LMFDB - Embedded newform 315.2.t.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	315.101
Dual form			315.2.t.c.131.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62557i q^{2} +(-1.73024 - 0.0792089i) q^{3} -4.89362 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.207969 + 4.54286i) q^{6} +(1.43974 + 2.21972i) q^{7} +7.59741i q^{8} +(2.98745 + 0.274101i) q^{9} +O(q^{10})$	\(q-2.62557i q^{2} +(-1.73024 - 0.0792089i) q^{3} -4.89362 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.207969 + 4.54286i) q^{6} +(1.43974 + 2.21972i) q^{7} +7.59741i q^{8} +(2.98745 + 0.274101i) q^{9} +(2.27381 + 1.31279i) q^{10} +(0.0934713 - 0.0539657i) q^{11} +(8.46714 + 0.387619i) q^{12} +(-5.35335 + 3.09076i) q^{13} +(5.82803 - 3.78014i) q^{14} +(0.933716 - 1.45883i) q^{15} +10.1603 q^{16} +(0.643963 - 1.11538i) q^{17} +(0.719671 - 7.84377i) q^{18} +(-2.22804 + 1.28636i) q^{19} +(2.44681 - 4.23800i) q^{20} +(-2.31527 - 3.95468i) q^{21} +(-0.141691 - 0.245416i) q^{22} +(0.661990 + 0.382200i) q^{23} +(0.601783 - 13.1453i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(8.11501 + 14.0556i) q^{26} +(-5.14729 - 0.710892i) q^{27} +(-7.04555 - 10.8625i) q^{28} +(8.71958 + 5.03425i) q^{29} +(-3.83025 - 2.45154i) q^{30} +5.37088i q^{31} -11.4818i q^{32} +(-0.166002 + 0.0859698i) q^{33} +(-2.92850 - 1.69077i) q^{34} +(-2.64220 + 0.136993i) q^{35} +(-14.6195 - 1.34135i) q^{36} +(-0.952679 - 1.65009i) q^{37} +(3.37743 + 5.84988i) q^{38} +(9.50740 - 4.92372i) q^{39} +(-6.57955 - 3.79871i) q^{40} +(3.87282 + 6.70793i) q^{41} +(-10.3833 + 6.07892i) q^{42} +(-3.74174 + 6.48088i) q^{43} +(-0.457414 + 0.264088i) q^{44} +(-1.73110 + 2.45016i) q^{45} +(1.00349 - 1.73810i) q^{46} -7.71436 q^{47} +(-17.5797 - 0.804786i) q^{48} +(-2.85429 + 6.39164i) q^{49} +(-2.27381 + 1.31279i) q^{50} +(-1.20256 + 1.87886i) q^{51} +(26.1973 - 15.1250i) q^{52} +(-4.83694 - 2.79261i) q^{53} +(-1.86650 + 13.5146i) q^{54} +0.107931i q^{55} +(-16.8641 + 10.9383i) q^{56} +(3.95694 - 2.04923i) q^{57} +(13.2178 - 22.8939i) q^{58} +2.37037 q^{59} +(-4.56926 + 7.13895i) q^{60} -8.37710i q^{61} +14.1016 q^{62} +(3.69273 + 7.02593i) q^{63} -9.82559 q^{64} -6.18152i q^{65} +(0.225720 + 0.435851i) q^{66} -8.43763 q^{67} +(-3.15131 + 5.45823i) q^{68} +(-1.11513 - 0.713733i) q^{69} +(0.359686 + 6.93729i) q^{70} -10.2356i q^{71} +(-2.08246 + 22.6969i) q^{72} +(9.71863 + 5.61106i) q^{73} +(-4.33242 + 2.50133i) q^{74} +(0.796522 + 1.53804i) q^{75} +(10.9032 - 6.29496i) q^{76} +(0.254363 + 0.129783i) q^{77} +(-12.9276 - 24.9623i) q^{78} -10.1831 q^{79} +(-5.08015 + 8.79908i) q^{80} +(8.84974 + 1.63773i) q^{81} +(17.6121 - 10.1684i) q^{82} +(-7.13623 + 12.3603i) q^{83} +(11.3301 + 19.3527i) q^{84} +(0.643963 + 1.11538i) q^{85} +(17.0160 + 9.82420i) q^{86} +(-14.6882 - 9.40113i) q^{87} +(0.410000 + 0.710140i) q^{88} +(-0.334543 - 0.579445i) q^{89} +(6.43307 + 4.54514i) q^{90} +(-14.5681 - 7.43304i) q^{91} +(-3.23953 - 1.87034i) q^{92} +(0.425422 - 9.29291i) q^{93} +20.2546i q^{94} -2.57272i q^{95} +(-0.909458 + 19.8662i) q^{96} +(7.16437 + 4.13635i) q^{97} +(16.7817 + 7.49415i) q^{98} +(0.294033 - 0.135599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	2.62557i		−	1.85656i	−0.371883	−	0.928280i	$-0.621288\pi$
$2$		−	2.62557i		−	1.85656i	0.371883	−	0.928280i	$-0.378712\pi$
$3$	−1.73024	−	0.0792089i	−0.998954	−	0.0457313i
$3$	−1.73024	−	0.0792089i	−0.998954	−	0.0457313i
$4$	−4.89362			−2.44681
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.207969	+	4.54286i	−0.0849028	+	1.85462i
$7$	1.43974	+	2.21972i	0.544171	+	0.838974i
$7$	1.43974	+	2.21972i	0.544171	+	0.838974i
$8$			7.59741i			2.68609i
$9$	2.98745	+	0.274101i	0.995817	+	0.0913669i
$10$	2.27381	+	1.31279i	0.719042	+	0.415139i
$11$	0.0934713	−	0.0539657i	0.0281827	−	0.0162713i	−0.485842	−	0.874046i	$-0.661487\pi$
$11$	0.0934713	−	0.0539657i	0.0281827	−	0.0162713i	0.514025	+	0.857775i	$0.328154\pi$
$12$	8.46714	+	0.387619i	2.44425	+	0.111896i
$13$	−5.35335	+	3.09076i	−1.48475	+	0.857223i	−0.999850	−	0.0173448i	$-0.994479\pi$
$13$	−5.35335	+	3.09076i	−1.48475	+	0.857223i	−0.484904	+	0.874568i	$0.661145\pi$
$14$	5.82803	−	3.78014i	1.55761	−	1.01029i
$15$	0.933716	−	1.45883i	0.241085	−	0.376667i
$16$	10.1603			2.54008
$17$	0.643963	−	1.11538i	0.156184	−	0.270519i	−0.777306	−	0.629123i	$-0.783414\pi$
$17$	0.643963	−	1.11538i	0.156184	−	0.270519i	0.933490	+	0.358605i	$0.116747\pi$
$18$	0.719671	−	7.84377i	0.169628	−	1.84879i
$19$	−2.22804	+	1.28636i	−0.511148	+	0.295111i	−0.733305	−	0.679899i	$-0.762023\pi$
$19$	−2.22804	+	1.28636i	−0.511148	+	0.295111i	0.222158	+	0.975011i	$0.428690\pi$
$20$	2.44681	−	4.23800i	0.547124	−	0.947646i
$21$	−2.31527	−	3.95468i	−0.505234	−	0.862982i
$22$	−0.141691	−	0.245416i	−0.0302086	−	0.0523228i
$23$	0.661990	+	0.382200i	0.138034	+	0.0796942i	0.567427	−	0.823424i	$-0.307939\pi$
$23$	0.661990	+	0.382200i	0.138034	+	0.0796942i	−0.429392	+	0.903118i	$0.641272\pi$
$24$	0.601783	−	13.1453i	0.122838	−	2.68328i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	8.11501	+	14.0556i	1.59148	+	2.75653i
$27$	−5.14729	−	0.710892i	−0.990597	−	0.136811i
$28$	−7.04555	−	10.8625i	−1.33148	−	2.05281i
$29$	8.71958	+	5.03425i	1.61919	+	0.934838i	0.987131	+	0.159914i	$0.0511217\pi$
$29$	8.71958	+	5.03425i	1.61919	+	0.934838i	0.632055	+	0.774923i	$0.282212\pi$
$30$	−3.83025	−	2.45154i	−0.699305	−	0.447588i
$31$			5.37088i			0.964639i	0.875995	+	0.482320i	$0.160206\pi$
$31$			5.37088i			0.964639i	−0.875995	+	0.482320i	$0.839794\pi$
$32$		−	11.4818i		−	2.02971i
$33$	−0.166002	+	0.0859698i	−0.0288973	+	0.0149654i
$34$	−2.92850	−	1.69077i	−0.502234	−	0.289965i
$35$	−2.64220	+	0.136993i	−0.446614	+	0.0231561i
$36$	−14.6195	−	1.34135i	−2.43658	−	0.223558i
$37$	−0.952679	−	1.65009i	−0.156619	−	0.271273i	0.777028	−	0.629466i	$-0.216726\pi$
$37$	−0.952679	−	1.65009i	−0.156619	−	0.271273i	−0.933648	+	0.358193i	$0.883393\pi$
$38$	3.37743	+	5.84988i	0.547892	+	0.948976i
$39$	9.50740	−	4.92372i	1.52240	−	0.788426i
$40$	−6.57955	−	3.79871i	−1.04032	−	0.600628i
$41$	3.87282	+	6.70793i	0.604834	+	1.04760i	0.992078	+	0.125625i	$0.0400937\pi$
$41$	3.87282	+	6.70793i	0.604834	+	1.04760i	−0.387244	+	0.921977i	$0.626573\pi$
$42$	−10.3833	+	6.07892i	−1.60218	+	0.937997i
$43$	−3.74174	+	6.48088i	−0.570610	+	0.988325i	0.425894	+	0.904773i	$0.359960\pi$
$43$	−3.74174	+	6.48088i	−0.570610	+	0.988325i	−0.996503	+	0.0835517i	$0.973374\pi$
$44$	−0.457414	+	0.264088i	−0.0689577	+	0.0398127i
$45$	−1.73110	+	2.45016i	−0.258058	+	0.365248i
$46$	1.00349	−	1.73810i	0.147957	−	0.256269i
$47$	−7.71436			−1.12525			−0.562627	−	0.826711i	$-0.690209\pi$
$47$	−7.71436			−1.12525			−0.562627	+	0.826711i	$0.690209\pi$
$48$	−17.5797	−	0.804786i	−2.53742	−	0.116161i
$49$	−2.85429	+	6.39164i	−0.407756	+	0.913091i
$50$	−2.27381	+	1.31279i	−0.321565	+	0.185656i
$51$	−1.20256	+	1.87886i	−0.168392	+	0.263093i
$52$	26.1973	−	15.1250i	3.63291	−	2.09746i
$53$	−4.83694	−	2.79261i	−0.664405	−	0.383595i	0.129548	−	0.991573i	$-0.458647\pi$
$53$	−4.83694	−	2.79261i	−0.664405	−	0.383595i	−0.793953	+	0.607979i	$0.791981\pi$
$54$	−1.86650	+	13.5146i	−0.253998	+	1.83910i
$55$			0.107931i			0.0145535i
$56$	−16.8641	+	10.9383i	−2.25356	+	1.46169i
$57$	3.95694	−	2.04923i	0.524109	−	0.271427i
$58$	13.2178	−	22.8939i	1.73558	−	3.00611i
$59$	2.37037			0.308596			0.154298	−	0.988024i	$-0.450688\pi$
$59$	2.37037			0.308596			0.154298	+	0.988024i	$0.450688\pi$
$60$	−4.56926	+	7.13895i	−0.589888	+	0.921634i
$61$		−	8.37710i		−	1.07258i	−0.844034	−	0.536289i	$-0.819826\pi$
$61$		−	8.37710i		−	1.07258i	0.844034	−	0.536289i	$-0.180174\pi$
$62$	14.1016			1.79091
$63$	3.69273	+	7.02593i	0.465240	+	0.885184i
$64$	−9.82559			−1.22820
$65$		−	6.18152i		−	0.766723i
$66$	0.225720	+	0.435851i	0.0277842	+	0.0536495i
$67$	−8.43763			−1.03082			−0.515410	−	0.856944i	$-0.672360\pi$
$67$	−8.43763			−1.03082			−0.515410	+	0.856944i	$0.672360\pi$
$68$	−3.15131	+	5.45823i	−0.382153	+	0.661908i
$69$	−1.11513	−	0.713733i	−0.134245	−	0.0859233i
$70$	0.359686	+	6.93729i	0.0429907	+	0.829165i
$71$		−	10.2356i		−	1.21474i	−0.794420	−	0.607368i	$-0.792225\pi$
$71$		−	10.2356i		−	1.21474i	0.794420	−	0.607368i	$-0.207775\pi$
$72$	−2.08246	+	22.6969i	−0.245420	+	2.67486i
$73$	9.71863	+	5.61106i	1.13748	+	0.656724i	0.945805	−	0.324734i	$-0.105275\pi$
$73$	9.71863	+	5.61106i	1.13748	+	0.656724i	0.191675	+	0.981459i	$0.438608\pi$
$74$	−4.33242	+	2.50133i	−0.503634	+	0.290773i
$75$	0.796522	+	1.53804i	0.0919745	+	0.177597i
$76$	10.9032	−	6.29496i	1.25068	−	0.722082i
$77$	0.254363	+	0.129783i	0.0289874	+	0.0147902i
$78$	−12.9276	−	24.9623i	−1.46376	−	2.82643i
$79$	−10.1831			−1.14569			−0.572845	−	0.819664i	$-0.694160\pi$
$79$	−10.1831			−1.14569			−0.572845	+	0.819664i	$0.694160\pi$
$80$	−5.08015	+	8.79908i	−0.567978	+	0.983767i
$81$	8.84974	+	1.63773i	0.983304	+	0.181969i
$82$	17.6121	−	10.1684i	1.94494	−	1.12291i
$83$	−7.13623	+	12.3603i	−0.783302	+	1.35672i	0.146705	+	0.989180i	$0.453133\pi$
$83$	−7.13623	+	12.3603i	−0.783302	+	1.35672i	−0.930008	+	0.367539i	$0.880200\pi$
$84$	11.3301	+	19.3527i	1.23621	+	2.11155i
$85$	0.643963	+	1.11538i	0.0698476	+	0.120980i
$86$	17.0160	+	9.82420i	1.83488	+	1.05937i
$87$	−14.6882	−	9.40113i	−1.57474	−	1.00791i
$88$	0.410000	+	0.710140i	0.0437061	+	0.0757012i
$89$	−0.334543	−	0.579445i	−0.0354615	−	0.0614211i	0.847750	−	0.530396i	$-0.177957\pi$
$89$	−0.334543	−	0.579445i	−0.0354615	−	0.0614211i	−0.883211	+	0.468975i	$0.844623\pi$
$90$	6.43307	+	4.54514i	0.678105	+	0.479099i
$91$	−14.5681	−	7.43304i	−1.52715	−	0.779194i
$92$	−3.23953	−	1.87034i	−0.337744	−	0.194997i
$93$	0.425422	−	9.29291i	0.0441142	−	0.963630i
$94$			20.2546i			2.08910i
$95$		−	2.57272i		−	0.263956i
$96$	−0.909458	+	19.8662i	−0.0928212	+	2.02758i
$97$	7.16437	+	4.13635i	0.727431	+	0.419983i	0.817482	−	0.575955i	$-0.195370\pi$
$97$	7.16437	+	4.13635i	0.727431	+	0.419983i	−0.0900505	+	0.995937i	$0.528703\pi$
$98$	16.7817	+	7.49415i	1.69521	+	0.757023i
$99$	0.294033	−	0.135599i	0.0295514	−	0.0136283i
$100$	2.44681	+	4.23800i	0.244681	+	0.423800i
$101$	−5.59462	−	9.69016i	−0.556685	−	0.964207i	−0.997770	−	0.0667415i	$-0.978740\pi$
$101$	−5.59462	−	9.69016i	−0.556685	−	0.964207i	0.441085	−	0.897465i	$-0.354594\pi$
$102$	4.93308	+	3.15740i	0.488448	+	0.312629i
$103$	−2.21297	−	1.27766i	−0.218050	−	0.125891i	0.386997	−	0.922081i	$-0.373512\pi$
$103$	−2.21297	−	1.27766i	−0.218050	−	0.125891i	−0.605047	+	0.796190i	$0.706846\pi$
$104$	−23.4818	−	40.6716i	−2.30258	−	3.98818i
$105$	4.58249	−	0.0277452i	0.447205	−	0.00270766i
$106$	−7.33220	+	12.6997i	−0.712166	+	1.23351i
$107$	−6.29942	+	3.63697i	−0.608988	+	0.351599i	−0.772569	−	0.634931i	$-0.781029\pi$
$107$	−6.29942	+	3.63697i	−0.608988	+	0.351599i	0.163581	+	0.986530i	$0.447695\pi$
$108$	25.1889	+	3.47884i	2.42380	+	0.334751i
$109$	−5.61363	+	9.72309i	−0.537688	+	0.931303i	0.461340	+	0.887223i	$0.347369\pi$
$109$	−5.61363	+	9.72309i	−0.537688	+	0.931303i	−0.999028	+	0.0440795i	$0.985965\pi$
$110$	0.283382			0.0270194
$111$	1.51766	+	2.93051i	0.144050	+	0.278151i
$112$	14.6282	+	22.5530i	1.38223	+	2.13106i
$113$	12.2520	−	7.07371i	1.15257	−	0.665438i	0.203060	−	0.979166i	$-0.434911\pi$
$113$	12.2520	−	7.07371i	1.15257	−	0.665438i	0.949513	+	0.313728i	$0.101578\pi$
$114$	−5.38040	−	10.3892i	−0.503921	−	0.973039i
$115$	−0.661990	+	0.382200i	−0.0617309	+	0.0356403i
$116$	−42.6704	−	24.6357i	−3.96184	−	2.28737i
$117$	−16.8401	+	7.76614i	−1.55686	+	0.717980i
$118$		−	6.22357i		−	0.572926i
$119$	3.40296	−	0.176437i	0.311949	−	0.0161740i
$120$	11.0833	+	7.09383i	1.01176	+	0.647575i
$121$	−5.49418	+	9.51619i	−0.499470	+	0.865108i
$122$	−21.9947			−1.99131
$123$	−6.16958	−	11.9131i	−0.556293	−	1.07417i
$124$		−	26.2831i		−	2.36029i
$125$	1.00000			0.0894427
$126$	18.4471	−	9.69553i	1.64340	−	0.863746i
$127$	−4.51354			−0.400512			−0.200256	−	0.979744i	$-0.564177\pi$
$127$	−4.51354			−0.400512			−0.200256	+	0.979744i	$0.564177\pi$
$128$			2.83425i			0.250514i
$129$	6.98744	−	10.9171i	0.615210	−	0.961196i
$130$	−16.2300			−1.42347
$131$	1.14246	−	1.97879i	0.0998169	−	0.172888i	−0.811792	−	0.583947i	$-0.801508\pi$
$131$	1.14246	−	1.97879i	0.0998169	−	0.172888i	0.911609	+	0.411059i	$0.134841\pi$
$132$	0.812353	−	0.420704i	0.0707062	−	0.0366176i
$133$	−6.06316	−	3.09360i	−0.525743	−	0.268249i
$134$			22.1536i			1.91378i
$135$	3.18930	−	4.10224i	0.274491	−	0.353065i
$136$	8.47398	+	4.89245i	0.726637	+	0.419524i
$137$	11.8336	−	6.83212i	1.01101	−	0.583707i	0.0995231	−	0.995035i	$-0.468268\pi$
$137$	11.8336	−	6.83212i	1.01101	−	0.583707i	0.911487	+	0.411328i	$0.134935\pi$
$138$	−1.87396	+	2.92784i	−0.159522	+	0.249235i
$139$	14.1970	−	8.19662i	1.20417	−	0.695229i	0.242691	−	0.970104i	$-0.421970\pi$
$139$	14.1970	−	8.19662i	1.20417	−	0.695229i	0.961480	+	0.274875i	$0.0886365\pi$
$140$	12.9299	−	0.670394i	1.09278	−	0.0566586i
$141$	13.3477	+	0.611046i	1.12408	+	0.0514593i
$142$	−26.8742			−2.25523
$143$	−0.333590	+	0.577795i	−0.0278962	+	0.0483177i
$144$	30.3534	+	2.78495i	2.52945	+	0.232079i
$145$	−8.71958	+	5.03425i	−0.724122	+	0.418072i
$146$	14.7322	−	25.5170i	1.21925	−	2.11180i
$147$	5.44488	−	10.8330i	0.449086	−	0.893488i
$148$	4.66205	+	8.07491i	0.383218	+	0.663754i
$149$	4.64855	+	2.68384i	0.380824	+	0.219869i	0.678177	−	0.734899i	$-0.262770\pi$
$149$	4.64855	+	2.68384i	0.380824	+	0.219869i	−0.297353	+	0.954768i	$0.596104\pi$
$150$	4.03822	−	2.09133i	0.329719	−	0.170756i
$151$	1.12253	+	1.94428i	0.0913501	+	0.158223i	0.908079	−	0.418798i	$-0.137548\pi$
$151$	1.12253	+	1.94428i	0.0913501	+	0.158223i	−0.816729	+	0.577021i	$0.804215\pi$
$152$	−9.77301	−	16.9274i	−0.792696	−	1.37299i
$153$	2.22953	−	3.15562i	0.180247	−	0.255117i
$154$	0.340755	−	0.667848i	0.0274589	−	0.0538168i
$155$	−4.65132	−	2.68544i	−0.373603	−	0.215700i
$156$	−46.5256	+	24.0948i	−3.72503	+	1.92913i
$157$		−	15.8193i		−	1.26252i	−0.775572	−	0.631259i	$-0.782539\pi$
$157$		−	15.8193i		−	1.26252i	0.775572	−	0.631259i	$-0.217461\pi$
$158$			26.7365i			2.12704i
$159$	8.14787	+	5.21501i	0.646168	+	0.413577i
$160$	9.94350	+	5.74088i	0.786103	+	0.453857i
$161$	0.104718	+	2.01970i	0.00825291	+	0.159175i
$162$	4.29996	−	23.2356i	0.337837	−	1.82556i
$163$	4.56650	+	7.90941i	0.357676	+	0.619513i	0.987572	−	0.157167i	$-0.0502360\pi$
$163$	4.56650	+	7.90941i	0.357676	+	0.619513i	−0.629896	+	0.776679i	$0.716903\pi$
$164$	−18.9521	−	32.8261i	−1.47991	−	2.56329i
$165$	0.00854913	−	0.186747i	0.000665549	−	0.0145382i
$166$	32.4529	+	18.7367i	2.51883	+	1.45425i
$167$	−1.79055	−	3.10133i	−0.138557	−	0.239988i	0.788394	−	0.615171i	$-0.210913\pi$
$167$	−1.79055	−	3.10133i	−0.138557	−	0.239988i	−0.926951	+	0.375183i	$0.877580\pi$
$168$	30.0453	−	17.5901i	2.31805	−	1.35711i
$169$	12.6056	−	21.8335i	0.969662	−	1.67950i
$170$	2.92850	−	1.69077i	0.224606	−	0.129676i
$171$	−7.00876	+	3.23223i	−0.535973	+	0.247175i
$172$	18.3107	−	31.7150i	1.39617	−	2.41824i
$173$	−0.110691			−0.00841570			−0.00420785	−	0.999991i	$-0.501339\pi$
$173$	−0.110691			−0.00841570			−0.00420785	+	0.999991i	$0.501339\pi$
$174$	−24.6833	+	38.5649i	−1.87124	+	2.92360i
$175$	1.20246	−	2.35671i	0.0908975	−	0.178151i
$176$	0.949697	−	0.548308i	0.0715861	−	0.0413303i
$177$	−4.10130	−	0.187754i	−0.308273	−	0.0141125i
$178$	−1.52137	+	0.878366i	−0.114032	+	0.0658363i
$179$	−0.238794	−	0.137868i	−0.0178483	−	0.0103047i	0.491049	−	0.871132i	$-0.336613\pi$
$179$	−0.238794	−	0.137868i	−0.0178483	−	0.0103047i	−0.508898	+	0.860827i	$0.669947\pi$
$180$	8.47137	−	11.9902i	0.631419	−	0.893693i
$181$			9.56064i			0.710637i	0.934745	+	0.355319i	$0.115628\pi$
$181$			9.56064i			0.710637i	−0.934745	+	0.355319i	$0.884372\pi$
$182$	−19.5160	+	38.2495i	−1.44662	+	2.83524i
$183$	−0.663541	+	14.4944i	−0.0490504	+	1.07146i
$184$	−2.90373	+	5.02941i	−0.214066	+	0.370773i
$185$	1.90536			0.140085
$186$	−24.3992	−	1.11698i	−1.78904	−	0.0819006i
$187$		−	0.139008i		−	0.0101652i
$188$	37.7512			2.75329
$189$	−5.83279	−	12.4490i	−0.424273	−	0.905534i
$190$	−6.75486			−0.490049
$191$		−	13.3403i		−	0.965268i	−0.875822	−	0.482634i	$-0.839680\pi$
$191$		−	13.3403i		−	0.965268i	0.875822	−	0.482634i	$-0.160320\pi$
$192$	17.0006	+	0.778274i	1.22691	+	0.0561671i
$193$	15.3866			1.10755			0.553775	−	0.832666i	$-0.313187\pi$
$193$	15.3866			1.10755			0.553775	+	0.832666i	$0.313187\pi$
$194$	10.8603	−	18.8106i	0.779722	−	1.35052i
$195$	−0.489632	+	10.6955i	−0.0350632	+	0.765921i
$196$	13.9678	−	31.2783i	0.997702	−	2.23416i
$197$		−	12.1119i		−	0.862940i	−0.902127	−	0.431470i	$-0.857995\pi$
$197$		−	12.1119i		−	0.862940i	0.902127	−	0.431470i	$-0.142005\pi$
$198$	−0.356026	−	0.772005i	−0.0253017	−	0.0548640i
$199$	0.805586	+	0.465105i	0.0571065	+	0.0329704i	0.528281	−	0.849069i	$-0.322837\pi$
$199$	0.805586	+	0.465105i	0.0571065	+	0.0329704i	−0.471175	+	0.882040i	$0.656170\pi$
$200$	6.57955	−	3.79871i	0.465245	−	0.268609i
$201$	14.5991	+	0.668335i	1.02974	+	0.0471407i
$202$	−25.4422	+	14.6891i	−1.79011	+	1.03352i
$203$	1.37932	+	26.6030i	0.0968092	+	1.86717i
$204$	5.88486	−	9.19443i	0.412023	−	0.643739i
$205$	−7.74565			−0.540980
$206$	−3.35458	+	5.81030i	−0.233724	+	0.404823i
$207$	1.87290	+	1.32326i	0.130176	+	0.0919726i
$208$	−54.3917	+	31.4031i	−3.77138	+	2.17741i
$209$	−0.138839	+	0.240476i	−0.00960367	+	0.0166341i
$210$	−0.0728471	−	12.0317i	−0.00502693	−	0.830263i
$211$	4.55602	+	7.89127i	0.313650	+	0.543257i	0.979150	−	0.203141i	$-0.0651149\pi$
$211$	4.55602	+	7.89127i	0.313650	+	0.543257i	−0.665500	+	0.746398i	$0.731782\pi$
$212$	23.6702	+	13.6660i	1.62567	+	0.938584i
$213$	−0.810747	+	17.7100i	−0.0555515	+	1.21347i
$214$	9.54913	+	16.5396i	0.652765	+	1.13062i
$215$	−3.74174	−	6.48088i	−0.255184	−	0.441992i
$216$	5.40094	−	39.1061i	0.367488	−	2.66083i
$217$	−11.9218	+	7.73268i	−0.809308	+	0.524929i
$218$	25.5287	+	14.7390i	1.72902	+	0.998249i
$219$	−16.3711	−	10.4783i	−1.10626	−	0.708056i
$220$		−	0.528176i		−	0.0356096i
$221$			7.96134i			0.535538i
$222$	7.69426	−	3.98473i	0.516405	−	0.267437i
$223$	5.56608	+	3.21358i	0.372732	+	0.215197i	0.674651	−	0.738137i	$-0.264294\pi$
$223$	5.56608	+	3.21358i	0.372732	+	0.215197i	−0.301919	+	0.953333i	$0.597627\pi$
$224$	25.4863	−	16.5308i	1.70287	−	1.10451i
$225$	−1.25635	−	2.72426i	−0.0837565	−	0.181617i
$226$	−18.5725	−	32.1686i	−1.23543	−	2.13982i
$227$	9.71303	+	16.8235i	0.644677	+	1.11661i	0.984376	+	0.176079i	$0.0563414\pi$
$227$	9.71303	+	16.8235i	0.644677	+	1.11661i	−0.339699	+	0.940534i	$0.610325\pi$
$228$	−19.3638	+	10.0282i	−1.28240	+	0.664131i
$229$	−0.0678442	−	0.0391699i	−0.00448327	−	0.00258842i	0.497757	−	0.867317i	$-0.334157\pi$
$229$	−0.0678442	−	0.0391699i	−0.00448327	−	0.00258842i	−0.502240	+	0.864728i	$0.667491\pi$
$230$	1.00349	+	1.73810i	0.0661684	+	0.114607i
$231$	−0.429829	−	0.244704i	−0.0282807	−	0.0161003i
$232$	−38.2473	+	66.2463i	−2.51106	+	4.34928i
$233$	−13.4942	+	7.79085i	−0.884031	+	0.510396i	−0.871985	−	0.489532i	$-0.837168\pi$
$233$	−13.4942	+	7.79085i	−0.884031	+	0.510396i	−0.0120459	+	0.999927i	$0.503834\pi$
$234$	20.3906	+	44.2148i	1.33297	+	2.89041i
$235$	3.85718	−	6.68083i	0.251615	−	0.435809i
$236$	−11.5997			−0.755076
$237$	17.6192	+	0.806594i	1.14449	+	0.0523939i
$238$	−0.463249	−	8.93471i	−0.0300279	−	0.579152i
$239$	−9.50772	+	5.48929i	−0.615003	+	0.355072i	−0.774921	−	0.632058i	$-0.782210\pi$
$239$	−9.50772	+	5.48929i	−0.615003	+	0.355072i	0.159918	+	0.987130i	$0.448877\pi$
$240$	9.48684	−	14.8221i	0.612373	−	0.956763i
$241$	−20.4879	+	11.8287i	−1.31974	+	0.761954i	−0.983687	−	0.179889i	$-0.942426\pi$
$241$	−20.4879	+	11.8287i	−1.31974	+	0.761954i	−0.336055	+	0.941842i	$0.609093\pi$
$242$	24.9854	+	14.4253i	1.60612	+	0.927296i
$243$	−15.1824	−	3.53463i	−0.973954	−	0.226747i
$244$			40.9944i			2.62440i
$245$	−4.10817	−	5.66771i	−0.262462	−	0.362097i
$246$	−31.2786	+	16.1987i	−1.99425	+	1.03279i
$247$	7.95166	−	13.7727i	0.505952	−	0.876335i
$248$	−40.8048			−2.59111
$249$	13.3264	−	20.8210i	0.844528	−	1.31948i
$250$		−	2.62557i		−	0.166056i
$251$	−10.0851			−0.636567			−0.318283	−	0.947996i	$-0.603106\pi$
$251$	−10.0851			−0.636567			−0.318283	+	0.947996i	$0.603106\pi$
$252$	−18.0708	−	34.3823i	−1.13836	−	2.16588i
$253$	0.0825028			0.00518690
$254$			11.8506i			0.743574i
$255$	−1.02586	−	1.98088i	−0.0642420	−	0.124047i
$256$	−12.2097			−0.763103
$257$	0.943020	−	1.63336i	0.0588240	−	0.101886i	−0.835114	−	0.550077i	$-0.814598\pi$
$257$	0.943020	−	1.63336i	0.0588240	−	0.101886i	0.893938	+	0.448191i	$0.147932\pi$
$258$	−28.6636	−	18.3460i	−1.78452	−	1.14217i
$259$	2.29112	−	4.49038i	0.142363	−	0.279019i
$260$			30.2500i			1.87603i
$261$	24.6694	+	17.4296i	1.52700	+	1.07887i
$262$	−5.19546	−	2.99960i	−0.320977	−	0.185316i
$263$	24.8390	−	14.3408i	1.53164	−	0.884291i	0.532350	−	0.846524i	$-0.321309\pi$
$263$	24.8390	−	14.3408i	1.53164	−	0.884291i	0.999287	−	0.0377663i	$-0.0120242\pi$
$264$	−0.653148	−	1.26119i	−0.0401985	−	0.0776208i
$265$	4.83694	−	2.79261i	0.297131	−	0.171549i
$266$	−8.12246	+	15.9193i	−0.498020	+	0.976072i
$267$	0.532942	+	1.02908i	0.0326155	+	0.0629785i
$268$	41.2906			2.52222
$269$	15.5910	−	27.0044i	0.950601	−	1.64649i	0.206472	−	0.978452i	$-0.433802\pi$
$269$	15.5910	−	27.0044i	0.950601	−	1.64649i	0.744129	−	0.668036i	$-0.232865\pi$
$270$	−10.7707	−	8.37373i	−0.655485	−	0.509609i
$271$	9.11994	−	5.26540i	0.553997	−	0.319850i	−0.196736	−	0.980457i	$-0.563034\pi$
$271$	9.11994	−	5.26540i	0.553997	−	0.319850i	0.750733	+	0.660606i	$0.229701\pi$
$272$	6.54286	−	11.3326i	0.396719	−	0.687137i
$273$	24.6175	+	14.0149i	1.48992	+	0.848218i
$274$	−17.9382	−	31.0699i	−1.08369	−	1.87700i
$275$	−0.0934713	−	0.0539657i	−0.00563653	−	0.00325425i
$276$	5.45701	+	3.49274i	0.328473	+	0.210238i
$277$	10.7303	+	18.5853i	0.644718	+	1.11668i	0.984367	+	0.176132i	$0.0563586\pi$
$277$	10.7303	+	18.5853i	0.644718	+	1.11668i	−0.339648	+	0.940553i	$0.610308\pi$
$278$	−21.5208	−	37.2751i	−1.29073	−	2.23561i
$279$	−1.47216	+	16.0453i	−0.0881361	+	0.960604i
$280$	−1.04080	−	20.0739i	−0.0621994	−	1.19965i
$281$	7.44154	+	4.29637i	0.443925	+	0.256300i	0.705261	−	0.708948i	$-0.250830\pi$
$281$	7.44154	+	4.29637i	0.443925	+	0.256300i	−0.261336	+	0.965248i	$0.584163\pi$
$282$	1.60434	−	35.0453i	0.0955373	−	2.08692i
$283$			4.57998i			0.272251i	0.990692	+	0.136126i	$0.0434651\pi$
$283$			4.57998i			0.272251i	−0.990692	+	0.136126i	$0.956535\pi$
$284$			50.0889i			2.97223i
$285$	−0.203782	+	4.45142i	−0.0120710	+	0.263679i
$286$	1.51704	+	0.875865i	0.0897046	+	0.0517910i
$287$	−9.31384	+	18.2543i	−0.549779	+	1.07751i
$288$	3.14716	−	34.3012i	0.185448	−	2.02122i
$289$	7.67062	+	13.2859i	0.451213	+	0.781524i
$290$	13.2178	+	22.8939i	0.776175	+	1.34438i
$291$	−12.0684	−	7.72435i	−0.707464	−	0.452810i
$292$	−47.5593	−	27.4584i	−2.78320	−	1.60688i
$293$	−3.19302	−	5.53047i	−0.186538	−	0.323094i	0.757556	−	0.652771i	$-0.226393\pi$
$293$	−3.19302	−	5.53047i	−0.186538	−	0.323094i	−0.944094	+	0.329677i	$0.893060\pi$
$294$	−28.4427	−	14.2959i	−1.65881	−	0.833755i
$295$	−1.18518	+	2.05280i	−0.0690041	+	0.119519i
$296$	12.5364	−	7.23790i	0.728664	−	0.420694i
$297$	−0.519488	+	0.211329i	−0.0301438	+	0.0122626i
$298$	7.04662	−	12.2051i	0.408200	−	0.707023i
$299$	−4.72515			−0.273263
$300$	−3.89788	−	7.52656i	−0.225044	−	0.434546i
$301$	−19.7729	+	1.02519i	−1.13969	+	0.0590908i
$302$	5.10484	−	2.94728i	0.293750	−	0.169597i
$303$	8.91247	+	17.2094i	0.512008	+	0.988656i
$304$	−22.6376	+	13.0698i	−1.29835	+	0.749605i
$305$	7.25479	+	4.18855i	0.415408	+	0.239836i
$306$	−8.28531	−	5.85380i	−0.473640	−	0.334639i
$307$		−	8.86419i		−	0.505906i	−0.967479	−	0.252953i	$-0.918598\pi$
$307$		−	8.86419i		−	0.505906i	0.967479	−	0.252953i	$-0.0814018\pi$
$308$	−1.24476	−	0.635111i	−0.0709266	−	0.0361888i
$309$	3.72776	+	2.38594i	0.212065	+	0.135731i
$310$	−7.05082	+	12.2124i	−0.400460	+	0.693616i
$311$	−6.81606			−0.386503			−0.193252	−	0.981149i	$-0.561903\pi$
$311$	−6.81606			−0.386503			−0.193252	+	0.981149i	$0.561903\pi$
$312$	37.4075	+	72.2316i	2.11778	+	4.08931i
$313$		−	12.1048i		−	0.684203i	−0.939663	−	0.342101i	$-0.888861\pi$
$313$		−	12.1048i		−	0.684203i	0.939663	−	0.342101i	$-0.111139\pi$
$314$	−41.5347			−2.34394
$315$	−7.93100	−	0.314968i	−0.446861	−	0.0177465i
$316$	49.8323			2.80329
$317$			10.8313i			0.608345i	0.952617	+	0.304172i	$0.0983798\pi$
$317$			10.8313i			0.608345i	−0.952617	+	0.304172i	$0.901620\pi$
$318$	13.6924	−	21.3928i	0.767831	−	1.19965i
$319$	1.08671			0.0608440
$320$	4.91279	−	8.50921i	0.274634	−	0.475679i
$321$	11.1876	−	5.79386i	0.624430	−	0.323382i
$322$	5.30286	−	0.274944i	0.295517	−	0.0153220i
$323$			3.31347i			0.184367i
$324$	−43.3073	−	8.01441i	−2.40596	−	0.445245i
$325$	5.35335	+	3.09076i	0.296951	+	0.171445i
$326$	20.7667	−	11.9897i	1.15016	−	0.664046i
$327$	10.4831	−	16.3786i	0.579715	−	0.905739i
$328$	−50.9629	+	29.4234i	−2.81396	+	1.62464i
$329$	−11.1067	−	17.1237i	−0.612331	−	0.944060i
$330$	−0.490318	−	0.0224463i	−0.0269911	−	0.00123563i
$331$	16.1476			0.887553			0.443777	−	0.896137i	$-0.353638\pi$
$331$	16.1476			0.887553			0.443777	+	0.896137i	$0.353638\pi$
$332$	34.9220	−	60.4867i	1.91659	−	3.31964i
$333$	−2.39379	−	5.19069i	−0.131179	−	0.284448i
$334$	−8.14275	+	4.70122i	−0.445552	+	0.257239i
$335$	4.21881	−	7.30720i	0.230498	−	0.399235i
$336$	−23.5239	−	40.1808i	−1.28333	−	2.19204i
$337$	11.4187	+	19.7777i	0.622015	+	1.07736i	0.989110	+	0.147178i	$0.0470189\pi$
$337$	11.4187	+	19.7777i	0.622015	+	1.07736i	−0.367096	+	0.930183i	$0.619648\pi$
$338$	−57.3255	−	33.0969i	−3.11810	−	1.80023i
$339$	−21.7592	+	11.2687i	−1.18180	+	0.612034i
$340$	−3.15131	−	5.45823i	−0.170904	−	0.296014i
$341$	0.289844	+	0.502024i	0.0156959	+	0.0271861i
$342$	8.48646	+	18.4020i	0.458895	+	0.995066i
$343$	−18.2971	+	2.86658i	−0.987949	+	0.154781i
$344$	−49.2379	−	28.4275i	−2.65473	−	1.53271i
$345$	1.17567	−	0.608862i	0.0632962	−	0.0327800i
$346$			0.290628i			0.0156243i
$347$			0.108044i			0.00580012i	0.999996	+	0.00290006i	$0.000923119\pi$
$347$			0.108044i			0.00580012i	−0.999996	+	0.00290006i	$0.999077\pi$
$348$	71.8785	+	46.0056i	3.85309	+	2.46616i
$349$	19.0311	+	10.9876i	1.01871	+	0.588153i	0.913730	−	0.406321i	$-0.133189\pi$
$349$	19.0311	+	10.9876i	1.01871	+	0.588153i	0.104981	+	0.994474i	$0.466522\pi$
$350$	−6.18771	−	3.15715i	−0.330747	−	0.168757i
$351$	29.7525	−	12.1034i	1.58807	−	0.646031i
$352$	−0.619622	−	1.07322i	−0.0330259	−	0.0572026i
$353$	−8.58978	−	14.8779i	−0.457188	−	0.791873i	0.541623	−	0.840621i	$-0.317810\pi$
$353$	−8.58978	−	14.8779i	−0.457188	−	0.791873i	−0.998811	+	0.0487487i	$0.984477\pi$
$354$	−0.492962	+	10.7683i	−0.0262007	+	0.572327i
$355$	8.86425	+	5.11778i	0.470466	+	0.271623i
$356$	1.63713	+	2.83559i	0.0867675	+	0.150286i
$357$	−5.90191	+	0.0357338i	−0.312362	+	0.00189123i
$358$	−0.361982	+	0.626970i	−0.0191313	+	0.0331364i
$359$	−14.1707	+	8.18146i	−0.747901	+	0.431801i	−0.824935	−	0.565228i	$-0.808788\pi$
$359$	−14.1707	+	8.18146i	−0.747901	+	0.431801i	0.0770340	+	0.997028i	$0.475455\pi$
$360$	−18.6149	−	13.1519i	−0.981090	−	0.693167i
$361$	−6.19055	+	10.7224i	−0.325819	+	0.564334i
$362$	25.1021			1.31934
$363$	10.2600	−	16.0301i	0.538510	−	0.841362i
$364$	71.2906	+	36.3745i	3.73664	+	1.90654i
$365$	−9.71863	+	5.61106i	−0.508697	+	0.293696i
$366$	38.0561	+	1.74218i	1.98922	+	0.0910649i
$367$	12.8670	−	7.42876i	0.671651	−	0.387778i	−0.125051	−	0.992150i	$-0.539909\pi$
$367$	12.8670	−	7.42876i	0.671651	−	0.387778i	0.796702	+	0.604372i	$0.206576\pi$
$368$	6.72602	+	3.88327i	0.350618	+	0.202429i
$369$	9.73123	+	21.1012i	0.506588	+	1.09848i
$370$		−	5.00265i		−	0.260076i
$371$	−0.765138	−	14.7573i	−0.0397240	−	0.766160i
$372$	−2.08185	+	45.4760i	−0.107939	+	2.35782i
$373$	1.26992	−	2.19957i	0.0657541	−	0.113889i	−0.831274	−	0.555863i	$-0.812388\pi$
$373$	1.26992	−	2.19957i	0.0657541	−	0.113889i	0.897028	+	0.441973i	$0.145721\pi$
$374$	−0.364974			−0.0188724
$375$	−1.73024	−	0.0792089i	−0.0893491	−	0.00409033i
$376$		−	58.6092i		−	3.02254i
$377$	−62.2387			−3.20546
$378$	−32.6858	+	15.3144i	−1.68118	+	0.787688i
$379$	−9.92334			−0.509728			−0.254864	−	0.966977i	$-0.582031\pi$
$379$	−9.92334			−0.509728			−0.254864	+	0.966977i	$0.582031\pi$
$380$			12.5899i			0.645850i
$381$	7.80950	+	0.357513i	0.400093	+	0.0183159i
$382$	−35.0258			−1.79208
$383$	7.98496	−	13.8303i	0.408012	−	0.706698i	−0.586655	−	0.809837i	$-0.699555\pi$
$383$	7.98496	−	13.8303i	0.408012	−	0.706698i	0.994667	+	0.103139i	$0.0328888\pi$
$384$	0.224498	−	4.90393i	0.0114564	−	0.250252i
$385$	−0.239577	+	0.155393i	−0.0122100	+	0.00791957i
$386$		−	40.3986i		−	2.05623i
$387$	−12.9547	+	18.3357i	−0.658523	+	0.932056i
$388$	−35.0597	−	20.2417i	−1.77989	−	1.02762i
$389$	18.4365	−	10.6443i	0.934768	−	0.539688i	0.0464514	−	0.998921i	$-0.485209\pi$
$389$	18.4365	−	10.6443i	0.934768	−	0.539688i	0.888316	+	0.459232i	$0.151875\pi$
$390$	28.0818	+	1.28556i	1.42198	+	0.0650970i
$391$	0.852594	−	0.492245i	0.0431175	−	0.0248939i
$392$	−48.5599	−	21.6852i	−2.45265	−	1.09527i
$393$	−2.13346	+	3.33329i	−0.107619	+	0.168142i
$394$	−31.8008			−1.60210
$395$	5.09156	−	8.81884i	0.256184	−	0.443724i
$396$	−1.43889	+	0.663572i	−0.0723068	+	0.0333458i
$397$	7.42803	−	4.28857i	0.372802	−	0.215237i	−0.301880	−	0.953346i	$-0.597614\pi$
$397$	7.42803	−	4.28857i	0.372802	−	0.215237i	0.674682	+	0.738109i	$0.264281\pi$
$398$	1.22117	−	2.11512i	0.0612115	−	0.106022i
$399$	10.2457	+	5.83292i	0.512925	+	0.292011i
$400$	−5.08015	−	8.79908i	−0.254008	−	0.439954i
$401$	−18.3829	−	10.6134i	−0.918000	−	0.530007i	−0.0350034	−	0.999387i	$-0.511144\pi$
$401$	−18.3829	−	10.6134i	−0.918000	−	0.530007i	−0.882996	+	0.469380i	$0.844478\pi$
$402$	1.75476	−	38.3310i	0.0875196	−	1.91178i
$403$	−16.6001	−	28.7522i	−0.826911	−	1.43225i
$404$	27.3779	+	47.4200i	1.36210	+	2.35923i
$405$	−5.84318	+	6.84524i	−0.290350	+	0.340142i
$406$	69.8482	−	3.62150i	3.46651	−	0.179732i
$407$	−0.178096	−	0.102824i	−0.00882791	−	0.00509680i
$408$	−14.2745	−	9.13632i	−0.706692	−	0.452315i
$409$			3.51938i			0.174022i	0.996207	+	0.0870112i	$0.0277316\pi$
$409$			3.51938i			0.174022i	−0.996207	+	0.0870112i	$0.972268\pi$
$410$			20.3368i			1.00436i
$411$	−21.0161	+	10.8839i	−1.03665	+	0.536862i
$412$	10.8294	+	6.25237i	0.533527	+	0.308032i
$413$	3.41272	+	5.26155i	0.167929	+	0.258904i
$414$	3.47430	−	4.91744i	0.170753	−	0.241679i
$415$	−7.13623	−	12.3603i	−0.350304	−	0.606743i
$416$	35.4874	+	61.4660i	1.73991	+	3.01362i
$417$	−25.2134	+	13.0576i	−1.23470	+	0.639433i
$418$	0.631386	+	0.364531i	0.0308821	+	0.0178298i
$419$	10.2456	+	17.7459i	0.500529	+	0.866942i	1.00000		0.000610964i	$0.000194476\pi$
$419$	10.2456	+	17.7459i	0.500529	+	0.866942i	−0.499471	+	0.866331i	$0.666472\pi$
$420$	−22.4250	+	0.135775i	−1.09423	+	0.00662513i
$421$	−13.7370	+	23.7931i	−0.669499	+	1.15961i	0.308546	+	0.951210i	$0.400158\pi$
$421$	−13.7370	+	23.7931i	−0.669499	+	1.15961i	−0.978044	+	0.208396i	$0.933176\pi$
$422$	20.7191	−	11.9622i	1.00859	−	0.582309i
$423$	−23.0463	−	2.11451i	−1.12055	−	0.102811i
$424$	21.2166	−	36.7483i	1.03037	−	1.78465i
$425$	−1.28793			−0.0624736
$426$	46.4987	+	2.12867i	2.25287	+	0.103135i
$427$	18.5948	−	12.0609i	0.899866	−	0.583666i
$428$	30.8270	−	17.7980i	1.49008	−	0.860297i
$429$	0.622957	−	0.973300i	0.0300767	−	0.0469914i
$430$	−17.0160	+	9.82420i	−0.820585	+	0.473765i
$431$	1.34674	+	0.777543i	0.0648704	+	0.0374529i	0.532084	−	0.846691i	$-0.321409\pi$
$431$	1.34674	+	0.777543i	0.0648704	+	0.0374529i	−0.467214	+	0.884144i	$0.654742\pi$
$432$	−52.2981	−	7.22288i	−2.51619	−	0.347511i
$433$			8.27463i			0.397653i	0.980035	+	0.198827i	$0.0637131\pi$
$433$			8.27463i			0.397653i	−0.980035	+	0.198827i	$0.936287\pi$
$434$	20.3027	+	31.3017i	0.974561	+	1.50253i
$435$	15.4857	−	8.01979i	0.742483	−	0.384520i
$436$	27.4710	−	47.5811i	1.31562	−	2.27872i
$437$	−1.96659			−0.0940747
$438$	−27.5114	+	42.9835i	−1.31455	+	2.05383i
$439$			3.57096i			0.170433i	0.996362	+	0.0852164i	$0.0271581\pi$
$439$			3.57096i			0.170433i	−0.996362	+	0.0852164i	$0.972842\pi$
$440$	−0.819999			−0.0390919
$441$	−10.2790	+	18.3123i	−0.489477	+	0.872016i
$442$	20.9031			0.994257
$443$			33.5935i			1.59607i	0.602608	+	0.798037i	$0.294128\pi$
$443$			33.5935i			1.59607i	−0.602608	+	0.798037i	$0.705872\pi$
$444$	−7.42686	−	14.3408i	−0.352463	−	0.680584i
$445$	0.669086			0.0317177
$446$	8.43747	−	14.6141i	0.399526	−	0.691999i
$447$	−7.83052	−	5.01189i	−0.370371	−	0.237054i
$448$	−14.1463	−	21.8100i	−0.668350	−	1.03043i
$449$			7.96280i			0.375788i	0.982189	+	0.187894i	$0.0601661\pi$
$449$			7.96280i			0.375788i	−0.982189	+	0.187894i	$0.939834\pi$
$450$	−7.15274	+	3.29863i	−0.337183	+	0.155499i
$451$	0.723996	+	0.417999i	0.0340917	+	0.0196828i
$452$	−59.9568	+	34.6161i	−2.82013	+	1.62820i
$453$	−1.78824	−	3.45298i	−0.0840188	−	0.162235i
$454$	44.1712	−	25.5023i	2.07306	−	1.19688i
$455$	13.7212	−	8.89979i	0.643261	−	0.417229i
$456$	15.5688	+	30.0625i	0.729078	+	1.40780i
$457$	36.6991			1.71671			0.858356	−	0.513055i	$-0.171486\pi$
$457$	36.6991			1.71671			0.858356	+	0.513055i	$0.171486\pi$
$458$	−0.102843	+	0.178130i	−0.00480555	+	0.00832346i
$459$	−4.10758	+	5.28338i	−0.191725	+	0.246607i
$460$	3.23953	−	1.87034i	0.151044	−	0.0872052i
$461$	−3.34188	+	5.78830i	−0.155647	+	0.269588i	−0.933294	−	0.359112i	$-0.883079\pi$
$461$	−3.34188	+	5.78830i	−0.155647	+	0.269588i	0.777648	+	0.628700i	$0.216413\pi$
$462$	−0.642488	+	1.12855i	−0.0298912	+	0.0525047i
$463$	3.45184	+	5.97877i	0.160421	+	0.277857i	0.935020	−	0.354596i	$-0.115382\pi$
$463$	3.45184	+	5.97877i	0.160421	+	0.277857i	−0.774599	+	0.632453i	$0.782048\pi$
$464$	88.5936	+	51.1495i	4.11285	+	2.37456i
$465$	7.83519	+	5.01488i	0.363348	+	0.232560i
$466$	20.4554	+	35.4299i	0.947580	+	1.64126i
$467$	3.63751	+	6.30035i	0.168324	+	0.291545i	0.937831	−	0.347093i	$-0.112831\pi$
$467$	3.63751	+	6.30035i	0.168324	+	0.291545i	−0.769507	+	0.638639i	$0.779498\pi$
$468$	82.4089	−	38.0046i	3.80935	−	1.75676i
$469$	−12.1480	−	18.7292i	−0.560942	−	0.864832i
$470$	−17.5410	−	10.1273i	−0.809106	−	0.467137i
$471$	−1.25303	+	27.3712i	−0.0577366	+	1.26120i
$472$			18.0087i			0.828916i
$473$			0.807702i			0.0371382i
$474$	2.11777	−	46.2605i	0.0972724	−	2.12482i
$475$	2.22804	+	1.28636i	0.102230	+	0.0590223i
$476$	−16.6528	+	0.863418i	−0.763280	+	0.0395747i
$477$	−13.6847	−	9.66860i	−0.626578	−	0.442695i
$478$	14.4125	+	24.9632i	0.659213	+	1.14179i
$479$	7.87363	+	13.6375i	0.359755	+	0.623114i	0.987920	−	0.154966i	$-0.0495268\pi$
$479$	7.87363	+	13.6375i	0.359755	+	0.623114i	−0.628164	+	0.778081i	$0.716194\pi$
$480$	−16.7499	−	10.7207i	−0.764525	−	0.489331i
$481$	10.2001	+	5.88901i	0.465083	+	0.268516i
$482$	31.0571	+	53.7925i	1.41461	+	2.45018i
$483$	−0.0212085	−	3.50286i	−0.000965018	−	0.159385i
$484$	26.8864	−	46.5687i	1.22211	−	2.11676i
$485$	−7.16437	+	4.13635i	−0.325317	+	0.187822i
$486$	−9.28043	+	39.8626i	−0.420969	+	1.80820i
$487$	7.41905	−	12.8502i	0.336189	−	0.582297i	−0.647523	−	0.762046i	$-0.724195\pi$
$487$	7.41905	−	12.8502i	0.336189	−	0.582297i	0.983713	+	0.179749i	$0.0575285\pi$
$488$	63.6443			2.88104
$489$	−7.27464	−	14.0469i	−0.328970	−	0.635221i
$490$	−14.8810	+	10.7863i	−0.672254	+	0.487275i
$491$	28.9366	−	16.7066i	1.30589	−	0.753956i	0.324483	−	0.945891i	$-0.394810\pi$
$491$	28.9366	−	16.7066i	1.30589	−	0.753956i	0.981408	+	0.191935i	$0.0614763\pi$
$492$	30.1916	+	58.2981i	1.36114	+	2.62828i
$493$	11.2302	−	6.48375i	0.505782	−	0.292013i
$494$	−36.1612	−	20.8777i	−1.62697	−	0.939330i
$495$	−0.0295841	+	0.322440i	−0.00132971	+	0.0144926i
$496$			54.5698i			2.45026i
$497$	22.7200	−	14.7365i	1.01913	−	0.661024i
$498$	−54.6671	−	34.9895i	−2.44969	−	1.56792i
$499$	5.34482	−	9.25750i	0.239267	−	0.414423i	−0.721237	−	0.692688i	$-0.756426\pi$
$499$	5.34482	−	9.25750i	0.239267	−	0.414423i	0.960504	+	0.278266i	$0.0897596\pi$
$500$	−4.89362			−0.218849
$501$	2.85243	+	5.50786i	0.127437	+	0.246073i
$502$			26.4792i			1.18182i
$503$	−2.28280			−0.101785			−0.0508925	−	0.998704i	$-0.516207\pi$
$503$	−2.28280			−0.101785			−0.0508925	+	0.998704i	$0.516207\pi$
$504$	−53.3789	+	28.0552i	−2.37769	+	1.24968i
$505$	11.1892			0.497914
$506$		−	0.216617i		−	0.00962980i
$507$	−23.5401	+	36.7788i	−1.04545	+	1.63340i
$508$	22.0876			0.979977
$509$	−11.5546	+	20.0132i	−0.512149	+	0.887067i	0.487752	+	0.872982i	$0.337817\pi$
$509$	−11.5546	+	20.0132i	−0.512149	+	0.887067i	−0.999901	+	0.0140852i	$0.995516\pi$
$510$	−5.20093	+	2.69347i	−0.230301	+	0.119269i
$511$	1.53735	+	29.6511i	0.0680086	+	1.31169i
$512$			37.7258i			1.66726i
$513$	12.3828	−	5.03738i	0.546716	−	0.222406i
$514$	−4.28850	−	2.47597i	−0.189158	−	0.109210i
$515$	2.21297	−	1.27766i	0.0975149	−	0.0563003i
$516$	−34.1939	+	53.4241i	−1.50530	+	2.35187i
$517$	−0.721071	+	0.416311i	−0.0317127	+	0.0183093i
$518$	−11.7898	−	6.01550i	−0.518014	−	0.264306i
$519$	0.191522	+	0.00876774i	0.00840690	+	0.000384861i
$520$	46.9636			2.05949
$521$	7.37414	−	12.7724i	0.323067	−	0.559569i	−0.658052	−	0.752972i	$-0.728619\pi$
$521$	7.37414	−	12.7724i	0.323067	−	0.559569i	0.981119	+	0.193404i	$0.0619527\pi$
$522$	45.7627	−	64.7714i	2.00298	−	2.83497i
$523$	−22.9326	+	13.2401i	−1.00277	+	0.578950i	−0.909067	−	0.416650i	$-0.863204\pi$
$523$	−22.9326	+	13.2401i	−1.00277	+	0.578950i	−0.0937044	+	0.995600i	$0.529871\pi$
$524$	−5.59075	+	9.68346i	−0.244233	+	0.423024i
$525$	−2.26722	+	3.98243i	−0.0989495	+	0.173807i
$526$	−37.6528	−	65.2165i	−1.64174	−	2.84357i
$527$	5.99056	+	3.45865i	0.260953	+	0.150661i
$528$	−1.68663	+	0.873479i	−0.0734013	+	0.0380133i
$529$	−11.2078	−	19.4126i	−0.487298	−	0.844024i
$530$	−7.33220	−	12.6997i	−0.318490	−	0.551641i
$531$	7.08136	+	0.649720i	0.307305	+	0.0281954i
$532$	29.6708	+	15.1389i	1.28639	+	0.656355i
$533$	−41.4652	−	23.9399i	−1.79606	−	1.03695i
$534$	2.70192	−	1.39928i	0.116923	−	0.0605526i
$535$		−	7.27394i		−	0.314480i
$536$		−	64.1041i		−	2.76888i
$537$	0.402250	+	0.257459i	0.0173584	+	0.0111102i
$538$	−70.9020	−	40.9353i	−3.05680	−	1.76485i
$539$	0.0781346	+	0.751469i	0.00336550	+	0.0323681i
$540$	−15.6072	+	20.0748i	−0.671628	+	0.863883i
$541$	−18.8183	−	32.5943i	−0.809062	−	1.40134i	−0.913514	−	0.406807i	$-0.866642\pi$
$541$	−18.8183	−	32.5943i	−0.809062	−	1.40134i	0.104452	−	0.994530i	$-0.466691\pi$
$542$	−13.8247	−	23.9451i	−0.593821	−	1.02853i
$543$	0.757288	−	16.5422i	0.0324983	−	0.709894i
$544$	−12.8065	−	7.39383i	−0.549074	−	0.317008i
$545$	−5.61363	−	9.72309i	−0.240461	−	0.416491i
$546$	36.7970	−	64.6349i	1.57477	−	2.76612i
$547$	15.4329	−	26.7305i	0.659862	−	1.14292i	−0.320788	−	0.947151i	$-0.603948\pi$
$547$	15.4329	−	26.7305i	0.659862	−	1.14292i	0.980651	−	0.195764i	$-0.0627188\pi$
$548$	−57.9091	+	33.4338i	−2.47375	+	1.42822i
$549$	2.29617	−	25.0262i	0.0979981	−	1.06809i
$550$	−0.141691	+	0.245416i	−0.00604172	+	0.0104646i
$551$	−25.9035			−1.10352
$552$	5.42252	−	8.47208i	0.230798	−	0.360596i
$553$	−14.6611	−	22.6036i	−0.623451	−	0.961205i
$554$	48.7971	−	28.1730i	2.07319	−	1.19696i
$555$	−3.29672	−	0.150921i	−0.139938	−	0.00640625i
$556$	−69.4746	+	40.1112i	−2.94638	+	1.70109i
$557$	0.431897	+	0.249356i	0.0183001	+	0.0105655i	0.509122	−	0.860694i	$-0.329970\pi$
$557$	0.431897	+	0.249356i	0.0183001	+	0.0105655i	−0.490822	+	0.871260i	$0.663303\pi$
$558$	42.1280	+	3.86527i	1.78342	+	0.163630i
$559$		−	46.2593i		−	1.95656i
$560$	−26.8456	+	1.39189i	−1.13443	+	0.0588182i
$561$	−0.0110106	+	0.240516i	−0.000464870	+	0.0101546i
$562$	11.2804	−	19.5383i	0.475837	−	0.824173i
$563$	−4.83117			−0.203610			−0.101805	−	0.994804i	$-0.532462\pi$
$563$	−4.83117			−0.203610			−0.101805	+	0.994804i	$0.532462\pi$
$564$	−65.3185	−	2.99023i	−2.75041	−	0.125911i
$565$			14.1474i			0.595186i
$566$	12.0251			0.505451
$567$	9.10604	+	22.0018i	0.382418	+	0.923990i
$568$	77.7637			3.26289
$569$			3.67339i			0.153997i	0.997031	+	0.0769983i	$0.0245336\pi$
$569$			3.67339i			0.153997i	−0.997031	+	0.0769983i	$0.975466\pi$
$570$	11.6875	+	0.535045i	0.489536	+	0.0224106i
$571$	−24.2791			−1.01605			−0.508025	−	0.861342i	$-0.669624\pi$
$571$	−24.2791			−1.01605			−0.508025	+	0.861342i	$0.669624\pi$
$572$	1.63246	−	2.82751i	0.0682568	−	0.118224i
$573$	−1.05667	+	23.0819i	−0.0441430	+	0.964258i
$574$	47.9278	+	24.4542i	2.00047	+	1.02070i
$575$		−	0.764400i		−	0.0318777i
$576$	−29.3535	−	2.69320i	−1.22306	−	0.112217i
$577$	25.8066	+	14.8995i	1.07434	+	0.620273i	0.929365	−	0.369162i	$-0.120355\pi$
$577$	25.8066	+	14.8995i	1.07434	+	0.620273i	0.144979	+	0.989435i	$0.453689\pi$
$578$	34.8831	−	20.1398i	1.45095	−	0.837704i
$579$	−26.6225	−	1.21875i	−1.10639	−	0.0506497i
$580$	42.6704	−	24.6357i	1.77179	−	1.02294i
$581$	−37.7107	+	1.95523i	−1.56450	+	0.0811166i
$582$	−20.2808	+	31.6865i	−0.840668	+	1.31345i
$583$	−0.602821			−0.0249663
$584$	−42.6295	+	73.8365i	−1.76402	+	3.05537i
$585$	1.69436	−	18.4670i	0.0700531	−	0.763516i
$586$	−14.5206	+	8.38350i	−0.599842	+	0.346319i
$587$	10.5048	−	18.1948i	0.433579	−	0.750981i	−0.563599	−	0.826048i	$-0.690584\pi$
$587$	10.5048	−	18.1948i	0.433579	−	0.750981i	0.997178	+	0.0750669i	$0.0239170\pi$
$588$	−26.6452	+	53.0125i	−1.09883	+	2.18620i
$589$	−6.90889	−	11.9666i	−0.284676	−	0.493073i
$590$	5.38977	+	3.11179i	0.221893	+	0.128110i
$591$	−0.959373	+	20.9565i	−0.0394633	+	0.862037i
$592$	−9.67951	−	16.7654i	−0.397825	−	0.689053i
$593$	0.141047	+	0.244300i	0.00579210	+	0.0100322i	0.868907	−	0.494976i	$-0.164823\pi$
$593$	0.141047	+	0.244300i	0.00579210	+	0.0100322i	−0.863115	+	0.505008i	$0.831490\pi$
$594$	0.554860	+	1.36395i	0.0227662	+	0.0559637i
$595$	−1.54868	+	3.03527i	−0.0634897	+	0.124434i
$596$	−22.7483	−	13.1337i	−0.931805	−	0.537978i
$597$	−1.35702	−	0.868552i	−0.0555389	−	0.0355475i
$598$			12.4062i			0.507328i
$599$			46.1600i			1.88604i	0.332729	+	0.943022i	$0.392030\pi$
$599$			46.1600i			1.88604i	−0.332729	+	0.943022i	$0.607970\pi$
$600$	−11.6851	+	6.05151i	−0.477042	+	0.247052i
$601$	−33.5229	−	19.3544i	−1.36743	−	0.789484i	−0.376827	−	0.926284i	$-0.622985\pi$
$601$	−33.5229	−	19.3544i	−1.36743	−	0.789484i	−0.990599	+	0.136800i	$0.956318\pi$
$602$	2.69170	+	51.9150i	0.109705	+	2.11590i
$603$	−25.2070	−	2.31276i	−1.02651	−	0.0941828i
$604$	−5.49323	−	9.51456i	−0.223516	−	0.387142i
$605$	−5.49418	−	9.51619i	−0.223370	−	0.386888i
$606$	45.1846	−	23.4003i	1.83550	−	0.950573i
$607$	2.49638	+	1.44129i	0.101325	+	0.0585000i	0.549806	−	0.835292i	$-0.314702\pi$
$607$	2.49638	+	1.44129i	0.101325	+	0.0585000i	−0.448481	+	0.893792i	$0.648035\pi$
$608$	14.7697	+	25.5819i	0.598990	+	1.03748i
$609$	−0.279353	−	46.1389i	−0.0113200	−	1.86964i
$610$	10.9973	−	19.0480i	0.445269	−	0.771229i
$611$	41.2977	−	23.8432i	1.67073	−	0.964594i
$612$	−10.9105	+	15.4424i	−0.441031	+	0.624223i
$613$	−4.23686	+	7.33845i	−0.171125	+	0.296397i	−0.938813	−	0.344426i	$-0.888074\pi$
$613$	−4.23686	+	7.33845i	−0.171125	+	0.296397i	0.767688	+	0.640823i	$0.221407\pi$
$614$	−23.2735			−0.939244
$615$	13.4018	+	0.613524i	0.540414	+	0.0247397i
$616$	−0.986018	+	1.93250i	−0.0397278	+	0.0778627i
$617$	−13.3572	+	7.71176i	−0.537739	+	0.310464i	−0.744162	−	0.667999i	$-0.767151\pi$
$617$	−13.3572	+	7.71176i	−0.537739	+	0.310464i	0.206423	+	0.978463i	$0.433818\pi$
$618$	6.26445	−	9.78749i	0.251993	−	0.393711i
$619$	24.5106	−	14.1512i	0.985162	−	0.568784i	0.0813377	−	0.996687i	$-0.474081\pi$
$619$	24.5106	−	14.1512i	0.985162	−	0.568784i	0.903825	+	0.427903i	$0.140747\pi$
$620$	22.7618	+	13.1415i	0.914137	+	0.527777i
$621$	−3.13575	−	2.43790i	−0.125833	−	0.0978295i
$622$			17.8960i			0.717566i
$623$	0.804550	−	1.57684i	0.0322336	−	0.0631748i
$624$	96.5980	−	50.0265i	3.86701	−	2.00266i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−31.7820			−1.27026
$627$	0.259272	−	0.405083i	0.0103543	−	0.0161775i
$628$			77.4137i			3.08914i
$629$	−2.45396			−0.0978458
$630$	−0.826972	+	20.8234i	−0.0329473	+	0.829624i
$631$	−10.3968			−0.413890			−0.206945	−	0.978353i	$-0.566352\pi$
$631$	−10.3968			−0.413890			−0.206945	+	0.978353i	$0.566352\pi$
$632$		−	77.3654i		−	3.07743i
$633$	−7.25795	−	14.0147i	−0.288478	−	0.557032i
$634$	28.4383			1.12943
$635$	2.25677	−	3.90884i	0.0895572	−	0.155118i
$636$	−39.8726	−	25.5203i	−1.58105	−	1.01195i
$637$	−4.47498	−	43.0386i	−0.177305	−	1.70525i
$638$		−	2.85323i		−	0.112960i
$639$	2.80557	−	30.5782i	0.110987	−	1.20966i
$640$	−2.45453	−	1.41712i	−0.0970238	−	0.0560167i
$641$	13.2230	−	7.63432i	0.522278	−	0.301538i	−0.215588	−	0.976484i	$-0.569167\pi$
$641$	13.2230	−	7.63432i	0.522278	−	0.301538i	0.737866	+	0.674947i	$0.235833\pi$
$642$	−15.2122	−	29.3738i	−0.600377	−	1.15929i
$643$	26.0206	−	15.0230i	1.02615	−	0.592450i	0.110273	−	0.993901i	$-0.464828\pi$
$643$	26.0206	−	15.0230i	1.02615	−	0.592450i	0.915880	+	0.401452i	$0.131494\pi$
$644$	−0.512449	−	9.88365i	−0.0201933	−	0.389470i
$645$	5.96076	+	11.5098i	0.234705	+	0.453200i
$646$	8.69976			0.342288
$647$	1.09203	−	1.89146i	0.0429323	−	0.0743608i	−0.843761	−	0.536719i	$-0.819663\pi$
$647$	1.09203	−	1.89146i	0.0429323	−	0.0743608i	0.886693	+	0.462359i	$0.152997\pi$
$648$	−12.4425	+	67.2351i	−0.488787	+	2.64124i
$649$	0.221562	−	0.127919i	0.00869705	−	0.00502125i
$650$	8.11501	−	14.0556i	0.318297	−	0.551306i
$651$	21.2401	−	12.4351i	0.832467	−	0.487369i
$652$	−22.3467	−	38.7057i	−0.875165	−	1.51583i
$653$	2.61135	+	1.50766i	0.102190	+	0.0589995i	0.550224	−	0.835017i	$-0.314542\pi$
$653$	2.61135	+	1.50766i	0.102190	+	0.0589995i	−0.448034	+	0.894017i	$0.647876\pi$
$654$	−43.0032	−	27.5240i	−1.68156	−	1.07628i
$655$	1.14246	+	1.97879i	0.0446395	+	0.0773178i
$656$	39.3491	+	68.1546i	1.53632	+	2.66099i
$657$	27.4960	+	19.4266i	1.07272	+	0.757906i
$658$	−44.9595	+	29.1614i	−1.75270	+	1.13683i
$659$	−17.4300	−	10.0632i	−0.678978	−	0.392008i	0.120492	−	0.992714i	$-0.461553\pi$
$659$	−17.4300	−	10.0632i	−0.678978	−	0.392008i	−0.799470	+	0.600706i	$0.794886\pi$
$660$	−0.0418362	+	0.913870i	−0.00162847	+	0.0355723i
$661$			27.5575i			1.07186i	0.844261	+	0.535932i	$0.180040\pi$
$661$			27.5575i			1.07186i	−0.844261	+	0.535932i	$0.819960\pi$
$662$		−	42.3967i		−	1.64780i
$663$	0.630609	−	13.7750i	0.0244908	−	0.534977i
$664$	−93.9063	−	54.2168i	−3.64427	−	2.10402i
$665$	5.71071	−	3.70405i	0.221452	−	0.143637i
$666$	−13.6285	+	6.28507i	−0.528095	+	0.243542i
$667$	3.84818	+	6.66525i	0.149002	+	0.258080i
$668$	8.76228	+	15.1767i	0.339023	+	0.587205i
$669$	−9.37610	−	6.00114i	−0.362501	−	0.232017i
$670$	−19.1856	−	11.0768i	−0.741203	−	0.427934i
$671$	−0.452076	−	0.783019i	−0.0174522	−	0.0302281i
$672$	−45.4067	+	26.5834i	−1.75160	+	1.02548i
$673$	−4.21453	+	7.29978i	−0.162458	+	0.281386i	−0.935750	−	0.352665i	$-0.885276\pi$
$673$	−4.21453	+	7.29978i	−0.162458	+	0.281386i	0.773292	+	0.634051i	$0.218609\pi$
$674$	51.9278	−	29.9805i	2.00018	−	1.15481i
$675$	1.95800	+	4.81313i	0.0753633	+	0.185258i
$676$	−61.6871	+	106.845i	−2.37258	+	4.10943i
$677$	5.69454			0.218859			0.109429	−	0.993995i	$-0.465098\pi$
$677$	5.69454			0.218859			0.109429	+	0.993995i	$0.465098\pi$
$678$	29.5869	+	57.1304i	1.13628	+	2.19408i
$679$	1.13330	+	21.8581i	0.0434922	+	0.838838i
$680$	−8.47398	+	4.89245i	−0.324962	+	0.187617i
$681$	−15.4733	−	29.8780i	−0.592938	−	1.14493i
$682$	1.31810	−	0.761005i	0.0504726	−	0.0291404i
$683$	−3.57383	−	2.06335i	−0.136749	−	0.0789519i	0.430065	−	0.902798i	$-0.358491\pi$
$683$	−3.57383	−	2.06335i	−0.136749	−	0.0789519i	−0.566814	+	0.823846i	$0.691824\pi$
$684$	34.2982	−	15.8173i	1.31143	−	0.604791i
$685$			13.6642i			0.522084i
$686$	7.52640	+	48.0403i	0.287359	+	1.83419i
$687$	0.114284	+	0.0731471i	0.00436021	+	0.00279074i
$688$	−38.0172	+	65.8477i	−1.44939	+	2.51042i
$689$	34.5252			1.31530
$690$	−1.59861	−	3.08682i	−0.0608580	−	0.117513i
$691$		−	32.8653i		−	1.25026i	−0.780523	−	0.625128i	$-0.785047\pi$
$691$		−	32.8653i		−	1.25026i	0.780523	−	0.625128i	$-0.214953\pi$
$692$	0.541682			0.0205916
$693$	0.724324	+	0.457443i	0.0275148	+	0.0173768i
$694$	0.283678			0.0107683
$695$			16.3932i			0.621831i
$696$	71.4243	−	111.592i	2.70733	−	4.22990i
$697$	9.97582			0.377861
$698$	28.8488	−	49.9675i	1.09194	−	1.89130i
$699$	23.9652	−	12.4112i	0.906448	−	0.469434i
$700$	−5.88439	+	11.5329i	−0.222409	+	0.435901i
$701$			14.8571i			0.561143i	0.959833	+	0.280572i	$0.0905240\pi$
$701$			14.8571i			0.561143i	−0.959833	+	0.280572i	$0.909476\pi$
$702$	−31.7783	−	78.1173i	−1.19940	−	2.94835i
$703$	4.24522	+	2.45098i	0.160111	+	0.0924404i
$704$	−0.918411	+	0.530245i	−0.0346139	+	0.0199844i
$705$	−7.20302	+	11.2539i	−0.271281	+	0.423847i
$706$	−39.0631	+	22.5531i	−1.47016	+	0.848796i
$707$	13.4546	−	26.3698i	0.506013	−	0.991738i
$708$	20.0702	+	0.918799i	0.754286	+	0.0345306i
$709$	−46.7657			−1.75632			−0.878161	−	0.478366i	$-0.841229\pi$
$709$	−46.7657			−1.75632			−0.878161	+	0.478366i	$0.841229\pi$
$710$	13.4371	−	23.2737i	0.504285	−	0.873447i
$711$	−30.4216	−	2.79120i	−1.14090	−	0.104678i
$712$	4.40228	−	2.54166i	0.164983	−	0.0952527i
$713$	−2.05275	+	3.55547i	−0.0768762	+	0.133153i
$714$	0.0938216	+	15.4959i	0.00351119	+	0.579919i
$715$	−0.333590	−	0.577795i	−0.0124756	−	0.0216083i
$716$	1.16857	+	0.674673i	0.0436714	+	0.0252137i
$717$	16.8854	−	8.74468i	0.630598	−	0.326576i
$718$	21.4810	+	37.2062i	0.801664	+	1.38852i
$719$	10.5490	+	18.2715i	0.393413	+	0.681410i	0.992897	−	0.118976i	$-0.0379611\pi$
$719$	10.5490	+	18.2715i	0.393413	+	0.681410i	−0.599485	+	0.800386i	$0.704628\pi$
$720$	−17.5885	+	24.8944i	−0.655486	+	0.927758i
$721$	−0.350061	−	6.75165i	−0.0130369	−	0.251445i
$722$	28.1523	+	16.2537i	1.04772	+	0.604901i
$723$	36.3859	−	18.8437i	1.35321	−	0.700803i
$724$		−	46.7862i		−	1.73879i
$725$		−	10.0685i		−	0.373935i
$726$	−42.0882	−	26.9384i	−1.56204	−	0.999776i
$727$	19.2054	+	11.0883i	0.712290	+	0.411241i	0.811908	−	0.583785i	$-0.198429\pi$
$727$	19.2054	+	11.0883i	0.712290	+	0.411241i	−0.0996181	+	0.995026i	$0.531762\pi$
$728$	56.4719	−	110.680i	2.09299	−	4.10206i
$729$	25.9893	+	7.31834i	0.962565	+	0.271050i
$730$	14.7322	+	25.5170i	0.545264	+	0.944425i
$731$	4.81908	+	8.34689i	0.178240	+	0.308721i
$732$	3.24712	−	70.9301i	0.120017	−	2.62165i
$733$	14.9077	+	8.60695i	0.550627	+	0.317905i	0.749375	−	0.662146i	$-0.230354\pi$
$733$	14.9077	+	8.60695i	0.550627	+	0.317905i	−0.198748	+	0.980051i	$0.563687\pi$
$734$	−19.5047	−	33.7832i	−0.719933	−	1.24696i
$735$	6.65919	+	10.1319i	0.245628	+	0.373720i
$736$	4.38833	−	7.60081i	0.161756	−	0.280170i
$737$	−0.788676	+	0.455343i	−0.0290513	+	0.0167728i
$738$	55.4026	−	25.5500i	2.03940	−	0.940510i
$739$	−23.2171	+	40.2133i	−0.854057	+	1.47927i	0.0234608	+	0.999725i	$0.492532\pi$
$739$	−23.2171	+	40.2133i	−0.854057	+	1.47927i	−0.877517	+	0.479545i	$0.840802\pi$
$740$	−9.32410			−0.342761
$741$	−14.8492	+	23.2002i	−0.545499	+	0.852280i
$742$	−38.7463	+	2.00892i	−1.42242	+	0.0737500i
$743$	−13.0366	+	7.52670i	−0.478267	+	0.276128i	−0.719694	−	0.694291i	$-0.755718\pi$
$743$	−13.0366	+	7.52670i	−0.478267	+	0.276128i	0.241427	+	0.970419i	$0.422385\pi$
$744$	70.6021	+	3.23211i	2.58840	+	0.118495i
$745$	−4.64855	+	2.68384i	−0.170310	+	0.0983284i
$746$	−5.77513	−	3.33427i	−0.211442	−	0.122076i
$747$	−24.7071	+	34.9698i	−0.903985	+	1.27948i
$748$			0.680251i			0.0248724i
$749$	−17.1426	−	8.74664i	−0.626376	−	0.319595i
$750$	−0.207969	+	4.54286i	−0.00759394	+	0.165882i
$751$	−13.2560	+	22.9601i	−0.483720	+	0.837827i	−0.999825	−	0.0186978i	$-0.994048\pi$
$751$	−13.2560	+	22.9601i	−0.483720	+	0.837827i	0.516105	+	0.856525i	$0.327381\pi$
$752$	−78.3802			−2.85823
$753$	17.4497	+	0.798831i	0.635901	+	0.0291110i
$754$			163.412i			5.95112i
$755$	−2.24506			−0.0817060
$756$	28.5435	+	60.9209i	1.03812	+	2.21567i
$757$	0.366541			0.0133222			0.00666108	−	0.999978i	$-0.497880\pi$
$757$	0.366541			0.0133222			0.00666108	+	0.999978i	$0.497880\pi$
$758$			26.0544i			0.946339i
$759$	−0.142749	−	0.00653496i	−0.00518148	−	0.000237204i
$760$	19.5460			0.709009
$761$	7.18394	−	12.4429i	0.260418	−	0.451056i	−0.705935	−	0.708276i	$-0.749473\pi$
$761$	7.18394	−	12.4429i	0.260418	−	0.451056i	0.966353	+	0.257220i	$0.0828065\pi$
$762$	0.938675	−	20.5044i	0.0340046	−	0.742796i
$763$	−29.6647	+	1.53806i	−1.07393	+	0.0556815i
$764$			65.2823i			2.36183i
$765$	1.61808	+	3.50864i	0.0585019	+	0.126855i
$766$	−36.3126	−	20.9651i	−1.31203	−	0.757499i
$767$	−12.6894	+	7.32624i	−0.458189	+	0.264535i
$768$	21.1256	+	0.967114i	0.762305	+	0.0348977i
$769$	16.6324	−	9.60274i	0.599781	−	0.346284i	−0.169174	−	0.985586i	$-0.554110\pi$
$769$	16.6324	−	9.60274i	0.599781	−	0.346284i	0.768955	+	0.639302i	$0.220777\pi$
$770$	0.407996	+	0.629027i	0.0147032	+	0.0226686i
$771$	−1.76103	+	2.75140i	−0.0634218	+	0.0990894i
$772$	−75.2961			−2.70997
$773$	−8.19251	+	14.1898i	−0.294664	+	0.510373i	−0.974907	−	0.222614i	$-0.928541\pi$
$773$	−8.19251	+	14.1898i	−0.294664	+	0.510373i	0.680243	+	0.732987i	$0.261874\pi$
$774$	48.1417	+	34.0134i	1.73042	+	1.22259i
$775$	4.65132	−	2.68544i	0.167080	−	0.0964639i
$776$	−31.4255	+	54.4306i	−1.12811	+	1.95395i
$777$	−4.31986	+	7.58795i	−0.154974	+	0.272216i
$778$	−27.9474	−	48.4063i	−1.00196	−	1.73545i
$779$	−17.2576	−	9.96370i	−0.618319	−	0.356987i
$780$	2.39607	−	52.3398i	0.0857931	−	1.87406i
$781$	−0.552369	−	0.956731i	−0.0197653	−	0.0342345i
$782$	−1.29242	−	2.23855i	−0.0462170	−	0.0800502i
$783$	−41.3034	−	32.1115i	−1.47606	−	1.14757i
$784$	−29.0005	+	64.9409i	−1.03573	+	2.31932i
$785$	13.6999	+	7.90965i	0.488971	+	0.282308i
$786$	8.75179	+	5.60155i	0.312166	+	0.199801i
$787$			23.5194i			0.838376i	0.907899	+	0.419188i	$0.137685\pi$
$787$			23.5194i			0.838376i	−0.907899	+	0.419188i	$0.862315\pi$
$788$			59.2713i			2.11145i
$789$	−44.1133	+	22.8455i	−1.57047	+	0.813322i
$790$	−23.1545	−	13.3683i	−0.823800	−	0.475621i
$791$	33.3414	+	17.0117i	1.18548	+	0.604867i
$792$	1.03020	+	2.23389i	0.0366067	+	0.0793779i
$793$	25.8916	+	44.8456i	0.919439	+	1.59251i
$794$	−11.2600	−	19.5028i	−0.399601	−	0.692129i
$795$	−8.59027	+	4.44875i	−0.304665	+	0.157781i
$796$	−3.94223	−	2.27605i	−0.139729	−	0.0806724i
$797$	−7.30322	−	12.6495i	−0.258693	−	0.448070i	0.707199	−	0.707015i	$-0.249959\pi$
$797$	−7.30322	−	12.6495i	−0.258693	−	0.448070i	−0.965892	+	0.258945i	$0.916625\pi$
$798$	15.3147	−	26.9007i	0.542136	−	0.952276i
$799$	−4.96776	+	8.60441i	−0.175747	+	0.304402i
$800$	−9.94350	+	5.74088i	−0.351556	+	0.202971i
$801$	−0.840604	−	1.82276i	−0.0297013	−	0.0644042i
$802$	−27.8662	+	48.2657i	−0.983990	+	1.70432i
$803$	1.21122			0.0427430
$804$	−71.4425	−	3.27058i	−2.51958	−	0.115345i
$805$	−1.80147	−	0.919162i	−0.0634935	−	0.0323962i
$806$	−75.4911	+	43.5848i	−2.65906	+	1.53521i
$807$	−29.1152	+	45.4892i	−1.02490	+	1.60129i
$808$	73.6201	−	42.5046i	2.58995	−	1.49531i
$809$	29.0893	+	16.7947i	1.02272	+	0.590471i	0.914892	−	0.403699i	$-0.132276\pi$
$809$	29.0893	+	16.7947i	1.02272	+	0.590471i	0.107833	+	0.994169i	$0.465609\pi$
$810$	17.9727	+	15.3417i	0.631495	+	0.539052i
$811$		−	39.1986i		−	1.37645i	−0.725499	−	0.688224i	$-0.758391\pi$
$811$		−	39.1986i		−	1.37645i	0.725499	−	0.688224i	$-0.241609\pi$
$812$	−6.74987	−	130.185i	−0.236874	−	4.56861i
$813$	−16.1967	+	8.38802i	−0.568045	+	0.294181i
$814$	−0.269972	+	0.467605i	−0.00946250	+	0.0163895i
$815$	−9.13300			−0.319915
$816$	−12.2183	+	19.0898i	−0.427728	+	0.668276i
$817$		−	19.2529i		−	0.673574i
$818$	9.24039			0.323083
$819$	−41.4840	−	26.1990i	−1.44957	−	0.915466i
$820$	37.9043			1.32368
$821$			20.3298i			0.709516i	0.934958	+	0.354758i	$0.115437\pi$
$821$			20.3298i			0.709516i	−0.934958	+	0.354758i	$0.884563\pi$
$822$	28.5764	+	55.1792i	0.996715	+	1.92460i
$823$	−25.3856			−0.884886			−0.442443	−	0.896797i	$-0.645888\pi$
$823$	−25.3856			−0.884886			−0.442443	+	0.896797i	$0.645888\pi$
$824$	9.70688	−	16.8128i	0.338155	−	0.585702i
$825$	0.157453	+	0.100777i	0.00548182	+	0.00350862i
$826$	13.8146	−	8.96033i	0.480670	−	0.311770i
$827$		−	2.03073i		−	0.0706153i	−0.999376	−	0.0353076i	$-0.988759\pi$
$827$		−	2.03073i		−	0.0706153i	0.999376	−	0.0353076i	$-0.0112411\pi$
$828$	−9.16527	−	6.47552i	−0.318515	−	0.225040i
$829$	31.5729	+	18.2286i	1.09657	+	0.633107i	0.935319	−	0.353806i	$-0.115113\pi$
$829$	31.5729	+	18.2286i	1.09657	+	0.633107i	0.161255	+	0.986913i	$0.448446\pi$
$830$	−32.4529	+	18.7367i	−1.12646	+	0.650359i
$831$	−17.0938	−	33.0070i	−0.592976	−	1.14500i
$832$	52.5998	−	30.3685i	1.82357	−	1.05284i
$833$	5.29102	+	7.29959i	0.183323	+	0.252916i
$834$	34.2836	+	66.1995i	1.18714	+	2.29230i
$835$	3.58110			0.123929
$836$	0.679424	−	1.17680i	0.0234984	−	0.0407004i
$837$	3.81812	−	27.6455i	0.131974	−	0.955569i
$838$	46.5930	−	26.9005i	1.60953	−	0.929262i
$839$	−25.1634	+	43.5842i	−0.868735	+	1.50469i	−0.00544570	+	0.999985i	$0.501733\pi$
$839$	−25.1634	+	43.5842i	−0.868735	+	1.50469i	−0.863290	+	0.504709i	$0.831600\pi$
$840$	0.210792	+	34.8151i	0.00727301	+	1.20123i
$841$	36.1874	+	62.6785i	1.24784	+	2.16133i
$842$	62.4705	+	36.0674i	2.15288	+	1.24296i
$843$	−12.5353	−	8.02319i	−0.431740	−	0.276333i
$844$	−22.2955	−	38.6169i	−0.767442	−	1.32925i
$845$	12.6056	+	21.8335i	0.433646	+	0.751097i
$846$	−5.55180	+	60.5096i	−0.190875	+	2.08036i
$847$	−29.0334	+	1.50533i	−0.997601	+	0.0517238i
$848$	−49.1448	−	28.3738i	−1.68764	−	0.974359i
$849$	0.362775	−	7.92446i	0.0124504	−	0.271967i
$850$			3.38154i			0.115986i
$851$		−	1.45646i		−	0.0499267i
$852$	3.96749	−	86.6658i	0.135924	−	2.96912i
$853$	−31.9795	−	18.4634i	−1.09496	−	0.632175i	−0.160066	−	0.987106i	$-0.551171\pi$
$853$	−31.9795	−	18.4634i	−1.09496	−	0.632175i	−0.934892	+	0.354932i	$0.884504\pi$
$854$	−31.6666	−	48.8220i	−1.08361	−	1.67065i
$855$	0.705185	−	7.68588i	0.0241168	−	0.262852i
$856$	−27.6316	−	47.8593i	−0.944428	−	1.63580i
$857$	19.8629	+	34.4036i	0.678505	+	1.17521i	0.975431	+	0.220305i	$0.0707052\pi$
$857$	19.8629	+	34.4036i	0.678505	+	1.17521i	−0.296926	+	0.954900i	$0.595961\pi$
$858$	−2.55547	−	1.63562i	−0.0872423	−	0.0558391i
$859$	−34.8483	−	20.1197i	−1.18901	−	0.686474i	−0.230926	−	0.972971i	$-0.574176\pi$
$859$	−34.8483	−	20.1197i	−1.18901	−	0.686474i	−0.958081	+	0.286498i	$0.907509\pi$
$860$	18.3107	+	31.7150i	0.624388	+	1.08147i
$861$	17.5611	−	30.8465i	0.598480	−	1.05125i
$862$	2.04150	−	3.53597i	0.0695336	−	0.120436i
$863$	38.0305	−	21.9569i	1.29457	−	0.747422i	0.315112	−	0.949054i	$-0.397958\pi$
$863$	38.0305	−	21.9569i	1.29457	−	0.747422i	0.979461	+	0.201632i	$0.0646245\pi$
$864$	−8.16230	+	59.1000i	−0.277687	+	2.01062i
$865$	0.0553457	−	0.0958615i	0.00188181	−	0.00325939i
$866$	21.7256			0.738267
$867$	−12.2196	−	23.5954i	−0.415001	−	0.801341i
$868$	58.3410	−	37.8408i	1.98022	−	1.28440i
$869$	−0.951830	+	0.549539i	−0.0322886	+	0.0186418i
$870$	−21.0565	−	40.6589i	−0.713883	−	1.37846i
$871$	45.1696	−	26.0787i	1.53051	−	0.883643i
$872$	−73.8703	−	42.6490i	−2.50156	−	1.44428i
$873$	20.2694	+	14.3209i	0.686016	+	0.484689i
$874$			5.16342i			0.174655i
$875$	1.43974	+	2.21972i	0.0486721	+	0.0750402i
$876$	80.1140	+	51.2767i	2.70680	+	1.73248i
$877$	6.26061	−	10.8437i	0.211406	−	0.366165i	−0.740749	−	0.671782i	$-0.765529\pi$
$877$	6.26061	−	10.8437i	0.211406	−	0.366165i	0.952155	+	0.305617i	$0.0988626\pi$
$878$	9.37582			0.316418
$879$	5.08662	+	9.82195i	0.171568	+	0.331286i
$880$			1.09662i			0.0369669i
$881$	−5.13011			−0.172838			−0.0864189	−	0.996259i	$-0.527542\pi$
$881$	−5.13011			−0.172838			−0.0864189	+	0.996259i	$0.527542\pi$
$882$	48.0804	+	26.9883i	1.61895	+	0.908743i
$883$	10.5436			0.354820			0.177410	−	0.984137i	$-0.443228\pi$
$883$	10.5436			0.354820			0.177410	+	0.984137i	$0.443228\pi$
$884$		−	38.9598i		−	1.31036i
$885$	2.21325	−	3.45796i	0.0743976	−	0.116238i
$886$	88.2021			2.96321
$887$	6.68256	−	11.5745i	0.224379	−	0.388635i	−0.731754	−	0.681569i	$-0.761298\pi$
$887$	6.68256	−	11.5745i	0.224379	−	0.388635i	0.956133	+	0.292934i	$0.0946315\pi$
$888$	−22.2643	+	11.5303i	−0.747140	+	0.386931i
$889$	−6.49833	−	10.0188i	−0.217947	−	0.336019i
$890$		−	1.75673i		−	0.0588858i
$891$	0.915578	−	0.324502i	0.0306730	−	0.0108712i
$892$	−27.2383	−	15.7260i	−0.912005	−	0.526546i
$893$	17.1879	−	9.92345i	0.575172	−	0.332075i
$894$	−13.1591	+	20.5596i	−0.440106	+	0.687615i
$895$	0.238794	−	0.137868i	0.00798200	−	0.00460841i
$896$	−6.29123	+	4.08058i	−0.210175	+	0.136323i
$897$	8.17565	+	0.374274i	0.272977	+	0.0124967i
$898$	20.9069			0.697672
$899$	−27.0384	+	46.8319i	−0.901781	+	1.56193i
$900$	6.14809	+	13.3315i	0.204936	+	0.444383i
$901$	−6.22963	+	3.59668i	−0.207539	+	0.119823i
$902$	1.09749	−	1.90090i	0.0365423	−	0.0632932i
$903$	34.2930	−	0.207631i	1.14120	−	0.00690952i
$904$	53.7419	+	93.0837i	1.78743	+	3.09592i
$905$	−8.27976	−	4.78032i	−0.275229	−	0.158903i
$906$	−9.06603	+	4.69515i	−0.301199	+	0.155986i
$907$	29.2716	+	50.6999i	0.971947	+	1.68346i	0.689664	+	0.724130i	$0.257758\pi$
$907$	29.2716	+	50.6999i	0.971947	+	1.68346i	0.282283	+	0.959331i	$0.408908\pi$
$908$	−47.5319	−	82.3277i	−1.57740	−	2.73214i
$909$	−14.0576	−	30.4824i	−0.466260	−	1.01104i
$910$	−23.3670	−	36.0261i	−0.774609	−	1.19425i
$911$	−42.7733	−	24.6952i	−1.41714	−	0.818188i	−0.421097	−	0.907016i	$-0.638355\pi$
$911$	−42.7733	−	24.6952i	−1.41714	−	0.818188i	−0.996047	+	0.0888275i	$0.971688\pi$
$912$	40.2037	−	20.8208i	1.33128	−	0.689445i
$913$			1.54045i			0.0509813i
$914$		−	96.3561i		−	3.18718i
$915$	−12.2207	−	7.82184i	−0.404005	−	0.258582i
$916$	0.332004	+	0.191683i	0.0109697	+	0.00633337i
$917$	6.03720	−	0.313018i	0.199366	−	0.0103368i
$918$	13.8719	+	10.7847i	0.457841	+	0.355949i
$919$	−14.0820	−	24.3908i	−0.464523	−	0.804577i	0.534657	−	0.845069i	$-0.320441\pi$
$919$	−14.0820	−	24.3908i	−0.464523	−	0.804577i	−0.999180	+	0.0404918i	$0.987108\pi$
$920$	−2.90373	−	5.02941i	−0.0957332	−	0.165815i
$921$	−0.702123	+	15.3372i	−0.0231357	+	0.505377i
$922$	15.1976	+	8.77434i	0.500506	+	0.288967i
$923$	31.6356	+	54.7945i	1.04130	+	1.80358i
$924$	2.10342	+	1.19749i	0.0691975	+	0.0393945i
$925$	−0.952679	+	1.65009i	−0.0313239	+	0.0542546i
$926$	15.6977	−	9.06306i	0.515858	−	0.297831i
$927$	−6.26092	−	4.42351i	−0.205636	−	0.145287i
$928$	57.8021	−	100.116i	1.89745	−	3.28648i
$929$	−24.2768			−0.796496			−0.398248	−	0.917278i	$-0.630382\pi$
$929$	−24.2768			−0.796496			−0.398248	+	0.917278i	$0.630382\pi$
$930$	13.1669	−	20.5718i	0.431761	−	0.674577i
$931$	−1.86247	−	17.9125i	−0.0610398	−	0.587058i
$932$	66.0353	−	38.1255i	2.16306	−	1.24884i
$933$	11.7934	+	0.539892i	0.386099	+	0.0176753i
$934$	16.5420	−	9.55054i	0.541271	−	0.312503i
$935$	0.120384	+	0.0695038i	0.00393698	+	0.00227302i
$936$	−59.0026	−	127.941i	−1.92856	−	4.18188i
$937$		−	40.1097i		−	1.31033i	−0.755487	−	0.655163i	$-0.772600\pi$
$937$		−	40.1097i		−	1.31033i	0.755487	−	0.655163i	$-0.227400\pi$
$938$	−49.1747	+	31.8954i	−1.60561	+	1.04142i
$939$	−0.958807	+	20.9442i	−0.0312895	+	0.683487i
$940$	−18.8756	+	32.6935i	−0.615654	+	1.06634i
$941$	14.5699			0.474965			0.237482	−	0.971392i	$-0.423678\pi$
$941$	14.5699			0.474965			0.237482	+	0.971392i	$0.423678\pi$
$942$	71.8649	+	3.28992i	2.34149	+	0.107191i
$943$			5.92077i			0.192807i
$944$	24.0837			0.783856
$945$	13.6976	+	1.17318i	0.445582	+	0.0381634i
$946$	2.12068			0.0689492
$947$			51.1440i			1.66196i	0.556306	+	0.830978i	$0.312218\pi$
$947$			51.1440i			1.66196i	−0.556306	+	0.830978i	$0.687782\pi$
$948$	−86.2218	−	3.94717i	−2.80036	−	0.128198i
$949$	−69.3697			−2.25184
$950$	3.37743	−	5.84988i	0.109578	−	0.189795i
$951$	0.857933	−	18.7407i	0.0278204	−	0.607708i
$952$	1.34047	+	25.8537i	0.0434448	+	0.837923i
$953$			11.2676i			0.364992i	0.983207	+	0.182496i	$0.0584177\pi$
$953$			11.2676i			0.364992i	−0.983207	+	0.182496i	$0.941582\pi$
$954$	−25.3856	+	35.9301i	−0.821889	+	1.16328i
$955$	11.5530	+	6.67014i	0.373847	+	0.215841i
$956$	46.5272	−	26.8625i	1.50480	−	0.868795i
$957$	−1.88026	−	0.0860770i	−0.0607803	−	0.00278247i
$958$	35.8063	−	20.6728i	1.15685	−	0.667907i
$959$	32.2027	+	16.4307i	1.03988	+	0.530575i
$960$	−9.17431	+	14.3338i	−0.296100	+	0.462622i
$961$	2.15360			0.0694711
$962$	15.4620	−	26.7810i	0.498515	−	0.863453i
$963$	−19.8161	+	9.13860i	−0.638565	+	0.294487i
$964$	100.260	−	57.8852i	3.22916	−	1.86436i
$965$	−7.69329	+	13.3252i	−0.247656	+	0.428952i
$966$	−9.19700	+	0.0556843i	−0.295909	+	0.00179161i
$967$	18.2443	+	31.6001i	0.586697	+	1.01619i	0.994661	+	0.103192i	$0.0329055\pi$
$967$	18.2443	+	31.6001i	0.586697	+	1.01619i	−0.407964	+	0.912998i	$0.633761\pi$
$968$	−72.2984	−	41.7415i	−2.32376	−	1.34162i
$969$	0.262457	−	5.73310i	0.00843132	−	0.184174i
$970$	10.8603	+	18.8106i	0.348702	+	0.603970i
$971$	15.7734	+	27.3203i	0.506193	+	0.876752i	0.999974	+	0.00716569i	$0.00228093\pi$
$971$	15.7734	+	27.3203i	0.506193	+	0.876752i	−0.493781	+	0.869586i	$0.664386\pi$
$972$	74.2971	+	17.2972i	2.38308	+	0.554807i
$973$	38.6341	+	19.7122i	1.23855	+	0.631946i
$974$	−33.7390	−	19.4792i	−1.08107	−	0.624155i
$975$	−9.01776	−	5.77179i	−0.288800	−	0.184845i
$976$		−	85.1139i		−	2.72443i
$977$			29.9836i			0.959260i	0.877471	+	0.479630i	$0.159229\pi$
$977$			29.9836i			0.959260i	−0.877471	+	0.479630i	$0.840771\pi$
$978$	−36.8811	+	19.1001i	−1.17933	+	0.610753i
$979$	−0.0625403	−	0.0361077i	−0.00199880	−	0.00115401i
$980$	20.1039	+	27.7356i	0.642194	+	0.885982i
$981$	−19.4355	+	27.5086i	−0.620529	+	0.878281i
$982$	−43.8643	−	75.9751i	−1.39976	−	2.42446i
$983$	0.623637	+	1.08017i	0.0198909	+	0.0344521i	0.875800	−	0.482675i	$-0.160335\pi$
$983$	0.623637	+	1.08017i	0.0198909	+	0.0344521i	−0.855909	+	0.517127i	$0.827001\pi$
$984$	90.5086	−	46.8729i	2.88531	−	1.49425i
$985$	10.4892	+	6.05597i	0.334215	+	0.192959i
$986$	−17.0235	−	29.4856i	−0.542140	−	0.939014i
$987$	17.8609	+	30.5078i	0.568517	+	0.971075i
$988$	−38.9124	+	67.3983i	−1.23797	+	2.14423i
$989$	−4.95398	+	2.86018i	−0.157528	+	0.0909486i
$990$	0.846589	+	0.0776751i	0.0269064	+	0.00246868i
$991$	3.10232	−	5.37338i	0.0985485	−	0.170691i	−0.812536	−	0.582912i	$-0.801913\pi$
$991$	3.10232	−	5.37338i	0.0985485	−	0.170691i	0.911084	+	0.412221i	$0.135247\pi$
$992$	61.6672			1.95794
$993$	−27.9392	−	1.27904i	−0.886625	−	0.0405890i
$994$	−38.6918	−	59.6531i	−1.22723	−	1.89208i
$995$	−0.805586	+	0.465105i	−0.0255388	+	0.0147448i
$996$	−65.2145	+	101.890i	−2.06640	+	3.22852i
$997$	−46.2205	+	26.6854i	−1.46382	+	0.845137i	−0.999185	−	0.0403661i	$-0.987148\pi$
$997$	−46.2205	+	26.6854i	−1.46382	+	0.845137i	−0.464634	+	0.885503i	$0.653814\pi$
$998$	−24.3062	−	14.0332i	−0.769400	−	0.444213i
$999$	3.73068	+	9.17074i	0.118034	+	0.290149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.101.1	✓	32
3.2	odd	2		945.2.t.c.521.16		32
7.5	odd	6		315.2.be.c.236.1	yes	32
9.4	even	3		945.2.be.c.206.16		32
9.5	odd	6		315.2.be.c.311.1	yes	32
21.5	even	6		945.2.be.c.656.16		32
63.5	even	6	inner	315.2.t.c.131.16	yes	32
63.40	odd	6		945.2.t.c.341.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.1	✓	32	1.1	even	1	trivial
315.2.t.c.131.16	yes	32	63.5	even	6	inner
315.2.be.c.236.1	yes	32	7.5	odd	6
315.2.be.c.311.1	yes	32	9.5	odd	6
945.2.t.c.341.1		32	63.40	odd	6
945.2.t.c.521.16		32	3.2	odd	2
945.2.be.c.206.16		32	9.4	even	3
945.2.be.c.656.16		32	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.62557i q^{2} +(-1.73024 - 0.0792089i) q^{3} -4.89362 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.207969 + 4.54286i) q^{6} +(1.43974 + 2.21972i) q^{7} +7.59741i q^{8} +(2.98745 + 0.274101i) q^{9} +O(q^{10})\)	\(q-2.62557i q^{2} +(-1.73024 - 0.0792089i) q^{3} -4.89362 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.207969 + 4.54286i) q^{6} +(1.43974 + 2.21972i) q^{7} +7.59741i q^{8} +(2.98745 + 0.274101i) q^{9} +(2.27381 + 1.31279i) q^{10} +(0.0934713 - 0.0539657i) q^{11} +(8.46714 + 0.387619i) q^{12} +(-5.35335 + 3.09076i) q^{13} +(5.82803 - 3.78014i) q^{14} +(0.933716 - 1.45883i) q^{15} +10.1603 q^{16} +(0.643963 - 1.11538i) q^{17} +(0.719671 - 7.84377i) q^{18} +(-2.22804 + 1.28636i) q^{19} +(2.44681 - 4.23800i) q^{20} +(-2.31527 - 3.95468i) q^{21} +(-0.141691 - 0.245416i) q^{22} +(0.661990 + 0.382200i) q^{23} +(0.601783 - 13.1453i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(8.11501 + 14.0556i) q^{26} +(-5.14729 - 0.710892i) q^{27} +(-7.04555 - 10.8625i) q^{28} +(8.71958 + 5.03425i) q^{29} +(-3.83025 - 2.45154i) q^{30} +5.37088i q^{31} -11.4818i q^{32} +(-0.166002 + 0.0859698i) q^{33} +(-2.92850 - 1.69077i) q^{34} +(-2.64220 + 0.136993i) q^{35} +(-14.6195 - 1.34135i) q^{36} +(-0.952679 - 1.65009i) q^{37} +(3.37743 + 5.84988i) q^{38} +(9.50740 - 4.92372i) q^{39} +(-6.57955 - 3.79871i) q^{40} +(3.87282 + 6.70793i) q^{41} +(-10.3833 + 6.07892i) q^{42} +(-3.74174 + 6.48088i) q^{43} +(-0.457414 + 0.264088i) q^{44} +(-1.73110 + 2.45016i) q^{45} +(1.00349 - 1.73810i) q^{46} -7.71436 q^{47} +(-17.5797 - 0.804786i) q^{48} +(-2.85429 + 6.39164i) q^{49} +(-2.27381 + 1.31279i) q^{50} +(-1.20256 + 1.87886i) q^{51} +(26.1973 - 15.1250i) q^{52} +(-4.83694 - 2.79261i) q^{53} +(-1.86650 + 13.5146i) q^{54} +0.107931i q^{55} +(-16.8641 + 10.9383i) q^{56} +(3.95694 - 2.04923i) q^{57} +(13.2178 - 22.8939i) q^{58} +2.37037 q^{59} +(-4.56926 + 7.13895i) q^{60} -8.37710i q^{61} +14.1016 q^{62} +(3.69273 + 7.02593i) q^{63} -9.82559 q^{64} -6.18152i q^{65} +(0.225720 + 0.435851i) q^{66} -8.43763 q^{67} +(-3.15131 + 5.45823i) q^{68} +(-1.11513 - 0.713733i) q^{69} +(0.359686 + 6.93729i) q^{70} -10.2356i q^{71} +(-2.08246 + 22.6969i) q^{72} +(9.71863 + 5.61106i) q^{73} +(-4.33242 + 2.50133i) q^{74} +(0.796522 + 1.53804i) q^{75} +(10.9032 - 6.29496i) q^{76} +(0.254363 + 0.129783i) q^{77} +(-12.9276 - 24.9623i) q^{78} -10.1831 q^{79} +(-5.08015 + 8.79908i) q^{80} +(8.84974 + 1.63773i) q^{81} +(17.6121 - 10.1684i) q^{82} +(-7.13623 + 12.3603i) q^{83} +(11.3301 + 19.3527i) q^{84} +(0.643963 + 1.11538i) q^{85} +(17.0160 + 9.82420i) q^{86} +(-14.6882 - 9.40113i) q^{87} +(0.410000 + 0.710140i) q^{88} +(-0.334543 - 0.579445i) q^{89} +(6.43307 + 4.54514i) q^{90} +(-14.5681 - 7.43304i) q^{91} +(-3.23953 - 1.87034i) q^{92} +(0.425422 - 9.29291i) q^{93} +20.2546i q^{94} -2.57272i q^{95} +(-0.909458 + 19.8662i) q^{96} +(7.16437 + 4.13635i) q^{97} +(16.7817 + 7.49415i) q^{98} +(0.294033 - 0.135599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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