LMFDB - Embedded newform 547.2.c.a.40.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.13
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.771252 - 1.33585i) q^{2} -0.116598 q^{3} +(-0.189661 + 0.328502i) q^{4} +(1.94811 - 3.37423i) q^{5} +(0.0899263 + 0.155757i) q^{6} +(-1.20784 - 2.09204i) q^{7} -2.49991 q^{8} -2.98640 q^{9} +O(q^{10})$	\(q+(-0.771252 - 1.33585i) q^{2} -0.116598 q^{3} +(-0.189661 + 0.328502i) q^{4} +(1.94811 - 3.37423i) q^{5} +(0.0899263 + 0.155757i) q^{6} +(-1.20784 - 2.09204i) q^{7} -2.49991 q^{8} -2.98640 q^{9} -6.00995 q^{10} +(-0.0264869 - 0.0458767i) q^{11} +(0.0221140 - 0.0383026i) q^{12} +(-0.704957 - 1.22102i) q^{13} +(-1.86310 + 3.22698i) q^{14} +(-0.227146 + 0.393428i) q^{15} +(2.30738 + 3.99650i) q^{16} +(3.07730 + 5.33005i) q^{17} +(2.30327 + 3.98938i) q^{18} +(-2.29720 + 3.97887i) q^{19} +(0.738960 + 1.27992i) q^{20} +(0.140831 + 0.243927i) q^{21} +(-0.0408562 + 0.0707651i) q^{22} +(4.50450 - 7.80202i) q^{23} +0.291483 q^{24} +(-5.09029 - 8.81664i) q^{25} +(-1.08740 + 1.88343i) q^{26} +0.698002 q^{27} +0.916318 q^{28} -2.75590 q^{29} +0.700747 q^{30} +7.03499 q^{31} +(1.05924 - 1.83465i) q^{32} +(0.00308832 + 0.00534913i) q^{33} +(4.74676 - 8.22162i) q^{34} -9.41203 q^{35} +(0.566403 - 0.981039i) q^{36} +(-1.30872 - 2.26677i) q^{37} +7.08689 q^{38} +(0.0821965 + 0.142368i) q^{39} +(-4.87010 + 8.43526i) q^{40} +(4.80754 + 8.32691i) q^{41} +(0.217233 - 0.376259i) q^{42} +(-3.16713 - 5.48563i) q^{43} +0.0200941 q^{44} +(-5.81785 + 10.0768i) q^{45} -13.8964 q^{46} +(-1.81536 + 3.14430i) q^{47} +(-0.269035 - 0.465983i) q^{48} +(0.582248 - 1.00848i) q^{49} +(-7.85180 + 13.5997i) q^{50} +(-0.358807 - 0.621472i) q^{51} +0.534810 q^{52} +(3.18468 + 5.51603i) q^{53} +(-0.538335 - 0.932424i) q^{54} -0.206398 q^{55} +(3.01948 + 5.22990i) q^{56} +(0.267849 - 0.463927i) q^{57} +(2.12549 + 3.68146i) q^{58} +(-6.17746 - 10.6997i) q^{59} +(-0.0861611 - 0.149235i) q^{60} +(1.38425 + 2.39760i) q^{61} +(-5.42575 - 9.39767i) q^{62} +(3.60710 + 6.24768i) q^{63} +5.96176 q^{64} -5.49335 q^{65} +(0.00476375 - 0.00825105i) q^{66} +(-7.29502 - 12.6353i) q^{67} -2.33457 q^{68} +(-0.525214 + 0.909698i) q^{69} +(7.25905 + 12.5730i) q^{70} +(-6.10276 - 10.5703i) q^{71} +7.46573 q^{72} +(-3.64459 - 6.31262i) q^{73} +(-2.01871 + 3.49651i) q^{74} +(0.593516 + 1.02800i) q^{75} +(-0.871377 - 1.50927i) q^{76} +(-0.0639840 + 0.110823i) q^{77} +(0.126788 - 0.219604i) q^{78} -15.2341 q^{79} +17.9801 q^{80} +8.87783 q^{81} +(7.41566 - 12.8443i) q^{82} +(6.56729 + 11.3749i) q^{83} -0.106841 q^{84} +23.9797 q^{85} +(-4.88532 + 8.46162i) q^{86} +0.321332 q^{87} +(0.0662148 + 0.114687i) q^{88} -14.4073 q^{89} +17.9481 q^{90} +(-1.70295 + 2.94960i) q^{91} +(1.70865 + 2.95947i) q^{92} -0.820264 q^{93} +5.60041 q^{94} +(8.95042 + 15.5026i) q^{95} +(-0.123505 + 0.213917i) q^{96} +(6.35308 - 11.0039i) q^{97} -1.79624 q^{98} +(0.0791007 + 0.137007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.771252	−	1.33585i	−0.545358	−	0.944587i	−0.998584	−	0.0531920i	$-0.983060\pi$
$2$	−0.771252	−	1.33585i	−0.545358	−	0.944587i	0.453226	−	0.891395i	$-0.350273\pi$
$3$	−0.116598			−0.0673178			−0.0336589	−	0.999433i	$-0.510716\pi$
$3$	−0.116598			−0.0673178			−0.0336589	+	0.999433i	$0.510716\pi$
$4$	−0.189661	+	0.328502i	−0.0948303	+	0.164251i
$5$	1.94811	−	3.37423i	0.871223	−	1.50900i	0.0104898	−	0.999945i	$-0.496661\pi$
$5$	1.94811	−	3.37423i	0.871223	−	1.50900i	0.860733	−	0.509057i	$-0.170006\pi$
$6$	0.0899263	+	0.155757i	0.0367123	+	0.0635875i
$7$	−1.20784	−	2.09204i	−0.456520	−	0.790717i	0.542254	−	0.840215i	$-0.317571\pi$
$7$	−1.20784	−	2.09204i	−0.456520	−	0.790717i	−0.998774	+	0.0494982i	$0.984238\pi$
$8$	−2.49991			−0.883850
$9$	−2.98640			−0.995468
$10$	−6.00995			−1.90051
$11$	−0.0264869	−	0.0458767i	−0.00798611	−	0.0138324i	0.862005	−	0.506900i	$-0.169209\pi$
$11$	−0.0264869	−	0.0458767i	−0.00798611	−	0.0138324i	−0.869991	+	0.493068i	$0.835875\pi$
$12$	0.0221140	−	0.0383026i	0.00638376	−	0.0110570i
$13$	−0.704957	−	1.22102i	−0.195520	−	0.338650i	0.751551	−	0.659675i	$-0.229306\pi$
$13$	−0.704957	−	1.22102i	−0.195520	−	0.338650i	−0.947071	+	0.321025i	$0.895973\pi$
$14$	−1.86310	+	3.22698i	−0.497934	+	0.862447i
$15$	−0.227146	+	0.393428i	−0.0586488	+	0.101583i
$16$	2.30738	+	3.99650i	0.576845	+	0.999124i
$17$	3.07730	+	5.33005i	0.746356	+	1.29273i	0.949559	+	0.313589i	$0.101532\pi$
$17$	3.07730	+	5.33005i	0.746356	+	1.29273i	−0.203203	+	0.979137i	$0.565135\pi$
$18$	2.30327	+	3.98938i	0.542886	+	0.940307i
$19$	−2.29720	+	3.97887i	−0.527014	+	0.912815i	0.472490	+	0.881336i	$0.343355\pi$
$19$	−2.29720	+	3.97887i	−0.527014	+	0.912815i	−0.999504	+	0.0314794i	$0.989978\pi$
$20$	0.738960	+	1.27992i	0.165237	+	0.286198i
$21$	0.140831	+	0.243927i	0.0307319	+	0.0532293i
$22$	−0.0408562	+	0.0707651i	−0.00871058	+	0.0150872i
$23$	4.50450	−	7.80202i	0.939252	−	1.62683i	0.172382	−	0.985030i	$-0.444854\pi$
$23$	4.50450	−	7.80202i	0.939252	−	1.62683i	0.766870	−	0.641803i	$-0.221813\pi$
$24$	0.291483			0.0594988
$25$	−5.09029	−	8.81664i	−1.01806	−	1.76333i
$26$	−1.08740	+	1.88343i	−0.213257	+	0.369371i
$27$	0.698002			0.134330
$28$	0.916318			0.173168
$29$	−2.75590			−0.511757			−0.255879	−	0.966709i	$-0.582365\pi$
$29$	−2.75590			−0.511757			−0.255879	+	0.966709i	$0.582365\pi$
$30$	0.700747			0.127938
$31$	7.03499			1.26352			0.631760	−	0.775164i	$-0.282333\pi$
$31$	7.03499			1.26352			0.631760	+	0.775164i	$0.282333\pi$
$32$	1.05924	−	1.83465i	0.187249	−	0.324324i
$33$	0.00308832	+	0.00534913i	0.000537607	+	0.000931163i
$34$	4.74676	−	8.22162i	0.814062	−	1.41000i
$35$	−9.41203			−1.59092
$36$	0.566403	−	0.981039i	0.0944005	−	0.163507i
$37$	−1.30872	−	2.26677i	−0.215153	−	0.372655i	0.738167	−	0.674618i	$-0.235692\pi$
$37$	−1.30872	−	2.26677i	−0.215153	−	0.372655i	−0.953320	+	0.301963i	$0.902358\pi$
$38$	7.08689			1.14965
$39$	0.0821965	+	0.142368i	0.0131620	+	0.0227972i
$40$	−4.87010	+	8.43526i	−0.770030	+	1.33373i
$41$	4.80754	+	8.32691i	0.750812	+	1.30044i	0.947430	+	0.319964i	$0.103671\pi$
$41$	4.80754	+	8.32691i	0.750812	+	1.30044i	−0.196618	+	0.980480i	$0.562996\pi$
$42$	0.217233	−	0.376259i	0.0335198	−	0.0580580i
$43$	−3.16713	−	5.48563i	−0.482983	−	0.836551i	0.516826	−	0.856091i	$-0.327113\pi$
$43$	−3.16713	−	5.48563i	−0.482983	−	0.836551i	−0.999809	+	0.0195391i	$0.993780\pi$
$44$	0.0200941			0.00302930
$45$	−5.81785	+	10.0768i	−0.867275	+	1.50216i
$46$	−13.8964			−2.04891
$47$	−1.81536	+	3.14430i	−0.264798	+	0.458643i	−0.967511	−	0.252831i	$-0.918638\pi$
$47$	−1.81536	+	3.14430i	−0.264798	+	0.458643i	0.702713	+	0.711473i	$0.251972\pi$
$48$	−0.269035	−	0.465983i	−0.0388319	−	0.0672588i
$49$	0.582248	−	1.00848i	0.0831782	−	0.144069i
$50$	−7.85180	+	13.5997i	−1.11041	+	1.92329i
$51$	−0.358807	−	0.621472i	−0.0502430	−	0.0870234i
$52$	0.534810			0.0741648
$53$	3.18468	+	5.51603i	0.437450	+	0.757685i	0.997492	−	0.0707788i	$-0.0225484\pi$
$53$	3.18468	+	5.51603i	0.437450	+	0.757685i	−0.560042	+	0.828464i	$0.689215\pi$
$54$	−0.538335	−	0.932424i	−0.0732582	−	0.126887i
$55$	−0.206398			−0.0278307
$56$	3.01948	+	5.22990i	0.403496	+	0.698875i
$57$	0.267849	−	0.463927i	0.0354774	−	0.0614487i
$58$	2.12549	+	3.68146i	0.279091	+	0.483400i
$59$	−6.17746	−	10.6997i	−0.804236	−	1.39298i	−0.916805	−	0.399334i	$-0.869241\pi$
$59$	−6.17746	−	10.6997i	−0.804236	−	1.39298i	0.112569	−	0.993644i	$-0.464092\pi$
$60$	−0.0861611	−	0.149235i	−0.0111234	−	0.0192662i
$61$	1.38425	+	2.39760i	0.177235	+	0.306981i	0.940933	−	0.338594i	$-0.109951\pi$
$61$	1.38425	+	2.39760i	0.177235	+	0.306981i	−0.763697	+	0.645575i	$0.776618\pi$
$62$	−5.42575	−	9.39767i	−0.689071	−	1.19351i
$63$	3.60710	+	6.24768i	0.454452	+	0.787133i
$64$	5.96176			0.745220
$65$	−5.49335			−0.681366
$66$	0.00476375	−	0.00825105i	0.000586377	−	0.00101563i
$67$	−7.29502	−	12.6353i	−0.891228	−	1.54365i	−0.838405	−	0.545048i	$-0.816511\pi$
$67$	−7.29502	−	12.6353i	−0.891228	−	1.54365i	−0.0528233	−	0.998604i	$-0.516822\pi$
$68$	−2.33457			−0.283108
$69$	−0.525214	+	0.909698i	−0.0632284	+	0.109515i
$70$	7.25905	+	12.5730i	0.867623	+	1.50277i
$71$	−6.10276	−	10.5703i	−0.724265	−	1.25446i	−0.959276	−	0.282471i	$-0.908846\pi$
$71$	−6.10276	−	10.5703i	−0.724265	−	1.25446i	0.235011	−	0.971993i	$-0.424487\pi$
$72$	7.46573			0.879845
$73$	−3.64459	−	6.31262i	−0.426567	−	0.738836i	0.569998	−	0.821646i	$-0.306944\pi$
$73$	−3.64459	−	6.31262i	−0.426567	−	0.738836i	−0.996565	+	0.0828098i	$0.973611\pi$
$74$	−2.01871	+	3.49651i	−0.234670	+	0.406461i
$75$	0.593516	+	1.02800i	0.0685334	+	0.118703i
$76$	−0.871377	−	1.50927i	−0.0999538	−	0.173125i
$77$	−0.0639840	+	0.110823i	−0.00729165	+	0.0126295i
$78$	0.126788	−	0.219604i	0.0143560	−	0.0248653i
$79$	−15.2341			−1.71397			−0.856983	−	0.515345i	$-0.827664\pi$
$79$	−15.2341			−1.71397			−0.856983	+	0.515345i	$0.827664\pi$
$80$	17.9801			2.01024
$81$	8.87783			0.986425
$82$	7.41566	−	12.8443i	0.818922	−	1.41842i
$83$	6.56729	+	11.3749i	0.720854	+	1.24856i	0.960658	+	0.277735i	$0.0895836\pi$
$83$	6.56729	+	11.3749i	0.720854	+	1.24856i	−0.239804	+	0.970821i	$0.577083\pi$
$84$	−0.106841			−0.0116573
$85$	23.9797			2.60097
$86$	−4.88532	+	8.46162i	−0.526797	+	0.912440i
$87$	0.321332			0.0344504
$88$	0.0662148	+	0.114687i	0.00705853	+	0.0122257i
$89$	−14.4073			−1.52717			−0.763583	−	0.645709i	$-0.776562\pi$
$89$	−14.4073			−1.52717			−0.763583	+	0.645709i	$0.776562\pi$
$90$	17.9481			1.89190
$91$	−1.70295	+	2.94960i	−0.178518	+	0.309202i
$92$	1.70865	+	2.95947i	0.178139	+	0.308546i
$93$	−0.820264			−0.0850574
$94$	5.60041			0.577638
$95$	8.95042	+	15.5026i	0.918293	+	1.59053i
$96$	−0.123505	+	0.213917i	−0.0126052	+	0.0218328i
$97$	6.35308	−	11.0039i	0.645057	−	1.11727i	−0.339231	−	0.940703i	$-0.610167\pi$
$97$	6.35308	−	11.0039i	0.645057	−	1.11727i	0.984288	−	0.176569i	$-0.0564999\pi$
$98$	−1.79624			−0.181448
$99$	0.0791007	+	0.137007i	0.00794992	+	0.0137697i
$100$	3.86171			0.386171
$101$	3.55027			0.353265			0.176633	−	0.984277i	$-0.443480\pi$
$101$	3.55027			0.353265			0.176633	+	0.984277i	$0.443480\pi$
$102$	−0.553461	+	0.958623i	−0.0548008	+	0.0949178i
$103$	0.495668			0.0488396			0.0244198	−	0.999702i	$-0.492226\pi$
$103$	0.495668			0.0488396			0.0244198	+	0.999702i	$0.492226\pi$
$104$	1.76233	+	3.05244i	0.172810	+	0.299316i
$105$	1.09742			0.107097
$106$	4.91239	−	8.50851i	0.477133	−	0.826419i
$107$	0.968446			0.0936232			0.0468116	−	0.998904i	$-0.485094\pi$
$107$	0.968446			0.0936232			0.0468116	+	0.998904i	$0.485094\pi$
$108$	−0.132383	+	0.229295i	−0.0127386	+	0.0220639i
$109$	0.984604	−	1.70538i	0.0943079	−	0.163346i	−0.815012	−	0.579445i	$-0.803270\pi$
$109$	0.984604	−	1.70538i	0.0943079	−	0.163346i	0.909320	+	0.416098i	$0.136603\pi$
$110$	0.159185	+	0.275717i	0.0151777	+	0.0262886i
$111$	0.152594	+	0.264301i	0.0144836	+	0.0250863i
$112$	5.57389	−	9.65425i	0.526683	−	0.912241i
$113$	1.55014	−	2.68493i	0.145825	−	0.252577i	−0.783855	−	0.620944i	$-0.786750\pi$
$113$	1.55014	−	2.68493i	0.145825	−	0.252577i	0.929681	+	0.368367i	$0.120083\pi$
$114$	−0.826316			−0.0773915
$115$	−17.5505	−	30.3984i	−1.63660	−	2.83467i
$116$	0.522685	−	0.905317i	0.0485301	−	0.0840566i
$117$	2.10529	+	3.64647i	0.194634	+	0.337116i
$118$	−9.52876	+	16.5043i	−0.877193	+	1.51934i
$119$	7.43378	−	12.8757i	0.681453	−	1.18031i
$120$	0.567843	−	0.983532i	0.0518367	−	0.0897838i
$121$	5.49860	−	9.52385i	0.499872	−	0.865804i
$122$	2.13522	−	3.69830i	0.193313	−	0.334829i
$123$	−0.560549	−	0.970899i	−0.0505430	−	0.0875430i
$124$	−1.33426	+	2.31100i	−0.119820	+	0.207534i
$125$	−20.1847			−1.80537
$126$	5.56397	−	9.63707i	0.495677	−	0.858539i
$127$	8.39973	−	14.5488i	0.745356	−	1.29099i	−0.204673	−	0.978830i	$-0.565613\pi$
$127$	8.39973	−	14.5488i	0.745356	−	1.29099i	0.950028	−	0.312163i	$-0.101054\pi$
$128$	−6.71649	−	11.6333i	−0.593660	−	1.02825i
$129$	0.369281	+	0.639613i	0.0325134	+	0.0563148i
$130$	4.23676	+	7.33828i	0.371588	+	0.643609i
$131$	−3.25456			−0.284352			−0.142176	−	0.989841i	$-0.545410\pi$
$131$	−3.25456			−0.284352			−0.142176	+	0.989841i	$0.545410\pi$
$132$	−0.00234293			−0.000203926
$133$	11.0986			0.962371
$134$	−11.2526	+	19.4901i	−0.972076	+	1.68369i
$135$	1.35979	−	2.35522i	0.117032	−	0.202705i
$136$	−7.69297	−	13.3246i	−0.659666	−	1.14258i
$137$	10.5013	+	18.1887i	0.897184	+	1.55397i	0.831078	+	0.556156i	$0.187724\pi$
$137$	10.5013	+	18.1887i	0.897184	+	1.55397i	0.0661057	+	0.997813i	$0.478943\pi$
$138$	1.62029			0.137928
$139$	−0.115159	−	0.199461i	−0.00976766	−	0.0169181i	0.861100	−	0.508435i	$-0.169776\pi$
$139$	−0.115159	−	0.199461i	−0.00976766	−	0.0169181i	−0.870868	+	0.491517i	$0.836443\pi$
$140$	1.78509	−	3.09187i	0.150868	−	0.261311i
$141$	0.211667	−	0.366618i	0.0178256	−	0.0308748i
$142$	−9.41354	+	16.3047i	−0.789967	+	1.36826i
$143$	−0.0373443	+	0.0646823i	−0.00312289	+	0.00540900i
$144$	−6.89077	−	11.9352i	−0.574231	−	0.994597i
$145$	−5.36880	+	9.29903i	−0.445855	+	0.772243i
$146$	−5.62180	+	9.73725i	−0.465264	+	0.805860i
$147$	−0.0678888	+	0.117587i	−0.00559937	+	0.00969840i
$148$	0.992852			0.0816119
$149$	5.29041			0.433407			0.216703	−	0.976237i	$-0.430470\pi$
$149$	5.29041			0.433407			0.216703	+	0.976237i	$0.430470\pi$
$150$	0.915502	−	1.58570i	0.0747504	−	0.129472i
$151$	6.39474			0.520397			0.260198	−	0.965555i	$-0.416212\pi$
$151$	6.39474			0.520397			0.260198	+	0.965555i	$0.416212\pi$
$152$	5.74279	−	9.94680i	0.465801	−	0.806792i
$153$	−9.19007	−	15.9177i	−0.742974	−	1.28687i
$154$	0.197391			0.0159062
$155$	13.7049	−	23.7377i	1.10081	−	1.90666i
$156$	−0.0623577			−0.00499261
$157$	10.5167	+	18.2154i	0.839322	+	1.45375i	0.890463	+	0.455056i	$0.150381\pi$
$157$	10.5167	+	18.2154i	0.839322	+	1.45375i	−0.0511410	+	0.998691i	$0.516286\pi$
$158$	11.7493	+	20.3504i	0.934725	+	1.61899i
$159$	−0.371327	−	0.643157i	−0.0294481	−	0.0510057i
$160$	−4.12703	−	7.14823i	−0.326270	−	0.565117i
$161$	−21.7628			−1.71515
$162$	−6.84705	−	11.8594i	−0.537955	−	0.931765i
$163$	2.16469	+	3.74936i	0.169552	+	0.293672i	0.938262	−	0.345924i	$-0.112435\pi$
$163$	2.16469	+	3.74936i	0.169552	+	0.293672i	−0.768711	+	0.639597i	$0.779101\pi$
$164$	−3.64720			−0.284799
$165$	0.0240656			0.00187350
$166$	10.1301	−	17.5458i	0.786247	−	1.36182i
$167$	10.3900			0.804004			0.402002	−	0.915639i	$-0.368314\pi$
$167$	10.3900			0.804004			0.402002	+	0.915639i	$0.368314\pi$
$168$	−0.352065	−	0.609795i	−0.0271624	−	0.0470467i
$169$	5.50607	−	9.53679i	0.423544	−	0.733600i
$170$	−18.4944	−	32.0333i	−1.41846	−	2.45684i
$171$	6.86037	−	11.8825i	0.524626	−	0.908679i
$172$	2.40272			0.183206
$173$	−5.64190			−0.428946			−0.214473	−	0.976730i	$-0.568803\pi$
$173$	−5.64190			−0.428946			−0.214473	+	0.976730i	$0.568803\pi$
$174$	−0.247828	−	0.429250i	−0.0187878	−	0.0325414i
$175$	−12.2965	+	21.2982i	−0.929528	+	1.60999i
$176$	0.122231	−	0.211710i	0.00921350	−	0.0159582i
$177$	0.720278	+	1.24756i	0.0541394	+	0.0937722i
$178$	11.1116	+	19.2459i	0.832852	+	1.44254i
$179$	−5.57799			−0.416918			−0.208459	−	0.978031i	$-0.566845\pi$
$179$	−5.57799			−0.416918			−0.208459	+	0.978031i	$0.566845\pi$
$180$	−2.20683	−	3.82235i	−0.164488	−	0.284901i
$181$	−7.02952	+	12.1755i	−0.522500	+	0.904997i	0.477157	+	0.878818i	$0.341667\pi$
$181$	−7.02952	+	12.1755i	−0.522500	+	0.904997i	−0.999657	+	0.0261788i	$0.991666\pi$
$182$	5.25362			0.389424
$183$	−0.161401	−	0.279554i	−0.0119311	−	0.0206653i
$184$	−11.2608	+	19.5043i	−0.830158	+	1.43788i
$185$	−10.1982			−0.749783
$186$	0.632630	+	1.09575i	0.0463867	+	0.0803442i
$187$	0.163017	−	0.282353i	0.0119210	−	0.0206477i
$188$	−0.688605	−	1.19270i	−0.0502217	−	0.0869865i
$189$	−0.843074	−	1.46025i	−0.0613246	−	0.106217i
$190$	13.8061	−	23.9128i	1.00160	−	1.73482i
$191$	−5.93751	+	10.2841i	−0.429623	+	0.744129i	−0.996840	−	0.0794396i	$-0.974687\pi$
$191$	−5.93751	+	10.2841i	−0.429623	+	0.744129i	0.567217	+	0.823569i	$0.308020\pi$
$192$	−0.695128			−0.0501665
$193$	6.87488	−	11.9076i	0.494864	−	0.857130i	−0.505118	−	0.863050i	$-0.668551\pi$
$193$	6.87488	−	11.9076i	0.494864	−	0.857130i	0.999982	+	0.00591988i	$0.00188437\pi$
$194$	−19.5993			−1.40715
$195$	0.640512			0.0458680
$196$	0.220859	+	0.382539i	0.0157756	+	0.0273242i
$197$	25.8098			1.83887			0.919436	−	0.393240i	$-0.128646\pi$
$197$	25.8098			1.83887			0.919436	+	0.393240i	$0.128646\pi$
$198$	0.122013	−	0.211333i	0.00867111	−	0.0150188i
$199$	−0.710831	+	1.23120i	−0.0503895	+	0.0872771i	−0.890120	−	0.455726i	$-0.849380\pi$
$199$	−0.710831	+	1.23120i	−0.0503895	+	0.0872771i	0.839731	+	0.543003i	$0.182713\pi$
$200$	12.7252	+	22.0408i	0.899810	+	1.55852i
$201$	0.850583	+	1.47325i	0.0599955	+	0.103915i
$202$	−2.73816	−	4.74263i	−0.192656	−	0.333690i
$203$	3.32868	+	5.76545i	0.233628	+	0.404655i
$204$	0.272206			0.0190582
$205$	37.4625			2.61650
$206$	−0.382285	−	0.662138i	−0.0266351	−	0.0461333i
$207$	−13.4522	+	23.3000i	−0.934996	+	1.61946i
$208$	3.25321	−	5.63472i	0.225569	−	0.390697i
$209$	0.243383			0.0168352
$210$	−0.846389	−	1.46599i	−0.0584064	−	0.101163i
$211$	3.84917	−	6.66695i	0.264988	−	0.458972i	−0.702573	−	0.711612i	$-0.747965\pi$
$211$	3.84917	−	6.66695i	0.264988	−	0.458972i	0.967560	+	0.252640i	$0.0812988\pi$
$212$	−2.41603			−0.165934
$213$	0.711569	+	1.23247i	0.0487559	+	0.0844477i
$214$	−0.746917	−	1.29370i	−0.0510582	−	0.0884353i
$215$	−24.6797			−1.68314
$216$	−1.74494			−0.118728
$217$	−8.49713	−	14.7175i	−0.576823	−	0.999087i
$218$	−3.03751			−0.205726
$219$	0.424951	+	0.736038i	0.0287156	+	0.0497368i
$220$	0.0391456	−	0.0678022i	0.00263920	−	0.00457122i
$221$	4.33873	−	7.51491i	0.291855	−	0.505508i
$222$	0.235377	−	0.407685i	0.0157975	−	0.0273620i
$223$	6.07148	−	10.5161i	0.406577	−	0.704211i	−0.587927	−	0.808914i	$-0.700056\pi$
$223$	6.07148	−	10.5161i	0.406577	−	0.704211i	0.994504	+	0.104703i	$0.0333891\pi$
$224$	−5.11756			−0.341931
$225$	15.2017	+	26.3301i	1.01344	+	1.75534i
$226$	−4.78221			−0.318108
$227$	10.7287	−	18.5827i	0.712090	−	1.23338i	−0.251981	−	0.967732i	$-0.581082\pi$
$227$	10.7287	−	18.5827i	0.712090	−	1.23338i	0.964071	−	0.265644i	$-0.0855847\pi$
$228$	0.101601	+	0.175977i	0.00672867	+	0.0116544i
$229$	−7.49087	+	12.9746i	−0.495010	+	0.857383i	−0.999983	−	0.00575189i	$-0.998169\pi$
$229$	−7.49087	+	12.9746i	−0.495010	+	0.857383i	0.504973	+	0.863135i	$0.331502\pi$
$230$	−27.0718	+	46.8897i	−1.78506	+	3.09182i
$231$	0.00746039	−	0.0129218i	0.000490858	−	0.000850190i
$232$	6.88948			0.452317
$233$	−6.61475	+	11.4571i	−0.433347	+	0.750579i	−0.997159	−	0.0753242i	$-0.976001\pi$
$233$	−6.61475	+	11.4571i	−0.433347	+	0.750579i	0.563812	+	0.825903i	$0.309334\pi$
$234$	3.24742	−	5.62469i	0.212290	−	0.367698i
$235$	7.07306	+	12.2509i	0.461395	+	0.799160i
$236$	4.68648			0.305064
$237$	1.77626			0.115380
$238$	−22.9333			−1.48654
$239$	−1.12830	−	1.95428i	−0.0729839	−	0.126412i	0.827224	−	0.561872i	$-0.189919\pi$
$239$	−1.12830	−	1.95428i	−0.0729839	−	0.126412i	−0.900208	+	0.435461i	$0.856585\pi$
$240$	−2.09644			−0.135325
$241$	−2.83602	+	4.91214i	−0.182684	+	0.316419i	−0.942794	−	0.333377i	$-0.891812\pi$
$241$	−2.83602	+	4.91214i	−0.182684	+	0.316419i	0.760109	+	0.649795i	$0.225145\pi$
$242$	−16.9632			−1.09044
$243$	−3.12914			−0.200734
$244$	−1.05015			−0.0672291
$245$	−2.26857	−	3.92928i	−0.144933	−	0.251032i
$246$	−0.864649	+	1.49762i	−0.0551280	+	0.0954845i
$247$	6.47771			0.412167
$248$	−17.5868			−1.11676
$249$	−0.765732	−	1.32629i	−0.0485263	−	0.0840500i
$250$	15.5675	+	26.9637i	0.984575	+	1.70533i
$251$	13.0827	+	22.6598i	0.825770	+	1.43028i	0.901330	+	0.433134i	$0.142592\pi$
$251$	13.0827	+	22.6598i	0.825770	+	1.43028i	−0.0755600	+	0.997141i	$0.524074\pi$
$252$	−2.73650			−0.172383
$253$	−0.477241			−0.0300039
$254$	−25.9132			−1.62594
$255$	−2.79599			−0.175091
$256$	−4.39847	+	7.61837i	−0.274904	+	0.476148i
$257$	−10.1939			−0.635875			−0.317938	−	0.948112i	$-0.602990\pi$
$257$	−10.1939			−0.635875			−0.317938	+	0.948112i	$0.602990\pi$
$258$	0.569617	−	0.986606i	0.0354628	−	0.0614234i
$259$	−3.16145	+	5.47580i	−0.196443	+	0.340250i
$260$	1.04187	−	1.80457i	0.0646141	−	0.111915i
$261$	8.23023			0.509438
$262$	2.51009	+	4.34760i	0.155074	+	0.268596i
$263$	4.00574			0.247005			0.123502	−	0.992344i	$-0.460587\pi$
$263$	4.00574			0.247005			0.123502	+	0.992344i	$0.460587\pi$
$264$	−0.00772051	−	0.0133723i	−0.000475164	−	0.000823009i
$265$	24.8165			1.52446
$266$	−8.55982	−	14.8260i	−0.524836	−	0.909043i
$267$	1.67985			0.102805
$268$	5.53431			0.338062
$269$	1.27366	−	2.20605i	0.0776567	−	0.134505i	−0.824582	−	0.565743i	$-0.808590\pi$
$269$	1.27366	−	2.20605i	0.0776567	−	0.134505i	0.902238	+	0.431237i	$0.141923\pi$
$270$	−4.19495			−0.255297
$271$	5.23975	+	9.07552i	0.318292	+	0.551299i	0.980132	−	0.198347i	$-0.0635573\pi$
$271$	5.23975	+	9.07552i	0.318292	+	0.551299i	−0.661840	+	0.749646i	$0.730224\pi$
$272$	−14.2010	+	24.5969i	−0.861063	+	1.49140i
$273$	0.198560	−	0.343916i	0.0120174	−	0.0208148i
$274$	16.1983	−	28.0562i	0.978573	−	1.69494i
$275$	−0.269652	+	0.467052i	−0.0162607	+	0.0281643i
$276$	−0.199225	−	0.345068i	−0.0119919	−	0.0207706i
$277$	12.1587			0.730547			0.365273	−	0.930900i	$-0.380976\pi$
$277$	12.1587			0.730547			0.365273	+	0.930900i	$0.380976\pi$
$278$	−0.177633	+	0.307670i	−0.0106537	+	0.0184528i
$279$	−21.0093			−1.25779
$280$	23.5292			1.40614
$281$	−7.40867	−	12.8322i	−0.441964	−	0.765504i	0.555871	−	0.831268i	$-0.312385\pi$
$281$	−7.40867	−	12.8322i	−0.441964	−	0.765504i	−0.997835	+	0.0657644i	$0.979051\pi$
$282$	−0.652995			−0.0388853
$283$	3.90866	+	6.76999i	0.232346	+	0.402434i	0.958498	−	0.285099i	$-0.0920266\pi$
$283$	3.90866	+	6.76999i	0.232346	+	0.402434i	−0.726152	+	0.687534i	$0.758693\pi$
$284$	4.62981			0.274729
$285$	−1.04360	−	1.80757i	−0.0618175	−	0.107071i
$286$	0.115208			0.00681237
$287$	11.6135	−	20.1151i	0.685522	−	1.18736i
$288$	−3.16331	+	5.47902i	−0.186400	+	0.322854i
$289$	−10.4396	+	18.0819i	−0.614094	+	1.06364i
$290$	16.5628			0.972601
$291$	−0.740755	+	1.28303i	−0.0434238	+	0.0752123i
$292$	2.76494			0.161806
$293$	29.6749			1.73363			0.866814	−	0.498632i	$-0.166164\pi$
$293$	29.6749			1.73363			0.866814	+	0.498632i	$0.166164\pi$
$294$	0.209438			0.0122146
$295$	−48.1375			−2.80268
$296$	3.27168	+	5.66672i	0.190163	+	0.329371i
$297$	−0.0184879	−	0.0320220i	−0.00107278	−	0.00185811i
$298$	−4.08024	−	7.06718i	−0.236362	−	0.409391i
$299$	−12.7019			−0.734570
$300$	−0.450267			−0.0259962
$301$	−7.65078	+	13.2515i	−0.440983	+	0.763806i
$302$	−4.93196	−	8.54241i	−0.283803	−	0.491560i
$303$	−0.413954			−0.0237810
$304$	−21.2021			−1.21602
$305$	10.7867			0.617646
$306$	−14.1757	+	24.5531i	−0.810373	+	1.40361i
$307$	14.8518			0.847640			0.423820	−	0.905746i	$-0.360689\pi$
$307$	14.8518			0.847640			0.423820	+	0.905746i	$0.360689\pi$
$308$	−0.0242705	−	0.0420377i	−0.00138294	−	0.00239532i
$309$	−0.0577938			−0.00328778
$310$	−42.2799			−2.40134
$311$	−14.3099			−0.811437			−0.405719	−	0.913998i	$-0.632979\pi$
$311$	−14.3099			−0.811437			−0.405719	+	0.913998i	$0.632979\pi$
$312$	−0.205483	−	0.355908i	−0.0116332	−	0.0201493i
$313$	−9.39841	+	16.2785i	−0.531230	+	0.920117i	0.468106	+	0.883672i	$0.344937\pi$
$313$	−9.39841	+	16.2785i	−0.531230	+	0.920117i	−0.999336	+	0.0364446i	$0.988397\pi$
$314$	16.2220	−	28.0974i	0.915461	−	1.58563i
$315$	28.1081			1.58371
$316$	2.88930	−	5.00442i	0.162536	−	0.281520i
$317$	1.24110	−	2.14965i	0.0697071	−	0.120736i	−0.829065	−	0.559152i	$-0.811127\pi$
$317$	1.24110	−	2.14965i	0.0697071	−	0.120736i	0.898772	+	0.438416i	$0.144460\pi$
$318$	−0.572774	+	0.992073i	−0.0321195	+	0.0556327i
$319$	0.0729953	+	0.126432i	0.00408695	+	0.00707881i
$320$	11.6142	−	20.1163i	0.649252	−	1.12454i
$321$	−0.112919			−0.00630251
$322$	16.7846	+	29.0718i	0.935371	+	1.62011i
$323$	−28.2767			−1.57336
$324$	−1.68377	+	2.91638i	−0.0935430	+	0.162021i
$325$	−7.17687	+	12.4307i	−0.398101	+	0.689532i
$326$	3.33905	−	5.78340i	0.184933	−	0.320313i
$327$	−0.114803	+	0.198844i	−0.00634860	+	0.0109961i
$328$	−12.0184	−	20.8165i	−0.663605	−	1.14940i
$329$	8.77066			0.483542
$330$	−0.0185606	−	0.0321480i	−0.00102173	−	0.00176969i
$331$	8.47351			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$331$	8.47351			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$332$	−4.98223			−0.273435
$333$	3.90838	+	6.76950i	0.214178	+	0.370967i
$334$	−8.01333	−	13.8795i	−0.438470	−	0.759452i
$335$	−56.8461			−3.10583
$336$	−0.649903	+	1.12566i	−0.0354551	+	0.0614101i
$337$	−14.0568	−	24.3471i	−0.765724	−	1.32627i	−0.939863	−	0.341552i	$-0.889048\pi$
$337$	−14.0568	−	24.3471i	−0.765724	−	1.32627i	0.174139	−	0.984721i	$-0.444286\pi$
$338$	−16.9863			−0.923932
$339$	−0.180743	+	0.313057i	−0.00981664	+	0.0170029i
$340$	−4.54801	+	7.87739i	−0.246651	+	0.427211i
$341$	−0.186335	−	0.322742i	−0.0100906	−	0.0174775i
$342$	−21.1643			−1.14444
$343$	−19.7228			−1.06493
$344$	7.91753	+	13.7136i	0.426885	+	0.739386i
$345$	2.04635	+	3.54439i	0.110172	+	0.190823i
$346$	4.35133	+	7.53672i	0.233929	+	0.405177i
$347$	−0.202160	−	0.350152i	−0.0108525	−	0.0187971i	0.860548	−	0.509369i	$-0.170121\pi$
$347$	−0.202160	−	0.350152i	−0.0108525	−	0.0187971i	−0.871401	+	0.490572i	$0.836788\pi$
$348$	−0.0609439	+	0.105558i	−0.00326694	+	0.00565850i
$349$	−5.68033	+	9.83862i	−0.304061	+	0.526649i	−0.977052	−	0.213002i	$-0.931676\pi$
$349$	−5.68033	+	9.83862i	−0.304061	+	0.526649i	0.672991	+	0.739651i	$0.265009\pi$
$350$	37.9348			2.02770
$351$	−0.492061	−	0.852275i	−0.0262643	−	0.0454911i
$352$	−0.112224			−0.00598155
$353$	23.9547			1.27498			0.637489	−	0.770459i	$-0.279973\pi$
$353$	23.9547			1.27498			0.637489	+	0.770459i	$0.279973\pi$
$354$	1.11103	−	1.92436i	0.0590507	−	0.102279i
$355$	−47.5555			−2.52398
$356$	2.73249	−	4.73281i	0.144822	−	0.250838i
$357$	−0.866762	+	1.50128i	−0.0458739	+	0.0794560i
$358$	4.30204	+	7.45134i	0.227370	+	0.393816i
$359$	−1.84362	−	3.19324i	−0.0973024	−	0.168533i	0.813265	−	0.581894i	$-0.197688\pi$
$359$	−1.84362	−	3.19324i	−0.0973024	−	0.168533i	−0.910567	+	0.413361i	$0.864355\pi$
$360$	14.5441	−	25.1911i	0.766541	−	1.32769i
$361$	−1.05427	−	1.82605i	−0.0554878	−	0.0961077i
$362$	21.6861			1.13980
$363$	−0.641124	+	1.11046i	−0.0336503	+	0.0582840i
$364$	−0.645965	−	1.11884i	−0.0338578	−	0.0586434i
$365$	−28.4003			−1.48654
$366$	−0.248962	+	0.431214i	−0.0130134	+	0.0225399i
$367$	−4.33413	−	7.50694i	−0.226240	−	0.391859i	0.730451	−	0.682965i	$-0.239310\pi$
$367$	−4.33413	−	7.50694i	−0.226240	−	0.391859i	−0.956691	+	0.291106i	$0.905977\pi$
$368$	41.5743			2.16721
$369$	−14.3573	−	24.8675i	−0.747409	−	1.29455i
$370$	7.86535	+	13.6232i	0.408900	+	0.708236i
$371$	7.69317	−	13.3250i	0.399410	−	0.691798i
$372$	0.155572	−	0.269458i	0.00806602	−	0.0139708i
$373$	−16.2563	−	28.1568i	−0.841721	−	1.45790i	−0.888438	−	0.458996i	$-0.848209\pi$
$373$	−16.2563	−	28.1568i	−0.841721	−	1.45790i	0.0467170	−	0.998908i	$-0.485124\pi$
$374$	−0.502908			−0.0260048
$375$	2.35349			0.121534
$376$	4.53823	−	7.86044i	0.234041	−	0.405371i
$377$	1.94279	+	3.36501i	0.100059	+	0.173307i
$378$	−1.30045	+	2.25244i	−0.0668877	+	0.115853i
$379$	9.66142	+	16.7341i	0.496274	+	0.859571i	0.999991	−	0.00429745i	$-0.00136793\pi$
$379$	9.66142	+	16.7341i	0.496274	+	0.859571i	−0.503717	+	0.863869i	$0.668035\pi$
$380$	−6.79016			−0.348328
$381$	−0.979390	+	1.69635i	−0.0501757	+	0.0869068i
$382$	18.3173			0.937193
$383$	13.1274			0.670776			0.335388	−	0.942080i	$-0.391133\pi$
$383$	13.1274			0.670776			0.335388	+	0.942080i	$0.391133\pi$
$384$	0.783128	+	1.35642i	0.0399639	+	0.0692194i
$385$	0.249296	+	0.431793i	0.0127053	+	0.0220062i
$386$	−21.2091			−1.07951
$387$	9.45834	+	16.3823i	0.480794	+	0.832760i
$388$	2.40986	+	4.17399i	0.122342	+	0.211902i
$389$	6.23842	+	10.8053i	0.316300	+	0.547848i	0.979713	−	0.200405i	$-0.0642259\pi$
$389$	6.23842	+	10.8053i	0.316300	+	0.547848i	−0.663413	+	0.748254i	$0.730893\pi$
$390$	−0.493996	−	0.855627i	−0.0250145	−	0.0433264i
$391$	55.4468			2.80407
$392$	−1.45556	+	2.52111i	−0.0735171	+	0.127335i
$393$	0.379475			0.0191420
$394$	−19.9059	−	34.4780i	−1.00284	−	1.73698i
$395$	−29.6777	+	51.4032i	−1.49325	+	2.58638i
$396$	−0.0600092			−0.00301557
$397$	10.2372	−	17.7313i	0.513788	−	0.889907i	−0.486084	−	0.873912i	$-0.661575\pi$
$397$	10.2372	−	17.7313i	0.513788	−	0.889907i	0.999872	−	0.0159952i	$-0.00509164\pi$
$398$	2.19292			0.109921
$399$	−1.29407			−0.0647847
$400$	23.4905	−	40.6867i	1.17452	−	2.03433i
$401$	−2.85362	+	4.94261i	−0.142503	+	0.246822i	−0.928439	−	0.371486i	$-0.878848\pi$
$401$	−2.85362	+	4.94261i	−0.142503	+	0.246822i	0.785936	+	0.618308i	$0.212182\pi$
$402$	1.31203	−	2.27250i	0.0654380	−	0.113342i
$403$	−4.95936	−	8.58987i	−0.247044	−	0.427892i
$404$	−0.673347	+	1.16627i	−0.0335002	+	0.0580241i
$405$	17.2950	−	29.9558i	0.859396	−	1.48852i
$406$	5.13451	−	8.89323i	0.254821	−	0.441364i
$407$	−0.0693281	+	0.120080i	−0.00343647	+	0.00595214i
$408$	0.896983	+	1.55362i	0.0444073	+	0.0769157i
$409$	−0.854254			−0.0422401			−0.0211201	−	0.999777i	$-0.506723\pi$
$409$	−0.854254			−0.0422401			−0.0211201	+	0.999777i	$0.506723\pi$
$410$	−28.8931	−	50.0443i	−1.42693	−	2.47151i
$411$	−1.22442	−	2.12077i	−0.0603964	−	0.104610i
$412$	−0.0940087	+	0.162828i	−0.00463148	+	0.00802195i
$413$	−14.9228	+	25.8470i	−0.734301	+	1.27185i
$414$	41.5003			2.03963
$415$	51.1753			2.51210
$416$	−2.98687			−0.146443
$417$	0.0134273	+	0.0232567i	0.000657537	+	0.00113889i
$418$	−0.187710	−	0.325123i	−0.00918120	−	0.0159023i
$419$	5.93385	+	10.2777i	0.289887	+	0.502100i	0.973783	−	0.227481i	$-0.0730488\pi$
$419$	5.93385	+	10.2777i	0.289887	+	0.502100i	−0.683895	+	0.729580i	$0.739715\pi$
$420$	−0.208138	+	0.360505i	−0.0101561	+	0.0175908i
$421$	−9.67954	+	16.7655i	−0.471752	+	0.817098i	−0.999478	−	0.0323166i	$-0.989712\pi$
$421$	−9.67954	+	16.7655i	−0.471752	+	0.817098i	0.527726	+	0.849415i	$0.323045\pi$
$422$	−11.8747			−0.578052
$423$	5.42140	−	9.39015i	0.263598	−	0.456564i
$424$	−7.96140	−	13.7896i	−0.386640	−	0.669680i
$425$	31.3287	−	54.2630i	1.51967	−	2.63214i
$426$	1.09760	−	1.90110i	0.0531788	−	0.0921084i
$427$	3.34391	−	5.79182i	0.161823	−	0.280286i
$428$	−0.183676	+	0.318136i	−0.00887832	+	0.0153777i
$429$	0.00435427	−	0.00754181i	0.000210226	−	0.000364122i
$430$	19.0343	+	32.9684i	0.917916	+	1.58988i
$431$	−0.738795	+	1.27963i	−0.0355865	+	0.0616377i	−0.883270	−	0.468864i	$-0.844663\pi$
$431$	−0.738795	+	1.27963i	−0.0355865	+	0.0616377i	0.847684	+	0.530502i	$0.177997\pi$
$432$	1.61055	+	2.78956i	0.0774878	+	0.134213i
$433$	22.3025			1.07179			0.535896	−	0.844284i	$-0.319974\pi$
$433$	22.3025			1.07179			0.535896	+	0.844284i	$0.319974\pi$
$434$	−13.1069	+	22.7018i	−0.629150	+	1.08972i
$435$	0.625990	−	1.08425i	0.0300139	−	0.0519857i
$436$	0.373481	+	0.646888i	0.0178865	+	0.0309803i
$437$	20.6955	+	35.8456i	0.989998	+	1.71473i
$438$	0.655490	−	1.13534i	0.0313205	−	0.0542487i
$439$	1.49736	−	2.59351i	0.0714652	−	0.123781i	−0.828078	−	0.560612i	$-0.810566\pi$
$439$	1.49736	−	2.59351i	0.0714652	−	0.123781i	0.899544	+	0.436831i	$0.143899\pi$
$440$	0.515976			0.0245982
$441$	−1.73883	+	3.01174i	−0.0828013	+	0.143416i
$442$	−13.3850			−0.636661
$443$	−3.46120	−	5.99498i	−0.164447	−	0.284830i	0.772012	−	0.635608i	$-0.219251\pi$
$443$	−3.46120	−	5.99498i	−0.164447	−	0.284830i	−0.936459	+	0.350778i	$0.885917\pi$
$444$	−0.115764			−0.00549393
$445$	−28.0670	+	48.6134i	−1.33050	+	2.30450i
$446$	−18.7306			−0.886919
$447$	−0.616850			−0.0291760
$448$	−7.20084	−	12.4722i	−0.340208	−	0.589257i
$449$	25.9886			1.22648			0.613239	−	0.789897i	$-0.289866\pi$
$449$	25.9886			1.22648			0.613239	+	0.789897i	$0.289866\pi$
$450$	23.4486	−	40.6142i	1.10538	−	1.91457i
$451$	0.254674	−	0.441109i	0.0119921	−	0.0207710i
$452$	0.588002	+	1.01845i	0.0276573	+	0.0479039i
$453$	−0.745613			−0.0350320
$454$	−33.0982			−1.55338
$455$	6.63508	+	11.4923i	0.311057	+	0.538767i
$456$	−0.669596	+	1.15977i	−0.0313567	+	0.0543114i
$457$	−32.0668			−1.50002			−0.750010	−	0.661427i	$-0.769951\pi$
$457$	−32.0668			−1.50002			−0.750010	+	0.661427i	$0.769951\pi$
$458$	23.1094			1.07983
$459$	2.14796	+	3.72038i	0.100258	+	0.173653i
$460$	13.3146			0.620795
$461$	−4.38226	+	7.59030i	−0.204102	+	0.353515i	−0.949846	−	0.312717i	$-0.898761\pi$
$461$	−4.38226	+	7.59030i	−0.204102	+	0.353515i	0.745744	+	0.666232i	$0.232094\pi$
$462$	−0.0230154			−0.00107077
$463$	21.9665			1.02087			0.510436	−	0.859916i	$-0.329484\pi$
$463$	21.9665			1.02087			0.510436	+	0.859916i	$0.329484\pi$
$464$	−6.35890	−	11.0139i	−0.295205	−	0.511309i
$465$	−1.59797	+	2.76776i	−0.0741039	+	0.128352i
$466$	20.4066			0.945316
$467$	−26.9409			−1.24667			−0.623337	−	0.781953i	$-0.714224\pi$
$467$	−26.9409			−1.24667			−0.623337	+	0.781953i	$0.714224\pi$
$468$	−1.59716			−0.0738287
$469$	−17.6224	+	30.5229i	−0.813728	+	1.40942i
$470$	10.9102	−	18.8971i	0.503251	−	0.871656i
$471$	−1.22622	−	2.12388i	−0.0565013	−	0.0978631i
$472$	15.4431	+	26.7482i	0.710824	+	1.23118i
$473$	−0.167775	+	0.290595i	−0.00771432	+	0.0133616i
$474$	−1.36994	−	2.37281i	−0.0629236	−	0.108987i
$475$	46.7737			2.14612
$476$	2.81979	+	4.88402i	0.129245	+	0.223859i
$477$	−9.51075	−	16.4731i	−0.435467	−	0.754252i
$478$	−1.74041	+	3.01448i	−0.0796046	+	0.137879i
$479$	11.5273			0.526695			0.263348	−	0.964701i	$-0.415173\pi$
$479$	11.5273			0.526695			0.263348	+	0.964701i	$0.415173\pi$
$480$	0.481203	+	0.833467i	0.0219638	+	0.0380424i
$481$	−1.84519	+	3.19596i	−0.0841333	+	0.145723i
$482$	8.74916			0.398513
$483$	2.53750			0.115460
$484$	2.08573	+	3.61260i	0.0948061	+	0.164209i
$485$	−24.7530	−	42.8735i	−1.12398	−	1.94679i
$486$	2.41336	+	4.18006i	0.109472	+	0.189611i
$487$	−16.5456	−	28.6578i	−0.749753	−	1.29861i	−0.947941	−	0.318446i	$-0.896839\pi$
$487$	−16.5456	−	28.6578i	−0.749753	−	1.29861i	0.198188	−	0.980164i	$-0.436494\pi$
$488$	−3.46050	−	5.99376i	−0.156649	−	0.271325i
$489$	−0.252398	−	0.437167i	−0.0114139	−	0.0197694i
$490$	−3.49928	+	6.06093i	−0.158081	+	0.273805i
$491$	−1.95655	−	3.38885i	−0.0882979	−	0.152937i	0.818494	−	0.574515i	$-0.194809\pi$
$491$	−1.95655	−	3.38885i	−0.0882979	−	0.152937i	−0.906792	+	0.421579i	$0.861476\pi$
$492$	0.425256			0.0191720
$493$	−8.48073	−	14.6891i	−0.381953	−	0.661562i
$494$	−4.99595	−	8.65324i	−0.224779	−	0.389328i
$495$	0.616389			0.0277046
$496$	16.2324	+	28.1153i	0.728855	+	1.26241i
$497$	−14.7423	+	25.5344i	−0.661283	+	1.14538i
$498$	−1.18115	+	2.04580i	−0.0529284	+	0.0916747i
$499$	1.15193	+	1.99520i	0.0515673	+	0.0893172i	0.890657	−	0.454676i	$-0.150245\pi$
$499$	1.15193	+	1.99520i	0.0515673	+	0.0893172i	−0.839090	+	0.543993i	$0.816912\pi$
$500$	3.82824	−	6.63071i	0.171204	−	0.296534i
$501$	−1.21145			−0.0541238
$502$	20.1801	−	34.9529i	0.900680	−	1.56002i
$503$	−23.0098			−1.02596			−0.512978	−	0.858402i	$-0.671458\pi$
$503$	−23.0098			−1.02596			−0.512978	+	0.858402i	$0.671458\pi$
$504$	−9.01740	−	15.6186i	−0.401667	−	0.695708i
$505$	6.91633	−	11.9794i	0.307773	−	0.533078i
$506$	0.368074	+	0.637522i	0.0163629	+	0.0283413i
$507$	−0.641996	+	1.11197i	−0.0285120	+	0.0493843i
$508$	3.18619	+	5.51865i	0.141365	+	0.244851i
$509$	19.5103			0.864778			0.432389	−	0.901687i	$-0.357671\pi$
$509$	19.5103			0.864778			0.432389	+	0.901687i	$0.357671\pi$
$510$	2.15641	+	3.73501i	0.0954875	+	0.165389i
$511$	−8.80417	+	15.2493i	−0.389473	+	0.674588i
$512$	−13.2967			−0.587635
$513$	−1.60345	+	2.77726i	−0.0707941	+	0.122619i
$514$	7.86203	+	13.6174i	0.346779	+	0.600640i
$515$	0.965618	−	1.67250i	0.0425502	−	0.0736991i
$516$	−0.280152			−0.0123330
$517$	0.192333			0.00845882
$518$	9.75311			0.428527
$519$	0.657833			0.0288757
$520$	13.7328			0.602225
$521$	−3.32548	+	5.75989i	−0.145692	+	0.252346i	−0.929631	−	0.368492i	$-0.879874\pi$
$521$	−3.32548	+	5.75989i	−0.145692	+	0.252346i	0.783939	+	0.620838i	$0.213207\pi$
$522$	−6.34758	−	10.9943i	−0.277826	−	0.481209i
$523$	−4.52613			−0.197914			−0.0989570	−	0.995092i	$-0.531551\pi$
$523$	−4.52613			−0.197914			−0.0989570	+	0.995092i	$0.531551\pi$
$524$	0.617262	−	1.06913i	0.0269652	−	0.0467051i
$525$	1.43375	−	2.48332i	0.0625738	−	0.108381i
$526$	−3.08944	−	5.35106i	−0.134706	−	0.233317i
$527$	21.6488	+	37.4968i	0.943036	+	1.63339i
$528$	−0.0142518	+	0.0246849i	−0.000620232	+	0.00107427i
$529$	−29.0810	−	50.3697i	−1.26439	−	2.18999i
$530$	−19.1398	−	33.1511i	−0.831379	−	1.43999i
$531$	18.4484	+	31.9535i	0.800592	+	1.38667i
$532$	−2.10497	+	3.64591i	−0.0912619	+	0.158070i
$533$	6.77822	−	11.7402i	0.293597	−	0.508526i
$534$	−1.29559	−	2.24403i	−0.0560658	−	0.0971087i
$535$	1.88664	−	3.26776i	0.0815667	−	0.141278i
$536$	18.2368	+	31.5871i	0.787712	+	1.36436i
$537$	0.650381			0.0280660
$538$	−3.92927			−0.169403
$539$	−0.0616878			−0.00265708
$540$	0.515796	+	0.893384i	0.0221963	+	0.0384451i
$541$	−2.79768	−	4.84573i	−0.120282	−	0.208334i	0.799597	−	0.600537i	$-0.205046\pi$
$541$	−2.79768	−	4.84573i	−0.120282	−	0.208334i	−0.919879	+	0.392203i	$0.871713\pi$
$542$	8.08234	−	13.9990i	0.347166	−	0.601310i
$543$	0.819627	−	1.41964i	0.0351735	−	0.0609224i
$544$	13.0384			0.559016
$545$	−3.83624	−	6.64456i	−0.164326	−	0.284622i
$546$	−0.612560			−0.0262152
$547$	−23.3770	+	0.717419i	−0.999529	+	0.0306746i
$547$	−23.3770	+	0.717419i	−0.999529	+	0.0306746i
$548$	−7.96671			−0.340321
$549$	−4.13394	−	7.16019i	−0.176432	−	0.305590i
$550$	0.831880			0.0354715
$551$	6.33085	−	10.9654i	0.269703	−	0.467140i
$552$	1.31299	−	2.27416i	0.0558844	−	0.0967946i
$553$	18.4003	+	31.8703i	0.782461	+	1.35526i
$554$	−9.37744	−	16.2422i	−0.398409	−	0.690065i
$555$	1.18908			0.0504738
$556$	0.0873645			0.00370508
$557$	43.1360			1.82773			0.913866	−	0.406016i	$-0.133082\pi$
$557$	43.1360			1.82773			0.913866	+	0.406016i	$0.133082\pi$
$558$	16.2035	+	28.0653i	0.685948	+	1.18810i
$559$	−4.46539	+	7.73428i	−0.188866	+	0.327125i
$560$	−21.7171	−	37.6152i	−0.917716	−	1.58953i
$561$	−0.0190074	+	0.0329218i	−0.000802493	+	0.00138996i
$562$	−11.4279	+	19.7937i	−0.482057	+	0.834947i
$563$	5.49997	+	9.52622i	0.231796	+	0.401482i	0.958337	−	0.285641i	$-0.0922065\pi$
$563$	5.49997	+	9.52622i	0.231796	+	0.401482i	−0.726541	+	0.687123i	$0.758873\pi$
$564$	0.0802898	+	0.139066i	0.00338081	+	0.00585573i
$565$	−6.03971	−	10.4611i	−0.254093	−	0.440101i
$566$	6.02912	−	10.4427i	0.253423	−	0.438941i
$567$	−10.7230	−	18.5728i	−0.450323	−	0.779983i
$568$	15.2563	+	26.4247i	0.640141	+	1.10876i
$569$	−11.4695	+	19.8658i	−0.480827	+	0.832817i	−0.999758	−	0.0219989i	$-0.992997\pi$
$569$	−11.4695	+	19.8658i	−0.480827	+	0.832817i	0.518931	+	0.854816i	$0.326330\pi$
$570$	−1.60976	+	2.78818i	−0.0674253	+	0.116784i
$571$	−1.09760			−0.0459329			−0.0229665	−	0.999736i	$-0.507311\pi$
$571$	−1.09760			−0.0459329			−0.0229665	+	0.999736i	$0.507311\pi$
$572$	−0.0141655	−	0.0245353i	−0.000592289	−	0.00102587i
$573$	0.692301	−	1.19910i	0.0289213	−	0.0500931i
$574$	−35.8277			−1.49542
$575$	−91.7167			−3.82485
$576$	−17.8042			−0.741842
$577$	22.8553			0.951478			0.475739	−	0.879586i	$-0.342181\pi$
$577$	22.8553			0.951478			0.475739	+	0.879586i	$0.342181\pi$
$578$	32.2063			1.33960
$579$	−0.801596	+	1.38840i	−0.0333132	+	0.0577001i
$580$	−2.03650	−	3.52732i	−0.0845610	−	0.146464i
$581$	15.8645	−	27.4781i	0.658169	−	1.13998i
$582$	2.28524			0.0947261
$583$	0.168705	−	0.292206i	0.00698705	−	0.0121019i
$584$	9.11114	+	15.7809i	0.377021	+	0.653020i
$585$	16.4054			0.678278
$586$	−22.8869	−	39.6412i	−0.945447	−	1.63756i
$587$	6.78022	−	11.7437i	0.279850	−	0.484714i	−0.691497	−	0.722379i	$-0.743049\pi$
$587$	6.78022	−	11.7437i	0.279850	−	0.484714i	0.971347	+	0.237665i	$0.0763820\pi$
$588$	−0.0257516	−	0.0446032i	−0.00106198	−	0.00183940i
$589$	−16.1608	+	27.9913i	−0.665893	+	1.15336i
$590$	37.1262	+	64.3045i	1.52846	+	2.64737i
$591$	−3.00937			−0.123789
$592$	6.03944	−	10.4606i	0.248219	−	0.429929i
$593$	40.7403			1.67300			0.836501	−	0.547965i	$-0.184597\pi$
$593$	40.7403			1.67300			0.836501	+	0.547965i	$0.184597\pi$
$594$	−0.0285177	+	0.0493941i	−0.00117010	+	0.00202667i
$595$	−28.9637	−	50.1666i	−1.18740	−	2.05663i
$596$	−1.00338	+	1.73791i	−0.0411001	+	0.0711875i
$597$	0.0828813	−	0.143555i	0.00339211	−	0.00587530i
$598$	9.79638	+	16.9678i	0.400604	+	0.693866i
$599$	43.8075			1.78993			0.894963	−	0.446140i	$-0.147202\pi$
$599$	43.8075			1.78993			0.894963	+	0.446140i	$0.147202\pi$
$600$	−1.48373	−	2.56990i	−0.0605732	−	0.104916i
$601$	−9.13175	−	15.8167i	−0.372492	−	0.645175i	0.617456	−	0.786605i	$-0.288163\pi$
$601$	−9.13175	−	15.8167i	−0.372492	−	0.645175i	−0.989948	+	0.141430i	$0.954830\pi$
$602$	23.6027			0.961975
$603$	21.7859	+	37.7342i	0.887189	+	1.53666i
$604$	−1.21283	+	2.10068i	−0.0493494	+	0.0854756i
$605$	−21.4238	−	37.1071i	−0.871000	−	1.50862i
$606$	0.319263	+	0.552980i	0.0129692	+	0.0224633i
$607$	−1.41276	−	2.44697i	−0.0573422	−	0.0993195i	0.835929	−	0.548837i	$-0.184929\pi$
$607$	−1.41276	−	2.44697i	−0.0573422	−	0.0993195i	−0.893272	+	0.449518i	$0.851596\pi$
$608$	4.86657	+	8.42914i	0.197365	+	0.341847i
$609$	−0.388117	−	0.672238i	−0.0157273	−	0.0272405i
$610$	−8.31929	−	14.4094i	−0.336838	−	0.583421i
$611$	5.11901			0.207093
$612$	6.97198			0.281826
$613$	−14.4476	+	25.0240i	−0.583534	+	1.01071i	0.411523	+	0.911400i	$0.364997\pi$
$613$	−14.4476	+	25.0240i	−0.583534	+	1.01071i	−0.995056	+	0.0993108i	$0.968336\pi$
$614$	−11.4545	−	19.8398i	−0.462267	−	0.800670i
$615$	−4.36805			−0.176137
$616$	0.159954	−	0.277048i	0.00644472	−	0.0111626i
$617$	7.98954	+	13.8383i	0.321647	+	0.557109i	0.980828	−	0.194875i	$-0.0624303\pi$
$617$	7.98954	+	13.8383i	0.321647	+	0.557109i	−0.659181	+	0.751984i	$0.729097\pi$
$618$	0.0445736	+	0.0772038i	0.00179301	+	0.00310559i
$619$	−22.1239			−0.889233			−0.444617	−	0.895721i	$-0.646660\pi$
$619$	−22.1239			−0.889233			−0.444617	+	0.895721i	$0.646660\pi$
$620$	5.19858	+	9.00420i	0.208780	+	0.361617i
$621$	3.14415	−	5.44582i	0.126170	−	0.218533i
$622$	11.0365	+	19.1158i	0.442524	+	0.766474i
$623$	17.4017	+	30.1406i	0.697183	+	1.20756i
$624$	−0.379317	+	0.656996i	−0.0151848	+	0.0263009i
$625$	−13.8706	+	24.0247i	−0.554826	+	0.960986i
$626$	28.9942			1.15884
$627$	−0.0283780			−0.00113331
$628$	−7.97839			−0.318372
$629$	8.05467	−	13.9511i	0.321161	−	0.556267i
$630$	−21.6785	−	37.5482i	−0.863691	−	1.49596i
$631$	22.6748			0.902671			0.451336	−	0.892354i	$-0.350948\pi$
$631$	22.6748			0.902671			0.451336	+	0.892354i	$0.350948\pi$
$632$	38.0837			1.51489
$633$	−0.448804	+	0.777352i	−0.0178384	+	0.0308970i
$634$	−3.82880			−0.152061
$635$	−32.7272	−	56.6853i	−1.29874	−	2.24949i
$636$	0.281704			0.0111703
$637$	−1.64184			−0.0650520
$638$	0.112596	−	0.195021i	0.00445770	−	0.00772097i
$639$	18.2253	+	31.5672i	0.720983	+	1.24878i
$640$	−52.3380			−2.06884
$641$	4.66082			0.184091			0.0920456	−	0.995755i	$-0.470659\pi$
$641$	4.66082			0.184091			0.0920456	+	0.995755i	$0.470659\pi$
$642$	0.0870888	+	0.150842i	0.00343712	+	0.00595327i
$643$	−12.3613	+	21.4104i	−0.487481	+	0.844343i	−0.999896	−	0.0143954i	$-0.995418\pi$
$643$	−12.3613	+	21.4104i	−0.487481	+	0.844343i	0.512415	+	0.858738i	$0.328751\pi$
$644$	4.12755	−	7.14913i	0.162648	−	0.281715i
$645$	2.87760			0.113305
$646$	21.8085	+	37.7734i	0.858044	+	1.48618i
$647$	−3.57401			−0.140509			−0.0702545	−	0.997529i	$-0.522381\pi$
$647$	−3.57401			−0.140509			−0.0702545	+	0.997529i	$0.522381\pi$
$648$	−22.1937			−0.871852
$649$	−0.327244	+	0.566803i	−0.0128454	+	0.0222490i
$650$	22.1407			0.868430
$651$	0.990747	+	1.71602i	0.0388304	+	0.0672563i
$652$	−1.64223			−0.0643146
$653$	−6.41231	+	11.1064i	−0.250933	+	0.434629i	−0.963783	−	0.266688i	$-0.914071\pi$
$653$	−6.41231	+	11.1064i	−0.250933	+	0.434629i	0.712850	+	0.701317i	$0.247404\pi$
$654$	0.354167			0.0138490
$655$	−6.34026	+	10.9816i	−0.247734	+	0.429088i
$656$	−22.1856	+	38.4267i	−0.866204	+	1.50031i
$657$	10.8842	+	18.8520i	0.424634	+	0.735488i
$658$	−6.76439	−	11.7163i	−0.263703	−	0.456748i
$659$	−10.2618	+	17.7740i	−0.399743	+	0.692376i	−0.993694	−	0.112126i	$-0.964234\pi$
$659$	−10.2618	+	17.7740i	−0.399743	+	0.692376i	0.593951	+	0.804501i	$0.297567\pi$
$660$	−0.00456429	+	0.00790558i	−0.000177665	+	0.000307724i
$661$	2.83203			0.110153			0.0550767	−	0.998482i	$-0.482460\pi$
$661$	2.83203			0.110153			0.0550767	+	0.998482i	$0.482460\pi$
$662$	−6.53521	−	11.3193i	−0.253998	−	0.439938i
$663$	−0.505887	+	0.876222i	−0.0196470	+	0.0340296i
$664$	−16.4176	−	28.4361i	−0.637127	−	1.10354i
$665$	21.6213	−	37.4492i	0.838439	−	1.45222i
$666$	6.02869	−	10.4420i	0.233607	−	0.404619i
$667$	−12.4139	+	21.5016i	−0.480669	+	0.832544i
$668$	−1.97058	+	3.41314i	−0.0762439	+	0.132058i
$669$	−0.707921	+	1.22616i	−0.0273698	+	0.0474059i
$670$	43.8427	+	75.9377i	1.69379	+	2.93373i
$671$	0.0733292	−	0.127010i	0.00283084	−	0.00490317i
$672$	0.596696			0.0230180
$673$	−12.1254	+	21.0019i	−0.467402	+	0.809563i	−0.999306	−	0.0372408i	$-0.988143\pi$
$673$	−12.1254	+	21.0019i	−0.467402	+	0.809563i	0.531905	+	0.846804i	$0.321476\pi$
$674$	−21.6827	+	37.5556i	−0.835187	+	1.44659i
$675$	−3.55303	−	6.15403i	−0.136756	−	0.236869i
$676$	2.08857	+	3.61751i	0.0803296	+	0.139135i
$677$	14.1269	+	24.4684i	0.542939	+	0.940398i	0.998733	+	0.0503131i	$0.0160219\pi$
$677$	14.1269	+	24.4684i	0.542939	+	0.940398i	−0.455794	+	0.890085i	$0.650645\pi$
$678$	0.557595			0.0214143
$679$	−30.6940			−1.17793
$680$	−59.9471			−2.29887
$681$	−1.25095	+	2.16670i	−0.0479363	+	0.0830282i
$682$	−0.287423	+	0.497831i	−0.0110060	+	0.0190629i
$683$	−8.63352	−	14.9537i	−0.330352	−	0.572187i	0.652229	−	0.758022i	$-0.273834\pi$
$683$	−8.63352	−	14.9537i	−0.330352	−	0.572187i	−0.982581	+	0.185835i	$0.940501\pi$
$684$	2.60228	+	4.50729i	0.0995008	+	0.172340i
$685$	81.8306			3.12659
$686$	15.2113	+	26.3467i	0.580768	+	1.00592i
$687$	0.873419	−	1.51281i	0.0333230	−	0.0577171i
$688$	14.6156	−	25.3149i	0.557213	−	0.965121i
$689$	4.49013	−	7.77713i	0.171060	−	0.296285i
$690$	3.15651	−	5.46724i	0.120166	−	0.208134i
$691$	−18.2729	−	31.6496i	−0.695135	−	1.20401i	−0.970135	−	0.242565i	$-0.922011\pi$
$691$	−18.2729	−	31.6496i	−0.695135	−	1.20401i	0.275000	−	0.961444i	$-0.411322\pi$
$692$	1.07005	−	1.85337i	0.0406770	−	0.0704547i
$693$	0.191082	−	0.330964i	0.00725860	−	0.0125723i
$694$	−0.311833	+	0.540111i	−0.0118370	+	0.0205023i
$695$	−0.897371			−0.0340392
$696$	−0.803298			−0.0304490
$697$	−29.5885	+	51.2488i	−1.12075	+	1.94119i
$698$	17.5239			0.663288
$699$	0.771266	−	1.33587i	0.0291719	−	0.0505273i
$700$	−4.66432	−	8.07884i	−0.176295	−	0.305352i
$701$	11.1353			0.420574			0.210287	−	0.977640i	$-0.432560\pi$
$701$	11.1353			0.420574			0.210287	+	0.977640i	$0.432560\pi$
$702$	−0.759007	+	1.31464i	−0.0286469	+	0.0496178i
$703$	12.0256			0.453554
$704$	−0.157909	−	0.273506i	−0.00595141	−	0.0103081i
$705$	−0.824703	−	1.42843i	−0.0310601	−	0.0537977i
$706$	−18.4751	−	31.9998i	−0.695320	−	1.20433i
$707$	−4.28816	−	7.42731i	−0.161273	−	0.279333i
$708$	−0.546433			−0.0205362
$709$	−17.4784	−	30.2734i	−0.656413	−	1.13694i	−0.981538	−	0.191270i	$-0.938739\pi$
$709$	−17.4784	−	30.2734i	−0.656413	−	1.13694i	0.325124	−	0.945671i	$-0.394594\pi$
$710$	36.6773	+	63.5269i	1.37647	+	2.38412i
$711$	45.4951			1.70620
$712$	36.0168			1.34979
$713$	31.6891	−	54.8871i	1.18676	−	2.05554i
$714$	2.67397			0.100071
$715$	0.145502	+	0.252017i	0.00544146	+	0.00942489i
$716$	1.05792	−	1.83238i	0.0395365	−	0.0684792i
$717$	0.131558	+	0.227865i	0.00491311	+	0.00850976i
$718$	−2.84379	+	4.92559i	−0.106129	+	0.183821i
$719$	5.13839			0.191630			0.0958149	−	0.995399i	$-0.469454\pi$
$719$	5.13839			0.191630			0.0958149	+	0.995399i	$0.469454\pi$
$720$	−53.6960			−2.00113
$721$	−0.598688	−	1.03696i	−0.0222963	−	0.0386183i
$722$	−1.62621	+	2.81668i	−0.0605214	+	0.104826i
$723$	0.330674	−	0.572744i	0.0122979	−	0.0213006i
$724$	−2.66645	−	4.61842i	−0.0990977	−	0.171642i
$725$	14.0283	+	24.2978i	0.520999	+	0.902396i
$726$	1.97787			0.0734058
$727$	−5.11478	−	8.85905i	−0.189697	−	0.328564i	0.755453	−	0.655203i	$-0.227417\pi$
$727$	−5.11478	−	8.85905i	−0.189697	−	0.328564i	−0.945149	+	0.326639i	$0.894084\pi$
$728$	4.25721	−	7.37371i	0.157783	−	0.273288i
$729$	−26.2686			−0.972912
$730$	21.9038	+	37.9385i	0.810696	+	1.40417i
$731$	19.4925	−	33.7619i	0.720955	−	1.24873i
$732$	0.122445			0.00452571
$733$	17.6548	+	30.5790i	0.652094	+	1.12946i	0.982614	+	0.185661i	$0.0594426\pi$
$733$	17.6548	+	30.5790i	0.652094	+	1.12946i	−0.330520	+	0.943799i	$0.607224\pi$
$734$	−6.68542	+	11.5795i	−0.246763	+	0.427407i
$735$	0.264510	+	0.458145i	0.00975660	+	0.0168989i
$736$	−9.54267	−	16.5284i	−0.351747	−	0.609244i
$737$	−0.386445	+	0.669343i	−0.0142349	+	0.0246556i
$738$	−22.1462	+	38.3583i	−0.815211	+	1.41199i
$739$	10.1824			0.374567			0.187284	−	0.982306i	$-0.440032\pi$
$739$	10.1824			0.374567			0.187284	+	0.982306i	$0.440032\pi$
$740$	1.93419	−	3.35011i	0.0711022	−	0.123153i
$741$	−0.755287			−0.0277462
$742$	−23.7335			−0.871284
$743$	−9.20720	−	15.9473i	−0.337779	−	0.585051i	0.646235	−	0.763138i	$-0.276342\pi$
$743$	−9.20720	−	15.9473i	−0.337779	−	0.585051i	−0.984015	+	0.178087i	$0.943009\pi$
$744$	2.05058			0.0751780
$745$	10.3063	−	17.8511i	0.377594	−	0.654012i
$746$	−25.0755	+	43.4320i	−0.918079	+	1.59016i
$747$	−19.6126	−	33.9700i	−0.717587	−	1.24290i
$748$	0.0618357	+	0.107103i	0.00226094	+	0.00391606i
$749$	−1.16973	−	2.02603i	−0.0427409	−	0.0740294i
$750$	−1.81514	−	3.14391i	−0.0662794	−	0.114799i
$751$	−18.4161			−0.672014			−0.336007	−	0.941860i	$-0.609077\pi$
$751$	−18.4161			−0.672014			−0.336007	+	0.941860i	$0.609077\pi$
$752$	−16.7549			−0.610988
$753$	−1.52541	−	2.64208i	−0.0555890	−	0.0962829i
$754$	2.99676	−	5.19055i	0.109136	−	0.189029i
$755$	12.4577	−	21.5773i	0.453382	−	0.785280i
$756$	0.639591			0.0232617
$757$	3.20025	+	5.54300i	0.116315	+	0.201464i	0.918305	−	0.395874i	$-0.129558\pi$
$757$	3.20025	+	5.54300i	0.116315	+	0.201464i	−0.801990	+	0.597338i	$0.796225\pi$
$758$	14.9028	−	25.8124i	0.541293	−	0.937548i
$759$	0.0556453			0.00201980
$760$	−22.3752	−	38.7550i	−0.811633	−	1.40579i
$761$	3.51270	+	6.08417i	0.127335	+	0.220551i	0.922643	−	0.385654i	$-0.126024\pi$
$761$	3.51270	+	6.08417i	0.127335	+	0.220551i	−0.795308	+	0.606205i	$0.792691\pi$
$762$	3.02143			0.109455
$763$	−4.75697			−0.172214
$764$	−2.25222	−	3.90096i	−0.0814825	−	0.141132i
$765$	−71.6132			−2.58918
$766$	−10.1245	−	17.5362i	−0.365813	−	0.633607i
$767$	−8.70969	+	15.0856i	−0.314489	+	0.544710i
$768$	0.512852	−	0.888285i	0.0185059	−	0.0320532i
$769$	−5.90459	+	10.2271i	−0.212925	+	0.368797i	−0.952629	−	0.304136i	$-0.901632\pi$
$769$	−5.90459	+	10.2271i	−0.212925	+	0.368797i	0.739704	+	0.672933i	$0.234966\pi$
$770$	0.384540	−	0.666043i	0.0138579	−	0.0240025i
$771$	1.18858			0.0428057
$772$	2.60779	+	4.51682i	0.0938563	+	0.162564i
$773$	−25.0388			−0.900582			−0.450291	−	0.892882i	$-0.648680\pi$
$773$	−25.0388			−0.900582			−0.450291	+	0.892882i	$0.648680\pi$
$774$	14.5895	−	25.2698i	0.524410	−	0.908305i
$775$	−35.8101	−	62.0249i	−1.28634	−	2.22800i
$776$	−15.8821	+	27.5086i	−0.570134	+	0.987501i
$777$	0.368619	−	0.638466i	0.0132241	−	0.0229048i
$778$	9.62279	−	16.6672i	0.344994	−	0.597547i
$779$	−44.1756			−1.58275
$780$	−0.121480	+	0.210409i	−0.00434968	+	0.00753386i
$781$	−0.323287	+	0.559950i	−0.0115681	+	0.0200366i
$782$	−42.7635	−	74.0685i	−1.52922	−	2.64868i
$783$	−1.92362			−0.0687446
$784$	5.37386			0.191924
$785$	81.9507			2.92494
$786$	−0.292671	−	0.506921i	−0.0104392	−	0.0180813i
$787$	−36.0170			−1.28387			−0.641935	−	0.766759i	$-0.721868\pi$
$787$	−36.0170			−1.28387			−0.641935	+	0.766759i	$0.721868\pi$
$788$	−4.89510	+	8.47856i	−0.174381	+	0.302036i
$789$	−0.467061			−0.0166278
$790$	91.5559			3.25741
$791$	−7.48930			−0.266289
$792$	−0.197744	−	0.342503i	−0.00702654	−	0.0121703i
$793$	1.95168	−	3.38041i	0.0693061	−	0.120042i
$794$	−31.5817			−1.12079
$795$	−2.89355			−0.102624
$796$	−0.269633	−	0.467018i	−0.00955689	−	0.0165530i
$797$	−17.7327	−	30.7140i	−0.628126	−	1.08795i	−0.987928	−	0.154917i	$-0.950489\pi$
$797$	−17.7327	−	30.7140i	−0.628126	−	1.08795i	0.359802	−	0.933029i	$-0.382844\pi$
$798$	0.998057	+	1.72868i	0.0353308	+	0.0611948i
$799$	−22.3457			−0.790533
$800$	−21.5673			−0.762520
$801$	43.0259			1.52025
$802$	8.80344			0.310860
$803$	−0.193068	+	0.334404i	−0.00681323	+	0.0118009i
$804$	−0.645288			−0.0227576
$805$	−42.3965	+	73.4328i	−1.49428	+	2.58817i
$806$	−7.64984	+	13.2499i	−0.269454	+	0.466708i
$807$	−0.148506	+	0.257221i	−0.00522768	+	0.00905460i
$808$	−8.87534			−0.312234
$809$	10.8706	+	18.8284i	0.382189	+	0.661970i	0.991375	−	0.131057i	$-0.0418371\pi$
$809$	10.8706	+	18.8284i	0.382189	+	0.661970i	−0.609186	+	0.793027i	$0.708504\pi$
$810$	−53.3553			−1.87471
$811$	9.93190	+	17.2026i	0.348756	+	0.604063i	0.986029	−	0.166575i	$-0.0532708\pi$
$811$	9.93190	+	17.2026i	0.348756	+	0.604063i	−0.637273	+	0.770638i	$0.719937\pi$
$812$	−2.52528			−0.0886199
$813$	−0.610944	−	1.05819i	−0.0214267	−	0.0371122i
$814$	0.213878			0.00749642
$815$	16.8683			0.590870
$816$	1.65581	−	2.86794i	0.0579648	−	0.100398i
$817$	29.1022			1.01816
$818$	0.658845	+	1.14115i	0.0230360	+	0.0398995i
$819$	5.08570	−	8.80869i	0.177709	−	0.307801i
$820$	−7.10517	+	12.3065i	−0.248123	+	0.429762i
$821$	3.82022	−	6.61682i	0.133327	−	0.230929i	−0.791630	−	0.611000i	$-0.790767\pi$
$821$	3.82022	−	6.61682i	0.133327	−	0.230929i	0.924957	+	0.380072i	$0.124101\pi$
$822$	−1.88868	+	3.27129i	−0.0658753	+	0.114099i
$823$	−1.31759	−	2.28213i	−0.0459282	−	0.0795499i	0.842147	−	0.539247i	$-0.181291\pi$
$823$	−1.31759	−	2.28213i	−0.0459282	−	0.0795499i	−0.888076	+	0.459697i	$0.847958\pi$
$824$	−1.23912			−0.0431669
$825$	0.0314409	−	0.0544572i	0.00109463	−	0.00189596i
$826$	46.0368			1.60183
$827$	−22.2687			−0.774359			−0.387180	−	0.922004i	$-0.626551\pi$
$827$	−22.2687			−0.774359			−0.387180	+	0.922004i	$0.626551\pi$
$828$	−5.10272	−	8.83817i	−0.177332	−	0.307148i
$829$	31.7938			1.10424			0.552122	−	0.833763i	$-0.313818\pi$
$829$	31.7938			1.10424			0.552122	+	0.833763i	$0.313818\pi$
$830$	−39.4691	−	68.3625i	−1.36999	−	2.37290i
$831$	−1.41768			−0.0491788
$832$	−4.20278	−	7.27943i	−0.145705	−	0.252369i
$833$	7.16701			0.248322
$834$	0.0207117	−	0.0358736i	0.000717186	−	0.00124220i
$835$	20.2409	−	35.0583i	0.700467	−	1.21324i
$836$	−0.0461602	+	0.0799519i	−0.00159648	+	0.00276519i
$837$	4.91043			0.169729
$838$	9.15299	−	15.8534i	0.316185	−	0.547648i
$839$	46.2956			1.59830			0.799152	−	0.601130i	$-0.205282\pi$
$839$	46.2956			1.59830			0.799152	+	0.601130i	$0.205282\pi$
$840$	−2.74345			−0.0946581
$841$	−21.4050			−0.738104
$842$	29.8615			1.02909
$843$	0.863834	+	1.49620i	0.0297520	+	0.0515320i
$844$	1.46007	+	2.52892i	0.0502577	+	0.0870489i
$845$	−21.4529	−	37.1575i	−0.738002	−	1.27826i
$846$	−16.7251			−0.575020
$847$	−26.5657			−0.912808
$848$	−14.6965	+	25.4551i	−0.504681	+	0.874133i
$849$	−0.455741	−	0.789366i	−0.0156410	−	0.0270910i
$850$	−96.6494			−3.31505
$851$	−23.5805			−0.808330
$852$	−0.539826			−0.0184941
$853$	−18.5701	+	32.1644i	−0.635830	+	1.10129i	0.350509	+	0.936559i	$0.386009\pi$
$853$	−18.5701	+	32.1644i	−0.635830	+	1.10129i	−0.986339	+	0.164730i	$0.947325\pi$
$854$	−10.3160			−0.353006
$855$	−26.7296	−	46.2970i	−0.914132	−	1.58332i
$856$	−2.42102			−0.0827489
$857$	−7.02589			−0.240000			−0.120000	−	0.992774i	$-0.538289\pi$
$857$	−7.02589			−0.240000			−0.120000	+	0.992774i	$0.538289\pi$
$858$	−0.0134330			−0.000458593
$859$	4.24018	+	7.34420i	0.144673	+	0.250581i	0.929251	−	0.369449i	$-0.120454\pi$
$859$	4.24018	+	7.34420i	0.144673	+	0.250581i	−0.784578	+	0.620030i	$0.787120\pi$
$860$	4.68077	−	8.10733i	0.159613	−	0.276458i
$861$	−1.35411	+	2.34538i	−0.0461478	+	0.0799303i
$862$	2.27919			0.0776296
$863$	−0.202064	+	0.349986i	−0.00687835	+	0.0119136i	−0.869444	−	0.494031i	$-0.835523\pi$
$863$	−0.202064	+	0.349986i	−0.00687835	+	0.0119136i	0.862566	+	0.505945i	$0.168856\pi$
$864$	0.739350	−	1.28059i	0.0251532	−	0.0435666i
$865$	−10.9911	+	19.0371i	−0.373707	+	0.647280i
$866$	−17.2009	−	29.7928i	−0.584510	−	1.01240i
$867$	1.21723	−	2.10831i	0.0413394	−	0.0716020i
$868$	6.44628			0.218801
$869$	0.403504	+	0.698889i	0.0136879	+	0.0237082i
$870$	−1.93119			−0.0654733
$871$	−10.2853	+	17.8147i	−0.348506	+	0.603630i
$872$	−2.46142	+	4.26330i	−0.0833541	+	0.144373i
$873$	−18.9729	+	32.8620i	−0.642134	+	1.11221i
$874$	31.9229	−	55.2920i	1.07981	−	1.87028i
$875$	24.3799	+	42.2272i	0.824190	+	1.42754i
$876$	−0.322386			−0.0108924
$877$	7.90030	+	13.6837i	0.266774	+	0.462066i	0.968027	−	0.250846i	$-0.0807089\pi$
$877$	7.90030	+	13.6837i	0.266774	+	0.462066i	−0.701253	+	0.712913i	$0.747376\pi$
$878$	−4.61937			−0.155896
$879$	−3.46003			−0.116704
$880$	−0.476239	−	0.824870i	−0.0160540	−	0.0278064i
$881$	−5.13653	−	8.89673i	−0.173054	−	0.299739i	0.766432	−	0.642325i	$-0.222030\pi$
$881$	−5.13653	−	8.89673i	−0.173054	−	0.299739i	−0.939486	+	0.342587i	$0.888697\pi$
$882$	5.36430			0.180625
$883$	6.78870	−	11.7584i	0.228458	−	0.395701i	−0.728893	−	0.684627i	$-0.759965\pi$
$883$	6.78870	−	11.7584i	0.228458	−	0.395701i	0.957351	+	0.288926i	$0.0932983\pi$
$884$	1.64577	+	2.85056i	0.0553534	+	0.0958748i
$885$	5.61273			0.188670
$886$	−5.33892	+	9.24729i	−0.179365	+	0.310669i
$887$	1.70040	−	2.94518i	0.0570939	−	0.0988895i	−0.836066	−	0.548629i	$-0.815150\pi$
$887$	1.70040	−	2.94518i	0.0570939	−	0.0988895i	0.893160	+	0.449740i	$0.148483\pi$
$888$	−0.381471	−	0.660727i	−0.0128013	−	0.0221725i
$889$	−40.5821			−1.36108
$890$	86.5869			2.90240
$891$	−0.235147	−	0.407286i	−0.00787771	−	0.0136446i
$892$	2.30304	+	3.98898i	0.0771115	+	0.133561i
$893$	−8.34050	−	14.4462i	−0.279104	−	0.483423i
$894$	0.475747	+	0.824018i	0.0159114	+	0.0275593i
$895$	−10.8665	+	18.8214i	−0.363229	+	0.629130i
$896$	−16.2249	+	28.1023i	−0.542036	+	0.938833i
$897$	1.48101			0.0494496
$898$	−20.0438	−	34.7168i	−0.668870	−	1.15852i
$899$	−19.3877			−0.646616
$900$	−11.5326			−0.384421
$901$	−19.6005	+	33.9490i	−0.652986	+	1.13101i
$902$	−0.785672			−0.0261600
$903$	0.892064	−	1.54510i	0.0296860	−	0.0514177i
$904$	−3.87521	+	6.71207i	−0.128888	+	0.223240i
$905$	27.3886	+	47.4385i	0.910428	+	1.57691i
$906$	0.575056	+	0.996026i	0.0191050	+	0.0330908i
$907$	−20.7737	+	35.9811i	−0.689779	+	1.19473i	0.282130	+	0.959376i	$0.408959\pi$
$907$	−20.7737	+	35.9811i	−0.689779	+	1.19473i	−0.971909	+	0.235356i	$0.924374\pi$
$908$	4.06963	+	7.04881i	0.135055	+	0.233923i
$909$	−10.6026			−0.351664
$910$	10.2346	−	17.7269i	0.339275	−	0.587642i
$911$	17.1727	+	29.7441i	0.568958	+	0.985465i	0.996669	+	0.0815492i	$0.0259868\pi$
$911$	17.1727	+	29.7441i	0.568958	+	0.985465i	−0.427711	+	0.903916i	$0.640680\pi$
$912$	2.47211			0.0818598
$913$	0.347895	−	0.602572i	0.0115136	−	0.0199422i
$914$	24.7316	+	42.8363i	0.818048	+	1.41690i
$915$	−1.25771			−0.0415785
$916$	−2.84144	−	4.92153i	−0.0938839	−	0.162612i
$917$	3.93099	+	6.80867i	0.129813	+	0.224842i
$918$	3.31324	−	5.73871i	0.109353	−	0.189406i
$919$	29.2986	−	50.7466i	0.966470	−	1.67398i	0.260858	−	0.965377i	$-0.415994\pi$
$919$	29.2986	−	50.7466i	0.966470	−	1.67398i	0.705612	−	0.708599i	$-0.250672\pi$
$920$	43.8747	+	75.9932i	1.44650	+	2.50542i
$921$	−1.73169			−0.0570612
$922$	13.5193			0.445235
$923$	−8.60438	+	14.9032i	−0.283216	+	0.490545i
$924$	0.00282988	+	0.00490150i	9.30963e−5	+	0.000161248i
$925$	−13.3236	+	23.0771i	−0.438076	+	0.758769i
$926$	−16.9418	−	29.3440i	−0.556741	−	0.964303i
$927$	−1.48027			−0.0486183
$928$	−2.91915	+	5.05612i	−0.0958258	+	0.165975i
$929$	−22.3867			−0.734485			−0.367242	−	0.930125i	$-0.619698\pi$
$929$	−22.3867			−0.734485			−0.367242	+	0.930125i	$0.619698\pi$
$930$	4.92974			0.161653
$931$	2.67508	+	4.63337i	0.0876722	+	0.151853i
$932$	−2.50912	−	4.34591i	−0.0821888	−	0.142355i
$933$	1.66850			0.0546242
$934$	20.7782	+	35.9889i	0.679884	+	1.17759i
$935$	−0.635150	−	1.10011i	−0.0207716	−	0.0359775i
$936$	−5.26302	−	9.11582i	−0.172027	−	0.297960i
$937$	19.2638	+	33.3659i	0.629321	+	1.09002i	0.987688	+	0.156435i	$0.0500003\pi$
$937$	19.2638	+	33.3659i	0.629321	+	1.09002i	−0.358367	+	0.933581i	$0.616666\pi$
$938$	54.3653			1.77509
$939$	1.09583	−	1.89804i	0.0357612	−	0.0619402i
$940$	−5.36592			−0.175017
$941$	−23.0064	−	39.8483i	−0.749988	−	1.29902i	−0.947828	−	0.318783i	$-0.896726\pi$
$941$	−23.0064	−	39.8483i	−0.749988	−	1.29902i	0.197840	−	0.980234i	$-0.436607\pi$
$942$	−1.89145	+	3.27609i	−0.0616268	+	0.106741i
$943$	86.6222			2.82081
$944$	28.5075	−	49.3764i	0.927839	−	1.60706i
$945$	−6.56961			−0.213710
$946$	0.517589			0.0168283
$947$	15.7192	−	27.2265i	0.510806	−	0.884741i	−0.489116	−	0.872219i	$-0.662681\pi$
$947$	15.7192	−	27.2265i	0.510806	−	0.884741i	0.999922	−	0.0125224i	$-0.00398612\pi$
$948$	−0.336886	+	0.583504i	−0.0109416	+	0.0189513i
$949$	−5.13856	+	8.90025i	−0.166805	+	0.288914i
$950$	−36.0743	−	62.4825i	−1.17041	−	2.02720i
$951$	−0.144709	+	0.250644i	−0.00469253	+	0.00812769i
$952$	−18.5837	+	32.1880i	−0.602302	+	1.04322i
$953$	19.2165	−	33.2840i	0.622484	−	1.07817i	−0.366537	−	0.930403i	$-0.619457\pi$
$953$	19.2165	−	33.2840i	0.622484	−	1.07817i	0.989022	−	0.147771i	$-0.0472099\pi$
$954$	−14.6704	+	25.4098i	−0.474971	+	0.822674i
$955$	23.1339	+	40.0691i	0.748595	+	1.29660i
$956$	0.855978			0.0276843
$957$	−0.00851109	−	0.0147416i	−0.000275125	−	0.000476530i
$958$	−8.89045	−	15.3987i	−0.287237	−	0.497510i
$959$	25.3677	−	43.9381i	0.819166	−	1.41884i
$960$	−1.35419	+	2.34552i	−0.0437062	+	0.0757014i
$961$	18.4910			0.596485
$962$	5.69242			0.183531
$963$	−2.89217			−0.0931990
$964$	−1.07576	−	1.86328i	−0.0346480	−	0.0600121i
$965$	−26.7861	−	46.3948i	−0.862274	−	1.49350i
$966$	−1.95705	−	3.38971i	−0.0629671	−	0.109062i
$967$	8.87068	−	15.3645i	0.285262	−	0.494088i	−0.687411	−	0.726269i	$-0.741253\pi$
$967$	8.87068	−	15.3645i	0.285262	−	0.494088i	0.972673	+	0.232181i	$0.0745861\pi$
$968$	−13.7460	+	23.8087i	−0.441812	+	0.765241i
$969$	3.29701			0.105915
$970$	−38.1817	+	66.1326i	−1.22594	+	2.12339i
$971$	1.94406	+	3.36721i	0.0623878	+	0.108059i	0.895532	−	0.444997i	$-0.146795\pi$
$971$	1.94406	+	3.36721i	0.0623878	+	0.108059i	−0.833144	+	0.553055i	$0.813462\pi$
$972$	0.593474	−	1.02793i	0.0190357	−	0.0329708i
$973$	−0.278187	+	0.481834i	−0.00891827	+	0.0154469i
$974$	−25.5217	+	44.2048i	−0.817767	+	1.41641i
$975$	0.836807	−	1.44939i	0.0267993	−	0.0464177i
$976$	−6.38799	+	11.0643i	−0.204475	+	0.354160i
$977$	3.78645	+	6.55832i	0.121139	+	0.209819i	0.920217	−	0.391408i	$-0.128012\pi$
$977$	3.78645	+	6.55832i	0.121139	+	0.209819i	−0.799078	+	0.601227i	$0.794679\pi$
$978$	−0.389326	+	0.674332i	−0.0124493	+	0.0215628i
$979$	0.381604	+	0.660958i	0.0121961	+	0.0211243i
$980$	1.72103			0.0549763
$981$	−2.94043	+	5.09297i	−0.0938806	+	0.162606i
$982$	−3.01799	+	5.22731i	−0.0963079	+	0.166810i
$983$	−7.00931	−	12.1405i	−0.223562	−	0.387221i	0.732325	−	0.680955i	$-0.238435\pi$
$983$	−7.00931	−	12.1405i	−0.223562	−	0.387221i	−0.955887	+	0.293734i	$0.905102\pi$
$984$	1.40132	+	2.42716i	0.0446724	+	0.0773749i
$985$	50.2804	−	87.0882i	1.60207	−	2.77486i
$986$	−13.0816	+	22.6579i	−0.416602	+	0.721576i
$987$	−1.02264			−0.0325510
$988$	−1.22857	+	2.12794i	−0.0390859	+	0.0676988i
$989$	−57.0653			−1.81457
$990$	−0.475391	−	0.823402i	−0.0151089	−	0.0261694i
$991$	48.2140			1.53157			0.765785	−	0.643097i	$-0.222351\pi$
$991$	48.2140			1.53157			0.765785	+	0.643097i	$0.222351\pi$
$992$	7.45172	−	12.9068i	0.236592	−	0.409790i
$993$	−0.987992			−0.0313530
$994$	45.4802			1.44254
$995$	2.76956	+	4.79701i	0.0878009	+	0.152076i
$996$	0.580917			0.0184070
$997$	−27.2435	+	47.1871i	−0.862810	+	1.49443i	0.00639473	+	0.999980i	$0.497964\pi$
$997$	−27.2435	+	47.1871i	−0.862810	+	1.49443i	−0.869205	+	0.494452i	$0.835369\pi$
$998$	1.77685	−	3.07760i	0.0562453	−	0.0974197i
$999$	−0.913490	−	1.58221i	−0.0289016	−	0.0500590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.13	✓	90
547.506	even	3	inner	547.2.c.a.506.13	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.13	✓	90	1.1	even	1	trivial
547.2.c.a.506.13	yes	90	547.506	even	3	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.771252 - 1.33585i) q^{2} -0.116598 q^{3} +(-0.189661 + 0.328502i) q^{4} +(1.94811 - 3.37423i) q^{5} +(0.0899263 + 0.155757i) q^{6} +(-1.20784 - 2.09204i) q^{7} -2.49991 q^{8} -2.98640 q^{9} +O(q^{10})\)	\(q+(-0.771252 - 1.33585i) q^{2} -0.116598 q^{3} +(-0.189661 + 0.328502i) q^{4} +(1.94811 - 3.37423i) q^{5} +(0.0899263 + 0.155757i) q^{6} +(-1.20784 - 2.09204i) q^{7} -2.49991 q^{8} -2.98640 q^{9} -6.00995 q^{10} +(-0.0264869 - 0.0458767i) q^{11} +(0.0221140 - 0.0383026i) q^{12} +(-0.704957 - 1.22102i) q^{13} +(-1.86310 + 3.22698i) q^{14} +(-0.227146 + 0.393428i) q^{15} +(2.30738 + 3.99650i) q^{16} +(3.07730 + 5.33005i) q^{17} +(2.30327 + 3.98938i) q^{18} +(-2.29720 + 3.97887i) q^{19} +(0.738960 + 1.27992i) q^{20} +(0.140831 + 0.243927i) q^{21} +(-0.0408562 + 0.0707651i) q^{22} +(4.50450 - 7.80202i) q^{23} +0.291483 q^{24} +(-5.09029 - 8.81664i) q^{25} +(-1.08740 + 1.88343i) q^{26} +0.698002 q^{27} +0.916318 q^{28} -2.75590 q^{29} +0.700747 q^{30} +7.03499 q^{31} +(1.05924 - 1.83465i) q^{32} +(0.00308832 + 0.00534913i) q^{33} +(4.74676 - 8.22162i) q^{34} -9.41203 q^{35} +(0.566403 - 0.981039i) q^{36} +(-1.30872 - 2.26677i) q^{37} +7.08689 q^{38} +(0.0821965 + 0.142368i) q^{39} +(-4.87010 + 8.43526i) q^{40} +(4.80754 + 8.32691i) q^{41} +(0.217233 - 0.376259i) q^{42} +(-3.16713 - 5.48563i) q^{43} +0.0200941 q^{44} +(-5.81785 + 10.0768i) q^{45} -13.8964 q^{46} +(-1.81536 + 3.14430i) q^{47} +(-0.269035 - 0.465983i) q^{48} +(0.582248 - 1.00848i) q^{49} +(-7.85180 + 13.5997i) q^{50} +(-0.358807 - 0.621472i) q^{51} +0.534810 q^{52} +(3.18468 + 5.51603i) q^{53} +(-0.538335 - 0.932424i) q^{54} -0.206398 q^{55} +(3.01948 + 5.22990i) q^{56} +(0.267849 - 0.463927i) q^{57} +(2.12549 + 3.68146i) q^{58} +(-6.17746 - 10.6997i) q^{59} +(-0.0861611 - 0.149235i) q^{60} +(1.38425 + 2.39760i) q^{61} +(-5.42575 - 9.39767i) q^{62} +(3.60710 + 6.24768i) q^{63} +5.96176 q^{64} -5.49335 q^{65} +(0.00476375 - 0.00825105i) q^{66} +(-7.29502 - 12.6353i) q^{67} -2.33457 q^{68} +(-0.525214 + 0.909698i) q^{69} +(7.25905 + 12.5730i) q^{70} +(-6.10276 - 10.5703i) q^{71} +7.46573 q^{72} +(-3.64459 - 6.31262i) q^{73} +(-2.01871 + 3.49651i) q^{74} +(0.593516 + 1.02800i) q^{75} +(-0.871377 - 1.50927i) q^{76} +(-0.0639840 + 0.110823i) q^{77} +(0.126788 - 0.219604i) q^{78} -15.2341 q^{79} +17.9801 q^{80} +8.87783 q^{81} +(7.41566 - 12.8443i) q^{82} +(6.56729 + 11.3749i) q^{83} -0.106841 q^{84} +23.9797 q^{85} +(-4.88532 + 8.46162i) q^{86} +0.321332 q^{87} +(0.0662148 + 0.114687i) q^{88} -14.4073 q^{89} +17.9481 q^{90} +(-1.70295 + 2.94960i) q^{91} +(1.70865 + 2.95947i) q^{92} -0.820264 q^{93} +5.60041 q^{94} +(8.95042 + 15.5026i) q^{95} +(-0.123505 + 0.213917i) q^{96} +(6.35308 - 11.0039i) q^{97} -1.79624 q^{98} +(0.0791007 + 0.137007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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