LMFDB - Embedded newform 287.2.h.b.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (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:	$2.29170653801$
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			141.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	287.141
Dual form			287.2.h.b.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 2.48990i) q^{2} +2.61803 q^{3} +(-3.92705 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.11803 + 6.51864i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-6.04508 - 4.39201i) q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+(0.809017 + 2.48990i) q^{2} +2.61803 q^{3} +(-3.92705 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.11803 + 6.51864i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-6.04508 - 4.39201i) q^{8} +3.85410 q^{9} +(-1.30902 - 0.951057i) q^{10} +(2.30902 + 1.67760i) q^{11} +(-10.2812 + 7.46969i) q^{12} +(-0.690983 - 2.12663i) q^{13} +2.61803 q^{14} +(-1.30902 + 0.951057i) q^{15} +(3.04508 - 9.37181i) q^{16} +(-6.04508 - 4.39201i) q^{17} +(3.11803 + 9.59632i) q^{18} +(1.61803 - 4.97980i) q^{19} +(0.927051 - 2.85317i) q^{20} +(0.809017 - 2.48990i) q^{21} +(-2.30902 + 7.10642i) q^{22} +(1.30902 + 4.02874i) q^{23} +(-15.8262 - 11.4984i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(4.73607 - 3.44095i) q^{26} +2.23607 q^{27} +(1.50000 + 4.61653i) q^{28} +(3.23607 - 2.35114i) q^{29} +(-3.42705 - 2.48990i) q^{30} +(3.80902 + 2.76741i) q^{31} +10.8541 q^{32} +(6.04508 + 4.39201i) q^{33} +(6.04508 - 18.6049i) q^{34} +(0.190983 + 0.587785i) q^{35} +(-15.1353 + 10.9964i) q^{36} +(6.16312 - 4.47777i) q^{37} +13.7082 q^{38} +(-1.80902 - 5.56758i) q^{39} +4.61803 q^{40} +(-5.89919 + 2.48990i) q^{41} +6.85410 q^{42} +(-1.38197 - 4.25325i) q^{43} -13.8541 q^{44} +(-1.92705 + 1.40008i) q^{45} +(-8.97214 + 6.51864i) q^{46} +(2.64590 + 8.14324i) q^{47} +(7.97214 - 24.5357i) q^{48} +(-0.809017 - 0.587785i) q^{49} -12.0902 q^{50} +(-15.8262 - 11.4984i) q^{51} +(8.78115 + 6.37988i) q^{52} +(-5.47214 + 3.97574i) q^{53} +(1.80902 + 5.56758i) q^{54} -1.76393 q^{55} +(-6.04508 + 4.39201i) q^{56} +(4.23607 - 13.0373i) q^{57} +(8.47214 + 6.15537i) q^{58} +(-2.35410 - 7.24518i) q^{59} +(2.42705 - 7.46969i) q^{60} +(3.54508 - 10.9106i) q^{61} +(-3.80902 + 11.7229i) q^{62} +(1.19098 - 3.66547i) q^{63} +(2.69098 + 8.28199i) q^{64} +(1.11803 + 0.812299i) q^{65} +(-6.04508 + 18.6049i) q^{66} +(-11.2812 + 8.19624i) q^{67} +36.2705 q^{68} +(3.42705 + 10.5474i) q^{69} +(-1.30902 + 0.951057i) q^{70} +(12.7812 + 9.28605i) q^{71} +(-23.2984 - 16.9273i) q^{72} -2.70820 q^{73} +(16.1353 + 11.7229i) q^{74} +(-3.73607 + 11.4984i) q^{75} +(7.85410 + 24.1724i) q^{76} +(2.30902 - 1.67760i) q^{77} +(12.3992 - 9.00854i) q^{78} -0.909830 q^{79} +(1.88197 + 5.79210i) q^{80} -5.70820 q^{81} +(-10.9721 - 12.6740i) q^{82} -0.145898 q^{83} +(3.92705 + 12.0862i) q^{84} +4.61803 q^{85} +(9.47214 - 6.88191i) q^{86} +(8.47214 - 6.15537i) q^{87} +(-6.59017 - 20.2825i) q^{88} +(1.88197 - 5.79210i) q^{89} +(-5.04508 - 3.66547i) q^{90} -2.23607 q^{91} +(-16.6353 - 12.0862i) q^{92} +(9.97214 + 7.24518i) q^{93} +(-18.1353 + 13.1760i) q^{94} +(1.00000 + 3.07768i) q^{95} +28.4164 q^{96} +(-5.97214 + 4.33901i) q^{97} +(0.809017 - 2.48990i) q^{98} +(8.89919 + 6.46564i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9} - 3 q^{10} + 7 q^{11} - 21 q^{12} - 5 q^{13} + 6 q^{14} - 3 q^{15} + q^{16} - 13 q^{17} + 8 q^{18} + 2 q^{19} - 3 q^{20} + q^{21} - 7 q^{22} + 3 q^{23} - 32 q^{24} + q^{25} + 10 q^{26} + 6 q^{28} + 4 q^{29} - 7 q^{30} + 13 q^{31} + 30 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} - 27 q^{36} + 9 q^{37} + 28 q^{38} - 5 q^{39} + 14 q^{40} + q^{41} + 14 q^{42} - 10 q^{43} - 42 q^{44} - q^{45} - 18 q^{46} + 24 q^{47} + 14 q^{48} - q^{49} - 26 q^{50} - 32 q^{51} + 15 q^{52} - 4 q^{53} + 5 q^{54} - 16 q^{55} - 13 q^{56} + 8 q^{57} + 16 q^{58} + 4 q^{59} + 3 q^{60} + 3 q^{61} - 13 q^{62} + 7 q^{63} + 13 q^{64} - 13 q^{66} - 25 q^{67} + 78 q^{68} + 7 q^{69} - 3 q^{70} + 31 q^{71} - 44 q^{72} + 16 q^{73} + 31 q^{74} - 6 q^{75} + 18 q^{76} + 7 q^{77} + 25 q^{78} - 26 q^{79} + 12 q^{80} + 4 q^{81} - 26 q^{82} - 14 q^{83} + 9 q^{84} + 14 q^{85} + 20 q^{86} + 16 q^{87} - 4 q^{88} + 12 q^{89} - 9 q^{90} - 33 q^{92} + 22 q^{93} - 39 q^{94} + 4 q^{95} + 60 q^{96} - 6 q^{97} + q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9 - 3 * q^10 + 7 * q^11 - 21 * q^12 - 5 * q^13 + 6 * q^14 - 3 * q^15 + q^16 - 13 * q^17 + 8 * q^18 + 2 * q^19 - 3 * q^20 + q^21 - 7 * q^22 + 3 * q^23 - 32 * q^24 + q^25 + 10 * q^26 + 6 * q^28 + 4 * q^29 - 7 * q^30 + 13 * q^31 + 30 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 - 27 * q^36 + 9 * q^37 + 28 * q^38 - 5 * q^39 + 14 * q^40 + q^41 + 14 * q^42 - 10 * q^43 - 42 * q^44 - q^45 - 18 * q^46 + 24 * q^47 + 14 * q^48 - q^49 - 26 * q^50 - 32 * q^51 + 15 * q^52 - 4 * q^53 + 5 * q^54 - 16 * q^55 - 13 * q^56 + 8 * q^57 + 16 * q^58 + 4 * q^59 + 3 * q^60 + 3 * q^61 - 13 * q^62 + 7 * q^63 + 13 * q^64 - 13 * q^66 - 25 * q^67 + 78 * q^68 + 7 * q^69 - 3 * q^70 + 31 * q^71 - 44 * q^72 + 16 * q^73 + 31 * q^74 - 6 * q^75 + 18 * q^76 + 7 * q^77 + 25 * q^78 - 26 * q^79 + 12 * q^80 + 4 * q^81 - 26 * q^82 - 14 * q^83 + 9 * q^84 + 14 * q^85 + 20 * q^86 + 16 * q^87 - 4 * q^88 + 12 * q^89 - 9 * q^90 - 33 * q^92 + 22 * q^93 - 39 * q^94 + 4 * q^95 + 60 * q^96 - 6 * q^97 + q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	0.645974	+	0.763359i	$0.276451\pi$
$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	−0.0739128	+	0.997265i	$0.523549\pi$
$3$	2.61803			1.51152			0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803			1.51152			0.755761	+	0.654847i	$0.227267\pi$
$4$	−3.92705	+	2.85317i	−1.96353	+	1.42658i
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	−0.693949	−	0.720024i	$-0.744131\pi$
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	0.470342	+	0.882484i	$0.344131\pi$
$6$	2.11803	+	6.51864i	0.864684	+	2.66122i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$	3.85410			1.28470
$10$	−1.30902	−	0.951057i	−0.413948	−	0.300750i
$11$	2.30902	+	1.67760i	0.696195	+	0.505815i	0.878691	−	0.477391i	$-0.158418\pi$
$11$	2.30902	+	1.67760i	0.696195	+	0.505815i	−0.182496	+	0.983207i	$0.558418\pi$
$12$	−10.2812	+	7.46969i	−2.96791	+	2.15632i
$13$	−0.690983	−	2.12663i	−0.191644	−	0.589820i	−0.999999	−	0.00112510i	$-0.999642\pi$
$13$	−0.690983	−	2.12663i	−0.191644	−	0.589820i	0.808355	−	0.588695i	$-0.200358\pi$
$14$	2.61803			0.699699
$15$	−1.30902	+	0.951057i	−0.337987	+	0.245562i
$16$	3.04508	−	9.37181i	0.761271	−	2.34295i
$17$	−6.04508	−	4.39201i	−1.46615	−	1.06522i	−0.981708	−	0.190395i	$-0.939023\pi$
$17$	−6.04508	−	4.39201i	−1.46615	−	1.06522i	−0.484441	−	0.874824i	$-0.660977\pi$
$18$	3.11803	+	9.59632i	0.734928	+	2.26187i
$19$	1.61803	−	4.97980i	0.371202	−	1.14244i	−0.574803	−	0.818292i	$-0.694921\pi$
$19$	1.61803	−	4.97980i	0.371202	−	1.14244i	0.946005	−	0.324152i	$-0.105079\pi$
$20$	0.927051	−	2.85317i	0.207295	−	0.637988i
$21$	0.809017	−	2.48990i	0.176542	−	0.543340i
$22$	−2.30902	+	7.10642i	−0.492284	+	1.51509i
$23$	1.30902	+	4.02874i	0.272949	+	0.840050i	0.989755	+	0.142778i	$0.0456034\pi$
$23$	1.30902	+	4.02874i	0.272949	+	0.840050i	−0.716806	+	0.697273i	$0.754397\pi$
$24$	−15.8262	−	11.4984i	−3.23052	−	2.34711i
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$	4.73607	−	3.44095i	0.928819	−	0.674827i
$27$	2.23607			0.430331
$28$	1.50000	+	4.61653i	0.283473	+	0.872441i
$29$	3.23607	−	2.35114i	0.600923	−	0.436596i	−0.245284	−	0.969451i	$-0.578881\pi$
$29$	3.23607	−	2.35114i	0.600923	−	0.436596i	0.846206	+	0.532855i	$0.178881\pi$
$30$	−3.42705	−	2.48990i	−0.625691	−	0.454591i
$31$	3.80902	+	2.76741i	0.684120	+	0.497042i	0.874722	−	0.484625i	$-0.161044\pi$
$31$	3.80902	+	2.76741i	0.684120	+	0.497042i	−0.190602	+	0.981667i	$0.561044\pi$
$32$	10.8541			1.91875
$33$	6.04508	+	4.39201i	1.05231	+	0.764551i
$34$	6.04508	−	18.6049i	1.03672	−	3.19071i
$35$	0.190983	+	0.587785i	0.0322820	+	0.0993538i
$36$	−15.1353	+	10.9964i	−2.52254	+	1.83273i
$37$	6.16312	−	4.47777i	1.01321	−	0.736141i	0.0483305	−	0.998831i	$-0.484610\pi$
$37$	6.16312	−	4.47777i	1.01321	−	0.736141i	0.964880	+	0.262691i	$0.0846099\pi$
$38$	13.7082			2.22376
$39$	−1.80902	−	5.56758i	−0.289675	−	0.891527i
$40$	4.61803			0.730175
$41$	−5.89919	+	2.48990i	−0.921298	+	0.388857i
$41$	−5.89919	+	2.48990i	−0.921298	+	0.388857i
$42$	6.85410			1.05761
$43$	−1.38197	−	4.25325i	−0.210748	−	0.648615i	−0.999428	−	0.0338117i	$-0.989235\pi$
$43$	−1.38197	−	4.25325i	−0.210748	−	0.648615i	0.788680	−	0.614803i	$-0.210765\pi$
$44$	−13.8541			−2.08858
$45$	−1.92705	+	1.40008i	−0.287268	+	0.208712i
$46$	−8.97214	+	6.51864i	−1.32287	+	0.961121i
$47$	2.64590	+	8.14324i	0.385944	+	1.18781i	0.935793	+	0.352549i	$0.114685\pi$
$47$	2.64590	+	8.14324i	0.385944	+	1.18781i	−0.549849	+	0.835264i	$0.685315\pi$
$48$	7.97214	−	24.5357i	1.15068	−	3.54142i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−12.0902			−1.70981
$51$	−15.8262	−	11.4984i	−2.21612	−	1.61010i
$52$	8.78115	+	6.37988i	1.21773	+	0.884730i
$53$	−5.47214	+	3.97574i	−0.751656	+	0.546110i	−0.896340	−	0.443368i	$-0.853783\pi$
$53$	−5.47214	+	3.97574i	−0.751656	+	0.546110i	0.144684	+	0.989478i	$0.453783\pi$
$54$	1.80902	+	5.56758i	0.246176	+	0.757652i
$55$	−1.76393			−0.237849
$56$	−6.04508	+	4.39201i	−0.807808	+	0.586907i
$57$	4.23607	−	13.0373i	0.561081	−	1.72683i
$58$	8.47214	+	6.15537i	1.11245	+	0.808239i
$59$	−2.35410	−	7.24518i	−0.306478	−	0.943242i	−0.979122	−	0.203276i	$-0.934841\pi$
$59$	−2.35410	−	7.24518i	−0.306478	−	0.943242i	0.672644	−	0.739967i	$-0.265159\pi$
$60$	2.42705	−	7.46969i	0.313331	−	0.964333i
$61$	3.54508	−	10.9106i	0.453902	−	1.39697i	−0.418518	−	0.908208i	$-0.637450\pi$
$61$	3.54508	−	10.9106i	0.453902	−	1.39697i	0.872420	−	0.488757i	$-0.162550\pi$
$62$	−3.80902	+	11.7229i	−0.483746	+	1.48882i
$63$	1.19098	−	3.66547i	0.150050	−	0.461806i
$64$	2.69098	+	8.28199i	0.336373	+	1.03525i
$65$	1.11803	+	0.812299i	0.138675	+	0.100753i
$66$	−6.04508	+	18.6049i	−0.744099	+	2.29010i
$67$	−11.2812	+	8.19624i	−1.37821	+	1.00133i	−0.381168	+	0.924506i	$0.624478\pi$
$67$	−11.2812	+	8.19624i	−1.37821	+	1.00133i	−0.997045	+	0.0768238i	$0.975522\pi$
$68$	36.2705			4.39845
$69$	3.42705	+	10.5474i	0.412568	+	1.26976i
$70$	−1.30902	+	0.951057i	−0.156457	+	0.113673i
$71$	12.7812	+	9.28605i	1.51684	+	1.10205i	0.963024	+	0.269415i	$0.0868303\pi$
$71$	12.7812	+	9.28605i	1.51684	+	1.10205i	0.553820	+	0.832637i	$0.313170\pi$
$72$	−23.2984	−	16.9273i	−2.74574	−	1.99490i
$73$	−2.70820			−0.316971			−0.158486	−	0.987361i	$-0.550661\pi$
$73$	−2.70820			−0.316971			−0.158486	+	0.987361i	$0.550661\pi$
$74$	16.1353	+	11.7229i	1.87569	+	1.36277i
$75$	−3.73607	+	11.4984i	−0.431404	+	1.32772i
$76$	7.85410	+	24.1724i	0.900927	+	2.77277i
$77$	2.30902	−	1.67760i	0.263137	−	0.191180i
$78$	12.3992	−	9.00854i	1.40393	−	1.02002i
$79$	−0.909830			−0.102364			−0.0511819	−	0.998689i	$-0.516299\pi$
$79$	−0.909830			−0.102364			−0.0511819	+	0.998689i	$0.516299\pi$
$80$	1.88197	+	5.79210i	0.210410	+	0.647576i
$81$	−5.70820			−0.634245
$82$	−10.9721	−	12.6740i	−1.21167	−	1.39961i
$83$	−0.145898			−0.0160144			−0.00800719	−	0.999968i	$-0.502549\pi$
$83$	−0.145898			−0.0160144			−0.00800719	+	0.999968i	$0.502549\pi$
$84$	3.92705	+	12.0862i	0.428476	+	1.31871i
$85$	4.61803			0.500896
$86$	9.47214	−	6.88191i	1.02141	−	0.742095i
$87$	8.47214	−	6.15537i	0.908308	−	0.659925i
$88$	−6.59017	−	20.2825i	−0.702514	−	2.16212i
$89$	1.88197	−	5.79210i	0.199488	−	0.613961i	−0.800407	−	0.599457i	$-0.795383\pi$
$89$	1.88197	−	5.79210i	0.199488	−	0.613961i	0.999895	−	0.0145037i	$-0.00461684\pi$
$90$	−5.04508	−	3.66547i	−0.531799	−	0.386374i
$91$	−2.23607			−0.234404
$92$	−16.6353	−	12.0862i	−1.73435	−	1.26008i
$93$	9.97214	+	7.24518i	1.03406	+	0.751290i
$94$	−18.1353	+	13.1760i	−1.87051	+	1.35900i
$95$	1.00000	+	3.07768i	0.102598	+	0.315764i
$96$	28.4164			2.90024
$97$	−5.97214	+	4.33901i	−0.606379	+	0.440560i	−0.848137	−	0.529777i	$-0.822276\pi$
$97$	−5.97214	+	4.33901i	−0.606379	+	0.440560i	0.241759	+	0.970336i	$0.422276\pi$
$98$	0.809017	−	2.48990i	0.0817231	−	0.251518i
$99$	8.89919	+	6.46564i	0.894402	+	0.649821i
$100$	−6.92705	−	21.3193i	−0.692705	−	2.13193i
$101$	−5.01722	+	15.4414i	−0.499232	+	1.53648i	0.311024	+	0.950402i	$0.399328\pi$
$101$	−5.01722	+	15.4414i	−0.499232	+	1.53648i	−0.810256	+	0.586076i	$0.800672\pi$
$102$	15.8262	−	48.7082i	1.56703	−	4.82283i
$103$	0.572949	−	1.76336i	0.0564543	−	0.173749i	−0.918853	−	0.394599i	$-0.870883\pi$
$103$	0.572949	−	1.76336i	0.0564543	−	0.173749i	0.975308	+	0.220851i	$0.0708834\pi$
$104$	−5.16312	+	15.8904i	−0.506285	+	1.55819i
$105$	0.500000	+	1.53884i	0.0487950	+	0.150176i
$106$	−14.3262	−	10.4086i	−1.39149	−	1.01097i
$107$	0.972136	−	2.99193i	0.0939799	−	0.289240i	−0.893007	−	0.450044i	$-0.851408\pi$
$107$	0.972136	−	2.99193i	0.0939799	−	0.289240i	0.986986	+	0.160803i	$0.0514084\pi$
$108$	−8.78115	+	6.37988i	−0.844967	+	0.613904i
$109$	−4.90983			−0.470276			−0.235138	−	0.971962i	$-0.575554\pi$
$109$	−4.90983			−0.470276			−0.235138	+	0.971962i	$0.575554\pi$
$110$	−1.42705	−	4.39201i	−0.136064	−	0.418762i
$111$	16.1353	−	11.7229i	1.53149	−	1.11269i
$112$	−7.97214	−	5.79210i	−0.753296	−	0.547302i
$113$	−4.04508	−	2.93893i	−0.380530	−	0.276471i	0.381034	−	0.924561i	$-0.375568\pi$
$113$	−4.04508	−	2.93893i	−0.380530	−	0.276471i	−0.761564	+	0.648090i	$0.775568\pi$
$114$	35.8885			3.36127
$115$	−2.11803	−	1.53884i	−0.197508	−	0.143498i
$116$	−6.00000	+	18.4661i	−0.557086	+	1.71453i
$117$	−2.66312	−	8.19624i	−0.246205	−	0.757742i
$118$	16.1353	−	11.7229i	1.48537	−	1.07918i
$119$	−6.04508	+	4.39201i	−0.554152	+	0.402615i
$120$	12.0902			1.10368
$121$	−0.881966	−	2.71441i	−0.0801787	−	0.246765i
$122$	30.0344			2.71919
$123$	−15.4443	+	6.51864i	−1.39256	+	0.587766i
$124$	−22.8541			−2.05236
$125$	−1.83688	−	5.65334i	−0.164296	−	0.505650i
$126$	10.0902			0.898904
$127$	−9.23607	+	6.71040i	−0.819569	+	0.595451i	−0.916589	−	0.399831i	$-0.869069\pi$
$127$	−9.23607	+	6.71040i	−0.819569	+	0.595451i	0.0970204	+	0.995282i	$0.469069\pi$
$128$	−0.881966	+	0.640786i	−0.0779555	+	0.0566380i
$129$	−3.61803	−	11.1352i	−0.318550	−	0.980396i
$130$	−1.11803	+	3.44095i	−0.0980581	+	0.301792i
$131$	4.92705	+	3.57971i	0.430478	+	0.312761i	0.781840	−	0.623479i	$-0.214281\pi$
$131$	4.92705	+	3.57971i	0.430478	+	0.312761i	−0.351362	+	0.936240i	$0.614281\pi$
$132$	−36.2705			−3.15694
$133$	−4.23607	−	3.07768i	−0.367314	−	0.266869i
$134$	−29.5344	−	21.4580i	−2.55139	−	1.85369i
$135$	−1.11803	+	0.812299i	−0.0962250	+	0.0699116i
$136$	17.2533	+	53.1002i	1.47946	+	4.55330i
$137$	7.61803			0.650853			0.325426	−	0.945567i	$-0.394492\pi$
$137$	7.61803			0.650853			0.325426	+	0.945567i	$0.394492\pi$
$138$	−23.4894	+	17.0660i	−1.99955	+	1.45276i
$139$	−0.409830	+	1.26133i	−0.0347613	+	0.106984i	−0.966932	−	0.255036i	$-0.917913\pi$
$139$	−0.409830	+	1.26133i	−0.0347613	+	0.106984i	0.932170	+	0.362020i	$0.117913\pi$
$140$	−2.42705	−	1.76336i	−0.205123	−	0.149031i
$141$	6.92705	+	21.3193i	0.583363	+	1.79541i
$142$	−12.7812	+	39.3363i	−1.07257	+	3.30103i
$143$	1.97214	−	6.06961i	0.164918	−	0.507566i
$144$	11.7361	−	36.1199i	0.978006	−	3.00999i
$145$	−0.763932	+	2.35114i	−0.0634411	+	0.195252i
$146$	−2.19098	−	6.74315i	−0.181327	−	0.558067i
$147$	−2.11803	−	1.53884i	−0.174692	−	0.126922i
$148$	−11.4271	+	35.1688i	−0.939298	+	2.89086i
$149$	−10.2082	+	7.41669i	−0.836289	+	0.607599i	−0.921331	−	0.388778i	$-0.872897\pi$
$149$	−10.2082	+	7.41669i	−0.836289	+	0.607599i	0.0850428	+	0.996377i	$0.472897\pi$
$150$	−31.6525			−2.58441
$151$	−6.07295	−	18.6906i	−0.494210	−	1.52102i	−0.818185	−	0.574955i	$-0.805019\pi$
$151$	−6.07295	−	18.6906i	−0.494210	−	1.52102i	0.323975	−	0.946066i	$-0.394981\pi$
$152$	−31.6525	+	22.9969i	−2.56735	+	1.86529i
$153$	−23.2984	−	16.9273i	−1.88356	−	1.36849i
$154$	6.04508	+	4.39201i	0.487127	+	0.353918i
$155$	−2.90983			−0.233723
$156$	22.9894	+	16.7027i	1.84062	+	1.33729i
$157$	1.98278	−	6.10237i	0.158243	−	0.487022i	−0.840232	−	0.542227i	$-0.817581\pi$
$157$	1.98278	−	6.10237i	0.158243	−	0.487022i	0.998475	+	0.0552051i	$0.0175813\pi$
$158$	−0.736068	−	2.26538i	−0.0585584	−	0.180224i
$159$	−14.3262	+	10.4086i	−1.13614	+	0.825457i
$160$	−5.42705	+	3.94298i	−0.429046	+	0.311720i
$161$	4.23607			0.333849
$162$	−4.61803	−	14.2128i	−0.362827	−	1.11667i
$163$	−19.2361			−1.50669			−0.753343	−	0.657628i	$-0.771560\pi$
$163$	−19.2361			−1.50669			−0.753343	+	0.657628i	$0.771560\pi$
$164$	16.0623	−	26.6093i	1.25426	−	2.07784i
$165$	−4.61803			−0.359513
$166$	−0.118034	−	0.363271i	−0.00916121	−	0.0281953i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	−15.8262	+	11.4984i	−1.22102	+	0.887124i
$169$	6.47214	−	4.70228i	0.497857	−	0.361714i
$170$	3.73607	+	11.4984i	0.286543	+	0.881890i
$171$	6.23607	−	19.1926i	0.476884	−	1.46770i
$172$	17.5623	+	12.7598i	1.33911	+	0.972923i
$173$	−1.00000			−0.0760286			−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000			−0.0760286			−0.0380143	+	0.999277i	$0.512103\pi$
$174$	22.1803	+	16.1150i	1.68149	+	1.22167i
$175$	3.73607	+	2.71441i	0.282420	+	0.205190i
$176$	22.7533	−	16.5312i	1.71509	−	1.24609i
$177$	−6.16312	−	18.9681i	−0.463248	−	1.42573i
$178$	15.9443			1.19507
$179$	20.1353	−	14.6291i	1.50498	−	1.09343i	0.536635	−	0.843814i	$-0.319695\pi$
$179$	20.1353	−	14.6291i	1.50498	−	1.09343i	0.968345	−	0.249617i	$-0.0803048\pi$
$180$	3.57295	−	10.9964i	0.266312	−	0.819624i
$181$	12.0902	+	8.78402i	0.898655	+	0.652911i	0.938120	−	0.346310i	$-0.112565\pi$
$181$	12.0902	+	8.78402i	0.898655	+	0.652911i	−0.0394650	+	0.999221i	$0.512565\pi$
$182$	−1.80902	−	5.56758i	−0.134093	−	0.412697i
$183$	9.28115	−	28.5645i	0.686083	−	2.11155i
$184$	9.78115	−	30.1033i	0.721076	−	2.21924i
$185$	−1.45492	+	4.47777i	−0.106967	+	0.329212i
$186$	−9.97214	+	30.6911i	−0.731192	+	2.25038i
$187$	−6.59017	−	20.2825i	−0.481921	−	1.48320i
$188$	−33.6246	−	24.4297i	−2.45233	−	1.78172i
$189$	0.690983	−	2.12663i	0.0502616	−	0.154689i
$190$	−6.85410	+	4.97980i	−0.497249	+	0.361272i
$191$	−15.7082			−1.13661			−0.568303	−	0.822819i	$-0.692400\pi$
$191$	−15.7082			−1.13661			−0.568303	+	0.822819i	$0.692400\pi$
$192$	7.04508	+	21.6825i	0.508435	+	1.56480i
$193$	−13.5902	+	9.87384i	−0.978242	+	0.710734i	−0.957315	−	0.289047i	$-0.906662\pi$
$193$	−13.5902	+	9.87384i	−0.978242	+	0.710734i	−0.0209268	+	0.999781i	$0.506662\pi$
$194$	−15.6353	−	11.3597i	−1.12255	−	0.815577i
$195$	2.92705	+	2.12663i	0.209610	+	0.152291i
$196$	4.85410			0.346722
$197$	14.3262	+	10.4086i	1.02070	+	0.741584i	0.966427	−	0.256942i	$-0.0827151\pi$
$197$	14.3262	+	10.4086i	1.02070	+	0.741584i	0.0542755	+	0.998526i	$0.482715\pi$
$198$	−8.89919	+	27.3889i	−0.632438	+	1.94644i
$199$	2.61803	+	8.05748i	0.185588	+	0.571180i	0.999958	−	0.00916572i	$-0.00291758\pi$
$199$	2.61803	+	8.05748i	0.185588	+	0.571180i	−0.814370	+	0.580345i	$0.802918\pi$
$200$	27.9164	−	20.2825i	1.97399	−	1.43419i
$201$	−29.5344	+	21.4580i	−2.08320	+	1.51353i
$202$	−42.5066			−2.99075
$203$	−1.23607	−	3.80423i	−0.0867550	−	0.267004i
$204$	94.9574			6.64835
$205$	2.04508	−	3.38795i	0.142835	−	0.236625i
$206$	4.85410			0.338201
$207$	5.04508	+	15.5272i	0.350658	+	1.07921i
$208$	−22.0344			−1.52781
$209$	12.0902	−	8.78402i	0.836295	−	0.607604i
$210$	−3.42705	+	2.48990i	−0.236489	+	0.171819i
$211$	4.54508	+	13.9883i	0.312897	+	0.962997i	0.976612	+	0.215011i	$0.0689788\pi$
$211$	4.54508	+	13.9883i	0.312897	+	0.962997i	−0.663715	+	0.747986i	$0.731021\pi$
$212$	10.1459	−	31.2259i	0.696823	−	2.14460i
$213$	33.4615	+	24.3112i	2.29274	+	1.66578i
$214$	8.23607			0.563006
$215$	2.23607	+	1.62460i	0.152499	+	0.110797i
$216$	−13.5172	−	9.82084i	−0.919730	−	0.668223i
$217$	3.80902	−	2.76741i	0.258573	−	0.187864i
$218$	−3.97214	−	12.2250i	−0.269027	−	0.827980i
$219$	−7.09017			−0.479109
$220$	6.92705	−	5.03280i	0.467022	−	0.339311i
$221$	−5.16312	+	15.8904i	−0.347309	+	1.06891i
$222$	42.2426	+	30.6911i	2.83514	+	2.05985i
$223$	−3.63525	−	11.1882i	−0.243435	−	0.749215i	−0.995890	−	0.0905715i	$-0.971131\pi$
$223$	−3.63525	−	11.1882i	−0.243435	−	0.749215i	0.752455	−	0.658643i	$-0.228869\pi$
$224$	3.35410	−	10.3229i	0.224105	−	0.689725i
$225$	−5.50000	+	16.9273i	−0.366667	+	1.12848i
$226$	4.04508	−	12.4495i	0.269075	−	0.828128i
$227$	−2.98278	+	9.18005i	−0.197974	+	0.609301i	0.801955	+	0.597384i	$0.203793\pi$
$227$	−2.98278	+	9.18005i	−0.197974	+	0.609301i	−0.999929	+	0.0119169i	$0.996207\pi$
$228$	20.5623	+	63.2843i	1.36177	+	4.19110i
$229$	8.35410	+	6.06961i	0.552055	+	0.401091i	0.828542	−	0.559926i	$-0.189171\pi$
$229$	8.35410	+	6.06961i	0.552055	+	0.401091i	−0.276488	+	0.961017i	$0.589171\pi$
$230$	2.11803	−	6.51864i	0.139659	−	0.429826i
$231$	6.04508	−	4.39201i	0.397737	−	0.288973i
$232$	−29.8885			−1.96228
$233$	5.64590	+	17.3763i	0.369875	+	1.13836i	0.946872	+	0.321612i	$0.104225\pi$
$233$	5.64590	+	17.3763i	0.369875	+	1.13836i	−0.576997	+	0.816747i	$0.695775\pi$
$234$	18.2533	−	13.2618i	1.19325	−	0.866950i
$235$	−4.28115	−	3.11044i	−0.279272	−	0.202903i
$236$	29.9164	+	21.7355i	1.94739	+	1.41486i
$237$	−2.38197			−0.154725
$238$	−15.8262	−	11.4984i	−1.02586	−	0.745333i
$239$	6.18034	−	19.0211i	0.399773	−	1.23037i	−0.525409	−	0.850850i	$-0.676088\pi$
$239$	6.18034	−	19.0211i	0.399773	−	1.23037i	0.925182	−	0.379525i	$-0.123912\pi$
$240$	4.92705	+	15.1639i	0.318040	+	0.978826i
$241$	3.07295	−	2.23263i	0.197946	−	0.143816i	−0.484397	−	0.874848i	$-0.660961\pi$
$241$	3.07295	−	2.23263i	0.197946	−	0.143816i	0.682343	+	0.731032i	$0.260961\pi$
$242$	6.04508	−	4.39201i	0.388593	−	0.282329i
$243$	−21.6525			−1.38901
$244$	17.2082	+	52.9614i	1.10164	+	3.39051i
$245$	0.618034			0.0394847
$246$	−28.7254	−	33.1810i	−1.83147	−	2.11554i
$247$	−11.7082			−0.744975
$248$	−10.8713	−	33.4585i	−0.690330	−	2.12462i
$249$	−0.381966			−0.0242061
$250$	12.5902	−	9.14729i	0.796272	−	0.578526i
$251$	−6.28115	+	4.56352i	−0.396463	+	0.288047i	−0.768099	−	0.640331i	$-0.778797\pi$
$251$	−6.28115	+	4.56352i	−0.396463	+	0.288047i	0.371636	+	0.928379i	$0.378797\pi$
$252$	5.78115	+	17.7926i	0.364178	+	1.12083i
$253$	−3.73607	+	11.4984i	−0.234885	+	0.722900i
$254$	−24.1803	−	17.5680i	−1.51721	−	1.10232i
$255$	12.0902			0.757116
$256$	11.7812	+	8.55951i	0.736322	+	0.534969i
$257$	21.7533	+	15.8047i	1.35693	+	0.985869i	0.998633	+	0.0522628i	$0.0166433\pi$
$257$	21.7533	+	15.8047i	1.35693	+	0.985869i	0.358300	+	0.933607i	$0.383357\pi$
$258$	24.7984	−	18.0171i	1.54388	−	1.12169i
$259$	−2.35410	−	7.24518i	−0.146277	−	0.450194i
$260$	−6.70820			−0.416025
$261$	12.4721	−	9.06154i	0.772006	−	0.560895i
$262$	−4.92705	+	15.1639i	−0.304394	+	0.936829i
$263$	−1.97214	−	1.43284i	−0.121607	−	0.0883527i	0.525319	−	0.850905i	$-0.323946\pi$
$263$	−1.97214	−	1.43284i	−0.121607	−	0.0883527i	−0.646926	+	0.762552i	$0.723946\pi$
$264$	−17.2533	−	53.1002i	−1.06187	−	3.26809i
$265$	1.29180	−	3.97574i	0.0793544	−	0.244228i
$266$	4.23607	−	13.0373i	0.259730	−	0.799367i
$267$	4.92705	−	15.1639i	0.301531	−	0.928016i
$268$	20.9164	−	64.3741i	1.27767	−	3.93227i
$269$	−3.55573	−	10.9434i	−0.216797	−	0.667231i	−0.999021	−	0.0442347i	$-0.985915\pi$
$269$	−3.55573	−	10.9434i	−0.216797	−	0.667231i	0.782225	−	0.622997i	$-0.214085\pi$
$270$	−2.92705	−	2.12663i	−0.178135	−	0.129422i
$271$	4.60739	−	14.1801i	0.279879	−	0.861379i	−0.708008	−	0.706204i	$-0.750406\pi$
$271$	4.60739	−	14.1801i	0.279879	−	0.861379i	0.987887	−	0.155175i	$-0.0495941\pi$
$272$	−59.5689	+	43.2793i	−3.61189	+	2.62419i
$273$	−5.85410			−0.354306
$274$	6.16312	+	18.9681i	0.372328	+	1.14591i
$275$	−10.6631	+	7.74721i	−0.643010	+	0.467174i
$276$	−43.5517	−	31.6421i	−2.62150	−	1.90463i
$277$	15.8262	+	11.4984i	0.950906	+	0.690874i	0.951021	−	0.309126i	$-0.100036\pi$
$277$	15.8262	+	11.4984i	0.950906	+	0.690874i	−0.000114615		1.00000i	$0.500036\pi$
$278$	−3.47214			−0.208245
$279$	14.6803	+	10.6659i	0.878889	+	0.638550i
$280$	1.42705	−	4.39201i	0.0852826	−	0.262473i
$281$	2.33688	+	7.19218i	0.139407	+	0.429050i	0.996249	−	0.0865283i	$-0.0275773\pi$
$281$	2.33688	+	7.19218i	0.139407	+	0.429050i	−0.856843	+	0.515578i	$0.827577\pi$
$282$	−47.4787	+	34.4953i	−2.82732	+	2.05417i
$283$	22.2984	−	16.2007i	1.32550	−	0.963033i	0.325655	−	0.945489i	$-0.394415\pi$
$283$	22.2984	−	16.2007i	1.32550	−	0.963033i	0.999846	−	0.0175439i	$-0.00558467\pi$
$284$	−76.6869			−4.55053
$285$	2.61803	+	8.05748i	0.155079	+	0.477284i
$286$	16.7082			0.987977
$287$	0.545085	+	6.37988i	0.0321753	+	0.376592i
$288$	41.8328			2.46502
$289$	12.0000	+	36.9322i	0.705882	+	2.17248i
$290$	−6.47214			−0.380057
$291$	−15.6353	+	11.3597i	−0.916555	+	0.665916i
$292$	10.6353	−	7.72696i	0.622381	−	0.452186i
$293$	−0.635255	−	1.95511i	−0.0371120	−	0.114219i	0.930784	−	0.365569i	$-0.119126\pi$
$293$	−0.635255	−	1.95511i	−0.0371120	−	0.114219i	−0.967896	+	0.251350i	$0.919126\pi$
$294$	2.11803	−	6.51864i	0.123526	−	0.380175i
$295$	3.80902	+	2.76741i	0.221770	+	0.161125i
$296$	−56.9230			−3.30858
$297$	5.16312	+	3.75123i	0.299595	+	0.217668i
$298$	−26.7254	−	19.4172i	−1.54816	−	1.12481i
$299$	7.66312	−	5.56758i	0.443170	−	0.321982i
$300$	−18.1353	−	55.8146i	−1.04704	−	3.22246i
$301$	−4.47214			−0.257770
$302$	41.6246	−	30.2421i	2.39523	−	1.74023i
$303$	−13.1353	+	40.4262i	−0.754601	+	2.32242i
$304$	−41.7426	−	30.3278i	−2.39410	−	1.73942i
$305$	2.19098	+	6.74315i	0.125455	+	0.386112i
$306$	23.2984	−	71.7050i	1.33188	−	4.09910i
$307$	7.09017	−	21.8213i	0.404657	−	1.24541i	−0.516524	−	0.856273i	$-0.672774\pi$
$307$	7.09017	−	21.8213i	0.404657	−	1.24541i	0.921181	−	0.389134i	$-0.127226\pi$
$308$	−4.28115	+	13.1760i	−0.243941	+	0.750774i
$309$	1.50000	−	4.61653i	0.0853320	−	0.262625i
$310$	−2.35410	−	7.24518i	−0.133704	−	0.411499i
$311$	6.97214	+	5.06555i	0.395354	+	0.287241i	0.767646	−	0.640874i	$-0.221428\pi$
$311$	6.97214	+	5.06555i	0.395354	+	0.287241i	−0.372292	+	0.928116i	$0.621428\pi$
$312$	−13.5172	+	41.6017i	−0.765262	+	2.35523i
$313$	−14.6803	+	10.6659i	−0.829782	+	0.602872i	−0.919498	−	0.393096i	$-0.871404\pi$
$313$	−14.6803	+	10.6659i	−0.829782	+	0.602872i	0.0897157	+	0.995967i	$0.471404\pi$
$314$	16.7984			0.947987
$315$	0.736068	+	2.26538i	0.0414727	+	0.127640i
$316$	3.57295	−	2.59590i	0.200994	−	0.146031i
$317$	0.0729490	+	0.0530006i	0.00409722	+	0.00297681i	0.589832	−	0.807526i	$-0.299194\pi$
$317$	0.0729490	+	0.0530006i	0.00409722	+	0.00297681i	−0.585735	+	0.810503i	$0.699194\pi$
$318$	−37.5066	−	27.2501i	−2.10326	−	1.52811i
$319$	11.4164			0.639196
$320$	−4.35410	−	3.16344i	−0.243402	−	0.176842i
$321$	2.54508	−	7.83297i	0.142053	−	0.437194i
$322$	3.42705	+	10.5474i	0.190982	+	0.587782i
$323$	−31.6525	+	22.9969i	−1.76119	+	1.27958i
$324$	22.4164	−	16.2865i	1.24536	−	0.904804i
$325$	10.3262			0.572797
$326$	−15.5623	−	47.8959i	−0.861916	−	2.65271i
$327$	−12.8541			−0.710833
$328$	46.5967	+	10.8576i	2.57287	+	0.599513i
$329$	8.56231			0.472055
$330$	−3.73607	−	11.4984i	−0.205664	−	0.632968i
$331$	14.7639			0.811499			0.405750	−	0.913984i	$-0.367011\pi$
$331$	14.7639			0.811499			0.405750	+	0.913984i	$0.367011\pi$
$332$	0.572949	−	0.416272i	0.0314447	−	0.0228459i
$333$	23.7533	−	17.2578i	1.30167	−	0.945720i
$334$	9.70820	+	29.8788i	0.531209	+	1.63489i
$335$	2.66312	−	8.19624i	0.145502	−	0.447808i
$336$	−20.8713	−	15.1639i	−1.13862	−	0.827259i
$337$	36.0000			1.96104			0.980522	−	0.196407i	$-0.0629273\pi$
$337$	36.0000			1.96104			0.980522	+	0.196407i	$0.0629273\pi$
$338$	16.9443	+	12.3107i	0.921647	+	0.669616i
$339$	−10.5902	−	7.69421i	−0.575179	−	0.417892i
$340$	−18.1353	+	13.1760i	−0.983522	+	0.714571i
$341$	4.15248	+	12.7800i	0.224869	+	0.692076i
$342$	52.8328			2.85687
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−10.3262	+	31.7809i	−0.556753	+	1.71351i
$345$	−5.54508	−	4.02874i	−0.298537	−	0.216900i
$346$	−0.809017	−	2.48990i	−0.0434930	−	0.133858i
$347$	−8.48936	+	26.1276i	−0.455733	+	1.40260i	0.414540	+	0.910031i	$0.363942\pi$
$347$	−8.48936	+	26.1276i	−0.455733	+	1.40260i	−0.870273	+	0.492570i	$0.836058\pi$
$348$	−15.7082	+	48.3449i	−0.842048	+	2.59156i
$349$	−2.29837	+	7.07367i	−0.123029	+	0.378645i	−0.993537	−	0.113510i	$-0.963791\pi$
$349$	−2.29837	+	7.07367i	−0.123029	+	0.378645i	0.870508	+	0.492155i	$0.163791\pi$
$350$	−3.73607	+	11.4984i	−0.199701	+	0.614617i
$351$	−1.54508	−	4.75528i	−0.0824705	−	0.253818i
$352$	25.0623	+	18.2088i	1.33583	+	0.970534i
$353$	−1.69098	+	5.20431i	−0.0900019	+	0.276998i	−0.985919	−	0.167224i	$-0.946520\pi$
$353$	−1.69098	+	5.20431i	−0.0900019	+	0.276998i	0.895917	+	0.444222i	$0.146520\pi$
$354$	42.2426	−	30.6911i	2.24517	−	1.63121i
$355$	−9.76393			−0.518216
$356$	9.13525	+	28.1154i	0.484168	+	1.49011i
$357$	−15.8262	+	11.4984i	−0.837613	+	0.608562i
$358$	52.7148	+	38.2995i	2.78606	+	2.02419i
$359$	−4.85410	−	3.52671i	−0.256190	−	0.186133i	0.452276	−	0.891878i	$-0.350612\pi$
$359$	−4.85410	−	3.52671i	−0.256190	−	0.186133i	−0.708466	+	0.705745i	$0.750612\pi$
$360$	17.7984			0.938057
$361$	−6.80902	−	4.94704i	−0.358369	−	0.260371i
$362$	−12.0902	+	37.2097i	−0.635445	+	1.95570i
$363$	−2.30902	−	7.10642i	−0.121192	−	0.372991i
$364$	8.78115	−	6.37988i	0.460257	−	0.334397i
$365$	1.35410	−	0.983813i	0.0708769	−	0.0514951i
$366$	78.6312			4.11012
$367$	−3.31966	−	10.2169i	−0.173285	−	0.533316i	0.826266	−	0.563280i	$-0.190461\pi$
$367$	−3.31966	−	10.2169i	−0.173285	−	0.533316i	−0.999551	+	0.0299640i	$0.990461\pi$
$368$	41.7426			2.17599
$369$	−22.7361	+	9.59632i	−1.18359	+	0.499565i
$370$	−12.3262			−0.640811
$371$	2.09017	+	6.43288i	0.108516	+	0.333979i
$372$	−59.8328			−3.10219
$373$	12.5451	−	9.11454i	0.649560	−	0.471933i	−0.213561	−	0.976930i	$-0.568506\pi$
$373$	12.5451	−	9.11454i	0.649560	−	0.471933i	0.863121	+	0.504997i	$0.168506\pi$
$374$	45.1697	−	32.8177i	2.33567	−	1.69696i
$375$	−4.80902	−	14.8006i	−0.248337	−	0.764301i
$376$	19.7705	−	60.8474i	1.01959	−	3.13796i
$377$	−7.23607	−	5.25731i	−0.372676	−	0.270765i
$378$	5.85410			0.301103
$379$	−10.7533	−	7.81272i	−0.552359	−	0.401313i	0.276295	−	0.961073i	$-0.410893\pi$
$379$	−10.7533	−	7.81272i	−0.552359	−	0.401313i	−0.828655	+	0.559760i	$0.810893\pi$
$380$	−12.7082	−	9.23305i	−0.651917	−	0.473646i
$381$	−24.1803	+	17.5680i	−1.23880	+	0.900038i
$382$	−12.7082	−	39.1118i	−0.650208	−	2.00114i
$383$	−13.8885			−0.709671			−0.354836	−	0.934929i	$-0.615463\pi$
$383$	−13.8885			−0.709671			−0.354836	+	0.934929i	$0.615463\pi$
$384$	−2.30902	+	1.67760i	−0.117832	+	0.0856096i
$385$	−0.545085	+	1.67760i	−0.0277801	+	0.0854984i
$386$	−35.5795	−	25.8500i	−1.81095	−	1.31573i
$387$	−5.32624	−	16.3925i	−0.270748	−	0.833276i
$388$	11.0729	−	34.0790i	0.562144	−	1.73010i
$389$	−0.555728	+	1.71036i	−0.0281765	+	0.0867185i	−0.964156	−	0.265336i	$-0.914517\pi$
$389$	−0.555728	+	1.71036i	−0.0281765	+	0.0867185i	0.935979	+	0.352055i	$0.114517\pi$
$390$	−2.92705	+	9.00854i	−0.148217	+	0.456165i
$391$	9.78115	−	30.1033i	0.494654	−	1.52239i
$392$	2.30902	+	7.10642i	0.116623	+	0.358929i
$393$	12.8992	+	9.37181i	0.650678	+	0.472745i
$394$	−14.3262	+	44.0916i	−0.721745	+	2.22130i
$395$	0.454915	−	0.330515i	0.0228893	−	0.0166300i
$396$	−53.3951			−2.68321
$397$	8.07295	+	24.8460i	0.405170	+	1.24698i	0.920753	+	0.390145i	$0.127575\pi$
$397$	8.07295	+	24.8460i	0.405170	+	1.24698i	−0.515584	+	0.856839i	$0.672425\pi$
$398$	−17.9443	+	13.0373i	−0.899465	+	0.653500i
$399$	−11.0902	−	8.05748i	−0.555203	−	0.403379i
$400$	36.8156	+	26.7481i	1.84078	+	1.33740i
$401$	8.38197			0.418575			0.209288	−	0.977854i	$-0.432885\pi$
$401$	8.38197			0.418575			0.209288	+	0.977854i	$0.432885\pi$
$402$	−77.3222	−	56.1778i	−3.85648	−	2.80190i
$403$	3.25329	−	10.0126i	0.162058	−	0.498763i
$404$	−24.3541	−	74.9542i	−1.21166	−	3.72911i
$405$	2.85410	−	2.07363i	0.141821	−	0.103039i
$406$	8.47214	−	6.15537i	0.420465	−	0.305486i
$407$	21.7426			1.07774
$408$	45.1697	+	139.018i	2.23623	+	6.88242i
$409$	−25.5623			−1.26397			−0.631987	−	0.774979i	$-0.717761\pi$
$409$	−25.5623			−1.26397			−0.631987	+	0.774979i	$0.717761\pi$
$410$	10.0902	+	2.35114i	0.498318	+	0.116115i
$411$	19.9443			0.983778
$412$	2.78115	+	8.55951i	0.137018	+	0.421697i
$413$	−7.61803			−0.374859
$414$	−34.5795	+	25.1235i	−1.69949	+	1.23475i
$415$	0.0729490	−	0.0530006i	0.00358093	−	0.00260170i
$416$	−7.50000	−	23.0826i	−0.367718	−	1.13172i
$417$	−1.07295	+	3.30220i	−0.0525425	+	0.161709i
$418$	31.6525	+	22.9969i	1.54817	+	1.12481i
$419$	8.94427			0.436956			0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427			0.436956			0.218478	+	0.975842i	$0.429891\pi$
$420$	−6.35410	−	4.61653i	−0.310048	−	0.225263i
$421$	−16.4164	−	11.9272i	−0.800087	−	0.581297i	0.110853	−	0.993837i	$-0.464642\pi$
$421$	−16.4164	−	11.9272i	−0.800087	−	0.581297i	−0.910940	+	0.412540i	$0.864642\pi$
$422$	−31.1525	+	22.6336i	−1.51648	+	1.10179i
$423$	10.1976	+	31.3849i	0.495822	+	1.52598i
$424$	50.5410			2.45449
$425$	27.9164	−	20.2825i	1.35414	−	0.983844i
$426$	−33.4615	+	102.984i	−1.62121	+	4.98959i
$427$	−9.28115	−	6.74315i	−0.449146	−	0.326324i
$428$	4.71885	+	14.5231i	0.228094	+	0.702001i
$429$	5.16312	−	15.8904i	0.249278	−	0.767198i
$430$	−2.23607	+	6.88191i	−0.107833	+	0.331875i
$431$	−3.73607	+	11.4984i	−0.179960	+	0.553860i	−0.999825	−	0.0186966i	$-0.994048\pi$
$431$	−3.73607	+	11.4984i	−0.179960	+	0.553860i	0.819865	+	0.572557i	$0.194048\pi$
$432$	6.80902	−	20.9560i	0.327599	−	1.00825i
$433$	0.0835921	+	0.257270i	0.00401718	+	0.0123636i	0.953045	−	0.302829i	$-0.0979310\pi$
$433$	0.0835921	+	0.257270i	0.00401718	+	0.0123636i	−0.949028	+	0.315192i	$0.897931\pi$
$434$	9.97214	+	7.24518i	0.478678	+	0.347780i
$435$	−2.00000	+	6.15537i	−0.0958927	+	0.295127i
$436$	19.2812	−	14.0086i	0.923400	−	0.670889i
$437$	22.1803			1.06103
$438$	−5.73607	−	17.6538i	−0.274080	−	0.843531i
$439$	−25.0623	+	18.2088i	−1.19616	+	0.869060i	−0.993901	−	0.110272i	$-0.964828\pi$
$439$	−25.0623	+	18.2088i	−1.19616	+	0.869060i	−0.202257	+	0.979332i	$0.564828\pi$
$440$	10.6631	+	7.74721i	0.508344	+	0.369334i
$441$	−3.11803	−	2.26538i	−0.148478	−	0.107875i
$442$	−43.7426			−2.08063
$443$	1.26393	+	0.918300i	0.0600512	+	0.0436298i	0.617406	−	0.786645i	$-0.288184\pi$
$443$	1.26393	+	0.918300i	0.0600512	+	0.0436298i	−0.557355	+	0.830275i	$0.688184\pi$
$444$	−29.9164	+	92.0732i	−1.41977	+	4.36960i
$445$	1.16312	+	3.57971i	0.0551371	+	0.169695i
$446$	24.9164	−	18.1028i	1.17983	−	0.857194i
$447$	−26.7254	+	19.4172i	−1.26407	+	0.918400i
$448$	8.70820			0.411424
$449$	2.92705	+	9.00854i	0.138136	+	0.425139i	0.996065	−	0.0886299i	$-0.0282488\pi$
$449$	2.92705	+	9.00854i	0.138136	+	0.425139i	−0.857929	+	0.513769i	$0.828249\pi$
$450$	−46.5967			−2.19659
$451$	−17.7984	−	4.14725i	−0.838093	−	0.195287i
$452$	24.2705			1.14159
$453$	−15.8992	−	48.9327i	−0.747009	−	2.29906i
$454$	−25.2705			−1.18600
$455$	1.11803	−	0.812299i	0.0524142	−	0.0380812i
$456$	−82.8673	+	60.2066i	−3.88061	+	2.81943i
$457$	−0.510643	−	1.57160i	−0.0238869	−	0.0735162i	0.938402	−	0.345544i	$-0.112306\pi$
$457$	−0.510643	−	1.57160i	−0.0238869	−	0.0735162i	−0.962289	+	0.272028i	$0.912306\pi$
$458$	−8.35410	+	25.7113i	−0.390362	+	1.20141i
$459$	−13.5172	−	9.82084i	−0.630930	−	0.458397i
$460$	12.7082			0.592523
$461$	4.54508	+	3.30220i	0.211686	+	0.153799i	0.688576	−	0.725164i	$-0.258236\pi$
$461$	4.54508	+	3.30220i	0.211686	+	0.153799i	−0.476890	+	0.878963i	$0.658236\pi$
$462$	15.8262	+	11.4984i	0.736303	+	0.534956i
$463$	−4.28115	+	3.11044i	−0.198962	+	0.144554i	−0.682806	−	0.730600i	$-0.739240\pi$
$463$	−4.28115	+	3.11044i	−0.198962	+	0.144554i	0.483844	+	0.875155i	$0.339240\pi$
$464$	−12.1803	−	37.4872i	−0.565458	−	1.74030i
$465$	−7.61803			−0.353278
$466$	−38.6976	+	28.1154i	−1.79263	+	1.30242i
$467$	12.1976	−	37.5402i	0.564436	−	1.73715i	−0.105186	−	0.994453i	$-0.533544\pi$
$467$	12.1976	−	37.5402i	0.564436	−	1.73715i	0.669622	−	0.742702i	$-0.266456\pi$
$468$	33.8435	+	24.5887i	1.56441	+	1.13661i
$469$	4.30902	+	13.2618i	0.198972	+	0.612373i
$470$	4.28115	−	13.1760i	0.197475	−	0.607765i
$471$	5.19098	−	15.9762i	0.239188	−	0.736145i
$472$	−17.5902	+	54.1370i	−0.809653	+	2.49186i
$473$	3.94427	−	12.1392i	0.181358	−	0.558162i
$474$	−1.92705	−	5.93085i	−0.0885124	−	0.272413i
$475$	19.5623	+	14.2128i	0.897580	+	0.652130i
$476$	11.2082	−	34.4953i	0.513727	−	1.58109i
$477$	−21.0902	+	15.3229i	−0.965653	+	0.701588i
$478$	52.3607			2.39492
$479$	10.5517	+	32.4747i	0.482118	+	1.48381i	0.836112	+	0.548558i	$0.184823\pi$
$479$	10.5517	+	32.4747i	0.482118	+	1.48381i	−0.353994	+	0.935248i	$0.615177\pi$
$480$	−14.2082	+	10.3229i	−0.648513	+	0.471172i
$481$	−13.7812	−	10.0126i	−0.628366	−	0.456535i
$482$	8.04508	+	5.84510i	0.366444	+	0.266237i
$483$	11.0902			0.504620
$484$	11.2082	+	8.14324i	0.509464	+	0.370147i
$485$	1.40983	−	4.33901i	0.0640171	−	0.197024i
$486$	−17.5172	−	53.9125i	−0.794597	−	2.44552i
$487$	−5.20820	+	3.78398i	−0.236006	+	0.171469i	−0.699502	−	0.714630i	$-0.746595\pi$
$487$	−5.20820	+	3.78398i	−0.236006	+	0.171469i	0.463496	+	0.886099i	$0.346595\pi$
$488$	−69.3500	+	50.3858i	−3.13933	+	2.28086i
$489$	−50.3607			−2.27739
$490$	0.500000	+	1.53884i	0.0225877	+	0.0695178i
$491$	−1.79837			−0.0811595			−0.0405797	−	0.999176i	$-0.512920\pi$
$491$	−1.79837			−0.0811595			−0.0405797	+	0.999176i	$0.512920\pi$
$492$	42.0517	−	69.6642i	1.89584	−	3.14070i
$493$	−29.8885			−1.34611
$494$	−9.47214	−	29.1522i	−0.426172	−	1.31162i
$495$	−6.79837			−0.305564
$496$	37.5344	−	27.2704i	1.68535	−	1.22448i
$497$	12.7812	−	9.28605i	0.573313	−	0.416536i
$498$	−0.309017	−	0.951057i	−0.0138474	−	0.0426179i
$499$	11.9271	−	36.7077i	0.533928	−	1.64326i	−0.212026	−	0.977264i	$-0.568006\pi$
$499$	11.9271	−	36.7077i	0.533928	−	1.64326i	0.745954	−	0.665998i	$-0.231994\pi$
$500$	23.3435	+	16.9600i	1.04395	+	0.758475i
$501$	31.4164			1.40358
$502$	−16.4443	−	11.9475i	−0.733944	−	0.533241i
$503$	27.0172	+	19.6292i	1.20464	+	0.875221i	0.994733	−	0.102501i	$-0.0326844\pi$
$503$	27.0172	+	19.6292i	1.20464	+	0.875221i	0.209905	+	0.977722i	$0.432684\pi$
$504$	−23.2984	+	16.9273i	−1.03779	+	0.754000i
$505$	−3.10081	−	9.54332i	−0.137984	−	0.424672i
$506$	−31.6525			−1.40712
$507$	16.9443	−	12.3107i	0.752522	−	0.546739i
$508$	17.1246	−	52.7041i	0.759782	−	2.33837i
$509$	−11.9271	−	8.66551i	−0.528657	−	0.384092i	0.291198	−	0.956663i	$-0.405946\pi$
$509$	−11.9271	−	8.66551i	−0.528657	−	0.384092i	−0.819855	+	0.572571i	$0.805946\pi$
$510$	9.78115	+	30.1033i	0.433117	+	1.33300i
$511$	−0.836881	+	2.57565i	−0.0370214	+	0.113940i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$	3.61803	−	11.1352i	0.159740	−	0.491629i
$514$	−21.7533	+	66.9497i	−0.959496	+	2.95303i
$515$	0.354102	+	1.08981i	0.0156036	+	0.0480229i
$516$	45.9787	+	33.4055i	2.02410	+	1.47059i
$517$	−7.55166	+	23.2416i	−0.332122	+	1.02217i
$518$	16.1353	−	11.7229i	0.708942	−	0.515077i
$519$	−2.61803			−0.114919
$520$	−3.19098	−	9.82084i	−0.139934	−	0.430672i
$521$	−0.881966	+	0.640786i	−0.0386396	+	0.0280733i	−0.606937	−	0.794750i	$-0.707602\pi$
$521$	−0.881966	+	0.640786i	−0.0386396	+	0.0280733i	0.568298	+	0.822823i	$0.307602\pi$
$522$	32.6525	+	23.7234i	1.42916	+	1.03835i
$523$	9.35410	+	6.79615i	0.409026	+	0.297175i	0.773208	−	0.634153i	$-0.218651\pi$
$523$	9.35410	+	6.79615i	0.409026	+	0.297175i	−0.364181	+	0.931328i	$0.618651\pi$
$524$	−29.5623			−1.29144
$525$	9.78115	+	7.10642i	0.426885	+	0.310150i
$526$	1.97214	−	6.06961i	0.0859892	−	0.264648i
$527$	−10.8713	−	33.4585i	−0.473562	−	1.45747i
$528$	59.5689	−	43.2793i	2.59240	−	1.88349i
$529$	4.09017	−	2.97168i	0.177833	−	0.129204i
$530$	10.9443			0.475389
$531$	−9.07295	−	27.9237i	−0.393732	−	1.21178i
$532$	25.4164			1.10194
$533$	9.37132	+	10.8249i	0.405917	+	0.468878i
$534$	41.7426			1.80638
$535$	0.600813	+	1.84911i	0.0259754	+	0.0799441i
$536$	104.193			4.50047
$537$	52.7148	−	38.2995i	2.27481	−	1.65275i
$538$	24.3713	−	17.7068i	1.05072	−	0.763394i
$539$	−0.881966	−	2.71441i	−0.0379890	−	0.116918i
$540$	2.07295	−	6.37988i	0.0892055	−	0.274546i
$541$	−2.38197	−	1.73060i	−0.102409	−	0.0744043i	0.535402	−	0.844597i	$-0.320160\pi$
$541$	−2.38197	−	1.73060i	−0.102409	−	0.0744043i	−0.637811	+	0.770193i	$0.720160\pi$
$542$	39.0344			1.67667
$543$	31.6525	+	22.9969i	1.35834	+	0.986890i
$544$	−65.6140	−	47.6713i	−2.81318	−	2.04389i
$545$	2.45492	−	1.78360i	0.105157	−	0.0764010i
$546$	−4.73607	−	14.5761i	−0.202685	−	0.623800i
$547$	21.7639			0.930559			0.465279	−	0.885164i	$-0.345954\pi$
$547$	21.7639			0.930559			0.465279	+	0.885164i	$0.345954\pi$
$548$	−29.9164	+	21.7355i	−1.27797	+	0.928496i
$549$	13.6631	−	42.0508i	0.583128	−	1.79468i
$550$	−27.9164	−	20.2825i	−1.19036	−	0.864847i
$551$	−6.47214	−	19.9192i	−0.275722	−	0.848586i
$552$	25.6074	−	78.8114i	1.08992	−	3.35444i
$553$	−0.281153	+	0.865300i	−0.0119558	+	0.0367963i
$554$	−15.8262	+	48.7082i	−0.672392	+	2.06941i
$555$	−3.80902	+	11.7229i	−0.161684	+	0.497611i
$556$	−1.98936	−	6.12261i	−0.0843675	−	0.259657i
$557$	−14.7533	−	10.7189i	−0.625117	−	0.454174i	0.229588	−	0.973288i	$-0.426262\pi$
$557$	−14.7533	−	10.7189i	−0.625117	−	0.454174i	−0.854705	+	0.519114i	$0.826262\pi$
$558$	−14.6803	+	45.1814i	−0.621468	+	1.91268i
$559$	−8.09017	+	5.87785i	−0.342178	+	0.248607i
$560$	6.09017			0.257357
$561$	−17.2533	−	53.1002i	−0.728434	−	2.24189i
$562$	−16.0172	+	11.6372i	−0.675646	+	0.490885i
$563$	−12.5172	−	9.09429i	−0.527538	−	0.383279i	0.291898	−	0.956449i	$-0.405713\pi$
$563$	−12.5172	−	9.09429i	−0.527538	−	0.383279i	−0.819436	+	0.573171i	$0.805713\pi$
$564$	−88.0304	−	63.9578i	−3.70675	−	2.69311i
$565$	3.09017			0.130004
$566$	58.3779	+	42.4140i	2.45381	+	1.78279i
$567$	−1.76393	+	5.42882i	−0.0740782	+	0.227989i
$568$	−36.4787	−	112.270i	−1.53061	−	4.71074i
$569$	−7.06231	+	5.13107i	−0.296067	+	0.215105i	−0.725895	−	0.687805i	$-0.758574\pi$
$569$	−7.06231	+	5.13107i	−0.296067	+	0.215105i	0.429828	+	0.902911i	$0.358574\pi$
$570$	−17.9443	+	13.0373i	−0.751603	+	0.546071i
$571$	28.8885			1.20895			0.604474	−	0.796625i	$-0.293383\pi$
$571$	28.8885			1.20895			0.604474	+	0.796625i	$0.293383\pi$
$572$	9.57295	+	29.4625i	0.400265	+	1.23189i
$573$	−41.1246			−1.71801
$574$	−15.4443	+	6.51864i	−0.644631	+	0.272083i
$575$	−19.5623			−0.815805
$576$	10.3713	+	31.9196i	0.432138	+	1.32999i
$577$	−25.3607			−1.05578			−0.527889	−	0.849313i	$-0.677016\pi$
$577$	−25.3607			−1.05578			−0.527889	+	0.849313i	$0.677016\pi$
$578$	−82.2492	+	59.7576i	−3.42112	+	2.48559i
$579$	−35.5795	+	25.8500i	−1.47863	+	1.07429i
$580$	−3.70820	−	11.4127i	−0.153975	−	0.473886i
$581$	−0.0450850	+	0.138757i	−0.00187044	+	0.00575662i
$582$	−40.9336	−	29.7400i	−1.69675	−	1.23276i
$583$	−19.3050			−0.799529
$584$	16.3713	+	11.8945i	0.677450	+	0.492196i
$585$	4.30902	+	3.13068i	0.178156	+	0.129438i
$586$	4.35410	−	3.16344i	0.179866	−	0.130681i
$587$	−5.60081	−	17.2375i	−0.231170	−	0.711469i	−0.997606	−	0.0691484i	$-0.977972\pi$
$587$	−5.60081	−	17.2375i	−0.231170	−	0.711469i	0.766436	−	0.642321i	$-0.222028\pi$
$588$	12.7082			0.524077
$589$	19.9443	−	14.4904i	0.821789	−	0.597065i
$590$	−3.80902	+	11.7229i	−0.156815	+	0.482626i
$591$	37.5066	+	27.2501i	1.54281	+	1.12092i
$592$	−23.1976	−	71.3948i	−0.953414	−	2.93431i
$593$	1.73607	−	5.34307i	0.0712918	−	0.219413i	−0.909062	−	0.416661i	$-0.863200\pi$
$593$	1.73607	−	5.34307i	0.0712918	−	0.219413i	0.980354	+	0.197247i	$0.0632002\pi$
$594$	−5.16312	+	15.8904i	−0.211845	+	0.651993i
$595$	1.42705	−	4.39201i	0.0585034	−	0.180055i
$596$	18.9271	−	58.2515i	0.775282	−	2.38607i
$597$	6.85410	+	21.0948i	0.280520	+	0.863351i
$598$	20.0623	+	14.5761i	0.820409	+	0.596062i
$599$	3.03851	−	9.35156i	0.124150	−	0.382095i	−0.869595	−	0.493765i	$-0.835620\pi$
$599$	3.03851	−	9.35156i	0.124150	−	0.382095i	0.993745	+	0.111671i	$0.0356202\pi$
$600$	73.0861	−	53.1002i	2.98373	−	2.16781i
$601$	−17.2361			−0.703074			−0.351537	−	0.936174i	$-0.614341\pi$
$601$	−17.2361			−0.703074			−0.351537	+	0.936174i	$0.614341\pi$
$602$	−3.61803	−	11.1352i	−0.147460	−	0.453835i
$603$	−43.4787	+	31.5891i	−1.77059	+	1.28641i
$604$	77.1763	+	56.0718i	3.14026	+	2.28153i
$605$	1.42705	+	1.03681i	0.0580179	+	0.0421525i
$606$	−111.284			−4.52059
$607$	−20.3262	−	14.7679i	−0.825017	−	0.599410i	0.0931285	−	0.995654i	$-0.470313\pi$
$607$	−20.3262	−	14.7679i	−0.825017	−	0.599410i	−0.918145	+	0.396244i	$0.870313\pi$
$608$	17.5623	−	54.0512i	0.712246	−	2.19207i
$609$	−3.23607	−	9.95959i	−0.131132	−	0.403583i
$610$	−15.0172	+	10.9106i	−0.608030	+	0.441759i
$611$	15.4894	−	11.2537i	0.626632	−	0.455275i
$612$	139.790			5.65069
$613$	−1.21885	−	3.75123i	−0.0492288	−	0.151511i	0.923420	−	0.383790i	$-0.125381\pi$
$613$	−1.21885	−	3.75123i	−0.0492288	−	0.151511i	−0.972649	+	0.232280i	$0.925381\pi$
$614$	60.0689			2.42418
$615$	5.35410	−	8.86978i	0.215898	−	0.357664i
$616$	−21.3262			−0.859259
$617$	−0.618034	−	1.90211i	−0.0248811	−	0.0765762i	0.937845	−	0.347055i	$-0.112818\pi$
$617$	−0.618034	−	1.90211i	−0.0248811	−	0.0765762i	−0.962726	+	0.270478i	$0.912818\pi$
$618$	12.7082			0.511199
$619$	−2.82624	+	2.05338i	−0.113596	+	0.0825324i	−0.643133	−	0.765755i	$-0.722366\pi$
$619$	−2.82624	+	2.05338i	−0.113596	+	0.0825324i	0.529537	+	0.848287i	$0.322366\pi$
$620$	11.4271	−	8.30224i	0.458921	−	0.333426i
$621$	2.92705	+	9.00854i	0.117459	+	0.361500i
$622$	−6.97214	+	21.4580i	−0.279557	+	0.860389i
$623$	−4.92705	−	3.57971i	−0.197398	−	0.143418i
$624$	−57.6869			−2.30932
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$	−38.4336	−	27.9237i	−1.53612	−	1.11605i
$627$	31.6525	−	22.9969i	1.26408	−	0.918407i
$628$	9.62461	+	29.6215i	0.384064	+	1.18203i
$629$	−56.9230			−2.26967
$630$	−5.04508	+	3.66547i	−0.201001	+	0.146036i
$631$	9.39919	−	28.9277i	0.374176	−	1.15159i	−0.569857	−	0.821744i	$-0.693002\pi$
$631$	9.39919	−	28.9277i	0.374176	−	1.15159i	0.944033	−	0.329851i	$-0.106998\pi$
$632$	5.50000	+	3.99598i	0.218778	+	0.158952i
$633$	11.8992	+	36.6219i	0.472950	+	1.45559i
$634$	−0.0729490	+	0.224514i	−0.00289718	+	0.00891659i
$635$	2.18034	−	6.71040i	0.0865241	−	0.266294i
$636$	26.5623	−	81.7504i	1.05326	−	3.24161i
$637$	−0.690983	+	2.12663i	−0.0273777	+	0.0842600i
$638$	9.23607	+	28.4257i	0.365659	+	1.12538i
$639$	49.2599	+	35.7894i	1.94869	+	1.41581i
$640$	0.208204	−	0.640786i	0.00822998	−	0.0253293i
$641$	30.8435	−	22.4091i	1.21824	−	0.885106i	0.222290	−	0.974981i	$-0.428647\pi$
$641$	30.8435	−	22.4091i	1.21824	−	0.885106i	0.995953	+	0.0898749i	$0.0286467\pi$
$642$	21.5623			0.850996
$643$	−6.16312	−	18.9681i	−0.243050	−	0.748030i	−0.995951	−	0.0898967i	$-0.971346\pi$
$643$	−6.16312	−	18.9681i	−0.243050	−	0.748030i	0.752901	−	0.658133i	$-0.228654\pi$
$644$	−16.6353	+	12.0862i	−0.655521	+	0.476264i
$645$	5.85410	+	4.25325i	0.230505	+	0.167472i
$646$	−82.8673	−	60.2066i	−3.26037	−	2.36880i
$647$	−17.2148			−0.676783			−0.338391	−	0.941005i	$-0.609883\pi$
$647$	−17.2148			−0.676783			−0.338391	+	0.941005i	$0.609883\pi$
$648$	34.5066	+	25.0705i	1.35555	+	0.984862i
$649$	6.71885	−	20.6785i	0.263738	−	0.811702i
$650$	8.35410	+	25.7113i	0.327675	+	1.00848i
$651$	9.97214	−	7.24518i	0.390839	−	0.283961i
$652$	75.5410	−	54.8838i	2.95841	−	2.14941i
$653$	−7.70820			−0.301645			−0.150823	−	0.988561i	$-0.548192\pi$
$653$	−7.70820			−0.301645			−0.150823	+	0.988561i	$0.548192\pi$
$654$	−10.3992	−	32.0054i	−0.406640	−	1.25151i
$655$	−3.76393			−0.147069
$656$	5.37132	+	62.8680i	0.209715	+	2.45458i
$657$	−10.4377			−0.407213
$658$	6.92705	+	21.3193i	0.270045	+	0.831112i
$659$	−20.5066			−0.798823			−0.399411	−	0.916772i	$-0.630785\pi$
$659$	−20.5066			−0.798823			−0.399411	+	0.916772i	$0.630785\pi$
$660$	18.1353	−	13.1760i	0.705914	−	0.512876i
$661$	10.7533	−	7.81272i	0.418254	−	0.303880i	−0.358681	−	0.933460i	$-0.616773\pi$
$661$	10.7533	−	7.81272i	0.418254	−	0.303880i	0.776935	+	0.629581i	$0.216773\pi$
$662$	11.9443	+	36.7607i	0.464227	+	1.42874i
$663$	−13.5172	+	41.6017i	−0.524965	+	1.61568i
$664$	0.881966	+	0.640786i	0.0342269	+	0.0248673i
$665$	3.23607			0.125489
$666$	62.1869	+	45.1814i	2.40969	+	1.75075i
$667$	13.7082	+	9.95959i	0.530784	+	0.385637i
$668$	−47.1246	+	34.2380i	−1.82331	+	1.32471i
$669$	−9.51722	−	29.2910i	−0.367957	−	1.13246i
$670$	22.5623			0.871658
$671$	26.4894	−	19.2456i	1.02261	−	0.742970i
$672$	8.78115	−	27.0256i	0.338740	−	1.04254i
$673$	5.87132	+	4.26577i	0.226323	+	0.164433i	0.695168	−	0.718847i	$-0.255330\pi$
$673$	5.87132	+	4.26577i	0.226323	+	0.164433i	−0.468845	+	0.883280i	$0.655330\pi$
$674$	29.1246	+	89.6363i	1.12184	+	3.45266i
$675$	−3.19098	+	9.82084i	−0.122821	+	0.378004i
$676$	−12.0000	+	36.9322i	−0.461538	+	1.42047i
$677$	−5.45492	+	16.7885i	−0.209649	+	0.645235i	0.789841	+	0.613312i	$0.210163\pi$
$677$	−5.45492	+	16.7885i	−0.209649	+	0.645235i	−0.999490	+	0.0319228i	$0.989837\pi$
$678$	10.5902	−	32.5932i	0.406713	−	1.25173i
$679$	2.28115	+	7.02067i	0.0875426	+	0.269428i
$680$	−27.9164	−	20.2825i	−1.07055	−	0.777797i
$681$	−7.80902	+	24.0337i	−0.299242	+	0.920973i
$682$	−28.4615	+	20.6785i	−1.08985	+	0.791820i
$683$	−41.1591			−1.57491			−0.787454	−	0.616374i	$-0.788601\pi$
$683$	−41.1591			−1.57491			−0.787454	+	0.616374i	$0.788601\pi$
$684$	30.2705	+	93.1630i	1.15742	+	3.56218i
$685$	−3.80902	+	2.76741i	−0.145535	+	0.105737i
$686$	−2.11803	−	1.53884i	−0.0808669	−	0.0587533i
$687$	21.8713	+	15.8904i	0.834443	+	0.606258i
$688$	−44.0689			−1.68011
$689$	12.2361	+	8.89002i	0.466157	+	0.338683i
$690$	5.54508	−	17.0660i	0.211098	−	0.649692i
$691$	−0.135255	−	0.416272i	−0.00514534	−	0.0158357i	0.948451	−	0.316924i	$-0.102650\pi$
$691$	−0.135255	−	0.416272i	−0.00514534	−	0.0158357i	−0.953596	+	0.301088i	$0.902650\pi$
$692$	3.92705	−	2.85317i	0.149284	−	0.108461i
$693$	8.89919	−	6.46564i	0.338052	−	0.245609i
$694$	−71.9230			−2.73016
$695$	−0.253289	−	0.779543i	−0.00960780	−	0.0295698i
$696$	−78.2492			−2.96603
$697$	46.5967	+	10.8576i	1.76498	+	0.411263i
$698$	−19.4721			−0.737031
$699$	14.7812	+	45.4917i	0.559075	+	1.72065i
$700$	−22.4164			−0.847261
$701$	−3.33688	+	2.42439i	−0.126032	+	0.0915678i	−0.649016	−	0.760775i	$-0.724819\pi$
$701$	−3.33688	+	2.42439i	−0.126032	+	0.0915678i	0.522983	+	0.852343i	$0.324819\pi$
$702$	10.5902	−	7.69421i	0.399700	−	0.290399i
$703$	−12.3262	−	37.9363i	−0.464893	−	1.43079i
$704$	−7.68034	+	23.6377i	−0.289464	+	0.890878i
$705$	−11.2082	−	8.14324i	−0.422125	−	0.306692i
$706$	−14.3262			−0.539175
$707$	13.1353	+	9.54332i	0.494002	+	0.358914i
$708$	78.3222	+	56.9044i	2.94353	+	2.13860i
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	−0.139200	−	0.990264i	$-0.544453\pi$
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	0.898782	+	0.438396i	$0.144453\pi$
$710$	−7.89919	−	24.3112i	−0.296451	−	0.912383i
$711$	−3.50658			−0.131507
$712$	−36.8156	+	26.7481i	−1.37972	+	1.00243i
$713$	−6.16312	+	18.9681i	−0.230811	+	0.710362i
$714$	−41.4336	−	30.1033i	−1.55061	−	1.12659i
$715$	1.21885	+	3.75123i	0.0455823	+	0.140288i
$716$	−37.3328	+	114.899i	−1.39519	+	4.29396i
$717$	16.1803	−	49.7980i	0.604266	−	1.85974i
$718$	4.85410	−	14.9394i	0.181153	−	0.557533i
$719$	14.3926	−	44.2959i	0.536754	−	1.65196i	−0.203075	−	0.979163i	$-0.565094\pi$
$719$	14.3926	−	44.2959i	0.536754	−	1.65196i	0.739829	−	0.672795i	$-0.234906\pi$
$720$	7.25329	+	22.3233i	0.270314	+	0.831941i
$721$	−1.50000	−	1.08981i	−0.0558629	−	0.0405868i
$722$	6.80902	−	20.9560i	0.253405	−	0.779902i
$723$	8.04508	−	5.84510i	0.299200	−	0.217381i
$724$	−72.5410			−2.69597
$725$	5.70820	+	17.5680i	0.211997	+	0.652461i
$726$	15.8262	−	11.4984i	0.587367	−	0.426747i
$727$	18.4894	+	13.4333i	0.685732	+	0.498214i	0.875254	−	0.483663i	$-0.160694\pi$
$727$	18.4894	+	13.4333i	0.685732	+	0.498214i	−0.189522	+	0.981876i	$0.560694\pi$
$728$	13.5172	+	9.82084i	0.500982	+	0.363984i
$729$	−39.5623			−1.46527
$730$	3.54508	+	2.57565i	0.131209	+	0.0953293i
$731$	−10.3262	+	31.7809i	−0.381930	+	1.17546i
$732$	45.0517	+	138.655i	1.66516	+	5.12483i
$733$	33.0066	−	23.9807i	1.21913	−	0.885747i	0.223099	−	0.974796i	$-0.428383\pi$
$733$	33.0066	−	23.9807i	1.21913	−	0.885747i	0.996027	+	0.0890492i	$0.0283828\pi$
$734$	22.7533	−	16.5312i	0.839839	−	0.610179i
$735$	1.61803			0.0596821
$736$	14.2082	+	43.7284i	0.523721	+	1.61185i
$737$	−39.7984			−1.46599
$738$	−42.2877	−	48.8469i	−1.55663	−	1.79808i
$739$	−38.7426			−1.42517			−0.712586	−	0.701585i	$-0.752476\pi$
$739$	−38.7426			−1.42517			−0.712586	+	0.701585i	$0.752476\pi$
$740$	−7.06231	−	21.7355i	−0.259616	−	0.799014i
$741$	−30.6525			−1.12605
$742$	−14.3262	+	10.4086i	−0.525933	+	0.382113i
$743$	−5.50000	+	3.99598i	−0.201775	+	0.146598i	−0.684085	−	0.729403i	$-0.739798\pi$
$743$	−5.50000	+	3.99598i	−0.201775	+	0.146598i	0.482309	+	0.876001i	$0.339798\pi$
$744$	−28.4615	−	87.5955i	−1.04345	−	3.21141i
$745$	2.40983	−	7.41669i	0.0882893	−	0.271727i
$746$	32.8435	+	23.8622i	1.20248	+	0.873656i
$747$	−0.562306			−0.0205737
$748$	83.7492	+	60.8474i	3.06217	+	2.22480i
$749$	−2.54508	−	1.84911i	−0.0929954	−	0.0675651i
$750$	32.9615	−	23.9479i	1.20358	−	0.874455i
$751$	6.34346	+	19.5232i	0.231476	+	0.712410i	0.997569	+	0.0696807i	$0.0221981\pi$
$751$	6.34346	+	19.5232i	0.231476	+	0.712410i	−0.766093	+	0.642729i	$0.777802\pi$
$752$	84.3738			3.07680
$753$	−16.4443	+	11.9475i	−0.599263	+	0.435390i
$754$	7.23607	−	22.2703i	0.263522	−	0.811037i
$755$	9.82624	+	7.13918i	0.357613	+	0.259821i
$756$	3.35410	+	10.3229i	0.121988	+	0.375439i
$757$	4.71885	−	14.5231i	0.171509	−	0.527852i	−0.827947	−	0.560806i	$-0.810491\pi$
$757$	4.71885	−	14.5231i	0.171509	−	0.527852i	0.999457	+	0.0329540i	$0.0104915\pi$
$758$	10.7533	−	33.0952i	0.390577	−	1.20207i
$759$	−9.78115	+	30.1033i	−0.355033	+	1.09268i
$760$	7.47214	−	22.9969i	0.271043	−	0.834184i
$761$	−8.59675	−	26.4581i	−0.311632	−	0.959104i	−0.977119	−	0.212695i	$-0.931776\pi$
$761$	−8.59675	−	26.4581i	−0.311632	−	0.959104i	0.665487	−	0.746410i	$-0.268224\pi$
$762$	−63.3050	−	45.9937i	−2.29330	−	1.66618i
$763$	−1.51722	+	4.66953i	−0.0549271	+	0.169048i
$764$	61.6869	−	44.8182i	2.23175	−	1.62146i
$765$	17.7984			0.643502
$766$	−11.2361	−	34.5811i	−0.405976	−	1.24946i
$767$	−13.7812	+	10.0126i	−0.497609	+	0.361534i
$768$	30.8435	+	22.4091i	1.11297	+	0.808618i
$769$	−12.8541	−	9.33905i	−0.463531	−	0.336775i	0.331384	−	0.943496i	$-0.392484\pi$
$769$	−12.8541	−	9.33905i	−0.463531	−	0.336775i	−0.794915	+	0.606721i	$0.792484\pi$
$770$	−4.61803			−0.166422
$771$	56.9508	+	41.3772i	2.05103	+	1.49016i
$772$	25.1976	−	77.5501i	0.906880	−	2.79109i
$773$	−2.31966	−	7.13918i	−0.0834324	−	0.256778i	0.900634	−	0.434578i	$-0.143102\pi$
$773$	−2.31966	−	7.13918i	−0.0834324	−	0.256778i	−0.984067	+	0.177799i	$0.943102\pi$
$774$	36.5066	−	26.5236i	1.31220	−	0.953370i
$775$	−17.5902	+	12.7800i	−0.631858	+	0.459071i
$776$	55.1591			1.98009
$777$	−6.16312	−	18.9681i	−0.221101	−	0.680478i
$778$	−4.70820			−0.168797
$779$	2.85410	+	33.4055i	0.102259	+	1.19688i
$780$	−17.5623			−0.628831
$781$	13.9336	+	42.8833i	0.498584	+	1.53449i
$782$	82.8673			2.96333
$783$	7.23607	−	5.25731i	0.258596	−	0.187881i
$784$	−7.97214	+	5.79210i	−0.284719	+	0.206861i
$785$	1.22542	+	3.77147i	0.0437373	+	0.134610i
$786$	−12.8992	+	39.6996i	−0.460099	+	1.41604i
$787$	−10.0451	−	7.29818i	−0.358069	−	0.260152i	0.394177	−	0.919034i	$-0.371030\pi$
$787$	−10.0451	−	7.29818i	−0.358069	−	0.260152i	−0.752246	+	0.658882i	$0.771030\pi$
$788$	−85.9574			−3.06211
$789$	−5.16312	−	3.75123i	−0.183812	−	0.133547i
$790$	1.19098	+	0.865300i	0.0423733	+	0.0307860i
$791$	−4.04508	+	2.93893i	−0.143827	+	0.104496i
$792$	−25.3992	−	78.1707i	−0.902521	−	2.77767i
$793$	−25.6525			−0.910946
$794$	−55.3328	+	40.2016i	−1.96369	+	1.42670i
$795$	3.38197	−	10.4086i	0.119946	−	0.369156i
$796$	−33.2705	−	24.1724i	−1.17924	−	0.856769i
$797$	3.14590	+	9.68208i	0.111433	+	0.342957i	0.991186	−	0.132474i	$-0.0422921\pi$
$797$	3.14590	+	9.68208i	0.111433	+	0.342957i	−0.879753	+	0.475431i	$0.842292\pi$
$798$	11.0902	−	34.1320i	0.392588	−	1.20826i
$799$	19.7705	−	60.8474i	0.699430	−	2.15263i
$800$	−15.4894	+	47.6713i	−0.547631	+	1.68544i
$801$	7.25329	−	22.3233i	0.256282	−	0.788756i
$802$	6.78115	+	20.8702i	0.239451	+	0.736954i
$803$	−6.25329	−	4.54328i	−0.220674	−	0.160329i
$804$	54.7599	−	168.534i	1.93123	−	5.94372i
$805$	−2.11803	+	1.53884i	−0.0746509	+	0.0542370i
$806$	27.5623			0.970841
$807$	−9.30902	−	28.6502i	−0.327693	−	1.00854i
$808$	98.1484	−	71.3090i	3.45285	−	2.50864i
$809$	−26.0795	−	18.9479i	−0.916907	−	0.666172i	0.0258450	−	0.999666i	$-0.491772\pi$
$809$	−26.0795	−	18.9479i	−0.916907	−	0.666172i	−0.942752	+	0.333494i	$0.891772\pi$
$810$	7.47214	+	5.42882i	0.262544	+	0.190749i
$811$	−2.05573			−0.0721864			−0.0360932	−	0.999348i	$-0.511491\pi$
$811$	−2.05573			−0.0721864			−0.0360932	+	0.999348i	$0.511491\pi$
$812$	15.7082	+	11.4127i	0.551250	+	0.400506i
$813$	12.0623	−	37.1240i	0.423044	−	1.30199i
$814$	17.5902	+	54.1370i	0.616535	+	1.89750i
$815$	9.61803	−	6.98791i	0.336905	−	0.244776i
$816$	−155.953	+	113.307i	−5.45946	+	3.96653i
$817$	−23.4164			−0.819236
$818$	−20.6803	−	63.6475i	−0.723071	−	2.22538i
$819$	−8.61803			−0.301138
$820$	1.63525	+	19.1396i	0.0571056	+	0.668385i
$821$	29.3951			1.02590			0.512948	−	0.858419i	$-0.328553\pi$
$821$	29.3951			1.02590			0.512948	+	0.858419i	$0.328553\pi$
$822$	16.1353	+	49.6592i	0.562782	+	1.73206i
$823$	−3.96556			−0.138231			−0.0691153	−	0.997609i	$-0.522018\pi$
$823$	−3.96556			−0.138231			−0.0691153	+	0.997609i	$0.522018\pi$
$824$	−11.2082	+	8.14324i	−0.390456	+	0.283683i
$825$	−27.9164	+	20.2825i	−0.971925	+	0.706145i
$826$	−6.16312	−	18.9681i	−0.214442	−	0.659986i
$827$	−9.32624	+	28.7032i	−0.324305	+	0.998108i	0.647448	+	0.762109i	$0.275836\pi$
$827$	−9.32624	+	28.7032i	−0.324305	+	0.998108i	−0.971753	+	0.235999i	$0.924164\pi$
$828$	−64.1140	−	46.5815i	−2.22811	−	1.61882i
$829$	8.02129			0.278591			0.139295	−	0.990251i	$-0.455516\pi$
$829$	8.02129			0.278591			0.139295	+	0.990251i	$0.455516\pi$
$830$	0.190983	+	0.138757i	0.00662912	+	0.00481634i
$831$	41.4336	+	30.1033i	1.43732	+	1.04427i
$832$	15.7533	−	11.4454i	0.546147	−	0.396799i
$833$	2.30902	+	7.10642i	0.0800027	+	0.246223i
$834$	−9.09017			−0.314767
$835$	−6.00000	+	4.35926i	−0.207639	+	0.150858i
$836$	−22.4164	+	68.9906i	−0.775288	+	2.38609i
$837$	8.51722	+	6.18812i	0.294398	+	0.213893i
$838$	7.23607	+	22.2703i	0.249966	+	0.769316i
$839$	−7.60081	+	23.3929i	−0.262409	+	0.807613i	0.729870	+	0.683586i	$0.239581\pi$
$839$	−7.60081	+	23.3929i	−0.262409	+	0.807613i	−0.992279	+	0.124026i	$0.960419\pi$
$840$	3.73607	−	11.4984i	0.128907	−	0.396734i
$841$	−4.01722	+	12.3637i	−0.138525	+	0.426336i
$842$	16.4164	−	50.5245i	0.565747	−	1.74119i
$843$	6.11803	+	18.8294i	0.210716	+	0.648518i
$844$	−57.7599	−	41.9650i	−1.98818	−	1.44449i
$845$	−1.52786	+	4.70228i	−0.0525601	+	0.161763i
$846$	−69.8951	+	50.7818i	−2.40304	+	1.74591i
$847$	−2.85410			−0.0980681
$848$	20.5967	+	63.3903i	0.707295	+	2.17683i
$849$	58.3779	−	42.4140i	2.00352	−	1.45565i
$850$	73.0861	+	53.1002i	2.50683	+	1.82132i
$851$	26.1074	+	18.9681i	0.894950	+	0.650219i
$852$	−200.769			−6.87823
$853$	−11.9164	−	8.65778i	−0.408010	−	0.296437i	0.364786	−	0.931092i	$-0.381142\pi$
$853$	−11.9164	−	8.65778i	−0.408010	−	0.296437i	−0.772796	+	0.634655i	$0.781142\pi$
$854$	9.28115	−	28.5645i	0.317595	−	0.977455i
$855$	3.85410	+	11.8617i	0.131808	+	0.405662i
$856$	−19.0172	+	13.8168i	−0.649995	+	0.472249i
$857$	−41.8156	+	30.3808i	−1.42839	+	1.03779i	−0.438080	+	0.898936i	$0.644342\pi$
$857$	−41.8156	+	30.3808i	−1.42839	+	1.03779i	−0.990313	+	0.138853i	$0.955658\pi$
$858$	43.7426			1.49335
$859$	−0.656541	−	2.02063i	−0.0224009	−	0.0689429i	0.939231	−	0.343285i	$-0.111540\pi$
$859$	−0.656541	−	2.02063i	−0.0224009	−	0.0689429i	−0.961632	+	0.274343i	$0.911540\pi$
$860$	−13.4164			−0.457496
$861$	1.42705	+	16.7027i	0.0486338	+	0.569228i
$862$	−31.6525			−1.07809
$863$	−9.59017	−	29.5155i	−0.326453	−	1.00472i	−0.970780	−	0.239970i	$-0.922863\pi$
$863$	−9.59017	−	29.5155i	−0.326453	−	1.00472i	0.644327	−	0.764750i	$-0.277137\pi$
$864$	24.2705			0.825700
$865$	0.500000	−	0.363271i	0.0170005	−	0.0123516i
$866$	−0.572949	+	0.416272i	−0.0194696	+	0.0141455i
$867$	31.4164	+	96.6898i	1.06696	+	3.28376i
$868$	−7.06231	+	21.7355i	−0.239710	+	0.737752i
$869$	−2.10081	−	1.52633i	−0.0712652	−	0.0517772i
$870$	−16.9443			−0.574465
$871$	25.2254	+	18.3273i	0.854731	+	0.620998i
$872$	29.6803	+	21.5640i	1.00510	+	0.730250i
$873$	−23.0172	+	16.7230i	−0.779015	+	0.565987i
$874$	17.9443	+	55.2268i	0.606974	+	1.86807i
$875$	−5.94427			−0.200953
$876$	27.8435	−	20.2295i	0.940743	−	0.683490i
$877$	5.29837	−	16.3067i	0.178913	−	0.550639i	−0.820877	−	0.571105i	$-0.806515\pi$
$877$	5.29837	−	16.3067i	0.178913	−	0.550639i	0.999791	+	0.0204660i	$0.00651499\pi$
$878$	−65.6140	−	47.6713i	−2.21436	−	1.60883i
$879$	−1.66312	−	5.11855i	−0.0560956	−	0.172645i
$880$	−5.37132	+	16.5312i	−0.181067	+	0.557268i
$881$	−0.628677	+	1.93487i	−0.0211807	+	0.0651874i	−0.961088	−	0.276242i	$-0.910911\pi$
$881$	−0.628677	+	1.93487i	−0.0211807	+	0.0651874i	0.939908	+	0.341429i	$0.110911\pi$
$882$	3.11803	−	9.59632i	0.104990	−	0.323125i
$883$	3.46149	−	10.6534i	0.116489	−	0.358515i	−0.875766	−	0.482736i	$-0.839643\pi$
$883$	3.46149	−	10.6534i	0.116489	−	0.358515i	0.992255	+	0.124221i	$0.0396432\pi$
$884$	−25.0623	−	77.1338i	−0.842937	−	2.59429i
$885$	9.97214	+	7.24518i	0.335210	+	0.243544i
$886$	−1.26393	+	3.88998i	−0.0424626	+	0.130687i
$887$	−18.4894	+	13.4333i	−0.620812	+	0.451046i	−0.853205	−	0.521576i	$-0.825344\pi$
$887$	−18.4894	+	13.4333i	−0.620812	+	0.451046i	0.232393	+	0.972622i	$0.425344\pi$
$888$	−149.026			−5.00100
$889$	3.52786	+	10.8576i	0.118321	+	0.364154i
$890$	−7.97214	+	5.79210i	−0.267227	+	0.194151i
$891$	−13.1803	−	9.57608i	−0.441558	−	0.320811i
$892$	46.1976	+	33.5645i	1.54681	+	1.12382i
$893$	44.8328			1.50027
$894$	−69.9681	−	50.8348i	−2.34008	−	1.70017i
$895$	−4.75329	+	14.6291i	−0.158885	+	0.488998i
$896$	0.336881	+	1.03681i	0.0112544	+	0.0346375i
$897$	20.0623	−	14.5761i	0.669861	−	0.486682i
$898$	−20.0623	+	14.5761i	−0.669488	+	0.486411i
$899$	18.8328			0.628110
$900$	−26.6976	−	82.1666i	−0.889919	−	2.73889i
$901$	50.5410			1.68377
$902$	−4.07295	−	47.6713i	−0.135614	−	1.58728i
$903$	−11.7082			−0.389625
$904$	11.5451	+	35.5321i	0.383984	+	1.18178i
$905$	−9.23607			−0.307017
$906$	108.975	−	79.1747i	3.62044	−	2.63040i
$907$	−0.354102	+	0.257270i	−0.0117578	+	0.00854251i	−0.593649	−	0.804724i	$-0.702313\pi$
$907$	−0.354102	+	0.257270i	−0.0117578	+	0.00854251i	0.581891	+	0.813267i	$0.302313\pi$
$908$	−14.4787	−	44.5609i	−0.480493	−	1.47881i
$909$	−19.3369	+	59.5128i	−0.641364	+	1.97391i
$910$	2.92705	+	2.12663i	0.0970308	+	0.0704970i
$911$	31.3951			1.04017			0.520083	−	0.854115i	$-0.325901\pi$
$911$	31.3951			1.04017			0.520083	+	0.854115i	$0.325901\pi$
$912$	−109.284	−	79.3992i	−3.61874	−	2.62917i
$913$	−0.336881	−	0.244758i	−0.0111491	−	0.00810032i
$914$	3.50000	−	2.54290i	0.115770	−	0.0841116i
$915$	5.73607	+	17.6538i	0.189629	+	0.583617i
$916$	−50.1246			−1.65616
$917$	4.92705	−	3.57971i	0.162706	−	0.118213i
$918$	13.5172	−	41.6017i	0.446135	−	1.37306i
$919$	22.7082	+	16.4985i	0.749075	+	0.544235i	0.895540	−	0.444981i	$-0.146790\pi$
$919$	22.7082	+	16.4985i	0.749075	+	0.544235i	−0.146465	+	0.989216i	$0.546790\pi$
$920$	6.04508	+	18.6049i	0.199301	+	0.613384i
$921$	18.5623	−	57.1289i	0.611649	−	1.88246i
$922$	−4.54508	+	13.9883i	−0.149684	+	0.460681i
$923$	10.9164	−	33.5972i	0.359318	−	1.10587i
$924$	−11.2082	+	34.4953i	−0.368723	+	1.13481i
$925$	10.8713	+	33.4585i	0.357447	+	1.10011i
$926$	−11.2082	−	8.14324i	−0.368324	−	0.267603i
$927$	2.20820	−	6.79615i	0.0725269	−	0.223215i
$928$	35.1246	−	25.5195i	1.15302	−	0.837719i
$929$	25.2148			0.827270			0.413635	−	0.910443i	$-0.364259\pi$
$929$	25.2148			0.827270			0.413635	+	0.910443i	$0.364259\pi$
$930$	−6.16312	−	18.9681i	−0.202097	−	0.621989i
$931$	−4.23607	+	3.07768i	−0.138832	+	0.100867i
$932$	−71.7492	−	52.1289i	−2.35022	−	1.70754i
$933$	18.2533	+	13.2618i	0.597586	+	0.434172i
$934$	103.339			3.38137
$935$	10.6631	+	7.74721i	0.348721	+	0.253361i
$936$	−19.8992	+	61.2434i	−0.650425	+	2.00180i
$937$	−5.09017	−	15.6659i	−0.166289	−	0.511784i	0.832840	−	0.553513i	$-0.186713\pi$
$937$	−5.09017	−	15.6659i	−0.166289	−	0.511784i	−0.999129	+	0.0417296i	$0.986713\pi$
$938$	−29.5344	+	21.4580i	−0.964334	+	0.700629i
$939$	−38.4336	+	27.9237i	−1.25423	+	0.911254i
$940$	25.6869			0.837815
$941$	−8.48936	−	26.1276i	−0.276745	−	0.851734i	−0.988752	−	0.149562i	$-0.952214\pi$
$941$	−8.48936	−	26.1276i	−0.276745	−	0.851734i	0.712007	−	0.702172i	$-0.247786\pi$
$942$	43.9787			1.43290
$943$	−17.7533	−	20.5070i	−0.578127	−	0.667799i
$944$	−75.0689			−2.44328
$945$	0.427051	+	1.31433i	0.0138920	+	0.0427551i
$946$	33.4164			1.08646
$947$	−3.50000	+	2.54290i	−0.113735	+	0.0826331i	−0.643199	−	0.765699i	$-0.722393\pi$
$947$	−3.50000	+	2.54290i	−0.113735	+	0.0826331i	0.529464	+	0.848332i	$0.322393\pi$
$948$	9.35410	−	6.79615i	0.303807	−	0.220729i
$949$	1.87132	+	5.75934i	0.0607457	+	0.186956i
$950$	−19.5623	+	60.2066i	−0.634685	+	1.95336i
$951$	0.190983	+	0.138757i	0.00619305	+	0.00449951i
$952$	55.8328			1.80955
$953$	0.236068	+	0.171513i	0.00764699	+	0.00555586i	0.591602	−	0.806230i	$-0.298496\pi$
$953$	0.236068	+	0.171513i	0.00764699	+	0.00555586i	−0.583955	+	0.811786i	$0.698496\pi$
$954$	−55.2148	−	40.1159i	−1.78764	−	1.29880i
$955$	7.85410	−	5.70634i	0.254153	−	0.184653i
$956$	30.0000	+	92.3305i	0.970269	+	2.98618i
$957$	29.8885			0.966159
$958$	−72.3222	+	52.5451i	−2.33662	+	1.69766i
$959$	2.35410	−	7.24518i	0.0760179	−	0.233959i
$960$	−11.3992	−	8.28199i	−0.367907	−	0.267300i
$961$	−2.72949	−	8.40051i	−0.0880481	−	0.270984i
$962$	13.7812	−	42.4140i	0.444322	−	1.36748i
$963$	3.74671	−	11.5312i	0.120736	−	0.371587i
$964$	−5.69756	+	17.5353i	−0.183506	+	0.564774i
$965$	3.20820	−	9.87384i	0.103276	−	0.317850i
$966$	8.97214	+	27.6134i	0.288674	+	0.888446i
$967$	13.4721	+	9.78808i	0.433235	+	0.314763i	0.782941	−	0.622096i	$-0.213719\pi$
$967$	13.4721	+	9.78808i	0.433235	+	0.314763i	−0.349706	+	0.936859i	$0.613719\pi$
$968$	−6.59017	+	20.2825i	−0.211816	+	0.651903i
$969$	−82.8673	+	60.2066i	−2.66208	+	1.93411i
$970$	11.9443			0.383507
$971$	−4.16970	−	12.8330i	−0.133812	−	0.411831i	0.861591	−	0.507602i	$-0.169468\pi$
$971$	−4.16970	−	12.8330i	−0.133812	−	0.411831i	−0.995403	+	0.0957717i	$0.969468\pi$
$972$	85.0304	−	61.7782i	2.72735	−	1.98154i
$973$	1.07295	+	0.779543i	0.0343972	+	0.0249910i
$974$	−13.6353	−	9.90659i	−0.436902	−	0.317428i
$975$	27.0344			0.865795
$976$	−91.4574	−	66.4477i	−2.92748	−	2.12694i
$977$	0.770510	−	2.37139i	0.0246508	−	0.0758673i	−0.937974	−	0.346705i	$-0.887301\pi$
$977$	0.770510	−	2.37139i	0.0246508	−	0.0758673i	0.962625	+	0.270837i	$0.0873006\pi$
$978$	−40.7426	−	125.393i	−1.30281	−	4.00963i
$979$	14.0623	−	10.2169i	0.449433	−	0.326532i
$980$	−2.42705	+	1.76336i	−0.0775293	+	0.0563283i
$981$	−18.9230			−0.604164
$982$	−1.45492	−	4.47777i	−0.0464282	−	0.142891i
$983$	−58.1246			−1.85389			−0.926944	−	0.375201i	$-0.877574\pi$
$983$	−58.1246			−1.85389			−0.926944	+	0.375201i	$0.877574\pi$
$984$	121.992	+	28.4257i	3.88896	+	0.906178i
$985$	−10.9443			−0.348713
$986$	−24.1803	−	74.4194i	−0.770059	−	2.37000i
$987$	22.4164			0.713522
$988$	45.9787	−	33.4055i	1.46278	−	1.06277i
$989$	15.3262	−	11.1352i	0.487346	−	0.354078i
$990$	−5.50000	−	16.9273i	−0.174801	−	0.537984i
$991$	3.99342	−	12.2905i	0.126855	−	0.390420i	−0.867379	−	0.497648i	$-0.834197\pi$
$991$	3.99342	−	12.2905i	0.126855	−	0.390420i	0.994235	+	0.107227i	$0.0341973\pi$
$992$	41.3435	+	30.0378i	1.31266	+	0.953701i
$993$	38.6525			1.22660
$994$	33.4615	+	24.3112i	1.06133	+	0.771104i
$995$	−4.23607	−	3.07768i	−0.134292	−	0.0975691i
$996$	1.50000	−	1.08981i	0.0475293	−	0.0345321i
$997$	10.5836	+	32.5729i	0.335186	+	1.03160i	0.966630	+	0.256175i	$0.0824622\pi$
$997$	10.5836	+	32.5729i	0.335186	+	1.03160i	−0.631445	+	0.775421i	$0.717538\pi$
$998$	101.048			3.19861
$999$	13.7812	−	10.0126i	0.436016	−	0.316784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.b.141.1	yes	4
41.16	even	5	inner	287.2.h.b.57.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.b.57.1	✓	4	41.16	even	5	inner
287.2.h.b.141.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 2.48990i) q^{2} +2.61803 q^{3} +(-3.92705 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.11803 + 6.51864i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-6.04508 - 4.39201i) q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+(0.809017 + 2.48990i) q^{2} +2.61803 q^{3} +(-3.92705 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.11803 + 6.51864i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-6.04508 - 4.39201i) q^{8} +3.85410 q^{9} +(-1.30902 - 0.951057i) q^{10} +(2.30902 + 1.67760i) q^{11} +(-10.2812 + 7.46969i) q^{12} +(-0.690983 - 2.12663i) q^{13} +2.61803 q^{14} +(-1.30902 + 0.951057i) q^{15} +(3.04508 - 9.37181i) q^{16} +(-6.04508 - 4.39201i) q^{17} +(3.11803 + 9.59632i) q^{18} +(1.61803 - 4.97980i) q^{19} +(0.927051 - 2.85317i) q^{20} +(0.809017 - 2.48990i) q^{21} +(-2.30902 + 7.10642i) q^{22} +(1.30902 + 4.02874i) q^{23} +(-15.8262 - 11.4984i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(4.73607 - 3.44095i) q^{26} +2.23607 q^{27} +(1.50000 + 4.61653i) q^{28} +(3.23607 - 2.35114i) q^{29} +(-3.42705 - 2.48990i) q^{30} +(3.80902 + 2.76741i) q^{31} +10.8541 q^{32} +(6.04508 + 4.39201i) q^{33} +(6.04508 - 18.6049i) q^{34} +(0.190983 + 0.587785i) q^{35} +(-15.1353 + 10.9964i) q^{36} +(6.16312 - 4.47777i) q^{37} +13.7082 q^{38} +(-1.80902 - 5.56758i) q^{39} +4.61803 q^{40} +(-5.89919 + 2.48990i) q^{41} +6.85410 q^{42} +(-1.38197 - 4.25325i) q^{43} -13.8541 q^{44} +(-1.92705 + 1.40008i) q^{45} +(-8.97214 + 6.51864i) q^{46} +(2.64590 + 8.14324i) q^{47} +(7.97214 - 24.5357i) q^{48} +(-0.809017 - 0.587785i) q^{49} -12.0902 q^{50} +(-15.8262 - 11.4984i) q^{51} +(8.78115 + 6.37988i) q^{52} +(-5.47214 + 3.97574i) q^{53} +(1.80902 + 5.56758i) q^{54} -1.76393 q^{55} +(-6.04508 + 4.39201i) q^{56} +(4.23607 - 13.0373i) q^{57} +(8.47214 + 6.15537i) q^{58} +(-2.35410 - 7.24518i) q^{59} +(2.42705 - 7.46969i) q^{60} +(3.54508 - 10.9106i) q^{61} +(-3.80902 + 11.7229i) q^{62} +(1.19098 - 3.66547i) q^{63} +(2.69098 + 8.28199i) q^{64} +(1.11803 + 0.812299i) q^{65} +(-6.04508 + 18.6049i) q^{66} +(-11.2812 + 8.19624i) q^{67} +36.2705 q^{68} +(3.42705 + 10.5474i) q^{69} +(-1.30902 + 0.951057i) q^{70} +(12.7812 + 9.28605i) q^{71} +(-23.2984 - 16.9273i) q^{72} -2.70820 q^{73} +(16.1353 + 11.7229i) q^{74} +(-3.73607 + 11.4984i) q^{75} +(7.85410 + 24.1724i) q^{76} +(2.30902 - 1.67760i) q^{77} +(12.3992 - 9.00854i) q^{78} -0.909830 q^{79} +(1.88197 + 5.79210i) q^{80} -5.70820 q^{81} +(-10.9721 - 12.6740i) q^{82} -0.145898 q^{83} +(3.92705 + 12.0862i) q^{84} +4.61803 q^{85} +(9.47214 - 6.88191i) q^{86} +(8.47214 - 6.15537i) q^{87} +(-6.59017 - 20.2825i) q^{88} +(1.88197 - 5.79210i) q^{89} +(-5.04508 - 3.66547i) q^{90} -2.23607 q^{91} +(-16.6353 - 12.0862i) q^{92} +(9.97214 + 7.24518i) q^{93} +(-18.1353 + 13.1760i) q^{94} +(1.00000 + 3.07768i) q^{95} +28.4164 q^{96} +(-5.97214 + 4.33901i) q^{97} +(0.809017 - 2.48990i) q^{98} +(8.89919 + 6.46564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9} - 3 q^{10} + 7 q^{11} - 21 q^{12} - 5 q^{13} + 6 q^{14} - 3 q^{15} + q^{16} - 13 q^{17} + 8 q^{18} + 2 q^{19} - 3 q^{20} + q^{21} - 7 q^{22} + 3 q^{23} - 32 q^{24} + q^{25} + 10 q^{26} + 6 q^{28} + 4 q^{29} - 7 q^{30} + 13 q^{31} + 30 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} - 27 q^{36} + 9 q^{37} + 28 q^{38} - 5 q^{39} + 14 q^{40} + q^{41} + 14 q^{42} - 10 q^{43} - 42 q^{44} - q^{45} - 18 q^{46} + 24 q^{47} + 14 q^{48} - q^{49} - 26 q^{50} - 32 q^{51} + 15 q^{52} - 4 q^{53} + 5 q^{54} - 16 q^{55} - 13 q^{56} + 8 q^{57} + 16 q^{58} + 4 q^{59} + 3 q^{60} + 3 q^{61} - 13 q^{62} + 7 q^{63} + 13 q^{64} - 13 q^{66} - 25 q^{67} + 78 q^{68} + 7 q^{69} - 3 q^{70} + 31 q^{71} - 44 q^{72} + 16 q^{73} + 31 q^{74} - 6 q^{75} + 18 q^{76} + 7 q^{77} + 25 q^{78} - 26 q^{79} + 12 q^{80} + 4 q^{81} - 26 q^{82} - 14 q^{83} + 9 q^{84} + 14 q^{85} + 20 q^{86} + 16 q^{87} - 4 q^{88} + 12 q^{89} - 9 q^{90} - 33 q^{92} + 22 q^{93} - 39 q^{94} + 4 q^{95} + 60 q^{96} - 6 q^{97} + q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9 - 3 * q^10 + 7 * q^11 - 21 * q^12 - 5 * q^13 + 6 * q^14 - 3 * q^15 + q^16 - 13 * q^17 + 8 * q^18 + 2 * q^19 - 3 * q^20 + q^21 - 7 * q^22 + 3 * q^23 - 32 * q^24 + q^25 + 10 * q^26 + 6 * q^28 + 4 * q^29 - 7 * q^30 + 13 * q^31 + 30 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 - 27 * q^36 + 9 * q^37 + 28 * q^38 - 5 * q^39 + 14 * q^40 + q^41 + 14 * q^42 - 10 * q^43 - 42 * q^44 - q^45 - 18 * q^46 + 24 * q^47 + 14 * q^48 - q^49 - 26 * q^50 - 32 * q^51 + 15 * q^52 - 4 * q^53 + 5 * q^54 - 16 * q^55 - 13 * q^56 + 8 * q^57 + 16 * q^58 + 4 * q^59 + 3 * q^60 + 3 * q^61 - 13 * q^62 + 7 * q^63 + 13 * q^64 - 13 * q^66 - 25 * q^67 + 78 * q^68 + 7 * q^69 - 3 * q^70 + 31 * q^71 - 44 * q^72 + 16 * q^73 + 31 * q^74 - 6 * q^75 + 18 * q^76 + 7 * q^77 + 25 * q^78 - 26 * q^79 + 12 * q^80 + 4 * q^81 - 26 * q^82 - 14 * q^83 + 9 * q^84 + 14 * q^85 + 20 * q^86 + 16 * q^87 - 4 * q^88 + 12 * q^89 - 9 * q^90 - 33 * q^92 + 22 * q^93 - 39 * q^94 + 4 * q^95 + 60 * q^96 - 6 * q^97 + q^98 + 11 * q^99

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