LMFDB - Embedded newform 31.2.c.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(5,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("31.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			5.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	31.5
Dual form			31.2.c.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} +(-0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.207107 - 0.358719i) q^{7} -1.58579 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+0.414214 q^{2} +(-0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.207107 - 0.358719i) q^{7} -1.58579 q^{8} +(1.41421 + 2.44949i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(-1.62132 - 2.80821i) q^{11} +(0.378680 - 0.655892i) q^{12} +(1.91421 + 3.31552i) q^{13} +(0.0857864 - 0.148586i) q^{14} +0.414214 q^{15} +3.00000 q^{16} +(2.91421 - 5.04757i) q^{17} +(0.585786 + 1.01461i) q^{18} +(-2.20711 + 3.82282i) q^{19} +(0.914214 + 1.58346i) q^{20} +(0.0857864 + 0.148586i) q^{21} +(-0.671573 - 1.16320i) q^{22} -4.00000 q^{23} +(0.328427 - 0.568852i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} -2.41421 q^{27} +(-0.378680 + 0.655892i) q^{28} -6.82843 q^{29} +0.171573 q^{30} +(-5.00000 + 2.44949i) q^{31} +4.41421 q^{32} +1.34315 q^{33} +(1.20711 - 2.09077i) q^{34} -0.414214 q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-0.914214 + 1.58346i) q^{38} -1.58579 q^{39} +(0.792893 + 1.37333i) q^{40} +(3.74264 + 6.48244i) q^{41} +(0.0355339 + 0.0615465i) q^{42} +(5.44975 - 9.43924i) q^{43} +(2.96447 + 5.13461i) q^{44} +(1.41421 - 2.44949i) q^{45} -1.65685 q^{46} +9.65685 q^{47} +(-0.621320 + 1.07616i) q^{48} +(3.41421 + 5.91359i) q^{49} +(0.828427 - 1.43488i) q^{50} +(1.20711 + 2.09077i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(-2.91421 - 5.04757i) q^{53} -1.00000 q^{54} +(-1.62132 + 2.80821i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} -2.82843 q^{58} +(-2.03553 + 3.52565i) q^{59} -0.757359 q^{60} -2.82843 q^{61} +(-2.07107 + 1.01461i) q^{62} +1.17157 q^{63} -4.17157 q^{64} +(1.91421 - 3.31552i) q^{65} +0.556349 q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(0.828427 - 1.43488i) q^{69} -0.171573 q^{70} +(-0.0355339 - 0.0615465i) q^{71} +(-2.24264 - 3.88437i) q^{72} +(0.914214 + 1.58346i) q^{73} +(-0.207107 + 0.358719i) q^{74} +(0.828427 + 1.43488i) q^{75} +(4.03553 - 6.98975i) q^{76} -1.34315 q^{77} -0.656854 q^{78} +(3.37868 - 5.85204i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(1.55025 + 2.68512i) q^{82} +(5.03553 + 8.72180i) q^{83} +(-0.156854 - 0.271680i) q^{84} -5.82843 q^{85} +(2.25736 - 3.90986i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +4.48528 q^{89} +(0.585786 - 1.01461i) q^{90} +1.58579 q^{91} +7.31371 q^{92} +(0.156854 - 2.30090i) q^{93} +4.00000 q^{94} +4.41421 q^{95} +(-0.914214 + 1.58346i) q^{96} +5.17157 q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} - 4 q^{15} + 12 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21} - 14 q^{22} - 16 q^{23} - 10 q^{24} + 8 q^{25} + 6 q^{26} - 4 q^{27} - 10 q^{28} - 16 q^{29} + 12 q^{30} - 20 q^{31} + 12 q^{32} + 28 q^{33} + 2 q^{34} + 4 q^{35} - 16 q^{36} - 2 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} + 16 q^{46} + 16 q^{47} + 6 q^{48} + 8 q^{49} - 8 q^{50} + 2 q^{51} - 14 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 10 q^{56} + 2 q^{57} + 6 q^{59} - 20 q^{60} + 20 q^{62} + 16 q^{63} - 28 q^{64} + 2 q^{65} - 60 q^{66} + 2 q^{67} - 10 q^{68} - 8 q^{69} - 12 q^{70} + 14 q^{71} + 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} + 2 q^{76} - 28 q^{77} + 20 q^{78} + 22 q^{79} - 6 q^{80} + 2 q^{81} + 26 q^{82} + 6 q^{83} + 22 q^{84} - 12 q^{85} + 26 q^{86} - 18 q^{88} - 16 q^{89} + 8 q^{90} + 12 q^{91} - 16 q^{92} - 22 q^{93} + 16 q^{94} + 12 q^{95} + 2 q^{96} + 32 q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 - 4 * q^15 + 12 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 - 16 * q^23 - 10 * q^24 + 8 * q^25 + 6 * q^26 - 4 * q^27 - 10 * q^28 - 16 * q^29 + 12 * q^30 - 20 * q^31 + 12 * q^32 + 28 * q^33 + 2 * q^34 + 4 * q^35 - 16 * q^36 - 2 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 + 16 * q^46 + 16 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 10 * q^56 + 2 * q^57 + 6 * q^59 - 20 * q^60 + 20 * q^62 + 16 * q^63 - 28 * q^64 + 2 * q^65 - 60 * q^66 + 2 * q^67 - 10 * q^68 - 8 * q^69 - 12 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 - 28 * q^77 + 20 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 - 12 * q^85 + 26 * q^86 - 18 * q^88 - 16 * q^89 + 8 * q^90 + 12 * q^91 - 16 * q^92 - 22 * q^93 + 16 * q^94 + 12 * q^95 + 2 * q^96 + 32 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.414214			0.292893			0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214			0.292893			0.146447	+	0.989219i	$0.453216\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$	−1.82843			−0.914214
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−0.0857864	+	0.148586i	−0.0350222	+	0.0606602i
$7$	0.207107	−	0.358719i	0.0782790	−	0.135583i	−0.824228	−	0.566257i	$-0.808391\pi$
$7$	0.207107	−	0.358719i	0.0782790	−	0.135583i	0.902507	+	0.430674i	$0.141724\pi$
$8$	−1.58579			−0.560660
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	−1.62132	−	2.80821i	−0.488846	−	0.846707i	0.511071	−	0.859538i	$-0.329249\pi$
$11$	−1.62132	−	2.80821i	−0.488846	−	0.846707i	−0.999918	+	0.0128314i	$0.995916\pi$
$12$	0.378680	−	0.655892i	0.109315	−	0.189340i
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	0.999349	+	0.0360643i	$0.0114821\pi$
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	−0.468442	+	0.883494i	$0.655185\pi$
$14$	0.0857864	−	0.148586i	0.0229274	−	0.0397114i
$15$	0.414214			0.106949
$16$	3.00000			0.750000
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	−0.259237	−	0.965814i	$-0.583471\pi$
$17$	2.91421	−	5.04757i	0.706801	−	1.22421i	0.966038	−	0.258401i	$-0.0831955\pi$
$18$	0.585786	+	1.01461i	0.138071	+	0.239146i
$19$	−2.20711	+	3.82282i	−0.506345	+	0.877015i	0.493628	+	0.869673i	$0.335670\pi$
$19$	−2.20711	+	3.82282i	−0.506345	+	0.877015i	−0.999973	+	0.00734216i	$0.997663\pi$
$20$	0.914214	+	1.58346i	0.204424	+	0.354073i
$21$	0.0857864	+	0.148586i	0.0187201	+	0.0324242i
$22$	−0.671573	−	1.16320i	−0.143180	−	0.247995i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	0.328427	−	0.568852i	0.0670399	−	0.116117i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	0.792893	+	1.37333i	0.155499	+	0.269332i
$27$	−2.41421			−0.464616
$28$	−0.378680	+	0.655892i	−0.0715637	+	0.123952i
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$	0.171573			0.0313248
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$32$	4.41421			0.780330
$33$	1.34315			0.233812
$34$	1.20711	−	2.09077i	0.207017	−	0.358564i
$35$	−0.414214			−0.0700149
$36$	−2.58579	−	4.47871i	−0.430964	−	0.746452i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	−0.914214	+	1.58346i	−0.148305	+	0.256872i
$39$	−1.58579			−0.253929
$40$	0.792893	+	1.37333i	0.125367	+	0.217143i
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	0.994937	+	0.100498i	$0.0320435\pi$
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	−0.410435	+	0.911890i	$0.634623\pi$
$42$	0.0355339	+	0.0615465i	0.00548300	+	0.00949684i
$43$	5.44975	−	9.43924i	0.831079	−	1.43947i	−0.0661049	−	0.997813i	$-0.521057\pi$
$43$	5.44975	−	9.43924i	0.831079	−	1.43947i	0.897184	−	0.441658i	$-0.145609\pi$
$44$	2.96447	+	5.13461i	0.446910	+	0.774071i
$45$	1.41421	−	2.44949i	0.210819	−	0.365148i
$46$	−1.65685			−0.244290
$47$	9.65685			1.40860			0.704298	−	0.709904i	$-0.251262\pi$
$47$	9.65685			1.40860			0.704298	+	0.709904i	$0.251262\pi$
$48$	−0.621320	+	1.07616i	−0.0896799	+	0.155330i
$49$	3.41421	+	5.91359i	0.487745	+	0.844799i
$50$	0.828427	−	1.43488i	0.117157	−	0.202922i
$51$	1.20711	+	2.09077i	0.169029	+	0.292766i
$52$	−3.50000	−	6.06218i	−0.485363	−	0.840673i
$53$	−2.91421	−	5.04757i	−0.400298	−	0.693337i	0.593464	−	0.804861i	$-0.297760\pi$
$53$	−2.91421	−	5.04757i	−0.400298	−	0.693337i	−0.993762	+	0.111524i	$0.964427\pi$
$54$	−1.00000			−0.136083
$55$	−1.62132	+	2.80821i	−0.218619	+	0.378659i
$56$	−0.328427	+	0.568852i	−0.0438879	+	0.0760161i
$57$	−0.914214	−	1.58346i	−0.121091	−	0.209735i
$58$	−2.82843			−0.371391
$59$	−2.03553	+	3.52565i	−0.265004	+	0.459000i	−0.967565	−	0.252624i	$-0.918707\pi$
$59$	−2.03553	+	3.52565i	−0.265004	+	0.459000i	0.702561	+	0.711624i	$0.252040\pi$
$60$	−0.757359			−0.0977747
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$	−2.07107	+	1.01461i	−0.263026	+	0.128856i
$63$	1.17157			0.147604
$64$	−4.17157			−0.521447
$65$	1.91421	−	3.31552i	0.237429	−	0.411239i
$66$	0.556349			0.0684819
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$	−5.32843	+	9.22911i	−0.646167	+	1.11919i
$69$	0.828427	−	1.43488i	0.0997309	−	0.172739i
$70$	−0.171573			−0.0205069
$71$	−0.0355339	−	0.0615465i	−0.00421710	−	0.00730423i	0.863909	−	0.503648i	$-0.168009\pi$
$71$	−0.0355339	−	0.0615465i	−0.00421710	−	0.00730423i	−0.868126	+	0.496343i	$0.834676\pi$
$72$	−2.24264	−	3.88437i	−0.264298	−	0.457777i
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	0.914554	−	0.404464i	$-0.132542\pi$
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	−0.807553	+	0.589795i	$0.799209\pi$
$74$	−0.207107	+	0.358719i	−0.0240757	+	0.0417003i
$75$	0.828427	+	1.43488i	0.0956585	+	0.165685i
$76$	4.03553	−	6.98975i	0.462907	−	0.801779i
$77$	−1.34315			−0.153066
$78$	−0.656854			−0.0743741
$79$	3.37868	−	5.85204i	0.380131	−	0.658406i	−0.610950	−	0.791670i	$-0.709212\pi$
$79$	3.37868	−	5.85204i	0.380131	−	0.658406i	0.991081	+	0.133263i	$0.0425455\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	1.55025	+	2.68512i	0.171197	+	0.296521i
$83$	5.03553	+	8.72180i	0.552722	+	0.957342i	0.998077	+	0.0619880i	$0.0197441\pi$
$83$	5.03553	+	8.72180i	0.552722	+	0.957342i	−0.445355	+	0.895354i	$0.646923\pi$
$84$	−0.156854	−	0.271680i	−0.0171142	−	0.0296427i
$85$	−5.82843			−0.632182
$86$	2.25736	−	3.90986i	0.243417	−	0.421611i
$87$	1.41421	−	2.44949i	0.151620	−	0.262613i
$88$	2.57107	+	4.45322i	0.274077	+	0.474715i
$89$	4.48528			0.475439			0.237719	−	0.971334i	$-0.423600\pi$
$89$	4.48528			0.475439			0.237719	+	0.971334i	$0.423600\pi$
$90$	0.585786	−	1.01461i	0.0617473	−	0.106949i
$91$	1.58579			0.166236
$92$	7.31371			0.762507
$93$	0.156854	−	2.30090i	0.0162650	−	0.238593i
$94$	4.00000			0.412568
$95$	4.41421			0.452889
$96$	−0.914214	+	1.58346i	−0.0933065	+	0.161612i
$97$	5.17157			0.525094			0.262547	−	0.964919i	$-0.415438\pi$
$97$	5.17157			0.525094			0.262547	+	0.964919i	$0.415438\pi$
$98$	1.41421	+	2.44949i	0.142857	+	0.247436i
$99$	4.58579	−	7.94282i	0.460889	−	0.798283i
$100$	−3.65685	+	6.33386i	−0.365685	+	0.633386i
$101$	−8.48528			−0.844317			−0.422159	−	0.906522i	$-0.638727\pi$
$101$	−8.48528			−0.844317			−0.422159	+	0.906522i	$0.638727\pi$
$102$	0.500000	+	0.866025i	0.0495074	+	0.0857493i
$103$	−1.03553	−	1.79360i	−0.102034	−	0.176728i	0.810488	−	0.585755i	$-0.199202\pi$
$103$	−1.03553	−	1.79360i	−0.102034	−	0.176728i	−0.912523	+	0.409026i	$0.865868\pi$
$104$	−3.03553	−	5.25770i	−0.297659	−	0.515560i
$105$	0.0857864	−	0.148586i	0.00837190	−	0.0145006i
$106$	−1.20711	−	2.09077i	−0.117245	−	0.203074i
$107$	−6.20711	+	10.7510i	−0.600064	+	1.03934i	0.392747	+	0.919646i	$0.371525\pi$
$107$	−6.20711	+	10.7510i	−0.600064	+	1.03934i	−0.992811	+	0.119694i	$0.961809\pi$
$108$	4.41421			0.424758
$109$	−10.8284			−1.03718			−0.518588	−	0.855024i	$-0.673542\pi$
$109$	−10.8284			−1.03718			−0.518588	+	0.855024i	$0.673542\pi$
$110$	−0.671573	+	1.16320i	−0.0640320	+	0.110907i
$111$	−0.207107	−	0.358719i	−0.0196577	−	0.0340481i
$112$	0.621320	−	1.07616i	0.0587093	−	0.101687i
$113$	−8.32843	−	14.4253i	−0.783473	−	1.35701i	−0.929907	−	0.367794i	$-0.880113\pi$
$113$	−8.32843	−	14.4253i	−0.783473	−	1.35701i	0.146435	−	0.989220i	$-0.453220\pi$
$114$	−0.378680	−	0.655892i	−0.0354666	−	0.0614300i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	12.4853			1.15923
$117$	−5.41421	+	9.37769i	−0.500544	+	0.866968i
$118$	−0.843146	+	1.46037i	−0.0776179	+	0.134438i
$119$	−1.20711	−	2.09077i	−0.110655	−	0.191661i
$120$	−0.656854			−0.0599623
$121$	0.242641	−	0.420266i	0.0220582	−	0.0382060i
$122$	−1.17157			−0.106069
$123$	−3.10051			−0.279563
$124$	9.14214	−	4.47871i	0.820988	−	0.402200i
$125$	−9.00000			−0.804984
$126$	0.485281			0.0432323
$127$	−4.44975	+	7.70719i	−0.394851	+	0.683902i	−0.993082	−	0.117421i	$-0.962537\pi$
$127$	−4.44975	+	7.70719i	−0.394851	+	0.683902i	0.598231	+	0.801324i	$0.295871\pi$
$128$	−10.5563			−0.933058
$129$	2.25736	+	3.90986i	0.198749	+	0.344244i
$130$	0.792893	−	1.37333i	0.0695413	−	0.120449i
$131$	6.62132	−	11.4685i	0.578507	−	1.00200i	−0.417143	−	0.908841i	$-0.636969\pi$
$131$	6.62132	−	11.4685i	0.578507	−	1.00200i	0.995651	−	0.0931636i	$-0.0296980\pi$
$132$	−2.45584			−0.213754
$133$	0.914214	+	1.58346i	0.0792724	+	0.137304i
$134$	−0.671573	−	1.16320i	−0.0580151	−	0.100485i
$135$	1.20711	+	2.09077i	0.103891	+	0.179945i
$136$	−4.62132	+	8.00436i	−0.396275	+	0.686368i
$137$	−4.74264	−	8.21449i	−0.405191	−	0.701812i	0.589153	−	0.808022i	$-0.299462\pi$
$137$	−4.74264	−	8.21449i	−0.405191	−	0.701812i	−0.994344	+	0.106210i	$0.966128\pi$
$138$	0.343146	−	0.594346i	0.0292105	−	0.0505941i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	0.757359			0.0640085
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	−0.0147186	−	0.0254934i	−0.00123516	−	0.00213936i
$143$	6.20711	−	10.7510i	0.519064	−	0.899046i
$144$	4.24264	+	7.34847i	0.353553	+	0.612372i
$145$	3.41421	+	5.91359i	0.283535	+	0.491097i
$146$	0.378680	+	0.655892i	0.0313398	+	0.0542820i
$147$	−2.82843			−0.233285
$148$	0.914214	−	1.58346i	0.0751479	−	0.130160i
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$	0.343146	+	0.594346i	0.0280177	+	0.0485281i
$151$	5.31371			0.432423			0.216212	−	0.976346i	$-0.430630\pi$
$151$	5.31371			0.432423			0.216212	+	0.976346i	$0.430630\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$	16.4853			1.33276
$154$	−0.556349			−0.0448319
$155$	4.62132	+	3.10538i	0.371193	+	0.249430i
$156$	2.89949			0.232145
$157$	9.17157			0.731971			0.365986	−	0.930621i	$-0.380732\pi$
$157$	9.17157			0.731971			0.365986	+	0.930621i	$0.380732\pi$
$158$	1.39949	−	2.42400i	0.111338	−	0.192843i
$159$	2.41421			0.191460
$160$	−2.20711	−	3.82282i	−0.174487	−	0.302221i
$161$	−0.828427	+	1.43488i	−0.0652892	+	0.113084i
$162$	−1.55025	+	2.68512i	−0.121799	+	0.210963i
$163$	20.9706			1.64254			0.821271	−	0.570539i	$-0.193266\pi$
$163$	20.9706			1.64254			0.821271	+	0.570539i	$0.193266\pi$
$164$	−6.84315	−	11.8527i	−0.534360	−	0.925539i
$165$	−0.671573	−	1.16320i	−0.0522819	−	0.0905549i
$166$	2.08579	+	3.61269i	0.161888	+	0.280399i
$167$	−11.2782	+	19.5344i	−0.872731	+	1.51162i	−0.0135714	+	0.999908i	$0.504320\pi$
$167$	−11.2782	+	19.5344i	−0.872731	+	1.51162i	−0.859160	+	0.511707i	$0.829013\pi$
$168$	−0.136039	−	0.235626i	−0.0104956	−	0.0181790i
$169$	−0.828427	+	1.43488i	−0.0637252	+	0.110375i
$170$	−2.41421			−0.185162
$171$	−12.4853			−0.954773
$172$	−9.96447	+	17.2590i	−0.759783	+	1.31598i
$173$	−4.15685	−	7.19988i	−0.316040	−	0.547397i	0.663618	−	0.748071i	$-0.269020\pi$
$173$	−4.15685	−	7.19988i	−0.316040	−	0.547397i	−0.979658	+	0.200674i	$0.935687\pi$
$174$	0.585786	−	1.01461i	0.0444084	−	0.0769175i
$175$	−0.828427	−	1.43488i	−0.0626232	−	0.108467i
$176$	−4.86396	−	8.42463i	−0.366635	−	0.635030i
$177$	−0.843146	−	1.46037i	−0.0633747	−	0.109768i
$178$	1.85786			0.139253
$179$	7.62132	−	13.2005i	0.569644	−	0.986653i	−0.426957	−	0.904272i	$-0.640414\pi$
$179$	7.62132	−	13.2005i	0.569644	−	0.986653i	0.996601	−	0.0823807i	$-0.0262523\pi$
$180$	−2.58579	+	4.47871i	−0.192733	+	0.333824i
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$	0.656854			0.0486893
$183$	0.585786	−	1.01461i	0.0433026	−	0.0750023i
$184$	6.34315			0.467623
$185$	1.00000			0.0735215
$186$	0.0649712	−	0.953065i	0.00476392	−	0.0698821i
$187$	−18.8995			−1.38207
$188$	−17.6569			−1.28776
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	1.82843			0.132648
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	0.944817	+	0.327599i	$0.106239\pi$
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	−0.188700	+	0.982035i	$0.560427\pi$
$192$	0.863961	−	1.49642i	0.0623510	−	0.107995i
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	−0.965451	−	0.260586i	$-0.916084\pi$
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	0.708400	+	0.705812i	$0.249418\pi$
$194$	2.14214			0.153796
$195$	0.792893	+	1.37333i	0.0567803	+	0.0983463i
$196$	−6.24264	−	10.8126i	−0.445903	−	0.772326i
$197$	6.74264	+	11.6786i	0.480393	+	0.832066i	0.999747	−	0.0224938i	$-0.00716061\pi$
$197$	6.74264	+	11.6786i	0.480393	+	0.832066i	−0.519354	+	0.854559i	$0.673827\pi$
$198$	1.89949	−	3.29002i	0.134991	−	0.233812i
$199$	−9.20711	−	15.9472i	−0.652674	−	1.13047i	−0.982471	−	0.186413i	$-0.940314\pi$
$199$	−9.20711	−	15.9472i	−0.652674	−	1.13047i	0.329797	−	0.944052i	$-0.393020\pi$
$200$	−3.17157	+	5.49333i	−0.224264	+	0.388437i
$201$	1.34315			0.0947382
$202$	−3.51472			−0.247295
$203$	−1.41421	+	2.44949i	−0.0992583	+	0.171920i
$204$	−2.20711	−	3.82282i	−0.154528	−	0.267651i
$205$	3.74264	−	6.48244i	0.261397	−	0.452754i
$206$	−0.428932	−	0.742932i	−0.0298851	−	0.0517625i
$207$	−5.65685	−	9.79796i	−0.393179	−	0.681005i
$208$	5.74264	+	9.94655i	0.398180	+	0.689669i
$209$	14.3137			0.990100
$210$	0.0355339	−	0.0615465i	0.00245207	−	0.00424711i
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	5.32843	+	9.22911i	0.365958	+	0.633858i
$213$	0.0294373			0.00201701
$214$	−2.57107	+	4.45322i	−0.175755	+	0.304416i
$215$	−10.8995			−0.743339
$216$	3.82843			0.260491
$217$	−0.156854	+	2.30090i	−0.0106480	+	0.156195i
$218$	−4.48528			−0.303782
$219$	−0.757359			−0.0511776
$220$	2.96447	−	5.13461i	0.199864	−	0.346175i
$221$	22.3137			1.50098
$222$	−0.0857864	−	0.148586i	−0.00575761	−	0.00997247i
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	−0.128706	−	0.991683i	$-0.541082\pi$
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	0.923175	−	0.384379i	$-0.125584\pi$
$224$	0.914214	−	1.58346i	0.0610835	−	0.105800i
$225$	11.3137			0.754247
$226$	−3.44975	−	5.97514i	−0.229474	−	0.397460i
$227$	9.20711	+	15.9472i	0.611097	+	1.05845i	0.991056	+	0.133448i	$0.0426049\pi$
$227$	9.20711	+	15.9472i	0.611097	+	1.05845i	−0.379959	+	0.925003i	$0.624062\pi$
$228$	1.67157	+	2.89525i	0.110703	+	0.191743i
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	−0.761064	−	0.648677i	$-0.775323\pi$
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	0.942303	+	0.334762i	$0.108656\pi$
$230$	0.828427	+	1.43488i	0.0546249	+	0.0946130i
$231$	0.278175	−	0.481813i	0.0183025	−	0.0317009i
$232$	10.8284			0.710921
$233$	−9.17157			−0.600850			−0.300425	−	0.953805i	$-0.597128\pi$
$233$	−9.17157			−0.600850			−0.300425	+	0.953805i	$0.597128\pi$
$234$	−2.24264	+	3.88437i	−0.146606	+	0.253929i
$235$	−4.82843	−	8.36308i	−0.314972	−	0.545547i
$236$	3.72183	−	6.44639i	0.242270	−	0.419624i
$237$	1.39949	+	2.42400i	0.0909070	+	0.157455i
$238$	−0.500000	−	0.866025i	−0.0324102	−	0.0561361i
$239$	10.6213	+	18.3967i	0.687036	+	1.18998i	0.972792	+	0.231679i	$0.0744219\pi$
$239$	10.6213	+	18.3967i	0.687036	+	1.18998i	−0.285756	+	0.958302i	$0.592245\pi$
$240$	1.24264			0.0802121
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	−0.996851	−	0.0792954i	$-0.974733\pi$
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	0.567097	+	0.823651i	$0.308066\pi$
$242$	0.100505	−	0.174080i	0.00646071	−	0.0111903i
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$	5.17157			0.331076
$245$	3.41421	−	5.91359i	0.218126	−	0.377805i
$246$	−1.28427			−0.0818821
$247$	−16.8995			−1.07529
$248$	7.92893	−	3.88437i	0.503488	−	0.246658i
$249$	−4.17157			−0.264363
$250$	−3.72792			−0.235774
$251$	−3.20711	+	5.55487i	−0.202431	+	0.350620i	−0.949311	−	0.314338i	$-0.898217\pi$
$251$	−3.20711	+	5.55487i	−0.202431	+	0.350620i	0.746880	+	0.664958i	$0.231551\pi$
$252$	−2.14214			−0.134942
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$	−1.84315	+	3.19242i	−0.115649	+	0.200310i
$255$	1.20711	−	2.09077i	0.0755920	−	0.130929i
$256$	3.97056			0.248160
$257$	−11.1569	−	19.3242i	−0.695945	−	1.20541i	−0.969861	−	0.243659i	$-0.921652\pi$
$257$	−11.1569	−	19.3242i	−0.695945	−	1.20541i	0.273915	−	0.961754i	$-0.411681\pi$
$258$	0.935029	+	1.61952i	0.0582124	+	0.100827i
$259$	0.207107	+	0.358719i	0.0128690	+	0.0222897i
$260$	−3.50000	+	6.06218i	−0.217061	+	0.375960i
$261$	−9.65685	−	16.7262i	−0.597744	−	1.03532i
$262$	2.74264	−	4.75039i	0.169441	−	0.293480i
$263$	−23.3137			−1.43758			−0.718792	−	0.695225i	$-0.755305\pi$
$263$	−23.3137			−1.43758			−0.718792	+	0.695225i	$0.755305\pi$
$264$	−2.12994			−0.131089
$265$	−2.91421	+	5.04757i	−0.179019	+	0.310070i
$266$	0.378680	+	0.655892i	0.0232183	+	0.0402153i
$267$	−0.928932	+	1.60896i	−0.0568497	+	0.0984666i
$268$	2.96447	+	5.13461i	0.181084	+	0.313646i
$269$	13.0858	+	22.6652i	0.797854	+	1.38192i	0.921011	+	0.389537i	$0.127365\pi$
$269$	13.0858	+	22.6652i	0.797854	+	1.38192i	−0.123156	+	0.992387i	$0.539302\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−0.686292			−0.0416892			−0.0208446	−	0.999783i	$-0.506636\pi$
$271$	−0.686292			−0.0416892			−0.0208446	+	0.999783i	$0.506636\pi$
$272$	8.74264	−	15.1427i	0.530100	−	0.918161i
$273$	−0.328427	+	0.568852i	−0.0198773	+	0.0344285i
$274$	−1.96447	−	3.40256i	−0.118678	−	0.205556i
$275$	−12.9706			−0.782154
$276$	−1.51472	+	2.62357i	−0.0911753	+	0.157920i
$277$	14.1421			0.849719			0.424859	−	0.905259i	$-0.360324\pi$
$277$	14.1421			0.849719			0.424859	+	0.905259i	$0.360324\pi$
$278$		0			0
$279$	−13.0711	−	8.78335i	−0.782544	−	0.525845i
$280$	0.656854			0.0392545
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−0.828427	+	1.43488i	−0.0493321	+	0.0854457i
$283$	−13.6569			−0.811816			−0.405908	−	0.913914i	$-0.633045\pi$
$283$	−13.6569			−0.811816			−0.405908	+	0.913914i	$0.633045\pi$
$284$	0.0649712	+	0.112533i	0.00385533	+	0.00667763i
$285$	−0.914214	+	1.58346i	−0.0541533	+	0.0937963i
$286$	2.57107	−	4.45322i	0.152030	−	0.263324i
$287$	3.10051			0.183017
$288$	6.24264	+	10.8126i	0.367851	+	0.637137i
$289$	−8.48528	−	14.6969i	−0.499134	−	0.864526i
$290$	1.41421	+	2.44949i	0.0830455	+	0.143839i
$291$	−1.07107	+	1.85514i	−0.0627871	+	0.108750i
$292$	−1.67157	−	2.89525i	−0.0978214	−	0.169432i
$293$	−7.39949	+	12.8163i	−0.432283	+	0.748736i	−0.997070	−	0.0765008i	$-0.975625\pi$
$293$	−7.39949	+	12.8163i	−0.432283	+	0.748736i	0.564786	+	0.825237i	$0.308959\pi$
$294$	−1.17157			−0.0683275
$295$	4.07107			0.237027
$296$	0.792893	−	1.37333i	0.0460860	−	0.0798233i
$297$	3.91421	+	6.77962i	0.227126	+	0.393393i
$298$	−0.207107	+	0.358719i	−0.0119974	+	0.0207801i
$299$	−7.65685	−	13.2621i	−0.442807	−	0.766965i
$300$	−1.51472	−	2.62357i	−0.0874523	−	0.151472i
$301$	−2.25736	−	3.90986i	−0.130112	−	0.225361i
$302$	2.20101			0.126654
$303$	1.75736	−	3.04384i	0.100958	−	0.174864i
$304$	−6.62132	+	11.4685i	−0.379759	+	0.657761i
$305$	1.41421	+	2.44949i	0.0809776	+	0.140257i
$306$	6.82843			0.390355
$307$	5.62132	−	9.73641i	0.320826	−	0.555686i	−0.659833	−	0.751412i	$-0.729373\pi$
$307$	5.62132	−	9.73641i	0.320826	−	0.555686i	0.980659	+	0.195726i	$0.0627063\pi$
$308$	2.45584			0.139935
$309$	0.857864			0.0488022
$310$	1.91421	+	1.28629i	0.108720	+	0.0730564i
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$	2.51472			0.142368
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	−0.839031	−	0.544083i	$-0.816878\pi$
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	0.890706	+	0.454581i	$0.150211\pi$
$314$	3.79899			0.214389
$315$	−0.585786	−	1.01461i	−0.0330053	−	0.0571669i
$316$	−6.17767	+	10.7000i	−0.347521	+	0.601924i
$317$	3.91421	−	6.77962i	0.219844	−	0.380781i	−0.734916	−	0.678158i	$-0.762778\pi$
$317$	3.91421	−	6.77962i	0.219844	−	0.380781i	0.954760	+	0.297377i	$0.0961118\pi$
$318$	1.00000			0.0560772
$319$	11.0711	+	19.1757i	0.619861	+	1.07363i
$320$	2.08579	+	3.61269i	0.116599	+	0.201955i
$321$	−2.57107	−	4.45322i	−0.143503	−	0.248555i
$322$	−0.343146	+	0.594346i	−0.0191228	+	0.0331216i
$323$	12.8640	+	22.2810i	0.715770	+	1.23975i
$324$	6.84315	−	11.8527i	0.380175	−	0.658482i
$325$	15.3137			0.849452
$326$	8.68629			0.481089
$327$	2.24264	−	3.88437i	0.124018	−	0.214806i
$328$	−5.93503	−	10.2798i	−0.327707	−	0.567605i
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$	−0.278175	−	0.481813i	−0.0153130	−	0.0265229i
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	0.710616	−	0.703580i	$-0.248417\pi$
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	−0.964626	+	0.263621i	$0.915083\pi$
$332$	−9.20711	−	15.9472i	−0.505306	−	0.875215i
$333$	−2.82843			−0.154997
$334$	−4.67157	+	8.09140i	−0.255617	+	0.442742i
$335$	−1.62132	+	2.80821i	−0.0885822	+	0.153429i
$336$	0.257359	+	0.445759i	0.0140401	+	0.0243182i
$337$	9.31371			0.507350			0.253675	−	0.967290i	$-0.418361\pi$
$337$	9.31371			0.507350			0.253675	+	0.967290i	$0.418361\pi$
$338$	−0.343146	+	0.594346i	−0.0186647	+	0.0323282i
$339$	6.89949			0.374729
$340$	10.6569			0.577949
$341$	14.9853	+	10.0696i	0.811498	+	0.545301i
$342$	−5.17157			−0.279647
$343$	5.72792			0.309279
$344$	−8.64214	+	14.9686i	−0.465953	+	0.807054i
$345$	−1.65685			−0.0892020
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	−0.728044	−	0.685530i	$-0.759570\pi$
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	0.957709	+	0.287740i	$0.0929038\pi$
$348$	−2.58579	+	4.47871i	−0.138613	+	0.240084i
$349$	−27.1127			−1.45131			−0.725655	−	0.688059i	$-0.758463\pi$
$349$	−27.1127			−1.45131			−0.725655	+	0.688059i	$0.758463\pi$
$350$	−0.343146	−	0.594346i	−0.0183419	−	0.0317691i
$351$	−4.62132	−	8.00436i	−0.246668	−	0.427241i
$352$	−7.15685	−	12.3960i	−0.381462	−	0.660711i
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$	−0.349242	−	0.604906i	−0.0185620	−	0.0321504i
$355$	−0.0355339	+	0.0615465i	−0.00188594	+	0.00326655i
$356$	−8.20101			−0.434653
$357$	1.00000			0.0529256
$358$	3.15685	−	5.46783i	0.166845	−	0.288984i
$359$	−3.55025	−	6.14922i	−0.187375	−	0.324543i	0.756999	−	0.653416i	$-0.226665\pi$
$359$	−3.55025	−	6.14922i	−0.187375	−	0.324543i	−0.944374	+	0.328873i	$0.893331\pi$
$360$	−2.24264	+	3.88437i	−0.118198	+	0.204724i
$361$	−0.242641	−	0.420266i	−0.0127706	−	0.0221193i
$362$	−2.55025	−	4.41717i	−0.134038	−	0.232161i
$363$	0.100505	+	0.174080i	0.00527515	+	0.00913682i
$364$	−2.89949			−0.151975
$365$	0.914214	−	1.58346i	0.0478521	−	0.0828823i
$366$	0.242641	−	0.420266i	0.0126830	−	0.0219677i
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	0.987151	+	0.159792i	$0.0510824\pi$
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	−0.355191	+	0.934794i	$0.615584\pi$
$368$	−12.0000			−0.625543
$369$	−10.5858	+	18.3351i	−0.551074	+	0.954488i
$370$	0.414214			0.0215339
$371$	−2.41421			−0.125340
$372$	−0.286797	+	4.20703i	−0.0148697	+	0.218125i
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−7.82843			−0.404798
$375$	1.86396	−	3.22848i	0.0962545	−	0.166718i
$376$	−15.3137			−0.789744
$377$	−13.0711	−	22.6398i	−0.673194	−	1.16601i
$378$	−0.207107	+	0.358719i	−0.0106524	+	0.0184505i
$379$	−3.69239	+	6.39540i	−0.189665	+	0.328510i	−0.945139	−	0.326669i	$-0.894074\pi$
$379$	−3.69239	+	6.39540i	−0.189665	+	0.328510i	0.755473	+	0.655179i	$0.227407\pi$
$380$	−8.07107			−0.414037
$381$	−1.84315	−	3.19242i	−0.0944272	−	0.163553i
$382$	4.32843	+	7.49706i	0.221462	+	0.383583i
$383$	−2.55025	−	4.41717i	−0.130312	−	0.225707i	0.793485	−	0.608590i	$-0.208265\pi$
$383$	−2.55025	−	4.41717i	−0.130312	−	0.225707i	−0.923797	+	0.382883i	$0.874931\pi$
$384$	2.18629	−	3.78677i	0.111569	−	0.193243i
$385$	0.671573	+	1.16320i	0.0342265	+	0.0592821i
$386$	−1.47918	+	2.56202i	−0.0752885	+	0.130404i
$387$	30.8284			1.56710
$388$	−9.45584			−0.480048
$389$	5.57107	−	9.64937i	0.282464	−	0.489243i	−0.689527	−	0.724260i	$-0.742181\pi$
$389$	5.57107	−	9.64937i	0.282464	−	0.489243i	0.971991	+	0.235018i	$0.0755148\pi$
$390$	0.328427	+	0.568852i	0.0166306	+	0.0288050i
$391$	−11.6569	+	20.1903i	−0.589512	+	1.02107i
$392$	−5.41421	−	9.37769i	−0.273459	−	0.473645i
$393$	2.74264	+	4.75039i	0.138348	+	0.239626i
$394$	2.79289	+	4.83743i	0.140704	+	0.243706i
$395$	−6.75736			−0.340000
$396$	−8.38478	+	14.5229i	−0.421351	+	0.729801i
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$	−3.81371	−	6.60554i	−0.191164	−	0.331106i
$399$	−0.757359			−0.0379154
$400$	6.00000	−	10.3923i	0.300000	−	0.519615i
$401$	−26.8284			−1.33975			−0.669874	−	0.742475i	$-0.733652\pi$
$401$	−26.8284			−1.33975			−0.669874	+	0.742475i	$0.733652\pi$
$402$	0.556349			0.0277482
$403$	−17.6924	−	11.8887i	−0.881321	−	0.592220i
$404$	15.5147			0.771886
$405$	7.48528			0.371947
$406$	−0.585786	+	1.01461i	−0.0290721	+	0.0503543i
$407$	3.24264			0.160732
$408$	−1.91421	−	3.31552i	−0.0947677	−	0.164142i
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	0.489215	+	0.872163i	$0.337283\pi$
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	−0.999923	+	0.0124088i	$0.996050\pi$
$410$	1.55025	−	2.68512i	0.0765615	−	0.132608i
$411$	3.92893			0.193800
$412$	1.89340	+	3.27946i	0.0932810	+	0.161567i
$413$	0.843146	+	1.46037i	0.0414885	+	0.0718602i
$414$	−2.34315	−	4.05845i	−0.115159	−	0.199462i
$415$	5.03553	−	8.72180i	0.247185	−	0.428136i
$416$	8.44975	+	14.6354i	0.414283	+	0.717559i
$417$		0			0
$418$	5.92893			0.289994
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$	−0.156854	+	0.271680i	−0.00765370	+	0.0132566i
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	0.943418	+	0.331605i	$0.107590\pi$
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	−0.184531	+	0.982827i	$0.559077\pi$
$422$	−2.15685	+	3.73578i	−0.104994	+	0.181855i
$423$	13.6569	+	23.6544i	0.664019	+	1.15011i
$424$	4.62132	+	8.00436i	0.224431	+	0.388726i
$425$	−11.6569	−	20.1903i	−0.565440	−	0.979372i
$426$	0.0121933			0.000590768
$427$	−0.585786	+	1.01461i	−0.0283482	+	0.0491005i
$428$	11.3492	−	19.6575i	0.548586	−	0.950179i
$429$	2.57107	+	4.45322i	0.124132	+	0.215003i
$430$	−4.51472			−0.217719
$431$	8.37868	−	14.5123i	0.403587	−	0.699033i	−0.590569	−	0.806987i	$-0.701097\pi$
$431$	8.37868	−	14.5123i	0.403587	−	0.699033i	0.994156	+	0.107954i	$0.0344300\pi$
$432$	−7.24264			−0.348462
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$	−0.0649712	+	0.953065i	−0.00311872	+	0.0457486i
$435$	−2.82843			−0.135613
$436$	19.7990			0.948200
$437$	8.82843	−	15.2913i	0.422321	−	0.731481i
$438$	−0.313708			−0.0149896
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	0.840255	−	0.542191i	$-0.182405\pi$
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	−0.889679	+	0.456587i	$0.849072\pi$
$440$	2.57107	−	4.45322i	0.122571	−	0.212299i
$441$	−9.65685	+	16.7262i	−0.459850	+	0.796484i
$442$	9.24264			0.439628
$443$	2.37868	+	4.11999i	0.113014	+	0.195747i	0.916984	−	0.398923i	$-0.130616\pi$
$443$	2.37868	+	4.11999i	0.113014	+	0.195747i	−0.803970	+	0.594670i	$0.797283\pi$
$444$	0.378680	+	0.655892i	0.0179713	+	0.0311273i
$445$	−2.24264	−	3.88437i	−0.106311	−	0.184137i
$446$	4.91421	−	8.51167i	0.232695	−	0.403039i
$447$	−0.207107	−	0.358719i	−0.00979581	−	0.0169668i
$448$	−0.863961	+	1.49642i	−0.0408183	+	0.0706994i
$449$	−40.6274			−1.91733			−0.958663	−	0.284543i	$-0.908158\pi$
$449$	−40.6274			−1.91733			−0.958663	+	0.284543i	$0.908158\pi$
$450$	4.68629			0.220914
$451$	12.1360	−	21.0202i	0.571464	−	0.989804i
$452$	15.2279	+	26.3755i	0.716261	+	1.24060i
$453$	−1.10051	+	1.90613i	−0.0517062	+	0.0895578i
$454$	3.81371	+	6.60554i	0.178986	+	0.310013i
$455$	−0.792893	−	1.37333i	−0.0371714	−	0.0643828i
$456$	1.44975	+	2.51104i	0.0678906	+	0.117590i
$457$	−31.1127			−1.45539			−0.727695	−	0.685901i	$-0.759409\pi$
$457$	−31.1127			−1.45539			−0.727695	+	0.685901i	$0.759409\pi$
$458$	1.13604	−	1.96768i	0.0530836	−	0.0919435i
$459$	−7.03553	+	12.1859i	−0.328391	+	0.568789i
$460$	−3.65685	−	6.33386i	−0.170502	−	0.295318i
$461$	−2.14214			−0.0997692			−0.0498846	−	0.998755i	$-0.515885\pi$
$461$	−2.14214			−0.0997692			−0.0498846	+	0.998755i	$0.515885\pi$
$462$	0.115224	−	0.199573i	0.00536069	−	0.00928499i
$463$	−8.97056			−0.416897			−0.208449	−	0.978033i	$-0.566841\pi$
$463$	−8.97056			−0.416897			−0.208449	+	0.978033i	$0.566841\pi$
$464$	−20.4853			−0.951005
$465$	−2.07107	+	1.01461i	−0.0960435	+	0.0470515i
$466$	−3.79899			−0.175985
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	9.89949	−	17.1464i	0.457604	−	0.792594i
$469$	−1.34315			−0.0620207
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	−1.89949	+	3.29002i	−0.0875241	+	0.151596i
$472$	3.22792	−	5.59093i	0.148577	−	0.257343i
$473$	−35.3431			−1.62508
$474$	0.579690	+	1.00405i	0.0266260	+	0.0461176i
$475$	8.82843	+	15.2913i	0.405076	+	0.701612i
$476$	2.20711	+	3.82282i	0.101163	+	0.175219i
$477$	8.24264	−	14.2767i	0.377405	−	0.653684i
$478$	4.39949	+	7.62015i	0.201228	+	0.348537i
$479$	7.86396	−	13.6208i	0.359314	−	0.622349i	−0.628533	−	0.777783i	$-0.716344\pi$
$479$	7.86396	−	13.6208i	0.359314	−	0.622349i	0.987846	+	0.155434i	$0.0496775\pi$
$480$	1.82843			0.0834559
$481$	−3.82843			−0.174561
$482$	−2.76346	+	4.78645i	−0.125872	+	0.218017i
$483$	−0.343146	−	0.594346i	−0.0156137	−	0.0270437i
$484$	−0.443651	+	0.768426i	−0.0201659	+	0.0349284i
$485$	−2.58579	−	4.47871i	−0.117415	−	0.203368i
$486$	−2.14214	−	3.71029i	−0.0971692	−	0.168302i
$487$	−9.69239	−	16.7877i	−0.439204	−	0.760724i	0.558424	−	0.829556i	$-0.311406\pi$
$487$	−9.69239	−	16.7877i	−0.439204	−	0.760724i	−0.997628	+	0.0688318i	$0.978073\pi$
$488$	4.48528			0.203039
$489$	−4.34315	+	7.52255i	−0.196404	+	0.340181i
$490$	1.41421	−	2.44949i	0.0638877	−	0.110657i
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	0.847579	−	0.530669i	$-0.178059\pi$
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	−0.883362	+	0.468691i	$0.844726\pi$
$492$	5.66905			0.255580
$493$	−19.8995	+	34.4669i	−0.896228	+	1.55231i
$494$	−7.00000			−0.314945
$495$	−9.17157			−0.412232
$496$	−15.0000	+	7.34847i	−0.673520	+	0.329956i
$497$	−0.0294373			−0.00132044
$498$	−1.72792			−0.0774300
$499$	1.10660	−	1.91669i	0.0495383	−	0.0858028i	−0.840193	−	0.542288i	$-0.817558\pi$
$499$	1.10660	−	1.91669i	0.0495383	−	0.0858028i	0.889731	+	0.456485i	$0.150892\pi$
$500$	16.4558			0.735928
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$	−1.32843	+	2.30090i	−0.0592906	+	0.102694i
$503$	6.69239	−	11.5916i	0.298399	−	0.516842i	−0.677371	−	0.735642i	$-0.736881\pi$
$503$	6.69239	−	11.5916i	0.298399	−	0.516842i	0.975770	+	0.218800i	$0.0702141\pi$
$504$	−1.85786			−0.0827559
$505$	4.24264	+	7.34847i	0.188795	+	0.327003i
$506$	2.68629	+	4.65279i	0.119420	+	0.206842i
$507$	−0.343146	−	0.594346i	−0.0152396	−	0.0263958i
$508$	8.13604	−	14.0920i	0.360978	−	0.625233i
$509$	16.3995	+	28.4048i	0.726895	+	1.25902i	0.958189	+	0.286135i	$0.0923706\pi$
$509$	16.3995	+	28.4048i	0.726895	+	1.25902i	−0.231294	+	0.972884i	$0.574296\pi$
$510$	0.500000	−	0.866025i	0.0221404	−	0.0383482i
$511$	0.757359			0.0335036
$512$	22.7574			1.00574
$513$	5.32843	−	9.22911i	0.235256	−	0.407475i
$514$	−4.62132	−	8.00436i	−0.203838	−	0.353057i
$515$	−1.03553	+	1.79360i	−0.0456311	+	0.0790353i
$516$	−4.12742	−	7.14890i	−0.181699	−	0.314713i
$517$	−15.6569	−	27.1185i	−0.688588	−	1.19267i
$518$	0.0857864	+	0.148586i	0.00376924	+	0.00652851i
$519$	3.44365			0.151159
$520$	−3.03553	+	5.25770i	−0.133117	+	0.230565i
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	−8.00000			−0.349816			−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000			−0.349816			−0.174908	+	0.984585i	$0.555963\pi$
$524$	−12.1066	+	20.9692i	−0.528879	+	0.916046i
$525$	0.686292			0.0299522
$526$	−9.65685			−0.421059
$527$	−2.20711	+	32.3762i	−0.0961431	+	1.41033i
$528$	4.02944			0.175359
$529$	−7.00000			−0.304348
$530$	−1.20711	+	2.09077i	−0.0524334	+	0.0908173i
$531$	−11.5147			−0.499696
$532$	−1.67157	−	2.89525i	−0.0724719	−	0.125525i
$533$	−14.3284	+	24.8176i	−0.620633	+	1.07497i
$534$	−0.384776	+	0.666452i	−0.0166509	+	0.0288402i
$535$	12.4142			0.536713
$536$	2.57107	+	4.45322i	0.111053	+	0.192350i
$537$	3.15685	+	5.46783i	0.136228	+	0.235954i
$538$	5.42031	+	9.38825i	0.233686	+	0.404756i
$539$	11.0711	−	19.1757i	0.476865	−	0.825954i
$540$	−2.20711	−	3.82282i	−0.0949788	−	0.164508i
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	−0.304683	−	0.952454i	$-0.598550\pi$
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	0.977191	−	0.212364i	$-0.0681162\pi$
$542$	−0.284271			−0.0122105
$543$	5.10051			0.218884
$544$	12.8640	−	22.2810i	0.551538	−	0.955291i
$545$	5.41421	+	9.37769i	0.231919	+	0.401696i
$546$	−0.136039	+	0.235626i	−0.00582193	+	0.0100839i
$547$	9.86396	+	17.0849i	0.421753	+	0.730497i	0.996111	−	0.0881071i	$-0.0280818\pi$
$547$	9.86396	+	17.0849i	0.421753	+	0.730497i	−0.574358	+	0.818604i	$0.694748\pi$
$548$	8.67157	+	15.0196i	0.370431	+	0.641606i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	−5.37258			−0.229088
$551$	15.0711	−	26.1039i	0.642049	−	1.11206i
$552$	−1.31371	+	2.27541i	−0.0559151	+	0.0968479i
$553$	−1.39949	−	2.42400i	−0.0595126	−	0.103079i
$554$	5.85786			0.248877
$555$	−0.207107	+	0.358719i	−0.00879119	+	0.0152268i
$556$		0			0
$557$	27.5147			1.16584			0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147			1.16584			0.582918	+	0.812531i	$0.301911\pi$
$558$	−5.41421	−	3.63818i	−0.229202	−	0.154017i
$559$	41.7279			1.76490
$560$	−1.24264			−0.0525112
$561$	3.91421	−	6.77962i	0.165258	−	0.286236i
$562$	0.828427			0.0349451
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	0.692095	−	0.721807i	$-0.256688\pi$
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	−0.971150	+	0.238468i	$0.923355\pi$
$564$	3.65685	−	6.33386i	0.153981	−	0.266704i
$565$	−8.32843	+	14.4253i	−0.350380	+	0.606875i
$566$	−5.65685			−0.237775
$567$	1.55025	+	2.68512i	0.0651045	+	0.112764i
$568$	0.0563492	+	0.0975997i	0.00236436	+	0.00409519i
$569$	6.57107	+	11.3814i	0.275473	+	0.477134i	0.970254	−	0.242087i	$-0.0778320\pi$
$569$	6.57107	+	11.3814i	0.275473	+	0.477134i	−0.694781	+	0.719221i	$0.744499\pi$
$570$	−0.378680	+	0.655892i	−0.0158611	+	0.0274723i
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	0.997802	−	0.0662645i	$-0.0211081\pi$
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	−0.556288	+	0.830990i	$0.687775\pi$
$572$	−11.3492	+	19.6575i	−0.474536	+	0.821920i
$573$	−8.65685			−0.361645
$574$	1.28427			0.0536044
$575$	−8.00000	+	13.8564i	−0.333623	+	0.577852i
$576$	−5.89949	−	10.2182i	−0.245812	−	0.425759i
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	−0.865719	−	0.500531i	$-0.833138\pi$
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	0.866332	+	0.499469i	$0.166472\pi$
$578$	−3.51472	−	6.08767i	−0.146193	−	0.253214i
$579$	−1.47918	−	2.56202i	−0.0614728	−	0.106474i
$580$	−6.24264	−	10.8126i	−0.259212	−	0.448968i
$581$	4.17157			0.173066
$582$	−0.443651	+	0.768426i	−0.0183899	+	0.0318523i
$583$	−9.44975	+	16.3674i	−0.391369	+	0.677870i
$584$	−1.44975	−	2.51104i	−0.0599910	−	0.103907i
$585$	10.8284			0.447700
$586$	−3.06497	+	5.30869i	−0.126613	+	0.219300i
$587$	−31.6569			−1.30662			−0.653309	−	0.757091i	$-0.726620\pi$
$587$	−31.6569			−1.30662			−0.653309	+	0.757091i	$0.726620\pi$
$588$	5.17157			0.213272
$589$	1.67157	−	24.5204i	0.0688760	−	1.01035i
$590$	1.68629			0.0694235
$591$	−5.58579			−0.229769
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	−1.31371			−0.0539475			−0.0269738	−	0.999636i	$-0.508587\pi$
$593$	−1.31371			−0.0539475			−0.0269738	+	0.999636i	$0.508587\pi$
$594$	1.62132	+	2.80821i	0.0665236	+	0.115222i
$595$	−1.20711	+	2.09077i	−0.0494866	+	0.0857132i
$596$	0.914214	−	1.58346i	0.0374476	−	0.0648612i
$597$	7.62742			0.312169
$598$	−3.17157	−	5.49333i	−0.129695	−	0.224639i
$599$	−7.55025	−	13.0774i	−0.308495	−	0.534329i	0.669538	−	0.742777i	$-0.266492\pi$
$599$	−7.55025	−	13.0774i	−0.308495	−	0.534329i	−0.978033	+	0.208449i	$0.933159\pi$
$600$	−1.31371	−	2.27541i	−0.0536319	−	0.0928932i
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	−0.791911	−	0.610636i	$-0.790914\pi$
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	0.924782	+	0.380498i	$0.124247\pi$
$602$	−0.935029	−	1.61952i	−0.0381089	−	0.0660066i
$603$	4.58579	−	7.94282i	0.186748	−	0.323456i
$604$	−9.71573			−0.395327
$605$	−0.485281			−0.0197295
$606$	0.727922	−	1.26080i	0.0295698	−	0.0512164i
$607$	0.792893	+	1.37333i	0.0321825	+	0.0557418i	0.881668	−	0.471870i	$-0.156421\pi$
$607$	0.792893	+	1.37333i	0.0321825	+	0.0557418i	−0.849486	+	0.527612i	$0.823088\pi$
$608$	−9.74264	+	16.8747i	−0.395116	+	0.684361i
$609$	−0.585786	−	1.01461i	−0.0237373	−	0.0411141i
$610$	0.585786	+	1.01461i	0.0237178	+	0.0410804i
$611$	18.4853	+	32.0174i	0.747834	+	1.29529i
$612$	−30.1421			−1.21842
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	−0.963158	−	0.268937i	$-0.913328\pi$
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	0.714485	+	0.699651i	$0.246661\pi$
$614$	2.32843	−	4.03295i	0.0939677	−	0.162757i
$615$	1.55025	+	2.68512i	0.0625122	+	0.108274i
$616$	2.12994			0.0858178
$617$	16.6421	−	28.8250i	0.669987	−	1.16045i	−0.307920	−	0.951412i	$-0.599633\pi$
$617$	16.6421	−	28.8250i	0.669987	−	1.16045i	0.977907	−	0.209040i	$-0.0670337\pi$
$618$	0.355339			0.0142938
$619$	−20.3431			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$619$	−20.3431			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$620$	−8.44975	−	5.67796i	−0.339350	−	0.228033i
$621$	9.65685			0.387516
$622$	4.68629			0.187903
$623$	0.928932	−	1.60896i	0.0372169	−	0.0644615i
$624$	−4.75736			−0.190447
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.378680	−	0.655892i	0.0151351	−	0.0262147i
$627$	−2.96447	+	5.13461i	−0.118389	+	0.205056i
$628$	−16.7696			−0.669178
$629$	2.91421	+	5.04757i	0.116197	+	0.201260i
$630$	−0.242641	−	0.420266i	−0.00966704	−	0.0167438i
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.580013	−	0.814607i	$-0.696953\pi$
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.415464	−	0.909610i	$-0.636381\pi$
$632$	−5.35786	+	9.28009i	−0.213124	+	0.369142i
$633$	−2.15685	−	3.73578i	−0.0857273	−	0.148484i
$634$	1.62132	−	2.80821i	0.0643909	−	0.111528i
$635$	8.89949			0.353166
$636$	−4.41421			−0.175035
$637$	−13.0711	+	22.6398i	−0.517895	+	0.897020i
$638$	4.58579	+	7.94282i	0.181553	+	0.314459i
$639$	0.100505	−	0.174080i	0.00397592	−	0.00688649i
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	0.970362	−	0.241655i	$-0.0776901\pi$
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	−0.694460	+	0.719531i	$0.744357\pi$
$642$	−1.06497	−	1.84458i	−0.0420311	−	0.0727999i
$643$	35.3137			1.39264			0.696318	−	0.717733i	$-0.254820\pi$
$643$	35.3137			1.39264			0.696318	+	0.717733i	$0.254820\pi$
$644$	1.51472	−	2.62357i	0.0596883	−	0.103383i
$645$	2.25736	−	3.90986i	0.0888834	−	0.153951i
$646$	5.32843	+	9.22911i	0.209644	+	0.363114i
$647$	−45.3137			−1.78147			−0.890733	−	0.454527i	$-0.849808\pi$
$647$	−45.3137			−1.78147			−0.890733	+	0.454527i	$0.849808\pi$
$648$	5.93503	−	10.2798i	0.233150	−	0.403828i
$649$	13.2010			0.518185
$650$	6.34315			0.248799
$651$	−0.792893	−	0.532799i	−0.0310759	−	0.0208821i
$652$	−38.3431			−1.50163
$653$	−6.14214			−0.240360			−0.120180	−	0.992752i	$-0.538347\pi$
$653$	−6.14214			−0.240360			−0.120180	+	0.992752i	$0.538347\pi$
$654$	0.928932	−	1.60896i	0.0363241	−	0.0629152i
$655$	−13.2426			−0.517433
$656$	11.2279	+	19.4473i	0.438377	+	0.759291i
$657$	−2.58579	+	4.47871i	−0.100881	+	0.174731i
$658$	0.828427	−	1.43488i	0.0322955	−	0.0559374i
$659$	−1.65685			−0.0645419			−0.0322709	−	0.999479i	$-0.510274\pi$
$659$	−1.65685			−0.0645419			−0.0322709	+	0.999479i	$0.510274\pi$
$660$	1.22792	+	2.12682i	0.0477968	+	0.0827865i
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	0.814915	−	0.579581i	$-0.196784\pi$
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	−0.909389	+	0.415946i	$0.863450\pi$
$662$	−1.91421	−	3.31552i	−0.0743980	−	0.128861i
$663$	−4.62132	+	8.00436i	−0.179477	+	0.310864i
$664$	−7.98528	−	13.8309i	−0.309889	−	0.536744i
$665$	0.914214	−	1.58346i	0.0354517	−	0.0614041i
$666$	−1.17157			−0.0453975
$667$	27.3137			1.05759
$668$	20.6213	−	35.7172i	0.797863	−	1.38194i
$669$	4.91421	+	8.51167i	0.189994	+	0.329080i
$670$	−0.671573	+	1.16320i	−0.0259451	+	0.0449383i
$671$	4.58579	+	7.94282i	0.177032	+	0.306629i
$672$	0.378680	+	0.655892i	0.0146079	+	0.0253016i
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	0.761830	−	0.647777i	$-0.224301\pi$
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	−0.941906	+	0.335876i	$0.890968\pi$
$674$	3.85786			0.148599
$675$	−4.82843	+	8.36308i	−0.185846	+	0.321895i
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	0.951711	+	0.306994i	$0.0993232\pi$
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	−0.209991	+	0.977703i	$0.567343\pi$
$678$	2.85786			0.109756
$679$	1.07107	−	1.85514i	0.0411038	−	0.0711939i
$680$	9.24264			0.354439
$681$	−7.62742			−0.292283
$682$	6.20711	+	4.17098i	0.237682	+	0.159715i
$683$	−1.37258			−0.0525204			−0.0262602	−	0.999655i	$-0.508360\pi$
$683$	−1.37258			−0.0525204			−0.0262602	+	0.999655i	$0.508360\pi$
$684$	22.8284			0.872867
$685$	−4.74264	+	8.21449i	−0.181207	+	0.313860i
$686$	2.37258			0.0905856
$687$	1.13604	+	1.96768i	0.0433426	+	0.0750716i
$688$	16.3492	−	28.3177i	0.623309	−	1.07960i
$689$	11.1569	−	19.3242i	0.425042	−	0.736195i
$690$	−0.686292			−0.0261267
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	0.866700	−	0.498829i	$-0.166236\pi$
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	−0.865349	+	0.501170i	$0.832903\pi$
$692$	7.60051	+	13.1645i	0.288928	+	0.500438i
$693$	−1.89949	−	3.29002i	−0.0721558	−	0.124978i
$694$	1.77208	−	3.06933i	0.0672672	−	0.116510i
$695$		0			0
$696$	−2.24264	+	3.88437i	−0.0850071	+	0.147237i
$697$	43.6274			1.65251
$698$	−11.2304			−0.425079
$699$	1.89949	−	3.29002i	0.0718455	−	0.124440i
$700$	1.51472	+	2.62357i	0.0572510	+	0.0991616i
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	−0.710139	−	0.704062i	$-0.751368\pi$
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	0.964805	+	0.262967i	$0.0847011\pi$
$702$	−1.91421	−	3.31552i	−0.0722473	−	0.125136i
$703$	−2.20711	−	3.82282i	−0.0832426	−	0.144180i
$704$	6.76346	+	11.7146i	0.254907	+	0.441512i
$705$	4.00000			0.150649
$706$	−0.621320	+	1.07616i	−0.0233837	+	0.0405018i
$707$	−1.75736	+	3.04384i	−0.0660923	+	0.114475i
$708$	1.54163	+	2.67018i	0.0579380	+	0.100352i
$709$	17.3137			0.650230			0.325115	−	0.945674i	$-0.394597\pi$
$709$	17.3137			0.650230			0.325115	+	0.945674i	$0.394597\pi$
$710$	−0.0147186	+	0.0254934i	−0.000552380	+	0.000956751i
$711$	19.1127			0.716782
$712$	−7.11270			−0.266560
$713$	20.0000	−	9.79796i	0.749006	−	0.366936i
$714$	0.414214			0.0155016
$715$	−12.4142			−0.464265
$716$	−13.9350	+	24.1362i	−0.520776	+	0.902011i
$717$	−8.79899			−0.328604
$718$	−1.47056	−	2.54709i	−0.0548809	−	0.0950565i
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	−0.780911	−	0.624642i	$-0.785245\pi$
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	0.931411	+	0.363968i	$0.118578\pi$
$720$	4.24264	−	7.34847i	0.158114	−	0.273861i
$721$	−0.857864			−0.0319485
$722$	−0.100505	−	0.174080i	−0.00374041	−	0.00647858i
$723$	−2.76346	−	4.78645i	−0.102774	−	0.178010i
$724$	11.2574	+	19.4983i	0.418376	+	0.724649i
$725$	−13.6569	+	23.6544i	−0.507203	+	0.878501i
$726$	0.0416306	+	0.0721062i	0.00154506	+	0.00267611i
$727$	−20.4203	+	35.3690i	−0.757347	+	1.31176i	0.186851	+	0.982388i	$0.440172\pi$
$727$	−20.4203	+	35.3690i	−0.757347	+	1.31176i	−0.944199	+	0.329376i	$0.893162\pi$
$728$	−2.51472			−0.0932017
$729$	−18.1716			−0.673021
$730$	0.378680	−	0.655892i	0.0140156	−	0.0242757i
$731$	−31.7635	−	55.0159i	−1.17481	−	2.03484i
$732$	−1.07107	+	1.85514i	−0.0395878	+	0.0685681i
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	0.684871	−	0.728664i	$-0.259858\pi$
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	−0.973477	+	0.228784i	$0.926525\pi$
$734$	5.01472	+	8.68575i	0.185097	+	0.320597i
$735$	1.41421	+	2.44949i	0.0521641	+	0.0903508i
$736$	−17.6569			−0.650840
$737$	−5.25736	+	9.10601i	−0.193657	+	0.335424i
$738$	−4.38478	+	7.59466i	−0.161406	+	0.279563i
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	−0.886764	−	0.462223i	$-0.847052\pi$
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	0.0430851	−	0.999071i	$-0.486281\pi$
$740$	−1.82843			−0.0672143
$741$	3.50000	−	6.06218i	0.128576	−	0.222700i
$742$	−1.00000			−0.0367112
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$	−0.248737	+	3.64874i	−0.00911915	+	0.133769i
$745$	1.00000			0.0366372
$746$	4.14214			0.151654
$747$	−14.2426	+	24.6690i	−0.521111	+	0.902591i
$748$	34.5563			1.26351
$749$	2.57107	+	4.45322i	0.0939448	+	0.162717i
$750$	0.772078	−	1.33728i	0.0281923	−	0.0488305i
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	−0.924503	−	0.381175i	$-0.875519\pi$
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	0.792359	+	0.610055i	$0.208853\pi$
$752$	28.9706			1.05645
$753$	−1.32843	−	2.30090i	−0.0484106	−	0.0838496i
$754$	−5.41421	−	9.37769i	−0.197174	−	0.341515i
$755$	−2.65685	−	4.60181i	−0.0966928	−	0.167477i
$756$	0.914214	−	1.58346i	0.0332496	−	0.0575900i
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	0.572136	−	0.820159i	$-0.306115\pi$
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	−0.996346	+	0.0854047i	$0.972782\pi$
$758$	−1.52944	+	2.64906i	−0.0555517	+	0.0962183i
$759$	−5.37258			−0.195012
$760$	−7.00000			−0.253917
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	0.446118	+	0.894974i	$0.352806\pi$
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	−0.998129	+	0.0611380i	$0.980527\pi$
$762$	−0.763456	−	1.32234i	−0.0276571	−	0.0479035i
$763$	−2.24264	+	3.88437i	−0.0811890	+	0.140624i
$764$	−19.1066	−	33.0936i	−0.691253	−	1.19728i
$765$	−8.24264	−	14.2767i	−0.298013	−	0.516174i
$766$	−1.05635	−	1.82965i	−0.0381674	−	0.0661080i
$767$	−15.5858			−0.562770
$768$	−0.822330	+	1.42432i	−0.0296733	+	0.0513957i
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$	0.278175	+	0.481813i	0.0100247	+	0.0173633i
$771$	9.24264			0.332866
$772$	6.52944	−	11.3093i	0.235000	−	0.407031i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	12.7696			0.458992
$775$	−1.51472	+	22.2195i	−0.0544103	+	0.798148i
$776$	−8.20101			−0.294399
$777$	−0.171573			−0.00615514
$778$	2.30761	−	3.99690i	0.0827319	−	0.143296i
$779$	−33.0416			−1.18384
$780$	−1.44975	−	2.51104i	−0.0519093	−	0.0899095i
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$	−4.82843	+	8.36308i	−0.172664	+	0.299063i
$783$	16.4853			0.589136
$784$	10.2426	+	17.7408i	0.365809	+	0.633599i
$785$	−4.58579	−	7.94282i	−0.163674	−	0.283491i
$786$	1.13604	+	1.96768i	0.0405212	+	0.0701847i
$787$	−21.2071	+	36.7318i	−0.755952	+	1.30935i	0.188948	+	0.981987i	$0.439492\pi$
$787$	−21.2071	+	36.7318i	−0.755952	+	1.30935i	−0.944900	+	0.327360i	$0.893841\pi$
$788$	−12.3284	−	21.3535i	−0.439182	−	0.760686i
$789$	4.82843	−	8.36308i	0.171897	−	0.297734i
$790$	−2.79899			−0.0995836
$791$	−6.89949			−0.245318
$792$	−7.27208	+	12.5956i	−0.258402	+	0.447565i
$793$	−5.41421	−	9.37769i	−0.192264	−	0.333012i
$794$	6.93503	−	12.0118i	0.246115	−	0.426284i
$795$	−1.20711	−	2.09077i	−0.0428117	−	0.0741520i
$796$	16.8345	+	29.1583i	0.596684	+	1.03349i
$797$	−14.2279	−	24.6435i	−0.503979	−	0.872917i	−0.999989	−	0.00460050i	$-0.998536\pi$
$797$	−14.2279	−	24.6435i	−0.503979	−	0.872917i	0.496011	−	0.868316i	$-0.334798\pi$
$798$	−0.313708			−0.0111052
$799$	28.1421	−	48.7436i	0.995597	−	1.72442i
$800$	8.82843	−	15.2913i	0.312132	−	0.540629i
$801$	6.34315	+	10.9867i	0.224124	+	0.388194i
$802$	−11.1127			−0.392403
$803$	2.96447	−	5.13461i	0.104614	−	0.181196i
$804$	−2.45584			−0.0866109
$805$	1.65685			0.0583964
$806$	−7.32843	−	4.92447i	−0.258133	−	0.173457i
$807$	−10.8406			−0.381608
$808$	13.4558			0.473375
$809$	6.01472	−	10.4178i	0.211466	−	0.366270i	−0.740707	−	0.671828i	$-0.765509\pi$
$809$	6.01472	−	10.4178i	0.211466	−	0.366270i	0.952174	+	0.305558i	$0.0988428\pi$
$810$	3.10051			0.108941
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	2.58579	−	4.47871i	0.0907433	−	0.157172i
$813$	0.142136	−	0.246186i	0.00498491	−	0.00863412i
$814$	1.34315			0.0470772
$815$	−10.4853	−	18.1610i	−0.367283	−	0.636153i
$816$	3.62132	+	6.27231i	0.126772	+	0.219575i
$817$	24.0563	+	41.6668i	0.841625	+	1.45774i
$818$	−4.27817	+	7.41002i	−0.149583	+	0.259085i
$819$	2.24264	+	3.88437i	0.0783642	+	0.135731i
$820$	−6.84315	+	11.8527i	−0.238973	+	0.413913i
$821$	8.48528			0.296138			0.148069	−	0.988977i	$-0.452694\pi$
$821$	8.48528			0.296138			0.148069	+	0.988977i	$0.452694\pi$
$822$	1.62742			0.0567627
$823$	−18.1066	+	31.3616i	−0.631156	+	1.09320i	0.356159	+	0.934425i	$0.384086\pi$
$823$	−18.1066	+	31.3616i	−0.631156	+	1.09320i	−0.987316	+	0.158770i	$0.949247\pi$
$824$	1.64214	+	2.84426i	0.0572065	+	0.0990846i
$825$	2.68629	−	4.65279i	0.0935247	−	0.161989i
$826$	0.349242	+	0.604906i	0.0121517	+	0.0210474i
$827$	−18.4497	−	31.9559i	−0.641561	−	1.11122i	−0.985084	−	0.172072i	$-0.944954\pi$
$827$	−18.4497	−	31.9559i	−0.641561	−	1.11122i	0.343524	−	0.939144i	$-0.388379\pi$
$828$	10.3431	+	17.9149i	0.359449	+	0.622584i
$829$	38.4264			1.33460			0.667302	−	0.744787i	$-0.267449\pi$
$829$	38.4264			1.33460			0.667302	+	0.744787i	$0.267449\pi$
$830$	2.08579	−	3.61269i	0.0723987	−	0.125398i
$831$	−2.92893	+	5.07306i	−0.101604	+	0.175982i
$832$	−7.98528	−	13.8309i	−0.276840	−	0.479501i
$833$	39.7990			1.37895
$834$		0			0
$835$	22.5563			0.780595
$836$	−26.1716			−0.905163
$837$	12.0711	−	5.91359i	0.417237	−	0.204404i
$838$	11.5980			0.400646
$839$	−14.6274			−0.504995			−0.252497	−	0.967598i	$-0.581252\pi$
$839$	−14.6274			−0.504995			−0.252497	+	0.967598i	$0.581252\pi$
$840$	−0.136039	+	0.235626i	−0.00469379	+	0.00812988i
$841$	17.6274			0.607842
$842$	6.44975	+	11.1713i	0.222273	+	0.384988i
$843$	−0.414214	+	0.717439i	−0.0142663	+	0.0247099i
$844$	9.52082	−	16.4905i	0.327720	−	0.567628i
$845$	1.65685			0.0569975
$846$	5.65685	+	9.79796i	0.194487	+	0.336861i
$847$	−0.100505	−	0.174080i	−0.00345339	−	0.00598146i
$848$	−8.74264	−	15.1427i	−0.300224	−	0.520002i
$849$	2.82843	−	4.89898i	0.0970714	−	0.168133i
$850$	−4.82843	−	8.36308i	−0.165614	−	0.286851i
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$	−0.0538239			−0.00184398
$853$	−15.5147			−0.531214			−0.265607	−	0.964081i	$-0.585572\pi$
$853$	−15.5147			−0.531214			−0.265607	+	0.964081i	$0.585572\pi$
$854$	−0.242641	+	0.420266i	−0.00830299	+	0.0143812i
$855$	6.24264	+	10.8126i	0.213494	+	0.369782i
$856$	9.84315	−	17.0488i	0.336432	−	0.582717i
$857$	9.74264	+	16.8747i	0.332802	+	0.576430i	0.983060	−	0.183283i	$-0.0586725\pi$
$857$	9.74264	+	16.8747i	0.332802	+	0.576430i	−0.650258	+	0.759714i	$0.725339\pi$
$858$	1.06497	+	1.84458i	0.0363575	+	0.0629731i
$859$	24.6924	+	42.7685i	0.842493	+	1.45924i	0.887780	+	0.460267i	$0.152246\pi$
$859$	24.6924	+	42.7685i	0.842493	+	1.45924i	−0.0452869	+	0.998974i	$0.514420\pi$
$860$	19.9289			0.679571
$861$	−0.642136	+	1.11221i	−0.0218839	+	0.0379041i
$862$	3.47056	−	6.01119i	0.118208	−	0.204742i
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	0.887423	−	0.460956i	$-0.152493\pi$
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	−0.842911	+	0.538053i	$0.819160\pi$
$864$	−10.6569			−0.362554
$865$	−4.15685	+	7.19988i	−0.141337	+	0.244803i
$866$	11.2304			0.381626
$867$	7.02944			0.238732
$868$	0.286797	−	4.20703i	0.00973451	−	0.142796i
$869$	−21.9117			−0.743303
$870$	−1.17157			−0.0397200
$871$	6.20711	−	10.7510i	0.210320	−	0.364285i
$872$	17.1716			0.581503
$873$	7.31371	+	12.6677i	0.247532	+	0.428737i
$874$	3.65685	−	6.33386i	0.123695	−	0.214246i
$875$	−1.86396	+	3.22848i	−0.0630134	+	0.109142i
$876$	1.38478			0.0467873
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.815694	−	0.578483i	$-0.803645\pi$
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.0931343	−	0.995654i	$-0.529689\pi$
$878$	−0.428932	−	0.742932i	−0.0144758	−	0.0250728i
$879$	−3.06497	−	5.30869i	−0.103379	−	0.179058i
$880$	−4.86396	+	8.42463i	−0.163964	+	0.283994i
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	0.750648	−	0.660702i	$-0.229741\pi$
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	−0.947509	+	0.319729i	$0.896408\pi$
$882$	−4.00000	+	6.92820i	−0.134687	+	0.233285i
$883$	−30.2843			−1.01915			−0.509573	−	0.860427i	$-0.670197\pi$
$883$	−30.2843			−1.01915			−0.509573	+	0.860427i	$0.670197\pi$
$884$	−40.7990			−1.37222
$885$	−0.843146	+	1.46037i	−0.0283420	+	0.0490898i
$886$	0.985281	+	1.70656i	0.0331012	+	0.0573329i
$887$	25.6630	−	44.4495i	0.861678	−	1.49247i	−0.00863117	−	0.999963i	$-0.502747\pi$
$887$	25.6630	−	44.4495i	0.861678	−	1.49247i	0.870309	−	0.492507i	$-0.163919\pi$
$888$	0.328427	+	0.568852i	0.0110213	+	0.0190894i
$889$	1.84315	+	3.19242i	0.0618171	+	0.107070i
$890$	−0.928932	−	1.60896i	−0.0311379	−	0.0539324i
$891$	24.2721			0.813145
$892$	−21.6924	+	37.5723i	−0.726315	+	1.25801i
$893$	−21.3137	+	36.9164i	−0.713236	+	1.23536i
$894$	−0.0857864	−	0.148586i	−0.00286913	−	0.00496947i
$895$	−15.2426			−0.509505
$896$	−2.18629	+	3.78677i	−0.0730389	+	0.126507i
$897$	6.34315			0.211791
$898$	−16.8284			−0.561572
$899$	34.1421	−	16.7262i	1.13870	−	0.557849i
$900$	−20.6863			−0.689543
$901$	−33.9706			−1.13172
$902$	5.02691	−	8.70687i	0.167378	−	0.289907i
$903$	1.87006			0.0622316
$904$	13.2071	+	22.8754i	0.439262	+	0.760824i
$905$	−6.15685	+	10.6640i	−0.204661	+	0.354483i
$906$	−0.455844	+	0.789545i	−0.0151444	+	0.0262309i
$907$	32.6863			1.08533			0.542665	−	0.839949i	$-0.317415\pi$
$907$	32.6863			1.08533			0.542665	+	0.839949i	$0.317415\pi$
$908$	−16.8345	−	29.1583i	−0.558673	−	0.967651i
$909$	−12.0000	−	20.7846i	−0.398015	−	0.689382i
$910$	−0.328427	−	0.568852i	−0.0108873	−	0.0188573i
$911$	−0.479185	+	0.829972i	−0.0158761	+	0.0274982i	−0.873854	−	0.486188i	$-0.838387\pi$
$911$	−0.479185	+	0.829972i	−0.0158761	+	0.0274982i	0.857978	+	0.513686i	$0.171720\pi$
$912$	−2.74264	−	4.75039i	−0.0908179	−	0.157301i
$913$	16.3284	−	28.2817i	0.540392	−	0.935987i
$914$	−12.8873			−0.426274
$915$	−1.17157			−0.0387310
$916$	−5.01472	+	8.68575i	−0.165691	+	0.286985i
$917$	−2.74264	−	4.75039i	−0.0905700	−	0.156872i
$918$	−2.91421	+	5.04757i	−0.0961834	+	0.166595i
$919$	17.4497	+	30.2238i	0.575614	+	0.996993i	0.995975	+	0.0896356i	$0.0285703\pi$
$919$	17.4497	+	30.2238i	0.575614	+	0.996993i	−0.420361	+	0.907357i	$0.638096\pi$
$920$	−3.17157	−	5.49333i	−0.104564	−	0.181110i
$921$	2.32843	+	4.03295i	0.0767243	+	0.132890i
$922$	−0.887302			−0.0292217
$923$	0.136039	−	0.235626i	0.00447778	−	0.00775574i
$924$	−0.508622	+	0.880959i	−0.0167324	+	0.0289814i
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	−3.71573			−0.122106
$927$	2.92893	−	5.07306i	0.0961988	−	0.166621i
$928$	−30.1421			−0.989464
$929$	7.51472			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$929$	7.51472			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$930$	−0.857864	+	0.420266i	−0.0281305	+	0.0137811i
$931$	−30.1421			−0.987869
$932$	16.7696			0.549305
$933$	−2.34315	+	4.05845i	−0.0767111	+	0.132868i
$934$	−3.31371			−0.108428
$935$	9.44975	+	16.3674i	0.309040	+	0.535273i
$936$	8.58579	−	14.8710i	0.280635	−	0.486074i
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	−0.965227	−	0.261412i	$-0.915812\pi$
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	0.709003	+	0.705206i	$0.249145\pi$
$938$	−0.556349			−0.0181654
$939$	0.378680	+	0.655892i	0.0123577	+	0.0214042i
$940$	8.82843	+	15.2913i	0.287952	+	0.498747i
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	0.996516	+	0.0833989i	$0.0265776\pi$
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	−0.426033	+	0.904708i	$0.640089\pi$
$942$	−0.786797	+	1.36277i	−0.0256352	+	0.0444015i
$943$	−14.9706	−	25.9298i	−0.487509	−	0.844390i
$944$	−6.10660	+	10.5769i	−0.198753	+	0.344250i
$945$	1.00000			0.0325300
$946$	−14.6396			−0.475975
$947$	−9.55025	+	16.5415i	−0.310342	+	0.537527i	−0.978436	−	0.206549i	$-0.933777\pi$
$947$	−9.55025	+	16.5415i	−0.310342	+	0.537527i	0.668095	+	0.744076i	$0.267110\pi$
$948$	−2.55887	−	4.43210i	−0.0831084	−	0.143948i
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$	3.65685	+	6.33386i	0.118644	+	0.205497i
$951$	1.62132	+	2.80821i	0.0525749	+	0.0910624i
$952$	1.91421	+	3.31552i	0.0620400	+	0.107456i
$953$	3.51472			0.113853			0.0569265	−	0.998378i	$-0.481870\pi$
$953$	3.51472			0.113853			0.0569265	+	0.998378i	$0.481870\pi$
$954$	3.41421	−	5.91359i	0.110539	−	0.191460i
$955$	10.4497	−	18.0995i	0.338146	−	0.585686i
$956$	−19.4203	−	33.6370i	−0.628098	−	1.08790i
$957$	−9.17157			−0.296475
$958$	3.25736	−	5.64191i	0.105241	−	0.182282i
$959$	−3.92893			−0.126872
$960$	−1.72792			−0.0557684
$961$	19.0000	−	24.4949i	0.612903	−	0.790158i
$962$	−1.58579			−0.0511278
$963$	−35.1127			−1.13149
$964$	12.1985	−	21.1284i	0.392887	−	0.680500i
$965$	7.14214			0.229913
$966$	−0.142136	−	0.246186i	−0.00457314	−	0.00792091i
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	−0.714742	−	0.699388i	$-0.753456\pi$
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	0.963059	+	0.269290i	$0.0867892\pi$
$968$	−0.384776	+	0.666452i	−0.0123672	+	0.0214206i
$969$	−10.6569			−0.342347
$970$	−1.07107	−	1.85514i	−0.0343899	−	0.0595651i
$971$	0.349242	+	0.604906i	0.0112077	+	0.0194123i	0.871575	−	0.490262i	$-0.163099\pi$
$971$	0.349242	+	0.604906i	0.0112077	+	0.0194123i	−0.860367	+	0.509675i	$0.829766\pi$
$972$	9.45584	+	16.3780i	0.303296	+	0.525325i
$973$		0			0
$974$	−4.01472	−	6.95370i	−0.128640	−	0.222811i
$975$	−3.17157	+	5.49333i	−0.101572	+	0.175927i
$976$	−8.48528			−0.271607
$977$	−0.485281			−0.0155255			−0.00776276	−	0.999970i	$-0.502471\pi$
$977$	−0.485281			−0.0155255			−0.00776276	+	0.999970i	$0.502471\pi$
$978$	−1.79899	+	3.11594i	−0.0575254	+	0.0996368i
$979$	−7.27208	−	12.5956i	−0.232417	−	0.402557i
$980$	−6.24264	+	10.8126i	−0.199414	+	0.345395i
$981$	−15.3137	−	26.5241i	−0.488929	−	0.846850i
$982$	−0.328427	−	0.568852i	−0.0104805	−	0.0181528i
$983$	19.4203	+	33.6370i	0.619412	+	1.07285i	0.989593	+	0.143893i	$0.0459621\pi$
$983$	19.4203	+	33.6370i	0.619412	+	1.07285i	−0.370182	+	0.928959i	$0.620705\pi$
$984$	4.91674			0.156740
$985$	6.74264	−	11.6786i	0.214838	−	0.372111i
$986$	−8.24264	+	14.2767i	−0.262499	+	0.454662i
$987$	0.828427	+	1.43488i	0.0263691	+	0.0456727i
$988$	30.8995			0.983044
$989$	−21.7990	+	37.7570i	−0.693168	+	1.20060i
$990$	−3.79899			−0.120740
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$	−22.0711	+	10.8126i	−0.700757	+	0.343299i
$993$	3.82843			0.121491
$994$	−0.0121933			−0.000386748
$995$	−9.20711	+	15.9472i	−0.291885	+	0.505559i
$996$	7.62742			0.241684
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$	0.458369	−	0.793919i	0.0145094	−	0.0251311i
$999$	1.20711	−	2.09077i	0.0381912	−	0.0661490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.c.a.5.2	✓	4
3.2	odd	2		279.2.h.c.253.1		4
4.3	odd	2		496.2.i.h.129.2		4
5.2	odd	4		775.2.o.d.749.3		8
5.3	odd	4		775.2.o.d.749.2		8
5.4	even	2		775.2.e.e.501.1		4
31.2	even	5		961.2.g.o.547.2		16
31.3	odd	30		961.2.g.r.448.2		16
31.4	even	5		961.2.g.o.235.1		16
31.5	even	3		961.2.a.a.1.2		2
31.6	odd	6		961.2.c.a.521.2		4
31.7	even	15		961.2.g.o.338.1		16
31.8	even	5		961.2.g.o.816.1		16
31.9	even	15		961.2.d.l.374.1		8
31.10	even	15		961.2.d.l.531.2		8
31.11	odd	30		961.2.d.i.388.1		8
31.12	odd	30		961.2.g.r.844.2		16
31.13	odd	30		961.2.d.i.628.2		8
31.14	even	15		961.2.g.o.732.1		16
31.15	odd	10		961.2.g.r.846.2		16
31.16	even	5		961.2.g.o.846.2		16
31.17	odd	30		961.2.g.r.732.1		16
31.18	even	15		961.2.d.l.628.2		8
31.19	even	15		961.2.g.o.844.2		16
31.20	even	15		961.2.d.l.388.1		8
31.21	odd	30		961.2.d.i.531.2		8
31.22	odd	30		961.2.d.i.374.1		8
31.23	odd	10		961.2.g.r.816.1		16
31.24	odd	30		961.2.g.r.338.1		16
31.25	even	3	inner	31.2.c.a.25.2	yes	4
31.26	odd	6		961.2.a.c.1.2		2
31.27	odd	10		961.2.g.r.235.1		16
31.28	even	15		961.2.g.o.448.2		16
31.29	odd	10		961.2.g.r.547.2		16
31.30	odd	2		961.2.c.a.439.2		4
93.5	odd	6		8649.2.a.l.1.1		2
93.26	even	6		8649.2.a.k.1.1		2
93.56	odd	6		279.2.h.c.118.1		4
124.87	odd	6		496.2.i.h.273.2		4
155.87	odd	12		775.2.o.d.149.3		8
155.118	odd	12		775.2.o.d.149.2		8
155.149	even	6		775.2.e.e.676.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	1.1	even	1	trivial
31.2.c.a.25.2	yes	4	31.25	even	3	inner
279.2.h.c.118.1		4	93.56	odd	6
279.2.h.c.253.1		4	3.2	odd	2
496.2.i.h.129.2		4	4.3	odd	2
496.2.i.h.273.2		4	124.87	odd	6
775.2.e.e.501.1		4	5.4	even	2
775.2.e.e.676.1		4	155.149	even	6
775.2.o.d.149.2		8	155.118	odd	12
775.2.o.d.149.3		8	155.87	odd	12
775.2.o.d.749.2		8	5.3	odd	4
775.2.o.d.749.3		8	5.2	odd	4
961.2.a.a.1.2		2	31.5	even	3
961.2.a.c.1.2		2	31.26	odd	6
961.2.c.a.439.2		4	31.30	odd	2
961.2.c.a.521.2		4	31.6	odd	6
961.2.d.i.374.1		8	31.22	odd	30
961.2.d.i.388.1		8	31.11	odd	30
961.2.d.i.531.2		8	31.21	odd	30
961.2.d.i.628.2		8	31.13	odd	30
961.2.d.l.374.1		8	31.9	even	15
961.2.d.l.388.1		8	31.20	even	15
961.2.d.l.531.2		8	31.10	even	15
961.2.d.l.628.2		8	31.18	even	15
961.2.g.o.235.1		16	31.4	even	5
961.2.g.o.338.1		16	31.7	even	15
961.2.g.o.448.2		16	31.28	even	15
961.2.g.o.547.2		16	31.2	even	5
961.2.g.o.732.1		16	31.14	even	15
961.2.g.o.816.1		16	31.8	even	5
961.2.g.o.844.2		16	31.19	even	15
961.2.g.o.846.2		16	31.16	even	5
961.2.g.r.235.1		16	31.27	odd	10
961.2.g.r.338.1		16	31.24	odd	30
961.2.g.r.448.2		16	31.3	odd	30
961.2.g.r.547.2		16	31.29	odd	10
961.2.g.r.732.1		16	31.17	odd	30
961.2.g.r.816.1		16	31.23	odd	10
961.2.g.r.844.2		16	31.12	odd	30
961.2.g.r.846.2		16	31.15	odd	10
8649.2.a.k.1.1		2	93.26	even	6
8649.2.a.l.1.1		2	93.5	odd	6

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

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} +(-0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.207107 - 0.358719i) q^{7} -1.58579 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} +(-0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(0.207107 - 0.358719i) q^{7} -1.58579 q^{8} +(1.41421 + 2.44949i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(-1.62132 - 2.80821i) q^{11} +(0.378680 - 0.655892i) q^{12} +(1.91421 + 3.31552i) q^{13} +(0.0857864 - 0.148586i) q^{14} +0.414214 q^{15} +3.00000 q^{16} +(2.91421 - 5.04757i) q^{17} +(0.585786 + 1.01461i) q^{18} +(-2.20711 + 3.82282i) q^{19} +(0.914214 + 1.58346i) q^{20} +(0.0857864 + 0.148586i) q^{21} +(-0.671573 - 1.16320i) q^{22} -4.00000 q^{23} +(0.328427 - 0.568852i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} -2.41421 q^{27} +(-0.378680 + 0.655892i) q^{28} -6.82843 q^{29} +0.171573 q^{30} +(-5.00000 + 2.44949i) q^{31} +4.41421 q^{32} +1.34315 q^{33} +(1.20711 - 2.09077i) q^{34} -0.414214 q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-0.914214 + 1.58346i) q^{38} -1.58579 q^{39} +(0.792893 + 1.37333i) q^{40} +(3.74264 + 6.48244i) q^{41} +(0.0355339 + 0.0615465i) q^{42} +(5.44975 - 9.43924i) q^{43} +(2.96447 + 5.13461i) q^{44} +(1.41421 - 2.44949i) q^{45} -1.65685 q^{46} +9.65685 q^{47} +(-0.621320 + 1.07616i) q^{48} +(3.41421 + 5.91359i) q^{49} +(0.828427 - 1.43488i) q^{50} +(1.20711 + 2.09077i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(-2.91421 - 5.04757i) q^{53} -1.00000 q^{54} +(-1.62132 + 2.80821i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} -2.82843 q^{58} +(-2.03553 + 3.52565i) q^{59} -0.757359 q^{60} -2.82843 q^{61} +(-2.07107 + 1.01461i) q^{62} +1.17157 q^{63} -4.17157 q^{64} +(1.91421 - 3.31552i) q^{65} +0.556349 q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(0.828427 - 1.43488i) q^{69} -0.171573 q^{70} +(-0.0355339 - 0.0615465i) q^{71} +(-2.24264 - 3.88437i) q^{72} +(0.914214 + 1.58346i) q^{73} +(-0.207107 + 0.358719i) q^{74} +(0.828427 + 1.43488i) q^{75} +(4.03553 - 6.98975i) q^{76} -1.34315 q^{77} -0.656854 q^{78} +(3.37868 - 5.85204i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(1.55025 + 2.68512i) q^{82} +(5.03553 + 8.72180i) q^{83} +(-0.156854 - 0.271680i) q^{84} -5.82843 q^{85} +(2.25736 - 3.90986i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +4.48528 q^{89} +(0.585786 - 1.01461i) q^{90} +1.58579 q^{91} +7.31371 q^{92} +(0.156854 - 2.30090i) q^{93} +4.00000 q^{94} +4.41421 q^{95} +(-0.914214 + 1.58346i) q^{96} +5.17157 q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} - 4 q^{15} + 12 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21} - 14 q^{22} - 16 q^{23} - 10 q^{24} + 8 q^{25} + 6 q^{26} - 4 q^{27} - 10 q^{28} - 16 q^{29} + 12 q^{30} - 20 q^{31} + 12 q^{32} + 28 q^{33} + 2 q^{34} + 4 q^{35} - 16 q^{36} - 2 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} + 16 q^{46} + 16 q^{47} + 6 q^{48} + 8 q^{49} - 8 q^{50} + 2 q^{51} - 14 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 10 q^{56} + 2 q^{57} + 6 q^{59} - 20 q^{60} + 20 q^{62} + 16 q^{63} - 28 q^{64} + 2 q^{65} - 60 q^{66} + 2 q^{67} - 10 q^{68} - 8 q^{69} - 12 q^{70} + 14 q^{71} + 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} + 2 q^{76} - 28 q^{77} + 20 q^{78} + 22 q^{79} - 6 q^{80} + 2 q^{81} + 26 q^{82} + 6 q^{83} + 22 q^{84} - 12 q^{85} + 26 q^{86} - 18 q^{88} - 16 q^{89} + 8 q^{90} + 12 q^{91} - 16 q^{92} - 22 q^{93} + 16 q^{94} + 12 q^{95} + 2 q^{96} + 32 q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 - 4 * q^15 + 12 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 - 16 * q^23 - 10 * q^24 + 8 * q^25 + 6 * q^26 - 4 * q^27 - 10 * q^28 - 16 * q^29 + 12 * q^30 - 20 * q^31 + 12 * q^32 + 28 * q^33 + 2 * q^34 + 4 * q^35 - 16 * q^36 - 2 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 + 16 * q^46 + 16 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 10 * q^56 + 2 * q^57 + 6 * q^59 - 20 * q^60 + 20 * q^62 + 16 * q^63 - 28 * q^64 + 2 * q^65 - 60 * q^66 + 2 * q^67 - 10 * q^68 - 8 * q^69 - 12 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 - 28 * q^77 + 20 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 - 12 * q^85 + 26 * q^86 - 18 * q^88 - 16 * q^89 + 8 * q^90 + 12 * q^91 - 16 * q^92 - 22 * q^93 + 16 * q^94 + 12 * q^95 + 2 * q^96 + 32 * q^97 + 24 * q^99

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