LMFDB - Embedded newform 731.2.d.d.560.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.8
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90092 q^{2} +2.97496i q^{3} +1.61349 q^{4} +1.24660i q^{5} -5.65517i q^{6} -4.11114i q^{7} +0.734723 q^{8} -5.85042 q^{9} +O(q^{10})$	\(q-1.90092 q^{2} +2.97496i q^{3} +1.61349 q^{4} +1.24660i q^{5} -5.65517i q^{6} -4.11114i q^{7} +0.734723 q^{8} -5.85042 q^{9} -2.36968i q^{10} -1.10979i q^{11} +4.80008i q^{12} +5.49572 q^{13} +7.81495i q^{14} -3.70859 q^{15} -4.62363 q^{16} +(-0.277222 + 4.11378i) q^{17} +11.1212 q^{18} +8.40135 q^{19} +2.01137i q^{20} +12.2305 q^{21} +2.10963i q^{22} -3.45536i q^{23} +2.18577i q^{24} +3.44599 q^{25} -10.4469 q^{26} -8.47989i q^{27} -6.63329i q^{28} +1.83216i q^{29} +7.04972 q^{30} +3.35766i q^{31} +7.31970 q^{32} +3.30160 q^{33} +(0.526976 - 7.81995i) q^{34} +5.12494 q^{35} -9.43959 q^{36} -3.35492i q^{37} -15.9703 q^{38} +16.3496i q^{39} +0.915904i q^{40} +0.843138i q^{41} -23.2492 q^{42} -1.00000 q^{43} -1.79064i q^{44} -7.29312i q^{45} +6.56836i q^{46} -7.88113 q^{47} -13.7551i q^{48} -9.90149 q^{49} -6.55055 q^{50} +(-12.2383 - 0.824726i) q^{51} +8.86729 q^{52} +6.03871 q^{53} +16.1196i q^{54} +1.38347 q^{55} -3.02055i q^{56} +24.9937i q^{57} -3.48278i q^{58} +8.31630 q^{59} -5.98377 q^{60} -8.77808i q^{61} -6.38264i q^{62} +24.0519i q^{63} -4.66689 q^{64} +6.85095i q^{65} -6.27607 q^{66} -6.67152 q^{67} +(-0.447295 + 6.63754i) q^{68} +10.2796 q^{69} -9.74210 q^{70} +6.75335i q^{71} -4.29843 q^{72} +9.72765i q^{73} +6.37743i q^{74} +10.2517i q^{75} +13.5555 q^{76} -4.56252 q^{77} -31.0792i q^{78} -10.5257i q^{79} -5.76381i q^{80} +7.67612 q^{81} -1.60274i q^{82} +3.49714 q^{83} +19.7338 q^{84} +(-5.12823 - 0.345584i) q^{85} +1.90092 q^{86} -5.45060 q^{87} -0.815391i q^{88} +2.18136 q^{89} +13.8636i q^{90} -22.5937i q^{91} -5.57519i q^{92} -9.98892 q^{93} +14.9814 q^{94} +10.4731i q^{95} +21.7758i q^{96} +2.51952i q^{97} +18.8219 q^{98} +6.49275i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.90092			−1.34415			−0.672076	−	0.740482i	$-0.734597\pi$
$2$	−1.90092			−1.34415			−0.672076	+	0.740482i	$0.734597\pi$
$3$			2.97496i			1.71760i	0.512314	+	0.858798i	$0.328789\pi$
$3$			2.97496i			1.71760i	−0.512314	+	0.858798i	$0.671211\pi$
$4$	1.61349			0.806745
$5$			1.24660i			0.557496i	0.960364	+	0.278748i	$0.0899194\pi$
$5$			1.24660i			0.557496i	−0.960364	+	0.278748i	$0.910081\pi$
$6$		−	5.65517i		−	2.30871i
$7$		−	4.11114i		−	1.55387i	−0.629583	−	0.776933i	$-0.716774\pi$
$7$		−	4.11114i		−	1.55387i	0.629583	−	0.776933i	$-0.283226\pi$
$8$	0.734723			0.259764
$9$	−5.85042			−1.95014
$10$		−	2.36968i		−	0.749359i
$11$		−	1.10979i		−	0.334615i	−0.985905	−	0.167308i	$-0.946493\pi$
$11$		−	1.10979i		−	0.334615i	0.985905	−	0.167308i	$-0.0535073\pi$
$12$			4.80008i			1.38566i
$13$	5.49572			1.52424			0.762119	−	0.647437i	$-0.224159\pi$
$13$	5.49572			1.52424			0.762119	+	0.647437i	$0.224159\pi$
$14$			7.81495i			2.08863i
$15$	−3.70859			−0.957553
$16$	−4.62363			−1.15591
$17$	−0.277222	+	4.11378i	−0.0672362	+	0.997737i
$17$	−0.277222	+	4.11378i	−0.0672362	+	0.997737i
$18$	11.1212			2.62128
$19$	8.40135			1.92740			0.963701	−	0.266985i	$-0.0860276\pi$
$19$	8.40135			1.92740			0.963701	+	0.266985i	$0.0860276\pi$
$20$			2.01137i			0.449757i
$21$	12.2305			2.66891
$22$			2.10963i			0.449774i
$23$		−	3.45536i		−	0.720493i	−0.932857	−	0.360246i	$-0.882693\pi$
$23$		−	3.45536i		−	0.720493i	0.932857	−	0.360246i	$-0.117307\pi$
$24$			2.18577i			0.446169i
$25$	3.44599			0.689199
$26$	−10.4469			−2.04881
$27$		−	8.47989i		−	1.63195i
$28$		−	6.63329i		−	1.25357i
$29$			1.83216i			0.340223i	0.985425	+	0.170111i	$0.0544127\pi$
$29$			1.83216i			0.340223i	−0.985425	+	0.170111i	$0.945587\pi$
$30$	7.04972			1.28710
$31$			3.35766i			0.603053i	0.953458	+	0.301527i	$0.0974962\pi$
$31$			3.35766i			0.603053i	−0.953458	+	0.301527i	$0.902504\pi$
$32$	7.31970			1.29395
$33$	3.30160			0.574734
$34$	0.526976	−	7.81995i	0.0903757	−	1.34111i
$35$	5.12494			0.866273
$36$	−9.43959			−1.57327
$37$		−	3.35492i		−	0.551545i	−0.961223	−	0.275773i	$-0.911066\pi$
$37$		−	3.35492i		−	0.551545i	0.961223	−	0.275773i	$-0.0889337\pi$
$38$	−15.9703			−2.59072
$39$			16.3496i			2.61803i
$40$			0.915904i			0.144817i
$41$			0.843138i			0.131676i	0.997830	+	0.0658380i	$0.0209720\pi$
$41$			0.843138i			0.131676i	−0.997830	+	0.0658380i	$0.979028\pi$
$42$	−23.2492			−3.58743
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$		−	1.79064i		−	0.269949i
$45$		−	7.29312i		−	1.08719i
$46$			6.56836i			0.968452i
$47$	−7.88113			−1.14958			−0.574790	−	0.818301i	$-0.694916\pi$
$47$	−7.88113			−1.14958			−0.574790	+	0.818301i	$0.694916\pi$
$48$		−	13.7551i		−	1.98538i
$49$	−9.90149			−1.41450
$50$	−6.55055			−0.926388
$51$	−12.2383	−	0.824726i	−1.71371	−	0.115485i
$52$	8.86729			1.22967
$53$	6.03871			0.829480			0.414740	−	0.909940i	$-0.363872\pi$
$53$	6.03871			0.829480			0.414740	+	0.909940i	$0.363872\pi$
$54$			16.1196i			2.19360i
$55$	1.38347			0.186547
$56$		−	3.02055i		−	0.403638i
$57$			24.9937i			3.31050i
$58$		−	3.48278i		−	0.457311i
$59$	8.31630			1.08269			0.541345	−	0.840801i	$-0.317915\pi$
$59$	8.31630			1.08269			0.541345	+	0.840801i	$0.317915\pi$
$60$	−5.98377			−0.772501
$61$		−	8.77808i		−	1.12392i	−0.827165	−	0.561959i	$-0.810048\pi$
$61$		−	8.77808i		−	1.12392i	0.827165	−	0.561959i	$-0.189952\pi$
$62$		−	6.38264i		−	0.810596i
$63$			24.0519i			3.03025i
$64$	−4.66689			−0.583361
$65$			6.85095i			0.849756i
$66$	−6.27607			−0.772530
$67$	−6.67152			−0.815056			−0.407528	−	0.913193i	$-0.633609\pi$
$67$	−6.67152			−0.815056			−0.407528	+	0.913193i	$0.633609\pi$
$68$	−0.447295	+	6.63754i	−0.0542425	+	0.804920i
$69$	10.2796			1.23752
$70$	−9.74210			−1.16440
$71$			6.75335i			0.801476i	0.916193	+	0.400738i	$0.131246\pi$
$71$			6.75335i			0.801476i	−0.916193	+	0.400738i	$0.868754\pi$
$72$	−4.29843			−0.506575
$73$			9.72765i			1.13854i	0.822152	+	0.569268i	$0.192773\pi$
$73$			9.72765i			1.13854i	−0.822152	+	0.569268i	$0.807227\pi$
$74$			6.37743i			0.741361i
$75$			10.2517i			1.18377i
$76$	13.5555			1.55492
$77$	−4.56252			−0.519947
$78$		−	31.0792i		−	3.51903i
$79$		−	10.5257i		−	1.18423i	−0.805853	−	0.592115i	$-0.798293\pi$
$79$		−	10.5257i		−	1.18423i	0.805853	−	0.592115i	$-0.201707\pi$
$80$		−	5.76381i		−	0.644413i
$81$	7.67612			0.852902
$82$		−	1.60274i		−	0.176993i
$83$	3.49714			0.383861			0.191931	−	0.981409i	$-0.438525\pi$
$83$	3.49714			0.383861			0.191931	+	0.981409i	$0.438525\pi$
$84$	19.7338			2.15313
$85$	−5.12823	−	0.345584i	−0.556234	−	0.0374839i
$86$	1.90092			0.204981
$87$	−5.45060			−0.584365
$88$		−	0.815391i		−	0.0869209i
$89$	2.18136			0.231224			0.115612	−	0.993294i	$-0.463117\pi$
$89$	2.18136			0.231224			0.115612	+	0.993294i	$0.463117\pi$
$90$			13.8636i			1.46135i
$91$		−	22.5937i		−	2.36846i
$92$		−	5.57519i		−	0.581254i
$93$	−9.98892			−1.03580
$94$	14.9814			1.54521
$95$			10.4731i			1.07452i
$96$			21.7758i			2.22249i
$97$			2.51952i			0.255818i	0.991786	+	0.127909i	$0.0408266\pi$
$97$			2.51952i			0.255818i	−0.991786	+	0.127909i	$0.959173\pi$
$98$	18.8219			1.90130
$99$			6.49275i			0.652546i
$100$	5.56008			0.556008
$101$	7.44052			0.740359			0.370179	−	0.928960i	$-0.379296\pi$
$101$	7.44052			0.740359			0.370179	+	0.928960i	$0.379296\pi$
$102$	23.2641	+	1.56774i	2.30349	+	0.155229i
$103$	1.28748			0.126859			0.0634294	−	0.997986i	$-0.479796\pi$
$103$	1.28748			0.126859			0.0634294	+	0.997986i	$0.479796\pi$
$104$	4.03783			0.395942
$105$			15.2465i			1.48791i
$106$	−11.4791			−1.11495
$107$			12.8787i			1.24503i	0.782607	+	0.622516i	$0.213890\pi$
$107$			12.8787i			1.24503i	−0.782607	+	0.622516i	$0.786110\pi$
$108$		−	13.6822i		−	1.31657i
$109$			8.05950i			0.771960i	0.922507	+	0.385980i	$0.126137\pi$
$109$			8.05950i			0.771960i	−0.922507	+	0.385980i	$0.873863\pi$
$110$	−2.62986			−0.250747
$111$	9.98077			0.947333
$112$			19.0084i			1.79612i
$113$			3.74565i			0.352361i	0.984358	+	0.176180i	$0.0563742\pi$
$113$			3.74565i			0.352361i	−0.984358	+	0.176180i	$0.943626\pi$
$114$		−	47.5110i		−	4.44981i
$115$	4.30745			0.401672
$116$			2.95616i			0.274473i
$117$	−32.1522			−2.97247
$118$	−15.8086			−1.45530
$119$	16.9123	+	1.13970i	1.55035	+	0.104476i
$120$	−2.72478			−0.248738
$121$	9.76836			0.888033
$122$			16.6864i			1.51072i
$123$	−2.50830			−0.226166
$124$			5.41755i			0.486510i
$125$			10.5288i			0.941721i
$126$		−	45.7207i		−	4.07312i
$127$	19.2180			1.70532			0.852662	−	0.522463i	$-0.174987\pi$
$127$	19.2180			1.70532			0.852662	+	0.522463i	$0.174987\pi$
$128$	−5.76802			−0.509826
$129$		−	2.97496i		−	0.261931i
$130$		−	13.0231i		−	1.14220i
$131$			10.9760i			0.958980i	0.877547	+	0.479490i	$0.159178\pi$
$131$			10.9760i			0.958980i	−0.877547	+	0.479490i	$0.840822\pi$
$132$	5.32709			0.463664
$133$		−	34.5391i		−	2.99492i
$134$	12.6820			1.09556
$135$	10.5710			0.909808
$136$	−0.203681	+	3.02248i	−0.0174655	+	0.259176i
$137$	−18.6309			−1.59175			−0.795873	−	0.605463i	$-0.792988\pi$
$137$	−18.6309			−1.59175			−0.795873	+	0.605463i	$0.792988\pi$
$138$	−19.5406			−1.66341
$139$		−	10.1600i		−	0.861761i	−0.902409	−	0.430881i	$-0.858203\pi$
$139$		−	10.1600i		−	0.861761i	0.902409	−	0.430881i	$-0.141797\pi$
$140$	8.26905			0.698862
$141$		−	23.4461i		−	1.97452i
$142$		−	12.8376i		−	1.07731i
$143$		−	6.09911i		−	0.510033i
$144$	27.0502			2.25418
$145$	−2.28396			−0.189673
$146$		−	18.4915i		−	1.53037i
$147$		−	29.4566i		−	2.42954i
$148$		−	5.41313i		−	0.444957i
$149$	−0.472890			−0.0387407			−0.0193703	−	0.999812i	$-0.506166\pi$
$149$	−0.472890			−0.0387407			−0.0193703	+	0.999812i	$0.506166\pi$
$150$		−	19.4877i		−	1.59116i
$151$	−17.1005			−1.39162			−0.695810	−	0.718226i	$-0.744955\pi$
$151$	−17.1005			−1.39162			−0.695810	+	0.718226i	$0.744955\pi$
$152$	6.17266			0.500669
$153$	1.62186	−	24.0673i	0.131120	−	1.94573i
$154$	8.67298			0.698888
$155$	−4.18565			−0.336200
$156$			26.3799i			2.11208i
$157$	−22.6328			−1.80629			−0.903146	−	0.429334i	$-0.858748\pi$
$157$	−22.6328			−1.80629			−0.903146	+	0.429334i	$0.858748\pi$
$158$			20.0084i			1.59179i
$159$			17.9649i			1.42471i
$160$			9.12472i			0.721372i
$161$	−14.2055			−1.11955
$162$	−14.5917			−1.14643
$163$			23.3785i			1.83114i	0.402155	+	0.915572i	$0.368261\pi$
$163$			23.3785i			1.83114i	−0.402155	+	0.915572i	$0.631739\pi$
$164$			1.36039i			0.106229i
$165$			4.11576i			0.320412i
$166$	−6.64778			−0.515968
$167$		−	25.2447i		−	1.95349i	−0.214396	−	0.976747i	$-0.568778\pi$
$167$		−	25.2447i		−	1.95349i	0.214396	−	0.976747i	$-0.431222\pi$
$168$	8.98603			0.693287
$169$	17.2029			1.32330
$170$	9.74834	+	0.656928i	0.747663	+	0.0503841i
$171$	−49.1514			−3.75870
$172$	−1.61349			−0.123028
$173$			11.1128i			0.844890i	0.906389	+	0.422445i	$0.138828\pi$
$173$			11.1128i			0.844890i	−0.906389	+	0.422445i	$0.861172\pi$
$174$	10.3611			0.785476
$175$		−	14.1670i		−	1.07092i
$176$			5.13127i			0.386784i
$177$			24.7407i			1.85963i
$178$	−4.14659			−0.310800
$179$	15.7030			1.17370			0.586849	−	0.809697i	$-0.300368\pi$
$179$	15.7030			1.17370			0.586849	+	0.809697i	$0.300368\pi$
$180$		−	11.7674i		−	0.877088i
$181$			1.17623i			0.0874286i	0.999044	+	0.0437143i	$0.0139191\pi$
$181$			1.17623i			0.0874286i	−0.999044	+	0.0437143i	$0.986081\pi$
$182$			42.9487i			3.18357i
$183$	26.1145			1.93044
$184$		−	2.53873i		−	0.187158i
$185$	4.18224			0.307484
$186$	18.9881			1.39228
$187$	4.56544	+	0.307659i	0.333858	+	0.0224983i
$188$	−12.7161			−0.927419
$189$	−34.8620			−2.53584
$190$		−	19.9085i		−	1.44432i
$191$	8.73539			0.632071			0.316035	−	0.948747i	$-0.397648\pi$
$191$	8.73539			0.632071			0.316035	+	0.948747i	$0.397648\pi$
$192$		−	13.8838i		−	1.00198i
$193$			3.85380i			0.277402i	0.990334	+	0.138701i	$0.0442928\pi$
$193$			3.85380i			0.277402i	−0.990334	+	0.138701i	$0.955707\pi$
$194$		−	4.78940i		−	0.343859i
$195$	−20.3813			−1.45954
$196$	−15.9760			−1.14114
$197$			2.57620i			0.183546i	0.995780	+	0.0917731i	$0.0292535\pi$
$197$			2.57620i			0.183546i	−0.995780	+	0.0917731i	$0.970747\pi$
$198$		−	12.3422i		−	0.877121i
$199$		−	4.52207i		−	0.320561i	−0.987071	−	0.160281i	$-0.948760\pi$
$199$		−	4.52207i		−	0.320561i	0.987071	−	0.160281i	$-0.0512399\pi$
$200$	2.53185			0.179029
$201$		−	19.8475i		−	1.39994i
$202$	−14.1438			−0.995155
$203$	7.53225			0.528660
$204$	−19.7464	−	1.33069i	−1.38253	−	0.0931667i
$205$	−1.05105			−0.0734088
$206$	−2.44739			−0.170518
$207$			20.2153i			1.40506i
$208$	−25.4102			−1.76188
$209$		−	9.32376i		−	0.644938i
$210$		−	28.9824i		−	1.99998i
$211$		−	27.2931i		−	1.87893i	−0.342642	−	0.939466i	$-0.611322\pi$
$211$		−	27.2931i		−	1.87893i	0.342642	−	0.939466i	$-0.388678\pi$
$212$	9.74340			0.669179
$213$	−20.0910			−1.37661
$214$		−	24.4814i		−	1.67351i
$215$		−	1.24660i		−	0.0850173i
$216$		−	6.23037i		−	0.423923i
$217$	13.8038			0.937064
$218$		−	15.3204i		−	1.03763i
$219$	−28.9394			−1.95554
$220$	2.23221			0.150496
$221$	−1.52353	+	22.6081i	−0.102484	+	1.52079i
$222$	−18.9726			−1.27336
$223$	−0.629403			−0.0421479			−0.0210740	−	0.999778i	$-0.506709\pi$
$223$	−0.629403			−0.0421479			−0.0210740	+	0.999778i	$0.506709\pi$
$224$		−	30.0923i		−	2.01063i
$225$	−20.1605			−1.34403
$226$		−	7.12017i		−	0.473627i
$227$		−	21.1904i		−	1.40646i	−0.710964	−	0.703228i	$-0.751741\pi$
$227$		−	21.1904i		−	1.40646i	0.710964	−	0.703228i	$-0.248259\pi$
$228$			40.3271i			2.67073i
$229$	23.1073			1.52697			0.763486	−	0.645825i	$-0.223486\pi$
$229$	23.1073			1.52697			0.763486	+	0.645825i	$0.223486\pi$
$230$	−8.18811			−0.539908
$231$		−	13.5733i		−	0.893060i
$232$			1.34613i			0.0883775i
$233$			19.6670i			1.28843i	0.764845	+	0.644215i	$0.222816\pi$
$233$			19.6670i			1.28843i	−0.764845	+	0.644215i	$0.777184\pi$
$234$	61.1188			3.99546
$235$		−	9.82460i		−	0.640886i
$236$	13.4183			0.873455
$237$	31.3135			2.03403
$238$	−32.1489	−	2.16647i	−2.08391	−	0.140432i
$239$	20.5965			1.33228			0.666138	−	0.745829i	$-0.267946\pi$
$239$	20.5965			1.33228			0.666138	+	0.745829i	$0.267946\pi$
$240$	17.1471			1.10684
$241$			11.5422i			0.743497i	0.928333	+	0.371749i	$0.121242\pi$
$241$			11.5422i			0.743497i	−0.928333	+	0.371749i	$0.878758\pi$
$242$	−18.5689			−1.19365
$243$		−	2.60348i		−	0.167014i
$244$		−	14.1633i		−	0.906715i
$245$		−	12.3432i		−	0.788577i
$246$	4.76808			0.304002
$247$	46.1714			2.93782
$248$			2.46695i			0.156651i
$249$			10.4039i			0.659319i
$250$		−	20.0143i		−	1.26582i
$251$	−3.02409			−0.190879			−0.0954396	−	0.995435i	$-0.530426\pi$
$251$	−3.02409			−0.190879			−0.0954396	+	0.995435i	$0.530426\pi$
$252$			38.8075i			2.44464i
$253$	−3.83474			−0.241088
$254$	−36.5319			−2.29221
$255$	1.02810	−	15.2563i	0.0643822	−	0.955386i
$256$	20.2983			1.26864
$257$	−20.3887			−1.27181			−0.635907	−	0.771766i	$-0.719374\pi$
$257$	−20.3887			−1.27181			−0.635907	+	0.771766i	$0.719374\pi$
$258$			5.65517i			0.352075i
$259$	−13.7926			−0.857028
$260$			11.0539i			0.685537i
$261$		−	10.7189i		−	0.663481i
$262$		−	20.8645i		−	1.28902i
$263$	12.2122			0.753035			0.376517	−	0.926410i	$-0.377121\pi$
$263$	12.2122			0.753035			0.376517	+	0.926410i	$0.377121\pi$
$264$	2.42576			0.149295
$265$			7.52784i			0.462432i
$266$			65.6561i			4.02563i
$267$			6.48947i			0.397149i
$268$	−10.7644			−0.657543
$269$		−	21.7780i		−	1.32783i	−0.747808	−	0.663915i	$-0.768894\pi$
$269$		−	21.7780i		−	1.32783i	0.747808	−	0.663915i	$-0.231106\pi$
$270$	−20.0946			−1.22292
$271$	−2.04153			−0.124014			−0.0620071	−	0.998076i	$-0.519750\pi$
$271$	−2.04153			−0.124014			−0.0620071	+	0.998076i	$0.519750\pi$
$272$	1.28177	−	19.0206i	0.0777188	−	1.15329i
$273$	67.2154			4.06806
$274$	35.4159			2.13955
$275$		−	3.82434i		−	0.230616i
$276$	16.5860			0.998360
$277$			24.1605i			1.45167i	0.687871	+	0.725833i	$0.258545\pi$
$277$			24.1605i			1.45167i	−0.687871	+	0.725833i	$0.741455\pi$
$278$			19.3134i			1.15834i
$279$		−	19.6437i		−	1.17604i
$280$	3.76541			0.225026
$281$	−11.6725			−0.696321			−0.348160	−	0.937435i	$-0.613193\pi$
$281$	−11.6725			−0.696321			−0.348160	+	0.937435i	$0.613193\pi$
$282$			44.5691i			2.65405i
$283$			19.4354i			1.15532i	0.816279	+	0.577658i	$0.196033\pi$
$283$			19.4354i			1.15532i	−0.816279	+	0.577658i	$0.803967\pi$
$284$			10.8965i			0.646587i
$285$	−31.1571			−1.84559
$286$			11.5939i			0.685562i
$287$	3.46626			0.204607
$288$	−42.8233			−2.52339
$289$	−16.8463	−	2.28086i	−0.990959	−	0.134168i
$290$	4.34162			0.254949
$291$	−7.49547			−0.439392
$292$			15.6955i			0.918508i
$293$	8.11387			0.474018			0.237009	−	0.971508i	$-0.423833\pi$
$293$	8.11387			0.474018			0.237009	+	0.971508i	$0.423833\pi$
$294$			55.9946i			3.26567i
$295$			10.3671i			0.603595i
$296$		−	2.46494i		−	0.143272i
$297$	−9.41092			−0.546077
$298$	0.898926			0.0520734
$299$		−	18.9897i		−	1.09820i
$300$			16.5410i			0.954997i
$301$			4.11114i			0.236962i
$302$	32.5067			1.87055
$303$			22.1353i			1.27164i
$304$	−38.8447			−2.22790
$305$	10.9427			0.626579
$306$	−3.08303	+	45.7500i	−0.176245	+	2.61535i
$307$	28.7371			1.64011			0.820056	−	0.572283i	$-0.193942\pi$
$307$	28.7371			1.64011			0.820056	+	0.572283i	$0.193942\pi$
$308$	−7.36158			−0.419465
$309$			3.83020i			0.217892i
$310$	7.95658			0.451904
$311$		−	31.4137i		−	1.78131i	−0.454681	−	0.890654i	$-0.650247\pi$
$311$		−	31.4137i		−	1.78131i	0.454681	−	0.890654i	$-0.349753\pi$
$312$			12.0124i			0.680068i
$313$			15.8739i			0.897249i	0.893720	+	0.448624i	$0.148086\pi$
$313$			15.8739i			0.897249i	−0.893720	+	0.448624i	$0.851914\pi$
$314$	43.0230			2.42793
$315$	−29.9830			−1.68935
$316$		−	16.9831i		−	0.955372i
$317$			1.82217i			0.102343i	0.998690	+	0.0511717i	$0.0162956\pi$
$317$			1.82217i			0.102343i	−0.998690	+	0.0511717i	$0.983704\pi$
$318$		−	34.1499i		−	1.91503i
$319$	2.03331			0.113844
$320$		−	5.81773i		−	0.325221i
$321$	−38.3137			−2.13846
$322$	27.0035			1.50484
$323$	−2.32904	+	34.5613i	−0.129591	+	1.92304i
$324$	12.3853			0.688075
$325$	18.9382			1.05050
$326$		−	44.4406i		−	2.46134i
$327$	−23.9767			−1.32592
$328$			0.619472i			0.0342046i
$329$			32.4004i			1.78629i
$330$		−	7.82373i		−	0.430682i
$331$	3.13221			0.172162			0.0860810	−	0.996288i	$-0.472566\pi$
$331$	3.13221			0.172162			0.0860810	+	0.996288i	$0.472566\pi$
$332$	5.64260			0.309678
$333$			19.6277i			1.07559i
$334$			47.9881i			2.62579i
$335$		−	8.31671i		−	0.454390i
$336$	−56.5493			−3.08502
$337$		−	16.8231i		−	0.916415i	−0.888845	−	0.458208i	$-0.848492\pi$
$337$		−	16.8231i		−	0.916415i	0.888845	−	0.458208i	$-0.151508\pi$
$338$	−32.7013			−1.77872
$339$	−11.1432			−0.605214
$340$	−8.27434	−	0.557597i	−0.448739	−	0.0302400i
$341$	3.72631			0.201791
$342$	93.4327			5.05226
$343$			11.9284i			0.644075i
$344$	−0.734723			−0.0396136
$345$			12.8145i			0.689910i
$346$		−	21.1245i		−	1.13566i
$347$		−	14.1416i		−	0.759160i	−0.925159	−	0.379580i	$-0.876069\pi$
$347$		−	14.1416i		−	0.759160i	0.925159	−	0.379580i	$-0.123931\pi$
$348$	−8.79449			−0.471434
$349$	4.80977			0.257461			0.128731	−	0.991680i	$-0.458910\pi$
$349$	4.80977			0.257461			0.128731	+	0.991680i	$0.458910\pi$
$350$			26.9302i			1.43948i
$351$		−	46.6031i		−	2.48749i
$352$		−	8.12335i		−	0.432976i
$353$	−19.4920			−1.03745			−0.518727	−	0.854940i	$-0.673594\pi$
$353$	−19.4920			−1.03745			−0.518727	+	0.854940i	$0.673594\pi$
$354$		−	47.0301i		−	2.49962i
$355$	−8.41872			−0.446819
$356$	3.51960			0.186539
$357$	−3.39056	+	50.3135i	−0.179448	+	2.66288i
$358$	−29.8501			−1.57763
$359$	−6.94436			−0.366509			−0.183255	−	0.983066i	$-0.558663\pi$
$359$	−6.94436			−0.366509			−0.183255	+	0.983066i	$0.558663\pi$
$360$		−	5.35842i		−	0.282414i
$361$	51.5826			2.71488
$362$		−	2.23592i		−	0.117517i
$363$			29.0605i			1.52528i
$364$		−	36.4547i		−	1.91074i
$365$	−12.1265			−0.634729
$366$	−49.6415			−2.59480
$367$		−	2.13183i		−	0.111281i	−0.998451	−	0.0556403i	$-0.982280\pi$
$367$		−	2.13183i		−	0.111281i	0.998451	−	0.0556403i	$-0.0177200\pi$
$368$			15.9763i			0.832823i
$369$		−	4.93270i		−	0.256786i
$370$	−7.95009			−0.413306
$371$		−	24.8260i		−	1.28890i
$372$	−16.1170			−0.835629
$373$	0.0383465			0.00198551			0.000992753	−	1.00000i	$-0.499684\pi$
$373$	0.0383465			0.00198551			0.000992753		1.00000i	$0.499684\pi$
$374$	−8.67853	−	0.584835i	−0.448756	−	0.0302411i
$375$	−31.3227			−1.61750
$376$	−5.79045			−0.298619
$377$			10.0690i			0.518580i
$378$	66.2699			3.40855
$379$			0.663889i			0.0341017i	0.999855	+	0.0170508i	$0.00542772\pi$
$379$			0.663889i			0.0341017i	−0.999855	+	0.0170508i	$0.994572\pi$
$380$			16.8983i			0.866862i
$381$			57.1729i			2.92906i
$382$	−16.6053			−0.849599
$383$	22.0244			1.12539			0.562697	−	0.826663i	$-0.309764\pi$
$383$	22.0244			1.12539			0.562697	+	0.826663i	$0.309764\pi$
$384$		−	17.1597i		−	0.875675i
$385$		−	5.68763i		−	0.289868i
$386$		−	7.32575i		−	0.372871i
$387$	5.85042			0.297393
$388$			4.06522i			0.206380i
$389$	−3.73584			−0.189415			−0.0947074	−	0.995505i	$-0.530192\pi$
$389$	−3.73584			−0.189415			−0.0947074	+	0.995505i	$0.530192\pi$
$390$	38.7433			1.96184
$391$	14.2146	+	0.957902i	0.718862	+	0.0484432i
$392$	−7.27485			−0.367436
$393$	−32.6533			−1.64714
$394$		−	4.89714i		−	0.246714i
$395$	13.1213			0.660203
$396$			10.4760i			0.526439i
$397$		−	26.6637i		−	1.33821i	−0.743166	−	0.669107i	$-0.766677\pi$
$397$		−	26.6637i		−	1.33821i	0.743166	−	0.669107i	$-0.233323\pi$
$398$			8.59609i			0.430883i
$399$	102.753			5.14407
$400$	−15.9330			−0.796650
$401$			17.7191i			0.884850i	0.896806	+	0.442425i	$0.145882\pi$
$401$			17.7191i			0.884850i	−0.896806	+	0.442425i	$0.854118\pi$
$402$			37.7286i			1.88173i
$403$			18.4527i			0.919197i
$404$	12.0052			0.597281
$405$			9.56903i			0.475489i
$406$	−14.3182			−0.710600
$407$	−3.72327			−0.184556
$408$	−8.99179	−	0.605945i	−0.445160	−	0.0299987i
$409$	−16.2171			−0.801885			−0.400943	−	0.916103i	$-0.631317\pi$
$409$	−16.2171			−0.801885			−0.400943	+	0.916103i	$0.631317\pi$
$410$	1.99797			0.0986726
$411$		−	55.4263i		−	2.73398i
$412$	2.07733			0.102343
$413$		−	34.1895i		−	1.68236i
$414$		−	38.4276i		−	1.88862i
$415$			4.35953i			0.214001i
$416$	40.2270			1.97229
$417$	30.2257			1.48016
$418$			17.7237i			0.866895i
$419$			2.21972i			0.108440i	0.998529	+	0.0542201i	$0.0172673\pi$
$419$			2.21972i			0.108440i	−0.998529	+	0.0542201i	$0.982733\pi$
$420$			24.6001i			1.20036i
$421$	−18.1349			−0.883841			−0.441920	−	0.897054i	$-0.645703\pi$
$421$	−18.1349			−0.883841			−0.441920	+	0.897054i	$0.645703\pi$
$422$			51.8819i			2.52557i
$423$	46.1079			2.24184
$424$	4.43678			0.215469
$425$	−0.955305	+	14.1760i	−0.0463391	+	0.687639i
$426$	38.1913			1.85038
$427$	−36.0879			−1.74642
$428$			20.7797i			1.00442i
$429$	18.1446			0.876032
$430$			2.36968i			0.114276i
$431$			6.98546i			0.336478i	0.985746	+	0.168239i	$0.0538080\pi$
$431$			6.98546i			0.336478i	−0.985746	+	0.168239i	$0.946192\pi$
$432$			39.2079i			1.88639i
$433$	−40.3787			−1.94048			−0.970238	−	0.242153i	$-0.922146\pi$
$433$	−40.3787			−1.94048			−0.970238	+	0.242153i	$0.922146\pi$
$434$	−26.2399			−1.25956
$435$		−	6.79470i		−	0.325781i
$436$			13.0039i			0.622775i
$437$		−	29.0297i		−	1.38868i
$438$	55.0115			2.62855
$439$			6.16913i			0.294437i	0.989104	+	0.147218i	$0.0470320\pi$
$439$			6.16913i			0.294437i	−0.989104	+	0.147218i	$0.952968\pi$
$440$	1.01646			0.0484580
$441$	57.9278			2.75847
$442$	2.89611	−	42.9762i	0.137754	−	2.04417i
$443$	7.83374			0.372192			0.186096	−	0.982532i	$-0.440416\pi$
$443$	7.83374			0.372192			0.186096	+	0.982532i	$0.440416\pi$
$444$	16.1039			0.764256
$445$			2.71928i			0.128906i
$446$	1.19644			0.0566533
$447$		−	1.40683i		−	0.0665409i
$448$			19.1862i			0.906464i
$449$		−	23.5285i		−	1.11038i	−0.831724	−	0.555190i	$-0.812646\pi$
$449$		−	23.5285i		−	1.11038i	0.831724	−	0.555190i	$-0.187354\pi$
$450$	38.3234			1.80658
$451$	0.935708			0.0440608
$452$			6.04357i			0.284265i
$453$		−	50.8734i		−	2.39024i
$454$			40.2812i			1.89049i
$455$	28.1652			1.32041
$456$			18.3635i			0.859947i
$457$	−27.8695			−1.30368			−0.651840	−	0.758357i	$-0.726002\pi$
$457$	−27.8695			−1.30368			−0.651840	+	0.758357i	$0.726002\pi$
$458$	−43.9250			−2.05248
$459$	34.8843	+	2.35081i	1.62826	+	0.109726i
$460$	6.95003			0.324047
$461$	−12.9678			−0.603970			−0.301985	−	0.953313i	$-0.597649\pi$
$461$	−12.9678			−0.603970			−0.301985	+	0.953313i	$0.597649\pi$
$462$			25.8018i			1.20041i
$463$	−12.6666			−0.588669			−0.294334	−	0.955703i	$-0.595098\pi$
$463$	−12.6666			−0.588669			−0.294334	+	0.955703i	$0.595098\pi$
$464$		−	8.47121i		−	0.393266i
$465$		−	12.4522i		−	0.577455i
$466$		−	37.3854i		−	1.73185i
$467$	−36.5826			−1.69284			−0.846419	−	0.532517i	$-0.821246\pi$
$467$	−36.5826			−1.69284			−0.846419	+	0.532517i	$0.821246\pi$
$468$	−51.8773			−2.39803
$469$			27.4276i			1.26649i
$470$			18.6758i			0.861449i
$471$		−	67.3317i		−	3.10248i
$472$	6.11018			0.281244
$473$			1.10979i			0.0510284i
$474$	−59.5244			−2.73405
$475$	28.9510			1.32836
$476$	27.2879	+	1.83889i	1.25074	+	0.0842856i
$477$	−35.3290			−1.61760
$478$	−39.1522			−1.79078
$479$		−	9.00865i		−	0.411616i	−0.978592	−	0.205808i	$-0.934018\pi$
$479$		−	9.00865i		−	0.411616i	0.978592	−	0.205808i	$-0.0659822\pi$
$480$	−27.1457			−1.23903
$481$		−	18.4377i		−	0.840686i
$482$		−	21.9408i		−	0.999374i
$483$		−	42.2608i		−	1.92293i
$484$	15.7612			0.716416
$485$	−3.14083			−0.142618
$486$			4.94901i			0.224492i
$487$		−	6.20798i		−	0.281310i	−0.990059	−	0.140655i	$-0.955079\pi$
$487$		−	6.20798i		−	0.281310i	0.990059	−	0.140655i	$-0.0449209\pi$
$488$		−	6.44945i		−	0.291953i
$489$	−69.5501			−3.14517
$490$			23.4634i			1.05997i
$491$	12.7631			0.575990			0.287995	−	0.957632i	$-0.407011\pi$
$491$	12.7631			0.575990			0.287995	+	0.957632i	$0.407011\pi$
$492$	−4.04713			−0.182459
$493$	−7.53707	−	0.507914i	−0.339453	−	0.0228753i
$494$	−87.7681			−3.94887
$495$	−8.09385			−0.363792
$496$		−	15.5246i		−	0.697074i
$497$	27.7640			1.24539
$498$		−	19.7769i		−	0.886224i
$499$			22.8754i			1.02404i	0.858972	+	0.512022i	$0.171103\pi$
$499$			22.8754i			1.02404i	−0.858972	+	0.512022i	$0.828897\pi$
$500$			16.9881i			0.759729i
$501$	75.1021			3.35531
$502$	5.74856			0.256571
$503$		−	37.0364i		−	1.65137i	−0.564129	−	0.825687i	$-0.690788\pi$
$503$		−	37.0364i		−	1.65137i	0.564129	−	0.825687i	$-0.309212\pi$
$504$			17.6715i			0.787150i
$505$			9.27533i			0.412747i
$506$	7.28952			0.324059
$507$			51.1781i			2.27290i
$508$	31.0081			1.37576
$509$	8.60869			0.381573			0.190787	−	0.981632i	$-0.438896\pi$
$509$	8.60869			0.381573			0.190787	+	0.981632i	$0.438896\pi$
$510$	−1.95434	+	29.0010i	−0.0865395	+	1.28418i
$511$	39.9918			1.76913
$512$	−27.0494			−1.19543
$513$		−	71.2425i		−	3.14543i
$514$	38.7573			1.70951
$515$			1.60497i			0.0707232i
$516$		−	4.80008i		−	0.211312i
$517$			8.74642i			0.384667i
$518$	26.2185			1.15198
$519$	−33.0601			−1.45118
$520$			5.03355i			0.220736i
$521$		−	24.9224i		−	1.09187i	−0.837827	−	0.545935i	$-0.816174\pi$
$521$		−	24.9224i		−	1.09187i	0.837827	−	0.545935i	$-0.183826\pi$
$522$			20.3757i			0.891820i
$523$	25.3151			1.10695			0.553475	−	0.832865i	$-0.313301\pi$
$523$	25.3151			1.10695			0.553475	+	0.832865i	$0.313301\pi$
$524$			17.7097i			0.773653i
$525$	42.1462			1.83941
$526$	−23.2143			−1.01219
$527$	−13.8127	−	0.930817i	−0.601689	−	0.0405470i
$528$	−15.2654			−0.664339
$529$	11.0605			0.480890
$530$		−	14.3098i		−	0.621579i
$531$	−48.6538			−2.11140
$532$		−	55.7286i		−	2.41614i
$533$			4.63365i			0.200705i
$534$		−	12.3359i		−	0.533829i
$535$	−16.0546			−0.694100
$536$	−4.90172			−0.211722
$537$			46.7159i			2.01594i
$538$			41.3982i			1.78480i
$539$			10.9886i			0.473313i
$540$	17.0562			0.733983
$541$		−	24.4873i		−	1.05279i	−0.850240	−	0.526395i	$-0.823543\pi$
$541$		−	24.4873i		−	1.05279i	0.850240	−	0.526395i	$-0.176457\pi$
$542$	3.88079			0.166694
$543$	−3.49925			−0.150167
$544$	−2.02918	+	30.1116i	−0.0870004	+	1.29102i
$545$	−10.0470			−0.430364
$546$	−127.771			−5.46809
$547$		−	30.2863i		−	1.29495i	−0.762087	−	0.647475i	$-0.775825\pi$
$547$		−	30.2863i		−	1.29495i	0.762087	−	0.647475i	$-0.224175\pi$
$548$	−30.0608			−1.28413
$549$			51.3554i			2.19179i
$550$			7.26976i			0.309984i
$551$			15.3926i			0.655746i
$552$	7.55264			0.321462
$553$	−43.2725			−1.84014
$554$		−	45.9272i		−	1.95126i
$555$			12.4420i			0.528134i
$556$		−	16.3931i		−	0.695222i
$557$	−45.1760			−1.91417			−0.957084	−	0.289810i	$-0.906408\pi$
$557$	−45.1760			−1.91417			−0.957084	+	0.289810i	$0.906408\pi$
$558$			37.3411i			1.58077i
$559$	−5.49572			−0.232444
$560$	−23.6958			−1.00133
$561$	−0.915275	+	13.5820i	−0.0386429	+	0.573434i
$562$	22.1884			0.935961
$563$	−37.4521			−1.57842			−0.789209	−	0.614125i	$-0.789509\pi$
$563$	−37.4521			−1.57842			−0.789209	+	0.614125i	$0.789509\pi$
$564$		−	37.8300i		−	1.59293i
$565$	−4.66932			−0.196440
$566$		−	36.9452i		−	1.55292i
$567$		−	31.5576i		−	1.32529i
$568$			4.96184i			0.208194i
$569$	−15.1128			−0.633561			−0.316780	−	0.948499i	$-0.602602\pi$
$569$	−15.1128			−0.633561			−0.316780	+	0.948499i	$0.602602\pi$
$570$	59.2271			2.48075
$571$		−	1.22584i		−	0.0512998i	−0.999671	−	0.0256499i	$-0.991834\pi$
$571$		−	1.22584i		−	0.0512998i	0.999671	−	0.0256499i	$-0.00816551\pi$
$572$		−	9.84086i		−	0.411467i
$573$			25.9875i			1.08564i
$574$	−6.58907			−0.275023
$575$		−	11.9071i		−	0.496562i
$576$	27.3032			1.13763
$577$	−9.39602			−0.391161			−0.195581	−	0.980688i	$-0.562659\pi$
$577$	−9.39602			−0.391161			−0.195581	+	0.980688i	$0.562659\pi$
$578$	32.0234	+	4.33572i	1.33200	+	0.180342i
$579$	−11.4649			−0.476465
$580$	−3.68515			−0.153018
$581$		−	14.3772i		−	0.596469i
$582$	14.2483			0.590610
$583$		−	6.70172i		−	0.277557i
$584$			7.14713i			0.295750i
$585$		−	40.0809i		−	1.65714i
$586$	−15.4238			−0.637152
$587$	−27.1728			−1.12154			−0.560771	−	0.827971i	$-0.689495\pi$
$587$	−27.1728			−1.12154			−0.560771	+	0.827971i	$0.689495\pi$
$588$		−	47.5279i		−	1.96002i
$589$			28.2089i			1.16233i
$590$		−	19.7070i		−	0.811324i
$591$	−7.66409			−0.315259
$592$			15.5119i			0.637535i
$593$	28.1250			1.15496			0.577478	−	0.816406i	$-0.304037\pi$
$593$	28.1250			1.15496			0.577478	+	0.816406i	$0.304037\pi$
$594$	17.8894			0.734011
$595$	−1.42075	+	21.0829i	−0.0582449	+	0.864313i
$596$	−0.763004			−0.0312539
$597$	13.4530			0.550595
$598$			36.0978i			1.47615i
$599$	−41.8565			−1.71021			−0.855105	−	0.518455i	$-0.826507\pi$
$599$	−41.8565			−1.71021			−0.855105	+	0.518455i	$0.826507\pi$
$600$			7.53216i			0.307499i
$601$		−	33.8784i		−	1.38193i	−0.722890	−	0.690964i	$-0.757187\pi$
$601$		−	33.8784i		−	1.38193i	0.722890	−	0.690964i	$-0.242813\pi$
$602$		−	7.81495i		−	0.318513i
$603$	39.0312			1.58947
$604$	−27.5915			−1.12268
$605$			12.1772i			0.495074i
$606$		−	42.0773i		−	1.70928i
$607$			5.11768i			0.207720i	0.994592	+	0.103860i	$0.0331194\pi$
$607$			5.11768i			0.207720i	−0.994592	+	0.103860i	$0.966881\pi$
$608$	61.4953			2.49396
$609$			22.4082i			0.908025i
$610$	−20.8012			−0.842218
$611$	−43.3125			−1.75223
$612$	2.61686	−	38.8324i	0.105780	−	1.56970i
$613$	−1.59672			−0.0644910			−0.0322455	−	0.999480i	$-0.510266\pi$
$613$	−1.59672			−0.0644910			−0.0322455	+	0.999480i	$0.510266\pi$
$614$	−54.6269			−2.20456
$615$		−	3.12685i		−	0.126087i
$616$	−3.35219			−0.135063
$617$			14.6284i			0.588919i	0.955664	+	0.294459i	$0.0951396\pi$
$617$			14.6284i			0.588919i	−0.955664	+	0.294459i	$0.904860\pi$
$618$		−	7.28089i		−	0.292880i
$619$		−	19.2775i		−	0.774827i	−0.921906	−	0.387413i	$-0.873369\pi$
$619$		−	19.2775i		−	0.774827i	0.921906	−	0.387413i	$-0.126631\pi$
$620$	−6.75351			−0.271227
$621$	−29.3011			−1.17581
$622$			59.7149i			2.39435i
$623$		−	8.96788i		−	0.359290i
$624$		−	75.5943i		−	3.02620i
$625$	4.10483			0.164193
$626$		−	30.1751i		−	1.20604i
$627$	27.7379			1.10774
$628$	−36.5178			−1.45722
$629$	13.8014	+	0.930058i	0.550297	+	0.0370838i
$630$	56.9953			2.27075
$631$	34.6217			1.37827			0.689134	−	0.724634i	$-0.257991\pi$
$631$	34.6217			1.37827			0.689134	+	0.724634i	$0.257991\pi$
$632$		−	7.73345i		−	0.307620i
$633$	81.1959			3.22725
$634$		−	3.46380i		−	0.137565i
$635$			23.9572i			0.950711i
$636$			28.9863i			1.14938i
$637$	−54.4158			−2.15603
$638$	−3.86516			−0.153023
$639$		−	39.5099i		−	1.56299i
$640$		−	7.19041i		−	0.284226i
$641$		−	24.0135i		−	0.948476i	−0.880397	−	0.474238i	$-0.842724\pi$
$641$		−	24.0135i		−	0.948476i	0.880397	−	0.474238i	$-0.157276\pi$
$642$	72.8313			2.87442
$643$			17.7255i			0.699026i	0.936931	+	0.349513i	$0.113653\pi$
$643$			17.7255i			0.699026i	−0.936931	+	0.349513i	$0.886347\pi$
$644$	−22.9204			−0.903191
$645$	3.70859			0.146025
$646$	4.42731	−	65.6981i	0.174190	−	2.58486i
$647$	−23.6388			−0.929339			−0.464669	−	0.885484i	$-0.653827\pi$
$647$	−23.6388			−0.929339			−0.464669	+	0.885484i	$0.653827\pi$
$648$	5.63982			0.221553
$649$		−	9.22938i		−	0.362285i
$650$	−36.0000			−1.41204
$651$			41.0659i			1.60950i
$652$			37.7209i			1.47727i
$653$		−	41.7525i		−	1.63390i	−0.576707	−	0.816951i	$-0.695663\pi$
$653$		−	41.7525i		−	1.63390i	0.576707	−	0.816951i	$-0.304337\pi$
$654$	45.5778			1.78223
$655$	−13.6827			−0.534627
$656$		−	3.89836i		−	0.152205i
$657$		−	56.9108i		−	2.22030i
$658$		−	61.5906i		−	2.40105i
$659$	−14.8431			−0.578203			−0.289102	−	0.957298i	$-0.593357\pi$
$659$	−14.8431			−0.578203			−0.289102	+	0.957298i	$0.593357\pi$
$660$			6.64075i			0.258491i
$661$	43.1426			1.67805			0.839026	−	0.544091i	$-0.183125\pi$
$661$	43.1426			1.67805			0.839026	+	0.544091i	$0.183125\pi$
$662$	−5.95408			−0.231412
$663$	−67.2584	−	4.53246i	−2.61210	−	0.176026i
$664$	2.56943			0.0997132
$665$	43.0564			1.66966
$666$		−	37.3106i		−	1.44576i
$667$	6.33076			0.245128
$668$		−	40.7321i		−	1.57597i
$669$		−	1.87245i		−	0.0723932i
$670$			15.8094i			0.610770i
$671$	−9.74185			−0.376080
$672$	89.5236			3.45345
$673$		−	27.4313i		−	1.05740i	−0.848809	−	0.528700i	$-0.822680\pi$
$673$		−	27.4313i		−	1.05740i	0.848809	−	0.528700i	$-0.177320\pi$
$674$			31.9794i			1.23180i
$675$		−	29.2216i		−	1.12474i
$676$	27.7567			1.06757
$677$			45.0014i			1.72954i	0.502165	+	0.864772i	$0.332537\pi$
$677$			45.0014i			1.72954i	−0.502165	+	0.864772i	$0.667463\pi$
$678$	21.1823			0.813500
$679$	10.3581			0.397507
$680$	−3.76782	−	0.253909i	−0.144489	−	0.00973696i
$681$	63.0407			2.41572
$682$	−7.08341			−0.271238
$683$			11.2708i			0.431263i	0.976475	+	0.215632i	$0.0691810\pi$
$683$			11.2708i			0.431263i	−0.976475	+	0.215632i	$0.930819\pi$
$684$	−79.3053			−3.03231
$685$		−	23.2253i		−	0.887392i
$686$		−	22.6750i		−	0.865735i
$687$			68.7433i			2.62272i
$688$	4.62363			0.176274
$689$	33.1870			1.26433
$690$		−	24.3593i		−	0.927344i
$691$			14.6577i			0.557607i	0.960348	+	0.278804i	$0.0899378\pi$
$691$			14.6577i			0.557607i	−0.960348	+	0.278804i	$0.910062\pi$
$692$			17.9304i			0.681611i
$693$	26.6926			1.01397
$694$			26.8820i			1.02043i
$695$	12.6655			0.480428
$696$	−4.00468			−0.151797
$697$	−3.46848	−	0.233736i	−0.131378	−	0.00885339i
$698$	−9.14298			−0.346067
$699$	−58.5087			−2.21300
$700$		−	22.8583i		−	0.863961i
$701$	−18.9092			−0.714192			−0.357096	−	0.934068i	$-0.616233\pi$
$701$	−18.9092			−0.714192			−0.357096	+	0.934068i	$0.616233\pi$
$702$			88.5886i			3.34356i
$703$		−	28.1858i		−	1.06305i
$704$			5.17928i			0.195201i
$705$	29.2278			1.10078
$706$	37.0527			1.39450
$707$		−	30.5890i		−	1.15042i
$708$			39.9189i			1.50024i
$709$			39.0119i			1.46512i	0.680702	+	0.732560i	$0.261675\pi$
$709$			39.0119i			1.46512i	−0.680702	+	0.732560i	$0.738325\pi$
$710$	16.0033			0.600593
$711$			61.5796i			2.30941i
$712$	1.60269			0.0600635
$713$	11.6019			0.434495
$714$	6.44519	−	95.6419i	0.241205	−	3.57931i
$715$	7.60314			0.284341
$716$	25.3366			0.946875
$717$			61.2738i			2.28831i
$718$	13.2007			0.492644
$719$		−	12.4705i		−	0.465073i	−0.972588	−	0.232536i	$-0.925298\pi$
$719$		−	12.4705i		−	0.465073i	0.972588	−	0.232536i	$-0.0747025\pi$
$720$			33.7207i			1.25670i
$721$		−	5.29300i		−	0.197122i
$722$	−98.0544			−3.64921
$723$	−34.3376			−1.27703
$724$			1.89784i			0.0705326i
$725$			6.31359i			0.234481i
$726$		−	55.2417i		−	2.05021i
$727$	1.57869			0.0585504			0.0292752	−	0.999571i	$-0.490680\pi$
$727$	1.57869			0.0585504			0.0292752	+	0.999571i	$0.490680\pi$
$728$		−	16.6001i		−	0.615240i
$729$	30.7736			1.13976
$730$	23.0514			0.853172
$731$	0.277222	−	4.11378i	0.0102534	−	0.152153i
$732$	42.1354			1.55737
$733$	−22.4620			−0.829654			−0.414827	−	0.909900i	$-0.636158\pi$
$733$	−22.4620			−0.829654			−0.414827	+	0.909900i	$0.636158\pi$
$734$			4.05243i			0.149578i
$735$	36.7205			1.35446
$736$		−	25.2922i		−	0.932283i
$737$			7.40401i			0.272730i
$738$			9.37667i			0.345160i
$739$	−30.6777			−1.12850			−0.564249	−	0.825605i	$-0.690834\pi$
$739$	−30.6777			−1.12850			−0.564249	+	0.825605i	$0.690834\pi$
$740$	6.74800			0.248061
$741$			137.358i			5.04599i
$742$			47.1922i			1.73248i
$743$			34.1975i			1.25458i	0.778784	+	0.627292i	$0.215837\pi$
$743$			34.1975i			1.25458i	−0.778784	+	0.627292i	$0.784163\pi$
$744$	−7.33909			−0.269064
$745$		−	0.589504i		−	0.0215978i
$746$	−0.0728935			−0.00266882
$747$	−20.4597			−0.748582
$748$	7.36630	+	0.496405i	0.269338	+	0.0181504i
$749$	52.9463			1.93461
$750$	59.5419			2.17416
$751$			27.0975i			0.988803i	0.869234	+	0.494402i	$0.164613\pi$
$751$			27.0975i			0.988803i	−0.869234	+	0.494402i	$0.835387\pi$
$752$	36.4394			1.32881
$753$		−	8.99658i		−	0.327853i
$754$		−	19.1404i		−	0.697051i
$755$		−	21.3175i		−	0.775823i
$756$	−56.2495			−2.04578
$757$	−19.7524			−0.717914			−0.358957	−	0.933354i	$-0.616868\pi$
$757$	−19.7524			−0.717914			−0.358957	+	0.933354i	$0.616868\pi$
$758$		−	1.26200i		−	0.0458379i
$759$		−	11.4082i		−	0.414092i
$760$			7.69483i			0.279121i
$761$	24.3702			0.883420			0.441710	−	0.897158i	$-0.354372\pi$
$761$	24.3702			0.883420			0.441710	+	0.897158i	$0.354372\pi$
$762$		−	108.681i		−	3.93710i
$763$	33.1337			1.19952
$764$	14.0945			0.509920
$765$	30.0022	+	2.02181i	1.08473	+	0.0730988i
$766$	−41.8666			−1.51270
$767$	45.7040			1.65028
$768$			60.3868i			2.17902i
$769$	−13.5182			−0.487477			−0.243739	−	0.969841i	$-0.578374\pi$
$769$	−13.5182			−0.487477			−0.243739	+	0.969841i	$0.578374\pi$
$770$			10.8117i			0.389627i
$771$		−	60.6557i		−	2.18446i
$772$			6.21806i			0.223793i
$773$	−4.03566			−0.145153			−0.0725763	−	0.997363i	$-0.523122\pi$
$773$	−4.03566			−0.145153			−0.0725763	+	0.997363i	$0.523122\pi$
$774$	−11.1212			−0.399742
$775$			11.5705i			0.415624i
$776$			1.85115i			0.0664523i
$777$		−	41.0324i		−	1.47203i
$778$	7.10154			0.254602
$779$			7.08349i			0.253792i
$780$	−32.8851			−1.17748
$781$	7.49483			0.268186
$782$	−27.0208	−	1.82089i	−0.966260	−	0.0651150i
$783$	15.5365			0.555228
$784$	45.7808			1.63503
$785$		−	28.2140i		−	1.00700i
$786$	62.0712			2.21401
$787$		−	44.4258i		−	1.58361i	−0.610775	−	0.791805i	$-0.709142\pi$
$787$		−	44.4258i		−	1.58361i	0.610775	−	0.791805i	$-0.290858\pi$
$788$			4.15667i			0.148075i
$789$			36.3308i			1.29341i
$790$	−24.9425			−0.887414
$791$	15.3989			0.547522
$792$			4.77037i			0.169508i
$793$		−	48.2418i		−	1.71312i
$794$			50.6855i			1.79876i
$795$	−22.3951			−0.794271
$796$		−	7.29632i		−	0.258611i
$797$	−27.1887			−0.963074			−0.481537	−	0.876426i	$-0.659921\pi$
$797$	−27.1887			−0.963074			−0.481537	+	0.876426i	$0.659921\pi$
$798$	−195.324			−6.91441
$799$	2.18482	−	32.4212i	0.0772935	−	1.14698i
$800$	25.2236			0.891790
$801$	−12.7619			−0.450918
$802$		−	33.6826i		−	1.18937i
$803$	10.7957			0.380971
$804$		−	32.0238i		−	1.12939i
$805$		−	17.7085i		−	0.624144i
$806$		−	35.0772i		−	1.23554i
$807$	64.7888			2.28067
$808$	5.46672			0.192318
$809$		−	30.0021i		−	1.05482i	−0.849612	−	0.527408i	$-0.823164\pi$
$809$		−	30.0021i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$810$		−	18.1900i		−	0.639130i
$811$			55.5095i			1.94920i	0.223945	+	0.974602i	$0.428107\pi$
$811$			55.5095i			1.94920i	−0.223945	+	0.974602i	$0.571893\pi$
$812$	12.1532			0.426494
$813$		−	6.07349i		−	0.213007i
$814$	7.07763			0.248071
$815$	−29.1436			−1.02085
$816$	56.5855	+	3.81323i	1.98089	+	0.133490i
$817$	−8.40135			−0.293926
$818$	30.8274			1.07786
$819$			132.182i			4.61883i
$820$	−1.69587			−0.0592222
$821$			16.4633i			0.574574i	0.957845	+	0.287287i	$0.0927533\pi$
$821$			16.4633i			0.574574i	−0.957845	+	0.287287i	$0.907247\pi$
$822$			105.361i			3.67488i
$823$			41.0952i			1.43249i	0.697849	+	0.716245i	$0.254141\pi$
$823$			41.0952i			1.43249i	−0.697849	+	0.716245i	$0.745859\pi$
$824$	0.945938			0.0329533
$825$	11.3773			0.396106
$826$			64.9914i			2.26134i
$827$			5.56887i			0.193649i	0.995301	+	0.0968244i	$0.0308685\pi$
$827$			5.56887i			0.193649i	−0.995301	+	0.0968244i	$0.969131\pi$
$828$			32.6172i			1.13353i
$829$	6.78514			0.235658			0.117829	−	0.993034i	$-0.462407\pi$
$829$	6.78514			0.235658			0.117829	+	0.993034i	$0.462407\pi$
$830$		−	8.28711i		−	0.287650i
$831$	−71.8767			−2.49338
$832$	−25.6479			−0.889181
$833$	2.74491	−	40.7325i	0.0951055	−	1.41130i
$834$	−57.4566			−1.98956
$835$	31.4700			1.08906
$836$		−	15.0438i		−	0.520301i
$837$	28.4726			0.984156
$838$		−	4.21950i		−	0.145760i
$839$			6.68292i			0.230720i	0.993324	+	0.115360i	$0.0368021\pi$
$839$			6.68292i			0.230720i	−0.993324	+	0.115360i	$0.963198\pi$
$840$			11.2020i			0.386505i
$841$	25.6432			0.884249
$842$	34.4729			1.18802
$843$		−	34.7252i		−	1.19600i
$844$		−	44.0371i		−	1.51582i
$845$			21.4451i			0.737735i
$846$	−87.6473			−3.01338
$847$		−	40.1591i		−	1.37988i
$848$	−27.9208			−0.958803
$849$	−57.8197			−1.98437
$850$	1.81596	−	26.9475i	0.0622868	−	0.924291i
$851$	−11.5925			−0.397384
$852$	−32.4166			−1.11058
$853$		−	36.5424i		−	1.25119i	−0.780149	−	0.625594i	$-0.784857\pi$
$853$		−	36.5424i		−	1.25119i	0.780149	−	0.625594i	$-0.215143\pi$
$854$	68.6002			2.34745
$855$		−	61.2720i		−	2.09546i
$856$			9.46229i			0.323414i
$857$			46.5824i			1.59123i	0.605806	+	0.795613i	$0.292851\pi$
$857$			46.5824i			1.59123i	−0.605806	+	0.795613i	$0.707149\pi$
$858$	−34.4915			−1.17752
$859$	18.0620			0.616269			0.308134	−	0.951343i	$-0.400295\pi$
$859$	18.0620			0.616269			0.308134	+	0.951343i	$0.400295\pi$
$860$		−	2.01137i		−	0.0685873i
$861$			10.3120i			0.351432i
$862$		−	13.2788i		−	0.452277i
$863$	21.6544			0.737125			0.368562	−	0.929603i	$-0.379850\pi$
$863$	21.6544			0.737125			0.368562	+	0.929603i	$0.379850\pi$
$864$		−	62.0702i		−	2.11167i
$865$	−13.8532			−0.471022
$866$	76.7566			2.60830
$867$	6.78547	−	50.1171i	0.230447	−	1.70207i
$868$	22.2723			0.755972
$869$	−11.6813			−0.396262
$870$			12.9162i			0.437899i
$871$	−36.6648			−1.24234
$872$			5.92150i			0.200527i
$873$		−	14.7402i		−	0.498881i
$874$			55.1831i			1.86659i
$875$	43.2852			1.46331
$876$	−46.6935			−1.57763
$877$			2.23178i			0.0753619i	0.999290	+	0.0376810i	$0.0119971\pi$
$877$			2.23178i			0.0753619i	−0.999290	+	0.0376810i	$0.988003\pi$
$878$		−	11.7270i		−	0.395768i
$879$			24.1385i			0.814171i
$880$	−6.39664			−0.215631
$881$			19.2669i			0.649120i	0.945865	+	0.324560i	$0.105216\pi$
$881$			19.2669i			0.649120i	−0.945865	+	0.324560i	$0.894784\pi$
$882$	−110.116			−3.70780
$883$	−1.52706			−0.0513896			−0.0256948	−	0.999670i	$-0.508180\pi$
$883$	−1.52706			−0.0513896			−0.0256948	+	0.999670i	$0.508180\pi$
$884$	−2.45821	+	36.4780i	−0.0826785	+	1.22689i
$885$	−30.8417			−1.03673
$886$	−14.8913			−0.500283
$887$		−	42.8862i		−	1.43998i	−0.693986	−	0.719989i	$-0.744147\pi$
$887$		−	42.8862i		−	1.43998i	0.693986	−	0.719989i	$-0.255853\pi$
$888$	7.33310			0.246083
$889$		−	79.0080i		−	2.64984i
$890$		−	5.16913i		−	0.173270i
$891$		−	8.51890i		−	0.285394i
$892$	−1.01554			−0.0340027
$893$	−66.2121			−2.21570
$894$			2.67427i			0.0894411i
$895$			19.5753i			0.654331i
$896$			23.7132i			0.792201i
$897$	56.4937			1.88627
$898$			44.7258i			1.49252i
$899$	−6.15175			−0.205172
$900$	−32.5288			−1.08429
$901$	−1.67406	+	24.8419i	−0.0557711	+	0.827603i
$902$	−1.77871			−0.0592244
$903$	−12.2305			−0.407006
$904$			2.75201i			0.0915306i
$905$	−1.46629			−0.0487411
$906$			96.7063i			3.21285i
$907$			14.3884i			0.477759i	0.971049	+	0.238880i	$0.0767801\pi$
$907$			14.3884i			0.477759i	−0.971049	+	0.238880i	$0.923220\pi$
$908$		−	34.1905i		−	1.13465i
$909$	−43.5301			−1.44380
$910$	−53.5398			−1.77483
$911$			16.6825i			0.552715i	0.961055	+	0.276358i	$0.0891274\pi$
$911$			16.6825i			0.552715i	−0.961055	+	0.276358i	$0.910873\pi$
$912$		−	115.562i		−	3.82663i
$913$		−	3.88110i		−	0.128446i
$914$	52.9776			1.75234
$915$			32.5542i			1.07621i
$916$	37.2834			1.23188
$917$	45.1240			1.49013
$918$	−66.3123	−	4.46870i	−2.18863	−	0.147489i
$919$	−21.3260			−0.703480			−0.351740	−	0.936098i	$-0.614410\pi$
$919$	−21.3260			−0.703480			−0.351740	+	0.936098i	$0.614410\pi$
$920$	3.16478			0.104340
$921$			85.4918i			2.81705i
$922$	24.6507			0.811827
$923$			37.1145i			1.22164i
$924$		−	21.9004i		−	0.720472i
$925$		−	11.5610i		−	0.380124i
$926$	24.0783			0.791260
$927$	−7.53227			−0.247392
$928$			13.4108i			0.440232i
$929$		−	3.41070i		−	0.111902i	−0.998434	−	0.0559508i	$-0.982181\pi$
$929$		−	3.41070i		−	0.111902i	0.998434	−	0.0559508i	$-0.0178190\pi$
$930$			23.6706i			0.776188i
$931$	−83.1859			−2.72631
$932$			31.7326i			1.03943i
$933$	93.4547			3.05957
$934$	69.5404			2.27543
$935$	−0.383527	+	5.69127i	−0.0125427	+	0.186124i
$936$	−23.6230			−0.772141
$937$	22.6489			0.739907			0.369954	−	0.929050i	$-0.379374\pi$
$937$	22.6489			0.739907			0.369954	+	0.929050i	$0.379374\pi$
$938$		−	52.1376i		−	1.70235i
$939$	−47.2244			−1.54111
$940$		−	15.8519i		−	0.517032i
$941$		−	8.23011i		−	0.268294i	−0.990961	−	0.134147i	$-0.957171\pi$
$941$		−	8.23011i		−	0.268294i	0.990961	−	0.134147i	$-0.0428294\pi$
$942$			127.992i			4.17021i
$943$	2.91334			0.0948716
$944$	−38.4515			−1.25149
$945$		−	43.4589i		−	1.41372i
$946$		−	2.10963i		−	0.0685899i
$947$		−	32.2036i		−	1.04647i	−0.852187	−	0.523237i	$-0.824724\pi$
$947$		−	32.2036i		−	1.04647i	0.852187	−	0.523237i	$-0.175276\pi$
$948$	50.5240			1.64094
$949$			53.4604i			1.73540i
$950$	−55.0334			−1.78552
$951$	−5.42090			−0.175785
$952$	12.4259	+	0.837363i	0.402725	+	0.0271391i
$953$	−26.6991			−0.864870			−0.432435	−	0.901665i	$-0.642345\pi$
$953$	−26.6991			−0.864870			−0.432435	+	0.901665i	$0.642345\pi$
$954$	67.1575			2.17430
$955$			10.8895i			0.352377i
$956$	33.2322			1.07481
$957$			6.04904i			0.195538i
$958$			17.1247i			0.553274i
$959$			76.5943i			2.47336i
$960$	17.3075			0.558599
$961$	19.7261			0.636327
$962$			35.0486i			1.13001i
$963$		−	75.3459i		−	2.42799i
$964$			18.6232i			0.599813i
$965$	−4.80414			−0.154651
$966$			80.3343i			2.58472i
$967$	10.5265			0.338509			0.169255	−	0.985572i	$-0.445864\pi$
$967$	10.5265			0.338509			0.169255	+	0.985572i	$0.445864\pi$
$968$	7.17704			0.230679
$969$	−102.819	−	6.92881i	−3.30301	−	0.222585i
$970$	5.97045			0.191700
$971$	17.8900			0.574116			0.287058	−	0.957913i	$-0.407323\pi$
$971$	17.8900			0.574116			0.287058	+	0.957913i	$0.407323\pi$
$972$		−	4.20070i		−	0.134737i
$973$	−41.7693			−1.33906
$974$			11.8009i			0.378124i
$975$			56.3405i			1.80434i
$976$			40.5866i			1.29914i
$977$	21.0041			0.671981			0.335990	−	0.941865i	$-0.390929\pi$
$977$	21.0041			0.671981			0.335990	+	0.941865i	$0.390929\pi$
$978$	132.209			4.22758
$979$		−	2.42086i		−	0.0773710i
$980$		−	19.9156i		−	0.636181i
$981$		−	47.1514i		−	1.50543i
$982$	−24.2616			−0.774218
$983$		−	44.3152i		−	1.41344i	−0.707495	−	0.706718i	$-0.750175\pi$
$983$		−	44.3152i		−	1.41344i	0.707495	−	0.706718i	$-0.249825\pi$
$984$	−1.84291			−0.0587498
$985$	−3.21148			−0.102326
$986$	14.3274	+	0.965502i	0.456276	+	0.0307479i
$987$	−96.3902			−3.06813
$988$	74.4972			2.37007
$989$			3.45536i			0.109874i
$990$	15.3858			0.488991
$991$			20.9956i			0.666946i	0.942760	+	0.333473i	$0.108221\pi$
$991$			20.9956i			0.666946i	−0.942760	+	0.333473i	$0.891779\pi$
$992$			24.5770i			0.780322i
$993$			9.31822i			0.295705i
$994$	−52.7771			−1.67399
$995$	5.63721			0.178712
$996$			16.7865i			0.531902i
$997$		−	38.2100i		−	1.21012i	−0.796179	−	0.605062i	$-0.793148\pi$
$997$		−	38.2100i		−	1.21012i	0.796179	−	0.605062i	$-0.206852\pi$
$998$		−	43.4843i		−	1.37647i
$999$	−28.4493			−0.900097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.8	yes	34
17.16	even	2	inner	731.2.d.d.560.7	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.7	✓	34	17.16	even	2	inner
731.2.d.d.560.8	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90092 q^{2} +2.97496i q^{3} +1.61349 q^{4} +1.24660i q^{5} -5.65517i q^{6} -4.11114i q^{7} +0.734723 q^{8} -5.85042 q^{9} +O(q^{10})\)	\(q-1.90092 q^{2} +2.97496i q^{3} +1.61349 q^{4} +1.24660i q^{5} -5.65517i q^{6} -4.11114i q^{7} +0.734723 q^{8} -5.85042 q^{9} -2.36968i q^{10} -1.10979i q^{11} +4.80008i q^{12} +5.49572 q^{13} +7.81495i q^{14} -3.70859 q^{15} -4.62363 q^{16} +(-0.277222 + 4.11378i) q^{17} +11.1212 q^{18} +8.40135 q^{19} +2.01137i q^{20} +12.2305 q^{21} +2.10963i q^{22} -3.45536i q^{23} +2.18577i q^{24} +3.44599 q^{25} -10.4469 q^{26} -8.47989i q^{27} -6.63329i q^{28} +1.83216i q^{29} +7.04972 q^{30} +3.35766i q^{31} +7.31970 q^{32} +3.30160 q^{33} +(0.526976 - 7.81995i) q^{34} +5.12494 q^{35} -9.43959 q^{36} -3.35492i q^{37} -15.9703 q^{38} +16.3496i q^{39} +0.915904i q^{40} +0.843138i q^{41} -23.2492 q^{42} -1.00000 q^{43} -1.79064i q^{44} -7.29312i q^{45} +6.56836i q^{46} -7.88113 q^{47} -13.7551i q^{48} -9.90149 q^{49} -6.55055 q^{50} +(-12.2383 - 0.824726i) q^{51} +8.86729 q^{52} +6.03871 q^{53} +16.1196i q^{54} +1.38347 q^{55} -3.02055i q^{56} +24.9937i q^{57} -3.48278i q^{58} +8.31630 q^{59} -5.98377 q^{60} -8.77808i q^{61} -6.38264i q^{62} +24.0519i q^{63} -4.66689 q^{64} +6.85095i q^{65} -6.27607 q^{66} -6.67152 q^{67} +(-0.447295 + 6.63754i) q^{68} +10.2796 q^{69} -9.74210 q^{70} +6.75335i q^{71} -4.29843 q^{72} +9.72765i q^{73} +6.37743i q^{74} +10.2517i q^{75} +13.5555 q^{76} -4.56252 q^{77} -31.0792i q^{78} -10.5257i q^{79} -5.76381i q^{80} +7.67612 q^{81} -1.60274i q^{82} +3.49714 q^{83} +19.7338 q^{84} +(-5.12823 - 0.345584i) q^{85} +1.90092 q^{86} -5.45060 q^{87} -0.815391i q^{88} +2.18136 q^{89} +13.8636i q^{90} -22.5937i q^{91} -5.57519i q^{92} -9.98892 q^{93} +14.9814 q^{94} +10.4731i q^{95} +21.7758i q^{96} +2.51952i q^{97} +18.8219 q^{98} +6.49275i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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