LMFDB - Embedded newform 946.2.f.a.603.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.55384803121$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			603.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	946.603
Dual form			946.2.f.a.775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(1.00000 + 3.07768i) q^{6} +(-3.61803 - 2.62866i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.30902 - 7.10642i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(1.00000 + 3.07768i) q^{6} +(-3.61803 - 2.62866i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.30902 - 7.10642i) q^{9} -3.23607 q^{10} +(-3.23607 + 0.726543i) q^{11} +3.23607 q^{12} +(-0.190983 + 0.587785i) q^{13} +(-3.61803 + 2.62866i) q^{14} +(8.47214 + 6.15537i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-6.04508 - 4.39201i) q^{18} +(-1.61803 + 1.17557i) q^{19} +(-1.00000 + 3.07768i) q^{20} +14.4721 q^{21} +(-0.309017 + 3.30220i) q^{22} +7.09017 q^{23} +(1.00000 - 3.07768i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(0.500000 + 0.363271i) q^{26} +(4.47214 + 13.7638i) q^{27} +(1.38197 + 4.25325i) q^{28} +(-8.47214 - 6.15537i) q^{29} +(8.47214 - 6.15537i) q^{30} +(0.118034 - 0.363271i) q^{31} +1.00000 q^{32} +(7.09017 - 8.05748i) q^{33} -4.85410 q^{34} +(-4.47214 + 13.7638i) q^{35} +(-6.04508 + 4.39201i) q^{36} +(6.47214 + 4.70228i) q^{37} +(0.618034 + 1.90211i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(2.61803 + 1.90211i) q^{40} +(-0.381966 + 0.277515i) q^{41} +(4.47214 - 13.7638i) q^{42} -1.00000 q^{43} +(3.04508 + 1.31433i) q^{44} -24.1803 q^{45} +(2.19098 - 6.74315i) q^{46} +(-0.927051 + 0.673542i) q^{47} +(-2.61803 - 1.90211i) q^{48} +(4.01722 + 12.3637i) q^{49} +(1.69098 + 5.20431i) q^{50} +(12.7082 + 9.23305i) q^{51} +(0.500000 - 0.363271i) q^{52} +(-4.26393 + 13.1230i) q^{53} +14.4721 q^{54} +(5.47214 + 9.23305i) q^{55} +4.47214 q^{56} +(2.00000 - 6.15537i) q^{57} +(-8.47214 + 6.15537i) q^{58} +(-3.50000 - 2.54290i) q^{59} +(-3.23607 - 9.95959i) q^{60} +(-2.61803 - 8.05748i) q^{61} +(-0.309017 - 0.224514i) q^{62} +(-27.0344 + 19.6417i) q^{63} +(0.309017 - 0.951057i) q^{64} +2.00000 q^{65} +(-5.47214 - 9.23305i) q^{66} +4.32624 q^{67} +(-1.50000 + 4.61653i) q^{68} +(-18.5623 + 13.4863i) q^{69} +(11.7082 + 8.50651i) q^{70} +(-0.763932 - 2.35114i) q^{71} +(2.30902 + 7.10642i) q^{72} +(1.23607 + 0.898056i) q^{73} +(6.47214 - 4.70228i) q^{74} +(5.47214 - 16.8415i) q^{75} +2.00000 q^{76} +(13.6180 + 5.87785i) q^{77} -2.00000 q^{78} +(-0.645898 + 1.98787i) q^{79} +(2.61803 - 1.90211i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(0.145898 + 0.449028i) q^{82} +(0.118034 + 0.363271i) q^{83} +(-11.7082 - 8.50651i) q^{84} +(-12.7082 + 9.23305i) q^{85} +(-0.309017 + 0.951057i) q^{86} +33.8885 q^{87} +(2.19098 - 2.48990i) q^{88} +5.23607 q^{89} +(-7.47214 + 22.9969i) q^{90} +(2.23607 - 1.62460i) q^{91} +(-5.73607 - 4.16750i) q^{92} +(0.381966 + 1.17557i) q^{93} +(0.354102 + 1.08981i) q^{94} +(5.23607 + 3.80423i) q^{95} +(-2.61803 + 1.90211i) q^{96} +(3.42705 - 10.5474i) q^{97} +13.0000 q^{98} +(-2.30902 + 24.6745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 6 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{7} - q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - q^2 - 6 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 10 * q^7 - q^8 + 7 * q^9	\( 4 q - q^{2} - 6 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{7} - q^{8} + 7 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 10 q^{14} + 16 q^{15} - q^{16} - 6 q^{17} - 13 q^{18} - 2 q^{19} - 4 q^{20} + 40 q^{21} + q^{22} + 6 q^{23} + 4 q^{24} - 11 q^{25} + 2 q^{26} + 10 q^{28} - 16 q^{29} + 16 q^{30} - 4 q^{31} + 4 q^{32} + 6 q^{33} - 6 q^{34} - 13 q^{36} + 8 q^{37} - 2 q^{38} + 2 q^{39} + 6 q^{40} - 6 q^{41} - 4 q^{43} + q^{44} - 52 q^{45} + 11 q^{46} + 3 q^{47} - 6 q^{48} - 13 q^{49} + 9 q^{50} + 24 q^{51} + 2 q^{52} - 26 q^{53} + 40 q^{54} + 4 q^{55} + 8 q^{57} - 16 q^{58} - 14 q^{59} - 4 q^{60} - 6 q^{61} + q^{62} - 50 q^{63} - q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} - 6 q^{68} - 34 q^{69} + 20 q^{70} - 12 q^{71} + 7 q^{72} - 4 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} + 50 q^{77} - 8 q^{78} - 16 q^{79} + 6 q^{80} - 41 q^{81} + 14 q^{82} - 4 q^{83} - 20 q^{84} - 24 q^{85} + q^{86} + 64 q^{87} + 11 q^{88} + 12 q^{89} - 12 q^{90} - 14 q^{92} + 6 q^{93} - 12 q^{94} + 12 q^{95} - 6 q^{96} + 7 q^{97} + 52 q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - q^2 - 6 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 10 * q^7 - q^8 + 7 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 10 * q^14 + 16 * q^15 - q^16 - 6 * q^17 - 13 * q^18 - 2 * q^19 - 4 * q^20 + 40 * q^21 + q^22 + 6 * q^23 + 4 * q^24 - 11 * q^25 + 2 * q^26 + 10 * q^28 - 16 * q^29 + 16 * q^30 - 4 * q^31 + 4 * q^32 + 6 * q^33 - 6 * q^34 - 13 * q^36 + 8 * q^37 - 2 * q^38 + 2 * q^39 + 6 * q^40 - 6 * q^41 - 4 * q^43 + q^44 - 52 * q^45 + 11 * q^46 + 3 * q^47 - 6 * q^48 - 13 * q^49 + 9 * q^50 + 24 * q^51 + 2 * q^52 - 26 * q^53 + 40 * q^54 + 4 * q^55 + 8 * q^57 - 16 * q^58 - 14 * q^59 - 4 * q^60 - 6 * q^61 + q^62 - 50 * q^63 - q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 - 6 * q^68 - 34 * q^69 + 20 * q^70 - 12 * q^71 + 7 * q^72 - 4 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 + 50 * q^77 - 8 * q^78 - 16 * q^79 + 6 * q^80 - 41 * q^81 + 14 * q^82 - 4 * q^83 - 20 * q^84 - 24 * q^85 + q^86 + 64 * q^87 + 11 * q^88 + 12 * q^89 - 12 * q^90 - 14 * q^92 + 6 * q^93 - 12 * q^94 + 12 * q^95 - 6 * q^96 + 7 * q^97 + 52 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.546027	+	0.837768i	$0.683860\pi$
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.965496	+	0.260418i	$0.916140\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000	−	3.07768i	−0.447214	−	1.37638i	−0.880038	−	0.474904i	$-0.842483\pi$
$5$	−1.00000	−	3.07768i	−0.447214	−	1.37638i	0.432824	−	0.901478i	$-0.357517\pi$
$6$	1.00000	+	3.07768i	0.408248	+	1.25646i
$7$	−3.61803	−	2.62866i	−1.36749	−	0.993538i	−0.997929	−	0.0643314i	$-0.979509\pi$
$7$	−3.61803	−	2.62866i	−1.36749	−	0.993538i	−0.369560	−	0.929207i	$-0.620491\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	2.30902	−	7.10642i	0.769672	−	2.36881i
$10$	−3.23607			−1.02333
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$12$	3.23607			0.934172
$13$	−0.190983	+	0.587785i	−0.0529692	+	0.163022i	−0.974042	−	0.226369i	$-0.927315\pi$
$13$	−0.190983	+	0.587785i	−0.0529692	+	0.163022i	0.921073	+	0.389391i	$0.127315\pi$
$14$	−3.61803	+	2.62866i	−0.966960	+	0.702538i
$15$	8.47214	+	6.15537i	2.18750	+	1.58931i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.50000	−	4.61653i	−0.363803	−	1.11967i	−0.950727	−	0.310029i	$-0.899661\pi$
$17$	−1.50000	−	4.61653i	−0.363803	−	1.11967i	0.586924	−	0.809642i	$-0.300339\pi$
$18$	−6.04508	−	4.39201i	−1.42484	−	1.03521i
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	−0.757709	−	0.652592i	$-0.773682\pi$
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	0.386507	+	0.922287i	$0.373682\pi$
$20$	−1.00000	+	3.07768i	−0.223607	+	0.688191i
$21$	14.4721			3.15808
$22$	−0.309017	+	3.30220i	−0.0658826	+	0.704031i
$23$	7.09017			1.47840			0.739201	−	0.673485i	$-0.235203\pi$
$23$	7.09017			1.47840			0.739201	+	0.673485i	$0.235203\pi$
$24$	1.00000	−	3.07768i	0.204124	−	0.628230i
$25$	−4.42705	+	3.21644i	−0.885410	+	0.643288i
$26$	0.500000	+	0.363271i	0.0980581	+	0.0712434i
$27$	4.47214	+	13.7638i	0.860663	+	2.64885i
$28$	1.38197	+	4.25325i	0.261167	+	0.803789i
$29$	−8.47214	−	6.15537i	−1.57324	−	1.14302i	−0.923972	−	0.382460i	$-0.875077\pi$
$29$	−8.47214	−	6.15537i	−1.57324	−	1.14302i	−0.649264	−	0.760563i	$-0.724923\pi$
$30$	8.47214	−	6.15537i	1.54679	−	1.12381i
$31$	0.118034	−	0.363271i	0.0211995	−	0.0652454i	−0.939897	−	0.341458i	$-0.889079\pi$
$31$	0.118034	−	0.363271i	0.0211995	−	0.0652454i	0.961097	+	0.276212i	$0.0890793\pi$
$32$	1.00000			0.176777
$33$	7.09017	−	8.05748i	1.23424	−	1.40263i
$34$	−4.85410			−0.832472
$35$	−4.47214	+	13.7638i	−0.755929	+	2.32651i
$36$	−6.04508	+	4.39201i	−1.00751	+	0.732002i
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.974827	−	0.222965i	$-0.0715734\pi$
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.0891861	+	0.996015i	$0.471573\pi$
$38$	0.618034	+	1.90211i	0.100258	+	0.308563i
$39$	−0.618034	−	1.90211i	−0.0989646	−	0.304582i
$40$	2.61803	+	1.90211i	0.413948	+	0.300750i
$41$	−0.381966	+	0.277515i	−0.0596531	+	0.0433405i	−0.617212	−	0.786797i	$-0.711738\pi$
$41$	−0.381966	+	0.277515i	−0.0596531	+	0.0433405i	0.557559	+	0.830137i	$0.311738\pi$
$42$	4.47214	−	13.7638i	0.690066	−	2.12380i
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$	3.04508	+	1.31433i	0.459064	+	0.198142i
$45$	−24.1803			−3.60459
$46$	2.19098	−	6.74315i	0.323043	−	0.994224i
$47$	−0.927051	+	0.673542i	−0.135224	+	0.0982462i	−0.653341	−	0.757064i	$-0.726633\pi$
$47$	−0.927051	+	0.673542i	−0.135224	+	0.0982462i	0.518117	+	0.855310i	$0.326633\pi$
$48$	−2.61803	−	1.90211i	−0.377881	−	0.274546i
$49$	4.01722	+	12.3637i	0.573889	+	1.76625i
$50$	1.69098	+	5.20431i	0.239141	+	0.736001i
$51$	12.7082	+	9.23305i	1.77950	+	1.29289i
$52$	0.500000	−	0.363271i	0.0693375	−	0.0503767i
$53$	−4.26393	+	13.1230i	−0.585696	+	1.80259i	0.0107607	+	0.999942i	$0.496575\pi$
$53$	−4.26393	+	13.1230i	−0.585696	+	1.80259i	−0.596457	+	0.802645i	$0.703425\pi$
$54$	14.4721			1.96941
$55$	5.47214	+	9.23305i	0.737863	+	1.24498i
$56$	4.47214			0.597614
$57$	2.00000	−	6.15537i	0.264906	−	0.815298i
$58$	−8.47214	+	6.15537i	−1.11245	+	0.808239i
$59$	−3.50000	−	2.54290i	−0.455661	−	0.331057i	0.336166	−	0.941803i	$-0.390870\pi$
$59$	−3.50000	−	2.54290i	−0.455661	−	0.331057i	−0.791827	+	0.610746i	$0.790870\pi$
$60$	−3.23607	−	9.95959i	−0.417775	−	1.28578i
$61$	−2.61803	−	8.05748i	−0.335205	−	1.03165i	−0.966621	−	0.256210i	$-0.917526\pi$
$61$	−2.61803	−	8.05748i	−0.335205	−	1.03165i	0.631416	−	0.775444i	$-0.282474\pi$
$62$	−0.309017	−	0.224514i	−0.0392452	−	0.0285133i
$63$	−27.0344	+	19.6417i	−3.40602	+	2.47462i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.00000			0.248069
$66$	−5.47214	−	9.23305i	−0.673573	−	1.13651i
$67$	4.32624			0.528534			0.264267	−	0.964450i	$-0.414870\pi$
$67$	4.32624			0.528534			0.264267	+	0.964450i	$0.414870\pi$
$68$	−1.50000	+	4.61653i	−0.181902	+	0.559836i
$69$	−18.5623	+	13.4863i	−2.23464	+	1.62356i
$70$	11.7082	+	8.50651i	1.39940	+	1.01672i
$71$	−0.763932	−	2.35114i	−0.0906621	−	0.279029i	0.895437	−	0.445189i	$-0.146863\pi$
$71$	−0.763932	−	2.35114i	−0.0906621	−	0.279029i	−0.986099	+	0.166159i	$0.946863\pi$
$72$	2.30902	+	7.10642i	0.272120	+	0.837500i
$73$	1.23607	+	0.898056i	0.144671	+	0.105109i	0.657766	−	0.753222i	$-0.271501\pi$
$73$	1.23607	+	0.898056i	0.144671	+	0.105109i	−0.513096	+	0.858331i	$0.671501\pi$
$74$	6.47214	−	4.70228i	0.752371	−	0.546629i
$75$	5.47214	−	16.8415i	0.631868	−	1.94469i
$76$	2.00000			0.229416
$77$	13.6180	+	5.87785i	1.55192	+	0.669843i
$78$	−2.00000			−0.226455
$79$	−0.645898	+	1.98787i	−0.0726692	+	0.223653i	−0.980794	−	0.195047i	$-0.937514\pi$
$79$	−0.645898	+	1.98787i	−0.0726692	+	0.223653i	0.908125	+	0.418700i	$0.137514\pi$
$80$	2.61803	−	1.90211i	0.292705	−	0.212663i
$81$	−19.7533	−	14.3516i	−2.19481	−	1.59462i
$82$	0.145898	+	0.449028i	0.0161117	+	0.0495868i
$83$	0.118034	+	0.363271i	0.0129559	+	0.0398742i	0.957325	−	0.289012i	$-0.0933267\pi$
$83$	0.118034	+	0.363271i	0.0129559	+	0.0398742i	−0.944370	+	0.328886i	$0.893327\pi$
$84$	−11.7082	−	8.50651i	−1.27747	−	0.928136i
$85$	−12.7082	+	9.23305i	−1.37840	+	1.00146i
$86$	−0.309017	+	0.951057i	−0.0333222	+	0.102555i
$87$	33.8885			3.63323
$88$	2.19098	−	2.48990i	0.233560	−	0.265424i
$89$	5.23607			0.555022			0.277511	−	0.960722i	$-0.410490\pi$
$89$	5.23607			0.555022			0.277511	+	0.960722i	$0.410490\pi$
$90$	−7.47214	+	22.9969i	−0.787632	+	2.42408i
$91$	2.23607	−	1.62460i	0.234404	−	0.170304i
$92$	−5.73607	−	4.16750i	−0.598026	−	0.434492i
$93$	0.381966	+	1.17557i	0.0396080	+	0.121901i
$94$	0.354102	+	1.08981i	0.0365228	+	0.112406i
$95$	5.23607	+	3.80423i	0.537209	+	0.390305i
$96$	−2.61803	+	1.90211i	−0.267202	+	0.194134i
$97$	3.42705	−	10.5474i	0.347964	−	1.07092i	−0.612013	−	0.790847i	$-0.709640\pi$
$97$	3.42705	−	10.5474i	0.347964	−	1.07092i	0.959978	−	0.280077i	$-0.0903599\pi$
$98$	13.0000			1.31320
$99$	−2.30902	+	24.6745i	−0.232065	+	2.47988i
$100$	5.47214			0.547214
$101$	−0.663119	+	2.04087i	−0.0659828	+	0.203074i	−0.978612	−	0.205714i	$-0.934048\pi$
$101$	−0.663119	+	2.04087i	−0.0659828	+	0.203074i	0.912629	+	0.408788i	$0.134048\pi$
$102$	12.7082	−	9.23305i	1.25830	−	0.914208i
$103$	0.454915	+	0.330515i	0.0448241	+	0.0325666i	0.609972	−	0.792423i	$-0.291181\pi$
$103$	0.454915	+	0.330515i	0.0448241	+	0.0325666i	−0.565148	+	0.824990i	$0.691181\pi$
$104$	−0.190983	−	0.587785i	−0.0187274	−	0.0576371i
$105$	−14.4721	−	44.5407i	−1.41234	−	4.34672i
$106$	11.1631	+	8.11048i	1.08426	+	0.787760i
$107$	2.50000	−	1.81636i	0.241684	−	0.175594i	−0.460349	−	0.887738i	$-0.652276\pi$
$107$	2.50000	−	1.81636i	0.241684	−	0.175594i	0.702033	+	0.712144i	$0.252276\pi$
$108$	4.47214	−	13.7638i	0.430331	−	1.32442i
$109$	4.09017			0.391767			0.195884	−	0.980627i	$-0.437243\pi$
$109$	4.09017			0.391767			0.195884	+	0.980627i	$0.437243\pi$
$110$	10.4721	−	2.35114i	0.998479	−	0.224172i
$111$	−25.8885			−2.45723
$112$	1.38197	−	4.25325i	0.130584	−	0.401895i
$113$	9.32624	−	6.77591i	0.877339	−	0.637424i	−0.0552074	−	0.998475i	$-0.517582\pi$
$113$	9.32624	−	6.77591i	0.877339	−	0.637424i	0.932546	+	0.361051i	$0.117582\pi$
$114$	−5.23607	−	3.80423i	−0.490403	−	0.356298i
$115$	−7.09017	−	21.8213i	−0.661162	−	2.03485i
$116$	3.23607	+	9.95959i	0.300461	+	0.924725i
$117$	3.73607	+	2.71441i	0.345400	+	0.250948i
$118$	−3.50000	+	2.54290i	−0.322201	+	0.234093i
$119$	−6.70820	+	20.6457i	−0.614940	+	1.89259i
$120$	−10.4721			−0.955971
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$	−8.47214			−0.767031
$123$	0.472136	−	1.45309i	0.0425711	−	0.131020i
$124$	−0.309017	+	0.224514i	−0.0277505	+	0.0201620i
$125$	1.23607	+	0.898056i	0.110557	+	0.0803246i
$126$	10.3262	+	31.7809i	0.919934	+	2.83127i
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	0.969579	+	0.244778i	$0.0787150\pi$
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	−0.640529	+	0.767934i	$0.721285\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	2.61803	−	1.90211i	0.230505	−	0.167472i
$130$	0.618034	−	1.90211i	0.0542052	−	0.166826i
$131$	1.05573			0.0922394			0.0461197	−	0.998936i	$-0.485314\pi$
$131$	1.05573			0.0922394			0.0461197	+	0.998936i	$0.485314\pi$
$132$	−10.4721	+	2.35114i	−0.911482	+	0.204641i
$133$	8.94427			0.775567
$134$	1.33688	−	4.11450i	0.115489	−	0.355438i
$135$	37.8885	−	27.5276i	3.26093	−	2.36920i
$136$	3.92705	+	2.85317i	0.336742	+	0.244657i
$137$	−7.00000	−	21.5438i	−0.598050	−	1.84061i	−0.538916	−	0.842360i	$-0.681166\pi$
$137$	−7.00000	−	21.5438i	−0.598050	−	1.84061i	−0.0591347	−	0.998250i	$-0.518834\pi$
$138$	7.09017	+	21.8213i	0.603555	+	1.85755i
$139$	−16.4443	−	11.9475i	−1.39478	−	1.01337i	−0.995321	−	0.0966216i	$-0.969196\pi$
$139$	−16.4443	−	11.9475i	−1.39478	−	1.01337i	−0.399464	−	0.916749i	$-0.630804\pi$
$140$	11.7082	−	8.50651i	0.989524	−	0.718931i
$141$	1.14590	−	3.52671i	0.0965020	−	0.297003i
$142$	−2.47214			−0.207457
$143$	0.190983	−	2.04087i	0.0159708	−	0.170666i
$144$	7.47214			0.622678
$145$	−10.4721	+	32.2299i	−0.869664	+	2.67655i
$146$	1.23607	−	0.898056i	0.102298	−	0.0743236i
$147$	−34.0344	−	24.7275i	−2.80711	−	2.03949i
$148$	−2.47214	−	7.60845i	−0.203208	−	0.625411i
$149$	−3.52786	−	10.8576i	−0.289014	−	0.889493i	−0.985167	−	0.171600i	$-0.945106\pi$
$149$	−3.52786	−	10.8576i	−0.289014	−	0.889493i	0.696153	−	0.717894i	$-0.254894\pi$
$150$	−14.3262	−	10.4086i	−1.16973	−	0.849860i
$151$	−8.32624	+	6.04937i	−0.677580	+	0.492290i	−0.872554	−	0.488518i	$-0.837538\pi$
$151$	−8.32624	+	6.04937i	−0.677580	+	0.492290i	0.194974	+	0.980808i	$0.437538\pi$
$152$	0.618034	−	1.90211i	0.0501292	−	0.154282i
$153$	−36.2705			−2.93230
$154$	9.79837	−	11.1352i	0.789575	−	0.897297i
$155$	−1.23607			−0.0992834
$156$	−0.618034	+	1.90211i	−0.0494823	+	0.152291i
$157$	−4.00000	+	2.90617i	−0.319235	+	0.231938i	−0.735849	−	0.677146i	$-0.763217\pi$
$157$	−4.00000	+	2.90617i	−0.319235	+	0.231938i	0.416614	+	0.909083i	$0.363217\pi$
$158$	1.69098	+	1.22857i	0.134527	+	0.0977399i
$159$	−13.7984	−	42.4670i	−1.09428	−	3.36785i
$160$	−1.00000	−	3.07768i	−0.0790569	−	0.243312i
$161$	−25.6525	−	18.6376i	−2.02170	−	1.46885i
$162$	−19.7533	+	14.3516i	−1.55196	+	1.12757i
$163$	−3.23607	+	9.95959i	−0.253468	+	0.780096i	0.740659	+	0.671881i	$0.234513\pi$
$163$	−3.23607	+	9.95959i	−0.253468	+	0.780096i	−0.994128	+	0.108215i	$0.965487\pi$
$164$	0.472136			0.0368676
$165$	−31.8885	−	13.7638i	−2.48252	−	1.07151i
$166$	0.381966			0.0296463
$167$	3.71885	−	11.4454i	0.287773	−	0.885674i	−0.697781	−	0.716311i	$-0.745829\pi$
$167$	3.71885	−	11.4454i	0.287773	−	0.885674i	0.985554	−	0.169363i	$-0.0541710\pi$
$168$	−11.7082	+	8.50651i	−0.903308	+	0.656291i
$169$	10.2082	+	7.41669i	0.785246	+	0.570515i
$170$	4.85410	+	14.9394i	0.372293	+	1.14580i
$171$	4.61803	+	14.2128i	0.353150	+	1.08688i
$172$	0.809017	+	0.587785i	0.0616870	+	0.0448182i
$173$	5.30902	−	3.85723i	0.403637	−	0.293260i	−0.367384	−	0.930069i	$-0.619746\pi$
$173$	5.30902	−	3.85723i	0.403637	−	0.293260i	0.771021	+	0.636810i	$0.219746\pi$
$174$	10.4721	−	32.2299i	0.793891	−	2.44334i
$175$	24.4721			1.84992
$176$	−1.69098	−	2.85317i	−0.127463	−	0.215066i
$177$	14.0000			1.05230
$178$	1.61803	−	4.97980i	0.121277	−	0.373252i
$179$	1.76393	−	1.28157i	0.131842	−	0.0957892i	−0.519909	−	0.854221i	$-0.674034\pi$
$179$	1.76393	−	1.28157i	0.131842	−	0.0957892i	0.651752	+	0.758432i	$0.274034\pi$
$180$	19.5623	+	14.2128i	1.45809	+	1.05936i
$181$	6.66312	+	20.5070i	0.495266	+	1.52427i	0.816542	+	0.577286i	$0.195888\pi$
$181$	6.66312	+	20.5070i	0.495266	+	1.52427i	−0.321276	+	0.946985i	$0.604112\pi$
$182$	−0.854102	−	2.62866i	−0.0633102	−	0.194849i
$183$	22.1803	+	16.1150i	1.63962	+	1.19125i
$184$	−5.73607	+	4.16750i	−0.422869	+	0.307232i
$185$	8.00000	−	24.6215i	0.588172	−	1.81021i
$186$	1.23607			0.0906329
$187$	8.20820	+	13.8496i	0.600243	+	1.01278i
$188$	1.14590			0.0835732
$189$	20.0000	−	61.5537i	1.45479	−	4.47737i
$190$	5.23607	−	3.80423i	0.379864	−	0.275988i
$191$	10.8541	+	7.88597i	0.785375	+	0.570609i	0.906587	−	0.422018i	$-0.138678\pi$
$191$	10.8541	+	7.88597i	0.785375	+	0.570609i	−0.121212	+	0.992627i	$0.538678\pi$
$192$	1.00000	+	3.07768i	0.0721688	+	0.222113i
$193$	5.20820	+	16.0292i	0.374895	+	1.15381i	0.943550	+	0.331231i	$0.107464\pi$
$193$	5.20820	+	16.0292i	0.374895	+	1.15381i	−0.568655	+	0.822576i	$0.692536\pi$
$194$	−8.97214	−	6.51864i	−0.644162	−	0.468011i
$195$	−5.23607	+	3.80423i	−0.374963	+	0.272426i
$196$	4.01722	−	12.3637i	0.286944	−	0.883124i
$197$	17.8541			1.27205			0.636026	−	0.771668i	$-0.280577\pi$
$197$	17.8541			1.27205			0.636026	+	0.771668i	$0.280577\pi$
$198$	22.7533	+	9.82084i	1.61701	+	0.697936i
$199$	−19.4164			−1.37639			−0.688196	−	0.725525i	$-0.741597\pi$
$199$	−19.4164			−1.37639			−0.688196	+	0.725525i	$0.741597\pi$
$200$	1.69098	−	5.20431i	0.119571	−	0.368000i
$201$	−11.3262	+	8.22899i	−0.798891	+	0.580428i
$202$	1.73607	+	1.26133i	0.122149	+	0.0887467i
$203$	14.4721	+	44.5407i	1.01574	+	3.12614i
$204$	−4.85410	−	14.9394i	−0.339855	−	1.04597i
$205$	1.23607	+	0.898056i	0.0863307	+	0.0627229i
$206$	0.454915	−	0.330515i	0.0316954	−	0.0230281i
$207$	16.3713	−	50.3858i	1.13789	−	3.50205i
$208$	−0.618034			−0.0428529
$209$	4.38197	−	4.97980i	0.303107	−	0.344460i
$210$	−46.8328			−3.23177
$211$	6.09017	−	18.7436i	0.419265	−	1.29036i	−0.489116	−	0.872219i	$-0.662680\pi$
$211$	6.09017	−	18.7436i	0.419265	−	1.29036i	0.908380	−	0.418145i	$-0.137320\pi$
$212$	11.1631	−	8.11048i	0.766686	−	0.557030i
$213$	6.47214	+	4.70228i	0.443463	+	0.322195i
$214$	−0.954915	−	2.93893i	−0.0652766	−	0.200901i
$215$	1.00000	+	3.07768i	0.0681994	+	0.209896i
$216$	−11.7082	−	8.50651i	−0.796642	−	0.578795i
$217$	−1.38197	+	1.00406i	−0.0938140	+	0.0681598i
$218$	1.26393	−	3.88998i	0.0856043	−	0.263463i
$219$	−4.94427			−0.334103
$220$	1.00000	−	10.6861i	0.0674200	−	0.720459i
$221$	3.00000			0.201802
$222$	−8.00000	+	24.6215i	−0.536925	+	1.65248i
$223$	−11.4721	+	8.33499i	−0.768231	+	0.558153i	−0.901424	−	0.432938i	$-0.857477\pi$
$223$	−11.4721	+	8.33499i	−0.768231	+	0.558153i	0.133193	+	0.991090i	$0.457477\pi$
$224$	−3.61803	−	2.62866i	−0.241740	−	0.175634i
$225$	12.6353	+	38.8873i	0.842350	+	2.59249i
$226$	−3.56231	−	10.9637i	−0.236961	−	0.729291i
$227$	6.09017	+	4.42477i	0.404219	+	0.293682i	0.771257	−	0.636524i	$-0.219628\pi$
$227$	6.09017	+	4.42477i	0.404219	+	0.293682i	−0.367038	+	0.930206i	$0.619628\pi$
$228$	−5.23607	+	3.80423i	−0.346767	+	0.251941i
$229$	−6.57295	+	20.2295i	−0.434353	+	1.33680i	0.459396	+	0.888232i	$0.348066\pi$
$229$	−6.57295	+	20.2295i	−0.434353	+	1.33680i	−0.893748	+	0.448568i	$0.851934\pi$
$230$	−22.9443			−1.51290
$231$	−46.8328	+	10.5146i	−3.08137	+	0.691811i
$232$	10.4721			0.687529
$233$	−1.94427	+	5.98385i	−0.127373	+	0.392015i	−0.994326	−	0.106375i	$-0.966075\pi$
$233$	−1.94427	+	5.98385i	−0.127373	+	0.392015i	0.866953	+	0.498391i	$0.166075\pi$
$234$	3.73607	−	2.71441i	0.244234	−	0.177447i
$235$	3.00000	+	2.17963i	0.195698	+	0.142183i
$236$	1.33688	+	4.11450i	0.0870235	+	0.267831i
$237$	−2.09017	−	6.43288i	−0.135771	−	0.417861i
$238$	17.5623	+	12.7598i	1.13840	+	0.827093i
$239$	−13.6803	+	9.93935i	−0.884908	+	0.642923i	−0.934545	−	0.355844i	$-0.884193\pi$
$239$	−13.6803	+	9.93935i	−0.884908	+	0.642923i	0.0496376	+	0.998767i	$0.484193\pi$
$240$	−3.23607	+	9.95959i	−0.208887	+	0.642889i
$241$	−17.7082			−1.14069			−0.570343	−	0.821407i	$-0.693190\pi$
$241$	−17.7082			−1.14069			−0.570343	+	0.821407i	$0.693190\pi$
$242$	−1.39919	−	10.9106i	−0.0899431	−	0.701363i
$243$	35.5967			2.28353
$244$	−2.61803	+	8.05748i	−0.167602	+	0.515827i
$245$	34.0344	−	24.7275i	2.17438	−	1.57978i
$246$	−1.23607	−	0.898056i	−0.0788088	−	0.0572580i
$247$	−0.381966	−	1.17557i	−0.0243039	−	0.0747998i
$248$	0.118034	+	0.363271i	0.00749517	+	0.0230677i
$249$	−1.00000	−	0.726543i	−0.0633724	−	0.0460428i
$250$	1.23607	−	0.898056i	0.0781758	−	0.0567980i
$251$	4.64590	−	14.2986i	0.293246	−	0.902520i	−0.690558	−	0.723277i	$-0.742635\pi$
$251$	4.64590	−	14.2986i	0.293246	−	0.902520i	0.983805	−	0.179243i	$-0.0573649\pi$
$252$	33.4164			2.10504
$253$	−22.9443	+	5.15131i	−1.44249	+	0.323860i
$254$	12.0000			0.752947
$255$	15.7082	−	48.3449i	0.983686	−	3.02747i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.4721	+	9.06154i	0.777990	+	0.565243i	0.904375	−	0.426738i	$-0.140337\pi$
$257$	12.4721	+	9.06154i	0.777990	+	0.565243i	−0.126385	+	0.991981i	$0.540337\pi$
$258$	−1.00000	−	3.07768i	−0.0622573	−	0.191608i
$259$	−11.0557	−	34.0260i	−0.686970	−	2.11427i
$260$	−1.61803	−	1.17557i	−0.100346	−	0.0729058i
$261$	−63.3050	+	45.9937i	−3.91848	+	2.84694i
$262$	0.326238	−	1.00406i	0.0201550	−	0.0620309i
$263$	−23.8885			−1.47303			−0.736515	−	0.676421i	$-0.763530\pi$
$263$	−23.8885			−1.47303			−0.736515	+	0.676421i	$0.763530\pi$
$264$	−1.00000	+	10.6861i	−0.0615457	+	0.657686i
$265$	44.6525			2.74298
$266$	2.76393	−	8.50651i	0.169468	−	0.521567i
$267$	−13.7082	+	9.95959i	−0.838928	+	0.609517i
$268$	−3.50000	−	2.54290i	−0.213797	−	0.155332i
$269$	−3.79180	−	11.6699i	−0.231190	−	0.711529i	−0.997604	−	0.0691825i	$-0.977961\pi$
$269$	−3.79180	−	11.6699i	−0.231190	−	0.711529i	0.766414	−	0.642347i	$-0.222039\pi$
$270$	−14.4721	−	44.5407i	−0.880746	−	2.71066i
$271$	−13.8713	−	10.0781i	−0.842623	−	0.612201i	0.0804792	−	0.996756i	$-0.474355\pi$
$271$	−13.8713	−	10.0781i	−0.842623	−	0.612201i	−0.923102	+	0.384555i	$0.874355\pi$
$272$	3.92705	−	2.85317i	0.238112	−	0.172999i
$273$	−2.76393	+	8.50651i	−0.167281	+	0.514837i
$274$	−22.6525			−1.36849
$275$	11.9894	−	13.6251i	0.722985	−	0.821622i
$276$	22.9443			1.38108
$277$	−7.14590	+	21.9928i	−0.429355	+	1.32142i	0.469406	+	0.882982i	$0.344468\pi$
$277$	−7.14590	+	21.9928i	−0.429355	+	1.32142i	−0.898762	+	0.438438i	$0.855532\pi$
$278$	−16.4443	+	11.9475i	−0.986262	+	0.716561i
$279$	−2.30902	−	1.67760i	−0.138237	−	0.100435i
$280$	−4.47214	−	13.7638i	−0.267261	−	0.822546i
$281$	0.663119	+	2.04087i	0.0395584	+	0.121748i	0.968886	−	0.247509i	$-0.0796121\pi$
$281$	0.663119	+	2.04087i	0.0395584	+	0.121748i	−0.929327	+	0.369257i	$0.879612\pi$
$282$	−3.00000	−	2.17963i	−0.178647	−	0.129795i
$283$	−16.1803	+	11.7557i	−0.961821	+	0.698804i	−0.953573	−	0.301162i	$-0.902626\pi$
$283$	−16.1803	+	11.7557i	−0.961821	+	0.698804i	−0.00824833	+	0.999966i	$0.502626\pi$
$284$	−0.763932	+	2.35114i	−0.0453310	+	0.139515i
$285$	−20.9443			−1.24063
$286$	−1.88197	−	0.812299i	−0.111283	−	0.0480323i
$287$	2.11146			0.124635
$288$	2.30902	−	7.10642i	0.136060	−	0.418750i
$289$	−5.30902	+	3.85723i	−0.312295	+	0.226896i
$290$	27.4164	+	19.9192i	1.60995	+	1.16969i
$291$	11.0902	+	34.1320i	0.650117	+	2.00086i
$292$	−0.472136	−	1.45309i	−0.0276297	−	0.0850354i
$293$	14.8541	+	10.7921i	0.867786	+	0.630483i	0.929992	−	0.367580i	$-0.119814\pi$
$293$	14.8541	+	10.7921i	0.867786	+	0.630483i	−0.0622060	+	0.998063i	$0.519814\pi$
$294$	−34.0344	+	24.7275i	−1.98493	+	1.44214i
$295$	−4.32624	+	13.3148i	−0.251883	+	0.775217i
$296$	−8.00000			−0.464991
$297$	−24.4721	−	41.2915i	−1.42002	−	2.39597i
$298$	−11.4164			−0.661335
$299$	−1.35410	+	4.16750i	−0.0783097	+	0.241013i
$300$	−14.3262	+	10.4086i	−0.827126	+	0.600942i
$301$	3.61803	+	2.62866i	0.208540	+	0.151513i
$302$	3.18034	+	9.78808i	0.183008	+	0.563241i
$303$	−2.14590	−	6.60440i	−0.123279	−	0.379413i
$304$	−1.61803	−	1.17557i	−0.0928006	−	0.0674236i
$305$	−22.1803	+	16.1150i	−1.27004	+	0.922740i
$306$	−11.2082	+	34.4953i	−0.640730	+	1.97197i
$307$	10.8541			0.619476			0.309738	−	0.950822i	$-0.399759\pi$
$307$	10.8541			0.619476			0.309738	+	0.950822i	$0.399759\pi$
$308$	−7.56231	−	12.7598i	−0.430902	−	0.727055i
$309$	−1.81966			−0.103517
$310$	−0.381966	+	1.17557i	−0.0216942	+	0.0667679i
$311$	−11.9721	+	8.69827i	−0.678878	+	0.493233i	−0.872985	−	0.487747i	$-0.837819\pi$
$311$	−11.9721	+	8.69827i	−0.678878	+	0.493233i	0.194108	+	0.980980i	$0.437819\pi$
$312$	1.61803	+	1.17557i	0.0916031	+	0.0665536i
$313$	−1.23607	−	3.80423i	−0.0698667	−	0.215028i	0.910027	−	0.414550i	$-0.136061\pi$
$313$	−1.23607	−	3.80423i	−0.0698667	−	0.215028i	−0.979893	+	0.199522i	$0.936061\pi$
$314$	1.52786	+	4.70228i	0.0862224	+	0.265365i
$315$	87.4853	+	63.5618i	4.92924	+	3.58130i
$316$	1.69098	−	1.22857i	0.0951252	−	0.0691125i
$317$	−3.26393	+	10.0453i	−0.183321	+	0.564203i	−0.999915	−	0.0130084i	$-0.995859\pi$
$317$	−3.26393	+	10.0453i	−0.183321	+	0.564203i	0.816595	+	0.577211i	$0.195859\pi$
$318$	−44.6525			−2.50399
$319$	31.8885	+	13.7638i	1.78542	+	0.770626i
$320$	−3.23607			−0.180902
$321$	−3.09017	+	9.51057i	−0.172476	+	0.530828i
$322$	−25.6525	+	18.6376i	−1.42956	+	1.03863i
$323$	7.85410	+	5.70634i	0.437014	+	0.317509i
$324$	7.54508	+	23.2214i	0.419171	+	1.29008i
$325$	−1.04508	−	3.21644i	−0.0579709	−	0.178416i
$326$	8.47214	+	6.15537i	0.469228	+	0.340914i
$327$	−10.7082	+	7.77997i	−0.592165	+	0.430233i
$328$	0.145898	−	0.449028i	0.00805587	−	0.0247934i
$329$	5.12461			0.282529
$330$	−22.9443	+	26.0746i	−1.26304	+	1.43536i
$331$	−21.8885			−1.20310			−0.601552	−	0.798834i	$-0.705451\pi$
$331$	−21.8885			−1.20310			−0.601552	+	0.798834i	$0.705451\pi$
$332$	0.118034	−	0.363271i	0.00647796	−	0.0199371i
$333$	48.3607	−	35.1361i	2.65015	−	1.92545i
$334$	−9.73607	−	7.07367i	−0.532734	−	0.387054i
$335$	−4.32624	−	13.3148i	−0.236368	−	0.727465i
$336$	4.47214	+	13.7638i	0.243975	+	0.750878i
$337$	−19.6803	−	14.2986i	−1.07206	−	0.778895i	−0.0957757	−	0.995403i	$-0.530533\pi$
$337$	−19.6803	−	14.2986i	−1.07206	−	0.778895i	−0.976281	+	0.216508i	$0.930533\pi$
$338$	10.2082	−	7.41669i	0.555253	−	0.403415i
$339$	−11.5279	+	35.4791i	−0.626108	+	1.92696i
$340$	15.7082			0.851897
$341$	−0.118034	+	1.26133i	−0.00639190	+	0.0683047i
$342$	14.9443			0.808094
$343$	8.29180	−	25.5195i	0.447715	−	1.37792i
$344$	0.809017	−	0.587785i	0.0436193	−	0.0316913i
$345$	60.0689	+	43.6426i	3.23400	+	2.34964i
$346$	−2.02786	−	6.24112i	−0.109019	−	0.335525i
$347$	10.2705	+	31.6094i	0.551350	+	1.69688i	0.705393	+	0.708816i	$0.250770\pi$
$347$	10.2705	+	31.6094i	0.551350	+	1.69688i	−0.154043	+	0.988064i	$0.549230\pi$
$348$	−27.4164	−	19.9192i	−1.46967	−	1.06778i
$349$	0.145898	−	0.106001i	0.00780974	−	0.00567411i	−0.583874	−	0.811845i	$-0.698464\pi$
$349$	0.145898	−	0.106001i	0.00780974	−	0.00567411i	0.591683	+	0.806171i	$0.298464\pi$
$350$	7.56231	−	23.2744i	0.404222	−	1.24407i
$351$	−8.94427			−0.477410
$352$	−3.23607	+	0.726543i	−0.172483	+	0.0387248i
$353$	−8.03444			−0.427630			−0.213815	−	0.976874i	$-0.568589\pi$
$353$	−8.03444			−0.427630			−0.213815	+	0.976874i	$0.568589\pi$
$354$	4.32624	−	13.3148i	0.229937	−	0.707673i
$355$	−6.47214	+	4.70228i	−0.343505	+	0.249571i
$356$	−4.23607	−	3.07768i	−0.224511	−	0.163117i
$357$	−21.7082	−	66.8110i	−1.14892	−	3.53601i
$358$	−0.673762	−	2.07363i	−0.0356094	−	0.109595i
$359$	17.1074	+	12.4292i	0.902894	+	0.655991i	0.939208	−	0.343350i	$-0.111562\pi$
$359$	17.1074	+	12.4292i	0.902894	+	0.655991i	−0.0363140	+	0.999340i	$0.511562\pi$
$360$	19.5623	−	14.2128i	1.03102	−	0.749083i
$361$	−4.63525	+	14.2658i	−0.243961	+	0.750834i
$362$	21.5623			1.13329
$363$	−17.0902	+	31.2259i	−0.897001	+	1.63893i
$364$	−2.76393			−0.144869
$365$	1.52786	−	4.70228i	0.0799721	−	0.246129i
$366$	22.1803	−	16.1150i	1.15938	−	0.842342i
$367$	−11.9721	−	8.69827i	−0.624940	−	0.454046i	0.229703	−	0.973261i	$-0.426224\pi$
$367$	−11.9721	−	8.69827i	−0.624940	−	0.454046i	−0.854644	+	0.519215i	$0.826224\pi$
$368$	2.19098	+	6.74315i	0.114213	+	0.351511i
$369$	1.09017	+	3.35520i	0.0567520	+	0.174665i
$370$	−20.9443	−	15.2169i	−1.08884	−	0.791089i
$371$	49.9230	−	36.2712i	2.59187	−	1.88311i
$372$	0.381966	−	1.17557i	0.0198040	−	0.0609505i
$373$	−20.1803			−1.04490			−0.522449	−	0.852670i	$-0.674982\pi$
$373$	−20.1803			−1.04490			−0.522449	+	0.852670i	$0.674982\pi$
$374$	15.7082	−	3.52671i	0.812252	−	0.182362i
$375$	−4.94427			−0.255321
$376$	0.354102	−	1.08981i	0.0182614	−	0.0562029i
$377$	5.23607	−	3.80423i	0.269671	−	0.195928i
$378$	−52.3607	−	38.0423i	−2.69314	−	1.95668i
$379$	2.40983	+	7.41669i	0.123785	+	0.380970i	0.993678	−	0.112270i	$-0.0358123\pi$
$379$	2.40983	+	7.41669i	0.123785	+	0.380970i	−0.869893	+	0.493240i	$0.835812\pi$
$380$	−2.00000	−	6.15537i	−0.102598	−	0.315764i
$381$	−31.4164	−	22.8254i	−1.60951	−	1.16938i
$382$	10.8541	−	7.88597i	0.555344	−	0.403481i
$383$	4.94427	−	15.2169i	0.252640	−	0.777547i	−0.741645	−	0.670793i	$-0.765954\pi$
$383$	4.94427	−	15.2169i	0.252640	−	0.777547i	0.994285	−	0.106755i	$-0.0340460\pi$
$384$	3.23607			0.165140
$385$	4.47214	−	47.7899i	0.227921	−	2.43560i
$386$	16.8541			0.857851
$387$	−2.30902	+	7.10642i	−0.117374	+	0.361240i
$388$	−8.97214	+	6.51864i	−0.455491	+	0.330934i
$389$	12.0902	+	8.78402i	0.612996	+	0.445368i	0.850468	−	0.526027i	$-0.176319\pi$
$389$	12.0902	+	8.78402i	0.612996	+	0.445368i	−0.237472	+	0.971394i	$0.576319\pi$
$390$	2.00000	+	6.15537i	0.101274	+	0.311689i
$391$	−10.6353	−	32.7319i	−0.537848	−	1.65533i
$392$	−10.5172	−	7.64121i	−0.531200	−	0.385939i
$393$	−2.76393	+	2.00811i	−0.139422	+	0.101296i
$394$	5.51722	−	16.9803i	0.277954	−	0.855453i
$395$	6.76393			0.340330
$396$	16.3713	−	18.6049i	0.822690	−	0.934929i
$397$	−1.79837			−0.0902578			−0.0451289	−	0.998981i	$-0.514370\pi$
$397$	−1.79837			−0.0902578			−0.0451289	+	0.998981i	$0.514370\pi$
$398$	−6.00000	+	18.4661i	−0.300753	+	0.925622i
$399$	−23.4164	+	17.0130i	−1.17229	+	0.851716i
$400$	−4.42705	−	3.21644i	−0.221353	−	0.160822i
$401$	−5.68034	−	17.4823i	−0.283663	−	0.873024i	−0.986796	−	0.161966i	$-0.948216\pi$
$401$	−5.68034	−	17.4823i	−0.283663	−	0.873024i	0.703134	−	0.711058i	$-0.251784\pi$
$402$	4.32624	+	13.3148i	0.215773	+	0.664081i
$403$	0.190983	+	0.138757i	0.00951354	+	0.00691199i
$404$	1.73607	−	1.26133i	0.0863726	−	0.0627534i
$405$	−24.4164	+	75.1460i	−1.21326	+	3.73403i
$406$	46.8328			2.32427
$407$	−24.3607	−	10.5146i	−1.20751	−	0.521190i
$408$	−15.7082			−0.777672
$409$	4.14590	−	12.7598i	0.205001	−	0.630930i	−0.794712	−	0.606987i	$-0.792378\pi$
$409$	4.14590	−	12.7598i	0.205001	−	0.630930i	0.999713	−	0.0239428i	$-0.00762195\pi$
$410$	1.23607	−	0.898056i	0.0610450	−	0.0443518i
$411$	59.3050	+	43.0876i	2.92530	+	2.12535i
$412$	−0.173762	−	0.534785i	−0.00856064	−	0.0263470i
$413$	5.97871	+	18.4006i	0.294193	+	0.905434i
$414$	−42.8607	−	31.1401i	−2.10649	−	1.53045i
$415$	1.00000	−	0.726543i	0.0490881	−	0.0356646i
$416$	−0.190983	+	0.587785i	−0.00936371	+	0.0288185i
$417$	65.7771			3.22112
$418$	−3.38197	−	5.70634i	−0.165417	−	0.279106i
$419$	−37.8885			−1.85098			−0.925488	−	0.378776i	$-0.876345\pi$
$419$	−37.8885			−1.85098			−0.925488	+	0.378776i	$0.876345\pi$
$420$	−14.4721	+	44.5407i	−0.706168	+	2.17336i
$421$	−5.85410	+	4.25325i	−0.285311	+	0.207291i	−0.721231	−	0.692695i	$-0.756423\pi$
$421$	−5.85410	+	4.25325i	−0.285311	+	0.207291i	0.435919	+	0.899986i	$0.356423\pi$
$422$	−15.9443	−	11.5842i	−0.776155	−	0.563910i
$423$	2.64590	+	8.14324i	0.128648	+	0.395938i
$424$	−4.26393	−	13.1230i	−0.207075	−	0.637311i
$425$	21.4894	+	15.6129i	1.04239	+	0.757338i
$426$	6.47214	−	4.70228i	0.313576	−	0.227826i
$427$	−11.7082	+	36.0341i	−0.566600	+	1.74381i
$428$	−3.09017			−0.149369
$429$	3.38197	+	5.70634i	0.163283	+	0.275505i
$430$	3.23607			0.156057
$431$	4.28115	−	13.1760i	0.206216	−	0.634667i	−0.793445	−	0.608641i	$-0.791715\pi$
$431$	4.28115	−	13.1760i	0.206216	−	0.634667i	0.999661	−	0.0260258i	$-0.00828520\pi$
$432$	−11.7082	+	8.50651i	−0.563311	+	0.409270i
$433$	3.47214	+	2.52265i	0.166860	+	0.121231i	0.668082	−	0.744088i	$-0.267116\pi$
$433$	3.47214	+	2.52265i	0.166860	+	0.121231i	−0.501221	+	0.865319i	$0.667116\pi$
$434$	0.527864	+	1.62460i	0.0253383	+	0.0779832i
$435$	−33.8885	−	104.298i	−1.62483	−	5.00072i
$436$	−3.30902	−	2.40414i	−0.158473	−	0.115137i
$437$	−11.4721	+	8.33499i	−0.548787	+	0.398717i
$438$	−1.52786	+	4.70228i	−0.0730042	+	0.224684i
$439$	23.2148			1.10798			0.553991	−	0.832523i	$-0.313104\pi$
$439$	23.2148			1.10798			0.553991	+	0.832523i	$0.313104\pi$
$440$	−9.85410	−	4.25325i	−0.469776	−	0.202766i
$441$	97.1378			4.62561
$442$	0.927051	−	2.85317i	0.0440953	−	0.135711i
$443$	18.6353	−	13.5393i	0.885388	−	0.643272i	−0.0492836	−	0.998785i	$-0.515694\pi$
$443$	18.6353	−	13.5393i	0.885388	−	0.643272i	0.934671	+	0.355513i	$0.115694\pi$
$444$	20.9443	+	15.2169i	0.993971	+	0.722162i
$445$	−5.23607	−	16.1150i	−0.248213	−	0.763922i
$446$	4.38197	+	13.4863i	0.207492	+	0.638595i
$447$	29.8885	+	21.7153i	1.41368	+	1.02710i
$448$	−3.61803	+	2.62866i	−0.170936	+	0.124192i
$449$	3.70820	−	11.4127i	0.175001	−	0.538598i	−0.824633	−	0.565669i	$-0.808618\pi$
$449$	3.70820	−	11.4127i	0.175001	−	0.538598i	0.999634	+	0.0270712i	$0.00861808\pi$
$450$	40.8885			1.92750
$451$	1.03444	−	1.17557i	0.0487100	−	0.0553555i
$452$	−11.5279			−0.542225
$453$	10.2918	−	31.6749i	0.483551	−	1.48822i
$454$	6.09017	−	4.42477i	0.285826	−	0.207665i
$455$	−7.23607	−	5.25731i	−0.339232	−	0.246467i
$456$	2.00000	+	6.15537i	0.0936586	+	0.288251i
$457$	7.23607	+	22.2703i	0.338489	+	1.04176i	0.964978	+	0.262332i	$0.0844914\pi$
$457$	7.23607	+	22.2703i	0.338489	+	1.04176i	−0.626489	+	0.779430i	$0.715509\pi$
$458$	17.2082	+	12.5025i	0.804087	+	0.584203i
$459$	56.8328	−	41.2915i	2.65273	−	1.92732i
$460$	−7.09017	+	21.8213i	−0.330581	+	1.01742i
$461$	−33.8541			−1.57674			−0.788371	−	0.615200i	$-0.789075\pi$
$461$	−33.8541			−1.57674			−0.788371	+	0.615200i	$0.789075\pi$
$462$	−4.47214	+	47.7899i	−0.208063	+	2.22339i
$463$	−27.4164			−1.27415			−0.637074	−	0.770802i	$-0.719856\pi$
$463$	−27.4164			−1.27415			−0.637074	+	0.770802i	$0.719856\pi$
$464$	3.23607	−	9.95959i	0.150231	−	0.462363i
$465$	3.23607	−	2.35114i	0.150069	−	0.109032i
$466$	5.09017	+	3.69822i	0.235798	+	0.171317i
$467$	−11.0902	−	34.1320i	−0.513192	−	1.57944i	−0.786548	−	0.617529i	$-0.788134\pi$
$467$	−11.0902	−	34.1320i	−0.513192	−	1.57944i	0.273356	−	0.961913i	$-0.411866\pi$
$468$	−1.42705	−	4.39201i	−0.0659655	−	0.203021i
$469$	−15.6525	−	11.3722i	−0.722764	−	0.525119i
$470$	3.00000	−	2.17963i	0.138380	−	0.100539i
$471$	4.94427	−	15.2169i	0.227820	−	0.701158i
$472$	4.32624			0.199131
$473$	3.23607	−	0.726543i	0.148795	−	0.0334065i
$474$	−6.76393			−0.310678
$475$	3.38197	−	10.4086i	0.155175	−	0.477580i
$476$	17.5623	−	12.7598i	0.804967	−	0.584843i
$477$	83.4123	+	60.6026i	3.81919	+	2.77480i
$478$	5.22542	+	16.0822i	0.239005	+	0.735583i
$479$	5.60739	+	17.2578i	0.256208	+	0.788528i	0.993589	+	0.113051i	$0.0360623\pi$
$479$	5.60739	+	17.2578i	0.256208	+	0.788528i	−0.737381	+	0.675477i	$0.763938\pi$
$480$	8.47214	+	6.15537i	0.386698	+	0.280953i
$481$	−4.00000	+	2.90617i	−0.182384	+	0.132510i
$482$	−5.47214	+	16.8415i	−0.249249	+	0.767109i
$483$	102.610			4.66891
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$	−35.8885			−1.62961
$486$	11.0000	−	33.8545i	0.498970	−	1.53567i
$487$	17.9164	−	13.0170i	0.811870	−	0.589858i	−0.102502	−	0.994733i	$-0.532685\pi$
$487$	17.9164	−	13.0170i	0.811870	−	0.589858i	0.914372	+	0.404875i	$0.132685\pi$
$488$	6.85410	+	4.97980i	0.310271	+	0.225425i
$489$	−10.4721	−	32.2299i	−0.473566	−	1.45749i
$490$	−13.0000	−	40.0099i	−0.587280	−	1.80746i
$491$	9.56231	+	6.94742i	0.431541	+	0.313533i	0.782265	−	0.622946i	$-0.214064\pi$
$491$	9.56231	+	6.94742i	0.431541	+	0.313533i	−0.350724	+	0.936479i	$0.614064\pi$
$492$	−1.23607	+	0.898056i	−0.0557262	+	0.0404875i
$493$	−15.7082	+	48.3449i	−0.707462	+	2.17734i
$494$	−1.23607			−0.0556133
$495$	78.2492	−	17.5680i	3.51704	−	0.789625i
$496$	0.381966			0.0171508
$497$	−3.41641	+	10.5146i	−0.153247	+	0.471645i
$498$	−1.00000	+	0.726543i	−0.0448111	+	0.0325571i
$499$	26.5623	+	19.2986i	1.18909	+	0.863926i	0.993168	−	0.116693i	$-0.0372294\pi$
$499$	26.5623	+	19.2986i	1.18909	+	0.863926i	0.195924	+	0.980619i	$0.437229\pi$
$500$	−0.472136	−	1.45309i	−0.0211146	−	0.0649839i
$501$	12.0344	+	37.0382i	0.537659	+	1.65474i
$502$	−12.1631	−	8.83702i	−0.542867	−	0.394416i
$503$	32.5066	−	23.6174i	1.44940	−	1.05305i	0.463425	−	0.886136i	$-0.346620\pi$
$503$	32.5066	−	23.6174i	1.44940	−	1.05305i	0.985972	−	0.166912i	$-0.0533796\pi$
$504$	10.3262	−	31.7809i	0.459967	−	1.41563i
$505$	6.94427			0.309016
$506$	−2.19098	+	23.4131i	−0.0974011	+	1.04084i
$507$	−40.8328			−1.81345
$508$	3.70820	−	11.4127i	0.164525	−	0.506356i
$509$	−24.6803	+	17.9313i	−1.09394	+	0.794792i	−0.980060	−	0.198703i	$-0.936327\pi$
$509$	−24.6803	+	17.9313i	−1.09394	+	0.794792i	−0.113877	+	0.993495i	$0.536327\pi$
$510$	−41.1246	−	29.8788i	−1.82103	−	1.32305i
$511$	−2.11146	−	6.49839i	−0.0934053	−	0.287472i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−23.4164	−	17.0130i	−1.03386	−	0.751143i
$514$	12.4721	−	9.06154i	0.550122	−	0.399687i
$515$	0.562306	−	1.73060i	0.0247782	−	0.0762593i
$516$	−3.23607			−0.142460
$517$	2.51064	−	2.85317i	0.110418	−	0.125482i
$518$	−35.7771			−1.57195
$519$	−6.56231	+	20.1967i	−0.288053	+	0.886537i
$520$	−1.61803	+	1.17557i	−0.0709555	+	0.0515522i
$521$	−11.7984	−	8.57202i	−0.516896	−	0.375547i	0.298537	−	0.954398i	$-0.403501\pi$
$521$	−11.7984	−	8.57202i	−0.516896	−	0.375547i	−0.815433	+	0.578851i	$0.803501\pi$
$522$	24.1803	+	74.4194i	1.05834	+	3.25725i
$523$	0.201626	+	0.620541i	0.00881649	+	0.0271344i	0.955368	−	0.295418i	$-0.0954590\pi$
$523$	0.201626	+	0.620541i	0.00881649	+	0.0271344i	−0.946551	+	0.322553i	$0.895459\pi$
$524$	−0.854102	−	0.620541i	−0.0373116	−	0.0271085i
$525$	−64.0689	+	46.5488i	−2.79620	+	2.03155i
$526$	−7.38197	+	22.7194i	−0.321869	+	0.990611i
$527$	−1.85410			−0.0807660
$528$	9.85410	+	4.25325i	0.428845	+	0.185099i
$529$	27.2705			1.18567
$530$	13.7984	−	42.4670i	0.599363	−	1.84465i
$531$	−26.1525	+	19.0009i	−1.13492	+	0.824568i
$532$	−7.23607	−	5.25731i	−0.313723	−	0.227933i
$533$	−0.0901699	−	0.277515i	−0.00390569	−	0.0120205i
$534$	5.23607	+	16.1150i	0.226587	+	0.697363i
$535$	−8.09017	−	5.87785i	−0.349769	−	0.254122i
$536$	−3.50000	+	2.54290i	−0.151177	+	0.109837i
$537$	−2.18034	+	6.71040i	−0.0940886	+	0.289575i
$538$	−12.2705			−0.529019
$539$	−21.9828	−	37.0912i	−0.946865	−	1.59763i
$540$	−46.8328			−2.01536
$541$	9.27051	−	28.5317i	0.398570	−	1.22667i	−0.527576	−	0.849508i	$-0.676899\pi$
$541$	9.27051	−	28.5317i	0.398570	−	1.22667i	0.926146	−	0.377165i	$-0.123101\pi$
$542$	−13.8713	+	10.0781i	−0.595824	+	0.432892i
$543$	−56.4508	−	41.0139i	−2.42254	−	1.76008i
$544$	−1.50000	−	4.61653i	−0.0643120	−	0.197932i
$545$	−4.09017	−	12.5882i	−0.175204	−	0.539221i
$546$	7.23607	+	5.25731i	0.309675	+	0.224992i
$547$	−3.39919	+	2.46965i	−0.145339	+	0.105595i	−0.658079	−	0.752949i	$-0.728631\pi$
$547$	−3.39919	+	2.46965i	−0.145339	+	0.105595i	0.512740	+	0.858544i	$0.328631\pi$
$548$	−7.00000	+	21.5438i	−0.299025	+	0.920305i
$549$	−63.3050			−2.70179
$550$	−9.25329	−	15.6129i	−0.394562	−	0.665738i
$551$	20.9443			0.892256
$552$	7.09017	−	21.8213i	0.301778	−	0.928776i
$553$	7.56231	−	5.49434i	0.321582	−	0.233643i
$554$	18.7082	+	13.5923i	0.794835	+	0.577482i
$555$	25.8885	+	79.6767i	1.09891	+	3.38209i
$556$	6.28115	+	19.3314i	0.266380	+	0.819834i
$557$	28.5623	+	20.7517i	1.21022	+	0.879279i	0.995251	−	0.0973411i	$-0.0310338\pi$
$557$	28.5623	+	20.7517i	1.21022	+	0.879279i	0.214973	+	0.976620i	$0.431034\pi$
$558$	−2.30902	+	1.67760i	−0.0977485	+	0.0710184i
$559$	0.190983	−	0.587785i	0.00807772	−	0.0248607i
$560$	−14.4721			−0.611559
$561$	−47.8328	−	20.6457i	−2.01950	−	0.871663i
$562$	2.14590			0.0905192
$563$	−3.71885	+	11.4454i	−0.156731	+	0.482368i	−0.998332	−	0.0577316i	$-0.981613\pi$
$563$	−3.71885	+	11.4454i	−0.156731	+	0.482368i	0.841601	+	0.540099i	$0.181613\pi$
$564$	−3.00000	+	2.17963i	−0.126323	+	0.0917789i
$565$	−30.1803	−	21.9273i	−1.26970	−	0.922488i
$566$	6.18034	+	19.0211i	0.259779	+	0.799518i
$567$	33.7426	+	103.849i	1.41706	+	4.36126i
$568$	2.00000	+	1.45309i	0.0839181	+	0.0609701i
$569$	−0.690983	+	0.502029i	−0.0289675	+	0.0210461i	−0.602175	−	0.798364i	$-0.705699\pi$
$569$	−0.690983	+	0.502029i	−0.0289675	+	0.0210461i	0.573207	+	0.819410i	$0.305699\pi$
$570$	−6.47214	+	19.9192i	−0.271088	+	0.834323i
$571$	5.52786			0.231334			0.115667	−	0.993288i	$-0.463099\pi$
$571$	5.52786			0.231334			0.115667	+	0.993288i	$0.463099\pi$
$572$	−1.35410	+	1.53884i	−0.0566178	+	0.0643422i
$573$	−43.4164			−1.81375
$574$	0.652476	−	2.00811i	0.0272338	−	0.0838171i
$575$	−31.3885	+	22.8051i	−1.30899	+	0.951039i
$576$	−6.04508	−	4.39201i	−0.251879	−	0.183000i
$577$	−3.50658	−	10.7921i	−0.145981	−	0.449283i	0.851155	−	0.524914i	$-0.175903\pi$
$577$	−3.50658	−	10.7921i	−0.145981	−	0.449283i	−0.997136	+	0.0756318i	$0.975903\pi$
$578$	2.02786	+	6.24112i	0.0843480	+	0.259597i
$579$	−44.1246	−	32.0584i	−1.83376	−	1.33230i
$580$	27.4164	−	19.9192i	1.13840	−	0.827099i
$581$	0.527864	−	1.62460i	0.0218995	−	0.0673997i
$582$	35.8885			1.48763
$583$	4.26393	−	45.5650i	0.176594	−	1.88711i
$584$	−1.52786			−0.0632235
$585$	4.61803	−	14.2128i	0.190932	−	0.587629i
$586$	14.8541	−	10.7921i	0.613617	−	0.445819i
$587$	−6.32624	−	4.59628i	−0.261112	−	0.189709i	0.449525	−	0.893268i	$-0.351593\pi$
$587$	−6.32624	−	4.59628i	−0.261112	−	0.189709i	−0.710637	+	0.703559i	$0.751593\pi$
$588$	13.0000	+	40.0099i	0.536111	+	1.64998i
$589$	0.236068	+	0.726543i	0.00972701	+	0.0299367i
$590$	11.3262	+	8.22899i	0.466294	+	0.338782i
$591$	−46.7426	+	33.9605i	−1.92274	+	1.39695i
$592$	−2.47214	+	7.60845i	−0.101604	+	0.312705i
$593$	8.76393			0.359892			0.179946	−	0.983677i	$-0.442408\pi$
$593$	8.76393			0.359892			0.179946	+	0.983677i	$0.442408\pi$
$594$	−46.8328	+	10.5146i	−1.92157	+	0.431420i
$595$	70.2492			2.87994
$596$	−3.52786	+	10.8576i	−0.144507	+	0.444747i
$597$	50.8328	−	36.9322i	2.08045	−	1.51153i
$598$	3.54508	+	2.57565i	0.144969	+	0.105326i
$599$	−4.66312	−	14.3516i	−0.190530	−	0.586391i	0.809470	−	0.587161i	$-0.199755\pi$
$599$	−4.66312	−	14.3516i	−0.190530	−	0.586391i	−1.00000		0.000770814i	$0.999755\pi$
$600$	5.47214	+	16.8415i	0.223399	+	0.687551i
$601$	−1.38197	−	1.00406i	−0.0563716	−	0.0409563i	0.559243	−	0.829004i	$-0.311092\pi$
$601$	−1.38197	−	1.00406i	−0.0563716	−	0.0409563i	−0.615614	+	0.788048i	$0.711092\pi$
$602$	3.61803	−	2.62866i	0.147460	−	0.107136i
$603$	9.98936	−	30.7441i	0.406798	−	1.25200i
$604$	10.2918			0.418767
$605$	−24.4164	−	25.9030i	−0.992668	−	1.05311i
$606$	−6.94427			−0.282092
$607$	−13.1803	+	40.5649i	−0.534973	+	1.64648i	0.208733	+	0.977973i	$0.433066\pi$
$607$	−13.1803	+	40.5649i	−0.534973	+	1.64648i	−0.743706	+	0.668506i	$0.766934\pi$
$608$	−1.61803	+	1.17557i	−0.0656199	+	0.0476757i
$609$	−122.610	−	89.0813i	−4.96840	−	3.60976i
$610$	8.47214	+	26.0746i	0.343027	+	1.05573i
$611$	−0.218847	−	0.673542i	−0.00885360	−	0.0272486i
$612$	29.3435	+	21.3193i	1.18614	+	0.861780i
$613$	−5.92705	+	4.30625i	−0.239391	+	0.173928i	−0.701012	−	0.713149i	$-0.747268\pi$
$613$	−5.92705	+	4.30625i	−0.239391	+	0.173928i	0.461621	+	0.887077i	$0.347268\pi$
$614$	3.35410	−	10.3229i	0.135361	−	0.416597i
$615$	−4.94427			−0.199372
$616$	−14.4721	+	3.24920i	−0.583099	+	0.130914i
$617$	39.1033			1.57424			0.787120	−	0.616800i	$-0.211571\pi$
$617$	39.1033			1.57424			0.787120	+	0.616800i	$0.211571\pi$
$618$	−0.562306	+	1.73060i	−0.0226193	+	0.0696149i
$619$	8.63525	−	6.27388i	0.347080	−	0.252169i	−0.400563	−	0.916269i	$-0.631185\pi$
$619$	8.63525	−	6.27388i	0.347080	−	0.252169i	0.747643	+	0.664101i	$0.231185\pi$
$620$	1.00000	+	0.726543i	0.0401610	+	0.0291787i
$621$	31.7082	+	97.5878i	1.27241	+	3.91606i
$622$	4.57295	+	14.0741i	0.183359	+	0.564320i
$623$	−18.9443	−	13.7638i	−0.758986	−	0.551436i
$624$	1.61803	−	1.17557i	0.0647732	−	0.0470605i
$625$	−6.92705	+	21.3193i	−0.277082	+	0.852771i
$626$	−4.00000			−0.159872
$627$	−2.00000	+	21.3723i	−0.0798723	+	0.853526i
$628$	4.94427			0.197298
$629$	12.0000	−	36.9322i	0.478471	−	1.47258i
$630$	87.4853	−	63.5618i	3.48550	−	2.53236i
$631$	19.7984	+	14.3844i	0.788161	+	0.572632i	0.907417	−	0.420231i	$-0.138051\pi$
$631$	19.7984	+	14.3844i	0.788161	+	0.572632i	−0.119256	+	0.992864i	$0.538051\pi$
$632$	−0.645898	−	1.98787i	−0.0256924	−	0.0790732i
$633$	19.7082	+	60.6556i	0.783331	+	2.41084i
$634$	8.54508	+	6.20837i	0.339369	+	0.246566i
$635$	31.4164	−	22.8254i	1.24672	−	0.905797i
$636$	−13.7984	+	42.4670i	−0.547141	+	1.68393i
$637$	−8.03444			−0.318336
$638$	22.9443	−	26.0746i	0.908372	−	1.03230i
$639$	−18.4721			−0.730746
$640$	−1.00000	+	3.07768i	−0.0395285	+	0.121656i
$641$	−36.6525	+	26.6296i	−1.44769	+	1.05181i	−0.461321	+	0.887233i	$0.652624\pi$
$641$	−36.6525	+	26.6296i	−1.44769	+	1.05181i	−0.986365	+	0.164572i	$0.947376\pi$
$642$	8.09017	+	5.87785i	0.319294	+	0.231980i
$643$	4.11803	+	12.6740i	0.162399	+	0.499814i	0.998835	−	0.0482509i	$-0.0153647\pi$
$643$	4.11803	+	12.6740i	0.162399	+	0.499814i	−0.836436	+	0.548065i	$0.815365\pi$
$644$	9.79837	+	30.1563i	0.386110	+	1.18832i
$645$	−8.47214	−	6.15537i	−0.333590	−	0.242367i
$646$	7.85410	−	5.70634i	0.309016	−	0.224513i
$647$	−11.2361	+	34.5811i	−0.441735	+	1.35952i	0.444289	+	0.895883i	$0.353456\pi$
$647$	−11.2361	+	34.5811i	−0.441735	+	1.35952i	−0.886025	+	0.463638i	$0.846544\pi$
$648$	24.4164			0.959167
$649$	13.1738	+	5.68609i	0.517115	+	0.223199i
$650$	−3.38197			−0.132652
$651$	1.70820	−	5.25731i	0.0669498	−	0.206050i
$652$	8.47214	−	6.15537i	0.331794	−	0.241063i
$653$	15.5623	+	11.3067i	0.609000	+	0.442464i	0.849062	−	0.528293i	$-0.177168\pi$
$653$	15.5623	+	11.3067i	0.609000	+	0.442464i	−0.240062	+	0.970758i	$0.577168\pi$
$654$	4.09017	+	12.5882i	0.159938	+	0.492239i
$655$	−1.05573	−	3.24920i	−0.0412507	−	0.126957i
$656$	−0.381966	−	0.277515i	−0.0149133	−	0.0108351i
$657$	9.23607	−	6.71040i	0.360333	−	0.261797i
$658$	1.58359	−	4.87380i	0.0617348	−	0.190000i
$659$	7.96556			0.310294			0.155147	−	0.987891i	$-0.450415\pi$
$659$	7.96556			0.310294			0.155147	+	0.987891i	$0.450415\pi$
$660$	17.7082	+	29.8788i	0.689291	+	1.16303i
$661$	−32.0344			−1.24600			−0.622998	−	0.782224i	$-0.714085\pi$
$661$	−32.0344			−1.24600			−0.622998	+	0.782224i	$0.714085\pi$
$662$	−6.76393	+	20.8172i	−0.262888	+	0.809085i
$663$	−7.85410	+	5.70634i	−0.305028	+	0.221616i
$664$	−0.309017	−	0.224514i	−0.0119922	−	0.00871283i
$665$	−8.94427	−	27.5276i	−0.346844	−	1.06748i
$666$	−18.4721	−	56.8514i	−0.715781	−	2.20295i
$667$	−60.0689	−	43.6426i	−2.32588	−	1.68985i
$668$	−9.73607	+	7.07367i	−0.376700	+	0.273688i
$669$	14.1803	−	43.6426i	0.548244	−	1.68732i
$670$	−14.0000			−0.540867
$671$	14.3262	+	24.1724i	0.553058	+	0.933167i
$672$	14.4721			0.558275
$673$	−1.81966	+	5.60034i	−0.0701427	+	0.215877i	−0.979983	−	0.199082i	$-0.936204\pi$
$673$	−1.81966	+	5.60034i	−0.0701427	+	0.215877i	0.909840	+	0.414959i	$0.136204\pi$
$674$	−19.6803	+	14.2986i	−0.758058	+	0.550762i
$675$	−64.0689	−	46.5488i	−2.46601	−	1.79166i
$676$	−3.89919	−	12.0005i	−0.149969	−	0.461556i
$677$	8.52786	+	26.2461i	0.327752	+	1.00872i	0.970183	+	0.242374i	$0.0779262\pi$
$677$	8.52786	+	26.2461i	0.327752	+	1.00872i	−0.642430	+	0.766344i	$0.722074\pi$
$678$	30.1803	+	21.9273i	1.15907	+	0.842113i
$679$	−40.1246	+	29.1522i	−1.53984	+	1.11876i
$680$	4.85410	−	14.9394i	0.186146	−	0.572899i
$681$	−24.3607			−0.933503
$682$	1.16312	+	0.502029i	0.0445381	+	0.0192237i
$683$	−11.7984			−0.451452			−0.225726	−	0.974191i	$-0.572475\pi$
$683$	−11.7984			−0.451452			−0.225726	+	0.974191i	$0.572475\pi$
$684$	4.61803	−	14.2128i	0.176575	−	0.543442i
$685$	−59.3050	+	43.0876i	−2.26593	+	1.64629i
$686$	−21.7082	−	15.7719i	−0.828823	−	0.602175i
$687$	−21.2705	−	65.4639i	−0.811521	−	2.49760i
$688$	−0.309017	−	0.951057i	−0.0117812	−	0.0362587i
$689$	−6.89919	−	5.01255i	−0.262838	−	0.190963i
$690$	60.0689	−	43.6426i	2.28678	−	1.66145i
$691$	12.8885	−	39.6669i	0.490303	−	1.50900i	−0.333847	−	0.942627i	$-0.608347\pi$
$691$	12.8885	−	39.6669i	0.490303	−	1.50900i	0.824150	−	0.566371i	$-0.191653\pi$
$692$	−6.56231			−0.249461
$693$	73.2148	−	83.2035i	2.78120	−	3.16064i
$694$	33.2361			1.26162
$695$	−20.3262	+	62.5577i	−0.771018	+	2.37295i
$696$	−27.4164	+	19.9192i	−1.03922	+	0.755035i
$697$	1.85410	+	1.34708i	0.0702291	+	0.0510244i
$698$	−0.0557281	−	0.171513i	−0.00210934	−	0.00649188i
$699$	−6.29180	−	19.3642i	−0.237978	−	0.732420i
$700$	−19.7984	−	14.3844i	−0.748308	−	0.543678i
$701$	7.16312	−	5.20431i	0.270547	−	0.196564i	−0.444237	−	0.895909i	$-0.646525\pi$
$701$	7.16312	−	5.20431i	0.270547	−	0.196564i	0.714784	+	0.699345i	$0.246525\pi$
$702$	−2.76393	+	8.50651i	−0.104318	+	0.321057i
$703$	−16.0000			−0.603451
$704$	−0.309017	+	3.30220i	−0.0116465	+	0.124456i
$705$	−12.0000			−0.451946
$706$	−2.48278	+	7.64121i	−0.0934406	+	0.287581i
$707$	7.76393	−	5.64083i	0.291993	−	0.212145i
$708$	−11.3262	−	8.22899i	−0.425666	−	0.309265i
$709$	1.33688	+	4.11450i	0.0502076	+	0.154523i	0.973017	−	0.230734i	$-0.0741127\pi$
$709$	1.33688	+	4.11450i	0.0502076	+	0.154523i	−0.922809	+	0.385257i	$0.874113\pi$
$710$	2.47214	+	7.60845i	0.0927776	+	0.285540i
$711$	12.6353	+	9.18005i	0.473859	+	0.344279i
$712$	−4.23607	+	3.07768i	−0.158753	+	0.115341i
$713$	0.836881	−	2.57565i	0.0313414	−	0.0964590i
$714$	−70.2492			−2.62901
$715$	−6.47214	+	1.45309i	−0.242044	+	0.0543423i
$716$	−2.18034			−0.0814831
$717$	16.9098	−	52.0431i	0.631509	−	1.94359i
$718$	17.1074	−	12.4292i	0.638442	−	0.463855i
$719$	−29.1525	−	21.1805i	−1.08720	−	0.789900i	−0.108279	−	0.994121i	$-0.534534\pi$
$719$	−29.1525	−	21.1805i	−1.08720	−	0.789900i	−0.978925	+	0.204221i	$0.934534\pi$
$720$	−7.47214	−	22.9969i	−0.278470	−	0.857043i
$721$	−0.777088	−	2.39163i	−0.0289403	−	0.0890689i
$722$	12.1353	+	8.81678i	0.451627	+	0.328127i
$723$	46.3607	−	33.6830i	1.72417	−	1.25268i
$724$	6.66312	−	20.5070i	0.247633	−	0.762136i
$725$	57.3050			2.12825
$726$	24.4164	+	25.9030i	0.906178	+	0.961352i
$727$	−15.5279			−0.575897			−0.287948	−	0.957646i	$-0.592973\pi$
$727$	−15.5279			−0.575897			−0.287948	+	0.957646i	$0.592973\pi$
$728$	−0.854102	+	2.62866i	−0.0316551	+	0.0974245i
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	−4.00000	−	2.90617i	−0.148047	−	0.107562i
$731$	1.50000	+	4.61653i	0.0554795	+	0.170748i
$732$	−8.47214	−	26.0746i	−0.313139	−	0.963743i
$733$	2.14590	+	1.55909i	0.0792606	+	0.0575862i	0.626710	−	0.779253i	$-0.284401\pi$
$733$	2.14590	+	1.55909i	0.0792606	+	0.0575862i	−0.547449	+	0.836839i	$0.684401\pi$
$734$	−11.9721	+	8.69827i	−0.441900	+	0.321059i
$735$	−42.0689	+	129.475i	−1.55173	+	4.77575i
$736$	7.09017			0.261347
$737$	−14.0000	+	3.14320i	−0.515697	+	0.115781i
$738$	3.52786			0.129862
$739$	−13.4377	+	41.3570i	−0.494314	+	1.52134i	0.323710	+	0.946156i	$0.395070\pi$
$739$	−13.4377	+	41.3570i	−0.494314	+	1.52134i	−0.818024	+	0.575184i	$0.804930\pi$
$740$	−20.9443	+	15.2169i	−0.769927	+	0.559385i
$741$	3.23607	+	2.35114i	0.118880	+	0.0863713i
$742$	−19.0689	−	58.6880i	−0.700041	−	2.15450i
$743$	−9.61803	−	29.6013i	−0.352851	−	1.08597i	−0.957245	−	0.289279i	$-0.906584\pi$
$743$	−9.61803	−	29.6013i	−0.352851	−	1.08597i	0.604393	−	0.796686i	$-0.293416\pi$
$744$	−1.00000	−	0.726543i	−0.0366618	−	0.0266363i
$745$	−29.8885	+	21.7153i	−1.09503	+	0.795587i
$746$	−6.23607	+	19.1926i	−0.228319	+	0.702693i
$747$	2.85410			0.104426
$748$	1.50000	−	16.0292i	0.0548454	−	0.586086i
$749$	−13.8197			−0.504959
$750$	−1.52786	+	4.70228i	−0.0557897	+	0.171703i
$751$	4.47214	−	3.24920i	0.163191	−	0.118565i	−0.503193	−	0.864174i	$-0.667841\pi$
$751$	4.47214	−	3.24920i	0.163191	−	0.118565i	0.666383	+	0.745609i	$0.267841\pi$
$752$	−0.927051	−	0.673542i	−0.0338061	−	0.0245615i
$753$	15.0344	+	46.2713i	0.547886	+	1.68622i
$754$	−2.00000	−	6.15537i	−0.0728357	−	0.224165i
$755$	26.9443	+	19.5762i	0.980602	+	0.712449i
$756$	−52.3607	+	38.0423i	−1.90434	+	1.38358i
$757$	−0.888544	+	2.73466i	−0.0322947	+	0.0993928i	−0.965905	−	0.258898i	$-0.916641\pi$
$757$	−0.888544	+	2.73466i	−0.0322947	+	0.0993928i	0.933610	+	0.358291i	$0.116641\pi$
$758$	7.79837			0.283250
$759$	50.2705	−	57.1289i	1.82470	−	2.07365i
$760$	−6.47214			−0.234769
$761$	−5.52786	+	17.0130i	−0.200385	+	0.616721i	0.799486	+	0.600684i	$0.205105\pi$
$761$	−5.52786	+	17.0130i	−0.200385	+	0.616721i	−0.999871	+	0.0160373i	$0.994895\pi$
$762$	−31.4164	+	22.8254i	−1.13810	+	0.826875i
$763$	−14.7984	−	10.7516i	−0.535737	−	0.389236i
$764$	−4.14590	−	12.7598i	−0.149993	−	0.461632i
$765$	36.2705	+	111.629i	1.31136	+	4.03596i
$766$	−12.9443	−	9.40456i	−0.467696	−	0.339801i
$767$	2.16312	−	1.57160i	0.0781057	−	0.0567471i
$768$	1.00000	−	3.07768i	0.0360844	−	0.111056i
$769$	39.3262			1.41814			0.709070	−	0.705138i	$-0.249115\pi$
$769$	39.3262			1.41814			0.709070	+	0.705138i	$0.249115\pi$
$770$	−44.0689	−	19.0211i	−1.58813	−	0.685474i
$771$	−49.8885			−1.79669
$772$	5.20820	−	16.0292i	0.187447	−	0.576904i
$773$	36.9787	−	26.8666i	1.33003	−	0.966325i	0.330284	−	0.943882i	$-0.392856\pi$
$773$	36.9787	−	26.8666i	1.33003	−	0.966325i	0.999748	−	0.0224430i	$-0.00714444\pi$
$774$	6.04508	+	4.39201i	0.217286	+	0.157868i
$775$	0.645898	+	1.98787i	0.0232013	+	0.0714064i
$776$	3.42705	+	10.5474i	0.123024	+	0.378629i
$777$	93.6656	+	68.0521i	3.36024	+	2.44135i
$778$	12.0902	−	8.78402i	0.433454	−	0.314922i
$779$	0.291796	−	0.898056i	0.0104547	−	0.0321762i
$780$	6.47214			0.231740
$781$	4.18034	+	7.05342i	0.149584	+	0.252391i
$782$	−34.4164			−1.23073
$783$	46.8328	−	144.137i	1.67367	−	5.15102i
$784$	−10.5172	+	7.64121i	−0.375615	+	0.272900i
$785$	12.9443	+	9.40456i	0.462001	+	0.335663i
$786$	1.05573	+	3.24920i	0.0376566	+	0.115895i
$787$	−4.07953	−	12.5555i	−0.145419	−	0.447555i	0.851645	−	0.524119i	$-0.175605\pi$
$787$	−4.07953	−	12.5555i	−0.145419	−	0.447555i	−0.997065	+	0.0765637i	$0.975605\pi$
$788$	−14.4443	−	10.4944i	−0.514556	−	0.373847i
$789$	62.5410	−	45.4387i	2.22652	−	1.61766i
$790$	2.09017	−	6.43288i	0.0743649	−	0.228872i
$791$	−51.5542			−1.83306
$792$	−12.6353	−	21.3193i	−0.448974	−	0.757547i
$793$	5.23607			0.185938
$794$	−0.555728	+	1.71036i	−0.0197221	+	0.0606982i
$795$	−116.902	+	84.9341i	−4.14608	+	3.01230i
$796$	15.7082	+	11.4127i	0.556763	+	0.404512i
$797$	14.8435	+	45.6835i	0.525782	+	1.61819i	0.762764	+	0.646677i	$0.223842\pi$
$797$	14.8435	+	45.6835i	0.525782	+	1.61819i	−0.236981	+	0.971514i	$0.576158\pi$
$798$	8.94427	+	27.5276i	0.316624	+	0.974468i
$799$	4.50000	+	3.26944i	0.159199	+	0.115665i
$800$	−4.42705	+	3.21644i	−0.156520	+	0.113718i
$801$	12.0902	−	37.2097i	0.427185	−	1.31474i
$802$	−18.3820			−0.649090
$803$	−4.65248	−	2.00811i	−0.164182	−	0.0708648i
$804$	14.0000			0.493742
$805$	−31.7082	+	97.5878i	−1.11757	+	3.43952i
$806$	0.190983	−	0.138757i	0.00672709	−	0.00488752i
$807$	32.1246	+	23.3399i	1.13084	+	0.821603i
$808$	−0.663119	−	2.04087i	−0.0233284	−	0.0717976i
$809$	−1.38197	−	4.25325i	−0.0485873	−	0.149536i	0.923819	−	0.382829i	$-0.125050\pi$
$809$	−1.38197	−	4.25325i	−0.0485873	−	0.149536i	−0.972407	+	0.233292i	$0.925050\pi$
$810$	63.9230	+	46.4428i	2.24602	+	1.63183i
$811$	17.2705	−	12.5478i	0.606450	−	0.440611i	−0.241713	−	0.970348i	$-0.577709\pi$
$811$	17.2705	−	12.5478i	0.606450	−	0.440611i	0.848162	+	0.529736i	$0.177709\pi$
$812$	14.4721	−	44.5407i	0.507872	−	1.56307i
$813$	55.4853			1.94595
$814$	−17.5279	+	19.9192i	−0.614351	+	0.698167i
$815$	33.8885			1.18706
$816$	−4.85410	+	14.9394i	−0.169928	+	0.522983i
$817$	1.61803	−	1.17557i	0.0566078	−	0.0411280i
$818$	−10.8541	−	7.88597i	−0.379505	−	0.275726i
$819$	−6.38197	−	19.6417i	−0.223004	−	0.686336i
$820$	−0.472136	−	1.45309i	−0.0164877	−	0.0507439i
$821$	28.7254	+	20.8702i	1.00252	+	0.728376i	0.962628	−	0.270827i	$-0.0872972\pi$
$821$	28.7254	+	20.8702i	1.00252	+	0.728376i	0.0398963	+	0.999204i	$0.487297\pi$
$822$	59.3050	−	43.0876i	2.06850	−	1.50285i
$823$	−9.46556	+	29.1320i	−0.329949	+	1.01548i	0.639208	+	0.769034i	$0.279262\pi$
$823$	−9.46556	+	29.1320i	−0.329949	+	1.01548i	−0.969157	+	0.246444i	$0.920738\pi$
$824$	−0.562306			−0.0195889
$825$	−5.47214	+	58.4760i	−0.190515	+	2.03587i
$826$	19.3475			0.673186
$827$	6.35410	−	19.5559i	0.220954	−	0.680026i	−0.777723	−	0.628607i	$-0.783626\pi$
$827$	6.35410	−	19.5559i	0.220954	−	0.680026i	0.998677	−	0.0514191i	$-0.0163744\pi$
$828$	−42.8607	+	31.1401i	−1.48951	+	1.08219i
$829$	26.1803	+	19.0211i	0.909281	+	0.660631i	0.940833	−	0.338871i	$-0.110045\pi$
$829$	26.1803	+	19.0211i	0.909281	+	0.660631i	−0.0315521	+	0.999502i	$0.510045\pi$
$830$	−0.381966	−	1.17557i	−0.0132582	−	0.0408046i
$831$	−23.1246	−	71.1702i	−0.802184	−	2.46887i
$832$	0.500000	+	0.363271i	0.0173344	+	0.0125942i
$833$	51.0517	−	37.0912i	1.76884	−	1.28513i
$834$	20.3262	−	62.5577i	0.703840	−	2.16620i
$835$	−38.9443			−1.34772
$836$	−6.47214	+	1.45309i	−0.223844	+	0.0502560i
$837$	5.52786			0.191071
$838$	−11.7082	+	36.0341i	−0.404453	+	1.24478i
$839$	−29.1803	+	21.2008i	−1.00742	+	0.731931i	−0.963666	−	0.267111i	$-0.913931\pi$
$839$	−29.1803	+	21.2008i	−1.00742	+	0.731931i	−0.0437514	+	0.999042i	$0.513931\pi$
$840$	37.8885	+	27.5276i	1.30728	+	0.949794i
$841$	24.9271	+	76.7176i	0.859553	+	2.64543i
$842$	2.23607	+	6.88191i	0.0770600	+	0.237166i
$843$	−5.61803	−	4.08174i	−0.193495	−	0.140583i
$844$	−15.9443	+	11.5842i	−0.548824	+	0.398744i
$845$	12.6180	−	38.8343i	0.434074	−	1.33594i
$846$	8.56231			0.294378
$847$	−48.3394	−	9.12705i	−1.66096	−	0.313609i
$848$	−13.7984			−0.473838
$849$	20.0000	−	61.5537i	0.686398	−	2.11252i
$850$	21.4894	−	15.6129i	0.737079	−	0.535519i
$851$	45.8885	+	33.3400i	1.57304	+	1.14288i
$852$	−2.47214	−	7.60845i	−0.0846940	−	0.260661i
$853$	−4.43769	−	13.6578i	−0.151944	−	0.467635i	0.845895	−	0.533350i	$-0.179067\pi$
$853$	−4.43769	−	13.6578i	−0.151944	−	0.467635i	−0.997838	+	0.0657152i	$0.979067\pi$
$854$	30.6525	+	22.2703i	1.04891	+	0.762075i
$855$	39.1246	−	28.4257i	1.33803	−	0.972138i
$856$	−0.954915	+	2.93893i	−0.0326383	+	0.100450i
$857$	−49.9787			−1.70724			−0.853620	−	0.520896i	$-0.825598\pi$
$857$	−49.9787			−1.70724			−0.853620	+	0.520896i	$0.825598\pi$
$858$	6.47214	−	1.45309i	0.220955	−	0.0496075i
$859$	9.81966			0.335042			0.167521	−	0.985868i	$-0.446424\pi$
$859$	9.81966			0.335042			0.167521	+	0.985868i	$0.446424\pi$
$860$	1.00000	−	3.07768i	0.0340997	−	0.104948i
$861$	−5.52786	+	4.01623i	−0.188389	+	0.136873i
$862$	−11.2082	−	8.14324i	−0.381753	−	0.277360i
$863$	1.52786	+	4.70228i	0.0520091	+	0.160068i	0.973688	−	0.227887i	$-0.0731817\pi$
$863$	1.52786	+	4.70228i	0.0520091	+	0.160068i	−0.921678	+	0.387955i	$0.873182\pi$
$864$	4.47214	+	13.7638i	0.152145	+	0.468255i
$865$	−17.1803	−	12.4822i	−0.584149	−	0.424409i
$866$	3.47214	−	2.52265i	0.117988	−	0.0857233i
$867$	6.56231	−	20.1967i	0.222868	−	0.685916i
$868$	1.70820			0.0579802
$869$	0.645898	−	6.90215i	0.0219106	−	0.234140i
$870$	−109.666			−3.71801
$871$	−0.826238	+	2.54290i	−0.0279960	+	0.0861628i
$872$	−3.30902	+	2.40414i	−0.112057	+	0.0814145i
$873$	−67.0410	−	48.7082i	−2.26899	−	1.64852i
$874$	4.38197	+	13.4863i	0.148222	+	0.456181i
$875$	−2.11146	−	6.49839i	−0.0713802	−	0.219686i
$876$	4.00000	+	2.90617i	0.135147	+	0.0981904i
$877$	−12.9721	+	9.42481i	−0.438038	+	0.318253i	−0.784855	−	0.619680i	$-0.787263\pi$
$877$	−12.9721	+	9.42481i	−0.438038	+	0.318253i	0.346817	+	0.937933i	$0.387263\pi$
$878$	7.17376	−	22.0786i	0.242103	−	0.745116i
$879$	−59.4164			−2.00407
$880$	−7.09017	+	8.05748i	−0.239010	+	0.271618i
$881$	23.3820			0.787758			0.393879	−	0.919162i	$-0.371133\pi$
$881$	23.3820			0.787758			0.393879	+	0.919162i	$0.371133\pi$
$882$	30.0172	−	92.3835i	1.01073	−	3.11071i
$883$	−26.3435	+	19.1396i	−0.886528	+	0.644100i	−0.934970	−	0.354726i	$-0.884574\pi$
$883$	−26.3435	+	19.1396i	−0.886528	+	0.644100i	0.0484424	+	0.998826i	$0.484574\pi$
$884$	−2.42705	−	1.76336i	−0.0816306	−	0.0593081i
$885$	−14.0000	−	43.0876i	−0.470605	−	1.44837i
$886$	−7.11803	−	21.9071i	−0.239135	−	0.735982i
$887$	22.6525	+	16.4580i	0.760596	+	0.552605i	0.899093	−	0.437758i	$-0.144227\pi$
$887$	22.6525	+	16.4580i	0.760596	+	0.552605i	−0.138497	+	0.990363i	$0.544227\pi$
$888$	20.9443	−	15.2169i	0.702844	−	0.510646i
$889$	16.5836	−	51.0390i	0.556196	−	1.71179i
$890$	−16.9443			−0.567973
$891$	74.3500	+	32.0912i	2.49082	+	1.07509i
$892$	14.1803			0.474793
$893$	0.708204	−	2.17963i	0.0236991	−	0.0729385i
$894$	29.8885	−	21.7153i	0.999622	−	0.726268i
$895$	−5.70820	−	4.14725i	−0.190804	−	0.138627i
$896$	1.38197	+	4.25325i	0.0461682	+	0.142091i
$897$	−4.38197	−	13.4863i	−0.146310	−	0.450295i
$898$	−9.70820	−	7.05342i	−0.323967	−	0.235376i
$899$	−3.23607	+	2.35114i	−0.107929	+	0.0784149i
$900$	12.6353	−	38.8873i	0.421175	−	1.29624i
$901$	66.9787			2.23138
$902$	−0.798374	−	1.34708i	−0.0265829	−	0.0448530i
$903$	−14.4721			−0.481603
$904$	−3.56231	+	10.9637i	−0.118481	+	0.364646i
$905$	56.4508	−	41.0139i	1.87649	−	1.36335i
$906$	−26.9443	−	19.5762i	−0.895163	−	0.650374i
$907$	−1.71885	−	5.29007i	−0.0570734	−	0.175654i	0.918456	−	0.395523i	$-0.129437\pi$
$907$	−1.71885	−	5.29007i	−0.0570734	−	0.175654i	−0.975529	+	0.219870i	$0.929437\pi$
$908$	−2.32624	−	7.15942i	−0.0771989	−	0.237594i
$909$	12.9721	+	9.42481i	0.430259	+	0.312601i
$910$	−7.23607	+	5.25731i	−0.239873	+	0.174278i
$911$	12.5967	−	38.7688i	0.417349	−	1.28447i	−0.492784	−	0.870152i	$-0.664021\pi$
$911$	12.5967	−	38.7688i	0.417349	−	1.28447i	0.910133	−	0.414316i	$-0.135979\pi$
$912$	6.47214			0.214314
$913$	−0.645898	−	1.08981i	−0.0213761	−	0.0360676i
$914$	23.4164			0.774546
$915$	27.4164	−	84.3790i	0.906358	−	2.78948i
$916$	17.2082	−	12.5025i	0.568575	−	0.413094i
$917$	−3.81966	−	2.77515i	−0.126136	−	0.0916434i
$918$	−21.7082	−	66.8110i	−0.716477	−	2.20509i
$919$	−9.69756	−	29.8460i	−0.319893	−	0.984529i	−0.973693	−	0.227862i	$-0.926826\pi$
$919$	−9.69756	−	29.8460i	−0.319893	−	0.984529i	0.653800	−	0.756667i	$-0.273174\pi$
$920$	18.5623	+	13.4863i	0.611981	+	0.444630i
$921$	−28.4164	+	20.6457i	−0.936352	+	0.680300i
$922$	−10.4615	+	32.1972i	−0.344531	+	1.06036i
$923$	1.52786			0.0502903
$924$	44.0689	+	19.0211i	1.44976	+	0.625749i
$925$	−43.7771			−1.43938
$926$	−8.47214	+	26.0746i	−0.278412	+	0.856863i
$927$	3.39919	−	2.46965i	0.111644	−	0.0811141i
$928$	−8.47214	−	6.15537i	−0.278111	−	0.202060i
$929$	2.67376	+	8.22899i	0.0877233	+	0.269985i	0.985289	−	0.170896i	$-0.0546662\pi$
$929$	2.67376	+	8.22899i	0.0877233	+	0.269985i	−0.897566	+	0.440881i	$0.854666\pi$
$930$	−1.23607	−	3.80423i	−0.0405323	−	0.124745i
$931$	−21.0344	−	15.2824i	−0.689376	−	0.500861i
$932$	5.09017	−	3.69822i	0.166734	−	0.121139i
$933$	14.7984	−	45.5447i	0.484477	−	1.49107i
$934$	−35.8885			−1.17431
$935$	34.4164	−	39.1118i	1.12554	−	1.27909i
$936$	−4.61803			−0.150945
$937$	3.61803	−	11.1352i	0.118196	−	0.363770i	−0.874404	−	0.485198i	$-0.838747\pi$
$937$	3.61803	−	11.1352i	0.118196	−	0.363770i	0.992600	+	0.121428i	$0.0387474\pi$
$938$	−15.6525	+	11.3722i	−0.511071	+	0.371315i
$939$	10.4721	+	7.60845i	0.341745	+	0.248292i
$940$	−1.14590	−	3.52671i	−0.0373751	−	0.115029i
$941$	−6.50000	−	20.0049i	−0.211894	−	0.652143i	−0.999360	−	0.0357839i	$-0.988607\pi$
$941$	−6.50000	−	20.0049i	−0.211894	−	0.652143i	0.787466	−	0.616359i	$-0.211393\pi$
$942$	−12.9443	−	9.40456i	−0.421747	−	0.306417i
$943$	−2.70820	+	1.96763i	−0.0881913	+	0.0640747i
$944$	1.33688	−	4.11450i	0.0435118	−	0.133915i
$945$	−209.443			−6.81317
$946$	0.309017	−	3.30220i	0.0100470	−	0.107364i
$947$	−51.0344			−1.65840			−0.829198	−	0.558955i	$-0.811203\pi$
$947$	−51.0344			−1.65840			−0.829198	+	0.558955i	$0.811203\pi$
$948$	−2.09017	+	6.43288i	−0.0678856	+	0.208930i
$949$	−0.763932	+	0.555029i	−0.0247983	+	0.0180170i
$950$	−8.85410	−	6.43288i	−0.287265	−	0.208710i
$951$	−10.5623	−	32.5074i	−0.342506	−	1.05413i
$952$	−6.70820	−	20.6457i	−0.217414	−	0.669132i
$953$	−8.79837	−	6.39239i	−0.285007	−	0.207070i	0.436091	−	0.899902i	$-0.356362\pi$
$953$	−8.79837	−	6.39239i	−0.285007	−	0.207070i	−0.721099	+	0.692833i	$0.756362\pi$
$954$	83.4123	−	60.6026i	2.70057	−	1.96208i
$955$	13.4164	−	41.2915i	0.434145	−	1.33616i
$956$	16.9098			0.546903
$957$	−109.666	+	24.6215i	−3.54499	+	0.795899i
$958$	18.1459			0.586267
$959$	−31.3050	+	96.3467i	−1.01089	+	3.11120i
$960$	8.47214	−	6.15537i	0.273437	−	0.198664i
$961$	24.9615	+	18.1356i	0.805209	+	0.585019i
$962$	1.52786	+	4.70228i	0.0492603	+	0.151608i
$963$	−7.13525	−	21.9601i	−0.229930	−	0.707653i
$964$	14.3262	+	10.4086i	0.461417	+	0.335239i
$965$	44.1246	−	32.0584i	1.42042	−	1.03200i
$966$	31.7082	−	97.5878i	1.02019	−	3.13984i
$967$	−15.2148			−0.489274			−0.244637	−	0.969615i	$-0.578669\pi$
$967$	−15.2148			−0.489274			−0.244637	+	0.969615i	$0.578669\pi$
$968$	−5.28115	+	9.64932i	−0.169743	+	0.310141i
$969$	−31.4164			−1.00924
$970$	−11.0902	+	34.1320i	−0.356084	+	1.09591i
$971$	19.9164	−	14.4701i	0.639148	−	0.464368i	−0.220409	−	0.975407i	$-0.570739\pi$
$971$	19.9164	−	14.4701i	0.639148	−	0.464368i	0.859557	+	0.511039i	$0.170739\pi$
$972$	−28.7984	−	20.9232i	−0.923708	−	0.671113i
$973$	28.0902	+	86.4527i	0.900530	+	2.77154i
$974$	−6.84346	−	21.0620i	−0.219279	−	0.674870i
$975$	8.85410	+	6.43288i	0.283558	+	0.206017i
$976$	6.85410	−	4.97980i	0.219394	−	0.159399i
$977$	2.55166	−	7.85321i	0.0816349	−	0.251246i	−0.901906	−	0.431933i	$-0.857832\pi$
$977$	2.55166	−	7.85321i	0.0816349	−	0.251246i	0.983541	+	0.180686i	$0.0578318\pi$
$978$	−33.8885			−1.08364
$979$	−16.9443	+	3.80423i	−0.541541	+	0.121584i
$980$	−42.0689			−1.34384
$981$	9.44427	−	29.0665i	0.301532	−	0.928021i
$982$	9.56231	−	6.94742i	0.305145	−	0.221701i
$983$	−14.1803	−	10.3026i	−0.452283	−	0.328603i	0.338214	−	0.941069i	$-0.390177\pi$
$983$	−14.1803	−	10.3026i	−0.452283	−	0.328603i	−0.790496	+	0.612467i	$0.790177\pi$
$984$	0.472136	+	1.45309i	0.0150511	+	0.0463227i
$985$	−17.8541	−	54.9493i	−0.568879	−	1.75083i
$986$	41.1246	+	29.8788i	1.30967	+	0.951534i
$987$	−13.4164	+	9.74759i	−0.427049	+	0.310269i
$988$	−0.381966	+	1.17557i	−0.0121520	+	0.0373999i
$989$	−7.09017			−0.225454
$990$	7.47214	−	79.8483i	0.237480	−	2.53774i
$991$	−6.29180			−0.199865			−0.0999327	−	0.994994i	$-0.531863\pi$
$991$	−6.29180			−0.199865			−0.0999327	+	0.994994i	$0.531863\pi$
$992$	0.118034	−	0.363271i	0.00374758	−	0.0115339i
$993$	57.3050	−	41.6345i	1.81852	−	1.32123i
$994$	8.94427	+	6.49839i	0.283695	+	0.206117i
$995$	19.4164	+	59.7576i	0.615542	+	1.89444i
$996$	0.381966	+	1.17557i	0.0121031	+	0.0372494i
$997$	−43.5066	−	31.6094i	−1.37787	−	1.00108i	−0.997076	−	0.0764181i	$-0.975652\pi$
$997$	−43.5066	−	31.6094i	−1.37787	−	1.00108i	−0.380791	−	0.924661i	$-0.624348\pi$
$998$	26.5623	−	19.2986i	0.840815	−	0.610888i
$999$	−35.7771	+	110.111i	−1.13194	+	3.48374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.a.603.1	✓	4
11.5	even	5	inner	946.2.f.a.775.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.a.603.1	✓	4	1.1	even	1	trivial
946.2.f.a.775.1	yes	4	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(1.00000 + 3.07768i) q^{6} +(-3.61803 - 2.62866i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.30902 - 7.10642i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(1.00000 + 3.07768i) q^{6} +(-3.61803 - 2.62866i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.30902 - 7.10642i) q^{9} -3.23607 q^{10} +(-3.23607 + 0.726543i) q^{11} +3.23607 q^{12} +(-0.190983 + 0.587785i) q^{13} +(-3.61803 + 2.62866i) q^{14} +(8.47214 + 6.15537i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-6.04508 - 4.39201i) q^{18} +(-1.61803 + 1.17557i) q^{19} +(-1.00000 + 3.07768i) q^{20} +14.4721 q^{21} +(-0.309017 + 3.30220i) q^{22} +7.09017 q^{23} +(1.00000 - 3.07768i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(0.500000 + 0.363271i) q^{26} +(4.47214 + 13.7638i) q^{27} +(1.38197 + 4.25325i) q^{28} +(-8.47214 - 6.15537i) q^{29} +(8.47214 - 6.15537i) q^{30} +(0.118034 - 0.363271i) q^{31} +1.00000 q^{32} +(7.09017 - 8.05748i) q^{33} -4.85410 q^{34} +(-4.47214 + 13.7638i) q^{35} +(-6.04508 + 4.39201i) q^{36} +(6.47214 + 4.70228i) q^{37} +(0.618034 + 1.90211i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(2.61803 + 1.90211i) q^{40} +(-0.381966 + 0.277515i) q^{41} +(4.47214 - 13.7638i) q^{42} -1.00000 q^{43} +(3.04508 + 1.31433i) q^{44} -24.1803 q^{45} +(2.19098 - 6.74315i) q^{46} +(-0.927051 + 0.673542i) q^{47} +(-2.61803 - 1.90211i) q^{48} +(4.01722 + 12.3637i) q^{49} +(1.69098 + 5.20431i) q^{50} +(12.7082 + 9.23305i) q^{51} +(0.500000 - 0.363271i) q^{52} +(-4.26393 + 13.1230i) q^{53} +14.4721 q^{54} +(5.47214 + 9.23305i) q^{55} +4.47214 q^{56} +(2.00000 - 6.15537i) q^{57} +(-8.47214 + 6.15537i) q^{58} +(-3.50000 - 2.54290i) q^{59} +(-3.23607 - 9.95959i) q^{60} +(-2.61803 - 8.05748i) q^{61} +(-0.309017 - 0.224514i) q^{62} +(-27.0344 + 19.6417i) q^{63} +(0.309017 - 0.951057i) q^{64} +2.00000 q^{65} +(-5.47214 - 9.23305i) q^{66} +4.32624 q^{67} +(-1.50000 + 4.61653i) q^{68} +(-18.5623 + 13.4863i) q^{69} +(11.7082 + 8.50651i) q^{70} +(-0.763932 - 2.35114i) q^{71} +(2.30902 + 7.10642i) q^{72} +(1.23607 + 0.898056i) q^{73} +(6.47214 - 4.70228i) q^{74} +(5.47214 - 16.8415i) q^{75} +2.00000 q^{76} +(13.6180 + 5.87785i) q^{77} -2.00000 q^{78} +(-0.645898 + 1.98787i) q^{79} +(2.61803 - 1.90211i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(0.145898 + 0.449028i) q^{82} +(0.118034 + 0.363271i) q^{83} +(-11.7082 - 8.50651i) q^{84} +(-12.7082 + 9.23305i) q^{85} +(-0.309017 + 0.951057i) q^{86} +33.8885 q^{87} +(2.19098 - 2.48990i) q^{88} +5.23607 q^{89} +(-7.47214 + 22.9969i) q^{90} +(2.23607 - 1.62460i) q^{91} +(-5.73607 - 4.16750i) q^{92} +(0.381966 + 1.17557i) q^{93} +(0.354102 + 1.08981i) q^{94} +(5.23607 + 3.80423i) q^{95} +(-2.61803 + 1.90211i) q^{96} +(3.42705 - 10.5474i) q^{97} +13.0000 q^{98} +(-2.30902 + 24.6745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 6 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{7} - q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - q^2 - 6 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 10 * q^7 - q^8 + 7 * q^9	\( 4 q - q^{2} - 6 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{7} - q^{8} + 7 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} - 10 q^{14} + 16 q^{15} - q^{16} - 6 q^{17} - 13 q^{18} - 2 q^{19} - 4 q^{20} + 40 q^{21} + q^{22} + 6 q^{23} + 4 q^{24} - 11 q^{25} + 2 q^{26} + 10 q^{28} - 16 q^{29} + 16 q^{30} - 4 q^{31} + 4 q^{32} + 6 q^{33} - 6 q^{34} - 13 q^{36} + 8 q^{37} - 2 q^{38} + 2 q^{39} + 6 q^{40} - 6 q^{41} - 4 q^{43} + q^{44} - 52 q^{45} + 11 q^{46} + 3 q^{47} - 6 q^{48} - 13 q^{49} + 9 q^{50} + 24 q^{51} + 2 q^{52} - 26 q^{53} + 40 q^{54} + 4 q^{55} + 8 q^{57} - 16 q^{58} - 14 q^{59} - 4 q^{60} - 6 q^{61} + q^{62} - 50 q^{63} - q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} - 6 q^{68} - 34 q^{69} + 20 q^{70} - 12 q^{71} + 7 q^{72} - 4 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} + 50 q^{77} - 8 q^{78} - 16 q^{79} + 6 q^{80} - 41 q^{81} + 14 q^{82} - 4 q^{83} - 20 q^{84} - 24 q^{85} + q^{86} + 64 q^{87} + 11 q^{88} + 12 q^{89} - 12 q^{90} - 14 q^{92} + 6 q^{93} - 12 q^{94} + 12 q^{95} - 6 q^{96} + 7 q^{97} + 52 q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - q^2 - 6 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 10 * q^7 - q^8 + 7 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 - 10 * q^14 + 16 * q^15 - q^16 - 6 * q^17 - 13 * q^18 - 2 * q^19 - 4 * q^20 + 40 * q^21 + q^22 + 6 * q^23 + 4 * q^24 - 11 * q^25 + 2 * q^26 + 10 * q^28 - 16 * q^29 + 16 * q^30 - 4 * q^31 + 4 * q^32 + 6 * q^33 - 6 * q^34 - 13 * q^36 + 8 * q^37 - 2 * q^38 + 2 * q^39 + 6 * q^40 - 6 * q^41 - 4 * q^43 + q^44 - 52 * q^45 + 11 * q^46 + 3 * q^47 - 6 * q^48 - 13 * q^49 + 9 * q^50 + 24 * q^51 + 2 * q^52 - 26 * q^53 + 40 * q^54 + 4 * q^55 + 8 * q^57 - 16 * q^58 - 14 * q^59 - 4 * q^60 - 6 * q^61 + q^62 - 50 * q^63 - q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 - 6 * q^68 - 34 * q^69 + 20 * q^70 - 12 * q^71 + 7 * q^72 - 4 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 + 50 * q^77 - 8 * q^78 - 16 * q^79 + 6 * q^80 - 41 * q^81 + 14 * q^82 - 4 * q^83 - 20 * q^84 - 24 * q^85 + q^86 + 64 * q^87 + 11 * q^88 + 12 * q^89 - 12 * q^90 - 14 * q^92 + 6 * q^93 - 12 * q^94 + 12 * q^95 - 6 * q^96 + 7 * q^97 + 52 * q^98 - 7 * q^99

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