LMFDB - Embedded newform 350.2.m.b.169.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	350.169
Dual form			350.2.m.b.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.578028 + 0.795587i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.99915 + 1.00169i) q^{5} +(0.795587 + 0.578028i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.628209 - 1.93343i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.578028 + 0.795587i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.99915 + 1.00169i) q^{5} +(0.795587 + 0.578028i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.628209 - 1.93343i) q^{9} +(2.21085 + 0.334894i) q^{10} +(1.14389 + 3.52052i) q^{11} +(0.935268 + 0.303887i) q^{12} +(-6.30751 - 2.04944i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.358633 + 2.16951i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.84817 + 2.54379i) q^{17} -2.03293i q^{18} +(1.50421 + 1.09287i) q^{19} +(2.20613 - 0.364687i) q^{20} +(0.795587 - 0.578028i) q^{21} +(2.17580 + 2.99474i) q^{22} +(3.99353 - 1.29758i) q^{23} +0.983399 q^{24} +(2.99323 + 4.00507i) q^{25} -6.63211 q^{26} +(4.70714 - 1.52944i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-1.14049 + 0.828616i) q^{29} +(1.01149 + 1.95250i) q^{30} +(-7.02973 - 5.10740i) q^{31} -1.00000i q^{32} +(-2.13968 + 2.94502i) q^{33} +(-0.971641 + 2.99040i) q^{34} +(1.00169 - 1.99915i) q^{35} +(-0.628209 - 1.93343i) q^{36} +(-4.73624 - 1.53890i) q^{37} +(1.76830 + 0.574557i) q^{38} +(-2.01541 - 6.20280i) q^{39} +(1.98546 - 1.02857i) q^{40} +(-2.79307 + 8.59617i) q^{41} +(0.578028 - 0.795587i) q^{42} -4.81491i q^{43} +(2.99474 + 2.17580i) q^{44} +(3.19258 - 3.23595i) q^{45} +(3.39710 - 2.46814i) q^{46} +(-3.21041 - 4.41875i) q^{47} +(0.935268 - 0.303887i) q^{48} -1.00000 q^{49} +(4.08436 + 2.88409i) q^{50} -3.09210 q^{51} +(-6.30751 + 2.04944i) q^{52} +(-2.27323 - 3.12884i) q^{53} +(4.00413 - 2.90917i) q^{54} +(-1.23967 + 8.18389i) q^{55} +(-0.809017 - 0.587785i) q^{56} +1.82844i q^{57} +(-0.828616 + 1.14049i) q^{58} +(2.30888 - 7.10600i) q^{59} +(1.56534 + 1.54437i) q^{60} +(4.36431 + 13.4320i) q^{61} +(-8.26394 - 2.68512i) q^{62} +(-1.93343 - 0.628209i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-10.5568 - 10.4153i) q^{65} +(-1.12490 + 3.46208i) q^{66} +(0.688568 - 0.947733i) q^{67} +3.14430i q^{68} +(3.34071 + 2.42716i) q^{69} +(0.334894 - 2.21085i) q^{70} +(-6.63784 + 4.82267i) q^{71} +(-1.19492 - 1.64467i) q^{72} +(-11.3598 + 3.69101i) q^{73} -4.97997 q^{74} +(-1.45622 + 4.69641i) q^{75} +1.85931 q^{76} +(3.52052 - 1.14389i) q^{77} +(-3.83354 - 5.27642i) q^{78} +(9.20323 - 6.68654i) q^{79} +(1.57044 - 1.59177i) q^{80} +(-0.996359 - 0.723897i) q^{81} +9.03855i q^{82} +(-1.60022 + 2.20251i) q^{83} +(0.303887 - 0.935268i) q^{84} +(-6.24287 + 3.23413i) q^{85} +(-1.48789 - 4.57925i) q^{86} +(-1.31847 - 0.428397i) q^{87} +(3.52052 + 1.14389i) q^{88} +(-1.91415 - 5.89114i) q^{89} +(2.03637 - 4.06413i) q^{90} +(-2.04944 + 6.30751i) q^{91} +(2.46814 - 3.39710i) q^{92} -8.54497i q^{93} +(-4.41875 - 3.21041i) q^{94} +(1.91242 + 3.69157i) q^{95} +(0.795587 - 0.578028i) q^{96} +(-1.07383 - 1.47800i) q^{97} +(-0.951057 + 0.309017i) q^{98} +7.52528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	0.578028	+	0.795587i	0.333724	+	0.459332i	0.942595	−	0.333937i	$-0.108377\pi$
$3$	0.578028	+	0.795587i	0.333724	+	0.459332i	−0.608871	+	0.793269i	$0.708377\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.99915	+	1.00169i	0.894048	+	0.447970i
$5$	1.99915	+	1.00169i	0.894048	+	0.447970i
$6$	0.795587	+	0.578028i	0.324797	+	0.235979i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.628209	−	1.93343i	0.209403	−	0.644476i
$10$	2.21085	+	0.334894i	0.699131	+	0.105903i
$11$	1.14389	+	3.52052i	0.344895	+	1.06148i	0.961640	+	0.274315i	$0.0884510\pi$
$11$	1.14389	+	3.52052i	0.344895	+	1.06148i	−0.616745	+	0.787163i	$0.711549\pi$
$12$	0.935268	+	0.303887i	0.269989	+	0.0877246i
$13$	−6.30751	−	2.04944i	−1.74939	−	0.568411i	−0.753374	−	0.657592i	$-0.771575\pi$
$13$	−6.30751	−	2.04944i	−1.74939	−	0.568411i	−0.996015	+	0.0891806i	$0.971575\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.358633	+	2.16951i	0.0925985	+	0.560164i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.84817	+	2.54379i	−0.448248	+	0.616960i	−0.972020	−	0.234898i	$-0.924524\pi$
$17$	−1.84817	+	2.54379i	−0.448248	+	0.616960i	0.523772	+	0.851858i	$0.324524\pi$
$18$		−	2.03293i		−	0.479165i
$19$	1.50421	+	1.09287i	0.345089	+	0.250722i	0.746806	−	0.665042i	$-0.231586\pi$
$19$	1.50421	+	1.09287i	0.345089	+	0.250722i	−0.401717	+	0.915764i	$0.631586\pi$
$20$	2.20613	−	0.364687i	0.493305	−	0.0815464i
$21$	0.795587	−	0.578028i	0.173611	−	0.126136i
$22$	2.17580	+	2.99474i	0.463883	+	0.638480i
$23$	3.99353	−	1.29758i	0.832709	−	0.270564i	0.138523	−	0.990359i	$-0.455765\pi$
$23$	3.99353	−	1.29758i	0.832709	−	0.270564i	0.694186	+	0.719796i	$0.255765\pi$
$24$	0.983399			0.200736
$25$	2.99323	+	4.00507i	0.598645	+	0.801014i
$26$	−6.63211			−1.30066
$27$	4.70714	−	1.52944i	0.905889	−	0.294341i
$28$	−0.587785	−	0.809017i	−0.111081	−	0.152890i
$29$	−1.14049	+	0.828616i	−0.211784	+	0.153870i	−0.688621	−	0.725122i	$-0.741783\pi$
$29$	−1.14049	+	0.828616i	−0.211784	+	0.153870i	0.476836	+	0.878992i	$0.341783\pi$
$30$	1.01149	+	1.95250i	0.184673	+	0.356476i
$31$	−7.02973	−	5.10740i	−1.26258	−	0.917315i	−0.263695	−	0.964606i	$-0.584941\pi$
$31$	−7.02973	−	5.10740i	−1.26258	−	0.917315i	−0.998881	+	0.0472906i	$0.984941\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.13968	+	2.94502i	−0.372471	+	0.512662i
$34$	−0.971641	+	2.99040i	−0.166635	+	0.512850i
$35$	1.00169	−	1.99915i	0.169317	−	0.337919i
$36$	−0.628209	−	1.93343i	−0.104701	−	0.322238i
$37$	−4.73624	−	1.53890i	−0.778633	−	0.252993i	−0.107376	−	0.994218i	$-0.534245\pi$
$37$	−4.73624	−	1.53890i	−0.778633	−	0.252993i	−0.671256	+	0.741225i	$0.734245\pi$
$38$	1.76830	+	0.574557i	0.286857	+	0.0932055i
$39$	−2.01541	−	6.20280i	−0.322724	−	0.993244i
$40$	1.98546	−	1.02857i	0.313929	−	0.162631i
$41$	−2.79307	+	8.59617i	−0.436204	+	1.34250i	0.455645	+	0.890162i	$0.349409\pi$
$41$	−2.79307	+	8.59617i	−0.436204	+	1.34250i	−0.891848	+	0.452335i	$0.850591\pi$
$42$	0.578028	−	0.795587i	0.0891916	−	0.122762i
$43$		−	4.81491i		−	0.734267i	−0.930168	−	0.367133i	$-0.880339\pi$
$43$		−	4.81491i		−	0.734267i	0.930168	−	0.367133i	$-0.119661\pi$
$44$	2.99474	+	2.17580i	0.451473	+	0.328015i
$45$	3.19258	−	3.23595i	0.475922	−	0.482386i
$46$	3.39710	−	2.46814i	0.500875	−	0.363907i
$47$	−3.21041	−	4.41875i	−0.468286	−	0.644540i	0.507915	−	0.861407i	$-0.330416\pi$
$47$	−3.21041	−	4.41875i	−0.468286	−	0.644540i	−0.976201	+	0.216867i	$0.930416\pi$
$48$	0.935268	−	0.303887i	0.134994	−	0.0438623i
$49$	−1.00000			−0.142857
$50$	4.08436	+	2.88409i	0.577616	+	0.407872i
$51$	−3.09210			−0.432981
$52$	−6.30751	+	2.04944i	−0.874695	+	0.284206i
$53$	−2.27323	−	3.12884i	−0.312253	−	0.429779i	0.623829	−	0.781561i	$-0.285576\pi$
$53$	−2.27323	−	3.12884i	−0.312253	−	0.429779i	−0.936082	+	0.351782i	$0.885576\pi$
$54$	4.00413	−	2.90917i	0.544893	−	0.395888i
$55$	−1.23967	+	8.18389i	−0.167158	+	1.10352i
$56$	−0.809017	−	0.587785i	−0.108109	−	0.0785461i
$57$			1.82844i			0.242183i
$58$	−0.828616	+	1.14049i	−0.108803	+	0.149754i
$59$	2.30888	−	7.10600i	0.300591	−	0.925123i	−0.680695	−	0.732567i	$-0.738322\pi$
$59$	2.30888	−	7.10600i	0.300591	−	0.925123i	0.981286	−	0.192556i	$-0.0616778\pi$
$60$	1.56534	+	1.54437i	0.202085	+	0.199377i
$61$	4.36431	+	13.4320i	0.558793	+	1.71979i	0.685711	+	0.727874i	$0.259491\pi$
$61$	4.36431	+	13.4320i	0.558793	+	1.71979i	−0.126918	+	0.991913i	$0.540509\pi$
$62$	−8.26394	−	2.68512i	−1.04952	−	0.341010i
$63$	−1.93343	−	0.628209i	−0.243589	−	0.0791469i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−10.5568	−	10.4153i	−1.30941	−	1.29186i
$66$	−1.12490	+	3.46208i	−0.138465	+	0.426152i
$67$	0.688568	−	0.947733i	0.0841220	−	0.115784i	−0.764882	−	0.644170i	$-0.777203\pi$
$67$	0.688568	−	0.947733i	0.0841220	−	0.115784i	0.849004	+	0.528386i	$0.177203\pi$
$68$			3.14430i			0.381302i
$69$	3.34071	+	2.42716i	0.402174	+	0.292196i
$70$	0.334894	−	2.21085i	0.0400274	−	0.264247i
$71$	−6.63784	+	4.82267i	−0.787767	+	0.572346i	−0.907300	−	0.420484i	$-0.861860\pi$
$71$	−6.63784	+	4.82267i	−0.787767	+	0.572346i	0.119533	+	0.992830i	$0.461860\pi$
$72$	−1.19492	−	1.64467i	−0.140823	−	0.193826i
$73$	−11.3598	+	3.69101i	−1.32956	+	0.432000i	−0.885767	−	0.464129i	$-0.846367\pi$
$73$	−11.3598	+	3.69101i	−1.32956	+	0.432000i	−0.443793	+	0.896130i	$0.646367\pi$
$74$	−4.97997			−0.578910
$75$	−1.45622	+	4.69641i	−0.168149	+	0.542295i
$76$	1.85931			0.213277
$77$	3.52052	−	1.14389i	0.401201	−	0.130358i
$78$	−3.83354	−	5.27642i	−0.434063	−	0.597437i
$79$	9.20323	−	6.68654i	1.03544	−	0.752294i	0.0660533	−	0.997816i	$-0.478959\pi$
$79$	9.20323	−	6.68654i	1.03544	−	0.752294i	0.969391	+	0.245522i	$0.0789593\pi$
$80$	1.57044	−	1.59177i	0.175580	−	0.177965i
$81$	−0.996359	−	0.723897i	−0.110707	−	0.0804330i
$82$			9.03855i			0.998141i
$83$	−1.60022	+	2.20251i	−0.175646	+	0.241757i	−0.887759	−	0.460309i	$-0.847739\pi$
$83$	−1.60022	+	2.20251i	−0.175646	+	0.241757i	0.712112	+	0.702066i	$0.247739\pi$
$84$	0.303887	−	0.935268i	0.0331568	−	0.102046i
$85$	−6.24287	+	3.23413i	−0.677135	+	0.350790i
$86$	−1.48789	−	4.57925i	−0.160443	−	0.493793i
$87$	−1.31847	−	0.428397i	−0.141355	−	0.0459290i
$88$	3.52052	+	1.14389i	0.375289	+	0.121939i
$89$	−1.91415	−	5.89114i	−0.202899	−	0.624460i	−0.999793	−	0.0203403i	$-0.993525\pi$
$89$	−1.91415	−	5.89114i	−0.202899	−	0.624460i	0.796894	−	0.604119i	$-0.206475\pi$
$90$	2.03637	−	4.06413i	0.214652	−	0.428397i
$91$	−2.04944	+	6.30751i	−0.214839	+	0.661207i
$92$	2.46814	−	3.39710i	0.257321	−	0.354172i
$93$		−	8.54497i		−	0.886072i
$94$	−4.41875	−	3.21041i	−0.455759	−	0.331128i
$95$	1.91242	+	3.69157i	0.196211	+	0.378748i
$96$	0.795587	−	0.578028i	0.0811992	−	0.0589947i
$97$	−1.07383	−	1.47800i	−0.109031	−	0.150068i	0.751015	−	0.660286i	$-0.229565\pi$
$97$	−1.07383	−	1.47800i	−0.109031	−	0.150068i	−0.860045	+	0.510218i	$0.829565\pi$
$98$	−0.951057	+	0.309017i	−0.0960712	+	0.0312154i
$99$	7.52528			0.756319
$100$	4.77569	+	1.48080i	0.477569	+	0.148080i
$101$	10.9783			1.09238			0.546190	−	0.837661i	$-0.316078\pi$
$101$	10.9783			1.09238			0.546190	+	0.837661i	$0.316078\pi$
$102$	−2.94076	+	0.955511i	−0.291179	+	0.0946097i
$103$	6.12937	+	8.43635i	0.603945	+	0.831258i	0.996062	−	0.0886567i	$-0.0282574\pi$
$103$	6.12937	+	8.43635i	0.603945	+	0.831258i	−0.392118	+	0.919915i	$0.628257\pi$
$104$	−5.36549	+	3.89826i	−0.526130	+	0.382256i
$105$	2.16951	−	0.358633i	0.211722	−	0.0349989i
$106$	−3.12884	−	2.27323i	−0.303900	−	0.220796i
$107$		−	7.57062i		−	0.731879i	−0.930639	−	0.365940i	$-0.880748\pi$
$107$		−	7.57062i		−	0.731879i	0.930639	−	0.365940i	$-0.119252\pi$
$108$	2.90917	−	4.00413i	0.279935	−	0.385297i
$109$	2.90864	−	8.95187i	0.278597	−	0.857434i	−0.709648	−	0.704556i	$-0.751146\pi$
$109$	2.90864	−	8.95187i	0.278597	−	0.857434i	0.988245	−	0.152877i	$-0.0488539\pi$
$110$	1.34996	+	8.16642i	0.128714	+	0.778638i
$111$	−1.51335	−	4.65761i	−0.143641	−	0.442081i
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	4.61426	+	1.49926i	0.434073	+	0.141039i	0.517899	−	0.855441i	$-0.326714\pi$
$113$	4.61426	+	1.49926i	0.434073	+	0.141039i	−0.0838264	+	0.996480i	$0.526714\pi$
$114$	0.565019	+	1.73895i	0.0529189	+	0.162868i
$115$	9.28345	+	1.40623i	0.865686	+	0.131132i
$116$	−0.435629	+	1.34073i	−0.0404472	+	0.124484i
$117$	−7.92487	+	10.9077i	−0.732655	+	1.00841i
$118$		−	7.47170i		−	0.687825i
$119$	2.54379	+	1.84817i	0.233189	+	0.169422i
$120$	1.96597	+	0.985063i	0.179467	+	0.0899236i
$121$	−2.18642	+	1.58852i	−0.198765	+	0.144411i
$122$	8.30141	+	11.4259i	0.751575	+	1.03445i
$123$	−8.45347	+	2.74670i	−0.762224	+	0.247661i
$124$	−8.68922			−0.780315
$125$	1.97207	+	11.0050i	0.176387	+	0.984321i
$126$	−2.03293			−0.181107
$127$	−17.2896	+	5.61773i	−1.53420	+	0.498493i	−0.949770	−	0.312949i	$-0.898683\pi$
$127$	−17.2896	+	5.61773i	−1.53420	+	0.498493i	−0.584433	+	0.811442i	$0.698683\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	3.83068	−	2.78315i	0.337272	−	0.245043i
$130$	−13.2586	−	6.64334i	−1.16286	−	0.582659i
$131$	10.9608	+	7.96348i	0.957649	+	0.695772i	0.952603	−	0.304215i	$-0.0983941\pi$
$131$	10.9608	+	7.96348i	0.957649	+	0.695772i	0.00504513	+	0.999987i	$0.498394\pi$
$132$			3.64025i			0.316843i
$133$	1.09287	−	1.50421i	0.0947641	−	0.130432i
$134$	0.362002	−	1.11413i	0.0312722	−	0.0962459i
$135$	10.9423	+	1.65751i	0.941764	+	0.142656i
$136$	0.971641	+	2.99040i	0.0833176	+	0.256425i
$137$	−11.1087	−	3.60944i	−0.949082	−	0.308375i	−0.206740	−	0.978396i	$-0.566285\pi$
$137$	−11.1087	−	3.60944i	−0.949082	−	0.308375i	−0.742343	+	0.670021i	$0.766285\pi$
$138$	3.92724	+	1.27604i	0.334308	+	0.108623i
$139$	4.20932	+	12.9550i	0.357030	+	1.09883i	0.954823	+	0.297175i	$0.0960444\pi$
$139$	4.20932	+	12.9550i	0.357030	+	1.09883i	−0.597793	+	0.801650i	$0.703956\pi$
$140$	−0.364687	−	2.20613i	−0.0308216	−	0.186452i
$141$	1.65979	−	5.10831i	0.139780	−	0.430198i
$142$	−4.82267	+	6.63784i	−0.404710	+	0.557035i
$143$		−	24.5501i		−	2.05298i
$144$	−1.64467	−	1.19492i	−0.137056	−	0.0995770i
$145$	−3.11004	+	0.514108i	−0.258275	+	0.0426944i
$146$	−9.66319	+	7.02072i	−0.799732	+	0.581039i
$147$	−0.578028	−	0.795587i	−0.0476749	−	0.0656189i
$148$	−4.73624	+	1.53890i	−0.389316	+	0.126497i
$149$	−1.69133			−0.138559			−0.0692797	−	0.997597i	$-0.522070\pi$
$149$	−1.69133			−0.138559			−0.0692797	+	0.997597i	$0.522070\pi$
$150$	0.0663283	+	4.91655i	0.00541568	+	0.401434i
$151$	15.9724			1.29982			0.649909	−	0.760012i	$-0.274807\pi$
$151$	15.9724			1.29982			0.649909	+	0.760012i	$0.274807\pi$
$152$	1.76830	−	0.574557i	0.143428	−	0.0466027i
$153$	3.75720	+	5.17134i	0.303751	+	0.418078i
$154$	2.99474	−	2.17580i	0.241323	−	0.175331i
$155$	−8.93746	−	17.2521i	−0.717874	−	1.38572i
$156$	−5.27642	−	3.83354i	−0.422452	−	0.306929i
$157$		−	19.4023i		−	1.54848i	−0.632895	−	0.774238i	$-0.718134\pi$
$157$		−	19.4023i		−	1.54848i	0.632895	−	0.774238i	$-0.281866\pi$
$158$	6.68654	−	9.20323i	0.531952	−	0.732170i
$159$	1.17527	−	3.61711i	0.0932050	−	0.286855i
$160$	1.00169	−	1.99915i	0.0791907	−	0.158047i
$161$	−1.29758	−	3.99353i	−0.102263	−	0.314734i
$162$	−1.17129	−	0.380575i	−0.0920252	−	0.0299008i
$163$	20.7747	+	6.75012i	1.62720	+	0.528710i	0.973626	−	0.228151i	$-0.0732679\pi$
$163$	20.7747	+	6.75012i	1.62720	+	0.528710i	0.653576	+	0.756861i	$0.273268\pi$
$164$	2.79307	+	8.59617i	0.218102	+	0.671248i
$165$	−7.22756	+	3.74424i	−0.562665	+	0.291489i
$166$	−0.841283	+	2.58920i	−0.0652962	+	0.200961i
$167$	8.23728	−	11.3376i	0.637420	−	0.877333i	−0.361055	−	0.932545i	$-0.617583\pi$
$167$	8.23728	−	11.3376i	0.637420	−	0.877333i	0.998475	+	0.0552113i	$0.0175832\pi$
$168$		−	0.983399i		−	0.0758709i
$169$	25.0673	+	18.2125i	1.92826	+	1.40096i
$170$	−4.93793	+	5.00499i	−0.378722	+	0.383865i
$171$	3.05795	−	2.22173i	0.233847	−	0.169900i
$172$	−2.83013	−	3.89534i	−0.215796	−	0.297017i
$173$	−3.71859	+	1.20824i	−0.282719	+	0.0918611i	−0.446944	−	0.894562i	$-0.647488\pi$
$173$	−3.71859	+	1.20824i	−0.282719	+	0.0918611i	0.164225	+	0.986423i	$0.447488\pi$
$174$	−1.38632			−0.105097
$175$	4.00507	−	2.99323i	0.302755	−	0.226267i
$176$	3.70170			0.279026
$177$	6.98804	−	2.27055i	0.525253	−	0.170665i
$178$	−3.64092	−	5.01130i	−0.272899	−	0.375613i
$179$	13.2833	−	9.65090i	0.992842	−	0.721342i	0.0323007	−	0.999478i	$-0.489717\pi$
$179$	13.2833	−	9.65090i	0.992842	−	0.721342i	0.960542	+	0.278136i	$0.0897166\pi$
$180$	0.680814	−	4.49449i	0.0507449	−	0.334999i
$181$	5.58264	+	4.05602i	0.414954	+	0.301482i	0.775604	−	0.631219i	$-0.217445\pi$
$181$	5.58264	+	4.05602i	0.414954	+	0.301482i	−0.360650	+	0.932701i	$0.617445\pi$
$182$			6.63211i			0.491605i
$183$	−8.16360	+	11.2362i	−0.603471	+	0.830606i
$184$	1.29758	−	3.99353i	0.0956586	−	0.294407i
$185$	−7.92696	−	7.82074i	−0.582802	−	0.574992i
$186$	−2.64054	−	8.12675i	−0.193614	−	0.595882i
$187$	−11.0696	−	3.59672i	−0.809487	−	0.263018i
$188$	−5.19455	−	1.68781i	−0.378851	−	0.123096i
$189$	−1.52944	−	4.70714i	−0.111250	−	0.342394i
$190$	2.95958	+	2.91992i	0.214711	+	0.211834i
$191$	1.21534	−	3.74043i	0.0879388	−	0.270648i	−0.897410	−	0.441197i	$-0.854554\pi$
$191$	1.21534	−	3.74043i	0.0879388	−	0.270648i	0.985349	+	0.170549i	$0.0545541\pi$
$192$	0.578028	−	0.795587i	0.0417155	−	0.0574165i
$193$			15.8141i			1.13832i	0.822226	+	0.569161i	$0.192732\pi$
$193$			15.8141i			1.13832i	−0.822226	+	0.569161i	$0.807268\pi$
$194$	−1.47800	−	1.07383i	−0.106114	−	0.0770963i
$195$	2.18418	−	14.4192i	0.156412	−	1.03258i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	14.1910	+	19.5322i	1.01107	+	1.39161i	0.918282	+	0.395926i	$0.129576\pi$
$197$	14.1910	+	19.5322i	1.01107	+	1.39161i	0.0927834	+	0.995686i	$0.470424\pi$
$198$	7.15696	−	2.32544i	0.508623	−	0.165262i
$199$	−14.7972			−1.04895			−0.524473	−	0.851427i	$-0.675737\pi$
$199$	−14.7972			−1.04895			−0.524473	+	0.851427i	$0.675737\pi$
$200$	4.99955	−	0.0674480i	0.353521	−	0.00476929i
$201$	1.15201			0.0812569
$202$	10.4410	−	3.39248i	0.734624	−	0.238694i
$203$	0.828616	+	1.14049i	0.0581575	+	0.0800469i
$204$	−2.50156	+	1.81749i	−0.175144	+	0.127250i
$205$	−14.1945	+	14.3873i	−0.991386	+	1.00485i
$206$	8.43635	+	6.12937i	0.587788	+	0.427053i
$207$		−	8.53635i		−	0.593318i
$208$	−3.89826	+	5.36549i	−0.270296	+	0.372030i
$209$	−2.12684	+	6.54573i	−0.147116	+	0.452778i
$210$	1.95250	−	1.01149i	0.134735	−	0.0697997i
$211$	8.22779	+	25.3225i	0.566425	+	1.74328i	0.663681	+	0.748016i	$0.268993\pi$
$211$	8.22779	+	25.3225i	0.566425	+	1.74328i	−0.0972562	+	0.995259i	$0.531007\pi$
$212$	−3.67817	−	1.19511i	−0.252618	−	0.0820805i
$213$	−7.67371	−	2.49334i	−0.525794	−	0.170841i
$214$	−2.33945	−	7.20008i	−0.159921	−	0.492188i
$215$	4.82306	−	9.62574i	0.328930	−	0.656470i
$216$	1.52944	−	4.70714i	0.104065	−	0.320280i
$217$	−5.10740	+	7.02973i	−0.346713	+	0.477209i
$218$		−	9.41255i		−	0.637499i
$219$	−9.50278	−	6.90417i	−0.642138	−	0.466541i
$220$	3.80745	+	7.34957i	0.256698	+	0.495508i
$221$	16.8707	−	12.2573i	1.13485	−	0.824514i
$222$	−2.87856	−	3.96200i	−0.193196	−	0.265912i
$223$	3.47755	−	1.12992i	0.232874	−	0.0756653i	−0.190255	−	0.981735i	$-0.560932\pi$
$223$	3.47755	−	1.12992i	0.232874	−	0.0756653i	0.423129	+	0.906069i	$0.360932\pi$
$224$	−1.00000			−0.0668153
$225$	9.62389	−	3.27116i	0.641592	−	0.218078i
$226$	4.85172			0.322732
$227$	12.7005	−	4.12665i	0.842963	−	0.273895i	0.144467	−	0.989510i	$-0.453853\pi$
$227$	12.7005	−	4.12665i	0.842963	−	0.273895i	0.698496	+	0.715614i	$0.253853\pi$
$228$	1.07473	+	1.47924i	0.0711757	+	0.0979650i
$229$	−1.20294	+	0.873987i	−0.0794925	+	0.0577547i	−0.626822	−	0.779163i	$-0.715645\pi$
$229$	−1.20294	+	0.873987i	−0.0794925	+	0.0577547i	0.547329	+	0.836917i	$0.315645\pi$
$230$	9.26364	−	1.53134i	0.610826	−	0.100973i
$231$	2.94502	+	2.13968i	0.193768	+	0.140781i
$232$			1.40973i			0.0925530i
$233$	0.672315	−	0.925362i	0.0440448	−	0.0606225i	−0.786427	−	0.617684i	$-0.788071\pi$
$233$	0.672315	−	0.925362i	0.0440448	−	0.0606225i	0.830471	+	0.557061i	$0.188071\pi$
$234$	−4.16635	+	12.8227i	−0.272363	+	0.838247i
$235$	−1.99187	−	12.0496i	−0.129935	−	0.786029i
$236$	−2.30888	−	7.10600i	−0.150295	−	0.462561i
$237$	10.6394	+	3.45696i	0.691106	+	0.224554i
$238$	2.99040	+	0.971641i	0.193839	+	0.0629822i
$239$	1.46632	+	4.51286i	0.0948482	+	0.291913i	0.987214	−	0.159400i	$-0.0509559\pi$
$239$	1.46632	+	4.51286i	0.0948482	+	0.291913i	−0.892366	+	0.451313i	$0.850956\pi$
$240$	2.17415	+	0.329334i	0.140340	+	0.0212584i
$241$	−1.50592	+	4.63475i	−0.0970050	+	0.298551i	−0.987771	−	0.155911i	$-0.950169\pi$
$241$	−1.50592	+	4.63475i	−0.0970050	+	0.298551i	0.890766	+	0.454462i	$0.150169\pi$
$242$	−1.58852	+	2.18642i	−0.102114	+	0.140548i
$243$		−	16.0592i		−	1.03020i
$244$	11.4259	+	8.30141i	0.731469	+	0.531444i
$245$	−1.99915	−	1.00169i	−0.127721	−	0.0639958i
$246$	−7.19095	+	5.22453i	−0.458478	+	0.333104i
$247$	−7.24805	−	9.97609i	−0.461183	−	0.634764i
$248$	−8.26394	+	2.68512i	−0.524761	+	0.170505i
$249$	−2.67725			−0.169664
$250$	5.27629	+	9.85702i	0.333702	+	0.623412i
$251$	−8.45824			−0.533880			−0.266940	−	0.963713i	$-0.586012\pi$
$251$	−8.45824			−0.533880			−0.266940	+	0.963713i	$0.586012\pi$
$252$	−1.93343	+	0.628209i	−0.121794	+	0.0395734i
$253$	9.13630	+	12.5750i	0.574394	+	0.790586i
$254$	−14.7074	+	10.6856i	−0.922824	+	0.670471i
$255$	−6.18158	−	3.09733i	−0.387106	−	0.193962i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			12.0286i			0.750326i	0.926959	+	0.375163i	$0.122413\pi$
$257$			12.0286i			0.750326i	−0.926959	+	0.375163i	$0.877587\pi$
$258$	2.78315	−	3.83068i	0.173271	−	0.238488i
$259$	−1.53890	+	4.73624i	−0.0956224	+	0.294295i
$260$	−14.6626	−	2.22105i	−0.909335	−	0.137744i
$261$	0.885602	+	2.72560i	0.0548174	+	0.168711i
$262$	12.8852	+	4.18665i	0.796049	+	0.258652i
$263$	9.79077	+	3.18122i	0.603725	+	0.196162i	0.594901	−	0.803799i	$-0.297191\pi$
$263$	9.79077	+	3.18122i	0.603725	+	0.196162i	0.00882394	+	0.999961i	$0.497191\pi$
$264$	1.12490	+	3.46208i	0.0692327	+	0.213076i
$265$	−1.41041	−	8.53211i	−0.0866408	−	0.524123i
$266$	0.574557	−	1.76830i	0.0352284	−	0.108422i
$267$	3.58048	−	4.92811i	0.219122	−	0.301596i
$268$		−	1.17146i		−	0.0715584i
$269$	11.3325	+	8.23353i	0.690954	+	0.502007i	0.876973	−	0.480539i	$-0.159559\pi$
$269$	11.3325	+	8.23353i	0.690954	+	0.502007i	−0.186020	+	0.982546i	$0.559559\pi$
$270$	10.9190	−	1.80497i	0.664507	−	0.109847i
$271$	7.49155	−	5.44293i	0.455080	−	0.330635i	−0.336518	−	0.941677i	$-0.609249\pi$
$271$	7.49155	−	5.44293i	0.455080	−	0.330635i	0.791598	+	0.611042i	$0.209249\pi$
$272$	1.84817	+	2.54379i	0.112062	+	0.154240i
$273$	−6.20280	+	2.01541i	−0.375411	+	0.121978i
$274$	−11.6804			−0.705639
$275$	−10.6760	+	15.1191i	−0.643789	+	0.911714i
$276$	4.12934			0.248557
$277$	−27.2795	+	8.86366i	−1.63907	+	0.532565i	−0.976330	−	0.216286i	$-0.930606\pi$
$277$	−27.2795	+	8.86366i	−1.63907	+	0.532565i	−0.662738	+	0.748852i	$0.730606\pi$
$278$	8.00660	+	11.0201i	0.480204	+	0.660944i
$279$	−14.2909	+	10.3830i	−0.855575	+	0.621612i
$280$	−1.02857	−	1.98546i	−0.0614687	−	0.118654i
$281$	−23.7553	−	17.2592i	−1.41712	−	1.02960i	−0.992238	−	0.124352i	$-0.960315\pi$
$281$	−23.7553	−	17.2592i	−1.41712	−	1.02960i	−0.424884	−	0.905248i	$-0.639685\pi$
$282$		−	5.37120i		−	0.319850i
$283$	−9.37467	+	12.9031i	−0.557266	+	0.767011i	−0.990976	−	0.134042i	$-0.957204\pi$
$283$	−9.37467	+	12.9031i	−0.557266	+	0.767011i	0.433710	+	0.901053i	$0.357204\pi$
$284$	−2.53543	+	7.80325i	−0.150450	+	0.463038i
$285$	−1.83153	+	3.65533i	−0.108491	+	0.216523i
$286$	−7.58639	−	23.3485i	−0.448593	−	1.38063i
$287$	8.59617	+	2.79307i	0.507416	+	0.164869i
$288$	−1.93343	−	0.628209i	−0.113928	−	0.0370176i
$289$	2.19816	+	6.76524i	0.129303	+	0.397955i
$290$	−2.79895	+	1.45000i	−0.164360	+	0.0851469i
$291$	0.555172	−	1.70864i	0.0325448	−	0.100163i
$292$	−7.02072	+	9.66319i	−0.410857	+	0.565496i
$293$		−	32.7191i		−	1.91147i	−0.294233	−	0.955734i	$-0.595064\pi$
$293$		−	32.7191i		−	1.91147i	0.294233	−	0.955734i	$-0.404936\pi$
$294$	−0.795587	−	0.578028i	−0.0463996	−	0.0337112i
$295$	11.7338	−	11.8932i	0.683170	−	0.692449i
$296$	−4.02888	+	2.92716i	−0.234174	+	0.170137i
$297$	10.7689	+	14.8221i	0.624873	+	0.860064i
$298$	−1.60855	+	0.522651i	−0.0931810	+	0.0302764i
$299$	−27.8486			−1.61052
$300$	1.58238	+	4.65542i	0.0913587	+	0.268781i
$301$	−4.81491			−0.277527
$302$	15.1907	−	4.93575i	0.874126	−	0.284021i
$303$	6.34575	+	8.73418i	0.364554	+	0.501766i
$304$	1.50421	−	1.09287i	0.0862724	−	0.0626805i
$305$	−4.72977	+	31.2243i	−0.270826	+	1.78790i
$306$	5.17134	+	3.75720i	0.295626	+	0.214785i
$307$		−	9.20156i		−	0.525161i	−0.964910	−	0.262580i	$-0.915427\pi$
$307$		−	9.20156i		−	0.525161i	0.964910	−	0.262580i	$-0.0845735\pi$
$308$	2.17580	−	2.99474i	0.123978	−	0.170641i
$309$	−3.16890	+	9.75289i	−0.180273	+	0.554822i
$310$	−13.8312	−	13.6459i	−0.785561	−	0.775034i
$311$	2.92190	+	8.99267i	0.165686	+	0.509928i	0.999086	−	0.0427417i	$-0.0136092\pi$
$311$	2.92190	+	8.99267i	0.165686	+	0.509928i	−0.833401	+	0.552669i	$0.813609\pi$
$312$	−6.20280	−	2.01541i	−0.351165	−	0.114100i
$313$	−3.35815	−	1.09113i	−0.189814	−	0.0616742i	0.212568	−	0.977146i	$-0.431817\pi$
$313$	−3.35815	−	1.09113i	−0.189814	−	0.0616742i	−0.402381	+	0.915472i	$0.631817\pi$
$314$	−5.99565	−	18.4527i	−0.338354	−	1.04135i
$315$	−3.23595	−	3.19258i	−0.182325	−	0.179882i
$316$	3.51532	−	10.8190i	0.197752	−	0.608619i
$317$	14.9295	−	20.5487i	0.838526	−	1.15413i	−0.147750	−	0.989025i	$-0.547203\pi$
$317$	14.9295	−	20.5487i	0.838526	−	1.15413i	0.986276	−	0.165107i	$-0.0527969\pi$
$318$		−	3.80325i		−	0.213276i
$319$	−4.22176	−	3.06729i	−0.236373	−	0.171735i
$320$	0.334894	−	2.21085i	0.0187211	−	0.123590i
$321$	6.02308	−	4.37603i	0.336176	−	0.244246i
$322$	−2.46814	−	3.39710i	−0.137544	−	0.189313i
$323$	−5.56008	+	1.80658i	−0.309371	+	0.100521i
$324$	−1.23157			−0.0684204
$325$	−10.6717	−	31.3965i	−0.591958	−	1.74156i
$326$	21.8438			1.20982
$327$	8.80326	−	2.86035i	0.486821	−	0.158178i
$328$	5.31273	+	7.31234i	0.293346	+	0.403756i
$329$	−4.41875	+	3.21041i	−0.243613	+	0.176996i
$330$	−5.71678	+	5.79442i	−0.314698	+	0.318973i
$331$	−22.4067	−	16.2794i	−1.23158	−	0.894796i	−0.234574	−	0.972098i	$-0.575370\pi$
$331$	−22.4067	−	16.2794i	−1.23158	−	0.894796i	−0.997008	+	0.0773018i	$0.975370\pi$
$332$			2.72245i			0.149414i
$333$	−5.95069	+	8.19042i	−0.326096	+	0.448832i
$334$	4.33060	−	13.3282i	0.236960	−	0.729287i
$335$	2.32589	−	1.20493i	0.127077	−	0.0658323i
$336$	−0.303887	−	0.935268i	−0.0165784	−	0.0510231i
$337$	20.3987	+	6.62795i	1.11119	+	0.361047i	0.806399	−	0.591372i	$-0.201414\pi$
$337$	20.3987	+	6.62795i	1.11119	+	0.361047i	0.304790	+	0.952419i	$0.401414\pi$
$338$	29.4684	+	9.57487i	1.60287	+	0.520804i
$339$	1.47437	+	4.53766i	0.0800770	+	0.246452i
$340$	−3.14962	+	6.28593i	−0.170812	+	0.340903i
$341$	9.93949	−	30.5906i	0.538254	−	1.65657i
$342$	2.22173	−	3.05795i	0.120137	−	0.165355i
$343$			1.00000i			0.0539949i
$344$	−3.89534	−	2.83013i	−0.210023	−	0.152591i
$345$	4.24731	+	8.19863i	0.228667	+	0.441400i
$346$	−3.16322	+	2.29822i	−0.170056	+	0.123553i
$347$	−0.867175	−	1.19356i	−0.0465524	−	0.0640739i	0.785106	−	0.619361i	$-0.212608\pi$
$347$	−0.867175	−	1.19356i	−0.0465524	−	0.0640739i	−0.831659	+	0.555287i	$0.812608\pi$
$348$	−1.31847	+	0.428397i	−0.0706775	+	0.0229645i
$349$	−23.2874			−1.24654			−0.623272	−	0.782005i	$-0.714197\pi$
$349$	−23.2874			−1.24654			−0.623272	+	0.782005i	$0.714197\pi$
$350$	2.88409	−	4.08436i	0.154161	−	0.218318i
$351$	−32.8248			−1.75206
$352$	3.52052	−	1.14389i	0.187644	−	0.0609694i
$353$	−2.91596	−	4.01347i	−0.155201	−	0.213616i	0.724335	−	0.689448i	$-0.242147\pi$
$353$	−2.91596	−	4.01347i	−0.155201	−	0.213616i	−0.879536	+	0.475832i	$0.842147\pi$
$354$	5.94438	−	4.31885i	0.315940	−	0.229544i
$355$	−18.1009	+	2.99219i	−0.960696	+	0.158809i
$356$	−5.01130	−	3.64092i	−0.265599	−	0.192969i
$357$			3.09210i			0.163651i
$358$	9.65090	−	13.2833i	0.510066	−	0.702046i
$359$	−7.08923	+	21.8184i	−0.374155	+	1.15153i	0.569891	+	0.821720i	$0.306985\pi$
$359$	−7.08923	+	21.8184i	−0.374155	+	1.15153i	−0.944047	+	0.329812i	$0.893015\pi$
$360$	−0.741381	−	4.48490i	−0.0390742	−	0.236375i
$361$	−4.80305	−	14.7823i	−0.252792	−	0.778013i
$362$	6.56278	+	2.13238i	0.344932	+	0.112075i
$363$	−2.52762	−	0.821273i	−0.132665	−	0.0431056i
$364$	2.04944	+	6.30751i	0.107420	+	0.330604i
$365$	−26.4072	−	4.00009i	−1.38221	−	0.209374i
$366$	−4.29186	+	13.2090i	−0.224339	+	0.690445i
$367$	−12.6207	+	17.3709i	−0.658795	+	0.906754i	−0.999441	−	0.0334381i	$-0.989354\pi$
$367$	−12.6207	+	17.3709i	−0.658795	+	0.906754i	0.340646	+	0.940192i	$0.389354\pi$
$368$		−	4.19905i		−	0.218890i
$369$	14.8654	+	10.8004i	0.773864	+	0.562245i
$370$	−9.95573	−	4.98840i	−0.517574	−	0.259335i
$371$	−3.12884	+	2.27323i	−0.162441	+	0.118020i
$372$	−5.02261	−	6.91303i	−0.260410	−	0.358424i
$373$	−26.7013	+	8.67579i	−1.38254	+	0.449215i	−0.903504	−	0.428579i	$-0.859014\pi$
$373$	−26.7013	+	8.67579i	−1.38254	+	0.449215i	−0.479038	+	0.877794i	$0.659014\pi$
$374$	−11.6392			−0.601851
$375$	−7.61556	+	7.93017i	−0.393266	+	0.409512i
$376$	−5.46187			−0.281675
$377$	8.89187	−	2.88914i	0.457954	−	0.148798i
$378$	−2.90917	−	4.00413i	−0.149632	−	0.205950i
$379$	13.6734	−	9.93429i	0.702354	−	0.510290i	−0.178344	−	0.983968i	$-0.557074\pi$
$379$	13.6734	−	9.93429i	0.702354	−	0.510290i	0.880698	+	0.473678i	$0.157074\pi$
$380$	3.71704	+	1.86245i	0.190680	+	0.0955418i
$381$	−14.4632	−	10.5082i	−0.740974	−	0.538349i
$382$		−	3.93292i		−	0.201226i
$383$	−4.48077	+	6.16724i	−0.228956	+	0.315131i	−0.908003	−	0.418964i	$-0.862393\pi$
$383$	−4.48077	+	6.16724i	−0.228956	+	0.315131i	0.679047	+	0.734095i	$0.262393\pi$
$384$	0.303887	−	0.935268i	0.0155077	−	0.0477277i
$385$	8.18389	+	1.23967i	0.417089	+	0.0631797i
$386$	4.88682	+	15.0401i	0.248733	+	0.765521i
$387$	−9.30928	−	3.02477i	−0.473217	−	0.153758i
$388$	−1.73749	−	0.564544i	−0.0882076	−	0.0286604i
$389$	−10.4414	−	32.1353i	−0.529400	−	1.62933i	−0.755447	−	0.655210i	$-0.772580\pi$
$389$	−10.4414	−	32.1353i	−0.529400	−	1.62933i	0.226046	−	0.974117i	$-0.427420\pi$
$390$	−2.37849	−	14.3884i	−0.120440	−	0.728585i
$391$	−4.07997	+	12.5569i	−0.206333	+	0.635027i
$392$	−0.587785	+	0.809017i	−0.0296876	+	0.0408615i
$393$			13.3234i			0.672075i
$394$	19.5322	+	14.1910i	0.984019	+	0.714931i
$395$	25.0965	−	4.14861i	1.26274	−	0.208739i
$396$	6.08808	−	4.42325i	0.305937	−	0.222276i
$397$	−7.64669	−	10.5248i	−0.383776	−	0.528223i	0.572804	−	0.819692i	$-0.305856\pi$
$397$	−7.64669	−	10.5248i	−0.383776	−	0.528223i	−0.956580	+	0.291470i	$0.905856\pi$
$398$	−14.0730	+	4.57258i	−0.705414	+	0.229203i
$399$	1.82844			0.0915365
$400$	4.73401	−	1.60909i	0.236700	−	0.0804546i
$401$	−14.0173			−0.699992			−0.349996	−	0.936751i	$-0.613817\pi$
$401$	−14.0173			−0.699992			−0.349996	+	0.936751i	$0.613817\pi$
$402$	1.09563	−	0.355992i	0.0546451	−	0.0177553i
$403$	33.8728	+	46.6220i	1.68733	+	2.32240i
$404$	8.88162	−	6.45288i	0.441877	−	0.321043i
$405$	−1.26675	−	2.44523i	−0.0629454	−	0.121504i
$406$	1.14049	+	0.828616i	0.0566017	+	0.0411235i
$407$		−	18.4344i		−	0.913757i
$408$	−1.81749	+	2.50156i	−0.0899792	+	0.123846i
$409$	−0.307724	+	0.947078i	−0.0152160	+	0.0468300i	−0.958376	−	0.285508i	$-0.907838\pi$
$409$	−0.307724	+	0.947078i	−0.0152160	+	0.0468300i	0.943160	+	0.332338i	$0.107838\pi$
$410$	−9.05385	+	18.0694i	−0.447138	+	0.892386i
$411$	−3.54952	−	10.9243i	−0.175085	−	0.538856i
$412$	9.91752	+	3.22240i	0.488601	+	0.158756i
$413$	−7.10600	−	2.30888i	−0.349664	−	0.113613i
$414$	−2.63788	−	8.11855i	−0.129645	−	0.399005i
$415$	−5.40531	+	2.80023i	−0.265336	+	0.137458i
$416$	−2.04944	+	6.30751i	−0.100482	+	0.309251i
$417$	−7.87369	+	10.8372i	−0.385576	+	0.530700i
$418$			6.88259i			0.336638i
$419$	5.84182	+	4.24433i	0.285392	+	0.207349i	0.721266	−	0.692659i	$-0.243561\pi$
$419$	5.84182	+	4.24433i	0.285392	+	0.207349i	−0.435874	+	0.900008i	$0.643561\pi$
$420$	1.54437	−	1.56534i	0.0753574	−	0.0763809i
$421$	19.1841	−	13.9381i	0.934976	−	0.679300i	−0.0122299	−	0.999925i	$-0.503893\pi$
$421$	19.1841	−	13.9381i	0.934976	−	0.679300i	0.947206	+	0.320625i	$0.103893\pi$
$422$	15.6502	+	21.5406i	0.761839	+	1.04858i
$423$	−10.5601	+	3.43120i	−0.513451	+	0.166830i
$424$	−3.86746			−0.187820
$425$	−15.7201	+	0.212077i	−0.762535	+	0.0102872i
$426$	−8.06861			−0.390926
$427$	13.4320	−	4.36431i	0.650019	−	0.211204i
$428$	−4.44990	−	6.12476i	−0.215094	−	0.296051i
$429$	19.5317	−	14.1906i	0.943000	−	0.685129i
$430$	1.61248	−	10.6450i	0.0777608	−	0.513349i
$431$	24.6853	+	17.9349i	1.18905	+	0.863894i	0.993163	−	0.116733i	$-0.0372423\pi$
$431$	24.6853	+	17.9349i	1.18905	+	0.863894i	0.195884	+	0.980627i	$0.437242\pi$
$432$		−	4.94938i		−	0.238127i
$433$	−6.05268	+	8.33079i	−0.290873	+	0.400352i	−0.929297	−	0.369332i	$-0.879586\pi$
$433$	−6.05268	+	8.33079i	−0.290873	+	0.400352i	0.638424	+	0.769685i	$0.279586\pi$
$434$	−2.68512	+	8.26394i	−0.128890	+	0.396682i
$435$	−2.20670	−	2.17713i	−0.105803	−	0.104386i
$436$	−2.90864	−	8.95187i	−0.139299	−	0.428717i
$437$	7.42520	+	2.41259i	0.355195	+	0.115410i
$438$	−11.1712	−	3.62974i	−0.533780	−	0.173436i
$439$	−9.31743	−	28.6761i	−0.444697	−	1.36864i	−0.882816	−	0.469719i	$-0.844355\pi$
$439$	−9.31743	−	28.6761i	−0.444697	−	1.36864i	0.438119	−	0.898917i	$-0.355645\pi$
$440$	5.89224	+	5.81329i	0.280902	+	0.277138i
$441$	−0.628209	+	1.93343i	−0.0299147	+	0.0920680i
$442$	12.2573	−	16.8707i	0.583020	−	0.802458i
$443$			28.2679i			1.34305i	0.740983	+	0.671524i	$0.234360\pi$
$443$			28.2679i			1.34305i	−0.740983	+	0.671524i	$0.765640\pi$
$444$	−3.96200	−	2.87856i	−0.188028	−	0.136611i
$445$	2.07444	−	13.6947i	0.0983377	−	0.649190i
$446$	2.95818	−	2.14924i	0.140074	−	0.101770i
$447$	−0.977637	−	1.34560i	−0.0462407	−	0.0636448i
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−24.8102			−1.17086			−0.585432	−	0.810721i	$-0.699075\pi$
$449$	−24.8102			−1.17086			−0.585432	+	0.810721i	$0.699075\pi$
$450$	8.14202	−	6.08501i	0.383818	−	0.286850i
$451$	−33.4580			−1.57547
$452$	4.61426	−	1.49926i	0.217037	−	0.0705194i
$453$	9.23250	+	12.7075i	0.433781	+	0.597048i
$454$	10.8037	−	7.84935i	0.507043	−	0.368388i
$455$	−10.4153	+	10.5568i	−0.488278	+	0.494910i
$456$	1.47924	+	1.07473i	0.0692717	+	0.0503288i
$457$			20.0351i			0.937202i	0.883410	+	0.468601i	$0.155242\pi$
$457$			20.0351i			0.937202i	−0.883410	+	0.468601i	$0.844758\pi$
$458$	−0.873987	+	1.20294i	−0.0408387	+	0.0562097i
$459$	−4.80902	+	14.8006i	−0.224466	+	0.690835i
$460$	8.33704	−	4.31901i	0.388716	−	0.201375i
$461$	1.69493	+	5.21646i	0.0789408	+	0.242955i	0.982737	−	0.185008i	$-0.0592312\pi$
$461$	1.69493	+	5.21646i	0.0789408	+	0.242955i	−0.903796	+	0.427963i	$0.859231\pi$
$462$	3.46208	+	1.12490i	0.161070	+	0.0523350i
$463$	−0.963999	−	0.313222i	−0.0448008	−	0.0145567i	0.286531	−	0.958071i	$-0.407498\pi$
$463$	−0.963999	−	0.313222i	−0.0448008	−	0.0145567i	−0.331332	+	0.943514i	$0.607498\pi$
$464$	0.435629	+	1.34073i	0.0202236	+	0.0622418i
$465$	8.55943	−	17.0827i	0.396934	−	0.792192i
$466$	0.353457	−	1.08783i	0.0163736	−	0.0503927i
$467$	3.74494	−	5.15447i	0.173295	−	0.238521i	−0.713531	−	0.700624i	$-0.752905\pi$
$467$	3.74494	−	5.15447i	0.173295	−	0.238521i	0.886826	+	0.462103i	$0.152905\pi$
$468$			13.4826i			0.623233i
$469$	−0.947733	−	0.688568i	−0.0437622	−	0.0317951i
$470$	−5.61791	−	10.8443i	−0.259135	−	0.500211i
$471$	15.4362	−	11.2151i	0.711264	−	0.516764i
$472$	−4.39175	−	6.04473i	−0.202147	−	0.278231i
$473$	16.9510	−	5.50771i	0.779408	−	0.253245i
$474$	11.1870			0.513835
$475$	0.125406	+	9.29568i	0.00575404	+	0.426515i
$476$	3.14430			0.144119
$477$	−7.47745	+	2.42957i	−0.342369	+	0.111242i
$478$	2.78910	+	3.83887i	0.127571	+	0.175586i
$479$	−0.136486	+	0.0991627i	−0.00623619	+	0.00453086i	−0.590899	−	0.806746i	$-0.701227\pi$
$479$	−0.136486	+	0.0991627i	−0.00623619	+	0.00453086i	0.584663	+	0.811276i	$0.301227\pi$
$480$	2.16951	−	0.358633i	0.0990239	−	0.0163693i
$481$	26.7200	+	19.4132i	1.21833	+	0.885167i
$482$			4.87327i			0.221971i
$483$	2.42716	−	3.34071i	0.110440	−	0.152007i
$484$	−0.835137	+	2.57029i	−0.0379608	+	0.116831i
$485$	−0.666247	−	4.03038i	−0.0302527	−	0.183010i
$486$	−4.96258	−	15.2733i	−0.225107	−	0.692809i
$487$	12.4992	+	4.06125i	0.566395	+	0.184033i	0.578197	−	0.815897i	$-0.303757\pi$
$487$	12.4992	+	4.06125i	0.566395	+	0.184033i	−0.0118017	+	0.999930i	$0.503757\pi$
$488$	13.4320	+	4.36431i	0.608037	+	0.197563i
$489$	6.63806	+	20.4298i	0.300183	+	0.923870i
$490$	−2.21085	−	0.334894i	−0.0998759	−	0.0151290i
$491$	5.44539	−	16.7592i	0.245747	−	0.756332i	−0.749766	−	0.661703i	$-0.769834\pi$
$491$	5.44539	−	16.7592i	0.245747	−	0.756332i	0.995513	−	0.0946281i	$-0.0301662\pi$
$492$	−5.22453	+	7.19095i	−0.235540	+	0.324193i
$493$		−	4.43260i		−	0.199634i
$494$	−9.97609	−	7.24805i	−0.448846	−	0.326105i
$495$	15.0442	+	7.53801i	0.676186	+	0.338808i
$496$	−7.02973	+	5.10740i	−0.315644	+	0.229329i
$497$	4.82267	+	6.63784i	0.216326	+	0.297748i
$498$	−2.54622	+	0.827317i	−0.114099	+	0.0370730i
$499$	−2.28015			−0.102074			−0.0510368	−	0.998697i	$-0.516253\pi$
$499$	−2.28015			−0.102074			−0.0510368	+	0.998697i	$0.516253\pi$
$500$	8.06404	+	7.74411i	0.360635	+	0.346327i
$501$	13.7815			0.615710
$502$	−8.04427	+	2.61374i	−0.359033	+	0.116657i
$503$	−14.6478	−	20.1610i	−0.653115	−	0.898935i	0.346114	−	0.938192i	$-0.387501\pi$
$503$	−14.6478	−	20.1610i	−0.653115	−	0.898935i	−0.999229	+	0.0392569i	$0.987501\pi$
$504$	−1.64467	+	1.19492i	−0.0732595	+	0.0532261i
$505$	21.9473	+	10.9969i	0.976641	+	0.489354i
$506$	12.5750	+	9.13630i	0.559029	+	0.406158i
$507$			30.4706i			1.35324i
$508$	−10.6856	+	14.7074i	−0.474095	+	0.652535i
$509$	9.09910	−	28.0041i	0.403310	−	1.24126i	−0.518987	−	0.854782i	$-0.673691\pi$
$509$	9.09910	−	28.0041i	0.403310	−	1.24126i	0.922298	−	0.386480i	$-0.126309\pi$
$510$	−6.83616	−	1.03552i	−0.302710	−	0.0458538i
$511$	3.69101	+	11.3598i	0.163281	+	0.502526i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	8.75200	+	2.84370i	0.386410	+	0.125552i
$514$	3.71706	+	11.4399i	0.163952	+	0.504593i
$515$	3.80292	+	23.0053i	0.167577	+	1.01373i
$516$	1.46319	−	4.50323i	0.0644133	−	0.198244i
$517$	11.8840	−	16.3569i	0.522656	−	0.719374i
$518$			4.97997i			0.218808i
$519$	−3.11071	−	2.26006i	−0.136545	−	0.0992058i
$520$	−14.6313	+	2.41864i	−0.641625	+	0.106065i
$521$	−11.7603	+	8.54435i	−0.515228	+	0.374335i	−0.814803	−	0.579738i	$-0.803155\pi$
$521$	−11.7603	+	8.54435i	−0.515228	+	0.374335i	0.299575	+	0.954073i	$0.403155\pi$
$522$	1.68452	+	2.31854i	0.0737292	+	0.101480i
$523$	3.91933	−	1.27347i	0.171380	−	0.0556848i	−0.222070	−	0.975031i	$-0.571281\pi$
$523$	3.91933	−	1.27347i	0.171380	−	0.0556848i	0.393450	+	0.919346i	$0.371281\pi$
$524$	13.5483			0.591859
$525$	4.69641	+	1.45622i	0.204968	+	0.0635544i
$526$	10.2946			0.448867
$527$	25.9843	−	8.44281i	1.13189	−	0.367774i
$528$	2.13968	+	2.94502i	0.0931177	+	0.128166i
$529$	−4.34280	+	3.15523i	−0.188818	+	0.137184i
$530$	−3.97795	−	7.67867i	−0.172791	−	0.333540i
$531$	−12.2885	−	8.92811i	−0.533275	−	0.387447i
$532$		−	1.85931i		−	0.0806111i
$533$	35.2346	−	48.4963i	1.52618	−	2.10061i
$534$	1.88237	−	5.79334i	0.0814582	−	0.250702i
$535$	7.58343	−	15.1348i	0.327860	−	0.654335i
$536$	−0.362002	−	1.11413i	−0.0156361	−	0.0481229i
$537$	15.3563	+	4.98955i	0.662671	+	0.215315i
$538$	13.3221	+	4.32862i	0.574358	+	0.186620i
$539$	−1.14389	−	3.52052i	−0.0492707	−	0.151640i
$540$	9.82678	−	5.09077i	0.422877	−	0.219072i
$541$	10.9698	−	33.7617i	0.471630	−	1.45153i	−0.378819	−	0.925471i	$-0.623670\pi$
$541$	10.9698	−	33.7617i	0.471630	−	1.45153i	0.850449	−	0.526057i	$-0.176330\pi$
$542$	5.44293	−	7.49155i	0.233794	−	0.321790i
$543$			6.78596i			0.291214i
$544$	2.54379	+	1.84817i	0.109064	+	0.0792397i
$545$	14.7818	−	14.9826i	0.633184	−	0.641784i
$546$	−5.27642	+	3.83354i	−0.225810	+	0.164061i
$547$	−8.13690	−	11.1995i	−0.347909	−	0.478855i	0.598822	−	0.800882i	$-0.295636\pi$
$547$	−8.13690	−	11.1995i	−0.347909	−	0.478855i	−0.946731	+	0.322027i	$0.895636\pi$
$548$	−11.1087	+	3.60944i	−0.474541	+	0.154188i
$549$	28.7114			1.22537
$550$	−5.48146	+	17.6782i	−0.233730	+	0.753799i
$551$	−2.62111			−0.111663
$552$	3.92724	−	1.27604i	0.167154	−	0.0543117i
$553$	−6.68654	−	9.20323i	−0.284341	−	0.391361i
$554$	−23.2054	+	16.8597i	−0.985901	+	0.716299i
$555$	1.64008	−	10.8272i	0.0696173	−	0.459589i
$556$	11.0201	+	8.00660i	0.467358	+	0.339556i
$557$		−	4.69405i		−	0.198893i	−0.995043	−	0.0994466i	$-0.968293\pi$
$557$		−	4.69405i		−	0.198893i	0.995043	−	0.0994466i	$-0.0317072\pi$
$558$	−10.3830	+	14.2909i	−0.439546	+	0.604983i
$559$	−9.86785	+	30.3701i	−0.417365	+	1.28452i
$560$	−1.59177	−	1.57044i	−0.0672645	−	0.0663631i
$561$	−3.53701	−	10.8858i	−0.149333	−	0.459599i
$562$	−27.9260	−	9.07372i	−1.17799	−	0.382752i
$563$	41.2665	+	13.4083i	1.73917	+	0.565092i	0.994724	−	0.102587i	$-0.0327119\pi$
$563$	41.2665	+	13.4083i	1.73917	+	0.565092i	0.744450	+	0.667678i	$0.232712\pi$
$564$	−1.65979	−	5.10831i	−0.0698899	−	0.215099i
$565$	7.72281	+	7.61933i	0.324901	+	0.320547i
$566$	−4.92855	+	15.1685i	−0.207163	+	0.637581i
$567$	−0.723897	+	0.996359i	−0.0304008	+	0.0418431i
$568$			8.20482i			0.344267i
$569$	−15.3489	−	11.1517i	−0.643461	−	0.467502i	0.217576	−	0.976043i	$-0.430185\pi$
$569$	−15.3489	−	11.1517i	−0.643461	−	0.467502i	−0.861038	+	0.508541i	$0.830185\pi$
$570$	−0.612333	+	4.04240i	−0.0256478	+	0.169318i
$571$	4.40938	−	3.20361i	0.184527	−	0.134067i	−0.491687	−	0.870772i	$-0.663620\pi$
$571$	4.40938	−	3.20361i	0.184527	−	0.134067i	0.676214	+	0.736705i	$0.263620\pi$
$572$	−14.4302	−	19.8614i	−0.603356	−	0.830448i
$573$	3.67833	−	1.19516i	0.153665	−	0.0499286i
$574$	9.03855			0.377262
$575$	17.1504	+	12.1104i	0.715222	+	0.505040i
$576$	−2.03293			−0.0847053
$577$	25.8650	−	8.40405i	1.07677	−	0.349865i	0.283652	−	0.958927i	$-0.408454\pi$
$577$	25.8650	−	8.40405i	1.07677	−	0.349865i	0.793122	+	0.609062i	$0.208454\pi$
$578$	4.18115	+	5.75485i	0.173913	+	0.239370i
$579$	−12.5815	+	9.14098i	−0.522868	+	0.379886i
$580$	−2.21389	+	2.24396i	−0.0919267	+	0.0931752i
$581$	2.20251	+	1.60022i	0.0913754	+	0.0663881i
$582$		−	1.79658i		−	0.0744704i
$583$	8.41482	−	11.5820i	0.348506	−	0.479678i
$584$	−3.69101	+	11.3598i	−0.152735	+	0.470070i
$585$	−26.7691	+	13.8678i	−1.10677	+	0.573362i
$586$	−10.1107	−	31.1177i	−0.417671	−	1.28546i
$587$	14.7740	+	4.80038i	0.609790	+	0.198133i	0.597602	−	0.801793i	$-0.296120\pi$
$587$	14.7740	+	4.80038i	0.609790	+	0.198133i	0.0121882	+	0.999926i	$0.496120\pi$
$588$	−0.935268	−	0.303887i	−0.0385698	−	0.0125321i
$589$	−4.99245	−	15.3652i	−0.205710	−	0.633112i
$590$	7.48434	−	14.9371i	0.308125	−	0.614949i
$591$	−7.33679	+	22.5803i	−0.301795	+	0.928830i
$592$	−2.92716	+	4.02888i	−0.120305	+	0.165586i
$593$		−	38.4738i		−	1.57993i	−0.613153	−	0.789964i	$-0.710099\pi$
$593$		−	38.4738i		−	1.57993i	0.613153	−	0.789964i	$-0.289901\pi$
$594$	14.8221	+	10.7689i	0.608157	+	0.441852i
$595$	3.23413	+	6.24287i	0.132586	+	0.255933i
$596$	−1.36832	+	0.994141i	−0.0560485	+	0.0407216i
$597$	−8.55318	−	11.7724i	−0.350058	−	0.481814i
$598$	−26.4856	+	8.60568i	−1.08307	+	0.351912i
$599$	−19.4462			−0.794551			−0.397275	−	0.917699i	$-0.630044\pi$
$599$	−19.4462			−0.794551			−0.397275	+	0.917699i	$0.630044\pi$
$600$	2.94354	+	3.93858i	0.120169	+	0.160792i
$601$	25.6569			1.04657			0.523284	−	0.852158i	$-0.324707\pi$
$601$	25.6569			1.04657			0.523284	+	0.852158i	$0.324707\pi$
$602$	−4.57925	+	1.48789i	−0.186636	+	0.0606418i
$603$	−1.39981	−	1.92667i	−0.0570046	−	0.0784601i
$604$	12.9220	−	9.38836i	0.525787	−	0.382007i
$605$	−5.96219	+	0.985587i	−0.242398	+	0.0400698i
$606$	8.73418	+	6.34575i	0.354802	+	0.257779i
$607$		−	41.7573i		−	1.69488i	−0.530893	−	0.847439i	$-0.678143\pi$
$607$		−	41.7573i		−	1.69488i	0.530893	−	0.847439i	$-0.321857\pi$
$608$	1.09287	−	1.50421i	0.0443218	−	0.0610038i
$609$	−0.428397	+	1.31847i	−0.0173595	+	0.0534272i
$610$	5.15054	+	31.1576i	0.208539	+	1.26153i
$611$	11.1938	+	34.4508i	0.452851	+	1.39373i
$612$	6.07927	+	1.97528i	0.245740	+	0.0798458i
$613$	23.8932	+	7.76338i	0.965039	+	0.313560i	0.748812	−	0.662783i	$-0.230625\pi$
$613$	23.8932	+	7.76338i	0.965039	+	0.313560i	0.216227	+	0.976343i	$0.430625\pi$
$614$	−2.84344	−	8.75120i	−0.114752	−	0.353170i
$615$	−19.6511	−	2.97670i	−0.792410	−	0.120032i
$616$	1.14389	−	3.52052i	0.0460885	−	0.141846i
$617$	−13.3065	+	18.3148i	−0.535700	+	0.737328i	−0.987986	−	0.154545i	$-0.950609\pi$
$617$	−13.3065	+	18.3148i	−0.535700	+	0.737328i	0.452286	+	0.891873i	$0.350609\pi$
$618$			10.2548i			0.412508i
$619$	−17.6264	−	12.8063i	−0.708463	−	0.514729i	0.174214	−	0.984708i	$-0.444261\pi$
$619$	−17.6264	−	12.8063i	−0.708463	−	0.514729i	−0.882678	+	0.469979i	$0.844261\pi$
$620$	−17.3711	−	8.70393i	−0.697640	−	0.349558i
$621$	16.8135	−	12.2157i	0.674704	−	0.490201i
$622$	5.55778	+	7.64962i	0.222847	+	0.306722i
$623$	−5.89114	+	1.91415i	−0.236024	+	0.0766887i
$624$	−6.52201			−0.261090
$625$	−7.08120	+	23.9762i	−0.283248	+	0.959047i
$626$	−3.53096			−0.141126
$627$	−6.43706	+	2.09153i	−0.257072	+	0.0835276i
$628$	−11.4044	−	15.6968i	−0.455085	−	0.626371i
$629$	12.6680	−	9.20385i	0.505107	−	0.366981i
$630$	−4.06413	−	2.03637i	−0.161919	−	0.0811308i
$631$	−7.63404	−	5.54646i	−0.303907	−	0.220801i	0.425371	−	0.905019i	$-0.360144\pi$
$631$	−7.63404	−	5.54646i	−0.303907	−	0.220801i	−0.729277	+	0.684218i	$0.760144\pi$
$632$		−	11.3758i		−	0.452506i
$633$	−15.3904	+	21.1830i	−0.611713	+	0.841950i
$634$	7.84892	−	24.1565i	0.311720	−	0.959376i
$635$	−40.1918	−	6.08815i	−1.59496	−	0.241601i
$636$	−1.17527	−	3.61711i	−0.0466025	−	0.143428i
$637$	6.30751	+	2.04944i	0.249913	+	0.0812016i
$638$	−4.96297	−	1.61257i	−0.196486	−	0.0638422i
$639$	5.15434	+	15.8634i	0.203903	+	0.627548i
$640$	−0.364687	−	2.20613i	−0.0144155	−	0.0872049i
$641$	−3.80327	+	11.7053i	−0.150220	+	0.462330i	−0.997645	−	0.0685847i	$-0.978152\pi$
$641$	−3.80327	+	11.7053i	−0.150220	+	0.462330i	0.847425	+	0.530915i	$0.178152\pi$
$642$	4.37603	−	6.02308i	0.172708	−	0.237712i
$643$		−	31.7705i		−	1.25291i	−0.779459	−	0.626453i	$-0.784506\pi$
$643$		−	31.7705i		−	1.25291i	0.779459	−	0.626453i	$-0.215494\pi$
$644$	−3.39710	−	2.46814i	−0.133865	−	0.0972583i
$645$	10.4460	−	1.72678i	0.411310	−	0.0679920i
$646$	−4.72968	+	3.43632i	−0.186087	+	0.135200i
$647$	1.44892	+	1.99427i	0.0569630	+	0.0784028i	0.836548	−	0.547893i	$-0.184570\pi$
$647$	1.44892	+	1.99427i	0.0569630	+	0.0784028i	−0.779585	+	0.626296i	$0.784570\pi$
$648$	−1.17129	+	0.380575i	−0.0460126	+	0.0149504i
$649$	27.6579			1.08567
$650$	−19.8514	−	26.5621i	−0.778636	−	1.04185i
$651$	−8.54497			−0.334904
$652$	20.7747	−	6.75012i	0.813601	−	0.264355i
$653$	−3.29779	−	4.53903i	−0.129053	−	0.177626i	0.739601	−	0.673046i	$-0.235014\pi$
$653$	−3.29779	−	4.53903i	−0.129053	−	0.177626i	−0.868654	+	0.495420i	$0.835014\pi$
$654$	7.48850	−	5.44071i	0.292824	−	0.212749i
$655$	13.9353	+	26.8996i	0.544499	+	1.05105i
$656$	7.31234	+	5.31273i	0.285499	+	0.207427i
$657$			24.2820i			0.947332i
$658$	−3.21041	+	4.41875i	−0.125155	+	0.172261i
$659$	−5.37687	+	16.5483i	−0.209453	+	0.644631i	0.790048	+	0.613045i	$0.210056\pi$
$659$	−5.37687	+	16.5483i	−0.209453	+	0.644631i	−0.999501	+	0.0315856i	$0.989944\pi$
$660$	−3.64641	+	7.27741i	−0.141936	+	0.283273i
$661$	−6.12216	−	18.8421i	−0.238124	−	0.732871i	−0.996692	−	0.0812767i	$-0.974100\pi$
$661$	−6.12216	−	18.8421i	−0.238124	−	0.732871i	0.758567	−	0.651595i	$-0.225900\pi$
$662$	−26.3406	−	8.55858i	−1.02376	−	0.332639i
$663$	19.5035	+	6.33706i	0.757452	+	0.246111i
$664$	0.841283	+	2.58920i	0.0326481	+	0.100481i
$665$	3.69157	−	1.91242i	0.143153	−	0.0741606i
$666$	−3.12846	+	9.62842i	−0.121225	+	0.373094i
$667$	−3.47940	+	4.78898i	−0.134723	+	0.185430i
$668$		−	14.0141i		−	0.542222i
$669$	2.90907	+	2.11356i	0.112471	+	0.0817150i
$670$	1.83971	−	1.86470i	0.0710742	−	0.0720395i
$671$	−42.2953	+	30.7293i	−1.63279	+	1.18629i
$672$	−0.578028	−	0.795587i	−0.0222979	−	0.0306904i
$673$	−23.6906	+	7.69755i	−0.913206	+	0.296719i	−0.727677	−	0.685920i	$-0.759400\pi$
$673$	−23.6906	+	7.69755i	−0.913206	+	0.296719i	−0.185529	+	0.982639i	$0.559400\pi$
$674$	21.4485			0.826165
$675$	20.2150	+	14.2745i	0.778077	+	0.549424i
$676$	30.9849			1.19173
$677$	−23.9413	+	7.77899i	−0.920138	+	0.298971i	−0.730523	−	0.682888i	$-0.760724\pi$
$677$	−23.9413	+	7.77899i	−0.920138	+	0.298971i	−0.189614	+	0.981859i	$0.560724\pi$
$678$	2.80443	+	3.85996i	0.107703	+	0.148241i
$679$	−1.47800	+	1.07383i	−0.0567203	+	0.0412097i
$680$	−1.05301	+	6.95156i	−0.0403809	+	0.266580i
$681$	10.6244	+	7.71905i	0.407126	+	0.295794i
$682$		−	32.1649i		−	1.23166i
$683$	−19.3082	+	26.5755i	−0.738808	+	1.01688i	0.259878	+	0.965641i	$0.416318\pi$
$683$	−19.3082	+	26.5755i	−0.738808	+	1.01688i	−0.998686	+	0.0512411i	$0.983682\pi$
$684$	1.16803	−	3.59483i	0.0446608	−	0.137452i
$685$	−18.5925	−	18.3433i	−0.710382	−	0.700863i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−1.39067	−	0.451854i	−0.0530572	−	0.0172393i
$688$	−4.57925	−	1.48789i	−0.174582	−	0.0567252i
$689$	7.92610	+	24.3940i	0.301960	+	0.929339i
$690$	6.57295	+	6.48487i	0.250228	+	0.246875i
$691$	1.38797	−	4.27174i	0.0528010	−	0.162505i	−0.921179	−	0.389140i	$-0.872772\pi$
$691$	1.38797	−	4.27174i	0.0528010	−	0.162505i	0.973980	+	0.226635i	$0.0727724\pi$
$692$	−2.29822	+	3.16322i	−0.0873651	+	0.120248i
$693$		−	7.52528i		−	0.285862i
$694$	−1.19356	−	0.867175i	−0.0453071	−	0.0329175i
$695$	−4.56180	+	30.1154i	−0.173039	+	1.14234i
$696$	−1.12156	+	0.814860i	−0.0425126	+	0.0308872i
$697$	−16.7048	−	22.9922i	−0.632739	−	0.870891i
$698$	−22.1476	+	7.19619i	−0.838299	+	0.272380i
$699$	1.12482			0.0425447
$700$	1.48080	−	4.77569i	0.0559689	−	0.180504i
$701$	−16.8109			−0.634937			−0.317469	−	0.948269i	$-0.602833\pi$
$701$	−16.8109			−0.634937			−0.317469	+	0.948269i	$0.602833\pi$
$702$	−31.2183	+	10.1434i	−1.17826	+	0.382839i
$703$	−5.44248	−	7.49093i	−0.205267	−	0.282526i
$704$	2.99474	−	2.17580i	0.112868	−	0.0820037i
$705$	8.43514	−	8.54970i	0.317686	−	0.322000i
$706$	−4.01347	−	2.91596i	−0.151049	−	0.109744i
$707$		−	10.9783i		−	0.412881i
$708$	4.31885	−	5.94438i	0.162312	−	0.223404i
$709$	−4.20718	+	12.9484i	−0.158004	+	0.486287i	−0.998453	−	0.0556043i	$-0.982291\pi$
$709$	−4.20718	+	12.9484i	−0.158004	+	0.486287i	0.840449	+	0.541891i	$0.182291\pi$
$710$	−16.2903	+	8.43922i	−0.611365	+	0.316718i
$711$	−7.14639	−	21.9943i	−0.268011	−	0.824852i
$712$	−5.89114	−	1.91415i	−0.220780	−	0.0717357i
$713$	−34.7007	−	11.2749i	−1.29955	−	0.422250i
$714$	0.955511	+	2.94076i	0.0357591	+	0.110055i
$715$	24.5916	−	49.0794i	0.919674	−	1.83546i
$716$	5.07378	−	15.6155i	0.189616	−	0.583578i
$717$	−2.74280	+	3.77514i	−0.102432	+	0.140985i
$718$			22.9412i			0.856159i
$719$	−28.1421	−	20.4464i	−1.04952	−	0.762524i	−0.0774022	−	0.997000i	$-0.524663\pi$
$719$	−28.1421	−	20.4464i	−1.04952	−	0.762524i	−0.972122	+	0.234476i	$0.924663\pi$
$720$	−2.09100	−	4.03629i	−0.0779271	−	0.150424i
$721$	8.43635	−	6.12937i	0.314186	−	0.228270i
$722$	−9.13594	−	12.5745i	−0.340004	−	0.467976i
$723$	−4.55781	+	1.48092i	−0.169507	+	0.0550761i
$724$	6.90052			0.256456
$725$	−6.73242	−	2.08752i	−0.250036	−	0.0775285i
$726$	−2.65769			−0.0986363
$727$	−21.3844	+	6.94822i	−0.793105	+	0.257695i	−0.677426	−	0.735591i	$-0.736904\pi$
$727$	−21.3844	+	6.94822i	−0.793105	+	0.257695i	−0.115679	+	0.993287i	$0.536904\pi$
$728$	3.89826	+	5.36549i	0.144479	+	0.198858i
$729$	9.78745	−	7.11100i	0.362498	−	0.263370i
$730$	−26.3508	+	4.35595i	−0.975287	+	0.161221i
$731$	12.2481	+	8.89878i	0.453013	+	0.329133i
$732$			13.8887i			0.513343i
$733$	13.3003	−	18.3062i	0.491256	−	0.676156i	−0.489363	−	0.872080i	$-0.662771\pi$
$733$	13.3003	−	18.3062i	0.491256	−	0.676156i	0.980619	+	0.195924i	$0.0627707\pi$
$734$	−6.63509	+	20.4207i	−0.244906	+	0.753742i
$735$	−0.358633	−	2.16951i	−0.0132284	−	0.0800234i
$736$	−1.29758	−	3.99353i	−0.0478293	−	0.147204i
$737$	4.12416	+	1.34002i	0.151915	+	0.0493603i
$738$	17.4754	+	5.67810i	0.643278	+	0.209014i
$739$	−13.7863	−	42.4300i	−0.507138	−	1.56081i	−0.797146	−	0.603787i	$-0.793658\pi$
$739$	−13.7863	−	42.4300i	−0.507138	−	1.56081i	0.290007	−	0.957024i	$-0.406342\pi$
$740$	−11.0100	−	1.66776i	−0.404734	−	0.0613081i
$741$	3.74727	−	11.5329i	0.137659	−	0.423672i
$742$	−2.27323	+	3.12884i	−0.0834530	+	0.114863i
$743$			8.17564i			0.299935i	0.988691	+	0.149967i	$0.0479169\pi$
$743$			8.17564i			0.299935i	−0.988691	+	0.149967i	$0.952083\pi$
$744$	−6.91303	−	5.02261i	−0.253444	−	0.184138i
$745$	−3.38123	−	1.69420i	−0.123879	−	0.0620705i
$746$	−22.7135	+	16.5023i	−0.831601	+	0.604193i
$747$	3.25312	+	4.47753i	0.119025	+	0.163824i
$748$	−11.0696	+	3.59672i	−0.404744	+	0.131509i
$749$	−7.57062			−0.276624
$750$	−4.79227	+	9.89537i	−0.174989	+	0.361328i
$751$	30.3011			1.10570			0.552851	−	0.833280i	$-0.313540\pi$
$751$	30.3011			1.10570			0.552851	+	0.833280i	$0.313540\pi$
$752$	−5.19455	+	1.68781i	−0.189426	+	0.0615481i
$753$	−4.88910	−	6.72927i	−0.178169	−	0.245228i
$754$	7.56387	−	5.49548i	0.275460	−	0.200133i
$755$	31.9313	+	15.9995i	1.16210	+	0.582280i
$756$	−4.00413	−	2.90917i	−0.145629	−	0.105805i
$757$			24.6437i			0.895692i	0.894111	+	0.447846i	$0.147809\pi$
$757$			24.6437i			0.895692i	−0.894111	+	0.447846i	$0.852191\pi$
$758$	9.93429	−	13.6734i	0.360830	−	0.496639i
$759$	−4.72350	+	14.5374i	−0.171452	+	0.527675i
$760$	4.11064	+	0.622670i	0.149109	+	0.0225866i
$761$	11.0683	+	34.0647i	0.401226	+	1.23485i	0.924006	+	0.382378i	$0.124895\pi$
$761$	11.0683	+	34.0647i	0.401226	+	1.23485i	−0.522780	+	0.852467i	$0.675105\pi$
$762$	−17.0026	−	5.52447i	−0.615938	−	0.200130i
$763$	−8.95187	−	2.90864i	−0.324079	−	0.105300i
$764$	−1.21534	−	3.74043i	−0.0439694	−	0.135324i
$765$	2.33112	+	14.1019i	0.0842819	+	0.509853i
$766$	−2.35568	+	7.25003i	−0.0851141	+	0.261954i
$767$	−29.1266	+	40.0893i	−1.05170	+	1.44754i
$768$		−	0.983399i		−	0.0354854i
$769$	19.0049	+	13.8078i	0.685333	+	0.497923i	0.875123	−	0.483901i	$-0.160781\pi$
$769$	19.0049	+	13.8078i	0.685333	+	0.497923i	−0.189790	+	0.981825i	$0.560781\pi$
$770$	8.16642	−	1.34996i	0.294297	−	0.0486492i
$771$	−9.56983	+	6.95289i	−0.344649	+	0.250402i
$772$	9.29529	+	12.7939i	0.334545	+	0.460461i
$773$	−4.03710	+	1.31173i	−0.145204	+	0.0471798i	−0.380717	−	0.924691i	$-0.624323\pi$
$773$	−4.03710	+	1.31173i	−0.145204	+	0.0471798i	0.235513	+	0.971871i	$0.424323\pi$
$774$	−9.78836			−0.351835
$775$	−0.586071	−	43.4422i	−0.0210523	−	1.56049i
$776$	−1.82690			−0.0655820
$777$	−4.65761	+	1.51335i	−0.167091	+	0.0542911i
$778$	−19.8607	−	27.3360i	−0.712042	−	0.980041i
$779$	−13.5959	+	9.87798i	−0.487123	+	0.353915i
$780$	−6.70834	−	12.9492i	−0.240197	−	0.463655i
$781$	−24.5713	−	17.8521i	−0.879229	−	0.638797i
$782$			13.2031i			0.472140i
$783$	−4.10113	+	5.64472i	−0.146563	+	0.201726i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	19.4352	−	38.7882i	0.693671	−	1.38441i
$786$	4.11715	+	12.6713i	0.146854	+	0.451969i
$787$	−26.3312	−	8.55552i	−0.938605	−	0.304971i	−0.200528	−	0.979688i	$-0.564266\pi$
$787$	−26.3312	−	8.55552i	−0.938605	−	0.304971i	−0.738077	+	0.674717i	$0.764266\pi$
$788$	22.9615	+	7.46064i	0.817969	+	0.265774i
$789$	3.12840	+	9.62824i	0.111374	+	0.342774i
$790$	22.5862	−	11.7008i	0.803582	−	0.416296i
$791$	1.49926	−	4.61426i	0.0533077	−	0.164064i
$792$	4.42325	−	6.08808i	0.157173	−	0.216330i
$793$		−	93.6667i		−	3.32620i
$794$	−10.5248	−	7.64669i	−0.373510	−	0.271371i
$795$	5.97277	−	6.05390i	0.211832	−	0.214710i
$796$	−11.9712	+	8.69757i	−0.424307	+	0.308277i
$797$	29.1219	+	40.0829i	1.03155	+	1.41981i	0.903776	+	0.428005i	$0.140783\pi$
$797$	29.1219	+	40.0829i	1.03155	+	1.41981i	0.127774	+	0.991803i	$0.459217\pi$
$798$	1.73895	−	0.565019i	0.0615581	−	0.0200015i
$799$	17.1738			0.607564
$800$	4.00507	−	2.99323i	0.141601	−	0.105826i
$801$	−12.5926			−0.444937
$802$	−13.3313	+	4.33159i	−0.470744	+	0.152954i
$803$	−25.9886	−	35.7702i	−0.917117	−	1.26230i
$804$	0.932000	−	0.677137i	0.0328691	−	0.0238808i
$805$	1.40623	−	9.28345i	0.0495632	−	0.327199i
$806$	46.6220	+	33.8728i	1.64219	+	1.19312i
$807$			13.7752i			0.484909i
$808$	6.45288	−	8.88162i	0.227011	−	0.312454i
$809$	4.44701	−	13.6865i	0.156349	−	0.481192i	−0.841946	−	0.539561i	$-0.818590\pi$
$809$	4.44701	−	13.6865i	0.156349	−	0.481192i	0.998295	+	0.0583694i	$0.0185901\pi$
$810$	−1.96037	−	1.93410i	−0.0688803	−	0.0679573i
$811$	−5.40708	−	16.6413i	−0.189868	−	0.584354i	0.810130	−	0.586250i	$-0.199396\pi$
$811$	−5.40708	−	16.6413i	−0.189868	−	0.584354i	−0.999998	+	0.00189612i	$0.999396\pi$
$812$	1.34073	+	0.435629i	0.0470504	+	0.0152876i
$813$	8.66065	+	2.81402i	0.303742	+	0.0986918i
$814$	−5.69653	−	17.5321i	−0.199663	−	0.614500i
$815$	34.7703	+	34.3044i	1.21795	+	1.20163i
$816$	−0.955511	+	2.94076i	−0.0334496	+	0.102947i
$817$	5.26208	−	7.24263i	0.184097	−	0.253388i
$818$			0.995817i			0.0348179i
$819$	10.9077	+	7.92487i	0.381144	+	0.276917i
$820$	−3.02695	+	19.9829i	−0.105706	+	0.697832i
$821$	−1.49364	+	1.08519i	−0.0521284	+	0.0378735i	−0.613544	−	0.789660i	$-0.710257\pi$
$821$	−1.49364	+	1.08519i	−0.0521284	+	0.0378735i	0.561416	+	0.827534i	$0.310257\pi$
$822$	−6.75159	−	9.29277i	−0.235489	−	0.324123i
$823$	39.5938	−	12.8648i	1.38015	−	0.448439i	0.477434	−	0.878668i	$-0.341567\pi$
$823$	39.5938	−	12.8648i	1.38015	−	0.448439i	0.902720	+	0.430229i	$0.141567\pi$
$824$	10.4279			0.363273
$825$	−18.1996	+	0.245527i	−0.633628	+	0.00854816i
$826$	−7.47170			−0.259974
$827$	−14.7730	+	4.80005i	−0.513709	+	0.166914i	−0.554388	−	0.832258i	$-0.687048\pi$
$827$	−14.7730	+	4.80005i	−0.513709	+	0.166914i	0.0406794	+	0.999172i	$0.487048\pi$
$828$	−5.01754	−	6.90605i	−0.174372	−	0.240002i
$829$	−37.8056	+	27.4674i	−1.31304	+	0.953981i	−0.313051	+	0.949736i	$0.601351\pi$
$829$	−37.8056	+	27.4674i	−1.31304	+	0.953981i	−0.999991	+	0.00424479i	$0.998649\pi$
$830$	−4.27544	+	4.33351i	−0.148403	+	0.150418i
$831$	−22.8201	−	16.5798i	−0.791621	−	0.575146i
$832$			6.63211i			0.229927i
$833$	1.84817	−	2.54379i	0.0640354	−	0.0881371i
$834$	−4.13944	+	12.7399i	−0.143337	+	0.441146i
$835$	27.8244	−	14.4145i	0.962904	−	0.498833i
$836$	2.12684	+	6.54573i	0.0735582	+	0.226389i
$837$	−40.9013	−	13.2897i	−1.41376	−	0.459358i
$838$	6.86747	+	2.23138i	0.237233	+	0.0770817i
$839$	−11.4400	−	35.2088i	−0.394954	−	1.21554i	−0.928998	−	0.370086i	$-0.879328\pi$
$839$	−11.4400	−	35.2088i	−0.394954	−	1.21554i	0.534044	−	0.845457i	$-0.320672\pi$
$840$	0.985063	−	1.96597i	0.0339879	−	0.0678322i
$841$	−8.34737	+	25.6906i	−0.287841	+	0.885882i
$842$	13.9381	−	19.1841i	0.480338	−	0.661128i
$843$		−	28.8757i		−	0.994532i
$844$	21.5406	+	15.6502i	0.741459	+	0.538702i
$845$	31.8701	+	61.5193i	1.09637	+	2.11633i
$846$	−8.98299	+	6.52652i	−0.308841	+	0.224386i
$847$	1.58852	+	2.18642i	0.0545823	+	0.0751261i
$848$	−3.67817	+	1.19511i	−0.126309	+	0.0410402i
$849$	−15.6844			−0.538286
$850$	−14.8851	+	5.05946i	−0.510556	+	0.173538i
$851$	−20.9111			−0.716825
$852$	−7.67371	+	2.49334i	−0.262897	+	0.0854204i
$853$	17.4790	+	24.0577i	0.598468	+	0.823720i	0.995567	−	0.0940553i	$-0.0299831\pi$
$853$	17.4790	+	24.0577i	0.598468	+	0.823720i	−0.397099	+	0.917776i	$0.629983\pi$
$854$	11.4259	−	8.30141i	0.390987	−	0.284069i
$855$	8.33879	−	1.37845i	0.285181	−	0.0471421i
$856$	−6.12476	−	4.44990i	−0.209340	−	0.152094i
$857$			37.2615i			1.27283i	0.771348	+	0.636414i	$0.219583\pi$
$857$			37.2615i			1.27283i	−0.771348	+	0.636414i	$0.780417\pi$
$858$	14.1906	−	19.5317i	0.484460	−	0.666802i
$859$	−2.10856	+	6.48949i	−0.0719432	+	0.221418i	−0.980563	−	0.196207i	$-0.937138\pi$
$859$	−2.10856	+	6.48949i	−0.0719432	+	0.221418i	0.908619	+	0.417625i	$0.137138\pi$
$860$	−1.75593	−	10.6223i	−0.0598768	−	0.362218i
$861$	2.74670	+	8.45347i	0.0936072	+	0.288093i
$862$	29.0193	+	9.42893i	0.988401	+	0.321151i
$863$	−30.8928	−	10.0377i	−1.05160	−	0.341687i	−0.268306	−	0.963334i	$-0.586464\pi$
$863$	−30.8928	−	10.0377i	−1.05160	−	0.341687i	−0.783298	+	0.621647i	$0.786464\pi$
$864$	−1.52944	−	4.70714i	−0.0520326	−	0.160140i
$865$	−8.64433	−	1.30942i	−0.293916	−	0.0445216i
$866$	−3.18208	+	9.79343i	−0.108131	+	0.332794i
$867$	−4.11174	+	5.65932i	−0.139642	+	0.192201i
$868$			8.68922i			0.294931i
$869$	34.0676	+	24.7515i	1.15566	+	0.839638i
$870$	−2.77147	−	1.38867i	−0.0939617	−	0.0470803i
$871$	−6.28547	+	4.56666i	−0.212975	+	0.154735i
$872$	−5.53256	−	7.61492i	−0.187356	−	0.257874i
$873$	−3.53219	+	1.14768i	−0.119546	+	0.0388430i
$874$	7.80731			0.264086
$875$	11.0050	−	1.97207i	0.372038	−	0.0666680i
$876$	−11.7461			−0.396863
$877$	−39.5213	+	12.8413i	−1.33454	+	0.433619i	−0.887464	−	0.460877i	$-0.847535\pi$
$877$	−39.5213	+	12.8413i	−1.33454	+	0.433619i	−0.447077	+	0.894495i	$0.647535\pi$
$878$	−17.7228	−	24.3934i	−0.598116	−	0.823236i
$879$	26.0308	−	18.9125i	0.877999	−	0.637903i
$880$	7.40026	+	3.70796i	0.249463	+	0.124995i
$881$	−9.87040	−	7.17127i	−0.332542	−	0.241606i	0.408966	−	0.912550i	$-0.365889\pi$
$881$	−9.87040	−	7.17127i	−0.332542	−	0.241606i	−0.741509	+	0.670943i	$0.765889\pi$
$882$			2.03293i			0.0684522i
$883$	−11.1473	+	15.3429i	−0.375136	+	0.516330i	−0.954288	−	0.298890i	$-0.903384\pi$
$883$	−11.1473	+	15.3429i	−0.375136	+	0.516330i	0.579152	+	0.815220i	$0.303384\pi$
$884$	6.44404	−	19.8327i	0.216736	−	0.667046i
$885$	16.2446	+	2.46068i	0.546055	+	0.0827150i
$886$	8.73526	+	26.8844i	0.293467	+	0.903198i
$887$	14.6562	+	4.76208i	0.492107	+	0.159895i	0.544549	−	0.838729i	$-0.316701\pi$
$887$	14.6562	+	4.76208i	0.492107	+	0.159895i	−0.0524428	+	0.998624i	$0.516701\pi$
$888$	−4.65761	−	1.51335i	−0.156299	−	0.0507847i
$889$	5.61773	+	17.2896i	0.188413	+	0.579874i
$890$	−2.25898	−	13.6654i	−0.0757213	−	0.458067i
$891$	1.40877	−	4.33576i	0.0471957	−	0.145253i
$892$	2.14924	−	2.95818i	0.0719619	−	0.0990471i
$893$		−	10.1553i		−	0.339834i
$894$	−1.34560	−	0.977637i	−0.0450037	−	0.0326971i
$895$	36.2226	−	5.98782i	1.21079	−	0.200151i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−16.0972	−	22.1559i	−0.537471	−	0.739765i
$898$	−23.5959	+	7.66677i	−0.787405	+	0.255843i
$899$	12.2494			0.408541
$900$	5.86315	−	8.30321i	0.195438	−	0.276774i
$901$	12.1604			0.405123
$902$	−31.8204	+	10.3391i	−1.05950	+	0.344254i
$903$	−2.78315	−	3.83068i	−0.0926174	−	0.127477i
$904$	3.92512	−	2.85177i	0.130548	−	0.0948484i
$905$	7.09766	+	13.7007i	0.235934	+	0.455426i
$906$	12.7075	+	9.23250i	0.422177	+	0.306729i
$907$			4.84955i			0.161027i	0.996754	+	0.0805134i	$0.0256560\pi$
$907$			4.84955i			0.161027i	−0.996754	+	0.0805134i	$0.974344\pi$
$908$	7.84935	−	10.8037i	0.260490	−	0.358534i
$909$	6.89666	−	21.2257i	0.228748	−	0.704013i
$910$	−6.64334	+	13.2586i	−0.220224	+	0.439519i
$911$	4.78127	+	14.7152i	0.158410	+	0.487537i	0.998490	−	0.0549253i	$-0.0174921\pi$
$911$	4.78127	+	14.7152i	0.158410	+	0.487537i	−0.840080	+	0.542462i	$0.817492\pi$
$912$	1.73895	+	0.565019i	0.0575824	+	0.0187096i
$913$	−9.58444	−	3.11417i	−0.317199	−	0.103064i
$914$	6.19118	+	19.0545i	0.204786	+	0.630267i
$915$	−27.5755	+	14.2855i	−0.911619	+	0.472265i
$916$	−0.459482	+	1.41414i	−0.0151817	+	0.0467245i
$917$	7.96348	−	10.9608i	0.262977	−	0.361957i
$918$			15.5623i			0.513633i
$919$	−9.37286	−	6.80978i	−0.309182	−	0.224634i	0.422363	−	0.906427i	$-0.361201\pi$
$919$	−9.37286	−	6.80978i	−0.309182	−	0.224634i	−0.731546	+	0.681793i	$0.761201\pi$
$920$	6.59434	−	6.68391i	0.217409	−	0.220362i
$921$	7.32064	−	5.31875i	0.241223	−	0.175259i
$922$	3.22395	+	4.43739i	0.106175	+	0.146138i
$923$	51.7520	−	16.8153i	1.70344	−	0.553481i
$924$	3.64025			0.119755
$925$	−8.01323	−	23.5752i	−0.263473	−	0.775149i
$926$	−1.01361			−0.0333093
$927$	20.1616	−	6.55090i	0.662194	−	0.215160i
$928$	0.828616	+	1.14049i	0.0272007	+	0.0374385i
$929$	−15.7013	+	11.4077i	−0.515144	+	0.374274i	−0.814771	−	0.579782i	$-0.803138\pi$
$929$	−15.7013	+	11.4077i	−0.515144	+	0.374274i	0.299628	+	0.954056i	$0.403138\pi$
$930$	2.86166	−	18.8916i	0.0938374	−	0.619481i
$931$	−1.50421	−	1.09287i	−0.0492985	−	0.0358175i
$932$		−	1.14381i		−	0.0374667i
$933$	−5.46551	+	7.52263i	−0.178933	+	0.246280i
$934$	1.96883	−	6.05945i	0.0644222	−	0.198271i
$935$	−18.5270	−	18.2787i	−0.605896	−	0.597777i
$936$	4.16635	+	12.8227i	0.136181	+	0.419123i
$937$	9.83604	+	3.19592i	0.321329	+	0.104406i	0.465240	−	0.885184i	$-0.345968\pi$
$937$	9.83604	+	3.19592i	0.321329	+	0.104406i	−0.143911	+	0.989591i	$0.545968\pi$
$938$	−1.11413	−	0.362002i	−0.0363775	−	0.0118198i
$939$	−1.07301	−	3.30240i	−0.0350165	−	0.107770i
$940$	−8.69403	−	8.57753i	−0.283568	−	0.279768i
$941$	−3.24248	+	9.97933i	−0.105702	+	0.325317i	−0.989895	−	0.141805i	$-0.954709\pi$
$941$	−3.24248	+	9.97933i	−0.105702	+	0.325317i	0.884193	+	0.467122i	$0.154709\pi$
$942$	11.2151	−	15.4362i	0.365407	−	0.502940i
$943$			37.9533i			1.23593i
$944$	−6.04473	−	4.39175i	−0.196739	−	0.142939i
$945$	1.65751	−	10.9423i	0.0539189	−	0.355953i
$946$	14.4194	−	10.4763i	0.468814	−	0.340614i
$947$	16.8404	+	23.1788i	0.547240	+	0.753211i	0.989634	−	0.143609i	$-0.0458709\pi$
$947$	16.8404	+	23.1788i	0.547240	+	0.753211i	−0.442394	+	0.896821i	$0.645871\pi$
$948$	10.6394	−	3.45696i	0.345553	−	0.112277i
$949$	79.2164			2.57147
$950$	2.99179	+	8.80197i	0.0970666	+	0.285574i
$951$	24.9780			0.809966
$952$	2.99040	−	0.971641i	0.0969196	−	0.0314911i
$953$	−10.1565	−	13.9792i	−0.329000	−	0.452830i	0.612188	−	0.790712i	$-0.290289\pi$
$953$	−10.1565	−	13.9792i	−0.329000	−	0.452830i	−0.941188	+	0.337882i	$0.890289\pi$
$954$	−6.36070	+	4.62132i	−0.205935	+	0.149621i
$955$	6.17640	−	6.26029i	0.199864	−	0.202578i
$956$	3.83887	+	2.78910i	0.124158	+	0.0902060i
$957$		−	5.13175i		−	0.165886i
$958$	−0.0991627	+	0.136486i	−0.00320380	+	0.00440965i
$959$	−3.60944	+	11.1087i	−0.116555	+	0.358719i
$960$	1.95250	−	1.01149i	0.0630166	−	0.0326458i
$961$	13.7521	+	42.3245i	0.443615	+	1.36531i
$962$	31.4113	+	10.2061i	1.01274	+	0.329059i
$963$	−14.6372	−	4.75593i	−0.471678	−	0.153258i
$964$	1.50592	+	4.63475i	0.0485025	+	0.149275i
$965$	−15.8408	+	31.6148i	−0.509935	+	1.01772i
$966$	1.27604	−	3.92724i	0.0410558	−	0.126357i
$967$	2.65264	−	3.65105i	0.0853032	−	0.117410i	−0.764233	−	0.644941i	$-0.776882\pi$
$967$	2.65264	−	3.65105i	0.0853032	−	0.117410i	0.849536	+	0.527531i	$0.176882\pi$
$968$			2.70256i			0.0868635i
$969$	−4.65117	−	3.37927i	−0.149417	−	0.108558i
$970$	−1.87910	−	3.62724i	−0.0603341	−	0.116464i
$971$	28.9879	−	21.0610i	0.930266	−	0.675878i	−0.0157916	−	0.999875i	$-0.505027\pi$
$971$	28.9879	−	21.0610i	0.930266	−	0.675878i	0.946058	+	0.323997i	$0.105027\pi$
$972$	−9.43939	−	12.9922i	−0.302769	−	0.416725i
$973$	12.9550	−	4.20932i	0.415317	−	0.134945i
$974$	13.1425			0.421112
$975$	18.8101	−	26.6383i	0.602405	−	0.853107i
$976$	14.1232			0.452073
$977$	27.6931	−	8.99803i	0.885980	−	0.287873i	0.169542	−	0.985523i	$-0.445771\pi$
$977$	27.6931	−	8.99803i	0.885980	−	0.287873i	0.716438	+	0.697650i	$0.245771\pi$
$978$	12.6263	+	17.3787i	0.403746	+	0.555708i
$979$	18.5503	−	13.4776i	0.592871	−	0.430746i
$980$	−2.20613	+	0.364687i	−0.0704722	+	0.0116495i
$981$	−15.4806	−	11.2473i	−0.494256	−	0.359098i
$982$		−	17.6217i		−	0.562330i
$983$	−0.676388	+	0.930968i	−0.0215734	+	0.0296933i	−0.819667	−	0.572840i	$-0.805842\pi$
$983$	−0.676388	+	0.930968i	−0.0215734	+	0.0296933i	0.798094	+	0.602533i	$0.205842\pi$
$984$	−2.74670	+	8.45347i	−0.0875615	+	0.269487i
$985$	8.80468	+	53.2629i	0.280540	+	1.69710i
$986$	−1.36975	−	4.21565i	−0.0436217	−	0.134254i
$987$	−5.10831	−	1.65979i	−0.162599	−	0.0528318i
$988$	−11.7276	−	3.81053i	−0.373105	−	0.121229i
$989$	−6.24772	−	19.2285i	−0.198666	−	0.611430i
$990$	16.6372	+	2.52017i	0.528766	+	0.0800962i
$991$	1.90072	−	5.84981i	0.0603783	−	0.185825i	−0.916318	−	0.400451i	$-0.868853\pi$
$991$	1.90072	−	5.84981i	0.0603783	−	0.185825i	0.976696	+	0.214626i	$0.0688533\pi$
$992$	−5.10740	+	7.02973i	−0.162160	+	0.223194i
$993$		−	27.2364i		−	0.864320i
$994$	6.63784	+	4.82267i	0.210540	+	0.152966i
$995$	−29.5818	−	14.8222i	−0.937808	−	0.469896i
$996$	−2.16594	+	1.57365i	−0.0686305	+	0.0498630i
$997$	−15.5403	−	21.3894i	−0.492166	−	0.677408i	0.488620	−	0.872497i	$-0.337501\pi$
$997$	−15.5403	−	21.3894i	−0.492166	−	0.677408i	−0.980786	+	0.195089i	$0.937501\pi$
$998$	−2.16855	+	0.704606i	−0.0686444	+	0.0223039i
$999$	−24.6478			−0.779821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.169.9	yes	40
25.2	odd	20		8750.2.a.bf.1.7		20
25.4	even	10	inner	350.2.m.b.29.9	✓	40
25.23	odd	20		8750.2.a.be.1.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.9	✓	40	25.4	even	10	inner
350.2.m.b.169.9	yes	40	1.1	even	1	trivial
8750.2.a.be.1.14		20	25.23	odd	20
8750.2.a.bf.1.7		20	25.2	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.578028 + 0.795587i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.99915 + 1.00169i) q^{5} +(0.795587 + 0.578028i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.628209 - 1.93343i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.578028 + 0.795587i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.99915 + 1.00169i) q^{5} +(0.795587 + 0.578028i) q^{6} -1.00000i q^{7} +(0.587785 - 0.809017i) q^{8} +(0.628209 - 1.93343i) q^{9} +(2.21085 + 0.334894i) q^{10} +(1.14389 + 3.52052i) q^{11} +(0.935268 + 0.303887i) q^{12} +(-6.30751 - 2.04944i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.358633 + 2.16951i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.84817 + 2.54379i) q^{17} -2.03293i q^{18} +(1.50421 + 1.09287i) q^{19} +(2.20613 - 0.364687i) q^{20} +(0.795587 - 0.578028i) q^{21} +(2.17580 + 2.99474i) q^{22} +(3.99353 - 1.29758i) q^{23} +0.983399 q^{24} +(2.99323 + 4.00507i) q^{25} -6.63211 q^{26} +(4.70714 - 1.52944i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-1.14049 + 0.828616i) q^{29} +(1.01149 + 1.95250i) q^{30} +(-7.02973 - 5.10740i) q^{31} -1.00000i q^{32} +(-2.13968 + 2.94502i) q^{33} +(-0.971641 + 2.99040i) q^{34} +(1.00169 - 1.99915i) q^{35} +(-0.628209 - 1.93343i) q^{36} +(-4.73624 - 1.53890i) q^{37} +(1.76830 + 0.574557i) q^{38} +(-2.01541 - 6.20280i) q^{39} +(1.98546 - 1.02857i) q^{40} +(-2.79307 + 8.59617i) q^{41} +(0.578028 - 0.795587i) q^{42} -4.81491i q^{43} +(2.99474 + 2.17580i) q^{44} +(3.19258 - 3.23595i) q^{45} +(3.39710 - 2.46814i) q^{46} +(-3.21041 - 4.41875i) q^{47} +(0.935268 - 0.303887i) q^{48} -1.00000 q^{49} +(4.08436 + 2.88409i) q^{50} -3.09210 q^{51} +(-6.30751 + 2.04944i) q^{52} +(-2.27323 - 3.12884i) q^{53} +(4.00413 - 2.90917i) q^{54} +(-1.23967 + 8.18389i) q^{55} +(-0.809017 - 0.587785i) q^{56} +1.82844i q^{57} +(-0.828616 + 1.14049i) q^{58} +(2.30888 - 7.10600i) q^{59} +(1.56534 + 1.54437i) q^{60} +(4.36431 + 13.4320i) q^{61} +(-8.26394 - 2.68512i) q^{62} +(-1.93343 - 0.628209i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-10.5568 - 10.4153i) q^{65} +(-1.12490 + 3.46208i) q^{66} +(0.688568 - 0.947733i) q^{67} +3.14430i q^{68} +(3.34071 + 2.42716i) q^{69} +(0.334894 - 2.21085i) q^{70} +(-6.63784 + 4.82267i) q^{71} +(-1.19492 - 1.64467i) q^{72} +(-11.3598 + 3.69101i) q^{73} -4.97997 q^{74} +(-1.45622 + 4.69641i) q^{75} +1.85931 q^{76} +(3.52052 - 1.14389i) q^{77} +(-3.83354 - 5.27642i) q^{78} +(9.20323 - 6.68654i) q^{79} +(1.57044 - 1.59177i) q^{80} +(-0.996359 - 0.723897i) q^{81} +9.03855i q^{82} +(-1.60022 + 2.20251i) q^{83} +(0.303887 - 0.935268i) q^{84} +(-6.24287 + 3.23413i) q^{85} +(-1.48789 - 4.57925i) q^{86} +(-1.31847 - 0.428397i) q^{87} +(3.52052 + 1.14389i) q^{88} +(-1.91415 - 5.89114i) q^{89} +(2.03637 - 4.06413i) q^{90} +(-2.04944 + 6.30751i) q^{91} +(2.46814 - 3.39710i) q^{92} -8.54497i q^{93} +(-4.41875 - 3.21041i) q^{94} +(1.91242 + 3.69157i) q^{95} +(0.795587 - 0.578028i) q^{96} +(-1.07383 - 1.47800i) q^{97} +(-0.951057 + 0.309017i) q^{98} +7.52528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

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