LMFDB - Embedded newform 525.2.n.d.106.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			106.6
Character	$\chi$	$=$	525.106
Dual form			525.2.n.d.421.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.276260 + 0.850242i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.971442 - 0.705794i) q^{4} +(-1.96138 - 1.07378i) q^{5} +(-0.723259 - 0.525478i) q^{6} -1.00000 q^{7} +(2.31498 + 1.68193i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.276260 + 0.850242i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.971442 - 0.705794i) q^{4} +(-1.96138 - 1.07378i) q^{5} +(-0.723259 - 0.525478i) q^{6} -1.00000 q^{7} +(2.31498 + 1.68193i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.371124 - 1.96429i) q^{10} +(1.94869 + 5.99744i) q^{11} +(-0.371058 + 1.14200i) q^{12} +(0.740817 - 2.28000i) q^{13} +(-0.276260 - 0.850242i) q^{14} +(2.21794 - 0.284160i) q^{15} +(-0.0483972 + 0.148951i) q^{16} +(2.03581 + 1.47910i) q^{17} +0.893997 q^{18} +(4.58302 + 3.32976i) q^{19} +(-2.66323 + 0.341210i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-4.56093 + 3.31371i) q^{22} +(1.81286 + 5.57941i) q^{23} -2.86148 q^{24} +(2.69398 + 4.21218i) q^{25} +2.14321 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.971442 + 0.705794i) q^{28} +(5.81870 - 4.22754i) q^{29} +(0.854333 + 1.80728i) q^{30} +(-0.990652 - 0.719751i) q^{31} +5.58294 q^{32} +(-5.10172 - 3.70662i) q^{33} +(-0.695180 + 2.13954i) q^{34} +(1.96138 + 1.07378i) q^{35} +(-0.371058 - 1.14200i) q^{36} +(0.386855 - 1.19062i) q^{37} +(-1.56499 + 4.81656i) q^{38} +(0.740817 + 2.28000i) q^{39} +(-2.73452 - 5.78469i) q^{40} +(2.27327 - 6.99639i) q^{41} +(0.723259 + 0.525478i) q^{42} -10.5351 q^{43} +(6.12599 + 4.45079i) q^{44} +(-1.62733 + 1.53356i) q^{45} +(-4.24303 + 3.08274i) q^{46} +(-8.54769 + 6.21026i) q^{47} +(-0.0483972 - 0.148951i) q^{48} +1.00000 q^{49} +(-2.83713 + 3.45420i) q^{50} -2.51640 q^{51} +(-0.889550 - 2.73775i) q^{52} +(-5.42642 + 3.94252i) q^{53} +(-0.723259 + 0.525478i) q^{54} +(2.61784 - 13.8557i) q^{55} +(-2.31498 - 1.68193i) q^{56} -5.66492 q^{57} +(5.20191 + 3.77941i) q^{58} +(1.81147 - 5.57512i) q^{59} +(1.95404 - 1.84145i) q^{60} +(-0.237051 - 0.729567i) q^{61} +(0.338285 - 1.04113i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(1.63914 + 5.04475i) q^{64} +(-3.90124 + 3.67646i) q^{65} +(1.74212 - 5.36169i) q^{66} +(-2.45298 - 1.78220i) q^{67} +3.02161 q^{68} +(-4.74613 - 3.44827i) q^{69} +(-0.371124 + 1.96429i) q^{70} +(-4.50020 + 3.26959i) q^{71} +(2.31498 - 1.68193i) q^{72} +(-1.19250 - 3.67013i) q^{73} +1.11919 q^{74} +(-4.65534 - 1.82424i) q^{75} +6.80226 q^{76} +(-1.94869 - 5.99744i) q^{77} +(-1.73389 + 1.25975i) q^{78} +(13.5956 - 9.87777i) q^{79} +(0.254866 - 0.240181i) q^{80} +(-0.809017 - 0.587785i) q^{81} +6.57664 q^{82} +(6.91824 + 5.02639i) q^{83} +(0.371058 - 1.14200i) q^{84} +(-2.40475 - 5.08708i) q^{85} +(-2.91043 - 8.95739i) q^{86} +(-2.22255 + 6.84030i) q^{87} +(-5.57612 + 17.1615i) q^{88} +(4.40854 + 13.5681i) q^{89} +(-1.75346 - 0.959958i) q^{90} +(-0.740817 + 2.28000i) q^{91} +(5.69901 + 4.14057i) q^{92} +1.22451 q^{93} +(-7.64161 - 5.55195i) q^{94} +(-5.41359 - 11.4521i) q^{95} +(-4.51670 + 3.28157i) q^{96} +(4.66125 - 3.38660i) q^{97} +(0.276260 + 0.850242i) q^{98} +6.30608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.276260	+	0.850242i	0.195346	+	0.601212i	0.999972	+	0.00743102i	$0.00236539\pi$
$2$	0.276260	+	0.850242i	0.195346	+	0.601212i	−0.804627	+	0.593781i	$0.797635\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.971442	−	0.705794i	0.485721	−	0.352897i
$5$	−1.96138	−	1.07378i	−0.877154	−	0.480210i
$5$	−1.96138	−	1.07378i	−0.877154	−	0.480210i
$6$	−0.723259	−	0.525478i	−0.295269	−	0.214526i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.31498	+	1.68193i	0.818471	+	0.594654i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.371124	−	1.96429i	0.117360	−	0.621162i
$11$	1.94869	+	5.99744i	0.587551	+	1.80830i	0.588776	+	0.808296i	$0.299610\pi$
$11$	1.94869	+	5.99744i	0.587551	+	1.80830i	−0.00122570	+	0.999999i	$0.500390\pi$
$12$	−0.371058	+	1.14200i	−0.107115	+	0.329667i
$13$	0.740817	−	2.28000i	0.205466	−	0.632358i	−0.794228	−	0.607619i	$-0.792125\pi$
$13$	0.740817	−	2.28000i	0.205466	−	0.632358i	0.999694	−	0.0247387i	$-0.00787539\pi$
$14$	−0.276260	−	0.850242i	−0.0738337	−	0.227237i
$15$	2.21794	−	0.284160i	0.572669	−	0.0733697i
$16$	−0.0483972	+	0.148951i	−0.0120993	+	0.0372378i
$17$	2.03581	+	1.47910i	0.493756	+	0.358734i	0.806627	−	0.591061i	$-0.201291\pi$
$17$	2.03581	+	1.47910i	0.493756	+	0.358734i	−0.312871	+	0.949796i	$0.601291\pi$
$18$	0.893997			0.210717
$19$	4.58302	+	3.32976i	1.05142	+	0.763899i	0.972481	−	0.232981i	$-0.0748479\pi$
$19$	4.58302	+	3.32976i	1.05142	+	0.763899i	0.0789353	+	0.996880i	$0.474848\pi$
$20$	−2.66323	+	0.341210i	−0.595517	+	0.0762969i
$21$	0.809017	−	0.587785i	0.176542	−	0.128265i
$22$	−4.56093	+	3.31371i	−0.972393	+	0.706485i
$23$	1.81286	+	5.57941i	0.378008	+	1.16339i	0.941427	+	0.337217i	$0.109486\pi$
$23$	1.81286	+	5.57941i	0.378008	+	1.16339i	−0.563419	+	0.826171i	$0.690514\pi$
$24$	−2.86148			−0.584097
$25$	2.69398	+	4.21218i	0.538797	+	0.842436i
$26$	2.14321			0.420318
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.971442	+	0.705794i	−0.183585	+	0.133383i
$29$	5.81870	−	4.22754i	1.08051	−	0.785034i	0.102735	−	0.994709i	$-0.467241\pi$
$29$	5.81870	−	4.22754i	1.08051	−	0.785034i	0.977771	+	0.209675i	$0.0672406\pi$
$30$	0.854333	+	1.80728i	0.155979	+	0.329963i
$31$	−0.990652	−	0.719751i	−0.177926	−	0.129271i	0.495257	−	0.868746i	$-0.335074\pi$
$31$	−0.990652	−	0.719751i	−0.177926	−	0.129271i	−0.673184	+	0.739475i	$0.735074\pi$
$32$	5.58294			0.986934
$33$	−5.10172	−	3.70662i	−0.888096	−	0.645240i
$34$	−0.695180	+	2.13954i	−0.119222	+	0.366929i
$35$	1.96138	+	1.07378i	0.331533	+	0.181502i
$36$	−0.371058	−	1.14200i	−0.0618430	−	0.190333i
$37$	0.386855	−	1.19062i	0.0635986	−	0.195736i	−0.914208	−	0.405245i	$-0.867186\pi$
$37$	0.386855	−	1.19062i	0.0635986	−	0.195736i	0.977807	+	0.209508i	$0.0671864\pi$
$38$	−1.56499	+	4.81656i	−0.253875	+	0.781348i
$39$	0.740817	+	2.28000i	0.118626	+	0.365092i
$40$	−2.73452	−	5.78469i	−0.432366	−	0.914640i
$41$	2.27327	−	6.99639i	0.355025	−	1.09265i	−0.600971	−	0.799271i	$-0.705219\pi$
$41$	2.27327	−	6.99639i	0.355025	−	1.09265i	0.955995	−	0.293382i	$-0.0947808\pi$
$42$	0.723259	+	0.525478i	0.111601	+	0.0810831i
$43$	−10.5351			−1.60659			−0.803294	−	0.595582i	$-0.796921\pi$
$43$	−10.5351			−1.60659			−0.803294	+	0.595582i	$0.796921\pi$
$44$	6.12599	+	4.45079i	0.923528	+	0.670982i
$45$	−1.62733	+	1.53356i	−0.242587	+	0.228610i
$46$	−4.24303	+	3.08274i	−0.625600	+	0.454525i
$47$	−8.54769	+	6.21026i	−1.24681	+	0.905859i	−0.998032	−	0.0627016i	$-0.980028\pi$
$47$	−8.54769	+	6.21026i	−1.24681	+	0.905859i	−0.248776	+	0.968561i	$0.580028\pi$
$48$	−0.0483972	−	0.148951i	−0.00698554	−	0.0214993i
$49$	1.00000			0.142857
$50$	−2.83713	+	3.45420i	−0.401231	+	0.488497i
$51$	−2.51640			−0.352366
$52$	−0.889550	−	2.73775i	−0.123358	−	0.379658i
$53$	−5.42642	+	3.94252i	−0.745376	+	0.541547i	−0.894390	−	0.447288i	$-0.852390\pi$
$53$	−5.42642	+	3.94252i	−0.745376	+	0.541547i	0.149014	+	0.988835i	$0.452390\pi$
$54$	−0.723259	+	0.525478i	−0.0984231	+	0.0715086i
$55$	2.61784	−	13.8557i	0.352989	−	1.86830i
$56$	−2.31498	−	1.68193i	−0.309353	−	0.224758i
$57$	−5.66492			−0.750337
$58$	5.20191	+	3.77941i	0.683044	+	0.496260i
$59$	1.81147	−	5.57512i	0.235833	−	0.725819i	−0.761177	−	0.648544i	$-0.775378\pi$
$59$	1.81147	−	5.57512i	0.235833	−	0.725819i	0.997010	−	0.0772749i	$-0.0246219\pi$
$60$	1.95404	−	1.84145i	0.252266	−	0.237731i
$61$	−0.237051	−	0.729567i	−0.0303512	−	0.0934115i	0.934733	−	0.355350i	$-0.115638\pi$
$61$	−0.237051	−	0.729567i	−0.0303512	−	0.0934115i	−0.965085	+	0.261938i	$0.915638\pi$
$62$	0.338285	−	1.04113i	0.0429622	−	0.132224i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	1.63914	+	5.04475i	0.204893	+	0.630594i
$65$	−3.90124	+	3.67646i	−0.483890	+	0.456009i
$66$	1.74212	−	5.36169i	0.214440	−	0.659979i
$67$	−2.45298	−	1.78220i	−0.299680	−	0.217730i	0.427776	−	0.903885i	$-0.359297\pi$
$67$	−2.45298	−	1.78220i	−0.299680	−	0.217730i	−0.727456	+	0.686155i	$0.759297\pi$
$68$	3.02161			0.366424
$69$	−4.74613	−	3.44827i	−0.571367	−	0.415122i
$70$	−0.371124	+	1.96429i	−0.0443578	+	0.234777i
$71$	−4.50020	+	3.26959i	−0.534076	+	0.388029i	−0.821880	−	0.569660i	$-0.807075\pi$
$71$	−4.50020	+	3.26959i	−0.534076	+	0.388029i	0.287804	+	0.957689i	$0.407075\pi$
$72$	2.31498	−	1.68193i	0.272824	−	0.198218i
$73$	−1.19250	−	3.67013i	−0.139571	−	0.429556i	0.856702	−	0.515812i	$-0.172510\pi$
$73$	−1.19250	−	3.67013i	−0.139571	−	0.429556i	−0.996273	+	0.0862559i	$0.972510\pi$
$74$	1.11919			0.130103
$75$	−4.65534	−	1.82424i	−0.537552	−	0.210645i
$76$	6.80226			0.780273
$77$	−1.94869	−	5.99744i	−0.222073	−	0.683471i
$78$	−1.73389	+	1.25975i	−0.196325	+	0.142638i
$79$	13.5956	−	9.87777i	1.52962	−	1.11134i	0.573174	−	0.819434i	$-0.305712\pi$
$79$	13.5956	−	9.87777i	1.52962	−	1.11134i	0.956448	−	0.291902i	$-0.0942882\pi$
$80$	0.254866	−	0.240181i	0.0284949	−	0.0268531i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	6.57664			0.726268
$83$	6.91824	+	5.02639i	0.759375	+	0.551718i	0.898719	−	0.438526i	$-0.144499\pi$
$83$	6.91824	+	5.02639i	0.759375	+	0.551718i	−0.139343	+	0.990244i	$0.544499\pi$
$84$	0.371058	−	1.14200i	0.0404857	−	0.124602i
$85$	−2.40475	−	5.08708i	−0.260832	−	0.551772i
$86$	−2.91043	−	8.95739i	−0.313840	−	0.965900i
$87$	−2.22255	+	6.84030i	−0.238282	+	0.733357i
$88$	−5.57612	+	17.1615i	−0.594417	+	1.82943i
$89$	4.40854	+	13.5681i	0.467304	+	1.43821i	0.856061	+	0.516874i	$0.172905\pi$
$89$	4.40854	+	13.5681i	0.467304	+	1.43821i	−0.388757	+	0.921340i	$0.627095\pi$
$90$	−1.75346	−	0.959958i	−0.184831	−	0.101188i
$91$	−0.740817	+	2.28000i	−0.0776587	+	0.239009i
$92$	5.69901	+	4.14057i	0.594162	+	0.431684i
$93$	1.22451			0.126976
$94$	−7.64161	−	5.55195i	−0.788172	−	0.572640i
$95$	−5.41359	−	11.4521i	−0.555422	−	1.17496i
$96$	−4.51670	+	3.28157i	−0.460983	+	0.334924i
$97$	4.66125	−	3.38660i	0.473279	−	0.343857i	−0.325439	−	0.945563i	$-0.605512\pi$
$97$	4.66125	−	3.38660i	0.473279	−	0.343857i	0.798718	+	0.601706i	$0.205512\pi$
$98$	0.276260	+	0.850242i	0.0279065	+	0.0858874i
$99$	6.30608			0.633785
$100$	5.58998	+	2.19049i	0.558998	+	0.219049i
$101$	−16.8187			−1.67352			−0.836760	−	0.547571i	$-0.815553\pi$
$101$	−16.8187			−1.67352			−0.836760	+	0.547571i	$0.815553\pi$
$102$	−0.695180	−	2.13954i	−0.0688331	−	0.211847i
$103$	2.53020	−	1.83830i	0.249308	−	0.181133i	−0.456112	−	0.889922i	$-0.650758\pi$
$103$	2.53020	−	1.83830i	0.249308	−	0.181133i	0.705420	+	0.708789i	$0.250758\pi$
$104$	5.54979	−	4.03216i	0.544202	−	0.395386i
$105$	−2.21794	+	0.284160i	−0.216449	+	0.0277311i
$106$	−4.85120	−	3.52461i	−0.471190	−	0.342340i
$107$	1.50549			0.145541			0.0727705	−	0.997349i	$-0.476816\pi$
$107$	1.50549			0.145541			0.0727705	+	0.997349i	$0.476816\pi$
$108$	0.971442	+	0.705794i	0.0934771	+	0.0679151i
$109$	3.27528	−	10.0803i	0.313715	−	0.965516i	−0.662565	−	0.749005i	$-0.730532\pi$
$109$	3.27528	−	10.0803i	0.313715	−	0.965516i	0.976280	−	0.216512i	$-0.0694679\pi$
$110$	12.5039	−	1.60198i	1.19220	−	0.152743i
$111$	0.386855	+	1.19062i	0.0367186	+	0.113008i
$112$	0.0483972	−	0.148951i	0.00457311	−	0.0140746i
$113$	4.71945	−	14.5250i	0.443969	−	1.36640i	−0.439642	−	0.898173i	$-0.644895\pi$
$113$	4.71945	−	14.5250i	0.443969	−	1.36640i	0.883611	−	0.468223i	$-0.155105\pi$
$114$	−1.56499	−	4.81656i	−0.146575	−	0.451112i
$115$	2.43537	−	12.8899i	0.227100	−	1.20199i
$116$	2.66876	−	8.21361i	0.247789	−	0.762615i
$117$	−1.93948	−	1.40912i	−0.179305	−	0.130273i
$118$	5.24064			0.482440
$119$	−2.03581	−	1.47910i	−0.186622	−	0.135589i
$120$	5.61243	+	3.07260i	0.512343	+	0.280489i
$121$	−23.2727	+	16.9086i	−2.11570	+	1.53715i
$122$	0.554821	−	0.403101i	0.0502311	−	0.0364951i
$123$	2.27327	+	6.99639i	0.204974	+	0.630844i
$124$	−1.47036			−0.132042
$125$	−0.760954	−	11.1544i	−0.0680618	−	0.997681i
$126$	−0.893997			−0.0796436
$127$	−3.11640	−	9.59129i	−0.276536	−	0.851089i	−0.988809	−	0.149187i	$-0.952334\pi$
$127$	−3.11640	−	9.59129i	−0.276536	−	0.851089i	0.712273	−	0.701902i	$-0.247666\pi$
$128$	5.19696	−	3.77581i	0.459351	−	0.333738i
$129$	8.52308	−	6.19238i	0.750415	−	0.545209i
$130$	−4.20364	−	2.30134i	−0.368683	−	0.201841i
$131$	0.0894129	+	0.0649623i	0.00781204	+	0.00567578i	0.591684	−	0.806170i	$-0.298463\pi$
$131$	0.0894129	+	0.0649623i	0.00781204	+	0.00567578i	−0.583872	+	0.811845i	$0.698463\pi$
$132$	−7.57214			−0.659070
$133$	−4.58302	−	3.32976i	−0.397398	−	0.288727i
$134$	0.837636	−	2.57798i	0.0723608	−	0.222703i
$135$	0.415129	−	2.19720i	0.0357286	−	0.189104i
$136$	2.22511	+	6.84819i	0.190802	+	0.587227i
$137$	−3.00500	+	9.24844i	−0.256734	+	0.790147i	0.736748	+	0.676167i	$0.236360\pi$
$137$	−3.00500	+	9.24844i	−0.256734	+	0.790147i	−0.993483	+	0.113981i	$0.963640\pi$
$138$	1.62069	−	4.98798i	0.137963	−	0.424605i
$139$	3.67613	+	11.3140i	0.311805	+	0.959637i	0.977050	+	0.213012i	$0.0683273\pi$
$139$	3.67613	+	11.3140i	0.311805	+	0.959637i	−0.665245	+	0.746626i	$0.731673\pi$
$140$	2.66323	−	0.341210i	0.225084	−	0.0288375i
$141$	3.26493	−	10.0484i	0.274956	−	0.846229i
$142$	−4.02317	−	2.92300i	−0.337617	−	0.245293i
$143$	15.1178			1.26421
$144$	0.126706	+	0.0920570i	0.0105588	+	0.00767141i
$145$	−15.9521	+	2.04376i	−1.32475	+	0.169725i
$146$	2.79106	−	2.02782i	0.230990	−	0.167824i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−0.464523	−	1.42966i	−0.0381836	−	0.117517i
$149$	−0.139971			−0.0114668			−0.00573342	−	0.999984i	$-0.501825\pi$
$149$	−0.139971			−0.0114668			−0.00573342	+	0.999984i	$0.501825\pi$
$150$	0.264960	−	4.46213i	0.0216339	−	0.364331i
$151$	7.16559			0.583127			0.291564	−	0.956551i	$-0.405825\pi$
$151$	7.16559			0.583127			0.291564	+	0.956551i	$0.405825\pi$
$152$	5.00918	+	15.4167i	0.406298	+	1.25046i
$153$	2.03581	−	1.47910i	0.164585	−	0.119578i
$154$	4.56093	−	3.31371i	0.367530	−	0.267026i
$155$	1.17019	+	2.47545i	0.0939915	+	0.198833i
$156$	2.32887	+	1.69202i	0.186459	+	0.135470i
$157$	−10.8993			−0.869862			−0.434931	−	0.900464i	$-0.643227\pi$
$157$	−10.8993			−0.869862			−0.434931	+	0.900464i	$0.643227\pi$
$158$	12.1544	+	8.83070i	0.966953	+	0.702533i
$159$	2.07271	−	6.37914i	0.164376	−	0.505898i
$160$	−10.9502	−	5.99486i	−0.865693	−	0.473936i
$161$	−1.81286	−	5.57941i	−0.142873	−	0.439719i
$162$	0.276260	−	0.850242i	0.0217051	−	0.0668013i
$163$	1.13671	−	3.49844i	0.0890343	−	0.274019i	−0.896619	−	0.442803i	$-0.853984\pi$
$163$	1.13671	−	3.49844i	0.0890343	−	0.274019i	0.985653	+	0.168784i	$0.0539840\pi$
$164$	−2.72967	−	8.40105i	−0.213151	−	0.656012i
$165$	6.02629	+	12.7482i	0.469146	+	0.992447i
$166$	−2.36242	+	7.27077i	−0.183359	+	0.564321i
$167$	−18.7559	−	13.6270i	−1.45138	−	1.05449i	−0.985507	−	0.169634i	$-0.945742\pi$
$167$	−18.7559	−	13.6270i	−1.45138	−	1.05449i	−0.465870	−	0.884853i	$-0.654258\pi$
$168$	2.86148			0.220768
$169$	5.86763	+	4.26308i	0.451356	+	0.327930i
$170$	3.66091	−	3.44998i	0.280779	−	0.264601i
$171$	4.58302	−	3.32976i	0.350472	−	0.254633i
$172$	−10.2342	+	7.43562i	−0.780354	+	0.566960i
$173$	0.224361	+	0.690513i	0.0170579	+	0.0524987i	0.959223	−	0.282650i	$-0.0912135\pi$
$173$	0.224361	+	0.690513i	0.0170579	+	0.0524987i	−0.942165	+	0.335149i	$0.891213\pi$
$174$	−6.42991			−0.487450
$175$	−2.69398	−	4.21218i	−0.203646	−	0.318411i
$176$	−0.987637			−0.0744459
$177$	1.81147	+	5.57512i	0.136158	+	0.419052i
$178$	−10.3183	+	7.49665i	−0.773386	+	0.561898i
$179$	−19.1101	+	13.8843i	−1.42835	+	1.03776i	−0.438035	+	0.898958i	$0.644325\pi$
$179$	−19.1101	+	13.8843i	−1.42835	+	1.03776i	−0.990320	+	0.138802i	$0.955675\pi$
$180$	−0.498474	+	2.63832i	−0.0371541	+	0.196649i
$181$	−4.00779	−	2.91183i	−0.297897	−	0.216435i	0.428789	−	0.903405i	$-0.358940\pi$
$181$	−4.00779	−	2.91183i	−0.297897	−	0.216435i	−0.726686	+	0.686970i	$0.758940\pi$
$182$	−2.14321			−0.158865
$183$	0.620607	+	0.450897i	0.0458766	+	0.0333313i
$184$	−5.18746	+	15.9654i	−0.382425	+	1.17698i
$185$	−2.03723	+	1.91985i	−0.149780	+	0.141150i
$186$	0.338285	+	1.04113i	0.0248042	+	0.0763396i
$187$	−4.90366	+	15.0919i	−0.358591	+	1.10363i
$188$	−3.92042	+	12.0658i	−0.285926	+	0.879990i
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	8.24147	−	7.76661i	0.597899	−	0.563449i
$191$	4.63941	−	14.2786i	0.335696	−	1.03317i	−0.630683	−	0.776041i	$-0.717225\pi$
$191$	4.63941	−	14.2786i	0.335696	−	1.03317i	0.966378	−	0.257124i	$-0.0827750\pi$
$192$	−4.29132	−	3.11783i	−0.309700	−	0.225010i
$193$	15.3511			1.10500			0.552498	−	0.833515i	$-0.313675\pi$
$193$	15.3511			1.10500			0.552498	+	0.833515i	$0.313675\pi$
$194$	4.16715	+	3.02761i	0.299184	+	0.217370i
$195$	0.995203	−	5.26741i	0.0712680	−	0.377207i
$196$	0.971442	−	0.705794i	0.0693887	−	0.0504139i
$197$	13.5236	−	9.82547i	0.963516	−	0.700036i	0.00955164	−	0.999954i	$-0.496960\pi$
$197$	13.5236	−	9.82547i	0.963516	−	0.700036i	0.953965	+	0.299919i	$0.0969596\pi$
$198$	1.74212	+	5.36169i	0.123807	+	0.381039i
$199$	15.6999			1.11293			0.556467	−	0.830870i	$-0.312157\pi$
$199$	15.6999			1.11293			0.556467	+	0.830870i	$0.312157\pi$
$200$	−0.848076	+	14.2822i	−0.0599680	+	1.00991i
$201$	3.03205			0.213865
$202$	−4.64633	−	14.2999i	−0.326915	−	1.00614i
$203$	−5.81870	+	4.22754i	−0.408393	+	0.296715i
$204$	−2.44453	+	1.77606i	−0.171152	+	0.124349i
$205$	−11.9713	+	11.2816i	−0.836114	+	0.787938i
$206$	2.26199	+	1.64343i	0.157600	+	0.114503i
$207$	5.86654			0.407753
$208$	0.303755	+	0.220691i	0.0210616	+	0.0153022i
$209$	−11.0392	+	33.9750i	−0.763594	+	2.35010i
$210$	−0.854333	−	1.80728i	−0.0589546	−	0.124714i
$211$	−3.11297	−	9.58073i	−0.214306	−	0.659565i	−0.999202	−	0.0399381i	$-0.987284\pi$
$211$	−3.11297	−	9.58073i	−0.214306	−	0.659565i	0.784897	−	0.619627i	$-0.212716\pi$
$212$	−2.48884	+	7.65987i	−0.170934	+	0.526082i
$213$	1.71892	−	5.29031i	0.117779	−	0.362486i
$214$	0.415906	+	1.28003i	0.0284308	+	0.0875009i
$215$	20.6633	+	11.3124i	1.40922	+	0.771500i
$216$	−0.884246	+	2.72143i	−0.0601653	+	0.185170i
$217$	0.990652	+	0.719751i	0.0672499	+	0.0488599i
$218$	9.47551			0.641763
$219$	3.12200	+	2.26826i	0.210965	+	0.153275i
$220$	−7.23619	−	15.3077i	−0.487864	−	1.03204i
$221$	4.88051	−	3.54590i	0.328298	−	0.238523i
$222$	−0.905440	+	0.657841i	−0.0607691	+	0.0441514i
$223$	−2.41649	−	7.43719i	−0.161820	−	0.498031i	0.836968	−	0.547252i	$-0.184326\pi$
$223$	−2.41649	−	7.43719i	−0.161820	−	0.498031i	−0.998788	+	0.0492209i	$0.984326\pi$
$224$	−5.58294			−0.373026
$225$	4.83851	−	1.26050i	0.322567	−	0.0840331i
$226$	13.6536			0.908221
$227$	1.74847	+	5.38123i	0.116050	+	0.357165i	0.992165	−	0.124938i	$-0.0398732\pi$
$227$	1.74847	+	5.38123i	0.116050	+	0.357165i	−0.876115	+	0.482103i	$0.839873\pi$
$228$	−5.50315	+	3.99827i	−0.364455	+	0.264792i
$229$	−5.47890	+	3.98065i	−0.362056	+	0.263049i	−0.753909	−	0.656979i	$-0.771834\pi$
$229$	−5.47890	+	3.98065i	−0.362056	+	0.263049i	0.391853	+	0.920028i	$0.371834\pi$
$230$	11.6324	−	1.49032i	0.767015	−	0.0982690i
$231$	5.10172	+	3.70662i	0.335669	+	0.243878i
$232$	20.5806			1.35119
$233$	−7.13229	−	5.18191i	−0.467252	−	0.339478i	0.329117	−	0.944289i	$-0.393249\pi$
$233$	−7.13229	−	5.18191i	−0.467252	−	0.339478i	−0.796369	+	0.604811i	$0.793249\pi$
$234$	0.662288	−	2.03831i	0.0432951	−	0.133249i
$235$	23.4337	−	3.00229i	1.52865	−	0.195848i
$236$	−2.17515	−	6.69444i	−0.141590	−	0.435771i
$237$	−5.19305	+	15.9826i	−0.337325	+	1.03818i
$238$	0.695180	−	2.13954i	0.0450618	−	0.138686i
$239$	−0.710729	−	2.18740i	−0.0459732	−	0.141491i	0.925435	−	0.378906i	$-0.123700\pi$
$239$	−0.710729	−	2.18740i	−0.0459732	−	0.141491i	−0.971408	+	0.237415i	$0.923700\pi$
$240$	−0.0650161	+	0.344117i	−0.00419677	+	0.0222127i
$241$	−3.79683	+	11.6854i	−0.244575	+	0.752725i	0.751131	+	0.660153i	$0.229509\pi$
$241$	−3.79683	+	11.6854i	−0.244575	+	0.752725i	−0.995706	+	0.0925714i	$0.970491\pi$
$242$	−20.8057	−	15.1162i	−1.33744	−	0.971709i
$243$	1.00000			0.0641500
$244$	−0.745206	−	0.541424i	−0.0477069	−	0.0346611i
$245$	−1.96138	−	1.07378i	−0.125308	−	0.0686014i
$246$	−5.32061	+	3.86565i	−0.339230	+	0.246465i
$247$	10.9870	−	7.98254i	0.699088	−	0.507917i
$248$	−1.08277	−	3.33243i	−0.0687560	−	0.211609i
$249$	−8.55141			−0.541924
$250$	9.27373	−	3.72852i	0.586522	−	0.235812i
$251$	−20.2254			−1.27662			−0.638309	−	0.769780i	$-0.720366\pi$
$251$	−20.2254			−1.27662			−0.638309	+	0.769780i	$0.720366\pi$
$252$	0.371058	+	1.14200i	0.0233745	+	0.0719392i
$253$	−29.9295	+	21.7450i	−1.88165	+	1.36710i
$254$	7.29398	−	5.29938i	0.457665	−	0.332513i
$255$	4.93560	+	2.70206i	0.309079	+	0.169210i
$256$	13.2287	+	9.61122i	0.826795	+	0.600702i
$257$	17.9361			1.11882			0.559411	−	0.828891i	$-0.311027\pi$
$257$	17.9361			1.11882			0.559411	+	0.828891i	$0.311027\pi$
$258$	7.61961	+	5.53597i	0.474376	+	0.344654i
$259$	−0.386855	+	1.19062i	−0.0240380	+	0.0739813i
$260$	−1.19501	+	6.32494i	−0.0741113	+	0.392256i
$261$	−2.22255	−	6.84030i	−0.137572	−	0.423404i
$262$	−0.0305324	+	0.0939691i	−0.00188630	+	0.00580543i
$263$	5.04043	−	15.5128i	0.310806	−	0.956563i	−0.666640	−	0.745380i	$-0.732268\pi$
$263$	5.04043	−	15.5128i	0.310806	−	0.956563i	0.977446	−	0.211184i	$-0.0677318\pi$
$264$	−5.57612	−	17.1615i	−0.343187	−	1.05622i
$265$	14.8767	−	1.90598i	0.913865	−	0.117083i
$266$	1.56499	−	4.81656i	0.0959559	−	0.295322i
$267$	−11.5417	−	8.38554i	−0.706341	−	0.513187i
$268$	−3.64080			−0.222397
$269$	−20.2685	−	14.7259i	−1.23579	−	0.897855i	−0.238481	−	0.971147i	$-0.576650\pi$
$269$	−20.2685	−	14.7259i	−1.23579	−	0.897855i	−0.997311	+	0.0732919i	$0.976650\pi$
$270$	1.98283	−	0.254038i	0.120671	−	0.0154603i
$271$	−14.8568	+	10.7941i	−0.902489	+	0.655697i	−0.939104	−	0.343633i	$-0.888343\pi$
$271$	−14.8568	+	10.7941i	−0.902489	+	0.655697i	0.0366149	+	0.999329i	$0.488343\pi$
$272$	−0.318841	+	0.231652i	−0.0193326	+	0.0140459i
$273$	−0.740817	−	2.28000i	−0.0448363	−	0.137992i
$274$	−8.69357			−0.525198
$275$	−20.0125	+	24.3652i	−1.20680	+	1.46928i
$276$	−7.04436			−0.424021
$277$	4.79471	+	14.7566i	0.288086	+	0.886638i	0.985457	+	0.169927i	$0.0543533\pi$
$277$	4.79471	+	14.7566i	0.288086	+	0.886638i	−0.697370	+	0.716711i	$0.745647\pi$
$278$	−8.60403	+	6.25120i	−0.516036	+	0.374922i
$279$	−0.990652	+	0.719751i	−0.0593088	+	0.0430904i
$280$	2.73452	+	5.78469i	0.163419	+	0.345702i
$281$	−16.7865	−	12.1961i	−1.00140	−	0.727560i	−0.0390127	−	0.999239i	$-0.512421\pi$
$281$	−16.7865	−	12.1961i	−1.00140	−	0.727560i	−0.962388	+	0.271678i	$0.912421\pi$
$282$	9.44555			0.562474
$283$	3.47729	+	2.52640i	0.206703	+	0.150179i	0.686321	−	0.727299i	$-0.259225\pi$
$283$	3.47729	+	2.52640i	0.206703	+	0.150179i	−0.479618	+	0.877478i	$0.659225\pi$
$284$	−2.06403	+	6.35244i	−0.122478	+	0.376948i
$285$	11.1110	+	6.08289i	0.658161	+	0.360319i
$286$	4.17644	+	12.8538i	0.246958	+	0.760059i
$287$	−2.27327	+	6.99639i	−0.134187	+	0.412984i
$288$	1.72522	−	5.30969i	0.101660	−	0.312877i
$289$	−3.29652	−	10.1456i	−0.193913	−	0.596802i
$290$	−6.14463	−	12.9985i	−0.360825	−	0.763301i
$291$	−1.78044	+	5.47963i	−0.104371	+	0.321222i
$292$	−3.74880	−	2.72366i	−0.219382	−	0.159390i
$293$	−4.71707			−0.275574			−0.137787	−	0.990462i	$-0.543999\pi$
$293$	−4.71707			−0.275574			−0.137787	+	0.990462i	$0.543999\pi$
$294$	−0.723259	−	0.525478i	−0.0421813	−	0.0306465i
$295$	−9.53943	+	8.98979i	−0.555407	+	0.523406i
$296$	2.89810	−	2.10560i	0.168449	−	0.122385i
$297$	−5.10172	+	3.70662i	−0.296032	+	0.215080i
$298$	−0.0386683	−	0.119009i	−0.00224000	−	0.00689400i
$299$	14.0641			0.813345
$300$	−5.80993	+	1.51357i	−0.335436	+	0.0873858i
$301$	10.5351			0.607233
$302$	1.97957	+	6.09248i	0.113911	+	0.350583i
$303$	13.6066	−	9.88576i	0.781678	−	0.567922i
$304$	−0.717777	+	0.521496i	−0.0411673	+	0.0299098i
$305$	−0.318451	+	1.68550i	−0.0182344	+	0.0965112i
$306$	1.82001	+	1.32231i	0.104043	+	0.0755915i
$307$	11.4432			0.653100			0.326550	−	0.945180i	$-0.394114\pi$
$307$	11.4432			0.653100			0.326550	+	0.945180i	$0.394114\pi$
$308$	−6.12599	−	4.45079i	−0.349061	−	0.253607i
$309$	−0.966450	+	2.97443i	−0.0549794	+	0.169209i
$310$	−1.78145	+	1.67881i	−0.101180	+	0.0953499i
$311$	2.41678	+	7.43809i	0.137043	+	0.421775i	0.995902	−	0.0904366i	$-0.0288262\pi$
$311$	2.41678	+	7.43809i	0.137043	+	0.421775i	−0.858859	+	0.512212i	$0.828826\pi$
$312$	−2.11983	+	6.52417i	−0.120012	+	0.369358i
$313$	−3.98620	+	12.2683i	−0.225313	+	0.693443i	0.772946	+	0.634471i	$0.218782\pi$
$313$	−3.98620	+	12.2683i	−0.225313	+	0.693443i	−0.998260	+	0.0589717i	$0.981218\pi$
$314$	−3.01106	−	9.26708i	−0.169924	−	0.522971i
$315$	1.62733	−	1.53356i	0.0916894	−	0.0864064i
$316$	6.23565	−	19.1914i	0.350783	−	1.07960i
$317$	−27.4021	−	19.9088i	−1.53906	−	1.11819i	−0.950923	−	0.309428i	$-0.899862\pi$
$317$	−27.4021	−	19.9088i	−1.53906	−	1.11819i	−0.588135	−	0.808763i	$-0.700138\pi$
$318$	5.99642			0.336262
$319$	36.6932	+	26.6592i	2.05442	+	1.49263i
$320$	2.20200	−	11.6547i	0.123095	−	0.651520i
$321$	−1.21796	+	0.884903i	−0.0679802	+	0.0493905i
$322$	4.24303	−	3.08274i	0.236455	−	0.171794i
$323$	4.40509	+	13.5575i	0.245106	+	0.754359i
$324$	−1.20077			−0.0667094
$325$	11.5995	−	3.02183i	0.643425	−	0.167621i
$326$	3.28855			0.182136
$327$	3.27528	+	10.0803i	0.181124	+	0.557441i
$328$	17.0301	−	12.3731i	0.940328	−	0.683188i
$329$	8.54769	−	6.21026i	0.471249	−	0.342383i
$330$	−9.17424	+	8.64563i	−0.505025	+	0.475926i
$331$	−7.33077	−	5.32612i	−0.402936	−	0.292750i	0.367800	−	0.929905i	$-0.380111\pi$
$331$	−7.33077	−	5.32612i	−0.402936	−	0.292750i	−0.770736	+	0.637155i	$0.780111\pi$
$332$	10.2683			0.563544
$333$	−1.01280	−	0.735842i	−0.0555011	−	0.0403239i
$334$	6.40471	−	19.7117i	0.350450	−	1.07857i
$335$	2.89753	+	6.12952i	0.158309	+	0.334892i
$336$	0.0483972	+	0.148951i	0.00264028	+	0.00812596i
$337$	−0.248311	+	0.764222i	−0.0135264	+	0.0416298i	−0.957592	−	0.288128i	$-0.906967\pi$
$337$	−0.248311	+	0.764222i	−0.0135264	+	0.0416298i	0.944066	+	0.329758i	$0.106967\pi$
$338$	−2.00366	+	6.16663i	−0.108985	+	0.335420i
$339$	4.71945	+	14.5250i	0.256326	+	0.788889i
$340$	−5.92651	−	3.24455i	−0.321410	−	0.175960i
$341$	2.38619	−	7.34394i	0.129220	−	0.397697i
$342$	4.09721	+	2.97679i	0.221552	+	0.160967i
$343$	−1.00000			−0.0539949
$344$	−24.3886	−	17.7194i	−1.31495	−	0.955364i
$345$	5.60626	+	11.8597i	0.301831	+	0.638502i
$346$	−0.525121	+	0.381523i	−0.0282307	+	0.0205108i
$347$	−19.1009	+	13.8776i	−1.02539	+	0.744989i	−0.967381	−	0.253327i	$-0.918475\pi$
$347$	−19.1009	+	13.8776i	−1.02539	+	0.744989i	−0.0580086	+	0.998316i	$0.518475\pi$
$348$	2.66876	+	8.21361i	0.143061	+	0.440296i
$349$	−9.74933			−0.521870			−0.260935	−	0.965356i	$-0.584031\pi$
$349$	−9.74933			−0.521870			−0.260935	+	0.965356i	$0.584031\pi$
$350$	2.83713	−	3.45420i	0.151651	−	0.184635i
$351$	2.39733			0.127960
$352$	10.8794	+	33.4833i	0.579874	+	1.78467i
$353$	20.0559	−	14.5715i	1.06747	−	0.775561i	0.0920121	−	0.995758i	$-0.470670\pi$
$353$	20.0559	−	14.5715i	1.06747	−	0.775561i	0.975455	+	0.220197i	$0.0706701\pi$
$354$	−4.23977	+	3.08037i	−0.225341	+	0.163720i
$355$	12.3374	−	1.58065i	0.654802	−	0.0838924i
$356$	13.8589	+	10.0691i	0.734521	+	0.533661i
$357$	2.51640			0.133182
$358$	−17.0844	−	12.4125i	−0.902937	−	0.656022i
$359$	4.24669	−	13.0700i	0.224132	−	0.689807i	−0.774247	−	0.632884i	$-0.781871\pi$
$359$	4.24669	−	13.0700i	0.224132	−	0.689807i	0.998379	−	0.0569231i	$-0.0181290\pi$
$360$	−6.34659	+	0.813117i	−0.334494	+	0.0428550i
$361$	4.04545	+	12.4506i	0.212918	+	0.655296i
$362$	1.36857	−	4.21202i	0.0719303	−	0.221379i
$363$	8.88937	−	27.3587i	0.466571	−	1.43596i
$364$	0.889550	+	2.73775i	0.0466251	+	0.143497i
$365$	−1.60198	+	8.47898i	−0.0838517	+	0.443810i
$366$	−0.211923	+	0.652231i	−0.0110774	+	0.0340927i
$367$	22.4811	+	16.3335i	1.17351	+	0.852602i	0.991424	−	0.130681i	$-0.0417164\pi$
$367$	22.4811	+	16.3335i	1.17351	+	0.852602i	0.182082	+	0.983283i	$0.441716\pi$
$368$	−0.918798			−0.0478957
$369$	−5.95149	−	4.32401i	−0.309822	−	0.225099i
$370$	−2.19514	−	1.20176i	−0.114120	−	0.0624766i
$371$	5.42642	−	3.94252i	0.281726	−	0.204686i
$372$	1.18954	−	0.864255i	0.0616750	−	0.0448095i
$373$	3.69865	+	11.3833i	0.191509	+	0.589404i	1.00000		0.000894937i	$0.000284867\pi$
$373$	3.69865	+	11.3833i	0.191509	+	0.589404i	−0.808491	+	0.588509i	$0.799715\pi$
$374$	−14.1865			−0.733565
$375$	7.17202	+	8.57683i	0.370362	+	0.442906i
$376$	−30.2330			−1.55915
$377$	−5.32819	−	16.3985i	−0.274416	−	0.844564i
$378$	0.723259	−	0.525478i	0.0372004	−	0.0270277i
$379$	14.7718	−	10.7323i	0.758776	−	0.551283i	−0.139759	−	0.990186i	$-0.544633\pi$
$379$	14.7718	−	10.7323i	0.758776	−	0.551283i	0.898535	+	0.438903i	$0.144633\pi$
$380$	−13.3418	−	7.30415i	−0.684419	−	0.374695i
$381$	8.15884	+	5.92774i	0.417990	+	0.303687i
$382$	13.4220			0.686728
$383$	1.49282	+	1.08460i	0.0762797	+	0.0554204i	0.625272	−	0.780407i	$-0.284988\pi$
$383$	1.49282	+	1.08460i	0.0762797	+	0.0554204i	−0.548992	+	0.835828i	$0.684988\pi$
$384$	−1.98506	+	6.10939i	−0.101300	+	0.311769i
$385$	−2.61784	+	13.8557i	−0.133417	+	0.706151i
$386$	4.24090	+	13.0521i	0.215856	+	0.664336i
$387$	−3.25553	+	10.0195i	−0.165488	+	0.509319i
$388$	2.13790	−	6.57977i	0.108535	−	0.334037i
$389$	0.813691	+	2.50428i	0.0412558	+	0.126972i	0.969563	−	0.244842i	$-0.0787360\pi$
$389$	0.813691	+	2.50428i	0.0412558	+	0.126972i	−0.928307	+	0.371814i	$0.878736\pi$
$390$	4.75351	−	0.609014i	0.240703	−	0.0308386i
$391$	−4.56187	+	14.0400i	−0.230704	+	0.710034i
$392$	2.31498	+	1.68193i	0.116924	+	0.0849505i
$393$	−0.110520			−0.00557502
$394$	12.0901	+	8.78394i	0.609088	+	0.442529i
$395$	−37.2726	+	4.77532i	−1.87539	+	0.240272i
$396$	6.12599	−	4.45079i	0.307843	−	0.223661i
$397$	22.7962	−	16.5624i	1.14411	−	0.831242i	0.156421	−	0.987691i	$-0.450004\pi$
$397$	22.7962	−	16.5624i	1.14411	−	0.831242i	0.987686	+	0.156448i	$0.0500044\pi$
$398$	4.33725	+	13.3487i	0.217407	+	0.669109i
$399$	5.66492			0.283601
$400$	−0.757791	+	0.197415i	−0.0378895	+	0.00987074i
$401$	2.21165			0.110444			0.0552222	−	0.998474i	$-0.482413\pi$
$401$	2.21165			0.110444			0.0552222	+	0.998474i	$0.482413\pi$
$402$	0.837636	+	2.57798i	0.0417775	+	0.128578i
$403$	−2.37492	+	1.72548i	−0.118303	+	0.0859525i
$404$	−16.3384	+	11.8705i	−0.812864	+	0.590580i
$405$	0.955633	+	2.02158i	0.0474858	+	0.100453i
$406$	−5.20191	−	3.77941i	−0.258166	−	0.187569i
$407$	7.89451			0.391316
$408$	−5.82542	−	4.23241i	−0.288401	−	0.209536i
$409$	1.76938	−	5.44558i	0.0874900	−	0.269267i	−0.897734	−	0.440538i	$-0.854788\pi$
$409$	1.76938	−	5.44558i	0.0874900	−	0.269267i	0.985224	+	0.171272i	$0.0547876\pi$
$410$	−12.8993	−	7.06188i	−0.637049	−	0.348761i
$411$	−3.00500	−	9.24844i	−0.148226	−	0.456192i
$412$	1.16048	−	3.57160i	0.0571729	−	0.175960i
$413$	−1.81147	+	5.57512i	−0.0891365	+	0.274334i
$414$	1.62069	+	4.98798i	0.0796527	+	0.245146i
$415$	−8.17201	−	17.2873i	−0.401148	−	0.848601i
$416$	4.13594	−	12.7291i	0.202781	−	0.624096i
$417$	−9.62423	−	6.99241i	−0.471300	−	0.342420i
$418$	−31.9367			−1.56207
$419$	−21.1357	−	15.3560i	−1.03254	−	0.750188i	−0.0637283	−	0.997967i	$-0.520299\pi$
$419$	−21.1357	−	15.3560i	−1.03254	−	0.750188i	−0.968816	+	0.247780i	$0.920299\pi$
$420$	−1.95404	+	1.84145i	−0.0953475	+	0.0898537i
$421$	−2.63187	+	1.91217i	−0.128270	+	0.0931933i	−0.650070	−	0.759874i	$-0.725261\pi$
$421$	−2.63187	+	1.91217i	−0.128270	+	0.0931933i	0.521801	+	0.853067i	$0.325261\pi$
$422$	7.28595	−	5.29355i	0.354675	−	0.257686i
$423$	3.26493	+	10.0484i	0.158746	+	0.488570i
$424$	−19.1931			−0.932101
$425$	−0.745801	+	12.5599i	−0.0361767	+	0.609242i
$426$	4.97291			0.240938
$427$	0.237051	+	0.729567i	0.0114717	+	0.0353062i
$428$	1.46249	−	1.06256i	0.0706923	−	0.0513610i
$429$	−12.2305	+	8.88600i	−0.590496	+	0.429020i
$430$	−3.90983	+	20.6940i	−0.188549	+	0.997952i
$431$	16.6281	+	12.0810i	0.800949	+	0.581923i	0.911192	−	0.411981i	$-0.135163\pi$
$431$	16.6281	+	12.0810i	0.800949	+	0.581923i	−0.110244	+	0.993905i	$0.535163\pi$
$432$	−0.156617			−0.00753522
$433$	−26.8058	−	19.4755i	−1.28820	−	0.935934i	−0.288435	−	0.957499i	$-0.593135\pi$
$433$	−26.8058	−	19.4755i	−1.28820	−	0.935934i	−0.999767	+	0.0215655i	$0.993135\pi$
$434$	−0.338285	+	1.04113i	−0.0162382	+	0.0499760i
$435$	11.7042	−	11.0299i	0.561175	−	0.528841i
$436$	−3.93286	−	12.1041i	−0.188350	−	0.579681i
$437$	−10.2697	+	31.6069i	−0.491267	+	1.51196i
$438$	−1.06609	+	3.28109i	−0.0509397	+	0.156776i
$439$	−9.96232	−	30.6609i	−0.475475	−	1.46336i	−0.845316	−	0.534267i	$-0.820588\pi$
$439$	−9.96232	−	30.6609i	−0.475475	−	1.46336i	0.369840	−	0.929095i	$-0.379412\pi$
$440$	29.3646	−	27.6727i	1.39990	−	1.31924i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	4.36316	+	3.17002i	0.207534	+	0.150783i
$443$	−13.4392			−0.638517			−0.319259	−	0.947668i	$-0.603434\pi$
$443$	−13.4392			−0.638517			−0.319259	+	0.947668i	$0.603434\pi$
$444$	1.21614	+	0.883576i	0.0577153	+	0.0419327i
$445$	5.92237	−	31.3459i	0.280747	−	1.48594i
$446$	5.65583	−	4.10920i	0.267812	−	0.194576i
$447$	0.113239	−	0.0822726i	0.00535600	−	0.00389136i
$448$	−1.63914	−	5.04475i	−0.0774421	−	0.238342i
$449$	27.3998			1.29308			0.646538	−	0.762882i	$-0.276216\pi$
$449$	27.3998			1.29308			0.646538	+	0.762882i	$0.276216\pi$
$450$	2.40842	+	3.76568i	0.113534	+	0.177516i
$451$	46.3903			2.18443
$452$	−5.66697	−	17.4412i	−0.266552	−	0.820363i
$453$	−5.79708	+	4.21183i	−0.272371	+	0.197889i
$454$	−4.09232	+	2.97324i	−0.192062	+	0.139541i
$455$	3.90124	−	3.67646i	0.182893	−	0.172355i
$456$	−13.1142	−	9.52803i	−0.614129	−	0.446191i
$457$	2.89385			0.135369			0.0676843	−	0.997707i	$-0.478439\pi$
$457$	2.89385			0.135369			0.0676843	+	0.997707i	$0.478439\pi$
$458$	−4.89812	−	3.55869i	−0.228874	−	0.166287i
$459$	−0.777609	+	2.39323i	−0.0362957	+	0.111707i
$460$	−6.73182	−	14.2407i	−0.313873	−	0.663976i
$461$	11.0677	+	34.0628i	0.515473	+	1.58646i	0.782419	+	0.622753i	$0.213986\pi$
$461$	11.0677	+	34.0628i	0.515473	+	1.58646i	−0.266945	+	0.963712i	$0.586014\pi$
$462$	−1.74212	+	5.36169i	−0.0810507	+	0.249448i
$463$	1.08054	−	3.32557i	0.0502170	−	0.154552i	−0.922803	−	0.385271i	$-0.874108\pi$
$463$	1.08054	−	3.32557i	0.0502170	−	0.154552i	0.973020	+	0.230719i	$0.0741079\pi$
$464$	0.348088	+	1.07130i	0.0161596	+	0.0497341i
$465$	−2.40173	−	1.31486i	−0.111378	−	0.0609752i
$466$	2.43551	−	7.49573i	0.112823	−	0.347233i
$467$	11.4625	+	8.32800i	0.530421	+	0.385374i	0.820515	−	0.571624i	$-0.193687\pi$
$467$	11.4625	+	8.32800i	0.530421	+	0.385374i	−0.290094	+	0.956998i	$0.593687\pi$
$468$	−2.87864			−0.133065
$469$	2.45298	+	1.78220i	0.113268	+	0.0822942i
$470$	9.02648	+	19.0949i	0.416360	+	0.880782i
$471$	8.81775	−	6.40647i	0.406301	−	0.295195i
$472$	13.5705	−	9.85956i	0.624634	−	0.453823i
$473$	−20.5296	−	63.1836i	−0.943952	−	2.90519i
$474$	−15.0237			−0.690061
$475$	−1.67895	+	28.2748i	−0.0770356	+	1.29734i
$476$	−3.02161			−0.138495
$477$	2.07271	+	6.37914i	0.0949027	+	0.292081i
$478$	1.66347	−	1.20858i	0.0760854	−	0.0552793i
$479$	8.68377	−	6.30913i	0.396772	−	0.288271i	−0.371453	−	0.928452i	$-0.621140\pi$
$479$	8.68377	−	6.30913i	0.396772	−	0.288271i	0.768225	+	0.640180i	$0.221140\pi$
$480$	12.3826	−	1.58645i	0.565187	−	0.0724110i
$481$	−2.42802	−	1.76406i	−0.110708	−	0.0804341i
$482$	−10.9844			−0.500324
$483$	4.74613	+	3.44827i	0.215956	+	0.156902i
$484$	−10.6741	+	32.8515i	−0.485186	+	1.49325i
$485$	−12.7789	+	1.63722i	−0.580261	+	0.0743424i
$486$	0.276260	+	0.850242i	0.0125314	+	0.0385678i
$487$	10.9576	−	33.7239i	0.496535	−	1.52818i	−0.318017	−	0.948085i	$-0.603017\pi$
$487$	10.9576	−	33.7239i	0.496535	−	1.52818i	0.814551	−	0.580091i	$-0.196983\pi$
$488$	0.678316	−	2.08764i	0.0307059	−	0.0945031i
$489$	1.13671	+	3.49844i	0.0514039	+	0.158205i
$490$	0.371124	−	1.96429i	0.0167657	−	0.0887374i
$491$	5.44517	−	16.7585i	0.245737	−	0.756301i	−0.749777	−	0.661690i	$-0.769839\pi$
$491$	5.44517	−	16.7585i	0.245737	−	0.756301i	0.995514	−	0.0946107i	$-0.0301606\pi$
$492$	7.14636	+	5.19214i	0.322183	+	0.234080i
$493$	18.0987			0.815125
$494$	9.82237	+	7.13637i	0.441929	+	0.321080i
$495$	−12.3686	−	6.77135i	−0.555927	−	0.304350i
$496$	0.155153	−	0.112725i	0.00696656	−	0.00506150i
$497$	4.50020	−	3.26959i	0.201862	−	0.146661i
$498$	−2.36242	−	7.27077i	−0.105862	−	0.325811i
$499$	18.0173			0.806567			0.403283	−	0.915075i	$-0.367869\pi$
$499$	18.0173			0.806567			0.403283	+	0.915075i	$0.367869\pi$
$500$	−8.61194	−	10.2988i	−0.385138	−	0.460576i
$501$	23.1836			1.03577
$502$	−5.58748	−	17.1965i	−0.249382	−	0.767518i
$503$	27.0540	−	19.6558i	1.20628	−	0.876411i	0.211389	−	0.977402i	$-0.432201\pi$
$503$	27.0540	−	19.6558i	1.20628	−	0.876411i	0.994887	+	0.100991i	$0.0322013\pi$
$504$	−2.31498	+	1.68193i	−0.103118	+	0.0749193i
$505$	32.9877	+	18.0596i	1.46793	+	0.803640i
$506$	−26.7569	−	19.4400i	−1.18949	−	0.864213i
$507$	−7.25279			−0.322108
$508$	−9.79687	−	7.11785i	−0.434666	−	0.315803i
$509$	4.56682	−	14.0552i	0.202421	−	0.622987i	−0.797389	−	0.603466i	$-0.793786\pi$
$509$	4.56682	−	14.0552i	0.202421	−	0.622987i	0.999809	−	0.0195211i	$-0.00621414\pi$
$510$	−0.933895	+	4.94292i	−0.0413536	+	0.218876i
$511$	1.19250	+	3.67013i	0.0527530	+	0.162357i
$512$	−0.547174	+	1.68403i	−0.0241819	+	0.0744242i
$513$	−1.75056	+	5.38766i	−0.0772890	+	0.237871i
$514$	4.95503	+	15.2500i	0.218557	+	0.672649i
$515$	−6.93660	+	0.888709i	−0.305663	+	0.0391612i
$516$	3.90913	−	12.0311i	0.172090	−	0.529639i
$517$	−53.9024	−	39.1624i	−2.37062	−	1.72236i
$518$	−1.11919			−0.0491742
$519$	−0.587385	−	0.426760i	−0.0257833	−	0.0187327i
$520$	−15.2149	+	1.94931i	−0.667217	+	0.0854830i
$521$	−22.4534	+	16.3133i	−0.983700	+	0.714700i	−0.958532	−	0.284984i	$-0.908012\pi$
$521$	−22.4534	+	16.3133i	−0.983700	+	0.714700i	−0.0251672	+	0.999683i	$0.508012\pi$
$522$	5.20191	−	3.77941i	0.227681	−	0.165420i
$523$	−6.75695	−	20.7958i	−0.295461	−	0.909335i	−0.983066	−	0.183250i	$-0.941338\pi$
$523$	−6.75695	−	20.7958i	−0.295461	−	0.909335i	0.687605	−	0.726085i	$-0.258662\pi$
$524$	0.132710			0.00579744
$525$	4.65534	+	1.82424i	0.203176	+	0.0796163i
$526$	14.5821			0.635812
$527$	−0.952193	−	2.93055i	−0.0414782	−	0.127657i
$528$	0.799015	−	0.580518i	0.0347727	−	0.0252638i
$529$	−9.23598	+	6.71033i	−0.401564	+	0.291753i
$530$	5.73037	+	12.1222i	0.248911	+	0.526555i
$531$	−4.74248	−	3.44562i	−0.205806	−	0.149527i
$532$	−6.80226			−0.294915
$533$	−14.2677	−	10.3661i	−0.618003	−	0.449005i
$534$	3.94122	−	12.1298i	0.170553	−	0.524909i
$535$	−2.95282	−	1.61656i	−0.127662	−	0.0698902i
$536$	−2.68108	−	8.25152i	−0.115805	−	0.356411i
$537$	7.29940	−	22.4653i	0.314992	−	0.969447i
$538$	6.92122	−	21.3013i	0.298395	−	0.918365i
$539$	1.94869	+	5.99744i	0.0839358	+	0.258328i
$540$	−1.14749	−	2.42744i	−0.0493803	−	0.104461i
$541$	5.34705	−	16.4565i	0.229888	−	0.707522i	−0.767871	−	0.640605i	$-0.778684\pi$
$541$	5.34705	−	16.4565i	0.229888	−	0.707522i	0.997759	−	0.0669169i	$-0.0213163\pi$
$542$	−13.2820	−	9.64993i	−0.570510	−	0.414500i
$543$	4.95391			0.212592
$544$	11.3658	+	8.25773i	0.487304	+	0.354047i
$545$	−17.2481	+	16.2543i	−0.738827	+	0.696257i
$546$	1.73389	−	1.25975i	0.0742038	−	0.0539122i
$547$	0.591294	−	0.429600i	0.0252819	−	0.0183684i	−0.575073	−	0.818102i	$-0.695026\pi$
$547$	0.591294	−	0.429600i	0.0252819	−	0.0183684i	0.600354	+	0.799734i	$0.295026\pi$
$548$	3.60831	+	11.1052i	0.154139	+	0.474392i
$549$	−0.767113			−0.0327396
$550$	−26.2450	−	10.2844i	−1.11909	−	0.438527i
$551$	40.7439			1.73575
$552$	−5.18746	−	15.9654i	−0.220793	−	0.679531i
$553$	−13.5956	+	9.87777i	−0.578143	+	0.420045i
$554$	−11.2221	+	8.15333i	−0.476781	+	0.346402i
$555$	0.519695	−	2.75064i	0.0220598	−	0.116758i
$556$	11.5565	+	8.39627i	0.490104	+	0.356081i
$557$	−13.5939			−0.575990			−0.287995	−	0.957632i	$-0.592989\pi$
$557$	−13.5939			−0.575990			−0.287995	+	0.957632i	$0.592989\pi$
$558$	−0.885641	−	0.643456i	−0.0374922	−	0.0272396i
$559$	−7.80458	+	24.0200i	−0.330099	+	1.01594i
$560$	−0.254866	+	0.240181i	−0.0107701	+	0.0101495i
$561$	−4.90366	−	15.0919i	−0.207033	−	0.637181i
$562$	5.73221	−	17.6419i	0.241799	−	0.744180i
$563$	6.21811	−	19.1374i	0.262062	−	0.806544i	−0.730294	−	0.683133i	$-0.760617\pi$
$563$	6.21811	−	19.1374i	0.262062	−	0.806544i	0.992356	−	0.123411i	$-0.0393833\pi$
$564$	−3.92042	−	12.0658i	−0.165080	−	0.508063i
$565$	−24.8533	+	23.4213i	−1.04559	+	0.985341i
$566$	−1.18741	+	3.65448i	−0.0499107	+	0.153609i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	−15.9171			−0.667868
$569$	−28.3587	−	20.6038i	−1.18886	−	0.863756i	−0.195715	−	0.980661i	$-0.562703\pi$
$569$	−28.3587	−	20.6038i	−1.18886	−	0.863756i	−0.993143	+	0.116905i	$0.962703\pi$
$570$	−2.10239	+	11.1275i	−0.0880594	+	0.466081i
$571$	−36.7196	+	26.6784i	−1.53667	+	1.11645i	−0.584286	+	0.811547i	$0.698626\pi$
$571$	−36.7196	+	26.6784i	−1.53667	+	1.11645i	−0.952382	+	0.304908i	$0.901374\pi$
$572$	14.6860	−	10.6700i	0.614054	−	0.446137i
$573$	4.63941	+	14.2786i	0.193814	+	0.596498i
$574$	−6.57664			−0.274504
$575$	−18.6177	+	22.6669i	−0.776410	+	0.945277i
$576$	5.30437			0.221015
$577$	−11.3616	−	34.9675i	−0.472991	−	1.45572i	−0.848648	−	0.528958i	$-0.822583\pi$
$577$	−11.3616	−	34.9675i	−0.472991	−	1.45572i	0.375657	−	0.926759i	$-0.377417\pi$
$578$	7.71555	−	5.60567i	0.320925	−	0.233165i
$579$	−12.4193	+	9.02314i	−0.516128	+	0.374989i
$580$	−14.0541	+	13.2443i	−0.583564	+	0.549940i
$581$	−6.91824	−	5.02639i	−0.287017	−	0.208530i
$582$	−5.15088			−0.213511
$583$	−34.2194	−	24.8619i	−1.41722	−	1.02967i
$584$	3.41231	−	10.5020i	0.141202	−	0.434576i
$585$	2.29097	+	4.84639i	0.0947200	+	0.200374i
$586$	−1.30314	−	4.01065i	−0.0538322	−	0.165678i
$587$	−1.59454	+	4.90749i	−0.0658137	+	0.202554i	−0.978556	−	0.205983i	$-0.933961\pi$
$587$	−1.59454	+	4.90749i	−0.0658137	+	0.202554i	0.912742	+	0.408537i	$0.133961\pi$
$588$	−0.371058	+	1.14200i	−0.0153022	+	0.0470952i
$589$	−2.14358	−	6.59727i	−0.0883247	−	0.271836i
$590$	−10.2789	−	5.62731i	−0.423174	−	0.231673i
$591$	−5.16555	+	15.8979i	−0.212483	+	0.653954i
$592$	0.158621	+	0.115245i	0.00651929	+	0.00473654i
$593$	4.68920			0.192562			0.0962811	−	0.995354i	$-0.469305\pi$
$593$	4.68920			0.192562			0.0962811	+	0.995354i	$0.469305\pi$
$594$	−4.56093	−	3.31371i	−0.187137	−	0.135963i
$595$	2.40475	+	5.08708i	0.0985851	+	0.208550i
$596$	−0.135973	+	0.0987904i	−0.00556968	+	0.00404661i
$597$	−12.7015	+	9.22814i	−0.519836	+	0.377683i
$598$	3.88534	+	11.9578i	0.158883	+	0.488993i
$599$	−21.8046			−0.890911			−0.445455	−	0.895304i	$-0.646958\pi$
$599$	−21.8046			−0.890911			−0.445455	+	0.895304i	$0.646958\pi$
$600$	−7.70878	−	12.0531i	−0.314710	−	0.492064i
$601$	10.6310			0.433649			0.216824	−	0.976211i	$-0.430430\pi$
$601$	10.6310			0.433649			0.216824	+	0.976211i	$0.430430\pi$
$602$	2.91043	+	8.95739i	0.118620	+	0.365076i
$603$	−2.45298	+	1.78220i	−0.0998932	+	0.0725767i
$604$	6.96095	−	5.05743i	0.283237	−	0.205784i
$605$	63.8026	−	8.17431i	2.59394	−	0.332333i
$606$	12.1642	+	8.83784i	0.494139	+	0.359013i
$607$	34.9300			1.41777			0.708883	−	0.705326i	$-0.249199\pi$
$607$	34.9300			1.41777			0.708883	+	0.705326i	$0.249199\pi$
$608$	25.5867	+	18.5898i	1.03768	+	0.753918i
$609$	2.22255	−	6.84030i	0.0900621	−	0.277183i
$610$	−1.52105	+	0.194876i	−0.0615857	+	0.00789028i
$611$	7.82712	+	24.0894i	0.316651	+	0.974552i
$612$	0.933729	−	2.87372i	0.0377437	−	0.116163i
$613$	−6.59841	+	20.3078i	−0.266507	+	0.820225i	0.724835	+	0.688923i	$0.241916\pi$
$613$	−6.59841	+	20.3078i	−0.266507	+	0.820225i	−0.991342	+	0.131303i	$0.958084\pi$
$614$	3.16131	+	9.72951i	0.127580	+	0.392651i
$615$	3.05387	−	16.1635i	0.123144	−	0.651777i
$616$	5.57612	−	17.1615i	0.224668	−	0.691458i
$617$	19.4405	+	14.1244i	0.782646	+	0.568626i	0.905772	−	0.423765i	$-0.139292\pi$
$617$	19.4405	+	14.1244i	0.782646	+	0.568626i	−0.123126	+	0.992391i	$0.539292\pi$
$618$	−2.79598			−0.112471
$619$	−12.1983	−	8.86261i	−0.490292	−	0.356218i	0.315004	−	0.949090i	$-0.397994\pi$
$619$	−12.1983	−	8.86261i	−0.490292	−	0.356218i	−0.805297	+	0.592872i	$0.797994\pi$
$620$	2.88392	+	1.57884i	0.115821	+	0.0634079i
$621$	−4.74613	+	3.44827i	−0.190456	+	0.138374i
$622$	−5.65651	+	4.10970i	−0.226806	+	0.164784i
$623$	−4.40854	−	13.5681i	−0.176624	−	0.543594i
$624$	−0.375462			−0.0150305
$625$	−10.4849	+	22.6951i	−0.419396	+	0.907804i
$626$	−11.5322			−0.460920
$627$	−11.0392	−	33.9750i	−0.440861	−	1.35683i
$628$	−10.5881	+	7.69269i	−0.422510	+	0.306972i
$629$	2.54860	−	1.85167i	0.101619	−	0.0738309i
$630$	1.75346	+	0.959958i	0.0698597	+	0.0382456i
$631$	23.7310	+	17.2416i	0.944717	+	0.686377i	0.949551	−	0.313611i	$-0.101539\pi$
$631$	23.7310	+	17.2416i	0.944717	+	0.686377i	−0.00483472	+	0.999988i	$0.501539\pi$
$632$	48.0873			1.91281
$633$	8.14986	+	5.92122i	0.323928	+	0.235347i
$634$	9.35719	−	28.7985i	0.371622	−	1.14373i
$635$	−4.18652	+	22.1584i	−0.166137	+	0.879331i
$636$	−2.48884	−	7.65987i	−0.0986890	−	0.303734i
$637$	0.740817	−	2.28000i	0.0293522	−	0.0903369i
$638$	−12.5299	+	38.5630i	−0.496062	+	1.52672i
$639$	1.71892	+	5.29031i	0.0679996	+	0.209281i
$640$	−14.2476	+	1.82538i	−0.563185	+	0.0721546i
$641$	3.07172	−	9.45378i	0.121326	−	0.373402i	−0.871888	−	0.489705i	$-0.837104\pi$
$641$	3.07172	−	9.45378i	0.121326	−	0.373402i	0.993214	+	0.116303i	$0.0371044\pi$
$642$	−1.08886	−	0.791101i	−0.0429738	−	0.0312223i
$643$	41.8923			1.65207			0.826036	−	0.563617i	$-0.190591\pi$
$643$	41.8923			1.65207			0.826036	+	0.563617i	$0.190591\pi$
$644$	−5.69901	−	4.14057i	−0.224572	−	0.163161i
$645$	−23.3662	+	2.99365i	−0.920044	+	0.117875i
$646$	−10.3102	+	7.49079i	−0.405649	+	0.294721i
$647$	2.92887	−	2.12795i	0.115146	−	0.0836583i	−0.528722	−	0.848795i	$-0.677329\pi$
$647$	2.92887	−	2.12795i	0.115146	−	0.0836583i	0.643868	+	0.765137i	$0.277329\pi$
$648$	−0.884246	−	2.72143i	−0.0347364	−	0.106908i
$649$	36.9664			1.45106
$650$	5.77377	+	9.02758i	0.226466	+	0.354091i
$651$	−1.22451			−0.0479925
$652$	−1.36493	−	4.20082i	−0.0534548	−	0.164517i
$653$	−17.1436	+	12.4555i	−0.670880	+	0.487423i	−0.870320	−	0.492487i	$-0.836088\pi$
$653$	−17.1436	+	12.4555i	−0.670880	+	0.487423i	0.199440	+	0.979910i	$0.436088\pi$
$654$	−7.66585	+	5.56957i	−0.299758	+	0.217787i
$655$	−0.105617	−	0.223425i	−0.00412680	−	0.00872995i
$656$	0.932102	+	0.677212i	0.0363925	+	0.0264407i
$657$	−3.85900			−0.150554
$658$	7.64161	+	5.55195i	0.297901	+	0.216438i
$659$	−3.48049	+	10.7119i	−0.135581	+	0.417275i	−0.995680	−	0.0928522i	$-0.970402\pi$
$659$	−3.48049	+	10.7119i	−0.135581	+	0.417275i	0.860099	+	0.510127i	$0.170402\pi$
$660$	14.8518	+	8.13083i	0.578106	+	0.316492i
$661$	9.14010	+	28.1303i	0.355509	+	1.09414i	0.955714	+	0.294297i	$0.0950856\pi$
$661$	9.14010	+	28.1303i	0.355509	+	1.09414i	−0.600205	+	0.799846i	$0.704914\pi$
$662$	2.50329	−	7.70433i	0.0972930	−	0.299437i
$663$	−1.86419	+	5.73738i	−0.0723991	+	0.222821i
$664$	7.56155	+	23.2720i	0.293445	+	0.903131i
$665$	5.41359	+	11.4521i	0.209930	+	0.444092i
$666$	0.345847	−	1.06441i	0.0134013	−	0.0412450i
$667$	34.1357	+	24.8010i	1.32174	+	0.960299i
$668$	−27.8381			−1.07709
$669$	6.32646	+	4.59644i	0.244595	+	0.177709i
$670$	−4.41111	+	4.15695i	−0.170416	+	0.160597i
$671$	3.91360	−	2.84339i	0.151083	−	0.109768i
$672$	4.51670	−	3.28157i	0.174235	−	0.126589i
$673$	−0.379638	−	1.16841i	−0.0146340	−	0.0450387i	0.943473	−	0.331450i	$-0.107538\pi$
$673$	−0.379638	−	1.16841i	−0.0146340	−	0.0450387i	−0.958107	+	0.286411i	$0.907538\pi$
$674$	−0.718372			−0.0276707
$675$	−3.17353	+	3.86377i	−0.122149	+	0.148716i
$676$	8.70893			0.334959
$677$	11.6709	+	35.9192i	0.448548	+	1.38049i	0.878546	+	0.477658i	$0.158514\pi$
$677$	11.6709	+	35.9192i	0.448548	+	1.38049i	−0.429998	+	0.902830i	$0.641486\pi$
$678$	−11.0460	+	8.02536i	−0.424217	+	0.308212i
$679$	−4.66125	+	3.38660i	−0.178882	+	0.129966i
$680$	2.98918	−	15.8212i	0.114630	−	0.606713i
$681$	−4.57755	−	3.32578i	−0.175412	−	0.127444i
$682$	6.90334			0.264343
$683$	10.9383	+	7.94715i	0.418543	+	0.304089i	0.777051	−	0.629437i	$-0.216714\pi$
$683$	10.9383	+	7.94715i	0.418543	+	0.304089i	−0.358508	+	0.933527i	$0.616714\pi$
$684$	2.10201	−	6.46934i	0.0803725	−	0.247361i
$685$	15.8247	−	14.9129i	0.604632	−	0.569794i
$686$	−0.276260	−	0.850242i	−0.0105477	−	0.0324624i
$687$	2.09275	−	6.44083i	0.0798435	−	0.245733i
$688$	0.509870	−	1.56922i	0.0194386	−	0.0598259i
$689$	4.96897	+	15.2929i	0.189303	+	0.582614i
$690$	−8.53479	+	8.04303i	−0.324914	+	0.306193i
$691$	−3.02886	+	9.32187i	−0.115223	+	0.354621i	−0.991994	−	0.126289i	$-0.959693\pi$
$691$	−3.02886	+	9.32187i	−0.115223	+	0.354621i	0.876770	+	0.480909i	$0.159693\pi$
$692$	0.705314	+	0.512440i	0.0268120	+	0.0194801i
$693$	−6.30608			−0.239548
$694$	−17.0761	−	12.4065i	−0.648201	−	0.470946i
$695$	4.93846	−	26.1383i	0.187326	−	0.991481i
$696$	−16.6501	+	12.0970i	−0.631120	+	0.458536i
$697$	14.9763	−	10.8809i	0.567268	−	0.412144i
$698$	−2.69335	−	8.28929i	−0.101945	−	0.313754i
$699$	8.81600			0.333452
$700$	−5.58998	−	2.19049i	−0.211281	−	0.0827927i
$701$	23.5411			0.889136			0.444568	−	0.895745i	$-0.353357\pi$
$701$	23.5411			0.889136			0.444568	+	0.895745i	$0.353357\pi$
$702$	0.662288	+	2.03831i	0.0249965	+	0.0769312i
$703$	5.73743	−	4.16849i	0.216391	−	0.157217i
$704$	−27.0614	+	19.6613i	−1.01992	+	0.741012i
$705$	−17.1935	+	16.2029i	−0.647546	+	0.610236i
$706$	17.9299	+	13.0268i	0.674801	+	0.490272i
$707$	16.8187			0.632531
$708$	5.69463	+	4.13739i	0.214017	+	0.155493i
$709$	−2.76815	+	8.51948i	−0.103960	+	0.319956i	−0.989485	−	0.144636i	$-0.953799\pi$
$709$	−2.76815	+	8.51948i	−0.103960	+	0.319956i	0.885525	+	0.464592i	$0.153799\pi$
$710$	4.75228	+	10.0531i	0.178350	+	0.377287i
$711$	−5.19305	−	15.9826i	−0.194755	−	0.599393i
$712$	−12.6149	+	38.8248i	−0.472765	+	1.45502i
$713$	2.21987	−	6.83207i	0.0831349	−	0.255863i
$714$	0.695180	+	2.13954i	0.0260165	+	0.0800705i
$715$	−29.6516	−	16.2332i	−1.10891	−	0.607087i
$716$	−8.76489	+	26.9756i	−0.327560	+	1.00812i
$717$	1.86071	+	1.35189i	0.0694896	+	0.0504871i
$718$	12.2858			0.458503
$719$	−13.8567	−	10.0675i	−0.516767	−	0.375453i	0.298618	−	0.954373i	$-0.403474\pi$
$719$	−13.8567	−	10.0675i	−0.516767	−	0.375453i	−0.815384	+	0.578920i	$0.803474\pi$
$720$	−0.149668	−	0.316612i	−0.00557780	−	0.0117994i
$721$	−2.53020	+	1.83830i	−0.0942296	+	0.0684618i
$722$	−9.46844	+	6.87922i	−0.352379	+	0.256018i
$723$	−3.79683	−	11.6854i	−0.141205	−	0.434586i
$724$	−5.94850			−0.221074
$725$	33.4826	+	13.1205i	1.24351	+	0.487283i
$726$	25.7173			0.954458
$727$	−11.0937	−	34.1430i	−0.411444	−	1.26629i	−0.915394	−	0.402560i	$-0.868120\pi$
$727$	−11.0937	−	34.1430i	−0.411444	−	1.26629i	0.503950	−	0.863733i	$-0.331880\pi$
$728$	−5.54979	+	4.03216i	−0.205689	+	0.149442i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−7.65175	+	0.980333i	−0.283204	+	0.0362837i
$731$	−21.4474	−	15.5825i	−0.793262	−	0.576339i
$732$	0.921125			0.0340458
$733$	7.60593	+	5.52603i	0.280931	+	0.204109i	0.719324	−	0.694675i	$-0.244452\pi$
$733$	7.60593	+	5.52603i	0.280931	+	0.204109i	−0.438392	+	0.898784i	$0.644452\pi$
$734$	−7.67678	+	23.6267i	−0.283355	+	0.872078i
$735$	2.21794	−	0.284160i	0.0818099	−	0.0104814i
$736$	10.1211	+	31.1495i	0.373069	+	1.14819i
$737$	5.90852	−	18.1846i	0.217643	−	0.669837i
$738$	2.03229	−	6.25476i	0.0748098	−	0.230241i
$739$	−4.64099	−	14.2835i	−0.170722	−	0.525427i	0.828691	−	0.559707i	$-0.189086\pi$
$739$	−4.64099	−	14.2835i	−0.170722	−	0.525427i	−0.999412	+	0.0342797i	$0.989086\pi$
$740$	−0.624034	+	3.30289i	−0.0229399	+	0.121417i
$741$	−4.19667	+	12.9160i	−0.154169	+	0.474482i
$742$	4.85120	+	3.52461i	0.178093	+	0.129392i
$743$	−8.53404			−0.313084			−0.156542	−	0.987671i	$-0.550035\pi$
$743$	−8.53404			−0.313084			−0.156542	+	0.987671i	$0.550035\pi$
$744$	2.83473	+	2.05955i	0.103926	+	0.0755069i
$745$	0.274535	+	0.150298i	0.0100582	+	0.00550649i
$746$	−8.65675	+	6.28950i	−0.316946	+	0.230275i
$747$	6.91824	−	5.02639i	0.253125	−	0.183906i
$748$	5.88817	+	18.1219i	0.215293	+	0.662603i
$749$	−1.50549			−0.0550093
$750$	−5.31104	+	8.46740i	−0.193932	+	0.309186i
$751$	−53.7325			−1.96073			−0.980364	−	0.197196i	$-0.936816\pi$
$751$	−53.7325			−1.96073			−0.980364	+	0.197196i	$0.936816\pi$
$752$	−0.511342	−	1.57375i	−0.0186467	−	0.0573887i
$753$	16.3627	−	11.8882i	0.596290	−	0.433230i
$754$	12.4707	−	9.06050i	0.454156	−	0.329964i
$755$	−14.0544	−	7.69428i	−0.511492	−	0.280023i
$756$	−0.971442	−	0.705794i	−0.0353310	−	0.0256695i
$757$	19.6619			0.714624			0.357312	−	0.933985i	$-0.383693\pi$
$757$	19.6619			0.714624			0.357312	+	0.933985i	$0.383693\pi$
$758$	13.2059	+	9.59468i	0.479661	+	0.348494i
$759$	11.4320	−	35.1842i	0.414957	−	1.27711i
$760$	6.72927	−	35.6167i	0.244096	−	1.29195i
$761$	6.57823	+	20.2457i	0.238461	+	0.733907i	0.996643	+	0.0818645i	$0.0260875\pi$
$761$	6.57823	+	20.2457i	0.238461	+	0.733907i	−0.758183	+	0.652042i	$0.773913\pi$
$762$	−2.78605	+	8.57458i	−0.100928	+	0.310624i
$763$	−3.27528	+	10.0803i	−0.118573	+	0.364931i
$764$	−5.57086	−	17.1453i	−0.201546	−	0.620296i
$765$	−5.58121	+	0.715058i	−0.201789	+	0.0258530i
$766$	−0.509764	+	1.56889i	−0.0184185	+	0.0566864i
$767$	−11.3693	−	8.26029i	−0.410522	−	0.298262i
$768$	−16.3516			−0.590037
$769$	23.9049	+	17.3679i	0.862033	+	0.626304i	0.928437	−	0.371489i	$-0.121153\pi$
$769$	23.9049	+	17.3679i	0.862033	+	0.626304i	−0.0664040	+	0.997793i	$0.521153\pi$
$770$	−12.5039	+	1.60198i	−0.450609	+	0.0577314i
$771$	−14.5106	+	10.5426i	−0.522586	+	0.379681i
$772$	14.9127	−	10.8347i	0.536720	−	0.389950i
$773$	4.73679	+	14.5783i	0.170370	+	0.524346i	0.999392	−	0.0348706i	$-0.0111019\pi$
$773$	4.73679	+	14.5783i	0.170370	+	0.524346i	−0.829021	+	0.559217i	$0.811102\pi$
$774$	−9.41836			−0.338536
$775$	0.362917	−	6.11180i	0.0130364	−	0.219542i
$776$	16.4868			0.591840
$777$	−0.386855	−	1.19062i	−0.0138783	−	0.0427131i
$778$	−1.90446	+	1.38367i	−0.0682780	+	0.0496069i
$779$	33.7147	−	24.4952i	1.20796	−	0.877631i
$780$	−2.75093	−	5.81939i	−0.0984989	−	0.208368i
$781$	−28.3786	−	20.6183i	−1.01547	−	0.737780i
$782$	−13.1977			−0.471948
$783$	5.81870	+	4.22754i	0.207943	+	0.151080i
$784$	−0.0483972	+	0.148951i	−0.00172847	+	0.00531969i
$785$	21.3777	+	11.7035i	0.763003	+	0.417716i
$786$	−0.0305324	−	0.0939691i	−0.00108906	−	0.00335177i
$787$	−10.7196	+	32.9914i	−0.382111	+	1.17602i	0.556443	+	0.830886i	$0.312166\pi$
$787$	−10.7196	+	32.9914i	−0.382111	+	1.17602i	−0.938554	+	0.345132i	$0.887834\pi$
$788$	6.20264	−	19.0898i	0.220960	−	0.680044i
$789$	5.04043	+	15.5128i	0.179444	+	0.552272i
$790$	−14.3571	−	30.3715i	−0.510803	−	1.08057i
$791$	−4.71945	+	14.5250i	−0.167804	+	0.516449i
$792$	14.5985	+	10.6064i	0.518734	+	0.376882i
$793$	−1.83902			−0.0653057
$794$	20.3797	+	14.8067i	0.723249	+	0.525471i
$795$	−10.9152	+	10.2862i	−0.387121	+	0.364816i
$796$	15.2515	−	11.0809i	0.540575	−	0.392751i
$797$	18.5794	−	13.4987i	0.658116	−	0.478149i	−0.207910	−	0.978148i	$-0.566666\pi$
$797$	18.5794	−	13.4987i	0.658116	−	0.478149i	0.866026	+	0.499999i	$0.166666\pi$
$798$	1.56499	+	4.81656i	0.0554002	+	0.170504i
$799$	−26.5870			−0.940582
$800$	15.0404	+	23.5163i	0.531757	+	0.831429i
$801$	14.2663			0.504076
$802$	0.610991	+	1.88044i	0.0215748	+	0.0664005i
$803$	19.6876	−	14.3039i	0.694759	−	0.504772i
$804$	2.94547	−	2.14001i	0.103879	−	0.0754722i
$805$	−2.43537	+	12.8899i	−0.0858356	+	0.454311i
$806$	−2.12318	−	1.54258i	−0.0747857	−	0.0543350i
$807$	25.0532			0.881916
$808$	−38.9349	−	28.2879i	−1.36973	−	0.995164i
$809$	3.92525	−	12.0807i	0.138004	−	0.424734i	−0.858041	−	0.513581i	$-0.828318\pi$
$809$	3.92525	−	12.0807i	0.138004	−	0.424734i	0.996045	+	0.0888476i	$0.0283184\pi$
$810$	−1.45482	+	1.37100i	−0.0511173	+	0.0481720i
$811$	10.9420	+	33.6761i	0.384227	+	1.18253i	0.937039	+	0.349223i	$0.113555\pi$
$811$	10.9420	+	33.6761i	0.384227	+	1.18253i	−0.552813	+	0.833306i	$0.686445\pi$
$812$	−2.66876	+	8.21361i	−0.0936553	+	0.288241i
$813$	5.67481	−	17.4653i	0.199024	−	0.612534i
$814$	2.18094	+	6.71224i	0.0764419	+	0.235264i
$815$	−5.98609	+	5.64118i	−0.209683	+	0.197602i
$816$	0.121787	−	0.374820i	0.00426338	−	0.0131213i
$817$	−48.2826	−	35.0794i	−1.68919	−	1.22727i
$818$	5.11887			0.178977
$819$	1.93948	+	1.40912i	0.0677710	+	0.0492385i
$820$	−3.66700	+	19.4087i	−0.128057	+	0.677781i
$821$	33.3970	−	24.2644i	1.16556	−	0.846832i	0.175093	−	0.984552i	$-0.443977\pi$
$821$	33.3970	−	24.2644i	1.16556	−	0.846832i	0.990471	+	0.137720i	$0.0439773\pi$
$822$	7.03325	−	5.10995i	0.245313	−	0.178230i
$823$	5.34632	+	16.4543i	0.186361	+	0.573560i	0.999969	−	0.00785369i	$-0.00249993\pi$
$823$	5.34632	+	16.4543i	0.186361	+	0.573560i	−0.813608	+	0.581413i	$0.802500\pi$
$824$	8.94927			0.311763
$825$	1.86898	−	31.4749i	0.0650694	−	1.09582i
$826$	−5.24064			−0.182345
$827$	−10.1659	−	31.2875i	−0.353504	−	1.08797i	−0.956872	−	0.290510i	$-0.906175\pi$
$827$	−10.1659	−	31.2875i	−0.353504	−	1.08797i	0.603369	−	0.797462i	$-0.293825\pi$
$828$	5.69901	−	4.14057i	0.198054	−	0.143895i
$829$	−30.2985	+	22.0132i	−1.05231	+	0.764549i	−0.972651	−	0.232273i	$-0.925384\pi$
$829$	−30.2985	+	22.0132i	−1.05231	+	0.764549i	−0.0796607	+	0.996822i	$0.525384\pi$
$830$	12.4408	−	11.7240i	0.431827	−	0.406945i
$831$	−12.5527	−	9.12008i	−0.435449	−	0.316372i
$832$	12.7163			0.440860
$833$	2.03581	+	1.47910i	0.0705365	+	0.0512478i
$834$	3.28645	−	10.1146i	0.113800	−	0.350242i
$835$	22.1550	+	46.8674i	0.766705	+	1.62191i
$836$	13.2555	+	40.7961i	0.458450	+	1.41096i
$837$	0.378396	−	1.16458i	0.0130793	−	0.0402538i
$838$	7.21733	−	22.2127i	0.249319	−	0.767324i
$839$	4.34721	+	13.3793i	0.150082	+	0.461906i	0.997629	−	0.0688143i	$-0.0219216\pi$
$839$	4.34721	+	13.3793i	0.150082	+	0.461906i	−0.847547	+	0.530720i	$0.821922\pi$
$840$	−5.61243	−	3.07260i	−0.193647	−	0.106015i
$841$	7.02376	−	21.6169i	0.242199	−	0.745411i
$842$	−2.35289	−	1.70947i	−0.0810858	−	0.0589123i
$843$	20.7493			0.714644
$844$	−9.78610	−	7.11002i	−0.336851	−	0.244737i
$845$	−6.93100	−	14.6621i	−0.238434	−	0.504390i
$846$	−7.64161	+	5.55195i	−0.262724	+	0.190880i
$847$	23.2727	−	16.9086i	0.799659	−	0.580986i
$848$	−0.324620	−	0.999079i	−0.0111475	−	0.0343085i
$849$	−4.29816			−0.147513
$850$	−10.8849	+	2.83568i	−0.373351	+	0.0972630i
$851$	7.34426			0.251758
$852$	−2.06403	−	6.35244i	−0.0707125	−	0.217631i
$853$	−38.4599	+	27.9428i	−1.31684	+	0.956742i	−0.316876	+	0.948467i	$0.602634\pi$
$853$	−38.4599	+	27.9428i	−1.31684	+	0.956742i	−0.999966	+	0.00827486i	$0.997366\pi$
$854$	−0.554821	+	0.403101i	−0.0189856	+	0.0137938i
$855$	−12.5645	+	1.60974i	−0.429695	+	0.0550520i
$856$	3.48518	+	2.53213i	0.119121	+	0.0865465i
$857$	−29.3217			−1.00161			−0.500806	−	0.865560i	$-0.666963\pi$
$857$	−29.3217			−1.00161			−0.500806	+	0.865560i	$0.666963\pi$
$858$	−10.9341	−	7.94406i	−0.373283	−	0.271206i
$859$	2.98991	−	9.20201i	0.102015	−	0.313968i	−0.887004	−	0.461762i	$-0.847217\pi$
$859$	2.98991	−	9.20201i	0.102015	−	0.313968i	0.989018	+	0.147794i	$0.0472173\pi$
$860$	28.0574	−	3.59468i	0.956750	−	0.122578i
$861$	−2.27327	−	6.99639i	−0.0774727	−	0.238436i
$862$	−5.67812	+	17.4754i	−0.193397	+	0.595216i
$863$	4.45690	−	13.7169i	0.151715	−	0.466930i	−0.846098	−	0.533027i	$-0.821055\pi$
$863$	4.45690	−	13.7169i	0.151715	−	0.466930i	0.997813	+	0.0660966i	$0.0210545\pi$
$864$	1.72522	+	5.30969i	0.0586933	+	0.180639i
$865$	0.301404	−	1.59527i	0.0102480	−	0.0542408i
$866$	9.15354	−	28.1717i	0.311050	−	0.957313i
$867$	8.63039	+	6.27035i	0.293104	+	0.212952i
$868$	1.47036			0.0499072
$869$	85.7348	+	62.2900i	2.90835	+	2.11304i
$870$	12.6115	+	6.90432i	0.427569	+	0.234078i
$871$	−5.88062	+	4.27252i	−0.199257	+	0.144769i
$872$	24.5366	−	17.8269i	0.830914	−	0.603695i
$873$	−1.78044	−	5.47963i	−0.0602588	−	0.185457i
$874$	−29.7107			−1.00498
$875$	0.760954	+	11.1544i	0.0257249	+	0.377088i
$876$	4.63377			0.156561
$877$	−0.384117	−	1.18219i	−0.0129707	−	0.0399197i	0.944362	−	0.328909i	$-0.106681\pi$
$877$	−0.384117	−	1.18219i	−0.0129707	−	0.0399197i	−0.957332	+	0.288989i	$0.906681\pi$
$878$	23.3170	−	16.9408i	0.786909	−	0.571723i
$879$	3.81619	−	2.77262i	0.128717	−	0.0935183i
$880$	1.93713	+	1.06051i	0.0653005	+	0.0357497i
$881$	24.1688	+	17.5597i	0.814268	+	0.591600i	0.915065	−	0.403307i	$-0.132139\pi$
$881$	24.1688	+	17.5597i	0.814268	+	0.591600i	−0.100797	+	0.994907i	$0.532139\pi$
$882$	0.893997			0.0301025
$883$	−9.25172	−	6.72177i	−0.311345	−	0.226206i	0.421128	−	0.907001i	$-0.361634\pi$
$883$	−9.25172	−	6.72177i	−0.311345	−	0.226206i	−0.732474	+	0.680796i	$0.761634\pi$
$884$	2.23846	−	6.88927i	0.0752875	−	0.231711i
$885$	2.43350	−	12.8800i	0.0818012	−	0.432957i
$886$	−3.71273	−	11.4266i	−0.124731	−	0.383884i
$887$	−7.63393	+	23.4948i	−0.256322	+	0.788879i	0.737244	+	0.675627i	$0.236127\pi$
$887$	−7.63393	+	23.4948i	−0.256322	+	0.788879i	−0.993566	+	0.113252i	$0.963873\pi$
$888$	−1.10698	+	3.40693i	−0.0371477	+	0.114329i
$889$	3.11640	+	9.59129i	0.104521	+	0.321681i
$890$	28.2877	−	3.62419i	0.948207	−	0.121483i
$891$	1.94869	−	5.99744i	0.0652834	−	0.200922i
$892$	−7.59661	−	5.51926i	−0.254353	−	0.184799i
$893$	−59.8529			−2.00290
$894$	0.101235	+	0.0735515i	0.00338580	+	0.00245993i
$895$	52.3907	−	6.71224i	1.75123	−	0.224365i
$896$	−5.19696	+	3.77581i	−0.173618	+	0.126141i
$897$	−11.3781	+	8.26664i	−0.379902	+	0.276015i
$898$	7.56947	+	23.2964i	0.252597	+	0.777412i
$899$	−8.80709			−0.293733
$900$	3.81068	−	4.63949i	0.127023	−	0.154650i
$901$	−16.8785			−0.562305
$902$	12.8158	+	39.4430i	0.426720	+	1.31331i
$903$	−8.52308	+	6.19238i	−0.283630	+	0.206069i
$904$	35.3555	−	25.6873i	1.17591	−	0.854347i
$905$	4.73411	+	10.0147i	0.157367	+	0.332900i
$906$	−5.18257	−	3.76536i	−0.172179	−	0.125096i
$907$	−49.1208			−1.63103			−0.815515	−	0.578736i	$-0.803546\pi$
$907$	−49.1208			−1.63103			−0.815515	+	0.578736i	$0.803546\pi$
$908$	5.49658	+	3.99350i	0.182410	+	0.132529i
$909$	−5.19725	+	15.9955i	−0.172382	+	0.530537i
$910$	4.20364	+	2.30134i	0.139349	+	0.0762887i
$911$	13.6989	+	42.1608i	0.453864	+	1.39685i	0.872464	+	0.488679i	$0.162521\pi$
$911$	13.6989	+	42.1608i	0.453864	+	1.39685i	−0.418599	+	0.908171i	$0.637479\pi$
$912$	0.274166	−	0.843798i	0.00907856	−	0.0279409i
$913$	−16.6640	+	51.2865i	−0.551498	+	1.69734i
$914$	0.799456	+	2.46047i	0.0264437	+	0.0813852i
$915$	−0.733078	−	1.55078i	−0.0242348	−	0.0512671i
$916$	−2.51291	+	7.73395i	−0.0830290	+	0.255537i
$917$	−0.0894129	−	0.0649623i	−0.00295267	−	0.00214524i
$918$	−2.24965			−0.0742495
$919$	−43.6459	−	31.7106i	−1.43974	−	1.04604i	−0.988096	−	0.153840i	$-0.950836\pi$
$919$	−43.6459	−	31.7106i	−1.43974	−	1.04604i	−0.451649	−	0.892196i	$-0.649164\pi$
$920$	27.3179	−	25.7439i	0.900644	−	0.848750i
$921$	−9.25777	+	6.72616i	−0.305054	+	0.221635i
$922$	−25.9041	+	18.8204i	−0.853106	+	0.619818i
$923$	4.12084	+	12.6826i	0.135639	+	0.417454i
$924$	7.57214			0.249105
$925$	6.05727	−	1.57800i	0.199162	−	0.0518844i
$926$	3.12605			0.102728
$927$	−0.966450	−	2.97443i	−0.0317424	−	0.0976930i
$928$	32.4855	−	23.6021i	1.06639	−	0.774776i
$929$	−24.9082	+	18.0969i	−0.817212	+	0.593739i	−0.915913	−	0.401378i	$-0.868531\pi$
$929$	−24.9082	+	18.0969i	−0.817212	+	0.593739i	0.0987004	+	0.995117i	$0.468531\pi$
$930$	0.454447	−	2.40530i	0.0149019	−	0.0788728i
$931$	4.58302	+	3.32976i	0.150202	+	0.109128i
$932$	−10.5860			−0.346755
$933$	−6.32722	−	4.59699i	−0.207144	−	0.150499i
$934$	−3.91418	+	12.0466i	−0.128076	+	0.394177i
$935$	25.8234	−	24.3355i	0.844514	−	0.795855i
$936$	−2.11983	−	6.52417i	−0.0692889	−	0.213249i
$937$	−3.60000	+	11.0797i	−0.117607	+	0.361957i	−0.992482	−	0.122392i	$-0.960943\pi$
$937$	−3.60000	+	11.0797i	−0.117607	+	0.361957i	0.874875	+	0.484349i	$0.160943\pi$
$938$	−0.837636	+	2.57798i	−0.0273498	+	0.0841740i
$939$	−3.98620	−	12.2683i	−0.130085	−	0.400360i
$940$	20.6455	−	19.4559i	0.673381	−	0.634582i
$941$	1.28967	−	3.96918i	0.0420419	−	0.129392i	−0.927833	−	0.372997i	$-0.878330\pi$
$941$	1.28967	−	3.96918i	0.0420419	−	0.129392i	0.969874	+	0.243605i	$0.0783302\pi$
$942$	7.88305	+	5.72737i	0.256843	+	0.186608i
$943$	43.1569			1.40538
$944$	0.742752	+	0.539641i	0.0241745	+	0.0175638i
$945$	−0.415129	+	2.19720i	−0.0135041	+	0.0714748i
$946$	48.0499	−	34.9103i	1.56224	−	1.13503i
$947$	−31.6990	+	23.0307i	−1.03008	+	0.748397i	−0.968325	−	0.249694i	$-0.919670\pi$
$947$	−31.6990	+	23.0307i	−1.03008	+	0.748397i	−0.0617553	+	0.998091i	$0.519670\pi$
$948$	6.23565	+	19.1914i	0.202525	+	0.623307i
$949$	−9.25132			−0.300310
$950$	−24.5043	+	6.38369i	−0.795023	+	0.207114i
$951$	33.8709			1.09834
$952$	−2.22511	−	6.84819i	−0.0721163	−	0.221951i
$953$	−1.79828	+	1.30653i	−0.0582521	+	0.0423226i	−0.616530	−	0.787331i	$-0.711462\pi$
$953$	−1.79828	+	1.30653i	−0.0582521	+	0.0423226i	0.558278	+	0.829654i	$0.311462\pi$
$954$	−4.85120	+	3.52461i	−0.157063	+	0.114113i
$955$	−24.4317	+	23.0240i	−0.790593	+	0.745040i
$956$	−2.23428	−	1.62330i	−0.0722619	−	0.0525014i
$957$	−45.3553			−1.46613
$958$	7.76327	+	5.64034i	0.250820	+	0.182231i
$959$	3.00500	−	9.24844i	0.0970365	−	0.298648i
$960$	5.06903	+	10.7232i	0.163602	+	0.346089i
$961$	−9.11618	−	28.0567i	−0.294070	−	0.905055i
$962$	0.829111	−	2.55174i	0.0267316	−	0.0822715i
$963$	0.465221	−	1.43180i	0.0149915	−	0.0461392i
$964$	4.55911	+	14.0315i	0.146839	+	0.451924i
$965$	−30.1092	−	16.4837i	−0.969250	−	0.530630i
$966$	−1.62069	+	4.98798i	−0.0521449	+	0.160486i
$967$	5.50734	+	4.00132i	0.177104	+	0.128674i	0.672806	−	0.739819i	$-0.265089\pi$
$967$	5.50734	+	4.00132i	0.177104	+	0.128674i	−0.495702	+	0.868493i	$0.665089\pi$
$968$	−82.3151			−2.64571
$969$	−11.5327	−	8.37899i	−0.370483	−	0.269172i
$970$	−4.92235	−	10.4129i	−0.158047	−	0.334338i
$971$	−14.3174	+	10.4022i	−0.459468	+	0.333823i	−0.793323	−	0.608801i	$-0.791651\pi$
$971$	−14.3174	+	10.4022i	−0.459468	+	0.333823i	0.333854	+	0.942625i	$0.391651\pi$
$972$	0.971442	−	0.705794i	0.0311590	−	0.0226384i
$973$	−3.67613	−	11.3140i	−0.117851	−	0.362709i
$974$	31.7006			1.01575
$975$	−7.60802	+	9.26274i	−0.243652	+	0.296645i
$976$	0.120143			0.00384567
$977$	−6.89724	−	21.2275i	−0.220662	−	0.679128i	−0.998703	−	0.0509146i	$-0.983786\pi$
$977$	−6.89724	−	21.2275i	−0.220662	−	0.679128i	0.778041	−	0.628214i	$-0.216214\pi$
$978$	−2.66049	+	1.93296i	−0.0850732	+	0.0618093i
$979$	−72.7829	+	52.8799i	−2.32615	+	1.69005i
$980$	−2.66323	+	0.341210i	−0.0850738	+	0.0108996i
$981$	−8.57480	−	6.22996i	−0.273772	−	0.198907i
$982$	15.7531			0.502701
$983$	5.42130	+	3.93881i	0.172913	+	0.125628i	0.670876	−	0.741570i	$-0.265918\pi$
$983$	5.42130	+	3.93881i	0.172913	+	0.125628i	−0.497963	+	0.867198i	$0.665918\pi$
$984$	−6.50490	+	20.0200i	−0.207369	+	0.638215i
$985$	−37.0753	+	4.75004i	−1.18132	+	0.151349i
$986$	4.99995	+	15.3883i	0.159231	+	0.490063i
$987$	−3.26493	+	10.0484i	−0.103924	+	0.319844i
$988$	5.03923	−	15.5092i	0.160319	−	0.493412i
$989$	−19.0987	−	58.7797i	−0.607303	−	1.86909i
$990$	2.34034	−	12.3869i	0.0743808	−	0.393683i
$991$	−6.49330	+	19.9843i	−0.206267	+	0.634823i	0.793392	+	0.608711i	$0.208313\pi$
$991$	−6.49330	+	19.9843i	−0.206267	+	0.634823i	−0.999659	+	0.0261128i	$0.991687\pi$
$992$	−5.53076	−	4.01833i	−0.175602	−	0.127582i
$993$	9.06133			0.287553
$994$	4.02317	+	2.92300i	0.127607	+	0.0927121i
$995$	−30.7933	−	16.8582i	−0.976214	−	0.534442i
$996$	−8.30720	+	6.03554i	−0.263224	+	0.191243i
$997$	26.0988	−	18.9619i	0.826558	−	0.600530i	−0.0920252	−	0.995757i	$-0.529334\pi$
$997$	26.0988	−	18.9619i	0.826558	−	0.600530i	0.918584	+	0.395227i	$0.129334\pi$
$998$	4.97747	+	15.3191i	0.157559	+	0.484917i
$999$	1.25189			0.0396080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.106.6	✓	32
25.21	even	5	inner	525.2.n.d.421.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.106.6	✓	32	1.1	even	1	trivial
525.2.n.d.421.6	yes	32	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.276260 + 0.850242i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.971442 - 0.705794i) q^{4} +(-1.96138 - 1.07378i) q^{5} +(-0.723259 - 0.525478i) q^{6} -1.00000 q^{7} +(2.31498 + 1.68193i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.276260 + 0.850242i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.971442 - 0.705794i) q^{4} +(-1.96138 - 1.07378i) q^{5} +(-0.723259 - 0.525478i) q^{6} -1.00000 q^{7} +(2.31498 + 1.68193i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.371124 - 1.96429i) q^{10} +(1.94869 + 5.99744i) q^{11} +(-0.371058 + 1.14200i) q^{12} +(0.740817 - 2.28000i) q^{13} +(-0.276260 - 0.850242i) q^{14} +(2.21794 - 0.284160i) q^{15} +(-0.0483972 + 0.148951i) q^{16} +(2.03581 + 1.47910i) q^{17} +0.893997 q^{18} +(4.58302 + 3.32976i) q^{19} +(-2.66323 + 0.341210i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-4.56093 + 3.31371i) q^{22} +(1.81286 + 5.57941i) q^{23} -2.86148 q^{24} +(2.69398 + 4.21218i) q^{25} +2.14321 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.971442 + 0.705794i) q^{28} +(5.81870 - 4.22754i) q^{29} +(0.854333 + 1.80728i) q^{30} +(-0.990652 - 0.719751i) q^{31} +5.58294 q^{32} +(-5.10172 - 3.70662i) q^{33} +(-0.695180 + 2.13954i) q^{34} +(1.96138 + 1.07378i) q^{35} +(-0.371058 - 1.14200i) q^{36} +(0.386855 - 1.19062i) q^{37} +(-1.56499 + 4.81656i) q^{38} +(0.740817 + 2.28000i) q^{39} +(-2.73452 - 5.78469i) q^{40} +(2.27327 - 6.99639i) q^{41} +(0.723259 + 0.525478i) q^{42} -10.5351 q^{43} +(6.12599 + 4.45079i) q^{44} +(-1.62733 + 1.53356i) q^{45} +(-4.24303 + 3.08274i) q^{46} +(-8.54769 + 6.21026i) q^{47} +(-0.0483972 - 0.148951i) q^{48} +1.00000 q^{49} +(-2.83713 + 3.45420i) q^{50} -2.51640 q^{51} +(-0.889550 - 2.73775i) q^{52} +(-5.42642 + 3.94252i) q^{53} +(-0.723259 + 0.525478i) q^{54} +(2.61784 - 13.8557i) q^{55} +(-2.31498 - 1.68193i) q^{56} -5.66492 q^{57} +(5.20191 + 3.77941i) q^{58} +(1.81147 - 5.57512i) q^{59} +(1.95404 - 1.84145i) q^{60} +(-0.237051 - 0.729567i) q^{61} +(0.338285 - 1.04113i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(1.63914 + 5.04475i) q^{64} +(-3.90124 + 3.67646i) q^{65} +(1.74212 - 5.36169i) q^{66} +(-2.45298 - 1.78220i) q^{67} +3.02161 q^{68} +(-4.74613 - 3.44827i) q^{69} +(-0.371124 + 1.96429i) q^{70} +(-4.50020 + 3.26959i) q^{71} +(2.31498 - 1.68193i) q^{72} +(-1.19250 - 3.67013i) q^{73} +1.11919 q^{74} +(-4.65534 - 1.82424i) q^{75} +6.80226 q^{76} +(-1.94869 - 5.99744i) q^{77} +(-1.73389 + 1.25975i) q^{78} +(13.5956 - 9.87777i) q^{79} +(0.254866 - 0.240181i) q^{80} +(-0.809017 - 0.587785i) q^{81} +6.57664 q^{82} +(6.91824 + 5.02639i) q^{83} +(0.371058 - 1.14200i) q^{84} +(-2.40475 - 5.08708i) q^{85} +(-2.91043 - 8.95739i) q^{86} +(-2.22255 + 6.84030i) q^{87} +(-5.57612 + 17.1615i) q^{88} +(4.40854 + 13.5681i) q^{89} +(-1.75346 - 0.959958i) q^{90} +(-0.740817 + 2.28000i) q^{91} +(5.69901 + 4.14057i) q^{92} +1.22451 q^{93} +(-7.64161 - 5.55195i) q^{94} +(-5.41359 - 11.4521i) q^{95} +(-4.51670 + 3.28157i) q^{96} +(4.66125 - 3.38660i) q^{97} +(0.276260 + 0.850242i) q^{98} +6.30608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

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