LMFDB - Embedded newform 950.2.l.a.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	950.301
Dual form			950.2.l.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.76604 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.76604 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +(2.97178 - 5.14728i) q^{11} +(-0.939693 - 1.62760i) q^{12} +(-3.09240 - 1.12554i) q^{13} +(0.0603074 - 0.342020i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.23783 - 3.55596i) q^{17} +0.532089 q^{18} +(-4.11721 + 1.43128i) q^{19} +(0.500000 + 0.419550i) q^{21} +(5.58512 - 2.03282i) q^{22} +(0.492726 + 2.79439i) q^{23} +(0.326352 - 1.85083i) q^{24} +(-1.64543 - 2.84997i) q^{26} +(2.31908 - 4.01676i) q^{27} +(0.266044 - 0.223238i) q^{28} +(5.46064 - 4.58202i) q^{29} +(-1.52094 - 2.63435i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-1.93969 + 11.0005i) q^{33} +(-0.960637 - 5.44804i) q^{34} +(0.407604 + 0.342020i) q^{36} -1.82295 q^{37} +(-4.07398 - 1.55007i) q^{38} +6.18479 q^{39} +(6.41147 - 2.33359i) q^{41} +(0.113341 + 0.642788i) q^{42} +(-0.0923963 + 0.524005i) q^{43} +(5.58512 + 2.03282i) q^{44} +(-1.41875 + 2.45734i) q^{46} +(3.56418 - 2.99070i) q^{47} +(1.43969 - 1.20805i) q^{48} +(3.43969 - 5.95772i) q^{49} +(9.76991 + 3.55596i) q^{51} +(0.571452 - 3.24086i) q^{52} +(-0.539363 - 3.05888i) q^{53} +(4.35844 - 1.58634i) q^{54} +0.347296 q^{56} +(6.35117 - 5.17420i) q^{57} +7.12836 q^{58} +(-2.10741 - 1.76833i) q^{59} +(-2.14156 - 12.1454i) q^{61} +(0.528218 - 2.99568i) q^{62} +(-0.173648 - 0.0632028i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-8.55690 + 7.18009i) q^{66} +(-3.86231 + 3.24086i) q^{67} +(2.76604 - 4.79093i) q^{68} +(-2.66637 - 4.61830i) q^{69} +(-2.26991 + 12.8733i) q^{71} +(0.0923963 + 0.524005i) q^{72} +(-2.06670 + 0.752219i) q^{73} +(-1.39646 - 1.17177i) q^{74} +(-2.12449 - 3.80612i) q^{76} -2.06418 q^{77} +(4.73783 + 3.97551i) q^{78} +(0.939693 - 0.342020i) q^{79} +(-1.79086 + 10.1565i) q^{81} +(6.41147 + 2.33359i) q^{82} +(-4.67752 - 8.10170i) q^{83} +(-0.326352 + 0.565258i) q^{84} +(-0.407604 + 0.342020i) q^{86} +(-6.69846 + 11.6021i) q^{87} +(2.97178 + 5.14728i) q^{88} +(-10.6493 - 3.87603i) q^{89} +(0.198463 + 1.12554i) q^{91} +(-2.66637 + 0.970481i) q^{92} +(4.37939 + 3.67474i) q^{93} +4.65270 q^{94} +1.87939 q^{96} +(-4.38326 - 3.67799i) q^{97} +(6.46451 - 2.35289i) q^{98} +(-0.549163 - 3.11446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9	$ 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 15 q^{13} + 6 q^{14} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{21} + 12 q^{22} - 15 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} - 3 q^{28} + 24 q^{29} - 6 q^{31} - 6 q^{33} + 3 q^{34} + 6 q^{36} + 30 q^{37} - 9 q^{38} + 30 q^{39} + 18 q^{41} - 6 q^{42} + 3 q^{43} + 12 q^{44} - 6 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 30 q^{51} + 3 q^{52} - 12 q^{53} + 18 q^{54} + 12 q^{57} + 6 q^{58} + 21 q^{59} - 21 q^{61} + 18 q^{62} - 3 q^{64} - 15 q^{66} + 9 q^{67} + 12 q^{68} + 3 q^{69} + 15 q^{71} - 3 q^{72} + 21 q^{73} - 18 q^{74} + 6 q^{77} + 9 q^{78} + 21 q^{81} + 18 q^{82} - 3 q^{83} - 3 q^{84} - 6 q^{86} - 12 q^{87} + 3 q^{88} - 24 q^{89} - 27 q^{91} + 3 q^{92} + 15 q^{93} + 30 q^{94} + 9 q^{97} + 6 q^{98} - 15 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 15 * q^13 + 6 * q^14 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^21 + 12 * q^22 - 15 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 - 3 * q^28 + 24 * q^29 - 6 * q^31 - 6 * q^33 + 3 * q^34 + 6 * q^36 + 30 * q^37 - 9 * q^38 + 30 * q^39 + 18 * q^41 - 6 * q^42 + 3 * q^43 + 12 * q^44 - 6 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 30 * q^51 + 3 * q^52 - 12 * q^53 + 18 * q^54 + 12 * q^57 + 6 * q^58 + 21 * q^59 - 21 * q^61 + 18 * q^62 - 3 * q^64 - 15 * q^66 + 9 * q^67 + 12 * q^68 + 3 * q^69 + 15 * q^71 - 3 * q^72 + 21 * q^73 - 18 * q^74 + 6 * q^77 + 9 * q^78 + 21 * q^81 + 18 * q^82 - 3 * q^83 - 3 * q^84 - 6 * q^86 - 12 * q^87 + 3 * q^88 - 24 * q^89 - 27 * q^91 + 3 * q^92 + 15 * q^93 + 30 * q^94 + 9 * q^97 + 6 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.76604	+	0.642788i	−1.01963	+	0.371114i	−0.797122	−	0.603818i	$-0.793645\pi$
$3$	−1.76604	+	0.642788i	−1.01963	+	0.371114i	−0.222504	+	0.974932i	$0.571423\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	−1.76604	−	0.642788i	−0.720985	−	0.262417i
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	0.831342	−	0.555762i	$-0.187573\pi$
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	−0.896975	+	0.442082i	$0.854240\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.407604	−	0.342020i	0.135868	−	0.114007i
$10$		0			0
$11$	2.97178	−	5.14728i	0.896026	−	1.55196i	0.0634960	−	0.997982i	$-0.479775\pi$
$11$	2.97178	−	5.14728i	0.896026	−	1.55196i	0.832530	−	0.553980i	$-0.186892\pi$
$12$	−0.939693	−	1.62760i	−0.271266	−	0.469846i
$13$	−3.09240	−	1.12554i	−0.857676	−	0.312169i	−0.124510	−	0.992218i	$-0.539736\pi$
$13$	−3.09240	−	1.12554i	−0.857676	−	0.312169i	−0.733166	+	0.680050i	$0.761958\pi$
$14$	0.0603074	−	0.342020i	0.0161178	−	0.0914087i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.23783	−	3.55596i	−1.02782	−	0.862447i	−0.0372334	−	0.999307i	$-0.511854\pi$
$17$	−4.23783	−	3.55596i	−1.02782	−	0.862447i	−0.990590	+	0.136860i	$0.956299\pi$
$18$	0.532089			0.125415
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$20$		0			0
$21$	0.500000	+	0.419550i	0.109109	+	0.0915533i
$22$	5.58512	−	2.03282i	1.19075	−	0.433398i
$23$	0.492726	+	2.79439i	0.102740	+	0.582670i	0.992099	+	0.125459i	$0.0400404\pi$
$23$	0.492726	+	2.79439i	0.102740	+	0.582670i	−0.889358	+	0.457211i	$0.848848\pi$
$24$	0.326352	−	1.85083i	0.0666163	−	0.377800i
$25$		0			0
$26$	−1.64543	−	2.84997i	−0.322695	−	0.558925i
$27$	2.31908	−	4.01676i	0.446307	−	0.773026i
$28$	0.266044	−	0.223238i	0.0502777	−	0.0421880i
$29$	5.46064	−	4.58202i	1.01401	−	0.850859i	0.0251512	−	0.999684i	$-0.491993\pi$
$29$	5.46064	−	4.58202i	1.01401	−	0.850859i	0.988864	+	0.148824i	$0.0475488\pi$
$30$		0			0
$31$	−1.52094	−	2.63435i	−0.273170	−	0.473144i	0.696502	−	0.717555i	$-0.254739\pi$
$31$	−1.52094	−	2.63435i	−0.273170	−	0.473144i	−0.969672	+	0.244411i	$0.921405\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−1.93969	+	11.0005i	−0.337657	+	1.91495i
$34$	−0.960637	−	5.44804i	−0.164748	−	0.934332i
$35$		0			0
$36$	0.407604	+	0.342020i	0.0679340	+	0.0570034i
$37$	−1.82295			−0.299691			−0.149845	−	0.988709i	$-0.547878\pi$
$37$	−1.82295			−0.299691			−0.149845	+	0.988709i	$0.547878\pi$
$38$	−4.07398	−	1.55007i	−0.660886	−	0.251454i
$39$	6.18479			0.990359
$40$		0			0
$41$	6.41147	−	2.33359i	1.00130	−	0.364445i	0.211217	−	0.977439i	$-0.432257\pi$
$41$	6.41147	−	2.33359i	1.00130	−	0.364445i	0.790087	+	0.612994i	$0.210035\pi$
$42$	0.113341	+	0.642788i	0.0174889	+	0.0991843i
$43$	−0.0923963	+	0.524005i	−0.0140903	+	0.0799101i	−0.991042	−	0.133550i	$-0.957362\pi$
$43$	−0.0923963	+	0.524005i	−0.0140903	+	0.0799101i	0.976952	+	0.213460i	$0.0684734\pi$
$44$	5.58512	+	2.03282i	0.841989	+	0.306459i
$45$		0			0
$46$	−1.41875	+	2.45734i	−0.209183	+	0.362316i
$47$	3.56418	−	2.99070i	0.519889	−	0.436238i	−0.344704	−	0.938711i	$-0.612021\pi$
$47$	3.56418	−	2.99070i	0.519889	−	0.436238i	0.864593	+	0.502473i	$0.167576\pi$
$48$	1.43969	−	1.20805i	0.207802	−	0.174366i
$49$	3.43969	−	5.95772i	0.491385	−	0.851103i
$50$		0			0
$51$	9.76991	+	3.55596i	1.36806	+	0.497934i
$52$	0.571452	−	3.24086i	0.0792461	−	0.449427i
$53$	−0.539363	−	3.05888i	−0.0740872	−	0.420169i	−0.999182	−	0.0404337i	$-0.987126\pi$
$53$	−0.539363	−	3.05888i	−0.0740872	−	0.420169i	0.925095	−	0.379736i	$-0.123985\pi$
$54$	4.35844	−	1.58634i	0.593109	−	0.215874i
$55$		0			0
$56$	0.347296			0.0464094
$57$	6.35117	−	5.17420i	0.841233	−	0.685340i
$58$	7.12836			0.935999
$59$	−2.10741	−	1.76833i	−0.274362	−	0.230217i	0.495216	−	0.868770i	$-0.335089\pi$
$59$	−2.10741	−	1.76833i	−0.274362	−	0.230217i	−0.769578	+	0.638553i	$0.779533\pi$
$60$		0			0
$61$	−2.14156	−	12.1454i	−0.274199	−	1.55506i	−0.741496	−	0.670957i	$-0.765883\pi$
$61$	−2.14156	−	12.1454i	−0.274199	−	1.55506i	0.467297	−	0.884100i	$-0.345228\pi$
$62$	0.528218	−	2.99568i	0.0670838	−	0.380451i
$63$	−0.173648	−	0.0632028i	−0.0218776	−	0.00796280i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−8.55690	+	7.18009i	−1.05328	+	0.883809i
$67$	−3.86231	+	3.24086i	−0.471856	+	0.395935i	−0.847471	−	0.530841i	$-0.821876\pi$
$67$	−3.86231	+	3.24086i	−0.471856	+	0.395935i	0.375615	+	0.926776i	$0.377432\pi$
$68$	2.76604	−	4.79093i	0.335432	−	0.580986i
$69$	−2.66637	−	4.61830i	−0.320994	−	0.555977i
$70$		0			0
$71$	−2.26991	+	12.8733i	−0.269389	+	1.52778i	0.486849	+	0.873486i	$0.338146\pi$
$71$	−2.26991	+	12.8733i	−0.269389	+	1.52778i	−0.756238	+	0.654297i	$0.772965\pi$
$72$	0.0923963	+	0.524005i	0.0108890	+	0.0617546i
$73$	−2.06670	+	0.752219i	−0.241889	+	0.0880405i	−0.460120	−	0.887857i	$-0.652194\pi$
$73$	−2.06670	+	0.752219i	−0.241889	+	0.0880405i	0.218231	+	0.975897i	$0.429971\pi$
$74$	−1.39646	−	1.17177i	−0.162335	−	0.136215i
$75$		0			0
$76$	−2.12449	−	3.80612i	−0.243695	−	0.436592i
$77$	−2.06418			−0.235235
$78$	4.73783	+	3.97551i	0.536453	+	0.450138i
$79$	0.939693	−	0.342020i	0.105724	−	0.0384803i	−0.288617	−	0.957445i	$-0.593195\pi$
$79$	0.939693	−	0.342020i	0.105724	−	0.0384803i	0.394340	+	0.918964i	$0.370973\pi$
$80$		0			0
$81$	−1.79086	+	10.1565i	−0.198984	+	1.12850i
$82$	6.41147	+	2.33359i	0.708029	+	0.257701i
$83$	−4.67752	−	8.10170i	−0.513424	−	0.889277i	−0.999879	−	0.0155711i	$-0.995043\pi$
$83$	−4.67752	−	8.10170i	−0.513424	−	0.889277i	0.486454	−	0.873706i	$-0.338290\pi$
$84$	−0.326352	+	0.565258i	−0.0356079	+	0.0616747i
$85$		0			0
$86$	−0.407604	+	0.342020i	−0.0439530	+	0.0368810i
$87$	−6.69846	+	11.6021i	−0.718151	+	1.24387i
$88$	2.97178	+	5.14728i	0.316793	+	0.548702i
$89$	−10.6493	−	3.87603i	−1.12882	−	0.410858i	−0.290959	−	0.956736i	$-0.593974\pi$
$89$	−10.6493	−	3.87603i	−1.12882	−	0.410858i	−0.837865	+	0.545877i	$0.816196\pi$
$90$		0			0
$91$	0.198463	+	1.12554i	0.0208046	+	0.117989i
$92$	−2.66637	+	0.970481i	−0.277989	+	0.101180i
$93$	4.37939	+	3.67474i	0.454121	+	0.381053i
$94$	4.65270			0.479890
$95$		0			0
$96$	1.87939			0.191814
$97$	−4.38326	−	3.67799i	−0.445052	−	0.373443i	0.392544	−	0.919733i	$-0.371595\pi$
$97$	−4.38326	−	3.67799i	−0.445052	−	0.373443i	−0.837596	+	0.546290i	$0.816040\pi$
$98$	6.46451	−	2.35289i	0.653014	−	0.237678i
$99$	−0.549163	−	3.11446i	−0.0551930	−	0.313015i
$100$		0			0
$101$	−4.45336	−	1.62089i	−0.443126	−	0.161285i	0.110814	−	0.993841i	$-0.464654\pi$
$101$	−4.45336	−	1.62089i	−0.443126	−	0.161285i	−0.553940	+	0.832556i	$0.686876\pi$
$102$	5.19846	+	9.00400i	0.514725	+	0.891529i
$103$	1.58512	−	2.74551i	0.156187	−	0.270523i	−0.777304	−	0.629125i	$-0.783413\pi$
$103$	1.58512	−	2.74551i	0.156187	−	0.270523i	0.933491	+	0.358602i	$0.116747\pi$
$104$	2.52094	−	2.11532i	0.247199	−	0.207425i
$105$		0			0
$106$	1.55303	−	2.68993i	0.150844	−	0.261269i
$107$	6.69846	+	11.6021i	0.647565	+	1.12162i	0.983703	+	0.179802i	$0.0575459\pi$
$107$	6.69846	+	11.6021i	0.647565	+	1.12162i	−0.336138	+	0.941813i	$0.609121\pi$
$108$	4.35844	+	1.58634i	0.419391	+	0.152646i
$109$	−2.37551	+	13.4722i	−0.227533	+	1.29040i	0.630250	+	0.776392i	$0.282952\pi$
$109$	−2.37551	+	13.4722i	−0.227533	+	1.29040i	−0.857783	+	0.514012i	$0.828159\pi$
$110$		0			0
$111$	3.21941	−	1.17177i	0.305573	−	0.111219i
$112$	0.266044	+	0.223238i	0.0251388	+	0.0210940i
$113$	−13.5202			−1.27188			−0.635938	−	0.771740i	$-0.719387\pi$
$113$	−13.5202			−1.27188			−0.635938	+	0.771740i	$0.719387\pi$
$114$	8.19119	+	0.118782i	0.767175	+	0.0111250i
$115$		0			0
$116$	5.46064	+	4.58202i	0.507007	+	0.425430i
$117$	−1.64543	+	0.598887i	−0.152120	+	0.0553672i
$118$	−0.477711	−	2.70924i	−0.0439769	−	0.249405i
$119$	−0.333626	+	1.89209i	−0.0305834	+	0.173447i
$120$		0			0
$121$	−12.1630	−	21.0669i	−1.10572	−	1.91517i
$122$	6.16637	−	10.6805i	0.558277	−	0.966965i
$123$	−9.82295	+	8.24243i	−0.885705	+	0.743195i
$124$	2.33022	−	1.95529i	0.209260	−	0.175590i
$125$		0			0
$126$	−0.0923963	−	0.160035i	−0.00823131	−	0.0142571i
$127$	18.1694	+	6.61311i	1.61227	+	0.586819i	0.981887	−	0.189466i	$-0.0606755\pi$
$127$	18.1694	+	6.61311i	1.61227	+	0.586819i	0.630383	+	0.776284i	$0.282898\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−0.173648	−	0.984808i	−0.0152889	−	0.0867075i
$130$		0			0
$131$	13.0817	+	10.9769i	1.14296	+	0.959053i	0.999531	−	0.0306082i	$-0.00974442\pi$
$131$	13.0817	+	10.9769i	1.14296	+	0.959053i	0.143424	+	0.989661i	$0.454189\pi$
$132$	−11.1702			−0.972245
$133$	1.14543	+	0.989783i	0.0993213	+	0.0858251i
$134$	−5.04189			−0.435553
$135$		0			0
$136$	5.19846	−	1.89209i	0.445765	−	0.162245i
$137$	−2.66637	−	15.1218i	−0.227804	−	1.29194i	−0.857252	−	0.514897i	$-0.827830\pi$
$137$	−2.66637	−	15.1218i	−0.227804	−	1.29194i	0.629448	−	0.777042i	$-0.283281\pi$
$138$	0.926022	−	5.25173i	0.0788282	−	0.447057i
$139$	−4.84477	−	1.76335i	−0.410928	−	0.149566i	0.128280	−	0.991738i	$-0.459054\pi$
$139$	−4.84477	−	1.76335i	−0.410928	−	0.149566i	−0.539208	+	0.842172i	$0.681276\pi$
$140$		0			0
$141$	−4.37211	+	7.57272i	−0.368198	+	0.637738i
$142$	−10.0137	+	8.40247i	−0.840329	+	0.705119i
$143$	−14.9834	+	12.5726i	−1.25297	+	1.05137i
$144$	−0.266044	+	0.460802i	−0.0221704	+	0.0384002i
$145$		0			0
$146$	−2.06670	−	0.752219i	−0.171042	−	0.0622541i
$147$	−2.24510	+	12.7326i	−0.185173	+	1.05017i
$148$	−0.316552	−	1.79525i	−0.0260204	−	0.147569i
$149$	−10.9829	+	3.99746i	−0.899756	+	0.327485i	−0.750155	−	0.661262i	$-0.770021\pi$
$149$	−10.9829	+	3.99746i	−0.899756	+	0.327485i	−0.149601	+	0.988746i	$0.547799\pi$
$150$		0			0
$151$	−7.14290			−0.581281			−0.290641	−	0.956832i	$-0.593868\pi$
$151$	−7.14290			−0.581281			−0.290641	+	0.956832i	$0.593868\pi$
$152$	0.819078	−	4.28125i	0.0664360	−	0.347255i
$153$	−2.94356			−0.237973
$154$	−1.58125	−	1.32683i	−0.127421	−	0.106919i
$155$		0			0
$156$	1.07398	+	6.09083i	0.0859871	+	0.487657i
$157$	0.533433	−	3.02525i	0.0425726	−	0.241441i	−0.956094	−	0.293059i	$-0.905327\pi$
$157$	0.533433	−	3.02525i	0.0425726	−	0.241441i	0.998667	+	0.0516180i	$0.0164378\pi$
$158$	0.939693	+	0.342020i	0.0747579	+	0.0272097i
$159$	2.91875	+	5.05542i	0.231472	+	0.400921i
$160$		0			0
$161$	0.754900	−	0.633436i	0.0594945	−	0.0499218i
$162$	−7.90033	+	6.62916i	−0.620709	+	0.520836i
$163$	9.53462	−	16.5144i	0.746809	−	1.29351i	−0.202536	−	0.979275i	$-0.564918\pi$
$163$	9.53462	−	16.5144i	0.746809	−	1.29351i	0.949345	−	0.314236i	$-0.101748\pi$
$164$	3.41147	+	5.90885i	0.266391	+	0.461403i
$165$		0			0
$166$	1.62449	−	9.21291i	0.126085	−	0.715061i
$167$	2.30453	+	13.0696i	0.178330	+	1.01136i	0.934230	+	0.356672i	$0.116089\pi$
$167$	2.30453	+	13.0696i	0.178330	+	1.01136i	−0.755900	+	0.654687i	$0.772800\pi$
$168$	−0.613341	+	0.223238i	−0.0473203	+	0.0172232i
$169$	−1.66250	−	1.39501i	−0.127885	−	0.107308i
$170$		0			0
$171$	−1.18866	+	1.99157i	−0.0908993	+	0.152299i
$172$	−0.532089			−0.0405714
$173$	0.798133	+	0.669713i	0.0606810	+	0.0509174i	0.672624	−	0.739985i	$-0.265167\pi$
$173$	0.798133	+	0.669713i	0.0606810	+	0.0509174i	−0.611943	+	0.790902i	$0.709612\pi$
$174$	−12.5890	+	4.58202i	−0.954369	+	0.347362i
$175$		0			0
$176$	−1.03209	+	5.85327i	−0.0777966	+	0.441207i
$177$	4.85844	+	1.76833i	0.365183	+	0.132916i
$178$	−5.66637	−	9.81445i	−0.424713	−	0.735624i
$179$	−6.48293	+	11.2288i	−0.484557	+	0.839277i	−0.999843	−	0.0177416i	$-0.994352\pi$
$179$	−6.48293	+	11.2288i	−0.484557	+	0.839277i	0.515286	+	0.857018i	$0.327686\pi$
$180$		0			0
$181$	14.2456	−	11.9534i	1.05886	−	0.888493i	0.0648669	−	0.997894i	$-0.479338\pi$
$181$	14.2456	−	11.9534i	1.05886	−	0.888493i	0.993998	+	0.109401i	$0.0348933\pi$
$182$	−0.571452	+	0.989783i	−0.0423588	+	0.0733676i
$183$	11.5890	+	20.0727i	0.856683	+	1.48382i
$184$	−2.66637	−	0.970481i	−0.196568	−	0.0715448i
$185$		0			0
$186$	0.992726	+	5.63003i	0.0727902	+	0.412814i
$187$	−30.8974	+	11.2457i	−2.25944	+	0.822369i
$188$	3.56418	+	2.99070i	0.259944	+	0.218119i
$189$	−1.61081			−0.117170
$190$		0			0
$191$	−23.5645			−1.70507			−0.852533	−	0.522673i	$-0.824935\pi$
$191$	−23.5645			−1.70507			−0.852533	+	0.522673i	$0.824935\pi$
$192$	1.43969	+	1.20805i	0.103901	+	0.0871832i
$193$	3.92989	−	1.43036i	0.282880	−	0.102960i	−0.196684	−	0.980467i	$-0.563017\pi$
$193$	3.92989	−	1.43036i	0.282880	−	0.102960i	0.479564	+	0.877507i	$0.340795\pi$
$194$	−0.993603	−	5.63500i	−0.0713366	−	0.404570i
$195$		0			0
$196$	6.46451	+	2.35289i	0.461751	+	0.168063i
$197$	−12.8512	−	22.2589i	−0.915608	−	1.58588i	−0.806009	−	0.591903i	$-0.798377\pi$
$197$	−12.8512	−	22.2589i	−0.915608	−	1.58588i	−0.109599	−	0.993976i	$-0.534957\pi$
$198$	1.58125	−	2.73881i	0.112375	−	0.194639i
$199$	−20.0385	+	16.8143i	−1.42049	+	1.19193i	−0.469414	+	0.882978i	$0.655535\pi$
$199$	−20.0385	+	16.8143i	−1.42049	+	1.19193i	−0.951077	+	0.308955i	$0.900021\pi$
$200$		0			0
$201$	4.73783	−	8.20616i	0.334180	−	0.578818i
$202$	−2.36959	−	4.10424i	−0.166723	−	0.288773i
$203$	−2.32635	−	0.846723i	−0.163278	−	0.0594283i
$204$	−1.80541	+	10.2390i	−0.126404	+	0.716872i
$205$		0			0
$206$	2.97906	−	1.08429i	0.207561	−	0.0755459i
$207$	1.15657	+	0.970481i	0.0803875	+	0.0674531i
$208$	3.29086			0.228180
$209$	−4.86824	+	25.4459i	−0.336743	+	1.76013i
$210$		0			0
$211$	5.03983	+	4.22892i	0.346956	+	0.291131i	0.799566	−	0.600578i	$-0.205063\pi$
$211$	5.03983	+	4.22892i	0.346956	+	0.291131i	−0.452610	+	0.891708i	$0.649507\pi$
$212$	2.91875	−	1.06234i	0.200460	−	0.0729616i
$213$	−4.26604	−	24.1939i	−0.292305	−	1.65774i
$214$	−2.32635	+	13.1934i	−0.159026	+	0.901882i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	−0.528218	+	0.914901i	−0.0358578	+	0.0621075i
$218$	−10.4795	+	8.79336i	−0.709763	+	0.595562i
$219$	3.16637	−	2.65690i	0.213964	−	0.179537i
$220$		0			0
$221$	9.10266	+	15.7663i	0.612311	+	1.06055i
$222$	3.21941	+	1.17177i	0.216072	+	0.0786440i
$223$	3.67112	−	20.8200i	0.245837	−	1.39421i	−0.572705	−	0.819761i	$-0.694106\pi$
$223$	3.67112	−	20.8200i	0.245837	−	1.39421i	0.818542	−	0.574447i	$-0.194783\pi$
$224$	0.0603074	+	0.342020i	0.00402946	+	0.0228522i
$225$		0			0
$226$	−10.3571	−	8.69064i	−0.688944	−	0.578092i
$227$	3.24216			0.215190			0.107595	−	0.994195i	$-0.465685\pi$
$227$	3.24216			0.215190			0.107595	+	0.994195i	$0.465685\pi$
$228$	6.19846	+	5.35619i	0.410503	+	0.354722i
$229$	8.56717			0.566135			0.283067	−	0.959100i	$-0.408648\pi$
$229$	8.56717			0.566135			0.283067	+	0.959100i	$0.408648\pi$
$230$		0			0
$231$	3.64543	−	1.32683i	0.239852	−	0.0872989i
$232$	1.23783	+	7.02006i	0.0812673	+	0.460890i
$233$	−0.193715	+	1.09861i	−0.0126907	+	0.0719726i	−0.990495	−	0.137546i	$-0.956079\pi$
$233$	−0.193715	+	1.09861i	−0.0126907	+	0.0719726i	0.977805	+	0.209519i	$0.0671897\pi$
$234$	−1.64543	−	0.598887i	−0.107565	−	0.0391505i
$235$		0			0
$236$	1.37551	−	2.38246i	0.0895384	−	0.155085i
$237$	−1.43969	+	1.20805i	−0.0935181	+	0.0784710i
$238$	−1.47178	+	1.23497i	−0.0954014	+	0.0800513i
$239$	−2.09879	+	3.63522i	−0.135760	+	0.235143i	−0.925887	−	0.377800i	$-0.876681\pi$
$239$	−2.09879	+	3.63522i	−0.135760	+	0.235143i	0.790128	+	0.612942i	$0.210014\pi$
$240$		0			0
$241$	−14.5842	−	5.30823i	−0.939454	−	0.341933i	−0.173504	−	0.984833i	$-0.555509\pi$
$241$	−14.5842	−	5.30823i	−0.939454	−	0.341933i	−0.765950	+	0.642900i	$0.777731\pi$
$242$	4.22416	−	23.9564i	0.271539	−	1.53997i
$243$	−0.949493	−	5.38484i	−0.0609100	−	0.345438i
$244$	11.5890	−	4.21805i	0.741909	−	0.270033i
$245$		0			0
$246$	−12.8229			−0.817561
$247$	14.3430	+	0.207991i	0.912624	+	0.0132342i
$248$	3.04189			0.193160
$249$	13.4684	+	11.3013i	0.853524	+	0.716191i
$250$		0			0
$251$	1.27244	+	7.21637i	0.0803158	+	0.455493i	0.998269	+	0.0588058i	$0.0187293\pi$
$251$	1.27244	+	7.21637i	0.0803158	+	0.455493i	−0.917954	+	0.396688i	$0.870160\pi$
$252$	0.0320889	−	0.181985i	0.00202141	−	0.0114640i
$253$	15.8478	+	5.76811i	0.996340	+	0.362638i
$254$	9.66772	+	16.7450i	0.606607	+	1.05067i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.9368	+	20.0853i	−1.49313	+	1.25289i	−0.602540	+	0.798089i	$0.705845\pi$
$257$	−23.9368	+	20.0853i	−1.49313	+	1.25289i	−0.890594	+	0.454799i	$0.849711\pi$
$258$	0.500000	−	0.866025i	0.0311286	−	0.0539164i
$259$	0.316552	+	0.548284i	0.0196696	+	0.0340687i
$260$		0			0
$261$	0.658633	−	3.73530i	0.0407684	−	0.231209i
$262$	2.96538	+	16.8175i	0.183202	+	1.03899i
$263$	20.5719	−	7.48757i	1.26852	−	0.461703i	0.381900	−	0.924204i	$-0.375270\pi$
$263$	20.5719	−	7.48757i	1.26852	−	0.461703i	0.886619	+	0.462501i	$0.153048\pi$
$264$	−8.55690	−	7.18009i	−0.526641	−	0.441904i
$265$		0			0
$266$	0.241230	+	1.49449i	0.0147907	+	0.0916328i
$267$	21.2986			1.30345
$268$	−3.86231	−	3.24086i	−0.235928	−	0.197967i
$269$	19.1411	−	6.96681i	1.16706	−	0.424774i	0.315443	−	0.948944i	$-0.397847\pi$
$269$	19.1411	−	6.96681i	1.16706	−	0.424774i	0.851613	+	0.524171i	$0.175625\pi$
$270$		0			0
$271$	−3.93835	+	22.3355i	−0.239238	+	1.35678i	0.594265	+	0.804269i	$0.297443\pi$
$271$	−3.93835	+	22.3355i	−0.239238	+	1.35678i	−0.833503	+	0.552515i	$0.813668\pi$
$272$	5.19846	+	1.89209i	0.315203	+	0.114725i
$273$	−1.07398	−	1.86018i	−0.0650001	−	0.112583i
$274$	7.67752	−	13.2979i	0.463816	−	0.803353i
$275$		0			0
$276$	4.08512	−	3.42782i	0.245895	−	0.206331i
$277$	10.4076	−	18.0265i	0.625332	−	1.08311i	−0.363144	−	0.931733i	$-0.618297\pi$
$277$	10.4076	−	18.0265i	0.625332	−	1.08311i	0.988477	−	0.151374i	$-0.0483699\pi$
$278$	−2.57785	−	4.46496i	−0.154609	−	0.267791i
$279$	−1.52094	−	0.553579i	−0.0910566	−	0.0331419i
$280$		0			0
$281$	3.16028	+	17.9229i	0.188527	+	1.06919i	0.921340	+	0.388758i	$0.127096\pi$
$281$	3.16028	+	17.9229i	0.188527	+	1.06919i	−0.732813	+	0.680430i	$0.761793\pi$
$282$	−8.21688	+	2.99070i	−0.489308	+	0.178094i
$283$	−13.9422	−	11.6989i	−0.828779	−	0.695428i	0.126231	−	0.992001i	$-0.459712\pi$
$283$	−13.9422	−	11.6989i	−0.828779	−	0.695428i	−0.955010	+	0.296573i	$0.904156\pi$
$284$	−13.0719			−0.775676
$285$		0			0
$286$	−19.5594			−1.15657
$287$	−1.81521	−	1.52314i	−0.107148	−	0.0899081i
$288$	−0.500000	+	0.181985i	−0.0294628	+	0.0107236i
$289$	2.36231	+	13.3973i	0.138959	+	0.788078i
$290$		0			0
$291$	10.1052	+	3.67799i	0.592377	+	0.215607i
$292$	−1.09967	−	1.90468i	−0.0643533	−	0.111463i
$293$	14.9003	−	25.8081i	0.870487	−	1.50773i	0.00899234	−	0.999960i	$-0.497138\pi$
$293$	14.9003	−	25.8081i	0.870487	−	1.50773i	0.861494	−	0.507767i	$-0.169529\pi$
$294$	−9.90420	+	8.31061i	−0.577625	+	0.484685i
$295$		0			0
$296$	0.911474	−	1.57872i	0.0529784	−	0.0917612i
$297$	−13.7836	−	23.8739i	−0.799805	−	1.38530i
$298$	−10.9829	−	3.99746i	−0.636224	−	0.231567i
$299$	1.62149	−	9.19594i	0.0937733	−	0.531815i
$300$		0			0
$301$	0.173648	−	0.0632028i	0.0100089	−	0.00364295i
$302$	−5.47178	−	4.59137i	−0.314866	−	0.264204i
$303$	8.90673			0.511678
$304$	3.37939	−	2.75314i	0.193821	−	0.157903i
$305$		0			0
$306$	−2.25490	−	1.89209i	−0.128904	−	0.108163i
$307$	−4.37464	+	1.59224i	−0.249674	+	0.0908738i	−0.463825	−	0.885927i	$-0.653524\pi$
$307$	−4.37464	+	1.59224i	−0.249674	+	0.0908738i	0.214152	+	0.976800i	$0.431301\pi$
$308$	−0.358441	−	2.03282i	−0.0204241	−	0.115831i
$309$	−1.03462	+	5.86759i	−0.0588572	+	0.333796i
$310$		0			0
$311$	−7.02869	−	12.1740i	−0.398560	−	0.690326i	0.594988	−	0.803734i	$-0.297157\pi$
$311$	−7.02869	−	12.1740i	−0.398560	−	0.690326i	−0.993549	+	0.113408i	$0.963823\pi$
$312$	−3.09240	+	5.35619i	−0.175072	+	0.303234i
$313$	5.63223	−	4.72600i	0.318352	−	0.267129i	−0.469582	−	0.882889i	$-0.655595\pi$
$313$	5.63223	−	4.72600i	0.318352	−	0.267129i	0.787934	+	0.615760i	$0.211151\pi$
$314$	2.35323	−	1.97459i	0.132800	−	0.111433i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	5.08037	+	1.84911i	0.285342	+	0.103856i	0.480726	−	0.876871i	$-0.340373\pi$
$317$	5.08037	+	1.84911i	0.285342	+	0.103856i	−0.195384	+	0.980727i	$0.562595\pi$
$318$	−1.01367	+	5.74881i	−0.0568438	+	0.322377i
$319$	−7.35710	−	41.7242i	−0.411918	−	2.33610i
$320$		0			0
$321$	−19.2875	−	16.1841i	−1.07652	−	0.903308i
$322$	0.985452			0.0549171
$323$	22.5376	+	8.57510i	1.25403	+	0.477131i
$324$	−10.3131			−0.572953
$325$		0			0
$326$	17.9192	−	6.52206i	0.992454	−	0.361224i
$327$	−4.46451	−	25.3195i	−0.246888	−	1.40017i
$328$	−1.18479	+	6.71929i	−0.0654192	+	0.371011i
$329$	−1.51842	−	0.552659i	−0.0837131	−	0.0304691i
$330$		0			0
$331$	12.8562	−	22.2676i	0.706642	−	1.22394i	−0.259454	−	0.965755i	$-0.583543\pi$
$331$	12.8562	−	22.2676i	0.706642	−	1.22394i	0.966096	−	0.258184i	$-0.0831240\pi$
$332$	7.16637	−	6.01330i	0.393306	−	0.330023i
$333$	−0.743041	+	0.623485i	−0.0407184	+	0.0341668i
$334$	−6.63563	+	11.4932i	−0.363085	+	0.628883i
$335$		0			0
$336$	−0.613341	−	0.223238i	−0.0334605	−	0.0121786i
$337$	−3.10519	+	17.6104i	−0.169150	+	0.959300i	0.775531	+	0.631310i	$0.217482\pi$
$337$	−3.10519	+	17.6104i	−0.169150	+	0.959300i	−0.944681	+	0.327990i	$0.893629\pi$
$338$	−0.376859	−	2.13727i	−0.0204984	−	0.116252i
$339$	23.8773	−	8.69064i	1.29684	−	0.472011i
$340$		0			0
$341$	−18.0797			−0.979068
$342$	−2.19072	+	0.761570i	−0.118461	+	0.0411810i
$343$	−4.82026			−0.260270
$344$	−0.407604	−	0.342020i	−0.0219765	−	0.0184405i
$345$		0			0
$346$	0.180922	+	1.02606i	0.00972643	+	0.0551614i
$347$	2.39440	−	13.5793i	0.128538	−	0.728976i	−0.850605	−	0.525805i	$-0.823764\pi$
$347$	2.39440	−	13.5793i	0.128538	−	0.728976i	0.979143	−	0.203171i	$-0.0651247\pi$
$348$	−12.5890	−	4.58202i	−0.674841	−	0.245622i
$349$	4.40760	+	7.63419i	0.235934	+	0.408649i	0.959544	−	0.281560i	$-0.0908519\pi$
$349$	4.40760	+	7.63419i	0.235934	+	0.408649i	−0.723610	+	0.690209i	$0.757519\pi$
$350$		0			0
$351$	−11.6925	+	9.81120i	−0.624101	+	0.523683i
$352$	−4.55303	+	3.82045i	−0.242677	+	0.203631i
$353$	−0.306589	+	0.531028i	−0.0163181	+	0.0282638i	−0.874069	−	0.485802i	$-0.838528\pi$
$353$	−0.306589	+	0.531028i	−0.0163181	+	0.0282638i	0.857751	+	0.514065i	$0.171861\pi$
$354$	2.58512	+	4.47756i	0.137398	+	0.237980i
$355$		0			0
$356$	1.96791	−	11.1606i	0.104299	−	0.591509i
$357$	−0.627011	−	3.55596i	−0.0331850	−	0.188201i
$358$	−12.1839	+	4.43458i	−0.643940	+	0.234375i
$359$	−11.9834	−	10.0553i	−0.632459	−	0.530696i	0.269233	−	0.963075i	$-0.413230\pi$
$359$	−11.9834	−	10.0553i	−0.632459	−	0.530696i	−0.901692	+	0.432379i	$0.857674\pi$
$360$		0			0
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$	18.5963			0.977398
$363$	35.0219	+	29.3868i	1.83817	+	1.54241i
$364$	−1.07398	+	0.390896i	−0.0562917	+	0.0204885i
$365$		0			0
$366$	−4.02481	+	22.8259i	−0.210380	+	1.19313i
$367$	32.9440	+	11.9906i	1.71966	+	0.625907i	0.997810	−	0.0661388i	$-0.0210680\pi$
$367$	32.9440	+	11.9906i	1.71966	+	0.625907i	0.721854	+	0.692045i	$0.243290\pi$
$368$	−1.41875	−	2.45734i	−0.0739574	−	0.128098i
$369$	1.81521	−	3.14403i	0.0944959	−	0.163672i
$370$		0			0
$371$	−0.826352	+	0.693392i	−0.0429020	+	0.0359991i
$372$	−2.85844	+	4.95096i	−0.148203	+	0.256696i
$373$	12.9231	+	22.3834i	0.669132	+	1.15897i	0.978147	+	0.207914i	$0.0666673\pi$
$373$	12.9231	+	22.3834i	0.669132	+	1.15897i	−0.309015	+	0.951057i	$0.599999\pi$
$374$	−30.8974	−	11.2457i	−1.59767	−	0.581503i
$375$		0			0
$376$	0.807934	+	4.58202i	0.0416660	+	0.236300i
$377$	−22.0437	+	8.02325i	−1.13531	+	0.413218i
$378$	−1.23396	−	1.03541i	−0.0634678	−	0.0532558i
$379$	4.44562			0.228356			0.114178	−	0.993460i	$-0.463577\pi$
$379$	4.44562			0.228356			0.114178	+	0.993460i	$0.463577\pi$
$380$		0			0
$381$	−36.3387			−1.86169
$382$	−18.0514	−	15.1470i	−0.923592	−	0.774986i
$383$	−25.7922	+	9.38759i	−1.31792	+	0.479684i	−0.902791	−	0.430079i	$-0.858486\pi$
$383$	−25.7922	+	9.38759i	−1.31792	+	0.479684i	−0.415129	+	0.909763i	$0.636263\pi$
$384$	0.326352	+	1.85083i	0.0166541	+	0.0944499i
$385$		0			0
$386$	3.92989	+	1.43036i	0.200026	+	0.0728036i
$387$	0.141559	+	0.245188i	0.00719586	+	0.0124636i
$388$	2.86097	−	4.95534i	0.145244	−	0.251569i
$389$	17.6250	−	14.7891i	0.893621	−	0.749837i	−0.0753125	−	0.997160i	$-0.523995\pi$
$389$	17.6250	−	14.7891i	0.893621	−	0.749837i	0.968933	+	0.247323i	$0.0795510\pi$
$390$		0			0
$391$	7.84864	−	13.5942i	0.396923	−	0.687490i
$392$	3.43969	+	5.95772i	0.173731	+	0.300910i
$393$	−30.1587	−	10.9769i	−1.52130	−	0.553710i
$394$	4.46316	−	25.3119i	0.224851	−	1.27519i
$395$		0			0
$396$	2.97178	−	1.08164i	0.149338	−	0.0543545i
$397$	28.0522	+	23.5386i	1.40790	+	1.18137i	0.957463	+	0.288557i	$0.0931754\pi$
$397$	28.0522	+	23.5386i	1.40790	+	1.18137i	0.450435	+	0.892809i	$0.351269\pi$
$398$	−26.1584			−1.31120
$399$	−2.65910	−	1.01173i	−0.133122	−	0.0506500i
$400$		0			0
$401$	27.1195	+	22.7560i	1.35428	+	1.13638i	0.977703	+	0.209994i	$0.0673444\pi$
$401$	27.1195	+	22.7560i	1.35428	+	1.13638i	0.376580	+	0.926384i	$0.377100\pi$
$402$	8.90420	−	3.24086i	0.444101	−	0.161640i
$403$	1.73829	+	9.85835i	0.0865905	+	0.491079i
$404$	0.822948	−	4.66717i	0.0409432	−	0.232200i
$405$		0			0
$406$	−1.23783	−	2.14398i	−0.0614323	−	0.106404i
$407$	−5.41740	+	9.38322i	−0.268531	+	0.465109i
$408$	−7.96451	+	6.68302i	−0.394302	+	0.330859i
$409$	1.28833	−	1.08104i	0.0637040	−	0.0534540i	−0.610380	−	0.792109i	$-0.708983\pi$
$409$	1.28833	−	1.08104i	0.0637040	−	0.0534540i	0.674084	+	0.738655i	$0.264539\pi$
$410$		0			0
$411$	14.4290	+	24.9918i	0.711731	+	1.23275i
$412$	2.97906	+	1.08429i	0.146768	+	0.0534190i
$413$	−0.165907	+	0.940908i	−0.00816377	+	0.0462990i
$414$	0.262174	+	1.48686i	0.0128852	+	0.0730753i
$415$		0			0
$416$	2.52094	+	2.11532i	0.123599	+	0.103712i
$417$	9.68954			0.474499
$418$	−20.0856	+	16.3634i	−0.982418	+	0.800362i
$419$	33.7033			1.64651			0.823256	−	0.567670i	$-0.192155\pi$
$419$	33.7033			1.64651			0.823256	+	0.567670i	$0.192155\pi$
$420$		0			0
$421$	−6.71941	+	2.44566i	−0.327484	+	0.119194i	−0.500530	−	0.865719i	$-0.666861\pi$
$421$	−6.71941	+	2.44566i	−0.327484	+	0.119194i	0.173046	+	0.984914i	$0.444639\pi$
$422$	1.14244	+	6.47908i	0.0556129	+	0.315397i
$423$	0.429892	−	2.43804i	0.0209021	−	0.118542i
$424$	2.91875	+	1.06234i	0.141747	+	0.0515917i
$425$		0			0
$426$	12.2836	−	21.2758i	0.595142	−	1.03082i
$427$	−3.28106	+	2.75314i	−0.158782	+	0.133234i
$428$	−10.2626	+	8.61138i	−0.496063	+	0.416247i
$429$	18.3799	−	31.8348i	0.887388	−	1.53700i
$430$		0			0
$431$	21.2738	+	7.74302i	1.02472	+	0.372968i	0.799069	−	0.601239i	$-0.205326\pi$
$431$	21.2738	+	7.74302i	1.02472	+	0.372968i	0.225653	+	0.974208i	$0.427548\pi$
$432$	−0.805407	+	4.56769i	−0.0387502	+	0.219763i
$433$	−0.827696	−	4.69410i	−0.0397765	−	0.225584i	0.958439	−	0.285297i	$-0.0920924\pi$
$433$	−0.827696	−	4.69410i	−0.0397765	−	0.225584i	−0.998216	+	0.0597135i	$0.980981\pi$
$434$	−0.992726	+	0.361323i	−0.0476524	+	0.0173440i
$435$		0			0
$436$	−13.6800			−0.655155
$437$	−6.02822	−	10.7999i	−0.288369	−	0.516627i
$438$	4.13341			0.197502
$439$	−4.68866	−	3.93426i	−0.223778	−	0.187772i	0.524005	−	0.851715i	$-0.324437\pi$
$439$	−4.68866	−	3.93426i	−0.223778	−	0.187772i	−0.747783	+	0.663943i	$0.768882\pi$
$440$		0			0
$441$	−0.635630	−	3.60483i	−0.0302681	−	0.171659i
$442$	−3.16132	+	17.9287i	−0.150369	+	0.852784i
$443$	23.3011	+	8.48092i	1.10707	+	0.402940i	0.829918	−	0.557886i	$-0.188387\pi$
$443$	23.3011	+	8.48092i	1.10707	+	0.402940i	0.277152	+	0.960826i	$0.410609\pi$
$444$	1.71301	+	2.96702i	0.0812959	+	0.140809i
$445$		0			0
$446$	16.1951	−	13.5893i	0.766858	−	0.643471i
$447$	16.8268	−	14.1194i	0.795881	−	0.667824i
$448$	−0.173648	+	0.300767i	−0.00820411	+	0.0142099i
$449$	0.333626	+	0.577857i	0.0157448	+	0.0272707i	0.873790	−	0.486303i	$-0.161655\pi$
$449$	0.333626	+	0.577857i	0.0157448	+	0.0272707i	−0.858046	+	0.513573i	$0.828321\pi$
$450$		0			0
$451$	7.04189	−	39.9365i	0.331590	−	1.88054i
$452$	−2.34776	−	13.3148i	−0.110429	−	0.626277i
$453$	12.6147	−	4.59137i	0.592690	−	0.215721i
$454$	2.48364	+	2.08402i	0.116563	+	0.0978080i
$455$		0			0
$456$	1.30541	+	8.08737i	0.0611313	+	0.378726i
$457$	13.1967			0.617313			0.308657	−	0.951174i	$-0.400121\pi$
$457$	13.1967			0.617313			0.308657	+	0.951174i	$0.400121\pi$
$458$	6.56283	+	5.50687i	0.306661	+	0.257319i
$459$	−24.1113	+	8.77579i	−1.12542	+	0.409619i
$460$		0			0
$461$	−2.50346	+	14.1978i	−0.116598	+	0.661259i	0.869349	+	0.494199i	$0.164538\pi$
$461$	−2.50346	+	14.1978i	−0.116598	+	0.661259i	−0.985947	+	0.167060i	$0.946573\pi$
$462$	3.64543	+	1.32683i	0.169601	+	0.0617296i
$463$	−3.26470	−	5.65463i	−0.151723	−	0.262793i	0.780138	−	0.625608i	$-0.215149\pi$
$463$	−3.26470	−	5.65463i	−0.151723	−	0.262793i	−0.931861	+	0.362815i	$0.881816\pi$
$464$	−3.56418	+	6.17334i	−0.165463	+	0.286590i
$465$		0			0
$466$	−0.854570	+	0.717070i	−0.0395872	+	0.0332176i
$467$	−12.5890	+	21.8048i	−0.582549	+	1.00900i	0.412627	+	0.910900i	$0.364611\pi$
$467$	−12.5890	+	21.8048i	−0.582549	+	1.00900i	−0.995176	+	0.0981046i	$0.968722\pi$
$468$	−0.875515	−	1.51644i	−0.0404707	−	0.0700973i
$469$	1.64543	+	0.598887i	0.0759789	+	0.0276541i
$470$		0			0
$471$	1.00253	+	5.68561i	0.0461940	+	0.261979i
$472$	2.58512	−	0.940908i	0.118990	−	0.0433088i
$473$	2.42262	+	2.03282i	0.111392	+	0.0934691i
$474$	−1.87939			−0.0863230
$475$		0			0
$476$	−1.92127			−0.0880615
$477$	−1.26604	−	1.06234i	−0.0579682	−	0.0486411i
$478$	−3.94444	+	1.43566i	−0.180415	+	0.0656655i
$479$	−1.61246	−	9.14473i	−0.0736753	−	0.417834i	−0.999231	−	0.0392210i	$-0.987512\pi$
$479$	−1.61246	−	9.14473i	−0.0736753	−	0.417834i	0.925555	−	0.378613i	$-0.123599\pi$
$480$		0			0
$481$	5.63728	+	2.05180i	0.257038	+	0.0935541i
$482$	−7.76011	−	13.4409i	−0.353464	−	0.612217i
$483$	−0.926022	+	1.60392i	−0.0421355	+	0.0729808i
$484$	18.6348	−	15.6364i	0.847034	−	0.710746i
$485$		0			0
$486$	2.73396	−	4.73535i	0.124015	−	0.214800i
$487$	−7.96585	−	13.7973i	−0.360967	−	0.625214i	0.627153	−	0.778896i	$-0.284220\pi$
$487$	−7.96585	−	13.7973i	−0.360967	−	0.625214i	−0.988120	+	0.153682i	$0.950887\pi$
$488$	11.5890	+	4.21805i	0.524609	+	0.190942i
$489$	−6.22328	+	35.2940i	−0.281426	+	1.59605i
$490$		0			0
$491$	−1.50640	+	0.548284i	−0.0679827	+	0.0247437i	−0.375788	−	0.926706i	$-0.622628\pi$
$491$	−1.50640	+	0.548284i	−0.0679827	+	0.0247437i	0.307805	+	0.951449i	$0.400406\pi$
$492$	−9.82295	−	8.24243i	−0.442853	−	0.371598i
$493$	−39.4347			−1.77605
$494$	10.8537	+	9.37884i	0.488331	+	0.421974i
$495$		0			0
$496$	2.33022	+	1.95529i	0.104630	+	0.0877950i
$497$	4.26604	−	1.55271i	0.191358	−	0.0696487i
$498$	3.05303	+	17.3146i	0.136810	+	0.775886i
$499$	5.78652	−	32.8170i	0.259040	−	1.46909i	−0.526444	−	0.850210i	$-0.676475\pi$
$499$	5.78652	−	32.8170i	0.259040	−	1.46909i	0.785485	−	0.618881i	$-0.212414\pi$
$500$		0			0
$501$	−12.4709	−	21.6002i	−0.557159	−	0.965028i
$502$	−3.66385	+	6.34597i	−0.163526	+	0.283235i
$503$	−27.5424	+	23.1108i	−1.22805	+	1.03046i	−0.229690	+	0.973264i	$0.573771\pi$
$503$	−27.5424	+	23.1108i	−1.22805	+	1.03046i	−0.998363	+	0.0571949i	$0.981784\pi$
$504$	0.141559	−	0.118782i	0.00630555	−	0.00529099i
$505$		0			0
$506$	8.43242	+	14.6054i	0.374867	+	0.649288i
$507$	3.83275	+	1.39501i	0.170218	+	0.0619544i
$508$	−3.35756	+	19.0417i	−0.148968	+	0.844838i
$509$	−0.504337	−	2.86024i	−0.0223544	−	0.126778i	0.971588	−	0.236677i	$-0.0760583\pi$
$509$	−0.504337	−	2.86024i	−0.0223544	−	0.126778i	−0.993943	+	0.109899i	$0.964947\pi$
$510$		0			0
$511$	0.585122	+	0.490976i	0.0258843	+	0.0217195i
$512$	1.00000			0.0441942
$513$	−3.79901	+	19.8571i	−0.167730	+	0.876713i
$514$	−31.2472			−1.37826
$515$		0			0
$516$	0.939693	−	0.342020i	0.0413677	−	0.0150566i
$517$	−4.80200	−	27.2335i	−0.211192	−	1.19773i
$518$	−0.109937	+	0.623485i	−0.00483036	+	0.0273944i
$519$	−1.84002	−	0.669713i	−0.0807680	−	0.0293972i
$520$		0			0
$521$	3.43330	−	5.94664i	0.150415	−	0.260527i	−0.780965	−	0.624575i	$-0.785272\pi$
$521$	3.43330	−	5.94664i	0.150415	−	0.260527i	0.931380	+	0.364048i	$0.118606\pi$
$522$	2.90554	−	2.43804i	0.127172	−	0.106710i
$523$	25.6930	−	21.5590i	1.12348	−	0.942709i	0.124702	−	0.992194i	$-0.460203\pi$
$523$	25.6930	−	21.5590i	1.12348	−	0.942709i	0.998775	+	0.0494856i	$0.0157582\pi$
$524$	−8.53849	+	14.7891i	−0.373005	+	0.646064i
$525$		0			0
$526$	20.5719	+	7.48757i	0.896978	+	0.326473i
$527$	−2.92215	+	16.5723i	−0.127291	+	0.721903i
$528$	−1.93969	−	11.0005i	−0.0844143	−	0.478737i
$529$	14.0471	−	5.11273i	0.610744	−	0.222293i
$530$		0			0
$531$	−1.46379			−0.0635232
$532$	−0.775845	+	1.29990i	−0.0336371	+	0.0563579i
$533$	−22.4534			−0.972563
$534$	16.3157	+	13.6905i	0.706048	+	0.592445i
$535$		0			0
$536$	−0.875515	−	4.96529i	−0.0378165	−	0.214468i
$537$	4.23143	−	23.9976i	0.182600	−	1.03557i
$538$	19.1411	+	6.96681i	0.825234	+	0.300360i
$539$	−20.4440	−	35.4101i	−0.880587	−	1.52522i
$540$		0			0
$541$	−24.3744	+	20.4525i	−1.04794	+	0.879323i	−0.992875	−	0.119160i	$-0.961980\pi$
$541$	−24.3744	+	20.4525i	−1.04794	+	0.879323i	−0.0550617	+	0.998483i	$0.517536\pi$
$542$	−17.3739	+	14.5785i	−0.746274	+	0.626198i
$543$	−17.4748	+	30.2672i	−0.749914	+	1.29889i
$544$	2.76604	+	4.79093i	0.118593	+	0.205409i
$545$		0			0
$546$	0.372989	−	2.11532i	0.0159624	−	0.0905275i
$547$	1.02734	+	5.82634i	0.0439259	+	0.249116i	0.998862	−	0.0476955i	$-0.0151877\pi$
$547$	1.02734	+	5.82634i	0.0439259	+	0.249116i	−0.954936	+	0.296812i	$0.904077\pi$
$548$	14.4290	−	5.25173i	0.616377	−	0.224343i
$549$	−5.02687	−	4.21805i	−0.214542	−	0.180022i
$550$		0			0
$551$	−15.9244	+	26.6809i	−0.678404	+	1.13664i
$552$	5.33275			0.226977
$553$	−0.266044	−	0.223238i	−0.0113134	−	0.00949304i
$554$	19.5599	−	7.11922i	0.831020	−	0.302467i
$555$		0			0
$556$	0.895277	−	5.07737i	0.0379682	−	0.215328i
$557$	−24.0590	−	8.75677i	−1.01941	−	0.371036i	−0.222373	−	0.974962i	$-0.571380\pi$
$557$	−24.0590	−	8.75677i	−1.01941	−	0.371036i	−0.797041	+	0.603926i	$0.793602\pi$
$558$	−0.809278	−	1.40171i	−0.0342595	−	0.0593391i
$559$	0.875515	−	1.51644i	0.0370303	−	0.0641384i
$560$		0			0
$561$	47.3376	−	39.7209i	1.99859	−	1.67702i
$562$	−9.09967	+	15.7611i	−0.383846	+	0.664842i
$563$	10.9231	+	18.9193i	0.460353	+	0.797355i	0.998978	−	0.0451904i	$-0.0143895\pi$
$563$	10.9231	+	18.9193i	0.460353	+	0.797355i	−0.538625	+	0.842545i	$0.681056\pi$
$564$	−8.21688	−	2.99070i	−0.345993	−	0.125931i
$565$		0			0
$566$	−3.16044	−	17.9238i	−0.132843	−	0.753392i
$567$	3.36571	−	1.22502i	0.141347	−	0.0514460i
$568$	−10.0137	−	8.40247i	−0.420164	−	0.352560i
$569$	−15.5175			−0.650529			−0.325265	−	0.945623i	$-0.605453\pi$
$569$	−15.5175			−0.650529			−0.325265	+	0.945623i	$0.605453\pi$
$570$		0			0
$571$	−37.2317			−1.55810			−0.779050	−	0.626962i	$-0.784298\pi$
$571$	−37.2317			−1.55810			−0.779050	+	0.626962i	$0.784298\pi$
$572$	−14.9834	−	12.5726i	−0.626487	−	0.525685i
$573$	41.6159	−	15.1470i	1.73853	−	0.632773i
$574$	−0.411474	−	2.33359i	−0.0171746	−	0.0974020i
$575$		0			0
$576$	−0.500000	−	0.181985i	−0.0208333	−	0.00758271i
$577$	14.2306	+	24.6480i	0.592426	+	1.02611i	0.993905	+	0.110243i	$0.0351629\pi$
$577$	14.2306	+	24.6480i	0.592426	+	1.02611i	−0.401479	+	0.915868i	$0.631504\pi$
$578$	−6.80200	+	11.7814i	−0.282926	+	0.490042i
$579$	−6.02094	+	5.05217i	−0.250222	+	0.209961i
$580$		0			0
$581$	−1.62449	+	2.81369i	−0.0673950	+	0.116732i
$582$	5.37686	+	9.31299i	0.222878	+	0.386036i
$583$	−17.3478	−	6.31407i	−0.718471	−	0.261502i
$584$	0.381911	−	2.16593i	0.0158036	−	0.0896267i
$585$		0			0
$586$	28.0035	−	10.1924i	1.15681	−	0.421045i
$587$	21.4743	+	18.0191i	0.886340	+	0.743727i	0.967473	−	0.252976i	$-0.0814094\pi$
$587$	21.4743	+	18.0191i	0.886340	+	0.743727i	−0.0811330	+	0.996703i	$0.525854\pi$
$588$	−12.9290			−0.533184
$589$	10.0326	+	8.66929i	0.413384	+	0.357212i
$590$		0			0
$591$	37.0035	+	31.0496i	1.52212	+	1.27721i
$592$	1.71301	−	0.623485i	0.0704043	−	0.0256251i
$593$	4.14559	+	23.5108i	0.170239	+	0.965474i	0.943497	+	0.331382i	$0.107515\pi$
$593$	4.14559	+	23.5108i	0.170239	+	0.965474i	−0.773258	+	0.634092i	$0.781374\pi$
$594$	4.78699	−	27.1484i	0.196413	−	1.11391i
$595$		0			0
$596$	−5.84389	−	10.1219i	−0.239375	−	0.414610i
$597$	24.5808	−	42.5753i	1.00603	−	1.74249i
$598$	7.15317	−	6.00222i	0.292515	−	0.245449i
$599$	30.3182	−	25.4400i	1.23877	−	1.03945i	0.241149	−	0.970488i	$-0.422476\pi$
$599$	30.3182	−	25.4400i	1.23877	−	1.03945i	0.997619	−	0.0689617i	$-0.0219686\pi$
$600$		0			0
$601$	−18.2083	−	31.5376i	−0.742731	−	1.28645i	−0.951248	−	0.308428i	$-0.900197\pi$
$601$	−18.2083	−	31.5376i	−0.742731	−	1.28645i	0.208517	−	0.978019i	$-0.433136\pi$
$602$	0.173648	+	0.0632028i	0.00707737	+	0.00257595i
$603$	−0.465852	+	2.64198i	−0.0189709	+	0.107590i
$604$	−1.24035	−	7.03439i	−0.0504692	−	0.286225i
$605$		0			0
$606$	6.82295	+	5.72513i	0.277163	+	0.232568i
$607$	8.97266			0.364189			0.182094	−	0.983281i	$-0.441712\pi$
$607$	8.97266			0.364189			0.182094	+	0.983281i	$0.441712\pi$
$608$	4.35844	+	0.0632028i	0.176758	+	0.00256321i
$609$	4.65270			0.188537
$610$		0			0
$611$	−14.3880	+	5.23680i	−0.582076	+	0.211858i
$612$	−0.511144	−	2.89884i	−0.0206618	−	0.117179i
$613$	4.75402	−	26.9614i	0.192013	−	1.08896i	−0.724595	−	0.689175i	$-0.757973\pi$
$613$	4.75402	−	26.9614i	0.192013	−	1.08896i	0.916608	−	0.399786i	$-0.130916\pi$
$614$	−4.37464	−	1.59224i	−0.176546	−	0.0642575i
$615$		0			0
$616$	1.03209	−	1.78763i	0.0415840	−	0.0720257i
$617$	16.1452	−	13.5474i	0.649981	−	0.545398i	−0.257085	−	0.966389i	$-0.582762\pi$
$617$	16.1452	−	13.5474i	0.649981	−	0.545398i	0.907065	+	0.420991i	$0.138317\pi$
$618$	−4.56418	+	3.82980i	−0.183598	+	0.154057i
$619$	17.0064	−	29.4559i	0.683545	−	1.18393i	−0.290347	−	0.956921i	$-0.593771\pi$
$619$	17.0064	−	29.4559i	0.683545	−	1.18393i	0.973892	−	0.227013i	$-0.0728959\pi$
$620$		0			0
$621$	12.3671	+	4.50124i	0.496273	+	0.180629i
$622$	2.44104	−	13.8438i	0.0978767	−	0.555086i
$623$	0.683448	+	3.87603i	0.0273818	+	0.155290i
$624$	−5.81180	+	2.11532i	−0.232658	+	0.0846807i
$625$		0			0
$626$	7.35235			0.293859
$627$	−7.75877	−	48.0678i	−0.309855	−	1.91964i
$628$	3.07192			0.122583
$629$	7.72534	+	6.48233i	0.308029	+	0.258467i
$630$		0			0
$631$	−2.68551	−	15.2303i	−0.106908	−	0.606308i	−0.990441	−	0.137938i	$-0.955953\pi$
$631$	−2.68551	−	15.2303i	−0.106908	−	0.606308i	0.883533	−	0.468370i	$-0.155158\pi$
$632$	−0.173648	+	0.984808i	−0.00690735	+	0.0391735i
$633$	−11.6189	−	4.22892i	−0.461808	−	0.168084i
$634$	2.70321	+	4.68210i	0.107358	+	0.185950i
$635$		0			0
$636$	−4.47178	+	3.75227i	−0.177318	+	0.148787i
$637$	−17.3425	+	14.5521i	−0.687137	+	0.576576i
$638$	21.1839	−	36.6916i	0.838679	−	1.45264i
$639$	3.47771	+	6.02357i	0.137576	+	0.238289i
$640$		0			0
$641$	−6.35545	+	36.0435i	−0.251025	+	1.42363i	0.555048	+	0.831818i	$0.312700\pi$
$641$	−6.35545	+	36.0435i	−0.251025	+	1.42363i	−0.806073	+	0.591816i	$0.798411\pi$
$642$	−4.37211	−	24.7955i	−0.172553	−	0.978599i
$643$	−22.9884	+	8.36711i	−0.906576	+	0.329967i	−0.752885	−	0.658152i	$-0.771338\pi$
$643$	−22.9884	+	8.36711i	−0.906576	+	0.329967i	−0.153691	+	0.988119i	$0.549116\pi$
$644$	0.754900	+	0.633436i	0.0297472	+	0.0249609i
$645$		0			0
$646$	11.7528	+	21.0558i	0.462409	+	0.828430i
$647$	17.2787			0.679295			0.339647	−	0.940553i	$-0.389692\pi$
$647$	17.2787			0.679295			0.339647	+	0.940553i	$0.389692\pi$
$648$	−7.90033	−	6.62916i	−0.310354	−	0.260418i
$649$	−15.3648	+	5.59234i	−0.603123	+	0.219519i
$650$		0			0
$651$	0.344770	−	1.95529i	0.0135126	−	0.0766338i
$652$	17.9192	+	6.52206i	0.701771	+	0.255424i
$653$	−4.24422	−	7.35121i	−0.166089	−	0.287675i	0.770952	−	0.636893i	$-0.219781\pi$
$653$	−4.24422	−	7.35121i	−0.166089	−	0.287675i	−0.937042	+	0.349218i	$0.886447\pi$
$654$	12.8550	−	22.2656i	0.502672	−	0.870653i
$655$		0			0
$656$	−5.22668	+	4.38571i	−0.204068	+	0.171233i
$657$	−0.585122	+	1.01346i	−0.0228278	+	0.0395389i
$658$	−0.807934	−	1.39938i	−0.0314965	−	0.0545536i
$659$	29.8859	+	10.8776i	1.16419	+	0.423731i	0.850593	−	0.525825i	$-0.176243\pi$
$659$	29.8859	+	10.8776i	1.16419	+	0.423731i	0.313598	+	0.949556i	$0.398465\pi$
$660$		0			0
$661$	−3.88114	−	22.0110i	−0.150959	−	0.856130i	−0.962388	−	0.271679i	$-0.912421\pi$
$661$	−3.88114	−	22.0110i	−0.150959	−	0.856130i	0.811429	−	0.584451i	$-0.198690\pi$
$662$	24.1618	−	8.79417i	0.939075	−	0.341795i
$663$	−26.2101	−	21.9929i	−1.01791	−	0.854132i
$664$	9.35504			0.363046
$665$		0			0
$666$	−0.969971			−0.0375856
$667$	15.4945	+	13.0015i	0.599951	+	0.503419i
$668$	−12.4709	+	4.53904i	−0.482514	+	0.175621i
$669$	6.89945	+	39.1287i	0.266748	+	1.51280i
$670$		0			0
$671$	−68.8799	−	25.0702i	−2.65908	−	0.967826i
$672$	−0.326352	−	0.565258i	−0.0125893	−	0.0218053i
$673$	21.0253	−	36.4169i	0.810465	−	1.40377i	−0.102074	−	0.994777i	$-0.532548\pi$
$673$	21.0253	−	36.4169i	0.810465	−	1.40377i	0.912539	−	0.408990i	$-0.134119\pi$
$674$	−13.6985	+	11.4944i	−0.527645	+	0.442747i
$675$		0			0
$676$	1.08512	−	1.87949i	0.0417355	−	0.0722880i
$677$	6.12970	+	10.6170i	0.235583	+	0.408043i	0.959442	−	0.281906i	$-0.0909666\pi$
$677$	6.12970	+	10.6170i	0.235583	+	0.408043i	−0.723859	+	0.689948i	$0.757633\pi$
$678$	23.8773	+	8.69064i	0.917003	+	0.333762i
$679$	−0.345075	+	1.95702i	−0.0132428	+	0.0751034i
$680$		0			0
$681$	−5.72580	+	2.08402i	−0.219413	+	0.0798599i
$682$	−13.8498	−	11.6214i	−0.530337	−	0.445006i
$683$	10.1652			0.388960			0.194480	−	0.980906i	$-0.437698\pi$
$683$	10.1652			0.388960			0.194480	+	0.980906i	$0.437698\pi$
$684$	−2.16772	−	0.824773i	−0.0828848	−	0.0315360i
$685$		0			0
$686$	−3.69253	−	3.09840i	−0.140982	−	0.118298i
$687$	−15.1300	+	5.50687i	−0.577246	+	0.210100i
$688$	−0.0923963	−	0.524005i	−0.00352257	−	0.0199775i
$689$	−1.77497	+	10.0663i	−0.0676209	+	0.383497i
$690$		0			0
$691$	0.740763	+	1.28304i	0.0281799	+	0.0488091i	0.879771	−	0.475397i	$-0.157696\pi$
$691$	0.740763	+	1.28304i	0.0281799	+	0.0488091i	−0.851592	+	0.524206i	$0.824362\pi$
$692$	−0.520945	+	0.902302i	−0.0198033	+	0.0343004i
$693$	−0.841367	+	0.705990i	−0.0319609	+	0.0268184i
$694$	10.5628	−	8.86327i	0.400960	−	0.336445i
$695$		0			0
$696$	−6.69846	−	11.6021i	−0.253905	−	0.439776i
$697$	−35.4688	−	12.9096i	−1.34348	−	0.488986i
$698$	−1.53074	+	8.68128i	−0.0579395	+	0.328591i
$699$	−0.364066	−	2.06472i	−0.0137702	−	0.0780949i
$700$		0			0
$701$	−21.7101	−	18.2169i	−0.819978	−	0.688043i	0.132989	−	0.991118i	$-0.457543\pi$
$701$	−21.7101	−	18.2169i	−0.819978	−	0.688043i	−0.952967	+	0.303074i	$0.901987\pi$
$702$	−15.2635			−0.576084
$703$	7.50546	−	2.60916i	0.283074	−	0.0984062i
$704$	−5.94356			−0.224006
$705$		0			0
$706$	−0.576199	+	0.209719i	−0.0216856	+	0.00789290i
$707$	0.285807	+	1.62089i	0.0107489	+	0.0609599i
$708$	−0.897804	+	5.09170i	−0.0337415	+	0.191358i
$709$	12.2852	+	4.47146i	0.461382	+	0.167929i	0.562244	−	0.826971i	$-0.309938\pi$
$709$	12.2852	+	4.47146i	0.461382	+	0.167929i	−0.100863	+	0.994900i	$0.532160\pi$
$710$		0			0
$711$	0.266044	−	0.460802i	0.00997745	−	0.0172814i
$712$	8.68139	−	7.28455i	0.325349	−	0.273000i
$713$	6.61200	−	5.54812i	0.247621	−	0.207779i
$714$	1.80541	−	3.12706i	0.0675657	−	0.117027i
$715$		0			0
$716$	−12.1839	−	4.43458i	−0.455334	−	0.165728i
$717$	1.36989	−	7.76903i	0.0511595	−	0.290140i
$718$	−2.71641	−	15.4056i	−0.101376	−	0.574930i
$719$	−26.4722	+	9.63511i	−0.987248	+	0.359329i	−0.784654	−	0.619934i	$-0.787159\pi$
$719$	−26.4722	+	9.63511i	−0.987248	+	0.359329i	−0.202594	+	0.979263i	$0.564937\pi$
$720$		0			0
$721$	−1.10101			−0.0410039
$722$	18.9920	+	0.550931i	0.706809	+	0.0205035i
$723$	29.1685			1.08479
$724$	14.2456	+	11.9534i	0.529432	+	0.444246i
$725$		0			0
$726$	7.93882	+	45.0233i	0.294637	+	1.67097i
$727$	5.89218	−	33.4162i	0.218529	−	1.23934i	−0.656148	−	0.754632i	$-0.727815\pi$
$727$	5.89218	−	33.4162i	0.218529	−	1.23934i	0.874677	−	0.484706i	$-0.161074\pi$
$728$	−1.07398	−	0.390896i	−0.0398043	−	0.0144876i
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$		0			0
$731$	2.25490	−	1.89209i	0.0834005	−	0.0699813i
$732$	−17.7554	+	14.8985i	−0.656257	+	0.550665i
$733$	17.5706	−	30.4331i	0.648984	−	1.12407i	−0.334382	−	0.942438i	$-0.608528\pi$
$733$	17.5706	−	30.4331i	0.648984	−	1.12407i	0.983366	−	0.181636i	$-0.0581391\pi$
$734$	17.5292	+	30.3614i	0.647013	+	1.12066i
$735$		0			0
$736$	0.492726	−	2.79439i	0.0181621	−	0.103003i
$737$	5.20368	+	29.5115i	0.191680	+	1.08707i
$738$	3.41147	−	1.24168i	0.125578	−	0.0457067i
$739$	12.6511	+	10.6155i	0.465379	+	0.390499i	0.845105	−	0.534600i	$-0.179538\pi$
$739$	12.6511	+	10.6155i	0.465379	+	0.390499i	−0.379727	+	0.925099i	$0.623982\pi$
$740$		0			0
$741$	−25.4641	+	8.85219i	−0.935447	+	0.325193i
$742$	−1.07873			−0.0396013
$743$	29.3161	+	24.5992i	1.07550	+	0.902456i	0.995540	−	0.0943419i	$-0.0300747\pi$
$743$	29.3161	+	24.5992i	1.07550	+	0.902456i	0.0799651	+	0.996798i	$0.474519\pi$
$744$	−5.37211	+	1.95529i	−0.196951	+	0.0716844i
$745$		0			0
$746$	−4.48814	+	25.4535i	−0.164322	+	0.931919i
$747$	−4.67752	−	1.70248i	−0.171141	−	0.0622904i
$748$	−16.4402	−	28.4752i	−0.601112	−	1.04116i
$749$	2.32635	−	4.02936i	0.0850030	−	0.147230i
$750$		0			0
$751$	8.77972	−	7.36706i	0.320376	−	0.268828i	−0.468389	−	0.883523i	$-0.655165\pi$
$751$	8.77972	−	7.36706i	0.320376	−	0.268828i	0.788765	+	0.614695i	$0.210721\pi$
$752$	−2.32635	+	4.02936i	−0.0848333	+	0.146936i
$753$	−6.88578	−	11.9265i	−0.250932	−	0.434627i
$754$	−22.0437	−	8.02325i	−0.802784	−	0.292190i
$755$		0			0
$756$	−0.279715	−	1.58634i	−0.0101731	−	0.0576947i
$757$	−18.2417	+	6.63943i	−0.663006	+	0.241314i	−0.651534	−	0.758620i	$-0.725874\pi$
$757$	−18.2417	+	6.63943i	−0.663006	+	0.241314i	−0.0114722	+	0.999934i	$0.503652\pi$
$758$	3.40554	+	2.85759i	0.123695	+	0.103792i
$759$	−31.6955			−1.15047
$760$		0			0
$761$	14.6441			0.530850			0.265425	−	0.964132i	$-0.414488\pi$
$761$	14.6441			0.530850			0.265425	+	0.964132i	$0.414488\pi$
$762$	−27.8371	−	23.3581i	−1.00843	−	0.846174i
$763$	4.46451	−	1.62495i	0.161626	−	0.0588271i
$764$	−4.09193	−	23.2065i	−0.148041	−	0.839581i
$765$		0			0
$766$	−25.7922	−	9.38759i	−0.931910	−	0.339188i
$767$	4.52663	+	7.84035i	0.163447	+	0.283098i
$768$	−0.939693	+	1.62760i	−0.0339082	+	0.0587308i
$769$	−31.6024	+	26.5176i	−1.13961	+	0.956248i	−0.999426	−	0.0338770i	$-0.989215\pi$
$769$	−31.6024	+	26.5176i	−1.13961	+	0.956248i	−0.140186	+	0.990125i	$0.544770\pi$
$770$		0			0
$771$	29.3628	−	50.8578i	1.05747	−	1.83160i
$772$	2.09105	+	3.62181i	0.0752586	+	0.130352i
$773$	18.8380	+	6.85646i	0.677554	+	0.246610i	0.657797	−	0.753195i	$-0.271488\pi$
$773$	18.8380	+	6.85646i	0.677554	+	0.246610i	0.0197573	+	0.999805i	$0.493711\pi$
$774$	−0.0491630	+	0.278817i	−0.00176713	+	0.0100219i
$775$		0			0
$776$	5.37686	−	1.95702i	0.193018	−	0.0702528i
$777$	−0.911474	−	0.764818i	−0.0326990	−	0.0274377i
$778$	23.0077			0.824867
$779$	−23.0574	+	18.7845i	−0.826116	+	0.673025i
$780$		0			0
$781$	59.5169	+	49.9406i	2.12968	+	1.78701i
$782$	14.7506	−	5.36879i	0.527481	−	0.191987i
$783$	−5.74123	−	32.5601i	−0.205175	−	1.16360i
$784$	−1.19459	+	6.77487i	−0.0426640	+	0.241960i
$785$		0			0
$786$	−16.0471	−	27.7944i	−0.572381	−	0.991393i
$787$	−17.4413	+	30.2093i	−0.621717	+	1.07684i	0.367449	+	0.930044i	$0.380231\pi$
$787$	−17.4413	+	30.2093i	−0.621717	+	1.07684i	−0.989166	+	0.146801i	$0.953102\pi$
$788$	19.6891	−	16.5211i	0.701396	−	0.588541i
$789$	−31.5180	+	26.4467i	−1.12207	+	0.941529i
$790$		0			0
$791$	2.34776	+	4.06645i	0.0834768	+	0.144586i
$792$	2.97178	+	1.08164i	0.105598	+	0.0384344i
$793$	−7.04757	+	39.9688i	−0.250267	+	1.41933i
$794$	6.35891	+	36.0632i	0.225669	+	1.27983i
$795$		0			0
$796$	−20.0385	−	16.8143i	−0.710245	−	0.595967i
$797$	42.3979			1.50181			0.750905	−	0.660411i	$-0.229618\pi$
$797$	42.3979			1.50181			0.750905	+	0.660411i	$0.229618\pi$
$798$	−1.38666	−	2.48427i	−0.0490872	−	0.0879422i
$799$	−25.7392			−0.910586
$800$		0			0
$801$	−5.66637	+	2.06239i	−0.200211	+	0.0728710i
$802$	6.14749	+	34.8641i	0.217075	+	1.23110i
$803$	−2.26991	+	12.8733i	−0.0801036	+	0.454290i
$804$	8.90420	+	3.24086i	0.314027	+	0.114296i
$805$		0			0
$806$	−5.00521	+	8.66929i	−0.176301	+	0.305363i
$807$	−29.3259	+	24.6074i	−1.03232	+	0.866221i
$808$	3.63041	−	3.04628i	0.127718	−	0.107168i
$809$	−3.97384	+	6.88289i	−0.139713	+	0.241990i	−0.927388	−	0.374101i	$-0.877951\pi$
$809$	−3.97384	+	6.88289i	−0.139713	+	0.241990i	0.787675	+	0.616091i	$0.211285\pi$
$810$		0			0
$811$	−2.68510	−	0.977295i	−0.0942865	−	0.0343175i	0.294446	−	0.955668i	$-0.404865\pi$
$811$	−2.68510	−	0.977295i	−0.0942865	−	0.0343175i	−0.388733	+	0.921351i	$0.627087\pi$
$812$	0.429892	−	2.43804i	0.0150863	−	0.0855585i
$813$	−7.40167	−	41.9770i	−0.259588	−	1.47220i
$814$	−10.1814	+	3.70572i	−0.356857	+	0.129886i
$815$		0			0
$816$	−10.3969			−0.363965
$817$	−0.369585	−	2.28969i	−0.0129301	−	0.0801060i
$818$	1.68180			0.0588027
$819$	0.465852	+	0.390896i	0.0162782	+	0.0136590i
$820$		0			0
$821$	6.34183	+	35.9663i	0.221332	+	1.25523i	0.869575	+	0.493800i	$0.164393\pi$
$821$	6.34183	+	35.9663i	0.221332	+	1.25523i	−0.648244	+	0.761433i	$0.724496\pi$
$822$	−5.01114	+	28.4196i	−0.174784	+	0.991248i
$823$	−35.2148	−	12.8171i	−1.22751	−	0.446778i	−0.354767	−	0.934955i	$-0.615440\pi$
$823$	−35.2148	−	12.8171i	−1.22751	−	0.446778i	−0.872745	+	0.488177i	$0.837662\pi$
$824$	1.58512	+	2.74551i	0.0552204	+	0.0956445i
$825$		0			0
$826$	−0.731896	+	0.614134i	−0.0254659	+	0.0213684i
$827$	−14.1951	+	11.9111i	−0.493611	+	0.414188i	−0.855318	−	0.518103i	$-0.826638\pi$
$827$	−14.1951	+	11.9111i	−0.493611	+	0.414188i	0.361708	+	0.932292i	$0.382194\pi$
$828$	−0.754900	+	1.30753i	−0.0262346	+	0.0454396i
$829$	0.458578	+	0.794280i	0.0159271	+	0.0275865i	0.873879	−	0.486143i	$-0.161597\pi$
$829$	0.458578	+	0.794280i	0.0159271	+	0.0275865i	−0.857952	+	0.513730i	$0.828263\pi$
$830$		0			0
$831$	−6.79308	+	38.5255i	−0.235649	+	1.33643i
$832$	0.571452	+	3.24086i	0.0198115	+	0.112357i
$833$	−35.7622	+	13.0164i	−1.23909	+	0.450991i
$834$	7.42262	+	6.22832i	0.257024	+	0.215669i
$835$		0			0
$836$	−25.9047	−	0.375650i	−0.895932	−	0.0129921i
$837$	−14.1088			−0.487670
$838$	25.8182	+	21.6640i	0.891875	+	0.748372i
$839$	25.5462	−	9.29807i	0.881954	−	0.321005i	0.138956	−	0.990299i	$-0.455625\pi$
$839$	25.5462	−	9.29807i	0.881954	−	0.321005i	0.742998	+	0.669294i	$0.233403\pi$
$840$		0			0
$841$	3.78787	−	21.4821i	0.130616	−	0.740761i
$842$	−6.71941	−	2.44566i	−0.231566	−	0.0842832i
$843$	−17.1018	−	29.6212i	−0.589017	−	1.02021i
$844$	−3.28952	+	5.69761i	−0.113230	+	0.196120i
$845$		0			0
$846$	1.89646	−	1.59132i	0.0652016	−	0.0547107i
$847$	−4.22416	+	7.31645i	−0.145144	+	0.251396i
$848$	1.55303	+	2.68993i	0.0533314	+	0.0923727i
$849$	32.1425	+	11.6989i	1.10313	+	0.401506i
$850$		0			0
$851$	−0.898214	−	5.09403i	−0.0307904	−	0.174621i
$852$	23.0856	−	8.40247i	0.790899	−	0.287864i
$853$	10.4272	+	8.74946i	0.357021	+	0.299576i	0.803602	−	0.595167i	$-0.202914\pi$
$853$	10.4272	+	8.74946i	0.357021	+	0.299576i	−0.446581	+	0.894743i	$0.647359\pi$
$854$	−4.28312			−0.146565
$855$		0			0
$856$	−13.3969			−0.457898
$857$	−5.44562	−	4.56942i	−0.186019	−	0.156088i	0.545023	−	0.838421i	$-0.316521\pi$
$857$	−5.44562	−	4.56942i	−0.186019	−	0.156088i	−0.731042	+	0.682333i	$0.760965\pi$
$858$	34.5428	−	12.5726i	1.17927	−	0.429220i
$859$	2.95605	+	16.7646i	0.100859	+	0.572001i	0.992794	+	0.119836i	$0.0382369\pi$
$859$	2.95605	+	16.7646i	0.100859	+	0.572001i	−0.891935	+	0.452165i	$0.850652\pi$
$860$		0			0
$861$	4.18479	+	1.52314i	0.142617	+	0.0519085i
$862$	11.3195	+	19.6060i	0.385545	+	0.667784i
$863$	−5.43423	+	9.41236i	−0.184983	+	0.320401i	−0.943571	−	0.331171i	$-0.892556\pi$
$863$	−5.43423	+	9.41236i	−0.184983	+	0.320401i	0.758588	+	0.651571i	$0.225890\pi$
$864$	−3.55303	+	2.98135i	−0.120877	+	0.101428i
$865$		0			0
$866$	2.38326	−	4.12792i	0.0809863	−	0.140272i
$867$	−12.7836	−	22.1418i	−0.434153	−	0.751976i
$868$	−0.992726	−	0.361323i	−0.0336953	−	0.0122641i
$869$	1.03209	−	5.85327i	0.0350112	−	0.198558i
$870$		0			0
$871$	15.5915	−	5.67485i	0.528298	−	0.192285i
$872$	−10.4795	−	8.79336i	−0.354881	−	0.297781i
$873$	−3.04458			−0.103043
$874$	2.32413	−	12.1480i	0.0786149	−	0.410913i
$875$		0			0
$876$	3.16637	+	2.65690i	0.106982	+	0.0897684i
$877$	−11.7922	+	4.29201i	−0.398194	+	0.144931i	−0.533352	−	0.845893i	$-0.679068\pi$
$877$	−11.7922	+	4.29201i	−0.398194	+	0.144931i	0.135158	+	0.990824i	$0.456846\pi$
$878$	−1.06283	−	6.02763i	−0.0358689	−	0.203423i
$879$	−9.72550	+	55.1560i	−0.328033	+	1.86037i
$880$		0			0
$881$	−17.7408	−	30.7280i	−0.597703	−	1.03525i	−0.993159	−	0.116768i	$-0.962747\pi$
$881$	−17.7408	−	30.7280i	−0.597703	−	1.03525i	0.395456	−	0.918485i	$-0.370587\pi$
$882$	1.83022	−	3.17004i	0.0616268	−	0.106741i
$883$	−12.9304	+	10.8499i	−0.435141	+	0.365127i	−0.833888	−	0.551934i	$-0.813890\pi$
$883$	−12.9304	+	10.8499i	−0.435141	+	0.365127i	0.398746	+	0.917061i	$0.369445\pi$
$884$	−13.9461	+	11.7022i	−0.469058	+	0.393586i
$885$		0			0
$886$	12.3983	+	21.4744i	0.416528	+	0.721448i
$887$	−54.8462	−	19.9624i	−1.84155	−	0.670271i	−0.989056	−	0.147541i	$-0.952864\pi$
$887$	−54.8462	−	19.9624i	−1.84155	−	0.670271i	−0.852498	−	0.522730i	$-0.824914\pi$
$888$	−0.594922	+	3.37397i	−0.0199643	+	0.113223i
$889$	−1.16607	−	6.61311i	−0.0391087	−	0.221797i
$890$		0			0
$891$	46.9561	+	39.4009i	1.57309	+	1.31998i
$892$	21.1411			0.707858
$893$	−10.3939	+	17.4147i	−0.347820	+	0.582760i
$894$	21.9659			0.734648
$895$		0			0
$896$	−0.326352	+	0.118782i	−0.0109026	+	0.00396824i
$897$	3.04741	+	17.2827i	0.101750	+	0.577053i
$898$	−0.115867	+	0.657115i	−0.00386653	+	0.0219282i
$899$	−20.3760	−	7.41625i	−0.679577	−	0.247346i
$900$		0			0
$901$	−8.59152	+	14.8809i	−0.286225	+	0.495756i
$902$	31.0651	−	26.0667i	1.03436	−	0.867927i
$903$	−0.266044	+	0.223238i	−0.00885340	+	0.00742889i
$904$	6.76011	−	11.7089i	0.224838	−	0.389431i
$905$		0			0
$906$	12.6147	+	4.59137i	0.419095	+	0.152538i
$907$	−0.283119	+	1.60565i	−0.00940080	+	0.0533146i	−0.989147	−	0.146927i	$-0.953062\pi$
$907$	−0.283119	+	1.60565i	−0.00940080	+	0.0533146i	0.979747	+	0.200242i	$0.0641728\pi$
$908$	0.562996	+	3.19291i	0.0186837	+	0.105960i
$909$	−2.36959	+	0.862458i	−0.0785942	+	0.0286059i
$910$		0			0
$911$	21.6016			0.715694			0.357847	−	0.933780i	$-0.383511\pi$
$911$	21.6016			0.715694			0.357847	+	0.933780i	$0.383511\pi$
$912$	−4.19846	+	7.03439i	−0.139025	+	0.232932i
$913$	−55.6023			−1.84017
$914$	10.1092	+	8.48264i	0.334383	+	0.280581i
$915$		0			0
$916$	1.48767	+	8.43702i	0.0491541	+	0.278767i
$917$	1.02987	−	5.84067i	0.0340092	−	0.192876i
$918$	−24.1113	−	8.77579i	−0.795791	−	0.289644i
$919$	−17.8152	−	30.8568i	−0.587669	−	1.01787i	−0.994537	−	0.104386i	$-0.966712\pi$
$919$	−17.8152	−	30.8568i	−0.587669	−	1.01787i	0.406867	−	0.913487i	$-0.366621\pi$
$920$		0			0
$921$	6.70233	−	5.62393i	0.220849	−	0.185315i
$922$	−11.0439	+	9.26697i	−0.363713	+	0.305192i
$923$	21.5089	−	37.2545i	0.707975	−	1.22625i
$924$	1.93969	+	3.35965i	0.0638112	+	0.110524i
$925$		0			0
$926$	1.13382	−	6.43020i	0.0372596	−	0.211310i
$927$	−0.292919	−	1.66122i	−0.00962071	−	0.0545618i
$928$	−6.69846	+	2.43804i	−0.219888	+	0.0800326i
$929$	22.0271	+	18.4829i	0.722685	+	0.606405i	0.928127	−	0.372264i	$-0.121419\pi$
$929$	22.0271	+	18.4829i	0.722685	+	0.606405i	−0.205441	+	0.978669i	$0.565863\pi$
$930$		0			0
$931$	−5.63475	+	29.4524i	−0.184672	+	0.965263i
$932$	−1.11556			−0.0365415
$933$	20.2383	+	16.9819i	0.662572	+	0.555964i
$934$	−23.6596	+	8.61138i	−0.774165	+	0.281773i
$935$		0			0
$936$	0.304063	−	1.72443i	0.00993861	−	0.0563647i
$937$	−33.9334	−	12.3507i	−1.10855	−	0.403481i	−0.278091	−	0.960555i	$-0.589702\pi$
$937$	−33.9334	−	12.3507i	−1.10855	−	0.403481i	−0.830463	+	0.557074i	$0.811924\pi$
$938$	0.875515	+	1.51644i	0.0285866	+	0.0495134i
$939$	−6.90895	+	11.9666i	−0.225465	+	0.390517i
$940$		0			0
$941$	35.1018	−	29.4539i	1.14429	−	0.960170i	0.144715	−	0.989473i	$-0.453773\pi$
$941$	35.1018	−	29.4539i	1.14429	−	0.960170i	0.999571	+	0.0293038i	$0.00932903\pi$
$942$	−2.88666	+	4.99984i	−0.0940524	+	0.162904i
$943$	9.68004	+	16.7663i	0.315226	+	0.545987i
$944$	2.58512	+	0.940908i	0.0841386	+	0.0306239i
$945$		0			0
$946$	0.549163	+	3.11446i	0.0178548	+	0.101260i
$947$	20.7322	−	7.54590i	0.673706	−	0.245209i	0.0175633	−	0.999846i	$-0.494409\pi$
$947$	20.7322	−	7.54590i	0.673706	−	0.245209i	0.656143	+	0.754637i	$0.272187\pi$
$948$	−1.43969	−	1.20805i	−0.0467590	−	0.0392355i
$949$	7.23772			0.234946
$950$		0			0
$951$	−10.1607			−0.329485
$952$	−1.47178	−	1.23497i	−0.0477007	−	0.0400257i
$953$	−50.8119	+	18.4940i	−1.64596	+	0.599080i	−0.988066	−	0.154033i	$-0.950774\pi$
$953$	−50.8119	+	18.4940i	−1.64596	+	0.599080i	−0.657892	+	0.753112i	$0.728552\pi$
$954$	−0.286989	−	1.62760i	−0.00929161	−	0.0526953i
$955$		0			0
$956$	−3.94444	−	1.43566i	−0.127572	−	0.0464325i
$957$	39.8127	+	68.9577i	1.28696	+	2.22909i
$958$	4.64290	−	8.04174i	0.150005	−	0.259817i
$959$	−4.08512	+	3.42782i	−0.131915	+	0.110690i
$960$		0			0
$961$	10.8735	−	18.8334i	0.350757	−	0.607528i
$962$	2.99953	+	5.19534i	0.0967088	+	0.167505i
$963$	6.69846	+	2.43804i	0.215855	+	0.0785648i
$964$	2.69506	−	15.2844i	0.0868020	−	0.492279i
$965$		0			0
$966$	−1.74035	+	0.633436i	−0.0559949	+	0.0203805i
$967$	1.21507	+	1.01957i	0.0390740	+	0.0327870i	0.662116	−	0.749402i	$-0.269659\pi$
$967$	1.21507	+	1.01957i	0.0390740	+	0.0327870i	−0.623042	+	0.782189i	$0.714103\pi$
$968$	24.3259			0.781865
$969$	−45.3144	−	0.657115i	−1.45571	−	0.0211096i
$970$		0			0
$971$	8.74944	+	7.34165i	0.280783	+	0.235605i	0.772292	−	0.635268i	$-0.219110\pi$
$971$	8.74944	+	7.34165i	0.280783	+	0.235605i	−0.491509	+	0.870872i	$0.663555\pi$
$972$	5.13816	−	1.87014i	0.164806	−	0.0599846i
$973$	0.310927	+	1.76335i	0.00996785	+	0.0565305i
$974$	2.76651	−	15.6897i	0.0886447	−	0.502729i
$975$		0			0
$976$	6.16637	+	10.6805i	0.197381	+	0.341874i
$977$	−22.8344	+	39.5503i	−0.730537	+	1.26533i	0.226117	+	0.974100i	$0.427397\pi$
$977$	−22.8344	+	39.5503i	−0.730537	+	1.26533i	−0.956654	+	0.291227i	$0.905936\pi$
$978$	−27.4538	+	23.0365i	−0.877877	+	0.736626i
$979$	−51.5984	+	43.2962i	−1.64909	+	1.38375i
$980$		0			0
$981$	3.63950	+	6.30380i	0.116200	+	0.201265i
$982$	−1.50640	−	0.548284i	−0.0480710	−	0.0174964i
$983$	3.88397	−	22.0271i	0.123879	−	0.702555i	−0.858088	−	0.513503i	$-0.828347\pi$
$983$	3.88397	−	22.0271i	0.123879	−	0.702555i	0.981967	−	0.189052i	$-0.0605415\pi$
$984$	−2.22668	−	12.6281i	−0.0709840	−	0.402570i
$985$		0			0
$986$	−30.2087	−	25.3481i	−0.962042	−	0.807249i
$987$	3.03684			0.0966636
$988$	2.28581	+	14.1612i	0.0727212	+	0.450529i
$989$	−1.50980			−0.0480089
$990$		0			0
$991$	28.2511	−	10.2826i	0.897425	−	0.326636i	0.148205	−	0.988957i	$-0.452651\pi$
$991$	28.2511	−	10.2826i	0.897425	−	0.326636i	0.749221	+	0.662321i	$0.230428\pi$
$992$	0.528218	+	2.99568i	0.0167710	+	0.0951128i
$993$	−8.39130	+	47.5894i	−0.266290	+	1.51021i
$994$	4.26604	+	1.55271i	0.135311	+	0.0492491i
$995$		0			0
$996$	−8.79086	+	15.2262i	−0.278549	+	0.482461i
$997$	−14.2362	+	11.9456i	−0.450866	+	0.378322i	−0.839757	−	0.542962i	$-0.817303\pi$
$997$	−14.2362	+	11.9456i	−0.450866	+	0.378322i	0.388891	+	0.921284i	$0.372858\pi$
$998$	25.5271	−	21.4198i	0.808046	−	0.678031i
$999$	−4.22756	+	7.32235i	−0.133754	+	0.231669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.a.301.1	yes	6
5.2	odd	4		950.2.u.a.149.1		12
5.3	odd	4		950.2.u.a.149.2		12
5.4	even	2		950.2.l.f.301.1	yes	6
19.6	even	9	inner	950.2.l.a.101.1	✓	6
95.44	even	18		950.2.l.f.101.1	yes	6
95.63	odd	36		950.2.u.a.899.1		12
95.82	odd	36		950.2.u.a.899.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.a.101.1	✓	6	19.6	even	9	inner
950.2.l.a.301.1	yes	6	1.1	even	1	trivial
950.2.l.f.101.1	yes	6	95.44	even	18
950.2.l.f.301.1	yes	6	5.4	even	2
950.2.u.a.149.1		12	5.2	odd	4
950.2.u.a.149.2		12	5.3	odd	4
950.2.u.a.899.1		12	95.63	odd	36
950.2.u.a.899.2		12	95.82	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.76604 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.76604 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +(2.97178 - 5.14728i) q^{11} +(-0.939693 - 1.62760i) q^{12} +(-3.09240 - 1.12554i) q^{13} +(0.0603074 - 0.342020i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.23783 - 3.55596i) q^{17} +0.532089 q^{18} +(-4.11721 + 1.43128i) q^{19} +(0.500000 + 0.419550i) q^{21} +(5.58512 - 2.03282i) q^{22} +(0.492726 + 2.79439i) q^{23} +(0.326352 - 1.85083i) q^{24} +(-1.64543 - 2.84997i) q^{26} +(2.31908 - 4.01676i) q^{27} +(0.266044 - 0.223238i) q^{28} +(5.46064 - 4.58202i) q^{29} +(-1.52094 - 2.63435i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-1.93969 + 11.0005i) q^{33} +(-0.960637 - 5.44804i) q^{34} +(0.407604 + 0.342020i) q^{36} -1.82295 q^{37} +(-4.07398 - 1.55007i) q^{38} +6.18479 q^{39} +(6.41147 - 2.33359i) q^{41} +(0.113341 + 0.642788i) q^{42} +(-0.0923963 + 0.524005i) q^{43} +(5.58512 + 2.03282i) q^{44} +(-1.41875 + 2.45734i) q^{46} +(3.56418 - 2.99070i) q^{47} +(1.43969 - 1.20805i) q^{48} +(3.43969 - 5.95772i) q^{49} +(9.76991 + 3.55596i) q^{51} +(0.571452 - 3.24086i) q^{52} +(-0.539363 - 3.05888i) q^{53} +(4.35844 - 1.58634i) q^{54} +0.347296 q^{56} +(6.35117 - 5.17420i) q^{57} +7.12836 q^{58} +(-2.10741 - 1.76833i) q^{59} +(-2.14156 - 12.1454i) q^{61} +(0.528218 - 2.99568i) q^{62} +(-0.173648 - 0.0632028i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-8.55690 + 7.18009i) q^{66} +(-3.86231 + 3.24086i) q^{67} +(2.76604 - 4.79093i) q^{68} +(-2.66637 - 4.61830i) q^{69} +(-2.26991 + 12.8733i) q^{71} +(0.0923963 + 0.524005i) q^{72} +(-2.06670 + 0.752219i) q^{73} +(-1.39646 - 1.17177i) q^{74} +(-2.12449 - 3.80612i) q^{76} -2.06418 q^{77} +(4.73783 + 3.97551i) q^{78} +(0.939693 - 0.342020i) q^{79} +(-1.79086 + 10.1565i) q^{81} +(6.41147 + 2.33359i) q^{82} +(-4.67752 - 8.10170i) q^{83} +(-0.326352 + 0.565258i) q^{84} +(-0.407604 + 0.342020i) q^{86} +(-6.69846 + 11.6021i) q^{87} +(2.97178 + 5.14728i) q^{88} +(-10.6493 - 3.87603i) q^{89} +(0.198463 + 1.12554i) q^{91} +(-2.66637 + 0.970481i) q^{92} +(4.37939 + 3.67474i) q^{93} +4.65270 q^{94} +1.87939 q^{96} +(-4.38326 - 3.67799i) q^{97} +(6.46451 - 2.35289i) q^{98} +(-0.549163 - 3.11446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9	\( 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 15 q^{13} + 6 q^{14} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{21} + 12 q^{22} - 15 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} - 3 q^{28} + 24 q^{29} - 6 q^{31} - 6 q^{33} + 3 q^{34} + 6 q^{36} + 30 q^{37} - 9 q^{38} + 30 q^{39} + 18 q^{41} - 6 q^{42} + 3 q^{43} + 12 q^{44} - 6 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 30 q^{51} + 3 q^{52} - 12 q^{53} + 18 q^{54} + 12 q^{57} + 6 q^{58} + 21 q^{59} - 21 q^{61} + 18 q^{62} - 3 q^{64} - 15 q^{66} + 9 q^{67} + 12 q^{68} + 3 q^{69} + 15 q^{71} - 3 q^{72} + 21 q^{73} - 18 q^{74} + 6 q^{77} + 9 q^{78} + 21 q^{81} + 18 q^{82} - 3 q^{83} - 3 q^{84} - 6 q^{86} - 12 q^{87} + 3 q^{88} - 24 q^{89} - 27 q^{91} + 3 q^{92} + 15 q^{93} + 30 q^{94} + 9 q^{97} + 6 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 15 * q^13 + 6 * q^14 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^21 + 12 * q^22 - 15 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 - 3 * q^28 + 24 * q^29 - 6 * q^31 - 6 * q^33 + 3 * q^34 + 6 * q^36 + 30 * q^37 - 9 * q^38 + 30 * q^39 + 18 * q^41 - 6 * q^42 + 3 * q^43 + 12 * q^44 - 6 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 30 * q^51 + 3 * q^52 - 12 * q^53 + 18 * q^54 + 12 * q^57 + 6 * q^58 + 21 * q^59 - 21 * q^61 + 18 * q^62 - 3 * q^64 - 15 * q^66 + 9 * q^67 + 12 * q^68 + 3 * q^69 + 15 * q^71 - 3 * q^72 + 21 * q^73 - 18 * q^74 + 6 * q^77 + 9 * q^78 + 21 * q^81 + 18 * q^82 - 3 * q^83 - 3 * q^84 - 6 * q^86 - 12 * q^87 + 3 * q^88 - 24 * q^89 - 27 * q^91 + 3 * q^92 + 15 * q^93 + 30 * q^94 + 9 * q^97 + 6 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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