LMFDB - Embedded newform 287.2.h.c.78.5

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			78.5
Character	$\chi$	$=$	287.78
Dual form			287.2.h.c.92.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.224492 + 0.163103i) q^{2} -2.77195 q^{3} +(-0.594240 + 1.82888i) q^{4} +(-1.20463 + 3.70748i) q^{5} +(0.622280 - 0.452113i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.336391 - 1.03531i) q^{8} +4.68369 q^{9} +O(q^{10})$	\(q+(-0.224492 + 0.163103i) q^{2} -2.77195 q^{3} +(-0.594240 + 1.82888i) q^{4} +(-1.20463 + 3.70748i) q^{5} +(0.622280 - 0.452113i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.336391 - 1.03531i) q^{8} +4.68369 q^{9} +(-0.334271 - 1.02878i) q^{10} +(-1.39475 - 4.29259i) q^{11} +(1.64720 - 5.06956i) q^{12} +(1.84826 - 1.34284i) q^{13} +0.277488 q^{14} +(3.33918 - 10.2769i) q^{15} +(-2.86710 - 2.08307i) q^{16} +(2.45122 + 7.54409i) q^{17} +(-1.05145 + 0.763924i) q^{18} +(-2.15251 - 1.56389i) q^{19} +(-6.06470 - 4.40626i) q^{20} +(2.24255 + 1.62931i) q^{21} +(1.01325 + 0.736166i) q^{22} +(-2.71950 + 1.97583i) q^{23} +(0.932458 + 2.86981i) q^{24} +(-8.24917 - 5.99337i) q^{25} +(-0.195899 + 0.602915i) q^{26} -4.66710 q^{27} +(1.55574 - 1.13031i) q^{28} +(1.39680 - 4.29890i) q^{29} +(0.926581 + 2.85172i) q^{30} +(-0.0231121 - 0.0711316i) q^{31} +3.16057 q^{32} +(3.86617 + 11.8988i) q^{33} +(-1.78074 - 1.29379i) q^{34} +(3.15377 - 2.29135i) q^{35} +(-2.78323 + 8.56591i) q^{36} +(1.21693 - 3.74531i) q^{37} +0.738296 q^{38} +(-5.12329 + 3.72229i) q^{39} +4.24360 q^{40} +(-1.73287 - 6.16418i) q^{41} -0.769181 q^{42} +(-3.85986 + 2.80435i) q^{43} +8.67946 q^{44} +(-5.64212 + 17.3647i) q^{45} +(0.288242 - 0.887119i) q^{46} +(-3.52636 + 2.56205i) q^{47} +(7.94745 + 5.77416i) q^{48} +(0.309017 + 0.951057i) q^{49} +2.82941 q^{50} +(-6.79466 - 20.9118i) q^{51} +(1.35759 + 4.17823i) q^{52} +(-2.16858 + 6.67421i) q^{53} +(1.04773 - 0.761218i) q^{54} +17.5949 q^{55} +(-0.336391 + 1.03531i) q^{56} +(5.96663 + 4.33501i) q^{57} +(0.387594 + 1.19289i) q^{58} +(-1.66921 + 1.21275i) q^{59} +(16.8110 + 12.2139i) q^{60} +(-10.8747 - 7.90090i) q^{61} +(0.0167903 + 0.0121988i) q^{62} +(-3.78918 - 2.75300i) q^{63} +(5.02468 - 3.65064i) q^{64} +(2.75208 + 8.47003i) q^{65} +(-2.80866 - 2.04061i) q^{66} +(2.66222 - 8.19348i) q^{67} -15.2539 q^{68} +(7.53831 - 5.47691i) q^{69} +(-0.334271 + 1.02878i) q^{70} +(3.34001 + 10.2795i) q^{71} +(-1.57555 - 4.84905i) q^{72} -8.29646 q^{73} +(0.337682 + 1.03928i) q^{74} +(22.8663 + 16.6133i) q^{75} +(4.13927 - 3.00736i) q^{76} +(-1.39475 + 4.29259i) q^{77} +(0.543022 - 1.67125i) q^{78} -5.90977 q^{79} +(11.1767 - 8.12038i) q^{80} -1.11413 q^{81} +(1.39441 + 1.10117i) q^{82} -6.17044 q^{83} +(-4.31243 + 3.13316i) q^{84} -30.9224 q^{85} +(0.409110 - 1.25911i) q^{86} +(-3.87184 + 11.9163i) q^{87} +(-3.97496 + 2.88798i) q^{88} +(-8.79968 - 6.39334i) q^{89} +(-1.56562 - 4.81848i) q^{90} -2.28458 q^{91} +(-1.99753 - 6.14777i) q^{92} +(0.0640654 + 0.197173i) q^{93} +(0.373762 - 1.15032i) q^{94} +(8.39106 - 6.09646i) q^{95} -8.76092 q^{96} +(-0.884678 + 2.72276i) q^{97} +(-0.224492 - 0.163103i) q^{98} +(-6.53257 - 20.1052i) 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 $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.224492	+	0.163103i	−0.158740	+	0.115331i	−0.664320	−	0.747449i	$-0.731279\pi$
$2$	−0.224492	+	0.163103i	−0.158740	+	0.115331i	0.505580	+	0.862780i	$0.331279\pi$
$3$	−2.77195			−1.60038			−0.800192	−	0.599744i	$-0.795269\pi$
$3$	−2.77195			−1.60038			−0.800192	+	0.599744i	$0.795269\pi$
$4$	−0.594240	+	1.82888i	−0.297120	+	0.914441i
$5$	−1.20463	+	3.70748i	−0.538728	+	1.65803i	0.196725	+	0.980459i	$0.436969\pi$
$5$	−1.20463	+	3.70748i	−0.538728	+	1.65803i	−0.735453	+	0.677576i	$0.763031\pi$
$6$	0.622280	−	0.452113i	0.254045	−	0.184574i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−0.336391	−	1.03531i	−0.118932	−	0.366036i
$9$	4.68369			1.56123
$10$	−0.334271	−	1.02878i	−0.105706	−	0.325329i
$11$	−1.39475	−	4.29259i	−0.420532	−	1.29427i	−0.907208	−	0.420683i	$-0.861791\pi$
$11$	−1.39475	−	4.29259i	−0.420532	−	1.29427i	0.486676	−	0.873583i	$-0.338209\pi$
$12$	1.64720	−	5.06956i	0.475506	−	1.46346i
$13$	1.84826	−	1.34284i	0.512616	−	0.372438i	−0.301199	−	0.953561i	$-0.597387\pi$
$13$	1.84826	−	1.34284i	0.512616	−	0.372438i	0.813815	+	0.581124i	$0.197387\pi$
$14$	0.277488			0.0741617
$15$	3.33918	−	10.2769i	0.862172	−	2.65349i
$16$	−2.86710	−	2.08307i	−0.716775	−	0.520768i
$17$	2.45122	+	7.54409i	0.594509	+	1.82971i	0.557156	+	0.830408i	$0.311892\pi$
$17$	2.45122	+	7.54409i	0.594509	+	1.82971i	0.0373523	+	0.999302i	$0.488108\pi$
$18$	−1.05145	+	0.763924i	−0.247830	+	0.180059i
$19$	−2.15251	−	1.56389i	−0.493819	−	0.358780i	0.312832	−	0.949808i	$-0.398722\pi$
$19$	−2.15251	−	1.56389i	−0.493819	−	0.358780i	−0.806651	+	0.591028i	$0.798722\pi$
$20$	−6.06470	−	4.40626i	−1.35611	−	0.985270i
$21$	2.24255	+	1.62931i	0.489365	+	0.355544i
$22$	1.01325	+	0.736166i	0.216025	+	0.156951i
$23$	−2.71950	+	1.97583i	−0.567055	+	0.411990i	−0.834034	−	0.551713i	$-0.813975\pi$
$23$	−2.71950	+	1.97583i	−0.567055	+	0.411990i	0.266979	+	0.963702i	$0.413975\pi$
$24$	0.932458	+	2.86981i	0.190337	+	0.585798i
$25$	−8.24917	−	5.99337i	−1.64983	−	1.19867i
$26$	−0.195899	+	0.602915i	−0.0384190	+	0.118241i
$27$	−4.66710			−0.898183
$28$	1.55574	−	1.13031i	0.294007	−	0.213609i
$29$	1.39680	−	4.29890i	0.259378	−	0.798285i	−0.733557	−	0.679628i	$-0.762141\pi$
$29$	1.39680	−	4.29890i	0.259378	−	0.798285i	0.992935	−	0.118657i	$-0.0378588\pi$
$30$	0.926581	+	2.85172i	0.169170	+	0.520651i
$31$	−0.0231121	−	0.0711316i	−0.00415105	−	0.0127756i	0.948960	−	0.315398i	$-0.102138\pi$
$31$	−0.0231121	−	0.0711316i	−0.00415105	−	0.0127756i	−0.953111	+	0.302622i	$0.902138\pi$
$32$	3.16057			0.558714
$33$	3.86617	+	11.8988i	0.673013	+	2.07132i
$34$	−1.78074	−	1.29379i	−0.305395	−	0.221883i
$35$	3.15377	−	2.29135i	0.533084	−	0.387308i
$36$	−2.78323	+	8.56591i	−0.463872	+	1.42765i
$37$	1.21693	−	3.74531i	0.200061	−	0.615725i	−0.799819	−	0.600241i	$-0.795071\pi$
$37$	1.21693	−	3.74531i	0.200061	−	0.615725i	0.999880	−	0.0154838i	$-0.00492886\pi$
$38$	0.738296			0.119767
$39$	−5.12329	+	3.72229i	−0.820383	+	0.596043i
$40$	4.24360			0.670972
$41$	−1.73287	−	6.16418i	−0.270629	−	0.962684i
$41$	−1.73287	−	6.16418i	−0.270629	−	0.962684i
$42$	−0.769181			−0.118687
$43$	−3.85986	+	2.80435i	−0.588623	+	0.427660i	−0.841822	−	0.539755i	$-0.818517\pi$
$43$	−3.85986	+	2.80435i	−0.588623	+	0.427660i	0.253200	+	0.967414i	$0.418517\pi$
$44$	8.67946			1.30848
$45$	−5.64212	+	17.3647i	−0.841078	+	2.58857i
$46$	0.288242	−	0.887119i	0.0424990	−	0.130798i
$47$	−3.52636	+	2.56205i	−0.514373	+	0.373714i	−0.814480	−	0.580192i	$-0.802978\pi$
$47$	−3.52636	+	2.56205i	−0.514373	+	0.373714i	0.300107	+	0.953906i	$0.402978\pi$
$48$	7.94745	+	5.77416i	1.14712	+	0.833429i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	2.82941			0.400139
$51$	−6.79466	−	20.9118i	−0.951442	−	2.92824i
$52$	1.35759	+	4.17823i	0.188264	+	0.579416i
$53$	−2.16858	+	6.67421i	−0.297878	+	0.916773i	0.684362	+	0.729142i	$0.260081\pi$
$53$	−2.16858	+	6.67421i	−0.297878	+	0.916773i	−0.982240	+	0.187631i	$0.939919\pi$
$54$	1.04773	−	0.761218i	0.142578	−	0.103589i
$55$	17.5949			2.37249
$56$	−0.336391	+	1.03531i	−0.0449521	+	0.138348i
$57$	5.96663	+	4.33501i	0.790300	+	0.574186i
$58$	0.387594	+	1.19289i	0.0508935	+	0.156634i
$59$	−1.66921	+	1.21275i	−0.217312	+	0.157886i	−0.691116	−	0.722744i	$-0.742881\pi$
$59$	−1.66921	+	1.21275i	−0.217312	+	0.157886i	0.473804	+	0.880630i	$0.342881\pi$
$60$	16.8110	+	12.2139i	2.17029	+	1.57681i
$61$	−10.8747	−	7.90090i	−1.39236	−	1.01161i	−0.995602	−	0.0936829i	$-0.970136\pi$
$61$	−10.8747	−	7.90090i	−1.39236	−	1.01161i	−0.396756	−	0.917924i	$-0.629864\pi$
$62$	0.0167903	+	0.0121988i	0.00213237	+	0.00154925i
$63$	−3.78918	−	2.75300i	−0.477392	−	0.346846i
$64$	5.02468	−	3.65064i	0.628085	−	0.456331i
$65$	2.75208	+	8.47003i	0.341354	+	1.05058i
$66$	−2.80866	−	2.04061i	−0.345722	−	0.251182i
$67$	2.66222	−	8.19348i	0.325242	−	1.00099i	−0.646089	−	0.763262i	$-0.723596\pi$
$67$	2.66222	−	8.19348i	0.325242	−	1.00099i	0.971331	−	0.237731i	$-0.0764036\pi$
$68$	−15.2539			−1.84980
$69$	7.53831	−	5.47691i	0.907506	−	0.659342i
$70$	−0.334271	+	1.02878i	−0.0399530	+	0.122963i
$71$	3.34001	+	10.2795i	0.396386	+	1.21995i	0.927877	+	0.372887i	$0.121632\pi$
$71$	3.34001	+	10.2795i	0.396386	+	1.21995i	−0.531491	+	0.847064i	$0.678368\pi$
$72$	−1.57555	−	4.84905i	−0.185680	−	0.571466i
$73$	−8.29646			−0.971028			−0.485514	−	0.874229i	$-0.661367\pi$
$73$	−8.29646			−0.971028			−0.485514	+	0.874229i	$0.661367\pi$
$74$	0.337682	+	1.03928i	0.0392547	+	0.120814i
$75$	22.8663	+	16.6133i	2.64037	+	1.91834i
$76$	4.13927	−	3.00736i	0.474807	−	0.344967i
$77$	−1.39475	+	4.29259i	−0.158946	+	0.489186i
$78$	0.543022	−	1.67125i	0.0614851	−	0.189232i
$79$	−5.90977			−0.664901			−0.332450	−	0.943121i	$-0.607875\pi$
$79$	−5.90977			−0.664901			−0.332450	+	0.943121i	$0.607875\pi$
$80$	11.1767	−	8.12038i	1.24960	−	0.907886i
$81$	−1.11413			−0.123792
$82$	1.39441	+	1.10117i	0.153987	+	0.121604i
$83$	−6.17044			−0.677294			−0.338647	−	0.940913i	$-0.609969\pi$
$83$	−6.17044			−0.677294			−0.338647	+	0.940913i	$0.609969\pi$
$84$	−4.31243	+	3.13316i	−0.470525	+	0.341856i
$85$	−30.9224			−3.35400
$86$	0.409110	−	1.25911i	0.0441154	−	0.135773i
$87$	−3.87184	+	11.9163i	−0.415105	+	1.27756i
$88$	−3.97496	+	2.88798i	−0.423732	+	0.307860i
$89$	−8.79968	−	6.39334i	−0.932764	−	0.677693i	0.0139042	−	0.999903i	$-0.495574\pi$
$89$	−8.79968	−	6.39334i	−0.932764	−	0.677693i	−0.946668	+	0.322211i	$0.895574\pi$
$90$	−1.56562	−	4.81848i	−0.165031	−	0.507913i
$91$	−2.28458			−0.239489
$92$	−1.99753	−	6.14777i	−0.208257	−	0.640949i
$93$	0.0640654	+	0.197173i	0.00664327	+	0.0204459i
$94$	0.373762	−	1.15032i	0.0385506	−	0.118647i
$95$	8.39106	−	6.09646i	0.860904	−	0.625483i
$96$	−8.76092			−0.894158
$97$	−0.884678	+	2.72276i	−0.0898254	+	0.276454i	−0.985871	−	0.167509i	$-0.946428\pi$
$97$	−0.884678	+	2.72276i	−0.0898254	+	0.276454i	0.896045	+	0.443963i	$0.146428\pi$
$98$	−0.224492	−	0.163103i	−0.0226771	−	0.0164759i
$99$	−6.53257	−	20.1052i	−0.656547	−	2.02065i
$100$	15.8632	−	11.5253i	1.58632	−	1.15253i
$101$	2.29505	+	1.66745i	0.228366	+	0.165917i	0.696084	−	0.717960i	$-0.254924\pi$
$101$	2.29505	+	1.66745i	0.228366	+	0.165917i	−0.467719	+	0.883877i	$0.654924\pi$
$102$	4.93613	+	3.58631i	0.488750	+	0.355097i
$103$	5.91798	+	4.29967i	0.583116	+	0.423659i	0.839846	−	0.542824i	$-0.182645\pi$
$103$	5.91798	+	4.29967i	0.583116	+	0.423659i	−0.256730	+	0.966483i	$0.582645\pi$
$104$	−2.01199	−	1.46180i	−0.197292	−	0.143341i
$105$	−8.74208	+	6.35149i	−0.853140	+	0.619842i
$106$	−0.601755	−	1.85201i	−0.0584476	−	0.179883i
$107$	−4.65790	−	3.38416i	−0.450296	−	0.327159i	0.339417	−	0.940636i	$-0.389770\pi$
$107$	−4.65790	−	3.38416i	−0.450296	−	0.327159i	−0.789713	+	0.613477i	$0.789770\pi$
$108$	2.77337	−	8.53557i	0.266868	−	0.821335i
$109$	0.713846			0.0683741			0.0341870	−	0.999415i	$-0.489116\pi$
$109$	0.713846			0.0683741			0.0341870	+	0.999415i	$0.489116\pi$
$110$	−3.94991	+	2.86978i	−0.376609	+	0.273622i
$111$	−3.37325	+	10.3818i	−0.320175	+	0.985397i
$112$	1.09514	+	3.37048i	0.103481	+	0.318480i
$113$	4.80796	+	14.7974i	0.452295	+	1.39202i	0.874282	+	0.485418i	$0.161333\pi$
$113$	4.80796	+	14.7974i	0.452295	+	1.39202i	−0.421987	+	0.906602i	$0.638667\pi$
$114$	−2.04652			−0.191674
$115$	−4.04936	−	12.4626i	−0.377605	−	1.16215i
$116$	7.03214	+	5.10915i	0.652918	+	0.474373i
$117$	8.65669	−	6.28946i	0.800312	−	0.581460i
$118$	0.176921	−	0.544505i	0.0162869	−	0.0501258i
$119$	2.45122	−	7.54409i	0.224703	−	0.691565i
$120$	−11.7630			−1.07381
$121$	−7.58184	+	5.50853i	−0.689259	+	0.500776i
$122$	3.72994			0.337693
$123$	4.80343	+	17.0868i	0.433111	+	1.54066i
$124$	0.143825			0.0129159
$125$	16.3887	−	11.9071i	1.46585	−	1.06500i
$126$	1.29967			0.115783
$127$	3.21329	−	9.88950i	0.285134	−	0.877551i	−0.701225	−	0.712940i	$-0.747363\pi$
$127$	3.21329	−	9.88950i	0.285134	−	0.877551i	0.986359	−	0.164611i	$-0.0526369\pi$
$128$	−2.48591	+	7.65084i	−0.219725	+	0.676245i
$129$	10.6993	−	7.77351i	0.942023	−	0.684420i
$130$	−1.99931	−	1.45258i	−0.175351	−	0.127400i
$131$	3.99428	+	12.2931i	0.348981	+	1.07405i	0.959418	+	0.281989i	$0.0909942\pi$
$131$	3.99428	+	12.2931i	0.348981	+	1.07405i	−0.610436	+	0.792065i	$0.709006\pi$
$132$	−24.0590			−2.09407
$133$	0.822184	+	2.53042i	0.0712924	+	0.219415i
$134$	0.738734	+	2.27359i	0.0638169	+	0.196408i
$135$	5.62214	−	17.3032i	0.483876	−	1.48922i
$136$	6.98586	−	5.07553i	0.599033	−	0.435223i
$137$	17.5205			1.49687			0.748437	−	0.663205i	$-0.230804\pi$
$137$	17.5205			1.49687			0.748437	+	0.663205i	$0.230804\pi$
$138$	−0.798992	+	2.45905i	−0.0680147	+	0.209328i
$139$	−10.5058	−	7.63289i	−0.891088	−	0.647414i	0.0450732	−	0.998984i	$-0.485648\pi$
$139$	−10.5058	−	7.63289i	−0.891088	−	0.647414i	−0.936162	+	0.351570i	$0.885648\pi$
$140$	2.31651	+	7.12948i	0.195781	+	0.602551i
$141$	9.77489	−	7.10188i	0.823195	−	0.598086i
$142$	−2.42642	−	1.76290i	−0.203621	−	0.147939i
$143$	−8.34214	−	6.06092i	−0.697605	−	0.506840i
$144$	−13.4286	−	9.75646i	−1.11905	−	0.813038i
$145$	14.2554	+	10.3572i	1.18385	+	0.860117i
$146$	1.86249	−	1.35318i	0.154141	−	0.111990i
$147$	−0.856579	−	2.63628i	−0.0706494	−	0.217437i
$148$	6.12659	+	4.45123i	0.503602	+	0.365889i
$149$	5.22414	−	16.0783i	0.427978	−	1.31718i	−0.472135	−	0.881526i	$-0.656517\pi$
$149$	5.22414	−	16.0783i	0.427978	−	1.31718i	0.900113	−	0.435656i	$-0.143483\pi$
$150$	−7.84298			−0.640377
$151$	2.48552	−	1.80584i	0.202269	−	0.146957i	−0.482040	−	0.876149i	$-0.660104\pi$
$151$	2.48552	−	1.80584i	0.202269	−	0.146957i	0.684309	+	0.729192i	$0.260104\pi$
$152$	−0.895017	+	2.75458i	−0.0725954	+	0.223426i
$153$	11.4808	+	35.3342i	0.928165	+	2.85660i
$154$	−0.387025	−	1.19114i	−0.0311874	−	0.0959849i
$155$	0.291560			0.0234187
$156$	−3.76316	−	11.5818i	−0.301294	−	0.927288i
$157$	−8.63569	−	6.27419i	−0.689203	−	0.500735i	0.187195	−	0.982323i	$-0.440060\pi$
$157$	−8.63569	−	6.27419i	−0.689203	−	0.500735i	−0.876398	+	0.481588i	$0.840060\pi$
$158$	1.32670	−	0.963901i	0.105546	−	0.0766839i
$159$	6.01119	−	18.5005i	0.476719	−	1.46719i
$160$	−3.80732	+	11.7177i	−0.300995	+	0.926368i
$161$	3.36149			0.264922
$162$	0.250113	−	0.181718i	0.0196507	−	0.0142771i
$163$	−10.8763			−0.851895			−0.425948	−	0.904748i	$-0.640059\pi$
$163$	−10.8763			−0.851895			−0.425948	+	0.904748i	$0.640059\pi$
$164$	12.3033	+	0.493783i	0.960727	+	0.0385580i
$165$	−48.7720			−3.79689
$166$	1.38522	−	1.00642i	0.107514	−	0.0781132i
$167$	−10.5722			−0.818102			−0.409051	−	0.912512i	$-0.634140\pi$
$167$	−10.5722			−0.818102			−0.409051	+	0.912512i	$0.634140\pi$
$168$	0.932458	−	2.86981i	0.0719407	−	0.221411i
$169$	−2.40437	+	7.39988i	−0.184951	+	0.569221i
$170$	6.94183	−	5.04353i	0.532414	−	0.386821i
$171$	−10.0817	−	7.32476i	−0.770964	−	0.560138i
$172$	−2.83515	−	8.72568i	−0.216178	−	0.665327i
$173$	−18.9039			−1.43724			−0.718619	−	0.695404i	$-0.755225\pi$
$173$	−18.9039			−1.43724			−0.718619	+	0.695404i	$0.755225\pi$
$174$	−1.07439	−	3.30663i	−0.0814492	−	0.250675i
$175$	3.15090	+	9.69748i	0.238186	+	0.733061i
$176$	−4.94289	+	15.2127i	−0.372585	+	1.14670i
$177$	4.62695	−	3.36168i	0.347783	−	0.252679i
$178$	3.01823			0.226226
$179$	−5.34420	+	16.4478i	−0.399445	+	1.22936i	0.526001	+	0.850484i	$0.323691\pi$
$179$	−5.34420	+	16.4478i	−0.399445	+	1.22936i	−0.925446	+	0.378880i	$0.876309\pi$
$180$	−28.4052	−	20.6376i	−2.11720	−	1.53823i
$181$	−3.72975	−	11.4790i	−0.277230	−	0.853227i	−0.988621	−	0.150430i	$-0.951934\pi$
$181$	−3.72975	−	11.4790i	−0.277230	−	0.853227i	0.711390	−	0.702797i	$-0.248066\pi$
$182$	0.512871	−	0.372622i	0.0380165	−	0.0276206i
$183$	30.1440	+	21.9009i	2.22831	+	1.61896i
$184$	2.96041	+	2.15086i	0.218244	+	0.158564i
$185$	12.4197	+	9.02345i	0.913115	+	0.663417i
$186$	−0.0465417	−	0.0338145i	−0.00341261	−	0.00247940i
$187$	28.9649	−	21.0442i	2.11812	−	1.53890i
$188$	−2.59019	−	7.97178i	−0.188909	−	0.581402i
$189$	3.77576	+	2.74325i	0.274646	+	0.199542i
$190$	−0.889375	+	2.73722i	−0.0645221	+	0.198578i
$191$	17.7474			1.28416			0.642079	−	0.766639i	$-0.278072\pi$
$191$	17.7474			1.28416			0.642079	+	0.766639i	$0.278072\pi$
$192$	−13.9281	+	10.1194i	−1.00518	+	0.730304i
$193$	4.02061	−	12.3742i	0.289410	−	0.890711i	−0.695633	−	0.718398i	$-0.744876\pi$
$193$	4.02061	−	12.3742i	0.289410	−	0.890711i	0.985042	−	0.172313i	$-0.0551241\pi$
$194$	−0.245487	−	0.755532i	−0.0176249	−	0.0542440i
$195$	−7.62862	−	23.4785i	−0.546297	−	1.68133i
$196$	−1.92300			−0.137357
$197$	−0.507517	−	1.56198i	−0.0361591	−	0.111286i	0.931348	−	0.364131i	$-0.118634\pi$
$197$	−0.507517	−	1.56198i	−0.0361591	−	0.111286i	−0.967507	+	0.252845i	$0.918634\pi$
$198$	4.74573	+	3.44797i	0.337264	+	0.245037i
$199$	−2.29456	+	1.66710i	−0.162657	+	0.118177i	−0.666136	−	0.745830i	$-0.732053\pi$
$199$	−2.29456	+	1.66710i	−0.162657	+	0.118177i	0.503479	+	0.864007i	$0.332053\pi$
$200$	−3.43002	+	10.5565i	−0.242539	+	0.746459i
$201$	−7.37954	+	22.7119i	−0.520513	+	1.60197i
$202$	−0.787186			−0.0553862
$203$	−3.65686	+	2.65686i	−0.256661	+	0.186475i
$204$	42.2829			2.96039
$205$	24.9410	+	1.00099i	1.74196	+	0.0699120i
$206$	−2.02983			−0.141425
$207$	−12.7373	+	9.25419i	−0.885303	+	0.643211i
$208$	−8.09640			−0.561384
$209$	−3.71093	+	11.4211i	−0.256690	+	0.790011i
$210$	0.926581	−	2.85172i	0.0639401	−	0.196787i
$211$	0.210017	−	0.152586i	0.0144581	−	0.0105044i	−0.580533	−	0.814237i	$-0.697156\pi$
$211$	0.210017	−	0.152586i	0.0144581	−	0.0105044i	0.594991	+	0.803732i	$0.297156\pi$
$212$	−10.9177	−	7.93216i	−0.749830	−	0.544783i
$213$	−9.25833	−	28.4942i	−0.634370	−	1.95239i
$214$	1.59763			0.109212
$215$	−5.74736	−	17.6886i	−0.391967	−	1.20635i
$216$	1.56997	+	4.83187i	0.106823	+	0.328767i
$217$	−0.0231121	+	0.0711316i	−0.00156895	+	0.00482873i
$218$	−0.160253	+	0.116431i	−0.0108537	+	0.00788567i
$219$	22.9974			1.55402
$220$	−10.4556	+	32.1789i	−0.704914	+	2.16950i
$221$	14.6610	+	10.6519i	0.986207	+	0.716522i
$222$	−0.936036	−	2.88082i	−0.0628226	−	0.193348i
$223$	2.26064	−	1.64245i	0.151384	−	0.109987i	−0.509515	−	0.860462i	$-0.670175\pi$
$223$	2.26064	−	1.64245i	0.151384	−	0.109987i	0.660899	+	0.750475i	$0.270175\pi$
$224$	−2.55695	−	1.85773i	−0.170844	−	0.124125i
$225$	−38.6365	−	28.0711i	−2.57577	−	1.87141i
$226$	−3.49285	−	2.53770i	−0.232341	−	0.168805i
$227$	−20.4302	−	14.8434i	−1.35600	−	0.985193i	−0.998688	−	0.0512091i	$-0.983693\pi$
$227$	−20.4302	−	14.8434i	−1.35600	−	0.985193i	−0.357314	−	0.933984i	$-0.616307\pi$
$228$	−11.4738	+	8.33623i	−0.759873	+	0.552080i
$229$	1.15766	+	3.56291i	0.0765002	+	0.235443i	0.981993	−	0.188919i	$-0.0604983\pi$
$229$	1.15766	+	3.56291i	0.0765002	+	0.235443i	−0.905492	+	0.424362i	$0.860498\pi$
$230$	2.94175	+	2.13730i	0.193973	+	0.140930i
$231$	3.86617	−	11.8988i	0.254375	−	0.782886i
$232$	−4.92054			−0.323049
$233$	−12.1285	+	8.81184i	−0.794561	+	0.577283i	−0.909314	−	0.416112i	$-0.863393\pi$
$233$	−12.1285	+	8.81184i	−0.794561	+	0.577283i	0.114752	+	0.993394i	$0.463393\pi$
$234$	−0.917530	+	2.82387i	−0.0599808	+	0.184602i
$235$	−5.25078	−	16.1603i	−0.342523	−	1.05418i
$236$	−1.22607	−	3.77344i	−0.0798101	−	0.245630i
$237$	16.3816			1.06410
$238$	0.680184	+	2.09339i	0.0440898	+	0.135694i
$239$	−11.4556	−	8.32296i	−0.740999	−	0.538368i	0.152025	−	0.988377i	$-0.451421\pi$
$239$	−11.4556	−	8.32296i	−0.740999	−	0.538368i	−0.893024	+	0.450009i	$0.851421\pi$
$240$	−30.9813	+	22.5093i	−1.99984	+	1.45297i
$241$	−1.70607	+	5.25074i	−0.109898	+	0.338230i	−0.990849	−	0.134977i	$-0.956904\pi$
$241$	−1.70607	+	5.25074i	−0.109898	+	0.338230i	0.880951	+	0.473207i	$0.156904\pi$
$242$	0.803606	−	2.47325i	0.0516578	−	0.158986i
$243$	17.0896			1.09630
$244$	20.9120	−	15.1934i	1.33875	−	0.972661i
$245$	−3.89827			−0.249052
$246$	−3.86524	−	3.05240i	−0.246439	−	0.194614i
$247$	−6.07845			−0.386763
$248$	−0.0658682	+	0.0478561i	−0.00418264	+	0.00303886i
$249$	17.1041			1.08393
$250$	−1.73705	+	5.34609i	−0.109861	+	0.338116i
$251$	−9.61757	+	29.5998i	−0.607055	+	1.86832i	−0.125064	+	0.992149i	$0.539914\pi$
$251$	−9.61757	+	29.5998i	−0.607055	+	1.86832i	−0.481992	+	0.876176i	$0.660086\pi$
$252$	7.28660	−	5.29403i	0.459013	−	0.333492i
$253$	12.2745	+	8.91792i	0.771689	+	0.560665i
$254$	0.891649	+	2.74421i	0.0559470	+	0.172187i
$255$	85.7151			5.36769
$256$	3.14871	+	9.69072i	0.196794	+	0.605670i
$257$	9.37843	+	28.8638i	0.585011	+	1.80048i	0.599228	+	0.800578i	$0.295474\pi$
$257$	9.37843	+	28.8638i	0.585011	+	1.80048i	−0.0142176	+	0.999899i	$0.504526\pi$
$258$	−1.13403	+	3.49019i	−0.0706016	+	0.217289i
$259$	−3.18595	+	2.31473i	−0.197965	+	0.143830i
$260$	−17.1261			−1.06211
$261$	6.54216	−	20.1347i	0.404949	−	1.24631i
$262$	−2.90173	−	2.10823i	−0.179269	−	0.130247i
$263$	−2.80635	−	8.63705i	−0.173047	−	0.532584i	0.826492	−	0.562948i	$-0.190333\pi$
$263$	−2.80635	−	8.63705i	−0.173047	−	0.532584i	−0.999539	+	0.0303649i	$0.990333\pi$
$264$	11.0184	−	8.00532i	0.678135	−	0.492694i
$265$	−22.1321	−	16.0799i	−1.35957	−	0.987783i
$266$	−0.597294	−	0.433959i	−0.0366224	−	0.0266078i
$267$	24.3922	+	17.7220i	1.49278	+	1.08457i
$268$	13.4029	+	9.73779i	0.818713	+	0.594830i
$269$	9.48676	−	6.89253i	0.578418	−	0.420245i	−0.259735	−	0.965680i	$-0.583635\pi$
$269$	9.48676	−	6.89253i	0.578418	−	0.420245i	0.838153	+	0.545435i	$0.183635\pi$
$270$	1.56007	+	4.80141i	0.0949430	+	0.292205i
$271$	21.5706	+	15.6719i	1.31032	+	0.952002i	0.999999	+	0.00136889i	$0.000435730\pi$
$271$	21.5706	+	15.6719i	1.31032	+	0.952002i	0.310319	+	0.950633i	$0.399564\pi$
$272$	8.68697	−	26.7357i	0.526725	−	1.62109i
$273$	6.33273			0.383275
$274$	−3.93321	+	2.85764i	−0.237614	+	0.172637i
$275$	−14.2216	+	43.7696i	−0.857595	+	2.63940i
$276$	5.53705	+	17.0413i	0.333291	+	1.02576i
$277$	3.62329	+	11.1513i	0.217702	+	0.670019i	0.998951	+	0.0457986i	$0.0145833\pi$
$277$	3.62329	+	11.1513i	0.217702	+	0.670019i	−0.781248	+	0.624220i	$0.785417\pi$
$278$	3.60341			0.216118
$279$	−0.108250	−	0.333158i	−0.00648074	−	0.0199457i
$280$	−3.43314	−	2.49432i	−0.205170	−	0.149064i
$281$	−5.33096	+	3.87317i	−0.318018	+	0.231054i	−0.735329	−	0.677710i	$-0.762973\pi$
$281$	−5.33096	+	3.87317i	−0.318018	+	0.231054i	0.417311	+	0.908764i	$0.362973\pi$
$282$	−1.03605	+	3.18863i	−0.0616958	+	0.189880i
$283$	−5.08359	+	15.6457i	−0.302188	+	0.930040i	0.678523	+	0.734579i	$0.262620\pi$
$283$	−5.08359	+	15.6457i	−0.302188	+	0.930040i	−0.980712	+	0.195461i	$0.937380\pi$
$284$	−20.7847			−1.23335
$285$	−23.2596	+	16.8991i	−1.37778	+	1.00101i
$286$	2.86130			0.169192
$287$	−2.22129	+	6.00549i	−0.131119	+	0.354493i
$288$	14.8031			0.872281
$289$	−37.1515	+	26.9921i	−2.18538	+	1.58777i
$290$	−4.88952			−0.287123
$291$	2.45228	−	7.54734i	0.143755	−	0.442433i
$292$	4.93009	−	15.1733i	0.288512	−	0.887948i
$293$	−8.01023	+	5.81977i	−0.467963	+	0.339995i	−0.796647	−	0.604445i	$-0.793395\pi$
$293$	−8.01023	+	5.81977i	−0.467963	+	0.339995i	0.328684	+	0.944440i	$0.393395\pi$
$294$	0.622280	+	0.452113i	0.0362921	+	0.0263678i
$295$	−2.48546	−	7.64946i	−0.144709	−	0.445369i
$296$	−4.28690			−0.249171
$297$	6.50942	+	20.0339i	0.377715	+	1.16249i
$298$	1.44963	+	4.46152i	0.0839751	+	0.258449i
$299$	−2.37312	+	7.30373i	−0.137241	+	0.422385i
$300$	−43.9718	+	31.9474i	−2.53871	+	1.84448i
$301$	4.77105			0.274999
$302$	−0.263443	+	0.810793i	−0.0151594	+	0.0466559i
$303$	−6.36175	−	4.62208i	−0.365473	−	0.265532i
$304$	2.91376	+	8.96765i	0.167116	+	0.514330i
$305$	42.3924	−	30.7999i	2.42738	−	1.76360i
$306$	−8.34045	−	6.05969i	−0.476792	−	0.346410i
$307$	20.8411	+	15.1420i	1.18947	+	0.864198i	0.993208	−	0.116354i	$-0.0371206\pi$
$307$	20.8411	+	15.1420i	1.18947	+	0.864198i	0.196259	+	0.980552i	$0.437121\pi$
$308$	−7.02183	−	5.10166i	−0.400106	−	0.290694i
$309$	−16.4043	−	11.9184i	−0.933210	−	0.678017i
$310$	−0.0654531	+	0.0475544i	−0.00371748	+	0.00270091i
$311$	−1.43755	−	4.42432i	−0.0815159	−	0.250880i	0.901990	−	0.431757i	$-0.142106\pi$
$311$	−1.43755	−	4.42432i	−0.0815159	−	0.250880i	−0.983506	+	0.180877i	$0.942106\pi$
$312$	5.57713	+	4.05202i	0.315743	+	0.229401i
$313$	−0.0790585	+	0.243317i	−0.00446865	+	0.0137531i	−0.953266	−	0.302132i	$-0.902302\pi$
$313$	−0.0790585	+	0.243317i	−0.00446865	+	0.0137531i	0.948797	+	0.315885i	$0.102302\pi$
$314$	2.96199			0.167155
$315$	14.7713	−	10.7320i	0.832267	−	0.604677i
$316$	3.51182	−	10.8083i	0.197555	−	0.608012i
$317$	−0.0575650	−	0.177167i	−0.00323317	−	0.00995069i	0.949427	−	0.313988i	$-0.101665\pi$
$317$	−0.0575650	−	0.177167i	−0.00323317	−	0.00995069i	−0.952660	+	0.304037i	$0.901665\pi$
$318$	1.66803	+	5.13367i	0.0935386	+	0.287882i
$319$	−20.4016			−1.14227
$320$	7.48179	+	23.0266i	0.418245	+	1.28722i
$321$	12.9114	+	9.38072i	0.720647	+	0.523580i
$322$	−0.754628	+	0.548269i	−0.0420538	+	0.0305539i
$323$	6.52183	−	20.0721i	0.362884	−	1.11684i
$324$	0.662059	−	2.03761i	0.0367810	−	0.113200i
$325$	−23.2948			−1.29216
$326$	2.44164	−	1.77395i	0.135230	−	0.0982502i
$327$	−1.97874			−0.109425
$328$	−5.79889	+	3.86763i	−0.320190	+	0.213554i
$329$	4.35883			0.240310
$330$	10.9489	−	7.95487i	0.602719	−	0.437901i
$331$	16.9344			0.930801			0.465400	−	0.885100i	$-0.345910\pi$
$331$	16.9344			0.930801			0.465400	+	0.885100i	$0.345910\pi$
$332$	3.66672	−	11.2850i	0.201238	−	0.619346i
$333$	5.69970	−	17.5419i	0.312342	−	0.961289i
$334$	2.37338	−	1.72436i	0.129865	−	0.0943528i
$335$	27.1702	+	19.7403i	1.48446	+	1.07853i
$336$	−3.03566	−	9.34279i	−0.165609	−	0.509691i
$337$	−5.38365			−0.293266			−0.146633	−	0.989191i	$-0.546844\pi$
$337$	−5.38365			−0.293266			−0.146633	+	0.989191i	$0.546844\pi$
$338$	−0.667182	−	2.05337i	−0.0362899	−	0.111689i
$339$	−13.3274	−	41.0175i	−0.723845	−	2.22777i
$340$	18.3753	−	56.5534i	0.996541	−	3.06704i
$341$	−0.273104	+	0.198421i	−0.0147894	+	0.0107451i
$342$	3.45795			0.186984
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	4.20178	+	3.05277i	0.226545	+	0.164594i
$345$	11.2246	+	34.5458i	0.604313	+	1.85988i
$346$	4.24378	−	3.08329i	0.228147	−	0.165759i
$347$	−11.3264	−	8.22910i	−0.608032	−	0.441761i	0.240689	−	0.970602i	$-0.422627\pi$
$347$	−11.3264	−	8.22910i	−0.608032	−	0.441761i	−0.848721	+	0.528841i	$0.822627\pi$
$348$	−19.4927	−	14.1623i	−1.04492	−	0.759179i
$349$	8.12493	+	5.90311i	0.434917	+	0.315986i	0.783612	−	0.621250i	$-0.213375\pi$
$349$	8.12493	+	5.90311i	0.434917	+	0.315986i	−0.348695	+	0.937236i	$0.613375\pi$
$350$	−2.28904	−	1.66309i	−0.122354	−	0.0888957i
$351$	−8.62603	+	6.26717i	−0.460423	+	0.334517i
$352$	−4.40819	−	13.5670i	−0.234957	−	0.723125i
$353$	−16.6971	−	12.1312i	−0.888699	−	0.645678i	0.0468395	−	0.998902i	$-0.485085\pi$
$353$	−16.6971	−	12.1312i	−0.888699	−	0.645678i	−0.935538	+	0.353225i	$0.885085\pi$
$354$	−0.490414	+	1.50934i	−0.0260652	+	0.0802205i
$355$	−42.1345			−2.23627
$356$	16.9218	−	12.2944i	0.896853	−	0.651602i
$357$	−6.79466	+	20.9118i	−0.359611	+	1.10677i
$358$	−1.48295	−	4.56405i	−0.0783764	−	0.241218i
$359$	0.949440	+	2.92208i	0.0501095	+	0.154221i	0.972980	−	0.230889i	$-0.0741634\pi$
$359$	0.949440	+	2.92208i	0.0501095	+	0.154221i	−0.922871	+	0.385110i	$0.874163\pi$
$360$	19.8757			1.04754
$361$	−3.68378	−	11.3375i	−0.193883	−	0.596712i
$362$	2.70956	+	1.96861i	0.142411	+	0.103468i
$363$	21.0165	−	15.2694i	1.10308	−	0.801433i
$364$	1.35759	−	4.17823i	0.0711570	−	0.218999i
$365$	9.99419	−	30.7590i	0.523120	−	1.61000i
$366$	−10.3392			−0.540438
$367$	−16.5305	+	12.0101i	−0.862885	+	0.626923i	−0.928668	−	0.370911i	$-0.879045\pi$
$367$	−16.5305	+	12.0101i	−0.862885	+	0.626923i	0.0657830	+	0.997834i	$0.479045\pi$
$368$	11.9129			0.621002
$369$	−8.11624	−	28.8711i	−0.422514	−	1.50297i
$370$	−4.25988			−0.221461
$371$	5.67742	−	4.12489i	0.294757	−	0.214153i
$372$	−0.398677			−0.0206704
$373$	−1.42799	+	4.39491i	−0.0739386	+	0.227560i	−0.981195	−	0.193018i	$-0.938173\pi$
$373$	−1.42799	+	4.39491i	−0.0739386	+	0.227560i	0.907257	+	0.420577i	$0.138173\pi$
$374$	−3.07001	+	9.44852i	−0.158746	+	0.488571i
$375$	−45.4285	+	33.0058i	−2.34592	+	1.70441i
$376$	3.83874	+	2.78901i	0.197968	+	0.143832i
$377$	−3.19109	−	9.82117i	−0.164350	−	0.505816i
$378$	−1.29506			−0.0666108
$379$	7.28427	+	22.4187i	0.374168	+	1.15157i	0.944038	+	0.329836i	$0.106993\pi$
$379$	7.28427	+	22.4187i	0.374168	+	1.15157i	−0.569871	+	0.821734i	$0.693007\pi$
$380$	6.16341	+	18.9690i	0.316176	+	0.973090i
$381$	−8.90708	+	27.4132i	−0.456323	+	1.40442i
$382$	−3.98416	+	2.89466i	−0.203847	+	0.148104i
$383$	−1.19292			−0.0609554			−0.0304777	−	0.999535i	$-0.509703\pi$
$383$	−1.19292			−0.0609554			−0.0304777	+	0.999535i	$0.509703\pi$
$384$	6.89080	−	21.2077i	0.351645	−	1.08225i
$385$	−14.2345	−	10.3420i	−0.725459	−	0.527077i
$386$	1.11567	+	3.43367i	0.0567860	+	0.174769i
$387$	−18.0784	+	13.1347i	−0.918975	+	0.667675i
$388$	−4.45389	−	3.23594i	−0.226112	−	0.164280i
$389$	−2.37169	−	1.72313i	−0.120249	−	0.0873663i	0.526035	−	0.850463i	$-0.323678\pi$
$389$	−2.37169	−	1.72313i	−0.120249	−	0.0873663i	−0.646284	+	0.763097i	$0.723678\pi$
$390$	5.54198	+	4.02648i	0.280629	+	0.203889i
$391$	−21.5720	−	15.6729i	−1.09094	−	0.792615i
$392$	0.880683	−	0.639854i	0.0444812	−	0.0323175i
$393$	−11.0719	−	34.0759i	−0.558504	−	1.71890i
$394$	0.368697	+	0.267874i	0.0185747	+	0.0134953i
$395$	7.11910	−	21.9103i	0.358201	−	1.10243i
$396$	40.6519			2.04283
$397$	10.0219	−	7.28134i	0.502985	−	0.365440i	−0.307171	−	0.951654i	$-0.599382\pi$
$397$	10.0219	−	7.28134i	0.502985	−	0.365440i	0.810156	+	0.586215i	$0.199382\pi$
$398$	0.243202	−	0.748500i	0.0121906	−	0.0375189i
$399$	−2.27905	−	7.01420i	−0.114095	−	0.351149i
$400$	11.1666	+	34.3672i	0.558329	+	1.71836i
$401$	3.17644			0.158624			0.0793119	−	0.996850i	$-0.474728\pi$
$401$	3.17644			0.158624			0.0793119	+	0.996850i	$0.474728\pi$
$402$	−2.04773	−	6.30227i	−0.102132	−	0.314329i
$403$	−0.138236	−	0.100434i	−0.00688601	−	0.00500298i
$404$	−4.41338	+	3.20651i	−0.219574	+	0.159530i
$405$	1.34211	−	4.13060i	0.0666902	−	0.205251i
$406$	0.387594	−	1.19289i	0.0192359	−	0.0592022i
$407$	−17.7744			−0.881044
$408$	−19.3644	+	14.0691i	−0.958683	+	0.696524i
$409$	14.0948			0.696943			0.348471	−	0.937319i	$-0.386701\pi$
$409$	14.0948			0.696943			0.348471	+	0.937319i	$0.386701\pi$
$410$	−5.76234	+	3.84325i	−0.284581	+	0.189805i
$411$	−48.5658			−2.39557
$412$	−11.3803	+	8.26826i	−0.560666	+	0.407348i
$413$	2.06325			0.101526
$414$	1.35004	−	4.15499i	0.0663507	−	0.204206i
$415$	7.43312	−	22.8768i	0.364877	−	1.12298i
$416$	5.84156	−	4.24414i	0.286406	−	0.208086i
$417$	29.1215	+	21.1580i	1.42608	+	1.03611i
$418$	−1.02974	−	3.16920i	−0.0503661	−	0.155011i
$419$	13.8054			0.674439			0.337219	−	0.941426i	$-0.390514\pi$
$419$	13.8054			0.674439			0.337219	+	0.941426i	$0.390514\pi$
$420$	−6.42124	−	19.7625i	−0.313324	−	0.964314i
$421$	11.5049	+	35.4083i	0.560712	+	1.72569i	0.680360	+	0.732878i	$0.261823\pi$
$421$	11.5049	+	35.4083i	0.560712	+	1.72569i	−0.119648	+	0.992816i	$0.538177\pi$
$422$	−0.0222598	+	0.0685087i	−0.00108359	+	0.00333495i
$423$	−16.5164	+	11.9999i	−0.803054	+	0.583453i
$424$	7.63933			0.370999
$425$	24.9940	−	76.9235i	1.21239	−	3.73134i
$426$	6.72592	+	4.88666i	0.325872	+	0.236760i
$427$	4.15375	+	12.7839i	0.201014	+	0.618658i
$428$	8.95714	−	6.50774i	0.432960	−	0.314564i
$429$	23.1240	+	16.8005i	1.11644	+	0.811138i
$430$	4.17530	+	3.03353i	0.201351	+	0.146290i
$431$	−26.6699	−	19.3768i	−1.28464	−	0.933347i	−0.284960	−	0.958540i	$-0.591980\pi$
$431$	−26.6699	−	19.3768i	−1.28464	−	0.933347i	−0.999683	+	0.0251923i	$0.991980\pi$
$432$	13.3810	+	9.72189i	0.643795	+	0.467745i
$433$	1.23938	−	0.900463i	0.0595609	−	0.0432735i	−0.557606	−	0.830105i	$-0.688280\pi$
$433$	1.23938	−	0.900463i	0.0595609	−	0.0432735i	0.617167	+	0.786832i	$0.288280\pi$
$434$	−0.00641331	−	0.0197381i	−0.000307849	−	0.000947461i
$435$	−39.5153	−	28.7096i	−1.89461	−	1.37652i
$436$	−0.424196	+	1.30554i	−0.0203153	+	0.0625241i
$437$	8.94372			0.427836
$438$	−5.16273	+	3.75094i	−0.246685	+	0.179227i
$439$	3.10987	−	9.57121i	0.148426	−	0.456809i	−0.849009	−	0.528378i	$-0.822801\pi$
$439$	3.10987	−	9.57121i	0.148426	−	0.456809i	0.997436	+	0.0715688i	$0.0228005\pi$
$440$	−5.91875	−	18.2160i	−0.282165	−	0.868416i
$441$	1.44734	+	4.45445i	0.0689209	+	0.212117i
$442$	−5.02864			−0.239188
$443$	0.0295564	+	0.0909652i	0.00140427	+	0.00432189i	0.951756	−	0.306855i	$-0.0992768\pi$
$443$	0.0295564	+	0.0909652i	0.00140427	+	0.00432189i	−0.950352	+	0.311177i	$0.899277\pi$
$444$	−16.9826	−	12.3386i	−0.805957	−	0.585562i
$445$	34.3035	−	24.9230i	1.62614	−	1.18146i
$446$	−0.239607	+	0.737436i	−0.0113457	+	0.0349186i
$447$	−14.4810	+	44.5681i	−0.684930	+	2.10800i
$448$	−6.21085			−0.293435
$449$	−7.29492	+	5.30007i	−0.344268	+	0.250126i	−0.746461	−	0.665430i	$-0.768248\pi$
$449$	−7.29492	+	5.30007i	−0.344268	+	0.250126i	0.402192	+	0.915555i	$0.368248\pi$
$450$	13.2521			0.624709
$451$	−24.0434	+	16.0360i	−1.13216	+	0.755106i
$452$	−29.9197			−1.40731
$453$	−6.88974	+	5.00569i	−0.323708	+	0.235188i
$454$	7.00744			0.328875
$455$	2.75208	−	8.47003i	0.129020	−	0.397081i
$456$	2.48094	−	7.63554i	0.116181	−	0.357567i
$457$	−16.6007	+	12.0611i	−0.776546	+	0.564194i	−0.903940	−	0.427658i	$-0.859339\pi$
$457$	−16.6007	+	12.0611i	−0.776546	+	0.564194i	0.127394	+	0.991852i	$0.459339\pi$
$458$	−0.841007	−	0.611027i	−0.0392977	−	0.0285514i
$459$	−11.4401	−	35.2090i	−0.533978	−	1.64341i
$460$	25.1990			1.17491
$461$	−13.1493	−	40.4695i	−0.612426	−	1.88485i	−0.434042	−	0.900893i	$-0.642913\pi$
$461$	−13.1493	−	40.4695i	−0.612426	−	1.88485i	−0.178384	−	0.983961i	$-0.557087\pi$
$462$	1.07281	+	3.30178i	0.0499118	+	0.153613i
$463$	−10.7189	+	32.9895i	−0.498151	+	1.53315i	0.313837	+	0.949477i	$0.398385\pi$
$463$	−10.7189	+	32.9895i	−0.498151	+	1.53315i	−0.811988	+	0.583674i	$0.801615\pi$
$464$	−12.9597	+	9.41574i	−0.601637	+	0.437115i
$465$	−0.808190			−0.0374789
$466$	1.28550	−	3.95638i	0.0595499	−	0.183276i
$467$	23.3097	+	16.9355i	1.07864	+	0.783679i	0.977446	−	0.211187i	$-0.0677330\pi$
$467$	23.3097	+	16.9355i	1.07864	+	0.783679i	0.101196	+	0.994866i	$0.467733\pi$
$468$	6.35852	+	19.5695i	0.293923	+	0.904601i
$469$	−6.96979	+	5.06385i	−0.321835	+	0.233827i
$470$	3.81455	+	2.77143i	0.175952	+	0.127837i
$471$	23.9377	+	17.3917i	1.10299	+	0.801369i
$472$	1.81707	+	1.32018i	0.0836375	+	0.0607662i
$473$	17.4215	+	12.6574i	0.801040	+	0.581990i
$474$	−3.67753	+	2.67188i	−0.168915	+	0.122724i
$475$	8.38343	+	25.8015i	0.384658	+	1.18386i
$476$	12.3406	+	8.96599i	0.565632	+	0.410956i
$477$	−10.1570	+	31.2599i	−0.465055	+	1.43129i
$478$	3.92919			0.179717
$479$	−6.17760	+	4.48829i	−0.282262	+	0.205075i	−0.719903	−	0.694074i	$-0.755814\pi$
$479$	−6.17760	+	4.48829i	−0.282262	+	0.205075i	0.437642	+	0.899150i	$0.355814\pi$
$480$	10.5537	−	32.4809i	0.481708	−	1.48254i
$481$	−2.78016	−	8.55646i	−0.126765	−	0.390141i
$482$	−0.473413	−	1.45702i	−0.0215634	−	0.0663653i
$483$	−9.31787			−0.423978
$484$	−5.56902	−	17.1397i	−0.253137	−	0.779077i
$485$	−9.02885	−	6.55985i	−0.409979	−	0.297867i
$486$	−3.83648	+	2.78737i	−0.174026	+	0.126437i
$487$	−2.85418	+	8.78426i	−0.129335	+	0.398053i	−0.994666	−	0.103148i	$-0.967108\pi$
$487$	−2.85418	+	8.78426i	−0.129335	+	0.398053i	0.865331	+	0.501201i	$0.167108\pi$
$488$	−4.52171	+	13.9164i	−0.204688	+	0.629965i
$489$	30.1484			1.36336
$490$	0.875132	−	0.635821i	0.0395344	−	0.0287234i
$491$	−21.0083			−0.948090			−0.474045	−	0.880501i	$-0.657207\pi$
$491$	−21.0083			−0.948090			−0.474045	+	0.880501i	$0.657207\pi$
$492$	−34.1041	−	1.36874i	−1.53753	−	0.0617075i
$493$	35.8551			1.61483
$494$	1.36457	−	0.991415i	0.0613947	−	0.0446059i
$495$	82.4088			3.70400
$496$	−0.0819076	+	0.252086i	−0.00367776	+	0.0113190i
$497$	3.34001	−	10.2795i	0.149820	−	0.461098i
$498$	−3.83975	+	2.78974i	−0.172063	+	0.125011i
$499$	−24.5519	−	17.8380i	−1.09909	−	0.798538i	−0.118182	−	0.992992i	$-0.537706\pi$
$499$	−24.5519	−	17.8380i	−1.09909	−	0.798538i	−0.980912	+	0.194454i	$0.937706\pi$
$500$	12.0378	+	37.0486i	0.538348	+	1.65686i
$501$	29.3056			1.30928
$502$	−2.66876	−	8.21359i	−0.119112	−	0.366590i
$503$	−7.61845	−	23.4472i	−0.339690	−	1.04546i	−0.964366	−	0.264573i	$-0.914769\pi$
$503$	−7.61845	−	23.4472i	−0.339690	−	1.04546i	0.624676	−	0.780884i	$-0.285231\pi$
$504$	−1.57555	+	4.84905i	−0.0701806	+	0.215994i
$505$	−8.94672	+	6.50017i	−0.398124	+	0.289254i
$506$	−4.21006			−0.187160
$507$	6.66478	−	20.5121i	0.295993	−	0.910973i
$508$	16.1773	+	11.7535i	0.717750	+	0.521476i
$509$	−7.61018	−	23.4217i	−0.337315	−	1.03815i	−0.965570	−	0.260143i	$-0.916230\pi$
$509$	−7.61018	−	23.4217i	−0.337315	−	1.03815i	0.628255	−	0.778008i	$-0.283770\pi$
$510$	−19.2424	+	13.9804i	−0.852067	+	0.619063i
$511$	6.71198	+	4.87654i	0.296921	+	0.215725i
$512$	−15.3038	−	11.1189i	−0.676340	−	0.491390i
$513$	10.0459	+	7.29881i	0.443539	+	0.322250i
$514$	−6.81317	−	4.95006i	−0.300516	−	0.218338i
$515$	−23.0699	+	16.7613i	−1.01658	+	0.738590i
$516$	7.85887	+	24.1871i	0.345968	+	1.06478i
$517$	15.9162	+	11.5638i	0.699996	+	0.508577i
$518$	0.337682	−	1.03928i	0.0148369	−	0.0456632i
$519$	52.4006			2.30013
$520$	7.84329	−	5.69849i	0.343951	−	0.249895i
$521$	8.26793	−	25.4461i	0.362225	−	1.11481i	−0.589476	−	0.807786i	$-0.700666\pi$
$521$	8.26793	−	25.4461i	0.362225	−	1.11481i	0.951701	−	0.307027i	$-0.0993343\pi$
$522$	1.81537	+	5.58713i	0.0794565	+	0.244542i
$523$	−4.55230	−	14.0105i	−0.199058	−	0.612638i	−0.999905	−	0.0137692i	$-0.995617\pi$
$523$	−4.55230	−	14.0105i	−0.199058	−	0.612638i	0.800847	−	0.598869i	$-0.204383\pi$
$524$	−24.8562			−1.08585
$525$	−8.73413	−	26.8809i	−0.381189	−	1.17318i
$526$	2.03873	+	1.48123i	0.0888930	+	0.0645846i
$527$	0.479970	−	0.348719i	0.0209078	−	0.0151904i
$528$	13.7014	−	42.1687i	0.596278	−	1.83516i
$529$	−3.61562	+	11.1277i	−0.157201	+	0.483815i
$530$	7.59118			0.329740
$531$	−7.81804	+	5.68014i	−0.339274	+	0.246497i
$532$	−5.11642			−0.221825
$533$	−11.4803	−	9.06606i	−0.497268	−	0.392695i
$534$	−8.36638			−0.362049
$535$	18.1578	−	13.1924i	0.785029	−	0.570357i
$536$	−9.37830			−0.405081
$537$	14.8139	−	45.5923i	0.639265	−	1.96745i
$538$	−1.00551	+	3.09464i	−0.0433506	+	0.133419i
$539$	3.65150	−	2.65297i	0.157281	−	0.114271i
$540$	28.3045	+	20.5644i	1.21803	+	0.884953i
$541$	4.36051	+	13.4203i	0.187473	+	0.576982i	0.999982	−	0.00596594i	$-0.00189903\pi$
$541$	4.36051	+	13.4203i	0.187473	+	0.576982i	−0.812509	+	0.582948i	$0.801899\pi$
$542$	−7.39856			−0.317795
$543$	10.3387	+	31.8192i	0.443675	+	1.36549i
$544$	7.74725	+	23.8436i	0.332161	+	1.02229i
$545$	−0.859922	+	2.64657i	−0.0368350	+	0.113367i
$546$	−1.42165	+	1.03289i	−0.0608410	+	0.0442036i
$547$	−14.8318			−0.634163			−0.317081	−	0.948398i	$-0.602703\pi$
$547$	−14.8318			−0.634163			−0.317081	+	0.948398i	$0.602703\pi$
$548$	−10.4114	+	32.0429i	−0.444751	+	1.36880i
$549$	−50.9335	−	37.0054i	−2.17379	−	1.57935i
$550$	−3.94632	−	12.1455i	−0.168272	−	0.517887i
$551$	−9.72960	+	7.06897i	−0.414495	+	0.301148i
$552$	−8.20609	−	5.96207i	−0.349274	−	0.253763i
$553$	4.78110	+	3.47367i	0.203313	+	0.147716i
$554$	−2.63222	−	1.91242i	−0.111832	−	0.0812509i
$555$	−34.4268	−	25.0125i	−1.46134	−	1.06172i
$556$	20.2026	−	14.6781i	0.856782	−	0.622488i
$557$	2.88421	+	8.87668i	0.122208	+	0.376117i	0.993382	−	0.114857i	$-0.0366410\pi$
$557$	2.88421	+	8.87668i	0.122208	+	0.376117i	−0.871174	+	0.490974i	$0.836641\pi$
$558$	0.0786404	+	0.0571356i	0.00332911	+	0.00241874i
$559$	−3.36824	+	10.3664i	−0.142461	+	0.438450i
$560$	−13.8152			−0.583800
$561$	−80.2890	+	58.3334i	−3.38981	+	2.46284i
$562$	0.565033	−	1.73899i	0.0238345	−	0.0733549i
$563$	7.05353	+	21.7085i	0.297271	+	0.914906i	0.982449	+	0.186530i	$0.0597242\pi$
$563$	7.05353	+	21.7085i	0.297271	+	0.914906i	−0.685178	+	0.728375i	$0.740276\pi$
$564$	7.17986	+	22.0973i	0.302327	+	0.930466i
$565$	−60.6528			−2.55168
$566$	−1.41063	−	4.34149i	−0.0592934	−	0.182486i
$567$	0.901348	+	0.654867i	0.0378530	+	0.0275018i
$568$	9.51886	−	6.91586i	0.399402	−	0.290183i
$569$	11.9639	−	36.8211i	0.501553	−	1.54362i	−0.304936	−	0.952373i	$-0.598635\pi$
$569$	11.9639	−	36.8211i	0.501553	−	1.54362i	0.806489	−	0.591249i	$-0.201365\pi$
$570$	2.46530	−	7.58741i	0.103260	−	0.317802i
$571$	18.8698			0.789678			0.394839	−	0.918750i	$-0.370800\pi$
$571$	18.8698			0.789678			0.394839	+	0.918750i	$0.370800\pi$
$572$	16.0419	−	11.6552i	0.670747	−	0.487326i
$573$	−49.1949			−2.05515
$574$	−0.480851	−	1.71048i	−0.0200703	−	0.0713942i
$575$	34.2755			1.42939
$576$	23.5340	−	17.0985i	0.980585	−	0.712437i
$577$	16.5800			0.690236			0.345118	−	0.938559i	$-0.387839\pi$
$577$	16.5800			0.690236			0.345118	+	0.938559i	$0.387839\pi$
$578$	3.93772	−	12.1190i	0.163787	−	0.504086i
$579$	−11.1449	+	34.3005i	−0.463166	+	1.42548i
$580$	−27.4132	+	19.9169i	−1.13827	+	0.827003i
$581$	4.99199	+	3.62690i	0.207103	+	0.150469i
$582$	0.680477	+	2.09429i	0.0282067	+	0.0868113i
$583$	31.6743			1.31181
$584$	2.79086	+	8.58937i	0.115486	+	0.355431i
$585$	12.8899	+	39.6710i	0.532931	+	1.64019i
$586$	0.849011	−	2.61299i	0.0350723	−	0.107942i
$587$	−4.78825	+	3.47887i	−0.197632	+	0.143588i	−0.682200	−	0.731165i	$-0.738977\pi$
$587$	−4.78825	+	3.47887i	−0.197632	+	0.143588i	0.484568	+	0.874754i	$0.338977\pi$
$588$	5.33046			0.219824
$589$	−0.0614930	+	0.189256i	−0.00253377	+	0.00779815i
$590$	1.80562	+	1.31186i	0.0743361	+	0.0540083i
$591$	1.40681	+	4.32972i	0.0578684	+	0.178101i
$592$	−11.2908	+	8.20325i	−0.464049	+	0.337151i
$593$	7.74866	+	5.62973i	0.318199	+	0.231185i	0.735407	−	0.677626i	$-0.236991\pi$
$593$	7.74866	+	5.62973i	0.318199	+	0.231185i	−0.417207	+	0.908811i	$0.636991\pi$
$594$	−4.72891	−	3.43576i	−0.194030	−	0.140971i
$595$	25.0167	+	18.1757i	1.02559	+	0.745131i
$596$	26.3008	+	19.1087i	1.07732	+	0.782722i
$597$	6.36040	−	4.62110i	0.260314	−	0.189129i
$598$	−0.658513	−	2.02669i	−0.0269286	−	0.0828777i
$599$	−11.7657	−	8.54827i	−0.480733	−	0.349273i	0.320877	−	0.947121i	$-0.396023\pi$
$599$	−11.7657	−	8.54827i	−0.480733	−	0.349273i	−0.801609	+	0.597848i	$0.796023\pi$
$600$	9.50784	−	29.2621i	0.388156	−	1.19462i
$601$	−5.00887			−0.204316			−0.102158	−	0.994768i	$-0.532575\pi$
$601$	−5.00887			−0.204316			−0.102158	+	0.994768i	$0.532575\pi$
$602$	−1.07106	+	0.778173i	−0.0436533	+	0.0317160i
$603$	12.4690	−	38.3757i	0.507778	−	1.56278i
$604$	1.82567	+	5.61883i	0.0742854	+	0.228627i
$605$	−11.2894	−	34.7453i	−0.458980	−	1.41260i
$606$	2.18204			0.0886393
$607$	−2.12931	−	6.55333i	−0.0864259	−	0.265992i	0.898499	−	0.438976i	$-0.144659\pi$
$607$	−2.12931	−	6.55333i	−0.0864259	−	0.265992i	−0.984924	+	0.172985i	$0.944659\pi$
$608$	−6.80314	−	4.94277i	−0.275904	−	0.200456i
$609$	10.1366	−	7.36468i	0.410756	−	0.298432i
$610$	−4.49321	+	13.8287i	−0.181925	+	0.559906i
$611$	−3.07722	+	9.47070i	−0.124491	+	0.383144i
$612$	−71.4443			−2.88797
$613$	−12.4016	+	9.01028i	−0.500896	+	0.363922i	−0.809359	−	0.587314i	$-0.800185\pi$
$613$	−12.4016	+	9.01028i	−0.500896	+	0.363922i	0.308463	+	0.951236i	$0.400185\pi$
$614$	−7.14838			−0.288485
$615$	−69.1353	−	2.77469i	−2.78780	−	0.111886i
$616$	4.91332			0.197963
$617$	24.2546	−	17.6220i	0.976452	−	0.709434i	0.0195390	−	0.999809i	$-0.493780\pi$
$617$	24.2546	−	17.6220i	0.976452	−	0.709434i	0.956913	+	0.290375i	$0.0937802\pi$
$618$	5.62658			0.226334
$619$	2.30954	−	7.10803i	0.0928282	−	0.285696i	−0.893853	−	0.448359i	$-0.852009\pi$
$619$	2.30954	−	7.10803i	0.0928282	−	0.285696i	0.986682	+	0.162664i	$0.0520085\pi$
$620$	−0.173257	+	0.533230i	−0.00695816	+	0.0214150i
$621$	12.6922	−	9.22140i	0.509319	−	0.370042i
$622$	1.04434	+	0.758757i	0.0418742	+	0.0304234i
$623$	3.36118	+	10.3446i	0.134663	+	0.414449i
$624$	22.4428			0.898430
$625$	8.64835	+	26.6169i	0.345934	+	1.06468i
$626$	−0.0219378	−	0.0675175i	−0.000876810	−	0.00269854i
$627$	10.2865	−	31.6586i	0.410803	−	1.26432i
$628$	16.6064	−	12.0653i	0.662669	−	0.481457i
$629$	31.2379			1.24554
$630$	−1.56562	+	4.81848i	−0.0623758	+	0.191973i
$631$	−6.61888	−	4.80890i	−0.263494	−	0.191439i	0.448192	−	0.893937i	$-0.352068\pi$
$631$	−6.61888	−	4.80890i	−0.263494	−	0.191439i	−0.711686	+	0.702498i	$0.752068\pi$
$632$	1.98799	+	6.11841i	0.0790781	+	0.243377i
$633$	−0.582155	+	0.422960i	−0.0231386	+	0.0168112i
$634$	0.0418194	+	0.0303836i	0.00166086	+	0.00120669i
$635$	32.7943	+	23.8264i	1.30140	+	0.945523i
$636$	30.2632	+	21.9875i	1.20002	+	0.871862i
$637$	1.84826	+	1.34284i	0.0732309	+	0.0532054i
$638$	4.58000	−	3.32756i	0.181324	−	0.131739i
$639$	15.6436	+	48.1459i	0.618850	+	1.90462i
$640$	−25.3707	−	18.4329i	−1.00287	−	0.728624i
$641$	−12.8210	+	39.4589i	−0.506398	+	1.55853i	0.292010	+	0.956415i	$0.405676\pi$
$641$	−12.8210	+	39.4589i	−0.506398	+	1.55853i	−0.798408	+	0.602117i	$0.794324\pi$
$642$	−4.42854			−0.174781
$643$	34.5200	−	25.0802i	1.36134	−	0.989068i	0.362977	−	0.931798i	$-0.381760\pi$
$643$	34.5200	−	25.0802i	1.36134	−	0.989068i	0.998359	−	0.0572700i	$-0.0182396\pi$
$644$	−1.99753	+	6.14777i	−0.0787137	+	0.242256i
$645$	15.9314	+	49.0317i	0.627297	+	1.93062i
$646$	1.80973	+	5.56977i	0.0712028	+	0.219140i
$647$	15.3680			0.604177			0.302089	−	0.953280i	$-0.402316\pi$
$647$	15.3680			0.604177			0.302089	+	0.953280i	$0.402316\pi$
$648$	0.374782	+	1.15346i	0.0147228	+	0.0453122i
$649$	7.53396	+	5.47374i	0.295734	+	0.214863i
$650$	5.22950	−	3.79946i	0.205118	−	0.149027i
$651$	0.0640654	−	0.197173i	0.00251092	−	0.00772782i
$652$	6.46311	−	19.8914i	0.253115	−	0.779008i
$653$	8.35675			0.327025			0.163512	−	0.986541i	$-0.447718\pi$
$653$	8.35675			0.327025			0.163512	+	0.986541i	$0.447718\pi$
$654$	0.444213	−	0.322739i	0.0173701	−	0.0126201i
$655$	−50.3881			−1.96883
$656$	−7.87211	+	21.2830i	−0.307354	+	0.830963i
$657$	−38.8581			−1.51600
$658$	−0.978523	+	0.710938i	−0.0381468	+	0.0277153i
$659$	16.3737			0.637828			0.318914	−	0.947784i	$-0.396682\pi$
$659$	16.3737			0.637828			0.318914	+	0.947784i	$0.396682\pi$
$660$	28.9823	−	89.1982i	1.12813	−	3.47204i
$661$	6.56144	−	20.1940i	0.255210	−	0.785457i	−0.738578	−	0.674168i	$-0.764502\pi$
$661$	6.56144	−	20.1940i	0.255210	−	0.785457i	0.993788	−	0.111288i	$-0.0354977\pi$
$662$	−3.80165	+	2.76206i	−0.147755	+	0.107351i
$663$	−40.6396	−	29.5264i	−1.57831	−	1.14671i
$664$	2.07568	+	6.38829i	0.0805521	+	0.247914i
$665$	−10.3719			−0.402206
$666$	1.58160	+	4.86765i	0.0612856	+	0.188618i
$667$	4.69531	+	14.4507i	0.181803	+	0.559533i
$668$	6.28243	−	19.3353i	0.243074	−	0.748106i
$669$	−6.26638	+	4.55279i	−0.242272	+	0.176021i
$670$	−9.31919			−0.360032
$671$	−18.7480	+	57.7003i	−0.723757	+	2.22749i
$672$	7.08773	+	5.14954i	0.273415	+	0.198648i
$673$	−10.9000	−	33.5468i	−0.420165	−	1.29314i	−0.907548	−	0.419948i	$-0.862048\pi$
$673$	−10.9000	−	33.5468i	−0.420165	−	1.29314i	0.487383	−	0.873188i	$-0.337952\pi$
$674$	1.20859	−	0.878091i	0.0465531	−	0.0338228i
$675$	38.4997	+	27.9716i	1.48185	+	1.07663i
$676$	−12.1047	−	8.79461i	−0.465567	−	0.338254i
$677$	−2.28128	−	1.65745i	−0.0876769	−	0.0637010i	0.543083	−	0.839679i	$-0.317257\pi$
$677$	−2.28128	−	1.65745i	−0.0876769	−	0.0637010i	−0.630760	+	0.775978i	$0.717257\pi$
$678$	9.68199	+	7.03438i	0.371834	+	0.270154i
$679$	2.31612	−	1.68276i	0.0888844	−	0.0645783i
$680$	10.4020	+	32.0141i	0.398899	+	1.22768i
$681$	56.6315	+	41.1452i	2.17012	+	1.57669i
$682$	0.0289465	−	0.0890881i	0.00110842	−	0.00341136i
$683$	−42.9119			−1.64198			−0.820988	−	0.570945i	$-0.806577\pi$
$683$	−42.9119			−1.64198			−0.820988	+	0.570945i	$0.806577\pi$
$684$	19.3871	−	14.0855i	0.741282	−	0.538573i
$685$	−21.1057	+	64.9568i	−0.806409	+	2.48187i
$686$	0.0857484	+	0.263906i	0.00327389	+	0.0100760i
$687$	−3.20897	−	9.87619i	−0.122430	−	0.376800i
$688$	16.9083			0.644622
$689$	4.95430	+	15.2478i	0.188744	+	0.580894i
$690$	−8.15437	−	5.92449i	−0.310431	−	0.225542i
$691$	−21.5557	+	15.6612i	−0.820019	+	0.595779i	−0.916718	−	0.399535i	$-0.869172\pi$
$691$	−21.5557	+	15.6612i	−0.820019	+	0.595779i	0.0966989	+	0.995314i	$0.469172\pi$
$692$	11.2335	−	34.5730i	0.427032	−	1.31427i
$693$	−6.53257	+	20.1052i	−0.248152	+	0.763732i
$694$	3.88488			0.147468
$695$	40.9544	−	29.7551i	1.55349	−	1.12868i
$696$	13.6395			0.517003
$697$	42.2555	−	28.1827i	1.60054	−	1.06750i
$698$	−2.78680			−0.105482
$699$	33.6194	−	24.4259i	1.27160	−	0.923874i
$700$	−19.6079			−0.741111
$701$	−13.1210	+	40.3822i	−0.495572	+	1.52521i	0.320492	+	0.947251i	$0.396152\pi$
$701$	−13.1210	+	40.3822i	−0.495572	+	1.52521i	−0.816064	+	0.577962i	$0.803848\pi$
$702$	0.914280	−	2.81386i	0.0345073	−	0.106202i
$703$	−8.47668	+	6.15867i	−0.319704	+	0.232279i
$704$	−22.6789	−	16.4772i	−0.854743	−	0.621007i
$705$	14.5549	+	44.7954i	0.548169	+	1.68709i
$706$	5.72701			0.215539
$707$	−0.876630	−	2.69799i	−0.0329691	−	0.101468i
$708$	3.39859	+	10.4598i	0.127727	+	0.393103i
$709$	2.85067	−	8.77347i	0.107059	−	0.329494i	−0.883149	−	0.469093i	$-0.844581\pi$
$709$	2.85067	−	8.77347i	0.107059	−	0.329494i	0.990208	+	0.139598i	$0.0445811\pi$
$710$	9.45886	−	6.87227i	0.354985	−	0.257912i
$711$	−27.6795			−1.03806
$712$	−3.65892	+	11.2610i	−0.137124	+	0.422024i
$713$	0.203398	+	0.147777i	0.00761730	+	0.00553429i
$714$	−1.88543	−	5.80277i	−0.0705606	−	0.217163i
$715$	32.5199	−	23.6271i	1.21618	−	0.883604i
$716$	−26.9053	−	19.5478i	−1.00550	−	0.730537i
$717$	31.7542	+	23.0708i	1.18588	+	0.861595i
$718$	−0.689742	−	0.501127i	−0.0257409	−	0.0187019i
$719$	−13.5359	−	9.83440i	−0.504804	−	0.366761i	0.306045	−	0.952017i	$-0.400994\pi$
$719$	−13.5359	−	9.83440i	−0.504804	−	0.366761i	−0.810849	+	0.585256i	$0.800994\pi$
$720$	52.3484	−	38.0333i	1.95091	−	1.41742i
$721$	−2.26047	−	6.95701i	−0.0841842	−	0.259092i
$722$	2.67617	+	1.94435i	0.0995966	+	0.0723612i
$723$	4.72914	−	14.5548i	0.175878	−	0.541298i
$724$	23.2101			0.862597
$725$	−37.2873	+	27.0908i	−1.38482	+	1.00613i
$726$	−2.22755	+	6.85570i	−0.0826723	+	0.254439i
$727$	−3.03692	−	9.34668i	−0.112633	−	0.346649i	0.878813	−	0.477167i	$-0.158336\pi$
$727$	−3.03692	−	9.34668i	−0.112633	−	0.346649i	−0.991446	+	0.130517i	$0.958336\pi$
$728$	0.768512	+	2.36524i	0.0284830	+	0.0876615i
$729$	−44.0290			−1.63071
$730$	2.77326	+	8.53523i	0.102643	+	0.315903i
$731$	−30.6176	−	22.2450i	−1.13243	−	0.822762i
$732$	−57.9669	+	42.1154i	−2.14252	+	1.55663i
$733$	1.06052	−	3.26395i	0.0391713	−	0.120557i	−0.929559	−	0.368674i	$-0.879812\pi$
$733$	1.06052	−	3.26395i	0.0391713	−	0.120557i	0.968730	+	0.248117i	$0.0798118\pi$
$734$	1.75208	−	5.39235i	0.0646705	−	0.199035i
$735$	10.8058			0.398578
$736$	−8.59516	+	6.24475i	−0.316822	+	0.230185i
$737$	−38.8844			−1.43233
$738$	6.53100	+	5.15756i	0.240409	+	0.189852i
$739$	19.3385			0.711378			0.355689	−	0.934604i	$-0.384246\pi$
$739$	19.3385			0.711378			0.355689	+	0.934604i	$0.384246\pi$
$740$	−23.8831	+	17.3521i	−0.877961	+	0.637876i
$741$	16.8491			0.618969
$742$	−0.601755	+	1.85201i	−0.0220911	+	0.0679894i
$743$	−1.63276	+	5.02513i	−0.0599003	+	0.184354i	−0.976529	−	0.215385i	$-0.930899\pi$
$743$	−1.63276	+	5.02513i	−0.0599003	+	0.184354i	0.916629	+	0.399739i	$0.130899\pi$
$744$	0.182583	−	0.132654i	0.00669383	−	0.00486335i
$745$	53.3166	+	38.7368i	1.95337	+	1.41921i
$746$	−0.396250	−	1.21953i	−0.0145078	−	0.0446503i
$747$	−28.9004			−1.05741
$748$	21.2753	+	65.4786i	0.777902	+	2.39414i
$749$	1.77916	+	5.47569i	0.0650091	+	0.200077i
$750$	4.81501	−	14.8191i	0.175819	−	0.541116i
$751$	20.7683	−	15.0891i	0.757847	−	0.550608i	−0.140402	−	0.990095i	$-0.544839\pi$
$751$	20.7683	−	15.0891i	0.757847	−	0.550608i	0.898249	+	0.439486i	$0.144839\pi$
$752$	15.4474			0.563308
$753$	26.6594	−	82.0491i	0.971522	−	2.99004i
$754$	2.31824	+	1.68430i	0.0844253	+	0.0613386i
$755$	3.70096	+	11.3904i	0.134692	+	0.414539i
$756$	−7.26079	+	5.27527i	−0.264072	+	0.191860i
$757$	33.7244	+	24.5022i	1.22573	+	0.890547i	0.996563	−	0.0828397i	$-0.0263989\pi$
$757$	33.7244	+	24.5022i	1.22573	+	0.890547i	0.229170	+	0.973386i	$0.426399\pi$
$758$	−5.29182	−	3.84473i	−0.192208	−	0.139647i
$759$	−34.0242	−	24.7200i	−1.23500	−	0.897279i
$760$	−9.13437	−	6.63651i	−0.331338	−	0.240731i
$761$	−8.99846	+	6.53777i	−0.326194	+	0.236994i	−0.738814	−	0.673909i	$-0.764614\pi$
$761$	−8.99846	+	6.53777i	−0.326194	+	0.236994i	0.412620	+	0.910903i	$0.364614\pi$
$762$	−2.47160	−	7.60681i	−0.0895368	−	0.275566i
$763$	−0.577514	−	0.419588i	−0.0209074	−	0.0151901i
$764$	−10.5462	+	32.4579i	−0.381549	+	1.17429i
$765$	−144.831			−5.23637
$766$	0.267801	−	0.194569i	0.00967606	−	0.00703007i
$767$	−1.45660	+	4.48296i	−0.0525949	+	0.161870i
$768$	−8.72805	−	26.8622i	−0.314946	−	0.969305i
$769$	11.0514	+	34.0126i	0.398522	+	1.22652i	0.926185	+	0.377070i	$0.123069\pi$
$769$	11.0514	+	34.0126i	0.398522	+	1.22652i	−0.527663	+	0.849454i	$0.676931\pi$
$770$	4.88235			0.175948
$771$	−25.9965	−	80.0090i	−0.936242	−	2.88146i
$772$	20.2417	+	14.7064i	0.728513	+	0.529296i
$773$	−28.8582	+	20.9667i	−1.03796	+	0.754119i	−0.969886	−	0.243561i	$-0.921684\pi$
$773$	−28.8582	+	20.9667i	−1.03796	+	0.754119i	−0.0680707	+	0.997680i	$0.521684\pi$
$774$	1.91614	−	5.89728i	0.0688743	−	0.211973i
$775$	−0.235663	+	0.725296i	−0.00846526	+	0.0260534i
$776$	3.11648			0.111875
$777$	8.83129	−	6.41631i	0.316821	−	0.230184i
$778$	0.813474			0.0291645
$779$	−5.91007	+	15.9785i	−0.211750	+	0.572488i
$780$	47.4726			1.69979
$781$	39.4672	−	28.6746i	1.41225	−	1.02606i
$782$	7.39905			0.264589
$783$	−6.51898	+	20.0634i	−0.232969	+	0.717006i
$784$	1.09514	−	3.37048i	0.0391120	−	0.120374i
$785$	33.6643	−	24.4585i	1.20153	−	0.872962i
$786$	8.04344	+	5.84390i	0.286900	+	0.208445i
$787$	9.70947	+	29.8827i	0.346105	+	1.06520i	0.960990	+	0.276585i	$0.0892027\pi$
$787$	9.70947	+	29.8827i	0.346105	+	1.06520i	−0.614884	+	0.788617i	$0.710797\pi$
$788$	3.15826			0.112508
$789$	7.77905	+	23.9415i	0.276942	+	0.852338i
$790$	1.97546	+	6.07985i	0.0702838	+	0.216311i
$791$	4.80796	−	14.7974i	0.170951	−	0.526134i
$792$	−18.6175	+	13.5264i	−0.661544	+	0.480640i
$793$	−30.7089			−1.09051
$794$	−1.06223	+	3.26921i	−0.0376971	+	0.116020i
$795$	61.3491	+	44.5727i	2.17583	+	1.58083i
$796$	−1.68540	−	5.18713i	−0.0597375	−	0.183853i
$797$	−4.25670	+	3.09267i	−0.150780	+	0.109548i	−0.660618	−	0.750723i	$-0.729706\pi$
$797$	−4.25670	+	3.09267i	−0.150780	+	0.109548i	0.509838	+	0.860271i	$0.329706\pi$
$798$	1.65567	+	1.20291i	0.0586100	+	0.0425826i
$799$	−27.9723	−	20.3230i	−0.989587	−	0.718977i
$800$	−26.0720	−	18.9425i	−0.921786	−	0.669717i
$801$	−41.2149	−	29.9444i	−1.45626	−	1.05803i
$802$	−0.713086	+	0.518087i	−0.0251799	+	0.0182943i
$803$	11.5715	+	35.6133i	0.408349	+	1.25677i
$804$	−37.1522	−	26.9926i	−1.31026	−	0.951956i
$805$	−4.04936	+	12.4626i	−0.142721	+	0.439251i
$806$	0.0474140			0.00167009
$807$	−26.2968	+	19.1057i	−0.925691	+	0.672554i
$808$	0.954286	−	2.93699i	0.0335716	−	0.103323i
$809$	1.96604	+	6.05084i	0.0691222	+	0.212736i	0.979651	−	0.200710i	$-0.0643249\pi$
$809$	1.96604	+	6.05084i	0.0691222	+	0.212736i	−0.910528	+	0.413446i	$0.864325\pi$
$810$	0.372420	+	1.14619i	0.0130855	+	0.0402730i
$811$	−17.7986			−0.624994			−0.312497	−	0.949919i	$-0.601165\pi$
$811$	−17.7986			−0.624994			−0.312497	+	0.949919i	$0.601165\pi$
$812$	−2.68604	−	8.26678i	−0.0942615	−	0.290107i
$813$	−59.7924	−	43.4417i	−2.09701	−	1.52357i
$814$	3.99021	−	2.89906i	0.139857	−	0.101612i
$815$	13.1019	−	40.3235i	0.458940	−	1.41247i
$816$	−24.0798	+	74.1100i	−0.842962	+	2.59437i
$817$	12.6941			0.444109
$818$	−3.16417	+	2.29891i	−0.110633	+	0.0803793i
$819$	−10.7003			−0.373897
$820$	−16.6517	+	45.0194i	−0.581501	+	1.57215i
$821$	−10.8829			−0.379817			−0.189908	−	0.981802i	$-0.560819\pi$
$821$	−10.8829			−0.379817			−0.189908	+	0.981802i	$0.560819\pi$
$822$	10.9026	−	7.92124i	0.380273	−	0.276285i
$823$	11.3999			0.397374			0.198687	−	0.980063i	$-0.436332\pi$
$823$	11.3999			0.397374			0.198687	+	0.980063i	$0.436332\pi$
$824$	2.46071	−	7.57329i	0.0857229	−	0.263828i
$825$	39.4215	−	121.327i	1.37248	−	4.22406i
$826$	−0.463184	+	0.336523i	−0.0161162	+	0.0117091i
$827$	−14.7582	−	10.7224i	−0.513191	−	0.372855i	0.300841	−	0.953674i	$-0.402732\pi$
$827$	−14.7582	−	10.7224i	−0.513191	−	0.372855i	−0.814033	+	0.580819i	$0.802732\pi$
$828$	−9.35581	−	28.7942i	−0.325137	−	1.00067i
$829$	−47.6662			−1.65552			−0.827759	−	0.561085i	$-0.810384\pi$
$829$	−47.6662			−1.65552			−0.827759	+	0.561085i	$0.810384\pi$
$830$	2.06260	+	6.34803i	0.0715938	+	0.220343i
$831$	−10.0436	−	30.9109i	−0.348407	−	1.07229i
$832$	4.38470	−	13.4947i	0.152012	−	0.467845i
$833$	−6.41738	+	4.66250i	−0.222349	+	0.161546i
$834$	−9.98847			−0.345872
$835$	12.7356	−	39.1962i	0.440734	−	1.35644i
$836$	−18.6826	−	13.5737i	−0.646151	−	0.469456i
$837$	0.107866	+	0.331978i	0.00372840	+	0.0114748i
$838$	−3.09921	+	2.25171i	−0.107060	+	0.0777839i
$839$	17.5470	+	12.7486i	0.605789	+	0.440132i	0.847929	−	0.530110i	$-0.177849\pi$
$839$	17.5470	+	12.7486i	0.605789	+	0.440132i	−0.242140	+	0.970241i	$0.577849\pi$
$840$	9.51649	+	6.91414i	0.328350	+	0.238560i
$841$	6.93203	+	5.03641i	0.239036	+	0.173669i
$842$	−8.35795	−	6.07241i	−0.288034	−	0.209269i
$843$	14.7771	−	10.7362i	0.508951	−	0.369775i
$844$	0.154262	+	0.474768i	0.00530990	+	0.0163422i
$845$	−24.5385	−	17.8283i	−0.844150	−	0.613311i
$846$	1.75059	−	5.38775i	0.0601864	−	0.185235i
$847$	9.37168			0.322015
$848$	20.1204	−	14.6183i	0.690937	−	0.501995i
$849$	14.0914	−	43.3690i	0.483617	−	1.48842i
$850$	6.93552	+	21.3453i	0.237886	+	0.732139i
$851$	4.09068	+	12.5898i	0.140227	+	0.431574i
$852$	57.6142			1.97383
$853$	−8.38029	−	25.7919i	−0.286936	−	0.883097i	−0.985812	−	0.167854i	$-0.946316\pi$
$853$	−8.38029	−	25.7919i	−0.286936	−	0.883097i	0.698876	−	0.715243i	$-0.253684\pi$
$854$	−3.01758	−	2.19240i	−0.103260	−	0.0750225i
$855$	39.3011	−	28.5539i	1.34407	−	0.976523i
$856$	−1.93676	+	5.96075i	−0.0661972	+	0.203734i
$857$	−6.55173	+	20.1642i	−0.223803	+	0.688795i	0.774608	+	0.632442i	$0.217947\pi$
$857$	−6.55173	+	20.1642i	−0.223803	+	0.688795i	−0.998411	+	0.0563530i	$0.982053\pi$
$858$	−7.93137			−0.270773
$859$	4.87697	−	3.54333i	0.166400	−	0.120897i	−0.501469	−	0.865176i	$-0.667207\pi$
$859$	4.87697	−	3.54333i	0.166400	−	0.120897i	0.667869	+	0.744279i	$0.267207\pi$
$860$	35.7656			1.21960
$861$	6.15730	−	16.6469i	0.209840	−	0.567324i
$862$	9.14759			0.311568
$863$	−21.8874	+	15.9021i	−0.745056	+	0.541315i	−0.894291	−	0.447487i	$-0.852319\pi$
$863$	−21.8874	+	15.9021i	−0.745056	+	0.541315i	0.149234	+	0.988802i	$0.452319\pi$
$864$	−14.7507			−0.501828
$865$	22.7723	−	70.0858i	0.774280	−	2.38299i
$866$	−0.131363	+	0.404294i	−0.00446390	+	0.0137385i
$867$	102.982	−	74.8207i	3.49745	−	2.54104i
$868$	−0.116357	−	0.0845385i	−0.00394942	−	0.00286942i
$869$	8.24263	+	25.3682i	0.279612	+	0.860558i
$870$	13.5535			0.459507
$871$	−6.08206	−	18.7187i	−0.206083	−	0.634258i
$872$	−0.240131	−	0.739049i	−0.00813188	−	0.0250273i
$873$	−4.14355	+	12.7525i	−0.140238	+	0.431608i
$874$	−2.00780	+	1.45875i	−0.0679147	+	0.0493429i
$875$	−20.2575			−0.684829
$876$	−13.6659	+	42.0595i	−0.461730	+	1.42106i
$877$	−28.9344	−	21.0221i	−0.977045	−	0.709865i	−0.0199991	−	0.999800i	$-0.506366\pi$
$877$	−28.9344	−	21.0221i	−0.977045	−	0.709865i	−0.957046	+	0.289935i	$0.906366\pi$
$878$	0.862952	+	2.65589i	0.0291232	+	0.0896320i
$879$	22.2039	−	16.1321i	0.748920	−	0.544122i
$880$	−50.4462	−	36.6513i	−1.70054	−	1.23552i
$881$	−43.0022	−	31.2429i	−1.44878	−	1.05260i	−0.986114	−	0.166070i	$-0.946892\pi$
$881$	−43.0022	−	31.2429i	−1.44878	−	1.05260i	−0.462668	−	0.886532i	$-0.653108\pi$
$882$	−1.05145	−	0.763924i	−0.0354042	−	0.0257227i
$883$	−18.0950	−	13.1468i	−0.608946	−	0.442425i	0.240097	−	0.970749i	$-0.422821\pi$
$883$	−18.0950	−	13.1468i	−0.608946	−	0.442425i	−0.849043	+	0.528324i	$0.822821\pi$
$884$	−28.1932	+	20.4835i	−0.948239	+	0.688936i
$885$	6.88956	+	21.2039i	0.231590	+	0.712761i
$886$	−0.0214719	−	0.0156002i	−0.000721362	−	0.000524100i
$887$	14.9434	−	45.9912i	0.501751	−	1.54423i	−0.304413	−	0.952540i	$-0.598460\pi$
$887$	14.9434	−	45.9912i	0.501751	−	1.54423i	0.806164	−	0.591692i	$-0.201540\pi$
$888$	11.8831			0.398770
$889$	−8.41251	+	6.11205i	−0.282147	+	0.204991i
$890$	−3.63586	+	11.1900i	−0.121874	+	0.375091i
$891$	1.55393	+	4.78249i	0.0520585	+	0.160220i
$892$	1.66049	+	5.11046i	0.0555973	+	0.171111i
$893$	11.5973			0.388088
$894$	−4.01831	−	12.3671i	−0.134392	−	0.413617i
$895$	−54.5419	−	39.6270i	−1.82314	−	1.32459i
$896$	6.50819	−	4.72848i	0.217423	−	0.157967i
$897$	6.57817	−	20.2455i	0.219639	−	0.675979i
$898$	0.773194	−	2.37965i	0.0258018	−	0.0794099i
$899$	−0.338070			−0.0112753
$900$	74.2981	−	53.9807i	2.47660	−	1.79936i
$901$	−55.6665			−1.85452
$902$	2.78204	−	7.52151i	0.0926317	−	0.250439i
$903$	−13.2251			−0.440103
$904$	13.7024	−	9.95541i	0.455736	−	0.331112i
$905$	47.0511			1.56403
$906$	0.730249	−	2.24748i	0.0242609	−	0.0746674i
$907$	−15.2702	+	46.9969i	−0.507039	+	1.56051i	0.290277	+	0.956943i	$0.406253\pi$
$907$	−15.2702	+	46.9969i	−0.507039	+	1.56051i	−0.797316	+	0.603562i	$0.793747\pi$
$908$	39.2874	−	28.5439i	1.30380	−	0.947264i
$909$	10.7493	+	7.80981i	0.356531	+	0.259035i
$910$	0.763668	+	2.35033i	0.0253154	+	0.0779127i
$911$	13.0163			0.431251			0.215625	−	0.976476i	$-0.430821\pi$
$911$	13.0163			0.431251			0.215625	+	0.976476i	$0.430821\pi$
$912$	−8.07680	−	24.8578i	−0.267450	−	0.823125i
$913$	8.60621	+	26.4872i	0.284824	+	0.876598i
$914$	1.75952	−	5.41524i	0.0581997	−	0.179120i
$915$	−117.509	+	85.3756i	−3.88474	+	2.82243i
$916$	−7.20406			−0.238029
$917$	3.99428	−	12.2931i	0.131903	−	0.405954i
$918$	8.31090	+	6.03823i	0.274301	+	0.199291i
$919$	−7.18955	−	22.1272i	−0.237161	−	0.729907i	−0.996827	−	0.0795941i	$-0.974638\pi$
$919$	−7.18955	−	22.1272i	−0.237161	−	0.729907i	0.759666	−	0.650313i	$-0.225362\pi$
$920$	−11.5405	+	8.38465i	−0.380478	+	0.276434i
$921$	−57.7705	−	41.9728i	−1.90360	−	1.38305i
$922$	9.55263	+	6.94039i	0.314599	+	0.228570i
$923$	19.9770	+	14.5141i	0.657550	+	0.477738i
$924$	19.4641	+	14.1415i	0.640323	+	0.465222i
$925$	−32.4857	+	23.6022i	−1.06812	+	0.776036i
$926$	−2.97437	−	9.15417i	−0.0977439	−	0.300825i
$927$	27.7180	+	20.1383i	0.910378	+	0.661428i
$928$	4.41467	−	13.5869i	0.144918	−	0.446013i
$929$	44.7190			1.46718			0.733592	−	0.679590i	$-0.237842\pi$
$929$	44.7190			1.46718			0.733592	+	0.679590i	$0.237842\pi$
$930$	0.181432	−	0.131818i	0.00594940	−	0.00432249i
$931$	0.822184	−	2.53042i	0.0269460	−	0.0829312i
$932$	−8.90860	−	27.4179i	−0.291811	−	0.898102i
$933$	3.98481	+	12.2640i	0.130457	+	0.401505i
$934$	−7.99506			−0.261606
$935$	43.1289	+	132.737i	1.41047	+	4.34097i
$936$	−9.42354	−	6.84660i	−0.308018	−	0.223788i
$937$	36.2713	−	26.3526i	1.18493	−	0.860903i	0.192212	−	0.981354i	$-0.438434\pi$
$937$	36.2713	−	26.3526i	1.18493	−	0.860903i	0.992719	+	0.120451i	$0.0384340\pi$
$938$	0.738734	−	2.27359i	0.0241205	−	0.0742353i
$939$	0.219146	−	0.674462i	0.00715156	−	0.0220102i
$940$	32.6754			1.06575
$941$	−23.0265	+	16.7297i	−0.750643	+	0.545374i	−0.896026	−	0.444002i	$-0.853558\pi$
$941$	−23.0265	+	16.7297i	−0.750643	+	0.545374i	0.145383	+	0.989375i	$0.453558\pi$
$942$	−8.21047			−0.267511
$943$	16.8920	+	13.3396i	0.550078	+	0.434398i
$944$	7.31202			0.237986
$945$	−14.7189	+	10.6939i	−0.478807	+	0.347874i
$946$	−5.97545			−0.194279
$947$	1.89879	−	5.84386i	0.0617022	−	0.189900i	−0.915454	−	0.402423i	$-0.868168\pi$
$947$	1.89879	−	5.84386i	0.0617022	−	0.189900i	0.977156	+	0.212523i	$0.0681681\pi$
$948$	−9.73457	+	29.9599i	−0.316164	+	0.973054i
$949$	−15.3341	+	11.1408i	−0.497765	+	0.361647i
$950$	−6.09033	−	4.42488i	−0.197596	−	0.143562i
$951$	0.159567	+	0.491097i	0.00517432	+	0.0159249i
$952$	−8.63500			−0.279862
$953$	3.83568	+	11.8050i	0.124250	+	0.382402i	0.993764	−	0.111507i	$-0.0355677\pi$
$953$	3.83568	+	11.8050i	0.124250	+	0.382402i	−0.869514	+	0.493909i	$0.835568\pi$
$954$	−2.81843	−	8.67424i	−0.0912501	−	0.280839i
$955$	−21.3791	+	65.7981i	−0.691812	+	2.12918i
$956$	22.0291	−	16.0051i	0.712471	−	0.517641i
$957$	56.5521			1.82807
$958$	0.654769	−	2.01517i	0.0211546	−	0.0651073i
$959$	−14.1744	−	10.2983i	−0.457714	−	0.332549i
$960$	−20.7391	−	63.8285i	−0.669352	−	2.06005i
$961$	25.0750	−	18.2181i	0.808871	−	0.587679i
$962$	2.01971	+	1.46741i	0.0651181	+	0.0473111i
$963$	−21.8161	−	15.8504i	−0.703016	−	0.510771i
$964$	−8.58918	−	6.24040i	−0.276639	−	0.200990i
$965$	41.0335	+	29.8126i	1.32092	+	0.959702i
$966$	2.09179	−	1.51977i	0.0673022	−	0.0488979i
$967$	−0.265656	−	0.817604i	−0.00854291	−	0.0262924i	0.946694	−	0.322134i	$-0.104400\pi$
$967$	−0.265656	−	0.817604i	−0.00854291	−	0.0262924i	−0.955237	+	0.295841i	$0.904400\pi$
$968$	8.25348	+	5.99650i	0.265277	+	0.192735i
$969$	−18.0782	+	55.6389i	−0.580754	+	1.78738i
$970$	3.09684			0.0994335
$971$	15.1143	−	10.9812i	0.485041	−	0.352403i	−0.318233	−	0.948013i	$-0.603089\pi$
$971$	15.1143	−	10.9812i	0.485041	−	0.352403i	0.803274	+	0.595609i	$0.203089\pi$
$972$	−10.1553	+	31.2548i	−0.325732	+	1.00250i
$973$	4.01285	+	12.3503i	0.128646	+	0.395932i
$974$	−0.791999	−	2.43752i	−0.0253773	−	0.0781033i
$975$	64.5720			2.06796
$976$	14.7206	+	45.3054i	0.471195	+	1.45019i
$977$	34.1051	+	24.7788i	1.09112	+	0.792745i	0.979588	−	0.201016i	$-0.0644243\pi$
$977$	34.1051	+	24.7788i	1.09112	+	0.792745i	0.111532	+	0.993761i	$0.464424\pi$
$978$	−6.76809	+	4.91731i	−0.216420	+	0.157238i
$979$	−15.1707	+	46.6905i	−0.484857	+	1.49224i
$980$	2.31651	−	7.12948i	0.0739982	−	0.227743i
$981$	3.34343			0.106748
$982$	4.71619	−	3.42652i	0.150500	−	0.109345i
$983$	12.2646			0.391181			0.195590	−	0.980686i	$-0.437338\pi$
$983$	12.2646			0.391181			0.195590	+	0.980686i	$0.437338\pi$
$984$	16.0742	−	10.7209i	0.512427	−	0.341768i
$985$	6.40237			0.203996
$986$	−8.04919	+	5.84808i	−0.256338	+	0.186241i
$987$	−12.0824			−0.384588
$988$	3.61206	−	11.1168i	0.114915	−	0.353672i
$989$	4.95596	−	15.2529i	0.157590	−	0.485013i
$990$	−18.5001	+	13.4411i	−0.587973	+	0.427187i
$991$	23.2652	+	16.9032i	0.739045	+	0.536948i	0.892412	−	0.451222i	$-0.149012\pi$
$991$	23.2652	+	16.9032i	0.739045	+	0.536948i	−0.153367	+	0.988169i	$0.549012\pi$
$992$	−0.0730472	−	0.224816i	−0.00231925	−	0.00713792i
$993$	−46.9414			−1.48964
$994$	0.926811	+	2.85243i	0.0293967	+	0.0904736i
$995$	−3.41662	−	10.5153i	−0.108314	−	0.333356i
$996$	−10.1640	+	31.2815i	−0.322057	+	0.991191i
$997$	3.35412	−	2.43691i	0.106226	−	0.0771777i	−0.533404	−	0.845860i	$-0.679088\pi$
$997$	3.35412	−	2.43691i	0.106226	−	0.0771777i	0.639630	+	0.768683i	$0.279088\pi$
$998$	8.42114			0.266566
$999$	−5.67951	+	17.4797i	−0.179692	+	0.553034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.c.78.5	✓	40
41.10	even	5	inner	287.2.h.c.92.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.c.78.5	✓	40	1.1	even	1	trivial
287.2.h.c.92.5	yes	40	41.10	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)

\(f(q)\)	\(=\)	\(q+(-0.224492 + 0.163103i) q^{2} -2.77195 q^{3} +(-0.594240 + 1.82888i) q^{4} +(-1.20463 + 3.70748i) q^{5} +(0.622280 - 0.452113i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.336391 - 1.03531i) q^{8} +4.68369 q^{9} +O(q^{10})\)	\(q+(-0.224492 + 0.163103i) q^{2} -2.77195 q^{3} +(-0.594240 + 1.82888i) q^{4} +(-1.20463 + 3.70748i) q^{5} +(0.622280 - 0.452113i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.336391 - 1.03531i) q^{8} +4.68369 q^{9} +(-0.334271 - 1.02878i) q^{10} +(-1.39475 - 4.29259i) q^{11} +(1.64720 - 5.06956i) q^{12} +(1.84826 - 1.34284i) q^{13} +0.277488 q^{14} +(3.33918 - 10.2769i) q^{15} +(-2.86710 - 2.08307i) q^{16} +(2.45122 + 7.54409i) q^{17} +(-1.05145 + 0.763924i) q^{18} +(-2.15251 - 1.56389i) q^{19} +(-6.06470 - 4.40626i) q^{20} +(2.24255 + 1.62931i) q^{21} +(1.01325 + 0.736166i) q^{22} +(-2.71950 + 1.97583i) q^{23} +(0.932458 + 2.86981i) q^{24} +(-8.24917 - 5.99337i) q^{25} +(-0.195899 + 0.602915i) q^{26} -4.66710 q^{27} +(1.55574 - 1.13031i) q^{28} +(1.39680 - 4.29890i) q^{29} +(0.926581 + 2.85172i) q^{30} +(-0.0231121 - 0.0711316i) q^{31} +3.16057 q^{32} +(3.86617 + 11.8988i) q^{33} +(-1.78074 - 1.29379i) q^{34} +(3.15377 - 2.29135i) q^{35} +(-2.78323 + 8.56591i) q^{36} +(1.21693 - 3.74531i) q^{37} +0.738296 q^{38} +(-5.12329 + 3.72229i) q^{39} +4.24360 q^{40} +(-1.73287 - 6.16418i) q^{41} -0.769181 q^{42} +(-3.85986 + 2.80435i) q^{43} +8.67946 q^{44} +(-5.64212 + 17.3647i) q^{45} +(0.288242 - 0.887119i) q^{46} +(-3.52636 + 2.56205i) q^{47} +(7.94745 + 5.77416i) q^{48} +(0.309017 + 0.951057i) q^{49} +2.82941 q^{50} +(-6.79466 - 20.9118i) q^{51} +(1.35759 + 4.17823i) q^{52} +(-2.16858 + 6.67421i) q^{53} +(1.04773 - 0.761218i) q^{54} +17.5949 q^{55} +(-0.336391 + 1.03531i) q^{56} +(5.96663 + 4.33501i) q^{57} +(0.387594 + 1.19289i) q^{58} +(-1.66921 + 1.21275i) q^{59} +(16.8110 + 12.2139i) q^{60} +(-10.8747 - 7.90090i) q^{61} +(0.0167903 + 0.0121988i) q^{62} +(-3.78918 - 2.75300i) q^{63} +(5.02468 - 3.65064i) q^{64} +(2.75208 + 8.47003i) q^{65} +(-2.80866 - 2.04061i) q^{66} +(2.66222 - 8.19348i) q^{67} -15.2539 q^{68} +(7.53831 - 5.47691i) q^{69} +(-0.334271 + 1.02878i) q^{70} +(3.34001 + 10.2795i) q^{71} +(-1.57555 - 4.84905i) q^{72} -8.29646 q^{73} +(0.337682 + 1.03928i) q^{74} +(22.8663 + 16.6133i) q^{75} +(4.13927 - 3.00736i) q^{76} +(-1.39475 + 4.29259i) q^{77} +(0.543022 - 1.67125i) q^{78} -5.90977 q^{79} +(11.1767 - 8.12038i) q^{80} -1.11413 q^{81} +(1.39441 + 1.10117i) q^{82} -6.17044 q^{83} +(-4.31243 + 3.13316i) q^{84} -30.9224 q^{85} +(0.409110 - 1.25911i) q^{86} +(-3.87184 + 11.9163i) q^{87} +(-3.97496 + 2.88798i) q^{88} +(-8.79968 - 6.39334i) q^{89} +(-1.56562 - 4.81848i) q^{90} -2.28458 q^{91} +(-1.99753 - 6.14777i) q^{92} +(0.0640654 + 0.197173i) q^{93} +(0.373762 - 1.15032i) q^{94} +(8.39106 - 6.09646i) q^{95} -8.76092 q^{96} +(-0.884678 + 2.72276i) q^{97} +(-0.224492 - 0.163103i) q^{98} +(-6.53257 - 20.1052i) 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

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