LMFDB - Embedded newform 43.2.c.b.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	43.36
Dual form			43.2.c.b.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61803 q^{2} +(0.190983 + 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 + 2.80252i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 + 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})$	\(q-2.61803 q^{2} +(0.190983 + 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 + 2.80252i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 + 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +(-4.23607 - 7.33708i) q^{10} -1.38197 q^{11} +(0.927051 + 1.60570i) q^{12} +(-1.80902 + 3.13331i) q^{13} +(0.309017 - 0.535233i) q^{14} +(-0.618034 + 1.07047i) q^{15} +9.85410 q^{16} +(2.54508 - 4.40822i) q^{17} +(-3.73607 + 6.47106i) q^{18} +(-1.61803 - 2.80252i) q^{19} +(7.85410 + 13.6037i) q^{20} -0.0901699 q^{21} +3.61803 q^{22} +(-3.30902 - 5.73139i) q^{23} +(-1.42705 - 2.47172i) q^{24} +(-2.73607 + 4.73901i) q^{25} +(4.73607 - 8.20311i) q^{26} +2.23607 q^{27} +(-0.572949 + 0.992377i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(1.61803 - 2.80252i) q^{30} -10.8541 q^{32} +(-0.263932 - 0.457144i) q^{33} +(-6.66312 + 11.5409i) q^{34} -0.763932 q^{35} +(6.92705 - 11.9980i) q^{36} +(-0.927051 - 1.60570i) q^{37} +(4.23607 + 7.33708i) q^{38} -1.38197 q^{39} +(-12.0902 - 20.9408i) q^{40} +0.527864 q^{41} +0.236068 q^{42} +(-6.50000 - 0.866025i) q^{43} -6.70820 q^{44} +9.23607 q^{45} +(8.66312 + 15.0050i) q^{46} +7.85410 q^{47} +(1.88197 + 3.25966i) q^{48} +(3.47214 + 6.01392i) q^{49} +(7.16312 - 12.4069i) q^{50} +1.94427 q^{51} +(-8.78115 + 15.2094i) q^{52} +(1.80902 + 3.13331i) q^{53} -5.85410 q^{54} +(-2.23607 - 3.87298i) q^{55} +(0.881966 - 1.52761i) q^{56} +(0.618034 - 1.07047i) q^{57} +(3.92705 - 6.80185i) q^{58} -6.09017 q^{59} +(-3.00000 + 5.19615i) q^{60} +(1.92705 - 3.33775i) q^{61} +(0.336881 + 0.583495i) q^{63} +8.70820 q^{64} -11.7082 q^{65} +(0.690983 + 1.19682i) q^{66} +(-1.42705 - 2.47172i) q^{67} +(12.3541 - 21.3979i) q^{68} +(1.26393 - 2.18919i) q^{69} +2.00000 q^{70} +(-6.89919 + 11.9497i) q^{71} +(-10.6631 + 18.4691i) q^{72} +(2.42705 - 4.20378i) q^{73} +(2.42705 + 4.20378i) q^{74} -2.09017 q^{75} +(-7.85410 - 13.6037i) q^{76} +(0.163119 - 0.282530i) q^{77} +3.61803 q^{78} +(1.80902 - 3.13331i) q^{79} +(15.9443 + 27.6163i) q^{80} +(-3.85410 - 6.67550i) q^{81} -1.38197 q^{82} +(6.51722 + 11.2882i) q^{83} -0.437694 q^{84} +16.4721 q^{85} +(17.0172 + 2.26728i) q^{86} -1.14590 q^{87} +10.3262 q^{88} +(-2.42705 - 4.20378i) q^{89} -24.1803 q^{90} +(-0.427051 - 0.739674i) q^{91} +(-16.0623 - 27.8207i) q^{92} -20.5623 q^{94} +(5.23607 - 9.06914i) q^{95} +(-2.07295 - 3.59045i) q^{96} -4.76393 q^{97} +(-9.09017 - 15.7446i) q^{98} +(-1.97214 + 3.41584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9} - 8 q^{10} - 10 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} + 2 q^{15} + 26 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 22 q^{21} + 10 q^{22} - 11 q^{23} + q^{24} - 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} - 30 q^{32} - 10 q^{33} - 11 q^{34} - 12 q^{35} + 21 q^{36} + 3 q^{37} + 8 q^{38} - 10 q^{39} - 26 q^{40} + 20 q^{41} - 8 q^{42} - 26 q^{43} + 28 q^{45} + 19 q^{46} + 18 q^{47} + 12 q^{48} - 4 q^{49} + 13 q^{50} - 28 q^{51} - 15 q^{52} + 5 q^{53} - 10 q^{54} + 8 q^{56} - 2 q^{57} + 9 q^{58} - 2 q^{59} - 12 q^{60} + q^{61} + 17 q^{63} + 8 q^{64} - 20 q^{65} + 5 q^{66} + q^{67} + 36 q^{68} + 14 q^{69} + 8 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} + 3 q^{74} + 14 q^{75} - 18 q^{76} - 15 q^{77} + 10 q^{78} + 5 q^{79} + 28 q^{80} - 2 q^{81} - 10 q^{82} - 3 q^{83} - 42 q^{84} + 48 q^{85} + 39 q^{86} - 18 q^{87} + 10 q^{88} - 3 q^{89} - 52 q^{90} + 5 q^{91} - 24 q^{92} - 42 q^{94} + 12 q^{95} - 15 q^{96} - 28 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9 - 8 * q^10 - 10 * q^11 - 3 * q^12 - 5 * q^13 - q^14 + 2 * q^15 + 26 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 22 * q^21 + 10 * q^22 - 11 * q^23 + q^24 - 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 - 30 * q^32 - 10 * q^33 - 11 * q^34 - 12 * q^35 + 21 * q^36 + 3 * q^37 + 8 * q^38 - 10 * q^39 - 26 * q^40 + 20 * q^41 - 8 * q^42 - 26 * q^43 + 28 * q^45 + 19 * q^46 + 18 * q^47 + 12 * q^48 - 4 * q^49 + 13 * q^50 - 28 * q^51 - 15 * q^52 + 5 * q^53 - 10 * q^54 + 8 * q^56 - 2 * q^57 + 9 * q^58 - 2 * q^59 - 12 * q^60 + q^61 + 17 * q^63 + 8 * q^64 - 20 * q^65 + 5 * q^66 + q^67 + 36 * q^68 + 14 * q^69 + 8 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 + 3 * q^74 + 14 * q^75 - 18 * q^76 - 15 * q^77 + 10 * q^78 + 5 * q^79 + 28 * q^80 - 2 * q^81 - 10 * q^82 - 3 * q^83 - 42 * q^84 + 48 * q^85 + 39 * q^86 - 18 * q^87 + 10 * q^88 - 3 * q^89 - 52 * q^90 + 5 * q^91 - 24 * q^92 - 42 * q^94 + 12 * q^95 - 15 * q^96 - 28 * q^97 - 14 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.61803			−1.85123			−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803			−1.85123			−0.925615	+	0.378467i	$0.876451\pi$
$3$	0.190983	+	0.330792i	0.110264	+	0.190983i	0.915877	−	0.401460i	$-0.131497\pi$
$3$	0.190983	+	0.330792i	0.110264	+	0.190983i	−0.805613	+	0.592443i	$0.798164\pi$
$4$	4.85410			2.42705
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	0.959545	+	0.281556i	$0.0908504\pi$
$5$	1.61803	+	2.80252i	0.723607	+	1.25332i	−0.235938	+	0.971768i	$0.575816\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	−0.887469	−	0.460866i	$-0.847539\pi$
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	0.842857	+	0.538138i	$0.180872\pi$
$8$	−7.47214			−2.64180
$9$	1.42705	−	2.47172i	0.475684	−	0.823908i
$10$	−4.23607	−	7.33708i	−1.33956	−	2.32019i
$11$	−1.38197			−0.416678			−0.208339	−	0.978057i	$-0.566806\pi$
$11$	−1.38197			−0.416678			−0.208339	+	0.978057i	$0.566806\pi$
$12$	0.927051	+	1.60570i	0.267617	+	0.463525i
$13$	−1.80902	+	3.13331i	−0.501731	+	0.869024i	0.498267	+	0.867024i	$0.333970\pi$
$13$	−1.80902	+	3.13331i	−0.501731	+	0.869024i	−0.999998	+	0.00199999i	$0.999363\pi$
$14$	0.309017	−	0.535233i	0.0825883	−	0.143047i
$15$	−0.618034	+	1.07047i	−0.159576	+	0.276393i
$16$	9.85410			2.46353
$17$	2.54508	−	4.40822i	0.617274	−	1.06915i	−0.372707	−	0.927949i	$-0.621570\pi$
$17$	2.54508	−	4.40822i	0.617274	−	1.06915i	0.989981	−	0.141201i	$-0.0450962\pi$
$18$	−3.73607	+	6.47106i	−0.880600	+	1.52524i
$19$	−1.61803	−	2.80252i	−0.371202	−	0.642942i	0.618548	−	0.785747i	$-0.287721\pi$
$19$	−1.61803	−	2.80252i	−0.371202	−	0.642942i	−0.989751	+	0.142805i	$0.954388\pi$
$20$	7.85410	+	13.6037i	1.75623	+	3.04188i
$21$	−0.0901699			−0.0196767
$22$	3.61803			0.771367
$23$	−3.30902	−	5.73139i	−0.689978	−	1.19508i	−0.971845	−	0.235623i	$-0.924287\pi$
$23$	−3.30902	−	5.73139i	−0.689978	−	1.19508i	0.281867	−	0.959454i	$-0.409046\pi$
$24$	−1.42705	−	2.47172i	−0.291296	−	0.504539i
$25$	−2.73607	+	4.73901i	−0.547214	+	0.947802i
$26$	4.73607	−	8.20311i	0.928819	−	1.60876i
$27$	2.23607			0.430331
$28$	−0.572949	+	0.992377i	−0.108277	+	0.187542i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	1.61803	−	2.80252i	0.295411	−	0.511667i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−10.8541			−1.91875
$33$	−0.263932	−	0.457144i	−0.0459447	−	0.0795785i
$34$	−6.66312	+	11.5409i	−1.14272	+	1.97924i
$35$	−0.763932			−0.129128
$36$	6.92705	−	11.9980i	1.15451	−	1.99967i
$37$	−0.927051	−	1.60570i	−0.152406	−	0.263975i	0.779705	−	0.626147i	$-0.215369\pi$
$37$	−0.927051	−	1.60570i	−0.152406	−	0.263975i	−0.932112	+	0.362171i	$0.882036\pi$
$38$	4.23607	+	7.33708i	0.687181	+	1.19023i
$39$	−1.38197			−0.221292
$40$	−12.0902	−	20.9408i	−1.91162	−	3.31103i
$41$	0.527864			0.0824385			0.0412193	−	0.999150i	$-0.486876\pi$
$41$	0.527864			0.0824385			0.0412193	+	0.999150i	$0.486876\pi$
$42$	0.236068			0.0364261
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$44$	−6.70820			−1.01130
$45$	9.23607			1.37683
$46$	8.66312	+	15.0050i	1.27731	+	2.21236i
$47$	7.85410			1.14564			0.572819	−	0.819682i	$-0.305850\pi$
$47$	7.85410			1.14564			0.572819	+	0.819682i	$0.305850\pi$
$48$	1.88197	+	3.25966i	0.271638	+	0.470492i
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$	7.16312	−	12.4069i	1.01302	−	1.75460i
$51$	1.94427			0.272253
$52$	−8.78115	+	15.2094i	−1.21773	+	2.10916i
$53$	1.80902	+	3.13331i	0.248488	+	0.430393i	0.963106	−	0.269121i	$-0.0867331\pi$
$53$	1.80902	+	3.13331i	0.248488	+	0.430393i	−0.714619	+	0.699514i	$0.753400\pi$
$54$	−5.85410			−0.796642
$55$	−2.23607	−	3.87298i	−0.301511	−	0.522233i
$56$	0.881966	−	1.52761i	0.117858	−	0.204135i
$57$	0.618034	−	1.07047i	0.0818606	−	0.141787i
$58$	3.92705	−	6.80185i	0.515647	−	0.893127i
$59$	−6.09017			−0.792873			−0.396436	−	0.918062i	$-0.629753\pi$
$59$	−6.09017			−0.792873			−0.396436	+	0.918062i	$0.629753\pi$
$60$	−3.00000	+	5.19615i	−0.387298	+	0.670820i
$61$	1.92705	−	3.33775i	0.246734	−	0.427355i	−0.715884	−	0.698219i	$-0.753976\pi$
$61$	1.92705	−	3.33775i	0.246734	−	0.427355i	0.962618	+	0.270864i	$0.0873094\pi$
$62$		0			0
$63$	0.336881	+	0.583495i	0.0424430	+	0.0735135i
$64$	8.70820			1.08853
$65$	−11.7082			−1.45222
$66$	0.690983	+	1.19682i	0.0850541	+	0.147318i
$67$	−1.42705	−	2.47172i	−0.174342	−	0.301969i	0.765591	−	0.643327i	$-0.222447\pi$
$67$	−1.42705	−	2.47172i	−0.174342	−	0.301969i	−0.939933	+	0.341358i	$0.889113\pi$
$68$	12.3541	−	21.3979i	1.49815	−	2.59488i
$69$	1.26393	−	2.18919i	0.152160	−	0.263548i
$70$	2.00000			0.239046
$71$	−6.89919	+	11.9497i	−0.818783	+	1.41817i	0.0877966	+	0.996138i	$0.472017\pi$
$71$	−6.89919	+	11.9497i	−0.818783	+	1.41817i	−0.906580	+	0.422035i	$0.861316\pi$
$72$	−10.6631	+	18.4691i	−1.25666	+	2.17660i
$73$	2.42705	−	4.20378i	0.284065	−	0.492015i	−0.688317	−	0.725410i	$-0.741650\pi$
$73$	2.42705	−	4.20378i	0.284065	−	0.492015i	0.972382	+	0.233395i	$0.0749836\pi$
$74$	2.42705	+	4.20378i	0.282139	+	0.488679i
$75$	−2.09017			−0.241352
$76$	−7.85410	−	13.6037i	−0.900927	−	1.56045i
$77$	0.163119	−	0.282530i	0.0185891	−	0.0321973i
$78$	3.61803			0.409662
$79$	1.80902	−	3.13331i	0.203530	−	0.352525i	−0.746133	−	0.665797i	$-0.768092\pi$
$79$	1.80902	−	3.13331i	0.203530	−	0.352525i	0.949663	+	0.313272i	$0.101425\pi$
$80$	15.9443	+	27.6163i	1.78262	+	3.08759i
$81$	−3.85410	−	6.67550i	−0.428234	−	0.741722i
$82$	−1.38197			−0.152613
$83$	6.51722	+	11.2882i	0.715358	+	1.23904i	0.962821	+	0.270139i	$0.0870697\pi$
$83$	6.51722	+	11.2882i	0.715358	+	1.23904i	−0.247463	+	0.968897i	$0.579597\pi$
$84$	−0.437694			−0.0477563
$85$	16.4721			1.78665
$86$	17.0172	+	2.26728i	1.83501	+	0.244488i
$87$	−1.14590			−0.122853
$88$	10.3262			1.10078
$89$	−2.42705	−	4.20378i	−0.257267	−	0.445599i	0.708242	−	0.705970i	$-0.249489\pi$
$89$	−2.42705	−	4.20378i	−0.257267	−	0.445599i	−0.965509	+	0.260371i	$0.916155\pi$
$90$	−24.1803			−2.54883
$91$	−0.427051	−	0.739674i	−0.0447671	−	0.0775389i
$92$	−16.0623	−	27.8207i	−1.67461	−	2.90051i
$93$		0			0
$94$	−20.5623			−2.12084
$95$	5.23607	−	9.06914i	0.537209	−	0.930474i
$96$	−2.07295	−	3.59045i	−0.211569	−	0.366449i
$97$	−4.76393			−0.483704			−0.241852	−	0.970313i	$-0.577755\pi$
$97$	−4.76393			−0.483704			−0.241852	+	0.970313i	$0.577755\pi$
$98$	−9.09017	−	15.7446i	−0.918246	−	1.59045i
$99$	−1.97214	+	3.41584i	−0.198207	+	0.343305i
$100$	−13.2812	+	23.0036i	−1.32812	+	2.30036i
$101$	−4.11803	+	7.13264i	−0.409760	+	0.709725i	−0.994863	−	0.101234i	$-0.967721\pi$
$101$	−4.11803	+	7.13264i	−0.409760	+	0.709725i	0.585103	+	0.810959i	$0.301054\pi$
$102$	−5.09017			−0.504002
$103$	−5.20820	+	9.02087i	−0.513180	+	0.888853i	0.486704	+	0.873567i	$0.338199\pi$
$103$	−5.20820	+	9.02087i	−0.513180	+	0.888853i	−0.999883	+	0.0152859i	$0.995134\pi$
$104$	13.5172	−	23.4125i	1.32547	−	2.29579i
$105$	−0.145898	−	0.252703i	−0.0142382	−	0.0246613i
$106$	−4.73607	−	8.20311i	−0.460008	−	0.796757i
$107$	16.4721			1.59242			0.796211	−	0.605019i	$-0.206835\pi$
$107$	16.4721			1.59242			0.796211	+	0.605019i	$0.206835\pi$
$108$	10.8541			1.04444
$109$	3.57295	+	6.18853i	0.342226	+	0.592754i	0.984846	−	0.173432i	$-0.0554857\pi$
$109$	3.57295	+	6.18853i	0.342226	+	0.592754i	−0.642619	+	0.766186i	$0.722152\pi$
$110$	5.85410	+	10.1396i	0.558167	+	0.966773i
$111$	0.354102	−	0.613323i	0.0336099	−	0.0582140i
$112$	−1.16312	+	2.01458i	−0.109904	+	0.190360i
$113$	−13.3820			−1.25887			−0.629435	−	0.777053i	$-0.716714\pi$
$113$	−13.3820			−1.25887			−0.629435	+	0.777053i	$0.716714\pi$
$114$	−1.61803	+	2.80252i	−0.151543	+	0.262480i
$115$	10.7082	−	18.5472i	0.998545	−	1.72953i
$116$	−7.28115	+	12.6113i	−0.676038	+	1.17093i
$117$	5.16312	+	8.94278i	0.477331	+	0.826761i
$118$	15.9443			1.46779
$119$	0.600813	+	1.04064i	0.0550764	+	0.0953952i
$120$	4.61803	−	7.99867i	0.421567	−	0.730175i
$121$	−9.09017			−0.826379
$122$	−5.04508	+	8.73834i	−0.456761	+	0.791132i
$123$	0.100813	+	0.174613i	0.00909001	+	0.0157444i
$124$		0			0
$125$	−1.52786			−0.136656
$126$	−0.881966	−	1.52761i	−0.0785718	−	0.136090i
$127$	16.6525			1.47767			0.738834	−	0.673887i	$-0.235377\pi$
$127$	16.6525			1.47767			0.738834	+	0.673887i	$0.235377\pi$
$128$	−1.09017			−0.0963583
$129$	−0.954915	−	2.31555i	−0.0840756	−	0.203872i
$130$	30.6525			2.68840
$131$	−7.94427			−0.694094			−0.347047	−	0.937848i	$-0.612816\pi$
$131$	−7.94427			−0.694094			−0.347047	+	0.937848i	$0.612816\pi$
$132$	−1.28115	−	2.21902i	−0.111510	−	0.193141i
$133$	0.763932			0.0662413
$134$	3.73607	+	6.47106i	0.322747	+	0.559014i
$135$	3.61803	+	6.26662i	0.311391	+	0.539345i
$136$	−19.0172	+	32.9388i	−1.63071	+	2.82448i
$137$	−9.70820			−0.829428			−0.414714	−	0.909952i	$-0.636118\pi$
$137$	−9.70820			−0.829428			−0.414714	+	0.909952i	$0.636118\pi$
$138$	−3.30902	+	5.73139i	−0.281682	+	0.487888i
$139$	9.35410	+	16.2018i	0.793405	+	1.37422i	0.923847	+	0.382761i	$0.125027\pi$
$139$	9.35410	+	16.2018i	0.793405	+	1.37422i	−0.130443	+	0.991456i	$0.541640\pi$
$140$	−3.70820			−0.313400
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	18.0623	−	31.2848i	1.51576	−	2.62536i
$143$	2.50000	−	4.33013i	0.209061	−	0.362103i
$144$	14.0623	−	24.3566i	1.17186	−	2.02972i
$145$	−9.70820			−0.806222
$146$	−6.35410	+	11.0056i	−0.525869	+	0.910832i
$147$	−1.32624	+	2.29711i	−0.109386	+	0.189463i
$148$	−4.50000	−	7.79423i	−0.369898	−	0.640682i
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$	5.47214			0.446798
$151$	−2.14590			−0.174631			−0.0873154	−	0.996181i	$-0.527829\pi$
$151$	−2.14590			−0.174631			−0.0873154	+	0.996181i	$0.527829\pi$
$152$	12.0902	+	20.9408i	0.980642	+	1.69852i
$153$	−7.26393	−	12.5815i	−0.587254	−	1.01715i
$154$	−0.427051	+	0.739674i	−0.0344127	+	0.0596046i
$155$		0			0
$156$	−6.70820			−0.537086
$157$	5.92705	−	10.2660i	0.473030	−	0.819312i	−0.526493	−	0.850179i	$-0.676493\pi$
$157$	5.92705	−	10.2660i	0.473030	−	0.819312i	0.999524	+	0.0308670i	$0.00982682\pi$
$158$	−4.73607	+	8.20311i	−0.376781	+	0.652604i
$159$	−0.690983	+	1.19682i	−0.0547985	+	0.0949138i
$160$	−17.5623	−	30.4188i	−1.38842	−	2.40482i
$161$	1.56231			0.123127
$162$	10.0902	+	17.4767i	0.792759	+	1.37310i
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$	2.56231			0.200082
$165$	0.854102	−	1.47935i	0.0664917	−	0.115167i
$166$	−17.0623	−	29.5528i	−1.32429	−	2.29374i
$167$	−4.88197	−	8.45581i	−0.377778	−	0.654330i	0.612961	−	0.790113i	$-0.289978\pi$
$167$	−4.88197	−	8.45581i	−0.377778	−	0.654330i	−0.990739	+	0.135783i	$0.956645\pi$
$168$	0.673762			0.0519819
$169$	−0.0450850	−	0.0780895i	−0.00346807	−	0.00600688i
$170$	−43.1246			−3.30751
$171$	−9.23607			−0.706300
$172$	−31.5517	−	4.20378i	−2.40579	−	0.320535i
$173$	−8.23607			−0.626177			−0.313088	−	0.949724i	$-0.601364\pi$
$173$	−8.23607			−0.626177			−0.313088	+	0.949724i	$0.601364\pi$
$174$	3.00000			0.227429
$175$	−0.645898	−	1.11873i	−0.0488253	−	0.0845679i
$176$	−13.6180			−1.02650
$177$	−1.16312	−	2.01458i	−0.0874254	−	0.151425i
$178$	6.35410	+	11.0056i	0.476260	+	0.824907i
$179$	10.8262	−	18.7516i	0.809191	−	1.40156i	−0.104234	−	0.994553i	$-0.533239\pi$
$179$	10.8262	−	18.7516i	0.809191	−	1.40156i	0.913425	−	0.407007i	$-0.133428\pi$
$180$	44.8328			3.34164
$181$	10.8090	−	18.7218i	0.803428	−	1.39158i	−0.113919	−	0.993490i	$-0.536341\pi$
$181$	10.8090	−	18.7218i	0.803428	−	1.39158i	0.917347	−	0.398088i	$-0.130326\pi$
$182$	1.11803	+	1.93649i	0.0828742	+	0.143542i
$183$	1.47214			0.108823
$184$	24.7254	+	42.8257i	1.82278	+	3.15715i
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	−3.51722	+	6.09201i	−0.257205	+	0.445492i
$188$	38.1246			2.78052
$189$	−0.263932	+	0.457144i	−0.0191982	+	0.0332523i
$190$	−13.7082	+	23.7433i	−0.994498	+	1.72252i
$191$	11.7361	+	20.3275i	0.849192	+	1.47084i	0.881930	+	0.471380i	$0.156244\pi$
$191$	11.7361	+	20.3275i	0.849192	+	1.47084i	−0.0327382	+	0.999464i	$0.510423\pi$
$192$	1.66312	+	2.88061i	0.120025	+	0.207890i
$193$	−10.7082			−0.770793			−0.385397	−	0.922751i	$-0.625935\pi$
$193$	−10.7082			−0.770793			−0.385397	+	0.922751i	$0.625935\pi$
$194$	12.4721			0.895447
$195$	−2.23607	−	3.87298i	−0.160128	−	0.277350i
$196$	16.8541	+	29.1922i	1.20386	+	2.08515i
$197$	−7.47214	+	12.9421i	−0.532368	+	0.922088i	0.466918	+	0.884301i	$0.345364\pi$
$197$	−7.47214	+	12.9421i	−0.532368	+	0.922088i	−0.999286	+	0.0377873i	$0.987969\pi$
$198$	5.16312	−	8.94278i	0.366927	−	0.635536i
$199$	−15.9443			−1.13026			−0.565130	−	0.825002i	$-0.691174\pi$
$199$	−15.9443			−1.13026			−0.565130	+	0.825002i	$0.691174\pi$
$200$	20.4443	−	35.4105i	1.44563	−	2.50390i
$201$	0.545085	−	0.944115i	0.0384473	−	0.0665927i
$202$	10.7812	−	18.6735i	0.758559	−	1.31386i
$203$	−0.354102	−	0.613323i	−0.0248531	−	0.0430468i
$204$	9.43769			0.660771
$205$	0.854102	+	1.47935i	0.0596531	+	0.103322i
$206$	13.6353	−	23.6170i	0.950013	−	1.64547i
$207$	−18.8885			−1.31284
$208$	−17.8262	+	30.8759i	−1.23603	+	2.14086i
$209$	2.23607	+	3.87298i	0.154672	+	0.267900i
$210$	0.381966	+	0.661585i	0.0263582	+	0.0456537i
$211$	−4.76393			−0.327963			−0.163981	−	0.986463i	$-0.552434\pi$
$211$	−4.76393			−0.327963			−0.163981	+	0.986463i	$0.552434\pi$
$212$	8.78115	+	15.2094i	0.603092	+	1.04459i
$213$	−5.27051			−0.361129
$214$	−43.1246			−2.94794
$215$	−8.09017	−	19.6176i	−0.551745	−	1.33791i
$216$	−16.7082			−1.13685
$217$		0			0
$218$	−9.35410	−	16.2018i	−0.633540	−	1.09732i
$219$	1.85410			0.125289
$220$	−10.8541	−	18.7999i	−0.731783	−	1.26749i
$221$	9.20820	+	15.9491i	0.619411	+	1.07285i
$222$	−0.927051	+	1.60570i	−0.0622196	+	0.107767i
$223$	7.23607			0.484563			0.242281	−	0.970206i	$-0.422104\pi$
$223$	7.23607			0.484563			0.242281	+	0.970206i	$0.422104\pi$
$224$	1.28115	−	2.21902i	0.0856006	−	0.148265i
$225$	7.80902	+	13.5256i	0.520601	+	0.901708i
$226$	35.0344			2.33046
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	0.714991	−	0.699133i	$-0.246431\pi$
$227$	−3.73607	−	6.47106i	−0.247972	−	0.429499i	−0.962963	+	0.269634i	$0.913097\pi$
$228$	3.00000	−	5.19615i	0.198680	−	0.344124i
$229$	7.85410	−	13.6037i	0.519014	−	0.898958i	−0.480742	−	0.876862i	$-0.659633\pi$
$229$	7.85410	−	13.6037i	0.519014	−	0.898958i	0.999756	−	0.0220961i	$-0.00703396\pi$
$230$	−28.0344	+	48.5571i	−1.84854	+	3.20176i
$231$	0.124612			0.00819885
$232$	11.2082	−	19.4132i	0.735855	−	1.27454i
$233$	5.51722	−	9.55611i	0.361445	−	0.626041i	−0.626754	−	0.779217i	$-0.715617\pi$
$233$	5.51722	−	9.55611i	0.361445	−	0.626041i	0.988199	+	0.153176i	$0.0489501\pi$
$234$	−13.5172	−	23.4125i	−0.883648	−	1.53052i
$235$	12.7082	+	22.0113i	0.828992	+	1.43586i
$236$	−29.5623			−1.92434
$237$	1.38197			0.0897683
$238$	−1.57295	−	2.72443i	−0.101959	−	0.176598i
$239$	10.8541	+	18.7999i	0.702093	+	1.21606i	0.967730	+	0.251988i	$0.0810845\pi$
$239$	10.8541	+	18.7999i	0.702093	+	1.21606i	−0.265637	+	0.964073i	$0.585582\pi$
$240$	−6.09017	+	10.5485i	−0.393119	+	0.680902i
$241$	14.6353	−	25.3490i	0.942740	−	1.63287i	0.182525	−	0.983201i	$-0.441573\pi$
$241$	14.6353	−	25.3490i	0.942740	−	1.63287i	0.760215	−	0.649672i	$-0.225094\pi$
$242$	23.7984			1.52982
$243$	4.82624	−	8.35929i	0.309603	−	0.536249i
$244$	9.35410	−	16.2018i	0.598835	−	1.03721i
$245$	−11.2361	+	19.4614i	−0.717846	+	1.24335i
$246$	−0.263932	−	0.457144i	−0.0168277	−	0.0291464i
$247$	11.7082			0.744975
$248$		0			0
$249$	−2.48936	+	4.31169i	−0.157757	+	0.273242i
$250$	4.00000			0.252982
$251$	3.40983	−	5.90600i	0.215227	−	0.372783i	−0.738116	−	0.674674i	$-0.764284\pi$
$251$	3.40983	−	5.90600i	0.215227	−	0.372783i	0.953343	+	0.301890i	$0.0976177\pi$
$252$	1.63525	+	2.83234i	0.103011	+	0.178421i
$253$	4.57295	+	7.92058i	0.287499	+	0.497963i
$254$	−43.5967			−2.73550
$255$	3.14590	+	5.44886i	0.197004	+	0.341221i
$256$	−14.5623			−0.910144
$257$	23.5623			1.46978			0.734888	−	0.678188i	$-0.237235\pi$
$257$	23.5623			1.46978			0.734888	+	0.678188i	$0.237235\pi$
$258$	2.50000	+	6.06218i	0.155643	+	0.377415i
$259$	0.437694			0.0271970
$260$	−56.8328			−3.52462
$261$	4.28115	+	7.41517i	0.264997	+	0.458988i
$262$	20.7984			1.28493
$263$	5.25329	+	9.09896i	0.323932	+	0.561066i	0.981296	−	0.192507i	$-0.0616619\pi$
$263$	5.25329	+	9.09896i	0.323932	+	0.561066i	−0.657364	+	0.753573i	$0.728329\pi$
$264$	1.97214	+	3.41584i	0.121377	+	0.210230i
$265$	−5.85410	+	10.1396i	−0.359615	+	0.622871i
$266$	−2.00000			−0.122628
$267$	0.927051	−	1.60570i	0.0567346	−	0.0982672i
$268$	−6.92705	−	11.9980i	−0.423137	−	0.732895i
$269$	−8.56231			−0.522053			−0.261027	−	0.965332i	$-0.584061\pi$
$269$	−8.56231			−0.522053			−0.261027	+	0.965332i	$0.584061\pi$
$270$	−9.47214	−	16.4062i	−0.576456	−	0.998451i
$271$	−3.57295	+	6.18853i	−0.217041	+	0.375926i	−0.953902	−	0.300118i	$-0.902974\pi$
$271$	−3.57295	+	6.18853i	−0.217041	+	0.375926i	0.736861	+	0.676044i	$0.236307\pi$
$272$	25.0795	−	43.4390i	1.52067	−	2.63388i
$273$	0.163119	−	0.282530i	0.00987241	−	0.0170995i
$274$	25.4164			1.53546
$275$	3.78115	−	6.54915i	0.228012	−	0.394929i
$276$	6.13525	−	10.6266i	0.369299	−	0.639645i
$277$	1.76393	+	3.05522i	0.105984	+	0.183570i	0.914140	−	0.405399i	$-0.132867\pi$
$277$	1.76393	+	3.05522i	0.105984	+	0.183570i	−0.808156	+	0.588969i	$0.799534\pi$
$278$	−24.4894	−	42.4168i	−1.46877	−	2.54399i
$279$		0			0
$280$	5.70820			0.341130
$281$	0.736068	+	1.27491i	0.0439101	+	0.0760546i	0.887145	−	0.461490i	$-0.152685\pi$
$281$	0.736068	+	1.27491i	0.0439101	+	0.0760546i	−0.843235	+	0.537545i	$0.819352\pi$
$282$	−3.92705	−	6.80185i	−0.233852	−	0.405044i
$283$	−7.61803	+	13.1948i	−0.452845	+	0.784351i	−0.998561	−	0.0536192i	$-0.982924\pi$
$283$	−7.61803	+	13.1948i	−0.452845	+	0.784351i	0.545716	+	0.837970i	$0.316258\pi$
$284$	−33.4894	+	58.0053i	−1.98723	+	3.44198i
$285$	4.00000			0.236940
$286$	−6.54508	+	11.3364i	−0.387019	+	0.670337i
$287$	−0.0623059	+	0.107917i	−0.00367780	+	0.00637014i
$288$	−15.4894	+	26.8284i	−0.912719	+	1.58088i
$289$	−4.45492	−	7.71614i	−0.262054	−	0.453891i
$290$	25.4164			1.49250
$291$	−0.909830	−	1.57587i	−0.0533352	−	0.0923792i
$292$	11.7812	−	20.4056i	0.689440	−	1.19414i
$293$	−0.909830			−0.0531528			−0.0265764	−	0.999647i	$-0.508461\pi$
$293$	−0.909830			−0.0531528			−0.0265764	+	0.999647i	$0.508461\pi$
$294$	3.47214	−	6.01392i	0.202499	−	0.350739i
$295$	−9.85410	−	17.0678i	−0.573728	−	0.993726i
$296$	6.92705	+	11.9980i	0.402627	+	0.697370i
$297$	−3.09017			−0.179310
$298$	11.7812	+	20.4056i	0.682464	+	1.18206i
$299$	23.9443			1.38473
$300$	−10.1459			−0.585774
$301$	0.944272	−	1.22665i	0.0544269	−	0.0707027i
$302$	5.61803			0.323282
$303$	−3.14590			−0.180727
$304$	−15.9443	−	27.6163i	−0.914467	−	1.58390i
$305$	12.4721			0.714152
$306$	19.0172	+	32.9388i	1.08714	+	1.88299i
$307$	−14.1074	−	24.4347i	−0.805151	−	1.39456i	−0.916189	−	0.400747i	$-0.868751\pi$
$307$	−14.1074	−	24.4347i	−0.805151	−	1.39456i	0.111038	−	0.993816i	$-0.464583\pi$
$308$	0.791796	−	1.37143i	0.0451168	−	0.0781445i
$309$	−3.97871			−0.226341
$310$		0			0
$311$	−11.9164	−	20.6398i	−0.675717	−	1.17038i	−0.976259	−	0.216608i	$-0.930501\pi$
$311$	−11.9164	−	20.6398i	−0.675717	−	1.17038i	0.300541	−	0.953769i	$-0.402833\pi$
$312$	10.3262			0.584608
$313$	13.5623	+	23.4906i	0.766587	+	1.32777i	0.939404	+	0.342813i	$0.111380\pi$
$313$	13.5623	+	23.4906i	0.766587	+	1.32777i	−0.172817	+	0.984954i	$0.555287\pi$
$314$	−15.5172	+	26.8766i	−0.875687	+	1.51674i
$315$	−1.09017	+	1.88823i	−0.0614241	+	0.106390i
$316$	8.78115	−	15.2094i	0.493978	−	0.855596i
$317$	−29.3050			−1.64593			−0.822965	−	0.568092i	$-0.807682\pi$
$317$	−29.3050			−1.64593			−0.822965	+	0.568092i	$0.807682\pi$
$318$	1.80902	−	3.13331i	0.101445	−	0.175707i
$319$	2.07295	−	3.59045i	0.116063	−	0.201027i
$320$	14.0902	+	24.4049i	0.787664	+	1.36427i
$321$	3.14590	+	5.44886i	0.175587	+	0.304125i
$322$	−4.09017			−0.227936
$323$	−16.4721			−0.916534
$324$	−18.7082	−	32.4036i	−1.03934	−	1.80020i
$325$	−9.89919	−	17.1459i	−0.549108	−	0.951083i
$326$	18.3262	−	31.7420i	1.01500	−	1.75803i
$327$	−1.36475	+	2.36381i	−0.0754706	+	0.130719i
$328$	−3.94427			−0.217786
$329$	−0.927051	+	1.60570i	−0.0511100	+	0.0885251i
$330$	−2.23607	+	3.87298i	−0.123091	+	0.213201i
$331$	−1.73607	+	3.00696i	−0.0954229	+	0.165277i	−0.909785	−	0.415080i	$-0.863754\pi$
$331$	−1.73607	+	3.00696i	−0.0954229	+	0.165277i	0.814362	+	0.580357i	$0.197087\pi$
$332$	31.6353	+	54.7939i	1.73621	+	3.00720i
$333$	−5.29180			−0.289989
$334$	12.7812	+	22.1376i	0.699354	+	1.21132i
$335$	4.61803	−	7.99867i	0.252310	−	0.437014i
$336$	−0.888544			−0.0484740
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	0.178863	+	0.983874i	$0.442758\pi$
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	−0.941491	+	0.337037i	$0.890575\pi$
$338$	0.118034	+	0.204441i	0.00642020	+	0.0111201i
$339$	−2.55573	−	4.42665i	−0.138808	−	0.240423i
$340$	79.9574			4.33630
$341$		0			0
$342$	24.1803			1.30752
$343$	−3.29180			−0.177740
$344$	48.5689	+	6.47106i	2.61866	+	0.348896i
$345$	8.18034			0.440415
$346$	21.5623			1.15920
$347$	0.545085	+	0.944115i	0.0292617	+	0.0506827i	0.880285	−	0.474445i	$-0.157351\pi$
$347$	0.545085	+	0.944115i	0.0292617	+	0.0506827i	−0.851024	+	0.525127i	$0.824018\pi$
$348$	−5.56231			−0.298171
$349$	−3.64590	−	6.31488i	−0.195160	−	0.338028i	0.751793	−	0.659400i	$-0.229189\pi$
$349$	−3.64590	−	6.31488i	−0.195160	−	0.338028i	−0.946953	+	0.321372i	$0.895856\pi$
$350$	1.69098	+	2.92887i	0.0903868	+	0.156555i
$351$	−4.04508	+	7.00629i	−0.215911	+	0.373968i
$352$	15.0000			0.799503
$353$	6.38197	−	11.0539i	0.339678	−	0.588339i	−0.644694	−	0.764441i	$-0.723015\pi$
$353$	6.38197	−	11.0539i	0.339678	−	0.588339i	0.984372	+	0.176101i	$0.0563486\pi$
$354$	3.04508	+	5.27424i	0.161844	+	0.280323i
$355$	−44.6525			−2.36991
$356$	−11.7812	−	20.4056i	−0.624400	−	1.08149i
$357$	−0.229490	+	0.397489i	−0.0121459	+	0.0210373i
$358$	−28.3435	+	49.0923i	−1.49800	+	2.59461i
$359$	18.3262	−	31.7420i	0.967222	−	1.67528i	0.263699	−	0.964605i	$-0.415058\pi$
$359$	18.3262	−	31.7420i	0.967222	−	1.67528i	0.703523	−	0.710672i	$-0.251609\pi$
$360$	−69.0132			−3.63731
$361$	4.26393	−	7.38535i	0.224417	−	0.388702i
$362$	−28.2984	+	49.0142i	−1.48733	+	2.57613i
$363$	−1.73607	−	3.00696i	−0.0911199	−	0.157824i
$364$	−2.07295	−	3.59045i	−0.108652	−	0.188191i
$365$	15.7082			0.822205
$366$	−3.85410			−0.201457
$367$	1.59017	+	2.75426i	0.0830062	+	0.143771i	0.904540	−	0.426389i	$-0.140215\pi$
$367$	1.59017	+	2.75426i	0.0830062	+	0.143771i	−0.821534	+	0.570160i	$0.806881\pi$
$368$	−32.6074	−	56.4777i	−1.69978	−	2.94410i
$369$	0.753289	−	1.30473i	0.0392147	−	0.0679218i
$370$	−7.85410	+	13.6037i	−0.408315	+	0.707223i
$371$	−0.854102			−0.0443428
$372$		0			0
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	9.20820	−	15.9491i	0.476145	−	0.824707i
$375$	−0.291796	−	0.505406i	−0.0150683	−	0.0260990i
$376$	−58.6869			−3.02655
$377$	−5.42705	−	9.39993i	−0.279507	−	0.484121i
$378$	0.690983	−	1.19682i	0.0355403	−	0.0615577i
$379$	17.3607			0.891758			0.445879	−	0.895093i	$-0.352891\pi$
$379$	17.3607			0.891758			0.445879	+	0.895093i	$0.352891\pi$
$380$	25.4164	−	44.0225i	1.30383	−	2.25831i
$381$	3.18034	+	5.50851i	0.162934	+	0.282210i
$382$	−30.7254	−	53.2180i	−1.57205	−	2.72287i
$383$	−2.12461			−0.108563			−0.0542813	−	0.998526i	$-0.517287\pi$
$383$	−2.12461			−0.108563			−0.0542813	+	0.998526i	$0.517287\pi$
$384$	−0.208204	−	0.360620i	−0.0106249	−	0.0184028i
$385$	1.05573			0.0538049
$386$	28.0344			1.42692
$387$	−11.4164	+	14.8303i	−0.580329	+	0.753869i
$388$	−23.1246			−1.17397
$389$	23.0689			1.16964			0.584819	−	0.811164i	$-0.301165\pi$
$389$	23.0689			1.16964			0.584819	+	0.811164i	$0.301165\pi$
$390$	5.85410	+	10.1396i	0.296434	+	0.513439i
$391$	−33.6869			−1.70362
$392$	−25.9443	−	44.9368i	−1.31038	−	2.26965i
$393$	−1.51722	−	2.62790i	−0.0765337	−	0.132560i
$394$	19.5623	−	33.8829i	0.985535	−	1.70700i
$395$	11.7082			0.589104
$396$	−9.57295	+	16.5808i	−0.481059	+	0.833218i
$397$	−2.79180	−	4.83553i	−0.140116	−	0.242688i	0.787424	−	0.616412i	$-0.211414\pi$
$397$	−2.79180	−	4.83553i	−0.140116	−	0.242688i	−0.927540	+	0.373723i	$0.878081\pi$
$398$	41.7426			2.09237
$399$	0.145898	+	0.252703i	0.00730404	+	0.0126510i
$400$	−26.9615	+	46.6987i	−1.34807	+	2.33493i
$401$	−0.708204	+	1.22665i	−0.0353660	+	0.0612557i	−0.883167	−	0.469059i	$-0.844593\pi$
$401$	−0.708204	+	1.22665i	−0.0353660	+	0.0612557i	0.847801	+	0.530315i	$0.177926\pi$
$402$	−1.42705	+	2.47172i	−0.0711748	+	0.123278i
$403$		0			0
$404$	−19.9894	+	34.6226i	−0.994508	+	1.72254i
$405$	12.4721	−	21.6024i	0.619745	−	1.07343i
$406$	0.927051	+	1.60570i	0.0460088	+	0.0796895i
$407$	1.28115	+	2.21902i	0.0635044	+	0.109993i
$408$	−14.5279			−0.719236
$409$	20.0902			0.993395			0.496697	−	0.867924i	$-0.334546\pi$
$409$	20.0902			0.993395			0.496697	+	0.867924i	$0.334546\pi$
$410$	−2.23607	−	3.87298i	−0.110432	−	0.191273i
$411$	−1.85410	−	3.21140i	−0.0914561	−	0.158407i
$412$	−25.2812	+	43.7882i	−1.24551	+	2.15729i
$413$	0.718847	−	1.24508i	0.0353722	−	0.0612664i
$414$	49.4508			2.43038
$415$	−21.0902	+	36.5292i	−1.03528	+	1.79315i
$416$	19.6353	−	34.0093i	0.962698	−	1.66744i
$417$	−3.57295	+	6.18853i	−0.174968	+	0.303054i
$418$	−5.85410	−	10.1396i	−0.286333	−	0.495944i
$419$	−5.76393			−0.281587			−0.140793	−	0.990039i	$-0.544965\pi$
$419$	−5.76393			−0.281587			−0.140793	+	0.990039i	$0.544965\pi$
$420$	−0.708204	−	1.22665i	−0.0345568	−	0.0598542i
$421$	−11.8262	+	20.4836i	−0.576376	+	0.998312i	0.419515	+	0.907748i	$0.362200\pi$
$421$	−11.8262	+	20.4836i	−0.576376	+	0.998312i	−0.995891	+	0.0905634i	$0.971133\pi$
$422$	12.4721			0.607134
$423$	11.2082	−	19.4132i	0.544962	−	0.943901i
$424$	−13.5172	−	23.4125i	−0.656454	−	1.13701i
$425$	13.9271	+	24.1224i	0.675561	+	1.17011i
$426$	13.7984			0.668533
$427$	0.454915	+	0.787936i	0.0220149	+	0.0381309i
$428$	79.9574			3.86489
$429$	1.90983			0.0922075
$430$	21.1803	+	51.3596i	1.02141	+	2.47678i
$431$	−0.201626			−0.00971199			−0.00485599	−	0.999988i	$-0.501546\pi$
$431$	−0.201626			−0.00971199			−0.00485599	+	0.999988i	$0.501546\pi$
$432$	22.0344			1.06013
$433$	10.6459	+	18.4392i	0.511609	+	0.886133i	0.999909	+	0.0134574i	$0.00428377\pi$
$433$	10.6459	+	18.4392i	0.511609	+	0.886133i	−0.488300	+	0.872676i	$0.662383\pi$
$434$		0			0
$435$	−1.85410	−	3.21140i	−0.0888974	−	0.153975i
$436$	17.3435	+	30.0398i	0.830601	+	1.43864i
$437$	−10.7082	+	18.5472i	−0.512243	+	0.887231i
$438$	−4.85410			−0.231938
$439$	−3.92705	+	6.80185i	−0.187428	+	0.324635i	−0.944392	−	0.328822i	$-0.893348\pi$
$439$	−3.92705	+	6.80185i	−0.187428	+	0.324635i	0.756964	+	0.653457i	$0.226682\pi$
$440$	16.7082	+	28.9395i	0.796532	+	1.37963i
$441$	19.8197			0.943793
$442$	−24.1074	−	41.7552i	−1.14667	−	1.98609i
$443$	3.23607	−	5.60503i	0.153750	−	0.266303i	−0.778853	−	0.627206i	$-0.784198\pi$
$443$	3.23607	−	5.60503i	0.153750	−	0.266303i	0.932603	+	0.360903i	$0.117532\pi$
$444$	1.71885	−	2.97713i	0.0815729	−	0.141288i
$445$	7.85410	−	13.6037i	0.372320	−	0.644877i
$446$	−18.9443			−0.897037
$447$	1.71885	−	2.97713i	0.0812987	−	0.140813i
$448$	−1.02786	+	1.78031i	−0.0485620	+	0.0841119i
$449$	−10.4164	−	18.0417i	−0.491581	−	0.851443i	0.508372	−	0.861137i	$-0.330247\pi$
$449$	−10.4164	−	18.0417i	−0.491581	−	0.851443i	−0.999953	+	0.00969466i	$0.996914\pi$
$450$	−20.4443	−	35.4105i	−0.963752	−	1.66927i
$451$	−0.729490			−0.0343504
$452$	−64.9574			−3.05534
$453$	−0.409830	−	0.709846i	−0.0192555	−	0.0333515i
$454$	9.78115	+	16.9415i	0.459052	+	0.795102i
$455$	1.38197	−	2.39364i	0.0647876	−	0.112215i
$456$	−4.61803	+	7.99867i	−0.216259	+	0.374572i
$457$	−2.29180			−0.107206			−0.0536028	−	0.998562i	$-0.517070\pi$
$457$	−2.29180			−0.107206			−0.0536028	+	0.998562i	$0.517070\pi$
$458$	−20.5623	+	35.6150i	−0.960813	+	1.66418i
$459$	5.69098	−	9.85707i	0.265632	−	0.460089i
$460$	51.9787	−	90.0298i	2.42352	−	4.19766i
$461$	−8.79837	−	15.2392i	−0.409781	−	0.709762i	0.585084	−	0.810973i	$-0.301062\pi$
$461$	−8.79837	−	15.2392i	−0.409781	−	0.709762i	−0.994865	+	0.101211i	$0.967728\pi$
$462$	−0.326238			−0.0151780
$463$	−11.9164	−	20.6398i	−0.553802	−	0.959214i	−0.997996	−	0.0632829i	$-0.979843\pi$
$463$	−11.9164	−	20.6398i	−0.553802	−	0.959214i	0.444193	−	0.895931i	$-0.353490\pi$
$464$	−14.7812	+	25.6017i	−0.686198	+	1.18853i
$465$		0			0
$466$	−14.4443	+	25.0182i	−0.669118	+	1.15895i
$467$	16.4721	+	28.5306i	0.762240	+	1.32024i	0.941694	+	0.336471i	$0.109234\pi$
$467$	16.4721	+	28.5306i	0.762240	+	1.32024i	−0.179454	+	0.983766i	$0.557433\pi$
$468$	25.0623	+	43.4092i	1.15851	+	2.00659i
$469$	0.673762			0.0311114
$470$	−33.2705	−	57.6262i	−1.53465	−	2.65810i
$471$	4.52786			0.208633
$472$	45.5066			2.09461
$473$	8.98278	+	1.19682i	0.413029	+	0.0550297i
$474$	−3.61803			−0.166182
$475$	17.7082			0.812508
$476$	2.91641	+	5.05137i	0.133673	+	0.231529i
$477$	10.3262			0.472806
$478$	−28.4164	−	49.2187i	−1.29974	−	2.25121i
$479$	18.0902	+	31.3331i	0.826561	+	1.43165i	0.900720	+	0.434399i	$0.143039\pi$
$479$	18.0902	+	31.3331i	0.826561	+	1.43165i	−0.0741595	+	0.997246i	$0.523627\pi$
$480$	6.70820	−	11.6190i	0.306186	−	0.530330i
$481$	6.70820			0.305868
$482$	−38.3156	+	66.3646i	−1.74523	+	3.02282i
$483$	0.298374	+	0.516799i	0.0135765	+	0.0235152i
$484$	−44.1246			−2.00566
$485$	−7.70820	−	13.3510i	−0.350012	−	0.606238i
$486$	−12.6353	+	21.8849i	−0.573147	+	0.992719i
$487$	7.16312	−	12.4069i	0.324592	−	0.562210i	−0.656838	−	0.754032i	$-0.728106\pi$
$487$	7.16312	−	12.4069i	0.324592	−	0.562210i	0.981430	+	0.191822i	$0.0614397\pi$
$488$	−14.3992	+	24.9401i	−0.651821	+	1.12899i
$489$	−5.34752			−0.241823
$490$	29.4164	−	50.9507i	1.32890	−	2.30172i
$491$	4.82624	−	8.35929i	0.217805	−	0.377249i	−0.736332	−	0.676621i	$-0.763444\pi$
$491$	4.82624	−	8.35929i	0.217805	−	0.377249i	0.954137	+	0.299371i	$0.0967770\pi$
$492$	0.489357	+	0.847591i	0.0220619	+	0.0382124i
$493$	7.63525	+	13.2246i	0.343875	+	0.595608i
$494$	−30.6525			−1.37912
$495$	−12.7639			−0.573696
$496$		0			0
$497$	−1.62868	−	2.82095i	−0.0730562	−	0.126537i
$498$	6.51722	−	11.2882i	0.292044	−	0.505834i
$499$	−3.57295	+	6.18853i	−0.159947	+	0.277037i	−0.934849	−	0.355044i	$-0.884466\pi$
$499$	−3.57295	+	6.18853i	−0.159947	+	0.277037i	0.774902	+	0.632081i	$0.217799\pi$
$500$	−7.41641			−0.331672
$501$	1.86475	−	3.22983i	0.0833107	−	0.144298i
$502$	−8.92705	+	15.4621i	−0.398434	+	0.690108i
$503$	2.26393	−	3.92125i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$503$	2.26393	−	3.92125i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$504$	−2.51722	−	4.35995i	−0.112126	−	0.194208i
$505$	−26.6525			−1.18602
$506$	−11.9721	−	20.7363i	−0.532226	−	0.921843i
$507$	0.0172209	−	0.0298275i	0.000764808	−	0.00132469i
$508$	80.8328			3.58638
$509$	−2.64590	+	4.58283i	−0.117277	+	0.203130i	−0.918688	−	0.394984i	$-0.870750\pi$
$509$	−2.64590	+	4.58283i	−0.117277	+	0.203130i	0.801410	+	0.598115i	$0.204083\pi$
$510$	−8.23607	−	14.2653i	−0.364699	−	0.631678i
$511$	0.572949	+	0.992377i	0.0253458	+	0.0439002i
$512$	40.3050			1.78124
$513$	−3.61803	−	6.26662i	−0.159740	−	0.276678i
$514$	−61.6869			−2.72089
$515$	−33.7082			−1.48536
$516$	−4.63525	−	11.2399i	−0.204056	−	0.494809i
$517$	−10.8541			−0.477363
$518$	−1.14590			−0.0503479
$519$	−1.57295	−	2.72443i	−0.0690448	−	0.119589i
$520$	87.4853			3.83648
$521$	−3.51722	−	6.09201i	−0.154092	−	0.266896i	0.778636	−	0.627476i	$-0.215912\pi$
$521$	−3.51722	−	6.09201i	−0.154092	−	0.266896i	−0.932728	+	0.360580i	$0.882579\pi$
$522$	−11.2082	−	19.4132i	−0.490570	−	0.849692i
$523$	8.91641	−	15.4437i	0.389887	−	0.675305i	−0.602547	−	0.798084i	$-0.705847\pi$
$523$	8.91641	−	15.4437i	0.389887	−	0.675305i	0.992434	+	0.122779i	$0.0391806\pi$
$524$	−38.5623			−1.68460
$525$	0.246711	−	0.427316i	0.0107674	−	0.0186496i
$526$	−13.7533	−	23.8214i	−0.599672	−	1.03866i
$527$		0			0
$528$	−2.60081	−	4.50474i	−0.113186	−	0.196044i
$529$	−10.3992	+	18.0119i	−0.452139	+	0.783127i
$530$	15.3262	−	26.5458i	0.665729	−	1.15308i
$531$	−8.69098	+	15.0532i	−0.377157	+	0.653254i
$532$	3.70820			0.160771
$533$	−0.954915	+	1.65396i	−0.0413620	+	0.0716410i
$534$	−2.42705	+	4.20378i	−0.105029	+	0.181915i
$535$	26.6525	+	46.1634i	1.15229	+	1.99582i
$536$	10.6631	+	18.4691i	0.460577	+	0.797742i
$537$	8.27051			0.356899
$538$	22.4164			0.966440
$539$	−4.79837	−	8.31103i	−0.206681	−	0.357981i
$540$	17.5623	+	30.4188i	0.755761	+	1.30902i
$541$	10.0279	−	17.3688i	0.431132	−	0.746742i	−0.565839	−	0.824515i	$-0.691448\pi$
$541$	10.0279	−	17.3688i	0.431132	−	0.746742i	0.996971	+	0.0777737i	$0.0247812\pi$
$542$	9.35410	−	16.2018i	0.401793	−	0.695926i
$543$	8.25735			0.354357
$544$	−27.6246	+	47.8472i	−1.18440	+	2.05143i
$545$	−11.5623	+	20.0265i	−0.495275	+	0.857841i
$546$	−0.427051	+	0.739674i	−0.0182761	+	0.0316551i
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	0.549370	−	0.835579i	$-0.314868\pi$
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	−0.998318	+	0.0579790i	$0.981534\pi$
$548$	−47.1246			−2.01306
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$	−9.89919	+	17.1459i	−0.422103	+	0.731103i
$551$	9.70820			0.413583
$552$	−9.44427	+	16.3580i	−0.401975	+	0.696241i
$553$	0.427051	+	0.739674i	0.0181601	+	0.0314541i
$554$	−4.61803	−	7.99867i	−0.196201	−	0.339831i
$555$	2.29180			0.0972813
$556$	45.4058	+	78.6451i	1.92563	+	3.33529i
$557$	−18.4377			−0.781230			−0.390615	−	0.920554i	$-0.627738\pi$
$557$	−18.4377			−0.781230			−0.390615	+	0.920554i	$0.627738\pi$
$558$		0			0
$559$	14.4721	−	18.7999i	0.612106	−	0.795149i
$560$	−7.52786			−0.318110
$561$	−2.68692			−0.113442
$562$	−1.92705	−	3.33775i	−0.0812877	−	0.140794i
$563$	14.3262			0.603779			0.301889	−	0.953343i	$-0.402383\pi$
$563$	14.3262			0.603779			0.301889	+	0.953343i	$0.402383\pi$
$564$	7.28115	+	12.6113i	0.306592	+	0.531033i
$565$	−21.6525	−	37.5032i	−0.910927	−	1.57777i
$566$	19.9443	−	34.5445i	0.838320	−	1.45201i
$567$	1.81966			0.0764185
$568$	51.5517	−	89.2901i	2.16306	−	3.74653i
$569$	4.02786	+	6.97647i	0.168857	+	0.292469i	0.938018	−	0.346586i	$-0.112659\pi$
$569$	4.02786	+	6.97647i	0.168857	+	0.292469i	−0.769161	+	0.639055i	$0.779326\pi$
$570$	−10.4721			−0.438630
$571$	10.4098	+	18.0304i	0.435638	+	0.754547i	0.997347	−	0.0727876i	$-0.0231895\pi$
$571$	10.4098	+	18.0304i	0.435638	+	0.754547i	−0.561710	+	0.827334i	$0.689856\pi$
$572$	12.1353	−	21.0189i	0.507400	−	0.878843i
$573$	−4.48278	+	7.76440i	−0.187271	+	0.324363i
$574$	0.163119	−	0.282530i	0.00680845	−	0.0117926i
$575$	36.2148			1.51026
$576$	12.4271	−	21.5243i	0.517794	−	0.896845i
$577$	−11.6074	+	20.1046i	−0.483222	+	0.836965i	−0.999814	−	0.0192664i	$-0.993867\pi$
$577$	−11.6074	+	20.1046i	−0.483222	+	0.836965i	0.516592	+	0.856231i	$0.327200\pi$
$578$	11.6631	+	20.2011i	0.485122	+	0.840256i
$579$	−2.04508	−	3.54219i	−0.0849908	−	0.147208i
$580$	−47.1246			−1.95674
$581$	−3.07701			−0.127656
$582$	2.38197	+	4.12569i	0.0987357	+	0.171015i
$583$	−2.50000	−	4.33013i	−0.103539	−	0.179336i
$584$	−18.1353	+	31.4112i	−0.750442	+	1.29980i
$585$	−16.7082	+	28.9395i	−0.690799	+	1.19650i
$586$	2.38197			0.0983981
$587$	13.3713	−	23.1598i	0.551894	−	0.955908i	−0.446244	−	0.894911i	$-0.647239\pi$
$587$	13.3713	−	23.1598i	0.551894	−	0.955908i	0.998138	−	0.0609966i	$-0.0194279\pi$
$588$	−6.43769	+	11.1504i	−0.265486	+	0.459835i
$589$		0			0
$590$	25.7984	+	44.6841i	1.06210	+	1.83962i
$591$	−5.70820			−0.234804
$592$	−9.13525	−	15.8227i	−0.375457	−	0.650310i
$593$	10.7639	−	18.6437i	0.442022	−	0.765604i	−0.555818	−	0.831304i	$-0.687595\pi$
$593$	10.7639	−	18.6437i	0.442022	−	0.765604i	0.997839	+	0.0657001i	$0.0209281\pi$
$594$	8.09017			0.331944
$595$	−1.94427	+	3.36758i	−0.0797074	+	0.138057i
$596$	−21.8435	−	37.8340i	−0.894743	−	1.54974i
$597$	−3.04508	−	5.27424i	−0.124627	−	0.215860i
$598$	−62.6869			−2.56346
$599$	−15.8820	−	27.5084i	−0.648920	−	1.12396i	−0.983381	−	0.181552i	$-0.941888\pi$
$599$	−15.8820	−	27.5084i	−0.648920	−	1.12396i	0.334462	−	0.942409i	$-0.391445\pi$
$600$	15.6180			0.637604
$601$	2.58359			0.105387			0.0526935	−	0.998611i	$-0.483219\pi$
$601$	2.58359			0.105387			0.0526935	+	0.998611i	$0.483219\pi$
$602$	−2.47214	+	3.21140i	−0.100757	+	0.130887i
$603$	−8.14590			−0.331727
$604$	−10.4164			−0.423838
$605$	−14.7082	−	25.4754i	−0.597974	−	1.03572i
$606$	8.23607			0.334567
$607$	8.57295	+	14.8488i	0.347965	+	0.602694i	0.985888	−	0.167407i	$-0.0535394\pi$
$607$	8.57295	+	14.8488i	0.347965	+	0.602694i	−0.637923	+	0.770100i	$0.720206\pi$
$608$	17.5623	+	30.4188i	0.712246	+	1.23365i
$609$	0.135255	−	0.234268i	0.00548081	−	0.00949303i
$610$	−32.6525			−1.32206
$611$	−14.2082	+	24.6093i	−0.574802	+	0.995587i
$612$	−35.2599	−	61.0719i	−1.42530	−	2.46868i
$613$	29.7984			1.20354			0.601772	−	0.798668i	$-0.294461\pi$
$613$	29.7984			1.20354			0.601772	+	0.798668i	$0.294461\pi$
$614$	36.9336	+	63.9709i	1.49052	+	2.58166i
$615$	−0.326238	+	0.565061i	−0.0131552	+	0.0227854i
$616$	−1.21885	+	2.11111i	−0.0491087	+	0.0850588i
$617$	1.85410	−	3.21140i	0.0746433	−	0.129286i	−0.826288	−	0.563248i	$-0.809552\pi$
$617$	1.85410	−	3.21140i	0.0746433	−	0.129286i	0.900931	+	0.433962i	$0.142885\pi$
$618$	10.4164			0.419009
$619$	−1.63525	+	2.83234i	−0.0657264	+	0.113842i	−0.897016	−	0.441998i	$-0.854270\pi$
$619$	−1.63525	+	2.83234i	−0.0657264	+	0.113842i	0.831290	+	0.555840i	$0.187603\pi$
$620$		0			0
$621$	−7.39919	−	12.8158i	−0.296919	−	0.514279i
$622$	31.1976	+	54.0358i	1.25091	+	2.16664i
$623$	1.14590			0.0459094
$624$	−13.6180			−0.545158
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$	−35.5066	−	61.4992i	−1.41913	−	2.45800i
$627$	−0.854102	+	1.47935i	−0.0341095	+	0.0590795i
$628$	28.7705	−	49.8320i	1.14807	−	1.98851i
$629$	−9.43769			−0.376306
$630$	2.85410	−	4.94345i	0.113710	−	0.196952i
$631$	7.95492	−	13.7783i	0.316680	−	0.548506i	−0.663113	−	0.748519i	$-0.730765\pi$
$631$	7.95492	−	13.7783i	0.316680	−	0.548506i	0.979793	+	0.200013i	$0.0640985\pi$
$632$	−13.5172	+	23.4125i	−0.537686	+	0.931300i
$633$	−0.909830	−	1.57587i	−0.0361625	−	0.0626353i
$634$	76.7214			3.04699
$635$	26.9443	+	46.6688i	1.06925	+	1.85200i
$636$	−3.35410	+	5.80948i	−0.132999	+	0.230361i
$637$	−25.1246			−0.995473
$638$	−5.42705	+	9.39993i	−0.214859	+	0.372147i
$639$	19.6910	+	34.1058i	0.778963	+	1.34920i
$640$	−1.76393	−	3.05522i	−0.0697255	−	0.120768i
$641$	33.1803			1.31054			0.655272	−	0.755393i	$-0.272554\pi$
$641$	33.1803			1.31054			0.655272	+	0.755393i	$0.272554\pi$
$642$	−8.23607	−	14.2653i	−0.325052	−	0.563006i
$643$	29.5623			1.16582			0.582912	−	0.812535i	$-0.301913\pi$
$643$	29.5623			1.16582			0.582912	+	0.812535i	$0.301913\pi$
$644$	7.58359			0.298835
$645$	4.94427	−	6.42280i	0.194681	−	0.252897i
$646$	43.1246			1.69672
$647$	−37.3262			−1.46745			−0.733723	−	0.679449i	$-0.762219\pi$
$647$	−37.3262			−1.46745			−0.733723	+	0.679449i	$0.762219\pi$
$648$	28.7984	+	49.8802i	1.13131	+	1.95948i
$649$	8.41641			0.330373
$650$	25.9164	+	44.8885i	1.01653	+	1.76067i
$651$		0			0
$652$	−33.9787	+	58.8529i	−1.33071	+	2.30486i
$653$	2.88854			0.113037			0.0565187	−	0.998402i	$-0.482000\pi$
$653$	2.88854			0.113037			0.0565187	+	0.998402i	$0.482000\pi$
$654$	3.57295	−	6.18853i	0.139713	−	0.241991i
$655$	−12.8541	−	22.2640i	−0.502251	−	0.869925i
$656$	5.20163			0.203089
$657$	−6.92705	−	11.9980i	−0.270250	−	0.468087i
$658$	2.42705	−	4.20378i	0.0946163	−	0.163880i
$659$	−7.68034	+	13.3027i	−0.299184	+	0.518201i	−0.975949	−	0.217997i	$-0.930048\pi$
$659$	−7.68034	+	13.3027i	−0.299184	+	0.518201i	0.676766	+	0.736198i	$0.263381\pi$
$660$	4.14590	−	7.18091i	0.161379	−	0.279516i
$661$	30.3951			1.18223			0.591117	−	0.806586i	$-0.298687\pi$
$661$	30.3951			1.18223			0.591117	+	0.806586i	$0.298687\pi$
$662$	4.54508	−	7.87232i	0.176650	−	0.305966i
$663$	−3.51722	+	6.09201i	−0.136598	+	0.236594i
$664$	−48.6976	−	84.3466i	−1.88983	−	3.27328i
$665$	1.23607	+	2.14093i	0.0479327	+	0.0830218i
$666$	13.8541			0.536836
$667$	19.8541			0.768754
$668$	−23.6976	−	41.0454i	−0.916886	−	1.58809i
$669$	1.38197	+	2.39364i	0.0534299	+	0.0925433i
$670$	−12.0902	+	20.9408i	−0.467084	+	0.809013i
$671$	−2.66312	+	4.61266i	−0.102809	+	0.178070i
$672$	0.978714			0.0377547
$673$	19.9164	−	34.4962i	0.767721	−	1.32973i	−0.171075	−	0.985258i	$-0.554724\pi$
$673$	19.9164	−	34.4962i	0.767721	−	1.32973i	0.938796	−	0.344474i	$-0.111943\pi$
$674$	36.6525	−	63.4840i	1.41180	−	2.44531i
$675$	−6.11803	+	10.5967i	−0.235483	+	0.407869i
$676$	−0.218847	−	0.379054i	−0.00841719	−	0.0145790i
$677$	−36.2361			−1.39267			−0.696333	−	0.717719i	$-0.745186\pi$
$677$	−36.2361			−1.39267			−0.696333	+	0.717719i	$0.745186\pi$
$678$	6.69098	+	11.5891i	0.256966	+	0.445078i
$679$	0.562306	−	0.973942i	0.0215793	−	0.0373765i
$680$	−123.082			−4.71998
$681$	1.42705	−	2.47172i	0.0546847	−	0.0947167i
$682$		0			0
$683$	−14.5623	−	25.2227i	−0.557211	−	0.965118i	−0.997728	−	0.0673736i	$-0.978538\pi$
$683$	−14.5623	−	25.2227i	−0.557211	−	0.965118i	0.440517	−	0.897744i	$-0.354795\pi$
$684$	−44.8328			−1.71423
$685$	−15.7082	−	27.2074i	−0.600180	−	1.03954i
$686$	8.61803			0.329038
$687$	6.00000			0.228914
$688$	−64.0517	−	8.53390i	−2.44195	−	0.325352i
$689$	−13.0902			−0.498696
$690$	−21.4164			−0.815309
$691$	−24.6353	−	42.6695i	−0.937169	−	1.62322i	−0.770719	−	0.637175i	$-0.780103\pi$
$691$	−24.6353	−	42.6695i	−0.937169	−	1.62322i	−0.166450	−	0.986050i	$-0.553230\pi$
$692$	−39.9787			−1.51976
$693$	−0.465558	−	0.806370i	−0.0176851	−	0.0306315i
$694$	−1.42705	−	2.47172i	−0.0541701	−	0.0938254i
$695$	−30.2705	+	52.4301i	−1.14823	+	1.98879i
$696$	8.56231			0.324553
$697$	1.34346	−	2.32694i	0.0508871	−	0.0881391i
$698$	9.54508	+	16.5326i	0.361287	+	0.625767i
$699$	4.21478			0.159418
$700$	−3.13525	−	5.43042i	−0.118501	−	0.205251i
$701$	−11.7533	+	20.3573i	−0.443916	+	0.768884i	−0.997976	−	0.0635921i	$-0.979744\pi$
$701$	−11.7533	+	20.3573i	−0.443916	+	0.768884i	0.554060	+	0.832476i	$0.313078\pi$
$702$	10.5902	−	18.3427i	0.399700	−	0.692301i
$703$	−3.00000	+	5.19615i	−0.113147	+	0.195977i
$704$	−12.0344			−0.453565
$705$	−4.85410	+	8.40755i	−0.182816	+	0.316647i
$706$	−16.7082	+	28.9395i	−0.628822	+	1.08915i
$707$	−0.972136	−	1.68379i	−0.0365609	−	0.0633254i
$708$	−5.64590	−	9.77898i	−0.212186	−	0.367517i
$709$	−6.88854			−0.258705			−0.129352	−	0.991599i	$-0.541290\pi$
$709$	−6.88854			−0.258705			−0.129352	+	0.991599i	$0.541290\pi$
$710$	116.902			4.38724
$711$	−5.16312	−	8.94278i	−0.193632	−	0.335381i
$712$	18.1353	+	31.4112i	0.679647	+	1.17718i
$713$		0			0
$714$	0.600813	−	1.04064i	0.0224849	−	0.0389449i
$715$	16.1803			0.605110
$716$	52.5517	−	91.0221i	1.96395	−	3.40166i
$717$	−4.14590	+	7.18091i	−0.154831	+	0.268176i
$718$	−47.9787	+	83.1016i	−1.79055	+	3.10132i
$719$	−6.89919	−	11.9497i	−0.257296	−	0.445650i	0.708220	−	0.705991i	$-0.249498\pi$
$719$	−6.89919	−	11.9497i	−0.257296	−	0.445650i	−0.965517	+	0.260341i	$0.916165\pi$
$720$	91.0132			3.39186
$721$	−1.22949	−	2.12954i	−0.0457886	−	0.0793082i
$722$	−11.1631	+	19.3351i	−0.415448	+	0.719578i
$723$	11.1803			0.415801
$724$	52.4681	−	90.8774i	1.94996	−	3.37743i
$725$	−8.20820	−	14.2170i	−0.304845	−	0.528007i
$726$	4.54508	+	7.87232i	0.168684	+	0.292169i
$727$	28.9787			1.07476			0.537381	−	0.843340i	$-0.319414\pi$
$727$	28.9787			1.07476			0.537381	+	0.843340i	$0.319414\pi$
$728$	3.19098	+	5.52694i	0.118266	+	0.204842i
$729$	−19.4377			−0.719915
$730$	−41.1246			−1.52209
$731$	−20.3607	+	26.4493i	−0.753067	+	0.978263i
$732$	7.14590			0.264120
$733$	−42.5410			−1.57129			−0.785644	−	0.618679i	$-0.787668\pi$
$733$	−42.5410			−1.57129			−0.785644	+	0.618679i	$0.787668\pi$
$734$	−4.16312	−	7.21073i	−0.153664	−	0.266153i
$735$	−8.58359			−0.316611
$736$	35.9164	+	62.2090i	1.32390	+	2.29306i
$737$	1.97214	+	3.41584i	0.0726446	+	0.125824i
$738$	−1.97214	+	3.41584i	−0.0725953	+	0.125739i
$739$	−17.5410			−0.645257			−0.322628	−	0.946526i	$-0.604566\pi$
$739$	−17.5410			−0.645257			−0.322628	+	0.946526i	$0.604566\pi$
$740$	14.5623	−	25.2227i	0.535321	−	0.927203i
$741$	2.23607	+	3.87298i	0.0821440	+	0.142278i
$742$	2.23607			0.0820886
$743$	5.68034	+	9.83864i	0.208391	+	0.360945i	0.951208	−	0.308550i	$-0.0998439\pi$
$743$	5.68034	+	9.83864i	0.208391	+	0.360945i	−0.742817	+	0.669495i	$0.766511\pi$
$744$		0			0
$745$	14.5623	−	25.2227i	0.533522	−	0.924087i
$746$	7.85410	−	13.6037i	0.287559	−	0.498067i
$747$	37.2016			1.36114
$748$	−17.0729	+	29.5712i	−0.624249	+	1.08123i
$749$	−1.94427	+	3.36758i	−0.0710421	+	0.123049i
$750$	0.763932	+	1.32317i	0.0278949	+	0.0483153i
$751$	−4.48936	−	7.77579i	−0.163819	−	0.283743i	0.772416	−	0.635117i	$-0.219048\pi$
$751$	−4.48936	−	7.77579i	−0.163819	−	0.283743i	−0.936235	+	0.351374i	$0.885715\pi$
$752$	77.3951			2.82231
$753$	2.60488			0.0949270
$754$	14.2082	+	24.6093i	0.517432	+	0.896219i
$755$	−3.47214	−	6.01392i	−0.126364	−	0.218869i
$756$	−1.28115	+	2.21902i	−0.0465951	+	0.0807050i
$757$	−7.98936	+	13.8380i	−0.290378	+	0.502950i	−0.973899	−	0.226981i	$-0.927114\pi$
$757$	−7.98936	+	13.8380i	−0.290378	+	0.502950i	0.683521	+	0.729931i	$0.260448\pi$
$758$	−45.4508			−1.65085
$759$	−1.74671	+	3.02539i	−0.0634016	+	0.109815i
$760$	−39.1246	+	67.7658i	−1.41920	+	2.45812i
$761$	5.04508	−	8.73834i	0.182884	−	0.316765i	−0.759977	−	0.649950i	$-0.774790\pi$
$761$	5.04508	−	8.73834i	0.182884	−	0.316765i	0.942862	+	0.333185i	$0.108123\pi$
$762$	−8.32624	−	14.4215i	−0.301628	−	0.522435i
$763$	−1.68692			−0.0610705
$764$	56.9681	+	98.6716i	2.06103	+	3.56981i
$765$	23.5066	−	40.7146i	0.849882	−	1.47204i
$766$	5.56231			0.200974
$767$	11.0172	−	19.0824i	0.397809	−	0.689025i
$768$	−2.78115	−	4.81710i	−0.100356	−	0.173822i
$769$	7.94427	+	13.7599i	0.286478	+	0.496194i	0.972966	−	0.230946i	$-0.0741822\pi$
$769$	7.94427	+	13.7599i	0.286478	+	0.496194i	−0.686489	+	0.727140i	$0.740849\pi$
$770$	−2.76393			−0.0996052
$771$	4.50000	+	7.79423i	0.162064	+	0.280702i
$772$	−51.9787			−1.87075
$773$	−33.5967			−1.20839			−0.604196	−	0.796836i	$-0.706505\pi$
$773$	−33.5967			−1.20839			−0.604196	+	0.796836i	$0.706505\pi$
$774$	29.8885	−	38.8264i	1.07432	−	1.39558i
$775$		0			0
$776$	35.5967			1.27785
$777$	0.0835921	+	0.144786i	0.00299885	+	0.00519416i
$778$	−60.3951			−2.16527
$779$	−0.854102	−	1.47935i	−0.0306014	−	0.0530031i
$780$	−10.8541	−	18.7999i	−0.388639	−	0.673143i
$781$	9.53444	−	16.5141i	0.341169	−	0.590922i
$782$	88.1935			3.15379
$783$	−3.35410	+	5.80948i	−0.119866	+	0.207614i
$784$	34.2148	+	59.2617i	1.22196	+	2.11649i
$785$	38.3607			1.36915
$786$	3.97214	+	6.87994i	0.141681	+	0.245399i
$787$	22.7254	−	39.3616i	0.810074	−	1.40309i	−0.102738	−	0.994708i	$-0.532760\pi$
$787$	22.7254	−	39.3616i	0.810074	−	1.40309i	0.912812	−	0.408381i	$-0.133906\pi$
$788$	−36.2705	+	62.8224i	−1.29208	+	2.23795i
$789$	−2.00658	+	3.47549i	−0.0714361	+	0.123731i
$790$	−30.6525			−1.09057
$791$	1.57953	−	2.73582i	0.0561615	−	0.0972746i
$792$	14.7361	−	25.5236i	0.523623	−	0.906942i
$793$	6.97214	+	12.0761i	0.247588	+	0.428835i
$794$	7.30902	+	12.6596i	0.259387	+	0.449272i
$795$	−4.47214			−0.158610
$796$	−77.3951			−2.74320
$797$	1.88197	+	3.25966i	0.0666627	+	0.115463i	0.897430	−	0.441156i	$-0.145432\pi$
$797$	1.88197	+	3.25966i	0.0666627	+	0.115463i	−0.830768	+	0.556619i	$0.812098\pi$
$798$	−0.381966	−	0.661585i	−0.0135215	−	0.0234198i
$799$	19.9894	−	34.6226i	0.707173	−	1.22486i
$800$	29.6976	−	51.4377i	1.04997	−	1.81860i
$801$	−13.8541			−0.489511
$802$	1.85410	−	3.21140i	0.0654706	−	0.113398i
$803$	−3.35410	+	5.80948i	−0.118364	+	0.205012i
$804$	2.64590	−	4.58283i	0.0933136	−	0.161624i
$805$	2.52786	+	4.37839i	0.0890955	+	0.154318i
$806$		0			0
$807$	−1.63525	−	2.83234i	−0.0575637	−	0.0997033i
$808$	30.7705	−	53.2961i	1.08250	−	1.87495i
$809$	−37.7426			−1.32696			−0.663480	−	0.748194i	$-0.730921\pi$
$809$	−37.7426			−1.32696			−0.663480	+	0.748194i	$0.730921\pi$
$810$	−32.6525	+	56.5557i	−1.14729	+	1.98717i
$811$	13.1976	+	22.8588i	0.463429	+	0.802683i	0.999129	−	0.0417257i	$-0.0132856\pi$
$811$	13.1976	+	22.8588i	0.463429	+	0.802683i	−0.535700	+	0.844408i	$0.679952\pi$
$812$	−1.71885	−	2.97713i	−0.0603197	−	0.104477i
$813$	−2.72949			−0.0957274
$814$	−3.35410	−	5.80948i	−0.117561	−	0.203622i
$815$	−45.3050			−1.58696
$816$	19.1591			0.670701
$817$	8.09017	+	19.6176i	0.283039	+	0.686334i
$818$	−52.5967			−1.83900
$819$	−2.43769			−0.0851799
$820$	4.14590	+	7.18091i	0.144781	+	0.250768i
$821$	−15.3262			−0.534889			−0.267445	−	0.963573i	$-0.586179\pi$
$821$	−15.3262			−0.534889			−0.267445	+	0.963573i	$0.586179\pi$
$822$	4.85410	+	8.40755i	0.169306	+	0.293247i
$823$	12.0066	+	20.7960i	0.418523	+	0.724903i	0.995791	−	0.0916516i	$-0.0292146\pi$
$823$	12.0066	+	20.7960i	0.418523	+	0.724903i	−0.577268	+	0.816555i	$0.695881\pi$
$824$	38.9164	−	67.4052i	1.35572	−	2.34817i
$825$	2.88854			0.100566
$826$	−1.88197	+	3.25966i	−0.0654820	+	0.113418i
$827$	6.59017	+	11.4145i	0.229163	+	0.396921i	0.957560	−	0.288233i	$-0.0930679\pi$
$827$	6.59017	+	11.4145i	0.229163	+	0.396921i	−0.728398	+	0.685155i	$0.759735\pi$
$828$	−91.6869			−3.18634
$829$	20.5795	+	35.6448i	0.714757	+	1.23799i	0.963053	+	0.269311i	$0.0867958\pi$
$829$	20.5795	+	35.6448i	0.714757	+	1.23799i	−0.248297	+	0.968684i	$0.579871\pi$
$830$	55.2148	−	95.6348i	1.91653	−	3.31953i
$831$	−0.673762	+	1.16699i	−0.0233725	+	0.0404824i
$832$	−15.7533	+	27.2855i	−0.546147	+	0.945954i
$833$	35.3475			1.22472
$834$	9.35410	−	16.2018i	0.323906	−	0.561022i
$835$	15.7984	−	27.3636i	0.546725	−	0.946956i
$836$	10.8541	+	18.7999i	0.375397	+	0.650207i
$837$		0			0
$838$	15.0902			0.521281
$839$	−9.88854			−0.341390			−0.170695	−	0.985324i	$-0.554601\pi$
$839$	−9.88854			−0.341390			−0.170695	+	0.985324i	$0.554601\pi$
$840$	1.09017	+	1.88823i	0.0376144	+	0.0651501i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	30.9615	−	53.6269i	1.06700	−	1.84810i
$843$	−0.281153	+	0.486971i	−0.00968342	+	0.0167722i
$844$	−23.1246			−0.795982
$845$	0.145898	−	0.252703i	0.00501904	−	0.00869324i
$846$	−29.3435	+	50.8244i	−1.00885	+	1.74738i
$847$	1.07295	−	1.85840i	0.0368670	−	0.0638555i
$848$	17.8262	+	30.8759i	0.612156	+	1.06028i
$849$	−5.81966			−0.199730
$850$	−36.4615	−	63.1532i	−1.25062	−	2.16614i
$851$	−6.13525	+	10.6266i	−0.210314	+	0.364274i
$852$	−25.5836			−0.876479
$853$	−26.8713	+	46.5425i	−0.920057	+	1.59358i	−0.120732	+	0.992685i	$0.538524\pi$
$853$	−26.8713	+	46.5425i	−0.920057	+	1.59358i	−0.799325	+	0.600900i	$0.794809\pi$
$854$	−1.19098	−	2.06284i	−0.0407546	−	0.0705890i
$855$	−14.9443	−	25.8842i	−0.511083	−	0.885222i
$856$	−123.082			−4.20686
$857$	6.90983	+	11.9682i	0.236035	+	0.408825i	0.959573	−	0.281460i	$-0.0908186\pi$
$857$	6.90983	+	11.9682i	0.236035	+	0.408825i	−0.723538	+	0.690285i	$0.757485\pi$
$858$	−5.00000			−0.170697
$859$	−22.5836			−0.770542			−0.385271	−	0.922803i	$-0.625892\pi$
$859$	−22.5836			−0.770542			−0.385271	+	0.922803i	$0.625892\pi$
$860$	−39.2705	−	95.2259i	−1.33911	−	3.24718i
$861$	−0.0475975			−0.00162212
$862$	0.527864			0.0179791
$863$	14.2533	+	24.6874i	0.485188	+	0.840370i	0.999855	−	0.0170203i	$-0.00541798\pi$
$863$	14.2533	+	24.6874i	0.485188	+	0.840370i	−0.514668	+	0.857390i	$0.672085\pi$
$864$	−24.2705			−0.825700
$865$	−13.3262	−	23.0817i	−0.453106	−	0.784802i
$866$	−27.8713	−	48.2745i	−0.947106	−	1.64044i
$867$	1.70163	−	2.94730i	0.0577903	−	0.100096i
$868$		0			0
$869$	−2.50000	+	4.33013i	−0.0848067	+	0.146889i
$870$	4.85410	+	8.40755i	0.164569	+	0.285043i
$871$	10.3262			0.349891
$872$	−26.6976	−	46.2415i	−0.904093	−	1.56594i
$873$	−6.79837	+	11.7751i	−0.230090	+	0.398528i
$874$	28.0344	−	48.5571i	0.948279	−	1.64247i
$875$	0.180340	−	0.312358i	0.00609660	−	0.0105596i
$876$	9.00000			0.304082
$877$	−11.8262	+	20.4836i	−0.399344	+	0.691684i	−0.993645	−	0.112559i	$-0.964095\pi$
$877$	−11.8262	+	20.4836i	−0.399344	+	0.691684i	0.594301	+	0.804242i	$0.297429\pi$
$878$	10.2812	−	17.8075i	0.346972	−	0.600973i
$879$	−0.173762	−	0.300965i	−0.00586085	−	0.0101513i
$880$	−22.0344	−	38.1648i	−0.742781	−	1.28653i
$881$	38.2361			1.28821			0.644103	−	0.764939i	$-0.277231\pi$
$881$	38.2361			1.28821			0.644103	+	0.764939i	$0.277231\pi$
$882$	−51.8885			−1.74718
$883$	13.5623	+	23.4906i	0.456408	+	0.790522i	0.998768	−	0.0496245i	$-0.0158024\pi$
$883$	13.5623	+	23.4906i	0.456408	+	0.790522i	−0.542360	+	0.840146i	$0.682469\pi$
$884$	44.6976	+	77.4184i	1.50334	+	2.60386i
$885$	3.76393	−	6.51932i	0.126523	−	0.219145i
$886$	−8.47214	+	14.6742i	−0.284627	+	0.492988i
$887$	40.9574			1.37522			0.687608	−	0.726082i	$-0.258661\pi$
$887$	40.9574			1.37522			0.687608	+	0.726082i	$0.258661\pi$
$888$	−2.64590	+	4.58283i	−0.0887905	+	0.153790i
$889$	−1.96556	+	3.40445i	−0.0659227	+	0.114181i
$890$	−20.5623	+	35.6150i	−0.689250	+	1.19382i
$891$	5.32624	+	9.22531i	0.178436	+	0.309060i
$892$	35.1246			1.17606
$893$	−12.7082	−	22.0113i	−0.425264	−	0.736579i
$894$	−4.50000	+	7.79423i	−0.150503	+	0.260678i
$895$	70.0689			2.34214
$896$	0.128677	−	0.222875i	0.00429880	−	0.00744574i
$897$	4.57295	+	7.92058i	0.152686	+	0.264460i
$898$	27.2705	+	47.2339i	0.910029	+	1.57622i
$899$		0			0
$900$	37.9058	+	65.6547i	1.26353	+	2.18849i
$901$	18.4164			0.613540
$902$	1.90983			0.0635904
$903$	0.586105	+	0.0780895i	0.0195043	+	0.00259865i
$904$	99.9919			3.32568
$905$	69.9574			2.32546
$906$	1.07295	+	1.85840i	0.0356463	+	0.0617413i
$907$	−8.29180			−0.275325			−0.137662	−	0.990479i	$-0.543959\pi$
$907$	−8.29180			−0.275325			−0.137662	+	0.990479i	$0.543959\pi$
$908$	−18.1353	−	31.4112i	−0.601840	−	1.04242i
$909$	11.7533	+	20.3573i	0.389832	+	0.675209i
$910$	−3.61803	+	6.26662i	−0.119937	+	0.207736i
$911$	3.97871			0.131821			0.0659103	−	0.997826i	$-0.479005\pi$
$911$	3.97871			0.131821			0.0659103	+	0.997826i	$0.479005\pi$
$912$	6.09017	−	10.5485i	0.201666	−	0.349295i
$913$	−9.00658	−	15.5999i	−0.298074	−	0.516280i
$914$	6.00000			0.198462
$915$	2.38197	+	4.12569i	0.0787454	+	0.136391i
$916$	38.1246	−	66.0338i	1.25967	−	2.18182i
$917$	0.937694	−	1.62413i	0.0309654	−	0.0536336i
$918$	−14.8992	+	25.8061i	−0.491746	+	0.851730i
$919$	−44.3951			−1.46446			−0.732230	−	0.681057i	$-0.761520\pi$
$919$	−44.3951			−1.46446			−0.732230	+	0.681057i	$0.761520\pi$
$920$	−80.0132	+	138.587i	−2.63796	+	4.56907i
$921$	5.38854	−	9.33323i	0.177559	−	0.307540i
$922$	23.0344	+	39.8968i	0.758599	+	1.31393i
$923$	−24.9615	−	43.2346i	−0.821618	−	1.42308i
$924$	0.604878			0.0198990
$925$	10.1459			0.333595
$926$	31.1976	+	54.0358i	1.02522	+	1.77573i
$927$	14.8647	+	25.7465i	0.488222	+	0.845626i
$928$	16.2812	−	28.1998i	0.534455	−	0.925703i
$929$	−15.3820	+	26.6423i	−0.504666	+	0.874107i	0.495320	+	0.868711i	$0.335051\pi$
$929$	−15.3820	+	26.6423i	−0.504666	+	0.874107i	−0.999985	+	0.00539616i	$0.998282\pi$
$930$		0			0
$931$	11.2361	−	19.4614i	0.368247	−	0.637823i
$932$	26.7812	−	46.3863i	0.877246	−	1.51943i
$933$	4.55166	−	7.88371i	0.149015	−	0.258101i
$934$	−43.1246	−	74.6940i	−1.41108	−	2.44406i
$935$	−22.7639			−0.744460
$936$	−38.5795	−	66.8217i	−1.26101	−	2.18414i
$937$	19.8369	−	34.3585i	0.648043	−	1.12244i	−0.335547	−	0.942023i	$-0.608921\pi$
$937$	19.8369	−	34.3585i	0.648043	−	1.12244i	0.983590	−	0.180419i	$-0.0577455\pi$
$938$	−1.76393			−0.0575944
$939$	−5.18034	+	8.97261i	−0.169054	+	0.292810i
$940$	61.6869	+	106.845i	2.01201	+	3.48490i
$941$	10.8820	+	18.8481i	0.354742	+	0.614431i	0.987074	−	0.160267i	$-0.0512354\pi$
$941$	10.8820	+	18.8481i	0.354742	+	0.614431i	−0.632332	+	0.774698i	$0.717902\pi$
$942$	−11.8541			−0.386228
$943$	−1.74671	−	3.02539i	−0.0568807	−	0.0985203i
$944$	−60.0132			−1.95326
$945$	−1.70820			−0.0555679
$946$	−23.5172	−	3.13331i	−0.764611	−	0.101873i
$947$	−19.3607			−0.629138			−0.314569	−	0.949235i	$-0.601860\pi$
$947$	−19.3607			−0.629138			−0.314569	+	0.949235i	$0.601860\pi$
$948$	6.70820			0.217872
$949$	8.78115	+	15.2094i	0.285048	+	0.493718i
$950$	−46.3607			−1.50414
$951$	−5.59675	−	9.69385i	−0.181487	−	0.314345i
$952$	−4.48936	−	7.77579i	−0.145501	−	0.252015i
$953$	1.55573	−	2.69460i	0.0503950	−	0.0872867i	−0.839728	−	0.543008i	$-0.817285\pi$
$953$	1.55573	−	2.69460i	0.0503950	−	0.0872867i	0.890122	+	0.455721i	$0.150619\pi$
$954$	−27.0344			−0.875272
$955$	−37.9787	+	65.7811i	−1.22896	+	2.12863i
$956$	52.6869	+	91.2564i	1.70402	+	2.95144i
$957$	1.58359			0.0511903
$958$	−47.3607	−	82.0311i	−1.53015	−	2.65030i
$959$	1.14590	−	1.98475i	0.0370030	−	0.0640910i
$960$	−5.38197	+	9.32184i	−0.173702	+	0.300861i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−17.5623			−0.566231
$963$	23.5066	−	40.7146i	0.757489	−	1.31201i
$964$	71.0410	−	123.047i	2.28808	−	3.96307i
$965$	−17.3262	−	30.0099i	−0.557751	−	0.966054i
$966$	−0.781153	−	1.35300i	−0.0251332	−	0.0435320i
$967$	−49.1033			−1.57906			−0.789528	−	0.613714i	$-0.789675\pi$
$967$	−49.1033			−1.57906			−0.789528	+	0.613714i	$0.789675\pi$
$968$	67.9230			2.18313
$969$	−3.14590	−	5.44886i	−0.101061	−	0.175042i
$970$	20.1803	+	34.9534i	0.647952	+	1.12229i
$971$	−13.6803	+	23.6950i	−0.439023	+	0.760410i	−0.997614	−	0.0690328i	$-0.978009\pi$
$971$	−13.6803	+	23.6950i	−0.439023	+	0.760410i	0.558591	+	0.829443i	$0.311342\pi$
$972$	23.4271	−	40.5768i	0.751423	−	1.30150i
$973$	−4.41641			−0.141584
$974$	−18.7533	+	32.4816i	−0.600894	+	1.04078i
$975$	3.78115	−	6.54915i	0.121094	−	0.209741i
$976$	18.9894	−	32.8905i	0.607835	−	1.05280i
$977$	−18.3820	−	31.8385i	−0.588091	−	1.01860i	−0.994482	−	0.104905i	$-0.966546\pi$
$977$	−18.3820	−	31.8385i	−0.588091	−	1.01860i	0.406391	−	0.913699i	$-0.366787\pi$
$978$	14.0000			0.447671
$979$	3.35410	+	5.80948i	0.107198	+	0.185672i
$980$	−54.5410	+	94.4678i	−1.74225	+	3.01766i
$981$	20.3951			0.651166
$982$	−12.6353	+	21.8849i	−0.403207	+	0.698375i
$983$	0.763932	+	1.32317i	0.0243656	+	0.0422025i	0.877951	−	0.478750i	$-0.158910\pi$
$983$	0.763932	+	1.32317i	0.0243656	+	0.0422025i	−0.853585	+	0.520953i	$0.825577\pi$
$984$	−0.753289	−	1.30473i	−0.0240140	−	0.0415934i
$985$	−48.3607			−1.54090
$986$	−19.9894	−	34.6226i	−0.636591	−	1.10261i
$987$	−0.708204			−0.0225424
$988$	56.8328			1.80809
$989$	16.5451	+	40.1197i	0.526103	+	1.27573i
$990$	33.4164			1.06204
$991$	−33.1803			−1.05401			−0.527004	−	0.849863i	$-0.676685\pi$
$991$	−33.1803			−1.05401			−0.527004	+	0.849863i	$0.676685\pi$
$992$		0			0
$993$	−1.32624			−0.0420869
$994$	4.26393	+	7.38535i	0.135244	+	0.234249i
$995$	−25.7984	−	44.6841i	−0.817863	−	1.41658i
$996$	−12.0836	+	20.9294i	−0.382883	+	0.663173i
$997$	36.4508			1.15441			0.577205	−	0.816599i	$-0.304143\pi$
$997$	36.4508			1.15441			0.577205	+	0.816599i	$0.304143\pi$
$998$	9.35410	−	16.2018i	0.296099	−	0.512858i
$999$	−2.07295	−	3.59045i	−0.0655852	−	0.113597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.c.b.36.1	yes	4
3.2	odd	2		387.2.h.d.208.2		4
4.3	odd	2		688.2.i.e.337.2		4
43.6	even	3	inner	43.2.c.b.6.1	✓	4
43.7	odd	6		1849.2.a.h.1.2		2
43.36	even	3		1849.2.a.e.1.1		2
129.92	odd	6		387.2.h.d.307.2		4
172.135	odd	6		688.2.i.e.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.1	✓	4	43.6	even	3	inner
43.2.c.b.36.1	yes	4	1.1	even	1	trivial
387.2.h.d.208.2		4	3.2	odd	2
387.2.h.d.307.2		4	129.92	odd	6
688.2.i.e.49.2		4	172.135	odd	6
688.2.i.e.337.2		4	4.3	odd	2
1849.2.a.e.1.1		2	43.36	even	3
1849.2.a.h.1.2		2	43.7	odd	6

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} +(0.190983 + 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 + 2.80252i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 + 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\)	\(q-2.61803 q^{2} +(0.190983 + 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 + 2.80252i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 + 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +(-4.23607 - 7.33708i) q^{10} -1.38197 q^{11} +(0.927051 + 1.60570i) q^{12} +(-1.80902 + 3.13331i) q^{13} +(0.309017 - 0.535233i) q^{14} +(-0.618034 + 1.07047i) q^{15} +9.85410 q^{16} +(2.54508 - 4.40822i) q^{17} +(-3.73607 + 6.47106i) q^{18} +(-1.61803 - 2.80252i) q^{19} +(7.85410 + 13.6037i) q^{20} -0.0901699 q^{21} +3.61803 q^{22} +(-3.30902 - 5.73139i) q^{23} +(-1.42705 - 2.47172i) q^{24} +(-2.73607 + 4.73901i) q^{25} +(4.73607 - 8.20311i) q^{26} +2.23607 q^{27} +(-0.572949 + 0.992377i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(1.61803 - 2.80252i) q^{30} -10.8541 q^{32} +(-0.263932 - 0.457144i) q^{33} +(-6.66312 + 11.5409i) q^{34} -0.763932 q^{35} +(6.92705 - 11.9980i) q^{36} +(-0.927051 - 1.60570i) q^{37} +(4.23607 + 7.33708i) q^{38} -1.38197 q^{39} +(-12.0902 - 20.9408i) q^{40} +0.527864 q^{41} +0.236068 q^{42} +(-6.50000 - 0.866025i) q^{43} -6.70820 q^{44} +9.23607 q^{45} +(8.66312 + 15.0050i) q^{46} +7.85410 q^{47} +(1.88197 + 3.25966i) q^{48} +(3.47214 + 6.01392i) q^{49} +(7.16312 - 12.4069i) q^{50} +1.94427 q^{51} +(-8.78115 + 15.2094i) q^{52} +(1.80902 + 3.13331i) q^{53} -5.85410 q^{54} +(-2.23607 - 3.87298i) q^{55} +(0.881966 - 1.52761i) q^{56} +(0.618034 - 1.07047i) q^{57} +(3.92705 - 6.80185i) q^{58} -6.09017 q^{59} +(-3.00000 + 5.19615i) q^{60} +(1.92705 - 3.33775i) q^{61} +(0.336881 + 0.583495i) q^{63} +8.70820 q^{64} -11.7082 q^{65} +(0.690983 + 1.19682i) q^{66} +(-1.42705 - 2.47172i) q^{67} +(12.3541 - 21.3979i) q^{68} +(1.26393 - 2.18919i) q^{69} +2.00000 q^{70} +(-6.89919 + 11.9497i) q^{71} +(-10.6631 + 18.4691i) q^{72} +(2.42705 - 4.20378i) q^{73} +(2.42705 + 4.20378i) q^{74} -2.09017 q^{75} +(-7.85410 - 13.6037i) q^{76} +(0.163119 - 0.282530i) q^{77} +3.61803 q^{78} +(1.80902 - 3.13331i) q^{79} +(15.9443 + 27.6163i) q^{80} +(-3.85410 - 6.67550i) q^{81} -1.38197 q^{82} +(6.51722 + 11.2882i) q^{83} -0.437694 q^{84} +16.4721 q^{85} +(17.0172 + 2.26728i) q^{86} -1.14590 q^{87} +10.3262 q^{88} +(-2.42705 - 4.20378i) q^{89} -24.1803 q^{90} +(-0.427051 - 0.739674i) q^{91} +(-16.0623 - 27.8207i) q^{92} -20.5623 q^{94} +(5.23607 - 9.06914i) q^{95} +(-2.07295 - 3.59045i) q^{96} -4.76393 q^{97} +(-9.09017 - 15.7446i) q^{98} +(-1.97214 + 3.41584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9	\( 4 q - 6 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - q^{9} - 8 q^{10} - 10 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} + 2 q^{15} + 26 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 22 q^{21} + 10 q^{22} - 11 q^{23} + q^{24} - 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} - 30 q^{32} - 10 q^{33} - 11 q^{34} - 12 q^{35} + 21 q^{36} + 3 q^{37} + 8 q^{38} - 10 q^{39} - 26 q^{40} + 20 q^{41} - 8 q^{42} - 26 q^{43} + 28 q^{45} + 19 q^{46} + 18 q^{47} + 12 q^{48} - 4 q^{49} + 13 q^{50} - 28 q^{51} - 15 q^{52} + 5 q^{53} - 10 q^{54} + 8 q^{56} - 2 q^{57} + 9 q^{58} - 2 q^{59} - 12 q^{60} + q^{61} + 17 q^{63} + 8 q^{64} - 20 q^{65} + 5 q^{66} + q^{67} + 36 q^{68} + 14 q^{69} + 8 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} + 3 q^{74} + 14 q^{75} - 18 q^{76} - 15 q^{77} + 10 q^{78} + 5 q^{79} + 28 q^{80} - 2 q^{81} - 10 q^{82} - 3 q^{83} - 42 q^{84} + 48 q^{85} + 39 q^{86} - 18 q^{87} + 10 q^{88} - 3 q^{89} - 52 q^{90} + 5 q^{91} - 24 q^{92} - 42 q^{94} + 12 q^{95} - 15 q^{96} - 28 q^{97} - 14 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - q^9 - 8 * q^10 - 10 * q^11 - 3 * q^12 - 5 * q^13 - q^14 + 2 * q^15 + 26 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 22 * q^21 + 10 * q^22 - 11 * q^23 + q^24 - 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 - 30 * q^32 - 10 * q^33 - 11 * q^34 - 12 * q^35 + 21 * q^36 + 3 * q^37 + 8 * q^38 - 10 * q^39 - 26 * q^40 + 20 * q^41 - 8 * q^42 - 26 * q^43 + 28 * q^45 + 19 * q^46 + 18 * q^47 + 12 * q^48 - 4 * q^49 + 13 * q^50 - 28 * q^51 - 15 * q^52 + 5 * q^53 - 10 * q^54 + 8 * q^56 - 2 * q^57 + 9 * q^58 - 2 * q^59 - 12 * q^60 + q^61 + 17 * q^63 + 8 * q^64 - 20 * q^65 + 5 * q^66 + q^67 + 36 * q^68 + 14 * q^69 + 8 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 + 3 * q^74 + 14 * q^75 - 18 * q^76 - 15 * q^77 + 10 * q^78 + 5 * q^79 + 28 * q^80 - 2 * q^81 - 10 * q^82 - 3 * q^83 - 42 * q^84 + 48 * q^85 + 39 * q^86 - 18 * q^87 + 10 * q^88 - 3 * q^89 - 52 * q^90 + 5 * q^91 - 24 * q^92 - 42 * q^94 + 12 * q^95 - 15 * q^96 - 28 * q^97 - 14 * q^98 + 10 * q^99

Introduction

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