LMFDB - Embedded newform 560.2.bb.d.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 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("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41250 + 0.0695215i) q^{2} +(0.861811 - 0.861811i) q^{3} +(1.99033 - 0.196399i) q^{4} +(-1.76836 - 1.36854i) q^{5} +(-1.15740 + 1.27722i) q^{6} +1.00000 q^{7} +(-2.79770 + 0.415785i) q^{8} +1.51457i q^{9} +O(q^{10})$	\(q+(-1.41250 + 0.0695215i) q^{2} +(0.861811 - 0.861811i) q^{3} +(1.99033 - 0.196399i) q^{4} +(-1.76836 - 1.36854i) q^{5} +(-1.15740 + 1.27722i) q^{6} +1.00000 q^{7} +(-2.79770 + 0.415785i) q^{8} +1.51457i q^{9} +(2.59295 + 1.81014i) q^{10} +(-4.46879 + 4.46879i) q^{11} +(1.54603 - 1.88455i) q^{12} +(-2.57718 + 2.57718i) q^{13} +(-1.41250 + 0.0695215i) q^{14} +(-2.70341 + 0.344562i) q^{15} +(3.92286 - 0.781798i) q^{16} +3.17844i q^{17} +(-0.105295 - 2.13933i) q^{18} +(0.755057 + 0.755057i) q^{19} +(-3.78840 - 2.37656i) q^{20} +(0.861811 - 0.861811i) q^{21} +(6.00150 - 6.62285i) q^{22} +0.384857 q^{23} +(-2.05276 + 2.76941i) q^{24} +(1.25417 + 4.84015i) q^{25} +(3.46111 - 3.81945i) q^{26} +(3.89070 + 3.89070i) q^{27} +(1.99033 - 0.196399i) q^{28} +(0.364625 + 0.364625i) q^{29} +(3.79463 - 0.674641i) q^{30} +6.65377 q^{31} +(-5.48670 + 1.37701i) q^{32} +7.70250i q^{33} +(-0.220970 - 4.48956i) q^{34} +(-1.76836 - 1.36854i) q^{35} +(0.297459 + 3.01449i) q^{36} +(-3.28660 - 3.28660i) q^{37} +(-1.11901 - 1.01403i) q^{38} +4.44209i q^{39} +(5.51635 + 3.09352i) q^{40} -9.62324i q^{41} +(-1.15740 + 1.27722i) q^{42} +(-5.54209 - 5.54209i) q^{43} +(-8.01671 + 9.77204i) q^{44} +(2.07275 - 2.67829i) q^{45} +(-0.543613 + 0.0267559i) q^{46} +5.93369i q^{47} +(2.70700 - 4.05452i) q^{48} +1.00000 q^{49} +(-2.10802 - 6.74954i) q^{50} +(2.73921 + 2.73921i) q^{51} +(-4.62330 + 5.63561i) q^{52} +(5.22510 + 5.22510i) q^{53} +(-5.76612 - 5.22514i) q^{54} +(14.0181 - 1.78668i) q^{55} +(-2.79770 + 0.415785i) q^{56} +1.30143 q^{57} +(-0.540383 - 0.489685i) q^{58} +(-8.39229 + 8.39229i) q^{59} +(-5.31303 + 1.21674i) q^{60} +(5.49892 + 5.49892i) q^{61} +(-9.39847 + 0.462580i) q^{62} +1.51457i q^{63} +(7.65425 - 2.32648i) q^{64} +(8.08437 - 1.03039i) q^{65} +(-0.535489 - 10.8798i) q^{66} +(-9.71951 + 9.71951i) q^{67} +(0.624242 + 6.32616i) q^{68} +(0.331674 - 0.331674i) q^{69} +(2.59295 + 1.81014i) q^{70} -11.7154i q^{71} +(-0.629733 - 4.23730i) q^{72} +1.01014 q^{73} +(4.87083 + 4.41385i) q^{74} +(5.25215 + 3.09043i) q^{75} +(1.65111 + 1.35452i) q^{76} +(-4.46879 + 4.46879i) q^{77} +(-0.308820 - 6.27447i) q^{78} -16.9731 q^{79} +(-8.00693 - 3.98610i) q^{80} +2.16240 q^{81} +(0.669021 + 13.5929i) q^{82} +(-9.36697 + 9.36697i) q^{83} +(1.54603 - 1.88455i) q^{84} +(4.34984 - 5.62062i) q^{85} +(8.21351 + 7.44292i) q^{86} +0.628475 q^{87} +(10.6443 - 14.3604i) q^{88} +7.52367i q^{89} +(-2.74157 + 3.92720i) q^{90} +(-2.57718 + 2.57718i) q^{91} +(0.765995 - 0.0755855i) q^{92} +(5.73429 - 5.73429i) q^{93} +(-0.412519 - 8.38136i) q^{94} +(-0.301881 - 2.36854i) q^{95} +(-3.54177 + 5.91522i) q^{96} +8.65054i q^{97} +(-1.41250 + 0.0695215i) q^{98} +(-6.76827 - 6.76827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41250	+	0.0695215i	−0.998791	+	0.0491591i
$2$	−1.41250	+	0.0695215i	−0.998791	+	0.0491591i
$3$	0.861811	−	0.861811i	0.497567	−	0.497567i	−0.413113	−	0.910680i	$-0.635559\pi$
$3$	0.861811	−	0.861811i	0.497567	−	0.497567i	0.910680	+	0.413113i	$0.135559\pi$
$4$	1.99033	−	0.196399i	0.995167	−	0.0981993i
$5$	−1.76836	−	1.36854i	−0.790833	−	0.612032i
$5$	−1.76836	−	1.36854i	−0.790833	−	0.612032i
$6$	−1.15740	+	1.27722i	−0.472505	+	0.521425i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.79770	+	0.415785i	−0.989136	+	0.147002i
$9$			1.51457i			0.504855i
$10$	2.59295	+	1.81014i	0.819964	+	0.572415i
$11$	−4.46879	+	4.46879i	−1.34739	+	1.34739i	−0.458904	+	0.888486i	$0.651758\pi$
$11$	−4.46879	+	4.46879i	−1.34739	+	1.34739i	−0.888486	+	0.458904i	$0.848242\pi$
$12$	1.54603	−	1.88455i	0.446301	−	0.544022i
$13$	−2.57718	+	2.57718i	−0.714782	+	0.714782i	−0.967532	−	0.252750i	$-0.918665\pi$
$13$	−2.57718	+	2.57718i	−0.714782	+	0.714782i	0.252750	+	0.967532i	$0.418665\pi$
$14$	−1.41250	+	0.0695215i	−0.377507	+	0.0185804i
$15$	−2.70341	+	0.344562i	−0.698019	+	0.0889656i
$16$	3.92286	−	0.781798i	0.980714	−	0.195449i
$17$			3.17844i			0.770885i	0.922732	+	0.385443i	$0.125951\pi$
$17$			3.17844i			0.770885i	−0.922732	+	0.385443i	$0.874049\pi$
$18$	−0.105295	−	2.13933i	−0.0248182	−	0.504245i
$19$	0.755057	+	0.755057i	0.173222	+	0.173222i	0.788393	−	0.615171i	$-0.210913\pi$
$19$	0.755057	+	0.755057i	0.173222	+	0.173222i	−0.615171	+	0.788393i	$0.710913\pi$
$20$	−3.78840	−	2.37656i	−0.847112	−	0.531414i
$21$	0.861811	−	0.861811i	0.188062	−	0.188062i
$22$	6.00150	−	6.62285i	1.27952	−	1.41200i
$23$	0.384857			0.0802483			0.0401242	−	0.999195i	$-0.487225\pi$
$23$	0.384857			0.0802483			0.0401242	+	0.999195i	$0.487225\pi$
$24$	−2.05276	+	2.76941i	−0.419018	+	0.565304i
$25$	1.25417	+	4.84015i	0.250834	+	0.968030i
$26$	3.46111	−	3.81945i	0.678780	−	0.749056i
$27$	3.89070	+	3.89070i	0.748766	+	0.748766i
$28$	1.99033	−	0.196399i	0.376138	−	0.0371159i
$29$	0.364625	+	0.364625i	0.0677091	+	0.0677091i	0.740150	−	0.672441i	$-0.234754\pi$
$29$	0.364625	+	0.364625i	0.0677091	+	0.0677091i	−0.672441	+	0.740150i	$0.734754\pi$
$30$	3.79463	−	0.674641i	0.692801	−	0.123172i
$31$	6.65377			1.19505			0.597526	−	0.801850i	$-0.296151\pi$
$31$	6.65377			1.19505			0.597526	+	0.801850i	$0.296151\pi$
$32$	−5.48670	+	1.37701i	−0.969920	+	0.243424i
$33$			7.70250i			1.34083i
$34$	−0.220970	−	4.48956i	−0.0378960	−	0.769953i
$35$	−1.76836	−	1.36854i	−0.298907	−	0.231326i
$36$	0.297459	+	3.01449i	0.0495764	+	0.502415i
$37$	−3.28660	−	3.28660i	−0.540314	−	0.540314i	0.383307	−	0.923621i	$-0.374785\pi$
$37$	−3.28660	−	3.28660i	−0.540314	−	0.540314i	−0.923621	+	0.383307i	$0.874785\pi$
$38$	−1.11901	−	1.01403i	−0.181528	−	0.164497i
$39$			4.44209i			0.711303i
$40$	5.51635	+	3.09352i	0.872212	+	0.489129i
$41$		−	9.62324i		−	1.50290i	−0.659792	−	0.751448i	$-0.729356\pi$
$41$		−	9.62324i		−	1.50290i	0.659792	−	0.751448i	$-0.270644\pi$
$42$	−1.15740	+	1.27722i	−0.178590	+	0.197080i
$43$	−5.54209	−	5.54209i	−0.845160	−	0.845160i	0.144364	−	0.989525i	$-0.453886\pi$
$43$	−5.54209	−	5.54209i	−0.845160	−	0.845160i	−0.989525	+	0.144364i	$0.953886\pi$
$44$	−8.01671	+	9.77204i	−1.20856	+	1.47319i
$45$	2.07275	−	2.67829i	0.308987	−	0.399256i
$46$	−0.543613	+	0.0267559i	−0.0801513	+	0.00394494i
$47$			5.93369i			0.865518i	0.901510	+	0.432759i	$0.142460\pi$
$47$			5.93369i			0.865518i	−0.901510	+	0.432759i	$0.857540\pi$
$48$	2.70700	−	4.05452i	0.390721	−	0.585219i
$49$	1.00000			0.142857
$50$	−2.10802	−	6.74954i	−0.298119	−	0.954529i
$51$	2.73921	+	2.73921i	0.383567	+	0.383567i
$52$	−4.62330	+	5.63561i	−0.641136	+	0.781519i
$53$	5.22510	+	5.22510i	0.717722	+	0.717722i	0.968138	−	0.250416i	$-0.0805674\pi$
$53$	5.22510	+	5.22510i	0.717722	+	0.717722i	−0.250416	+	0.968138i	$0.580567\pi$
$54$	−5.76612	−	5.22514i	−0.784669	−	0.711052i
$55$	14.0181	−	1.78668i	1.89021	−	0.240915i
$56$	−2.79770	+	0.415785i	−0.373858	+	0.0555616i
$57$	1.30143			0.172379
$58$	−0.540383	−	0.489685i	−0.0709558	−	0.0642988i
$59$	−8.39229	+	8.39229i	−1.09258	+	1.09258i	−0.0973309	+	0.995252i	$0.531031\pi$
$59$	−8.39229	+	8.39229i	−1.09258	+	1.09258i	−0.995252	+	0.0973309i	$0.968969\pi$
$60$	−5.31303	+	1.21674i	−0.685909	+	0.157081i
$61$	5.49892	+	5.49892i	0.704065	+	0.704065i	0.965280	−	0.261216i	$-0.0841234\pi$
$61$	5.49892	+	5.49892i	0.704065	+	0.704065i	−0.261216	+	0.965280i	$0.584123\pi$
$62$	−9.39847	+	0.462580i	−1.19361	+	0.0587477i
$63$			1.51457i			0.190817i
$64$	7.65425	−	2.32648i	0.956781	−	0.290810i
$65$	8.08437	−	1.03039i	1.00274	−	0.127804i
$66$	−0.535489	−	10.8798i	−0.0659141	−	1.33921i
$67$	−9.71951	+	9.71951i	−1.18743	+	1.18743i	−0.209651	+	0.977776i	$0.567233\pi$
$67$	−9.71951	+	9.71951i	−1.18743	+	1.18743i	−0.977776	+	0.209651i	$0.932767\pi$
$68$	0.624242	+	6.32616i	0.0757004	+	0.767159i
$69$	0.331674	−	0.331674i	0.0399289	−	0.0399289i
$70$	2.59295	+	1.81014i	0.309917	+	0.216353i
$71$		−	11.7154i		−	1.39037i	−0.718832	−	0.695184i	$-0.755323\pi$
$71$		−	11.7154i		−	1.39037i	0.718832	−	0.695184i	$-0.244677\pi$
$72$	−0.629733	−	4.23730i	−0.0742148	−	0.499370i
$73$	1.01014			0.118227			0.0591137	−	0.998251i	$-0.481173\pi$
$73$	1.01014			0.118227			0.0591137	+	0.998251i	$0.481173\pi$
$74$	4.87083	+	4.41385i	0.566222	+	0.513100i
$75$	5.25215	+	3.09043i	0.606466	+	0.356853i
$76$	1.65111	+	1.35452i	0.189395	+	0.155374i
$77$	−4.46879	+	4.46879i	−0.509266	+	0.509266i
$78$	−0.308820	−	6.27447i	−0.0349670	−	0.710443i
$79$	−16.9731			−1.90962			−0.954812	−	0.297211i	$-0.903944\pi$
$79$	−16.9731			−1.90962			−0.954812	+	0.297211i	$0.903944\pi$
$80$	−8.00693	−	3.98610i	−0.895202	−	0.445660i
$81$	2.16240			0.240266
$82$	0.669021	+	13.5929i	0.0738811	+	1.50108i
$83$	−9.36697	+	9.36697i	−1.02816	+	1.02816i	−0.0285672	+	0.999592i	$0.509094\pi$
$83$	−9.36697	+	9.36697i	−1.02816	+	1.02816i	−0.999592	+	0.0285672i	$0.990906\pi$
$84$	1.54603	−	1.88455i	0.168686	−	0.205621i
$85$	4.34984	−	5.62062i	0.471806	−	0.609642i
$86$	8.21351	+	7.44292i	0.885686	+	0.802591i
$87$	0.628475			0.0673796
$88$	10.6443	−	14.3604i	1.13468	−	1.53082i
$89$			7.52367i			0.797507i	0.917058	+	0.398754i	$0.130557\pi$
$89$			7.52367i			0.797507i	−0.917058	+	0.398754i	$0.869443\pi$
$90$	−2.74157	+	3.92720i	−0.288987	+	0.413963i
$91$	−2.57718	+	2.57718i	−0.270162	+	0.270162i
$92$	0.765995	−	0.0755855i	0.0798605	−	0.00788033i
$93$	5.73429	−	5.73429i	0.594618	−	0.594618i
$94$	−0.412519	−	8.38136i	−0.0425481	−	0.864471i
$95$	−0.301881	−	2.36854i	−0.0309723	−	0.243007i
$96$	−3.54177	+	5.91522i	−0.361480	+	0.603719i
$97$			8.65054i			0.878329i	0.898407	+	0.439164i	$0.144725\pi$
$97$			8.65054i			0.878329i	−0.898407	+	0.439164i	$0.855275\pi$
$98$	−1.41250	+	0.0695215i	−0.142684	+	0.00702273i
$99$	−6.76827	−	6.76827i	−0.680237	−	0.680237i
$100$	3.44682	+	9.38720i	0.344682	+	0.938720i
$101$	9.63329	−	9.63329i	0.958548	−	0.958548i	−0.0406266	−	0.999174i	$-0.512935\pi$
$101$	9.63329	−	9.63329i	0.958548	−	0.958548i	0.999174	+	0.0406266i	$0.0129354\pi$
$102$	−4.05958	−	3.67872i	−0.401959	−	0.364247i
$103$	3.00769			0.296356			0.148178	−	0.988961i	$-0.452659\pi$
$103$	3.00769			0.296356			0.148178	+	0.988961i	$0.452659\pi$
$104$	6.13863	−	8.28174i	0.601942	−	0.812091i
$105$	−2.70341	+	0.344562i	−0.263826	+	0.0336258i
$106$	−7.74373	−	7.01721i	−0.752137	−	0.681572i
$107$	3.85453	+	3.85453i	0.372632	+	0.372632i	0.868435	−	0.495803i	$-0.165126\pi$
$107$	3.85453	+	3.85453i	0.372632	+	0.372632i	−0.495803	+	0.868435i	$0.665126\pi$
$108$	8.50792	+	6.97966i	0.818675	+	0.671618i
$109$	3.00543	+	3.00543i	0.287868	+	0.287868i	0.836237	−	0.548369i	$-0.184751\pi$
$109$	3.00543	+	3.00543i	0.287868	+	0.287868i	−0.548369	+	0.836237i	$0.684751\pi$
$110$	−19.6765	+	3.49825i	−1.87608	+	0.333545i
$111$	−5.66486			−0.537684
$112$	3.92286	−	0.781798i	0.370675	−	0.0738729i
$113$			3.03344i			0.285362i	0.989769	+	0.142681i	$0.0455723\pi$
$113$			3.03344i			0.285362i	−0.989769	+	0.142681i	$0.954428\pi$
$114$	−1.83828	+	0.0904775i	−0.172171	+	0.00847399i
$115$	−0.680565	−	0.526695i	−0.0634630	−	0.0491145i
$116$	0.797337	+	0.654113i	0.0740309	+	0.0607329i
$117$	−3.90331	−	3.90331i	−0.360861	−	0.360861i
$118$	11.2707	−	12.4376i	1.03755	−	1.14497i
$119$			3.17844i			0.291367i
$120$	7.42008	−	2.08802i	0.677357	−	0.190609i
$121$		−	28.9401i		−	2.63092i
$122$	−8.14954	−	7.38495i	−0.737824	−	0.668602i
$123$	−8.29341	−	8.29341i	−0.747791	−	0.747791i
$124$	13.2432	−	1.30679i	1.18928	−	0.117353i
$125$	4.40614	−	10.2755i	0.394097	−	0.919069i
$126$	−0.105295	−	2.13933i	−0.00938041	−	0.190587i
$127$		−	5.51304i		−	0.489203i	−0.969624	−	0.244602i	$-0.921343\pi$
$127$		−	5.51304i		−	0.489203i	0.969624	−	0.244602i	$-0.0786572\pi$
$128$	−10.6499	+	3.81830i	−0.941328	+	0.337493i
$129$	−9.55246			−0.841047
$130$	−11.3476	+	2.01747i	−0.995248	+	0.176943i
$131$	−10.0465	−	10.0465i	−0.877766	−	0.877766i	0.115537	−	0.993303i	$-0.463141\pi$
$131$	−10.0465	−	10.0465i	−0.877766	−	0.877766i	−0.993303	+	0.115537i	$0.963141\pi$
$132$	1.51276	+	15.3305i	0.131669	+	1.33435i
$133$	0.755057	+	0.755057i	0.0654718	+	0.0654718i
$134$	13.0531	−	14.4046i	1.12762	−	1.24436i
$135$	−1.55555	−	12.2047i	−0.133880	−	1.05042i
$136$	−1.32155	−	8.89232i	−0.113322	−	0.762510i
$137$	11.0865			0.947183			0.473592	−	0.880745i	$-0.342957\pi$
$137$	11.0865			0.947183			0.473592	+	0.880745i	$0.342957\pi$
$138$	−0.445433	+	0.491550i	−0.0379177	+	0.0418435i
$139$	3.35709	−	3.35709i	0.284745	−	0.284745i	−0.550253	−	0.834998i	$-0.685469\pi$
$139$	3.35709	−	3.35709i	0.284745	−	0.284745i	0.834998	+	0.550253i	$0.185469\pi$
$140$	−3.78840	−	2.37656i	−0.320178	−	0.200856i
$141$	5.11372	+	5.11372i	0.430653	+	0.430653i
$142$	0.814475	+	16.5481i	0.0683492	+	1.38869i
$143$		−	23.0338i		−	1.92618i
$144$	1.18408	+	5.94142i	0.0986736	+	0.495118i
$145$	−0.145782	−	1.14379i	−0.0121065	−	0.0949868i
$146$	−1.42682	+	0.0702261i	−0.118085	+	0.00581196i
$147$	0.861811	−	0.861811i	0.0710809	−	0.0710809i
$148$	−7.18692	−	5.89595i	−0.590761	−	0.484644i
$149$	−0.693994	+	0.693994i	−0.0568542	+	0.0568542i	−0.734962	−	0.678108i	$-0.762800\pi$
$149$	−0.693994	+	0.693994i	−0.0568542	+	0.0568542i	0.678108	+	0.734962i	$0.262800\pi$
$150$	−7.63353	−	4.00011i	−0.623275	−	0.326608i
$151$			11.7111i			0.953032i	0.879166	+	0.476516i	$0.158101\pi$
$151$			11.7111i			0.953032i	−0.879166	+	0.476516i	$0.841899\pi$
$152$	−2.42636	−	1.79848i	−0.196804	−	0.145876i
$153$	−4.81396			−0.389185
$154$	6.00150	−	6.62285i	0.483615	−	0.533685i
$155$	−11.7662	−	9.10598i	−0.945087	−	0.731410i
$156$	0.872420	+	8.84124i	0.0698495	+	0.707865i
$157$	6.15319	−	6.15319i	0.491078	−	0.491078i	−0.417568	−	0.908646i	$-0.637117\pi$
$157$	6.15319	−	6.15319i	0.491078	−	0.491078i	0.908646	+	0.417568i	$0.137117\pi$
$158$	23.9746	−	1.18000i	1.90731	−	0.0938754i
$159$	9.00609			0.714229
$160$	11.5869	+	5.07373i	0.916028	+	0.401114i
$161$	0.384857			0.0303310
$162$	−3.05439	+	0.150333i	−0.239976	+	0.0118113i
$163$	−2.61475	+	2.61475i	−0.204803	+	0.204803i	−0.802054	−	0.597251i	$-0.796260\pi$
$163$	−2.61475	+	2.61475i	−0.204803	+	0.204803i	0.597251	+	0.802054i	$0.296260\pi$
$164$	−1.88999	−	19.1534i	−0.147583	−	1.49563i
$165$	10.5412	−	13.6208i	0.820632	−	1.06037i
$166$	12.5797	−	13.8821i	0.976373	−	1.07746i
$167$	1.25268			0.0969351			0.0484675	−	0.998825i	$-0.484566\pi$
$167$	1.25268			0.0969351			0.0484675	+	0.998825i	$0.484566\pi$
$168$	−2.05276	+	2.76941i	−0.158374	+	0.213665i
$169$		−	0.283750i		−	0.0218269i
$170$	−5.75341	+	8.24155i	−0.441266	+	0.632098i
$171$	−1.14358	+	1.14358i	−0.0874520	+	0.0874520i
$172$	−12.1191	−	9.94214i	−0.924069	−	0.758081i
$173$	11.7397	−	11.7397i	0.892554	−	0.892554i	−0.102209	−	0.994763i	$-0.532591\pi$
$173$	11.7397	−	11.7397i	0.892554	−	0.892554i	0.994763	+	0.102209i	$0.0325909\pi$
$174$	−0.887724	+	0.0436925i	−0.0672982	+	0.00331232i
$175$	1.25417	+	4.84015i	0.0948065	+	0.365881i
$176$	−14.0367	+	21.0241i	−1.05806	+	1.58475i
$177$			14.4651i			1.08727i
$178$	−0.523056	−	10.6272i	−0.0392047	−	0.796543i
$179$	3.61528	+	3.61528i	0.270219	+	0.270219i	0.829188	−	0.558969i	$-0.188803\pi$
$179$	3.61528	+	3.61528i	0.270219	+	0.270219i	−0.558969	+	0.829188i	$0.688803\pi$
$180$	3.59945	−	5.73778i	0.268287	−	0.427669i
$181$	−10.4829	+	10.4829i	−0.779188	+	0.779188i	−0.979693	−	0.200505i	$-0.935742\pi$
$181$	−10.4829	+	10.4829i	−0.779188	+	0.779188i	0.200505	+	0.979693i	$0.435742\pi$
$182$	3.46111	−	3.81945i	0.256555	−	0.283117i
$183$	9.47805			0.700638
$184$	−1.07672	+	0.160018i	−0.0793765	+	0.0117967i
$185$	1.31402	+	10.3097i	0.0966090	+	0.757988i
$186$	−7.70105	+	8.49836i	−0.564668	+	0.623130i
$187$	−14.2038	−	14.2038i	−1.03868	−	1.03868i
$188$	1.16537	+	11.8100i	0.0849933	+	0.861334i
$189$	3.89070	+	3.89070i	0.283007	+	0.283007i
$190$	0.591072	+	3.32458i	0.0428809	+	0.241191i
$191$	−6.45816			−0.467296			−0.233648	−	0.972321i	$-0.575066\pi$
$191$	−6.45816			−0.467296			−0.233648	+	0.972321i	$0.575066\pi$
$192$	4.59152	−	8.60150i	0.331365	−	0.620760i
$193$		−	6.07558i		−	0.437330i	−0.975800	−	0.218665i	$-0.929830\pi$
$193$		−	6.07558i		−	0.437330i	0.975800	−	0.218665i	$-0.0701702\pi$
$194$	−0.601398	−	12.2189i	−0.0431779	−	0.877267i
$195$	6.07920	−	7.85520i	0.435340	−	0.562522i
$196$	1.99033	−	0.196399i	0.142167	−	0.0140285i
$197$	−19.3031	−	19.3031i	−1.37529	−	1.37529i	−0.852404	−	0.522883i	$-0.824856\pi$
$197$	−19.3031	−	19.3031i	−1.37529	−	1.37529i	−0.522883	−	0.852404i	$-0.675144\pi$
$198$	10.0307	+	9.08966i	0.712854	+	0.645974i
$199$			13.4844i			0.955885i	0.878391	+	0.477942i	$0.158617\pi$
$199$			13.4844i			0.955885i	−0.878391	+	0.477942i	$0.841383\pi$
$200$	−5.52126	−	13.0198i	−0.390412	−	0.920640i
$201$			16.7528i			1.18165i
$202$	−12.9373	+	14.2768i	−0.910268	+	1.00451i
$203$	0.364625	+	0.364625i	0.0255917	+	0.0255917i
$204$	5.98993	+	4.91397i	0.419379	+	0.344047i
$205$	−13.1698	+	17.0173i	−0.919821	+	1.18854i
$206$	−4.24837	+	0.209099i	−0.295998	+	0.0145686i
$207$			0.582892i			0.0405138i
$208$	−8.09508	+	12.1248i	−0.561293	+	0.840700i
$209$	−6.74838			−0.466795
$210$	3.79463	−	0.674641i	0.261854	−	0.0465547i
$211$	14.3838	+	14.3838i	0.990224	+	0.990224i	0.999953	−	0.00972876i	$-0.00309681\pi$
$211$	14.3838	+	14.3838i	0.990224	+	0.990224i	−0.00972876	+	0.999953i	$0.503097\pi$
$212$	11.4259	+	9.37348i	0.784733	+	0.643774i
$213$	−10.0965	−	10.0965i	−0.691800	−	0.691800i
$214$	−5.71251	−	5.17657i	−0.390499	−	0.353863i
$215$	2.21579	+	17.3850i	0.151116	+	1.18565i
$216$	−12.5027	−	9.26732i	−0.850701	−	0.630561i
$217$	6.65377			0.451687
$218$	−4.45412	−	4.03624i	−0.301671	−	0.273369i
$219$	0.870546	−	0.870546i	0.0588260	−	0.0588260i
$220$	27.5499	−	6.30923i	1.85741	−	0.425368i
$221$	−8.19143	−	8.19143i	−0.551015	−	0.551015i
$222$	8.00163	−	0.393829i	0.537034	−	0.0264321i
$223$			4.58754i			0.307204i	0.988133	+	0.153602i	$0.0490874\pi$
$223$			4.58754i			0.307204i	−0.988133	+	0.153602i	$0.950913\pi$
$224$	−5.48670	+	1.37701i	−0.366595	+	0.0920057i
$225$	−7.33072	+	1.89952i	−0.488715	+	0.126635i
$226$	−0.210889	−	4.28474i	−0.0140281	−	0.285017i
$227$	8.61146	−	8.61146i	0.571563	−	0.571563i	−0.361002	−	0.932565i	$-0.617565\pi$
$227$	8.61146	−	8.61146i	0.571563	−	0.571563i	0.932565	+	0.361002i	$0.117565\pi$
$228$	2.59028	−	0.255600i	0.171546	−	0.0169275i
$229$	4.93592	−	4.93592i	0.326175	−	0.326175i	−0.524955	−	0.851130i	$-0.675918\pi$
$229$	4.93592	−	4.93592i	0.326175	−	0.326175i	0.851130	+	0.524955i	$0.175918\pi$
$230$	0.997918	+	0.696644i	0.0658007	+	0.0459354i
$231$			7.70250i			0.506787i
$232$	−1.17172	−	0.868506i	−0.0769270	−	0.0570202i
$233$	27.3076			1.78898			0.894490	−	0.447087i	$-0.147539\pi$
$233$	27.3076			1.78898			0.894490	+	0.447087i	$0.147539\pi$
$234$	5.78481	+	5.24208i	0.378165	+	0.342685i
$235$	8.12052	−	10.4929i	0.529724	−	0.684480i
$236$	−15.0552	+	18.3517i	−0.980011	+	1.19459i
$237$	−14.6276	+	14.6276i	−0.950165	+	0.950165i
$238$	−0.220970	−	4.48956i	−0.0143234	−	0.291015i
$239$	2.21374			0.143195			0.0715974	−	0.997434i	$-0.477190\pi$
$239$	2.21374			0.143195			0.0715974	+	0.997434i	$0.477190\pi$
$240$	−10.3357	+	3.46519i	−0.667168	+	0.223677i
$241$	7.34980			0.473442			0.236721	−	0.971578i	$-0.423927\pi$
$241$	7.34980			0.473442			0.236721	+	0.971578i	$0.423927\pi$
$242$	2.01196	+	40.8780i	0.129334	+	2.62774i
$243$	−9.80852	+	9.80852i	−0.629217	+	0.629217i
$244$	12.0247	+	9.86470i	0.769800	+	0.631523i
$245$	−1.76836	−	1.36854i	−0.112976	−	0.0874331i
$246$	12.2910	+	11.1379i	0.783648	+	0.710126i
$247$	−3.89184			−0.247632
$248$	−18.6152	+	2.76653i	−1.18207	+	0.175675i
$249$			16.1451i			1.02316i
$250$	−5.50932	+	14.8205i	−0.348440	+	0.937331i
$251$	7.82501	−	7.82501i	0.493910	−	0.493910i	−0.415626	−	0.909536i	$-0.636437\pi$
$251$	7.82501	−	7.82501i	0.493910	−	0.493910i	0.909536	+	0.415626i	$0.136437\pi$
$252$	0.297459	+	3.01449i	0.0187381	+	0.189895i
$253$	−1.71985	+	1.71985i	−0.108126	+	0.108126i
$254$	0.383275	+	7.78719i	0.0240488	+	0.488612i
$255$	−1.09517	−	8.59264i	−0.0685823	−	0.538092i
$256$	14.7776	−	6.13376i	0.923599	−	0.383360i
$257$			27.6112i			1.72234i	0.508317	+	0.861170i	$0.330268\pi$
$257$			27.6112i			1.72234i	−0.508317	+	0.861170i	$0.669732\pi$
$258$	13.4929	−	0.664101i	0.840030	−	0.0413451i
$259$	−3.28660	−	3.28660i	−0.204220	−	0.204220i
$260$	15.8882	−	3.63858i	0.985346	−	0.225655i
$261$	−0.552248	+	0.552248i	−0.0341833	+	0.0341833i
$262$	14.8892	+	13.4923i	0.919855	+	0.833555i
$263$	−10.7048			−0.660084			−0.330042	−	0.943966i	$-0.607063\pi$
$263$	−10.7048			−0.660084			−0.330042	+	0.943966i	$0.607063\pi$
$264$	−3.20258	−	21.5493i	−0.197105	−	1.32627i
$265$	−2.08906	−	16.3906i	−0.128330	−	1.00687i
$266$	−1.11901	−	1.01403i	−0.0686111	−	0.0621741i
$267$	6.48398	+	6.48398i	0.396813	+	0.396813i
$268$	−17.4362	+	21.2540i	−1.06508	+	1.29829i
$269$	18.2550	+	18.2550i	1.11303	+	1.11303i	0.992739	+	0.120289i	$0.0383820\pi$
$269$	18.2550	+	18.2550i	1.11303	+	1.11303i	0.120289	+	0.992739i	$0.461618\pi$
$270$	3.04571	+	17.1311i	0.185356	+	1.04257i
$271$	−7.52231			−0.456948			−0.228474	−	0.973550i	$-0.573374\pi$
$271$	−7.52231			−0.456948			−0.228474	+	0.973550i	$0.573374\pi$
$272$	2.48490	+	12.4686i	0.150669	+	0.756018i
$273$			4.44209i			0.268847i
$274$	−15.6597	+	0.770750i	−0.946038	+	0.0465627i
$275$	−27.2342	−	16.0250i	−1.64229	−	0.966342i
$276$	0.595002	−	0.725283i	0.0358149	−	0.0436569i
$277$	−4.04046	−	4.04046i	−0.242768	−	0.242768i	0.575226	−	0.817994i	$-0.304914\pi$
$277$	−4.04046	−	4.04046i	−0.242768	−	0.242768i	−0.817994	+	0.575226i	$0.804914\pi$
$278$	−4.50852	+	4.97530i	−0.270403	+	0.298399i
$279$			10.0776i			0.603328i
$280$	5.51635	+	3.09352i	0.329665	+	0.184873i
$281$			4.33763i			0.258762i	0.991595	+	0.129381i	$0.0412989\pi$
$281$			4.33763i			0.258762i	−0.991595	+	0.129381i	$0.958701\pi$
$282$	−7.57866	−	6.86763i	−0.451302	−	0.408961i
$283$	3.90728	+	3.90728i	0.232263	+	0.232263i	0.813637	−	0.581373i	$-0.197484\pi$
$283$	3.90728	+	3.90728i	0.232263	+	0.232263i	−0.581373	+	0.813637i	$0.697484\pi$
$284$	−2.30090	−	23.3176i	−0.136533	−	1.38365i
$285$	−2.30140	−	1.78107i	−0.136323	−	0.105501i
$286$	1.60134	+	32.5353i	0.0946893	+	1.92385i
$287$		−	9.62324i		−	0.568042i
$288$	−2.08558	−	8.30996i	−0.122894	−	0.489669i
$289$	6.89751			0.405736
$290$	0.285435	+	1.60548i	0.0167613	+	0.0942768i
$291$	7.45512	+	7.45512i	0.437027	+	0.437027i
$292$	2.01051	−	0.198389i	0.117656	−	0.0116099i
$293$	0.173800	+	0.173800i	0.0101535	+	0.0101535i	0.712165	−	0.702012i	$-0.247715\pi$
$293$	0.173800	+	0.173800i	0.0101535	+	0.0101535i	−0.702012	+	0.712165i	$0.747715\pi$
$294$	−1.15740	+	1.27722i	−0.0675007	+	0.0744893i
$295$	26.3258	−	3.35534i	1.53275	−	0.195355i
$296$	10.5614	+	7.82841i	0.613872	+	0.455017i
$297$	−34.7734			−2.01776
$298$	0.932021	−	1.02852i	0.0539905	−	0.0595803i
$299$	−0.991848	+	0.991848i	−0.0573601	+	0.0573601i
$300$	11.0605	+	5.11948i	0.638578	+	0.295573i
$301$	−5.54209	−	5.54209i	−0.319440	−	0.319440i
$302$	−0.814169	−	16.5419i	−0.0468502	−	0.951880i
$303$		−	16.6041i		−	0.953883i
$304$	3.55228	+	2.37168i	0.203737	+	0.136025i
$305$	−2.19854	−	17.2496i	−0.125888	−	0.987707i
$306$	6.79973	−	0.334673i	0.388715	−	0.0191320i
$307$	1.35307	−	1.35307i	0.0772239	−	0.0772239i	−0.667440	−	0.744664i	$-0.732610\pi$
$307$	1.35307	−	1.35307i	0.0772239	−	0.0772239i	0.744664	+	0.667440i	$0.232610\pi$
$308$	−8.01671	+	9.77204i	−0.456795	+	0.556814i
$309$	2.59206	−	2.59206i	0.147457	−	0.147457i
$310$	17.2529	+	12.0442i	0.979899	+	0.684066i
$311$		−	7.25985i		−	0.411668i	−0.978587	−	0.205834i	$-0.934009\pi$
$311$		−	7.25985i		−	0.411668i	0.978587	−	0.205834i	$-0.0659907\pi$
$312$	−1.84695	−	12.4276i	−0.104563	−	0.703576i
$313$	14.3909			0.813419			0.406710	−	0.913558i	$-0.366676\pi$
$313$	14.3909			0.813419			0.406710	+	0.913558i	$0.366676\pi$
$314$	−8.26362	+	9.11918i	−0.466343	+	0.514625i
$315$	2.07275	−	2.67829i	0.116786	−	0.150905i
$316$	−33.7821	+	3.33350i	−1.90039	+	0.187524i
$317$	22.4649	−	22.4649i	1.26175	−	1.26175i	0.311512	−	0.950242i	$-0.399165\pi$
$317$	22.4649	−	22.4649i	1.26175	−	1.26175i	0.950242	−	0.311512i	$-0.100835\pi$
$318$	−12.7211	+	0.626116i	−0.713366	+	0.0351109i
$319$	−3.25886			−0.182461
$320$	−16.7193	−	6.36113i	−0.934639	−	0.355598i
$321$	6.64375			0.370818
$322$	−0.543613	+	0.0267559i	−0.0302943	+	0.00149105i
$323$	−2.39990	+	2.39990i	−0.133534	+	0.133534i
$324$	4.30389	−	0.424692i	0.239105	−	0.0235940i
$325$	−15.7062	−	9.24173i	−0.871222	−	0.512639i
$326$	3.51156	−	3.87513i	0.194487	−	0.214623i
$327$	5.18022			0.286467
$328$	4.00119	+	26.9229i	0.220929	+	1.48657i
$329$			5.93369i			0.327135i
$330$	−13.9426	+	19.9722i	−0.767513	+	1.09943i
$331$	11.2958	−	11.2958i	0.620873	−	0.620873i	−0.324881	−	0.945755i	$-0.605324\pi$
$331$	11.2958	−	11.2958i	0.620873	−	0.620873i	0.945755	+	0.324881i	$0.105324\pi$
$332$	−16.8037	+	20.4831i	−0.922225	+	1.12415i
$333$	4.97777	−	4.97777i	0.272780	−	0.272780i
$334$	−1.76941	+	0.0870880i	−0.0968179	+	0.00476524i
$335$	30.4892	−	3.88598i	1.66580	−	0.212314i
$336$	2.70700	−	4.05452i	0.147679	−	0.221192i
$337$		−	23.1286i		−	1.25989i	−0.776638	−	0.629947i	$-0.783077\pi$
$337$		−	23.1286i		−	1.25989i	0.776638	−	0.629947i	$-0.216923\pi$
$338$	0.0197267	+	0.400798i	0.00107299	+	0.0218005i
$339$	2.61425	+	2.61425i	0.141986	+	0.141986i
$340$	7.55375	−	12.0412i	0.409659	−	0.653026i
$341$	−29.7343	+	29.7343i	−1.61020	+	1.61020i
$342$	1.53581	−	1.69482i	0.0830472	−	0.0916453i
$343$	1.00000			0.0539949
$344$	17.8094	+	13.2008i	0.960219	+	0.711738i
$345$	−1.04043	+	0.132607i	−0.0560148	+	0.00713934i
$346$	−15.7662	+	17.3986i	−0.847598	+	0.935352i
$347$	−0.738346	−	0.738346i	−0.0396365	−	0.0396365i	0.687011	−	0.726647i	$-0.258923\pi$
$347$	−0.738346	−	0.738346i	−0.0396365	−	0.0396365i	−0.726647	+	0.687011i	$0.758923\pi$
$348$	1.25088	−	0.123432i	0.0670540	−	0.00661663i
$349$	−22.1534	−	22.1534i	−1.18585	−	1.18585i	−0.978205	−	0.207640i	$-0.933422\pi$
$349$	−22.1534	−	22.1534i	−1.18585	−	1.18585i	−0.207640	−	0.978205i	$-0.566578\pi$
$350$	−2.10802	−	6.74954i	−0.112678	−	0.360778i
$351$	−20.0541			−1.07041
$352$	18.3653	−	30.6725i	0.978873	−	1.63485i
$353$			6.26050i			0.333213i	0.986023	+	0.166606i	$0.0532809\pi$
$353$			6.26050i			0.333213i	−0.986023	+	0.166606i	$0.946719\pi$
$354$	−1.00564	−	20.4320i	−0.0534490	−	1.08595i
$355$	−16.0331	+	20.7171i	−0.850949	+	1.09955i
$356$	1.47764	+	14.9746i	0.0783147	+	0.793653i
$357$	2.73921	+	2.73921i	0.144975	+	0.144975i
$358$	−5.35794	−	4.85526i	−0.283176	−	0.256608i
$359$		−	4.35961i		−	0.230091i	−0.993360	−	0.115046i	$-0.963299\pi$
$359$		−	4.35961i		−	0.230091i	0.993360	−	0.115046i	$-0.0367015\pi$
$360$	−4.68534	+	8.35487i	−0.246939	+	0.440340i
$361$		−	17.8598i		−	0.939988i
$362$	14.0783	−	15.5359i	0.739942	−	0.816550i
$363$	−24.9409	−	24.9409i	−1.30906	−	1.30906i
$364$	−4.62330	+	5.63561i	−0.242327	+	0.295386i
$365$	−1.78628	−	1.38242i	−0.0934982	−	0.0723590i
$366$	−13.3878	+	0.658928i	−0.699791	+	0.0344427i
$367$			24.5630i			1.28218i	0.767467	+	0.641089i	$0.221517\pi$
$367$			24.5630i			1.28218i	−0.767467	+	0.641089i	$0.778483\pi$
$368$	1.50974	−	0.300881i	0.0787006	−	0.0156845i
$369$	14.5750			0.758745
$370$	−2.57281	−	14.4712i	−0.133754	−	0.752322i
$371$	5.22510	+	5.22510i	0.271274	+	0.271274i
$372$	10.2869	−	12.5393i	0.533353	−	0.650135i
$373$	7.07734	+	7.07734i	0.366451	+	0.366451i	0.866181	−	0.499730i	$-0.166568\pi$
$373$	7.07734	+	7.07734i	0.366451	+	0.366451i	−0.499730	+	0.866181i	$0.666568\pi$
$374$	21.0504	+	19.0754i	1.08849	+	0.986366i
$375$	−5.05828	−	12.6528i	−0.261208	−	0.653387i
$376$	−2.46714	−	16.6007i	−0.127233	−	0.856115i
$377$	−1.87941			−0.0967946
$378$	−5.76612	−	5.22514i	−0.296577	−	0.268752i
$379$	−4.33329	+	4.33329i	−0.222586	+	0.222586i	−0.809587	−	0.587000i	$-0.800309\pi$
$379$	−4.33329	+	4.33329i	−0.222586	+	0.222586i	0.587000	+	0.809587i	$0.300309\pi$
$380$	−1.06602	−	4.65489i	−0.0546858	−	0.238791i
$381$	−4.75120	−	4.75120i	−0.243411	−	0.243411i
$382$	9.12218	−	0.448981i	0.466731	−	0.0229719i
$383$		−	7.32293i		−	0.374184i	−0.982342	−	0.187092i	$-0.940094\pi$
$383$		−	7.32293i		−	0.374184i	0.982342	−	0.187092i	$-0.0599062\pi$
$384$	−5.88756	+	12.4689i	−0.300448	+	0.636299i
$385$	14.0181	−	1.78668i	0.714431	−	0.0910574i
$386$	0.422383	+	8.58178i	0.0214987	+	0.436801i
$387$	8.39385	−	8.39385i	0.426683	−	0.426683i
$388$	1.69895	+	17.2175i	0.0862513	+	0.874084i
$389$	−20.9917	+	20.9917i	−1.06432	+	1.06432i	−0.0665375	+	0.997784i	$0.521195\pi$
$389$	−20.9917	+	20.9917i	−1.06432	+	1.06432i	−0.997784	+	0.0665375i	$0.978805\pi$
$390$	−8.04078	+	11.5181i	−0.407161	+	0.583243i
$391$			1.22325i			0.0618623i
$392$	−2.79770	+	0.415785i	−0.141305	+	0.0210003i
$393$	−17.3164			−0.873494
$394$	28.6077	+	25.9237i	1.44123	+	1.30602i
$395$	30.0145	+	23.2285i	1.51019	+	1.16875i
$396$	−14.8004	−	12.1418i	−0.743748	−	0.610150i
$397$	19.8861	−	19.8861i	0.998057	−	0.998057i	−0.00194128	−	0.999998i	$-0.500618\pi$
$397$	19.8861	−	19.8861i	0.998057	−	0.998057i	0.999998	+	0.00194128i	$0.000617930\pi$
$398$	−0.937456	−	19.0468i	−0.0469904	−	0.954729i
$399$	1.30143			0.0651531
$400$	8.70395	+	18.0067i	0.435198	+	0.900335i
$401$	−7.30430			−0.364760			−0.182380	−	0.983228i	$-0.558380\pi$
$401$	−7.30430			−0.364760			−0.182380	+	0.983228i	$0.558380\pi$
$402$	−1.16468	−	23.6633i	−0.0580888	−	1.18022i
$403$	−17.1480	+	17.1480i	−0.854202	+	0.854202i
$404$	17.2815	−	21.0654i	0.859786	−	1.04804i
$405$	−3.82389	−	2.95934i	−0.190011	−	0.147051i
$406$	−0.540383	−	0.489685i	−0.0268188	−	0.0243026i
$407$	29.3743			1.45603
$408$	−8.80242	−	6.52458i	−0.435785	−	0.323015i
$409$			7.26905i			0.359432i	0.983719	+	0.179716i	$0.0575178\pi$
$409$			7.26905i			0.359432i	−0.983719	+	0.179716i	$0.942482\pi$
$410$	17.4194	−	24.9526i	0.860281	−	1.23232i
$411$	9.55446	−	9.55446i	0.471287	−	0.471287i
$412$	5.98631	−	0.590706i	0.294924	−	0.0291020i
$413$	−8.39229	+	8.39229i	−0.412958	+	0.412958i
$414$	−0.0405235	−	0.823337i	−0.00199162	−	0.0404648i
$415$	29.3833	−	3.74503i	1.44237	−	0.183836i
$416$	10.5914	−	17.6890i	0.519286	−	0.867277i
$417$		−	5.78636i		−	0.283359i
$418$	9.53211	−	0.469157i	0.466231	−	0.0229472i
$419$	−4.50077	−	4.50077i	−0.219877	−	0.219877i	0.588570	−	0.808446i	$-0.299691\pi$
$419$	−4.50077	−	4.50077i	−0.219877	−	0.219877i	−0.808446	+	0.588570i	$0.799691\pi$
$420$	−5.31303	+	1.21674i	−0.259249	+	0.0593709i
$421$	14.6650	−	14.6650i	0.714731	−	0.714731i	−0.252790	−	0.967521i	$-0.581348\pi$
$421$	14.6650	−	14.6650i	0.714731	−	0.714731i	0.967521	+	0.252790i	$0.0813483\pi$
$422$	−21.3172	−	19.3172i	−1.03771	−	0.940348i
$423$	−8.98696			−0.436961
$424$	−16.7908	−	12.4457i	−0.815432	−	0.604418i
$425$	−15.3841	+	3.98631i	−0.746240	+	0.193364i
$426$	14.9633	+	13.5594i	0.724972	+	0.656956i
$427$	5.49892	+	5.49892i	0.266111	+	0.266111i
$428$	8.42883	+	6.91478i	0.407423	+	0.334238i
$429$	−19.8507	−	19.8507i	−0.958403	−	0.958403i
$430$	−4.33845	−	24.4023i	−0.209218	−	1.17678i
$431$	7.22097			0.347822			0.173911	−	0.984761i	$-0.444359\pi$
$431$	7.22097			0.347822			0.173911	+	0.984761i	$0.444359\pi$
$432$	18.3044	+	12.2209i	0.880670	+	0.587979i
$433$			13.1606i			0.632457i	0.948683	+	0.316229i	$0.102417\pi$
$433$			13.1606i			0.632457i	−0.948683	+	0.316229i	$0.897583\pi$
$434$	−9.39847	+	0.462580i	−0.451141	+	0.0222045i
$435$	−1.11137	−	0.860096i	−0.0532860	−	0.0412385i
$436$	6.57207	+	5.39155i	0.314745	+	0.258208i
$437$	0.290589	+	0.290589i	0.0139008	+	0.0139008i
$438$	−1.16913	+	1.29017i	−0.0558631	+	0.0616467i
$439$			11.0196i			0.525936i	0.964805	+	0.262968i	$0.0847013\pi$
$439$			11.0196i			0.525936i	−0.964805	+	0.262968i	$0.915299\pi$
$440$	−38.4757	+	10.8271i	−1.83426	+	0.516162i
$441$			1.51457i			0.0721221i
$442$	12.1399	+	11.0009i	0.577436	+	0.523261i
$443$	7.83150	+	7.83150i	0.372086	+	0.372086i	0.868237	−	0.496151i	$-0.165254\pi$
$443$	7.83150	+	7.83150i	0.372086	+	0.372086i	−0.496151	+	0.868237i	$0.665254\pi$
$444$	−11.2750	+	1.11257i	−0.535086	+	0.0528003i
$445$	10.2965	−	13.3045i	0.488100	−	0.630695i
$446$	−0.318932	−	6.47991i	−0.0151019	−	0.306833i
$447$			1.19618i			0.0565775i
$448$	7.65425	−	2.32648i	0.361629	−	0.109916i
$449$	−20.0547			−0.946440			−0.473220	−	0.880944i	$-0.656908\pi$
$449$	−20.0547			−0.946440			−0.473220	+	0.880944i	$0.656908\pi$
$450$	10.2226	−	3.19273i	0.481899	−	0.150507i
$451$	43.0042	+	43.0042i	2.02499	+	2.02499i
$452$	0.595763	+	6.03755i	0.0280223	+	0.283983i
$453$	10.0927	+	10.0927i	0.474197	+	0.474197i
$454$	−11.5650	+	12.7624i	−0.542774	+	0.598969i
$455$	8.08437	−	1.03039i	0.379001	−	0.0483054i
$456$	−3.64102	+	0.541116i	−0.170506	+	0.0253401i
$457$	−18.0865			−0.846049			−0.423024	−	0.906118i	$-0.639032\pi$
$457$	−18.0865			−0.846049			−0.423024	+	0.906118i	$0.639032\pi$
$458$	−6.62885	+	7.31516i	−0.309746	+	0.341815i
$459$	−12.3664	+	12.3664i	−0.577212	+	0.577212i
$460$	−1.45799	−	0.914636i	−0.0679793	−	0.0426451i
$461$	0.211098	+	0.211098i	0.00983180	+	0.00983180i	0.712006	−	0.702174i	$-0.247787\pi$
$461$	0.211098	+	0.211098i	0.00983180	+	0.00983180i	−0.702174	+	0.712006i	$0.747787\pi$
$462$	−0.535489	−	10.8798i	−0.0249132	−	0.506174i
$463$		−	0.0595355i		−	0.00276685i	−0.999999	−	0.00138342i	$-0.999560\pi$
$463$		−	0.0595355i		−	0.00276685i	0.999999	−	0.00138342i	$-0.000440358\pi$
$464$	1.71543	+	1.14531i	0.0796370	+	0.0531696i
$465$	−17.9879	+	2.29264i	−0.834168	+	0.106319i
$466$	−38.5721	+	1.89846i	−1.78682	+	0.0879447i
$467$	3.00128	−	3.00128i	0.138883	−	0.138883i	−0.634247	−	0.773130i	$-0.718690\pi$
$467$	3.00128	−	3.00128i	0.138883	−	0.138883i	0.773130	+	0.634247i	$0.218690\pi$
$468$	−8.53550	−	7.00229i	−0.394554	−	0.323681i
$469$	−9.71951	+	9.71951i	−0.448805	+	0.448805i
$470$	−10.7408	+	15.3858i	−0.495435	+	0.709693i
$471$		−	10.6058i		−	0.488688i
$472$	19.9897	−	26.9685i	0.920101	−	1.24133i
$473$	49.5328			2.27752
$474$	19.6446	−	21.6785i	0.902307	−	0.995725i
$475$	−2.70762	+	4.60156i	−0.124234	+	0.211134i
$476$	0.624242	+	6.32616i	0.0286121	+	0.289959i
$477$	−7.91375	+	7.91375i	−0.362346	+	0.362346i
$478$	−3.12691	+	0.153902i	−0.143022	+	0.00703933i
$479$	15.4830			0.707434			0.353717	−	0.935352i	$-0.384918\pi$
$479$	15.4830			0.707434			0.353717	+	0.935352i	$0.384918\pi$
$480$	14.3583	−	5.61315i	0.655366	−	0.256204i
$481$	16.9404			0.772414
$482$	−10.3816	+	0.510969i	−0.472870	+	0.0232740i
$483$	0.331674	−	0.331674i	0.0150917	−	0.0150917i
$484$	−5.68380	−	57.6005i	−0.258354	−	2.61820i
$485$	11.8386	−	15.2972i	0.537565	−	0.694612i
$486$	13.1727	−	14.5365i	0.597525	−	0.659388i
$487$	−28.8777			−1.30858			−0.654288	−	0.756246i	$-0.727031\pi$
$487$	−28.8777			−1.30858			−0.654288	+	0.756246i	$0.727031\pi$
$488$	−17.6707	−	13.0980i	−0.799915	−	0.592917i
$489$			4.50684i			0.203806i
$490$	2.59295	+	1.81014i	0.117138	+	0.0817736i
$491$	13.7382	−	13.7382i	0.619995	−	0.619995i	−0.325535	−	0.945530i	$-0.605544\pi$
$491$	13.7382	−	13.7382i	0.619995	−	0.619995i	0.945530	+	0.325535i	$0.105544\pi$
$492$	−18.1355	−	14.8778i	−0.817610	−	0.670744i
$493$	−1.15894	+	1.15894i	−0.0521960	+	0.0521960i
$494$	5.49724	−	0.270567i	0.247333	−	0.0121734i
$495$	2.70604	+	21.2314i	0.121627	+	0.954280i
$496$	26.1018	−	5.20190i	1.17200	−	0.233572i
$497$		−	11.7154i		−	0.525509i
$498$	−1.12243	−	22.8050i	−0.0502974	−	1.02192i
$499$	−18.7148	−	18.7148i	−0.837788	−	0.837788i	0.150780	−	0.988567i	$-0.451822\pi$
$499$	−18.7148	−	18.7148i	−0.837788	−	0.837788i	−0.988567	+	0.150780i	$0.951822\pi$
$500$	6.75159	−	21.3170i	0.301940	−	0.953327i
$501$	1.07957	−	1.07957i	0.0482317	−	0.0482317i
$502$	−10.5089	+	11.5969i	−0.469033	+	0.517593i
$503$	34.3986			1.53376			0.766878	−	0.641792i	$-0.221809\pi$
$503$	34.3986			1.53376			0.766878	+	0.641792i	$0.221809\pi$
$504$	−0.629733	−	4.23730i	−0.0280505	−	0.188744i
$505$	−30.2187	+	3.85151i	−1.34471	+	0.171390i
$506$	2.30972	−	2.54886i	0.102680	−	0.113310i
$507$	−0.244539	−	0.244539i	−0.0108603	−	0.0108603i
$508$	−1.08275	−	10.9728i	−0.0480395	−	0.486839i
$509$	1.51820	+	1.51820i	0.0672929	+	0.0672929i	0.739952	−	0.672659i	$-0.234848\pi$
$509$	1.51820	+	1.51820i	0.0672929	+	0.0672929i	−0.672659	+	0.739952i	$0.734848\pi$
$510$	2.14431	+	12.0610i	0.0949515	+	0.534070i
$511$	1.01014			0.0446858
$512$	−20.4470	+	9.69132i	−0.903637	+	0.428300i
$513$			5.87540i			0.259405i
$514$	−1.91957	−	39.0009i	−0.0846687	−	1.72026i
$515$	−5.31867	−	4.11616i	−0.234369	−	0.181380i
$516$	−19.0126	+	1.87609i	−0.836982	+	0.0825902i
$517$	−26.5164	−	26.5164i	−1.16619	−	1.16619i
$518$	4.87083	+	4.41385i	0.214012	+	0.193933i
$519$		−	20.2348i		−	0.888210i
$520$	−22.1892	+	6.24408i	−0.973062	+	0.273821i
$521$		−	3.64734i		−	0.159793i	−0.996803	−	0.0798964i	$-0.974541\pi$
$521$		−	3.64734i		−	0.159793i	0.996803	−	0.0798964i	$-0.0254589\pi$
$522$	0.741660	−	0.818446i	0.0324616	−	0.0358224i
$523$	−10.0679	−	10.0679i	−0.440237	−	0.440237i	0.451855	−	0.892092i	$-0.350763\pi$
$523$	−10.0679	−	10.0679i	−0.440237	−	0.440237i	−0.892092	+	0.451855i	$0.850763\pi$
$524$	−21.9690	−	18.0228i	−0.959720	−	0.787328i
$525$	5.25215	+	3.09043i	0.229223	+	0.134878i
$526$	15.1205	−	0.744211i	0.659286	−	0.0324491i
$527$			21.1486i			0.921248i
$528$	6.02179	+	30.2158i	0.262065	+	1.31497i
$529$	−22.8519			−0.993560
$530$	4.09030	+	23.0066i	0.177671	+	0.999341i
$531$	−12.7107	−	12.7107i	−0.551596	−	0.551596i
$532$	1.65111	+	1.35452i	0.0715846	+	0.0587260i
$533$	24.8008	+	24.8008i	1.07424	+	1.07424i
$534$	−9.60941	−	8.70786i	−0.415840	−	0.376826i
$535$	−1.54109	−	12.0913i	−0.0666271	−	0.522752i
$536$	23.1511	−	31.2335i	0.999973	−	1.34908i
$537$	6.23138			0.268904
$538$	−27.0544	−	24.5162i	−1.16640	−	1.05697i
$539$	−4.46879	+	4.46879i	−0.192484	+	0.192484i
$540$	−5.49306	−	23.9860i	−0.236384	−	1.03219i
$541$	−19.7189	−	19.7189i	−0.847783	−	0.847783i	0.142073	−	0.989856i	$-0.454623\pi$
$541$	−19.7189	−	19.7189i	−0.847783	−	0.847783i	−0.989856	+	0.142073i	$0.954623\pi$
$542$	10.6253	−	0.522962i	0.456395	−	0.0224631i
$543$			18.0685i			0.775396i
$544$	−4.37676	−	17.4391i	−0.187652	−	0.747697i
$545$	−1.20161	−	9.42774i	−0.0514712	−	0.403840i
$546$	−0.308820	−	6.27447i	−0.0132163	−	0.268522i
$547$	3.17570	−	3.17570i	0.135783	−	0.135783i	−0.635949	−	0.771731i	$-0.719391\pi$
$547$	3.17570	−	3.17570i	0.135783	−	0.135783i	0.771731	+	0.635949i	$0.219391\pi$
$548$	22.0658	−	2.17737i	0.942605	−	0.0930128i
$549$	−8.32847	+	8.32847i	−0.355451	+	0.355451i
$550$	39.5825	+	20.7420i	1.68780	+	0.884441i
$551$			0.550625i			0.0234574i
$552$	−0.790020	+	1.06583i	−0.0336255	+	0.0453647i
$553$	−16.9731			−0.721770
$554$	5.98807	+	5.42627i	0.254409	+	0.230540i
$555$	10.0175	+	7.75261i	0.425219	+	0.329080i
$556$	6.02241	−	7.34107i	0.255407	−	0.311331i
$557$	−4.16926	+	4.16926i	−0.176657	+	0.176657i	−0.789897	−	0.613240i	$-0.789866\pi$
$557$	−4.16926	+	4.16926i	−0.176657	+	0.176657i	0.613240	+	0.789897i	$0.289866\pi$
$558$	−0.700607	−	14.2346i	−0.0296591	−	0.602598i
$559$	28.5659			1.20821
$560$	−8.00693	−	3.98610i	−0.338355	−	0.168444i
$561$	−24.4819			−1.03363
$562$	−0.301559	−	6.12692i	−0.0127205	−	0.258449i
$563$	12.7195	−	12.7195i	0.536063	−	0.536063i	−0.386307	−	0.922370i	$-0.626250\pi$
$563$	12.7195	−	12.7195i	0.536063	−	0.536063i	0.922370	+	0.386307i	$0.126250\pi$
$564$	11.1823	+	9.17368i	0.470861	+	0.386281i
$565$	4.15139	−	5.36420i	0.174650	−	0.225674i
$566$	−5.79068	−	5.24740i	−0.243400	−	0.220565i
$567$	2.16240			0.0908121
$568$	4.87110	+	32.7763i	0.204387	+	1.37526i
$569$			40.3346i			1.69091i	0.534044	+	0.845457i	$0.320672\pi$
$569$			40.3346i			1.69091i	−0.534044	+	0.845457i	$0.679328\pi$
$570$	3.37455	+	2.35577i	0.141345	+	0.0986723i
$571$	16.3410	−	16.3410i	0.683849	−	0.683849i	−0.277016	−	0.960865i	$-0.589346\pi$
$571$	16.3410	−	16.3410i	0.683849	−	0.683849i	0.960865	+	0.277016i	$0.0893456\pi$
$572$	−4.52380	−	45.8449i	−0.189150	−	1.91687i
$573$	−5.56571	+	5.56571i	−0.232511	+	0.232511i
$574$	0.669021	+	13.5929i	0.0279244	+	0.567355i
$575$	0.482677	+	1.86277i	0.0201290	+	0.0776828i
$576$	3.52361	+	11.5929i	0.146817	+	0.483036i
$577$			40.3862i			1.68130i	0.541579	+	0.840650i	$0.317827\pi$
$577$			40.3862i			1.68130i	−0.541579	+	0.840650i	$0.682173\pi$
$578$	−9.74276	+	0.479525i	−0.405245	+	0.0199456i
$579$	−5.23600	−	5.23600i	−0.217601	−	0.217601i
$580$	−0.514793	−	2.24790i	−0.0213756	−	0.0933388i
$581$	−9.36697	+	9.36697i	−0.388608	+	0.388608i
$582$	−11.0487	−	10.0121i	−0.457983	−	0.415015i
$583$	−46.6997			−1.93410
$584$	−2.82606	+	0.419999i	−0.116943	+	0.0173797i
$585$	1.56059	+	12.2443i	0.0645225	+	0.506240i
$586$	−0.257576	−	0.233411i	−0.0106404	−	0.00964211i
$587$	25.6459	+	25.6459i	1.05852	+	1.05852i	0.998178	+	0.0603409i	$0.0192188\pi$
$587$	25.6459	+	25.6459i	1.05852	+	1.05852i	0.0603409	+	0.998178i	$0.480781\pi$
$588$	1.54603	−	1.88455i	0.0637573	−	0.0777175i
$589$	5.02397	+	5.02397i	0.207009	+	0.207009i
$590$	−36.9520	+	6.56964i	−1.52129	+	0.270468i
$591$	−33.2712			−1.36859
$592$	−15.4623	−	10.3234i	−0.635498	−	0.424289i
$593$		−	0.408237i		−	0.0167643i	−0.999965	−	0.00838213i	$-0.997332\pi$
$593$		−	0.408237i		−	0.0167643i	0.999965	−	0.00838213i	$-0.00266815\pi$
$594$	49.1176	−	2.41750i	2.01532	−	0.0991912i
$595$	4.34984	−	5.62062i	0.178326	−	0.230423i
$596$	−1.24498	+	1.51758i	−0.0509963	+	0.0621624i
$597$	11.6210	+	11.6210i	0.475616	+	0.475616i
$598$	1.33203	−	1.46994i	0.0544709	−	0.0601105i
$599$		−	33.9533i		−	1.38730i	−0.720314	−	0.693648i	$-0.756002\pi$
$599$		−	33.9533i		−	1.38730i	0.720314	−	0.693648i	$-0.243998\pi$
$600$	−15.9789	−	6.46234i	−0.652336	−	0.263824i
$601$			17.1008i			0.697557i	0.937205	+	0.348779i	$0.113403\pi$
$601$			17.1008i			0.697557i	−0.937205	+	0.348779i	$0.886597\pi$
$602$	8.21351	+	7.44292i	0.334758	+	0.303351i
$603$	−14.7208	−	14.7208i	−0.599479	−	0.599479i
$604$	2.30003	+	23.3089i	0.0935871	+	0.948426i
$605$	−39.6058	+	51.1764i	−1.61021	+	2.08062i
$606$	1.15434	+	23.4534i	0.0468920	+	0.952729i
$607$			7.05606i			0.286397i	0.989694	+	0.143198i	$0.0457387\pi$
$607$			7.05606i			0.286397i	−0.989694	+	0.143198i	$0.954261\pi$
$608$	−5.18249	−	3.10304i	−0.210178	−	0.125845i
$609$	0.628475			0.0254671
$610$	4.30465	+	24.2122i	0.174290	+	0.980325i
$611$	−15.2922	−	15.2922i	−0.618657	−	0.618657i
$612$	−9.58138	+	0.945455i	−0.387304	+	0.0382177i
$613$	21.9759	+	21.9759i	0.887600	+	0.887600i	0.994292	−	0.106692i	$-0.0340259\pi$
$613$	21.9759	+	21.9759i	0.887600	+	0.887600i	−0.106692	+	0.994292i	$0.534026\pi$
$614$	−1.81715	+	2.00529i	−0.0733343	+	0.0809268i
$615$	3.31581	+	26.0156i	0.133706	+	1.04905i
$616$	10.6443	−	14.3604i	0.428870	−	0.578596i
$617$	39.3186			1.58291			0.791453	−	0.611230i	$-0.209325\pi$
$617$	39.3186			1.58291			0.791453	+	0.611230i	$0.209325\pi$
$618$	−3.48109	+	3.84150i	−0.140030	+	0.154528i
$619$	−21.3483	+	21.3483i	−0.858062	+	0.858062i	−0.991110	−	0.133048i	$-0.957524\pi$
$619$	−21.3483	+	21.3483i	−0.858062	+	0.858062i	0.133048	+	0.991110i	$0.457524\pi$
$620$	−25.2071	−	15.8131i	−1.01234	−	0.635068i
$621$	1.49736	+	1.49736i	0.0600872	+	0.0600872i
$622$	0.504715	+	10.2546i	0.0202372	+	0.411170i
$623$			7.52367i			0.301429i
$624$	3.47281	+	17.4257i	0.139024	+	0.697585i
$625$	−21.8541	+	12.1408i	−0.874164	+	0.485630i
$626$	−20.3271	+	1.00047i	−0.812436	+	0.0399870i
$627$	−5.81582	+	5.81582i	−0.232262	+	0.232262i
$628$	11.0384	−	13.4554i	0.440481	−	0.536928i
$629$	10.4463	−	10.4463i	0.416520	−	0.416520i
$630$	−2.74157	+	3.92720i	−0.109227	+	0.156463i
$631$		−	20.6470i		−	0.821945i	−0.911648	−	0.410973i	$-0.865189\pi$
$631$		−	20.6470i		−	0.821945i	0.911648	−	0.410973i	$-0.134811\pi$
$632$	47.4857	−	7.05716i	1.88888	−	0.280719i
$633$	24.7923			0.985405
$634$	−30.1700	+	33.2935i	−1.19820	+	1.32226i
$635$	−7.54484	+	9.74903i	−0.299408	+	0.386878i
$636$	17.9251	−	1.76878i	0.710777	−	0.0701368i
$637$	−2.57718	+	2.57718i	−0.102112	+	0.102112i
$638$	4.60315	−	0.226561i	0.182241	−	0.00896963i
$639$	17.7438			0.701934
$640$	24.0584	+	7.82276i	0.950990	+	0.309222i
$641$	19.9799			0.789158			0.394579	−	0.918862i	$-0.370890\pi$
$641$	19.9799			0.789158			0.394579	+	0.918862i	$0.370890\pi$
$642$	−9.38432	+	0.461883i	−0.370370	+	0.0182291i
$643$	31.6675	−	31.6675i	1.24884	−	1.24884i	0.292613	−	0.956231i	$-0.405475\pi$
$643$	31.6675	−	31.6675i	1.24884	−	1.24884i	0.956231	−	0.292613i	$-0.0945248\pi$
$644$	0.765995	−	0.0755855i	0.0301844	−	0.00297849i
$645$	16.8921	+	13.0730i	0.665128	+	0.514747i
$646$	3.22303	−	3.55672i	0.126808	−	0.139937i
$647$	4.19096			0.164764			0.0823819	−	0.996601i	$-0.473747\pi$
$647$	4.19096			0.164764			0.0823819	+	0.996601i	$0.473747\pi$
$648$	−6.04974	+	0.899092i	−0.237656	+	0.0353197i
$649$		−	75.0067i		−	2.94427i
$650$	22.8275	+	11.9621i	0.895370	+	0.469190i
$651$	5.73429	−	5.73429i	0.224744	−	0.224744i
$652$	−4.69069	+	5.71776i	−0.183702	+	0.223925i
$653$	−6.55071	+	6.55071i	−0.256349	+	0.256349i	−0.823567	−	0.567218i	$-0.808020\pi$
$653$	−6.55071	+	6.55071i	−0.256349	+	0.256349i	0.567218	+	0.823567i	$0.308020\pi$
$654$	−7.31709	+	0.360137i	−0.286121	+	0.0140825i
$655$	4.01671	+	31.5149i	0.156946	+	1.23139i
$656$	−7.52342	−	37.7506i	−0.293740	−	1.47391i
$657$			1.52992i			0.0596877i
$658$	−0.412519	−	8.38136i	−0.0160817	−	0.326739i
$659$	25.9264	+	25.9264i	1.00995	+	1.00995i	0.999950	+	0.0100002i	$0.00318321\pi$
$659$	25.9264	+	25.9264i	1.00995	+	1.00995i	0.0100002	+	0.999950i	$0.496817\pi$
$660$	18.3054	−	29.1801i	0.712538	−	1.13584i
$661$	−19.6011	+	19.6011i	−0.762396	+	0.762396i	−0.976755	−	0.214359i	$-0.931234\pi$
$661$	−19.6011	+	19.6011i	−0.762396	+	0.762396i	0.214359	+	0.976755i	$0.431234\pi$
$662$	−15.1701	+	16.7407i	−0.589601	+	0.650644i
$663$	−14.1189			−0.548333
$664$	22.3113	−	30.1006i	0.865848	−	1.16813i
$665$	−0.301881	−	2.36854i	−0.0117064	−	0.0918480i
$666$	−6.68506	+	7.37719i	−0.259041	+	0.285860i
$667$	0.140329	+	0.140329i	0.00543355	+	0.00543355i
$668$	2.49325	−	0.246024i	0.0964666	−	0.00951896i
$669$	3.95359	+	3.95359i	0.152854	+	0.152854i
$670$	−42.7959	+	7.60861i	−1.65335	+	0.293946i
$671$	−49.1470			−1.89730
$672$	−3.54177	+	5.91522i	−0.136627	+	0.228184i
$673$			37.3306i			1.43899i	0.694499	+	0.719494i	$0.255626\pi$
$673$			37.3306i			1.43899i	−0.694499	+	0.719494i	$0.744374\pi$
$674$	1.60793	+	32.6692i	0.0619353	+	1.25837i
$675$	−13.9520	+	23.7112i	−0.537011	+	0.912644i
$676$	−0.0557281	−	0.564757i	−0.00214339	−	0.0217214i
$677$	−2.54427	−	2.54427i	−0.0977841	−	0.0977841i	0.656522	−	0.754307i	$-0.272027\pi$
$677$	−2.54427	−	2.54427i	−0.0977841	−	0.0977841i	−0.754307	+	0.656522i	$0.772027\pi$
$678$	−3.87438	−	3.51089i	−0.148795	−	0.134835i
$679$			8.65054i			0.331977i
$680$	−9.83257	+	17.5334i	−0.377062	+	0.672375i
$681$		−	14.8429i		−	0.568781i
$682$	39.9326	−	44.0669i	1.52910	−	1.68741i
$683$	−3.95611	−	3.95611i	−0.151376	−	0.151376i	0.627356	−	0.778732i	$-0.284137\pi$
$683$	−3.95611	−	3.95611i	−0.151376	−	0.151376i	−0.778732	+	0.627356i	$0.784137\pi$
$684$	−2.05151	+	2.50071i	−0.0784416	+	0.0956170i
$685$	−19.6049	−	15.1724i	−0.749064	−	0.579706i
$686$	−1.41250	+	0.0695215i	−0.0539296	+	0.00265434i
$687$		−	8.50766i		−	0.324587i
$688$	−26.0736	−	17.4080i	−0.994046	−	0.663674i
$689$	−26.9321			−1.02603
$690$	1.46039	−	0.259641i	0.0555961	−	0.00988435i
$691$	12.1085	+	12.1085i	0.460629	+	0.460629i	0.898862	−	0.438232i	$-0.144395\pi$
$691$	12.1085	+	12.1085i	0.460629	+	0.460629i	−0.438232	+	0.898862i	$0.644395\pi$
$692$	21.0603	−	25.6716i	0.800592	−	0.975889i
$693$	−6.76827	−	6.76827i	−0.257105	−	0.257105i
$694$	1.09425	+	0.991586i	0.0415371	+	0.0376401i
$695$	−10.5309	+	1.34221i	−0.399459	+	0.0509128i
$696$	−1.75828	+	0.261310i	−0.0666476	+	0.00990495i
$697$	30.5869			1.15856
$698$	32.8319	+	29.7517i	1.24271	+	1.12612i
$699$	23.5340	−	23.5340i	0.890137	−	0.890137i
$700$	3.44682	+	9.38720i	0.130278	+	0.354803i
$701$	14.2677	+	14.2677i	0.538885	+	0.538885i	0.923202	−	0.384316i	$-0.125563\pi$
$701$	14.2677	+	14.2677i	0.538885	+	0.538885i	−0.384316	+	0.923202i	$0.625563\pi$
$702$	28.3265	−	1.39419i	1.06911	−	0.0526203i
$703$		−	4.96315i		−	0.187189i
$704$	−23.8086	+	44.6017i	−0.897322	+	1.68099i
$705$	−2.04453	−	16.0412i	−0.0770013	−	0.604148i
$706$	−0.435239	−	8.84298i	−0.0163804	−	0.332810i
$707$	9.63329	−	9.63329i	0.362297	−	0.362297i
$708$	2.84093	+	28.7904i	0.106769	+	1.08201i
$709$	6.58737	−	6.58737i	0.247394	−	0.247394i	−0.572506	−	0.819900i	$-0.694029\pi$
$709$	6.58737	−	6.58737i	0.247394	−	0.247394i	0.819900	+	0.572506i	$0.194029\pi$
$710$	21.2065	−	30.3776i	0.795867	−	1.14005i
$711$		−	25.7069i		−	0.964083i
$712$	−3.12823	−	21.0490i	−0.117235	−	0.788843i
$713$	2.56075			0.0959009
$714$	−4.05958	−	3.67872i	−0.151926	−	0.137672i
$715$	−31.5227	+	40.7319i	−1.17888	+	1.52329i
$716$	7.90565	+	6.48558i	0.295448	+	0.242378i
$717$	1.90782	−	1.90782i	0.0712489	−	0.0712489i
$718$	0.303087	+	6.15797i	0.0113111	+	0.229813i
$719$	14.0833			0.525220			0.262610	−	0.964902i	$-0.415417\pi$
$719$	14.0833			0.525220			0.262610	+	0.964902i	$0.415417\pi$
$720$	6.03722	−	12.1270i	0.224994	−	0.451947i
$721$	3.00769			0.112012
$722$	1.24164	+	25.2270i	0.0462090	+	0.938852i
$723$	6.33413	−	6.33413i	0.235569	−	0.235569i
$724$	−18.8056	+	22.9233i	−0.698906	+	0.851938i
$725$	−1.30754	+	2.22214i	−0.0485607	+	0.0825283i
$726$	36.9630	+	33.4952i	1.37183	+	1.24312i
$727$	−5.61438			−0.208226			−0.104113	−	0.994565i	$-0.533200\pi$
$727$	−5.61438			−0.208226			−0.104113	+	0.994565i	$0.533200\pi$
$728$	6.13863	−	8.28174i	0.227513	−	0.306942i
$729$			23.3934i			0.866421i
$730$	2.61924	+	1.82848i	0.0969423	+	0.0676752i
$731$	17.6152	−	17.6152i	0.651521	−	0.651521i
$732$	18.8645	−	1.86148i	0.697252	−	0.0688022i
$733$	15.3017	−	15.3017i	0.565181	−	0.565181i	−0.365593	−	0.930775i	$-0.619134\pi$
$733$	15.3017	−	15.3017i	0.565181	−	0.565181i	0.930775	+	0.365593i	$0.119134\pi$
$734$	−1.70765	−	34.6953i	−0.0630307	−	1.28063i
$735$	−2.70341	+	0.344562i	−0.0997170	+	0.0127094i
$736$	−2.11160	+	0.529954i	−0.0778345	+	0.0195344i
$737$		−	86.8689i		−	3.19986i
$738$	−20.5873	+	1.01328i	−0.757828	+	0.0372992i
$739$	15.6006	+	15.6006i	0.573879	+	0.573879i	0.933210	−	0.359331i	$-0.116995\pi$
$739$	15.6006	+	15.6006i	0.573879	+	0.573879i	−0.359331	+	0.933210i	$0.616995\pi$
$740$	4.64017	+	20.2618i	0.170576	+	0.744837i
$741$	−3.35403	+	3.35403i	−0.123213	+	0.123213i
$742$	−7.74373	−	7.01721i	−0.284281	−	0.257610i
$743$	−38.1908			−1.40109			−0.700543	−	0.713611i	$-0.747059\pi$
$743$	−38.1908			−1.40109			−0.700543	+	0.713611i	$0.747059\pi$
$744$	−13.6586	+	18.4270i	−0.500748	+	0.675568i
$745$	2.17699	−	0.277467i	0.0797587	−	0.0101656i
$746$	−10.4888	−	9.50474i	−0.384022	−	0.347993i
$747$	−14.1869	−	14.1869i	−0.519071	−	0.519071i
$748$	−31.0599	−	25.4807i	−1.13566	−	0.931665i
$749$	3.85453	+	3.85453i	0.140841	+	0.140841i
$750$	8.02448	+	17.5205i	0.293013	+	0.639757i
$751$	29.4385			1.07423			0.537113	−	0.843510i	$-0.319515\pi$
$751$	29.4385			1.07423			0.537113	+	0.843510i	$0.319515\pi$
$752$	4.63895	+	23.2770i	0.169165	+	0.848825i
$753$		−	13.4874i		−	0.491507i
$754$	2.65467	−	0.130659i	0.0966775	−	0.00475833i
$755$	16.0271	−	20.7093i	0.583286	−	0.753689i
$756$	8.50792	+	6.97966i	0.309430	+	0.253848i
$757$	3.46413	+	3.46413i	0.125906	+	0.125906i	0.767252	−	0.641346i	$-0.221624\pi$
$757$	3.46413	+	3.46413i	0.125906	+	0.125906i	−0.641346	+	0.767252i	$0.721624\pi$
$758$	5.81953	−	6.42205i	0.211375	−	0.233259i
$759$			2.96436i			0.107600i
$760$	1.82938	+	6.50094i	0.0663584	+	0.235814i
$761$		−	27.4999i		−	0.996871i	−0.866927	−	0.498436i	$-0.833908\pi$
$761$		−	27.4999i		−	0.996871i	0.866927	−	0.498436i	$-0.166092\pi$
$762$	7.04140	+	6.38078i	0.255083	+	0.231151i
$763$	3.00543	+	3.00543i	0.108804	+	0.108804i
$764$	−12.8539	+	1.26837i	−0.465038	+	0.0458882i
$765$	8.51279	+	6.58811i	0.307781	+	0.238194i
$766$	0.509100	+	10.3437i	0.0183945	+	0.373732i
$767$		−	43.2569i		−	1.56192i
$768$	7.44934	−	18.0216i	0.268805	−	0.650299i
$769$	14.6461			0.528150			0.264075	−	0.964502i	$-0.414933\pi$
$769$	14.6461			0.528150			0.264075	+	0.964502i	$0.414933\pi$
$770$	−19.6765	+	3.49825i	−0.709091	+	0.126068i
$771$	23.7956	+	23.7956i	0.856979	+	0.856979i
$772$	−1.19324	−	12.0924i	−0.0429455	−	0.435216i
$773$	22.6836	+	22.6836i	0.815873	+	0.815873i	0.985507	−	0.169634i	$-0.0542586\pi$
$773$	22.6836	+	22.6836i	0.815873	+	0.815873i	−0.169634	+	0.985507i	$0.554259\pi$
$774$	−11.2728	+	12.4399i	−0.405192	+	0.447143i
$775$	8.34497	+	32.2052i	0.299760	+	1.15685i
$776$	−3.59676	−	24.2016i	−0.129116	−	0.868787i
$777$	−5.66486			−0.203226
$778$	28.1915	−	31.1102i	1.01071	−	1.11536i
$779$	7.26609	−	7.26609i	0.260335	−	0.260335i
$780$	10.5569	−	16.8284i	0.377997	−	0.602554i
$781$	52.3538	+	52.3538i	1.87337	+	1.87337i
$782$	−0.0850419	−	1.72784i	−0.00304109	−	0.0617875i
$783$			2.83729i			0.101397i
$784$	3.92286	−	0.781798i	0.140102	−	0.0279213i
$785$	−19.3019	+	2.46012i	−0.688916	+	0.0878055i
$786$	24.4594	−	1.20386i	0.872438	−	0.0429402i
$787$	10.6620	−	10.6620i	0.380059	−	0.380059i	−0.491065	−	0.871123i	$-0.663392\pi$
$787$	10.6620	−	10.6620i	0.380059	−	0.380059i	0.871123	+	0.491065i	$0.163392\pi$
$788$	−42.2107	−	34.6285i	−1.50369	−	1.23359i
$789$	−9.22548	+	9.22548i	−0.328436	+	0.328436i
$790$	−44.0105	−	30.7236i	−1.56582	−	1.09310i
$791$			3.03344i			0.107857i
$792$	21.7497	+	16.1214i	0.772843	+	0.572850i
$793$	−28.3435			−1.00651
$794$	−26.7067	+	29.4718i	−0.947787	+	1.04591i
$795$	−15.9260	−	12.3252i	−0.564836	−	0.437131i
$796$	2.64832	+	26.8385i	0.0938672	+	0.951264i
$797$	−0.678424	+	0.678424i	−0.0240310	+	0.0240310i	−0.719020	−	0.694989i	$-0.755409\pi$
$797$	−0.678424	+	0.678424i	−0.0240310	+	0.0240310i	0.694989	+	0.719020i	$0.255409\pi$
$798$	−1.83828	+	0.0904775i	−0.0650743	+	0.00320287i
$799$	−18.8599			−0.667215
$800$	−13.5462	−	24.8294i	−0.478931	−	0.877853i
$801$	−11.3951			−0.402625
$802$	10.3174	−	0.507806i	0.364319	−	0.0179313i
$803$	−4.51408	+	4.51408i	−0.159298	+	0.159298i
$804$	3.29022	+	33.3436i	0.116037	+	1.17594i
$805$	−0.680565	−	0.526695i	−0.0239868	−	0.0185635i
$806$	23.0294	−	25.4137i	0.811177	−	0.895161i
$807$	31.4647			1.10761
$808$	−22.9457	+	30.9564i	−0.807226	+	1.08904i
$809$			12.3721i			0.434981i	0.976062	+	0.217491i	$0.0697872\pi$
$809$			12.3721i			0.434981i	−0.976062	+	0.217491i	$0.930213\pi$
$810$	5.60700	+	3.91423i	0.197010	+	0.137532i
$811$	−19.4550	+	19.4550i	−0.683156	+	0.683156i	−0.960710	−	0.277554i	$-0.910476\pi$
$811$	−19.4550	+	19.4550i	−0.683156	+	0.683156i	0.277554	+	0.960710i	$0.410476\pi$
$812$	0.797337	+	0.654113i	0.0279810	+	0.0229549i
$813$	−6.48281	+	6.48281i	−0.227362	+	0.227362i
$814$	−41.4912	+	2.04214i	−1.45427	+	0.0715770i
$815$	8.20221	−	1.04541i	0.287311	−	0.0366191i
$816$	12.8871	+	8.60403i	0.451137	+	0.301201i
$817$		−	8.36918i		−	0.292801i
$818$	−0.505355	−	10.2676i	−0.0176693	−	0.358997i
$819$	−3.90331	−	3.90331i	−0.136393	−	0.136393i
$820$	−22.8702	+	36.4567i	−0.798661	+	1.27312i
$821$	−29.6285	+	29.6285i	−1.03404	+	1.03404i	−0.0346417	+	0.999400i	$0.511029\pi$
$821$	−29.6285	+	29.6285i	−1.03404	+	1.03404i	−0.999400	+	0.0346417i	$0.988971\pi$
$822$	−12.8315	+	14.1600i	−0.447549	+	0.493885i
$823$	−44.5013			−1.55122			−0.775610	−	0.631213i	$-0.782557\pi$
$823$	−44.5013			−1.55122			−0.775610	+	0.631213i	$0.782557\pi$
$824$	−8.41461	+	1.25055i	−0.293137	+	0.0435650i
$825$	−37.2812	+	9.66025i	−1.29797	+	0.336327i
$826$	11.2707	−	12.4376i	0.392158	−	0.432759i
$827$	17.5441	+	17.5441i	0.610069	+	0.610069i	0.942964	−	0.332895i	$-0.108025\pi$
$827$	17.5441	+	17.5441i	0.610069	+	0.610069i	−0.332895	+	0.942964i	$0.608025\pi$
$828$	0.114479	+	1.16015i	0.00397843	+	0.0403180i
$829$	−18.3639	−	18.3639i	−0.637804	−	0.637804i	0.312209	−	0.950013i	$-0.398931\pi$
$829$	−18.3639	−	18.3639i	−0.637804	−	0.637804i	−0.950013	+	0.312209i	$0.898931\pi$
$830$	−41.2436	+	7.33264i	−1.43159	+	0.254520i
$831$	−6.96423			−0.241586
$832$	−13.7306	+	25.7222i	−0.476024	+	0.891756i
$833$			3.17844i			0.110126i
$834$	0.402276	+	8.17325i	0.0139297	+	0.283017i
$835$	−2.21518	−	1.71434i	−0.0766595	−	0.0593273i
$836$	−13.4315	+	1.32537i	−0.464539	+	0.0458390i
$837$	25.8878	+	25.8878i	0.894814	+	0.894814i
$838$	6.67025	+	6.04445i	0.230420	+	0.208802i
$839$			34.3386i			1.18550i	0.805386	+	0.592751i	$0.201958\pi$
$839$			34.3386i			1.18550i	−0.805386	+	0.592751i	$0.798042\pi$
$840$	7.42008	−	2.08802i	0.256017	−	0.0720436i
$841$		−	28.7341i		−	0.990831i
$842$	−19.6949	+	21.7340i	−0.678731	+	0.749002i
$843$	3.73822	+	3.73822i	0.128751	+	0.128751i
$844$	31.4536	+	25.8037i	1.08268	+	0.888199i
$845$	−0.388324	+	0.501771i	−0.0133588	+	0.0172614i
$846$	12.6941	−	0.624787i	0.436433	−	0.0214806i
$847$		−	28.9401i		−	0.994394i
$848$	24.5823	+	16.4123i	0.844159	+	0.563602i
$849$	6.73466			0.231133
$850$	21.4530	−	6.70021i	0.735832	−	0.229815i
$851$	−1.26487	−	1.26487i	−0.0433593	−	0.0433593i
$852$	−22.0783	−	18.1125i	−0.756391	−	0.620522i
$853$	16.4735	+	16.4735i	0.564043	+	0.564043i	0.930453	−	0.366410i	$-0.119413\pi$
$853$	16.4735	+	16.4735i	0.564043	+	0.564043i	−0.366410	+	0.930453i	$0.619413\pi$
$854$	−8.14954	−	7.38495i	−0.278871	−	0.252708i
$855$	3.58731	−	0.457219i	0.122683	−	0.0156365i
$856$	−12.3865	−	9.18116i	−0.423361	−	0.313806i
$857$	−47.1582			−1.61089			−0.805446	−	0.592669i	$-0.798074\pi$
$857$	−47.1582			−1.61089			−0.805446	+	0.592669i	$0.798074\pi$
$858$	29.4193	+	26.6592i	1.00436	+	0.910130i
$859$	17.8971	−	17.8971i	0.610640	−	0.610640i	−0.332473	−	0.943113i	$-0.607883\pi$
$859$	17.8971	−	17.8971i	0.610640	−	0.610640i	0.943113	+	0.332473i	$0.107883\pi$
$860$	7.82455	+	34.1667i	0.266815	+	1.16508i
$861$	−8.29341	−	8.29341i	−0.282639	−	0.282639i
$862$	−10.1997	+	0.502013i	−0.347402	+	0.0170986i
$863$		−	11.9441i		−	0.406583i	−0.979118	−	0.203292i	$-0.934836\pi$
$863$		−	11.9441i		−	0.406583i	0.979118	−	0.203292i	$-0.0651640\pi$
$864$	−26.7046	−	15.9895i	−0.908510	−	0.543975i
$865$	−36.8263	+	4.69368i	−1.25213	+	0.159590i
$866$	−0.914943	−	18.5894i	−0.0310910	−	0.631693i
$867$	5.94435	−	5.94435i	0.201881	−	0.201881i
$868$	13.2432	−	1.30679i	0.449504	−	0.0443554i
$869$	75.8492	−	75.8492i	2.57301	−	2.57301i
$870$	1.62961	+	1.13763i	0.0552489	+	0.0385691i
$871$		−	50.0979i		−	1.69750i
$872$	−9.65791	−	7.15868i	−0.327058	−	0.242424i
$873$	−13.1018			−0.443429
$874$	−0.430661	−	0.390256i	−0.0145673	−	0.0132006i
$875$	4.40614	−	10.2755i	0.148955	−	0.347375i
$876$	1.56170	−	1.90365i	0.0527650	−	0.0643184i
$877$	−12.4578	+	12.4578i	−0.420670	+	0.420670i	−0.885434	−	0.464764i	$-0.846139\pi$
$877$	−12.4578	+	12.4578i	−0.420670	+	0.420670i	0.464764	+	0.885434i	$0.346139\pi$
$878$	−0.766097	−	15.5652i	−0.0258545	−	0.525300i
$879$	0.299566			0.0101041
$880$	53.5943	−	17.9682i	1.80666	−	0.605709i
$881$	44.0596			1.48441			0.742203	−	0.670175i	$-0.233781\pi$
$881$	44.0596			1.48441			0.742203	+	0.670175i	$0.233781\pi$
$882$	−0.105295	−	2.13933i	−0.00354546	−	0.0720350i
$883$	−26.8849	+	26.8849i	−0.904750	+	0.904750i	−0.995842	−	0.0910925i	$-0.970964\pi$
$883$	−26.8849	+	26.8849i	−0.904750	+	0.904750i	0.0910925	+	0.995842i	$0.470964\pi$
$884$	−17.9125	−	14.6949i	−0.602461	−	0.494242i
$885$	19.7962	−	25.5795i	0.665441	−	0.859846i
$886$	−11.6065	−	10.5176i	−0.389928	−	0.353345i
$887$	−41.1360			−1.38121			−0.690606	−	0.723232i	$-0.742656\pi$
$887$	−41.1360			−1.38121			−0.690606	+	0.723232i	$0.742656\pi$
$888$	15.8486	−	2.35536i	0.531843	−	0.0790408i
$889$		−	5.51304i		−	0.184902i
$890$	−13.6189	+	19.5085i	−0.456505	+	0.653927i
$891$	−9.66329	+	9.66329i	−0.323732	+	0.323732i
$892$	0.900986	+	9.13073i	0.0301672	+	0.305719i
$893$	−4.48027	+	4.48027i	−0.149927	+	0.149927i
$894$	−0.0831603	−	1.68961i	−0.00278130	−	0.0565091i
$895$	−1.44543	−	11.3408i	−0.0483155	−	0.379081i
$896$	−10.6499	+	3.81830i	−0.355789	+	0.127560i
$897$			1.70957i			0.0570809i
$898$	28.3273	−	1.39423i	0.945296	−	0.0465261i
$899$	2.42613	+	2.42613i	0.0809159	+	0.0809159i
$900$	−14.2175	+	5.22043i	−0.473917	+	0.174014i
$901$	−16.6077	+	16.6077i	−0.553282	+	0.553282i
$902$	−63.7333	−	57.7539i	−2.12209	−	1.92299i
$903$	−9.55246			−0.317886
$904$	−1.26126	−	8.48665i	−0.0419488	−	0.282262i
$905$	32.8838	−	4.19119i	1.09310	−	0.139320i
$906$	−14.9576	−	13.5543i	−0.496935	−	0.450312i
$907$	28.2186	+	28.2186i	0.936982	+	0.936982i	0.998129	−	0.0611467i	$-0.0194758\pi$
$907$	28.2186	+	28.2186i	0.936982	+	0.936982i	−0.0611467	+	0.998129i	$0.519476\pi$
$908$	15.4484	−	18.8310i	0.512673	−	0.624928i
$909$	14.5902	+	14.5902i	0.483928	+	0.483928i
$910$	−11.3476	+	2.01747i	−0.376168	+	0.0668784i
$911$	26.4582			0.876598			0.438299	−	0.898829i	$-0.355581\pi$
$911$	26.4582			0.876598			0.438299	+	0.898829i	$0.355581\pi$
$912$	5.10533	−	1.01746i	0.169054	−	0.0336914i
$913$		−	83.7180i		−	2.77066i
$914$	25.5472	−	1.25740i	0.845026	−	0.0415910i
$915$	−16.7606	−	12.9711i	−0.554088	−	0.428813i
$916$	8.85472	−	10.7935i	0.292568	−	0.356628i
$917$	−10.0465	−	10.0465i	−0.331764	−	0.331764i
$918$	16.6078	−	18.3273i	0.548139	−	0.604890i
$919$			42.5058i			1.40214i	0.713093	+	0.701069i	$0.247294\pi$
$919$			42.5058i			1.40214i	−0.713093	+	0.701069i	$0.752706\pi$
$920$	2.12301	+	1.19056i	0.0699935	+	0.0392518i
$921$		−	2.33218i		−	0.0768481i
$922$	−0.312852	−	0.283501i	−0.0103032	−	0.00933659i
$923$	30.1928	+	30.1928i	0.993810	+	0.993810i
$924$	1.51276	+	15.3305i	0.0497661	+	0.504338i
$925$	11.7857	−	20.0296i	0.387511	−	0.658570i
$926$	0.00413900	+	0.0840941i	0.000136016	+	0.00276350i
$927$			4.55534i			0.149617i
$928$	−2.50268	−	1.49849i	−0.0821545	−	0.0491904i
$929$	49.8886			1.63679			0.818395	−	0.574656i	$-0.194864\pi$
$929$	49.8886			1.63679			0.818395	+	0.574656i	$0.194864\pi$
$930$	25.2486	−	4.48890i	0.827933	−	0.147197i
$931$	0.755057	+	0.755057i	0.0247460	+	0.0247460i
$932$	54.3512	−	5.36318i	1.78033	−	0.175677i
$933$	−6.25661	−	6.25661i	−0.204832	−	0.204832i
$934$	−4.03067	+	4.44798i	−0.131888	+	0.145542i
$935$	5.67884	+	44.5558i	0.185718	+	1.45713i
$936$	12.5432	+	9.29736i	0.409988	+	0.303894i
$937$	−12.7198			−0.415539			−0.207769	−	0.978178i	$-0.566620\pi$
$937$	−12.7198			−0.415539			−0.207769	+	0.978178i	$0.566620\pi$
$938$	13.0531	−	14.4046i	0.426200	−	0.470326i
$939$	12.4022	−	12.4022i	0.404730	−	0.404730i
$940$	14.1018	−	22.4792i	0.459949	−	0.733190i
$941$	41.8791	+	41.8791i	1.36522	+	1.36522i	0.867120	+	0.498099i	$0.165968\pi$
$941$	41.8791	+	41.8791i	1.36522	+	1.36522i	0.498099	+	0.867120i	$0.334032\pi$
$942$	0.737329	+	14.9807i	0.0240235	+	0.488097i
$943$		−	3.70357i		−	0.120605i
$944$	−26.3607	+	39.4828i	−0.857966	+	1.28506i
$945$	−1.55555	−	12.2047i	−0.0506020	−	0.397020i
$946$	−69.9653	+	3.44359i	−2.27477	+	0.111961i
$947$	−18.3407	+	18.3407i	−0.595994	+	0.595994i	−0.939244	−	0.343250i	$-0.888472\pi$
$947$	−18.3407	+	18.3407i	−0.595994	+	0.595994i	0.343250	+	0.939244i	$0.388472\pi$
$948$	−26.2410	+	31.9867i	−0.852267	+	1.03888i
$949$	−2.60331	+	2.60331i	−0.0845069	+	0.0845069i
$950$	3.50461	−	6.68796i	0.113705	−	0.216986i
$951$		−	38.7210i		−	1.25561i
$952$	−1.32155	−	8.89232i	−0.0428316	−	0.288202i
$953$	−21.8205			−0.706836			−0.353418	−	0.935465i	$-0.614981\pi$
$953$	−21.8205			−0.706836			−0.353418	+	0.935465i	$0.614981\pi$
$954$	10.6280	−	11.7284i	0.344095	−	0.379720i
$955$	11.4203	+	8.83829i	0.369553	+	0.286000i
$956$	4.40608	−	0.434775i	0.142503	−	0.0140616i
$957$	−2.80852	+	2.80852i	−0.0907866	+	0.0907866i
$958$	−21.8697	+	1.07640i	−0.706579	+	0.0347768i
$959$	11.0865			0.358002
$960$	−19.8910	+	8.92681i	−0.641979	+	0.288112i
$961$	13.2726			0.428149
$962$	−23.9283	+	1.17772i	−0.771480	+	0.0379712i
$963$	−5.83794	+	5.83794i	−0.188125	+	0.188125i
$964$	14.6285	−	1.44349i	0.471154	−	0.0464917i
$965$	−8.31470	+	10.7438i	−0.267660	+	0.345855i
$966$	−0.445433	+	0.491550i	−0.0143316	+	0.0158153i
$967$	−16.2248			−0.521754			−0.260877	−	0.965372i	$-0.584012\pi$
$967$	−16.2248			−0.521754			−0.260877	+	0.965372i	$0.584012\pi$
$968$	12.0329	+	80.9657i	0.386751	+	2.60234i
$969$			4.13653i			0.132884i
$970$	−15.6586	+	22.4304i	−0.502769	+	0.720198i
$971$	−22.9082	+	22.9082i	−0.735160	+	0.735160i	−0.971637	−	0.236477i	$-0.924007\pi$
$971$	−22.9082	+	22.9082i	−0.735160	+	0.735160i	0.236477	+	0.971637i	$0.424007\pi$
$972$	−17.5959	+	21.4486i	−0.564387	+	0.687965i
$973$	3.35709	−	3.35709i	0.107623	−	0.107623i
$974$	40.7899	−	2.00762i	1.30699	−	0.0643284i
$975$	−21.5004	+	5.57114i	−0.688563	+	0.178419i
$976$	25.8705	+	17.2724i	0.828095	+	0.552877i
$977$		−	39.9065i		−	1.27672i	−0.769738	−	0.638360i	$-0.779613\pi$
$977$		−	39.9065i		−	1.27672i	0.769738	−	0.638360i	$-0.220387\pi$
$978$	−0.313322	−	6.36593i	−0.0100189	−	0.203560i
$979$	−33.6217	−	33.6217i	−1.07455	−	1.07455i
$980$	−3.78840	−	2.37656i	−0.121016	−	0.0759163i
$981$	−4.55192	+	4.55192i	−0.145332	+	0.145332i
$982$	−18.4501	+	20.3603i	−0.588767	+	0.649724i
$983$	37.5222			1.19677			0.598386	−	0.801208i	$-0.295809\pi$
$983$	37.5222			1.19677			0.598386	+	0.801208i	$0.295809\pi$
$984$	26.6507	+	19.7542i	0.849594	+	0.629741i
$985$	7.71761	+	60.5519i	0.245903	+	1.92934i
$986$	1.55643	−	1.71758i	0.0495670	−	0.0546988i
$987$	5.11372	+	5.11372i	0.162771	+	0.162771i
$988$	−7.74606	+	0.764352i	−0.246435	+	0.0243173i
$989$	−2.13291	−	2.13291i	−0.0678227	−	0.0678227i
$990$	−5.29832	−	29.8013i	−0.168392	−	0.947147i
$991$	−38.1475			−1.21179			−0.605897	−	0.795543i	$-0.707186\pi$
$991$	−38.1475			−1.21179			−0.605897	+	0.795543i	$0.707186\pi$
$992$	−36.5072	+	9.16234i	−1.15910	+	0.290904i
$993$		−	19.4697i		−	0.617852i
$994$	0.814475	+	16.5481i	0.0258336	+	0.524874i
$995$	18.4540	−	23.8452i	0.585032	−	0.755945i
$996$	3.17088	+	32.1342i	0.100473	+	1.01821i
$997$	41.7955	+	41.7955i	1.32368	+	1.32368i	0.910775	+	0.412903i	$0.135485\pi$
$997$	41.7955	+	41.7955i	1.32368	+	1.32368i	0.412903	+	0.910775i	$0.364515\pi$
$998$	27.7357	+	25.1336i	0.877959	+	0.795590i
$999$		−	25.5744i		−	0.809137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.1	yes	70
5.4	even	2		560.2.bb.c.29.35	✓	70
16.5	even	4		560.2.bb.c.309.35	yes	70
80.69	even	4	inner	560.2.bb.d.309.1	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.35	✓	70	5.4	even	2
560.2.bb.c.309.35	yes	70	16.5	even	4
560.2.bb.d.29.1	yes	70	1.1	even	1	trivial
560.2.bb.d.309.1	yes	70	80.69	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41250 + 0.0695215i) q^{2} +(0.861811 - 0.861811i) q^{3} +(1.99033 - 0.196399i) q^{4} +(-1.76836 - 1.36854i) q^{5} +(-1.15740 + 1.27722i) q^{6} +1.00000 q^{7} +(-2.79770 + 0.415785i) q^{8} +1.51457i q^{9} +O(q^{10})\)	\(q+(-1.41250 + 0.0695215i) q^{2} +(0.861811 - 0.861811i) q^{3} +(1.99033 - 0.196399i) q^{4} +(-1.76836 - 1.36854i) q^{5} +(-1.15740 + 1.27722i) q^{6} +1.00000 q^{7} +(-2.79770 + 0.415785i) q^{8} +1.51457i q^{9} +(2.59295 + 1.81014i) q^{10} +(-4.46879 + 4.46879i) q^{11} +(1.54603 - 1.88455i) q^{12} +(-2.57718 + 2.57718i) q^{13} +(-1.41250 + 0.0695215i) q^{14} +(-2.70341 + 0.344562i) q^{15} +(3.92286 - 0.781798i) q^{16} +3.17844i q^{17} +(-0.105295 - 2.13933i) q^{18} +(0.755057 + 0.755057i) q^{19} +(-3.78840 - 2.37656i) q^{20} +(0.861811 - 0.861811i) q^{21} +(6.00150 - 6.62285i) q^{22} +0.384857 q^{23} +(-2.05276 + 2.76941i) q^{24} +(1.25417 + 4.84015i) q^{25} +(3.46111 - 3.81945i) q^{26} +(3.89070 + 3.89070i) q^{27} +(1.99033 - 0.196399i) q^{28} +(0.364625 + 0.364625i) q^{29} +(3.79463 - 0.674641i) q^{30} +6.65377 q^{31} +(-5.48670 + 1.37701i) q^{32} +7.70250i q^{33} +(-0.220970 - 4.48956i) q^{34} +(-1.76836 - 1.36854i) q^{35} +(0.297459 + 3.01449i) q^{36} +(-3.28660 - 3.28660i) q^{37} +(-1.11901 - 1.01403i) q^{38} +4.44209i q^{39} +(5.51635 + 3.09352i) q^{40} -9.62324i q^{41} +(-1.15740 + 1.27722i) q^{42} +(-5.54209 - 5.54209i) q^{43} +(-8.01671 + 9.77204i) q^{44} +(2.07275 - 2.67829i) q^{45} +(-0.543613 + 0.0267559i) q^{46} +5.93369i q^{47} +(2.70700 - 4.05452i) q^{48} +1.00000 q^{49} +(-2.10802 - 6.74954i) q^{50} +(2.73921 + 2.73921i) q^{51} +(-4.62330 + 5.63561i) q^{52} +(5.22510 + 5.22510i) q^{53} +(-5.76612 - 5.22514i) q^{54} +(14.0181 - 1.78668i) q^{55} +(-2.79770 + 0.415785i) q^{56} +1.30143 q^{57} +(-0.540383 - 0.489685i) q^{58} +(-8.39229 + 8.39229i) q^{59} +(-5.31303 + 1.21674i) q^{60} +(5.49892 + 5.49892i) q^{61} +(-9.39847 + 0.462580i) q^{62} +1.51457i q^{63} +(7.65425 - 2.32648i) q^{64} +(8.08437 - 1.03039i) q^{65} +(-0.535489 - 10.8798i) q^{66} +(-9.71951 + 9.71951i) q^{67} +(0.624242 + 6.32616i) q^{68} +(0.331674 - 0.331674i) q^{69} +(2.59295 + 1.81014i) q^{70} -11.7154i q^{71} +(-0.629733 - 4.23730i) q^{72} +1.01014 q^{73} +(4.87083 + 4.41385i) q^{74} +(5.25215 + 3.09043i) q^{75} +(1.65111 + 1.35452i) q^{76} +(-4.46879 + 4.46879i) q^{77} +(-0.308820 - 6.27447i) q^{78} -16.9731 q^{79} +(-8.00693 - 3.98610i) q^{80} +2.16240 q^{81} +(0.669021 + 13.5929i) q^{82} +(-9.36697 + 9.36697i) q^{83} +(1.54603 - 1.88455i) q^{84} +(4.34984 - 5.62062i) q^{85} +(8.21351 + 7.44292i) q^{86} +0.628475 q^{87} +(10.6443 - 14.3604i) q^{88} +7.52367i q^{89} +(-2.74157 + 3.92720i) q^{90} +(-2.57718 + 2.57718i) q^{91} +(0.765995 - 0.0755855i) q^{92} +(5.73429 - 5.73429i) q^{93} +(-0.412519 - 8.38136i) q^{94} +(-0.301881 - 2.36854i) q^{95} +(-3.54177 + 5.91522i) q^{96} +8.65054i q^{97} +(-1.41250 + 0.0695215i) q^{98} +(-6.76827 - 6.76827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

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