LMFDB - Embedded newform 403.2.f.c.94.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.4
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00222 - 1.73589i) q^{2} +(-0.398982 - 0.691057i) q^{3} +(-1.00888 + 1.74743i) q^{4} -2.51167 q^{5} +(-0.799734 + 1.38518i) q^{6} +(2.36824 - 4.10191i) q^{7} +0.0356005 q^{8} +(1.18163 - 2.04664i) q^{9} +O(q^{10})$	\(q+(-1.00222 - 1.73589i) q^{2} +(-0.398982 - 0.691057i) q^{3} +(-1.00888 + 1.74743i) q^{4} -2.51167 q^{5} +(-0.799734 + 1.38518i) q^{6} +(2.36824 - 4.10191i) q^{7} +0.0356005 q^{8} +(1.18163 - 2.04664i) q^{9} +(2.51724 + 4.35999i) q^{10} +(-1.57113 - 2.72128i) q^{11} +1.61010 q^{12} +(2.62127 - 2.47567i) q^{13} -9.49397 q^{14} +(1.00211 + 1.73571i) q^{15} +(1.98208 + 3.43307i) q^{16} +(-2.08364 + 3.60897i) q^{17} -4.73699 q^{18} +(-3.78499 + 6.55580i) q^{19} +(2.53398 - 4.38897i) q^{20} -3.77954 q^{21} +(-3.14924 + 5.45464i) q^{22} +(0.893759 + 1.54804i) q^{23} +(-0.0142040 - 0.0246020i) q^{24} +1.30849 q^{25} +(-6.92458 - 2.06909i) q^{26} -4.27968 q^{27} +(4.77854 + 8.27668i) q^{28} +(1.52239 + 2.63685i) q^{29} +(2.00867 - 3.47912i) q^{30} +1.00000 q^{31} +(4.00855 - 6.94302i) q^{32} +(-1.25371 + 2.17149i) q^{33} +8.35304 q^{34} +(-5.94824 + 10.3027i) q^{35} +(2.38424 + 4.12962i) q^{36} +(-3.21672 - 5.57152i) q^{37} +15.1735 q^{38} +(-2.75667 - 0.823704i) q^{39} -0.0894167 q^{40} +(-3.81104 - 6.60091i) q^{41} +(3.78792 + 6.56088i) q^{42} +(1.66136 - 2.87756i) q^{43} +6.34034 q^{44} +(-2.96786 + 5.14048i) q^{45} +(1.79148 - 3.10294i) q^{46} +4.68762 q^{47} +(1.58163 - 2.73946i) q^{48} +(-7.71713 - 13.3665i) q^{49} +(-1.31139 - 2.27140i) q^{50} +3.32534 q^{51} +(1.68151 + 7.07815i) q^{52} +5.60718 q^{53} +(4.28918 + 7.42907i) q^{54} +(3.94617 + 6.83497i) q^{55} +(0.0843105 - 0.146030i) q^{56} +6.04058 q^{57} +(3.05152 - 5.28540i) q^{58} +(-3.47851 + 6.02495i) q^{59} -4.04404 q^{60} +(-0.933529 + 1.61692i) q^{61} +(-1.00222 - 1.73589i) q^{62} +(-5.59675 - 9.69386i) q^{63} -8.14145 q^{64} +(-6.58378 + 6.21806i) q^{65} +5.02595 q^{66} +(1.05175 + 1.82169i) q^{67} +(-4.20429 - 7.28204i) q^{68} +(0.713188 - 1.23528i) q^{69} +23.8457 q^{70} +(2.16446 - 3.74895i) q^{71} +(0.0420665 - 0.0728613i) q^{72} +11.3493 q^{73} +(-6.44770 + 11.1678i) q^{74} +(-0.522064 - 0.904241i) q^{75} +(-7.63721 - 13.2280i) q^{76} -14.8833 q^{77} +(1.33292 + 5.61081i) q^{78} -4.81485 q^{79} +(-4.97834 - 8.62273i) q^{80} +(-1.83736 - 3.18240i) q^{81} +(-7.63898 + 13.2311i) q^{82} -2.04957 q^{83} +(3.81311 - 6.60449i) q^{84} +(5.23342 - 9.06455i) q^{85} -6.66019 q^{86} +(1.21481 - 2.10411i) q^{87} +(-0.0559331 - 0.0968790i) q^{88} +(-9.32100 - 16.1444i) q^{89} +11.8978 q^{90} +(-3.94716 - 16.6152i) q^{91} -3.60678 q^{92} +(-0.398982 - 0.691057i) q^{93} +(-4.69802 - 8.13720i) q^{94} +(9.50665 - 16.4660i) q^{95} -6.39737 q^{96} +(-2.35701 + 4.08246i) q^{97} +(-15.4685 + 26.7922i) q^{98} -7.42597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00222	−	1.73589i	−0.708675	−	1.22746i	−0.965349	−	0.260963i	$-0.915960\pi$
$2$	−1.00222	−	1.73589i	−0.708675	−	1.22746i	0.256674	−	0.966498i	$-0.417373\pi$
$3$	−0.398982	−	0.691057i	−0.230352	−	0.398982i	0.727559	−	0.686045i	$-0.240655\pi$
$3$	−0.398982	−	0.691057i	−0.230352	−	0.398982i	−0.957912	+	0.287063i	$0.907321\pi$
$4$	−1.00888	+	1.74743i	−0.504440	+	0.873716i
$5$	−2.51167			−1.12325			−0.561627	−	0.827391i	$-0.689824\pi$
$5$	−2.51167			−1.12325			−0.561627	+	0.827391i	$0.689824\pi$
$6$	−0.799734	+	1.38518i	−0.326490	+	0.565497i
$7$	2.36824	−	4.10191i	0.895111	−	1.55038i	0.0614434	−	0.998111i	$-0.480430\pi$
$7$	2.36824	−	4.10191i	0.895111	−	1.55038i	0.833667	−	0.552267i	$-0.186237\pi$
$8$	0.0356005			0.0125867
$9$	1.18163	−	2.04664i	0.393876	−	0.682212i
$10$	2.51724	+	4.35999i	0.796021	+	1.37875i
$11$	−1.57113	−	2.72128i	−0.473715	−	0.820498i	0.525833	−	0.850588i	$-0.323754\pi$
$11$	−1.57113	−	2.72128i	−0.473715	−	0.820498i	−0.999547	+	0.0300904i	$0.990420\pi$
$12$	1.61010			0.464796
$13$	2.62127	−	2.47567i	0.727010	−	0.686626i
$13$	2.62127	−	2.47567i	0.727010	−	0.686626i
$14$	−9.49397			−2.53737
$15$	1.00211	+	1.73571i	0.258744	+	0.448158i
$16$	1.98208	+	3.43307i	0.495520	+	0.858266i
$17$	−2.08364	+	3.60897i	−0.505357	+	0.875304i	0.494624	+	0.869107i	$0.335306\pi$
$17$	−2.08364	+	3.60897i	−0.505357	+	0.875304i	−0.999981	+	0.00619684i	$0.998027\pi$
$18$	−4.73699			−1.11652
$19$	−3.78499	+	6.55580i	−0.868337	+	1.50400i	−0.00464155	+	0.999989i	$0.501477\pi$
$19$	−3.78499	+	6.55580i	−0.868337	+	1.50400i	−0.863695	+	0.504014i	$0.831856\pi$
$20$	2.53398	−	4.38897i	0.566614	−	0.981404i
$21$	−3.77954			−0.824764
$22$	−3.14924	+	5.45464i	−0.671419	+	1.16293i
$23$	0.893759	+	1.54804i	0.186362	+	0.322788i	0.944034	−	0.329847i	$-0.106997\pi$
$23$	0.893759	+	1.54804i	0.186362	+	0.322788i	−0.757673	+	0.652634i	$0.773664\pi$
$24$	−0.0142040	−	0.0246020i	−0.00289937	−	0.00502186i
$25$	1.30849			0.261698
$26$	−6.92458	−	2.06909i	−1.35802	−	0.405782i
$27$	−4.27968			−0.823626
$28$	4.77854	+	8.27668i	0.903060	+	1.56415i
$29$	1.52239	+	2.63685i	0.282700	+	0.489651i	0.972049	−	0.234779i	$-0.0754366\pi$
$29$	1.52239	+	2.63685i	0.282700	+	0.489651i	−0.689349	+	0.724430i	$0.742103\pi$
$30$	2.00867	−	3.47912i	0.366731	−	0.635197i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	4.00855	−	6.94302i	0.708619	−	1.22736i
$33$	−1.25371	+	2.17149i	−0.218243	+	0.378007i
$34$	8.35304			1.43254
$35$	−5.94824	+	10.3027i	−1.00544	+	1.74147i
$36$	2.38424	+	4.12962i	0.397373	+	0.688271i
$37$	−3.21672	−	5.57152i	−0.528825	−	0.915952i	−0.999435	−	0.0336107i	$-0.989299\pi$
$37$	−3.21672	−	5.57152i	−0.528825	−	0.915952i	0.470610	−	0.882341i	$-0.344034\pi$
$38$	15.1735			2.46147
$39$	−2.75667	−	0.823704i	−0.441420	−	0.131898i
$40$	−0.0894167			−0.0141380
$41$	−3.81104	−	6.60091i	−0.595184	−	1.03089i	−0.993521	−	0.113650i	$-0.963746\pi$
$41$	−3.81104	−	6.60091i	−0.595184	−	1.03089i	0.398337	−	0.917239i	$-0.369587\pi$
$42$	3.78792	+	6.56088i	0.584489	+	1.01237i
$43$	1.66136	−	2.87756i	0.253355	−	0.438824i	−0.711092	−	0.703099i	$-0.751799\pi$
$43$	1.66136	−	2.87756i	0.253355	−	0.438824i	0.964448	+	0.264274i	$0.0851325\pi$
$44$	6.34034			0.955843
$45$	−2.96786	+	5.14048i	−0.442422	+	0.766297i
$46$	1.79148	−	3.10294i	0.264140	−	0.457503i
$47$	4.68762			0.683760			0.341880	−	0.939744i	$-0.388936\pi$
$47$	4.68762			0.683760			0.341880	+	0.939744i	$0.388936\pi$
$48$	1.58163	−	2.73946i	0.228289	−	0.395408i
$49$	−7.71713	−	13.3665i	−1.10245	−	1.90949i
$50$	−1.31139	−	2.27140i	−0.185459	−	0.321224i
$51$	3.32534			0.465641
$52$	1.68151	+	7.07815i	0.233183	+	0.981563i
$53$	5.60718			0.770205			0.385102	−	0.922874i	$-0.374166\pi$
$53$	5.60718			0.770205			0.385102	+	0.922874i	$0.374166\pi$
$54$	4.28918	+	7.42907i	0.583683	+	1.01097i
$55$	3.94617	+	6.83497i	0.532101	+	0.921627i
$56$	0.0843105	−	0.146030i	0.0112665	−	0.0195141i
$57$	6.04058			0.800094
$58$	3.05152	−	5.28540i	0.400685	−	0.694006i
$59$	−3.47851	+	6.02495i	−0.452863	+	0.784381i	−0.998563	−	0.0535994i	$-0.982931\pi$
$59$	−3.47851	+	6.02495i	−0.452863	+	0.784381i	0.545700	+	0.837981i	$0.316264\pi$
$60$	−4.04404			−0.522084
$61$	−0.933529	+	1.61692i	−0.119526	+	0.207025i	−0.919580	−	0.392903i	$-0.871471\pi$
$61$	−0.933529	+	1.61692i	−0.119526	+	0.207025i	0.800054	+	0.599928i	$0.204804\pi$
$62$	−1.00222	−	1.73589i	−0.127282	−	0.220458i
$63$	−5.59675	−	9.69386i	−0.705124	−	1.22131i
$64$	−8.14145			−1.01768
$65$	−6.58378	+	6.21806i	−0.816617	+	0.771255i
$66$	5.02595			0.618652
$67$	1.05175	+	1.82169i	0.128492	+	0.222555i	0.923093	−	0.384578i	$-0.125653\pi$
$67$	1.05175	+	1.82169i	0.128492	+	0.222555i	−0.794600	+	0.607133i	$0.792320\pi$
$68$	−4.20429	−	7.28204i	−0.509845	−	0.883077i
$69$	0.713188	−	1.23528i	0.0858577	−	0.148710i
$70$	23.8457			2.85011
$71$	2.16446	−	3.74895i	0.256874	−	0.444918i	−0.708529	−	0.705682i	$-0.750641\pi$
$71$	2.16446	−	3.74895i	0.256874	−	0.444918i	0.965403	+	0.260763i	$0.0839743\pi$
$72$	0.0420665	−	0.0728613i	0.00495758	−	0.00858679i
$73$	11.3493			1.32833			0.664166	−	0.747585i	$-0.268787\pi$
$73$	11.3493			1.32833			0.664166	+	0.747585i	$0.268787\pi$
$74$	−6.44770	+	11.1678i	−0.749530	+	1.29822i
$75$	−0.522064	−	0.904241i	−0.0602828	−	0.104413i
$76$	−7.63721	−	13.2280i	−0.876048	−	1.51736i
$77$	−14.8833			−1.69611
$78$	1.33292	+	5.61081i	0.150924	+	0.635299i
$79$	−4.81485			−0.541713			−0.270857	−	0.962620i	$-0.587307\pi$
$79$	−4.81485			−0.541713			−0.270857	+	0.962620i	$0.587307\pi$
$80$	−4.97834	−	8.62273i	−0.556595	−	0.964051i
$81$	−1.83736	−	3.18240i	−0.204151	−	0.353600i
$82$	−7.63898	+	13.2311i	−0.843584	+	1.46113i
$83$	−2.04957			−0.224969			−0.112485	−	0.993653i	$-0.535881\pi$
$83$	−2.04957			−0.224969			−0.112485	+	0.993653i	$0.535881\pi$
$84$	3.81311	−	6.60449i	0.416044	−	0.720609i
$85$	5.23342	−	9.06455i	0.567644	−	0.983188i
$86$	−6.66019			−0.718186
$87$	1.21481	−	2.10411i	0.130241	−	0.225585i
$88$	−0.0559331	−	0.0968790i	−0.00596249	−	0.0103273i
$89$	−9.32100	−	16.1444i	−0.988024	−	1.71131i	−0.627639	−	0.778505i	$-0.715979\pi$
$89$	−9.32100	−	16.1444i	−0.988024	−	1.71131i	−0.360385	−	0.932804i	$-0.617355\pi$
$90$	11.8978			1.25413
$91$	−3.94716	−	16.6152i	−0.413775	−	1.74175i
$92$	−3.60678			−0.376033
$93$	−0.398982	−	0.691057i	−0.0413725	−	0.0716593i
$94$	−4.69802	−	8.13720i	−0.484563	−	0.839289i
$95$	9.50665	−	16.4660i	0.975362	−	1.68938i
$96$	−6.39737			−0.652928
$97$	−2.35701	+	4.08246i	−0.239318	+	0.414511i	−0.960519	−	0.278215i	$-0.910257\pi$
$97$	−2.35701	+	4.08246i	−0.239318	+	0.414511i	0.721201	+	0.692726i	$0.243591\pi$
$98$	−15.4685	+	26.7922i	−1.56255	+	2.70642i
$99$	−7.42597			−0.746338
$100$	−1.32011	+	2.28650i	−0.132011	+	0.228650i
$101$	2.08977	+	3.61959i	0.207940	+	0.360163i	0.951065	−	0.308989i	$-0.0999908\pi$
$101$	2.08977	+	3.61959i	0.207940	+	0.360163i	−0.743125	+	0.669152i	$0.766657\pi$
$102$	−3.33272	−	5.77243i	−0.329988	−	0.571556i
$103$	1.25291			0.123453			0.0617263	−	0.998093i	$-0.480339\pi$
$103$	1.25291			0.123453			0.0617263	+	0.998093i	$0.480339\pi$
$104$	0.0933186	−	0.0881350i	0.00915065	−	0.00864234i
$105$	9.49297			0.926419
$106$	−5.61961	−	9.73345i	−0.545825	−	0.945396i
$107$	5.90312	+	10.2245i	0.570676	+	0.988440i	0.996497	+	0.0836321i	$0.0266520\pi$
$107$	5.90312	+	10.2245i	0.570676	+	0.988440i	−0.425821	+	0.904807i	$0.640015\pi$
$108$	4.31769	−	7.47846i	0.415470	−	0.719615i
$109$	3.18338			0.304912			0.152456	−	0.988310i	$-0.451282\pi$
$109$	3.18338			0.304912			0.152456	+	0.988310i	$0.451282\pi$
$110$	7.90984	−	13.7002i	0.754174	−	1.30627i
$111$	−2.56683	+	4.44587i	−0.243632	+	0.421984i
$112$	18.7762			1.77418
$113$	7.73086	−	13.3902i	0.727258	−	1.25965i	−0.230780	−	0.973006i	$-0.574128\pi$
$113$	7.73086	−	13.3902i	0.727258	−	1.25965i	0.958038	−	0.286642i	$-0.0925390\pi$
$114$	−6.05397	−	10.4858i	−0.567007	−	0.982084i
$115$	−2.24483	−	3.88816i	−0.209331	−	0.362572i
$116$	−6.14362			−0.570421
$117$	−1.96942	−	8.29011i	−0.182073	−	0.766421i
$118$	13.9449			1.28373
$119$	9.86912	+	17.0938i	0.904701	+	1.56699i
$120$	0.0356757	+	0.0617921i	0.00325673	+	0.00564082i
$121$	0.563080	−	0.975284i	0.0511891	−	0.0886621i
$122$	3.74240			0.338821
$123$	−3.04107	+	5.26729i	−0.274204	+	0.474936i
$124$	−1.00888	+	1.74743i	−0.0906001	+	0.156924i
$125$	9.27186			0.829300
$126$	−11.2183	+	19.4307i	−0.999408	+	1.73103i
$127$	−7.23315	−	12.5282i	−0.641838	−	1.11170i	−0.985022	−	0.172428i	$-0.944839\pi$
$127$	−7.23315	−	12.5282i	−0.641838	−	1.11170i	0.343184	−	0.939268i	$-0.388495\pi$
$128$	0.142396	+	0.246638i	0.0125862	+	0.0217999i
$129$	−2.65142			−0.233444
$130$	17.3923	+	5.19687i	1.52540	+	0.455796i
$131$	−4.31667			−0.377149			−0.188575	−	0.982059i	$-0.560387\pi$
$131$	−4.31667			−0.377149			−0.188575	+	0.982059i	$0.560387\pi$
$132$	−2.52968	−	4.38154i	−0.220181	−	0.381364i
$133$	17.9275	+	31.0514i	1.55452	+	2.69250i
$134$	2.10817	−	3.65146i	0.182118	−	0.315438i
$135$	10.7492			0.925140
$136$	−0.0741786	+	0.128481i	−0.00636077	+	0.0110172i
$137$	0.831703	−	1.44055i	0.0710572	−	0.123075i	−0.828308	−	0.560273i	$-0.810696\pi$
$137$	0.831703	−	1.44055i	0.0710572	−	0.123075i	0.899365	+	0.437199i	$0.144029\pi$
$138$	−2.85908			−0.243381
$139$	1.33625	−	2.31445i	0.113339	−	0.196309i	−0.803775	−	0.594933i	$-0.797179\pi$
$139$	1.33625	−	2.31445i	0.113339	−	0.196309i	0.917115	+	0.398624i	$0.130512\pi$
$140$	−12.0021	−	20.7883i	−1.01436	−	1.75693i
$141$	−1.87028	−	3.23942i	−0.157506	−	0.272808i
$142$	−8.67702			−0.728160
$143$	−10.8554	−	3.24362i	−0.907771	−	0.271245i
$144$	9.36832			0.780693
$145$	−3.82373	−	6.62290i	−0.317544	−	0.550002i
$146$	−11.3744	−	19.7011i	−0.941356	−	1.63048i
$147$	−6.15799	+	10.6660i	−0.507903	+	0.879713i
$148$	12.9811			1.06704
$149$	3.40263	−	5.89353i	0.278754	−	0.482817i	−0.692321	−	0.721590i	$-0.743412\pi$
$149$	3.40263	−	5.89353i	0.278754	−	0.482817i	0.971075	+	0.238773i	$0.0767452\pi$
$150$	−1.04644	+	1.81249i	−0.0854418	+	0.147989i
$151$	−13.4701			−1.09618			−0.548092	−	0.836418i	$-0.684645\pi$
$151$	−13.4701			−1.09618			−0.548092	+	0.836418i	$0.684645\pi$
$152$	−0.134748	+	0.233390i	−0.0109295	+	0.0189304i
$153$	4.92417	+	8.52891i	0.398096	+	0.689522i
$154$	14.9163	+	25.8358i	1.20199	+	2.08191i
$155$	−2.51167			−0.201742
$156$	4.22052	−	3.98607i	0.337912	−	0.319141i
$157$	−17.0604			−1.36157			−0.680786	−	0.732482i	$-0.738362\pi$
$157$	−17.0604			−1.36157			−0.680786	+	0.732482i	$0.738362\pi$
$158$	4.82553	+	8.35806i	0.383899	+	0.664932i
$159$	−2.23716	−	3.87488i	−0.177419	−	0.307298i
$160$	−10.0682	+	17.4386i	−0.795959	+	1.37864i
$161$	8.46654			0.667257
$162$	−3.68287	+	6.37892i	−0.289354	+	0.501176i
$163$	−3.94560	+	6.83397i	−0.309043	+	0.535278i	−0.978153	−	0.207885i	$-0.933342\pi$
$163$	−3.94560	+	6.83397i	−0.309043	+	0.535278i	0.669110	+	0.743163i	$0.266675\pi$
$164$	15.3795			1.20094
$165$	3.14890	−	5.45406i	0.245142	−	0.424598i
$166$	2.05411	+	3.55782i	0.159430	+	0.276141i
$167$	−7.92344	−	13.7238i	−0.613134	−	1.06198i	−0.990709	−	0.136000i	$-0.956575\pi$
$167$	−7.92344	−	13.7238i	−0.613134	−	1.06198i	0.377575	−	0.925979i	$-0.376758\pi$
$168$	−0.134554			−0.0103810
$169$	0.742150	−	12.9788i	0.0570885	−	0.998369i
$170$	−20.9801			−1.60910
$171$	8.94490	+	15.4930i	0.684033	+	1.18478i
$172$	3.35223	+	5.80624i	0.255605	+	0.442721i
$173$	−11.3002	+	19.5725i	−0.859138	+	1.48807i	0.0136149	+	0.999907i	$0.495666\pi$
$173$	−11.3002	+	19.5725i	−0.859138	+	1.48807i	−0.872753	+	0.488163i	$0.837667\pi$
$174$	−4.87002			−0.369195
$175$	3.09882	−	5.36731i	0.234249	−	0.405731i
$176$	6.22823	−	10.7876i	0.469470	−	0.813147i
$177$	5.55145			0.417272
$178$	−18.6833	+	32.3605i	−1.40038	+	2.42552i
$179$	−6.45043	−	11.1725i	−0.482127	−	0.835069i	0.517662	−	0.855585i	$-0.326802\pi$
$179$	−6.45043	−	11.1725i	−0.482127	−	0.835069i	−0.999790	+	0.0205159i	$0.993469\pi$
$180$	−5.98843	−	10.3723i	−0.446351	−	0.773102i
$181$	25.5513			1.89921			0.949607	−	0.313442i	$-0.101482\pi$
$181$	25.5513			1.89921			0.949607	+	0.313442i	$0.101482\pi$
$182$	−24.8863	+	23.5039i	−1.84469	+	1.74223i
$183$	1.48985			0.110133
$184$	0.0318183	+	0.0551108i	0.00234567	+	0.00406282i
$185$	8.07934	+	13.9938i	0.594005	+	1.02885i
$186$	−0.799734	+	1.38518i	−0.0586393	+	0.101566i
$187$	13.0947			0.957580
$188$	−4.72925	+	8.19130i	−0.344916	+	0.597412i
$189$	−10.1353	+	17.5549i	−0.737236	+	1.27693i
$190$	−38.1109			−2.76486
$191$	2.02232	−	3.50277i	0.146330	−	0.253451i	−0.783538	−	0.621344i	$-0.786587\pi$
$191$	2.02232	−	3.50277i	0.146330	−	0.253451i	0.929868	+	0.367892i	$0.119920\pi$
$192$	3.24829	+	5.62621i	0.234425	+	0.406037i
$193$	6.71071	+	11.6233i	0.483048	+	0.836663i	0.999811	−	0.0194654i	$-0.00619642\pi$
$193$	6.71071	+	11.6233i	0.483048	+	0.836663i	−0.516763	+	0.856129i	$0.672863\pi$
$194$	9.44895			0.678395
$195$	6.92384	+	2.06887i	0.495827	+	0.148155i
$196$	31.1426			2.22447
$197$	−5.95880	−	10.3209i	−0.424547	−	0.735336i	0.571831	−	0.820371i	$-0.306233\pi$
$197$	−5.95880	−	10.3209i	−0.424547	−	0.735336i	−0.996378	+	0.0850348i	$0.972900\pi$
$198$	7.44244	+	12.8907i	0.528911	+	0.916101i
$199$	−10.5704	+	18.3085i	−0.749318	+	1.29786i	0.198833	+	0.980033i	$0.436285\pi$
$199$	−10.5704	+	18.3085i	−0.749318	+	1.29786i	−0.948150	+	0.317823i	$0.897048\pi$
$200$	0.0465829			0.00329391
$201$	0.839262	−	1.45365i	0.0591970	−	0.102532i
$202$	4.18881	−	7.25523i	0.294724	−	0.510476i
$203$	14.4215			1.01219
$204$	−3.35487	+	5.81081i	−0.234888	+	0.406838i
$205$	9.57207	+	16.5793i	0.668542	+	1.15795i
$206$	−1.25569	−	2.17491i	−0.0874878	−	0.151533i
$207$	4.22436			0.293613
$208$	13.6947	+	4.09203i	0.949557	+	0.283731i
$209$	23.7869			1.64538
$210$	−9.51402	−	16.4788i	−0.656530	−	1.13714i
$211$	−12.3806	−	21.4438i	−0.852315	−	1.47625i	−0.879114	−	0.476612i	$-0.841865\pi$
$211$	−12.3806	−	21.4438i	−0.852315	−	1.47625i	0.0267986	−	0.999641i	$-0.491469\pi$
$212$	−5.65697	+	9.79816i	−0.388522	+	0.672940i
$213$	−3.45432			−0.236686
$214$	11.8324	−	20.4943i	0.808847	−	1.40096i
$215$	−4.17280	+	7.22749i	−0.284582	+	0.492911i
$216$	−0.152359			−0.0103667
$217$	2.36824	−	4.10191i	0.160767	−	0.278456i
$218$	−3.19044	−	5.52600i	−0.216084	−	0.374268i
$219$	−4.52816	−	7.84300i	−0.305985	−	0.529981i
$220$	−15.9249			−1.07365
$221$	3.47282	+	14.6185i	0.233607	+	0.983347i
$222$	10.2901			0.690625
$223$	6.83194	+	11.8333i	0.457501	+	0.792414i	0.998828	−	0.0483975i	$-0.0154114\pi$
$223$	6.83194	+	11.8333i	0.457501	+	0.792414i	−0.541328	+	0.840812i	$0.682078\pi$
$224$	−18.9864	−	32.8855i	−1.26859	−	2.19725i
$225$	1.54615	−	2.67800i	0.103076	−	0.178534i
$226$	−30.9920			−2.06156
$227$	8.83435	−	15.3015i	0.586357	−	1.01560i	−0.408348	−	0.912826i	$-0.633895\pi$
$227$	8.83435	−	15.3015i	0.586357	−	1.01560i	0.994705	−	0.102773i	$-0.0327716\pi$
$228$	−6.09422	+	10.5555i	−0.403600	+	0.699055i
$229$	−23.2252			−1.53476			−0.767381	−	0.641191i	$-0.778441\pi$
$229$	−23.2252			−1.53476			−0.767381	+	0.641191i	$0.778441\pi$
$230$	−4.49961	+	7.79356i	−0.296696	+	0.513892i
$231$	5.93817	+	10.2852i	0.390703	+	0.676717i
$232$	0.0541977	+	0.0938732i	0.00355825	+	0.00616308i
$233$	2.55783			0.167569			0.0837845	−	0.996484i	$-0.473299\pi$
$233$	2.55783			0.167569			0.0837845	+	0.996484i	$0.473299\pi$
$234$	−12.4169	+	11.7272i	−0.811721	+	0.766631i
$235$	−11.7738			−0.768036
$236$	−7.01879	−	12.1569i	−0.456884	−	0.791347i
$237$	1.92104	+	3.32734i	0.124785	+	0.216134i
$238$	19.7820	−	34.2635i	1.28228	−	2.22097i
$239$	5.81730			0.376290			0.188145	−	0.982141i	$-0.439753\pi$
$239$	5.81730			0.376290			0.188145	+	0.982141i	$0.439753\pi$
$240$	−3.97253	+	6.88063i	−0.256426	+	0.444143i
$241$	10.9200	−	18.9139i	0.703417	−	1.21835i	−0.263842	−	0.964566i	$-0.584990\pi$
$241$	10.9200	−	18.9139i	0.703417	−	1.21835i	0.967260	−	0.253789i	$-0.0816767\pi$
$242$	−2.25732			−0.145106
$243$	−7.88568	+	13.6584i	−0.505866	+	0.876186i
$244$	−1.88364	−	3.26256i	−0.120588	−	0.208864i
$245$	19.3829	+	33.5721i	1.23833	+	2.14484i
$246$	12.1913			0.777286
$247$	6.30847	+	26.5549i	0.401399	+	1.68965i
$248$	0.0356005			0.00226063
$249$	0.817740	+	1.41637i	0.0518222	+	0.0897586i
$250$	−9.29242	−	16.0949i	−0.587704	−	1.01793i
$251$	2.00702	−	3.47627i	0.126682	−	0.219420i	−0.795707	−	0.605682i	$-0.792900\pi$
$251$	2.00702	−	3.47627i	0.126682	−	0.219420i	0.922389	+	0.386262i	$0.126234\pi$
$252$	22.5858			1.42277
$253$	2.80843	−	4.86434i	0.176564	−	0.305818i
$254$	−14.4984	+	25.1119i	−0.909709	+	1.57566i
$255$	−8.35216			−0.523033
$256$	−7.85603	+	13.6070i	−0.491002	+	0.850440i
$257$	14.8347	+	25.6945i	0.925365	+	1.60278i	0.790973	+	0.611851i	$0.209575\pi$
$257$	14.8347	+	25.6945i	0.925365	+	1.60278i	0.134392	+	0.990928i	$0.457092\pi$
$258$	2.65730	+	4.60257i	0.165436	+	0.286544i
$259$	−30.4719			−1.89343
$260$	−4.22339	−	17.7780i	−0.261924	−	1.10254i
$261$	7.19557			0.445394
$262$	4.32624	+	7.49327i	0.267276	+	0.462936i
$263$	−7.00947	−	12.1408i	−0.432222	−	0.748631i	0.564842	−	0.825199i	$-0.308937\pi$
$263$	−7.00947	−	12.1408i	−0.432222	−	0.748631i	−0.997064	+	0.0765679i	$0.975604\pi$
$264$	−0.0446326	+	0.0773060i	−0.00274695	+	0.00475786i
$265$	−14.0834			−0.865135
$266$	35.9346	−	62.2406i	2.20329	−	3.81621i
$267$	−7.43783	+	12.8827i	−0.455188	+	0.788408i
$268$	−4.24438			−0.259267
$269$	3.18597	−	5.51826i	0.194252	−	0.336454i	−0.752403	−	0.658703i	$-0.771105\pi$
$269$	3.18597	−	5.51826i	0.194252	−	0.336454i	0.946655	+	0.322249i	$0.104439\pi$
$270$	−10.7730	−	18.6594i	−0.655624	−	1.13557i
$271$	−7.45830	−	12.9182i	−0.453059	−	0.784722i	0.545515	−	0.838101i	$-0.316334\pi$
$271$	−7.45830	−	12.9182i	−0.453059	−	0.784722i	−0.998574	+	0.0533792i	$0.983001\pi$
$272$	−16.5198			−1.00166
$273$	−9.90722	+	9.35689i	−0.599612	+	0.566305i
$274$	−3.33419			−0.201426
$275$	−2.05581	−	3.56077i	−0.123970	−	0.214723i
$276$	1.43904	+	2.49249i	0.0866201	+	0.150030i
$277$	9.52555	−	16.4987i	0.572335	−	0.991313i	−0.423991	−	0.905666i	$-0.639371\pi$
$277$	9.52555	−	16.4987i	0.572335	−	0.991313i	0.996326	−	0.0856461i	$-0.0272955\pi$
$278$	−5.35685			−0.321282
$279$	1.18163	−	2.04664i	0.0707421	−	0.122529i
$280$	−0.211760	+	0.366780i	−0.0126551	+	0.0219193i
$281$	28.7378			1.71435			0.857177	−	0.515022i	$-0.172216\pi$
$281$	28.7378			1.71435			0.857177	+	0.515022i	$0.172216\pi$
$282$	−3.74885	+	6.49320i	−0.223241	+	0.386664i
$283$	−8.50585	−	14.7326i	−0.505620	−	0.875760i	−0.999979	−	0.00650182i	$-0.997930\pi$
$283$	−8.50585	−	14.7326i	−0.505620	−	0.875760i	0.494359	−	0.869258i	$-0.335403\pi$
$284$	4.36735	+	7.56448i	0.259155	+	0.448869i
$285$	−15.1719			−0.898708
$286$	5.24885	+	22.0945i	0.310371	+	1.30648i
$287$	−36.1018			−2.13102
$288$	−9.47323	−	16.4081i	−0.558215	−	0.966857i
$289$	−0.183115	−	0.317164i	−0.0107714	−	0.0186567i
$290$	−7.66443	+	13.2752i	−0.450071	+	0.779545i
$291$	3.76162			0.220510
$292$	−11.4501	+	19.8321i	−0.670064	+	1.16059i
$293$	13.4401	−	23.2789i	0.785177	−	1.35997i	−0.143716	−	0.989619i	$-0.545905\pi$
$293$	13.4401	−	23.2789i	0.785177	−	1.35997i	0.928893	−	0.370348i	$-0.120761\pi$
$294$	24.6866			1.43975
$295$	8.73686	−	15.1327i	0.508680	−	0.881059i
$296$	−0.114517	−	0.198349i	−0.00665615	−	0.0115288i
$297$	6.72395	+	11.6462i	0.390163	+	0.675783i
$298$	−13.6407			−0.790185
$299$	6.17521	+	1.84518i	0.357121	+	0.106709i
$300$	2.10680			0.121636
$301$	−7.86901	−	13.6295i	−0.453562	−	0.785593i
$302$	13.5000	+	23.3827i	0.776837	+	1.34552i
$303$	1.66756	−	2.88830i	0.0957990	−	0.165929i
$304$	−30.0087			−1.72111
$305$	2.34472	−	4.06117i	0.134258	−	0.232542i
$306$	9.87018	−	17.0957i	0.564241	−	0.977293i
$307$	2.53272			0.144550			0.0722748	−	0.997385i	$-0.476974\pi$
$307$	2.53272			0.144550			0.0722748	+	0.997385i	$0.476974\pi$
$308$	15.0155	−	26.0075i	0.855585	−	1.48192i
$309$	−0.499888	−	0.865831i	−0.0284376	−	0.0492554i
$310$	2.51724	+	4.35999i	0.142970	+	0.247631i
$311$	−5.32901			−0.302181			−0.151090	−	0.988520i	$-0.548278\pi$
$311$	−5.32901			−0.302181			−0.151090	+	0.988520i	$0.548278\pi$
$312$	−0.0981388	−	0.0293243i	−0.00555601	−	0.00166016i
$313$	23.0482			1.30276			0.651381	−	0.758751i	$-0.274190\pi$
$313$	23.0482			1.30276			0.651381	+	0.758751i	$0.274190\pi$
$314$	17.0983	+	29.6151i	0.964912	+	1.67128i
$315$	14.0572	+	24.3478i	0.792033	+	1.37184i
$316$	4.85761	−	8.41363i	0.273262	−	0.473304i
$317$	3.94491			0.221568			0.110784	−	0.993844i	$-0.464664\pi$
$317$	3.94491			0.221568			0.110784	+	0.993844i	$0.464664\pi$
$318$	−4.48425	+	7.76695i	−0.251464	+	0.435549i
$319$	4.78374	−	8.28569i	0.267838	−	0.463909i
$320$	20.4486			1.14311
$321$	4.71048	−	8.15878i	0.262913	−	0.455379i
$322$	−8.48532	−	14.6970i	−0.472868	−	0.819032i
$323$	−15.7731	−	27.3199i	−0.877640	−	1.52012i
$324$	7.41471			0.411929
$325$	3.42991	−	3.23938i	0.190257	−	0.179689i
$326$	15.8174			0.876044
$327$	−1.27011	−	2.19990i	−0.0702373	−	0.121655i
$328$	−0.135675	−	0.234996i	−0.00749139	−	0.0129755i
$329$	11.1014	−	19.2282i	0.612041	−	1.06009i
$330$	−12.6235			−0.694903
$331$	−13.9100	+	24.0928i	−0.764562	+	1.32426i	0.175916	+	0.984405i	$0.443711\pi$
$331$	−13.9100	+	24.0928i	−0.764562	+	1.32426i	−0.940478	+	0.339855i	$0.889622\pi$
$332$	2.06777	−	3.58148i	0.113483	−	0.196559i
$333$	−15.2038			−0.833165
$334$	−15.8820	+	27.5085i	−0.869025	+	1.50520i
$335$	−2.64166	−	4.57549i	−0.144329	−	0.249986i
$336$	−7.49136	−	12.9754i	−0.408687	−	0.707867i
$337$	34.1651			1.86109			0.930546	−	0.366174i	$-0.119333\pi$
$337$	34.1651			1.86109			0.930546	+	0.366174i	$0.119333\pi$
$338$	−23.2736	+	11.7193i	−1.26592	+	0.637445i
$339$	−12.3379			−0.670103
$340$	10.5598	+	18.2901i	0.572685	+	0.991919i
$341$	−1.57113	−	2.72128i	−0.0850816	−	0.147366i
$342$	17.9295	−	31.0547i	0.969514	−	1.67925i
$343$	−39.9487			−2.15703
$344$	0.0591453	−	0.102443i	0.00318890	−	0.00552334i
$345$	−1.79129	+	3.10261i	−0.0964399	+	0.167039i
$346$	45.3010			2.43540
$347$	−0.698207	+	1.20933i	−0.0374817	+	0.0649202i	−0.884158	−	0.467189i	$-0.845267\pi$
$347$	−0.698207	+	1.20933i	−0.0374817	+	0.0649202i	0.846676	+	0.532109i	$0.178600\pi$
$348$	2.45120	+	4.24560i	0.131398	+	0.227588i
$349$	1.87444	+	3.24662i	0.100336	+	0.173788i	0.911823	−	0.410583i	$-0.134675\pi$
$349$	1.87444	+	3.24662i	0.100336	+	0.173788i	−0.811487	+	0.584371i	$0.801341\pi$
$350$	−12.4228			−0.664025
$351$	−11.2182	+	10.5951i	−0.598784	+	0.565523i
$352$	−25.1919			−1.34273
$353$	−5.02948	−	8.71131i	−0.267692	−	0.463656i	0.700573	−	0.713580i	$-0.252928\pi$
$353$	−5.02948	−	8.71131i	−0.267692	−	0.463656i	−0.968265	+	0.249924i	$0.919594\pi$
$354$	−5.56376	−	9.63671i	−0.295710	−	0.512185i
$355$	−5.43640	+	9.41612i	−0.288534	+	0.499756i
$356$	37.6151			1.99360
$357$	7.87521	−	13.6403i	0.416800	−	0.721919i
$358$	−12.9295	+	22.3945i	−0.683343	+	1.18359i
$359$	10.0606			0.530977			0.265489	−	0.964114i	$-0.414467\pi$
$359$	10.0606			0.530977			0.265489	+	0.964114i	$0.414467\pi$
$360$	−0.105657	+	0.183004i	−0.00556862	+	0.00964514i
$361$	−19.1523	−	33.1728i	−1.00802	−	1.74594i
$362$	−25.6080	−	44.3543i	−1.34593	−	2.33121i
$363$	−0.898636			−0.0471661
$364$	33.0162	+	9.86536i	1.73052	+	0.517085i
$365$	−28.5056			−1.49205
$366$	−1.49315	−	2.58621i	−0.0780482	−	0.135183i
$367$	6.59720	+	11.4267i	0.344371	+	0.596468i	0.985239	−	0.171183i	$-0.0547589\pi$
$367$	6.59720	+	11.4267i	0.344371	+	0.596468i	−0.640868	+	0.767651i	$0.721426\pi$
$368$	−3.54301	+	6.13667i	−0.184692	+	0.319896i
$369$	−18.0129			−0.937713
$370$	16.1945	−	28.0497i	0.841912	−	1.45824i
$371$	13.2791	−	23.0001i	0.689419	−	1.19411i
$372$	1.61010			0.0834799
$373$	−9.13856	+	15.8285i	−0.473177	+	0.819566i	−0.999529	−	0.0307007i	$-0.990226\pi$
$373$	−9.13856	+	15.8285i	−0.473177	+	0.819566i	0.526352	+	0.850267i	$0.323559\pi$
$374$	−13.1237	−	22.7310i	−0.678613	−	1.17539i
$375$	−3.69931	−	6.40739i	−0.191031	−	0.330876i
$376$	0.166882			0.00860626
$377$	10.5186	+	3.14299i	0.541733	+	0.161872i
$378$	40.6312			2.08984
$379$	14.1093	+	24.4380i	0.724745	+	1.25530i	0.959079	+	0.283139i	$0.0913757\pi$
$379$	14.1093	+	24.4380i	0.724745	+	1.25530i	−0.234334	+	0.972156i	$0.575291\pi$
$380$	19.1822	+	33.2245i	0.984024	+	1.70438i
$381$	−5.77179	+	9.99704i	−0.295698	+	0.512164i
$382$	−8.10723			−0.414802
$383$	9.15782	−	15.8618i	0.467943	−	0.810501i	−0.531386	−	0.847130i	$-0.678329\pi$
$383$	9.15782	−	15.8618i	0.467943	−	0.810501i	0.999329	+	0.0366291i	$0.0116620\pi$
$384$	0.113627	−	0.196808i	0.00579851	−	0.0100433i
$385$	37.3819			1.90516
$386$	13.4512	−	23.2981i	0.684648	−	1.18584i
$387$	−3.92622	−	6.80041i	−0.199581	−	0.345684i
$388$	−4.75589	−	8.23744i	−0.241444	−	0.418192i
$389$	−25.4670			−1.29123			−0.645615	−	0.763663i	$-0.723399\pi$
$389$	−25.4670			−1.29123			−0.645615	+	0.763663i	$0.723399\pi$
$390$	−3.34786	−	14.0925i	−0.169526	−	0.713602i
$391$	−7.44909			−0.376717
$392$	−0.274734	−	0.475852i	−0.0138761	−	0.0240342i
$393$	1.72227	+	2.98307i	0.0868772	+	0.150476i
$394$	−11.9440	+	20.6877i	−0.601731	+	1.04223i
$395$	12.0933			0.608481
$396$	7.49192	−	12.9764i	0.376483	−	0.652088i
$397$	1.86896	−	3.23713i	0.0938004	−	0.162467i	−0.815307	−	0.579029i	$-0.803432\pi$
$397$	1.86896	−	3.23713i	0.0938004	−	0.162467i	0.909107	+	0.416562i	$0.136765\pi$
$398$	42.3755			2.12409
$399$	14.3055	−	24.7779i	0.716173	−	1.24045i
$400$	2.59353	+	4.49213i	0.129677	+	0.224607i
$401$	−6.07369	−	10.5199i	−0.303306	−	0.525341i	0.673577	−	0.739117i	$-0.264757\pi$
$401$	−6.07369	−	10.5199i	−0.303306	−	0.525341i	−0.976883	+	0.213776i	$0.931424\pi$
$402$	−3.36449			−0.167806
$403$	2.62127	−	2.47567i	0.130575	−	0.123322i
$404$	−8.43332			−0.419573
$405$	4.61485	+	7.99315i	0.229314	+	0.397183i
$406$	−14.4535	−	25.0342i	−0.717315	−	1.24243i
$407$	−10.1078	+	17.5072i	−0.501024	+	0.867800i
$408$	0.118384			0.00586087
$409$	−11.9720	+	20.7361i	−0.591976	+	1.02533i	0.401990	+	0.915644i	$0.368319\pi$
$409$	−11.9720	+	20.7361i	−0.591976	+	1.02533i	−0.993966	+	0.109688i	$0.965015\pi$
$410$	19.1866	−	33.2322i	0.947558	−	1.64122i
$411$	−1.32734			−0.0654728
$412$	−1.26403	+	2.18937i	−0.0622745	+	0.107863i
$413$	16.4759	+	28.5371i	0.810725	+	1.40422i
$414$	−4.23372	−	7.33303i	−0.208076	−	0.360399i
$415$	5.14783			0.252697
$416$	−6.68108	−	28.1234i	−0.327567	−	1.37886i
$417$	−2.13256			−0.104432
$418$	−23.8397	−	41.2915i	−1.16604	−	2.01963i
$419$	−2.32047	−	4.01918i	−0.113363	−	0.196350i	0.803761	−	0.594952i	$-0.202829\pi$
$419$	−2.32047	−	4.01918i	−0.113363	−	0.196350i	−0.917124	+	0.398602i	$0.869495\pi$
$420$	−9.57727	+	16.5883i	−0.467323	+	0.809427i
$421$	5.38642			0.262518			0.131259	−	0.991348i	$-0.458098\pi$
$421$	5.38642			0.262518			0.131259	+	0.991348i	$0.458098\pi$
$422$	−24.8161	+	42.9827i	−1.20803	+	2.09237i
$423$	5.53902	−	9.59386i	0.269316	−	0.466469i
$424$	0.199618			0.00969432
$425$	−2.72642	+	4.72230i	−0.132251	+	0.229065i
$426$	3.46198	+	5.99632i	0.167733	+	0.290523i
$427$	4.42164	+	7.65851i	0.213978	+	0.370621i
$428$	−23.8222			−1.15149
$429$	2.08956	+	8.79582i	0.100885	+	0.424666i
$430$	16.7282			0.806705
$431$	6.95350	+	12.0438i	0.334938	+	0.580130i	0.983473	−	0.181055i	$-0.0579511\pi$
$431$	6.95350	+	12.0438i	0.334938	+	0.580130i	−0.648535	+	0.761185i	$0.724618\pi$
$432$	−8.48268	−	14.6924i	−0.408123	−	0.706890i
$433$	18.2753	−	31.6538i	0.878256	−	1.52118i	0.0250030	−	0.999687i	$-0.492040\pi$
$433$	18.2753	−	31.6538i	0.878256	−	1.52118i	0.853253	−	0.521497i	$-0.174626\pi$
$434$	−9.49397			−0.455725
$435$	−3.05120	+	5.28484i	−0.146294	+	0.253389i
$436$	−3.21165	+	5.56274i	−0.153810	+	0.266407i
$437$	−13.5315			−0.647299
$438$	−9.07640	+	15.7208i	−0.433687	+	0.751168i
$439$	7.23109	+	12.5246i	0.345121	+	0.597767i	0.985376	−	0.170395i	$-0.0545045\pi$
$439$	7.23109	+	12.5246i	0.345121	+	0.597767i	−0.640255	+	0.768163i	$0.721171\pi$
$440$	0.140486	+	0.243328i	0.00669739	+	0.0116002i
$441$	−36.4750			−1.73691
$442$	21.8956	−	20.6794i	1.04147	−	0.983617i
$443$	−26.3377			−1.25134			−0.625672	−	0.780086i	$-0.715175\pi$
$443$	−26.3377			−1.25134			−0.625672	+	0.780086i	$0.715175\pi$
$444$	−5.17924	−	8.97071i	−0.245796	−	0.425731i
$445$	23.4113	+	40.5495i	1.10980	+	1.92223i
$446$	13.6942	−	23.7190i	0.648438	−	1.12313i
$447$	−5.43035			−0.256847
$448$	−19.2809	+	33.3955i	−0.910938	+	1.57779i
$449$	−6.85478	+	11.8728i	−0.323497	+	0.560313i	−0.981207	−	0.192958i	$-0.938192\pi$
$449$	−6.85478	+	11.8728i	−0.323497	+	0.560313i	0.657710	+	0.753271i	$0.271525\pi$
$450$	−6.19830			−0.292191
$451$	−11.9753	+	20.7418i	−0.563895	+	0.976694i
$452$	15.5990	+	27.0183i	0.733716	+	1.27083i
$453$	5.37434	+	9.30863i	0.252508	+	0.437357i
$454$	−35.4158			−1.66214
$455$	9.91397	+	41.7319i	0.464774	+	1.95642i
$456$	0.215048			0.0100705
$457$	0.0483712	+	0.0837814i	0.00226271	+	0.00391913i	0.867155	−	0.498039i	$-0.165946\pi$
$457$	0.0483712	+	0.0837814i	0.00226271	+	0.00391913i	−0.864892	+	0.501958i	$0.832613\pi$
$458$	23.2767	+	40.3164i	1.08765	+	1.88386i
$459$	8.91732	−	15.4453i	0.416225	−	0.720923i
$460$	9.05905			0.422380
$461$	−14.6286	+	25.3375i	−0.681323	+	1.18009i	0.293255	+	0.956034i	$0.405262\pi$
$461$	−14.6286	+	25.3375i	−0.681323	+	1.18009i	−0.974577	+	0.224051i	$0.928072\pi$
$462$	11.9027	−	20.6160i	0.553762	−	0.959144i
$463$	14.0482			0.652877			0.326439	−	0.945218i	$-0.394151\pi$
$463$	14.0482			0.652877			0.326439	+	0.945218i	$0.394151\pi$
$464$	−6.03499	+	10.4529i	−0.280167	+	0.485264i
$465$	1.00211	+	1.73571i	0.0464718	+	0.0804916i
$466$	−2.56350	−	4.44012i	−0.118752	−	0.205684i
$467$	40.6266			1.87998			0.939988	−	0.341208i	$-0.110836\pi$
$467$	40.6266			1.87998			0.939988	+	0.341208i	$0.110836\pi$
$468$	16.4733	+	4.92229i	0.761479	+	0.227533i
$469$	9.96323			0.460059
$470$	11.7999	+	20.4380i	0.544287	+	0.942734i
$471$	6.80681	+	11.7897i	0.313641	+	0.543243i
$472$	−0.123837	+	0.214491i	−0.00570004	+	0.00987275i
$473$	−10.4409			−0.480073
$474$	3.85060	−	6.66944i	0.176864	−	0.306337i
$475$	−4.95262	+	8.57820i	−0.227242	+	0.393595i
$476$	−39.8271			−1.82547
$477$	6.62559	−	11.4759i	0.303365	−	0.525443i
$478$	−5.83020	−	10.0982i	−0.266667	−	0.461881i
$479$	20.0700	+	34.7622i	0.917021	+	1.58833i	0.803916	+	0.594743i	$0.202746\pi$
$479$	20.0700	+	34.7622i	0.917021	+	1.58833i	0.113105	+	0.993583i	$0.463920\pi$
$480$	16.0681			0.733404
$481$	−22.2251	−	6.64095i	−1.01338	−	0.302801i
$482$	−43.7768			−1.99398
$483$	−3.37800	−	5.85087i	−0.153704	−	0.266224i
$484$	1.13616	+	1.96789i	0.0516437	+	0.0894495i
$485$	5.92004	−	10.2538i	0.268815	−	0.465601i
$486$	31.6127			1.43398
$487$	−19.2009	+	33.2569i	−0.870075	+	1.50701i	−0.00815706	+	0.999967i	$0.502597\pi$
$487$	−19.2009	+	33.2569i	−0.870075	+	1.50701i	−0.861918	+	0.507048i	$0.830737\pi$
$488$	−0.0332341	+	0.0575631i	−0.00150444	+	0.00260576i
$489$	6.29689			0.284755
$490$	38.8517	−	67.2932i	1.75514	−	3.04000i
$491$	−7.76628	−	13.4516i	−0.350487	−	0.607062i	0.635847	−	0.771815i	$-0.280651\pi$
$491$	−7.76628	−	13.4516i	−0.350487	−	0.607062i	−0.986335	+	0.164753i	$0.947317\pi$
$492$	−6.13615	−	10.6281i	−0.276639	−	0.479153i
$493$	−12.6884			−0.571458
$494$	39.7740	−	37.5646i	1.78952	−	1.69011i
$495$	18.6516			0.838327
$496$	1.98208	+	3.43307i	0.0889981	+	0.154149i
$497$	−10.2519	−	17.7568i	−0.459861	−	0.796502i
$498$	1.63911	−	2.83902i	0.0734501	−	0.127219i
$499$	−6.88749			−0.308326			−0.154163	−	0.988045i	$-0.549268\pi$
$499$	−6.88749			−0.308326			−0.154163	+	0.988045i	$0.549268\pi$
$500$	−9.35420	+	16.2019i	−0.418332	+	0.724573i
$501$	−6.32262	+	10.9511i	−0.282474	+	0.489259i
$502$	−8.04590			−0.359106
$503$	−0.0419183	+	0.0726046i	−0.00186905	+	0.00323728i	−0.866958	−	0.498380i	$-0.833928\pi$
$503$	−0.0419183	+	0.0726046i	−0.00186905	+	0.00323728i	0.865089	+	0.501618i	$0.167262\pi$
$504$	−0.199247	−	0.345106i	−0.00887517	−	0.0153723i
$505$	−5.24882	−	9.09122i	−0.233569	−	0.404554i
$506$	−11.2586			−0.500507
$507$	−9.26520	+	4.66544i	−0.411482	+	0.207199i
$508$	29.1895			1.29508
$509$	4.65197	+	8.05744i	0.206195	+	0.357140i	0.950513	−	0.310686i	$-0.100559\pi$
$509$	4.65197	+	8.05744i	0.206195	+	0.357140i	−0.744318	+	0.667825i	$0.767225\pi$
$510$	8.37068	+	14.4985i	0.370660	+	0.642002i
$511$	26.8778	−	46.5537i	1.18900	−	2.05942i
$512$	32.0634			1.41701
$513$	16.1986	−	28.0568i	0.715184	−	1.23874i
$514$	29.7353	−	51.5030i	1.31157	−	2.27170i
$515$	−3.14689			−0.138669
$516$	2.67496	−	4.63317i	0.117759	−	0.203964i
$517$	−7.36488	−	12.7563i	−0.323907	−	0.561023i
$518$	30.5394	+	52.8958i	1.34183	+	2.32411i
$519$	18.0343			0.791618
$520$	−0.234386	+	0.221366i	−0.0102785	+	0.00970754i
$521$	43.7274			1.91573			0.957866	−	0.287217i	$-0.0927300\pi$
$521$	43.7274			1.91573			0.957866	+	0.287217i	$0.0927300\pi$
$522$	−7.21152	−	12.4907i	−0.315640	−	0.546704i
$523$	−0.607239	−	1.05177i	−0.0265527	−	0.0459906i	0.852444	−	0.522819i	$-0.175120\pi$
$523$	−0.607239	−	1.05177i	−0.0265527	−	0.0459906i	−0.878996	+	0.476828i	$0.841786\pi$
$524$	4.35500	−	7.54309i	0.190249	−	0.329521i
$525$	−4.94549			−0.215839
$526$	−14.0500	+	24.3354i	−0.612610	+	1.06107i
$527$	−2.08364	+	3.60897i	−0.0907648	+	0.157209i
$528$	−9.93981			−0.432575
$529$	9.90239	−	17.1514i	0.430539	−	0.745715i
$530$	14.1146	+	24.4472i	0.613100	+	1.06192i
$531$	8.22059	+	14.2385i	0.356743	+	0.617897i
$532$	−72.3470			−3.13664
$533$	−26.3314	−	7.86793i	−1.14054	−	0.340798i
$534$	29.8173			1.29032
$535$	−14.8267	−	25.6806i	−0.641014	−	1.11027i
$536$	0.0374430	+	0.0648531i	0.00161729	+	0.00280123i
$537$	−5.14721	+	8.91523i	−0.222118	+	0.384720i
$538$	−12.7721			−0.550646
$539$	−24.2493	+	42.0010i	−1.04449	+	1.80911i
$540$	−10.8446	+	18.7834i	−0.466678	+	0.808310i
$541$	−12.4568			−0.535558			−0.267779	−	0.963480i	$-0.586290\pi$
$541$	−12.4568			−0.535558			−0.267779	+	0.963480i	$0.586290\pi$
$542$	−14.9497	+	25.8936i	−0.642144	+	1.11223i
$543$	−10.1945	−	17.6574i	−0.437489	−	0.757753i
$544$	16.7048	+	28.9335i	0.716211	+	1.24051i
$545$	−7.99560			−0.342494
$546$	26.1717	+	7.82022i	1.12005	+	0.334674i
$547$	17.2013			0.735473			0.367736	−	0.929930i	$-0.380133\pi$
$547$	17.2013			0.735473			0.367736	+	0.929930i	$0.380133\pi$
$548$	1.67818	+	2.90669i	0.0716882	+	0.124168i
$549$	2.20616	+	3.82119i	0.0941568	+	0.163084i
$550$	−4.12074	+	7.13733i	−0.175709	+	0.304337i
$551$	−23.0489			−0.981915
$552$	0.0253898	−	0.0439765i	0.00108066	−	0.00187176i
$553$	−11.4027	+	19.7501i	−0.484893	+	0.839860i
$554$	−38.1867			−1.62240
$555$	6.44702	−	11.1666i	0.273661	−	0.473995i
$556$	2.69623	+	4.67001i	0.114346	+	0.198052i
$557$	17.6361	+	30.5466i	0.747265	+	1.29430i	0.949129	+	0.314887i	$0.101967\pi$
$557$	17.6361	+	30.5466i	0.747265	+	1.29430i	−0.201864	+	0.979414i	$0.564700\pi$
$558$	−4.73699			−0.200533
$559$	−2.76900	−	11.6559i	−0.117116	−	0.492990i
$560$	−47.1596			−1.99286
$561$	−5.22455	−	9.04919i	−0.220581	−	0.382057i
$562$	−28.8015	−	49.8857i	−1.21492	−	2.10430i
$563$	4.08034	−	7.06736i	0.171966	−	0.297854i	−0.767141	−	0.641478i	$-0.778321\pi$
$563$	4.08034	−	7.06736i	0.171966	−	0.297854i	0.939107	+	0.343625i	$0.111655\pi$
$564$	7.54754			0.317809
$565$	−19.4174	+	33.6319i	−0.816895	+	1.41490i
$566$	−17.0494	+	29.5305i	−0.716641	+	1.24126i
$567$	−17.4053			−0.730952
$568$	0.0770557	−	0.133464i	0.00323319	−	0.00560004i
$569$	5.22839	+	9.05584i	0.219186	+	0.379641i	0.954559	−	0.298021i	$-0.0963266\pi$
$569$	5.22839	+	9.05584i	0.219186	+	0.379641i	−0.735374	+	0.677662i	$0.762993\pi$
$570$	15.2056	+	26.3369i	0.636892	+	1.10313i
$571$	41.0089			1.71617			0.858084	−	0.513510i	$-0.171655\pi$
$571$	41.0089			1.71617			0.858084	+	0.513510i	$0.171655\pi$
$572$	16.6198	−	15.6966i	0.694908	−	0.656307i
$573$	−3.22748			−0.134830
$574$	36.1819	+	62.6688i	1.51020	+	2.61575i
$575$	1.16947	+	2.02559i	0.0487704	+	0.0844729i
$576$	−9.62015	+	16.6626i	−0.400840	+	0.694275i
$577$	−15.9855			−0.665486			−0.332743	−	0.943018i	$-0.607974\pi$
$577$	−15.9855			−0.665486			−0.332743	+	0.943018i	$0.607974\pi$
$578$	−0.367041	+	0.635734i	−0.0152669	+	0.0264431i
$579$	5.35491	−	9.27498i	0.222542	−	0.385455i
$580$	15.4308			0.640727
$581$	−4.85386	+	8.40714i	−0.201372	+	0.348787i
$582$	−3.76996	−	6.52977i	−0.156270	−	0.270668i
$583$	−8.80962	−	15.2587i	−0.364857	−	0.631951i
$584$	0.404040			0.0167193
$585$	4.94655	+	20.8220i	0.204515	+	0.860885i
$586$	−53.8795			−2.22574
$587$	−14.4851	−	25.0889i	−0.597863	−	1.03553i	−0.993136	−	0.116965i	$-0.962683\pi$
$587$	−14.4851	−	25.0889i	−0.597863	−	1.03553i	0.395273	−	0.918564i	$-0.370650\pi$
$588$	−12.4254	−	21.5213i	−0.512413	−	0.887525i
$589$	−3.78499	+	6.55580i	−0.155958	+	0.270127i
$590$	−35.0249			−1.44195
$591$	−4.75491	+	8.23574i	−0.195591	+	0.338773i
$592$	12.7516	−	22.0864i	0.524087	−	0.907746i
$593$	−16.5350			−0.679012			−0.339506	−	0.940604i	$-0.610260\pi$
$593$	−16.5350			−0.679012			−0.339506	+	0.940604i	$0.610260\pi$
$594$	13.4777	−	23.3441i	0.552998	−	0.957821i
$595$	−24.7880	−	42.9341i	−1.01621	−	1.76012i
$596$	6.86569	+	11.8917i	0.281230	+	0.487104i
$597$	16.8696			0.690429
$598$	−2.98587	−	12.5688i	−0.122101	−	0.513975i
$599$	−0.970307			−0.0396457			−0.0198228	−	0.999804i	$-0.506310\pi$
$599$	−0.970307			−0.0396457			−0.0198228	+	0.999804i	$0.506310\pi$
$600$	−0.0185857	−	0.0321914i	−0.000758760	−	0.00131421i
$601$	−17.7114	−	30.6770i	−0.722462	−	1.25134i	−0.960010	−	0.279965i	$-0.909677\pi$
$601$	−17.7114	−	30.6770i	−0.722462	−	1.25134i	0.237549	−	0.971376i	$-0.423656\pi$
$602$	−15.7729	+	27.3195i	−0.642856	+	1.11346i
$603$	4.97112			0.202440
$604$	13.5897	−	23.5381i	0.552959	−	0.957753i
$605$	−1.41427	+	2.44959i	−0.0574983	+	0.0995900i
$606$	−6.68504			−0.271561
$607$	18.8756	−	32.6935i	0.766138	−	1.32699i	−0.173505	−	0.984833i	$-0.555509\pi$
$607$	18.8756	−	32.6935i	0.766138	−	1.32699i	0.939643	−	0.342156i	$-0.111157\pi$
$608$	30.3447	+	52.5586i	1.23064	+	2.13153i
$609$	−5.75392	−	9.96609i	−0.233161	−	0.403846i
$610$	−9.39967			−0.380581
$611$	12.2875	−	11.6050i	0.497101	−	0.469488i
$612$	−19.8716			−0.803262
$613$	−16.4304	−	28.4582i	−0.663616	−	1.14942i	−0.979659	−	0.200672i	$-0.935688\pi$
$613$	−16.4304	−	28.4582i	−0.663616	−	1.14942i	0.316043	−	0.948745i	$-0.397646\pi$
$614$	−2.53833	−	4.39652i	−0.102439	−	0.177429i
$615$	7.63817	−	13.2297i	0.308001	−	0.533473i
$616$	−0.529852			−0.0213484
$617$	−9.44749	+	16.3635i	−0.380342	+	0.658771i	−0.991111	−	0.133037i	$-0.957527\pi$
$617$	−9.44749	+	16.3635i	−0.380342	+	0.658771i	0.610769	+	0.791809i	$0.290860\pi$
$618$	−1.00199	+	1.73550i	−0.0403061	+	0.0698121i
$619$	15.2034			0.611078			0.305539	−	0.952180i	$-0.401163\pi$
$619$	15.2034			0.611078			0.305539	+	0.952180i	$0.401163\pi$
$620$	2.53398	−	4.38897i	0.101767	−	0.176265i
$621$	−3.82501	−	6.62510i	−0.153492	−	0.265856i
$622$	5.34083	+	9.25059i	0.214148	+	0.370915i
$623$	−88.2975			−3.53756
$624$	−2.63611	−	11.0965i	−0.105529	−	0.444214i
$625$	−29.8303			−1.19321
$626$	−23.0993	−	40.0092i	−0.923234	−	1.59909i
$627$	−9.49055	−	16.4381i	−0.379016	−	0.656475i
$628$	17.2120	−	29.8120i	0.686832	−	1.18963i
$629$	26.8099			1.06898
$630$	28.1767	−	48.8035i	1.12259	−	1.94438i
$631$	−9.87481	+	17.1037i	−0.393110	+	0.680886i	−0.992858	−	0.119303i	$-0.961934\pi$
$631$	−9.87481	+	17.1037i	−0.393110	+	0.680886i	0.599748	+	0.800189i	$0.295267\pi$
$632$	−0.171411			−0.00681837
$633$	−9.87927	+	17.1114i	−0.392666	+	0.680117i
$634$	−3.95366	−	6.84794i	−0.157020	−	0.271967i
$635$	18.1673	+	31.4667i	0.720947	+	1.24872i
$636$	9.02812			0.357988
$637$	−53.3196	−	15.9321i	−2.11260	−	0.631253i
$638$	−19.1774			−0.759241
$639$	−5.11516	−	8.85971i	−0.202352	−	0.350485i
$640$	−0.357653	−	0.619473i	−0.0141375	−	0.0244868i
$641$	6.64572	−	11.5107i	0.262490	−	0.454646i	−0.704413	−	0.709790i	$-0.748790\pi$
$641$	6.64572	−	11.5107i	0.262490	−	0.454646i	0.966903	+	0.255144i	$0.0821230\pi$
$642$	−18.8837			−0.745280
$643$	−17.0663	+	29.5597i	−0.673030	+	1.16572i	0.304010	+	0.952669i	$0.401674\pi$
$643$	−17.0663	+	29.5597i	−0.673030	+	1.16572i	−0.977040	+	0.213054i	$0.931659\pi$
$644$	−8.54173	+	14.7947i	−0.336591	+	0.582993i
$645$	6.65948			0.262217
$646$	−31.6162	+	54.7609i	−1.24392	+	2.15454i
$647$	18.3365	+	31.7597i	0.720881	+	1.24860i	0.960647	+	0.277772i	$0.0895960\pi$
$647$	18.3365	+	31.7597i	0.720881	+	1.24860i	−0.239766	+	0.970831i	$0.577071\pi$
$648$	−0.0654110	−	0.113295i	−0.00256959	−	0.00445065i
$649$	21.8608			0.858111
$650$	−9.06074	−	2.70738i	−0.355391	−	0.106192i
$651$	−3.77954			−0.148132
$652$	−7.96127	−	13.7893i	−0.311787	−	0.540032i
$653$	−3.76829	−	6.52687i	−0.147465	−	0.255416i	0.782825	−	0.622242i	$-0.213778\pi$
$653$	−3.76829	−	6.52687i	−0.147465	−	0.255416i	−0.930290	+	0.366825i	$0.880445\pi$
$654$	−2.54585	+	4.40955i	−0.0995508	+	0.172427i
$655$	10.8421			0.423634
$656$	15.1076	−	26.1671i	0.589852	−	1.02165i
$657$	13.4106	−	23.2279i	0.523198	−	0.906205i
$658$	−44.5041			−1.73495
$659$	5.11468	−	8.85889i	0.199240	−	0.345093i	−0.749042	−	0.662522i	$-0.769486\pi$
$659$	5.11468	−	8.85889i	0.199240	−	0.345093i	0.948282	+	0.317429i	$0.102819\pi$
$660$	6.35373	+	11.0050i	0.247319	+	0.428369i
$661$	−7.85731	−	13.6093i	−0.305614	−	0.529339i	0.671784	−	0.740747i	$-0.265528\pi$
$661$	−7.85731	−	13.6093i	−0.305614	−	0.529339i	−0.977398	+	0.211408i	$0.932195\pi$
$662$	55.7633			2.16730
$663$	8.71663	−	8.23244i	0.338526	−	0.319721i
$664$	−0.0729656			−0.00283161
$665$	−45.0281	−	77.9909i	−1.74611	−	3.02436i
$666$	15.2376	+	26.3922i	0.590443	+	1.02268i
$667$	−2.72129	+	4.71342i	−0.105369	+	0.182504i
$668$	31.9752			1.23716
$669$	5.45164	−	9.44253i	0.210773	−	0.365069i
$670$	−5.29504	+	9.17128i	−0.204565	+	0.354317i
$671$	5.86679			0.226485
$672$	−15.1505	+	26.2414i	−0.584443	+	1.01229i
$673$	3.06051	+	5.30095i	0.117974	+	0.204337i	0.918965	−	0.394340i	$-0.129027\pi$
$673$	3.06051	+	5.30095i	0.117974	+	0.204337i	−0.800991	+	0.598677i	$0.795693\pi$
$674$	−34.2409	−	59.3070i	−1.31891	−	2.28442i
$675$	−5.59992			−0.215541
$676$	21.9308	+	14.3909i	0.843493	+	0.553497i
$677$	21.8244			0.838781			0.419391	−	0.907806i	$-0.362244\pi$
$677$	21.8244			0.838781			0.419391	+	0.907806i	$0.362244\pi$
$678$	12.3653	+	21.4173i	0.474885	+	0.822525i
$679$	11.1639	+	19.3365i	0.428433	+	0.742067i
$680$	0.186312	−	0.322702i	0.00714475	−	0.0123751i
$681$	−14.0990			−0.540275
$682$	−3.14924	+	5.45464i	−0.120590	+	0.208869i
$683$	10.8503	−	18.7932i	0.415174	−	0.719103i	−0.580273	−	0.814422i	$-0.697054\pi$
$683$	10.8503	−	18.7932i	0.415174	−	0.719103i	0.995447	+	0.0953197i	$0.0303873\pi$
$684$	−36.0973			−1.38022
$685$	−2.08896	+	3.61819i	−0.0798152	+	0.138244i
$686$	40.0373	+	69.3466i	1.52863	+	2.64767i
$687$	9.26643	+	16.0499i	0.353536	+	0.612343i
$688$	13.1718			0.502171
$689$	14.6979	−	13.8815i	0.559947	−	0.528843i
$690$	7.18106			0.273378
$691$	15.7211	+	27.2298i	0.598060	+	1.03587i	0.993107	+	0.117209i	$0.0373948\pi$
$691$	15.7211	+	27.2298i	0.598060	+	1.03587i	−0.395047	+	0.918661i	$0.629272\pi$
$692$	−22.8011	−	39.4926i	−0.866767	−	1.50128i
$693$	−17.5865	+	30.4607i	−0.668055	+	1.15711i
$694$	2.79902			0.106249
$695$	−3.35622	+	5.81314i	−0.127309	+	0.220505i
$696$	0.0432478	−	0.0749074i	0.00163930	−	0.00283936i
$697$	31.7633			1.20312
$698$	3.75719	−	6.50765i	0.142212	−	0.246318i
$699$	−1.02053	−	1.76761i	−0.0385999	−	0.0668570i
$700$	6.25267	+	10.8299i	0.236329	+	0.409334i
$701$	27.7932			1.04973			0.524867	−	0.851185i	$-0.324115\pi$
$701$	27.7932			1.04973			0.524867	+	0.851185i	$0.324115\pi$
$702$	29.6350	+	8.85506i	1.11850	+	0.334213i
$703$	48.7010			1.83679
$704$	12.7913	+	22.1552i	0.482090	+	0.835005i
$705$	4.69752	+	8.13634i	0.176919	+	0.306432i
$706$	−10.0813	+	17.4613i	−0.379413	+	0.657163i
$707$	19.7963			0.744517
$708$	−5.60074	+	9.70077i	−0.210489	+	0.364577i
$709$	4.47028	−	7.74276i	0.167885	−	0.290785i	−0.769791	−	0.638296i	$-0.779640\pi$
$709$	4.47028	−	7.74276i	0.167885	−	0.290785i	0.937676	+	0.347511i	$0.112973\pi$
$710$	21.7938			0.817908
$711$	−5.68936	+	9.85426i	−0.213368	+	0.369563i
$712$	−0.331832	−	0.574750i	−0.0124359	−	0.0215397i
$713$	0.893759	+	1.54804i	0.0334715	+	0.0579744i
$714$	−31.5707			−1.18150
$715$	27.2651	+	8.14692i	1.01966	+	0.304677i
$716$	26.0308			0.972818
$717$	−2.32100	−	4.02008i	−0.0866792	−	0.150133i
$718$	−10.0829	−	17.4641i	−0.376290	−	0.651754i
$719$	−20.6401	+	35.7497i	−0.769747	+	1.33324i	0.167953	+	0.985795i	$0.446284\pi$
$719$	−20.6401	+	35.7497i	−0.769747	+	1.33324i	−0.937700	+	0.347446i	$0.887049\pi$
$720$	−23.5301			−0.876916
$721$	2.96719	−	5.13932i	0.110504	−	0.191398i
$722$	−38.3896	+	66.4928i	−1.42871	+	2.47460i
$723$	−17.4275			−0.648136
$724$	−25.7782	+	44.6492i	−0.958040	+	1.65937i
$725$	1.99203	+	3.45029i	0.0739820	+	0.128141i
$726$	0.900629	+	1.55993i	0.0334255	+	0.0578946i
$727$	38.5841			1.43101			0.715503	−	0.698610i	$-0.246198\pi$
$727$	38.5841			1.43101			0.715503	+	0.698610i	$0.246198\pi$
$728$	−0.140521	−	0.591510i	−0.00520805	−	0.0219228i
$729$	1.56080			0.0578075
$730$	28.5689	+	49.4827i	1.05738	+	1.83144i
$731$	6.92336	+	11.9916i	0.256070	+	0.443526i
$732$	−1.50308	+	2.60340i	−0.0555553	+	0.0962246i
$733$	18.5311			0.684462			0.342231	−	0.939616i	$-0.388818\pi$
$733$	18.5311			0.684462			0.342231	+	0.939616i	$0.388818\pi$
$734$	13.2237	−	22.9040i	0.488094	−	0.845404i
$735$	15.4668	−	26.7894i	0.570503	−	0.988141i
$736$	14.3307			0.528237
$737$	3.30489	−	5.72424i	0.121737	−	0.210855i
$738$	18.0528	+	31.2684i	0.664534	+	1.15101i
$739$	−0.257950	−	0.446782i	−0.00948884	−	0.0164352i	0.861242	−	0.508195i	$-0.169687\pi$
$739$	−0.257950	−	0.446782i	−0.00948884	−	0.0164352i	−0.870731	+	0.491760i	$0.836354\pi$
$740$	−32.6043			−1.19856
$741$	15.8340	−	14.9545i	0.581677	−	0.549366i
$742$	−53.2344			−1.95429
$743$	−21.3054	−	36.9020i	−0.781619	−	1.35380i	−0.930998	−	0.365024i	$-0.881061\pi$
$743$	−21.3054	−	36.9020i	−0.781619	−	1.35380i	0.149379	−	0.988780i	$-0.452272\pi$
$744$	−0.0142040	−	0.0246020i	−0.000520743	−	0.000901953i
$745$	−8.54628	+	14.8026i	−0.313112	+	0.542325i
$746$	36.6353			1.34131
$747$	−2.42182	+	4.19472i	−0.0886098	+	0.153477i
$748$	−13.2110	+	22.8821i	−0.483042	+	0.836653i
$749$	55.9200			2.04327
$750$	−7.41502	+	12.8432i	−0.270758	+	0.468967i
$751$	−0.672295	−	1.16445i	−0.0245324	−	0.0424913i	0.853499	−	0.521095i	$-0.174476\pi$
$751$	−0.672295	−	1.16445i	−0.0245324	−	0.0424913i	−0.878031	+	0.478604i	$0.841143\pi$
$752$	9.29125	+	16.0929i	0.338817	+	0.586848i
$753$	−3.20307			−0.116726
$754$	−5.08600	−	21.4090i	−0.185221	−	0.779671i
$755$	33.8325			1.23129
$756$	−20.4507	−	35.4216i	−0.743783	−	1.28827i
$757$	−1.93214	−	3.34656i	−0.0702247	−	0.121633i	0.828775	−	0.559582i	$-0.189038\pi$
$757$	−1.93214	−	3.34656i	−0.0702247	−	0.121633i	−0.899000	+	0.437949i	$0.855705\pi$
$758$	28.2811	−	48.9844i	1.02722	−	1.77919i
$759$	−4.48205			−0.162688
$760$	0.338442	−	0.586198i	0.0122766	−	0.0212636i
$761$	−14.1782	+	24.5574i	−0.513960	+	0.890205i	0.485909	+	0.874010i	$0.338489\pi$
$761$	−14.1782	+	24.5574i	−0.513960	+	0.890205i	−0.999869	+	0.0161956i	$0.994845\pi$
$762$	23.1384			0.838215
$763$	7.53900	−	13.0579i	0.272930	−	0.472729i
$764$	4.08056	+	7.06774i	0.147630	+	0.255702i
$765$	−12.3679	−	21.4218i	−0.447162	−	0.774507i
$766$	−36.7125			−1.32648
$767$	5.79765	+	24.4047i	0.209341	+	0.881201i
$768$	12.5377			0.452414
$769$	5.87853	+	10.1819i	0.211985	+	0.367169i	0.952336	−	0.305052i	$-0.0986738\pi$
$769$	5.87853	+	10.1819i	0.211985	+	0.367169i	−0.740351	+	0.672221i	$0.765341\pi$
$770$	−37.4648	−	64.8910i	−1.35014	−	2.33851i
$771$	11.8376	−	20.5033i	0.426320	−	0.738408i
$772$	−27.0812			−0.974675
$773$	0.782019	−	1.35450i	0.0281273	−	0.0487178i	−0.851619	−	0.524161i	$-0.824379\pi$
$773$	0.782019	−	1.35450i	0.0281273	−	0.0487178i	0.879746	+	0.475443i	$0.157712\pi$
$774$	−7.86985	+	13.6310i	−0.282876	+	0.489956i
$775$	1.30849			0.0470023
$776$	−0.0839108	+	0.145338i	−0.00301222	+	0.00521732i
$777$	12.1577	+	21.0578i	0.436156	+	0.755444i
$778$	25.5235	+	44.2080i	0.915063	+	1.58493i
$779$	57.6990			2.06728
$780$	−10.6005	+	10.0117i	−0.379560	+	0.358477i
$781$	−13.6026			−0.486739
$782$	7.46561	+	12.9308i	0.266970	+	0.462405i
$783$	−6.51533	−	11.2849i	−0.232839	−	0.403289i
$784$	30.5919	−	52.9868i	1.09257	−	1.89239i
$785$	42.8502			1.52939
$786$	3.45219	−	5.97936i	0.123135	−	0.213277i
$787$	−17.5953	+	30.4760i	−0.627206	+	1.08635i	0.360904	+	0.932603i	$0.382468\pi$
$787$	−17.5953	+	30.4760i	−0.627206	+	1.08635i	−0.988110	+	0.153749i	$0.950865\pi$
$788$	24.0469			0.856634
$789$	−5.59331	+	9.68789i	−0.199127	+	0.344898i
$790$	−12.1201	−	20.9927i	−0.431215	−	0.746887i
$791$	−36.6171	−	63.4226i	−1.30195	−	2.25505i
$792$	−0.264368			−0.00939392
$793$	1.55592	+	6.54949i	0.0552523	+	0.232579i
$794$	−7.49242			−0.265896
$795$	5.61902	+	9.73242i	0.199286	+	0.345173i
$796$	−21.3286	−	36.9422i	−0.755972	−	1.30938i
$797$	12.1364	−	21.0208i	0.429892	−	0.744595i	−0.566971	−	0.823738i	$-0.691885\pi$
$797$	12.1364	−	21.0208i	0.429892	−	0.744595i	0.996863	+	0.0791428i	$0.0252183\pi$
$798$	−57.3491			−2.03013
$799$	−9.76732	+	16.9175i	−0.345543	+	0.598498i
$800$	5.24515	−	9.08487i	0.185444	−	0.321199i
$801$	−44.0558			−1.55663
$802$	−12.1743	+	21.0865i	−0.429890	+	0.744591i
$803$	−17.8312	−	30.8846i	−0.629250	−	1.08989i
$804$	1.69343	+	2.93311i	0.0597227	+	0.103443i
$805$	−21.2652			−0.749499
$806$	−6.92458	−	2.06909i	−0.243908	−	0.0728806i
$807$	−5.08458			−0.178986
$808$	0.0743969	+	0.128859i	0.00261727	+	0.00453325i
$809$	16.1507	+	27.9738i	0.567828	+	0.983507i	0.996780	+	0.0801798i	$0.0255494\pi$
$809$	16.1507	+	27.9738i	0.567828	+	0.983507i	−0.428952	+	0.903327i	$0.641117\pi$
$810$	9.25016	−	16.0218i	0.325018	−	0.562947i
$811$	0.702297			0.0246610			0.0123305	−	0.999924i	$-0.496075\pi$
$811$	0.702297			0.0246610			0.0123305	+	0.999924i	$0.496075\pi$
$812$	−14.5496	+	25.2006i	−0.510590	+	0.884368i
$813$	−5.95146	+	10.3082i	−0.208727	+	0.361525i
$814$	40.5208			1.42025
$815$	9.91004	−	17.1647i	0.347134	−	0.601253i
$816$	6.59110	+	11.4161i	0.230735	+	0.399644i
$817$	12.5765	+	21.7831i	0.439996	+	0.762095i
$818$	47.9941			1.67807
$819$	−38.6694	−	11.5546i	−1.35122	−	0.403749i
$820$	−38.6283			−1.34896
$821$	−2.77860	−	4.81268i	−0.0969739	−	0.167964i	0.813457	−	0.581625i	$-0.197583\pi$
$821$	−2.77860	−	4.81268i	−0.0969739	−	0.167964i	−0.910431	+	0.413662i	$0.864250\pi$
$822$	1.33028	+	2.30412i	0.0463989	+	0.0803653i
$823$	16.3813	−	28.3732i	0.571016	−	0.989029i	−0.425446	−	0.904984i	$-0.639883\pi$
$823$	16.3813	−	28.3732i	0.571016	−	0.989029i	0.996462	−	0.0840452i	$-0.0267840\pi$
$824$	0.0446041			0.00155386
$825$	−1.64046	+	2.84137i	−0.0571136	+	0.0989237i
$826$	33.0248	−	57.2007i	1.14908	−	1.99027i
$827$	4.74689			0.165066			0.0825328	−	0.996588i	$-0.473699\pi$
$827$	4.74689			0.165066			0.0825328	+	0.996588i	$0.473699\pi$
$828$	−4.26187	+	7.38178i	−0.148110	+	0.256534i
$829$	−17.9817	−	31.1453i	−0.624532	−	1.08172i	−0.988631	−	0.150360i	$-0.951957\pi$
$829$	−17.9817	−	31.1453i	−0.624532	−	1.08172i	0.364100	−	0.931360i	$-0.381377\pi$
$830$	−5.15925	−	8.93608i	−0.179080	−	0.310176i
$831$	−15.2021			−0.527355
$832$	−21.3410	+	20.1555i	−0.739865	+	0.698767i
$833$	64.3189			2.22852
$834$	2.13729	+	3.70189i	0.0740082	+	0.128186i
$835$	19.9011	+	34.4696i	0.688705	+	1.19287i
$836$	−23.9981	+	41.5660i	−0.829993	+	1.43759i
$837$	−4.27968			−0.147928
$838$	−4.65124	+	8.05618i	−0.160674	+	0.278296i
$839$	2.44715	−	4.23859i	0.0844850	−	0.146332i	−0.820687	−	0.571379i	$-0.806409\pi$
$839$	2.44715	−	4.23859i	0.0844850	−	0.146332i	0.905172	+	0.425046i	$0.139742\pi$
$840$	0.337954			0.0116605
$841$	9.86468	−	17.0861i	0.340161	−	0.589177i
$842$	−5.39837	−	9.35025i	−0.186040	−	0.322231i
$843$	−11.4659	−	19.8595i	−0.394906	−	0.683997i
$844$	49.9621			1.71977
$845$	−1.86404	+	32.5985i	−0.0641248	+	1.12142i
$846$	−22.2052			−0.763431
$847$	−2.66702	−	4.61941i	−0.0916399	−	0.158725i
$848$	11.1139	+	19.2498i	0.381652	+	0.661041i
$849$	−6.78736	+	11.7561i	−0.232942	+	0.403467i
$850$	10.9299			0.374892
$851$	5.74994	−	9.95919i	0.197105	−	0.341397i
$852$	3.48499	−	6.03618i	0.119394	−	0.206796i
$853$	19.8721			0.680408			0.340204	−	0.940352i	$-0.389504\pi$
$853$	19.8721			0.680408			0.340204	+	0.940352i	$0.389504\pi$
$854$	8.86289	−	15.3510i	0.303282	−	0.525300i
$855$	−22.4666	−	38.9133i	−0.768343	−	1.33081i
$856$	0.210154	+	0.363997i	0.00718291	+	0.0124412i
$857$	15.9063			0.543348			0.271674	−	0.962389i	$-0.412423\pi$
$857$	15.9063			0.543348			0.271674	+	0.962389i	$0.412423\pi$
$858$	13.1744	−	12.4426i	0.449767	−	0.424783i
$859$	−22.1555			−0.755937			−0.377969	−	0.925818i	$-0.623377\pi$
$859$	−22.1555			−0.755937			−0.377969	+	0.925818i	$0.623377\pi$
$860$	−8.41970	−	14.5834i	−0.287109	−	0.497288i
$861$	14.4040	+	24.9484i	0.490886	+	0.850240i
$862$	13.9378	−	24.1411i	0.474725	−	0.822248i
$863$	−19.1946			−0.653392			−0.326696	−	0.945129i	$-0.605935\pi$
$863$	−19.1946			−0.653392			−0.326696	+	0.945129i	$0.605935\pi$
$864$	−17.1553	+	29.7139i	−0.583637	+	1.01089i
$865$	28.3824	−	49.1597i	0.965029	−	1.67148i
$866$	−73.2634			−2.48959
$867$	−0.146119	+	0.253085i	−0.00496246	+	0.00859523i
$868$	4.77854	+	8.27668i	0.162194	+	0.280929i
$869$	7.56477	+	13.1026i	0.256617	+	0.444474i
$870$	12.2319			0.414699
$871$	7.26684	+	2.17136i	0.246227	+	0.0735737i
$872$	0.113330			0.00383783
$873$	5.57021	+	9.64789i	0.188523	+	0.326532i
$874$	13.5615	+	23.4892i	0.458724	+	0.794534i
$875$	21.9580	−	38.0324i	0.742316	−	1.28573i
$876$	18.2735			0.617404
$877$	21.8794	−	37.8962i	0.738815	−	1.27966i	−0.214215	−	0.976787i	$-0.568719\pi$
$877$	21.8794	−	37.8962i	0.738815	−	1.27966i	0.953029	−	0.302878i	$-0.0979475\pi$
$878$	14.4943	−	25.1048i	0.489157	−	0.847245i
$879$	−21.4494			−0.723470
$880$	−15.6433	+	27.0949i	−0.527334	+	0.913370i
$881$	2.32401	+	4.02531i	0.0782980	+	0.135616i	0.902516	−	0.430657i	$-0.141718\pi$
$881$	2.32401	+	4.02531i	0.0782980	+	0.135616i	−0.824218	+	0.566273i	$0.808385\pi$
$882$	36.5559	+	63.3167i	1.23090	+	2.13199i
$883$	−22.9690			−0.772970			−0.386485	−	0.922296i	$-0.626311\pi$
$883$	−22.9690			−0.772970			−0.386485	+	0.922296i	$0.626311\pi$
$884$	−29.0485	−	8.67980i	−0.977007	−	0.291933i
$885$	−13.9434			−0.468702
$886$	26.3961	+	45.7195i	0.886796	+	1.53598i
$887$	14.9380	+	25.8734i	0.501570	+	0.868745i	0.999998	+	0.00181399i	$0.000577412\pi$
$887$	14.9380	+	25.8734i	0.501570	+	0.868745i	−0.498428	+	0.866931i	$0.666089\pi$
$888$	−0.0913803	+	0.158275i	−0.00306652	+	0.00531137i
$889$	−68.5193			−2.29807
$890$	46.9264	−	81.2789i	1.57298	−	2.72448i
$891$	−5.77348	+	9.99996i	−0.193419	+	0.335011i
$892$	−27.5704			−0.923127
$893$	−17.7426	+	30.7311i	−0.593734	+	1.02838i
$894$	5.44240	+	9.42651i	0.182021	+	0.315270i
$895$	16.2013	+	28.0616i	0.541551	+	0.937994i
$896$	1.34892			0.0450641
$897$	−1.18867	−	5.00361i	−0.0396887	−	0.167066i
$898$	27.4799			0.917017
$899$	1.52239	+	2.63685i	0.0507744	+	0.0879439i
$900$	3.11975	+	5.40357i	0.103992	+	0.180119i
$901$	−11.6833	+	20.2361i	−0.389228	+	0.674163i
$902$	48.0074			1.59847
$903$	−6.27919	+	10.8759i	−0.208958	+	0.361926i
$904$	0.275222	−	0.476699i	0.00915376	−	0.0158548i
$905$	−64.1765			−2.13330
$906$	10.7725	−	18.6585i	0.357893	−	0.619889i
$907$	−18.4482	−	31.9532i	−0.612561	−	1.06099i	−0.990807	−	0.135282i	$-0.956806\pi$
$907$	−18.4482	−	31.9532i	−0.612561	−	1.06099i	0.378246	−	0.925705i	$-0.376527\pi$
$908$	17.8256	+	30.8749i	0.591564	+	1.02462i
$909$	9.87731			0.327610
$910$	62.5062	−	59.0341i	2.07206	−	1.95696i
$911$	−53.7266			−1.78004			−0.890021	−	0.455919i	$-0.849311\pi$
$911$	−53.7266			−1.78004			−0.890021	+	0.455919i	$0.849311\pi$
$912$	11.9729	+	20.7377i	0.396463	+	0.686694i
$913$	3.22014	+	5.57745i	0.106571	+	0.184587i
$914$	0.0969570	−	0.167934i	0.00320705	−	0.00555478i
$915$	−3.74200			−0.123707
$916$	23.4314	−	40.5844i	0.774196	−	1.34095i
$917$	−10.2229	+	17.7066i	−0.337590	+	0.584724i
$918$	−35.7484			−1.17987
$919$	13.8008	−	23.9037i	0.455247	−	0.788512i	−0.543455	−	0.839438i	$-0.682884\pi$
$919$	13.8008	−	23.9037i	0.455247	−	0.788512i	0.998702	+	0.0509267i	$0.0162175\pi$
$920$	−0.0799170	−	0.138420i	−0.00263478	−	0.00456358i
$921$	−1.01051	−	1.75025i	−0.0332974	−	0.0576727i
$922$	58.6442			1.93135
$923$	−3.60751	−	15.1855i	−0.118743	−	0.499836i
$924$	−23.9636			−0.788344
$925$	−4.20904	−	7.29028i	−0.138392	−	0.239703i
$926$	−14.0794	−	24.3862i	−0.462678	−	0.801381i
$927$	1.48047	−	2.56425i	0.0486250	−	0.0842209i
$928$	24.4103			0.801306
$929$	−19.7860	+	34.2704i	−0.649158	+	1.12438i	0.334166	+	0.942514i	$0.391545\pi$
$929$	−19.7860	+	34.2704i	−0.649158	+	1.12438i	−0.983324	+	0.181861i	$0.941788\pi$
$930$	2.00867	−	3.47912i	0.0658668	−	0.114085i
$931$	116.837			3.82918
$932$	−2.58054	+	4.46963i	−0.0845285	+	0.146408i
$933$	2.12618	+	3.68265i	0.0696081	+	0.120565i
$934$	−40.7167	−	70.5234i	−1.33229	−	2.30760i
$935$	−32.8896			−1.07560
$936$	−0.0701125	−	0.295132i	−0.00229170	−	0.00964669i
$937$	−11.1521			−0.364324			−0.182162	−	0.983268i	$-0.558310\pi$
$937$	−11.1521			−0.364324			−0.182162	+	0.983268i	$0.558310\pi$
$938$	−9.98533	−	17.2951i	−0.326032	−	0.564705i
$939$	−9.19582	−	15.9276i	−0.300094	−	0.519778i
$940$	11.8783	−	20.5738i	0.387428	−	0.671045i
$941$	22.6106			0.737083			0.368542	−	0.929611i	$-0.379857\pi$
$941$	22.6106			0.737083			0.368542	+	0.929611i	$0.379857\pi$
$942$	13.6438	−	23.6318i	0.444540	−	0.769965i
$943$	6.81229	−	11.7992i	0.221839	−	0.384236i
$944$	−27.5787			−0.897611
$945$	25.4566	−	44.0921i	0.828103	−	1.43432i
$946$	10.4640	+	18.1243i	0.340215	+	0.589270i
$947$	22.6012	+	39.1464i	0.734441	+	1.27209i	0.954968	+	0.296708i	$0.0958887\pi$
$947$	22.6012	+	39.1464i	0.734441	+	1.27209i	−0.220528	+	0.975381i	$0.570778\pi$
$948$	−7.75240			−0.251786
$949$	29.7496	−	28.0970i	0.965712	−	0.912068i
$950$	19.8544			0.644163
$951$	−1.57395	−	2.72616i	−0.0510388	−	0.0884018i
$952$	0.351346	+	0.608549i	0.0113872	+	0.0197232i
$953$	−12.1523	+	21.0484i	−0.393652	+	0.681825i	−0.992928	−	0.118718i	$-0.962122\pi$
$953$	−12.1523	+	21.0484i	−0.393652	+	0.681825i	0.599276	+	0.800542i	$0.295455\pi$
$954$	−26.5611			−0.859948
$955$	−5.07941	+	8.79779i	−0.164366	+	0.284690i
$956$	−5.86896	+	10.1653i	−0.189816	+	0.328770i
$957$	−7.63451			−0.246789
$958$	40.2290	−	69.6786i	1.29974	−	2.25121i
$959$	−3.93935	−	6.82315i	−0.127208	−	0.220331i
$960$	−8.15864	−	14.1312i	−0.263319	−	0.456082i
$961$	1.00000			0.0322581
$962$	10.7464	+	45.2361i	0.346479	+	1.45847i
$963$	27.9011			0.899101
$964$	22.0339	+	38.1638i	0.709664	+	1.22917i
$965$	−16.8551	−	29.1939i	−0.542585	−	0.939785i
$966$	−6.77098	+	11.7277i	−0.217853	+	0.377332i
$967$	−16.3396			−0.525445			−0.262722	−	0.964871i	$-0.584620\pi$
$967$	−16.3396			−0.525445			−0.262722	+	0.964871i	$0.584620\pi$
$968$	0.0200459	−	0.0347206i	0.000644301	−	0.00111596i
$969$	−12.5864	+	21.8003i	−0.404333	+	0.700326i
$970$	−23.7327			−0.762010
$971$	2.78114	−	4.81707i	0.0892510	−	0.154587i	−0.817944	−	0.575298i	$-0.804886\pi$
$971$	2.78114	−	4.81707i	0.0892510	−	0.154587i	0.907195	+	0.420711i	$0.138219\pi$
$972$	−15.9114	−	27.5594i	−0.510359	−	0.883967i
$973$	−6.32912	−	10.9624i	−0.202902	−	0.351437i
$974$	76.9739			2.46640
$975$	−3.60707	−	1.07781i	−0.115519	−	0.0345175i
$976$	−7.40132			−0.236910
$977$	−20.4027	−	35.3385i	−0.652739	−	1.13058i	−0.982455	−	0.186497i	$-0.940286\pi$
$977$	−20.4027	−	35.3385i	−0.652739	−	1.13058i	0.329716	−	0.944080i	$-0.393047\pi$
$978$	−6.31086	−	10.9307i	−0.201799	−	0.349526i
$979$	−29.2891	+	50.7302i	−0.936083	+	1.62134i
$980$	−78.2200			−2.49865
$981$	3.76156	−	6.51522i	0.120097	−	0.208015i
$982$	−15.5670	+	26.9629i	−0.496763	+	0.860419i
$983$	−2.59252			−0.0826887			−0.0413443	−	0.999145i	$-0.513164\pi$
$983$	−2.59252			−0.0826887			−0.0413443	+	0.999145i	$0.513164\pi$
$984$	−0.108264	+	0.187518i	−0.00345132	+	0.00597786i
$985$	14.9665	+	25.9228i	0.476873	+	0.825969i
$986$	12.7166	+	22.0257i	0.404978	+	0.701442i
$987$	−17.7171			−0.563940
$988$	−52.7674	−	15.7671i	−1.67876	−	0.501619i
$989$	5.93943			0.188863
$990$	−18.6930	−	32.3772i	−0.594101	−	1.02901i
$991$	−28.5756	−	49.4944i	−0.907733	−	1.57224i	−0.817205	−	0.576346i	$-0.804478\pi$
$991$	−28.5756	−	49.4944i	−0.907733	−	1.57224i	−0.0905280	−	0.995894i	$-0.528855\pi$
$992$	4.00855	−	6.94302i	0.127272	−	0.220441i
$993$	22.1993			0.704475
$994$	−20.5493	+	35.5924i	−0.651783	+	1.12892i
$995$	26.5494	−	45.9850i	0.841673	−	1.45782i
$996$	−3.30001			−0.104565
$997$	9.00754	−	15.6015i	0.285272	−	0.494105i	−0.687403	−	0.726276i	$-0.741250\pi$
$997$	9.00754	−	15.6015i	0.285272	−	0.494105i	0.972675	+	0.232171i	$0.0745829\pi$
$998$	6.90277	+	11.9559i	0.218503	+	0.378459i
$999$	13.7665	+	23.8443i	0.435554	+	0.754402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.4	✓	36
13.3	even	3		5239.2.a.p.1.15		18
13.9	even	3	inner	403.2.f.c.373.4	yes	36
13.10	even	6		5239.2.a.o.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.4	✓	36	1.1	even	1	trivial
403.2.f.c.373.4	yes	36	13.9	even	3	inner
5239.2.a.o.1.4		18	13.10	even	6
5239.2.a.p.1.15		18	13.3	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00222 - 1.73589i) q^{2} +(-0.398982 - 0.691057i) q^{3} +(-1.00888 + 1.74743i) q^{4} -2.51167 q^{5} +(-0.799734 + 1.38518i) q^{6} +(2.36824 - 4.10191i) q^{7} +0.0356005 q^{8} +(1.18163 - 2.04664i) q^{9} +O(q^{10})\)	\(q+(-1.00222 - 1.73589i) q^{2} +(-0.398982 - 0.691057i) q^{3} +(-1.00888 + 1.74743i) q^{4} -2.51167 q^{5} +(-0.799734 + 1.38518i) q^{6} +(2.36824 - 4.10191i) q^{7} +0.0356005 q^{8} +(1.18163 - 2.04664i) q^{9} +(2.51724 + 4.35999i) q^{10} +(-1.57113 - 2.72128i) q^{11} +1.61010 q^{12} +(2.62127 - 2.47567i) q^{13} -9.49397 q^{14} +(1.00211 + 1.73571i) q^{15} +(1.98208 + 3.43307i) q^{16} +(-2.08364 + 3.60897i) q^{17} -4.73699 q^{18} +(-3.78499 + 6.55580i) q^{19} +(2.53398 - 4.38897i) q^{20} -3.77954 q^{21} +(-3.14924 + 5.45464i) q^{22} +(0.893759 + 1.54804i) q^{23} +(-0.0142040 - 0.0246020i) q^{24} +1.30849 q^{25} +(-6.92458 - 2.06909i) q^{26} -4.27968 q^{27} +(4.77854 + 8.27668i) q^{28} +(1.52239 + 2.63685i) q^{29} +(2.00867 - 3.47912i) q^{30} +1.00000 q^{31} +(4.00855 - 6.94302i) q^{32} +(-1.25371 + 2.17149i) q^{33} +8.35304 q^{34} +(-5.94824 + 10.3027i) q^{35} +(2.38424 + 4.12962i) q^{36} +(-3.21672 - 5.57152i) q^{37} +15.1735 q^{38} +(-2.75667 - 0.823704i) q^{39} -0.0894167 q^{40} +(-3.81104 - 6.60091i) q^{41} +(3.78792 + 6.56088i) q^{42} +(1.66136 - 2.87756i) q^{43} +6.34034 q^{44} +(-2.96786 + 5.14048i) q^{45} +(1.79148 - 3.10294i) q^{46} +4.68762 q^{47} +(1.58163 - 2.73946i) q^{48} +(-7.71713 - 13.3665i) q^{49} +(-1.31139 - 2.27140i) q^{50} +3.32534 q^{51} +(1.68151 + 7.07815i) q^{52} +5.60718 q^{53} +(4.28918 + 7.42907i) q^{54} +(3.94617 + 6.83497i) q^{55} +(0.0843105 - 0.146030i) q^{56} +6.04058 q^{57} +(3.05152 - 5.28540i) q^{58} +(-3.47851 + 6.02495i) q^{59} -4.04404 q^{60} +(-0.933529 + 1.61692i) q^{61} +(-1.00222 - 1.73589i) q^{62} +(-5.59675 - 9.69386i) q^{63} -8.14145 q^{64} +(-6.58378 + 6.21806i) q^{65} +5.02595 q^{66} +(1.05175 + 1.82169i) q^{67} +(-4.20429 - 7.28204i) q^{68} +(0.713188 - 1.23528i) q^{69} +23.8457 q^{70} +(2.16446 - 3.74895i) q^{71} +(0.0420665 - 0.0728613i) q^{72} +11.3493 q^{73} +(-6.44770 + 11.1678i) q^{74} +(-0.522064 - 0.904241i) q^{75} +(-7.63721 - 13.2280i) q^{76} -14.8833 q^{77} +(1.33292 + 5.61081i) q^{78} -4.81485 q^{79} +(-4.97834 - 8.62273i) q^{80} +(-1.83736 - 3.18240i) q^{81} +(-7.63898 + 13.2311i) q^{82} -2.04957 q^{83} +(3.81311 - 6.60449i) q^{84} +(5.23342 - 9.06455i) q^{85} -6.66019 q^{86} +(1.21481 - 2.10411i) q^{87} +(-0.0559331 - 0.0968790i) q^{88} +(-9.32100 - 16.1444i) q^{89} +11.8978 q^{90} +(-3.94716 - 16.6152i) q^{91} -3.60678 q^{92} +(-0.398982 - 0.691057i) q^{93} +(-4.69802 - 8.13720i) q^{94} +(9.50665 - 16.4660i) q^{95} -6.39737 q^{96} +(-2.35701 + 4.08246i) q^{97} +(-15.4685 + 26.7922i) q^{98} -7.42597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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