$601$	36.2146			1.47723			0.738613	−	0.674130i	$-0.235481\pi$
$601$	36.2146			1.47723			0.738613	+	0.674130i	$0.235481\pi$
$602$	0.421290	−	1.29660i	0.0171705	−	0.0528453i
$603$	−72.7989	−	52.8915i	−2.96460	−	2.15391i
$604$	−7.43712	+	5.40339i	−0.302612	+	0.219861i
$605$	−27.2523	+	19.8000i	−1.10796	+	0.804983i
$606$	52.0512			2.11444
$607$	11.7336	−	8.52499i	0.476254	−	0.346018i	−0.323620	−	0.946187i	$-0.604900\pi$
$607$	11.7336	−	8.52499i	0.476254	−	0.346018i	0.799873	+	0.600169i	$0.204900\pi$
$608$	−13.8930	−	42.7583i	−0.563437	−	1.73408i
$609$	−1.25216	+	3.85374i	−0.0507399	+	0.156161i
$610$	−70.5165	−	51.2332i	−2.85513	−	2.07437i
$611$	1.32629	+	0.963603i	0.0536558	+	0.0389832i
$612$	−41.4738			−1.67648
$613$	2.14381	−	6.59796i	0.0865876	−	0.266489i	−0.898383	−	0.439214i	$-0.855257\pi$
$613$	2.14381	−	6.59796i	0.0865876	−	0.266489i	0.984970	+	0.172725i	$0.0552570\pi$
$614$	3.53347			0.142599
$615$	62.1620	−	24.5452i	2.50661	−	0.989758i
$616$	−1.06318			−0.0428368
$617$	8.34272	−	25.6763i	0.335865	−	1.03369i	−0.630429	−	0.776247i	$-0.717121\pi$
$617$	8.34272	−	25.6763i	0.335865	−	1.03369i	0.966294	−	0.257440i	$-0.0828791\pi$
$618$	37.7878			1.52005
$619$	−3.43243	−	2.49381i	−0.137961	−	0.100234i	0.516664	−	0.856188i	$-0.327174\pi$
$619$	−3.43243	−	2.49381i	−0.137961	−	0.100234i	−0.654625	+	0.755954i	$0.727174\pi$
$620$	−10.4343	−	7.58099i	−0.419053	−	0.304460i
$621$	−21.5475	+	66.3165i	−0.864673	+	2.66119i
$622$	16.3983	+	50.4688i	0.657512	+	2.02361i
$623$	−1.33037	+	0.966568i	−0.0533000	+	0.0387247i
$624$	−6.41648			−0.256865
$625$	13.5199	−	9.82282i	0.540798	−	0.392913i
$626$	−48.0756	+	34.9290i	−1.92149	+	1.39604i
$627$	16.5268	+	12.0074i	0.660017	+	0.479531i
$628$	−10.7930	+	33.2174i	−0.430687	+	1.32552i
$629$	31.9616			1.27439
$630$	33.3660	+	24.2418i	1.32933	+	0.965818i
$631$	14.6386	+	45.0530i	0.582754	+	1.79353i	0.608110	+	0.793853i	$0.291928\pi$
$631$	14.6386	+	45.0530i	0.582754	+	1.79353i	−0.0253564	+	0.999678i	$0.508072\pi$
$632$	−1.11856	+	0.812685i	−0.0444941	+	0.0323269i
$633$	−10.1876	+	31.3542i	−0.404920	+	1.24622i
$634$	9.66435	+	29.7438i	0.383820	+	1.18128i
$635$	3.82649	+	11.7767i	0.151850	+	0.467345i
$636$	12.2919	+	37.8304i	0.487404	+	1.50007i
$637$	−0.132482	−	0.407738i	−0.00524913	−	0.0161551i
$638$	0.740613	−	2.27937i	0.0293212	−	0.0902413i
$639$	−23.1156	+	16.7945i	−0.914439	+	0.664379i
$640$	−8.53451	−	26.2665i	−0.337356	−	1.03827i
$641$	13.1040	+	9.52064i	0.517578	+	0.376043i	0.815691	−	0.578488i	$-0.196357\pi$
$641$	13.1040	+	9.52064i	0.517578	+	0.376043i	−0.298113	+	0.954531i	$0.596357\pi$
$642$	2.99368			0.118151
$643$	−1.47885	+	4.55143i	−0.0583201	+	0.179491i	−0.975973	−	0.217893i	$-0.930082\pi$
$643$	−1.47885	+	4.55143i	−0.0583201	+	0.179491i	0.917653	+	0.397383i	$0.130082\pi$
$644$	−7.11546	−	5.16969i	−0.280388	−	0.203714i
$645$	−6.22431	+	4.52223i	−0.245082	+	0.178062i
$646$	43.7037	−	31.7526i	1.71950	−	1.24929i
$647$	20.6289			0.811007			0.405504	−	0.914093i	$-0.367096\pi$
$647$	20.6289			0.811007			0.405504	+	0.914093i	$0.367096\pi$
$648$	13.0569	−	9.48641i	0.512925	−	0.372662i
$649$	−4.64386	−	14.2923i	−0.182287	−	0.561023i
$650$	−1.54685	+	4.76072i	−0.0606725	+	0.186731i
$651$	−6.77591	−	4.92298i	−0.265569	−	0.192947i
$652$	−4.07507	−	2.96071i	−0.159592	−	0.115950i
$653$	−0.603414			−0.0236134			−0.0118067	−	0.999930i	$-0.503758\pi$
$653$	−0.603414			−0.0236134			−0.0118067	+	0.999930i	$0.503758\pi$
$654$	9.88556	−	30.4246i	0.386556	−	1.18970i
$655$	−34.0787			−1.33156
$656$	29.9047	+	7.70772i	1.16758	+	0.300936i
$657$	−106.316			−4.14779
$658$	2.18549	−	6.72623i	0.0851991	−	0.262216i
$659$	−2.77721			−0.108185			−0.0540923	−	0.998536i	$-0.517227\pi$
$659$	−2.77721			−0.108185			−0.0540923	+	0.998536i	$0.517227\pi$
$660$	−11.9056	−	8.64993i	−0.463425	−	0.336698i
$661$	−5.00508	−	3.63640i	−0.194675	−	0.141440i	0.486178	−	0.873860i	$-0.338391\pi$
$661$	−5.00508	−	3.63640i	−0.194675	−	0.141440i	−0.680853	+	0.732420i	$0.738391\pi$
$662$	−4.27160	+	13.1466i	−0.166021	+	0.510959i
$663$	−1.81018	−	5.57116i	−0.0703016	−	0.216366i
$664$	7.43801	−	5.40403i	0.288651	−	0.209717i
$665$	−22.3116			−0.865206
$666$	72.0094	−	52.3179i	2.79031	−	2.02728i
$667$	−6.53963	+	4.75132i	−0.253215	+	0.183972i
$668$	−8.87657	−	6.44921i	−0.343445	−	0.249527i
$669$	−12.4790	+	38.4066i	−0.482468	+	1.48488i
$670$	−84.4339			−3.26196
$671$	11.2492	+	8.17305i	0.434272	+	0.315517i
$672$	6.49924	+	20.0026i	0.250713	+	0.771617i
$673$	−20.6018	+	14.9681i	−0.794141	+	0.576977i	−0.909189	−	0.416383i	$-0.863298\pi$
$673$	−20.6018	+	14.9681i	−0.794141	+	0.576977i	0.115049	+	0.993360i	$0.463298\pi$
$674$	−10.5599	+	32.5001i	−0.406753	+	1.25186i
$675$	−21.9736	−	67.6277i	−0.845764	−	2.60299i
$676$	−5.62677	−	17.3174i	−0.216414	−	0.666055i
$677$	−5.84959	−	18.0032i	−0.224818	−	0.691918i	−0.998310	−	0.0581124i	$-0.981492\pi$
$677$	−5.84959	−	18.0032i	−0.224818	−	0.691918i	0.773492	−	0.633806i	$-0.218508\pi$
$678$	−11.0944	−	34.1450i	−0.426077	−	1.31133i
$679$	4.29334	−	13.2135i	0.164763	−	0.507089i
$680$	12.8360	−	9.32588i	0.492237	−	0.357631i
$681$	−5.56200	−	17.1181i	−0.213136	−	0.655967i
$682$	4.00775	+	2.91180i	0.153465	+	0.111499i
$683$	13.6687			0.523017			0.261509	−	0.965201i	$-0.415780\pi$
$683$	13.6687			0.523017			0.261509	+	0.965201i	$0.415780\pi$
$684$	19.3082	−	59.4245i	0.738267	−	2.27215i
$685$	9.28813	+	6.74822i	0.354881	+	0.257836i
$686$	−1.49630	+	1.08712i	−0.0571290	+	0.0415066i
$687$	−55.2790	+	40.1626i	−2.10903	+	1.53230i
$688$	−3.55510			−0.135537
$689$	−3.12926	+	2.27354i	−0.119215	+	0.0866149i
$690$	36.9289	+	113.655i	1.40586	+	4.32679i
$691$	14.4549	−	44.4878i	0.549892	−	1.69239i	−0.159173	−	0.987251i	$-0.550883\pi$
$691$	14.4549	−	44.4878i	0.549892	−	1.69239i	0.709065	−	0.705143i	$-0.249117\pi$
$692$	5.45252	+	3.96149i	0.207274	+	0.150593i
$693$	−5.32276	−	3.86721i	−0.202195	−	0.146903i
$694$	52.6073			1.99695
$695$	−3.07656	+	9.46867i	−0.116700	+	0.359167i
$696$	4.34112			0.164550
$697$	1.74426	+	28.1395i	0.0660687	+	1.06586i
$698$	59.1627			2.23934
$699$	−21.8552	+	67.2635i	−0.826641	+	2.54414i
$700$	8.96910			0.339000
$701$	4.20896	+	3.05799i	0.158970	+	0.115499i	0.664427	−	0.747354i	$-0.268676\pi$
$701$	4.20896	+	3.05799i	0.158970	+	0.115499i	−0.505456	+	0.862852i	$0.668676\pi$
$702$	−7.22571	−	5.24978i	−0.272717	−	0.198140i
$703$	−14.8798	+	45.7953i	−0.561202	+	1.72720i
$704$	−0.886045	−	2.72697i	−0.0333941	−	0.102776i
$705$	−32.2893	+	23.4595i	−1.21608	+	0.883537i
$706$	4.49769			0.169273
$707$	7.33702	−	5.33066i	0.275937	−	0.200480i
$708$	−54.0131	+	39.2428i	−2.02994	+	1.47484i
$709$	4.29031	+	3.11710i	0.161126	+	0.117065i	0.665427	−	0.746463i	$-0.268250\pi$
$709$	4.29031	+	3.11710i	0.161126	+	0.117065i	−0.504301	+	0.863528i	$0.668250\pi$
$710$	−8.28475	+	25.4978i	−0.310921	+	0.956917i
$711$	−8.55610			−0.320879
$712$	1.42527	+	1.03552i	0.0534143	+	0.0388078i
$713$	−5.16311	−	15.8904i	−0.193360	−	0.595101i
$714$	−20.4448	+	14.8540i	−0.765129	+	0.555898i
$715$	0.442206	−	1.36097i	0.0165376	−	0.0508974i
$716$	4.30752	+	13.2572i	0.160980	+	0.495444i
$717$	23.8310	+	73.3441i	0.889983	+	2.73909i
$718$	−0.169135	−	0.520545i	−0.00631208	−	0.0194266i
$719$	9.39401	+	28.9118i	0.350337	+	1.07823i	0.958664	+	0.284541i	$0.0918411\pi$
$719$	9.39401	+	28.9118i	0.350337	+	1.07823i	−0.608327	+	0.793687i	$0.708159\pi$
$720$	33.2340	−	102.284i	1.23856	−	3.81189i
$721$	5.32649	−	3.86992i	0.198369	−	0.144123i
$722$	14.2903	+	43.9810i	0.531829	+	1.63680i
$723$	25.1552	+	18.2763i	0.935533	+	0.679705i
$724$	22.8023			0.847440
$725$	2.54731	−	7.83980i	0.0946045	−	0.291163i
$726$	−46.5034	−	33.7867i	−1.72590	−	1.25394i
$727$	18.0391	−	13.1062i	0.669034	−	0.486082i	−0.200668	−	0.979659i	$-0.564311\pi$
$727$	18.0391	−	13.1062i	0.669034	−	0.486082i	0.869702	+	0.493578i	$0.164311\pi$
$728$	−0.371585	+	0.269972i	−0.0137719	+	0.0100058i
$729$	−4.98694			−0.184702
$730$	−80.7061	+	58.6364i	−2.98707	+	2.17023i
$731$	−1.00295	−	3.08675i	−0.0370953	−	0.114168i
$732$	19.0894	−	58.7512i	0.705566	−	2.17151i
$733$	24.6262	+	17.8920i	0.909589	+	0.660855i	0.940911	−	0.338654i	$-0.109972\pi$
$733$	24.6262	+	17.8920i	0.909589	+	0.660855i	−0.0313220	+	0.999509i	$0.509972\pi$
$734$	−9.88807	−	7.18410i	−0.364975	−	0.265170i
$735$	10.4375			0.384992
$736$	−12.9653	+	39.9030i	−0.477907	+	1.47085i
$737$	13.4694			0.496153
$738$	49.9912	+	60.5429i	1.84020	+	2.22862i
$739$	−8.68944			−0.319646			−0.159823	−	0.987146i	$-0.551092\pi$
$739$	−8.68944			−0.319646			−0.159823	+	0.987146i	$0.551092\pi$
$740$	10.7191	−	32.9901i	0.394043	−	1.21274i
$741$	8.82521			0.324202
$742$	13.4998	+	9.80818i	0.495593	+	0.360070i
$743$	−18.0877	−	13.1415i	−0.663573	−	0.482114i	0.204295	−	0.978909i	$-0.434510\pi$
$743$	−18.0877	−	13.1415i	−0.663573	−	0.482114i	−0.867868	+	0.496795i	$0.834510\pi$
$744$	−2.77280	+	8.53380i	−0.101656	+	0.312864i
$745$	17.8790	+	55.0258i	0.655034	+	2.01599i
$746$	8.66000	−	6.29186i	0.317065	−	0.230361i
$747$	56.8946			2.08167
$748$	5.02242	−	3.64900i	0.183638	−	0.133421i
$749$	0.421983	−	0.306588i	0.0154189	−	0.0112025i
$750$	−20.5048	−	14.8976i	−0.748729	−	0.543983i
$751$	−0.726273	+	2.23524i	−0.0265021	+	0.0815650i	−0.963433	−	0.267950i	$-0.913654\pi$
$751$	−0.726273	+	2.23524i	−0.0265021	+	0.0815650i	0.936931	+	0.349515i	$0.113654\pi$
$752$	−18.4425			−0.672528
$753$	27.9494	+	20.3064i	1.01853	+	0.740008i
$754$	−0.319952	−	0.984712i	−0.0116520	−	0.0358611i
$755$	17.6066	−	12.7919i	0.640769	−	0.465546i
$756$	−4.94524	+	15.2199i	−0.179857	+	0.553542i
$757$	1.41888	+	4.36687i	0.0515701	+	0.158716i	0.973525	−	0.228581i	$-0.0734086\pi$
$757$	1.41888	+	4.36687i	0.0515701	+	0.158716i	−0.921955	+	0.387298i	$0.873409\pi$
$758$	−5.22135	−	16.0697i	−0.189648	−	0.583677i
$759$	−5.89113	−	18.1310i	−0.213835	−	0.658115i
$760$	7.38650	+	22.7333i	0.267937	+	0.824624i
$761$	1.79029	−	5.50994i	0.0648979	−	0.199735i	−0.913350	−	0.407176i	$-0.866513\pi$
$761$	1.79029	−	5.50994i	0.0648979	−	0.199735i	0.978248	+	0.207441i	$0.0665135\pi$
$762$	−17.0945	+	12.4199i	−0.619269	+	0.449925i
$763$	−1.72239	−	5.30098i	−0.0623549	−	0.191909i
$764$	−7.84999	−	5.70335i	−0.284003	−	0.206340i
$765$	98.1846			3.54987
$766$	3.65672	−	11.2542i	0.132123	−	0.406631i
$767$	−5.25228	−	3.81601i	−0.189649	−	0.137788i
$768$	52.6346	−	38.2412i	1.89929	−	1.37991i
$769$	22.2272	−	16.1490i	0.801532	−	0.582347i	−0.109831	−	0.993950i	$-0.535031\pi$
$769$	22.2272	−	16.1490i	0.801532	−	0.582347i	0.911363	+	0.411603i	$0.135031\pi$
$770$	−6.17347			−0.222476
$771$	40.5386	−	29.4530i	1.45996	−	1.06072i
$772$	−1.47895	−	4.55175i	−0.0532287	−	0.163821i
$773$	2.04459	−	6.29259i	0.0735386	−	0.226329i	−0.907531	−	0.419986i	$-0.862035\pi$
$773$	2.04459	−	6.29259i	0.0735386	−	0.226329i	0.981069	+	0.193657i	$0.0620350\pi$
$774$	−7.31232	−	5.31271i	−0.262836	−	0.190961i
$775$	13.7845	+	10.0150i	0.495153	+	0.359750i
$776$	−14.8847			−0.534328
$777$	6.96085	−	21.4233i	0.249719	−	0.768556i
$778$	−25.7565			−0.923417
$779$	−41.1309	−	10.6012i	−1.47367	−	0.379827i
$780$	−6.35752			−0.227636
$781$	1.32164	−	4.06758i	0.0472919	−	0.145549i
$782$	−50.4133			−1.80278
$783$	11.8991	+	8.64518i	0.425238	+	0.308954i
$784$	3.90186	+	2.83487i	0.139352	+	0.101245i
$785$	25.5512	−	78.6386i	0.911962	−	2.80673i
$786$	−17.9699	−	55.3058i	−0.640966	−	1.97269i
$787$	−15.8515	+	11.5168i	−0.565044	+	0.410528i	−0.833302	−	0.552819i	$-0.813552\pi$
$787$	−15.8515	+	11.5168i	−0.565044	+	0.410528i	0.268258	+	0.963347i	$0.413552\pi$
$788$	1.78811			0.0636988
$789$	−16.1979	+	11.7685i	−0.576662	+	0.418970i
$790$	−6.49506	+	4.71894i	−0.231084	+	0.167892i
$791$	−5.06069	−	3.67681i	−0.179937	−	0.130732i
$792$	−2.17815	+	6.70366i	−0.0773973	+	0.238204i
$793$	6.00702			0.213316
$794$	10.7993	+	7.84614i	0.383252	+	0.278449i
$795$	−29.0996	−	89.5594i	−1.03206	−	3.17634i
$796$	−0.435434	+	0.316361i	−0.0154335	+	0.0112131i
$797$	−14.1085	+	43.4215i	−0.499749	+	1.53807i	0.309674	+	0.950843i	$0.399780\pi$
$797$	−14.1085	+	43.4215i	−0.499749	+	1.53807i	−0.809423	+	0.587226i	$0.800220\pi$
$798$	−11.7651	−	36.2091i	−0.416478	−	1.28179i
$799$	−5.20289	−	16.0128i	−0.184065	−	0.566494i
$800$	−13.2216	−	40.6920i	−0.467455	−	1.43868i
$801$	3.36895	+	10.3686i	0.119036	+	0.366355i
$802$	12.4926	−	38.4482i	0.441128	−	1.35765i
$803$	12.8748	−	9.35406i	0.454340	−	0.330097i
$804$	−18.4917	−	56.9116i	−0.652152	−	2.00712i
$805$	16.8451	+	12.2387i	0.593711	+	0.431356i
$806$	2.14011			0.0753823
$807$	9.78936	−	30.1286i	0.344602	−	1.06058i
$808$	−7.86043	−	5.71094i	−0.276529	−	0.200910i
$809$	−37.6131	+	27.3276i	−1.32241	+	0.960786i	−0.322509	+	0.946566i	$0.604526\pi$
$809$	−37.6131	+	27.3276i	−1.32241	+	0.960786i	−0.999899	+	0.0142192i	$0.995474\pi$
$810$	75.8164	−	55.0838i	2.66392	−	1.93545i
$811$	−30.9540			−1.08694			−0.543471	−	0.839428i	$-0.682890\pi$
$811$	−30.9540			−1.08694			−0.543471	+	0.839428i	$0.682890\pi$
$812$	−1.50087	+	1.09045i	−0.0526702	+	0.0382672i
$813$	6.94262	+	21.3672i	0.243488	+	0.749380i
$814$	−4.11714	+	12.6713i	−0.144306	+	0.444127i
$815$	9.64728	+	7.00916i	0.337929	+	0.245520i
$816$	53.3135	+	38.7345i	1.86635	+	1.35598i
$817$	4.88968			0.171068
$818$	−10.3375	+	31.8156i	−0.361443	+	1.11241i
$819$	−2.84232			−0.0993187
$820$	29.6299	+	7.63689i	1.03472	+	0.266692i
$821$	−28.6365			−0.999420			−0.499710	−	0.866193i	$-0.666560\pi$
$821$	−28.6365			−0.999420			−0.499710	+	0.866193i	$0.666560\pi$
$822$	−6.05389	+	18.6320i	−0.211154	+	0.649864i
$823$	−27.2146			−0.948642			−0.474321	−	0.880352i	$-0.657306\pi$
$823$	−27.2146			−0.948642			−0.474321	+	0.880352i	$0.657306\pi$
$824$	−5.70647	−	4.14599i	−0.198794	−	0.144432i
$825$	15.7281	+	11.4272i	0.547584	+	0.397843i
$826$	−8.65484	+	26.6369i	−0.301140	+	0.926815i
$827$	3.27153	+	10.0687i	0.113762	+	0.350124i	0.991687	−	0.128675i	$-0.0410724\pi$
$827$	3.27153	+	10.0687i	0.113762	+	0.350124i	−0.877925	+	0.478799i	$0.841072\pi$
$828$	−47.1739	+	34.2738i	−1.63941	+	1.19110i
$829$	17.7149			0.615263			0.307631	−	0.951506i	$-0.400464\pi$
$829$	17.7149			0.615263			0.307631	+	0.951506i	$0.400464\pi$
$830$	43.1895	−	31.3790i	1.49913	−	1.08918i
$831$	62.2735	−	45.2444i	2.16024	−	1.56951i
$832$	−1.00213	−	0.728091i	−0.0347427	−	0.0252420i
$833$	−1.36063	+	4.18758i	−0.0471430	+	0.145091i
$834$	−16.9888			−0.588276
$835$	21.0143	+	15.2678i	0.727230	+	0.528364i
$836$	2.89017	+	8.89503i	0.0999587	+	0.307641i
$837$	−24.5950	+	17.8693i	−0.850128	+	0.617654i
$838$	14.6460	−	45.0757i	0.505937	−	1.55711i
$839$	−1.50784	−	4.64066i	−0.0520565	−	0.160213i	0.921649	−	0.388026i	$-0.126843\pi$
$839$	−1.50784	−	4.64066i	−0.0520565	−	0.160213i	−0.973705	+	0.227812i	$0.926843\pi$
$840$	−3.45545	−	10.6348i	−0.119224	−	0.366935i
$841$	−8.43461	−	25.9590i	−0.290848	−	0.895140i
$842$	−11.1438	−	34.2971i	−0.384041	−	1.18196i
$843$	0.255507	−	0.786369i	0.00880012	−	0.0270840i
$844$	−12.2111	+	8.87191i	−0.420325	+	0.305384i
$845$	13.3208	+	40.9971i	0.458248	+	1.41034i
$846$	−37.9334	−	27.5602i	−1.30418	−	0.947541i
$847$	−10.0152			−0.344125
$848$	13.4464	−	41.3838i	0.461751	−	1.42112i
$849$	−66.0875	−	48.0154i	−2.26812	−	1.64788i
$850$	41.5917	−	30.2181i	1.42658	−	1.03647i
$851$	36.3544	−	26.4130i	1.24621	−	0.905427i
$852$	−19.0009			−0.650961
$853$	−35.4170	+	25.7320i	−1.21266	+	0.881045i	−0.995469	−	0.0950848i	$-0.969688\pi$
$853$	−35.4170	+	25.7320i	−1.21266	+	0.881045i	−0.217186	+	0.976130i	$0.569688\pi$
$854$	−8.00807	−	24.6463i	−0.274030	−	0.843379i
$855$	−45.7100	+	140.681i	−1.56325	+	4.81119i
$856$	−0.452086	−	0.328460i	−0.0154520	−	0.0112265i
$857$	25.1203	+	18.2510i	0.858093	+	0.623441i	0.927365	−	0.374157i	$-0.122068\pi$
$857$	25.1203	+	18.2510i	0.858093	+	0.623441i	−0.0692725	+	0.997598i	$0.522068\pi$
$858$	2.44188			0.0833643
$859$	−0.386759	+	1.19032i	−0.0131960	+	0.0406132i	−0.957438	−	0.288640i	$-0.906797\pi$
$859$	−0.386759	+	1.19032i	−0.0131960	+	0.0406132i	0.944242	+	0.329253i	$0.106797\pi$
$860$	−3.52244			−0.120114
$861$	19.2413	+	4.95929i	0.655740	+	0.169012i
$862$	6.59833			0.224740
$863$	−6.90348	+	21.2467i	−0.234997	+	0.723247i	0.762124	+	0.647431i	$0.224156\pi$
$863$	−6.90348	+	21.2467i	−0.234997	+	0.723247i	−0.997122	+	0.0758169i	$0.975844\pi$
$864$	76.3413			2.59718
$865$	−12.9082	−	9.37838i	−0.438893	−	0.318875i
$866$	−51.0690	−	37.1038i	−1.73540	−	1.26084i
$867$	−2.28914	+	7.04526i	−0.0777434	+	0.239270i
$868$	−1.18496	−	3.64692i	−0.0402200	−	0.123784i
$869$	1.03613	−	0.752795i	0.0351484	−	0.0255368i
$870$	25.2072			0.854603
$871$	4.70761	−	3.42028i	0.159511	−	0.115892i
$872$	−4.83097	+	3.50990i	−0.163597	+	0.118860i
$873$	−74.5193	−	54.1414i	−2.52210	−	1.83241i
$874$	23.4700	−	72.2333i	0.793885	−	2.44333i
$875$	−4.41600			−0.149288
$876$	−57.1984	−	41.5571i	−1.93256	−	1.40408i
$877$	6.78382	+	20.8785i	0.229073	+	0.705015i	0.997853	+	0.0655009i	$0.0208645\pi$
$877$	6.78382	+	20.8785i	0.229073	+	0.705015i	−0.768779	+	0.639514i	$0.779135\pi$
$878$	−0.0702226	+	0.0510197i	−0.00236990	+	0.00172183i
$879$	5.55912	−	17.1092i	0.187504	−	0.577079i
$880$	4.97468	+	15.3105i	0.167696	+	0.516117i
$881$	−9.63657	−	29.6583i	−0.324664	−	0.999214i	−0.971592	−	0.236663i	$-0.923946\pi$
$881$	−9.63657	−	29.6583i	−0.324664	−	0.999214i	0.646927	−	0.762552i	$-0.276054\pi$
$882$	3.78915	+	11.6618i	0.127587	+	0.392673i
$883$	−5.32685	−	16.3943i	−0.179263	−	0.551714i	0.820540	−	0.571589i	$-0.193673\pi$
$883$	−5.32685	−	16.3943i	−0.179263	−	0.551714i	−0.999802	+	0.0198757i	$0.993673\pi$
$884$	0.828766	−	2.55068i	0.0278744	−	0.0857886i
$885$	127.870	−	92.9031i	4.29831	−	3.12290i
$886$	11.8427	+	36.4481i	0.397864	+	1.22450i
$887$	−39.4160	−	28.6374i	−1.32346	−	0.961550i	−0.999882	−	0.0153480i	$-0.995114\pi$
$887$	−39.4160	−	28.6374i	−1.32346	−	0.961550i	−0.323577	−	0.946202i	$-0.604886\pi$
$888$	−24.1327			−0.809841
$889$	−1.13766	+	3.50136i	−0.0381559	+	0.117432i
$890$	8.27598	+	6.01285i	0.277412	+	0.201551i
$891$	−12.0947	+	8.78732i	−0.405188	+	0.294386i
$892$	−14.9578	+	10.8674i	−0.500823	+	0.363869i
$893$	25.3657			0.848832
$894$	−79.8727	+	58.0309i	−2.67134	+	1.94085i
$895$	−10.1976	−	31.3849i	−0.340867	−	1.04908i
$896$	2.53741	−	7.80935i	0.0847690	−	0.260892i
$897$	−6.66297	−	4.84093i	−0.222470	−	0.161634i
$898$	−32.4860	−	23.6024i	−1.08407	−	0.787624i
$899$	−3.52427			−0.117541
$900$	18.3751	−	56.5528i	0.612503	−	1.88509i
$901$	39.7252			1.32344
$902$	−11.3806	−	2.93327i	−0.378934	−	0.0976674i
$903$	−2.28742			−0.0761206
$904$	−2.07091	+	6.37360i	−0.0688774	+	0.211983i
$905$	−53.9819			−1.79442
$906$	30.0439	+	21.8282i	0.998141	+	0.725192i
$907$	−45.8131	−	33.2851i	−1.52120	−	1.10522i	−0.960890	−	0.276931i	$-0.910683\pi$
$907$	−45.8131	−	33.2851i	−1.52120	−	1.10522i	−0.560308	−	0.828284i	$-0.689317\pi$
$908$	2.54648	−	7.83727i	0.0845081	−	0.260089i
$909$	−18.5799	−	57.1831i	−0.616256	−	1.89664i
$910$	−2.15765	+	1.56762i	−0.0715253	+	0.0519662i
$911$	21.9052			0.725752			0.362876	−	0.931837i	$-0.381795\pi$
$911$	21.9052			0.725752			0.362876	+	0.931837i	$0.381795\pi$
$912$	−80.3198	+	58.3558i	−2.65966	+	1.93235i
$913$	−6.88987	+	5.00578i	−0.228021	+	0.165667i
$914$	3.61095	+	2.62351i	0.119440	+	0.0867779i
$915$	−45.1921	+	139.087i	−1.49400	+	4.59807i
$916$	−31.2833			−1.03363
$917$	−8.19696	−	5.95544i	−0.270688	−	0.196666i
$918$	28.3457	+	87.2392i	0.935549	+	2.87932i
$919$	1.04677	−	0.760525i	0.0345299	−	0.0250874i	−0.570386	−	0.821376i	$-0.693207\pi$
$919$	1.04677	−	0.760525i	0.0345299	−	0.0250874i	0.604916	+	0.796289i	$0.293207\pi$
$920$	6.89325	−	21.2152i	0.227264	−	0.699446i
$921$	−1.83202	−	5.63839i	−0.0603673	−	0.185791i
$922$	−4.33638	−	13.3460i	−0.142811	−	0.439527i
$923$	−0.570960	−	1.75723i	−0.0187934	−	0.0578401i
$924$	−1.35204	−	4.16115i	−0.0444788	−	0.136892i
$925$	−14.1607	+	43.5822i	−0.465601	+	1.43297i
$926$	41.7069	−	30.3019i	1.37057	−	0.995781i
$927$	−13.4885	−	41.5134i	−0.443021	−	1.36348i
$928$	7.15974	+	5.20186i	0.235030	+	0.170759i
$929$	56.1233			1.84135			0.920673	−	0.390334i	$-0.127640\pi$
$929$	56.1233			1.84135			0.920673	+	0.390334i	$0.127640\pi$
$930$	−16.1005	+	49.5524i	−0.527957	+	1.62489i
$931$	−5.36661	−	3.89907i	−0.175884	−	0.127787i
$932$	−26.1963	+	19.0327i	−0.858089	+	0.623438i
$933$	72.0314	−	52.3339i	2.35820	−	1.71333i
$934$	26.4693			0.866102
$935$	−11.8900	+	8.63862i	−0.388846	+	0.282513i
$936$	0.940983	+	2.89605i	0.0307570	+	0.0946603i
$937$	7.64263	−	23.5216i	0.249674	−	0.768417i	−0.745159	−	0.666887i	$-0.767626\pi$
$937$	7.64263	−	23.5216i	0.249674	−	0.768417i	0.994832	−	0.101530i	$-0.0323738\pi$
$938$	−20.3089	−	14.7553i	−0.663110	−	0.481777i
$939$	80.6626	+	58.6048i	2.63232	+	1.91249i
$940$	−18.2730			−0.596000
$941$	−10.7058	+	32.9492i	−0.349000	+	1.07411i	0.610407	+	0.792088i	$0.291006\pi$
$941$	−10.7058	+	32.9492i	−0.349000	+	1.07411i	−0.959407	+	0.282024i	$0.908994\pi$
$942$	141.095			4.59711
$943$	25.2384	+	30.5655i	0.821876	+	0.995350i
$944$	73.0349			2.37708
$945$	11.7073	−	36.0314i	0.380839	−	1.17210i
$946$	1.35294			0.0439880
$947$	−44.0419	−	31.9983i	−1.43117	−	1.03981i	−0.989798	−	0.142480i	$-0.954492\pi$
$947$	−44.0419	−	31.9983i	−1.43117	−	1.03981i	−0.441371	−	0.897325i	$-0.645508\pi$
$948$	−4.60321	−	3.34443i	−0.149505	−	0.108622i
$949$	2.12450	−	6.53855i	0.0689643	−	0.212250i
$950$	23.9341	+	73.6615i	0.776524	+	2.38990i
$951$	42.4517	−	30.8430i	1.37659	−	1.00015i
$952$	4.71719			0.152885
$953$	11.9417	−	8.67615i	0.386830	−	0.281048i	−0.377326	−	0.926081i	$-0.623156\pi$
$953$	11.9417	−	8.67615i	0.386830	−	0.281048i	0.764155	+	0.645033i	$0.223156\pi$
$954$	89.5007	−	65.0260i	2.89769	−	2.10530i
$955$	18.5840	+	13.5020i	0.601363	+	0.436916i
$956$	−10.9107	+	33.5796i	−0.352876	+	1.08604i
$957$	−4.02121			−0.129987
$958$	24.4332	+	17.7518i	0.789401	+	0.573533i
$959$	1.05479	+	3.24631i	0.0340609	+	0.104829i
$960$	24.3975	−	17.7258i	0.787427	−	0.572099i
$961$	−7.32847	+	22.5547i	−0.236402	+	0.727572i
$962$	1.77864	+	5.47411i	0.0573458	+	0.176492i
$963$	−1.06861	−	3.28884i	−0.0344354	−	0.105981i
$964$	4.39909	+	13.5390i	0.141685	+	0.436062i
$965$	3.50126	+	10.7758i	0.112709	+	0.346884i
$966$	−10.9794	+	33.7911i	−0.353257	+	1.08721i
$967$	−29.2738	+	21.2686i	−0.941381	+	0.683953i	−0.948753	−	0.316020i	$-0.897653\pi$
$967$	−29.2738	+	21.2686i	−0.941381	+	0.683953i	0.00737178	+	0.999973i	$0.497653\pi$
$968$	3.31564	+	10.2045i	0.106569	+	0.327984i
$969$	−73.3273	−	53.2754i	−2.35561	−	1.71145i
$970$	−86.4292			−2.77508
$971$	2.95577	−	9.09692i	0.0948551	−	0.291934i	−0.892361	−	0.451323i	$-0.850952\pi$
$971$	2.95577	−	9.09692i	0.0948551	−	0.291934i	0.987216	+	0.159389i	$0.0509523\pi$
$972$	14.8925	+	10.8200i	0.477676	+	0.347052i
$973$	−2.39471	+	1.73986i	−0.0767708	+	0.0557773i
$974$	−32.1358	+	23.3480i	−1.02970	+	0.748119i
$975$	8.39872			0.268974
$976$	−54.6710	+	39.7208i	−1.74998	+	1.27143i
$977$	12.4216	+	38.2297i	0.397402	+	1.22308i	0.927075	+	0.374876i	$0.122315\pi$
$977$	12.4216	+	38.2297i	0.397402	+	1.22308i	−0.529673	+	0.848202i	$0.677685\pi$
$978$	−6.28797	+	19.3524i	−0.201067	+	0.618821i
$979$	−1.32024	−	0.959209i	−0.0421950	−	0.0306564i
$980$	3.86601	+	2.80882i	0.123495	+	0.0897245i
$981$	−36.9529			−1.17982
$982$	15.3853	−	47.3512i	0.490966	−	1.51104i
$983$	9.99653			0.318840			0.159420	−	0.987211i	$-0.449038\pi$
$983$	9.99653			0.318840			0.159420	+	0.987211i	$0.449038\pi$
$984$	−1.31701	−	21.2468i	−0.0419848	−	0.677323i
$985$	−4.23315			−0.134879
$986$	−3.28600	+	10.1133i	−0.104648	+	0.322072i
$987$	−11.8662			−0.377706
$988$	3.26883	+	2.37495i	0.103995	+	0.0755571i
$989$	−3.69167	−	2.68216i	−0.117388	−	0.0852876i
$990$	−12.6477	+	38.9255i	−0.401969	+	1.23713i
$991$	−3.22460	−	9.92429i	−0.102433	−	0.315256i	0.886687	−	0.462371i	$-0.153001\pi$
$991$	−3.22460	−	9.92429i	−0.102433	−	0.315256i	−0.989119	+	0.147115i	$0.953001\pi$
$992$	−14.7990	+	10.7521i	−0.469867	+	0.341379i
$993$	23.1929			0.736006
$994$	−6.44863	+	4.68520i	−0.204538	+	0.148606i
$995$	1.03084	−	0.748950i	0.0326799	−	0.0237433i
$996$	30.6095	+	22.2391i	0.969899	+	0.704673i
$997$	−11.1507	+	34.3185i	−0.353148	+	1.08688i	0.603928	+	0.797039i	$0.293601\pi$
$997$	−11.1507	+	34.3185i	−0.353148	+	1.08688i	−0.957076	+	0.289838i	$0.906399\pi$
$998$	15.8096			0.500444
$999$	−66.1481	−	48.0594i	−2.09283	−	1.52053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.c.57.9	✓	40
41.18	even	5	inner	287.2.h.c.141.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.c.57.9	✓	40	1.1	even	1	trivial
287.2.h.c.141.9	yes	40	41.18	even	5	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.571535 - 1.75900i) q^{2} -3.10319 q^{3} +(-1.14941 - 0.835096i) q^{4} +(2.72110 + 1.97700i) q^{5} +(-1.77358 + 5.45852i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.866730 - 0.629716i) q^{8} +6.62977 q^{9} +O(q^{10})\)	\(q+(0.571535 - 1.75900i) q^{2} -3.10319 q^{3} +(-1.14941 - 0.835096i) q^{4} +(2.72110 + 1.97700i) q^{5} +(-1.77358 + 5.45852i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.866730 - 0.629716i) q^{8} +6.62977 q^{9} +(5.03276 - 3.65651i) q^{10} +(-0.802857 + 0.583310i) q^{11} +(3.56684 + 2.59146i) q^{12} +(-0.132482 + 0.407738i) q^{13} +1.84953 q^{14} +(-8.44410 - 6.13500i) q^{15} +(-1.49038 - 4.58692i) q^{16} +(3.56217 - 2.58807i) q^{17} +(3.78915 - 11.6618i) q^{18} +(2.04986 + 6.30883i) q^{19} +(-1.47668 - 4.54477i) q^{20} +(-0.958938 - 2.95131i) q^{21} +(0.567184 + 1.74561i) q^{22} +(1.91298 - 5.88754i) q^{23} +(-2.68963 + 1.95413i) q^{24} +(1.95080 + 6.00395i) q^{25} +(0.641494 + 0.466073i) q^{26} -11.2639 q^{27} +(0.439036 - 1.35121i) q^{28} +(-1.05639 - 0.767514i) q^{29} +(-15.6176 + 11.3468i) q^{30} +(2.18353 - 1.58643i) q^{31} -6.77754 q^{32} +(2.49142 - 1.81012i) q^{33} +(-2.51652 - 7.74505i) q^{34} +(-1.03937 + 3.19885i) q^{35} +(-7.62034 - 5.53650i) q^{36} +(5.87259 + 4.26668i) q^{37} +12.2688 q^{38} +(0.411116 - 1.26529i) q^{39} +3.60341 q^{40} +(-3.43596 + 5.40316i) q^{41} -5.73943 q^{42} +(0.227782 - 0.701042i) q^{43} +1.40993 q^{44} +(18.0403 + 13.1070i) q^{45} +(-9.26288 - 6.72988i) q^{46} +(1.18165 - 3.63673i) q^{47} +(4.62493 + 14.2341i) q^{48} +(-0.809017 + 0.587785i) q^{49} +11.6759 q^{50} +(-11.0541 + 8.03126i) q^{51} +(0.492776 - 0.358023i) q^{52} +(7.29906 + 5.30308i) q^{53} +(-6.43770 + 19.8132i) q^{54} -3.33786 q^{55} +(0.866730 + 0.629716i) q^{56} +(-6.36111 - 19.5775i) q^{57} +(-1.95383 + 1.41954i) q^{58} +(-4.67949 + 14.4020i) q^{59} +(4.58243 + 14.1033i) q^{60} +(-4.32979 - 13.3257i) q^{61} +(-1.54257 - 4.74754i) q^{62} +(2.04871 + 6.30529i) q^{63} +(-0.892843 + 2.74789i) q^{64} +(-1.16659 + 0.847580i) q^{65} +(-1.76008 - 5.41696i) q^{66} +(-10.9806 - 7.97787i) q^{67} -6.25569 q^{68} +(-5.93633 + 18.2701i) q^{69} +(5.03276 + 3.65651i) q^{70} +(-3.48664 + 2.53319i) q^{71} +(5.74623 - 4.17488i) q^{72} -16.0362 q^{73} +(10.8615 - 7.89135i) q^{74} +(-6.05371 - 18.6314i) q^{75} +(2.91235 - 8.96328i) q^{76} +(-0.802857 - 0.583310i) q^{77} +(-1.99068 - 1.44631i) q^{78} -1.29056 q^{79} +(5.01285 - 15.4280i) q^{80} +15.0646 q^{81} +(7.54041 + 9.13197i) q^{82} +8.58168 q^{83} +(-1.36241 + 4.19307i) q^{84} +14.8096 q^{85} +(-1.10295 - 0.801341i) q^{86} +(3.27818 + 2.38174i) q^{87} +(-0.328541 + 1.01115i) q^{88} +(0.508155 + 1.56394i) q^{89} +(33.3660 - 24.2418i) q^{90} -0.428721 q^{91} +(-7.11546 + 5.16969i) q^{92} +(-6.77591 + 4.92298i) q^{93} +(-5.72168 - 4.15704i) q^{94} +(-6.89466 + 21.2196i) q^{95} +21.0320 q^{96} +(-11.2401 - 8.16641i) q^{97} +(0.571535 + 1.75900i) q^{98} +(-5.32276 + 3.86721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more