LMFDB - Embedded newform 700.2.be.e.443.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(107,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.4
Character	$\chi$	$=$	700.443
Dual form			700.2.be.e.207.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18977 + 0.764487i) q^{2} +(2.38471 + 0.638980i) q^{3} +(0.831118 - 1.81913i) q^{4} +(-3.32575 + 1.06284i) q^{6} +(2.10106 - 1.60796i) q^{7} +(0.401862 + 2.79973i) q^{8} +(2.68045 + 1.54756i) q^{9} +(4.09588 - 2.36476i) q^{11} +(3.14436 - 3.80703i) q^{12} +(-0.0592655 - 0.0592655i) q^{13} +(-1.27053 + 3.51934i) q^{14} +(-2.61849 - 3.02383i) q^{16} +(-4.77484 - 1.27942i) q^{17} +(-4.37222 + 0.207927i) q^{18} +(1.31544 - 2.27842i) q^{19} +(6.03788 - 2.49197i) q^{21} +(-3.06534 + 5.94478i) q^{22} +(-0.292774 - 1.09265i) q^{23} +(-0.830651 + 6.93332i) q^{24} +(0.115820 + 0.0252047i) q^{26} +(0.166053 + 0.166053i) q^{27} +(-1.17885 - 5.15852i) q^{28} +7.27332i q^{29} +(4.01558 - 2.31840i) q^{31} +(5.42708 + 1.59587i) q^{32} +(11.2785 - 3.02207i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(0.596933 + 2.22779i) q^{37} +(0.176741 + 3.71644i) q^{38} +(-0.103461 - 0.179200i) q^{39} -5.71767 q^{41} +(-5.27862 + 7.58075i) q^{42} +(-1.57302 + 1.57302i) q^{43} +(-0.897647 - 9.41635i) q^{44} +(1.18365 + 1.07618i) q^{46} +(2.67468 - 0.716679i) q^{47} +(-4.31215 - 8.88410i) q^{48} +(1.82895 - 6.75684i) q^{49} +(-10.5691 - 6.10206i) q^{51} +(-0.157068 + 0.0585551i) q^{52} +(-2.44441 + 9.12265i) q^{53} +(-0.324510 - 0.0706197i) q^{54} +(5.34619 + 5.23624i) q^{56} +(4.59281 - 4.59281i) q^{57} +(-5.56036 - 8.65360i) q^{58} +(1.67748 + 2.90547i) q^{59} +(-0.978771 + 1.69528i) q^{61} +(-3.00524 + 5.82822i) q^{62} +(8.12021 - 1.05853i) q^{63} +(-7.67701 + 2.25021i) q^{64} +(-11.1085 + 12.2179i) q^{66} +(-0.131802 + 0.491893i) q^{67} +(-6.29589 + 7.62273i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(-3.25558 + 8.12646i) q^{72} +(2.48257 - 9.26507i) q^{73} +(-2.41333 - 2.19421i) q^{74} +(-3.05145 - 4.28660i) q^{76} +(4.80329 - 11.5545i) q^{77} +(0.260092 + 0.134113i) q^{78} +(-3.05204 + 5.28630i) q^{79} +(-4.35280 - 7.53927i) q^{81} +(6.80273 - 4.37109i) q^{82} +(-5.62620 + 5.62620i) q^{83} +(0.484971 - 13.0548i) q^{84} +(0.668982 - 3.07409i) q^{86} +(-4.64751 + 17.3447i) q^{87} +(8.26668 + 10.5171i) q^{88} +(14.4482 + 8.34169i) q^{89} +(-0.219817 - 0.0292243i) q^{91} +(-2.23100 - 0.375524i) q^{92} +(11.0574 - 2.96282i) q^{93} +(-2.63437 + 2.89745i) q^{94} +(11.9223 + 7.27348i) q^{96} +(-5.81505 + 5.81505i) q^{97} +(2.98949 + 9.43732i) q^{98} +14.6384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.18977	+	0.764487i	−0.841296	+	0.540574i
$2$	−1.18977	+	0.764487i	−0.841296	+	0.540574i
$3$	2.38471	+	0.638980i	1.37681	+	0.368915i	0.869962	−	0.493119i	$-0.164143\pi$
$3$	2.38471	+	0.638980i	1.37681	+	0.368915i	0.506849	+	0.862035i	$0.330810\pi$
$4$	0.831118	−	1.81913i	0.415559	−	0.909566i
$5$		0			0
$5$		0			0
$6$	−3.32575	+	1.06284i	−1.35773	+	0.433901i
$7$	2.10106	−	1.60796i	0.794128	−	0.607751i
$7$	2.10106	−	1.60796i	0.794128	−	0.607751i
$8$	0.401862	+	2.79973i	0.142080	+	0.989855i
$9$	2.68045	+	1.54756i	0.893484	+	0.515853i
$10$		0			0
$11$	4.09588	−	2.36476i	1.23496	−	0.713002i	0.266897	−	0.963725i	$-0.414002\pi$
$11$	4.09588	−	2.36476i	1.23496	−	0.713002i	0.968059	+	0.250723i	$0.0806684\pi$
$12$	3.14436	−	3.80703i	0.907699	−	1.09899i
$13$	−0.0592655	−	0.0592655i	−0.0164373	−	0.0164373i	0.698840	−	0.715278i	$-0.253700\pi$
$13$	−0.0592655	−	0.0592655i	−0.0164373	−	0.0164373i	−0.715278	+	0.698840i	$0.753700\pi$
$14$	−1.27053	+	3.51934i	−0.339563	+	0.940583i
$15$		0			0
$16$	−2.61849	−	3.02383i	−0.654621	−	0.755957i
$17$	−4.77484	−	1.27942i	−1.15807	−	0.310304i	−0.371875	−	0.928283i	$-0.621285\pi$
$17$	−4.77484	−	1.27942i	−1.15807	−	0.310304i	−0.786195	+	0.617979i	$0.787952\pi$
$18$	−4.37222	+	0.207927i	−1.03054	+	0.0490090i
$19$	1.31544	−	2.27842i	0.301784	−	0.522705i	−0.674756	−	0.738041i	$-0.735751\pi$
$19$	1.31544	−	2.27842i	0.301784	−	0.522705i	0.976540	+	0.215336i	$0.0690846\pi$
$20$		0			0
$21$	6.03788	−	2.49197i	1.31757	−	0.543792i
$22$	−3.06534	+	5.94478i	−0.653533	+	1.26743i
$23$	−0.292774	−	1.09265i	−0.0610475	−	0.227832i	0.928661	−	0.370929i	$-0.120961\pi$
$23$	−0.292774	−	1.09265i	−0.0610475	−	0.227832i	−0.989709	+	0.143097i	$0.954294\pi$
$24$	−0.830651	+	6.93332i	−0.169556	+	1.41526i
$25$		0			0
$26$	0.115820	+	0.0252047i	0.0227142	+	0.00494306i
$27$	0.166053	+	0.166053i	0.0319568	+	0.0319568i
$28$	−1.17885	−	5.15852i	−0.222782	−	0.974868i
$29$			7.27332i			1.35062i	0.737533	+	0.675311i	$0.235991\pi$
$29$			7.27332i			1.35062i	−0.737533	+	0.675311i	$0.764009\pi$
$30$		0			0
$31$	4.01558	−	2.31840i	0.721219	−	0.416396i	−0.0939821	−	0.995574i	$-0.529960\pi$
$31$	4.01558	−	2.31840i	0.721219	−	0.416396i	0.815201	+	0.579178i	$0.196626\pi$
$32$	5.42708	+	1.59587i	0.959381	+	0.282112i
$33$	11.2785	−	3.02207i	1.96334	−	0.526075i
$34$	6.65908	−	2.12809i	1.14202	−	0.364965i
$35$		0			0
$36$	5.04299	−	3.58989i	0.840498	−	0.598315i
$37$	0.596933	+	2.22779i	0.0981352	+	0.366246i	0.997476	−	0.0710024i	$-0.0226198\pi$
$37$	0.596933	+	2.22779i	0.0981352	+	0.366246i	−0.899341	+	0.437248i	$0.855953\pi$
$38$	0.176741	+	3.71644i	0.0286712	+	0.602886i
$39$	−0.103461	−	0.179200i	−0.0165671	−	0.0286950i
$40$		0			0
$41$	−5.71767			−0.892950			−0.446475	−	0.894796i	$-0.647321\pi$
$41$	−5.71767			−0.892950			−0.446475	+	0.894796i	$0.647321\pi$
$42$	−5.27862	+	7.58075i	−0.814509	+	1.16974i
$43$	−1.57302	+	1.57302i	−0.239883	+	0.239883i	−0.816802	−	0.576918i	$-0.804255\pi$
$43$	−1.57302	+	1.57302i	−0.239883	+	0.239883i	0.576918	+	0.816802i	$0.304255\pi$
$44$	−0.897647	−	9.41635i	−0.135325	−	1.41957i
$45$		0			0
$46$	1.18365	+	1.07618i	0.174519	+	0.158674i
$47$	2.67468	−	0.716679i	0.390143	−	0.104538i	−0.0584148	−	0.998292i	$-0.518605\pi$
$47$	2.67468	−	0.716679i	0.390143	−	0.104538i	0.448558	+	0.893754i	$0.351938\pi$
$48$	−4.31215	−	8.88410i	−0.622406	−	1.28231i
$49$	1.82895	−	6.75684i	0.261278	−	0.965264i
$50$		0			0
$51$	−10.5691	−	6.10206i	−1.47997	−	0.854459i
$52$	−0.157068	+	0.0585551i	−0.0217815	+	0.00812014i
$53$	−2.44441	+	9.12265i	−0.335765	+	1.25309i	0.567272	+	0.823530i	$0.307999\pi$
$53$	−2.44441	+	9.12265i	−0.335765	+	1.25309i	−0.903037	+	0.429562i	$0.858668\pi$
$54$	−0.324510	−	0.0706197i	−0.0441602	−	0.00961013i
$55$		0			0
$56$	5.34619	+	5.23624i	0.714415	+	0.699723i
$57$	4.59281	−	4.59281i	0.608333	−	0.608333i
$58$	−5.56036	−	8.65360i	−0.730112	−	1.13627i
$59$	1.67748	+	2.90547i	0.218389	+	0.378260i	0.954315	−	0.298801i	$-0.0965866\pi$
$59$	1.67748	+	2.90547i	0.218389	+	0.378260i	−0.735927	+	0.677061i	$0.763253\pi$
$60$		0			0
$61$	−0.978771	+	1.69528i	−0.125319	+	0.217058i	−0.921857	−	0.387529i	$-0.873329\pi$
$61$	−0.978771	+	1.69528i	−0.125319	+	0.217058i	0.796539	+	0.604587i	$0.206662\pi$
$62$	−3.00524	+	5.82822i	−0.381666	+	0.740185i
$63$	8.12021	−	1.05853i	1.02305	−	0.133362i
$64$	−7.67701	+	2.25021i	−0.959627	+	0.281277i
$65$		0			0
$66$	−11.1085	+	12.2179i	−1.36737	+	1.50391i
$67$	−0.131802	+	0.491893i	−0.0161022	+	0.0600943i	−0.973509	−	0.228647i	$-0.926570\pi$
$67$	−0.131802	+	0.491893i	−0.0161022	+	0.0600943i	0.957407	+	0.288741i	$0.0932366\pi$
$68$	−6.29589	+	7.62273i	−0.763488	+	0.924392i
$69$		−	2.79272i		−	0.336204i
$70$		0			0
$71$			14.4625i			1.71638i	0.513329	+	0.858192i	$0.328412\pi$
$71$			14.4625i			1.71638i	−0.513329	+	0.858192i	$0.671588\pi$
$72$	−3.25558	+	8.12646i	−0.383674	+	0.957712i
$73$	2.48257	−	9.26507i	0.290563	−	1.08439i	−0.654115	−	0.756395i	$-0.726959\pi$
$73$	2.48257	−	9.26507i	0.290563	−	1.08439i	0.944678	−	0.327999i	$-0.106374\pi$
$74$	−2.41333	−	2.19421i	−0.280544	−	0.255072i
$75$		0			0
$76$	−3.05145	−	4.28660i	−0.350026	−	0.491707i
$77$	4.80329	−	11.5545i	0.547385	−	1.31676i
$78$	0.260092	+	0.134113i	0.0294496	+	0.0151853i
$79$	−3.05204	+	5.28630i	−0.343382	+	0.594755i	−0.985058	−	0.172221i	$-0.944906\pi$
$79$	−3.05204	+	5.28630i	−0.343382	+	0.594755i	0.641677	+	0.766975i	$0.278239\pi$
$80$		0			0
$81$	−4.35280	−	7.53927i	−0.483644	−	0.837696i
$82$	6.80273	−	4.37109i	0.751235	−	0.482706i
$83$	−5.62620	+	5.62620i	−0.617555	+	0.617555i	−0.944904	−	0.327348i	$-0.893845\pi$
$83$	−5.62620	+	5.62620i	−0.617555	+	0.617555i	0.327348	+	0.944904i	$0.393845\pi$
$84$	0.484971	−	13.0548i	0.0529146	−	1.42440i
$85$		0			0
$86$	0.668982	−	3.07409i	0.0721382	−	0.331488i
$87$	−4.64751	+	17.3447i	−0.498265	+	1.85955i
$88$	8.26668	+	10.5171i	0.881231	+	1.12112i
$89$	14.4482	+	8.34169i	1.53151	+	0.884218i	0.999292	+	0.0376100i	$0.0119745\pi$
$89$	14.4482	+	8.34169i	1.53151	+	0.884218i	0.532217	+	0.846608i	$0.321359\pi$
$90$		0			0
$91$	−0.219817	−	0.0292243i	−0.0230431	−	0.00306354i
$92$	−2.23100	−	0.375524i	−0.232598	−	0.0391511i
$93$	11.0574	−	2.96282i	1.14660	−	0.307230i
$94$	−2.63437	+	2.89745i	−0.271715	+	0.298849i
$95$		0			0
$96$	11.9223	+	7.27348i	1.21681	+	0.742346i
$97$	−5.81505	+	5.81505i	−0.590429	+	0.590429i	−0.937747	−	0.347318i	$-0.887092\pi$
$97$	−5.81505	+	5.81505i	−0.590429	+	0.590429i	0.347318	+	0.937747i	$0.387092\pi$
$98$	2.98949	+	9.43732i	0.301984	+	0.953313i
$99$	14.6384			1.47122
$100$		0			0
$101$	4.28723	+	7.42571i	0.426596	+	0.738885i	0.996568	−	0.0827785i	$-0.0263794\pi$
$101$	4.28723	+	7.42571i	0.426596	+	0.738885i	−0.569972	+	0.821664i	$0.693046\pi$
$102$	17.2398	−	0.819862i	1.70699	−	0.0811785i
$103$	0.845330	+	3.15482i	0.0832929	+	0.310853i	0.994985	−	0.100020i	$-0.0318906\pi$
$103$	0.845330	+	3.15482i	0.0832929	+	0.310853i	−0.911693	+	0.410873i	$0.865224\pi$
$104$	0.142111	−	0.189744i	0.0139351	−	0.0186059i
$105$		0			0
$106$	−4.06586	−	12.7226i	−0.394911	−	1.23573i
$107$	6.56081	−	1.75796i	0.634257	−	0.169949i	0.0726563	−	0.997357i	$-0.476852\pi$
$107$	6.56081	−	1.75796i	0.634257	−	0.169949i	0.561601	+	0.827408i	$0.310186\pi$
$108$	0.440081	−	0.164062i	0.0423468	−	0.0157869i
$109$	−3.39423	+	1.95966i	−0.325108	+	0.187701i	−0.653667	−	0.756782i	$-0.726770\pi$
$109$	−3.39423	+	1.95966i	−0.325108	+	0.187701i	0.328559	+	0.944483i	$0.393437\pi$
$110$		0			0
$111$			5.69404i			0.540455i
$112$	−10.3638	−	2.14285i	−0.979286	−	0.202480i
$113$	0.0280186	+	0.0280186i	0.00263577	+	0.00263577i	0.708423	−	0.705788i	$-0.249407\pi$
$113$	0.0280186	+	0.0280186i	0.00263577	+	0.00263577i	−0.705788	+	0.708423i	$0.749407\pi$
$114$	−1.95326	+	8.97555i	−0.182939	+	0.840637i
$115$		0			0
$116$	13.2311	+	6.04499i	1.22848	+	0.561263i
$117$	−0.0671414	−	0.250575i	−0.00620723	−	0.0231657i
$118$	−4.21701	−	2.17444i	−0.388207	−	0.200174i
$119$	−12.0895	+	4.98961i	−1.10824	+	0.457397i
$120$		0			0
$121$	5.68418	−	9.84529i	0.516744	−	0.895026i
$122$	−0.131506	−	2.76526i	−0.0119060	−	0.250355i
$123$	−13.6350	−	3.65348i	−1.22942	−	0.329423i
$124$	−0.880048	−	9.23173i	−0.0790306	−	0.829034i
$125$		0			0
$126$	−8.85198	+	7.46721i	−0.788597	+	0.665232i
$127$	−6.53450	−	6.53450i	−0.579843	−	0.579843i	0.355017	−	0.934860i	$-0.384475\pi$
$127$	−6.53450	−	6.53450i	−0.579843	−	0.579843i	−0.934860	+	0.355017i	$0.884475\pi$
$128$	7.41364	−	8.54622i	0.655280	−	0.755386i
$129$	−4.75632	+	2.74606i	−0.418770	+	0.241777i
$130$		0			0
$131$	−3.19588	−	1.84514i	−0.279225	−	0.161211i	0.353847	−	0.935303i	$-0.384873\pi$
$131$	−3.19588	−	1.84514i	−0.279225	−	0.161211i	−0.633073	+	0.774092i	$0.718207\pi$
$132$	3.87624	−	23.0288i	0.337383	−	2.00440i
$133$	−0.899762	−	6.90228i	−0.0780193	−	0.598504i
$134$	−0.219231	−	0.686002i	−0.0189387	−	0.0592616i
$135$		0			0
$136$	1.66319	−	13.8824i	0.142618	−	1.19041i
$137$	−19.1819	−	5.13977i	−1.63882	−	0.439120i	−0.682366	−	0.731010i	$-0.739049\pi$
$137$	−19.1819	−	5.13977i	−1.63882	−	0.439120i	−0.956452	+	0.291890i	$0.905716\pi$
$138$	2.13500	+	3.32270i	0.181743	+	0.282847i
$139$	−1.15593			−0.0980447			−0.0490223	−	0.998798i	$-0.515611\pi$
$139$	−1.15593			−0.0980447			−0.0490223	+	0.998798i	$0.515611\pi$
$140$		0			0
$141$	6.83628			0.575719
$142$	−11.0564	−	17.2071i	−0.927833	−	1.44399i
$143$	−0.382893	−	0.102596i	−0.0320191	−	0.00857950i
$144$	−2.33917	−	12.1575i	−0.194931	−	1.01312i
$145$		0			0
$146$	4.12934	+	12.9212i	0.341746	+	1.06937i
$147$	8.67899	−	14.9444i	0.715831	−	1.23260i
$148$	4.54876	+	0.765652i	0.373906	+	0.0629362i
$149$	−5.37045	−	3.10063i	−0.439965	−	0.254014i	0.263618	−	0.964627i	$-0.415084\pi$
$149$	−5.37045	−	3.10063i	−0.439965	−	0.254014i	−0.703583	+	0.710613i	$0.748418\pi$
$150$		0			0
$151$	−8.72300	+	5.03623i	−0.709868	+	0.409842i	−0.811012	−	0.585029i	$-0.801083\pi$
$151$	−8.72300	+	5.03623i	−0.709868	+	0.409842i	0.101144	+	0.994872i	$0.467750\pi$
$152$	6.90759	+	2.76729i	0.560279	+	0.224457i
$153$	−10.8188	−	10.8188i	−0.874646	−	0.874646i
$154$	3.11847	+	17.4193i	0.251293	+	1.40369i
$155$		0			0
$156$	−0.411977	+	0.0392732i	−0.0329846	+	0.00314438i
$157$	14.0732	+	3.77089i	1.12316	+	0.300950i	0.772162	−	0.635426i	$-0.219175\pi$
$157$	14.0732	+	3.77089i	1.12316	+	0.300950i	0.350999	+	0.936376i	$0.385842\pi$
$158$	−0.410067	−	8.62274i	−0.0326232	−	0.685988i
$159$	−11.6584	+	20.1929i	−0.924570	+	1.60140i
$160$		0			0
$161$	−2.37206	−	1.82495i	−0.186945	−	0.143826i
$162$	10.9425	+	5.64235i	0.859725	+	0.443305i
$163$	−0.763938	−	2.85106i	−0.0598363	−	0.223312i	0.929533	−	0.368740i	$-0.120211\pi$
$163$	−0.763938	−	2.85106i	−0.0598363	−	0.223312i	−0.989369	+	0.145428i	$0.953544\pi$
$164$	−4.75206	+	10.4012i	−0.371073	+	0.812197i
$165$		0			0
$166$	2.39274	−	10.9950i	0.185713	−	0.853381i
$167$	−6.13096	−	6.13096i	−0.474428	−	0.474428i	0.428916	−	0.903344i	$-0.358895\pi$
$167$	−6.13096	−	6.13096i	−0.474428	−	0.474428i	−0.903344	+	0.428916i	$0.858895\pi$
$168$	9.40323	+	15.9030i	0.725475	+	1.22694i
$169$		−	12.9930i		−	0.999460i
$170$		0			0
$171$	7.05197	−	4.07146i	0.539278	−	0.311352i
$172$	1.55417	+	4.16890i	0.118504	+	0.317875i
$173$	−1.73431	+	0.464708i	−0.131857	+	0.0353311i	−0.324144	−	0.946008i	$-0.605076\pi$
$173$	−1.73431	+	0.464708i	−0.131857	+	0.0353311i	0.192287	+	0.981339i	$0.438410\pi$
$174$	−7.73035	−	24.1893i	−0.586037	−	1.83378i
$175$		0			0
$176$	−17.8756	−	6.19316i	−1.34743	−	0.466827i
$177$	2.14375	+	8.00057i	0.161134	+	0.601360i
$178$	−23.5672	+	1.12078i	−1.76644	+	0.0840057i
$179$	−10.7713	−	18.6564i	−0.805084	−	1.39445i	−0.916234	−	0.400643i	$-0.868787\pi$
$179$	−10.7713	−	18.6564i	−0.805084	−	1.39445i	0.111150	−	0.993804i	$-0.464547\pi$
$180$		0			0
$181$	−16.2122			−1.20504			−0.602520	−	0.798104i	$-0.705837\pi$
$181$	−16.2122			−1.20504			−0.602520	+	0.798104i	$0.705837\pi$
$182$	0.283874	−	0.133277i	0.0210421	−	0.00987915i
$183$	−3.41733	+	3.41733i	−0.252616	+	0.252616i
$184$	2.94146	−	1.25878i	0.216848	−	0.0927986i
$185$		0			0
$186$	−10.8907	+	11.9783i	−0.798548	+	0.878292i
$187$	−22.5827	+	6.05102i	−1.65141	+	0.442495i
$188$	0.919244	−	5.46125i	0.0670427	−	0.398303i
$189$	0.615893	+	0.0818818i	0.0447996	+	0.00595603i
$190$		0			0
$191$	14.2331	+	8.21746i	1.02987	+	0.594595i	0.916947	−	0.399009i	$-0.130646\pi$
$191$	14.2331	+	8.21746i	1.02987	+	0.594595i	0.112921	+	0.993604i	$0.463979\pi$
$192$	−19.7453	+	0.460637i	−1.42499	+	0.0332436i
$193$	−1.28369	+	4.79080i	−0.0924021	+	0.344849i	−0.996613	−	0.0822374i	$-0.973793\pi$
$193$	−1.28369	+	4.79080i	−0.0924021	+	0.344849i	0.904211	+	0.427087i	$0.140460\pi$
$194$	2.47306	−	11.3641i	0.177555	−	0.815897i
$195$		0			0
$196$	−10.7715	−	8.94283i	−0.769395	−	0.638774i
$197$	3.89922	−	3.89922i	0.277808	−	0.277808i	−0.554425	−	0.832233i	$-0.687062\pi$
$197$	3.89922	−	3.89922i	0.277808	−	0.277808i	0.832233	+	0.554425i	$0.187062\pi$
$198$	−17.4164	+	11.1909i	−1.23773	+	0.795302i
$199$	−9.44788	−	16.3642i	−0.669743	−	1.16003i	−0.977976	−	0.208717i	$-0.933071\pi$
$199$	−9.44788	−	16.3642i	−0.669743	−	1.16003i	0.308233	−	0.951311i	$-0.400262\pi$
$200$		0			0
$201$	−0.628620	+	1.08880i	−0.0443394	+	0.0767981i
$202$	−10.7777	−	5.55737i	−0.758316	−	0.391015i
$203$	11.6952	+	15.2817i	0.820842	+	1.07257i
$204$	−19.8846	+	14.1550i	−1.39220	+	0.991050i
$205$		0			0
$206$	−3.41757	−	3.10727i	−0.238113	−	0.216494i
$207$	0.906169	−	3.38187i	0.0629831	−	0.235056i
$208$	−0.0240228	+	0.334394i	−0.00166568	+	0.0231861i
$209$		−	12.4428i		−	0.860690i
$210$		0			0
$211$			10.9795i			0.755859i	0.925834	+	0.377929i	$0.123364\pi$
$211$			10.9795i			0.755859i	−0.925834	+	0.377929i	$0.876636\pi$
$212$	14.5637	+	12.0287i	1.00024	+	0.826135i
$213$	−9.24126	+	34.4888i	−0.633201	+	2.36314i
$214$	−6.46193	+	7.10723i	−0.441728	+	0.485840i
$215$		0			0
$216$	−0.398173	+	0.531633i	−0.0270922	+	0.0361731i
$217$	4.70911	−	11.3280i	0.319675	−	0.768993i
$218$	2.54022	−	4.92639i	0.172046	−	0.333657i
$219$	11.8404	−	20.5082i	0.800099	−	1.38581i
$220$		0			0
$221$	0.207158	+	0.358809i	0.0139350	+	0.0241361i
$222$	−4.35302	−	6.77462i	−0.292156	−	0.454683i
$223$	13.6990	−	13.6990i	0.917356	−	0.917356i	−0.0794806	−	0.996836i	$-0.525326\pi$
$223$	13.6990	−	13.6990i	0.917356	−	0.917356i	0.996836	+	0.0794806i	$0.0253262\pi$
$224$	13.9687	−	5.37349i	0.933326	−	0.359031i
$225$		0			0
$226$	−0.0547556	−	0.0119159i	−0.00364229	−	0.000792634i
$227$	5.94107	−	22.1724i	0.394322	−	1.47163i	−0.428609	−	0.903490i	$-0.640996\pi$
$227$	5.94107	−	22.1724i	0.394322	−	1.47163i	0.822931	−	0.568141i	$-0.192337\pi$
$228$	−4.53776	−	12.1721i	−0.300521	−	0.806117i
$229$	−10.3396	−	5.96955i	−0.683258	−	0.394479i	0.117824	−	0.993035i	$-0.462408\pi$
$229$	−10.3396	−	5.96955i	−0.683258	−	0.394479i	−0.801081	+	0.598556i	$0.795742\pi$
$230$		0			0
$231$	18.8375	−	24.4849i	1.23942	−	1.61099i
$232$	−20.3634	+	2.92287i	−1.33692	+	0.191896i
$233$	−22.9805	+	6.15761i	−1.50550	+	0.403399i	−0.914939	−	0.403592i	$-0.867762\pi$
$233$	−22.9805	+	6.15761i	−1.50550	+	0.403399i	−0.590565	+	0.806990i	$0.701095\pi$
$234$	0.271445	+	0.246799i	0.0177449	+	0.0161337i
$235$		0			0
$236$	6.67962	−	0.636759i	0.434806	−	0.0414495i
$237$	−10.6561	+	10.6561i	−0.692186	+	0.692186i
$238$	10.5693	−	15.1788i	0.685104	−	0.983894i
$239$	−1.50749			−0.0975113			−0.0487556	−	0.998811i	$-0.515526\pi$
$239$	−1.50749			−0.0975113			−0.0487556	+	0.998811i	$0.515526\pi$
$240$		0			0
$241$	9.26556	+	16.0484i	0.596847	+	1.03377i	0.993283	+	0.115708i	$0.0369136\pi$
$241$	9.26556	+	16.0484i	0.596847	+	1.03377i	−0.396436	+	0.918062i	$0.629753\pi$
$242$	0.763716	+	16.0591i	0.0490935	+	1.03232i
$243$	−5.74504	−	21.4408i	−0.368544	−	1.37543i
$244$	2.27047	+	3.18949i	0.145352	+	0.204186i
$245$		0			0
$246$	19.0155	−	6.07695i	1.21239	−	0.387452i
$247$	−0.212992	+	0.0570710i	−0.0135524	+	0.00363134i
$248$	8.10460	+	10.3109i	0.514642	+	0.654741i
$249$	−17.0119	+	9.82180i	−1.07808	+	0.622431i
$250$		0			0
$251$		−	18.0219i		−	1.13753i	−0.822500	−	0.568765i	$-0.807421\pi$
$251$		−	18.0219i		−	1.13753i	0.822500	−	0.568765i	$-0.192579\pi$
$252$	4.82325	−	15.6515i	0.303836	−	0.985952i
$253$	−3.78301	−	3.78301i	−0.237836	−	0.237836i
$254$	12.7701	+	2.77903i	0.801268	+	0.174372i
$255$		0			0
$256$	−2.28707	+	15.8357i	−0.142942	+	0.989731i
$257$	3.85933	+	14.4032i	0.240738	+	0.898448i	0.975478	+	0.220098i	$0.0706378\pi$
$257$	3.85933	+	14.4032i	0.240738	+	0.898448i	−0.734739	+	0.678350i	$0.762696\pi$
$258$	3.55961	−	6.90333i	0.221611	−	0.429783i
$259$	4.83638	+	3.72088i	0.300518	+	0.231204i
$260$		0			0
$261$	−11.2559	+	19.4958i	−0.696723	+	1.20676i
$262$	5.21295	−	0.247910i	0.322057	−	0.0153159i
$263$	−6.84826	−	1.83499i	−0.422282	−	0.113150i	0.0414191	−	0.999142i	$-0.486812\pi$
$263$	−6.84826	−	1.83499i	−0.422282	−	0.113150i	−0.463701	+	0.885992i	$0.653479\pi$
$264$	12.9934	+	30.3624i	0.799688	+	1.86868i
$265$		0			0
$266$	6.34722	+	7.52429i	0.389173	+	0.461344i
$267$	29.1246	+	29.1246i	1.78240	+	1.78240i
$268$	0.785275	+	0.648587i	0.0479683	+	0.0396188i
$269$	5.23463	−	3.02221i	0.319161	−	0.184268i	−0.331858	−	0.943329i	$-0.607675\pi$
$269$	5.23463	−	3.02221i	0.319161	−	0.184268i	0.651019	+	0.759062i	$0.274342\pi$
$270$		0			0
$271$	−20.3476	−	11.7477i	−1.23603	−	0.713622i	−0.267750	−	0.963488i	$-0.586280\pi$
$271$	−20.3476	−	11.7477i	−1.23603	−	0.713622i	−0.968280	+	0.249866i	$0.919613\pi$
$272$	8.63413	+	17.7884i	0.523521	+	1.07858i
$273$	−0.505525	−	0.210150i	−0.0305958	−	0.0127189i
$274$	26.7514	−	8.54914i	1.61611	−	0.516473i
$275$		0			0
$276$	−5.08032	−	2.32108i	−0.305799	−	0.139712i
$277$	22.5298	+	6.03684i	1.35369	+	0.362719i	0.861494	−	0.507768i	$-0.169529\pi$
$277$	22.5298	+	6.03684i	1.35369	+	0.362719i	0.492191	+	0.870487i	$0.336196\pi$
$278$	1.37529	−	0.883694i	0.0824846	−	0.0530004i
$279$	14.3514			0.859197
$280$		0			0
$281$	−19.3011			−1.15141			−0.575703	−	0.817659i	$-0.695272\pi$
$281$	−19.3011			−1.15141			−0.575703	+	0.817659i	$0.695272\pi$
$282$	−8.13362	+	5.22625i	−0.484350	+	0.311219i
$283$	6.88593	+	1.84508i	0.409326	+	0.109679i	0.457606	−	0.889155i	$-0.348707\pi$
$283$	6.88593	+	1.84508i	0.409326	+	0.109679i	−0.0482794	+	0.998834i	$0.515374\pi$
$284$	26.3092	+	12.0201i	1.56117	+	0.713259i
$285$		0			0
$286$	0.533989	−	0.170651i	0.0315754	−	0.0100908i
$287$	−12.0132	+	9.19377i	−0.709116	+	0.542691i
$288$	12.0773	+	12.6764i	0.711663	+	0.746963i
$289$	6.43980	+	3.71802i	0.378812	+	0.218707i
$290$		0			0
$291$	−17.5829	+	10.1515i	−1.03073	+	0.595091i
$292$	−14.7911	−	12.2165i	−0.865583	−	0.714916i
$293$	−1.29442	−	1.29442i	−0.0756208	−	0.0756208i	0.668285	−	0.743906i	$-0.267029\pi$
$293$	−1.29442	−	1.29442i	−0.0756208	−	0.0756208i	−0.743906	+	0.668285i	$0.767029\pi$
$294$	1.09880	+	24.4155i	0.0640832	+	1.42394i
$295$		0			0
$296$	−5.99732	+	2.56652i	−0.348587	+	0.149176i
$297$	1.07281	+	0.287458i	0.0622506	+	0.0166800i
$298$	8.76001	−	0.416596i	0.507454	−	0.0241327i
$299$	−0.0474048	+	0.0821076i	−0.00274149	+	0.00474840i
$300$		0			0
$301$	−0.775668	+	5.83436i	−0.0447088	+	0.336287i
$302$	6.52826	−	12.6606i	0.375659	−	0.728535i
$303$	5.47891	+	20.4476i	0.314755	+	1.17468i
$304$	−10.3340	+	1.98832i	−0.592696	+	0.114038i
$305$		0			0
$306$	21.1427	+	4.60106i	1.20865	+	0.263025i
$307$	3.86175	+	3.86175i	0.220402	+	0.220402i	0.808667	−	0.588266i	$-0.200189\pi$
$307$	3.86175	+	3.86175i	0.220402	+	0.220402i	−0.588266	+	0.808667i	$0.700189\pi$
$308$	−17.0271	−	18.3410i	−0.970209	−	1.04507i
$309$			8.06346i			0.458714i
$310$		0			0
$311$	17.7808	−	10.2657i	1.00826	−	0.582116i	0.0975749	−	0.995228i	$-0.468891\pi$
$311$	17.7808	−	10.2657i	1.00826	−	0.582116i	0.910680	+	0.413112i	$0.135558\pi$
$312$	0.460136	−	0.361678i	0.0260501	−	0.0204760i
$313$	26.9598	−	7.22385i	1.52386	−	0.408316i	0.602847	−	0.797856i	$-0.294033\pi$
$313$	26.9598	−	7.22385i	1.52386	−	0.408316i	0.921009	+	0.389540i	$0.127366\pi$
$314$	−19.6267	+	6.27225i	−1.10760	+	0.353964i
$315$		0			0
$316$	7.07986	+	9.94561i	0.398273	+	0.559484i
$317$	3.35388	+	12.5169i	0.188373	+	0.703016i	0.993883	+	0.110435i	$0.0352244\pi$
$317$	3.35388	+	12.5169i	0.188373	+	0.703016i	−0.805511	+	0.592581i	$0.798109\pi$
$318$	−1.56640	−	32.9377i	−0.0878394	−	1.84705i
$319$	17.1997	+	29.7907i	0.962996	+	1.66796i
$320$		0			0
$321$	16.7689			0.935949
$322$	4.21737	+	0.357866i	0.235025	+	0.0199431i
$323$	−9.19609	+	9.19609i	−0.511684	+	0.511684i
$324$	−17.3326	+	1.65229i	−0.962923	+	0.0917941i
$325$		0			0
$326$	3.08851	+	2.80809i	0.171057	+	0.155526i
$327$	−9.34642	+	2.50436i	−0.516858	+	0.138492i
$328$	−2.29771	−	16.0079i	−0.126870	−	0.883891i
$329$	4.46729	−	5.80657i	0.246290	−	0.320126i
$330$		0			0
$331$	6.41324	+	3.70269i	0.352504	+	0.203518i	0.665787	−	0.746142i	$-0.268096\pi$
$331$	6.41324	+	3.70269i	0.352504	+	0.203518i	−0.313284	+	0.949660i	$0.601429\pi$
$332$	5.55876	+	14.9108i	0.305077	+	0.818338i
$333$	−1.84758	+	6.89526i	−0.101247	+	0.377858i
$334$	11.9815	+	2.60741i	0.655598	+	0.142671i
$335$		0			0
$336$	−23.3454	−	11.7323i	−1.27359	−	0.640050i
$337$	5.81990	−	5.81990i	0.317030	−	0.317030i	−0.530595	−	0.847625i	$-0.678032\pi$
$337$	5.81990	−	5.81990i	0.317030	−	0.317030i	0.847625	+	0.530595i	$0.178032\pi$
$338$	9.93297	+	15.4587i	0.540282	+	0.840842i
$339$	0.0489128	+	0.0847195i	0.00265658	+	0.00460133i
$340$		0			0
$341$	10.9649	−	18.9918i	0.593782	−	1.02846i
$342$	−5.27767	+	10.2353i	−0.285384	+	0.553459i
$343$	−7.02198	−	17.1374i	−0.379151	−	0.925335i
$344$	−5.03617	−	3.77190i	−0.271532	−	0.203367i
$345$		0			0
$346$	1.70817	−	1.87876i	0.0918320	−	0.101003i
$347$	−2.85823	+	10.6671i	−0.153438	+	0.572638i	0.845796	+	0.533506i	$0.179126\pi$
$347$	−2.85823	+	10.6671i	−0.153438	+	0.572638i	−0.999234	+	0.0391317i	$0.987541\pi$
$348$	27.6897	+	22.8700i	1.48433	+	1.22596i
$349$			10.3995i			0.556672i	0.960484	+	0.278336i	$0.0897829\pi$
$349$			10.3995i			0.556672i	−0.960484	+	0.278336i	$0.910217\pi$
$350$		0			0
$351$		−	0.0196824i		−	0.00105057i
$352$	26.0025	−	6.29725i	1.38594	−	0.335644i
$353$	1.95306	−	7.28892i	0.103951	−	0.387950i	−0.894273	−	0.447522i	$-0.852307\pi$
$353$	1.95306	−	7.28892i	0.103951	−	0.387950i	0.998224	+	0.0595714i	$0.0189734\pi$
$354$	−8.66691	−	7.87999i	−0.460641	−	0.418817i
$355$		0			0
$356$	27.1828	−	19.3503i	1.44069	−	1.02556i
$357$	−32.0182	+	4.17380i	−1.69458	+	0.220901i
$358$	27.0780	+	13.9624i	1.43112	+	0.737935i
$359$	5.74179	−	9.94507i	0.303040	−	0.524881i	−0.673783	−	0.738929i	$-0.735332\pi$
$359$	5.74179	−	9.94507i	0.303040	−	0.524881i	0.976823	+	0.214049i	$0.0686651\pi$
$360$		0			0
$361$	6.03921	+	10.4602i	0.317853	+	0.550538i
$362$	19.2888	−	12.3940i	1.01380	−	0.651413i
$363$	19.8460	−	19.8460i	1.04165	−	1.04165i
$364$	−0.235857	+	0.375587i	−0.0123622	+	0.0196861i
$365$		0			0
$366$	1.45334	−	6.67835i	0.0759673	−	0.349083i
$367$	3.27735	−	12.2312i	0.171076	−	0.638465i	−0.826111	−	0.563508i	$-0.809451\pi$
$367$	3.27735	−	12.2312i	0.171076	−	0.638465i	0.997187	−	0.0749570i	$-0.0238820\pi$
$368$	−2.53735	+	3.74637i	−0.132269	+	0.195293i
$369$	−15.3259	−	8.84843i	−0.797836	−	0.460631i
$370$		0			0
$371$	9.53297	+	23.0978i	0.494927	+	1.19918i
$372$	3.80024	−	22.5773i	0.197033	−	1.17058i
$373$	−24.0550	+	6.44552i	−1.24552	+	0.333737i	−0.820605	−	0.571496i	$-0.806363\pi$
$373$	−24.0550	+	6.44552i	−1.24552	+	0.333737i	−0.424917	+	0.905232i	$0.639697\pi$
$374$	22.2424	−	24.4635i	1.15013	−	1.26498i
$375$		0			0
$376$	3.08137	+	7.20040i	0.158909	+	0.371332i
$377$	0.431057	−	0.431057i	0.0222006	−	0.0222006i
$378$	−0.795370	+	0.373422i	−0.0409094	+	0.0192067i
$379$	−4.18354			−0.214894			−0.107447	−	0.994211i	$-0.534268\pi$
$379$	−4.18354			−0.214894			−0.107447	+	0.994211i	$0.534268\pi$
$380$		0			0
$381$	−11.4074	−	19.7583i	−0.584421	−	1.01225i
$382$	−23.2163	+	1.10408i	−1.18785	+	0.0564898i
$383$	3.47535	+	12.9702i	0.177582	+	0.662745i	0.996097	+	0.0882604i	$0.0281308\pi$
$383$	3.47535	+	12.9702i	0.177582	+	0.662745i	−0.818515	+	0.574484i	$0.805203\pi$
$384$	23.1402	−	15.6431i	1.18087	−	0.798282i
$385$		0			0
$386$	−2.13521	−	6.68133i	−0.108679	−	0.340071i
$387$	−6.65075	+	1.78206i	−0.338076	+	0.0905873i
$388$	5.74535	+	15.4113i	0.291676	+	0.782393i
$389$	−15.5106	+	8.95506i	−0.786419	+	0.454039i	−0.838700	−	0.544593i	$-0.816684\pi$
$389$	−15.5106	+	8.95506i	−0.786419	+	0.454039i	0.0522811	+	0.998632i	$0.483351\pi$
$390$		0			0
$391$			5.59179i			0.282789i
$392$	19.6523	+	2.40525i	0.992593	+	0.121483i
$393$	−6.44222	−	6.44222i	−0.324967	−	0.324967i
$394$	−1.65828	+	7.62009i	−0.0835430	+	0.383895i
$395$		0			0
$396$	12.1663	−	26.6292i	0.611378	−	1.33817i
$397$	1.58258	+	5.90626i	0.0794273	+	0.296427i	0.994201	−	0.107541i	$-0.0342976\pi$
$397$	1.58258	+	5.90626i	0.0794273	+	0.296427i	−0.914773	+	0.403967i	$0.867631\pi$
$398$	23.7511	+	12.2469i	1.19053	+	0.613882i
$399$	2.26475	−	17.0348i	0.113379	−	0.852809i
$400$		0			0
$401$	−9.81777	+	17.0049i	−0.490276	+	0.849183i	−0.999937	−	0.0111923i	$-0.996437\pi$
$401$	−9.81777	+	17.0049i	−0.490276	+	0.849183i	0.509662	+	0.860375i	$0.329771\pi$
$402$	−0.0844603	−	1.77600i	−0.00421250	−	0.0885788i
$403$	−0.375386	−	0.100584i	−0.0186993	−	0.00501046i
$404$	17.0715	−	1.62741i	0.849341	−	0.0809665i
$405$		0			0
$406$	−25.5973	−	9.24095i	−1.27037	−	0.458621i
$407$	7.71315	+	7.71315i	0.382327	+	0.382327i
$408$	12.8368	−	32.0428i	0.635518	−	1.58635i
$409$	8.70611	−	5.02647i	0.430489	−	0.248543i	−0.269066	−	0.963122i	$-0.586715\pi$
$409$	8.70611	−	5.02647i	0.430489	−	0.248543i	0.699555	+	0.714579i	$0.253382\pi$
$410$		0			0
$411$	−42.4589	−	24.5137i	−2.09434	−	1.20917i
$412$	6.44160	+	1.08426i	0.317355	+	0.0534175i
$413$	8.19636	+	3.40728i	0.403316	+	0.167661i
$414$	1.50726	+	4.71641i	0.0740779	+	0.231799i
$415$		0			0
$416$	−0.227059	−	0.416218i	−0.0111325	−	0.0204068i
$417$	−2.75655	−	0.738616i	−0.134989	−	0.0361702i
$418$	9.51240	+	14.8042i	0.465267	+	0.724095i
$419$	17.7853			0.868870			0.434435	−	0.900703i	$-0.356948\pi$
$419$	17.7853			0.868870			0.434435	+	0.900703i	$0.356948\pi$
$420$		0			0
$421$	39.6482			1.93234			0.966168	−	0.257913i	$-0.0830348\pi$
$421$	39.6482			1.93234			0.966168	+	0.257913i	$0.0830348\pi$
$422$	−8.39368	−	13.0631i	−0.408598	−	0.635901i
$423$	8.27847	+	2.21821i	0.402513	+	0.107853i
$424$	−26.5233	−	3.17764i	−1.28809	−	0.154320i
$425$		0			0
$426$	−15.3713	−	48.0987i	−0.744741	−	2.33039i
$427$	0.669478	+	5.13572i	0.0323983	+	0.248535i
$428$	2.25484	−	13.3960i	0.108992	−	0.647522i
$429$	−0.847531	−	0.489322i	−0.0409192	−	0.0236247i
$430$		0			0
$431$	−21.7939	+	12.5827i	−1.04977	+	0.606087i	−0.922586	−	0.385792i	$-0.873928\pi$
$431$	−21.7939	+	12.5827i	−1.04977	+	0.606087i	−0.127187	+	0.991879i	$0.540595\pi$
$432$	0.0673082	−	0.936921i	0.00323837	−	0.0450776i
$433$	−9.19231	−	9.19231i	−0.441754	−	0.441754i	0.450847	−	0.892601i	$-0.351122\pi$
$433$	−9.19231	−	9.19231i	−0.441754	−	0.441754i	−0.892601	+	0.450847i	$0.851122\pi$
$434$	3.05732	+	17.0778i	0.146756	+	0.819759i
$435$		0			0
$436$	0.743873	+	7.80325i	0.0356251	+	0.373708i
$437$	−2.87463	−	0.770255i	−0.137512	−	0.0368463i
$438$	1.59085	+	33.4519i	0.0760139	+	1.59839i
$439$	−14.8997	+	25.8071i	−0.711125	+	1.23170i	0.253310	+	0.967385i	$0.418481\pi$
$439$	−14.8997	+	25.8071i	−0.711125	+	1.23170i	−0.964435	+	0.264320i	$0.914853\pi$
$440$		0			0
$441$	15.3590	−	15.2810i	0.731382	−	0.727666i
$442$	−0.520776	−	0.268531i	−0.0247708	−	0.0127727i
$443$	−10.5682	−	39.4412i	−0.502112	−	1.87391i	−0.485856	−	0.874039i	$-0.661492\pi$
$443$	−10.5682	−	39.4412i	−0.502112	−	1.87391i	−0.0162556	−	0.999868i	$-0.505175\pi$
$444$	10.3582	+	4.73242i	0.491579	+	0.224591i
$445$		0			0
$446$	−5.82600	+	26.7715i	−0.275869	+	1.26767i
$447$	−10.8257	−	10.8257i	−0.512039	−	0.512039i
$448$	−12.5117	+	17.0722i	−0.591120	+	0.806583i
$449$			20.7052i			0.977139i	0.872525	+	0.488570i	$0.162481\pi$
$449$			20.7052i			0.977139i	−0.872525	+	0.488570i	$0.837519\pi$
$450$		0			0
$451$	−23.4189	+	13.5209i	−1.10275	+	0.636675i
$452$	0.0742563	−	0.0276828i	0.00349272	−	0.00130209i
$453$	−24.0199	+	6.43610i	−1.12855	+	0.302394i
$454$	9.88197	+	30.9219i	0.463784	+	1.45124i
$455$		0			0
$456$	14.7043	+	11.0130i	0.688593	+	0.515730i
$457$	−0.969683	−	3.61891i	−0.0453599	−	0.169285i	0.939530	−	0.342466i	$-0.111262\pi$
$457$	−0.969683	−	3.61891i	−0.0453599	−	0.169285i	−0.984890	+	0.173181i	$0.944596\pi$
$458$	16.8654	−	0.802058i	0.788067	−	0.0374777i
$459$	−0.580425	−	1.00533i	−0.0270919	−	0.0469246i
$460$		0			0
$461$	−6.66823			−0.310570			−0.155285	−	0.987870i	$-0.549630\pi$
$461$	−6.66823			−0.310570			−0.155285	+	0.987870i	$0.549630\pi$
$462$	−3.69396	+	43.5326i	−0.171859	+	2.02532i
$463$	−14.7884	+	14.7884i	−0.687277	+	0.687277i	−0.961629	−	0.274353i	$-0.911536\pi$
$463$	−14.7884	+	14.7884i	−0.687277	+	0.687277i	0.274353	+	0.961629i	$0.411536\pi$
$464$	21.9933	−	19.0451i	1.02101	−	0.884146i
$465$		0			0
$466$	22.6342	−	24.8945i	1.04851	−	1.15321i
$467$	27.1281	−	7.26895i	1.25534	−	0.336367i	0.430941	−	0.902380i	$-0.358182\pi$
$467$	27.1281	−	7.26895i	1.25534	−	0.336367i	0.824396	+	0.566013i	$0.191515\pi$
$468$	−0.511632	−	0.0861184i	−0.0236502	−	0.00398083i
$469$	0.514018	+	1.24543i	0.0237351	+	0.0575087i
$470$		0			0
$471$	31.1509	+	17.9850i	1.43536	+	0.828703i
$472$	−7.46043	+	5.86408i	−0.343394	+	0.269916i
$473$	−2.72309	+	10.1627i	−0.125208	+	0.467282i
$474$	4.53187	−	20.8247i	0.208156	−	0.956511i
$475$		0			0
$476$	−0.971046	+	26.1394i	−0.0445078	+	1.19810i
$477$	−20.6700	+	20.6700i	−0.946413	+	0.946413i
$478$	1.79357	−	1.15246i	0.0820359	−	0.0527121i
$479$	5.27141	+	9.13034i	0.240857	+	0.417176i	0.960959	−	0.276692i	$-0.0892383\pi$
$479$	5.27141	+	9.13034i	0.240857	+	0.417176i	−0.720102	+	0.693868i	$0.755905\pi$
$480$		0			0
$481$	0.0966532	−	0.167408i	0.00440701	−	0.00763316i
$482$	−23.2927	−	12.0106i	−1.06096	−	0.547067i
$483$	−4.49057	−	5.86768i	−0.204328	−	0.266989i
$484$	−13.1857	−	18.5229i	−0.599348	−	0.841949i
$485$		0			0
$486$	23.2265	+	21.1176i	1.05358	+	0.957916i
$487$	−9.85078	+	36.7636i	−0.446381	+	1.66592i	0.265882	+	0.964006i	$0.414337\pi$
$487$	−9.85078	+	36.7636i	−0.446381	+	1.66592i	−0.712263	+	0.701913i	$0.752330\pi$
$488$	−5.13966	−	2.05903i	−0.232662	−	0.0932078i
$489$		−	7.28707i		−	0.329533i
$490$		0			0
$491$		−	3.59770i		−	0.162362i	−0.996699	−	0.0811809i	$-0.974131\pi$
$491$		−	3.59770i		−	0.162362i	0.996699	−	0.0811809i	$-0.0258691\pi$
$492$	−17.9784	+	21.7673i	−0.810530	+	0.981347i
$493$	9.30560	−	34.7290i	0.419103	−	1.56411i
$494$	0.209782	−	0.230731i	0.00943854	−	0.0103811i
$495$		0			0
$496$	−17.5252	−	6.07173i	−0.786903	−	0.272629i
$497$	23.2551	+	30.3867i	1.04313	+	1.36303i
$498$	12.7316	−	24.6910i	0.570516	−	1.10643i
$499$	5.11616	−	8.86145i	0.229031	−	0.396693i	−0.728490	−	0.685056i	$-0.759778\pi$
$499$	5.11616	−	8.86145i	0.229031	−	0.396693i	0.957521	+	0.288363i	$0.0931110\pi$
$500$		0			0
$501$	−10.7030	−	18.5381i	−0.478174	−	0.828221i
$502$	13.7775	+	21.4419i	0.614920	+	0.957000i
$503$	−30.0943	+	30.0943i	−1.34184	+	1.34184i	−0.447605	+	0.894231i	$0.647723\pi$
$503$	−30.0943	+	30.0943i	−1.34184	+	1.34184i	−0.894231	+	0.447605i	$0.852277\pi$
$504$	6.22680	+	22.3091i	0.277364	+	0.993724i
$505$		0			0
$506$	7.39299	+	1.60886i	0.328659	+	0.0715225i
$507$	8.30225	−	30.9844i	0.368716	−	1.37607i
$508$	−17.3181	+	6.45618i	−0.768365	+	0.286447i
$509$	0.0145211	+	0.00838376i	0.000643637	+	0.000371604i	0.500322	−	0.865840i	$-0.333215\pi$
$509$	0.0145211	+	0.00838376i	0.000643637	+	0.000371604i	−0.499678	+	0.866211i	$0.666548\pi$
$510$		0			0
$511$	−9.68180	−	23.4584i	−0.428298	−	1.03774i
$512$	−9.38510	−	20.5893i	−0.414767	−	0.909928i
$513$	0.596770	−	0.159904i	0.0263481	−	0.00705994i
$514$	−15.6028	−	14.1861i	−0.688210	−	0.625724i
$515$		0			0
$516$	1.04239	+	10.9347i	0.0458885	+	0.481372i
$517$	9.26042	−	9.26042i	0.407273	−	0.407273i
$518$	−8.59876	−	0.729649i	−0.377808	−	0.0320589i
$519$	−4.43276			−0.194577
$520$		0			0
$521$	0.00830997	+	0.0143933i	0.000364066	+	0.000630582i	0.866207	−	0.499685i	$-0.166551\pi$
$521$	0.00830997	+	0.0143933i	0.000364066	+	0.000630582i	−0.865843	+	0.500315i	$0.833217\pi$
$522$	−1.51232	−	31.8006i	−0.0661926	−	1.39187i
$523$	−8.00409	−	29.8717i	−0.349994	−	1.30620i	−0.886668	−	0.462407i	$-0.846986\pi$
$523$	−8.00409	−	29.8717i	−0.349994	−	1.30620i	0.536674	−	0.843790i	$-0.319681\pi$
$524$	−6.01271	+	4.28019i	−0.262666	+	0.186981i
$525$		0			0
$526$	9.55070	−	3.05219i	0.416430	−	0.133082i
$527$	−22.1400	+	5.93238i	−0.964432	+	0.258419i
$528$	−38.6708	−	26.1910i	−1.68293	−	1.13982i
$529$	18.8104	−	10.8602i	0.817845	−	0.472183i
$530$		0			0
$531$			10.3840i			0.450626i
$532$	−13.3040	−	4.09983i	−0.576800	−	0.177750i
$533$	0.338860	+	0.338860i	0.0146777	+	0.0146777i
$534$	−56.9171	−	12.3863i	−2.46304	−	0.536007i
$535$		0			0
$536$	−1.43014	−	0.171338i	−0.0617725	−	0.00740069i
$537$	−13.7653	−	51.3727i	−0.594016	−	2.21690i
$538$	−3.91757	+	7.59756i	−0.168899	+	0.327554i
$539$	−8.48716	−	32.0003i	−0.365568	−	1.37835i
$540$		0			0
$541$	−14.5885	+	25.2681i	−0.627211	+	1.08636i	0.360898	+	0.932605i	$0.382470\pi$
$541$	−14.5885	+	25.2681i	−0.627211	+	1.08636i	−0.988109	+	0.153756i	$0.950863\pi$
$542$	33.1900	−	1.57840i	1.42563	−	0.0677981i
$543$	−38.6612	−	10.3592i	−1.65911	−	0.444558i
$544$	−23.8717	−	14.5635i	−1.02349	−	0.624406i
$545$		0			0
$546$	0.762117	−	0.136437i	0.0326156	−	0.00583896i
$547$	0.913792	+	0.913792i	0.0390709	+	0.0390709i	0.726372	−	0.687301i	$-0.241205\pi$
$547$	0.913792	+	0.913792i	0.0390709	+	0.0390709i	−0.687301	+	0.726372i	$0.741205\pi$
$548$	−25.2923	+	30.6226i	−1.08043	+	1.30813i
$549$	−5.24710	+	3.02941i	−0.223941	+	0.129292i
$550$		0			0
$551$	16.5717	+	9.56766i	0.705977	+	0.407596i
$552$	7.81886	−	1.12229i	0.332793	−	0.0477677i
$553$	2.08759	+	16.0144i	0.0887735	+	0.681002i
$554$	−31.4204	+	10.0413i	−1.33493	+	0.426613i
$555$		0			0
$556$	−0.960714	+	2.10279i	−0.0407434	+	0.0891781i
$557$	2.78027	+	0.744970i	0.117804	+	0.0315654i	0.317239	−	0.948346i	$-0.397244\pi$
$557$	2.78027	+	0.744970i	0.117804	+	0.0315654i	−0.199436	+	0.979911i	$0.563911\pi$
$558$	−17.0749	+	10.9715i	−0.722839	+	0.464460i
$559$	0.186452			0.00788606
$560$		0			0
$561$	−57.7196			−2.43693
$562$	22.9639	−	14.7554i	0.968674	−	0.622421i
$563$	26.9945	+	7.23315i	1.13768	+	0.304841i	0.778018	−	0.628241i	$-0.216225\pi$
$563$	26.9945	+	7.23315i	1.13768	+	0.304841i	0.359663	+	0.933082i	$0.382892\pi$
$564$	5.68176	−	12.4361i	0.239245	−	0.523654i
$565$		0			0
$566$	−9.60324	+	3.06898i	−0.403654	+	0.128999i
$567$	−21.2683	−	8.84138i	−0.893186	−	0.371303i
$568$	−40.4912	+	5.81193i	−1.69897	+	0.243863i
$569$	−31.8950	−	18.4146i	−1.33711	−	0.771981i	−0.350732	−	0.936476i	$-0.614067\pi$
$569$	−31.8950	−	18.4146i	−1.33711	−	0.771981i	−0.986378	+	0.164495i	$0.947400\pi$
$570$		0			0
$571$	35.5147	−	20.5044i	1.48624	−	0.858084i	0.486367	−	0.873754i	$-0.338322\pi$
$571$	35.5147	−	20.5044i	1.48624	−	0.858084i	0.999877	+	0.0156706i	$0.00498830\pi$
$572$	−0.504865	+	0.611264i	−0.0211095	+	0.0255582i
$573$	28.6909	+	28.6909i	1.19858	+	1.19858i
$574$	7.26445	−	20.1224i	0.303212	−	0.839894i
$575$		0			0
$576$	−24.0602	−	5.84905i	−1.00251	−	0.243710i
$577$	20.6267	+	5.52692i	0.858703	+	0.230089i	0.661196	−	0.750213i	$-0.270049\pi$
$577$	20.6267	+	5.52692i	0.858703	+	0.230089i	0.197506	+	0.980302i	$0.436716\pi$
$578$	−10.5043	+	0.499547i	−0.436921	+	0.0207784i
$579$	−6.12245	+	10.6044i	−0.254440	+	0.440704i
$580$		0			0
$581$	−2.77432	+	20.8677i	−0.115098	+	0.865737i
$582$	13.1590	−	25.5199i	0.545457	−	1.05783i
$583$	11.5609	+	43.1458i	0.478802	+	1.78691i
$584$	26.9374	+	3.22725i	1.11468	+	0.133545i
$585$		0			0
$586$	2.52963	+	0.550498i	0.104498	+	0.0227408i
$587$	−0.870374	−	0.870374i	−0.0359242	−	0.0359242i	0.688917	−	0.724841i	$-0.258087\pi$
$587$	−0.870374	−	0.870374i	−0.0359242	−	0.0359242i	−0.724841	+	0.688917i	$0.758087\pi$
$588$	−19.9726	−	28.2088i	−0.823657	−	1.16331i
$589$		−	12.1989i		−	0.502646i
$590$		0			0
$591$	11.7900	−	6.80697i	0.484977	−	0.280001i
$592$	5.17338	−	7.63845i	0.212625	−	0.313938i
$593$	2.04214	−	0.547190i	0.0838607	−	0.0224704i	−0.216645	−	0.976251i	$-0.569511\pi$
$593$	2.04214	−	0.547190i	0.0838607	−	0.0224704i	0.300505	+	0.953780i	$0.402845\pi$
$594$	−1.49615	+	0.478138i	−0.0613880	+	0.0196182i
$595$		0			0
$596$	−10.1039	+	7.19257i	−0.413874	+	0.294619i
$597$	−12.0740	−	45.0608i	−0.494157	−	1.84422i
$598$	−0.00636923	−	0.133930i	−0.000260457	−	0.00547679i
$599$	12.9248	+	22.3864i	0.528092	+	0.914683i	0.999464	+	0.0327479i	$0.0104258\pi$
$599$	12.9248	+	22.3864i	0.528092	+	0.914683i	−0.471371	+	0.881935i	$0.656241\pi$
$600$		0			0
$601$	20.5570			0.838537			0.419269	−	0.907862i	$-0.362287\pi$
$601$	20.5570			0.838537			0.419269	+	0.907862i	$0.362287\pi$
$602$	−3.53743	−	7.53456i	−0.144175	−	0.307086i
$603$	−1.11452	+	1.11452i	−0.0453869	+	0.0453869i
$604$	1.91172	+	20.0540i	0.0777868	+	0.815986i
$605$		0			0
$606$	−22.1506	−	20.1394i	−0.899806	−	0.818108i
$607$	21.6414	−	5.79881i	0.878399	−	0.235366i	0.208683	−	0.977983i	$-0.433082\pi$
$607$	21.6414	−	5.79881i	0.878399	−	0.235366i	0.669716	+	0.742617i	$0.266416\pi$
$608$	10.7751	−	10.2659i	0.436987	−	0.416336i
$609$	18.1249	+	43.9154i	0.734457	+	1.77954i
$610$		0			0
$611$	−0.200991	−	0.116042i	−0.00813122	−	0.00469456i
$612$	−28.6725	+	10.6891i	−1.15902	+	0.432081i
$613$	8.56832	−	31.9774i	0.346071	−	1.29156i	−0.545285	−	0.838251i	$-0.683578\pi$
$613$	8.56832	−	31.9774i	0.346071	−	1.29156i	0.891356	−	0.453304i	$-0.149755\pi$
$614$	−7.54686	−	1.64234i	−0.304566	−	0.0662796i
$615$		0			0
$616$	34.2798	+	8.80460i	1.38117	+	0.354747i
$617$	−27.2948	+	27.2948i	−1.09885	+	1.09885i	−0.104300	+	0.994546i	$0.533260\pi$
$617$	−27.2948	+	27.2948i	−1.09885	+	1.09885i	−0.994546	+	0.104300i	$0.966740\pi$
$618$	−6.16441	−	9.59368i	−0.247969	−	0.385914i
$619$	−18.1903	−	31.5065i	−0.731130	−	1.26635i	−0.956400	−	0.292059i	$-0.905660\pi$
$619$	−18.1903	−	31.5065i	−0.731130	−	1.26635i	0.225270	−	0.974296i	$-0.427674\pi$
$620$		0			0
$621$	0.132821	−	0.230053i	0.00532992	−	0.00923169i
$622$	−13.3071	+	25.8071i	−0.533564	+	1.03477i
$623$	43.7698	−	5.70571i	1.75360	−	0.228594i
$624$	−0.270959	+	0.782082i	−0.0108470	+	0.0313083i
$625$		0			0
$626$	−26.5535	+	29.2052i	−1.06129	+	1.16727i
$627$	7.95073	−	29.6725i	0.317522	−	1.18501i
$628$	18.5562	−	22.4669i	0.740474	−	0.896527i
$629$		−	11.4011i		−	0.454590i
$630$		0			0
$631$			10.6984i			0.425897i	0.977063	+	0.212949i	$0.0683067\pi$
$631$			10.6984i			0.425897i	−0.977063	+	0.212949i	$0.931693\pi$
$632$	−16.0267	−	6.42055i	−0.637509	−	0.255396i
$633$	−7.01567	+	26.1828i	−0.278848	+	1.04067i
$634$	−13.5593	−	12.3282i	−0.538510	−	0.489616i
$635$		0			0
$636$	27.0441	+	37.9908i	1.07237	+	1.50643i
$637$	−0.508841	+	0.292054i	−0.0201610	+	0.0115716i
$638$	−43.2383	−	22.2952i	−1.71182	−	0.882676i
$639$	−22.3816	+	38.7661i	−0.885402	+	1.53356i
$640$		0			0
$641$	−2.64450	−	4.58042i	−0.104452	−	0.180916i	0.809062	−	0.587723i	$-0.199975\pi$
$641$	−2.64450	−	4.58042i	−0.104452	−	0.180916i	−0.913514	+	0.406807i	$0.866642\pi$
$642$	−19.9512	+	12.8196i	−0.787410	+	0.505950i
$643$	−6.36844	+	6.36844i	−0.251147	+	0.251147i	−0.821441	−	0.570294i	$-0.806829\pi$
$643$	−6.36844	+	6.36844i	−0.251147	+	0.251147i	0.570294	+	0.821441i	$0.306829\pi$
$644$	−5.29130	+	2.79835i	−0.208506	+	0.110270i
$645$		0			0
$646$	3.91096	−	17.9715i	0.153875	−	0.707081i
$647$	1.58576	−	5.91812i	0.0623425	−	0.232665i	−0.927724	−	0.373268i	$-0.878237\pi$
$647$	1.58576	−	5.91812i	0.0623425	−	0.232665i	0.990066	+	0.140602i	$0.0449039\pi$
$648$	19.3587	−	15.2164i	0.760482	−	0.597757i
$649$	13.7415	+	7.93365i	0.539401	+	0.311423i
$650$		0			0
$651$	18.4682	−	24.0049i	0.723826	−	0.940825i
$652$	−5.82137	−	0.979860i	−0.227983	−	0.0383743i
$653$	37.7871	−	10.1250i	1.47872	−	0.396223i	0.572812	−	0.819687i	$-0.305853\pi$
$653$	37.7871	−	10.1250i	1.47872	−	0.396223i	0.905913	+	0.423464i	$0.139186\pi$
$654$	9.20555	−	10.1248i	0.359966	−	0.395913i
$655$		0			0
$656$	14.9716	+	17.2892i	0.584544	+	0.675032i
$657$	20.9927	−	20.9927i	0.819001	−	0.819001i
$658$	−0.876018	+	10.3237i	−0.0341508	+	0.402459i
$659$	7.96382			0.310226			0.155113	−	0.987897i	$-0.450426\pi$
$659$	7.96382			0.310226			0.155113	+	0.987897i	$0.450426\pi$
$660$		0			0
$661$	−17.8362	−	30.8932i	−0.693748	−	1.20161i	−0.970601	−	0.240694i	$-0.922625\pi$
$661$	−17.8362	−	30.8932i	−0.693748	−	1.20161i	0.276854	−	0.960912i	$-0.410708\pi$
$662$	−10.4610	+	0.497486i	−0.406577	+	0.0193354i
$663$	0.264740	+	0.988023i	0.0102817	+	0.0383716i
$664$	−18.0128	−	13.4909i	−0.699032	−	0.523548i
$665$		0			0
$666$	−3.07314	−	9.61625i	−0.119082	−	0.372622i
$667$	7.94717	−	2.12944i	0.307716	−	0.0824521i
$668$	−16.2486	+	6.05747i	−0.628676	+	0.234371i
$669$	41.4216	−	23.9148i	1.60145	−	0.924599i
$670$		0			0
$671$			9.25823i			0.357410i
$672$	36.7449	−	3.88844i	1.41746	−	0.150000i
$673$	29.4853	+	29.4853i	1.13657	+	1.13657i	0.989060	+	0.147515i	$0.0471275\pi$
$673$	29.4853	+	29.4853i	1.13657	+	1.13657i	0.147515	+	0.989060i	$0.452873\pi$
$674$	−2.47512	+	11.3736i	−0.0953380	+	0.438094i
$675$		0			0
$676$	−23.6359	−	10.7987i	−0.909075	−	0.415335i
$677$	−11.9320	−	44.5308i	−0.458584	−	1.71146i	−0.677333	−	0.735676i	$-0.736864\pi$
$677$	−11.9320	−	44.5308i	−0.458584	−	1.71146i	0.218750	−	0.975781i	$-0.429802\pi$
$678$	−0.122962	−	0.0634037i	−0.00472233	−	0.00243500i
$679$	−2.86745	+	21.5682i	−0.110043	+	0.827710i
$680$		0			0
$681$	28.3354	−	49.0783i	1.08581	−	1.88069i
$682$	1.47322	+	30.9784i	0.0564127	+	1.18622i
$683$	40.1276	+	10.7522i	1.53544	+	0.411420i	0.924790	−	0.380479i	$-0.124241\pi$
$683$	40.1276	+	10.7522i	1.53544	+	0.411420i	0.610652	+	0.791899i	$0.290907\pi$
$684$	−1.54550	−	16.2123i	−0.0590936	−	0.619894i
$685$		0			0
$686$	21.4559	+	15.0214i	0.819191	+	0.573521i
$687$	−20.8424	−	20.8424i	−0.795187	−	0.795187i
$688$	8.87547	+	0.637612i	0.338374	+	0.0243087i
$689$	0.685527	−	0.395789i	0.0261165	−	0.0150784i
$690$		0			0
$691$	−15.8798	−	9.16821i	−0.604096	−	0.348775i	0.166555	−	0.986032i	$-0.446736\pi$
$691$	−15.8798	−	9.16821i	−0.604096	−	0.348775i	−0.770651	+	0.637257i	$0.780069\pi$
$692$	−0.596054	+	3.54117i	−0.0226586	+	0.134615i
$693$	30.7563	−	23.5380i	1.16833	−	0.894133i
$694$	−4.75419	−	14.8765i	−0.180466	−	0.564703i
$695$		0			0
$696$	−50.4283	−	6.04159i	−1.91148	−	0.229006i
$697$	27.3010	+	7.31528i	1.03410	+	0.277086i
$698$	−7.95028	−	12.3730i	−0.300922	−	0.468326i
$699$	−58.7364			−2.22161
$700$		0			0
$701$	3.42628			0.129409			0.0647045	−	0.997904i	$-0.479390\pi$
$701$	3.42628			0.129409			0.0647045	+	0.997904i	$0.479390\pi$
$702$	0.0150469	+	0.0234176i	0.000567910	+	0.000883839i
$703$	5.86106	+	1.57047i	0.221054	+	0.0592312i
$704$	−26.1229	+	27.3709i	−0.984546	+	1.03158i
$705$		0			0
$706$	3.24859	+	10.1653i	0.122262	+	0.382574i
$707$	20.9480	+	8.70820i	0.787830	+	0.327506i
$708$	16.3358	+	2.74966i	0.613937	+	0.103339i
$709$	26.8261	+	15.4881i	1.00748	+	0.581667i	0.910452	−	0.413615i	$-0.135734\pi$
$709$	26.8261	+	15.4881i	1.00748	+	0.581667i	0.0970248	+	0.995282i	$0.469067\pi$
$710$		0			0
$711$	−16.3617	+	9.44644i	−0.613612	+	0.354269i
$712$	−17.5483	+	43.8034i	−0.657651	+	1.64160i
$713$	−3.70884	−	3.70884i	−0.138897	−	0.138897i
$714$	34.9035	−	29.4434i	1.30623	−	1.10189i
$715$		0			0
$716$	−42.8907	+	4.08871i	−1.60290	+	0.152802i
$717$	−3.59492	−	0.963255i	−0.134255	−	0.0359734i
$718$	0.771456	+	16.2219i	0.0287905	+	0.605396i
$719$	21.3674	−	37.0094i	0.796869	−	1.38022i	−0.124777	−	0.992185i	$-0.539821\pi$
$719$	21.3674	−	37.0094i	0.796869	−	1.38022i	0.921646	−	0.388033i	$-0.126845\pi$
$720$		0			0
$721$	6.84890	+	5.26922i	0.255066	+	0.196236i
$722$	−15.1820	−	7.82838i	−0.565015	−	0.291342i
$723$	11.8410	+	44.1913i	0.440372	+	1.64349i
$724$	−13.4742	+	29.4920i	−0.500765	+	1.09606i
$725$		0			0
$726$	−8.44023	+	38.7843i	−0.313246	+	1.43942i
$727$	21.7303	+	21.7303i	0.805931	+	0.805931i	0.984015	−	0.178084i	$-0.0569900\pi$
$727$	21.7303	+	21.7303i	0.805931	+	0.805931i	−0.178084	+	0.984015i	$0.556990\pi$
$728$	−0.00651592	−	0.627173i	−0.000241496	−	0.0232446i
$729$		−	28.6841i		−	1.06238i
$730$		0			0
$731$	9.52347	−	5.49838i	0.352238	−	0.203365i
$732$	3.37637	+	9.05678i	0.124794	+	0.334748i
$733$	3.68215	−	0.986629i	0.136003	−	0.0364420i	−0.190175	−	0.981750i	$-0.560906\pi$
$733$	3.68215	−	0.986629i	0.136003	−	0.0364420i	0.326179	+	0.945308i	$0.394239\pi$
$734$	5.45132	+	17.0579i	0.201212	+	0.629618i
$735$		0			0
$736$	0.154814	−	6.39711i	0.00570652	−	0.235800i
$737$	0.623362	+	2.32642i	0.0229618	+	0.0856947i
$738$	24.9989	−	1.18886i	0.920222	−	0.0437625i
$739$	−6.00177	−	10.3954i	−0.220779	−	0.382400i	0.734266	−	0.678862i	$-0.237526\pi$
$739$	−6.00177	−	10.3954i	−0.220779	−	0.382400i	−0.955045	+	0.296462i	$0.904193\pi$
$740$		0			0
$741$	−0.544391			−0.0199987
$742$	−29.0000	−	20.1933i	−1.06462	−	0.741318i
$743$	−7.86007	+	7.86007i	−0.288358	+	0.288358i	−0.836431	−	0.548073i	$-0.815362\pi$
$743$	−7.86007	+	7.86007i	−0.288358	+	0.288358i	0.548073	+	0.836431i	$0.315362\pi$
$744$	12.7386	+	29.7671i	0.467021	+	1.09131i
$745$		0			0
$746$	23.6925	−	26.0585i	0.867443	−	0.954068i
$747$	−23.7876	+	6.37387i	−0.870344	+	0.233208i
$748$	−7.76130	+	46.1101i	−0.283781	+	1.68595i
$749$	10.9580	−	14.2431i	0.400395	−	0.520431i
$750$		0			0
$751$	−1.00430	−	0.579834i	−0.0366475	−	0.0211584i	0.481564	−	0.876411i	$-0.340069\pi$
$751$	−1.00430	−	0.579834i	−0.0366475	−	0.0211584i	−0.518212	+	0.855252i	$0.673402\pi$
$752$	−9.17074	−	6.21117i	−0.334422	−	0.226498i
$753$	11.5156	−	42.9769i	0.419653	−	1.56616i
$754$	−0.183322	+	0.842397i	−0.00667620	+	0.0306783i
$755$		0			0
$756$	0.660834	−	1.05234i	0.0240343	−	0.0382731i
$757$	15.7431	−	15.7431i	0.572192	−	0.572192i	−0.360549	−	0.932740i	$-0.617410\pi$
$757$	15.7431	−	15.7431i	0.572192	−	0.572192i	0.932740	+	0.360549i	$0.117410\pi$
$758$	4.97747	−	3.19827i	0.180790	−	0.116166i
$759$	−6.60410	−	11.4386i	−0.239714	−	0.415196i
$760$		0			0
$761$	9.62047	−	16.6631i	0.348742	−	0.604039i	−0.637284	−	0.770629i	$-0.719942\pi$
$761$	9.62047	−	16.6631i	0.348742	−	0.604039i	0.986026	+	0.166590i	$0.0532757\pi$
$762$	28.6772	+	14.7870i	1.03887	+	0.535677i
$763$	−3.98044	+	9.57514i	−0.144102	+	0.346643i
$764$	26.7780	−	19.0621i	0.968794	−	0.689644i
$765$		0			0
$766$	−14.0504	−	12.7747i	−0.507662	−	0.461569i
$767$	0.0727778	−	0.271611i	0.00262786	−	0.00980729i
$768$	−15.5727	+	36.3021i	−0.561931	+	1.30994i
$769$			30.8833i			1.11368i	0.830620	+	0.556840i	$0.187986\pi$
$769$			30.8833i			1.11368i	−0.830620	+	0.556840i	$0.812014\pi$
$770$		0			0
$771$			36.8135i			1.32580i
$772$	7.64820	+	6.31693i	0.275265	+	0.227351i
$773$	4.19873	−	15.6699i	0.151018	−	0.563607i	−0.848396	−	0.529363i	$-0.822431\pi$
$773$	4.19873	−	15.6699i	0.151018	−	0.563607i	0.999414	−	0.0342438i	$-0.0109023\pi$
$774$	6.55051	−	7.20466i	0.235453	−	0.258966i
$775$		0			0
$776$	−18.6174	−	13.9437i	−0.668327	−	0.500551i
$777$	9.15578	+	11.9636i	0.328462	+	0.429190i
$778$	11.6081	−	22.5122i	0.416170	−	0.807100i
$779$	−7.52128	+	13.0272i	−0.269478	+	0.466749i
$780$		0			0
$781$	34.2004	+	59.2368i	1.22379	+	2.11966i
$782$	−4.27486	−	6.65296i	−0.152869	−	0.237910i
$783$	−1.20775	+	1.20775i	−0.0431616	+	0.0431616i
$784$	−25.2206	+	12.1623i	−0.900736	+	0.434367i
$785$		0			0
$786$	12.5898	+	2.73978i	0.449062	+	0.0977248i
$787$	−10.8721	+	40.5750i	−0.387547	+	1.44634i	0.446566	+	0.894751i	$0.352647\pi$
$787$	−10.8721	+	40.5750i	−0.387547	+	1.44634i	−0.834113	+	0.551594i	$0.814020\pi$
$788$	−3.85249	−	10.3339i	−0.137239	−	0.368130i
$789$	−15.1586	−	8.75180i	−0.539659	−	0.311572i
$790$		0			0
$791$	0.103922	+	0.0138162i	0.00369503	+	0.000491247i
$792$	5.88263	+	40.9837i	0.209030	+	1.45629i
$793$	0.158479	−	0.0424643i	0.00562775	−	0.00150795i
$794$	−6.39817	−	5.81724i	−0.227062	−	0.206446i
$795$		0			0
$796$	−37.6210	+	3.58635i	−1.33344	+	0.127115i
$797$	−5.01705	+	5.01705i	−0.177713	+	0.177713i	−0.790358	−	0.612645i	$-0.790106\pi$
$797$	−5.01705	+	5.01705i	−0.177713	+	0.177713i	0.612645	+	0.790358i	$0.290106\pi$
$798$	10.3284	+	21.9990i	0.365621	+	0.778755i
$799$	−13.6881			−0.484251
$800$		0			0
$801$	25.8185	+	44.7190i	0.912253	+	1.58007i
$802$	−1.31910	−	27.7375i	−0.0465790	−	0.979445i
$803$	−11.7414	−	43.8193i	−0.414343	−	1.54635i
$804$	1.45822	+	2.04847i	0.0514273	+	0.0722438i
$805$		0			0
$806$	0.523519	−	0.167305i	0.0184402	−	0.00589308i
$807$	14.4142	−	3.86227i	0.507403	−	0.135958i
$808$	−19.0671	+	14.9872i	−0.670779	+	0.527249i
$809$	−16.3576	+	9.44409i	−0.575104	+	0.332036i	−0.759185	−	0.650875i	$-0.774402\pi$
$809$	−16.3576	+	9.44409i	−0.575104	+	0.332036i	0.184081	+	0.982911i	$0.441069\pi$
$810$		0			0
$811$			21.4189i			0.752118i	0.926596	+	0.376059i	$0.122721\pi$
$811$			21.4189i			0.752118i	−0.926596	+	0.376059i	$0.877279\pi$
$812$	37.5196	−	8.57418i	1.31668	−	0.300895i
$813$	−41.0166	−	41.0166i	−1.43851	−	1.43851i
$814$	−15.0735	−	3.28029i	−0.528326	−	0.114974i
$815$		0			0
$816$	9.22340	+	47.9372i	0.322883	+	1.67814i
$817$	1.51477	+	5.65322i	0.0529953	+	0.197781i
$818$	−6.51561	+	12.6361i	−0.227813	+	0.441810i
$819$	−0.543983	−	0.418514i	−0.0190083	−	0.0146241i
$820$		0			0
$821$	20.8528	−	36.1180i	0.727766	−	1.26053i	−0.230059	−	0.973177i	$-0.573892\pi$
$821$	20.8528	−	36.1180i	0.727766	−	1.26053i	0.957825	−	0.287351i	$-0.0927747\pi$
$822$	69.2569	−	3.29361i	2.41561	−	0.114878i
$823$	39.0933	+	10.4750i	1.36271	+	0.365136i	0.864809	−	0.502100i	$-0.167439\pi$
$823$	39.0933	+	10.4750i	1.36271	+	0.365136i	0.497897	+	0.867236i	$0.334106\pi$
$824$	−8.49294	+	3.63450i	−0.295865	+	0.126614i
$825$		0			0
$826$	−12.3566	+	2.21213i	−0.429942	+	0.0769697i
$827$	−30.7849	−	30.7849i	−1.07050	−	1.07050i	−0.997319	−	0.0731766i	$-0.976686\pi$
$827$	−30.7849	−	30.7849i	−1.07050	−	1.07050i	−0.0731766	−	0.997319i	$-0.523314\pi$
$828$	−5.39894	−	4.45918i	−0.187626	−	0.154967i
$829$	36.1486	−	20.8704i	1.25549	−	0.724859i	0.283298	−	0.959032i	$-0.408571\pi$
$829$	36.1486	−	20.8704i	1.25549	−	0.724859i	0.972195	+	0.234172i	$0.0752380\pi$
$830$		0			0
$831$	49.8696	+	28.7922i	1.72996	+	0.998790i
$832$	0.588342	+	0.321622i	0.0203971	+	0.0111502i
$833$	−17.3778	+	29.9229i	−0.602104	+	1.03677i
$834$	3.84433	−	1.22856i	0.133118	−	0.0425417i
$835$		0			0
$836$	−22.6352	−	10.3415i	−0.782854	−	0.357667i
$837$	1.05177	+	0.281822i	0.0363546	+	0.00974118i
$838$	−21.1605	+	13.5967i	−0.730977	+	0.469689i
$839$	20.9842			0.724456			0.362228	−	0.932090i	$-0.382016\pi$
$839$	20.9842			0.724456			0.362228	+	0.932090i	$0.382016\pi$
$840$		0			0
$841$	−23.9012			−0.824180
$842$	−47.1724	+	30.3106i	−1.62567	+	1.04457i
$843$	−46.0274	−	12.3330i	−1.58527	−	0.424772i
$844$	19.9731	+	9.12525i	0.687504	+	0.314104i
$845$		0			0
$846$	−11.5453	+	3.68962i	−0.396935	+	0.126852i
$847$	−3.88797	−	29.8255i	−0.133592	−	1.02482i
$848$	33.9860	−	16.4961i	1.16708	−	0.566477i
$849$	15.2420	+	8.79995i	0.523103	+	0.302014i
$850$		0			0
$851$	2.25941	−	1.30447i	0.0774517	−	0.0447168i
$852$	55.0592	+	45.4754i	1.88630	+	1.55796i
$853$	−19.9509	−	19.9509i	−0.683106	−	0.683106i	0.277593	−	0.960699i	$-0.410463\pi$
$853$	−19.9509	−	19.9509i	−0.683106	−	0.683106i	−0.960699	+	0.277593i	$0.910463\pi$
$854$	−4.72272	−	5.59853i	−0.161608	−	0.191578i
$855$		0			0
$856$	7.55837	+	17.6620i	0.258340	+	0.603676i
$857$	−37.0531	−	9.92835i	−1.26571	−	0.339146i	−0.437324	−	0.899304i	$-0.644074\pi$
$857$	−37.0531	−	9.92835i	−1.26571	−	0.339146i	−0.828386	+	0.560158i	$0.810740\pi$
$858$	1.38245	−	0.0657445i	0.0471961	−	0.00224448i
$859$	−3.51740	+	6.09232i	−0.120012	+	0.207867i	−0.919772	−	0.392453i	$-0.871627\pi$
$859$	−3.51740	+	6.09232i	−0.120012	+	0.207867i	0.799760	+	0.600320i	$0.204960\pi$
$860$		0			0
$861$	−34.5226	+	14.2482i	−1.17653	+	0.485579i
$862$	16.3104	−	31.6317i	0.555536	−	1.07738i
$863$	−11.5958	−	43.2762i	−0.394726	−	1.47314i	−0.822246	−	0.569132i	$-0.807279\pi$
$863$	−11.5958	−	43.2762i	−0.394726	−	1.47314i	0.427520	−	0.904006i	$-0.359387\pi$
$864$	0.636183	+	1.16618i	0.0216434	+	0.0396742i
$865$		0			0
$866$	17.9642	+	3.90936i	0.610447	+	0.132845i
$867$	12.9813	+	12.9813i	0.440868	+	0.440868i
$868$	−16.6933	−	17.9814i	−0.566606	−	0.610328i
$869$			28.8694i			0.979328i
$870$		0			0
$871$	0.0369636	−	0.0213410i	0.00125246	−	0.000723111i
$872$	−6.85053	−	8.71542i	−0.231988	−	0.295141i
$873$	−24.5861	+	6.58783i	−0.832114	+	0.222964i
$874$	4.00901	−	1.28119i	0.135607	−	0.0433369i
$875$		0			0
$876$	−27.4663	−	38.5839i	−0.928000	−	1.30363i
$877$	−1.48622	−	5.54663i	−0.0501860	−	0.187297i	0.936282	−	0.351248i	$-0.114243\pi$
$877$	−1.48622	−	5.54663i	−0.0501860	−	0.187297i	−0.986468	+	0.163951i	$0.947576\pi$
$878$	−2.00190	−	42.0952i	−0.0675609	−	1.42064i
$879$	−2.25970	−	3.91392i	−0.0762179	−	0.132013i
$880$		0			0
$881$	3.68416			0.124122			0.0620612	−	0.998072i	$-0.480233\pi$
$881$	3.68416			0.124122			0.0620612	+	0.998072i	$0.480233\pi$
$882$	−6.59163	+	29.9227i	−0.221952	+	1.00755i
$883$	−10.4605	+	10.4605i	−0.352023	+	0.352023i	−0.860862	−	0.508839i	$-0.830075\pi$
$883$	−10.4605	+	10.4605i	−0.352023	+	0.352023i	0.508839	+	0.860862i	$0.330075\pi$
$884$	0.824893	−	0.0786359i	0.0277442	−	0.00264481i
$885$		0			0
$886$	42.7261	+	38.8468i	1.43541	+	1.30508i
$887$	−30.8995	+	8.27950i	−1.03750	+	0.277998i	−0.737079	−	0.675807i	$-0.763795\pi$
$887$	−30.8995	+	8.27950i	−1.03750	+	0.277998i	−0.300426	+	0.953805i	$0.597129\pi$
$888$	−15.9418	+	2.28822i	−0.534972	+	0.0767876i
$889$	−24.2366	−	3.22221i	−0.812869	−	0.108070i
$890$		0			0
$891$	−35.6571	−	20.5866i	−1.19456	−	0.689678i
$892$	−13.5348	−	36.3059i	−0.453180	−	1.21561i
$893$	1.88550	−	7.03680i	0.0630960	−	0.235477i
$894$	21.1563	+	4.60402i	0.707571	+	0.153981i
$895$		0			0
$896$	1.83459	−	29.8770i	0.0612892	−	0.998120i
$897$	−0.165512	+	0.165512i	−0.00552627	+	0.00552627i
$898$	−15.8289	−	24.6345i	−0.528216	−	0.822064i
$899$	16.8624	+	29.2066i	0.562394	+	0.974095i
$900$		0			0
$901$	23.3433	−	40.4318i	0.777679	−	1.34698i
$902$	17.5266	−	33.9903i	0.583572	−	1.13175i
$903$	−5.57778	+	13.4176i	−0.185617	+	0.446510i
$904$	−0.0671850	+	0.0897042i	−0.00223454	+	0.00298352i
$905$		0			0
$906$	23.6578	−	26.0204i	0.785979	−	0.864469i
$907$	3.58771	−	13.3895i	0.119128	−	0.444592i	−0.880435	−	0.474168i	$-0.842749\pi$
$907$	3.58771	−	13.3895i	0.119128	−	0.444592i	0.999563	+	0.0295760i	$0.00941571\pi$
$908$	−35.3967	−	29.2354i	−1.17468	−	0.970212i
$909$			26.5390i			0.880243i
$910$		0			0
$911$		−	47.8573i		−	1.58558i	−0.609494	−	0.792791i	$-0.708627\pi$
$911$		−	47.8573i		−	1.58558i	0.609494	−	0.792791i	$-0.291373\pi$
$912$	−25.9141	−	1.86166i	−0.858101	−	0.0616458i
$913$	−9.73964	+	36.3488i	−0.322335	+	1.20297i
$914$	3.92031	+	3.56437i	0.129672	+	0.117899i
$915$		0			0
$916$	−19.4528	+	13.8476i	−0.642739	+	0.457539i
$917$	−9.68165	+	1.26207i	−0.319716	+	0.0416773i
$918$	1.45913	+	0.752382i	0.0481586	+	0.0248323i
$919$	3.56719	−	6.17855i	0.117671	−	0.203812i	−0.801173	−	0.598432i	$-0.795791\pi$
$919$	3.56719	−	6.17855i	0.117671	−	0.203812i	0.918844	+	0.394620i	$0.129124\pi$
$920$		0			0
$921$	6.74155	+	11.6767i	0.222142	+	0.384761i
$922$	7.93367	−	5.09778i	0.261282	−	0.167886i
$923$	0.857128	−	0.857128i	0.0282127	−	0.0282127i
$924$	−28.8851	−	54.6178i	−0.950251	−	1.79680i
$925$		0			0
$926$	6.28930	−	28.9004i	0.206679	−	0.949727i
$927$	−2.61640	+	9.76453i	−0.0859338	+	0.320709i
$928$	−11.6073	+	39.4729i	−0.381027	+	1.29576i
$929$	−22.9712	−	13.2625i	−0.753662	−	0.435127i	0.0733534	−	0.997306i	$-0.476630\pi$
$929$	−22.9712	−	13.2625i	−0.753662	−	0.435127i	−0.827016	+	0.562179i	$0.809963\pi$
$930$		0			0
$931$	−12.9890	−	13.0554i	−0.425698	−	0.427872i
$932$	−7.89802	+	46.9223i	−0.258708	+	1.53699i
$933$	48.9615	−	13.1192i	1.60293	−	0.429503i
$934$	−26.7192	+	29.3875i	−0.874280	+	0.961587i
$935$		0			0
$936$	0.674562	−	0.288675i	0.0220487	−	0.00943563i
$937$	−4.34151	+	4.34151i	−0.141831	+	0.141831i	−0.774457	−	0.632626i	$-0.781977\pi$
$937$	−4.34151	+	4.34151i	−0.141831	+	0.141831i	0.632626	+	0.774457i	$0.281977\pi$
$938$	−1.56368	−	1.08882i	−0.0510560	−	0.0355513i
$939$	68.9071			2.24870
$940$		0			0
$941$	−12.9331	−	22.4008i	−0.421607	−	0.730245i	0.574490	−	0.818512i	$-0.305200\pi$
$941$	−12.9331	−	22.4008i	−0.421607	−	0.730245i	−0.996097	+	0.0882670i	$0.971867\pi$
$942$	−50.8117	+	2.41643i	−1.65553	+	0.0787314i
$943$	1.67398	+	6.24739i	0.0545124	+	0.203443i
$944$	4.39320	−	12.6803i	0.142987	−	0.412710i
$945$		0			0
$946$	−4.52941	−	14.1731i	−0.147264	−	0.460807i
$947$	28.6706	−	7.68227i	0.931670	−	0.249640i	0.239103	−	0.970994i	$-0.423147\pi$
$947$	28.6706	−	7.68227i	0.931670	−	0.249640i	0.692567	+	0.721354i	$0.256480\pi$
$948$	10.5283	+	28.2413i	0.341945	+	0.917233i
$949$	−0.696229	+	0.401968i	−0.0226006	+	0.0130484i
$950$		0			0
$951$			31.9921i			1.03741i
$952$	−18.8279	−	31.8423i	−0.610215	−	1.03201i
$953$	33.9836	+	33.9836i	1.10084	+	1.10084i	0.994310	+	0.106528i	$0.0339734\pi$
$953$	33.9836	+	33.9836i	1.10084	+	1.10084i	0.106528	+	0.994310i	$0.466027\pi$
$954$	8.79063	−	40.3945i	0.284607	−	1.30782i
$955$		0			0
$956$	−1.25290	+	2.74232i	−0.0405217	+	0.0886930i
$957$	21.9805	+	82.0323i	0.710528	+	2.65173i
$958$	−13.2518	−	6.83311i	−0.428146	−	0.220768i
$959$	−48.5669	+	20.0446i	−1.56831	+	0.647275i
$960$		0			0
$961$	−4.75009	+	8.22739i	−0.153229	+	0.265400i
$962$	0.0129862	+	0.273068i	0.000418691	+	0.00880407i
$963$	20.3065	+	5.44110i	0.654367	+	0.175337i
$964$	36.8950	−	3.51715i	1.18831	−	0.113280i
$965$		0			0
$966$	9.82852	+	3.54822i	0.316228	+	0.114162i
$967$	26.2766	+	26.2766i	0.844999	+	0.844999i	0.989504	−	0.144505i	$-0.0461589\pi$
$967$	26.2766	+	26.2766i	0.844999	+	0.844999i	−0.144505	+	0.989504i	$0.546159\pi$
$968$	29.8484	+	11.9577i	0.959365	+	0.384336i
$969$	−27.8061	+	16.0539i	−0.893260	+	0.515724i
$970$		0			0
$971$	−40.7412	−	23.5219i	−1.30745	−	0.754855i	−0.325778	−	0.945446i	$-0.605626\pi$
$971$	−40.7412	−	23.5219i	−1.30745	−	0.754855i	−0.981670	+	0.190591i	$0.938960\pi$
$972$	−43.7784	−	7.36883i	−1.40419	−	0.236355i
$973$	−2.42868	+	1.85869i	−0.0778600	+	0.0595867i
$974$	−16.3851	−	51.2711i	−0.525013	−	1.64283i
$975$		0			0
$976$	7.68913	−	1.47943i	0.246123	−	0.0473555i
$977$	−21.3849	−	5.73007i	−0.684163	−	0.183321i	−0.100037	−	0.994984i	$-0.531896\pi$
$977$	−21.3849	−	5.73007i	−0.684163	−	0.183321i	−0.584126	+	0.811663i	$0.698563\pi$
$978$	5.57087	+	8.66996i	0.178137	+	0.277235i
$979$	78.9044			2.52180
$980$		0			0
$981$	−12.1307			−0.387305
$982$	2.75039	+	4.28044i	0.0877686	+	0.136594i
$983$	−17.0668	−	4.57305i	−0.544348	−	0.145858i	−0.0238421	−	0.999716i	$-0.507590\pi$
$983$	−17.0668	−	4.57305i	−0.544348	−	0.145858i	−0.520506	+	0.853858i	$0.674257\pi$
$984$	4.74939	−	39.6424i	0.151405	−	1.26376i
$985$		0			0
$986$	15.4783	+	48.4336i	0.492930	+	1.54244i
$987$	14.3635	−	10.9924i	0.457194	−	0.349893i
$988$	−0.0732017	+	0.434893i	−0.00232886	+	0.0138358i
$989$	2.17929	+	1.25821i	0.0692975	+	0.0400089i
$990$		0			0
$991$	3.59673	−	2.07657i	0.114254	−	0.0659645i	−0.441784	−	0.897121i	$-0.645654\pi$
$991$	3.59673	−	2.07657i	0.114254	−	0.0659645i	0.556038	+	0.831157i	$0.312321\pi$
$992$	25.4927	−	6.17378i	0.809395	−	0.196018i
$993$	12.9278	+	12.9278i	0.410250	+	0.410250i
$994$	−50.8985	−	18.3750i	−1.61440	−	0.582820i
$995$		0			0
$996$	3.72829	+	39.1099i	0.118135	+	1.23924i
$997$	−23.3879	−	6.26677i	−0.740702	−	0.198471i	−0.131312	−	0.991341i	$-0.541919\pi$
$997$	−23.3879	−	6.26677i	−0.740702	−	0.198471i	−0.609390	+	0.792870i	$0.708586\pi$
$998$	0.687398	+	14.4544i	0.0217592	+	0.457545i
$999$	−0.270807	+	0.469052i	−0.00856796	+	0.0148401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.443.4		72
4.3	odd	2	inner	700.2.be.e.443.18		72
5.2	odd	4	inner	700.2.be.e.107.7		72
5.3	odd	4		140.2.w.b.107.12	yes	72
5.4	even	2		140.2.w.b.23.15	yes	72
7.4	even	3	inner	700.2.be.e.543.10		72
20.3	even	4		140.2.w.b.107.9	yes	72
20.7	even	4	inner	700.2.be.e.107.10		72
20.19	odd	2		140.2.w.b.23.1	✓	72
28.11	odd	6	inner	700.2.be.e.543.7		72
35.3	even	12		980.2.x.m.67.1		72
35.4	even	6		140.2.w.b.123.9	yes	72
35.9	even	6		980.2.k.k.883.4		36
35.13	even	4		980.2.x.m.667.12		72
35.18	odd	12		140.2.w.b.67.1	yes	72
35.19	odd	6		980.2.k.j.883.4		36
35.23	odd	12		980.2.k.k.687.14		36
35.24	odd	6		980.2.x.m.263.9		72
35.32	odd	12	inner	700.2.be.e.207.18		72
35.33	even	12		980.2.k.j.687.14		36
35.34	odd	2		980.2.x.m.863.15		72
140.3	odd	12		980.2.x.m.67.15		72
140.19	even	6		980.2.k.j.883.14		36
140.23	even	12		980.2.k.k.687.4		36
140.39	odd	6		140.2.w.b.123.12	yes	72
140.59	even	6		980.2.x.m.263.12		72
140.67	even	12	inner	700.2.be.e.207.4		72
140.79	odd	6		980.2.k.k.883.14		36
140.83	odd	4		980.2.x.m.667.9		72
140.103	odd	12		980.2.k.j.687.4		36
140.123	even	12		140.2.w.b.67.15	yes	72
140.139	even	2		980.2.x.m.863.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.1	✓	72	20.19	odd	2
140.2.w.b.23.15	yes	72	5.4	even	2
140.2.w.b.67.1	yes	72	35.18	odd	12
140.2.w.b.67.15	yes	72	140.123	even	12
140.2.w.b.107.9	yes	72	20.3	even	4
140.2.w.b.107.12	yes	72	5.3	odd	4
140.2.w.b.123.9	yes	72	35.4	even	6
140.2.w.b.123.12	yes	72	140.39	odd	6
700.2.be.e.107.7		72	5.2	odd	4	inner
700.2.be.e.107.10		72	20.7	even	4	inner
700.2.be.e.207.4		72	140.67	even	12	inner
700.2.be.e.207.18		72	35.32	odd	12	inner
700.2.be.e.443.4		72	1.1	even	1	trivial
700.2.be.e.443.18		72	4.3	odd	2	inner
700.2.be.e.543.7		72	28.11	odd	6	inner
700.2.be.e.543.10		72	7.4	even	3	inner
980.2.k.j.687.4		36	140.103	odd	12
980.2.k.j.687.14		36	35.33	even	12
980.2.k.j.883.4		36	35.19	odd	6
980.2.k.j.883.14		36	140.19	even	6
980.2.k.k.687.4		36	140.23	even	12
980.2.k.k.687.14		36	35.23	odd	12
980.2.k.k.883.4		36	35.9	even	6
980.2.k.k.883.14		36	140.79	odd	6
980.2.x.m.67.1		72	35.3	even	12
980.2.x.m.67.15		72	140.3	odd	12
980.2.x.m.263.9		72	35.24	odd	6
980.2.x.m.263.12		72	140.59	even	6
980.2.x.m.667.9		72	140.83	odd	4
980.2.x.m.667.12		72	35.13	even	4
980.2.x.m.863.1		72	140.139	even	2
980.2.x.m.863.15		72	35.34	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18977 + 0.764487i) q^{2} +(2.38471 + 0.638980i) q^{3} +(0.831118 - 1.81913i) q^{4} +(-3.32575 + 1.06284i) q^{6} +(2.10106 - 1.60796i) q^{7} +(0.401862 + 2.79973i) q^{8} +(2.68045 + 1.54756i) q^{9} +(4.09588 - 2.36476i) q^{11} +(3.14436 - 3.80703i) q^{12} +(-0.0592655 - 0.0592655i) q^{13} +(-1.27053 + 3.51934i) q^{14} +(-2.61849 - 3.02383i) q^{16} +(-4.77484 - 1.27942i) q^{17} +(-4.37222 + 0.207927i) q^{18} +(1.31544 - 2.27842i) q^{19} +(6.03788 - 2.49197i) q^{21} +(-3.06534 + 5.94478i) q^{22} +(-0.292774 - 1.09265i) q^{23} +(-0.830651 + 6.93332i) q^{24} +(0.115820 + 0.0252047i) q^{26} +(0.166053 + 0.166053i) q^{27} +(-1.17885 - 5.15852i) q^{28} +7.27332i q^{29} +(4.01558 - 2.31840i) q^{31} +(5.42708 + 1.59587i) q^{32} +(11.2785 - 3.02207i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(0.596933 + 2.22779i) q^{37} +(0.176741 + 3.71644i) q^{38} +(-0.103461 - 0.179200i) q^{39} -5.71767 q^{41} +(-5.27862 + 7.58075i) q^{42} +(-1.57302 + 1.57302i) q^{43} +(-0.897647 - 9.41635i) q^{44} +(1.18365 + 1.07618i) q^{46} +(2.67468 - 0.716679i) q^{47} +(-4.31215 - 8.88410i) q^{48} +(1.82895 - 6.75684i) q^{49} +(-10.5691 - 6.10206i) q^{51} +(-0.157068 + 0.0585551i) q^{52} +(-2.44441 + 9.12265i) q^{53} +(-0.324510 - 0.0706197i) q^{54} +(5.34619 + 5.23624i) q^{56} +(4.59281 - 4.59281i) q^{57} +(-5.56036 - 8.65360i) q^{58} +(1.67748 + 2.90547i) q^{59} +(-0.978771 + 1.69528i) q^{61} +(-3.00524 + 5.82822i) q^{62} +(8.12021 - 1.05853i) q^{63} +(-7.67701 + 2.25021i) q^{64} +(-11.1085 + 12.2179i) q^{66} +(-0.131802 + 0.491893i) q^{67} +(-6.29589 + 7.62273i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(-3.25558 + 8.12646i) q^{72} +(2.48257 - 9.26507i) q^{73} +(-2.41333 - 2.19421i) q^{74} +(-3.05145 - 4.28660i) q^{76} +(4.80329 - 11.5545i) q^{77} +(0.260092 + 0.134113i) q^{78} +(-3.05204 + 5.28630i) q^{79} +(-4.35280 - 7.53927i) q^{81} +(6.80273 - 4.37109i) q^{82} +(-5.62620 + 5.62620i) q^{83} +(0.484971 - 13.0548i) q^{84} +(0.668982 - 3.07409i) q^{86} +(-4.64751 + 17.3447i) q^{87} +(8.26668 + 10.5171i) q^{88} +(14.4482 + 8.34169i) q^{89} +(-0.219817 - 0.0292243i) q^{91} +(-2.23100 - 0.375524i) q^{92} +(11.0574 - 2.96282i) q^{93} +(-2.63437 + 2.89745i) q^{94} +(11.9223 + 7.27348i) q^{96} +(-5.81505 + 5.81505i) q^{97} +(2.98949 + 9.43732i) q^{98} +14.6384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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