LMFDB - Embedded newform 1000.2.o.a.149.22

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			149.22
Character	$\chi$	$=$	1000.149
Dual form			1000.2.o.a.349.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08090 - 0.911952i) q^{2} +(-2.58107 - 1.87526i) q^{3} +(0.336688 - 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769i q^{7} +(-1.43395 - 2.43799i) q^{8} +(2.21828 + 6.82716i) q^{9} +O(q^{10})$	\(q+(1.08090 - 0.911952i) q^{2} +(-2.58107 - 1.87526i) q^{3} +(0.336688 - 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769i q^{7} +(-1.43395 - 2.43799i) q^{8} +(2.21828 + 6.82716i) q^{9} +(0.263378 + 0.0855768i) q^{11} +(-4.56600 + 4.45709i) q^{12} +(1.36304 + 4.19500i) q^{13} +(2.71551 + 3.21858i) q^{14} +(-3.77328 - 1.32753i) 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} +(0.362728 - 0.147688i) 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} +(5.87038 + 1.00255i) 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} +(7.03655 + 1.73431i) q^{34} +(14.2063 - 2.07461i) q^{36} +(1.24835 + 3.84202i) q^{37} +(1.92699 + 0.474948i) q^{38} +(4.34861 - 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(-0.973245 - 13.3996i) q^{42} -10.9079 q^{43} +(0.257387 - 0.490426i) q^{44} +(0.423062 - 0.172254i) q^{46} +(-1.67150 + 2.30062i) q^{47} +(7.24963 + 10.5023i) q^{48} -1.86662 q^{49} -16.3491i q^{51} +(8.72919 - 1.27476i) q^{52} +(0.378304 + 0.274854i) q^{53} +(-7.10942 - 17.4610i) q^{54} +(7.25957 - 4.26984i) q^{56} -4.47727i q^{57} +(0.451815 + 6.22060i) q^{58} +(5.09147 - 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(-1.27568 + 5.17578i) q^{62} +(-20.3291 + 6.60534i) q^{63} +(-3.88759 + 6.99190i) q^{64} +(-1.21318 - 0.299013i) 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} +(13.4636 - 15.1979i) 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} +(-7.50482 - 18.4321i) 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} +(-13.2718 - 13.5961i) q^{84} +(-11.7903 + 9.94745i) q^{86} +(13.3816 - 4.34795i) q^{87} +(-0.169035 - 0.764826i) q^{88} +(0.992059 - 3.05324i) q^{89} +(-12.4914 + 4.05871i) q^{91} +(0.300200 - 0.572001i) q^{92} +12.0257 q^{93} +(0.291332 + 4.01107i) q^{94} +(17.4137 + 4.74064i) q^{96} +(-9.69449 + 13.3433i) q^{97} +(-2.01763 + 1.70227i) 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.08090	−	0.911952i	0.764312	−	0.644847i
$2$	1.08090	−	0.911952i	0.764312	−	0.644847i
$3$	−2.58107	−	1.87526i	−1.49018	−	1.08268i	−0.974094	−	0.226143i	$-0.927388\pi$
$3$	−2.58107	−	1.87526i	−1.49018	−	1.08268i	−0.516086	−	0.856537i	$-0.672612\pi$
$4$	0.336688	−	1.97146i	0.168344	−	0.985728i
$5$		0			0
$5$		0			0
$6$	−4.50002	+	0.326846i	−1.83712	+	0.133434i
$7$			2.97769i			1.12546i	0.826641	+	0.562730i	$0.190249\pi$
$7$			2.97769i			1.12546i	−0.826641	+	0.562730i	$0.809751\pi$
$8$	−1.43395	−	2.43799i	−0.506977	−	0.861960i
$9$	2.21828	+	6.82716i	0.739426	+	2.27572i
$10$		0			0
$11$	0.263378	+	0.0855768i	0.0794116	+	0.0258024i	0.348453	−	0.937326i	$-0.386707\pi$
$11$	0.263378	+	0.0855768i	0.0794116	+	0.0258024i	−0.269042	+	0.963129i	$0.586707\pi$
$12$	−4.56600	+	4.45709i	−1.31809	+	1.28665i
$13$	1.36304	+	4.19500i	0.378039	+	1.16349i	0.941405	+	0.337278i	$0.109506\pi$
$13$	1.36304	+	4.19500i	0.378039	+	1.16349i	−0.563366	+	0.826207i	$0.690494\pi$
$14$	2.71551	+	3.21858i	0.725750	+	0.860202i
$15$		0			0
$16$	−3.77328	−	1.32753i	−0.943320	−	0.331883i
$17$	3.01210	+	4.14580i	0.730542	+	1.00551i	0.999107	+	0.0422436i	$0.0134505\pi$
$17$	3.01210	+	4.14580i	0.730542	+	1.00551i	−0.268565	+	0.963262i	$0.586549\pi$
$18$	8.62377	+	5.35651i	2.03264	+	1.26254i
$19$	0.824879	+	1.13535i	0.189240	+	0.260467i	0.893086	−	0.449886i	$-0.148535\pi$
$19$	0.824879	+	1.13535i	0.189240	+	0.260467i	−0.703846	+	0.710353i	$0.748535\pi$
$20$		0			0
$21$	5.58392	−	7.68561i	1.21851	−	1.67714i
$22$	0.362728	−	0.147688i	0.0773338	−	0.0314873i
$23$	0.307187	+	0.0998113i	0.0640530	+	0.0208121i	0.340868	−	0.940111i	$-0.389279\pi$
$23$	0.307187	+	0.0998113i	0.0640530	+	0.0208121i	−0.276815	+	0.960923i	$0.589279\pi$
$24$	−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
$28$	5.87038	+	1.00255i	1.10940	+	0.189465i
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	−0.978768	−	0.204973i	$-0.934289\pi$
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	0.497397	+	0.867523i	$0.334289\pi$
$30$		0			0
$31$	−3.04947	+	2.21557i	−0.547702	+	0.397929i	−0.826937	−	0.562294i	$-0.809919\pi$
$31$	−3.04947	+	2.21557i	−0.547702	+	0.397929i	0.279236	+	0.960223i	$0.409919\pi$
$32$	−5.28919	+	2.00612i	−0.935005	+	0.354635i
$33$	−0.519319	−	0.714781i	−0.0904018	−	0.124427i
$34$	7.03655	+	1.73431i	1.20676	+	0.297431i
$35$		0			0
$36$	14.2063	−	2.07461i	2.36772	−	0.345769i
$37$	1.24835	+	3.84202i	0.205227	+	0.631625i	0.999704	+	0.0243301i	$0.00774527\pi$
$37$	1.24835	+	3.84202i	0.205227	+	0.631625i	−0.794477	+	0.607295i	$0.792255\pi$
$38$	1.92699	+	0.474948i	0.312600	+	0.0770467i
$39$	4.34861	−	13.3836i	0.696335	−	2.14310i
$40$		0			0
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	−0.978138	−	0.207958i	$-0.933318\pi$
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	0.669095	−	0.743177i	$-0.266682\pi$
$42$	−0.973245	−	13.3996i	−0.150175	−	2.06761i
$43$	−10.9079			−1.66343			−0.831717	−	0.555199i	$-0.812642\pi$
$43$	−10.9079			−1.66343			−0.831717	+	0.555199i	$0.812642\pi$
$44$	0.257387	−	0.490426i	0.0388026	−	0.0739345i
$45$		0			0
$46$	0.423062	−	0.172254i	0.0623771	−	0.0253975i
$47$	−1.67150	+	2.30062i	−0.243813	+	0.335580i	−0.913333	−	0.407214i	$-0.866500\pi$
$47$	−1.67150	+	2.30062i	−0.243813	+	0.335580i	0.669519	+	0.742795i	$0.266500\pi$
$48$	7.24963	+	10.5023i	1.04639	+	1.51588i
$49$	−1.86662			−0.266660
$50$		0			0
$51$		−	16.3491i		−	2.28933i
$52$	8.72919	−	1.27476i	1.21052	−	0.176778i
$53$	0.378304	+	0.274854i	0.0519641	+	0.0377541i	0.613464	−	0.789723i	$-0.289776\pi$
$53$	0.378304	+	0.274854i	0.0519641	+	0.0377541i	−0.561500	+	0.827477i	$0.689776\pi$
$54$	−7.10942	−	17.4610i	−0.967470	−	2.37614i
$55$		0			0
$56$	7.25957	−	4.26984i	0.970101	−	0.570582i
$57$		−	4.47727i		−	0.593029i
$58$	0.451815	+	6.22060i	0.0593263	+	0.816805i
$59$	5.09147	−	1.65432i	0.662853	−	0.215374i	0.0417804	−	0.999127i	$-0.486697\pi$
$59$	5.09147	−	1.65432i	0.662853	−	0.215374i	0.621073	+	0.783753i	$0.286697\pi$
$60$		0			0
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	0.432049	−	0.901850i	$-0.357791\pi$
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	−0.180560	+	0.983564i	$0.557791\pi$
$62$	−1.27568	+	5.17578i	−0.162012	+	0.657325i
$63$	−20.3291	+	6.60534i	−2.56123	+	0.832194i
$64$	−3.88759	+	6.99190i	−0.485949	+	0.873987i
$65$		0			0
$66$	−1.21318	−	0.299013i	−0.149332	−	0.0368060i
$67$	1.25093	−	0.908853i	0.152825	−	0.111034i	−0.508745	−	0.860917i	$-0.669890\pi$
$67$	1.25093	−	0.908853i	0.152825	−	0.111034i	0.661570	+	0.749883i	$0.269890\pi$
$68$	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	0.945302	−	0.326195i	$-0.105767\pi$
$71$	7.81261	+	5.67620i	0.927187	+	0.673640i	−0.0181158	+	0.999836i	$0.505767\pi$
$72$	13.4636	−	15.1979i	1.58671	−	1.79109i
$73$	8.54291	+	2.77576i	0.999872	+	0.324878i	0.762814	−	0.646618i	$-0.223817\pi$
$73$	8.54291	+	2.77576i	0.999872	+	0.324878i	0.237057	+	0.971496i	$0.423817\pi$
$74$	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
$78$	−7.50482	−	18.4321i	−0.849754	−	2.08702i
$79$	4.49455	+	3.26548i	0.505677	+	0.367396i	0.811181	−	0.584795i	$-0.198825\pi$
$79$	4.49455	+	3.26548i	0.505677	+	0.367396i	−0.305504	+	0.952191i	$0.598825\pi$
$80$		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	$-0.440053\pi$
$83$	10.7440	−	7.80599i	1.17931	−	0.856819i	0.992094	+	0.125500i	$0.0400534\pi$
$84$	−13.2718	−	13.5961i	−1.44807	−	1.48346i
$85$		0			0
$86$	−11.7903	+	9.94745i	−1.27138	+	1.07266i
$87$	13.3816	−	4.34795i	1.43466	−	0.466149i
$88$	−0.169035	−	0.764826i	−0.0180192	−	0.0815308i
$89$	0.992059	−	3.05324i	0.105158	−	0.323643i	−0.884610	−	0.466333i	$-0.845575\pi$
$89$	0.992059	−	3.05324i	0.105158	−	0.323643i	0.989768	+	0.142689i	$0.0455750\pi$
$90$		0			0
$91$	−12.4914	+	4.05871i	−1.30946	+	0.425468i
$92$	0.300200	−	0.572001i	0.0312980	−	0.0596353i
$93$	12.0257			1.24700
$94$	0.291332	+	4.01107i	0.0300486	+	0.413710i
$95$		0			0
$96$	17.4137	+	4.74064i	1.77728	+	0.483840i
$97$	−9.69449	+	13.3433i	−0.984327	+	1.35481i	−0.0498611	+	0.998756i	$0.515878\pi$
$97$	−9.69449	+	13.3433i	−0.984327	+	1.35481i	−0.934466	+	0.356053i	$0.884122\pi$
$98$	−2.01763	+	1.70227i	−0.203811	+	0.171955i
$99$			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	$0.578770\pi$
$102$	−14.9096	−	17.6717i	−1.47627	−	1.74976i
$103$	4.15447	−	5.71814i	0.409352	−	0.563425i	−0.553708	−	0.832711i	$-0.686788\pi$
$103$	4.15447	−	5.71814i	0.409352	−	0.563425i	0.963060	+	0.269286i	$0.0867877\pi$
$104$	8.27286	−	9.33849i	0.811220	−	0.915714i
$105$		0			0
$106$	0.659563	−	0.0479054i	0.0640624	−	0.00465299i
$107$	−11.2557			−1.08813			−0.544064	−	0.839044i	$-0.683115\pi$
$107$	−11.2557			−1.08813			−0.544064	+	0.839044i	$0.683115\pi$
$108$	−23.6081	−	12.3901i	−2.27169	−	1.19224i
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.709642	−	0.704563i	$-0.751143\pi$
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.159981	+	0.987120i	$0.551143\pi$
$110$		0			0
$111$	3.98270	−	12.2575i	0.378021	−	1.16343i
$112$	3.95298	−	11.2357i	0.373521	−	1.06167i
$113$	10.0510	−	3.26576i	0.945517	−	0.307217i	0.204624	−	0.978841i	$-0.434403\pi$
$113$	10.0510	−	3.26576i	0.945517	−	0.307217i	0.740892	+	0.671624i	$0.234403\pi$
$114$	−4.08305	−	4.83948i	−0.382413	−	0.453259i
$115$		0			0
$116$	6.16125	+	6.31181i	0.572058	+	0.586037i
$117$	−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
$122$	2.70511	−	1.10141i	0.244909	−	0.0997172i
$123$	−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	0.251185	−	0.967939i	$-0.419180\pi$
$127$	−1.29082	−	0.419412i	−0.114542	−	0.0372168i	−0.365727	+	0.930722i	$0.619180\pi$
$128$	2.17417	+	11.1028i	0.192171	+	0.981361i
$129$	28.1540	+	20.4550i	2.47882	+	1.80097i
$130$		0			0
$131$	0.471129	+	0.648453i	0.0411627	+	0.0566556i	0.829102	−	0.559097i	$-0.188852\pi$
$131$	0.471129	+	0.648453i	0.0411627	+	0.0566556i	−0.787940	+	0.615753i	$0.788852\pi$
$132$	−1.58401	+	0.783156i	−0.137870	+	0.0681650i
$133$	−3.38071	+	2.45623i	−0.293145	+	0.212982i
$134$	0.523299	−	2.12317i	0.0452061	−	0.183414i
$135$		0			0
$136$	5.78824	−	13.2883i	0.496337	−	1.13947i
$137$	6.89354	−	2.23985i	0.588955	−	0.191363i	0.000646705	−	1.00000i	$-0.499794\pi$
$137$	6.89354	−	2.23985i	0.588955	−	0.191363i	0.588308	+	0.808637i	$0.299794\pi$
$138$	−1.41497	−	0.348750i	−0.120450	−	0.0296875i
$139$	−0.417329	−	0.135598i	−0.0353973	−	0.0115013i	0.291265	−	0.956642i	$-0.405924\pi$
$139$	−0.417329	−	0.135598i	−0.0353973	−	0.0115013i	−0.326662	+	0.945141i	$0.605924\pi$
$140$		0			0
$141$	8.62851	−	2.80357i	0.726652	−	0.236103i
$142$	13.6211	−	0.989327i	1.14305	−	0.0830225i
$143$			1.22152i			0.102148i
$144$	0.693091	−	28.7056i	0.0577576	−	2.39214i
$145$		0			0
$146$	11.7654	−	4.79040i	0.973710	−	0.396456i
$147$	4.81787	+	3.50039i	0.397372	+	0.288707i
$148$	7.99469	−	1.16750i	0.657159	−	0.0959680i
$149$			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	$0.693914\pi$
$152$	1.58514	−	3.63908i	0.128572	−	0.295168i
$153$	−21.6224	+	29.7606i	−1.74806	+	2.40600i
$154$	0.439770	+	1.08009i	0.0354377	+	0.0870361i
$155$		0			0
$156$	−24.9211	−	13.0792i	−1.99529	−	1.04717i
$157$	9.56521			0.763387			0.381693	−	0.924289i	$-0.375341\pi$
$157$	9.56521			0.763387			0.381693	+	0.924289i	$0.375341\pi$
$158$	7.83613	−	0.569154i	0.623409	−	0.0452795i
$159$	−0.461007	−	1.41883i	−0.0365603	−	0.112521i
$160$		0			0
$161$	−0.297207	+	0.914708i	−0.0234232	+	0.0720891i
$162$	−7.10554	+	28.8291i	−0.558264	+	2.26503i
$163$	−1.69722	−	5.22350i	−0.132936	−	0.409136i	0.862327	−	0.506352i	$-0.169006\pi$
$163$	−1.69722	−	5.22350i	−0.132936	−	0.409136i	−0.995263	+	0.0972156i	$0.969006\pi$
$164$	−12.6729	+	1.85068i	−0.989586	+	0.144514i
$165$		0			0
$166$	4.49453	−	18.2355i	0.348843	−	1.41535i
$167$	7.07399	+	9.73651i	0.547401	+	0.753433i	0.989657	−	0.143456i	$-0.0458215\pi$
$167$	7.07399	+	9.73651i	0.547401	+	0.753433i	−0.442255	+	0.896889i	$0.645821\pi$
$168$	−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
$172$	−3.67255	+	21.5044i	−0.280030	+	1.63969i
$173$	5.37296	−	16.5363i	0.408498	−	1.25723i	−0.509440	−	0.860506i	$-0.670148\pi$
$173$	5.37296	−	16.5363i	0.408498	−	1.25723i	0.917939	−	0.396722i	$-0.129852\pi$
$174$	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
$178$	−1.71209	−	4.20496i	−0.128327	−	0.315175i
$179$	−12.5073	+	17.2148i	−0.934841	+	1.28670i	0.0231007	+	0.999733i	$0.492646\pi$
$179$	−12.5073	+	17.2148i	−0.934841	+	1.28670i	−0.957941	+	0.286964i	$0.907354\pi$
$180$		0			0
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	0.949860	−	0.312676i	$-0.101225\pi$
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	−0.590896	+	0.806748i	$0.701225\pi$
$182$	−9.80062	+	15.7786i	−0.726470	+	1.16959i
$183$	−3.87291	−	5.33061i	−0.286294	−	0.394050i
$184$	−0.197152	−	0.892044i	−0.0145342	−	0.0657624i
$185$		0			0
$186$	12.9985	−	10.9668i	0.953099	−	0.804127i
$187$	0.438538	+	1.34968i	0.0320691	+	0.0986985i
$188$	3.97280	+	4.06988i	0.289746	+	0.296827i
$189$	37.7526	+	12.2666i	2.74610	+	0.892262i
$190$		0			0
$191$	−1.09517	−	3.37058i	−0.0792436	−	0.243887i	0.903585	−	0.428410i	$-0.140926\pi$
$191$	−1.09517	−	3.37058i	−0.0792436	−	0.243887i	−0.982828	+	0.184523i	$0.940926\pi$
$192$	23.1457	−	10.7563i	1.67040	−	0.776271i
$193$			13.3961i			0.964273i	0.876096	+	0.482137i	$0.160139\pi$
$193$			13.3961i			0.964273i	−0.876096	+	0.482137i	$0.839861\pi$
$194$	1.68969	+	23.2637i	0.121313	+	1.67024i
$195$		0			0
$196$	−0.628469	+	3.67996i	−0.0448907	+	0.262854i
$197$	4.15379	+	3.01790i	0.295945	+	0.215017i	0.725842	−	0.687861i	$-0.241450\pi$
$197$	4.15379	+	3.01790i	0.295945	+	0.215017i	−0.429897	+	0.902878i	$0.641450\pi$
$198$	1.81292	+	2.14878i	0.128839	+	0.152707i
$199$	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
$202$	17.7716	+	21.0640i	1.25041	+	1.48206i
$203$	−10.6242	−	7.71894i	−0.745673	−	0.541763i
$204$	−32.2315	−	5.50454i	−2.25665	−	0.385395i
$205$		0			0
$206$	−0.724099	−	9.96941i	−0.0504504	−	0.694601i
$207$			2.31863i			0.161156i
$208$	0.425876	−	17.6384i	0.0295292	−	1.22300i
$209$	0.120096	+	0.369617i	0.00830719	+	0.0255669i
$210$		0			0
$211$	−7.25107	−	2.35602i	−0.499184	−	0.162195i	0.0485936	−	0.998819i	$-0.484526\pi$
$211$	−7.25107	−	2.35602i	−0.499184	−	0.162195i	−0.547778	+	0.836624i	$0.684526\pi$
$212$	0.669234	−	0.653270i	0.0459632	−	0.0448668i
$213$	−9.52057	−	29.3013i	−0.652339	−	2.00769i
$214$	−12.1663	+	10.2646i	−0.831668	+	0.701676i
$215$		0			0
$216$	−36.8172	+	8.13701i	−2.50509	+	0.553653i
$217$	−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
$222$	−6.87334	−	16.8812i	−0.461309	−	1.13299i
$223$	−18.3487	−	5.96185i	−1.22872	−	0.399235i	−0.378469	−	0.925614i	$-0.623549\pi$
$223$	−18.3487	−	5.96185i	−1.22872	−	0.399235i	−0.850250	+	0.526379i	$0.823549\pi$
$224$	−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	0.324212	+	0.945984i	$0.394901\pi$
$227$	−7.44462	+	22.9122i	−0.494117	+	1.52073i	−0.818329	+	0.574751i	$0.805099\pi$
$228$	−8.82674	−	1.50744i	−0.584565	−	0.0998330i
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.117113	−	0.993119i	$-0.462636\pi$
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.908322	−	0.418272i	$-0.137364\pi$
$230$		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	−0.959339	−	0.282256i	$-0.908917\pi$
$233$	−14.2161	−	19.5668i	−0.931328	−	1.28186i	0.0280108	−	0.999608i	$-0.491083\pi$
$234$	−10.7160	+	43.4779i	−0.700529	+	2.84224i
$235$		0			0
$236$	−1.54718	−	10.5946i	−0.100713	−	0.689650i
$237$	−5.47713	−	16.8569i	−0.355778	−	1.09497i
$238$	−5.16422	+	20.9527i	−0.334747	+	1.35816i
$239$	4.76280	−	14.6584i	0.308080	−	0.948173i	−0.670430	−	0.741973i	$-0.733890\pi$
$239$	4.76280	−	14.6584i	0.308080	−	0.948173i	0.978510	−	0.206200i	$-0.0661097\pi$
$240$		0			0
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	0.977526	+	0.210813i	$0.0676111\pi$
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	−0.666923	+	0.745127i	$0.732389\pi$
$242$	−15.4073	+	1.11907i	−0.990419	+	0.0719362i
$243$	26.9901			1.73141
$244$	1.91951	−	3.65744i	0.122884	−	0.234144i
$245$		0			0
$246$	10.8954	+	26.7594i	0.694663	+	1.70612i
$247$	−3.63845	+	5.00790i	−0.231509	+	0.318645i
$248$	9.77433	+	4.25758i	0.620670	+	0.270356i
$249$	−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	$0.973930\pi$
$252$	6.17755	+	42.3019i	0.389149	+	2.66477i
$253$	0.0723650	+	0.0525763i	0.00454955	+	0.00330544i
$254$	−1.77773	+	0.723821i	−0.111545	+	0.0454166i
$255$		0			0
$256$	12.4753	+	10.0183i	0.779707	+	0.626145i
$257$		−	1.98944i		−	0.124098i	−0.998073	−	0.0620490i	$-0.980236\pi$
$257$		−	1.98944i		−	0.124098i	0.998073	−	0.0620490i	$-0.0197635\pi$
$258$	49.0856	−	3.56519i	3.05594	−	0.221959i
$259$	−11.4403	+	3.71719i	−0.710868	+	0.230975i
$260$		0			0
$261$	−30.1092	−	9.78308i	−1.86371	−	0.605558i
$262$	1.10060	+	0.271266i	0.0679954	+	0.0167589i
$263$	14.8066	−	4.81097i	0.913017	−	0.296657i	0.185418	−	0.982660i	$-0.440636\pi$
$263$	14.8066	−	4.81097i	0.913017	−	0.296657i	0.727599	+	0.686003i	$0.240636\pi$
$264$	−0.997954	+	2.29105i	−0.0614198	+	0.141005i
$265$		0			0
$266$	−1.41425	+	5.73798i	−0.0867130	+	0.351818i
$267$	−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	$-0.212828\pi$
$269$	−0.776787	−	1.06916i	−0.0473616	−	0.0651876i	−0.832041	+	0.554714i	$0.812828\pi$
$270$		0			0
$271$	11.7169	+	8.51285i	0.711753	+	0.517119i	0.883739	−	0.467981i	$-0.155018\pi$
$271$	11.7169	+	8.51285i	0.711753	+	0.517119i	−0.171986	+	0.985099i	$0.555018\pi$
$272$	−5.86182	−	19.6420i	−0.355425	−	1.19097i
$273$	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	−0.759070	−	0.651009i	$-0.774346\pi$
$277$	3.95585	−	12.1748i	0.237684	−	0.731516i	0.996754	−	0.0805069i	$-0.0256539\pi$
$278$	−0.574749	+	0.234015i	−0.0344712	+	0.0140353i
$279$	−21.8906	−	15.9045i	−1.31056	−	0.952176i
$280$		0			0
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	−0.661198	−	0.750212i	$-0.729952\pi$
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	0.509172	+	0.860665i	$0.329952\pi$
$282$	6.76983	−	10.8992i	0.403138	−	0.649036i
$283$	−10.1940	+	7.40638i	−0.605971	+	0.440264i	−0.847993	−	0.530007i	$-0.822189\pi$
$283$	−10.1940	+	7.40638i	−0.605971	+	0.440264i	0.242022	+	0.970271i	$0.422189\pi$
$284$	13.8208	−	13.4911i	0.820113	−	0.800550i
$285$		0			0
$286$	1.11397	+	1.32034i	0.0658702	+	0.0780733i
$287$	18.1348	−	5.89236i	1.07046	−	0.347815i
$288$	−25.4290	−	31.6600i	−1.49842	−	1.86558i
$289$	−2.86164	+	8.80721i	−0.168332	+	0.518071i
$290$		0			0
$291$	50.0443	−	16.2604i	2.93365	−	0.953200i
$292$	8.34859	−	15.9074i	0.488564	−	0.930910i
$293$	−9.19701			−0.537295			−0.268647	−	0.963239i	$-0.586577\pi$
$293$	−9.19701			−0.537295			−0.268647	+	0.963239i	$0.586577\pi$
$294$	8.39983	−	0.610097i	0.489888	−	0.0355816i
$295$		0			0
$296$	7.57675	−	8.55272i	0.440390	−	0.497117i
$297$	2.16997	−	2.98671i	0.125915	−	0.173307i
$298$	1.50971	+	1.78940i	0.0874551	+	0.103657i
$299$			1.42470i			0.0823925i
$300$		0			0
$301$		−	32.4802i		−	1.87213i
$302$	−15.2006	+	12.8247i	−0.874695	+	0.737977i
$303$	36.5440	−	50.2984i	2.09940	−	2.88957i
$304$	−1.60529	−	5.37904i	−0.0920695	−	0.308509i
$305$		0			0
$306$	3.76865	+	51.8868i	0.215439	+	2.96617i
$307$	24.3699			1.39087			0.695433	−	0.718591i	$-0.255213\pi$
$307$	24.3699			1.39087			0.695433	+	0.718591i	$0.255213\pi$
$308$	1.46034	+	0.766419i	0.0832104	+	0.0436708i
$309$	−21.4459	+	6.96821i	−1.22002	+	0.396407i
$310$		0			0
$311$	7.74867	−	23.8479i	0.439387	−	1.35229i	−0.449138	−	0.893463i	$-0.648269\pi$
$311$	7.74867	−	23.8479i	0.439387	−	1.35229i	0.888524	−	0.458830i	$-0.151731\pi$
$312$	−38.8649	+	8.58956i	−2.20029	+	0.486288i
$313$	−10.3764	+	3.37148i	−0.586506	+	0.190567i	−0.587213	−	0.809432i	$-0.699775\pi$
$313$	−10.3764	+	3.37148i	−0.586506	+	0.190567i	0.000706882		1.00000i	$0.499775\pi$
$314$	10.3390	−	8.72301i	0.583465	−	0.492268i
$315$		0			0
$316$	7.95102	−	7.76137i	0.447280	−	0.436611i
$317$	−0.695505	+	0.505314i	−0.0390635	+	0.0283813i	−0.607146	−	0.794591i	$-0.707686\pi$
$317$	−0.695505	+	0.505314i	−0.0390635	+	0.0283813i	0.568082	+	0.822972i	$0.307686\pi$
$318$	−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
$322$	0.512919	+	1.25975i	0.0285839	+	0.0702029i
$323$	−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
$328$	−12.0104	+	13.5575i	−0.663163	+	0.748585i
$329$	−6.85053	−	4.97720i	−0.377682	−	0.274402i
$330$		0			0
$331$	4.98309	+	6.85864i	0.273895	+	0.376985i	0.923700	−	0.383117i	$-0.125149\pi$
$331$	4.98309	+	6.85864i	0.273895	+	0.376985i	−0.649805	+	0.760101i	$0.725149\pi$
$332$	−11.7718	−	23.8096i	−0.646061	−	1.30672i
$333$	−23.4609	+	17.0453i	−1.28565	+	0.934079i
$334$	16.5255	+	4.07305i	0.904235	+	0.222868i
$335$		0			0
$336$	−31.2726	+	21.5871i	−1.70606	+	1.17767i
$337$	−15.9864	+	5.19430i	−0.870835	+	0.282951i	−0.710147	−	0.704054i	$-0.751371\pi$
$337$	−15.9864	+	5.19430i	−0.870835	+	0.282951i	−0.160688	+	0.987005i	$0.551371\pi$
$338$	−2.18491	+	8.86479i	−0.118844	+	0.482181i
$339$	−32.0664	−	10.4190i	−1.74161	−	0.565883i
$340$		0			0
$341$	−0.992767	+	0.322570i	−0.0537613	+	0.0174681i
$342$	1.03206	+	14.2095i	0.0558076	+	0.768359i
$343$			15.2856i			0.825345i
$344$	15.6413	+	26.5933i	0.843323	+	1.43381i
$345$		0			0
$346$	−9.27264	−	22.7739i	−0.498500	−	1.22433i
$347$	14.2663	+	10.3651i	0.765856	+	0.556427i	0.900701	−	0.434440i	$-0.143054\pi$
$347$	14.2663	+	10.3651i	0.765856	+	0.556427i	−0.134845	+	0.990867i	$0.543054\pi$
$348$	−4.06636	−	27.8451i	−0.217980	−	1.49266i
$349$		−	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
$352$	−1.56473	+	0.0757370i	−0.0834006	+	0.00403679i
$353$	16.7024	−	22.9889i	0.888980	−	1.22358i	−0.0848720	−	0.996392i	$-0.527048\pi$
$353$	16.7024	−	22.9889i	0.888980	−	1.22358i	0.973852	−	0.227184i	$-0.0729519\pi$
$354$	−22.3710	+	9.10860i	−1.18901	+	0.484117i
$355$		0			0
$356$	−5.68532	−	2.98379i	−0.301321	−	0.158141i
$357$	48.6824			2.57655
$358$	2.17995	+	30.0136i	0.115214	+	1.58627i
$359$	3.94315	+	12.1358i	0.208112	+	0.640501i	0.999571	+	0.0292801i	$0.00932147\pi$
$359$	3.94315	+	12.1358i	0.208112	+	0.640501i	−0.791460	+	0.611221i	$0.790679\pi$
$360$		0			0
$361$	5.26273	−	16.1970i	0.276986	−	0.852475i
$362$	11.2819	+	2.78065i	0.592961	+	0.146148i
$363$	10.7691	+	33.1438i	0.565230	+	1.73960i
$364$	3.79585	+	25.9928i	0.198956	+	1.36239i
$365$		0			0
$366$	−9.04749	−	2.22994i	−0.472920	−	0.116561i
$367$	−12.5338	−	17.2512i	−0.654257	−	0.900507i	0.345018	−	0.938596i	$-0.387873\pi$
$367$	−12.5338	−	17.2512i	−0.654257	−	0.900507i	−0.999274	+	0.0380891i	$0.987873\pi$
$368$	−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
$372$	4.04890	−	23.7081i	0.209926	−	1.22921i
$373$	3.63793	−	11.1964i	0.188365	−	0.579727i	−0.811625	−	0.584178i	$-0.801417\pi$
$373$	3.63793	−	11.1964i	0.188365	−	0.579727i	0.999990	+	0.00445132i	$0.00141691\pi$
$374$	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
$378$	51.9933	−	21.1696i	2.67425	−	1.08885i
$379$	−10.7274	+	14.7650i	−0.551030	+	0.758428i	−0.990152	−	0.140000i	$-0.955290\pi$
$379$	−10.7274	+	14.7650i	−0.551030	+	0.758428i	0.439121	+	0.898428i	$0.355290\pi$
$380$		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	0.859087	+	0.511830i	$0.171032\pi$
$383$	21.1437	+	29.1018i	1.08039	+	1.48703i	0.221307	+	0.975204i	$0.428968\pi$
$384$	15.2090	−	32.7343i	0.776130	−	1.67047i
$385$		0			0
$386$	12.2166	+	14.4799i	0.621809	+	0.737005i
$387$	−24.1967	−	74.4697i	−1.22999	−	3.78551i
$388$	23.0418	+	23.6048i	1.16977	+	1.19835i
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	0.240408	−	0.970672i	$-0.422719\pi$
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	−0.376053	+	0.926598i	$0.622719\pi$
$390$		0			0
$391$	0.511482	+	1.57418i	0.0258668	+	0.0796097i
$392$	2.67663	+	4.55080i	0.135190	+	0.229850i
$393$		−	2.55719i		−	0.128993i
$394$	7.24201	−	0.526002i	0.364847	−	0.0264996i
$395$		0			0
$396$	3.91917	+	0.669323i	0.196946	+	0.0336347i
$397$	6.36873	+	4.62715i	0.319637	+	0.232230i	0.736021	−	0.676959i	$-0.236703\pi$
$397$	6.36873	+	4.62715i	0.319637	+	0.232230i	−0.416383	+	0.909189i	$0.636703\pi$
$398$	13.5709	−	11.4497i	0.680246	−	0.573922i
$399$	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	$0.553884\pi$
$402$	−5.33215	+	4.49872i	−0.265943	+	0.224376i
$403$	−13.4509	−	9.77264i	−0.670037	−	0.486810i
$404$	38.4187	+	6.56120i	1.91140	+	0.326432i
$405$		0			0
$406$	−18.5230	+	1.34536i	−0.919281	+	0.0667693i
$407$			1.11874i			0.0554537i
$408$	−39.8589	+	23.4437i	−1.97331	+	1.16064i
$409$	−8.52623	−	26.2411i	−0.421595	−	1.29754i	−0.906217	−	0.422813i	$-0.861043\pi$
$409$	−8.52623	−	26.2411i	−0.421595	−	1.29754i	0.484622	−	0.874724i	$-0.338957\pi$
$410$		0			0
$411$	−21.9930	−	7.14596i	−1.08483	−	0.352484i
$412$	−9.87430	−	10.1156i	−0.486472	−	0.498359i
$413$	4.92605	+	15.1608i	0.242395	+	0.746015i
$414$	2.11447	+	2.50620i	0.103921	+	0.123173i
$415$		0			0
$416$	−15.6251	−	19.4537i	−0.766081	−	0.953798i
$417$	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	0.999908	+	0.0135851i	$0.00432441\pi$
$419$	14.4072	+	19.8299i	0.703839	+	0.968752i	−0.296068	+	0.955167i	$0.595676\pi$
$420$		0			0
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	0.218514	+	0.975834i	$0.429879\pi$
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	−0.995598	+	0.0937303i	$0.970121\pi$
$422$	−9.98625	+	4.06601i	−0.486123	+	0.197930i
$423$	−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
$428$	−3.78966	+	22.1901i	−0.183180	+	1.07260i
$429$	2.29066	−	3.15282i	0.110594	−	0.152220i
$430$		0			0
$431$	−6.94699	+	5.04728i	−0.334625	+	0.243119i	−0.742390	−	0.669968i	$-0.766308\pi$
$431$	−6.94699	+	5.04728i	−0.334625	+	0.243119i	0.407766	+	0.913087i	$0.366308\pi$
$432$	−32.3752	+	42.3708i	−1.55765	+	2.03857i
$433$	−17.2045	−	23.6800i	−0.826797	−	1.13799i	−0.988511	−	0.151150i	$-0.951702\pi$
$433$	−17.2045	−	23.6800i	−0.826797	−	1.13799i	0.161714	−	0.986838i	$-0.448298\pi$
$434$	−15.4119	−	3.79858i	−0.739793	−	0.182338i
$435$		0			0
$436$	2.75894	+	18.8923i	0.132129	+	0.904779i
$437$	0.140072	+	0.431097i	0.00670055	+	0.0206222i
$438$	−39.3505	−	9.69875i	−1.88024	−	0.463424i
$439$	3.98757	−	12.2725i	0.190317	−	0.585734i	−0.809683	−	0.586868i	$-0.800361\pi$
$439$	3.98757	−	12.2725i	0.190317	−	0.585734i	0.999999	+	0.00113362i	$0.000360843\pi$
$440$		0			0
$441$	−4.14068	−	12.7437i	−0.197175	−	0.606843i
$442$	2.31568	+	31.8823i	0.110146	+	1.51649i
$443$	1.10768			0.0526274			0.0263137	−	0.999654i	$-0.491623\pi$
$443$	1.10768			0.0526274			0.0263137	+	0.999654i	$0.491623\pi$
$444$	−22.8242	−	11.9787i	−1.08319	−	0.568483i
$445$		0			0
$446$	−25.2700	+	10.2890i	−1.19657	+	0.487196i
$447$	3.10443	−	4.27288i	0.146834	−	0.202100i
$448$	−20.8197	−	11.5760i	−0.983637	−	0.546916i
$449$	−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
$452$	−3.05426	−	20.9146i	−0.143660	−	0.983741i
$453$	36.2973	+	26.3715i	1.70539	+	1.23904i
$454$	12.8479	+	31.5549i	0.602983	+	1.48095i
$455$		0			0
$456$	−10.9155	+	6.42017i	−0.511167	+	0.300652i
$457$		−	36.8695i		−	1.72468i	−0.506328	−	0.862341i	$-0.668997\pi$
$457$		−	36.8695i		−	1.72468i	0.506328	−	0.862341i	$-0.331003\pi$
$458$	−2.70463	−	37.2374i	−0.126379	−	1.73999i
$459$	64.9710	−	21.1103i	3.03258	−	0.985347i
$460$		0			0
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.943177	−	0.332291i	$-0.107822\pi$
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.567730	+	0.823215i	$0.307822\pi$
$462$	0.890367	−	3.61246i	0.0414236	−	0.168067i
$463$	−39.9752	+	12.9887i	−1.85780	+	0.603637i	−0.862591	+	0.505902i	$0.831160\pi$
$463$	−39.9752	+	12.9887i	−1.85780	+	0.603637i	−0.995212	+	0.0977353i	$0.968840\pi$
$464$	14.5179	−	10.0215i	0.673976	−	0.465238i
$465$		0			0
$466$	−33.2102	−	8.18534i	−1.53843	−	0.379179i
$467$	−9.30036	+	6.75711i	−0.430370	+	0.312682i	−0.781797	−	0.623533i	$-0.785696\pi$
$467$	−9.30036	+	6.75711i	−0.430370	+	0.312682i	0.351427	+	0.936215i	$0.385696\pi$
$468$	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
$472$	−11.3341	−	10.0408i	−0.521695	−	0.462163i
$473$	−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
$478$	−8.21964	−	20.1877i	−0.375957	−	0.923364i
$479$	9.62460	+	6.99268i	0.439759	+	0.319504i	0.785539	−	0.618812i	$-0.212386\pi$
$479$	9.62460	+	6.99268i	0.439759	+	0.319504i	−0.345780	+	0.938316i	$0.612386\pi$
$480$		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
$484$	−15.6332	+	15.2603i	−0.710601	+	0.693651i
$485$		0			0
$486$	29.1735	−	24.6136i	1.32334	−	1.11650i
$487$	−20.8019	+	6.75894i	−0.942622	+	0.306277i	−0.739714	−	0.672921i	$-0.765039\pi$
$487$	−20.8019	+	6.75894i	−0.942622	+	0.306277i	−0.202908	+	0.979198i	$0.565039\pi$
$488$	−1.26061	−	5.70383i	−0.0570651	−	0.258200i
$489$	−5.41477	+	16.6649i	−0.244864	+	0.753615i
$490$		0			0
$491$	−3.07965	+	1.00064i	−0.138983	+	0.0451582i	−0.377682	−	0.925935i	$-0.623279\pi$
$491$	−3.07965	+	1.00064i	−0.138983	+	0.0451582i	0.238700	+	0.971093i	$0.423279\pi$
$492$	36.1801	+	18.9882i	1.63112	+	0.856053i
$493$	−22.6001			−1.01786
$494$	0.634160	+	8.73112i	0.0285322	+	0.392832i
$495$		0			0
$496$	14.4478	−	4.31170i	0.648724	−	0.193601i
$497$	−16.9019	+	23.2635i	−0.758155	+	1.04351i
$498$	−45.7970	+	38.6388i	−2.05221	+	1.73144i
$499$		−	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
$502$	2.36400	+	2.80195i	0.105510	+	0.125057i
$503$	−7.58802	+	10.4440i	−0.338333	+	0.465676i	−0.943954	−	0.330078i	$-0.892925\pi$
$503$	−7.58802	+	10.4440i	−0.338333	+	0.465676i	0.605621	+	0.795754i	$0.292925\pi$
$504$	45.2546	+	40.0905i	2.01580	+	1.78577i
$505$		0			0
$506$	0.126166	−	0.00916373i	0.00560878	−	0.000407377i
$507$	20.5969			0.914740
$508$	−1.26146	+	2.40358i	−0.0559681	+	0.106642i
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	−0.499008	−	0.866597i	$-0.666302\pi$
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	0.105667	+	0.994402i	$0.466302\pi$
$510$		0			0
$511$	−8.26534	+	25.4381i	−0.365637	+	1.12532i
$512$	22.6208	−	0.548087i	0.999707	−	0.0242223i
$513$	17.7926	−	5.78117i	0.785563	−	0.255245i
$514$	−1.81428	−	2.15039i	−0.0800243	−	0.0948495i
$515$		0			0
$516$	49.8054	−	48.6173i	2.19256	−	2.14026i
$517$	−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	0.218045	−	0.975939i	$-0.430032\pi$
$521$	−14.6710	−	10.6591i	−0.642748	−	0.466984i	−0.860793	+	0.508955i	$0.830032\pi$
$522$	−41.4668	+	16.8836i	−1.81495	+	0.738977i
$523$	7.22455	−	22.2349i	0.315908	−	0.972264i	−0.659472	−	0.751729i	$-0.729220\pi$
$523$	7.22455	−	22.2349i	0.315908	−	0.972264i	0.975379	−	0.220534i	$-0.0707800\pi$
$524$	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
$528$	1.01064	+	3.38648i	0.0439825	+	0.147378i
$529$	−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
$534$	−3.46634	+	14.0639i	−0.150003	+	0.608604i
$535$		0			0
$536$	−4.00954	−	1.74651i	−0.173186	−	0.0754376i
$537$	64.5645	−	20.9783i	2.78616	−	0.905279i
$538$	−1.81465	−	0.447258i	−0.0782350	−	0.0192827i
$539$	−0.491627	−	0.159739i	−0.0211759	−	0.00688046i
$540$		0			0
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	−0.282322	−	0.959320i	$-0.591104\pi$
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	0.335471	+	0.942050i	$0.391104\pi$
$542$	20.4281	−	1.48374i	0.877464	−	0.0637320i
$543$		−	26.2128i		−	1.12490i
$544$	−24.2485	−	15.8853i	−1.03965	−	0.681076i
$545$		0			0
$546$	54.8850	−	22.3470i	2.34886	−	0.956364i
$547$	1.78489	+	1.29680i	0.0763163	+	0.0554470i	0.625289	−	0.780393i	$-0.284981\pi$
$547$	1.78489	+	1.29680i	0.0763163	+	0.0554470i	−0.548973	+	0.835840i	$0.684981\pi$
$548$	−2.09479	−	14.3444i	−0.0894848	−	0.612764i
$549$			14.8256i			0.632739i
$550$		0			0
$551$	−6.18915			−0.263667
$552$	−1.16395	+	2.67214i	−0.0495410	+	0.113734i
$553$	−9.72359	+	13.3834i	−0.413489	+	0.569119i
$554$	−6.82700	−	16.7673i	−0.290051	−	0.712376i
$555$		0			0
$556$	−0.407836	+	0.777091i	−0.0172961	+	0.0329560i
$557$	−22.2912			−0.944509			−0.472255	−	0.881462i	$-0.656560\pi$
$557$	−22.2912			−0.944509			−0.472255	+	0.881462i	$0.656560\pi$
$558$	−38.1657	+	2.77206i	−1.61568	+	0.117350i
$559$	−14.8679	−	45.7586i	−0.628844	−	1.93538i
$560$		0			0
$561$	1.39910	−	4.30599i	0.0590701	−	0.181799i
$562$	−1.06607	+	4.32534i	−0.0449695	+	0.182453i
$563$	6.54968	+	20.1578i	0.276036	+	0.849551i	0.988943	+	0.148293i	$0.0473780\pi$
$563$	6.54968	+	20.1578i	0.276036	+	0.849551i	−0.712907	+	0.701258i	$0.752622\pi$
$564$	−2.62200	−	17.9547i	−0.110406	−	0.756028i
$565$		0			0
$566$	−4.26444	+	17.3020i	−0.179248	+	0.727258i
$567$	−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	−0.559164	−	0.829057i	$-0.688878\pi$
$569$	1.34832	−	0.979610i	0.0565244	−	0.0410674i	0.615689	+	0.787989i	$0.288878\pi$
$570$		0			0
$571$	2.18726	−	3.01051i	0.0915340	−	0.125986i	−0.760794	−	0.648994i	$-0.775190\pi$
$571$	2.18726	−	3.01051i	0.0915340	−	0.125986i	0.852328	+	0.523008i	$0.175190\pi$
$572$	2.40817	+	0.411271i	0.100691	+	0.0171961i
$573$	−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	0.749181	−	0.662366i	$-0.230447\pi$
$577$	23.2030	+	7.53910i	0.965952	+	0.313857i	0.216771	+	0.976222i	$0.430447\pi$
$578$	4.93861	+	12.1294i	0.205419	+	0.504516i
$579$	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
$584$	−5.48280	−	24.8078i	−0.226880	−	1.02655i
$585$		0			0
$586$	−9.94104	+	8.38722i	−0.410661	+	0.346473i
$587$	4.25195	+	13.0862i	0.175497	+	0.540123i	0.999656	−	0.0262350i	$-0.00835183\pi$
$587$	4.25195	+	13.0862i	0.175497	+	0.540123i	−0.824159	+	0.566358i	$0.808352\pi$
$588$	8.52299	−	8.31969i	0.351482	−	0.343098i
$589$	−5.03089	−	1.63464i	−0.207294	−	0.0673540i
$590$		0			0
$591$	−5.06187	−	15.5788i	−0.208217	−	0.640827i
$592$	0.390041	−	16.1543i	0.0160306	−	0.663936i
$593$		−	18.8934i		−	0.775861i	−0.921689	−	0.387930i	$-0.873190\pi$
$593$		−	18.8934i		−	0.775861i	0.921689	−	0.387930i	$-0.126810\pi$
$594$	−0.378213	−	5.20725i	−0.0155183	−	0.213656i
$595$		0			0
$596$	3.26369	+	0.557378i	0.133686	+	0.0228311i
$597$	−32.4057	−	23.5441i	−1.32628	−	0.963598i
$598$	1.29926	+	1.53996i	0.0531306	+	0.0629735i
$599$	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	$0.412177\pi$
$602$	−29.6204	−	35.1079i	−1.20724	−	1.43089i
$603$	8.97979	+	6.52420i	0.365685	+	0.265686i
$604$	−4.73481	+	27.7244i	−0.192657	+	1.12809i
$605$		0			0
$606$	−6.36939	−	87.6939i	−0.258739	−	3.56232i
$607$			22.7175i			0.922076i	0.887380	+	0.461038i	$0.152523\pi$
$607$			22.7175i			0.922076i	−0.887380	+	0.461038i	$0.847477\pi$
$608$	−6.64058	−	4.35026i	−0.269311	−	0.176426i
$609$	12.9468	+	39.8462i	0.524632	+	1.61465i
$610$		0			0
$611$	−11.9294	−	3.87611i	−0.482614	−	0.156811i
$612$	51.3918	+	52.6476i	2.07739	+	2.12815i
$613$	9.25887	+	28.4959i	0.373962	+	1.15094i	0.944176	+	0.329441i	$0.106860\pi$
$613$	9.25887	+	28.4959i	0.373962	+	1.15094i	−0.570214	+	0.821496i	$0.693140\pi$
$614$	26.3415	−	22.2242i	1.06306	−	0.896896i
$615$		0			0
$616$	2.27741	−	0.503333i	0.0917596	−	0.0202799i
$617$	−14.2585	−	19.6251i	−0.574025	−	0.790077i	0.419000	−	0.907986i	$-0.362381\pi$
$617$	−14.2585	−	19.6251i	−0.574025	−	0.790077i	−0.993024	+	0.117909i	$0.962381\pi$
$618$	−16.8262	+	27.0896i	−0.676851	+	1.08970i
$619$	20.9345	+	28.8138i	0.841428	+	1.15813i	0.985687	+	0.168586i	$0.0539201\pi$
$619$	20.9345	+	28.8138i	0.841428	+	1.15813i	−0.144259	+	0.989540i	$0.546080\pi$
$620$		0			0
$621$	2.53092	−	3.48351i	0.101562	−	0.139788i
$622$	−13.3726	−	32.8436i	−0.536194	−	1.31691i
$623$	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
$628$	3.22049	−	18.8574i	0.128512	−	0.752492i
$629$	−12.1681	+	16.7480i	−0.485175	+	0.667786i
$630$		0			0
$631$	−5.35186	+	3.88835i	−0.213054	+	0.154793i	−0.689194	−	0.724576i	$-0.742035\pi$
$631$	−5.35186	+	3.88835i	−0.213054	+	0.154793i	0.476140	+	0.879369i	$0.342035\pi$
$632$	1.51627	−	15.6402i	0.0603140	−	0.622134i
$633$	14.2974	+	19.6786i	0.568270	+	0.782156i
$634$	−0.290949	+	1.18046i	−0.0115551	+	0.0468821i
$635$		0			0
$636$	−2.95239	+	0.431151i	−0.117070	+	0.0170962i
$637$	−2.54428	−	7.83048i	−0.100808	−	0.310255i
$638$	−0.413341	+	1.67704i	−0.0163643	+	0.0663945i
$639$	−21.4217	+	65.9293i	−0.847430	+	2.60812i
$640$		0			0
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	0.990947	+	0.134251i	$0.0428629\pi$
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	−0.722782	+	0.691076i	$0.757137\pi$
$642$	50.6508	−	3.67887i	1.99903	−	0.145193i
$643$	−32.6614			−1.28804			−0.644019	−	0.765009i	$-0.722734\pi$
$643$	−32.6614			−1.28804			−0.644019	+	0.765009i	$0.722734\pi$
$644$	1.70324	+	0.893902i	0.0671171	+	0.0352247i
$645$		0			0
$646$	3.83526	+	9.41953i	0.150896	+	0.370606i
$647$	20.5295	−	28.2564i	0.807098	−	1.11088i	−0.184666	−	0.982801i	$-0.559120\pi$
$647$	20.5295	−	28.2564i	0.807098	−	1.11088i	0.991765	−	0.128074i	$-0.0408795\pi$
$648$	54.4430	+	23.7147i	2.13872	+	0.931602i
$649$	1.48256			0.0581954
$650$		0			0
$651$			35.8087i			1.40345i
$652$	−10.8693	+	1.58730i	−0.425676	+	0.0621635i
$653$	31.5991	+	22.9581i	1.23657	+	0.898420i	0.997365	−	0.0725499i	$-0.0231137\pi$
$653$	31.5991	+	22.9581i	1.23657	+	0.898420i	0.239204	+	0.970969i	$0.423114\pi$
$654$	39.8921	−	16.2425i	1.55990	−	0.635131i
$655$		0			0
$656$	−0.618279	+	25.6071i	−0.0241397	+	0.999791i
$657$			64.4812i			2.51565i
$658$	−11.9437	+	0.867497i	−0.465614	+	0.0338185i
$659$	40.4722	−	13.1502i	1.57657	−	0.512260i	0.615402	−	0.788213i	$-0.288994\pi$
$659$	40.4722	−	13.1502i	1.57657	−	0.512260i	0.961171	+	0.275953i	$0.0889936\pi$
$660$		0			0
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.589071	−	0.808082i	$-0.299494\pi$
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.00158966	+	0.999999i	$0.499494\pi$
$662$	11.6410	+	2.86916i	0.452439	+	0.111513i
$663$	68.5844	−	22.2844i	2.66360	−	0.865455i
$664$	−34.4373	−	15.0005i	−1.33643	−	0.582131i
$665$		0			0
$666$	−9.81436	+	39.8195i	−0.380299	+	1.54298i
$667$	−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
$672$	−14.1162	+	51.8527i	−0.544542	+	2.00026i
$673$	8.44939	+	2.74537i	0.325700	+	0.105826i	0.467303	−	0.884097i	$-0.345226\pi$
$673$	8.44939	+	2.74537i	0.325700	+	0.105826i	−0.141603	+	0.989924i	$0.545226\pi$
$674$	−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	−0.707862	−	0.706351i	$-0.750340\pi$
$677$	7.28520	−	22.4216i	0.279993	−	0.861730i	0.987855	−	0.155379i	$-0.0496600\pi$
$678$	−44.1622	+	17.9811i	−1.69604	+	0.690560i
$679$	−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	$-0.535903\pi$
$683$	20.8468	−	15.1461i	0.797680	−	0.579548i	0.910233	+	0.414097i	$0.135903\pi$
$684$	14.0739	+	14.4178i	0.538129	+	0.551279i
$685$		0			0
$686$	13.9397	+	16.5222i	0.532221	+	0.630821i
$687$	−80.1042	+	26.0274i	−3.05617	+	0.993009i
$688$	41.1585	+	14.4806i	1.56915	+	0.552066i
$689$	−0.637371	+	1.96163i	−0.0242819	+	0.0747320i
$690$		0			0
$691$	−28.3342	+	9.20634i	−1.07788	+	0.350225i	−0.793553	−	0.608501i	$-0.791771\pi$
$691$	−28.3342	+	9.20634i	−1.07788	+	0.350225i	−0.284330	+	0.958726i	$0.591771\pi$
$692$	−30.7915	−	16.1601i	−1.17052	−	0.614315i
$693$	−5.91952			−0.224864
$694$	24.8729	−	1.80657i	0.944163	−	0.0685766i
$695$		0			0
$696$	−29.7887	−	26.3895i	−1.12914	−	1.00029i
$697$	19.2885	−	26.5483i	0.730602	−	1.00559i
$698$	−32.0967	−	38.0429i	−1.21488	−	1.43995i
$699$			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	$0.964788\pi$
$702$	63.5585	−	53.6241i	2.39886	−	2.02391i
$703$	−3.33230	+	4.58651i	−0.125680	+	0.172984i
$704$	−1.62225	+	1.50883i	−0.0611409	+	0.0568660i
$705$		0			0
$706$	−2.91113	−	40.0805i	−0.109562	−	1.50845i
$707$	−58.0275			−2.18235
$708$	−15.8742	+	30.2468i	−0.596590	+	1.13674i
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.0611529	−	0.998128i	$-0.480522\pi$
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.636159	+	0.771558i	$0.280522\pi$
$710$		0			0
$711$	−12.3238	+	37.9288i	−0.462179	+	1.42244i
$712$	−8.86633	+	1.95956i	−0.332280	+	0.0734375i
$713$	−1.15790	+	0.376224i	−0.0433637	+	0.0140897i
$714$	52.6208	−	44.3960i	1.96928	−	1.66148i
$715$		0			0
$716$	29.7272	+	30.4537i	1.11096	+	1.13811i
$717$	−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	0.398408	−	0.917208i	$-0.369563\pi$
$719$	37.3747	−	27.1543i	1.39384	−	1.01268i	0.995432	−	0.0954761i	$-0.0304373\pi$
$720$		0			0
$721$	17.0268	+	12.3707i	0.634112	+	0.460709i
$722$	−9.08242	−	22.3067i	−0.338013	−	0.830170i
$723$	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	0.179300	−	0.983795i	$-0.442617\pi$
$727$	−6.84600	−	2.22440i	−0.253904	−	0.0824984i	−0.433204	+	0.901296i	$0.642617\pi$
$728$	27.8071	+	24.6340i	1.03060	+	0.912996i
$729$	−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	$-0.526475\pi$
$733$	22.7156	−	16.5038i	0.839018	−	0.609582i	0.922096	+	0.386961i	$0.126475\pi$
$734$	−29.2800	−	7.21668i	−1.08075	−	0.266372i
$735$		0			0
$736$	−1.82500	+	0.0883347i	−0.0672706	+	0.00325606i
$737$	0.407244	−	0.132322i	0.0150010	−	0.00487413i
$738$	15.5574	−	63.1204i	0.572674	−	2.32350i
$739$	−37.8363	−	12.2937i	−1.39183	−	0.452233i	−0.485290	−	0.874353i	$-0.661286\pi$
$739$	−37.8363	−	12.2937i	−1.39183	−	0.452233i	−0.906540	+	0.422121i	$0.861286\pi$
$740$		0			0
$741$	18.7822	−	6.10270i	0.689980	−	0.224188i
$742$	0.142647	+	1.96397i	0.00523675	+	0.0720997i
$743$			20.8383i			0.764482i	0.924063	+	0.382241i	$0.124848\pi$
$743$			20.8383i			0.764482i	−0.924063	+	0.382241i	$0.875152\pi$
$744$	−17.2442	−	29.3185i	−0.632202	−	1.07487i
$745$		0			0
$746$	−6.27833	−	15.4198i	−0.229866	−	0.564558i
$747$	77.1260	+	56.0353i	2.82189	+	2.05022i
$748$	2.80849	−	0.410137i	0.102689	−	0.0149961i
$749$		−	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	$0.850516\pi$
$752$	9.36119	−	6.46192i	0.341368	−	0.235642i
$753$	4.86111	−	6.69075i	0.177149	−	0.243824i
$754$	−25.4796	+	10.3743i	−0.927913	+	0.377809i
$755$		0			0
$756$	36.8939	−	70.2977i	1.34182	−	2.55670i
$757$	−18.6251			−0.676942			−0.338471	−	0.940977i	$-0.609910\pi$
$757$	−18.6251			−0.676942			−0.338471	+	0.940977i	$0.609910\pi$
$758$	1.86972	+	25.7424i	0.0679114	+	0.935005i
$759$	−0.0881851	−	0.271406i	−0.00320092	−	0.00985141i
$760$		0			0
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	−0.416115	−	0.909312i	$-0.636609\pi$
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	0.871124	−	0.491063i	$-0.163391\pi$
$762$	5.94579	+	1.46546i	0.215393	+	0.0530882i
$763$	−8.78414	−	27.0348i	−0.318007	−	0.978726i
$764$	−7.01369	+	1.02424i	−0.253746	+	0.0370557i
$765$		0			0
$766$	49.3937	+	12.1741i	1.78467	+	0.439869i
$767$	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	−0.287179	−	0.957877i	$-0.592718\pi$
$769$	14.8380	−	10.7804i	0.535072	−	0.388753i	0.822252	+	0.569124i	$0.192718\pi$
$770$		0			0
$771$	−3.73071	+	5.13489i	−0.134358	+	0.184928i
$772$	26.4099	+	4.51032i	0.950511	+	0.162330i
$773$	−10.0305	+	30.8706i	−0.360770	+	1.11034i	0.591817	+	0.806072i	$0.298411\pi$
$773$	−10.0305	+	30.8706i	−0.360770	+	1.11034i	−0.952588	+	0.304265i	$0.901589\pi$
$774$	−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
$778$	−3.68450	+	1.50018i	−0.132096	+	0.0537842i
$779$	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
$784$	7.04328	+	2.47800i	0.251546	+	0.0885000i
$785$		0			0
$786$	−2.33203	−	2.76406i	−0.0831809	−	0.0985909i
$787$	−11.5801	−	35.6398i	−0.412785	−	1.27042i	−0.914217	−	0.405224i	$-0.867193\pi$
$787$	−11.5801	−	35.6398i	−0.412785	−	1.27042i	0.501432	−	0.865197i	$-0.332807\pi$
$788$	7.34820	−	7.17292i	0.261769	−	0.255525i
$789$	−47.2388	−	15.3488i	−1.68174	−	0.546432i
$790$		0			0
$791$	9.72441	+	29.9287i	0.345760	+	1.06414i
$792$	4.84662	−	2.85063i	0.172217	−	0.101293i
$793$			9.10969i			0.323495i
$794$	11.1037	−	0.806485i	0.394056	−	0.0286211i
$795$		0			0
$796$	4.22718	−	24.7520i	0.149828	−	0.877310i
$797$	44.1511	+	32.0777i	1.56391	+	1.13625i	0.932707	+	0.360636i	$0.117440\pi$
$797$	44.1511	+	32.0777i	1.56391	+	1.13625i	0.631207	+	0.775614i	$0.282560\pi$
$798$	14.4105	−	12.1581i	0.510125	−	0.430390i
$799$	−14.5727			−0.515544
$800$		0			0
$801$	23.0456			0.814277
$802$	−7.29319	+	6.15324i	−0.257531	+	0.217278i
$803$	2.01248	+	1.46215i	0.0710187	+	0.0515981i
$804$	−1.66091	+	9.72532i	−0.0585756	+	0.342986i
$805$		0			0
$806$	−23.4512	+	1.70331i	−0.826035	+	0.0599967i
$807$			4.21624i			0.148419i
$808$	47.5102	−	27.9440i	1.67140	−	0.983065i
$809$	−2.50898	−	7.72183i	−0.0882109	−	0.271485i	0.897214	−	0.441596i	$-0.145587\pi$
$809$	−2.50898	−	7.72183i	−0.0882109	−	0.271485i	−0.985425	+	0.170111i	$0.945587\pi$
$810$		0			0
$811$	−1.71354	−	0.556763i	−0.0601705	−	0.0195506i	0.278777	−	0.960356i	$-0.410071\pi$
$811$	−1.71354	−	0.556763i	−0.0601705	−	0.0195506i	−0.338948	+	0.940805i	$0.610071\pi$
$812$	−18.7946	+	18.3463i	−0.659561	+	0.643828i
$813$	−14.2784	−	43.9445i	−0.500766	−	1.54120i
$814$	1.02023	+	1.20924i	0.0357591	+	0.0423839i
$815$		0			0
$816$	−21.7039	+	61.6896i	−0.759789	+	2.15957i
$817$	−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	$-0.663786\pi$
$821$	13.9783	−	19.2395i	0.487848	−	0.671465i	0.979989	+	0.199051i	$0.0637858\pi$
$822$	−30.2890	+	12.3325i	−1.05645	+	0.430145i
$823$	22.5499	+	7.32692i	0.786042	+	0.255400i	0.674418	−	0.738350i	$-0.264395\pi$
$823$	22.5499	+	7.32692i	0.786042	+	0.255400i	0.111624	+	0.993751i	$0.464395\pi$
$824$	−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	$-0.949144\pi$
$827$	−2.73313	+	8.41171i	−0.0950402	+	0.292504i	0.892224	+	0.451593i	$0.149144\pi$
$828$	4.57107	+	0.780655i	0.158856	+	0.0271296i
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	−0.882660	−	0.470012i	$-0.844250\pi$
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	0.719765	+	0.694218i	$0.244250\pi$
$830$		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
$834$	1.92231	+	0.473793i	0.0665640	+	0.0164061i
$835$		0			0
$836$	0.769118	−	0.112318i	0.0266005	−	0.00388459i
$837$	15.5279	+	47.7898i	0.536721	+	1.65186i
$838$	33.6566	+	8.29539i	1.16265	+	0.286559i
$839$	−14.2160	+	43.7523i	−0.490790	+	1.51050i	0.332627	+	0.943058i	$0.392065\pi$
$839$	−14.2160	+	43.7523i	−0.490790	+	1.51050i	−0.823417	+	0.567437i	$0.807935\pi$
$840$		0			0
$841$	2.95111	+	9.08258i	0.101762	+	0.313193i
$842$	2.77902	+	38.2616i	0.0957713	+	1.31858i
$843$	10.0497			0.346130
$844$	−7.08613	+	13.5019i	−0.243915	+	0.464756i
$845$		0			0
$846$	−26.7379	+	10.8866i	−0.919269	+	0.374290i
$847$	19.1184	−	26.3142i	0.656917	−	0.904168i
$848$	−1.06257	−	1.53931i	−0.0364888	−	0.0528603i
$849$	40.2003			1.37967
$850$		0			0
$851$			1.30482i			0.0447287i
$852$	−60.9717	+	8.90398i	−2.08886	+	0.305045i
$853$	−37.0549	−	26.9220i	−1.26874	−	0.921790i	−0.269584	−	0.962977i	$-0.586886\pi$
$853$	−37.0549	−	26.9220i	−1.26874	−	0.921790i	−0.999151	+	0.0411867i	$0.986886\pi$
$854$	3.27966	+	8.05496i	0.112228	+	0.275635i
$855$		0			0
$856$	16.1400	+	27.4412i	0.551655	+	0.937922i
$857$			46.7189i			1.59589i	0.602733	+	0.797943i	$0.294078\pi$
$857$			46.7189i			1.59589i	−0.602733	+	0.797943i	$0.705922\pi$
$858$	−0.399248	−	5.49685i	−0.0136301	−	0.187659i
$859$	35.3436	−	11.4838i	1.20591	−	0.391824i	0.363978	−	0.931408i	$-0.381418\pi$
$859$	35.3436	−	11.4838i	1.20591	−	0.391824i	0.841932	+	0.539584i	$0.181418\pi$
$860$		0			0
$861$	−57.8569	−	18.7988i	−1.97176	−	0.640662i
$862$	−2.90612	+	11.7909i	−0.0989828	+	0.401600i
$863$	−47.5068	+	15.4359i	−1.61715	+	0.525444i	−0.971267	−	0.237992i	$-0.923511\pi$
$863$	−47.5068	+	15.4359i	−1.61715	+	0.525444i	−0.645883	+	0.763436i	$0.723511\pi$
$864$	3.64583	+	75.3232i	0.124034	+	2.56255i
$865$		0			0
$866$	−40.1914	−	9.90601i	−1.36576	−	0.336620i
$867$	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
$872$	20.2110	+	17.9047i	0.684432	+	0.606330i
$873$	−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	−0.715050	−	0.699073i	$-0.753596\pi$
$877$	8.12444	−	25.0044i	0.274343	−	0.844340i	0.989393	−	0.145267i	$-0.0464040\pi$
$878$	−6.88175	−	16.9018i	−0.232248	−	0.570408i
$879$	23.7381	+	17.2467i	0.800666	+	0.581718i
$880$		0			0
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	−0.789086	−	0.614282i	$-0.789446\pi$
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	0.340376	+	0.940289i	$0.389446\pi$
$882$	−16.0973	−	9.99857i	−0.542024	−	0.336669i
$883$	5.10972	−	3.71243i	0.171956	−	0.124933i	−0.498479	−	0.866902i	$-0.666108\pi$
$883$	5.10972	−	3.71243i	0.171956	−	0.124933i	0.670434	+	0.741969i	$0.266108\pi$
$884$	31.5781	+	32.3498i	1.06209	+	1.08804i
$885$		0			0
$886$	1.19729	−	1.01015i	0.0402237	−	0.0339366i
$887$	26.2498	−	8.52907i	0.881381	−	0.286378i	0.166850	−	0.985982i	$-0.446640\pi$
$887$	26.2498	−	8.52907i	0.881381	−	0.286378i	0.714531	+	0.699604i	$0.246640\pi$
$888$	−35.5946	+	7.86681i	−1.19448	+	0.263993i
$889$	1.24888	−	3.84365i	0.0418860	−	0.128912i
$890$		0			0
$891$	−5.52971	+	1.79671i	−0.185252	+	0.0601922i
$892$	−17.9313	+	34.1664i	−0.600385	+	1.14397i
$893$	−3.99079			−0.133547
$894$	−0.541083	−	7.44964i	−0.0180965	−	0.249153i
$895$		0			0
$896$	−33.0608	+	6.47400i	−1.10448	+	0.216281i
$897$	2.67168	−	3.67725i	0.0892047	−	0.122780i
$898$	−6.49916	+	5.48332i	−0.216880	+	0.182981i
$899$		−	16.6237i		−	0.554431i
$900$		0			0
$901$			2.39626i			0.0798312i
$902$	−1.61724	−	1.91684i	−0.0538480	−	0.0638239i
$903$	−60.9087	+	83.8337i	−2.02692	+	2.78981i
$904$	−22.3745	−	19.8213i	−0.744164	−	0.659245i
$905$		0			0
$906$	63.2833	−	4.59640i	2.10245	−	0.152705i
$907$	15.5893			0.517636			0.258818	−	0.965926i	$-0.416667\pi$
$907$	15.5893			0.517636			0.258818	+	0.965926i	$0.416667\pi$
$908$	42.6639	+	22.3910i	1.41585	+	0.743072i
$909$	−133.044	+	43.2286i	−4.41279	+	1.43380i
$910$		0			0
$911$	8.96903	−	27.6038i	0.297157	−	0.914556i	−0.685331	−	0.728232i	$-0.740342\pi$
$911$	8.96903	−	27.6038i	0.297157	−	0.914556i	0.982488	−	0.186324i	$-0.0596575\pi$
$912$	−5.94372	+	16.8940i	−0.196816	+	0.559416i
$913$	3.49776	−	1.13649i	0.115759	−	0.0376123i
$914$	−33.6232	−	39.8522i	−1.11216	−	1.31819i
$915$		0			0
$916$	−36.8822	−	37.7834i	−1.21862	−	1.24840i
$917$	−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	0.153304	−	0.988179i	$-0.451009\pi$
$919$	34.5740	−	25.1195i	1.14049	−	0.828616i	0.987188	+	0.159563i	$0.0510086\pi$
$920$		0			0
$921$	−62.9005	−	45.6999i	−2.07264	−	1.50586i
$922$	44.6775	−	18.1909i	1.47137	−	0.599086i
$923$	−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
$928$	6.55323	−	24.0719i	0.215120	−	0.790198i
$929$	−7.83492	−	5.69240i	−0.257055	−	0.186762i	0.451792	−	0.892123i	$-0.350785\pi$
$929$	−7.83492	−	5.69240i	−0.257055	−	0.186762i	−0.708848	+	0.705361i	$0.750785\pi$
$930$		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
$934$	−3.89060	+	15.7852i	−0.127304	+	0.516509i
$935$		0			0
$936$	82.1068	+	35.7647i	2.68375	+	1.16901i
$937$	−45.0827	+	14.6482i	−1.47279	+	0.478537i	−0.931949	−	0.362590i	$-0.881893\pi$
$937$	−45.0827	+	14.6482i	−1.47279	+	0.478537i	−0.540837	+	0.841127i	$0.681893\pi$
$938$	6.32212	+	1.55822i	0.206425	+	0.0508777i
$939$	33.1045	+	10.7563i	1.08032	+	0.351018i
$940$		0			0
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	−0.531804	−	0.846867i	$-0.678486\pi$
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	0.0675373	+	0.997717i	$0.478486\pi$
$942$	−43.0436	+	3.12635i	−1.40244	+	0.101862i
$943$		−	2.06835i		−	0.0673549i
$944$	−21.4077	−	0.516885i	−0.696762	−	0.0168232i
$945$		0			0
$946$	−3.95658	+	1.61097i	−0.128640	+	0.0523770i
$947$	−21.2273	−	15.4226i	−0.689796	−	0.501166i	0.186797	−	0.982398i	$-0.440189\pi$
$947$	−21.2273	−	15.4226i	−0.689796	−	0.501166i	−0.876593	+	0.481233i	$0.840189\pi$
$948$	−35.0767	+	5.12241i	−1.13924	+	0.166368i
$949$			39.6210i			1.28615i
$950$		0			0
$951$	2.74274			0.0889394
$952$	39.5685	+	17.2356i	1.28242	+	0.558607i
$953$	17.5587	−	24.1675i	0.568782	−	0.782861i	−0.423628	−	0.905836i	$-0.639244\pi$
$953$	17.5587	−	24.1675i	0.568782	−	0.782861i	0.992410	+	0.122975i	$0.0392436\pi$
$954$	1.79015	+	4.39667i	0.0579583	+	0.142347i
$955$		0			0
$956$	−27.2948	−	14.3250i	−0.882777	−	0.463303i
$957$	3.89651			0.125956
$958$	16.7802	−	1.21878i	0.542144	−	0.0393771i
$959$	6.66957	+	20.5268i	0.215371	+	0.662845i
$960$		0			0
$961$	−5.18900	+	15.9701i	−0.167387	+	0.515164i
$962$	−6.03052	+	24.4675i	−0.194432	+	0.788862i
$963$	−24.9682	−	76.8443i	−0.804590	−	2.47627i
$964$	30.8802	−	4.50958i	0.994585	−	0.145244i
$965$		0			0
$966$	1.03847	−	4.21334i	0.0334121	−	0.135562i
$967$	−15.3115	−	21.0745i	−0.492385	−	0.677710i	0.488440	−	0.872597i	$-0.337566\pi$
$967$	−15.3115	−	21.0745i	−0.492385	−	0.677710i	−0.980826	+	0.194887i	$0.937566\pi$
$968$	−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	$-0.787966\pi$
$971$	1.38452	−	1.90563i	0.0444314	−	0.0611546i	0.830655	+	0.556788i	$0.187966\pi$
$972$	9.08724	−	53.2097i	0.291473	−	1.70670i
$973$	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	0.448269	−	0.893899i	$-0.352041\pi$
$977$	8.92406	+	2.89960i	0.285506	+	0.0927665i	−0.162763	+	0.986665i	$0.552041\pi$
$978$	9.34480	+	22.9511i	0.298814	+	0.733896i
$979$	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	−0.909503	−	0.415698i	$-0.863537\pi$
$983$	−32.0991	−	44.1807i	−1.02380	−	1.40914i	−0.114301	−	0.993446i	$-0.536463\pi$
$984$	56.4233	−	12.4702i	1.79871	−	0.397535i
$985$		0			0
$986$	−24.4285	+	20.6102i	−0.777961	+	0.656363i
$987$	8.34816	+	25.6930i	0.265725	+	0.817817i
$988$	8.64782	+	8.85914i	0.275124	+	0.281847i
$989$	−3.35076	−	1.08873i	−0.106548	−	0.0346196i
$990$		0			0
$991$	19.1415	+	58.9116i	0.608051	+	1.87139i	0.474273	+	0.880378i	$0.342711\pi$
$991$	19.1415	+	58.9116i	0.608051	+	1.87139i	0.133778	+	0.991011i	$0.457289\pi$
$992$	11.6845	−	17.8362i	0.370984	−	0.566299i
$993$		−	27.0472i		−	0.858316i
$994$	2.94591	+	40.5593i	0.0934385	+	1.28646i
$995$		0			0
$996$	−14.2653	+	83.5292i	−0.452012	+	2.64673i
$997$	−24.8911	−	18.0845i	−0.788310	−	0.572741i	0.119151	−	0.992876i	$-0.461983\pi$
$997$	−24.8911	−	18.0845i	−0.788310	−	0.572741i	−0.907462	+	0.420135i	$0.861983\pi$
$998$	−4.29368	−	5.08913i	−0.135914	−	0.161094i
$999$	53.8537			1.70386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.149.22		112
5.2	odd	4		1000.2.t.b.101.40		224
5.3	odd	4		1000.2.t.b.101.17		224
5.4	even	2		200.2.o.a.29.7	✓	112
8.5	even	2	inner	1000.2.o.a.149.16		112
20.19	odd	2		800.2.be.a.529.1		112
25.6	even	5		200.2.o.a.69.13	yes	112
25.8	odd	20		1000.2.t.b.901.51		224
25.17	odd	20		1000.2.t.b.901.6		224
25.19	even	10	inner	1000.2.o.a.349.16		112
40.13	odd	4		1000.2.t.b.101.51		224
40.19	odd	2		800.2.be.a.529.28		112
40.29	even	2		200.2.o.a.29.13	yes	112
40.37	odd	4		1000.2.t.b.101.6		224
100.31	odd	10		800.2.be.a.369.28		112
200.69	even	10	inner	1000.2.o.a.349.22		112
200.117	odd	20		1000.2.t.b.901.40		224
200.131	odd	10		800.2.be.a.369.1		112
200.133	odd	20		1000.2.t.b.901.17		224
200.181	even	10		200.2.o.a.69.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	5.4	even	2
200.2.o.a.29.13	yes	112	40.29	even	2
200.2.o.a.69.7	yes	112	200.181	even	10
200.2.o.a.69.13	yes	112	25.6	even	5
800.2.be.a.369.1		112	200.131	odd	10
800.2.be.a.369.28		112	100.31	odd	10
800.2.be.a.529.1		112	20.19	odd	2
800.2.be.a.529.28		112	40.19	odd	2
1000.2.o.a.149.16		112	8.5	even	2	inner
1000.2.o.a.149.22		112	1.1	even	1	trivial
1000.2.o.a.349.16		112	25.19	even	10	inner
1000.2.o.a.349.22		112	200.69	even	10	inner
1000.2.t.b.101.6		224	40.37	odd	4
1000.2.t.b.101.17		224	5.3	odd	4
1000.2.t.b.101.40		224	5.2	odd	4
1000.2.t.b.101.51		224	40.13	odd	4
1000.2.t.b.901.6		224	25.17	odd	20
1000.2.t.b.901.17		224	200.133	odd	20
1000.2.t.b.901.40		224	200.117	odd	20
1000.2.t.b.901.51		224	25.8	odd	20

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)

\(f(q)\)	\(=\)	\(q+(1.08090 - 0.911952i) q^{2} +(-2.58107 - 1.87526i) q^{3} +(0.336688 - 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769i q^{7} +(-1.43395 - 2.43799i) q^{8} +(2.21828 + 6.82716i) q^{9} +O(q^{10})\)	\(q+(1.08090 - 0.911952i) q^{2} +(-2.58107 - 1.87526i) q^{3} +(0.336688 - 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769i q^{7} +(-1.43395 - 2.43799i) q^{8} +(2.21828 + 6.82716i) q^{9} +(0.263378 + 0.0855768i) q^{11} +(-4.56600 + 4.45709i) q^{12} +(1.36304 + 4.19500i) q^{13} +(2.71551 + 3.21858i) q^{14} +(-3.77328 - 1.32753i) 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} +(0.362728 - 0.147688i) 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} +(5.87038 + 1.00255i) 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} +(7.03655 + 1.73431i) q^{34} +(14.2063 - 2.07461i) q^{36} +(1.24835 + 3.84202i) q^{37} +(1.92699 + 0.474948i) q^{38} +(4.34861 - 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(-0.973245 - 13.3996i) q^{42} -10.9079 q^{43} +(0.257387 - 0.490426i) q^{44} +(0.423062 - 0.172254i) q^{46} +(-1.67150 + 2.30062i) q^{47} +(7.24963 + 10.5023i) q^{48} -1.86662 q^{49} -16.3491i q^{51} +(8.72919 - 1.27476i) q^{52} +(0.378304 + 0.274854i) q^{53} +(-7.10942 - 17.4610i) q^{54} +(7.25957 - 4.26984i) q^{56} -4.47727i q^{57} +(0.451815 + 6.22060i) q^{58} +(5.09147 - 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(-1.27568 + 5.17578i) q^{62} +(-20.3291 + 6.60534i) q^{63} +(-3.88759 + 6.99190i) q^{64} +(-1.21318 - 0.299013i) 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} +(13.4636 - 15.1979i) 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} +(-7.50482 - 18.4321i) 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} +(-13.2718 - 13.5961i) q^{84} +(-11.7903 + 9.94745i) q^{86} +(13.3816 - 4.34795i) q^{87} +(-0.169035 - 0.764826i) q^{88} +(0.992059 - 3.05324i) q^{89} +(-12.4914 + 4.05871i) q^{91} +(0.300200 - 0.572001i) q^{92} +12.0257 q^{93} +(0.291332 + 4.01107i) q^{94} +(17.4137 + 4.74064i) q^{96} +(-9.69449 + 13.3433i) q^{97} +(-2.01763 + 1.70227i) 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

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Database

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