LMFDB - Embedded newform 738.2.i.b.409.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(409,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.409"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			409.13
Character	$\chi$	$=$	738.409
Dual form			738.2.i.b.655.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.793227 + 1.53974i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18467 + 2.05191i) q^{5} +(0.936838 - 1.45682i) q^{6} +(-4.22182 + 2.43747i) q^{7} +1.00000 q^{8} +(-1.74158 + 2.44272i) q^{9} +2.36934 q^{10} +(3.26477 - 1.88492i) q^{11} +(-1.73007 - 0.0829143i) q^{12} +(0.883519 + 0.510100i) q^{13} +(4.22182 + 2.43747i) q^{14} +(-4.09911 - 0.196452i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.79124i q^{17} +(2.98625 + 0.286894i) q^{18} -8.27391i q^{19} +(-1.18467 - 2.05191i) q^{20} +(-7.10192 - 4.56703i) q^{21} +(-3.26477 - 1.88492i) q^{22} +(-3.96640 + 6.87000i) q^{23} +(0.793227 + 1.53974i) q^{24} +(-0.306879 - 0.531530i) q^{25} -1.02020i q^{26} +(-5.14262 - 0.743949i) q^{27} -4.87494i q^{28} +(-7.89342 + 4.55727i) q^{29} +(1.87942 + 3.64816i) q^{30} +(2.79358 - 4.83863i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.49198 + 3.53173i) q^{33} +(-1.55126 + 0.895620i) q^{34} -11.5504i q^{35} +(-1.24467 - 2.72962i) q^{36} -6.27081 q^{37} +(-7.16542 + 4.13696i) q^{38} +(-0.0845891 + 1.76501i) q^{39} +(-1.18467 + 2.05191i) q^{40} +(-5.17282 - 3.77385i) q^{41} +(-0.404202 + 8.43396i) q^{42} +(3.17911 + 5.50637i) q^{43} +3.76984i q^{44} +(-2.94904 - 6.46738i) q^{45} +7.93279 q^{46} +(0.755744 - 0.436329i) q^{47} +(0.936838 - 1.45682i) q^{48} +(8.38252 - 14.5189i) q^{49} +(-0.306879 + 0.531530i) q^{50} +(2.75804 - 1.42086i) q^{51} +(-0.883519 + 0.510100i) q^{52} -2.59870i q^{53} +(1.92703 + 4.82561i) q^{54} +8.93201i q^{55} +(-4.22182 + 2.43747i) q^{56} +(12.7397 - 6.56309i) q^{57} +(7.89342 + 4.55727i) q^{58} +(-1.99784 + 3.46037i) q^{59} +(2.21969 - 3.45171i) q^{60} +(-0.584806 - 1.01291i) q^{61} -5.58717 q^{62} +(1.39859 - 14.5578i) q^{63} +1.00000 q^{64} +(-2.09335 + 1.20860i) q^{65} +(0.312573 - 6.52206i) q^{66} +(-3.06655 - 1.77047i) q^{67} +(1.55126 + 0.895620i) q^{68} +(-13.7242 - 0.657742i) q^{69} +(-10.0029 + 5.77519i) q^{70} +4.65070i q^{71} +(-1.74158 + 2.44272i) q^{72} +2.14855 q^{73} +(3.13541 + 5.43068i) q^{74} +(0.574992 - 0.894137i) q^{75} +(7.16542 + 4.13696i) q^{76} +(-9.18886 + 15.9156i) q^{77} +(1.57084 - 0.809250i) q^{78} +(2.47565 - 1.42931i) q^{79} +2.36934 q^{80} +(-2.93378 - 8.50840i) q^{81} +(-0.681841 + 6.36672i) q^{82} +(7.31381 + 12.6679i) q^{83} +(7.50613 - 3.86693i) q^{84} +(3.67546 + 2.12203i) q^{85} +(3.17911 - 5.50637i) q^{86} +(-13.2783 - 8.53885i) q^{87} +(3.26477 - 1.88492i) q^{88} +13.5197i q^{89} +(-4.12640 + 5.78763i) q^{90} -4.97341 q^{91} +(-3.96640 - 6.87000i) q^{92} +(9.66617 + 0.463256i) q^{93} +(-0.755744 - 0.436329i) q^{94} +(16.9773 + 9.80184i) q^{95} +(-1.73007 - 0.0829143i) q^{96} +(-1.48001 + 0.854487i) q^{97} -16.7650 q^{98} +(-1.08154 + 11.2577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 4 q^{5} + 36 q^{8} - 14 q^{9} - 8 q^{10} - 18 q^{16} + 4 q^{18} + 4 q^{20} - 16 q^{21} - 4 q^{23} - 26 q^{25} + 8 q^{31} - 18 q^{32} - 6 q^{33} + 10 q^{36} - 60 q^{37} - 64 q^{39}+ \cdots - 76 q^{98}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 4 * q^5 + 36 * q^8 - 14 * q^9 - 8 * q^10 - 18 * q^16 + 4 * q^18 + 4 * q^20 - 16 * q^21 - 4 * q^23 - 26 * q^25 + 8 * q^31 - 18 * q^32 - 6 * q^33 + 10 * q^36 - 60 * q^37 - 64 * q^39 + 4 * q^40 - 6 * q^41 + 26 * q^42 + 6 * q^43 + 28 * q^45 + 8 * q^46 + 38 * q^49 - 26 * q^50 + 18 * q^51 + 28 * q^57 + 22 * q^59 - 46 * q^61 - 16 * q^62 + 36 * q^64 - 30 * q^66 - 14 * q^72 + 64 * q^73 + 30 * q^74 - 2 * q^77 + 14 * q^78 - 8 * q^80 - 22 * q^81 + 12 * q^82 + 68 * q^83 - 10 * q^84 + 6 * q^86 - 142 * q^87 - 80 * q^90 + 36 * q^91 - 4 * q^92 - 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.793227	+	1.53974i	0.457970	+	0.888968i
$3$	0.793227	+	1.53974i	0.457970	+	0.888968i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.18467	+	2.05191i	−0.529800	+	0.917640i	0.469596	+	0.882881i	$0.344400\pi$
$5$	−1.18467	+	2.05191i	−0.529800	+	0.917640i	−0.999396	+	0.0347588i	$0.988934\pi$
$6$	0.936838	−	1.45682i	0.382463	−	0.594746i
$7$	−4.22182	+	2.43747i	−1.59570	+	0.921277i	−0.603396	+	0.797442i	$0.706186\pi$
$7$	−4.22182	+	2.43747i	−1.59570	+	0.921277i	−0.992303	+	0.123835i	$0.960481\pi$
$8$	1.00000			0.353553
$9$	−1.74158	+	2.44272i	−0.580528	+	0.814241i
$10$	2.36934			0.749250
$11$	3.26477	−	1.88492i	0.984366	−	0.568324i	0.0807808	−	0.996732i	$-0.474259\pi$
$11$	3.26477	−	1.88492i	0.984366	−	0.568324i	0.903586	+	0.428408i	$0.140925\pi$
$12$	−1.73007	−	0.0829143i	−0.499427	−	0.0239353i
$13$	0.883519	+	0.510100i	0.245044	+	0.141476i	0.617493	−	0.786577i	$-0.288148\pi$
$13$	0.883519	+	0.510100i	0.245044	+	0.141476i	−0.372449	+	0.928053i	$0.621482\pi$
$14$	4.22182	+	2.43747i	1.12833	+	0.651441i
$15$	−4.09911	−	0.196452i	−1.05838	−	0.0507237i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	1.79124i		−	0.434440i	−0.976123	−	0.217220i	$-0.930301\pi$
$17$		−	1.79124i		−	0.434440i	0.976123	−	0.217220i	$-0.0696988\pi$
$18$	2.98625	+	0.286894i	0.703866	+	0.0676216i
$19$		−	8.27391i		−	1.89817i	−0.315027	−	0.949083i	$-0.602014\pi$
$19$		−	8.27391i		−	1.89817i	0.315027	−	0.949083i	$-0.397986\pi$
$20$	−1.18467	−	2.05191i	−0.264900	−	0.458820i
$21$	−7.10192	−	4.56703i	−1.54977	−	0.996608i
$22$	−3.26477	−	1.88492i	−0.696052	−	0.401866i
$23$	−3.96640	+	6.87000i	−0.827051	+	1.43249i	0.0732914	+	0.997311i	$0.476650\pi$
$23$	−3.96640	+	6.87000i	−0.827051	+	1.43249i	−0.900342	+	0.435183i	$0.856684\pi$
$24$	0.793227	+	1.53974i	0.161917	+	0.314298i
$25$	−0.306879	−	0.531530i	−0.0613758	−	0.106306i
$26$		−	1.02020i		−	0.200078i
$27$	−5.14262	−	0.743949i	−0.989698	−	0.143173i
$28$		−	4.87494i		−	0.921277i
$29$	−7.89342	+	4.55727i	−1.46577	+	0.846263i	−0.999268	−	0.0382562i	$-0.987820\pi$
$29$	−7.89342	+	4.55727i	−1.46577	+	0.846263i	−0.466503	+	0.884520i	$0.654486\pi$
$30$	1.87942	+	3.64816i	0.343134	+	0.666059i
$31$	2.79358	−	4.83863i	0.501743	−	0.869044i	−0.498255	−	0.867030i	$-0.666026\pi$
$31$	2.79358	−	4.83863i	0.501743	−	0.869044i	0.999998	−	0.00201334i	$-0.000640866\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.49198	+	3.53173i	0.956032	+	0.614795i
$34$	−1.55126	+	0.895620i	−0.266039	+	0.153598i
$35$		−	11.5504i		−	1.95237i
$36$	−1.24467	−	2.72962i	−0.207445	−	0.454936i
$37$	−6.27081			−1.03092			−0.515458	−	0.856915i	$-0.672378\pi$
$37$	−6.27081			−1.03092			−0.515458	+	0.856915i	$0.672378\pi$
$38$	−7.16542	+	4.13696i	−1.16238	+	0.671103i
$39$	−0.0845891	+	1.76501i	−0.0135451	+	0.282628i
$40$	−1.18467	+	2.05191i	−0.187313	+	0.324435i
$41$	−5.17282	−	3.77385i	−0.807859	−	0.589376i
$41$	−5.17282	−	3.77385i	−0.807859	−	0.589376i
$42$	−0.404202	+	8.43396i	−0.0623698	+	1.30139i
$43$	3.17911	+	5.50637i	0.484809	+	0.839714i	0.999848	−	0.0174529i	$-0.00555570\pi$
$43$	3.17911	+	5.50637i	0.484809	+	0.839714i	−0.515038	+	0.857167i	$0.672222\pi$
$44$			3.76984i			0.568324i
$45$	−2.94904	−	6.46738i	−0.439616	−	0.964100i
$46$	7.93279			1.16963
$47$	0.755744	−	0.436329i	0.110237	−	0.0636452i	−0.443868	−	0.896092i	$-0.646394\pi$
$47$	0.755744	−	0.436329i	0.110237	−	0.0636452i	0.554105	+	0.832447i	$0.313061\pi$
$48$	0.936838	−	1.45682i	0.135221	−	0.210274i
$49$	8.38252	−	14.5189i	1.19750	−	2.07413i
$50$	−0.306879	+	0.531530i	−0.0433992	+	0.0751697i
$51$	2.75804	−	1.42086i	0.386203	−	0.198960i
$52$	−0.883519	+	0.510100i	−0.122522	+	0.0707381i
$53$		−	2.59870i		−	0.356959i	−0.983944	−	0.178479i	$-0.942882\pi$
$53$		−	2.59870i		−	0.356959i	0.983944	−	0.178479i	$-0.0571178\pi$
$54$	1.92703	+	4.82561i	0.262236	+	0.656683i
$55$			8.93201i			1.20439i
$56$	−4.22182	+	2.43747i	−0.564165	+	0.325721i
$57$	12.7397	−	6.56309i	1.68741	−	0.869302i
$58$	7.89342	+	4.55727i	1.03646	+	0.598399i
$59$	−1.99784	+	3.46037i	−0.260097	+	0.450501i	−0.966267	−	0.257541i	$-0.917088\pi$
$59$	−1.99784	+	3.46037i	−0.260097	+	0.450501i	0.706170	+	0.708042i	$0.250421\pi$
$60$	2.21969	−	3.45171i	0.286560	−	0.445613i
$61$	−0.584806	−	1.01291i	−0.0748768	−	0.129690i	0.826156	−	0.563442i	$-0.190523\pi$
$61$	−0.584806	−	1.01291i	−0.0748768	−	0.129690i	−0.901033	+	0.433751i	$0.857190\pi$
$62$	−5.58717			−0.709571
$63$	1.39859	−	14.5578i	0.176206	−	1.83411i
$64$	1.00000			0.125000
$65$	−2.09335	+	1.20860i	−0.259649	+	0.149908i
$66$	0.312573	−	6.52206i	0.0384751	−	0.802810i
$67$	−3.06655	−	1.77047i	−0.374638	−	0.216297i	0.300845	−	0.953673i	$-0.402731\pi$
$67$	−3.06655	−	1.77047i	−0.374638	−	0.216297i	−0.675483	+	0.737376i	$0.736065\pi$
$68$	1.55126	+	0.895620i	0.188118	+	0.108610i
$69$	−13.7242	−	0.657742i	−1.65220	−	0.0791828i
$70$	−10.0029	+	5.77519i	−1.19558	+	0.690267i
$71$			4.65070i			0.551937i	0.961167	+	0.275968i	$0.0889985\pi$
$71$			4.65070i			0.551937i	−0.961167	+	0.275968i	$0.911001\pi$
$72$	−1.74158	+	2.44272i	−0.205248	+	0.287878i
$73$	2.14855			0.251468			0.125734	−	0.992064i	$-0.459871\pi$
$73$	2.14855			0.251468			0.125734	+	0.992064i	$0.459871\pi$
$74$	3.13541	+	5.43068i	0.364484	+	0.631304i
$75$	0.574992	−	0.894137i	0.0663943	−	0.103246i
$76$	7.16542	+	4.13696i	0.821930	+	0.474541i
$77$	−9.18886	+	15.9156i	−1.04717	+	1.81375i
$78$	1.57084	−	0.809250i	0.177863	−	0.0916295i
$79$	2.47565	−	1.42931i	0.278532	−	0.160810i	−0.354227	−	0.935160i	$-0.615256\pi$
$79$	2.47565	−	1.42931i	0.278532	−	0.160810i	0.632759	+	0.774349i	$0.281923\pi$
$80$	2.36934			0.264900
$81$	−2.93378	−	8.50840i	−0.325975	−	0.945378i
$82$	−0.681841	+	6.36672i	−0.0752967	+	0.703086i
$83$	7.31381	+	12.6679i	0.802794	+	1.39048i	0.917770	+	0.397112i	$0.129988\pi$
$83$	7.31381	+	12.6679i	0.802794	+	1.39048i	−0.114976	+	0.993368i	$0.536679\pi$
$84$	7.50613	−	3.86693i	0.818986	−	0.421917i
$85$	3.67546	+	2.12203i	0.398659	+	0.230166i
$86$	3.17911	−	5.50637i	0.342812	−	0.593768i
$87$	−13.2783	−	8.53885i	−1.42358	−	0.915460i
$88$	3.26477	−	1.88492i	0.348026	−	0.200933i
$89$			13.5197i			1.43309i	0.697542	+	0.716543i	$0.254277\pi$
$89$			13.5197i			1.43309i	−0.697542	+	0.716543i	$0.745723\pi$
$90$	−4.12640	+	5.78763i	−0.434960	+	0.610070i
$91$	−4.97341			−0.521355
$92$	−3.96640	−	6.87000i	−0.413525	−	0.716247i
$93$	9.66617	+	0.463256i	1.00233	+	0.0480374i
$94$	−0.755744	−	0.436329i	−0.0779491	−	0.0450039i
$95$	16.9773	+	9.80184i	1.74183	+	1.00565i
$96$	−1.73007	−	0.0829143i	−0.176574	−	0.00846241i
$97$	−1.48001	+	0.854487i	−0.150273	+	0.0867600i	−0.573251	−	0.819380i	$-0.694318\pi$
$97$	−1.48001	+	0.854487i	−0.150273	+	0.0867600i	0.422978	+	0.906140i	$0.360985\pi$
$98$	−16.7650			−1.69352
$99$	−1.08154	+	11.2577i	−0.108699	+	1.13144i
$100$	0.613758			0.0613758
$101$	−4.29909	+	2.48208i	−0.427775	+	0.246976i	−0.698398	−	0.715709i	$-0.746104\pi$
$101$	−4.29909	+	2.48208i	−0.427775	+	0.246976i	0.270623	+	0.962685i	$0.412770\pi$
$102$	−2.60952	−	1.67810i	−0.258381	−	0.166157i
$103$	−6.24403	+	10.8150i	−0.615242	+	1.06563i	0.375100	+	0.926984i	$0.377608\pi$
$103$	−6.24403	+	10.8150i	−0.615242	+	1.06563i	−0.990342	+	0.138646i	$0.955725\pi$
$104$	0.883519	+	0.510100i	0.0866361	+	0.0500194i
$105$	17.7845	−	9.16206i	1.73559	−	0.894126i
$106$	−2.25054	+	1.29935i	−0.218592	+	0.126204i
$107$	2.56768			0.248227			0.124113	−	0.992268i	$-0.460391\pi$
$107$	2.56768			0.248227			0.124113	+	0.992268i	$0.460391\pi$
$108$	3.21559	−	4.08167i	0.309420	−	0.392758i
$109$		−	12.8485i		−	1.23066i	−0.788269	−	0.615330i	$-0.789023\pi$
$109$		−	12.8485i		−	1.23066i	0.788269	−	0.615330i	$-0.210977\pi$
$110$	7.73535	−	4.46601i	0.737537	−	0.425817i
$111$	−4.97418	−	9.65541i	−0.472128	−	0.916451i
$112$	4.22182	+	2.43747i	0.398925	+	0.230319i
$113$	−6.06365	+	10.5025i	−0.570420	+	0.987996i	0.426103	+	0.904675i	$0.359886\pi$
$113$	−6.06365	+	10.5025i	−0.570420	+	0.987996i	−0.996523	+	0.0833216i	$0.973447\pi$
$114$	−12.0536	−	7.75132i	−1.12893	−	0.725977i
$115$	−9.39773	−	16.2773i	−0.876343	−	1.51787i
$116$		−	9.11454i		−	0.846263i
$117$	−2.78475	+	1.26981i	−0.257451	+	0.117394i
$118$	3.99569			0.367833
$119$	4.36609	+	7.56230i	0.400239	+	0.693235i
$120$	−4.09911	−	0.196452i	−0.374196	−	0.0179335i
$121$	1.60583	−	2.78138i	0.145985	−	0.252853i
$122$	−0.584806	+	1.01291i	−0.0529459	+	0.0917050i
$123$	1.70752	−	10.9583i	0.153962	−	0.988077i
$124$	2.79358	+	4.83863i	0.250871	+	0.434522i
$125$	−10.3925			−0.929532
$126$	−13.3067	+	6.06768i	−1.18546	+	0.540552i
$127$	19.9429			1.76965			0.884824	−	0.465925i	$-0.154278\pi$
$127$	19.9429			1.76965			0.884824	+	0.465925i	$0.154278\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.95662	+	9.26279i	−0.524451	+	0.815543i
$130$	2.09335	+	1.20860i	0.183599	+	0.106001i
$131$	−2.06415	+	3.57521i	−0.180345	+	0.312367i	−0.941998	−	0.335618i	$-0.891055\pi$
$131$	−2.06415	+	3.57521i	−0.180345	+	0.312367i	0.761653	+	0.647985i	$0.224388\pi$
$132$	−5.80456	+	2.99033i	−0.505222	+	0.260275i
$133$	20.1674	+	34.9310i	1.74874	+	3.02890i
$134$			3.54094i			0.305891i
$135$	7.61881	−	9.67084i	0.655723	−	0.832333i
$136$		−	1.79124i		−	0.153598i
$137$	5.91355	−	3.41419i	0.505228	−	0.291694i	−0.225642	−	0.974210i	$-0.572448\pi$
$137$	5.91355	−	3.41419i	0.505228	−	0.291694i	0.730870	+	0.682517i	$0.239115\pi$
$138$	6.29250	+	12.2144i	0.535653	+	1.03976i
$139$	−9.29993	+	16.1080i	−0.788810	+	1.36626i	0.137886	+	0.990448i	$0.455969\pi$
$139$	−9.29993	+	16.1080i	−0.788810	+	1.36626i	−0.926696	+	0.375811i	$0.877364\pi$
$140$	10.0029	+	5.77519i	0.845401	+	0.488092i
$141$	1.27131	+	0.817540i	0.107064	+	0.0688493i
$142$	4.02763	−	2.32535i	0.337991	−	0.195139i
$143$	3.84599			0.321617
$144$	2.98625	+	0.286894i	0.248854	+	0.0239079i
$145$		−	21.5954i		−	1.79340i
$146$	−1.07427	−	1.86070i	−0.0889075	−	0.153992i
$147$	29.0046	+	1.39006i	2.39226	+	0.114650i
$148$	3.13541	−	5.43068i	0.257729	−	0.446399i
$149$	−3.24993	−	1.87635i	−0.266245	−	0.153716i	0.360935	−	0.932591i	$-0.382458\pi$
$149$	−3.24993	−	1.87635i	−0.266245	−	0.153716i	−0.627180	+	0.778874i	$0.715791\pi$
$150$	−1.06184	−	0.0508893i	−0.0866989	−	0.00415509i
$151$	−10.6094	+	6.12536i	−0.863384	+	0.498475i	−0.865144	−	0.501524i	$-0.832773\pi$
$151$	−10.6094	+	6.12536i	−0.863384	+	0.498475i	0.00176024	+	0.999998i	$0.499440\pi$
$152$		−	8.27391i		−	0.671103i
$153$	4.37550	+	3.11959i	0.353738	+	0.252204i
$154$	18.3777			1.48092
$155$	6.61894	+	11.4643i	0.531646	+	0.920838i
$156$	−1.48625	−	0.955762i	−0.118995	−	0.0765222i
$157$	−1.69151	−	0.976594i	−0.134997	−	0.0779407i	0.430980	−	0.902361i	$-0.358168\pi$
$157$	−1.69151	−	0.976594i	−0.134997	−	0.0779407i	−0.565978	+	0.824421i	$0.691501\pi$
$158$	−2.47565	−	1.42931i	−0.196952	−	0.113710i
$159$	4.00132	−	2.06136i	0.317325	−	0.163476i
$160$	−1.18467	−	2.05191i	−0.0936563	−	0.162217i
$161$		−	38.6719i		−	3.04777i
$162$	−5.90161	+	6.79493i	−0.463674	+	0.533860i
$163$	−15.0198			−1.17644			−0.588220	−	0.808701i	$-0.700171\pi$
$163$	−15.0198			−1.17644			−0.588220	+	0.808701i	$0.700171\pi$
$164$	5.85466	−	2.59287i	0.457172	−	0.202469i
$165$	−13.7530	+	7.08511i	−1.07067	+	0.551575i
$166$	7.31381	−	12.6679i	0.567661	−	0.983218i
$167$	14.0692	+	8.12285i	1.08871	+	0.628565i	0.933232	−	0.359275i	$-0.116976\pi$
$167$	14.0692	+	8.12285i	1.08871	+	0.628565i	0.155474	+	0.987840i	$0.450309\pi$
$168$	−7.10192	−	4.56703i	−0.547925	−	0.352354i
$169$	−5.97960	−	10.3570i	−0.459969	−	0.796690i
$170$		−	4.24405i		−	0.325504i
$171$	20.2109	+	14.4097i	1.54556	+	1.10194i
$172$	−6.35821			−0.484809
$173$	−3.45113	−	5.97753i	−0.262385	−	0.454464i	0.704490	−	0.709713i	$-0.251176\pi$
$173$	−3.45113	−	5.97753i	−0.262385	−	0.454464i	−0.966875	+	0.255250i	$0.917842\pi$
$174$	−0.755725	+	15.7687i	−0.0572914	+	1.19543i
$175$	2.59118	+	1.49602i	0.195874	+	0.113088i
$176$	−3.26477	−	1.88492i	−0.246092	−	0.142081i
$177$	−6.91280	−	0.331300i	−0.519598	−	0.0249020i
$178$	11.7084	−	6.75986i	0.877583	−	0.506673i
$179$			14.8852i			1.11257i	0.830990	+	0.556287i	$0.187775\pi$
$179$			14.8852i			1.11257i	−0.830990	+	0.556287i	$0.812225\pi$
$180$	7.07543	+	0.679749i	0.527372	+	0.0506655i
$181$		−	0.411674i		−	0.0305995i	−0.999883	−	0.0152997i	$-0.995130\pi$
$181$		−	0.411674i		−	0.0305995i	0.999883	−	0.0152997i	$-0.00487025\pi$
$182$	2.48671	+	4.30710i	0.184327	+	0.319264i
$183$	1.09574	−	1.70392i	0.0809993	−	0.125957i
$184$	−3.96640	+	6.87000i	−0.292407	+	0.506463i
$185$	7.42884	−	12.8671i	0.546179	−	0.946010i
$186$	−4.43189	−	8.60277i	−0.324962	−	0.630786i
$187$	−3.37634	−	5.84799i	−0.246902	−	0.427648i
$188$			0.872659i			0.0636452i
$189$	23.5246	−	9.39416i	1.71116	−	0.683325i
$190$		−	19.6037i		−	1.42220i
$191$	−3.79497	+	2.19103i	−0.274594	+	0.158537i	−0.630974	−	0.775804i	$-0.717344\pi$
$191$	−3.79497	+	2.19103i	−0.274594	+	0.158537i	0.356379	+	0.934341i	$0.384011\pi$
$192$	0.793227	+	1.53974i	0.0572462	+	0.111121i
$193$	−11.6920	−	6.75038i	−0.841608	−	0.485903i	0.0162022	−	0.999869i	$-0.494842\pi$
$193$	−11.6920	−	6.75038i	−0.841608	−	0.485903i	−0.857811	+	0.513966i	$0.828176\pi$
$194$	1.48001	+	0.854487i	0.106259	+	0.0613486i
$195$	−3.52143	−	2.26452i	−0.252175	−	0.162166i
$196$	8.38252	+	14.5189i	0.598751	+	1.03707i
$197$	−11.8168			−0.841911			−0.420955	−	0.907081i	$-0.638305\pi$
$197$	−11.8168			−0.841911			−0.420955	+	0.907081i	$0.638305\pi$
$198$	10.2902	−	4.69219i	0.731293	−	0.333460i
$199$			0.995626i			0.0705780i	0.999377	+	0.0352890i	$0.0112352\pi$
$199$			0.995626i			0.0705780i	−0.999377	+	0.0352890i	$0.988765\pi$
$200$	−0.306879	−	0.531530i	−0.0216996	−	0.0375848i
$201$	0.293595	−	6.12606i	0.0207086	−	0.432099i
$202$	4.29909	+	2.48208i	0.302483	+	0.174638i
$203$	22.2164	−	38.4799i	1.55929	−	2.70076i
$204$	−0.148519	+	3.09896i	−0.0103984	+	0.216971i
$205$	13.8717	−	6.14338i	0.968839	−	0.429072i
$206$	12.4881			0.870084
$207$	−9.87369	−	21.6535i	−0.686269	−	1.50502i
$208$		−	1.02020i		−	0.0707381i
$209$	−15.5956	−	27.0124i	−1.07877	−	1.86849i
$210$	−16.8269	−	10.8208i	−1.16116	−	0.746709i
$211$	3.63947	+	2.10125i	0.250552	+	0.144656i	0.620017	−	0.784588i	$-0.287126\pi$
$211$	3.63947	+	2.10125i	0.250552	+	0.144656i	−0.369465	+	0.929245i	$0.620459\pi$
$212$	2.25054	+	1.29935i	0.154568	+	0.0892397i
$213$	−7.16086	+	3.68906i	−0.490654	+	0.252770i
$214$	−1.28384	−	2.22368i	−0.0877615	−	0.152007i
$215$	−15.0647			−1.02741
$216$	−5.14262	−	0.743949i	−0.349911	−	0.0506193i
$217$			27.2371i			1.84898i
$218$	−11.1271	+	6.42424i	−0.753623	+	0.435104i
$219$	1.70428	+	3.30820i	0.115165	+	0.223547i
$220$	−7.73535	−	4.46601i	−0.521517	−	0.301098i
$221$	0.913711	−	1.58259i	0.0614629	−	0.106457i
$222$	−5.87474	+	9.13547i	−0.394287	+	0.613132i
$223$	−6.73892	−	11.6721i	−0.451271	−	0.781625i	0.547194	−	0.837006i	$-0.315696\pi$
$223$	−6.73892	−	11.6721i	−0.451271	−	0.781625i	−0.998465	+	0.0553810i	$0.982363\pi$
$224$		−	4.87494i		−	0.325721i
$225$	1.83283	+	0.176084i	0.122189	+	0.0117389i
$226$	12.1273			0.806696
$227$	13.4763	−	7.78057i	0.894456	−	0.516414i	0.0190585	−	0.999818i	$-0.493933\pi$
$227$	13.4763	−	7.78057i	0.894456	−	0.516414i	0.875397	+	0.483404i	$0.160600\pi$
$228$	−0.686026	+	14.3144i	−0.0454332	+	0.947995i
$229$	19.7946	+	11.4284i	1.30806	+	0.755212i	0.981773	−	0.190058i	$-0.0608675\pi$
$229$	19.7946	+	11.4284i	1.30806	+	0.755212i	0.326292	+	0.945269i	$0.394201\pi$
$230$	−9.39773	+	16.2773i	−0.619668	+	1.07330i
$231$	−31.7947	−	1.52378i	−2.09193	−	0.100257i
$232$	−7.89342	+	4.55727i	−0.518228	+	0.299199i
$233$			6.30922i			0.413331i	0.978412	+	0.206665i	$0.0662612\pi$
$233$			6.30922i			0.413331i	−0.978412	+	0.206665i	$0.933739\pi$
$234$	2.49206	+	1.77676i	0.162911	+	0.116151i
$235$			2.06762i			0.134877i
$236$	−1.99784	−	3.46037i	−0.130049	−	0.225251i
$237$	4.16452	+	2.67807i	0.270514	+	0.173960i
$238$	4.36609	−	7.56230i	0.283012	−	0.490191i
$239$	15.9212	+	9.19209i	1.02985	+	0.594587i	0.916943	−	0.399018i	$-0.130649\pi$
$239$	15.9212	+	9.19209i	1.02985	+	0.594587i	0.112912	+	0.993605i	$0.463982\pi$
$240$	1.87942	+	3.64816i	0.121316	+	0.235488i
$241$	9.73255	+	16.8573i	0.626929	+	1.08587i	0.988164	+	0.153398i	$0.0490217\pi$
$241$	9.73255	+	16.8573i	0.626929	+	1.08587i	−0.361236	+	0.932475i	$0.617645\pi$
$242$	−3.21166			−0.206454
$243$	10.7736	−	11.2663i	0.691124	−	0.722736i
$244$	1.16961			0.0748768
$245$	19.8610	+	34.4003i	1.26887	+	2.19775i
$246$	−10.3439	+	4.00039i	−0.659505	+	0.255056i
$247$	4.22052	−	7.31016i	0.268545	−	0.465134i
$248$	2.79358	−	4.83863i	0.177393	−	0.307253i
$249$	−13.7037	+	21.3098i	−0.868437	+	1.35046i
$250$	5.19624	+	9.00016i	0.328639	+	0.569220i
$251$	−1.76288			−0.111272			−0.0556361	−	0.998451i	$-0.517719\pi$
$251$	−1.76288			−0.111272			−0.0556361	+	0.998451i	$0.517719\pi$
$252$	11.9081	+	8.49011i	0.750141	+	0.534827i
$253$			29.9053i			1.88013i
$254$	−9.97146	−	17.2711i	−0.625665	−	1.08368i
$255$	−0.351893	+	7.34249i	−0.0220364	+	0.459804i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.28762	−	3.63016i	−0.392211	−	0.226443i	0.290907	−	0.956751i	$-0.406043\pi$
$257$	−6.28762	−	3.63016i	−0.392211	−	0.226443i	−0.683118	+	0.730308i	$0.739376\pi$
$258$	11.0001	+	0.527187i	0.684838	+	0.0328212i
$259$	26.4743	−	15.2849i	1.64503	−	0.949759i
$260$		−	2.41720i		−	0.149908i
$261$	2.61491	−	27.2183i	0.161859	−	1.68477i
$262$	4.12829			0.255047
$263$	4.65782	−	2.68919i	0.287213	−	0.165823i	−0.349471	−	0.936947i	$-0.613639\pi$
$263$	4.65782	−	2.68919i	0.287213	−	0.165823i	0.636685	+	0.771124i	$0.280305\pi$
$264$	5.49198	+	3.53173i	0.338008	+	0.217363i
$265$	5.33229	+	3.07860i	0.327560	+	0.189117i
$266$	20.1674	−	34.9310i	1.23654	−	2.14176i
$267$	−20.8168	+	10.7242i	−1.27397	+	0.656310i
$268$	3.06655	−	1.77047i	0.187319	−	0.108149i
$269$	1.23141			0.0750805			0.0375403	−	0.999295i	$-0.488048\pi$
$269$	1.23141			0.0750805			0.0375403	+	0.999295i	$0.488048\pi$
$270$	−12.1846	−	1.76267i	−0.741531	−	0.107272i
$271$	−7.39532			−0.449233			−0.224617	−	0.974447i	$-0.572113\pi$
$271$	−7.39532			−0.449233			−0.224617	+	0.974447i	$0.572113\pi$
$272$	−1.55126	+	0.895620i	−0.0940589	+	0.0543049i
$273$	−3.94504	−	7.65775i	−0.238765	−	0.463468i
$274$	−5.91355	−	3.41419i	−0.357250	−	0.206259i
$275$	−2.00378	−	1.15688i	−0.120832	−	0.0697627i
$276$	7.43174	−	11.5567i	0.447338	−	0.695630i
$277$	−8.51360	−	14.7460i	−0.511532	−	0.886000i	−0.999911	−	0.0133682i	$-0.995745\pi$
$277$	−8.51360	−	14.7460i	−0.511532	−	0.886000i	0.488378	−	0.872632i	$-0.337589\pi$
$278$	18.5999			1.11555
$279$	6.95417	+	15.2508i	0.416335	+	0.913043i
$280$		−	11.5504i		−	0.690267i
$281$	−19.5785	+	11.3037i	−1.16796	+	0.674320i	−0.953198	−	0.302347i	$-0.902230\pi$
$281$	−19.5785	+	11.3037i	−1.16796	+	0.674320i	−0.214759	+	0.976667i	$0.568897\pi$
$282$	0.0723559	−	1.50976i	0.00430873	−	0.0899047i
$283$	−2.14984	+	3.72362i	−0.127794	+	0.221346i	−0.922822	−	0.385227i	$-0.874123\pi$
$283$	−2.14984	+	3.72362i	−0.127794	+	0.221346i	0.795027	+	0.606574i	$0.207456\pi$
$284$	−4.02763	−	2.32535i	−0.238996	−	0.137984i
$285$	−1.62543	+	33.9156i	−0.0962819	+	2.00899i
$286$	−1.92299	−	3.33072i	−0.113709	−	0.196950i
$287$	31.0374	+	3.32393i	1.83208	+	0.196206i
$288$	−1.24467	−	2.72962i	−0.0733427	−	0.160844i
$289$	13.7915			0.811262
$290$	−18.7022	+	10.7977i	−1.09823	+	0.634063i
$291$	−2.48967	−	1.60103i	−0.145947	−	0.0938542i
$292$	−1.07427	+	1.86070i	−0.0628671	+	0.108889i
$293$	9.22331	+	5.32508i	0.538832	+	0.311095i	0.744605	−	0.667505i	$-0.232638\pi$
$293$	9.22331	+	5.32508i	0.538832	+	0.311095i	−0.205774	+	0.978600i	$0.565971\pi$
$294$	−13.2985	−	25.8137i	−0.775583	−	1.50549i
$295$	−4.73356	−	8.19877i	−0.275599	−	0.477351i
$296$	−6.27081			−0.364484
$297$	−18.1918	+	7.26459i	−1.05559	+	0.421534i
$298$			3.75270i			0.217388i
$299$	−7.00877	+	4.04652i	−0.405328	+	0.234016i
$300$	0.486849	+	0.945026i	0.0281082	+	0.0545611i
$301$	−26.8432	−	15.4980i	−1.54722	−	0.893287i
$302$	10.6094	+	6.12536i	0.610504	+	0.352475i
$303$	−7.23190	−	4.65061i	−0.415462	−	0.267171i
$304$	−7.16542	+	4.13696i	−0.410965	+	0.237271i
$305$	2.77121			0.158679
$306$	0.513897	−	5.34909i	0.0293775	−	0.305787i
$307$	14.6398			0.835535			0.417768	−	0.908554i	$-0.362813\pi$
$307$	14.6398			0.835535			0.417768	+	0.908554i	$0.362813\pi$
$308$	−9.18886	−	15.9156i	−0.523584	−	0.906874i
$309$	−21.6051	−	1.03544i	−1.22907	−	0.0589040i
$310$	6.61894	−	11.4643i	0.375931	−	0.651131i
$311$	−8.57490	−	4.95072i	−0.486238	−	0.280730i	0.236775	−	0.971565i	$-0.423910\pi$
$311$	−8.57490	−	4.95072i	−0.486238	−	0.280730i	−0.723012	+	0.690835i	$0.757243\pi$
$312$	−0.0845891	+	1.76501i	−0.00478892	+	0.0999241i
$313$	−16.8234	+	9.71299i	−0.950915	+	0.549011i	−0.893365	−	0.449332i	$-0.851662\pi$
$313$	−16.8234	+	9.71299i	−0.950915	+	0.549011i	−0.0575498	+	0.998343i	$0.518329\pi$
$314$			1.95319i			0.110225i
$315$	28.2143	+	20.1159i	1.58970	+	1.13340i
$316$			2.85863i			0.160810i
$317$	−26.8971	+	15.5290i	−1.51069	+	0.872197i	−0.510768	+	0.859719i	$0.670639\pi$
$317$	−26.8971	+	15.5290i	−1.51069	+	0.872197i	−0.999922	+	0.0124789i	$0.996028\pi$
$318$	−3.78585	−	2.43456i	−0.212300	−	0.136523i
$319$	−17.1802	+	29.7569i	−0.961904	+	1.66607i
$320$	−1.18467	+	2.05191i	−0.0662250	+	0.114705i
$321$	2.03675	+	3.95355i	0.113680	+	0.220666i
$322$	−33.4908	+	19.3359i	−1.86637	+	1.07755i
$323$	−14.8206			−0.824638
$324$	8.83538	+	1.71348i	0.490855	+	0.0951931i
$325$		−	0.626155i		−	0.0347329i
$326$	7.50989	+	13.0075i	0.415934	+	0.720419i
$327$	19.7833	−	10.1918i	1.09402	−	0.563605i
$328$	−5.17282	−	3.77385i	−0.285621	−	0.208376i
$329$	−2.12708	+	3.68421i	−0.117270	+	0.203117i
$330$	13.0124	+	8.36785i	0.716307	+	0.460635i
$331$	22.0103	−	12.7077i	1.20980	−	0.698477i	0.247082	−	0.968995i	$-0.420528\pi$
$331$	22.0103	−	12.7077i	1.20980	−	0.698477i	0.962715	+	0.270518i	$0.0871950\pi$
$332$	−14.6276			−0.802794
$333$	10.9211	−	15.3179i	0.598475	−	0.839413i
$334$		−	16.2457i		−	0.888925i
$335$	7.26568	−	4.19484i	0.396967	−	0.229189i
$336$	−0.404202	+	8.43396i	−0.0220510	+	0.460110i
$337$	−11.4954	+	19.9107i	−0.626195	+	1.08460i	0.362113	+	0.932134i	$0.382055\pi$
$337$	−11.4954	+	19.9107i	−0.626195	+	1.08460i	−0.988308	+	0.152468i	$0.951278\pi$
$338$	−5.97960	+	10.3570i	−0.325247	+	0.563345i
$339$	−20.9810	−	1.00553i	−1.13953	−	0.0546127i
$340$	−3.67546	+	2.12203i	−0.199330	+	0.115083i
$341$		−	21.0627i		−	1.14061i
$342$	2.37374	−	24.7080i	0.128357	−	1.33605i
$343$			47.6039i			2.57037i
$344$	3.17911	+	5.50637i	0.171406	+	0.296884i
$345$	17.6083	−	27.3817i	0.947999	−	1.47418i
$346$	−3.45113	+	5.97753i	−0.185534	+	0.321354i
$347$	−25.5614	−	14.7579i	−1.37221	−	0.792244i	−0.381001	−	0.924575i	$-0.624420\pi$
$347$	−25.5614	−	14.7579i	−1.37221	−	0.792244i	−0.991206	+	0.132331i	$0.957754\pi$
$348$	14.0340	−	7.22989i	0.752301	−	0.387563i
$349$	4.54328	+	7.86919i	0.243196	+	0.421228i	0.961623	−	0.274375i	$-0.0884708\pi$
$349$	4.54328	+	7.86919i	0.243196	+	0.421228i	−0.718427	+	0.695603i	$0.755137\pi$
$350$		−	2.99203i		−	0.159931i
$351$	−4.16411	−	3.28054i	−0.222264	−	0.175102i
$352$			3.76984i			0.200933i
$353$	10.5516	+	18.2760i	0.561607	+	0.972732i	0.997356	+	0.0726642i	$0.0231501\pi$
$353$	10.5516	+	18.2760i	0.561607	+	0.972732i	−0.435749	+	0.900068i	$0.643517\pi$
$354$	3.16948	+	6.15231i	0.168456	+	0.326991i
$355$	−9.54280	−	5.50954i	−0.506479	−	0.292416i
$356$	−11.7084	−	6.75986i	−0.620545	−	0.358272i
$357$	−8.18065	+	12.7213i	−0.432966	+	0.673280i
$358$	12.8910	−	7.44262i	0.681310	−	0.393355i
$359$	17.0214			0.898354			0.449177	−	0.893443i	$-0.351717\pi$
$359$	17.0214			0.898354			0.449177	+	0.893443i	$0.351717\pi$
$360$	−2.94904	−	6.46738i	−0.155428	−	0.340861i
$361$	−49.4576			−2.60303
$362$	−0.356520	+	0.205837i	−0.0187383	+	0.0108185i
$363$	5.55639	+	0.266293i	0.291635	+	0.0139767i
$364$	2.48671	−	4.30710i	0.130339	−	0.225753i
$365$	−2.54532	+	4.40862i	−0.133228	+	0.230757i
$366$	−2.02351	−	0.0969776i	−0.105770	−	0.00506910i
$367$	7.18379	+	12.4427i	0.374991	+	0.649503i	0.990326	−	0.138763i	$-0.0443125\pi$
$367$	7.18379	+	12.4427i	0.374991	+	0.649503i	−0.615335	+	0.788266i	$0.710979\pi$
$368$	7.93279			0.413525
$369$	18.2274	−	6.06328i	0.948878	−	0.315642i
$370$	−14.8577			−0.772414
$371$	6.33425	+	10.9712i	0.328858	+	0.569599i
$372$	−5.23427	+	8.13952i	−0.271385	+	0.422014i
$373$	15.6241	−	27.0617i	0.808983	−	1.40120i	−0.104585	−	0.994516i	$-0.533352\pi$
$373$	15.6241	−	27.0617i	0.808983	−	1.40120i	0.913569	−	0.406684i	$-0.133315\pi$
$374$	−3.37634	+	5.84799i	−0.174586	+	0.302393i
$375$	−8.24360	−	16.0017i	−0.425698	−	0.826324i
$376$	0.755744	−	0.436329i	0.0389745	−	0.0225020i
$377$	−9.29865			−0.478905
$378$	−19.8979	−	15.6758i	−1.02344	−	0.806276i
$379$	10.8106			0.555303			0.277651	−	0.960682i	$-0.410444\pi$
$379$	10.8106			0.555303			0.277651	+	0.960682i	$0.410444\pi$
$380$	−16.9773	+	9.80184i	−0.870917	+	0.502824i
$381$	15.8193	+	30.7069i	0.810445	+	1.57316i
$382$	3.79497	+	2.19103i	0.194167	+	0.112103i
$383$	−9.04861	−	5.22422i	−0.462362	−	0.266945i	0.250675	−	0.968071i	$-0.419348\pi$
$383$	−9.04861	−	5.22422i	−0.462362	−	0.266945i	−0.713037	+	0.701126i	$0.752681\pi$
$384$	0.936838	−	1.45682i	0.0478078	−	0.0743432i
$385$	−21.7715	−	37.7094i	−1.10958	−	1.92185i
$386$			13.5008i			0.687170i
$387$	−18.9872	−	1.82414i	−0.965174	−	0.0927260i
$388$		−	1.70897i		−	0.0867600i
$389$	−8.03655	−	13.9197i	−0.407469	−	0.705757i	0.587136	−	0.809488i	$-0.300255\pi$
$389$	−8.03655	−	13.9197i	−0.407469	−	0.705757i	−0.994605	+	0.103731i	$0.966922\pi$
$390$	−0.200420	+	4.18191i	−0.0101487	+	0.211759i
$391$	12.3058	+	7.10477i	0.622332	+	0.359304i
$392$	8.38252	−	14.5189i	0.423381	−	0.733317i
$393$	−7.14222	−	0.342295i	−0.360277	−	0.0172665i
$394$	5.90839	+	10.2336i	0.297660	+	0.515563i
$395$			6.77305i			0.340789i
$396$	−9.20866	−	6.56548i	−0.462753	−	0.329928i
$397$		−	27.5081i		−	1.38059i	−0.723528	−	0.690295i	$-0.757481\pi$
$397$		−	27.5081i		−	1.38059i	0.723528	−	0.690295i	$-0.242519\pi$
$398$	0.862237	−	0.497813i	0.0432200	−	0.0249531i
$399$	−37.7872	+	58.7607i	−1.89173	+	2.94171i
$400$	−0.306879	+	0.531530i	−0.0153439	+	0.0265765i
$401$	−5.26643	+	9.12173i	−0.262993	+	0.455517i	−0.967036	−	0.254640i	$-0.918043\pi$
$401$	−5.26643	+	9.12173i	−0.262993	+	0.455517i	0.704043	+	0.710158i	$0.251376\pi$
$402$	−5.45212	+	2.80877i	−0.271927	+	0.140089i
$403$	4.93637	−	2.85001i	0.245898	−	0.141969i
$404$		−	4.96416i		−	0.246976i
$405$	20.9340	+	4.05980i	1.04022	+	0.201733i
$406$	−44.4328			−2.20516
$407$	−20.4728	+	11.8200i	−1.01480	+	0.585894i
$408$	2.75804	−	1.42086i	0.136543	−	0.0703430i
$409$	7.41896	−	12.8500i	0.366844	−	0.635392i	−0.622226	−	0.782837i	$-0.713772\pi$
$409$	7.41896	−	12.8500i	0.366844	−	0.635392i	0.989070	+	0.147445i	$0.0471049\pi$
$410$	−12.2562	−	8.94152i	−0.605288	−	0.441590i
$411$	9.94774	+	6.39708i	0.490686	+	0.315545i
$412$	−6.24403	−	10.8150i	−0.307621	−	0.532815i
$413$		−	19.4787i		−	0.958486i
$414$	−13.8156	+	19.3776i	−0.679000	+	0.952357i
$415$	−34.6577			−1.70128
$416$	−0.883519	+	0.510100i	−0.0433181	+	0.0250097i
$417$	−32.1790	−	1.54220i	−1.57581	−	0.0755216i
$418$	−15.5956	+	27.0124i	−0.762808	+	1.32122i
$419$	10.8374	−	18.7709i	0.529442	−	0.917020i	−0.469969	−	0.882683i	$-0.655735\pi$
$419$	10.8374	−	18.7709i	0.529442	−	0.917020i	0.999410	−	0.0343369i	$-0.0109319\pi$
$420$	−0.957691	+	19.9829i	−0.0467305	+	0.975066i
$421$	−34.1977	+	19.7441i	−1.66669	+	0.962267i	−0.697293	+	0.716786i	$0.745612\pi$
$421$	−34.1977	+	19.7441i	−1.66669	+	0.962267i	−0.969402	+	0.245480i	$0.921054\pi$
$422$		−	4.20250i		−	0.204575i
$423$	−0.250361	+	2.60598i	−0.0121730	+	0.126707i
$424$		−	2.59870i		−	0.126204i
$425$	−0.952098	+	0.549694i	−0.0461835	+	0.0266641i
$426$	6.77525	+	4.35696i	0.328262	+	0.211095i
$427$	4.93790	+	2.85090i	0.238962	+	0.137965i
$428$	−1.28384	+	2.22368i	−0.0620567	+	0.107485i
$429$	3.05074	+	5.92181i	0.147291	+	0.285908i
$430$	7.53237	+	13.0465i	0.363243	+	0.629156i
$431$	14.1510			0.681627			0.340814	−	0.940131i	$-0.389297\pi$
$431$	14.1510			0.681627			0.340814	+	0.940131i	$0.389297\pi$
$432$	1.92703	+	4.82561i	0.0927143	+	0.232172i
$433$	−36.1991			−1.73962			−0.869810	−	0.493387i	$-0.835759\pi$
$433$	−36.1991			−1.73962			−0.869810	+	0.493387i	$0.835759\pi$
$434$	23.5880	−	13.6186i	1.13226	−	0.653712i
$435$	33.2513	−	17.1301i	1.59428	−	0.821323i
$436$	11.1271	+	6.42424i	0.532892	+	0.307665i
$437$	56.8418	+	32.8176i	2.71911	+	1.56988i
$438$	2.01284	−	3.13005i	0.0961773	−	0.149560i
$439$	7.35009	−	4.24358i	0.350801	−	0.202535i	−0.314237	−	0.949345i	$-0.601749\pi$
$439$	7.35009	−	4.24358i	0.350801	−	0.202535i	0.665038	+	0.746810i	$0.268415\pi$
$440$			8.93201i			0.425817i
$441$	20.8669	+	45.7621i	0.993662	+	2.17915i
$442$	−1.82742			−0.0869216
$443$	−2.05505	−	3.55945i	−0.0976385	−	0.169115i	0.813068	−	0.582168i	$-0.197796\pi$
$443$	−2.05505	−	3.55945i	−0.0976385	−	0.169115i	−0.910707	+	0.413054i	$0.864462\pi$
$444$	10.8489	+	0.519940i	0.514867	+	0.0246753i
$445$	−27.7412	−	16.0164i	−1.31506	−	0.759249i
$446$	−6.73892	+	11.6721i	−0.319097	+	0.552692i
$447$	0.311152	−	6.49241i	0.0147170	−	0.307080i
$448$	−4.22182	+	2.43747i	−0.199462	+	0.115160i
$449$	22.2112			1.04821			0.524106	−	0.851653i	$-0.324399\pi$
$449$	22.2112			1.04821			0.524106	+	0.851653i	$0.324399\pi$
$450$	−0.763924	−	1.67532i	−0.0360117	−	0.0789755i
$451$	−24.0015	−	2.57043i	−1.13019	−	0.121037i
$452$	−6.06365	−	10.5025i	−0.285210	−	0.493998i
$453$	−17.8471	−	11.4769i	−0.838532	−	0.539234i
$454$	−13.4763	−	7.78057i	−0.632476	−	0.365160i
$455$	5.89184	−	10.2050i	0.276214	−	0.478416i
$456$	12.7397	−	6.56309i	0.596589	−	0.307345i
$457$	−5.18852	+	2.99559i	−0.242709	+	0.140128i	−0.616421	−	0.787417i	$-0.711418\pi$
$457$	−5.18852	+	2.99559i	−0.242709	+	0.140128i	0.373712	+	0.927545i	$0.378085\pi$
$458$		−	22.8568i		−	1.06803i
$459$	−1.33259	+	9.21167i	−0.0622000	+	0.429964i
$460$	18.7955			0.876343
$461$	−10.3050	−	17.8487i	−0.479950	−	0.831299i	0.519785	−	0.854297i	$-0.326012\pi$
$461$	−10.3050	−	17.8487i	−0.479950	−	0.831299i	−0.999735	+	0.0229985i	$0.992679\pi$
$462$	14.5777	+	28.2969i	0.678216	+	1.31649i
$463$	−2.61596	−	1.51032i	−0.121574	−	0.0701907i	0.437980	−	0.898985i	$-0.355694\pi$
$463$	−2.61596	−	1.51032i	−0.121574	−	0.0701907i	−0.559554	+	0.828794i	$0.689027\pi$
$464$	7.89342	+	4.55727i	0.366443	+	0.211566i
$465$	−12.4018	+	19.2853i	−0.575118	+	0.894332i
$466$	5.46395	−	3.15461i	0.253112	−	0.146135i
$467$	38.3929			1.77661			0.888306	−	0.459252i	$-0.151882\pi$
$467$	38.3929			1.77661			0.888306	+	0.459252i	$0.151882\pi$
$468$	0.292689	−	3.04657i	0.0135296	−	0.140828i
$469$	17.2619			0.797079
$470$	1.79061	−	1.03381i	0.0825948	−	0.0476861i
$471$	0.161947	−	3.37914i	0.00746213	−	0.155703i
$472$	−1.99784	+	3.46037i	−0.0919582	+	0.159276i
$473$	20.7581	+	11.9847i	0.954460	+	0.551058i
$474$	0.237021	−	4.94561i	0.0108867	−	0.227160i
$475$	−4.39783	+	2.53909i	−0.201786	+	0.116501i
$476$	−8.73219			−0.400239
$477$	6.34790	+	4.52585i	0.290650	+	0.207225i
$478$		−	18.3842i		−	0.840873i
$479$	14.8658	−	8.58280i	0.679237	−	0.392158i	−0.120330	−	0.992734i	$-0.538395\pi$
$479$	14.8658	−	8.58280i	0.679237	−	0.392158i	0.799568	+	0.600576i	$0.205062\pi$
$480$	2.21969	−	3.45171i	0.101314	−	0.157548i
$481$	−5.54038	−	3.19874i	−0.252620	−	0.145850i
$482$	9.73255	−	16.8573i	0.443306	−	0.767828i
$483$	59.5445	−	30.6756i	2.70937	−	1.39579i
$484$	1.60583	+	2.78138i	0.0729923	+	0.126426i
$485$		−	4.04913i		−	0.183862i
$486$	−15.1437	−	3.69701i	−0.686933	−	0.167700i
$487$	8.83968			0.400564			0.200282	−	0.979738i	$-0.435814\pi$
$487$	8.83968			0.400564			0.200282	+	0.979738i	$0.435814\pi$
$488$	−0.584806	−	1.01291i	−0.0264729	−	0.0458525i
$489$	−11.9141	−	23.1265i	−0.538774	−	1.04582i
$490$	19.8610	−	34.4003i	0.897229	−	1.55405i
$491$	−18.4092	+	31.8858i	−0.830798	+	1.43898i	0.0666087	+	0.997779i	$0.478782\pi$
$491$	−18.4092	+	31.8858i	−0.830798	+	1.43898i	−0.897406	+	0.441205i	$0.854551\pi$
$492$	8.63641	+	6.95791i	0.389359	+	0.313687i
$493$	8.16316	+	14.1390i	0.367650	+	0.636789i
$494$	−8.44104			−0.379780
$495$	−21.8184	−	15.5558i	−0.980665	−	0.699183i
$496$	−5.58717			−0.250871
$497$	−11.3359	−	19.6344i	−0.508487	−	0.880725i
$498$	25.3067	+	1.21284i	1.13402	+	0.0543486i
$499$	−0.131128	−	0.0757069i	−0.00587010	−	0.00338910i	0.497062	−	0.867715i	$-0.334412\pi$
$499$	−0.131128	−	0.0757069i	−0.00587010	−	0.00338910i	−0.502932	+	0.864326i	$0.667745\pi$
$500$	5.19624	−	9.00016i	0.232383	−	0.402499i
$501$	−1.34700	+	28.1061i	−0.0601795	+	1.25569i
$502$	0.881442	+	1.52670i	0.0393407	+	0.0681401i
$503$		−	17.8020i		−	0.793750i	−0.917873	−	0.396875i	$-0.870095\pi$
$503$		−	17.8020i		−	0.793750i	0.917873	−	0.396875i	$-0.129905\pi$
$504$	1.39859	−	14.5578i	0.0622982	−	0.648455i
$505$		−	11.7618i		−	0.523391i
$506$	25.8988	−	14.9527i	1.15134	−	0.664727i
$507$	11.2038	−	17.4224i	0.497580	−	0.773757i
$508$	−9.97146	+	17.2711i	−0.442412	+	0.766280i
$509$	12.7907	+	7.38472i	0.566939	+	0.327322i	0.755926	−	0.654657i	$-0.227187\pi$
$509$	12.7907	+	7.38472i	0.566939	+	0.327322i	−0.188987	+	0.981980i	$0.560520\pi$
$510$	6.53473	−	3.36649i	0.289363	−	0.149071i
$511$	−9.07078	+	5.23702i	−0.401268	+	0.231672i
$512$	1.00000			0.0441942
$513$	−6.15537	+	42.5496i	−0.271766	+	1.87861i
$514$			7.26031i			0.320239i
$515$	−14.7942	−	25.6243i	−0.651910	−	1.12914i
$516$	−5.04350	−	9.78998i	−0.222028	−	0.430980i
$517$	1.64489	−	2.84903i	0.0723422	−	0.125300i
$518$	−26.4743	−	15.2849i	−1.16321	−	0.671581i
$519$	6.46630	−	10.0554i	0.283839	−	0.441382i
$520$	−2.09335	+	1.20860i	−0.0917996	+	0.0530005i
$521$			35.9628i			1.57556i	0.615958	+	0.787779i	$0.288769\pi$
$521$			35.9628i			1.57556i	−0.615958	+	0.787779i	$0.711231\pi$
$522$	−24.8792	+	11.3446i	−1.08893	+	0.496538i
$523$	31.3935			1.37274			0.686371	−	0.727252i	$-0.259203\pi$
$523$	31.3935			1.37274			0.686371	+	0.727252i	$0.259203\pi$
$524$	−2.06415	−	3.57521i	−0.0901727	−	0.156184i
$525$	−0.248082	+	5.17641i	−0.0108272	+	0.225917i
$526$	−4.65782	−	2.68919i	−0.203091	−	0.117254i
$527$	−8.66715	−	5.00398i	−0.377547	−	0.217977i
$528$	0.312573	−	6.52206i	0.0136030	−	0.283836i
$529$	−19.9646	−	34.5797i	−0.868025	−	1.50346i
$530$		−	6.15720i		−	0.267452i
$531$	−4.97330	−	10.9067i	−0.215823	−	0.473310i
$532$	−40.3348			−1.74874
$533$	−2.64524	−	5.97292i	−0.114578	−	0.258716i
$534$	19.6958	+	12.6658i	0.852322	+	0.548102i
$535$	−3.04185	+	5.26864i	−0.131511	+	0.227783i
$536$	−3.06655	−	1.77047i	−0.132455	−	0.0764727i
$537$	−22.9194	+	11.8074i	−0.989043	+	0.509526i
$538$	−0.615706	−	1.06643i	−0.0265450	−	0.0459772i
$539$		−	63.2014i		−	2.72228i
$540$	4.56579	+	11.4335i	0.196480	+	0.492020i
$541$	35.1456			1.51103			0.755514	−	0.655133i	$-0.227387\pi$
$541$	35.1456			1.51103			0.755514	+	0.655133i	$0.227387\pi$
$542$	3.69766	+	6.40453i	0.158828	+	0.275098i
$543$	0.633870	−	0.326551i	0.0272019	−	0.0140136i
$544$	1.55126	+	0.895620i	0.0665097	+	0.0383994i
$545$	26.3639	+	15.2212i	1.12930	+	0.652004i
$546$	−4.65928	+	7.24538i	−0.199399	+	0.310074i
$547$	28.0707	−	16.2066i	1.20022	−	0.692946i	0.239614	−	0.970868i	$-0.422979\pi$
$547$	28.0707	−	16.2066i	1.20022	−	0.692946i	0.960604	+	0.277922i	$0.0896457\pi$
$548$			6.82838i			0.291694i
$549$	3.49276	+	0.335555i	0.149067	+	0.0143211i
$550$			2.31377i			0.0986593i
$551$	37.7064	+	65.3095i	1.60635	+	2.78228i
$552$	−13.7242	−	0.657742i	−0.584143	−	0.0279954i
$553$	−6.96782	+	12.0686i	−0.296302	+	0.513210i
$554$	−8.51360	+	14.7460i	−0.361708	+	0.626497i
$555$	25.7047	+	1.23191i	1.09111	+	0.0522918i
$556$	−9.29993	−	16.1080i	−0.394405	−	0.683130i
$557$			10.9092i			0.462237i	0.972926	+	0.231118i	$0.0742384\pi$
$557$			10.9092i			0.462237i	−0.972926	+	0.231118i	$0.925762\pi$
$558$	9.73052	−	13.6479i	0.411926	−	0.577762i
$559$			6.48665i			0.274356i
$560$	−10.0029	+	5.77519i	−0.422700	+	0.244046i
$561$	6.32617	−	9.83746i	0.267091	−	0.415338i
$562$	19.5785	+	11.3037i	0.825870	+	0.476816i
$563$	−3.87933	−	2.23973i	−0.163494	−	0.0943935i	0.416020	−	0.909355i	$-0.363425\pi$
$563$	−3.87933	−	2.23973i	−0.163494	−	0.0943935i	−0.579515	+	0.814962i	$0.696758\pi$
$564$	−1.34367	+	0.692216i	−0.0565785	+	0.0291476i
$565$	−14.3668	−	24.8841i	−0.604417	−	1.04688i
$566$	4.29967			0.180729
$567$	33.1249	+	28.7700i	1.39111	+	1.20823i
$568$			4.65070i			0.195139i
$569$	−14.7509	−	25.5493i	−0.618390	−	1.07108i	−0.989780	−	0.142606i	$-0.954452\pi$
$569$	−14.7509	−	25.5493i	−0.618390	−	1.07108i	0.371390	−	0.928477i	$-0.378881\pi$
$570$	30.1845	−	15.5502i	1.26429	−	0.651325i
$571$	7.52372	+	4.34382i	0.314858	+	0.181783i	0.649098	−	0.760705i	$-0.275146\pi$
$571$	7.52372	+	4.34382i	0.314858	+	0.181783i	−0.334240	+	0.942488i	$0.608480\pi$
$572$	−1.92299	+	3.33072i	−0.0804044	+	0.139264i
$573$	−6.38387	−	4.10527i	−0.266690	−	0.171500i
$574$	−12.6401	−	28.5411i	−0.527586	−	1.19128i
$575$	4.86881			0.203044
$576$	−1.74158	+	2.44272i	−0.0725660	+	0.101780i
$577$			31.3335i			1.30443i	0.758034	+	0.652215i	$0.226160\pi$
$577$			31.3335i			1.30443i	−0.758034	+	0.652215i	$0.773840\pi$
$578$	−6.89573	−	11.9438i	−0.286825	−	0.496795i
$579$	1.11941	−	23.3572i	0.0465209	−	0.970692i
$580$	18.7022	+	10.7977i	0.776565	+	0.448350i
$581$	−61.7552	−	35.6544i	−2.56204	−	1.47919i
$582$	−0.141698	+	2.95664i	−0.00587359	+	0.122556i
$583$	−4.89834	−	8.48417i	−0.202868	−	0.351378i
$584$	2.14855			0.0889075
$585$	0.693480	−	7.21835i	0.0286719	−	0.298442i
$586$		−	10.6502i		−	0.439954i
$587$	−10.0003	+	5.77368i	−0.412757	+	0.238305i	−0.691974	−	0.721923i	$-0.743259\pi$
$587$	−10.0003	+	5.77368i	−0.412757	+	0.238305i	0.279217	+	0.960228i	$0.409925\pi$
$588$	−15.7061	+	24.4237i	−0.647710	+	1.00722i
$589$	−40.0344	−	23.1139i	−1.64959	−	0.952390i
$590$	−4.73356	+	8.19877i	−0.194878	+	0.337538i
$591$	−9.37338	−	18.1947i	−0.385569	−	0.748431i
$592$	3.13541	+	5.43068i	0.128864	+	0.223200i
$593$		−	2.38737i		−	0.0980375i	−0.998798	−	0.0490187i	$-0.984391\pi$
$593$		−	2.38737i		−	0.0980375i	0.998798	−	0.0490187i	$-0.0156094\pi$
$594$	15.3872	+	12.1222i	0.631345	+	0.497382i
$595$	−20.6895			−0.848187
$596$	3.24993	−	1.87635i	0.133122	−	0.0768582i
$597$	−1.53300	+	0.789757i	−0.0627416	+	0.0323226i
$598$	7.00877	+	4.04652i	0.286610	+	0.165474i
$599$	12.4875	−	21.6290i	0.510225	−	0.883736i	−0.489705	−	0.871888i	$-0.662895\pi$
$599$	12.4875	−	21.6290i	0.510225	−	0.883736i	0.999930	−	0.0118473i	$-0.00377121\pi$
$600$	0.574992	−	0.894137i	0.0234739	−	0.0365030i
$601$	2.68855	−	1.55223i	0.109668	−	0.0633169i	−0.444163	−	0.895946i	$-0.646499\pi$
$601$	2.68855	−	1.55223i	0.109668	−	0.0633169i	0.553831	+	0.832629i	$0.313165\pi$
$602$			30.9959i			1.26330i
$603$	9.66541	−	4.40730i	0.393606	−	0.179479i
$604$		−	12.2507i		−	0.498475i
$605$	3.80476	+	6.59003i	0.154685	+	0.267923i
$606$	−0.411600	+	8.58831i	−0.0167201	+	0.348876i
$607$	−15.9613	+	27.6458i	−0.647850	+	1.12211i	0.335786	+	0.941938i	$0.390998\pi$
$607$	−15.9613	+	27.6458i	−0.647850	+	1.12211i	−0.983635	+	0.180170i	$0.942335\pi$
$608$	7.16542	+	4.13696i	0.290596	+	0.167776i
$609$	76.8716	+	3.68412i	3.11500	+	0.149288i
$610$	−1.38560	−	2.39994i	−0.0561014	−	0.0971706i
$611$	0.890286			0.0360171
$612$	−4.88940	+	2.22950i	−0.197642	+	0.0901221i
$613$	40.2200			1.62447			0.812236	−	0.583330i	$-0.198250\pi$
$613$	40.2200			1.62447			0.812236	+	0.583330i	$0.198250\pi$
$614$	−7.31988	−	12.6784i	−0.295406	−	0.511659i
$615$	20.4626	+	16.4856i	0.825130	+	0.664765i
$616$	−9.18886	+	15.9156i	−0.370230	+	0.641257i
$617$	9.19582	−	15.9276i	0.370210	−	0.641222i	−0.619388	−	0.785085i	$-0.712619\pi$
$617$	9.19582	−	15.9276i	0.370210	−	0.641222i	0.989598	+	0.143863i	$0.0459525\pi$
$618$	9.90585	+	19.2283i	0.398472	+	0.773476i
$619$	−8.32782	−	14.4242i	−0.334723	−	0.579758i	0.648708	−	0.761037i	$-0.275310\pi$
$619$	−8.32782	−	14.4242i	−0.334723	−	0.579758i	−0.983432	+	0.181279i	$0.941976\pi$
$620$	−13.2379			−0.531646
$621$	25.5086	−	32.3790i	1.02362	−	1.29932i
$622$			9.90144i			0.397012i
$623$	−32.9539	−	57.0778i	−1.32027	−	2.28677i
$624$	1.57084	−	0.809250i	0.0628839	−	0.0323959i
$625$	13.8460	−	23.9821i	0.553842	−	0.959282i
$626$	16.8234	+	9.71299i	0.672398	+	0.388209i
$627$	29.2212	−	45.4402i	1.16698	−	1.81471i
$628$	1.69151	−	0.976594i	0.0674986	−	0.0389703i
$629$			11.2325i			0.447870i
$630$	3.31374	−	34.4923i	0.132022	−	1.37421i
$631$	1.18152			0.0470356			0.0235178	−	0.999723i	$-0.492513\pi$
$631$	1.18152			0.0470356			0.0235178	+	0.999723i	$0.492513\pi$
$632$	2.47565	−	1.42931i	0.0984759	−	0.0568551i
$633$	−0.348448	+	7.27060i	−0.0138496	+	0.288981i
$634$	26.8971	+	15.5290i	1.06822	+	0.616737i
$635$	−23.6258	+	40.9210i	−0.937560	+	1.62390i
$636$	−0.215469	+	4.49592i	−0.00854392	+	0.178275i
$637$	14.8122	−	8.55184i	0.586882	−	0.338836i
$638$	34.3603			1.36034
$639$	−11.3604	−	8.09958i	−0.449409	−	0.320415i
$640$	2.36934			0.0936563
$641$	−14.2317	+	8.21670i	−0.562120	+	0.324540i	−0.753996	−	0.656879i	$-0.771876\pi$
$641$	−14.2317	+	8.21670i	−0.562120	+	0.324540i	0.191876	+	0.981419i	$0.438543\pi$
$642$	2.40550	−	3.74065i	0.0949375	−	0.147632i
$643$	14.0501	+	8.11186i	0.554084	+	0.319900i	0.750767	−	0.660567i	$-0.229684\pi$
$643$	14.0501	+	8.11186i	0.554084	+	0.319900i	−0.196684	+	0.980467i	$0.563017\pi$
$644$	33.4908	+	19.3359i	1.31972	+	0.761943i
$645$	−11.9498	−	23.1958i	−0.470521	−	0.913332i
$646$	7.41028	+	12.8350i	0.291554	+	0.504986i
$647$	2.79497			0.109882			0.0549408	−	0.998490i	$-0.482503\pi$
$647$	2.79497			0.109882			0.0549408	+	0.998490i	$0.482503\pi$
$648$	−2.93378	−	8.50840i	−0.115250	−	0.334242i
$649$			15.0631i			0.591278i
$650$	−0.542267	+	0.313078i	−0.0212694	+	0.0122799i
$651$	−41.9380	+	21.6052i	−1.64368	+	0.846775i
$652$	7.50989	−	13.0075i	0.294110	−	0.509413i
$653$	29.2270	+	16.8742i	1.14374	+	0.660340i	0.947355	−	0.320186i	$-0.103745\pi$
$653$	29.2270	+	16.8742i	1.14374	+	0.660340i	0.196388	+	0.980526i	$0.437079\pi$
$654$	−18.7180	−	12.0369i	−0.731930	−	0.470682i
$655$	−4.89066	−	8.47087i	−0.191094	−	0.330984i
$656$	−0.681841	+	6.36672i	−0.0266214	+	0.248579i
$657$	−3.74187	+	5.24830i	−0.145984	+	0.204756i
$658$	4.25416			0.165844
$659$	−11.6023	+	6.69857i	−0.451960	+	0.260939i	−0.708658	−	0.705553i	$-0.750699\pi$
$659$	−11.6023	+	6.69857i	−0.451960	+	0.260939i	0.256698	+	0.966492i	$0.417366\pi$
$660$	0.740592	−	15.4530i	0.0288275	−	0.601506i
$661$	−3.00112	+	5.19808i	−0.116730	+	0.202182i	−0.918470	−	0.395491i	$-0.870575\pi$
$661$	−3.00112	+	5.19808i	−0.116730	+	0.202182i	0.801740	+	0.597673i	$0.203908\pi$
$662$	−22.0103	−	12.7077i	−0.855456	−	0.493898i
$663$	3.16156	+	0.151519i	0.122785	+	0.00588453i
$664$	7.31381	+	12.6679i	0.283831	+	0.491609i
$665$	−95.5668			−3.70592
$666$	−18.7262	−	1.79906i	−0.725626	−	0.0697122i
$667$		−	72.3037i		−	2.79961i
$668$	−14.0692	+	8.12285i	−0.544353	+	0.314282i
$669$	12.6266	−	19.6348i	0.488171	−	0.759126i
$670$	−7.26568	−	4.19484i	−0.280698	−	0.162061i
$671$	−3.81852	−	2.20462i	−0.147412	−	0.0851086i
$672$	7.50613	−	3.86693i	0.289555	−	0.149170i
$673$	17.1253	−	9.88732i	0.660134	−	0.381128i	−0.132194	−	0.991224i	$-0.542202\pi$
$673$	17.1253	−	9.88732i	0.660134	−	0.381128i	0.792328	+	0.610095i	$0.208869\pi$
$674$	22.9908			0.885574
$675$	1.18273	+	2.96176i	0.0455233	+	0.113998i
$676$	11.9592			0.459969
$677$	1.57334	+	2.72511i	0.0604684	+	0.104734i	0.894675	−	0.446718i	$-0.147407\pi$
$677$	1.57334	+	2.72511i	0.0604684	+	0.104734i	−0.834206	+	0.551452i	$0.814074\pi$
$678$	9.61969	+	18.6729i	0.369442	+	0.717127i
$679$	4.16557	−	7.21498i	0.159860	−	0.276886i
$680$	3.67546	+	2.12203i	0.140947	+	0.0813760i
$681$	22.6698	+	14.5783i	0.868709	+	0.558640i
$682$	−18.2408	+	10.5314i	−0.698478	+	0.403266i
$683$			27.0410i			1.03470i	0.855775	+	0.517348i	$0.173081\pi$
$683$			27.0410i			1.03470i	−0.855775	+	0.517348i	$0.826919\pi$
$684$	−22.5846	+	10.2983i	−0.863544	+	0.393764i
$685$			16.1787i			0.618157i
$686$	41.2262	−	23.8020i	1.57402	−	0.908764i
$687$	−1.89516	+	39.5438i	−0.0723048	+	1.50869i
$688$	3.17911	−	5.50637i	0.121202	−	0.209929i
$689$	1.32560	−	2.29600i	0.0505012	−	0.0874707i
$690$	−32.5174	−	1.55841i	−1.23791	−	0.0593277i
$691$	5.89775	−	3.40506i	0.224361	−	0.129535i	−0.383607	−	0.923496i	$-0.625318\pi$
$691$	5.89775	−	3.40506i	0.224361	−	0.129535i	0.607968	+	0.793962i	$0.291985\pi$
$692$	6.90226			0.262385
$693$	−22.8742	−	50.1641i	−0.868917	−	1.90558i
$694$			29.5157i			1.12040i
$695$	−22.0347	−	38.1652i	−0.835823	−	1.44769i
$696$	−13.2783	−	8.53885i	−0.503311	−	0.323664i
$697$	−6.75987	+	9.26576i	−0.256048	+	0.350966i
$698$	4.54328	−	7.86919i	0.171966	−	0.297853i
$699$	−9.71455	+	5.00464i	−0.367438	+	0.189293i
$700$	−2.59118	+	1.49602i	−0.0979372	+	0.0565441i
$701$	24.5252			0.926303			0.463151	−	0.886279i	$-0.346719\pi$
$701$	24.5252			0.926303			0.463151	+	0.886279i	$0.346719\pi$
$702$	−0.758976	+	5.24650i	−0.0286457	+	0.198016i
$703$			51.8842i			1.95685i
$704$	3.26477	−	1.88492i	0.123046	−	0.0710405i
$705$	−3.18360	+	1.64009i	−0.119901	+	0.0617695i
$706$	10.5516	−	18.2760i	0.397116	−	0.687826i
$707$	12.1000	−	20.9578i	0.455067	−	0.788199i
$708$	3.74331	−	5.82101i	0.140682	−	0.218767i
$709$	−8.31381	+	4.79998i	−0.312232	+	0.180267i	−0.647925	−	0.761704i	$-0.724363\pi$
$709$	−8.31381	+	4.79998i	−0.312232	+	0.180267i	0.335693	+	0.941971i	$0.391030\pi$
$710$			11.0191i			0.413539i
$711$	−0.820124	+	8.53658i	−0.0307571	+	0.320147i
$712$			13.5197i			0.506673i
$713$	22.1609	+	38.3838i	0.829933	+	1.43749i
$714$	15.1073	+	0.724023i	0.565375	+	0.0270959i
$715$	−4.55622	+	7.89160i	−0.170393	+	0.295129i
$716$	−12.8910	−	7.44262i	−0.481759	−	0.278144i
$717$	−1.52431	+	31.8058i	−0.0569265	+	1.18781i
$718$	−8.51069	−	14.7409i	−0.317616	−	0.550127i
$719$			50.1862i			1.87163i	0.352495	+	0.935814i	$0.385333\pi$
$719$			50.1862i			1.87163i	−0.352495	+	0.935814i	$0.614667\pi$
$720$	−4.12640	+	5.78763i	−0.153782	+	0.215692i
$721$		−	60.8785i		−	2.26723i
$722$	24.7288	+	42.8315i	0.920311	+	1.59403i
$723$	−18.2357	+	28.3572i	−0.678192	+	1.05462i
$724$	0.356520	+	0.205837i	0.0132500	+	0.00764987i
$725$	4.84465	+	2.79706i	0.179926	+	0.103880i
$726$	−2.54758	−	4.94512i	−0.0945494	−	0.183531i
$727$	38.0592	−	21.9735i	1.41154	−	0.814952i	0.416005	−	0.909362i	$-0.363430\pi$
$727$	38.0592	−	21.9735i	1.41154	−	0.814952i	0.995533	+	0.0944103i	$0.0300965\pi$
$728$	−4.97341			−0.184327
$729$	25.8931	+	7.65169i	0.959003	+	0.283396i
$730$	5.09063			0.188413
$731$	9.86324	−	5.69454i	0.364805	−	0.210620i
$732$	0.927768	+	1.80090i	0.0342913	+	0.0665631i
$733$	−21.8748	+	37.8883i	−0.807964	+	1.39943i	0.106308	+	0.994333i	$0.466097\pi$
$733$	−21.8748	+	37.8883i	−0.807964	+	1.39943i	−0.914272	+	0.405101i	$0.867236\pi$
$734$	7.18379	−	12.4427i	0.265159	−	0.459268i
$735$	−37.2131	+	57.8679i	−1.37263	+	2.13449i
$736$	−3.96640	−	6.87000i	−0.146203	−	0.253231i
$737$	−13.3488			−0.491708
$738$	−14.3646	−	12.7537i	−0.528770	−	0.469471i
$739$	15.0259			0.552738			0.276369	−	0.961052i	$-0.410869\pi$
$739$	15.0259			0.552738			0.276369	+	0.961052i	$0.410869\pi$
$740$	7.42884	+	12.8671i	0.273089	+	0.473005i
$741$	14.6036	+	0.699883i	0.536475	+	0.0257108i
$742$	6.33425	−	10.9712i	0.232538	−	0.402767i
$743$	3.10453	−	5.37720i	0.113894	−	0.197270i	−0.803443	−	0.595382i	$-0.797001\pi$
$743$	3.10453	−	5.37720i	0.113894	−	0.197270i	0.917337	+	0.398111i	$0.130334\pi$
$744$	9.66617	+	0.463256i	0.354379	+	0.0169838i
$745$	7.70018	−	4.44570i	0.282113	−	0.162878i
$746$	−31.2481			−1.14408
$747$	−43.6817	−	4.19658i	−1.59823	−	0.153545i
$748$	6.75268			0.246902
$749$	−10.8403	+	6.25864i	−0.396095	+	0.228686i
$750$	−9.73608	+	15.1400i	−0.355511	+	0.552835i
$751$	−13.3710	−	7.71976i	−0.487915	−	0.281698i	0.235794	−	0.971803i	$-0.424231\pi$
$751$	−13.3710	−	7.71976i	−0.487915	−	0.281698i	−0.723709	+	0.690105i	$0.757564\pi$
$752$	−0.755744	−	0.436329i	−0.0275592	−	0.0159113i
$753$	−1.39837	−	2.71438i	−0.0509593	−	0.0989174i
$754$	4.64932	+	8.05286i	0.169318	+	0.293268i
$755$		−	29.0261i		−	1.05637i
$756$	−3.62670	+	25.0700i	−0.131902	+	0.911786i
$757$			51.1223i			1.85807i	0.369992	+	0.929035i	$0.379361\pi$
$757$			51.1223i			1.85807i	−0.369992	+	0.929035i	$0.620639\pi$
$758$	−5.40529	−	9.36225i	−0.196329	−	0.340052i
$759$	−46.0463	+	23.7217i	−1.67138	+	0.861043i
$760$	16.9773	+	9.80184i	0.615831	+	0.355550i
$761$	10.2952	−	17.8318i	0.373201	−	0.646403i	−0.616855	−	0.787077i	$-0.711594\pi$
$761$	10.2952	−	17.8318i	0.373201	−	0.646403i	0.990056	+	0.140674i	$0.0449268\pi$
$762$	18.6833	−	29.0533i	0.676825	−	1.05249i
$763$	31.3178	+	54.2440i	1.13378	+	1.96376i
$764$		−	4.38205i		−	0.158537i
$765$	−11.5846	+	5.28243i	−0.418843	+	0.190987i
$766$			10.4484i			0.377517i
$767$	−3.53026	+	2.03820i	−0.127470	+	0.0735951i
$768$	−1.73007	−	0.0829143i	−0.0624283	−	0.00299191i
$769$	15.5878	−	26.9989i	0.562111	−	0.973605i	−0.435201	−	0.900333i	$-0.643323\pi$
$769$	15.5878	−	26.9989i	0.562111	−	0.973605i	0.997312	−	0.0732713i	$-0.0233439\pi$
$770$	−21.7715	+	37.7094i	−0.784591	+	1.35895i
$771$	0.601984	−	12.5608i	0.0216799	−	0.452367i
$772$	11.6920	−	6.75038i	0.420804	−	0.242951i
$773$		−	37.8592i		−	1.36170i	−0.732423	−	0.680850i	$-0.761611\pi$
$773$		−	37.8592i		−	1.36170i	0.732423	−	0.680850i	$-0.238389\pi$
$774$	7.91386	+	17.3555i	0.284458	+	0.623830i
$775$	−3.42917			−0.123179
$776$	−1.48001	+	0.854487i	−0.0531294	+	0.0306743i
$777$	44.5348	+	28.6390i	1.59768	+	1.02742i
$778$	−8.03655	+	13.9197i	−0.288124	+	0.499046i
$779$	−31.2245	+	42.7994i	−1.11873	+	1.53345i
$780$	3.72185	−	1.91738i	0.133264	−	0.0686534i
$781$	8.76619	+	15.1835i	0.313679	+	0.543308i
$782$		−	14.2095i		−	0.508132i
$783$	43.9832	−	17.5640i	1.57183	−	0.627686i
$784$	−16.7650			−0.598751
$785$	4.00776	−	2.31388i	0.143043	−	0.0825859i
$786$	3.27467	+	6.35649i	0.116804	+	0.226728i
$787$	1.00283	−	1.73695i	0.0357470	−	0.0619156i	−0.847598	−	0.530638i	$-0.821952\pi$
$787$	1.00283	−	1.73695i	0.0357470	−	0.0619156i	0.883345	+	0.468723i	$0.155286\pi$
$788$	5.90839	−	10.2336i	0.210478	−	0.364558i
$789$	7.83536	+	5.03868i	0.278946	+	0.179382i
$790$	5.86564	−	3.38653i	0.208690	−	0.120487i
$791$		−	59.1198i		−	2.10206i
$792$	−1.08154	+	11.2577i	−0.0384310	+	0.400024i
$793$		−	1.19324i		−	0.0423731i
$794$	−23.8227	+	13.7540i	−0.845435	+	0.488112i
$795$	−0.510520	+	10.6524i	−0.0181063	+	0.377800i
$796$	−0.862237	−	0.497813i	−0.0305612	−	0.0176445i
$797$	11.7865	−	20.4149i	0.417501	−	0.723132i	−0.578187	−	0.815904i	$-0.696240\pi$
$797$	11.7865	−	20.4149i	0.417501	−	0.723132i	0.995687	+	0.0927722i	$0.0295728\pi$
$798$	69.7819	+	3.34433i	2.47025	+	0.118388i
$799$	−0.781571	−	1.35372i	−0.0276500	−	0.0478912i
$800$	0.613758			0.0216996
$801$	−33.0249	−	23.5457i	−1.16688	−	0.831947i
$802$	10.5329			0.371928
$803$	7.01452	−	4.04983i	0.247537	−	0.142916i
$804$	5.15853	+	3.31729i	0.181927	+	0.116992i
$805$	79.3511	+	45.8134i	2.79676	+	1.61471i
$806$	−4.93637	−	2.85001i	−0.173876	−	0.100387i
$807$	0.976789	+	1.89605i	0.0343846	+	0.0667442i
$808$	−4.29909	+	2.48208i	−0.151241	+	0.0873192i
$809$		−	6.06955i		−	0.213394i	−0.994292	−	0.106697i	$-0.965973\pi$
$809$		−	6.06955i		−	0.213394i	0.994292	−	0.106697i	$-0.0340275\pi$
$810$	−6.95111	−	20.1593i	−0.244237	−	0.708325i
$811$	−39.1375			−1.37430			−0.687152	−	0.726514i	$-0.741139\pi$
$811$	−39.1375			−1.37430			−0.687152	+	0.726514i	$0.741139\pi$
$812$	22.2164	+	38.4799i	0.779643	+	1.35038i
$813$	−5.86616	−	11.3868i	−0.205735	−	0.399354i
$814$	20.4728	+	11.8200i	0.717571	+	0.414290i
$815$	17.7935	−	30.8192i	0.623277	−	1.07955i
$816$	−2.60952	−	1.67810i	−0.0913515	−	0.0587453i
$817$	45.5593	−	26.3036i	1.59392	−	0.920248i
$818$	−14.8379			−0.518796
$819$	8.66161	−	12.1487i	0.302661	−	0.424508i
$820$	−1.61551	+	15.0849i	−0.0564161	+	0.526788i
$821$	3.20799	+	5.55640i	0.111960	+	0.193920i	0.916560	−	0.399896i	$-0.130954\pi$
$821$	3.20799	+	5.55640i	0.111960	+	0.193920i	−0.804601	+	0.593816i	$0.797621\pi$
$822$	0.566170	−	11.8135i	0.0197474	−	0.412044i
$823$	−34.8428	−	20.1165i	−1.21454	−	0.701217i	−0.250797	−	0.968040i	$-0.580693\pi$
$823$	−34.8428	−	20.1165i	−1.21454	−	0.701217i	−0.963746	+	0.266823i	$0.914026\pi$
$824$	−6.24403	+	10.8150i	−0.217521	+	0.376757i
$825$	0.191844	−	4.00297i	0.00667916	−	0.139365i
$826$	−16.8691	+	9.73936i	−0.586950	+	0.338876i
$827$			42.8896i			1.49142i	0.666272	+	0.745709i	$0.267889\pi$
$827$			42.8896i			1.49142i	−0.666272	+	0.745709i	$0.732111\pi$
$828$	23.6893	+	2.27587i	0.823260	+	0.0790920i
$829$	−14.0068			−0.486476			−0.243238	−	0.969967i	$-0.578210\pi$
$829$	−14.0068			−0.486476			−0.243238	+	0.969967i	$0.578210\pi$
$830$	17.3289	+	30.0145i	0.601494	+	1.04182i
$831$	15.9517	−	24.8056i	0.553359	−	0.860497i
$832$	0.883519	+	0.510100i	0.0306305	+	0.0176845i
$833$	−26.0069	−	15.0151i	−0.901086	−	0.520242i
$834$	14.7539	+	28.6389i	0.510886	+	0.991684i
$835$	−33.3346	+	19.2458i	−1.15359	+	0.666027i
$836$	31.1913			1.07877
$837$	−17.9660	+	22.8050i	−0.620997	+	0.788255i
$838$	−21.6748			−0.748744
$839$	−13.0827	+	7.55328i	−0.451664	+	0.260768i	−0.708533	−	0.705678i	$-0.750642\pi$
$839$	−13.0827	+	7.55328i	−0.451664	+	0.260768i	0.256869	+	0.966446i	$0.417309\pi$
$840$	17.7845	−	9.16206i	0.613625	−	0.316121i
$841$	27.0374	−	46.8301i	0.932323	−	1.61483i
$842$	34.1977	+	19.7441i	1.17853	+	0.680425i
$843$	−32.9349	−	21.1794i	−1.13434	−	0.729458i
$844$	−3.63947	+	2.10125i	−0.125276	+	0.0723281i
$845$	28.3354			0.974766
$846$	2.38202	−	1.08617i	0.0818956	−	0.0373433i
$847$			15.6567i			0.537969i
$848$	−2.25054	+	1.29935i	−0.0772839	+	0.0446199i
$849$	−7.43871	−	0.356504i	−0.255296	−	0.0122352i
$850$	0.952098	+	0.549694i	0.0326567	+	0.0188543i
$851$	24.8725	−	43.0805i	0.852619	−	1.47678i
$852$	0.385610	−	8.04602i	0.0132108	−	0.275652i
$853$	12.8734	+	22.2974i	0.440776	+	0.763447i	0.997747	−	0.0670849i	$-0.0213698\pi$
$853$	12.8734	+	22.2974i	0.440776	+	0.763447i	−0.556971	+	0.830532i	$0.688036\pi$
$854$		−	5.70179i		−	0.195111i
$855$	−53.5105	+	24.4001i	−1.83002	+	0.834465i
$856$	2.56768			0.0877615
$857$	13.3942	+	23.1994i	0.457536	+	0.792475i	0.998830	−	0.0483583i	$-0.0153989\pi$
$857$	13.3942	+	23.1994i	0.457536	+	0.792475i	−0.541295	+	0.840833i	$0.682066\pi$
$858$	3.60307	−	5.60292i	0.123007	−	0.191281i
$859$	−15.0584	+	26.0819i	−0.513786	+	0.889903i	0.486086	+	0.873911i	$0.338424\pi$
$859$	−15.0584	+	26.0819i	−0.513786	+	0.889903i	−0.999872	+	0.0159924i	$0.994909\pi$
$860$	7.53237	−	13.0465i	0.256852	−	0.444880i
$861$	19.5017	+	50.4260i	0.664615	+	1.71851i
$862$	−7.07548	−	12.2551i	−0.240992	−	0.417410i
$863$	−36.4107			−1.23943			−0.619717	−	0.784825i	$-0.712753\pi$
$863$	−36.4107			−1.23943			−0.619717	+	0.784825i	$0.712753\pi$
$864$	3.21559	−	4.08167i	0.109397	−	0.138861i
$865$	16.3538			0.556045
$866$	18.0996	+	31.3494i	0.615048	+	1.06530i
$867$	10.9398	+	21.2352i	0.371533	+	0.721186i
$868$	−23.5880	−	13.6186i	−0.800630	−	0.462244i
$869$	5.38828	−	9.33278i	0.182785	−	0.316593i
$870$	−31.4607	−	20.2314i	−1.06662	−	0.685909i
$871$	−1.80623	−	3.12849i	−0.0612019	−	0.106005i
$872$		−	12.8485i		−	0.435104i
$873$	0.490295	−	5.10342i	0.0165940	−	0.172725i
$874$		−	65.6352i		−	2.22014i
$875$	43.8752	−	25.3314i	1.48325	−	0.856357i
$876$	−3.71712	−	0.178145i	−0.125590	−	0.00601897i
$877$	21.4618	−	37.1729i	0.724713	−	1.25524i	−0.234379	−	0.972145i	$-0.575306\pi$
$877$	21.4618	−	37.1729i	0.724713	−	1.25524i	0.959092	−	0.283095i	$-0.0913611\pi$
$878$	−7.35009	−	4.24358i	−0.248054	−	0.143214i
$879$	−0.883051	+	18.4255i	−0.0297846	+	0.621476i
$880$	7.73535	−	4.46601i	0.260759	−	0.150549i
$881$	−8.22436			−0.277086			−0.138543	−	0.990356i	$-0.544242\pi$
$881$	−8.22436			−0.277086			−0.138543	+	0.990356i	$0.544242\pi$
$882$	29.1977	−	40.9523i	0.983138	−	1.37894i
$883$			0.0492990i			0.00165904i	1.00000		0.000829522i	$0.000264045\pi$
$883$			0.0492990i			0.00165904i	−1.00000		0.000829522i	$0.999736\pi$
$884$	0.913711	+	1.58259i	0.0307314	+	0.0532284i
$885$	8.86917	−	13.7919i	0.298134	−	0.463611i
$886$	−2.05505	+	3.55945i	−0.0690408	+	0.119582i
$887$	11.9207	+	6.88244i	0.400259	+	0.231090i	0.686596	−	0.727039i	$-0.259104\pi$
$887$	11.9207	+	6.88244i	0.400259	+	0.231090i	−0.286337	+	0.958129i	$0.592438\pi$
$888$	−4.97418	−	9.65541i	−0.166922	−	0.324014i
$889$	−84.1955	+	48.6103i	−2.82383	+	1.63034i
$890$			32.0328i			1.07374i
$891$	−25.6158	−	22.2481i	−0.858160	−	0.745339i
$892$	13.4778			0.451271
$893$	−3.61015	−	6.25296i	−0.120809	−	0.209247i
$894$	−5.77817	+	2.97674i	−0.193251	+	0.0995571i
$895$	−30.5431	−	17.6341i	−1.02094	−	0.589442i
$896$	4.22182	+	2.43747i	0.141041	+	0.0814301i
$897$	−11.7901	−	7.58186i	−0.393660	−	0.253151i
$898$	−11.1056	−	19.2355i	−0.370599	−	0.641896i
$899$			50.9244i			1.69843i
$900$	−1.06891	+	1.49924i	−0.0356303	+	0.0499746i
$901$	−4.65490			−0.155077
$902$	9.77468	+	22.0711i	0.325461	+	0.734887i
$903$	2.57000	−	53.6249i	0.0855244	−	1.78453i
$904$	−6.06365	+	10.5025i	−0.201674	+	0.349309i
$905$	0.844716	+	0.487697i	0.0280793	+	0.0162116i
$906$	−1.01576	+	21.1945i	−0.0337464	+	0.704142i
$907$	−18.1325	−	31.4065i	−0.602081	−	1.04284i	−0.992505	−	0.122200i	$-0.961005\pi$
$907$	−18.1325	−	31.4065i	−0.602081	−	1.04284i	0.390424	−	0.920635i	$-0.372328\pi$
$908$			15.5611i			0.516414i
$909$	1.42419	−	14.8242i	0.0472373	−	0.491688i
$910$	−11.7837			−0.390625
$911$	−11.9582	−	20.7121i	−0.396192	−	0.686224i	0.597061	−	0.802196i	$-0.296335\pi$
$911$	−11.9582	−	20.7121i	−0.396192	−	0.686224i	−0.993253	+	0.115972i	$0.963002\pi$
$912$	−12.0536	−	7.75132i	−0.399135	−	0.256672i
$913$	47.7558	+	27.5718i	1.58049	+	0.912495i
$914$	5.18852	+	2.99559i	0.171621	+	0.0990854i
$915$	2.19820	+	4.26693i	0.0726701	+	0.141060i
$916$	−19.7946	+	11.4284i	−0.654032	+	0.377606i
$917$		−	20.1252i		−	0.664592i
$918$	8.64383	−	3.45178i	0.285289	−	0.113926i
$919$			22.1114i			0.729387i	0.931128	+	0.364693i	$0.118826\pi$
$919$			22.1114i			0.729387i	−0.931128	+	0.364693i	$0.881174\pi$
$920$	−9.39773	−	16.2773i	−0.309834	−	0.536648i
$921$	11.6127	+	22.5414i	0.382650	+	0.742764i
$922$	−10.3050	+	17.8487i	−0.339376	+	0.587817i
$923$	−2.37232	+	4.10898i	−0.0780859	+	0.135249i
$924$	17.2170	−	26.7731i	0.566396	−	0.880770i
$925$	1.92438	+	3.33312i	0.0632732	+	0.109592i
$926$			3.02065i			0.0992647i
$927$	−15.5435	−	34.0876i	−0.510515	−	1.11958i
$928$		−	9.11454i		−	0.299199i
$929$	19.5249	−	11.2727i	0.640591	−	0.369845i	−0.144251	−	0.989541i	$-0.546077\pi$
$929$	19.5249	−	11.2727i	0.640591	−	0.369845i	0.784842	+	0.619696i	$0.212744\pi$
$930$	22.9024	+	1.09761i	0.750999	+	0.0359921i
$931$	−120.128	−	69.3562i	−3.93705	−	2.27306i
$932$	−5.46395	−	3.15461i	−0.178978	−	0.103333i
$933$	0.820971	−	17.1301i	0.0268774	−	0.560815i
$934$	−19.1965	−	33.2492i	−0.628127	−	1.08795i
$935$	15.9994			0.523236
$936$	−2.78475	+	1.26981i	−0.0910225	+	0.0415050i
$937$			30.5206i			0.997063i	0.866872	+	0.498532i	$0.166127\pi$
$937$			30.5206i			0.997063i	−0.866872	+	0.498532i	$0.833873\pi$
$938$	−8.63094	−	14.9492i	−0.281810	−	0.488109i
$939$	−28.3002	−	18.1990i	−0.923543	−	0.593902i
$940$	−1.79061	−	1.03381i	−0.0584034	−	0.0337192i
$941$	1.50505	−	2.60683i	0.0490634	−	0.0849803i	−0.840451	−	0.541888i	$-0.817710\pi$
$941$	1.50505	−	2.60683i	0.0490634	−	0.0849803i	0.889514	+	0.456908i	$0.151043\pi$
$942$	−3.00740	+	1.54932i	−0.0979863	+	0.0504796i
$943$	46.4438	−	20.5687i	1.51242	−	0.669808i
$944$	3.99569			0.130049
$945$	−8.59289	+	59.3992i	−0.279527	+	1.93226i
$946$		−	23.9694i		−	0.779313i
$947$	−11.2653	−	19.5120i	−0.366072	−	0.634055i	0.622876	−	0.782321i	$-0.285964\pi$
$947$	−11.2653	−	19.5120i	−0.366072	−	0.634055i	−0.988948	+	0.148266i	$0.952631\pi$
$948$	−4.40154	+	2.26754i	−0.142955	+	0.0736463i
$949$	1.89828	+	1.09597i	0.0616208	+	0.0355768i
$950$	4.39783	+	2.53909i	0.142684	+	0.0823789i
$951$	−45.2461	−	29.0964i	−1.46721	−	0.943515i
$952$	4.36609	+	7.56230i	0.141506	+	0.245095i
$953$	−8.27459			−0.268040			−0.134020	−	0.990979i	$-0.542789\pi$
$953$	−8.27459			−0.268040			−0.134020	+	0.990979i	$0.542789\pi$
$954$	0.745552	−	7.76037i	0.0241381	−	0.251251i
$955$		−	10.3826i		−	0.335972i
$956$	−15.9212	+	9.19209i	−0.514927	+	0.297293i
$957$	−59.4456	−	2.84896i	−1.92160	−	0.0920938i
$958$	−14.8658	−	8.58280i	−0.480293	−	0.277298i
$959$	−16.6440	+	28.8282i	−0.537461	+	0.930911i
$960$	−4.09911	−	0.196452i	−0.132298	−	0.00634046i
$961$	−0.108229	−	0.187458i	−0.00349125	−	0.00604702i
$962$			6.39748i			0.206263i
$963$	−4.47183	+	6.27213i	−0.144103	+	0.202116i
$964$	−19.4651			−0.626929
$965$	27.7023	−	15.9939i	0.891768	−	0.514863i
$966$	−56.3381	−	36.2293i	−1.81265	−	1.16566i
$967$	−2.43201	−	1.40412i	−0.0782082	−	0.0451535i	0.460386	−	0.887719i	$-0.347711\pi$
$967$	−2.43201	−	1.40412i	−0.0782082	−	0.0451535i	−0.538594	+	0.842565i	$0.681044\pi$
$968$	1.60583	−	2.78138i	0.0516134	−	0.0893970i
$969$	−11.7561	−	22.8198i	−0.377659	−	0.733077i
$970$	−3.50665	+	2.02457i	−0.112592	+	0.0650049i
$971$		−	33.4875i		−	1.07467i	−0.843370	−	0.537333i	$-0.819432\pi$
$971$		−	33.4875i		−	1.07467i	0.843370	−	0.537333i	$-0.180568\pi$
$972$	4.37016	+	14.9633i	0.140173	+	0.479950i
$973$		−	90.6732i		−	2.90685i
$974$	−4.41984	−	7.65539i	−0.141621	−	0.245294i
$975$	0.964115	−	0.496683i	0.0308764	−	0.0159066i
$976$	−0.584806	+	1.01291i	−0.0187192	+	0.0324226i
$977$	−26.2539	−	15.1577i	−0.839937	−	0.484938i	0.0173059	−	0.999850i	$-0.494491\pi$
$977$	−26.2539	−	15.1577i	−0.839937	−	0.484938i	−0.857243	+	0.514913i	$0.827824\pi$
$978$	−14.0711	+	21.8812i	−0.449944	+	0.699682i
$979$	25.4836	+	44.1388i	0.814458	+	1.41068i
$980$	−39.7220			−1.26887
$981$	31.3852	+	22.3767i	1.00205	+	0.714433i
$982$	36.8185			1.17493
$983$	9.39214	+	16.2677i	0.299563	+	0.518858i	0.976036	−	0.217609i	$-0.0698259\pi$
$983$	9.39214	+	16.2677i	0.299563	+	0.518858i	−0.676473	+	0.736467i	$0.736493\pi$
$984$	1.70752	−	10.9583i	0.0544338	−	0.349338i
$985$	13.9990	−	24.2469i	0.446044	−	0.772571i
$986$	8.16316	−	14.1390i	0.259968	−	0.450278i
$987$	−7.35997	−	0.352730i	−0.234270	−	0.0112275i
$988$	4.22052	+	7.31016i	0.134273	+	0.232567i
$989$	−50.4384			−1.60385
$990$	−2.56254	+	26.6732i	−0.0814430	+	0.847731i
$991$			9.81733i			0.311858i	0.987768	+	0.155929i	$0.0498371\pi$
$991$			9.81733i			0.311858i	−0.987768	+	0.155929i	$0.950163\pi$
$992$	2.79358	+	4.83863i	0.0886964	+	0.153627i
$993$	37.0256	+	23.8101i	1.17497	+	0.755589i
$994$	−11.3359	+	19.6344i	−0.359554	+	0.622766i
$995$	−2.04293	−	1.17949i	−0.0647652	−	0.0373922i
$996$	−11.6030	−	22.5227i	−0.367655	−	0.713658i
$997$	7.91332	−	4.56875i	0.250617	−	0.144694i	−0.369430	−	0.929259i	$-0.620447\pi$
$997$	7.91332	−	4.56875i	0.250617	−	0.144694i	0.620047	+	0.784565i	$0.287114\pi$
$998$			0.151414i			0.00479292i
$999$	32.2484	+	4.66516i	1.02029	+	0.147599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.i.b.409.13	yes	36
3.2	odd	2		2214.2.i.b.901.13		36
9.2	odd	6		2214.2.i.b.1639.14		36
9.7	even	3	inner	738.2.i.b.655.6	yes	36
41.40	even	2	inner	738.2.i.b.409.6	✓	36
123.122	odd	2		2214.2.i.b.901.14		36
369.245	odd	6		2214.2.i.b.1639.13		36
369.286	even	6	inner	738.2.i.b.655.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.6	✓	36	41.40	even	2	inner
738.2.i.b.409.13	yes	36	1.1	even	1	trivial
738.2.i.b.655.6	yes	36	9.7	even	3	inner
738.2.i.b.655.13	yes	36	369.286	even	6	inner
2214.2.i.b.901.13		36	3.2	odd	2
2214.2.i.b.901.14		36	123.122	odd	2
2214.2.i.b.1639.13		36	369.245	odd	6
2214.2.i.b.1639.14		36	9.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.793227 + 1.53974i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18467 + 2.05191i) q^{5} +(0.936838 - 1.45682i) q^{6} +(-4.22182 + 2.43747i) q^{7} +1.00000 q^{8} +(-1.74158 + 2.44272i) q^{9} +2.36934 q^{10} +(3.26477 - 1.88492i) q^{11} +(-1.73007 - 0.0829143i) q^{12} +(0.883519 + 0.510100i) q^{13} +(4.22182 + 2.43747i) q^{14} +(-4.09911 - 0.196452i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.79124i q^{17} +(2.98625 + 0.286894i) q^{18} -8.27391i q^{19} +(-1.18467 - 2.05191i) q^{20} +(-7.10192 - 4.56703i) q^{21} +(-3.26477 - 1.88492i) q^{22} +(-3.96640 + 6.87000i) q^{23} +(0.793227 + 1.53974i) q^{24} +(-0.306879 - 0.531530i) q^{25} -1.02020i q^{26} +(-5.14262 - 0.743949i) q^{27} -4.87494i q^{28} +(-7.89342 + 4.55727i) q^{29} +(1.87942 + 3.64816i) q^{30} +(2.79358 - 4.83863i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.49198 + 3.53173i) q^{33} +(-1.55126 + 0.895620i) q^{34} -11.5504i q^{35} +(-1.24467 - 2.72962i) q^{36} -6.27081 q^{37} +(-7.16542 + 4.13696i) q^{38} +(-0.0845891 + 1.76501i) q^{39} +(-1.18467 + 2.05191i) q^{40} +(-5.17282 - 3.77385i) q^{41} +(-0.404202 + 8.43396i) q^{42} +(3.17911 + 5.50637i) q^{43} +3.76984i q^{44} +(-2.94904 - 6.46738i) q^{45} +7.93279 q^{46} +(0.755744 - 0.436329i) q^{47} +(0.936838 - 1.45682i) q^{48} +(8.38252 - 14.5189i) q^{49} +(-0.306879 + 0.531530i) q^{50} +(2.75804 - 1.42086i) q^{51} +(-0.883519 + 0.510100i) q^{52} -2.59870i q^{53} +(1.92703 + 4.82561i) q^{54} +8.93201i q^{55} +(-4.22182 + 2.43747i) q^{56} +(12.7397 - 6.56309i) q^{57} +(7.89342 + 4.55727i) q^{58} +(-1.99784 + 3.46037i) q^{59} +(2.21969 - 3.45171i) q^{60} +(-0.584806 - 1.01291i) q^{61} -5.58717 q^{62} +(1.39859 - 14.5578i) q^{63} +1.00000 q^{64} +(-2.09335 + 1.20860i) q^{65} +(0.312573 - 6.52206i) q^{66} +(-3.06655 - 1.77047i) q^{67} +(1.55126 + 0.895620i) q^{68} +(-13.7242 - 0.657742i) q^{69} +(-10.0029 + 5.77519i) q^{70} +4.65070i q^{71} +(-1.74158 + 2.44272i) q^{72} +2.14855 q^{73} +(3.13541 + 5.43068i) q^{74} +(0.574992 - 0.894137i) q^{75} +(7.16542 + 4.13696i) q^{76} +(-9.18886 + 15.9156i) q^{77} +(1.57084 - 0.809250i) q^{78} +(2.47565 - 1.42931i) q^{79} +2.36934 q^{80} +(-2.93378 - 8.50840i) q^{81} +(-0.681841 + 6.36672i) q^{82} +(7.31381 + 12.6679i) q^{83} +(7.50613 - 3.86693i) q^{84} +(3.67546 + 2.12203i) q^{85} +(3.17911 - 5.50637i) q^{86} +(-13.2783 - 8.53885i) q^{87} +(3.26477 - 1.88492i) q^{88} +13.5197i q^{89} +(-4.12640 + 5.78763i) q^{90} -4.97341 q^{91} +(-3.96640 - 6.87000i) q^{92} +(9.66617 + 0.463256i) q^{93} +(-0.755744 - 0.436329i) q^{94} +(16.9773 + 9.80184i) q^{95} +(-1.73007 - 0.0829143i) q^{96} +(-1.48001 + 0.854487i) q^{97} -16.7650 q^{98} +(-1.08154 + 11.2577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 4 q^{5} + 36 q^{8} - 14 q^{9} - 8 q^{10} - 18 q^{16} + 4 q^{18} + 4 q^{20} - 16 q^{21} - 4 q^{23} - 26 q^{25} + 8 q^{31} - 18 q^{32} - 6 q^{33} + 10 q^{36} - 60 q^{37} - 64 q^{39}+ \cdots - 76 q^{98}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 4 * q^5 + 36 * q^8 - 14 * q^9 - 8 * q^10 - 18 * q^16 + 4 * q^18 + 4 * q^20 - 16 * q^21 - 4 * q^23 - 26 * q^25 + 8 * q^31 - 18 * q^32 - 6 * q^33 + 10 * q^36 - 60 * q^37 - 64 * q^39 + 4 * q^40 - 6 * q^41 + 26 * q^42 + 6 * q^43 + 28 * q^45 + 8 * q^46 + 38 * q^49 - 26 * q^50 + 18 * q^51 + 28 * q^57 + 22 * q^59 - 46 * q^61 - 16 * q^62 + 36 * q^64 - 30 * q^66 - 14 * q^72 + 64 * q^73 + 30 * q^74 - 2 * q^77 + 14 * q^78 - 8 * q^80 - 22 * q^81 + 12 * q^82 + 68 * q^83 - 10 * q^84 + 6 * q^86 - 142 * q^87 - 80 * q^90 + 36 * q^91 - 4 * q^92 - 76 * q^98

Introduction

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