LMFDB - Embedded newform 570.2.k.b.77.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.7
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) q^{3} -1.00000i q^{4} +(1.61979 - 1.54152i) q^{5} +(0.408116 + 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.37395 - 2.66688i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) q^{3} -1.00000i q^{4} +(1.61979 - 1.54152i) q^{5} +(0.408116 + 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.37395 - 2.66688i) q^{9} +(-0.0553424 + 2.23538i) q^{10} +3.67926i q^{11} +(-1.47884 - 0.901679i) q^{12} +(2.60584 - 2.60584i) q^{13} +2.76100 q^{14} +(-0.819140 - 3.78537i) q^{15} -1.00000 q^{16} +(1.52607 - 1.52607i) q^{17} +(2.85730 + 0.914240i) q^{18} -1.00000i q^{19} +(-1.54152 - 1.61979i) q^{20} +(-4.64754 + 1.12681i) q^{21} +(-2.60163 - 2.60163i) q^{22} +(-0.483241 - 0.483241i) q^{23} +(1.68328 - 0.408116i) q^{24} +(0.247423 - 4.99387i) q^{25} +3.68522i q^{26} +(-5.18276 - 0.372814i) q^{27} +(-1.95232 + 1.95232i) q^{28} -8.02750 q^{29} +(3.25588 + 2.09744i) q^{30} -3.06305 q^{31} +(0.707107 - 0.707107i) q^{32} +(5.44104 + 3.31751i) q^{33} +2.15819i q^{34} +(-6.17189 - 0.152800i) q^{35} +(-2.66688 + 1.37395i) q^{36} +(7.32517 + 7.32517i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-1.50400 - 6.20326i) q^{39} +(2.23538 + 0.0553424i) q^{40} -5.46374i q^{41} +(2.48954 - 4.08308i) q^{42} +(-3.11201 + 3.11201i) q^{43} +3.67926 q^{44} +(-6.33656 - 2.20181i) q^{45} +0.683406 q^{46} +(3.44995 - 3.44995i) q^{47} +(-0.901679 + 1.47884i) q^{48} +0.623122i q^{49} +(3.35625 + 3.70616i) q^{50} +(-0.880794 - 3.63285i) q^{51} +(-2.60584 - 2.60584i) q^{52} +(-7.51422 - 7.51422i) q^{53} +(3.92838 - 3.40115i) q^{54} +(5.67165 + 5.95961i) q^{55} -2.76100i q^{56} +(-1.47884 - 0.901679i) q^{57} +(5.67630 - 5.67630i) q^{58} +11.1184 q^{59} +(-3.78537 + 0.819140i) q^{60} +0.989652 q^{61} +(2.16590 - 2.16590i) q^{62} +(-2.52422 + 7.88901i) q^{63} +1.00000i q^{64} +(0.203949 - 8.23787i) q^{65} +(-6.19323 + 1.50156i) q^{66} +(8.05094 + 8.05094i) q^{67} +(-1.52607 - 1.52607i) q^{68} +(-1.15037 + 0.278909i) q^{69} +(4.47223 - 4.25614i) q^{70} +4.07805i q^{71} +(0.914240 - 2.85730i) q^{72} +(11.1477 - 11.1477i) q^{73} -10.3593 q^{74} +(-7.16206 - 4.86877i) q^{75} -1.00000 q^{76} +(7.18309 - 7.18309i) q^{77} +(5.44985 + 3.32288i) q^{78} +7.15671i q^{79} +(-1.61979 + 1.54152i) q^{80} +(-5.22452 + 7.32833i) q^{81} +(3.86345 + 3.86345i) q^{82} +(2.66585 + 2.66585i) q^{83} +(1.12681 + 4.64754i) q^{84} +(0.119439 - 4.82439i) q^{85} -4.40105i q^{86} +(-7.23823 + 11.8714i) q^{87} +(-2.60163 + 2.60163i) q^{88} +1.05913 q^{89} +(6.03754 - 2.92371i) q^{90} -10.1749 q^{91} +(-0.483241 + 0.483241i) q^{92} +(-2.76188 + 4.52976i) q^{93} +4.87897i q^{94} +(-1.54152 - 1.61979i) q^{95} +(-0.408116 - 1.68328i) q^{96} +(5.51911 + 5.51911i) q^{97} +(-0.440614 - 0.440614i) q^{98} +(9.81214 - 5.05512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.901679	−	1.47884i	0.520584	−	0.853810i
$3$	0.901679	−	1.47884i	0.520584	−	0.853810i
$4$		−	1.00000i		−	0.500000i
$5$	1.61979	−	1.54152i	0.724391	−	0.689389i
$5$	1.61979	−	1.54152i	0.724391	−	0.689389i
$6$	0.408116	+	1.68328i	0.166613	+	0.687197i
$7$	−1.95232	−	1.95232i	−0.737908	−	0.737908i	0.234265	−	0.972173i	$-0.424732\pi$
$7$	−1.95232	−	1.95232i	−0.737908	−	0.737908i	−0.972173	+	0.234265i	$0.924732\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.37395	−	2.66688i	−0.457984	−	0.888961i
$10$	−0.0553424	+	2.23538i	−0.0175008	+	0.706890i
$11$			3.67926i			1.10934i	0.832071	+	0.554669i	$0.187155\pi$
$11$			3.67926i			1.10934i	−0.832071	+	0.554669i	$0.812845\pi$
$12$	−1.47884	−	0.901679i	−0.426905	−	0.260292i
$13$	2.60584	−	2.60584i	0.722730	−	0.722730i	−0.246430	−	0.969161i	$-0.579258\pi$
$13$	2.60584	−	2.60584i	0.722730	−	0.722730i	0.969161	+	0.246430i	$0.0792576\pi$
$14$	2.76100			0.737908
$15$	−0.819140	−	3.78537i	−0.211501	−	0.977378i
$16$	−1.00000			−0.250000
$17$	1.52607	−	1.52607i	0.370127	−	0.370127i	−0.497396	−	0.867523i	$-0.665711\pi$
$17$	1.52607	−	1.52607i	0.370127	−	0.370127i	0.867523	+	0.497396i	$0.165711\pi$
$18$	2.85730	+	0.914240i	0.673472	+	0.215489i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.54152	−	1.61979i	−0.344695	−	0.362195i
$21$	−4.64754	+	1.12681i	−1.01418	+	0.245890i
$22$	−2.60163	−	2.60163i	−0.554669	−	0.554669i
$23$	−0.483241	−	0.483241i	−0.100763	−	0.100763i	0.654928	−	0.755691i	$-0.272699\pi$
$23$	−0.483241	−	0.483241i	−0.100763	−	0.100763i	−0.755691	+	0.654928i	$0.772699\pi$
$24$	1.68328	−	0.408116i	0.343599	−	0.0833064i
$25$	0.247423	−	4.99387i	0.0494845	−	0.998775i
$26$			3.68522i			0.722730i
$27$	−5.18276	−	0.372814i	−0.997423	−	0.0717481i
$28$	−1.95232	+	1.95232i	−0.368954	+	0.368954i
$29$	−8.02750			−1.49067			−0.745335	−	0.666691i	$-0.767710\pi$
$29$	−8.02750			−1.49067			−0.745335	+	0.666691i	$0.767710\pi$
$30$	3.25588	+	2.09744i	0.594439	+	0.382938i
$31$	−3.06305			−0.550139			−0.275070	−	0.961424i	$-0.588701\pi$
$31$	−3.06305			−0.550139			−0.275070	+	0.961424i	$0.588701\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.44104	+	3.31751i	0.947163	+	0.577504i
$34$			2.15819i			0.370127i
$35$	−6.17189	−	0.152800i	−1.04324	−	0.0258280i
$36$	−2.66688	+	1.37395i	−0.444480	+	0.228992i
$37$	7.32517	+	7.32517i	1.20425	+	1.20425i	0.972861	+	0.231389i	$0.0743269\pi$
$37$	7.32517	+	7.32517i	1.20425	+	1.20425i	0.231389	+	0.972861i	$0.425673\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	−1.50400	−	6.20326i	−0.240832	−	0.993317i
$40$	2.23538	+	0.0553424i	0.353445	+	0.00875039i
$41$		−	5.46374i		−	0.853293i	−0.904419	−	0.426646i	$-0.859695\pi$
$41$		−	5.46374i		−	0.853293i	0.904419	−	0.426646i	$-0.140305\pi$
$42$	2.48954	−	4.08308i	0.384144	−	0.630034i
$43$	−3.11201	+	3.11201i	−0.474577	+	0.474577i	−0.903392	−	0.428815i	$-0.858931\pi$
$43$	−3.11201	+	3.11201i	−0.474577	+	0.474577i	0.428815	+	0.903392i	$0.358931\pi$
$44$	3.67926			0.554669
$45$	−6.33656	−	2.20181i	−0.944599	−	0.328226i
$46$	0.683406			0.100763
$47$	3.44995	−	3.44995i	0.503227	−	0.503227i	−0.409212	−	0.912439i	$-0.634196\pi$
$47$	3.44995	−	3.44995i	0.503227	−	0.503227i	0.912439	+	0.409212i	$0.134196\pi$
$48$	−0.901679	+	1.47884i	−0.130146	+	0.213453i
$49$			0.623122i			0.0890174i
$50$	3.35625	+	3.70616i	0.474645	+	0.524130i
$51$	−0.880794	−	3.63285i	−0.123336	−	0.508700i
$52$	−2.60584	−	2.60584i	−0.361365	−	0.361365i
$53$	−7.51422	−	7.51422i	−1.03216	−	1.03216i	−0.999465	−	0.0326918i	$-0.989592\pi$
$53$	−7.51422	−	7.51422i	−1.03216	−	1.03216i	−0.0326918	−	0.999465i	$-0.510408\pi$
$54$	3.92838	−	3.40115i	0.534585	−	0.462837i
$55$	5.67165	+	5.95961i	0.764765	+	0.803594i
$56$		−	2.76100i		−	0.368954i
$57$	−1.47884	−	0.901679i	−0.195877	−	0.119430i
$58$	5.67630	−	5.67630i	0.745335	−	0.745335i
$59$	11.1184			1.44749			0.723744	−	0.690068i	$-0.242420\pi$
$59$	11.1184			1.44749			0.723744	+	0.690068i	$0.242420\pi$
$60$	−3.78537	+	0.819140i	−0.488689	+	0.105750i
$61$	0.989652			0.126712			0.0633559	−	0.997991i	$-0.479820\pi$
$61$	0.989652			0.126712			0.0633559	+	0.997991i	$0.479820\pi$
$62$	2.16590	−	2.16590i	0.275070	−	0.275070i
$63$	−2.52422	+	7.88901i	−0.318022	+	0.993921i
$64$			1.00000i			0.125000i
$65$	0.203949	−	8.23787i	0.0252967	−	1.02178i
$66$	−6.19323	+	1.50156i	−0.762334	+	0.184830i
$67$	8.05094	+	8.05094i	0.983579	+	0.983579i	0.999867	−	0.0162886i	$-0.00518506\pi$
$67$	8.05094	+	8.05094i	0.983579	+	0.983579i	−0.0162886	+	0.999867i	$0.505185\pi$
$68$	−1.52607	−	1.52607i	−0.185063	−	0.185063i
$69$	−1.15037	+	0.278909i	−0.138488	+	0.0335767i
$70$	4.47223	−	4.25614i	0.534534	−	0.508706i
$71$			4.07805i			0.483975i	0.970279	+	0.241988i	$0.0777993\pi$
$71$			4.07805i			0.483975i	−0.970279	+	0.241988i	$0.922201\pi$
$72$	0.914240	−	2.85730i	0.107744	−	0.336736i
$73$	11.1477	−	11.1477i	1.30474	−	1.30474i	0.379579	−	0.925159i	$-0.376069\pi$
$73$	11.1477	−	11.1477i	1.30474	−	1.30474i	0.925159	−	0.379579i	$-0.123931\pi$
$74$	−10.3593			−1.20425
$75$	−7.16206	−	4.86877i	−0.827003	−	0.562197i
$76$	−1.00000			−0.114708
$77$	7.18309	−	7.18309i	0.818589	−	0.818589i
$78$	5.44985	+	3.32288i	0.617074	+	0.376242i
$79$			7.15671i			0.805193i	0.915378	+	0.402596i	$0.131892\pi$
$79$			7.15671i			0.805193i	−0.915378	+	0.402596i	$0.868108\pi$
$80$	−1.61979	+	1.54152i	−0.181098	+	0.172347i
$81$	−5.22452	+	7.32833i	−0.580502	+	0.814259i
$82$	3.86345	+	3.86345i	0.426646	+	0.426646i
$83$	2.66585	+	2.66585i	0.292615	+	0.292615i	0.838113	−	0.545497i	$-0.183659\pi$
$83$	2.66585	+	2.66585i	0.292615	+	0.292615i	−0.545497	+	0.838113i	$0.683659\pi$
$84$	1.12681	+	4.64754i	0.122945	+	0.507089i
$85$	0.119439	−	4.82439i	0.0129550	−	0.523278i
$86$		−	4.40105i		−	0.474577i
$87$	−7.23823	+	11.8714i	−0.776019	+	1.27275i
$88$	−2.60163	+	2.60163i	−0.277334	+	0.277334i
$89$	1.05913			0.112267			0.0561336	−	0.998423i	$-0.482123\pi$
$89$	1.05913			0.112267			0.0561336	+	0.998423i	$0.482123\pi$
$90$	6.03754	−	2.92371i	0.636413	−	0.308187i
$91$	−10.1749			−1.06662
$92$	−0.483241	+	0.483241i	−0.0503814	+	0.0503814i
$93$	−2.76188	+	4.52976i	−0.286394	+	0.469714i
$94$			4.87897i			0.503227i
$95$	−1.54152	−	1.61979i	−0.158157	−	0.166187i
$96$	−0.408116	−	1.68328i	−0.0416532	−	0.171799i
$97$	5.51911	+	5.51911i	0.560381	+	0.560381i	0.929416	−	0.369035i	$-0.120312\pi$
$97$	5.51911	+	5.51911i	0.560381	+	0.560381i	−0.369035	+	0.929416i	$0.620312\pi$
$98$	−0.440614	−	0.440614i	−0.0445087	−	0.0445087i
$99$	9.81214	−	5.05512i	0.986157	−	0.508058i
$100$	−4.99387	−	0.247423i	−0.499387	−	0.0247423i
$101$			7.18857i			0.715289i	0.933858	+	0.357645i	$0.116420\pi$
$101$			7.18857i			0.715289i	−0.933858	+	0.357645i	$0.883580\pi$
$102$	3.19163	+	1.94600i	0.316018	+	0.192682i
$103$	5.24203	−	5.24203i	0.516512	−	0.516512i	−0.400002	−	0.916514i	$-0.630991\pi$
$103$	5.24203	−	5.24203i	0.516512	−	0.516512i	0.916514	+	0.400002i	$0.130991\pi$
$104$	3.68522			0.361365
$105$	−5.79103	+	8.98948i	−0.565147	+	0.877284i
$106$	10.6267			1.03216
$107$	3.71052	−	3.71052i	0.358709	−	0.358709i	−0.504628	−	0.863337i	$-0.668370\pi$
$107$	3.71052	−	3.71052i	0.358709	−	0.358709i	0.863337	+	0.504628i	$0.168370\pi$
$108$	−0.372814	+	5.18276i	−0.0358740	+	0.498711i
$109$		−	1.39041i		−	0.133178i	−0.997781	−	0.0665888i	$-0.978788\pi$
$109$		−	1.39041i		−	0.133178i	0.997781	−	0.0665888i	$-0.0212116\pi$
$110$	−8.22455	−	0.203619i	−0.784180	−	0.0194143i
$111$	17.4377	−	4.22782i	1.65511	−	0.401287i
$112$	1.95232	+	1.95232i	0.184477	+	0.184477i
$113$	10.6045	+	10.6045i	0.997589	+	0.997589i	0.999997	−	0.00240835i	$-0.000766603\pi$
$113$	10.6045	+	10.6045i	0.997589	+	0.997589i	−0.00240835	+	0.999997i	$0.500767\pi$
$114$	1.68328	−	0.408116i	0.157654	−	0.0382236i
$115$	−1.52767	−	0.0378213i	−0.142456	−	0.00352685i
$116$			8.02750i			0.745335i
$117$	−10.5298	−	3.36917i	−0.973477	−	0.311480i
$118$	−7.86188	+	7.86188i	−0.723744	+	0.723744i
$119$	−5.95877			−0.546239
$120$	2.09744	−	3.25588i	0.191469	−	0.297220i
$121$	−2.53692			−0.230629
$122$	−0.699789	+	0.699789i	−0.0633559	+	0.0633559i
$123$	−8.08001	−	4.92654i	−0.728550	−	0.444211i
$124$			3.06305i			0.275070i
$125$	−7.29739	−	8.47042i	−0.652699	−	0.757618i
$126$	−3.79348	−	7.36326i	−0.337950	−	0.655971i
$127$	13.6390	+	13.6390i	1.21027	+	1.21027i	0.970938	+	0.239330i	$0.0769276\pi$
$127$	13.6390	+	13.6390i	1.21027	+	1.21027i	0.239330	+	0.970938i	$0.423072\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.79614	+	7.40821i	0.158141	+	0.652256i
$130$	5.68084	+	5.96927i	0.498243	+	0.523539i
$131$			15.8526i			1.38505i	0.721396	+	0.692523i	$0.243501\pi$
$131$			15.8526i			1.38505i	−0.721396	+	0.692523i	$0.756499\pi$
$132$	3.31751	−	5.44104i	0.288752	−	0.473582i
$133$	−1.95232	+	1.95232i	−0.169288	+	0.169288i
$134$	−11.3857			−0.983579
$135$	−8.96967	+	7.38546i	−0.771986	+	0.635639i
$136$	2.15819			0.185063
$137$	−0.0250882	+	0.0250882i	−0.00214343	+	0.00214343i	−0.708178	−	0.706034i	$-0.750482\pi$
$137$	−0.0250882	+	0.0250882i	−0.00214343	+	0.00214343i	0.706034	+	0.708178i	$0.250482\pi$
$138$	0.616213	−	1.01065i	0.0524555	−	0.0860322i
$139$		−	15.9440i		−	1.35235i	−0.736739	−	0.676177i	$-0.763635\pi$
$139$		−	15.9440i		−	1.35235i	0.736739	−	0.676177i	$-0.236365\pi$
$140$	−0.152800	+	6.17189i	−0.0129140	+	0.521620i
$141$	−1.99119	−	8.21268i	−0.167688	−	0.691633i
$142$	−2.88361	−	2.88361i	−0.241988	−	0.241988i
$143$	9.58756	+	9.58756i	0.801752	+	0.801752i
$144$	1.37395	+	2.66688i	0.114496	+	0.222240i
$145$	−13.0028	+	12.3746i	−1.07983	+	1.02765i
$146$			15.7652i			1.30474i
$147$	0.921499	+	0.561856i	0.0760039	+	0.0463411i
$148$	7.32517	−	7.32517i	0.602125	−	0.602125i
$149$	−17.7034			−1.45032			−0.725160	−	0.688580i	$-0.758234\pi$
$149$	−17.7034			−1.45032			−0.725160	+	0.688580i	$0.758234\pi$
$150$	8.50708	−	1.62160i	0.694600	−	0.132403i
$151$	−13.6930			−1.11432			−0.557160	−	0.830405i	$-0.688109\pi$
$151$	−13.6930			−1.11432			−0.557160	+	0.830405i	$0.688109\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	−6.16660	−	1.97311i	−0.498540	−	0.159516i
$154$			10.1584i			0.818589i
$155$	−4.96148	+	4.72175i	−0.398516	+	0.379260i
$156$	−6.20326	+	1.50400i	−0.496658	+	0.120416i
$157$	−1.10214	−	1.10214i	−0.0879600	−	0.0879600i	0.661758	−	0.749718i	$-0.269811\pi$
$157$	−1.10214	−	1.10214i	−0.0879600	−	0.0879600i	−0.749718	+	0.661758i	$0.769811\pi$
$158$	−5.06056	−	5.06056i	−0.402596	−	0.402596i
$159$	−17.8878	+	4.33693i	−1.41859	+	0.343941i
$160$	0.0553424	−	2.23538i	0.00437520	−	0.176723i
$161$			1.88688i			0.148707i
$162$	−1.48762	−	8.87620i	−0.116878	−	0.697380i
$163$	−11.0666	+	11.0666i	−0.866806	+	0.866806i	−0.992117	−	0.125311i	$-0.960007\pi$
$163$	−11.0666	+	11.0666i	−0.866806	+	0.866806i	0.125311	+	0.992117i	$0.460007\pi$
$164$	−5.46374			−0.426646
$165$	13.9273	−	3.01382i	1.08424	−	0.234626i
$166$	−3.77008			−0.292615
$167$	6.38610	−	6.38610i	0.494171	−	0.494171i	−0.415446	−	0.909618i	$-0.636375\pi$
$167$	6.38610	−	6.38610i	0.494171	−	0.494171i	0.909618	+	0.415446i	$0.136375\pi$
$168$	−4.08308	−	2.48954i	−0.315017	−	0.192072i
$169$		−	0.580815i		−	0.0446781i
$170$	3.32690	+	3.49581i	0.255162	+	0.268117i
$171$	−2.66688	+	1.37395i	−0.203942	+	0.105069i
$172$	3.11201	+	3.11201i	0.237289	+	0.237289i
$173$	0.393098	+	0.393098i	0.0298867	+	0.0298867i	0.721892	−	0.692006i	$-0.243273\pi$
$173$	0.393098	+	0.393098i	0.0298867	+	0.0298867i	−0.692006	+	0.721892i	$0.743273\pi$
$174$	−3.27615	−	13.5126i	−0.248365	−	1.02438i
$175$	−10.2327	+	9.26660i	−0.773519	+	0.700489i
$176$		−	3.67926i		−	0.277334i
$177$	10.0252	−	16.4423i	0.753540	−	1.23588i
$178$	−0.748916	+	0.748916i	−0.0561336	+	0.0561336i
$179$	−7.26370			−0.542915			−0.271457	−	0.962450i	$-0.587506\pi$
$179$	−7.26370			−0.542915			−0.271457	+	0.962450i	$0.587506\pi$
$180$	−2.20181	+	6.33656i	−0.164113	+	0.472300i
$181$	11.4499			0.851061			0.425531	−	0.904944i	$-0.360087\pi$
$181$	11.4499			0.851061			0.425531	+	0.904944i	$0.360087\pi$
$182$	7.19473	−	7.19473i	0.533309	−	0.533309i
$183$	0.892348	−	1.46354i	0.0659642	−	0.108188i
$184$		−	0.683406i		−	0.0503814i
$185$	23.1571	+	0.573311i	1.70254	+	0.0421506i
$186$	−1.25008	−	5.15597i	−0.0916603	−	0.378054i
$187$	5.61481	+	5.61481i	0.410596	+	0.410596i
$188$	−3.44995	−	3.44995i	−0.251614	−	0.251614i
$189$	9.39056	+	10.8463i	0.683063	+	0.788950i
$190$	2.23538	+	0.0553424i	0.162172	+	0.00401496i
$191$			14.1961i			1.02720i	0.858031	+	0.513598i	$0.171688\pi$
$191$			14.1961i			1.02720i	−0.858031	+	0.513598i	$0.828312\pi$
$192$	1.47884	+	0.901679i	0.106726	+	0.0650731i
$193$	−11.5541	+	11.5541i	−0.831685	+	0.831685i	−0.987747	−	0.156063i	$-0.950120\pi$
$193$	−11.5541	+	11.5541i	−0.831685	+	0.831685i	0.156063	+	0.987747i	$0.450120\pi$
$194$	−7.80520			−0.560381
$195$	−11.9986	−	7.72952i	−0.859239	−	0.553522i
$196$	0.623122			0.0445087
$197$	18.1909	−	18.1909i	1.29605	−	1.29605i	0.365065	−	0.930982i	$-0.381047\pi$
$197$	18.1909	−	18.1909i	1.29605	−	1.29605i	0.930982	−	0.365065i	$-0.118953\pi$
$198$	−3.36372	+	10.5127i	−0.239049	+	0.747108i
$199$		−	0.0497425i		−	0.00352616i	−0.999998	−	0.00176308i	$-0.999439\pi$
$199$		−	0.0497425i		−	0.00352616i	0.999998	−	0.00176308i	$-0.000561205\pi$
$200$	3.70616	−	3.35625i	0.262065	−	0.237323i
$201$	19.1654	−	4.64671i	1.35183	−	0.327754i
$202$	−5.08309	−	5.08309i	−0.357645	−	0.357645i
$203$	15.6723	+	15.6723i	1.09998	+	1.09998i
$204$	−3.63285	+	0.880794i	−0.254350	+	0.0616679i
$205$	−8.42247	−	8.85010i	−0.588251	−	0.618117i
$206$			7.41335i			0.516512i
$207$	−0.624797	+	1.95270i	−0.0434264	+	0.135722i
$208$	−2.60584	+	2.60584i	−0.180683	+	0.180683i
$209$	3.67926			0.254499
$210$	−2.26164	−	10.4514i	−0.156068	−	0.721215i
$211$	27.0957			1.86535			0.932674	−	0.360721i	$-0.117469\pi$
$211$	27.0957			1.86535			0.932674	+	0.360721i	$0.117469\pi$
$212$	−7.51422	+	7.51422i	−0.516079	+	0.516079i
$213$	6.03079	+	3.67709i	0.413223	+	0.251950i
$214$			5.24746i			0.358709i
$215$	−0.243564	+	9.83803i	−0.0166109	+	0.670948i
$216$	−3.40115	−	3.92838i	−0.231419	−	0.267293i
$217$	5.98005	+	5.98005i	0.405952	+	0.405952i
$218$	0.983171	+	0.983171i	0.0665888	+	0.0665888i
$219$	−6.43404	−	26.5373i	−0.434772	−	1.79323i
$220$	5.95961	−	5.67165i	0.401797	−	0.382383i
$221$		−	7.95340i		−	0.535004i
$222$	−9.34081	+	15.3198i	−0.626914	+	1.02820i
$223$	19.2124	−	19.2124i	1.28656	−	1.28656i	0.349689	−	0.936866i	$-0.386287\pi$
$223$	19.2124	−	19.2124i	1.28656	−	1.28656i	0.936866	−	0.349689i	$-0.113713\pi$
$224$	−2.76100			−0.184477
$225$	−13.6580	+	6.20149i	−0.910535	+	0.413433i
$226$	−14.9970			−0.997589
$227$	−3.11027	+	3.11027i	−0.206436	+	0.206436i	−0.802751	−	0.596315i	$-0.796631\pi$
$227$	−3.11027	+	3.11027i	−0.206436	+	0.206436i	0.596315	+	0.802751i	$0.296631\pi$
$228$	−0.901679	+	1.47884i	−0.0597151	+	0.0979387i
$229$			6.10439i			0.403389i	0.979448	+	0.201695i	$0.0646448\pi$
$229$			6.10439i			0.403389i	−0.979448	+	0.201695i	$0.935355\pi$
$230$	1.10697	−	1.05348i	0.0729916	−	0.0694647i
$231$	−4.14582	−	17.0995i	−0.272775	−	1.12506i
$232$	−5.67630	−	5.67630i	−0.372667	−	0.372667i
$233$	−10.7007	−	10.7007i	−0.701026	−	0.701026i	0.263605	−	0.964631i	$-0.415088\pi$
$233$	−10.7007	−	10.7007i	−0.701026	−	0.701026i	−0.964631	+	0.263605i	$0.915088\pi$
$234$	9.82804	−	5.06330i	0.642479	−	0.330999i
$235$	0.270014	−	10.9064i	0.0176137	−	0.711452i
$236$		−	11.1184i		−	0.723744i
$237$	10.5836	+	6.45305i	0.687482	+	0.419171i
$238$	4.21349	−	4.21349i	0.273120	−	0.273120i
$239$	−7.74663			−0.501088			−0.250544	−	0.968105i	$-0.580609\pi$
$239$	−7.74663			−0.501088			−0.250544	+	0.968105i	$0.580609\pi$
$240$	0.819140	+	3.78537i	0.0528752	+	0.244344i
$241$	11.5977			0.747071			0.373535	−	0.927616i	$-0.378145\pi$
$241$	11.5977			0.747071			0.373535	+	0.927616i	$0.378145\pi$
$242$	1.79388	−	1.79388i	0.115315	−	0.115315i
$243$	6.12661	+	14.3340i	0.393022	+	0.919529i
$244$		−	0.989652i		−	0.0633559i
$245$	0.960555	+	1.00932i	0.0613676	+	0.0644834i
$246$	9.19702	−	2.22984i	0.586380	−	0.142169i
$247$	−2.60584	−	2.60584i	−0.165806	−	0.165806i
$248$	−2.16590	−	2.16590i	−0.137535	−	0.137535i
$249$	6.34612	−	1.53863i	0.402169	−	0.0975069i
$250$	11.1495	+	0.829457i	0.705158	+	0.0524595i
$251$			16.8253i			1.06200i	0.847371	+	0.531001i	$0.178184\pi$
$251$			16.8253i			1.06200i	−0.847371	+	0.531001i	$0.821816\pi$
$252$	7.88901	+	2.52422i	0.496961	+	0.159011i
$253$	1.77797	−	1.77797i	0.111780	−	0.111780i
$254$	−19.2885			−1.21027
$255$	−7.02681	−	4.52668i	−0.440036	−	0.283472i
$256$	1.00000			0.0625000
$257$	14.5714	−	14.5714i	0.908942	−	0.908942i	−0.0872448	−	0.996187i	$-0.527806\pi$
$257$	14.5714	−	14.5714i	0.908942	−	0.908942i	0.996187	+	0.0872448i	$0.0278062\pi$
$258$	−6.50846	−	3.96833i	−0.405199	−	0.247058i
$259$		−	28.6022i		−	1.77725i
$260$	−8.23787	−	0.203949i	−0.510891	−	0.0126484i
$261$	11.0294	+	21.4084i	0.682702	+	1.32515i
$262$	−11.2095	−	11.2095i	−0.692523	−	0.692523i
$263$	−17.7679	−	17.7679i	−1.09562	−	1.09562i	−0.994917	−	0.100700i	$-0.967892\pi$
$263$	−17.7679	−	17.7679i	−1.09562	−	1.09562i	−0.100700	−	0.994917i	$-0.532108\pi$
$264$	1.50156	+	6.19323i	0.0924149	+	0.381167i
$265$	−23.7548	−	0.588107i	−1.45924	−	0.0361271i
$266$		−	2.76100i		−	0.169288i
$267$	0.954992	−	1.56628i	0.0584446	−	0.0958549i
$268$	8.05094	−	8.05094i	0.491789	−	0.491789i
$269$	27.3733			1.66898			0.834488	−	0.551026i	$-0.185763\pi$
$269$	27.3733			1.66898			0.834488	+	0.551026i	$0.185763\pi$
$270$	1.12021	−	11.5648i	0.0681737	−	0.703813i
$271$	−25.6490			−1.55807			−0.779034	−	0.626981i	$-0.784290\pi$
$271$	−25.6490			−1.55807			−0.779034	+	0.626981i	$0.784290\pi$
$272$	−1.52607	+	1.52607i	−0.0925317	+	0.0925317i
$273$	−9.17447	+	15.0470i	−0.555264	+	0.910689i
$274$		−	0.0354800i		−	0.00214343i
$275$	18.3737	+	0.910331i	1.10798	+	0.0548951i
$276$	0.278909	+	1.15037i	0.0167884	+	0.0692439i
$277$	−10.7585	−	10.7585i	−0.646419	−	0.646419i	0.305707	−	0.952126i	$-0.401107\pi$
$277$	−10.7585	−	10.7585i	−0.646419	−	0.646419i	−0.952126	+	0.305707i	$0.901107\pi$
$278$	11.2741	+	11.2741i	0.676177	+	0.676177i
$279$	4.20847	+	8.16878i	0.251955	+	0.489052i
$280$	−4.25614	−	4.47223i	−0.254353	−	0.267267i
$281$			14.9620i			0.892559i	0.894894	+	0.446279i	$0.147251\pi$
$281$			14.9620i			0.892559i	−0.894894	+	0.446279i	$0.852749\pi$
$282$	7.21522	+	4.39926i	0.429660	+	0.261972i
$283$	−14.6425	+	14.6425i	−0.870404	+	0.870404i	−0.992516	−	0.122112i	$-0.961033\pi$
$283$	−14.6425	+	14.6425i	−0.870404	+	0.870404i	0.122112	+	0.992516i	$0.461033\pi$
$284$	4.07805			0.241988
$285$	−3.78537	+	0.819140i	−0.224226	+	0.0485216i
$286$	−13.5589			−0.801752
$287$	−10.6670	+	10.6670i	−0.629652	+	0.629652i
$288$	−2.85730	−	0.914240i	−0.168368	−	0.0538721i
$289$			12.3422i			0.726012i
$290$	0.444261	−	17.9445i	0.0260879	−	1.05374i
$291$	13.1384	−	3.18543i	0.770184	−	0.186733i
$292$	−11.1477	−	11.1477i	−0.652369	−	0.652369i
$293$	2.83956	+	2.83956i	0.165889	+	0.165889i	0.785170	−	0.619281i	$-0.212576\pi$
$293$	2.83956	+	2.83956i	0.165889	+	0.165889i	−0.619281	+	0.785170i	$0.712576\pi$
$294$	−1.04889	+	0.254306i	−0.0611725	+	0.0148314i
$295$	18.0094	−	17.1392i	1.04855	−	0.997883i
$296$			10.3593i			0.602125i
$297$	1.37168	−	19.0687i	0.0795928	−	1.10648i
$298$	12.5182	−	12.5182i	0.725160	−	0.725160i
$299$	−2.51850			−0.145649
$300$	−4.86877	+	7.16206i	−0.281099	+	0.413502i
$301$	12.1513			0.700389
$302$	9.68240	−	9.68240i	0.557160	−	0.557160i
$303$	10.6308	+	6.48178i	0.610721	+	0.372369i
$304$			1.00000i			0.0573539i
$305$	1.60303	−	1.52557i	0.0917890	−	0.0873538i
$306$	5.75564	−	2.96525i	0.329028	−	0.169512i
$307$	−13.1684	−	13.1684i	−0.751562	−	0.751562i	0.223209	−	0.974771i	$-0.428347\pi$
$307$	−13.1684	−	13.1684i	−0.751562	−	0.751562i	−0.974771	+	0.223209i	$0.928347\pi$
$308$	−7.18309	−	7.18309i	−0.409295	−	0.409295i
$309$	−3.02551	−	12.4788i	−0.172115	−	0.709892i
$310$	0.169516	−	6.84708i	0.00962787	−	0.388888i
$311$		−	22.0732i		−	1.25166i	−0.779961	−	0.625828i	$-0.784761\pi$
$311$		−	22.0732i		−	1.25166i	0.779961	−	0.625828i	$-0.215239\pi$
$312$	3.32288	−	5.44985i	0.188121	−	0.308537i
$313$	10.3013	−	10.3013i	0.582265	−	0.582265i	−0.353260	−	0.935525i	$-0.614927\pi$
$313$	10.3013	−	10.3013i	0.582265	−	0.582265i	0.935525	+	0.353260i	$0.114927\pi$
$314$	1.55866			0.0879600
$315$	8.07238	+	16.6696i	0.454827	+	0.939228i
$316$	7.15671			0.402596
$317$	13.0482	−	13.0482i	0.732860	−	0.732860i	−0.238325	−	0.971185i	$-0.576598\pi$
$317$	13.0482	−	13.0482i	0.732860	−	0.732860i	0.971185	+	0.238325i	$0.0765985\pi$
$318$	9.58188	−	15.7152i	0.537325	−	0.881266i
$319$		−	29.5352i		−	1.65365i
$320$	1.54152	+	1.61979i	0.0861737	+	0.0905489i
$321$	−2.14158	−	8.83297i	−0.119531	−	0.493008i
$322$	−1.33423	−	1.33423i	−0.0743536	−	0.0743536i
$323$	−1.52607	−	1.52607i	−0.0849129	−	0.0849129i
$324$	7.32833	+	5.22452i	0.407129	+	0.290251i
$325$	−12.3685	−	13.6580i	−0.686081	−	0.757609i
$326$		−	15.6506i		−	0.866806i
$327$	−2.05620	−	1.25371i	−0.113708	−	0.0693301i
$328$	3.86345	−	3.86345i	0.213323	−	0.213323i
$329$	−13.4708			−0.742671
$330$	−7.71702	+	11.9792i	−0.424808	+	0.659434i
$331$	−24.9937			−1.37378			−0.686888	−	0.726763i	$-0.741024\pi$
$331$	−24.9937			−1.37378			−0.686888	+	0.726763i	$0.741024\pi$
$332$	2.66585	−	2.66585i	0.146308	−	0.146308i
$333$	9.47094	−	29.5998i	0.519004	−	1.62206i
$334$			9.03131i			0.494171i
$335$	25.4515	+	0.630114i	1.39056	+	0.0344268i
$336$	4.64754	−	1.12681i	0.253544	−	0.0614725i
$337$	−1.90830	−	1.90830i	−0.103952	−	0.103952i	0.653218	−	0.757170i	$-0.273419\pi$
$337$	−1.90830	−	1.90830i	−0.103952	−	0.103952i	−0.757170	+	0.653218i	$0.773419\pi$
$338$	0.410698	+	0.410698i	0.0223390	+	0.0223390i
$339$	25.2443	−	6.12054i	1.37108	−	0.332422i
$340$	−4.82439	−	0.119439i	−0.261639	−	0.00647751i
$341$		−	11.2697i		−	0.610290i
$342$	0.914240	−	2.85730i	0.0494365	−	0.154505i
$343$	−12.4497	+	12.4497i	−0.672222	+	0.672222i
$344$	−4.40105			−0.237289
$345$	−1.43340	+	2.22509i	−0.0771718	+	0.119795i
$346$	−0.555924			−0.0298867
$347$	−13.4880	+	13.4880i	−0.724074	+	0.724074i	−0.969432	−	0.245358i	$-0.921094\pi$
$347$	−13.4880	+	13.4880i	−0.724074	+	0.724074i	0.245358	+	0.969432i	$0.421094\pi$
$348$	11.8714	+	7.23823i	0.636374	+	0.388010i
$349$			3.83364i			0.205210i	0.994722	+	0.102605i	$0.0327178\pi$
$349$			3.83364i			0.205210i	−0.994722	+	0.102605i	$0.967282\pi$
$350$	0.683134	−	13.7881i	0.0365151	−	0.737004i
$351$	−14.4769	+	12.5340i	−0.772722	+	0.669013i
$352$	2.60163	+	2.60163i	0.138667	+	0.138667i
$353$	22.0113	+	22.0113i	1.17155	+	1.17155i	0.981841	+	0.189704i	$0.0607527\pi$
$353$	22.0113	+	22.0113i	1.17155	+	1.17155i	0.189704	+	0.981841i	$0.439247\pi$
$354$	4.53759	+	18.7154i	0.241170	+	0.994710i
$355$	6.28640	+	6.60557i	0.333647	+	0.350587i
$356$		−	1.05913i		−	0.0561336i
$357$	−5.37290	+	8.81208i	−0.284364	+	0.466385i
$358$	5.13621	−	5.13621i	0.271457	−	0.271457i
$359$	−2.29765			−0.121265			−0.0606327	−	0.998160i	$-0.519312\pi$
$359$	−2.29765			−0.121265			−0.0606327	+	0.998160i	$0.519312\pi$
$360$	−2.92371	−	6.03754i	−0.154093	−	0.318206i
$361$	−1.00000			−0.0526316
$362$	−8.09627	+	8.09627i	−0.425531	+	0.425531i
$363$	−2.28749	+	3.75171i	−0.120062	+	0.196914i
$364$			10.1749i			0.533309i
$365$	0.872484	−	35.2413i	0.0456679	−	1.84461i
$366$	0.403893	+	1.66586i	0.0211118	+	0.0870761i
$367$	8.45018	+	8.45018i	0.441096	+	0.441096i	0.892380	−	0.451284i	$-0.149034\pi$
$367$	8.45018	+	8.45018i	0.441096	+	0.441096i	−0.451284	+	0.892380i	$0.649034\pi$
$368$	0.483241	+	0.483241i	0.0251907	+	0.0251907i
$369$	−14.5711	+	7.50691i	−0.758544	+	0.390794i
$370$	−16.7799	+	15.9692i	−0.872348	+	0.830197i
$371$			29.3403i			1.52327i
$372$	4.52976	+	2.76188i	0.234857	+	0.143197i
$373$	−16.3447	+	16.3447i	−0.846298	+	0.846298i	−0.989669	−	0.143371i	$-0.954206\pi$
$373$	−16.3447	+	16.3447i	−0.846298	+	0.846298i	0.143371	+	0.989669i	$0.454206\pi$
$374$	−7.94054			−0.410596
$375$	−19.1063	+	3.15409i	−0.986646	+	0.162877i
$376$	4.87897			0.251614
$377$	−20.9184	+	20.9184i	−1.07735	+	1.07735i
$378$	−14.3096	−	1.02934i	−0.736007	−	0.0529435i
$379$			19.6159i			1.00760i	0.863821	+	0.503800i	$0.168065\pi$
$379$			19.6159i			1.00760i	−0.863821	+	0.503800i	$0.831935\pi$
$380$	−1.61979	+	1.54152i	−0.0830933	+	0.0790784i
$381$	32.4680	−	7.87195i	1.66339	−	0.403292i
$382$	−10.0382	−	10.0382i	−0.513598	−	0.513598i
$383$	−23.4876	−	23.4876i	−1.20016	−	1.20016i	−0.974117	−	0.226045i	$-0.927420\pi$
$383$	−23.4876	−	23.4876i	−1.20016	−	1.20016i	−0.226045	−	0.974117i	$-0.572580\pi$
$384$	−1.68328	+	0.408116i	−0.0858997	+	0.0208266i
$385$	0.562191	−	22.7080i	0.0286519	−	1.15731i
$386$		−	16.3400i		−	0.831685i
$387$	12.5751	+	4.02362i	0.639229	+	0.204532i
$388$	5.51911	−	5.51911i	0.280190	−	0.280190i
$389$	26.9154			1.36466			0.682332	−	0.731043i	$-0.260966\pi$
$389$	26.9154			1.36466			0.682332	+	0.731043i	$0.260966\pi$
$390$	13.9499	−	3.01871i	0.706381	−	0.152858i
$391$	−1.47492			−0.0745900
$392$	−0.440614	+	0.440614i	−0.0222543	+	0.0222543i
$393$	23.4435	+	14.2939i	1.18257	+	0.721033i
$394$			25.7258i			1.29605i
$395$	11.0322	+	11.5923i	0.555091	+	0.583274i
$396$	−5.05512	−	9.81214i	−0.254029	−	0.493079i
$397$	−17.6233	−	17.6233i	−0.884487	−	0.884487i	0.109500	−	0.993987i	$-0.465075\pi$
$397$	−17.6233	−	17.6233i	−0.884487	−	0.884487i	−0.993987	+	0.109500i	$0.965075\pi$
$398$	0.0351733	+	0.0351733i	0.00176308	+	0.00176308i
$399$	1.12681	+	4.64754i	0.0564110	+	0.232668i
$400$	−0.247423	+	4.99387i	−0.0123711	+	0.249694i
$401$		−	5.28634i		−	0.263987i	−0.991251	−	0.131994i	$-0.957862\pi$
$401$		−	5.28634i		−	0.263987i	0.991251	−	0.131994i	$-0.0421378\pi$
$402$	−10.2663	+	16.8377i	−0.512036	+	0.839789i
$403$	−7.98181	+	7.98181i	−0.397602	+	0.397602i
$404$	7.18857			0.357645
$405$	2.83417	+	19.9240i	0.140831	+	0.990034i
$406$	−22.1639			−1.09998
$407$	−26.9512	+	26.9512i	−1.33592	+	1.33592i
$408$	1.94600	−	3.19163i	0.0963412	−	0.158009i
$409$			15.6120i			0.771963i	0.922507	+	0.385981i	$0.126137\pi$
$409$			15.6120i			0.771963i	−0.922507	+	0.385981i	$0.873863\pi$
$410$	12.2135	+	0.302376i	0.603184	+	0.0149333i
$411$	0.0144800	+	0.0597229i	0.000714245	+	0.00294591i
$412$	−5.24203	−	5.24203i	−0.258256	−	0.258256i
$413$	−21.7066	−	21.7066i	−1.06811	−	1.06811i
$414$	−0.938966	−	1.82256i	−0.0461477	−	0.0895741i
$415$	8.42758	+	0.208645i	0.413694	+	0.0102420i
$416$		−	3.68522i		−	0.180683i
$417$	−23.5787	−	14.3764i	−1.15465	−	0.704015i
$418$	−2.60163	+	2.60163i	−0.127250	+	0.127250i
$419$	13.9765			0.682795			0.341397	−	0.939919i	$-0.389100\pi$
$419$	13.9765			0.682795			0.341397	+	0.939919i	$0.389100\pi$
$420$	8.98948	+	5.79103i	0.438642	+	0.282573i
$421$	20.4247			0.995439			0.497719	−	0.867338i	$-0.334171\pi$
$421$	20.4247			0.995439			0.497719	+	0.867338i	$0.334171\pi$
$422$	−19.1596	+	19.1596i	−0.932674	+	0.932674i
$423$	−13.9407	−	4.46055i	−0.677819	−	0.216879i
$424$		−	10.6267i		−	0.516079i
$425$	−7.24343	−	7.99860i	−0.351358	−	0.387989i
$426$	−6.86450	+	1.66432i	−0.332586	+	0.0806364i
$427$	−1.93212	−	1.93212i	−0.0935018	−	0.0935018i
$428$	−3.71052	−	3.71052i	−0.179355	−	0.179355i
$429$	22.8234	−	5.53359i	1.10192	−	0.267164i
$430$	−6.78431	−	7.12876i	−0.327168	−	0.343779i
$431$		−	15.5840i		−	0.750654i	−0.926892	−	0.375327i	$-0.877530\pi$
$431$		−	15.5840i		−	0.750654i	0.926892	−	0.375327i	$-0.122470\pi$
$432$	5.18276	+	0.372814i	0.249356	+	0.0179370i
$433$	−23.3156	+	23.3156i	−1.12048	+	1.12048i	−0.128806	+	0.991670i	$0.541114\pi$
$433$	−23.3156	+	23.3156i	−1.12048	+	1.12048i	−0.991670	+	0.128806i	$0.958886\pi$
$434$	−8.45707			−0.405952
$435$	6.57564	+	30.3870i	0.315278	+	1.45695i
$436$	−1.39041			−0.0665888
$437$	−0.483241	+	0.483241i	−0.0231165	+	0.0231165i
$438$	23.3143	+	14.2152i	1.11400	+	0.679227i
$439$		−	18.2344i		−	0.870279i	−0.900363	−	0.435139i	$-0.856699\pi$
$439$		−	18.2344i		−	0.870279i	0.900363	−	0.435139i	$-0.143301\pi$
$440$	−0.203619	+	8.22455i	−0.00970714	+	0.392090i
$441$	1.66179	−	0.856138i	0.0791329	−	0.0407685i
$442$	5.62391	+	5.62391i	0.267502	+	0.267502i
$443$	4.95807	+	4.95807i	0.235565	+	0.235565i	0.815011	−	0.579446i	$-0.196731\pi$
$443$	4.95807	+	4.95807i	0.235565	+	0.235565i	−0.579446	+	0.815011i	$0.696731\pi$
$444$	−4.22782	−	17.4377i	−0.200643	−	0.827557i
$445$	1.71556	−	1.63267i	0.0813254	−	0.0773959i
$446$			27.1704i			1.28656i
$447$	−15.9628	+	26.1806i	−0.755014	+	1.23830i
$448$	1.95232	−	1.95232i	0.0922385	−	0.0922385i
$449$	−32.0557			−1.51280			−0.756401	−	0.654109i	$-0.773044\pi$
$449$	−32.0557			−1.51280			−0.756401	+	0.654109i	$0.773044\pi$
$450$	5.27256	−	14.0428i	0.248551	−	0.661984i
$451$	20.1025			0.946589
$452$	10.6045	−	10.6045i	0.498794	−	0.498794i
$453$	−12.3467	+	20.2498i	−0.580097	+	0.951417i
$454$		−	4.39859i		−	0.206436i
$455$	−16.4811	+	15.6848i	−0.772648	+	0.735315i
$456$	−0.408116	−	1.68328i	−0.0191118	−	0.0788269i
$457$	4.40540	+	4.40540i	0.206076	+	0.206076i	0.802597	−	0.596521i	$-0.203451\pi$
$457$	4.40540	+	4.40540i	0.206076	+	0.206076i	−0.596521	+	0.802597i	$0.703451\pi$
$458$	−4.31645	−	4.31645i	−0.201695	−	0.201695i
$459$	−8.47821	+	7.34033i	−0.395729	+	0.342617i
$460$	−0.0378213	+	1.52767i	−0.00176343	+	0.0712282i
$461$		−	8.34487i		−	0.388659i	−0.980936	−	0.194330i	$-0.937747\pi$
$461$		−	8.34487i		−	0.388659i	0.980936	−	0.194330i	$-0.0622532\pi$
$462$	15.0227	+	9.15964i	0.698920	+	0.426145i
$463$	−0.884571	+	0.884571i	−0.0411095	+	0.0411095i	−0.727363	−	0.686253i	$-0.759254\pi$
$463$	−0.884571	+	0.884571i	−0.0411095	+	0.0411095i	0.686253	+	0.727363i	$0.259254\pi$
$464$	8.02750			0.372667
$465$	2.50906	+	11.5948i	0.116355	+	0.537694i
$466$	15.1331			0.701026
$467$	−2.44668	+	2.44668i	−0.113219	+	0.113219i	−0.761447	−	0.648228i	$-0.775511\pi$
$467$	−2.44668	+	2.44668i	−0.113219	+	0.113219i	0.648228	+	0.761447i	$0.275511\pi$
$468$	−3.36917	+	10.5298i	−0.155740	+	0.486739i
$469$		−	31.4360i		−	1.45158i
$470$	7.52103	+	7.90289i	0.346919	+	0.364533i
$471$	−2.62366	+	0.636113i	−0.120892	+	0.0293105i
$472$	7.86188	+	7.86188i	0.361872	+	0.361872i
$473$	−11.4499	−	11.4499i	−0.526466	−	0.526466i
$474$	−12.0468	+	2.92077i	−0.553326	+	0.134155i
$475$	−4.99387	−	0.247423i	−0.229135	−	0.0113525i
$476$			5.95877i			0.273120i
$477$	−9.71537	+	30.3637i	−0.444836	+	1.39026i
$478$	5.47769	−	5.47769i	0.250544	−	0.250544i
$479$	1.05345			0.0481333			0.0240667	−	0.999710i	$-0.492339\pi$
$479$	1.05345			0.0481333			0.0240667	+	0.999710i	$0.492339\pi$
$480$	−3.25588	−	2.09744i	−0.148610	−	0.0957346i
$481$	38.1764			1.74070
$482$	−8.20078	+	8.20078i	−0.373535	+	0.373535i
$483$	2.79040	+	1.70136i	0.126968	+	0.0774147i
$484$			2.53692i			0.115315i
$485$	17.4476	+	0.431958i	0.792255	+	0.0196142i
$486$	−14.4679	−	5.80353i	−0.656276	−	0.263254i
$487$	−6.07963	−	6.07963i	−0.275494	−	0.275494i	0.555813	−	0.831307i	$-0.312407\pi$
$487$	−6.07963	−	6.07963i	−0.275494	−	0.275494i	−0.831307	+	0.555813i	$0.812407\pi$
$488$	0.699789	+	0.699789i	0.0316780	+	0.0316780i
$489$	6.38727	+	26.3444i	0.288842	+	1.19133i
$490$	−1.39292	−	0.0344850i	−0.0629255	−	0.00155787i
$491$			18.2097i			0.821794i	0.911682	+	0.410897i	$0.134784\pi$
$491$			18.2097i			0.821794i	−0.911682	+	0.410897i	$0.865216\pi$
$492$	−4.92654	+	8.08001i	−0.222105	+	0.364275i
$493$	−12.2505	+	12.2505i	−0.551737	+	0.551737i
$494$	3.68522			0.165806
$495$	8.10101	−	23.3138i	0.364113	−	1.04788i
$496$	3.06305			0.137535
$497$	7.96166	−	7.96166i	0.357129	−	0.357129i
$498$	−3.39940	+	5.57536i	−0.152331	+	0.249838i
$499$			8.59031i			0.384555i	0.981341	+	0.192278i	$0.0615874\pi$
$499$			8.59031i			0.384555i	−0.981341	+	0.192278i	$0.938413\pi$
$500$	−8.47042	+	7.29739i	−0.378809	+	0.326349i
$501$	−3.68583	−	15.2022i	−0.164671	−	0.679186i
$502$	−11.8973	−	11.8973i	−0.531001	−	0.531001i
$503$	−22.4745	−	22.4745i	−1.00209	−	1.00209i	−0.999998	−	0.00209079i	$-0.999334\pi$
$503$	−22.4745	−	22.4745i	−1.00209	−	1.00209i	−0.00209079	−	0.999998i	$-0.500666\pi$
$504$	−7.36326	+	3.79348i	−0.327986	+	0.168975i
$505$	11.0813	+	11.6440i	0.493113	+	0.518149i
$506$			2.51443i			0.111780i
$507$	−0.858934	−	0.523709i	−0.0381466	−	0.0232587i
$508$	13.6390	−	13.6390i	0.605134	−	0.605134i
$509$	22.2471			0.986087			0.493043	−	0.870005i	$-0.335884\pi$
$509$	22.2471			0.986087			0.493043	+	0.870005i	$0.335884\pi$
$510$	8.16955	−	1.76786i	0.361754	−	0.0782822i
$511$	−43.5278			−1.92555
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.372814	+	5.18276i	−0.0164601	+	0.228824i
$514$			20.6071i			0.908942i
$515$	0.410272	−	16.5717i	0.0180787	−	0.730235i
$516$	7.40821	−	1.79614i	0.326128	−	0.0790706i
$517$	12.6933	+	12.6933i	0.558249	+	0.558249i
$518$	20.2248	+	20.2248i	0.888626	+	0.888626i
$519$	0.935778	−	0.226882i	0.0410761	−	0.00995900i
$520$	5.96927	−	5.68084i	0.261770	−	0.249121i
$521$			11.3759i			0.498385i	0.968454	+	0.249193i	$0.0801653\pi$
$521$			11.3759i			0.498385i	−0.968454	+	0.249193i	$0.919835\pi$
$522$	−22.9370	−	7.33906i	−1.00392	−	0.321222i
$523$	−9.78826	+	9.78826i	−0.428011	+	0.428011i	−0.887950	−	0.459940i	$-0.847871\pi$
$523$	−9.78826	+	9.78826i	−0.428011	+	0.428011i	0.459940	+	0.887950i	$0.347871\pi$
$524$	15.8526			0.692523
$525$	4.47724	+	23.4880i	0.195403	+	1.02510i
$526$	25.1276			1.09562
$527$	−4.67443	+	4.67443i	−0.203621	+	0.203621i
$528$	−5.44104	−	3.31751i	−0.236791	−	0.144376i
$529$		−	22.5330i		−	0.979694i
$530$	17.2130	−	16.3813i	0.747685	−	0.711558i
$531$	−15.2761	−	29.6514i	−0.662926	−	1.28676i
$532$	1.95232	+	1.95232i	0.0846439	+	0.0846439i
$533$	−14.2376	−	14.2376i	−0.616700	−	0.616700i
$534$	0.432247	+	1.78281i	0.0187052	+	0.0771498i
$535$	0.290407	−	11.7301i	0.0125554	−	0.507136i
$536$			11.3857i			0.491789i
$537$	−6.54953	+	10.7419i	−0.282633	+	0.463546i
$538$	−19.3558	+	19.3558i	−0.834488	+	0.834488i
$539$	−2.29262			−0.0987503
$540$	7.38546	+	8.96967i	0.317820	+	0.385993i
$541$	−29.7432			−1.27876			−0.639380	−	0.768891i	$-0.720809\pi$
$541$	−29.7432			−1.27876			−0.639380	+	0.768891i	$0.720809\pi$
$542$	18.1366	−	18.1366i	0.779034	−	0.779034i
$543$	10.3241	−	16.9325i	0.443049	−	0.726645i
$544$		−	2.15819i		−	0.0925317i
$545$	−2.14335	−	2.25218i	−0.0918112	−	0.0964726i
$546$	−4.15254	−	17.1272i	−0.177712	−	0.732977i
$547$	27.7770	+	27.7770i	1.18766	+	1.18766i	0.977713	+	0.209945i	$0.0673286\pi$
$547$	27.7770	+	27.7770i	1.18766	+	1.18766i	0.209945	+	0.977713i	$0.432671\pi$
$548$	0.0250882	+	0.0250882i	0.00107171	+	0.00107171i
$549$	−1.35973	−	2.63928i	−0.0580320	−	0.112642i
$550$	−13.6359	+	12.3485i	−0.581437	+	0.526542i
$551$			8.02750i			0.341983i
$552$	−1.01065	−	0.616213i	−0.0430161	−	0.0262278i
$553$	13.9722	−	13.9722i	0.594158	−	0.594158i
$554$	15.2149			0.646419
$555$	21.7281	−	33.7288i	0.922307	−	1.43171i
$556$	−15.9440			−0.676177
$557$	−18.6904	+	18.6904i	−0.791939	+	0.791939i	−0.981809	−	0.189871i	$-0.939193\pi$
$557$	−18.6904	+	18.6904i	−0.791939	+	0.791939i	0.189871	+	0.981809i	$0.439193\pi$
$558$	−8.75204	−	2.80036i	−0.370503	−	0.118549i
$559$			16.2188i			0.685983i
$560$	6.17189	+	0.152800i	0.260810	+	0.00645699i
$561$	13.3662	−	3.24067i	0.564320	−	0.136821i
$562$	−10.5797	−	10.5797i	−0.446279	−	0.446279i
$563$	−12.1886	−	12.1886i	−0.513687	−	0.513687i	0.401967	−	0.915654i	$-0.368327\pi$
$563$	−12.1886	−	12.1886i	−0.513687	−	0.513687i	−0.915654	+	0.401967i	$0.868327\pi$
$564$	−8.21268	+	1.99119i	−0.345816	+	0.0838441i
$565$	33.5241	+	0.829972i	1.41037	+	0.0349172i
$566$		−	20.7076i		−	0.870404i
$567$	24.5072	−	4.10731i	1.02921	−	0.172491i
$568$	−2.88361	+	2.88361i	−0.120994	+	0.120994i
$569$	−15.7219			−0.659095			−0.329548	−	0.944139i	$-0.606896\pi$
$569$	−15.7219			−0.659095			−0.329548	+	0.944139i	$0.606896\pi$
$570$	2.09744	−	3.25588i	0.0878521	−	0.136374i
$571$	−9.79901			−0.410076			−0.205038	−	0.978754i	$-0.565732\pi$
$571$	−9.79901			−0.410076			−0.205038	+	0.978754i	$0.565732\pi$
$572$	9.58756	−	9.58756i	0.400876	−	0.400876i
$573$	20.9938	+	12.8004i	0.877031	+	0.534742i
$574$		−	15.0854i		−	0.629652i
$575$	−2.53281	+	2.29368i	−0.105625	+	0.0956531i
$576$	2.66688	−	1.37395i	0.111120	−	0.0572479i
$577$	3.10041	+	3.10041i	0.129072	+	0.129072i	0.768691	−	0.639620i	$-0.220908\pi$
$577$	3.10041	+	3.10041i	0.129072	+	0.129072i	−0.639620	+	0.768691i	$0.720908\pi$
$578$	−8.72726	−	8.72726i	−0.363006	−	0.363006i
$579$	6.66863	+	27.5049i	0.277139	+	1.14306i
$580$	12.3746	+	13.0028i	0.513826	+	0.539914i
$581$		−	10.4092i		−	0.431846i
$582$	−7.03778	+	11.5427i	−0.291725	+	0.478459i
$583$	27.6467	−	27.6467i	1.14501	−	1.14501i
$584$	15.7652			0.652369
$585$	−22.2496	+	10.7745i	−0.919909	+	0.445472i
$586$	−4.01575			−0.165889
$587$	9.84222	−	9.84222i	0.406232	−	0.406232i	−0.474190	−	0.880422i	$-0.657259\pi$
$587$	9.84222	−	9.84222i	0.406232	−	0.406232i	0.880422	+	0.474190i	$0.157259\pi$
$588$	0.561856	−	0.921499i	0.0231705	−	0.0380020i
$589$			3.06305i			0.126211i
$590$	−0.615317	+	24.8538i	−0.0253322	+	1.02322i
$591$	−10.4991	−	43.3038i	−0.431876	−	1.78128i
$592$	−7.32517	−	7.32517i	−0.301062	−	0.301062i
$593$	−26.6020	−	26.6020i	−1.09241	−	1.09241i	−0.995271	−	0.0971411i	$-0.969030\pi$
$593$	−26.6020	−	26.6020i	−1.09241	−	1.09241i	−0.0971411	−	0.995271i	$-0.530970\pi$
$594$	12.5137	+	14.4535i	0.513443	+	0.593036i
$595$	−9.65194	+	9.18557i	−0.395691	+	0.376572i
$596$			17.7034i			0.725160i
$597$	−0.0735614	−	0.0448518i	−0.00301067	−	0.00183566i
$598$	1.78085	−	1.78085i	0.0728243	−	0.0728243i
$599$	−1.72077			−0.0703088			−0.0351544	−	0.999382i	$-0.511192\pi$
$599$	−1.72077			−0.0703088			−0.0351544	+	0.999382i	$0.511192\pi$
$600$	−1.62160	−	8.50708i	−0.0662015	−	0.347300i
$601$	22.1111			0.901930			0.450965	−	0.892542i	$-0.351080\pi$
$601$	22.1111			0.901930			0.450965	+	0.892542i	$0.351080\pi$
$602$	−8.59226	+	8.59226i	−0.350194	+	0.350194i
$603$	10.4093	−	32.5325i	0.423900	−	1.32483i
$604$			13.6930i			0.557160i
$605$	−4.10928	+	3.91072i	−0.167066	+	0.158993i
$606$	−12.1004	+	2.93377i	−0.491545	+	0.119176i
$607$	19.6650	+	19.6650i	0.798178	+	0.798178i	0.982808	−	0.184630i	$-0.0591088\pi$
$607$	19.6650	+	19.6650i	0.798178	+	0.798178i	−0.184630	+	0.982808i	$0.559109\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	37.3082	−	9.04546i	1.51180	−	0.366541i
$610$	−0.0547696	+	2.21225i	−0.00221756	+	0.0895714i
$611$		−	17.9800i		−	0.727395i
$612$	−1.97311	+	6.16660i	−0.0797581	+	0.249270i
$613$	−14.6901	+	14.6901i	−0.593327	+	0.593327i	−0.938529	−	0.345201i	$-0.887811\pi$
$613$	−14.6901	+	14.6901i	−0.593327	+	0.593327i	0.345201	+	0.938529i	$0.387811\pi$
$614$	18.6230			0.751562
$615$	−20.6823	+	4.47557i	−0.833989	+	0.180472i
$616$	10.1584			0.409295
$617$	12.2561	−	12.2561i	0.493413	−	0.493413i	−0.415967	−	0.909380i	$-0.636557\pi$
$617$	12.2561	−	12.2561i	0.493413	−	0.493413i	0.909380	+	0.415967i	$0.136557\pi$
$618$	10.9632	+	6.68446i	0.441003	+	0.268888i
$619$		−	1.71268i		−	0.0688385i	−0.999407	−	0.0344193i	$-0.989042\pi$
$619$		−	1.71268i		−	0.0688385i	0.999407	−	0.0344193i	$-0.0109582\pi$
$620$	4.72175	+	4.96148i	0.189630	+	0.199258i
$621$	2.32436	+	2.68468i	0.0932735	+	0.107733i
$622$	15.6081	+	15.6081i	0.625828	+	0.625828i
$623$	−2.06776	−	2.06776i	−0.0828429	−	0.0828429i
$624$	1.50400	+	6.20326i	0.0602081	+	0.248329i
$625$	−24.8776	−	2.47120i	−0.995103	−	0.0988478i
$626$			14.5683i			0.582265i
$627$	3.31751	−	5.44104i	0.132488	−	0.217294i
$628$	−1.10214	+	1.10214i	−0.0439800	+	0.0439800i
$629$	22.3575			0.891451
$630$	−17.4953	−	6.07919i	−0.697028	−	0.242201i
$631$	−16.1064			−0.641187			−0.320594	−	0.947217i	$-0.603882\pi$
$631$	−16.1064			−0.641187			−0.320594	+	0.947217i	$0.603882\pi$
$632$	−5.06056	+	5.06056i	−0.201298	+	0.201298i
$633$	24.4317	−	40.0703i	0.971071	−	1.59265i
$634$			18.4529i			0.732860i
$635$	43.1172	+	1.06747i	1.71105	+	0.0423613i
$636$	4.33693	+	17.8878i	0.171971	+	0.709296i
$637$	1.62376	+	1.62376i	0.0643356	+	0.0643356i
$638$	20.8846	+	20.8846i	0.826827	+	0.826827i
$639$	10.8757	−	5.60303i	0.430235	−	0.221653i
$640$	−2.23538	−	0.0553424i	−0.0883613	−	0.00218760i
$641$			36.1619i			1.42831i	0.699988	+	0.714155i	$0.253189\pi$
$641$			36.1619i			1.42831i	−0.699988	+	0.714155i	$0.746811\pi$
$642$	7.76017	+	4.73153i	0.306270	+	0.186739i
$643$	12.4536	−	12.4536i	0.491122	−	0.491122i	−0.417537	−	0.908660i	$-0.637107\pi$
$643$	12.4536	−	12.4536i	0.491122	−	0.491122i	0.908660	+	0.417537i	$0.137107\pi$
$644$	1.88688			0.0743536
$645$	14.3293	+	9.23093i	0.564215	+	0.363468i
$646$	2.15819			0.0849129
$647$	−4.82277	+	4.82277i	−0.189603	+	0.189603i	−0.795524	−	0.605922i	$-0.792804\pi$
$647$	−4.82277	+	4.82277i	−0.189603	+	0.189603i	0.605922	+	0.795524i	$0.292804\pi$
$648$	−8.87620	+	1.48762i	−0.348690	+	0.0584392i
$649$			40.9073i			1.60575i
$650$	18.4035	+	0.911806i	0.721845	+	0.0357640i
$651$	14.2356	−	3.45147i	0.557939	−	0.135274i
$652$	11.0666	+	11.0666i	0.433403	+	0.433403i
$653$	−23.8973	−	23.8973i	−0.935174	−	0.935174i	0.0628489	−	0.998023i	$-0.479981\pi$
$653$	−23.8973	−	23.8973i	−0.935174	−	0.935174i	−0.998023	+	0.0628489i	$0.979981\pi$
$654$	2.34046	−	0.567451i	0.0915192	−	0.0221891i
$655$	24.4371	+	25.6778i	0.954836	+	1.00331i
$656$			5.46374i			0.213323i
$657$	−45.0460	−	14.4132i	−1.75741	−	0.562312i
$658$	9.52531	−	9.52531i	0.371335	−	0.371335i
$659$	5.45910			0.212656			0.106328	−	0.994331i	$-0.466091\pi$
$659$	5.45910			0.212656			0.106328	+	0.994331i	$0.466091\pi$
$660$	−3.01382	−	13.9273i	−0.117313	−	0.542121i
$661$	13.7047			0.533053			0.266526	−	0.963828i	$-0.414124\pi$
$661$	13.7047			0.533053			0.266526	+	0.963828i	$0.414124\pi$
$662$	17.6732	−	17.6732i	0.686888	−	0.686888i
$663$	−11.7618	−	7.17142i	−0.456792	−	0.278515i
$664$			3.77008i			0.146308i
$665$	−0.152800	+	6.17189i	−0.00592534	+	0.239336i
$666$	14.2332	+	27.6272i	0.551527	+	1.07053i
$667$	3.87922	+	3.87922i	0.150204	+	0.150204i
$668$	−6.38610	−	6.38610i	−0.247086	−	0.247086i
$669$	−11.0887	−	45.7354i	−0.428713	−	1.76823i
$670$	−18.4425	+	17.5514i	−0.712496	+	0.678069i
$671$			3.64118i			0.140566i
$672$	−2.48954	+	4.08308i	−0.0960359	+	0.157508i
$673$	21.2329	−	21.2329i	0.818469	−	0.818469i	−0.167417	−	0.985886i	$-0.553543\pi$
$673$	21.2329	−	21.2329i	0.818469	−	0.818469i	0.985886	+	0.167417i	$0.0535427\pi$
$674$	2.69875			0.103952
$675$	−3.14412	+	25.7898i	−0.121017	+	0.992650i
$676$	−0.580815			−0.0223390
$677$	−31.7382	+	31.7382i	−1.21980	+	1.21980i	−0.252097	+	0.967702i	$0.581120\pi$
$677$	−31.7382	+	31.7382i	−1.21980	+	1.21980i	−0.967702	+	0.252097i	$0.918880\pi$
$678$	−13.5225	+	22.1783i	−0.519329	+	0.851751i
$679$		−	21.5502i		−	0.827019i
$680$	3.49581	−	3.32690i	0.134058	−	0.127581i
$681$	1.79514	+	7.40407i	0.0687898	+	0.283725i
$682$	7.96890	+	7.96890i	0.305145	+	0.305145i
$683$	−20.1518	−	20.1518i	−0.771089	−	0.771089i	0.207208	−	0.978297i	$-0.433562\pi$
$683$	−20.1518	−	20.1518i	−0.771089	−	0.771089i	−0.978297	+	0.207208i	$0.933562\pi$
$684$	1.37395	+	2.66688i	0.0525343	+	0.101971i
$685$	−0.00196355	+	0.0793114i	−7.50233e−5	+	0.00303033i
$686$		−	17.6066i		−	0.672222i
$687$	9.02743	+	5.50420i	0.344418	+	0.209998i
$688$	3.11201	−	3.11201i	0.118644	−	0.118644i
$689$	−39.1617			−1.49194
$690$	−0.559805	−	2.58694i	−0.0213114	−	0.0984832i
$691$	−31.1608			−1.18541			−0.592707	−	0.805418i	$-0.701941\pi$
$691$	−31.1608			−1.18541			−0.592707	+	0.805418i	$0.701941\pi$
$692$	0.393098	−	0.393098i	0.0149433	−	0.0149433i
$693$	−29.0257	−	9.28724i	−1.10259	−	0.352793i
$694$		−	19.0749i		−	0.724074i
$695$	−24.5781	−	25.8259i	−0.932299	−	0.979633i
$696$	−13.5126	+	3.27615i	−0.512192	+	0.124182i
$697$	−8.33806	−	8.33806i	−0.315827	−	0.315827i
$698$	−2.71079	−	2.71079i	−0.102605	−	0.102605i
$699$	−25.4732	+	6.17605i	−0.963486	+	0.233600i
$700$	9.26660	+	10.2327i	0.350245	+	0.386760i
$701$			10.0481i			0.379513i	0.981831	+	0.189757i	$0.0607699\pi$
$701$			10.0481i			0.379513i	−0.981831	+	0.189757i	$0.939230\pi$
$702$	1.37390	−	19.0996i	0.0518545	−	0.720868i
$703$	7.32517	−	7.32517i	0.276274	−	0.276274i
$704$	−3.67926			−0.138667
$705$	−15.8853	−	10.2333i	−0.598276	−	0.385410i
$706$	−31.1287			−1.17155
$707$	14.0344	−	14.0344i	0.527818	−	0.527818i
$708$	−16.4423	−	10.0252i	−0.617940	−	0.376770i
$709$			28.4137i			1.06710i	0.845768	+	0.533550i	$0.179142\pi$
$709$			28.4137i			1.06710i	−0.845768	+	0.533550i	$0.820858\pi$
$710$	−9.11599	−	0.225689i	−0.342117	−	0.00846994i
$711$	19.0861	−	9.83296i	0.715784	−	0.368765i
$712$	0.748916	+	0.748916i	0.0280668	+	0.0280668i
$713$	1.48019	+	1.48019i	0.0554335	+	0.0554335i
$714$	−2.43187	−	10.0303i	−0.0910105	−	0.375374i
$715$	30.3092	+	0.750379i	1.13350	+	0.0280626i
$716$			7.26370i			0.271457i
$717$	−6.98497	+	11.4560i	−0.260858	+	0.427834i
$718$	1.62469	−	1.62469i	0.0606327	−	0.0606327i
$719$	4.57697			0.170692			0.0853460	−	0.996351i	$-0.472800\pi$
$719$	4.57697			0.170692			0.0853460	+	0.996351i	$0.472800\pi$
$720$	6.33656	+	2.20181i	0.236150	+	0.0820565i
$721$	−20.4682			−0.762277
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	10.4574	−	17.1511i	0.388914	−	0.637857i
$724$		−	11.4499i		−	0.425531i
$725$	−1.98619	+	40.0883i	−0.0737651	+	1.48884i
$726$	−1.03536	−	4.27036i	−0.0384258	−	0.158488i
$727$	−35.7671	−	35.7671i	−1.32653	−	1.32653i	−0.908378	−	0.418149i	$-0.862679\pi$
$727$	−35.7671	−	35.7671i	−1.32653	−	1.32653i	−0.418149	−	0.908378i	$-0.637321\pi$
$728$	−7.19473	−	7.19473i	−0.266654	−	0.266654i
$729$	26.7220	+	3.86441i	0.989704	+	0.143126i
$730$	24.3024	+	25.5363i	0.899473	+	0.945141i
$731$			9.49831i			0.351308i
$732$	−1.46354	−	0.892348i	−0.0540940	−	0.0329821i
$733$	−20.7681	+	20.7681i	−0.767088	+	0.767088i	−0.977593	−	0.210505i	$-0.932489\pi$
$733$	−20.7681	+	20.7681i	−0.767088	+	0.767088i	0.210505	+	0.977593i	$0.432489\pi$
$734$	−11.9504			−0.441096
$735$	2.35874	−	0.510424i	0.0870036	−	0.0188273i
$736$	−0.683406			−0.0251907
$737$	−29.6215	+	29.6215i	−1.09112	+	1.09112i
$738$	4.99517	−	15.6115i	0.183875	−	0.574669i
$739$		−	6.83000i		−	0.251246i	−0.992078	−	0.125623i	$-0.959907\pi$
$739$		−	6.83000i		−	0.251246i	0.992078	−	0.125623i	$-0.0400929\pi$
$740$	0.573311	−	23.1571i	0.0210753	−	0.851272i
$741$	−6.20326	+	1.50400i	−0.227882	+	0.0552507i
$742$	−20.7468	−	20.7468i	−0.761637	−	0.761637i
$743$	23.8484	+	23.8484i	0.874912	+	0.874912i	0.993003	−	0.118091i	$-0.0376775\pi$
$743$	23.8484	+	23.8484i	0.874912	+	0.874912i	−0.118091	+	0.993003i	$0.537678\pi$
$744$	−5.15597	+	1.25008i	−0.189027	+	0.0458301i
$745$	−28.6758	+	27.2902i	−1.05060	+	0.999836i
$746$		−	23.1149i		−	0.846298i
$747$	3.44676	−	10.7723i	0.126110	−	0.394136i
$748$	5.61481	−	5.61481i	0.205298	−	0.205298i
$749$	−14.4883			−0.529389
$750$	11.2799	−	15.7405i	0.411885	−	0.574762i
$751$	−26.8233			−0.978797			−0.489399	−	0.872060i	$-0.662784\pi$
$751$	−26.8233			−0.978797			−0.489399	+	0.872060i	$0.662784\pi$
$752$	−3.44995	+	3.44995i	−0.125807	+	0.125807i
$753$	24.8819	+	15.1710i	0.906748	+	0.552862i
$754$		−	29.5831i		−	1.07735i
$755$	−22.1797	+	21.1080i	−0.807203	+	0.768200i
$756$	10.8463	−	9.39056i	0.394475	−	0.341532i
$757$	−17.2746	−	17.2746i	−0.627856	−	0.627856i	0.319672	−	0.947528i	$-0.396427\pi$
$757$	−17.2746	−	17.2746i	−0.627856	−	0.627856i	−0.947528	+	0.319672i	$0.896427\pi$
$758$	−13.8705	−	13.8705i	−0.503800	−	0.503800i
$759$	−1.02618	−	4.23249i	−0.0372479	−	0.153630i
$760$	0.0553424	−	2.23538i	0.00200748	−	0.0810859i
$761$		−	47.3018i		−	1.71469i	−0.514744	−	0.857344i	$-0.672113\pi$
$761$		−	47.3018i		−	1.71469i	0.514744	−	0.857344i	$-0.327887\pi$
$762$	−17.3920	+	28.5247i	−0.630047	+	1.03334i
$763$	−2.71454	+	2.71454i	−0.0982728	+	0.0982728i
$764$	14.1961			0.513598
$765$	−13.0302	+	6.30994i	−0.471107	+	0.228136i
$766$	33.2165			1.20016
$767$	28.9727	−	28.9727i	1.04614	−	1.04614i
$768$	0.901679	−	1.47884i	0.0325365	−	0.0533631i
$769$		−	14.3683i		−	0.518135i	−0.965859	−	0.259068i	$-0.916585\pi$
$769$		−	14.3683i		−	0.518135i	0.965859	−	0.259068i	$-0.0834153\pi$
$770$	15.6594	+	16.4545i	0.564327	+	0.592979i
$771$	−8.41011	−	34.6876i	−0.302883	−	1.24925i
$772$	11.5541	+	11.5541i	0.415842	+	0.415842i
$773$	11.3662	+	11.3662i	0.408814	+	0.408814i	0.881325	−	0.472511i	$-0.156652\pi$
$773$	11.3662	+	11.3662i	0.408814	+	0.408814i	−0.472511	+	0.881325i	$0.656652\pi$
$774$	−11.7371	+	6.04682i	−0.421880	+	0.217349i
$775$	−0.757867	+	15.2965i	−0.0272234	+	0.549465i
$776$			7.80520i			0.280190i
$777$	−42.2981	−	25.7900i	−1.51744	−	0.925210i
$778$	−19.0320	+	19.0320i	−0.682332	+	0.682332i
$779$	−5.46374			−0.195759
$780$	−7.72952	+	11.9986i	−0.276761	+	0.429619i
$781$	−15.0042			−0.536892
$782$	1.04293	−	1.04293i	0.0372950	−	0.0372950i
$783$	41.6046	+	2.99276i	1.48683	+	0.106953i
$784$		−	0.623122i		−	0.0222543i
$785$	−3.48419	−	0.0862597i	−0.124356	−	0.00307874i
$786$	−26.6844	+	6.46969i	−0.951800	+	0.230766i
$787$	−11.9002	−	11.9002i	−0.424195	−	0.424195i	0.462450	−	0.886645i	$-0.346970\pi$
$787$	−11.9002	−	11.9002i	−0.424195	−	0.424195i	−0.886645	+	0.462450i	$0.846970\pi$
$788$	−18.1909	−	18.1909i	−0.648024	−	0.648024i
$789$	−42.2969	+	10.2550i	−1.50581	+	0.365088i
$790$	−15.9980	−	0.396069i	−0.569183	−	0.0140915i
$791$		−	41.4068i		−	1.47226i
$792$	10.5127	+	3.36372i	0.373554	+	0.119525i
$793$	2.57887	−	2.57887i	0.0915785	−	0.0915785i
$794$	24.9231			0.884487
$795$	−22.2889	+	34.5993i	−0.790505	+	1.22711i
$796$	−0.0497425			−0.00176308
$797$	16.2267	−	16.2267i	0.574780	−	0.574780i	−0.358680	−	0.933460i	$-0.616773\pi$
$797$	16.2267	−	16.2267i	0.574780	−	0.574780i	0.933460	+	0.358680i	$0.116773\pi$
$798$	−4.08308	−	2.48954i	−0.144540	−	0.0881286i
$799$		−	10.5297i		−	0.372516i
$800$	−3.35625	−	3.70616i	−0.118661	−	0.131032i
$801$	−1.45519	−	2.82457i	−0.0514166	−	0.0998012i
$802$	3.73800	+	3.73800i	0.131994	+	0.131994i
$803$	41.0152	+	41.0152i	1.44740	+	1.44740i
$804$	−4.64671	−	19.1654i	−0.163877	−	0.675913i
$805$	2.90867	+	3.05635i	0.102517	+	0.107722i
$806$		−	11.2880i		−	0.397602i
$807$	24.6819	−	40.4807i	0.868843	−	1.42499i
$808$	−5.08309	+	5.08309i	−0.178822	+	0.178822i
$809$	5.67777			0.199620			0.0998099	−	0.995007i	$-0.468177\pi$
$809$	5.67777			0.199620			0.0998099	+	0.995007i	$0.468177\pi$
$810$	−16.0925	−	12.0844i	−0.565432	−	0.424601i
$811$	51.2315			1.79898			0.899491	−	0.436939i	$-0.143937\pi$
$811$	51.2315			1.79898			0.899491	+	0.436939i	$0.143937\pi$
$812$	15.6723	−	15.6723i	0.549989	−	0.549989i
$813$	−23.1272	+	37.9309i	−0.811106	+	1.33029i
$814$		−	38.1147i		−	1.33592i
$815$	−0.866141	+	34.9851i	−0.0303396	+	1.22547i
$816$	0.880794	+	3.63285i	0.0308339	+	0.127175i
$817$	3.11201	+	3.11201i	0.108875	+	0.108875i
$818$	−11.0393	−	11.0393i	−0.385981	−	0.385981i
$819$	13.9798	+	27.1352i	0.488493	+	0.948181i
$820$	−8.85010	+	8.42247i	−0.309059	+	0.294125i
$821$			33.7096i			1.17647i	0.808688	+	0.588237i	$0.200178\pi$
$821$			33.7096i			1.17647i	−0.808688	+	0.588237i	$0.799822\pi$
$822$	−0.0524694	−	0.0319916i	−0.00183008	−	0.00111583i
$823$	30.6367	−	30.6367i	1.06793	−	1.06793i	0.0704107	−	0.997518i	$-0.477569\pi$
$823$	30.6367	−	30.6367i	1.06793	−	1.06793i	0.997518	−	0.0704107i	$-0.0224310\pi$
$824$	7.41335			0.258256
$825$	17.9134	−	26.3510i	0.623666	−	0.917426i
$826$	30.6978			1.06811
$827$	−12.6509	+	12.6509i	−0.439913	+	0.439913i	−0.891983	−	0.452069i	$-0.850686\pi$
$827$	−12.6509	+	12.6509i	−0.439913	+	0.439913i	0.452069	+	0.891983i	$0.350686\pi$
$828$	1.95270	+	0.624797i	0.0678609	+	0.0217132i
$829$			9.54714i			0.331586i	0.986161	+	0.165793i	$0.0530183\pi$
$829$			9.54714i			0.331586i	−0.986161	+	0.165793i	$0.946982\pi$
$830$	−6.10673	+	5.81167i	−0.211968	+	0.201726i
$831$	−25.6110	+	6.20945i	−0.888434	+	0.215403i
$832$	2.60584	+	2.60584i	0.0903413	+	0.0903413i
$833$	0.950929	+	0.950929i	0.0329477	+	0.0329477i
$834$	26.8383	−	6.50702i	0.929334	−	0.225320i
$835$	0.499814	−	20.1884i	0.0172968	−	0.698649i
$836$		−	3.67926i		−	0.127250i
$837$	15.8750	+	1.14195i	0.548721	+	0.0394714i
$838$	−9.88285	+	9.88285i	−0.341397	+	0.341397i
$839$	5.90307			0.203796			0.101898	−	0.994795i	$-0.467508\pi$
$839$	5.90307			0.203796			0.101898	+	0.994795i	$0.467508\pi$
$840$	−10.4514	+	2.26164i	−0.360608	+	0.0780342i
$841$	35.4407			1.22209
$842$	−14.4424	+	14.4424i	−0.497719	+	0.497719i
$843$	22.1265	+	13.4909i	0.762076	+	0.464652i
$844$		−	27.0957i		−	0.932674i
$845$	−0.895339	−	0.940797i	−0.0308006	−	0.0323644i
$846$	13.0116	−	6.70346i	0.447349	−	0.230470i
$847$	4.95289	+	4.95289i	0.170183	+	0.170183i
$848$	7.51422	+	7.51422i	0.258039	+	0.258039i
$849$	8.45110	+	34.8567i	0.290041	+	1.19628i
$850$	10.7777	+	0.533986i	0.369673	+	0.0183156i
$851$		−	7.07964i		−	0.242687i
$852$	3.67709	−	6.03079i	0.125975	−	0.206611i
$853$	2.34098	−	2.34098i	0.0801538	−	0.0801538i	−0.665893	−	0.746047i	$-0.731949\pi$
$853$	2.34098	−	2.34098i	0.0801538	−	0.0801538i	0.746047	+	0.665893i	$0.231949\pi$
$854$	2.73243			0.0935018
$855$	−2.20181	+	6.33656i	−0.0753002	+	0.216706i
$856$	5.24746			0.179355
$857$	4.58336	−	4.58336i	0.156565	−	0.156565i	−0.624478	−	0.781042i	$-0.714688\pi$
$857$	4.58336	−	4.58336i	0.156565	−	0.156565i	0.781042	+	0.624478i	$0.214688\pi$
$858$	−12.2257	+	20.0514i	−0.417379	+	0.684544i
$859$		−	0.916695i		−	0.0312772i	−0.999878	−	0.0156386i	$-0.995022\pi$
$859$		−	0.916695i		−	0.0312772i	0.999878	−	0.0156386i	$-0.00497813\pi$
$860$	9.83803	+	0.243564i	0.335474	+	0.00830547i
$861$	6.15659	+	25.3930i	0.209816	+	0.865390i
$862$	11.0195	+	11.0195i	0.375327	+	0.375327i
$863$	6.51118	+	6.51118i	0.221643	+	0.221643i	0.809190	−	0.587547i	$-0.199906\pi$
$863$	6.51118	+	6.51118i	0.221643	+	0.221643i	−0.587547	+	0.809190i	$0.699906\pi$
$864$	−3.92838	+	3.40115i	−0.133646	+	0.115709i
$865$	1.24270	+	0.0307662i	0.0422532	+	0.00104608i
$866$		−	32.9732i		−	1.12048i
$867$	18.2522	+	11.1287i	0.619877	+	0.377951i
$868$	5.98005	−	5.98005i	0.202976	−	0.202976i
$869$	−26.3314			−0.893230
$870$	−26.1366	−	16.8372i	−0.886112	−	0.570834i
$871$	41.9589			1.42172
$872$	0.983171	−	0.983171i	0.0332944	−	0.0332944i
$873$	7.13583	−	22.3018i	0.241511	−	0.754801i
$874$		−	0.683406i		−	0.0231165i
$875$	−2.29013	+	30.7839i	−0.0774206	+	1.04068i
$876$	−26.5373	+	6.43404i	−0.896613	+	0.217386i
$877$	−12.0072	−	12.0072i	−0.405454	−	0.405454i	0.474696	−	0.880150i	$-0.342558\pi$
$877$	−12.0072	−	12.0072i	−0.405454	−	0.405454i	−0.880150	+	0.474696i	$0.842558\pi$
$878$	12.8936	+	12.8936i	0.435139	+	0.435139i
$879$	6.75964	−	1.63889i	0.227997	−	0.0552785i
$880$	−5.67165	−	5.95961i	−0.191191	−	0.200898i
$881$			14.1946i			0.478229i	0.970991	+	0.239114i	$0.0768571\pi$
$881$			14.1946i			0.478229i	−0.970991	+	0.239114i	$0.923143\pi$
$882$	−0.569683	+	1.78045i	−0.0191822	+	0.0599507i
$883$	9.98977	−	9.98977i	0.336183	−	0.336183i	−0.518746	−	0.854928i	$-0.673601\pi$
$883$	9.98977	−	9.98977i	0.336183	−	0.336183i	0.854928	+	0.518746i	$0.173601\pi$
$884$	−7.95340			−0.267502
$885$	−9.10750	−	42.0871i	−0.306145	−	1.41474i
$886$	−7.01177			−0.235565
$887$	−33.6571	+	33.6571i	−1.13009	+	1.13009i	−0.139933	+	0.990161i	$0.544689\pi$
$887$	−33.6571	+	33.6571i	−1.13009	+	1.13009i	−0.990161	+	0.139933i	$0.955311\pi$
$888$	15.3198	+	9.34081i	0.514100	+	0.313457i
$889$		−	53.2555i		−	1.78613i
$890$	−0.0586146	+	2.36755i	−0.00196477	+	0.0793606i
$891$	−26.9628	−	19.2223i	−0.903288	−	0.643973i
$892$	−19.2124	−	19.2124i	−0.643278	−	0.643278i
$893$	−3.44995	−	3.44995i	−0.115448	−	0.115448i
$894$	−7.22506	−	29.7999i	−0.241642	−	0.996656i
$895$	−11.7657	+	11.1972i	−0.393282	+	0.374280i
$896$			2.76100i			0.0922385i
$897$	−2.27088	+	3.72446i	−0.0758224	+	0.124356i
$898$	22.6668	−	22.6668i	0.756401	−	0.756401i
$899$	24.5886			0.820076
$900$	6.20149	+	13.6580i	0.206716	+	0.455267i
$901$	−22.9345			−0.764058
$902$	−14.2146	+	14.2146i	−0.473295	+	0.473295i
$903$	10.9566	−	17.9698i	0.364612	−	0.597999i
$904$			14.9970i			0.498794i
$905$	18.5463	−	17.6502i	0.616501	−	0.586713i
$906$	−5.58833	−	23.0492i	−0.185660	−	0.765757i
$907$	21.1853	+	21.1853i	0.703446	+	0.703446i	0.965149	−	0.261703i	$-0.0842840\pi$
$907$	21.1853	+	21.1853i	0.703446	+	0.703446i	−0.261703	+	0.965149i	$0.584284\pi$
$908$	3.11027	+	3.11027i	0.103218	+	0.103218i
$909$	19.1711	−	9.87674i	0.635864	−	0.327591i
$910$	0.563102	−	22.7448i	0.0186666	−	0.753981i
$911$		−	26.7273i		−	0.885515i	−0.896641	−	0.442757i	$-0.854000\pi$
$911$		−	26.7273i		−	0.885515i	0.896641	−	0.442757i	$-0.146000\pi$
$912$	1.47884	+	0.901679i	0.0489694	+	0.0298576i
$913$	−9.80835	+	9.80835i	−0.324609	+	0.324609i
$914$	−6.23017			−0.206076
$915$	−0.810663	−	3.74620i	−0.0267997	−	0.123845i
$916$	6.10439			0.201695
$917$	30.9493	−	30.9493i	1.02204	−	1.02204i
$918$	0.804604	−	11.1854i	0.0265559	−	0.369173i
$919$			54.3196i			1.79184i	0.444218	+	0.895919i	$0.353482\pi$
$919$			54.3196i			1.79184i	−0.444218	+	0.895919i	$0.646518\pi$
$920$	−1.05348	−	1.10697i	−0.0347324	−	0.0364958i
$921$	−31.3477	+	7.60034i	−1.03294	+	0.250440i
$922$	5.90072	+	5.90072i	0.194330	+	0.194330i
$923$	10.6267	+	10.6267i	0.349783	+	0.349783i
$924$	−17.0995	+	4.14582i	−0.562532	+	0.136387i
$925$	38.3934	−	34.7685i	1.26237	−	1.14318i
$926$		−	1.25097i		−	0.0411095i
$927$	−21.1822	−	6.77758i	−0.695713	−	0.222605i
$928$	−5.67630	+	5.67630i	−0.186334	+	0.186334i
$929$	−53.5187			−1.75589			−0.877946	−	0.478760i	$-0.841087\pi$
$929$	−53.5187			−1.75589			−0.877946	+	0.478760i	$0.841087\pi$
$930$	−9.97291	−	6.42456i	−0.327024	−	0.210669i
$931$	0.623122			0.0204220
$932$	−10.7007	+	10.7007i	−0.350513	+	0.350513i
$933$	−32.6428	−	19.9029i	−1.06868	−	0.651593i
$934$		−	3.46013i		−	0.113219i
$935$	17.7501	+	0.439448i	0.580492	+	0.0143715i
$936$	−5.06330	−	9.82804i	−0.165499	−	0.321239i
$937$	19.5835	+	19.5835i	0.639766	+	0.639766i	0.950498	−	0.310732i	$-0.100574\pi$
$937$	19.5835	+	19.5835i	0.639766	+	0.639766i	−0.310732	+	0.950498i	$0.600574\pi$
$938$	22.2286	+	22.2286i	0.725791	+	0.725791i
$939$	−5.94555	−	24.5225i	−0.194026	−	0.800262i
$940$	−10.9064	−	0.270014i	−0.355726	−	0.00880687i
$941$		−	0.189949i		−	0.00619216i	−0.999995	−	0.00309608i	$-0.999014\pi$
$941$		−	0.189949i		−	0.00619216i	0.999995	−	0.00309608i	$-0.000985514\pi$
$942$	1.40541	−	2.30501i	0.0457906	−	0.0751012i
$943$	−2.64030	+	2.64030i	−0.0859801	+	0.0859801i
$944$	−11.1184			−0.361872
$945$	31.9305	+	3.09290i	1.03870	+	0.100612i
$946$	16.1926			0.526466
$947$	27.1729	−	27.1729i	0.883001	−	0.883001i	−0.110838	−	0.993839i	$-0.535353\pi$
$947$	27.1729	−	27.1729i	0.883001	−	0.883001i	0.993839	+	0.110838i	$0.0353534\pi$
$948$	6.45305	−	10.5836i	0.209585	−	0.343741i
$949$		−	58.0982i		−	1.88595i
$950$	3.70616	−	3.35625i	0.120244	−	0.108891i
$951$	−7.53095	−	31.0615i	−0.244208	−	1.00724i
$952$	−4.21349	−	4.21349i	−0.136560	−	0.136560i
$953$	40.9711	+	40.9711i	1.32718	+	1.32718i	0.907816	+	0.419369i	$0.137748\pi$
$953$	40.9711	+	40.9711i	1.32718	+	1.32718i	0.419369	+	0.907816i	$0.362252\pi$
$954$	−14.6006	−	28.3402i	−0.472711	−	0.917547i
$955$	21.8836	+	22.9947i	0.708138	+	0.744092i
$956$			7.74663i			0.250544i
$957$	−43.6779	−	26.6313i	−1.41191	−	0.860867i
$958$	−0.744901	+	0.744901i	−0.0240667	+	0.0240667i
$959$	0.0979604			0.00316330
$960$	3.78537	−	0.819140i	0.122172	−	0.0264376i
$961$	−21.6178			−0.697347
$962$	−26.9948	+	26.9948i	−0.870348	+	0.870348i
$963$	−14.9936	−	4.79744i	−0.483161	−	0.154595i
$964$		−	11.5977i		−	0.373535i
$965$	−0.904295	+	36.5262i	−0.0291103	+	1.17582i
$966$	−3.17616	+	0.770068i	−0.102191	+	0.0247765i
$967$	−20.4865	−	20.4865i	−0.658800	−	0.658800i	0.296296	−	0.955096i	$-0.404248\pi$
$967$	−20.4865	−	20.4865i	−0.658800	−	0.658800i	−0.955096	+	0.296296i	$0.904248\pi$
$968$	−1.79388	−	1.79388i	−0.0576573	−	0.0576573i
$969$	−3.63285	+	0.880794i	−0.116704	+	0.0282952i
$970$	−12.6428	+	12.0319i	−0.405935	+	0.386320i
$971$			24.5415i			0.787575i	0.919202	+	0.393787i	$0.128835\pi$
$971$			24.5415i			0.787575i	−0.919202	+	0.393787i	$0.871165\pi$
$972$	14.3340	−	6.12661i	0.459765	−	0.196511i
$973$	−31.1279	+	31.1279i	−0.997914	+	0.997914i
$974$	8.59789			0.275494
$975$	−31.3504	+	5.97595i	−1.00402	+	0.191383i
$976$	−0.989652			−0.0316780
$977$	−40.9755	+	40.9755i	−1.31092	+	1.31092i	−0.390189	+	0.920735i	$0.627590\pi$
$977$	−40.9755	+	40.9755i	−1.31092	+	1.31092i	−0.920735	+	0.390189i	$0.872410\pi$
$978$	−23.1448	−	14.1118i	−0.740088	−	0.451246i
$979$			3.89680i			0.124542i
$980$	1.00932	−	0.960555i	0.0322417	−	0.0306838i
$981$	−3.70807	+	1.91036i	−0.118390	+	0.0609931i
$982$	−12.8762	−	12.8762i	−0.410897	−	0.410897i
$983$	22.7648	+	22.7648i	0.726085	+	0.726085i	0.969838	−	0.243752i	$-0.0783783\pi$
$983$	22.7648	+	22.7648i	0.726085	+	0.726085i	−0.243752	+	0.969838i	$0.578378\pi$
$984$	−2.22984	−	9.19702i	−0.0710847	−	0.293190i
$985$	1.42373	−	57.5070i	0.0453637	−	1.83233i
$986$		−	17.3249i		−	0.551737i
$987$	−12.1464	+	19.9212i	−0.386623	+	0.634100i
$988$	−2.60584	+	2.60584i	−0.0829028	+	0.0829028i
$989$	3.00770			0.0956394
$990$	10.7571	+	22.2137i	0.341883	+	0.705996i
$991$	34.9385			1.10986			0.554930	−	0.831897i	$-0.312745\pi$
$991$	34.9385			1.10986			0.554930	+	0.831897i	$0.312745\pi$
$992$	−2.16590	+	2.16590i	−0.0687674	+	0.0687674i
$993$	−22.5363	+	36.9617i	−0.715167	+	1.17294i
$994$			11.2595i			0.357129i
$995$	−0.0766792	−	0.0805724i	−0.00243089	−	0.00255432i
$996$	−1.53863	−	6.34612i	−0.0487535	−	0.201084i
$997$	23.0397	+	23.0397i	0.729676	+	0.729676i	0.970555	−	0.240879i	$-0.0774357\pi$
$997$	23.0397	+	23.0397i	0.729676	+	0.729676i	−0.240879	+	0.970555i	$0.577436\pi$
$998$	−6.07427	−	6.07427i	−0.192278	−	0.192278i
$999$	−35.2337	−	40.6955i	−1.11474	−	1.28755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.7	✓	36
3.2	odd	2	inner	570.2.k.b.77.17	yes	36
5.3	odd	4	inner	570.2.k.b.533.17	yes	36
15.8	even	4	inner	570.2.k.b.533.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.7	✓	36	1.1	even	1	trivial
570.2.k.b.77.17	yes	36	3.2	odd	2	inner
570.2.k.b.533.7	yes	36	15.8	even	4	inner
570.2.k.b.533.17	yes	36	5.3	odd	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) q^{3} -1.00000i q^{4} +(1.61979 - 1.54152i) q^{5} +(0.408116 + 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.37395 - 2.66688i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.901679 - 1.47884i) q^{3} -1.00000i q^{4} +(1.61979 - 1.54152i) q^{5} +(0.408116 + 1.68328i) q^{6} +(-1.95232 - 1.95232i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.37395 - 2.66688i) q^{9} +(-0.0553424 + 2.23538i) q^{10} +3.67926i q^{11} +(-1.47884 - 0.901679i) q^{12} +(2.60584 - 2.60584i) q^{13} +2.76100 q^{14} +(-0.819140 - 3.78537i) q^{15} -1.00000 q^{16} +(1.52607 - 1.52607i) q^{17} +(2.85730 + 0.914240i) q^{18} -1.00000i q^{19} +(-1.54152 - 1.61979i) q^{20} +(-4.64754 + 1.12681i) q^{21} +(-2.60163 - 2.60163i) q^{22} +(-0.483241 - 0.483241i) q^{23} +(1.68328 - 0.408116i) q^{24} +(0.247423 - 4.99387i) q^{25} +3.68522i q^{26} +(-5.18276 - 0.372814i) q^{27} +(-1.95232 + 1.95232i) q^{28} -8.02750 q^{29} +(3.25588 + 2.09744i) q^{30} -3.06305 q^{31} +(0.707107 - 0.707107i) q^{32} +(5.44104 + 3.31751i) q^{33} +2.15819i q^{34} +(-6.17189 - 0.152800i) q^{35} +(-2.66688 + 1.37395i) q^{36} +(7.32517 + 7.32517i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-1.50400 - 6.20326i) q^{39} +(2.23538 + 0.0553424i) q^{40} -5.46374i q^{41} +(2.48954 - 4.08308i) q^{42} +(-3.11201 + 3.11201i) q^{43} +3.67926 q^{44} +(-6.33656 - 2.20181i) q^{45} +0.683406 q^{46} +(3.44995 - 3.44995i) q^{47} +(-0.901679 + 1.47884i) q^{48} +0.623122i q^{49} +(3.35625 + 3.70616i) q^{50} +(-0.880794 - 3.63285i) q^{51} +(-2.60584 - 2.60584i) q^{52} +(-7.51422 - 7.51422i) q^{53} +(3.92838 - 3.40115i) q^{54} +(5.67165 + 5.95961i) q^{55} -2.76100i q^{56} +(-1.47884 - 0.901679i) q^{57} +(5.67630 - 5.67630i) q^{58} +11.1184 q^{59} +(-3.78537 + 0.819140i) q^{60} +0.989652 q^{61} +(2.16590 - 2.16590i) q^{62} +(-2.52422 + 7.88901i) q^{63} +1.00000i q^{64} +(0.203949 - 8.23787i) q^{65} +(-6.19323 + 1.50156i) q^{66} +(8.05094 + 8.05094i) q^{67} +(-1.52607 - 1.52607i) q^{68} +(-1.15037 + 0.278909i) q^{69} +(4.47223 - 4.25614i) q^{70} +4.07805i q^{71} +(0.914240 - 2.85730i) q^{72} +(11.1477 - 11.1477i) q^{73} -10.3593 q^{74} +(-7.16206 - 4.86877i) q^{75} -1.00000 q^{76} +(7.18309 - 7.18309i) q^{77} +(5.44985 + 3.32288i) q^{78} +7.15671i q^{79} +(-1.61979 + 1.54152i) q^{80} +(-5.22452 + 7.32833i) q^{81} +(3.86345 + 3.86345i) q^{82} +(2.66585 + 2.66585i) q^{83} +(1.12681 + 4.64754i) q^{84} +(0.119439 - 4.82439i) q^{85} -4.40105i q^{86} +(-7.23823 + 11.8714i) q^{87} +(-2.60163 + 2.60163i) q^{88} +1.05913 q^{89} +(6.03754 - 2.92371i) q^{90} -10.1749 q^{91} +(-0.483241 + 0.483241i) q^{92} +(-2.76188 + 4.52976i) q^{93} +4.87897i q^{94} +(-1.54152 - 1.61979i) q^{95} +(-0.408116 - 1.68328i) q^{96} +(5.51911 + 5.51911i) q^{97} +(-0.440614 - 0.440614i) q^{98} +(9.81214 - 5.05512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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