LMFDB - Embedded newform 605.2.g.n.366.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.n.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04238 - 1.48388i) q^{2} +(-0.762262 - 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-5.03801 - 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +O(q^{10})$	\(q+(2.04238 - 1.48388i) q^{2} +(-0.762262 - 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-5.03801 - 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} -2.52452 q^{10} -10.7876 q^{12} +(1.04238 - 0.757336i) q^{13} +(1.63319 + 5.02644i) q^{14} +(-0.762262 + 2.34600i) q^{15} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(-2.40649 + 7.40641i) q^{18} +(-0.664789 - 2.04601i) q^{19} +(-3.53801 + 2.57052i) q^{20} +5.16413 q^{21} +8.77882 q^{23} +(-11.9563 + 8.68677i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.00515 - 3.09354i) q^{26} +(0.169161 + 0.122903i) q^{27} +(7.40686 + 5.38140i) q^{28} +(0.189313 - 0.582646i) q^{29} +(1.92435 + 5.92254i) q^{30} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(1.69369 - 1.23053i) q^{35} +(4.16875 + 12.8301i) q^{36} +(-0.578100 + 1.77921i) q^{37} +(-4.39378 - 3.19227i) q^{38} +(-2.57128 - 1.86814i) q^{39} +(-1.85140 + 5.69802i) q^{40} +(1.57810 + 4.85689i) q^{41} +(10.5471 - 7.66294i) q^{42} -5.17287 q^{43} +3.08477 q^{45} +(17.9297 - 13.0267i) q^{46} +(-2.25789 - 6.94907i) q^{47} +(-4.86218 + 14.9643i) q^{48} +(2.11737 + 1.53836i) q^{49} +(2.04238 + 1.48388i) q^{50} +(-2.28012 + 7.01749i) q^{51} +(-1.74122 - 5.35892i) q^{52} +(2.38030 - 1.72939i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(-4.29320 + 3.11919i) q^{57} +(-0.477925 - 1.47090i) q^{58} +(-2.00682 + 6.17636i) q^{59} +(8.72732 + 6.34077i) q^{60} +(-0.406490 - 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(-1.99563 - 6.14191i) q^{63} +(1.90523 - 1.38423i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(-6.69176 - 20.5951i) q^{69} +(1.63319 - 5.02644i) q^{70} +(9.14526 + 6.64442i) q^{71} +(14.9519 + 10.8632i) q^{72} +(3.43539 - 10.5730i) q^{73} +(1.45943 + 4.49166i) q^{74} +(1.99563 - 1.44991i) q^{75} -9.40812 q^{76} -8.02363 q^{78} +(4.33558 - 3.14998i) q^{79} +(1.97110 + 6.06643i) q^{80} +(-2.70035 + 8.31082i) q^{81} +(10.4301 + 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(6.97880 - 21.4785i) q^{84} +(0.924349 + 2.84485i) q^{85} +(-10.5650 + 7.67591i) q^{86} -1.51119 q^{87} -4.32336 q^{89} +(6.30027 - 4.57742i) q^{90} +(0.833541 + 2.56538i) q^{91} +(11.8637 - 36.5127i) q^{92} +(-7.27408 - 5.28493i) q^{93} +(-14.9230 - 10.8422i) q^{94} +(-0.664789 + 2.04601i) q^{95} +(3.14089 + 9.66666i) q^{96} +(0.284493 - 0.206696i) q^{97} +6.60723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.457035	−	0.889449i	$-0.348911\pi$
$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.987148	−	0.159812i	$-0.0510887\pi$
$3$	−0.762262	−	2.34600i	−0.440092	−	1.35446i	−0.887777	−	0.460273i	$-0.847751\pi$
$3$	−0.762262	−	2.34600i	−0.440092	−	1.35446i	0.447685	−	0.894191i	$-0.352249\pi$
$4$	1.35140	−	4.15918i	0.675700	−	2.07959i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−5.03801	−	3.66033i	−2.05676	−	1.49432i
$7$	−0.646930	+	1.99105i	−0.244517	+	0.752545i	0.751199	+	0.660076i	$0.229476\pi$
$7$	−0.646930	+	1.99105i	−0.244517	+	0.752545i	−0.995716	+	0.0924689i	$0.970524\pi$
$8$	−1.85140	−	5.69802i	−0.654569	−	2.01456i
$9$	−2.49563	+	1.81318i	−0.831876	+	0.604393i
$10$	−2.52452			−0.798325
$11$		0			0
$11$		0			0
$12$	−10.7876			−3.11410
$13$	1.04238	−	0.757336i	0.289105	−	0.210047i	−0.433774	−	0.901022i	$-0.642818\pi$
$13$	1.04238	−	0.757336i	0.289105	−	0.210047i	0.722879	+	0.690975i	$0.242818\pi$
$14$	1.63319	+	5.02644i	0.436489	+	1.34337i
$15$	−0.762262	+	2.34600i	−0.196815	+	0.605735i
$16$	−5.16042	−	3.74926i	−1.29010	−	0.937316i
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	0.254285	−	0.967129i	$-0.418160\pi$
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	−0.841216	+	0.540699i	$0.818160\pi$
$18$	−2.40649	+	7.40641i	−0.567215	+	1.74571i
$19$	−0.664789	−	2.04601i	−0.152513	−	0.469387i	0.845387	−	0.534154i	$-0.179370\pi$
$19$	−0.664789	−	2.04601i	−0.152513	−	0.469387i	−0.997900	+	0.0647668i	$0.979370\pi$
$20$	−3.53801	+	2.57052i	−0.791123	+	0.574785i
$21$	5.16413			1.12690
$22$		0			0
$23$	8.77882			1.83051			0.915255	−	0.402874i	$-0.131989\pi$
$23$	8.77882			1.83051			0.915255	+	0.402874i	$0.131989\pi$
$24$	−11.9563	+	8.68677i	−2.44057	+	1.77318i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.00515	−	3.09354i	0.197126	−	0.606693i
$27$	0.169161	+	0.122903i	0.0325550	+	0.0236526i
$28$	7.40686	+	5.38140i	1.39977	+	1.01699i
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	−0.931939	−	0.362614i	$-0.881884\pi$
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	0.967094	+	0.254419i	$0.0818844\pi$
$30$	1.92435	+	5.92254i	0.351336	+	1.08130i
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	−0.290587	−	0.956848i	$-0.593851\pi$
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	0.820221	+	0.572047i	$0.193851\pi$
$32$	−4.12048			−0.728405
$33$		0			0
$34$	−7.55150			−1.29507
$35$	1.69369	−	1.23053i	0.286285	−	0.207998i
$36$	4.16875	+	12.8301i	0.694792	+	2.13835i
$37$	−0.578100	+	1.77921i	−0.0950391	+	0.292500i	−0.987264	−	0.159091i	$-0.949144\pi$
$37$	−0.578100	+	1.77921i	−0.0950391	+	0.292500i	0.892225	+	0.451592i	$0.149144\pi$
$38$	−4.39378	−	3.19227i	−0.712766	−	0.517855i
$39$	−2.57128	−	1.86814i	−0.411734	−	0.299142i
$40$	−1.85140	+	5.69802i	−0.292732	+	0.900937i
$41$	1.57810	+	4.85689i	0.246458	+	0.758519i	0.995393	+	0.0958763i	$0.0305653\pi$
$41$	1.57810	+	4.85689i	0.246458	+	0.758519i	−0.748935	+	0.662643i	$0.769435\pi$
$42$	10.5471	−	7.66294i	1.62746	−	1.18242i
$43$	−5.17287			−0.788856			−0.394428	−	0.918927i	$-0.629057\pi$
$43$	−5.17287			−0.788856			−0.394428	+	0.918927i	$0.629057\pi$
$44$		0			0
$45$	3.08477			0.459850
$46$	17.9297	−	13.0267i	2.64359	−	1.92068i
$47$	−2.25789	−	6.94907i	−0.329347	−	1.01363i	−0.969440	−	0.245329i	$-0.921104\pi$
$47$	−2.25789	−	6.94907i	−0.329347	−	1.01363i	0.640093	−	0.768298i	$-0.278896\pi$
$48$	−4.86218	+	14.9643i	−0.701796	+	2.15991i
$49$	2.11737	+	1.53836i	0.302482	+	0.219766i
$50$	2.04238	+	1.48388i	0.288837	+	0.209852i
$51$	−2.28012	+	7.01749i	−0.319281	+	0.982645i
$52$	−1.74122	−	5.35892i	−0.241464	−	0.743149i
$53$	2.38030	−	1.72939i	0.326959	−	0.237549i	−0.412180	−	0.911102i	$-0.635233\pi$
$53$	2.38030	−	1.72939i	0.326959	−	0.237549i	0.739139	+	0.673553i	$0.235233\pi$
$54$	0.527864			0.0718332
$55$		0			0
$56$	12.5428			1.67610
$57$	−4.29320	+	3.11919i	−0.568648	+	0.413147i
$58$	−0.477925	−	1.47090i	−0.0627547	−	0.193139i
$59$	−2.00682	+	6.17636i	−0.261266	+	0.804094i	0.731264	+	0.682094i	$0.238931\pi$
$59$	−2.00682	+	6.17636i	−0.261266	+	0.804094i	−0.992530	+	0.121999i	$0.961069\pi$
$60$	8.72732	+	6.34077i	1.12669	+	0.818590i
$61$	−0.406490	−	0.295332i	−0.0520457	−	0.0378134i	0.561458	−	0.827505i	$-0.310241\pi$
$61$	−0.406490	−	0.295332i	−0.0520457	−	0.0378134i	−0.613504	+	0.789692i	$0.710241\pi$
$62$	2.84355	−	8.75154i	0.361131	−	1.11145i
$63$	−1.99563	−	6.14191i	−0.251425	−	0.773808i
$64$	1.90523	−	1.38423i	0.238154	−	0.173029i
$65$	−1.28846			−0.159813
$66$		0			0
$67$	−7.80964			−0.954099			−0.477050	−	0.878876i	$-0.658294\pi$
$67$	−7.80964			−0.954099			−0.477050	+	0.878876i	$0.658294\pi$
$68$	−10.5831	+	7.68907i	−1.28339	+	0.932437i
$69$	−6.69176	−	20.5951i	−0.805594	−	2.47936i
$70$	1.63319	−	5.02644i	0.195204	−	0.600775i
$71$	9.14526	+	6.64442i	1.08534	+	0.788548i	0.978607	−	0.205740i	$-0.0659600\pi$
$71$	9.14526	+	6.64442i	1.08534	+	0.788548i	0.106736	+	0.994287i	$0.465960\pi$
$72$	14.9519	+	10.8632i	1.76210	+	1.28024i
$73$	3.43539	−	10.5730i	0.402082	−	1.23748i	−0.521226	−	0.853419i	$-0.674525\pi$
$73$	3.43539	−	10.5730i	0.402082	−	1.23748i	0.923308	−	0.384061i	$-0.125475\pi$
$74$	1.45943	+	4.49166i	0.169655	+	0.522145i
$75$	1.99563	−	1.44991i	0.230435	−	0.167421i
$76$	−9.40812			−1.07919
$77$		0			0
$78$	−8.02363			−0.908498
$79$	4.33558	−	3.14998i	0.487791	−	0.354401i	−0.316543	−	0.948578i	$-0.602522\pi$
$79$	4.33558	−	3.14998i	0.487791	−	0.354401i	0.804334	+	0.594177i	$0.202522\pi$
$80$	1.97110	+	6.06643i	0.220376	+	0.678248i
$81$	−2.70035	+	8.31082i	−0.300039	+	0.923425i
$82$	10.4301	+	7.57793i	1.15181	+	0.836842i
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.953864	−	0.300239i	$-0.0970664\pi$
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.00921619	+	0.999958i	$0.497066\pi$
$84$	6.97880	−	21.4785i	0.761450	−	2.34350i
$85$	0.924349	+	2.84485i	0.100260	+	0.308568i
$86$	−10.5650	+	7.67591i	−1.13925	+	0.827715i
$87$	−1.51119			−0.162017
$88$		0			0
$89$	−4.32336			−0.458275			−0.229137	−	0.973394i	$-0.573591\pi$
$89$	−4.32336			−0.458275			−0.229137	+	0.973394i	$0.573591\pi$
$90$	6.30027	−	4.57742i	0.664107	−	0.482502i
$91$	0.833541	+	2.56538i	0.0873788	+	0.268924i
$92$	11.8637	−	36.5127i	1.23688	−	3.80671i
$93$	−7.27408	−	5.28493i	−0.754287	−	0.548021i
$94$	−14.9230	−	10.8422i	−1.53920	−	1.11829i
$95$	−0.664789	+	2.04601i	−0.0682059	+	0.209916i
$96$	3.14089	+	9.66666i	0.320566	+	0.986599i
$97$	0.284493	−	0.206696i	0.0288859	−	0.0209868i	−0.573249	−	0.819381i	$-0.694317\pi$
$97$	0.284493	−	0.206696i	0.0288859	−	0.0209868i	0.602135	+	0.798395i	$0.294317\pi$
$98$	6.60723			0.667431
$99$		0			0
$100$	4.37322			0.437322
$101$	−12.7011	+	9.22791i	−1.26381	+	0.918211i	−0.998938	−	0.0460722i	$-0.985330\pi$
$101$	−12.7011	+	9.22791i	−1.26381	+	0.918211i	−0.264872	+	0.964284i	$0.585330\pi$
$102$	5.75622	+	17.7158i	0.569951	+	1.75413i
$103$	2.06420	−	6.35297i	0.203392	−	0.625977i	−0.796383	−	0.604792i	$-0.793256\pi$
$103$	2.06420	−	6.35297i	0.203392	−	0.625977i	0.999776	−	0.0211846i	$-0.00674378\pi$
$104$	−6.24518	−	4.53739i	−0.612391	−	0.444928i
$105$	−4.17787	−	3.03540i	−0.407718	−	0.296225i
$106$	2.29528	−	7.06414i	0.222937	−	0.686130i
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	−0.857379	−	0.514685i	$-0.827909\pi$
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	0.391110	−	0.920344i	$-0.372091\pi$
$108$	0.739779	−	0.537481i	0.0711852	−	0.0517191i
$109$	−11.5070			−1.10217			−0.551087	−	0.834448i	$-0.685787\pi$
$109$	−11.5070			−1.10217			−0.551087	+	0.834448i	$0.685787\pi$
$110$		0			0
$111$	4.61469			0.438007
$112$	10.8034	−	7.84912i	1.02082	−	0.741672i
$113$	2.79606	+	8.60538i	0.263031	+	0.809526i	0.992140	+	0.125129i	$0.0399345\pi$
$113$	2.79606	+	8.60538i	0.263031	+	0.809526i	−0.729110	+	0.684397i	$0.760066\pi$
$114$	−4.13986	+	12.7412i	−0.387733	+	1.19332i
$115$	−7.10222	−	5.16006i	−0.662285	−	0.481178i
$116$	−2.16749	−	1.57477i	−0.201246	−	0.146214i
$117$	−1.22821	+	3.78006i	−0.113548	+	0.349466i
$118$	5.06627	+	15.5924i	0.466388	+	1.43539i
$119$	5.06625	−	3.68084i	0.464422	−	0.337422i
$120$	14.7788			1.34912
$121$		0			0
$122$	−1.26845			−0.114840
$123$	10.1914	−	7.40445i	0.918923	−	0.667637i
$124$	−4.92586	−	15.1602i	−0.442356	−	1.36143i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−13.1897	−	9.58287i	−1.17503	−	0.853710i
$127$	15.2371	+	11.0704i	1.35207	+	0.982339i	0.998905	+	0.0467796i	$0.0148959\pi$
$127$	15.2371	+	11.0704i	1.35207	+	0.982339i	0.353169	+	0.935560i	$0.385104\pi$
$128$	4.38378	−	13.4919i	0.387475	−	1.19252i
$129$	3.94308	+	12.1356i	0.347169	+	1.06848i
$130$	−2.63152	+	1.91191i	−0.230800	+	0.167686i
$131$	20.0997			1.75612			0.878058	−	0.478555i	$-0.158839\pi$
$131$	20.0997			1.75612			0.878058	+	0.478555i	$0.158839\pi$
$132$		0			0
$133$	4.50377			0.390527
$134$	−15.9503	+	11.5886i	−1.37789	+	1.00110i
$135$	−0.0646137	−	0.198861i	−0.00556107	−	0.0171152i
$136$	−5.53801	+	17.0442i	−0.474881	+	1.46153i
$137$	14.5390	+	10.5632i	1.24215	+	0.902478i	0.997740	−	0.0671930i	$-0.0214043\pi$
$137$	14.5390	+	10.5632i	1.24215	+	0.902478i	0.244414	+	0.969671i	$0.421404\pi$
$138$	−44.2278	−	32.1334i	−3.76492	−	2.73537i
$139$	−5.21098	+	16.0377i	−0.441989	+	1.36030i	0.443762	+	0.896145i	$0.353643\pi$
$139$	−5.21098	+	16.0377i	−0.441989	+	1.36030i	−0.885752	+	0.464159i	$0.846357\pi$
$140$	−2.82917	−	8.70729i	−0.239108	−	0.735900i
$141$	−14.5814	+	10.5940i	−1.22798	+	0.892178i
$142$	28.5376			2.39482
$143$		0			0
$144$	19.6766			1.63971
$145$	−0.495628	+	0.360095i	−0.0411597	+	0.0299042i
$146$	−8.67272	−	26.6919i	−0.717759	−	2.20904i
$147$	1.99500	−	6.13999i	0.164545	−	0.506418i
$148$	6.61881	+	4.80885i	0.544063	+	0.395285i
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	0.662428	−	0.749126i	$-0.269526\pi$
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	−0.507759	+	0.861499i	$0.669526\pi$
$150$	1.92435	−	5.92254i	0.157122	−	0.483573i
$151$	1.21718	+	3.74609i	0.0990525	+	0.304852i	0.988289	−	0.152596i	$-0.0487634\pi$
$151$	1.21718	+	3.74609i	0.0990525	+	0.304852i	−0.889236	+	0.457448i	$0.848763\pi$
$152$	−10.4274	+	7.57597i	−0.845776	+	0.614492i
$153$	9.22732			0.745985
$154$		0			0
$155$	−3.64501			−0.292774
$156$	−11.2448	+	8.16981i	−0.900302	+	0.654108i
$157$	−1.50834	−	4.64218i	−0.120378	−	0.370486i	0.872652	−	0.488342i	$-0.162398\pi$
$157$	−1.50834	−	4.64218i	−0.120378	−	0.370486i	−0.993031	+	0.117856i	$0.962398\pi$
$158$	4.18073	−	12.8669i	0.332601	−	1.02364i
$159$	−5.87155	−	4.26593i	−0.465644	−	0.338310i
$160$	3.33354	+	2.42196i	0.263540	+	0.191473i
$161$	−5.67928	+	17.4790i	−0.447590	+	1.37754i
$162$	6.81710	+	20.9809i	0.535602	+	1.64841i
$163$	5.69202	−	4.13549i	0.445833	−	0.323917i	−0.342115	−	0.939658i	$-0.611143\pi$
$163$	5.69202	−	4.13549i	0.445833	−	0.323917i	0.787948	+	0.615741i	$0.211143\pi$
$164$	22.3333			1.74394
$165$		0			0
$166$	27.3794			2.12505
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	−0.199308	−	0.979937i	$-0.563869\pi$
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	0.870386	+	0.492370i	$0.163869\pi$
$168$	−9.56086	−	29.4253i	−0.737637	−	2.27021i
$169$	−3.50422	+	10.7849i	−0.269555	+	0.829605i
$170$	6.10929	+	4.43866i	0.468561	+	0.340430i
$171$	5.36885	+	3.90070i	0.410566	+	0.298294i
$172$	−6.99062	+	21.5149i	−0.533030	+	1.64050i
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	−0.999936	−	0.0113267i	$-0.996395\pi$
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	0.802307	−	0.596911i	$-0.203605\pi$
$174$	−3.08644	+	2.24243i	−0.233982	+	0.169998i
$175$	−2.09351			−0.158254
$176$		0			0
$177$	16.0195			1.20410
$178$	−8.82995	+	6.41533i	−0.661833	+	0.480850i
$179$	6.50062	+	20.0069i	0.485879	+	1.49538i	0.830703	+	0.556716i	$0.187939\pi$
$179$	6.50062	+	20.0069i	0.485879	+	1.49538i	−0.344824	+	0.938667i	$0.612061\pi$
$180$	4.16875	−	12.8301i	0.310720	−	0.956299i
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	0.638960	−	0.769240i	$-0.279365\pi$
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	−0.534141	+	0.845395i	$0.679365\pi$
$182$	5.50911	+	4.00261i	0.408363	+	0.296693i
$183$	−0.382998	+	1.17875i	−0.0283120	+	0.0871355i
$184$	−16.2531	−	50.0219i	−1.19820	−	3.68767i
$185$	1.51349	−	1.09961i	0.111274	−	0.0808451i
$186$	−22.6986			−1.66435
$187$		0			0
$188$	−31.9538			−2.33047
$189$	−0.354140	+	0.257298i	−0.0257599	+	0.0187157i
$190$	1.67828	+	5.16520i	0.121755	+	0.374723i
$191$	0.00771200	−	0.0237351i	0.000558021	−	0.00171741i	−0.950777	−	0.309876i	$-0.899713\pi$
$191$	0.00771200	−	0.0237351i	0.000558021	−	0.00171741i	0.951335	+	0.308158i	$0.0997126\pi$
$192$	−4.69969	−	3.41452i	−0.339171	−	0.246422i
$193$	1.17894	+	0.856548i	0.0848618	+	0.0616557i	0.629407	−	0.777076i	$-0.283298\pi$
$193$	1.17894	+	0.856548i	0.0848618	+	0.0616557i	−0.544545	+	0.838731i	$0.683298\pi$
$194$	0.274331	−	0.844306i	0.0196959	−	0.0606176i
$195$	0.982141	+	3.02272i	0.0703326	+	0.216461i
$196$	9.25974	−	6.72759i	0.661410	−	0.480542i
$197$	−22.7027			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$197$	−22.7027			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$198$		0			0
$199$	−6.62834			−0.469870			−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834			−0.469870			−0.234935	+	0.972011i	$0.575488\pi$
$200$	4.84703	−	3.52157i	0.342737	−	0.249013i
$201$	5.95299	+	18.3214i	0.419892	+	1.29229i
$202$	−12.2475	+	37.6939i	−0.861729	+	2.65213i
$203$	1.03760	+	0.753862i	0.0728254	+	0.0529107i
$204$	26.1057	+	18.9669i	1.82776	+	1.32795i
$205$	1.57810	−	4.85689i	0.110219	−	0.339220i
$206$	−5.21114	−	16.0382i	−0.363077	−	1.11744i
$207$	−21.9087	+	15.9176i	−1.52276	+	1.10635i
$208$	−8.21858			−0.569856
$209$		0			0
$210$	−13.0370			−0.899636
$211$	4.57709	−	3.32545i	0.315100	−	0.228934i	−0.418982	−	0.907995i	$-0.637613\pi$
$211$	4.57709	−	3.32545i	0.315100	−	0.228934i	0.734082	+	0.679061i	$0.237613\pi$
$212$	−3.97610	−	12.2372i	−0.273080	−	0.840453i
$213$	8.61673	−	26.5196i	0.590409	−	1.81709i
$214$	−31.8774	−	23.1603i	−2.17910	−	1.58321i
$215$	4.18494	+	3.04054i	0.285411	+	0.207363i
$216$	0.387117	−	1.19143i	0.0263400	−	0.0810662i
$217$	2.35807	+	7.25738i	0.160076	+	0.492663i
$218$	−23.5018	+	17.0750i	−1.59174	+	1.15647i
$219$	−27.4230			−1.85308
$220$		0			0
$221$	−3.85410			−0.259255
$222$	9.42497	−	6.84764i	0.632563	−	0.459584i
$223$	2.43642	+	7.49852i	0.163155	+	0.502138i	0.998896	−	0.0469856i	$-0.0149615\pi$
$223$	2.43642	+	7.49852i	0.163155	+	0.502138i	−0.835741	+	0.549124i	$0.814961\pi$
$224$	2.66566	−	8.20407i	0.178107	−	0.548158i
$225$	−2.49563	−	1.81318i	−0.166375	−	0.120879i
$226$	18.4800	+	13.4265i	1.22927	+	0.893116i
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	−0.767804	−	0.640685i	$-0.778650\pi$
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	0.997752	−	0.0670213i	$-0.0213495\pi$
$228$	7.17145	+	22.0715i	0.474941	+	1.46172i
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.455547	+	0.890212i	$0.650556\pi$
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.987413	+	0.158160i	$0.949444\pi$
$230$	−22.1623			−1.46134
$231$		0			0
$232$	−3.67042			−0.240975
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	−0.836953	−	0.547275i	$-0.815665\pi$
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	0.261857	+	0.965107i	$0.415665\pi$
$234$	3.10066	+	9.54284i	0.202696	+	0.623835i
$235$	−2.25789	+	6.94907i	−0.147289	+	0.453307i
$236$	22.9766	+	16.6935i	1.49565	+	1.08665i
$237$	−10.6947	−	7.77017i	−0.694697	−	0.504727i
$238$	4.88529	−	15.0354i	0.316666	−	0.974599i
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	0.997839	+	0.0657129i	$0.0209322\pi$
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	−0.768643	+	0.639678i	$0.779068\pi$
$240$	12.7294	−	9.24842i	0.821677	−	0.596983i
$241$	−12.7542			−0.821572			−0.410786	−	0.911732i	$-0.634746\pi$
$241$	−12.7542			−0.821572			−0.410786	+	0.911732i	$0.634746\pi$
$242$		0			0
$243$	22.1829			1.42303
$244$	−1.77767	+	1.29155i	−0.113804	+	0.0826833i
$245$	−0.808764	−	2.48912i	−0.0516701	−	0.159024i
$246$	9.82734	−	30.2455i	0.626568	−	1.92838i
$247$	−2.24248	−	1.62926i	−0.142686	−	0.103667i
$248$	−17.6675	−	12.8362i	−1.12188	−	0.815097i
$249$	8.26700	−	25.4432i	0.523900	−	1.61240i
$250$	−0.780121	−	2.40097i	−0.0493392	−	0.151850i
$251$	9.87130	−	7.17192i	0.623071	−	0.452687i	−0.230922	−	0.972972i	$-0.574174\pi$
$251$	9.87130	−	7.17192i	0.623071	−	0.452687i	0.853993	+	0.520285i	$0.174174\pi$
$252$	−28.2422			−1.77909
$253$		0			0
$254$	47.5471			2.98337
$255$	5.96943	−	4.33705i	0.373820	−	0.271596i
$256$	−9.61149	−	29.5811i	−0.600718	−	1.84882i
$257$	−1.82198	+	5.60747i	−0.113652	+	0.349784i	−0.991663	−	0.128855i	$-0.958870\pi$
$257$	−1.82198	+	5.60747i	−0.113652	+	0.349784i	0.878012	+	0.478639i	$0.158870\pi$
$258$	26.0610	+	18.9344i	1.62249	+	1.17881i
$259$	−3.16850	−	2.30205i	−0.196881	−	0.143042i
$260$	−1.74122	+	5.35892i	−0.107986	+	0.332346i
$261$	0.583986	+	1.79733i	0.0361478	+	0.111252i
$262$	41.0512	−	29.8254i	2.53615	−	1.84262i
$263$	21.7305			1.33996			0.669980	−	0.742379i	$-0.266302\pi$
$263$	21.7305			1.33996			0.669980	+	0.742379i	$0.266302\pi$
$264$		0			0
$265$	−2.94221			−0.180738
$266$	9.19843	−	6.68305i	0.563992	−	0.409764i
$267$	3.29553	+	10.1426i	0.201683	+	0.620717i
$268$	−10.5539	+	32.4817i	−0.644685	+	1.98414i
$269$	3.66042	+	2.65945i	0.223180	+	0.162149i	0.693757	−	0.720209i	$-0.255954\pi$
$269$	3.66042	+	2.65945i	0.223180	+	0.162149i	−0.470577	+	0.882359i	$0.655954\pi$
$270$	−0.427051	−	0.310271i	−0.0259895	−	0.0188825i
$271$	6.72447	−	20.6958i	0.408482	−	1.25718i	−0.509470	−	0.860488i	$-0.670159\pi$
$271$	6.72447	−	20.6958i	0.408482	−	1.25718i	0.917952	−	0.396691i	$-0.129841\pi$
$272$	5.89608	+	18.1463i	0.357502	+	1.10028i
$273$	5.38300	−	3.91098i	0.325794	−	0.236703i
$274$	45.3688			2.74083
$275$		0			0
$276$	−94.7021			−5.70040
$277$	−10.5452	+	7.66154i	−0.633600	+	0.460337i	−0.857645	−	0.514241i	$-0.828074\pi$
$277$	−10.5452	+	7.66154i	−0.633600	+	0.460337i	0.224046	+	0.974579i	$0.428074\pi$
$278$	13.1552	+	40.4877i	0.788999	+	2.42829i
$279$	−3.47459	+	10.6937i	−0.208018	+	0.640214i
$280$	−10.1473	−	7.37245i	−0.606417	−	0.440588i
$281$	7.59310	+	5.51671i	0.452966	+	0.329099i	0.790766	−	0.612119i	$-0.209683\pi$
$281$	7.59310	+	5.51671i	0.452966	+	0.329099i	−0.337799	+	0.941218i	$0.609683\pi$
$282$	−14.0606	+	43.2741i	−0.837297	+	2.57694i
$283$	−4.30760	−	13.2574i	−0.256060	−	0.788072i	−0.993619	−	0.112789i	$-0.964021\pi$
$283$	−4.30760	−	13.2574i	−0.256060	−	0.788072i	0.737559	−	0.675283i	$-0.235979\pi$
$284$	39.9943	−	29.0575i	2.37322	−	1.72425i
$285$	5.30669			0.314341
$286$		0			0
$287$	−10.6912			−0.631083
$288$	10.2832	−	7.47118i	0.605943	−	0.440243i
$289$	−2.48832	−	7.65828i	−0.146372	−	0.450487i
$290$	−0.477925	+	1.47090i	−0.0280647	+	0.0863744i
$291$	−0.701768	−	0.509864i	−0.0411383	−	0.0298888i
$292$	−39.3326	−	28.5768i	−2.30176	−	1.67233i
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	0.158534	+	0.987354i	$0.449323\pi$
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	−0.708608	+	0.705602i	$0.750677\pi$
$294$	−5.03644	−	15.5006i	−0.293731	−	0.904011i
$295$	5.25393	−	3.81720i	0.305895	−	0.222246i
$296$	11.2083			0.651468
$297$		0			0
$298$	5.89138			0.341278
$299$	9.15089	−	6.64851i	0.529210	−	0.384493i
$300$	−3.33354	−	10.2596i	−0.192462	−	0.592337i
$301$	3.34649	−	10.2994i	0.192888	−	0.593649i
$302$	8.04468	+	5.84480i	0.462919	+	0.336330i
$303$	31.3303	+	22.7628i	1.79988	+	1.30769i
$304$	−4.24044	+	13.0507i	−0.243206	+	0.748511i
$305$	0.155265	+	0.477858i	0.00889047	+	0.0273621i
$306$	18.8457	−	13.6922i	1.07734	−	0.782732i
$307$	−5.08609			−0.290278			−0.145139	−	0.989411i	$-0.546363\pi$
$307$	−5.08609			−0.290278			−0.145139	+	0.989411i	$0.546363\pi$
$308$		0			0
$309$	−16.4775			−0.937375
$310$	−7.44450	+	5.40875i	−0.422819	+	0.307196i
$311$	4.25249	+	13.0878i	0.241136	+	0.742141i	0.996248	+	0.0865451i	$0.0275827\pi$
$311$	4.25249	+	13.0878i	0.241136	+	0.742141i	−0.755112	+	0.655596i	$0.772417\pi$
$312$	−5.88426	+	18.1099i	−0.333131	+	1.02527i
$313$	−12.9060	−	9.37676i	−0.729491	−	0.530006i	0.159912	−	0.987131i	$-0.448879\pi$
$313$	−12.9060	−	9.37676i	−0.729491	−	0.530006i	−0.889402	+	0.457125i	$0.848879\pi$
$314$	−9.96903	−	7.24292i	−0.562585	−	0.408742i
$315$	−1.99563	+	6.14191i	−0.112441	+	0.346057i
$316$	−7.24225	−	22.2894i	−0.407408	−	1.25387i
$317$	−8.66246	+	6.29364i	−0.486532	+	0.353486i	−0.803849	−	0.594833i	$-0.797218\pi$
$317$	−8.66246	+	6.29364i	−0.486532	+	0.353486i	0.317317	+	0.948320i	$0.397218\pi$
$318$	−18.3221			−1.02745
$319$		0			0
$320$	−2.35499			−0.131648
$321$	−31.1477	+	22.6301i	−1.73849	+	1.26309i
$322$	14.3375	+	44.1263i	0.798997	+	2.45906i
$323$	−1.98855	+	6.12014i	−0.110646	+	0.340534i
$324$	30.9170	+	22.4625i	1.71761	+	1.24792i
$325$	1.04238	+	0.757336i	0.0578210	+	0.0420094i
$326$	5.48871	−	16.8925i	0.303992	−	0.935590i
$327$	8.77138	+	26.9955i	0.485058	+	1.49286i
$328$	24.7530	−	17.9841i	1.36676	−	0.993006i
$329$	15.2966			0.843330
$330$		0			0
$331$	−8.84618			−0.486230			−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618			−0.486230			−0.243115	+	0.969997i	$0.578169\pi$
$332$	38.3710	−	27.8782i	2.10588	−	1.53001i
$333$	−1.78330	−	5.48845i	−0.0977245	−	0.300765i
$334$	8.36248	−	25.7371i	0.457575	−	1.40827i
$335$	6.31813	+	4.59039i	0.345196	+	0.250800i
$336$	−26.6491	−	19.3617i	−1.45382	−	1.05627i
$337$	3.58143	−	11.0225i	0.195093	−	0.600434i	−0.804883	−	0.593434i	$-0.797772\pi$
$337$	3.58143	−	11.0225i	0.195093	−	0.600434i	0.999976	−	0.00699978i	$-0.00222812\pi$
$338$	8.84648	+	27.2267i	0.481185	+	1.48093i
$339$	18.0569	−	13.1191i	0.980716	−	0.712532i
$340$	13.0814			0.709440
$341$		0			0
$342$	16.7534			0.905920
$343$	−16.2885	+	11.8343i	−0.879498	+	0.638993i
$344$	9.57705	+	29.4751i	0.516360	+	1.58919i
$345$	−6.69176	+	20.5951i	−0.360272	+	1.10880i
$346$	−17.1802	−	12.4821i	−0.923611	−	0.671043i
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	0.476537	−	0.879155i	$-0.341892\pi$
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	−0.688868	+	0.724887i	$0.741892\pi$
$348$	−2.04223	+	6.28533i	−0.109475	+	0.336929i
$349$	−0.294654	−	0.906853i	−0.0157725	−	0.0485427i	0.942861	−	0.333188i	$-0.108124\pi$
$349$	−0.294654	−	0.906853i	−0.0157725	−	0.0485427i	−0.958633	+	0.284645i	$0.908124\pi$
$350$	−4.27575	+	3.10651i	−0.228548	+	0.166050i
$351$	0.269409			0.0143800
$352$		0			0
$353$	−15.5166			−0.825865			−0.412933	−	0.910762i	$-0.635495\pi$
$353$	−15.5166			−0.825865			−0.412933	+	0.910762i	$0.635495\pi$
$354$	32.7179	−	23.7709i	1.73894	−	1.26341i
$355$	−3.49318	−	10.7509i	−0.185399	−	0.570598i
$356$	−5.84258	+	17.9816i	−0.309656	+	0.953024i
$357$	−12.4971	−	9.07965i	−0.661415	−	0.480546i
$358$	42.9645	+	31.2155i	2.27074	+	1.64979i
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	0.638624	+	0.769519i	$0.279504\pi$
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	−0.968970	+	0.247180i	$0.920496\pi$
$360$	−5.71114	−	17.5771i	−0.301003	−	0.926393i
$361$	11.6271	−	8.44759i	0.611953	−	0.444610i
$362$	4.40051			0.231286
$363$		0			0
$364$	11.7963			0.618295
$365$	−8.99396	+	6.53449i	−0.470765	+	0.342031i
$366$	0.966888	+	2.97578i	0.0505400	+	0.155546i
$367$	11.0180	−	33.9099i	0.575135	−	1.77008i	−0.0605844	−	0.998163i	$-0.519296\pi$
$367$	11.0180	−	33.9099i	0.575135	−	1.77008i	0.635719	−	0.771920i	$-0.280704\pi$
$368$	−45.3024	−	32.9141i	−2.36155	−	1.71577i
$369$	−12.7448	−	9.25962i	−0.663466	−	0.482037i
$370$	1.45943	−	4.49166i	0.0758721	−	0.233510i
$371$	1.90340	+	5.85807i	0.0988198	+	0.304136i
$372$	−31.8112	+	23.1122i	−1.64933	+	1.19831i
$373$	−12.1358			−0.628370			−0.314185	−	0.949362i	$-0.601731\pi$
$373$	−12.1358			−0.628370			−0.314185	+	0.949362i	$0.601731\pi$
$374$		0			0
$375$	−2.46673			−0.127381
$376$	−35.4157	+	25.7310i	−1.82643	+	1.32698i
$377$	−0.243922	−	0.750713i	−0.0125626	−	0.0386637i
$378$	−0.341491	+	1.05100i	−0.0175644	+	0.0540577i
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	0.429364	−	0.903131i	$-0.358738\pi$
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	−0.726248	+	0.687433i	$0.758738\pi$
$380$	7.61133	+	5.52996i	0.390453	+	0.283681i
$381$	14.3565	−	44.1848i	0.735506	−	2.26366i
$382$	−0.0194691	−	0.0599198i	−0.000996127	−	0.00306576i
$383$	−12.9143	+	9.38279i	−0.659890	+	0.479438i	−0.866626	−	0.498959i	$-0.833716\pi$
$383$	−12.9143	+	9.38279i	−0.659890	+	0.479438i	0.206736	+	0.978397i	$0.433716\pi$
$384$	−34.9936			−1.78576
$385$		0			0
$386$	3.67885			0.187249
$387$	12.9096	−	9.37935i	0.656230	−	0.476779i
$388$	−0.475223	−	1.46259i	−0.0241258	−	0.0742516i
$389$	−7.75336	+	23.8624i	−0.393111	+	1.20987i	0.537312	+	0.843384i	$0.319440\pi$
$389$	−7.75336	+	23.8624i	−0.393111	+	1.20987i	−0.930423	+	0.366488i	$0.880560\pi$
$390$	6.49126	+	4.71617i	0.328698	+	0.238813i
$391$	−21.2445	−	15.4351i	−1.07438	−	0.780585i
$392$	4.84551	−	14.9130i	0.244735	−	0.753218i
$393$	−15.3212	−	47.1538i	−0.772853	−	2.37860i
$394$	−46.3677	+	33.6881i	−2.33597	+	1.69718i
$395$	−5.35907			−0.269644
$396$		0			0
$397$	3.57490			0.179419			0.0897094	−	0.995968i	$-0.471406\pi$
$397$	3.57490			0.179419			0.0897094	+	0.995968i	$0.471406\pi$
$398$	−13.5376	+	9.83564i	−0.678579	+	0.493016i
$399$	−3.43305	−	10.5659i	−0.171868	−	0.528954i
$400$	1.97110	−	6.06643i	0.0985552	−	0.303322i
$401$	−23.3675	−	16.9775i	−1.16692	−	0.847815i	−0.176281	−	0.984340i	$-0.556407\pi$
$401$	−23.3675	−	16.9775i	−1.16692	−	0.847815i	−0.990637	+	0.136524i	$0.956407\pi$
$402$	39.3451	+	28.5859i	1.96235	+	1.42573i
$403$	1.45128	−	4.46657i	0.0722933	−	0.222496i
$404$	21.2162	+	65.2969i	1.05555	+	3.24864i
$405$	7.06961	−	5.13637i	0.351292	−	0.255228i
$406$	3.23782			0.160690
$407$		0			0
$408$	44.2072			2.18858
$409$	7.78197	−	5.65393i	0.384794	−	0.279569i	−0.378525	−	0.925591i	$-0.623569\pi$
$409$	7.78197	−	5.65393i	0.384794	−	0.279569i	0.763319	+	0.646022i	$0.223569\pi$
$410$	−3.98395	−	12.2613i	−0.196753	−	0.605545i
$411$	13.6988	−	42.1606i	0.675712	−	2.07963i
$412$	−23.6336	−	17.1708i	−1.16434	−	0.845945i
$413$	−10.9991	−	7.99135i	−0.541233	−	0.393229i
$414$	−21.1261	+	65.0196i	−1.03829	+	3.19554i
$415$	−3.35140	−	10.3145i	−0.164514	−	0.506321i
$416$	−4.29512	+	3.12059i	−0.210586	+	0.152999i
$417$	41.5967			2.03700
$418$		0			0
$419$	−30.6537			−1.49753			−0.748765	−	0.662836i	$-0.769353\pi$
$419$	−30.6537			−1.49753			−0.748765	+	0.662836i	$0.769353\pi$
$420$	−18.2707	+	13.2745i	−0.891521	+	0.647728i
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	0.884986	−	0.465617i	$-0.154168\pi$
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	−0.989652	+	0.143490i	$0.954168\pi$
$422$	4.41361	−	13.5837i	0.214851	−	0.661244i
$423$	18.2348	+	13.2483i	0.886605	+	0.644156i
$424$	−14.2610	−	10.3612i	−0.692574	−	0.503184i
$425$	0.924349	−	2.84485i	0.0448375	−	0.137996i
$426$	−21.7532	−	66.9493i	−1.05394	−	3.24371i
$427$	0.850991	−	0.618281i	0.0411823	−	0.0299207i
$428$	−68.2571			−3.29933
$429$		0			0
$430$	13.0590			0.629763
$431$	−2.61636	+	1.90090i	−0.126026	+	0.0915631i	−0.649013	−	0.760778i	$-0.724818\pi$
$431$	−2.61636	+	1.90090i	−0.126026	+	0.0915631i	0.522987	+	0.852341i	$0.324818\pi$
$432$	−0.412147	−	1.26846i	−0.0198294	−	0.0610287i
$433$	−9.39161	+	28.9044i	−0.451332	+	1.38906i	0.424056	+	0.905636i	$0.360606\pi$
$433$	−9.39161	+	28.9044i	−0.451332	+	1.38906i	−0.875388	+	0.483421i	$0.839394\pi$
$434$	15.5851	+	11.3233i	0.748110	+	0.543534i
$435$	1.22258	+	0.888257i	0.0586183	+	0.0425887i
$436$	−15.5506	+	47.8598i	−0.744739	+	2.29207i
$437$	−5.83606	−	17.9616i	−0.279177	−	0.859218i
$438$	−56.0083	+	40.6924i	−2.67618	+	1.94436i
$439$	−36.5311			−1.74353			−0.871767	−	0.489921i	$-0.837026\pi$
$439$	−36.5311			−1.74353			−0.871767	+	0.489921i	$0.837026\pi$
$440$		0			0
$441$	−8.07350			−0.384452
$442$	−7.87155	+	5.71902i	−0.374412	+	0.272026i
$443$	−0.667949	−	2.05574i	−0.0317352	−	0.0976710i	0.933934	−	0.357445i	$-0.116352\pi$
$443$	−0.667949	−	2.05574i	−0.0317352	−	0.0976710i	−0.965669	+	0.259774i	$0.916352\pi$
$444$	6.23630	−	19.1933i	0.295962	−	0.910876i
$445$	3.49767	+	2.54120i	0.165805	+	0.120465i
$446$	16.1030	+	11.6995i	0.762499	+	0.553988i
$447$	1.77886	−	5.47477i	0.0841372	−	0.258948i
$448$	1.52352	+	4.68890i	0.0719793	+	0.221530i
$449$	9.32124	−	6.77228i	0.439897	−	0.319604i	−0.345697	−	0.938346i	$-0.612358\pi$
$449$	9.32124	−	6.77228i	0.439897	−	0.319604i	0.785594	+	0.618742i	$0.212358\pi$
$450$	−7.78757			−0.367109
$451$		0			0
$452$	39.5699			1.86121
$453$	7.86051	−	5.71100i	0.369319	−	0.268326i
$454$	−8.74624	−	26.9182i	−0.410482	−	1.26333i
$455$	0.833541	−	2.56538i	0.0390770	−	0.120267i
$456$	25.7217	+	18.6879i	1.20453	+	0.875140i
$457$	−12.8888	−	9.36427i	−0.602913	−	0.438042i	0.243999	−	0.969776i	$-0.421541\pi$
$457$	−12.8888	−	9.36427i	−0.602913	−	0.438042i	−0.846912	+	0.531734i	$0.821541\pi$
$458$	−21.0560	+	64.8038i	−0.983883	+	3.02808i
$459$	−0.193276	−	0.594843i	−0.00902136	−	0.0277649i
$460$	−31.0596	+	22.5661i	−1.44816	+	1.05215i
$461$	−1.52527			−0.0710387			−0.0355193	−	0.999369i	$-0.511309\pi$
$461$	−1.52527			−0.0710387			−0.0355193	+	0.999369i	$0.511309\pi$
$462$		0			0
$463$	14.2073			0.660268			0.330134	−	0.943934i	$-0.392906\pi$
$463$	14.2073			0.660268			0.330134	+	0.943934i	$0.392906\pi$
$464$	−3.16143	+	2.29691i	−0.146765	+	0.106631i
$465$	2.77845	+	8.55119i	0.128848	+	0.396552i
$466$	−8.46491	+	26.0523i	−0.392129	+	1.20685i
$467$	4.90020	+	3.56020i	0.226754	+	0.164746i	0.695362	−	0.718660i	$-0.255244\pi$
$467$	4.90020	+	3.56020i	0.226754	+	0.164746i	−0.468608	+	0.883406i	$0.655244\pi$
$468$	14.0621	+	10.2167i	0.650022	+	0.472269i
$469$	5.05229	−	15.5494i	0.233293	−	0.718002i
$470$	5.70010	+	17.5431i	0.262926	+	0.809203i
$471$	−9.74081	+	7.07711i	−0.448833	+	0.326096i
$472$	38.9085			1.79091
$473$		0			0
$474$	−33.3727			−1.53286
$475$	1.74044	−	1.26450i	0.0798569	−	0.0580194i
$476$	−8.46277	−	26.0457i	−0.387890	−	1.19380i
$477$	−2.80464	+	8.63181i	−0.128416	+	0.395223i
$478$	23.4185	+	17.0146i	1.07114	+	0.778227i
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	0.212681	−	0.977122i	$-0.431780\pi$
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	−0.863576	+	0.504219i	$0.831780\pi$
$480$	3.14089	−	9.66666i	0.143361	−	0.441221i
$481$	0.744857	+	2.29243i	0.0339626	+	0.104526i
$482$	−26.0490	+	18.9257i	−1.18650	+	0.862043i
$483$	45.3350			2.06281
$484$		0			0
$485$	−0.351653			−0.0159677
$486$	45.3059	−	32.9167i	2.05512	−	1.49313i
$487$	2.09619	+	6.45140i	0.0949874	+	0.292341i	0.987250	−	0.159175i	$-0.0508834\pi$
$487$	2.09619	+	6.45140i	0.0949874	+	0.292341i	−0.892263	+	0.451516i	$0.850883\pi$
$488$	−0.930235	+	2.86297i	−0.0421097	+	0.129600i
$489$	−14.0407	−	10.2011i	−0.634941	−	0.461312i
$490$	−5.34536	−	3.88363i	−0.241479	−	0.175445i
$491$	−0.160261	+	0.493232i	−0.00723247	+	0.0222592i	−0.954608	−	0.297866i	$-0.903725\pi$
$491$	−0.160261	+	0.493232i	−0.00723247	+	0.0222592i	0.947375	+	0.320125i	$0.103725\pi$
$492$	−17.0239	−	52.3941i	−0.767495	−	2.36211i
$493$	−1.48255	+	1.07714i	−0.0667707	+	0.0485117i
$494$	−6.99762			−0.314838
$495$		0			0
$496$	−23.2501			−1.04396
$497$	−19.1457	+	13.9102i	−0.858802	+	0.623956i
$498$	−20.8703	−	64.2320i	−0.935218	−	2.87831i
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	−0.678220	−	0.734859i	$-0.737248\pi$
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	0.980631	−	0.195866i	$-0.0627516\pi$
$500$	−3.53801	−	2.57052i	−0.158225	−	0.114957i
$501$	−21.3921	−	15.5423i	−0.955727	−	0.694377i
$502$	9.51872	−	29.2956i	0.424841	−	1.30753i
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	0.928121	−	0.372279i	$-0.121424\pi$
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	−0.969686	+	0.244356i	$0.921424\pi$
$504$	−31.3020	+	22.7423i	−1.39430	+	1.01302i
$505$	15.6995			0.698617
$506$		0			0
$507$	27.9724			1.24230
$508$	66.6352	−	48.4133i	2.95646	−	2.14799i
$509$	−7.94418	−	24.4497i	−0.352119	−	1.08371i	−0.957661	−	0.287898i	$-0.907043\pi$
$509$	−7.94418	−	24.4497i	−0.352119	−	1.08371i	0.605542	−	0.795814i	$-0.292957\pi$
$510$	5.75622	−	17.7158i	0.254890	−	0.784470i
$511$	18.8289	+	13.6800i	0.832943	+	0.605169i
$512$	−40.5713	−	29.4768i	−1.79302	−	1.30270i
$513$	0.139004	−	0.427809i	0.00613716	−	0.0188882i
$514$	4.59962	+	14.1562i	0.202881	+	0.624403i
$515$	−5.40416	+	3.92635i	−0.238136	+	0.173016i
$516$	55.8027			2.45658
$517$		0			0
$518$	−9.88725			−0.434421
$519$	−16.7869	+	12.1964i	−0.736862	+	0.535361i
$520$	2.38545	+	7.34165i	0.104609	+	0.321953i
$521$	3.44017	−	10.5877i	0.150716	−	0.463858i	−0.846985	−	0.531616i	$-0.821585\pi$
$521$	3.44017	−	10.5877i	0.150716	−	0.463858i	0.997702	+	0.0677588i	$0.0215848\pi$
$522$	3.85974	+	2.80426i	0.168936	+	0.122739i
$523$	−5.28968	−	3.84318i	−0.231302	−	0.168050i	0.466098	−	0.884733i	$-0.345660\pi$
$523$	−5.28968	−	3.84318i	−0.231302	−	0.168050i	−0.697399	+	0.716683i	$0.745660\pi$
$524$	27.1627	−	83.5981i	1.18661	−	3.65200i
$525$	1.59580	+	4.91138i	0.0696466	+	0.214350i
$526$	44.3820	−	32.2454i	1.93515	−	1.40597i
$527$	−10.9032			−0.474949
$528$		0			0
$529$	54.0677			2.35077
$530$	−6.00911	+	4.36588i	−0.261019	+	0.189642i
$531$	−6.19057	−	19.0526i	−0.268648	−	0.826814i
$532$	6.08640	−	18.7320i	0.263879	−	0.812135i
$533$	5.32328	+	3.86759i	0.230577	+	0.167524i
$534$	21.7811	+	15.8249i	0.942561	+	0.684811i
$535$	−4.82313	+	14.8441i	−0.208522	+	0.641765i
$536$	14.4588	+	44.4995i	0.624524	+	1.92209i
$537$	41.9809	−	30.5009i	1.81161	−	1.31621i
$538$	11.4223			0.492449
$539$		0			0
$540$	−0.914417			−0.0393502
$541$	33.7684	−	24.5342i	1.45182	−	1.05481i	0.466413	−	0.884567i	$-0.345546\pi$
$541$	33.7684	−	24.5342i	1.45182	−	1.05481i	0.985403	−	0.170239i	$-0.0544538\pi$
$542$	−16.9761	−	52.2470i	−0.729185	−	2.24420i
$543$	1.32870	−	4.08932i	0.0570201	−	0.175490i
$544$	9.97147	+	7.24470i	0.427523	+	0.310614i
$545$	9.30939	+	6.76367i	0.398770	+	0.289724i
$546$	5.19073	−	15.9754i	0.222143	−	0.683685i
$547$	1.37703	+	4.23806i	0.0588775	+	0.181206i	0.976170	−	0.217008i	$-0.0696299\pi$
$547$	1.37703	+	4.23806i	0.0588775	+	0.181206i	−0.917292	+	0.398215i	$0.869630\pi$
$548$	63.5825	−	46.1954i	2.71611	−	1.97337i
$549$	1.54994			0.0661498
$550$		0			0
$551$	−1.31795			−0.0561466
$552$	−104.962	+	76.2596i	−4.46750	+	3.24583i
$553$	3.46695	+	10.6702i	0.147430	+	0.453742i
$554$	−10.1686	+	31.2956i	−0.432020	+	1.32962i
$555$	−3.73337	−	2.71245i	−0.158473	−	0.115137i
$556$	59.6618	+	43.3468i	2.53022	+	1.83831i
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	0.740456	+	0.672104i	$0.234609\pi$
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	−0.994095	+	0.108514i	$0.965391\pi$
$558$	8.77167	+	26.9964i	0.371335	+	1.14285i
$559$	−5.39211	+	3.91760i	−0.228062	+	0.165697i
$560$	−13.3537			−0.564298
$561$		0			0
$562$	23.6941			0.999477
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	−0.175030	−	0.984563i	$-0.556002\pi$
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	0.882288	+	0.470710i	$0.156002\pi$
$564$	24.3571	+	74.9636i	1.02562	+	3.15654i
$565$	2.79606	−	8.60538i	0.117631	−	0.362031i
$566$	−28.4702	−	20.6848i	−1.19669	−	0.869447i
$567$	−14.8003	−	10.7530i	−0.621554	−	0.451585i
$568$	20.9285	−	64.4114i	0.878141	−	2.70264i
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	0.711408	+	0.702779i	$0.248058\pi$
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	−0.162458	+	0.986716i	$0.551942\pi$
$570$	10.8383	−	7.87447i	0.453966	−	0.329825i
$571$	5.03980			0.210909			0.105455	−	0.994424i	$-0.466370\pi$
$571$	5.03980			0.210909			0.105455	+	0.994424i	$0.466370\pi$
$572$		0			0
$573$	−0.0615611			−0.00257175
$574$	−21.8356	+	15.8645i	−0.911399	+	0.662170i
$575$	2.71281	+	8.34916i	0.113132	+	0.348184i
$576$	−2.24488	+	6.90905i	−0.0935369	+	0.287877i
$577$	−28.1877	−	20.4796i	−1.17347	−	0.852576i	−0.182050	−	0.983289i	$-0.558273\pi$
$577$	−28.1877	−	20.4796i	−1.17347	−	0.852576i	−0.991420	+	0.130713i	$0.958273\pi$
$578$	−16.4461	−	11.9488i	−0.684066	−	0.497003i
$579$	1.11080	−	3.41870i	0.0461634	−	0.142076i
$580$	0.827908	+	2.54804i	0.0343770	+	0.105802i
$581$	−18.3686	+	13.3456i	−0.762059	+	0.553668i
$582$	−2.18985			−0.0907724
$583$		0			0
$584$	−66.6057			−2.75616
$585$	3.21551	−	2.33620i	0.132945	−	0.0965901i
$586$	23.7703	+	73.1575i	0.981943	+	3.02211i
$587$	−4.25772	+	13.1039i	−0.175735	+	0.540857i	−0.999666	−	0.0258331i	$-0.991776\pi$
$587$	−4.25772	+	13.1039i	−0.175735	+	0.540857i	0.823931	+	0.566690i	$0.191776\pi$
$588$	−22.8413	−	16.5952i	−0.941959	−	0.684373i
$589$	−6.34392	−	4.60913i	−0.261397	−	0.189916i
$590$	5.06627	−	15.5924i	0.208575	−	0.641928i
$591$	17.3054	+	53.2606i	0.711850	+	2.19085i
$592$	9.65397	−	7.01402i	0.396776	−	0.288274i
$593$	25.1595			1.03318			0.516588	−	0.856234i	$-0.327202\pi$
$593$	25.1595			1.03318			0.516588	+	0.856234i	$0.327202\pi$
$594$		0			0
$595$	−6.26222			−0.256726
$596$	8.25651	−	5.99871i	0.338200	−	0.245717i
$597$	5.05253	+	15.5501i	0.206786	+	0.636423i
$598$	8.82405	−	27.1576i	0.360842	−	1.11056i
$599$	13.3539	+	9.70216i	0.545624	+	0.396419i	0.826170	−	0.563421i	$-0.190515\pi$
$599$	13.3539	+	9.70216i	0.545624	+	0.396419i	−0.280545	+	0.959841i	$0.590515\pi$
$600$	−11.9563	−	8.68677i	−0.488115	−	0.354636i
$601$	−12.2509	+	37.7045i	−0.499726	+	1.53800i	0.309734	+	0.950823i	$0.399760\pi$
$601$	−12.2509	+	37.7045i	−0.499726	+	1.53800i	−0.809460	+	0.587175i	$0.800240\pi$
$602$	−8.44829	−	26.0011i	−0.344326	−	1.05973i
$603$	19.4900	−	14.1603i	0.793692	−	0.576651i
$604$	17.2255			0.700897
$605$		0			0
$606$	97.7656			3.97146
$607$	11.4795	−	8.34036i	0.465939	−	0.338525i	−0.329917	−	0.944010i	$-0.607021\pi$
$607$	11.4795	−	8.34036i	0.465939	−	0.338525i	0.795857	+	0.605485i	$0.207021\pi$
$608$	2.73925	+	8.43055i	0.111091	+	0.341904i
$609$	0.977637	−	3.00886i	0.0396158	−	0.121925i
$610$	1.02619	+	0.745574i	0.0415494	+	0.0301874i
$611$	−7.61636	−	5.53361i	−0.308125	−	0.223866i
$612$	12.4698	−	38.3781i	0.504062	−	1.55134i
$613$	−9.31820	−	28.6785i	−0.376359	−	1.15831i	−0.942557	−	0.334044i	$-0.891586\pi$
$613$	−9.31820	−	28.6785i	−0.376359	−	1.15831i	0.566199	−	0.824269i	$-0.308414\pi$
$614$	−10.3877	+	7.54714i	−0.419215	+	0.304578i
$615$	−12.5972			−0.507968
$616$		0			0
$617$	−31.3844			−1.26349			−0.631744	−	0.775177i	$-0.717661\pi$
$617$	−31.3844			−1.26349			−0.631744	+	0.775177i	$0.717661\pi$
$618$	−33.6534	+	24.4507i	−1.35374	+	0.983550i
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	0.890387	+	0.455205i	$0.150434\pi$
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	−0.452775	+	0.891625i	$0.649566\pi$
$620$	−4.92586	+	15.1602i	−0.197827	+	0.608850i
$621$	1.48503	+	1.07894i	0.0595924	+	0.0432964i
$622$	28.1059	+	20.4201i	1.12694	+	0.818773i
$623$	2.79691	−	8.60800i	0.112056	−	0.344872i
$624$	6.26471	+	19.2808i	0.250789	+	0.771850i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−40.2730			−1.60963
$627$		0			0
$628$	−21.3460			−0.851799
$629$	4.52723	−	3.28922i	0.180512	−	0.131150i
$630$	5.03801	+	15.5054i	0.200719	+	0.617750i
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	−0.909567	−	0.415558i	$-0.863586\pi$
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	0.980114	+	0.198436i	$0.0635863\pi$
$632$	−25.9756	−	18.8724i	−1.03325	−	0.750702i
$633$	−11.2905	−	8.20300i	−0.448755	−	0.326040i
$634$	−8.35306	+	25.7081i	−0.331742	+	1.02100i
$635$	−5.82005	−	17.9123i	−0.230962	−	0.710827i
$636$	−25.6776	+	18.6559i	−1.01818	+	0.739753i
$637$	3.37217			0.133610
$638$		0			0
$639$	−34.8707			−1.37946
$640$	−11.4769	+	8.33844i	−0.453663	+	0.329606i
$641$	−2.20167	−	6.77605i	−0.0869608	−	0.267638i	0.898115	−	0.439762i	$-0.144937\pi$
$641$	−2.20167	−	6.77605i	−0.0869608	−	0.267638i	−0.985075	+	0.172124i	$0.944937\pi$
$642$	−30.0352	+	92.4388i	−1.18539	+	3.64827i
$643$	17.1427	+	12.4549i	0.676042	+	0.491173i	0.872042	−	0.489431i	$-0.162795\pi$
$643$	17.1427	+	12.4549i	0.676042	+	0.491173i	−0.196000	+	0.980604i	$0.562795\pi$
$644$	65.0235	+	47.2423i	2.56229	+	1.86161i
$645$	3.94308	−	12.1356i	0.155259	−	0.477837i
$646$	5.02015	+	15.4504i	0.197515	+	0.607889i
$647$	4.57074	−	3.32083i	0.179694	−	0.130555i	−0.494302	−	0.869290i	$-0.664576\pi$
$647$	4.57074	−	3.32083i	0.179694	−	0.130555i	0.673996	+	0.738735i	$0.264576\pi$
$648$	52.3547			2.05669
$649$		0			0
$650$	3.25274			0.127583
$651$	15.2284	−	11.0640i	0.596846	−	0.433634i
$652$	−9.50807	−	29.2628i	−0.372365	−	1.14602i
$653$	−4.85563	+	14.9441i	−0.190016	+	0.584808i	−0.999999	−	0.00164558i	$-0.999476\pi$
$653$	−4.85563	+	14.9441i	−0.190016	+	0.584808i	0.809983	+	0.586453i	$0.199476\pi$
$654$	57.9726	+	42.1195i	2.26691	+	1.64700i
$655$	−16.2610	−	11.8143i	−0.635368	−	0.461622i
$656$	10.0661	−	30.9803i	0.393016	−	1.20958i
$657$	10.5974	+	32.6153i	0.413442	+	1.27245i
$658$	31.2416	−	22.6983i	1.21792	−	0.884872i
$659$	41.7884			1.62784			0.813922	−	0.580975i	$-0.197329\pi$
$659$	41.7884			1.62784			0.813922	+	0.580975i	$0.197329\pi$
$660$		0			0
$661$	15.8742			0.617435			0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742			0.617435			0.308717	+	0.951154i	$0.400100\pi$
$662$	−18.0673	+	13.1266i	−0.702205	+	0.510182i
$663$	2.93784	+	9.04173i	0.114096	+	0.351152i
$664$	20.0791	−	61.7971i	0.779220	−	2.39819i
$665$	−3.64363	−	2.64725i	−0.141294	−	0.102656i
$666$	−11.7864	−	8.56330i	−0.456713	−	0.331821i
$667$	1.66195	−	5.11494i	0.0643508	−	0.198051i
$668$	−14.4863	−	44.5842i	−0.560491	−	1.72502i
$669$	15.7344	−	11.4317i	0.608325	−	0.441974i
$670$	19.7156			0.761681
$671$		0			0
$672$	−21.2787			−0.820844
$673$	26.0864	−	18.9529i	1.00556	−	0.730580i	0.0422850	−	0.999106i	$-0.486536\pi$
$673$	26.0864	−	18.9529i	1.00556	−	0.730580i	0.963273	+	0.268525i	$0.0865363\pi$
$674$	−9.04140	−	27.8266i	−0.348262	−	1.07184i
$675$	−0.0646137	+	0.198861i	−0.00248698	+	0.00765415i
$676$	40.1206	+	29.1493i	1.54310	+	1.12113i
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	0.826336	−	0.563178i	$-0.190422\pi$
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	−0.280263	+	0.959923i	$0.590422\pi$
$678$	17.4120	−	53.5885i	0.668702	−	2.05805i
$679$	0.227495	+	0.700157i	0.00873044	+	0.0268695i
$680$	14.4987	−	10.5339i	0.556000	−	0.403957i
$681$	−27.6555			−1.05976
$682$		0			0
$683$	−5.93856			−0.227233			−0.113616	−	0.993525i	$-0.536243\pi$
$683$	−5.93856			−0.227233			−0.113616	+	0.993525i	$0.536243\pi$
$684$	23.4792	−	17.0586i	0.897749	−	0.652253i
$685$	−5.55342	−	17.0917i	−0.212185	−	0.653039i
$686$	−15.7067	+	48.3404i	−0.599686	+	1.84565i
$687$	53.8634	+	39.1341i	2.05502	+	1.49306i
$688$	26.6942	+	19.3945i	1.01771	+	0.739407i
$689$	1.17145	−	3.60537i	0.0446289	−	0.137353i
$690$	16.8935	+	51.9929i	0.643125	+	1.97934i
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	−0.871728	−	0.489989i	$-0.837001\pi$
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	0.196629	+	0.980478i	$0.437001\pi$
$692$	−36.7868			−1.39842
$693$		0			0
$694$	−12.3424			−0.468511
$695$	13.6425	−	9.91187i	0.517490	−	0.375979i
$696$	2.79782	+	8.61082i	0.106051	+	0.326392i
$697$	4.72050	−	14.5282i	0.178802	−	0.550295i
$698$	−1.94746	−	1.41491i	−0.0737123	−	0.0535551i
$699$	21.6541	+	15.7326i	0.819033	+	0.595062i
$700$	−2.82917	+	8.70729i	−0.106933	+	0.329105i
$701$	−10.0186	−	30.8341i	−0.378397	−	1.16459i	−0.941158	−	0.337967i	$-0.890261\pi$
$701$	−10.0186	−	30.8341i	−0.378397	−	1.16459i	0.562761	−	0.826620i	$-0.309739\pi$
$702$	0.550236	−	0.399770i	0.0207673	−	0.0150884i
$703$	4.02460			0.151791
$704$		0			0
$705$	18.0236			0.678809
$706$	−31.6908	+	23.0247i	−1.19270	+	0.866547i
$707$	−10.1565	−	31.2584i	−0.381973	−	1.17559i
$708$	21.6487	−	66.6279i	0.813609	−	2.50403i
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	0.804871	−	0.593450i	$-0.202235\pi$
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	−0.315686	+	0.948864i	$0.602235\pi$
$710$	−23.0874	−	16.7740i	−0.866456	−	0.629517i
$711$	−5.10851	+	15.7224i	−0.191584	+	0.589635i
$712$	8.00426	+	24.6346i	0.299972	+	0.923220i
$713$	25.8876	−	18.8085i	0.969499	−	0.704383i
$714$	−38.9969			−1.45942
$715$		0			0
$716$	91.9971			3.43809
$717$	22.8824	−	16.6250i	0.854559	−	0.620874i
$718$	15.8014	+	48.6316i	0.589702	+	1.81492i
$719$	−2.41409	+	7.42981i	−0.0900304	+	0.277085i	−0.985927	−	0.167178i	$-0.946534\pi$
$719$	−2.41409	+	7.42981i	−0.0900304	+	0.277085i	0.895896	+	0.444263i	$0.146534\pi$
$720$	−15.9187	−	11.5656i	−0.593254	−	0.431024i
$721$	11.3137	+	8.21985i	0.421343	+	0.306123i
$722$	11.2118	−	34.5064i	0.417261	−	1.28420i
$723$	9.72206	+	29.9214i	0.361567	+	1.11279i
$724$	6.16712	−	4.48068i	0.229199	−	0.166523i
$725$	0.612630			0.0227525
$726$		0			0
$727$	−49.1218			−1.82183			−0.910914	−	0.412597i	$-0.864622\pi$
$727$	−49.1218			−1.82183			−0.910914	+	0.412597i	$0.864622\pi$
$728$	13.0744	−	9.49907i	0.484568	−	0.352059i
$729$	−8.80810	−	27.1086i	−0.326226	−	1.00402i
$730$	−8.67272	+	26.6919i	−0.320992	+	0.987911i
$731$	12.5182	+	9.09503i	0.463003	+	0.336392i
$732$	4.38504	+	3.18592i	0.162076	+	0.117755i
$733$	0.206407	−	0.635255i	0.00762382	−	0.0234637i	−0.947172	−	0.320725i	$-0.896073\pi$
$733$	0.206407	−	0.635255i	0.00762382	−	0.0234637i	0.954796	+	0.297262i	$0.0960734\pi$
$734$	−27.8152	−	85.6064i	−1.02668	−	3.15979i
$735$	−5.22299	+	3.79472i	−0.192653	+	0.139971i
$736$	−36.1730			−1.33335
$737$		0			0
$738$	−39.7699			−1.46395
$739$	30.8186	−	22.3911i	1.13368	−	0.823668i	0.147456	−	0.989069i	$-0.452892\pi$
$739$	30.8186	−	22.3911i	1.13368	−	0.823668i	0.986227	+	0.165400i	$0.0528916\pi$
$740$	−2.52816	−	7.78088i	−0.0929371	−	0.286031i
$741$	−2.11288	+	6.50278i	−0.0776187	+	0.238886i
$742$	12.5801	+	9.14001i	0.461832	+	0.335540i
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	0.0159622	−	0.999873i	$-0.494919\pi$
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	−0.946003	+	0.324159i	$0.894919\pi$
$744$	−16.6464	+	51.2324i	−0.610287	+	1.87827i
$745$	−0.721140	−	2.21944i	−0.0264205	−	0.0813140i
$746$	−24.7860	+	18.0081i	−0.907480	+	0.659323i
$747$	−33.4554			−1.22407
$748$		0			0
$749$	32.6754			1.19393
$750$	−5.03801	+	3.66033i	−0.183962	+	0.133656i
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	−0.908318	−	0.418280i	$-0.862633\pi$
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	0.488986	−	0.872292i	$-0.337367\pi$
$752$	−14.4022	+	44.3255i	−0.525196	+	1.61639i
$753$	−24.3498	−	17.6912i	−0.887358	−	0.644703i
$754$	−1.61215	−	1.17129i	−0.0587110	−	0.0426560i
$755$	1.21718	−	3.74609i	0.0442976	−	0.136334i
$756$	0.591564	+	1.82065i	0.0215150	+	0.0662162i
$757$	−5.40478	+	3.92680i	−0.196440	+	0.142722i	−0.681657	−	0.731672i	$-0.738741\pi$
$757$	−5.40478	+	3.92680i	−0.196440	+	0.142722i	0.485217	+	0.874394i	$0.338741\pi$
$758$	−18.0355			−0.655079
$759$		0			0
$760$	12.8890			0.467533
$761$	−18.5213	+	13.4565i	−0.671398	+	0.487799i	−0.870493	−	0.492181i	$-0.836200\pi$
$761$	−18.5213	+	13.4565i	−0.671398	+	0.487799i	0.199095	+	0.979980i	$0.436200\pi$
$762$	−36.2434	−	111.546i	−1.31296	−	4.04087i
$763$	7.44425	−	22.9110i	0.269500	−	0.829435i
$764$	−0.0882966	−	0.0641512i	−0.00319446	−	0.00232091i
$765$	−7.46506	−	5.42368i	−0.269900	−	0.196094i
$766$	−12.4530	+	38.3265i	−0.449947	+	1.38479i
$767$	2.58570	+	7.95797i	0.0933643	+	0.287346i
$768$	−62.0709	+	45.0971i	−2.23979	+	1.62730i
$769$	13.1946			0.475808			0.237904	−	0.971289i	$-0.423540\pi$
$769$	13.1946			0.475808			0.237904	+	0.971289i	$0.423540\pi$
$770$		0			0
$771$	14.5440			0.523788
$772$	5.15575	−	3.74587i	0.185560	−	0.134817i
$773$	−3.83827	−	11.8130i	−0.138053	−	0.424883i	0.857999	−	0.513651i	$-0.171707\pi$
$773$	−3.83827	−	11.8130i	−0.138053	−	0.424883i	−0.996052	+	0.0887673i	$0.971707\pi$
$774$	12.4485	−	38.3124i	0.447451	−	1.37711i
$775$	2.94887	+	2.14248i	0.105927	+	0.0769602i
$776$	−1.70447	−	1.23837i	−0.0611869	−	0.0444549i
$777$	−2.98538	+	9.18807i	−0.107100	+	0.329620i
$778$	19.5735	+	60.2412i	0.701746	+	2.15975i
$779$	8.88815	−	6.45762i	0.318451	−	0.231368i
$780$	13.8993			0.497675
$781$		0			0
$782$	−66.2932			−2.37064
$783$	0.103633	−	0.0752938i	0.00370354	−	0.00269078i
$784$	−5.15881	−	15.8772i	−0.184243	−	0.567042i
$785$	−1.50834	+	4.64218i	−0.0538348	+	0.165686i
$786$	−101.262	−	73.5714i	−3.61191	−	2.62420i
$787$	17.3818	+	12.6286i	0.619595	+	0.450162i	0.852780	−	0.522270i	$-0.174915\pi$
$787$	17.3818	+	12.6286i	0.619595	+	0.450162i	−0.233185	+	0.972432i	$0.574915\pi$
$788$	−30.6805	+	94.4247i	−1.09295	+	3.36374i
$789$	−16.5643	−	50.9798i	−0.589706	−	1.81493i
$790$	−10.9453	+	7.95221i	−0.389416	+	0.282927i
$791$	−18.9426			−0.673520
$792$		0			0
$793$	−0.647384			−0.0229893
$794$	7.30130	−	5.30471i	0.259114	−	0.188257i
$795$	2.24273	+	6.90242i	0.0795416	+	0.244804i
$796$	−8.95753	+	27.5685i	−0.317491	+	0.977138i
$797$	−1.72264	−	1.25157i	−0.0610191	−	0.0443330i	0.556858	−	0.830608i	$-0.312007\pi$
$797$	−1.72264	−	1.25157i	−0.0610191	−	0.0443330i	−0.617877	+	0.786275i	$0.712007\pi$
$798$	−22.6901	−	16.4853i	−0.803219	−	0.583573i
$799$	−6.75393	+	20.7864i	−0.238937	+	0.735372i
$800$	−1.27330	−	3.91881i	−0.0450179	−	0.138551i
$801$	10.7895	−	7.83902i	0.381228	−	0.276978i
$802$	−72.9179			−2.57482
$803$		0			0
$804$	84.2470			2.97116
$805$	14.8686	−	10.8026i	0.524048	−	0.380743i
$806$	−3.66378	−	11.2760i	−0.129051	−	0.397179i
$807$	3.44887	−	10.6145i	0.121406	−	0.373649i
$808$	76.0957	+	55.2868i	2.67704	+	1.94498i
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	0.508906	−	0.860822i	$-0.330050\pi$
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	−0.661430	+	0.750007i	$0.730050\pi$
$810$	6.81710	−	20.9809i	0.239528	−	0.737193i
$811$	−6.05047	−	18.6214i	−0.212461	−	0.653887i	−0.999324	−	0.0367600i	$-0.988296\pi$
$811$	−6.05047	−	18.6214i	−0.212461	−	0.653887i	0.786863	−	0.617127i	$-0.211704\pi$
$812$	4.53766	−	3.29681i	0.159241	−	0.115695i
$813$	−53.6781			−1.88257
$814$		0			0
$815$	−7.03572			−0.246450
$816$	38.0768	−	27.6644i	1.33295	−	0.968448i
$817$	3.43887	+	10.5837i	0.120311	+	0.370278i
$818$	7.50402	−	23.0950i	0.262372	−	0.807497i
$819$	−6.73170	−	4.89086i	−0.235224	−	0.170901i
$820$	−18.0681	−	13.1272i	−0.630964	−	0.458422i
$821$	5.14095	−	15.8222i	0.179420	−	0.552199i	−0.820387	−	0.571808i	$-0.806242\pi$
$821$	5.14095	−	15.8222i	0.179420	−	0.552199i	0.999808	+	0.0196092i	$0.00624219\pi$
$822$	−34.5829	−	106.435i	−1.20622	−	3.71236i
$823$	14.7993	−	10.7523i	0.515870	−	0.374801i	−0.299176	−	0.954198i	$-0.596712\pi$
$823$	14.7993	−	10.7523i	0.515870	−	0.374801i	0.815046	+	0.579397i	$0.196712\pi$
$824$	−40.0210			−1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.975830	−	0.218530i	$-0.929874\pi$
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.0937136	+	0.995599i	$0.529874\pi$
$828$	36.5967	+	112.633i	1.27182	+	3.91427i
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	−0.141389	−	0.989954i	$-0.545157\pi$
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	0.696267	−	0.717783i	$-0.254843\pi$
$830$	−22.1504	−	16.0932i	−0.768851	−	0.558603i
$831$	26.0122	+	18.8990i	0.902353	+	0.655598i
$832$	0.937652	−	2.88580i	0.0325072	−	0.100047i
$833$	−2.41922	−	7.44560i	−0.0838210	−	0.257975i
$834$	84.9564	−	61.7244i	2.94180	−	2.13734i
$835$	−10.7195			−0.370963
$836$		0			0
$837$	0.762151			0.0263438
$838$	−62.6065	+	45.4863i	−2.16271	+	1.57130i
$839$	11.9288	+	36.7132i	0.411829	+	1.26748i	0.915056	+	0.403326i	$0.132146\pi$
$839$	11.9288	+	36.7132i	0.411829	+	1.26748i	−0.503227	+	0.864154i	$0.667854\pi$
$840$	−9.56086	+	29.4253i	−0.329881	+	1.01527i
$841$	23.1579	+	16.8252i	0.798547	+	0.580178i
$842$	−14.1938	−	10.3124i	−0.489151	−	0.355389i
$843$	7.15428	−	22.0186i	0.246406	−	0.758361i
$844$	−7.64568	−	23.5310i	−0.263175	−	0.809969i
$845$	9.17416	−	6.66541i	0.315601	−	0.229297i
$846$	56.9013			1.95631
$847$		0			0
$848$	−18.7672			−0.644470
$849$	−27.8184	+	20.2113i	−0.954726	+	0.693649i
$850$	−2.33354	−	7.18190i	−0.0800398	−	0.246337i
$851$	−5.07504	+	15.6194i	−0.173970	+	0.535425i
$852$	−98.6551	−	71.6771i	−3.37987	−	2.45562i
$853$	27.4303	+	19.9293i	0.939197	+	0.682366i	0.948227	−	0.317593i	$-0.102874\pi$
$853$	27.4303	+	19.9293i	0.939197	+	0.682366i	−0.00903033	+	0.999959i	$0.502874\pi$
$854$	0.820596	−	2.52553i	0.0280802	−	0.0864220i
$855$	−2.05072	−	6.31146i	−0.0701331	−	0.215847i
$856$	−75.6523	+	54.9646i	−2.58574	+	1.87865i
$857$	56.7117			1.93723			0.968617	−	0.248558i	$-0.0799568\pi$
$857$	56.7117			1.93723			0.968617	+	0.248558i	$0.0799568\pi$
$858$		0			0
$859$	−25.7505			−0.878597			−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505			−0.878597			−0.439298	+	0.898341i	$0.644773\pi$
$860$	18.3017	−	13.2969i	0.624082	−	0.453422i
$861$	8.14951	+	25.0816i	0.277735	+	0.854779i
$862$	−2.52291	+	7.76473i	−0.0859308	+	0.264468i
$863$	−28.9345	−	21.0222i	−0.984942	−	0.715603i	−0.0261347	−	0.999658i	$-0.508320\pi$
$863$	−28.9345	−	21.0222i	−0.984942	−	0.715603i	−0.958808	+	0.284056i	$0.908320\pi$
$864$	−0.697025	−	0.506418i	−0.0237133	−	0.0172287i
$865$	−2.59940	+	8.00012i	−0.0883821	+	0.272012i
$866$	23.7093	+	72.9698i	0.805676	+	2.47962i
$867$	−16.0696	+	11.6752i	−0.545751	+	0.396511i
$868$	33.3714			1.13270
$869$		0			0
$870$	3.81504			0.129342
$871$	−8.14064	+	5.91452i	−0.275835	+	0.200406i
$872$	21.3041	+	65.5674i	0.721449	+	2.22039i
$873$	−0.335211	+	1.03167i	−0.0113452	+	0.0349169i
$874$	−38.5722	−	28.0244i	−1.30473	−	0.947938i
$875$	1.69369	+	1.23053i	0.0572570	+	0.0415996i
$876$	−37.0595	+	114.057i	−1.25212	+	3.85364i
$877$	−5.34913	−	16.4629i	−0.180627	−	0.555913i	0.819218	−	0.573482i	$-0.194408\pi$
$877$	−5.34913	−	16.4629i	−0.180627	−	0.555913i	−0.999846	+	0.0175682i	$0.994408\pi$
$878$	−74.6105	+	54.2077i	−2.51798	+	1.82942i
$879$	75.1614			2.53513
$880$		0			0
$881$	−4.15822			−0.140094			−0.0700470	−	0.997544i	$-0.522315\pi$
$881$	−4.15822			−0.140094			−0.0700470	+	0.997544i	$0.522315\pi$
$882$	−16.4892	+	11.9801i	−0.555219	+	0.403391i
$883$	−12.7533	−	39.2505i	−0.429182	−	1.32088i	−0.898933	−	0.438086i	$-0.855656\pi$
$883$	−12.7533	−	39.2505i	−0.429182	−	1.32088i	0.469751	−	0.882799i	$-0.344344\pi$
$884$	−5.20843	+	16.0299i	−0.175179	+	0.539144i
$885$	−12.9600	−	9.41601i	−0.435647	−	0.316516i
$886$	−4.41467	−	3.20744i	−0.148314	−	0.107756i
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	0.658996	+	0.752146i	$0.270981\pi$
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	−0.975240	+	0.221151i	$0.929019\pi$
$888$	−8.54364	−	26.2946i	−0.286706	−	0.882390i
$889$	−31.8990	+	23.1760i	−1.06986	+	0.777298i
$890$	10.9144			0.365852
$891$		0			0
$892$	34.4803			1.15449
$893$	−12.7168	+	9.23933i	−0.425553	+	0.309182i
$894$	−4.49077	−	13.8212i	−0.150194	−	0.462249i
$895$	6.50062	−	20.0069i	0.217292	−	0.668756i
$896$	24.0270	+	17.4566i	0.802684	+	0.583184i
$897$	−22.5728	−	16.4001i	−0.753684	−	0.547583i
$898$	8.98831	−	27.6632i	0.299944	−	0.923132i
$899$	−0.690047	−	2.12375i	−0.0230144	−	0.0708309i
$900$	−10.9139	+	7.92944i	−0.363798	+	0.264315i
$901$	−8.80090			−0.293200
$902$		0			0
$903$	−26.7134			−0.888965
$904$	43.8570	−	31.8640i	1.45866	−	1.05978i
$905$	−0.538649	−	1.65779i	−0.0179053	−	0.0551068i
$906$	7.57976	−	23.3281i	0.251821	−	0.775024i
$907$	−9.13337	−	6.63578i	−0.303269	−	0.220338i	0.425734	−	0.904848i	$-0.360016\pi$
$907$	−9.13337	−	6.63578i	−0.303269	−	0.220338i	−0.729003	+	0.684511i	$0.760016\pi$
$908$	−39.6660	−	28.8191i	−1.31636	−	0.956394i
$909$	14.9654	−	46.0589i	0.496372	−	1.52768i
$910$	−2.10429	−	6.47635i	−0.0697567	−	0.214689i
$911$	−40.9417	+	29.7459i	−1.35646	+	0.985525i	−0.357797	+	0.933799i	$0.616472\pi$
$911$	−40.9417	+	29.7459i	−1.35646	+	0.985525i	−0.998661	+	0.0517251i	$0.983528\pi$
$912$	33.8494			1.12086
$913$		0			0
$914$	−40.2193			−1.33034
$915$	1.00270	−	0.728506i	0.0331483	−	0.0240837i
$916$	36.4753	+	112.259i	1.20518	+	3.70915i
$917$	−13.0031	+	40.0193i	−0.429399	+	1.32156i
$918$	−1.27742	−	0.928099i	−0.0421611	−	0.0306318i
$919$	−22.0198	−	15.9983i	−0.726366	−	0.527736i	0.162046	−	0.986783i	$-0.448191\pi$
$919$	−22.0198	−	15.9983i	−0.726366	−	0.527736i	−0.888412	+	0.459048i	$0.848191\pi$
$920$	−16.2531	+	50.0219i	−0.535849	+	1.64917i
$921$	3.87693	+	11.9320i	0.127749	+	0.393172i
$922$	−3.11518	+	2.26331i	−0.102593	+	0.0745381i
$923$	14.5649			0.479410
$924$		0			0
$925$	−1.87077			−0.0615106
$926$	29.0167	−	21.0819i	0.953547	−	0.692793i
$927$	6.36759	+	19.5974i	0.209139	+	0.643664i
$928$	−0.780061	+	2.40078i	−0.0256068	+	0.0788095i
$929$	18.7776	+	13.6427i	0.616073	+	0.447603i	0.851548	−	0.524277i	$-0.175664\pi$
$929$	18.7776	+	13.6427i	0.616073	+	0.447603i	−0.235475	+	0.971880i	$0.575664\pi$
$930$	18.3636	+	13.3419i	0.602166	+	0.437499i
$931$	1.73990	−	5.35485i	0.0570228	−	0.175498i
$932$	14.6637	+	45.1303i	0.480326	+	1.47829i
$933$	27.4625	−	19.9527i	0.899082	−	0.653221i
$934$	15.2910			0.500336
$935$		0			0
$936$	23.8128			0.778344
$937$	−34.1500	+	24.8114i	−1.11563	+	0.810554i	−0.983541	−	0.180684i	$-0.942169\pi$
$937$	−34.1500	+	24.8114i	−1.11563	+	0.810554i	−0.132090	+	0.991238i	$0.542169\pi$
$938$	−12.7546	−	39.2547i	−0.416453	−	1.28171i
$939$	−12.1601	+	37.4251i	−0.396831	+	1.22132i
$940$	25.8511	+	18.7819i	0.843171	+	0.612600i
$941$	−23.6336	−	17.1708i	−0.770435	−	0.559754i	0.131658	−	0.991295i	$-0.457970\pi$
$941$	−23.6336	−	17.1708i	−0.770435	−	0.559754i	−0.902093	+	0.431542i	$0.857970\pi$
$942$	−9.39289	+	28.9083i	−0.306037	+	0.941885i
$943$	13.8539	+	42.6378i	0.451144	+	1.38848i
$944$	33.5128	−	24.3485i	1.09075	−	0.792476i
$945$	0.437741			0.0142397
$946$		0			0
$947$	9.63809			0.313196			0.156598	−	0.987662i	$-0.449947\pi$
$947$	9.63809			0.313196			0.156598	+	0.987662i	$0.449947\pi$
$948$	−46.7704	+	33.9807i	−1.51903	+	1.10364i
$949$	−4.42634	−	13.6229i	−0.143685	−	0.442218i
$950$	1.67828	−	5.16520i	0.0544505	−	0.167581i
$951$	21.3680	+	15.5247i	0.692904	+	0.503424i
$952$	−30.3532	−	22.0529i	−0.983752	−	0.714738i
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	−0.973783	−	0.227479i	$-0.926952\pi$
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	0.921516	+	0.388341i	$0.126952\pi$
$954$	7.08039	+	21.7912i	0.229236	+	0.705517i
$955$	−0.0201903	+	0.0146691i	−0.000653342	+	0.000474681i
$956$	50.1446			1.62179
$957$		0			0
$958$	−44.4529			−1.43621
$959$	−30.4376	+	22.1142i	−0.982882	+	0.714106i
$960$	1.79512	+	5.52482i	0.0579373	+	0.178313i
$961$	−5.47390	+	16.8469i	−0.176577	+	0.543450i
$962$	4.92298	+	3.57675i	0.158723	+	0.115319i
$963$	38.9517	+	28.3001i	1.25520	+	0.911956i
$964$	−17.2361	+	53.0471i	−0.555136	+	1.70853i
$965$	−0.450314	−	1.38592i	−0.0144961	−	0.0446145i
$966$	92.5913	−	67.2715i	2.97908	−	2.16443i
$967$	−38.4583			−1.23674			−0.618368	−	0.785889i	$-0.712206\pi$
$967$	−38.4583			−1.23674			−0.618368	+	0.785889i	$0.712206\pi$
$968$		0			0
$969$	15.8737			0.509935
$970$	−0.718209	+	0.521810i	−0.0230603	+	0.0167543i
$971$	13.4928	+	41.5267i	0.433006	+	1.33265i	0.895116	+	0.445832i	$0.147092\pi$
$971$	13.4928	+	41.5267i	0.433006	+	1.33265i	−0.462111	+	0.886822i	$0.652908\pi$
$972$	29.9779	−	92.2625i	0.961542	−	2.95932i
$973$	−28.5608	−	20.7506i	−0.915616	−	0.665234i
$974$	13.8543	+	10.0658i	0.443921	+	0.322527i
$975$	0.982141	−	3.02272i	0.0314537	−	0.0968045i
$976$	0.990380	+	3.04808i	0.0317013	+	0.0975665i
$977$	9.50330	−	6.90455i	0.304038	−	0.220896i	−0.425296	−	0.905054i	$-0.639830\pi$
$977$	9.50330	−	6.90455i	0.304038	−	0.220896i	0.729334	+	0.684158i	$0.239830\pi$
$978$	−43.8137			−1.40101
$979$		0			0
$980$	−11.4457			−0.365618
$981$	28.7173	−	20.8643i	0.916872	−	0.666147i
$982$	0.404582	+	1.24518i	0.0129107	+	0.0397351i
$983$	2.88989	−	8.89417i	0.0921733	−	0.283680i	−0.894333	−	0.447401i	$-0.852350\pi$
$983$	2.88989	−	8.89417i	0.0921733	−	0.283680i	0.986507	+	0.163721i	$0.0523497\pi$
$984$	−61.0590	−	44.3620i	−1.94649	−	1.41421i
$985$	18.3669	+	13.3443i	0.585218	+	0.425186i
$986$	−1.42960	+	4.39985i	−0.0455276	+	0.140120i
$987$	−11.6600	−	35.8859i	−0.371143	−	1.14226i
$988$	−9.80687	+	7.12510i	−0.311998	+	0.226680i
$989$	−45.4117			−1.44401
$990$		0			0
$991$	−32.3450			−1.02747			−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450			−1.02747			−0.513737	+	0.857948i	$0.671739\pi$
$992$	−12.1508	+	8.82806i	−0.385788	+	0.280291i
$993$	6.74310	+	20.7531i	0.213986	+	0.658581i
$994$	−18.4619	+	56.8197i	−0.585574	+	1.80221i
$995$	5.36244	+	3.89604i	0.170001	+	0.123513i
$996$	−94.6510	−	68.7679i	−2.99913	−	2.17900i
$997$	8.99777	−	27.6923i	0.284962	−	0.877023i	−0.701448	−	0.712721i	$-0.747463\pi$
$997$	8.99777	−	27.6923i	0.284962	−	0.877023i	0.986410	−	0.164302i	$-0.0525373\pi$
$998$	−17.0540	−	52.4869i	−0.539836	−	1.66144i
$999$	−0.316462	+	0.229923i	−0.0100124	+	0.00727444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.n.366.2		8
11.2	odd	10		605.2.a.l.1.4		4
11.3	even	5		605.2.g.g.511.1		8
11.4	even	5	inner	605.2.g.n.81.2		8
11.5	even	5		605.2.g.g.251.1		8
11.6	odd	10		605.2.g.j.251.2		8
11.7	odd	10		55.2.g.a.26.1	✓	8
11.8	odd	10		605.2.g.j.511.2		8
11.9	even	5		605.2.a.i.1.1		4
11.10	odd	2		55.2.g.a.36.1	yes	8
33.2	even	10		5445.2.a.bg.1.1		4
33.20	odd	10		5445.2.a.bu.1.4		4
33.29	even	10		495.2.n.f.136.2		8
33.32	even	2		495.2.n.f.91.2		8
44.7	even	10		880.2.bo.e.81.2		8
44.31	odd	10		9680.2.a.cv.1.4		4
44.35	even	10		9680.2.a.cs.1.4		4
44.43	even	2		880.2.bo.e.641.2		8
55.7	even	20		275.2.z.b.224.4		16
55.9	even	10		3025.2.a.be.1.4		4
55.18	even	20		275.2.z.b.224.1		16
55.24	odd	10		3025.2.a.v.1.1		4
55.29	odd	10		275.2.h.b.26.2		8
55.32	even	4		275.2.z.b.124.1		16
55.43	even	4		275.2.z.b.124.4		16
55.54	odd	2		275.2.h.b.201.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	11.7	odd	10
55.2.g.a.36.1	yes	8	11.10	odd	2
275.2.h.b.26.2		8	55.29	odd	10
275.2.h.b.201.2		8	55.54	odd	2
275.2.z.b.124.1		16	55.32	even	4
275.2.z.b.124.4		16	55.43	even	4
275.2.z.b.224.1		16	55.18	even	20
275.2.z.b.224.4		16	55.7	even	20
495.2.n.f.91.2		8	33.32	even	2
495.2.n.f.136.2		8	33.29	even	10
605.2.a.i.1.1		4	11.9	even	5
605.2.a.l.1.4		4	11.2	odd	10
605.2.g.g.251.1		8	11.5	even	5
605.2.g.g.511.1		8	11.3	even	5
605.2.g.j.251.2		8	11.6	odd	10
605.2.g.j.511.2		8	11.8	odd	10
605.2.g.n.81.2		8	11.4	even	5	inner
605.2.g.n.366.2		8	1.1	even	1	trivial
880.2.bo.e.81.2		8	44.7	even	10
880.2.bo.e.641.2		8	44.43	even	2
3025.2.a.v.1.1		4	55.24	odd	10
3025.2.a.be.1.4		4	55.9	even	10
5445.2.a.bg.1.1		4	33.2	even	10
5445.2.a.bu.1.4		4	33.20	odd	10
9680.2.a.cs.1.4		4	44.35	even	10
9680.2.a.cv.1.4		4	44.31	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.04238 - 1.48388i) q^{2} +(-0.762262 - 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-5.03801 - 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +O(q^{10})\)	\(q+(2.04238 - 1.48388i) q^{2} +(-0.762262 - 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-5.03801 - 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} -2.52452 q^{10} -10.7876 q^{12} +(1.04238 - 0.757336i) q^{13} +(1.63319 + 5.02644i) q^{14} +(-0.762262 + 2.34600i) q^{15} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(-2.40649 + 7.40641i) q^{18} +(-0.664789 - 2.04601i) q^{19} +(-3.53801 + 2.57052i) q^{20} +5.16413 q^{21} +8.77882 q^{23} +(-11.9563 + 8.68677i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.00515 - 3.09354i) q^{26} +(0.169161 + 0.122903i) q^{27} +(7.40686 + 5.38140i) q^{28} +(0.189313 - 0.582646i) q^{29} +(1.92435 + 5.92254i) q^{30} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} -7.55150 q^{34} +(1.69369 - 1.23053i) q^{35} +(4.16875 + 12.8301i) q^{36} +(-0.578100 + 1.77921i) q^{37} +(-4.39378 - 3.19227i) q^{38} +(-2.57128 - 1.86814i) q^{39} +(-1.85140 + 5.69802i) q^{40} +(1.57810 + 4.85689i) q^{41} +(10.5471 - 7.66294i) q^{42} -5.17287 q^{43} +3.08477 q^{45} +(17.9297 - 13.0267i) q^{46} +(-2.25789 - 6.94907i) q^{47} +(-4.86218 + 14.9643i) q^{48} +(2.11737 + 1.53836i) q^{49} +(2.04238 + 1.48388i) q^{50} +(-2.28012 + 7.01749i) q^{51} +(-1.74122 - 5.35892i) q^{52} +(2.38030 - 1.72939i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(-4.29320 + 3.11919i) q^{57} +(-0.477925 - 1.47090i) q^{58} +(-2.00682 + 6.17636i) q^{59} +(8.72732 + 6.34077i) q^{60} +(-0.406490 - 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(-1.99563 - 6.14191i) q^{63} +(1.90523 - 1.38423i) q^{64} -1.28846 q^{65} -7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(-6.69176 - 20.5951i) q^{69} +(1.63319 - 5.02644i) q^{70} +(9.14526 + 6.64442i) q^{71} +(14.9519 + 10.8632i) q^{72} +(3.43539 - 10.5730i) q^{73} +(1.45943 + 4.49166i) q^{74} +(1.99563 - 1.44991i) q^{75} -9.40812 q^{76} -8.02363 q^{78} +(4.33558 - 3.14998i) q^{79} +(1.97110 + 6.06643i) q^{80} +(-2.70035 + 8.31082i) q^{81} +(10.4301 + 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(6.97880 - 21.4785i) q^{84} +(0.924349 + 2.84485i) q^{85} +(-10.5650 + 7.67591i) q^{86} -1.51119 q^{87} -4.32336 q^{89} +(6.30027 - 4.57742i) q^{90} +(0.833541 + 2.56538i) q^{91} +(11.8637 - 36.5127i) q^{92} +(-7.27408 - 5.28493i) q^{93} +(-14.9230 - 10.8422i) q^{94} +(-0.664789 + 2.04601i) q^{95} +(3.14089 + 9.66666i) q^{96} +(0.284493 - 0.206696i) q^{97} +6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

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