LMFDB - Embedded newform 403.2.l.c.129.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.23
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.921357i q^{2} +(-0.264605 + 0.458309i) q^{3} +1.15110 q^{4} +(-2.89414 + 1.67093i) q^{5} +(-0.422266 - 0.243795i) q^{6} +(-0.336375 - 0.194206i) q^{7} +2.90329i q^{8} +(1.35997 + 2.35553i) q^{9} +O(q^{10})$	\(q+0.921357i q^{2} +(-0.264605 + 0.458309i) q^{3} +1.15110 q^{4} +(-2.89414 + 1.67093i) q^{5} +(-0.422266 - 0.243795i) q^{6} +(-0.336375 - 0.194206i) q^{7} +2.90329i q^{8} +(1.35997 + 2.35553i) q^{9} +(-1.53952 - 2.66653i) q^{10} +(1.48736 - 0.858726i) q^{11} +(-0.304587 + 0.527560i) q^{12} +(-2.58614 - 2.51235i) q^{13} +(0.178933 - 0.309921i) q^{14} -1.76854i q^{15} -0.372763 q^{16} +(-3.39637 + 5.88269i) q^{17} +(-2.17029 + 1.25302i) q^{18} +(-3.04784 - 1.75967i) q^{19} +(-3.33144 + 1.92341i) q^{20} +(0.178013 - 0.102776i) q^{21} +(0.791193 + 1.37039i) q^{22} -5.13958 q^{23} +(-1.33060 - 0.768224i) q^{24} +(3.08402 - 5.34167i) q^{25} +(2.31477 - 2.38276i) q^{26} -3.02705 q^{27} +(-0.387201 - 0.223551i) q^{28} +6.43390 q^{29} +1.62946 q^{30} +(1.53653 + 5.35155i) q^{31} +5.46313i q^{32} +0.908892i q^{33} +(-5.42006 - 3.12927i) q^{34} +1.29802 q^{35} +(1.56546 + 2.71146i) q^{36} +(8.23736 + 4.75584i) q^{37} +(1.62128 - 2.80815i) q^{38} +(1.83574 - 0.520472i) q^{39} +(-4.85119 - 8.40251i) q^{40} +(-2.23586 + 1.29088i) q^{41} +(0.0946930 + 0.164013i) q^{42} +(-0.0134584 + 0.0233107i) q^{43} +(1.71210 - 0.988481i) q^{44} +(-7.87187 - 4.54483i) q^{45} -4.73539i q^{46} -8.52072i q^{47} +(0.0986349 - 0.170841i) q^{48} +(-3.42457 - 5.93153i) q^{49} +(4.92159 + 2.84148i) q^{50} +(-1.79739 - 3.11317i) q^{51} +(-2.97691 - 2.89196i) q^{52} +(5.34839 + 9.26368i) q^{53} -2.78899i q^{54} +(-2.86974 + 4.97054i) q^{55} +(0.563836 - 0.976592i) q^{56} +(1.61294 - 0.931234i) q^{57} +5.92791i q^{58} +(2.19840 + 1.26924i) q^{59} -2.03577i q^{60} +9.90394 q^{61} +(-4.93069 + 1.41569i) q^{62} -1.05646i q^{63} -5.77902 q^{64} +(11.6826 + 2.94981i) q^{65} -0.837414 q^{66} +(-1.42755 + 0.824195i) q^{67} +(-3.90957 + 6.77157i) q^{68} +(1.35996 - 2.35551i) q^{69} +1.19594i q^{70} +(13.4306 - 7.75418i) q^{71} +(-6.83880 + 3.94838i) q^{72} +(0.522668 - 0.301763i) q^{73} +(-4.38183 + 7.58955i) q^{74} +(1.63209 + 2.82686i) q^{75} +(-3.50837 - 2.02556i) q^{76} -0.667079 q^{77} +(0.479541 + 1.69137i) q^{78} +(-1.05400 + 1.82557i) q^{79} +(1.07883 - 0.622861i) q^{80} +(-3.27894 + 5.67928i) q^{81} +(-1.18936 - 2.06003i) q^{82} +(14.4287 - 8.33039i) q^{83} +(0.204911 - 0.118305i) q^{84} -22.7004i q^{85} +(-0.0214775 - 0.0124000i) q^{86} +(-1.70244 + 2.94871i) q^{87} +(2.49313 + 4.31823i) q^{88} +12.7022i q^{89} +(4.18741 - 7.25280i) q^{90} +(0.381999 + 1.34733i) q^{91} -5.91617 q^{92} +(-2.85924 - 0.711841i) q^{93} +7.85063 q^{94} +11.7611 q^{95} +(-2.50380 - 1.44557i) q^{96} -1.89406i q^{97} +(5.46505 - 3.15525i) q^{98} +(4.04552 + 2.33568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			0.921357i			0.651498i	0.945456	+	0.325749i	$0.105616\pi$
$2$			0.921357i			0.651498i	−0.945456	+	0.325749i	$0.894384\pi$
$3$	−0.264605	+	0.458309i	−0.152770	+	0.264605i	−0.932245	−	0.361829i	$-0.882153\pi$
$3$	−0.264605	+	0.458309i	−0.152770	+	0.264605i	0.779475	+	0.626433i	$0.215486\pi$
$4$	1.15110			0.575551
$5$	−2.89414	+	1.67093i	−1.29430	+	0.747263i	−0.979413	−	0.201867i	$-0.935299\pi$
$5$	−2.89414	+	1.67093i	−1.29430	+	0.747263i	−0.314884	+	0.949130i	$0.601966\pi$
$6$	−0.422266	−	0.243795i	−0.172389	−	0.0995291i
$7$	−0.336375	−	0.194206i	−0.127138	−	0.0734029i	0.435082	−	0.900391i	$-0.356719\pi$
$7$	−0.336375	−	0.194206i	−0.127138	−	0.0734029i	−0.562220	+	0.826988i	$0.690053\pi$
$8$			2.90329i			1.02647i
$9$	1.35997	+	2.35553i	0.453323	+	0.785178i
$10$	−1.53952	−	2.66653i	−0.486840	−	0.843232i
$11$	1.48736	−	0.858726i	0.448455	−	0.258916i	−0.258722	−	0.965952i	$-0.583301\pi$
$11$	1.48736	−	0.858726i	0.448455	−	0.258916i	0.707178	+	0.707036i	$0.249968\pi$
$12$	−0.304587	+	0.527560i	−0.0879267	+	0.152293i
$13$	−2.58614	−	2.51235i	−0.717266	−	0.696799i
$13$	−2.58614	−	2.51235i	−0.717266	−	0.696799i
$14$	0.178933	−	0.309921i	0.0478218	−	0.0828299i
$15$		−	1.76854i		−	0.456636i
$16$	−0.372763			−0.0931908
$17$	−3.39637	+	5.88269i	−0.823741	+	1.42676i	0.0791365	+	0.996864i	$0.474784\pi$
$17$	−3.39637	+	5.88269i	−0.823741	+	1.42676i	−0.902878	+	0.429898i	$0.858550\pi$
$18$	−2.17029	+	1.25302i	−0.511542	+	0.295339i
$19$	−3.04784	−	1.75967i	−0.699222	−	0.403696i	0.107836	−	0.994169i	$-0.465608\pi$
$19$	−3.04784	−	1.75967i	−0.699222	−	0.403696i	−0.807057	+	0.590473i	$0.798941\pi$
$20$	−3.33144	+	1.92341i	−0.744934	+	0.430088i
$21$	0.178013	−	0.102776i	0.0388455	−	0.0224275i
$22$	0.791193	+	1.37039i	0.168683	+	0.292167i
$23$	−5.13958			−1.07168			−0.535838	−	0.844321i	$-0.680004\pi$
$23$	−5.13958			−1.07168			−0.535838	+	0.844321i	$0.680004\pi$
$24$	−1.33060	−	0.768224i	−0.271608	−	0.156813i
$25$	3.08402	−	5.34167i	0.616803	−	1.06833i
$26$	2.31477	−	2.38276i	0.453963	−	0.467297i
$27$	−3.02705			−0.582555
$28$	−0.387201	−	0.223551i	−0.0731741	−	0.0422471i
$29$	6.43390			1.19474			0.597372	−	0.801964i	$-0.296212\pi$
$29$	6.43390			1.19474			0.597372	+	0.801964i	$0.296212\pi$
$30$	1.62946			0.297498
$31$	1.53653	+	5.35155i	0.275969	+	0.961167i
$31$	1.53653	+	5.35155i	0.275969	+	0.961167i
$32$			5.46313i			0.965754i
$33$			0.908892i			0.158218i
$34$	−5.42006	−	3.12927i	−0.929532	−	0.536665i
$35$	1.29802			0.219405
$36$	1.56546	+	2.71146i	0.260910	+	0.451910i
$37$	8.23736	+	4.75584i	1.35421	+	0.781855i	0.988837	−	0.149004i	$-0.0476068\pi$
$37$	8.23736	+	4.75584i	1.35421	+	0.781855i	0.365377	+	0.930860i	$0.380940\pi$
$38$	1.62128	−	2.80815i	0.263007	−	0.455541i
$39$	1.83574	−	0.520472i	0.293953	−	0.0833423i
$40$	−4.85119	−	8.40251i	−0.767041	−	1.32855i
$41$	−2.23586	+	1.29088i	−0.349183	+	0.201601i	−0.664326	−	0.747443i	$-0.731281\pi$
$41$	−2.23586	+	1.29088i	−0.349183	+	0.201601i	0.315142	+	0.949044i	$0.397948\pi$
$42$	0.0946930	+	0.164013i	0.0146115	+	0.0253078i
$43$	−0.0134584	+	0.0233107i	−0.00205239	+	0.00355485i	−0.867050	−	0.498222i	$-0.833987\pi$
$43$	−0.0134584	+	0.0233107i	−0.00205239	+	0.00355485i	0.864997	+	0.501776i	$0.167320\pi$
$44$	1.71210	−	0.988481i	0.258109	−	0.149019i
$45$	−7.87187	−	4.54483i	−1.17347	−	0.677503i
$46$		−	4.73539i		−	0.698194i
$47$		−	8.52072i		−	1.24287i	−0.783464	−	0.621437i	$-0.786549\pi$
$47$		−	8.52072i		−	1.24287i	0.783464	−	0.621437i	$-0.213451\pi$
$48$	0.0986349	−	0.170841i	0.0142367	−	0.0246587i
$49$	−3.42457	−	5.93153i	−0.489224	−	0.847361i
$50$	4.92159	+	2.84148i	0.696018	+	0.401846i
$51$	−1.79739	−	3.11317i	−0.251685	−	0.435932i
$52$	−2.97691	−	2.89196i	−0.412823	−	0.401043i
$53$	5.34839	+	9.26368i	0.734658	+	1.27246i	0.954873	+	0.297013i	$0.0959905\pi$
$53$	5.34839	+	9.26368i	0.734658	+	1.27246i	−0.220216	+	0.975451i	$0.570676\pi$
$54$		−	2.78899i		−	0.379533i
$55$	−2.86974	+	4.97054i	−0.386956	+	0.670228i
$56$	0.563836	−	0.976592i	0.0753457	−	0.130503i
$57$	1.61294	−	0.931234i	0.213640	−	0.123345i
$58$			5.92791i			0.778373i
$59$	2.19840	+	1.26924i	0.286207	+	0.165242i	0.636230	−	0.771499i	$-0.280493\pi$
$59$	2.19840	+	1.26924i	0.286207	+	0.165242i	−0.350023	+	0.936741i	$0.613826\pi$
$60$		−	2.03577i		−	0.262817i
$61$	9.90394			1.26807			0.634035	−	0.773304i	$-0.281398\pi$
$61$	9.90394			1.26807			0.634035	+	0.773304i	$0.281398\pi$
$62$	−4.93069	+	1.41569i	−0.626198	+	0.179793i
$63$		−	1.05646i		−	0.133101i
$64$	−5.77902			−0.722377
$65$	11.6826	+	2.94981i	1.44905	+	0.365879i
$66$	−0.837414			−0.103079
$67$	−1.42755	+	0.824195i	−0.174403	+	0.100691i	−0.584660	−	0.811278i	$-0.698772\pi$
$67$	−1.42755	+	0.824195i	−0.174403	+	0.100691i	0.410257	+	0.911970i	$0.365439\pi$
$68$	−3.90957	+	6.77157i	−0.474105	+	0.821173i
$69$	1.35996	−	2.35551i	0.163720	−	0.283571i
$70$			1.19594i			0.142942i
$71$	13.4306	−	7.75418i	1.59392	−	0.920252i	0.601298	−	0.799025i	$-0.294651\pi$
$71$	13.4306	−	7.75418i	1.59392	−	0.920252i	0.992625	−	0.121226i	$-0.0386827\pi$
$72$	−6.83880	+	3.94838i	−0.805960	+	0.465321i
$73$	0.522668	−	0.301763i	0.0611737	−	0.0353187i	−0.469101	−	0.883144i	$-0.655422\pi$
$73$	0.522668	−	0.301763i	0.0611737	−	0.0353187i	0.530275	+	0.847826i	$0.322089\pi$
$74$	−4.38183	+	7.58955i	−0.509377	+	0.882267i
$75$	1.63209	+	2.82686i	0.188458	+	0.326418i
$76$	−3.50837	−	2.02556i	−0.402437	−	0.232347i
$77$	−0.667079			−0.0760207
$78$	0.479541	+	1.69137i	0.0542973	+	0.191510i
$79$	−1.05400	+	1.82557i	−0.118584	+	0.205393i	−0.919207	−	0.393775i	$-0.871169\pi$
$79$	−1.05400	+	1.82557i	−0.118584	+	0.205393i	0.800623	+	0.599169i	$0.204502\pi$
$80$	1.07883	−	0.622861i	0.120617	−	0.0696380i
$81$	−3.27894	+	5.67928i	−0.364326	+	0.631031i
$82$	−1.18936	−	2.06003i	−0.131343	−	0.227492i
$83$	14.4287	−	8.33039i	1.58375	−	0.914379i	0.589446	−	0.807808i	$-0.299346\pi$
$83$	14.4287	−	8.33039i	1.58375	−	0.914379i	0.994305	−	0.106571i	$-0.0339871\pi$
$84$	0.204911	−	0.118305i	0.0223576	−	0.0129082i
$85$		−	22.7004i		−	2.46220i
$86$	−0.0214775	−	0.0124000i	−0.00231598	−	0.00133713i
$87$	−1.70244	+	2.94871i	−0.182521	+	0.316135i
$88$	2.49313	+	4.31823i	0.265769	+	0.460325i
$89$			12.7022i			1.34643i	0.739446	+	0.673216i	$0.235088\pi$
$89$			12.7022i			1.34643i	−0.739446	+	0.673216i	$0.764912\pi$
$90$	4.18741	−	7.25280i	0.441391	−	0.764512i
$91$	0.381999	+	1.34733i	0.0400444	+	0.141239i
$92$	−5.91617			−0.616804
$93$	−2.85924	−	0.711841i	−0.296489	−	0.0738145i
$94$	7.85063			0.809730
$95$	11.7611			1.20667
$96$	−2.50380	−	1.44557i	−0.255543	−	0.147538i
$97$		−	1.89406i		−	0.192313i	−0.995366	−	0.0961564i	$-0.969345\pi$
$97$		−	1.89406i		−	0.192313i	0.995366	−	0.0961564i	$-0.0306549\pi$
$98$	5.46505	−	3.15525i	0.552054	−	0.318728i
$99$	4.04552	+	2.33568i	0.406590	+	0.234745i
$100$	3.55002	−	6.14881i	0.355002	−	0.614881i
$101$	7.21921			0.718338			0.359169	−	0.933272i	$-0.383060\pi$
$101$	7.21921			0.718338			0.359169	+	0.933272i	$0.383060\pi$
$102$	2.86835	−	1.65604i	0.284009	−	0.163972i
$103$	5.75322	+	9.96487i	0.566882	+	0.981868i	0.996872	+	0.0790344i	$0.0251837\pi$
$103$	5.75322	+	9.96487i	0.566882	+	0.981868i	−0.429990	+	0.902834i	$0.641483\pi$
$104$	7.29407	−	7.50831i	0.715242	−	0.736251i
$105$	−0.343462	+	0.594893i	−0.0335184	+	0.0580556i
$106$	−8.53516	+	4.92777i	−0.829008	+	0.478628i
$107$	−5.39261	+	9.34028i	−0.521324	+	0.902959i	0.478369	+	0.878159i	$0.341228\pi$
$107$	−5.39261	+	9.34028i	−0.521324	+	0.902959i	−0.999692	+	0.0247999i	$0.992105\pi$
$108$	−3.48444			−0.335290
$109$		−	5.01983i		−	0.480813i	−0.970672	−	0.240406i	$-0.922719\pi$
$109$		−	5.01983i		−	0.480813i	0.970672	−	0.240406i	$-0.0772807\pi$
$110$	−4.57964	−	2.64406i	−0.436652	−	0.252101i
$111$	−4.35929	+	2.51684i	−0.413765	+	0.238888i
$112$	0.125388	+	0.0723928i	0.0118481	+	0.00684048i
$113$	−5.61711	−	9.72911i	−0.528413	−	0.915238i	−0.999451	−	0.0331252i	$-0.989454\pi$
$113$	−5.61711	−	9.72911i	−0.528413	−	0.915238i	0.471038	−	0.882113i	$-0.343879\pi$
$114$	0.857999	+	1.48610i	0.0803589	+	0.139186i
$115$	14.8746	−	8.58787i	1.38707	−	0.800823i
$116$	7.40607			0.687636
$117$	2.40085	−	9.50845i	0.221958	−	0.879057i
$118$	−1.16943	+	2.02551i	−0.107655	+	0.186463i
$119$	2.28491	−	1.31919i	0.209457	−	0.120930i
$120$	5.13460			0.468722
$121$	−4.02518	+	6.97181i	−0.365925	+	0.633801i
$122$			9.12507i			0.826145i
$123$		−	1.36629i		−	0.123194i
$124$	1.76870	+	6.16018i	0.158834	+	0.553200i
$125$			3.90340i			0.349131i
$126$	0.973373			0.0867149
$127$	8.40593	−	14.5595i	0.745906	−	1.29195i	−0.203865	−	0.978999i	$-0.565350\pi$
$127$	8.40593	−	14.5595i	0.745906	−	1.29195i	0.949770	−	0.312948i	$-0.101316\pi$
$128$			5.60172i			0.495127i
$129$	−0.00712234	−	0.0123362i	−0.000627087	−	0.00108615i
$130$	−2.71783	+	10.7638i	−0.238369	+	0.944051i
$131$	−4.51417	+	7.81877i	−0.394405	+	0.683129i	−0.993025	−	0.117904i	$-0.962382\pi$
$131$	−4.51417	+	7.81877i	−0.394405	+	0.683129i	0.598620	+	0.801033i	$0.295716\pi$
$132$			1.04623i			0.0910624i
$133$	0.683476	+	1.18382i	0.0592649	+	0.102650i
$134$	−0.759378	−	1.31528i	−0.0656003	−	0.113623i
$135$	8.76068	−	5.05798i	0.753999	−	0.435322i
$136$	−17.0791	−	9.86065i	−1.46452	−	0.845544i
$137$	−14.3387	+	8.27844i	−1.22504	+	0.707274i	−0.965987	−	0.258590i	$-0.916742\pi$
$137$	−14.3387	+	8.27844i	−1.22504	+	0.707274i	−0.259048	+	0.965864i	$0.583409\pi$
$138$	2.17027	+	1.25301i	0.184746	+	0.106663i
$139$	9.68159			0.821182			0.410591	−	0.911820i	$-0.365322\pi$
$139$	9.68159			0.821182			0.410591	+	0.911820i	$0.365322\pi$
$140$	1.49415			0.126279
$141$	3.90512	+	2.25462i	0.328871	+	0.189874i
$142$	7.14437	+	12.3744i	0.599542	+	1.03844i
$143$	−6.00393	−	1.51597i	−0.502074	−	0.126772i
$144$	−0.506946	−	0.878056i	−0.0422455	−	0.0731714i
$145$	−18.6206	+	10.7506i	−1.54635	+	0.892788i
$146$	0.278031	+	0.481564i	0.0230100	+	0.0398545i
$147$	3.62463			0.298954
$148$	9.48203	+	5.47445i	0.779418	+	0.449997i
$149$	−10.0003	−	5.77366i	−0.819255	−	0.472997i	0.0309046	−	0.999522i	$-0.490161\pi$
$149$	−10.0003	−	5.77366i	−0.819255	−	0.472997i	−0.850159	+	0.526525i	$0.823495\pi$
$150$	−2.60455	+	1.50374i	−0.212661	+	0.122780i
$151$			2.65833i			0.216332i	0.994133	+	0.108166i	$0.0344977\pi$
$151$			2.65833i			0.216332i	−0.994133	+	0.108166i	$0.965502\pi$
$152$	5.10883	−	8.84875i	0.414381	−	0.717728i
$153$	−18.4758			−1.49368
$154$		−	0.614618i		−	0.0495273i
$155$	−13.3890	−	12.9207i	−1.07543	−	1.03781i
$156$	2.11312	−	0.599116i	0.169185	−	0.0479677i
$157$	1.35432			0.108087			0.0540434	−	0.998539i	$-0.482789\pi$
$157$	1.35432			0.108087			0.0540434	+	0.998539i	$0.482789\pi$
$158$	−1.68201	−	0.971107i	−0.133813	−	0.0772571i
$159$	−5.66084			−0.448934
$160$	−9.12851	−	15.8110i	−0.721672	−	1.24997i
$161$	1.72882	+	0.998136i	0.136250	+	0.0786642i
$162$	−5.23265	−	3.02107i	−0.411116	−	0.237358i
$163$			4.10278i			0.321355i	0.987007	+	0.160677i	$0.0513679\pi$
$163$			4.10278i			0.321355i	−0.987007	+	0.160677i	$0.948632\pi$
$164$	−2.57371	+	1.48593i	−0.200973	+	0.116032i
$165$	−1.51870	−	2.63046i	−0.118230	−	0.204781i
$166$	7.67526	+	13.2939i	0.595716	+	1.03181i
$167$	14.3558	+	8.28830i	1.11088	+	0.641368i	0.939058	−	0.343759i	$-0.111700\pi$
$167$	14.3558	+	8.28830i	1.11088	+	0.641368i	0.171824	+	0.985128i	$0.445034\pi$
$168$	0.298387	+	0.516822i	0.0230211	+	0.0398737i
$169$	0.376239	+	12.9946i	0.0289415	+	0.999581i
$170$	20.9152			1.60412
$171$		−	9.57238i		−	0.732018i
$172$	−0.0154920	+	0.0268330i	−0.00118126	+	0.00204600i
$173$	−8.61739	−	14.9257i	−0.655168	−	1.13478i	−0.981852	−	0.189650i	$-0.939265\pi$
$173$	−8.61739	−	14.9257i	−0.655168	−	1.13478i	0.326684	−	0.945134i	$-0.394069\pi$
$174$	−2.71682	−	1.56855i	−0.205961	−	0.118912i
$175$	−2.07477	+	1.19787i	−0.156838	+	0.0905503i
$176$	−0.554432	+	0.320101i	−0.0417919	+	0.0241286i
$177$	−1.16341	+	0.671697i	−0.0874474	+	0.0504878i
$178$	−11.7033			−0.877198
$179$	−6.46323	+	11.1946i	−0.483084	+	0.836726i	−0.999811	−	0.0194238i	$-0.993817\pi$
$179$	−6.46323	+	11.1946i	−0.483084	+	0.836726i	0.516727	+	0.856150i	$0.327150\pi$
$180$	−9.06132	−	5.23155i	−0.675391	−	0.389937i
$181$	−0.617119	−	1.06888i	−0.0458701	−	0.0794493i	0.842179	−	0.539198i	$-0.181273\pi$
$181$	−0.617119	−	1.06888i	−0.0458701	−	0.0794493i	−0.888049	+	0.459749i	$0.847939\pi$
$182$	−1.24137	+	0.351958i	−0.0920168	+	0.0260888i
$183$	−2.62063	+	4.53906i	−0.193723	+	0.335537i
$184$		−	14.9217i		−	1.10004i
$185$	−31.7867			−2.33701
$186$	0.655860	−	2.63438i	0.0480900	−	0.193162i
$187$			11.6662i			0.853118i
$188$		−	9.80821i		−	0.715337i
$189$	1.01822	+	0.587870i	0.0740647	+	0.0427613i
$190$			10.8362i			0.786141i
$191$	−12.0037	−	20.7911i	−0.868559	−	1.50439i	−0.863469	−	0.504402i	$-0.831713\pi$
$191$	−12.0037	−	20.7911i	−0.868559	−	1.50439i	−0.00509028	−	0.999987i	$-0.501620\pi$
$192$	1.52916	−	2.64858i	0.110357	−	0.191145i
$193$	−1.07300	−	0.619496i	−0.0772361	−	0.0445923i	0.460885	−	0.887460i	$-0.347532\pi$
$193$	−1.07300	−	0.619496i	−0.0772361	−	0.0445923i	−0.538121	+	0.842868i	$0.680866\pi$
$194$	1.74511			0.125291
$195$	−4.44320	+	4.57370i	−0.318184	+	0.327530i
$196$	−3.94202	−	6.82779i	−0.281573	−	0.487699i
$197$	−1.23210	+	0.711351i	−0.0877832	+	0.0506816i	−0.543249	−	0.839572i	$-0.682806\pi$
$197$	−1.23210	+	0.711351i	−0.0877832	+	0.0506816i	0.455466	+	0.890253i	$0.349473\pi$
$198$	−2.15200	+	3.72737i	−0.152936	+	0.264892i
$199$	1.53028	+	2.65052i	0.108479	+	0.187890i	0.915154	−	0.403104i	$-0.132069\pi$
$199$	1.53028	+	2.65052i	0.108479	+	0.187890i	−0.806675	+	0.590995i	$0.798735\pi$
$200$	15.5084	+	8.95379i	1.09661	+	0.633129i
$201$		−	0.872344i		−	0.0615304i
$202$			6.65147i			0.467996i
$203$	−2.16420	−	1.24950i	−0.151897	−	0.0876977i
$204$	−2.06898	−	3.58358i	−0.144858	−	0.250901i
$205$	4.31393	−	7.47195i	0.301298	−	0.521863i
$206$	−9.18120	+	5.30077i	−0.639685	+	0.369322i
$207$	−6.98966	−	12.1065i	−0.485815	−	0.841457i
$208$	0.964018	+	0.936510i	0.0668426	+	0.0649353i
$209$	−6.04430			−0.418093
$210$	−0.548109	−	0.316451i	−0.0378231	−	0.0218372i
$211$	12.5242	−	21.6926i	0.862203	−	1.49338i	−0.00759518	−	0.999971i	$-0.502418\pi$
$211$	12.5242	−	21.6926i	0.862203	−	1.49338i	0.869798	−	0.493408i	$-0.164249\pi$
$212$	6.15654	+	10.6634i	0.422833	+	0.732368i
$213$			8.20717i			0.562346i
$214$	−8.60573	−	4.96852i	−0.588276	−	0.339641i
$215$		−	0.0899525i		−	0.00613471i
$216$		−	8.78839i		−	0.597974i
$217$	0.522454	−	2.09853i	0.0354665	−	0.142457i
$218$	4.62506			0.313248
$219$			0.319391i			0.0215825i
$220$	−3.30337	+	5.72160i	−0.222713	+	0.385750i
$221$	23.5628	−	6.68060i	1.58501	−	0.449385i
$222$	−2.31890	−	4.01646i	−0.155635	−	0.269567i
$223$	−18.5559	−	10.7133i	−1.24260	−	0.717414i	−0.272976	−	0.962021i	$-0.588008\pi$
$223$	−18.5559	−	10.7133i	−1.24260	−	0.717414i	−0.969622	+	0.244607i	$0.921341\pi$
$224$	1.06097	−	1.83766i	0.0708892	−	0.122784i
$225$	16.7767			1.11844
$226$	8.96399	−	5.17536i	0.596275	−	0.344260i
$227$	−17.2233	+	9.94388i	−1.14315	+	0.659998i	−0.947209	−	0.320617i	$-0.896110\pi$
$227$	−17.2233	+	9.94388i	−1.14315	+	0.659998i	−0.195942	+	0.980616i	$0.562776\pi$
$228$	1.85666	−	1.07194i	0.122960	−	0.0709913i
$229$	8.91245	+	5.14561i	0.588951	+	0.340031i	0.764683	−	0.644407i	$-0.222896\pi$
$229$	8.91245	+	5.14561i	0.588951	+	0.340031i	−0.175731	+	0.984438i	$0.556229\pi$
$230$	7.91250	+	13.7048i	0.521735	+	0.903671i
$231$	0.176512	−	0.305728i	0.0116137	−	0.0201154i
$232$			18.6795i			1.22637i
$233$	−8.82706			−0.578280			−0.289140	−	0.957287i	$-0.593369\pi$
$233$	−8.82706			−0.578280			−0.289140	+	0.957287i	$0.593369\pi$
$234$	8.76068	+	2.21204i	0.572704	+	0.144605i
$235$	14.2375	+	24.6601i	0.928754	+	1.60865i
$236$	2.53058	+	1.46103i	0.164727	+	0.0951049i
$237$	−0.557785	−	0.966112i	−0.0362320	−	0.0627557i
$238$	1.21545	+	2.10521i	0.0787856	+	0.136461i
$239$	−8.56756	+	4.94648i	−0.554190	+	0.319961i	−0.750810	−	0.660518i	$-0.770337\pi$
$239$	−8.56756	+	4.94648i	−0.554190	+	0.319961i	0.196621	+	0.980480i	$0.437003\pi$
$240$			0.659248i			0.0425543i
$241$	−3.89676	−	2.24979i	−0.251012	−	0.144922i	0.369215	−	0.929344i	$-0.379626\pi$
$241$	−3.89676	−	2.24979i	−0.251012	−	0.144922i	−0.620228	+	0.784422i	$0.712960\pi$
$242$	−6.42353	−	3.70863i	−0.412920	−	0.238400i
$243$	−6.27581	−	10.8700i	−0.402594	−	0.697312i
$244$	11.4004			0.729838
$245$	19.8223	+	11.4444i	1.26640	+	0.731158i
$246$	1.25884			0.0802607
$247$	3.46123	+	12.2080i	0.220233	+	0.776774i
$248$	−15.5371	+	4.46099i	−0.986607	+	0.283273i
$249$			8.81704i			0.558757i
$250$	−3.59643			−0.227458
$251$	−0.203866	+	0.353106i	−0.0128679	+	0.0222879i	−0.872388	−	0.488815i	$-0.837429\pi$
$251$	−0.203866	+	0.353106i	−0.0128679	+	0.0222879i	0.859520	+	0.511103i	$0.170763\pi$
$252$		−	1.21609i		−	0.0766063i
$253$	−7.64439	+	4.41349i	−0.480599	+	0.277474i
$254$	13.4145	+	7.74486i	0.841700	+	0.485956i
$255$	10.4038	+	6.00663i	0.651511	+	0.376150i
$256$	−16.7192			−1.04495
$257$	4.56174	+	7.90116i	0.284553	+	0.492861i	0.972501	−	0.232900i	$-0.0748214\pi$
$257$	4.56174	+	7.90116i	0.284553	+	0.492861i	−0.687948	+	0.725760i	$0.741488\pi$
$258$	0.0113661	−	0.00656221i	0.000707622	−	0.000408546i
$259$	−1.84722	−	3.19949i	−0.114781	−	0.198806i
$260$	13.4479	+	3.39553i	0.834000	+	0.210582i
$261$	8.74990	+	15.1553i	0.541605	+	0.938087i
$262$	−7.20387	−	4.15916i	−0.445057	−	0.256954i
$263$	14.8123			0.913367			0.456684	−	0.889629i	$-0.349037\pi$
$263$	14.8123			0.913367			0.456684	+	0.889629i	$0.349037\pi$
$264$	−2.63878			−0.162405
$265$	−30.9579	−	17.8736i	−1.90173	−	1.09796i
$266$	−1.09072	+	0.629726i	−0.0668761	+	0.0386110i
$267$	−5.82154	−	3.36107i	−0.356272	−	0.205694i
$268$	−1.64325	+	0.948732i	−0.100378	+	0.0579530i
$269$	5.59402	+	9.68913i	0.341074	+	0.590757i	0.984632	−	0.174640i	$-0.0558761\pi$
$269$	5.59402	+	9.68913i	0.341074	+	0.590757i	−0.643559	+	0.765397i	$0.722543\pi$
$270$	4.66021	+	8.07172i	0.283611	+	0.491229i
$271$		−	21.4231i		−	1.30136i	−0.759352	−	0.650680i	$-0.774484\pi$
$271$		−	21.4231i		−	1.30136i	0.759352	−	0.650680i	$-0.225516\pi$
$272$	1.26604	−	2.19285i	0.0767651	−	0.132961i
$273$	−0.718573	−	0.181437i	−0.0434900	−	0.0109811i
$274$	−7.62739	−	13.2110i	−0.460788	−	0.798108i
$275$		−	10.5933i		−	0.638800i
$276$	1.56545	−	2.71144i	0.0942289	−	0.163209i
$277$	−7.73496			−0.464749			−0.232374	−	0.972626i	$-0.574649\pi$
$277$	−7.73496			−0.464749			−0.232374	+	0.972626i	$0.574649\pi$
$278$			8.92020i			0.534998i
$279$	−10.5161	+	10.8973i	−0.629584	+	0.652403i
$280$			3.76852i			0.225212i
$281$		−	22.6650i		−	1.35208i	−0.736866	−	0.676039i	$-0.763695\pi$
$281$		−	22.6650i		−	1.35208i	0.736866	−	0.676039i	$-0.236305\pi$
$282$	−2.07731	+	3.59801i	−0.123702	+	0.214258i
$283$	13.8479			0.823175			0.411587	−	0.911370i	$-0.364975\pi$
$283$	13.8479			0.823175			0.411587	+	0.911370i	$0.364975\pi$
$284$	15.4600	−	8.92584i	0.917383	−	0.529651i
$285$	−3.11205	+	5.39023i	−0.184342	+	0.319290i
$286$	1.39675	−	5.53176i	0.0825915	−	0.327100i
$287$	1.00278			0.0591925
$288$	−12.8686	+	7.42969i	−0.758289	+	0.437798i
$289$	−14.5707	−	25.2372i	−0.857099	−	1.48454i
$290$	−9.90513	−	17.1562i	−0.581649	−	1.00745i
$291$	0.868065	+	0.501178i	0.0508869	+	0.0293795i
$292$	0.601644	−	0.347359i	0.0352086	−	0.0203277i
$293$	−24.8644	−	14.3555i	−1.45260	−	0.838656i	−0.453967	−	0.891018i	$-0.649992\pi$
$293$	−24.8644	−	14.3555i	−1.45260	−	0.838656i	−0.998628	+	0.0523623i	$0.983325\pi$
$294$			3.33958i			0.194768i
$295$	−8.48328			−0.493916
$296$	−13.8076	+	23.9154i	−0.802549	+	1.39006i
$297$	−4.50230	+	2.59940i	−0.261250	+	0.150833i
$298$	5.31961	−	9.21383i	0.308156	−	0.533743i
$299$	13.2917	+	12.9124i	0.768677	+	0.746743i
$300$	1.87870	+	3.25401i	0.108467	+	0.187870i
$301$	0.00905415	−	0.00522742i	0.000521873	−	0.000301303i
$302$	−2.44927			−0.140940
$303$	−1.91024	+	3.30863i	−0.109740	+	0.190076i
$304$	1.13612	+	0.655940i	0.0651610	+	0.0376207i
$305$	−28.6634	+	16.5488i	−1.64126	+	0.947581i
$306$		−	17.0228i		−	0.973131i
$307$	12.9627	+	7.48403i	0.739821	+	0.427136i	0.822004	−	0.569481i	$-0.192856\pi$
$307$	12.9627	+	7.48403i	0.739821	+	0.427136i	−0.0821829	+	0.996617i	$0.526189\pi$
$308$	−0.767875			−0.0437538
$309$	−6.08932			−0.346409
$310$	11.9046	−	12.3360i	0.676134	−	0.700640i
$311$	23.3031			1.32140			0.660698	−	0.750651i	$-0.270260\pi$
$311$	23.3031			1.32140			0.660698	+	0.750651i	$0.270260\pi$
$312$	1.51108	+	5.32967i	0.0855482	+	0.301733i
$313$	5.37275	−	9.30588i	0.303686	−	0.526000i	−0.673282	−	0.739386i	$-0.735116\pi$
$313$	5.37275	−	9.30588i	0.303686	−	0.526000i	0.976968	+	0.213386i	$0.0684493\pi$
$314$			1.24782i			0.0704183i
$315$	1.76526	+	3.05753i	0.0994614	+	0.172272i
$316$	−1.21326	+	2.10142i	−0.0682510	+	0.118214i
$317$	9.81125	+	5.66453i	0.551055	+	0.318152i	0.749547	−	0.661951i	$-0.230271\pi$
$317$	9.81125	+	5.66453i	0.551055	+	0.318152i	−0.198492	+	0.980102i	$0.563605\pi$
$318$		−	5.21565i		−	0.292479i
$319$	9.56950	−	5.52495i	0.535789	−	0.309338i
$320$	16.7253	−	9.65634i	0.934971	−	0.539806i
$321$	−2.85382	−	4.94297i	−0.159285	−	0.275889i
$322$	−0.919640	+	1.59286i	−0.0512495	+	0.0887668i
$323$	20.7032	−	11.9530i	1.15196	−	0.665082i
$324$	−3.77439	+	6.53743i	−0.209688	+	0.363191i
$325$	−21.3958	+	6.06620i	−1.18683	+	0.336492i
$326$	−3.78013			−0.209362
$327$	2.30063	+	1.32827i	0.127225	+	0.0734536i
$328$	−3.74779	−	6.49136i	−0.206937	−	0.358425i
$329$	−1.65477	+	2.86615i	−0.0912307	+	0.158016i
$330$	2.42359	−	1.39926i	0.133414	−	0.0770268i
$331$	1.52114	−	0.878228i	0.0836092	−	0.0482718i	−0.457613	−	0.889152i	$-0.651295\pi$
$331$	1.52114	−	0.878228i	0.0836092	−	0.0482718i	0.541222	+	0.840880i	$0.317962\pi$
$332$	16.6088	−	9.58912i	0.911529	−	0.526271i
$333$			25.8712i			1.41773i
$334$	−7.63649	+	13.2268i	−0.417850	+	0.723737i
$335$	2.75435	−	4.77067i	0.150486	−	0.260649i
$336$	−0.0663565	+	0.0383110i	−0.00362005	+	0.00209003i
$337$	3.68645			0.200814			0.100407	−	0.994946i	$-0.467986\pi$
$337$	3.68645			0.200814			0.100407	+	0.994946i	$0.467986\pi$
$338$	−11.9726	+	0.346651i	−0.651225	+	0.0188553i
$339$	5.94525			0.322902
$340$		−	26.1305i		−	1.41712i
$341$	6.88088	+	6.64021i	0.372621	+	0.359587i
$342$	8.81958			0.476908
$343$			5.37917i			0.290448i
$344$	−0.0676777	−	0.0390737i	−0.00364894	−	0.00210672i
$345$			9.08957i			0.489366i
$346$	13.7519	−	7.93969i	0.739309	−	0.426840i
$347$	5.42934	−	9.40389i	0.291462	−	0.504827i	−0.682693	−	0.730705i	$-0.739192\pi$
$347$	5.42934	−	9.40389i	0.291462	−	0.504827i	0.974156	+	0.225877i	$0.0725249\pi$
$348$	−1.95968	+	3.39427i	−0.105050	+	0.181952i
$349$			24.3630i			1.30412i	0.758166	+	0.652061i	$0.226096\pi$
$349$			24.3630i			1.30412i	−0.758166	+	0.652061i	$0.773904\pi$
$350$	−1.10366	−	1.91160i	−0.0589933	−	0.102179i
$351$	7.82836	+	7.60498i	0.417847	+	0.405924i
$352$	4.69133	+	8.12563i	0.250049	+	0.433097i
$353$	4.53924	+	2.62073i	0.241599	+	0.139487i	0.615912	−	0.787815i	$-0.288788\pi$
$353$	4.53924	+	2.62073i	0.241599	+	0.139487i	−0.374312	+	0.927303i	$0.622121\pi$
$354$	−0.618872	−	1.07192i	−0.0328927	−	0.0569718i
$355$	−25.9134	+	44.8833i	−1.37534	+	2.38216i
$356$			14.6215i			0.774940i
$357$			1.39626i			0.0738978i
$358$	−10.3143	−	5.95494i	−0.545125	−	0.314728i
$359$	−3.34965	+	1.93392i	−0.176788	+	0.102069i	−0.585783	−	0.810468i	$-0.699213\pi$
$359$	−3.34965	+	1.93392i	−0.176788	+	0.102069i	0.408995	+	0.912537i	$0.365879\pi$
$360$	13.1949	−	22.8543i	0.695435	−	1.20453i
$361$	−3.30713	−	5.72812i	−0.174059	−	0.301480i
$362$	0.984822	−	0.568587i	0.0517611	−	0.0298843i
$363$	−2.13016	−	3.68955i	−0.111805	−	0.193651i
$364$	0.439720	+	1.55092i	0.0230476	+	0.0812901i
$365$	−1.00845	+	1.74668i	−0.0527846	+	0.0914257i
$366$	−4.18210	−	2.41454i	−0.218602	−	0.126210i
$367$	10.5358	+	18.2485i	0.549963	+	0.952564i	0.998276	+	0.0586874i	$0.0186915\pi$
$367$	10.5358	+	18.2485i	0.549963	+	0.952564i	−0.448313	+	0.893876i	$0.647975\pi$
$368$	1.91584			0.0998703
$369$	−6.08141	−	3.51110i	−0.316586	−	0.182781i
$370$		−	29.2869i		−	1.52255i
$371$		−	4.15475i		−	0.215704i
$372$	−3.29127	−	0.819401i	−0.170644	−	0.0424840i
$373$	7.00707			0.362812			0.181406	−	0.983408i	$-0.441935\pi$
$373$	7.00707			0.362812			0.181406	+	0.983408i	$0.441935\pi$
$374$	−10.7487			−0.555804
$375$	−1.78896	−	1.03286i	−0.0923817	−	0.0533366i
$376$	24.7381			1.27577
$377$	−16.6390	−	16.1642i	−0.856950	−	0.832497i
$378$	−0.541638	+	0.938145i	−0.0278589	+	0.0482530i
$379$	28.1273	+	16.2393i	1.44480	+	0.834157i	0.998165	−	0.0605577i	$-0.0192879\pi$
$379$	28.1273	+	16.2393i	1.44480	+	0.834157i	0.446638	+	0.894715i	$0.352621\pi$
$380$	13.5383			0.694498
$381$	4.44850	+	7.70503i	0.227904	+	0.394740i
$382$	19.1560	−	11.0597i	0.980106	−	0.565864i
$383$	12.4776	−	7.20397i	0.637578	−	0.368106i	−0.146103	−	0.989269i	$-0.546673\pi$
$383$	12.4776	−	7.20397i	0.637578	−	0.368106i	0.783681	+	0.621164i	$0.213340\pi$
$384$	−2.56732	−	1.48224i	−0.131013	−	0.0756404i
$385$	1.93062	−	1.11464i	0.0983933	−	0.0568074i
$386$	0.570777	−	0.988614i	0.0290518	−	0.0503191i
$387$	−0.0732122			−0.00372159
$388$		−	2.18026i		−	0.110686i
$389$	7.09412	−	12.2874i	0.359686	−	0.622995i	−0.628222	−	0.778034i	$-0.716217\pi$
$389$	7.09412	−	12.2874i	0.359686	−	0.622995i	0.987908	+	0.155039i	$0.0495504\pi$
$390$	−4.21401	−	4.09377i	−0.213385	−	0.207296i
$391$	17.4559	−	30.2345i	0.882783	−	1.52903i
$392$	17.2209	−	9.94251i	0.869789	−	0.502173i
$393$	−2.38894	−	4.13777i	−0.120506	−	0.208723i
$394$	−0.655408	−	1.13520i	−0.0330190	−	0.0571905i
$395$		−	7.04462i		−	0.354453i
$396$	4.65680	+	2.68861i	0.234013	+	0.135108i
$397$	18.6860	+	10.7883i	0.937822	+	0.541452i	0.889277	−	0.457369i	$-0.151208\pi$
$397$	18.6860	+	10.7883i	0.937822	+	0.541452i	0.0485448	+	0.998821i	$0.484542\pi$
$398$	−2.44208	+	1.40993i	−0.122410	+	0.0706736i
$399$	−0.723404			−0.0362155
$400$	−1.14961	+	1.99118i	−0.0574804	+	0.0995589i
$401$			18.3217i			0.914940i	0.889225	+	0.457470i	$0.151244\pi$
$401$			18.3217i			0.914940i	−0.889225	+	0.457470i	$0.848756\pi$
$402$	0.803740			0.0400869
$403$	9.47126	−	17.7001i	0.471797	−	0.881707i
$404$	8.31004			0.413440
$405$		−	21.9155i		−	1.08899i
$406$	1.15124	−	1.99400i	0.0571349	−	0.0989605i
$407$	16.3359			0.809738
$408$	9.03845	−	5.21835i	0.447470	−	0.258347i
$409$	−31.1134	−	17.9633i	−1.53846	−	0.888229i	−0.998929	−	0.0462613i	$-0.985269\pi$
$409$	−31.1134	−	17.9633i	−1.53846	−	0.888229i	−0.539528	−	0.841968i	$-0.681397\pi$
$410$	6.88433	+	3.97467i	0.339993	+	0.196295i
$411$		−	8.76205i		−	0.432200i
$412$	6.62254	+	11.4706i	0.326269	+	0.565115i
$413$	−0.492990	−	0.853883i	−0.0242584	−	0.0420169i
$414$	11.1544	−	6.43998i	0.548207	−	0.316508i
$415$	−27.8390	+	48.2186i	−1.36656	+	2.36696i
$416$	13.7253	−	14.1284i	0.672937	−	0.692703i
$417$	−2.56180	+	4.43716i	−0.125452	+	0.217289i
$418$		−	5.56895i		−	0.272386i
$419$	19.8072			0.967647			0.483824	−	0.875165i	$-0.339248\pi$
$419$	19.8072			0.967647			0.483824	+	0.875165i	$0.339248\pi$
$420$	−0.395359	+	0.684782i	−0.0192916	+	0.0334140i
$421$	2.64724	−	1.52839i	0.129019	−	0.0744889i	−0.434102	−	0.900864i	$-0.642934\pi$
$421$	2.64724	−	1.52839i	0.129019	−	0.0744889i	0.563120	+	0.826375i	$0.309601\pi$
$422$	19.9866	+	11.5393i	0.972933	+	0.561723i
$423$	20.0709	−	11.5879i	0.975878	−	0.563424i
$424$	−26.8951	+	15.5279i	−1.30614	+	0.754102i
$425$	20.9489	+	36.2846i	1.01617	+	1.76006i
$426$	−7.56173			−0.366367
$427$	−3.33143	−	1.92340i	−0.161219	−	0.0930800i
$428$	−6.20744	+	10.7516i	−0.300048	+	0.519699i
$429$	2.28345	−	2.35052i	0.110246	−	0.113484i
$430$	0.0828783			0.00399675
$431$	−24.6899	−	14.2547i	−1.18927	−	0.686625i	−0.231129	−	0.972923i	$-0.574242\pi$
$431$	−24.6899	−	14.2547i	−1.18927	−	0.686625i	−0.958141	+	0.286298i	$0.907575\pi$
$432$	1.12837			0.0542888
$433$	−9.48475			−0.455808			−0.227904	−	0.973684i	$-0.573187\pi$
$433$	−9.48475			−0.455808			−0.227904	+	0.973684i	$0.573187\pi$
$434$	1.93349	+	0.481366i	0.0928106	+	0.0231063i
$435$		−	11.3786i		−	0.545564i
$436$		−	5.77834i		−	0.276732i
$437$	15.6646	+	9.04395i	0.749339	+	0.432631i
$438$	−0.294274			−0.0140609
$439$	−6.64973	−	11.5177i	−0.317374	−	0.549709i	0.662565	−	0.749004i	$-0.269468\pi$
$439$	−6.64973	−	11.5177i	−0.317374	−	0.549709i	−0.979939	+	0.199296i	$0.936135\pi$
$440$	−14.4309	−	8.33169i	−0.687967	−	0.397198i
$441$	9.31461	−	16.1334i	0.443553	−	0.768256i
$442$	6.15521	+	21.7098i	0.292774	+	1.03263i
$443$	−20.4933	−	35.4955i	−0.973668	−	1.68644i	−0.684262	−	0.729236i	$-0.739876\pi$
$443$	−20.4933	−	35.4955i	−0.973668	−	1.68644i	−0.289406	−	0.957207i	$-0.593458\pi$
$444$	−5.01798	+	2.89713i	−0.238143	+	0.137492i
$445$	−21.2245	−	36.7619i	−1.00614	−	1.74268i
$446$	9.87076	−	17.0967i	0.467394	−	0.809550i
$447$	5.29224	−	3.05548i	0.250315	−	0.144519i
$448$	1.94391	+	1.12232i	0.0918413	+	0.0530246i
$449$			15.5080i			0.731869i	0.930641	+	0.365935i	$0.119251\pi$
$449$			15.5080i			0.731869i	−0.930641	+	0.365935i	$0.880749\pi$
$450$			15.4573i			0.728664i
$451$	−2.21702	+	3.83999i	−0.104395	+	0.180818i
$452$	−6.46586	−	11.1992i	−0.304128	−	0.526766i
$453$	−1.21834	−	0.703406i	−0.0572424	−	0.0330489i
$454$	−9.16186	−	15.8688i	−0.429987	−	0.744760i
$455$	−3.35686	−	3.26107i	−0.157372	−	0.152881i
$456$	2.70364	+	4.68284i	0.126610	+	0.219294i
$457$			21.1888i			0.991170i	0.868559	+	0.495585i	$0.165046\pi$
$457$			21.1888i			0.991170i	−0.868559	+	0.495585i	$0.834954\pi$
$458$	−4.74094	+	8.21155i	−0.221530	+	0.383701i
$459$	10.2810	−	17.8072i	0.479875	−	0.831167i
$460$	17.1222	−	9.88551i	0.798327	−	0.460914i
$461$		−	21.1258i		−	0.983926i	−0.870616	−	0.491963i	$-0.836280\pi$
$461$		−	21.1258i		−	0.983926i	0.870616	−	0.491963i	$-0.163720\pi$
$462$	0.281685	+	0.162631i	0.0131052	+	0.00756627i
$463$			5.56614i			0.258681i	0.991600	+	0.129340i	$0.0412860\pi$
$463$			5.56614i			0.258681i	−0.991600	+	0.129340i	$0.958714\pi$
$464$	−2.39832			−0.111339
$465$	9.46445	−	2.71742i	0.438904	−	0.126017i
$466$		−	8.13287i		−	0.376748i
$467$	−16.1924			−0.749294			−0.374647	−	0.927167i	$-0.622236\pi$
$467$	−16.1924			−0.749294			−0.374647	+	0.927167i	$0.622236\pi$
$468$	2.76362	−	10.9452i	0.127748	−	0.505942i
$469$	0.640254			0.0295642
$470$	−22.7208	+	13.1178i	−1.04803	+	0.605081i
$471$	−0.358361	+	0.620699i	−0.0165124	+	0.0286003i
$472$	−3.68499	+	6.38258i	−0.169615	+	0.293782i
$473$			0.0462285i			0.00212559i
$474$	0.890134	−	0.513919i	0.0408852	−	0.0236051i
$475$	−18.7992	+	10.8537i	−0.862564	+	0.498002i
$476$	2.63016	−	1.51852i	0.120553	−	0.0696014i
$477$	−14.5473	+	25.1966i	−0.666074	+	1.15367i
$478$	−4.55748	−	7.89378i	−0.208454	−	0.361053i
$479$	14.9827	+	8.65028i	0.684578	+	0.395241i	0.801578	−	0.597891i	$-0.203994\pi$
$479$	14.9827	+	8.65028i	0.684578	+	0.395241i	−0.117000	+	0.993132i	$0.537328\pi$
$480$	9.66179			0.440998
$481$	−9.35464	−	32.9944i	−0.426535	−	1.50441i
$482$	2.07286	−	3.59031i	0.0944164	−	0.163534i
$483$	−0.914909	+	0.528223i	−0.0416298	+	0.0240350i
$484$	−4.63339	+	8.02526i	−0.210609	+	0.364785i
$485$	3.16484	+	5.48167i	0.143708	+	0.248910i
$486$	10.0152	−	5.78226i	0.454298	−	0.262289i
$487$	−18.3177	+	10.5757i	−0.830054	+	0.479232i	−0.853871	−	0.520485i	$-0.825751\pi$
$487$	−18.3177	+	10.5757i	−0.830054	+	0.479232i	0.0238175	+	0.999716i	$0.492418\pi$
$488$			28.7540i			1.30163i
$489$	−1.88034	−	1.08562i	−0.0850320	−	0.0490933i
$490$	−10.5444	+	18.2634i	−0.476348	+	0.825058i
$491$	−6.82944	−	11.8289i	−0.308208	−	0.533833i	0.669762	−	0.742576i	$-0.266396\pi$
$491$	−6.82944	−	11.8289i	−0.308208	−	0.533833i	−0.977971	+	0.208743i	$0.933063\pi$
$492$		−	1.57274i		−	0.0709045i
$493$	−21.8519	+	37.8486i	−0.984160	+	1.70462i
$494$	−11.2479	+	3.18903i	−0.506067	+	0.143481i
$495$	−15.6110			−0.701664
$496$	−0.572761	−	1.99486i	−0.0257177	−	0.0895719i
$497$	−6.02363			−0.270197
$498$	−8.12364			−0.364029
$499$	23.8353	+	13.7613i	1.06701	+	0.616041i	0.927364	−	0.374160i	$-0.122069\pi$
$499$	23.8353	+	13.7613i	1.06701	+	0.616041i	0.139650	+	0.990201i	$0.455402\pi$
$500$			4.49321i			0.200943i
$501$	−7.59721	+	4.38625i	−0.339418	+	0.195963i
$502$	−0.325337	−	0.187833i	−0.0145205	−	0.00838342i
$503$	0.838225	−	1.45185i	0.0373746	−	0.0647347i	−0.846733	−	0.532018i	$-0.821434\pi$
$503$	0.838225	−	1.45185i	0.0373746	−	0.0647347i	0.884108	+	0.467283i	$0.154767\pi$
$504$	3.06720			0.136624
$505$	−20.8934	+	12.0628i	−0.929743	+	0.536787i
$506$	−4.06640	−	7.04321i	−0.180773	−	0.313109i
$507$	−6.05508	−	3.26599i	−0.268915	−	0.145048i
$508$	9.67608	−	16.7595i	0.429307	−	0.743581i
$509$	−8.24747	+	4.76168i	−0.365563	+	0.211058i	−0.671518	−	0.740988i	$-0.734357\pi$
$509$	−8.24747	+	4.76168i	−0.365563	+	0.211058i	0.305956	+	0.952046i	$0.401024\pi$
$510$	−5.53426	+	9.58561i	−0.245061	+	0.424458i
$511$	−0.234416			−0.0103700
$512$		−	4.20093i		−	0.185657i
$513$	9.22594	+	5.32660i	0.407335	+	0.235175i
$514$	−7.27979	+	4.20299i	−0.321098	+	0.185386i
$515$	−33.3012	−	19.2265i	−1.46743	−	0.847219i
$516$	−0.00819853	−	0.0142003i	−0.000360920	−	0.000625132i
$517$	−7.31697	−	12.6734i	−0.321800	−	0.557374i
$518$	2.94787	−	1.70195i	0.129522	−	0.0747795i
$519$	9.12081			0.400359
$520$	−8.56415	+	33.9180i	−0.375563	+	1.48740i
$521$	−9.95759	+	17.2471i	−0.436250	+	0.755607i	−0.997397	−	0.0721092i	$-0.977027\pi$
$521$	−9.95759	+	17.2471i	−0.436250	+	0.755607i	0.561147	+	0.827716i	$0.310360\pi$
$522$	−13.9634	+	8.06178i	−0.611162	+	0.352854i
$523$	39.1926			1.71377			0.856886	−	0.515505i	$-0.172396\pi$
$523$	39.1926			1.71377			0.856886	+	0.515505i	$0.172396\pi$
$524$	−5.19626	+	9.00019i	−0.227000	+	0.393175i
$525$		−	1.26785i		−	0.0553334i
$526$			13.6474i			0.595057i
$527$	−36.7001	−	9.13693i	−1.59868	−	0.398011i
$528$		−	0.338802i		−	0.0147444i
$529$	3.41525			0.148489
$530$	16.4679	−	28.5233i	0.715321	−	1.23897i
$531$			6.90453i			0.299631i
$532$	0.786750	+	1.36269i	0.0341100	+	0.0590802i
$533$	9.02539	+	2.27888i	0.390933	+	0.0987091i
$534$	3.09674	−	5.36372i	0.134009	−	0.232111i
$535$		−	36.0427i		−	1.55826i
$536$	−2.39288	−	4.14458i	−0.103357	−	0.179019i
$537$	−3.42040	−	5.92431i	−0.147601	−	0.255653i
$538$	−8.92715	+	5.15409i	−0.384877	+	0.222209i
$539$	−10.1871	−	5.88153i	−0.438790	−	0.253336i
$540$	10.0844	−	5.82225i	0.433965	−	0.250550i
$541$	16.0461	+	9.26419i	0.689874	+	0.398299i	0.803565	−	0.595217i	$-0.202934\pi$
$541$	16.0461	+	9.26419i	0.689874	+	0.398299i	−0.113691	+	0.993516i	$0.536267\pi$
$542$	19.7383			0.847833
$543$	0.653171			0.0280302
$544$	−32.1379	−	18.5548i	−1.37790	−	0.795531i
$545$	8.38779	+	14.5281i	0.359294	+	0.622315i
$546$	0.167168	−	0.662063i	0.00715414	−	0.0283337i
$547$	−19.0486	−	32.9932i	−0.814460	−	1.41069i	−0.909715	−	0.415233i	$-0.863700\pi$
$547$	−19.0486	−	32.9932i	−0.814460	−	1.41069i	0.0952552	−	0.995453i	$-0.469633\pi$
$548$	−16.5053	+	9.52932i	−0.705070	+	0.407072i
$549$	13.4690	+	23.3291i	0.574845	+	0.995661i
$550$	9.76021			0.416177
$551$	−19.6095	−	11.3215i	−0.835391	−	0.482313i
$552$	6.83874	+	3.94835i	0.291076	+	0.168053i
$553$	0.709075	−	0.409385i	0.0301529	−	0.0174088i
$554$		−	7.12666i		−	0.302783i
$555$	8.41092	−	14.5681i	0.357024	−	0.618383i
$556$	11.1445			0.472632
$557$		−	4.65769i		−	0.197353i	−0.995120	−	0.0986763i	$-0.968539\pi$
$557$		−	4.65769i		−	0.197353i	0.995120	−	0.0986763i	$-0.0314608\pi$
$558$	−10.0403	−	9.68911i	−0.425039	−	0.410173i
$559$	0.0933700	−	0.0264725i	0.00394913	−	0.00111967i
$560$	−0.483853			−0.0204465
$561$	−5.34673	−	3.08694i	−0.225739	−	0.130331i
$562$	20.8825			0.880876
$563$	10.9845	+	19.0258i	0.462943	+	0.801840i	0.999106	−	0.0422741i	$-0.0134603\pi$
$563$	10.9845	+	19.0258i	0.462943	+	0.801840i	−0.536163	+	0.844114i	$0.680127\pi$
$564$	4.49519	+	2.59530i	0.189282	+	0.109282i
$565$	32.5133	+	18.7716i	1.36785	+	0.789727i
$566$			12.7589i			0.536296i
$567$	2.20590	−	1.27358i	0.0926391	−	0.0534852i
$568$	22.5126	+	38.9930i	0.944609	+	1.63611i
$569$	−6.14942	−	10.6511i	−0.257797	−	0.446518i	0.707854	−	0.706358i	$-0.249663\pi$
$569$	−6.14942	−	10.6511i	−0.257797	−	0.446518i	−0.965652	+	0.259841i	$0.916330\pi$
$570$	−4.96633	−	2.86731i	−0.208017	−	0.120098i
$571$	11.4470	+	19.8267i	0.479040	+	0.829722i	0.999711	−	0.0240353i	$-0.00765139\pi$
$571$	11.4470	+	19.8267i	0.479040	+	0.829722i	−0.520671	+	0.853758i	$0.674318\pi$
$572$	−6.91113	−	1.74503i	−0.288969	−	0.0729636i
$573$	12.7050			0.530758
$574$			0.923922i			0.0385638i
$575$	−15.8505	+	27.4539i	−0.661013	+	1.14491i
$576$	−7.85929	−	13.6127i	−0.327470	−	0.567195i
$577$	−13.5289	−	7.81090i	−0.563214	−	0.325172i	0.191220	−	0.981547i	$-0.438756\pi$
$577$	−13.5289	−	7.81090i	−0.563214	−	0.325172i	−0.754435	+	0.656375i	$0.772089\pi$
$578$	23.2524	−	13.4248i	0.967174	−	0.558398i
$579$	0.567841	−	0.327843i	0.0235987	−	0.0136247i
$580$	−21.4342	+	12.3750i	−0.890005	+	0.513845i
$581$	−6.47124			−0.268472
$582$	−0.461763	+	0.799798i	−0.0191407	+	0.0331527i
$583$	15.9099	+	9.18560i	0.658922	+	0.380429i
$584$	0.876104	+	1.51746i	0.0362535	+	0.0627928i
$585$	8.93958	+	31.5304i	0.369606	+	1.30362i
$586$	13.2265	−	22.9090i	0.546383	−	0.946363i
$587$			15.9702i			0.659159i	0.944128	+	0.329580i	$0.106907\pi$
$587$			15.9702i			0.659159i	−0.944128	+	0.329580i	$0.893093\pi$
$588$	4.17231			0.172063
$589$	4.73387	−	19.0144i	0.195056	−	0.783476i
$590$		−	7.81613i		−	0.321785i
$591$		−	0.752907i		−	0.0309705i
$592$	−3.07058	−	1.77280i	−0.126200	−	0.0728617i
$593$		−	9.00794i		−	0.369912i	−0.982747	−	0.184956i	$-0.940786\pi$
$593$		−	9.00794i		−	0.369912i	0.982747	−	0.184956i	$-0.0592142\pi$
$594$	−2.39498	−	4.14822i	−0.0982671	−	0.170204i
$595$	−4.40855	+	7.63584i	−0.180733	+	0.313039i
$596$	−11.5113	−	6.64607i	−0.471523	−	0.272234i
$597$	−1.61968			−0.0662890
$598$	−11.8969	+	12.2464i	−0.486501	+	0.500791i
$599$	−8.82768	−	15.2900i	−0.360689	−	0.624732i	0.627385	−	0.778709i	$-0.284125\pi$
$599$	−8.82768	−	15.2900i	−0.360689	−	0.624732i	−0.988074	+	0.153977i	$0.950792\pi$
$600$	−8.20721	+	4.73843i	−0.335058	+	0.193446i
$601$	12.1027	−	20.9626i	0.493681	−	0.855080i	−0.506293	−	0.862362i	$-0.668984\pi$
$601$	12.1027	−	20.9626i	0.493681	−	0.855080i	0.999973	+	0.00728131i	$0.00231773\pi$
$602$	0.00481632	+	0.00834211i	0.000196298	+	0.000339999i
$603$	−3.88284	−	2.24176i	−0.158121	−	0.0912915i
$604$			3.06000i			0.124510i
$605$		−	26.9032i		−	1.09377i
$606$	−3.04843	−	1.76001i	−0.123834	−	0.0714956i
$607$	4.10722	+	7.11392i	0.166707	+	0.288745i	0.937260	−	0.348631i	$-0.113353\pi$
$607$	4.10722	+	7.11392i	0.166707	+	0.288745i	−0.770553	+	0.637376i	$0.780020\pi$
$608$	9.61330	−	16.6507i	0.389871	−	0.675276i
$609$	1.14531	−	0.661248i	0.0464105	−	0.0267951i
$610$	−15.2473	−	26.4092i	−0.617347	−	1.06928i
$611$	−21.4070	+	22.0358i	−0.866034	+	0.891472i
$612$	−21.2676			−0.859690
$613$	28.3749	+	16.3822i	1.14605	+	0.661672i	0.947922	−	0.318504i	$-0.103180\pi$
$613$	28.3749	+	16.3822i	1.14605	+	0.661672i	0.198129	+	0.980176i	$0.436514\pi$
$614$	−6.89546	+	11.9433i	−0.278278	+	0.481992i
$615$	2.28297	+	3.95423i	0.0920584	+	0.159450i
$616$		−	1.93672i		−	0.0780328i
$617$	19.1584	+	11.0611i	0.771288	+	0.445303i	0.833334	−	0.552770i	$-0.186429\pi$
$617$	19.1584	+	11.0611i	0.771288	+	0.445303i	−0.0620459	+	0.998073i	$0.519763\pi$
$618$		−	5.61044i		−	0.225685i
$619$			19.7208i			0.792645i	0.918111	+	0.396323i	$0.129714\pi$
$619$			19.7208i			0.792645i	−0.918111	+	0.396323i	$0.870286\pi$
$620$	−15.4121	−	14.8730i	−0.618964	−	0.597315i
$621$	15.5577			0.624310
$622$			21.4705i			0.860887i
$623$	2.46685	−	4.27270i	0.0988321	−	0.171182i
$624$	−0.684294	+	0.194013i	−0.0273937	+	0.00776673i
$625$	8.89777	+	15.4114i	0.355911	+	0.616455i
$626$	8.57404	+	4.95023i	0.342688	+	0.197851i
$627$	1.59935	−	2.77015i	0.0638719	−	0.110629i
$628$	1.55896			0.0622094
$629$	−55.9543	+	32.3052i	−2.23104	+	1.28809i
$630$	−2.81707	+	1.62644i	−0.112235	+	0.0647989i
$631$	−17.9143	+	10.3428i	−0.713156	+	0.411741i	−0.812228	−	0.583340i	$-0.801746\pi$
$631$	−17.9143	+	10.3428i	−0.713156	+	0.411741i	0.0990727	+	0.995080i	$0.468412\pi$
$632$	−5.30017	−	3.06006i	−0.210830	−	0.121722i
$633$	6.62794	+	11.4799i	0.263437	+	0.456286i
$634$	−5.21905	+	9.03967i	−0.207275	+	0.359011i
$635$			56.1829i			2.22955i
$636$	−6.51620			−0.258384
$637$	−6.04563	+	23.9435i	−0.239537	+	0.948674i
$638$	5.09046	+	8.81693i	0.201533	+	0.349066i
$639$	36.5305	+	21.0909i	1.44512	+	0.834342i
$640$	−9.36009	−	16.2121i	−0.369990	−	0.640841i
$641$	−13.7787	−	23.8653i	−0.544224	−	0.942624i	−0.998655	−	0.0518422i	$-0.983491\pi$
$641$	−13.7787	−	23.8653i	−0.544224	−	0.942624i	0.454431	−	0.890782i	$-0.349843\pi$
$642$	4.55424	−	2.62939i	0.179741	−	0.103774i
$643$		−	1.24221i		−	0.0489881i	−0.999700	−	0.0244940i	$-0.992203\pi$
$643$		−	1.24221i		−	0.0489881i	0.999700	−	0.0244940i	$-0.00779748\pi$
$644$	1.99005	+	1.14896i	0.0784190	+	0.0452752i
$645$	0.0412260	+	0.0238019i	0.00162327	+	0.000937197i
$646$	11.0130	+	19.0750i	0.433299	+	0.750496i
$647$	−25.4546			−1.00072			−0.500362	−	0.865816i	$-0.666800\pi$
$647$	−25.4546			−1.00072			−0.500362	+	0.865816i	$0.666800\pi$
$648$	−16.4886	−	9.51970i	−0.647733	−	0.373969i
$649$	4.35974			0.171135
$650$	−5.58913	−	19.7132i	−0.219224	−	0.773215i
$651$	0.823530	+	0.794726i	0.0322767	+	0.0311478i
$652$			4.72272i			0.184956i
$653$	43.7442			1.71184			0.855921	−	0.517107i	$-0.172991\pi$
$653$	43.7442			1.71184			0.855921	+	0.517107i	$0.172991\pi$
$654$	−1.22381	+	2.11971i	−0.0478549	+	0.0828870i
$655$		−	30.1714i		−	1.17890i
$656$	0.833448	−	0.481191i	0.0325407	−	0.0187874i
$657$	1.42163	+	0.820776i	0.0554629	+	0.0320215i
$658$	−2.64075	−	1.52464i	−0.102947	−	0.0594366i
$659$	−20.2139			−0.787420			−0.393710	−	0.919235i	$-0.628809\pi$
$659$	−20.2139			−0.787420			−0.393710	+	0.919235i	$0.628809\pi$
$660$	−1.74817	−	3.02792i	−0.0680475	−	0.117862i
$661$	14.7989	−	8.54414i	0.575610	−	0.332328i	−0.183777	−	0.982968i	$-0.558832\pi$
$661$	14.7989	−	8.54414i	0.575610	−	0.332328i	0.759387	+	0.650640i	$0.225499\pi$
$662$	0.809162	+	1.40151i	0.0314490	+	0.0544712i
$663$	−3.17306	+	12.5668i	−0.123232	+	0.488053i
$664$	24.1855	+	41.8906i	0.938580	+	1.62567i
$665$	−3.95615	−	2.28408i	−0.153413	−	0.0885729i
$666$	−23.8366			−0.923649
$667$	−33.0675			−1.28038
$668$	16.5249	+	9.54068i	0.639369	+	0.369140i
$669$	9.81998	−	5.66957i	0.379663	−	0.219198i
$670$	4.39549	+	2.53774i	0.169812	+	0.0980413i
$671$	14.7307	−	8.50477i	0.568672	−	0.328323i
$672$	0.561477	+	0.972506i	0.0216594	+	0.0375152i
$673$	11.1009	+	19.2272i	0.427907	+	0.741156i	0.996687	−	0.0813336i	$-0.0259179\pi$
$673$	11.1009	+	19.2272i	0.427907	+	0.741156i	−0.568780	+	0.822489i	$0.692585\pi$
$674$			3.39653i			0.130830i
$675$	−9.33546	+	16.1695i	−0.359322	+	0.622364i
$676$	0.433089	+	14.9580i	0.0166573	+	0.575310i
$677$	2.21818	+	3.84200i	0.0852515	+	0.147660i	0.905498	−	0.424350i	$-0.139497\pi$
$677$	2.21818	+	3.84200i	0.0852515	+	0.147660i	−0.820247	+	0.572010i	$0.806164\pi$
$678$			5.47770i			0.210370i
$679$	−0.367838	+	0.637114i	−0.0141163	+	0.0244502i
$680$	65.9058			2.52737
$681$		−	10.5248i		−	0.403311i
$682$	−6.11800	+	6.33975i	−0.234270	+	0.242762i
$683$		−	43.5287i		−	1.66558i	−0.553590	−	0.832789i	$-0.686743\pi$
$683$		−	43.5287i		−	1.66558i	0.553590	−	0.832789i	$-0.313257\pi$
$684$		−	11.0188i		−	0.421314i
$685$	27.6654	−	47.9178i	1.05704	−	1.83085i
$686$	−4.95613			−0.189226
$687$	−4.71656	+	2.72310i	−0.179948	+	0.103893i
$688$	0.00501681	−	0.00868937i	0.000191264	−	0.000331279i
$689$	9.44189	−	37.3942i	0.359707	−	1.42460i
$690$	−8.37474			−0.318821
$691$	23.4368	−	13.5312i	0.891577	−	0.514752i	0.0171191	−	0.999853i	$-0.494551\pi$
$691$	23.4368	−	13.5312i	0.891577	−	0.514752i	0.874458	+	0.485101i	$0.161217\pi$
$692$	−9.91948	−	17.1811i	−0.377082	−	0.653126i
$693$	−0.907206	−	1.57133i	−0.0344619	−	0.0596898i
$694$	8.66434	+	5.00236i	0.328894	+	0.189887i
$695$	−28.0199	+	16.1773i	−1.06285	+	0.613639i
$696$	−8.56096	−	4.94267i	−0.324502	−	0.187352i
$697$		−	17.5372i		−	0.664269i
$698$	−22.4470			−0.849633
$699$	2.33568	−	4.04552i	0.0883436	−	0.153016i
$700$	−2.38827	+	1.37887i	−0.0902681	+	0.0521163i
$701$	−15.3204	+	26.5358i	−0.578644	+	1.00224i	0.416991	+	0.908911i	$0.363085\pi$
$701$	−15.3204	+	26.5358i	−0.578644	+	1.00224i	−0.995635	+	0.0933308i	$0.970249\pi$
$702$	−7.00691	+	7.21272i	−0.264459	+	0.272226i
$703$	−16.7374	−	28.9900i	−0.631263	−	1.09338i
$704$	−8.59547	+	4.96260i	−0.323954	+	0.187035i
$705$	−15.0693			−0.567542
$706$	−2.41463	+	4.18226i	−0.0908757	+	0.157401i
$707$	−2.42836	−	1.40201i	−0.0913278	−	0.0527281i
$708$	−1.33921	+	0.773191i	−0.0503304	+	0.0290583i
$709$			4.56728i			0.171528i	0.996315	+	0.0857638i	$0.0273331\pi$
$709$			4.56728i			0.171528i	−0.996315	+	0.0857638i	$0.972667\pi$
$710$	−41.3535	−	23.8755i	−1.55197	−	0.896031i
$711$	−5.73361			−0.215027
$712$	−36.8782			−1.38207
$713$	−7.89711	−	27.5047i	−0.295749	−	1.03006i
$714$	−1.28645			−0.0481442
$715$	19.9093	−	5.64473i	0.744565	−	0.211101i
$716$	−7.43983	+	12.8862i	−0.278039	+	0.481578i
$717$		−	5.23545i		−	0.195522i
$718$	−1.78183	−	3.08623i	−0.0664974	−	0.115177i
$719$	−10.1438	+	17.5695i	−0.378299	+	0.655233i	−0.990815	−	0.135225i	$-0.956824\pi$
$719$	−10.1438	+	17.5695i	−0.378299	+	0.655233i	0.612516	+	0.790458i	$0.290157\pi$
$720$	2.93434	+	1.69414i	0.109356	+	0.0631370i
$721$		−	4.46924i		−	0.166443i
$722$	5.27764	−	3.04705i	0.196413	−	0.113399i
$723$	2.06220	−	1.19061i	0.0766941	−	0.0442794i
$724$	−0.710367	−	1.23039i	−0.0264006	−	0.0457271i
$725$	19.8422	−	34.3678i	0.736922	−	1.27639i
$726$	3.39939	−	1.96264i	0.126163	−	0.0728404i
$727$	4.81063	−	8.33226i	0.178417	−	0.309026i	−0.762922	−	0.646491i	$-0.776236\pi$
$727$	4.81063	−	8.33226i	0.178417	−	0.309026i	0.941338	+	0.337464i	$0.109569\pi$
$728$	−3.91170	+	1.10905i	−0.144977	+	0.0411043i
$729$	−13.0312			−0.482636
$730$	−1.60932	−	0.929142i	−0.0595636	−	0.0343891i
$731$	−0.0914197	−	0.158344i	−0.00338128	−	0.00585655i
$732$	−3.01661	+	5.22492i	−0.111497	+	0.193119i
$733$	−40.9888	+	23.6649i	−1.51396	+	0.874083i	−0.514089	+	0.857737i	$0.671870\pi$
$733$	−40.9888	+	23.6649i	−1.51396	+	0.874083i	−0.999866	+	0.0163462i	$0.994797\pi$
$734$	−16.8134	+	9.70721i	−0.620593	+	0.358300i
$735$	−10.4902	+	6.05650i	−0.386936	+	0.223397i
$736$		−	28.0782i		−	1.03498i
$737$	−1.41552	+	2.45175i	−0.0521412	+	0.0903112i
$738$	3.23498	−	5.60315i	0.119081	−	0.206255i
$739$	8.17341	−	4.71892i	0.300664	−	0.173588i	−0.342077	−	0.939672i	$-0.611130\pi$
$739$	8.17341	−	4.71892i	0.300664	−	0.173588i	0.642741	+	0.766083i	$0.277797\pi$
$740$	−36.5897			−1.34507
$741$	−6.51088	−	1.64397i	−0.239183	−	0.0603928i
$742$	3.82801			0.140531
$743$			10.0321i			0.368044i	0.982922	+	0.184022i	$0.0589117\pi$
$743$			10.0321i			0.368044i	−0.982922	+	0.184022i	$0.941088\pi$
$744$	2.06668	−	8.30119i	0.0757682	−	0.304336i
$745$	38.5896			1.41381
$746$			6.45601i			0.236371i
$747$	39.2450	+	22.6581i	1.43590	+	0.829018i
$748$			13.4290i			0.491013i
$749$	3.62787	−	2.09455i	0.132560	−	0.0765334i
$750$	0.951632	−	1.64827i	0.0347487	−	0.0601865i
$751$	−2.93092	+	5.07650i	−0.106951	+	0.185244i	−0.914534	−	0.404510i	$-0.867442\pi$
$751$	−2.93092	+	5.07650i	−0.106951	+	0.185244i	0.807583	+	0.589754i	$0.200775\pi$
$752$			3.17621i			0.115824i
$753$	−0.107888	−	0.186867i	−0.00393165	−	0.00680982i
$754$	14.8930	−	15.3304i	0.542370	−	0.558301i
$755$	−4.44188	−	7.69356i	−0.161657	−	0.279997i
$756$	1.17208	+	0.676698i	0.0426280	+	0.0246113i
$757$	8.29928	+	14.3748i	0.301642	+	0.522460i	0.976508	−	0.215481i	$-0.0691318\pi$
$757$	8.29928	+	14.3748i	0.301642	+	0.522460i	−0.674866	+	0.737941i	$0.735798\pi$
$758$	−14.9622	+	25.9153i	−0.543451	+	0.941286i
$759$		−	4.67132i		−	0.169558i
$760$			34.1460i			1.23861i
$761$	14.5945	+	8.42614i	0.529050	+	0.305447i	0.740630	−	0.671914i	$-0.234527\pi$
$761$	14.5945	+	8.42614i	0.529050	+	0.305447i	−0.211580	+	0.977361i	$0.567861\pi$
$762$	−7.09908	+	4.09866i	−0.257173	+	0.148479i
$763$	−0.974881	+	1.68854i	−0.0352931	+	0.0611294i
$764$	−13.8175	−	23.9326i	−0.499900	−	0.865852i
$765$	53.4716	−	30.8718i	1.93327	−	1.11617i
$766$	6.63743	+	11.4964i	0.239820	+	0.415381i
$767$	−2.49658	−	8.80558i	−0.0901463	−	0.317951i
$768$	4.42399	−	7.66257i	0.159637	−	0.276499i
$769$	−7.22585	−	4.17185i	−0.260571	−	0.150441i	0.364024	−	0.931390i	$-0.381403\pi$
$769$	−7.22585	−	4.17185i	−0.260571	−	0.150441i	−0.624595	+	0.780949i	$0.714736\pi$
$770$	1.02698	+	1.77879i	0.0370099	+	0.0641030i
$771$	−4.82823			−0.173884
$772$	−1.23513	−	0.713102i	−0.0444533	−	0.0256651i
$773$		−	37.6289i		−	1.35342i	−0.736251	−	0.676709i	$-0.763406\pi$
$773$		−	37.6289i		−	1.35342i	0.736251	−	0.676709i	$-0.236594\pi$
$774$		−	0.0674546i		−	0.00242461i
$775$	33.3249	+	8.29663i	1.19707	+	0.298024i
$776$	5.49901			0.197403
$777$	1.95514			0.0701402
$778$	11.3211	+	6.53622i	0.405880	+	0.234335i
$779$	9.08607			0.325542
$780$	−5.11457	+	5.26480i	−0.183131	+	0.188510i
$781$	13.3174	−	23.0665i	0.476535	−	0.825383i
$782$	27.8568	+	16.0831i	0.996157	+	0.575131i
$783$	−19.4757			−0.696005
$784$	1.27655	+	2.21105i	0.0455912	+	0.0789662i
$785$	−3.91960	+	2.26298i	−0.139896	+	0.0807693i
$786$	3.81236	−	2.20107i	0.135982	−	0.0785094i
$787$	−39.6702	−	22.9036i	−1.41409	−	0.816425i	−0.418319	−	0.908300i	$-0.637381\pi$
$787$	−39.6702	−	22.9036i	−1.41409	−	0.816425i	−0.995771	+	0.0918750i	$0.970714\pi$
$788$	−1.41827	+	0.818837i	−0.0505237	+	0.0291698i
$789$	−3.91941	+	6.78862i	−0.139535	+	0.241681i
$790$	6.49061			0.230925
$791$			4.36350i			0.155148i
$792$	−6.78116	+	11.7453i	−0.240958	+	0.417351i
$793$	−25.6130	−	24.8821i	−0.909544	−	0.883590i
$794$	−9.93992	+	17.2164i	−0.352754	+	0.610989i
$795$	16.3832	−	9.45886i	0.581053	−	0.335471i
$796$	1.76151	+	3.05102i	0.0624349	+	0.108140i
$797$	−12.7555	−	22.0932i	−0.451824	−	0.782582i	0.546676	−	0.837345i	$-0.315893\pi$
$797$	−12.7555	−	22.0932i	−0.451824	−	0.782582i	−0.998499	+	0.0547627i	$0.982560\pi$
$798$		−	0.666514i		−	0.0235943i
$799$	50.1247	+	28.9395i	1.77329	+	1.02381i
$800$	29.1823	+	16.8484i	1.03175	+	0.595680i
$801$	−29.9205	+	17.2746i	−1.05719	+	0.610368i
$802$	−16.8808			−0.596081
$803$	0.518263	−	0.897658i	0.0182891	−	0.0316777i
$804$		−	1.00416i		−	0.0354139i
$805$	−6.67126			−0.235131
$806$	16.3082	+	8.72642i	0.574430	+	0.307375i
$807$	−5.92082			−0.208423
$808$			20.9595i			0.737351i
$809$	2.50873	−	4.34525i	0.0882022	−	0.152771i	−0.818549	−	0.574437i	$-0.805221\pi$
$809$	2.50873	−	4.34525i	0.0882022	−	0.152771i	0.906751	+	0.421666i	$0.138554\pi$
$810$	20.1920			0.709474
$811$	17.3151	−	9.99687i	0.608015	−	0.351037i	−0.164173	−	0.986432i	$-0.552496\pi$
$811$	17.3151	−	9.99687i	0.608015	−	0.351037i	0.772188	+	0.635394i	$0.219162\pi$
$812$	−2.49121	−	1.43830i	−0.0874244	−	0.0504745i
$813$	9.81839	+	5.66865i	0.344346	+	0.198808i
$814$			15.0512i			0.527543i
$815$	−6.85547	−	11.8740i	−0.240136	−	0.415929i
$816$	0.670002	+	1.16048i	0.0234547	+	0.0406248i
$817$	0.0820383	−	0.0473648i	0.00287016	−	0.00165708i
$818$	16.5506	−	28.6665i	0.578679	−	1.00230i
$819$	−2.65418	+	2.73214i	−0.0927446	+	0.0954688i
$820$	4.96577	−	8.60097i	0.173412	−	0.300359i
$821$		−	55.0809i		−	1.92234i	−0.275961	−	0.961169i	$-0.588996\pi$
$821$		−	55.0809i		−	1.92234i	0.275961	−	0.961169i	$-0.411004\pi$
$822$	8.07298			0.281578
$823$	7.76866	−	13.4557i	0.270798	−	0.469037i	−0.698268	−	0.715836i	$-0.746046\pi$
$823$	7.76866	−	13.4557i	0.270798	−	0.469037i	0.969067	+	0.246800i	$0.0793790\pi$
$824$	−28.9309	+	16.7033i	−1.00786	+	0.581886i
$825$	4.85501	+	2.80304i	0.169030	+	0.0975893i
$826$	0.786731	−	0.454220i	0.0273739	−	0.0158043i
$827$	37.8451	−	21.8499i	1.31600	−	0.759795i	0.332920	−	0.942955i	$-0.391966\pi$
$827$	37.8451	−	21.8499i	1.31600	−	0.759795i	0.983083	+	0.183160i	$0.0586328\pi$
$828$	−8.04581	−	13.9358i	−0.279611	−	0.484301i
$829$	3.66182			0.127180			0.0635901	−	0.997976i	$-0.479745\pi$
$829$	3.66182			0.127180			0.0635901	+	0.997976i	$0.479745\pi$
$830$	−44.4265	−	25.6497i	−1.54207	−	0.890312i
$831$	2.04671	−	3.54500i	0.0709995	−	0.122975i
$832$	14.9454	+	14.5189i	0.518137	+	0.503352i
$833$	46.5244			1.61198
$834$	−4.08821	−	2.36033i	−0.141563	−	0.0817315i
$835$	−55.3967			−1.91708
$836$	−6.95760			−0.240634
$837$	−4.65114	−	16.1994i	−0.160767	−	0.559933i
$838$			18.2495i			0.630420i
$839$			4.45862i			0.153929i	0.997034	+	0.0769643i	$0.0245227\pi$
$839$			4.45862i			0.153929i	−0.997034	+	0.0769643i	$0.975477\pi$
$840$	−1.72715	−	0.997169i	−0.0595922	−	0.0344056i
$841$	12.3950			0.427414
$842$	1.40819	+	2.43905i	0.0485294	+	0.0840554i
$843$	10.3876	+	5.99726i	0.357766	+	0.206557i
$844$	14.4166	−	24.9704i	0.496241	−	0.859515i
$845$	−22.8019	−	36.9793i	−0.784409	−	1.27213i
$846$	10.6766	+	18.4924i	0.367069	+	0.635783i
$847$	2.70794	−	1.56343i	0.0930457	−	0.0537200i
$848$	−1.99368	−	3.45316i	−0.0684633	−	0.118582i
$849$	−3.66423	+	6.34664i	−0.125756	+	0.217816i
$850$	−33.4311	+	19.3014i	−1.14668	+	0.662034i
$851$	−42.3365	−	24.4430i	−1.45128	−	0.837896i
$852$			9.44728i			0.323659i
$853$		−	20.4210i		−	0.699203i	−0.936899	−	0.349601i	$-0.886317\pi$
$853$		−	20.4210i		−	0.699203i	0.936899	−	0.349601i	$-0.113683\pi$
$854$	1.77214	−	3.06944i	0.0606414	−	0.105034i
$855$	15.9948	+	27.7038i	0.547010	+	0.947449i
$856$	−27.1175	−	15.6563i	−0.926858	−	0.535122i
$857$	12.3972	+	21.4726i	0.423481	+	0.733491i	0.996277	−	0.0862068i	$-0.0274746\pi$
$857$	12.3972	+	21.4726i	0.423481	+	0.733491i	−0.572796	+	0.819698i	$0.694141\pi$
$858$	2.16567	+	2.10387i	0.0739348	+	0.0718251i
$859$	19.0481	+	32.9923i	0.649913	+	1.12568i	0.983143	+	0.182837i	$0.0585280\pi$
$859$	19.0481	+	32.9923i	0.649913	+	1.12568i	−0.333230	+	0.942845i	$0.608139\pi$
$860$		−	0.103544i		−	0.00353084i
$861$	−0.265341	+	0.459585i	−0.00904281	+	0.0156626i
$862$	13.1337	−	22.7482i	0.447335	−	0.774806i
$863$	17.6592	−	10.1955i	0.601125	−	0.347060i	−0.168359	−	0.985726i	$-0.553847\pi$
$863$	17.6592	−	10.1955i	0.601125	−	0.347060i	0.769484	+	0.638666i	$0.220513\pi$
$864$		−	16.5371i		−	0.562605i
$865$	49.8798	+	28.7981i	1.69596	+	0.979165i
$866$		−	8.73884i		−	0.296958i
$867$	15.4219			0.523755
$868$	0.601397	−	2.41562i	0.0204127	−	0.0819914i
$869$			3.62038i			0.122813i
$870$	10.4838			0.355434
$871$	5.76250	+	1.45501i	0.195255	+	0.0493011i
$872$	14.5740			0.493539
$873$	4.46153	−	2.57586i	0.151000	−	0.0871798i
$874$	−8.33271	+	14.4327i	−0.281858	+	0.488193i
$875$	0.758064	−	1.31301i	0.0256272	−	0.0443877i
$876$			0.367652i			0.0124218i
$877$	34.2446	−	19.7711i	1.15636	−	0.667624i	0.205930	−	0.978567i	$-0.433978\pi$
$877$	34.2446	−	19.7711i	1.15636	−	0.667624i	0.950429	+	0.310943i	$0.100645\pi$
$878$	10.6119	−	6.12678i	0.358134	−	0.206769i
$879$	13.1585	−	7.59706i	0.443825	−	0.256242i
$880$	1.06973	−	1.85283i	0.0360607	−	0.0624590i
$881$	23.5855	+	40.8512i	0.794614	+	1.37631i	0.923084	+	0.384599i	$0.125660\pi$
$881$	23.5855	+	40.8512i	0.794614	+	1.37631i	−0.128470	+	0.991713i	$0.541006\pi$
$882$	14.8646	+	8.58208i	0.500517	+	0.288974i
$883$	31.8717			1.07257			0.536285	−	0.844037i	$-0.319827\pi$
$883$	31.8717			1.07257			0.536285	+	0.844037i	$0.319827\pi$
$884$	27.1232	−	7.69004i	0.912252	−	0.258644i
$885$	2.24472	−	3.88796i	0.0754553	−	0.130692i
$886$	32.7040	−	18.8817i	1.09871	−	0.634343i
$887$	27.6379	−	47.8702i	0.927989	−	1.60732i	0.141306	−	0.989966i	$-0.454870\pi$
$887$	27.6379	−	47.8702i	0.927989	−	1.60732i	0.786683	−	0.617357i	$-0.211797\pi$
$888$	−7.30710	−	12.6563i	−0.245210	−	0.424717i
$889$	−5.65508	+	3.26496i	−0.189665	+	0.109503i
$890$	33.8709	−	19.5554i	1.13535	−	0.655497i
$891$			11.2628i			0.377319i
$892$	−21.3598	−	12.3321i	−0.715178	−	0.412908i
$893$	−14.9936	+	25.9698i	−0.501743	+	0.869045i
$894$	2.81519	+	4.87605i	0.0941539	+	0.163079i
$895$		−	43.1984i		−	1.44396i
$896$	1.08789	−	1.88428i	0.0363438	−	0.0629492i
$897$	−9.43490	+	2.67501i	−0.315022	+	0.0893159i
$898$	−14.2884			−0.476811
$899$	9.88586	+	34.4313i	0.329712	+	1.14835i
$900$	19.3116			0.643721
$901$	−72.6605			−2.42067
$902$	−3.53800	−	2.04267i	−0.117803	−	0.0680134i
$903$			0.00553280i			0.000184120i
$904$	28.2464	−	16.3081i	0.939462	−	0.542399i
$905$	3.57205	+	2.06233i	0.118739	+	0.0685540i
$906$	0.648088	−	1.12252i	0.0215313	−	0.0372933i
$907$	10.7677			0.357535			0.178768	−	0.983891i	$-0.442789\pi$
$907$	10.7677			0.357535			0.178768	+	0.983891i	$0.442789\pi$
$908$	−19.8258	+	11.4464i	−0.657941	+	0.379862i
$909$	9.81790	+	17.0051i	0.325639	+	0.564024i
$910$	3.00461	−	3.09286i	0.0996018	−	0.102527i
$911$	−10.6815	+	18.5008i	−0.353893	+	0.612960i	−0.986928	−	0.161163i	$-0.948476\pi$
$911$	−10.6815	+	18.5008i	−0.353893	+	0.612960i	0.633035	+	0.774123i	$0.281809\pi$
$912$	−0.601246	+	0.347130i	−0.0199092	+	0.0114946i
$913$	14.3070	−	24.7805i	0.473494	−	0.820116i
$914$	−19.5224			−0.645745
$915$		−	17.5156i		−	0.579047i
$916$	10.2591	+	5.92311i	0.338971	+	0.195705i
$917$	3.03690	−	1.75336i	0.100287	−	0.0579009i
$918$	16.4068	+	9.47244i	0.541504	+	0.312637i
$919$	0.476889	+	0.825996i	0.0157311	+	0.0272471i	0.873784	−	0.486315i	$-0.161659\pi$
$919$	0.476889	+	0.825996i	0.0157311	+	0.0272471i	−0.858053	+	0.513562i	$0.828326\pi$
$920$	24.9331	+	43.1854i	0.822019	+	1.42378i
$921$	−6.86000	+	3.96062i	−0.226045	+	0.130507i
$922$	19.4644			0.641025
$923$	−54.2147	−	13.6890i	−1.78450	−	0.450579i
$924$	0.203183	−	0.351924i	0.00668425	−	0.0115775i
$925$	50.8083	−	29.3342i	1.67057	−	0.964502i
$926$	−5.12840			−0.168530
$927$	−15.6484	+	27.1038i	−0.513961	+	0.890206i
$928$			35.1492i			1.15383i
$929$		−	8.40497i		−	0.275758i	−0.990449	−	0.137879i	$-0.955971\pi$
$929$		−	8.40497i		−	0.275758i	0.990449	−	0.137879i	$-0.0440285\pi$
$930$	2.50371	+	8.72014i	0.0821000	+	0.285945i
$931$			24.1044i			0.789991i
$932$	−10.1608			−0.332829
$933$	−6.16611	+	10.6800i	−0.201869	+	0.349648i
$934$		−	14.9190i		−	0.488164i
$935$	−19.4934	−	33.7636i	−0.637503	−	1.10419i
$936$	27.6058	+	6.97036i	0.902323	+	0.227833i
$937$	−9.87366	+	17.1017i	−0.322558	+	0.558687i	−0.981015	−	0.193931i	$-0.937876\pi$
$937$	−9.87366	+	17.1017i	−0.322558	+	0.558687i	0.658457	+	0.752619i	$0.271210\pi$
$938$			0.589903i			0.0192610i
$939$	2.84331	+	4.92476i	0.0927880	+	0.160714i
$940$	16.3888	+	28.3863i	0.534545	+	0.925859i
$941$	4.69039	−	2.70800i	0.152902	−	0.0882782i	−0.421597	−	0.906783i	$-0.638530\pi$
$941$	4.69039	−	2.70800i	0.152902	−	0.0882782i	0.574499	+	0.818505i	$0.305197\pi$
$942$	−0.571885	−	0.330178i	−0.0186330	−	0.0107578i
$943$	11.4914	−	6.63456i	0.374211	−	0.216051i
$944$	−0.819481	−	0.473128i	−0.0266718	−	0.0153990i
$945$	−3.92916			−0.127816
$946$	−0.0425929			−0.00138482
$947$	−37.2271	−	21.4931i	−1.20972	−	0.698431i	−0.247020	−	0.969010i	$-0.579451\pi$
$947$	−37.2271	−	21.4931i	−1.20972	−	0.698431i	−0.962698	+	0.270580i	$0.912785\pi$
$948$	−0.642067	−	1.11209i	−0.0208534	−	0.0361191i
$949$	−2.10983	−	0.532723i	−0.0684878	−	0.0172929i
$950$	−10.0001	−	17.3207i	−0.324447	−	0.561959i
$951$	−5.19221	+	2.99772i	−0.168369	+	0.0972078i
$952$	3.82999	+	6.63374i	0.124131	+	0.215001i
$953$	0.870073			0.0281844			0.0140922	−	0.999901i	$-0.495514\pi$
$953$	0.870073			0.0281844			0.0140922	+	0.999901i	$0.495514\pi$
$954$	−23.2151	−	13.4032i	−0.751616	−	0.433946i
$955$	69.4809	+	40.1148i	2.24835	+	1.29808i
$956$	−9.86213	+	5.69390i	−0.318964	+	0.184154i
$957$			5.84772i			0.189030i
$958$	−7.97000	+	13.8044i	−0.257499	+	0.446001i
$959$	6.43088			0.207664
$960$			10.2205i			0.329864i
$961$	−26.2782	+	16.4456i	−0.847683	+	0.530504i
$962$	30.3996	−	8.61897i	0.980122	−	0.277887i
$963$	−29.3351			−0.945312
$964$	−4.48556	−	2.58974i	−0.144470	−	0.0834100i
$965$	4.14054			0.133289
$966$	−0.486682	−	0.842958i	−0.0156587	−	0.0271217i
$967$	−20.6969	−	11.9493i	−0.665567	−	0.384265i	0.128828	−	0.991667i	$-0.458878\pi$
$967$	−20.6969	−	11.9493i	−0.665567	−	0.384265i	−0.794395	+	0.607402i	$0.792212\pi$
$968$	−20.2412	−	11.6863i	−0.650577	−	0.375611i
$969$			12.6513i			0.406417i
$970$	−5.05057	+	2.91595i	−0.162164	+	0.0936255i
$971$	−18.0930	−	31.3379i	−0.580631	−	1.00568i	−0.995405	−	0.0957579i	$-0.969473\pi$
$971$	−18.0930	−	31.3379i	−0.580631	−	1.00568i	0.414774	−	0.909925i	$-0.363861\pi$
$972$	−7.22410	−	12.5125i	−0.231713	−	0.401339i
$973$	−3.25664	−	1.88022i	−0.104403	−	0.0602772i
$974$	−9.74401	−	16.8771i	−0.312218	−	0.540778i
$975$	2.88125	−	11.4110i	0.0922737	−	0.365446i
$976$	−3.69182			−0.118172
$977$			42.1760i			1.34933i	0.738123	+	0.674666i	$0.235712\pi$
$977$			42.1760i			1.34933i	−0.738123	+	0.674666i	$0.764288\pi$
$978$	1.00024	−	1.73247i	0.0319842	−	0.0553982i
$979$	10.9077	+	18.8927i	0.348612	+	0.603814i
$980$	22.8175	+	13.1737i	0.728879	+	0.420818i
$981$	11.8244	−	6.82682i	0.377524	−	0.217963i
$982$	10.8987	−	6.29236i	0.347791	−	0.200797i
$983$	−43.5851	+	25.1639i	−1.39015	+	0.802604i	−0.993331	−	0.115293i	$-0.963219\pi$
$983$	−43.5851	+	25.1639i	−1.39015	+	0.802604i	−0.396819	+	0.917897i	$0.629886\pi$
$984$	3.96673			0.126455
$985$	2.37723	−	4.11749i	0.0757450	−	0.131194i
$986$	−34.8721	−	20.1334i	−1.11055	−	0.641178i
$987$	−0.875722	−	1.51680i	−0.0278746	−	0.0482801i
$988$	3.98423	+	14.0526i	0.126755	+	0.447073i
$989$	0.0691707	−	0.119807i	0.00219950	−	0.00380965i
$990$		−	14.3833i		−	0.457133i
$991$	−16.3695			−0.519995			−0.259997	−	0.965609i	$-0.583722\pi$
$991$	−16.3695			−0.519995			−0.259997	+	0.965609i	$0.583722\pi$
$992$	−29.2362	+	8.39426i	−0.928251	+	0.266518i
$993$			0.929533i			0.0294979i
$994$		−	5.54991i		−	0.176033i
$995$	−8.85767	−	5.11398i	−0.280807	−	0.162124i
$996$			10.1493i			0.321593i
$997$	−6.78633	−	11.7543i	−0.214925	−	0.372262i	0.738324	−	0.674446i	$-0.235617\pi$
$997$	−6.78633	−	11.7543i	−0.214925	−	0.372262i	−0.953249	+	0.302184i	$0.902284\pi$
$998$	−12.6791	+	21.9608i	−0.401349	+	0.695158i
$999$	−24.9349	−	14.3961i	−0.788904	−	0.455474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.23	yes	68
13.12	even	2	inner	403.2.l.c.129.12	yes	68
31.25	even	3	inner	403.2.l.c.25.23	yes	68
403.25	even	6	inner	403.2.l.c.25.12	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.12	✓	68	403.25	even	6	inner
403.2.l.c.25.23	yes	68	31.25	even	3	inner
403.2.l.c.129.12	yes	68	13.12	even	2	inner
403.2.l.c.129.23	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.921357i q^{2} +(-0.264605 + 0.458309i) q^{3} +1.15110 q^{4} +(-2.89414 + 1.67093i) q^{5} +(-0.422266 - 0.243795i) q^{6} +(-0.336375 - 0.194206i) q^{7} +2.90329i q^{8} +(1.35997 + 2.35553i) q^{9} +O(q^{10})\)	\(q+0.921357i q^{2} +(-0.264605 + 0.458309i) q^{3} +1.15110 q^{4} +(-2.89414 + 1.67093i) q^{5} +(-0.422266 - 0.243795i) q^{6} +(-0.336375 - 0.194206i) q^{7} +2.90329i q^{8} +(1.35997 + 2.35553i) q^{9} +(-1.53952 - 2.66653i) q^{10} +(1.48736 - 0.858726i) q^{11} +(-0.304587 + 0.527560i) q^{12} +(-2.58614 - 2.51235i) q^{13} +(0.178933 - 0.309921i) q^{14} -1.76854i q^{15} -0.372763 q^{16} +(-3.39637 + 5.88269i) q^{17} +(-2.17029 + 1.25302i) q^{18} +(-3.04784 - 1.75967i) q^{19} +(-3.33144 + 1.92341i) q^{20} +(0.178013 - 0.102776i) q^{21} +(0.791193 + 1.37039i) q^{22} -5.13958 q^{23} +(-1.33060 - 0.768224i) q^{24} +(3.08402 - 5.34167i) q^{25} +(2.31477 - 2.38276i) q^{26} -3.02705 q^{27} +(-0.387201 - 0.223551i) q^{28} +6.43390 q^{29} +1.62946 q^{30} +(1.53653 + 5.35155i) q^{31} +5.46313i q^{32} +0.908892i q^{33} +(-5.42006 - 3.12927i) q^{34} +1.29802 q^{35} +(1.56546 + 2.71146i) q^{36} +(8.23736 + 4.75584i) q^{37} +(1.62128 - 2.80815i) q^{38} +(1.83574 - 0.520472i) q^{39} +(-4.85119 - 8.40251i) q^{40} +(-2.23586 + 1.29088i) q^{41} +(0.0946930 + 0.164013i) q^{42} +(-0.0134584 + 0.0233107i) q^{43} +(1.71210 - 0.988481i) q^{44} +(-7.87187 - 4.54483i) q^{45} -4.73539i q^{46} -8.52072i q^{47} +(0.0986349 - 0.170841i) q^{48} +(-3.42457 - 5.93153i) q^{49} +(4.92159 + 2.84148i) q^{50} +(-1.79739 - 3.11317i) q^{51} +(-2.97691 - 2.89196i) q^{52} +(5.34839 + 9.26368i) q^{53} -2.78899i q^{54} +(-2.86974 + 4.97054i) q^{55} +(0.563836 - 0.976592i) q^{56} +(1.61294 - 0.931234i) q^{57} +5.92791i q^{58} +(2.19840 + 1.26924i) q^{59} -2.03577i q^{60} +9.90394 q^{61} +(-4.93069 + 1.41569i) q^{62} -1.05646i q^{63} -5.77902 q^{64} +(11.6826 + 2.94981i) q^{65} -0.837414 q^{66} +(-1.42755 + 0.824195i) q^{67} +(-3.90957 + 6.77157i) q^{68} +(1.35996 - 2.35551i) q^{69} +1.19594i q^{70} +(13.4306 - 7.75418i) q^{71} +(-6.83880 + 3.94838i) q^{72} +(0.522668 - 0.301763i) q^{73} +(-4.38183 + 7.58955i) q^{74} +(1.63209 + 2.82686i) q^{75} +(-3.50837 - 2.02556i) q^{76} -0.667079 q^{77} +(0.479541 + 1.69137i) q^{78} +(-1.05400 + 1.82557i) q^{79} +(1.07883 - 0.622861i) q^{80} +(-3.27894 + 5.67928i) q^{81} +(-1.18936 - 2.06003i) q^{82} +(14.4287 - 8.33039i) q^{83} +(0.204911 - 0.118305i) q^{84} -22.7004i q^{85} +(-0.0214775 - 0.0124000i) q^{86} +(-1.70244 + 2.94871i) q^{87} +(2.49313 + 4.31823i) q^{88} +12.7022i q^{89} +(4.18741 - 7.25280i) q^{90} +(0.381999 + 1.34733i) q^{91} -5.91617 q^{92} +(-2.85924 - 0.711841i) q^{93} +7.85063 q^{94} +11.7611 q^{95} +(-2.50380 - 1.44557i) q^{96} -1.89406i q^{97} +(5.46505 - 3.15525i) q^{98} +(4.04552 + 2.33568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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