LMFDB - Embedded newform 425.2.k.b.86.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.5
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38672 + 1.00751i) q^{2} +(-0.537884 + 1.65544i) q^{3} +(0.289884 - 0.892173i) q^{4} +(0.0918514 - 2.23418i) q^{5} +(-0.921979 - 2.83756i) q^{6} +3.20986 q^{7} +(-0.562476 - 1.73112i) q^{8} +(-0.0241012 - 0.0175105i) q^{9} +(2.12360 + 3.19073i) q^{10} +(-4.93687 + 3.58684i) q^{11} +(1.32101 + 0.959771i) q^{12} +(3.52554 + 2.56146i) q^{13} +(-4.45118 + 3.23397i) q^{14} +(3.64914 + 1.35378i) q^{15} +(4.04198 + 2.93667i) q^{16} +(0.309017 + 0.951057i) q^{17} +0.0510638 q^{18} +(0.920995 + 2.83453i) q^{19} +(-1.96665 - 0.729602i) q^{20} +(-1.72653 + 5.31372i) q^{21} +(3.23228 - 9.94792i) q^{22} +(2.19271 - 1.59310i) q^{23} +3.16831 q^{24} +(-4.98313 - 0.410425i) q^{25} -7.46966 q^{26} +(-4.18265 + 3.03887i) q^{27} +(0.930488 - 2.86375i) q^{28} +(-1.60747 + 4.94728i) q^{29} +(-6.42430 + 1.79923i) q^{30} +(-0.190938 - 0.587648i) q^{31} -4.92343 q^{32} +(-3.28233 - 10.1020i) q^{33} +(-1.38672 - 1.00751i) q^{34} +(0.294830 - 7.17140i) q^{35} +(-0.0226090 + 0.0164264i) q^{36} +(-7.42013 - 5.39104i) q^{37} +(-4.13299 - 3.00279i) q^{38} +(-6.13667 + 4.45855i) q^{39} +(-3.91931 + 1.09767i) q^{40} +(5.53783 + 4.02347i) q^{41} +(-2.95942 - 9.10816i) q^{42} +8.48358 q^{43} +(1.76896 + 5.44431i) q^{44} +(-0.0413354 + 0.0522380i) q^{45} +(-1.43562 + 4.41837i) q^{46} +(-3.10048 + 9.54230i) q^{47} +(-7.03560 + 5.11166i) q^{48} +3.30318 q^{49} +(7.32373 - 4.45142i) q^{50} -1.74063 q^{51} +(3.30726 - 2.40287i) q^{52} +(3.67190 - 11.3009i) q^{53} +(2.73847 - 8.42814i) q^{54} +(7.56020 + 11.3593i) q^{55} +(-1.80547 - 5.55666i) q^{56} -5.18777 q^{57} +(-2.75534 - 8.48006i) q^{58} +(-1.43495 - 1.04256i) q^{59} +(2.26564 - 2.86322i) q^{60} +(-10.9331 + 7.94340i) q^{61} +(0.856842 + 0.622532i) q^{62} +(-0.0773614 - 0.0562063i) q^{63} +(-1.25653 + 0.912922i) q^{64} +(6.04658 - 7.64143i) q^{65} +(14.7296 + 10.7017i) q^{66} +(3.17954 + 9.78563i) q^{67} +0.938086 q^{68} +(1.45785 + 4.48680i) q^{69} +(6.81644 + 10.2418i) q^{70} +(-1.15895 + 3.56687i) q^{71} +(-0.0167566 + 0.0515714i) q^{72} +(6.83140 - 4.96331i) q^{73} +15.7212 q^{74} +(3.35978 - 8.02849i) q^{75} +2.79587 q^{76} +(-15.8466 + 11.5133i) q^{77} +(4.01781 - 12.3655i) q^{78} +(-2.41647 + 7.43714i) q^{79} +(6.93232 - 8.76078i) q^{80} +(-2.80850 - 8.64366i) q^{81} -11.7331 q^{82} +(2.40134 + 7.39057i) q^{83} +(4.24026 + 3.08073i) q^{84} +(2.15322 - 0.603044i) q^{85} +(-11.7644 + 8.54733i) q^{86} +(-7.32528 - 5.32213i) q^{87} +(8.98614 + 6.52881i) q^{88} +(7.49634 - 5.44641i) q^{89} +(0.00469028 - 0.114086i) q^{90} +(11.3165 + 8.22191i) q^{91} +(-0.785685 - 2.41809i) q^{92} +1.07552 q^{93} +(-5.31449 - 16.3563i) q^{94} +(6.41745 - 1.79731i) q^{95} +(2.64824 - 8.15043i) q^{96} +(2.66273 - 8.19503i) q^{97} +(-4.58060 + 3.32800i) q^{98} +0.181792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.38672	+	1.00751i	−0.980562	+	0.712420i	−0.957834	−	0.287322i	$-0.907235\pi$
$2$	−1.38672	+	1.00751i	−0.980562	+	0.712420i	−0.0227276	+	0.999742i	$0.507235\pi$
$3$	−0.537884	+	1.65544i	−0.310548	+	0.955767i	0.667001	+	0.745057i	$0.267578\pi$
$3$	−0.537884	+	1.65544i	−0.310548	+	0.955767i	−0.977549	+	0.210710i	$0.932422\pi$
$4$	0.289884	−	0.892173i	0.144942	−	0.446086i
$5$	0.0918514	−	2.23418i	0.0410772	−	0.999156i
$5$	0.0918514	−	2.23418i	0.0410772	−	0.999156i
$6$	−0.921979	−	2.83756i	−0.376396	−	1.15843i
$7$	3.20986			1.21321			0.606606	−	0.795003i	$-0.292531\pi$
$7$	3.20986			1.21321			0.606606	+	0.795003i	$0.292531\pi$
$8$	−0.562476	−	1.73112i	−0.198865	−	0.612044i
$9$	−0.0241012	−	0.0175105i	−0.00803373	−	0.00583685i
$10$	2.12360	+	3.19073i	0.671540	+	1.00900i
$11$	−4.93687	+	3.58684i	−1.48852	+	1.08147i	−0.513837	+	0.857888i	$0.671777\pi$
$11$	−4.93687	+	3.58684i	−1.48852	+	1.08147i	−0.974684	+	0.223587i	$0.928223\pi$
$12$	1.32101	+	0.959771i	0.381343	+	0.277062i
$13$	3.52554	+	2.56146i	0.977810	+	0.710420i	0.957218	−	0.289367i	$-0.0934450\pi$
$13$	3.52554	+	2.56146i	0.977810	+	0.710420i	0.0205918	+	0.999788i	$0.493445\pi$
$14$	−4.45118	+	3.23397i	−1.18963	+	0.864316i
$15$	3.64914	+	1.35378i	0.942204	+	0.349546i
$16$	4.04198	+	2.93667i	1.01050	+	0.734168i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	0.0510638			0.0120359
$19$	0.920995	+	2.83453i	0.211291	+	0.650286i	0.999396	+	0.0347456i	$0.0110621\pi$
$19$	0.920995	+	2.83453i	0.211291	+	0.650286i	−0.788106	+	0.615540i	$0.788938\pi$
$20$	−1.96665	−	0.729602i	−0.439756	−	0.163144i
$21$	−1.72653	+	5.31372i	−0.376760	+	1.15955i
$22$	3.23228	−	9.94792i	0.689124	−	2.12090i
$23$	2.19271	−	1.59310i	0.457212	−	0.332184i	−0.335225	−	0.942138i	$-0.608812\pi$
$23$	2.19271	−	1.59310i	0.457212	−	0.332184i	0.792437	+	0.609954i	$0.208812\pi$
$24$	3.16831			0.646729
$25$	−4.98313	−	0.410425i	−0.996625	−	0.0820850i
$26$	−7.46966			−1.46492
$27$	−4.18265	+	3.03887i	−0.804950	+	0.584831i
$28$	0.930488	−	2.86375i	0.175846	−	0.541197i
$29$	−1.60747	+	4.94728i	−0.298500	+	0.918688i	0.683524	+	0.729928i	$0.260447\pi$
$29$	−1.60747	+	4.94728i	−0.298500	+	0.918688i	−0.982023	+	0.188759i	$0.939553\pi$
$30$	−6.42430	+	1.79923i	−1.17291	+	0.328494i
$31$	−0.190938	−	0.587648i	−0.0342935	−	0.105545i	0.932445	−	0.361313i	$-0.117671\pi$
$31$	−0.190938	−	0.587648i	−0.0342935	−	0.105545i	−0.966738	+	0.255769i	$0.917671\pi$
$32$	−4.92343			−0.870348
$33$	−3.28233	−	10.1020i	−0.571381	−	1.75853i
$34$	−1.38672	−	1.00751i	−0.237821	−	0.172787i
$35$	0.294830	−	7.17140i	0.0498353	−	1.21219i
$36$	−0.0226090	+	0.0164264i	−0.00376816	+	0.00273773i
$37$	−7.42013	−	5.39104i	−1.21986	−	0.886281i	−0.223773	−	0.974641i	$-0.571837\pi$
$37$	−7.42013	−	5.39104i	−1.21986	−	0.886281i	−0.996089	+	0.0883603i	$0.971837\pi$
$38$	−4.13299	−	3.00279i	−0.670460	−	0.487118i
$39$	−6.13667	+	4.45855i	−0.982653	+	0.713939i
$40$	−3.91931	+	1.09767i	−0.619697	+	0.173556i
$41$	5.53783	+	4.02347i	0.864863	+	0.628360i	0.929204	−	0.369568i	$-0.120494\pi$
$41$	5.53783	+	4.02347i	0.864863	+	0.628360i	−0.0643404	+	0.997928i	$0.520494\pi$
$42$	−2.95942	−	9.10816i	−0.456648	−	1.40542i
$43$	8.48358			1.29373			0.646867	−	0.762603i	$-0.276079\pi$
$43$	8.48358			1.29373			0.646867	+	0.762603i	$0.276079\pi$
$44$	1.76896	+	5.44431i	0.266681	+	0.820760i
$45$	−0.0413354	+	0.0522380i	−0.00616192	+	0.00778719i
$46$	−1.43562	+	4.41837i	−0.211670	+	0.651453i
$47$	−3.10048	+	9.54230i	−0.452252	+	1.39189i	0.422080	+	0.906558i	$0.361300\pi$
$47$	−3.10048	+	9.54230i	−0.452252	+	1.39189i	−0.874332	+	0.485329i	$0.838700\pi$
$48$	−7.03560	+	5.11166i	−1.01550	+	0.737804i
$49$	3.30318			0.471883
$50$	7.32373	−	4.45142i	1.03573	−	0.629526i
$51$	−1.74063			−0.243737
$52$	3.30726	−	2.40287i	0.458635	−	0.333218i
$53$	3.67190	−	11.3009i	0.504374	−	1.55230i	−0.297447	−	0.954738i	$-0.596135\pi$
$53$	3.67190	−	11.3009i	0.504374	−	1.55230i	0.801821	−	0.597565i	$-0.203865\pi$
$54$	2.73847	−	8.42814i	0.372659	−	1.14693i
$55$	7.56020	+	11.3593i	1.01942	+	1.53169i
$56$	−1.80547	−	5.55666i	−0.241266	−	0.742540i
$57$	−5.18777			−0.687137
$58$	−2.75534	−	8.48006i	−0.361794	−	1.11349i
$59$	−1.43495	−	1.04256i	−0.186815	−	0.135729i	0.490447	−	0.871471i	$-0.336834\pi$
$59$	−1.43495	−	1.04256i	−0.186815	−	0.135729i	−0.677262	+	0.735742i	$0.736834\pi$
$60$	2.26564	−	2.86322i	0.292493	−	0.369640i
$61$	−10.9331	+	7.94340i	−1.39985	+	1.01705i	−0.405143	+	0.914253i	$0.632778\pi$
$61$	−10.9331	+	7.94340i	−1.39985	+	1.01705i	−0.994703	+	0.102795i	$0.967222\pi$
$62$	0.856842	+	0.622532i	0.108819	+	0.0790616i
$63$	−0.0773614	−	0.0562063i	−0.00974662	−	0.00708133i
$64$	−1.25653	+	0.912922i	−0.157066	+	0.114115i
$65$	6.04658	−	7.64143i	0.749987	−	0.947803i
$66$	14.7296	+	10.7017i	1.81308	+	1.31728i
$67$	3.17954	+	9.78563i	0.388443	+	1.19550i	0.933952	+	0.357400i	$0.116337\pi$
$67$	3.17954	+	9.78563i	0.388443	+	1.19550i	−0.545509	+	0.838105i	$0.683663\pi$
$68$	0.938086			0.113760
$69$	1.45785	+	4.48680i	0.175504	+	0.540147i
$70$	6.81644	+	10.2418i	0.814720	+	1.22413i
$71$	−1.15895	+	3.56687i	−0.137542	+	0.423310i	−0.995977	−	0.0896126i	$-0.971437\pi$
$71$	−1.15895	+	3.56687i	−0.137542	+	0.423310i	0.858435	+	0.512922i	$0.171437\pi$
$72$	−0.0167566	+	0.0515714i	−0.00197478	+	0.00607775i
$73$	6.83140	−	4.96331i	0.799555	−	0.580911i	−0.111228	−	0.993795i	$-0.535478\pi$
$73$	6.83140	−	4.96331i	0.799555	−	0.580911i	0.910784	+	0.412884i	$0.135478\pi$
$74$	15.7212			1.82755
$75$	3.35978	−	8.02849i	0.387954	−	0.927050i
$76$	2.79587			0.320709
$77$	−15.8466	+	11.5133i	−1.80589	+	1.31206i
$78$	4.01781	−	12.3655i	0.454927	−	1.40012i
$79$	−2.41647	+	7.43714i	−0.271874	+	0.836743i	0.718155	+	0.695883i	$0.244987\pi$
$79$	−2.41647	+	7.43714i	−0.271874	+	0.836743i	−0.990029	+	0.140860i	$0.955013\pi$
$80$	6.93232	−	8.76078i	0.775057	−	0.979485i
$81$	−2.80850	−	8.64366i	−0.312055	−	0.960407i
$82$	−11.7331			−1.29571
$83$	2.40134	+	7.39057i	0.263582	+	0.811221i	0.992017	+	0.126106i	$0.0402480\pi$
$83$	2.40134	+	7.39057i	0.263582	+	0.811221i	−0.728435	+	0.685115i	$0.759752\pi$
$84$	4.24026	+	3.08073i	0.462650	+	0.336135i
$85$	2.15322	−	0.603044i	0.233549	−	0.0654093i
$86$	−11.7644	+	8.54733i	−1.26859	+	0.921682i
$87$	−7.32528	−	5.32213i	−0.785353	−	0.570592i
$88$	8.98614	+	6.52881i	0.957926	+	0.695974i
$89$	7.49634	−	5.44641i	0.794610	−	0.577318i	−0.114718	−	0.993398i	$-0.536596\pi$
$89$	7.49634	−	5.44641i	0.794610	−	0.577318i	0.909328	+	0.416080i	$0.136596\pi$
$90$	0.00469028	−	0.114086i	0.000494399	−	0.0120257i
$91$	11.3165	+	8.22191i	1.18629	+	0.861891i
$92$	−0.785685	−	2.41809i	−0.0819134	−	0.252103i
$93$	1.07552			0.111526
$94$	−5.31449	−	16.3563i	−0.548147	−	1.68702i
$95$	6.41745	−	1.79731i	0.658416	−	0.184400i
$96$	2.64824	−	8.15043i	0.270284	−	0.831850i
$97$	2.66273	−	8.19503i	0.270359	−	0.832079i	−0.720051	−	0.693921i	$-0.755882\pi$
$97$	2.66273	−	8.19503i	0.270359	−	0.832079i	0.990410	−	0.138158i	$-0.0441183\pi$
$98$	−4.58060	+	3.32800i	−0.462711	+	0.336179i
$99$	0.181792			0.0182708
$100$	−1.81070	+	4.32683i	−0.181070	+	0.432683i
$101$	−4.90472			−0.488038			−0.244019	−	0.969770i	$-0.578466\pi$
$101$	−4.90472			−0.488038			−0.244019	+	0.969770i	$0.578466\pi$
$102$	2.41377	−	1.75371i	0.238999	−	0.173643i
$103$	1.59577	−	4.91129i	0.157236	−	0.483924i	−0.841144	−	0.540811i	$-0.818118\pi$
$103$	1.59577	−	4.91129i	0.157236	−	0.483924i	0.998381	+	0.0568871i	$0.0181175\pi$
$104$	2.45116	−	7.54391i	0.240356	−	0.739741i
$105$	11.7132	+	4.34545i	1.14309	+	0.424073i
$106$	6.29394	+	19.3708i	0.611322	+	1.88145i
$107$	5.90573			0.570929			0.285464	−	0.958389i	$-0.407852\pi$
$107$	5.90573			0.570929			0.285464	+	0.958389i	$0.407852\pi$
$108$	1.49871	+	4.61256i	0.144214	+	0.443844i
$109$	−3.32390	−	2.41496i	−0.318372	−	0.231311i	0.417109	−	0.908857i	$-0.363044\pi$
$109$	−3.32390	−	2.41496i	−0.318372	−	0.231311i	−0.735480	+	0.677546i	$0.763044\pi$
$110$	−21.9286	−	8.13522i	−2.09081	−	0.775663i
$111$	12.9157	−	9.38380i	1.22590	−	0.890671i
$112$	12.9742	+	9.42630i	1.22595	+	0.890702i
$113$	12.0014	+	8.71951i	1.12899	+	0.820263i	0.985548	−	0.169395i	$-0.0541814\pi$
$113$	12.0014	+	8.71951i	1.12899	+	0.820263i	0.143447	+	0.989658i	$0.454181\pi$
$114$	7.19401	−	5.22675i	0.673781	−	0.489530i
$115$	−3.35786	−	5.04524i	−0.313123	−	0.470471i
$116$	3.94785	+	2.86828i	0.366549	+	0.266313i
$117$	−0.0401173	−	0.123468i	−0.00370885	−	0.0114147i
$118$	3.04027			0.279880
$119$	0.991900	+	3.05276i	0.0909274	+	0.279846i
$120$	0.291014	−	7.07858i	0.0265658	−	0.646183i
$121$	8.10802	−	24.9539i	0.737093	−	2.26854i
$122$	7.15817	−	22.0306i	0.648070	−	1.99456i
$123$	−9.63930	+	7.00336i	−0.869147	+	0.631472i
$124$	−0.579633			−0.0520526
$125$	−1.37467	+	11.0955i	−0.122954	+	0.992412i
$126$	0.163908			0.0146020
$127$	2.41742	−	1.75636i	0.214511	−	0.155852i	−0.475341	−	0.879802i	$-0.657675\pi$
$127$	2.41742	−	1.75636i	0.214511	−	0.155852i	0.689853	+	0.723950i	$0.257675\pi$
$128$	3.86553	−	11.8969i	0.341667	−	1.05154i
$129$	−4.56318	+	14.0440i	−0.401766	+	1.23651i
$130$	−0.686098	+	16.6886i	−0.0601748	+	1.46368i
$131$	−3.74882	−	11.5377i	−0.327535	−	1.00805i	−0.970283	−	0.241973i	$-0.922206\pi$
$131$	−3.74882	−	11.5377i	−0.327535	−	1.00805i	0.642748	−	0.766078i	$-0.277794\pi$
$132$	−9.96421			−0.867273
$133$	2.95626	+	9.09844i	0.256340	+	0.788934i
$134$	−14.2683	−	10.3665i	−1.23259	−	0.895532i
$135$	6.40520	+	9.62391i	0.551272	+	0.828294i
$136$	1.47258	−	1.06989i	0.126273	−	0.0917426i
$137$	−4.60732	−	3.34741i	−0.393630	−	0.285989i	0.373312	−	0.927706i	$-0.378222\pi$
$137$	−4.60732	−	3.34741i	−0.393630	−	0.285989i	−0.766941	+	0.641717i	$0.778222\pi$
$138$	−6.54214	−	4.75314i	−0.556904	−	0.404614i
$139$	7.69632	−	5.59170i	0.652793	−	0.474282i	−0.211428	−	0.977394i	$-0.567811\pi$
$139$	7.69632	−	5.59170i	0.652793	−	0.474282i	0.864222	+	0.503111i	$0.167811\pi$
$140$	−6.31266	−	2.34192i	−0.533517	−	0.197928i
$141$	−14.1290	−	10.2653i	−1.18987	−	0.864494i
$142$	−1.98653	−	6.11392i	−0.166706	−	0.513069i
$143$	−26.5927			−2.22379
$144$	−0.0459939	−	0.141555i	−0.00383282	−	0.0117962i
$145$	10.9055	+	4.04579i	0.905651	+	0.335985i
$146$	−4.47267	+	13.7655i	−0.370161	+	1.13924i
$147$	−1.77673	+	5.46821i	−0.146542	+	0.451011i
$148$	−6.96072	+	5.05726i	−0.572167	+	0.415704i
$149$	6.52143			0.534256			0.267128	−	0.963661i	$-0.413925\pi$
$149$	6.52143			0.534256			0.267128	+	0.963661i	$0.413925\pi$
$150$	3.42973	+	14.5183i	0.280036	+	1.18542i
$151$	1.75870			0.143121			0.0715605	−	0.997436i	$-0.477202\pi$
$151$	1.75870			0.143121			0.0715605	+	0.997436i	$0.477202\pi$
$152$	4.38888	−	3.18871i	0.355985	−	0.258639i
$153$	0.00920584	−	0.0283326i	0.000744248	−	0.00229056i
$154$	10.3751	−	31.9314i	0.836053	−	2.57311i
$155$	−1.33045	+	0.372614i	−0.106864	+	0.0299291i
$156$	2.19887	+	6.76743i	0.176051	+	0.541828i
$157$	−12.6295			−1.00795			−0.503973	−	0.863719i	$-0.668129\pi$
$157$	−12.6295			−1.00795			−0.503973	+	0.863719i	$0.668129\pi$
$158$	−4.14204	−	12.7479i	−0.329523	−	1.01417i
$159$	16.7329	+	12.1572i	1.32701	+	0.964128i
$160$	−0.452224	+	10.9998i	−0.0357514	+	0.869613i
$161$	7.03829	−	5.11362i	0.554695	−	0.403009i
$162$	12.6032	+	9.15677i	0.990202	+	0.719424i
$163$	1.66385	+	1.20886i	0.130323	+	0.0946850i	0.651037	−	0.759046i	$-0.274334\pi$
$163$	1.66385	+	1.20886i	0.130323	+	0.0946850i	−0.520714	+	0.853731i	$0.674334\pi$
$164$	5.19496	−	3.77436i	0.405658	−	0.294728i
$165$	−22.8711	+	6.40544i	−1.78052	+	0.498663i
$166$	−10.7761	−	7.82930i	−0.836388	−	0.607671i
$167$	1.69506	+	5.21686i	0.131168	+	0.403693i	0.994974	−	0.100131i	$-0.0319262\pi$
$167$	1.69506	+	5.21686i	0.131168	+	0.403693i	−0.863807	+	0.503824i	$0.831926\pi$
$168$	10.1698			0.784619
$169$	1.85117	+	5.69733i	0.142398	+	0.438256i
$170$	−2.37834	+	3.00565i	−0.182410	+	0.230523i
$171$	0.0274371	−	0.0844427i	0.00209817	−	0.00645749i
$172$	2.45926	−	7.56882i	0.187517	−	0.577117i
$173$	−14.2235	+	10.3340i	−1.08139	+	0.785677i	−0.977925	−	0.208956i	$-0.932994\pi$
$173$	−14.2235	+	10.3340i	−1.08139	+	0.785677i	−0.103467	+	0.994633i	$0.532994\pi$
$174$	15.5203			1.17659
$175$	−15.9951	−	1.31741i	−1.20912	−	0.0995865i
$176$	−30.4881			−2.29813
$177$	2.49772	−	1.81470i	0.187740	−	0.136401i
$178$	−4.90802	+	15.1053i	−0.367872	+	1.13219i
$179$	3.54679	−	10.9159i	0.265100	−	0.815893i	−0.726571	−	0.687092i	$-0.758887\pi$
$179$	3.54679	−	10.9159i	0.265100	−	0.815893i	0.991670	−	0.128802i	$-0.0411130\pi$
$180$	0.0346229	+	0.0520213i	0.00258064	+	0.00387744i
$181$	2.16564	+	6.66517i	0.160971	+	0.495418i	0.998717	−	0.0506425i	$-0.0161269\pi$
$181$	2.16564	+	6.66517i	0.160971	+	0.495418i	−0.837746	+	0.546060i	$0.816127\pi$
$182$	−23.9765			−1.77726
$183$	−7.26903	−	22.3718i	−0.537342	−	1.65377i
$184$	−3.99120	−	2.89977i	−0.294235	−	0.213774i
$185$	−12.7261	+	16.0827i	−0.935641	+	1.18243i
$186$	−1.49144	+	1.08360i	−0.109358	+	0.0794532i
$187$	−4.93687	−	3.58684i	−0.361019	−	0.262296i
$188$	7.61460	+	5.53233i	0.555351	+	0.403486i
$189$	−13.4257	+	9.75434i	−0.976576	+	0.709524i
$190$	−7.08841	+	8.95804i	−0.514247	+	0.649885i
$191$	5.90855	+	4.29281i	0.427528	+	0.310617i	0.780660	−	0.624957i	$-0.214883\pi$
$191$	5.90855	+	4.29281i	0.427528	+	0.310617i	−0.353132	+	0.935574i	$0.614883\pi$
$192$	−0.835418	−	2.57115i	−0.0602911	−	0.185557i
$193$	26.5147			1.90857			0.954284	−	0.298902i	$-0.0966205\pi$
$193$	26.5147			1.90857			0.954284	+	0.298902i	$0.0966205\pi$
$194$	4.56414	+	14.0470i	0.327686	+	1.00851i
$195$	9.39754	+	14.1199i	0.672972	+	1.01115i
$196$	0.957542	−	2.94701i	0.0683958	−	0.210501i
$197$	4.57711	−	14.0869i	0.326106	−	1.00365i	−0.644833	−	0.764323i	$-0.723073\pi$
$197$	4.57711	−	14.0869i	0.326106	−	1.00365i	0.970939	−	0.239327i	$-0.0769267\pi$
$198$	−0.252095	+	0.183158i	−0.0179156	+	0.0130165i
$199$	10.1440			0.719090			0.359545	−	0.933128i	$-0.382932\pi$
$199$	10.1440			0.719090			0.359545	+	0.933128i	$0.382932\pi$
$200$	2.09239	+	8.85726i	0.147955	+	0.626303i
$201$	−17.9097			−1.26325
$202$	6.80149	−	4.94157i	0.478551	−	0.347688i
$203$	−5.15975	+	15.8801i	−0.362143	+	1.11456i
$204$	−0.504581	+	1.55294i	−0.0353278	+	0.108728i
$205$	9.49781	−	12.0029i	0.663356	−	0.838322i
$206$	2.73529	+	8.41836i	0.190577	+	0.586535i
$207$	−0.0807429			−0.00561202
$208$	6.72803	+	20.7067i	0.466505	+	1.43575i
$209$	−14.7138	−	10.6902i	−1.01778	−	0.739459i
$210$	−20.6211	+	5.77528i	−1.42299	+	0.398532i
$211$	−5.28903	+	3.84270i	−0.364112	+	0.264543i	−0.754765	−	0.655995i	$-0.772249\pi$
$211$	−5.28903	+	3.84270i	−0.364112	+	0.264543i	0.390653	+	0.920538i	$0.372249\pi$
$212$	−9.01796	−	6.55193i	−0.619356	−	0.449989i
$213$	−5.28135	−	3.83713i	−0.361872	−	0.262916i
$214$	−8.18962	+	5.95011i	−0.559831	+	0.406741i
$215$	0.779229	−	18.9539i	0.0531429	−	1.29264i
$216$	7.61329	+	5.53138i	0.518019	+	0.376363i
$217$	−0.612885	−	1.88627i	−0.0416053	−	0.128048i
$218$	7.04243			0.476974
$219$	4.54194	+	13.9786i	0.306916	+	0.944589i
$220$	12.3261	−	3.45212i	0.831022	−	0.232742i
$221$	−1.34664	+	4.14453i	−0.0905847	+	0.278791i
$222$	−8.45619	+	26.0255i	−0.567542	+	1.74671i
$223$	5.63520	−	4.09421i	0.377361	−	0.274169i	−0.382896	−	0.923792i	$-0.625073\pi$
$223$	5.63520	−	4.09421i	0.377361	−	0.274169i	0.760257	+	0.649623i	$0.225073\pi$
$224$	−15.8035			−1.05592
$225$	0.112913	+	0.0971490i	0.00752750	+	0.00647660i
$226$	−25.4276			−1.69142
$227$	18.5064	−	13.4457i	1.22832	−	0.892423i	0.231552	−	0.972822i	$-0.425620\pi$
$227$	18.5064	−	13.4457i	1.22832	−	0.892423i	0.996763	+	0.0803992i	$0.0256195\pi$
$228$	−1.50385	+	4.62839i	−0.0995952	+	0.306523i
$229$	5.45980	−	16.8035i	0.360793	−	1.11041i	−0.591780	−	0.806099i	$-0.701575\pi$
$229$	5.45980	−	16.8035i	0.360793	−	1.11041i	0.952574	−	0.304309i	$-0.0984254\pi$
$230$	9.73958	+	3.61326i	0.642209	+	0.238251i
$231$	−10.5358	−	32.4259i	−0.693206	−	2.13347i
$232$	9.46852			0.621639
$233$	−6.55299	−	20.1680i	−0.429301	−	1.32125i	−0.898815	−	0.438327i	$-0.855571\pi$
$233$	−6.55299	−	20.1680i	−0.429301	−	1.32125i	0.469515	−	0.882925i	$-0.344429\pi$
$234$	0.180028	+	0.130798i	0.0117688	+	0.00855052i
$235$	21.0344	+	7.80351i	1.37214	+	0.509045i
$236$	−1.34611	+	0.978006i	−0.0876243	+	0.0636628i
$237$	−11.0119	−	8.00063i	−0.715302	−	0.519697i
$238$	−4.45118	−	3.23397i	−0.288527	−	0.209627i
$239$	6.41470	−	4.66055i	0.414932	−	0.301466i	−0.360663	−	0.932696i	$-0.617450\pi$
$239$	6.41470	−	4.66055i	0.414932	−	0.301466i	0.775596	+	0.631230i	$0.217450\pi$
$240$	10.7741	+	16.1883i	0.695468	+	1.04495i
$241$	−8.02414	−	5.82988i	−0.516880	−	0.375535i	0.298547	−	0.954395i	$-0.403498\pi$
$241$	−8.02414	−	5.82988i	−0.516880	−	0.375535i	−0.815427	+	0.578860i	$0.803498\pi$
$242$	13.8978	+	42.7731i	0.893387	+	2.74956i
$243$	0.309583			0.0198597
$244$	3.91753	+	12.0569i	0.250794	+	0.771865i
$245$	0.303402	−	7.37991i	0.0193836	−	0.471485i
$246$	6.31106	−	19.4235i	0.402379	−	1.23839i
$247$	−4.01352	+	12.3523i	−0.255374	+	0.785961i
$248$	−0.909892	+	0.661075i	−0.0577782	+	0.0419783i
$249$	−13.5263			−0.857193
$250$	−9.27259	−	16.7714i	−0.586450	−	1.06072i
$251$	11.1127			0.701427			0.350713	−	0.936483i	$-0.385939\pi$
$251$	11.1127			0.701427			0.350713	+	0.936483i	$0.385939\pi$
$252$	−0.0725716	+	0.0527264i	−0.00457158	+	0.00332145i
$253$	−5.11093	+	15.7298i	−0.321321	+	0.988926i
$254$	−1.58274	+	4.87117i	−0.0993099	+	0.305644i
$255$	−0.159879	+	3.88888i	−0.0100120	+	0.243531i
$256$	5.66593	+	17.4380i	0.354121	+	1.08987i
$257$	−1.48745			−0.0927847			−0.0463924	−	0.998923i	$-0.514772\pi$
$257$	−1.48745			−0.0927847			−0.0463924	+	0.998923i	$0.514772\pi$
$258$	−7.82168	−	24.0727i	−0.486957	−	1.49870i
$259$	−23.8175	−	17.3045i	−1.47995	−	1.07525i
$260$	−5.06466	−	7.60973i	−0.314097	−	0.471935i
$261$	0.125372	−	0.0910878i	0.00776030	−	0.00563819i
$262$	16.8229	+	12.2226i	1.03932	+	0.755113i
$263$	−16.5434	−	12.0195i	−1.02011	−	0.741154i	−0.0538050	−	0.998551i	$-0.517135\pi$
$263$	−16.5434	−	12.0195i	−1.02011	−	0.741154i	−0.966306	+	0.257398i	$0.917135\pi$
$264$	−15.6415	+	11.3642i	−0.962670	+	0.699421i
$265$	−24.9111	−	9.24169i	−1.53027	−	0.567712i
$266$	−13.2663	−	9.63854i	−0.813410	−	0.590977i
$267$	4.98403	+	15.3393i	0.305017	+	0.938747i
$268$	9.65217			0.589600
$269$	−1.06550	−	3.27928i	−0.0649648	−	0.199941i	0.913305	−	0.407276i	$-0.133521\pi$
$269$	−1.06550	−	3.27928i	−0.0649648	−	0.199941i	−0.978270	+	0.207335i	$0.933521\pi$
$270$	−18.5785	−	6.89237i	−1.13065	−	0.419456i
$271$	6.54333	−	20.1383i	0.397479	−	1.22331i	−0.529535	−	0.848288i	$-0.677634\pi$
$271$	6.54333	−	20.1383i	0.397479	−	1.22331i	0.927014	−	0.375027i	$-0.122366\pi$
$272$	−1.54390	+	4.75164i	−0.0936127	+	0.288110i
$273$	−19.6978	+	14.3113i	−1.19217	+	0.866159i
$274$	9.76164			0.589722
$275$	26.0732	−	15.8475i	1.57227	−	0.955639i
$276$	4.42561			0.266390
$277$	−19.9266	+	14.4775i	−1.19727	+	0.869868i	−0.994014	−	0.109257i	$-0.965153\pi$
$277$	−19.9266	+	14.4775i	−1.19727	+	0.869868i	−0.203257	+	0.979125i	$0.565153\pi$
$278$	−5.03895	+	15.5083i	−0.302216	+	0.930126i
$279$	−0.00568819	+	0.0175064i	−0.000340543	+	0.00104808i
$280$	−12.5804	+	3.52335i	−0.751823	+	0.210561i
$281$	1.25636	+	3.86669i	0.0749484	+	0.230668i	0.981512	−	0.191403i	$-0.0613036\pi$
$281$	1.25636	+	3.86669i	0.0749484	+	0.230668i	−0.906563	+	0.422070i	$0.861304\pi$
$282$	29.9354			1.78263
$283$	−3.63224	−	11.1789i	−0.215914	−	0.664516i	−0.999087	−	0.0427125i	$-0.986400\pi$
$283$	−3.63224	−	11.1789i	−0.215914	−	0.664516i	0.783173	−	0.621804i	$-0.213600\pi$
$284$	2.84630	+	2.06796i	0.168897	+	0.122711i
$285$	−0.476504	+	11.5904i	−0.0282257	+	0.686557i
$286$	36.8767	−	26.7925i	2.18057	−	1.58427i
$287$	17.7756	+	12.9148i	1.04926	+	0.762334i
$288$	0.118661	+	0.0862119i	0.00699214	+	0.00508009i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−19.1991	+	5.37702i	−1.12741	+	0.315750i
$291$	12.1341	+	8.81595i	0.711315	+	0.516800i
$292$	−2.44781	−	7.53358i	−0.143247	−	0.440869i
$293$	29.5392			1.72570			0.862850	−	0.505461i	$-0.168678\pi$
$293$	29.5392			1.72570			0.862850	+	0.505461i	$0.168678\pi$
$294$	−3.04547	−	9.37298i	−0.177615	−	0.546643i
$295$	−2.46106	+	3.11019i	−0.143288	+	0.181082i
$296$	−5.15891	+	15.8775i	−0.299855	+	0.922860i
$297$	9.74921	−	30.0050i	0.565707	−	1.74107i
$298$	−9.04342	+	6.57043i	−0.523871	+	0.380615i
$299$	11.8112			0.683056
$300$	−6.18885	−	5.32484i	−0.357314	−	0.307430i
$301$	27.2311			1.56957
$302$	−2.43883	+	1.77191i	−0.140339	+	0.101962i
$303$	2.63817	−	8.11945i	0.151559	−	0.466450i
$304$	−4.60144	+	14.1618i	−0.263911	+	0.812234i
$305$	16.7428	+	25.1562i	0.958688	+	1.44044i
$306$	0.0157796	+	0.0485646i	0.000902059	+	0.00277625i
$307$	19.5387			1.11513			0.557565	−	0.830133i	$-0.311736\pi$
$307$	19.5387			1.11513			0.557565	+	0.830133i	$0.311736\pi$
$308$	5.67812	+	17.4755i	0.323541	+	0.995756i
$309$	7.27199	+	5.28341i	0.413689	+	0.300563i
$310$	1.46955	−	1.85716i	0.0834649	−	0.105480i
$311$	−1.85635	+	1.34871i	−0.105264	+	0.0764785i	−0.639172	−	0.769064i	$-0.720723\pi$
$311$	−1.85635	+	1.34871i	−0.105264	+	0.0764785i	0.533908	+	0.845542i	$0.320723\pi$
$312$	11.1700	+	8.11550i	0.632378	+	0.459450i
$313$	−26.4598	−	19.2242i	−1.49560	−	1.08662i	−0.972094	−	0.234592i	$-0.924625\pi$
$313$	−26.4598	−	19.2242i	−1.49560	−	1.08662i	−0.523504	−	0.852023i	$-0.675375\pi$
$314$	17.5137	−	12.7244i	0.988353	−	0.718081i
$315$	−0.132681	+	0.167677i	−0.00747572	+	0.00944751i
$316$	5.93471	+	4.31182i	0.333854	+	0.242559i
$317$	0.373315	+	1.14894i	0.0209674	+	0.0645311i	0.960993	−	0.276574i	$-0.0891989\pi$
$317$	0.373315	+	1.14894i	0.0209674	+	0.0645311i	−0.940025	+	0.341105i	$0.889199\pi$
$318$	−35.4525			−1.98808
$319$	−9.80927	−	30.1898i	−0.549214	−	1.69031i
$320$	1.92422	+	2.89117i	0.107567	+	0.161621i
$321$	−3.17660	+	9.77657i	−0.177300	+	0.545675i
$322$	−4.60812	+	14.1823i	−0.256801	+	0.790351i
$323$	−2.41119	+	1.75184i	−0.134162	+	0.0974747i
$324$	−8.52578			−0.473654
$325$	−16.5169	−	14.2110i	−0.916195	−	0.788287i
$326$	−3.52524			−0.195245
$327$	5.78568	−	4.20354i	0.319949	−	0.232456i
$328$	3.85022	−	11.8498i	0.212593	−	0.654294i
$329$	−9.95210	+	30.6294i	−0.548677	+	1.68865i
$330$	25.2624	−	31.9256i	1.39065	−	1.75744i
$331$	9.96449	+	30.6675i	0.547698	+	1.68564i	0.714487	+	0.699648i	$0.246660\pi$
$331$	9.96449	+	30.6675i	0.547698	+	1.68564i	−0.166789	+	0.985993i	$0.553340\pi$
$332$	7.28978			0.400079
$333$	0.0844339	+	0.259861i	0.00462695	+	0.0142403i
$334$	−7.60664	−	5.52655i	−0.416217	−	0.302399i
$335$	22.1549	−	6.20485i	1.21045	−	0.339007i
$336$	−22.5833	+	16.4077i	−1.23202	+	0.895113i
$337$	−15.1711	−	11.0224i	−0.826420	−	0.600430i	0.0921239	−	0.995748i	$-0.470634\pi$
$337$	−15.1711	−	11.0224i	−0.826420	−	0.600430i	−0.918544	+	0.395318i	$0.870634\pi$
$338$	−8.30720	−	6.03553i	−0.451852	−	0.328290i
$339$	−20.8900	+	15.1774i	−1.13459	+	0.824325i
$340$	0.0861645	−	2.09585i	0.00467292	−	0.113664i
$341$	3.05044	+	2.21627i	0.165190	+	0.120018i
$342$	0.0470295	+	0.144742i	0.00254306	+	0.00782674i
$343$	−11.8663			−0.640717
$344$	−4.77181	−	14.6861i	−0.257279	−	0.791823i
$345$	10.1582	−	2.84498i	0.546900	−	0.153169i
$346$	9.31243	−	28.6607i	0.500639	−	1.54081i
$347$	−3.05777	+	9.41086i	−0.164150	+	0.505201i	−0.998973	−	0.0453174i	$-0.985570\pi$
$347$	−3.05777	+	9.41086i	−0.164150	+	0.505201i	0.834823	+	0.550519i	$0.185570\pi$
$348$	−6.87175	+	4.99262i	−0.368364	+	0.267632i
$349$	4.83782			0.258963			0.129481	−	0.991582i	$-0.458669\pi$
$349$	4.83782			0.258963			0.129481	+	0.991582i	$0.458669\pi$
$350$	23.5081	−	14.2884i	1.25656	−	0.763749i
$351$	−22.5300			−1.20256
$352$	24.3063	−	17.6596i	1.29553	−	0.941259i
$353$	4.55142	−	14.0078i	0.242247	−	0.745561i	−0.753830	−	0.657070i	$-0.771796\pi$
$353$	4.55142	−	14.0078i	0.242247	−	0.745561i	0.996077	−	0.0884909i	$-0.0282044\pi$
$354$	−1.63531	+	5.03298i	−0.0869160	+	0.267500i
$355$	7.86258	+	2.91692i	0.417303	+	0.154814i
$356$	−2.68607	−	8.26686i	−0.142361	−	0.438143i
$357$	−5.58717			−0.295704
$358$	6.07951	+	18.7108i	0.321312	+	0.988896i
$359$	8.16996	+	5.93582i	0.431194	+	0.313281i	0.782126	−	0.623120i	$-0.214135\pi$
$359$	8.16996	+	5.93582i	0.431194	+	0.313281i	−0.350932	+	0.936401i	$0.614135\pi$
$360$	0.113681	+	0.0421741i	0.00599150	+	0.00222277i
$361$	8.18500	−	5.94675i	0.430789	−	0.312987i
$362$	−9.71839	−	7.06083i	−0.510787	−	0.371109i
$363$	36.9485	+	26.8446i	1.93929	+	1.40898i
$364$	10.6158	−	7.71286i	0.556421	−	0.404264i
$365$	−10.4614	−	15.7185i	−0.547577	−	0.822743i
$366$	32.6200	+	23.6998i	1.70507	+	1.23881i
$367$	−1.83273	−	5.64057i	−0.0956679	−	0.294436i	0.891759	−	0.452510i	$-0.149471\pi$
$367$	−1.83273	−	5.64057i	−0.0956679	−	0.294436i	−0.987427	+	0.158075i	$0.949471\pi$
$368$	13.5413			0.705890
$369$	−0.0630151	−	0.193941i	−0.00328044	−	0.0100961i
$370$	1.44401	−	35.1240i	0.0750707	−	1.82601i
$371$	11.7863	−	36.2744i	0.611912	−	1.88327i
$372$	0.311776	−	0.959546i	0.0161648	−	0.0497502i
$373$	1.44159	−	1.04738i	0.0746429	−	0.0542313i	−0.549838	−	0.835271i	$-0.685311\pi$
$373$	1.44159	−	1.04738i	0.0746429	−	0.0542313i	0.624481	+	0.781040i	$0.285311\pi$
$374$	10.4599			0.540867
$375$	−17.6285	−	8.24378i	−0.910332	−	0.425707i
$376$	18.2628			0.941834
$377$	−18.3395	+	13.3244i	−0.944530	+	0.686241i
$378$	8.79010	−	27.0531i	0.452114	−	1.39146i
$379$	6.18212	−	19.0266i	0.317554	−	0.977331i	−0.657136	−	0.753772i	$-0.728232\pi$
$379$	6.18212	−	19.0266i	0.317554	−	0.977331i	0.974690	−	0.223559i	$-0.0717676\pi$
$380$	0.256805	−	6.24648i	0.0131738	−	0.320438i
$381$	1.60725	+	4.94660i	0.0823419	+	0.253422i
$382$	−12.5186			−0.640507
$383$	0.624380	+	1.92164i	0.0319043	+	0.0981915i	0.965741	−	0.259509i	$-0.0835608\pi$
$383$	0.624380	+	1.92164i	0.0319043	+	0.0981915i	−0.933836	+	0.357701i	$0.883561\pi$
$384$	17.6153	+	12.7983i	0.898927	+	0.653109i
$385$	24.2672	+	36.4618i	1.23677	+	1.85826i
$386$	−36.7685	+	26.7139i	−1.87147	+	1.35970i
$387$	−0.204464	−	0.148552i	−0.0103935	−	0.00755133i
$388$	−6.53950	−	4.75122i	−0.331993	−	0.241207i
$389$	−2.56831	+	1.86599i	−0.130219	+	0.0946093i	−0.650988	−	0.759088i	$-0.725645\pi$
$389$	−2.56831	+	1.86599i	−0.130219	+	0.0946093i	0.520769	+	0.853697i	$0.325645\pi$
$390$	−27.2578	−	10.1123i	−1.38025	−	0.512056i
$391$	2.19271	+	1.59310i	0.110890	+	0.0805664i
$392$	−1.85796	−	5.71822i	−0.0938412	−	0.288814i
$393$	21.1163			1.06518
$394$	7.84556	+	24.1461i	0.395253	+	1.21646i
$395$	16.3940	+	6.08195i	0.824869	+	0.306016i
$396$	0.0526987	−	0.162190i	0.00264821	−	0.00815035i
$397$	7.46715	−	22.9815i	0.374766	−	1.15341i	−0.568871	−	0.822427i	$-0.692620\pi$
$397$	7.46715	−	22.9815i	0.374766	−	1.15341i	0.943637	−	0.330983i	$-0.107380\pi$
$398$	−14.0669	+	10.2202i	−0.705112	+	0.512294i
$399$	−16.6520			−0.833643
$400$	−18.9364	−	16.2927i	−0.946822	−	0.814637i
$401$	12.5700			0.627717			0.313859	−	0.949470i	$-0.398378\pi$
$401$	12.5700			0.627717			0.313859	+	0.949470i	$0.398378\pi$
$402$	24.8358	−	18.0443i	1.23870	−	0.899967i
$403$	0.832073	−	2.56086i	0.0414485	−	0.127565i
$404$	−1.42180	+	4.37586i	−0.0707373	+	0.217707i
$405$	−19.5695	+	5.48076i	−0.972415	+	0.272341i
$406$	−8.84425	−	27.2198i	−0.438933	−	1.35090i
$407$	55.9690			2.77428
$408$	0.979062	+	3.01324i	0.0484708	+	0.149178i
$409$	15.6328	+	11.3579i	0.772995	+	0.561613i	0.902868	−	0.429917i	$-0.141457\pi$
$409$	15.6328	+	11.3579i	0.772995	+	0.561613i	−0.129874	+	0.991531i	$0.541457\pi$
$410$	−1.07770	+	26.2139i	−0.0532240	+	1.29461i
$411$	8.01963	−	5.82660i	0.395579	−	0.287405i
$412$	−3.91913	−	2.84741i	−0.193082	−	0.140282i
$413$	−4.60600	−	3.34645i	−0.226646	−	0.164668i
$414$	0.111968	−	0.0813496i	0.00550293	−	0.00399812i
$415$	16.7324	−	4.68620i	0.821363	−	0.230036i
$416$	−17.3578	−	12.6112i	−0.851035	−	0.618313i
$417$	5.11698	+	15.7485i	0.250580	+	0.771205i
$418$	31.1746			1.52480
$419$	−0.0443465	−	0.136484i	−0.00216647	−	0.00666770i	0.949967	−	0.312349i	$-0.101116\pi$
$419$	−0.0443465	−	0.136484i	−0.00216647	−	0.00666770i	−0.952134	+	0.305681i	$0.901116\pi$
$420$	7.27238	−	9.19053i	0.354856	−	0.448452i
$421$	−10.7639	+	33.1278i	−0.524598	+	1.61455i	0.240510	+	0.970647i	$0.422685\pi$
$421$	−10.7639	+	33.1278i	−0.524598	+	1.61455i	−0.765109	+	0.643901i	$0.777315\pi$
$422$	3.46284	−	10.6575i	0.168569	−	0.518801i
$423$	0.241816	−	0.175690i	0.0117575	−	0.00854232i
$424$	−21.6287			−1.05038
$425$	−1.14953	−	4.86606i	−0.0557606	−	0.236039i
$426$	11.1897			0.542144
$427$	−35.0938	+	25.4972i	−1.69831	+	1.23389i
$428$	1.71198	−	5.26893i	0.0827517	−	0.254683i
$429$	14.3038	−	44.0225i	0.690593	−	2.12543i
$430$	18.0157	+	27.0688i	0.868794	+	1.30538i
$431$	−5.58719	−	17.1956i	−0.269125	−	0.828283i	−0.990714	−	0.135961i	$-0.956588\pi$
$431$	−5.58719	−	17.1956i	−0.269125	−	0.828283i	0.721589	−	0.692322i	$-0.243412\pi$
$432$	−25.8303			−1.24276
$433$	5.78802	+	17.8137i	0.278155	+	0.856072i	0.988367	+	0.152085i	$0.0485987\pi$
$433$	5.78802	+	17.8137i	0.278155	+	0.856072i	−0.710213	+	0.703987i	$0.751401\pi$
$434$	2.75034	+	1.99824i	0.132021	+	0.0959185i
$435$	−12.5634	+	15.8772i	−0.602371	+	0.761252i
$436$	−3.11810	+	2.26544i	−0.149330	+	0.108495i
$437$	6.53516	+	4.74807i	0.312619	+	0.227131i
$438$	−20.3821	−	14.8084i	−0.973893	−	0.707575i
$439$	−8.54142	+	6.20571i	−0.407660	+	0.296182i	−0.772654	−	0.634828i	$-0.781071\pi$
$439$	−8.54142	+	6.20571i	−0.407660	+	0.296182i	0.364994	+	0.931010i	$0.381071\pi$
$440$	15.4119	−	19.4770i	0.734735	−	0.928528i
$441$	−0.0796107	−	0.0578405i	−0.00379098	−	0.00275431i
$442$	−2.30825	−	7.10407i	−0.109792	−	0.337906i
$443$	11.5541			0.548950			0.274475	−	0.961594i	$-0.411496\pi$
$443$	11.5541			0.548950			0.274475	+	0.961594i	$0.411496\pi$
$444$	−4.62791	−	14.2432i	−0.219631	−	0.675954i
$445$	−11.4797	−	17.2484i	−0.544191	−	0.817654i
$446$	−3.68949	+	11.3551i	−0.174702	+	0.537678i
$447$	−3.50777	+	10.7958i	−0.165912	+	0.510625i
$448$	−4.03328	+	2.93035i	−0.190555	+	0.138446i
$449$	4.06213			0.191704			0.0958519	−	0.995396i	$-0.469442\pi$
$449$	4.06213			0.191704			0.0958519	+	0.995396i	$0.469442\pi$
$450$	−0.254457	−	0.0209579i	−0.0119952	−	0.000987963i
$451$	−41.7711			−1.96692
$452$	11.2583	−	8.17965i	0.529547	−	0.384739i
$453$	−0.945977	+	2.91142i	−0.0444459	+	0.136790i
$454$	−12.1166	+	37.2910i	−0.568659	+	1.75015i
$455$	19.4087	−	24.5279i	0.909893	−	1.14989i
$456$	2.91800	+	8.98067i	0.136648	+	0.420559i
$457$	−4.27532			−0.199991			−0.0999955	−	0.994988i	$-0.531883\pi$
$457$	−4.27532			−0.199991			−0.0999955	+	0.994988i	$0.531883\pi$
$458$	9.35855	+	28.8027i	0.437296	+	1.34586i
$459$	−4.18265	−	3.03887i	−0.195229	−	0.141842i
$460$	−5.47462	+	1.53326i	−0.255255	+	0.0714885i
$461$	−1.24504	+	0.904575i	−0.0579874	+	0.0421303i	−0.616401	−	0.787432i	$-0.711410\pi$
$461$	−1.24504	+	0.904575i	−0.0579874	+	0.0421303i	0.558414	+	0.829562i	$0.311410\pi$
$462$	47.2798	+	34.3508i	2.19966	+	1.59814i
$463$	−10.9750	−	7.97378i	−0.510050	−	0.370573i	0.302793	−	0.953056i	$-0.402081\pi$
$463$	−10.9750	−	7.97378i	−0.510050	−	0.370573i	−0.812843	+	0.582483i	$0.802081\pi$
$464$	−21.0259	+	15.2762i	−0.976104	+	0.709181i
$465$	0.0987876	−	2.40290i	0.00458117	−	0.111432i
$466$	29.4068	+	21.3653i	1.36224	+	0.989727i
$467$	−2.41200	−	7.42338i	−0.111614	−	0.343513i	0.879612	−	0.475692i	$-0.157802\pi$
$467$	−2.41200	−	7.42338i	−0.111614	−	0.343513i	−0.991226	+	0.132180i	$0.957802\pi$
$468$	−0.121784			−0.00562949
$469$	10.2059	+	31.4105i	0.471264	+	1.45040i
$470$	−37.0311	+	10.3712i	−1.70812	+	0.478386i
$471$	6.79322	−	20.9074i	0.313015	−	0.963361i
$472$	−0.997664	+	3.07049i	−0.0459212	+	0.141331i
$473$	−41.8823	+	30.4293i	−1.92575	+	1.39914i
$474$	23.3312			1.07164
$475$	−3.42607	−	14.5028i	−0.157199	−	0.665435i
$476$	3.01112			0.138015
$477$	−0.286383	+	0.208069i	−0.0131126	+	0.00952683i
$478$	−4.19984	+	12.9258i	−0.192096	+	0.591212i
$479$	−6.94510	+	21.3748i	−0.317330	+	0.976641i	0.657455	+	0.753494i	$0.271633\pi$
$479$	−6.94510	+	21.3748i	−0.317330	+	0.976641i	−0.974785	+	0.223147i	$0.928367\pi$
$480$	−17.9663	−	6.66526i	−0.820045	−	0.304226i
$481$	−12.3511	−	38.0127i	−0.563160	−	1.73323i
$482$	17.0009			0.774371
$483$	4.67949	+	14.4020i	0.212924	+	0.655313i
$484$	−19.9128	−	14.4675i	−0.905128	−	0.657614i
$485$	−18.0646	−	6.70174i	−0.820271	−	0.304310i
$486$	−0.429306	+	0.311909i	−0.0194737	+	0.0141485i
$487$	−25.9670	−	18.8661i	−1.17668	−	0.854905i	−0.184883	−	0.982761i	$-0.559191\pi$
$487$	−25.9670	−	18.8661i	−1.17668	−	0.854905i	−0.991793	+	0.127856i	$0.959191\pi$
$488$	19.9006	+	14.4587i	0.900859	+	0.654513i
$489$	−2.89614	+	2.10417i	−0.130968	+	0.0951539i
$490$	7.01462	+	10.5396i	0.316888	+	0.476130i
$491$	−33.6599	−	24.4553i	−1.51905	−	1.10365i	−0.961956	−	0.273205i	$-0.911916\pi$
$491$	−33.6599	−	24.4553i	−1.51905	−	1.10365i	−0.557094	−	0.830449i	$-0.688084\pi$
$492$	3.45393	+	10.6301i	0.155715	+	0.479241i
$493$	−5.20188			−0.234281
$494$	−6.87951	−	21.1730i	−0.309524	−	0.952617i
$495$	0.0166978	−	0.406156i	0.000750512	−	0.0182554i
$496$	0.953960	−	2.93599i	0.0428341	−	0.131830i
$497$	−3.72005	+	11.4491i	−0.166867	+	0.513564i
$498$	18.7572	−	13.6279i	0.840530	−	0.610681i
$499$	−40.1689			−1.79821			−0.899105	−	0.437734i	$-0.855781\pi$
$499$	−40.1689			−1.79821			−0.899105	+	0.437734i	$0.855781\pi$
$500$	9.50061	+	4.44286i	0.424880	+	0.198691i
$501$	−9.54793			−0.426570
$502$	−15.4102	+	11.1962i	−0.687792	+	0.499710i
$503$	−0.0732554	+	0.225457i	−0.00326630	+	0.0100526i	−0.952676	−	0.303986i	$-0.901682\pi$
$503$	−0.0732554	+	0.225457i	−0.00326630	+	0.0100526i	0.949410	+	0.314039i	$0.101682\pi$
$504$	−0.0537862	+	0.165537i	−0.00239583	+	0.00737359i
$505$	−0.450505	+	10.9580i	−0.0200472	+	0.487626i
$506$	−8.76057	−	26.9622i	−0.389455	−	1.19862i
$507$	−10.4273			−0.463092
$508$	−0.866203	−	2.66590i	−0.0384315	−	0.118280i
$509$	18.1976	+	13.2213i	0.806594	+	0.586025i	0.912841	−	0.408315i	$-0.133884\pi$
$509$	18.1976	+	13.2213i	0.806594	+	0.586025i	−0.106247	+	0.994340i	$0.533884\pi$
$510$	−3.69639	−	5.55388i	−0.163679	−	0.245930i
$511$	21.9278	−	15.9315i	0.970030	−	0.704768i
$512$	−5.18590	−	3.76778i	−0.229187	−	0.166514i
$513$	−12.4660	−	9.05705i	−0.550386	−	0.399878i
$514$	2.06269	−	1.49863i	0.0909812	−	0.0661017i
$515$	−10.8261	−	4.01636i	−0.477056	−	0.176982i
$516$	11.2069	+	8.14230i	0.493357	+	0.358445i
$517$	−18.9201	−	58.2300i	−0.832104	−	2.56095i
$518$	50.4628			2.21721
$519$	−9.45665	−	29.1046i	−0.415101	−	1.27755i
$520$	−16.6293	−	6.16926i	−0.729244	−	0.270540i
$521$	−2.43773	+	7.50256i	−0.106799	+	0.328693i	−0.990148	−	0.140022i	$-0.955283\pi$
$521$	−2.43773	+	7.50256i	−0.106799	+	0.328693i	0.883350	+	0.468715i	$0.155283\pi$
$522$	−0.0820835	+	0.252627i	−0.00359270	+	0.0110572i
$523$	−6.12768	+	4.45202i	−0.267945	+	0.194673i	−0.713642	−	0.700510i	$-0.752956\pi$
$523$	−6.12768	+	4.45202i	−0.267945	+	0.194673i	0.445697	+	0.895184i	$0.352956\pi$
$524$	−11.3803			−0.497151
$525$	10.7844	−	25.7703i	0.470670	−	1.12471i
$526$	35.0509			1.52829
$527$	0.499883	−	0.363186i	0.0217752	−	0.0158206i
$528$	16.3991	−	50.4712i	0.713678	−	2.19648i
$529$	−4.83737	+	14.8879i	−0.210320	+	0.647300i
$530$	43.8559	−	12.2826i	1.90498	−	0.533521i
$531$	0.0163284	+	0.0502536i	0.000708592	+	0.00218082i
$532$	8.97435			0.389087
$533$	9.21791	+	28.3698i	0.399272	+	1.22883i
$534$	−22.3660	−	16.2498i	−0.967870	−	0.703199i
$535$	0.542449	−	13.1945i	0.0234521	−	0.570447i
$536$	15.1517	−	11.0084i	0.654454	−	0.475489i
$537$	16.1628	+	11.7430i	0.697478	+	0.506747i
$538$	4.78147	+	3.47394i	0.206144	+	0.149772i
$539$	−16.3074	+	11.8480i	−0.702409	+	0.510330i
$540$	10.4430	−	2.92472i	0.449393	−	0.125860i
$541$	1.61401	+	1.17265i	0.0693919	+	0.0504161i	0.621940	−	0.783065i	$-0.286345\pi$
$541$	1.61401	+	1.17265i	0.0693919	+	0.0504161i	−0.552549	+	0.833481i	$0.686345\pi$
$542$	11.2158	+	34.5188i	0.481761	+	1.48271i
$543$	−12.1986			−0.523493
$544$	−1.52142	−	4.68246i	−0.0652305	−	0.200759i
$545$	−5.70075	+	7.20438i	−0.244193	+	0.308602i
$546$	12.8966	−	39.6916i	0.551923	−	1.69865i
$547$	−4.40640	+	13.5615i	−0.188404	+	0.579849i	−0.999990	−	0.00438418i	$-0.998604\pi$
$547$	−4.40640	+	13.5615i	−0.188404	+	0.579849i	0.811586	+	0.584233i	$0.198604\pi$
$548$	−4.32206	+	3.14016i	−0.184629	+	0.134141i
$549$	0.402595			0.0171823
$550$	−20.1897	+	48.2451i	−0.860892	+	2.05718i
$551$	−15.5037			−0.660480
$552$	6.94719	−	5.04743i	0.295692	−	0.214833i
$553$	−7.75653	+	23.8721i	−0.329841	+	1.01515i
$554$	13.0464	−	40.1526i	0.554287	−	1.70592i
$555$	−19.7788	−	29.7179i	−0.839562	−	1.26145i
$556$	−2.75772	−	8.48739i	−0.116953	−	0.359946i
$557$	21.9776			0.931222			0.465611	−	0.884989i	$-0.345835\pi$
$557$	21.9776			0.931222			0.465611	+	0.884989i	$0.345835\pi$
$558$	−0.00975003	−	0.0300075i	−0.000412752	−	0.00127032i
$559$	29.9092	+	21.7303i	1.26503	+	0.919095i
$560$	22.2518	−	28.1209i	0.940308	−	1.18832i
$561$	8.59326	−	6.24337i	0.362808	−	0.263595i
$562$	−5.63798	−	4.09623i	−0.237824	−	0.172789i
$563$	−9.94186	−	7.22318i	−0.418999	−	0.304421i	0.358236	−	0.933631i	$-0.383378\pi$
$563$	−9.94186	−	7.22318i	−0.418999	−	0.304421i	−0.777235	+	0.629210i	$0.783378\pi$
$564$	−13.2542	+	9.62973i	−0.558102	+	0.405485i
$565$	20.5833	−	26.0124i	0.865946	−	1.09435i
$566$	16.2998	+	11.8425i	0.685132	+	0.497778i
$567$	−9.01487	−	27.7449i	−0.378589	−	1.16518i
$568$	6.82657			0.286437
$569$	11.1733	+	34.3879i	0.468410	+	1.44162i	0.854643	+	0.519216i	$0.173776\pi$
$569$	11.1733	+	34.3879i	0.468410	+	1.44162i	−0.386233	+	0.922401i	$0.626224\pi$
$570$	−11.0167	−	16.5528i	−0.461440	−	0.693320i
$571$	0.196244	−	0.603978i	0.00821257	−	0.0252757i	−0.946866	−	0.321628i	$-0.895770\pi$
$571$	0.196244	−	0.603978i	0.00821257	−	0.0252757i	0.955079	+	0.296352i	$0.0957701\pi$
$572$	−7.70881	+	23.7253i	−0.322321	+	0.992003i
$573$	−10.2846	+	7.47220i	−0.429645	+	0.312155i
$574$	−37.6617			−1.57197
$575$	−11.5804	+	7.03866i	−0.482936	+	0.293533i
$576$	0.0462696			0.00192790
$577$	29.8157	−	21.6624i	1.24125	−	0.901818i	0.243565	−	0.969885i	$-0.421683\pi$
$577$	29.8157	−	21.6624i	1.24125	−	0.901818i	0.997681	+	0.0680670i	$0.0216832\pi$
$578$	0.529681	−	1.63019i	0.0220318	−	0.0678070i
$579$	−14.2618	+	43.8934i	−0.592701	+	1.82415i
$580$	6.77087	−	8.55676i	0.281145	−	0.355300i
$581$	7.70797	+	23.7227i	0.319780	+	0.984183i
$582$	−25.7089			−1.06567
$583$	22.4070	+	68.9617i	0.928004	+	2.85610i
$584$	−12.4346	−	9.03426i	−0.514547	−	0.373840i
$585$	−0.279535	+	0.0782886i	−0.0115574	+	0.00323683i
$586$	−40.9627	+	29.7612i	−1.69215	+	1.22942i
$587$	−6.56738	−	4.77148i	−0.271065	−	0.196940i	0.443946	−	0.896054i	$-0.353578\pi$
$587$	−6.56738	−	4.77148i	−0.271065	−	0.196940i	−0.715011	+	0.699114i	$0.753578\pi$
$588$	4.36354	+	3.17030i	0.179950	+	0.130741i
$589$	1.48985	−	1.08244i	0.0613883	−	0.0446012i
$590$	0.279253	−	6.79252i	0.0114967	−	0.279644i
$591$	20.8580	+	15.1542i	0.857984	+	0.623362i
$592$	−14.1603	−	43.5810i	−0.581985	−	1.79117i
$593$	44.7608			1.83811			0.919053	−	0.394134i	$-0.128955\pi$
$593$	44.7608			1.83811			0.919053	+	0.394134i	$0.128955\pi$
$594$	16.7110	+	51.4311i	0.685660	+	2.11024i
$595$	6.91152	−	1.93569i	0.283344	−	0.0793554i
$596$	1.89046	−	5.81824i	0.0774363	−	0.238324i
$597$	−5.45631	+	16.7928i	−0.223312	+	0.687283i
$598$	−16.3788	+	11.8999i	−0.669779	+	0.486623i
$599$	−32.8001			−1.34017			−0.670087	−	0.742283i	$-0.733743\pi$
$599$	−32.8001			−1.34017			−0.670087	+	0.742283i	$0.733743\pi$
$600$	−15.7881	−	1.30035i	−0.644546	−	0.0530868i
$601$	−3.25822			−0.132905			−0.0664527	−	0.997790i	$-0.521168\pi$
$601$	−3.25822			−0.132905			−0.0664527	+	0.997790i	$0.521168\pi$
$602$	−37.7620	+	27.4357i	−1.53906	+	1.11820i
$603$	0.0947209	−	0.291521i	0.00385733	−	0.0118716i
$604$	0.509820	−	1.56906i	0.0207443	−	0.0638443i
$605$	−55.0068	−	20.4068i	−2.23635	−	0.829656i
$606$	4.52205	+	13.9174i	0.183696	+	0.565357i
$607$	−5.66298			−0.229853			−0.114927	−	0.993374i	$-0.536663\pi$
$607$	−5.66298			−0.229853			−0.114927	+	0.993374i	$0.536663\pi$
$608$	−4.53445	−	13.9556i	−0.183896	−	0.565975i
$609$	−23.5131	−	17.0833i	−0.952800	−	0.692249i
$610$	−48.5628	−	18.0162i	−1.96625	−	0.729454i
$611$	−35.3731	+	25.7000i	−1.43104	+	1.03971i
$612$	−0.0226090	−	0.0164264i	−0.000913914	−	0.000663997i
$613$	−18.3794	−	13.3534i	−0.742336	−	0.539339i	0.151106	−	0.988518i	$-0.451717\pi$
$613$	−18.3794	−	13.3534i	−0.742336	−	0.539339i	−0.893442	+	0.449179i	$0.851717\pi$
$614$	−27.0947	+	19.6855i	−1.09345	+	0.794441i
$615$	14.7614	+	22.1792i	0.595237	+	0.894352i
$616$	28.8442	+	20.9566i	1.16217	+	0.844364i
$617$	−6.75538	−	20.7909i	−0.271961	−	0.837011i	−0.990007	−	0.141015i	$-0.954963\pi$
$617$	−6.75538	−	20.7909i	−0.271961	−	0.837011i	0.718046	−	0.695996i	$-0.245037\pi$
$618$	−15.4073			−0.619774
$619$	−0.00642664	−	0.0197792i	−0.000258308	−	0.000794991i	0.950927	−	0.309414i	$-0.100133\pi$
$619$	−0.00642664	−	0.0197792i	−0.000258308	−	0.000794991i	−0.951186	+	0.308619i	$0.900133\pi$
$620$	−0.0532401	+	1.29501i	−0.00213817	+	0.0520087i
$621$	−4.33012	+	13.3267i	−0.173762	+	0.534783i
$622$	1.21539	−	3.74059i	0.0487327	−	0.149984i
$623$	24.0622	−	17.4822i	0.964031	−	0.700409i
$624$	−37.8976			−1.51712
$625$	24.6631	+	4.09040i	0.986524	+	0.163616i
$626$	56.0611			2.24065
$627$	25.6113	−	18.6077i	1.02282	−	0.743121i
$628$	−3.66110	+	11.2677i	−0.146094	+	0.449631i
$629$	2.83424	−	8.72288i	0.113008	−	0.347804i
$630$	0.0150551	−	0.366199i	0.000599811	−	0.0145897i
$631$	11.7980	+	36.3104i	0.469670	+	1.44549i	0.853014	+	0.521889i	$0.174772\pi$
$631$	11.7980	+	36.3104i	0.469670	+	1.44549i	−0.383344	+	0.923606i	$0.625228\pi$
$632$	14.2338			0.566190
$633$	−3.51647	−	10.8226i	−0.139767	−	0.430159i
$634$	−1.67526	−	1.21715i	−0.0665331	−	0.0483391i
$635$	−3.70198	−	5.56228i	−0.146909	−	0.220732i
$636$	15.6969	−	11.4045i	0.622424	−	0.452217i
$637$	11.6455	+	8.46096i	0.461412	+	0.335236i
$638$	44.0194	+	31.9820i	1.74275	+	1.26618i
$639$	0.0903898	−	0.0656721i	0.00357577	−	0.00259795i
$640$	−26.2247	−	9.72903i	−1.03662	−	0.384573i
$641$	6.34200	+	4.60773i	0.250494	+	0.181994i	0.705946	−	0.708266i	$-0.250522\pi$
$641$	6.34200	+	4.60773i	0.250494	+	0.181994i	−0.455452	+	0.890260i	$0.650522\pi$
$642$	−5.44496	−	16.7579i	−0.214895	−	0.661380i
$643$	0.639161			0.0252061			0.0126030	−	0.999921i	$-0.495988\pi$
$643$	0.639161			0.0252061			0.0126030	+	0.999921i	$0.495988\pi$
$644$	−2.52194	−	7.76173i	−0.0993783	−	0.305855i
$645$	30.9578	+	11.4849i	1.21896	+	0.452219i
$646$	1.57866	−	4.85862i	0.0621116	−	0.191160i
$647$	−14.3060	+	44.0295i	−0.562429	+	1.73098i	0.113042	+	0.993590i	$0.463941\pi$
$647$	−14.3060	+	44.0295i	−0.562429	+	1.73098i	−0.675470	+	0.737387i	$0.736059\pi$
$648$	−13.3835	+	9.72371i	−0.525755	+	0.381983i
$649$	10.8237			0.424866
$650$	37.2223	+	3.06573i	1.45998	+	0.120248i
$651$	3.45225			0.135305
$652$	1.56083	−	1.13401i	0.0611269	−	0.0444113i
$653$	−10.6396	+	32.7453i	−0.416360	+	1.28142i	0.494669	+	0.869081i	$0.335289\pi$
$653$	−10.6396	+	32.7453i	−0.416360	+	1.28142i	−0.911029	+	0.412342i	$0.864711\pi$
$654$	−3.78801	+	11.6583i	−0.148123	+	0.455876i
$655$	−26.1216	+	7.31578i	−1.02065	+	0.285851i
$656$	10.5682	+	32.5256i	0.412619	+	1.26991i
$657$	−0.251555			−0.00981410
$658$	−17.0587	−	52.5014i	−0.665019	−	2.04672i
$659$	8.73488	+	6.34626i	0.340263	+	0.247215i	0.744773	−	0.667318i	$-0.232558\pi$
$659$	8.73488	+	6.34626i	0.340263	+	0.247215i	−0.404510	+	0.914534i	$0.632558\pi$
$660$	−0.915226	+	22.2618i	−0.0356251	+	0.866541i
$661$	15.5003	−	11.2616i	0.602890	−	0.438025i	−0.244013	−	0.969772i	$-0.578464\pi$
$661$	15.5003	−	11.2616i	0.602890	−	0.438025i	0.846904	+	0.531747i	$0.178464\pi$
$662$	−44.7160	−	32.4881i	−1.73794	−	1.26268i
$663$	−6.13667	−	4.45855i	−0.238328	−	0.173156i
$664$	11.4433	−	8.31404i	0.444086	−	0.322647i
$665$	20.5991	−	5.76912i	0.798798	−	0.223717i
$666$	−0.378900	−	0.275287i	−0.0146821	−	0.0106671i
$667$	4.35679	+	13.4088i	0.168696	+	0.519192i
$668$	5.14571			0.199094
$669$	3.74662	+	11.5309i	0.144853	+	0.445811i
$670$	−24.4713	+	30.9258i	−0.945407	+	1.19477i
$671$	25.4838	−	78.4310i	0.983790	−	3.02779i
$672$	8.50046	−	26.1617i	0.327912	−	1.00921i
$673$	1.61648	−	1.17444i	0.0623106	−	0.0452713i	−0.556194	−	0.831053i	$-0.687739\pi$
$673$	1.61648	−	1.17444i	0.0623106	−	0.0452713i	0.618505	+	0.785781i	$0.287739\pi$
$674$	32.1433			1.23811
$675$	22.0899	−	13.4264i	0.850240	−	0.516783i
$676$	5.61962			0.216139
$677$	−36.5910	+	26.5849i	−1.40630	+	1.02174i	−0.412458	+	0.910977i	$0.635330\pi$
$677$	−36.5910	+	26.5849i	−1.40630	+	1.02174i	−0.993847	+	0.110763i	$0.964670\pi$
$678$	13.6771	−	42.0938i	0.525266	−	1.61660i
$679$	8.54697	−	26.3049i	0.328003	−	1.00949i
$680$	−2.25508	−	3.38828i	−0.0864782	−	0.129935i
$681$	12.3042	+	37.8685i	0.471498	+	1.45112i
$682$	−6.46304			−0.247483
$683$	−0.335329	−	1.03204i	−0.0128310	−	0.0394898i	0.944436	−	0.328695i	$-0.106609\pi$
$683$	−0.335329	−	1.03204i	−0.0128310	−	0.0394898i	−0.957267	+	0.289205i	$0.906609\pi$
$684$	−0.0673838	−	0.0489572i	−0.00257649	−	0.00187193i
$685$	−7.90191	+	9.98611i	−0.301916	+	0.381550i
$686$	16.4552	−	11.9554i	0.628263	−	0.456460i
$687$	24.8804	+	18.0767i	0.949248	+	0.689669i
$688$	34.2905	+	24.9135i	1.30731	+	0.949819i
$689$	41.8923	−	30.4365i	1.59597	−	1.15954i
$690$	−11.2203	+	14.1797i	−0.427149	+	0.539814i
$691$	−2.28456	−	1.65983i	−0.0869089	−	0.0631430i	0.543482	−	0.839421i	$-0.317105\pi$
$691$	−2.28456	−	1.65983i	−0.0869089	−	0.0631430i	−0.630391	+	0.776278i	$0.717105\pi$
$692$	5.09652	+	15.6855i	0.193741	+	0.596272i
$693$	0.583526			0.0221663
$694$	−5.24128	−	16.1310i	−0.198956	−	0.612325i
$695$	−11.7860	−	17.7086i	−0.447067	−	0.671724i
$696$	−5.09297	+	15.6745i	−0.193048	+	0.594142i
$697$	−2.11526	+	6.51011i	−0.0801212	+	0.246588i
$698$	−6.70872	+	4.87417i	−0.253929	+	0.184490i
$699$	36.9117			1.39613
$700$	−5.81209	+	13.8885i	−0.219676	+	0.524937i
$701$	14.3009			0.540136			0.270068	−	0.962841i	$-0.412954\pi$
$701$	14.3009			0.540136			0.270068	+	0.962841i	$0.412954\pi$
$702$	31.2429	−	22.6993i	1.17919	−	0.856730i
$703$	8.44716	−	25.9977i	0.318591	−	0.980521i
$704$	2.92881	−	9.01395i	0.110384	−	0.339726i
$705$	−24.2323	+	30.6238i	−0.912641	+	1.15336i
$706$	7.80151	+	24.0106i	0.293614	+	0.903650i
$707$	−15.7434			−0.592093
$708$	−0.894976	−	2.75445i	−0.0336353	−	0.103519i
$709$	−2.53683	−	1.84312i	−0.0952728	−	0.0692197i	0.539129	−	0.842223i	$-0.318754\pi$
$709$	−2.53683	−	1.84312i	−0.0952728	−	0.0692197i	−0.634402	+	0.773003i	$0.718754\pi$
$710$	−13.8421	+	3.87670i	−0.519483	+	0.145490i
$711$	0.188468	−	0.136930i	0.00706811	−	0.00513528i
$712$	−13.6449	−	9.91361i	−0.511365	−	0.371528i
$713$	−1.35485	−	0.984358i	−0.0507396	−	0.0368645i
$714$	7.74786	−	5.62915i	0.289956	−	0.210666i
$715$	−2.44257	+	59.4129i	−0.0913471	+	2.22192i
$716$	−8.71072	−	6.32871i	−0.325535	−	0.236515i
$717$	4.26488	+	13.1260i	0.159275	+	0.490198i
$718$	−17.3099			−0.645999
$719$	9.14823	+	28.1554i	0.341171	+	1.05002i	0.963602	+	0.267342i	$0.0861455\pi$
$719$	9.14823	+	28.1554i	0.341171	+	1.05002i	−0.622430	+	0.782675i	$0.713855\pi$
$720$	−0.320483	+	0.0897567i	−0.0119437	+	0.00334503i
$721$	5.12221	−	15.7645i	0.190761	−	0.587102i
$722$	−5.35890	+	16.4930i	−0.199437	+	0.613805i
$723$	13.9670	−	10.1477i	0.519440	−	0.377395i
$724$	6.57426			0.244331
$725$	10.0407	−	23.9932i	0.372903	−	0.891085i
$726$	−78.2836			−2.90538
$727$	−16.3419	+	11.8731i	−0.606089	+	0.440350i	−0.848035	−	0.529940i	$-0.822214\pi$
$727$	−16.3419	+	11.8731i	−0.606089	+	0.440350i	0.241946	+	0.970290i	$0.422214\pi$
$728$	7.86789	−	24.2149i	0.291603	−	0.897463i
$729$	8.25897	−	25.4185i	0.305888	−	0.941426i
$730$	30.3437	+	11.2571i	1.12307	+	0.416645i
$731$	2.62157	+	8.06837i	0.0969623	+	0.298419i
$732$	−22.0667			−0.815607
$733$	−4.39735	−	13.5336i	−0.162420	−	0.499877i	0.836417	−	0.548093i	$-0.184646\pi$
$733$	−4.39735	−	13.5336i	−0.162420	−	0.499877i	−0.998837	+	0.0482168i	$0.984646\pi$
$734$	8.22445	+	5.97541i	0.303570	+	0.220557i
$735$	12.0538	+	4.47180i	0.444610	+	0.164945i
$736$	−10.7957	+	7.84351i	−0.397933	+	0.289115i
$737$	−50.7965	−	36.9058i	−1.87111	−	1.35944i
$738$	0.282782	+	0.205453i	0.0104094	+	0.00756285i
$739$	9.30003	−	6.75686i	0.342107	−	0.248555i	−0.403443	−	0.915005i	$-0.632187\pi$
$739$	9.30003	−	6.75686i	0.342107	−	0.248555i	0.745550	+	0.666449i	$0.232187\pi$
$740$	10.6595	+	16.0160i	0.391850	+	0.588760i
$741$	−18.2897	−	13.2883i	−0.671890	−	0.488156i
$742$	20.2027	+	62.1774i	0.741663	+	2.28260i
$743$	9.57498			0.351272			0.175636	−	0.984455i	$-0.443802\pi$
$743$	9.57498			0.351272			0.175636	+	0.984455i	$0.443802\pi$
$744$	−0.604952	−	1.86185i	−0.0221786	−	0.0682588i
$745$	0.599002	−	14.5701i	0.0219457	−	0.533805i
$746$	−0.943844	+	2.90485i	−0.0345566	+	0.106354i
$747$	0.0715377	−	0.220170i	0.00261743	−	0.00805561i
$748$	−4.63121	+	3.36477i	−0.169334	+	0.123028i
$749$	18.9566			0.692657
$750$	32.7516	−	6.32911i	1.19592	−	0.231107i
$751$	1.99936			0.0729575			0.0364788	−	0.999334i	$-0.488386\pi$
$751$	1.99936			0.0729575			0.0364788	+	0.999334i	$0.488386\pi$
$752$	−40.5547	+	29.4647i	−1.47888	+	1.07447i
$753$	−5.97734	+	18.3964i	−0.217826	+	0.670400i
$754$	12.0073	−	36.9545i	0.437278	−	1.34580i
$755$	0.161539	−	3.92925i	0.00587900	−	0.143000i
$756$	4.81065	+	14.8057i	0.174962	+	0.538477i
$757$	−25.1099			−0.912634			−0.456317	−	0.889817i	$-0.650832\pi$
$757$	−25.1099			−0.912634			−0.456317	+	0.889817i	$0.650832\pi$
$758$	10.5967	+	32.6132i	0.384889	+	1.18457i
$759$	−23.2906	−	16.9216i	−0.845397	−	0.614217i
$760$	−6.72103	−	10.0984i	−0.243797	−	0.366309i
$761$	−4.58671	+	3.33244i	−0.166268	+	0.120801i	−0.667808	−	0.744334i	$-0.732767\pi$
$761$	−4.58671	+	3.33244i	−0.166268	+	0.120801i	0.501540	+	0.865135i	$0.332767\pi$
$762$	−7.21258	−	5.24025i	−0.261284	−	0.189834i
$763$	−10.6692	−	7.75166i	−0.386253	−	0.280629i
$764$	5.54273	−	4.02703i	0.200529	−	0.145693i
$765$	−0.0624547	−	0.0231699i	−0.00225805	−	0.000837709i
$766$	−2.80193	−	2.03572i	−0.101238	−	0.0735535i
$767$	−2.38853	−	7.35115i	−0.0862449	−	0.265435i
$768$	−31.9150			−1.15164
$769$	−10.3850	−	31.9616i	−0.374491	−	1.15257i	−0.943821	−	0.330457i	$-0.892797\pi$
$769$	−10.3850	−	31.9616i	−0.374491	−	1.15257i	0.569330	−	0.822109i	$-0.307203\pi$
$770$	−70.3876	−	26.1129i	−2.53659	−	0.941043i
$771$	0.800077	−	2.46238i	0.0288141	−	0.0886806i
$772$	7.68619	−	23.6557i	0.276632	−	0.851386i
$773$	−3.75152	+	2.72564i	−0.134933	+	0.0980345i	−0.653204	−	0.757182i	$-0.726576\pi$
$773$	−3.75152	+	2.72564i	−0.134933	+	0.0980345i	0.518271	+	0.855216i	$0.326576\pi$
$774$	0.433204			0.0155712
$775$	0.710284	+	3.00669i	0.0255142	+	0.108003i
$776$	−15.6843			−0.563035
$777$	41.4575	−	30.1207i	1.48728	−	1.08057i
$778$	1.68153	−	5.17522i	0.0602858	−	0.185541i
$779$	−6.30433	+	19.4027i	−0.225876	+	0.695175i
$780$	15.3216	−	4.29108i	0.548602	−	0.153645i
$781$	−7.07224	−	21.7661i	−0.253065	−	0.778853i
$782$	−4.64575			−0.166132
$783$	−8.31067	−	25.5776i	−0.296999	−	0.914070i
$784$	13.3514	+	9.70037i	0.476836	+	0.346442i
$785$	−1.16004	+	28.2166i	−0.0414036	+	1.00710i
$786$	−29.2825	+	21.2750i	−1.04447	+	0.758853i
$787$	20.6331	+	14.9909i	0.735492	+	0.534366i	0.891296	−	0.453422i	$-0.149797\pi$
$787$	20.6331	+	14.9909i	0.735492	+	0.534366i	−0.155804	+	0.987788i	$0.549797\pi$
$788$	−11.2411	−	8.16715i	−0.400448	−	0.290943i
$789$	28.7960	−	20.9215i	1.02516	−	0.744825i
$790$	−28.8615	+	8.08315i	−1.02685	+	0.287586i
$791$	38.5227	+	27.9884i	1.36971	+	0.995153i
$792$	−0.102254	−	0.314704i	−0.00363342	−	0.0111825i
$793$	−58.8920			−2.09131
$794$	12.7993	+	39.3923i	0.454231	+	1.39798i
$795$	28.6983	−	36.2677i	1.01782	−	1.28628i
$796$	2.94059	−	9.05022i	0.104227	−	0.320776i
$797$	0.732815	−	2.25537i	0.0259577	−	0.0798894i	−0.937238	−	0.348689i	$-0.886627\pi$
$797$	0.732815	−	2.25537i	0.0259577	−	0.0798894i	0.963196	+	0.268800i	$0.0866269\pi$
$798$	23.0917	−	16.7771i	0.817439	−	0.593904i
$799$	−10.0334			−0.354955
$800$	24.5341	+	2.02070i	0.867411	+	0.0714425i
$801$	−0.276040			−0.00975340
$802$	−17.4311	+	12.6645i	−0.615515	+	0.447198i
$803$	−15.9231	+	49.0064i	−0.561915	+	1.72940i
$804$	−5.19175	+	15.9786i	−0.183099	+	0.563520i
$805$	−10.7783	−	16.1945i	−0.379884	−	0.570781i
$806$	1.42624	+	4.38953i	0.0502373	+	0.154614i
$807$	6.00175			0.211272
$808$	2.75879	+	8.49067i	0.0970538	+	0.298701i
$809$	−29.6797	−	21.5636i	−1.04348	−	0.758135i	−0.0725212	−	0.997367i	$-0.523104\pi$
$809$	−29.6797	−	21.5636i	−1.04348	−	0.758135i	−0.970963	+	0.239232i	$0.923104\pi$
$810$	21.6155	−	27.3168i	0.759491	−	0.959814i
$811$	1.80080	−	1.30836i	0.0632346	−	0.0459426i	−0.555719	−	0.831370i	$-0.687557\pi$
$811$	1.80080	−	1.30836i	0.0632346	−	0.0459426i	0.618953	+	0.785428i	$0.287557\pi$
$812$	12.6720	+	9.20677i	0.444701	+	0.323094i
$813$	29.8181	+	21.6641i	1.04577	+	0.759795i
$814$	−77.6135	+	56.3895i	−2.72035	+	1.97645i
$815$	2.85363	−	3.60630i	0.0999584	−	0.126323i
$816$	−7.03560	−	5.11166i	−0.246295	−	0.178944i
$817$	7.81333	+	24.0470i	0.273354	+	0.841297i
$818$	−33.1217			−1.15807
$819$	−0.128771	−	0.396316i	−0.00449962	−	0.0138484i
$820$	−7.95543	−	11.9532i	−0.277816	−	0.417422i
$821$	8.86978	−	27.2984i	0.309557	−	0.952720i	−0.668380	−	0.743820i	$-0.733012\pi$
$821$	8.86978	−	27.2984i	0.309557	−	0.952720i	0.977937	−	0.208899i	$-0.0669881\pi$
$822$	−5.25063	+	16.1598i	−0.183137	+	0.563637i
$823$	31.4692	−	22.8637i	1.09695	−	0.796979i	0.116389	−	0.993204i	$-0.462868\pi$
$823$	31.4692	−	22.8637i	1.09695	−	0.796979i	0.980559	+	0.196225i	$0.0628682\pi$
$824$	−9.39963			−0.327452
$825$	12.2102	+	51.6866i	0.425104	+	1.79950i
$826$	9.75884			0.339554
$827$	32.3688	−	23.5173i	1.12557	−	0.817778i	0.140530	−	0.990076i	$-0.455119\pi$
$827$	32.3688	−	23.5173i	1.12557	−	0.817778i	0.985045	+	0.172299i	$0.0551195\pi$
$828$	−0.0234061	+	0.0720367i	−0.000813419	+	0.00250345i
$829$	−5.55837	+	17.1069i	−0.193050	+	0.594147i	0.806944	+	0.590628i	$0.201120\pi$
$829$	−5.55837	+	17.1069i	−0.193050	+	0.594147i	−0.999994	+	0.00351880i	$0.998880\pi$
$830$	−18.4819	+	23.3566i	−0.641515	+	0.810720i
$831$	−13.2484	−	40.7744i	−0.459582	−	1.41445i
$832$	−6.76836			−0.234651
$833$	1.02074	+	3.14151i	0.0353665	+	0.108847i
$834$	−22.9626	−	16.6833i	−0.795131	−	0.577696i
$835$	11.8111	−	3.30790i	0.408740	−	0.114474i
$836$	−13.8028	+	10.0284i	−0.477381	+	0.346838i
$837$	2.58441	+	1.87769i	0.0893303	+	0.0649023i
$838$	0.199006	+	0.144587i	0.00687456	+	0.00499466i
$839$	18.1184	−	13.1638i	0.625516	−	0.454464i	−0.229328	−	0.973349i	$-0.573653\pi$
$839$	18.1184	−	13.1638i	0.625516	−	0.454464i	0.854844	+	0.518885i	$0.173653\pi$
$840$	0.934113	−	22.7212i	0.0322299	−	0.783957i
$841$	1.56983	+	1.14055i	0.0541322	+	0.0393294i
$842$	−18.4502	−	56.7838i	−0.635835	−	1.95690i
$843$	−7.07685			−0.243739
$844$	1.89515	+	5.83266i	0.0652337	+	0.200769i
$845$	12.8989	−	3.61255i	0.443735	−	0.124275i
$846$	−0.158322	+	0.487266i	−0.00544323	+	0.0167525i
$847$	26.0256	−	80.0985i	0.894250	−	2.75222i
$848$	48.0289	−	34.8950i	1.64932	−	1.19830i
$849$	20.4597			0.702175
$850$	6.49671	+	5.58971i	0.222835	+	0.191726i
$851$	−24.8586			−0.852143
$852$	−4.95436	+	3.59955i	−0.169734	+	0.123319i
$853$	8.69966	−	26.7748i	0.297871	−	0.916752i	−0.684371	−	0.729134i	$-0.739923\pi$
$853$	8.69966	−	26.7748i	0.297871	−	0.916752i	0.982242	−	0.187618i	$-0.0600768\pi$
$854$	22.9767	−	70.7150i	0.786247	−	2.41982i
$855$	−0.186140	−	0.0690556i	−0.00636585	−	0.00236165i
$856$	−3.32183	−	10.2235i	−0.113538	−	0.349434i
$857$	−8.56298			−0.292506			−0.146253	−	0.989247i	$-0.546721\pi$
$857$	−8.56298			−0.292506			−0.146253	+	0.989247i	$0.546721\pi$
$858$	24.5179	+	75.4583i	0.837027	+	2.57610i
$859$	−3.93806	−	2.86117i	−0.134365	−	0.0976219i	0.518573	−	0.855034i	$-0.326464\pi$
$859$	−3.93806	−	2.86117i	−0.134365	−	0.0976219i	−0.652938	+	0.757412i	$0.726464\pi$
$860$	−16.6842	−	6.18964i	−0.568927	−	0.211065i
$861$	−30.9408	+	22.4798i	−1.05446	+	0.766110i
$862$	25.0727	+	18.2164i	0.853979	+	0.620452i
$863$	−15.6225	−	11.3504i	−0.531796	−	0.386373i	0.289233	−	0.957259i	$-0.406600\pi$
$863$	−15.6225	−	11.3504i	−0.531796	−	0.386373i	−0.821029	+	0.570886i	$0.806600\pi$
$864$	20.5930	−	14.9617i	0.700587	−	0.509006i
$865$	21.7815	+	32.7270i	0.740594	+	1.11275i
$866$	−25.9739	−	18.8712i	−0.882630	−	0.641268i
$867$	−0.537884	−	1.65544i	−0.0182675	−	0.0562216i
$868$	−1.86054			−0.0631508
$869$	−14.7460	−	45.3837i	−0.500225	−	1.53954i
$870$	1.42556	−	34.6751i	0.0483309	−	1.17560i
$871$	−13.8559	+	42.6439i	−0.469488	+	1.44493i
$872$	−2.31097	+	7.11244i	−0.0782593	+	0.240857i
$873$	−0.207674	+	0.150884i	−0.00702871	+	0.00510666i
$874$	−13.8462			−0.468355
$875$	−4.41250	+	35.6150i	−0.149170	+	1.20401i
$876$	13.7880			0.465853
$877$	−29.9042	+	21.7266i	−1.00979	+	0.733657i	−0.964165	−	0.265302i	$-0.914528\pi$
$877$	−29.9042	+	21.7266i	−1.00979	+	0.733657i	−0.0456264	+	0.998959i	$0.514528\pi$
$878$	5.59226	−	17.2112i	0.188730	−	0.580850i
$879$	−15.8887	+	48.9003i	−0.535912	+	1.64937i
$880$	−2.80038	+	68.1160i	−0.0944006	+	2.29619i
$881$	−11.2530	−	34.6332i	−0.379124	−	1.16682i	−0.940654	−	0.339367i	$-0.889787\pi$
$881$	−11.2530	−	34.6332i	−0.379124	−	1.16682i	0.561530	−	0.827456i	$-0.310213\pi$
$882$	0.168673			0.00567952
$883$	−5.93397	−	18.2629i	−0.199694	−	0.614595i	−0.999890	−	0.0148559i	$-0.995271\pi$
$883$	−5.93397	−	18.2629i	−0.199694	−	0.614595i	0.800196	−	0.599739i	$-0.204729\pi$
$884$	3.30726	+	2.40287i	0.111235	+	0.0808172i
$885$	−3.82495	−	5.74705i	−0.128574	−	0.193185i
$886$	−16.0223	+	11.6409i	−0.538279	+	0.391083i
$887$	−9.78269	−	7.10754i	−0.328471	−	0.238648i	0.411311	−	0.911495i	$-0.365071\pi$
$887$	−9.78269	−	7.10754i	−0.328471	−	0.238648i	−0.739781	+	0.672847i	$0.765071\pi$
$888$	−23.5093	−	17.0805i	−0.788920	−	0.573184i
$889$	7.75958	−	5.63766i	0.260248	−	0.189081i
$890$	33.2972	+	12.3528i	1.11613	+	0.414068i
$891$	44.8686	+	32.5990i	1.50316	+	1.09211i
$892$	−2.01919	−	6.21442i	−0.0676074	−	0.208074i
$893$	−29.9034			−1.00068
$894$	−6.01262	−	18.5049i	−0.201092	−	0.618898i
$895$	−24.0623	−	8.92682i	−0.804315	−	0.298391i
$896$	12.4078	−	38.1872i	0.414515	−	1.27575i
$897$	−6.35303	+	19.5526i	−0.212121	+	0.652843i
$898$	−5.63305	+	4.09265i	−0.187977	+	0.136574i
$899$	3.21419			0.107199
$900$	0.119405	−	0.0725755i	0.00398017	−	0.00241918i
$901$	11.8825			0.395864
$902$	57.9249	−	42.0849i	1.92869	−	1.40127i
$903$	−14.6472	+	45.0794i	−0.487427	+	1.50015i
$904$	8.34406	−	25.6804i	0.277519	−	0.854117i
$905$	15.0901	−	4.22623i	0.501612	−	0.140485i
$906$	−1.62148	−	4.99041i	−0.0538702	−	0.165795i
$907$	49.8428			1.65500			0.827501	−	0.561464i	$-0.189762\pi$
$907$	49.8428			1.65500			0.827501	+	0.561464i	$0.189762\pi$
$908$	−6.63117	−	20.4086i	−0.220063	−	0.677284i
$909$	0.118210	+	0.0858843i	0.00392076	+	0.00284860i
$910$	−2.20228	+	53.5679i	−0.0730048	+	1.77576i
$911$	−22.4901	+	16.3400i	−0.745132	+	0.541370i	−0.894314	−	0.447440i	$-0.852336\pi$
$911$	−22.4901	+	16.3400i	−0.745132	+	0.541370i	0.149182	+	0.988810i	$0.452336\pi$
$912$	−20.9689	−	15.2348i	−0.694350	−	0.504474i
$913$	−38.3639	−	27.8730i	−1.26966	−	0.922463i
$914$	5.92868	−	4.30744i	0.196103	−	0.142478i
$915$	−50.6502	+	14.1854i	−1.67444	+	0.468956i
$916$	−13.4089	−	9.74216i	−0.443044	−	0.321890i
$917$	−12.0332	−	37.0343i	−0.397370	−	1.22298i
$918$	8.86187			0.292485
$919$	−6.69222	−	20.5965i	−0.220756	−	0.679417i	−0.998695	−	0.0510769i	$-0.983735\pi$
$919$	−6.69222	−	20.5965i	−0.220756	−	0.679417i	0.777939	−	0.628340i	$-0.216265\pi$
$920$	−6.84521	+	8.65070i	−0.225680	+	0.285205i
$921$	−10.5095	+	32.3450i	−0.346301	+	1.06580i
$922$	0.815156	−	2.50879i	0.0268457	−	0.0826227i
$923$	−13.2223	+	9.60657i	−0.435217	+	0.316204i
$924$	−31.9837			−1.05219
$925$	34.7628	+	29.9096i	1.14299	+	0.983422i
$926$	23.2529			0.764139
$927$	−0.124459	+	0.0904250i	−0.00408778	+	0.00296995i
$928$	7.91427	−	24.3576i	0.259799	−	0.799578i
$929$	0.746600	−	2.29780i	0.0244952	−	0.0753883i	−0.938062	−	0.346468i	$-0.887381\pi$
$929$	0.746600	−	2.29780i	0.0244952	−	0.0753883i	0.962557	+	0.271080i	$0.0873808\pi$
$930$	2.28396	+	3.43168i	0.0748940	+	0.112529i
$931$	3.04221	+	9.36297i	0.0997045	+	0.306859i
$932$	−19.8930			−0.651616
$933$	−1.23421	−	3.79851i	−0.0404063	−	0.124358i
$934$	10.8239	+	7.86405i	0.354170	+	0.257319i
$935$	−8.46712	+	10.7004i	−0.276904	+	0.349940i
$936$	−0.191174	+	0.138896i	−0.00624871	+	0.00453996i
$937$	37.4713	+	27.2245i	1.22413	+	0.889385i	0.996436	−	0.0843473i	$-0.0268805\pi$
$937$	37.4713	+	27.2245i	1.22413	+	0.889385i	0.227697	+	0.973732i	$0.426881\pi$
$938$	−45.7992	−	33.2751i	−1.49540	−	1.08647i
$939$	46.0568	−	33.4622i	1.50301	−	1.09200i
$940$	13.0596	−	16.5042i	0.425958	−	0.538309i
$941$	10.0543	+	7.30487i	0.327761	+	0.238132i	0.739480	−	0.673179i	$-0.235072\pi$
$941$	10.0543	+	7.30487i	0.327761	+	0.238132i	−0.411719	+	0.911311i	$0.635072\pi$
$942$	11.6442	+	35.8370i	0.379387	+	1.16763i
$943$	18.5526			0.604157
$944$	−2.73842	−	8.42798i	−0.0891279	−	0.274307i
$945$	20.5598	+	30.8914i	0.668810	+	1.00490i
$946$	27.4213	−	84.3940i	0.891543	−	2.74389i
$947$	−12.8436	+	39.5286i	−0.417361	+	1.28451i	0.492761	+	0.870165i	$0.335988\pi$
$947$	−12.8436	+	39.5286i	−0.417361	+	1.28451i	−0.910122	+	0.414341i	$0.864012\pi$
$948$	−10.3301	+	7.50528i	−0.335507	+	0.243760i
$949$	36.7977			1.19450
$950$	19.3628	+	16.6596i	0.628212	+	0.540508i
$951$	−2.10280			−0.0681881
$952$	4.72678	−	3.43420i	0.153196	−	0.111303i
$953$	−2.19975	+	6.77015i	−0.0712570	+	0.219307i	−0.980343	−	0.197303i	$-0.936782\pi$
$953$	−2.19975	+	6.77015i	−0.0712570	+	0.219307i	0.909086	+	0.416610i	$0.136782\pi$
$954$	0.187501	−	0.577069i	0.00607057	−	0.0186833i
$955$	10.1336	−	12.8065i	0.327916	−	0.414408i
$956$	−2.29849	−	7.07404i	−0.0743386	−	0.228791i
$957$	55.2536			1.78610
$958$	−11.9045	−	36.6383i	−0.384617	−	1.18373i
$959$	−14.7888	−	10.7447i	−0.477556	−	0.346965i
$960$	−5.82115	+	1.63031i	−0.187877	+	0.0526181i
$961$	24.7707	−	17.9969i	0.799053	−	0.580546i
$962$	55.4258	+	40.2692i	1.78700	+	1.29833i
$963$	−0.142335	−	0.103413i	−0.00458669	−	0.00333242i
$964$	−7.52733	+	5.46892i	−0.242439	+	0.176142i
$965$	2.43541	−	59.2386i	0.0783986	−	1.90696i
$966$	−20.9993	−	15.2569i	−0.675643	−	0.490883i
$967$	−11.3423	−	34.9081i	−0.364745	−	1.12257i	−0.950141	−	0.311821i	$-0.899061\pi$
$967$	−11.3423	−	34.9081i	−0.364745	−	1.12257i	0.585396	−	0.810748i	$-0.300939\pi$
$968$	−47.7589			−1.53503
$969$	−1.60311	−	4.93387i	−0.0514993	−	0.158499i
$970$	31.8027	−	8.90688i	1.02112	−	0.285983i
$971$	−3.01001	+	9.26386i	−0.0965958	+	0.297291i	−0.987666	−	0.156574i	$-0.949955\pi$
$971$	−3.01001	+	9.26386i	−0.0965958	+	0.297291i	0.891070	+	0.453865i	$0.149955\pi$
$972$	0.0897432	−	0.276201i	0.00287852	−	0.00885916i
$973$	24.7041	−	17.9486i	0.791977	−	0.575405i
$974$	55.0169			1.76285
$975$	32.4097	−	19.6989i	1.03794	−	0.630869i
$976$	−67.5188			−2.16122
$977$	−9.43215	+	6.85286i	−0.301761	+	0.219242i	−0.728353	−	0.685202i	$-0.759714\pi$
$977$	−9.43215	+	6.85286i	−0.301761	+	0.219242i	0.426592	+	0.904444i	$0.359714\pi$
$978$	1.89617	−	5.83581i	0.0606328	−	0.186609i
$979$	−17.4730	+	53.7764i	−0.558440	+	1.71870i
$980$	−6.49620	−	2.41001i	−0.207514	−	0.0769849i
$981$	0.0378228	+	0.116407i	0.00120759	+	0.00371658i
$982$	71.3161			2.27579
$983$	16.0947	+	49.5343i	0.513340	+	1.57990i	0.786283	+	0.617867i	$0.212003\pi$
$983$	16.0947	+	49.5343i	0.513340	+	1.57990i	−0.272943	+	0.962030i	$0.587997\pi$
$984$	17.5456	+	12.7476i	0.559332	+	0.406379i
$985$	−31.0523	−	11.5200i	−0.989407	−	0.367058i
$986$	7.21357	−	5.24097i	0.229727	−	0.166906i
$987$	−45.3520	−	32.9501i	−1.44357	−	1.04881i
$988$	9.85697	+	7.16151i	0.313592	+	0.227838i
$989$	18.6020	−	13.5152i	0.591511	−	0.429758i
$990$	0.386052	+	0.580049i	0.0122696	+	0.0184352i
$991$	19.0389	+	13.8325i	0.604789	+	0.439405i	0.847576	−	0.530675i	$-0.178061\pi$
$991$	19.0389	+	13.8325i	0.604789	+	0.439405i	−0.242786	+	0.970080i	$0.578061\pi$
$992$	0.940072	+	2.89324i	0.0298473	+	0.0918606i
$993$	−56.1279			−1.78117
$994$	−6.37649	−	19.6248i	−0.202250	−	0.622461i
$995$	0.931742	−	22.6636i	0.0295382	−	0.718484i
$996$	−3.92106	+	12.0678i	−0.124243	+	0.382382i
$997$	15.6395	−	48.1334i	0.495307	−	1.52440i	−0.321170	−	0.947022i	$-0.604076\pi$
$997$	15.6395	−	48.1334i	0.495307	−	1.52440i	0.816477	−	0.577378i	$-0.195924\pi$
$998$	55.7032	−	40.4708i	1.76325	−	1.28108i
$999$	47.4184			1.50025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.5	✓	76
25.16	even	5	inner	425.2.k.b.341.5	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.5	✓	76	1.1	even	1	trivial
425.2.k.b.341.5	yes	76	25.16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38672 + 1.00751i) q^{2} +(-0.537884 + 1.65544i) q^{3} +(0.289884 - 0.892173i) q^{4} +(0.0918514 - 2.23418i) q^{5} +(-0.921979 - 2.83756i) q^{6} +3.20986 q^{7} +(-0.562476 - 1.73112i) q^{8} +(-0.0241012 - 0.0175105i) q^{9} +(2.12360 + 3.19073i) q^{10} +(-4.93687 + 3.58684i) q^{11} +(1.32101 + 0.959771i) q^{12} +(3.52554 + 2.56146i) q^{13} +(-4.45118 + 3.23397i) q^{14} +(3.64914 + 1.35378i) q^{15} +(4.04198 + 2.93667i) q^{16} +(0.309017 + 0.951057i) q^{17} +0.0510638 q^{18} +(0.920995 + 2.83453i) q^{19} +(-1.96665 - 0.729602i) q^{20} +(-1.72653 + 5.31372i) q^{21} +(3.23228 - 9.94792i) q^{22} +(2.19271 - 1.59310i) q^{23} +3.16831 q^{24} +(-4.98313 - 0.410425i) q^{25} -7.46966 q^{26} +(-4.18265 + 3.03887i) q^{27} +(0.930488 - 2.86375i) q^{28} +(-1.60747 + 4.94728i) q^{29} +(-6.42430 + 1.79923i) q^{30} +(-0.190938 - 0.587648i) q^{31} -4.92343 q^{32} +(-3.28233 - 10.1020i) q^{33} +(-1.38672 - 1.00751i) q^{34} +(0.294830 - 7.17140i) q^{35} +(-0.0226090 + 0.0164264i) q^{36} +(-7.42013 - 5.39104i) q^{37} +(-4.13299 - 3.00279i) q^{38} +(-6.13667 + 4.45855i) q^{39} +(-3.91931 + 1.09767i) q^{40} +(5.53783 + 4.02347i) q^{41} +(-2.95942 - 9.10816i) q^{42} +8.48358 q^{43} +(1.76896 + 5.44431i) q^{44} +(-0.0413354 + 0.0522380i) q^{45} +(-1.43562 + 4.41837i) q^{46} +(-3.10048 + 9.54230i) q^{47} +(-7.03560 + 5.11166i) q^{48} +3.30318 q^{49} +(7.32373 - 4.45142i) q^{50} -1.74063 q^{51} +(3.30726 - 2.40287i) q^{52} +(3.67190 - 11.3009i) q^{53} +(2.73847 - 8.42814i) q^{54} +(7.56020 + 11.3593i) q^{55} +(-1.80547 - 5.55666i) q^{56} -5.18777 q^{57} +(-2.75534 - 8.48006i) q^{58} +(-1.43495 - 1.04256i) q^{59} +(2.26564 - 2.86322i) q^{60} +(-10.9331 + 7.94340i) q^{61} +(0.856842 + 0.622532i) q^{62} +(-0.0773614 - 0.0562063i) q^{63} +(-1.25653 + 0.912922i) q^{64} +(6.04658 - 7.64143i) q^{65} +(14.7296 + 10.7017i) q^{66} +(3.17954 + 9.78563i) q^{67} +0.938086 q^{68} +(1.45785 + 4.48680i) q^{69} +(6.81644 + 10.2418i) q^{70} +(-1.15895 + 3.56687i) q^{71} +(-0.0167566 + 0.0515714i) q^{72} +(6.83140 - 4.96331i) q^{73} +15.7212 q^{74} +(3.35978 - 8.02849i) q^{75} +2.79587 q^{76} +(-15.8466 + 11.5133i) q^{77} +(4.01781 - 12.3655i) q^{78} +(-2.41647 + 7.43714i) q^{79} +(6.93232 - 8.76078i) q^{80} +(-2.80850 - 8.64366i) q^{81} -11.7331 q^{82} +(2.40134 + 7.39057i) q^{83} +(4.24026 + 3.08073i) q^{84} +(2.15322 - 0.603044i) q^{85} +(-11.7644 + 8.54733i) q^{86} +(-7.32528 - 5.32213i) q^{87} +(8.98614 + 6.52881i) q^{88} +(7.49634 - 5.44641i) q^{89} +(0.00469028 - 0.114086i) q^{90} +(11.3165 + 8.22191i) q^{91} +(-0.785685 - 2.41809i) q^{92} +1.07552 q^{93} +(-5.31449 - 16.3563i) q^{94} +(6.41745 - 1.79731i) q^{95} +(2.64824 - 8.15043i) q^{96} +(2.66273 - 8.19503i) q^{97} +(-4.58060 + 3.32800i) q^{98} +0.181792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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