LMFDB - Embedded newform 276.2.c.b.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27564 + 0.610520i) q^{2} +(0.436111 + 1.67625i) q^{3} +(1.25453 - 1.55761i) q^{4} +3.87509i q^{5} +(-1.57971 - 1.87204i) q^{6} -0.468259i q^{7} +(-0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +O(q^{10})$	\(q+(-1.27564 + 0.610520i) q^{2} +(0.436111 + 1.67625i) q^{3} +(1.25453 - 1.55761i) q^{4} +3.87509i q^{5} +(-1.57971 - 1.87204i) q^{6} -0.468259i q^{7} +(-0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +(-2.36582 - 4.94323i) q^{10} -0.650350 q^{11} +(3.15806 + 1.42361i) q^{12} +3.42468 q^{13} +(0.285881 + 0.597331i) q^{14} +(-6.49561 + 1.68997i) q^{15} +(-0.852308 - 3.90814i) q^{16} -6.36961i q^{17} +(2.44908 - 3.46439i) q^{18} +7.16356i q^{19} +(6.03589 + 4.86142i) q^{20} +(0.784918 - 0.204213i) q^{21} +(0.829614 - 0.397052i) q^{22} -1.00000 q^{23} +(-4.89770 + 0.112037i) q^{24} -10.0163 q^{25} +(-4.36867 + 2.09084i) q^{26} +(-3.59322 - 3.75350i) q^{27} +(-0.729365 - 0.587445i) q^{28} +0.0999734i q^{29} +(7.25432 - 6.12150i) q^{30} -3.26002i q^{31} +(3.47324 + 4.46504i) q^{32} +(-0.283625 - 1.09015i) q^{33} +(3.88878 + 8.12535i) q^{34} +1.81455 q^{35} +(-1.00906 + 5.91454i) q^{36} -3.38856 q^{37} +(-4.37350 - 9.13814i) q^{38} +(1.49354 + 5.74062i) q^{39} +(-10.6676 - 2.51640i) q^{40} +6.03791i q^{41} +(-0.876599 + 0.739711i) q^{42} +6.56050i q^{43} +(-0.815884 + 1.01299i) q^{44} +(-5.66562 - 10.1512i) q^{45} +(1.27564 - 0.610520i) q^{46} +0.906570 q^{47} +(6.17931 - 3.13306i) q^{48} +6.78073 q^{49} +(12.7773 - 6.11517i) q^{50} +(10.6770 - 2.77786i) q^{51} +(4.29637 - 5.33433i) q^{52} -6.73216i q^{53} +(6.87525 + 2.59440i) q^{54} -2.52017i q^{55} +(1.28906 + 0.304078i) q^{56} +(-12.0079 + 3.12411i) q^{57} +(-0.0610358 - 0.127530i) q^{58} +11.2912 q^{59} +(-5.51663 + 12.2378i) q^{60} +11.3593 q^{61} +(1.99031 + 4.15862i) q^{62} +(0.684623 + 1.22666i) q^{63} +(-7.15661 - 3.57532i) q^{64} +13.2710i q^{65} +(1.02736 + 1.21748i) q^{66} +6.94878i q^{67} +(-9.92138 - 7.99087i) q^{68} +(-0.436111 - 1.67625i) q^{69} +(-2.31471 + 1.10782i) q^{70} +9.43849 q^{71} +(-2.32374 - 8.16090i) q^{72} +2.07235 q^{73} +(4.32259 - 2.06879i) q^{74} +(-4.36823 - 16.7899i) q^{75} +(11.1580 + 8.98690i) q^{76} +0.304532i q^{77} +(-5.40999 - 6.41114i) q^{78} +5.03913i q^{79} +(15.1444 - 3.30277i) q^{80} +(4.72476 - 7.66007i) q^{81} +(-3.68627 - 7.70222i) q^{82} -4.30093 q^{83} +(0.666619 - 1.47879i) q^{84} +24.6828 q^{85} +(-4.00532 - 8.36886i) q^{86} +(-0.167580 + 0.0435995i) q^{87} +(0.422324 - 1.79033i) q^{88} -1.13288i q^{89} +(13.4248 + 9.49039i) q^{90} -1.60364i q^{91} +(-1.25453 + 1.55761i) q^{92} +(5.46460 - 1.42173i) q^{93} +(-1.15646 + 0.553479i) q^{94} -27.7594 q^{95} +(-5.96980 + 7.76927i) q^{96} +9.48994 q^{97} +(-8.64980 + 4.13977i) q^{98} +(1.70367 - 0.950851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.27564	+	0.610520i	−0.902016	+	0.431703i
$2$	−1.27564	+	0.610520i	−0.902016	+	0.431703i
$3$	0.436111	+	1.67625i	0.251789	+	0.967782i
$3$	0.436111	+	1.67625i	0.251789	+	0.967782i
$4$	1.25453	−	1.55761i	0.627265	−	0.778806i
$5$			3.87509i			1.73299i	0.499183	+	0.866497i	$0.333634\pi$
$5$			3.87509i			1.73299i	−0.499183	+	0.866497i	$0.666366\pi$
$6$	−1.57971	−	1.87204i	−0.644912	−	0.764257i
$7$		−	0.468259i		−	0.176985i	−0.996077	−	0.0884926i	$-0.971795\pi$
$7$		−	0.468259i		−	0.176985i	0.996077	−	0.0884926i	$-0.0282050\pi$
$8$	−0.649379	+	2.75287i	−0.229590	+	0.973287i
$9$	−2.61961	+	1.46206i	−0.873205	+	0.487353i
$10$	−2.36582	−	4.94323i	−0.748138	−	1.56319i
$11$	−0.650350			−0.196088			−0.0980439	−	0.995182i	$-0.531259\pi$
$11$	−0.650350			−0.196088			−0.0980439	+	0.995182i	$0.531259\pi$
$12$	3.15806	+	1.42361i	0.911653	+	0.410961i
$13$	3.42468			0.949836			0.474918	−	0.880030i	$-0.342478\pi$
$13$	3.42468			0.949836			0.474918	+	0.880030i	$0.342478\pi$
$14$	0.285881	+	0.597331i	0.0764050	+	0.159643i
$15$	−6.49561	+	1.68997i	−1.67716	+	0.436348i
$16$	−0.852308	−	3.90814i	−0.213077	−	0.977035i
$17$		−	6.36961i		−	1.54486i	−0.635101	−	0.772429i	$-0.719042\pi$
$17$		−	6.36961i		−	1.54486i	0.635101	−	0.772429i	$-0.280958\pi$
$18$	2.44908	−	3.46439i	0.577253	−	0.816566i
$19$			7.16356i			1.64343i	0.569896	+	0.821717i	$0.306983\pi$
$19$			7.16356i			1.64343i	−0.569896	+	0.821717i	$0.693017\pi$
$20$	6.03589	+	4.86142i	1.34967	+	1.08705i
$21$	0.784918	−	0.204213i	0.171283	−	0.0445629i
$22$	0.829614	−	0.397052i	0.176874	−	0.0846517i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−4.89770	+	0.112037i	−0.999738	+	0.0228695i
$25$	−10.0163			−2.00327
$26$	−4.36867	+	2.09084i	−0.856767	+	0.410047i
$27$	−3.59322	−	3.75350i	−0.691515	−	0.722362i
$28$	−0.729365	−	0.587445i	−0.137837	−	0.111017i
$29$			0.0999734i			0.0185646i	0.999957	+	0.00928230i	$0.00295469\pi$
$29$			0.0999734i			0.0185646i	−0.999957	+	0.00928230i	$0.997045\pi$
$30$	7.25432	−	6.12150i	1.32445	−	1.11763i
$31$		−	3.26002i		−	0.585516i	−0.956187	−	0.292758i	$-0.905427\pi$
$31$		−	3.26002i		−	0.585516i	0.956187	−	0.292758i	$-0.0945731\pi$
$32$	3.47324	+	4.46504i	0.613988	+	0.789315i
$33$	−0.283625	−	1.09015i	−0.0493727	−	0.189770i
$34$	3.88878	+	8.12535i	0.666920	+	1.39349i
$35$	1.81455			0.306714
$36$	−1.00906	+	5.91454i	−0.168177	+	0.985757i
$37$	−3.38856			−0.557076			−0.278538	−	0.960425i	$-0.589850\pi$
$37$	−3.38856			−0.557076			−0.278538	+	0.960425i	$0.589850\pi$
$38$	−4.37350	−	9.13814i	−0.709475	−	1.48240i
$39$	1.49354	+	5.74062i	0.239158	+	0.919235i
$40$	−10.6676	−	2.51640i	−1.68670	−	0.397879i
$41$			6.03791i			0.942963i	0.881876	+	0.471481i	$0.156281\pi$
$41$			6.03791i			0.942963i	−0.881876	+	0.471481i	$0.843719\pi$
$42$	−0.876599	+	0.739711i	−0.135262	+	0.114140i
$43$			6.56050i			1.00047i	0.865890	+	0.500234i	$0.166753\pi$
$43$			6.56050i			1.00047i	−0.865890	+	0.500234i	$0.833247\pi$
$44$	−0.815884	+	1.01299i	−0.122999	+	0.152714i
$45$	−5.66562	−	10.1512i	−0.844580	−	1.51326i
$46$	1.27564	−	0.610520i	0.188083	−	0.0900163i
$47$	0.906570			0.132237			0.0661184	−	0.997812i	$-0.478938\pi$
$47$	0.906570			0.132237			0.0661184	+	0.997812i	$0.478938\pi$
$48$	6.17931	−	3.13306i	0.891907	−	0.452219i
$49$	6.78073			0.968676
$50$	12.7773	−	6.11517i	1.80698	−	0.864816i
$51$	10.6770	−	2.77786i	1.49509	−	0.388978i
$52$	4.29637	−	5.33433i	0.595799	−	0.739738i
$53$		−	6.73216i		−	0.924733i	−0.886689	−	0.462367i	$-0.847000\pi$
$53$		−	6.73216i		−	0.924733i	0.886689	−	0.462367i	$-0.153000\pi$
$54$	6.87525	+	2.59440i	0.935603	+	0.353053i
$55$		−	2.52017i		−	0.339819i
$56$	1.28906	+	0.304078i	0.172257	+	0.0406341i
$57$	−12.0079	+	3.12411i	−1.59049	+	0.413798i
$58$	−0.0610358	−	0.127530i	−0.00801439	−	0.0167456i
$59$	11.2912			1.46999			0.734997	−	0.678070i	$-0.237183\pi$
$59$	11.2912			1.46999			0.734997	+	0.678070i	$0.237183\pi$
$60$	−5.51663	+	12.2378i	−0.712194	+	1.57989i
$61$	11.3593			1.45441			0.727206	−	0.686419i	$-0.240819\pi$
$61$	11.3593			1.45441			0.727206	+	0.686419i	$0.240819\pi$
$62$	1.99031	+	4.15862i	0.252769	+	0.528145i
$63$	0.684623	+	1.22666i	0.0862543	+	0.154544i
$64$	−7.15661	−	3.57532i	−0.894577	−	0.446915i
$65$			13.2710i			1.64606i
$66$	1.02736	+	1.21748i	0.126459	+	0.149862i
$67$			6.94878i			0.848929i	0.905445	+	0.424465i	$0.139538\pi$
$67$			6.94878i			0.848929i	−0.905445	+	0.424465i	$0.860462\pi$
$68$	−9.92138	−	7.99087i	−1.20314	−	0.969035i
$69$	−0.436111	−	1.67625i	−0.0525016	−	0.201797i
$70$	−2.31471	+	1.10782i	−0.276661	+	0.132409i
$71$	9.43849			1.12014			0.560071	−	0.828444i	$-0.310774\pi$
$71$	9.43849			1.12014			0.560071	+	0.828444i	$0.310774\pi$
$72$	−2.32374	−	8.16090i	−0.273856	−	0.961771i
$73$	2.07235			0.242550			0.121275	−	0.992619i	$-0.461302\pi$
$73$	2.07235			0.242550			0.121275	+	0.992619i	$0.461302\pi$
$74$	4.32259	−	2.06879i	0.502491	−	0.240491i
$75$	−4.36823	−	16.7899i	−0.504400	−	1.93873i
$76$	11.1580	+	8.98690i	1.27992	+	1.03087i
$77$			0.304532i			0.0347046i
$78$	−5.40999	−	6.41114i	−0.612561	−	0.725919i
$79$			5.03913i			0.566946i	0.958980	+	0.283473i	$0.0914867\pi$
$79$			5.03913i			0.566946i	−0.958980	+	0.283473i	$0.908513\pi$
$80$	15.1444	−	3.30277i	1.69320	−	0.369261i
$81$	4.72476	−	7.66007i	0.524973	−	0.851119i
$82$	−3.68627	−	7.70222i	−0.407080	−	0.850568i
$83$	−4.30093			−0.472089			−0.236044	−	0.971742i	$-0.575851\pi$
$83$	−4.30093			−0.472089			−0.236044	+	0.971742i	$0.575851\pi$
$84$	0.666619	−	1.47879i	0.0727341	−	0.161349i
$85$	24.6828			2.67723
$86$	−4.00532	−	8.36886i	−0.431905	−	0.902438i
$87$	−0.167580	+	0.0435995i	−0.0179665	+	0.00467436i
$88$	0.422324	−	1.79033i	0.0450199	−	0.190850i
$89$		−	1.13288i		−	0.120085i	−0.998196	−	0.0600423i	$-0.980876\pi$
$89$		−	1.13288i		−	0.120085i	0.998196	−	0.0600423i	$-0.0191236\pi$
$90$	13.4248	+	9.49039i	1.41510	+	1.00038i
$91$		−	1.60364i		−	0.168107i
$92$	−1.25453	+	1.55761i	−0.130794	+	0.162392i
$93$	5.46460	−	1.42173i	0.566652	−	0.147426i
$94$	−1.15646	+	0.553479i	−0.119280	+	0.0570870i
$95$	−27.7594			−2.84806
$96$	−5.96980	+	7.76927i	−0.609290	+	0.792947i
$97$	9.48994			0.963557			0.481779	−	0.876293i	$-0.339991\pi$
$97$	9.48994			0.963557			0.481779	+	0.876293i	$0.339991\pi$
$98$	−8.64980	+	4.13977i	−0.873761	+	0.418180i
$99$	1.70367	−	0.950851i	0.171225	−	0.0955641i
$100$	−12.5658	+	15.6016i	−1.25658	+	1.56016i
$101$			1.26245i			0.125619i	0.998026	+	0.0628094i	$0.0200060\pi$
$101$			1.26245i			0.125619i	−0.998026	+	0.0628094i	$0.979994\pi$
$102$	−11.9242	+	10.0621i	−1.18067	+	0.996297i
$103$		−	12.5453i		−	1.23612i	−0.786129	−	0.618062i	$-0.787918\pi$
$103$		−	12.5453i		−	1.23612i	0.786129	−	0.618062i	$-0.212082\pi$
$104$	−2.22392	+	9.42772i	−0.218073	+	0.924464i
$105$	0.791343	+	3.04163i	0.0772272	+	0.296833i
$106$	4.11012	+	8.58783i	0.399210	+	0.834124i
$107$	4.01038			0.387698			0.193849	−	0.981031i	$-0.437903\pi$
$107$	4.01038			0.387698			0.193849	+	0.981031i	$0.437903\pi$
$108$	−10.3543	+	0.887956i	−0.996343	+	0.0854436i
$109$	−11.3082			−1.08313			−0.541565	−	0.840659i	$-0.682168\pi$
$109$	−11.3082			−1.08313			−0.541565	+	0.840659i	$0.682168\pi$
$110$	1.53861	+	3.21483i	0.146701	+	0.306522i
$111$	−1.47779	−	5.68007i	−0.140266	−	0.539128i
$112$	−1.83002	+	0.399101i	−0.172921	+	0.0377115i
$113$			5.70743i			0.536909i	0.963292	+	0.268455i	$0.0865130\pi$
$113$			5.70743i			0.536909i	−0.963292	+	0.268455i	$0.913487\pi$
$114$	13.4105	−	11.3163i	1.25601	−	1.05987i
$115$		−	3.87509i		−	0.361354i
$116$	0.155720	+	0.125420i	0.0144582	+	0.0116449i
$117$	−8.97135	+	5.00709i	−0.829402	+	0.462906i
$118$	−14.4036	+	6.89353i	−1.32596	+	0.634601i
$119$	−2.98263			−0.273417
$120$	−0.434154	−	18.9790i	−0.0396326	−	1.73254i
$121$	−10.5770			−0.961550
$122$	−14.4904	+	6.93509i	−1.31190	+	0.627874i
$123$	−10.1210	+	2.63320i	−0.912583	+	0.237428i
$124$	−5.07784	−	4.08979i	−0.456004	−	0.367274i
$125$		−	19.4388i		−	1.73865i
$126$	−1.62223	−	1.14680i	−0.144520	−	0.102165i
$127$		−	15.8316i		−	1.40482i	−0.711771	−	0.702412i	$-0.752107\pi$
$127$		−	15.8316i		−	1.40482i	0.711771	−	0.702412i	$-0.247893\pi$
$128$	11.3121	+	0.191572i	0.999857	+	0.0169327i
$129$	−10.9970	+	2.86111i	−0.968235	+	0.251907i
$130$	−8.10219	−	16.9290i	−0.710609	−	1.48477i
$131$	1.78820			0.156236			0.0781180	−	0.996944i	$-0.475109\pi$
$131$	1.78820			0.156236			0.0781180	+	0.996944i	$0.475109\pi$
$132$	−2.05384	−	0.925846i	−0.178764	−	0.0805845i
$133$	3.35440			0.290863
$134$	−4.24237	−	8.86417i	−0.366485	−	0.765747i
$135$	14.5452	−	13.9240i	1.25185	−	1.19839i
$136$	17.5347	+	4.13629i	1.50359	+	0.354684i
$137$			19.7014i			1.68320i	0.540101	+	0.841600i	$0.318386\pi$
$137$			19.7014i			1.68320i	−0.540101	+	0.841600i	$0.681614\pi$
$138$	1.57971	+	1.87204i	0.134473	+	0.159359i
$139$			18.6264i			1.57987i	0.613192	+	0.789934i	$0.289885\pi$
$139$			18.6264i			1.57987i	−0.613192	+	0.789934i	$0.710115\pi$
$140$	2.27640	−	2.82636i	0.192391	−	0.238871i
$141$	0.395365	+	1.51964i	0.0332957	+	0.127976i
$142$	−12.0401	+	5.76239i	−1.01039	+	0.483569i
$143$	−2.22724			−0.186251
$144$	7.94666	+	8.99170i	0.662221	+	0.749308i
$145$	−0.387406			−0.0321723
$146$	−2.64358	+	1.26521i	−0.218784	+	0.104710i
$147$	2.95715	+	11.3662i	0.243902	+	0.937468i
$148$	−4.25105	+	5.27806i	−0.349434	+	0.433854i
$149$		−	2.90017i		−	0.237591i	−0.992919	−	0.118795i	$-0.962097\pi$
$149$		−	2.90017i		−	0.237591i	0.992919	−	0.118795i	$-0.0379033\pi$
$150$	15.8229	+	18.7510i	1.29193	+	1.53101i
$151$			9.50248i			0.773301i	0.922226	+	0.386651i	$0.126368\pi$
$151$			9.50248i			0.773301i	−0.922226	+	0.386651i	$0.873632\pi$
$152$	−19.7204	−	4.65187i	−1.59953	−	0.377316i
$153$	9.31275	+	16.6859i	0.752892	+	1.34898i
$154$	−0.185923	−	0.388474i	−0.0149821	−	0.0313041i
$155$	12.6329			1.01470
$156$	10.8153	+	4.87542i	0.865921	+	0.390346i
$157$	−14.5494			−1.16117			−0.580583	−	0.814201i	$-0.697175\pi$
$157$	−14.5494			−1.16117			−0.580583	+	0.814201i	$0.697175\pi$
$158$	−3.07649	−	6.42813i	−0.244752	−	0.511395i
$159$	11.2848	−	2.93597i	0.894940	−	0.232837i
$160$	−17.3024	+	13.4591i	−1.36788	+	1.06404i
$161$			0.468259i			0.0369040i
$162$	−1.35048	+	12.6561i	−0.106104	+	0.994355i
$163$		−	23.4151i		−	1.83401i	−0.398876	−	0.917005i	$-0.630600\pi$
$163$		−	23.4151i		−	1.83401i	0.398876	−	0.917005i	$-0.369400\pi$
$164$	9.40472	+	7.57474i	0.734385	+	0.591488i
$165$	4.22442	−	1.09907i	0.328871	−	0.0855626i
$166$	5.48645	−	2.62581i	0.425831	−	0.203802i
$167$	−10.7461			−0.831557			−0.415778	−	0.909466i	$-0.636491\pi$
$167$	−10.7461			−0.831557			−0.415778	+	0.909466i	$0.636491\pi$
$168$	0.0524623	+	2.29339i	0.00404756	+	0.176939i
$169$	−1.27154			−0.0978111
$170$	−31.4865	+	15.0694i	−2.41490	+	1.15577i
$171$	−10.4736	−	18.7658i	−0.800933	−	1.43505i
$172$	10.2187	+	8.23035i	0.779170	+	0.627558i
$173$		−	8.11918i		−	0.617290i	−0.951177	−	0.308645i	$-0.900125\pi$
$173$		−	8.11918i		−	0.617290i	0.951177	−	0.308645i	$-0.0998755\pi$
$174$	0.187154	−	0.157929i	0.0141881	−	0.0119725i
$175$			4.69024i			0.354549i
$176$	0.554298	+	2.54166i	0.0417818	+	0.191585i
$177$	4.92423	+	18.9269i	0.370128	+	1.42263i
$178$	0.691644	+	1.44515i	0.0518409	+	0.108318i
$179$	5.62429			0.420379			0.210190	−	0.977661i	$-0.432592\pi$
$179$	5.62429			0.420379			0.210190	+	0.977661i	$0.432592\pi$
$180$	−22.9194	−	3.91021i	−1.70831	−	0.291450i
$181$	7.09966			0.527714			0.263857	−	0.964562i	$-0.415005\pi$
$181$	7.09966			0.527714			0.263857	+	0.964562i	$0.415005\pi$
$182$	0.979053	+	2.04567i	0.0725723	+	0.151635i
$183$	4.95392	+	19.0410i	0.366205	+	1.40755i
$184$	0.649379	−	2.75287i	0.0478729	−	0.202944i
$185$		−	13.1310i		−	0.965409i
$186$	−6.10288	+	5.14987i	−0.447485	+	0.377606i
$187$			4.14248i			0.302928i
$188$	1.13732	−	1.41208i	0.0829475	−	0.102987i
$189$	−1.75761	+	1.68256i	−0.127847	+	0.122388i
$190$	35.4111	−	16.9477i	2.56899	−	1.22952i
$191$	25.8417			1.86984			0.934919	−	0.354862i	$-0.115472\pi$
$191$	25.8417			1.86984			0.934919	+	0.354862i	$0.115472\pi$
$192$	2.87204	−	13.5555i	0.207272	−	0.978283i
$193$	21.7934			1.56872			0.784360	−	0.620306i	$-0.212991\pi$
$193$	21.7934			1.56872			0.784360	+	0.620306i	$0.212991\pi$
$194$	−12.1058	+	5.79380i	−0.869144	+	0.415971i
$195$	−22.2454	+	5.78761i	−1.59303	+	0.414460i
$196$	8.50664	−	10.5617i	0.607617	−	0.754411i
$197$		−	25.1954i		−	1.79510i	−0.440915	−	0.897549i	$-0.645346\pi$
$197$		−	25.1954i		−	1.79510i	0.440915	−	0.897549i	$-0.354654\pi$
$198$	−1.59276	+	2.25307i	−0.113192	+	0.160119i
$199$		−	8.27498i		−	0.586598i	−0.956021	−	0.293299i	$-0.905247\pi$
$199$		−	8.27498i		−	0.586598i	0.956021	−	0.293299i	$-0.0947531\pi$
$200$	6.50440	−	27.5737i	0.459931	−	1.94975i
$201$	−11.6479	+	3.03044i	−0.821578	+	0.213751i
$202$	−0.770754	−	1.61044i	−0.0542300	−	0.113310i
$203$	0.0468134			0.00328566
$204$	9.06785	−	20.1156i	0.634877	−	1.40837i
$205$	−23.3974			−1.63415
$206$	7.65916	+	16.0033i	0.533639	+	1.11500i
$207$	2.61961	−	1.46206i	0.182076	−	0.101620i
$208$	−2.91888	−	13.3841i	−0.202388	−	0.928024i
$209$		−	4.65882i		−	0.322257i
$210$	−2.86645	−	3.39690i	−0.197804	−	0.234408i
$211$		−	6.41193i		−	0.441415i	−0.975340	−	0.220708i	$-0.929163\pi$
$211$		−	6.41193i		−	0.441415i	0.975340	−	0.220708i	$-0.0708367\pi$
$212$	−10.4861	−	8.44570i	−0.720188	−	0.580053i
$213$	4.11623	+	15.8212i	0.282039	+	1.08405i
$214$	−5.11581	+	2.44842i	−0.349710	+	0.167370i
$215$	−25.4226			−1.73380
$216$	12.6663	−	7.45422i	0.861831	−	0.507196i
$217$	−1.52653			−0.103628
$218$	14.4252	−	6.90389i	0.977001	−	0.467591i
$219$	0.903775	+	3.47378i	0.0610715	+	0.234736i
$220$	−3.92544	−	3.16162i	−0.264653	−	0.213157i
$221$		−	21.8139i		−	1.46736i
$222$	5.35293	+	6.34352i	0.359265	+	0.425749i
$223$		−	19.2125i		−	1.28656i	−0.765630	−	0.643281i	$-0.777573\pi$
$223$		−	19.2125i		−	1.28656i	0.765630	−	0.643281i	$-0.222427\pi$
$224$	2.09080	−	1.62637i	0.139697	−	0.108667i
$225$	26.2389	−	14.6445i	1.74926	−	0.976299i
$226$	−3.48450	−	7.28064i	−0.231785	−	0.484301i
$227$	−14.4610			−0.959811			−0.479905	−	0.877320i	$-0.659329\pi$
$227$	−14.4610			−0.959811			−0.479905	+	0.877320i	$0.659329\pi$
$228$	−10.1981	+	22.6229i	−0.675388	+	1.49824i
$229$	−11.4885			−0.759183			−0.379592	−	0.925154i	$-0.623936\pi$
$229$	−11.4885			−0.759183			−0.379592	+	0.925154i	$0.623936\pi$
$230$	2.36582	+	4.94323i	0.155998	+	0.325947i
$231$	−0.510471	+	0.132810i	−0.0335865	+	0.00873824i
$232$	−0.275214	−	0.0649207i	−0.0180687	−	0.00426225i
$233$		−	1.02311i		−	0.0670260i	−0.999438	−	0.0335130i	$-0.989330\pi$
$233$		−	1.02311i		−	0.0670260i	0.999438	−	0.0335130i	$-0.0106695\pi$
$234$	8.38731	−	11.8645i	0.548295	−	0.775604i
$235$			3.51304i			0.229166i
$236$	14.1652	−	17.5874i	0.922076	−	1.14484i
$237$	−8.44683	+	2.19762i	−0.548681	+	0.142751i
$238$	3.80477	−	1.82095i	0.246626	−	0.118035i
$239$	−1.34526			−0.0870177			−0.0435089	−	0.999053i	$-0.513854\pi$
$239$	−1.34526			−0.0870177			−0.0435089	+	0.999053i	$0.513854\pi$
$240$	12.1409	+	23.9454i	0.783692	+	1.54567i
$241$	−2.24734			−0.144764			−0.0723819	−	0.997377i	$-0.523060\pi$
$241$	−2.24734			−0.144764			−0.0723819	+	0.997377i	$0.523060\pi$
$242$	13.4925	−	6.45750i	0.867333	−	0.415104i
$243$	14.9007	+	4.57923i	0.955880	+	0.293758i
$244$	14.2506	−	17.6934i	0.912302	−	1.13270i
$245$			26.2760i			1.67871i
$246$	11.3032	−	9.53812i	0.720666	−	0.608128i
$247$			24.5329i			1.56099i
$248$	8.97441	+	2.11699i	0.569876	+	0.134429i
$249$	−1.87568	−	7.20943i	−0.118867	−	0.456879i
$250$	11.8678	+	24.7969i	0.750582	+	1.56829i
$251$	−21.4504			−1.35394			−0.676968	−	0.736013i	$-0.736706\pi$
$251$	−21.4504			−1.35394			−0.676968	+	0.736013i	$0.736706\pi$
$252$	2.76954	+	0.472503i	0.174464	+	0.0297649i
$253$	0.650350			0.0408871
$254$	9.66548	+	20.1954i	0.606466	+	1.26717i
$255$	10.7645	+	41.3745i	0.674096	+	2.59097i
$256$	−14.5471	+	6.66188i	−0.909196	+	0.416367i
$257$		−	5.95991i		−	0.371769i	−0.982572	−	0.185884i	$-0.940485\pi$
$257$		−	5.95991i		−	0.371769i	0.982572	−	0.185884i	$-0.0595150\pi$
$258$	12.2815	−	10.3637i	0.764614	−	0.645213i
$259$			1.58672i			0.0985942i
$260$	20.6710	+	16.6488i	1.28196	+	1.03252i
$261$	−0.146167	−	0.261892i	−0.00904752	−	0.0162107i
$262$	−2.28111	+	1.09173i	−0.140927	+	0.0674475i
$263$	15.1457			0.933922			0.466961	−	0.884278i	$-0.345349\pi$
$263$	15.1457			0.933922			0.466961	+	0.884278i	$0.345349\pi$
$264$	3.18522	−	0.0728633i	0.196037	−	0.00448443i
$265$	26.0877			1.60256
$266$	−4.27902	+	2.04793i	−0.262363	+	0.125567i
$267$	1.89898	−	0.494060i	0.116216	−	0.0302360i
$268$	10.8235	+	8.71746i	0.661151	+	0.532504i
$269$		−	3.51147i		−	0.214098i	−0.994254	−	0.107049i	$-0.965860\pi$
$269$		−	3.51147i		−	0.214098i	0.994254	−	0.107049i	$-0.0341402\pi$
$270$	−10.0535	+	26.6422i	−0.611838	+	1.62139i
$271$			0.944202i			0.0573562i	0.999589	+	0.0286781i	$0.00912977\pi$
$271$			0.944202i			0.0573562i	−0.999589	+	0.0286781i	$0.990870\pi$
$272$	−24.8933	+	5.42887i	−1.50938	+	0.329174i
$273$	2.68809	−	0.699364i	0.162691	−	0.0423274i
$274$	−12.0281	−	25.1319i	−0.726643	−	1.51827i
$275$	6.51412			0.392816
$276$	−3.15806	−	1.42361i	−0.190093	−	0.0856914i
$277$	0.105667			0.00634892			0.00317446	−	0.999995i	$-0.498990\pi$
$277$	0.105667			0.00634892			0.00317446	+	0.999995i	$0.498990\pi$
$278$	−11.3718	−	23.7606i	−0.682033	−	1.42507i
$279$	4.76634	+	8.53999i	0.285353	+	0.511276i
$280$	−1.17833	+	4.99521i	−0.0704186	+	0.298521i
$281$			15.5345i			0.926713i	0.886172	+	0.463357i	$0.153355\pi$
$281$			15.5345i			0.926713i	−0.886172	+	0.463357i	$0.846645\pi$
$282$	−1.43211	−	1.69713i	−0.0852811	−	0.101063i
$283$			3.64088i			0.216428i	0.994128	+	0.108214i	$0.0345132\pi$
$283$			3.64088i			0.216428i	−0.994128	+	0.108214i	$0.965487\pi$
$284$	11.8409	−	14.7015i	0.702626	−	0.872374i
$285$	−12.1062	−	46.5317i	−0.717109	−	2.75630i
$286$	2.84117	−	1.35978i	0.168002	−	0.0804053i
$287$	2.82730			0.166890
$288$	−15.6267	−	6.61860i	−0.920813	−	0.390005i
$289$	−23.5719			−1.38658
$290$	0.494192	−	0.236519i	0.0290200	−	0.0138889i
$291$	4.13867	+	15.9075i	0.242613	+	0.932514i
$292$	2.59983	−	3.22792i	0.152143	−	0.188900i
$293$			3.46683i			0.202535i	0.994859	+	0.101267i	$0.0322897\pi$
$293$			3.46683i			0.202535i	−0.994859	+	0.101267i	$0.967710\pi$
$294$	−10.7116	−	12.6938i	−0.624711	−	0.740318i
$295$			43.7546i			2.54749i
$296$	2.20046	−	9.32828i	0.127899	−	0.542195i
$297$	2.33685	+	2.44109i	0.135598	+	0.141646i
$298$	1.77061	+	3.69958i	0.102569	+	0.214311i
$299$	−3.42468			−0.198055
$300$	−31.6322	−	14.2594i	−1.82628	−	0.823265i
$301$	3.07201			0.177068
$302$	−5.80146	−	12.1218i	−0.333836	−	0.697530i
$303$	−2.11619	+	0.550570i	−0.121572	+	0.0316294i
$304$	27.9962	−	6.10556i	1.60569	−	0.350178i
$305$			44.0184i			2.52049i
$306$	−22.0668	−	15.5997i	−1.26148	−	0.891773i
$307$		−	21.0789i		−	1.20303i	−0.798860	−	0.601517i	$-0.794563\pi$
$307$		−	21.0789i		−	1.20303i	0.798860	−	0.601517i	$-0.205437\pi$
$308$	0.474343	+	0.382045i	0.0270282	+	0.0217690i
$309$	21.0290	−	5.47114i	1.19630	−	0.311242i
$310$	−16.1150	+	7.71262i	−0.915272	+	0.438047i
$311$	11.4899			0.651533			0.325766	−	0.945450i	$-0.394378\pi$
$311$	11.4899			0.651533			0.325766	+	0.945450i	$0.394378\pi$
$312$	−16.7731	+	0.383691i	−0.949588	+	0.0217223i
$313$	−15.2720			−0.863226			−0.431613	−	0.902059i	$-0.642055\pi$
$313$	−15.2720			−0.863226			−0.431613	+	0.902059i	$0.642055\pi$
$314$	18.5598	−	8.88268i	1.04739	−	0.501279i
$315$	−4.75341	+	2.65298i	−0.267824	+	0.149478i
$316$	7.84901	+	6.32174i	0.441541	+	0.355626i
$317$			8.93528i			0.501855i	0.968006	+	0.250928i	$0.0807356\pi$
$317$			8.93528i			0.501855i	−0.968006	+	0.250928i	$0.919264\pi$
$318$	−12.6029	+	10.6348i	−0.706734	+	0.596371i
$319$		−	0.0650177i		−	0.00364029i
$320$	13.8547	−	27.7325i	0.774500	−	1.55030i
$321$	1.74897	+	6.72239i	0.0976180	+	0.375207i
$322$	−0.285881	−	0.597331i	−0.0159315	−	0.0332880i
$323$	45.6291			2.53887
$324$	−6.00406	−	16.9691i	−0.333559	−	0.942729i
$325$	−34.3028			−1.90278
$326$	14.2954	+	29.8693i	0.791747	+	1.65431i
$327$	−4.93164	−	18.9554i	−0.272720	−	1.04823i
$328$	−16.6216	−	3.92089i	−0.917774	−	0.216495i
$329$		−	0.424509i		−	0.0234040i
$330$	−4.71785	+	3.98112i	−0.259709	+	0.219153i
$331$		−	9.83726i		−	0.540705i	−0.962761	−	0.270352i	$-0.912860\pi$
$331$		−	9.83726i		−	0.540705i	0.962761	−	0.270352i	$-0.0871402\pi$
$332$	−5.39565	+	6.69918i	−0.296125	+	0.367665i
$333$	8.87672	−	4.95428i	0.486441	−	0.271493i
$334$	13.7082	−	6.56070i	0.750077	−	0.358985i
$335$	−26.9272			−1.47119
$336$	−1.46708	−	2.89352i	−0.0800360	−	0.157854i
$337$	−17.7897			−0.969067			−0.484534	−	0.874773i	$-0.661011\pi$
$337$	−17.7897			−0.969067			−0.484534	+	0.874773i	$0.661011\pi$
$338$	1.62204	−	0.776304i	0.0882272	−	0.0422253i
$339$	−9.56706	+	2.48907i	−0.519611	+	0.135188i
$340$	30.9653	−	38.4463i	1.67933	−	2.08504i
$341$			2.12015i			0.114813i
$342$	24.8174	+	17.5441i	1.34197	+	0.948676i
$343$		−	6.45295i		−	0.348427i
$344$	−18.0602	−	4.26026i	−0.973742	−	0.229698i
$345$	6.49561	−	1.68997i	0.349712	−	0.0909849i
$346$	4.95692	+	10.3572i	0.266486	+	0.556805i
$347$	−15.5194			−0.833127			−0.416564	−	0.909107i	$-0.636766\pi$
$347$	−15.5194			−0.833127			−0.416564	+	0.909107i	$0.636766\pi$
$348$	−0.142323	+	0.315722i	−0.00762933	+	0.0169245i
$349$	−4.08923			−0.218892			−0.109446	−	0.993993i	$-0.534908\pi$
$349$	−4.08923			−0.218892			−0.109446	+	0.993993i	$0.534908\pi$
$350$	−2.86348	−	5.98307i	−0.153060	−	0.319808i
$351$	−12.3056	−	12.8546i	−0.656826	−	0.686126i
$352$	−2.25882	−	2.90384i	−0.120396	−	0.154775i
$353$		−	24.0178i		−	1.27834i	−0.769065	−	0.639170i	$-0.779278\pi$
$353$		−	24.0178i		−	1.27834i	0.769065	−	0.639170i	$-0.220722\pi$
$354$	−17.8368	−	21.1376i	−0.948017	−	1.12345i
$355$			36.5750i			1.94120i
$356$	−1.76458	−	1.42123i	−0.0935226	−	0.0753249i
$357$	−1.30076	−	4.99962i	−0.0688433	−	0.264608i
$358$	−7.17459	+	3.43374i	−0.379189	+	0.181479i
$359$	0.968568			0.0511191			0.0255595	−	0.999673i	$-0.491863\pi$
$359$	0.968568			0.0511191			0.0255595	+	0.999673i	$0.491863\pi$
$360$	31.6242	−	9.00471i	1.66674	−	0.474590i
$361$	−32.3166			−1.70087
$362$	−9.05663	+	4.33449i	−0.476006	+	0.227815i
$363$	−4.61277	−	17.7298i	−0.242107	−	0.930571i
$364$	−2.49784	−	2.01181i	−0.130923	−	0.105448i
$365$			8.03055i			0.420338i
$366$	−17.9444	−	21.2651i	−0.937967	−	1.11154i
$367$		−	15.5983i		−	0.814226i	−0.913378	−	0.407113i	$-0.866536\pi$
$367$		−	15.5983i		−	0.814226i	0.913378	−	0.407113i	$-0.133464\pi$
$368$	0.852308	+	3.90814i	0.0444296	+	0.203726i
$369$	−8.82779	−	15.8170i	−0.459556	−	0.823400i
$370$	8.01673	+	16.7504i	0.416770	+	0.870814i
$371$	−3.15239			−0.163664
$372$	4.64100	−	10.2953i	0.240625	−	0.533788i
$373$	17.3782			0.899810			0.449905	−	0.893077i	$-0.351458\pi$
$373$	17.3782			0.899810			0.449905	+	0.893077i	$0.351458\pi$
$374$	−2.52906	−	5.28432i	−0.130775	−	0.273246i
$375$	32.5842	−	8.47745i	1.68264	−	0.437774i
$376$	−0.588708	+	2.49567i	−0.0303603	+	0.128704i
$377$			0.342377i			0.0176333i
$378$	1.21485	−	3.21940i	0.0624851	−	0.165588i
$379$			20.7558i			1.06615i	0.846067	+	0.533077i	$0.178964\pi$
$379$			20.7558i			1.06615i	−0.846067	+	0.533077i	$0.821036\pi$
$380$	−34.8251	+	43.2384i	−1.78649	+	2.21808i
$381$	26.5376	−	6.90431i	1.35956	−	0.353719i
$382$	−32.9647	+	15.7769i	−1.68662	+	0.807214i
$383$	−16.3694			−0.836437			−0.418218	−	0.908347i	$-0.637345\pi$
$383$	−16.3694			−0.836437			−0.418218	+	0.908347i	$0.637345\pi$
$384$	4.61220	+	19.0454i	0.235366	+	0.971907i
$385$	−1.18009			−0.0601429
$386$	−27.8005	+	13.3053i	−1.41501	+	0.677221i
$387$	−9.59185	−	17.1860i	−0.487581	−	0.873613i
$388$	11.9054	−	14.7816i	0.604406	−	0.750424i
$389$			1.05108i			0.0532918i	0.999645	+	0.0266459i	$0.00848266\pi$
$389$			1.05108i			0.0532918i	−0.999645	+	0.0266459i	$0.991517\pi$
$390$	24.8438	−	20.9642i	1.25801	−	1.06156i
$391$			6.36961i			0.322125i
$392$	−4.40327	+	18.6665i	−0.222399	+	0.942800i
$393$	0.779855	+	2.99747i	0.0393385	+	0.151202i
$394$	15.3823	+	32.1403i	0.774949	+	1.61921i
$395$	−19.5271			−0.982514
$396$	0.656244	−	3.84652i	0.0329775	−	0.193295i
$397$	30.7621			1.54391			0.771953	−	0.635679i	$-0.219280\pi$
$397$	30.7621			1.54391			0.771953	+	0.635679i	$0.219280\pi$
$398$	5.05204	+	10.5559i	0.253236	+	0.529120i
$399$	1.46289	+	5.62280i	0.0732361	+	0.281492i
$400$	8.53700	+	39.1453i	0.426850	+	1.95726i
$401$		−	12.8169i		−	0.640043i	−0.947410	−	0.320022i	$-0.896310\pi$
$401$		−	12.8169i		−	0.640043i	0.947410	−	0.320022i	$-0.103690\pi$
$402$	13.0084	−	10.9770i	0.648800	−	0.547484i
$403$		−	11.1645i		−	0.556145i
$404$	1.96641	+	1.58379i	0.0978327	+	0.0787963i
$405$	29.6835	+	18.3089i	1.47498	+	0.909775i
$406$	−0.0597172	+	0.0285805i	−0.00296372	+	0.00141843i
$407$	2.20375			0.109236
$408$	0.713632	+	31.1964i	0.0353301	+	1.54445i
$409$	−0.977376			−0.0483281			−0.0241641	−	0.999708i	$-0.507692\pi$
$409$	−0.977376			−0.0483281			−0.0241641	+	0.999708i	$0.507692\pi$
$410$	29.8468	−	14.2846i	1.47403	−	0.705467i
$411$	−33.0244	+	8.59198i	−1.62897	+	0.423811i
$412$	−19.5407	−	15.7385i	−0.962701	−	0.775378i
$413$		−	5.28722i		−	0.260167i
$414$	−2.44908	+	3.46439i	−0.120365	+	0.170266i
$415$		−	16.6665i		−	0.818127i
$416$	11.8947	+	15.2914i	0.583188	+	0.749720i
$417$	−31.2224	+	8.12316i	−1.52897	+	0.397793i
$418$	2.84430	+	5.94299i	0.139119	+	0.290681i
$419$	20.3108			0.992248			0.496124	−	0.868252i	$-0.334756\pi$
$419$	20.3108			0.992248			0.496124	+	0.868252i	$0.334756\pi$
$420$	5.73044	+	2.58321i	0.279617	+	0.126048i
$421$	14.6184			0.712457			0.356228	−	0.934399i	$-0.384063\pi$
$421$	14.6184			0.712457			0.356228	+	0.934399i	$0.384063\pi$
$422$	3.91461	+	8.17933i	0.190560	+	0.398164i
$423$	−2.37486	+	1.32546i	−0.115470	+	0.0644461i
$424$	18.5328	+	4.37173i	0.900031	+	0.212310i
$425$			63.8001i			3.09476i
$426$	−14.9100	−	17.6692i	−0.722393	−	0.856077i
$427$		−	5.31910i		−	0.257409i
$428$	5.03114	−	6.24661i	0.243189	−	0.301941i
$429$	−0.971325	−	3.73341i	−0.0468960	−	0.180251i
$430$	32.4301	−	15.5210i	1.56392	−	0.748488i
$431$	−4.81034			−0.231706			−0.115853	−	0.993266i	$-0.536960\pi$
$431$	−4.81034			−0.231706			−0.115853	+	0.993266i	$0.536960\pi$
$432$	−11.6067	+	17.2419i	−0.558427	+	0.829554i
$433$	−13.7872			−0.662570			−0.331285	−	0.943531i	$-0.607482\pi$
$433$	−13.7872			−0.662570			−0.331285	+	0.943531i	$0.607482\pi$
$434$	1.94731	−	0.931978i	0.0934738	−	0.0447364i
$435$	−0.168952	−	0.649389i	−0.00810063	−	0.0311358i
$436$	−14.1865	+	17.6138i	−0.679410	+	0.843548i
$437$		−	7.16356i		−	0.342680i
$438$	−3.27370	−	3.87952i	−0.156424	−	0.185371i
$439$		−	1.52839i		−	0.0729462i	−0.999335	−	0.0364731i	$-0.988388\pi$
$439$		−	1.52839i		−	0.0729462i	0.999335	−	0.0364731i	$-0.0116123\pi$
$440$	6.93769	+	1.63654i	0.330742	+	0.0780191i
$441$	−17.7629	+	9.91384i	−0.845853	+	0.472088i
$442$	13.3178	+	27.8267i	0.633464	+	1.32358i
$443$	22.5150			1.06972			0.534859	−	0.844941i	$-0.320365\pi$
$443$	22.5150			1.06972			0.534859	+	0.844941i	$0.320365\pi$
$444$	−10.7013	−	4.82400i	−0.507860	−	0.228937i
$445$	4.39000			0.208106
$446$	11.7296	+	24.5083i	0.555413	+	1.16050i
$447$	4.86140	−	1.26479i	0.229936	−	0.0598227i
$448$	−1.67417	+	3.35115i	−0.0790973	+	0.158327i
$449$		−	36.4375i		−	1.71959i	−0.510637	−	0.859797i	$-0.670590\pi$
$449$		−	36.4375i		−	1.71959i	0.510637	−	0.859797i	$-0.329410\pi$
$450$	−24.5308	+	34.7005i	−1.15639	+	1.63580i
$451$		−	3.92675i		−	0.184904i
$452$	8.88995	+	7.16014i	0.418148	+	0.336785i
$453$	−15.9285	+	4.14414i	−0.748387	+	0.194709i
$454$	18.4471	−	8.82874i	0.865765	−	0.414353i
$455$	6.21424			0.291328
$456$	−0.802584	−	35.0850i	−0.0375844	−	1.64300i
$457$	−2.40072			−0.112301			−0.0561504	−	0.998422i	$-0.517883\pi$
$457$	−2.40072			−0.112301			−0.0561504	+	0.998422i	$0.517883\pi$
$458$	14.6553	−	7.01398i	0.684795	−	0.327742i
$459$	−23.9083	+	22.8874i	−1.11595	+	1.06829i
$460$	−6.03589	−	4.86142i	−0.281425	−	0.226665i
$461$		−	21.2277i		−	0.988671i	−0.869271	−	0.494336i	$-0.835411\pi$
$461$		−	21.2277i		−	0.988671i	0.869271	−	0.494336i	$-0.164589\pi$
$462$	0.570096	−	0.481071i	0.0265233	−	0.0223814i
$463$		−	16.9713i		−	0.788724i	−0.918955	−	0.394362i	$-0.870966\pi$
$463$		−	16.9713i		−	0.788724i	0.918955	−	0.394362i	$-0.129034\pi$
$464$	0.390710	−	0.0852081i	0.0181383	−	0.00395569i
$465$	5.50933	+	21.1758i	0.255489	+	0.982005i
$466$	0.624628	+	1.30512i	0.0289353	+	0.0604585i
$467$	−38.8587			−1.79817			−0.899083	−	0.437779i	$-0.855765\pi$
$467$	−38.8587			−1.79817			−0.899083	+	0.437779i	$0.855765\pi$
$468$	−3.45572	+	20.2554i	−0.159741	+	0.936308i
$469$	3.25383			0.150248
$470$	−2.14478	−	4.48139i	−0.0989314	−	0.206711i
$471$	−6.34514	−	24.3883i	−0.292369	−	1.12376i
$472$	−7.33230	+	31.0833i	−0.337496	+	1.43073i
$473$		−	4.26662i		−	0.196180i
$474$	9.43345	−	7.96034i	0.433293	−	0.365631i
$475$		−	71.7526i		−	3.29224i
$476$	−3.74179	+	4.64577i	−0.171505	+	0.212939i
$477$	9.84282	+	17.6357i	0.450672	+	0.807481i
$478$	1.71607	−	0.821309i	0.0784914	−	0.0375658i
$479$	3.81359			0.174247			0.0871237	−	0.996198i	$-0.472232\pi$
$479$	3.81359			0.174247			0.0871237	+	0.996198i	$0.472232\pi$
$480$	−30.1066	−	23.1335i	−1.37417	−	1.05590i
$481$	−11.6047			−0.529131
$482$	2.86680	−	1.37205i	0.130579	−	0.0624950i
$483$	−0.784918	+	0.204213i	−0.0357150	+	0.00929200i
$484$	−13.2692	+	16.4749i	−0.603146	+	0.748860i
$485$			36.7744i			1.66984i
$486$	−21.8037	+	3.25572i	−0.989035	+	0.147682i
$487$		−	7.03221i		−	0.318660i	−0.987225	−	0.159330i	$-0.949067\pi$
$487$		−	7.03221i		−	0.318660i	0.987225	−	0.159330i	$-0.0509333\pi$
$488$	−7.37651	+	31.2708i	−0.333919	+	1.41556i
$489$	39.2495	−	10.2116i	1.77492	−	0.461783i
$490$	−16.0420	−	33.5187i	−0.724704	−	1.51422i
$491$	28.0066			1.26392			0.631960	−	0.775001i	$-0.282251\pi$
$491$	28.0066			1.26392			0.631960	+	0.775001i	$0.282251\pi$
$492$	−8.59564	+	19.0681i	−0.387521	+	0.859655i
$493$	0.636792			0.0286797
$494$	−14.9778	−	31.2952i	−0.673885	−	1.40804i
$495$	3.68463	+	6.60186i	0.165612	+	0.296732i
$496$	−12.7406	+	2.77854i	−0.572070	+	0.124760i
$497$		−	4.41965i		−	0.198249i
$498$	6.79421	+	8.05151i	0.304456	+	0.360797i
$499$		−	18.2415i		−	0.816603i	−0.912847	−	0.408302i	$-0.866121\pi$
$499$		−	18.2415i		−	0.816603i	0.912847	−	0.408302i	$-0.133879\pi$
$500$	−30.2780	−	24.3865i	−1.35407	−	1.09060i
$501$	−4.68648	−	18.0131i	−0.209377	−	0.804766i
$502$	27.3630	−	13.0959i	1.22127	−	0.584498i
$503$	38.4575			1.71474			0.857369	−	0.514703i	$-0.172098\pi$
$503$	38.4575			1.71474			0.857369	+	0.514703i	$0.172098\pi$
$504$	−3.82141	+	1.08811i	−0.170219	+	0.0484684i
$505$	−4.89212			−0.217697
$506$	−0.829614	+	0.397052i	−0.0368809	+	0.0176511i
$507$	−0.554535	−	2.13142i	−0.0246277	−	0.0946599i
$508$	−24.6594	−	19.8612i	−1.09408	−	0.881197i
$509$			3.95004i			0.175083i	0.996161	+	0.0875413i	$0.0279010\pi$
$509$			3.95004i			0.175083i	−0.996161	+	0.0875413i	$0.972099\pi$
$510$	−38.9916	−	46.2072i	−1.72658	−	2.04609i
$511$		−	0.970397i		−	0.0429278i
$512$	14.4897	−	17.3795i	0.640362	−	0.768073i
$513$	26.8884	−	25.7402i	1.18715	−	1.13646i
$514$	3.63865	+	7.60272i	0.160494	+	0.335341i
$515$	48.6142			2.14220
$516$	−9.33961	+	20.7185i	−0.411154	+	0.912079i
$517$	−0.589588			−0.0259300
$518$	−0.968727	−	2.02409i	−0.0425634	−	0.0889335i
$519$	13.6098	−	3.54086i	0.597402	−	0.155427i
$520$	−36.5333	−	8.61789i	−1.60209	−	0.377919i
$521$			0.586194i			0.0256816i	0.999918	+	0.0128408i	$0.00408747\pi$
$521$			0.586194i			0.0256816i	−0.999918	+	0.0128408i	$0.995913\pi$
$522$	0.346347	+	0.244842i	0.0151592	+	0.0107165i
$523$			30.2320i			1.32195i	0.750407	+	0.660976i	$0.229857\pi$
$523$			30.2320i			1.32195i	−0.750407	+	0.660976i	$0.770143\pi$
$524$	2.24335	−	2.78532i	0.0980013	−	0.121677i
$525$	−7.86200	+	2.04546i	−0.343126	+	0.0892713i
$526$	−19.3205	+	9.24674i	−0.842413	+	0.403177i
$527$	−20.7650			−0.904539
$528$	−4.01872	+	2.03759i	−0.174892	+	0.0886746i
$529$	1.00000			0.0434783
$530$	−33.2786	+	15.9271i	−1.44553	+	0.691828i
$531$	−29.5787	+	16.5085i	−1.28361	+	0.716407i
$532$	4.20820	−	5.22485i	0.182448	−	0.226526i
$533$			20.6779i			0.895660i
$534$	−2.12079	+	1.78961i	−0.0917755	+	0.0774440i
$535$			15.5406i			0.671878i
$536$	−19.1291	−	4.51240i	−0.826252	−	0.194906i
$537$	2.45282	+	9.42771i	0.105847	+	0.406836i
$538$	2.14382	+	4.47938i	0.0924268	+	0.193120i
$539$	−4.40985			−0.189946
$540$	−3.44091	−	40.1239i	−0.148073	−	1.72666i
$541$	34.8848			1.49981			0.749907	−	0.661543i	$-0.230098\pi$
$541$	34.8848			1.49981			0.749907	+	0.661543i	$0.230098\pi$
$542$	−0.576454	−	1.20446i	−0.0247608	−	0.0517362i
$543$	3.09624	+	11.9008i	0.132872	+	0.510712i
$544$	28.4406	−	22.1232i	1.21938	−	0.948524i
$545$		−	43.8204i		−	1.87706i
$546$	−3.00207	+	2.53328i	−0.128477	+	0.108414i
$547$		−	3.84448i		−	0.164378i	−0.996617	−	0.0821890i	$-0.973809\pi$
$547$		−	3.84448i		−	0.164378i	0.996617	−	0.0821890i	$-0.0261911\pi$
$548$	30.6871	+	24.7159i	1.31089	+	1.05581i
$549$	−29.7570	+	16.6080i	−1.27000	+	0.708813i
$550$	−8.30969	+	3.97700i	−0.354327	+	0.169580i
$551$	−0.716166			−0.0305097
$552$	4.89770	−	0.112037i	0.208460	−	0.00476861i
$553$	2.35962			0.100341
$554$	−0.134793	+	0.0645118i	−0.00572682	+	0.00274085i
$555$	22.0108	−	5.72657i	0.934306	−	0.243079i
$556$	29.0126	+	23.3673i	1.23041	+	0.990996i
$557$			3.00842i			0.127471i	0.997967	+	0.0637355i	$0.0203014\pi$
$557$			3.00842i			0.127471i	−0.997967	+	0.0637355i	$0.979699\pi$
$558$	−11.2940	−	7.98403i	−0.478113	−	0.337991i
$559$			22.4677i			0.950280i
$560$	−1.54655	−	7.09150i	−0.0653537	−	0.299671i
$561$	−6.94382	+	1.80658i	−0.293168	+	0.0762738i
$562$	−9.48416	−	19.8165i	−0.400065	−	0.835910i
$563$	−28.4680			−1.19978			−0.599892	−	0.800081i	$-0.704790\pi$
$563$	−28.4680			−1.19978			−0.599892	+	0.800081i	$0.704790\pi$
$564$	2.86300	+	1.29060i	0.120554	+	0.0543442i
$565$	−22.1168			−0.930461
$566$	−2.22283	−	4.64447i	−0.0934327	−	0.195222i
$567$	−3.58689	−	2.21241i	−0.150635	−	0.0929125i
$568$	−6.12916	+	25.9830i	−0.257174	+	1.09022i
$569$		−	37.1462i		−	1.55725i	−0.627489	−	0.778626i	$-0.715917\pi$
$569$		−	37.1462i		−	1.55725i	0.627489	−	0.778626i	$-0.284083\pi$
$570$	43.8517	+	51.9668i	1.83675	+	2.17665i
$571$		−	22.4199i		−	0.938242i	−0.883134	−	0.469121i	$-0.844571\pi$
$571$		−	22.4199i		−	0.938242i	0.883134	−	0.469121i	$-0.155429\pi$
$572$	−2.79414	+	3.46918i	−0.116829	+	0.145054i
$573$	11.2698	+	43.3170i	0.470804	+	1.80960i
$574$	−3.60663	+	1.72613i	−0.150538	+	0.0720471i
$575$	10.0163			0.417710
$576$	23.9749	−	1.09745i	0.998954	−	0.0457270i
$577$	35.1004			1.46125			0.730625	−	0.682779i	$-0.239229\pi$
$577$	35.1004			1.46125			0.730625	+	0.682779i	$0.239229\pi$
$578$	30.0694	−	14.3911i	1.25072	−	0.598593i
$579$	9.50432	+	36.5311i	0.394986	+	1.51818i
$580$	−0.486013	+	0.603428i	−0.0201806	+	0.0250560i
$581$			2.01395i			0.0835527i
$582$	−14.9913	−	17.7655i	−0.621410	−	0.736405i
$583$			4.37826i			0.181329i
$584$	−1.34574	+	5.70492i	−0.0556872	+	0.236071i
$585$	−19.4029	−	34.7648i	−0.802213	−	1.43735i
$586$	−2.11657	−	4.42244i	−0.0874348	−	0.182689i
$587$	22.5164			0.929350			0.464675	−	0.885481i	$-0.346171\pi$
$587$	22.5164			0.929350			0.464675	+	0.885481i	$0.346171\pi$
$588$	21.4139	+	9.65313i	0.883096	+	0.398089i
$589$	23.3533			0.962257
$590$	−26.7131	−	55.8152i	−1.09976	−	2.29788i
$591$	42.2337	−	10.9880i	1.73726	−	0.451986i
$592$	2.88810	+	13.2430i	0.118700	+	0.544283i
$593$			41.8700i			1.71939i	0.510805	+	0.859697i	$0.329347\pi$
$593$			41.8700i			1.71939i	−0.510805	+	0.859697i	$0.670653\pi$
$594$	−4.47132	−	1.68727i	−0.183460	−	0.0692294i
$595$		−	11.5579i		−	0.473830i
$596$	−4.51733	−	3.63835i	−0.185037	−	0.149032i
$597$	13.8709	−	3.60881i	0.567699	−	0.147699i
$598$	4.36867	−	2.09084i	0.178648	−	0.0855007i
$599$	−32.2616			−1.31817			−0.659086	−	0.752068i	$-0.729057\pi$
$599$	−32.2616			−1.31817			−0.659086	+	0.752068i	$0.729057\pi$
$600$	49.0570	−	1.12220i	2.00274	−	0.0458136i
$601$	2.67401			0.109075			0.0545375	−	0.998512i	$-0.482632\pi$
$601$	2.67401			0.109075			0.0545375	+	0.998512i	$0.482632\pi$
$602$	−3.91879	+	1.87553i	−0.159718	+	0.0764407i
$603$	−10.1595	−	18.2031i	−0.413729	−	0.741289i
$604$	14.8012	+	11.9212i	0.602251	+	0.485065i
$605$		−	40.9870i		−	1.66636i
$606$	2.36336	−	1.99431i	0.0960051	−	0.0810131i
$607$			16.0950i			0.653276i	0.945150	+	0.326638i	$0.105916\pi$
$607$			16.0950i			0.653276i	−0.945150	+	0.326638i	$0.894084\pi$
$608$	−31.9856	+	24.8808i	−1.29719	+	1.00905i
$609$	0.0204159	+	0.0784709i	0.000827292	+	0.00317980i
$610$	−26.8741	−	56.1518i	−1.08810	−	2.27352i
$611$	3.10471			0.125603
$612$	37.6733	+	6.42734i	1.52285	+	0.259810i
$613$	−35.6282			−1.43901			−0.719505	−	0.694487i	$-0.755631\pi$
$613$	−35.6282			−1.43901			−0.719505	+	0.694487i	$0.755631\pi$
$614$	12.8691	+	26.8891i	0.519354	+	1.08516i
$615$	−10.2039	−	39.2199i	−0.411460	−	1.58150i
$616$	−0.838338	−	0.197757i	−0.0337776	−	0.00796785i
$617$			19.9256i			0.802176i	0.916040	+	0.401088i	$0.131368\pi$
$617$			19.9256i			0.802176i	−0.916040	+	0.401088i	$0.868632\pi$
$618$	−23.4853	+	19.8179i	−0.944717	+	0.797192i
$619$			9.47590i			0.380869i	0.981700	+	0.190434i	$0.0609896\pi$
$619$			9.47590i			0.380869i	−0.981700	+	0.190434i	$0.939010\pi$
$620$	15.8483	−	19.6771i	0.636483	−	0.790251i
$621$	3.59322	+	3.75350i	0.144191	+	0.150623i
$622$	−14.6570	+	7.01482i	−0.587693	+	0.281269i
$623$	−0.530479			−0.0212532
$624$	21.1622	−	10.7297i	0.847166	−	0.429534i
$625$	25.2453			1.00981
$626$	19.4816	−	9.32388i	0.778643	−	0.372657i
$627$	7.80934	−	2.03176i	0.311875	−	0.0811408i
$628$	−18.2526	+	22.6623i	−0.728359	+	0.904323i
$629$			21.5838i			0.860603i
$630$	4.44396	−	6.28630i	0.177052	−	0.250452i
$631$		−	12.6249i		−	0.502588i	−0.967911	−	0.251294i	$-0.919144\pi$
$631$		−	12.6249i		−	0.502588i	0.967911	−	0.251294i	$-0.0808562\pi$
$632$	−13.8721	−	3.27231i	−0.551802	−	0.130165i
$633$	10.7480	−	2.79631i	0.427194	−	0.111143i
$634$	−5.45517	−	11.3982i	−0.216652	−	0.452681i
$635$	61.3487			2.43455
$636$	9.58398	−	21.2605i	0.380030	−	0.843036i
$637$	23.2219			0.920084
$638$	0.0396946	+	0.0829394i	0.00157153	+	0.00328360i
$639$	−24.7252	+	13.7996i	−0.978114	+	0.545905i
$640$	−0.742359	+	43.8354i	−0.0293443	+	1.73275i
$641$			0.879059i			0.0347208i	0.999849	+	0.0173604i	$0.00552626\pi$
$641$			0.879059i			0.0347208i	−0.999849	+	0.0173604i	$0.994474\pi$
$642$	−6.33521	−	7.50758i	−0.250031	−	0.296301i
$643$		−	21.1567i		−	0.834341i	−0.908828	−	0.417170i	$-0.863022\pi$
$643$		−	21.1567i		−	0.834341i	0.908828	−	0.417170i	$-0.136978\pi$
$644$	0.729365	+	0.587445i	0.0287410	+	0.0231486i
$645$	−11.0871	−	42.6145i	−0.436552	−	1.67794i
$646$	−58.2064	+	27.8575i	−2.29010	+	1.09604i
$647$	4.36350			0.171547			0.0857734	−	0.996315i	$-0.472664\pi$
$647$	4.36350			0.171547			0.0857734	+	0.996315i	$0.472664\pi$
$648$	18.0190	+	17.9809i	0.707854	+	0.706358i
$649$	−7.34326			−0.288248
$650$	43.7581	−	20.9425i	1.71633	−	0.821434i
$651$	−0.665737	−	2.55885i	−0.0260923	−	0.100289i
$652$	−36.4716	−	29.3749i	−1.42834	−	1.15041i
$653$		−	7.45159i		−	0.291603i	−0.989314	−	0.145802i	$-0.953424\pi$
$653$		−	7.45159i		−	0.291603i	0.989314	−	0.145802i	$-0.0465762\pi$
$654$	17.8636	+	21.1694i	0.698524	+	0.827790i
$655$			6.92945i			0.270756i
$656$	23.5970	−	5.14616i	0.921308	−	0.200924i
$657$	−5.42876	+	3.02990i	−0.211796	+	0.118208i
$658$	0.259171	+	0.541522i	0.0101036	+	0.0211107i
$659$	15.9899			0.622878			0.311439	−	0.950266i	$-0.399189\pi$
$659$	15.9899			0.622878			0.311439	+	0.950266i	$0.399189\pi$
$660$	3.58774	−	7.95883i	0.139653	−	0.309797i
$661$	8.79853			0.342223			0.171112	−	0.985252i	$-0.445264\pi$
$661$	8.79853			0.342223			0.171112	+	0.985252i	$0.445264\pi$
$662$	6.00585	+	12.5488i	0.233424	+	0.487724i
$663$	36.5655	−	9.51328i	1.42009	−	0.369465i
$664$	2.79294	−	11.8399i	0.108387	−	0.459478i
$665$			12.9986i			0.504064i
$666$	−8.29884	+	11.7393i	−0.321574	+	0.454889i
$667$		−	0.0999734i		−	0.00387099i
$668$	−13.4813	+	16.7382i	−0.521606	+	0.647621i
$669$	32.2049	−	8.37877i	1.24511	−	0.323942i
$670$	34.3495	−	16.4396i	1.32704	−	0.635116i
$671$	−7.38753			−0.285192
$672$	3.63803	+	2.79541i	0.140340	+	0.107835i
$673$	−14.1613			−0.545878			−0.272939	−	0.962031i	$-0.587996\pi$
$673$	−14.1613			−0.545878			−0.272939	+	0.962031i	$0.587996\pi$
$674$	22.6933	−	10.8610i	0.874114	−	0.418349i
$675$	35.9909	+	37.5963i	1.38529	+	1.44708i
$676$	−1.59519	+	1.98057i	−0.0613535	+	0.0761759i
$677$		−	21.2166i		−	0.815420i	−0.913112	−	0.407710i	$-0.866327\pi$
$677$		−	21.2166i		−	0.815420i	0.913112	−	0.407710i	$-0.133673\pi$
$678$	10.6845	−	9.01605i	0.410337	−	0.346259i
$679$		−	4.44375i		−	0.170535i
$680$	−16.0285	+	67.9487i	−0.614666	+	2.60571i
$681$	−6.30660	−	24.2402i	−0.241670	−	0.928888i
$682$	−1.29440	−	2.70456i	−0.0495650	−	0.103563i
$683$	−42.2844			−1.61797			−0.808984	−	0.587831i	$-0.799982\pi$
$683$	−42.2844			−1.61797			−0.808984	+	0.587831i	$0.799982\pi$
$684$	−42.3692	−	7.22848i	−1.62003	−	0.276388i
$685$	−76.3446			−2.91698
$686$	3.93966	+	8.23166i	0.150417	+	0.314286i
$687$	−5.01027	−	19.2576i	−0.191154	−	0.734724i
$688$	25.6394	−	5.59157i	0.977492	−	0.213177i
$689$		−	23.0555i		−	0.878345i
$690$	−7.25432	+	6.12150i	−0.276167	+	0.233042i
$691$		−	15.7530i		−	0.599273i	−0.954053	−	0.299637i	$-0.903135\pi$
$691$		−	15.7530i		−	0.599273i	0.954053	−	0.299637i	$-0.0968654\pi$
$692$	−12.6465	−	10.1858i	−0.480749	−	0.387204i
$693$	−0.445244	−	0.797756i	−0.0169134	−	0.0303043i
$694$	19.7973	−	9.47493i	0.751494	−	0.359664i
$695$	−72.1789			−2.73790
$696$	−0.0112007	−	0.489640i	−0.000424563	−	0.0185597i
$697$	38.4591			1.45674
$698$	5.21640	−	2.49656i	0.197444	−	0.0944962i
$699$	1.71498	−	0.446189i	0.0648666	−	0.0168764i
$700$	7.30557	+	5.88404i	0.276124	+	0.222396i
$701$			41.2671i			1.55864i	0.626627	+	0.779319i	$0.284435\pi$
$701$			41.2671i			1.55864i	−0.626627	+	0.779319i	$0.715565\pi$
$702$	23.5456	+	8.88499i	0.888670	+	0.335342i
$703$		−	24.2742i		−	0.915517i
$704$	4.65430	+	2.32521i	0.175416	+	0.0876345i
$705$	−5.88873	+	1.53208i	−0.221782	+	0.0577013i
$706$	14.6634	+	30.6382i	0.551863	+	1.15308i
$707$	0.591155			0.0222327
$708$	35.6584	+	16.0743i	1.34012	+	0.604111i
$709$	−28.7989			−1.08157			−0.540783	−	0.841162i	$-0.681872\pi$
$709$	−28.7989			−1.08157			−0.540783	+	0.841162i	$0.681872\pi$
$710$	−22.3298	−	46.6567i	−0.838022	−	1.75099i
$711$	−7.36751	−	13.2006i	−0.276303	−	0.495060i
$712$	3.11866	+	0.735667i	0.116877	+	0.0275703i
$713$			3.26002i			0.122089i
$714$	4.71167	+	5.58359i	0.176330	+	0.208961i
$715$		−	8.63077i		−	0.322772i
$716$	7.05584	−	8.76046i	0.263689	−	0.327394i
$717$	−0.586683	−	2.25499i	−0.0219101	−	0.0842142i
$718$	−1.23555	+	0.591331i	−0.0461102	+	0.0220683i
$719$	−44.8244			−1.67167			−0.835834	−	0.548982i	$-0.815016\pi$
$719$	−44.8244			−1.67167			−0.835834	+	0.548982i	$0.815016\pi$
$720$	−34.8437	+	30.7940i	−1.29855	+	1.14763i
$721$	−5.87444			−0.218776
$722$	41.2244	−	19.7299i	1.53421	−	0.734272i
$723$	−0.980089	−	3.76710i	−0.0364499	−	0.140100i
$724$	8.90674	−	11.0585i	0.331016	−	0.410986i
$725$		−	1.00137i		−	0.0371898i
$726$	16.7086	+	19.8006i	0.620115	+	0.734871i
$727$			40.1016i			1.48728i	0.668578	+	0.743642i	$0.266903\pi$
$727$			40.1016i			1.48728i	−0.668578	+	0.743642i	$0.733097\pi$
$728$	4.41461	+	1.04137i	0.163616	+	0.0385957i
$729$	−1.17756	+	26.9743i	−0.0436135	+	0.999048i
$730$	−4.90281	−	10.2441i	−0.181461	−	0.379152i
$731$	41.7879			1.54558
$732$	35.8734	+	16.1713i	1.32592	+	0.597707i
$733$	26.9303			0.994693			0.497346	−	0.867552i	$-0.334308\pi$
$733$	26.9303			0.994693			0.497346	+	0.867552i	$0.334308\pi$
$734$	9.52309	+	19.8979i	0.351504	+	0.734445i
$735$	−44.0450	+	11.4592i	−1.62463	+	0.422680i
$736$	−3.47324	−	4.46504i	−0.128025	−	0.164584i
$737$		−	4.51914i		−	0.166465i
$738$	20.9177	+	14.7873i	0.769991	+	0.544328i
$739$			37.2743i			1.37116i	0.727998	+	0.685579i	$0.240451\pi$
$739$			37.2743i			1.37116i	−0.727998	+	0.685579i	$0.759549\pi$
$740$	−20.4530	−	16.4732i	−0.751866	−	0.605568i
$741$	−41.1233	+	10.6991i	−1.51070	+	0.393040i
$742$	4.02133	−	1.92460i	0.147628	−	0.0706543i
$743$	−46.3046			−1.69875			−0.849375	−	0.527790i	$-0.823021\pi$
$743$	−46.3046			−1.69875			−0.849375	+	0.527790i	$0.823021\pi$
$744$	0.365243	+	15.9666i	0.0133904	+	0.585363i
$745$	11.2384			0.411744
$746$	−22.1684	+	10.6097i	−0.811643	+	0.388450i
$747$	11.2668	−	6.28822i	0.412230	−	0.230074i
$748$	6.45237	+	5.19686i	0.235922	+	0.190016i
$749$		−	1.87789i		−	0.0686168i
$750$	−36.3901	+	30.7075i	−1.32878	+	1.12128i
$751$			38.1533i			1.39223i	0.717928	+	0.696117i	$0.245091\pi$
$751$			38.1533i			1.39223i	−0.717928	+	0.696117i	$0.754909\pi$
$752$	−0.772677	−	3.54300i	−0.0281766	−	0.129200i
$753$	−9.35475	−	35.9562i	−0.340906	−	1.31031i
$754$	−0.209028	−	0.436751i	−0.00761236	−	0.0159055i
$755$	−36.8230			−1.34013
$756$	0.415793	+	4.84849i	0.0151223	+	0.176338i
$757$	25.8675			0.940172			0.470086	−	0.882621i	$-0.344223\pi$
$757$	25.8675			0.940172			0.470086	+	0.882621i	$0.344223\pi$
$758$	−12.6718	−	26.4770i	−0.460262	−	0.961688i
$759$	0.283625	+	1.09015i	0.0102949	+	0.0395699i
$760$	18.0264	−	76.4182i	0.653887	−	2.77198i
$761$			16.9393i			0.614050i	0.951701	+	0.307025i	$0.0993335\pi$
$761$			16.9393i			0.614050i	−0.951701	+	0.307025i	$0.900666\pi$
$762$	−29.6373	+	25.0092i	−1.07365	+	0.905987i
$763$			5.29517i			0.191698i
$764$	32.4192	−	40.2513i	1.17288	−	1.45624i
$765$	−64.6595	+	36.0878i	−2.33777	+	1.30476i
$766$	20.8815	−	9.99384i	0.754479	−	0.361092i
$767$	38.6689			1.39625
$768$	−17.5111	−	21.4793i	−0.631879	−	0.775067i
$769$	3.61736			0.130445			0.0652226	−	0.997871i	$-0.479224\pi$
$769$	3.61736			0.130445			0.0652226	+	0.997871i	$0.479224\pi$
$770$	1.50537	−	0.720468i	0.0542499	−	0.0259639i
$771$	9.99029	−	2.59918i	0.359791	−	0.0936073i
$772$	27.3404	−	33.9456i	0.984004	−	1.22173i
$773$		−	27.0482i		−	0.972855i	−0.873721	−	0.486427i	$-0.838300\pi$
$773$		−	27.0482i		−	0.972855i	0.873721	−	0.486427i	$-0.161700\pi$
$774$	22.7282	+	16.0672i	0.816947	+	0.577523i
$775$			32.6534i			1.17295i
$776$	−6.16257	+	26.1246i	−0.221223	+	0.937818i
$777$	−2.65974	+	0.691988i	−0.0954177	+	0.0248249i
$778$	−0.641705	−	1.34080i	−0.0230062	−	0.0480701i
$779$	−43.2529			−1.54970
$780$	−18.8927	+	41.9105i	−0.676467	+	1.50064i
$781$	−6.13832			−0.219646
$782$	−3.88878	−	8.12535i	−0.139062	−	0.290562i
$783$	0.375251	−	0.359226i	0.0134104	−	0.0128377i
$784$	−5.77927	−	26.5001i	−0.206403	−	0.946431i
$785$		−	56.3801i		−	2.01229i
$786$	−2.82483	−	3.34758i	−0.100758	−	0.119404i
$787$			36.2469i			1.29206i	0.763310	+	0.646032i	$0.223573\pi$
$787$			36.2469i			1.29206i	−0.763310	+	0.646032i	$0.776427\pi$
$788$	−39.2447	−	31.6084i	−1.39803	−	1.12600i
$789$	6.60520	+	25.3879i	0.235151	+	0.903833i
$790$	24.9096	−	11.9217i	0.886244	−	0.424154i
$791$	2.67255			0.0950250
$792$	1.51125	+	5.30744i	0.0536998	+	0.188592i
$793$	38.9021			1.38145
$794$	−39.2415	+	18.7809i	−1.39263	+	0.666509i
$795$	11.3771	+	43.7295i	0.403506	+	1.55093i
$796$	−12.8892	−	10.3812i	−0.456846	−	0.367952i
$797$			19.4459i			0.688810i	0.938821	+	0.344405i	$0.111919\pi$
$797$			19.4459i			0.688810i	−0.938821	+	0.344405i	$0.888081\pi$
$798$	−5.29896	−	6.27957i	−0.187581	−	0.222294i
$799$		−	5.77450i		−	0.204287i
$800$	−34.7891	−	44.7234i	−1.22998	−	1.58121i
$801$	1.65633	+	2.96770i	0.0585237	+	0.104858i
$802$	7.82495	+	16.3497i	0.276309	+	0.577329i
$803$	−1.34775			−0.0475612
$804$	−9.89237	+	21.9447i	−0.348877	+	0.773929i
$805$	−1.81455			−0.0639543
$806$	6.81617	+	14.2419i	0.240089	+	0.501651i
$807$	5.88609	−	1.53139i	0.207200	−	0.0539075i
$808$	−3.47537	−	0.819812i	−0.122263	−	0.0288409i
$809$			21.5826i			0.758804i	0.925232	+	0.379402i	$0.123870\pi$
$809$			21.5826i			0.758804i	−0.925232	+	0.379402i	$0.876130\pi$
$810$	−49.0434	−	5.23323i	−1.72321	−	0.183877i
$811$			23.6598i			0.830810i	0.909637	+	0.415405i	$0.136360\pi$
$811$			23.6598i			0.830810i	−0.909637	+	0.415405i	$0.863640\pi$
$812$	0.0587289	−	0.0729172i	0.00206098	−	0.00255889i
$813$	−1.58272	+	0.411777i	−0.0555083	+	0.0144416i
$814$	−2.81120	+	1.34543i	−0.0985325	+	0.0471574i
$815$	90.7355			3.17833
$816$	−19.9564	−	39.3598i	−0.698613	−	1.37787i
$817$	−46.9966			−1.64420
$818$	1.24678	−	0.596708i	0.0435927	−	0.0208634i
$819$	2.34462	+	4.20091i	0.0819275	+	0.146792i
$820$	−29.3528	+	36.4441i	−1.02504	+	1.27268i
$821$			41.6011i			1.45189i	0.687754	+	0.725944i	$0.258597\pi$
$821$			41.6011i			1.45189i	−0.687754	+	0.725944i	$0.741403\pi$
$822$	36.8817	−	31.1223i	1.28640	−	1.08552i
$823$		−	44.5987i		−	1.55461i	−0.629121	−	0.777307i	$-0.716585\pi$
$823$		−	44.5987i		−	1.55461i	0.629121	−	0.777307i	$-0.283415\pi$
$824$	34.5356	+	8.14666i	1.20310	+	0.283802i
$825$	2.84088	+	10.9193i	0.0989068	+	0.380161i
$826$	3.22796	+	6.74461i	0.112315	+	0.234675i
$827$	14.3259			0.498161			0.249081	−	0.968483i	$-0.419872\pi$
$827$	14.3259			0.498161			0.249081	+	0.968483i	$0.419872\pi$
$828$	1.00906	−	5.91454i	0.0350674	−	0.205544i
$829$	−25.3692			−0.881109			−0.440555	−	0.897726i	$-0.645218\pi$
$829$	−25.3692			−0.881109			−0.440555	+	0.897726i	$0.645218\pi$
$830$	10.1752	+	21.2605i	0.353188	+	0.737963i
$831$	0.0460826	+	0.177124i	0.00159859	+	0.00614437i
$832$	−24.5091	−	12.2443i	−0.849701	−	0.424496i
$833$		−	43.1906i		−	1.49647i
$834$	34.8693	−	29.4242i	1.20742	−	1.01888i
$835$		−	41.6420i		−	1.44108i
$836$	−7.25663	−	5.84463i	−0.250976	−	0.202141i
$837$	−12.2365	+	11.7140i	−0.422955	+	0.404893i
$838$	−25.9093	+	12.4002i	−0.895024	+	0.428357i
$839$	−20.5882			−0.710783			−0.355392	−	0.934717i	$-0.615652\pi$
$839$	−20.5882			−0.710783			−0.355392	+	0.934717i	$0.615652\pi$
$840$	−8.88710	+	0.203296i	−0.306634	+	0.00701439i
$841$	28.9900			0.999655
$842$	−18.6478	+	8.92482i	−0.642647	+	0.307570i
$843$	−26.0398	+	6.77479i	−0.896857	+	0.233336i
$844$	−9.98729	−	8.04396i	−0.343777	−	0.276884i
$845$		−	4.92735i		−	0.169506i
$846$	2.22026	−	3.14072i	0.0763340	−	0.107980i
$847$			4.95279i			0.170180i
$848$	−26.3102	+	5.73787i	−0.903497	+	0.197039i
$849$	−6.10303	+	1.58783i	−0.209455	+	0.0544942i
$850$	−38.9513	−	81.3862i	−1.33602	−	2.79152i
$851$	3.38856			0.116158
$852$	29.8073	+	13.4367i	1.02118	+	0.460335i
$853$	−23.4787			−0.803896			−0.401948	−	0.915662i	$-0.631667\pi$
$853$	−23.4787			−0.803896			−0.401948	+	0.915662i	$0.631667\pi$
$854$	3.24742	+	6.78527i	0.111124	+	0.232187i
$855$	72.7190	−	40.5860i	2.48694	−	1.38801i
$856$	−2.60426	+	11.0401i	−0.0890117	+	0.377341i
$857$			9.96436i			0.340376i	0.985412	+	0.170188i	$0.0544375\pi$
$857$			9.96436i			0.340376i	−0.985412	+	0.170188i	$0.945563\pi$
$858$	3.51839	+	4.16949i	0.120116	+	0.142344i
$859$			17.8715i			0.609767i	0.952390	+	0.304883i	$0.0986175\pi$
$859$			17.8715i			0.609767i	−0.952390	+	0.304883i	$0.901383\pi$
$860$	−31.8934	+	39.5985i	−1.08755	+	1.35030i
$861$	1.23302	+	4.73926i	0.0420212	+	0.161514i
$862$	6.13628	−	2.93681i	0.209003	−	0.100028i
$863$	−12.8326			−0.436826			−0.218413	−	0.975856i	$-0.570088\pi$
$863$	−12.8326			−0.436826			−0.218413	+	0.975856i	$0.570088\pi$
$864$	4.27944	−	29.0807i	0.145589	−	0.989345i
$865$	31.4626			1.06976
$866$	17.5875	−	8.41736i	0.597649	−	0.286034i
$867$	−10.2800	−	39.5124i	−0.349126	−	1.34191i
$868$	−1.91508	+	2.37774i	−0.0650020	+	0.0807059i
$869$		−	3.27720i		−	0.111171i
$870$	0.611988	+	0.725240i	0.0207483	+	0.0245879i
$871$			23.7974i			0.806344i
$872$	7.34332	−	31.1301i	0.248676	−	1.05420i
$873$	−24.8600	+	13.8749i	−0.841383	+	0.469593i
$874$	4.37350	+	9.13814i	0.147936	+	0.309102i
$875$	−9.10237			−0.307716
$876$	6.54461	+	2.95022i	0.221122	+	0.0996789i
$877$	45.1340			1.52407			0.762034	−	0.647537i	$-0.224201\pi$
$877$	45.1340			1.52407			0.762034	+	0.647537i	$0.224201\pi$
$878$	0.933115	+	1.94968i	0.0314911	+	0.0657986i
$879$	−5.81127	+	1.51192i	−0.196009	+	0.0509959i
$880$	−9.84916	+	2.14796i	−0.332015	+	0.0724076i
$881$		−	23.1168i		−	0.778826i	−0.921063	−	0.389413i	$-0.872678\pi$
$881$		−	23.1168i		−	0.778826i	0.921063	−	0.389413i	$-0.127322\pi$
$882$	16.6065	−	23.4911i	0.559171	−	0.790988i
$883$			9.18562i			0.309121i	0.987983	+	0.154560i	$0.0493961\pi$
$883$			9.18562i			0.309121i	−0.987983	+	0.154560i	$0.950604\pi$
$884$	−33.9776	−	27.3662i	−1.14279	−	0.920425i
$885$	−73.3435	+	19.0819i	−2.46542	+	0.641430i
$886$	−28.7211	+	13.7458i	−0.964903	+	0.461801i
$887$	−46.6115			−1.56506			−0.782531	−	0.622612i	$-0.786072\pi$
$887$	−46.6115			−1.56506			−0.782531	+	0.622612i	$0.786072\pi$
$888$	16.5962	−	0.379644i	0.556930	−	0.0127400i
$889$	−7.41326			−0.248633
$890$	−5.60007	+	2.68018i	−0.187715	+	0.0898399i
$891$	−3.07275	+	4.98172i	−0.102941	+	0.166894i
$892$	−29.9256	−	24.1026i	−1.00198	−	0.807015i
$893$			6.49427i			0.217322i
$894$	−5.42923	+	4.58141i	−0.181580	+	0.153225i
$895$			21.7946i			0.728515i
$896$	0.0897053	−	5.29698i	0.00299684	−	0.176960i
$897$	−1.49354	−	5.74062i	−0.0498679	−	0.191674i
$898$	22.2458	+	46.4813i	0.742353	+	1.55110i
$899$	0.325915			0.0108699
$900$	10.1071	−	59.2420i	0.336904	−	1.97473i
$901$	−42.8812			−1.42858
$902$	2.39736	+	5.00914i	0.0798234	+	0.166786i
$903$	1.33974	+	5.14946i	0.0445837	+	0.171363i
$904$	−15.7118	−	3.70628i	−0.522567	−	0.123269i
$905$			27.5118i			0.914524i
$906$	17.7890	−	15.0111i	0.591001	−	0.498711i
$907$			1.64835i			0.0547324i	0.999625	+	0.0273662i	$0.00871202\pi$
$907$			1.64835i			0.0547324i	−0.999625	+	0.0273662i	$0.991288\pi$
$908$	−18.1418	+	22.5246i	−0.602056	+	0.747506i
$909$	−1.84578	−	3.30714i	−0.0612208	−	0.109691i
$910$	−7.92716	+	3.79392i	−0.262783	+	0.125767i
$911$	−46.9920			−1.55691			−0.778457	−	0.627698i	$-0.783997\pi$
$911$	−46.9920			−1.55691			−0.778457	+	0.627698i	$0.783997\pi$
$912$	22.4439	+	44.2659i	0.743191	+	1.46579i
$913$	2.79711			0.0925709
$914$	3.06246	−	1.46569i	0.101297	−	0.0484806i
$915$	−73.7857	+	19.1969i	−2.43928	+	0.634630i
$916$	−14.4127	+	17.8947i	−0.476209	+	0.591256i
$917$		−	0.837341i		−	0.0276514i
$918$	16.5253	−	43.7927i	0.545416	−	1.44537i
$919$		−	20.7172i		−	0.683397i	−0.939810	−	0.341699i	$-0.888998\pi$
$919$		−	20.7172i		−	0.683397i	0.939810	−	0.341699i	$-0.111002\pi$
$920$	10.6676	+	2.51640i	0.351701	+	0.0829634i
$921$	35.3334	−	9.19273i	1.16428	−	0.302911i
$922$	12.9599	+	27.0789i	0.426812	+	0.891797i
$923$	32.3238			1.06395
$924$	−0.433535	+	0.961730i	−0.0142623	+	0.0316386i
$925$	33.9410			1.11597
$926$	10.3613	+	21.6493i	0.340495	+	0.711442i
$927$	18.3420	+	32.8638i	0.602430	+	1.07939i
$928$	−0.446386	+	0.347232i	−0.0146533	+	0.0113984i
$929$		−	60.1880i		−	1.97470i	−0.158547	−	0.987351i	$-0.550681\pi$
$929$		−	60.1880i		−	1.97470i	0.158547	−	0.987351i	$-0.449319\pi$
$930$	−19.9562	−	23.6492i	−0.654390	−	0.775488i
$931$			48.5742i			1.59195i
$932$	−1.59361	−	1.28352i	−0.0522003	−	0.0420431i
$933$	5.01087	+	19.2599i	0.164049	+	0.630542i
$934$	49.5698	−	23.7240i	1.62197	−	0.776273i
$935$	−16.0525			−0.524972
$936$	−7.95808	−	27.9485i	−0.260118	−	0.913525i
$937$	−5.07326			−0.165736			−0.0828681	−	0.996561i	$-0.526408\pi$
$937$	−5.07326			−0.165736			−0.0828681	+	0.996561i	$0.526408\pi$
$938$	−4.15072	+	1.98653i	−0.135526	+	0.0648624i
$939$	−6.66030	−	25.5997i	−0.217351	−	0.835414i
$940$	5.47195	+	4.40722i	0.178475	+	0.143748i
$941$		−	18.3359i		−	0.597732i	−0.954295	−	0.298866i	$-0.903392\pi$
$941$		−	18.3359i		−	0.597732i	0.954295	−	0.298866i	$-0.0966083\pi$
$942$	22.9837	+	27.2370i	0.748850	+	0.887429i
$943$		−	6.03791i		−	0.196621i
$944$	−9.62361	−	44.1278i	−0.313222	−	1.43624i
$945$	−6.52006	−	6.81090i	−0.212098	−	0.221559i
$946$	2.60486	+	5.44269i	0.0846913	+	0.176957i
$947$	−40.1661			−1.30522			−0.652611	−	0.757693i	$-0.726326\pi$
$947$	−40.1661			−1.30522			−0.652611	+	0.757693i	$0.726326\pi$
$948$	−7.17377	+	15.9139i	−0.232993	+	0.516858i
$949$	7.09715			0.230383
$950$	43.8064	+	91.5307i	1.42127	+	2.96965i
$951$	−14.9777	+	3.89677i	−0.485687	+	0.126362i
$952$	1.93686	−	8.21079i	0.0627739	−	0.266113i
$953$		−	24.2238i		−	0.784685i	−0.919819	−	0.392342i	$-0.871665\pi$
$953$		−	24.2238i		−	0.784685i	0.919819	−	0.392342i	$-0.128335\pi$
$954$	−23.3229	−	16.4876i	−0.755105	−	0.533805i
$955$			100.139i			3.24042i
$956$	−1.68767	+	2.09539i	−0.0545832	+	0.0677699i
$957$	0.108986	−	0.0283549i	0.00352301	−	0.000916585i
$958$	−4.86478	+	2.32827i	−0.157174	+	0.0752231i
$959$	9.22533			0.297901
$960$	52.5288	+	11.1294i	1.69536	+	0.359200i
$961$	20.3723			0.657171
$962$	14.8035	−	7.08493i	0.477285	−	0.228427i
$963$	−10.5056	+	5.86341i	−0.338540	+	0.188946i
$964$	−2.81936	+	3.50048i	−0.0908053	+	0.112743i
$965$			84.4513i			2.71858i
$966$	0.876599	−	0.739711i	0.0282041	−	0.0237998i
$967$			49.0486i			1.57730i	0.614844	+	0.788649i	$0.289219\pi$
$967$			49.0486i			1.57730i	−0.614844	+	0.788649i	$0.710781\pi$
$968$	6.86852	−	29.1173i	0.220762	−	0.935864i
$969$	19.8993	+	76.4857i	0.639259	+	2.45707i
$970$	−22.4515	−	46.9110i	−0.720874	−	1.50622i
$971$	38.0733			1.22183			0.610915	−	0.791696i	$-0.290802\pi$
$971$	38.0733			1.22183			0.610915	+	0.791696i	$0.290802\pi$
$972$	25.8260	−	17.4647i	0.828370	−	0.560181i
$973$	8.72196			0.279613
$974$	4.29330	+	8.97058i	0.137566	+	0.287436i
$975$	−14.9598	−	57.4999i	−0.479098	−	1.84147i
$976$	−9.68164	−	44.3938i	−0.309902	−	1.42101i
$977$			9.59681i			0.307029i	0.988146	+	0.153515i	$0.0490592\pi$
$977$			9.59681i			0.307029i	−0.988146	+	0.153515i	$0.950941\pi$
$978$	−43.8339	+	36.9889i	−1.40165	+	1.18277i
$979$			0.736766i			0.0235471i
$980$	40.9277	+	32.9640i	1.30739	+	1.05300i
$981$	29.6232	−	16.5333i	0.945795	−	0.527867i
$982$	−35.7264	+	17.0986i	−1.14008	+	0.545638i
$983$	−11.4276			−0.364483			−0.182242	−	0.983254i	$-0.558335\pi$
$983$	−11.4276			−0.364483			−0.182242	+	0.983254i	$0.558335\pi$
$984$	−0.676470	−	29.5719i	−0.0215651	−	0.942716i
$985$	97.6345			3.11089
$986$	−0.812319	+	0.388774i	−0.0258695	+	0.0123811i
$987$	0.711583	−	0.185133i	0.0226499	−	0.00589285i
$988$	38.2128	+	30.7773i	1.21571	+	0.979156i
$989$		−	6.56050i		−	0.208612i
$990$	−8.73085	−	6.17207i	−0.277485	−	0.196161i
$991$		−	34.0635i		−	1.08206i	−0.841003	−	0.541031i	$-0.818034\pi$
$991$		−	34.0635i		−	1.08206i	0.841003	−	0.541031i	$-0.181966\pi$
$992$	14.5561	−	11.3228i	0.462157	−	0.359500i
$993$	16.4897	−	4.29014i	0.523285	−	0.136143i
$994$	2.69829	+	5.63790i	0.0855845	+	0.178823i
$995$	32.0663			1.01657
$996$	−13.5826	−	6.12286i	−0.430381	−	0.194010i
$997$	−13.1782			−0.417359			−0.208679	−	0.977984i	$-0.566917\pi$
$997$	−13.1782			−0.417359			−0.208679	+	0.977984i	$0.566917\pi$
$998$	11.1368	+	23.2697i	0.352530	+	0.736589i
$999$	12.1758	+	12.7190i	0.385227	+	0.402411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.b.47.4	yes	22
3.2	odd	2		276.2.c.a.47.19	✓	22
4.3	odd	2		276.2.c.a.47.20	yes	22
12.11	even	2	inner	276.2.c.b.47.3	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.19	✓	22	3.2	odd	2
276.2.c.a.47.20	yes	22	4.3	odd	2
276.2.c.b.47.3	yes	22	12.11	even	2	inner
276.2.c.b.47.4	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27564 + 0.610520i) q^{2} +(0.436111 + 1.67625i) q^{3} +(1.25453 - 1.55761i) q^{4} +3.87509i q^{5} +(-1.57971 - 1.87204i) q^{6} -0.468259i q^{7} +(-0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +O(q^{10})\)	\(q+(-1.27564 + 0.610520i) q^{2} +(0.436111 + 1.67625i) q^{3} +(1.25453 - 1.55761i) q^{4} +3.87509i q^{5} +(-1.57971 - 1.87204i) q^{6} -0.468259i q^{7} +(-0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +(-2.36582 - 4.94323i) q^{10} -0.650350 q^{11} +(3.15806 + 1.42361i) q^{12} +3.42468 q^{13} +(0.285881 + 0.597331i) q^{14} +(-6.49561 + 1.68997i) q^{15} +(-0.852308 - 3.90814i) q^{16} -6.36961i q^{17} +(2.44908 - 3.46439i) q^{18} +7.16356i q^{19} +(6.03589 + 4.86142i) q^{20} +(0.784918 - 0.204213i) q^{21} +(0.829614 - 0.397052i) q^{22} -1.00000 q^{23} +(-4.89770 + 0.112037i) q^{24} -10.0163 q^{25} +(-4.36867 + 2.09084i) q^{26} +(-3.59322 - 3.75350i) q^{27} +(-0.729365 - 0.587445i) q^{28} +0.0999734i q^{29} +(7.25432 - 6.12150i) q^{30} -3.26002i q^{31} +(3.47324 + 4.46504i) q^{32} +(-0.283625 - 1.09015i) q^{33} +(3.88878 + 8.12535i) q^{34} +1.81455 q^{35} +(-1.00906 + 5.91454i) q^{36} -3.38856 q^{37} +(-4.37350 - 9.13814i) q^{38} +(1.49354 + 5.74062i) q^{39} +(-10.6676 - 2.51640i) q^{40} +6.03791i q^{41} +(-0.876599 + 0.739711i) q^{42} +6.56050i q^{43} +(-0.815884 + 1.01299i) q^{44} +(-5.66562 - 10.1512i) q^{45} +(1.27564 - 0.610520i) q^{46} +0.906570 q^{47} +(6.17931 - 3.13306i) q^{48} +6.78073 q^{49} +(12.7773 - 6.11517i) q^{50} +(10.6770 - 2.77786i) q^{51} +(4.29637 - 5.33433i) q^{52} -6.73216i q^{53} +(6.87525 + 2.59440i) q^{54} -2.52017i q^{55} +(1.28906 + 0.304078i) q^{56} +(-12.0079 + 3.12411i) q^{57} +(-0.0610358 - 0.127530i) q^{58} +11.2912 q^{59} +(-5.51663 + 12.2378i) q^{60} +11.3593 q^{61} +(1.99031 + 4.15862i) q^{62} +(0.684623 + 1.22666i) q^{63} +(-7.15661 - 3.57532i) q^{64} +13.2710i q^{65} +(1.02736 + 1.21748i) q^{66} +6.94878i q^{67} +(-9.92138 - 7.99087i) q^{68} +(-0.436111 - 1.67625i) q^{69} +(-2.31471 + 1.10782i) q^{70} +9.43849 q^{71} +(-2.32374 - 8.16090i) q^{72} +2.07235 q^{73} +(4.32259 - 2.06879i) q^{74} +(-4.36823 - 16.7899i) q^{75} +(11.1580 + 8.98690i) q^{76} +0.304532i q^{77} +(-5.40999 - 6.41114i) q^{78} +5.03913i q^{79} +(15.1444 - 3.30277i) q^{80} +(4.72476 - 7.66007i) q^{81} +(-3.68627 - 7.70222i) q^{82} -4.30093 q^{83} +(0.666619 - 1.47879i) q^{84} +24.6828 q^{85} +(-4.00532 - 8.36886i) q^{86} +(-0.167580 + 0.0435995i) q^{87} +(0.422324 - 1.79033i) q^{88} -1.13288i q^{89} +(13.4248 + 9.49039i) q^{90} -1.60364i q^{91} +(-1.25453 + 1.55761i) q^{92} +(5.46460 - 1.42173i) q^{93} +(-1.15646 + 0.553479i) q^{94} -27.7594 q^{95} +(-5.96980 + 7.76927i) q^{96} +9.48994 q^{97} +(-8.64980 + 4.13977i) q^{98} +(1.70367 - 0.950851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more