LMFDB - Embedded newform 1155.2.c.f.694.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.7
Root			$-1.28094i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28094i q^{2} -1.00000i q^{3} +0.359182 q^{4} +(2.05729 - 0.876110i) q^{5} -1.28094 q^{6} -1.00000i q^{7} -3.02198i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.28094i q^{2} -1.00000i q^{3} +0.359182 q^{4} +(2.05729 - 0.876110i) q^{5} -1.28094 q^{6} -1.00000i q^{7} -3.02198i q^{8} -1.00000 q^{9} +(-1.12225 - 2.63527i) q^{10} +1.00000 q^{11} -0.359182i q^{12} -4.33981i q^{13} -1.28094 q^{14} +(-0.876110 - 2.05729i) q^{15} -3.15262 q^{16} +6.42363i q^{17} +1.28094i q^{18} -2.73466 q^{19} +(0.738942 - 0.314683i) q^{20} -1.00000 q^{21} -1.28094i q^{22} -3.91136i q^{23} -3.02198 q^{24} +(3.46486 - 3.60482i) q^{25} -5.55905 q^{26} +1.00000i q^{27} -0.359182i q^{28} -4.11721 q^{29} +(-2.63527 + 1.12225i) q^{30} +8.94510 q^{31} -2.00563i q^{32} -1.00000i q^{33} +8.22831 q^{34} +(-0.876110 - 2.05729i) q^{35} -0.359182 q^{36} +11.0931i q^{37} +3.50295i q^{38} -4.33981 q^{39} +(-2.64759 - 6.21708i) q^{40} -3.74740 q^{41} +1.28094i q^{42} +10.5319i q^{43} +0.359182 q^{44} +(-2.05729 + 0.876110i) q^{45} -5.01023 q^{46} -11.8241i q^{47} +3.15262i q^{48} -1.00000 q^{49} +(-4.61757 - 4.43830i) q^{50} +6.42363 q^{51} -1.55878i q^{52} -8.18618i q^{53} +1.28094 q^{54} +(2.05729 - 0.876110i) q^{55} -3.02198 q^{56} +2.73466i q^{57} +5.27391i q^{58} +4.77529 q^{59} +(-0.314683 - 0.738942i) q^{60} +7.12528 q^{61} -11.4582i q^{62} +1.00000i q^{63} -8.87434 q^{64} +(-3.80215 - 8.92823i) q^{65} -1.28094 q^{66} -5.84372i q^{67} +2.30726i q^{68} -3.91136 q^{69} +(-2.63527 + 1.12225i) q^{70} -0.841269 q^{71} +3.02198i q^{72} -0.456368i q^{73} +14.2096 q^{74} +(-3.60482 - 3.46486i) q^{75} -0.982242 q^{76} -1.00000i q^{77} +5.55905i q^{78} +6.39928 q^{79} +(-6.48585 + 2.76204i) q^{80} +1.00000 q^{81} +4.80021i q^{82} +9.87744i q^{83} -0.359182 q^{84} +(5.62781 + 13.2153i) q^{85} +13.4908 q^{86} +4.11721i q^{87} -3.02198i q^{88} -8.67569 q^{89} +(1.12225 + 2.63527i) q^{90} -4.33981 q^{91} -1.40489i q^{92} -8.94510i q^{93} -15.1460 q^{94} +(-5.62598 + 2.39586i) q^{95} -2.00563 q^{96} +2.64440i q^{97} +1.28094i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.28094i		−	0.905764i	−0.891570	−	0.452882i	$-0.850396\pi$
$2$		−	1.28094i		−	0.905764i	0.891570	−	0.452882i	$-0.149604\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.359182			0.179591
$5$	2.05729	−	0.876110i	0.920047	−	0.391808i
$5$	2.05729	−	0.876110i	0.920047	−	0.391808i
$6$	−1.28094			−0.522943
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	3.02198i		−	1.06843i
$9$	−1.00000			−0.333333
$10$	−1.12225	−	2.63527i	−0.354886	−	0.833346i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.359182i		−	0.103687i
$13$		−	4.33981i		−	1.20365i	−0.798629	−	0.601823i	$-0.794441\pi$
$13$		−	4.33981i		−	1.20365i	0.798629	−	0.601823i	$-0.205559\pi$
$14$	−1.28094			−0.342347
$15$	−0.876110	−	2.05729i	−0.226211	−	0.531189i
$16$	−3.15262			−0.788156
$17$			6.42363i			1.55796i	0.627049	+	0.778980i	$0.284263\pi$
$17$			6.42363i			1.55796i	−0.627049	+	0.778980i	$0.715737\pi$
$18$			1.28094i			0.301921i
$19$	−2.73466			−0.627374			−0.313687	−	0.949526i	$-0.601564\pi$
$19$	−2.73466			−0.627374			−0.313687	+	0.949526i	$0.601564\pi$
$20$	0.738942	−	0.314683i	0.165232	−	0.0703653i
$21$	−1.00000			−0.218218
$22$		−	1.28094i		−	0.273098i
$23$		−	3.91136i		−	0.815574i	−0.913077	−	0.407787i	$-0.866301\pi$
$23$		−	3.91136i		−	0.815574i	0.913077	−	0.407787i	$-0.133699\pi$
$24$	−3.02198			−0.616859
$25$	3.46486	−	3.60482i	0.692973	−	0.720964i
$26$	−5.55905			−1.09022
$27$			1.00000i			0.192450i
$28$		−	0.359182i		−	0.0678791i
$29$	−4.11721			−0.764547			−0.382273	−	0.924049i	$-0.624859\pi$
$29$	−4.11721			−0.764547			−0.382273	+	0.924049i	$0.624859\pi$
$30$	−2.63527	+	1.12225i	−0.481132	+	0.204893i
$31$	8.94510			1.60659			0.803294	−	0.595583i	$-0.203079\pi$
$31$	8.94510			1.60659			0.803294	+	0.595583i	$0.203079\pi$
$32$		−	2.00563i		−	0.354548i
$33$		−	1.00000i		−	0.174078i
$34$	8.22831			1.41114
$35$	−0.876110	−	2.05729i	−0.148090	−	0.347745i
$36$	−0.359182			−0.0598637
$37$			11.0931i			1.82369i	0.410533	+	0.911846i	$0.365343\pi$
$37$			11.0931i			1.82369i	−0.410533	+	0.911846i	$0.634657\pi$
$38$			3.50295i			0.568253i
$39$	−4.33981			−0.694926
$40$	−2.64759	−	6.21708i	−0.418620	−	0.983007i
$41$	−3.74740			−0.585246			−0.292623	−	0.956228i	$-0.594528\pi$
$41$	−3.74740			−0.585246			−0.292623	+	0.956228i	$0.594528\pi$
$42$			1.28094i			0.197654i
$43$			10.5319i			1.60610i	0.595913	+	0.803049i	$0.296790\pi$
$43$			10.5319i			1.60610i	−0.595913	+	0.803049i	$0.703210\pi$
$44$	0.359182			0.0541488
$45$	−2.05729	+	0.876110i	−0.306682	+	0.130603i
$46$	−5.01023			−0.738718
$47$		−	11.8241i		−	1.72472i	−0.506299	−	0.862358i	$-0.668987\pi$
$47$		−	11.8241i		−	1.72472i	0.506299	−	0.862358i	$-0.331013\pi$
$48$			3.15262i			0.455042i
$49$	−1.00000			−0.142857
$50$	−4.61757	−	4.43830i	−0.653023	−	0.627670i
$51$	6.42363			0.899488
$52$		−	1.55878i		−	0.216164i
$53$		−	8.18618i		−	1.12446i	−0.826982	−	0.562229i	$-0.809944\pi$
$53$		−	8.18618i		−	1.12446i	0.826982	−	0.562229i	$-0.190056\pi$
$54$	1.28094			0.174314
$55$	2.05729	−	0.876110i	0.277405	−	0.118135i
$56$	−3.02198			−0.403829
$57$			2.73466i			0.362215i
$58$			5.27391i			0.692499i
$59$	4.77529			0.621690			0.310845	−	0.950461i	$-0.399388\pi$
$59$	4.77529			0.621690			0.310845	+	0.950461i	$0.399388\pi$
$60$	−0.314683	−	0.738942i	−0.0406254	−	0.0953970i
$61$	7.12528			0.912299			0.456149	−	0.889903i	$-0.349228\pi$
$61$	7.12528			0.912299			0.456149	+	0.889903i	$0.349228\pi$
$62$		−	11.4582i		−	1.45519i
$63$			1.00000i			0.125988i
$64$	−8.87434			−1.10929
$65$	−3.80215	−	8.92823i	−0.471599	−	1.10741i
$66$	−1.28094			−0.157673
$67$		−	5.84372i		−	0.713923i	−0.934119	−	0.356962i	$-0.883813\pi$
$67$		−	5.84372i		−	0.713923i	0.934119	−	0.356962i	$-0.116187\pi$
$68$			2.30726i			0.279796i
$69$	−3.91136			−0.470872
$70$	−2.63527	+	1.12225i	−0.314975	+	0.134134i
$71$	−0.841269			−0.0998403			−0.0499201	−	0.998753i	$-0.515897\pi$
$71$	−0.841269			−0.0998403			−0.0499201	+	0.998753i	$0.515897\pi$
$72$			3.02198i			0.356144i
$73$		−	0.456368i		−	0.0534138i	−0.999643	−	0.0267069i	$-0.991498\pi$
$73$		−	0.456368i		−	0.0534138i	0.999643	−	0.0267069i	$-0.00850208\pi$
$74$	14.2096			1.65183
$75$	−3.60482	−	3.46486i	−0.416249	−	0.400088i
$76$	−0.982242			−0.112671
$77$		−	1.00000i		−	0.113961i
$78$			5.55905i			0.629439i
$79$	6.39928			0.719976			0.359988	−	0.932957i	$-0.382781\pi$
$79$	6.39928			0.719976			0.359988	+	0.932957i	$0.382781\pi$
$80$	−6.48585	+	2.76204i	−0.725140	+	0.308806i
$81$	1.00000			0.111111
$82$			4.80021i			0.530095i
$83$			9.87744i			1.08419i	0.840317	+	0.542095i	$0.182369\pi$
$83$			9.87744i			1.08419i	−0.840317	+	0.542095i	$0.817631\pi$
$84$	−0.359182			−0.0391900
$85$	5.62781	+	13.2153i	0.610421	+	1.43340i
$86$	13.4908			1.45475
$87$			4.11721i			0.441411i
$88$		−	3.02198i		−	0.322144i
$89$	−8.67569			−0.919622			−0.459811	−	0.888017i	$-0.652083\pi$
$89$	−8.67569			−0.919622			−0.459811	+	0.888017i	$0.652083\pi$
$90$	1.12225	+	2.63527i	0.118295	+	0.277782i
$91$	−4.33981			−0.454936
$92$		−	1.40489i		−	0.146470i
$93$		−	8.94510i		−	0.927564i
$94$	−15.1460			−1.56219
$95$	−5.62598	+	2.39586i	−0.577214	+	0.245810i
$96$	−2.00563			−0.204699
$97$			2.64440i			0.268499i	0.990948	+	0.134249i	$0.0428623\pi$
$97$			2.64440i			0.268499i	−0.990948	+	0.134249i	$0.957138\pi$
$98$			1.28094i			0.129395i
$99$	−1.00000			−0.100504
$100$	1.24452	−	1.29479i	0.124452	−	0.129479i
$101$	−10.3492			−1.02978			−0.514892	−	0.857255i	$-0.672168\pi$
$101$	−10.3492			−1.02978			−0.514892	+	0.857255i	$0.672168\pi$
$102$		−	8.22831i		−	0.814724i
$103$			15.8744i			1.56415i	0.623183	+	0.782076i	$0.285839\pi$
$103$			15.8744i			1.56415i	−0.623183	+	0.782076i	$0.714161\pi$
$104$	−13.1148			−1.28601
$105$	−2.05729	+	0.876110i	−0.200771	+	0.0854996i
$106$	−10.4860			−1.01849
$107$			17.3023i			1.67267i	0.548217	+	0.836336i	$0.315307\pi$
$107$			17.3023i			1.67267i	−0.548217	+	0.836336i	$0.684693\pi$
$108$			0.359182i			0.0345624i
$109$	−0.827834			−0.0792921			−0.0396461	−	0.999214i	$-0.512623\pi$
$109$	−0.827834			−0.0792921			−0.0396461	+	0.999214i	$0.512623\pi$
$110$	−1.12225	−	2.63527i	−0.107002	−	0.251263i
$111$	11.0931			1.05291
$112$			3.15262i			0.297895i
$113$			4.26466i			0.401185i	0.979675	+	0.200593i	$0.0642868\pi$
$113$			4.26466i			0.401185i	−0.979675	+	0.200593i	$0.935713\pi$
$114$	3.50295			0.328081
$115$	−3.42678	−	8.04679i	−0.319549	−	0.750367i
$116$	−1.47883			−0.137306
$117$			4.33981i			0.401215i
$118$		−	6.11688i		−	0.563104i
$119$	6.42363			0.588853
$120$	−6.21708	+	2.64759i	−0.567539	+	0.241691i
$121$	1.00000			0.0909091
$122$		−	9.12709i		−	0.826328i
$123$			3.74740i			0.337892i
$124$	3.21292			0.288529
$125$	3.97000	−	10.4518i	0.355088	−	0.934833i
$126$	1.28094			0.114116
$127$		−	9.19937i		−	0.816312i	−0.912912	−	0.408156i	$-0.866172\pi$
$127$		−	9.19937i		−	0.816312i	0.912912	−	0.408156i	$-0.133828\pi$
$128$			7.35628i			0.650209i
$129$	10.5319			0.927281
$130$	−11.4366	+	4.87034i	−1.00305	+	0.427157i
$131$	22.1491			1.93518			0.967588	−	0.252534i	$-0.0812640\pi$
$131$	22.1491			1.93518			0.967588	+	0.252534i	$0.0812640\pi$
$132$		−	0.359182i		−	0.0312628i
$133$			2.73466i			0.237125i
$134$	−7.48547			−0.646646
$135$	0.876110	+	2.05729i	0.0754035	+	0.177063i
$136$	19.4121			1.66457
$137$		−	0.726444i		−	0.0620643i	−0.999518	−	0.0310321i	$-0.990121\pi$
$137$		−	0.726444i		−	0.0620643i	0.999518	−	0.0310321i	$-0.00987942\pi$
$138$			5.01023i			0.426499i
$139$	−6.13878			−0.520685			−0.260342	−	0.965516i	$-0.583835\pi$
$139$	−6.13878			−0.520685			−0.260342	+	0.965516i	$0.583835\pi$
$140$	−0.314683	−	0.738942i	−0.0265956	−	0.0624520i
$141$	−11.8241			−0.995765
$142$			1.07762i			0.0904317i
$143$		−	4.33981i		−	0.362913i
$144$	3.15262			0.262719
$145$	−8.47028	+	3.60713i	−0.703419	+	0.299556i
$146$	−0.584581			−0.0483803
$147$			1.00000i			0.0824786i
$148$			3.98444i			0.327519i
$149$	−6.17559			−0.505924			−0.252962	−	0.967476i	$-0.581405\pi$
$149$	−6.17559			−0.505924			−0.252962	+	0.967476i	$0.581405\pi$
$150$	−4.43830	+	4.61757i	−0.362385	+	0.377023i
$151$	−17.5788			−1.43054			−0.715272	−	0.698846i	$-0.753697\pi$
$151$	−17.5788			−1.43054			−0.715272	+	0.698846i	$0.753697\pi$
$152$			8.26409i			0.670306i
$153$		−	6.42363i		−	0.519320i
$154$	−1.28094			−0.103221
$155$	18.4026	−	7.83689i	1.47814	−	0.629474i
$156$	−1.55878			−0.124803
$157$		−	2.76188i		−	0.220422i	−0.993908	−	0.110211i	$-0.964847\pi$
$157$		−	2.76188i		−	0.220422i	0.993908	−	0.110211i	$-0.0351527\pi$
$158$		−	8.19713i		−	0.652128i
$159$	−8.18618			−0.649206
$160$	−1.75715	−	4.12615i	−0.138915	−	0.326201i
$161$	−3.91136			−0.308258
$162$		−	1.28094i		−	0.100640i
$163$			21.1439i			1.65612i	0.560641	+	0.828059i	$0.310555\pi$
$163$			21.1439i			1.65612i	−0.560641	+	0.828059i	$0.689445\pi$
$164$	−1.34600			−0.105105
$165$	−0.876110	−	2.05729i	−0.0682051	−	0.160160i
$166$	12.6524			0.982020
$167$		−	16.8639i		−	1.30497i	−0.757804	−	0.652483i	$-0.773728\pi$
$167$		−	16.8639i		−	1.30497i	0.757804	−	0.652483i	$-0.226272\pi$
$168$			3.02198i			0.233151i
$169$	−5.83394			−0.448764
$170$	16.9280	−	7.20891i	1.29832	−	0.552898i
$171$	2.73466			0.209125
$172$			3.78287i			0.288441i
$173$		−	21.3369i		−	1.62221i	−0.584900	−	0.811105i	$-0.698866\pi$
$173$		−	21.3369i		−	1.62221i	0.584900	−	0.811105i	$-0.301134\pi$
$174$	5.27391			0.399814
$175$	−3.60482	−	3.46486i	−0.272499	−	0.261919i
$176$	−3.15262			−0.237638
$177$		−	4.77529i		−	0.358933i
$178$			11.1131i			0.832960i
$179$	−6.41551			−0.479518			−0.239759	−	0.970832i	$-0.577068\pi$
$179$	−6.41551			−0.479518			−0.239759	+	0.970832i	$0.577068\pi$
$180$	−0.738942	+	0.314683i	−0.0550775	+	0.0234551i
$181$	19.2317			1.42948			0.714742	−	0.699388i	$-0.246544\pi$
$181$	19.2317			1.42948			0.714742	+	0.699388i	$0.246544\pi$
$182$			5.55905i			0.412064i
$183$		−	7.12528i		−	0.526716i
$184$	−11.8200			−0.871385
$185$	9.71876	+	22.8217i	0.714537	+	1.67788i
$186$	−11.4582			−0.840154
$187$			6.42363i			0.469743i
$188$		−	4.24699i		−	0.309744i
$189$	1.00000			0.0727393
$190$	3.06897	+	7.20657i	0.222646	+	0.522819i
$191$	14.0877			1.01935			0.509674	−	0.860368i	$-0.329766\pi$
$191$	14.0877			1.01935			0.509674	+	0.860368i	$0.329766\pi$
$192$			8.87434i			0.640451i
$193$			8.61967i			0.620458i	0.950662	+	0.310229i	$0.100406\pi$
$193$			8.61967i			0.620458i	−0.950662	+	0.310229i	$0.899594\pi$
$194$	3.38733			0.243196
$195$	−8.92823	+	3.80215i	−0.639364	+	0.272278i
$196$	−0.359182			−0.0256559
$197$		−	4.21976i		−	0.300645i	−0.988637	−	0.150323i	$-0.951969\pi$
$197$		−	4.21976i		−	0.300645i	0.988637	−	0.150323i	$-0.0480313\pi$
$198$			1.28094i			0.0910327i
$199$	23.6115			1.67378			0.836889	−	0.547373i	$-0.184372\pi$
$199$	23.6115			1.67378			0.836889	+	0.547373i	$0.184372\pi$
$200$	−10.8937	−	10.4707i	−0.770301	−	0.740394i
$201$	−5.84372			−0.412184
$202$			13.2568i			0.932742i
$203$			4.11721i			0.288971i
$204$	2.30726			0.161540
$205$	−7.70948	+	3.28314i	−0.538454	+	0.229304i
$206$	20.3342			1.41675
$207$			3.91136i			0.271858i
$208$			13.6818i			0.948661i
$209$	−2.73466			−0.189160
$210$	1.12225	+	2.63527i	0.0774424	+	0.181851i
$211$	11.2812			0.776628			0.388314	−	0.921527i	$-0.373058\pi$
$211$	11.2812			0.776628			0.388314	+	0.921527i	$0.373058\pi$
$212$		−	2.94033i		−	0.201943i
$213$			0.841269i			0.0576428i
$214$	22.1632			1.51505
$215$	9.22709	+	21.6671i	0.629282	+	1.47769i
$216$	3.02198			0.205620
$217$		−	8.94510i		−	0.607233i
$218$			1.06041i			0.0718200i
$219$	−0.456368			−0.0308385
$220$	0.738942	−	0.314683i	0.0498194	−	0.0212159i
$221$	27.8773			1.87523
$222$		−	14.2096i		−	0.953687i
$223$		−	19.8197i		−	1.32722i	−0.748077	−	0.663612i	$-0.769023\pi$
$223$		−	19.8197i		−	1.32722i	0.748077	−	0.663612i	$-0.230977\pi$
$224$	−2.00563			−0.134007
$225$	−3.46486	+	3.60482i	−0.230991	+	0.240321i
$226$	5.46279			0.363379
$227$		−	15.0022i		−	0.995732i	−0.867254	−	0.497866i	$-0.834117\pi$
$227$		−	15.0022i		−	0.995732i	0.867254	−	0.497866i	$-0.165883\pi$
$228$			0.982242i			0.0650506i
$229$	16.9868			1.12252			0.561260	−	0.827640i	$-0.310317\pi$
$229$	16.9868			1.12252			0.561260	+	0.827640i	$0.310317\pi$
$230$	−10.3075	+	4.38951i	−0.679655	+	0.289436i
$231$	−1.00000			−0.0657952
$232$			12.4421i			0.816866i
$233$			9.99278i			0.654649i	0.944912	+	0.327324i	$0.106147\pi$
$233$			9.99278i			0.654649i	−0.944912	+	0.327324i	$0.893853\pi$
$234$	5.55905			0.363407
$235$	−10.3592	−	24.3255i	−0.675758	−	1.58682i
$236$	1.71520			0.111650
$237$		−	6.39928i		−	0.415678i
$238$		−	8.22831i		−	0.533362i
$239$	−1.81047			−0.117109			−0.0585547	−	0.998284i	$-0.518649\pi$
$239$	−1.81047			−0.117109			−0.0585547	+	0.998284i	$0.518649\pi$
$240$	2.76204	+	6.48585i	0.178289	+	0.418660i
$241$	18.7662			1.20884			0.604418	−	0.796667i	$-0.293406\pi$
$241$	18.7662			1.20884			0.604418	+	0.796667i	$0.293406\pi$
$242$		−	1.28094i		−	0.0823422i
$243$		−	1.00000i		−	0.0641500i
$244$	2.55928			0.163841
$245$	−2.05729	+	0.876110i	−0.131435	+	0.0559726i
$246$	4.80021			0.306050
$247$			11.8679i			0.755137i
$248$		−	27.0319i		−	1.71653i
$249$	9.87744			0.625957
$250$	−13.3881	−	5.08535i	−0.846738	−	0.321626i
$251$	17.9023			1.12998			0.564991	−	0.825097i	$-0.308880\pi$
$251$	17.9023			1.12998			0.564991	+	0.825097i	$0.308880\pi$
$252$			0.359182i			0.0226264i
$253$		−	3.91136i		−	0.245905i
$254$	−11.7839			−0.739386
$255$	13.2153	−	5.62781i	0.827572	−	0.352427i
$256$	−8.32570			−0.520356
$257$			10.6175i			0.662301i	0.943578	+	0.331151i	$0.107437\pi$
$257$			10.6175i			0.662301i	−0.943578	+	0.331151i	$0.892563\pi$
$258$		−	13.4908i		−	0.839898i
$259$	11.0931			0.689290
$260$	−1.36567	−	3.20687i	−0.0846950	−	0.198881i
$261$	4.11721			0.254849
$262$		−	28.3718i		−	1.75281i
$263$			6.42911i			0.396436i	0.980158	+	0.198218i	$0.0635154\pi$
$263$			6.42911i			0.396436i	−0.980158	+	0.198218i	$0.936485\pi$
$264$	−3.02198			−0.185990
$265$	−7.17199	−	16.8413i	−0.440572	−	1.03455i
$266$	3.50295			0.214779
$267$			8.67569i			0.530944i
$268$		−	2.09896i		−	0.128214i
$269$	−3.99523			−0.243594			−0.121797	−	0.992555i	$-0.538866\pi$
$269$	−3.99523			−0.243594			−0.121797	+	0.992555i	$0.538866\pi$
$270$	2.63527	−	1.12225i	0.160377	−	0.0682978i
$271$	29.6426			1.80066			0.900329	−	0.435209i	$-0.143326\pi$
$271$	29.6426			1.80066			0.900329	+	0.435209i	$0.143326\pi$
$272$		−	20.2513i		−	1.22791i
$273$			4.33981i			0.262657i
$274$	−0.930534			−0.0562156
$275$	3.46486	−	3.60482i	0.208939	−	0.217379i
$276$	−1.40489			−0.0845645
$277$		−	4.85544i		−	0.291735i	−0.989304	−	0.145867i	$-0.953403\pi$
$277$		−	4.85544i		−	0.291735i	0.989304	−	0.145867i	$-0.0465973\pi$
$278$			7.86344i			0.471618i
$279$	−8.94510			−0.535529
$280$	−6.21708	+	2.64759i	−0.371542	+	0.158224i
$281$	−28.3810			−1.69307			−0.846533	−	0.532336i	$-0.821314\pi$
$281$	−28.3810			−1.69307			−0.846533	+	0.532336i	$0.821314\pi$
$282$			15.1460i			0.901928i
$283$			18.0238i			1.07140i	0.844407	+	0.535701i	$0.179953\pi$
$283$			18.0238i			1.07140i	−0.844407	+	0.535701i	$0.820047\pi$
$284$	−0.302169			−0.0179304
$285$	2.39586	+	5.62598i	0.141919	+	0.333254i
$286$	−5.55905			−0.328714
$287$			3.74740i			0.221202i
$288$			2.00563i			0.118183i
$289$	−24.2631			−1.42724
$290$	4.62053	+	10.8500i	0.271327	+	0.637131i
$291$	2.64440			0.155018
$292$		−	0.163919i		−	0.00959265i
$293$		−	16.3356i		−	0.954335i	−0.878812	−	0.477167i	$-0.841664\pi$
$293$		−	16.3356i		−	0.954335i	0.878812	−	0.477167i	$-0.158336\pi$
$294$	1.28094			0.0747062
$295$	9.82414	−	4.18368i	0.571984	−	0.243583i
$296$	33.5231			1.94849
$297$			1.00000i			0.0580259i
$298$			7.91059i			0.458248i
$299$	−16.9745			−0.981663
$300$	−1.29479	−	1.24452i	−0.0747546	−	0.0718523i
$301$	10.5319			0.607048
$302$			22.5175i			1.29574i
$303$			10.3492i			0.594546i
$304$	8.62135			0.494469
$305$	14.6588	−	6.24253i	0.839358	−	0.357446i
$306$	−8.22831			−0.470381
$307$			7.60936i			0.434289i	0.976139	+	0.217145i	$0.0696743\pi$
$307$			7.60936i			0.434289i	−0.976139	+	0.217145i	$0.930326\pi$
$308$		−	0.359182i		−	0.0204663i
$309$	15.8744			0.903064
$310$	−10.0386	−	23.5728i	−0.570155	−	1.33884i
$311$	6.07092			0.344250			0.172125	−	0.985075i	$-0.444937\pi$
$311$	6.07092			0.344250			0.172125	+	0.985075i	$0.444937\pi$
$312$			13.1148i			0.742480i
$313$			21.4932i			1.21486i	0.794371	+	0.607432i	$0.207800\pi$
$313$			21.4932i			1.21486i	−0.794371	+	0.607432i	$0.792200\pi$
$314$	−3.53781			−0.199650
$315$	0.876110	+	2.05729i	0.0493632	+	0.115915i
$316$	2.29851			0.129301
$317$			8.76913i			0.492524i	0.969203	+	0.246262i	$0.0792023\pi$
$317$			8.76913i			0.492524i	−0.969203	+	0.246262i	$0.920798\pi$
$318$			10.4860i			0.588028i
$319$	−4.11721			−0.230519
$320$	−18.2571	+	7.77490i	−1.02060	+	0.434630i
$321$	17.3023			0.965718
$322$			5.01023i			0.279209i
$323$		−	17.5665i		−	0.977424i
$324$	0.359182			0.0199546
$325$	−15.6442	−	15.0368i	−0.867786	−	0.834094i
$326$	27.0841			1.50005
$327$			0.827834i			0.0457793i
$328$			11.3246i			0.625295i
$329$	−11.8241			−0.651881
$330$	−2.63527	+	1.12225i	−0.145067	+	0.0617777i
$331$	9.42284			0.517926			0.258963	−	0.965887i	$-0.416619\pi$
$331$	9.42284			0.517926			0.258963	+	0.965887i	$0.416619\pi$
$332$			3.54780i			0.194711i
$333$		−	11.0931i		−	0.607897i
$334$	−21.6017			−1.18199
$335$	−5.11974	−	12.0222i	−0.279721	−	0.656843i
$336$	3.15262			0.171990
$337$		−	6.52318i		−	0.355340i	−0.984090	−	0.177670i	$-0.943144\pi$
$337$		−	6.52318i		−	0.355340i	0.984090	−	0.177670i	$-0.0568560\pi$
$338$			7.47295i			0.406475i
$339$	4.26466			0.231624
$340$	2.02141	+	4.74669i	0.109626	+	0.257425i
$341$	8.94510			0.484404
$342$		−	3.50295i		−	0.189418i
$343$			1.00000i			0.0539949i
$344$	31.8272			1.71601
$345$	−8.04679	+	3.42678i	−0.433224	+	0.184492i
$346$	−27.3313			−1.46934
$347$			0.0883610i			0.00474347i	0.999997	+	0.00237173i	$0.000754947\pi$
$347$			0.0883610i			0.00474347i	−0.999997	+	0.00237173i	$0.999245\pi$
$348$			1.47883i			0.0792736i
$349$	−14.3541			−0.768357			−0.384179	−	0.923259i	$-0.625515\pi$
$349$	−14.3541			−0.768357			−0.384179	+	0.923259i	$0.625515\pi$
$350$	−4.43830	+	4.61757i	−0.237237	+	0.246820i
$351$	4.33981			0.231642
$352$		−	2.00563i		−	0.106900i
$353$			4.72823i			0.251658i	0.992052	+	0.125829i	$0.0401591\pi$
$353$			4.72823i			0.251658i	−0.992052	+	0.125829i	$0.959841\pi$
$354$	−6.11688			−0.325108
$355$	−1.73073	+	0.737044i	−0.0918577	+	0.0391182i
$356$	−3.11616			−0.165156
$357$		−	6.42363i		−	0.339975i
$358$			8.21791i			0.434330i
$359$	−21.8825			−1.15492			−0.577458	−	0.816420i	$-0.695955\pi$
$359$	−21.8825			−1.15492			−0.577458	+	0.816420i	$0.695955\pi$
$360$	2.64759	+	6.21708i	0.139540	+	0.327669i
$361$	−11.5216			−0.606402
$362$		−	24.6348i		−	1.29478i
$363$		−	1.00000i		−	0.0524864i
$364$	−1.55878			−0.0817024
$365$	−0.399828	−	0.938879i	−0.0209280	−	0.0491432i
$366$	−9.12709			−0.477081
$367$		−	5.39173i		−	0.281446i	−0.990049	−	0.140723i	$-0.955057\pi$
$367$		−	5.39173i		−	0.281446i	0.990049	−	0.140723i	$-0.0449427\pi$
$368$			12.3310i			0.642800i
$369$	3.74740			0.195082
$370$	29.2333	−	12.4492i	1.51976	−	0.647202i
$371$	−8.18618			−0.425005
$372$		−	3.21292i		−	0.166582i
$373$			19.0750i			0.987668i	0.869556	+	0.493834i	$0.164405\pi$
$373$			19.0750i			0.987668i	−0.869556	+	0.493834i	$0.835595\pi$
$374$	8.22831			0.425476
$375$	−10.4518	−	3.97000i	−0.539726	−	0.205010i
$376$	−35.7321			−1.84274
$377$			17.8679i			0.920244i
$378$		−	1.28094i		−	0.0658846i
$379$	34.3994			1.76698			0.883490	−	0.468450i	$-0.155188\pi$
$379$	34.3994			1.76698			0.883490	+	0.468450i	$0.155188\pi$
$380$	−2.02075	+	0.860552i	−0.103663	+	0.0441454i
$381$	−9.19937			−0.471298
$382$		−	18.0455i		−	0.923289i
$383$			13.5353i			0.691621i	0.938304	+	0.345811i	$0.112396\pi$
$383$			13.5353i			0.691621i	−0.938304	+	0.345811i	$0.887604\pi$
$384$	7.35628			0.375399
$385$	−0.876110	−	2.05729i	−0.0446507	−	0.104849i
$386$	11.0413			0.561988
$387$		−	10.5319i		−	0.535366i
$388$			0.949824i			0.0482200i
$389$	−13.0854			−0.663458			−0.331729	−	0.943375i	$-0.607632\pi$
$389$	−13.0854			−0.663458			−0.331729	+	0.943375i	$0.607632\pi$
$390$	4.87034	+	11.4366i	0.246619	+	0.579113i
$391$	25.1251			1.27063
$392$			3.02198i			0.152633i
$393$		−	22.1491i		−	1.11727i
$394$	−5.40527			−0.272314
$395$	13.1652	−	5.60648i	0.662411	−	0.282092i
$396$	−0.359182			−0.0180496
$397$		−	37.7082i		−	1.89252i	−0.323404	−	0.946261i	$-0.604827\pi$
$397$		−	37.7082i		−	1.89252i	0.323404	−	0.946261i	$-0.395173\pi$
$398$		−	30.2451i		−	1.51605i
$399$	2.73466			0.136904
$400$	−10.9234	+	11.3646i	−0.546170	+	0.568232i
$401$	1.18285			0.0590687			0.0295344	−	0.999564i	$-0.490598\pi$
$401$	1.18285			0.0590687			0.0295344	+	0.999564i	$0.490598\pi$
$402$			7.48547i			0.373341i
$403$		−	38.8200i		−	1.93376i
$404$	−3.71725			−0.184940
$405$	2.05729	−	0.876110i	0.102227	−	0.0435343i
$406$	5.27391			0.261740
$407$			11.0931i			0.549864i
$408$		−	19.4121i		−	0.961042i
$409$	−7.14274			−0.353186			−0.176593	−	0.984284i	$-0.556508\pi$
$409$	−7.14274			−0.353186			−0.176593	+	0.984284i	$0.556508\pi$
$410$	4.20551	+	9.87541i	0.207695	+	0.487712i
$411$	−0.726444			−0.0358328
$412$			5.70181i			0.280908i
$413$		−	4.77529i		−	0.234977i
$414$	5.01023			0.246239
$415$	8.65372	+	20.3207i	0.424794	+	0.997505i
$416$	−8.70404			−0.426751
$417$			6.13878i			0.300617i
$418$			3.50295i			0.171335i
$419$	36.4231			1.77938			0.889692	−	0.456562i	$-0.150919\pi$
$419$	36.4231			1.77938			0.889692	+	0.456562i	$0.150919\pi$
$420$	−0.738942	+	0.314683i	−0.0360567	+	0.0153550i
$421$	−31.0701			−1.51427			−0.757133	−	0.653261i	$-0.773400\pi$
$421$	−31.0701			−1.51427			−0.757133	+	0.653261i	$0.773400\pi$
$422$		−	14.4505i		−	0.703442i
$423$			11.8241i			0.574905i
$424$	−24.7385			−1.20141
$425$	23.1560	+	22.2570i	1.12323	+	1.07962i
$426$	1.07762			0.0522108
$427$		−	7.12528i		−	0.344817i
$428$			6.21467i			0.300397i
$429$	−4.33981			−0.209528
$430$	27.7544	−	11.8194i	1.33843	−	0.569981i
$431$	−4.27599			−0.205967			−0.102984	−	0.994683i	$-0.532839\pi$
$431$	−4.27599			−0.205967			−0.102984	+	0.994683i	$0.532839\pi$
$432$		−	3.15262i		−	0.151681i
$433$			13.2412i			0.636332i	0.948035	+	0.318166i	$0.103067\pi$
$433$			13.2412i			0.636332i	−0.948035	+	0.318166i	$0.896933\pi$
$434$	−11.4582			−0.550010
$435$	3.60713	+	8.47028i	0.172949	+	0.406119i
$436$	−0.297344			−0.0142402
$437$			10.6962i			0.511670i
$438$			0.584581i			0.0279324i
$439$	−13.1833			−0.629205			−0.314602	−	0.949224i	$-0.601871\pi$
$439$	−13.1833			−0.629205			−0.314602	+	0.949224i	$0.601871\pi$
$440$	−2.64759	−	6.21708i	−0.126219	−	0.296388i
$441$	1.00000			0.0476190
$442$		−	35.7093i		−	1.69852i
$443$		−	11.0326i		−	0.524176i	−0.965044	−	0.262088i	$-0.915589\pi$
$443$		−	11.0326i		−	0.524176i	0.965044	−	0.262088i	$-0.0844110\pi$
$444$	3.98444			0.189093
$445$	−17.8484	+	7.60086i	−0.846095	+	0.360315i
$446$	−25.3879			−1.20215
$447$			6.17559i			0.292095i
$448$			8.87434i			0.419273i
$449$	−31.9702			−1.50876			−0.754382	−	0.656435i	$-0.772063\pi$
$449$	−31.9702			−1.50876			−0.754382	+	0.656435i	$0.772063\pi$
$450$	4.61757	+	4.43830i	0.217674	+	0.209223i
$451$	−3.74740			−0.176458
$452$			1.53179i			0.0720494i
$453$			17.5788i			0.825925i
$454$	−19.2170			−0.901898
$455$	−8.92823	+	3.80215i	−0.418562	+	0.178247i
$456$	8.26409			0.387002
$457$			32.5736i			1.52373i	0.647737	+	0.761864i	$0.275715\pi$
$457$			32.5736i			1.52373i	−0.647737	+	0.761864i	$0.724285\pi$
$458$		−	21.7592i		−	1.01674i
$459$	−6.42363			−0.299829
$460$	−1.23084	−	2.89026i	−0.0573882	−	0.134759i
$461$	16.9553			0.789686			0.394843	−	0.918749i	$-0.370799\pi$
$461$	16.9553			0.789686			0.394843	+	0.918749i	$0.370799\pi$
$462$			1.28094i			0.0595949i
$463$			5.31939i			0.247213i	0.992331	+	0.123607i	$0.0394461\pi$
$463$			5.31939i			0.247213i	−0.992331	+	0.123607i	$0.960554\pi$
$464$	12.9800			0.602582
$465$	−7.83689	−	18.4026i	−0.363427	−	0.853402i
$466$	12.8002			0.592957
$467$			29.4668i			1.36356i	0.731557	+	0.681781i	$0.238794\pi$
$467$			29.4668i			1.36356i	−0.731557	+	0.681781i	$0.761206\pi$
$468$			1.55878i			0.0720548i
$469$	−5.84372			−0.269838
$470$	−31.1596	+	13.2695i	−1.43728	+	0.612077i
$471$	−2.76188			−0.127261
$472$		−	14.4308i		−	0.664233i
$473$			10.5319i			0.484257i
$474$	−8.19713			−0.376506
$475$	−9.47522	+	9.85796i	−0.434753	+	0.452314i
$476$	2.30726			0.105753
$477$			8.18618i			0.374819i
$478$			2.31911i			0.106073i
$479$	−16.3096			−0.745206			−0.372603	−	0.927991i	$-0.621535\pi$
$479$	−16.3096			−0.745206			−0.372603	+	0.927991i	$0.621535\pi$
$480$	−4.12615	+	1.75715i	−0.188332	+	0.0802026i
$481$	48.1418			2.19508
$482$		−	24.0384i		−	1.09492i
$483$			3.91136i			0.177973i
$484$	0.359182			0.0163265
$485$	2.31679	+	5.44030i	0.105200	+	0.247031i
$486$	−1.28094			−0.0581048
$487$		−	1.48078i		−	0.0671004i	−0.999437	−	0.0335502i	$-0.989319\pi$
$487$		−	1.48078i		−	0.0671004i	0.999437	−	0.0335502i	$-0.0106814\pi$
$488$		−	21.5325i		−	0.974729i
$489$	21.1439			0.956160
$490$	1.12225	+	2.63527i	0.0506980	+	0.119049i
$491$	−2.28511			−0.103125			−0.0515627	−	0.998670i	$-0.516420\pi$
$491$	−2.28511			−0.103125			−0.0515627	+	0.998670i	$0.516420\pi$
$492$			1.34600i			0.0606824i
$493$		−	26.4474i		−	1.19113i
$494$	15.2021			0.683976
$495$	−2.05729	+	0.876110i	−0.0924682	+	0.0393782i
$496$	−28.2005			−1.26624
$497$			0.841269i			0.0377361i
$498$		−	12.6524i		−	0.566969i
$499$	−1.60549			−0.0718718			−0.0359359	−	0.999354i	$-0.511441\pi$
$499$	−1.60549			−0.0718718			−0.0359359	+	0.999354i	$0.511441\pi$
$500$	1.42595	−	3.75409i	0.0637706	−	0.167888i
$501$	−16.8639			−0.753422
$502$		−	22.9318i		−	1.02350i
$503$			4.57455i			0.203969i	0.994786	+	0.101984i	$0.0325192\pi$
$503$			4.57455i			0.203969i	−0.994786	+	0.101984i	$0.967481\pi$
$504$	3.02198			0.134610
$505$	−21.2913	+	9.06704i	−0.947450	+	0.403478i
$506$	−5.01023			−0.222732
$507$			5.83394i			0.259094i
$508$		−	3.30425i		−	0.146603i
$509$	3.45483			0.153133			0.0765664	−	0.997064i	$-0.475604\pi$
$509$	3.45483			0.153133			0.0765664	+	0.997064i	$0.475604\pi$
$510$	−7.20891	−	16.9280i	−0.319216	−	0.749585i
$511$	−0.456368			−0.0201885
$512$			25.3773i			1.12153i
$513$		−	2.73466i		−	0.120738i
$514$	13.6004			0.599889
$515$	13.9077	+	32.6582i	0.612848	+	1.43909i
$516$	3.78287			0.166532
$517$		−	11.8241i		−	0.520021i
$518$		−	14.2096i		−	0.624335i
$519$	−21.3369			−0.936584
$520$	−26.9809	+	11.4900i	−1.18319	+	0.503871i
$521$	−35.4825			−1.55452			−0.777258	−	0.629182i	$-0.783390\pi$
$521$	−35.4825			−1.55452			−0.777258	+	0.629182i	$0.783390\pi$
$522$		−	5.27391i		−	0.230833i
$523$		−	33.3559i		−	1.45855i	−0.684219	−	0.729277i	$-0.739857\pi$
$523$		−	33.3559i		−	1.45855i	0.684219	−	0.729277i	$-0.260143\pi$
$524$	7.95557			0.347541
$525$	−3.46486	+	3.60482i	−0.151219	+	0.157327i
$526$	8.23533			0.359077
$527$			57.4600i			2.50300i
$528$			3.15262i			0.137200i
$529$	7.70128			0.334838
$530$	−21.5728	+	9.18692i	−0.937062	+	0.399054i
$531$	−4.77529			−0.207230
$532$			0.982242i			0.0425856i
$533$			16.2630i			0.704429i
$534$	11.1131			0.480910
$535$	15.1587	+	35.5957i	0.655367	+	1.53894i
$536$	−17.6596			−0.762778
$537$			6.41551i			0.276850i
$538$			5.11767i			0.220638i
$539$	−1.00000			−0.0430730
$540$	0.314683	+	0.738942i	0.0135418	+	0.0317990i
$541$	−21.8799			−0.940691			−0.470345	−	0.882482i	$-0.655871\pi$
$541$	−21.8799			−0.940691			−0.470345	+	0.882482i	$0.655871\pi$
$542$		−	37.9705i		−	1.63097i
$543$		−	19.2317i		−	0.825313i
$544$	12.8834			0.552372
$545$	−1.70309	+	0.725274i	−0.0729525	+	0.0310673i
$546$	5.55905			0.237905
$547$			27.3492i			1.16937i	0.811261	+	0.584684i	$0.198781\pi$
$547$			27.3492i			1.16937i	−0.811261	+	0.584684i	$0.801219\pi$
$548$		−	0.260926i		−	0.0111462i
$549$	−7.12528			−0.304100
$550$	−4.61757	−	4.43830i	−0.196894	−	0.189250i
$551$	11.2592			0.479657
$552$			11.8200i			0.503095i
$553$		−	6.39928i		−	0.272125i
$554$	−6.21954			−0.264243
$555$	22.8217	−	9.71876i	0.968725	−	0.412538i
$556$	−2.20494			−0.0935104
$557$			17.0977i			0.724454i	0.932090	+	0.362227i	$0.117983\pi$
$557$			17.0977i			0.724454i	−0.932090	+	0.362227i	$0.882017\pi$
$558$			11.4582i			0.485063i
$559$	45.7064			1.93317
$560$	2.76204	+	6.48585i	0.116718	+	0.274077i
$561$	6.42363			0.271206
$562$			36.3544i			1.53352i
$563$		−	5.05051i		−	0.212853i	−0.994321	−	0.106427i	$-0.966059\pi$
$563$		−	5.05051i		−	0.212853i	0.994321	−	0.106427i	$-0.0339410\pi$
$564$	−4.24699			−0.178831
$565$	3.73631	+	8.77363i	0.157188	+	0.369109i
$566$	23.0875			0.970438
$567$		−	1.00000i		−	0.0419961i
$568$			2.54230i			0.106672i
$569$	−28.9505			−1.21367			−0.606834	−	0.794829i	$-0.707561\pi$
$569$	−28.9505			−1.21367			−0.606834	+	0.794829i	$0.707561\pi$
$570$	7.20657	−	3.06897i	0.301850	−	0.128545i
$571$	5.45680			0.228360			0.114180	−	0.993460i	$-0.463576\pi$
$571$	5.45680			0.228360			0.114180	+	0.993460i	$0.463576\pi$
$572$		−	1.55878i		−	0.0651760i
$573$		−	14.0877i		−	0.588521i
$574$	4.80021			0.200357
$575$	−14.0997	−	13.5523i	−0.588000	−	0.565171i
$576$	8.87434			0.369764
$577$			10.3367i			0.430322i	0.976579	+	0.215161i	$0.0690277\pi$
$577$			10.3367i			0.430322i	−0.976579	+	0.215161i	$0.930972\pi$
$578$			31.0796i			1.29274i
$579$	8.61967			0.358221
$580$	−3.04238	+	1.29562i	−0.126328	+	0.0537976i
$581$	9.87744			0.409785
$582$		−	3.38733i		−	0.140409i
$583$		−	8.18618i		−	0.339037i
$584$	−1.37913			−0.0570690
$585$	3.80215	+	8.92823i	0.157200	+	0.369137i
$586$	−20.9250			−0.864402
$587$		−	44.0783i		−	1.81931i	−0.415368	−	0.909653i	$-0.636347\pi$
$587$		−	44.0783i		−	1.81931i	0.415368	−	0.909653i	$-0.363653\pi$
$588$			0.359182i			0.0148124i
$589$	−24.4618			−1.00793
$590$	−5.35906	−	12.5842i	−0.220629	−	0.518082i
$591$	−4.21976			−0.173578
$592$		−	34.9723i		−	1.43735i
$593$			31.4800i			1.29273i	0.763029	+	0.646365i	$0.223711\pi$
$593$			31.4800i			1.29273i	−0.763029	+	0.646365i	$0.776289\pi$
$594$	1.28094			0.0525578
$595$	13.2153	−	5.62781i	0.541773	−	0.230718i
$596$	−2.21816			−0.0908596
$597$		−	23.6115i		−	0.966356i
$598$			21.7434i			0.889155i
$599$	18.1237			0.740515			0.370257	−	0.928929i	$-0.379269\pi$
$599$	18.1237			0.740515			0.370257	+	0.928929i	$0.379269\pi$
$600$	−10.4707	+	10.8937i	−0.427467	+	0.444733i
$601$	−17.2185			−0.702357			−0.351179	−	0.936308i	$-0.614219\pi$
$601$	−17.2185			−0.702357			−0.351179	+	0.936308i	$0.614219\pi$
$602$		−	13.4908i		−	0.549842i
$603$			5.84372i			0.237974i
$604$	−6.31401			−0.256913
$605$	2.05729	−	0.876110i	0.0836406	−	0.0356189i
$606$	13.2568			0.538519
$607$		−	2.52209i		−	0.102368i	−0.998689	−	0.0511841i	$-0.983700\pi$
$607$		−	2.52209i		−	0.102368i	0.998689	−	0.0511841i	$-0.0162995\pi$
$608$			5.48471i			0.222434i
$609$	4.11721			0.166838
$610$	−7.99633	−	18.7770i	−0.323762	−	0.760260i
$611$	−51.3141			−2.07595
$612$		−	2.30726i		−	0.0932653i
$613$		−	38.6677i		−	1.56177i	−0.624673	−	0.780886i	$-0.714768\pi$
$613$		−	38.6677i		−	1.56177i	0.624673	−	0.780886i	$-0.285232\pi$
$614$	9.74717			0.393364
$615$	3.28314	+	7.70948i	0.132389	+	0.310876i
$616$	−3.02198			−0.121759
$617$			15.2060i			0.612170i	0.952004	+	0.306085i	$0.0990192\pi$
$617$			15.2060i			0.612170i	−0.952004	+	0.306085i	$0.900981\pi$
$618$		−	20.3342i		−	0.817963i
$619$	−29.7726			−1.19666			−0.598332	−	0.801248i	$-0.704170\pi$
$619$	−29.7726			−1.19666			−0.598332	+	0.801248i	$0.704170\pi$
$620$	6.60991	−	2.81487i	0.265460	−	0.113048i
$621$	3.91136			0.156957
$622$		−	7.77651i		−	0.311810i
$623$			8.67569i			0.347584i
$624$	13.6818			0.547710
$625$	−0.989450	−	24.9804i	−0.0395780	−	0.999216i
$626$	27.5315			1.10038
$627$			2.73466i			0.109212i
$628$		−	0.992019i		−	0.0395859i
$629$	−71.2579			−2.84124
$630$	2.63527	−	1.12225i	0.104992	−	0.0447114i
$631$	−33.2184			−1.32240			−0.661201	−	0.750208i	$-0.729953\pi$
$631$	−33.2184			−1.32240			−0.661201	+	0.750208i	$0.729953\pi$
$632$		−	19.3385i		−	0.769245i
$633$		−	11.2812i		−	0.448386i
$634$	11.2328			0.446110
$635$	−8.05966	−	18.9258i	−0.319838	−	0.751045i
$636$	−2.94033			−0.116592
$637$			4.33981i			0.171949i
$638$			5.27391i			0.208796i
$639$	0.841269			0.0332801
$640$	6.44491	+	15.1340i	0.254757	+	0.598223i
$641$	33.4579			1.32151			0.660753	−	0.750603i	$-0.270237\pi$
$641$	33.4579			1.32151			0.660753	+	0.750603i	$0.270237\pi$
$642$		−	22.1632i		−	0.874713i
$643$			13.1810i			0.519810i	0.965634	+	0.259905i	$0.0836912\pi$
$643$			13.1810i			0.519810i	−0.965634	+	0.259905i	$0.916309\pi$
$644$	−1.40489			−0.0553605
$645$	21.6671	−	9.22709i	0.853142	−	0.363316i
$646$	−22.5016			−0.885315
$647$			26.7231i			1.05059i	0.850919	+	0.525296i	$0.176046\pi$
$647$			26.7231i			1.05059i	−0.850919	+	0.525296i	$0.823954\pi$
$648$		−	3.02198i		−	0.118715i
$649$	4.77529			0.187446
$650$	−19.2614	+	20.0394i	−0.755492	+	0.786009i
$651$	−8.94510			−0.350586
$652$			7.59452i			0.297424i
$653$		−	9.78590i		−	0.382952i	−0.981497	−	0.191476i	$-0.938673\pi$
$653$		−	9.78590i		−	0.382952i	0.981497	−	0.191476i	$-0.0613274\pi$
$654$	1.06041			0.0414653
$655$	45.5671	−	19.4050i	1.78045	−	0.758218i
$656$	11.8141			0.461265
$657$			0.456368i			0.0178046i
$658$			15.1460i			0.590451i
$659$	0.159932			0.00623008			0.00311504	−	0.999995i	$-0.499008\pi$
$659$	0.159932			0.00623008			0.00311504	+	0.999995i	$0.499008\pi$
$660$	−0.314683	−	0.738942i	−0.0122490	−	0.0287633i
$661$	−7.90434			−0.307443			−0.153722	−	0.988114i	$-0.549126\pi$
$661$	−7.90434			−0.307443			−0.153722	+	0.988114i	$0.549126\pi$
$662$		−	12.0701i		−	0.469119i
$663$		−	27.8773i		−	1.08267i
$664$	29.8494			1.15838
$665$	2.39586	+	5.62598i	0.0929076	+	0.218166i
$666$	−14.2096			−0.550611
$667$			16.1039i			0.623545i
$668$		−	6.05720i		−	0.234360i
$669$	−19.8197			−0.766273
$670$	−15.3998	+	6.55810i	−0.594945	+	0.253361i
$671$	7.12528			0.275068
$672$			2.00563i			0.0773688i
$673$			32.2661i			1.24377i	0.783110	+	0.621883i	$0.213632\pi$
$673$			32.2661i			1.24377i	−0.783110	+	0.621883i	$0.786368\pi$
$674$	−8.35583			−0.321855
$675$	3.60482	+	3.46486i	0.138750	+	0.133363i
$676$	−2.09545			−0.0805942
$677$			15.6981i			0.603328i	0.953414	+	0.301664i	$0.0975421\pi$
$677$			15.6981i			0.603328i	−0.953414	+	0.301664i	$0.902458\pi$
$678$		−	5.46279i		−	0.209797i
$679$	2.64440			0.101483
$680$	39.9363	−	17.0071i	1.53149	−	0.652194i
$681$	−15.0022			−0.574886
$682$		−	11.4582i		−	0.438756i
$683$		−	4.54250i		−	0.173814i	−0.996216	−	0.0869070i	$-0.972302\pi$
$683$		−	4.54250i		−	0.173814i	0.996216	−	0.0869070i	$-0.0276983\pi$
$684$	0.982242			0.0375570
$685$	−0.636444	−	1.49450i	−0.0243173	−	0.0571020i
$686$	1.28094			0.0489067
$687$		−	16.9868i		−	0.648087i
$688$		−	33.2031i		−	1.26586i
$689$	−35.5265			−1.35345
$690$	4.38951	+	10.3075i	0.167106	+	0.392399i
$691$	−51.7044			−1.96693			−0.983463	−	0.181107i	$-0.942032\pi$
$691$	−51.7044			−1.96693			−0.983463	+	0.181107i	$0.942032\pi$
$692$		−	7.66382i		−	0.291335i
$693$			1.00000i			0.0379869i
$694$	0.113185			0.00429646
$695$	−12.6292	+	5.37825i	−0.479054	+	0.204009i
$696$	12.4421			0.471618
$697$		−	24.0719i		−	0.911789i
$698$			18.3868i			0.695951i
$699$	9.99278			0.377962
$700$	−1.29479	−	1.24452i	−0.0489384	−	0.0470384i
$701$	−11.3567			−0.428938			−0.214469	−	0.976731i	$-0.568802\pi$
$701$	−11.3567			−0.428938			−0.214469	+	0.976731i	$0.568802\pi$
$702$		−	5.55905i		−	0.209813i
$703$		−	30.3358i		−	1.14414i
$704$	−8.87434			−0.334464
$705$	−24.3255	+	10.3592i	−0.916151	+	0.390149i
$706$	6.05660			0.227943
$707$			10.3492i			0.389222i
$708$		−	1.71520i		−	0.0644612i
$709$	−17.1699			−0.644827			−0.322414	−	0.946599i	$-0.604494\pi$
$709$	−17.1699			−0.644827			−0.322414	+	0.946599i	$0.604494\pi$
$710$	0.944112	+	2.21697i	0.0354319	+	0.0832014i
$711$	−6.39928			−0.239992
$712$			26.2178i			0.982553i
$713$		−	34.9875i		−	1.31029i
$714$	−8.22831			−0.307937
$715$	−3.80215	−	8.92823i	−0.142192	−	0.333897i
$716$	−2.30434			−0.0861172
$717$			1.81047i			0.0676131i
$718$			28.0303i			1.04608i
$719$	−9.21717			−0.343743			−0.171871	−	0.985119i	$-0.554981\pi$
$719$	−9.21717			−0.343743			−0.171871	+	0.985119i	$0.554981\pi$
$720$	6.48585	−	2.76204i	0.241713	−	0.102935i
$721$	15.8744			0.591194
$722$			14.7586i			0.549257i
$723$		−	18.7662i		−	0.697922i
$724$	6.90770			0.256723
$725$	−14.2656	+	14.8418i	−0.529810	+	0.551211i
$726$	−1.28094			−0.0475403
$727$		−	1.45530i		−	0.0539741i	−0.999636	−	0.0269871i	$-0.991409\pi$
$727$		−	1.45530i		−	0.0539741i	0.999636	−	0.0269871i	$-0.00859129\pi$
$728$			13.1148i			0.486067i
$729$	−1.00000			−0.0370370
$730$	−1.20265	+	0.512157i	−0.0445121	+	0.0189558i
$731$	−67.6530			−2.50224
$732$		−	2.55928i		−	0.0945936i
$733$			32.9769i			1.21803i	0.793159	+	0.609015i	$0.208435\pi$
$733$			32.9769i			1.21803i	−0.793159	+	0.609015i	$0.791565\pi$
$734$	−6.90650			−0.254924
$735$	0.876110	+	2.05729i	0.0323158	+	0.0758842i
$736$	−7.84473			−0.289160
$737$		−	5.84372i		−	0.215256i
$738$		−	4.80021i		−	0.176698i
$739$	28.5928			1.05180			0.525902	−	0.850545i	$-0.323728\pi$
$739$	28.5928			1.05180			0.525902	+	0.850545i	$0.323728\pi$
$740$	3.49081	+	8.19714i	0.128325	+	0.301333i
$741$	11.8679			0.435978
$742$			10.4860i			0.384955i
$743$		−	37.5333i		−	1.37696i	−0.725254	−	0.688481i	$-0.758278\pi$
$743$		−	37.5333i		−	1.37696i	0.725254	−	0.688481i	$-0.241722\pi$
$744$	−27.0319			−0.991038
$745$	−12.7050	+	5.41050i	−0.465474	+	0.198225i
$746$	24.4340			0.894594
$747$		−	9.87744i		−	0.361396i
$748$			2.30726i			0.0843616i
$749$	17.3023			0.632211
$750$	−5.08535	+	13.3881i	−0.185691	+	0.488865i
$751$	1.59342			0.0581446			0.0290723	−	0.999577i	$-0.490745\pi$
$751$	1.59342			0.0581446			0.0290723	+	0.999577i	$0.490745\pi$
$752$			37.2768i			1.35934i
$753$		−	17.9023i		−	0.652395i
$754$	22.8878			0.833524
$755$	−36.1647	+	15.4010i	−1.31617	+	0.560499i
$756$	0.359182			0.0130633
$757$			2.92997i			0.106492i	0.998581	+	0.0532458i	$0.0169567\pi$
$757$			2.92997i			0.106492i	−0.998581	+	0.0532458i	$0.983043\pi$
$758$		−	44.0637i		−	1.60047i
$759$	−3.91136			−0.141973
$760$	7.24025	+	17.0016i	0.262632	+	0.616713i
$761$	15.0367			0.545080			0.272540	−	0.962144i	$-0.412136\pi$
$761$	15.0367			0.545080			0.272540	+	0.962144i	$0.412136\pi$
$762$			11.7839i			0.426885i
$763$			0.827834i			0.0299696i
$764$	5.06005			0.183066
$765$	−5.62781	−	13.2153i	−0.203474	−	0.477799i
$766$	17.3380			0.626446
$767$		−	20.7238i		−	0.748294i
$768$			8.32570i			0.300428i
$769$	−6.01857			−0.217035			−0.108518	−	0.994095i	$-0.534610\pi$
$769$	−6.01857			−0.217035			−0.108518	+	0.994095i	$0.534610\pi$
$770$	−2.63527	+	1.12225i	−0.0949685	+	0.0404430i
$771$	10.6175			0.382380
$772$			3.09604i			0.111429i
$773$		−	38.7223i		−	1.39275i	−0.717680	−	0.696373i	$-0.754796\pi$
$773$		−	38.7223i		−	1.39275i	0.717680	−	0.696373i	$-0.245204\pi$
$774$	−13.4908			−0.484915
$775$	30.9935	−	32.2455i	1.11332	−	1.15829i
$776$	7.99134			0.286872
$777$		−	11.0931i		−	0.397962i
$778$			16.7617i			0.600937i
$779$	10.2479			0.367168
$780$	−3.20687	+	1.36567i	−0.114824	+	0.0488987i
$781$	−0.841269			−0.0301030
$782$		−	32.1839i		−	1.15089i
$783$		−	4.11721i		−	0.147137i
$784$	3.15262			0.112594
$785$	−2.41971	−	5.68198i	−0.0863632	−	0.202799i
$786$	−28.3718			−1.01199
$787$		−	22.2233i		−	0.792174i	−0.918213	−	0.396087i	$-0.870368\pi$
$787$		−	22.2233i		−	0.792174i	0.918213	−	0.396087i	$-0.129632\pi$
$788$		−	1.51566i		−	0.0539933i
$789$	6.42911			0.228882
$790$	−7.18158	−	16.8638i	−0.255509	−	0.599989i
$791$	4.26466			0.151634
$792$			3.02198i			0.107381i
$793$		−	30.9224i		−	1.09809i
$794$	−48.3021			−1.71418
$795$	−16.8413	+	7.17199i	−0.597300	+	0.254364i
$796$	8.48085			0.300596
$797$			15.3201i			0.542665i	0.962486	+	0.271332i	$0.0874643\pi$
$797$			15.3201i			0.542665i	−0.962486	+	0.271332i	$0.912536\pi$
$798$		−	3.50295i		−	0.124003i
$799$	75.9534			2.68704
$800$	−7.22993	−	6.94923i	−0.255617	−	0.245692i
$801$	8.67569			0.306541
$802$		−	1.51516i		−	0.0535023i
$803$		−	0.456368i		−	0.0161049i
$804$	−2.09896			−0.0740246
$805$	−8.04679	+	3.42678i	−0.283612	+	0.120778i
$806$	−49.7263			−1.75153
$807$			3.99523i			0.140639i
$808$			31.2751i			1.10025i
$809$	39.7396			1.39717			0.698584	−	0.715528i	$-0.253814\pi$
$809$	39.7396			1.39717			0.698584	+	0.715528i	$0.253814\pi$
$810$	−1.12225	−	2.63527i	−0.0394318	−	0.0925939i
$811$	24.0448			0.844326			0.422163	−	0.906520i	$-0.361271\pi$
$811$	24.0448			0.844326			0.422163	+	0.906520i	$0.361271\pi$
$812$			1.47883i			0.0518967i
$813$		−	29.6426i		−	1.03961i
$814$	14.2096			0.498047
$815$	18.5244	+	43.4991i	0.648880	+	1.52371i
$816$	−20.2513			−0.708937
$817$		−	28.8011i		−	1.00762i
$818$			9.14946i			0.319903i
$819$	4.33981			0.151645
$820$	−2.76911	+	1.17924i	−0.0967015	+	0.0411810i
$821$	−3.09181			−0.107905			−0.0539525	−	0.998544i	$-0.517182\pi$
$821$	−3.09181			−0.107905			−0.0539525	+	0.998544i	$0.517182\pi$
$822$			0.930534i			0.0324561i
$823$			48.5002i			1.69061i	0.534283	+	0.845306i	$0.320582\pi$
$823$			48.5002i			1.69061i	−0.534283	+	0.845306i	$0.679418\pi$
$824$	47.9722			1.67119
$825$	−3.60482	−	3.46486i	−0.125504	−	0.120631i
$826$	−6.11688			−0.212833
$827$		−	33.0766i		−	1.15019i	−0.818088	−	0.575093i	$-0.804966\pi$
$827$		−	33.0766i		−	1.15019i	0.818088	−	0.575093i	$-0.195034\pi$
$828$			1.40489i			0.0488233i
$829$	−8.41011			−0.292095			−0.146048	−	0.989278i	$-0.546655\pi$
$829$	−8.41011			−0.292095			−0.146048	+	0.989278i	$0.546655\pi$
$830$	26.0297	−	11.0849i	0.903504	−	0.384764i
$831$	−4.85544			−0.168433
$832$			38.5129i			1.33520i
$833$		−	6.42363i		−	0.222566i
$834$	7.86344			0.272289
$835$	−14.7746	−	34.6938i	−0.511296	−	1.20063i
$836$	−0.982242			−0.0339716
$837$			8.94510i			0.309188i
$838$		−	46.6559i		−	1.61170i
$839$	−29.6188			−1.02255			−0.511277	−	0.859416i	$-0.670828\pi$
$839$	−29.6188			−1.02255			−0.511277	+	0.859416i	$0.670828\pi$
$840$	2.64759	+	6.21708i	0.0913504	+	0.214510i
$841$	−12.0486			−0.415469
$842$			39.7991i			1.37157i
$843$			28.3810i			0.977492i
$844$	4.05200			0.139476
$845$	−12.0021	+	5.11117i	−0.412884	+	0.175830i
$846$	15.1460			0.520729
$847$		−	1.00000i		−	0.0343604i
$848$			25.8079i			0.886248i
$849$	18.0238			0.618575
$850$	28.5100	−	29.6616i	0.977884	−	1.01738i
$851$	43.3890			1.48736
$852$			0.302169i			0.0103521i
$853$		−	36.4936i		−	1.24952i	−0.780818	−	0.624759i	$-0.785197\pi$
$853$		−	36.4936i		−	1.24952i	0.780818	−	0.624759i	$-0.214803\pi$
$854$	−9.12709			−0.312323
$855$	5.62598	−	2.39586i	0.192405	−	0.0819368i
$856$	52.2871			1.78714
$857$			33.2587i			1.13610i	0.822995	+	0.568048i	$0.192301\pi$
$857$			33.2587i			1.13610i	−0.822995	+	0.568048i	$0.807699\pi$
$858$			5.55905i			0.189783i
$859$	−43.1155			−1.47108			−0.735541	−	0.677481i	$-0.763072\pi$
$859$	−43.1155			−1.47108			−0.735541	+	0.677481i	$0.763072\pi$
$860$	3.31421	+	7.78245i	0.113014	+	0.265379i
$861$	3.74740			0.127711
$862$			5.47731i			0.186558i
$863$		−	16.6067i		−	0.565299i	−0.959223	−	0.282650i	$-0.908787\pi$
$863$		−	16.6067i		−	0.565299i	0.959223	−	0.282650i	$-0.0912134\pi$
$864$	2.00563			0.0682328
$865$	−18.6934	−	43.8960i	−0.635596	−	1.49251i
$866$	16.9613			0.576367
$867$			24.2631i			0.824017i
$868$		−	3.21292i		−	0.109054i
$869$	6.39928			0.217081
$870$	10.8500	−	4.62053i	0.367848	−	0.156651i
$871$	−25.3606			−0.859311
$872$			2.50170i			0.0847182i
$873$		−	2.64440i		−	0.0894995i
$874$	13.7013			0.463453
$875$	−10.4518	−	3.97000i	−0.353334	−	0.134211i
$876$	−0.163919			−0.00553832
$877$			26.8882i			0.907950i	0.891014	+	0.453975i	$0.149994\pi$
$877$			26.8882i			0.907950i	−0.891014	+	0.453975i	$0.850006\pi$
$878$			16.8871i			0.569911i
$879$	−16.3356			−0.550985
$880$	−6.48585	+	2.76204i	−0.218638	+	0.0931085i
$881$	−29.8864			−1.00690			−0.503450	−	0.864025i	$-0.667936\pi$
$881$	−29.8864			−1.00690			−0.503450	+	0.864025i	$0.667936\pi$
$882$		−	1.28094i		−	0.0431316i
$883$			21.6465i			0.728462i	0.931309	+	0.364231i	$0.118668\pi$
$883$			21.6465i			0.728462i	−0.931309	+	0.364231i	$0.881332\pi$
$884$	10.0131			0.336775
$885$	−4.18368	−	9.82414i	−0.140633	−	0.330235i
$886$	−14.1322			−0.474780
$887$			50.4897i			1.69528i	0.530574	+	0.847639i	$0.321976\pi$
$887$			50.4897i			1.69528i	−0.530574	+	0.847639i	$0.678024\pi$
$888$		−	33.5231i		−	1.12496i
$889$	−9.19937			−0.308537
$890$	9.73628	+	22.8628i	0.326361	+	0.766363i
$891$	1.00000			0.0335013
$892$		−	7.11888i		−	0.238358i
$893$			32.3348i			1.08204i
$894$	7.91059			0.264570
$895$	−13.1986	+	5.62069i	−0.441179	+	0.187879i
$896$	7.35628			0.245756
$897$			16.9745i			0.566763i
$898$			40.9520i			1.36658i
$899$	−36.8288			−1.22831
$900$	−1.24452	+	1.29479i	−0.0414839	+	0.0431596i
$901$	52.5850			1.75186
$902$			4.80021i			0.159830i
$903$		−	10.5319i		−	0.350479i
$904$	12.8877			0.428639
$905$	39.5652	−	16.8491i	1.31519	−	0.560084i
$906$	22.5175			0.748093
$907$		−	27.1135i		−	0.900289i	−0.892956	−	0.450145i	$-0.851372\pi$
$907$		−	27.1135i		−	0.900289i	0.892956	−	0.450145i	$-0.148628\pi$
$908$		−	5.38853i		−	0.178825i
$909$	10.3492			0.343262
$910$	4.87034	+	11.4366i	0.161450	+	0.379118i
$911$	−14.4981			−0.480345			−0.240172	−	0.970730i	$-0.577204\pi$
$911$	−14.4981			−0.480345			−0.240172	+	0.970730i	$0.577204\pi$
$912$		−	8.62135i		−	0.285482i
$913$			9.87744i			0.326895i
$914$	41.7249			1.38014
$915$	−6.24253	−	14.6588i	−0.206372	−	0.484603i
$916$	6.10137			0.201595
$917$		−	22.1491i		−	0.731428i
$918$			8.22831i			0.271575i
$919$	−50.1482			−1.65424			−0.827119	−	0.562027i	$-0.810022\pi$
$919$	−50.1482			−1.65424			−0.827119	+	0.562027i	$0.810022\pi$
$920$	−24.3172	+	10.3557i	−0.801715	+	0.341416i
$921$	7.60936			0.250737
$922$		−	21.7188i		−	0.715269i
$923$			3.65095i			0.120172i
$924$	−0.359182			−0.0118162
$925$	39.9886	+	38.4360i	1.31482	+	1.26377i
$926$	6.81384			0.223917
$927$		−	15.8744i		−	0.521384i
$928$			8.25759i			0.271069i
$929$	−5.32859			−0.174825			−0.0874127	−	0.996172i	$-0.527860\pi$
$929$	−5.32859			−0.174825			−0.0874127	+	0.996172i	$0.527860\pi$
$930$	−23.5728	+	10.0386i	−0.772981	+	0.329179i
$931$	2.73466			0.0896249
$932$			3.58923i			0.117569i
$933$		−	6.07092i		−	0.198753i
$934$	37.7453			1.23507
$935$	5.62781	+	13.2153i	0.184049	+	0.432185i
$936$	13.1148			0.428671
$937$		−	40.1279i		−	1.31092i	−0.755229	−	0.655461i	$-0.772474\pi$
$937$		−	40.1279i		−	1.31092i	0.755229	−	0.655461i	$-0.227526\pi$
$938$			7.48547i			0.244409i
$939$	21.4932			0.701403
$940$	−3.72083	−	8.73729i	−0.121360	−	0.284979i
$941$	36.7921			1.19939			0.599695	−	0.800229i	$-0.295289\pi$
$941$	36.7921			1.19939			0.599695	+	0.800229i	$0.295289\pi$
$942$			3.53781i			0.115268i
$943$			14.6574i			0.477311i
$944$	−15.0547			−0.489988
$945$	2.05729	−	0.876110i	0.0669236	−	0.0284999i
$946$	13.4908			0.438622
$947$			41.8643i			1.36041i	0.733024	+	0.680203i	$0.238108\pi$
$947$			41.8643i			1.36041i	−0.733024	+	0.680203i	$0.761892\pi$
$948$		−	2.29851i		−	0.0746522i
$949$	−1.98055			−0.0642913
$950$	12.6275	+	12.1372i	0.409690	+	0.393784i
$951$	8.76913			0.284359
$952$		−	19.4121i		−	0.629150i
$953$		−	12.5969i		−	0.408055i	−0.978965	−	0.204028i	$-0.934597\pi$
$953$		−	12.5969i		−	0.408055i	0.978965	−	0.204028i	$-0.0654032\pi$
$954$	10.4860			0.339498
$955$	28.9824	−	12.3423i	0.937848	−	0.399389i
$956$	−0.650288			−0.0210318
$957$			4.11721i			0.133090i
$958$			20.8917i			0.674981i
$959$	−0.726444			−0.0234581
$960$	7.77490	+	18.2571i	0.250934	+	0.589245i
$961$	49.0148			1.58112
$962$		−	61.6670i		−	1.98822i
$963$		−	17.3023i		−	0.557558i
$964$	6.74048			0.217096
$965$	7.55178	+	17.7331i	0.243100	+	0.570850i
$966$	5.01023			0.161201
$967$			7.29163i			0.234483i	0.993103	+	0.117241i	$0.0374052\pi$
$967$			7.29163i			0.234483i	−0.993103	+	0.117241i	$0.962595\pi$
$968$		−	3.02198i		−	0.0971301i
$969$	−17.5665			−0.564316
$970$	6.96872	−	2.96768i	0.223752	−	0.0952864i
$971$	−2.85734			−0.0916963			−0.0458482	−	0.998948i	$-0.514599\pi$
$971$	−2.85734			−0.0916963			−0.0458482	+	0.998948i	$0.514599\pi$
$972$		−	0.359182i		−	0.0115208i
$973$			6.13878i			0.196800i
$974$	−1.89679			−0.0607771
$975$	−15.0368	+	15.6442i	−0.481564	+	0.501016i
$976$	−22.4633			−0.719034
$977$		−	17.6664i		−	0.565199i	−0.959238	−	0.282599i	$-0.908803\pi$
$977$		−	17.6664i		−	0.565199i	0.959238	−	0.282599i	$-0.0911967\pi$
$978$		−	27.0841i		−	0.866055i
$979$	−8.67569			−0.277276
$980$	−0.738942	+	0.314683i	−0.0236046	+	0.0100522i
$981$	0.827834			0.0264307
$982$			2.92709i			0.0934073i
$983$			43.1783i			1.37717i	0.725154	+	0.688586i	$0.241768\pi$
$983$			43.1783i			1.37717i	−0.725154	+	0.688586i	$0.758232\pi$
$984$	11.3246			0.361014
$985$	−3.69697	−	8.68126i	−0.117795	−	0.276608i
$986$	−33.8777			−1.07889
$987$			11.8241i			0.376364i
$988$			4.26274i			0.135616i
$989$	41.1940			1.30989
$990$	1.12225	+	2.63527i	0.0356674	+	0.0837544i
$991$	−29.4281			−0.934814			−0.467407	−	0.884042i	$-0.654812\pi$
$991$	−29.4281			−0.934814			−0.467407	+	0.884042i	$0.654812\pi$
$992$		−	17.9405i		−	0.569613i
$993$		−	9.42284i		−	0.299025i
$994$	1.07762			0.0341800
$995$	48.5757	−	20.6863i	1.53995	−	0.655800i
$996$	3.54780			0.112416
$997$		−	21.3560i		−	0.676352i	−0.941083	−	0.338176i	$-0.890190\pi$
$997$		−	21.3560i		−	0.676352i	0.941083	−	0.338176i	$-0.109810\pi$
$998$			2.05655i			0.0650989i
$999$	−11.0931			−0.350970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.7	✓	20
5.2	odd	4		5775.2.a.cn.1.8		10
5.3	odd	4		5775.2.a.co.1.3		10
5.4	even	2	inner	1155.2.c.f.694.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.7	✓	20	1.1	even	1	trivial
1155.2.c.f.694.14	yes	20	5.4	even	2	inner
5775.2.a.cn.1.8		10	5.2	odd	4
5775.2.a.co.1.3		10	5.3	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.28094i q^{2} -1.00000i q^{3} +0.359182 q^{4} +(2.05729 - 0.876110i) q^{5} -1.28094 q^{6} -1.00000i q^{7} -3.02198i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.28094i q^{2} -1.00000i q^{3} +0.359182 q^{4} +(2.05729 - 0.876110i) q^{5} -1.28094 q^{6} -1.00000i q^{7} -3.02198i q^{8} -1.00000 q^{9} +(-1.12225 - 2.63527i) q^{10} +1.00000 q^{11} -0.359182i q^{12} -4.33981i q^{13} -1.28094 q^{14} +(-0.876110 - 2.05729i) q^{15} -3.15262 q^{16} +6.42363i q^{17} +1.28094i q^{18} -2.73466 q^{19} +(0.738942 - 0.314683i) q^{20} -1.00000 q^{21} -1.28094i q^{22} -3.91136i q^{23} -3.02198 q^{24} +(3.46486 - 3.60482i) q^{25} -5.55905 q^{26} +1.00000i q^{27} -0.359182i q^{28} -4.11721 q^{29} +(-2.63527 + 1.12225i) q^{30} +8.94510 q^{31} -2.00563i q^{32} -1.00000i q^{33} +8.22831 q^{34} +(-0.876110 - 2.05729i) q^{35} -0.359182 q^{36} +11.0931i q^{37} +3.50295i q^{38} -4.33981 q^{39} +(-2.64759 - 6.21708i) q^{40} -3.74740 q^{41} +1.28094i q^{42} +10.5319i q^{43} +0.359182 q^{44} +(-2.05729 + 0.876110i) q^{45} -5.01023 q^{46} -11.8241i q^{47} +3.15262i q^{48} -1.00000 q^{49} +(-4.61757 - 4.43830i) q^{50} +6.42363 q^{51} -1.55878i q^{52} -8.18618i q^{53} +1.28094 q^{54} +(2.05729 - 0.876110i) q^{55} -3.02198 q^{56} +2.73466i q^{57} +5.27391i q^{58} +4.77529 q^{59} +(-0.314683 - 0.738942i) q^{60} +7.12528 q^{61} -11.4582i q^{62} +1.00000i q^{63} -8.87434 q^{64} +(-3.80215 - 8.92823i) q^{65} -1.28094 q^{66} -5.84372i q^{67} +2.30726i q^{68} -3.91136 q^{69} +(-2.63527 + 1.12225i) q^{70} -0.841269 q^{71} +3.02198i q^{72} -0.456368i q^{73} +14.2096 q^{74} +(-3.60482 - 3.46486i) q^{75} -0.982242 q^{76} -1.00000i q^{77} +5.55905i q^{78} +6.39928 q^{79} +(-6.48585 + 2.76204i) q^{80} +1.00000 q^{81} +4.80021i q^{82} +9.87744i q^{83} -0.359182 q^{84} +(5.62781 + 13.2153i) q^{85} +13.4908 q^{86} +4.11721i q^{87} -3.02198i q^{88} -8.67569 q^{89} +(1.12225 + 2.63527i) q^{90} -4.33981 q^{91} -1.40489i q^{92} -8.94510i q^{93} -15.1460 q^{94} +(-5.62598 + 2.39586i) q^{95} -2.00563 q^{96} +2.64440i q^{97} +1.28094i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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