LMFDB - Embedded newform 731.2.d.d.560.14

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			560.14
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27937 q^{2} +0.638162i q^{3} -0.363207 q^{4} +1.64459i q^{5} -0.816447i q^{6} +4.36496i q^{7} +3.02342 q^{8} +2.59275 q^{9} +O(q^{10})$	\(q-1.27937 q^{2} +0.638162i q^{3} -0.363207 q^{4} +1.64459i q^{5} -0.816447i q^{6} +4.36496i q^{7} +3.02342 q^{8} +2.59275 q^{9} -2.10404i q^{10} +4.08349i q^{11} -0.231785i q^{12} -7.00534 q^{13} -5.58441i q^{14} -1.04951 q^{15} -3.14167 q^{16} +(3.80181 + 1.59570i) q^{17} -3.31709 q^{18} +5.02883 q^{19} -0.597325i q^{20} -2.78555 q^{21} -5.22430i q^{22} -5.58903i q^{23} +1.92943i q^{24} +2.29534 q^{25} +8.96244 q^{26} +3.56908i q^{27} -1.58538i q^{28} -3.44718i q^{29} +1.34272 q^{30} +1.85289i q^{31} -2.02748 q^{32} -2.60593 q^{33} +(-4.86392 - 2.04150i) q^{34} -7.17855 q^{35} -0.941704 q^{36} +2.73109i q^{37} -6.43375 q^{38} -4.47054i q^{39} +4.97228i q^{40} +6.36038i q^{41} +3.56376 q^{42} -1.00000 q^{43} -1.48315i q^{44} +4.26400i q^{45} +7.15044i q^{46} -8.92633 q^{47} -2.00489i q^{48} -12.0529 q^{49} -2.93659 q^{50} +(-1.01832 + 2.42617i) q^{51} +2.54439 q^{52} -6.95948 q^{53} -4.56618i q^{54} -6.71565 q^{55} +13.1971i q^{56} +3.20921i q^{57} +4.41023i q^{58} +3.93586 q^{59} +0.381190 q^{60} -11.5806i q^{61} -2.37054i q^{62} +11.3172i q^{63} +8.87724 q^{64} -11.5209i q^{65} +3.33395 q^{66} +1.27258 q^{67} +(-1.38084 - 0.579571i) q^{68} +3.56671 q^{69} +9.18403 q^{70} +10.6492i q^{71} +7.83897 q^{72} -14.0530i q^{73} -3.49407i q^{74} +1.46480i q^{75} -1.82651 q^{76} -17.8243 q^{77} +5.71949i q^{78} +9.62971i q^{79} -5.16674i q^{80} +5.50059 q^{81} -8.13730i q^{82} -4.62804 q^{83} +1.01173 q^{84} +(-2.62427 + 6.25240i) q^{85} +1.27937 q^{86} +2.19986 q^{87} +12.3461i q^{88} -5.75180 q^{89} -5.45524i q^{90} -30.5780i q^{91} +2.02997i q^{92} -1.18245 q^{93} +11.4201 q^{94} +8.27035i q^{95} -1.29386i q^{96} -7.14845i q^{97} +15.4201 q^{98} +10.5875i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.27937			−0.904653			−0.452326	−	0.891852i	$-0.649406\pi$
$2$	−1.27937			−0.904653			−0.452326	+	0.891852i	$0.649406\pi$
$3$			0.638162i			0.368443i	0.982885	+	0.184222i	$0.0589764\pi$
$3$			0.638162i			0.368443i	−0.982885	+	0.184222i	$0.941024\pi$
$4$	−0.363207			−0.181603
$5$			1.64459i			0.735481i	0.929928	+	0.367741i	$0.119869\pi$
$5$			1.64459i			0.735481i	−0.929928	+	0.367741i	$0.880131\pi$
$6$		−	0.816447i		−	0.333313i
$7$			4.36496i			1.64980i	0.565280	+	0.824899i	$0.308768\pi$
$7$			4.36496i			1.64980i	−0.565280	+	0.824899i	$0.691232\pi$
$8$	3.02342			1.06894
$9$	2.59275			0.864250
$10$		−	2.10404i		−	0.665355i
$11$			4.08349i			1.23122i	0.788052	+	0.615609i	$0.211090\pi$
$11$			4.08349i			1.23122i	−0.788052	+	0.615609i	$0.788910\pi$
$12$		−	0.231785i		−	0.0669105i
$13$	−7.00534			−1.94293			−0.971466	−	0.237178i	$-0.923777\pi$
$13$	−7.00534			−1.94293			−0.971466	+	0.237178i	$0.923777\pi$
$14$		−	5.58441i		−	1.49250i
$15$	−1.04951			−0.270983
$16$	−3.14167			−0.785417
$17$	3.80181	+	1.59570i	0.922073	+	0.387015i
$17$	3.80181	+	1.59570i	0.922073	+	0.387015i
$18$	−3.31709			−0.781846
$19$	5.02883			1.15369			0.576847	−	0.816853i	$-0.304283\pi$
$19$	5.02883			1.15369			0.576847	+	0.816853i	$0.304283\pi$
$20$		−	0.597325i		−	0.133566i
$21$	−2.78555			−0.607857
$22$		−	5.22430i		−	1.11383i
$23$		−	5.58903i		−	1.16539i	−0.812690	−	0.582696i	$-0.801998\pi$
$23$		−	5.58903i		−	1.16539i	0.812690	−	0.582696i	$-0.198002\pi$
$24$			1.92943i			0.393844i
$25$	2.29534			0.459068
$26$	8.96244			1.75768
$27$			3.56908i			0.686870i
$28$		−	1.58538i		−	0.299609i
$29$		−	3.44718i		−	0.640126i	−0.947396	−	0.320063i	$-0.896296\pi$
$29$		−	3.44718i		−	0.640126i	0.947396	−	0.320063i	$-0.103704\pi$
$30$	1.34272			0.245145
$31$			1.85289i			0.332789i	0.986059	+	0.166395i	$0.0532126\pi$
$31$			1.85289i			0.332789i	−0.986059	+	0.166395i	$0.946787\pi$
$32$	−2.02748			−0.358411
$33$	−2.60593			−0.453634
$34$	−4.86392	−	2.04150i	−0.834156	−	0.350114i
$35$	−7.17855			−1.21340
$36$	−0.941704			−0.156951
$37$			2.73109i			0.448988i	0.974476	+	0.224494i	$0.0720729\pi$
$37$			2.73109i			0.448988i	−0.974476	+	0.224494i	$0.927927\pi$
$38$	−6.43375			−1.04369
$39$		−	4.47054i		−	0.715860i
$40$			4.97228i			0.786186i
$41$			6.36038i			0.993325i	0.867944	+	0.496663i	$0.165441\pi$
$41$			6.36038i			0.993325i	−0.867944	+	0.496663i	$0.834559\pi$
$42$	3.56376			0.549900
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$		−	1.48315i		−	0.223594i
$45$			4.26400i			0.635639i
$46$			7.15044i			1.05428i
$47$	−8.92633			−1.30204			−0.651019	−	0.759061i	$-0.725658\pi$
$47$	−8.92633			−1.30204			−0.651019	+	0.759061i	$0.725658\pi$
$48$		−	2.00489i		−	0.289381i
$49$	−12.0529			−1.72184
$50$	−2.93659			−0.415297
$51$	−1.01832	+	2.42617i	−0.142593	+	0.339732i
$52$	2.54439			0.352843
$53$	−6.95948			−0.955958			−0.477979	−	0.878371i	$-0.658631\pi$
$53$	−6.95948			−0.955958			−0.477979	+	0.878371i	$0.658631\pi$
$54$		−	4.56618i		−	0.621379i
$55$	−6.71565			−0.905538
$56$			13.1971i			1.76354i
$57$			3.20921i			0.425070i
$58$			4.41023i			0.579092i
$59$	3.93586			0.512406			0.256203	−	0.966623i	$-0.417529\pi$
$59$	3.93586			0.512406			0.256203	+	0.966623i	$0.417529\pi$
$60$	0.381190			0.0492114
$61$		−	11.5806i		−	1.48274i	−0.671096	−	0.741370i	$-0.734176\pi$
$61$		−	11.5806i		−	1.48274i	0.671096	−	0.741370i	$-0.265824\pi$
$62$		−	2.37054i		−	0.301059i
$63$			11.3172i			1.42584i
$64$	8.87724			1.10965
$65$		−	11.5209i		−	1.42899i
$66$	3.33395			0.410381
$67$	1.27258			0.155471			0.0777353	−	0.996974i	$-0.475231\pi$
$67$	1.27258			0.155471			0.0777353	+	0.996974i	$0.475231\pi$
$68$	−1.38084	−	0.579571i	−0.167452	−	0.0702833i
$69$	3.56671			0.429381
$70$	9.18403			1.09770
$71$			10.6492i			1.26382i	0.775041	+	0.631911i	$0.217729\pi$
$71$			10.6492i			1.26382i	−0.775041	+	0.631911i	$0.782271\pi$
$72$	7.83897			0.923832
$73$		−	14.0530i		−	1.64478i	−0.568926	−	0.822388i	$-0.692641\pi$
$73$		−	14.0530i		−	1.64478i	0.568926	−	0.822388i	$-0.307359\pi$
$74$		−	3.49407i		−	0.406178i
$75$			1.46480i			0.169140i
$76$	−1.82651			−0.209515
$77$	−17.8243			−2.03126
$78$			5.71949i			0.647605i
$79$			9.62971i			1.08343i	0.840563	+	0.541713i	$0.182224\pi$
$79$			9.62971i			1.08343i	−0.840563	+	0.541713i	$0.817776\pi$
$80$		−	5.16674i		−	0.577659i
$81$	5.50059			0.611177
$82$		−	8.13730i		−	0.898614i
$83$	−4.62804			−0.507993			−0.253996	−	0.967205i	$-0.581745\pi$
$83$	−4.62804			−0.507993			−0.253996	+	0.967205i	$0.581745\pi$
$84$	1.01173			0.110389
$85$	−2.62427	+	6.25240i	−0.284642	+	0.678168i
$86$	1.27937			0.137958
$87$	2.19986			0.235850
$88$			12.3461i			1.31610i
$89$	−5.75180			−0.609689			−0.304845	−	0.952402i	$-0.598605\pi$
$89$	−5.75180			−0.609689			−0.304845	+	0.952402i	$0.598605\pi$
$90$		−	5.45524i		−	0.575033i
$91$		−	30.5780i		−	3.20545i
$92$			2.02997i			0.211639i
$93$	−1.18245			−0.122614
$94$	11.4201			1.17789
$95$			8.27035i			0.848519i
$96$		−	1.29386i		−	0.132054i
$97$		−	7.14845i		−	0.725815i	−0.931825	−	0.362908i	$-0.881784\pi$
$97$		−	7.14845i		−	0.725815i	0.931825	−	0.362908i	$-0.118216\pi$
$98$	15.4201			1.55766
$99$			10.5875i			1.06408i
$100$	−0.833682			−0.0833682
$101$	−0.785802			−0.0781902			−0.0390951	−	0.999235i	$-0.512448\pi$
$101$	−0.785802			−0.0781902			−0.0390951	+	0.999235i	$0.512448\pi$
$102$	1.30281	−	3.10397i	0.128997	−	0.307339i
$103$	10.9141			1.07540			0.537700	−	0.843136i	$-0.319293\pi$
$103$	10.9141			1.07540			0.537700	+	0.843136i	$0.319293\pi$
$104$	−21.1801			−2.07688
$105$		−	4.58108i		−	0.447067i
$106$	8.90377			0.864810
$107$		−	5.59924i		−	0.541299i	−0.962678	−	0.270649i	$-0.912762\pi$
$107$		−	5.59924i		−	0.541299i	0.962678	−	0.270649i	$-0.0872384\pi$
$108$		−	1.29631i		−	0.124738i
$109$			16.6963i			1.59922i	0.600522	+	0.799608i	$0.294960\pi$
$109$			16.6963i			1.59922i	−0.600522	+	0.799608i	$0.705040\pi$
$110$	8.59181			0.819197
$111$	−1.74288			−0.165426
$112$		−	13.7132i		−	1.29578i
$113$		−	12.3091i		−	1.15794i	−0.815348	−	0.578971i	$-0.803454\pi$
$113$		−	12.3091i		−	1.15794i	0.815348	−	0.578971i	$-0.196546\pi$
$114$		−	4.10577i		−	0.384541i
$115$	9.19163			0.857124
$116$			1.25204i			0.116249i
$117$	−18.1631			−1.67918
$118$	−5.03543			−0.463549
$119$	−6.96518	+	16.5947i	−0.638497	+	1.52124i
$120$	−3.17312			−0.289665
$121$	−5.67489			−0.515899
$122$			14.8159i			1.34136i
$123$	−4.05896			−0.365984
$124$		−	0.672983i		−	0.0604357i
$125$			11.9978i			1.07312i
$126$		−	14.4790i		−	1.28989i
$127$	17.8428			1.58329			0.791645	−	0.610982i	$-0.209225\pi$
$127$	17.8428			1.58329			0.791645	+	0.610982i	$0.209225\pi$
$128$	−7.30233			−0.645441
$129$		−	0.638162i		−	0.0561870i
$130$			14.7395i			1.29274i
$131$			13.3682i			1.16799i	0.811759	+	0.583993i	$0.198511\pi$
$131$			13.3682i			1.16799i	−0.811759	+	0.583993i	$0.801489\pi$
$132$	0.946491			0.0823815
$133$			21.9506i			1.90336i
$134$	−1.62811			−0.140647
$135$	−5.86966			−0.505180
$136$	11.4945	+	4.82449i	0.985642	+	0.413696i
$137$	−7.35985			−0.628794			−0.314397	−	0.949292i	$-0.601802\pi$
$137$	−7.35985			−0.628794			−0.314397	+	0.949292i	$0.601802\pi$
$138$	−4.56314			−0.388441
$139$		−	20.9254i		−	1.77487i	−0.460937	−	0.887433i	$-0.652486\pi$
$139$		−	20.9254i		−	1.77487i	0.460937	−	0.887433i	$-0.347514\pi$
$140$	2.60730			0.220357
$141$		−	5.69645i		−	0.479727i
$142$		−	13.6242i		−	1.14332i
$143$		−	28.6062i		−	2.39217i
$144$	−8.14555			−0.678796
$145$	5.66919			0.470801
$146$			17.9790i			1.48795i
$147$		−	7.69168i		−	0.634399i
$148$		−	0.991949i		−	0.0815377i
$149$	3.51367			0.287851			0.143926	−	0.989589i	$-0.454027\pi$
$149$	3.51367			0.287851			0.143926	+	0.989589i	$0.454027\pi$
$150$		−	1.87402i		−	0.153013i
$151$	15.3496			1.24913			0.624565	−	0.780973i	$-0.285276\pi$
$151$	15.3496			1.24913			0.624565	+	0.780973i	$0.285276\pi$
$152$	15.2043			1.23323
$153$	9.85713	+	4.13726i	0.796902	+	0.334478i
$154$	22.8039			1.83759
$155$	−3.04724			−0.244760
$156$			1.62373i			0.130003i
$157$	−12.5633			−1.00266			−0.501330	−	0.865256i	$-0.667156\pi$
$157$	−12.5633			−1.00266			−0.501330	+	0.865256i	$0.667156\pi$
$158$		−	12.3200i		−	0.980125i
$159$		−	4.44128i		−	0.352216i
$160$		−	3.33437i		−	0.263605i
$161$	24.3959			1.92266
$162$	−7.03731			−0.552903
$163$		−	11.2376i		−	0.880193i	−0.897950	−	0.440097i	$-0.854944\pi$
$163$		−	11.2376i		−	0.880193i	0.897950	−	0.440097i	$-0.145056\pi$
$164$		−	2.31014i		−	0.180391i
$165$		−	4.28567i		−	0.333639i
$166$	5.92098			0.459557
$167$		−	3.96035i		−	0.306461i	−0.988190	−	0.153231i	$-0.951032\pi$
$167$		−	3.96035i		−	0.306461i	0.988190	−	0.153231i	$-0.0489677\pi$
$168$	−8.42189			−0.649763
$169$	36.0748			2.77499
$170$	3.35742	−	7.99914i	0.257502	−	0.613506i
$171$	13.0385			0.997079
$172$	0.363207			0.0276943
$173$		−	10.9877i		−	0.835383i	−0.908589	−	0.417691i	$-0.862839\pi$
$173$		−	10.9877i		−	0.835383i	0.908589	−	0.417691i	$-0.137161\pi$
$174$	−2.81444			−0.213362
$175$			10.0191i			0.757369i
$176$		−	12.8290i		−	0.967020i
$177$			2.51172i			0.188792i
$178$	7.35869			0.551557
$179$	−5.59865			−0.418463			−0.209231	−	0.977866i	$-0.567096\pi$
$179$	−5.59865			−0.418463			−0.209231	+	0.977866i	$0.567096\pi$
$180$		−	1.54871i		−	0.115434i
$181$			6.32272i			0.469964i	0.972000	+	0.234982i	$0.0755031\pi$
$181$			6.32272i			0.469964i	−0.972000	+	0.234982i	$0.924497\pi$
$182$			39.1207i			2.89982i
$183$	7.39028			0.546305
$184$		−	16.8980i		−	1.24574i
$185$	−4.49150			−0.330222
$186$	1.51279			0.110923
$187$	−6.51604	+	15.5246i	−0.476500	+	1.13527i
$188$	3.24210			0.236455
$189$	−15.5789			−1.13320
$190$		−	10.5808i		−	0.767615i
$191$	10.8204			0.782938			0.391469	−	0.920191i	$-0.371967\pi$
$191$	10.8204			0.782938			0.391469	+	0.920191i	$0.371967\pi$
$192$			5.66512i			0.408845i
$193$			18.0258i			1.29752i	0.760992	+	0.648761i	$0.224713\pi$
$193$			18.0258i			1.29752i	−0.760992	+	0.648761i	$0.775287\pi$
$194$			9.14553i			0.656611i
$195$	7.35219			0.526501
$196$	4.37768			0.312691
$197$		−	5.22636i		−	0.372362i	−0.982515	−	0.186181i	$-0.940389\pi$
$197$		−	5.22636i		−	0.372362i	0.982515	−	0.186181i	$-0.0596112\pi$
$198$		−	13.5453i		−	0.962623i
$199$		−	9.40493i		−	0.666698i	−0.942804	−	0.333349i	$-0.891821\pi$
$199$		−	9.40493i		−	0.666698i	0.942804	−	0.333349i	$-0.108179\pi$
$200$	6.93977			0.490716
$201$			0.812114i			0.0572821i
$202$	1.00533			0.0707350
$203$	15.0468			1.05608
$204$	0.369860	−	0.881201i	0.0258954	−	0.0616964i
$205$	−10.4602			−0.730572
$206$	−13.9632			−0.972864
$207$		−	14.4909i		−	1.00719i
$208$	22.0085			1.52601
$209$			20.5352i			1.42045i
$210$			5.86090i			0.404441i
$211$		−	7.96572i		−	0.548383i	−0.961675	−	0.274192i	$-0.911590\pi$
$211$		−	7.96572i		−	0.548383i	0.961675	−	0.274192i	$-0.0884102\pi$
$212$	2.52773			0.173605
$213$	−6.79589			−0.465646
$214$			7.16351i			0.489687i
$215$		−	1.64459i		−	0.112160i
$216$			10.7908i			0.734223i
$217$	−8.08780			−0.549035
$218$		−	21.3608i		−	1.44674i
$219$	8.96808			0.606007
$220$	2.43917			0.164449
$221$	−26.6330	−	11.1785i	−1.79153	−	0.751944i
$222$	2.22979			0.149653
$223$	7.46115			0.499635			0.249818	−	0.968293i	$-0.419629\pi$
$223$	7.46115			0.499635			0.249818	+	0.968293i	$0.419629\pi$
$224$		−	8.84987i		−	0.591307i
$225$	5.95123			0.396749
$226$			15.7479i			1.04754i
$227$			17.7860i			1.18050i	0.807222	+	0.590248i	$0.200970\pi$
$227$			17.7860i			1.18050i	−0.807222	+	0.590248i	$0.799030\pi$
$228$		−	1.16561i		−	0.0771942i
$229$	−14.4964			−0.957949			−0.478975	−	0.877829i	$-0.658991\pi$
$229$	−14.4964			−0.957949			−0.478975	+	0.877829i	$0.658991\pi$
$230$	−11.7595			−0.775400
$231$		−	11.3748i		−	0.748405i
$232$		−	10.4223i		−	0.684257i
$233$			3.00043i			0.196564i	0.995159	+	0.0982822i	$0.0313348\pi$
$233$			3.00043i			0.196564i	−0.995159	+	0.0982822i	$0.968665\pi$
$234$	23.2374			1.51907
$235$		−	14.6801i		−	0.957625i
$236$	−1.42953			−0.0930546
$237$	−6.14532			−0.399181
$238$	8.91106	−	21.2308i	0.577618	−	1.37619i
$239$	−15.3981			−0.996020			−0.498010	−	0.867171i	$-0.665936\pi$
$239$	−15.3981			−0.996020			−0.498010	+	0.867171i	$0.665936\pi$
$240$	3.29722			0.212835
$241$			11.9715i			0.771151i	0.922676	+	0.385575i	$0.125997\pi$
$241$			11.9715i			0.771151i	−0.922676	+	0.385575i	$0.874003\pi$
$242$	7.26029			0.466709
$243$			14.2175i			0.912054i
$244$			4.20614i			0.269271i
$245$		−	19.8220i		−	1.26638i
$246$	5.19292			0.331088
$247$	−35.2287			−2.24155
$248$			5.60207i			0.355732i
$249$		−	2.95344i		−	0.187166i
$250$		−	15.3497i		−	0.970798i
$251$	1.19140			0.0752008			0.0376004	−	0.999293i	$-0.488029\pi$
$251$	1.19140			0.0752008			0.0376004	+	0.999293i	$0.488029\pi$
$252$		−	4.11050i		−	0.258937i
$253$	22.8227			1.43485
$254$	−22.8275			−1.43233
$255$	−3.99004	−	1.67471i	−0.249866	−	0.104874i
$256$	−8.41208			−0.525755
$257$	−12.5235			−0.781193			−0.390596	−	0.920562i	$-0.627731\pi$
$257$	−12.5235			−0.781193			−0.390596	+	0.920562i	$0.627731\pi$
$258$			0.816447i			0.0508298i
$259$	−11.9211			−0.740739
$260$			4.18446i			0.259509i
$261$		−	8.93769i		−	0.553229i
$262$		−	17.1029i		−	1.05662i
$263$	15.5108			0.956436			0.478218	−	0.878241i	$-0.341283\pi$
$263$	15.5108			0.956436			0.478218	+	0.878241i	$0.341283\pi$
$264$	−7.87882			−0.484908
$265$		−	11.4455i		−	0.703089i
$266$		−	28.0830i		−	1.72188i
$267$		−	3.67058i		−	0.224636i
$268$	−0.462211			−0.0282340
$269$			8.68854i			0.529750i	0.964283	+	0.264875i	$0.0853306\pi$
$269$			8.68854i			0.529750i	−0.964283	+	0.264875i	$0.914669\pi$
$270$	7.50948			0.457012
$271$	23.4055			1.42178			0.710890	−	0.703303i	$-0.248292\pi$
$271$	23.4055			1.42178			0.710890	+	0.703303i	$0.248292\pi$
$272$	−11.9440	−	5.01317i	−0.724212	−	0.303968i
$273$	19.5137			1.18103
$274$	9.41598			0.568840
$275$			9.37299i			0.565212i
$276$	−1.29545			−0.0779770
$277$			4.16913i			0.250499i	0.992125	+	0.125249i	$0.0399731\pi$
$277$			4.16913i			0.250499i	−0.992125	+	0.125249i	$0.960027\pi$
$278$			26.7713i			1.60564i
$279$			4.80408i			0.287613i
$280$	−21.7038			−1.29705
$281$	0.643601			0.0383940			0.0191970	−	0.999816i	$-0.493889\pi$
$281$	0.643601			0.0383940			0.0191970	+	0.999816i	$0.493889\pi$
$282$			7.28787i			0.433987i
$283$			10.3156i			0.613201i	0.951838	+	0.306601i	$0.0991916\pi$
$283$			10.3156i			0.613201i	−0.951838	+	0.306601i	$0.900808\pi$
$284$		−	3.86785i		−	0.229514i
$285$	−5.27782			−0.312631
$286$			36.5980i			2.16409i
$287$	−27.7628			−1.63879
$288$	−5.25675			−0.309757
$289$	11.9075	+	12.1331i	0.700439	+	0.713713i
$290$	−7.25301			−0.425911
$291$	4.56187			0.267422
$292$			5.10414i			0.298697i
$293$	12.9527			0.756706			0.378353	−	0.925661i	$-0.376491\pi$
$293$	12.9527			0.756706			0.378353	+	0.925661i	$0.376491\pi$
$294$			9.84052i			0.573911i
$295$			6.47286i			0.376865i
$296$			8.25722i			0.479941i
$297$	−14.5743			−0.845687
$298$	−4.49529			−0.260405
$299$			39.1530i			2.26428i
$300$		−	0.532025i		−	0.0307165i
$301$		−	4.36496i		−	0.251592i
$302$	−19.6378			−1.13003
$303$		−	0.501469i		−	0.0288086i
$304$	−15.7989			−0.906130
$305$	19.0452			1.09053
$306$	−12.6109	−	5.29310i	−0.720919	−	0.302586i
$307$	11.7956			0.673209			0.336605	−	0.941646i	$-0.390721\pi$
$307$	11.7956			0.673209			0.336605	+	0.941646i	$0.390721\pi$
$308$	6.47389			0.368884
$309$			6.96498i			0.396224i
$310$	3.89855			0.221423
$311$		−	25.7294i		−	1.45898i	−0.683990	−	0.729491i	$-0.739757\pi$
$311$		−	25.7294i		−	1.45898i	0.683990	−	0.729491i	$-0.260243\pi$
$312$		−	13.5163i		−	0.765212i
$313$		−	8.01432i		−	0.452996i	−0.974012	−	0.226498i	$-0.927272\pi$
$313$		−	8.01432i		−	0.452996i	0.974012	−	0.226498i	$-0.0727277\pi$
$314$	16.0731			0.907059
$315$	−18.6122			−1.04868
$316$		−	3.49758i		−	0.196754i
$317$			26.1344i			1.46786i	0.679227	+	0.733928i	$0.262315\pi$
$317$			26.1344i			1.46786i	−0.679227	+	0.733928i	$0.737685\pi$
$318$			5.68205i			0.318633i
$319$	14.0765			0.788135
$320$			14.5994i			0.816130i
$321$	3.57322			0.199438
$322$	−31.2114			−1.73934
$323$	19.1186	+	8.02453i	1.06379	+	0.446497i
$324$	−1.99785			−0.110992
$325$	−16.0796			−0.891937
$326$			14.3770i			0.796269i
$327$	−10.6550			−0.589220
$328$			19.2301i			1.06181i
$329$		−	38.9630i		−	2.14810i
$330$			5.48297i			0.301828i
$331$	25.0167			1.37504			0.687520	−	0.726165i	$-0.258699\pi$
$331$	25.0167			1.37504			0.687520	+	0.726165i	$0.258699\pi$
$332$	1.68093			0.0922532
$333$			7.08102i			0.388037i
$334$			5.06676i			0.277241i
$335$			2.09287i			0.114346i
$336$	8.75127			0.477421
$337$			27.6244i			1.50479i	0.658709	+	0.752397i	$0.271103\pi$
$337$			27.6244i			1.50479i	−0.658709	+	0.752397i	$0.728897\pi$
$338$	−46.1531			−2.51040
$339$	7.85520			0.426636
$340$	0.953154	−	2.27091i	0.0516920	−	0.123158i
$341$	−7.56627			−0.409736
$342$	−16.6811			−0.902010
$343$		−	22.0555i		−	1.19088i
$344$	−3.02342			−0.163012
$345$			5.86575i			0.315801i
$346$			14.0574i			0.755731i
$347$		−	11.9989i		−	0.644135i	−0.946717	−	0.322067i	$-0.895622\pi$
$347$		−	11.9989i		−	0.644135i	0.946717	−	0.322067i	$-0.104378\pi$
$348$	−0.799005			−0.0428312
$349$	0.760622			0.0407152			0.0203576	−	0.999793i	$-0.493520\pi$
$349$	0.760622			0.0407152			0.0203576	+	0.999793i	$0.493520\pi$
$350$		−	12.8181i		−	0.685156i
$351$		−	25.0026i		−	1.33454i
$352$		−	8.27920i		−	0.441283i
$353$	8.24539			0.438858			0.219429	−	0.975629i	$-0.429581\pi$
$353$	8.24539			0.438858			0.219429	+	0.975629i	$0.429581\pi$
$354$		−	3.21342i		−	0.170791i
$355$	−17.5134			−0.929517
$356$	2.08909			0.110722
$357$	−10.5901	−	4.44491i	−0.560489	−	0.235250i
$358$	7.16276			0.378564
$359$	−2.31432			−0.122145			−0.0610726	−	0.998133i	$-0.519452\pi$
$359$	−2.31432			−0.122145			−0.0610726	+	0.998133i	$0.519452\pi$
$360$			12.8919i			0.679461i
$361$	6.28915			0.331008
$362$		−	8.08911i		−	0.425154i
$363$		−	3.62150i		−	0.190079i
$364$			11.1061i			0.582120i
$365$	23.1113			1.20970
$366$	−9.45492			−0.494217
$367$			3.18184i			0.166091i	0.996546	+	0.0830454i	$0.0264647\pi$
$367$			3.18184i			0.166091i	−0.996546	+	0.0830454i	$0.973535\pi$
$368$			17.5589i			0.915319i
$369$			16.4909i			0.858481i
$370$	5.74631			0.298736
$371$		−	30.3778i		−	1.57714i
$372$	0.429472			0.0222671
$373$	−23.3715			−1.21013			−0.605065	−	0.796176i	$-0.706853\pi$
$373$	−23.3715			−1.21013			−0.605065	+	0.796176i	$0.706853\pi$
$374$	8.33644	−	19.8618i	0.431067	−	1.02703i
$375$	−7.65655			−0.395382
$376$	−26.9880			−1.39180
$377$			24.1487i			1.24372i
$378$	19.9312			1.02515
$379$		−	5.25383i		−	0.269871i	−0.990854	−	0.134936i	$-0.956917\pi$
$379$		−	5.25383i		−	0.269871i	0.990854	−	0.134936i	$-0.0430827\pi$
$380$		−	3.00385i		−	0.154094i
$381$			11.3866i			0.583352i
$382$	−13.8433			−0.708287
$383$	−29.0698			−1.48540			−0.742700	−	0.669624i	$-0.766455\pi$
$383$	−29.0698			−1.48540			−0.742700	+	0.669624i	$0.766455\pi$
$384$		−	4.66007i		−	0.237808i
$385$		−	29.3135i		−	1.49396i
$386$		−	23.0617i		−	1.17381i
$387$	−2.59275			−0.131797
$388$			2.59637i			0.131811i
$389$	−3.44596			−0.174717			−0.0873585	−	0.996177i	$-0.527843\pi$
$389$	−3.44596			−0.174717			−0.0873585	+	0.996177i	$0.527843\pi$
$390$	−9.40619			−0.476301
$391$	8.91843	−	21.2484i	0.451024	−	1.07458i
$392$	−36.4409			−1.84054
$393$	−8.53109			−0.430336
$394$			6.68645i			0.336859i
$395$	−15.8369			−0.796840
$396$		−	3.84544i		−	0.193241i
$397$			27.8143i			1.39596i	0.716117	+	0.697980i	$0.245918\pi$
$397$			27.8143i			1.39596i	−0.716117	+	0.697980i	$0.754082\pi$
$398$			12.0324i			0.603130i
$399$	−14.0081			−0.701280
$400$	−7.21119			−0.360559
$401$			19.9955i			0.998528i	0.866450	+	0.499264i	$0.166396\pi$
$401$			19.9955i			0.998528i	−0.866450	+	0.499264i	$0.833604\pi$
$402$		−	1.03900i		−	0.0518204i
$403$		−	12.9801i		−	0.646587i
$404$	0.285409			0.0141996
$405$			9.04620i			0.449509i
$406$	−19.2505			−0.955385
$407$	−11.1524			−0.552802
$408$	−3.07880	+	7.33533i	−0.152424	+	0.363153i
$409$	10.0834			0.498594			0.249297	−	0.968427i	$-0.419800\pi$
$409$	10.0834			0.498594			0.249297	+	0.968427i	$0.419800\pi$
$410$	13.3825			0.660914
$411$		−	4.69678i		−	0.231675i
$412$	−3.96409			−0.195296
$413$			17.1799i			0.845366i
$414$			18.5393i			0.911157i
$415$		−	7.61120i		−	0.373619i
$416$	14.2032			0.696369
$417$	13.3538			0.653937
$418$		−	26.2721i		−	1.28501i
$419$		−	1.20515i		−	0.0588753i	−0.999567	−	0.0294376i	$-0.990628\pi$
$419$		−	1.20515i		−	0.0588753i	0.999567	−	0.0294376i	$-0.00937165\pi$
$420$			1.66388i			0.0811890i
$421$	2.46964			0.120363			0.0601815	−	0.998187i	$-0.480832\pi$
$421$	2.46964			0.120363			0.0601815	+	0.998187i	$0.480832\pi$
$422$			10.1911i			0.496096i
$423$	−23.1437			−1.12529
$424$	−21.0414			−1.02186
$425$	8.72643	+	3.66268i	0.423294	+	0.177666i
$426$	8.69447			0.421248
$427$	50.5487			2.44622
$428$			2.03368i			0.0983017i
$429$	18.2554			0.881380
$430$			2.10404i			0.101466i
$431$			29.0254i			1.39810i	0.715071	+	0.699052i	$0.246394\pi$
$431$			29.0254i			1.39810i	−0.715071	+	0.699052i	$0.753606\pi$
$432$		−	11.2129i		−	0.539479i
$433$	−2.60437			−0.125158			−0.0625789	−	0.998040i	$-0.519933\pi$
$433$	−2.60437			−0.125158			−0.0625789	+	0.998040i	$0.519933\pi$
$434$	10.3473			0.496686
$435$			3.61786i			0.173463i
$436$		−	6.06422i		−	0.290423i
$437$		−	28.1063i		−	1.34451i
$438$	−11.4735			−0.548226
$439$		−	37.2076i		−	1.77582i	−0.460015	−	0.887911i	$-0.652156\pi$
$439$		−	37.2076i		−	1.77582i	0.460015	−	0.887911i	$-0.347844\pi$
$440$	−20.3042			−0.967966
$441$	−31.2500			−1.48810
$442$	34.0735	+	14.3014i	1.62071	+	0.680248i
$443$	−25.4824			−1.21071			−0.605353	−	0.795957i	$-0.706968\pi$
$443$	−25.4824			−1.21071			−0.605353	+	0.795957i	$0.706968\pi$
$444$	0.633024			0.0300420
$445$		−	9.45932i		−	0.448415i
$446$	−9.54558			−0.451997
$447$			2.24229i			0.106057i
$448$			38.7488i			1.83071i
$449$		−	3.94588i		−	0.186218i	−0.995656	−	0.0931088i	$-0.970320\pi$
$449$		−	3.94588i		−	0.186218i	0.995656	−	0.0931088i	$-0.0296804\pi$
$450$	−7.61384			−0.358920
$451$	−25.9726			−1.22300
$452$			4.47075i			0.210286i
$453$			9.79551i			0.460233i
$454$		−	22.7549i		−	1.06794i
$455$	50.2882			2.35755
$456$			9.70279i			0.454375i
$457$	−13.5234			−0.632598			−0.316299	−	0.948660i	$-0.602440\pi$
$457$	−13.5234			−0.632598			−0.316299	+	0.948660i	$0.602440\pi$
$458$	18.5463			0.866611
$459$	−5.69520	+	13.5690i	−0.265829	+	0.633345i
$460$	−3.33846			−0.155657
$461$	−3.91922			−0.182536			−0.0912682	−	0.995826i	$-0.529092\pi$
$461$	−3.91922			−0.182536			−0.0912682	+	0.995826i	$0.529092\pi$
$462$			14.5526i			0.677046i
$463$	21.6106			1.00433			0.502165	−	0.864772i	$-0.332537\pi$
$463$	21.6106			1.00433			0.502165	+	0.864772i	$0.332537\pi$
$464$			10.8299i			0.502766i
$465$		−	1.94463i		−	0.0901802i
$466$		−	3.83866i		−	0.177823i
$467$	−27.5769			−1.27611			−0.638054	−	0.769992i	$-0.720260\pi$
$467$	−27.5769			−1.27611			−0.638054	+	0.769992i	$0.720260\pi$
$468$	6.59696			0.304945
$469$			5.55477i			0.256495i
$470$			18.7813i			0.866318i
$471$		−	8.01742i		−	0.369423i
$472$	11.8998			0.547731
$473$		−	4.08349i		−	0.187759i
$474$	7.86215			0.361120
$475$	11.5429			0.529623
$476$	2.52980	−	6.02732i	0.115953	−	0.276262i
$477$	−18.0442			−0.826187
$478$	19.6999			0.901052
$479$			25.5684i			1.16825i	0.811664	+	0.584125i	$0.198562\pi$
$479$			25.5684i			1.16825i	−0.811664	+	0.584125i	$0.801438\pi$
$480$	2.12787			0.0971234
$481$		−	19.1322i		−	0.872353i
$482$		−	15.3160i		−	0.697623i
$483$			15.5685i			0.708392i
$484$	2.06116			0.0936890
$485$	11.7562			0.533823
$486$		−	18.1895i		−	0.825092i
$487$			26.8367i			1.21609i	0.793903	+	0.608044i	$0.208046\pi$
$487$			26.8367i			1.21609i	−0.793903	+	0.608044i	$0.791954\pi$
$488$		−	35.0129i		−	1.58496i
$489$	7.17138			0.324301
$490$			25.3597i			1.14563i
$491$	31.4104			1.41753			0.708766	−	0.705444i	$-0.249252\pi$
$491$	31.4104			1.41753			0.708766	+	0.705444i	$0.249252\pi$
$492$	1.47424			0.0664639
$493$	5.50069	−	13.1055i	0.247738	−	0.590243i
$494$	45.0706			2.02782
$495$	−17.4120			−0.782611
$496$		−	5.82117i		−	0.261378i
$497$	−46.4831			−2.08505
$498$			3.77855i			0.169321i
$499$			21.4315i			0.959407i	0.877431	+	0.479703i	$0.159256\pi$
$499$			21.4315i			0.959407i	−0.877431	+	0.479703i	$0.840744\pi$
$500$		−	4.35769i		−	0.194882i
$501$	2.52735			0.112914
$502$	−1.52425			−0.0680306
$503$			27.9389i			1.24573i	0.782328	+	0.622867i	$0.214032\pi$
$503$			27.9389i			1.24573i	−0.782328	+	0.622867i	$0.785968\pi$
$504$			34.2168i			1.52414i
$505$		−	1.29232i		−	0.0575074i
$506$	−29.1988			−1.29804
$507$			23.0216i			1.02242i
$508$	−6.48061			−0.287531
$509$	−29.7826			−1.32009			−0.660046	−	0.751225i	$-0.729463\pi$
$509$	−29.7826			−1.32009			−0.660046	+	0.751225i	$0.729463\pi$
$510$	5.10475	+	2.14258i	0.226042	+	0.0948750i
$511$	61.3407			2.71355
$512$	25.3668			1.12107
$513$			17.9483i			0.792437i
$514$	16.0222			0.706708
$515$			17.9492i			0.790937i
$516$			0.231785i			0.0102038i
$517$		−	36.4506i		−	1.60309i
$518$	15.2515			0.670112
$519$	7.01196			0.307791
$520$		−	34.8325i		−	1.52751i
$521$			22.8331i			1.00034i	0.865929	+	0.500168i	$0.166728\pi$
$521$			22.8331i			1.00034i	−0.865929	+	0.500168i	$0.833272\pi$
$522$			11.4346i			0.500480i
$523$	14.2575			0.623439			0.311720	−	0.950174i	$-0.399095\pi$
$523$	14.2575			0.623439			0.311720	+	0.950174i	$0.399095\pi$
$524$		−	4.85543i		−	0.212110i
$525$	−6.39378			−0.279047
$526$	−19.8441			−0.865242
$527$	−2.95667	+	7.04434i	−0.128794	+	0.306856i
$528$	8.18696			0.356292
$529$	−8.23721			−0.358140
$530$			14.6430i			0.636052i
$531$	10.2047			0.442846
$532$		−	7.97262i		−	0.345657i
$533$		−	44.5567i		−	1.92996i
$534$			4.69604i			0.203217i
$535$	9.20843			0.398115
$536$	3.84755			0.166189
$537$		−	3.57285i		−	0.154180i
$538$		−	11.1159i		−	0.479240i
$539$		−	49.2177i		−	2.11996i
$540$	2.13190			0.0917424
$541$		−	31.8209i		−	1.36809i	−0.729441	−	0.684043i	$-0.760220\pi$
$541$		−	31.8209i		−	1.36809i	0.729441	−	0.684043i	$-0.239780\pi$
$542$	−29.9443			−1.28622
$543$	−4.03492			−0.173155
$544$	−7.70809	−	3.23526i	−0.330482	−	0.138711i
$545$	−27.4585			−1.17619
$546$	−24.9653			−1.06842
$547$		−	8.43270i		−	0.360556i	−0.983616	−	0.180278i	$-0.942300\pi$
$547$		−	8.43270i		−	0.360556i	0.983616	−	0.180278i	$-0.0576997\pi$
$548$	2.67315			0.114191
$549$		−	30.0255i		−	1.28146i
$550$		−	11.9915i		−	0.511321i
$551$		−	17.3353i		−	0.738509i
$552$	10.7837			0.458983
$553$	−42.0333			−1.78744
$554$		−	5.33387i		−	0.226614i
$555$		−	2.86631i		−	0.121668i
$556$			7.60024i			0.322322i
$557$	39.2865			1.66462			0.832311	−	0.554308i	$-0.187017\pi$
$557$	39.2865			1.66462			0.832311	+	0.554308i	$0.187017\pi$
$558$		−	6.14621i		−	0.260190i
$559$	7.00534			0.296294
$560$	22.5526			0.953021
$561$	−9.90724	−	4.15829i	−0.418284	−	0.175563i
$562$	−0.823406			−0.0347333
$563$	31.6415			1.33353			0.666766	−	0.745267i	$-0.267678\pi$
$563$	31.6415			1.33353			0.666766	+	0.745267i	$0.267678\pi$
$564$			2.06899i			0.0871201i
$565$	20.2434			0.851645
$566$		−	13.1975i		−	0.554734i
$567$			24.0099i			1.00832i
$568$			32.1969i			1.35095i
$569$	45.9553			1.92655			0.963274	−	0.268520i	$-0.0865344\pi$
$569$	45.9553			1.92655			0.963274	+	0.268520i	$0.0865344\pi$
$570$	6.75230			0.282823
$571$		−	3.91761i		−	0.163947i	−0.996635	−	0.0819735i	$-0.973878\pi$
$571$		−	3.91761i		−	0.163947i	0.996635	−	0.0819735i	$-0.0261223\pi$
$572$			10.3900i			0.434427i
$573$			6.90519i			0.288468i
$574$	35.5190			1.48253
$575$		−	12.8287i		−	0.534994i
$576$	23.0164			0.959019
$577$	25.8931			1.07794			0.538972	−	0.842324i	$-0.318813\pi$
$577$	25.8931			1.07794			0.538972	+	0.842324i	$0.318813\pi$
$578$	−15.2341	−	15.5228i	−0.633654	−	0.645662i
$579$	−11.5034			−0.478063
$580$	−2.05909			−0.0854990
$581$		−	20.2012i		−	0.838086i
$582$	−5.83633			−0.241924
$583$		−	28.4190i		−	1.17699i
$584$		−	42.4881i		−	1.75817i
$585$		−	29.8708i		−	1.23500i
$586$	−16.5714			−0.684556
$587$	28.5942			1.18021			0.590104	−	0.807327i	$-0.299087\pi$
$587$	28.5942			1.18021			0.590104	+	0.807327i	$0.299087\pi$
$588$			2.79367i			0.115209i
$589$			9.31788i			0.383937i
$590$		−	8.28120i		−	0.340932i
$591$	3.33526			0.137194
$592$		−	8.58016i		−	0.352642i
$593$	−28.1528			−1.15610			−0.578049	−	0.816002i	$-0.696186\pi$
$593$	−28.1528			−1.15610			−0.578049	+	0.816002i	$0.696186\pi$
$594$	18.6460			0.765053
$595$	−27.2914	−	11.4548i	−1.11884	−	0.469602i
$596$	−1.27619			−0.0522748
$597$	6.00187			0.245640
$598$		−	50.0913i		−	2.04839i
$599$	36.0903			1.47461			0.737305	−	0.675560i	$-0.236098\pi$
$599$	36.0903			1.47461			0.737305	+	0.675560i	$0.236098\pi$
$600$			4.42870i			0.180801i
$601$		−	0.0241939i		−	0.000986888i	−1.00000		0.000493444i	$-0.999843\pi$
$601$		−	0.0241939i		−	0.000986888i	1.00000		0.000493444i	$-0.000157068\pi$
$602$			5.58441i			0.227603i
$603$	3.29949			0.134365
$604$	−5.57507			−0.226846
$605$		−	9.33284i		−	0.379434i
$606$			0.641565i			0.0260618i
$607$			13.9981i			0.568164i	0.958800	+	0.284082i	$0.0916888\pi$
$607$			13.9981i			0.568164i	−0.958800	+	0.284082i	$0.908311\pi$
$608$	−10.1959			−0.413497
$609$			9.60231i			0.389105i
$610$	−24.3660			−0.986549
$611$	62.5320			2.52977
$612$	−3.58018	−	1.50268i	−0.144720	−	0.0607423i
$613$	−7.92617			−0.320135			−0.160068	−	0.987106i	$-0.551171\pi$
$613$	−7.92617			−0.320135			−0.160068	+	0.987106i	$0.551171\pi$
$614$	−15.0909			−0.609021
$615$		−	6.67530i		−	0.269174i
$616$	−53.8902			−2.17130
$617$			13.1053i			0.527601i	0.964577	+	0.263800i	$0.0849760\pi$
$617$			13.1053i			0.527601i	−0.964577	+	0.263800i	$0.915024\pi$
$618$		−	8.91080i		−	0.358445i
$619$		−	23.7200i		−	0.953386i	−0.879070	−	0.476693i	$-0.841835\pi$
$619$		−	23.7200i		−	0.953386i	0.879070	−	0.476693i	$-0.158165\pi$
$620$	1.10678			0.0444493
$621$	19.9477			0.800473
$622$			32.9175i			1.31987i
$623$		−	25.1063i		−	1.00586i
$624$			14.0450i			0.562248i
$625$	−8.25473			−0.330189
$626$			10.2533i			0.409804i
$627$	−13.1048			−0.523354
$628$	4.56307			0.182086
$629$	−4.35800	+	10.3831i	−0.173765	+	0.414000i
$630$	23.8119			0.948688
$631$	1.38229			0.0550281			0.0275140	−	0.999621i	$-0.491241\pi$
$631$	1.38229			0.0550281			0.0275140	+	0.999621i	$0.491241\pi$
$632$			29.1147i			1.15812i
$633$	5.08342			0.202048
$634$		−	33.4357i		−	1.32790i
$635$			29.3440i			1.16448i
$636$			1.61310i			0.0639637i
$637$	84.4344			3.34541
$638$	−18.0091			−0.712989
$639$			27.6106i			1.09226i
$640$		−	12.0093i		−	0.474709i
$641$			20.4113i			0.806196i	0.915157	+	0.403098i	$0.132067\pi$
$641$			20.4113i			0.806196i	−0.915157	+	0.403098i	$0.867933\pi$
$642$	−4.57148			−0.180422
$643$			31.5236i			1.24317i	0.783347	+	0.621584i	$0.213511\pi$
$643$			31.5236i			1.24317i	−0.783347	+	0.621584i	$0.786489\pi$
$644$	−8.86074			−0.349162
$645$	1.04951			0.0413245
$646$	−24.4599	−	10.2664i	−0.962360	−	0.403924i
$647$	−21.8136			−0.857583			−0.428791	−	0.903404i	$-0.641060\pi$
$647$	−21.8136			−0.857583			−0.428791	+	0.903404i	$0.641060\pi$
$648$	16.6306			0.653312
$649$			16.0721i			0.630883i
$650$	20.5718			0.806893
$651$		−	5.16132i		−	0.202288i
$652$			4.08156i			0.159846i
$653$			46.1402i			1.80561i	0.430055	+	0.902803i	$0.358494\pi$
$653$			46.1402i			1.80561i	−0.430055	+	0.902803i	$0.641506\pi$
$654$	13.6317			0.533040
$655$	−21.9852			−0.859032
$656$		−	19.9822i		−	0.780174i
$657$		−	36.4358i		−	1.42150i
$658$			49.8482i			1.94329i
$659$	7.86210			0.306264			0.153132	−	0.988206i	$-0.451064\pi$
$659$	7.86210			0.306264			0.153132	+	0.988206i	$0.451064\pi$
$660$			1.55659i			0.0605900i
$661$	−31.1105			−1.21006			−0.605029	−	0.796203i	$-0.706839\pi$
$661$	−31.1105			−1.21006			−0.605029	+	0.796203i	$0.706839\pi$
$662$	−32.0056			−1.24393
$663$	7.13367	−	16.9961i	0.277049	−	0.660075i
$664$	−13.9925			−0.543014
$665$	−36.0997			−1.39989
$666$		−	9.05926i		−	0.351039i
$667$	−19.2664			−0.745998
$668$			1.43843i			0.0556544i
$669$			4.76142i			0.184087i
$670$		−	2.67756i		−	0.103443i
$671$	47.2891			1.82558
$672$	5.64765			0.217863
$673$		−	46.5492i		−	1.79434i	−0.441686	−	0.897170i	$-0.645619\pi$
$673$		−	46.5492i		−	1.79434i	0.441686	−	0.897170i	$-0.354381\pi$
$674$		−	35.3418i		−	1.36132i
$675$			8.19225i			0.315320i
$676$	−13.1026			−0.503947
$677$			8.60926i			0.330881i	0.986220	+	0.165440i	$0.0529045\pi$
$677$			8.60926i			0.330881i	−0.986220	+	0.165440i	$0.947095\pi$
$678$	−10.0497			−0.385958
$679$	31.2027			1.19745
$680$	−7.93428	+	18.9036i	−0.304266	+	0.724921i
$681$	−11.3503			−0.434945
$682$	9.68007			0.370669
$683$		−	13.9096i		−	0.532237i	−0.963940	−	0.266118i	$-0.914259\pi$
$683$		−	13.9096i		−	0.532237i	0.963940	−	0.266118i	$-0.0857412\pi$
$684$	−4.73567			−0.181073
$685$		−	12.1039i		−	0.462466i
$686$			28.2172i			1.07734i
$687$		−	9.25105i		−	0.352950i
$688$	3.14167			0.119775
$689$	48.7535			1.85736
$690$		−	7.50448i		−	0.285691i
$691$		−	0.423564i		−	0.0161131i	−0.999968	−	0.00805657i	$-0.997435\pi$
$691$		−	0.423564i		−	0.0161131i	0.999968	−	0.00805657i	$-0.00256451\pi$
$692$			3.99082i			0.151708i
$693$	−46.2138			−1.75552
$694$			15.3511i			0.582718i
$695$	34.4136			1.30538
$696$	6.65111			0.252110
$697$	−10.1493	+	24.1809i	−0.384432	+	0.915919i
$698$	−0.973119			−0.0368331
$699$	−1.91476			−0.0724228
$700$		−	3.63899i		−	0.137541i
$701$	−3.24682			−0.122631			−0.0613154	−	0.998118i	$-0.519530\pi$
$701$	−3.24682			−0.122631			−0.0613154	+	0.998118i	$0.519530\pi$
$702$			31.9877i			1.20730i
$703$			13.7342i			0.517994i
$704$			36.2501i			1.36623i
$705$	9.36829			0.352830
$706$	−10.5489			−0.397014
$707$		−	3.42999i		−	0.128998i
$708$		−	0.912273i		−	0.0342853i
$709$		−	19.4301i		−	0.729712i	−0.931064	−	0.364856i	$-0.881118\pi$
$709$		−	19.4301i		−	0.729712i	0.931064	−	0.364856i	$-0.118882\pi$
$710$	22.4062			0.840890
$711$			24.9674i			0.936351i
$712$	−17.3901			−0.651722
$713$	10.3559			0.387830
$714$	13.5487	+	5.68670i	0.507048	+	0.212819i
$715$	47.0454			1.75940
$716$	2.03347			0.0759943
$717$		−	9.82648i		−	0.366977i
$718$	2.96088			0.110499
$719$		−	32.5701i		−	1.21466i	−0.794450	−	0.607330i	$-0.792241\pi$
$719$		−	32.5701i		−	1.21466i	0.794450	−	0.607330i	$-0.207759\pi$
$720$		−	13.3961i		−	0.499242i
$721$			47.6397i			1.77419i
$722$	−8.04616			−0.299447
$723$	−7.63974			−0.284125
$724$		−	2.29646i		−	0.0853471i
$725$		−	7.91245i		−	0.293861i
$726$			4.63324i			0.171956i
$727$	24.0623			0.892420			0.446210	−	0.894928i	$-0.352773\pi$
$727$	24.0623			0.892420			0.446210	+	0.894928i	$0.352773\pi$
$728$		−	92.4502i		−	3.42643i
$729$	7.42870			0.275137
$730$	−29.5680			−1.09436
$731$	−3.80181	−	1.59570i	−0.140615	−	0.0590192i
$732$	−2.68420			−0.0992109
$733$	−19.9406			−0.736523			−0.368261	−	0.929722i	$-0.620047\pi$
$733$	−19.9406			−0.736523			−0.368261	+	0.929722i	$0.620047\pi$
$734$		−	4.07076i		−	0.150255i
$735$	12.6496			0.466588
$736$			11.3316i			0.417690i
$737$			5.19658i			0.191418i
$738$		−	21.0980i		−	0.776627i
$739$	−35.5023			−1.30597			−0.652987	−	0.757369i	$-0.726484\pi$
$739$	−35.5023			−1.30597			−0.652987	+	0.757369i	$0.726484\pi$
$740$	1.63135			0.0599694
$741$		−	22.4816i		−	0.825883i
$742$			38.8646i			1.42676i
$743$		−	15.3926i		−	0.564701i	−0.959311	−	0.282351i	$-0.908886\pi$
$743$		−	15.3926i		−	0.564701i	0.959311	−	0.282351i	$-0.0911141\pi$
$744$	−3.57503			−0.131067
$745$			5.77853i			0.211709i
$746$	29.9008			1.09475
$747$	−11.9993			−0.439033
$748$	2.36667	−	5.63865i	0.0865341	−	0.206170i
$749$	24.4404			0.893034
$750$	9.79557			0.357684
$751$			35.8646i			1.30872i	0.756184	+	0.654359i	$0.227061\pi$
$751$			35.8646i			1.30872i	−0.756184	+	0.654359i	$0.772939\pi$
$752$	28.0436			1.02264
$753$			0.760309i			0.0277072i
$754$		−	30.8952i		−	1.12514i
$755$			25.2437i			0.918711i
$756$	5.65836			0.205793
$757$	15.9757			0.580646			0.290323	−	0.956929i	$-0.406237\pi$
$757$	15.9757			0.580646			0.290323	+	0.956929i	$0.406237\pi$
$758$			6.72160i			0.244140i
$759$			14.5646i			0.528662i
$760$			25.0047i			0.907017i
$761$	−30.5967			−1.10913			−0.554564	−	0.832141i	$-0.687115\pi$
$761$	−30.5967			−1.10913			−0.554564	+	0.832141i	$0.687115\pi$
$762$		−	14.5677i		−	0.527731i
$763$	−72.8787			−2.63839
$764$	−3.93005			−0.142184
$765$	−6.80408	+	16.2109i	−0.246002	+	0.586106i
$766$	37.1912			1.34377
$767$	−27.5721			−0.995569
$768$		−	5.36827i		−	0.193711i
$769$	33.6044			1.21181			0.605903	−	0.795538i	$-0.292812\pi$
$769$	33.6044			1.21181			0.605903	+	0.795538i	$0.292812\pi$
$770$			37.5029i			1.35151i
$771$		−	7.99201i		−	0.287825i
$772$		−	6.54708i		−	0.235635i
$773$	17.2751			0.621342			0.310671	−	0.950518i	$-0.399446\pi$
$773$	17.2751			0.621342			0.310671	+	0.950518i	$0.399446\pi$
$774$	3.31709			0.119230
$775$			4.25301i			0.152773i
$776$		−	21.6128i		−	0.775853i
$777$		−	7.60758i		−	0.272920i
$778$	4.40867			0.158058
$779$			31.9853i			1.14599i
$780$	−2.67037			−0.0956145
$781$	−43.4857			−1.55604
$782$	−11.4100	+	27.1846i	−0.408020	+	0.972119i
$783$	12.3033			0.439683
$784$	37.8661			1.35236
$785$		−	20.6614i		−	0.737437i
$786$	10.9144			0.389305
$787$		−	13.4063i		−	0.477883i	−0.971034	−	0.238941i	$-0.923200\pi$
$787$		−	13.4063i		−	0.477883i	0.971034	−	0.238941i	$-0.0768004\pi$
$788$			1.89825i			0.0676223i
$789$			9.89839i			0.352392i
$790$	20.2613			0.720863
$791$	53.7287			1.91037
$792$			32.0104i			1.13744i
$793$			81.1259i			2.88086i
$794$		−	35.5848i		−	1.26286i
$795$	7.30406			0.259048
$796$			3.41594i			0.121075i
$797$	−21.3737			−0.757094			−0.378547	−	0.925582i	$-0.623576\pi$
$797$	−21.3737			−0.757094			−0.378547	+	0.925582i	$0.623576\pi$
$798$	17.9215			0.634415
$799$	−33.9362	−	14.2438i	−1.20058	−	0.503909i
$800$	−4.65375			−0.164535
$801$	−14.9130			−0.526924
$802$		−	25.5817i		−	0.903321i
$803$	57.3852			2.02508
$804$		−	0.294965i		−	0.0104026i
$805$			40.1211i			1.41408i
$806$			16.6064i			0.584937i
$807$	−5.54470			−0.195183
$808$	−2.37581			−0.0835807
$809$		−	24.0716i		−	0.846311i	−0.906057	−	0.423156i	$-0.860922\pi$
$809$		−	24.0716i		−	0.846311i	0.906057	−	0.423156i	$-0.139078\pi$
$810$		−	11.5735i		−	0.406650i
$811$			43.5495i			1.52923i	0.644487	+	0.764615i	$0.277071\pi$
$811$			43.5495i			1.52923i	−0.644487	+	0.764615i	$0.722929\pi$
$812$	−5.46511			−0.191788
$813$			14.9365i			0.523845i
$814$	14.2680			0.500094
$815$	18.4811			0.647366
$816$	3.19922	−	7.62221i	0.111995	−	0.266831i
$817$	−5.02883			−0.175937
$818$	−12.9005			−0.451055
$819$		−	79.2811i		−	2.77031i
$820$	3.79922			0.132674
$821$		−	34.3157i		−	1.19763i	−0.800889	−	0.598813i	$-0.795639\pi$
$821$		−	34.3157i		−	1.19763i	0.800889	−	0.598813i	$-0.204361\pi$
$822$			6.00893i			0.209585i
$823$		−	3.77001i		−	0.131414i	−0.997839	−	0.0657072i	$-0.979070\pi$
$823$		−	3.77001i		−	0.131414i	0.997839	−	0.0657072i	$-0.0209303\pi$
$824$	32.9980			1.14954
$825$	−5.98149			−0.208249
$826$		−	21.9795i		−	0.764763i
$827$			26.6591i			0.927028i	0.886090	+	0.463514i	$0.153412\pi$
$827$			26.6591i			0.927028i	−0.886090	+	0.463514i	$0.846588\pi$
$828$			5.26321i			0.182909i
$829$	31.3466			1.08871			0.544357	−	0.838854i	$-0.316774\pi$
$829$	31.3466			1.08871			0.544357	+	0.838854i	$0.316774\pi$
$830$			9.73756i			0.337996i
$831$	−2.66058			−0.0922945
$832$	−62.1881			−2.15598
$833$	−45.8226	−	19.2328i	−1.58766	−	0.666377i
$834$	−17.0844			−0.591586
$835$	6.51314			0.225396
$836$		−	7.45852i		−	0.257958i
$837$	−6.61312			−0.228583
$838$			1.54183i			0.0532617i
$839$		−	47.6809i		−	1.64613i	−0.567948	−	0.823065i	$-0.692262\pi$
$839$		−	47.6809i		−	1.64613i	0.567948	−	0.823065i	$-0.307738\pi$
$840$		−	13.8505i		−	0.477889i
$841$	17.1169			0.590238
$842$	−3.15959			−0.108887
$843$			0.410722i			0.0141460i
$844$			2.89321i			0.0995882i
$845$			59.3281i			2.04095i
$846$	29.6094			1.01799
$847$		−	24.7706i		−	0.851129i
$848$	21.8644			0.750826
$849$	−6.58305			−0.225930
$850$	−11.1644	−	4.68593i	−0.382934	−	0.160726i
$851$	15.2641			0.523247
$852$	2.46831			0.0845630
$853$		−	2.04817i		−	0.0701281i	−0.999385	−	0.0350641i	$-0.988836\pi$
$853$		−	2.04817i		−	0.0701281i	0.999385	−	0.0350641i	$-0.0111635\pi$
$854$	−64.6706			−2.21298
$855$			21.4429i			0.733333i
$856$		−	16.9289i		−	0.578616i
$857$			11.1823i			0.381980i	0.981592	+	0.190990i	$0.0611698\pi$
$857$			11.1823i			0.381980i	−0.981592	+	0.190990i	$0.938830\pi$
$858$	−23.3555			−0.797343
$859$	−38.8266			−1.32475			−0.662373	−	0.749174i	$-0.730451\pi$
$859$	−38.8266			−1.32475			−0.662373	+	0.749174i	$0.730451\pi$
$860$			0.597325i			0.0203686i
$861$		−	17.7172i		−	0.603800i
$862$		−	37.1343i		−	1.26480i
$863$	−38.0014			−1.29358			−0.646792	−	0.762666i	$-0.723890\pi$
$863$	−38.0014			−1.29358			−0.646792	+	0.762666i	$0.723890\pi$
$864$		−	7.23624i		−	0.246182i
$865$	18.0703			0.614408
$866$	3.33195			0.113224
$867$	−7.74289	+	7.59889i	−0.262962	+	0.258072i
$868$	2.93754			0.0997067
$869$	−39.3228			−1.33394
$870$		−	4.62859i		−	0.156924i
$871$	−8.91487			−0.302069
$872$			50.4800i			1.70947i
$873$		−	18.5341i		−	0.627286i
$874$			35.9584i			1.21631i
$875$	−52.3699			−1.77043
$876$	−3.25727			−0.110053
$877$		−	5.85862i		−	0.197831i	−0.995096	−	0.0989157i	$-0.968463\pi$
$877$		−	5.85862i		−	0.197831i	0.995096	−	0.0989157i	$-0.0315374\pi$
$878$			47.6024i			1.60650i
$879$			8.26594i			0.278803i
$880$	21.0983			0.711225
$881$		−	51.1521i		−	1.72336i	−0.507455	−	0.861678i	$-0.669414\pi$
$881$		−	51.1521i		−	1.72336i	0.507455	−	0.861678i	$-0.330586\pi$
$882$	39.9804			1.34621
$883$	41.4914			1.39630			0.698149	−	0.715953i	$-0.254007\pi$
$883$	41.4914			1.39630			0.698149	+	0.715953i	$0.254007\pi$
$884$	9.67327	+	4.06009i	0.325347	+	0.136556i
$885$	−4.13074			−0.138853
$886$	32.6015			1.09527
$887$		−	53.2655i		−	1.78848i	−0.447589	−	0.894240i	$-0.647717\pi$
$887$		−	53.2655i		−	1.78848i	0.447589	−	0.894240i	$-0.352283\pi$
$888$	−5.26945			−0.176831
$889$			77.8829i			2.61211i
$890$			12.1020i			0.405660i
$891$			22.4616i			0.752493i
$892$	−2.70994			−0.0907355
$893$	−44.8890			−1.50215
$894$		−	2.86873i		−	0.0959446i
$895$		−	9.20746i		−	0.307772i
$896$		−	31.8744i		−	1.06485i
$897$	−24.9860			−0.834258
$898$			5.04825i			0.168462i
$899$	6.38726			0.213027
$900$	−2.16153			−0.0720510
$901$	−26.4586	−	11.1053i	−0.881464	−	0.369970i
$902$	33.2286			1.10639
$903$	2.78555			0.0926973
$904$		−	37.2156i		−	1.23777i
$905$	−10.3983			−0.345650
$906$		−	12.5321i		−	0.416351i
$907$			10.4178i			0.345918i	0.984929	+	0.172959i	$0.0553328\pi$
$907$			10.4178i			0.345918i	−0.984929	+	0.172959i	$0.944667\pi$
$908$		−	6.45998i		−	0.214382i
$909$	−2.03739			−0.0675759
$910$	−64.3373			−2.13276
$911$			9.73793i			0.322632i	0.986903	+	0.161316i	$0.0515738\pi$
$911$			9.73793i			0.322632i	−0.986903	+	0.161316i	$0.948426\pi$
$912$		−	10.0823i		−	0.333857i
$913$		−	18.8985i		−	0.625450i
$914$	17.3015			0.572281
$915$			12.1540i			0.401797i
$916$	5.26519			0.173967
$917$	−58.3517			−1.92694
$918$	7.28628	−	17.3597i	0.240483	−	0.572957i
$919$	−20.5028			−0.676324			−0.338162	−	0.941088i	$-0.609805\pi$
$919$	−20.5028			−0.676324			−0.338162	+	0.941088i	$0.609805\pi$
$920$	27.7902			0.916215
$921$			7.52749i			0.248039i
$922$	5.01414			0.165132
$923$		−	74.6010i		−	2.45552i
$924$			4.13139i			0.135913i
$925$			6.26876i			0.206116i
$926$	−27.6480			−0.908569
$927$	28.2976			0.929415
$928$			6.98910i			0.229428i
$929$		−	38.9055i		−	1.27645i	−0.769850	−	0.638225i	$-0.779669\pi$
$929$		−	38.9055i		−	1.27645i	0.769850	−	0.638225i	$-0.220331\pi$
$930$			2.48791i			0.0815818i
$931$	−60.6118			−1.98647
$932$		−	1.08978i		−	0.0356968i
$933$	16.4196			0.537552
$934$	35.2811			1.15443
$935$	−25.5316	−	10.7162i	−0.834972	−	0.350457i
$936$	−54.9147			−1.79494
$937$	−26.4384			−0.863706			−0.431853	−	0.901944i	$-0.642140\pi$
$937$	−26.4384			−0.863706			−0.431853	+	0.901944i	$0.642140\pi$
$938$		−	7.10661i		−	0.232039i
$939$	5.11444			0.166903
$940$			5.33192i			0.173908i
$941$		−	43.1479i		−	1.40658i	−0.710902	−	0.703291i	$-0.751713\pi$
$941$		−	43.1479i		−	1.40658i	0.710902	−	0.703291i	$-0.248287\pi$
$942$			10.2573i			0.334200i
$943$	35.5484			1.15761
$944$	−12.3652			−0.402452
$945$		−	25.6208i		−	0.833445i
$946$			5.22430i			0.169857i
$947$			2.21854i			0.0720930i	0.999350	+	0.0360465i	$0.0114764\pi$
$947$			2.21854i			0.0720930i	−0.999350	+	0.0360465i	$0.988524\pi$
$948$	2.23202			0.0724927
$949$			98.4459i			3.19569i
$950$	−14.7676			−0.479125
$951$	−16.6780			−0.540822
$952$	−21.0587	+	50.1728i	−0.682515	+	1.62611i
$953$	9.58227			0.310400			0.155200	−	0.987883i	$-0.450398\pi$
$953$	9.58227			0.310400			0.155200	+	0.987883i	$0.450398\pi$
$954$	23.0852			0.747412
$955$			17.7951i			0.575836i
$956$	5.59269			0.180881
$957$			8.98312i			0.290383i
$958$		−	32.7115i		−	1.05686i
$959$		−	32.1254i		−	1.03738i
$960$	−9.31677			−0.300697
$961$	27.5668			0.889251
$962$			24.4772i			0.789176i
$963$		−	14.5174i		−	0.467817i
$964$		−	4.34812i		−	0.140044i
$965$	−29.6449			−0.954304
$966$		−	19.9179i		−	0.640849i
$967$	19.7816			0.636135			0.318067	−	0.948068i	$-0.396966\pi$
$967$	19.7816			0.636135			0.318067	+	0.948068i	$0.396966\pi$
$968$	−17.1576			−0.551465
$969$	−5.12095	+	12.2008i	−0.164509	+	0.391946i
$970$	−15.0406			−0.482925
$971$	5.52259			0.177228			0.0886142	−	0.996066i	$-0.471756\pi$
$971$	5.52259			0.177228			0.0886142	+	0.996066i	$0.471756\pi$
$972$		−	5.16390i		−	0.165632i
$973$	91.3383			2.92817
$974$		−	34.3342i		−	1.10014i
$975$		−	10.2614i		−	0.328628i
$976$			36.3823i			1.16457i
$977$	−41.8813			−1.33990			−0.669950	−	0.742406i	$-0.733685\pi$
$977$	−41.8813			−1.33990			−0.669950	+	0.742406i	$0.733685\pi$
$978$	−9.17487			−0.293380
$979$		−	23.4874i		−	0.750661i
$980$			7.19947i			0.229979i
$981$			43.2893i			1.38212i
$982$	−40.1856			−1.28237
$983$		−	17.2827i		−	0.551232i	−0.961268	−	0.275616i	$-0.911118\pi$
$983$		−	17.2827i		−	0.551232i	0.961268	−	0.275616i	$-0.0888818\pi$
$984$	−12.2719			−0.391215
$985$	8.59519			0.273866
$986$	−7.03743	+	16.7668i	−0.224117	+	0.533965i
$987$	24.8647			0.791453
$988$	12.7953			0.407073
$989$			5.58903i			0.177721i
$990$	22.2764			0.707991
$991$			59.5531i			1.89177i	0.324506	+	0.945884i	$0.394802\pi$
$991$			59.5531i			1.89177i	−0.324506	+	0.945884i	$0.605198\pi$
$992$		−	3.75670i		−	0.119275i
$993$			15.9647i			0.506624i
$994$	59.4692			1.88625
$995$	15.4672			0.490344
$996$			1.07271i			0.0339901i
$997$		−	16.0337i		−	0.507792i	−0.967232	−	0.253896i	$-0.918288\pi$
$997$		−	16.0337i		−	0.507792i	0.967232	−	0.253896i	$-0.0817121\pi$
$998$		−	27.4189i		−	0.867930i
$999$	−9.74747			−0.308396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.14	yes	34
17.16	even	2	inner	731.2.d.d.560.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.13	✓	34	17.16	even	2	inner
731.2.d.d.560.14	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)

\(f(q)\)	\(=\)	\(q-1.27937 q^{2} +0.638162i q^{3} -0.363207 q^{4} +1.64459i q^{5} -0.816447i q^{6} +4.36496i q^{7} +3.02342 q^{8} +2.59275 q^{9} +O(q^{10})\)	\(q-1.27937 q^{2} +0.638162i q^{3} -0.363207 q^{4} +1.64459i q^{5} -0.816447i q^{6} +4.36496i q^{7} +3.02342 q^{8} +2.59275 q^{9} -2.10404i q^{10} +4.08349i q^{11} -0.231785i q^{12} -7.00534 q^{13} -5.58441i q^{14} -1.04951 q^{15} -3.14167 q^{16} +(3.80181 + 1.59570i) q^{17} -3.31709 q^{18} +5.02883 q^{19} -0.597325i q^{20} -2.78555 q^{21} -5.22430i q^{22} -5.58903i q^{23} +1.92943i q^{24} +2.29534 q^{25} +8.96244 q^{26} +3.56908i q^{27} -1.58538i q^{28} -3.44718i q^{29} +1.34272 q^{30} +1.85289i q^{31} -2.02748 q^{32} -2.60593 q^{33} +(-4.86392 - 2.04150i) q^{34} -7.17855 q^{35} -0.941704 q^{36} +2.73109i q^{37} -6.43375 q^{38} -4.47054i q^{39} +4.97228i q^{40} +6.36038i q^{41} +3.56376 q^{42} -1.00000 q^{43} -1.48315i q^{44} +4.26400i q^{45} +7.15044i q^{46} -8.92633 q^{47} -2.00489i q^{48} -12.0529 q^{49} -2.93659 q^{50} +(-1.01832 + 2.42617i) q^{51} +2.54439 q^{52} -6.95948 q^{53} -4.56618i q^{54} -6.71565 q^{55} +13.1971i q^{56} +3.20921i q^{57} +4.41023i q^{58} +3.93586 q^{59} +0.381190 q^{60} -11.5806i q^{61} -2.37054i q^{62} +11.3172i q^{63} +8.87724 q^{64} -11.5209i q^{65} +3.33395 q^{66} +1.27258 q^{67} +(-1.38084 - 0.579571i) q^{68} +3.56671 q^{69} +9.18403 q^{70} +10.6492i q^{71} +7.83897 q^{72} -14.0530i q^{73} -3.49407i q^{74} +1.46480i q^{75} -1.82651 q^{76} -17.8243 q^{77} +5.71949i q^{78} +9.62971i q^{79} -5.16674i q^{80} +5.50059 q^{81} -8.13730i q^{82} -4.62804 q^{83} +1.01173 q^{84} +(-2.62427 + 6.25240i) q^{85} +1.27937 q^{86} +2.19986 q^{87} +12.3461i q^{88} -5.75180 q^{89} -5.45524i q^{90} -30.5780i q^{91} +2.02997i q^{92} -1.18245 q^{93} +11.4201 q^{94} +8.27035i q^{95} -1.29386i q^{96} -7.14845i q^{97} +15.4201 q^{98} +10.5875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 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

Properties

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