LMFDB - Embedded newform 403.2.l.c.25.12

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			25.12
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.23

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	0.921357i		−	0.651498i	−0.945456	−	0.325749i	$-0.894384\pi$
$2$		−	0.921357i		−	0.651498i	0.945456	−	0.325749i	$-0.105616\pi$
$3$	−0.264605	−	0.458309i	−0.152770	−	0.264605i	0.779475	−	0.626433i	$-0.215486\pi$
$3$	−0.264605	−	0.458309i	−0.152770	−	0.264605i	−0.932245	+	0.361829i	$0.882153\pi$
$4$	1.15110			0.575551
$5$	−2.89414	−	1.67093i	−1.29430	−	0.747263i	−0.314884	−	0.949130i	$-0.601966\pi$
$5$	−2.89414	−	1.67093i	−1.29430	−	0.747263i	−0.979413	+	0.201867i	$0.935299\pi$
$6$	−0.422266	+	0.243795i	−0.172389	+	0.0995291i
$7$	−0.336375	+	0.194206i	−0.127138	+	0.0734029i	−0.562220	−	0.826988i	$-0.690053\pi$
$7$	−0.336375	+	0.194206i	−0.127138	+	0.0734029i	0.435082	+	0.900391i	$0.356719\pi$
$8$		−	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	0.707178	−	0.707036i	$-0.249968\pi$
$11$	1.48736	+	0.858726i	0.448455	+	0.258916i	−0.258722	+	0.965952i	$0.583301\pi$
$12$	−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	−0.902878	−	0.429898i	$-0.858550\pi$
$17$	−3.39637	−	5.88269i	−0.823741	−	1.42676i	0.0791365	−	0.996864i	$-0.474784\pi$
$18$	−2.17029	−	1.25302i	−0.511542	−	0.295339i
$19$	−3.04784	+	1.75967i	−0.699222	+	0.403696i	−0.807057	−	0.590473i	$-0.798941\pi$
$19$	−3.04784	+	1.75967i	−0.699222	+	0.403696i	0.107836	+	0.994169i	$0.465608\pi$
$20$	−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	0.365377	−	0.930860i	$-0.380940\pi$
$37$	8.23736	−	4.75584i	1.35421	−	0.781855i	0.988837	+	0.149004i	$0.0476068\pi$
$38$	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	0.315142	−	0.949044i	$-0.397948\pi$
$41$	−2.23586	−	1.29088i	−0.349183	−	0.201601i	−0.664326	+	0.747443i	$0.731281\pi$
$42$	0.0946930	−	0.164013i	0.0146115	−	0.0253078i
$43$	−0.0134584	−	0.0233107i	−0.00205239	−	0.00355485i	0.864997	−	0.501776i	$-0.167320\pi$
$43$	−0.0134584	−	0.0233107i	−0.00205239	−	0.00355485i	−0.867050	+	0.498222i	$0.833987\pi$
$44$	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	$0.213451\pi$
$47$			8.52072i			1.24287i	−0.783464	+	0.621437i	$0.786549\pi$
$48$	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	−0.220216	−	0.975451i	$-0.570676\pi$
$53$	5.34839	−	9.26368i	0.734658	−	1.27246i	0.954873	−	0.297013i	$-0.0959905\pi$
$54$			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	−0.350023	−	0.936741i	$-0.613826\pi$
$59$	2.19840	−	1.26924i	0.286207	−	0.165242i	0.636230	+	0.771499i	$0.280493\pi$
$60$			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	0.410257	−	0.911970i	$-0.365439\pi$
$67$	−1.42755	−	0.824195i	−0.174403	−	0.100691i	−0.584660	+	0.811278i	$0.698772\pi$
$68$	−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	0.992625	+	0.121226i	$0.0386827\pi$
$71$	13.4306	+	7.75418i	1.59392	+	0.920252i	0.601298	+	0.799025i	$0.294651\pi$
$72$	−6.83880	−	3.94838i	−0.805960	−	0.465321i
$73$	0.522668	+	0.301763i	0.0611737	+	0.0353187i	0.530275	−	0.847826i	$-0.322089\pi$
$73$	0.522668	+	0.301763i	0.0611737	+	0.0353187i	−0.469101	+	0.883144i	$0.655422\pi$
$74$	−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	0.800623	−	0.599169i	$-0.204502\pi$
$79$	−1.05400	−	1.82557i	−0.118584	−	0.205393i	−0.919207	+	0.393775i	$0.871169\pi$
$80$	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	0.994305	+	0.106571i	$0.0339871\pi$
$83$	14.4287	+	8.33039i	1.58375	+	0.914379i	0.589446	+	0.807808i	$0.299346\pi$
$84$	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	$-0.764912\pi$
$89$		−	12.7022i		−	1.34643i	0.739446	−	0.673216i	$-0.235088\pi$
$90$	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	$0.0306549\pi$
$97$			1.89406i			0.192313i	−0.995366	+	0.0961564i	$0.969345\pi$
$98$	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	−0.429990	−	0.902834i	$-0.641483\pi$
$103$	5.75322	−	9.96487i	0.566882	−	0.981868i	0.996872	−	0.0790344i	$-0.0251837\pi$
$104$	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	−0.999692	−	0.0247999i	$-0.992105\pi$
$107$	−5.39261	−	9.34028i	−0.521324	−	0.902959i	0.478369	−	0.878159i	$-0.341228\pi$
$108$	−3.48444			−0.335290
$109$			5.01983i			0.480813i	0.970672	+	0.240406i	$0.0772807\pi$
$109$			5.01983i			0.480813i	−0.970672	+	0.240406i	$0.922719\pi$
$110$	−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	0.471038	+	0.882113i	$0.343879\pi$
$113$	−5.61711	+	9.72911i	−0.528413	+	0.915238i	−0.999451	+	0.0331252i	$0.989454\pi$
$114$	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	0.949770	+	0.312948i	$0.101316\pi$
$127$	8.40593	+	14.5595i	0.745906	+	1.29195i	−0.203865	+	0.978999i	$0.565350\pi$
$128$		−	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	0.598620	−	0.801033i	$-0.295716\pi$
$131$	−4.51417	−	7.81877i	−0.394405	−	0.683129i	−0.993025	+	0.117904i	$0.962382\pi$
$132$		−	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	−0.259048	−	0.965864i	$-0.583409\pi$
$137$	−14.3387	−	8.27844i	−1.22504	−	0.707274i	−0.965987	+	0.258590i	$0.916742\pi$
$138$	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	−0.850159	−	0.526525i	$-0.823495\pi$
$149$	−10.0003	+	5.77366i	−0.819255	+	0.472997i	0.0309046	+	0.999522i	$0.490161\pi$
$150$	−2.60455	−	1.50374i	−0.212661	−	0.122780i
$151$		−	2.65833i		−	0.216332i	−0.994133	−	0.108166i	$-0.965502\pi$
$151$		−	2.65833i		−	0.216332i	0.994133	−	0.108166i	$-0.0344977\pi$
$152$	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	$-0.948632\pi$
$163$		−	4.10278i		−	0.321355i	0.987007	−	0.160677i	$-0.0513679\pi$
$164$	−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	0.171824	−	0.985128i	$-0.445034\pi$
$167$	14.3558	−	8.28830i	1.11088	−	0.641368i	0.939058	+	0.343759i	$0.111700\pi$
$168$	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	0.326684	+	0.945134i	$0.394069\pi$
$173$	−8.61739	+	14.9257i	−0.655168	+	1.13478i	−0.981852	+	0.189650i	$0.939265\pi$
$174$	−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	0.516727	−	0.856150i	$-0.327150\pi$
$179$	−6.46323	−	11.1946i	−0.483084	−	0.836726i	−0.999811	+	0.0194238i	$0.993817\pi$
$180$	−9.06132	+	5.23155i	−0.675391	+	0.389937i
$181$	−0.617119	+	1.06888i	−0.0458701	+	0.0794493i	−0.888049	−	0.459749i	$-0.847939\pi$
$181$	−0.617119	+	1.06888i	−0.0458701	+	0.0794493i	0.842179	+	0.539198i	$0.181273\pi$
$182$	−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	−0.00509028	+	0.999987i	$0.501620\pi$
$191$	−12.0037	+	20.7911i	−0.868559	+	1.50439i	−0.863469	+	0.504402i	$0.831713\pi$
$192$	1.52916	+	2.64858i	0.110357	+	0.191145i
$193$	−1.07300	+	0.619496i	−0.0772361	+	0.0445923i	−0.538121	−	0.842868i	$-0.680866\pi$
$193$	−1.07300	+	0.619496i	−0.0772361	+	0.0445923i	0.460885	+	0.887460i	$0.347532\pi$
$194$	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	0.455466	−	0.890253i	$-0.349473\pi$
$197$	−1.23210	−	0.711351i	−0.0877832	−	0.0506816i	−0.543249	+	0.839572i	$0.682806\pi$
$198$	−2.15200	−	3.72737i	−0.152936	−	0.264892i
$199$	1.53028	−	2.65052i	0.108479	−	0.187890i	−0.806675	−	0.590995i	$-0.798735\pi$
$199$	1.53028	−	2.65052i	0.108479	−	0.187890i	0.915154	+	0.403104i	$0.132069\pi$
$200$	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	0.869798	+	0.493408i	$0.164249\pi$
$211$	12.5242	+	21.6926i	0.862203	+	1.49338i	−0.00759518	+	0.999971i	$0.502418\pi$
$212$	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	−0.969622	−	0.244607i	$-0.921341\pi$
$223$	−18.5559	+	10.7133i	−1.24260	+	0.717414i	−0.272976	+	0.962021i	$0.588008\pi$
$224$	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	−0.195942	−	0.980616i	$-0.562776\pi$
$227$	−17.2233	−	9.94388i	−1.14315	−	0.659998i	−0.947209	+	0.320617i	$0.896110\pi$
$228$	1.85666	+	1.07194i	0.122960	+	0.0709913i
$229$	8.91245	−	5.14561i	0.588951	−	0.340031i	−0.175731	−	0.984438i	$-0.556229\pi$
$229$	8.91245	−	5.14561i	0.588951	−	0.340031i	0.764683	+	0.644407i	$0.222896\pi$
$230$	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	0.196621	−	0.980480i	$-0.437003\pi$
$239$	−8.56756	−	4.94648i	−0.554190	−	0.319961i	−0.750810	+	0.660518i	$0.770337\pi$
$240$		−	0.659248i		−	0.0425543i
$241$	−3.89676	+	2.24979i	−0.251012	+	0.144922i	−0.620228	−	0.784422i	$-0.712960\pi$
$241$	−3.89676	+	2.24979i	−0.251012	+	0.144922i	0.369215	+	0.929344i	$0.379626\pi$
$242$	−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	0.859520	−	0.511103i	$-0.170763\pi$
$251$	−0.203866	−	0.353106i	−0.0128679	−	0.0222879i	−0.872388	+	0.488815i	$0.837429\pi$
$252$			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	−0.687948	−	0.725760i	$-0.741488\pi$
$257$	4.56174	−	7.90116i	0.284553	−	0.492861i	0.972501	+	0.232900i	$0.0748214\pi$
$258$	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	−0.643559	−	0.765397i	$-0.722543\pi$
$269$	5.59402	−	9.68913i	0.341074	−	0.590757i	0.984632	+	0.174640i	$0.0558761\pi$
$270$	4.66021	−	8.07172i	0.283611	−	0.491229i
$271$			21.4231i			1.30136i	0.759352	+	0.650680i	$0.225516\pi$
$271$			21.4231i			1.30136i	−0.759352	+	0.650680i	$0.774484\pi$
$272$	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	$0.236305\pi$
$281$			22.6650i			1.35208i	−0.736866	+	0.676039i	$0.763695\pi$
$282$	−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	−0.998628	−	0.0523623i	$-0.983325\pi$
$293$	−24.8644	+	14.3555i	−1.45260	+	0.838656i	−0.453967	+	0.891018i	$0.649992\pi$
$294$		−	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	−0.0821829	−	0.996617i	$-0.526189\pi$
$307$	12.9627	−	7.48403i	0.739821	−	0.427136i	0.822004	+	0.569481i	$0.192856\pi$
$308$	−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	0.976968	−	0.213386i	$-0.0684493\pi$
$313$	5.37275	+	9.30588i	0.303686	+	0.526000i	−0.673282	+	0.739386i	$0.735116\pi$
$314$		−	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	−0.198492	−	0.980102i	$-0.563605\pi$
$317$	9.81125	−	5.66453i	0.551055	−	0.318152i	0.749547	+	0.661951i	$0.230271\pi$
$318$			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	0.541222	−	0.840880i	$-0.317962\pi$
$331$	1.52114	+	0.878228i	0.0836092	+	0.0482718i	−0.457613	+	0.889152i	$0.651295\pi$
$332$	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	0.974156	−	0.225877i	$-0.0725249\pi$
$347$	5.42934	+	9.40389i	0.291462	+	0.504827i	−0.682693	+	0.730705i	$0.739192\pi$
$348$	−1.95968	−	3.39427i	−0.105050	−	0.181952i
$349$		−	24.3630i		−	1.30412i	−0.758166	−	0.652061i	$-0.773904\pi$
$349$		−	24.3630i		−	1.30412i	0.758166	−	0.652061i	$-0.226096\pi$
$350$	−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	−0.374312	−	0.927303i	$-0.622121\pi$
$353$	4.53924	−	2.62073i	0.241599	−	0.139487i	0.615912	+	0.787815i	$0.288788\pi$
$354$	−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	0.408995	−	0.912537i	$-0.365879\pi$
$359$	−3.34965	−	1.93392i	−0.176788	−	0.102069i	−0.585783	+	0.810468i	$0.699213\pi$
$360$	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	−0.448313	−	0.893876i	$-0.647975\pi$
$367$	10.5358	−	18.2485i	0.549963	−	0.952564i	0.998276	−	0.0586874i	$-0.0186915\pi$
$368$	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	0.446638	−	0.894715i	$-0.352621\pi$
$379$	28.1273	−	16.2393i	1.44480	−	0.834157i	0.998165	+	0.0605577i	$0.0192879\pi$
$380$	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	0.783681	−	0.621164i	$-0.213340\pi$
$383$	12.4776	+	7.20397i	0.637578	+	0.368106i	−0.146103	+	0.989269i	$0.546673\pi$
$384$	−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	0.987908	−	0.155039i	$-0.0495504\pi$
$389$	7.09412	+	12.2874i	0.359686	+	0.622995i	−0.628222	+	0.778034i	$0.716217\pi$
$390$	−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	0.0485448	−	0.998821i	$-0.484542\pi$
$397$	18.6860	−	10.7883i	0.937822	−	0.541452i	0.889277	+	0.457369i	$0.151208\pi$
$398$	−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	$-0.848756\pi$
$401$		−	18.3217i		−	0.914940i	0.889225	−	0.457470i	$-0.151244\pi$
$402$	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	−0.539528	+	0.841968i	$0.681397\pi$
$409$	−31.1134	+	17.9633i	−1.53846	+	0.888229i	−0.998929	+	0.0462613i	$0.985269\pi$
$410$	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	0.563120	−	0.826375i	$-0.309601\pi$
$421$	2.64724	+	1.52839i	0.129019	+	0.0744889i	−0.434102	+	0.900864i	$0.642934\pi$
$422$	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	−0.958141	−	0.286298i	$-0.907575\pi$
$431$	−24.6899	+	14.2547i	−1.18927	+	0.686625i	−0.231129	+	0.972923i	$0.574242\pi$
$432$	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	−0.979939	−	0.199296i	$-0.936135\pi$
$439$	−6.64973	+	11.5177i	−0.317374	+	0.549709i	0.662565	+	0.749004i	$0.269468\pi$
$440$	−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	−0.289406	+	0.957207i	$0.593458\pi$
$443$	−20.4933	+	35.4955i	−0.973668	+	1.68644i	−0.684262	+	0.729236i	$0.739876\pi$
$444$	−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	$-0.880749\pi$
$449$		−	15.5080i		−	0.731869i	0.930641	−	0.365935i	$-0.119251\pi$
$450$		−	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	$-0.834954\pi$
$457$		−	21.1888i		−	0.991170i	0.868559	−	0.495585i	$-0.165046\pi$
$458$	−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	$0.163720\pi$
$461$			21.1258i			0.983926i	−0.870616	+	0.491963i	$0.836280\pi$
$462$	0.281685	−	0.162631i	0.0131052	−	0.00756627i
$463$		−	5.56614i		−	0.258681i	−0.991600	−	0.129340i	$-0.958714\pi$
$463$		−	5.56614i		−	0.258681i	0.991600	−	0.129340i	$-0.0412860\pi$
$464$	−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	−0.117000	−	0.993132i	$-0.537328\pi$
$479$	14.9827	−	8.65028i	0.684578	−	0.395241i	0.801578	+	0.597891i	$0.203994\pi$
$480$	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	0.0238175	−	0.999716i	$-0.492418\pi$
$487$	−18.3177	−	10.5757i	−0.830054	−	0.479232i	−0.853871	+	0.520485i	$0.825751\pi$
$488$		−	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	−0.977971	−	0.208743i	$-0.933063\pi$
$491$	−6.82944	+	11.8289i	−0.308208	+	0.533833i	0.669762	+	0.742576i	$0.266396\pi$
$492$			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	0.139650	−	0.990201i	$-0.455402\pi$
$499$	23.8353	−	13.7613i	1.06701	−	0.616041i	0.927364	+	0.374160i	$0.122069\pi$
$500$		−	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	0.884108	−	0.467283i	$-0.154767\pi$
$503$	0.838225	+	1.45185i	0.0373746	+	0.0647347i	−0.846733	+	0.532018i	$0.821434\pi$
$504$	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	0.305956	−	0.952046i	$-0.401024\pi$
$509$	−8.24747	−	4.76168i	−0.365563	−	0.211058i	−0.671518	+	0.740988i	$0.734357\pi$
$510$	−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	0.561147	−	0.827716i	$-0.310360\pi$
$521$	−9.95759	−	17.2471i	−0.436250	−	0.755607i	−0.997397	+	0.0721092i	$0.977027\pi$
$522$	−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	−0.113691	−	0.993516i	$-0.536267\pi$
$541$	16.0461	−	9.26419i	0.689874	−	0.398299i	0.803565	+	0.595217i	$0.202934\pi$
$542$	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	0.0952552	+	0.995453i	$0.469633\pi$
$547$	−19.0486	+	32.9932i	−0.814460	+	1.41069i	−0.909715	+	0.415233i	$0.863700\pi$
$548$	−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	$0.0314608\pi$
$557$			4.65769i			0.197353i	−0.995120	+	0.0986763i	$0.968539\pi$
$558$	−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	−0.536163	−	0.844114i	$-0.680127\pi$
$563$	10.9845	−	19.0258i	0.462943	−	0.801840i	0.999106	+	0.0422741i	$0.0134603\pi$
$564$	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	−0.965652	−	0.259841i	$-0.916330\pi$
$569$	−6.14942	+	10.6511i	−0.257797	+	0.446518i	0.707854	+	0.706358i	$0.249663\pi$
$570$	−4.96633	+	2.86731i	−0.208017	+	0.120098i
$571$	11.4470	−	19.8267i	0.479040	−	0.829722i	−0.520671	−	0.853758i	$-0.674318\pi$
$571$	11.4470	−	19.8267i	0.479040	−	0.829722i	0.999711	+	0.0240353i	$0.00765139\pi$
$572$	−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	−0.754435	−	0.656375i	$-0.772089\pi$
$577$	−13.5289	+	7.81090i	−0.563214	+	0.325172i	0.191220	+	0.981547i	$0.438756\pi$
$578$	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	$-0.893093\pi$
$587$		−	15.9702i		−	0.659159i	0.944128	−	0.329580i	$-0.106907\pi$
$588$	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	$0.0592142\pi$
$593$			9.00794i			0.369912i	−0.982747	+	0.184956i	$0.940786\pi$
$594$	−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	−0.988074	−	0.153977i	$-0.950792\pi$
$599$	−8.82768	+	15.2900i	−0.360689	+	0.624732i	0.627385	+	0.778709i	$0.284125\pi$
$600$	−8.20721	−	4.73843i	−0.335058	−	0.193446i
$601$	12.1027	+	20.9626i	0.493681	+	0.855080i	0.999973	−	0.00728131i	$-0.00231773\pi$
$601$	12.1027	+	20.9626i	0.493681	+	0.855080i	−0.506293	+	0.862362i	$0.668984\pi$
$602$	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	−0.770553	−	0.637376i	$-0.780020\pi$
$607$	4.10722	−	7.11392i	0.166707	−	0.288745i	0.937260	+	0.348631i	$0.113353\pi$
$608$	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	0.198129	−	0.980176i	$-0.436514\pi$
$613$	28.3749	−	16.3822i	1.14605	−	0.661672i	0.947922	+	0.318504i	$0.103180\pi$
$614$	−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	−0.0620459	−	0.998073i	$-0.519763\pi$
$617$	19.1584	−	11.0611i	0.771288	−	0.445303i	0.833334	+	0.552770i	$0.186429\pi$
$618$			5.61044i			0.225685i
$619$		−	19.7208i		−	0.792645i	−0.918111	−	0.396323i	$-0.870286\pi$
$619$		−	19.7208i		−	0.792645i	0.918111	−	0.396323i	$-0.129714\pi$
$620$	−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	0.0990727	−	0.995080i	$-0.468412\pi$
$631$	−17.9143	−	10.3428i	−0.713156	−	0.411741i	−0.812228	+	0.583340i	$0.801746\pi$
$632$	−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	0.454431	+	0.890782i	$0.349843\pi$
$641$	−13.7787	+	23.8653i	−0.544224	+	0.942624i	−0.998655	+	0.0518422i	$0.983491\pi$
$642$	4.55424	+	2.62939i	0.179741	+	0.103774i
$643$			1.24221i			0.0489881i	0.999700	+	0.0244940i	$0.00779748\pi$
$643$			1.24221i			0.0489881i	−0.999700	+	0.0244940i	$0.992203\pi$
$644$	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	0.759387	−	0.650640i	$-0.225499\pi$
$661$	14.7989	+	8.54414i	0.575610	+	0.332328i	−0.183777	+	0.982968i	$0.558832\pi$
$662$	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	−0.568780	−	0.822489i	$-0.692585\pi$
$673$	11.1009	−	19.2272i	0.427907	−	0.741156i	0.996687	+	0.0813336i	$0.0259179\pi$
$674$		−	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	−0.820247	−	0.572010i	$-0.806164\pi$
$677$	2.21818	−	3.84200i	0.0852515	−	0.147660i	0.905498	+	0.424350i	$0.139497\pi$
$678$		−	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	$0.313257\pi$
$683$			43.5287i			1.66558i	−0.553590	+	0.832789i	$0.686743\pi$
$684$			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	0.874458	−	0.485101i	$-0.161217\pi$
$691$	23.4368	+	13.5312i	0.891577	+	0.514752i	0.0171191	+	0.999853i	$0.494551\pi$
$692$	−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	−0.995635	−	0.0933308i	$-0.970249\pi$
$701$	−15.3204	−	26.5358i	−0.578644	−	1.00224i	0.416991	−	0.908911i	$-0.363085\pi$
$702$	−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	$-0.972667\pi$
$709$		−	4.56728i		−	0.171528i	0.996315	−	0.0857638i	$-0.0273331\pi$
$710$	−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	0.612516	−	0.790458i	$-0.290157\pi$
$719$	−10.1438	−	17.5695i	−0.378299	−	0.655233i	−0.990815	+	0.135225i	$0.956824\pi$
$720$	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	0.941338	−	0.337464i	$-0.109569\pi$
$727$	4.81063	+	8.33226i	0.178417	+	0.309026i	−0.762922	+	0.646491i	$0.776236\pi$
$728$	−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	−0.999866	−	0.0163462i	$-0.994797\pi$
$733$	−40.9888	−	23.6649i	−1.51396	−	0.874083i	−0.514089	−	0.857737i	$-0.671870\pi$
$734$	−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	0.642741	−	0.766083i	$-0.277797\pi$
$739$	8.17341	+	4.71892i	0.300664	+	0.173588i	−0.342077	+	0.939672i	$0.611130\pi$
$740$	−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	$-0.941088\pi$
$743$		−	10.0321i		−	0.368044i	0.982922	−	0.184022i	$-0.0589117\pi$
$744$	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	0.807583	−	0.589754i	$-0.200775\pi$
$751$	−2.93092	−	5.07650i	−0.106951	−	0.185244i	−0.914534	+	0.404510i	$0.867442\pi$
$752$		−	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	−0.674866	−	0.737941i	$-0.735798\pi$
$757$	8.29928	−	14.3748i	0.301642	−	0.522460i	0.976508	+	0.215481i	$0.0691318\pi$
$758$	−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	−0.211580	−	0.977361i	$-0.567861\pi$
$761$	14.5945	−	8.42614i	0.529050	−	0.305447i	0.740630	+	0.671914i	$0.234527\pi$
$762$	−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	−0.624595	−	0.780949i	$-0.714736\pi$
$769$	−7.22585	+	4.17185i	−0.260571	+	0.150441i	0.364024	+	0.931390i	$0.381403\pi$
$770$	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	$0.236594\pi$
$773$			37.6289i			1.35342i	−0.736251	+	0.676709i	$0.763406\pi$
$774$			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	−0.995771	−	0.0918750i	$-0.970714\pi$
$787$	−39.6702	+	22.9036i	−1.41409	+	0.816425i	−0.418319	+	0.908300i	$0.637381\pi$
$788$	−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	−0.998499	−	0.0547627i	$-0.982560\pi$
$797$	−12.7555	+	22.0932i	−0.451824	+	0.782582i	0.546676	+	0.837345i	$0.315893\pi$
$798$			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	0.906751	−	0.421666i	$-0.138554\pi$
$809$	2.50873	+	4.34525i	0.0882022	+	0.152771i	−0.818549	+	0.574437i	$0.805221\pi$
$810$	20.1920			0.709474
$811$	17.3151	+	9.99687i	0.608015	+	0.351037i	0.772188	−	0.635394i	$-0.219162\pi$
$811$	17.3151	+	9.99687i	0.608015	+	0.351037i	−0.164173	+	0.986432i	$0.552496\pi$
$812$	−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	$0.411004\pi$
$821$			55.0809i			1.92234i	−0.275961	+	0.961169i	$0.588996\pi$
$822$	8.07298			0.281578
$823$	7.76866	+	13.4557i	0.270798	+	0.469037i	0.969067	−	0.246800i	$-0.0793790\pi$
$823$	7.76866	+	13.4557i	0.270798	+	0.469037i	−0.698268	+	0.715836i	$0.746046\pi$
$824$	−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	0.983083	−	0.183160i	$-0.0586328\pi$
$827$	37.8451	+	21.8499i	1.31600	+	0.759795i	0.332920	+	0.942955i	$0.391966\pi$
$828$	−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	$-0.975477\pi$
$839$		−	4.45862i		−	0.153929i	0.997034	−	0.0769643i	$-0.0245227\pi$
$840$	−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	$0.113683\pi$
$853$			20.4210i			0.699203i	−0.936899	+	0.349601i	$0.886317\pi$
$854$	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	−0.572796	−	0.819698i	$-0.694141\pi$
$857$	12.3972	−	21.4726i	0.423481	−	0.733491i	0.996277	+	0.0862068i	$0.0274746\pi$
$858$	2.16567	−	2.10387i	0.0739348	−	0.0718251i
$859$	19.0481	−	32.9923i	0.649913	−	1.12568i	−0.333230	−	0.942845i	$-0.608139\pi$
$859$	19.0481	−	32.9923i	0.649913	−	1.12568i	0.983143	−	0.182837i	$-0.0585280\pi$
$860$			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	0.769484	−	0.638666i	$-0.220513\pi$
$863$	17.6592	+	10.1955i	0.601125	+	0.347060i	−0.168359	+	0.985726i	$0.553847\pi$
$864$			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	0.950429	−	0.310943i	$-0.100645\pi$
$877$	34.2446	+	19.7711i	1.15636	+	0.667624i	0.205930	+	0.978567i	$0.433978\pi$
$878$	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	−0.128470	−	0.991713i	$-0.541006\pi$
$881$	23.5855	−	40.8512i	0.794614	−	1.37631i	0.923084	−	0.384599i	$-0.125660\pi$
$882$	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	0.786683	+	0.617357i	$0.211797\pi$
$887$	27.6379	+	47.8702i	0.927989	+	1.60732i	0.141306	+	0.989966i	$0.454870\pi$
$888$	−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	0.633035	−	0.774123i	$-0.281809\pi$
$911$	−10.6815	−	18.5008i	−0.353893	−	0.612960i	−0.986928	+	0.161163i	$0.948476\pi$
$912$	−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	−0.858053	−	0.513562i	$-0.828326\pi$
$919$	0.476889	−	0.825996i	0.0157311	−	0.0272471i	0.873784	+	0.486315i	$0.161659\pi$
$920$	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	$0.0440285\pi$
$929$			8.40497i			0.275758i	−0.990449	+	0.137879i	$0.955971\pi$
$930$	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	0.658457	−	0.752619i	$-0.271210\pi$
$937$	−9.87366	−	17.1017i	−0.322558	−	0.558687i	−0.981015	+	0.193931i	$0.937876\pi$
$938$		−	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	0.574499	−	0.818505i	$-0.305197\pi$
$941$	4.69039	+	2.70800i	0.152902	+	0.0882782i	−0.421597	+	0.906783i	$0.638530\pi$
$942$	−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	−0.962698	−	0.270580i	$-0.912785\pi$
$947$	−37.2271	+	21.4931i	−1.20972	+	0.698431i	−0.247020	+	0.969010i	$0.579451\pi$
$948$	−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	−0.794395	−	0.607402i	$-0.792212\pi$
$967$	−20.6969	+	11.9493i	−0.665567	+	0.384265i	0.128828	+	0.991667i	$0.458878\pi$
$968$	−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	0.414774	+	0.909925i	$0.363861\pi$
$971$	−18.0930	+	31.3379i	−0.580631	+	1.00568i	−0.995405	+	0.0957579i	$0.969473\pi$
$972$	−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	$-0.764288\pi$
$977$		−	42.1760i		−	1.34933i	0.738123	−	0.674666i	$-0.235712\pi$
$978$	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	−0.396819	−	0.917897i	$-0.629886\pi$
$983$	−43.5851	−	25.1639i	−1.39015	−	0.802604i	−0.993331	+	0.115293i	$0.963219\pi$
$984$	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	−0.953249	−	0.302184i	$-0.902284\pi$
$997$	−6.78633	+	11.7543i	−0.214925	+	0.372262i	0.738324	+	0.674446i	$0.235617\pi$
$998$	−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.25.12	✓	68
13.12	even	2	inner	403.2.l.c.25.23	yes	68
31.5	even	3	inner	403.2.l.c.129.12	yes	68
403.129	even	6	inner	403.2.l.c.129.23	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.12	✓	68	1.1	even	1	trivial
403.2.l.c.25.23	yes	68	13.12	even	2	inner
403.2.l.c.129.12	yes	68	31.5	even	3	inner
403.2.l.c.129.23	yes	68	403.129	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
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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