LMFDB - Embedded newform 385.2.n.b.246.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			246.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	385.246
Dual form			385.2.n.b.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 + 1.31433i) q^{2} +(0.190983 - 0.587785i) q^{3} +(0.927051 + 2.85317i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.11803 - 0.812299i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})$	\(q+(1.80902 + 1.31433i) q^{2} +(0.190983 - 0.587785i) q^{3} +(0.927051 + 2.85317i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.11803 - 0.812299i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.11803 + 1.53884i) q^{9} +2.23607 q^{10} +(3.04508 + 1.31433i) q^{11} +1.85410 q^{12} +(-3.73607 - 2.71441i) q^{13} +(0.690983 - 2.12663i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.54508 + 3.30220i) q^{17} +(1.80902 + 5.56758i) q^{18} +(-1.00000 + 3.07768i) q^{19} +(2.42705 + 1.76336i) q^{20} -0.618034 q^{21} +(3.78115 + 6.37988i) q^{22} -4.47214 q^{23} +(1.11803 + 0.812299i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-3.19098 - 9.82084i) q^{26} +(2.80902 - 2.04087i) q^{27} +(2.42705 - 1.76336i) q^{28} +(0.263932 + 0.812299i) q^{29} +(0.427051 - 1.31433i) q^{30} +(-2.61803 - 1.90211i) q^{31} +6.70820 q^{32} +(1.35410 - 1.53884i) q^{33} -12.5623 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-2.42705 + 7.46969i) q^{36} +(-2.23607 - 6.88191i) q^{37} +(-5.85410 + 4.25325i) q^{38} +(-2.30902 + 1.67760i) q^{39} +(0.690983 + 2.12663i) q^{40} +(0.763932 - 2.35114i) q^{41} +(-1.11803 - 0.812299i) q^{42} -5.23607 q^{43} +(-0.927051 + 9.90659i) q^{44} +2.61803 q^{45} +(-8.09017 - 5.87785i) q^{46} +(-0.354102 + 1.08981i) q^{47} +(-0.190983 - 0.587785i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.80902 - 1.31433i) q^{50} +(1.07295 + 3.30220i) q^{51} +(4.28115 - 13.1760i) q^{52} +(1.23607 + 0.898056i) q^{53} +7.76393 q^{54} +(3.23607 - 0.726543i) q^{55} +2.23607 q^{56} +(1.61803 + 1.17557i) q^{57} +(-0.590170 + 1.81636i) q^{58} +(-2.85410 - 8.78402i) q^{59} +(1.50000 - 1.08981i) q^{60} +(3.85410 - 2.80017i) q^{61} +(-2.23607 - 6.88191i) q^{62} +(0.809017 - 2.48990i) q^{63} +(10.5172 + 7.64121i) q^{64} -4.61803 q^{65} +(4.47214 - 1.00406i) q^{66} +8.18034 q^{67} +(-13.6353 - 9.90659i) q^{68} +(-0.854102 + 2.62866i) q^{69} +(-0.690983 - 2.12663i) q^{70} +(-13.2082 + 9.59632i) q^{71} +(-4.73607 + 3.44095i) q^{72} +(1.97214 + 6.06961i) q^{73} +(5.00000 - 15.3884i) q^{74} +(-0.500000 - 0.363271i) q^{75} -9.70820 q^{76} +(0.309017 - 3.30220i) q^{77} -6.38197 q^{78} +(-8.73607 - 6.34712i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.76393 + 5.42882i) q^{81} +(4.47214 - 3.24920i) q^{82} +(-7.73607 + 5.62058i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-1.73607 + 5.34307i) q^{85} +(-9.47214 - 6.88191i) q^{86} +0.527864 q^{87} +(-4.89919 + 5.56758i) q^{88} +12.7639 q^{89} +(4.73607 + 3.44095i) q^{90} +(-1.42705 + 4.39201i) q^{91} +(-4.14590 - 12.7598i) q^{92} +(-1.61803 + 1.17557i) q^{93} +(-2.07295 + 1.50609i) q^{94} +(1.00000 + 3.07768i) q^{95} +(1.28115 - 3.94298i) q^{96} +(12.3992 + 9.00854i) q^{97} -2.23607 q^{98} +(4.42705 + 7.46969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9	$ 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9} + q^{11} - 6 q^{12} - 6 q^{13} + 5 q^{14} - 3 q^{15} + q^{16} - 7 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 5 q^{22} - q^{25} - 15 q^{26} + 9 q^{27} + 3 q^{28} + 10 q^{29} - 5 q^{30} - 6 q^{31} - 8 q^{33} - 10 q^{34} - q^{35} - 3 q^{36} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 12 q^{41} - 12 q^{43} + 3 q^{44} + 6 q^{45} - 10 q^{46} + 12 q^{47} - 3 q^{48} - q^{49} + 5 q^{50} + 11 q^{51} - 3 q^{52} - 4 q^{53} + 40 q^{54} + 4 q^{55} + 2 q^{57} + 20 q^{58} + 2 q^{59} + 6 q^{60} + 2 q^{61} + q^{63} + 13 q^{64} - 14 q^{65} - 12 q^{67} - 21 q^{68} + 10 q^{69} - 5 q^{70} - 26 q^{71} - 10 q^{72} - 10 q^{73} + 20 q^{74} - 2 q^{75} - 12 q^{76} - q^{77} - 30 q^{78} - 26 q^{79} - q^{80} + 16 q^{81} - 22 q^{83} - 9 q^{84} + 2 q^{85} - 20 q^{86} + 20 q^{87} + 5 q^{88} + 60 q^{89} + 10 q^{90} + q^{91} - 30 q^{92} - 2 q^{93} - 15 q^{94} + 4 q^{95} - 15 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9 + q^11 - 6 * q^12 - 6 * q^13 + 5 * q^14 - 3 * q^15 + q^16 - 7 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 5 * q^22 - q^25 - 15 * q^26 + 9 * q^27 + 3 * q^28 + 10 * q^29 - 5 * q^30 - 6 * q^31 - 8 * q^33 - 10 * q^34 - q^35 - 3 * q^36 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 12 * q^41 - 12 * q^43 + 3 * q^44 + 6 * q^45 - 10 * q^46 + 12 * q^47 - 3 * q^48 - q^49 + 5 * q^50 + 11 * q^51 - 3 * q^52 - 4 * q^53 + 40 * q^54 + 4 * q^55 + 2 * q^57 + 20 * q^58 + 2 * q^59 + 6 * q^60 + 2 * q^61 + q^63 + 13 * q^64 - 14 * q^65 - 12 * q^67 - 21 * q^68 + 10 * q^69 - 5 * q^70 - 26 * q^71 - 10 * q^72 - 10 * q^73 + 20 * q^74 - 2 * q^75 - 12 * q^76 - q^77 - 30 * q^78 - 26 * q^79 - q^80 + 16 * q^81 - 22 * q^83 - 9 * q^84 + 2 * q^85 - 20 * q^86 + 20 * q^87 + 5 * q^88 + 60 * q^89 + 10 * q^90 + q^91 - 30 * q^92 - 2 * q^93 - 15 * q^94 + 4 * q^95 - 15 * q^96 + 25 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.999528	−	0.0307347i	$-0.00978469\pi$
$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.279641	+	0.960105i	$0.409785\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	−0.880666	−	0.473738i	$-0.842904\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	0.990930	+	0.134380i	$0.0429043\pi$
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	1.11803	−	0.812299i	0.456435	−	0.331620i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$	2.23607			0.707107
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$12$	1.85410			0.535233
$13$	−3.73607	−	2.71441i	−1.03620	−	0.752843i	−0.0666589	−	0.997776i	$-0.521234\pi$
$13$	−3.73607	−	2.71441i	−1.03620	−	0.752843i	−0.969540	+	0.244933i	$0.921234\pi$
$14$	0.690983	−	2.12663i	0.184673	−	0.568365i
$15$	−0.190983	−	0.587785i	−0.0493116	−	0.151765i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.981441	−	0.191764i	$-0.938579\pi$
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.120904	+	0.992664i	$0.538579\pi$
$18$	1.80902	+	5.56758i	0.426389	+	1.31229i
$19$	−1.00000	+	3.07768i	−0.229416	+	0.706069i	0.768398	+	0.639973i	$0.221054\pi$
$19$	−1.00000	+	3.07768i	−0.229416	+	0.706069i	−0.997813	+	0.0660962i	$0.978946\pi$
$20$	2.42705	+	1.76336i	0.542705	+	0.394298i
$21$	−0.618034			−0.134866
$22$	3.78115	+	6.37988i	0.806145	+	1.36020i
$23$	−4.47214			−0.932505			−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214			−0.932505			−0.466252	+	0.884652i	$0.654396\pi$
$24$	1.11803	+	0.812299i	0.228218	+	0.165810i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−3.19098	−	9.82084i	−0.625803	−	1.92602i
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$	2.42705	−	1.76336i	0.458670	−	0.333243i
$29$	0.263932	+	0.812299i	0.0490109	+	0.150840i	0.972567	−	0.232624i	$-0.0747311\pi$
$29$	0.263932	+	0.812299i	0.0490109	+	0.150840i	−0.923556	+	0.383464i	$0.874731\pi$
$30$	0.427051	−	1.31433i	0.0779685	−	0.239962i
$31$	−2.61803	−	1.90211i	−0.470213	−	0.341630i	0.327311	−	0.944917i	$-0.393857\pi$
$31$	−2.61803	−	1.90211i	−0.470213	−	0.341630i	−0.797524	+	0.603287i	$0.793857\pi$
$32$	6.70820			1.18585
$33$	1.35410	−	1.53884i	0.235719	−	0.267878i
$34$	−12.5623			−2.15442
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	−2.42705	+	7.46969i	−0.404508	+	1.24495i
$37$	−2.23607	−	6.88191i	−0.367607	−	1.13138i	−0.948332	−	0.317279i	$-0.897231\pi$
$37$	−2.23607	−	6.88191i	−0.367607	−	1.13138i	0.580725	−	0.814100i	$-0.302769\pi$
$38$	−5.85410	+	4.25325i	−0.949661	+	0.689969i
$39$	−2.30902	+	1.67760i	−0.369739	+	0.268631i
$40$	0.690983	+	2.12663i	0.109254	+	0.336249i
$41$	0.763932	−	2.35114i	0.119306	−	0.367187i	−0.873515	−	0.486798i	$-0.838165\pi$
$41$	0.763932	−	2.35114i	0.119306	−	0.367187i	0.992821	+	0.119611i	$0.0381648\pi$
$42$	−1.11803	−	0.812299i	−0.172516	−	0.125340i
$43$	−5.23607			−0.798493			−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607			−0.798493			−0.399246	+	0.916844i	$0.630728\pi$
$44$	−0.927051	+	9.90659i	−0.139758	+	1.49348i
$45$	2.61803			0.390273
$46$	−8.09017	−	5.87785i	−1.19283	−	0.866642i
$47$	−0.354102	+	1.08981i	−0.0516511	+	0.158966i	−0.973555	−	0.228453i	$-0.926633\pi$
$47$	−0.354102	+	1.08981i	−0.0516511	+	0.158966i	0.921904	+	0.387419i	$0.126633\pi$
$48$	−0.190983	−	0.587785i	−0.0275660	−	0.0848395i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	1.80902	−	1.31433i	0.255834	−	0.185874i
$51$	1.07295	+	3.30220i	0.150243	+	0.462400i
$52$	4.28115	−	13.1760i	0.593689	−	1.82719i
$53$	1.23607	+	0.898056i	0.169787	+	0.123357i	0.669434	−	0.742872i	$-0.266537\pi$
$53$	1.23607	+	0.898056i	0.169787	+	0.123357i	−0.499647	+	0.866229i	$0.666537\pi$
$54$	7.76393			1.05654
$55$	3.23607	−	0.726543i	0.436351	−	0.0979670i
$56$	2.23607			0.298807
$57$	1.61803	+	1.17557i	0.214314	+	0.155708i
$58$	−0.590170	+	1.81636i	−0.0774931	+	0.238499i
$59$	−2.85410	−	8.78402i	−0.371572	−	1.14358i	−0.945762	−	0.324860i	$-0.894683\pi$
$59$	−2.85410	−	8.78402i	−0.371572	−	1.14358i	0.574190	−	0.818722i	$-0.305317\pi$
$60$	1.50000	−	1.08981i	0.193649	−	0.140694i
$61$	3.85410	−	2.80017i	0.493467	−	0.358525i	−0.313049	−	0.949737i	$-0.601350\pi$
$61$	3.85410	−	2.80017i	0.493467	−	0.358525i	0.806516	+	0.591212i	$0.201350\pi$
$62$	−2.23607	−	6.88191i	−0.283981	−	0.874003i
$63$	0.809017	−	2.48990i	0.101927	−	0.313698i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	−4.61803			−0.572797
$66$	4.47214	−	1.00406i	0.550482	−	0.123591i
$67$	8.18034			0.999388			0.499694	−	0.866202i	$-0.333446\pi$
$67$	8.18034			0.999388			0.499694	+	0.866202i	$0.333446\pi$
$68$	−13.6353	−	9.90659i	−1.65352	−	1.20135i
$69$	−0.854102	+	2.62866i	−0.102822	+	0.316453i
$70$	−0.690983	−	2.12663i	−0.0825883	−	0.254181i
$71$	−13.2082	+	9.59632i	−1.56753	+	1.13887i	−0.638047	+	0.769997i	$0.720257\pi$
$71$	−13.2082	+	9.59632i	−1.56753	+	1.13887i	−0.929478	+	0.368876i	$0.879743\pi$
$72$	−4.73607	+	3.44095i	−0.558151	+	0.405520i
$73$	1.97214	+	6.06961i	0.230821	+	0.710394i	0.997648	+	0.0685406i	$0.0218343\pi$
$73$	1.97214	+	6.06961i	0.230821	+	0.710394i	−0.766827	+	0.641854i	$0.778166\pi$
$74$	5.00000	−	15.3884i	0.581238	−	1.78887i
$75$	−0.500000	−	0.363271i	−0.0577350	−	0.0419470i
$76$	−9.70820			−1.11361
$77$	0.309017	−	3.30220i	0.0352158	−	0.376320i
$78$	−6.38197			−0.722615
$79$	−8.73607	−	6.34712i	−0.982884	−	0.714107i	−0.0245330	−	0.999699i	$-0.507810\pi$
$79$	−8.73607	−	6.34712i	−0.982884	−	0.714107i	−0.958351	+	0.285592i	$0.907810\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$	4.47214	−	3.24920i	0.493865	−	0.358814i
$83$	−7.73607	+	5.62058i	−0.849144	+	0.616939i	−0.924910	−	0.380187i	$-0.875860\pi$
$83$	−7.73607	+	5.62058i	−0.849144	+	0.616939i	0.0757660	+	0.997126i	$0.475860\pi$
$84$	−0.572949	−	1.76336i	−0.0625139	−	0.192398i
$85$	−1.73607	+	5.34307i	−0.188303	+	0.579537i
$86$	−9.47214	−	6.88191i	−1.02141	−	0.742095i
$87$	0.527864			0.0565930
$88$	−4.89919	+	5.56758i	−0.522255	+	0.593506i
$89$	12.7639			1.35297			0.676487	−	0.736455i	$-0.263501\pi$
$89$	12.7639			1.35297			0.676487	+	0.736455i	$0.263501\pi$
$90$	4.73607	+	3.44095i	0.499225	+	0.362708i
$91$	−1.42705	+	4.39201i	−0.149596	+	0.460408i
$92$	−4.14590	−	12.7598i	−0.432240	−	1.33030i
$93$	−1.61803	+	1.17557i	−0.167782	+	0.121901i
$94$	−2.07295	+	1.50609i	−0.213808	+	0.155341i
$95$	1.00000	+	3.07768i	0.102598	+	0.315764i
$96$	1.28115	−	3.94298i	0.130757	−	0.402429i
$97$	12.3992	+	9.00854i	1.25895	+	0.914678i	0.998706	−	0.0508653i	$-0.0161979\pi$
$97$	12.3992	+	9.00854i	1.25895	+	0.914678i	0.260241	+	0.965544i	$0.416198\pi$
$98$	−2.23607			−0.225877
$99$	4.42705	+	7.46969i	0.444935	+	0.750733i
$100$	3.00000			0.300000
$101$	11.0902	+	8.05748i	1.10351	+	0.801749i	0.981630	−	0.190795i	$-0.0611066\pi$
$101$	11.0902	+	8.05748i	1.10351	+	0.801749i	0.121883	+	0.992544i	$0.461107\pi$
$102$	−2.39919	+	7.38394i	−0.237555	+	0.731119i
$103$	−5.35410	−	16.4782i	−0.527555	−	1.62365i	−0.759207	−	0.650850i	$-0.774413\pi$
$103$	−5.35410	−	16.4782i	−0.527555	−	1.62365i	0.231651	−	0.972799i	$-0.425587\pi$
$104$	8.35410	−	6.06961i	0.819187	−	0.595174i
$105$	−0.500000	+	0.363271i	−0.0487950	+	0.0354516i
$106$	1.05573	+	3.24920i	0.102541	+	0.315590i
$107$	−2.23607	+	6.88191i	−0.216169	+	0.665299i	0.782900	+	0.622148i	$0.213740\pi$
$107$	−2.23607	+	6.88191i	−0.216169	+	0.665299i	−0.999069	+	0.0431514i	$0.986260\pi$
$108$	8.42705	+	6.12261i	0.810893	+	0.589149i
$109$	−11.5279			−1.10417			−0.552085	−	0.833788i	$-0.686167\pi$
$109$	−11.5279			−1.10417			−0.552085	+	0.833788i	$0.686167\pi$
$110$	6.80902	+	2.93893i	0.649214	+	0.280216i
$111$	−4.47214			−0.424476
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	3.23607	−	9.95959i	0.304424	−	0.936920i	−0.675468	−	0.737389i	$-0.736058\pi$
$113$	3.23607	−	9.95959i	0.304424	−	0.936920i	0.979892	−	0.199530i	$-0.0639417\pi$
$114$	1.38197	+	4.25325i	0.129433	+	0.398354i
$115$	−3.61803	+	2.62866i	−0.337383	+	0.245123i
$116$	−2.07295	+	1.50609i	−0.192468	+	0.139837i
$117$	−3.73607	−	11.4984i	−0.345400	−	1.06303i
$118$	6.38197	−	19.6417i	0.587508	−	1.80816i
$119$	4.54508	+	3.30220i	0.416647	+	0.302712i
$120$	1.38197			0.126156
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	10.6525			0.964430
$123$	−1.23607	−	0.898056i	−0.111452	−	0.0809750i
$124$	3.00000	−	9.23305i	0.269408	−	0.829152i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	4.73607	−	3.44095i	0.421922	−	0.306545i
$127$	−7.47214	+	5.42882i	−0.663045	+	0.481730i	−0.867690	−	0.497106i	$-0.834396\pi$
$127$	−7.47214	+	5.42882i	−0.663045	+	0.481730i	0.204645	+	0.978836i	$0.434396\pi$
$128$	4.83688	+	14.8864i	0.427524	+	1.31578i
$129$	−1.00000	+	3.07768i	−0.0880451	+	0.270975i
$130$	−8.35410	−	6.06961i	−0.732703	−	0.532340i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$	5.64590	+	2.43690i	0.491412	+	0.212105i
$133$	3.23607			0.280603
$134$	14.7984	+	10.7516i	1.27838	+	0.928801i
$135$	1.07295	−	3.30220i	0.0923447	−	0.284208i
$136$	−3.88197	−	11.9475i	−0.332876	−	1.02449i
$137$	9.23607	−	6.71040i	0.789091	−	0.573308i	−0.118603	−	0.992942i	$-0.537842\pi$
$137$	9.23607	−	6.71040i	0.789091	−	0.573308i	0.907693	+	0.419634i	$0.137842\pi$
$138$	−5.00000	+	3.63271i	−0.425628	+	0.309237i
$139$	1.70820	+	5.25731i	0.144888	+	0.445919i	0.996997	−	0.0774457i	$-0.0246764\pi$
$139$	1.70820	+	5.25731i	0.144888	+	0.445919i	−0.852109	+	0.523365i	$0.824676\pi$
$140$	0.927051	−	2.85317i	0.0783501	−	0.241137i
$141$	0.572949	+	0.416272i	0.0482510	+	0.0350564i
$142$	−36.5066			−3.06356
$143$	−7.80902	−	13.1760i	−0.653023	−	1.10184i
$144$	2.61803			0.218169
$145$	0.690983	+	0.502029i	0.0573830	+	0.0416912i
$146$	−4.40983	+	13.5721i	−0.364960	+	1.12323i
$147$	0.190983	+	0.587785i	0.0157520	+	0.0484797i
$148$	17.5623	−	12.7598i	1.44361	−	1.04885i
$149$	14.4443	−	10.4944i	1.18332	−	0.859733i	0.190778	−	0.981633i	$-0.438899\pi$
$149$	14.4443	−	10.4944i	1.18332	−	0.859733i	0.992542	+	0.121900i	$0.0388988\pi$
$150$	−0.427051	−	1.31433i	−0.0348686	−	0.107314i
$151$	−0.118034	+	0.363271i	−0.00960547	+	0.0295626i	−0.955744	−	0.294198i	$-0.904947\pi$
$151$	−0.118034	+	0.363271i	−0.00960547	+	0.0295626i	0.946139	+	0.323761i	$0.104947\pi$
$152$	−5.85410	−	4.25325i	−0.474830	−	0.344984i
$153$	−14.7082			−1.18909
$154$	4.89919	−	5.56758i	0.394788	−	0.448649i
$155$	−3.23607			−0.259927
$156$	−6.92705	−	5.03280i	−0.554608	−	0.402946i
$157$	−4.97214	+	15.3027i	−0.396820	+	1.22129i	0.530716	+	0.847550i	$0.321923\pi$
$157$	−4.97214	+	15.3027i	−0.396820	+	1.22129i	−0.927535	+	0.373735i	$0.878077\pi$
$158$	−7.46149	−	22.9641i	−0.593604	−	1.82693i
$159$	0.763932	−	0.555029i	0.0605838	−	0.0440167i
$160$	5.42705	−	3.94298i	0.429046	−	0.311720i
$161$	1.38197	+	4.25325i	0.108914	+	0.335203i
$162$	−3.94427	+	12.1392i	−0.309891	+	0.953747i
$163$	17.9443	+	13.0373i	1.40550	+	1.02116i	0.993957	+	0.109770i	$0.0350113\pi$
$163$	17.9443	+	13.0373i	1.40550	+	1.02116i	0.411547	+	0.911389i	$0.364989\pi$
$164$	7.41641			0.579124
$165$	0.190983	−	2.04087i	0.0148680	−	0.158882i
$166$	−21.3820			−1.65956
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	0.896212	−	0.443626i	$-0.146308\pi$
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	−0.144969	+	0.989436i	$0.546308\pi$
$168$	0.427051	−	1.31433i	0.0329477	−	0.101403i
$169$	2.57295	+	7.91872i	0.197919	+	0.609133i
$170$	−10.1631	+	7.38394i	−0.779476	+	0.566322i
$171$	−6.85410	+	4.97980i	−0.524146	+	0.380815i
$172$	−4.85410	−	14.9394i	−0.370122	−	1.13912i
$173$	−0.482779	+	1.48584i	−0.0367050	+	0.112966i	−0.967730	−	0.251988i	$-0.918916\pi$
$173$	−0.482779	+	1.48584i	−0.0367050	+	0.112966i	0.931025	+	0.364955i	$0.118916\pi$
$174$	0.954915	+	0.693786i	0.0723919	+	0.0525958i
$175$	−1.00000			−0.0755929
$176$	3.23607	−	0.726543i	0.243928	−	0.0547652i
$177$	−5.70820			−0.429055
$178$	23.0902	+	16.7760i	1.73068	+	1.25741i
$179$	6.06231	−	18.6579i	0.453118	−	1.39455i	−0.420212	−	0.907426i	$-0.638044\pi$
$179$	6.06231	−	18.6579i	0.453118	−	1.39455i	0.873331	−	0.487128i	$-0.161956\pi$
$180$	2.42705	+	7.46969i	0.180902	+	0.556758i
$181$	−4.47214	+	3.24920i	−0.332411	+	0.241511i	−0.741453	−	0.671005i	$-0.765863\pi$
$181$	−4.47214	+	3.24920i	−0.332411	+	0.241511i	0.409042	+	0.912516i	$0.365863\pi$
$182$	−8.35410	+	6.06961i	−0.619247	+	0.449909i
$183$	−0.909830	−	2.80017i	−0.0672566	−	0.206994i
$184$	3.09017	−	9.51057i	0.227810	−	0.701128i
$185$	−5.85410	−	4.25325i	−0.430402	−	0.312705i
$186$	−4.47214			−0.327913
$187$	−18.1803	+	4.08174i	−1.32948	+	0.298486i
$188$	−3.43769			−0.250720
$189$	−2.80902	−	2.04087i	−0.204326	−	0.148451i
$190$	−2.23607	+	6.88191i	−0.162221	+	0.499266i
$191$	7.13525	+	21.9601i	0.516289	+	1.58897i	0.780924	+	0.624625i	$0.214748\pi$
$191$	7.13525	+	21.9601i	0.516289	+	1.58897i	−0.264636	+	0.964348i	$0.585252\pi$
$192$	6.50000	−	4.72253i	0.469097	−	0.340819i
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	−0.698131	−	0.715970i	$-0.745985\pi$
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	0.465194	+	0.885209i	$0.345985\pi$
$194$	10.5902	+	32.5932i	0.760330	+	2.34005i
$195$	−0.881966	+	2.71441i	−0.0631589	+	0.194383i
$196$	−2.42705	−	1.76336i	−0.173361	−	0.125954i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−1.80902	+	19.3314i	−0.128561	+	1.37382i
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	1.80902	+	1.31433i	0.127917	+	0.0929370i
$201$	1.56231	−	4.80828i	0.110197	−	0.339150i
$202$	9.47214	+	29.1522i	0.666457	+	2.05114i
$203$	0.690983	−	0.502029i	0.0484975	−	0.0352355i
$204$	−8.42705	+	6.12261i	−0.590012	+	0.428669i
$205$	−0.763932	−	2.35114i	−0.0533553	−	0.164211i
$206$	11.9721	−	36.8464i	0.834138	−	2.56721i
$207$	−9.47214	−	6.88191i	−0.658359	−	0.478326i
$208$	−4.61803			−0.320203
$209$	−7.09017	+	8.05748i	−0.490437	+	0.557348i
$210$	−1.38197			−0.0953647
$211$	−6.20820	−	4.51052i	−0.427390	−	0.310517i	0.353214	−	0.935542i	$-0.385089\pi$
$211$	−6.20820	−	4.51052i	−0.427390	−	0.310517i	−0.780605	+	0.625025i	$0.785089\pi$
$212$	−1.41641	+	4.35926i	−0.0972793	+	0.299395i
$213$	3.11803	+	9.59632i	0.213644	+	0.657529i
$214$	−13.0902	+	9.51057i	−0.894826	+	0.650129i
$215$	−4.23607	+	3.07768i	−0.288897	+	0.209896i
$216$	2.39919	+	7.38394i	0.163244	+	0.502413i
$217$	−1.00000	+	3.07768i	−0.0678844	+	0.208927i
$218$	−20.8541	−	15.1514i	−1.41242	−	1.02618i
$219$	3.94427			0.266529
$220$	5.07295	+	8.55951i	0.342018	+	0.577082i
$221$	25.9443			1.74520
$222$	−8.09017	−	5.87785i	−0.542977	−	0.394496i
$223$	0.472136	−	1.45309i	0.0316166	−	0.0973058i	−0.934003	−	0.357265i	$-0.883709\pi$
$223$	0.472136	−	1.45309i	0.0316166	−	0.0973058i	0.965620	+	0.259959i	$0.0837092\pi$
$224$	−2.07295	−	6.37988i	−0.138505	−	0.426274i
$225$	2.11803	−	1.53884i	0.141202	−	0.102589i
$226$	18.9443	−	13.7638i	1.26015	−	0.915556i
$227$	−3.33688	−	10.2699i	−0.221477	−	0.681635i	−0.998630	−	0.0523238i	$-0.983337\pi$
$227$	−3.33688	−	10.2699i	−0.221477	−	0.681635i	0.777154	−	0.629311i	$-0.216663\pi$
$228$	−1.85410	+	5.70634i	−0.122791	+	0.377912i
$229$	20.0344	+	14.5559i	1.32391	+	0.961879i	0.999875	+	0.0158354i	$0.00504076\pi$
$229$	20.0344	+	14.5559i	1.32391	+	0.961879i	0.324039	+	0.946044i	$0.394959\pi$
$230$	−10.0000			−0.659380
$231$	−1.88197	−	0.812299i	−0.123824	−	0.0534454i
$232$	−1.90983			−0.125386
$233$	−5.38197	−	3.91023i	−0.352584	−	0.256168i	0.397368	−	0.917659i	$-0.369924\pi$
$233$	−5.38197	−	3.91023i	−0.352584	−	0.256168i	−0.749952	+	0.661492i	$0.769924\pi$
$234$	8.35410	−	25.7113i	0.546125	−	1.68080i
$235$	0.354102	+	1.08981i	0.0230991	+	0.0710916i
$236$	22.4164	−	16.2865i	1.45918	−	1.06016i
$237$	−5.39919	+	3.92274i	−0.350715	+	0.254809i
$238$	3.88197	+	11.9475i	0.251630	+	0.774439i
$239$	7.71885	−	23.7562i	0.499291	−	1.53666i	−0.310871	−	0.950452i	$-0.600621\pi$
$239$	7.71885	−	23.7562i	0.499291	−	1.53666i	0.810162	−	0.586207i	$-0.199379\pi$
$240$	−0.500000	−	0.363271i	−0.0322749	−	0.0234491i
$241$	−17.1246			−1.10309			−0.551547	−	0.834144i	$-0.685962\pi$
$241$	−17.1246			−1.10309			−0.551547	+	0.834144i	$0.685962\pi$
$242$	3.12868	+	24.3970i	0.201119	+	1.56830i
$243$	13.9443			0.894525
$244$	11.5623	+	8.40051i	0.740201	+	0.537787i
$245$	−0.309017	+	0.951057i	−0.0197424	+	0.0607608i
$246$	−1.05573	−	3.24920i	−0.0673108	−	0.207161i
$247$	12.0902	−	8.78402i	0.769279	−	0.558914i
$248$	5.85410	−	4.25325i	0.371736	−	0.270082i
$249$	1.82624	+	5.62058i	0.115733	+	0.356190i
$250$	0.690983	−	2.12663i	0.0437016	−	0.134500i
$251$	6.23607	+	4.53077i	0.393617	+	0.285980i	0.766936	−	0.641723i	$-0.221780\pi$
$251$	6.23607	+	4.53077i	0.393617	+	0.285980i	−0.373319	+	0.927703i	$0.621780\pi$
$252$	7.85410			0.494762
$253$	−13.6180	−	5.87785i	−0.856158	−	0.369537i
$254$	−20.6525			−1.29585
$255$	2.80902	+	2.04087i	0.175907	+	0.127804i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	−0.736068	−	2.26538i	−0.0459147	−	0.141311i	0.925471	−	0.378818i	$-0.123670\pi$
$257$	−0.736068	−	2.26538i	−0.0459147	−	0.141311i	−0.971386	+	0.237508i	$0.923670\pi$
$258$	−5.85410	+	4.25325i	−0.364460	+	0.264796i
$259$	−5.85410	+	4.25325i	−0.363756	+	0.264284i
$260$	−4.28115	−	13.1760i	−0.265506	−	0.817143i
$261$	−0.690983	+	2.12663i	−0.0427708	+	0.131635i
$262$	14.4721	+	10.5146i	0.894092	+	0.649596i
$263$	14.1803			0.874397			0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803			0.874397			0.437199	+	0.899365i	$0.355971\pi$
$264$	2.33688	+	3.94298i	0.143825	+	0.242674i
$265$	1.52786			0.0938559
$266$	5.85410	+	4.25325i	0.358938	+	0.260784i
$267$	2.43769	−	7.50245i	0.149184	−	0.459143i
$268$	7.58359	+	23.3399i	0.463242	+	1.42571i
$269$	15.0902	−	10.9637i	0.920064	−	0.668466i	−0.0234760	−	0.999724i	$-0.507473\pi$
$269$	15.0902	−	10.9637i	0.920064	−	0.668466i	0.943540	+	0.331259i	$0.107473\pi$
$270$	6.28115	−	4.56352i	0.382259	−	0.277727i
$271$	7.18034	+	22.0988i	0.436175	+	1.34241i	0.891878	+	0.452276i	$0.149388\pi$
$271$	7.18034	+	22.0988i	0.436175	+	1.34241i	−0.455704	+	0.890132i	$0.650612\pi$
$272$	−1.73607	+	5.34307i	−0.105265	+	0.323971i
$273$	2.30902	+	1.67760i	0.139748	+	0.101533i
$274$	25.5279			1.54219
$275$	2.19098	−	2.48990i	0.132121	−	0.150147i
$276$	−8.29180			−0.499107
$277$	7.61803	+	5.53483i	0.457723	+	0.332555i	0.792638	−	0.609693i	$-0.208707\pi$
$277$	7.61803	+	5.53483i	0.457723	+	0.332555i	−0.334914	+	0.942249i	$0.608707\pi$
$278$	−3.81966	+	11.7557i	−0.229088	+	0.705060i
$279$	−2.61803	−	8.05748i	−0.156738	−	0.482389i
$280$	1.80902	−	1.31433i	0.108109	−	0.0785461i
$281$	6.85410	−	4.97980i	0.408881	−	0.297070i	−0.364267	−	0.931294i	$-0.618681\pi$
$281$	6.85410	−	4.97980i	0.408881	−	0.297070i	0.773149	+	0.634225i	$0.218681\pi$
$282$	0.489357	+	1.50609i	0.0291408	+	0.0896861i
$283$	−2.29837	+	7.07367i	−0.136624	+	0.420486i	−0.995839	−	0.0911289i	$-0.970952\pi$
$283$	−2.29837	+	7.07367i	−0.136624	+	0.420486i	0.859215	+	0.511615i	$0.170952\pi$
$284$	−39.6246	−	28.7890i	−2.35129	−	1.70831i
$285$	2.00000			0.118470
$286$	3.19098	−	34.0993i	0.188687	−	2.01633i
$287$	−2.47214			−0.145926
$288$	14.2082	+	10.3229i	0.837226	+	0.608281i
$289$	4.50000	−	13.8496i	0.264706	−	0.814681i
$290$	0.590170	+	1.81636i	0.0346560	+	0.106660i
$291$	7.66312	−	5.56758i	0.449220	−	0.326377i
$292$	−15.4894	+	11.2537i	−0.906446	+	0.658572i
$293$	−2.90983	−	8.95554i	−0.169994	−	0.523188i	0.829375	−	0.558692i	$-0.188696\pi$
$293$	−2.90983	−	8.95554i	−0.169994	−	0.523188i	−0.999370	+	0.0355036i	$0.988696\pi$
$294$	−0.427051	+	1.31433i	−0.0249061	+	0.0766532i
$295$	−7.47214	−	5.42882i	−0.435045	−	0.316078i
$296$	16.1803			0.940463
$297$	11.2361	−	2.52265i	0.651983	−	0.146379i
$298$	39.9230			2.31268
$299$	16.7082	+	12.1392i	0.966260	+	0.702029i
$300$	0.572949	−	1.76336i	0.0330792	−	0.101807i
$301$	1.61803	+	4.97980i	0.0932619	+	0.287031i
$302$	−0.690983	+	0.502029i	−0.0397616	+	0.0288885i
$303$	6.85410	−	4.97980i	0.393758	−	0.286082i
$304$	1.00000	+	3.07768i	0.0573539	+	0.176517i
$305$	1.47214	−	4.53077i	0.0842943	−	0.259431i
$306$	−26.6074	−	19.3314i	−1.52104	−	1.10510i
$307$	−20.5623			−1.17355			−0.586776	−	0.809749i	$-0.699603\pi$
$307$	−20.5623			−1.17355			−0.586776	+	0.809749i	$0.699603\pi$
$308$	9.70820	−	2.17963i	0.553176	−	0.124196i
$309$	−10.7082			−0.609168
$310$	−5.85410	−	4.25325i	−0.332491	−	0.241569i
$311$	4.05573	−	12.4822i	0.229979	−	0.707803i	−0.767769	−	0.640727i	$-0.778633\pi$
$311$	4.05573	−	12.4822i	0.229979	−	0.707803i	0.997748	−	0.0670761i	$-0.0213670\pi$
$312$	−1.97214	−	6.06961i	−0.111650	−	0.343624i
$313$	14.5623	−	10.5801i	0.823110	−	0.598025i	−0.0944915	−	0.995526i	$-0.530123\pi$
$313$	14.5623	−	10.5801i	0.823110	−	0.598025i	0.917602	+	0.397501i	$0.130123\pi$
$314$	−29.1074	+	21.1478i	−1.64263	+	1.19344i
$315$	−0.809017	−	2.48990i	−0.0455829	−	0.140290i
$316$	10.0106	−	30.8096i	0.563143	−	1.73317i
$317$	17.4164	+	12.6538i	0.978203	+	0.710706i	0.957306	−	0.289076i	$-0.0933479\pi$
$317$	17.4164	+	12.6538i	0.978203	+	0.710706i	0.0208967	+	0.999782i	$0.493348\pi$
$318$	2.11146			0.118405
$319$	−0.263932	+	2.82041i	−0.0147774	+	0.157913i
$320$	13.0000			0.726722
$321$	3.61803	+	2.62866i	0.201939	+	0.146717i
$322$	−3.09017	+	9.51057i	−0.172208	+	0.530003i
$323$	−5.61803	−	17.2905i	−0.312596	−	0.962071i
$324$	−13.8541	+	10.0656i	−0.769672	+	0.559200i
$325$	−3.73607	+	2.71441i	−0.207240	+	0.150569i
$326$	15.3262	+	47.1693i	0.848842	+	2.61247i
$327$	−2.20163	+	6.77591i	−0.121750	+	0.374709i
$328$	4.47214	+	3.24920i	0.246932	+	0.179407i
$329$	1.14590			0.0631754
$330$	3.02786	−	3.44095i	0.166678	−	0.189418i
$331$	−18.5066			−1.01721			−0.508607	−	0.860999i	$-0.669839\pi$
$331$	−18.5066			−1.01721			−0.508607	+	0.860999i	$0.669839\pi$
$332$	−23.2082	−	16.8617i	−1.27372	−	0.925409i
$333$	5.85410	−	18.0171i	0.320803	−	0.987330i
$334$	8.29180	+	25.5195i	0.453707	+	1.39637i
$335$	6.61803	−	4.80828i	0.361582	−	0.262705i
$336$	−0.500000	+	0.363271i	−0.0272772	+	0.0198181i
$337$	−9.70820	−	29.8788i	−0.528840	−	1.62760i	−0.756596	−	0.653883i	$-0.773139\pi$
$337$	−9.70820	−	29.8788i	−0.528840	−	1.62760i	0.227756	−	0.973718i	$-0.426861\pi$
$338$	−5.75329	+	17.7068i	−0.312938	+	0.963123i
$339$	−5.23607	−	3.80423i	−0.284384	−	0.206617i
$340$	−16.8541			−0.914042
$341$	−5.47214	−	9.23305i	−0.296333	−	0.499998i
$342$	−18.9443			−1.02439
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	3.61803	−	11.1352i	0.195071	−	0.600368i
$345$	0.854102	+	2.62866i	0.0459833	+	0.141522i
$346$	−2.82624	+	2.05338i	−0.151939	+	0.110391i
$347$	1.23607	−	0.898056i	0.0663556	−	0.0482102i	−0.554113	−	0.832441i	$-0.686942\pi$
$347$	1.23607	−	0.898056i	0.0663556	−	0.0482102i	0.620469	+	0.784231i	$0.286942\pi$
$348$	0.489357	+	1.50609i	0.0262323	+	0.0807347i
$349$	1.20163	−	3.69822i	0.0643216	−	0.197961i	−0.913731	−	0.406320i	$-0.866812\pi$
$349$	1.20163	−	3.69822i	0.0643216	−	0.197961i	0.978053	+	0.208358i	$0.0668120\pi$
$350$	−1.80902	−	1.31433i	−0.0966960	−	0.0702538i
$351$	−16.0344			−0.855855
$352$	20.4271	+	8.81678i	1.08877	+	0.469936i
$353$	−13.5623			−0.721849			−0.360924	−	0.932595i	$-0.617539\pi$
$353$	−13.5623			−0.721849			−0.360924	+	0.932595i	$0.617539\pi$
$354$	−10.3262	−	7.50245i	−0.548833	−	0.398751i
$355$	−5.04508	+	15.5272i	−0.267765	+	0.824097i
$356$	11.8328	+	36.4177i	0.627138	+	1.93013i
$357$	2.80902	−	2.04087i	0.148669	−	0.108014i
$358$	35.4894	−	25.7845i	1.87567	−	1.36275i
$359$	−4.01064	−	12.3435i	−0.211674	−	0.651465i	−0.999373	−	0.0354047i	$-0.988728\pi$
$359$	−4.01064	−	12.3435i	−0.211674	−	0.651465i	0.787699	−	0.616060i	$-0.211272\pi$
$360$	−1.80902	+	5.56758i	−0.0953436	+	0.293437i
$361$	6.89919	+	5.01255i	0.363115	+	0.263819i
$362$	−12.3607			−0.649663
$363$	6.14590	−	2.90617i	0.322576	−	0.152534i
$364$	−13.8541			−0.726152
$365$	5.16312	+	3.75123i	0.270250	+	0.196348i
$366$	2.03444	−	6.26137i	0.106342	−	0.327287i
$367$	−9.71885	−	29.9115i	−0.507320	−	1.56137i	−0.796836	−	0.604196i	$-0.793494\pi$
$367$	−9.71885	−	29.9115i	−0.507320	−	1.56137i	0.289516	−	0.957173i	$-0.406506\pi$
$368$	−3.61803	+	2.62866i	−0.188603	+	0.137028i
$369$	5.23607	−	3.80423i	0.272579	−	0.198040i
$370$	−5.00000	−	15.3884i	−0.259938	−	0.800006i
$371$	0.472136	−	1.45309i	0.0245121	−	0.0754404i
$372$	−4.85410	−	3.52671i	−0.251673	−	0.182851i
$373$	11.1246			0.576011			0.288005	−	0.957629i	$-0.407008\pi$
$373$	11.1246			0.576011			0.288005	+	0.957629i	$0.407008\pi$
$374$	−38.2533	−	16.5110i	−1.97803	−	0.853763i
$375$	−0.618034			−0.0319151
$376$	−2.07295	−	1.50609i	−0.106904	−	0.0776704i
$377$	1.21885	−	3.75123i	0.0627738	−	0.193198i
$378$	−2.39919	−	7.38394i	−0.123401	−	0.379789i
$379$	−20.0172	+	14.5434i	−1.02822	+	0.747042i	−0.967951	−	0.251140i	$-0.919195\pi$
$379$	−20.0172	+	14.5434i	−1.02822	+	0.747042i	−0.0602648	+	0.998182i	$0.519195\pi$
$380$	−7.85410	+	5.70634i	−0.402907	+	0.292729i
$381$	1.76393	+	5.42882i	0.0903690	+	0.278127i
$382$	−15.9549	+	49.1042i	−0.816324	+	2.51239i
$383$	−21.6803	−	15.7517i	−1.10781	−	0.804874i	−0.125496	−	0.992094i	$-0.540052\pi$
$383$	−21.6803	−	15.7517i	−1.10781	−	0.804874i	−0.982318	+	0.187220i	$0.940052\pi$
$384$	9.67376			0.493662
$385$	−1.69098	−	2.85317i	−0.0861805	−	0.145411i
$386$	−8.94427			−0.455251
$387$	−11.0902	−	8.05748i	−0.563745	−	0.409585i
$388$	−14.2082	+	43.7284i	−0.721312	+	2.21997i
$389$	−10.3713	−	31.9196i	−0.525847	−	1.61839i	−0.762635	−	0.646829i	$-0.776095\pi$
$389$	−10.3713	−	31.9196i	−0.525847	−	1.61839i	0.236788	−	0.971561i	$-0.423905\pi$
$390$	−5.16312	+	3.75123i	−0.261445	+	0.189951i
$391$	20.3262	−	14.7679i	1.02794	−	0.746844i
$392$	−0.690983	−	2.12663i	−0.0348999	−	0.107411i
$393$	1.52786	−	4.70228i	0.0770705	−	0.237199i
$394$	−21.7082	−	15.7719i	−1.09364	−	0.794579i
$395$	−10.7984			−0.543325
$396$	−17.2082	+	19.5559i	−0.864745	+	0.982722i
$397$	35.1591			1.76458			0.882291	−	0.470704i	$-0.156000\pi$
$397$	35.1591			1.76458			0.882291	+	0.470704i	$0.156000\pi$
$398$	−32.5623	−	23.6579i	−1.63220	−	1.18586i
$399$	0.618034	−	1.90211i	0.0309404	−	0.0952248i
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−12.5451	+	9.11454i	−0.626472	+	0.455158i	−0.855176	−	0.518338i	$-0.826551\pi$
$401$	−12.5451	+	9.11454i	−0.626472	+	0.455158i	0.228704	+	0.973496i	$0.426551\pi$
$402$	9.14590	−	6.64488i	0.456156	−	0.331417i
$403$	4.61803	+	14.2128i	0.230041	+	0.707992i
$404$	−12.7082	+	39.1118i	−0.632257	+	1.94589i
$405$	4.61803	+	3.35520i	0.229472	+	0.166721i
$406$	1.90983			0.0947833
$407$	2.23607	−	23.8949i	0.110838	−	1.18443i
$408$	−7.76393			−0.384372
$409$	2.61803	+	1.90211i	0.129453	+	0.0940534i	0.650628	−	0.759397i	$-0.274506\pi$
$409$	2.61803	+	1.90211i	0.129453	+	0.0940534i	−0.521174	+	0.853450i	$0.674506\pi$
$410$	1.70820	−	5.25731i	0.0843622	−	0.259640i
$411$	−2.18034	−	6.71040i	−0.107548	−	0.330999i
$412$	42.0517	−	30.5523i	2.07174	−	1.50520i
$413$	−7.47214	+	5.42882i	−0.367680	+	0.267135i
$414$	−8.09017	−	24.8990i	−0.397610	−	1.22372i
$415$	−2.95492	+	9.09429i	−0.145051	+	0.446421i
$416$	−25.0623	−	18.2088i	−1.22878	−	0.892761i
$417$	3.41641			0.167302
$418$	−23.4164	+	5.25731i	−1.14533	+	0.257143i
$419$	−35.3050			−1.72476			−0.862380	−	0.506262i	$-0.831027\pi$
$419$	−35.3050			−1.72476			−0.862380	+	0.506262i	$0.831027\pi$
$420$	−1.50000	−	1.08981i	−0.0731925	−	0.0531775i
$421$	−10.6631	+	32.8177i	−0.519689	+	1.59944i	0.254897	+	0.966968i	$0.417958\pi$
$421$	−10.6631	+	32.8177i	−0.519689	+	1.59944i	−0.774586	+	0.632469i	$0.782042\pi$
$422$	−5.30244	−	16.3192i	−0.258119	−	0.794408i
$423$	−2.42705	+	1.76336i	−0.118007	+	0.0857373i
$424$	−2.76393	+	2.00811i	−0.134228	+	0.0975226i
$425$	1.73607	+	5.34307i	0.0842117	+	0.259177i
$426$	−6.97214	+	21.4580i	−0.337801	+	1.03964i
$427$	−3.85410	−	2.80017i	−0.186513	−	0.135510i
$428$	−21.7082			−1.04931
$429$	−9.23607	+	2.07363i	−0.445922	+	0.100116i
$430$	−11.7082			−0.564620
$431$	4.30902	+	3.13068i	0.207558	+	0.150800i	0.686708	−	0.726933i	$-0.259055\pi$
$431$	4.30902	+	3.13068i	0.207558	+	0.150800i	−0.479150	+	0.877733i	$0.659055\pi$
$432$	1.07295	−	3.30220i	0.0516223	−	0.158877i
$433$	3.71885	+	11.4454i	0.178716	+	0.550032i	0.999784	−	0.0207989i	$-0.00662098\pi$
$433$	3.71885	+	11.4454i	0.178716	+	0.550032i	−0.821067	+	0.570831i	$0.806621\pi$
$434$	−5.85410	+	4.25325i	−0.281006	+	0.204163i
$435$	0.427051	−	0.310271i	0.0204755	−	0.0148763i
$436$	−10.6869	−	32.8910i	−0.511811	−	1.57519i
$437$	4.47214	−	13.7638i	0.213931	−	0.658413i
$438$	7.13525	+	5.18407i	0.340936	+	0.247704i
$439$	4.29180			0.204836			0.102418	−	0.994741i	$-0.467342\pi$
$439$	4.29180			0.204836			0.102418	+	0.994741i	$0.467342\pi$
$440$	−0.690983	+	7.38394i	−0.0329413	+	0.352015i
$441$	−2.61803			−0.124668
$442$	46.9336	+	34.0993i	2.23241	+	1.62194i
$443$	−1.03444	+	3.18368i	−0.0491478	+	0.151261i	−0.972618	−	0.232408i	$-0.925340\pi$
$443$	−1.03444	+	3.18368i	−0.0491478	+	0.151261i	0.923471	+	0.383669i	$0.125340\pi$
$444$	−4.14590	−	12.7598i	−0.196756	−	0.605552i
$445$	10.3262	−	7.50245i	0.489511	−	0.355650i
$446$	2.76393	−	2.00811i	0.130876	−	0.0950870i
$447$	−3.40983	−	10.4944i	−0.161279	−	0.496367i
$448$	4.01722	−	12.3637i	0.189796	−	0.584132i
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	0.750523	−	0.660844i	$-0.229802\pi$
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	−0.396576	+	0.918002i	$0.629802\pi$
$450$	5.85410			0.275965
$451$	5.41641	−	6.15537i	0.255049	−	0.289845i
$452$	31.4164			1.47770
$453$	0.190983	+	0.138757i	0.00897316	+	0.00651939i
$454$	7.46149	−	22.9641i	0.350185	−	1.07776i
$455$	1.42705	+	4.39201i	0.0669012	+	0.205901i
$456$	−3.61803	+	2.62866i	−0.169430	+	0.123098i
$457$	30.5623	−	22.2048i	1.42964	−	1.03870i	0.439562	−	0.898212i	$-0.355134\pi$
$457$	30.5623	−	22.2048i	1.42964	−	1.03870i	0.990083	−	0.140485i	$-0.0448662\pi$
$458$	17.1115	+	52.6636i	0.799566	+	2.46081i
$459$	−6.02786	+	18.5519i	−0.281357	+	0.865927i
$460$	−10.8541	−	7.88597i	−0.506075	−	0.367685i
$461$	16.2918			0.758785			0.379392	−	0.925236i	$-0.376133\pi$
$461$	16.2918			0.758785			0.379392	+	0.925236i	$0.376133\pi$
$462$	−2.33688	−	3.94298i	−0.108722	−	0.183444i
$463$	−17.1246			−0.795848			−0.397924	−	0.917418i	$-0.630269\pi$
$463$	−17.1246			−0.795848			−0.397924	+	0.917418i	$0.630269\pi$
$464$	0.690983	+	0.502029i	0.0320781	+	0.0233061i
$465$	−0.618034	+	1.90211i	−0.0286606	+	0.0882084i
$466$	−4.59675	−	14.1473i	−0.212940	−	0.655363i
$467$	26.1525	−	19.0009i	1.21019	−	0.879256i	0.214944	−	0.976626i	$-0.431043\pi$
$467$	26.1525	−	19.0009i	1.21019	−	0.879256i	0.995248	+	0.0973702i	$0.0310431\pi$
$468$	29.3435	−	21.3193i	1.35640	−	0.985484i
$469$	−2.52786	−	7.77997i	−0.116726	−	0.359245i
$470$	−0.791796	+	2.43690i	−0.0365228	+	0.112406i
$471$	8.04508	+	5.84510i	0.370698	+	0.269328i
$472$	20.6525			0.950607
$473$	−15.9443	−	6.88191i	−0.733118	−	0.316431i
$474$	−14.9230			−0.685435
$475$	2.61803	+	1.90211i	0.120124	+	0.0872749i
$476$	−5.20820	+	16.0292i	−0.238718	+	0.734697i
$477$	1.23607	+	3.80423i	0.0565957	+	0.174184i
$478$	45.1869	−	32.8302i	2.06680	−	1.50162i
$479$	−18.3262	+	13.3148i	−0.837347	+	0.608368i	−0.921628	−	0.388074i	$-0.873141\pi$
$479$	−18.3262	+	13.3148i	−0.837347	+	0.608368i	0.0842812	+	0.996442i	$0.473141\pi$
$480$	−1.28115	−	3.94298i	−0.0584764	−	0.179972i
$481$	−10.3262	+	31.7809i	−0.470836	+	1.44908i
$482$	−30.9787	−	22.5074i	−1.41104	−	1.02518i
$483$	2.76393			0.125763
$484$	−15.8435	+	28.9480i	−0.720157	+	1.31582i
$485$	15.3262			0.695929
$486$	25.2254	+	18.3273i	1.14425	+	0.831345i
$487$	−0.562306	+	1.73060i	−0.0254805	+	0.0784210i	−0.962988	−	0.269544i	$-0.913127\pi$
$487$	−0.562306	+	1.73060i	−0.0254805	+	0.0784210i	0.937508	+	0.347965i	$0.113127\pi$
$488$	3.29180	+	10.1311i	0.149013	+	0.458614i
$489$	11.0902	−	8.05748i	0.501515	−	0.364372i
$490$	−1.80902	+	1.31433i	−0.0817231	+	0.0593753i
$491$	0.652476	+	2.00811i	0.0294458	+	0.0906249i	0.964699	−	0.263354i	$-0.0848286\pi$
$491$	0.652476	+	2.00811i	0.0294458	+	0.0906249i	−0.935254	+	0.353979i	$0.884829\pi$
$492$	1.41641	−	4.35926i	0.0638566	−	0.196530i
$493$	−3.88197	−	2.82041i	−0.174835	−	0.127025i
$494$	33.4164			1.50348
$495$	7.97214	+	3.44095i	0.358321	+	0.154659i
$496$	−3.23607			−0.145304
$497$	13.2082	+	9.59632i	0.592469	+	0.430454i
$498$	−4.08359	+	12.5680i	−0.182990	+	0.563186i
$499$	−7.11803	−	21.9071i	−0.318647	−	0.980695i	−0.974227	−	0.225569i	$-0.927576\pi$
$499$	−7.11803	−	21.9071i	−0.318647	−	0.980695i	0.655580	−	0.755126i	$-0.272424\pi$
$500$	2.42705	−	1.76336i	0.108541	−	0.0788597i
$501$	6.00000	−	4.35926i	0.268060	−	0.194757i
$502$	5.32624	+	16.3925i	0.237722	+	0.731632i
$503$	0.954915	−	2.93893i	0.0425776	−	0.131040i	−0.927508	−	0.373803i	$-0.878054\pi$
$503$	0.954915	−	2.93893i	0.0425776	−	0.131040i	0.970086	+	0.242763i	$0.0780536\pi$
$504$	4.73607	+	3.44095i	0.210961	+	0.153272i
$505$	13.7082			0.610007
$506$	−16.9098	−	28.5317i	−0.751734	−	1.26839i
$507$	5.14590			0.228537
$508$	−22.4164	−	16.2865i	−0.994567	−	0.722595i
$509$	8.14590	−	25.0705i	0.361061	−	1.11123i	−0.591351	−	0.806414i	$-0.701405\pi$
$509$	8.14590	−	25.0705i	0.361061	−	1.11123i	0.952411	−	0.304816i	$-0.0985949\pi$
$510$	2.39919	+	7.38394i	0.106238	+	0.326966i
$511$	5.16312	−	3.75123i	0.228403	−	0.165944i
$512$	9.04508	−	6.57164i	0.399740	−	0.290428i
$513$	3.47214	+	10.6861i	0.153299	+	0.471804i
$514$	1.64590	−	5.06555i	0.0725975	−	0.223432i
$515$	−14.0172	−	10.1841i	−0.617673	−	0.448765i
$516$	−9.70820			−0.427380
$517$	−2.51064	+	2.85317i	−0.110418	+	0.125482i
$518$	−16.1803			−0.710923
$519$	0.781153	+	0.567541i	0.0342888	+	0.0249123i
$520$	3.19098	−	9.82084i	0.139934	−	0.430672i
$521$	−4.38197	−	13.4863i	−0.191977	−	0.590846i	−0.999999	−	0.00169226i	$-0.999461\pi$
$521$	−4.38197	−	13.4863i	−0.191977	−	0.590846i	0.808021	−	0.589153i	$-0.200539\pi$
$522$	−4.04508	+	2.93893i	−0.177049	+	0.128633i
$523$	−0.927051	+	0.673542i	−0.0405371	+	0.0294519i	−0.607869	−	0.794037i	$-0.707976\pi$
$523$	−0.927051	+	0.673542i	−0.0405371	+	0.0294519i	0.567332	+	0.823489i	$0.307976\pi$
$524$	7.41641	+	22.8254i	0.323987	+	0.997130i
$525$	−0.190983	+	0.587785i	−0.00833518	+	0.0256531i
$526$	25.6525	+	18.6376i	1.11850	+	0.812639i
$527$	18.1803			0.791948
$528$	0.190983	−	2.04087i	0.00831147	−	0.0888175i
$529$	−3.00000			−0.130435
$530$	2.76393	+	2.00811i	0.120058	+	0.0872269i
$531$	7.47214	−	22.9969i	0.324263	−	0.997979i
$532$	3.00000	+	9.23305i	0.130066	+	0.400304i
$533$	−9.23607	+	6.71040i	−0.400059	+	0.290660i
$534$	14.2705	−	10.3681i	0.617545	−	0.448673i
$535$	2.23607	+	6.88191i	0.0966736	+	0.297531i
$536$	−5.65248	+	17.3965i	−0.244150	+	0.751416i
$537$	−9.80902	−	7.12667i	−0.423290	−	0.307538i
$538$	41.7082			1.79817
$539$	−3.23607	+	0.726543i	−0.139387	+	0.0312944i
$540$	10.4164			0.448251
$541$	−4.97214	−	3.61247i	−0.213769	−	0.155312i	0.475748	−	0.879581i	$-0.342177\pi$
$541$	−4.97214	−	3.61247i	−0.213769	−	0.155312i	−0.689517	+	0.724269i	$0.742177\pi$
$542$	−16.0557	+	49.4145i	−0.689653	+	2.12253i
$543$	1.05573	+	3.24920i	0.0453056	+	0.139436i
$544$	−30.4894	+	22.1518i	−1.30722	+	0.949751i
$545$	−9.32624	+	6.77591i	−0.399492	+	0.290248i
$546$	1.97214	+	6.06961i	0.0843996	+	0.259755i
$547$	−5.58359	+	17.1845i	−0.238737	+	0.734757i	0.757866	+	0.652410i	$0.226242\pi$
$547$	−5.58359	+	17.1845i	−0.238737	+	0.734757i	−0.996604	+	0.0823478i	$0.973758\pi$
$548$	27.7082	+	20.1312i	1.18364	+	0.859962i
$549$	12.4721			0.532298
$550$	7.23607	−	1.62460i	0.308547	−	0.0692731i
$551$	−2.76393			−0.117747
$552$	−5.00000	−	3.63271i	−0.212814	−	0.154619i
$553$	−3.33688	+	10.2699i	−0.141899	+	0.436719i
$554$	6.50658	+	20.0252i	0.276438	+	0.850789i
$555$	−3.61803	+	2.62866i	−0.153577	+	0.111580i
$556$	−13.4164	+	9.74759i	−0.568982	+	0.413390i
$557$	−5.47214	−	16.8415i	−0.231862	−	0.713597i	−0.997522	−	0.0703523i	$-0.977588\pi$
$557$	−5.47214	−	16.8415i	−0.231862	−	0.713597i	0.765660	−	0.643245i	$-0.222412\pi$
$558$	5.85410	−	18.0171i	0.247824	−	0.762724i
$559$	19.5623	+	14.2128i	0.827397	+	0.601139i
$560$	−1.00000			−0.0422577
$561$	−1.07295	+	11.4657i	−0.0452999	+	0.484081i
$562$	18.9443			0.799116
$563$	19.1074	+	13.8823i	0.805281	+	0.585071i	0.912458	−	0.409169i	$-0.134181\pi$
$563$	19.1074	+	13.8823i	0.805281	+	0.585071i	−0.107178	+	0.994240i	$0.534181\pi$
$564$	−0.656541	+	2.02063i	−0.0276454	+	0.0850837i
$565$	−3.23607	−	9.95959i	−0.136142	−	0.419003i
$566$	−13.4549	+	9.77557i	−0.565552	+	0.410898i
$567$	4.61803	−	3.35520i	0.193939	−	0.140905i
$568$	−11.2812	−	34.7198i	−0.473347	−	1.45681i
$569$	−11.6803	+	35.9484i	−0.489665	+	1.50703i	0.335443	+	0.942060i	$0.391114\pi$
$569$	−11.6803	+	35.9484i	−0.489665	+	1.50703i	−0.825108	+	0.564974i	$0.808886\pi$
$570$	3.61803	+	2.62866i	0.151543	+	0.110102i
$571$	−35.9787			−1.50566			−0.752831	−	0.658214i	$-0.771312\pi$
$571$	−35.9787			−1.50566			−0.752831	+	0.658214i	$0.771312\pi$
$572$	30.3541	−	34.4953i	1.26917	−	1.44232i
$573$	14.2705			0.596159
$574$	−4.47214	−	3.24920i	−0.186663	−	0.135619i
$575$	−1.38197	+	4.25325i	−0.0576320	+	0.177373i
$576$	10.5172	+	32.3687i	0.438218	+	1.34869i
$577$	−26.8713	+	19.5232i	−1.11867	+	0.812760i	−0.984007	−	0.178132i	$-0.942995\pi$
$577$	−26.8713	+	19.5232i	−1.11867	+	0.812760i	−0.134661	+	0.990892i	$0.542995\pi$
$578$	26.3435	−	19.1396i	1.09574	−	0.796104i
$579$	0.763932	+	2.35114i	0.0317479	+	0.0977101i
$580$	−0.791796	+	2.43690i	−0.0328775	+	0.101187i
$581$	7.73607	+	5.62058i	0.320946	+	0.233181i
$582$	21.1803			0.877953
$583$	2.58359	+	4.35926i	0.107001	+	0.180542i
$584$	−14.2705			−0.590518
$585$	−9.78115	−	7.10642i	−0.404401	−	0.293814i
$586$	6.50658	−	20.0252i	0.268784	−	0.827233i
$587$	2.07953	+	6.40013i	0.0858313	+	0.264161i	0.984756	−	0.173942i	$-0.0556504\pi$
$587$	2.07953	+	6.40013i	0.0858313	+	0.264161i	−0.898925	+	0.438103i	$0.855650\pi$
$588$	−1.50000	+	1.08981i	−0.0618590	+	0.0449432i
$589$	8.47214	−	6.15537i	0.349088	−	0.253627i
$590$	−6.38197	−	19.6417i	−0.262741	−	0.808635i
$591$	−2.29180	+	7.05342i	−0.0942719	+	0.290139i
$592$	−5.85410	−	4.25325i	−0.240602	−	0.174808i
$593$	9.79837			0.402371			0.201185	−	0.979553i	$-0.435521\pi$
$593$	9.79837			0.402371			0.201185	+	0.979553i	$0.435521\pi$
$594$	23.6418	+	10.2044i	0.970036	+	0.418690i
$595$	5.61803			0.230317
$596$	43.3328	+	31.4831i	1.77498	+	1.28960i
$597$	−3.43769	+	10.5801i	−0.140695	+	0.433016i
$598$	14.2705	+	43.9201i	0.583565	+	1.79603i
$599$	−21.2533	+	15.4414i	−0.868386	+	0.630919i	−0.930153	−	0.367171i	$-0.880326\pi$
$599$	−21.2533	+	15.4414i	−0.868386	+	0.630919i	0.0617675	+	0.998091i	$0.480326\pi$
$600$	1.11803	−	0.812299i	0.0456435	−	0.0331620i
$601$	−4.76393	−	14.6619i	−0.194325	−	0.598070i	−0.999984	−	0.00569073i	$-0.998189\pi$
$601$	−4.76393	−	14.6619i	−0.194325	−	0.598070i	0.805659	−	0.592380i	$-0.201811\pi$
$602$	−3.61803	+	11.1352i	−0.147460	+	0.453835i
$603$	17.3262	+	12.5882i	0.705579	+	0.512633i
$604$	−1.14590			−0.0466259
$605$	10.8090	+	2.04087i	0.439449	+	0.0829732i
$606$	18.9443			0.769558
$607$	1.54508	+	1.12257i	0.0627131	+	0.0455637i	0.618700	−	0.785627i	$-0.287660\pi$
$607$	1.54508	+	1.12257i	0.0627131	+	0.0455637i	−0.555987	+	0.831191i	$0.687660\pi$
$608$	−6.70820	+	20.6457i	−0.272054	+	0.837295i
$609$	−0.163119	−	0.502029i	−0.00660991	−	0.0203432i
$610$	8.61803	−	6.26137i	0.348934	−	0.253515i
$611$	4.28115	−	3.11044i	0.173197	−	0.125835i
$612$	−13.6353	−	41.9650i	−0.551173	−	1.69633i
$613$	−12.6180	+	38.8343i	−0.509638	+	1.56850i	0.283194	+	0.959063i	$0.408606\pi$
$613$	−12.6180	+	38.8343i	−0.509638	+	1.56850i	−0.792832	+	0.609441i	$0.791394\pi$
$614$	−37.1976	−	27.0256i	−1.50117	−	1.09066i
$615$	−1.52786			−0.0616094
$616$	6.80902	+	2.93893i	0.274343	+	0.118413i
$617$	−2.76393			−0.111272			−0.0556359	−	0.998451i	$-0.517719\pi$
$617$	−2.76393			−0.111272			−0.0556359	+	0.998451i	$0.517719\pi$
$618$	−19.3713	−	14.0741i	−0.779229	−	0.566143i
$619$	−6.94427	+	21.3723i	−0.279114	+	0.859024i	0.708988	+	0.705221i	$0.249152\pi$
$619$	−6.94427	+	21.3723i	−0.279114	+	0.859024i	−0.988101	+	0.153803i	$0.950848\pi$
$620$	−3.00000	−	9.23305i	−0.120483	−	0.370808i
$621$	−12.5623	+	9.12705i	−0.504108	+	0.366256i
$622$	23.7426	−	17.2500i	0.951993	−	0.691664i
$623$	−3.94427	−	12.1392i	−0.158024	−	0.486348i
$624$	−0.881966	+	2.71441i	−0.0353069	+	0.108663i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	40.2492			1.60868
$627$	3.38197	+	5.70634i	0.135063	+	0.227889i
$628$	−48.2705			−1.92620
$629$	32.8885	+	23.8949i	1.31135	+	0.952753i
$630$	1.80902	−	5.56758i	0.0720730	−	0.221818i
$631$	−2.93769	−	9.04129i	−0.116948	−	0.359928i	0.875401	−	0.483398i	$-0.160598\pi$
$631$	−2.93769	−	9.04129i	−0.116948	−	0.359928i	−0.992348	+	0.123470i	$0.960598\pi$
$632$	19.5344	−	14.1926i	0.777038	−	0.564551i
$633$	−3.83688	+	2.78766i	−0.152502	+	0.110799i
$634$	14.8754	+	45.7817i	0.590777	+	1.81823i
$635$	−2.85410	+	8.78402i	−0.113262	+	0.348583i
$636$	2.29180	+	1.66509i	0.0908756	+	0.0660250i
$637$	4.61803			0.182973
$638$	−4.18441	+	4.75528i	−0.165662	+	0.188263i
$639$	−42.7426			−1.69087
$640$	12.6631	+	9.20029i	0.500554	+	0.363674i
$641$	6.48278	−	19.9519i	0.256054	−	0.788054i	−0.737566	−	0.675275i	$-0.764025\pi$
$641$	6.48278	−	19.9519i	0.256054	−	0.788054i	0.993620	−	0.112779i	$-0.0359752\pi$
$642$	3.09017	+	9.51057i	0.121959	+	0.375352i
$643$	−8.73607	+	6.34712i	−0.344517	+	0.250306i	−0.746565	−	0.665312i	$-0.768298\pi$
$643$	−8.73607	+	6.34712i	−0.344517	+	0.250306i	0.402048	+	0.915618i	$0.368298\pi$
$644$	−10.8541	+	7.88597i	−0.427712	+	0.310751i
$645$	1.00000	+	3.07768i	0.0393750	+	0.121184i
$646$	12.5623	−	38.6628i	0.494257	−	1.52117i
$647$	37.9058	+	27.5402i	1.49023	+	1.08272i	0.974077	+	0.226219i	$0.0726363\pi$
$647$	37.9058	+	27.5402i	1.49023	+	1.08272i	0.516153	+	0.856497i	$0.327364\pi$
$648$	−12.7639			−0.501415
$649$	2.85410	−	30.4993i	0.112033	−	1.19720i
$650$	−10.3262			−0.405028
$651$	1.61803	+	1.17557i	0.0634158	+	0.0460742i
$652$	−20.5623	+	63.2843i	−0.805282	+	2.47840i
$653$	−11.7984	−	36.3117i	−0.461706	−	1.42099i	−0.863078	−	0.505070i	$-0.831467\pi$
$653$	−11.7984	−	36.3117i	−0.461706	−	1.42099i	0.401372	−	0.915915i	$-0.368533\pi$
$654$	−12.8885	+	9.36408i	−0.503982	+	0.366164i
$655$	6.47214	−	4.70228i	0.252887	−	0.183733i
$656$	−0.763932	−	2.35114i	−0.0298265	−	0.0917966i
$657$	−5.16312	+	15.8904i	−0.201432	+	0.619945i
$658$	2.07295	+	1.50609i	0.0808120	+	0.0587133i
$659$	−4.03444			−0.157160			−0.0785798	−	0.996908i	$-0.525039\pi$
$659$	−4.03444			−0.157160			−0.0785798	+	0.996908i	$0.525039\pi$
$660$	6.00000	−	1.34708i	0.233550	−	0.0524352i
$661$	−6.58359			−0.256072			−0.128036	−	0.991770i	$-0.540867\pi$
$661$	−6.58359			−0.256072			−0.128036	+	0.991770i	$0.540867\pi$
$662$	−33.4787	−	24.3237i	−1.30119	−	0.945368i
$663$	4.95492	−	15.2497i	0.192433	−	0.592248i
$664$	−6.60739	−	20.3355i	−0.256416	−	0.789169i
$665$	2.61803	−	1.90211i	0.101523	−	0.0737608i
$666$	34.2705	−	24.8990i	1.32796	−	0.964816i
$667$	−1.18034	−	3.63271i	−0.0457029	−	0.140659i
$668$	−11.1246	+	34.2380i	−0.430424	+	1.32471i
$669$	−0.763932	−	0.555029i	−0.0295353	−	0.0214587i
$670$	18.2918			0.706674
$671$	15.4164	−	3.46120i	0.595144	−	0.133618i
$672$	−4.14590			−0.159931
$673$	−17.7082	−	12.8658i	−0.682601	−	0.495939i	0.191618	−	0.981469i	$-0.438626\pi$
$673$	−17.7082	−	12.8658i	−0.682601	−	0.495939i	−0.874220	+	0.485531i	$0.838626\pi$
$674$	21.7082	−	66.8110i	0.836169	−	2.57346i
$675$	−1.07295	−	3.30220i	−0.0412978	−	0.127102i
$676$	−20.2082	+	14.6821i	−0.777239	+	0.564697i
$677$	−39.5238	+	28.7157i	−1.51902	+	1.10363i	−0.557054	+	0.830476i	$0.688068\pi$
$677$	−39.5238	+	28.7157i	−1.51902	+	1.10363i	−0.961969	+	0.273158i	$0.911932\pi$
$678$	−4.47214	−	13.7638i	−0.171751	−	0.528596i
$679$	4.73607	−	14.5761i	0.181754	−	0.559380i
$680$	−10.1631	−	7.38394i	−0.389738	−	0.283161i
$681$	−6.67376			−0.255739
$682$	2.23607	−	23.8949i	0.0856235	−	0.914984i
$683$	34.7639			1.33020			0.665102	−	0.746752i	$-0.268388\pi$
$683$	34.7639			1.33020			0.665102	+	0.746752i	$0.268388\pi$
$684$	−20.5623	−	14.9394i	−0.786219	−	0.571222i
$685$	3.52786	−	10.8576i	0.134793	−	0.414849i
$686$	0.690983	+	2.12663i	0.0263819	+	0.0811950i
$687$	12.3820	−	8.99602i	0.472401	−	0.343220i
$688$	−4.23607	+	3.07768i	−0.161499	+	0.117336i
$689$	−2.18034	−	6.71040i	−0.0830643	−	0.255646i
$690$	−1.90983	+	5.87785i	−0.0727060	+	0.223766i
$691$	21.7082	+	15.7719i	0.825819	+	0.599993i	0.918373	−	0.395715i	$-0.129503\pi$
$691$	21.7082	+	15.7719i	0.825819	+	0.599993i	−0.0925544	+	0.995708i	$0.529503\pi$
$692$	−4.68692			−0.178170
$693$	5.73607	−	6.51864i	0.217895	−	0.247623i
$694$	3.41641			0.129685
$695$	4.47214	+	3.24920i	0.169638	+	0.123249i
$696$	−0.364745	+	1.12257i	−0.0138256	+	0.0425509i
$697$	4.29180	+	13.2088i	0.162563	+	0.500319i
$698$	7.03444	−	5.11082i	0.266258	−	0.193447i
$699$	−3.32624	+	2.41665i	−0.125810	+	0.0914062i
$700$	−0.927051	−	2.85317i	−0.0350392	−	0.107840i
$701$	−15.8541	+	48.7939i	−0.598801	+	1.84292i	−0.0639871	+	0.997951i	$0.520382\pi$
$701$	−15.8541	+	48.7939i	−0.598801	+	1.84292i	−0.534814	+	0.844970i	$0.679618\pi$
$702$	−29.0066	−	21.0745i	−1.09478	−	0.795406i
$703$	23.4164			0.883167
$704$	21.9828	+	37.0912i	0.828507	+	1.39793i
$705$	0.708204			0.0266725
$706$	−24.5344	−	17.8253i	−0.923366	−	0.670865i
$707$	4.23607	−	13.0373i	0.159314	−	0.490317i
$708$	−5.29180	−	16.2865i	−0.198878	−	0.612083i
$709$	−0.208204	+	0.151269i	−0.00781926	+	0.00568103i	−0.591688	−	0.806167i	$-0.701538\pi$
$709$	−0.208204	+	0.151269i	−0.00781926	+	0.00568103i	0.583869	+	0.811848i	$0.301538\pi$
$710$	−29.5344	+	21.4580i	−1.10841	+	0.805305i
$711$	−8.73607	−	26.8869i	−0.327628	−	1.00834i
$712$	−8.81966	+	27.1441i	−0.330531	+	1.01727i
$713$	11.7082	+	8.50651i	0.438476	+	0.318571i
$714$	7.76393			0.290558
$715$	−14.0623	−	6.06961i	−0.525900	−	0.226991i
$716$	58.8541			2.19948
$717$	−12.4894	−	9.07405i	−0.466424	−	0.338877i
$718$	8.96807	−	27.6009i	0.334685	−	1.03006i
$719$	6.76393	+	20.8172i	0.252252	+	0.776352i	0.994359	+	0.106070i	$0.0338268\pi$
$719$	6.76393	+	20.8172i	0.252252	+	0.776352i	−0.742107	+	0.670282i	$0.766173\pi$
$720$	2.11803	−	1.53884i	0.0789345	−	0.0573492i
$721$	−14.0172	+	10.1841i	−0.522029	+	0.379276i
$722$	5.89261	+	18.1356i	0.219300	+	0.674937i
$723$	−3.27051	+	10.0656i	−0.121632	+	0.374343i
$724$	−13.4164	−	9.74759i	−0.498617	−	0.362266i
$725$	0.854102			0.0317206
$726$	14.9377	+	2.82041i	0.554390	+	0.104675i
$727$	−41.5623			−1.54146			−0.770730	−	0.637162i	$-0.780108\pi$
$727$	−41.5623			−1.54146			−0.770730	+	0.637162i	$0.780108\pi$
$728$	−8.35410	−	6.06961i	−0.309624	−	0.224955i
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$	4.40983	+	13.5721i	0.163215	+	0.502325i
$731$	23.7984	−	17.2905i	0.880215	−	0.639513i
$732$	7.14590	−	5.19180i	0.264120	−	0.191894i
$733$	10.7746	+	33.1607i	0.397968	+	1.22482i	0.926626	+	0.375985i	$0.122695\pi$
$733$	10.7746	+	33.1607i	0.397968	+	1.22482i	−0.528658	+	0.848835i	$0.677305\pi$
$734$	21.7320	−	66.8842i	0.802143	−	2.46874i
$735$	0.500000	+	0.363271i	0.0184428	+	0.0133995i
$736$	−30.0000			−1.10581
$737$	24.9098	+	10.7516i	0.917565	+	0.396042i
$738$	14.4721			0.532727
$739$	−9.70820	−	7.05342i	−0.357122	−	0.259464i	0.394729	−	0.918798i	$-0.370839\pi$
$739$	−9.70820	−	7.05342i	−0.357122	−	0.259464i	−0.751851	+	0.659333i	$0.770839\pi$
$740$	6.70820	−	20.6457i	0.246598	−	0.758952i
$741$	−2.85410	−	8.78402i	−0.104848	−	0.322689i
$742$	2.76393	−	2.00811i	0.101467	−	0.0737202i
$743$	−4.32624	+	3.14320i	−0.158714	+	0.115313i	−0.664308	−	0.747459i	$-0.731274\pi$
$743$	−4.32624	+	3.14320i	−0.158714	+	0.115313i	0.505594	+	0.862772i	$0.331274\pi$
$744$	−1.38197	−	4.25325i	−0.0506653	−	0.155932i
$745$	5.51722	−	16.9803i	0.202135	−	0.622109i
$746$	20.1246	+	14.6214i	0.736814	+	0.535327i
$747$	−25.0344			−0.915962
$748$	−28.5000	−	48.0876i	−1.04206	−	1.75826i
$749$	7.23607			0.264400
$750$	−1.11803	−	0.812299i	−0.0408248	−	0.0296610i
$751$	11.5344	−	35.4994i	0.420898	−	1.29539i	−0.485970	−	0.873975i	$-0.661534\pi$
$751$	11.5344	−	35.4994i	0.420898	−	1.29539i	0.906868	−	0.421415i	$-0.138466\pi$
$752$	0.354102	+	1.08981i	0.0129128	+	0.0397414i
$753$	3.85410	−	2.80017i	0.140451	−	0.102044i
$754$	7.13525	−	5.18407i	0.259851	−	0.188793i
$755$	0.118034	+	0.363271i	0.00429570	+	0.0132208i
$756$	3.21885	−	9.90659i	0.117068	−	0.360299i
$757$	−3.38197	−	2.45714i	−0.122920	−	0.0893063i	0.524627	−	0.851332i	$-0.324205\pi$
$757$	−3.38197	−	2.45714i	−0.122920	−	0.0893063i	−0.647547	+	0.762026i	$0.724205\pi$
$758$	−55.3262			−2.00954
$759$	−6.05573	+	6.88191i	−0.219809	+	0.249797i
$760$	−7.23607			−0.262480
$761$	−39.5066	−	28.7032i	−1.43211	−	1.04049i	−0.989619	−	0.143719i	$-0.954094\pi$
$761$	−39.5066	−	28.7032i	−1.43211	−	1.04049i	−0.442494	−	0.896772i	$-0.645906\pi$
$762$	−3.94427	+	12.1392i	−0.142886	+	0.439758i
$763$	3.56231	+	10.9637i	0.128964	+	0.396911i
$764$	−56.0410	+	40.7162i	−2.02749	+	1.47306i
$765$	−11.8992	+	8.64527i	−0.430216	+	0.312570i
$766$	−18.5172	−	56.9901i	−0.669054	−	2.05914i
$767$	−13.1803	+	40.5649i	−0.475914	+	1.46471i
$768$	4.50000	+	3.26944i	0.162380	+	0.117976i
$769$	11.7082			0.422209			0.211104	−	0.977464i	$-0.432294\pi$
$769$	11.7082			0.422209			0.211104	+	0.977464i	$0.432294\pi$
$770$	0.690983	−	7.38394i	0.0249013	−	0.266099i
$771$	−1.47214			−0.0530177
$772$	−9.70820	−	7.05342i	−0.349406	−	0.253858i
$773$	−8.46149	+	26.0418i	−0.304339	+	0.936658i	0.675584	+	0.737283i	$0.263891\pi$
$773$	−8.46149	+	26.0418i	−0.304339	+	0.936658i	−0.979923	+	0.199376i	$0.936109\pi$
$774$	−9.47214	−	29.1522i	−0.340469	−	1.04786i
$775$	−2.61803	+	1.90211i	−0.0940426	+	0.0683259i
$776$	−27.7254	+	20.1437i	−0.995285	+	0.723117i
$777$	1.38197	+	4.25325i	0.0495778	+	0.152585i
$778$	23.1910	−	71.3745i	0.831437	−	2.55890i
$779$	6.47214	+	4.70228i	0.231888	+	0.168477i
$780$	−8.56231			−0.306580
$781$	−52.8328	+	11.8617i	−1.89051	+	0.424445i
$782$	56.1803			2.00900
$783$	2.39919	+	1.74311i	0.0857399	+	0.0622937i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	4.97214	+	15.3027i	0.177463	+	0.546175i
$786$	8.94427	−	6.49839i	0.319032	−	0.231790i
$787$	−32.3885	+	23.5317i	−1.15453	+	0.838813i	−0.989076	−	0.147405i	$-0.952908\pi$
$787$	−32.3885	+	23.5317i	−1.15453	+	0.838813i	−0.165451	+	0.986218i	$0.552908\pi$
$788$	−11.1246	−	34.2380i	−0.396298	−	1.21968i
$789$	2.70820	−	8.33499i	0.0964146	−	0.296734i
$790$	−19.5344	−	14.1926i	−0.695004	−	0.504950i
$791$	−10.4721			−0.372346
$792$	−18.9443	+	4.25325i	−0.673155	+	0.151133i
$793$	−22.0000			−0.781243
$794$	63.6033	+	46.2105i	2.25720	+	1.63995i
$795$	0.291796	−	0.898056i	0.0103489	−	0.0318508i
$796$	−16.6869	−	51.3571i	−0.591452	−	1.82030i
$797$	−35.6803	+	25.9233i	−1.26386	+	0.918250i	−0.998941	−	0.0460200i	$-0.985346\pi$
$797$	−35.6803	+	25.9233i	−1.26386	+	0.918250i	−0.264922	+	0.964270i	$0.585346\pi$
$798$	3.61803	−	2.62866i	0.128077	−	0.0930534i
$799$	−1.98936	−	6.12261i	−0.0703784	−	0.216602i
$800$	2.07295	−	6.37988i	0.0732898	−	0.225563i
$801$	27.0344	+	19.6417i	0.955215	+	0.694004i
$802$	−34.6738			−1.22437
$803$	−1.97214	+	21.0745i	−0.0695952	+	0.743703i
$804$	15.1672			0.534905
$805$	3.61803	+	2.62866i	0.127519	+	0.0926479i
$806$	−10.3262	+	31.7809i	−0.363726	+	1.11943i
$807$	−3.56231	−	10.9637i	−0.125399	−	0.385939i
$808$	−24.7984	+	18.0171i	−0.872404	+	0.633838i
$809$	2.50000	−	1.81636i	0.0878953	−	0.0638597i	−0.542970	−	0.839752i	$-0.682700\pi$
$809$	2.50000	−	1.81636i	0.0878953	−	0.0638597i	0.630865	+	0.775893i	$0.282700\pi$
$810$	3.94427	+	12.1392i	0.138588	+	0.426529i
$811$	9.70820	−	29.8788i	0.340901	−	1.04919i	−0.622841	−	0.782349i	$-0.714021\pi$
$811$	9.70820	−	29.8788i	0.340901	−	1.04919i	0.963742	−	0.266837i	$-0.0859785\pi$
$812$	2.07295	+	1.50609i	0.0727462	+	0.0528532i
$813$	14.3607			0.503651
$814$	35.4508	−	40.2874i	1.24255	−	1.41207i
$815$	22.1803			0.776943
$816$	2.80902	+	2.04087i	0.0983353	+	0.0714448i
$817$	5.23607	−	16.1150i	0.183187	−	0.563791i
$818$	2.23607	+	6.88191i	0.0781823	+	0.240620i
$819$	−9.78115	+	7.10642i	−0.341781	+	0.248319i
$820$	6.00000	−	4.35926i	0.209529	−	0.152232i
$821$	3.91641	+	12.0535i	0.136684	+	0.420669i	0.995848	−	0.0910307i	$-0.0290161\pi$
$821$	3.91641	+	12.0535i	0.136684	+	0.420669i	−0.859165	+	0.511699i	$0.829016\pi$
$822$	4.87539	−	15.0049i	0.170049	−	0.523356i
$823$	16.1803	+	11.7557i	0.564011	+	0.409778i	0.832925	−	0.553386i	$-0.186665\pi$
$823$	16.1803	+	11.7557i	0.564011	+	0.409778i	−0.268914	+	0.963164i	$0.586665\pi$
$824$	38.7426			1.34966
$825$	−1.04508	−	1.76336i	−0.0363852	−	0.0613922i
$826$	−20.6525			−0.718592
$827$	30.6525	+	22.2703i	1.06589	+	0.774415i	0.975169	−	0.221461i	$-0.0710826\pi$
$827$	30.6525	+	22.2703i	1.06589	+	0.774415i	0.0907218	+	0.995876i	$0.471083\pi$
$828$	10.8541	−	33.4055i	0.377206	−	1.16092i
$829$	10.4721	+	32.2299i	0.363712	+	1.11939i	0.950783	+	0.309856i	$0.100281\pi$
$829$	10.4721	+	32.2299i	0.363712	+	1.11939i	−0.587071	+	0.809535i	$0.699719\pi$
$830$	−17.2984	+	12.5680i	−0.600435	+	0.436242i
$831$	4.70820	−	3.42071i	0.163326	−	0.118663i
$832$	−18.5517	−	57.0961i	−0.643163	−	1.97945i
$833$	1.73607	−	5.34307i	0.0601512	−	0.185126i
$834$	6.18034	+	4.49028i	0.214008	+	0.155486i
$835$	12.0000			0.415277
$836$	−29.5623	−	12.7598i	−1.02243	−	0.441306i
$837$	−11.2361			−0.388375
$838$	−63.8673	−	46.4023i	−2.20626	−	1.60294i
$839$	2.36068	−	7.26543i	0.0814997	−	0.250830i	−0.902001	−	0.431734i	$-0.857902\pi$
$839$	2.36068	−	7.26543i	0.0814997	−	0.250830i	0.983501	+	0.180903i	$0.0579021\pi$
$840$	−0.427051	−	1.31433i	−0.0147347	−	0.0453486i
$841$	22.8713	−	16.6170i	0.788666	−	0.573000i
$842$	−62.4230	+	45.3530i	−2.15124	+	1.56297i
$843$	−1.61803	−	4.97980i	−0.0557281	−	0.171513i
$844$	7.11397	−	21.8945i	0.244873	−	0.753641i
$845$	6.73607	+	4.89404i	0.231728	+	0.168360i
$846$	−6.70820			−0.230633
$847$	5.28115	−	9.64932i	0.181463	−	0.331555i
$848$	1.52786			0.0524671
$849$	3.71885	+	2.70190i	0.127631	+	0.0927290i
$850$	−3.88197	+	11.9475i	−0.133150	+	0.409795i
$851$	10.0000	+	30.7768i	0.342796	+	1.05502i
$852$	−24.4894	+	17.7926i	−0.838992	+	0.609563i
$853$	−14.9164	+	10.8374i	−0.510728	+	0.371066i	−0.813100	−	0.582124i	$-0.802222\pi$
$853$	−14.9164	+	10.8374i	−0.510728	+	0.371066i	0.302372	+	0.953190i	$0.402222\pi$
$854$	−3.29180	−	10.1311i	−0.112643	−	0.346679i
$855$	−2.61803	+	8.05748i	−0.0895349	+	0.275560i
$856$	−13.0902	−	9.51057i	−0.447413	−	0.325064i
$857$	−57.1935			−1.95369			−0.976846	−	0.213942i	$-0.931370\pi$
$857$	−57.1935			−1.95369			−0.976846	+	0.213942i	$0.931370\pi$
$858$	−19.4336	−	8.38800i	−0.663453	−	0.286361i
$859$	−11.0557			−0.377217			−0.188608	−	0.982052i	$-0.560398\pi$
$859$	−11.0557			−0.377217			−0.188608	+	0.982052i	$0.560398\pi$
$860$	−12.7082	−	9.23305i	−0.433346	−	0.314844i
$861$	−0.472136	+	1.45309i	−0.0160904	+	0.0495210i
$862$	3.68034	+	11.3269i	0.125353	+	0.385796i
$863$	−2.47214	+	1.79611i	−0.0841525	+	0.0611404i	−0.629066	−	0.777352i	$-0.716562\pi$
$863$	−2.47214	+	1.79611i	−0.0841525	+	0.0611404i	0.544914	+	0.838492i	$0.316562\pi$
$864$	18.8435	−	13.6906i	0.641067	−	0.465763i
$865$	0.482779	+	1.48584i	0.0164150	+	0.0505201i
$866$	−8.31559	+	25.5928i	−0.282575	+	0.869678i
$867$	−7.28115	−	5.29007i	−0.247281	−	0.179660i
$868$	−9.70820			−0.329518
$869$	−18.2599	−	30.8096i	−0.619424	−	1.04514i
$870$	1.18034			0.0400173
$871$	−30.5623	−	22.2048i	−1.03556	−	0.752381i
$872$	7.96556	−	24.5155i	0.269748	−	0.830198i
$873$	12.3992	+	38.1608i	0.419649	+	1.29155i
$874$	26.1803	−	19.0211i	0.885563	−	0.643399i
$875$	−0.809017	+	0.587785i	−0.0273498	+	0.0198708i
$876$	3.65654	+	11.2537i	0.123543	+	0.380226i
$877$	17.0000	−	52.3206i	0.574049	−	1.76674i	−0.0653450	−	0.997863i	$-0.520815\pi$
$877$	17.0000	−	52.3206i	0.574049	−	1.76674i	0.639394	−	0.768879i	$-0.279185\pi$
$878$	7.76393	+	5.64083i	0.262020	+	0.190369i
$879$	−5.81966			−0.196292
$880$	2.19098	−	2.48990i	0.0738580	−	0.0839345i
$881$	−5.23607			−0.176408			−0.0882038	−	0.996102i	$-0.528113\pi$
$881$	−5.23607			−0.176408			−0.0882038	+	0.996102i	$0.528113\pi$
$882$	−4.73607	−	3.44095i	−0.159472	−	0.115863i
$883$	−3.14590	+	9.68208i	−0.105868	+	0.325828i	−0.989933	−	0.141536i	$-0.954796\pi$
$883$	−3.14590	+	9.68208i	−0.105868	+	0.325828i	0.884065	+	0.467363i	$0.154796\pi$
$884$	24.0517	+	74.0234i	0.808945	+	2.48968i
$885$	−4.61803	+	3.35520i	−0.155234	+	0.112784i
$886$	−6.05573	+	4.39974i	−0.203446	+	0.147812i
$887$	−6.53444	−	20.1109i	−0.219405	−	0.675259i	−0.998811	−	0.0487407i	$-0.984479\pi$
$887$	−6.53444	−	20.1109i	−0.219405	−	0.675259i	0.779406	−	0.626519i	$-0.215521\pi$
$888$	3.09017	−	9.51057i	0.103699	−	0.319154i
$889$	7.47214	+	5.42882i	0.250607	+	0.182077i
$890$	28.5410			0.956697
$891$	−1.76393	+	18.8496i	−0.0590939	+	0.631486i
$892$	4.58359			0.153470
$893$	−3.00000	−	2.17963i	−0.100391	−	0.0729385i
$894$	7.62461	−	23.4661i	0.255005	−	0.784825i
$895$	−6.06231	−	18.6579i	−0.202641	−	0.623663i
$896$	12.6631	−	9.20029i	0.423045	−	0.307360i
$897$	10.3262	−	7.50245i	0.344783	−	0.250500i
$898$	6.40576	+	19.7149i	0.213763	+	0.657895i
$899$	0.854102	−	2.62866i	0.0284859	−	0.0876706i
$900$	6.35410	+	4.61653i	0.211803	+	0.153884i
$901$	−8.58359			−0.285961
$902$	17.8885	−	4.01623i	0.595623	−	0.133726i
$903$	3.23607			0.107690
$904$	18.9443	+	13.7638i	0.630077	+	0.457778i
$905$	−1.70820	+	5.25731i	−0.0567826	+	0.174759i
$906$	0.163119	+	0.502029i	0.00541926	+	0.0166788i
$907$	−22.5623	+	16.3925i	−0.749169	+	0.544303i	−0.895569	−	0.444922i	$-0.853231\pi$
$907$	−22.5623	+	16.3925i	−0.749169	+	0.544303i	0.146400	+	0.989225i	$0.453231\pi$
$908$	26.2082	−	19.0414i	0.869750	−	0.631910i
$909$	11.0902	+	34.1320i	0.367838	+	1.13209i
$910$	−3.19098	+	9.82084i	−0.105780	+	0.325558i
$911$	1.21885	+	0.885544i	0.0403822	+	0.0293394i	0.607793	−	0.794095i	$-0.292055\pi$
$911$	1.21885	+	0.885544i	0.0403822	+	0.0293394i	−0.567411	+	0.823435i	$0.692055\pi$
$912$	2.00000			0.0662266
$913$	−30.9443	+	6.94742i	−1.02411	+	0.229926i
$914$	84.4721			2.79409
$915$	−2.38197	−	1.73060i	−0.0787454	−	0.0572119i
$916$	−22.9574	+	70.6557i	−0.758535	+	2.33453i
$917$	−2.47214	−	7.60845i	−0.0816371	−	0.251253i
$918$	−35.2877	+	25.6380i	−1.16467	+	0.846181i
$919$	−1.83688	+	1.33457i	−0.0605931	+	0.0440235i	−0.617670	−	0.786438i	$-0.711923\pi$
$919$	−1.83688	+	1.33457i	−0.0605931	+	0.0440235i	0.557076	+	0.830461i	$0.311923\pi$
$920$	−3.09017	−	9.51057i	−0.101880	−	0.313554i
$921$	−3.92705	+	12.0862i	−0.129401	+	0.398254i
$922$	29.4721	+	21.4128i	0.970613	+	0.705192i
$923$	75.3951			2.48166
$924$	0.572949	−	6.12261i	0.0188486	−	0.201419i
$925$	−7.23607			−0.237920
$926$	−30.9787	−	22.5074i	−1.01802	−	0.739638i
$927$	14.0172	−	43.1406i	0.460386	−	1.41692i
$928$	1.77051	+	5.44907i	0.0581198	+	0.178874i
$929$	14.4721	−	10.5146i	0.474815	−	0.344974i	−0.324500	−	0.945886i	$-0.605196\pi$
$929$	14.4721	−	10.5146i	0.474815	−	0.344974i	0.799315	+	0.600912i	$0.205196\pi$
$930$	−3.61803	+	2.62866i	−0.118640	+	0.0861970i
$931$	−1.00000	−	3.07768i	−0.0327737	−	0.100867i
$932$	6.16718	−	18.9806i	0.202013	−	0.621732i
$933$	−6.56231	−	4.76779i	−0.214840	−	0.156091i
$934$	72.2837			2.36519
$935$	−12.3090	+	13.9883i	−0.402548	+	0.457467i
$936$	27.0344			0.883648
$937$	−0.444272	−	0.322782i	−0.0145137	−	0.0105448i	0.580505	−	0.814257i	$-0.302855\pi$
$937$	−0.444272	−	0.322782i	−0.0145137	−	0.0105448i	−0.595018	+	0.803712i	$0.702855\pi$
$938$	5.65248	−	17.3965i	0.184560	−	0.568017i
$939$	−3.43769	−	10.5801i	−0.112185	−	0.345270i
$940$	−2.78115	+	2.02063i	−0.0907112	+	0.0659055i
$941$	24.7082	−	17.9516i	0.805464	−	0.585204i	−0.107048	−	0.994254i	$-0.534140\pi$
$941$	24.7082	−	17.9516i	0.805464	−	0.585204i	0.912512	+	0.409050i	$0.134140\pi$
$942$	6.87132	+	21.1478i	0.223880	+	0.689031i
$943$	−3.41641	+	10.5146i	−0.111254	+	0.342403i
$944$	−7.47214	−	5.42882i	−0.243197	−	0.176693i
$945$	−3.47214			−0.112949
$946$	−19.7984	−	33.4055i	−0.643701	−	1.08611i
$947$	34.0689			1.10709			0.553545	−	0.832819i	$-0.313275\pi$
$947$	34.0689			1.10709			0.553545	+	0.832819i	$0.313275\pi$
$948$	−16.1976	−	11.7682i	−0.526072	−	0.382214i
$949$	9.10739	−	28.0297i	0.295638	−	0.909881i
$950$	2.23607	+	6.88191i	0.0725476	+	0.223279i
$951$	10.7639	−	7.82045i	0.349044	−	0.253596i
$952$	−10.1631	+	7.38394i	−0.329389	+	0.239315i
$953$	13.2705	+	40.8424i	0.429874	+	1.32302i	0.898249	+	0.439486i	$0.144840\pi$
$953$	13.2705	+	40.8424i	0.429874	+	1.32302i	−0.468375	+	0.883530i	$0.655160\pi$
$954$	−2.76393	+	8.50651i	−0.0894856	+	0.275408i
$955$	18.6803	+	13.5721i	0.604482	+	0.439182i
$956$	74.9361			2.42361
$957$	1.60739	+	0.693786i	0.0519596	+	0.0224269i
$958$	−50.6525			−1.63651
$959$	−9.23607	−	6.71040i	−0.298248	−	0.216690i
$960$	2.48278	−	7.64121i	0.0801314	−	0.246619i
$961$	−6.34346	−	19.5232i	−0.204628	−	0.629779i
$962$	−60.4508	+	43.9201i	−1.94901	+	1.41604i
$963$	−15.3262	+	11.1352i	−0.493881	+	0.358826i
$964$	−15.8754	−	48.8594i	−0.511312	−	1.57366i
$965$	−1.23607	+	3.80423i	−0.0397904	+	0.122462i
$966$	5.00000	+	3.63271i	0.160872	+	0.116881i
$967$	−16.7639			−0.539092			−0.269546	−	0.962988i	$-0.586874\pi$
$967$	−16.7639			−0.539092			−0.269546	+	0.962988i	$0.586874\pi$
$968$	−22.2361	+	10.5146i	−0.714694	+	0.337953i
$969$	−11.2361			−0.360955
$970$	27.7254	+	20.1437i	0.890210	+	0.646775i
$971$	−0.798374	+	2.45714i	−0.0256210	+	0.0788534i	−0.963049	−	0.269325i	$-0.913200\pi$
$971$	−0.798374	+	2.45714i	−0.0256210	+	0.0788534i	0.937428	+	0.348178i	$0.113200\pi$
$972$	12.9271	+	39.7854i	0.414635	+	1.27612i
$973$	4.47214	−	3.24920i	0.143370	−	0.104164i
$974$	−3.29180	+	2.39163i	−0.105476	+	0.0766328i
$975$	0.881966	+	2.71441i	0.0282455	+	0.0869308i
$976$	1.47214	−	4.53077i	0.0471219	−	0.145026i
$977$	−33.3607	−	24.2380i	−1.06730	−	0.775441i	−0.0918772	−	0.995770i	$-0.529287\pi$
$977$	−33.3607	−	24.2380i	−1.06730	−	0.775441i	−0.975425	+	0.220330i	$0.929287\pi$
$978$	30.6525			0.980158
$979$	38.8673	+	16.7760i	1.24220	+	0.536163i
$980$	−3.00000			−0.0958315
$981$	−24.4164	−	17.7396i	−0.779556	−	0.566381i
$982$	−1.45898	+	4.49028i	−0.0465579	+	0.143291i
$983$	−8.64590	−	26.6093i	−0.275761	−	0.848706i	−0.989017	−	0.147802i	$-0.952780\pi$
$983$	−8.64590	−	26.6093i	−0.275761	−	0.848706i	0.713256	−	0.700904i	$-0.247220\pi$
$984$	2.76393	−	2.00811i	0.0881109	−	0.0640163i
$985$	−9.70820	+	7.05342i	−0.309329	+	0.224741i
$986$	−3.31559	−	10.2044i	−0.105590	−	0.324973i
$987$	0.218847	−	0.673542i	0.00696598	−	0.0214391i
$988$	36.2705	+	26.3521i	1.15392	+	0.838371i
$989$	23.4164			0.744598
$990$	9.89919	+	16.7027i	0.314617	+	0.530848i
$991$	13.8541			0.440090			0.220045	−	0.975490i	$-0.429380\pi$
$991$	13.8541			0.440090			0.220045	+	0.975490i	$0.429380\pi$
$992$	−17.5623	−	12.7598i	−0.557604	−	0.405123i
$993$	−3.53444	+	10.8779i	−0.112162	+	0.345200i
$994$	11.2812	+	34.7198i	0.357816	+	1.10125i
$995$	−14.5623	+	10.5801i	−0.461656	+	0.335413i
$996$	−14.3435	+	10.4211i	−0.454490	+	0.330206i
$997$	−7.79180	−	23.9807i	−0.246769	−	0.759476i	−0.995341	−	0.0964222i	$-0.969260\pi$
$997$	−7.79180	−	23.9807i	−0.246769	−	0.759476i	0.748572	−	0.663054i	$-0.230740\pi$
$998$	15.9164	−	48.9857i	0.503825	−	1.55061i
$999$	−20.3262	−	14.7679i	−0.643094	−	0.467235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.b.246.1	yes	4
11.3	even	5	inner	385.2.n.b.36.1	✓	4
11.5	even	5		4235.2.a.j.1.1		2
11.6	odd	10		4235.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.b.36.1	✓	4	11.3	even	5	inner
385.2.n.b.246.1	yes	4	1.1	even	1	trivial
4235.2.a.j.1.1		2	11.5	even	5
4235.2.a.k.1.2		2	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 + 1.31433i) q^{2} +(0.190983 - 0.587785i) q^{3} +(0.927051 + 2.85317i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.11803 - 0.812299i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})\)	\(q+(1.80902 + 1.31433i) q^{2} +(0.190983 - 0.587785i) q^{3} +(0.927051 + 2.85317i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.11803 - 0.812299i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(2.11803 + 1.53884i) q^{9} +2.23607 q^{10} +(3.04508 + 1.31433i) q^{11} +1.85410 q^{12} +(-3.73607 - 2.71441i) q^{13} +(0.690983 - 2.12663i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.54508 + 3.30220i) q^{17} +(1.80902 + 5.56758i) q^{18} +(-1.00000 + 3.07768i) q^{19} +(2.42705 + 1.76336i) q^{20} -0.618034 q^{21} +(3.78115 + 6.37988i) q^{22} -4.47214 q^{23} +(1.11803 + 0.812299i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-3.19098 - 9.82084i) q^{26} +(2.80902 - 2.04087i) q^{27} +(2.42705 - 1.76336i) q^{28} +(0.263932 + 0.812299i) q^{29} +(0.427051 - 1.31433i) q^{30} +(-2.61803 - 1.90211i) q^{31} +6.70820 q^{32} +(1.35410 - 1.53884i) q^{33} -12.5623 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-2.42705 + 7.46969i) q^{36} +(-2.23607 - 6.88191i) q^{37} +(-5.85410 + 4.25325i) q^{38} +(-2.30902 + 1.67760i) q^{39} +(0.690983 + 2.12663i) q^{40} +(0.763932 - 2.35114i) q^{41} +(-1.11803 - 0.812299i) q^{42} -5.23607 q^{43} +(-0.927051 + 9.90659i) q^{44} +2.61803 q^{45} +(-8.09017 - 5.87785i) q^{46} +(-0.354102 + 1.08981i) q^{47} +(-0.190983 - 0.587785i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.80902 - 1.31433i) q^{50} +(1.07295 + 3.30220i) q^{51} +(4.28115 - 13.1760i) q^{52} +(1.23607 + 0.898056i) q^{53} +7.76393 q^{54} +(3.23607 - 0.726543i) q^{55} +2.23607 q^{56} +(1.61803 + 1.17557i) q^{57} +(-0.590170 + 1.81636i) q^{58} +(-2.85410 - 8.78402i) q^{59} +(1.50000 - 1.08981i) q^{60} +(3.85410 - 2.80017i) q^{61} +(-2.23607 - 6.88191i) q^{62} +(0.809017 - 2.48990i) q^{63} +(10.5172 + 7.64121i) q^{64} -4.61803 q^{65} +(4.47214 - 1.00406i) q^{66} +8.18034 q^{67} +(-13.6353 - 9.90659i) q^{68} +(-0.854102 + 2.62866i) q^{69} +(-0.690983 - 2.12663i) q^{70} +(-13.2082 + 9.59632i) q^{71} +(-4.73607 + 3.44095i) q^{72} +(1.97214 + 6.06961i) q^{73} +(5.00000 - 15.3884i) q^{74} +(-0.500000 - 0.363271i) q^{75} -9.70820 q^{76} +(0.309017 - 3.30220i) q^{77} -6.38197 q^{78} +(-8.73607 - 6.34712i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.76393 + 5.42882i) q^{81} +(4.47214 - 3.24920i) q^{82} +(-7.73607 + 5.62058i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-1.73607 + 5.34307i) q^{85} +(-9.47214 - 6.88191i) q^{86} +0.527864 q^{87} +(-4.89919 + 5.56758i) q^{88} +12.7639 q^{89} +(4.73607 + 3.44095i) q^{90} +(-1.42705 + 4.39201i) q^{91} +(-4.14590 - 12.7598i) q^{92} +(-1.61803 + 1.17557i) q^{93} +(-2.07295 + 1.50609i) q^{94} +(1.00000 + 3.07768i) q^{95} +(1.28115 - 3.94298i) q^{96} +(12.3992 + 9.00854i) q^{97} -2.23607 q^{98} +(4.42705 + 7.46969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9	\( 4 q + 5 q^{2} + 3 q^{3} - 3 q^{4} + q^{5} + q^{7} - 5 q^{8} + 4 q^{9} + q^{11} - 6 q^{12} - 6 q^{13} + 5 q^{14} - 3 q^{15} + q^{16} - 7 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 5 q^{22} - q^{25} - 15 q^{26} + 9 q^{27} + 3 q^{28} + 10 q^{29} - 5 q^{30} - 6 q^{31} - 8 q^{33} - 10 q^{34} - q^{35} - 3 q^{36} - 10 q^{38} - 7 q^{39} + 5 q^{40} + 12 q^{41} - 12 q^{43} + 3 q^{44} + 6 q^{45} - 10 q^{46} + 12 q^{47} - 3 q^{48} - q^{49} + 5 q^{50} + 11 q^{51} - 3 q^{52} - 4 q^{53} + 40 q^{54} + 4 q^{55} + 2 q^{57} + 20 q^{58} + 2 q^{59} + 6 q^{60} + 2 q^{61} + q^{63} + 13 q^{64} - 14 q^{65} - 12 q^{67} - 21 q^{68} + 10 q^{69} - 5 q^{70} - 26 q^{71} - 10 q^{72} - 10 q^{73} + 20 q^{74} - 2 q^{75} - 12 q^{76} - q^{77} - 30 q^{78} - 26 q^{79} - q^{80} + 16 q^{81} - 22 q^{83} - 9 q^{84} + 2 q^{85} - 20 q^{86} + 20 q^{87} + 5 q^{88} + 60 q^{89} + 10 q^{90} + q^{91} - 30 q^{92} - 2 q^{93} - 15 q^{94} + 4 q^{95} - 15 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 + 3 * q^3 - 3 * q^4 + q^5 + q^7 - 5 * q^8 + 4 * q^9 + q^11 - 6 * q^12 - 6 * q^13 + 5 * q^14 - 3 * q^15 + q^16 - 7 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 5 * q^22 - q^25 - 15 * q^26 + 9 * q^27 + 3 * q^28 + 10 * q^29 - 5 * q^30 - 6 * q^31 - 8 * q^33 - 10 * q^34 - q^35 - 3 * q^36 - 10 * q^38 - 7 * q^39 + 5 * q^40 + 12 * q^41 - 12 * q^43 + 3 * q^44 + 6 * q^45 - 10 * q^46 + 12 * q^47 - 3 * q^48 - q^49 + 5 * q^50 + 11 * q^51 - 3 * q^52 - 4 * q^53 + 40 * q^54 + 4 * q^55 + 2 * q^57 + 20 * q^58 + 2 * q^59 + 6 * q^60 + 2 * q^61 + q^63 + 13 * q^64 - 14 * q^65 - 12 * q^67 - 21 * q^68 + 10 * q^69 - 5 * q^70 - 26 * q^71 - 10 * q^72 - 10 * q^73 + 20 * q^74 - 2 * q^75 - 12 * q^76 - q^77 - 30 * q^78 - 26 * q^79 - q^80 + 16 * q^81 - 22 * q^83 - 9 * q^84 + 2 * q^85 - 20 * q^86 + 20 * q^87 + 5 * q^88 + 60 * q^89 + 10 * q^90 + q^91 - 30 * q^92 - 2 * q^93 - 15 * q^94 + 4 * q^95 - 15 * q^96 + 25 * q^97 + 11 * q^99

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