LMFDB - Embedded newform 650.2.t.g.557.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(7,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{13} - 48 x^{12} + 16 x^{11} + 8 x^{10} + 80 x^{9} + 2208 x^{8} + 760 x^{7} + 192 x^{6} + \cdots + 4096 $ x^16 - 4x^13 - 48x^12 + 16x^11 + 8x^10 + 80x^9 + 2208x^8 + 760x^7 + 192x^6 + 1696x^5 - 2812x^4 - 2080x^3 + 128x^2 - 1024*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.3
Root			$0.935952 + 0.250788i$ of defining polynomial
Character	$\chi$	$=$	650.557
Dual form			650.2.t.g.643.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.935952 + 0.250788i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935952 - 0.250788i) q^{6} +(1.88470 - 3.26439i) q^{7} -1.00000i q^{8} +(-1.78496 - 1.03055i) q^{9} +(-1.91630 - 0.513470i) q^{11} +(0.685164 - 0.685164i) q^{12} +(0.930617 - 3.48338i) q^{13} -3.76940i q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.33261 + 4.97337i) q^{17} -2.06110 q^{18} +(0.103361 + 0.385747i) q^{19} +(2.58266 - 2.58266i) q^{21} +(-1.91630 + 0.513470i) q^{22} +(0.652430 - 2.43490i) q^{23} +(0.250788 - 0.935952i) q^{24} +(-0.935753 - 3.48201i) q^{26} +(-3.46769 - 3.46769i) q^{27} +(-1.88470 - 3.26439i) q^{28} +(-1.00654 + 0.581127i) q^{29} +(7.10352 + 7.10352i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.66479 - 0.961167i) q^{33} +(3.64076 + 3.64076i) q^{34} +(-1.78496 + 1.03055i) q^{36} +(5.39776 + 9.34919i) q^{37} +(0.282386 + 0.282386i) q^{38} +(1.74460 - 3.02689i) q^{39} +(-0.0903706 + 0.337268i) q^{41} +(0.945318 - 3.52797i) q^{42} +(4.86670 - 1.30403i) q^{43} +(-1.40283 + 1.40283i) q^{44} +(-0.652430 - 2.43490i) q^{46} -2.16571 q^{47} +(-0.250788 - 0.935952i) q^{48} +(-3.60417 - 6.24261i) q^{49} +4.98903i q^{51} +(-2.55139 - 2.54763i) q^{52} +(4.52928 - 4.52928i) q^{53} +(-4.73695 - 1.26926i) q^{54} +(-3.26439 - 1.88470i) q^{56} +0.386962i q^{57} +(-0.581127 + 1.00654i) q^{58} +(-12.2618 + 3.28554i) q^{59} +(0.985039 - 1.70614i) q^{61} +(9.70358 + 2.60007i) q^{62} +(-6.72824 + 3.88455i) q^{63} -1.00000 q^{64} -1.92233 q^{66} +(12.0484 - 6.95614i) q^{67} +(4.97337 + 1.33261i) q^{68} +(1.22129 - 2.11533i) q^{69} +(-0.875664 + 0.234633i) q^{71} +(-1.03055 + 1.78496i) q^{72} +8.38511i q^{73} +(9.34919 + 5.39776i) q^{74} +(0.385747 + 0.103361i) q^{76} +(-5.28781 + 5.28781i) q^{77} +(-0.00257603 - 3.49367i) q^{78} +3.10557i q^{79} +(0.715714 + 1.23965i) q^{81} +(0.0903706 + 0.337268i) q^{82} -4.98388 q^{83} +(-0.945318 - 3.52797i) q^{84} +(3.56267 - 3.56267i) q^{86} +(-1.08781 + 0.291479i) q^{87} +(-0.513470 + 1.91630i) q^{88} +(-4.22759 + 15.7776i) q^{89} +(-9.61719 - 9.60302i) q^{91} +(-1.78247 - 1.78247i) q^{92} +(4.86708 + 8.43002i) q^{93} +(-1.87556 + 1.08285i) q^{94} +(-0.685164 - 0.685164i) q^{96} +(-14.9854 - 8.65185i) q^{97} +(-6.24261 - 3.60417i) q^{98} +(2.89136 + 2.89136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 6 * q^33 - 14 * q^34 + 20 * q^37 - 6 * q^38 - 6 * q^39 - 44 * q^41 - 6 * q^42 + 6 * q^44 - 6 * q^46 - 52 * q^47 - 2 * q^49 - 10 * q^52 + 24 * q^53 + 6 * q^54 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.935952	+	0.250788i	0.540372	+	0.144792i	0.518674	−	0.854972i	$-0.326426\pi$
$3$	0.935952	+	0.250788i	0.540372	+	0.144792i	0.0216985	+	0.999765i	$0.493093\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.935952	−	0.250788i	0.382101	−	0.102384i
$7$	1.88470	−	3.26439i	0.712349	−	1.23382i	−0.251624	−	0.967825i	$-0.580965\pi$
$7$	1.88470	−	3.26439i	0.712349	−	1.23382i	0.963973	−	0.265999i	$-0.0857019\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.78496	−	1.03055i	−0.594988	−	0.343517i
$10$		0			0
$11$	−1.91630	−	0.513470i	−0.577785	−	0.154817i	−0.0419205	−	0.999121i	$-0.513348\pi$
$11$	−1.91630	−	0.513470i	−0.577785	−	0.154817i	−0.535865	+	0.844304i	$0.680014\pi$
$12$	0.685164	−	0.685164i	0.197790	−	0.197790i
$13$	0.930617	−	3.48338i	0.258107	−	0.966116i
$13$	0.930617	−	3.48338i	0.258107	−	0.966116i
$14$		−	3.76940i		−	1.00741i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.33261	+	4.97337i	0.323205	+	1.20622i	0.916104	+	0.400941i	$0.131317\pi$
$17$	1.33261	+	4.97337i	0.323205	+	1.20622i	−0.592899	+	0.805277i	$0.702017\pi$
$18$	−2.06110			−0.485806
$19$	0.103361	+	0.385747i	0.0237125	+	0.0884964i	0.976768	−	0.214299i	$-0.0687467\pi$
$19$	0.103361	+	0.385747i	0.0237125	+	0.0884964i	−0.953056	+	0.302796i	$0.902080\pi$
$20$		0			0
$21$	2.58266	−	2.58266i	0.563582	−	0.563582i
$22$	−1.91630	+	0.513470i	−0.408556	+	0.109472i
$23$	0.652430	−	2.43490i	0.136041	−	0.507712i	−0.863950	−	0.503577i	$-0.832017\pi$
$23$	0.652430	−	2.43490i	0.136041	−	0.507712i	0.999991	−	0.00413534i	$-0.00131632\pi$
$24$	0.250788	−	0.935952i	0.0511918	−	0.191050i
$25$		0			0
$26$	−0.935753	−	3.48201i	−0.183516	−	0.682878i
$27$	−3.46769	−	3.46769i	−0.667356	−	0.667356i
$28$	−1.88470	−	3.26439i	−0.356174	−	0.616912i
$29$	−1.00654	+	0.581127i	−0.186910	+	0.107913i	−0.590535	−	0.807012i	$-0.701083\pi$
$29$	−1.00654	+	0.581127i	−0.186910	+	0.107913i	0.403625	+	0.914924i	$0.367750\pi$
$30$		0			0
$31$	7.10352	+	7.10352i	1.27583	+	1.27583i	0.942980	+	0.332849i	$0.108010\pi$
$31$	7.10352	+	7.10352i	1.27583	+	1.27583i	0.332849	+	0.942980i	$0.391990\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.66479	−	0.961167i	−0.289803	−	0.167318i
$34$	3.64076	+	3.64076i	0.624384	+	0.624384i
$35$		0			0
$36$	−1.78496	+	1.03055i	−0.297494	+	0.171758i
$37$	5.39776	+	9.34919i	0.887386	+	1.53700i	0.842954	+	0.537985i	$0.180814\pi$
$37$	5.39776	+	9.34919i	0.887386	+	1.53700i	0.0444319	+	0.999012i	$0.485852\pi$
$38$	0.282386	+	0.282386i	0.0458091	+	0.0458091i
$39$	1.74460	−	3.02689i	0.279360	−	0.484691i
$40$		0			0
$41$	−0.0903706	+	0.337268i	−0.0141135	+	0.0526724i	−0.972623	−	0.232387i	$-0.925347\pi$
$41$	−0.0903706	+	0.337268i	−0.0141135	+	0.0526724i	0.958510	+	0.285059i	$0.0920132\pi$
$42$	0.945318	−	3.52797i	0.145866	−	0.544378i
$43$	4.86670	−	1.30403i	0.742165	−	0.198863i	0.132125	−	0.991233i	$-0.457820\pi$
$43$	4.86670	−	1.30403i	0.742165	−	0.198863i	0.610040	+	0.792370i	$0.291153\pi$
$44$	−1.40283	+	1.40283i	−0.211484	+	0.211484i
$45$		0			0
$46$	−0.652430	−	2.43490i	−0.0961956	−	0.359007i
$47$	−2.16571			−0.315901			−0.157950	−	0.987447i	$-0.550489\pi$
$47$	−2.16571			−0.315901			−0.157950	+	0.987447i	$0.550489\pi$
$48$	−0.250788	−	0.935952i	−0.0361981	−	0.135093i
$49$	−3.60417	−	6.24261i	−0.514882	−	0.891801i
$50$		0			0
$51$			4.98903i			0.698604i
$52$	−2.55139	−	2.54763i	−0.353814	−	0.353293i
$53$	4.52928	−	4.52928i	0.622145	−	0.622145i	−0.323935	−	0.946079i	$-0.605006\pi$
$53$	4.52928	−	4.52928i	0.622145	−	0.622145i	0.946079	+	0.323935i	$0.105006\pi$
$54$	−4.73695	−	1.26926i	−0.644617	−	0.172725i
$55$		0			0
$56$	−3.26439	−	1.88470i	−0.436223	−	0.251853i
$57$			0.386962i			0.0512544i
$58$	−0.581127	+	1.00654i	−0.0763058	+	0.132165i
$59$	−12.2618	+	3.28554i	−1.59635	+	0.427740i	−0.943937	−	0.330124i	$-0.892909\pi$
$59$	−12.2618	+	3.28554i	−1.59635	+	0.427740i	−0.652412	+	0.757865i	$0.726243\pi$
$60$		0			0
$61$	0.985039	−	1.70614i	0.126121	−	0.218449i	−0.796049	−	0.605232i	$-0.793080\pi$
$61$	0.985039	−	1.70614i	0.126121	−	0.218449i	0.922171	+	0.386783i	$0.126414\pi$
$62$	9.70358	+	2.60007i	1.23236	+	0.330209i
$63$	−6.72824	+	3.88455i	−0.847678	+	0.489407i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.92233			−0.236623
$67$	12.0484	−	6.95614i	1.47194	−	0.849827i	0.472441	−	0.881362i	$-0.343373\pi$
$67$	12.0484	−	6.95614i	1.47194	−	0.849827i	0.999503	+	0.0315350i	$0.0100396\pi$
$68$	4.97337	+	1.33261i	0.603109	+	0.161603i
$69$	1.22129	−	2.11533i	0.147026	−	0.254656i
$70$		0			0
$71$	−0.875664	+	0.234633i	−0.103922	+	0.0278459i	−0.310405	−	0.950604i	$-0.600465\pi$
$71$	−0.875664	+	0.234633i	−0.103922	+	0.0278459i	0.206483	+	0.978450i	$0.433798\pi$
$72$	−1.03055	+	1.78496i	−0.121451	+	0.210360i
$73$			8.38511i			0.981403i	0.871328	+	0.490701i	$0.163259\pi$
$73$			8.38511i			0.981403i	−0.871328	+	0.490701i	$0.836741\pi$
$74$	9.34919	+	5.39776i	1.08682	+	0.627477i
$75$		0			0
$76$	0.385747	+	0.103361i	0.0442482	+	0.0118563i
$77$	−5.28781	+	5.28781i	−0.602602	+	0.602602i
$78$	−0.00257603	−	3.49367i	−0.000291677	−	0.395580i
$79$			3.10557i			0.349403i	0.984621	+	0.174702i	$0.0558961\pi$
$79$			3.10557i			0.349403i	−0.984621	+	0.174702i	$0.944104\pi$
$80$		0			0
$81$	0.715714	+	1.23965i	0.0795238	+	0.137739i
$82$	0.0903706	+	0.337268i	0.00997976	+	0.0372450i
$83$	−4.98388			−0.547052			−0.273526	−	0.961865i	$-0.588190\pi$
$83$	−4.98388			−0.547052			−0.273526	+	0.961865i	$0.588190\pi$
$84$	−0.945318	−	3.52797i	−0.103143	−	0.384933i
$85$		0			0
$86$	3.56267	−	3.56267i	0.384173	−	0.384173i
$87$	−1.08781	+	0.291479i	−0.116626	+	0.0312498i
$88$	−0.513470	+	1.91630i	−0.0547361	+	0.204278i
$89$	−4.22759	+	15.7776i	−0.448124	+	1.67242i	0.259431	+	0.965762i	$0.416465\pi$
$89$	−4.22759	+	15.7776i	−0.448124	+	1.67242i	−0.707554	+	0.706659i	$0.750202\pi$
$90$		0			0
$91$	−9.61719	−	9.60302i	−1.00816	−	1.00667i
$92$	−1.78247	−	1.78247i	−0.185836	−	0.185836i
$93$	4.86708	+	8.43002i	0.504692	+	0.874153i
$94$	−1.87556	+	1.08285i	−0.193449	+	0.111688i
$95$		0			0
$96$	−0.685164	−	0.685164i	−0.0699293	−	0.0699293i
$97$	−14.9854	−	8.65185i	−1.52154	−	0.878462i	−0.999677	−	0.0254339i	$-0.991903\pi$
$97$	−14.9854	−	8.65185i	−1.52154	−	0.878462i	−0.521865	−	0.853028i	$-0.674763\pi$
$98$	−6.24261	−	3.60417i	−0.630599	−	0.364076i
$99$	2.89136	+	2.89136i	0.290593	+	0.290593i
$100$		0			0
$101$	−4.50466	+	2.60077i	−0.448230	+	0.258786i	−0.707083	−	0.707131i	$-0.749989\pi$
$101$	−4.50466	+	2.60077i	−0.448230	+	0.258786i	0.258852	+	0.965917i	$0.416656\pi$
$102$	2.49452	+	4.32063i	0.246994	+	0.427806i
$103$	3.96952	+	3.96952i	0.391129	+	0.391129i	0.875090	−	0.483961i	$-0.160802\pi$
$103$	3.96952	+	3.96952i	0.391129	+	0.391129i	−0.483961	+	0.875090i	$0.660802\pi$
$104$	−3.48338	−	0.930617i	−0.341574	−	0.0912545i
$105$		0			0
$106$	1.65783	−	6.18712i	0.161023	−	0.600946i
$107$	−2.39861	+	8.95175i	−0.231883	+	0.865398i	0.747647	+	0.664097i	$0.231184\pi$
$107$	−2.39861	+	8.95175i	−0.231883	+	0.865398i	−0.979529	+	0.201301i	$0.935483\pi$
$108$	−4.73695	+	1.26926i	−0.455813	+	0.122135i
$109$	3.96733	−	3.96733i	0.380001	−	0.380001i	−0.491101	−	0.871102i	$-0.663406\pi$
$109$	3.96733	−	3.96733i	0.380001	−	0.380001i	0.871102	+	0.491101i	$0.163406\pi$
$110$		0			0
$111$	2.70738	+	10.1041i	0.256973	+	0.959037i
$112$	−3.76940			−0.356174
$113$	−1.43269	−	5.34686i	−0.134776	−	0.502990i	−0.999999	−	0.00160293i	$-0.999490\pi$
$113$	−1.43269	−	5.34686i	−0.134776	−	0.502990i	0.865223	−	0.501388i	$-0.167177\pi$
$114$	0.193481	+	0.335119i	0.0181212	+	0.0313868i
$115$		0			0
$116$			1.16225i			0.107913i
$117$	−5.25092	+	5.25867i	−0.485447	+	0.486164i
$118$	−8.97625	+	8.97625i	−0.826331	+	0.826331i
$119$	18.7466	+	5.02313i	1.71850	+	0.460470i
$120$		0			0
$121$	−6.11774	−	3.53208i	−0.556158	−	0.321098i
$122$		−	1.97008i		−	0.178363i
$123$	−0.169165	+	0.293003i	−0.0152531	+	0.0264191i
$124$	9.70358	−	2.60007i	0.871407	−	0.233493i
$125$		0			0
$126$	−3.88455	+	6.72824i	−0.346063	+	0.599399i
$127$	−0.432529	−	0.115896i	−0.0383808	−	0.0102841i	0.239578	−	0.970877i	$-0.422991\pi$
$127$	−0.432529	−	0.115896i	−0.0383808	−	0.0102841i	−0.277958	+	0.960593i	$0.589658\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.88204			0.429839
$130$		0			0
$131$	14.7831			1.29161			0.645805	−	0.763503i	$-0.276522\pi$
$131$	14.7831			1.29161			0.645805	+	0.763503i	$0.276522\pi$
$132$	−1.66479	+	0.961167i	−0.144901	+	0.0836588i
$133$	1.45403	+	0.389607i	0.126081	+	0.0337832i
$134$	6.95614	−	12.0484i	0.600919	−	1.04082i
$135$		0			0
$136$	4.97337	−	1.33261i	0.426463	−	0.114270i
$137$	5.06901	−	8.77979i	0.433075	−	0.750108i	−0.564061	−	0.825733i	$-0.690762\pi$
$137$	5.06901	−	8.77979i	0.433075	−	0.750108i	0.997136	+	0.0756251i	$0.0240952\pi$
$138$		−	2.44257i		−	0.207926i
$139$	5.47729	+	3.16232i	0.464578	+	0.268224i	0.713967	−	0.700179i	$-0.246897\pi$
$139$	5.47729	+	3.16232i	0.464578	+	0.268224i	−0.249389	+	0.968403i	$0.580230\pi$
$140$		0			0
$141$	−2.02700	−	0.543132i	−0.170704	−	0.0457400i
$142$	−0.641030	+	0.641030i	−0.0537941	+	0.0537941i
$143$	−3.57195	+	6.19735i	−0.298702	+	0.518248i
$144$			2.06110i			0.171758i
$145$		0			0
$146$	4.19255	+	7.26172i	0.346978	+	0.600984i
$147$	−1.80776	−	6.74666i	−0.149102	−	0.556455i
$148$	10.7955			0.887386
$149$	−1.45148	−	5.41700i	−0.118910	−	0.443778i	0.880640	−	0.473787i	$-0.157113\pi$
$149$	−1.45148	−	5.41700i	−0.118910	−	0.443778i	−0.999550	+	0.0300087i	$0.990446\pi$
$150$		0			0
$151$	−8.56883	+	8.56883i	−0.697322	+	0.697322i	−0.963832	−	0.266510i	$-0.914129\pi$
$151$	−8.56883	+	8.56883i	−0.697322	+	0.697322i	0.266510	+	0.963832i	$0.414129\pi$
$152$	0.385747	−	0.103361i	0.0312882	−	0.00838365i
$153$	2.74664	−	10.2506i	0.222053	−	0.828712i
$154$	−1.93547	+	7.22328i	−0.155965	+	0.582068i
$155$		0			0
$156$	−1.74906	−	3.02432i	−0.140037	−	0.242139i
$157$	−2.39607	−	2.39607i	−0.191227	−	0.191227i	0.604999	−	0.796226i	$-0.293173\pi$
$157$	−2.39607	−	2.39607i	−0.191227	−	0.191227i	−0.796226	+	0.604999i	$0.793173\pi$
$158$	1.55278	+	2.68950i	0.123533	+	0.213965i
$159$	5.37508	−	3.10330i	0.426272	−	0.246108i
$160$		0			0
$161$	−6.71884	−	6.71884i	−0.529519	−	0.529519i
$162$	1.23965	+	0.715714i	0.0973964	+	0.0562318i
$163$	15.2707	+	8.81652i	1.19609	+	0.690563i	0.959681	−	0.281091i	$-0.0906961\pi$
$163$	15.2707	+	8.81652i	1.19609	+	0.690563i	0.236409	+	0.971654i	$0.424029\pi$
$164$	0.246897	+	0.246897i	0.0192794	+	0.0192794i
$165$		0			0
$166$	−4.31617	+	2.49194i	−0.335000	+	0.193412i
$167$	2.57973	+	4.46822i	0.199625	+	0.345761i	0.948407	−	0.317056i	$-0.102694\pi$
$167$	2.57973	+	4.46822i	0.199625	+	0.345761i	−0.748782	+	0.662817i	$0.769361\pi$
$168$	−2.58266	−	2.58266i	−0.199256	−	0.199256i
$169$	−11.2679	−	6.48339i	−0.866762	−	0.498722i
$170$		0			0
$171$	0.213036	−	0.795063i	0.0162913	−	0.0608000i
$172$	1.30403	−	4.86670i	0.0994313	−	0.371083i
$173$	1.09651	−	0.293810i	0.0833664	−	0.0223380i	−0.216895	−	0.976195i	$-0.569593\pi$
$173$	1.09651	−	0.293810i	0.0833664	−	0.0223380i	0.300261	+	0.953857i	$0.402926\pi$
$174$	−0.796336	+	0.796336i	−0.0603701	+	0.0603701i
$175$		0			0
$176$	0.513470	+	1.91630i	0.0387043	+	0.144446i
$177$	−12.3004			−0.924556
$178$	4.22759	+	15.7776i	0.316871	+	1.18258i
$179$	2.71932	+	4.71001i	0.203252	+	0.352042i	0.949574	−	0.313542i	$-0.101516\pi$
$179$	2.71932	+	4.71001i	0.203252	+	0.352042i	−0.746323	+	0.665584i	$0.768182\pi$
$180$		0			0
$181$			16.7849i			1.24761i	0.781580	+	0.623805i	$0.214414\pi$
$181$			16.7849i			1.24761i	−0.781580	+	0.623805i	$0.785586\pi$
$182$	−13.1302	−	3.50786i	−0.973279	−	0.260020i
$183$	1.34983	−	1.34983i	0.0997822	−	0.0997822i
$184$	−2.43490	−	0.652430i	−0.179503	−	0.0480978i
$185$		0			0
$186$	8.43002	+	4.86708i	0.618119	+	0.356871i
$187$		−	10.2147i		−	0.746973i
$188$	−1.08285	+	1.87556i	−0.0789752	+	0.136789i
$189$	−17.8554	+	4.78435i	−1.29879	+	0.348010i
$190$		0			0
$191$	−0.957583	+	1.65858i	−0.0692883	+	0.120011i	−0.898588	−	0.438793i	$-0.855406\pi$
$191$	−0.957583	+	1.65858i	−0.0692883	+	0.120011i	0.829300	+	0.558804i	$0.188739\pi$
$192$	−0.935952	−	0.250788i	−0.0675465	−	0.0180990i
$193$	−17.0820	+	9.86232i	−1.22959	+	0.709905i	−0.966945	−	0.254987i	$-0.917929\pi$
$193$	−17.0820	+	9.86232i	−1.22959	+	0.709905i	−0.262647	+	0.964892i	$0.584596\pi$
$194$	−17.3037			−1.24233
$195$		0			0
$196$	−7.20834			−0.514882
$197$	−9.48728	+	5.47748i	−0.675940	+	0.390254i	−0.798324	−	0.602228i	$-0.794280\pi$
$197$	−9.48728	+	5.47748i	−0.675940	+	0.390254i	0.122383	+	0.992483i	$0.460946\pi$
$198$	3.94968	+	1.05831i	0.280691	+	0.0752110i
$199$	5.90974	−	10.2360i	0.418930	−	0.725608i	−0.576902	−	0.816813i	$-0.695739\pi$
$199$	5.90974	−	10.2360i	0.418930	−	0.725608i	0.995832	+	0.0912052i	$0.0290719\pi$
$200$		0			0
$201$	13.0212	−	3.48902i	0.918446	−	0.246097i
$202$	−2.60077	+	4.50466i	−0.182989	+	0.316947i
$203$			4.38100i			0.307486i
$204$	4.32063	+	2.49452i	0.302505	+	0.174651i
$205$		0			0
$206$	5.42247	+	1.45295i	0.377801	+	0.101232i
$207$	−3.67385	+	3.67385i	−0.255350	+	0.255350i
$208$	−3.48201	+	0.935753i	−0.241434	+	0.0648828i
$209$		−	0.792278i		−	0.0548030i
$210$		0			0
$211$	−8.93348	−	15.4732i	−0.615006	−	1.06522i	−0.990383	−	0.138350i	$-0.955820\pi$
$211$	−8.93348	−	15.4732i	−0.615006	−	1.06522i	0.375377	−	0.926872i	$-0.377513\pi$
$212$	−1.65783	−	6.18712i	−0.113860	−	0.424933i
$213$	−0.878423			−0.0601885
$214$	2.39861	+	8.95175i	0.163966	+	0.611929i
$215$		0			0
$216$	−3.46769	+	3.46769i	−0.235946	+	0.235946i
$217$	36.5766	−	9.80068i	2.48298	−	0.665314i
$218$	1.45214	−	5.41947i	0.0983515	−	0.367053i
$219$	−2.10288	+	7.84806i	−0.142100	+	0.530323i
$220$		0			0
$221$	18.5643	−	0.0136882i	1.24877	−	0.000920769i
$222$	7.39671	+	7.39671i	0.496434	+	0.496434i
$223$	−4.42725	−	7.66822i	−0.296471	−	0.513502i	0.678855	−	0.734272i	$-0.262476\pi$
$223$	−4.42725	−	7.66822i	−0.296471	−	0.513502i	−0.975326	+	0.220770i	$0.929143\pi$
$224$	−3.26439	+	1.88470i	−0.218111	+	0.125927i
$225$		0			0
$226$	−3.91417	−	3.91417i	−0.260367	−	0.260367i
$227$	18.8658	+	10.8922i	1.25217	+	0.722941i	0.971540	−	0.236875i	$-0.0761232\pi$
$227$	18.8658	+	10.8922i	1.25217	+	0.722941i	0.280630	+	0.959816i	$0.409457\pi$
$228$	0.335119	+	0.193481i	0.0221938	+	0.0128136i
$229$	−7.92975	−	7.92975i	−0.524013	−	0.524013i	0.394768	−	0.918781i	$-0.370825\pi$
$229$	−7.92975	−	7.92975i	−0.524013	−	0.524013i	−0.918781	+	0.394768i	$0.870825\pi$
$230$		0			0
$231$	−6.27525	+	3.62302i	−0.412881	+	0.238377i
$232$	0.581127	+	1.00654i	0.0381529	+	0.0660827i
$233$	−1.89587	−	1.89587i	−0.124203	−	0.124203i	0.642273	−	0.766476i	$-0.277991\pi$
$233$	−1.89587	−	1.89587i	−0.124203	−	0.124203i	−0.766476	+	0.642273i	$0.777991\pi$
$234$	−1.91809	+	7.17960i	−0.125390	+	0.469345i
$235$		0			0
$236$	−3.28554	+	12.2618i	−0.213870	+	0.798175i
$237$	−0.778837	+	2.90666i	−0.0505909	+	0.188808i
$238$	18.7466	−	5.02313i	1.21516	−	0.325601i
$239$	2.43675	−	2.43675i	0.157620	−	0.157620i	−0.623891	−	0.781511i	$-0.714449\pi$
$239$	2.43675	−	2.43675i	0.157620	−	0.157620i	0.781511	+	0.623891i	$0.214449\pi$
$240$		0			0
$241$	−7.65372	−	28.5641i	−0.493019	−	1.83997i	−0.540852	−	0.841118i	$-0.681898\pi$
$241$	−7.65372	−	28.5641i	−0.493019	−	1.83997i	0.0478326	−	0.998855i	$-0.484769\pi$
$242$	−7.06416			−0.454101
$243$	4.16677	+	15.5506i	0.267298	+	0.997571i
$244$	−0.985039	−	1.70614i	−0.0630607	−	0.109224i
$245$		0			0
$246$			0.338330i			0.0215711i
$247$	1.43989	−	0.00106169i	0.0916182	−	6.75539e-5i
$248$	7.10352	−	7.10352i	0.451074	−	0.451074i
$249$	−4.66467	−	1.24990i	−0.295612	−	0.0792089i
$250$		0			0
$251$	22.7052	+	13.1089i	1.43314	+	0.827425i	0.997359	−	0.0726275i	$-0.0231384\pi$
$251$	22.7052	+	13.1089i	1.43314	+	0.827425i	0.435782	+	0.900052i	$0.356472\pi$
$252$			7.76910i			0.489407i
$253$	−2.50050	+	4.33099i	−0.157205	+	0.272287i
$254$	−0.432529	+	0.115896i	−0.0271393	+	0.00727196i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.0997	−	4.31389i	−1.00427	−	0.269093i	−0.281037	−	0.959697i	$-0.590678\pi$
$257$	−16.0997	−	4.31389i	−1.00427	−	0.269093i	−0.723233	+	0.690604i	$0.757345\pi$
$258$	4.22797	−	2.44102i	0.263222	−	0.151971i
$259$	40.6926			2.52851
$260$		0			0
$261$	2.39552			0.148279
$262$	12.8026	−	7.39157i	0.790946	−	0.456653i
$263$	−14.6464	−	3.92449i	−0.903136	−	0.241994i	−0.222773	−	0.974870i	$-0.571511\pi$
$263$	−14.6464	−	3.92449i	−0.903136	−	0.241994i	−0.680362	+	0.732876i	$0.738178\pi$
$264$	−0.961167	+	1.66479i	−0.0591557	+	0.102461i
$265$		0			0
$266$	1.45403	−	0.389607i	0.0891524	−	0.0238883i
$267$	−7.91365	+	13.7068i	−0.484307	+	0.838845i
$268$		−	13.9123i		−	0.849827i
$269$	13.9653	+	8.06288i	0.851480	+	0.491602i	0.861150	−	0.508351i	$-0.169745\pi$
$269$	13.9653	+	8.06288i	0.851480	+	0.491602i	−0.00966987	+	0.999953i	$0.503078\pi$
$270$		0			0
$271$	−15.1445	−	4.05795i	−0.919961	−	0.246503i	−0.232392	−	0.972622i	$-0.574655\pi$
$271$	−15.1445	−	4.05795i	−0.919961	−	0.246503i	−0.687569	+	0.726119i	$0.741322\pi$
$272$	3.64076	−	3.64076i	0.220753	−	0.220753i
$273$	−6.59291	−	11.3998i	−0.399021	−	0.689950i
$274$		−	10.1380i		−	0.612460i
$275$		0			0
$276$	−1.22129	−	2.11533i	−0.0735128	−	0.127328i
$277$	−5.48331	−	20.4640i	−0.329460	−	1.22956i	−0.909751	−	0.415154i	$-0.863728\pi$
$277$	−5.48331	−	20.4640i	−0.329460	−	1.22956i	0.580291	−	0.814409i	$-0.302939\pi$
$278$	6.32463			0.379326
$279$	−5.35900	−	20.0000i	−0.320835	−	1.19737i
$280$		0			0
$281$	−8.41983	+	8.41983i	−0.502285	+	0.502285i	−0.912147	−	0.409863i	$-0.865577\pi$
$281$	−8.41983	+	8.41983i	−0.502285	+	0.502285i	0.409863	+	0.912147i	$0.365577\pi$
$282$	−2.02700	+	0.543132i	−0.120706	+	0.0323431i
$283$	3.07011	−	11.4578i	0.182499	−	0.681095i	−0.812653	−	0.582748i	$-0.801978\pi$
$283$	3.07011	−	11.4578i	0.182499	−	0.681095i	0.995152	−	0.0983477i	$-0.0313557\pi$
$284$	−0.234633	+	0.875664i	−0.0139229	+	0.0519611i
$285$		0			0
$286$	0.00527423	+	7.15304i	0.000311872	+	0.422968i
$287$	0.930653	+	0.930653i	0.0549347	+	0.0549347i
$288$	1.03055	+	1.78496i	0.0607257	+	0.105180i
$289$	−8.23608	+	4.75510i	−0.484475	+	0.279712i
$290$		0			0
$291$	−11.8559	−	11.8559i	−0.695004	−	0.695004i
$292$	7.26172	+	4.19255i	0.424960	+	0.245351i
$293$	−23.1746	−	13.3799i	−1.35388	−	0.781661i	−0.365086	−	0.930974i	$-0.618960\pi$
$293$	−23.1746	−	13.3799i	−1.35388	−	0.781661i	−0.988790	+	0.149313i	$0.952294\pi$
$294$	−4.93890	−	4.93890i	−0.288043	−	0.288043i
$295$		0			0
$296$	9.34919	−	5.39776i	0.543411	−	0.313738i
$297$	4.86456	+	8.42567i	0.282270	+	0.488907i
$298$	−3.96552	−	3.96552i	−0.229716	−	0.229716i
$299$	−7.87454	−	4.53863i	−0.455396	−	0.262476i
$300$		0			0
$301$	4.91540	−	18.3445i	0.283319	−	1.05736i
$302$	−3.13641	+	11.7052i	−0.180480	+	0.673561i
$303$	−4.86839	+	1.30448i	−0.279681	+	0.0749404i
$304$	0.282386	−	0.282386i	0.0161960	−	0.0161960i
$305$		0			0
$306$	−2.74664	−	10.2506i	−0.157015	−	0.585988i
$307$	−0.284972			−0.0162642			−0.00813210	−	0.999967i	$-0.502589\pi$
$307$	−0.284972			−0.0162642			−0.00813210	+	0.999967i	$0.502589\pi$
$308$	1.93547	+	7.22328i	0.110284	+	0.411585i
$309$	2.71977	+	4.71079i	0.154723	+	0.267987i
$310$		0			0
$311$		−	1.02509i		−	0.0581274i	−0.999578	−	0.0290637i	$-0.990747\pi$
$311$		−	1.02509i		−	0.0581274i	0.999578	−	0.0290637i	$-0.00925257\pi$
$312$	−3.02689	−	1.74460i	−0.171364	−	0.0987686i
$313$	3.88598	−	3.88598i	0.219649	−	0.219649i	−0.588702	−	0.808350i	$-0.700361\pi$
$313$	3.88598	−	3.88598i	0.219649	−	0.219649i	0.808350	+	0.588702i	$0.200361\pi$
$314$	−3.27309	−	0.877022i	−0.184711	−	0.0494932i
$315$		0			0
$316$	2.68950	+	1.55278i	0.151296	+	0.0873509i
$317$			2.45686i			0.137991i	0.997617	+	0.0689956i	$0.0219794\pi$
$317$			2.45686i			0.137991i	−0.997617	+	0.0689956i	$0.978021\pi$
$318$	3.10330	−	5.37508i	0.174025	−	0.301420i
$319$	2.22723	−	0.596783i	0.124701	−	0.0334134i
$320$		0			0
$321$	−4.48997	+	7.77686i	−0.250606	+	0.434062i
$322$	−9.17811	−	2.45927i	−0.511476	−	0.137050i
$323$	−1.78072	+	1.02810i	−0.0990819	+	0.0572050i
$324$	1.43143			0.0795238
$325$		0			0
$326$	17.6330			0.976604
$327$	4.70818	−	2.71827i	0.260363	−	0.150321i
$328$	0.337268	+	0.0903706i	0.0186225	+	0.00498988i
$329$	−4.08170	+	7.06971i	−0.225031	+	0.389766i
$330$		0			0
$331$	6.49468	−	1.74025i	0.356980	−	0.0956525i	−0.0758718	−	0.997118i	$-0.524174\pi$
$331$	6.49468	−	1.74025i	0.356980	−	0.0956525i	0.432852	+	0.901465i	$0.357507\pi$
$332$	−2.49194	+	4.31617i	−0.136763	+	0.236880i
$333$		−	22.2506i		−	1.21933i
$334$	4.46822	+	2.57973i	0.244490	+	0.141156i
$335$		0			0
$336$	−3.52797	−	0.945318i	−0.192467	−	0.0515713i
$337$	−5.43489	+	5.43489i	−0.296057	+	0.296057i	−0.839467	−	0.543410i	$-0.817133\pi$
$337$	−5.43489	+	5.43489i	−0.296057	+	0.296057i	0.543410	+	0.839467i	$0.317133\pi$
$338$	−13.0000	+	0.0191709i	−0.707106	+	0.00104276i
$339$		−	5.36371i		−	0.291317i
$340$		0			0
$341$	−9.96500	−	17.2599i	−0.539635	−	0.934675i
$342$	−0.213036	−	0.795063i	−0.0115197	−	0.0429921i
$343$	−0.785328			−0.0424037
$344$	−1.30403	−	4.86670i	−0.0703086	−	0.262395i
$345$		0			0
$346$	0.802704	−	0.802704i	0.0431536	−	0.0431536i
$347$	34.5616	−	9.26076i	1.85537	−	0.497144i	0.855576	−	0.517677i	$-0.173203\pi$
$347$	34.5616	−	9.26076i	1.85537	−	0.497144i	0.999789	+	0.0205336i	$0.00653652\pi$
$348$	−0.291479	+	1.08781i	−0.0156249	+	0.0583130i
$349$	−5.42298	+	20.2388i	−0.290285	+	1.08336i	0.654604	+	0.755972i	$0.272835\pi$
$349$	−5.42298	+	20.2388i	−0.290285	+	1.08336i	−0.944890	+	0.327388i	$0.893831\pi$
$350$		0			0
$351$	−15.3064	+	8.85219i	−0.816993	+	0.472495i
$352$	1.40283	+	1.40283i	0.0747709	+	0.0747709i
$353$	3.65558	+	6.33165i	0.194567	+	0.336999i	0.946758	−	0.321945i	$-0.104337\pi$
$353$	3.65558	+	6.33165i	0.194567	+	0.336999i	−0.752192	+	0.658944i	$0.771003\pi$
$354$	−10.6525	+	6.15021i	−0.566173	+	0.326880i
$355$		0			0
$356$	11.5500	+	11.5500i	0.612148	+	0.612148i
$357$	16.2862	+	9.40282i	0.861955	+	0.497650i
$358$	4.71001	+	2.71932i	0.248932	+	0.143721i
$359$	−18.6180	−	18.6180i	−0.982620	−	0.982620i	0.0172312	−	0.999852i	$-0.494515\pi$
$359$	−18.6180	−	18.6180i	−0.982620	−	0.982620i	−0.999852	+	0.0172312i	$0.994515\pi$
$360$		0			0
$361$	16.3164	−	9.42026i	0.858756	−	0.495803i
$362$	8.39244	+	14.5361i	0.441097	+	0.764002i
$363$	−4.84011	−	4.84011i	−0.254040	−	0.254040i
$364$	−13.1251	+	3.52722i	−0.687940	+	0.184877i
$365$		0			0
$366$	0.494071	−	1.84390i	0.0258255	−	0.0963822i
$367$	2.28221	−	8.51733i	0.119130	−	0.444601i	−0.880432	−	0.474172i	$-0.842747\pi$
$367$	2.28221	−	8.51733i	0.119130	−	0.444601i	0.999563	+	0.0295711i	$0.00941416\pi$
$368$	−2.43490	+	0.652430i	−0.126928	+	0.0340103i
$369$	0.508879	−	0.508879i	0.0264912	−	0.0264912i
$370$		0			0
$371$	−6.24903	−	23.3217i	−0.324433	−	1.21080i
$372$	9.73415			0.504692
$373$	−6.64469	−	24.7983i	−0.344049	−	1.28401i	−0.893719	−	0.448627i	$-0.851913\pi$
$373$	−6.64469	−	24.7983i	−0.344049	−	1.28401i	0.549670	−	0.835382i	$-0.314753\pi$
$374$	−5.10735	−	8.84619i	−0.264095	−	0.457425i
$375$		0			0
$376$			2.16571i			0.111688i
$377$	1.08758	+	4.04698i	0.0560134	+	0.208430i
$378$	−13.0711	+	13.0711i	−0.672304	+	0.672304i
$379$	−11.5676	−	3.09953i	−0.594188	−	0.159212i	−0.0508216	−	0.998708i	$-0.516184\pi$
$379$	−11.5676	−	3.09953i	−0.594188	−	0.159212i	−0.543367	+	0.839495i	$0.682851\pi$
$380$		0			0
$381$	−0.375762	−	0.216946i	−0.0192508	−	0.0111145i
$382$			1.91517i			0.0979884i
$383$	17.1646	−	29.7300i	0.877073	−	1.51913i	0.0225340	−	0.999746i	$-0.492827\pi$
$383$	17.1646	−	29.7300i	0.877073	−	1.51913i	0.854538	−	0.519388i	$-0.173840\pi$
$384$	−0.935952	+	0.250788i	−0.0477626	+	0.0127980i
$385$		0			0
$386$	−9.86232	+	17.0820i	−0.501979	+	0.869453i
$387$	−10.0308	−	2.68773i	−0.509892	−	0.136625i
$388$	−14.9854	+	8.65185i	−0.760771	+	0.439231i
$389$	−33.2497			−1.68582			−0.842912	−	0.538051i	$-0.819161\pi$
$389$	−33.2497			−1.68582			−0.842912	+	0.538051i	$0.819161\pi$
$390$		0			0
$391$	12.9791			0.656381
$392$	−6.24261	+	3.60417i	−0.315299	+	0.182038i
$393$	13.8363	+	3.70743i	0.697950	+	0.187015i
$394$	−5.47748	+	9.48728i	−0.275952	+	0.477962i
$395$		0			0
$396$	3.94968	−	1.05831i	0.198479	−	0.0531822i
$397$	−3.18246	+	5.51217i	−0.159723	+	0.276648i	−0.934769	−	0.355257i	$-0.884393\pi$
$397$	−3.18246	+	5.51217i	−0.159723	+	0.276648i	0.775046	+	0.631905i	$0.217727\pi$
$398$		−	11.8195i		−	0.592457i
$399$	1.26320	+	0.729307i	0.0632389	+	0.0365110i
$400$		0			0
$401$	−12.2984	−	3.29534i	−0.614151	−	0.164561i	−0.0616838	−	0.998096i	$-0.519647\pi$
$401$	−12.2984	−	3.29534i	−0.614151	−	0.164561i	−0.552468	+	0.833534i	$0.686314\pi$
$402$	9.53219	−	9.53219i	0.475423	−	0.475423i
$403$	31.3549	−	18.1336i	1.56190	−	0.903299i
$404$			5.20153i			0.258786i
$405$		0			0
$406$	2.19050	+	3.79406i	0.108713	+	0.188296i
$407$	−5.54318	−	20.6874i	−0.274765	−	1.02544i
$408$	4.98903			0.246994
$409$	−5.36650	−	20.0280i	−0.265356	−	0.990323i	−0.962032	−	0.272937i	$-0.912005\pi$
$409$	−5.36650	−	20.0280i	−0.265356	−	0.990323i	0.696676	−	0.717386i	$-0.254662\pi$
$410$		0			0
$411$	6.94621	−	6.94621i	0.342631	−	0.342631i
$412$	5.42247	−	1.45295i	0.267146	−	0.0715815i
$413$	−12.3845	+	46.2195i	−0.609401	+	2.27431i
$414$	−1.34472	+	5.01858i	−0.0660896	+	0.246650i
$415$		0			0
$416$	−2.54763	+	2.55139i	−0.124908	+	0.125092i
$417$	4.33341	+	4.33341i	0.212208	+	0.212208i
$418$	−0.396139	−	0.686133i	−0.0193758	−	0.0335599i
$419$	12.0178	−	6.93846i	0.587106	−	0.338966i	−0.176846	−	0.984238i	$-0.556590\pi$
$419$	12.0178	−	6.93846i	0.587106	−	0.338966i	0.763952	+	0.645273i	$0.223256\pi$
$420$		0			0
$421$	7.42389	+	7.42389i	0.361818	+	0.361818i	0.864482	−	0.502664i	$-0.167647\pi$
$421$	7.42389	+	7.42389i	0.361818	+	0.361818i	−0.502664	+	0.864482i	$0.667647\pi$
$422$	−15.4732	−	8.93348i	−0.753226	−	0.434875i
$423$	3.86571	+	2.23187i	0.187957	+	0.108517i
$424$	−4.52928	−	4.52928i	−0.219961	−	0.219961i
$425$		0			0
$426$	−0.760736	+	0.439211i	−0.0368578	+	0.0212799i
$427$	−3.71300	−	6.43111i	−0.179685	−	0.311223i
$428$	6.55313	+	6.55313i	0.316758	+	0.316758i
$429$	−4.89739	+	4.90462i	−0.236448	+	0.236797i
$430$		0			0
$431$	−10.0156	+	37.3789i	−0.482436	+	1.80048i	0.108901	+	0.994053i	$0.465267\pi$
$431$	−10.0156	+	37.3789i	−0.482436	+	1.80048i	−0.591337	+	0.806424i	$0.701400\pi$
$432$	−1.26926	+	4.73695i	−0.0610673	+	0.227906i
$433$	17.3395	−	4.64610i	0.833282	−	0.223277i	0.183137	−	0.983087i	$-0.441375\pi$
$433$	17.3395	−	4.64610i	0.833282	−	0.223277i	0.650145	+	0.759810i	$0.274708\pi$
$434$	26.7760	−	26.7760i	1.28529	−	1.28529i
$435$		0			0
$436$	−1.45214	−	5.41947i	−0.0695450	−	0.259545i
$437$	1.00669			0.0481566
$438$	2.10288	+	7.84806i	0.100480	+	0.374995i
$439$	15.6117	+	27.0402i	0.745104	+	1.29056i	0.950146	+	0.311804i	$0.100933\pi$
$439$	15.6117	+	27.0402i	0.745104	+	1.29056i	−0.205043	+	0.978753i	$0.565733\pi$
$440$		0			0
$441$			14.8571i			0.707481i
$442$	16.0703	−	9.29399i	0.764386	−	0.442070i
$443$	14.2963	−	14.2963i	0.679238	−	0.679238i	−0.280589	−	0.959828i	$-0.590530\pi$
$443$	14.2963	−	14.2963i	0.679238	−	0.679238i	0.959828	+	0.280589i	$0.0905299\pi$
$444$	10.1041	+	2.70738i	0.479519	+	0.128487i
$445$		0			0
$446$	−7.66822	−	4.42725i	−0.363101	−	0.209636i
$447$		−	5.43406i		−	0.257022i
$448$	−1.88470	+	3.26439i	−0.0890436	+	0.154228i
$449$	20.6314	−	5.52817i	0.973657	−	0.260891i	0.263286	−	0.964718i	$-0.415194\pi$
$449$	20.6314	−	5.52817i	0.973657	−	0.260891i	0.710371	+	0.703827i	$0.248527\pi$
$450$		0			0
$451$	0.346354	−	0.599902i	0.0163092	−	0.0282483i
$452$	−5.34686	−	1.43269i	−0.251495	−	0.0673879i
$453$	−10.1690	+	5.87106i	−0.477780	+	0.275846i
$454$	21.7844			1.02239
$455$		0			0
$456$	0.386962			0.0181212
$457$	−10.2320	+	5.90744i	−0.478632	+	0.276338i	−0.719846	−	0.694134i	$-0.755788\pi$
$457$	−10.2320	+	5.90744i	−0.478632	+	0.276338i	0.241214	+	0.970472i	$0.422454\pi$
$458$	−10.8322	−	2.90249i	−0.506157	−	0.135624i
$459$	12.6250	−	21.8671i	0.589284	−	1.02067i
$460$		0			0
$461$	−6.93599	+	1.85849i	−0.323041	+	0.0865586i	−0.416695	−	0.909046i	$-0.636812\pi$
$461$	−6.93599	+	1.85849i	−0.323041	+	0.0865586i	0.0936542	+	0.995605i	$0.470145\pi$
$462$	−3.62302	+	6.27525i	−0.168558	+	0.291951i
$463$			29.7640i			1.38325i	0.722257	+	0.691625i	$0.243105\pi$
$463$			29.7640i			1.38325i	−0.722257	+	0.691625i	$0.756895\pi$
$464$	1.00654	+	0.581127i	0.0467276	+	0.0269782i
$465$		0			0
$466$	−2.58981	−	0.693937i	−0.119971	−	0.0321460i
$467$	16.9753	−	16.9753i	0.785525	−	0.785525i	−0.195232	−	0.980757i	$-0.562546\pi$
$467$	16.9753	−	16.9753i	0.785525	−	0.785525i	0.980757	+	0.195232i	$0.0625461\pi$
$468$	1.92868	+	7.17676i	0.0891533	+	0.331746i
$469$		−	52.4409i		−	2.42149i
$470$		0			0
$471$	−1.64170	−	2.84351i	−0.0756456	−	0.131022i
$472$	3.28554	+	12.2618i	0.151229	+	0.564395i
$473$	−9.99563			−0.459599
$474$	0.778837	+	2.90666i	0.0357732	+	0.133507i
$475$		0			0
$476$	13.7234	−	13.7234i	0.629013	−	0.629013i
$477$	−12.7523	+	3.41696i	−0.583886	+	0.156452i
$478$	0.891913	−	3.32867i	0.0407952	−	0.152250i
$479$	−8.07862	+	30.1498i	−0.369121	+	1.37758i	0.492625	+	0.870242i	$0.336037\pi$
$479$	−8.07862	+	30.1498i	−0.369121	+	1.37758i	−0.861747	+	0.507339i	$0.830629\pi$
$480$		0			0
$481$	37.5901	−	10.1019i	1.71396	−	0.460609i
$482$	−20.9103	−	20.9103i	−0.952440	−	0.952440i
$483$	−4.60351	−	7.97352i	−0.209467	−	0.362808i
$484$	−6.11774	+	3.53208i	−0.278079	+	0.160549i
$485$		0			0
$486$	11.3838	+	11.3838i	0.516381	+	0.516381i
$487$	−21.4064	−	12.3590i	−0.970015	−	0.560038i	−0.0707743	−	0.997492i	$-0.522547\pi$
$487$	−21.4064	−	12.3590i	−0.970015	−	0.560038i	−0.899241	+	0.437454i	$0.855880\pi$
$488$	−1.70614	−	0.985039i	−0.0772333	−	0.0445906i
$489$	12.0815	+	12.0815i	0.546346	+	0.546346i
$490$		0			0
$491$	−3.52957	+	2.03780i	−0.159287	+	0.0919645i	−0.577525	−	0.816373i	$-0.695981\pi$
$491$	−3.52957	+	2.03780i	−0.159287	+	0.0919645i	0.418238	+	0.908338i	$0.362648\pi$
$492$	0.169165	+	0.293003i	0.00762655	+	0.0132096i
$493$	−4.23149	−	4.23149i	−0.190577	−	0.190577i
$494$	1.24645	−	0.720866i	0.0560806	−	0.0324333i
$495$		0			0
$496$	2.60007	−	9.70358i	0.116746	−	0.435704i
$497$	−0.884426	+	3.30072i	−0.0396719	+	0.148058i
$498$	−4.66467	+	1.24990i	−0.209029	+	0.0560092i
$499$	−14.5534	+	14.5534i	−0.651500	+	0.651500i	−0.953354	−	0.301854i	$-0.902394\pi$
$499$	−14.5534	+	14.5534i	−0.651500	+	0.651500i	0.301854	+	0.953354i	$0.402394\pi$
$500$		0			0
$501$	1.29393	+	4.82900i	0.0578084	+	0.215744i
$502$	26.2177			1.17016
$503$	5.26719	+	19.6574i	0.234852	+	0.876481i	0.978215	+	0.207593i	$0.0665628\pi$
$503$	5.26719	+	19.6574i	0.234852	+	0.876481i	−0.743363	+	0.668888i	$0.766771\pi$
$504$	3.88455	+	6.72824i	0.173032	+	0.299699i
$505$		0			0
$506$			5.00100i			0.222322i
$507$	−8.92026	−	8.89399i	−0.396163	−	0.394996i
$508$	−0.316633	+	0.316633i	−0.0140483	+	0.0140483i
$509$	31.5138	+	8.44410i	1.39682	+	0.374278i	0.877203	−	0.480119i	$-0.159407\pi$
$509$	31.5138	+	8.44410i	1.39682	+	0.374278i	0.519621	+	0.854397i	$0.326073\pi$
$510$		0			0
$511$	27.3723	+	15.8034i	1.21088	+	0.699101i
$512$			1.00000i			0.0441942i
$513$	0.979227	−	1.69607i	0.0432339	−	0.0748833i
$514$	−16.0997	+	4.31389i	−0.710126	+	0.190278i
$515$		0			0
$516$	2.44102	−	4.22797i	0.107460	−	0.186126i
$517$	4.15013	+	1.11203i	0.182523	+	0.0489068i
$518$	35.2408	−	20.3463i	1.54839	−	0.893965i
$519$	1.09997			0.0482832
$520$		0			0
$521$	−44.2788			−1.93989			−0.969945	−	0.243325i	$-0.921762\pi$
$521$	−44.2788			−1.93989			−0.969945	+	0.243325i	$0.921762\pi$
$522$	2.07458	−	1.19776i	0.0908021	−	0.0524246i
$523$	−14.3107	−	3.83454i	−0.625764	−	0.167673i	−0.0680170	−	0.997684i	$-0.521667\pi$
$523$	−14.3107	−	3.83454i	−0.625764	−	0.167673i	−0.557747	+	0.830011i	$0.688334\pi$
$524$	7.39157	−	12.8026i	0.322902	−	0.559283i
$525$		0			0
$526$	−14.6464	+	3.92449i	−0.638613	+	0.171116i
$527$	−25.8622	+	44.7946i	−1.12657	+	1.95128i
$528$			1.92233i			0.0836588i
$529$	14.4155	+	8.32279i	0.626761	+	0.361860i
$530$		0			0
$531$	25.2728	+	6.77182i	1.09674	+	0.293872i
$532$	1.06443	−	1.06443i	0.0461487	−	0.0461487i
$533$	1.09073	+	0.628662i	0.0472448	+	0.0272304i
$534$			15.8273i			0.684914i
$535$		0			0
$536$	−6.95614	−	12.0484i	−0.300459	−	0.520411i
$537$	1.36395	+	5.09031i	0.0588586	+	0.219663i
$538$	16.1258			0.695231
$539$	3.70127	+	13.8133i	0.159425	+	0.594982i
$540$		0			0
$541$	−5.82293	+	5.82293i	−0.250347	+	0.250347i	−0.821113	−	0.570766i	$-0.806646\pi$
$541$	−5.82293	+	5.82293i	−0.250347	+	0.250347i	0.570766	+	0.821113i	$0.306646\pi$
$542$	−15.1445	+	4.05795i	−0.650511	+	0.174304i
$543$	−4.20944	+	15.7098i	−0.180644	+	0.674174i
$544$	1.33261	−	4.97337i	0.0571351	−	0.213231i
$545$		0			0
$546$	−11.4096	−	6.57610i	−0.488284	−	0.281431i
$547$	−4.24613	−	4.24613i	−0.181551	−	0.181551i	0.610480	−	0.792032i	$-0.290976\pi$
$547$	−4.24613	−	4.24613i	−0.181551	−	0.181551i	−0.792032	+	0.610480i	$0.790976\pi$
$548$	−5.06901	−	8.77979i	−0.216537	−	0.375054i
$549$	−3.51652	+	2.03026i	−0.150081	+	0.0866496i
$550$		0			0
$551$	−0.328205	−	0.328205i	−0.0139820	−	0.0139820i
$552$	−2.11533	−	1.22129i	−0.0900345	−	0.0519814i
$553$	10.1378	+	5.85305i	0.431102	+	0.248897i
$554$	−14.9807	−	14.9807i	−0.636469	−	0.636469i
$555$		0			0
$556$	5.47729	−	3.16232i	0.232289	−	0.134112i
$557$	11.4969	+	19.9132i	0.487140	+	0.843751i	0.999891	−	0.0147865i	$-0.00470686\pi$
$557$	11.4969	+	19.9132i	0.487140	+	0.843751i	−0.512751	+	0.858537i	$0.671374\pi$
$558$	−14.6411	−	14.6411i	−0.619805	−	0.619805i
$559$	−0.0133947	−	18.1661i	−0.000566533	−	0.768346i
$560$		0			0
$561$	2.56172	−	9.56047i	0.108156	−	0.403643i
$562$	−3.08187	+	11.5017i	−0.130001	+	0.485170i
$563$	−15.8729	+	4.25312i	−0.668962	+	0.179248i	−0.577287	−	0.816541i	$-0.695889\pi$
$563$	−15.8729	+	4.25312i	−0.668962	+	0.179248i	−0.0916745	+	0.995789i	$0.529222\pi$
$564$	−1.48386	+	1.48386i	−0.0624820	+	0.0624820i
$565$		0			0
$566$	−3.07011	−	11.4578i	−0.129046	−	0.481607i
$567$	5.39562			0.226595
$568$	0.234633	+	0.875664i	0.00984500	+	0.0367420i
$569$	−6.91493	−	11.9770i	−0.289889	−	0.502102i	0.683894	−	0.729581i	$-0.260285\pi$
$569$	−6.91493	−	11.9770i	−0.289889	−	0.502102i	−0.973783	+	0.227479i	$0.926952\pi$
$570$		0			0
$571$		−	7.17030i		−	0.300068i	−0.988681	−	0.150034i	$-0.952062\pi$
$571$		−	7.17030i		−	0.300068i	0.988681	−	0.150034i	$-0.0479383\pi$
$572$	3.58109	+	6.19207i	0.149733	+	0.258904i
$573$	−1.31220	+	1.31220i	−0.0548181	+	0.0548181i
$574$	1.27130	+	0.340643i	0.0530628	+	0.0142181i
$575$		0			0
$576$	1.78496	+	1.03055i	0.0743735	+	0.0429396i
$577$			1.60982i			0.0670175i	0.999438	+	0.0335088i	$0.0106682\pi$
$577$			1.60982i			0.0670175i	−0.999438	+	0.0335088i	$0.989332\pi$
$578$	−4.75510	+	8.23608i	−0.197786	+	0.342576i
$579$	−18.4613	+	4.94670i	−0.767226	+	0.205578i
$580$		0			0
$581$	−9.39311	+	16.2693i	−0.389692	+	0.674966i
$582$	−16.1954	−	4.33955i	−0.671322	−	0.179880i
$583$	−11.0051	+	6.35380i	−0.455785	+	0.263147i
$584$	8.38511			0.346978
$585$		0			0
$586$	−26.7598			−1.10544
$587$	−2.17897	+	1.25803i	−0.0899355	+	0.0519243i	−0.544293	−	0.838895i	$-0.683202\pi$
$587$	−2.17897	+	1.25803i	−0.0899355	+	0.0519243i	0.454358	+	0.890819i	$0.349869\pi$
$588$	−6.74666	−	1.80776i	−0.278228	−	0.0745509i
$589$	−2.00594	+	3.47438i	−0.0826531	+	0.143159i
$590$		0			0
$591$	−10.2533	+	2.74737i	−0.421765	+	0.113012i
$592$	5.39776	−	9.34919i	0.221847	−	0.384249i
$593$			17.2633i			0.708920i	0.935071	+	0.354460i	$0.115335\pi$
$593$			17.2633i			0.708920i	−0.935071	+	0.354460i	$0.884665\pi$
$594$	8.42567	+	4.86456i	0.345709	+	0.199595i
$595$		0			0
$596$	−5.41700	−	1.45148i	−0.221889	−	0.0594550i
$597$	8.09828	−	8.09828i	0.331441	−	0.331441i
$598$	−9.08886	+	0.00670159i	−0.371671	+	0.000274049i
$599$		−	22.8903i		−	0.935274i	−0.883921	−	0.467637i	$-0.845106\pi$
$599$		−	22.8903i		−	0.935274i	0.883921	−	0.467637i	$-0.154894\pi$
$600$		0			0
$601$	7.63567	+	13.2254i	0.311466	+	0.539474i	0.978680	−	0.205392i	$-0.0658468\pi$
$601$	7.63567	+	13.2254i	0.311466	+	0.539474i	−0.667214	+	0.744866i	$0.732513\pi$
$602$	−4.91540	−	18.3445i	−0.200337	−	0.747667i
$603$	−28.6746			−1.16772
$604$	3.13641	+	11.7052i	0.127619	+	0.476280i
$605$		0			0
$606$	−3.56391	+	3.56391i	−0.144774	+	0.144774i
$607$	4.67819	−	1.25352i	0.189882	−	0.0508787i	−0.162625	−	0.986688i	$-0.551996\pi$
$607$	4.67819	−	1.25352i	0.189882	−	0.0508787i	0.352507	+	0.935809i	$0.385329\pi$
$608$	0.103361	−	0.385747i	0.00419182	−	0.0156441i
$609$	−1.09870	+	4.10040i	−0.0445216	+	0.166157i
$610$		0			0
$611$	−2.01544	+	7.54398i	−0.0815361	+	0.305197i
$612$	−7.50396	−	7.50396i	−0.303330	−	0.303330i
$613$	19.0730	+	33.0354i	0.770352	+	1.33429i	0.937370	+	0.348335i	$0.113253\pi$
$613$	19.0730	+	33.0354i	0.770352	+	1.33429i	−0.167018	+	0.985954i	$0.553414\pi$
$614$	−0.246793	+	0.142486i	−0.00995974	+	0.00575026i
$615$		0			0
$616$	5.28781	+	5.28781i	0.213052	+	0.213052i
$617$	−18.1479	−	10.4777i	−0.730606	−	0.421816i	0.0880377	−	0.996117i	$-0.471940\pi$
$617$	−18.1479	−	10.4777i	−0.730606	−	0.421816i	−0.818644	+	0.574301i	$0.805274\pi$
$618$	4.71079	+	2.71977i	0.189496	+	0.109405i
$619$	28.5318	+	28.5318i	1.14679	+	1.14679i	0.987180	+	0.159612i	$0.0510242\pi$
$619$	28.5318	+	28.5318i	1.14679	+	1.14679i	0.159612	+	0.987180i	$0.448976\pi$
$620$		0			0
$621$	−10.7059	+	6.18105i	−0.429613	+	0.248037i
$622$	−0.512544	−	0.887753i	−0.0205512	−	0.0355956i
$623$	43.5365	+	43.5365i	1.74425	+	1.74425i
$624$	−3.49367	+	0.00257603i	−0.139859	+	0.000103124i
$625$		0			0
$626$	1.42237	−	5.30835i	0.0568492	−	0.212164i
$627$	0.198693	−	0.741534i	0.00793505	−	0.0296140i
$628$	−3.27309	+	0.877022i	−0.130610	+	0.0349970i
$629$	−39.3038	+	39.3038i	−1.56715	+	1.56715i
$630$		0			0
$631$	4.56935	+	17.0530i	0.181903	+	0.678870i	0.995272	+	0.0971231i	$0.0309641\pi$
$631$	4.56935	+	17.0530i	0.181903	+	0.678870i	−0.813370	+	0.581747i	$0.802369\pi$
$632$	3.10557			0.123533
$633$	−4.48081	−	16.7226i	−0.178096	−	0.664665i
$634$	1.22843	+	2.12771i	0.0487872	+	0.0845020i
$635$		0			0
$636$		−	6.20661i		−	0.246108i
$637$	−25.0995	+	6.74523i	−0.994478	+	0.267256i
$638$	1.63044	−	1.63044i	0.0645498	−	0.0645498i
$639$	1.80483	+	0.483603i	0.0713980	+	0.0191310i
$640$		0			0
$641$	−25.9381	−	14.9753i	−1.02449	−	0.591490i	−0.109090	−	0.994032i	$-0.534794\pi$
$641$	−25.9381	−	14.9753i	−1.02449	−	0.591490i	−0.915402	+	0.402542i	$0.868127\pi$
$642$			8.97995i			0.354410i
$643$	−7.61631	+	13.1918i	−0.300358	+	0.520235i	−0.976217	−	0.216796i	$-0.930439\pi$
$643$	−7.61631	+	13.1918i	−0.300358	+	0.520235i	0.675859	+	0.737031i	$0.263773\pi$
$644$	−9.17811	+	2.45927i	−0.361668	+	0.0969087i
$645$		0			0
$646$	−1.02810	+	1.78072i	−0.0404500	+	0.0700615i
$647$	20.4529	+	5.48034i	0.804086	+	0.215454i	0.637377	−	0.770552i	$-0.280019\pi$
$647$	20.4529	+	5.48034i	0.804086	+	0.215454i	0.166709	+	0.986006i	$0.446686\pi$
$648$	1.23965	−	0.715714i	0.0486982	−	0.0281159i
$649$	25.1842			0.988568
$650$		0			0
$651$	36.6919			1.43807
$652$	15.2707	−	8.81652i	0.598045	−	0.345282i
$653$	−5.78458	−	1.54997i	−0.226368	−	0.0606551i	0.143852	−	0.989599i	$-0.454051\pi$
$653$	−5.78458	−	1.54997i	−0.226368	−	0.0606551i	−0.370220	+	0.928944i	$0.620718\pi$
$654$	2.71827	−	4.70818i	0.106293	−	0.184105i
$655$		0			0
$656$	0.337268	−	0.0903706i	0.0131681	−	0.00352838i
$657$	8.64127	−	14.9671i	0.337128	−	0.583923i
$658$			8.16340i			0.318243i
$659$	11.1058	+	6.41196i	0.432622	+	0.249774i	0.700463	−	0.713689i	$-0.252977\pi$
$659$	11.1058	+	6.41196i	0.432622	+	0.249774i	−0.267841	+	0.963463i	$0.586310\pi$
$660$		0			0
$661$	−16.0707	−	4.30613i	−0.625077	−	0.167489i	−0.0676424	−	0.997710i	$-0.521548\pi$
$661$	−16.0707	−	4.30613i	−0.625077	−	0.167489i	−0.557435	+	0.830221i	$0.688214\pi$
$662$	4.75444	−	4.75444i	0.184787	−	0.184787i
$663$	17.3787	+	4.64288i	0.674933	+	0.180315i
$664$			4.98388i			0.193412i
$665$		0			0
$666$	−11.1253	−	19.2696i	−0.431097	−	0.746682i
$667$	0.758290	+	2.82998i	0.0293611	+	0.109577i
$668$	5.15946			0.199625
$669$	−2.22060	−	8.28739i	−0.0858533	−	0.320409i
$670$		0			0
$671$	−2.76368	+	2.76368i	−0.106691	+	0.106691i
$672$	−3.52797	+	0.945318i	−0.136095	+	0.0364664i
$673$	−2.55148	+	9.52225i	−0.0983523	+	0.367056i	−0.997506	−	0.0705765i	$-0.977516\pi$
$673$	−2.55148	+	9.52225i	−0.0983523	+	0.367056i	0.899154	+	0.437632i	$0.144183\pi$
$674$	−1.98931	+	7.42420i	−0.0766253	+	0.285970i
$675$		0			0
$676$	−11.2487	+	6.51660i	−0.432644	+	0.250638i
$677$	−7.43673	−	7.43673i	−0.285817	−	0.285817i	0.549607	−	0.835423i	$-0.314778\pi$
$677$	−7.43673	−	7.43673i	−0.285817	−	0.285817i	−0.835423	+	0.549607i	$0.814778\pi$
$678$	−2.68185	−	4.64511i	−0.102996	−	0.178394i
$679$	−56.4861	+	32.6122i	−2.16774	+	1.25154i
$680$		0			0
$681$	14.9259	+	14.9259i	0.571962	+	0.571962i
$682$	−17.2599	−	9.96500i	−0.660915	−	0.381580i
$683$	−33.2418	−	19.1922i	−1.27196	−	0.734368i	−0.296606	−	0.955000i	$-0.595855\pi$
$683$	−33.2418	−	19.1922i	−1.27196	−	0.734368i	−0.975357	+	0.220632i	$0.929188\pi$
$684$	−0.582026	−	0.582026i	−0.0222543	−	0.0222543i
$685$		0			0
$686$	−0.680114	+	0.392664i	−0.0259669	+	0.0149920i
$687$	−5.43318	−	9.41055i	−0.207289	−	0.359035i
$688$	−3.56267	−	3.56267i	−0.135826	−	0.135826i
$689$	−11.5622	−	19.9923i	−0.440485	−	0.761644i
$690$		0			0
$691$	0.195281	−	0.728798i	0.00742883	−	0.0277248i	−0.962112	−	0.272655i	$-0.912098\pi$
$691$	0.195281	−	0.728798i	0.00742883	−	0.0277248i	0.969541	+	0.244930i	$0.0787650\pi$
$692$	0.293810	−	1.09651i	0.0111690	−	0.0416832i
$693$	14.8879	−	3.98920i	0.565544	−	0.151537i
$694$	25.3009	−	25.3009i	0.960408	−	0.960408i
$695$		0			0
$696$	0.291479	+	1.08781i	0.0110485	+	0.0412335i
$697$	−1.79778			−0.0680959
$698$	5.42298	+	20.2388i	0.205263	+	0.766051i
$699$	−1.29898	−	2.24991i	−0.0491321	−	0.0850993i
$700$		0			0
$701$		−	28.2770i		−	1.06801i	−0.845482	−	0.534003i	$-0.820687\pi$
$701$		−	28.2770i		−	1.06801i	0.845482	−	0.534003i	$-0.179313\pi$
$702$	−8.82960	+	15.3194i	−0.333252	+	0.578193i
$703$	−3.04851	+	3.04851i	−0.114977	+	0.114977i
$704$	1.91630	+	0.513470i	0.0722231	+	0.0193521i
$705$		0			0
$706$	6.33165	+	3.65558i	0.238295	+	0.137579i
$707$			19.6066i			0.737384i
$708$	−6.15021	+	10.6525i	−0.231139	+	0.400345i
$709$	13.9738	−	3.74427i	0.524797	−	0.140619i	0.0133124	−	0.999911i	$-0.495762\pi$
$709$	13.9738	−	3.74427i	0.524797	−	0.140619i	0.511485	+	0.859292i	$0.329096\pi$
$710$		0			0
$711$	3.20044	−	5.54332i	0.120026	−	0.207891i
$712$	15.7776	+	4.22759i	0.591290	+	0.158436i
$713$	21.9309	−	12.6618i	0.821319	−	0.474189i
$714$	18.8056			0.703783
$715$		0			0
$716$	5.43865			0.203252
$717$	2.89179	−	1.66958i	0.107996	−	0.0623515i
$718$	−25.4327	−	6.81466i	−0.949138	−	0.254321i
$719$	−13.9121	+	24.0965i	−0.518835	+	0.898649i	0.480925	+	0.876762i	$0.340301\pi$
$719$	−13.9121	+	24.0965i	−0.518835	+	0.898649i	−0.999760	+	0.0218872i	$0.993033\pi$
$720$		0			0
$721$	20.4394	−	5.47673i	0.761204	−	0.203964i
$722$	9.42026	−	16.3164i	0.350586	−	0.607232i
$723$		−	28.6541i		−	1.06566i
$724$	14.5361	+	8.39244i	0.540231	+	0.311903i
$725$		0			0
$726$	−6.61171	−	1.77160i	−0.245384	−	0.0657503i
$727$	−1.02036	+	1.02036i	−0.0378431	+	0.0378431i	−0.725775	−	0.687932i	$-0.758519\pi$
$727$	−1.02036	+	1.02036i	−0.0378431	+	0.0378431i	0.687932	+	0.725775i	$0.258519\pi$
$728$	−9.60302	+	9.61719i	−0.355912	+	0.356437i
$729$			11.3053i			0.418715i
$730$		0			0
$731$	12.9708	+	22.4661i	0.479743	+	0.830940i
$732$	−0.494071	−	1.84390i	−0.0182614	−	0.0681525i
$733$	6.01412			0.222137			0.111068	−	0.993813i	$-0.464573\pi$
$733$	6.01412			0.222137			0.111068	+	0.993813i	$0.464573\pi$
$734$	−2.28221	−	8.51733i	−0.0842379	−	0.314380i
$735$		0			0
$736$	−1.78247	+	1.78247i	−0.0657028	+	0.0657028i
$737$	−26.6600	+	7.14353i	−0.982035	+	0.263135i
$738$	0.186263	−	0.695142i	0.00685643	−	0.0255885i
$739$	8.51002	−	31.7598i	0.313046	−	1.16830i	−0.612749	−	0.790278i	$-0.709936\pi$
$739$	8.51002	−	31.7598i	0.313046	−	1.16830i	0.925795	−	0.378026i	$-0.123397\pi$
$740$		0			0
$741$	1.34794	+	0.360114i	0.0495177	+	0.0132291i
$742$	−17.0727	−	17.0727i	−0.626757	−	0.626757i
$743$	9.20450	+	15.9427i	0.337680	+	0.584879i	0.983996	−	0.178191i	$-0.0570244\pi$
$743$	9.20450	+	15.9427i	0.337680	+	0.584879i	−0.646316	+	0.763070i	$0.723691\pi$
$744$	8.43002	−	4.86708i	0.309060	−	0.178436i
$745$		0			0
$746$	−18.1536	−	18.1536i	−0.664652	−	0.664652i
$747$	8.89605	+	5.13614i	0.325489	+	0.187921i
$748$	−8.84619	−	5.10735i	−0.323449	−	0.186743i
$749$	24.7014	+	24.7014i	0.902568	+	0.902568i
$750$		0			0
$751$	−35.4015	+	20.4390i	−1.29182	+	0.745831i	−0.978976	−	0.203974i	$-0.934614\pi$
$751$	−35.4015	+	20.4390i	−1.29182	+	0.745831i	−0.312841	+	0.949805i	$0.601281\pi$
$752$	1.08285	+	1.87556i	0.0394876	+	0.0683945i
$753$	17.9635	+	17.9635i	0.654625	+	0.654625i
$754$	2.96536	+	2.96099i	0.107992	+	0.107833i
$755$		0			0
$756$	−4.78435	+	17.8554i	−0.174005	+	0.649396i
$757$	0.768799	−	2.86920i	0.0279425	−	0.104283i	−0.950546	−	0.310583i	$-0.899476\pi$
$757$	0.768799	−	2.86920i	0.0279425	−	0.104283i	0.978489	+	0.206300i	$0.0661424\pi$
$758$	−11.5676	+	3.09953i	−0.420155	+	0.112580i
$759$	−3.42651	+	3.42651i	−0.124374	+	0.124374i
$760$		0			0
$761$	8.00523	+	29.8759i	0.290189	+	1.08300i	0.944963	+	0.327177i	$0.106097\pi$
$761$	8.00523	+	29.8759i	0.290189	+	1.08300i	−0.654774	+	0.755825i	$0.727236\pi$
$762$	−0.433892			−0.0157183
$763$	−5.47370	−	20.4281i	−0.198161	−	0.739548i
$764$	0.957583	+	1.65858i	0.0346441	+	0.0600054i
$765$		0			0
$766$		−	34.3293i		−	1.24037i
$767$	0.0337482	+	45.7701i	0.00121858	+	1.65266i
$768$	−0.685164	+	0.685164i	−0.0247237	+	0.0247237i
$769$	−5.34027	−	1.43092i	−0.192575	−	0.0516003i	0.161242	−	0.986915i	$-0.448450\pi$
$769$	−5.34027	−	1.43092i	−0.192575	−	0.0516003i	−0.353817	+	0.935315i	$0.615117\pi$
$770$		0			0
$771$	−13.9866	−	8.07520i	−0.503717	−	0.290821i
$772$			19.7246i			0.709905i
$773$	6.45097	−	11.1734i	0.232025	−	0.401880i	−0.726379	−	0.687295i	$-0.758798\pi$
$773$	6.45097	−	11.1734i	0.232025	−	0.401880i	0.958404	+	0.285415i	$0.0921314\pi$
$774$	−10.0308	+	2.68773i	−0.360548	+	0.0966086i
$775$		0			0
$776$	−8.65185	+	14.9854i	−0.310583	+	0.537946i
$777$	38.0863	+	10.2052i	1.36634	+	0.366109i
$778$	−28.7950	+	16.6248i	−1.03235	+	0.596029i
$779$	−0.139441			−0.00499598
$780$		0			0
$781$	1.79851			0.0643557
$782$	11.2402	−	6.48955i	0.401950	−	0.232066i
$783$	5.50554	+	1.47520i	0.196752	+	0.0527195i
$784$	−3.60417	+	6.24261i	−0.128720	+	0.222950i
$785$		0			0
$786$	13.8363	−	3.70743i	0.493525	−	0.132240i
$787$	−5.57437	+	9.65508i	−0.198705	+	0.344167i	−0.948109	−	0.317946i	$-0.897007\pi$
$787$	−5.57437	+	9.65508i	−0.198705	+	0.344167i	0.749404	+	0.662113i	$0.230340\pi$
$788$			10.9550i			0.390254i
$789$	−12.7241	−	7.34627i	−0.452990	−	0.261534i
$790$		0			0
$791$	−20.1544	−	5.40037i	−0.716609	−	0.192015i
$792$	2.89136	−	2.89136i	0.102740	−	0.102740i
$793$	−5.02644	−	5.01903i	−0.178494	−	0.178231i
$794$			6.36491i			0.225882i
$795$		0			0
$796$	−5.90974	−	10.2360i	−0.209465	−	0.362804i
$797$	7.31743	+	27.3090i	0.259197	+	0.967336i	0.965707	+	0.259633i	$0.0836016\pi$
$797$	7.31743	+	27.3090i	0.259197	+	0.967336i	−0.706511	+	0.707703i	$0.749732\pi$
$798$	1.45861			0.0516343
$799$	−2.88604	−	10.7708i	−0.102101	−	0.381045i
$800$		0			0
$801$	23.8057	−	23.8057i	0.841133	−	0.841133i
$802$	−12.2984	+	3.29534i	−0.434271	+	0.116362i
$803$	4.30550	−	16.0684i	0.151938	−	0.567040i
$804$	3.48902	−	13.0212i	0.123048	−	0.459223i
$805$		0			0
$806$	18.0873	−	31.3816i	0.637100	−	1.10537i
$807$	11.0488	+	11.0488i	0.388936	+	0.388936i
$808$	2.60077	+	4.50466i	0.0914947	+	0.158473i
$809$	18.5277	−	10.6970i	0.651399	−	0.376086i	−0.137593	−	0.990489i	$-0.543937\pi$
$809$	18.5277	−	10.6970i	0.651399	−	0.376086i	0.788992	+	0.614403i	$0.210603\pi$
$810$		0			0
$811$	−13.3183	−	13.3183i	−0.467667	−	0.467667i	0.433491	−	0.901158i	$-0.357282\pi$
$811$	−13.3183	−	13.3183i	−0.467667	−	0.467667i	−0.901158	+	0.433491i	$0.857282\pi$
$812$	3.79406	+	2.19050i	0.133145	+	0.0768715i
$813$	−13.1568	−	7.59609i	−0.461430	−	0.266407i
$814$	−15.1442	−	15.1442i	−0.530805	−	0.530805i
$815$		0			0
$816$	4.32063	−	2.49452i	0.151252	−	0.0873255i
$817$	1.00605	+	1.74253i	0.0351972	+	0.0609634i
$818$	−14.6615	−	14.6615i	−0.512629	−	0.512629i
$819$	7.26996	+	27.0520i	0.254033	+	0.945275i
$820$		0			0
$821$	−6.97890	+	26.0456i	−0.243565	+	0.908998i	0.730534	+	0.682876i	$0.239271\pi$
$821$	−6.97890	+	26.0456i	−0.243565	+	0.908998i	−0.974099	+	0.226121i	$0.927395\pi$
$822$	2.54249	−	9.48870i	0.0886795	−	0.330957i
$823$	−4.12123	+	1.10428i	−0.143657	+	0.0384928i	−0.329931	−	0.944005i	$-0.607025\pi$
$823$	−4.12123	+	1.10428i	−0.143657	+	0.0384928i	0.186274	+	0.982498i	$0.440359\pi$
$824$	3.96952	−	3.96952i	0.138285	−	0.138285i
$825$		0			0
$826$	12.3845	+	46.2195i	0.430911	+	1.60818i
$827$	−19.9242			−0.692831			−0.346415	−	0.938081i	$-0.612601\pi$
$827$	−19.9242			−0.692831			−0.346415	+	0.938081i	$0.612601\pi$
$828$	1.34472	+	5.01858i	0.0467324	+	0.174408i
$829$	6.80567	+	11.7878i	0.236371	+	0.409406i	0.959670	−	0.281129i	$-0.0907087\pi$
$829$	6.80567	+	11.7878i	0.236371	+	0.409406i	−0.723300	+	0.690534i	$0.757375\pi$
$830$		0			0
$831$		−	20.5285i		−	0.712125i
$832$	−0.930617	+	3.48338i	−0.0322633	+	0.120765i
$833$	26.2438	−	26.2438i	0.909294	−	0.909294i
$834$	5.91955	+	1.58614i	0.204977	+	0.0549235i
$835$		0			0
$836$	−0.686133	−	0.396139i	−0.0237304	−	0.0137008i
$837$		−	49.2655i		−	1.70287i
$838$	6.93846	−	12.0178i	0.239685	−	0.415147i
$839$	−39.2586	+	10.5193i	−1.35536	+	0.363167i	−0.862109	−	0.506722i	$-0.830857\pi$
$839$	−39.2586	+	10.5193i	−1.35536	+	0.363167i	−0.493248	+	0.869889i	$0.664190\pi$
$840$		0			0
$841$	−13.8246	+	23.9449i	−0.476710	+	0.825685i
$842$	10.1412	+	2.71733i	0.349489	+	0.0936454i
$843$	−9.99214	+	5.76897i	−0.344148	+	0.198694i
$844$	−17.8670			−0.615006
$845$		0			0
$846$	4.46373			0.153466
$847$	−23.0602	+	13.3138i	−0.792357	+	0.457468i
$848$	−6.18712	−	1.65783i	−0.212466	−	0.0569302i
$849$	5.74695	−	9.95401i	0.197235	−	0.341621i
$850$		0			0
$851$	26.2860	−	7.04332i	0.901074	−	0.241442i
$852$	−0.439211	+	0.760736i	−0.0150471	+	0.0260624i
$853$		−	16.8623i		−	0.577354i	−0.957426	−	0.288677i	$-0.906785\pi$
$853$		−	16.8623i		−	0.577354i	0.957426	−	0.288677i	$-0.0932155\pi$
$854$	−6.43111	−	3.71300i	−0.220068	−	0.127056i
$855$		0			0
$856$	8.95175	+	2.39861i	0.305964	+	0.0819829i
$857$	13.5795	−	13.5795i	0.463866	−	0.463866i	−0.436055	−	0.899920i	$-0.643625\pi$
$857$	13.5795	−	13.5795i	0.463866	−	0.463866i	0.899920	+	0.436055i	$0.143625\pi$
$858$	−1.78896	+	6.69622i	−0.0610740	+	0.228605i
$859$		−	2.04239i		−	0.0696855i	−0.999393	−	0.0348427i	$-0.988907\pi$
$859$		−	2.04239i		−	0.0696855i	0.999393	−	0.0348427i	$-0.0110930\pi$
$860$		0			0
$861$	0.637650	+	1.10444i	0.0217311	+	0.0376393i
$862$	10.0156	+	37.3789i	0.341134	+	1.27313i
$863$	−8.34696			−0.284134			−0.142067	−	0.989857i	$-0.545375\pi$
$863$	−8.34696			−0.284134			−0.142067	+	0.989857i	$0.545375\pi$
$864$	1.26926	+	4.73695i	0.0431811	+	0.161154i
$865$		0			0
$866$	12.6934	−	12.6934i	0.431338	−	0.431338i
$867$	−8.90110	+	2.38504i	−0.302297	+	0.0810003i
$868$	9.80068	−	36.5766i	0.332657	−	1.24149i
$869$	1.59461	−	5.95118i	0.0540936	−	0.201880i
$870$		0			0
$871$	−13.0184	−	48.4426i	−0.441113	−	1.64142i
$872$	−3.96733	−	3.96733i	−0.134351	−	0.134351i
$873$	17.8323	+	30.8865i	0.603533	+	1.04535i
$874$	0.871821	−	0.503346i	0.0294898	−	0.0170259i
$875$		0			0
$876$	5.74518	+	5.74518i	0.194112	+	0.194112i
$877$	−18.4158	−	10.6324i	−0.621857	−	0.359029i	0.155735	−	0.987799i	$-0.450225\pi$
$877$	−18.4158	−	10.6324i	−0.621857	−	0.359029i	−0.777591	+	0.628770i	$0.783559\pi$
$878$	27.0402	+	15.6117i	0.912562	+	0.526868i
$879$	−18.3348	−	18.3348i	−0.618419	−	0.618419i
$880$		0			0
$881$	8.65763	−	4.99848i	0.291683	−	0.168403i	−0.347018	−	0.937859i	$-0.612806\pi$
$881$	8.65763	−	4.99848i	0.291683	−	0.168403i	0.638701	+	0.769455i	$0.279472\pi$
$882$	7.42856	+	12.8666i	0.250132	+	0.433242i
$883$	0.0156717	+	0.0156717i	0.000527393	+	0.000527393i	0.707370	−	0.706843i	$-0.249881\pi$
$883$	0.0156717	+	0.0156717i	0.000527393	+	0.000527393i	−0.706843	+	0.707370i	$0.749881\pi$
$884$	9.27029	−	16.0840i	0.311793	−	0.540963i
$885$		0			0
$886$	5.23281	−	19.5291i	0.175800	−	0.656094i
$887$	6.43853	−	24.0289i	0.216185	−	0.806812i	−0.769562	−	0.638573i	$-0.779525\pi$
$887$	6.43853	−	24.0289i	0.216185	−	0.806812i	0.985746	−	0.168239i	$-0.0538081\pi$
$888$	10.1041	−	2.70738i	0.339071	−	0.0908538i
$889$	−1.19352	+	1.19352i	−0.0400293	+	0.0400293i
$890$		0			0
$891$	−0.734996	−	2.74304i	−0.0246233	−	0.0918953i
$892$	−8.85450			−0.296471
$893$	−0.223849	−	0.835414i	−0.00749081	−	0.0279561i
$894$	−2.71703	−	4.70604i	−0.0908711	−	0.157393i
$895$		0			0
$896$			3.76940i			0.125927i
$897$	−6.23196	−	6.22277i	−0.208079	−	0.207772i
$898$	15.1032	−	15.1032i	0.504002	−	0.504002i
$899$	−11.2780	−	3.02194i	−0.376144	−	0.100787i
$900$		0			0
$901$	28.5615	+	16.4900i	0.951523	+	0.549362i
$902$		−	0.692707i		−	0.0230646i
$903$	9.20116	−	15.9369i	0.306196	−	0.530346i
$904$	−5.34686	+	1.43269i	−0.177834	+	0.0476505i
$905$		0			0
$906$	−5.87106	+	10.1690i	−0.195053	+	0.337842i
$907$	24.4574	+	6.55335i	0.812096	+	0.217600i	0.640888	−	0.767635i	$-0.278566\pi$
$907$	24.4574	+	6.55335i	0.812096	+	0.217600i	0.171208	+	0.985235i	$0.445233\pi$
$908$	18.8658	−	10.8922i	0.626085	−	0.361470i
$909$	10.7209			0.355589
$910$		0			0
$911$	9.21903			0.305440			0.152720	−	0.988269i	$-0.451197\pi$
$911$	9.21903			0.305440			0.152720	+	0.988269i	$0.451197\pi$
$912$	0.335119	−	0.193481i	0.0110969	−	0.00640680i
$913$	9.55059	+	2.55907i	0.316079	+	0.0846930i
$914$	−5.90744	+	10.2320i	−0.195401	+	0.338444i
$915$		0			0
$916$	−10.8322	+	2.90249i	−0.357907	+	0.0959010i
$917$	27.8618	−	48.2580i	0.920077	−	1.59362i
$918$		−	25.2500i		−	0.833374i
$919$	−12.7906	−	7.38468i	−0.421924	−	0.243598i	0.273976	−	0.961737i	$-0.411661\pi$
$919$	−12.7906	−	7.38468i	−0.421924	−	0.243598i	−0.695900	+	0.718138i	$0.744994\pi$
$920$		0			0
$921$	−0.266720	−	0.0714674i	−0.00878872	−	0.00235493i
$922$	−5.07750	+	5.07750i	−0.167218	+	0.167218i
$923$	0.00241009	+	3.26863i	7.93292e−5	+	0.107588i
$924$			7.24604i			0.238377i
$925$		0			0
$926$	14.8820	+	25.7764i	0.489053	+	0.847064i
$927$	−2.99467	−	11.1762i	−0.0983577	−	0.367076i
$928$	1.16225			0.0381529
$929$	−0.864359	−	3.22583i	−0.0283587	−	0.105836i	0.950296	−	0.311348i	$-0.100781\pi$
$929$	−0.864359	−	3.22583i	−0.0283587	−	0.105836i	−0.978655	+	0.205512i	$0.934114\pi$
$930$		0			0
$931$	2.03554	−	2.03554i	0.0667120	−	0.0667120i
$932$	−2.58981	+	0.693937i	−0.0848320	+	0.0227307i
$933$	0.257080	−	0.959434i	0.00841641	−	0.0314105i
$934$	6.21340	−	23.1887i	0.203309	−	0.758758i
$935$		0			0
$936$	5.25867	+	5.25092i	0.171885	+	0.171632i
$937$	27.1529	+	27.1529i	0.887045	+	0.887045i	0.994238	−	0.107193i	$-0.0341863\pi$
$937$	27.1529	+	27.1529i	0.887045	+	0.887045i	−0.107193	+	0.994238i	$0.534186\pi$
$938$	−26.2204	−	45.4151i	−0.856127	−	1.48286i
$939$	4.61165	−	2.66253i	0.150495	−	0.0868885i
$940$		0			0
$941$	1.14387	+	1.14387i	0.0372890	+	0.0372890i	0.725505	−	0.688216i	$-0.241606\pi$
$941$	1.14387	+	1.14387i	0.0372890	+	0.0372890i	−0.688216	+	0.725505i	$0.741606\pi$
$942$	−2.84351	−	1.64170i	−0.0926465	−	0.0534895i
$943$	0.762254	+	0.440087i	0.0248224	+	0.0143312i
$944$	8.97625	+	8.97625i	0.292152	+	0.292152i
$945$		0			0
$946$	−8.65647	+	4.99781i	−0.281446	+	0.162493i
$947$	−23.0002	−	39.8374i	−0.747405	−	1.29454i	−0.949063	−	0.315087i	$-0.897966\pi$
$947$	−23.0002	−	39.8374i	−0.747405	−	1.29454i	0.201658	−	0.979456i	$-0.435367\pi$
$948$	2.12782	+	2.12782i	0.0691085	+	0.0691085i
$949$	29.2085	+	7.80333i	0.948149	+	0.253307i
$950$		0			0
$951$	−0.616151	+	2.29951i	−0.0199801	+	0.0745666i
$952$	5.02313	−	18.7466i	0.162801	−	0.607580i
$953$	−50.7459	+	13.5973i	−1.64382	+	0.440460i	−0.957873	−	0.287191i	$-0.907279\pi$
$953$	−50.7459	+	13.5973i	−1.64382	+	0.440460i	−0.685947	+	0.727651i	$0.740612\pi$
$954$	−9.33530	+	9.33530i	−0.302242	+	0.302242i
$955$		0			0
$956$	−0.891913	−	3.32867i	−0.0288465	−	0.107657i
$957$	2.23424			0.0722228
$958$	8.07862	+	30.1498i	0.261008	+	0.974096i
$959$	−19.1071	−	33.0945i	−0.617001	−	1.06868i
$960$		0			0
$961$			69.9199i			2.25548i
$962$	27.5030	−	27.5436i	0.886732	−	0.888040i
$963$	13.5067	−	13.5067i	0.435246	−	0.435246i
$964$	−28.5641	−	7.65372i	−0.919987	−	0.246510i
$965$		0			0
$966$	−7.97352	−	4.60351i	−0.256544	−	0.148116i
$967$		−	27.9143i		−	0.897662i	−0.893617	−	0.448831i	$-0.851840\pi$
$967$		−	27.9143i		−	0.897662i	0.893617	−	0.448831i	$-0.148160\pi$
$968$	−3.53208	+	6.11774i	−0.113525	+	0.196632i
$969$	−1.92450	+	0.515669i	−0.0618240	+	0.0165657i
$970$		0			0
$971$	22.1987	−	38.4493i	0.712390	−	1.23390i	−0.251568	−	0.967840i	$-0.580946\pi$
$971$	22.1987	−	38.4493i	0.712390	−	1.23390i	0.963958	−	0.266056i	$-0.0857205\pi$
$972$	15.5506	+	4.16677i	0.498785	+	0.133649i
$973$	20.6461	−	11.9200i	0.661883	−	0.382138i
$974$	−24.7179			−0.792014
$975$		0			0
$976$	−1.97008			−0.0630607
$977$	1.14585	−	0.661557i	0.0366590	−	0.0211651i	−0.481559	−	0.876414i	$-0.659929\pi$
$977$	1.14585	−	0.661557i	0.0366590	−	0.0211651i	0.518217	+	0.855249i	$0.326596\pi$
$978$	16.5037	+	4.42215i	0.527729	+	0.141405i
$979$	16.2026	−	28.0638i	0.517839	−	0.896923i
$980$		0			0
$981$	−11.1701	+	2.99301i	−0.356633	+	0.0955594i
$982$	−2.03780	+	3.52957i	−0.0650287	+	0.112633i
$983$			55.4069i			1.76721i	0.468237	+	0.883603i	$0.344889\pi$
$983$			55.4069i			1.76721i	−0.468237	+	0.883603i	$0.655111\pi$
$984$	0.293003	+	0.169165i	0.00934058	+	0.00539279i
$985$		0			0
$986$	−5.78032	−	1.54883i	−0.184083	−	0.0493248i
$987$	−5.59327	+	5.59327i	−0.178036	+	0.178036i
$988$	0.719027	−	1.24751i	0.0228753	−	0.0396887i
$989$		−	12.7007i		−	0.403860i
$990$		0			0
$991$	10.3910	+	17.9977i	0.330081	+	0.571716i	0.982527	−	0.186118i	$-0.0595907\pi$
$991$	10.3910	+	17.9977i	0.330081	+	0.571716i	−0.652447	+	0.757835i	$0.726257\pi$
$992$	−2.60007	−	9.70358i	−0.0825522	−	0.308089i
$993$	6.51515			0.206752
$994$	0.884426	+	3.30072i	0.0280523	+	0.104693i
$995$		0			0
$996$	−3.41478	+	3.41478i	−0.108201	+	0.108201i
$997$	19.6648	−	5.26916i	0.622790	−	0.166876i	0.0663940	−	0.997793i	$-0.478851\pi$
$997$	19.6648	−	5.26916i	0.622790	−	0.166876i	0.556396	+	0.830917i	$0.312184\pi$
$998$	−5.32692	+	19.8803i	−0.168621	+	0.629301i
$999$	13.7023	−	51.1378i	0.433522	−	1.61793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.t.g.557.3		16
5.2	odd	4		130.2.s.b.63.3	yes	16
5.3	odd	4		650.2.w.g.193.2		16
5.4	even	2		130.2.p.b.37.2	✓	16
13.6	odd	12		650.2.w.g.357.2		16
65.19	odd	12		130.2.s.b.97.3	yes	16
65.32	even	12		130.2.p.b.123.2	yes	16
65.58	even	12	inner	650.2.t.g.643.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.b.37.2	✓	16	5.4	even	2
130.2.p.b.123.2	yes	16	65.32	even	12
130.2.s.b.63.3	yes	16	5.2	odd	4
130.2.s.b.97.3	yes	16	65.19	odd	12
650.2.t.g.557.3		16	1.1	even	1	trivial
650.2.t.g.643.3		16	65.58	even	12	inner
650.2.w.g.193.2		16	5.3	odd	4
650.2.w.g.357.2		16	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.935952 + 0.250788i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.935952 - 0.250788i) q^{6} +(1.88470 - 3.26439i) q^{7} -1.00000i q^{8} +(-1.78496 - 1.03055i) q^{9} +(-1.91630 - 0.513470i) q^{11} +(0.685164 - 0.685164i) q^{12} +(0.930617 - 3.48338i) q^{13} -3.76940i q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.33261 + 4.97337i) q^{17} -2.06110 q^{18} +(0.103361 + 0.385747i) q^{19} +(2.58266 - 2.58266i) q^{21} +(-1.91630 + 0.513470i) q^{22} +(0.652430 - 2.43490i) q^{23} +(0.250788 - 0.935952i) q^{24} +(-0.935753 - 3.48201i) q^{26} +(-3.46769 - 3.46769i) q^{27} +(-1.88470 - 3.26439i) q^{28} +(-1.00654 + 0.581127i) q^{29} +(7.10352 + 7.10352i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.66479 - 0.961167i) q^{33} +(3.64076 + 3.64076i) q^{34} +(-1.78496 + 1.03055i) q^{36} +(5.39776 + 9.34919i) q^{37} +(0.282386 + 0.282386i) q^{38} +(1.74460 - 3.02689i) q^{39} +(-0.0903706 + 0.337268i) q^{41} +(0.945318 - 3.52797i) q^{42} +(4.86670 - 1.30403i) q^{43} +(-1.40283 + 1.40283i) q^{44} +(-0.652430 - 2.43490i) q^{46} -2.16571 q^{47} +(-0.250788 - 0.935952i) q^{48} +(-3.60417 - 6.24261i) q^{49} +4.98903i q^{51} +(-2.55139 - 2.54763i) q^{52} +(4.52928 - 4.52928i) q^{53} +(-4.73695 - 1.26926i) q^{54} +(-3.26439 - 1.88470i) q^{56} +0.386962i q^{57} +(-0.581127 + 1.00654i) q^{58} +(-12.2618 + 3.28554i) q^{59} +(0.985039 - 1.70614i) q^{61} +(9.70358 + 2.60007i) q^{62} +(-6.72824 + 3.88455i) q^{63} -1.00000 q^{64} -1.92233 q^{66} +(12.0484 - 6.95614i) q^{67} +(4.97337 + 1.33261i) q^{68} +(1.22129 - 2.11533i) q^{69} +(-0.875664 + 0.234633i) q^{71} +(-1.03055 + 1.78496i) q^{72} +8.38511i q^{73} +(9.34919 + 5.39776i) q^{74} +(0.385747 + 0.103361i) q^{76} +(-5.28781 + 5.28781i) q^{77} +(-0.00257603 - 3.49367i) q^{78} +3.10557i q^{79} +(0.715714 + 1.23965i) q^{81} +(0.0903706 + 0.337268i) q^{82} -4.98388 q^{83} +(-0.945318 - 3.52797i) q^{84} +(3.56267 - 3.56267i) q^{86} +(-1.08781 + 0.291479i) q^{87} +(-0.513470 + 1.91630i) q^{88} +(-4.22759 + 15.7776i) q^{89} +(-9.61719 - 9.60302i) q^{91} +(-1.78247 - 1.78247i) q^{92} +(4.86708 + 8.43002i) q^{93} +(-1.87556 + 1.08285i) q^{94} +(-0.685164 - 0.685164i) q^{96} +(-14.9854 - 8.65185i) q^{97} +(-6.24261 - 3.60417i) q^{98} +(2.89136 + 2.89136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 6 * q^33 - 14 * q^34 + 20 * q^37 - 6 * q^38 - 6 * q^39 - 44 * q^41 - 6 * q^42 + 6 * q^44 - 6 * q^46 - 52 * q^47 - 2 * q^49 - 10 * q^52 + 24 * q^53 + 6 * q^54 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Introduction

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