LMFDB - Embedded newform 946.2.f.g.861.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.55384803121$
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			861.6
Character	$\chi$	$=$	946.861
Dual form			946.2.f.g.345.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.536142 + 1.65007i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.42492 + 2.48835i) q^{5} +(-1.40364 - 1.01980i) q^{6} +(1.27999 - 3.93940i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.00824529 + 0.00599055i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.536142 + 1.65007i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.42492 + 2.48835i) q^{5} +(-1.40364 - 1.01980i) q^{6} +(1.27999 - 3.93940i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.00824529 + 0.00599055i) q^{9} -4.23344 q^{10} +(3.11523 + 1.13813i) q^{11} +1.73499 q^{12} +(-4.74642 + 3.44848i) q^{13} +(1.27999 + 3.93940i) q^{14} +(-2.26972 + 6.98549i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.60660 + 1.16726i) q^{17} +(0.00314942 - 0.00969292i) q^{18} +(-2.23601 - 6.88173i) q^{19} +(3.42492 - 2.48835i) q^{20} +7.18656 q^{21} +(-3.18925 + 0.910319i) q^{22} +0.946406 q^{23} +(-1.40364 + 1.01980i) q^{24} +(3.99312 + 12.2896i) q^{25} +(1.81297 - 5.57975i) q^{26} +(4.19660 + 3.04901i) q^{27} +(-3.35105 - 2.43468i) q^{28} +(-0.300873 + 0.925991i) q^{29} +(-2.26972 - 6.98549i) q^{30} +(1.54236 - 1.12059i) q^{31} +1.00000 q^{32} +(-0.207796 + 5.75056i) q^{33} -1.98586 q^{34} +(14.1865 - 10.3071i) q^{35} +(0.00314942 + 0.00969292i) q^{36} +(2.94819 - 9.07360i) q^{37} +(5.85395 + 4.25314i) q^{38} +(-8.23500 - 5.98308i) q^{39} +(-1.30820 + 4.02624i) q^{40} +(1.29057 + 3.97196i) q^{41} +(-5.81405 + 4.22415i) q^{42} -1.00000 q^{43} +(2.04509 - 2.61106i) q^{44} -0.0431461 q^{45} +(-0.765658 + 0.556283i) q^{46} +(2.56686 + 7.89999i) q^{47} +(0.536142 - 1.65007i) q^{48} +(-8.21738 - 5.97028i) q^{49} +(-10.4541 - 7.59536i) q^{50} +(-1.06470 + 3.27682i) q^{51} +(1.81297 + 5.57975i) q^{52} +(-3.17759 + 2.30865i) q^{53} -5.18729 q^{54} +(7.83735 + 11.6498i) q^{55} +4.14213 q^{56} +(10.1565 - 7.37916i) q^{57} +(-0.300873 - 0.925991i) q^{58} +(0.824876 - 2.53871i) q^{59} +(5.94221 + 4.31727i) q^{60} +(-7.76993 - 5.64518i) q^{61} +(-0.589128 + 1.81315i) q^{62} +(0.0130453 + 0.0401493i) q^{63} +(-0.809017 + 0.587785i) q^{64} -24.8372 q^{65} +(-3.21198 - 4.77444i) q^{66} -6.81637 q^{67} +(1.60660 - 1.16726i) q^{68} +(0.507407 + 1.56164i) q^{69} +(-5.41875 + 16.6772i) q^{70} +(-3.62716 - 2.63528i) q^{71} +(-0.00824529 - 0.00599055i) q^{72} +(-0.400075 + 1.23130i) q^{73} +(2.94819 + 9.07360i) q^{74} +(-18.1378 + 13.1779i) q^{75} -7.23588 q^{76} +(8.47101 - 10.8153i) q^{77} +10.1790 q^{78} +(-10.0848 + 7.32705i) q^{79} +(-1.30820 - 4.02624i) q^{80} +(-2.79057 + 8.58849i) q^{81} +(-3.37875 - 2.45481i) q^{82} +(5.37116 + 3.90238i) q^{83} +(2.22077 - 6.83482i) q^{84} +(2.59791 + 7.99556i) q^{85} +(0.809017 - 0.587785i) q^{86} -1.68926 q^{87} +(-0.119768 + 3.31446i) q^{88} -10.7529 q^{89} +(0.0349059 - 0.0253606i) q^{90} +(7.50957 + 23.1121i) q^{91} +(0.292455 - 0.900085i) q^{92} +(2.67597 + 1.94421i) q^{93} +(-6.72013 - 4.88246i) q^{94} +(9.46600 - 29.1334i) q^{95} +(0.536142 + 1.65007i) q^{96} +(-8.15781 + 5.92699i) q^{97} +10.1572 q^{98} +(-0.0325040 + 0.00927773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9}+O(q^{10}) $ 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 5 q^{14} - 23 q^{15} - 10 q^{16} - 5 q^{17} + 9 q^{18} - 21 q^{19} + 8 q^{20} + 20 q^{21} + 6 q^{22} + 24 q^{23} - 5 q^{24} - 16 q^{25} - 18 q^{26} - 10 q^{27} - 20 q^{28} + 7 q^{29} - 23 q^{30} - 15 q^{31} + 40 q^{32} + 36 q^{33} + 10 q^{34} + 50 q^{35} + 9 q^{36} + 2 q^{37} - 21 q^{38} - 70 q^{39} - 7 q^{40} - 20 q^{41} - 10 q^{42} - 40 q^{43} + 6 q^{44} - 14 q^{45} - q^{46} - 8 q^{47} + 5 q^{48} + 5 q^{49} - 11 q^{50} + 13 q^{51} - 18 q^{52} + 24 q^{53} + 38 q^{55} + 30 q^{56} + 62 q^{57} + 7 q^{58} - 27 q^{59} + 2 q^{60} - 49 q^{61} + 20 q^{62} - 5 q^{63} - 10 q^{64} - 4 q^{65} - 34 q^{66} - 26 q^{67} - 5 q^{68} + 73 q^{69} - 65 q^{70} - 5 q^{71} - 31 q^{72} + 22 q^{73} + 2 q^{74} - 60 q^{75} + 84 q^{76} - 20 q^{77} + 30 q^{78} + 81 q^{79} - 7 q^{80} - 38 q^{81} - 25 q^{82} + 3 q^{83} - 38 q^{85} + 10 q^{86} + 28 q^{87} - 14 q^{88} - 56 q^{89} - 4 q^{90} + 10 q^{91} - 11 q^{92} - 16 q^{93} - 23 q^{94} + 66 q^{95} + 5 q^{96} - 20 q^{97} + 50 q^{98} + 94 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 5 * q^14 - 23 * q^15 - 10 * q^16 - 5 * q^17 + 9 * q^18 - 21 * q^19 + 8 * q^20 + 20 * q^21 + 6 * q^22 + 24 * q^23 - 5 * q^24 - 16 * q^25 - 18 * q^26 - 10 * q^27 - 20 * q^28 + 7 * q^29 - 23 * q^30 - 15 * q^31 + 40 * q^32 + 36 * q^33 + 10 * q^34 + 50 * q^35 + 9 * q^36 + 2 * q^37 - 21 * q^38 - 70 * q^39 - 7 * q^40 - 20 * q^41 - 10 * q^42 - 40 * q^43 + 6 * q^44 - 14 * q^45 - q^46 - 8 * q^47 + 5 * q^48 + 5 * q^49 - 11 * q^50 + 13 * q^51 - 18 * q^52 + 24 * q^53 + 38 * q^55 + 30 * q^56 + 62 * q^57 + 7 * q^58 - 27 * q^59 + 2 * q^60 - 49 * q^61 + 20 * q^62 - 5 * q^63 - 10 * q^64 - 4 * q^65 - 34 * q^66 - 26 * q^67 - 5 * q^68 + 73 * q^69 - 65 * q^70 - 5 * q^71 - 31 * q^72 + 22 * q^73 + 2 * q^74 - 60 * q^75 + 84 * q^76 - 20 * q^77 + 30 * q^78 + 81 * q^79 - 7 * q^80 - 38 * q^81 - 25 * q^82 + 3 * q^83 - 38 * q^85 + 10 * q^86 + 28 * q^87 - 14 * q^88 - 56 * q^89 - 4 * q^90 + 10 * q^91 - 11 * q^92 - 16 * q^93 - 23 * q^94 + 66 * q^95 + 5 * q^96 - 20 * q^97 + 50 * q^98 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.536142	+	1.65007i	0.309541	+	0.952671i	0.977943	+	0.208870i	$0.0669787\pi$
$3$	0.536142	+	1.65007i	0.309541	+	0.952671i	−0.668402	+	0.743800i	$0.733021\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	3.42492	+	2.48835i	1.53167	+	1.11283i	0.955300	+	0.295638i	$0.0955321\pi$
$5$	3.42492	+	2.48835i	1.53167	+	1.11283i	0.576372	+	0.817187i	$0.304468\pi$
$6$	−1.40364	−	1.01980i	−0.573032	−	0.416332i
$7$	1.27999	−	3.93940i	0.483790	−	1.48895i	−0.349935	−	0.936774i	$-0.613796\pi$
$7$	1.27999	−	3.93940i	0.483790	−	1.48895i	0.833725	−	0.552179i	$-0.186204\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.00824529	+	0.00599055i	−0.00274843	+	0.00199685i
$10$	−4.23344			−1.33873
$11$	3.11523	+	1.13813i	0.939277	+	0.343159i
$11$	3.11523	+	1.13813i	0.939277	+	0.343159i
$12$	1.73499			0.500849
$13$	−4.74642	+	3.44848i	−1.31642	+	0.956436i	−0.316451	+	0.948609i	$0.602491\pi$
$13$	−4.74642	+	3.44848i	−1.31642	+	0.956436i	−0.999969	+	0.00782696i	$0.997509\pi$
$14$	1.27999	+	3.93940i	0.342091	+	1.05285i
$15$	−2.26972	+	6.98549i	−0.586040	+	1.80364i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.60660	+	1.16726i	0.389657	+	0.283102i	0.765315	−	0.643656i	$-0.222583\pi$
$17$	1.60660	+	1.16726i	0.389657	+	0.283102i	−0.375658	+	0.926758i	$0.622583\pi$
$18$	0.00314942	−	0.00969292i	0.000742326	−	0.00228464i
$19$	−2.23601	−	6.88173i	−0.512976	−	1.57878i	−0.786936	−	0.617035i	$-0.788334\pi$
$19$	−2.23601	−	6.88173i	−0.512976	−	1.57878i	0.273960	−	0.961741i	$-0.411666\pi$
$20$	3.42492	−	2.48835i	0.765836	−	0.556413i
$21$	7.18656			1.56824
$22$	−3.18925	+	0.910319i	−0.679951	+	0.194081i
$23$	0.946406			0.197339			0.0986696	−	0.995120i	$-0.468541\pi$
$23$	0.946406			0.197339			0.0986696	+	0.995120i	$0.468541\pi$
$24$	−1.40364	+	1.01980i	−0.286516	+	0.208166i
$25$	3.99312	+	12.2896i	0.798623	+	2.45791i
$26$	1.81297	−	5.57975i	0.355553	−	1.09428i
$27$	4.19660	+	3.04901i	0.807637	+	0.586783i
$28$	−3.35105	−	2.43468i	−0.633290	−	0.460112i
$29$	−0.300873	+	0.925991i	−0.0558707	+	0.171952i	−0.975098	−	0.221776i	$-0.928815\pi$
$29$	−0.300873	+	0.925991i	−0.0558707	+	0.171952i	0.919227	+	0.393728i	$0.128815\pi$
$30$	−2.26972	−	6.98549i	−0.414393	−	1.27537i
$31$	1.54236	−	1.12059i	0.277015	−	0.201263i	−0.440599	−	0.897704i	$-0.645234\pi$
$31$	1.54236	−	1.12059i	0.277015	−	0.201263i	0.717615	+	0.696441i	$0.245234\pi$
$32$	1.00000			0.176777
$33$	−0.207796	+	5.75056i	−0.0361726	+	1.00104i
$34$	−1.98586			−0.340573
$35$	14.1865	−	10.3071i	2.39795	−	1.74221i
$36$	0.00314942	+	0.00969292i	0.000524903	+	0.00161549i
$37$	2.94819	−	9.07360i	0.484680	−	1.49169i	−0.347765	−	0.937582i	$-0.613059\pi$
$37$	2.94819	−	9.07360i	0.484680	−	1.49169i	0.832444	−	0.554109i	$-0.186941\pi$
$38$	5.85395	+	4.25314i	0.949635	+	0.689951i
$39$	−8.23500	−	5.98308i	−1.31865	−	0.958059i
$40$	−1.30820	+	4.02624i	−0.206845	+	0.636604i
$41$	1.29057	+	3.97196i	0.201553	+	0.620316i	0.999837	+	0.0180353i	$0.00574113\pi$
$41$	1.29057	+	3.97196i	0.201553	+	0.620316i	−0.798285	+	0.602281i	$0.794259\pi$
$42$	−5.81405	+	4.22415i	−0.897127	+	0.651801i
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$	2.04509	−	2.61106i	0.308308	−	0.393632i
$45$	−0.0431461			−0.00643184
$46$	−0.765658	+	0.556283i	−0.112890	+	0.0820195i
$47$	2.56686	+	7.89999i	0.374415	+	1.15233i	0.943872	+	0.330311i	$0.107154\pi$
$47$	2.56686	+	7.89999i	0.374415	+	1.15233i	−0.569457	+	0.822021i	$0.692846\pi$
$48$	0.536142	−	1.65007i	0.0773854	−	0.238168i
$49$	−8.21738	−	5.97028i	−1.17391	−	0.852897i
$50$	−10.4541	−	7.59536i	−1.47844	−	1.07415i
$51$	−1.06470	+	3.27682i	−0.149088	+	0.458847i
$52$	1.81297	+	5.57975i	0.251414	+	0.773773i
$53$	−3.17759	+	2.30865i	−0.436475	+	0.317118i	−0.784233	−	0.620467i	$-0.786943\pi$
$53$	−3.17759	+	2.30865i	−0.436475	+	0.317118i	0.347757	+	0.937585i	$0.386943\pi$
$54$	−5.18729			−0.705901
$55$	7.83735	+	11.6498i	1.05679	+	1.57086i
$56$	4.14213			0.553515
$57$	10.1565	−	7.37916i	1.34527	−	0.977393i
$58$	−0.300873	−	0.925991i	−0.0395065	−	0.121589i
$59$	0.824876	−	2.53871i	0.107390	−	0.330511i	−0.882894	−	0.469572i	$-0.844408\pi$
$59$	0.824876	−	2.53871i	0.107390	−	0.330511i	0.990284	+	0.139061i	$0.0444083\pi$
$60$	5.94221	+	4.31727i	0.767136	+	0.557357i
$61$	−7.76993	−	5.64518i	−0.994837	−	0.722791i	−0.0338620	−	0.999427i	$-0.510781\pi$
$61$	−7.76993	−	5.64518i	−0.994837	−	0.722791i	−0.960975	+	0.276635i	$0.910781\pi$
$62$	−0.589128	+	1.81315i	−0.0748193	+	0.230270i
$63$	0.0130453	+	0.0401493i	0.00164355	+	0.00505834i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−24.8372			−3.08067
$66$	−3.21198	−	4.77444i	−0.395368	−	0.587693i
$67$	−6.81637			−0.832752			−0.416376	−	0.909192i	$-0.636700\pi$
$67$	−6.81637			−0.832752			−0.416376	+	0.909192i	$0.636700\pi$
$68$	1.60660	−	1.16726i	0.194828	−	0.141551i
$69$	0.507407	+	1.56164i	0.0610847	+	0.187999i
$70$	−5.41875	+	16.6772i	−0.647665	+	1.99331i
$71$	−3.62716	−	2.63528i	−0.430464	−	0.312751i	0.351370	−	0.936237i	$-0.385716\pi$
$71$	−3.62716	−	2.63528i	−0.430464	−	0.312751i	−0.781834	+	0.623486i	$0.785716\pi$
$72$	−0.00824529	−	0.00599055i	−0.000971717	−	0.000705994i
$73$	−0.400075	+	1.23130i	−0.0468252	+	0.144113i	−0.971736	−	0.236072i	$-0.924140\pi$
$73$	−0.400075	+	1.23130i	−0.0468252	+	0.144113i	0.924910	+	0.380185i	$0.124140\pi$
$74$	2.94819	+	9.07360i	0.342720	+	1.05478i
$75$	−18.1378	+	13.1779i	−2.09437	+	1.52165i
$76$	−7.23588			−0.830012
$77$	8.47101	−	10.8153i	0.965361	−	1.23252i
$78$	10.1790			1.15255
$79$	−10.0848	+	7.32705i	−1.13463	+	0.824357i	−0.986362	−	0.164590i	$-0.947370\pi$
$79$	−10.0848	+	7.32705i	−1.13463	+	0.824357i	−0.148268	+	0.988947i	$0.547370\pi$
$80$	−1.30820	−	4.02624i	−0.146262	−	0.450147i
$81$	−2.79057	+	8.58849i	−0.310063	+	0.954277i
$82$	−3.37875	−	2.45481i	−0.373121	−	0.271088i
$83$	5.37116	+	3.90238i	0.589562	+	0.428342i	0.842159	−	0.539230i	$-0.181285\pi$
$83$	5.37116	+	3.90238i	0.589562	+	0.428342i	−0.252597	+	0.967572i	$0.581285\pi$
$84$	2.22077	−	6.83482i	0.242306	−	0.745740i
$85$	2.59791	+	7.99556i	0.281783	+	0.867240i
$86$	0.809017	−	0.587785i	0.0872385	−	0.0633825i
$87$	−1.68926			−0.181108
$88$	−0.119768	+	3.31446i	−0.0127673	+	0.353323i
$89$	−10.7529			−1.13980			−0.569902	−	0.821713i	$-0.693019\pi$
$89$	−10.7529			−1.13980			−0.569902	+	0.821713i	$0.693019\pi$
$90$	0.0349059	−	0.0253606i	0.00367941	−	0.00267325i
$91$	7.50957	+	23.1121i	0.787216	+	2.42280i
$92$	0.292455	−	0.900085i	0.0304906	−	0.0938404i
$93$	2.67597	+	1.94421i	0.277485	+	0.201605i
$94$	−6.72013	−	4.88246i	−0.693129	−	0.503588i
$95$	9.46600	−	29.1334i	0.971191	−	2.98902i
$96$	0.536142	+	1.65007i	0.0547197	+	0.168410i
$97$	−8.15781	+	5.92699i	−0.828300	+	0.601795i	−0.919078	−	0.394076i	$-0.871065\pi$
$97$	−8.15781	+	5.92699i	−0.828300	+	0.601795i	0.0907779	+	0.995871i	$0.471065\pi$
$98$	10.1572			1.02604
$99$	−0.0325040	+	0.00927773i	−0.00326678	+	0.000932447i
$100$	12.9220			1.29220
$101$	8.18062	−	5.94357i	0.814002	−	0.591407i	−0.100986	−	0.994888i	$-0.532200\pi$
$101$	8.18062	−	5.94357i	0.814002	−	0.591407i	0.914988	+	0.403481i	$0.132200\pi$
$102$	−1.06470	−	3.27682i	−0.105421	−	0.324454i
$103$	4.94269	−	15.2120i	0.487017	−	1.49889i	−0.342020	−	0.939693i	$-0.611111\pi$
$103$	4.94269	−	15.2120i	0.487017	−	1.49889i	0.829038	−	0.559193i	$-0.188889\pi$
$104$	−4.74642	−	3.44848i	−0.465425	−	0.338151i
$105$	24.6134	+	17.8827i	2.40202	+	1.74517i
$106$	1.21373	−	3.73548i	0.117888	−	0.362822i
$107$	−1.22009	−	3.75504i	−0.117950	−	0.363014i	0.874601	−	0.484844i	$-0.161124\pi$
$107$	−1.22009	−	3.75504i	−0.117950	−	0.363014i	−0.992551	+	0.121830i	$0.961124\pi$
$108$	4.19660	−	3.04901i	0.403818	−	0.293391i
$109$	3.65734			0.350310			0.175155	−	0.984541i	$-0.443957\pi$
$109$	3.65734			0.350310			0.175155	+	0.984541i	$0.443957\pi$
$110$	−13.1881	−	4.81821i	−1.25744	−	0.459398i
$111$	16.5528			1.57112
$112$	−3.35105	+	2.43468i	−0.316645	+	0.230056i
$113$	0.230057	+	0.708043i	0.0216419	+	0.0666071i	0.961294	−	0.275524i	$-0.0888513\pi$
$113$	0.230057	+	0.708043i	0.0216419	+	0.0666071i	−0.939652	+	0.342131i	$0.888851\pi$
$114$	−3.87945	+	11.9397i	−0.363344	+	1.11826i
$115$	3.24137	+	2.35499i	0.302259	+	0.219604i
$116$	0.787695	+	0.572294i	0.0731357	+	0.0531362i
$117$	0.0184773	−	0.0568674i	0.00170823	−	0.00525739i
$118$	0.824876	+	2.53871i	0.0759360	+	0.233707i
$119$	6.65473	−	4.83495i	0.610038	−	0.443219i
$120$	−7.34497			−0.670501
$121$	8.40932	+	7.09108i	0.764483	+	0.644644i
$122$	9.60416			0.869519
$123$	−5.86210	+	4.25906i	−0.528568	+	0.384027i
$124$	−0.589128	−	1.81315i	−0.0529052	−	0.162826i
$125$	−10.3636	+	31.8959i	−0.926948	+	2.85285i
$126$	−0.0341531	−	0.0248137i	−0.00304260	−	0.00221058i
$127$	6.15188	+	4.46960i	0.545891	+	0.396613i	0.826268	−	0.563277i	$-0.190460\pi$
$127$	6.15188	+	4.46960i	0.545891	+	0.396613i	−0.280377	+	0.959890i	$0.590460\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.536142	−	1.65007i	−0.0472046	−	0.145281i
$130$	20.0937	−	14.5989i	1.76233	−	1.28041i
$131$	−16.2513			−1.41988			−0.709942	−	0.704260i	$-0.751279\pi$
$131$	−16.2513			−1.41988			−0.709942	+	0.704260i	$0.751279\pi$
$132$	5.40489	+	1.97465i	0.470436	+	0.171871i
$133$	−29.9719			−2.59890
$134$	5.51456	−	4.00656i	0.476385	−	0.346114i
$135$	6.78603	+	20.8853i	0.584049	+	1.79752i
$136$	−0.613665	+	1.88867i	−0.0526214	+	0.161952i
$137$	−1.34299	−	0.975738i	−0.114739	−	0.0833629i	0.528936	−	0.848662i	$-0.322591\pi$
$137$	−1.34299	−	0.975738i	−0.114739	−	0.0833629i	−0.643675	+	0.765299i	$0.722591\pi$
$138$	−1.32841	−	0.965146i	−0.113082	−	0.0821587i
$139$	4.31386	−	13.2767i	0.365897	−	1.12612i	−0.583520	−	0.812098i	$-0.698325\pi$
$139$	4.31386	−	13.2767i	0.365897	−	1.12612i	0.949417	−	0.314017i	$-0.101675\pi$
$140$	−5.41875	−	16.6772i	−0.457968	−	1.40948i
$141$	−11.6594	+	8.47103i	−0.981896	+	0.713389i
$142$	4.48341			0.376239
$143$	−18.7110	+	5.34075i	−1.56469	+	0.446616i
$144$	0.0101917			0.000849312
$145$	−3.33466	+	2.42277i	−0.276928	+	0.201200i
$146$	−0.400075	−	1.23130i	−0.0331104	−	0.101903i
$147$	5.44572	−	16.7602i	0.449155	−	1.38236i
$148$	−7.71847	−	5.60779i	−0.634454	−	0.460958i
$149$	−15.5900	−	11.3268i	−1.27718	−	0.927927i	−0.277718	−	0.960663i	$-0.589578\pi$
$149$	−15.5900	−	11.3268i	−1.27718	−	0.927927i	−0.999464	+	0.0327359i	$0.989578\pi$
$150$	6.92802	−	21.3223i	0.565670	−	1.74095i
$151$	2.06832	+	6.36564i	0.168318	+	0.518028i	0.999265	−	0.0383221i	$-0.0122013\pi$
$151$	2.06832	+	6.36564i	0.168318	+	0.518028i	−0.830948	+	0.556350i	$0.812201\pi$
$152$	5.85395	−	4.25314i	0.474818	−	0.344975i
$153$	−0.0202394			−0.00163626
$154$	−0.496093	+	13.7289i	−0.0399763	+	1.10631i
$155$	8.07087			0.648268
$156$	−8.23500	+	5.98308i	−0.659327	+	0.479029i
$157$	−5.56601	−	17.1304i	−0.444216	−	1.36716i	−0.883341	−	0.468731i	$-0.844712\pi$
$157$	−5.56601	−	17.1304i	−0.444216	−	1.36716i	0.439125	−	0.898426i	$-0.355288\pi$
$158$	3.85206	−	11.8554i	0.306453	−	0.943166i
$159$	−5.51309	−	4.00549i	−0.437216	−	0.317656i
$160$	3.42492	+	2.48835i	0.270764	+	0.196722i
$161$	1.21139	−	3.72827i	0.0954708	−	0.293829i
$162$	−2.79057	−	8.58849i	−0.219248	−	0.674775i
$163$	7.14536	−	5.19141i	0.559668	−	0.406623i	−0.271669	−	0.962391i	$-0.587576\pi$
$163$	7.14536	−	5.19141i	0.559668	−	0.406623i	0.831337	+	0.555768i	$0.187576\pi$
$164$	4.17637			0.326119
$165$	−15.0211	+	19.1782i	−1.16939	+	1.49302i
$166$	−6.63912			−0.515296
$167$	−20.3501	+	14.7852i	−1.57474	+	1.14411i	−0.652306	+	0.757956i	$0.726198\pi$
$167$	−20.3501	+	14.7852i	−1.57474	+	1.14411i	−0.922432	+	0.386158i	$0.873802\pi$
$168$	2.22077	+	6.83482i	0.171336	+	0.527318i
$169$	6.61931	−	20.3721i	0.509177	−	1.56709i
$170$	−6.80143	−	4.94153i	−0.521646	−	0.378998i
$171$	0.0596619	+	0.0433469i	0.00456246	+	0.00331482i
$172$	−0.309017	+	0.951057i	−0.0235623	+	0.0725174i
$173$	5.24166	+	16.1322i	0.398516	+	1.22651i	0.926190	+	0.377058i	$0.123064\pi$
$173$	5.24166	+	16.1322i	0.398516	+	1.22651i	−0.527674	+	0.849447i	$0.676936\pi$
$174$	1.36664	−	0.992925i	0.103605	−	0.0752734i
$175$	53.5246			4.04608
$176$	−1.85130	−	2.75185i	−0.139547	−	0.207429i
$177$	4.63130			0.348110
$178$	8.69927	−	6.32039i	0.652038	−	0.473733i
$179$	0.919861	+	2.83104i	0.0687537	+	0.211602i	0.979530	−	0.201298i	$-0.0645159\pi$
$179$	0.919861	+	2.83104i	0.0687537	+	0.211602i	−0.910776	+	0.412900i	$0.864516\pi$
$180$	−0.0133329	+	0.0410344i	−0.000993774	+	0.00305852i
$181$	−16.5594	−	12.0311i	−1.23085	−	0.894265i	−0.233896	−	0.972262i	$-0.575148\pi$
$181$	−16.5594	−	12.0311i	−1.23085	−	0.894265i	−0.996954	+	0.0779967i	$0.975148\pi$
$182$	−19.6603	−	14.2840i	−1.45732	−	1.05880i
$183$	5.14919	−	15.8476i	0.380639	−	1.17149i
$184$	0.292455	+	0.900085i	0.0215601	+	0.0663552i
$185$	32.6756	−	23.7402i	2.40236	−	1.74542i
$186$	−3.30768			−0.242531
$187$	3.67642	+	5.46480i	0.268847	+	0.399626i
$188$	8.30654			0.605817
$189$	17.3829	−	12.6294i	1.26442	−	0.918654i
$190$	9.46600	+	29.1334i	0.686736	+	2.11356i
$191$	1.16750	−	3.59320i	0.0844775	−	0.259995i	−0.899891	−	0.436114i	$-0.856354\pi$
$191$	1.16750	−	3.59320i	0.0844775	−	0.259995i	0.984369	+	0.176119i	$0.0563544\pi$
$192$	−1.40364	−	1.01980i	−0.101299	−	0.0735979i
$193$	1.10425	+	0.802288i	0.0794860	+	0.0577500i	0.626819	−	0.779165i	$-0.284357\pi$
$193$	1.10425	+	0.802288i	0.0794860	+	0.0577500i	−0.547333	+	0.836915i	$0.684357\pi$
$194$	3.11601	−	9.59008i	0.223716	−	0.688528i
$195$	−13.3162	−	40.9832i	−0.953595	−	2.93486i
$196$	−8.21738	+	5.97028i	−0.586956	+	0.426448i
$197$	−20.1156			−1.43318			−0.716590	−	0.697495i	$-0.754298\pi$
$197$	−20.1156			−1.43318			−0.716590	+	0.697495i	$0.754298\pi$
$198$	0.0208430	−	0.0266112i	0.00148125	−	0.00189118i
$199$	20.6270			1.46221			0.731103	−	0.682267i	$-0.239006\pi$
$199$	20.6270			1.46221			0.731103	+	0.682267i	$0.239006\pi$
$200$	−10.4541	+	7.59536i	−0.739218	+	0.537073i
$201$	−3.65454	−	11.2475i	−0.257771	−	0.793339i
$202$	−3.12472	+	9.61690i	−0.219855	+	0.676643i
$203$	3.26274	+	2.37052i	0.228999	+	0.166378i
$204$	2.78743	+	2.02519i	0.195159	+	0.141791i
$205$	−5.46354	+	16.8150i	−0.381590	+	1.17441i
$206$	4.94269	+	15.2120i	0.344373	+	1.05987i
$207$	−0.00780339	+	0.00566949i	−0.000542373	+	0.000394057i
$208$	5.86690			0.406796
$209$	0.866624	−	23.9830i	0.0599456	−	1.65894i
$210$	−30.4238			−2.09944
$211$	16.3826	−	11.9027i	1.12783	−	0.819414i	0.142449	−	0.989802i	$-0.454502\pi$
$211$	16.3826	−	11.9027i	1.12783	−	0.819414i	0.985377	+	0.170388i	$0.0545022\pi$
$212$	1.21373	+	3.73548i	0.0833594	+	0.256554i
$213$	2.40374	−	7.39796i	0.164702	−	0.506900i
$214$	3.19423	+	2.32074i	0.218353	+	0.158643i
$215$	−3.42492	−	2.48835i	−0.233578	−	0.169704i
$216$	−1.60296	+	4.93340i	−0.109068	+	0.335676i
$217$	−2.44024	−	7.51030i	−0.165655	−	0.509832i
$218$	−2.95885	+	2.14973i	−0.200399	+	0.145598i
$219$	−2.24624			−0.151787
$220$	13.5015	−	3.85378i	0.910271	−	0.259822i
$221$	−11.6509			−0.783722
$222$	−13.3915	+	9.72947i	−0.898776	+	0.652999i
$223$	−0.417564	−	1.28513i	−0.0279621	−	0.0860586i	0.936102	−	0.351730i	$-0.114406\pi$
$223$	−0.417564	−	1.28513i	−0.0279621	−	0.0860586i	−0.964064	+	0.265671i	$0.914406\pi$
$224$	1.27999	−	3.93940i	0.0855228	−	0.263212i
$225$	−0.106546	−	0.0774099i	−0.00710304	−	0.00516066i
$226$	−0.602297	−	0.437595i	−0.0400642	−	0.0291084i
$227$	0.723093	−	2.22545i	0.0479934	−	0.147708i	−0.924188	−	0.381938i	$-0.875257\pi$
$227$	0.723093	−	2.22545i	0.0479934	−	0.147708i	0.972181	+	0.234230i	$0.0752568\pi$
$228$	−3.87945	−	11.9397i	−0.256923	−	0.790728i
$229$	1.33567	−	0.970418i	0.0882633	−	0.0641270i	−0.542778	−	0.839876i	$-0.682628\pi$
$229$	1.33567	−	0.970418i	0.0882633	−	0.0641270i	0.631042	+	0.775749i	$0.282628\pi$
$230$	−4.00655			−0.264184
$231$	22.3878	+	8.17924i	1.47301	+	0.538155i
$232$	−0.973645			−0.0639229
$233$	9.47692	−	6.88538i	0.620853	−	0.451076i	−0.232366	−	0.972628i	$-0.574647\pi$
$233$	9.47692	−	6.88538i	0.620853	−	0.451076i	0.853220	+	0.521552i	$0.174647\pi$
$234$	0.0184773	+	0.0568674i	0.00120790	+	0.00371754i
$235$	−10.8667	+	33.4441i	−0.708862	+	2.18165i
$236$	−2.15955	−	1.56901i	−0.140575	−	0.102134i
$237$	−17.4971	−	12.7124i	−1.13656	−	0.825756i
$238$	−2.54188	+	7.82311i	−0.164766	+	0.507097i
$239$	−3.22895	−	9.93770i	−0.208864	−	0.642816i	−0.999533	−	0.0305723i	$-0.990267\pi$
$239$	−3.22895	−	9.93770i	−0.208864	−	0.642816i	0.790669	−	0.612244i	$-0.209733\pi$
$240$	5.94221	−	4.31727i	0.383568	−	0.278678i
$241$	17.1923			1.10745			0.553727	−	0.832698i	$-0.313205\pi$
$241$	17.1923			1.10745			0.553727	+	0.832698i	$0.313205\pi$
$242$	−10.9713	−	0.793931i	−0.705263	−	0.0510358i
$243$	−0.105915			−0.00679446
$244$	−7.76993	+	5.64518i	−0.497419	+	0.361396i
$245$	−13.2877	−	40.8955i	−0.848923	−	2.61272i
$246$	2.23912	−	6.89131i	0.142761	−	0.439374i
$247$	34.3445	+	24.9528i	2.18529	+	1.58771i
$248$	1.54236	+	1.12059i	0.0979397	+	0.0711574i
$249$	−3.55951	+	10.9550i	−0.225575	+	0.694248i
$250$	−10.3636	−	31.8959i	−0.655451	−	2.01727i
$251$	−14.4903	+	10.5278i	−0.914619	+	0.664510i	−0.942179	−	0.335111i	$-0.891226\pi$
$251$	−14.4903	+	10.5278i	−0.914619	+	0.664510i	0.0275598	+	0.999620i	$0.491226\pi$
$252$	0.0422155			0.00265933
$253$	2.94827	+	1.07713i	0.185356	+	0.0677188i
$254$	−7.60414			−0.477126
$255$	−11.8004	+	8.57350i	−0.738970	+	0.536893i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.91729	−	8.97851i	0.181976	−	0.560064i	−0.817907	−	0.575350i	$-0.804866\pi$
$257$	2.91729	−	8.97851i	0.181976	−	0.560064i	0.999883	+	0.0152860i	$0.00486589\pi$
$258$	1.40364	+	1.01980i	0.0873866	+	0.0634901i
$259$	−31.9709	−	23.2282i	−1.98657	−	1.44333i
$260$	−7.67511	+	23.6215i	−0.475990	+	1.46495i
$261$	−0.00306642	−	0.00943746i	−0.000189806	−	0.000584164i
$262$	13.1476	−	9.55228i	0.812261	−	0.590142i
$263$	19.2613			1.18770			0.593851	−	0.804575i	$-0.297607\pi$
$263$	19.2613			1.18770			0.593851	+	0.804575i	$0.297607\pi$
$264$	−5.53332	+	1.57939i	−0.340552	+	0.0972050i
$265$	−16.6277			−1.02143
$266$	24.2478	−	17.6171i	1.48673	−	1.08017i
$267$	−5.76507	−	17.7431i	−0.352817	−	1.08586i
$268$	−2.10637	+	6.48275i	−0.128667	+	0.395997i
$269$	−5.25979	−	3.82146i	−0.320695	−	0.232999i	0.415777	−	0.909467i	$-0.363510\pi$
$269$	−5.25979	−	3.82146i	−0.320695	−	0.232999i	−0.736472	+	0.676468i	$0.763510\pi$
$270$	−17.7661	−	12.9078i	−1.08121	−	0.785544i
$271$	5.34846	−	16.4609i	0.324896	−	0.999927i	−0.646592	−	0.762836i	$-0.723806\pi$
$271$	5.34846	−	16.4609i	0.324896	−	0.999927i	0.971488	−	0.237091i	$-0.0761938\pi$
$272$	−0.613665	−	1.88867i	−0.0372089	−	0.114517i
$273$	−34.1104	+	24.7827i	−2.06446	+	1.49992i
$274$	1.66002			0.100286
$275$	−1.54764	+	42.8295i	−0.0933261	+	2.58271i
$276$	1.64200			0.0988371
$277$	0.876862	−	0.637078i	0.0526856	−	0.0382783i	−0.561131	−	0.827727i	$-0.689634\pi$
$277$	0.876862	−	0.637078i	0.0526856	−	0.0382783i	0.613816	+	0.789449i	$0.289634\pi$
$278$	4.31386	+	13.2767i	0.258728	+	0.796284i
$279$	−0.00600423	+	0.0184791i	−0.000359464	+	0.00110632i
$280$	14.1865	+	10.3071i	0.847804	+	0.615966i
$281$	6.37656	+	4.63284i	0.380393	+	0.276372i	0.761508	−	0.648156i	$-0.224460\pi$
$281$	6.37656	+	4.63284i	0.380393	+	0.276372i	−0.381114	+	0.924528i	$0.624460\pi$
$282$	4.45348	−	13.7064i	0.265201	−	0.816205i
$283$	4.29419	+	13.2162i	0.255263	+	0.785619i	0.993778	+	0.111382i	$0.0355276\pi$
$283$	4.29419	+	13.2162i	0.255263	+	0.785619i	−0.738515	+	0.674237i	$0.764472\pi$
$284$	−3.62716	+	2.63528i	−0.215232	+	0.156375i
$285$	53.1473			3.14818
$286$	11.9983	−	15.3188i	0.709475	−	0.905821i
$287$	17.2990			1.02113
$288$	−0.00824529	+	0.00599055i	−0.000485858	+	0.000352997i
$289$	−4.03463	−	12.4173i	−0.237331	−	0.730431i
$290$	1.27373	−	3.92013i	0.0747958	−	0.230198i
$291$	−14.1537	−	10.2833i	−0.829706	−	0.602816i
$292$	1.04741	+	0.760988i	0.0612950	+	0.0445334i
$293$	−3.82590	+	11.7749i	−0.223511	+	0.687897i	0.774928	+	0.632049i	$0.217786\pi$
$293$	−3.82590	+	11.7749i	−0.223511	+	0.687897i	−0.998439	+	0.0558475i	$0.982214\pi$
$294$	5.44572	+	16.7602i	0.317601	+	0.977475i
$295$	9.14233	−	6.64229i	0.532287	−	0.386729i
$296$	9.54055			0.554533
$297$	9.60321	+	14.2747i	0.557235	+	0.828300i
$298$	19.2703			1.11630
$299$	−4.49204	+	3.26366i	−0.259781	+	0.188742i
$300$	6.92802	+	21.3223i	0.399989	+	1.23104i
$301$	−1.27999	+	3.93940i	−0.0737773	+	0.227063i
$302$	−5.41493	−	3.93418i	−0.311594	−	0.226387i
$303$	14.1933	+	10.3120i	0.815384	+	0.592411i
$304$	−2.23601	+	6.88173i	−0.128244	+	0.394694i
$305$	−12.5642	−	38.6686i	−0.719424	−	2.21416i
$306$	0.0163740	−	0.0118964i	0.000936040	−	0.000680073i
$307$	30.3557			1.73249			0.866245	−	0.499620i	$-0.166527\pi$
$307$	30.3557			1.73249			0.866245	+	0.499620i	$0.166527\pi$
$308$	−7.66832	−	11.3985i	−0.436943	−	0.649492i
$309$	27.7509			1.57870
$310$	−6.52947	+	4.74394i	−0.370849	+	0.269438i
$311$	−5.17073	−	15.9139i	−0.293205	−	0.902393i	−0.983818	−	0.179168i	$-0.942659\pi$
$311$	−5.17073	−	15.9139i	−0.293205	−	0.902393i	0.690613	−	0.723224i	$-0.257341\pi$
$312$	3.14549	−	9.68082i	0.178078	−	0.548069i
$313$	−9.24753	−	6.71872i	−0.522701	−	0.379765i	0.294919	−	0.955522i	$-0.404707\pi$
$313$	−9.24753	−	6.71872i	−0.522701	−	0.379765i	−0.817620	+	0.575758i	$0.804707\pi$
$314$	14.5720	+	10.5872i	0.822346	+	0.597469i
$315$	−0.0552265	+	0.169970i	−0.00311166	+	0.00957671i
$316$	3.85206	+	11.8554i	0.216695	+	0.666919i
$317$	4.64512	−	3.37488i	0.260896	−	0.189552i	−0.449646	−	0.893207i	$-0.648450\pi$
$317$	4.64512	−	3.37488i	0.260896	−	0.189552i	0.710542	+	0.703655i	$0.248450\pi$
$318$	6.81455			0.382141
$319$	−1.99119	+	2.54224i	−0.111485	+	0.142338i
$320$	−4.23344			−0.236656
$321$	5.54196	−	4.02647i	0.309322	−	0.224736i
$322$	1.21139	+	3.72827i	0.0675080	+	0.207768i
$323$	4.44041	−	13.6662i	0.247071	−	0.760406i
$324$	7.30580	+	5.30798i	0.405878	+	0.294888i
$325$	−61.3333	−	44.5612i	−3.40216	−	2.47181i
$326$	−2.72929	+	8.39988i	−0.151161	+	0.465226i
$327$	1.96085	+	6.03489i	0.108435	+	0.333730i
$328$	−3.37875	+	2.45481i	−0.186560	+	0.135544i
$329$	34.4068			1.89691
$330$	0.879691	−	24.3446i	0.0484254	−	1.34013i
$331$	−32.4697			−1.78470			−0.892348	−	0.451348i	$-0.850943\pi$
$331$	−32.4697			−1.78470			−0.892348	+	0.451348i	$0.850943\pi$
$332$	5.37116	−	3.90238i	0.294781	−	0.214171i
$333$	0.0300472	+	0.0924758i	0.00164658	+	0.00506764i
$334$	7.77305	−	23.9230i	0.425322	−	1.30901i
$335$	−23.3455	−	16.9615i	−1.27550	−	0.926708i
$336$	−5.81405	−	4.22415i	−0.317182	−	0.230446i
$337$	0.495052	−	1.52361i	0.0269672	−	0.0829965i	−0.936667	−	0.350221i	$-0.886107\pi$
$337$	0.495052	−	1.52361i	0.0269672	−	0.0829965i	0.963634	+	0.267224i	$0.0861065\pi$
$338$	6.61931	+	20.3721i	0.360043	+	1.10810i
$339$	−1.04498	+	0.759222i	−0.0567555	+	0.0412353i
$340$	8.40703			0.455935
$341$	6.08017	−	1.73548i	0.329260	−	0.0939817i
$342$	−0.0737461			−0.00398773
$343$	−10.5801	+	7.68688i	−0.571271	+	0.415053i
$344$	−0.309017	−	0.951057i	−0.0166611	−	0.0512775i
$345$	−2.14808	+	6.61110i	−0.115649	+	0.355930i
$346$	−13.7228	−	9.97022i	−0.737744	−	0.536002i
$347$	8.07771	+	5.86880i	0.433634	+	0.315054i	0.783100	−	0.621895i	$-0.213637\pi$
$347$	8.07771	+	5.86880i	0.433634	+	0.315054i	−0.349466	+	0.936949i	$0.613637\pi$
$348$	−0.522012	+	1.60659i	−0.0279828	+	0.0861221i
$349$	8.61351	+	26.5097i	0.461071	+	1.41903i	0.863858	+	0.503736i	$0.168042\pi$
$349$	8.61351	+	26.5097i	0.461071	+	1.41903i	−0.402787	+	0.915294i	$0.631958\pi$
$350$	−43.3023	+	31.4610i	−2.31461	+	1.68166i
$351$	−30.4333			−1.62441
$352$	3.11523	+	1.13813i	0.166042	+	0.0606626i
$353$	9.16023			0.487550			0.243775	−	0.969832i	$-0.421614\pi$
$353$	9.16023			0.487550			0.243775	+	0.969832i	$0.421614\pi$
$354$	−3.74680	+	2.72221i	−0.199140	+	0.144684i
$355$	−5.86522	−	18.0513i	−0.311293	−	0.958063i
$356$	−3.32283	+	10.2266i	−0.176109	+	0.542009i
$357$	11.5459	+	8.38858i	0.611074	+	0.443971i
$358$	−2.40823	−	1.74968i	−0.127279	−	0.0924735i
$359$	−1.81318	+	5.58041i	−0.0956962	+	0.294523i	−0.987434	−	0.158029i	$-0.949486\pi$
$359$	−1.81318	+	5.58041i	−0.0956962	+	0.294523i	0.891738	+	0.452551i	$0.149486\pi$
$360$	−0.0133329	−	0.0410344i	−0.000702704	−	0.00216270i
$361$	−26.9871	+	19.6073i	−1.42037	+	1.03196i
$362$	20.4685			1.07580
$363$	−7.19222	+	17.6778i	−0.377494	+	0.927845i
$364$	24.3015			1.27374
$365$	−4.43414	+	3.22159i	−0.232094	+	0.168626i
$366$	5.14919	+	15.8476i	0.269152	+	0.828366i
$367$	−7.88504	+	24.2677i	−0.411596	+	1.26676i	0.503665	+	0.863899i	$0.331985\pi$
$367$	−7.88504	+	24.2677i	−0.411596	+	1.26676i	−0.915261	+	0.402862i	$0.868015\pi$
$368$	−0.765658	−	0.556283i	−0.0399127	−	0.0289983i
$369$	−0.0344353	−	0.0250187i	−0.00179263	−	0.00130242i
$370$	−12.4810	+	38.4125i	−0.648856	+	1.99697i
$371$	5.02743	+	15.4728i	0.261011	+	0.803310i
$372$	2.67597	−	1.94421i	0.138743	−	0.100803i
$373$	−16.5902			−0.859009			−0.429505	−	0.903065i	$-0.641312\pi$
$373$	−16.5902			−0.859009			−0.429505	+	0.903065i	$0.641312\pi$
$374$	−6.18642	−	2.26017i	−0.319892	−	0.116871i
$375$	−58.1869			−3.00476
$376$	−6.72013	+	4.88246i	−0.346564	+	0.251794i
$377$	−1.76519	−	5.43270i	−0.0909120	−	0.279798i
$378$	−6.63967	+	20.4348i	−0.341508	+	1.05105i
$379$	9.12716	+	6.63127i	0.468831	+	0.340626i	0.796985	−	0.603998i	$-0.206427\pi$
$379$	9.12716	+	6.63127i	0.468831	+	0.340626i	−0.328155	+	0.944624i	$0.606427\pi$
$380$	−24.7823	−	18.0054i	−1.27131	−	0.923658i
$381$	−4.07689	+	12.5474i	−0.208866	+	0.642822i
$382$	1.16750	+	3.59320i	0.0597346	+	0.183844i
$383$	0.704937	−	0.512167i	0.0360206	−	0.0261705i	−0.569629	−	0.821902i	$-0.692913\pi$
$383$	0.704937	−	0.512167i	0.0360206	−	0.0261705i	0.605650	+	0.795731i	$0.292913\pi$
$384$	1.73499			0.0885384
$385$	55.9249	−	15.9629i	2.85020	−	0.813542i
$386$	−1.36493			−0.0694733
$387$	0.00824529	−	0.00599055i	0.000419132	−	0.000304517i
$388$	3.11601	+	9.59008i	0.158191	+	0.486862i
$389$	−5.75503	+	17.7122i	−0.291791	+	0.898042i	0.692489	+	0.721429i	$0.256514\pi$
$389$	−5.75503	+	17.7122i	−0.291791	+	0.898042i	−0.984280	+	0.176613i	$0.943486\pi$
$390$	34.8624	+	25.3290i	1.76532	+	1.28258i
$391$	1.52049	+	1.10470i	0.0768946	+	0.0558672i
$392$	3.13876	−	9.66011i	0.158531	−	0.487909i
$393$	−8.71300	−	26.8159i	−0.439513	−	1.35268i
$394$	16.2739	−	11.8237i	0.819867	−	0.595668i
$395$	−52.7720			−2.65525
$396$	−0.00122064	+	0.0337801i	−6.13395e−5	+	0.00169752i
$397$	26.1029			1.31007			0.655033	−	0.755601i	$-0.272655\pi$
$397$	26.1029			1.31007			0.655033	+	0.755601i	$0.272655\pi$
$398$	−16.6876	+	12.1242i	−0.836472	+	0.607733i
$399$	−16.0692	−	49.4559i	−0.804466	−	2.47589i
$400$	3.99312	−	12.2896i	0.199656	−	0.614478i
$401$	16.2093	+	11.7767i	0.809452	+	0.588102i	0.913672	−	0.406453i	$-0.133234\pi$
$401$	16.2093	+	11.7767i	0.809452	+	0.588102i	−0.104219	+	0.994554i	$0.533234\pi$
$402$	9.56771	+	6.95135i	0.477194	+	0.346702i
$403$	−3.45635	+	10.6376i	−0.172173	+	0.529895i
$404$	−3.12472	−	9.61690i	−0.155461	−	0.478459i
$405$	−30.9287	+	22.4710i	−1.53686	+	1.11659i
$406$	−4.03296			−0.200153
$407$	19.5112	−	24.9109i	0.967136	−	1.23479i
$408$	−3.44545			−0.170575
$409$	10.8850	−	7.90844i	0.538230	−	0.391047i	−0.285197	−	0.958469i	$-0.592059\pi$
$409$	10.8850	−	7.90844i	0.538230	−	0.391047i	0.823427	+	0.567422i	$0.192059\pi$
$410$	−5.46354	−	16.8150i	−0.269825	−	0.830436i
$411$	0.890008	−	2.73916i	0.0439009	−	0.135113i
$412$	−12.9401	−	9.40155i	−0.637514	−	0.463181i
$413$	−8.94515	−	6.49903i	−0.440162	−	0.319796i
$414$	0.00298063	−	0.00917343i	0.000146490	−	0.000450850i
$415$	8.68533	+	26.7307i	0.426346	+	1.31216i
$416$	−4.74642	+	3.44848i	−0.232713	+	0.169076i
$417$	24.2204			1.18608
$418$	13.3958	+	19.9121i	0.655208	+	0.973931i
$419$	14.6039			0.713446			0.356723	−	0.934210i	$-0.383894\pi$
$419$	14.6039			0.713446			0.356723	+	0.934210i	$0.383894\pi$
$420$	24.6134	−	17.8827i	1.20101	−	0.872586i
$421$	−11.0760	−	34.0884i	−0.539811	−	1.66137i	−0.733018	−	0.680209i	$-0.761889\pi$
$421$	−11.0760	−	34.0884i	−0.539811	−	1.66137i	0.193207	−	0.981158i	$-0.438111\pi$
$422$	−6.25761	+	19.2589i	−0.304615	+	0.937510i
$423$	−0.0684899	−	0.0497608i	−0.00333009	−	0.00241945i
$424$	−3.17759	−	2.30865i	−0.154317	−	0.112118i
$425$	−7.92978	+	24.4054i	−0.384651	+	1.18383i
$426$	2.40374	+	7.39796i	0.116462	+	0.358432i
$427$	−32.1840	+	23.3831i	−1.55750	+	1.13159i
$428$	−3.94829			−0.190848
$429$	−18.8444	−	28.0112i	−0.909816	−	1.35239i
$430$	4.23344			0.204155
$431$	−4.09569	+	2.97569i	−0.197283	+	0.143334i	−0.682041	−	0.731314i	$-0.738907\pi$
$431$	−4.09569	+	2.97569i	−0.197283	+	0.143334i	0.484759	+	0.874648i	$0.338907\pi$
$432$	−1.60296	−	4.93340i	−0.0771225	−	0.237359i
$433$	−4.78070	+	14.7135i	−0.229746	+	0.707085i	0.768029	+	0.640415i	$0.221237\pi$
$433$	−4.78070	+	14.7135i	−0.229746	+	0.707085i	−0.997775	+	0.0666699i	$0.978763\pi$
$434$	6.38864	+	4.64162i	0.306665	+	0.222805i
$435$	−5.78560	−	4.20349i	−0.277398	−	0.201542i
$436$	1.13018	−	3.47834i	0.0541259	−	0.166582i
$437$	−2.11617	−	6.51290i	−0.101230	−	0.311554i
$438$	1.81725	−	1.32031i	0.0868314	−	0.0630867i
$439$	16.6865			0.796404			0.398202	−	0.917298i	$-0.369634\pi$
$439$	16.6865			0.796404			0.398202	+	0.917298i	$0.369634\pi$
$440$	−8.65774	+	11.0538i	−0.412742	+	0.526967i
$441$	0.103520			0.00492952
$442$	9.42574	−	6.84820i	0.448337	−	0.325736i
$443$	−3.04064	−	9.35813i	−0.144465	−	0.444618i	0.852477	−	0.522765i	$-0.175100\pi$
$443$	−3.04064	−	9.35813i	−0.144465	−	0.444618i	−0.996942	+	0.0781471i	$0.975100\pi$
$444$	5.11508	−	15.7426i	0.242751	−	0.747111i
$445$	−36.8278	−	26.7570i	−1.74581	−	1.26840i
$446$	1.09320	+	0.794253i	0.0517643	+	0.0376090i
$447$	10.3316	−	31.7974i	0.488668	−	1.50397i
$448$	1.27999	+	3.93940i	0.0604738	+	0.186119i
$449$	−24.5335	+	17.8246i	−1.15781	+	0.841195i	−0.989499	−	0.144540i	$-0.953830\pi$
$449$	−24.5335	+	17.8246i	−1.15781	+	0.841195i	−0.168306	+	0.985735i	$0.553830\pi$
$450$	0.131698			0.00620829
$451$	−0.500194	+	13.8424i	−0.0235532	+	0.651813i
$452$	0.744480			0.0350174
$453$	−9.39486	+	6.82576i	−0.441409	+	0.320702i
$454$	0.723093	+	2.22545i	0.0339365	+	0.104446i
$455$	−31.7913	+	97.8435i	−1.49040	+	4.58697i
$456$	10.1565	+	7.37916i	0.475624	+	0.345561i
$457$	19.2512	+	13.9868i	0.900534	+	0.654276i	0.938603	−	0.344999i	$-0.112121\pi$
$457$	19.2512	+	13.9868i	0.900534	+	0.654276i	−0.0380692	+	0.999275i	$0.512121\pi$
$458$	−0.510179	+	1.57017i	−0.0238391	+	0.0733692i
$459$	3.18326	+	9.79706i	0.148582	+	0.457288i
$460$	3.24137	−	2.35499i	0.151129	−	0.109802i
$461$	14.8050			0.689537			0.344769	−	0.938688i	$-0.387957\pi$
$461$	14.8050			0.689537			0.344769	+	0.938688i	$0.387957\pi$
$462$	−22.9197	+	6.54206i	−1.06632	+	0.304364i
$463$	−18.7357			−0.870722			−0.435361	−	0.900256i	$-0.643379\pi$
$463$	−18.7357			−0.870722			−0.435361	+	0.900256i	$0.643379\pi$
$464$	0.787695	−	0.572294i	0.0365678	−	0.0265681i
$465$	4.32713	+	13.3175i	0.200666	+	0.617586i
$466$	−3.61986	+	11.1408i	−0.167687	+	0.516087i
$467$	7.53276	+	5.47287i	0.348575	+	0.253254i	0.748271	−	0.663393i	$-0.230884\pi$
$467$	7.53276	+	5.47287i	0.348575	+	0.253254i	−0.399696	+	0.916648i	$0.630884\pi$
$468$	−0.0483743	−	0.0351460i	−0.00223610	−	0.00162462i
$469$	−8.72488	+	26.8524i	−0.402877	+	1.23993i
$470$	−10.8667	−	33.4441i	−0.501241	−	1.54266i
$471$	25.2823	−	18.3687i	1.16495	−	0.846383i
$472$	2.66935			0.122867
$473$	−3.11523	−	1.13813i	−0.143238	−	0.0523313i
$474$	21.6276			0.993387
$475$	75.6447	−	54.9591i	3.47082	−	2.52170i
$476$	−2.54188	−	7.82311i	−0.116507	−	0.358572i
$477$	0.0123700	−	0.0380710i	0.000566385	−	0.00174315i
$478$	8.45351	+	6.14184i	0.386655	+	0.280921i
$479$	−9.26007	−	6.72784i	−0.423103	−	0.307403i	0.355782	−	0.934569i	$-0.384215\pi$
$479$	−9.26007	−	6.72784i	−0.423103	−	0.307403i	−0.778885	+	0.627166i	$0.784215\pi$
$480$	−2.26972	+	6.98549i	−0.103598	+	0.318842i
$481$	17.2967	+	53.2339i	0.788664	+	2.42726i
$482$	−13.9089	+	10.1054i	−0.633532	+	0.460288i
$483$	6.80140			0.309474
$484$	9.34264	−	5.80647i	0.424665	−	0.263931i
$485$	−42.6883			−1.93838
$486$	0.0856872	−	0.0622554i	0.00388685	−	0.00282396i
$487$	−1.07137	−	3.29735i	−0.0485486	−	0.149417i	0.923843	−	0.382771i	$-0.125030\pi$
$487$	−1.07137	−	3.29735i	−0.0485486	−	0.149417i	−0.972392	+	0.233354i	$0.925030\pi$
$488$	2.96785	−	9.13410i	0.134348	−	0.413481i
$489$	12.3971	+	9.00705i	0.560618	+	0.407313i
$490$	34.7878	+	25.2748i	1.57155	+	1.14180i
$491$	11.1635	−	34.3576i	0.503800	−	1.55054i	−0.298978	−	0.954260i	$-0.596646\pi$
$491$	11.1635	−	34.3576i	0.503800	−	1.55054i	0.802778	−	0.596278i	$-0.203354\pi$
$492$	2.23912	+	6.89131i	0.100947	+	0.310684i
$493$	−1.56425	+	1.13650i	−0.0704505	+	0.0511853i
$494$	−42.4522			−1.91001
$495$	−0.134410	−	0.0491059i	−0.00604128	−	0.00220715i
$496$	−1.90646			−0.0856024
$497$	−15.0242	+	10.9157i	−0.673925	+	0.489635i
$498$	−3.55951	−	10.9550i	−0.159505	−	0.490907i
$499$	3.11381	−	9.58331i	0.139393	−	0.429008i	−0.856854	−	0.515559i	$-0.827584\pi$
$499$	3.11381	−	9.58331i	0.139393	−	0.429008i	0.996247	+	0.0865506i	$0.0275844\pi$
$500$	27.1322	+	19.7127i	1.21339	+	0.881580i
$501$	−35.3072	−	25.6522i	−1.57741	−	1.14606i
$502$	5.53480	−	17.0344i	0.247030	−	0.760281i
$503$	1.82166	+	5.60648i	0.0812237	+	0.249981i	0.983419	−	0.181346i	$-0.0580455\pi$
$503$	1.82166	+	5.60648i	0.0812237	+	0.249981i	−0.902196	+	0.431327i	$0.858045\pi$
$504$	−0.0341531	+	0.0248137i	−0.00152130	+	0.00110529i
$505$	42.8077			1.90492
$506$	−3.01832	+	0.861531i	−0.134181	+	0.0382997i
$507$	37.1644			1.65053
$508$	6.15188	−	4.46960i	0.272945	−	0.198306i
$509$	6.73359	+	20.7239i	0.298461	+	0.918569i	0.982037	+	0.188689i	$0.0604239\pi$
$509$	6.73359	+	20.7239i	0.298461	+	0.918569i	−0.683576	+	0.729880i	$0.739576\pi$
$510$	4.50736	−	13.8722i	0.199589	−	0.614272i
$511$	4.33851	+	3.15211i	0.191924	+	0.139441i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	11.5988	−	35.6975i	0.512100	−	1.57608i
$514$	2.91729	+	8.97851i	0.128676	+	0.396025i
$515$	54.7812	−	39.8009i	2.41395	−	1.75384i
$516$	−1.73499			−0.0763787
$517$	−0.994856	+	27.5317i	−0.0437537	+	1.21084i
$518$	39.5182			1.73633
$519$	−23.8090	+	17.2982i	−1.04510	+	0.759308i
$520$	−7.67511	−	23.6215i	−0.336576	−	1.03587i
$521$	0.189792	−	0.584121i	0.00831496	−	0.0255908i	−0.946813	−	0.321784i	$-0.895717\pi$
$521$	0.189792	−	0.584121i	0.00831496	−	0.0255908i	0.955128	+	0.296194i	$0.0957174\pi$
$522$	0.00802799	+	0.00583267i	0.000351375	+	0.000255289i
$523$	−2.01164	−	1.46154i	−0.0879629	−	0.0639088i	0.542935	−	0.839775i	$-0.317313\pi$
$523$	−2.01164	−	1.46154i	−0.0879629	−	0.0639088i	−0.630897	+	0.775866i	$0.717313\pi$
$524$	−5.02193	+	15.4559i	−0.219384	+	0.675195i
$525$	28.6968	+	88.3195i	1.25243	+	3.85458i
$526$	−15.5827	+	11.3215i	−0.679438	+	0.493641i
$527$	3.78596			0.164919
$528$	3.54820	−	4.53016i	0.154416	−	0.197150i
$529$	−22.1043			−0.961057
$530$	13.4521	−	9.77354i	0.584323	−	0.424536i
$531$	0.00840692	+	0.0258738i	0.000364829	+	0.00112283i
$532$	−9.26184	+	28.5050i	−0.401552	+	1.23585i
$533$	−19.8228	−	14.4021i	−0.858621	−	0.623824i
$534$	15.0932	+	10.9658i	0.653145	+	0.474537i
$535$	5.16516	−	15.8967i	0.223310	−	0.687276i
$536$	−2.10637	−	6.48275i	−0.0909815	−	0.280012i
$537$	−4.17825	+	3.03568i	−0.180305	+	0.130999i
$538$	6.50146			0.280298
$539$	−18.8041	−	27.9512i	−0.809949	−	1.20395i
$540$	21.9601			0.945011
$541$	−30.3459	+	22.0476i	−1.30467	+	0.947901i	−0.999990	−	0.00455239i	$-0.998551\pi$
$541$	−30.3459	+	22.0476i	−1.30467	+	0.947901i	−0.304684	+	0.952453i	$0.598551\pi$
$542$	5.34846	+	16.4609i	0.229736	+	0.707055i
$543$	10.9740	−	33.7746i	0.470941	−	1.44941i
$544$	1.60660	+	1.16726i	0.0688823	+	0.0500459i
$545$	12.5261	+	9.10076i	0.536560	+	0.389834i
$546$	13.0290	−	40.0992i	0.557591	−	1.71609i
$547$	−6.62384	−	20.3861i	−0.283215	−	0.871646i	−0.986928	−	0.161162i	$-0.948476\pi$
$547$	−6.62384	−	20.3861i	−0.283215	−	0.871646i	0.703713	−	0.710484i	$-0.251524\pi$
$548$	−1.34299	+	0.975738i	−0.0573696	+	0.0416815i
$549$	0.0978831			0.00417755
$550$	−23.9225	−	35.5594i	−1.02006	−	1.51626i
$551$	7.04517			0.300135
$552$	−1.32841	+	0.965146i	−0.0565409	+	0.0410793i
$553$	15.9557	+	49.1067i	0.678506	+	2.08823i
$554$	−0.334932	+	1.03081i	−0.0142299	+	0.0437951i
$555$	56.6919	+	41.1891i	2.40644	+	1.74838i
$556$	−11.2938	−	8.20545i	−0.478965	−	0.347989i
$557$	3.88147	−	11.9459i	0.164463	−	0.506166i	−0.834533	−	0.550958i	$-0.814263\pi$
$557$	3.88147	−	11.9459i	0.164463	−	0.506166i	0.998996	+	0.0447921i	$0.0142625\pi$
$558$	−0.00600423	−	0.0184791i	−0.000254180	−	0.000782284i
$559$	4.74642	−	3.44848i	0.200752	−	0.145855i
$560$	−17.5355			−0.741008
$561$	−7.04625	+	8.99628i	−0.297493	+	0.379823i
$562$	−7.88186			−0.332476
$563$	14.1443	−	10.2764i	0.596111	−	0.433100i	−0.248385	−	0.968661i	$-0.579900\pi$
$563$	14.1443	−	10.2764i	0.596111	−	0.433100i	0.844496	+	0.535561i	$0.179900\pi$
$564$	4.45348	+	13.7064i	0.187525	+	0.577144i
$565$	−0.973932	+	2.99746i	−0.0409736	+	0.126104i
$566$	−11.2423	−	8.16803i	−0.472551	−	0.343328i
$567$	30.2616	+	21.9863i	1.27087	+	0.923339i
$568$	1.38545	−	4.26398i	0.0581322	−	0.178913i
$569$	0.151235	+	0.465454i	0.00634011	+	0.0195128i	0.954177	−	0.299244i	$-0.0967346\pi$
$569$	0.151235	+	0.465454i	0.00634011	+	0.0195128i	−0.947836	+	0.318757i	$0.896735\pi$
$570$	−42.9971	+	31.2392i	−1.80095	+	1.30847i
$571$	−24.8477			−1.03984			−0.519921	−	0.854214i	$-0.674039\pi$
$571$	−24.8477			−1.03984			−0.519921	+	0.854214i	$0.674039\pi$
$572$	−0.702665	+	19.4456i	−0.0293799	+	0.813062i
$573$	6.55500			0.273839
$574$	−13.9952	+	10.1681i	−0.584149	+	0.424409i
$575$	3.77911	+	11.6309i	0.157600	+	0.485042i
$576$	0.00314942	−	0.00969292i	0.000131226	−	0.000403872i
$577$	28.3876	+	20.6248i	1.18179	+	0.858621i	0.992373	−	0.123275i	$-0.0393398\pi$
$577$	28.3876	+	20.6248i	1.18179	+	0.858621i	0.189418	+	0.981896i	$0.439340\pi$
$578$	10.5628	+	7.67433i	0.439355	+	0.319210i
$579$	−0.731798	+	2.25224i	−0.0304125	+	0.0936000i
$580$	1.27373	+	3.92013i	0.0528886	+	0.162774i
$581$	22.2481	−	16.1642i	0.923005	−	0.670602i
$582$	17.4950			0.725189
$583$	−12.5265	+	3.57548i	−0.518793	+	0.148081i
$584$	−1.29467			−0.0535738
$585$	0.204790	−	0.148788i	0.00846701	−	0.00615164i
$586$	−3.82590	−	11.7749i	−0.158046	−	0.486417i
$587$	−3.67474	+	11.3097i	−0.151673	+	0.466801i	−0.997809	−	0.0661665i	$-0.978923\pi$
$587$	−3.67474	+	11.3097i	−0.151673	+	0.466801i	0.846136	+	0.532967i	$0.178923\pi$
$588$	−14.2571	−	10.3584i	−0.587952	−	0.427172i
$589$	−11.1603	−	8.10843i	−0.459852	−	0.334102i
$590$	−3.49206	+	10.7475i	−0.143766	+	0.442466i
$591$	−10.7848	−	33.1923i	−0.443629	−	1.36535i
$592$	−7.71847	+	5.60779i	−0.317227	+	0.230479i
$593$	31.1141			1.27770			0.638852	−	0.769330i	$-0.279410\pi$
$593$	31.1141			1.27770			0.638852	+	0.769330i	$0.279410\pi$
$594$	−16.1596	−	5.90381i	−0.663036	−	0.242236i
$595$	34.8230			1.42760
$596$	−15.5900	+	11.3268i	−0.638591	+	0.463963i
$597$	11.0590	+	34.0360i	0.452614	+	1.39300i
$598$	1.71581	−	5.28071i	0.0701646	−	0.215944i
$599$	0.760179	+	0.552302i	0.0310601	+	0.0225665i	0.603207	−	0.797585i	$-0.293889\pi$
$599$	0.760179	+	0.552302i	0.0310601	+	0.0225665i	−0.572147	+	0.820151i	$0.693889\pi$
$600$	−18.1378	−	13.1779i	−0.740472	−	0.537985i
$601$	−8.00532	+	24.6379i	−0.326544	+	1.00500i	0.644195	+	0.764861i	$0.277193\pi$
$601$	−8.00532	+	24.6379i	−0.326544	+	1.00500i	−0.970739	+	0.240138i	$0.922807\pi$
$602$	−1.27999	−	3.93940i	−0.0521684	−	0.160558i
$603$	0.0562030	−	0.0408338i	0.00228876	−	0.00166288i
$604$	6.69323			0.272344
$605$	11.1562	+	45.2117i	0.453562	+	1.83812i
$606$	−17.5439			−0.712672
$607$	15.8278	−	11.4995i	0.642429	−	0.466752i	−0.218255	−	0.975892i	$-0.570036\pi$
$607$	15.8278	−	11.4995i	0.642429	−	0.466752i	0.860684	+	0.509140i	$0.170036\pi$
$608$	−2.23601	−	6.88173i	−0.0906821	−	0.279091i
$609$	−2.16224	+	6.65469i	−0.0876184	+	0.269662i
$610$	32.8935	+	23.8985i	1.33182	+	0.967623i
$611$	−39.4264	−	28.6449i	−1.59502	−	1.15885i
$612$	−0.00625432	+	0.0192488i	−0.000252816	+	0.000778087i
$613$	−5.08681	−	15.6556i	−0.205454	−	0.632323i	−0.999694	−	0.0247192i	$-0.992131\pi$
$613$	−5.08681	−	15.6556i	−0.205454	−	0.632323i	0.794240	−	0.607604i	$-0.207869\pi$
$614$	−24.5583	+	17.8426i	−0.991091	+	0.720069i
$615$	−30.6753			−1.23695
$616$	12.9037	+	4.71429i	0.519904	+	0.189944i
$617$	−18.4241			−0.741725			−0.370863	−	0.928688i	$-0.620938\pi$
$617$	−18.4241			−0.741725			−0.370863	+	0.928688i	$0.620938\pi$
$618$	−22.4510	+	16.3116i	−0.903111	+	0.656149i
$619$	−3.15707	−	9.71647i	−0.126893	−	0.390538i	0.867348	−	0.497702i	$-0.165823\pi$
$619$	−3.15707	−	9.71647i	−0.126893	−	0.390538i	−0.994241	+	0.107165i	$0.965823\pi$
$620$	2.49404	−	7.67585i	0.100163	−	0.308270i
$621$	3.97169	+	2.88560i	0.159378	+	0.115795i
$622$	13.5371	+	9.83531i	0.542790	+	0.394360i
$623$	−13.7636	+	42.3599i	−0.551426	+	1.69712i
$624$	3.14549	+	9.68082i	0.125920	+	0.387543i
$625$	−62.5921	+	45.4758i	−2.50368	+	1.81903i
$626$	11.4306			0.456858
$627$	40.0384	−	11.4283i	1.59898	−	0.456403i
$628$	−18.0120			−0.718757
$629$	15.3278	−	11.1363i	0.611160	−	0.444034i
$630$	−0.0552265	−	0.169970i	−0.00220028	−	0.00677176i
$631$	10.3507	−	31.8563i	0.412056	−	1.26818i	−0.502802	−	0.864402i	$-0.667697\pi$
$631$	10.3507	−	31.8563i	0.412056	−	1.26818i	0.914858	−	0.403776i	$-0.132303\pi$
$632$	−10.0848	−	7.32705i	−0.401152	−	0.291454i
$633$	28.4237	+	20.6510i	1.12974	+	0.820805i
$634$	−1.77428	+	5.46067i	−0.0704656	+	0.216871i
$635$	9.94776	+	30.6161i	0.394765	+	1.21496i
$636$	−5.51309	+	4.00549i	−0.218608	+	0.158828i
$637$	59.5915			2.36110
$638$	0.116611	−	3.22711i	0.00461668	−	0.127762i
$639$	0.0456938			0.00180762
$640$	3.42492	−	2.48835i	0.135382	−	0.0983608i
$641$	−3.43382	−	10.5682i	−0.135628	−	0.417419i	0.860059	−	0.510194i	$-0.170426\pi$
$641$	−3.43382	−	10.5682i	−0.135628	−	0.417419i	−0.995687	+	0.0927747i	$0.970426\pi$
$642$	−2.11684	+	6.51496i	−0.0835450	+	0.257125i
$643$	−14.0666	−	10.2200i	−0.554734	−	0.403038i	0.274794	−	0.961503i	$-0.411390\pi$
$643$	−14.0666	−	10.2200i	−0.554734	−	0.403038i	−0.829528	+	0.558465i	$0.811390\pi$
$644$	−3.17146	−	2.30420i	−0.124973	−	0.0907981i
$645$	2.26972	−	6.98549i	0.0893702	−	0.275053i
$646$	4.44041	+	13.6662i	0.174705	+	0.537688i
$647$	−0.603738	+	0.438642i	−0.0237354	+	0.0172448i	−0.599590	−	0.800308i	$-0.704670\pi$
$647$	−0.603738	+	0.438642i	−0.0237354	+	0.0172448i	0.575854	+	0.817552i	$0.304670\pi$
$648$	−9.03047			−0.354750
$649$	5.45906	−	6.96984i	0.214287	−	0.273590i
$650$	75.8121			2.97359
$651$	11.0842	−	8.05316i	0.434425	−	0.315628i
$652$	−2.72929	−	8.39988i	−0.106887	−	0.328965i
$653$	11.1430	−	34.2946i	0.436059	−	1.34205i	−0.455938	−	0.890012i	$-0.650696\pi$
$653$	11.1430	−	34.2946i	0.436059	−	1.34205i	0.891997	−	0.452041i	$-0.149304\pi$
$654$	−5.13358	−	3.72977i	−0.200739	−	0.145845i
$655$	−55.6595	−	40.4390i	−2.17480	−	1.58008i
$656$	1.29057	−	3.97196i	0.0503882	−	0.155079i
$657$	−0.00407746	−	0.0125491i	−0.000159077	−	0.000489588i
$658$	−27.8357	+	20.2238i	−1.08515	+	0.788406i
$659$	−16.8000			−0.654436			−0.327218	−	0.944949i	$-0.606111\pi$
$659$	−16.8000			−0.654436			−0.327218	+	0.944949i	$0.606111\pi$
$660$	13.5977	+	20.2123i	0.529291	+	0.786762i
$661$	−29.0252			−1.12895			−0.564475	−	0.825450i	$-0.690921\pi$
$661$	−29.0252			−1.12895			−0.564475	+	0.825450i	$0.690921\pi$
$662$	26.2685	−	19.0852i	1.02096	−	0.741768i
$663$	−6.24651	−	19.2248i	−0.242594	−	0.746629i
$664$	−2.05160	+	6.31418i	−0.0796176	+	0.245038i
$665$	−102.652	−	74.5807i	−3.98066	−	2.89212i
$666$	−0.0786646	−	0.0571532i	−0.00304819	−	0.00221464i
$667$	−0.284748	+	0.876363i	−0.0110255	+	0.0339329i
$668$	7.77305	+	23.9230i	0.300748	+	0.925608i
$669$	1.89668	−	1.37802i	0.0733301	−	0.0532774i
$670$	28.8567			1.11483
$671$	−17.7802	−	26.4292i	−0.686395	−	1.02029i
$672$	7.18656			0.277227
$673$	−29.7965	+	21.6484i	−1.14857	+	0.834486i	−0.988290	−	0.152586i	$-0.951240\pi$
$673$	−29.7965	+	21.6484i	−1.14857	+	0.834486i	−0.160281	+	0.987071i	$0.551240\pi$
$674$	0.495052	+	1.52361i	0.0190687	+	0.0586874i
$675$	−20.7135	+	63.7494i	−0.797261	+	2.45372i
$676$	−17.3296	−	12.5907i	−0.666522	−	0.484257i
$677$	2.24540	+	1.63138i	0.0862978	+	0.0626990i	0.630098	−	0.776516i	$-0.283015\pi$
$677$	2.24540	+	1.63138i	0.0862978	+	0.0626990i	−0.543800	+	0.839215i	$0.683015\pi$
$678$	0.399147	−	1.22845i	0.0153291	−	0.0471782i
$679$	12.9069	+	39.7234i	0.495321	+	1.52444i
$680$	−6.80143	+	4.94153i	−0.260823	+	0.189499i
$681$	4.05984			0.155573
$682$	−3.89887	+	4.97787i	−0.149295	+	0.190612i
$683$	36.1428			1.38297			0.691483	−	0.722393i	$-0.256958\pi$
$683$	36.1428			1.38297			0.691483	+	0.722393i	$0.256958\pi$
$684$	0.0596619	−	0.0433469i	0.00228123	−	0.00165741i
$685$	−2.17165	−	6.68365i	−0.0829745	−	0.255369i
$686$	4.04123	−	12.4376i	0.154295	−	0.474871i
$687$	2.31737	+	1.68367i	0.0884131	+	0.0642359i
$688$	0.809017	+	0.587785i	0.0308435	+	0.0224091i
$689$	7.12084	−	21.9157i	0.271282	−	0.834921i
$690$	−2.14808	−	6.61110i	−0.0817759	−	0.251680i
$691$	5.49291	−	3.99084i	0.208960	−	0.151819i	−0.478383	−	0.878151i	$-0.658777\pi$
$691$	5.49291	−	3.99084i	0.208960	−	0.151819i	0.687343	+	0.726333i	$0.258777\pi$
$692$	16.9624			0.644812
$693$	−0.00505605	+	0.139922i	−0.000192064	+	0.00531519i
$694$	−9.98460			−0.379010
$695$	47.8118	−	34.7373i	1.81360	−	1.31766i
$696$	−0.522012	−	1.60659i	−0.0197868	−	0.0608975i
$697$	−2.56289	+	7.88777i	−0.0970764	+	0.298770i
$698$	−22.5505	−	16.3839i	−0.853548	−	0.620139i
$699$	16.4424	+	11.9461i	0.621907	+	0.451842i
$700$	16.5400	−	50.9049i	0.625154	−	1.92403i
$701$	−6.47203	−	19.9189i	−0.244445	−	0.752325i	−0.995727	−	0.0923436i	$-0.970564\pi$
$701$	−6.47203	−	19.9189i	−0.244445	−	0.752325i	0.751282	−	0.659981i	$-0.229436\pi$
$702$	24.6211	−	17.8883i	0.929262	−	0.675148i
$703$	−69.0342			−2.60367
$704$	−3.18925	+	0.910319i	−0.120199	+	0.0343089i
$705$	−61.0113			−2.29782
$706$	−7.41078	+	5.38425i	−0.278908	+	0.202639i
$707$	−12.9430	−	39.8344i	−0.486771	−	1.49813i
$708$	1.43115	−	4.40463i	0.0537860	−	0.165536i
$709$	5.50148	+	3.99706i	0.206612	+	0.150113i	0.686280	−	0.727338i	$-0.259243\pi$
$709$	5.50148	+	3.99706i	0.206612	+	0.150113i	−0.479667	+	0.877450i	$0.659243\pi$
$710$	15.3553	+	11.1563i	0.576276	+	0.418689i
$711$	0.0392592	−	0.120827i	0.00147233	−	0.00453138i
$712$	−3.32283	−	10.2266i	−0.124528	−	0.383258i
$713$	1.45969	−	1.06053i	0.0546660	−	0.0397172i
$714$	−14.2715			−0.534098
$715$	−77.3735	−	28.2679i	−2.89360	−	1.05716i
$716$	2.97673			0.111246
$717$	14.6668	−	10.6560i	0.547740	−	0.397957i
$718$	−1.81318	−	5.58041i	−0.0676674	−	0.208259i
$719$	10.5579	−	32.4940i	0.393745	−	1.21182i	−0.536190	−	0.844097i	$-0.680137\pi$
$719$	10.5579	−	32.4940i	0.393745	−	1.21182i	0.929935	−	0.367724i	$-0.119863\pi$
$720$	0.0349059	+	0.0253606i	0.00130087	+	0.000945135i
$721$	−53.5997	−	38.9424i	−1.99616	−	1.45029i
$722$	10.3082	−	31.7252i	0.383630	−	1.18069i
$723$	9.21751	+	28.3686i	0.342803	+	1.05504i
$724$	−16.5594	+	12.0311i	−0.615425	+	0.447132i
$725$	−12.5814			−0.467263
$726$	−4.57213	−	18.5291i	−0.169688	−	0.687681i
$727$	25.9341			0.961841			0.480920	−	0.876764i	$-0.340303\pi$
$727$	25.9341			0.961841			0.480920	+	0.876764i	$0.340303\pi$
$728$	−19.6603	+	14.2840i	−0.728659	+	0.529402i
$729$	8.31492	+	25.5907i	0.307960	+	0.947804i
$730$	1.69369	−	5.21265i	0.0626864	−	0.192929i
$731$	−1.60660	−	1.16726i	−0.0594221	−	0.0431727i
$732$	−13.4807	−	9.79434i	−0.498263	−	0.362009i
$733$	−5.87966	+	18.0957i	−0.217170	+	0.668381i	0.781822	+	0.623501i	$0.214290\pi$
$733$	−5.87966	+	18.0957i	−0.217170	+	0.668381i	−0.998992	+	0.0448796i	$0.985710\pi$
$734$	−7.88504	−	24.2677i	−0.291042	−	0.895736i
$735$	60.3565	−	43.8515i	2.22628	−	1.61749i
$736$	0.946406			0.0348850
$737$	−21.2346	−	7.75792i	−0.782185	−	0.285767i
$738$	0.0425644			0.00156682
$739$	−33.5333	+	24.3634i	−1.23354	+	0.896222i	−0.997151	−	0.0754355i	$-0.975965\pi$
$739$	−33.5333	+	24.3634i	−1.23354	+	0.896222i	−0.236393	+	0.971658i	$0.575965\pi$
$740$	−12.4810	−	38.4125i	−0.458810	−	1.41207i
$741$	−22.7604	+	70.0492i	−0.836123	+	2.57332i
$742$	−13.1620	−	9.56274i	−0.483192	−	0.351059i
$743$	−22.8617	−	16.6100i	−0.838714	−	0.609362i	0.0832970	−	0.996525i	$-0.473455\pi$
$743$	−22.8617	−	16.6100i	−0.838714	−	0.609362i	−0.922011	+	0.387163i	$0.873455\pi$
$744$	−1.02213	+	3.14580i	−0.0374731	+	0.115330i
$745$	−25.2095	−	77.5868i	−0.923604	−	2.84256i
$746$	13.4218	−	9.75149i	0.491406	−	0.357027i
$747$	−0.0676642			−0.00247570
$748$	6.33341	−	1.80777i	0.231573	−	0.0660986i
$749$	−16.3543			−0.597574
$750$	47.0742	−	34.2014i	1.71891	−	1.24886i
$751$	−13.0923	−	40.2941i	−0.477747	−	1.47035i	−0.842217	−	0.539138i	$-0.818750\pi$
$751$	−13.0923	−	40.2941i	−0.477747	−	1.47035i	0.364471	−	0.931215i	$-0.381250\pi$
$752$	2.56686	−	7.89999i	0.0936039	−	0.288083i
$753$	−25.1405	−	18.2657i	−0.916171	−	0.665637i
$754$	4.62133	+	3.35759i	0.168299	+	0.122276i
$755$	−8.75611	+	26.9485i	−0.318667	+	0.980757i
$756$	−6.63967	−	20.4348i	−0.241482	−	0.743207i
$757$	2.43786	−	1.77121i	0.0886055	−	0.0643757i	−0.542600	−	0.839991i	$-0.682560\pi$
$757$	2.43786	−	1.77121i	0.0886055	−	0.0643757i	0.631206	+	0.775615i	$0.282560\pi$
$758$	−11.2818			−0.409773
$759$	−0.196659	+	5.44236i	−0.00713827	+	0.197545i
$760$	30.6326			1.11116
$761$	13.7765	−	10.0092i	0.499398	−	0.362834i	−0.309389	−	0.950935i	$-0.600125\pi$
$761$	13.7765	−	10.0092i	0.499398	−	0.362834i	0.808787	+	0.588102i	$0.200125\pi$
$762$	−4.07689	−	12.5474i	−0.147690	−	0.454544i
$763$	4.68136	−	14.4077i	0.169477	−	0.521595i
$764$	−3.05656	−	2.22072i	−0.110582	−	0.0803429i
$765$	−0.0693184	−	0.0503627i	−0.00250621	−	0.00182087i
$766$	−0.269262	+	0.828704i	−0.00972884	+	0.0299423i
$767$	4.83946	+	14.8943i	0.174743	+	0.537803i
$768$	−1.40364	+	1.01980i	−0.0506494	+	0.0367989i
$769$	6.33542			0.228461			0.114231	−	0.993454i	$-0.463560\pi$
$769$	6.33542			0.228461			0.114231	+	0.993454i	$0.463560\pi$
$770$	−35.8615	+	45.7861i	−1.29236	+	1.65002i
$771$	16.3793			0.589885
$772$	1.10425	−	0.802288i	0.0397430	−	0.0288750i
$773$	9.68300	+	29.8012i	0.348273	+	1.07188i	0.959808	+	0.280658i	$0.0905525\pi$
$773$	9.68300	+	29.8012i	0.348273	+	1.07188i	−0.611535	+	0.791218i	$0.709447\pi$
$774$	−0.00314942	+	0.00969292i	−0.000113204	+	0.000348405i
$775$	19.9303	+	14.4802i	0.715918	+	0.520145i
$776$	−8.15781	−	5.92699i	−0.292848	−	0.212767i
$777$	21.1873	−	65.2079i	0.760092	−	2.33932i
$778$	−5.75503	−	17.7122i	−0.206328	−	0.635011i
$779$	24.4482	−	17.7627i	0.875948	−	0.636414i
$780$	−43.0922			−1.54295
$781$	−8.30013	−	12.3377i	−0.297002	−	0.441477i
$782$	−1.87943			−0.0672083
$783$	−4.08600	+	2.96866i	−0.146022	+	0.106091i
$784$	3.13876	+	9.66011i	0.112099	+	0.345004i
$785$	23.5634	−	72.5206i	0.841013	−	2.58837i
$786$	22.8109	+	16.5731i	0.813639	+	0.591144i
$787$	4.23180	+	3.07458i	0.150847	+	0.109597i	0.660649	−	0.750695i	$-0.270281\pi$
$787$	4.23180	+	3.07458i	0.150847	+	0.109597i	−0.509802	+	0.860292i	$0.670281\pi$
$788$	−6.21608	+	19.1311i	−0.221439	+	0.681518i
$789$	10.3268	+	31.7825i	0.367643	+	1.13149i
$790$	42.6934	−	31.0186i	1.51896	−	1.10359i
$791$	3.08373			0.109645
$792$	−0.0188679	−	0.0280462i	−0.000670443	−	0.000996577i
$793$	56.3466			2.00093
$794$	−21.1177	+	15.3429i	−0.749438	+	0.544498i
$795$	−8.91482	−	27.4370i	−0.316176	−	0.973090i
$796$	6.37408	−	19.6174i	0.225923	−	0.695321i
$797$	11.5493	+	8.39106i	0.409097	+	0.297227i	0.773236	−	0.634118i	$-0.218637\pi$
$797$	11.5493	+	8.39106i	0.409097	+	0.297227i	−0.364139	+	0.931345i	$0.618637\pi$
$798$	42.0697	+	30.5654i	1.48925	+	1.08200i
$799$	−5.09744	+	15.6883i	−0.180334	+	0.555012i
$800$	3.99312	+	12.2896i	0.141178	+	0.434501i
$801$	0.0886607	−	0.0644158i	0.00313267	−	0.00227602i
$802$	−20.0358			−0.707487
$803$	−2.64771	+	3.38046i	−0.0934357	+	0.119294i
$804$	−11.8263			−0.417083
$805$	13.4262	−	9.75468i	0.473210	−	0.343807i
$806$	−3.45635	−	10.6376i	−0.121745	−	0.374692i
$807$	3.48570	−	10.7279i	0.122703	−	0.377640i
$808$	8.18062	+	5.94357i	0.287793	+	0.209094i
$809$	41.6730	+	30.2772i	1.46514	+	1.06449i	0.981985	+	0.188957i	$0.0605107\pi$
$809$	41.6730	+	30.2772i	1.46514	+	1.06449i	0.483159	+	0.875533i	$0.339489\pi$
$810$	11.8137	−	36.3588i	0.415091	−	1.27752i
$811$	4.34651	+	13.3772i	0.152626	+	0.469736i	0.997913	−	0.0645779i	$-0.0205701\pi$
$811$	4.34651	+	13.3772i	0.152626	+	0.469736i	−0.845286	+	0.534314i	$0.820570\pi$
$812$	3.26274	−	2.37052i	0.114500	−	0.0831888i
$813$	30.0292			1.05317
$814$	−1.14265	+	31.6218i	−0.0400498	+	1.10834i
$815$	37.3904			1.30973
$816$	2.78743	−	2.02519i	0.0975796	−	0.0708957i
$817$	2.23601	+	6.88173i	0.0782280	+	0.240761i
$818$	−4.15771	+	12.7961i	−0.145371	+	0.447406i
$819$	−0.200373	−	0.145579i	−0.00700159	−	0.00508695i
$820$	14.3037	+	10.3923i	0.499508	+	0.362914i
$821$	−15.0416	+	46.2932i	−0.524954	+	1.61564i	0.239451	+	0.970908i	$0.423032\pi$
$821$	−15.0416	+	46.2932i	−0.524954	+	1.61564i	−0.764406	+	0.644735i	$0.776968\pi$
$822$	0.890008	+	2.73916i	0.0310426	+	0.0955393i
$823$	−19.7817	+	14.3722i	−0.689546	+	0.500985i	−0.876511	−	0.481382i	$-0.840135\pi$
$823$	−19.7817	+	14.3722i	−0.689546	+	0.500985i	0.186965	+	0.982367i	$0.440135\pi$
$824$	15.9949			0.557208
$825$	−71.5015	+	20.4089i	−2.48936	+	0.710548i
$826$	11.0568			0.384716
$827$	−16.2364	+	11.7965i	−0.564596	+	0.410203i	−0.833138	−	0.553065i	$-0.813458\pi$
$827$	−16.2364	+	11.7965i	−0.564596	+	0.410203i	0.268542	+	0.963268i	$0.413458\pi$
$828$	0.00298063	+	0.00917343i	0.000103584	+	0.000318799i
$829$	5.19073	−	15.9754i	0.180282	−	0.554850i	−0.819554	−	0.573002i	$-0.805779\pi$
$829$	5.19073	−	15.9754i	0.180282	−	0.554850i	0.999835	+	0.0181529i	$0.00577856\pi$
$830$	−22.7385	−	16.5205i	−0.789264	−	0.573434i
$831$	1.52135	+	1.10532i	0.0527750	+	0.0383433i
$832$	1.81297	−	5.57975i	0.0628535	−	0.193443i
$833$	−6.23315	−	19.1837i	−0.215966	−	0.664674i
$834$	−19.5947	+	14.2364i	−0.678509	+	0.492966i
$835$	−106.488			−3.68518
$836$	−22.5414	−	8.23537i	−0.779611	−	0.284826i
$837$	9.88934			0.341826
$838$	−11.8148	+	8.58394i	−0.408135	+	0.296527i
$839$	−1.72630	−	5.31300i	−0.0595985	−	0.183425i	0.916825	−	0.399289i	$-0.130743\pi$
$839$	−1.72630	−	5.31300i	−0.0595985	−	0.183425i	−0.976423	+	0.215864i	$0.930743\pi$
$840$	−9.40148	+	28.9348i	−0.324382	+	0.998345i
$841$	22.6946	+	16.4886i	0.782571	+	0.568571i
$842$	28.9973	+	21.0678i	0.999314	+	0.726044i
$843$	−4.22579	+	13.0056i	−0.145544	+	0.447938i
$844$	−6.25761	−	19.2589i	−0.215396	−	0.662920i
$845$	73.3637	−	53.3018i	2.52379	−	1.83364i
$846$	0.0846581			0.00291061
$847$	38.6984	−	24.0512i	1.32969	−	0.826408i
$848$	3.92772			0.134878
$849$	−19.5053	+	14.1715i	−0.669422	+	0.486363i
$850$	−7.92978	−	24.4054i	−0.271989	−	0.837097i
$851$	2.79018	−	8.58731i	0.0956463	−	0.294369i
$852$	−6.29308	−	4.57219i	−0.215597	−	0.156641i
$853$	9.34677	+	6.79083i	0.320027	+	0.232513i	0.736187	−	0.676778i	$-0.236624\pi$
$853$	9.34677	+	6.79083i	0.320027	+	0.232513i	−0.416160	+	0.909291i	$0.636624\pi$
$854$	12.2932	−	37.8346i	0.420665	−	1.29467i
$855$	0.0964750	+	0.296920i	0.00329938	+	0.0101544i
$856$	3.19423	−	2.32074i	0.109177	−	0.0793214i
$857$	−47.1315			−1.60998			−0.804991	−	0.593287i	$-0.797830\pi$
$857$	−47.1315			−1.60998			−0.804991	+	0.593287i	$0.797830\pi$
$858$	31.7100	+	11.5851i	1.08256	+	0.395507i
$859$	−47.4452			−1.61881			−0.809404	−	0.587252i	$-0.800210\pi$
$859$	−47.4452			−1.61881			−0.809404	+	0.587252i	$0.800210\pi$
$860$	−3.42492	+	2.48835i	−0.116789	+	0.0848521i
$861$	9.27474	+	28.5447i	0.316082	+	0.972801i
$862$	1.56442	−	4.81477i	0.0532842	−	0.163992i
$863$	−18.6189	−	13.5274i	−0.633795	−	0.460479i	0.223918	−	0.974608i	$-0.428115\pi$
$863$	−18.6189	−	13.5274i	−0.633795	−	0.460479i	−0.857713	+	0.514129i	$0.828115\pi$
$864$	4.19660	+	3.04901i	0.142771	+	0.103729i
$865$	−22.1902	+	68.2945i	−0.754490	+	2.32208i
$866$	−4.78070	−	14.7135i	−0.162455	−	0.499984i
$867$	18.3264	−	13.3149i	0.622396	−	0.452197i
$868$	−7.89679			−0.268035
$869$	−39.7557	+	11.3476i	−1.34862	+	0.384941i
$870$	7.15140			0.242455
$871$	32.3534	−	23.5061i	1.09625	−	0.796474i
$872$	1.13018	+	3.47834i	0.0382728	+	0.117791i
$873$	0.0317575	−	0.0977396i	0.00107483	−	0.00330798i
$874$	5.54021	+	4.02520i	0.187400	+	0.136154i
$875$	112.385	+	81.6527i	3.79931	+	2.76036i
$876$	−0.694126	+	2.13630i	−0.0234523	+	0.0721789i
$877$	−11.1383	−	34.2803i	−0.376115	−	1.15756i	−0.942723	−	0.333575i	$-0.891745\pi$
$877$	−11.1383	−	34.2803i	−0.376115	−	1.15756i	0.566609	−	0.823987i	$-0.308255\pi$
$878$	−13.4997	+	9.80809i	−0.455592	+	0.331007i
$879$	−21.4807			−0.724525
$880$	0.507029	−	14.0316i	0.0170919	−	0.473004i
$881$	53.5519			1.80421			0.902104	−	0.431518i	$-0.142022\pi$
$881$	53.5519			1.80421			0.902104	+	0.431518i	$0.142022\pi$
$882$	−0.0837494	+	0.0608475i	−0.00281999	+	0.00204884i
$883$	13.9459	+	42.9212i	0.469318	+	1.44441i	0.853469	+	0.521143i	$0.174494\pi$
$883$	13.9459	+	42.9212i	0.469318	+	1.44441i	−0.384151	+	0.923270i	$0.625506\pi$
$884$	−3.60031	+	11.0806i	−0.121092	+	0.372682i
$885$	15.8619	+	11.5243i	0.533191	+	0.387386i
$886$	7.96050	+	5.78364i	0.267438	+	0.194305i
$887$	3.85710	−	11.8709i	0.129509	−	0.398587i	−0.865187	−	0.501450i	$-0.832800\pi$
$887$	3.85710	−	11.8709i	0.129509	−	0.398587i	0.994696	+	0.102863i	$0.0328002\pi$
$888$	5.11508	+	15.7426i	0.171651	+	0.528287i
$889$	25.4819	−	18.5137i	0.854634	−	0.620928i
$890$	45.5217			1.52589
$891$	−18.4681	+	23.5791i	−0.618704	+	0.789929i
$892$	−1.35126			−0.0452437
$893$	48.6261	−	35.3289i	1.62721	−	1.18224i
$894$	10.3316	+	31.7974i	0.345540	+	1.06346i
$895$	−3.89418	+	11.9850i	−0.130168	+	0.400616i
$896$	−3.35105	−	2.43468i	−0.111951	−	0.0813371i
$897$	−7.79365	−	5.66242i	−0.260222	−	0.189063i
$898$	9.37094	−	28.8408i	0.312712	−	0.962430i
$899$	0.573601	+	1.76536i	0.0191307	+	0.0588782i
$900$	−0.106546	+	0.0774099i	−0.00355152	+	0.00258033i
$901$	−7.79990			−0.259853
$902$	−7.73170	−	11.4927i	−0.257437	−	0.382667i
$903$	−7.18656			−0.239154
$904$	−0.602297	+	0.437595i	−0.0200321	+	0.0145542i
$905$	−26.7770	−	82.4112i	−0.890098	−	2.73944i
$906$	3.58852	−	11.0443i	0.119220	−	0.366923i
$907$	32.0172	+	23.2618i	1.06311	+	0.772396i	0.974662	−	0.223684i	$-0.0718085\pi$
$907$	32.0172	+	23.2618i	1.06311	+	0.772396i	0.0884505	+	0.996081i	$0.471808\pi$
$908$	−1.89308	−	1.37541i	−0.0628242	−	0.0456444i
$909$	−0.0318463	+	0.0980129i	−0.00105628	+	0.00325088i
$910$	−31.7913	−	97.8435i	−1.05387	−	3.24348i
$911$	−8.88516	+	6.45545i	−0.294378	+	0.213878i	−0.725165	−	0.688576i	$-0.758236\pi$
$911$	−8.88516	+	6.45545i	−0.294378	+	0.213878i	0.430786	+	0.902454i	$0.358236\pi$
$912$	−12.5542			−0.415710
$913$	12.2910	+	18.2699i	0.406772	+	0.604645i
$914$	−23.7958			−0.787095
$915$	57.0699	−	41.4637i	1.88667	−	1.37075i
$916$	−0.510179	−	1.57017i	−0.0168568	−	0.0518799i
$917$	−20.8015	+	64.0204i	−0.686926	+	2.11414i
$918$	−8.33388	−	6.05492i	−0.275059	−	0.199842i
$919$	−18.3326	−	13.3194i	−0.604737	−	0.439367i	0.242820	−	0.970071i	$-0.421928\pi$
$919$	−18.3326	−	13.3194i	−0.604737	−	0.439367i	−0.847557	+	0.530704i	$0.821928\pi$
$920$	−1.23809	+	3.81045i	−0.0408187	+	0.125627i
$921$	16.2749	+	50.0891i	0.536277	+	1.65049i
$922$	−11.9775	+	8.70215i	−0.394458	+	0.286590i
$923$	26.3037			0.865798
$924$	14.6971	−	18.7645i	0.483500	−	0.617307i
$925$	123.283			4.05352
$926$	15.1575	−	11.0126i	0.498107	−	0.361896i
$927$	0.0503746	+	0.155037i	0.00165452	+	0.00509208i
$928$	−0.300873	+	0.925991i	−0.00987664	+	0.0303972i
$929$	−4.90316	−	3.56235i	−0.160867	−	0.116877i	0.504439	−	0.863447i	$-0.331699\pi$
$929$	−4.90316	−	3.56235i	−0.160867	−	0.116877i	−0.665307	+	0.746570i	$0.731699\pi$
$930$	−11.3286	−	8.23069i	−0.371478	−	0.269895i
$931$	−22.7117	+	69.8994i	−0.744345	+	2.29086i
$932$	−3.61986	−	11.1408i	−0.118572	−	0.364928i
$933$	23.4868	−	17.0642i	0.768924	−	0.558656i
$934$	−9.31101			−0.304666
$935$	−1.00689	+	27.8648i	−0.0329288	+	0.911275i
$936$	0.0597939			0.00195443
$937$	6.51892	−	4.73627i	0.212964	−	0.154727i	−0.476190	−	0.879342i	$-0.657982\pi$
$937$	6.51892	−	4.73627i	0.212964	−	0.154727i	0.689154	+	0.724615i	$0.257982\pi$
$938$	−8.72488	−	26.8524i	−0.284877	−	0.876762i
$939$	6.12840	−	18.8613i	0.199993	−	0.615515i
$940$	28.4493	+	20.6696i	0.927913	+	0.674168i
$941$	−24.2613	−	17.6269i	−0.790896	−	0.574619i	0.117333	−	0.993093i	$-0.462565\pi$
$941$	−24.2613	−	17.6269i	−0.790896	−	0.574619i	−0.908229	+	0.418473i	$0.862565\pi$
$942$	−9.65698	+	29.7211i	−0.314641	+	0.968366i
$943$	1.22140	+	3.75908i	0.0397743	+	0.122413i
$944$	−2.15955	+	1.56901i	−0.0702875	+	0.0510668i
$945$	90.9614			2.95898
$946$	3.18925	−	0.910319i	0.103691	−	0.0295970i
$947$	25.2629			0.820935			0.410468	−	0.911875i	$-0.365365\pi$
$947$	25.2629			0.820935			0.410468	+	0.911875i	$0.365365\pi$
$948$	−17.4971	+	12.7124i	−0.568278	+	0.412878i
$949$	−2.34720	−	7.22394i	−0.0761933	−	0.234499i
$950$	−28.8937	+	88.9257i	−0.937435	+	2.88513i
$951$	8.05924	+	5.85538i	0.261339	+	0.189874i
$952$	6.65473	+	4.83495i	0.215681	+	0.156701i
$953$	−11.2501	+	34.6242i	−0.364426	+	1.12159i	0.585914	+	0.810373i	$0.300736\pi$
$953$	−11.2501	+	34.6242i	−0.364426	+	1.12159i	−0.950340	+	0.311214i	$0.899264\pi$
$954$	0.0123700	+	0.0380710i	0.000400495	+	0.00123260i
$955$	12.9398	−	9.40129i	0.418721	−	0.304219i
$956$	−10.4491			−0.337949
$957$	−5.26245	−	1.92260i	−0.170111	−	0.0621490i
$958$	11.4461			0.369806
$959$	−5.56283	+	4.04163i	−0.179633	+	0.130511i
$960$	−2.26972	−	6.98549i	−0.0732550	−	0.225456i
$961$	−8.45638	+	26.0261i	−0.272786	+	0.839550i
$962$	−45.2835	−	32.9004i	−1.46000	−	1.06075i
$963$	0.0325548	+	0.0236524i	0.00104906	+	0.000762189i
$964$	5.31272	−	16.3509i	0.171111	−	0.526626i
$965$	1.78561	+	5.49555i	0.0574809	+	0.176908i
$966$	−5.50245	+	3.99776i	−0.177038	+	0.128626i
$967$	−23.1549			−0.744611			−0.372305	−	0.928110i	$-0.621433\pi$
$967$	−23.1549			−0.744611			−0.372305	+	0.928110i	$0.621433\pi$
$968$	−4.14539	+	10.1890i	−0.133238	+	0.327487i
$969$	24.9309			0.800895
$970$	34.5356	−	25.0916i	1.10887	−	0.805642i
$971$	−13.4766	−	41.4766i	−0.432483	−	1.33105i	−0.895644	−	0.444772i	$-0.853285\pi$
$971$	−13.4766	−	41.4766i	−0.432483	−	1.33105i	0.463160	−	0.886274i	$-0.346715\pi$
$972$	−0.0327296	+	0.100731i	−0.00104980	+	0.00323096i
$973$	−46.7805	−	33.9881i	−1.49972	−	1.08961i
$974$	2.80489	+	2.03787i	0.0898746	+	0.0652977i
$975$	40.6460	−	125.096i	1.30171	−	4.00626i
$976$	2.96785	+	9.13410i	0.0949985	+	0.292375i
$977$	−17.8190	+	12.9462i	−0.570079	+	0.414187i	−0.835134	−	0.550046i	$-0.814610\pi$
$977$	−17.8190	+	12.9462i	−0.570079	+	0.414187i	0.265055	+	0.964233i	$0.414610\pi$
$978$	−15.3237			−0.489998
$979$	−33.4977	−	12.2382i	−1.07059	−	0.391135i
$980$	−43.0001			−1.37359
$981$	−0.0301559	+	0.0219095i	−0.000962802	+	0.000699517i
$982$	11.1635	+	34.3576i	0.356241	+	1.09640i
$983$	−9.64044	+	29.6702i	−0.307482	+	0.946333i	0.671257	+	0.741225i	$0.265755\pi$
$983$	−9.64044	+	29.6702i	−0.307482	+	0.946333i	−0.978739	+	0.205108i	$0.934245\pi$
$984$	−5.86210	−	4.25906i	−0.186877	−	0.135774i
$985$	−68.8945	−	50.0548i	−2.19516	−	1.59488i
$986$	0.597492	−	1.83889i	0.0190280	−	0.0585622i
$987$	18.4469	+	56.7737i	0.587171	+	1.80713i
$988$	34.3445	−	24.9528i	1.09264	−	0.793853i
$989$	−0.946406			−0.0300939
$990$	0.137604	−	0.0392767i	0.00437333	−	0.00124830i
$991$	−31.1292			−0.988852			−0.494426	−	0.869220i	$-0.664622\pi$
$991$	−31.1292			−0.988852			−0.494426	+	0.869220i	$0.664622\pi$
$992$	1.54236	−	1.12059i	0.0489699	−	0.0355787i
$993$	−17.4083	−	53.5774i	−0.552437	−	1.70023i
$994$	5.73871	−	17.6619i	0.182021	−	0.560203i
$995$	70.6458	+	51.3272i	2.23962	+	1.62718i
$996$	9.31892	+	6.77059i	0.295281	+	0.214534i
$997$	−12.5899	+	38.7477i	−0.398726	+	1.22715i	0.527296	+	0.849682i	$0.323206\pi$
$997$	−12.5899	+	38.7477i	−0.398726	+	1.22715i	−0.926022	+	0.377470i	$0.876794\pi$
$998$	3.11381	+	9.58331i	0.0985658	+	0.303354i
$999$	40.0379	−	29.0892i	1.26674	−	0.920343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.g.861.6	yes	40
11.4	even	5	inner	946.2.f.g.345.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.g.345.6	✓	40	11.4	even	5	inner
946.2.f.g.861.6	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.536142 + 1.65007i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.42492 + 2.48835i) q^{5} +(-1.40364 - 1.01980i) q^{6} +(1.27999 - 3.93940i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.00824529 + 0.00599055i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.536142 + 1.65007i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.42492 + 2.48835i) q^{5} +(-1.40364 - 1.01980i) q^{6} +(1.27999 - 3.93940i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.00824529 + 0.00599055i) q^{9} -4.23344 q^{10} +(3.11523 + 1.13813i) q^{11} +1.73499 q^{12} +(-4.74642 + 3.44848i) q^{13} +(1.27999 + 3.93940i) q^{14} +(-2.26972 + 6.98549i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.60660 + 1.16726i) q^{17} +(0.00314942 - 0.00969292i) q^{18} +(-2.23601 - 6.88173i) q^{19} +(3.42492 - 2.48835i) q^{20} +7.18656 q^{21} +(-3.18925 + 0.910319i) q^{22} +0.946406 q^{23} +(-1.40364 + 1.01980i) q^{24} +(3.99312 + 12.2896i) q^{25} +(1.81297 - 5.57975i) q^{26} +(4.19660 + 3.04901i) q^{27} +(-3.35105 - 2.43468i) q^{28} +(-0.300873 + 0.925991i) q^{29} +(-2.26972 - 6.98549i) q^{30} +(1.54236 - 1.12059i) q^{31} +1.00000 q^{32} +(-0.207796 + 5.75056i) q^{33} -1.98586 q^{34} +(14.1865 - 10.3071i) q^{35} +(0.00314942 + 0.00969292i) q^{36} +(2.94819 - 9.07360i) q^{37} +(5.85395 + 4.25314i) q^{38} +(-8.23500 - 5.98308i) q^{39} +(-1.30820 + 4.02624i) q^{40} +(1.29057 + 3.97196i) q^{41} +(-5.81405 + 4.22415i) q^{42} -1.00000 q^{43} +(2.04509 - 2.61106i) q^{44} -0.0431461 q^{45} +(-0.765658 + 0.556283i) q^{46} +(2.56686 + 7.89999i) q^{47} +(0.536142 - 1.65007i) q^{48} +(-8.21738 - 5.97028i) q^{49} +(-10.4541 - 7.59536i) q^{50} +(-1.06470 + 3.27682i) q^{51} +(1.81297 + 5.57975i) q^{52} +(-3.17759 + 2.30865i) q^{53} -5.18729 q^{54} +(7.83735 + 11.6498i) q^{55} +4.14213 q^{56} +(10.1565 - 7.37916i) q^{57} +(-0.300873 - 0.925991i) q^{58} +(0.824876 - 2.53871i) q^{59} +(5.94221 + 4.31727i) q^{60} +(-7.76993 - 5.64518i) q^{61} +(-0.589128 + 1.81315i) q^{62} +(0.0130453 + 0.0401493i) q^{63} +(-0.809017 + 0.587785i) q^{64} -24.8372 q^{65} +(-3.21198 - 4.77444i) q^{66} -6.81637 q^{67} +(1.60660 - 1.16726i) q^{68} +(0.507407 + 1.56164i) q^{69} +(-5.41875 + 16.6772i) q^{70} +(-3.62716 - 2.63528i) q^{71} +(-0.00824529 - 0.00599055i) q^{72} +(-0.400075 + 1.23130i) q^{73} +(2.94819 + 9.07360i) q^{74} +(-18.1378 + 13.1779i) q^{75} -7.23588 q^{76} +(8.47101 - 10.8153i) q^{77} +10.1790 q^{78} +(-10.0848 + 7.32705i) q^{79} +(-1.30820 - 4.02624i) q^{80} +(-2.79057 + 8.58849i) q^{81} +(-3.37875 - 2.45481i) q^{82} +(5.37116 + 3.90238i) q^{83} +(2.22077 - 6.83482i) q^{84} +(2.59791 + 7.99556i) q^{85} +(0.809017 - 0.587785i) q^{86} -1.68926 q^{87} +(-0.119768 + 3.31446i) q^{88} -10.7529 q^{89} +(0.0349059 - 0.0253606i) q^{90} +(7.50957 + 23.1121i) q^{91} +(0.292455 - 0.900085i) q^{92} +(2.67597 + 1.94421i) q^{93} +(-6.72013 - 4.88246i) q^{94} +(9.46600 - 29.1334i) q^{95} +(0.536142 + 1.65007i) q^{96} +(-8.15781 + 5.92699i) q^{97} +10.1572 q^{98} +(-0.0325040 + 0.00927773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9}+O(q^{10}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 5 q^{14} - 23 q^{15} - 10 q^{16} - 5 q^{17} + 9 q^{18} - 21 q^{19} + 8 q^{20} + 20 q^{21} + 6 q^{22} + 24 q^{23} - 5 q^{24} - 16 q^{25} - 18 q^{26} - 10 q^{27} - 20 q^{28} + 7 q^{29} - 23 q^{30} - 15 q^{31} + 40 q^{32} + 36 q^{33} + 10 q^{34} + 50 q^{35} + 9 q^{36} + 2 q^{37} - 21 q^{38} - 70 q^{39} - 7 q^{40} - 20 q^{41} - 10 q^{42} - 40 q^{43} + 6 q^{44} - 14 q^{45} - q^{46} - 8 q^{47} + 5 q^{48} + 5 q^{49} - 11 q^{50} + 13 q^{51} - 18 q^{52} + 24 q^{53} + 38 q^{55} + 30 q^{56} + 62 q^{57} + 7 q^{58} - 27 q^{59} + 2 q^{60} - 49 q^{61} + 20 q^{62} - 5 q^{63} - 10 q^{64} - 4 q^{65} - 34 q^{66} - 26 q^{67} - 5 q^{68} + 73 q^{69} - 65 q^{70} - 5 q^{71} - 31 q^{72} + 22 q^{73} + 2 q^{74} - 60 q^{75} + 84 q^{76} - 20 q^{77} + 30 q^{78} + 81 q^{79} - 7 q^{80} - 38 q^{81} - 25 q^{82} + 3 q^{83} - 38 q^{85} + 10 q^{86} + 28 q^{87} - 14 q^{88} - 56 q^{89} - 4 q^{90} + 10 q^{91} - 11 q^{92} - 16 q^{93} - 23 q^{94} + 66 q^{95} + 5 q^{96} - 20 q^{97} + 50 q^{98} + 94 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 5 * q^14 - 23 * q^15 - 10 * q^16 - 5 * q^17 + 9 * q^18 - 21 * q^19 + 8 * q^20 + 20 * q^21 + 6 * q^22 + 24 * q^23 - 5 * q^24 - 16 * q^25 - 18 * q^26 - 10 * q^27 - 20 * q^28 + 7 * q^29 - 23 * q^30 - 15 * q^31 + 40 * q^32 + 36 * q^33 + 10 * q^34 + 50 * q^35 + 9 * q^36 + 2 * q^37 - 21 * q^38 - 70 * q^39 - 7 * q^40 - 20 * q^41 - 10 * q^42 - 40 * q^43 + 6 * q^44 - 14 * q^45 - q^46 - 8 * q^47 + 5 * q^48 + 5 * q^49 - 11 * q^50 + 13 * q^51 - 18 * q^52 + 24 * q^53 + 38 * q^55 + 30 * q^56 + 62 * q^57 + 7 * q^58 - 27 * q^59 + 2 * q^60 - 49 * q^61 + 20 * q^62 - 5 * q^63 - 10 * q^64 - 4 * q^65 - 34 * q^66 - 26 * q^67 - 5 * q^68 + 73 * q^69 - 65 * q^70 - 5 * q^71 - 31 * q^72 + 22 * q^73 + 2 * q^74 - 60 * q^75 + 84 * q^76 - 20 * q^77 + 30 * q^78 + 81 * q^79 - 7 * q^80 - 38 * q^81 - 25 * q^82 + 3 * q^83 - 38 * q^85 + 10 * q^86 + 28 * q^87 - 14 * q^88 - 56 * q^89 - 4 * q^90 + 10 * q^91 - 11 * q^92 - 16 * q^93 - 23 * q^94 + 66 * q^95 + 5 * q^96 - 20 * q^97 + 50 * q^98 + 94 * q^99

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