LMFDB - Embedded newform 1000.2.o.a.349.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.16
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.338435 - 1.37312i) q^{2} +(2.58107 - 1.87526i) q^{3} +(-1.77092 - 0.929423i) q^{4} +(-1.70143 - 4.17877i) q^{6} -2.97769i q^{7} +(-1.87555 + 2.11714i) q^{8} +(2.21828 - 6.82716i) q^{9} +O(q^{10})$	\(q+(0.338435 - 1.37312i) q^{2} +(2.58107 - 1.87526i) q^{3} +(-1.77092 - 0.929423i) q^{4} +(-1.70143 - 4.17877i) q^{6} -2.97769i q^{7} +(-1.87555 + 2.11714i) q^{8} +(2.21828 - 6.82716i) q^{9} +(-0.263378 + 0.0855768i) q^{11} +(-6.31378 + 0.922031i) q^{12} +(-1.36304 + 4.19500i) q^{13} +(-4.08873 - 1.00775i) q^{14} +(2.27234 + 3.29188i) q^{16} +(3.01210 - 4.14580i) q^{17} +(-8.62377 - 5.35651i) q^{18} +(-0.824879 + 1.13535i) q^{19} +(-5.58392 - 7.68561i) q^{21} +(0.0283710 + 0.390613i) q^{22} +(0.307187 - 0.0998113i) q^{23} +(-0.870742 + 8.98164i) q^{24} +(5.29895 + 3.29135i) q^{26} +(-4.11950 - 12.6785i) q^{27} +(-2.76753 + 5.27326i) q^{28} +(2.59226 + 3.56794i) q^{29} +(-3.04947 - 2.21557i) q^{31} +(5.28919 - 2.00612i) q^{32} +(-0.519319 + 0.714781i) q^{33} +(-4.67329 - 5.53907i) q^{34} +(-10.2737 + 10.0287i) q^{36} +(-1.24835 + 3.84202i) q^{37} +(1.27980 + 1.51690i) q^{38} +(4.34861 + 13.3836i) q^{39} +(-1.97884 + 6.09023i) q^{41} +(-12.4431 + 5.06633i) q^{42} +10.9079 q^{43} +(0.545960 + 0.0932399i) q^{44} +(-0.0330901 - 0.455585i) q^{46} +(-1.67150 - 2.30062i) q^{47} +(12.0382 + 4.23533i) q^{48} -1.86662 q^{49} -16.3491i q^{51} +(6.31278 - 6.16219i) q^{52} +(-0.378304 + 0.274854i) q^{53} +(-18.8033 + 1.36572i) q^{54} +(6.30419 + 5.58481i) q^{56} +4.47727i q^{57} +(5.77652 - 2.35197i) q^{58} +(-5.09147 - 1.65432i) q^{59} +(-1.96419 + 0.638204i) q^{61} +(-4.07430 + 3.43747i) q^{62} +(-20.3291 - 6.60534i) q^{63} +(-0.964603 - 7.94163i) q^{64} +(0.805726 + 0.954995i) q^{66} +(-1.25093 - 0.908853i) q^{67} +(-9.18741 + 4.54239i) q^{68} +(0.605700 - 0.833675i) q^{69} +(7.81261 - 5.67620i) q^{71} +(10.2936 + 17.5011i) q^{72} +(8.54291 - 2.77576i) q^{73} +(4.85308 + 3.01441i) q^{74} +(2.51602 - 1.24395i) q^{76} +(0.254821 + 0.784258i) q^{77} +(19.8491 - 1.44168i) q^{78} +(4.49455 - 3.26548i) q^{79} +(-16.9856 - 12.3407i) q^{81} +(7.69292 + 4.77833i) q^{82} +(-10.7440 - 7.80599i) q^{83} +(2.74552 + 18.8005i) q^{84} +(3.69160 - 14.9778i) q^{86} +(13.3816 + 4.34795i) q^{87} +(0.312802 - 0.718114i) q^{88} +(0.992059 + 3.05324i) q^{89} +(12.4914 + 4.05871i) q^{91} +(-0.636773 - 0.108749i) q^{92} -12.0257 q^{93} +(-3.72473 + 1.51656i) q^{94} +(9.88976 - 15.0965i) q^{96} +(-9.69449 - 13.3433i) q^{97} +(-0.631729 + 2.56310i) q^{98} +1.98796i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	0.338435	−	1.37312i	0.239309	−	0.970943i
$2$	0.338435	−	1.37312i	0.239309	−	0.970943i
$3$	2.58107	−	1.87526i	1.49018	−	1.08268i	0.516086	−	0.856537i	$-0.327388\pi$
$3$	2.58107	−	1.87526i	1.49018	−	1.08268i	0.974094	−	0.226143i	$-0.0726116\pi$
$4$	−1.77092	−	0.929423i	−0.885462	−	0.464712i
$5$		0			0
$5$		0			0
$6$	−1.70143	−	4.17877i	−0.694606	−	1.70598i
$7$		−	2.97769i		−	1.12546i	−0.826641	−	0.562730i	$-0.809751\pi$
$7$		−	2.97769i		−	1.12546i	0.826641	−	0.562730i	$-0.190249\pi$
$8$	−1.87555	+	2.11714i	−0.663108	+	0.748524i
$9$	2.21828	−	6.82716i	0.739426	−	2.27572i
$10$		0			0
$11$	−0.263378	+	0.0855768i	−0.0794116	+	0.0258024i	−0.348453	−	0.937326i	$-0.613293\pi$
$11$	−0.263378	+	0.0855768i	−0.0794116	+	0.0258024i	0.269042	+	0.963129i	$0.413293\pi$
$12$	−6.31378	+	0.922031i	−1.82263	+	0.266167i
$13$	−1.36304	+	4.19500i	−0.378039	+	1.16349i	0.563366	+	0.826207i	$0.309506\pi$
$13$	−1.36304	+	4.19500i	−0.378039	+	1.16349i	−0.941405	+	0.337278i	$0.890494\pi$
$14$	−4.08873	−	1.00775i	−1.09276	−	0.269333i
$15$		0			0
$16$	2.27234	+	3.29188i	0.568086	+	0.822969i
$17$	3.01210	−	4.14580i	0.730542	−	1.00551i	−0.268565	−	0.963262i	$-0.586549\pi$
$17$	3.01210	−	4.14580i	0.730542	−	1.00551i	0.999107	−	0.0422436i	$-0.0134505\pi$
$18$	−8.62377	−	5.35651i	−2.03264	−	1.26254i
$19$	−0.824879	+	1.13535i	−0.189240	+	0.260467i	−0.893086	−	0.449886i	$-0.851465\pi$
$19$	−0.824879	+	1.13535i	−0.189240	+	0.260467i	0.703846	+	0.710353i	$0.251465\pi$
$20$		0			0
$21$	−5.58392	−	7.68561i	−1.21851	−	1.67714i
$22$	0.0283710	+	0.390613i	0.00604872	+	0.0832789i
$23$	0.307187	−	0.0998113i	0.0640530	−	0.0208121i	−0.276815	−	0.960923i	$-0.589279\pi$
$23$	0.307187	−	0.0998113i	0.0640530	−	0.0208121i	0.340868	+	0.940111i	$0.389279\pi$
$24$	−0.870742	+	8.98164i	−0.177739	+	1.83337i
$25$		0			0
$26$	5.29895	+	3.29135i	1.03921	+	0.645488i
$27$	−4.11950	−	12.6785i	−0.792798	−	2.43998i
$28$	−2.76753	+	5.27326i	−0.523014	+	0.996552i
$29$	2.59226	+	3.56794i	0.481371	+	0.662550i	0.978768	−	0.204973i	$-0.0657107\pi$
$29$	2.59226	+	3.56794i	0.481371	+	0.662550i	−0.497397	+	0.867523i	$0.665711\pi$
$30$		0			0
$31$	−3.04947	−	2.21557i	−0.547702	−	0.397929i	0.279236	−	0.960223i	$-0.409919\pi$
$31$	−3.04947	−	2.21557i	−0.547702	−	0.397929i	−0.826937	+	0.562294i	$0.809919\pi$
$32$	5.28919	−	2.00612i	0.935005	−	0.354635i
$33$	−0.519319	+	0.714781i	−0.0904018	+	0.124427i
$34$	−4.67329	−	5.53907i	−0.801463	−	0.949942i
$35$		0			0
$36$	−10.2737	+	10.0287i	−1.71229	+	1.67144i
$37$	−1.24835	+	3.84202i	−0.205227	+	0.631625i	0.794477	+	0.607295i	$0.207745\pi$
$37$	−1.24835	+	3.84202i	−0.205227	+	0.631625i	−0.999704	+	0.0243301i	$0.992255\pi$
$38$	1.27980	+	1.51690i	0.207612	+	0.246074i
$39$	4.34861	+	13.3836i	0.696335	+	2.14310i
$40$		0			0
$41$	−1.97884	+	6.09023i	−0.309042	+	0.951135i	0.669095	+	0.743177i	$0.266682\pi$
$41$	−1.97884	+	6.09023i	−0.309042	+	0.951135i	−0.978138	+	0.207958i	$0.933318\pi$
$42$	−12.4431	+	5.06633i	−1.92001	+	0.781752i
$43$	10.9079			1.66343			0.831717	−	0.555199i	$-0.187358\pi$
$43$	10.9079			1.66343			0.831717	+	0.555199i	$0.187358\pi$
$44$	0.545960	+	0.0932399i	0.0823066	+	0.0140564i
$45$		0			0
$46$	−0.0330901	−	0.455585i	−0.00487887	−	0.0671724i
$47$	−1.67150	−	2.30062i	−0.243813	−	0.335580i	0.669519	−	0.742795i	$-0.266500\pi$
$47$	−1.67150	−	2.30062i	−0.243813	−	0.335580i	−0.913333	+	0.407214i	$0.866500\pi$
$48$	12.0382	+	4.23533i	1.73756	+	0.611317i
$49$	−1.86662			−0.266660
$50$		0			0
$51$		−	16.3491i		−	2.28933i
$52$	6.31278	−	6.16219i	0.875424	−	0.854543i
$53$	−0.378304	+	0.274854i	−0.0519641	+	0.0377541i	−0.613464	−	0.789723i	$-0.710224\pi$
$53$	−0.378304	+	0.274854i	−0.0519641	+	0.0377541i	0.561500	+	0.827477i	$0.310224\pi$
$54$	−18.8033	+	1.36572i	−2.55881	+	0.185852i
$55$		0			0
$56$	6.30419	+	5.58481i	0.842433	+	0.746302i
$57$			4.47727i			0.593029i
$58$	5.77652	−	2.35197i	0.758495	−	0.308829i
$59$	−5.09147	−	1.65432i	−0.662853	−	0.215374i	−0.0417804	−	0.999127i	$-0.513303\pi$
$59$	−5.09147	−	1.65432i	−0.662853	−	0.215374i	−0.621073	+	0.783753i	$0.713303\pi$
$60$		0			0
$61$	−1.96419	+	0.638204i	−0.251489	+	0.0817137i	−0.432049	−	0.901850i	$-0.642209\pi$
$61$	−1.96419	+	0.638204i	−0.251489	+	0.0817137i	0.180560	+	0.983564i	$0.442209\pi$
$62$	−4.07430	+	3.43747i	−0.517436	+	0.436559i
$63$	−20.3291	−	6.60534i	−2.56123	−	0.832194i
$64$	−0.964603	−	7.94163i	−0.120575	−	0.992704i
$65$		0			0
$66$	0.805726	+	0.954995i	0.0991780	+	0.117552i
$67$	−1.25093	−	0.908853i	−0.152825	−	0.111034i	0.508745	−	0.860917i	$-0.330110\pi$
$67$	−1.25093	−	0.908853i	−0.152825	−	0.111034i	−0.661570	+	0.749883i	$0.730110\pi$
$68$	−9.18741	+	4.54239i	−1.11414	+	0.550845i
$69$	0.605700	−	0.833675i	0.0729177	−	0.100363i
$70$		0			0
$71$	7.81261	−	5.67620i	0.927187	−	0.673640i	−0.0181158	−	0.999836i	$-0.505767\pi$
$71$	7.81261	−	5.67620i	0.927187	−	0.673640i	0.945302	+	0.326195i	$0.105767\pi$
$72$	10.2936	+	17.5011i	1.21311	+	2.06253i
$73$	8.54291	−	2.77576i	0.999872	−	0.324878i	0.237057	−	0.971496i	$-0.423817\pi$
$73$	8.54291	−	2.77576i	0.999872	−	0.324878i	0.762814	+	0.646618i	$0.223817\pi$
$74$	4.85308	+	3.01441i	0.564159	+	0.350418i
$75$		0			0
$76$	2.51602	−	1.24395i	0.288607	−	0.142691i
$77$	0.254821	+	0.784258i	0.0290395	+	0.0893745i
$78$	19.8491	−	1.44168i	2.24747	−	0.163238i
$79$	4.49455	−	3.26548i	0.505677	−	0.367396i	−0.305504	−	0.952191i	$-0.598825\pi$
$79$	4.49455	−	3.26548i	0.505677	−	0.367396i	0.811181	+	0.584795i	$0.198825\pi$
$80$		0			0
$81$	−16.9856	−	12.3407i	−1.88729	−	1.37119i
$82$	7.69292	+	4.77833i	0.849541	+	0.527678i
$83$	−10.7440	−	7.80599i	−1.17931	−	0.856819i	−0.187217	−	0.982319i	$-0.559947\pi$
$83$	−10.7440	−	7.80599i	−1.17931	−	0.856819i	−0.992094	+	0.125500i	$0.959947\pi$
$84$	2.74552	+	18.8005i	0.299561	+	2.05130i
$85$		0			0
$86$	3.69160	−	14.9778i	0.398075	−	1.61510i
$87$	13.3816	+	4.34795i	1.43466	+	0.466149i
$88$	0.312802	−	0.718114i	0.0333448	−	0.0765512i
$89$	0.992059	+	3.05324i	0.105158	+	0.323643i	0.989768	−	0.142689i	$-0.0455750\pi$
$89$	0.992059	+	3.05324i	0.105158	+	0.323643i	−0.884610	+	0.466333i	$0.845575\pi$
$90$		0			0
$91$	12.4914	+	4.05871i	1.30946	+	0.425468i
$92$	−0.636773	−	0.108749i	−0.0663881	−	0.0113379i
$93$	−12.0257			−1.24700
$94$	−3.72473	+	1.51656i	−0.384176	+	0.156421i
$95$		0			0
$96$	9.88976	−	15.0965i	1.00937	−	1.54078i
$97$	−9.69449	−	13.3433i	−0.984327	−	1.35481i	−0.934466	−	0.356053i	$-0.884122\pi$
$97$	−9.69449	−	13.3433i	−0.984327	−	1.35481i	−0.0498611	−	0.998756i	$-0.515878\pi$
$98$	−0.631729	+	2.56310i	−0.0638142	+	0.258912i
$99$			1.98796i			0.199797i
$100$		0			0
$101$			19.4874i			1.93907i	0.244946	+	0.969537i	$0.421230\pi$
$101$			19.4874i			1.93907i	−0.244946	+	0.969537i	$0.578770\pi$
$102$	−22.4492	−	5.53309i	−2.22281	−	0.547857i
$103$	4.15447	+	5.71814i	0.409352	+	0.563425i	0.963060	−	0.269286i	$-0.0867877\pi$
$103$	4.15447	+	5.71814i	0.409352	+	0.563425i	−0.553708	+	0.832711i	$0.686788\pi$
$104$	−6.32498	−	10.7537i	−0.620215	−	1.05449i
$105$		0			0
$106$	0.249377	+	0.612478i	0.0242216	+	0.0594891i
$107$	11.2557			1.08813			0.544064	−	0.839044i	$-0.316885\pi$
$107$	11.2557			1.08813			0.544064	+	0.839044i	$0.316885\pi$
$108$	−4.48838	+	26.2814i	−0.431895	+	2.52893i
$109$	9.07913	+	2.94999i	0.869623	+	0.282558i	0.709642	−	0.704563i	$-0.248857\pi$
$109$	9.07913	+	2.94999i	0.869623	+	0.282558i	0.159981	+	0.987120i	$0.448857\pi$
$110$		0			0
$111$	3.98270	+	12.2575i	0.378021	+	1.16343i
$112$	9.80218	−	6.76633i	0.926219	−	0.639358i
$113$	10.0510	+	3.26576i	0.945517	+	0.307217i	0.740892	−	0.671624i	$-0.234403\pi$
$113$	10.0510	+	3.26576i	0.945517	+	0.307217i	0.204624	+	0.978841i	$0.434403\pi$
$114$	6.14783	+	1.51526i	0.575797	+	0.141917i
$115$		0			0
$116$	−1.27457	−	8.72786i	−0.118341	−	0.810361i
$117$	25.6164	+	18.6114i	2.36823	+	1.72062i
$118$	−3.99471	+	6.43133i	−0.367743	+	0.592052i
$119$	−12.3449	−	8.96910i	−1.13166	−	0.822196i
$120$		0			0
$121$	−8.83714	+	6.42056i	−0.803377	+	0.583687i
$122$	0.211582	+	2.91306i	0.0191557	+	0.263736i
$123$	6.31323	+	19.4301i	0.569245	+	1.75196i
$124$	3.34118	+	6.75786i	0.300047	+	0.606874i
$125$		0			0
$126$	−15.9500	+	25.6789i	−1.42094	+	2.28766i
$127$	−1.29082	+	0.419412i	−0.114542	+	0.0372168i	−0.365727	−	0.930722i	$-0.619180\pi$
$127$	−1.29082	+	0.419412i	−0.114542	+	0.0372168i	0.251185	+	0.967939i	$0.419180\pi$
$128$	−11.2313	−	1.36321i	−0.992714	−	0.120491i
$129$	28.1540	−	20.4550i	2.47882	−	1.80097i
$130$		0			0
$131$	−0.471129	+	0.648453i	−0.0411627	+	0.0566556i	−0.829102	−	0.559097i	$-0.811148\pi$
$131$	−0.471129	+	0.648453i	−0.0411627	+	0.0566556i	0.787940	+	0.615753i	$0.211148\pi$
$132$	1.58401	−	0.783156i	0.137870	−	0.0681650i
$133$	3.38071	+	2.45623i	0.293145	+	0.212982i
$134$	−1.67132	+	1.41009i	−0.144380	+	0.121813i
$135$		0			0
$136$	3.12791	+	14.1527i	0.268216	+	1.21359i
$137$	6.89354	+	2.23985i	0.588955	+	0.191363i	0.588308	−	0.808637i	$-0.299794\pi$
$137$	6.89354	+	2.23985i	0.588955	+	0.191363i	0.000646705		1.00000i	$0.499794\pi$
$138$	−0.939747	−	1.11384i	−0.0799966	−	0.0948167i
$139$	0.417329	−	0.135598i	0.0353973	−	0.0115013i	−0.291265	−	0.956642i	$-0.594076\pi$
$139$	0.417329	−	0.135598i	0.0353973	−	0.0115013i	0.326662	+	0.945141i	$0.394076\pi$
$140$		0			0
$141$	−8.62851	−	2.80357i	−0.726652	−	0.236103i
$142$	−5.15005	−	12.6487i	−0.432182	−	1.06145i
$143$		−	1.22152i		−	0.102148i
$144$	27.5148	−	8.21136i	2.29290	−	0.684280i
$145$		0			0
$146$	−0.920239	−	12.6699i	−0.0761595	−	1.04856i
$147$	−4.81787	+	3.50039i	−0.397372	+	0.288707i
$148$	5.78160	−	5.64369i	0.475244	−	0.463908i
$149$			1.65547i			0.135621i	0.997698	+	0.0678107i	$0.0216014\pi$
$149$			1.65547i			0.135621i	−0.997698	+	0.0678107i	$0.978399\pi$
$150$		0			0
$151$	−14.0629			−1.14442			−0.572211	−	0.820107i	$-0.693914\pi$
$151$	−14.0629			−1.14442			−0.572211	+	0.820107i	$0.693914\pi$
$152$	−0.856593	−	3.87579i	−0.0694788	−	0.314368i
$153$	−21.6224	−	29.7606i	−1.74806	−	2.40600i
$154$	1.16312	−	0.0844800i	0.0937270	−	0.00680759i
$155$		0			0
$156$	4.73801	−	27.7431i	0.379345	−	2.22123i
$157$	−9.56521			−0.763387			−0.381693	−	0.924289i	$-0.624659\pi$
$157$	−9.56521			−0.763387			−0.381693	+	0.924289i	$0.624659\pi$
$158$	−2.96279	−	7.27672i	−0.235707	−	0.578905i
$159$	−0.461007	+	1.41883i	−0.0365603	+	0.112521i
$160$		0			0
$161$	−0.297207	−	0.914708i	−0.0234232	−	0.0720891i
$162$	−22.6938	+	19.1467i	−1.78300	+	1.50431i
$163$	1.69722	−	5.22350i	0.132936	−	0.409136i	−0.862327	−	0.506352i	$-0.830994\pi$
$163$	1.69722	−	5.22350i	0.132936	−	0.409136i	0.995263	+	0.0972156i	$0.0309936\pi$
$164$	9.16477	−	8.94616i	0.715649	−	0.698578i
$165$		0			0
$166$	−14.3547	+	12.1110i	−1.11414	+	0.939999i
$167$	7.07399	−	9.73651i	0.547401	−	0.753433i	−0.442255	−	0.896889i	$-0.645821\pi$
$167$	7.07399	−	9.73651i	0.547401	−	0.753433i	0.989657	+	0.143456i	$0.0458215\pi$
$168$	26.7445	+	2.59280i	2.06338	+	0.200039i
$169$	−5.22297	−	3.79471i	−0.401767	−	0.291901i
$170$		0			0
$171$	5.92139	+	8.15009i	0.452820	+	0.623253i
$172$	−19.3170	−	10.1380i	−1.47291	−	0.773018i
$173$	−5.37296	−	16.5363i	−0.408498	−	1.25723i	−0.917939	−	0.396722i	$-0.870148\pi$
$173$	−5.37296	−	16.5363i	−0.408498	−	1.25723i	0.509440	−	0.860506i	$-0.329852\pi$
$174$	10.4991	−	16.9031i	0.795931	−	1.28142i
$175$		0			0
$176$	−0.880195	−	0.672549i	−0.0663472	−	0.0506953i
$177$	−16.2437	+	5.27790i	−1.22095	+	0.396711i
$178$	4.52822	−	0.328894i	0.339404	−	0.0246517i
$179$	12.5073	+	17.2148i	0.934841	+	1.28670i	0.957941	+	0.286964i	$0.0926462\pi$
$179$	12.5073	+	17.2148i	0.934841	+	1.28670i	−0.0231007	+	0.999733i	$0.507354\pi$
$180$		0			0
$181$	−4.82937	+	6.64706i	−0.358964	+	0.494072i	−0.949860	−	0.312676i	$-0.898775\pi$
$181$	−4.82937	+	6.64706i	−0.358964	+	0.494072i	0.590896	+	0.806748i	$0.298775\pi$
$182$	9.80062	−	15.7786i	0.726470	−	1.16959i
$183$	−3.87291	+	5.33061i	−0.286294	+	0.394050i
$184$	−0.364831	+	0.837562i	−0.0268957	+	0.0617459i
$185$		0			0
$186$	−4.06990	+	16.5127i	−0.298420	+	1.21077i
$187$	−0.438538	+	1.34968i	−0.0320691	+	0.0986985i
$188$	0.821848	+	5.62776i	0.0599394	+	0.410446i
$189$	−37.7526	+	12.2666i	−2.74610	+	0.892262i
$190$		0			0
$191$	−1.09517	+	3.37058i	−0.0792436	+	0.243887i	−0.982828	−	0.184523i	$-0.940926\pi$
$191$	−1.09517	+	3.37058i	−0.0792436	+	0.243887i	0.903585	+	0.428410i	$0.140926\pi$
$192$	−17.3823	−	18.6890i	−1.25446	−	1.34876i
$193$		−	13.3961i		−	0.964273i	−0.876096	−	0.482137i	$-0.839861\pi$
$193$		−	13.3961i		−	0.964273i	0.876096	−	0.482137i	$-0.160139\pi$
$194$	−21.6030	+	8.79587i	−1.55100	+	0.631507i
$195$		0			0
$196$	3.30564	+	1.73488i	0.236117	+	0.123920i
$197$	−4.15379	+	3.01790i	−0.295945	+	0.215017i	−0.725842	−	0.687861i	$-0.758550\pi$
$197$	−4.15379	+	3.01790i	−0.295945	+	0.215017i	0.429897	+	0.902878i	$0.358550\pi$
$198$	2.72971	+	0.672794i	0.193992	+	0.0478134i
$199$	12.5552			0.890012			0.445006	−	0.895528i	$-0.353202\pi$
$199$	12.5552			0.890012			0.445006	+	0.895528i	$0.353202\pi$
$200$		0			0
$201$	−4.93307			−0.347952
$202$	26.7586	+	6.59523i	1.88273	+	0.464038i
$203$	10.6242	−	7.71894i	0.745673	−	0.541763i
$204$	−15.1952	+	28.9530i	−1.06388	+	2.02711i
$205$		0			0
$206$	9.25771	−	3.76938i	0.645015	−	0.262625i
$207$		−	2.31863i		−	0.161156i
$208$	−16.9067	+	5.04554i	−1.17227	+	0.349845i
$209$	0.120096	−	0.369617i	0.00830719	−	0.0255669i
$210$		0			0
$211$	7.25107	−	2.35602i	0.499184	−	0.162195i	−0.0485936	−	0.998819i	$-0.515474\pi$
$211$	7.25107	−	2.35602i	0.499184	−	0.162195i	0.547778	+	0.836624i	$0.315474\pi$
$212$	0.925404	−	0.135141i	0.0635570	−	0.00928153i
$213$	9.52057	−	29.3013i	0.652339	−	2.00769i
$214$	3.80931	−	15.4554i	0.260399	−	1.05651i
$215$		0			0
$216$	34.5686	+	15.0576i	2.35209	+	1.02454i
$217$	−6.59728	+	9.08038i	−0.447853	+	0.616416i
$218$	7.12338	−	11.4684i	0.482456	−	0.776736i
$219$	16.8446	−	23.1846i	1.13825	−	1.56667i
$220$		0			0
$221$	13.2861	+	18.2867i	0.893717	+	1.23010i
$222$	18.1789	−	1.32037i	1.22009	−	0.0886176i
$223$	−18.3487	+	5.96185i	−1.22872	+	0.399235i	−0.850250	−	0.526379i	$-0.823549\pi$
$223$	−18.3487	+	5.96185i	−1.22872	+	0.399235i	−0.378469	+	0.925614i	$0.623549\pi$
$224$	−5.97360	−	15.7495i	−0.399128	−	1.05231i
$225$		0			0
$226$	7.88588	−	12.6960i	0.524561	−	0.844523i
$227$	7.44462	+	22.9122i	0.494117	+	1.52073i	0.818329	+	0.574751i	$0.194901\pi$
$227$	7.44462	+	22.9122i	0.494117	+	1.52073i	−0.324212	+	0.945984i	$0.605099\pi$
$228$	4.16128	−	7.92890i	0.275587	−	0.525105i
$229$	−15.5176	−	21.3582i	−1.02544	−	1.41139i	−0.908322	−	0.418272i	$-0.862636\pi$
$229$	−15.5176	−	21.3582i	−1.02544	−	1.41139i	−0.117113	−	0.993119i	$-0.537364\pi$
$230$		0			0
$231$	2.12840	+	1.54637i	0.140038	+	0.101744i
$232$	−12.4158	−	1.20367i	−0.815135	−	0.0790248i
$233$	−14.2161	+	19.5668i	−0.931328	+	1.28186i	0.0280108	+	0.999608i	$0.491083\pi$
$233$	−14.2161	+	19.5668i	−0.931328	+	1.28186i	−0.959339	+	0.282256i	$0.908917\pi$
$234$	34.2251	−	28.8756i	2.23737	−	1.88766i
$235$		0			0
$236$	7.47905	+	7.66181i	0.486845	+	0.498741i
$237$	5.47713	−	16.8569i	0.355778	−	1.09497i
$238$	−16.4936	+	13.9156i	−1.06912	+	0.902014i
$239$	4.76280	+	14.6584i	0.308080	+	0.948173i	0.978510	+	0.206200i	$0.0661097\pi$
$239$	4.76280	+	14.6584i	0.308080	+	0.948173i	−0.670430	+	0.741973i	$0.733890\pi$
$240$		0			0
$241$	4.82186	−	14.8402i	0.310604	−	0.955940i	−0.666923	−	0.745127i	$-0.732389\pi$
$241$	4.82186	−	14.8402i	0.310604	−	0.955940i	0.977526	−	0.210813i	$-0.0676111\pi$
$242$	5.82541	+	14.3074i	0.374472	+	0.919715i
$243$	−26.9901			−1.73141
$244$	4.07160	+	0.695353i	0.260657	+	0.0445154i
$245$		0			0
$246$	28.8165	−	2.09301i	1.83728	−	0.133445i
$247$	−3.63845	−	5.00790i	−0.231509	−	0.318645i
$248$	10.4101	−	2.30075i	0.661044	−	0.146098i
$249$	−42.3693			−2.68505
$250$		0			0
$251$			2.59224i			0.163621i	0.996648	+	0.0818104i	$0.0260702\pi$
$251$			2.59224i			0.163621i	−0.996648	+	0.0818104i	$0.973930\pi$
$252$	29.8622	+	30.5919i	1.88114	+	1.92711i
$253$	−0.0723650	+	0.0525763i	−0.00454955	+	0.00330544i
$254$	0.139046	+	1.91439i	0.00872455	+	0.120120i
$255$		0			0
$256$	−5.67290	+	14.9606i	−0.354556	+	0.935035i
$257$			1.98944i			0.124098i	0.998073	+	0.0620490i	$0.0197635\pi$
$257$			1.98944i			0.124098i	−0.998073	+	0.0620490i	$0.980236\pi$
$258$	−18.5590	−	45.5815i	−1.15543	−	2.83778i
$259$	11.4403	+	3.71719i	0.710868	+	0.230975i
$260$		0			0
$261$	30.1092	−	9.78308i	1.86371	−	0.605558i
$262$	0.730959	+	0.866376i	0.0451588	+	0.0535249i
$263$	14.8066	+	4.81097i	0.913017	+	0.296657i	0.727599	−	0.686003i	$-0.240636\pi$
$263$	14.8066	+	4.81097i	0.913017	+	0.296657i	0.185418	+	0.982660i	$0.440636\pi$
$264$	−0.539285	−	2.44008i	−0.0331907	−	0.150177i
$265$		0			0
$266$	4.51685	−	3.81085i	0.276946	−	0.233658i
$267$	8.28618	+	6.02026i	0.507106	+	0.368434i
$268$	1.37059	+	2.77215i	0.0837222	+	0.169336i
$269$	0.776787	−	1.06916i	0.0473616	−	0.0651876i	−0.784679	−	0.619902i	$-0.787172\pi$
$269$	0.776787	−	1.06916i	0.0473616	−	0.0651876i	0.832041	+	0.554714i	$0.187172\pi$
$270$		0			0
$271$	11.7169	−	8.51285i	0.711753	−	0.517119i	−0.171986	−	0.985099i	$-0.555018\pi$
$271$	11.7169	−	8.51285i	0.711753	−	0.517119i	0.883739	+	0.467981i	$0.155018\pi$
$272$	20.4920	+	0.494775i	1.24251	+	0.0300001i
$273$	39.8523	−	12.9488i	2.41197	−	0.783697i
$274$	5.40859	−	8.70763i	0.326745	−	0.526047i
$275$		0			0
$276$	−1.84749	+	0.913423i	−0.111206	+	0.0549816i
$277$	−3.95585	−	12.1748i	−0.237684	−	0.731516i	−0.996754	−	0.0805069i	$-0.974346\pi$
$277$	−3.95585	−	12.1748i	−0.237684	−	0.731516i	0.759070	−	0.651009i	$-0.225654\pi$
$278$	−0.0449545	−	0.618934i	−0.00269619	−	0.0371212i
$279$	−21.8906	+	15.9045i	−1.31056	+	0.952176i
$280$		0			0
$281$	−2.54841	−	1.85153i	−0.152025	−	0.110453i	0.509172	−	0.860665i	$-0.329952\pi$
$281$	−2.54841	−	1.85153i	−0.152025	−	0.110453i	−0.661198	+	0.750212i	$0.729952\pi$
$282$	−6.76983	+	10.8992i	−0.403138	+	0.649036i
$283$	10.1940	+	7.40638i	0.605971	+	0.440264i	0.847993	−	0.530007i	$-0.177811\pi$
$283$	10.1940	+	7.40638i	0.605971	+	0.440264i	−0.242022	+	0.970271i	$0.577811\pi$
$284$	−19.1111	+	2.79089i	−1.13404	+	0.165609i
$285$		0			0
$286$	−1.67729	−	0.413404i	−0.0991804	−	0.0244451i
$287$	18.1348	+	5.89236i	1.07046	+	0.347815i
$288$	−1.96321	−	40.5602i	−0.115684	−	2.39003i
$289$	−2.86164	−	8.80721i	−0.168332	−	0.518071i
$290$		0			0
$291$	−50.0443	−	16.2604i	−2.93365	−	0.953200i
$292$	−17.7087	−	3.02432i	−1.03632	−	0.176985i
$293$	9.19701			0.537295			0.268647	−	0.963239i	$-0.413423\pi$
$293$	9.19701			0.537295			0.268647	+	0.963239i	$0.413423\pi$
$294$	3.17593	+	7.80018i	0.185224	+	0.454916i
$295$		0			0
$296$	−5.79278	−	9.84885i	−0.336698	−	0.572453i
$297$	2.16997	+	2.98671i	0.125915	+	0.173307i
$298$	2.27316	+	0.560268i	0.131681	+	0.0324555i
$299$			1.42470i			0.0823925i
$300$		0			0
$301$		−	32.4802i		−	1.87213i
$302$	−4.75937	+	19.3101i	−0.273871	+	1.11117i
$303$	36.5440	+	50.2984i	2.09940	+	2.88957i
$304$	−5.61183	−	0.135496i	−0.321861	−	0.00777126i
$305$		0			0
$306$	−48.1827	+	19.6181i	−2.75442	+	1.12149i
$307$	−24.3699			−1.39087			−0.695433	−	0.718591i	$-0.744787\pi$
$307$	−24.3699			−1.39087			−0.695433	+	0.718591i	$0.744787\pi$
$308$	0.277639	−	1.62570i	0.0158200	−	0.0926328i
$309$	21.4459	+	6.96821i	1.22002	+	0.396407i
$310$		0			0
$311$	7.74867	+	23.8479i	0.439387	+	1.35229i	0.888524	+	0.458830i	$0.151731\pi$
$311$	7.74867	+	23.8479i	0.439387	+	1.35229i	−0.449138	+	0.893463i	$0.648269\pi$
$312$	−36.4912	−	15.8951i	−2.06590	−	0.899882i
$313$	−10.3764	−	3.37148i	−0.586506	−	0.190567i	0.000706882	−	1.00000i	$-0.499775\pi$
$313$	−10.3764	−	3.37148i	−0.586506	−	0.190567i	−0.587213	+	0.809432i	$0.699775\pi$
$314$	−3.23720	+	13.1342i	−0.182686	+	0.741205i
$315$		0			0
$316$	−10.9945	+	1.60558i	−0.618491	+	0.0903210i
$317$	0.695505	+	0.505314i	0.0390635	+	0.0283813i	0.607146	−	0.794591i	$-0.292314\pi$
$317$	0.695505	+	0.505314i	0.0390635	+	0.0283813i	−0.568082	+	0.822972i	$0.692314\pi$
$318$	1.79221	+	1.11320i	0.100502	+	0.0624253i
$319$	−0.988078	−	0.717881i	−0.0553218	−	0.0401936i
$320$		0			0
$321$	29.0517	−	21.1073i	1.62151	−	1.17809i
$322$	−1.35659	+	0.0985320i	−0.0755998	+	0.00549098i
$323$	2.22231	+	6.83957i	0.123653	+	0.380564i
$324$	18.6104	+	37.6413i	1.03391	+	2.09118i
$325$		0			0
$326$	−6.59811	−	4.09830i	−0.365435	−	0.226984i
$327$	28.9658	−	9.41157i	1.60181	−	0.520461i
$328$	−9.18249	−	15.6120i	−0.507018	−	0.862031i
$329$	−6.85053	+	4.97720i	−0.377682	+	0.274402i
$330$		0			0
$331$	−4.98309	+	6.85864i	−0.273895	+	0.376985i	−0.923700	−	0.383117i	$-0.874851\pi$
$331$	−4.98309	+	6.85864i	−0.273895	+	0.376985i	0.649805	+	0.760101i	$0.274851\pi$
$332$	11.7718	+	23.8096i	0.646061	+	1.30672i
$333$	23.4609	+	17.0453i	1.28565	+	0.934079i
$334$	−10.9753	−	13.0086i	−0.600543	−	0.711799i
$335$		0			0
$336$	12.6115	−	35.8460i	0.688013	−	1.95556i
$337$	−15.9864	−	5.19430i	−0.870835	−	0.282951i	−0.160688	−	0.987005i	$-0.551371\pi$
$337$	−15.9864	−	5.19430i	−0.870835	−	0.282951i	−0.710147	+	0.704054i	$0.751371\pi$
$338$	−6.97823	+	5.88751i	−0.379566	+	0.320238i
$339$	32.0664	−	10.4190i	1.74161	−	0.565883i
$340$		0			0
$341$	0.992767	+	0.322570i	0.0537613	+	0.0174681i
$342$	13.1951	−	5.37251i	0.713508	−	0.290512i
$343$		−	15.2856i		−	0.825345i
$344$	−20.4583	+	23.0935i	−1.10304	+	1.24512i
$345$		0			0
$346$	−24.5247	+	1.78128i	−1.31845	+	0.0957622i
$347$	−14.2663	+	10.3651i	−0.765856	+	0.556427i	−0.900701	−	0.434440i	$-0.856946\pi$
$347$	−14.2663	+	10.3651i	−0.765856	+	0.556427i	0.134845	+	0.990867i	$0.456946\pi$
$348$	−19.6567	−	20.1371i	−1.05371	−	1.07946i
$349$		−	35.1956i		−	1.88398i	−0.335642	−	0.941990i	$-0.608953\pi$
$349$		−	35.1956i		−	1.88398i	0.335642	−	0.941990i	$-0.391047\pi$
$350$		0			0
$351$	58.8015			3.13859
$352$	−1.22138	+	0.981000i	−0.0650997	+	0.0522875i
$353$	16.7024	+	22.9889i	0.888980	+	1.22358i	0.973852	+	0.227184i	$0.0729519\pi$
$353$	16.7024	+	22.9889i	0.888980	+	1.22358i	−0.0848720	+	0.996392i	$0.527048\pi$
$354$	1.74977	+	24.0908i	0.0929991	+	1.28041i
$355$		0			0
$356$	1.08089	−	6.32910i	0.0572873	−	0.335442i
$357$	−48.6824			−2.57655
$358$	27.8710	−	11.3480i	1.47303	−	0.599758i
$359$	3.94315	−	12.1358i	0.208112	−	0.640501i	−0.791460	−	0.611221i	$-0.790679\pi$
$359$	3.94315	−	12.1358i	0.208112	−	0.640501i	0.999571	−	0.0292801i	$-0.00932147\pi$
$360$		0			0
$361$	5.26273	+	16.1970i	0.276986	+	0.852475i
$362$	7.49279	+	8.88091i	0.393812	+	0.466770i
$363$	−10.7691	+	33.1438i	−0.565230	+	1.73960i
$364$	−18.3491	−	18.7975i	−0.961753	−	0.985255i
$365$		0			0
$366$	6.00885	+	7.12204i	0.314087	+	0.372275i
$367$	−12.5338	+	17.2512i	−0.654257	+	0.900507i	−0.999274	−	0.0380891i	$-0.987873\pi$
$367$	−12.5338	+	17.2512i	−0.654257	+	0.900507i	0.345018	+	0.938596i	$0.387873\pi$
$368$	1.02660	+	0.784418i	0.0535153	+	0.0408906i
$369$	37.1894	+	27.0197i	1.93600	+	1.40659i
$370$		0			0
$371$	0.818430	+	1.12647i	0.0424908	+	0.0584835i
$372$	21.2965	+	11.1769i	1.10417	+	0.579497i
$373$	−3.63793	−	11.1964i	−0.188365	−	0.579727i	0.811625	−	0.584178i	$-0.198583\pi$
$373$	−3.63793	−	11.1964i	−0.188365	−	0.579727i	−0.999990	+	0.00445132i	$0.998583\pi$
$374$	1.70486	+	1.05894i	0.0881562	+	0.0547567i
$375$		0			0
$376$	8.00574	+	0.776131i	0.412864	+	0.0400259i
$377$	−18.5009	+	6.01130i	−0.952844	+	0.309598i
$378$	4.06670	+	55.9904i	0.209168	+	2.87983i
$379$	10.7274	+	14.7650i	0.551030	+	0.758428i	0.990152	−	0.140000i	$-0.0447102\pi$
$379$	10.7274	+	14.7650i	0.551030	+	0.758428i	−0.439121	+	0.898428i	$0.644710\pi$
$380$		0			0
$381$	−2.54518	+	3.50315i	−0.130394	+	0.179472i
$382$	4.25758	+	2.64452i	0.217836	+	0.135305i
$383$	21.1437	−	29.1018i	1.08039	−	1.48703i	0.221307	−	0.975204i	$-0.428968\pi$
$383$	21.1437	−	29.1018i	1.08039	−	1.48703i	0.859087	−	0.511830i	$-0.171032\pi$
$384$	−31.5451	+	17.5430i	−1.60978	+	0.895237i
$385$		0			0
$386$	−18.3945	−	4.53371i	−0.936255	−	0.230760i
$387$	24.1967	−	74.4697i	1.22999	−	3.78551i
$388$	4.76661	+	32.6403i	0.241988	+	1.65706i
$389$	2.67533	−	0.869269i	0.135645	−	0.0440737i	−0.240408	−	0.970672i	$-0.577281\pi$
$389$	2.67533	−	0.869269i	0.135645	−	0.0440737i	0.376053	+	0.926598i	$0.377281\pi$
$390$		0			0
$391$	0.511482	−	1.57418i	0.0258668	−	0.0796097i
$392$	3.50094	−	3.95190i	0.176824	−	0.199601i
$393$			2.55719i			0.128993i
$394$	2.73816	+	6.72501i	0.137947	+	0.338801i
$395$		0			0
$396$	1.84765	−	3.52052i	0.0928481	−	0.176913i
$397$	−6.36873	+	4.62715i	−0.319637	+	0.232230i	−0.736021	−	0.676959i	$-0.763297\pi$
$397$	−6.36873	+	4.62715i	−0.319637	+	0.232230i	0.416383	+	0.909189i	$0.363297\pi$
$398$	4.24910	−	17.2398i	0.212988	−	0.864151i
$399$	13.3319			0.667430
$400$		0			0
$401$	−6.74733			−0.336946			−0.168473	−	0.985706i	$-0.553884\pi$
$401$	−6.74733			−0.336946			−0.168473	+	0.985706i	$0.553884\pi$
$402$	−1.66952	+	6.77370i	−0.0832681	+	0.337841i
$403$	13.4509	−	9.77264i	0.670037	−	0.486810i
$404$	18.1121	−	34.5108i	0.901110	−	1.71698i
$405$		0			0
$406$	−7.00344	−	17.2007i	−0.347575	−	0.853655i
$407$		−	1.11874i		−	0.0554537i
$408$	34.6133	+	30.6635i	1.71362	+	1.51807i
$409$	−8.52623	+	26.2411i	−0.421595	+	1.29754i	0.484622	+	0.874724i	$0.338957\pi$
$409$	−8.52623	+	26.2411i	−0.421595	+	1.29754i	−0.906217	+	0.422813i	$0.861043\pi$
$410$		0			0
$411$	21.9930	−	7.14596i	1.08483	−	0.352484i
$412$	−2.04268	−	13.9876i	−0.100636	−	0.689122i
$413$	−4.92605	+	15.1608i	−0.242395	+	0.746015i
$414$	−3.18375	−	0.784703i	−0.156473	−	0.0385661i
$415$		0			0
$416$	1.20631	+	24.9226i	0.0591444	+	1.22193i
$417$	0.822872	−	1.13259i	0.0402962	−	0.0554630i
$418$	−0.466884	−	0.289997i	−0.0228360	−	0.0141842i
$419$	−14.4072	+	19.8299i	−0.703839	+	0.968752i	0.296068	+	0.955167i	$0.404324\pi$
$419$	−14.4072	+	19.8299i	−0.703839	+	0.968752i	−0.999908	+	0.0135851i	$0.995676\pi$
$420$		0			0
$421$	15.9444	+	21.9456i	0.777084	+	1.06956i	0.995598	+	0.0937303i	$0.0298792\pi$
$421$	15.9444	+	21.9456i	0.777084	+	1.06956i	−0.218514	+	0.975834i	$0.570121\pi$
$422$	−0.781083	−	10.7540i	−0.0380225	−	0.523494i
$423$	−19.4146	+	6.30817i	−0.943968	+	0.306714i
$424$	0.127624	−	1.31643i	0.00619795	−	0.0639314i
$425$		0			0
$426$	−37.0121	−	22.9895i	−1.79324	−	1.11384i
$427$	1.90037	+	5.84875i	0.0919655	+	0.283041i
$428$	−19.9330	−	10.4613i	−0.963496	−	0.505666i
$429$	−2.29066	−	3.15282i	−0.110594	−	0.152220i
$430$		0			0
$431$	−6.94699	−	5.04728i	−0.334625	−	0.243119i	0.407766	−	0.913087i	$-0.366308\pi$
$431$	−6.94699	−	5.04728i	−0.334625	−	0.243119i	−0.742390	+	0.669968i	$0.766308\pi$
$432$	32.3752	−	42.3708i	1.55765	−	2.03857i
$433$	−17.2045	+	23.6800i	−0.826797	+	1.13799i	0.161714	+	0.986838i	$0.448298\pi$
$433$	−17.2045	+	23.6800i	−0.826797	+	1.13799i	−0.988511	+	0.151150i	$0.951702\pi$
$434$	10.2357	+	12.1320i	0.491330	+	0.582354i
$435$		0			0
$436$	−13.3367	−	13.6626i	−0.638710	−	0.654318i
$437$	−0.140072	+	0.431097i	−0.00670055	+	0.0206222i
$438$	−26.1344	−	30.9761i	−1.24875	−	1.48009i
$439$	3.98757	+	12.2725i	0.190317	+	0.585734i	0.999999	−	0.00113362i	$-0.000360843\pi$
$439$	3.98757	+	12.2725i	0.190317	+	0.585734i	−0.809683	+	0.586868i	$0.800361\pi$
$440$		0			0
$441$	−4.14068	+	12.7437i	−0.197175	+	0.606843i
$442$	29.6063	−	12.0545i	1.40823	−	0.573375i
$443$	−1.10768			−0.0526274			−0.0263137	−	0.999654i	$-0.508377\pi$
$443$	−1.10768			−0.0526274			−0.0263137	+	0.999654i	$0.508377\pi$
$444$	4.33934	−	25.4087i	0.205936	−	1.20584i
$445$		0			0
$446$	1.97651	+	27.2127i	0.0935906	+	1.28856i
$447$	3.10443	+	4.27288i	0.146834	+	0.202100i
$448$	−23.6477	+	2.87229i	−1.11725	+	0.135703i
$449$	−6.01273			−0.283758			−0.141879	−	0.989884i	$-0.545314\pi$
$449$	−6.01273			−0.283758			−0.141879	+	0.989884i	$0.545314\pi$
$450$		0			0
$451$		−	1.77338i		−	0.0835051i
$452$	−14.7642	−	15.1250i	−0.694452	−	0.711422i
$453$	−36.2973	+	26.3715i	−1.70539	+	1.23904i
$454$	33.9807	−	2.46809i	1.59479	−	0.115833i
$455$		0			0
$456$	−9.47903	−	8.39736i	−0.443896	−	0.393242i
$457$			36.8695i			1.72468i	0.506328	+	0.862341i	$0.331003\pi$
$457$			36.8695i			1.72468i	−0.506328	+	0.862341i	$0.668997\pi$
$458$	−34.5791	+	14.0793i	−1.61578	+	0.657880i
$459$	−64.9710	−	21.1103i	−3.03258	−	0.985347i
$460$		0			0
$461$	−32.4405	+	10.5406i	−1.51091	+	0.490923i	−0.943177	−	0.332291i	$-0.892178\pi$
$461$	−32.4405	+	10.5406i	−1.51091	+	0.490923i	−0.567730	+	0.823215i	$0.692178\pi$
$462$	2.84368	−	2.39920i	0.132300	−	0.111621i
$463$	−39.9752	−	12.9887i	−1.85780	−	0.603637i	−0.995212	−	0.0977353i	$-0.968840\pi$
$463$	−39.9752	−	12.9887i	−1.85780	−	0.603637i	−0.862591	−	0.505902i	$-0.831160\pi$
$464$	−5.85471	+	16.6410i	−0.271798	+	0.772538i
$465$		0			0
$466$	22.0564	+	26.1425i	1.02174	+	1.21103i
$467$	9.30036	+	6.75711i	0.430370	+	0.312682i	0.781797	−	0.623533i	$-0.214304\pi$
$467$	9.30036	+	6.75711i	0.430370	+	0.312682i	−0.351427	+	0.936215i	$0.614304\pi$
$468$	−28.0668	−	56.7678i	−1.29739	−	2.62409i
$469$	−2.70628	+	3.72488i	−0.124964	+	0.171999i
$470$		0			0
$471$	−24.6884	+	17.9372i	−1.13758	+	0.826503i
$472$	13.0518	−	7.67662i	0.600756	−	0.353345i
$473$	−2.87290	+	0.933461i	−0.132096	+	0.0429206i
$474$	−21.2929	−	13.2257i	−0.978015	−	0.607477i
$475$		0			0
$476$	13.5258	+	27.3572i	0.619954	+	1.25392i
$477$	1.03729	+	3.19245i	0.0474942	+	0.146172i
$478$	21.7396	−	1.57900i	0.994348	−	0.0722216i
$479$	9.62460	−	6.99268i	0.439759	−	0.319504i	−0.345780	−	0.938316i	$-0.612386\pi$
$479$	9.62460	−	6.99268i	0.439759	−	0.319504i	0.785539	+	0.618812i	$0.212386\pi$
$480$		0			0
$481$	−14.4158	−	10.4737i	−0.657302	−	0.477558i
$482$	−18.7455	−	11.6434i	−0.853833	−	0.530344i
$483$	−2.48242	−	1.80359i	−0.112954	−	0.0820660i
$484$	21.6173	−	3.15688i	0.982606	−	0.143494i
$485$		0			0
$486$	−9.13437	+	37.0606i	−0.414343	+	1.68110i
$487$	−20.8019	−	6.75894i	−0.942622	−	0.306277i	−0.202908	−	0.979198i	$-0.565039\pi$
$487$	−20.8019	−	6.75894i	−0.942622	−	0.306277i	−0.739714	+	0.672921i	$0.765039\pi$
$488$	2.33277	−	5.35546i	0.105600	−	0.242430i
$489$	−5.41477	−	16.6649i	−0.244864	−	0.753615i
$490$		0			0
$491$	3.07965	+	1.00064i	0.138983	+	0.0451582i	0.377682	−	0.925935i	$-0.376721\pi$
$491$	3.07965	+	1.00064i	0.138983	+	0.0451582i	−0.238700	+	0.971093i	$0.576721\pi$
$492$	6.87856	−	40.2770i	0.310110	−	1.81583i
$493$	22.6001			1.01786
$494$	−8.10782	+	3.30119i	−0.364788	+	0.148527i
$495$		0			0
$496$	0.363935	−	15.0730i	0.0163412	−	0.676799i
$497$	−16.9019	−	23.2635i	−0.758155	−	1.04351i
$498$	−14.3392	+	58.1782i	−0.642556	+	2.60703i
$499$		−	4.70824i		−	0.210770i	−0.994432	−	0.105385i	$-0.966393\pi$
$499$		−	4.70824i		−	0.210770i	0.994432	−	0.105385i	$-0.0336074\pi$
$500$		0			0
$501$		−	38.3961i		−	1.71541i
$502$	3.55946	+	0.877304i	0.158867	+	0.0391560i
$503$	−7.58802	−	10.4440i	−0.338333	−	0.465676i	0.605621	−	0.795754i	$-0.292925\pi$
$503$	−7.58802	−	10.4440i	−0.338333	−	0.465676i	−0.943954	+	0.330078i	$0.892925\pi$
$504$	52.1128	−	30.6511i	2.32129	−	1.36531i
$505$		0			0
$506$	0.0477028	+	0.117160i	0.00212065	+	0.00520838i
$507$	−20.5969			−0.914740
$508$	2.67575	+	0.456969i	0.118717	+	0.0202747i
$509$	8.87419	+	2.88340i	0.393342	+	0.127804i	0.499008	−	0.866597i	$-0.333698\pi$
$509$	8.87419	+	2.88340i	0.393342	+	0.127804i	−0.105667	+	0.994402i	$0.533698\pi$
$510$		0			0
$511$	−8.26534	−	25.4381i	−0.365637	−	1.12532i
$512$	18.6228	+	12.8527i	0.823017	+	0.568017i
$513$	17.7926	+	5.78117i	0.785563	+	0.255245i
$514$	2.73175	+	0.673296i	0.120492	+	0.0296978i
$515$		0			0
$516$	−68.8699	+	10.0574i	−3.03183	+	0.442752i
$517$	0.637117	+	0.462892i	0.0280204	+	0.0203580i
$518$	8.97596	−	14.4510i	0.394381	−	0.634938i
$519$	−44.8777	−	32.6055i	−1.96991	−	1.43122i
$520$		0			0
$521$	−14.6710	+	10.6591i	−0.642748	+	0.466984i	−0.860793	−	0.508955i	$-0.830032\pi$
$521$	−14.6710	+	10.6591i	−0.642748	+	0.466984i	0.218045	+	0.975939i	$0.430032\pi$
$522$	−3.24336	−	44.6546i	−0.141958	−	1.95448i
$523$	−7.22455	−	22.2349i	−0.315908	−	0.972264i	−0.975379	−	0.220534i	$-0.929220\pi$
$523$	−7.22455	−	22.2349i	−0.315908	−	0.972264i	0.659472	−	0.751729i	$-0.270780\pi$
$524$	1.43702	−	0.710483i	0.0627766	−	0.0310376i
$525$		0			0
$526$	11.6171	−	18.7031i	0.506531	−	0.815495i
$527$	−18.3707	+	5.96899i	−0.800238	+	0.260013i
$528$	−3.53304	−	0.0853046i	−0.153756	−	0.00371240i
$529$	−18.5230	+	13.4577i	−0.805347	+	0.585119i
$530$		0			0
$531$	−22.5886	+	31.0905i	−0.980262	+	1.34921i
$532$	−3.70411	−	7.49191i	−0.160593	−	0.324816i
$533$	−22.8513	−	16.6025i	−0.989801	−	0.719132i
$534$	11.0709	−	9.34047i	0.479084	−	0.404202i
$535$		0			0
$536$	4.27036	−	0.943796i	0.184451	−	0.0407658i
$537$	64.5645	+	20.9783i	2.78616	+	0.905279i
$538$	−1.20519	−	1.42846i	−0.0519594	−	0.0615854i
$539$	0.491627	−	0.159739i	0.0211759	−	0.00688046i
$540$		0			0
$541$	−1.23623	−	0.401675i	−0.0531496	−	0.0172694i	0.282322	−	0.959320i	$-0.408896\pi$
$541$	−1.23623	−	0.401675i	−0.0531496	−	0.0172694i	−0.335471	+	0.942050i	$0.608896\pi$
$542$	−7.72376	−	18.9698i	−0.331764	−	0.814823i
$543$			26.2128i			1.12490i
$544$	7.61459	−	27.9706i	0.326473	−	1.19923i
$545$		0			0
$546$	−4.29287	−	59.1044i	−0.183718	−	2.52943i
$547$	−1.78489	+	1.29680i	−0.0763163	+	0.0554470i	−0.625289	−	0.780393i	$-0.715019\pi$
$547$	−1.78489	+	1.29680i	−0.0763163	+	0.0554470i	0.548973	+	0.835840i	$0.315019\pi$
$548$	−10.1262	−	10.3736i	−0.432569	−	0.443139i
$549$			14.8256i			0.632739i
$550$		0			0
$551$	−6.18915			−0.263667
$552$	0.628987	+	2.84596i	0.0267715	+	0.121132i
$553$	−9.72359	−	13.3834i	−0.413489	−	0.569119i
$554$	−18.0563	+	1.31147i	−0.767140	+	0.0557190i
$555$		0			0
$556$	−0.865085	−	0.147741i	−0.0366878	−	0.00626560i
$557$	22.2912			0.944509			0.472255	−	0.881462i	$-0.343440\pi$
$557$	22.2912			0.944509			0.472255	+	0.881462i	$0.343440\pi$
$558$	14.4302	+	35.4411i	0.610880	+	1.50034i
$559$	−14.8679	+	45.7586i	−0.628844	+	1.93538i
$560$		0			0
$561$	1.39910	+	4.30599i	0.0590701	+	0.181799i
$562$	−3.40484	+	2.87265i	−0.143624	+	0.121176i
$563$	−6.54968	+	20.1578i	−0.276036	+	0.849551i	0.712907	+	0.701258i	$0.247378\pi$
$563$	−6.54968	+	20.1578i	−0.276036	+	0.849551i	−0.988943	+	0.148293i	$0.952622\pi$
$564$	12.6747	+	12.9845i	0.533702	+	0.546744i
$565$		0			0
$566$	13.6199	−	11.4910i	0.572486	−	0.483004i
$567$	−36.7469	+	50.5777i	−1.54322	+	2.12406i
$568$	−2.63564	+	27.1864i	−0.110589	+	1.14072i
$569$	1.34832	+	0.979610i	0.0565244	+	0.0410674i	0.615689	−	0.787989i	$-0.288878\pi$
$569$	1.34832	+	0.979610i	0.0565244	+	0.0410674i	−0.559164	+	0.829057i	$0.688878\pi$
$570$		0			0
$571$	−2.18726	−	3.01051i	−0.0915340	−	0.125986i	0.760794	−	0.648994i	$-0.224810\pi$
$571$	−2.18726	−	3.01051i	−0.0915340	−	0.125986i	−0.852328	+	0.523008i	$0.824810\pi$
$572$	−1.13531	+	2.16322i	−0.0474696	+	0.0904486i
$573$	3.49400	+	10.7534i	0.145964	+	0.449231i
$574$	14.2284	−	22.9071i	0.593881	−	0.956124i
$575$		0			0
$576$	−56.3585	−	11.0312i	−2.34827	−	0.459635i
$577$	23.2030	−	7.53910i	0.965952	−	0.313857i	0.216771	−	0.976222i	$-0.430447\pi$
$577$	23.2030	−	7.53910i	0.965952	−	0.313857i	0.749181	+	0.662366i	$0.230447\pi$
$578$	−13.0618	+	0.948710i	−0.543301	+	0.0394611i
$579$	−25.1211	−	34.5763i	−1.04400	−	1.43694i
$580$		0			0
$581$	−23.2438	+	31.9924i	−0.964315	+	1.32727i
$582$	−39.2642	+	63.2138i	−1.62755	+	2.62030i
$583$	0.0761160	−	0.104765i	0.00315240	−	0.00433891i
$584$	−10.1460	+	23.2927i	−0.419844	+	0.963857i
$585$		0			0
$586$	3.11258	−	12.6286i	0.128580	−	0.521683i
$587$	−4.25195	+	13.0862i	−0.175497	+	0.540123i	−0.999656	−	0.0262350i	$-0.991648\pi$
$587$	−4.25195	+	13.0862i	−0.175497	+	0.540123i	0.824159	+	0.566358i	$0.191648\pi$
$588$	11.7854	−	1.72108i	0.486023	−	0.0709762i
$589$	5.03089	−	1.63464i	0.207294	−	0.0673540i
$590$		0			0
$591$	−5.06187	+	15.5788i	−0.208217	+	0.640827i
$592$	−15.4841	+	4.62099i	−0.636394	+	0.189922i
$593$			18.8934i			0.775861i	0.921689	+	0.387930i	$0.126810\pi$
$593$			18.8934i			0.775861i	−0.921689	+	0.387930i	$0.873190\pi$
$594$	4.83551	−	1.96883i	0.198403	−	0.0807821i
$595$		0			0
$596$	1.53863	−	2.93171i	0.0630248	−	0.120088i
$597$	32.4057	−	23.5441i	1.32628	−	0.963598i
$598$	1.95629	+	0.482168i	0.0799985	+	0.0197173i
$599$	33.9391			1.38671			0.693356	−	0.720595i	$-0.256131\pi$
$599$	33.9391			1.38671			0.693356	+	0.720595i	$0.256131\pi$
$600$		0			0
$601$	13.3568			0.544836			0.272418	−	0.962179i	$-0.412177\pi$
$601$	13.3568			0.544836			0.272418	+	0.962179i	$0.412177\pi$
$602$	−44.5993	−	10.9924i	−1.81773	−	0.448018i
$603$	−8.97979	+	6.52420i	−0.365685	+	0.265686i
$604$	24.9043	+	13.0704i	1.01334	+	0.531826i
$605$		0			0
$606$	81.4336	−	33.1565i	3.30801	−	1.34689i
$607$		−	22.7175i		−	0.922076i	−0.887380	−	0.461038i	$-0.847477\pi$
$607$		−	22.7175i		−	0.922076i	0.887380	−	0.461038i	$-0.152523\pi$
$608$	−2.08529	+	7.65987i	−0.0845697	+	0.310649i
$609$	12.9468	−	39.8462i	0.524632	−	1.61465i
$610$		0			0
$611$	11.9294	−	3.87611i	0.482614	−	0.156811i
$612$	10.6313	+	72.8002i	0.429747	+	2.94277i
$613$	−9.25887	+	28.4959i	−0.373962	+	1.15094i	0.570214	+	0.821496i	$0.306860\pi$
$613$	−9.25887	+	28.4959i	−0.373962	+	1.15094i	−0.944176	+	0.329441i	$0.893140\pi$
$614$	−8.24763	+	33.4629i	−0.332847	+	1.35045i
$615$		0			0
$616$	−2.13832	−	0.931425i	−0.0861553	−	0.0375282i
$617$	−14.2585	+	19.6251i	−0.574025	+	0.790077i	−0.993024	−	0.117909i	$-0.962381\pi$
$617$	−14.2585	+	19.6251i	−0.574025	+	0.790077i	0.419000	+	0.907986i	$0.362381\pi$
$618$	16.8262	−	27.0896i	0.676851	−	1.08970i
$619$	−20.9345	+	28.8138i	−0.841428	+	1.15813i	0.144259	+	0.989540i	$0.453920\pi$
$619$	−20.9345	+	28.8138i	−0.841428	+	1.15813i	−0.985687	+	0.168586i	$0.946080\pi$
$620$		0			0
$621$	−2.53092	−	3.48351i	−0.101562	−	0.139788i
$622$	35.3685	−	2.56889i	1.41815	−	0.103003i
$623$	9.09160	−	2.95404i	0.364247	−	0.118351i
$624$	−34.1758	+	44.7273i	−1.36813	+	1.79053i
$625$		0			0
$626$	−8.14117	+	13.1070i	−0.325387	+	0.523860i
$627$	−0.383150	−	1.17922i	−0.0153016	−	0.0470933i
$628$	16.9393	+	8.89013i	0.675950	+	0.354755i
$629$	12.1681	+	16.7480i	0.485175	+	0.667786i
$630$		0			0
$631$	−5.35186	−	3.88835i	−0.213054	−	0.154793i	0.476140	−	0.879369i	$-0.342035\pi$
$631$	−5.35186	−	3.88835i	−0.213054	−	0.154793i	−0.689194	+	0.724576i	$0.742035\pi$
$632$	−1.51627	+	15.6402i	−0.0603140	+	0.622134i
$633$	14.2974	−	19.6786i	0.568270	−	0.782156i
$634$	0.929240	−	0.783997i	0.0369049	−	0.0311365i
$635$		0			0
$636$	2.13511	−	2.08418i	0.0846625	−	0.0826430i
$637$	2.54428	−	7.83048i	0.100808	−	0.310255i
$638$	−1.32014	+	1.11380i	−0.0522647	+	0.0440956i
$639$	−21.4217	−	65.9293i	−0.847430	−	2.60812i
$640$		0			0
$641$	6.78939	−	20.8956i	0.268165	−	0.825327i	−0.722782	−	0.691076i	$-0.757137\pi$
$641$	6.78939	−	20.8956i	0.268165	−	0.825327i	0.990947	−	0.134251i	$-0.0428629\pi$
$642$	−19.1508	−	47.0349i	−0.755820	−	1.85632i
$643$	32.6614			1.28804			0.644019	−	0.765009i	$-0.277266\pi$
$643$	32.6614			1.28804			0.644019	+	0.765009i	$0.277266\pi$
$644$	−0.323821	+	1.89611i	−0.0127603	+	0.0747172i
$645$		0			0
$646$	10.1437	−	0.736756i	0.399097	−	0.0289873i
$647$	20.5295	+	28.2564i	0.807098	+	1.11088i	0.991765	+	0.128074i	$0.0408795\pi$
$647$	20.5295	+	28.2564i	0.807098	+	1.11088i	−0.184666	+	0.982801i	$0.559120\pi$
$648$	57.9845	−	12.8152i	2.27785	−	0.503429i
$649$	1.48256			0.0581954
$650$		0			0
$651$			35.8087i			1.40345i
$652$	−7.86049	+	7.67299i	−0.307841	+	0.300498i
$653$	−31.5991	+	22.9581i	−1.23657	+	0.898420i	−0.997365	−	0.0725499i	$-0.976886\pi$
$653$	−31.5991	+	22.9581i	−1.23657	+	0.898420i	−0.239204	+	0.970969i	$0.576886\pi$
$654$	−3.12019	−	42.9588i	−0.122009	−	1.67982i
$655$		0			0
$656$	−24.5449	+	7.32502i	−0.958317	+	0.285994i
$657$		−	64.4812i		−	2.51565i
$658$	4.51585	+	11.0911i	0.176046	+	0.432375i
$659$	−40.4722	−	13.1502i	−1.57657	−	0.512260i	−0.615402	−	0.788213i	$-0.711006\pi$
$659$	−40.4722	−	13.1502i	−1.57657	−	0.512260i	−0.961171	+	0.275953i	$0.911006\pi$
$660$		0			0
$661$	−15.1858	+	4.93417i	−0.590660	+	0.191917i	−0.589071	−	0.808082i	$-0.700506\pi$
$661$	−15.1858	+	4.93417i	−0.590660	+	0.191917i	−0.00158966	+	0.999999i	$0.500506\pi$
$662$	7.73129	+	9.16359i	0.300485	+	0.356153i
$663$	68.5844	+	22.2844i	2.66360	+	0.865455i
$664$	36.6774	−	8.10611i	1.42336	−	0.314578i
$665$		0			0
$666$	31.3453	−	26.4459i	1.21461	−	1.02476i
$667$	1.15243	+	0.837290i	0.0446223	+	0.0324200i
$668$	−21.5768	+	10.6679i	−0.834832	+	0.412753i
$669$	−36.1792	+	49.7964i	−1.39877	+	1.92524i
$670$		0			0
$671$	0.462710	−	0.336178i	0.0178627	−	0.0129780i
$672$	−44.9527	−	29.4486i	−1.73409	−	1.13600i
$673$	8.44939	−	2.74537i	0.325700	−	0.105826i	−0.141603	−	0.989924i	$-0.545226\pi$
$673$	8.44939	−	2.74537i	0.325700	−	0.105826i	0.467303	+	0.884097i	$0.345226\pi$
$674$	−12.5427	+	20.1933i	−0.483129	+	0.777818i
$675$		0			0
$676$	5.72259	+	11.5745i	0.220100	+	0.445173i
$677$	−7.28520	−	22.4216i	−0.279993	−	0.861730i	−0.987855	−	0.155379i	$-0.950340\pi$
$677$	−7.28520	−	22.4216i	−0.279993	−	0.861730i	0.707862	−	0.706351i	$-0.249660\pi$
$678$	−3.45418	−	47.5572i	−0.132657	−	1.82642i
$679$	−39.7323	+	28.8672i	−1.52478	+	1.10782i
$680$		0			0
$681$	62.1813	+	45.1773i	2.38279	+	1.73120i
$682$	0.778914	−	1.25402i	0.0298261	−	0.0480189i
$683$	−20.8468	−	15.1461i	−0.797680	−	0.579548i	0.112553	−	0.993646i	$-0.464097\pi$
$683$	−20.8468	−	15.1461i	−0.797680	−	0.579548i	−0.910233	+	0.414097i	$0.864097\pi$
$684$	−2.91144	−	19.9367i	−0.111322	−	0.762298i
$685$		0			0
$686$	−20.9890	−	5.17317i	−0.801363	−	0.197513i
$687$	−80.1042	−	26.0274i	−3.05617	−	0.993009i
$688$	24.7864	+	35.9074i	0.944974	+	1.36896i
$689$	−0.637371	−	1.96163i	−0.0242819	−	0.0747320i
$690$		0			0
$691$	28.3342	+	9.20634i	1.07788	+	0.350225i	0.793553	−	0.608501i	$-0.208229\pi$
$691$	28.3342	+	9.20634i	1.07788	+	0.350225i	0.284330	+	0.958726i	$0.408229\pi$
$692$	−5.85409	+	34.2782i	−0.222539	+	1.30306i
$693$	5.91952			0.224864
$694$	9.40431	+	23.0973i	0.356983	+	0.876761i
$695$		0			0
$696$	−34.3031	+	20.1760i	−1.30026	+	0.764769i
$697$	19.2885	+	26.5483i	0.730602	+	1.00559i
$698$	−48.3279	−	11.9114i	−1.82924	−	0.450854i
$699$			77.1621i			2.91854i
$700$		0			0
$701$			5.84579i			0.220792i	0.993888	+	0.110396i	$0.0352120\pi$
$701$			5.84579i			0.220792i	−0.993888	+	0.110396i	$0.964788\pi$
$702$	19.9004	−	80.7415i	0.751094	−	3.04739i
$703$	−3.33230	−	4.58651i	−0.125680	−	0.172984i
$704$	0.933675	+	2.00911i	0.0351892	+	0.0757211i
$705$		0			0
$706$	37.2192	−	15.1542i	1.40076	−	0.570336i
$707$	58.0275			2.18235
$708$	33.6718	+	5.75052i	1.26546	+	0.216118i
$709$	−18.5674	−	6.03290i	−0.697312	−	0.226570i	−0.0611529	−	0.998128i	$-0.519478\pi$
$709$	−18.5674	−	6.03290i	−0.697312	−	0.226570i	−0.636159	+	0.771558i	$0.719478\pi$
$710$		0			0
$711$	−12.3238	−	37.9288i	−0.462179	−	1.42244i
$712$	−8.32481	−	3.62619i	−0.311986	−	0.135897i
$713$	−1.15790	−	0.376224i	−0.0433637	−	0.0140897i
$714$	−16.4758	+	66.8468i	−0.616591	+	2.50168i
$715$		0			0
$716$	−6.14963	−	42.1108i	−0.229822	−	1.57375i
$717$	39.7814	+	28.9028i	1.48566	+	1.07940i
$718$	−15.3294	−	9.52159i	−0.572088	−	0.355342i
$719$	37.3747	+	27.1543i	1.39384	+	1.01268i	0.995432	+	0.0954761i	$0.0304373\pi$
$719$	37.3747	+	27.1543i	1.39384	+	1.01268i	0.398408	+	0.917208i	$0.369563\pi$
$720$		0			0
$721$	17.0268	−	12.3707i	0.634112	−	0.460709i
$722$	24.0216	−	1.74474i	0.893990	−	0.0649324i
$723$	−15.3836	−	47.3457i	−0.572121	−	1.76081i
$724$	14.7304	−	7.28291i	0.547450	−	0.270667i
$725$		0			0
$726$	41.8658	+	26.0043i	1.55379	+	0.965108i
$727$	−6.84600	+	2.22440i	−0.253904	+	0.0824984i	−0.433204	−	0.901296i	$-0.642617\pi$
$727$	−6.84600	+	2.22440i	−0.253904	+	0.0824984i	0.179300	+	0.983795i	$0.442617\pi$
$728$	−32.0212	+	18.8338i	−1.18678	+	0.698027i
$729$	−18.7064	+	13.5910i	−0.692831	+	0.503371i
$730$		0			0
$731$	32.8556	−	45.2219i	1.21521	−	1.67259i
$732$	11.8130	−	5.84053i	0.436622	−	0.215872i
$733$	−22.7156	−	16.5038i	−0.839018	−	0.609582i	0.0830781	−	0.996543i	$-0.473525\pi$
$733$	−22.7156	−	16.5038i	−0.839018	−	0.609582i	−0.922096	+	0.386961i	$0.873525\pi$
$734$	19.4462	+	23.0488i	0.717772	+	0.850746i
$735$		0			0
$736$	1.42454	−	1.14418i	0.0525092	−	0.0421749i
$737$	0.407244	+	0.132322i	0.0150010	+	0.00487413i
$738$	49.6874	−	41.9211i	1.82902	−	1.54314i
$739$	37.8363	−	12.2937i	1.39183	−	0.452233i	0.485290	−	0.874353i	$-0.338714\pi$
$739$	37.8363	−	12.2937i	1.39183	−	0.452233i	0.906540	+	0.422121i	$0.138714\pi$
$740$		0			0
$741$	−18.7822	−	6.10270i	−0.689980	−	0.224188i
$742$	1.82377	−	0.742566i	0.0669526	−	0.0272605i
$743$		−	20.8383i		−	0.764482i	−0.924063	−	0.382241i	$-0.875152\pi$
$743$		−	20.8383i		−	0.764482i	0.924063	−	0.382241i	$-0.124848\pi$
$744$	22.5548	−	25.4601i	0.826898	−	0.933411i
$745$		0			0
$746$	−16.6052	+	1.20607i	−0.607959	+	0.0441574i
$747$	−77.1260	+	56.0353i	−2.82189	+	2.05022i
$748$	2.03104	−	1.98260i	0.0742623	−	0.0724909i
$749$		−	33.5159i		−	1.22464i
$750$		0			0
$751$	−48.8753			−1.78348			−0.891742	−	0.452545i	$-0.850516\pi$
$751$	−48.8753			−1.78348			−0.891742	+	0.452545i	$0.850516\pi$
$752$	3.77514	−	10.7302i	0.137665	−	0.391289i
$753$	4.86111	+	6.69075i	0.177149	+	0.243824i
$754$	1.99291	+	27.4384i	0.0725774	+	0.999247i
$755$		0			0
$756$	78.2579	+	13.3650i	2.84621	+	0.486081i
$757$	18.6251			0.676942			0.338471	−	0.940977i	$-0.390090\pi$
$757$	18.6251			0.676942			0.338471	+	0.940977i	$0.390090\pi$
$758$	23.9047	−	9.73305i	0.868257	−	0.353520i
$759$	−0.0881851	+	0.271406i	−0.00320092	+	0.00985141i
$760$		0			0
$761$	12.5520	+	38.6311i	0.455009	+	1.40037i	0.871124	+	0.491063i	$0.163391\pi$
$761$	12.5520	+	38.6311i	0.455009	+	1.40037i	−0.416115	+	0.909312i	$0.636609\pi$
$762$	3.94887	+	4.68043i	0.143052	+	0.169554i
$763$	8.78414	−	27.0348i	0.318007	−	0.978726i
$764$	5.07216	−	4.95117i	0.183504	−	0.179127i
$765$		0			0
$766$	−32.8046	−	38.8820i	−1.18528	−	1.40486i
$767$	13.8798	−	19.1039i	0.501169	−	0.689800i
$768$	13.4127	+	49.2523i	0.483990	+	1.77724i
$769$	14.8380	+	10.7804i	0.535072	+	0.388753i	0.822252	−	0.569124i	$-0.192718\pi$
$769$	14.8380	+	10.7804i	0.535072	+	0.388753i	−0.287179	+	0.957877i	$0.592718\pi$
$770$		0			0
$771$	3.73071	+	5.13489i	0.134358	+	0.184928i
$772$	−12.4507	+	23.7235i	−0.448109	+	0.853827i
$773$	10.0305	+	30.8706i	0.360770	+	1.11034i	0.952588	+	0.304265i	$0.0984107\pi$
$773$	10.0305	+	30.8706i	0.360770	+	1.11034i	−0.591817	+	0.806072i	$0.701589\pi$
$774$	−94.0670	−	58.4281i	−3.38117	−	2.10016i
$775$		0			0
$776$	46.4323	+	4.50147i	1.66682	+	0.161593i
$777$	36.4990	−	11.8592i	1.30939	−	0.425448i
$778$	−0.288186	−	3.96775i	−0.0103320	−	0.142251i
$779$	−5.28223	−	7.27037i	−0.189256	−	0.260488i
$780$		0			0
$781$	−1.57192	+	2.16357i	−0.0562478	+	0.0774185i
$782$	−1.98844	−	1.23508i	−0.0711064	−	0.0441665i
$783$	34.5574	−	47.5641i	1.23498	−	1.69980i
$784$	−4.24160	−	6.14468i	−0.151486	−	0.219453i
$785$		0			0
$786$	3.51133	+	0.865441i	0.125245	+	0.0308693i
$787$	11.5801	−	35.6398i	0.412785	−	1.27042i	−0.501432	−	0.865197i	$-0.667193\pi$
$787$	11.5801	−	35.6398i	0.412785	−	1.27042i	0.914217	−	0.405224i	$-0.132807\pi$
$788$	10.1609	−	1.48385i	0.361969	−	0.0528600i
$789$	47.2388	−	15.3488i	1.68174	−	0.546432i
$790$		0			0
$791$	9.72441	−	29.9287i	0.345760	−	1.06414i
$792$	−4.20880	−	3.72852i	−0.149553	−	0.132487i
$793$		−	9.10969i		−	0.323495i
$794$	4.19824	+	10.3110i	0.148990	+	0.365925i
$795$		0			0
$796$	−22.2342	−	11.6691i	−0.788072	−	0.413599i
$797$	−44.1511	+	32.0777i	−1.56391	+	1.13625i	−0.631207	+	0.775614i	$0.717440\pi$
$797$	−44.1511	+	32.0777i	−1.56391	+	1.13625i	−0.932707	+	0.360636i	$0.882560\pi$
$798$	4.51198	−	18.3063i	0.159722	−	0.648037i
$799$	−14.5727			−0.515544
$800$		0			0
$801$	23.0456			0.814277
$802$	−2.28353	+	9.26490i	−0.0806342	+	0.327155i
$803$	−2.01248	+	1.46215i	−0.0710187	+	0.0515981i
$804$	8.73608	+	4.58491i	0.308098	+	0.161697i
$805$		0			0
$806$	−8.86678	−	21.7771i	−0.312319	−	0.767066i
$807$		−	4.21624i		−	0.148419i
$808$	−41.2577	−	36.5497i	−1.45144	−	1.28582i
$809$	−2.50898	+	7.72183i	−0.0882109	+	0.271485i	−0.985425	−	0.170111i	$-0.945587\pi$
$809$	−2.50898	+	7.72183i	−0.0882109	+	0.271485i	0.897214	+	0.441596i	$0.145587\pi$
$810$		0			0
$811$	1.71354	−	0.556763i	0.0601705	−	0.0195506i	−0.278777	−	0.960356i	$-0.589929\pi$
$811$	1.71354	−	0.556763i	0.0601705	−	0.0195506i	0.338948	+	0.940805i	$0.389929\pi$
$812$	−25.9888	+	3.79527i	−0.912029	+	0.133188i
$813$	14.2784	−	43.9445i	0.500766	−	1.54120i
$814$	−1.53616	−	0.378619i	−0.0538424	−	0.0132706i
$815$		0			0
$816$	53.8191	−	37.1507i	1.88405	−	1.30053i
$817$	−8.99767	+	12.3842i	−0.314789	+	0.433269i
$818$	33.1466	+	20.5884i	1.15894	+	0.719858i
$819$	55.4188	−	76.2775i	1.93649	−	2.66535i
$820$		0			0
$821$	−13.9783	−	19.2395i	−0.487848	−	0.671465i	0.492142	−	0.870515i	$-0.336214\pi$
$821$	−13.9783	−	19.2395i	−0.487848	−	0.671465i	−0.979989	+	0.199051i	$0.936214\pi$
$822$	−2.36908	−	32.6175i	−0.0826310	−	1.13767i
$823$	22.5499	−	7.32692i	0.786042	−	0.255400i	0.111624	−	0.993751i	$-0.464395\pi$
$823$	22.5499	−	7.32692i	0.786042	−	0.255400i	0.674418	+	0.738350i	$0.264395\pi$
$824$	−19.8980	−	1.92905i	−0.693181	−	0.0672018i
$825$		0			0
$826$	19.1505	+	11.8950i	0.666331	+	0.413880i
$827$	2.73313	+	8.41171i	0.0950402	+	0.292504i	0.987264	−	0.159089i	$-0.0508558\pi$
$827$	2.73313	+	8.41171i	0.0950402	+	0.292504i	−0.892224	+	0.451593i	$0.850856\pi$
$828$	−2.15499	+	4.10611i	−0.0748909	+	0.142697i
$829$	4.69015	+	6.45543i	0.162896	+	0.224206i	0.882660	−	0.470012i	$-0.155750\pi$
$829$	4.69015	+	6.45543i	0.162896	+	0.224206i	−0.719765	+	0.694218i	$0.755750\pi$
$830$		0			0
$831$	−33.0413	−	24.0059i	−1.14619	−	0.832755i
$832$	34.6300	+	6.77825i	1.20058	+	0.234993i
$833$	−5.62245	+	7.73864i	−0.194806	+	0.268128i
$834$	−1.27669	−	1.51321i	−0.0442082	−	0.0523982i
$835$		0			0
$836$	−0.556211	+	0.542943i	−0.0192370	+	0.0187781i
$837$	−15.5279	+	47.7898i	−0.536721	+	1.65186i
$838$	22.3529	+	26.4940i	0.772168	+	0.915220i
$839$	−14.2160	−	43.7523i	−0.490790	−	1.51050i	−0.823417	−	0.567437i	$-0.807935\pi$
$839$	−14.2160	−	43.7523i	−0.490790	−	1.51050i	0.332627	−	0.943058i	$-0.392065\pi$
$840$		0			0
$841$	2.95111	−	9.08258i	0.101762	−	0.313193i
$842$	35.5301	−	14.4665i	1.22445	−	0.498548i
$843$	−10.0497			−0.346130
$844$	−15.0308	−	2.56699i	−0.517383	−	0.0883594i
$845$		0			0
$846$	2.09133	+	28.7934i	0.0719014	+	0.989939i
$847$	19.1184	+	26.3142i	0.656917	+	0.904168i
$848$	−1.76442	−	0.620768i	−0.0605906	−	0.0213173i
$849$	40.2003			1.37967
$850$		0			0
$851$			1.30482i			0.0447287i
$852$	−44.0935	+	43.0417i	−1.51062	+	1.47459i
$853$	37.0549	−	26.9220i	1.26874	−	0.921790i	0.269584	−	0.962977i	$-0.413114\pi$
$853$	37.0549	−	26.9220i	1.26874	−	0.921790i	0.999151	+	0.0411867i	$0.0131138\pi$
$854$	8.67419	−	0.630025i	0.296825	−	0.0215590i
$855$		0			0
$856$	−21.1106	+	23.8299i	−0.721546	+	0.814489i
$857$		−	46.7189i		−	1.59589i	−0.602733	−	0.797943i	$-0.705922\pi$
$857$		−	46.7189i		−	1.59589i	0.602733	−	0.797943i	$-0.294078\pi$
$858$	−5.10444	+	2.07833i	−0.174263	+	0.0709530i
$859$	−35.3436	−	11.4838i	−1.20591	−	0.391824i	−0.363978	−	0.931408i	$-0.618582\pi$
$859$	−35.3436	−	11.4838i	−1.20591	−	0.391824i	−0.841932	+	0.539584i	$0.818582\pi$
$860$		0			0
$861$	57.8569	−	18.7988i	1.97176	−	0.640662i
$862$	−9.28163	+	7.83088i	−0.316133	+	0.266721i
$863$	−47.5068	−	15.4359i	−1.61715	−	0.525444i	−0.645883	−	0.763436i	$-0.723511\pi$
$863$	−47.5068	−	15.4359i	−1.61715	−	0.525444i	−0.971267	+	0.237992i	$0.923511\pi$
$864$	−47.2234	−	58.7948i	−1.60657	−	2.00024i
$865$		0			0
$866$	26.6929	+	31.6380i	0.907062	+	1.07510i
$867$	−23.9019	−	17.3657i	−0.811750	−	0.589771i
$868$	20.1228	−	9.94899i	0.683012	−	0.337691i
$869$	−0.904318	+	1.24469i	−0.0306769	+	0.0422231i
$870$		0			0
$871$	5.51771	−	4.00885i	0.186960	−	0.135835i
$872$	−23.2739	+	13.6890i	−0.788155	+	0.463567i
$873$	−112.602	+	36.5866i	−3.81100	+	1.23827i
$874$	0.544543	+	0.338234i	0.0184194	+	0.0114409i
$875$		0			0
$876$	−51.3787	+	25.4024i	−1.73593	+	0.858266i
$877$	−8.12444	−	25.0044i	−0.274343	−	0.844340i	−0.989393	−	0.145267i	$-0.953596\pi$
$877$	−8.12444	−	25.0044i	−0.274343	−	0.844340i	0.715050	−	0.699073i	$-0.246404\pi$
$878$	18.2012	−	1.32199i	0.614259	−	0.0446149i
$879$	23.7381	−	17.2467i	0.800666	−	0.581718i
$880$		0			0
$881$	−13.3185	−	9.67642i	−0.448710	−	0.326007i	0.340376	−	0.940289i	$-0.389446\pi$
$881$	−13.3185	−	9.67642i	−0.448710	−	0.326007i	−0.789086	+	0.614282i	$0.789446\pi$
$882$	16.0973	+	9.99857i	0.542024	+	0.336669i
$883$	−5.10972	−	3.71243i	−0.171956	−	0.124933i	0.498479	−	0.866902i	$-0.333892\pi$
$883$	−5.10972	−	3.71243i	−0.171956	−	0.124933i	−0.670434	+	0.741969i	$0.733892\pi$
$884$	−6.53252	−	44.7327i	−0.219712	−	1.50452i
$885$		0			0
$886$	−0.374877	+	1.52098i	−0.0125942	+	0.0510982i
$887$	26.2498	+	8.52907i	0.881381	+	0.286378i	0.714531	−	0.699604i	$-0.246640\pi$
$887$	26.2498	+	8.52907i	0.881381	+	0.286378i	0.166850	+	0.985982i	$0.446640\pi$
$888$	−33.4207	−	14.5576i	−1.12152	−	0.488522i
$889$	1.24888	+	3.84365i	0.0418860	+	0.128912i
$890$		0			0
$891$	5.52971	+	1.79671i	0.185252	+	0.0601922i
$892$	38.0352	+	6.49571i	1.27351	+	0.217493i
$893$	3.99079			0.133547
$894$	6.91783	−	2.81667i	0.231367	−	0.0942035i
$895$		0			0
$896$	−4.05920	+	33.4432i	−0.135608	+	1.11726i
$897$	2.67168	+	3.67725i	0.0892047	+	0.122780i
$898$	−2.03492	+	8.25621i	−0.0679060	+	0.275513i
$899$		−	16.6237i		−	0.554431i
$900$		0			0
$901$			2.39626i			0.0798312i
$902$	−2.43506	−	0.600172i	−0.0810787	−	0.0199836i
$903$	−60.9087	−	83.8337i	−2.02692	−	2.78981i
$904$	−25.7652	+	15.1543i	−0.856939	+	0.504024i
$905$		0			0
$906$	23.9270	+	58.7656i	0.794923	+	1.95236i
$907$	−15.5893			−0.517636			−0.258818	−	0.965926i	$-0.583333\pi$
$907$	−15.5893			−0.517636			−0.258818	+	0.965926i	$0.583333\pi$
$908$	8.11126	−	47.4949i	0.269182	−	1.57617i
$909$	133.044	+	43.2286i	4.41279	+	1.43380i
$910$		0			0
$911$	8.96903	+	27.6038i	0.297157	+	0.914556i	0.982488	+	0.186324i	$0.0596575\pi$
$911$	8.96903	+	27.6038i	0.297157	+	0.914556i	−0.685331	+	0.728232i	$0.740342\pi$
$912$	−14.7386	+	10.1739i	−0.488044	+	0.336891i
$913$	3.49776	+	1.13649i	0.115759	+	0.0376123i
$914$	50.6263	+	12.4779i	1.67457	+	0.412733i
$915$		0			0
$916$	7.62976	+	52.2462i	0.252094	+	1.72626i
$917$	1.93089	+	1.40287i	0.0637636	+	0.0463270i
$918$	−50.9755	+	82.0685i	−1.68244	+	2.70867i
$919$	34.5740	+	25.1195i	1.14049	+	0.828616i	0.987188	−	0.159563i	$-0.0510086\pi$
$919$	34.5740	+	25.1195i	1.14049	+	0.828616i	0.153304	+	0.988179i	$0.451009\pi$
$920$		0			0
$921$	−62.9005	+	45.6999i	−2.07264	+	1.50586i
$922$	3.49448	+	48.1121i	0.115085	+	1.58449i
$923$	13.1628	+	40.5108i	0.433258	+	1.33343i
$924$	−2.33199	−	4.71668i	−0.0767170	−	0.155167i
$925$		0			0
$926$	−31.3641	+	50.4949i	−1.03069	+	1.65937i
$927$	48.2544	−	15.6788i	1.58488	−	0.514959i
$928$	20.8687	+	13.6711i	0.685047	+	0.448776i
$929$	−7.83492	+	5.69240i	−0.257055	+	0.186762i	−0.708848	−	0.705361i	$-0.750785\pi$
$929$	−7.83492	+	5.69240i	−0.257055	+	0.186762i	0.451792	+	0.892123i	$0.350785\pi$
$930$		0			0
$931$	1.53974	−	2.11926i	0.0504628	−	0.0694561i
$932$	43.3615	−	21.4385i	1.42035	−	0.702242i
$933$	64.7208	+	47.0224i	2.11886	+	1.53945i
$934$	12.4259	−	10.4837i	0.406588	−	0.343037i
$935$		0			0
$936$	−87.4478	+	19.3269i	−2.85832	+	0.631720i
$937$	−45.0827	−	14.6482i	−1.47279	−	0.478537i	−0.540837	−	0.841127i	$-0.681893\pi$
$937$	−45.0827	−	14.6482i	−1.47279	−	0.478537i	−0.931949	+	0.362590i	$0.881893\pi$
$938$	4.19881	+	4.97668i	0.137096	+	0.162494i
$939$	−33.1045	+	10.7563i	−1.08032	+	0.351018i
$940$		0			0
$941$	14.2417	+	4.62742i	0.464267	+	0.150850i	0.531804	−	0.846867i	$-0.321514\pi$
$941$	14.2417	+	4.62742i	0.464267	+	0.150850i	−0.0675373	+	0.997717i	$0.521514\pi$
$942$	16.2745	+	39.9708i	0.530253	+	1.30232i
$943$			2.06835i			0.0673549i
$944$	−6.12377	−	20.5197i	−0.199312	−	0.667859i
$945$		0			0
$946$	0.309467	+	4.26075i	0.0100617	+	0.138529i
$947$	21.2273	−	15.4226i	0.689796	−	0.501166i	−0.186797	−	0.982398i	$-0.559811\pi$
$947$	21.2273	−	15.4226i	0.689796	−	0.501166i	0.876593	+	0.481233i	$0.159811\pi$
$948$	−25.3668	+	24.7617i	−0.823874	+	0.804222i
$949$			39.6210i			1.28615i
$950$		0			0
$951$	2.74274			0.0889394
$952$	42.1424	−	9.31393i	1.36584	−	0.301866i
$953$	17.5587	+	24.1675i	0.568782	+	0.782861i	0.992410	−	0.122975i	$-0.0392436\pi$
$953$	17.5587	+	24.1675i	0.568782	+	0.782861i	−0.423628	+	0.905836i	$0.639244\pi$
$954$	4.73467	−	0.343889i	0.153291	−	0.0111338i
$955$		0			0
$956$	5.18929	−	30.3856i	0.167834	−	0.982739i
$957$	−3.89651			−0.125956
$958$	−6.34450	−	15.5823i	−0.204982	−	0.503441i
$959$	6.66957	−	20.5268i	0.215371	−	0.662845i
$960$		0			0
$961$	−5.18900	−	15.9701i	−0.167387	−	0.515164i
$962$	−19.2604	+	16.2499i	−0.620980	+	0.523919i
$963$	24.9682	−	76.8443i	0.804590	−	2.47627i
$964$	−22.3320	+	21.7993i	−0.719264	+	0.702107i
$965$		0			0
$966$	−3.31668	+	2.79827i	−0.106712	+	0.0900329i
$967$	−15.3115	+	21.0745i	−0.492385	+	0.677710i	−0.980826	−	0.194887i	$-0.937566\pi$
$967$	−15.3115	+	21.0745i	−0.492385	+	0.677710i	0.488440	+	0.872597i	$0.337566\pi$
$968$	2.98127	−	30.7516i	0.0958217	−	0.988394i
$969$	18.5619	+	13.4860i	0.596294	+	0.433233i
$970$		0			0
$971$	−1.38452	−	1.90563i	−0.0444314	−	0.0611546i	0.786223	−	0.617943i	$-0.212034\pi$
$971$	−1.38452	−	1.90563i	−0.0444314	−	0.0611546i	−0.830655	+	0.556788i	$0.812034\pi$
$972$	47.7973	+	25.0852i	1.53310	+	0.804608i
$973$	−0.403769	−	1.24267i	−0.0129442	−	0.0398383i
$974$	−16.3209	+	26.2760i	−0.522956	+	0.841938i
$975$		0			0
$976$	−6.56421	−	5.01565i	−0.210115	−	0.160547i
$977$	8.92406	−	2.89960i	0.285506	−	0.0927665i	−0.162763	−	0.986665i	$-0.552041\pi$
$977$	8.92406	−	2.89960i	0.285506	−	0.0927665i	0.448269	+	0.893899i	$0.352041\pi$
$978$	−24.7155	+	1.79514i	−0.790315	+	0.0574023i
$979$	−0.522574	−	0.719261i	−0.0167015	−	0.0229877i
$980$		0			0
$981$	40.2801	−	55.4407i	1.28604	−	1.77009i
$982$	2.41626	−	3.89008i	0.0771059	−	0.124137i
$983$	−32.0991	+	44.1807i	−1.02380	+	1.40914i	−0.114301	+	0.993446i	$0.536463\pi$
$983$	−32.0991	+	44.1807i	−1.02380	+	1.40914i	−0.909503	+	0.415698i	$0.863537\pi$
$984$	−52.9772	−	23.0762i	−1.68885	−	0.735643i
$985$		0			0
$986$	7.64866	−	31.0327i	0.243583	−	0.988283i
$987$	−8.34816	+	25.6930i	−0.265725	+	0.817817i
$988$	1.78896	+	12.2503i	0.0569145	+	0.389733i
$989$	3.35076	−	1.08873i	0.106548	−	0.0346196i
$990$		0			0
$991$	19.1415	−	58.9116i	0.608051	−	1.87139i	0.133778	−	0.991011i	$-0.457289\pi$
$991$	19.1415	−	58.9116i	0.608051	−	1.87139i	0.474273	−	0.880378i	$-0.342711\pi$
$992$	−20.5739	−	5.60096i	−0.653223	−	0.177831i
$993$			27.0472i			0.858316i
$994$	−37.6638	+	15.3352i	−1.19462	+	0.486404i
$995$		0			0
$996$	75.0328	+	39.3790i	2.37751	+	1.24777i
$997$	24.8911	−	18.0845i	0.788310	−	0.572741i	−0.119151	−	0.992876i	$-0.538017\pi$
$997$	24.8911	−	18.0845i	0.788310	−	0.572741i	0.907462	+	0.420135i	$0.138017\pi$
$998$	−6.46498	−	1.59343i	−0.204645	−	0.0504391i
$999$	53.8537			1.70386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.349.16		112
5.2	odd	4		1000.2.t.b.901.51		224
5.3	odd	4		1000.2.t.b.901.6		224
5.4	even	2		200.2.o.a.69.13	yes	112
8.5	even	2	inner	1000.2.o.a.349.22		112
20.19	odd	2		800.2.be.a.369.28		112
25.3	odd	20		1000.2.t.b.101.40		224
25.4	even	10	inner	1000.2.o.a.149.22		112
25.21	even	5		200.2.o.a.29.7	✓	112
25.22	odd	20		1000.2.t.b.101.17		224
40.13	odd	4		1000.2.t.b.901.40		224
40.19	odd	2		800.2.be.a.369.1		112
40.29	even	2		200.2.o.a.69.7	yes	112
40.37	odd	4		1000.2.t.b.901.17		224
100.71	odd	10		800.2.be.a.529.1		112
200.21	even	10		200.2.o.a.29.13	yes	112
200.29	even	10	inner	1000.2.o.a.149.16		112
200.53	odd	20		1000.2.t.b.101.6		224
200.171	odd	10		800.2.be.a.529.28		112
200.197	odd	20		1000.2.t.b.101.51		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	25.21	even	5
200.2.o.a.29.13	yes	112	200.21	even	10
200.2.o.a.69.7	yes	112	40.29	even	2
200.2.o.a.69.13	yes	112	5.4	even	2
800.2.be.a.369.1		112	40.19	odd	2
800.2.be.a.369.28		112	20.19	odd	2
800.2.be.a.529.1		112	100.71	odd	10
800.2.be.a.529.28		112	200.171	odd	10
1000.2.o.a.149.16		112	200.29	even	10	inner
1000.2.o.a.149.22		112	25.4	even	10	inner
1000.2.o.a.349.16		112	1.1	even	1	trivial
1000.2.o.a.349.22		112	8.5	even	2	inner
1000.2.t.b.101.6		224	200.53	odd	20
1000.2.t.b.101.17		224	25.22	odd	20
1000.2.t.b.101.40		224	25.3	odd	20
1000.2.t.b.101.51		224	200.197	odd	20
1000.2.t.b.901.6		224	5.3	odd	4
1000.2.t.b.901.17		224	40.37	odd	4
1000.2.t.b.901.40		224	40.13	odd	4
1000.2.t.b.901.51		224	5.2	odd	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.338435 - 1.37312i) q^{2} +(2.58107 - 1.87526i) q^{3} +(-1.77092 - 0.929423i) q^{4} +(-1.70143 - 4.17877i) q^{6} -2.97769i q^{7} +(-1.87555 + 2.11714i) q^{8} +(2.21828 - 6.82716i) q^{9} +O(q^{10})\)	\(q+(0.338435 - 1.37312i) q^{2} +(2.58107 - 1.87526i) q^{3} +(-1.77092 - 0.929423i) q^{4} +(-1.70143 - 4.17877i) q^{6} -2.97769i q^{7} +(-1.87555 + 2.11714i) q^{8} +(2.21828 - 6.82716i) q^{9} +(-0.263378 + 0.0855768i) q^{11} +(-6.31378 + 0.922031i) q^{12} +(-1.36304 + 4.19500i) q^{13} +(-4.08873 - 1.00775i) q^{14} +(2.27234 + 3.29188i) q^{16} +(3.01210 - 4.14580i) q^{17} +(-8.62377 - 5.35651i) q^{18} +(-0.824879 + 1.13535i) q^{19} +(-5.58392 - 7.68561i) q^{21} +(0.0283710 + 0.390613i) q^{22} +(0.307187 - 0.0998113i) q^{23} +(-0.870742 + 8.98164i) q^{24} +(5.29895 + 3.29135i) q^{26} +(-4.11950 - 12.6785i) q^{27} +(-2.76753 + 5.27326i) q^{28} +(2.59226 + 3.56794i) q^{29} +(-3.04947 - 2.21557i) q^{31} +(5.28919 - 2.00612i) q^{32} +(-0.519319 + 0.714781i) q^{33} +(-4.67329 - 5.53907i) q^{34} +(-10.2737 + 10.0287i) q^{36} +(-1.24835 + 3.84202i) q^{37} +(1.27980 + 1.51690i) q^{38} +(4.34861 + 13.3836i) q^{39} +(-1.97884 + 6.09023i) q^{41} +(-12.4431 + 5.06633i) q^{42} +10.9079 q^{43} +(0.545960 + 0.0932399i) q^{44} +(-0.0330901 - 0.455585i) q^{46} +(-1.67150 - 2.30062i) q^{47} +(12.0382 + 4.23533i) q^{48} -1.86662 q^{49} -16.3491i q^{51} +(6.31278 - 6.16219i) q^{52} +(-0.378304 + 0.274854i) q^{53} +(-18.8033 + 1.36572i) q^{54} +(6.30419 + 5.58481i) q^{56} +4.47727i q^{57} +(5.77652 - 2.35197i) q^{58} +(-5.09147 - 1.65432i) q^{59} +(-1.96419 + 0.638204i) q^{61} +(-4.07430 + 3.43747i) q^{62} +(-20.3291 - 6.60534i) q^{63} +(-0.964603 - 7.94163i) q^{64} +(0.805726 + 0.954995i) q^{66} +(-1.25093 - 0.908853i) q^{67} +(-9.18741 + 4.54239i) q^{68} +(0.605700 - 0.833675i) q^{69} +(7.81261 - 5.67620i) q^{71} +(10.2936 + 17.5011i) q^{72} +(8.54291 - 2.77576i) q^{73} +(4.85308 + 3.01441i) q^{74} +(2.51602 - 1.24395i) q^{76} +(0.254821 + 0.784258i) q^{77} +(19.8491 - 1.44168i) q^{78} +(4.49455 - 3.26548i) q^{79} +(-16.9856 - 12.3407i) q^{81} +(7.69292 + 4.77833i) q^{82} +(-10.7440 - 7.80599i) q^{83} +(2.74552 + 18.8005i) q^{84} +(3.69160 - 14.9778i) q^{86} +(13.3816 + 4.34795i) q^{87} +(0.312802 - 0.718114i) q^{88} +(0.992059 + 3.05324i) q^{89} +(12.4914 + 4.05871i) q^{91} +(-0.636773 - 0.108749i) q^{92} -12.0257 q^{93} +(-3.72473 + 1.51656i) q^{94} +(9.88976 - 15.0965i) q^{96} +(-9.69449 - 13.3433i) q^{97} +(-0.631729 + 2.56310i) q^{98} +1.98796i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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