LMFDB - Embedded newform 357.2.p.a.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	357.16
Dual form			357.2.p.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955129 + 1.65433i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.824544 - 1.42815i) q^{4} +(-1.82126 - 1.05151i) q^{5} -1.91026i q^{6} +(-2.40522 + 1.10223i) q^{7} -0.670332 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.955129 + 1.65433i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.824544 - 1.42815i) q^{4} +(-1.82126 - 1.05151i) q^{5} -1.91026i q^{6} +(-2.40522 + 1.10223i) q^{7} -0.670332 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.47908 - 2.00865i) q^{10} +(-0.220275 + 0.127176i) q^{11} +(1.42815 + 0.824544i) q^{12} +4.96246 q^{13} +(0.473851 - 5.03181i) q^{14} +2.10301 q^{15} +(2.28934 - 3.96526i) q^{16} +(1.49619 - 3.84206i) q^{17} +(0.955129 + 1.65433i) q^{18} +(-0.346640 + 0.600398i) q^{19} +3.46805i q^{20} +(1.53187 - 2.15717i) q^{21} -0.485878i q^{22} +(-4.96251 - 2.86510i) q^{23} +(0.580525 - 0.335166i) q^{24} +(-0.288673 - 0.499996i) q^{25} +(-4.73979 + 8.20956i) q^{26} +1.00000i q^{27} +(3.55736 + 2.52619i) q^{28} -3.82787i q^{29} +(-2.00865 + 3.47908i) q^{30} +(7.44086 - 4.29598i) q^{31} +(3.70290 + 6.41362i) q^{32} +(0.127176 - 0.220275i) q^{33} +(4.92698 + 6.14486i) q^{34} +(5.53953 + 0.521664i) q^{35} -1.64909 q^{36} +(-0.0953196 - 0.0550328i) q^{37} +(-0.662172 - 1.14692i) q^{38} +(-4.29762 + 2.48123i) q^{39} +(1.22085 + 0.704858i) q^{40} +1.60009i q^{41} +(2.10554 + 4.59460i) q^{42} -8.41971 q^{43} +(0.363253 + 0.209724i) q^{44} +(-1.82126 + 1.05151i) q^{45} +(9.47967 - 5.47309i) q^{46} +(-5.32365 + 9.22084i) q^{47} +4.57868i q^{48} +(4.57020 - 5.30220i) q^{49} +1.10288 q^{50} +(0.625288 + 4.07542i) q^{51} +(-4.09177 - 7.08715i) q^{52} +(-1.54625 - 2.67818i) q^{53} +(-1.65433 - 0.955129i) q^{54} +0.534905 q^{55} +(1.61230 - 0.738858i) q^{56} -0.693280i q^{57} +(6.33256 + 3.65611i) q^{58} +(-6.03635 - 10.4553i) q^{59} +(-1.73403 - 3.00342i) q^{60} +(-3.23816 - 1.86955i) q^{61} +16.4129i q^{62} +(-0.248056 + 2.63410i) q^{63} -4.98964 q^{64} +(-9.03793 - 5.21805i) q^{65} +(0.242939 + 0.420782i) q^{66} +(-4.36617 - 7.56242i) q^{67} +(-6.72072 + 1.03116i) q^{68} +5.73021 q^{69} +(-6.15398 + 8.66598i) q^{70} -1.79392i q^{71} +(-0.335166 + 0.580525i) q^{72} +(-3.34020 + 1.92846i) q^{73} +(0.182085 - 0.105127i) q^{74} +(0.499996 + 0.288673i) q^{75} +1.14328 q^{76} +(0.389634 - 0.548679i) q^{77} -9.47958i q^{78} +(-11.1727 - 6.45057i) q^{79} +(-8.33898 + 4.81451i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.64708 - 1.52829i) q^{82} +6.41892 q^{83} +(-4.34386 - 0.409066i) q^{84} +(-6.76490 + 5.42413i) q^{85} +(8.04191 - 13.9290i) q^{86} +(1.91393 + 3.31503i) q^{87} +(0.147658 - 0.0852501i) q^{88} +(6.52655 - 11.3043i) q^{89} -4.01729i q^{90} +(-11.9358 + 5.46975i) q^{91} +9.44962i q^{92} +(-4.29598 + 7.44086i) q^{93} +(-10.1696 - 17.6142i) q^{94} +(1.26264 - 0.728988i) q^{95} +(-6.41362 - 3.70290i) q^{96} +6.18244i q^{97} +(4.40647 + 12.6249i) q^{98} +0.254352i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.955129	+	1.65433i	−0.675378	+	1.16979i	0.300980	+	0.953631i	$0.402686\pi$
$2$	−0.955129	+	1.65433i	−0.675378	+	1.16979i	−0.976358	+	0.216159i	$0.930647\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.824544	−	1.42815i	−0.412272	−	0.714076i
$5$	−1.82126	−	1.05151i	−0.814493	−	0.470247i	0.0340210	−	0.999421i	$-0.489169\pi$
$5$	−1.82126	−	1.05151i	−0.814493	−	0.470247i	−0.848514	+	0.529174i	$0.822502\pi$
$6$		−	1.91026i		−	0.779860i
$7$	−2.40522	+	1.10223i	−0.909089	+	0.416602i
$7$	−2.40522	+	1.10223i	−0.909089	+	0.416602i
$8$	−0.670332			−0.236998
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	3.47908	−	2.00865i	1.10018	−	0.635190i
$11$	−0.220275	+	0.127176i	−0.0664154	+	0.0383450i	−0.532840	−	0.846216i	$-0.678875\pi$
$11$	−0.220275	+	0.127176i	−0.0664154	+	0.0383450i	0.466425	+	0.884561i	$0.345542\pi$
$12$	1.42815	+	0.824544i	0.412272	+	0.238025i
$13$	4.96246			1.37634			0.688169	−	0.725550i	$-0.258415\pi$
$13$	4.96246			1.37634			0.688169	+	0.725550i	$0.258415\pi$
$14$	0.473851	−	5.03181i	0.126642	−	1.34481i
$15$	2.10301			0.542995
$16$	2.28934	−	3.96526i	0.572336	−	0.991314i
$17$	1.49619	−	3.84206i	0.362880	−	0.931836i
$17$	1.49619	−	3.84206i	0.362880	−	0.931836i
$18$	0.955129	+	1.65433i	0.225126	+	0.389930i
$19$	−0.346640	+	0.600398i	−0.0795247	+	0.137741i	−0.903045	−	0.429546i	$-0.858674\pi$
$19$	−0.346640	+	0.600398i	−0.0795247	+	0.137741i	0.823520	+	0.567287i	$0.192007\pi$
$20$			3.46805i			0.775480i
$21$	1.53187	−	2.15717i	0.334282	−	0.470732i
$22$		−	0.485878i		−	0.103589i
$23$	−4.96251	−	2.86510i	−1.03475	−	0.597415i	−0.116411	−	0.993201i	$-0.537139\pi$
$23$	−4.96251	−	2.86510i	−1.03475	−	0.597415i	−0.918343	+	0.395786i	$0.870472\pi$
$24$	0.580525	−	0.335166i	0.118499	−	0.0684155i
$25$	−0.288673	−	0.499996i	−0.0577346	−	0.0999993i
$26$	−4.73979	+	8.20956i	−0.929549	+	1.61003i
$27$			1.00000i			0.192450i
$28$	3.55736	+	2.52619i	0.672278	+	0.477405i
$29$		−	3.82787i		−	0.710817i	−0.934711	−	0.355408i	$-0.884342\pi$
$29$		−	3.82787i		−	0.710817i	0.934711	−	0.355408i	$-0.115658\pi$
$30$	−2.00865	+	3.47908i	−0.366727	+	0.635190i
$31$	7.44086	−	4.29598i	1.33642	−	0.771581i	0.350144	−	0.936696i	$-0.386133\pi$
$31$	7.44086	−	4.29598i	1.33642	−	0.771581i	0.986274	+	0.165115i	$0.0527994\pi$
$32$	3.70290	+	6.41362i	0.654587	+	1.13378i
$33$	0.127176	−	0.220275i	0.0221385	−	0.0383450i
$34$	4.92698	+	6.14486i	0.844971	+	1.05384i
$35$	5.53953	+	0.521664i	0.936352	+	0.0881773i
$36$	−1.64909			−0.274848
$37$	−0.0953196	−	0.0550328i	−0.0156704	−	0.00904733i	0.492144	−	0.870514i	$-0.336213\pi$
$37$	−0.0953196	−	0.0550328i	−0.0156704	−	0.00904733i	−0.507815	+	0.861466i	$0.669547\pi$
$38$	−0.662172	−	1.14692i	−0.107419	−	0.186054i
$39$	−4.29762	+	2.48123i	−0.688169	+	0.397315i
$40$	1.22085	+	0.704858i	0.193033	+	0.111448i
$41$			1.60009i			0.249892i	0.992164	+	0.124946i	$0.0398757\pi$
$41$			1.60009i			0.249892i	−0.992164	+	0.124946i	$0.960124\pi$
$42$	2.10554	+	4.59460i	0.324891	+	0.708962i
$43$	−8.41971			−1.28399			−0.641997	−	0.766707i	$-0.721894\pi$
$43$	−8.41971			−1.28399			−0.641997	+	0.766707i	$0.721894\pi$
$44$	0.363253	+	0.209724i	0.0547625	+	0.0316171i
$45$	−1.82126	+	1.05151i	−0.271498	+	0.156749i
$46$	9.47967	−	5.47309i	1.39770	−	0.806963i
$47$	−5.32365	+	9.22084i	−0.776535	+	1.34500i	0.157393	+	0.987536i	$0.449691\pi$
$47$	−5.32365	+	9.22084i	−0.776535	+	1.34500i	−0.933928	+	0.357462i	$0.883642\pi$
$48$			4.57868i			0.660876i
$49$	4.57020	−	5.30220i	0.652885	−	0.757457i
$50$	1.10288			0.155971
$51$	0.625288	+	4.07542i	0.0875579	+	0.570672i
$52$	−4.09177	−	7.08715i	−0.567426	−	0.982810i
$53$	−1.54625	−	2.67818i	−0.212393	−	0.367876i	0.740070	−	0.672530i	$-0.234793\pi$
$53$	−1.54625	−	2.67818i	−0.212393	−	0.367876i	−0.952463	+	0.304654i	$0.901459\pi$
$54$	−1.65433	−	0.955129i	−0.225126	−	0.129977i
$55$	0.534905			0.0721265
$56$	1.61230	−	0.738858i	0.215452	−	0.0987340i
$57$		−	0.693280i		−	0.0918272i
$58$	6.33256	+	3.65611i	0.831506	+	0.480070i
$59$	−6.03635	−	10.4553i	−0.785866	−	1.36116i	−0.928480	−	0.371381i	$-0.878884\pi$
$59$	−6.03635	−	10.4553i	−0.785866	−	1.36116i	0.142615	−	0.989778i	$-0.454449\pi$
$60$	−1.73403	−	3.00342i	−0.223862	−	0.387740i
$61$	−3.23816	−	1.86955i	−0.414603	−	0.239371i	0.278162	−	0.960534i	$-0.410275\pi$
$61$	−3.23816	−	1.86955i	−0.414603	−	0.239371i	−0.692766	+	0.721163i	$0.743608\pi$
$62$			16.4129i			2.08444i
$63$	−0.248056	+	2.63410i	−0.0312521	+	0.331865i
$64$	−4.98964			−0.623705
$65$	−9.03793	−	5.21805i	−1.12102	−	0.647220i
$66$	0.242939	+	0.420782i	0.0299037	+	0.0517947i
$67$	−4.36617	−	7.56242i	−0.533412	−	0.923897i	−0.999238	−	0.0390208i	$-0.987576\pi$
$67$	−4.36617	−	7.56242i	−0.533412	−	0.923897i	0.465826	−	0.884876i	$-0.345757\pi$
$68$	−6.72072	+	1.03116i	−0.815007	+	0.125046i
$69$	5.73021			0.689836
$70$	−6.15398	+	8.66598i	−0.735541	+	1.03578i
$71$		−	1.79392i		−	0.212899i	−0.994318	−	0.106449i	$-0.966052\pi$
$71$		−	1.79392i		−	0.212899i	0.994318	−	0.106449i	$-0.0339482\pi$
$72$	−0.335166	+	0.580525i	−0.0394997	+	0.0684155i
$73$	−3.34020	+	1.92846i	−0.390940	+	0.225709i	−0.682567	−	0.730823i	$-0.739137\pi$
$73$	−3.34020	+	1.92846i	−0.390940	+	0.225709i	0.291627	+	0.956532i	$0.405803\pi$
$74$	0.182085	−	0.105127i	0.0211670	−	0.0122207i
$75$	0.499996	+	0.288673i	0.0577346	+	0.0333331i
$76$	1.14328			0.131143
$77$	0.389634	−	0.548679i	0.0444029	−	0.0625278i
$78$		−	9.47958i		−	1.07335i
$79$	−11.1727	−	6.45057i	−1.25703	−	0.725745i	−0.284532	−	0.958666i	$-0.591838\pi$
$79$	−11.1727	−	6.45057i	−1.25703	−	0.725745i	−0.972496	+	0.232921i	$0.925172\pi$
$80$	−8.33898	+	4.81451i	−0.932326	+	0.538279i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.64708	−	1.52829i	−0.292321	−	0.168771i
$83$	6.41892			0.704568			0.352284	−	0.935893i	$-0.385405\pi$
$83$	6.41892			0.704568			0.352284	+	0.935893i	$0.385405\pi$
$84$	−4.34386	−	0.409066i	−0.473954	−	0.0446328i
$85$	−6.76490	+	5.42413i	−0.733756	+	0.588330i
$86$	8.04191	−	13.9290i	0.867182	−	1.50200i
$87$	1.91393	+	3.31503i	0.205195	+	0.355408i
$88$	0.147658	−	0.0852501i	0.0157403	−	0.00908769i
$89$	6.52655	−	11.3043i	0.691813	−	1.19826i	−0.279430	−	0.960166i	$-0.590146\pi$
$89$	6.52655	−	11.3043i	0.691813	−	1.19826i	0.971243	−	0.238090i	$-0.0765212\pi$
$90$		−	4.01729i		−	0.423460i
$91$	−11.9358	+	5.46975i	−1.25121	+	0.573386i
$92$			9.44962i			0.985191i
$93$	−4.29598	+	7.44086i	−0.445473	+	0.771581i
$94$	−10.1696	−	17.6142i	−1.04891	−	1.81676i
$95$	1.26264	−	0.728988i	0.129545	−	0.0747926i
$96$	−6.41362	−	3.70290i	−0.654587	−	0.377926i
$97$			6.18244i			0.627732i	0.949467	+	0.313866i	$0.101624\pi$
$97$			6.18244i			0.627732i	−0.949467	+	0.313866i	$0.898376\pi$
$98$	4.40647	+	12.6249i	0.445121	+	1.27531i
$99$			0.254352i			0.0255633i
$100$	−0.476047	+	0.824538i	−0.0476047	+	0.0824538i
$101$	−1.49014	−	2.58100i	−0.148275	−	0.256820i	0.782315	−	0.622883i	$-0.214039\pi$
$101$	−1.49014	−	2.58100i	−0.148275	−	0.256820i	−0.930590	+	0.366063i	$0.880705\pi$
$102$	−7.33932	−	2.85811i	−0.726701	−	0.282995i
$103$	6.75372	−	11.6978i	0.665463	−	1.15262i	−0.313696	−	0.949523i	$-0.601567\pi$
$103$	6.75372	−	11.6978i	0.665463	−	1.15262i	0.979159	−	0.203093i	$-0.0650994\pi$
$104$	−3.32650			−0.326190
$105$	−5.05821	+	2.31799i	−0.493631	+	0.226213i
$106$	5.90747			0.573784
$107$	12.7099	+	7.33805i	1.22871	+	0.709397i	0.966760	−	0.255685i	$-0.0823009\pi$
$107$	12.7099	+	7.33805i	1.22871	+	0.709397i	0.261951	+	0.965081i	$0.415634\pi$
$108$	1.42815	−	0.824544i	0.137424	−	0.0793418i
$109$	0.203806	−	0.117667i	0.0195211	−	0.0112705i	−0.490208	−	0.871606i	$-0.663079\pi$
$109$	0.203806	−	0.117667i	0.0195211	−	0.0112705i	0.509729	+	0.860335i	$0.329746\pi$
$110$	−0.510903	+	0.884910i	−0.0487127	+	0.0843729i
$111$	0.110066			0.0104470
$112$	−1.13577	+	12.0607i	−0.107320	+	1.13963i
$113$		−	4.84742i		−	0.456007i	−0.973660	−	0.228004i	$-0.926780\pi$
$113$		−	4.84742i		−	0.456007i	0.973660	−	0.228004i	$-0.0732198\pi$
$114$	1.14692	+	0.662172i	0.107419	+	0.0620181i
$115$	6.02534	+	10.4362i	0.561866	+	0.973181i
$116$	−5.46678	+	3.15624i	−0.507577	+	0.293050i
$117$	2.48123	−	4.29762i	0.229390	−	0.397315i
$118$	23.0620			2.12303
$119$	0.636140	+	10.8901i	0.0583148	+	0.998298i
$120$	−1.40972			−0.128689
$121$	−5.46765	+	9.47025i	−0.497059	+	0.860932i
$122$	6.18572	−	3.57132i	0.560028	−	0.323333i
$123$	−0.800044	−	1.38572i	−0.0721375	−	0.124946i
$124$	−12.2706	−	7.08445i	−1.10194	−	0.636203i
$125$			11.7292i			1.04909i
$126$	−4.12075	−	2.92627i	−0.367105	−	0.260693i
$127$	−21.8155			−1.93581			−0.967904	−	0.251319i	$-0.919136\pi$
$127$	−21.8155			−1.93581			−0.967904	+	0.251319i	$0.919136\pi$
$128$	−2.64006	+	4.57271i	−0.233350	+	0.404175i
$129$	7.29168	−	4.20985i	0.641997	−	0.370657i
$130$	17.2648	−	9.96783i	1.51422	−	0.874236i
$131$	8.30632	+	4.79566i	0.725727	+	0.418999i	0.816857	−	0.576840i	$-0.195715\pi$
$131$	8.30632	+	4.79566i	0.725727	+	0.418999i	−0.0911301	+	0.995839i	$0.529048\pi$
$132$	−0.419449			−0.0365083
$133$	0.171972	−	1.82617i	0.0149119	−	0.158349i
$134$	16.6810			1.44102
$135$	1.05151	−	1.82126i	0.0904992	−	0.156749i
$136$	−1.00295	+	2.57546i	−0.0860019	+	0.220843i
$137$	−7.65132	−	13.2525i	−0.653696	−	1.13223i	−0.982219	−	0.187739i	$-0.939884\pi$
$137$	−7.65132	−	13.2525i	−0.653696	−	1.13223i	0.328523	−	0.944496i	$-0.393449\pi$
$138$	−5.47309	+	9.47967i	−0.465900	+	0.806963i
$139$		−	15.7811i		−	1.33853i	−0.743022	−	0.669267i	$-0.766608\pi$
$139$		−	15.7811i		−	1.33853i	0.743022	−	0.669267i	$-0.233392\pi$
$140$	−3.82257	−	8.34143i	−0.323067	−	0.704980i
$141$		−	10.6473i		−	0.896665i
$142$	2.96773	+	1.71342i	0.249047	+	0.143787i
$143$	−1.09311	+	0.631105i	−0.0914101	+	0.0527757i
$144$	−2.28934	−	3.96526i	−0.190779	−	0.330438i
$145$	−4.02502	+	6.97154i	−0.334260	+	0.578955i
$146$		−	7.36772i		−	0.609757i
$147$	−1.30681	+	6.87694i	−0.107784	+	0.567200i
$148$			0.181508i			0.0149199i
$149$	0.257292	−	0.445643i	0.0210782	−	0.0365085i	−0.855294	−	0.518143i	$-0.826623\pi$
$149$	0.257292	−	0.445643i	0.0210782	−	0.0365085i	0.876372	+	0.481635i	$0.159957\pi$
$150$	−0.955122	+	0.551440i	−0.0779854	+	0.0450249i
$151$	7.43324	+	12.8748i	0.604909	+	1.04773i	0.992066	+	0.125719i	$0.0401237\pi$
$151$	7.43324	+	12.8748i	0.604909	+	1.04773i	−0.387157	+	0.922014i	$0.626543\pi$
$152$	0.232364	−	0.402466i	0.0188472	−	0.0326443i
$153$	−2.57922	−	3.21677i	−0.208518	−	0.260060i
$154$	0.535547	+	1.16864i	0.0431556	+	0.0941720i
$155$	−18.0690			−1.45134
$156$	7.08715	+	4.09177i	0.567426	+	0.327603i
$157$	5.20100	+	9.00840i	0.415085	+	0.718949i	0.995437	−	0.0954170i	$-0.0304185\pi$
$157$	5.20100	+	9.00840i	0.415085	+	0.718949i	−0.580352	+	0.814366i	$0.697085\pi$
$158$	21.3428	−	12.3222i	1.69794	−	0.980305i
$159$	2.67818	+	1.54625i	0.212393	+	0.122625i
$160$		−	15.5745i		−	1.23127i
$161$	15.0939	+	1.42141i	1.18957	+	0.112023i
$162$	1.91026			0.150084
$163$	10.9481	+	6.32091i	0.857524	+	0.495092i	0.863182	−	0.504892i	$-0.168468\pi$
$163$	10.9481	+	6.32091i	0.857524	+	0.495092i	−0.00565860	+	0.999984i	$0.501801\pi$
$164$	2.28517	−	1.31934i	0.178442	−	0.103023i
$165$	−0.463241	+	0.267452i	−0.0360633	+	0.0208211i
$166$	−6.13090	+	10.6190i	−0.475850	+	0.824196i
$167$			21.4382i			1.65894i	0.558552	+	0.829470i	$0.311357\pi$
$167$			21.4382i			1.65894i	−0.558552	+	0.829470i	$0.688643\pi$
$168$	−1.02686	+	1.44602i	−0.0792242	+	0.111563i
$169$	11.6260			0.894308
$170$	−2.51197	−	16.3721i	−0.192659	−	1.25569i
$171$	0.346640	+	0.600398i	0.0265082	+	0.0459136i
$172$	6.94242	+	12.0246i	0.529355	+	0.916869i
$173$	3.59217	+	2.07394i	0.273107	+	0.157679i	0.630299	−	0.776353i	$-0.282932\pi$
$173$	3.59217	+	2.07394i	0.273107	+	0.157679i	−0.357192	+	0.934031i	$0.616266\pi$
$174$	−7.31221			−0.554338
$175$	1.24543	+	0.884420i	0.0941458	+	0.0668558i
$176$			1.16460i			0.0877848i
$177$	10.4553	+	6.03635i	0.785866	+	0.453720i
$178$	12.4674	+	21.5942i	0.934471	+	1.61855i
$179$	4.03117	+	6.98219i	0.301304	+	0.521873i	0.976432	−	0.215827i	$-0.0692448\pi$
$179$	4.03117	+	6.98219i	0.301304	+	0.521873i	−0.675128	+	0.737701i	$0.735912\pi$
$180$	3.00342	+	1.73403i	0.223862	+	0.129247i
$181$		−	18.6845i		−	1.38880i	−0.719587	−	0.694402i	$-0.755669\pi$
$181$		−	18.6845i		−	1.38880i	0.719587	−	0.694402i	$-0.244331\pi$
$182$	2.35147	−	24.9701i	0.174302	−	1.85091i
$183$	3.73910			0.276402
$184$	3.32653	+	1.92057i	0.245235	+	0.141586i
$185$	0.115735	+	0.200458i	0.00850897	+	0.0147380i
$186$	−8.20644	−	14.2140i	−0.601725	−	1.04222i
$187$	0.159043	+	1.03659i	0.0116304	+	0.0758029i
$188$	17.5584			1.28057
$189$	−1.10223	−	2.40522i	−0.0801751	−	0.174954i
$190$			2.78511i			0.202053i
$191$	1.43812	−	2.49090i	0.104059	−	0.180235i	−0.809295	−	0.587403i	$-0.800150\pi$
$191$	1.43812	−	2.49090i	0.104059	−	0.180235i	0.913353	+	0.407168i	$0.133484\pi$
$192$	4.32115	−	2.49482i	0.311852	−	0.180048i
$193$	−2.46451	+	1.42289i	−0.177400	+	0.102422i	−0.586070	−	0.810260i	$-0.699326\pi$
$193$	−2.46451	+	1.42289i	−0.177400	+	0.102422i	0.408671	+	0.912682i	$0.365992\pi$
$194$	−10.2278	−	5.90503i	−0.734314	−	0.423957i
$195$	10.4361			0.747345
$196$	−11.3407	−	2.15504i	−0.810048	−	0.153931i
$197$		−	25.1011i		−	1.78838i	−0.447689	−	0.894189i	$-0.647753\pi$
$197$		−	25.1011i		−	1.78838i	0.447689	−	0.894189i	$-0.352247\pi$
$198$	−0.420782	−	0.242939i	−0.0299037	−	0.0172649i
$199$	−13.6874	+	7.90240i	−0.970271	+	0.560186i	−0.899319	−	0.437293i	$-0.855937\pi$
$199$	−13.6874	+	7.90240i	−0.970271	+	0.560186i	−0.0709523	+	0.997480i	$0.522604\pi$
$200$	0.193507	+	0.335164i	0.0136830	+	0.0236996i
$201$	7.56242	+	4.36617i	0.533412	+	0.307966i
$202$	5.69312			0.400566
$203$	4.21917	+	9.20687i	0.296128	+	0.646196i
$204$	5.30474	−	4.25337i	0.371406	−	0.297795i
$205$	1.68250	−	2.91418i	0.117511	−	0.203535i
$206$	12.9013	+	22.3458i	0.898879	+	1.55690i
$207$	−4.96251	+	2.86510i	−0.344918	+	0.199138i
$208$	11.3608	−	19.6774i	0.787727	−	1.36438i
$209$		−	0.176337i		−	0.0121975i
$210$	0.996514	−	10.5819i	0.0687660	−	0.730224i
$211$			4.39024i			0.302236i	0.988516	+	0.151118i	$0.0482874\pi$
$211$			4.39024i			0.302236i	−0.988516	+	0.151118i	$0.951713\pi$
$212$	−2.54990	+	4.41655i	−0.175128	+	0.303330i
$213$	0.896958	+	1.55358i	0.0614586	+	0.106449i
$214$	−24.2792	+	14.0176i	−1.65969	+	0.958222i
$215$	15.3345	+	8.85337i	1.04580	+	0.603795i
$216$		−	0.670332i		−	0.0456103i
$217$	−13.1618	+	18.5343i	−0.893480	+	1.25819i
$218$			0.449550i			0.0304474i
$219$	1.92846	−	3.34020i	0.130313	−	0.225709i
$220$	−0.441052	−	0.763925i	−0.0297357	−	0.0515038i
$221$	7.42479	−	19.0661i	0.499446	−	1.28252i
$222$	−0.105127	+	0.182085i	−0.00705565	+	0.0122207i
$223$	−19.4190			−1.30039			−0.650195	−	0.759768i	$-0.725313\pi$
$223$	−19.4190			−1.30039			−0.650195	+	0.759768i	$0.725313\pi$
$224$	−15.9756	−	11.3447i	−1.06741	−	0.758003i
$225$	−0.577346			−0.0384897
$226$	8.01925	+	4.62992i	0.533433	+	0.307977i
$227$	13.1519	−	7.59328i	0.872925	−	0.503984i	0.00460596	−	0.999989i	$-0.498534\pi$
$227$	13.1519	−	7.59328i	0.872925	−	0.503984i	0.868319	+	0.496006i	$0.165201\pi$
$228$	−0.990110	+	0.571640i	−0.0655716	+	0.0378578i
$229$	4.44200	−	7.69377i	0.293536	−	0.508419i	−0.681108	−	0.732183i	$-0.738501\pi$
$229$	4.44200	−	7.69377i	0.293536	−	0.508419i	0.974643	+	0.223765i	$0.0718347\pi$
$230$	−23.0199			−1.51789
$231$	−0.0630935	+	0.669987i	−0.00415124	+	0.0440819i
$232$			2.56594i			0.168462i
$233$	−12.7492	−	7.36075i	−0.835228	−	0.482219i	0.0204116	−	0.999792i	$-0.493502\pi$
$233$	−12.7492	−	7.36075i	−0.835228	−	0.482219i	−0.855639	+	0.517573i	$0.826836\pi$
$234$	4.73979	+	8.20956i	0.309850	+	0.536676i
$235$	19.3915	−	11.1957i	1.26496	−	0.730327i
$236$	−9.95447	+	17.2417i	−0.647981	+	1.12234i
$237$	12.9011			0.838019
$238$	−18.6235	−	9.34911i	−1.20718	−	0.606013i
$239$	−7.56041			−0.489042			−0.244521	−	0.969644i	$-0.578631\pi$
$239$	−7.56041			−0.489042			−0.244521	+	0.969644i	$0.578631\pi$
$240$	4.81451	−	8.33898i	0.310775	−	0.538279i
$241$	5.23166	−	3.02050i	0.337001	−	0.194568i	−0.321944	−	0.946759i	$-0.604336\pi$
$241$	5.23166	−	3.02050i	0.337001	−	0.194568i	0.658945	+	0.752191i	$0.271003\pi$
$242$	−10.4446	−	18.0906i	−0.671406	−	1.16291i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$			6.16611i			0.394745i
$245$	−13.8988	+	4.85110i	−0.887962	+	0.309925i
$246$	3.05658			0.194880
$247$	−1.72019	+	2.97945i	−0.109453	+	0.189578i
$248$	−4.98785	+	2.87974i	−0.316729	+	0.182863i
$249$	−5.55894	+	3.20946i	−0.352284	+	0.203391i
$250$	−19.4040	−	11.2029i	−1.22722	−	0.708535i
$251$	5.26763			0.332490			0.166245	−	0.986084i	$-0.446836\pi$
$251$	5.26763			0.332490			0.166245	+	0.986084i	$0.446836\pi$
$252$	3.96643	−	1.81767i	0.249861	−	0.114502i
$253$	1.45749			0.0916315
$254$	20.8366	−	36.0900i	1.30740	−	2.26449i
$255$	3.14651	−	8.07989i	0.197042	−	0.505982i
$256$	−10.0328	−	17.3774i	−0.627052	−	1.08609i
$257$	−3.49189	+	6.04814i	−0.217818	+	0.377272i	−0.954141	−	0.299358i	$-0.903227\pi$
$257$	−3.49189	+	6.04814i	−0.217818	+	0.377272i	0.736322	+	0.676631i	$0.236561\pi$
$258$			16.0838i			1.00133i
$259$	0.289923	+	0.0273024i	0.0180150	+	0.00169649i
$260$			17.2101i			1.06732i
$261$	−3.31503	−	1.91393i	−0.205195	−	0.118469i
$262$	−15.8672	+	9.16095i	−0.980280	+	0.565965i
$263$	4.60011	+	7.96762i	0.283655	+	0.491304i	0.972282	−	0.233811i	$-0.0751197\pi$
$263$	4.60011	+	7.96762i	0.283655	+	0.491304i	−0.688627	+	0.725115i	$0.741786\pi$
$264$	−0.0852501	+	0.147658i	−0.00524678	+	0.00908769i
$265$			6.50355i			0.399510i
$266$	2.85683	+	2.02873i	0.175164	+	0.124389i
$267$			13.0531i			0.798837i
$268$	−7.20019	+	12.4711i	−0.439822	+	0.761794i
$269$	−26.1117	+	15.0756i	−1.59206	+	0.919175i	−0.599104	+	0.800672i	$0.704476\pi$
$269$	−26.1117	+	15.0756i	−1.59206	+	0.919175i	−0.992954	+	0.118503i	$0.962190\pi$
$270$	2.00865	+	3.47908i	0.122242	+	0.211730i
$271$	−4.06926	+	7.04816i	−0.247190	+	0.428146i	−0.962745	−	0.270411i	$-0.912840\pi$
$271$	−4.06926	+	7.04816i	−0.247190	+	0.428146i	0.715555	+	0.698556i	$0.246174\pi$
$272$	−11.8095	−	14.7286i	−0.716053	−	0.893051i
$273$	7.60185	−	10.7049i	0.460085	−	0.647887i
$274$	29.2320			1.76597
$275$	0.127175	+	0.0734245i	0.00766894	+	0.00442766i
$276$	−4.72481	−	8.18361i	−0.284400	−	0.492595i
$277$	−13.3191	+	7.68976i	−0.800265	+	0.462033i	−0.843564	−	0.537029i	$-0.819547\pi$
$277$	−13.3191	+	7.68976i	−0.800265	+	0.462033i	0.0432991	+	0.999062i	$0.486213\pi$
$278$	26.1072	+	15.0730i	1.56580	+	0.904017i
$279$		−	8.59197i		−	0.514388i
$280$	−3.71333	−	0.349688i	−0.221914	−	0.0208979i
$281$	23.9654			1.42966			0.714829	−	0.699300i	$-0.246505\pi$
$281$	23.9654			1.42966			0.714829	+	0.699300i	$0.246505\pi$
$282$	17.6142	+	10.1696i	1.04891	+	0.605588i
$283$	17.4179	−	10.0562i	1.03539	−	0.597781i	0.116864	−	0.993148i	$-0.462716\pi$
$283$	17.4179	−	10.0562i	1.03539	−	0.597781i	0.918523	+	0.395367i	$0.129383\pi$
$284$	−2.56199	+	1.47916i	−0.152026	+	0.0877722i
$285$	−0.728988	+	1.26264i	−0.0431815	+	0.0747926i
$286$		−	2.41115i		−	0.142574i
$287$	−1.76366	−	3.84857i	−0.104105	−	0.227174i
$288$	7.40581			0.436391
$289$	−12.5228	−	11.4969i	−0.736636	−	0.676289i
$290$	−7.68883	−	13.3174i	−0.451504	−	0.782028i
$291$	−3.09122	−	5.35415i	−0.181211	−	0.313866i
$292$	5.50828	+	3.18020i	0.322347	+	0.186107i
$293$	−22.1274			−1.29270			−0.646348	−	0.763043i	$-0.723705\pi$
$293$	−22.1274			−1.29270			−0.646348	+	0.763043i	$0.723705\pi$
$294$	−10.1286	−	8.73026i	−0.590710	−	0.509159i
$295$			25.3890i			1.47821i
$296$	0.0638958	+	0.0368902i	0.00371387	+	0.00214420i
$297$	−0.127176	−	0.220275i	−0.00737949	−	0.0127817i
$298$	0.491494	+	0.851293i	0.0284715	+	0.0493141i
$299$	−24.6262	−	14.2180i	−1.42417	−	0.822246i
$300$		−	0.952094i		−	0.0549692i
$301$	20.2513	−	9.28042i	1.16726	−	0.534915i
$302$	−28.3988			−1.63417
$303$	2.58100	+	1.49014i	0.148275	+	0.0856065i
$304$	1.58716	+	2.74903i	0.0910296	+	0.157668i
$305$	3.93168	+	6.80988i	0.225128	+	0.389932i
$306$	7.78510	−	1.19446i	0.445044	−	0.0682829i
$307$	5.51415			0.314709			0.157355	−	0.987542i	$-0.449703\pi$
$307$	5.51415			0.314709			0.157355	+	0.987542i	$0.449703\pi$
$308$	−1.10487	−	0.104047i	−0.0629557	−	0.00592861i
$309$			13.5074i			0.768411i
$310$	17.2582	−	29.8921i	0.980201	−	1.69776i
$311$	−12.3813	+	7.14834i	−0.702078	+	0.405345i	−0.808121	−	0.589017i	$-0.799515\pi$
$311$	−12.3813	+	7.14834i	−0.702078	+	0.405345i	0.106043	+	0.994362i	$0.466182\pi$
$312$	2.88083	−	1.66325i	0.163095	−	0.0941629i
$313$	−3.80897	−	2.19911i	−0.215296	−	0.124301i	0.388474	−	0.921460i	$-0.373002\pi$
$313$	−3.80897	−	2.19911i	−0.215296	−	0.124301i	−0.603770	+	0.797158i	$0.706336\pi$
$314$	−19.8705			−1.12136
$315$	3.22154	−	4.53655i	0.181513	−	0.255605i
$316$			21.2751i			1.19682i
$317$	11.4923	+	6.63510i	0.645474	+	0.372664i	0.786720	−	0.617310i	$-0.211778\pi$
$317$	11.4923	+	6.63510i	0.645474	+	0.372664i	−0.141246	+	0.989974i	$0.545111\pi$
$318$	−5.11602	+	2.95373i	−0.286892	+	0.165637i
$319$	0.486812	+	0.843184i	0.0272563	+	0.0472092i
$320$	9.08743	+	5.24663i	0.508003	+	0.293296i
$321$	−14.6761			−0.819141
$322$	−16.7681	+	23.6127i	−0.934452	+	1.31589i
$323$	1.78812	+	2.23012i	0.0994939	+	0.124087i
$324$	−0.824544	+	1.42815i	−0.0458080	+	0.0793418i
$325$	−1.43253	−	2.48121i	−0.0794623	−	0.137633i
$326$	−20.9138	+	12.0746i	−1.15831	+	0.668748i
$327$	−0.117667	+	0.203806i	−0.00650702	+	0.0112705i
$328$		−	1.07259i		−	0.0592239i
$329$	2.64113	−	28.0460i	0.145610	−	1.54623i
$330$		−	1.02181i		−	0.0562486i
$331$	−2.42463	+	4.19959i	−0.133270	+	0.230830i	−0.924935	−	0.380125i	$-0.875881\pi$
$331$	−2.42463	+	4.19959i	−0.133270	+	0.230830i	0.791665	+	0.610955i	$0.209214\pi$
$332$	−5.29268	−	9.16719i	−0.290474	−	0.503115i
$333$	−0.0953196	+	0.0550328i	−0.00522348	+	0.00301578i
$334$	−35.4659	−	20.4763i	−1.94061	−	1.12041i
$335$			18.3642i			1.00334i
$336$	−5.04674	−	11.0128i	−0.275322	−	0.600795i
$337$		−	30.8247i		−	1.67913i	−0.543262	−	0.839563i	$-0.682811\pi$
$337$		−	30.8247i		−	1.67913i	0.543262	−	0.839563i	$-0.317189\pi$
$338$	−11.1043	+	19.2333i	−0.603996	+	1.04615i
$339$	2.42371	+	4.19799i	0.131638	+	0.228004i
$340$	13.3244	+	5.18887i	0.722620	+	0.281406i
$341$	−1.09269	+	1.89260i	−0.0591725	+	0.102490i
$342$	−1.32434			−0.0716123
$343$	−5.14812	+	17.7904i	−0.277972	+	0.960589i
$344$	5.64400			0.304304
$345$	−10.4362	−	6.02534i	−0.561866	−	0.324394i
$346$	−6.86197	+	3.96176i	−0.368902	+	0.212986i
$347$	11.3599	−	6.55865i	0.609832	−	0.352087i	−0.163068	−	0.986615i	$-0.552139\pi$
$347$	11.3599	−	6.55865i	0.609832	−	0.352087i	0.772900	+	0.634528i	$0.218806\pi$
$348$	3.15624	−	5.46678i	0.169192	−	0.293050i
$349$	31.1145			1.66552			0.832761	−	0.553633i	$-0.186759\pi$
$349$	31.1145			1.66552			0.832761	+	0.553633i	$0.186759\pi$
$350$	−2.65267	+	1.21562i	−0.141791	+	0.0649778i
$351$			4.96246i			0.264876i
$352$	−1.63132	−	0.941840i	−0.0869494	−	0.0502002i
$353$	−1.56742	−	2.71484i	−0.0834251	−	0.144496i	0.821294	−	0.570505i	$-0.193253\pi$
$353$	−1.56742	−	2.71484i	−0.0834251	−	0.144496i	−0.904719	+	0.426009i	$0.859919\pi$
$354$	−19.9723	+	11.5310i	−1.06151	+	0.612865i
$355$	−1.88631	+	3.26719i	−0.100115	+	0.173404i
$356$	−21.5257			−1.14086
$357$	−5.99599	−	9.11308i	−0.317341	−	0.482315i
$358$	−15.4012			−0.813976
$359$	−11.1271	+	19.2728i	−0.587268	+	1.01718i	0.407320	+	0.913285i	$0.366463\pi$
$359$	−11.1271	+	19.2728i	−0.587268	+	1.01718i	−0.994589	+	0.103893i	$0.966870\pi$
$360$	1.22085	−	0.704858i	0.0643444	−	0.0371493i
$361$	9.25968	+	16.0382i	0.487352	+	0.844118i
$362$	30.9103	+	17.8461i	1.62461	+	0.937969i
$363$		−	10.9353i		−	0.573955i
$364$	17.6532	+	12.5361i	0.925282	+	0.657071i
$365$	8.11115			0.424557
$366$	−3.57132	+	6.18572i	−0.186676	+	0.323333i
$367$	−16.2423	+	9.37750i	−0.847842	+	0.489502i	−0.859922	−	0.510425i	$-0.829488\pi$
$367$	−16.2423	+	9.37750i	−0.847842	+	0.489502i	0.0120804	+	0.999927i	$0.496155\pi$
$368$	−22.7217	+	13.1184i	−1.18445	+	0.683844i
$369$	1.38572	+	0.800044i	0.0721375	+	0.0416486i
$370$	−0.442166			−0.0229871
$371$	6.67103	+	4.73730i	0.346343	+	0.245949i
$372$	14.1689			0.734624
$373$	−0.205911	+	0.356648i	−0.0106617	+	0.0184665i	−0.871307	−	0.490738i	$-0.836727\pi$
$373$	−0.205911	+	0.356648i	−0.0106617	+	0.0184665i	0.860645	+	0.509205i	$0.170060\pi$
$374$	−1.86677	−	0.726966i	−0.0965284	−	0.0375905i
$375$	−5.86461	−	10.1578i	−0.302847	−	0.524547i
$376$	3.56862	−	6.18103i	0.184037	−	0.318762i
$377$		−	18.9956i		−	0.978325i
$378$	5.03181	+	0.473851i	0.258808	+	0.0243723i
$379$		−	14.0641i		−	0.722426i	−0.932483	−	0.361213i	$-0.882363\pi$
$379$		−	14.0641i		−	0.722426i	0.932483	−	0.361213i	$-0.117637\pi$
$380$	−2.08221	−	1.20217i	−0.106815	−	0.0616698i
$381$	18.8927	−	10.9077i	0.967904	−	0.558820i
$382$	2.74718	+	4.75825i	0.140558	+	0.243453i
$383$	12.5200	−	21.6854i	0.639745	−	1.10807i	−0.345744	−	0.938329i	$-0.612373\pi$
$383$	12.5200	−	21.6854i	0.639745	−	1.10807i	0.985489	−	0.169741i	$-0.0542932\pi$
$384$		−	5.28011i		−	0.269450i
$385$	−1.28656	+	0.589586i	−0.0655694	+	0.0300481i
$386$		−	5.43617i		−	0.276694i
$387$	−4.20985	+	7.29168i	−0.213999	+	0.370657i
$388$	8.82947	−	5.09770i	0.448248	−	0.258796i
$389$	1.50772	+	2.61145i	0.0764445	+	0.132406i	0.901714	−	0.432334i	$-0.142310\pi$
$389$	1.50772	+	2.61145i	0.0764445	+	0.132406i	−0.825269	+	0.564740i	$0.808977\pi$
$390$	−9.96783	+	17.2648i	−0.504741	+	0.874236i
$391$	−18.4328	+	14.7795i	−0.932185	+	0.747431i
$392$	−3.06355	+	3.55423i	−0.154733	+	0.179516i
$393$	−9.59131			−0.483818
$394$	41.5255	+	23.9748i	2.09203	+	1.20783i
$395$	13.5656	+	23.4963i	0.682560	+	1.18223i
$396$	0.363253	−	0.209724i	0.0182542	−	0.0105390i
$397$	−7.35195	−	4.24465i	−0.368984	−	0.213033i	0.304031	−	0.952662i	$-0.401667\pi$
$397$	−7.35195	−	4.24465i	−0.368984	−	0.213033i	−0.673014	+	0.739629i	$0.735001\pi$
$398$		−	30.1913i		−	1.51335i
$399$	0.764151	+	1.66749i	0.0382554	+	0.0834791i
$400$	−2.64349			−0.132174
$401$	16.7560	+	9.67410i	0.836756	+	0.483101i	0.856160	−	0.516710i	$-0.172844\pi$
$401$	16.7560	+	9.67410i	0.836756	+	0.483101i	−0.0194042	+	0.999812i	$0.506177\pi$
$402$	−14.4462	+	8.34051i	−0.720510	+	0.415987i
$403$	36.9250	−	21.3186i	1.83936	−	1.06196i
$404$	−2.45738	+	4.25630i	−0.122259	+	0.211759i
$405$			2.10301i			0.104499i
$406$	−19.2611	−	1.81384i	−0.955912	−	0.0900193i
$407$	0.0279954			0.00138768
$408$	−0.419151	−	2.73188i	−0.0207511	−	0.135248i
$409$	−17.6456	−	30.5630i	−0.872517	−	1.51124i	−0.859385	−	0.511330i	$-0.829153\pi$
$409$	−17.6456	−	30.5630i	−0.872517	−	1.51124i	−0.0131323	−	0.999914i	$-0.504180\pi$
$410$	3.21401	+	5.56683i	0.158729	+	0.274926i
$411$	13.2525	+	7.65132i	0.653696	+	0.377412i
$412$	−22.2749			−1.09741
$413$	26.0428	+	18.4938i	1.28148	+	0.910022i
$414$		−	10.9462i		−	0.537975i
$415$	−11.6905	−	6.74952i	−0.573865	−	0.331321i
$416$	18.3755	+	31.8273i	0.900933	+	1.56046i
$417$	7.89054	+	13.6668i	0.386402	+	0.669267i
$418$	0.291720	+	0.168425i	0.0142685	+	0.00823792i
$419$			0.819519i			0.0400361i	0.999800	+	0.0200181i	$0.00637238\pi$
$419$			0.819519i			0.0400361i	−0.999800	+	0.0200181i	$0.993628\pi$
$420$	7.48116	+	5.31261i	0.365043	+	0.259229i
$421$	7.93472			0.386714			0.193357	−	0.981128i	$-0.438062\pi$
$421$	7.93472			0.386714			0.193357	+	0.981128i	$0.438062\pi$
$422$	−7.26291	−	4.19324i	−0.353553	−	0.204124i
$423$	5.32365	+	9.22084i	0.258845	+	0.448333i
$424$	1.03650	+	1.79527i	0.0503369	+	0.0871860i
$425$	−2.35292	+	0.361008i	−0.114134	+	0.0175115i
$426$	−3.42684			−0.166031
$427$	9.84915	+	0.927506i	0.476634	+	0.0448852i
$428$		−	24.2022i		−	1.16986i
$429$	0.631105	−	1.09311i	0.0304700	−	0.0527757i
$430$	−29.2928	+	16.9122i	−1.41263	+	0.815580i
$431$	−9.10467	+	5.25658i	−0.438556	+	0.253201i	−0.702985	−	0.711205i	$-0.748150\pi$
$431$	−9.10467	+	5.25658i	−0.438556	+	0.253201i	0.264429	+	0.964405i	$0.414817\pi$
$432$	3.96526	+	2.28934i	0.190779	+	0.110146i
$433$	−4.33846			−0.208493			−0.104247	−	0.994551i	$-0.533243\pi$
$433$	−4.33846			−0.208493			−0.104247	+	0.994551i	$0.533243\pi$
$434$	−18.0907	−	39.4766i	−0.868381	−	1.89494i
$435$		−	8.05004i		−	0.385970i
$436$	−0.336094	−	0.194044i	−0.0160960	−	0.00929302i
$437$	3.44041	−	1.98632i	0.164577	−	0.0950185i
$438$	3.68386	+	6.38064i	0.176022	+	0.304879i
$439$	15.1191	+	8.72902i	0.721596	+	0.416614i	0.815340	−	0.578983i	$-0.196550\pi$
$439$	15.1191	+	8.72902i	0.721596	+	0.416614i	−0.0937439	+	0.995596i	$0.529883\pi$
$440$	−0.358564			−0.0170939
$441$	−2.30674	−	6.60901i	−0.109845	−	0.314715i
$442$	24.4500	+	30.4936i	1.16297	+	1.45043i
$443$	1.33101	−	2.30537i	0.0632381	−	0.109532i	−0.832673	−	0.553765i	$-0.813191\pi$
$443$	1.33101	−	2.30537i	0.0632381	−	0.109532i	0.895911	+	0.444233i	$0.146524\pi$
$444$	−0.0907539	−	0.157190i	−0.00430699	−	0.00745993i
$445$	−23.7731	+	13.7254i	−1.12695	+	0.650647i
$446$	18.5476	−	32.1254i	0.878255	−	1.52118i
$447$			0.514584i			0.0243390i
$448$	12.0012	−	5.49971i	0.567003	−	0.259837i
$449$			10.6803i			0.504036i	0.967723	+	0.252018i	$0.0810942\pi$
$449$			10.6803i			0.504036i	−0.967723	+	0.252018i	$0.918906\pi$
$450$	0.551440	−	0.955122i	0.0259951	−	0.0450249i
$451$	−0.203493	−	0.352459i	−0.00958209	−	0.0165967i
$452$	−6.92286	+	3.99691i	−0.325624	+	0.187999i
$453$	−12.8748	−	7.43324i	−0.604909	−	0.349244i
$454$			29.0103i			1.36152i
$455$	27.4897	+	2.58874i	1.28874	+	0.121362i
$456$			0.464728i			0.0217629i
$457$	−1.67921	+	2.90847i	−0.0785499	+	0.136052i	−0.902625	−	0.430429i	$-0.858362\pi$
$457$	−1.67921	+	2.90847i	−0.0785499	+	0.136052i	0.824075	+	0.566481i	$0.191696\pi$
$458$	8.48537	+	14.6971i	0.396495	+	0.686750i
$459$	3.84206	+	1.49619i	0.179332	+	0.0698363i
$460$	9.93632	−	17.2102i	0.463283	−	0.802430i
$461$	30.0368			1.39895			0.699477	−	0.714655i	$-0.253416\pi$
$461$	30.0368			1.39895			0.699477	+	0.714655i	$0.253416\pi$
$462$	−1.04812	−	0.744302i	−0.0487629	−	0.0346281i
$463$	−35.0010			−1.62663			−0.813317	−	0.581821i	$-0.802340\pi$
$463$	−35.0010			−1.62663			−0.813317	+	0.581821i	$0.802340\pi$
$464$	−15.1785	−	8.76330i	−0.704643	−	0.406826i
$465$	15.6482	−	9.03450i	0.725668	−	0.418965i
$466$	24.3543	−	14.0609i	1.12819	−	0.651360i
$467$	7.86735	−	13.6267i	0.364058	−	0.630566i	−0.624567	−	0.780971i	$-0.714724\pi$
$467$	7.86735	−	13.6267i	0.364058	−	0.630566i	0.988624	+	0.150405i	$0.0480578\pi$
$468$	−8.18353			−0.378284
$469$	18.8371	+	13.3768i	0.869817	+	0.617684i
$470$			42.7734i			1.97299i
$471$	−9.00840	−	5.20100i	−0.415085	−	0.239650i
$472$	4.04636	+	7.00850i	0.186249	+	0.322592i
$473$	1.85465	−	1.07078i	0.0852770	−	0.0492347i
$474$	−12.3222	+	21.3428i	−0.565980	+	0.980305i
$475$	0.400262			0.0183653
$476$	15.0283	−	9.88791i	0.688819	−	0.453212i
$477$	−3.09250			−0.141596
$478$	7.22117	−	12.5074i	0.330288	−	0.572076i
$479$	15.9142	−	9.18804i	0.727136	−	0.419812i	−0.0902374	−	0.995920i	$-0.528763\pi$
$479$	15.9142	−	9.18804i	0.727136	−	0.419812i	0.817374	+	0.576108i	$0.195429\pi$
$480$	7.78725	+	13.4879i	0.355438	+	0.615636i
$481$	−0.473019	−	0.273098i	−0.0215678	−	0.0124522i
$482$			11.5399i			0.525627i
$483$	−13.7824	+	6.31598i	−0.627122	+	0.287387i
$484$	18.0333			0.819695
$485$	6.50087	−	11.2598i	0.295189	−	0.511283i
$486$	−1.65433	+	0.955129i	−0.0750420	+	0.0433255i
$487$	30.7041	−	17.7270i	1.39133	−	0.803287i	0.397871	−	0.917441i	$-0.369749\pi$
$487$	30.7041	−	17.7270i	1.39133	−	0.803287i	0.993463	+	0.114154i	$0.0364158\pi$
$488$	2.17064	+	1.25322i	0.0982603	+	0.0567306i
$489$	−12.6418			−0.571682
$490$	5.24983	−	27.6267i	0.237163	−	1.24805i
$491$	−6.64618			−0.299938			−0.149969	−	0.988691i	$-0.547917\pi$
$491$	−6.64618			−0.299938			−0.149969	+	0.988691i	$0.547917\pi$
$492$	−1.31934	+	2.28517i	−0.0594805	+	0.103023i
$493$	−14.7069	−	5.72722i	−0.662365	−	0.257941i
$494$	−3.28600	−	5.69152i	−0.147844	−	0.256074i
$495$	0.267452	−	0.463241i	0.0120211	−	0.0208211i
$496$		−	39.3399i		−	1.76641i
$497$	1.97730	+	4.31477i	0.0886941	+	0.193544i
$498$		−	12.2618i		−	0.549464i
$499$	−37.8465	−	21.8507i	−1.69424	−	0.978172i	−0.951021	−	0.309128i	$-0.899963\pi$
$499$	−37.8465	−	21.8507i	−1.69424	−	0.978172i	−0.743223	−	0.669044i	$-0.766704\pi$
$500$	16.7511	−	9.67126i	0.749132	−	0.432512i
$501$	−10.7191	−	18.5660i	−0.478895	−	0.829470i
$502$	−5.03127	+	8.71442i	−0.224557	+	0.388943i
$503$		−	12.4728i		−	0.556136i	−0.960561	−	0.278068i	$-0.910306\pi$
$503$		−	12.4728i		−	0.556136i	0.960561	−	0.278068i	$-0.0896940\pi$
$504$	0.166280	−	1.76572i	0.00740669	−	0.0786514i
$505$			6.26758i			0.278903i
$506$	−1.39209	+	2.41117i	−0.0618859	+	0.107190i
$507$	−10.0684	+	5.81300i	−0.447154	+	0.258164i
$508$	17.9878	+	31.1558i	0.798080	+	1.38231i
$509$	−7.17075	+	12.4201i	−0.317838	+	0.550511i	−0.980037	−	0.198817i	$-0.936290\pi$
$509$	−7.17075	+	12.4201i	−0.317838	+	0.550511i	0.662199	+	0.749328i	$0.269623\pi$
$510$	10.3615	+	12.9227i	0.458815	+	0.572227i
$511$	5.90831	−	8.32003i	0.261368	−	0.368057i
$512$	27.7704			1.22729
$513$	−0.600398	−	0.346640i	−0.0265082	−	0.0153045i
$514$	−6.67042	−	11.5535i	−0.294220	−	0.509603i
$515$	−24.6006	+	14.2031i	−1.08403	+	0.625865i
$516$	−12.0246	−	6.94242i	−0.529355	−	0.305623i
$517$		−	2.70816i		−	0.119105i
$518$	−0.322082	+	0.453552i	−0.0141515	+	0.0199279i
$519$	−4.14788			−0.182072
$520$	6.05842	+	3.49783i	0.265679	+	0.153390i
$521$	−9.39525	+	5.42435i	−0.411613	+	0.237645i	−0.691483	−	0.722393i	$-0.743042\pi$
$521$	−9.39525	+	5.42435i	−0.411613	+	0.237645i	0.279869	+	0.960038i	$0.409709\pi$
$522$	6.33256	−	3.65611i	0.277169	−	0.160023i
$523$	11.8393	−	20.5062i	0.517695	−	0.896674i	−0.482094	−	0.876120i	$-0.660123\pi$
$523$	11.8393	−	20.5062i	0.517695	−	0.896674i	0.999789	−	0.0205547i	$-0.00654321\pi$
$524$		−	15.8169i		−	0.690966i
$525$	−1.52079	−	0.143214i	−0.0663725	−	0.00625037i
$526$	−17.5748			−0.766297
$527$	−5.37246	−	35.0158i	−0.234028	−	1.52531i
$528$	−0.582298	−	1.00857i	−0.0253413	−	0.0438924i
$529$	4.91764	+	8.51760i	0.213810	+	0.370330i
$530$	−10.7590	−	6.21173i	−0.467343	−	0.269820i
$531$	−12.0727			−0.523911
$532$	−2.74984	+	1.26015i	−0.119221	+	0.0546346i
$533$			7.94037i			0.343935i
$534$	−21.5942	−	12.4674i	−0.934471	−	0.539517i
$535$	−15.4320	−	26.7290i	−0.667184	−	1.15560i
$536$	2.92678	+	5.06934i	0.126418	+	0.218962i
$537$	−6.98219	−	4.03117i	−0.301304	−	0.173958i
$538$		−	57.5965i		−	2.48316i
$539$	−0.332389	+	1.74916i	−0.0143170	+	0.0753417i
$540$	−3.46805			−0.149241
$541$	−23.3872	−	13.5026i	−1.00549	−	0.580522i	−0.0956246	−	0.995417i	$-0.530485\pi$
$541$	−23.3872	−	13.5026i	−1.00549	−	0.580522i	−0.909869	+	0.414895i	$0.863818\pi$
$542$	−7.77334	−	13.4638i	−0.333894	−	0.578321i
$543$	9.34223	+	16.1812i	0.400913	+	0.694402i
$544$	30.1817	−	4.63077i	1.29403	−	0.198542i
$545$	−0.494911			−0.0211997
$546$	10.4486	+	22.8005i	0.447160	+	0.975772i
$547$		−	35.9985i		−	1.53918i	−0.638536	−	0.769592i	$-0.720460\pi$
$547$		−	35.9985i		−	1.53918i	0.638536	−	0.769592i	$-0.279540\pi$
$548$	−12.6177	+	21.8545i	−0.539001	+	0.933577i
$549$	−3.23816	+	1.86955i	−0.138201	+	0.0797905i
$550$	−0.242937	+	0.140260i	−0.0103589	+	0.00598070i
$551$	2.29824	+	1.32689i	0.0979085	+	0.0565275i
$552$	−3.84114			−0.163490
$553$	33.9828	+	3.20020i	1.44510	+	0.136086i
$554$		−	29.3789i		−	1.24819i
$555$	−0.200458	−	0.115735i	−0.00850897	−	0.00491266i
$556$	−22.5378	+	13.0122i	−0.955816	+	0.551840i
$557$	11.3741	+	19.7006i	0.481937	+	0.834739i	0.999785	−	0.0207333i	$-0.00660009\pi$
$557$	11.3741	+	19.7006i	0.481937	+	0.834739i	−0.517848	+	0.855473i	$0.673267\pi$
$558$	14.2140	+	8.20644i	0.601725	+	0.347406i
$559$	−41.7825			−1.76721
$560$	14.7504	−	20.7714i	0.623319	−	0.877752i
$561$	−0.656030	−	0.818191i	−0.0276976	−	0.0345441i
$562$	−22.8901	+	39.6468i	−0.965560	+	1.67240i
$563$	−15.5076	−	26.8600i	−0.653569	−	1.13201i	−0.982251	−	0.187573i	$-0.939938\pi$
$563$	−15.5076	−	26.8600i	−0.653569	−	1.13201i	0.328682	−	0.944441i	$-0.393396\pi$
$564$	−15.2060	+	8.77918i	−0.640287	+	0.369670i
$565$	−5.09709	+	8.82842i	−0.214436	+	0.371415i
$566$			38.4200i			1.61491i
$567$	2.15717	+	1.53187i	0.0905925	+	0.0643325i
$568$			1.20252i			0.0504566i
$569$	−16.2318	+	28.1143i	−0.680474	+	1.17861i	0.294363	+	0.955694i	$0.404893\pi$
$569$	−16.2318	+	28.1143i	−0.680474	+	1.17861i	−0.974836	+	0.222921i	$0.928441\pi$
$570$	−1.39256	−	2.41198i	−0.0583277	−	0.101027i
$571$	−1.19919	+	0.692353i	−0.0501846	+	0.0289741i	−0.524882	−	0.851175i	$-0.675891\pi$
$571$	−1.19919	+	0.692353i	−0.0501846	+	0.0289741i	0.474698	+	0.880149i	$0.342557\pi$
$572$	1.80263	+	1.04075i	0.0753717	+	0.0435159i
$573$			2.87624i			0.120157i
$574$	8.05133	+	0.758203i	0.336056	+	0.0316468i
$575$			3.30831i			0.137966i
$576$	−2.49482	+	4.32115i	−0.103951	+	0.180048i
$577$	−11.8295	−	20.4893i	−0.492470	−	0.852983i	0.507493	−	0.861656i	$-0.330572\pi$
$577$	−11.8295	−	20.4893i	−0.492470	−	0.852983i	−0.999962	+	0.00867345i	$0.997239\pi$
$578$	30.9806	−	9.73586i	1.28862	−	0.404959i
$579$	1.42289	−	2.46451i	0.0591332	−	0.102422i
$580$	13.2752			0.551224
$581$	−15.4389	+	7.07510i	−0.640515	+	0.293524i
$582$	11.8101			0.489543
$583$	0.681200	+	0.393291i	0.0282124	+	0.0162884i
$584$	2.23904	−	1.29271i	0.0926522	−	0.0534928i
$585$	−9.03793	+	5.21805i	−0.373672	+	0.215740i
$586$	21.1345	−	36.6061i	0.873059	−	1.51218i
$587$	42.7397			1.76405			0.882027	−	0.471198i	$-0.156178\pi$
$587$	42.7397			1.76405			0.882027	+	0.471198i	$0.156178\pi$
$588$	10.8988	−	3.80402i	0.449460	−	0.156875i
$589$			5.95664i			0.245439i
$590$	−42.0019	−	24.2498i	−1.72919	−	0.998348i
$591$	12.5505	+	21.7382i	0.516260	+	0.894189i
$592$	−0.436438	+	0.251978i	−0.0179375	+	0.0103562i
$593$	−1.21704	+	2.10797i	−0.0499778	+	0.0865640i	−0.889932	−	0.456093i	$-0.849248\pi$
$593$	−1.21704	+	2.10797i	−0.0499778	+	0.0865640i	0.839954	+	0.542657i	$0.182582\pi$
$594$	0.485878			0.0199358
$595$	10.2925	−	20.5027i	0.421950	−	0.840529i
$596$	−0.848594			−0.0347598
$597$	7.90240	−	13.6874i	0.323424	−	0.560186i
$598$	47.0425	−	27.1600i	1.92371	−	1.11065i
$599$	−6.83802	−	11.8438i	−0.279394	−	0.483925i	0.691840	−	0.722051i	$-0.256800\pi$
$599$	−6.83802	−	11.8438i	−0.279394	−	0.483925i	−0.971234	+	0.238126i	$0.923467\pi$
$600$	−0.335164	−	0.193507i	−0.0136830	−	0.00789988i
$601$			8.43737i			0.344168i	0.985082	+	0.172084i	$0.0550500\pi$
$601$			8.43737i			0.344168i	−0.985082	+	0.172084i	$0.944950\pi$
$602$	−3.98969	+	42.3663i	−0.162607	+	1.72672i
$603$	−8.73233			−0.355608
$604$	12.2581	−	21.2316i	0.498774	−	0.863902i
$605$	19.9160	−	11.4985i	0.809702	−	0.467482i
$606$	−4.93039	+	2.84656i	−0.200283	+	0.115634i
$607$	14.9433	+	8.62752i	0.606530	+	0.350180i	0.771606	−	0.636101i	$-0.219454\pi$
$607$	14.9433	+	8.62752i	0.606530	+	0.350180i	−0.165076	+	0.986281i	$0.552787\pi$
$608$	−5.13430			−0.208223
$609$	−8.25735	−	5.86380i	−0.334605	−	0.237613i
$610$	−15.0211			−0.608185
$611$	−26.4184	+	45.7580i	−1.06877	+	1.85117i
$612$	−2.46735	+	6.33589i	−0.0997368	+	0.256113i
$613$	19.9709	+	34.5906i	0.806618	+	1.39710i	0.915194	+	0.403014i	$0.132038\pi$
$613$	19.9709	+	34.5906i	0.806618	+	1.39710i	−0.108576	+	0.994088i	$0.534629\pi$
$614$	−5.26673	+	9.12224i	−0.212548	+	0.368144i
$615$			3.36500i			0.135690i
$616$	−0.261184	+	0.367797i	−0.0105234	+	0.0148190i
$617$		−	25.4840i		−	1.02595i	−0.858404	−	0.512974i	$-0.828544\pi$
$617$		−	25.4840i		−	1.02595i	0.858404	−	0.512974i	$-0.171456\pi$
$618$	−22.3458	−	12.9013i	−0.898879	−	0.518968i
$619$	28.6125	−	16.5194i	1.15003	−	0.663971i	0.201137	−	0.979563i	$-0.435536\pi$
$619$	28.6125	−	16.5194i	1.15003	−	0.663971i	0.948895	+	0.315592i	$0.102203\pi$
$620$	14.8987	+	25.8053i	0.598346	+	1.03636i
$621$	2.86510	−	4.96251i	0.114973	−	0.199138i
$622$		−	27.3103i		−	1.09504i
$623$	−3.23790	+	34.3831i	−0.129724	+	1.37753i
$624$			22.7215i			0.909589i
$625$	10.8900	−	18.8620i	0.435599	−	0.754479i
$626$	7.27612	−	4.20087i	0.290812	−	0.167901i
$627$	0.0881685	+	0.152712i	0.00352111	+	0.00609874i
$628$	8.57691	−	14.8556i	0.342256	−	0.592805i
$629$	−0.354056	+	0.283884i	−0.0141171	+	0.0113192i
$630$	4.42797	+	9.66249i	0.176414	+	0.384963i
$631$	−43.2725			−1.72265			−0.861326	−	0.508053i	$-0.830365\pi$
$631$	−43.2725			−1.72265			−0.861326	+	0.508053i	$0.830365\pi$
$632$	7.48943	+	4.32402i	0.297913	+	0.172000i
$633$	−2.19512	−	3.80206i	−0.0872481	−	0.151118i
$634$	−21.9533	+	12.6748i	−0.871878	+	0.503379i
$635$	39.7316	+	22.9391i	1.57670	+	0.910309i
$636$		−	5.09980i		−	0.202220i
$637$	22.6794	−	26.3119i	0.898591	−	1.04252i
$638$	−1.85987			−0.0736332
$639$	−1.55358	−	0.896958i	−0.0614586	−	0.0354831i
$640$	9.61646	−	5.55207i	0.380124	−	0.219465i
$641$	−27.2596	+	15.7383i	−1.07669	+	0.621627i	−0.930001	−	0.367556i	$-0.880194\pi$
$641$	−27.2596	+	15.7383i	−1.07669	+	0.621627i	−0.146687	+	0.989183i	$0.546861\pi$
$642$	14.0176	−	24.2792i	0.553230	−	0.958222i
$643$			20.4624i			0.806958i	0.914989	+	0.403479i	$0.132199\pi$
$643$			20.4624i			0.806958i	−0.914989	+	0.403479i	$0.867801\pi$
$644$	−10.4156	−	22.7284i	−0.410433	−	0.895626i
$645$	−17.7067			−0.697202
$646$	−5.39725	+	0.828097i	−0.212352	+	0.0325811i
$647$	4.38730	+	7.59903i	0.172483	+	0.298749i	0.939287	−	0.343132i	$-0.111488\pi$
$647$	4.38730	+	7.59903i	0.172483	+	0.298749i	−0.766805	+	0.641881i	$0.778154\pi$
$648$	0.335166	+	0.580525i	0.0131666	+	0.0228052i
$649$	2.65932	+	1.53536i	0.104387	+	0.0602680i
$650$	5.47300			0.214669
$651$	2.13129	−	22.6321i	0.0835317	−	0.887021i
$652$		−	20.8475i		−	0.816450i
$653$	22.0607	+	12.7367i	0.863300	+	0.498427i	0.865116	−	0.501572i	$-0.167245\pi$
$653$	22.0607	+	12.7367i	0.863300	+	0.498427i	−0.00181595	+	0.999998i	$0.500578\pi$
$654$	−0.224775	−	0.389322i	−0.00878940	−	0.0152237i
$655$	−10.0853	−	17.4683i	−0.394066	−	0.682542i
$656$	6.34476	+	3.66315i	0.247721	+	0.143022i
$657$			3.85693i			0.150473i
$658$	43.8749	+	31.1569i	1.71042	+	1.21462i
$659$	23.4678			0.914175			0.457088	−	0.889422i	$-0.348893\pi$
$659$	23.4678			0.914175			0.457088	+	0.889422i	$0.348893\pi$
$660$	0.763925	+	0.441052i	0.0297357	+	0.0171679i
$661$	13.8968	+	24.0699i	0.540521	+	0.936210i	0.998874	+	0.0474400i	$0.0151063\pi$
$661$	13.8968	+	24.0699i	0.540521	+	0.936210i	−0.458353	+	0.888770i	$0.651560\pi$
$662$	−4.63168	−	8.02230i	−0.180015	−	0.311796i
$663$	3.10297	+	20.2241i	0.120509	+	0.785438i
$664$	−4.30281			−0.166981
$665$	−2.23343	+	3.14510i	−0.0866087	+	0.121962i
$666$		−	0.210254i		−	0.00814717i
$667$	−10.9672	+	18.9958i	−0.424653	+	0.735521i
$668$	30.6170	−	17.6768i	1.18461	−	0.683934i
$669$	16.8173	−	9.70948i	0.650195	−	0.375390i
$670$	−30.3805	−	17.5402i	−1.17370	−	0.677636i
$671$	0.951047			0.0367148
$672$	19.5076	+	1.83705i	0.752523	+	0.0708659i
$673$			45.0659i			1.73716i	0.495546	+	0.868581i	$0.334968\pi$
$673$			45.0659i			1.73716i	−0.495546	+	0.868581i	$0.665032\pi$
$674$	50.9942	+	29.4415i	1.96422	+	1.13405i
$675$	0.499996	−	0.288673i	0.0192449	−	0.0111110i
$676$	−9.58615	−	16.6037i	−0.368698	−	0.638604i
$677$	−24.4330	−	14.1064i	−0.939037	−	0.542153i	−0.0493787	−	0.998780i	$-0.515724\pi$
$677$	−24.4330	−	14.1064i	−0.939037	−	0.542153i	−0.889658	+	0.456627i	$0.849057\pi$
$678$	−9.25983			−0.355622
$679$	−6.81445	−	14.8702i	−0.261515	−	0.570664i
$680$	4.53473	−	3.63597i	0.173899	−	0.139433i
$681$	−7.59328	+	13.1519i	−0.290975	+	0.503984i
$682$	−2.08732	−	3.61535i	−0.0799277	−	0.138439i
$683$	−33.1837	+	19.1586i	−1.26974	+	0.733084i	−0.974938	−	0.222475i	$-0.928586\pi$
$683$	−33.1837	+	19.1586i	−1.26974	+	0.733084i	−0.294800	+	0.955559i	$0.595253\pi$
$684$	0.571640	−	0.990110i	0.0218572	−	0.0378578i
$685$			32.1816i			1.22960i
$686$	−24.5140	−	25.5088i	−0.935951	−	0.973930i
$687$			8.88400i			0.338946i
$688$	−19.2756	+	33.3863i	−0.734875	+	1.27284i
$689$	−7.67319	−	13.2904i	−0.292325	−	0.506322i
$690$	19.9358	−	11.5100i	0.758945	−	0.438177i
$691$	22.8720	+	13.2052i	0.870093	+	0.502348i	0.867379	−	0.497648i	$-0.165803\pi$
$691$	22.8720	+	13.2052i	0.870093	+	0.502348i	0.00271357	+	0.999996i	$0.499136\pi$
$692$		−	6.84022i		−	0.260026i
$693$	−0.280353	−	0.611773i	−0.0106497	−	0.0232393i
$694$			25.0574i			0.951167i
$695$	−16.5939	+	28.7415i	−0.629443	+	1.09023i
$696$	−1.28297	−	2.22217i	−0.0486309	−	0.0842312i
$697$	6.14763	+	2.39404i	0.232858	+	0.0906806i
$698$	−29.7184	+	51.4738i	−1.12486	+	1.94831i
$699$	14.7215			0.556818
$700$	0.236173	−	2.50791i	0.00892649	−	0.0947901i
$701$	3.84574			0.145251			0.0726257	−	0.997359i	$-0.476862\pi$
$701$	3.84574			0.145251			0.0726257	+	0.997359i	$0.476862\pi$
$702$	−8.20956	−	4.73979i	−0.309850	−	0.178892i
$703$	0.0660832	−	0.0381531i	0.00249237	−	0.00143897i
$704$	1.09909	−	0.634562i	0.0414236	−	0.0239159i
$705$	−11.1957	+	19.3915i	−0.421655	+	0.730327i
$706$	5.98834			0.225374
$707$	6.42898	+	4.56542i	0.241787	+	0.171700i
$708$		−	19.9089i		−	0.748224i
$709$	−16.1087	−	9.30036i	−0.604974	−	0.349282i	0.166022	−	0.986122i	$-0.446908\pi$
$709$	−16.1087	−	9.30036i	−0.604974	−	0.349282i	−0.770996	+	0.636840i	$0.780241\pi$
$710$	−3.60334	−	6.24118i	−0.135231	−	0.234227i
$711$	−11.1727	+	6.45057i	−0.419009	+	0.241915i
$712$	−4.37496	+	7.57765i	−0.163959	+	0.283984i
$713$	−49.2337			−1.84382
$714$	20.8030	−	1.21519i	0.778533	−	0.0454774i
$715$	2.65444			0.0992705
$716$	6.64775	−	11.5142i	0.248438	−	0.430308i
$717$	6.54750	−	3.78020i	0.244521	−	0.141174i
$718$	−21.2557	−	36.8160i	−0.793256	−	1.37396i
$719$	−36.1061	−	20.8458i	−1.34653	−	0.777419i	−0.358773	−	0.933425i	$-0.616805\pi$
$719$	−36.1061	−	20.8458i	−1.34653	−	0.777419i	−0.987756	+	0.156006i	$0.950138\pi$
$720$			9.62902i			0.358852i
$721$	−3.35060	+	35.5799i	−0.124783	+	1.32506i
$722$	−35.3768			−1.31659
$723$	−3.02050	+	5.23166i	−0.112334	+	0.194568i
$724$	−26.6843	+	15.4062i	−0.991712	+	0.572565i
$725$	−1.91392	+	1.10500i	−0.0710812	+	0.0410387i
$726$	18.0906	+	10.4446i	0.671406	+	0.387637i
$727$	31.5480			1.17005			0.585025	−	0.811015i	$-0.301085\pi$
$727$	31.5480			1.17005			0.585025	+	0.811015i	$0.301085\pi$
$728$	8.00097	−	3.66655i	0.296536	−	0.135891i
$729$	−1.00000			−0.0370370
$730$	−7.74720	+	13.4185i	−0.286737	+	0.496643i
$731$	−12.5975	+	32.3490i	−0.465935	+	1.19647i
$732$	−3.08305	−	5.34001i	−0.113953	−	0.197372i
$733$	−6.23303	+	10.7959i	−0.230222	+	0.398757i	−0.957873	−	0.287191i	$-0.907279\pi$
$733$	−6.23303	+	10.7959i	−0.230222	+	0.398757i	0.727651	+	0.685947i	$0.240612\pi$
$734$		−	35.8269i		−	1.32240i
$735$	9.61117	−	11.1506i	0.354513	−	0.411295i
$736$		−	42.4368i		−	1.56424i
$737$	1.92352	+	1.11054i	0.0708536	+	0.0409074i
$738$	−2.64708	+	1.52829i	−0.0974402	+	0.0562571i
$739$	18.4135	+	31.8930i	0.677350	+	1.17320i	0.975776	+	0.218772i	$0.0702050\pi$
$739$	18.4135	+	31.8930i	0.677350	+	1.17320i	−0.298426	+	0.954433i	$0.596462\pi$
$740$	0.190856	−	0.330573i	0.00701602	−	0.0121521i
$741$		−	3.44037i		−	0.126385i
$742$	−14.2088	+	6.51136i	−0.521620	+	0.239040i
$743$		−	29.7969i		−	1.09314i	−0.837412	−	0.546572i	$-0.815932\pi$
$743$		−	29.7969i		−	1.09314i	0.837412	−	0.546572i	$-0.184068\pi$
$744$	2.87974	−	4.98785i	0.105576	−	0.182863i
$745$	−0.937191	+	0.541088i	−0.0343360	+	0.0198239i
$746$	−0.393343	−	0.681291i	−0.0144013	−	0.0249438i
$747$	3.20946	−	5.55894i	0.117428	−	0.203391i
$748$	1.34927	−	1.08185i	0.0493342	−	0.0395564i
$749$	−38.6583	−	3.64050i	−1.41254	−	0.133021i
$750$	22.4058			0.818146
$751$	13.4368	+	7.75771i	0.490314	+	0.283083i	0.724705	−	0.689059i	$-0.241976\pi$
$751$	13.4368	+	7.75771i	0.490314	+	0.283083i	−0.234391	+	0.972142i	$0.575309\pi$
$752$	24.3753	+	42.2193i	0.888877	+	1.53958i
$753$	−4.56190	+	2.63382i	−0.166245	+	0.0959816i
$754$	31.4251	+	18.1433i	1.14443	+	0.660739i
$755$		−	31.2644i		−	1.13783i
$756$	−2.52619	+	3.55736i	−0.0918767	+	0.129380i
$757$	27.4816			0.998837			0.499418	−	0.866361i	$-0.333547\pi$
$757$	27.4816			0.998837			0.499418	+	0.866361i	$0.333547\pi$
$758$	23.2668	+	13.4331i	0.845087	+	0.487911i
$759$	−1.26222	+	0.728744i	−0.0458158	+	0.0264517i
$760$	−0.846391	+	0.488664i	−0.0307018	+	0.0177257i
$761$	0.149277	−	0.258556i	0.00541130	−	0.00937264i	−0.863307	−	0.504679i	$-0.831611\pi$
$761$	0.149277	−	0.258556i	0.00541130	−	0.00937264i	0.868718	+	0.495306i	$0.164944\pi$
$762$			41.6732i			1.50966i
$763$	−0.360503	+	0.507656i	−0.0130511	+	0.0183784i
$764$	−4.74317			−0.171602
$765$	1.31499	+	8.57064i	0.0475435	+	0.309872i
$766$	23.9165	+	41.4246i	0.864139	+	1.49673i
$767$	−29.9551	−	51.8838i	−1.08162	−	1.87342i
$768$	17.3774	+	10.0328i	0.627052	+	0.362029i
$769$	33.1291			1.19466			0.597332	−	0.801994i	$-0.296227\pi$
$769$	33.1291			1.19466			0.597332	+	0.801994i	$0.296227\pi$
$770$	0.253465	−	2.69154i	0.00913424	−	0.0969962i
$771$		−	6.98379i		−	0.251515i
$772$	4.06420	+	2.34647i	0.146274	+	0.0844512i
$773$	−20.1794	−	34.9518i	−0.725804	−	1.25713i	−0.958642	−	0.284613i	$-0.908135\pi$
$773$	−20.1794	−	34.9518i	−0.725804	−	1.25713i	0.232839	−	0.972515i	$-0.425199\pi$
$774$	−8.04191	−	13.9290i	−0.289061	−	0.500667i
$775$	−4.29595	−	2.48027i	−0.154315	−	0.0890939i
$776$		−	4.14429i		−	0.148771i
$777$	−0.264732	+	0.121317i	−0.00949722	+	0.00435223i
$778$	−5.76027			−0.206516
$779$	−0.960689	−	0.554654i	−0.0344203	−	0.0198726i
$780$	−8.60503	−	14.9043i	−0.308109	−	0.533661i
$781$	0.228143	+	0.395155i	0.00816360	+	0.0141398i
$782$	−6.84452	−	44.6102i	−0.244760	−	1.59526i
$783$	3.82787			0.136797
$784$	−10.5618	−	30.2605i	−0.377208	−	1.08073i
$785$		−	21.8755i		−	0.780771i
$786$	9.16095	−	15.8672i	0.326760	−	0.565965i
$787$	6.13926	−	3.54450i	0.218841	−	0.126348i	−0.386573	−	0.922259i	$-0.626341\pi$
$787$	6.13926	−	3.54450i	0.218841	−	0.126348i	0.605413	+	0.795911i	$0.293008\pi$
$788$	−35.8482	+	20.6970i	−1.27704	+	0.737298i
$789$	−7.96762	−	4.60011i	−0.283655	−	0.163768i
$790$	−51.8276			−1.84394
$791$	5.34296	+	11.6591i	0.189974	+	0.414551i
$792$		−	0.170500i		−	0.00605846i
$793$	−16.0692	−	9.27757i	−0.570635	−	0.329456i
$794$	14.0441	−	8.10838i	0.498407	−	0.287756i
$795$	−3.25178	−	5.63224i	−0.115329	−	0.199755i
$796$	22.5717	+	13.0318i	0.800031	+	0.461898i
$797$	9.94431			0.352245			0.176123	−	0.984368i	$-0.443644\pi$
$797$	9.94431			0.352245			0.176123	+	0.984368i	$0.443644\pi$
$798$	−3.48845	−	0.328511i	−0.123490	−	0.0116292i
$799$	27.4618	+	34.2499i	0.971528	+	1.21168i
$800$	2.13786	−	3.70288i	0.0755846	−	0.130916i
$801$	−6.52655	−	11.3043i	−0.230604	−	0.399419i
$802$	−32.0083	+	18.4800i	−1.13025	+	0.652552i
$803$	0.490508	−	0.849585i	0.0173096	−	0.0299812i
$804$		−	14.4004i		−	0.507863i
$805$	−25.9953	−	18.4601i	−0.916216	−	0.650633i
$806$			81.4482i			2.86889i
$807$	15.0756	−	26.1117i	0.530686	−	0.919175i
$808$	0.998891	+	1.73013i	0.0351409	+	0.0608658i
$809$	−44.2324	+	25.5376i	−1.55513	+	0.897855i	−0.557419	+	0.830231i	$0.688208\pi$
$809$	−44.2324	+	25.5376i	−1.55513	+	0.897855i	−0.997711	+	0.0676231i	$0.978458\pi$
$810$	−3.47908	−	2.00865i	−0.122242	−	0.0705767i
$811$			0.351444i			0.0123409i	0.999981	+	0.00617043i	$0.00196412\pi$
$811$			0.351444i			0.0123409i	−0.999981	+	0.00617043i	$0.998036\pi$
$812$	9.66992	−	13.6171i	0.339348	−	0.477866i
$813$		−	8.13852i		−	0.285430i
$814$	−0.0267392	+	0.0463137i	−0.000937209	+	0.00162329i
$815$	−13.2929	−	23.0240i	−0.465631	−	0.806497i
$816$	17.5916	+	6.85059i	0.615828	+	0.239819i
$817$	2.91861	−	5.05518i	0.102109	−	0.176858i
$818$	67.4152			2.35712
$819$	−1.23097	+	13.0716i	−0.0430135	+	0.456759i
$820$	−5.54918			−0.193786
$821$	48.3346	+	27.9060i	1.68689	+	0.973926i	0.956878	+	0.290490i	$0.0938182\pi$
$821$	48.3346	+	27.9060i	1.68689	+	0.973926i	0.730010	+	0.683436i	$0.239515\pi$
$822$	−25.3156	+	14.6160i	−0.882984	+	0.509791i
$823$	−43.3963	+	25.0549i	−1.51270	+	0.873358i	−0.512811	+	0.858501i	$0.671396\pi$
$823$	−43.3963	+	25.0549i	−1.51270	+	0.873358i	−0.999890	+	0.0148567i	$0.995271\pi$
$824$	−4.52723	+	7.84140i	−0.157714	+	0.273168i
$825$	−0.146849			−0.00511263
$826$	−55.4692	+	25.4195i	−1.93002	+	0.884458i
$827$		−	10.4011i		−	0.361681i	−0.983512	−	0.180840i	$-0.942118\pi$
$827$		−	10.4011i		−	0.361681i	0.983512	−	0.180840i	$-0.0578818\pi$
$828$	8.18361	+	4.72481i	0.284400	+	0.164198i
$829$	−8.12629	−	14.0751i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$829$	−8.12629	−	14.0751i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$830$	22.3319	−	12.8933i	0.775152	−	0.447534i
$831$	7.68976	−	13.3191i	0.266755	−	0.462033i
$832$	−24.7609			−0.858429
$833$	−13.5335	−	25.4921i	−0.468907	−	0.883248i
$834$	−30.1460			−1.04387
$835$	22.5424	−	39.0446i	0.780112	−	1.35119i
$836$	−0.251836	+	0.145398i	−0.00870993	+	0.00502868i
$837$	4.29598	+	7.44086i	0.148491	+	0.257194i
$838$	−1.35576	−	0.782747i	−0.0468339	−	0.0270395i
$839$			20.8901i			0.721208i	0.932719	+	0.360604i	$0.117429\pi$
$839$			20.8901i			0.721208i	−0.932719	+	0.360604i	$0.882571\pi$
$840$	3.39068	−	1.55383i	0.116990	−	0.0536121i
$841$	14.3474			0.494739
$842$	−7.57868	+	13.1267i	−0.261179	+	0.452375i
$843$	−20.7547	+	11.9827i	−0.714829	+	0.412707i
$844$	6.26993	−	3.61994i	0.215820	−	0.124604i
$845$	−21.1740	−	12.2248i	−0.728407	−	0.420546i
$846$	−20.3391			−0.699273
$847$	2.71257	−	28.8047i	0.0932049	−	0.989740i
$848$	−14.1596			−0.486241
$849$	−10.0562	+	17.4179i	−0.345129	+	0.597781i
$850$	1.65012	−	4.23733i	0.0565987	−	0.145339i
$851$	0.315349	+	0.546201i	0.0108100	+	0.0187235i
$852$	1.47916	−	2.56199i	0.0506753	−	0.0877722i
$853$			43.0315i			1.47337i	0.676235	+	0.736686i	$0.263610\pi$
$853$			43.0315i			1.47337i	−0.676235	+	0.736686i	$0.736390\pi$
$854$	−10.9416	+	15.4079i	−0.374415	+	0.527247i
$855$		−	1.45798i		−	0.0498617i
$856$	−8.51985	−	4.91894i	−0.291202	−	0.168126i
$857$	28.7007	−	16.5704i	0.980397	−	0.566033i	0.0780073	−	0.996953i	$-0.475144\pi$
$857$	28.7007	−	16.5704i	0.980397	−	0.566033i	0.902390	+	0.430920i	$0.141811\pi$
$858$	1.20557	+	2.08812i	0.0411576	+	0.0712871i
$859$	−3.06433	+	5.30757i	−0.104553	+	0.181092i	−0.913556	−	0.406714i	$-0.866675\pi$
$859$	−3.06433	+	5.30757i	−0.104553	+	0.181092i	0.809002	+	0.587806i	$0.200008\pi$
$860$		−	29.2000i		−	0.995711i
$861$	3.45166	+	2.45113i	0.117632	+	0.0835342i
$862$		−	20.0829i		−	0.684025i
$863$	−17.6651	+	30.5968i	−0.601326	+	1.04153i	0.391294	+	0.920266i	$0.372027\pi$
$863$	−17.6651	+	30.5968i	−0.601326	+	1.04153i	−0.992621	+	0.121262i	$0.961306\pi$
$864$	−6.41362	+	3.70290i	−0.218196	+	0.125975i
$865$	−4.36152	−	7.55437i	−0.148296	−	0.256856i
$866$	4.14379	−	7.17725i	0.140812	−	0.243893i
$867$	16.5935	+	3.69521i	0.563546	+	0.125496i
$868$	37.3223	+	3.51468i	1.26680	+	0.119296i
$869$	3.28143			0.111315
$870$	13.3174	+	7.68883i	0.451504	+	0.260676i
$871$	−21.6669	−	37.5282i	−0.734156	−	1.27160i
$872$	−0.136618	+	0.0788762i	−0.00462646	+	0.00267109i
$873$	5.35415	+	3.09122i	0.181211	+	0.104622i
$874$			7.58877i			0.256694i
$875$	−12.9282	−	28.2114i	−0.437055	−	0.953719i
$876$	−6.36041			−0.214898
$877$	16.0747	+	9.28075i	0.542805	+	0.313389i	0.746215	−	0.665705i	$-0.231869\pi$
$877$	16.0747	+	9.28075i	0.542805	+	0.313389i	−0.203410	+	0.979094i	$0.565202\pi$
$878$	−28.8814	+	16.6747i	−0.974701	+	0.562744i
$879$	19.1629	−	11.0637i	0.646348	−	0.373169i
$880$	1.22458	−	2.12103i	0.0412806	−	0.0715000i
$881$			14.7520i			0.497008i	0.968631	+	0.248504i	$0.0799389\pi$
$881$			14.7520i			0.497008i	−0.968631	+	0.248504i	$0.920061\pi$
$882$	13.1367	+	2.49634i	0.442337	+	0.0840561i
$883$	−20.4041			−0.686652			−0.343326	−	0.939216i	$-0.611554\pi$
$883$	−20.4041			−0.686652			−0.343326	+	0.939216i	$0.611554\pi$
$884$	−33.3513	+	5.11707i	−1.12173	+	0.172106i
$885$	−12.6945	−	21.9875i	−0.426721	−	0.739103i
$886$	2.54257	+	4.40386i	0.0854192	+	0.147950i
$887$	−41.8821	−	24.1807i	−1.40626	−	0.811907i	−0.411239	−	0.911528i	$-0.634904\pi$
$887$	−41.8821	−	24.1807i	−1.40626	−	0.811907i	−0.995025	+	0.0996206i	$0.968237\pi$
$888$	−0.0737805			−0.00247591
$889$	52.4710	−	24.0456i	1.75982	−	0.806462i
$890$		−	52.4382i		−	1.75773i
$891$	0.220275	+	0.127176i	0.00737949	+	0.00426055i
$892$	16.0118	+	27.7332i	0.536114	+	0.928577i
$893$	−3.69078	−	6.39262i	−0.123507	−	0.213921i
$894$	−0.851293	−	0.491494i	−0.0284715	−	0.0164380i
$895$		−	16.9552i		−	0.566749i
$896$	1.30976	−	13.9083i	0.0437561	−	0.464645i
$897$	28.4359			0.949448
$898$	−17.6688	−	10.2011i	−0.589616	−	0.340415i
$899$	−16.4444	−	28.4826i	−0.548453	−	0.949948i
$900$	0.476047	+	0.824538i	0.0158682	+	0.0274846i
$901$	−12.6032	+	1.93370i	−0.419874	+	0.0644209i
$902$	0.777447			0.0258861
$903$	−12.8979	+	18.1627i	−0.429216	+	0.604417i
$904$			3.24938i			0.108073i
$905$	−19.6468	+	34.0293i	−0.653082	+	1.13117i
$906$	24.5941	−	14.1994i	0.817084	−	0.471744i
$907$	−9.94473	+	5.74159i	−0.330209	+	0.190646i	−0.655934	−	0.754818i	$-0.727725\pi$
$907$	−9.94473	+	5.74159i	−0.330209	+	0.190646i	0.325725	+	0.945465i	$0.394392\pi$
$908$	−21.6887	−	12.5220i	−0.719765	−	0.415557i
$909$	−2.98029			−0.0988499
$910$	−30.5389	+	43.0045i	−1.01235	+	1.42559i
$911$		−	24.4558i		−	0.810256i	−0.914260	−	0.405128i	$-0.867227\pi$
$911$		−	24.4558i		−	0.810256i	0.914260	−	0.405128i	$-0.132773\pi$
$912$	−2.74903	−	1.58716i	−0.0910296	−	0.0525560i
$913$	−1.41393	+	0.816331i	−0.0467942	+	0.0270166i
$914$	−3.20772	−	5.55593i	−0.106102	−	0.183774i
$915$	−6.80988	−	3.93168i	−0.225128	−	0.129977i
$916$	−14.6505			−0.484066
$917$	−25.2645	−	2.37918i	−0.834306	−	0.0785675i
$918$	−6.14486	+	4.92698i	−0.202811	+	0.162615i
$919$	13.2279	−	22.9114i	0.436349	−	0.755778i	−0.561056	−	0.827778i	$-0.689605\pi$
$919$	13.2279	−	22.9114i	0.436349	−	0.755778i	0.997405	+	0.0719998i	$0.0229381\pi$
$920$	−4.03898	−	6.99572i	−0.133161	−	0.230642i
$921$	−4.77539	+	2.75707i	−0.157355	+	0.0908487i
$922$	−28.6891	+	49.6909i	−0.944824	+	1.63648i
$923$		−	8.90224i		−	0.293021i
$924$	1.00887	−	0.462327i	0.0331893	−	0.0152094i
$925$			0.0635459i			0.00208938i
$926$	33.4305	−	57.9033i	1.09859	−	1.90282i
$927$	−6.75372	−	11.6978i	−0.221821	−	0.384205i
$928$	24.5505	−	14.1742i	0.805909	−	0.465292i
$929$	−14.5169	−	8.38135i	−0.476285	−	0.274983i	0.242582	−	0.970131i	$-0.422006\pi$
$929$	−14.5169	−	8.38135i	−0.476285	−	0.274983i	−0.718867	+	0.695148i	$0.755339\pi$
$930$			34.5165i			1.13184i
$931$	1.59922	+	4.58189i	0.0524122	+	0.150165i
$932$			24.2771i			0.795221i
$933$	7.14834	−	12.3813i	0.234026	−	0.405345i
$934$	15.0287	+	26.0304i	0.491753	+	0.851742i
$935$	0.800320	−	2.05513i	0.0261733	−	0.0672101i
$936$	−1.66325	+	2.88083i	−0.0543650	+	0.0941629i
$937$	−12.3742			−0.404248			−0.202124	−	0.979360i	$-0.564784\pi$
$937$	−12.3742			−0.404248			−0.202124	+	0.979360i	$0.564784\pi$
$938$	−40.1216	+	18.3863i	−1.31002	+	0.600332i
$939$	4.39822			0.143531
$940$	−31.9783	−	18.4627i	−1.04302	−	0.602187i
$941$	22.8586	−	13.1974i	0.745171	−	0.430224i	−0.0787756	−	0.996892i	$-0.525101\pi$
$941$	22.8586	−	13.1974i	0.745171	−	0.430224i	0.823946	+	0.566668i	$0.191768\pi$
$942$	17.2084	−	9.93526i	0.560679	−	0.323708i
$943$	4.58442	−	7.94044i	0.149289	−	0.258576i
$944$	−55.2771			−1.79912
$945$	−0.521664	+	5.53953i	−0.0169697	+	0.180201i
$946$			4.09095i			0.133008i
$947$	−25.1160	−	14.5007i	−0.816160	−	0.471210i	0.0329302	−	0.999458i	$-0.489516\pi$
$947$	−25.1160	−	14.5007i	−0.816160	−	0.471210i	−0.849091	+	0.528247i	$0.822849\pi$
$948$	−10.6376	−	18.4248i	−0.345492	−	0.598409i
$949$	−16.5756	+	9.56992i	−0.538066	+	0.310653i
$950$	−0.382302	+	0.662167i	−0.0124035	+	0.0214835i
$951$	−13.2702			−0.430316
$952$	−0.426425	−	7.30002i	−0.0138205	−	0.236595i
$953$	49.1905			1.59344			0.796718	−	0.604352i	$-0.206568\pi$
$953$	49.1905			1.59344			0.796718	+	0.604352i	$0.206568\pi$
$954$	2.95373	−	5.11602i	0.0956306	−	0.165637i
$955$	−5.23838	+	3.02438i	−0.169510	+	0.0978666i
$956$	6.23389	+	10.7974i	0.201618	+	0.349213i
$957$	−0.843184	−	0.486812i	−0.0272563	−	0.0157364i
$958$			35.1031i			1.13413i
$959$	33.0103	+	23.4417i	1.06596	+	0.756971i
$960$	−10.4933			−0.338669
$961$	21.4109	−	37.0848i	0.690675	−	1.19628i
$962$	0.903590	−	0.521688i	0.0291329	−	0.0168199i
$963$	12.7099	−	7.33805i	0.409570	−	0.236466i
$964$	−8.62748	−	4.98108i	−0.277872	−	0.160430i
$965$	5.98470			0.192654
$966$	2.71526	−	28.8333i	0.0873622	−	0.927696i
$967$	38.1833			1.22789			0.613946	−	0.789348i	$-0.289581\pi$
$967$	38.1833			1.22789			0.613946	+	0.789348i	$0.289581\pi$
$968$	3.66514	−	6.34822i	0.117802	−	0.204039i
$969$	−2.66362	−	1.03728i	−0.0855679	−	0.0333222i
$970$	12.4183	+	21.5092i	0.398729	+	0.690619i
$971$	6.22720	−	10.7858i	0.199840	−	0.346134i	−0.748636	−	0.662981i	$-0.769291\pi$
$971$	6.22720	−	10.7858i	0.199840	−	0.346134i	0.948477	+	0.316847i	$0.102624\pi$
$972$		−	1.64909i		−	0.0528945i
$973$	17.3943	+	37.9570i	0.557636	+	1.21685i
$974$			67.7263i			2.17009i
$975$	2.48121	+	1.43253i	0.0794623	+	0.0458776i
$976$	−14.8265	+	8.56008i	−0.474585	+	0.274002i
$977$	−14.7762	−	25.5932i	−0.472734	−	0.818799i	0.526779	−	0.850002i	$-0.323399\pi$
$977$	−14.7762	−	25.5932i	−0.472734	−	0.818799i	−0.999513	+	0.0312034i	$0.990066\pi$
$978$	12.0746	−	20.9138i	0.386102	−	0.668748i
$979$			3.32008i			0.106110i
$980$	18.3883	+	15.8497i	0.587392	+	0.506299i
$981$		−	0.235335i		−	0.00751366i
$982$	6.34796	−	10.9950i	0.202572	−	0.350864i
$983$	−18.4860	+	10.6729i	−0.589613	+	0.340413i	−0.764945	−	0.644096i	$-0.777234\pi$
$983$	−18.4860	+	10.6729i	−0.589613	+	0.340413i	0.175331	+	0.984509i	$0.443900\pi$
$984$	0.536295	+	0.928890i	0.0170965	+	0.0296119i
$985$	−26.3939	+	45.7156i	−0.840980	+	1.45662i
$986$	23.5217	−	18.8598i	0.749084	−	0.600620i
$987$	11.7357	+	25.6092i	0.373553	+	0.815148i
$988$	5.67348			0.180497
$989$	41.7828	+	24.1233i	1.32862	+	0.767077i
$990$	0.510903	+	0.884910i	0.0162376	+	0.0281243i
$991$	44.5622	−	25.7280i	1.41556	−	0.817276i	0.419658	−	0.907682i	$-0.362150\pi$
$991$	44.5622	−	25.7280i	1.41556	−	0.817276i	0.995905	+	0.0904062i	$0.0288165\pi$
$992$	55.1056	+	31.8152i	1.74960	+	1.01013i
$993$		−	4.84927i		−	0.153887i
$994$	−9.02664	−	0.850049i	−0.286308	−	0.0269619i
$995$	33.2377			1.05370
$996$	9.16719	+	5.29268i	0.290474	+	0.167705i
$997$	−15.9515	+	9.20961i	−0.505189	+	0.291671i	−0.730854	−	0.682534i	$-0.760878\pi$
$997$	−15.9515	+	9.20961i	−0.505189	+	0.291671i	0.225665	+	0.974205i	$0.427545\pi$
$998$	72.2967	−	41.7405i	2.28851	−	1.32127i
$999$	0.0550328	−	0.0953196i	0.00174116	−	0.00301578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.16.5	✓	48
7.4	even	3	inner	357.2.p.a.67.6	yes	48
17.16	even	2	inner	357.2.p.a.16.6	yes	48
119.67	even	6	inner	357.2.p.a.67.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.5	✓	48	1.1	even	1	trivial
357.2.p.a.16.6	yes	48	17.16	even	2	inner
357.2.p.a.67.5	yes	48	119.67	even	6	inner
357.2.p.a.67.6	yes	48	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.955129 + 1.65433i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.824544 - 1.42815i) q^{4} +(-1.82126 - 1.05151i) q^{5} -1.91026i q^{6} +(-2.40522 + 1.10223i) q^{7} -0.670332 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.955129 + 1.65433i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.824544 - 1.42815i) q^{4} +(-1.82126 - 1.05151i) q^{5} -1.91026i q^{6} +(-2.40522 + 1.10223i) q^{7} -0.670332 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.47908 - 2.00865i) q^{10} +(-0.220275 + 0.127176i) q^{11} +(1.42815 + 0.824544i) q^{12} +4.96246 q^{13} +(0.473851 - 5.03181i) q^{14} +2.10301 q^{15} +(2.28934 - 3.96526i) q^{16} +(1.49619 - 3.84206i) q^{17} +(0.955129 + 1.65433i) q^{18} +(-0.346640 + 0.600398i) q^{19} +3.46805i q^{20} +(1.53187 - 2.15717i) q^{21} -0.485878i q^{22} +(-4.96251 - 2.86510i) q^{23} +(0.580525 - 0.335166i) q^{24} +(-0.288673 - 0.499996i) q^{25} +(-4.73979 + 8.20956i) q^{26} +1.00000i q^{27} +(3.55736 + 2.52619i) q^{28} -3.82787i q^{29} +(-2.00865 + 3.47908i) q^{30} +(7.44086 - 4.29598i) q^{31} +(3.70290 + 6.41362i) q^{32} +(0.127176 - 0.220275i) q^{33} +(4.92698 + 6.14486i) q^{34} +(5.53953 + 0.521664i) q^{35} -1.64909 q^{36} +(-0.0953196 - 0.0550328i) q^{37} +(-0.662172 - 1.14692i) q^{38} +(-4.29762 + 2.48123i) q^{39} +(1.22085 + 0.704858i) q^{40} +1.60009i q^{41} +(2.10554 + 4.59460i) q^{42} -8.41971 q^{43} +(0.363253 + 0.209724i) q^{44} +(-1.82126 + 1.05151i) q^{45} +(9.47967 - 5.47309i) q^{46} +(-5.32365 + 9.22084i) q^{47} +4.57868i q^{48} +(4.57020 - 5.30220i) q^{49} +1.10288 q^{50} +(0.625288 + 4.07542i) q^{51} +(-4.09177 - 7.08715i) q^{52} +(-1.54625 - 2.67818i) q^{53} +(-1.65433 - 0.955129i) q^{54} +0.534905 q^{55} +(1.61230 - 0.738858i) q^{56} -0.693280i q^{57} +(6.33256 + 3.65611i) q^{58} +(-6.03635 - 10.4553i) q^{59} +(-1.73403 - 3.00342i) q^{60} +(-3.23816 - 1.86955i) q^{61} +16.4129i q^{62} +(-0.248056 + 2.63410i) q^{63} -4.98964 q^{64} +(-9.03793 - 5.21805i) q^{65} +(0.242939 + 0.420782i) q^{66} +(-4.36617 - 7.56242i) q^{67} +(-6.72072 + 1.03116i) q^{68} +5.73021 q^{69} +(-6.15398 + 8.66598i) q^{70} -1.79392i q^{71} +(-0.335166 + 0.580525i) q^{72} +(-3.34020 + 1.92846i) q^{73} +(0.182085 - 0.105127i) q^{74} +(0.499996 + 0.288673i) q^{75} +1.14328 q^{76} +(0.389634 - 0.548679i) q^{77} -9.47958i q^{78} +(-11.1727 - 6.45057i) q^{79} +(-8.33898 + 4.81451i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.64708 - 1.52829i) q^{82} +6.41892 q^{83} +(-4.34386 - 0.409066i) q^{84} +(-6.76490 + 5.42413i) q^{85} +(8.04191 - 13.9290i) q^{86} +(1.91393 + 3.31503i) q^{87} +(0.147658 - 0.0852501i) q^{88} +(6.52655 - 11.3043i) q^{89} -4.01729i q^{90} +(-11.9358 + 5.46975i) q^{91} +9.44962i q^{92} +(-4.29598 + 7.44086i) q^{93} +(-10.1696 - 17.6142i) q^{94} +(1.26264 - 0.728988i) q^{95} +(-6.41362 - 3.70290i) q^{96} +6.18244i q^{97} +(4.40647 + 12.6249i) q^{98} +0.254352i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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