LMFDB - Embedded newform 315.2.l.c.121.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.11
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.699049 q^{2} +(-1.56820 + 0.735367i) q^{3} -1.51133 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.09625 + 0.514057i) q^{6} +(2.62064 - 0.363625i) q^{7} -2.45459 q^{8} +(1.91847 - 2.30640i) q^{9} +O(q^{10})$	\(q+0.699049 q^{2} +(-1.56820 + 0.735367i) q^{3} -1.51133 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.09625 + 0.514057i) q^{6} +(2.62064 - 0.363625i) q^{7} -2.45459 q^{8} +(1.91847 - 2.30640i) q^{9} +(-0.349525 - 0.605394i) q^{10} +(1.91912 - 3.32401i) q^{11} +(2.37006 - 1.11138i) q^{12} +(2.28027 - 3.94954i) q^{13} +(1.83196 - 0.254192i) q^{14} +(1.42094 + 0.990413i) q^{15} +1.30678 q^{16} +(2.93173 + 5.07790i) q^{17} +(1.34111 - 1.61228i) q^{18} +(0.386961 - 0.670236i) q^{19} +(0.755665 + 1.30885i) q^{20} +(-3.84228 + 2.49737i) q^{21} +(1.34156 - 2.32364i) q^{22} +(-3.45266 - 5.98018i) q^{23} +(3.84928 - 1.80503i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.59402 - 2.76092i) q^{26} +(-1.31249 + 5.02766i) q^{27} +(-3.96066 + 0.549558i) q^{28} +(-3.95301 - 6.84682i) q^{29} +(0.993309 + 0.692347i) q^{30} -4.03789 q^{31} +5.82269 q^{32} +(-0.565184 + 6.62395i) q^{33} +(2.04942 + 3.54970i) q^{34} +(-1.62523 - 2.08773i) q^{35} +(-2.89944 + 3.48573i) q^{36} +(4.23407 - 7.33362i) q^{37} +(0.270505 - 0.468528i) q^{38} +(-0.671544 + 7.87048i) q^{39} +(1.22730 + 2.12574i) q^{40} +(-1.60838 + 2.78579i) q^{41} +(-2.68594 + 1.74578i) q^{42} +(4.19469 + 7.26541i) q^{43} +(-2.90042 + 5.02367i) q^{44} +(-2.95663 - 0.508246i) q^{45} +(-2.41358 - 4.18044i) q^{46} -3.33927 q^{47} +(-2.04929 + 0.960963i) q^{48} +(6.73555 - 1.90586i) q^{49} +(-0.349525 + 0.605394i) q^{50} +(-8.33164 - 5.80724i) q^{51} +(-3.44624 + 5.96906i) q^{52} +(1.32630 + 2.29721i) q^{53} +(-0.917494 + 3.51458i) q^{54} -3.83823 q^{55} +(-6.43261 + 0.892551i) q^{56} +(-0.113961 + 1.33562i) q^{57} +(-2.76335 - 4.78626i) q^{58} -6.73956 q^{59} +(-2.14752 - 1.49684i) q^{60} +7.01278 q^{61} -2.82268 q^{62} +(4.18897 - 6.74185i) q^{63} +1.45678 q^{64} -4.56054 q^{65} +(-0.395091 + 4.63046i) q^{66} +14.5703 q^{67} +(-4.43081 - 7.67439i) q^{68} +(9.81207 + 6.83912i) q^{69} +(-1.13612 - 1.45943i) q^{70} -9.67100 q^{71} +(-4.70906 + 5.66126i) q^{72} +(7.00941 + 12.1407i) q^{73} +(2.95982 - 5.12656i) q^{74} +(0.147251 - 1.72578i) q^{75} +(-0.584826 + 1.01295i) q^{76} +(3.82063 - 9.40888i) q^{77} +(-0.469442 + 5.50185i) q^{78} -13.3858 q^{79} +(-0.653390 - 1.13171i) q^{80} +(-1.63894 - 8.84951i) q^{81} +(-1.12433 + 1.94740i) q^{82} +(0.442527 + 0.766479i) q^{83} +(5.80696 - 3.77435i) q^{84} +(2.93173 - 5.07790i) q^{85} +(2.93229 + 5.07888i) q^{86} +(11.2340 + 7.83023i) q^{87} +(-4.71065 + 8.15908i) q^{88} +(0.950003 - 1.64545i) q^{89} +(-2.06683 - 0.355289i) q^{90} +(4.53962 - 11.1795i) q^{91} +(5.21811 + 9.03803i) q^{92} +(6.33220 - 2.96933i) q^{93} -2.33431 q^{94} -0.773922 q^{95} +(-9.13111 + 4.28181i) q^{96} +(-3.07725 - 5.32996i) q^{97} +(4.70848 - 1.33229i) q^{98} +(-3.98471 - 10.8033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.699049			0.494302			0.247151	−	0.968977i	$-0.420506\pi$
$2$	0.699049			0.494302			0.247151	+	0.968977i	$0.420506\pi$
$3$	−1.56820	+	0.735367i	−0.905398	+	0.424564i
$3$	−1.56820	+	0.735367i	−0.905398	+	0.424564i
$4$	−1.51133			−0.755665
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.09625	+	0.514057i	−0.447540	+	0.209863i
$7$	2.62064	−	0.363625i	0.990510	−	0.137437i
$7$	2.62064	−	0.363625i	0.990510	−	0.137437i
$8$	−2.45459			−0.867829
$9$	1.91847	−	2.30640i	0.639490	−	0.768799i
$10$	−0.349525	−	0.605394i	−0.110529	−	0.191442i
$11$	1.91912	−	3.32401i	0.578635	−	1.00223i	−0.417001	−	0.908906i	$-0.636919\pi$
$11$	1.91912	−	3.32401i	0.578635	−	1.00223i	0.995636	−	0.0933197i	$-0.0297479\pi$
$12$	2.37006	−	1.11138i	0.684178	−	0.320828i
$13$	2.28027	−	3.94954i	0.632432	−	1.09541i	−0.354621	−	0.935010i	$-0.615390\pi$
$13$	2.28027	−	3.94954i	0.632432	−	1.09541i	0.987053	−	0.160395i	$-0.0512767\pi$
$14$	1.83196	−	0.254192i	0.489612	−	0.0679356i
$15$	1.42094	+	0.990413i	0.366886	+	0.255724i
$16$	1.30678			0.326695
$17$	2.93173	+	5.07790i	0.711048	+	1.23157i	0.964464	+	0.264214i	$0.0851126\pi$
$17$	2.93173	+	5.07790i	0.711048	+	1.23157i	−0.253416	+	0.967357i	$0.581554\pi$
$18$	1.34111	−	1.61228i	0.316102	−	0.380019i
$19$	0.386961	−	0.670236i	0.0887750	−	0.153763i	−0.818219	−	0.574907i	$-0.805038\pi$
$19$	0.386961	−	0.670236i	0.0887750	−	0.153763i	0.906994	+	0.421144i	$0.138371\pi$
$20$	0.755665	+	1.30885i	0.168972	+	0.292668i
$21$	−3.84228	+	2.49737i	−0.838455	+	0.544971i
$22$	1.34156	−	2.32364i	0.286021	−	0.495403i
$23$	−3.45266	−	5.98018i	−0.719929	−	1.24695i	−0.961027	−	0.276453i	$-0.910841\pi$
$23$	−3.45266	−	5.98018i	−0.719929	−	1.24695i	0.241098	−	0.970501i	$-0.422492\pi$
$24$	3.84928	−	1.80503i	0.785731	−	0.368449i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.59402	−	2.76092i	0.312613	−	0.541461i
$27$	−1.31249	+	5.02766i	−0.252589	+	0.967574i
$28$	−3.96066	+	0.549558i	−0.748494	+	0.103857i
$29$	−3.95301	−	6.84682i	−0.734056	−	1.27142i	−0.955136	−	0.296167i	$-0.904292\pi$
$29$	−3.95301	−	6.84682i	−0.734056	−	1.27142i	0.221080	−	0.975256i	$-0.429042\pi$
$30$	0.993309	+	0.692347i	0.181353	+	0.126405i
$31$	−4.03789			−0.725226			−0.362613	−	0.931940i	$-0.618115\pi$
$31$	−4.03789			−0.725226			−0.362613	+	0.931940i	$0.618115\pi$
$32$	5.82269			1.02932
$33$	−0.565184	+	6.62395i	−0.0983859	+	1.15308i
$34$	2.04942	+	3.54970i	0.351473	+	0.608769i
$35$	−1.62523	−	2.08773i	−0.274714	−	0.352891i
$36$	−2.89944	+	3.48573i	−0.483241	+	0.580955i
$37$	4.23407	−	7.33362i	0.696076	−	1.20564i	−0.273740	−	0.961804i	$-0.588261\pi$
$37$	4.23407	−	7.33362i	0.696076	−	1.20564i	0.969816	−	0.243836i	$-0.0784059\pi$
$38$	0.270505	−	0.468528i	0.0438817	−	0.0760053i
$39$	−0.671544	+	7.87048i	−0.107533	+	1.26029i
$40$	1.22730	+	2.12574i	0.194053	+	0.336109i
$41$	−1.60838	+	2.78579i	−0.251186	+	0.435067i	−0.963853	−	0.266436i	$-0.914154\pi$
$41$	−1.60838	+	2.78579i	−0.251186	+	0.435067i	0.712667	+	0.701503i	$0.247487\pi$
$42$	−2.68594	+	1.74578i	−0.414450	+	0.269380i
$43$	4.19469	+	7.26541i	0.639683	+	1.10796i	0.985502	+	0.169663i	$0.0542679\pi$
$43$	4.19469	+	7.26541i	0.639683	+	1.10796i	−0.345819	+	0.938301i	$0.612399\pi$
$44$	−2.90042	+	5.02367i	−0.437255	+	0.757347i
$45$	−2.95663	−	0.508246i	−0.440749	−	0.0757649i
$46$	−2.41358	−	4.18044i	−0.355863	−	0.616372i
$47$	−3.33927			−0.487082			−0.243541	−	0.969891i	$-0.578309\pi$
$47$	−3.33927			−0.487082			−0.243541	+	0.969891i	$0.578309\pi$
$48$	−2.04929	+	0.960963i	−0.295789	+	0.138703i
$49$	6.73555	−	1.90586i	0.962222	−	0.272266i
$50$	−0.349525	+	0.605394i	−0.0494302	+	0.0856157i
$51$	−8.33164	−	5.80724i	−1.16666	−	0.813177i
$52$	−3.44624	+	5.96906i	−0.477907	+	0.827760i
$53$	1.32630	+	2.29721i	0.182181	+	0.315546i	0.942623	−	0.333859i	$-0.108351\pi$
$53$	1.32630	+	2.29721i	0.182181	+	0.315546i	−0.760442	+	0.649406i	$0.775018\pi$
$54$	−0.917494	+	3.51458i	−0.124855	+	0.478274i
$55$	−3.83823			−0.517547
$56$	−6.43261	+	0.892551i	−0.859594	+	0.119272i
$57$	−0.113961	+	1.33562i	−0.0150945	+	0.176907i
$58$	−2.76335	−	4.78626i	−0.362846	−	0.628467i
$59$	−6.73956			−0.877416			−0.438708	−	0.898630i	$-0.644564\pi$
$59$	−6.73956			−0.877416			−0.438708	+	0.898630i	$0.644564\pi$
$60$	−2.14752	−	1.49684i	−0.277243	−	0.193241i
$61$	7.01278			0.897894			0.448947	−	0.893558i	$-0.351799\pi$
$61$	7.01278			0.897894			0.448947	+	0.893558i	$0.351799\pi$
$62$	−2.82268			−0.358481
$63$	4.18897	−	6.74185i	0.527760	−	0.849393i
$64$	1.45678			0.182098
$65$	−4.56054			−0.565665
$66$	−0.395091	+	4.63046i	−0.0486324	+	0.569971i
$67$	14.5703			1.78004			0.890022	−	0.455918i	$-0.150689\pi$
$67$	14.5703			1.78004			0.890022	+	0.455918i	$0.150689\pi$
$68$	−4.43081	−	7.67439i	−0.537315	−	0.930656i
$69$	9.81207	+	6.83912i	1.18123	+	0.823333i
$70$	−1.13612	−	1.45943i	−0.135792	−	0.174435i
$71$	−9.67100			−1.14774			−0.573868	−	0.818948i	$-0.694558\pi$
$71$	−9.67100			−1.14774			−0.573868	+	0.818948i	$0.694558\pi$
$72$	−4.70906	+	5.66126i	−0.554969	+	0.667186i
$73$	7.00941	+	12.1407i	0.820389	+	1.42096i	0.905393	+	0.424575i	$0.139577\pi$
$73$	7.00941	+	12.1407i	0.820389	+	1.42096i	−0.0850031	+	0.996381i	$0.527090\pi$
$74$	2.95982	−	5.12656i	0.344072	−	0.595950i
$75$	0.147251	−	1.72578i	0.0170031	−	0.199276i
$76$	−0.584826	+	1.01295i	−0.0670842	+	0.116193i
$77$	3.82063	−	9.40888i	0.435401	−	1.07224i
$78$	−0.469442	+	5.50185i	−0.0531538	+	0.622962i
$79$	−13.3858			−1.50602			−0.753009	−	0.658010i	$-0.771398\pi$
$79$	−13.3858			−1.50602			−0.753009	+	0.658010i	$0.771398\pi$
$80$	−0.653390	−	1.13171i	−0.0730513	−	0.126529i
$81$	−1.63894	−	8.84951i	−0.182104	−	0.983279i
$82$	−1.12433	+	1.94740i	−0.124162	+	0.215055i
$83$	0.442527	+	0.766479i	0.0485736	+	0.0841320i	0.889290	−	0.457344i	$-0.151199\pi$
$83$	0.442527	+	0.766479i	0.0485736	+	0.0841320i	−0.840716	+	0.541476i	$0.817866\pi$
$84$	5.80696	−	3.77435i	0.633591	−	0.411816i
$85$	2.93173	−	5.07790i	0.317990	−	0.550776i
$86$	2.93229	+	5.07888i	0.316197	+	0.547669i
$87$	11.2340	+	7.83023i	1.20441	+	0.839489i
$88$	−4.71065	+	8.15908i	−0.502157	+	0.869761i
$89$	0.950003	−	1.64545i	0.100700	−	0.174418i	−0.811273	−	0.584667i	$-0.801225\pi$
$89$	0.950003	−	1.64545i	0.100700	−	0.174418i	0.911973	+	0.410250i	$0.134558\pi$
$90$	−2.06683	−	0.355289i	−0.217863	−	0.0374507i
$91$	4.53962	−	11.1795i	0.475881	−	1.17193i
$92$	5.21811	+	9.03803i	0.544025	+	0.942279i
$93$	6.33220	−	2.96933i	0.656618	−	0.307905i
$94$	−2.33431			−0.240766
$95$	−0.773922			−0.0794028
$96$	−9.13111	+	4.28181i	−0.931940	+	0.437011i
$97$	−3.07725	−	5.32996i	−0.312448	−	0.541176i	0.666444	−	0.745555i	$-0.267816\pi$
$97$	−3.07725	−	5.32996i	−0.312448	−	0.541176i	−0.978892	+	0.204380i	$0.934482\pi$
$98$	4.70848	−	1.33229i	0.475629	−	0.134582i
$99$	−3.98471	−	10.8033i	−0.400479	−	1.08577i
$100$	0.755665	−	1.30885i	0.0755665	−	0.130885i
$101$	0.772469	−	1.33795i	0.0768635	−	0.133131i	−0.825032	−	0.565087i	$-0.808843\pi$
$101$	0.772469	−	1.33795i	0.0768635	−	0.133131i	0.901895	+	0.431955i	$0.142176\pi$
$102$	−5.82423	−	4.05955i	−0.576684	−	0.401955i
$103$	5.90175	+	10.2221i	0.581516	+	1.00722i	0.995300	+	0.0968405i	$0.0308737\pi$
$103$	5.90175	+	10.2221i	0.581516	+	1.00722i	−0.413784	+	0.910375i	$0.635793\pi$
$104$	−5.59713	+	9.69451i	−0.548843	+	0.950625i
$105$	4.08393	+	2.07883i	0.398551	+	0.202873i
$106$	0.927146	+	1.60586i	0.0900524	+	0.155975i
$107$	−1.00776	+	1.74549i	−0.0974239	+	0.168743i	−0.910618	−	0.413250i	$-0.864394\pi$
$107$	−1.00776	+	1.74549i	−0.0974239	+	0.168743i	0.813194	+	0.581993i	$0.197727\pi$
$108$	1.98360	−	7.59846i	0.190872	−	0.731162i
$109$	−0.193245	−	0.334710i	−0.0185095	−	0.0320594i	0.856622	−	0.515944i	$-0.172559\pi$
$109$	−0.193245	−	0.334710i	−0.0185095	−	0.0320594i	−0.875132	+	0.483885i	$0.839225\pi$
$110$	−2.68311			−0.255825
$111$	−1.24694	+	14.6141i	−0.118355	+	1.38711i
$112$	3.42461	−	0.475178i	0.323595	−	0.0449001i
$113$	3.98925	−	6.90958i	0.375277	−	0.649998i	−0.615092	−	0.788456i	$-0.710881\pi$
$113$	3.98925	−	6.90958i	0.375277	−	0.649998i	0.990368	+	0.138457i	$0.0442144\pi$
$114$	−0.0796643	+	0.933664i	−0.00746124	+	0.0874456i
$115$	−3.45266	+	5.98018i	−0.321962	+	0.557655i
$116$	5.97431	+	10.3478i	0.554701	+	0.960770i
$117$	−4.73458	−	12.8363i	−0.437712	−	1.18671i
$118$	−4.71128			−0.433709
$119$	9.52947	+	12.2413i	0.873565	+	1.12216i
$120$	−3.48784	−	2.43106i	−0.318395	−	0.221924i
$121$	−1.86602	−	3.23203i	−0.169638	−	0.293821i
$122$	4.90228			0.443831
$123$	0.473670	−	5.55141i	0.0427094	−	0.500554i
$124$	6.10258			0.548028
$125$	1.00000			0.0894427
$126$	2.92829	−	4.71288i	0.260873	−	0.419857i
$127$	−1.89590			−0.168234			−0.0841170	−	0.996456i	$-0.526807\pi$
$127$	−1.89590			−0.168234			−0.0841170	+	0.996456i	$0.526807\pi$
$128$	−10.6270			−0.939304
$129$	−11.9208	−	8.30894i	−1.04957	−	0.731562i
$130$	−3.18804			−0.279609
$131$	3.66944	+	6.35565i	0.320600	+	0.555296i	0.980612	−	0.195959i	$-0.0627820\pi$
$131$	3.66944	+	6.35565i	0.320600	+	0.555296i	−0.660012	+	0.751255i	$0.729449\pi$
$132$	0.854180	−	10.0110i	0.0743468	−	0.871343i
$133$	0.770373	−	1.89716i	0.0667998	−	0.164505i
$134$	10.1853			0.879880
$135$	5.01033	−	1.37718i	0.431220	−	0.118529i
$136$	−7.19620	−	12.4642i	−0.617069	−	1.06879i
$137$	4.72601	−	8.18568i	0.403770	−	0.699350i	−0.590407	−	0.807105i	$-0.701033\pi$
$137$	4.72601	−	8.18568i	0.403770	−	0.699350i	0.994177	+	0.107755i	$0.0343663\pi$
$138$	6.85912	+	4.78088i	0.583887	+	0.406975i
$139$	3.28976	−	5.69803i	0.279034	−	0.483301i	−0.692111	−	0.721791i	$-0.743319\pi$
$139$	3.28976	−	5.69803i	0.279034	−	0.483301i	0.971145	+	0.238490i	$0.0766525\pi$
$140$	2.45626	+	3.15525i	0.207592	+	0.266668i
$141$	5.23662	−	2.45559i	0.441003	−	0.206798i
$142$	−6.76050			−0.567329
$143$	−8.75220	−	15.1593i	−0.731896	−	1.26768i
$144$	2.50702	−	3.01396i	0.208918	−	0.251163i
$145$	−3.95301	+	6.84682i	−0.328280	+	0.568597i
$146$	4.89992	+	8.48691i	0.405520	+	0.702382i
$147$	−9.16115	+	7.94187i	−0.755599	+	0.655034i
$148$	−6.39908	+	11.0835i	−0.526001	+	0.911060i
$149$	6.42839	+	11.1343i	0.526634	+	0.912158i	0.999518	+	0.0310329i	$0.00987967\pi$
$149$	6.42839	+	11.1343i	0.526634	+	0.912158i	−0.472884	+	0.881125i	$0.656787\pi$
$150$	0.102936	−	1.20640i	0.00840467	−	0.0985025i
$151$	−3.36398	+	5.82658i	−0.273756	+	0.474160i	−0.969821	−	0.243819i	$-0.921600\pi$
$151$	−3.36398	+	5.82658i	−0.273756	+	0.474160i	0.696064	+	0.717980i	$0.254933\pi$
$152$	−0.949832	+	1.64516i	−0.0770415	+	0.133440i
$153$	17.3361	+	2.98008i	1.40154	+	0.240925i
$154$	2.67081	−	6.57727i	0.215220	−	0.530011i
$155$	2.01894	+	3.49691i	0.162166	+	0.280879i
$156$	1.01492	−	11.8949i	0.0812590	−	0.952354i
$157$	−12.1116			−0.966614			−0.483307	−	0.875451i	$-0.660564\pi$
$157$	−12.1116			−0.966614			−0.483307	+	0.875451i	$0.660564\pi$
$158$	−9.35732			−0.744428
$159$	−3.76918	−	2.62716i	−0.298916	−	0.208348i
$160$	−2.91134	−	5.04260i	−0.230162	−	0.398652i
$161$	−11.2227	−	14.4164i	−0.884475	−	1.13618i
$162$	−1.14570	−	6.18624i	−0.0900145	−	0.486037i
$163$	−8.11477	+	14.0552i	−0.635598	+	1.10089i	0.350790	+	0.936454i	$0.385913\pi$
$163$	−8.11477	+	14.0552i	−0.635598	+	1.10089i	−0.986388	+	0.164434i	$0.947420\pi$
$164$	2.43079	−	4.21025i	0.189813	−	0.328765i
$165$	6.01910	−	2.82251i	0.468586	−	0.219732i
$166$	0.309348	+	0.535806i	0.0240101	+	0.0415866i
$167$	−8.60497	+	14.9042i	−0.665872	+	1.15332i	0.313176	+	0.949695i	$0.398607\pi$
$167$	−8.60497	+	14.9042i	−0.665872	+	1.15332i	−0.979048	+	0.203630i	$0.934726\pi$
$168$	9.43124	−	6.13003i	0.727636	−	0.472942i
$169$	−3.89924	−	6.75368i	−0.299942	−	0.519514i
$170$	2.04942	−	3.54970i	0.157183	−	0.272250i
$171$	−0.803458	−	2.17832i	−0.0614419	−	0.166580i
$172$	−6.33956	−	10.9804i	−0.483387	−	0.837250i
$173$	16.0306			1.21878			0.609390	−	0.792870i	$-0.291414\pi$
$173$	16.0306			1.21878			0.609390	+	0.792870i	$0.291414\pi$
$174$	7.85313	+	5.47372i	0.595344	+	0.414961i
$175$	−0.995414	+	2.45136i	−0.0752462	+	0.185305i
$176$	2.50786	−	4.34375i	0.189037	−	0.327422i
$177$	10.5689	−	4.95605i	0.794410	−	0.372519i
$178$	0.664099	−	1.15025i	0.0497763	−	0.0862151i
$179$	4.60018	+	7.96775i	0.343834	+	0.595538i	0.985141	−	0.171746i	$-0.0549410\pi$
$179$	4.60018	+	7.96775i	0.343834	+	0.595538i	−0.641307	+	0.767284i	$0.721608\pi$
$180$	4.46845	+	0.768128i	0.333059	+	0.0572529i
$181$	−5.76356			−0.428402			−0.214201	−	0.976790i	$-0.568715\pi$
$181$	−5.76356			−0.428402			−0.214201	+	0.976790i	$0.568715\pi$
$182$	3.17342	−	7.81502i	0.235229	−	0.579288i
$183$	−10.9974	+	5.15697i	−0.812952	+	0.381214i
$184$	8.47487	+	14.6789i	0.624776	+	1.08214i
$185$	−8.46813			−0.622590
$186$	4.42652	−	2.07571i	0.324568	−	0.152198i
$187$	22.5053			1.64575
$188$	5.04674			0.368071
$189$	−1.61138	+	13.6530i	−0.117211	+	0.993107i
$190$	−0.541010			−0.0392490
$191$	2.30298			0.166638			0.0833190	−	0.996523i	$-0.473448\pi$
$191$	2.30298			0.166638			0.0833190	+	0.996523i	$0.473448\pi$
$192$	−2.28452	+	1.07127i	−0.164871	+	0.0773122i
$193$	19.9528			1.43623			0.718117	−	0.695922i	$-0.245004\pi$
$193$	19.9528			1.43623			0.718117	+	0.695922i	$0.245004\pi$
$194$	−2.15115	−	3.72590i	−0.154444	−	0.267504i
$195$	7.15181	−	3.35367i	0.512152	−	0.240161i
$196$	−10.1796	+	2.88039i	−0.727118	+	0.205742i
$197$	0.261164			0.0186071			0.00930357	−	0.999957i	$-0.497039\pi$
$197$	0.261164			0.0186071			0.00930357	+	0.999957i	$0.497039\pi$
$198$	−2.78551	−	7.55201i	−0.197957	−	0.536698i
$199$	−1.81496	−	3.14360i	−0.128659	−	0.222844i	0.794498	−	0.607266i	$-0.207734\pi$
$199$	−1.81496	−	3.14360i	−0.128659	−	0.222844i	−0.923157	+	0.384423i	$0.874401\pi$
$200$	1.22730	−	2.12574i	0.0867829	−	0.150312i
$201$	−22.8491	+	10.7145i	−1.61165	+	0.755743i
$202$	0.539993	−	0.935296i	0.0379938	−	0.0658072i
$203$	−12.8491	−	16.5057i	−0.901831	−	1.15847i
$204$	12.5919	+	8.77666i	0.881607	+	0.614489i
$205$	3.21675			0.224668
$206$	4.12561	+	7.14577i	0.287445	+	0.497869i
$207$	−20.4165	−	3.50960i	−1.41904	−	0.243934i
$208$	2.97981	−	5.16118i	0.206613	−	0.357864i
$209$	−1.48525	−	2.57252i	−0.102737	−	0.177945i
$210$	2.85487	+	1.45320i	0.197004	+	0.100281i
$211$	2.25267	−	3.90174i	0.155080	−	0.268607i	−0.778008	−	0.628254i	$-0.783770\pi$
$211$	2.25267	−	3.90174i	0.155080	−	0.268607i	0.933088	+	0.359648i	$0.117103\pi$
$212$	−2.00447	−	3.47185i	−0.137668	−	0.238447i
$213$	15.1660	−	7.11173i	1.03916	−	0.487288i
$214$	−0.704474	+	1.22018i	−0.0481569	+	0.0834101i
$215$	4.19469	−	7.26541i	0.286075	−	0.495497i
$216$	3.22162	−	12.3409i	0.219204	−	0.839689i
$217$	−10.5819	+	1.46828i	−0.718344	+	0.0996732i
$218$	−0.135088	−	0.233979i	−0.00914929	−	0.0158470i
$219$	−19.9200	−	13.8844i	−1.34607	−	0.938223i
$220$	5.80084			0.391092
$221$	26.7405			1.79876
$222$	−0.871674	+	10.2160i	−0.0585029	+	0.685653i
$223$	−5.85329	−	10.1382i	−0.391966	−	0.678904i	0.600743	−	0.799442i	$-0.294871\pi$
$223$	−5.85329	−	10.1382i	−0.391966	−	0.678904i	−0.992709	+	0.120538i	$0.961538\pi$
$224$	15.2592	−	2.11728i	1.01955	−	0.141466i
$225$	1.03816	+	2.81464i	0.0692109	+	0.187643i
$226$	2.78868	−	4.83013i	0.185500	−	0.321296i
$227$	−4.63759	+	8.03254i	−0.307808	+	0.533138i	−0.977882	−	0.209155i	$-0.932929\pi$
$227$	−4.63759	+	8.03254i	−0.307808	+	0.533138i	0.670075	+	0.742294i	$0.266262\pi$
$228$	0.172233	−	2.01856i	0.0114064	−	0.133683i
$229$	−8.45325	−	14.6415i	−0.558606	−	0.967534i	−0.997613	−	0.0690507i	$-0.978003\pi$
$229$	−8.45325	−	14.6415i	−0.558606	−	0.967534i	0.439007	−	0.898484i	$-0.355330\pi$
$230$	−2.41358	+	4.18044i	−0.159147	+	0.275650i
$231$	0.927487	+	17.5645i	0.0610242	+	1.15566i
$232$	9.70303	+	16.8061i	0.637035	+	1.10338i
$233$	−3.50083	+	6.06362i	−0.229347	+	0.397241i	−0.957615	−	0.288052i	$-0.906992\pi$
$233$	−3.50083	+	6.06362i	−0.229347	+	0.397241i	0.728268	+	0.685293i	$0.240326\pi$
$234$	−3.30970	−	8.97319i	−0.216362	−	0.586596i
$235$	1.66963	+	2.89189i	0.108915	+	0.188646i
$236$	10.1857			0.663033
$237$	20.9915	−	9.84346i	1.36355	−	0.639402i
$238$	6.66156	+	8.55728i	0.431805	+	0.554686i
$239$	−8.00452	+	13.8642i	−0.517769	+	0.896803i	0.482017	+	0.876162i	$0.339904\pi$
$239$	−8.00452	+	13.8642i	−0.517769	+	0.896803i	−0.999787	+	0.0206414i	$0.993429\pi$
$240$	1.85686	+	1.29425i	0.119860	+	0.0835437i
$241$	3.67731	−	6.36928i	0.236876	−	0.410282i	−0.722940	−	0.690911i	$-0.757210\pi$
$241$	3.67731	−	6.36928i	0.236876	−	0.410282i	0.959816	+	0.280629i	$0.0905431\pi$
$242$	−1.30444	−	2.25935i	−0.0838523	−	0.145236i
$243$	9.07781	+	12.6725i	0.582342	+	0.812944i
$244$	−10.5986			−0.678508
$245$	−5.01830	−	4.88023i	−0.320608	−	0.311786i
$246$	0.331119	−	3.88071i	0.0211114	−	0.247425i
$247$	−1.76475	−	3.05664i	−0.112288	−	0.194489i
$248$	9.91137			0.629373
$249$	−1.25761	−	0.876569i	−0.0796979	−	0.0555503i
$250$	0.699049			0.0442117
$251$	15.4784			0.976991			0.488495	−	0.872566i	$-0.337546\pi$
$251$	15.4784			0.976991			0.488495	+	0.872566i	$0.337546\pi$
$252$	−6.33091	+	10.1892i	−0.398810	+	0.641857i
$253$	−26.5042			−1.66631
$254$	−1.32533			−0.0831584
$255$	−0.863400	+	10.1190i	−0.0540682	+	0.633678i
$256$	−10.3424			−0.646398
$257$	0.177951	+	0.308220i	0.0111003	+	0.0192262i	0.871522	−	0.490356i	$-0.163133\pi$
$257$	0.177951	+	0.308220i	0.0111003	+	0.0192262i	−0.860422	+	0.509582i	$0.829800\pi$
$258$	−8.33324	−	5.80836i	−0.518805	−	0.361613i
$259$	8.42930	−	20.7584i	0.523771	−	1.28987i
$260$	6.89248			0.427453
$261$	−23.3752	−	4.01821i	−1.44689	−	0.248721i
$262$	2.56512	+	4.44291i	0.158473	+	0.274484i
$263$	−9.58278	+	16.5979i	−0.590900	+	1.02347i	0.403212	+	0.915107i	$0.367894\pi$
$263$	−9.58278	+	16.5979i	−0.590900	+	1.02347i	−0.994112	+	0.108362i	$0.965440\pi$
$264$	1.38730	−	16.2591i	0.0853822	−	1.00068i
$265$	1.32630	−	2.29721i	0.0814737	−	0.141117i
$266$	0.538528	−	1.32621i	0.0330193	−	0.0813150i
$267$	−0.279778	+	3.27899i	−0.0171221	+	0.200671i
$268$	−22.0205			−1.34512
$269$	−4.18841	−	7.25453i	−0.255372	−	0.442317i	0.709625	−	0.704580i	$-0.248865\pi$
$269$	−4.18841	−	7.25453i	−0.255372	−	0.442317i	−0.964996	+	0.262263i	$0.915531\pi$
$270$	3.50246	−	0.962718i	0.213153	−	0.0585891i
$271$	−0.0397516	+	0.0688517i	−0.00241474	+	0.00418244i	−0.867230	−	0.497907i	$-0.834102\pi$
$271$	−0.0397516	+	0.0688517i	−0.00241474	+	0.00418244i	0.864816	+	0.502090i	$0.167435\pi$
$272$	3.83113	+	6.63570i	0.232296	+	0.402349i
$273$	1.10203	+	20.8699i	0.0666977	+	1.26311i
$274$	3.30371	−	5.72219i	0.199584	−	0.345690i
$275$	1.91912	+	3.32401i	0.115727	+	0.200445i
$276$	−14.8293	−	10.3362i	−0.892618	−	0.622164i
$277$	−10.6937	+	18.5221i	−0.642524	+	1.11288i	0.342343	+	0.939575i	$0.388779\pi$
$277$	−10.6937	+	18.5221i	−0.642524	+	1.11288i	−0.984867	+	0.173310i	$0.944554\pi$
$278$	2.29970	−	3.98320i	0.137927	−	0.238897i
$279$	−7.74657	+	9.31297i	−0.463775	+	0.557553i
$280$	3.98928	+	5.12453i	0.238405	+	0.306249i
$281$	2.12078	+	3.67329i	0.126515	+	0.219130i	0.922324	−	0.386417i	$-0.126288\pi$
$281$	2.12078	+	3.67329i	0.126515	+	0.219130i	−0.795809	+	0.605547i	$0.792954\pi$
$282$	3.66066	−	1.71658i	0.217989	−	0.102221i
$283$	−5.98783			−0.355940			−0.177970	−	0.984036i	$-0.556953\pi$
$283$	−5.98783			−0.355940			−0.177970	+	0.984036i	$0.556953\pi$
$284$	14.6161			0.867305
$285$	1.21366	−	0.569117i	0.0718911	−	0.0337116i
$286$	−6.11822	−	10.5971i	−0.361778	−	0.626617i
$287$	−3.20200	+	7.88541i	−0.189008	+	0.465461i
$288$	11.1707	−	13.4294i	0.658237	−	0.791337i
$289$	−8.69005	+	15.0516i	−0.511180	+	0.885389i
$290$	−2.76335	+	4.78626i	−0.162269	+	0.281059i
$291$	8.74521	+	6.09551i	0.512653	+	0.357325i
$292$	−10.5935	−	18.3485i	−0.619940	−	1.07377i
$293$	−6.26949	+	10.8591i	−0.366267	+	0.634393i	−0.988979	−	0.148058i	$-0.952698\pi$
$293$	−6.26949	+	10.8591i	−0.366267	+	0.634393i	0.622711	+	0.782452i	$0.286031\pi$
$294$	−6.40409	+	5.55176i	−0.373494	+	0.323785i
$295$	3.36978	+	5.83663i	0.196196	+	0.339822i
$296$	−10.3929	+	18.0010i	−0.604076	+	1.04629i
$297$	14.1932	+	14.0114i	0.823571	+	0.813023i
$298$	4.49376	+	7.78342i	0.260317	+	0.450882i
$299$	−31.4919			−1.82123
$300$	−0.222545	+	2.60822i	−0.0128486	+	0.150586i
$301$	13.6347	+	17.5148i	0.785889	+	1.00953i
$302$	−2.35158	+	4.07306i	−0.135318	+	0.234378i
$303$	−0.227494	+	2.66622i	−0.0130692	+	0.153170i
$304$	0.505673	−	0.875852i	0.0290024	−	0.0502336i
$305$	−3.50639	−	6.07324i	−0.200775	−	0.347753i
$306$	12.1188	+	2.08322i	0.692784	+	0.119090i
$307$	−21.0767			−1.20291			−0.601455	−	0.798906i	$-0.705412\pi$
$307$	−21.0767			−1.20291			−0.601455	+	0.798906i	$0.705412\pi$
$308$	−5.77423	+	14.2199i	−0.329017	+	0.810255i
$309$	−16.7721	−	11.6903i	−0.954131	−	0.665040i
$310$	1.41134	+	2.44451i	0.0801588	+	0.138839i
$311$	12.8347			0.727788			0.363894	−	0.931440i	$-0.381447\pi$
$311$	12.8347			0.727788			0.363894	+	0.931440i	$0.381447\pi$
$312$	1.64837	−	19.3188i	0.0933204	−	1.09371i
$313$	−14.8959			−0.841964			−0.420982	−	0.907069i	$-0.638315\pi$
$313$	−14.8959			−0.841964			−0.420982	+	0.907069i	$0.638315\pi$
$314$	−8.46663			−0.477799
$315$	−7.93310	−	0.256826i	−0.446979	−	0.0144705i
$316$	20.2303			1.13805
$317$	34.2397			1.92309			0.961545	−	0.274647i	$-0.0885609\pi$
$317$	34.2397			1.92309			0.961545	+	0.274647i	$0.0885609\pi$
$318$	−2.63484	−	1.83652i	−0.147755	−	0.102987i
$319$	−30.3452			−1.69900
$320$	−0.728391	−	1.26161i	−0.0407183	−	0.0705262i
$321$	0.296788	−	3.47835i	0.0165651	−	0.194142i
$322$	−7.84524	−	10.0778i	−0.437198	−	0.561614i
$323$	4.53786			0.252493
$324$	2.47698	+	13.3745i	0.137610	+	0.743030i
$325$	2.28027	+	3.94954i	0.126486	+	0.219081i
$326$	−5.67262	+	9.82527i	−0.314177	+	0.544171i
$327$	0.549180	+	0.382785i	0.0303697	+	0.0211680i
$328$	3.94791	−	6.83798i	0.217987	−	0.377564i
$329$	−8.75103	+	1.21424i	−0.482460	+	0.0669433i
$330$	4.20764	−	1.97307i	0.231623	−	0.108614i
$331$	33.1762			1.82353			0.911764	−	0.410716i	$-0.134721\pi$
$331$	33.1762			1.82353			0.911764	+	0.410716i	$0.134721\pi$
$332$	−0.668804	−	1.15840i	−0.0367054	−	0.0635756i
$333$	−8.79131	−	23.8348i	−0.481761	−	1.30614i
$334$	−6.01529	+	10.4188i	−0.329142	+	0.570091i
$335$	−7.28514	−	12.6182i	−0.398030	−	0.689408i
$336$	−5.02102	+	3.26352i	−0.273919	+	0.178039i
$337$	−10.8821	+	18.8484i	−0.592786	+	1.02674i	0.401069	+	0.916048i	$0.368639\pi$
$337$	−10.8821	+	18.8484i	−0.592786	+	1.02674i	−0.993855	+	0.110688i	$0.964695\pi$
$338$	−2.72576	−	4.72116i	−0.148262	−	0.256797i
$339$	−1.17484	+	13.7691i	−0.0638086	+	0.747836i
$340$	−4.43081	+	7.67439i	−0.240294	+	0.416202i
$341$	−7.74918	+	13.4220i	−0.419641	+	0.726840i
$342$	−0.561656	−	1.52275i	−0.0303709	−	0.0823408i
$343$	16.9585	−	7.44381i	0.915671	−	0.401928i
$344$	−10.2962	−	17.8336i	−0.555136	−	0.961524i
$345$	1.01682	−	11.9171i	0.0547435	−	0.641593i
$346$	11.2061			0.602446
$347$	4.81946			0.258722			0.129361	−	0.991598i	$-0.458707\pi$
$347$	4.81946			0.258722			0.129361	+	0.991598i	$0.458707\pi$
$348$	−16.9783	−	11.8341i	−0.910133	−	0.634373i
$349$	3.26983	+	5.66352i	0.175030	+	0.303161i	0.940172	−	0.340701i	$-0.110664\pi$
$349$	3.26983	+	5.66352i	0.175030	+	0.303161i	−0.765142	+	0.643862i	$0.777331\pi$
$350$	−0.695843	+	1.71362i	−0.0371944	+	0.0915968i
$351$	16.8641	+	16.6481i	0.900140	+	0.888612i
$352$	11.1744	−	19.3547i	0.595598	−	1.03161i
$353$	0.177217	−	0.306949i	0.00943233	−	0.0163373i	−0.861271	−	0.508146i	$-0.830331\pi$
$353$	0.177217	−	0.306949i	0.00943233	−	0.0163373i	0.870703	+	0.491809i	$0.163664\pi$
$354$	7.38821	−	3.46452i	0.392679	−	0.184137i
$355$	4.83550	+	8.37533i	0.256642	+	0.444516i
$356$	−1.43577	+	2.48683i	−0.0760956	+	0.131801i
$357$	−23.9459	−	12.1891i	−1.26735	−	0.645117i
$358$	3.21575	+	5.56985i	0.169958	+	0.294376i
$359$	6.26344	−	10.8486i	0.330572	−	0.572567i	−0.652052	−	0.758174i	$-0.726092\pi$
$359$	6.26344	−	10.8486i	0.330572	−	0.572567i	0.982624	+	0.185607i	$0.0594251\pi$
$360$	7.25733	+	1.24754i	0.382495	+	0.0657510i
$361$	9.20052	+	15.9358i	0.484238	+	0.838725i
$362$	−4.02901			−0.211760
$363$	5.30301	+	3.69625i	0.278336	+	0.194003i
$364$	−6.86086	+	16.8959i	−0.359607	+	0.885587i
$365$	7.00941	−	12.1407i	0.366889	−	0.635471i
$366$	−7.68772	+	3.60497i	−0.401844	+	0.188435i
$367$	−6.47698	+	11.2185i	−0.338096	+	0.585599i	−0.984075	−	0.177756i	$-0.943116\pi$
$367$	−6.47698	+	11.2185i	−0.338096	+	0.585599i	0.645979	+	0.763355i	$0.276449\pi$
$368$	−4.51187	−	7.81478i	−0.235197	−	0.407374i
$369$	3.33951	+	9.05401i	0.173848	+	0.471333i
$370$	−5.91964			−0.307747
$371$	4.31107	+	5.53790i	0.223820	+	0.287514i
$372$	−9.57004	+	4.48764i	−0.496184	+	0.232673i
$373$	−5.19019	−	8.98967i	−0.268738	−	0.465467i	0.699798	−	0.714340i	$-0.253273\pi$
$373$	−5.19019	−	8.98967i	−0.268738	−	0.465467i	−0.968536	+	0.248873i	$0.919940\pi$
$374$	15.7323			0.813498
$375$	−1.56820	+	0.735367i	−0.0809812	+	0.0379742i
$376$	8.19654			0.422704
$377$	−36.0557			−1.85696
$378$	−1.12644	+	9.54409i	−0.0579376	+	0.490895i
$379$	5.82342			0.299129			0.149564	−	0.988752i	$-0.452213\pi$
$379$	5.82342			0.299129			0.149564	+	0.988752i	$0.452213\pi$
$380$	1.16965			0.0600019
$381$	2.97314	−	1.39418i	0.152319	−	0.0714261i
$382$	1.60990			0.0823695
$383$	−13.0500	−	22.6032i	−0.666822	−	1.15497i	−0.978788	−	0.204877i	$-0.934321\pi$
$383$	−13.0500	−	22.6032i	−0.666822	−	1.15497i	0.311965	−	0.950094i	$-0.399013\pi$
$384$	16.6652	−	7.81475i	0.850444	−	0.398795i
$385$	−10.0586	+	1.39568i	−0.512636	+	0.0711303i
$386$	13.9480			0.709934
$387$	24.8043	+	4.26386i	1.26087	+	0.216744i
$388$	4.65075	+	8.05533i	0.236106	+	0.408948i
$389$	−0.0802449	+	0.138988i	−0.00406858	+	0.00704699i	−0.868053	−	0.496472i	$-0.834628\pi$
$389$	−0.0802449	+	0.138988i	−0.00406858	+	0.00704699i	0.863984	+	0.503519i	$0.167962\pi$
$390$	4.99946	−	2.34438i	0.253158	−	0.118712i
$391$	20.2445	−	35.0645i	1.02381	−	1.77329i
$392$	−16.5330	+	4.67812i	−0.835044	+	0.236281i
$393$	−10.4281	−	7.26852i	−0.526030	−	0.366648i
$394$	0.182566			0.00919755
$395$	6.69289	+	11.5924i	0.336756	+	0.583278i
$396$	6.02222	+	16.3273i	0.302628	+	0.820477i
$397$	6.09165	−	10.5510i	0.305731	−	0.529542i	−0.671693	−	0.740830i	$-0.734433\pi$
$397$	6.09165	−	10.5510i	0.305731	−	0.529542i	0.977424	+	0.211288i	$0.0677659\pi$
$398$	−1.26874	−	2.19753i	−0.0635964	−	0.110152i
$399$	0.187014	+	3.54162i	0.00936240	+	0.177303i
$400$	−0.653390	+	1.13171i	−0.0326695	+	0.0565853i
$401$	9.42081	+	16.3173i	0.470453	+	0.814848i	0.999429	−	0.0337883i	$-0.0107572\pi$
$401$	9.42081	+	16.3173i	0.470453	+	0.814848i	−0.528976	+	0.848637i	$0.677424\pi$
$402$	−15.9726	+	7.48997i	−0.796641	+	0.373566i
$403$	−9.20747	+	15.9478i	−0.458657	+	0.794416i
$404$	−1.16746	+	2.02209i	−0.0580831	+	0.100603i
$405$	−6.84443	+	5.84412i	−0.340103	+	0.290397i
$406$	−8.98216	−	11.5383i	−0.445777	−	0.572635i
$407$	−16.2513	−	28.1481i	−0.805549	−	1.39525i
$408$	20.4508	+	14.2544i	1.01246	+	0.705699i
$409$	−1.47525			−0.0729466			−0.0364733	−	0.999335i	$-0.511612\pi$
$409$	−1.47525			−0.0729466			−0.0364733	+	0.999335i	$0.511612\pi$
$410$	2.24867			0.111054
$411$	−1.39182	+	16.3121i	−0.0686534	+	0.804616i
$412$	−8.91949	−	15.4490i	−0.439432	−	0.761118i
$413$	−17.6620	+	2.45067i	−0.869089	+	0.120590i
$414$	−14.2721	−	2.45338i	−0.701437	−	0.120577i
$415$	0.442527	−	0.766479i	0.0217228	−	0.0376250i
$416$	13.2773	−	22.9969i	0.650973	−	1.12752i
$417$	−0.968842	+	11.3548i	−0.0474444	+	0.556047i
$418$	−1.03826	−	1.79832i	−0.0507830	−	0.0879587i
$419$	−2.29886	+	3.98174i	−0.112307	+	0.194521i	−0.916700	−	0.399576i	$-0.869157\pi$
$419$	−2.29886	+	3.98174i	−0.112307	+	0.194521i	0.804393	+	0.594097i	$0.202491\pi$
$420$	−6.17216	−	3.14180i	−0.301171	−	0.153304i
$421$	−8.56269	−	14.8310i	−0.417320	−	0.722819i	0.578349	−	0.815789i	$-0.303697\pi$
$421$	−8.56269	−	14.8310i	−0.417320	−	0.722819i	−0.995669	+	0.0929702i	$0.970364\pi$
$422$	1.57473	−	2.72750i	0.0766564	−	0.132773i
$423$	−6.40629	+	7.70168i	−0.311484	+	0.374468i
$424$	−3.25552	−	5.63872i	−0.158102	−	0.273840i
$425$	−5.86345			−0.284419
$426$	10.6018	−	4.97145i	0.513658	−	0.240868i
$427$	18.3780	−	2.55002i	0.889374	−	0.123404i
$428$	1.52306	−	2.63802i	0.0736199	−	0.127513i
$429$	24.8728	+	17.3366i	1.20087	+	0.837018i
$430$	2.93229	−	5.07888i	0.141408	−	0.244925i
$431$	−8.75901	−	15.1710i	−0.421907	−	0.730764i	0.574219	−	0.818701i	$-0.305306\pi$
$431$	−8.75901	−	15.1710i	−0.421907	−	0.730764i	−0.996126	+	0.0879379i	$0.971972\pi$
$432$	−1.71513	+	6.57005i	−0.0825195	+	0.316102i
$433$	31.4428			1.51104			0.755522	−	0.655124i	$-0.227383\pi$
$433$	31.4428			1.51104			0.755522	+	0.655124i	$0.227383\pi$
$434$	−7.39725	+	1.02640i	−0.355079	+	0.0492687i
$435$	1.16417	−	13.6441i	0.0558177	−	0.654183i
$436$	0.292057	+	0.505857i	0.0139870	+	0.0242262i
$437$	−5.34418			−0.255647
$438$	−13.9250	−	9.70589i	−0.665364	−	0.463766i
$439$	40.3355			1.92511			0.962555	−	0.271086i	$-0.0873827\pi$
$439$	40.3355			1.92511			0.962555	+	0.271086i	$0.0873827\pi$
$440$	9.42130			0.449143
$441$	8.52628	−	19.1912i	0.406014	−	0.913867i
$442$	18.6929			0.889131
$443$	36.1342			1.71679			0.858394	−	0.512991i	$-0.171462\pi$
$443$	36.1342			1.71679			0.858394	+	0.512991i	$0.171462\pi$
$444$	1.88454	−	22.0868i	0.0894364	−	1.04819i
$445$	−1.90001			−0.0900690
$446$	−4.09174	−	7.08710i	−0.193749	−	0.335584i
$447$	−18.2688	−	12.7335i	−0.864083	−	0.602275i
$448$	3.81771	−	0.529723i	0.180370	−	0.0250271i
$449$	17.2314			0.813202			0.406601	−	0.913606i	$-0.366714\pi$
$449$	17.2314			0.813202			0.406601	+	0.913606i	$0.366714\pi$
$450$	0.725727	+	1.96757i	0.0342111	+	0.0927523i
$451$	6.17332	+	10.6925i	0.290690	+	0.503491i
$452$	−6.02907	+	10.4427i	−0.283584	+	0.491181i
$453$	0.990698	−	11.6110i	0.0465471	−	0.545531i
$454$	−3.24190	+	5.61514i	−0.152150	+	0.263532i
$455$	−11.9515	+	1.65833i	−0.560297	+	0.0777435i
$456$	0.279728	−	3.27840i	0.0130994	−	0.153525i
$457$	9.17287			0.429089			0.214544	−	0.976714i	$-0.431173\pi$
$457$	9.17287			0.429089			0.214544	+	0.976714i	$0.431173\pi$
$458$	−5.90923	−	10.2351i	−0.276120	−	0.478254i
$459$	−29.3778	+	8.07504i	−1.37124	+	0.376911i
$460$	5.21811	−	9.03803i	0.243296	−	0.421400i
$461$	7.95525	+	13.7789i	0.370513	+	0.641747i	0.989645	−	0.143540i	$-0.0458486\pi$
$461$	7.95525	+	13.7789i	0.370513	+	0.641747i	−0.619132	+	0.785287i	$0.712515\pi$
$462$	0.648359	+	12.2785i	0.0301644	+	0.571246i
$463$	−4.80144	+	8.31634i	−0.223142	+	0.386493i	−0.955760	−	0.294146i	$-0.904965\pi$
$463$	−4.80144	+	8.31634i	−0.223142	+	0.386493i	0.732618	+	0.680640i	$0.238298\pi$
$464$	−5.16572	−	8.94729i	−0.239813	−	0.415368i
$465$	−5.73761	−	3.99918i	−0.266075	−	0.185457i
$466$	−2.44725	+	4.23877i	−0.113367	+	0.196357i
$467$	13.1371	−	22.7541i	0.607912	−	1.05294i	−0.383671	−	0.923470i	$-0.625340\pi$
$467$	13.1371	−	22.7541i	0.607912	−	1.05294i	0.991584	−	0.129466i	$-0.0413262\pi$
$468$	7.15551	+	19.3999i	0.330764	+	0.896759i
$469$	38.1835	−	5.29812i	1.76315	−	0.244645i
$470$	1.16716	+	2.02157i	0.0538369	+	0.0932482i
$471$	18.9934	−	8.90649i	0.875170	−	0.410390i
$472$	16.5429			0.761447
$473$	32.2004			1.48057
$474$	14.6741	−	6.88106i	0.674004	−	0.316058i
$475$	0.386961	+	0.670236i	0.0177550	+	0.0307526i
$476$	−14.4022	−	18.5007i	−0.660123	−	0.847977i
$477$	7.84274	+	1.34817i	0.359095	+	0.0617284i
$478$	−5.59555	+	9.69178i	−0.255935	+	0.443292i
$479$	3.66635	−	6.35030i	0.167520	−	0.290153i	−0.770027	−	0.638011i	$-0.779758\pi$
$479$	3.66635	−	6.35030i	0.167520	−	0.290153i	0.937547	+	0.347858i	$0.113091\pi$
$480$	8.27371	+	5.76687i	0.377642	+	0.263220i
$481$	−19.3096	−	33.4452i	−0.880443	−	1.52497i
$482$	2.57062	−	4.45244i	0.117088	−	0.202803i
$483$	28.2008	+	14.3550i	1.28318	+	0.653174i
$484$	2.82017	+	4.88467i	0.128189	+	0.222030i
$485$	−3.07725	+	5.32996i	−0.139731	+	0.242021i
$486$	6.34584	+	8.85873i	0.287853	+	0.401840i
$487$	−16.8879	−	29.2507i	−0.765262	−	1.32547i	−0.940108	−	0.340878i	$-0.889276\pi$
$487$	−16.8879	−	29.2507i	−0.765262	−	1.32547i	0.174845	−	0.984596i	$-0.444057\pi$
$488$	−17.2135			−0.779219
$489$	2.38982	−	28.0086i	0.108071	−	1.26659i
$490$	−3.50804	−	3.41152i	−0.158477	−	0.154117i
$491$	10.2358	−	17.7289i	0.461934	−	0.800093i	−0.537123	−	0.843504i	$-0.680489\pi$
$491$	10.2358	−	17.7289i	0.461934	−	0.800093i	0.999057	+	0.0434107i	$0.0138224\pi$
$492$	−0.715872	+	8.39001i	−0.0322740	+	0.378251i
$493$	23.1783	−	40.1460i	1.04390	−	1.80809i
$494$	−1.23365	−	2.13674i	−0.0555044	−	0.0961364i
$495$	−7.36354	+	8.85249i	−0.330966	+	0.397890i
$496$	−5.27663			−0.236928
$497$	−25.3443	+	3.51662i	−1.13685	+	0.157742i
$498$	−0.879132	−	0.612765i	−0.0393949	−	0.0274586i
$499$	−12.1698	−	21.0787i	−0.544796	−	0.943614i	−0.998620	−	0.0525229i	$-0.983274\pi$
$499$	−12.1698	−	21.0787i	−0.544796	−	0.943614i	0.453824	−	0.891091i	$-0.350060\pi$
$500$	−1.51133			−0.0675888
$501$	2.53418	−	29.7006i	0.113219	−	1.32692i
$502$	10.8202			0.482929
$503$	−23.7168			−1.05748			−0.528739	−	0.848784i	$-0.677335\pi$
$503$	−23.7168			−1.05748			−0.528739	+	0.848784i	$0.677335\pi$
$504$	−10.2822	+	16.5485i	−0.458006	+	0.737129i
$505$	−1.54494			−0.0687488
$506$	−18.5277			−0.823659
$507$	11.0812	+	7.72372i	0.492134	+	0.343022i
$508$	2.86533			0.127129
$509$	0.582806	+	1.00945i	0.0258324	+	0.0447431i	0.878653	−	0.477462i	$-0.158443\pi$
$509$	0.582806	+	1.00945i	0.0258324	+	0.0447431i	−0.852820	+	0.522205i	$0.825110\pi$
$510$	−0.603559	+	7.07370i	−0.0267260	+	0.313229i
$511$	22.7838	+	29.2675i	1.00790	+	1.29472i
$512$	14.0242			0.619788
$513$	2.86184	+	2.82519i	0.126353	+	0.124735i
$514$	0.124396	+	0.215461i	0.00548688	+	0.00950356i
$515$	5.90175	−	10.2221i	0.260062	−	0.450441i
$516$	18.0163	+	12.5576i	0.793124	+	0.552816i
$517$	−6.40844	+	11.0997i	−0.281843	+	0.488166i
$518$	5.89249	−	14.5112i	0.258901	−	0.637584i
$519$	−25.1390	+	11.7883i	−1.10348	+	0.517451i
$520$	11.1943			0.490900
$521$	15.6184	+	27.0519i	0.684254	+	1.18516i	0.973670	+	0.227960i	$0.0732055\pi$
$521$	15.6184	+	27.0519i	0.684254	+	1.18516i	−0.289416	+	0.957203i	$0.593461\pi$
$522$	−16.3404	−	2.80892i	−0.715201	−	0.122943i
$523$	−7.10144	+	12.3000i	−0.310524	+	0.537844i	−0.978476	−	0.206361i	$-0.933838\pi$
$523$	−7.10144	+	12.3000i	−0.310524	+	0.537844i	0.667952	+	0.744205i	$0.267171\pi$
$524$	−5.54573	−	9.60549i	−0.242267	−	0.419618i
$525$	−0.241644	−	4.57620i	−0.0105462	−	0.199722i
$526$	−6.69883	+	11.6027i	−0.292083	+	0.505903i
$527$	−11.8380	−	20.5040i	−0.515671	−	0.893168i
$528$	−0.738572	+	8.65605i	−0.0321422	+	0.376706i
$529$	−12.3417	+	21.3764i	−0.536595	+	0.929411i
$530$	0.927146	−	1.60586i	0.0402726	−	0.0697543i
$531$	−12.9296	+	15.5441i	−0.561099	+	0.674556i
$532$	−1.16429	+	2.86724i	−0.0504783	+	0.124310i
$533$	7.33506	+	12.7047i	0.317717	+	0.550301i
$534$	−0.195579	+	2.29218i	−0.00846351	+	0.0991922i
$535$	2.01552			0.0871386
$536$	−35.7641			−1.54477
$537$	−13.0732	−	9.11217i	−0.564151	−	0.393219i
$538$	−2.92790	−	5.07127i	−0.126231	−	0.218638i
$539$	6.59120	−	26.0466i	0.283903	−	1.12191i
$540$	−7.57226	+	2.08138i	−0.325858	+	0.0895682i
$541$	−1.38923	+	2.40621i	−0.0597275	+	0.103451i	−0.894343	−	0.447382i	$-0.852356\pi$
$541$	−1.38923	+	2.40621i	−0.0597275	+	0.103451i	0.834616	+	0.550833i	$0.185690\pi$
$542$	−0.0277883	+	0.0481307i	−0.00119361	+	0.00206739i
$543$	9.03839	−	4.23833i	0.387874	−	0.181884i
$544$	17.0705	+	29.5670i	0.731893	+	1.26768i
$545$	−0.193245	+	0.334710i	−0.00827770	+	0.0143374i
$546$	0.770371	+	14.5891i	0.0329688	+	0.624356i
$547$	−8.59132	−	14.8806i	−0.367338	−	0.636248i	0.621810	−	0.783168i	$-0.286398\pi$
$547$	−8.59132	−	14.8806i	−0.367338	−	0.636248i	−0.989148	+	0.146919i	$0.953064\pi$
$548$	−7.14256	+	12.3713i	−0.305115	+	0.528475i
$549$	13.4538	−	16.1743i	0.574195	−	0.690300i
$550$	1.34156	+	2.32364i	0.0572042	+	0.0990805i
$551$	−6.11865			−0.260663
$552$	−24.0846	−	16.7872i	−1.02511	−	0.714512i
$553$	−35.0794	+	4.86741i	−1.49173	+	0.206983i
$554$	−7.47545	+	12.9479i	−0.317601	+	0.550101i
$555$	13.2797	−	6.22719i	0.563691	−	0.264329i
$556$	−4.97191	+	8.61161i	−0.210856	+	0.365214i
$557$	12.1738	+	21.0857i	0.515822	+	0.893430i	0.999831	+	0.0183672i	$0.00584679\pi$
$557$	12.1738	+	21.0857i	0.515822	+	0.893430i	−0.484009	+	0.875063i	$0.660820\pi$
$558$	−5.41523	+	6.51023i	−0.229245	+	0.275600i
$559$	38.2600			1.61823
$560$	−2.12382	−	2.72821i	−0.0897478	−	0.115288i
$561$	−35.2927	+	16.5497i	−1.49006	+	0.698727i
$562$	1.48253	+	2.56781i	0.0625366	+	0.108317i
$563$	−26.2519			−1.10639			−0.553194	−	0.833053i	$-0.686591\pi$
$563$	−26.2519			−1.10639			−0.553194	+	0.833053i	$0.686591\pi$
$564$	−7.91427	+	3.71120i	−0.333251	+	0.156270i
$565$	−7.97849			−0.335658
$566$	−4.18579			−0.175942
$567$	−7.51298	−	22.5955i	−0.315515	−	0.948920i
$568$	23.7384			0.996039
$569$	−7.31630			−0.306715			−0.153358	−	0.988171i	$-0.549009\pi$
$569$	−7.31630			−0.306715			−0.153358	+	0.988171i	$0.549009\pi$
$570$	0.848409	−	0.397841i	0.0355359	−	0.0166637i
$571$	−11.4412			−0.478798			−0.239399	−	0.970921i	$-0.576950\pi$
$571$	−11.4412			−0.478798			−0.239399	+	0.970921i	$0.576950\pi$
$572$	13.2275	+	22.9106i	0.553068	+	0.957942i
$573$	−3.61153	+	1.69354i	−0.150874	+	0.0707485i
$574$	−2.23835	+	5.51229i	−0.0934271	+	0.230078i
$575$	6.90532			0.287972
$576$	2.79480	−	3.35992i	0.116450	−	0.139997i
$577$	17.3881	+	30.1170i	0.723875	+	1.25379i	0.959436	+	0.281928i	$0.0909739\pi$
$577$	17.3881	+	30.1170i	0.723875	+	1.25379i	−0.235561	+	0.971860i	$0.575693\pi$
$578$	−6.07477	+	10.5218i	−0.252677	+	0.437650i
$579$	−31.2899	+	14.6726i	−1.30036	+	0.609774i
$580$	5.97431	−	10.3478i	0.248070	−	0.429669i
$581$	1.43842	+	1.84776i	0.0596756	+	0.0766578i
$582$	6.11333	+	4.26106i	0.253406	+	0.176627i
$583$	10.1813			0.421665
$584$	−17.2052	−	29.8004i	−0.711958	−	1.23315i
$585$	−8.74925	+	10.5184i	−0.361737	+	0.434883i
$586$	−4.38268	+	7.59102i	−0.181047	+	0.313582i
$587$	−16.4446	−	28.4830i	−0.678743	−	1.17562i	−0.975360	−	0.220621i	$-0.929192\pi$
$587$	−16.4446	−	28.4830i	−0.678743	−	1.17562i	0.296616	−	0.954997i	$-0.404142\pi$
$588$	13.8455	−	12.0028i	0.570980	−	0.494987i
$589$	−1.56251	+	2.70634i	−0.0643819	+	0.111513i
$590$	2.35564	+	4.08009i	0.0969802	+	0.167975i
$591$	−0.409555	+	0.192051i	−0.0168469	+	0.00789992i
$592$	5.53300	−	9.58343i	0.227405	−	0.393877i
$593$	−11.6851	+	20.2392i	−0.479851	+	0.831125i	−0.999733	−	0.0231124i	$-0.992642\pi$
$593$	−11.6851	+	20.2392i	−0.479851	+	0.831125i	0.519882	+	0.854238i	$0.325976\pi$
$594$	9.92172	+	9.79465i	0.407093	+	0.401879i
$595$	5.83656	−	14.3734i	0.239276	−	0.589253i
$596$	−9.71543	−	16.8276i	−0.397959	−	0.689286i
$597$	5.15790	+	3.59511i	0.211099	+	0.147138i
$598$	−22.0144			−0.900236
$599$	−7.35558			−0.300541			−0.150270	−	0.988645i	$-0.548014\pi$
$599$	−7.35558			−0.300541			−0.150270	+	0.988645i	$0.548014\pi$
$600$	−0.361441	+	4.23609i	−0.0147558	+	0.172937i
$601$	−15.8014	−	27.3689i	−0.644553	−	1.11640i	−0.984405	−	0.175920i	$-0.943710\pi$
$601$	−15.8014	−	27.3689i	−0.644553	−	1.11640i	0.339851	−	0.940479i	$-0.389623\pi$
$602$	9.53130	+	12.2437i	0.388467	+	0.499015i
$603$	27.9527	−	33.6049i	1.13832	−	1.36850i
$604$	5.08408	−	8.80588i	0.206868	−	0.358306i
$605$	−1.86602	+	3.23203i	−0.0758643	+	0.131401i
$606$	−0.159029	+	1.86382i	−0.00646012	+	0.0757125i
$607$	0.998427	+	1.72933i	0.0405249	+	0.0701912i	0.885576	−	0.464494i	$-0.153764\pi$
$607$	0.998427	+	1.72933i	0.0405249	+	0.0701912i	−0.845052	+	0.534685i	$0.820430\pi$
$608$	2.25315	−	3.90258i	0.0913775	−	0.158270i
$609$	32.2876	+	16.4353i	1.30836	+	0.665991i
$610$	−2.45114	−	4.24550i	−0.0992437	−	0.171895i
$611$	−7.61442	+	13.1886i	−0.308047	+	0.533552i
$612$	−26.2006	−	4.50388i	−1.05909	−	0.182059i
$613$	−3.00257	−	5.20061i	−0.121273	−	0.210051i	0.798997	−	0.601335i	$-0.205364\pi$
$613$	−3.00257	−	5.20061i	−0.121273	−	0.210051i	−0.920270	+	0.391284i	$0.872031\pi$
$614$	−14.7336			−0.594601
$615$	−5.04450	+	2.36549i	−0.203414	+	0.0953859i
$616$	−9.37809	+	23.0950i	−0.377854	+	0.930522i
$617$	−3.65695	+	6.33402i	−0.147223	+	0.254998i	−0.930200	−	0.367053i	$-0.880367\pi$
$617$	−3.65695	+	6.33402i	−0.147223	+	0.254998i	0.782977	+	0.622051i	$0.213700\pi$
$618$	−11.7245	−	8.17212i	−0.471629	−	0.328731i
$619$	9.30116	−	16.1101i	0.373845	−	0.647519i	−0.616308	−	0.787505i	$-0.711373\pi$
$619$	9.30116	−	16.1101i	0.373845	−	0.647519i	0.990153	+	0.139986i	$0.0447059\pi$
$620$	−3.05129	−	5.28499i	−0.122543	−	0.212250i
$621$	34.5979	−	9.50988i	1.38837	−	0.381618i
$622$	8.97207			0.359747
$623$	1.89129	−	4.65760i	0.0757730	−	0.186603i
$624$	−0.877561	+	10.2850i	−0.0351305	+	0.411729i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.4129			−0.416185
$627$	4.22091	+	2.94202i	0.168567	+	0.117493i
$628$	18.3047			0.730436
$629$	49.6525			1.97978
$630$	−5.54562	−	0.179534i	−0.220943	−	0.00715279i
$631$	4.53109			0.180380			0.0901899	−	0.995925i	$-0.471253\pi$
$631$	4.53109			0.180380			0.0901899	+	0.995925i	$0.471253\pi$
$632$	32.8566			1.30697
$633$	−0.663416	+	7.77522i	−0.0263684	+	0.309037i
$634$	23.9352			0.950588
$635$	0.947950	+	1.64190i	0.0376183	+	0.0651567i
$636$	5.69648	+	3.97051i	0.225880	+	0.157441i
$637$	7.83158	−	30.9482i	0.310298	−	1.22621i
$638$	−21.2128			−0.839821
$639$	−18.5535	+	22.3052i	−0.733966	+	0.882379i
$640$	5.31351	+	9.20326i	0.210035	+	0.363791i
$641$	13.7709	−	23.8519i	0.543918	−	0.942093i	−0.454756	−	0.890616i	$-0.650274\pi$
$641$	13.7709	−	23.8519i	0.543918	−	0.942093i	0.998674	−	0.0514773i	$-0.0163930\pi$
$642$	0.207469	−	2.43153i	0.00818816	−	0.0959650i
$643$	1.10409	−	1.91233i	0.0435409	−	0.0754150i	−0.843434	−	0.537233i	$-0.819469\pi$
$643$	1.10409	−	1.91233i	0.0435409	−	0.0754150i	0.886975	+	0.461818i	$0.152803\pi$
$644$	16.9613	+	21.7880i	0.668367	+	0.858568i
$645$	−1.23534	+	14.4782i	−0.0486416	+	0.570079i
$646$	3.17219			0.124808
$647$	24.2181	+	41.9469i	0.952110	+	1.64910i	0.740847	+	0.671673i	$0.234424\pi$
$647$	24.2181	+	41.9469i	0.952110	+	1.64910i	0.211263	+	0.977429i	$0.432243\pi$
$648$	4.02292	+	21.7219i	0.158035	+	0.853319i
$649$	−12.9340	+	22.4023i	−0.507704	+	0.879369i
$650$	1.59402	+	2.76092i	0.0625226	+	0.108292i
$651$	15.5147	−	10.0841i	0.608069	−	0.395227i
$652$	12.2641	−	21.2420i	0.480299	−	0.831902i
$653$	9.72546	+	16.8450i	0.380587	+	0.659195i	0.991146	−	0.132775i	$-0.0423888\pi$
$653$	9.72546	+	16.8450i	0.380587	+	0.659195i	−0.610560	+	0.791970i	$0.709055\pi$
$654$	0.383904	+	0.267585i	0.0150118	+	0.0104634i
$655$	3.66944	−	6.35565i	0.143377	−	0.248336i
$656$	−2.10180	+	3.64042i	−0.0820613	+	0.142134i
$657$	41.4485	+	7.12501i	1.61706	+	0.277973i
$658$	−6.11740	+	0.848814i	−0.238481	+	0.0330902i
$659$	1.04114	+	1.80330i	0.0405569	+	0.0702467i	0.885591	−	0.464465i	$-0.153753\pi$
$659$	1.04114	+	1.80330i	0.0405569	+	0.0702467i	−0.845034	+	0.534712i	$0.820420\pi$
$660$	−9.09685	+	4.26574i	−0.354094	+	0.166044i
$661$	−45.4863			−1.76921			−0.884606	−	0.466339i	$-0.845573\pi$
$661$	−45.4863			−1.76921			−0.884606	+	0.466339i	$0.845573\pi$
$662$	23.1918			0.901374
$663$	−41.9343	+	19.6641i	−1.62859	+	0.763689i
$664$	−1.08622	−	1.88139i	−0.0421536	−	0.0730122i
$665$	−2.02818	+	0.281418i	−0.0786493	+	0.0109129i
$666$	−6.14555	−	16.6617i	−0.238135	−	0.645627i
$667$	−27.2968	+	47.2794i	−1.05694	+	1.83067i
$668$	13.0050	−	22.5252i	0.503177	−	0.871528i
$669$	16.6344	+	11.5944i	0.643123	+	0.448264i
$670$	−5.09267	−	8.82077i	−0.196747	−	0.340776i
$671$	13.4583	−	23.3105i	0.519553	−	0.899893i
$672$	−22.3724	+	14.5414i	−0.863035	+	0.560947i
$673$	−17.4910	−	30.2953i	−0.674229	−	1.16780i	−0.976694	−	0.214639i	$-0.931143\pi$
$673$	−17.4910	−	30.2953i	−0.674229	−	1.16780i	0.302464	−	0.953161i	$-0.402191\pi$
$674$	−7.60712	+	13.1759i	−0.293015	+	0.507518i
$675$	−3.69784	−	3.65048i	−0.142330	−	0.140507i
$676$	5.89304	+	10.2070i	0.226655	+	0.392579i
$677$	−11.8395			−0.455029			−0.227514	−	0.973775i	$-0.573060\pi$
$677$	−11.8395			−0.455029			−0.227514	+	0.973775i	$0.573060\pi$
$678$	−0.821272	+	9.62529i	−0.0315408	+	0.369657i
$679$	−10.0025	−	12.8490i	−0.383861	−	0.493098i
$680$	−7.19620	+	12.4642i	−0.275961	+	0.477979i
$681$	1.36578	−	16.0069i	0.0523368	−	0.613386i
$682$	−5.41705	+	9.38261i	−0.207430	+	0.359279i
$683$	0.504725	+	0.874210i	0.0193128	+	0.0334507i	0.875520	−	0.483181i	$-0.160519\pi$
$683$	0.504725	+	0.874210i	0.0193128	+	0.0334507i	−0.856207	+	0.516632i	$0.827186\pi$
$684$	1.21429	+	3.29215i	0.0464295	+	0.125879i
$685$	−9.45201			−0.361143
$686$	11.8548	−	5.20359i	0.452618	−	0.198674i
$687$	24.0232	+	16.7444i	0.916541	+	0.638839i
$688$	5.48153	+	9.49430i	0.208982	+	0.361967i
$689$	12.0972			0.460868
$690$	0.710804	−	8.33061i	0.0270598	−	0.317141i
$691$	−20.3392			−0.773739			−0.386870	−	0.922134i	$-0.626444\pi$
$691$	−20.3392			−0.773739			−0.386870	+	0.922134i	$0.626444\pi$
$692$	−24.2275			−0.920990
$693$	−14.3708	−	26.8626i	−0.545903	−	1.02042i
$694$	3.36904			0.127887
$695$	−6.57952			−0.249575
$696$	−27.5749	−	19.2200i	−1.04523	−	0.728533i
$697$	−18.8613			−0.714422
$698$	2.28577	+	3.95908i	0.0865178	+	0.149853i
$699$	1.03100	−	12.0833i	0.0389961	−	0.457034i
$700$	1.50440	−	3.70481i	0.0568609	−	0.140029i
$701$	−33.4009			−1.26154			−0.630768	−	0.775972i	$-0.717260\pi$
$701$	−33.4009			−1.26154			−0.630768	+	0.775972i	$0.717260\pi$
$702$	11.7888	+	11.6379i	0.444941	+	0.439243i
$703$	−3.27684	−	5.67565i	−0.123588	−	0.214061i
$704$	2.79574	−	4.84236i	0.105368	−	0.182503i
$705$	−4.74491	−	3.30726i	−0.178704	−	0.124558i
$706$	0.123884	−	0.214573i	0.00466242	−	0.00807555i
$707$	1.53785	−	3.78719i	0.0578369	−	0.142432i
$708$	−15.9732	+	7.49023i	−0.600308	+	0.281500i
$709$	−39.0631			−1.46705			−0.733523	−	0.679665i	$-0.762125\pi$
$709$	−39.0631			−1.46705			−0.733523	+	0.679665i	$0.762125\pi$
$710$	3.38025	+	5.85477i	0.126859	+	0.219725i
$711$	−25.6802	+	30.8729i	−0.963084	+	1.15783i
$712$	−2.33187	+	4.03892i	−0.0873906	+	0.151365i
$713$	13.9414	+	24.1473i	0.522111	+	0.904323i
$714$	−16.7394	−	8.52080i	−0.626455	−	0.318883i
$715$	−8.75220	+	15.1593i	−0.327314	+	0.566924i
$716$	−6.95240	−	12.0419i	−0.259823	−	0.450027i
$717$	2.35735	−	27.6281i	0.0880368	−	1.03179i
$718$	4.37845	−	7.58370i	0.163402	−	0.283021i
$719$	1.55174	−	2.68769i	0.0578702	−	0.100234i	−0.835639	−	0.549279i	$-0.814902\pi$
$719$	1.55174	−	2.68769i	0.0578702	−	0.100234i	0.893509	+	0.449045i	$0.148236\pi$
$720$	−3.86367	−	0.664166i	−0.143991	−	0.0247520i
$721$	19.1834	+	24.6425i	0.714427	+	0.917736i
$722$	6.43162	+	11.1399i	0.239360	+	0.414584i
$723$	−1.08298	+	12.6925i	−0.0402763	+	0.472037i
$724$	8.71064			0.323729
$725$	7.90603			0.293622
$726$	3.70706	+	2.58386i	0.137582	+	0.0958961i
$727$	21.5168	+	37.2683i	0.798015	+	1.38220i	0.920907	+	0.389783i	$0.127450\pi$
$727$	21.5168	+	37.2683i	0.798015	+	1.38220i	−0.122892	+	0.992420i	$0.539217\pi$
$728$	−11.1429	+	27.4411i	−0.412984	+	1.01704i
$729$	−23.5547	−	13.1975i	−0.872398	−	0.488796i
$730$	4.89992	−	8.48691i	0.181354	−	0.314115i
$731$	−24.5953	+	42.6004i	−0.909692	+	1.57563i
$732$	16.6207	−	7.79388i	0.614319	−	0.288070i
$733$	−11.9127	−	20.6333i	−0.440004	−	0.762110i	0.557685	−	0.830053i	$-0.311690\pi$
$733$	−11.9127	−	20.6333i	−0.440004	−	0.762110i	−0.997689	+	0.0679428i	$0.978356\pi$
$734$	−4.52773	+	7.84226i	−0.167122	+	0.289463i
$735$	11.4584	+	3.96286i	0.422651	+	0.146172i
$736$	−20.1038	−	34.8207i	−0.741034	−	1.28351i
$737$	27.9621	−	48.4317i	1.03000	−	1.78401i
$738$	2.33448	+	6.32920i	0.0859335	+	0.232981i
$739$	−0.522437	−	0.904887i	−0.0192181	−	0.0332868i	0.856256	−	0.516551i	$-0.172784\pi$
$739$	−0.522437	−	0.904887i	−0.0192181	−	0.0332868i	−0.875475	+	0.483264i	$0.839451\pi$
$740$	12.7982			0.470469
$741$	5.01522	+	3.49566i	0.184239	+	0.128416i
$742$	3.01365	+	3.87126i	0.110635	+	0.142119i
$743$	23.6637	−	40.9867i	0.868137	−	1.50366i	0.00423816	−	0.999991i	$-0.498651\pi$
$743$	23.6637	−	40.9867i	0.868137	−	1.50366i	0.863899	−	0.503666i	$-0.168016\pi$
$744$	−15.5430	+	7.28849i	−0.569833	+	0.267209i
$745$	6.42839	−	11.1343i	0.235518	−	0.407929i
$746$	−3.62820	−	6.28422i	−0.132838	−	0.230082i
$747$	2.61678	+	0.449825i	0.0957430	+	0.0164582i
$748$	−34.0130			−1.24364
$749$	−2.00628	+	4.94076i	−0.0733078	+	0.180532i
$750$	−1.09625	+	0.514057i	−0.0400292	+	0.0187707i
$751$	22.2479	+	38.5345i	0.811838	+	1.40614i	0.911576	+	0.411131i	$0.134866\pi$
$751$	22.2479	+	38.5345i	0.811838	+	1.40614i	−0.0997385	+	0.995014i	$0.531801\pi$
$752$	−4.36369			−0.159127
$753$	−24.2732	+	11.3823i	−0.884565	+	0.414795i
$754$	−25.2047			−0.917901
$755$	6.72795			0.244855
$756$	2.43533	−	20.6341i	0.0885721	−	0.750456i
$757$	15.8107			0.574650			0.287325	−	0.957833i	$-0.407234\pi$
$757$	15.8107			0.574650			0.287325	+	0.957833i	$0.407234\pi$
$758$	4.07086			0.147860
$759$	41.5638	−	19.4903i	1.50867	−	0.707454i
$760$	1.89966			0.0689080
$761$	−14.4379	−	25.0071i	−0.523372	−	0.906507i	−0.999630	−	0.0272015i	$-0.991340\pi$
$761$	−14.4379	−	25.0071i	−0.523372	−	0.906507i	0.476258	−	0.879306i	$-0.341993\pi$
$762$	2.07837	−	0.974602i	0.0752915	−	0.0353061i
$763$	−0.628135	−	0.806887i	−0.0227400	−	0.0292113i
$764$	−3.48057			−0.125923
$765$	−6.08722	−	16.5035i	−0.220084	−	0.596687i
$766$	−9.12257	−	15.8008i	−0.329612	−	0.570905i
$767$	−15.3680	+	26.6181i	−0.554906	+	0.961126i
$768$	16.2189	−	7.60544i	0.585247	−	0.274438i
$769$	−20.2272	+	35.0345i	−0.729411	+	1.26338i	0.227722	+	0.973726i	$0.426872\pi$
$769$	−20.2272	+	35.0345i	−0.729411	+	1.26338i	−0.957133	+	0.289650i	$0.906461\pi$
$770$	−7.03148	+	0.975647i	−0.253397	+	0.0351599i
$771$	−0.505716	−	0.352489i	−0.0182129	−	0.0126946i
$772$	−30.1553			−1.08531
$773$	0.958668	+	1.66046i	0.0344809	+	0.0597226i	0.882751	−	0.469841i	$-0.155689\pi$
$773$	0.958668	+	1.66046i	0.0344809	+	0.0597226i	−0.848270	+	0.529564i	$0.822356\pi$
$774$	17.3394	+	2.98065i	0.623253	+	0.107137i
$775$	2.01894	−	3.49691i	0.0725226	−	0.125613i
$776$	7.55340	+	13.0829i	0.271151	+	0.469648i
$777$	2.04628	+	38.7519i	0.0734098	+	1.39022i
$778$	−0.0560951	+	0.0971596i	−0.00201111	+	0.00348334i
$779$	1.24476	+	2.15598i	0.0445981	+	0.0772462i
$780$	−10.8087	+	5.06850i	−0.387015	+	0.181481i
$781$	−18.5598	+	32.1465i	−0.664121	+	1.15029i
$782$	14.1519	−	24.5118i	0.506071	−	0.876541i
$783$	39.6118	−	10.8880i	1.41561	−	0.389107i
$784$	8.80189	−	2.49055i	0.314353	−	0.0889481i
$785$	6.05582	+	10.4890i	0.216141	+	0.374368i
$786$	−7.28978	−	5.08105i	−0.260018	−	0.181235i
$787$	−19.0982			−0.680776			−0.340388	−	0.940285i	$-0.610558\pi$
$787$	−19.0982			−0.680776			−0.340388	+	0.940285i	$0.610558\pi$
$788$	−0.394705			−0.0140608
$789$	2.82215	−	33.0756i	0.100471	−	1.17752i
$790$	4.67866	+	8.10368i	0.166459	+	0.288316i
$791$	7.94190	−	19.5581i	0.282381	−	0.695407i
$792$	9.78084	+	26.5176i	0.347547	+	0.942261i
$793$	15.9910	−	27.6972i	0.567857	−	0.983558i
$794$	4.25836	−	7.37569i	0.151124	−	0.261754i
$795$	−0.390597	+	4.57779i	−0.0138531	+	0.162358i
$796$	2.74300	+	4.75101i	0.0972230	+	0.168395i
$797$	20.4912	−	35.4919i	0.725837	−	1.25719i	−0.232791	−	0.972527i	$-0.574786\pi$
$797$	20.4912	−	35.4919i	0.725837	−	1.25719i	0.958628	−	0.284660i	$-0.0918808\pi$
$798$	0.130732	+	2.47577i	0.00462786	+	0.0876413i
$799$	−9.78982	−	16.9565i	−0.346339	−	0.599877i
$800$	−2.91134	+	5.04260i	−0.102932	+	0.178283i
$801$	−1.97252	−	5.34784i	−0.0696955	−	0.188957i
$802$	6.58561	+	11.4066i	0.232546	+	0.402781i
$803$	53.8075			1.89883
$804$	34.5325	−	16.1932i	1.21787	−	0.571089i
$805$	−6.87365	+	16.9274i	−0.242264	+	0.596612i
$806$	−6.43647	+	11.1483i	−0.226715	+	0.392682i
$807$	11.9030	+	8.29651i	0.419005	+	0.292051i
$808$	−1.89610	+	3.28413i	−0.0667044	+	0.115535i
$809$	19.3458	+	33.5079i	0.680163	+	1.17808i	0.974931	+	0.222508i	$0.0714242\pi$
$809$	19.3458	+	33.5079i	0.680163	+	1.17808i	−0.294768	+	0.955569i	$0.595242\pi$
$810$	−4.78460	+	4.08532i	−0.168114	+	0.143544i
$811$	−48.0986			−1.68897			−0.844485	−	0.535580i	$-0.820093\pi$
$811$	−48.0986			−1.68897			−0.844485	+	0.535580i	$0.820093\pi$
$812$	19.4193	+	24.9455i	0.681482	+	0.875416i
$813$	0.0117069	−	0.137205i	0.000410580	−	0.00481199i
$814$	−11.3605	−	19.6769i	−0.398185	−	0.689676i
$815$	16.2295			0.568496
$816$	−10.8876	−	7.58879i	−0.381143	−	0.265661i
$817$	6.49272			0.227152
$818$	−1.03127			−0.0360576
$819$	−17.0752	−	31.9177i	−0.596657	−	1.11530i
$820$	−4.86158			−0.169774
$821$	21.6188			0.754502			0.377251	−	0.926111i	$-0.376869\pi$
$821$	21.6188			0.754502			0.377251	+	0.926111i	$0.376869\pi$
$822$	−0.972950	+	11.4030i	−0.0339355	+	0.397724i
$823$	25.9464			0.904434			0.452217	−	0.891908i	$-0.350633\pi$
$823$	25.9464			0.904434			0.452217	+	0.891908i	$0.350633\pi$
$824$	−14.4864	−	25.0911i	−0.504657	−	0.874091i
$825$	−5.45391	−	3.80144i	−0.189881	−	0.132349i
$826$	−12.3466	+	1.71314i	−0.429593	+	0.0596078i
$827$	−45.3663			−1.57754			−0.788770	−	0.614689i	$-0.789282\pi$
$827$	−45.3663			−1.57754			−0.788770	+	0.614689i	$0.789282\pi$
$828$	30.8561	+	5.30417i	1.07232	+	0.184332i
$829$	−20.8415	−	36.0986i	−0.723857	−	1.25376i	−0.959443	−	0.281903i	$-0.909034\pi$
$829$	−20.8415	−	36.0986i	−0.723857	−	1.25376i	0.235586	−	0.971853i	$-0.424299\pi$
$830$	0.309348	−	0.535806i	0.0107376	−	0.0185981i
$831$	3.14933	−	36.9101i	0.109249	−	1.28040i
$832$	3.32185	−	5.75362i	0.115165	−	0.199471i
$833$	29.4246	+	28.6150i	1.01950	+	0.991451i
$834$	−0.677268	+	7.93757i	−0.0234519	+	0.274855i
$835$	17.2099			0.595574
$836$	2.24470	+	3.88793i	0.0776345	+	0.134467i
$837$	5.29968	−	20.3011i	0.183184	−	0.701710i
$838$	−1.60702	+	2.78343i	−0.0555135	+	0.0961521i
$839$	−16.8414	−	29.1701i	−0.581429	−	1.00706i	−0.995310	−	0.0967337i	$-0.969160\pi$
$839$	−16.8414	−	29.1701i	−0.581429	−	1.00706i	0.413881	−	0.910331i	$-0.364173\pi$
$840$	−10.0244	−	5.10268i	−0.345874	−	0.176059i
$841$	−16.7526	+	29.0164i	−0.577677	+	1.00057i
$842$	−5.98574	−	10.3676i	−0.206282	−	0.357291i
$843$	−6.02701	−	4.20089i	−0.207581	−	0.144686i
$844$	−3.40453	+	5.89681i	−0.117189	+	0.202977i
$845$	−3.89924	+	6.75368i	−0.134138	+	0.232334i
$846$	−4.47831	+	5.38385i	−0.153967	+	0.185101i
$847$	−6.06541	−	7.79148i	−0.208410	−	0.267718i
$848$	1.73318	+	3.00195i	0.0595176	+	0.103087i
$849$	9.39009	−	4.40325i	0.322267	−	0.151119i
$850$	−4.09884			−0.140589
$851$	−58.4751			−2.00450
$852$	−22.9209	+	10.7482i	−0.785256	+	0.368227i
$853$	25.3194	+	43.8545i	0.866920	+	1.50155i	0.865128	+	0.501551i	$0.167237\pi$
$853$	25.3194	+	43.8545i	0.866920	+	1.50155i	0.00179188	+	0.999998i	$0.499430\pi$
$854$	12.8471	−	1.78259i	0.439619	−	0.0609990i
$855$	−1.48475	+	1.78497i	−0.0507773	+	0.0610448i
$856$	2.47364	−	4.28447i	0.0845473	−	0.146440i
$857$	−6.81082	+	11.7967i	−0.232653	+	0.402967i	−0.958588	−	0.284796i	$-0.908074\pi$
$857$	−6.81082	+	11.7967i	−0.232653	+	0.402967i	0.725935	+	0.687763i	$0.241407\pi$
$858$	17.3873	+	12.1191i	0.593592	+	0.413740i
$859$	−2.07174	−	3.58836i	−0.0706869	−	0.122433i	0.828516	−	0.559966i	$-0.189186\pi$
$859$	−2.07174	−	3.58836i	−0.0706869	−	0.122433i	−0.899203	+	0.437533i	$0.855852\pi$
$860$	−6.33956	+	10.9804i	−0.216177	+	0.374430i
$861$	−0.777310	−	14.7205i	−0.0264906	−	0.501673i
$862$	−6.12298	−	10.6053i	−0.208549	−	0.361218i
$863$	−12.8153	+	22.1968i	−0.436238	+	0.755587i	−0.997396	−	0.0721222i	$-0.977023\pi$
$863$	−12.8153	+	22.1968i	−0.436238	+	0.755587i	0.561158	+	0.827709i	$0.310356\pi$
$864$	−7.64221	+	29.2745i	−0.259993	+	0.995939i
$865$	−8.01528	−	13.8829i	−0.272528	−	0.472032i
$866$	21.9800			0.746912
$867$	2.55924	−	29.9942i	0.0869163	−	1.01866i
$868$	15.9927	−	2.21905i	0.542828	−	0.0753196i
$869$	−25.6889	+	44.4944i	−0.871436	+	1.50937i
$870$	0.813813	−	9.53787i	0.0275908	−	0.323364i
$871$	33.2242	−	57.5459i	1.12576	−	1.94987i
$872$	0.474337	+	0.821577i	0.0160631	+	0.0278221i
$873$	−18.1966	−	3.12800i	−0.615863	−	0.105867i
$874$	−3.73584			−0.126367
$875$	2.62064	−	0.363625i	0.0885939	−	0.0122928i
$876$	30.1056	+	20.9840i	1.01718	+	0.708982i
$877$	−4.94505	−	8.56509i	−0.166983	−	0.289222i	0.770375	−	0.637591i	$-0.220069\pi$
$877$	−4.94505	−	8.56509i	−0.166983	−	0.289222i	−0.937358	+	0.348369i	$0.886736\pi$
$878$	28.1965			0.951586
$879$	1.84638	−	21.6395i	0.0622768	−	0.729882i
$880$	−5.01573			−0.169080
$881$	−14.6040			−0.492022			−0.246011	−	0.969267i	$-0.579120\pi$
$881$	−14.6040			−0.492022			−0.246011	+	0.969267i	$0.579120\pi$
$882$	5.96029	−	13.4156i	0.200693	−	0.451727i
$883$	15.8128			0.532142			0.266071	−	0.963953i	$-0.414274\pi$
$883$	15.8128			0.532142			0.266071	+	0.963953i	$0.414274\pi$
$884$	−40.4137			−1.35926
$885$	−9.57653	−	6.67495i	−0.321912	−	0.224376i
$886$	25.2596			0.848612
$887$	10.9158	+	18.9067i	0.366517	+	0.634825i	0.989018	−	0.147793i	$-0.0472170\pi$
$887$	10.9158	+	18.9067i	0.366517	+	0.634825i	−0.622502	+	0.782618i	$0.713884\pi$
$888$	3.06073	−	35.8718i	0.102712	−	1.20378i
$889$	−4.96848	+	0.689397i	−0.166638	+	0.0231216i
$890$	−1.32820			−0.0445213
$891$	−32.5612	−	11.5354i	−1.09084	−	0.386451i
$892$	8.84626	+	15.3222i	0.296195	+	0.513024i
$893$	−1.29217	+	2.23810i	−0.0432407	+	0.0748951i
$894$	−12.7708	−	8.90136i	−0.427118	−	0.297706i
$895$	4.60018	−	7.96775i	0.153767	−	0.266333i
$896$	−27.8496	+	3.86425i	−0.930391	+	0.129096i
$897$	49.3855	−	23.1581i	1.64893	−	0.773227i
$898$	12.0456			0.401968
$899$	15.9618	+	27.6467i	0.532357	+	0.922069i
$900$	−1.56901	−	4.25386i	−0.0523003	−	0.141795i
$901$	−7.77668	+	13.4696i	−0.259079	+	0.448737i
$902$	4.31545	+	7.47459i	0.143689	+	0.248877i
$903$	−34.2616	−	17.4401i	−1.14015	−	0.580369i
$904$	−9.79197	+	16.9602i	−0.325676	+	0.564088i
$905$	2.88178	+	4.99139i	0.0957936	+	0.165919i
$906$	0.692547	−	8.11663i	0.0230083	−	0.269657i
$907$	22.7610	−	39.4232i	0.755767	−	1.30903i	−0.189226	−	0.981934i	$-0.560598\pi$
$907$	22.7610	−	39.4232i	0.755767	−	1.30903i	0.944992	−	0.327093i	$-0.106069\pi$
$908$	7.00893	−	12.1398i	0.232600	−	0.402874i
$909$	−1.60390	−	4.34845i	−0.0531979	−	0.144229i
$910$	−8.35471	+	1.15925i	−0.276956	+	0.0384288i
$911$	23.4277	+	40.5779i	0.776193	+	1.34441i	0.934121	+	0.356956i	$0.116185\pi$
$911$	23.4277	+	40.5779i	0.776193	+	1.34441i	−0.157928	+	0.987451i	$0.550481\pi$
$912$	−0.148922	+	1.74536i	−0.00493130	+	0.0577947i
$913$	3.39704			0.112426
$914$	6.41228			0.212100
$915$	9.96477	+	6.94555i	0.329425	+	0.229613i
$916$	12.7756	+	22.1281i	0.422119	+	0.731132i
$917$	11.9274	+	15.3216i	0.393876	+	0.505964i
$918$	−20.5365	+	5.64485i	−0.677807	+	0.186308i
$919$	−24.5539	+	42.5286i	−0.809958	+	1.40289i	0.102935	+	0.994688i	$0.467177\pi$
$919$	−24.5539	+	42.5286i	−0.809958	+	1.40289i	−0.912892	+	0.408200i	$0.866157\pi$
$920$	8.47487	−	14.6789i	0.279408	−	0.483949i
$921$	33.0524	−	15.4991i	1.08911	−	0.510713i
$922$	5.56111	+	9.63212i	0.183145	+	0.317217i
$923$	−22.0525	+	38.1960i	−0.725866	+	1.25724i
$924$	−1.40174	−	26.5458i	−0.0461138	−	0.873293i
$925$	4.23407	+	7.33362i	0.139215	+	0.241128i
$926$	−3.35644	+	5.81353i	−0.110300	+	0.191045i
$927$	34.8986	+	5.99908i	1.14622	+	0.197036i
$928$	−23.0172	−	39.8669i	−0.755575	−	1.30869i
$929$	52.9764			1.73810			0.869050	−	0.494725i	$-0.164731\pi$
$929$	52.9764			1.73810			0.869050	+	0.494725i	$0.164731\pi$
$930$	−4.01087	−	2.79562i	−0.131522	−	0.0916720i
$931$	1.32902	−	5.25191i	0.0435568	−	0.172124i
$932$	5.29091	−	9.16413i	0.173310	−	0.300181i
$933$	−20.1273	+	9.43820i	−0.658937	+	0.308993i
$934$	9.18348	−	15.9062i	0.300493	−	0.520468i
$935$	−11.2527	−	19.4902i	−0.368001	−	0.637397i
$936$	11.6215	+	31.5078i	0.379859	+	1.02987i
$937$	22.9340			0.749220			0.374610	−	0.927183i	$-0.377777\pi$
$937$	22.9340			0.749220			0.374610	+	0.927183i	$0.377777\pi$
$938$	26.6922	−	3.70365i	0.871530	−	0.120928i
$939$	23.3596	−	10.9539i	0.762313	−	0.357468i
$940$	−2.52337	−	4.37060i	−0.0823032	−	0.142553i
$941$	−30.9522			−1.00901			−0.504507	−	0.863408i	$-0.668326\pi$
$941$	−30.9522			−1.00901			−0.504507	+	0.863408i	$0.668326\pi$
$942$	13.2773	−	6.22608i	0.432598	−	0.202857i
$943$	22.2127			0.723345
$944$	−8.80712			−0.286648
$945$	12.6295	−	5.43098i	0.410838	−	0.176670i
$946$	22.5096			0.731851
$947$	12.8419			0.417304			0.208652	−	0.977990i	$-0.433092\pi$
$947$	12.8419			0.417304			0.208652	+	0.977990i	$0.433092\pi$
$948$	−31.7251	+	14.8767i	−1.03038	+	0.483174i
$949$	63.9333			2.07536
$950$	0.270505	+	0.468528i	0.00877634	+	0.0152011i
$951$	−53.6944	+	25.1787i	−1.74116	+	0.816475i
$952$	−23.3910	−	30.0475i	−0.758105	−	0.973844i
$953$	47.3316			1.53322			0.766611	−	0.642112i	$-0.221942\pi$
$953$	47.3316			1.53322			0.766611	+	0.642112i	$0.221942\pi$
$954$	5.48246	+	0.942437i	0.177501	+	0.0305125i
$955$	−1.15149	−	1.99444i	−0.0372614	−	0.0645386i
$956$	12.0975	−	20.9534i	0.391260	−	0.677683i
$957$	47.5871	−	22.3148i	1.53827	−	0.721336i
$958$	2.56296	−	4.43917i	0.0828054	−	0.143423i
$959$	9.40866	−	23.1703i	0.303822	−	0.748207i
$960$	2.07001	+	1.44282i	0.0668092	+	0.0465667i
$961$	−14.6955			−0.474047
$962$	−13.4984	−	23.3799i	−0.435205	−	0.753797i
$963$	2.09244	+	5.67297i	0.0674279	+	0.182809i
$964$	−5.55763	+	9.62609i	−0.178999	+	0.310036i
$965$	−9.97640	−	17.2796i	−0.321152	−	0.556251i
$966$	19.7138	+	10.0348i	0.634280	+	0.322865i
$967$	−10.2481	+	17.7503i	−0.329557	+	0.570810i	−0.982424	−	0.186663i	$-0.940233\pi$
$967$	−10.2481	+	17.7503i	−0.329557	+	0.570810i	0.652867	+	0.757473i	$0.273566\pi$
$968$	4.58031	+	7.93332i	0.147217	+	0.254987i
$969$	−7.11625	+	3.33699i	−0.228607	+	0.107200i
$970$	−2.15115	+	3.72590i	−0.0690693	+	0.119632i
$971$	28.6673	−	49.6533i	0.919979	−	1.59345i	0.120534	−	0.992709i	$-0.461539\pi$
$971$	28.6673	−	49.6533i	0.919979	−	1.59345i	0.799444	−	0.600740i	$-0.205127\pi$
$972$	−13.7196	−	19.1524i	−0.440056	−	0.614314i
$973$	6.54934	−	16.1288i	0.209962	−	0.517064i
$974$	−11.8054	−	20.4476i	−0.378271	−	0.655185i
$975$	−6.48026	−	4.51681i	−0.207535	−	0.144654i
$976$	9.16416			0.293338
$977$	−8.90306			−0.284834			−0.142417	−	0.989807i	$-0.545487\pi$
$977$	−8.90306			−0.284834			−0.142417	+	0.989807i	$0.545487\pi$
$978$	1.67060	−	19.5794i	0.0534199	−	0.626080i
$979$	−3.64633	−	6.31564i	−0.116537	−	0.201849i
$980$	7.58432	+	7.37564i	0.242272	+	0.235606i
$981$	−1.14271	−	0.196432i	−0.0364839	−	0.00627159i
$982$	7.15531	−	12.3934i	0.228335	−	0.395488i
$983$	−0.953307	+	1.65118i	−0.0304058	+	0.0526643i	−0.880828	−	0.473437i	$-0.843013\pi$
$983$	−0.953307	+	1.65118i	−0.0304058	+	0.0526643i	0.850422	+	0.526101i	$0.176347\pi$
$984$	−1.16267	+	13.6264i	−0.0370645	+	0.434395i
$985$	−0.130582	−	0.226174i	−0.00416068	−	0.00720651i
$986$	16.2028	−	28.0640i	0.516002	−	0.893741i
$987$	12.8304	−	8.33939i	0.408397	−	0.265446i
$988$	2.66712	+	4.61959i	0.0848524	+	0.146969i
$989$	28.9656	−	50.1699i	0.921053	−	1.59531i
$990$	−5.14747	+	6.18832i	−0.163597	+	0.196678i
$991$	−4.29788	−	7.44415i	−0.136527	−	0.236471i	0.789653	−	0.613554i	$-0.210261\pi$
$991$	−4.29788	−	7.44415i	−0.136527	−	0.236471i	−0.926180	+	0.377083i	$0.876927\pi$
$992$	−23.5114			−0.746487
$993$	−52.0267	+	24.3967i	−1.65102	+	0.774204i
$994$	−17.7169	+	2.45829i	−0.561945	+	0.0779722i
$995$	−1.81496	+	3.14360i	−0.0575380	+	0.0996587i
$996$	1.90067	+	1.32479i	0.0602249	+	0.0419774i
$997$	−21.7265	+	37.6314i	−0.688085	+	1.19180i	0.284371	+	0.958714i	$0.408215\pi$
$997$	−21.7265	+	37.6314i	−0.688085	+	1.19180i	−0.972456	+	0.233085i	$0.925118\pi$
$998$	−8.50730	−	14.7351i	−0.269294	−	0.466431i
$999$	31.3138	+	30.9127i	0.990724	+	0.978036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.11	yes	36
3.2	odd	2		945.2.l.c.226.8		36
7.4	even	3		315.2.k.c.256.8	yes	36
9.2	odd	6		945.2.k.c.856.11		36
9.7	even	3		315.2.k.c.16.8	✓	36
21.11	odd	6		945.2.k.c.361.11		36
63.11	odd	6		945.2.l.c.46.8		36
63.25	even	3	inner	315.2.l.c.151.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.8	✓	36	9.7	even	3
315.2.k.c.256.8	yes	36	7.4	even	3
315.2.l.c.121.11	yes	36	1.1	even	1	trivial
315.2.l.c.151.11	yes	36	63.25	even	3	inner
945.2.k.c.361.11		36	21.11	odd	6
945.2.k.c.856.11		36	9.2	odd	6
945.2.l.c.46.8		36	63.11	odd	6
945.2.l.c.226.8		36	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.699049 q^{2} +(-1.56820 + 0.735367i) q^{3} -1.51133 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.09625 + 0.514057i) q^{6} +(2.62064 - 0.363625i) q^{7} -2.45459 q^{8} +(1.91847 - 2.30640i) q^{9} +O(q^{10})\)	\(q+0.699049 q^{2} +(-1.56820 + 0.735367i) q^{3} -1.51133 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.09625 + 0.514057i) q^{6} +(2.62064 - 0.363625i) q^{7} -2.45459 q^{8} +(1.91847 - 2.30640i) q^{9} +(-0.349525 - 0.605394i) q^{10} +(1.91912 - 3.32401i) q^{11} +(2.37006 - 1.11138i) q^{12} +(2.28027 - 3.94954i) q^{13} +(1.83196 - 0.254192i) q^{14} +(1.42094 + 0.990413i) q^{15} +1.30678 q^{16} +(2.93173 + 5.07790i) q^{17} +(1.34111 - 1.61228i) q^{18} +(0.386961 - 0.670236i) q^{19} +(0.755665 + 1.30885i) q^{20} +(-3.84228 + 2.49737i) q^{21} +(1.34156 - 2.32364i) q^{22} +(-3.45266 - 5.98018i) q^{23} +(3.84928 - 1.80503i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.59402 - 2.76092i) q^{26} +(-1.31249 + 5.02766i) q^{27} +(-3.96066 + 0.549558i) q^{28} +(-3.95301 - 6.84682i) q^{29} +(0.993309 + 0.692347i) q^{30} -4.03789 q^{31} +5.82269 q^{32} +(-0.565184 + 6.62395i) q^{33} +(2.04942 + 3.54970i) q^{34} +(-1.62523 - 2.08773i) q^{35} +(-2.89944 + 3.48573i) q^{36} +(4.23407 - 7.33362i) q^{37} +(0.270505 - 0.468528i) q^{38} +(-0.671544 + 7.87048i) q^{39} +(1.22730 + 2.12574i) q^{40} +(-1.60838 + 2.78579i) q^{41} +(-2.68594 + 1.74578i) q^{42} +(4.19469 + 7.26541i) q^{43} +(-2.90042 + 5.02367i) q^{44} +(-2.95663 - 0.508246i) q^{45} +(-2.41358 - 4.18044i) q^{46} -3.33927 q^{47} +(-2.04929 + 0.960963i) q^{48} +(6.73555 - 1.90586i) q^{49} +(-0.349525 + 0.605394i) q^{50} +(-8.33164 - 5.80724i) q^{51} +(-3.44624 + 5.96906i) q^{52} +(1.32630 + 2.29721i) q^{53} +(-0.917494 + 3.51458i) q^{54} -3.83823 q^{55} +(-6.43261 + 0.892551i) q^{56} +(-0.113961 + 1.33562i) q^{57} +(-2.76335 - 4.78626i) q^{58} -6.73956 q^{59} +(-2.14752 - 1.49684i) q^{60} +7.01278 q^{61} -2.82268 q^{62} +(4.18897 - 6.74185i) q^{63} +1.45678 q^{64} -4.56054 q^{65} +(-0.395091 + 4.63046i) q^{66} +14.5703 q^{67} +(-4.43081 - 7.67439i) q^{68} +(9.81207 + 6.83912i) q^{69} +(-1.13612 - 1.45943i) q^{70} -9.67100 q^{71} +(-4.70906 + 5.66126i) q^{72} +(7.00941 + 12.1407i) q^{73} +(2.95982 - 5.12656i) q^{74} +(0.147251 - 1.72578i) q^{75} +(-0.584826 + 1.01295i) q^{76} +(3.82063 - 9.40888i) q^{77} +(-0.469442 + 5.50185i) q^{78} -13.3858 q^{79} +(-0.653390 - 1.13171i) q^{80} +(-1.63894 - 8.84951i) q^{81} +(-1.12433 + 1.94740i) q^{82} +(0.442527 + 0.766479i) q^{83} +(5.80696 - 3.77435i) q^{84} +(2.93173 - 5.07790i) q^{85} +(2.93229 + 5.07888i) q^{86} +(11.2340 + 7.83023i) q^{87} +(-4.71065 + 8.15908i) q^{88} +(0.950003 - 1.64545i) q^{89} +(-2.06683 - 0.355289i) q^{90} +(4.53962 - 11.1795i) q^{91} +(5.21811 + 9.03803i) q^{92} +(6.33220 - 2.96933i) q^{93} -2.33431 q^{94} -0.773922 q^{95} +(-9.13111 + 4.28181i) q^{96} +(-3.07725 - 5.32996i) q^{97} +(4.70848 - 1.33229i) q^{98} +(-3.98471 - 10.8033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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