LMFDB - Embedded newform 276.2.c.a.47.20

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			47.20
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27564 + 0.610520i) q^{2} +(-0.436111 - 1.67625i) q^{3} +(1.25453 + 1.55761i) q^{4} +3.87509i q^{5} +(0.467061 - 2.40455i) q^{6} +0.468259i q^{7} +(0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +O(q^{10})$	\(q+(1.27564 + 0.610520i) q^{2} +(-0.436111 - 1.67625i) q^{3} +(1.25453 + 1.55761i) q^{4} +3.87509i q^{5} +(0.467061 - 2.40455i) 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} +(2.06383 - 2.78220i) 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} +(-4.23431 + 0.265740i) 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} +(4.33130 - 2.28908i) 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} +(9.31785 + 1.80990i) 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} +(-5.56371 - 2.24614i) 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} +(1.12595 + 0.218706i) 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} +(6.92272 - 0.275704i) 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} +(2.29207 + 6.98186i) 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} +(10.7813 + 7.99753i) 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} +(0.303753 - 1.56380i) 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} +(-5.72599 - 6.26203i) 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} +(1.59954 - 8.23482i) 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} +(1.30279 + 0.966406i) 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} +(-1.02977 - 16.4083i) 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} +(8.99924 + 3.87476i) 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 - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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	$0.666366\pi$
$6$	0.467061	−	2.40455i	0.190677	−	0.981653i
$7$			0.468259i			0.176985i	0.996077	+	0.0884926i	$0.0282050\pi$
$7$			0.468259i			0.176985i	−0.996077	+	0.0884926i	$0.971795\pi$
$8$	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	$-0.468741\pi$
$11$	0.650350			0.196088			0.0980439	+	0.995182i	$0.468741\pi$
$12$	2.06383	−	2.78220i	0.595776	−	0.803151i
$13$	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	$-0.280958\pi$
$18$	−4.23431	+	0.265740i	−0.998036	+	0.0626354i
$19$		−	7.16356i		−	1.64343i	−0.569896	−	0.821717i	$-0.693017\pi$
$19$		−	7.16356i		−	1.64343i	0.569896	−	0.821717i	$-0.306983\pi$
$20$	−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
$24$	4.33130	−	2.28908i	0.884122	−	0.467256i
$25$	−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	$0.997045\pi$
$30$	9.31785	+	1.80990i	1.70120	+	0.330442i
$31$			3.26002i			0.585516i	0.956187	+	0.292758i	$0.0945731\pi$
$31$			3.26002i			0.585516i	−0.956187	+	0.292758i	$0.905427\pi$
$32$	−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
$36$	−5.56371	−	2.24614i	−0.927285	−	0.374357i
$37$	−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	$0.843719\pi$
$42$	1.12595	+	0.218706i	0.173738	+	0.0337470i
$43$		−	6.56050i		−	1.00047i	−0.865890	−	0.500234i	$-0.833247\pi$
$43$		−	6.56050i		−	1.00047i	0.865890	−	0.500234i	$-0.166753\pi$
$44$	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	$-0.521062\pi$
$47$	−0.906570			−0.132237			−0.0661184	+	0.997812i	$0.521062\pi$
$48$	6.92272	−	0.275704i	0.999208	−	0.0397945i
$49$	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	$-0.153000\pi$
$54$	2.29207	+	6.98186i	0.311912	+	0.950111i
$55$			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	$-0.762817\pi$
$59$	−11.2912			−1.46999			−0.734997	+	0.678070i	$0.762817\pi$
$60$	10.7813	+	7.99753i	1.39185	+	1.03248i
$61$	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
$66$	0.303753	−	1.56380i	0.0373894	−	0.192490i
$67$		−	6.94878i		−	0.848929i	−0.905445	−	0.424465i	$-0.860462\pi$
$67$		−	6.94878i		−	0.848929i	0.905445	−	0.424465i	$-0.139538\pi$
$68$	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	$-0.689226\pi$
$71$	−9.43849			−1.12014			−0.560071	+	0.828444i	$0.689226\pi$
$72$	−5.72599	−	6.26203i	−0.674814	−	0.737988i
$73$	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
$78$	1.59954	−	8.23482i	0.181112	−	0.932409i
$79$		−	5.03913i		−	0.566946i	−0.958980	−	0.283473i	$-0.908513\pi$
$79$		−	5.03913i		−	0.566946i	0.958980	−	0.283473i	$-0.0914867\pi$
$80$	−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	$-0.424149\pi$
$83$	4.30093			0.472089			0.236044	+	0.971742i	$0.424149\pi$
$84$	1.30279	+	0.966406i	0.142146	+	0.105444i
$85$	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	$-0.0191236\pi$
$90$	−1.02977	−	16.4083i	−0.108547	−	1.72959i
$91$			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
$96$	8.99924	+	3.87476i	0.918481	+	0.395466i
$97$	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	$0.979994\pi$
$102$	−15.3160	−	2.97500i	−1.51651	−	0.294569i
$103$			12.5453i			1.23612i	0.786129	+	0.618062i	$0.212082\pi$
$103$			12.5453i			1.23612i	−0.786129	+	0.618062i	$0.787918\pi$
$104$	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	$-0.562097\pi$
$107$	−4.01038			−0.387698			−0.193849	+	0.981031i	$0.562097\pi$
$108$	−1.33870	+	10.3057i	−0.128816	+	0.991668i
$109$	−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	$0.913487\pi$
$114$	−17.2251	−	3.34582i	−1.61328	−	0.313365i
$115$			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
$120$	8.87039	+	16.7842i	0.809752	+	1.53218i
$121$	−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
$126$	−0.124435	−	1.98275i	−0.0110855	−	0.176638i
$127$			15.8316i			1.40482i	0.711771	+	0.702412i	$0.247893\pi$
$127$			15.8316i			1.40482i	−0.711771	+	0.702412i	$0.752107\pi$
$128$	−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	$-0.524891\pi$
$131$	−1.78820			−0.156236			−0.0781180	+	0.996944i	$0.524891\pi$
$132$	1.34221	−	1.80940i	0.116824	−	0.157488i
$133$	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	$0.681614\pi$
$138$	0.467061	−	2.40455i	0.0397589	−	0.204689i
$139$		−	18.6264i		−	1.57987i	−0.613192	−	0.789934i	$-0.710115\pi$
$139$		−	18.6264i		−	1.57987i	0.613192	−	0.789934i	$-0.289885\pi$
$140$	−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
$144$	−3.48122	−	11.4839i	−0.290102	−	0.956996i
$145$	−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	$-0.0379033\pi$
$150$	−4.67824	+	24.0848i	−0.381977	+	1.96651i
$151$		−	9.50248i		−	0.773301i	−0.922226	−	0.386651i	$-0.873632\pi$
$151$		−	9.50248i		−	0.773301i	0.922226	−	0.386651i	$-0.126368\pi$
$152$	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
$156$	7.06796	−	9.52814i	0.565890	−	0.762862i
$157$	−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
$162$	10.7037	−	6.88695i	0.840965	−	0.541090i
$163$			23.4151i			1.83401i	0.398876	+	0.917005i	$0.369400\pi$
$163$			23.4151i			1.83401i	−0.398876	+	0.917005i	$0.630600\pi$
$164$	−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	$-0.363509\pi$
$167$	10.7461			0.831557			0.415778	+	0.909466i	$0.363509\pi$
$168$	1.07188	+	2.02817i	0.0826974	+	0.156476i
$169$	−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	$-0.0998755\pi$
$174$	0.240391	+	0.0466937i	0.0182240	+	0.00353984i
$175$		−	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	$-0.567408\pi$
$179$	−5.62429			−0.420379			−0.210190	+	0.977661i	$0.567408\pi$
$180$	8.70401	−	21.5599i	0.648759	−	1.60698i
$181$	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
$186$	7.83887	+	1.52263i	0.574774	+	0.111644i
$187$		−	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	$-0.884528\pi$
$191$	−25.8417			−1.86984			−0.934919	+	0.354862i	$0.884528\pi$
$192$	9.11420	+	10.4370i	0.657760	+	0.753227i
$193$	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	$-0.354654\pi$
$198$	−2.75378	+	0.172824i	−0.195703	+	0.0122821i
$199$			8.27498i			0.586598i	0.956021	+	0.293299i	$0.0947531\pi$
$199$			8.27498i			0.586598i	−0.956021	+	0.293299i	$0.905247\pi$
$200$	−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
$204$	−17.7215	−	13.1458i	−1.24075	−	0.920389i
$205$	−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
$210$	−0.847504	+	4.36316i	−0.0584833	+	0.301087i
$211$			6.41193i			0.441415i	0.975340	+	0.220708i	$0.0708367\pi$
$211$			6.41193i			0.441415i	−0.975340	+	0.220708i	$0.929163\pi$
$212$	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
$216$	−7.99955	+	12.3291i	−0.544301	+	0.838890i
$217$	−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
$222$	−1.58267	+	8.14796i	−0.106222	+	0.546855i
$223$			19.2125i			1.28656i	0.765630	+	0.643281i	$0.222427\pi$
$223$			19.2125i			1.28656i	−0.765630	+	0.643281i	$0.777573\pi$
$224$	−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	$-0.340671\pi$
$227$	14.4610			0.959811			0.479905	+	0.877320i	$0.340671\pi$
$228$	−19.9304	−	14.7844i	−1.31992	−	0.979118i
$229$	−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	$-0.0106695\pi$
$234$	−14.5012	+	0.910074i	−0.947971	+	0.0594934i
$235$		−	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	$-0.486146\pi$
$239$	1.34526			0.0870177			0.0435089	+	0.999053i	$0.486146\pi$
$240$	1.06838	+	26.8262i	0.0689636	+	1.73162i
$241$	−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
$246$	14.5184	+	2.82007i	0.925662	+	0.179801i
$247$		−	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	$-0.263294\pi$
$251$	21.4504			1.35394			0.676968	+	0.736013i	$0.263294\pi$
$252$	1.05178	−	2.60525i	0.0662557	−	0.164116i
$253$	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	$-0.0595150\pi$
$258$	−15.7751	−	3.06416i	−0.982112	−	0.190766i
$259$		−	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	$-0.654651\pi$
$263$	−15.1457			−0.933922			−0.466961	+	0.884278i	$0.654651\pi$
$264$	2.81686	−	1.48870i	0.173366	−	0.0916233i
$265$	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	$-0.0341402\pi$
$270$	−27.0554	+	8.88200i	−1.64654	+	0.540541i
$271$		−	0.944202i		−	0.0573562i	−0.999589	−	0.0286781i	$-0.990870\pi$
$271$		−	0.944202i		−	0.0573562i	0.999589	−	0.0286781i	$-0.00912977\pi$
$272$	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
$276$	2.06383	−	2.78220i	0.124228	−	0.167468i
$277$	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	$0.846645\pi$
$282$	−0.423424	+	2.17989i	−0.0252145	+	0.129811i
$283$		−	3.64088i		−	0.216428i	−0.994128	−	0.108214i	$-0.965487\pi$
$283$		−	3.64088i		−	0.216428i	0.994128	−	0.108214i	$-0.0345132\pi$
$284$	−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
$288$	2.57039	−	16.7748i	0.151462	−	0.988463i
$289$	−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	$0.967710\pi$
$294$	3.16702	−	16.3046i	0.184704	−	0.950904i
$295$		−	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
$300$	−20.6720	+	27.8674i	−1.19350	+	1.60892i
$301$	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
$306$	1.69266	+	26.9709i	0.0967628	+	1.54182i
$307$			21.0789i			1.20303i	0.798860	+	0.601517i	$0.205437\pi$
$307$			21.0789i			1.20303i	−0.798860	+	0.601517i	$0.794563\pi$
$308$	−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	$-0.605622\pi$
$311$	−11.4899			−0.651533			−0.325766	+	0.945450i	$0.605622\pi$
$312$	14.8333	−	7.83937i	0.839771	−	0.443817i
$313$	−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	$0.919264\pi$
$318$	−16.1878	−	3.14433i	−0.907767	−	0.176325i
$319$			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
$324$	17.8588	−	2.25045i	0.992154	−	0.125025i
$325$	−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
$330$	6.05986	+	1.17707i	0.333584	+	0.0647957i
$331$			9.83726i			0.540705i	0.962761	+	0.270352i	$0.0871402\pi$
$331$			9.83726i			0.540705i	−0.962761	+	0.270352i	$0.912860\pi$
$332$	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
$336$	0.129101	+	3.24162i	0.00704304	+	0.176845i
$337$	−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
$342$	1.90364	+	30.3327i	0.102937	+	1.64021i
$343$			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	$-0.363234\pi$
$347$	15.5194			0.833127			0.416564	+	0.909107i	$0.363234\pi$
$348$	0.278146	+	0.206328i	0.0149102	+	0.0110603i
$349$	−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	$-0.220722\pi$
$354$	−5.27370	+	27.1503i	−0.280294	+	1.44302i
$355$		−	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	$-0.508137\pi$
$359$	−0.968568			−0.0511191			−0.0255595	+	0.999673i	$0.508137\pi$
$360$	24.2659	−	22.1887i	1.27893	−	1.16945i
$361$	−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
$366$	5.30550	−	27.3140i	0.277323	−	1.42773i
$367$			15.5983i			0.814226i	0.913378	+	0.407113i	$0.133464\pi$
$367$			15.5983i			0.814226i	−0.913378	+	0.407113i	$0.866536\pi$
$368$	−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
$372$	9.07000	+	6.72812i	0.470258	+	0.348837i
$373$	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
$378$	−3.26932	+	1.07328i	−0.168156	+	0.0552038i
$379$		−	20.7558i		−	1.06615i	−0.846067	−	0.533077i	$-0.821036\pi$
$379$		−	20.7558i		−	1.06615i	0.846067	−	0.533077i	$-0.178964\pi$
$380$	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	$-0.362655\pi$
$383$	16.3694			0.836437			0.418218	+	0.908347i	$0.362655\pi$
$384$	5.25445	+	18.8783i	0.268140	+	0.963380i
$385$	−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	$0.991517\pi$
$390$	31.9107	+	6.19835i	1.61586	+	0.313866i
$391$		−	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
$396$	−3.61836	−	1.46078i	−0.181829	−	0.0734069i
$397$	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	$-0.103690\pi$
$402$	−16.7087	−	3.24551i	−0.833354	−	0.161871i
$403$			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
$408$	−14.5805	−	27.5887i	−0.721844	−	1.36584i
$409$	−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
$414$	−4.23431	+	0.265740i	−0.208105	+	0.0130604i
$415$			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	$-0.665244\pi$
$419$	−20.3108			−0.992248			−0.496124	+	0.868252i	$0.665244\pi$
$420$	−3.74491	+	5.04842i	−0.182733	+	0.246338i
$421$	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
$426$	−4.40835	+	22.6953i	−0.213585	+	1.09959i
$427$			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	$-0.463040\pi$
$431$	4.81034			0.231706			0.115853	+	0.993266i	$0.463040\pi$
$432$	−17.7317	+	10.8437i	−0.853119	+	0.521716i
$433$	−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
$438$	0.967915	−	4.98307i	0.0462488	−	0.238100i
$439$			1.52839i			0.0729462i	0.999335	+	0.0364731i	$0.0116123\pi$
$439$			1.52839i			0.0729462i	−0.999335	+	0.0364731i	$0.988388\pi$
$440$	−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	$-0.679635\pi$
$443$	−22.5150			−1.06972			−0.534859	+	0.844941i	$0.679635\pi$
$444$	−6.99341	+	9.42764i	−0.331893	+	0.447416i
$445$	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	$-0.329410\pi$
$450$	42.4123	−	2.66174i	1.99933	−	0.125476i
$451$			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
$456$	−16.3980	−	31.0275i	−0.767904	−	1.45300i
$457$	−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	$-0.164589\pi$
$462$	0.732262	+	0.142235i	0.0340679	+	0.00661738i
$463$			16.9713i			0.788724i	0.918955	+	0.394362i	$0.129034\pi$
$463$			16.9713i			0.788724i	−0.918955	+	0.394362i	$0.870966\pi$
$464$	−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	$-0.144235\pi$
$467$	38.8587			1.79817			0.899083	+	0.437779i	$0.144235\pi$
$468$	−19.0539	−	7.69233i	−0.880769	−	0.355578i
$469$	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
$474$	−12.1168	−	2.35358i	−0.556545	−	0.108104i
$475$			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	$-0.527768\pi$
$479$	−3.81359			−0.174247			−0.0871237	+	0.996198i	$0.527768\pi$
$480$	−15.0150	+	34.8729i	−0.685340	+	1.59172i
$481$	−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
$486$	−16.2123	−	14.9386i	−0.735403	−	0.677630i
$487$			7.03221i			0.318660i	0.987225	+	0.159330i	$0.0509333\pi$
$487$			7.03221i			0.318660i	−0.987225	+	0.159330i	$0.949067\pi$
$488$	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	$-0.717749\pi$
$491$	−28.0066			−1.26392			−0.631960	+	0.775001i	$0.717749\pi$
$492$	16.7986	+	12.4612i	0.757341	+	0.561795i
$493$	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
$498$	2.00880	−	10.3418i	0.0900164	−	0.463427i
$499$			18.2415i			0.816603i	0.912847	+	0.408302i	$0.133879\pi$
$499$			18.2415i			0.816603i	−0.912847	+	0.408302i	$0.866121\pi$
$500$	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	$-0.827902\pi$
$503$	−38.4575			−1.71474			−0.857369	+	0.514703i	$0.827902\pi$
$504$	2.93225	−	2.68124i	0.130613	−	0.119432i
$505$	−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	$0.972099\pi$
$510$	11.5284	−	59.3510i	0.510486	−	2.62811i
$511$			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
$516$	−18.2526	−	13.5398i	−0.803526	−	0.596055i
$517$	−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	$0.995913\pi$
$522$	−0.0265669	−	0.423319i	−0.00116280	−	0.0185281i
$523$		−	30.2320i		−	1.32195i	−0.750407	−	0.660976i	$-0.770143\pi$
$523$		−	30.2320i		−	1.32195i	0.750407	−	0.660976i	$-0.229857\pi$
$524$	−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
$528$	4.50219	−	0.179304i	0.195933	−	0.00780322i
$529$	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
$534$	−2.72406	−	0.529123i	−0.117881	−	0.0228974i
$535$		−	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
$540$	−39.9356	−	5.18758i	−1.71856	−	0.223238i
$541$	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
$546$	3.85603	+	0.748997i	0.165023	+	0.0320541i
$547$			3.84448i			0.164378i	0.996617	+	0.0821890i	$0.0261911\pi$
$547$			3.84448i			0.164378i	−0.996617	+	0.0821890i	$0.973809\pi$
$548$	−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
$552$	4.33130	−	2.28908i	0.184352	−	0.0974297i
$553$	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	$0.979699\pi$
$558$	−0.866316	−	13.8039i	−0.0366741	−	0.584367i
$559$		−	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	$-0.295210\pi$
$563$	28.4680			1.19978			0.599892	+	0.800081i	$0.295210\pi$
$564$	−1.87101	+	2.52225i	−0.0787835	+	0.106206i
$565$	−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	$-0.284083\pi$
$570$	12.9654	−	66.7489i	0.543059	−	2.79581i
$571$			22.4199i			0.938242i	0.883134	+	0.469121i	$0.155429\pi$
$571$			22.4199i			0.938242i	−0.883134	+	0.469121i	$0.844571\pi$
$572$	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
$576$	13.5202	−	19.8294i	0.563343	−	0.826223i
$577$	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
$582$	4.43238	−	22.8190i	0.183728	−	0.945879i
$583$		−	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	$-0.653829\pi$
$587$	−22.5164			−0.929350			−0.464675	+	0.885481i	$0.653829\pi$
$588$	13.9943	−	18.8653i	0.577114	−	0.777993i
$589$	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	$0.670653\pi$
$594$	1.49065	+	4.54065i	0.0611621	+	0.186305i
$595$			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	$-0.270943\pi$
$599$	32.2616			1.31817			0.659086	+	0.752068i	$0.270943\pi$
$600$	−43.3837	+	22.9282i	−1.77113	+	0.936039i
$601$	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
$606$	3.03563	+	0.589643i	0.123314	+	0.0239526i
$607$		−	16.0950i		−	0.653276i	−0.945150	−	0.326638i	$-0.894084\pi$
$607$		−	16.0950i		−	0.653276i	0.945150	−	0.326638i	$-0.105916\pi$
$608$	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
$612$	−14.3071	+	35.4386i	−0.578328	+	1.43252i
$613$	−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	$0.868632\pi$
$618$	30.1658	+	5.85942i	1.21345	+	0.235700i
$619$		−	9.47590i		−	0.380869i	−0.981700	−	0.190434i	$-0.939010\pi$
$619$		−	9.47590i		−	0.380869i	0.981700	−	0.190434i	$-0.0609896\pi$
$620$	−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
$624$	23.7081	−	0.944200i	0.949084	−	0.0377983i
$625$	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
$630$	7.68335	−	0.482197i	0.306112	−	0.0192112i
$631$			12.6249i			0.502588i	0.967911	+	0.251294i	$0.0808562\pi$
$631$			12.6249i			0.502588i	−0.967911	+	0.251294i	$0.919144\pi$
$632$	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
$636$	−18.7302	−	13.8940i	−0.742700	−	0.550934i
$637$	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	$0.994474\pi$
$642$	−1.87309	+	9.64315i	−0.0739250	+	0.380585i
$643$			21.1567i			0.834341i	0.908828	+	0.417170i	$0.136978\pi$
$643$			21.1567i			0.834341i	−0.908828	+	0.417170i	$0.863022\pi$
$644$	−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	$-0.527336\pi$
$647$	−4.36350			−0.171547			−0.0857734	+	0.996315i	$0.527336\pi$
$648$	24.1554	+	8.03237i	0.948912	+	0.315541i
$649$	−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	$-0.0465762\pi$
$654$	−5.28163	+	27.1912i	−0.206528	+	1.06326i
$655$		−	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	$-0.600811\pi$
$659$	−15.9899			−0.622878			−0.311439	+	0.950266i	$0.600811\pi$
$660$	7.01159	+	5.20119i	0.272926	+	0.202456i
$661$	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
$666$	14.3482	−	0.900475i	0.555982	−	0.0348927i
$667$			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
$672$	−1.81439	+	4.21397i	−0.0699916	+	0.162557i
$673$	−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	$-0.133673\pi$
$678$	13.7238	+	2.66572i	0.527059	+	0.102376i
$679$			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	$-0.200018\pi$
$683$	42.2844			1.61797			0.808984	+	0.587831i	$0.200018\pi$
$684$	−16.0904	+	39.8559i	−0.615231	+	1.52393i
$685$	−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
$690$	9.31785	+	1.80990i	0.354724	+	0.0689019i
$691$			15.7530i			0.599273i	0.954053	+	0.299637i	$0.0968654\pi$
$691$			15.7530i			0.599273i	−0.954053	+	0.299637i	$0.903135\pi$
$692$	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
$696$	0.228847	+	0.433014i	0.00867443	+	0.0164134i
$697$	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	$0.715565\pi$
$702$	7.84963	+	23.9107i	0.296265	+	0.902450i
$703$			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
$708$	−23.3032	+	31.4144i	−0.875787	+	1.18063i
$709$	−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
$714$	1.39307	−	7.17187i	0.0521343	−	0.268400i
$715$			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	$-0.184984\pi$
$719$	44.8244			1.67167			0.835834	+	0.548982i	$0.184984\pi$
$720$	44.5014	−	13.4901i	1.65847	−	0.502745i
$721$	−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
$726$	−4.94013	+	25.4330i	−0.183345	+	0.943908i
$727$		−	40.1016i		−	1.48728i	−0.668578	−	0.743642i	$-0.733097\pi$
$727$		−	40.1016i		−	1.48728i	0.668578	−	0.743642i	$-0.266903\pi$
$728$	−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
$732$	23.4437	−	31.6038i	0.866504	−	1.16811i
$733$	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
$738$	−1.60451	−	25.5664i	−0.0590629	−	0.941111i
$739$		−	37.2743i		−	1.37116i	−0.727998	−	0.685579i	$-0.759549\pi$
$739$		−	37.2743i		−	1.37116i	0.727998	−	0.685579i	$-0.240451\pi$
$740$	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	$-0.176979\pi$
$743$	46.3046			1.69875			0.849375	+	0.527790i	$0.176979\pi$
$744$	7.46244	+	14.1201i	0.273586	+	0.517668i
$745$	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
$750$	−46.7414	−	9.07909i	−1.70676	−	0.331521i
$751$		−	38.1533i		−	1.39223i	−0.717928	−	0.696117i	$-0.754909\pi$
$751$		−	38.1533i		−	1.39223i	0.717928	−	0.696117i	$-0.245091\pi$
$752$	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
$756$	−4.82574	−	0.626857i	−0.175511	−	0.0227986i
$757$	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	$0.900666\pi$
$762$	38.0677	+	7.39430i	1.37905	+	0.267867i
$763$		−	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
$768$	−4.82279	+	27.2899i	−0.174028	+	0.984741i
$769$	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	$-0.161700\pi$
$774$	1.74339	+	27.7792i	0.0626647	+	0.998503i
$775$		−	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
$780$	36.9224	+	27.3890i	1.32203	+	0.980683i
$781$	−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
$786$	−0.835200	+	4.29982i	−0.0297906	+	0.153369i
$787$		−	36.2469i		−	1.29206i	−0.763310	−	0.646032i	$-0.776427\pi$
$787$		−	36.2469i		−	1.29206i	0.763310	−	0.646032i	$-0.223573\pi$
$788$	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
$792$	−3.72390	−	4.07251i	−0.132323	−	0.144710i
$793$	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	$0.888081\pi$
$798$	1.56671	−	8.06582i	0.0554609	−	0.285527i
$799$			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
$804$	−19.3329	−	14.3411i	−0.681818	−	0.505772i
$805$	−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	$0.876130\pi$
$810$	26.6876	+	41.4779i	0.937706	+	1.45739i
$811$		−	23.6598i		−	0.830810i	−0.909637	−	0.415405i	$-0.863640\pi$
$811$		−	23.6598i		−	0.830810i	0.909637	−	0.415405i	$-0.136360\pi$
$812$	−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
$816$	−1.75613	−	44.0950i	−0.0614768	−	1.54363i
$817$	−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	$0.741403\pi$
$822$	47.3729	+	9.20174i	1.65232	+	0.320948i
$823$			44.5987i			1.55461i	0.629121	+	0.777307i	$0.283415\pi$
$823$			44.5987i			1.55461i	−0.629121	+	0.777307i	$0.716585\pi$
$824$	−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	$-0.580128\pi$
$827$	−14.3259			−0.498161			−0.249081	+	0.968483i	$0.580128\pi$
$828$	−5.56371	−	2.24614i	−0.193352	−	0.0780589i
$829$	−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
$834$	−44.7880	−	8.69965i	−1.55088	−	0.301244i
$835$			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	$-0.384348\pi$
$839$	20.5882			0.710783			0.355392	+	0.934717i	$0.384348\pi$
$840$	−7.85933	+	4.15364i	−0.271173	+	0.143314i
$841$	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
$846$	3.83870	−	0.240912i	0.131977	−	0.00828271i
$847$		−	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
$852$	−19.4794	+	26.2597i	−0.667354	+	0.899643i
$853$	−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	$0.945563\pi$
$858$	1.04026	−	5.35551i	0.0355138	−	0.182834i
$859$		−	17.8715i		−	0.609767i	−0.952390	−	0.304883i	$-0.901383\pi$
$859$		−	17.8715i		−	0.609767i	0.952390	−	0.304883i	$-0.0986175\pi$
$860$	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	$-0.429912\pi$
$863$	12.8326			0.436826			0.218413	+	0.975856i	$0.429912\pi$
$864$	−29.2397	+	3.00706i	−0.994753	+	0.102302i
$865$	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
$870$	−0.180942	+	0.931537i	−0.00613452	+	0.0315821i
$871$		−	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
$876$	4.27698	−	5.76569i	0.144506	−	0.194805i
$877$	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	$-0.127322\pi$
$882$	−28.7117	+	1.80191i	−0.966774	+	0.0606735i
$883$		−	9.18562i		−	0.309121i	−0.987983	−	0.154560i	$-0.950604\pi$
$883$		−	9.18562i		−	0.309121i	0.987983	−	0.154560i	$-0.0493961\pi$
$884$	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	$-0.213928\pi$
$887$	46.6115			1.56506			0.782531	+	0.622612i	$0.213928\pi$
$888$	−14.6769	+	7.75668i	−0.492523	+	0.260297i
$889$	−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
$894$	−6.97359	−	1.35456i	−0.233232	−	0.0453031i
$895$		−	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
$900$	55.7280	+	22.4981i	1.85760	+	0.749937i
$901$	−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
$906$	−22.8492	−	4.43824i	−0.759113	−	0.147451i
$907$		−	1.64835i		−	0.0547324i	−0.999625	−	0.0273662i	$-0.991288\pi$
$907$		−	1.64835i		−	0.0547324i	0.999625	−	0.0273662i	$-0.00871202\pi$
$908$	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	$-0.216003\pi$
$911$	46.9920			1.55691			0.778457	+	0.627698i	$0.216003\pi$
$912$	−1.97502	−	49.5913i	−0.0653996	−	1.64213i
$913$	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
$918$	44.4717	−	14.5996i	1.46779	−	0.481859i
$919$			20.7172i			0.683397i	0.939810	+	0.341699i	$0.111002\pi$
$919$			20.7172i			0.683397i	−0.939810	+	0.341699i	$0.888998\pi$
$920$	−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
$924$	0.847268	+	0.628502i	0.0278731	+	0.0206762i
$925$	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	$-0.449319\pi$
$930$	−5.90032	+	30.3763i	−0.193479	+	0.996079i
$931$		−	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
$936$	−19.6097	−	21.4455i	−0.640963	−	0.700967i
$937$	−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	$-0.0966083\pi$
$942$	−6.79544	+	34.9847i	−0.221408	+	1.13986i
$943$			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	$-0.273674\pi$
$947$	40.1661			1.30522			0.652611	+	0.757693i	$0.273674\pi$
$948$	−14.0198	−	10.3999i	−0.455343	−	0.337773i
$949$	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	$-0.128335\pi$
$954$	1.78900	+	28.5061i	0.0579211	+	0.922917i
$955$		−	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
$960$	−40.4444	+	35.3183i	−1.30534	+	1.13989i
$961$	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
$966$	1.12595	+	0.218706i	0.0362269	+	0.00703673i
$967$		−	49.0486i		−	1.57730i	−0.614844	−	0.788649i	$-0.710781\pi$
$967$		−	49.0486i		−	1.57730i	0.614844	−	0.788649i	$-0.289219\pi$
$968$	−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	$-0.709198\pi$
$971$	−38.0733			−1.22183			−0.610915	+	0.791696i	$0.709198\pi$
$972$	−11.5607	−	28.9543i	−0.370810	−	0.928709i
$973$	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	$0.950941\pi$
$978$	56.3027	+	10.9363i	1.80036	+	0.349703i
$979$		−	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	$-0.441665\pi$
$983$	11.4276			0.364483			0.182242	+	0.983254i	$0.441665\pi$
$984$	13.8212	+	26.1520i	0.440605	+	0.833694i
$985$	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
$990$	−0.669708	−	10.6712i	−0.0212847	−	0.339152i
$991$			34.0635i			1.08206i	0.841003	+	0.541031i	$0.181966\pi$
$991$			34.0635i			1.08206i	−0.841003	+	0.541031i	$0.818034\pi$
$992$	−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
$996$	8.87639	−	11.9660i	0.281259	−	0.379158i
$997$	−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.a.47.20	yes	22
3.2	odd	2		276.2.c.b.47.3	yes	22
4.3	odd	2		276.2.c.b.47.4	yes	22
12.11	even	2	inner	276.2.c.a.47.19	✓	22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.27564 + 0.610520i) q^{2} +(-0.436111 - 1.67625i) q^{3} +(1.25453 + 1.55761i) q^{4} +3.87509i q^{5} +(0.467061 - 2.40455i) q^{6} +0.468259i q^{7} +(0.649379 + 2.75287i) q^{8} +(-2.61961 + 1.46206i) q^{9} +O(q^{10})\)	\(q+(1.27564 + 0.610520i) q^{2} +(-0.436111 - 1.67625i) q^{3} +(1.25453 + 1.55761i) q^{4} +3.87509i q^{5} +(0.467061 - 2.40455i) 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} +(2.06383 - 2.78220i) 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} +(-4.23431 + 0.265740i) 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} +(4.33130 - 2.28908i) 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} +(9.31785 + 1.80990i) 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} +(-5.56371 - 2.24614i) 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} +(1.12595 + 0.218706i) 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} +(6.92272 - 0.275704i) 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} +(2.29207 + 6.98186i) 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} +(10.7813 + 7.99753i) 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} +(0.303753 - 1.56380i) 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} +(-5.72599 - 6.26203i) 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} +(1.59954 - 8.23482i) 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} +(1.30279 + 0.966406i) 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} +(-1.02977 - 16.4083i) 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} +(8.99924 + 3.87476i) q^{96} +9.48994 q^{97} +(8.64980 + 4.13977i) q^{98} +(-1.70367 + 0.950851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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