LMFDB - Embedded newform 731.2.d.d.560.18

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			560.18
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.335917 q^{2} +0.523814i q^{3} -1.88716 q^{4} +1.51365i q^{5} -0.175958i q^{6} -0.357736i q^{7} +1.30576 q^{8} +2.72562 q^{9} +O(q^{10})$	\(q-0.335917 q^{2} +0.523814i q^{3} -1.88716 q^{4} +1.51365i q^{5} -0.175958i q^{6} -0.357736i q^{7} +1.30576 q^{8} +2.72562 q^{9} -0.508460i q^{10} -2.34365i q^{11} -0.988522i q^{12} +2.14106 q^{13} +0.120169i q^{14} -0.792872 q^{15} +3.33569 q^{16} +(-0.486082 + 4.09435i) q^{17} -0.915581 q^{18} -4.97882 q^{19} -2.85650i q^{20} +0.187387 q^{21} +0.787272i q^{22} -0.807389i q^{23} +0.683977i q^{24} +2.70887 q^{25} -0.719217 q^{26} +2.99916i q^{27} +0.675105i q^{28} +8.18449i q^{29} +0.266339 q^{30} +3.43915i q^{31} -3.73204 q^{32} +1.22764 q^{33} +(0.163283 - 1.37536i) q^{34} +0.541487 q^{35} -5.14368 q^{36} +10.1722i q^{37} +1.67247 q^{38} +1.12152i q^{39} +1.97647i q^{40} +1.18063i q^{41} -0.0629465 q^{42} -1.00000 q^{43} +4.42284i q^{44} +4.12563i q^{45} +0.271216i q^{46} -4.86238 q^{47} +1.74728i q^{48} +6.87203 q^{49} -0.909953 q^{50} +(-2.14468 - 0.254617i) q^{51} -4.04052 q^{52} -2.67131 q^{53} -1.00747i q^{54} +3.54747 q^{55} -0.467118i q^{56} -2.60798i q^{57} -2.74931i q^{58} +9.76059 q^{59} +1.49628 q^{60} +4.64117i q^{61} -1.15527i q^{62} -0.975051i q^{63} -5.41773 q^{64} +3.24081i q^{65} -0.412384 q^{66} +2.25892 q^{67} +(0.917314 - 7.72670i) q^{68} +0.422922 q^{69} -0.181894 q^{70} +2.84290i q^{71} +3.55901 q^{72} -6.73975i q^{73} -3.41702i q^{74} +1.41894i q^{75} +9.39583 q^{76} -0.838408 q^{77} -0.376736i q^{78} -2.43002i q^{79} +5.04907i q^{80} +6.60585 q^{81} -0.396593i q^{82} -0.628850 q^{83} -0.353630 q^{84} +(-6.19741 - 0.735758i) q^{85} +0.335917 q^{86} -4.28715 q^{87} -3.06025i q^{88} +0.199232 q^{89} -1.38587i q^{90} -0.765933i q^{91} +1.52367i q^{92} -1.80148 q^{93} +1.63335 q^{94} -7.53619i q^{95} -1.95490i q^{96} +4.95539i q^{97} -2.30843 q^{98} -6.38790i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.335917			−0.237529			−0.118765	−	0.992922i	$-0.537893\pi$
$2$	−0.335917			−0.237529			−0.118765	+	0.992922i	$0.537893\pi$
$3$			0.523814i			0.302424i	0.988501	+	0.151212i	$0.0483177\pi$
$3$			0.523814i			0.302424i	−0.988501	+	0.151212i	$0.951682\pi$
$4$	−1.88716			−0.943580
$5$			1.51365i			0.676925i	0.940980	+	0.338462i	$0.109907\pi$
$5$			1.51365i			0.676925i	−0.940980	+	0.338462i	$0.890093\pi$
$6$		−	0.175958i		−	0.0718346i
$7$		−	0.357736i		−	0.135211i	−0.997712	−	0.0676057i	$-0.978464\pi$
$7$		−	0.357736i		−	0.135211i	0.997712	−	0.0676057i	$-0.0215360\pi$
$8$	1.30576			0.461657
$9$	2.72562			0.908539
$10$		−	0.508460i		−	0.160789i
$11$		−	2.34365i		−	0.706637i	−0.935503	−	0.353319i	$-0.885053\pi$
$11$		−	2.34365i		−	0.706637i	0.935503	−	0.353319i	$-0.114947\pi$
$12$		−	0.988522i		−	0.285362i
$13$	2.14106			0.593823			0.296911	−	0.954905i	$-0.404043\pi$
$13$	2.14106			0.593823			0.296911	+	0.954905i	$0.404043\pi$
$14$			0.120169i			0.0321166i
$15$	−0.792872			−0.204719
$16$	3.33569			0.833923
$17$	−0.486082	+	4.09435i	−0.117892	+	0.993026i
$17$	−0.486082	+	4.09435i	−0.117892	+	0.993026i
$18$	−0.915581			−0.215804
$19$	−4.97882			−1.14222			−0.571110	−	0.820873i	$-0.693487\pi$
$19$	−4.97882			−1.14222			−0.571110	+	0.820873i	$0.693487\pi$
$20$		−	2.85650i		−	0.638733i
$21$	0.187387			0.0408912
$22$			0.787272i			0.167847i
$23$		−	0.807389i		−	0.168352i	−0.996451	−	0.0841762i	$-0.973174\pi$
$23$		−	0.807389i		−	0.168352i	0.996451	−	0.0841762i	$-0.0268258\pi$
$24$			0.683977i			0.139616i
$25$	2.70887			0.541773
$26$	−0.719217			−0.141050
$27$			2.99916i			0.577189i
$28$			0.675105i			0.127583i
$29$			8.18449i			1.51982i	0.650027	+	0.759911i	$0.274757\pi$
$29$			8.18449i			1.51982i	−0.650027	+	0.759911i	$0.725243\pi$
$30$	0.266339			0.0486266
$31$			3.43915i			0.617690i	0.951112	+	0.308845i	$0.0999424\pi$
$31$			3.43915i			0.617690i	−0.951112	+	0.308845i	$0.900058\pi$
$32$	−3.73204			−0.659738
$33$	1.22764			0.213704
$34$	0.163283	−	1.37536i	0.0280028	−	0.235873i
$35$	0.541487			0.0915280
$36$	−5.14368			−0.857280
$37$			10.1722i			1.67230i	0.548500	+	0.836151i	$0.315199\pi$
$37$			10.1722i			1.67230i	−0.548500	+	0.836151i	$0.684801\pi$
$38$	1.67247			0.271310
$39$			1.12152i			0.179586i
$40$			1.97647i			0.312507i
$41$			1.18063i			0.184383i	0.995741	+	0.0921916i	$0.0293872\pi$
$41$			1.18063i			0.184383i	−0.995741	+	0.0921916i	$0.970613\pi$
$42$	−0.0629465			−0.00971286
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$			4.42284i			0.666769i
$45$			4.12563i			0.615013i
$46$			0.271216i			0.0399886i
$47$	−4.86238			−0.709250			−0.354625	−	0.935009i	$-0.615392\pi$
$47$	−4.86238			−0.709250			−0.354625	+	0.935009i	$0.615392\pi$
$48$			1.74728i			0.252199i
$49$	6.87203			0.981718
$50$	−0.909953			−0.128687
$51$	−2.14468	−	0.254617i	−0.300315	−	0.0356535i
$52$	−4.04052			−0.560319
$53$	−2.67131			−0.366932			−0.183466	−	0.983026i	$-0.558732\pi$
$53$	−2.67131			−0.366932			−0.183466	+	0.983026i	$0.558732\pi$
$54$		−	1.00747i		−	0.137099i
$55$	3.54747			0.478340
$56$		−	0.467118i		−	0.0624213i
$57$		−	2.60798i		−	0.345435i
$58$		−	2.74931i		−	0.361002i
$59$	9.76059			1.27072			0.635360	−	0.772216i	$-0.280852\pi$
$59$	9.76059			1.27072			0.635360	+	0.772216i	$0.280852\pi$
$60$	1.49628			0.193168
$61$			4.64117i			0.594241i	0.954840	+	0.297121i	$0.0960263\pi$
$61$			4.64117i			0.594241i	−0.954840	+	0.297121i	$0.903974\pi$
$62$		−	1.15527i		−	0.146719i
$63$		−	0.975051i		−	0.122845i
$64$	−5.41773			−0.677216
$65$			3.24081i			0.401973i
$66$	−0.412384			−0.0507610
$67$	2.25892			0.275971			0.137985	−	0.990434i	$-0.455937\pi$
$67$	2.25892			0.275971			0.137985	+	0.990434i	$0.455937\pi$
$68$	0.917314	−	7.72670i	0.111241	−	0.937000i
$69$	0.422922			0.0509139
$70$	−0.181894			−0.0217405
$71$			2.84290i			0.337390i	0.985668	+	0.168695i	$0.0539554\pi$
$71$			2.84290i			0.337390i	−0.985668	+	0.168695i	$0.946045\pi$
$72$	3.55901			0.419433
$73$		−	6.73975i		−	0.788828i	−0.918933	−	0.394414i	$-0.870948\pi$
$73$		−	6.73975i		−	0.788828i	0.918933	−	0.394414i	$-0.129052\pi$
$74$		−	3.41702i		−	0.397220i
$75$			1.41894i			0.163845i
$76$	9.39583			1.07778
$77$	−0.838408			−0.0955455
$78$		−	0.376736i		−	0.0426570i
$79$		−	2.43002i		−	0.273399i	−0.990613	−	0.136699i	$-0.956351\pi$
$79$		−	2.43002i		−	0.273399i	0.990613	−	0.136699i	$-0.0436495\pi$
$80$			5.04907i			0.564503i
$81$	6.60585			0.733983
$82$		−	0.396593i		−	0.0437964i
$83$	−0.628850			−0.0690252			−0.0345126	−	0.999404i	$-0.510988\pi$
$83$	−0.628850			−0.0690252			−0.0345126	+	0.999404i	$0.510988\pi$
$84$	−0.353630			−0.0385842
$85$	−6.19741	−	0.735758i	−0.672204	−	0.0798041i
$86$	0.335917			0.0362228
$87$	−4.28715			−0.459631
$88$		−	3.06025i		−	0.326224i
$89$	0.199232			0.0211186			0.0105593	−	0.999944i	$-0.496639\pi$
$89$	0.199232			0.0211186			0.0105593	+	0.999944i	$0.496639\pi$
$90$		−	1.38587i		−	0.146083i
$91$		−	0.765933i		−	0.0802916i
$92$			1.52367i			0.158854i
$93$	−1.80148			−0.186804
$94$	1.63335			0.168468
$95$		−	7.53619i		−	0.773197i
$96$		−	1.95490i		−	0.199521i
$97$			4.95539i			0.503143i	0.967839	+	0.251572i	$0.0809474\pi$
$97$			4.95539i			0.503143i	−0.967839	+	0.251572i	$0.919053\pi$
$98$	−2.30843			−0.233186
$99$		−	6.38790i		−	0.642008i
$100$	−5.11206			−0.511206
$101$	−9.32209			−0.927583			−0.463791	−	0.885944i	$-0.653511\pi$
$101$	−9.32209			−0.927583			−0.463791	+	0.885944i	$0.653511\pi$
$102$	0.720434	+	0.0855301i	0.0713336	+	0.00846874i
$103$	−7.56823			−0.745719			−0.372860	−	0.927888i	$-0.621623\pi$
$103$	−7.56823			−0.745719			−0.372860	+	0.927888i	$0.621623\pi$
$104$	2.79571			0.274142
$105$			0.283639i			0.0276803i
$106$	0.897336			0.0871570
$107$			5.42685i			0.524634i	0.964982	+	0.262317i	$0.0844866\pi$
$107$			5.42685i			0.524634i	−0.964982	+	0.262317i	$0.915513\pi$
$108$		−	5.65990i		−	0.544624i
$109$		−	17.1498i		−	1.64265i	−0.570458	−	0.821327i	$-0.693234\pi$
$109$		−	17.1498i		−	1.64265i	0.570458	−	0.821327i	$-0.306766\pi$
$110$	−1.19165			−0.113620
$111$	−5.32835			−0.505745
$112$		−	1.19330i		−	0.112756i
$113$			0.362438i			0.0340953i	0.999855	+	0.0170477i	$0.00542670\pi$
$113$			0.362438i			0.0340953i	−0.999855	+	0.0170477i	$0.994573\pi$
$114$			0.876064i			0.0820509i
$115$	1.22210			0.113962
$116$		−	15.4454i		−	1.43407i
$117$	5.83571			0.539511
$118$	−3.27875			−0.301833
$119$	1.46470	+	0.173889i	0.134269	+	0.0159404i
$120$	−1.03530			−0.0945097
$121$	5.50730			0.500663
$122$		−	1.55905i		−	0.141150i
$123$	−0.618431			−0.0557620
$124$		−	6.49023i		−	0.582840i
$125$			11.6685i			1.04366i
$126$			0.327536i			0.0291792i
$127$	19.9721			1.77224			0.886121	−	0.463455i	$-0.153390\pi$
$127$	19.9721			1.77224			0.886121	+	0.463455i	$0.153390\pi$
$128$	9.28399			0.820596
$129$		−	0.523814i		−	0.0461193i
$130$		−	1.08864i		−	0.0954803i
$131$			3.53090i			0.308496i	0.988032	+	0.154248i	$0.0492955\pi$
$131$			3.53090i			0.308496i	−0.988032	+	0.154248i	$0.950705\pi$
$132$	−2.31675			−0.201647
$133$			1.78110i			0.154441i
$134$	−0.758809			−0.0655511
$135$	−4.53968			−0.390713
$136$	−0.634708	+	5.34625i	−0.0544257	+	0.458437i
$137$	−1.01292			−0.0865398			−0.0432699	−	0.999063i	$-0.513778\pi$
$137$	−1.01292			−0.0865398			−0.0432699	+	0.999063i	$0.513778\pi$
$138$	−0.142067			−0.0120935
$139$			9.60563i			0.814739i	0.913263	+	0.407370i	$0.133554\pi$
$139$			9.60563i			0.814739i	−0.913263	+	0.407370i	$0.866446\pi$
$140$	−1.02187			−0.0863640
$141$		−	2.54698i		−	0.214495i
$142$		−	0.954979i		−	0.0801400i
$143$		−	5.01789i		−	0.419617i
$144$	9.09182			0.757652
$145$	−12.3884			−1.02880
$146$			2.26400i			0.187370i
$147$			3.59967i			0.296895i
$148$		−	19.1966i		−	1.57795i
$149$	8.05884			0.660206			0.330103	−	0.943945i	$-0.392917\pi$
$149$	8.05884			0.660206			0.330103	+	0.943945i	$0.392917\pi$
$150$		−	0.476647i		−	0.0389180i
$151$	−5.46967			−0.445116			−0.222558	−	0.974920i	$-0.571441\pi$
$151$	−5.46967			−0.445116			−0.222558	+	0.974920i	$0.571441\pi$
$152$	−6.50116			−0.527314
$153$	−1.32487	+	11.1596i	−0.107110	+	0.902204i
$154$	0.281635			0.0226948
$155$	−5.20567			−0.418129
$156$		−	2.11648i		−	0.169454i
$157$	5.91940			0.472420			0.236210	−	0.971702i	$-0.424095\pi$
$157$	5.91940			0.472420			0.236210	+	0.971702i	$0.424095\pi$
$158$			0.816286i			0.0649402i
$159$		−	1.39927i		−	0.110969i
$160$		−	5.64900i		−	0.446593i
$161$	−0.288832			−0.0227632
$162$	−2.21902			−0.174342
$163$		−	5.72123i		−	0.448121i	−0.974575	−	0.224060i	$-0.928069\pi$
$163$		−	5.72123i		−	0.448121i	0.974575	−	0.224060i	$-0.0719313\pi$
$164$		−	2.22804i		−	0.173980i
$165$			1.85821i			0.144662i
$166$	0.211241			0.0163955
$167$		−	5.97235i		−	0.462154i	−0.972935	−	0.231077i	$-0.925775\pi$
$167$		−	5.97235i		−	0.462154i	0.972935	−	0.231077i	$-0.0742250\pi$
$168$	0.244683			0.0188777
$169$	−8.41587			−0.647375
$170$	2.08182	+	0.247153i	0.159668	+	0.0189558i
$171$	−13.5704			−1.03775
$172$	1.88716			0.143895
$173$			13.7524i			1.04558i	0.852463	+	0.522788i	$0.175108\pi$
$173$			13.7524i			1.04558i	−0.852463	+	0.522788i	$0.824892\pi$
$174$	1.44013			0.109176
$175$		−	0.969058i		−	0.0732539i
$176$		−	7.81770i		−	0.589281i
$177$			5.11274i			0.384297i
$178$	−0.0669254			−0.00501627
$179$	−7.96035			−0.594984			−0.297492	−	0.954724i	$-0.596150\pi$
$179$	−7.96035			−0.594984			−0.297492	+	0.954724i	$0.596150\pi$
$180$		−	7.78573i		−	0.580314i
$181$		−	18.7239i		−	1.39174i	−0.718169	−	0.695869i	$-0.755020\pi$
$181$		−	18.7239i		−	1.39174i	0.718169	−	0.695869i	$-0.244980\pi$
$182$			0.257290i			0.0190716i
$183$	−2.43111			−0.179713
$184$		−	1.05426i		−	0.0777210i
$185$	−15.3972			−1.13202
$186$	0.605146			0.0443715
$187$	9.59574	+	1.13921i	0.701710	+	0.0833070i
$188$	9.17608			0.669235
$189$	1.07291			0.0780426
$190$			2.53153i			0.183657i
$191$	12.3029			0.890204			0.445102	−	0.895480i	$-0.353167\pi$
$191$	12.3029			0.890204			0.445102	+	0.895480i	$0.353167\pi$
$192$		−	2.83789i		−	0.204807i
$193$		−	17.5282i		−	1.26171i	−0.775902	−	0.630854i	$-0.782705\pi$
$193$		−	17.5282i		−	1.26171i	0.775902	−	0.630854i	$-0.217295\pi$
$194$		−	1.66460i		−	0.119511i
$195$	−1.69758			−0.121567
$196$	−12.9686			−0.926329
$197$		−	10.7914i		−	0.768857i	−0.923155	−	0.384428i	$-0.874399\pi$
$197$		−	10.7914i		−	0.768857i	0.923155	−	0.384428i	$-0.125601\pi$
$198$			2.14580i			0.152496i
$199$		−	11.3872i		−	0.807214i	−0.914932	−	0.403607i	$-0.867756\pi$
$199$		−	11.3872i		−	0.807214i	0.914932	−	0.403607i	$-0.132244\pi$
$200$	3.53713			0.250113
$201$			1.18325i			0.0834603i
$202$	3.13145			0.220328
$203$	2.92789			0.205497
$204$	4.04736	+	0.480503i	0.283372	+	0.0336419i
$205$	−1.78706			−0.124814
$206$	2.54229			0.177130
$207$		−	2.20064i		−	0.152955i
$208$	7.14191			0.495202
$209$			11.6686i			0.807136i
$210$		−	0.0952790i		−	0.00657487i
$211$		−	5.39864i		−	0.371658i	−0.982582	−	0.185829i	$-0.940503\pi$
$211$		−	5.39864i		−	0.371658i	0.982582	−	0.185829i	$-0.0594970\pi$
$212$	5.04118			0.346230
$213$	−1.48915			−0.102035
$214$		−	1.82297i		−	0.124616i
$215$		−	1.51365i		−	0.103230i
$216$			3.91619i			0.266463i
$217$	1.23031			0.0835187
$218$			5.76091i			0.390178i
$219$	3.53038			0.238561
$220$	−6.69464			−0.451352
$221$	−1.04073	+	8.76625i	−0.0700071	+	0.589682i
$222$	1.78988			0.120129
$223$	−19.7437			−1.32213			−0.661067	−	0.750327i	$-0.729896\pi$
$223$	−19.7437			−1.32213			−0.661067	+	0.750327i	$0.729896\pi$
$224$			1.33508i			0.0892041i
$225$	7.38333			0.492222
$226$		−	0.121749i		−	0.00809863i
$227$			0.379565i			0.0251926i	0.999921	+	0.0125963i	$0.00400964\pi$
$227$			0.379565i			0.0251926i	−0.999921	+	0.0125963i	$0.995990\pi$
$228$			4.92167i			0.325946i
$229$	12.9891			0.858342			0.429171	−	0.903223i	$-0.358806\pi$
$229$	12.9891			0.858342			0.429171	+	0.903223i	$0.358806\pi$
$230$	−0.410525			−0.0270692
$231$		−	0.439170i		−	0.0288953i
$232$			10.6870i			0.701636i
$233$			0.707708i			0.0463635i	0.999731	+	0.0231817i	$0.00737964\pi$
$233$			0.707708i			0.0463635i	−0.999731	+	0.0231817i	$0.992620\pi$
$234$	−1.96031			−0.128150
$235$		−	7.35993i		−	0.480109i
$236$	−18.4198			−1.19903
$237$	1.27288			0.0826825
$238$	−0.492016	−	0.0584122i	−0.0318927	−	0.00378630i
$239$	17.3288			1.12091			0.560453	−	0.828186i	$-0.310627\pi$
$239$	17.3288			1.12091			0.560453	+	0.828186i	$0.310627\pi$
$240$	−2.64478			−0.170720
$241$		−	21.7516i		−	1.40115i	−0.713581	−	0.700573i	$-0.752928\pi$
$241$		−	21.7516i		−	1.40115i	0.713581	−	0.700573i	$-0.247072\pi$
$242$	−1.84999			−0.118922
$243$			12.4577i			0.799163i
$244$		−	8.75863i		−	0.560714i
$245$			10.4018i			0.664549i
$246$	0.207741			0.0132451
$247$	−10.6599			−0.678276
$248$			4.49071i			0.285161i
$249$		−	0.329401i		−	0.0208749i
$250$		−	3.91965i		−	0.247901i
$251$	29.2455			1.84596			0.922981	−	0.384846i	$-0.125745\pi$
$251$	29.2455			1.84596			0.922981	+	0.384846i	$0.125745\pi$
$252$			1.84008i			0.115914i
$253$	−1.89224			−0.118964
$254$	−6.70898			−0.420959
$255$	0.385401	−	3.24630i	0.0241347	−	0.203291i
$256$	7.71681			0.482301
$257$	−14.0205			−0.874572			−0.437286	−	0.899322i	$-0.644060\pi$
$257$	−14.0205			−0.874572			−0.437286	+	0.899322i	$0.644060\pi$
$258$			0.175958i			0.0109547i
$259$	3.63896			0.226114
$260$		−	6.11593i		−	0.379294i
$261$			22.3078i			1.38082i
$262$		−	1.18609i		−	0.0732767i
$263$	12.3661			0.762527			0.381264	−	0.924466i	$-0.375489\pi$
$263$	12.3661			0.762527			0.381264	+	0.924466i	$0.375489\pi$
$264$	1.60300			0.0986581
$265$		−	4.04342i		−	0.248385i
$266$		−	0.598302i		−	0.0366843i
$267$			0.104361i			0.00638677i
$268$	−4.26294			−0.260401
$269$			10.2426i			0.624503i	0.949999	+	0.312251i	$0.101083\pi$
$269$			10.2426i			0.624503i	−0.949999	+	0.312251i	$0.898917\pi$
$270$	1.52495			0.0928058
$271$	−2.86669			−0.174139			−0.0870695	−	0.996202i	$-0.527750\pi$
$271$	−2.86669			−0.174139			−0.0870695	+	0.996202i	$0.527750\pi$
$272$	−1.62142	+	13.6575i	−0.0983130	+	0.828108i
$273$	0.401207			0.0242821
$274$	0.340258			0.0205557
$275$		−	6.34864i		−	0.382837i
$276$	−0.798122			−0.0480413
$277$		−	18.5066i		−	1.11195i	−0.831198	−	0.555977i	$-0.812344\pi$
$277$		−	18.5066i		−	1.11195i	0.831198	−	0.555977i	$-0.187656\pi$
$278$		−	3.22669i		−	0.193524i
$279$			9.37381i			0.561196i
$280$	0.707053			0.0422545
$281$	4.28914			0.255868			0.127934	−	0.991783i	$-0.459165\pi$
$281$	4.28914			0.255868			0.127934	+	0.991783i	$0.459165\pi$
$282$			0.855574i			0.0509487i
$283$		−	25.5384i		−	1.51810i	−0.651031	−	0.759051i	$-0.725663\pi$
$283$		−	25.5384i		−	1.51810i	0.651031	−	0.759051i	$-0.274337\pi$
$284$		−	5.36501i		−	0.318355i
$285$	3.94757			0.233834
$286$			1.68559i			0.0996713i
$287$	0.422353			0.0249307
$288$	−10.1721			−0.599398
$289$	−16.5274	−	3.98038i	−0.972203	−	0.234140i
$290$	4.16149			0.244371
$291$	−2.59570			−0.152163
$292$			12.7190i			0.744323i
$293$	−9.72313			−0.568031			−0.284016	−	0.958820i	$-0.591667\pi$
$293$	−9.72313			−0.568031			−0.284016	+	0.958820i	$0.591667\pi$
$294$		−	1.20919i		−	0.0705213i
$295$			14.7741i			0.860182i
$296$			13.2825i			0.772029i
$297$	7.02899			0.407863
$298$	−2.70710			−0.156818
$299$		−	1.72867i		−	0.0999714i
$300$		−	2.67777i		−	0.154601i
$301$			0.357736i			0.0206196i
$302$	1.83735			0.105728
$303$		−	4.88305i		−	0.280524i
$304$	−16.6078			−0.952524
$305$	−7.02511			−0.402256
$306$	0.445047	−	3.74871i	0.0254417	−	0.214300i
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$	1.58221			0.0901548
$309$		−	3.96435i		−	0.225524i
$310$	1.74867			0.0993179
$311$			14.1130i			0.800273i	0.916456	+	0.400137i	$0.131037\pi$
$311$			14.1130i			0.800273i	−0.916456	+	0.400137i	$0.868963\pi$
$312$			1.46443i			0.0829073i
$313$		−	15.0502i		−	0.850685i	−0.905033	−	0.425342i	$-0.860154\pi$
$313$		−	15.0502i		−	0.850685i	0.905033	−	0.425342i	$-0.139846\pi$
$314$	−1.98843			−0.112213
$315$	1.47589			0.0831568
$316$			4.58584i			0.257974i
$317$			23.8134i			1.33749i	0.743491	+	0.668746i	$0.233169\pi$
$317$			23.8134i			1.33749i	−0.743491	+	0.668746i	$0.766831\pi$
$318$			0.470038i			0.0263584i
$319$	19.1816			1.07396
$320$		−	8.20054i		−	0.458424i
$321$	−2.84266			−0.158662
$322$	0.0970236			0.00540691
$323$	2.42012	−	20.3851i	0.134659	−	1.13425i
$324$	−12.4663			−0.692572
$325$	5.79984			0.321717
$326$			1.92186i			0.106442i
$327$	8.98332			0.496779
$328$			1.54162i			0.0851218i
$329$			1.73945i			0.0958988i
$330$		−	0.624205i		−	0.0343614i
$331$	−18.7427			−1.03019			−0.515095	−	0.857133i	$-0.672244\pi$
$331$	−18.7427			−1.03019			−0.515095	+	0.857133i	$0.672244\pi$
$332$	1.18674			0.0651308
$333$			27.7256i			1.51935i
$334$			2.00621i			0.109775i
$335$			3.41921i			0.186811i
$336$	0.625066			0.0341002
$337$			27.4494i			1.49527i	0.664112	+	0.747633i	$0.268810\pi$
$337$			27.4494i			1.49527i	−0.664112	+	0.747633i	$0.731190\pi$
$338$	2.82703			0.153770
$339$	−0.189850			−0.0103113
$340$	11.6955	+	1.38849i	0.634278	+	0.0753016i
$341$	8.06017			0.436483
$342$	4.55851			0.246496
$343$		−	4.96252i		−	0.267951i
$344$	−1.30576			−0.0704020
$345$			0.640156i			0.0344648i
$346$		−	4.61967i		−	0.248355i
$347$			25.0976i			1.34731i	0.739045	+	0.673656i	$0.235277\pi$
$347$			25.0976i			1.34731i	−0.739045	+	0.673656i	$0.764723\pi$
$348$	8.09055			0.433699
$349$	−18.0375			−0.965524			−0.482762	−	0.875752i	$-0.660366\pi$
$349$	−18.0375			−0.965524			−0.482762	+	0.875752i	$0.660366\pi$
$350$			0.325523i			0.0173999i
$351$			6.42138i			0.342748i
$352$			8.74660i			0.466195i
$353$	16.1675			0.860510			0.430255	−	0.902707i	$-0.358424\pi$
$353$	16.1675			0.860510			0.430255	+	0.902707i	$0.358424\pi$
$354$		−	1.71745i		−	0.0912817i
$355$	−4.30316			−0.228388
$356$	−0.375983			−0.0199271
$357$	−0.0910856	+	0.767229i	−0.00482076	+	0.0406061i
$358$	2.67401			0.141326
$359$	2.77686			0.146557			0.0732784	−	0.997312i	$-0.476654\pi$
$359$	2.77686			0.146557			0.0732784	+	0.997312i	$0.476654\pi$
$360$			5.38709i			0.283925i
$361$	5.78867			0.304667
$362$			6.28967i			0.330578i
$363$			2.88480i			0.151413i
$364$			1.44544i			0.0757616i
$365$	10.2016			0.533977
$366$	0.816652			0.0426871
$367$		−	11.9415i		−	0.623342i	−0.950190	−	0.311671i	$-0.899111\pi$
$367$		−	11.9415i		−	0.623342i	0.950190	−	0.311671i	$-0.100889\pi$
$368$		−	2.69320i		−	0.140393i
$369$			3.21794i			0.167519i
$370$	5.17217			0.268888
$371$			0.955622i			0.0496134i
$372$	3.39968			0.176265
$373$	14.3217			0.741551			0.370776	−	0.928722i	$-0.379092\pi$
$373$	14.3217			0.741551			0.370776	+	0.928722i	$0.379092\pi$
$374$	−3.22337	−	0.382679i	−0.166676	−	0.0197878i
$375$	−6.11214			−0.315630
$376$	−6.34911			−0.327430
$377$			17.5235i			0.902504i
$378$	−0.360408			−0.0185374
$379$		−	31.0735i		−	1.59614i	−0.602564	−	0.798070i	$-0.705854\pi$
$379$		−	31.0735i		−	1.59614i	0.602564	−	0.798070i	$-0.294146\pi$
$380$			14.2220i			0.729573i
$381$			10.4617i			0.535969i
$382$	−4.13274			−0.211449
$383$	−36.5043			−1.86528			−0.932640	−	0.360807i	$-0.882501\pi$
$383$	−36.5043			−1.86528			−0.932640	+	0.360807i	$0.882501\pi$
$384$			4.86309i			0.248168i
$385$		−	1.26906i		−	0.0646771i
$386$			5.88801i			0.299692i
$387$	−2.72562			−0.138551
$388$		−	9.35161i		−	0.474756i
$389$	−15.0228			−0.761685			−0.380843	−	0.924640i	$-0.624366\pi$
$389$	−15.0228			−0.761685			−0.380843	+	0.924640i	$0.624366\pi$
$390$	0.570247			0.0288756
$391$	3.30574	+	0.392457i	0.167178	+	0.0198474i
$392$	8.97323			0.453217
$393$	−1.84953			−0.0932967
$394$			3.62502i			0.182626i
$395$	3.67820			0.185070
$396$			12.0550i			0.605786i
$397$			25.1966i			1.26458i	0.774732	+	0.632290i	$0.217885\pi$
$397$			25.1966i			1.26458i	−0.774732	+	0.632290i	$0.782115\pi$
$398$			3.82514i			0.191737i
$399$	−0.932968			−0.0467068
$400$	9.03594			0.451797
$401$			22.7457i			1.13586i	0.823076	+	0.567932i	$0.192256\pi$
$401$			22.7457i			1.13586i	−0.823076	+	0.567932i	$0.807744\pi$
$402$		−	0.397475i		−	0.0198243i
$403$			7.36342i			0.366798i
$404$	17.5923			0.875248
$405$			9.99894i			0.496851i
$406$	−0.983526			−0.0488116
$407$	23.8401			1.18171
$408$	−2.80044	−	0.332469i	−0.138643	−	0.0164597i
$409$	−10.3030			−0.509449			−0.254725	−	0.967014i	$-0.581985\pi$
$409$	−10.3030			−0.509449			−0.254725	+	0.967014i	$0.581985\pi$
$410$	0.600303			0.0296469
$411$		−	0.530583i		−	0.0261718i
$412$	14.2825			0.703646
$413$		−	3.49171i		−	0.171816i
$414$			0.739230i			0.0363312i
$415$		−	0.951858i		−	0.0467249i
$416$	−7.99051			−0.391767
$417$	−5.03157			−0.246397
$418$		−	3.91969i		−	0.191718i
$419$			28.0406i			1.36987i	0.728602	+	0.684937i	$0.240170\pi$
$419$			28.0406i			1.36987i	−0.728602	+	0.684937i	$0.759830\pi$
$420$		−	0.535271i		−	0.0261186i
$421$	19.6162			0.956035			0.478018	−	0.878350i	$-0.341355\pi$
$421$	19.6162			0.956035			0.478018	+	0.878350i	$0.341355\pi$
$422$			1.81349i			0.0882795i
$423$	−13.2530			−0.644382
$424$	−3.48809			−0.169397
$425$	−1.31673	+	11.0910i	−0.0638708	+	0.537995i
$426$	0.500232			0.0242363
$427$	1.66031			0.0803482
$428$		−	10.2413i		−	0.495034i
$429$	2.62845			0.126903
$430$			0.508460i			0.0245201i
$431$		−	6.67229i		−	0.321393i	−0.987004	−	0.160696i	$-0.948626\pi$
$431$		−	6.67229i		−	0.321393i	0.987004	−	0.160696i	$-0.0513740\pi$
$432$			10.0043i			0.481331i
$433$	27.6086			1.32678			0.663392	−	0.748272i	$-0.269116\pi$
$433$	27.6086			1.32678			0.663392	+	0.748272i	$0.269116\pi$
$434$	−0.413281			−0.0198381
$435$		−	6.48925i		−	0.311136i
$436$			32.3644i			1.54998i
$437$			4.01985i			0.192295i
$438$	−1.18591			−0.0566651
$439$		−	14.8716i		−	0.709783i	−0.934907	−	0.354892i	$-0.884518\pi$
$439$		−	14.8716i		−	0.709783i	0.934907	−	0.354892i	$-0.115482\pi$
$440$	4.63215			0.220829
$441$	18.7305			0.891929
$442$	0.349599	−	2.94473i	0.0166287	−	0.140066i
$443$	34.4247			1.63557			0.817783	−	0.575526i	$-0.195203\pi$
$443$	34.4247			1.63557			0.817783	+	0.575526i	$0.195203\pi$
$444$	10.0555			0.477211
$445$			0.301568i			0.0142957i
$446$	6.63223			0.314045
$447$			4.22134i			0.199662i
$448$			1.93812i			0.0915674i
$449$		−	33.2594i		−	1.56961i	−0.619745	−	0.784803i	$-0.712764\pi$
$449$		−	33.2594i		−	1.56961i	0.619745	−	0.784803i	$-0.287236\pi$
$450$	−2.48019			−0.116917
$451$	2.76698			0.130292
$452$		−	0.683979i		−	0.0321717i
$453$		−	2.86509i		−	0.134614i
$454$		−	0.127502i		−	0.00598398i
$455$	1.15935			0.0543514
$456$		−	3.40540i		−	0.159472i
$457$	−1.98029			−0.0926341			−0.0463171	−	0.998927i	$-0.514748\pi$
$457$	−1.98029			−0.0926341			−0.0463171	+	0.998927i	$0.514748\pi$
$458$	−4.36325			−0.203881
$459$	−12.2796	−	1.45784i	−0.573164	−	0.0680461i
$460$	−2.30631			−0.107532
$461$	−19.4725			−0.906926			−0.453463	−	0.891275i	$-0.649812\pi$
$461$	−19.4725			−0.906926			−0.453463	+	0.891275i	$0.649812\pi$
$462$			0.147525i			0.00686347i
$463$	12.6306			0.586993			0.293497	−	0.955960i	$-0.405181\pi$
$463$	12.6306			0.586993			0.293497	+	0.955960i	$0.405181\pi$
$464$			27.3009i			1.26741i
$465$		−	2.72681i		−	0.126453i
$466$		−	0.237731i		−	0.0110127i
$467$	9.70321			0.449011			0.224505	−	0.974473i	$-0.427923\pi$
$467$	9.70321			0.449011			0.224505	+	0.974473i	$0.427923\pi$
$468$	−11.0129			−0.509072
$469$		−	0.808096i		−	0.0373144i
$470$			2.47233i			0.114040i
$471$			3.10067i			0.142871i
$472$	12.7450			0.586636
$473$			2.34365i			0.107761i
$474$	−0.427582			−0.0196395
$475$	−13.4870			−0.618824
$476$	−2.76412	−	0.328156i	−0.126693	−	0.0150410i
$477$	−7.28096			−0.333372
$478$	−5.82103			−0.266248
$479$		−	30.0168i		−	1.37150i	−0.727836	−	0.685751i	$-0.759474\pi$
$479$		−	30.0168i		−	1.37150i	0.727836	−	0.685751i	$-0.240526\pi$
$480$	2.95903			0.135061
$481$			21.7793i			0.993050i
$482$			7.30674i			0.332813i
$483$		−	0.151294i		−	0.00688414i
$484$	−10.3932			−0.472416
$485$	−7.50072			−0.340590
$486$		−	4.18476i		−	0.189825i
$487$			34.4595i			1.56151i	0.624839	+	0.780754i	$0.285165\pi$
$487$			34.4595i			1.56151i	−0.624839	+	0.780754i	$0.714835\pi$
$488$			6.06027i			0.274335i
$489$	2.99686			0.135523
$490$		−	3.49415i		−	0.157850i
$491$	−20.5623			−0.927962			−0.463981	−	0.885845i	$-0.653579\pi$
$491$	−20.5623			−0.927962			−0.463981	+	0.885845i	$0.653579\pi$
$492$	1.16708			0.0526159
$493$	−33.5102	−	3.97833i	−1.50922	−	0.179175i
$494$	3.58085			0.161110
$495$	9.66904			0.434591
$496$			11.4720i			0.515106i
$497$	1.01701			0.0456191
$498$			0.110651i			0.00495840i
$499$		−	37.8770i		−	1.69561i	−0.530310	−	0.847804i	$-0.677924\pi$
$499$		−	37.8770i		−	1.69561i	0.530310	−	0.847804i	$-0.322076\pi$
$500$		−	22.0204i		−	0.984781i
$501$	3.12840			0.139767
$502$	−9.82407			−0.438470
$503$		−	17.4721i		−	0.779044i	−0.921017	−	0.389522i	$-0.872640\pi$
$503$		−	17.4721i		−	0.779044i	0.921017	−	0.389522i	$-0.127360\pi$
$504$		−	1.27319i		−	0.0567122i
$505$		−	14.1104i		−	0.627904i
$506$	0.635635			0.0282574
$507$		−	4.40835i		−	0.195782i
$508$	−37.6906			−1.67225
$509$	−2.14492			−0.0950717			−0.0475359	−	0.998870i	$-0.515137\pi$
$509$	−2.14492			−0.0950717			−0.0475359	+	0.998870i	$0.515137\pi$
$510$	−0.129463	+	1.09049i	−0.00573270	+	0.0482875i
$511$	−2.41105			−0.106659
$512$	−21.1602			−0.935157
$513$		−	14.9323i		−	0.659277i
$514$	4.70971			0.207736
$515$		−	11.4556i		−	0.504796i
$516$			0.988522i			0.0435172i
$517$			11.3957i			0.501183i
$518$	−1.22239			−0.0537087
$519$	−7.20371			−0.316208
$520$			4.23173i			0.185574i
$521$		−	32.6273i		−	1.42943i	−0.699416	−	0.714715i	$-0.746556\pi$
$521$		−	32.6273i		−	1.42943i	0.699416	−	0.714715i	$-0.253444\pi$
$522$		−	7.49356i		−	0.327984i
$523$	−21.7598			−0.951491			−0.475745	−	0.879583i	$-0.657822\pi$
$523$	−21.7598			−0.951491			−0.475745	+	0.879583i	$0.657822\pi$
$524$		−	6.66337i		−	0.291091i
$525$	0.507607			0.0221538
$526$	−4.15398			−0.181122
$527$	−14.0811	−	1.67171i	−0.613382	−	0.0728208i
$528$	4.09502			0.178213
$529$	22.3481			0.971657
$530$			1.35825i			0.0589987i
$531$	26.6036			1.15450
$532$		−	3.36123i		−	0.145728i
$533$			2.52780i			0.109491i
$534$		−	0.0350565i		−	0.00151704i
$535$	−8.21435			−0.355137
$536$	2.94961			0.127404
$537$		−	4.16974i		−	0.179938i
$538$		−	3.44066i		−	0.148338i
$539$		−	16.1056i		−	0.693719i
$540$	8.56710			0.368669
$541$		−	22.7358i		−	0.977490i	−0.872427	−	0.488745i	$-0.837455\pi$
$541$		−	22.7358i		−	0.977490i	0.872427	−	0.488745i	$-0.162545\pi$
$542$	0.962970			0.0413631
$543$	9.80785			0.420895
$544$	1.81408	−	15.2803i	0.0777779	−	0.655137i
$545$	25.9588			1.11195
$546$	−0.134772			−0.00576772
$547$			1.93237i			0.0826223i	0.999146	+	0.0413112i	$0.0131535\pi$
$547$			1.93237i			0.0826223i	−0.999146	+	0.0413112i	$0.986847\pi$
$548$	1.91155			0.0816572
$549$			12.6501i			0.539892i
$550$			2.13261i			0.0909349i
$551$		−	40.7491i		−	1.73597i
$552$	0.552236			0.0235047
$553$	−0.869306			−0.0369667
$554$			6.21667i			0.264121i
$555$		−	8.06526i		−	0.342351i
$556$		−	18.1274i		−	0.768772i
$557$	−34.4505			−1.45972			−0.729858	−	0.683598i	$-0.760414\pi$
$557$	−34.4505			−1.45972			−0.729858	+	0.683598i	$0.760414\pi$
$558$		−	3.14882i		−	0.133300i
$559$	−2.14106			−0.0905571
$560$	1.80623			0.0763273
$561$	−0.596733	+	5.02639i	−0.0251941	+	0.212214i
$562$	−1.44079			−0.0607762
$563$	−17.9044			−0.754582			−0.377291	−	0.926095i	$-0.623144\pi$
$563$	−17.9044			−0.754582			−0.377291	+	0.926095i	$0.623144\pi$
$564$			4.80656i			0.202393i
$565$	−0.548604			−0.0230800
$566$			8.57878i			0.360593i
$567$		−	2.36315i		−	0.0992430i
$568$			3.71215i			0.155759i
$569$	4.16005			0.174398			0.0871992	−	0.996191i	$-0.472208\pi$
$569$	4.16005			0.174398			0.0871992	+	0.996191i	$0.472208\pi$
$570$	−1.32605			−0.0555423
$571$		−	14.4902i		−	0.606398i	−0.952927	−	0.303199i	$-0.901945\pi$
$571$		−	14.4902i		−	0.606398i	0.952927	−	0.303199i	$-0.0980547\pi$
$572$			9.46957i			0.395943i
$573$			6.44442i			0.269219i
$574$	−0.141876			−0.00592177
$575$		−	2.18711i		−	0.0912088i
$576$	−14.7667			−0.615278
$577$	3.39765			0.141446			0.0707231	−	0.997496i	$-0.477469\pi$
$577$	3.39765			0.141446			0.0707231	+	0.997496i	$0.477469\pi$
$578$	5.55185	+	1.33708i	0.230926	+	0.0556151i
$579$	9.18152			0.381571
$580$	23.3790			0.970759
$581$			0.224962i			0.00933300i
$582$	0.871940			0.0361431
$583$			6.26061i			0.259288i
$584$		−	8.80051i		−	0.364168i
$585$			8.83322i			0.365208i
$586$	3.26616			0.134924
$587$	−12.7230			−0.525135			−0.262567	−	0.964914i	$-0.584569\pi$
$587$	−12.7230			−0.525135			−0.262567	+	0.964914i	$0.584569\pi$
$588$		−	6.79315i		−	0.280145i
$589$		−	17.1229i		−	0.705538i
$590$		−	4.96287i		−	0.204318i
$591$	5.65270			0.232521
$592$			33.9314i			1.39457i
$593$	−23.5893			−0.968694			−0.484347	−	0.874876i	$-0.660943\pi$
$593$	−23.5893			−0.968694			−0.484347	+	0.874876i	$0.660943\pi$
$594$	−2.36116			−0.0968794
$595$	−0.263207	+	2.21704i	−0.0107904	+	0.0908897i
$596$	−15.2083			−0.622957
$597$	5.96476			0.244121
$598$			0.580688i			0.0237461i
$599$	−3.92664			−0.160438			−0.0802191	−	0.996777i	$-0.525562\pi$
$599$	−3.92664			−0.160438			−0.0802191	+	0.996777i	$0.525562\pi$
$600$			1.85280i			0.0756403i
$601$		−	20.8010i		−	0.848492i	−0.905547	−	0.424246i	$-0.860539\pi$
$601$		−	20.8010i		−	0.848492i	0.905547	−	0.424246i	$-0.139461\pi$
$602$		−	0.120169i		−	0.00489774i
$603$	6.15695			0.250730
$604$	10.3221			0.420002
$605$			8.33612i			0.338911i
$606$			1.64030i			0.0666325i
$607$			30.0055i			1.21789i	0.793214	+	0.608944i	$0.208406\pi$
$607$			30.0055i			1.21789i	−0.793214	+	0.608944i	$0.791594\pi$
$608$	18.5812			0.753566
$609$			1.53367i			0.0621474i
$610$	2.35985			0.0955476
$611$	−10.4106			−0.421169
$612$	2.50025	−	21.0600i	0.101067	−	0.851301i
$613$	21.5003			0.868390			0.434195	−	0.900819i	$-0.357033\pi$
$613$	21.5003			0.868390			0.434195	+	0.900819i	$0.357033\pi$
$614$	3.32541			0.134202
$615$		−	0.936087i		−	0.0377467i
$616$	−1.09476			−0.0441092
$617$			2.34969i			0.0945951i	0.998881	+	0.0472976i	$0.0150609\pi$
$617$			2.34969i			0.0945951i	−0.998881	+	0.0472976i	$0.984939\pi$
$618$			1.33169i			0.0535684i
$619$		−	33.8952i		−	1.36236i	−0.732114	−	0.681182i	$-0.761466\pi$
$619$		−	33.8952i		−	1.36236i	0.732114	−	0.681182i	$-0.238534\pi$
$620$	9.82393			0.394539
$621$	2.42149			0.0971711
$622$		−	4.74078i		−	0.190088i
$623$		−	0.0712725i		−	0.00285547i
$624$			3.74104i			0.149761i
$625$	−4.11772			−0.164709
$626$			5.05560i			0.202062i
$627$	−6.11219			−0.244098
$628$	−11.1709			−0.445766
$629$	−41.6486	−	4.94453i	−1.66064	−	0.197151i
$630$	−0.495775			−0.0197521
$631$	24.2788			0.966525			0.483263	−	0.875475i	$-0.339452\pi$
$631$	24.2788			0.966525			0.483263	+	0.875475i	$0.339452\pi$
$632$		−	3.17303i		−	0.126216i
$633$	2.82789			0.112398
$634$		−	7.99932i		−	0.317693i
$635$			30.2308i			1.19967i
$636$			2.64064i			0.104708i
$637$	14.7134			0.582966
$638$	−6.44342			−0.255097
$639$			7.74867i			0.306533i
$640$			14.0527i			0.555482i
$641$		−	15.2313i		−	0.601600i	−0.953687	−	0.300800i	$-0.902746\pi$
$641$		−	15.2313i		−	0.601600i	0.953687	−	0.300800i	$-0.0972537\pi$
$642$	0.954899			0.0376868
$643$		−	14.7658i		−	0.582306i	−0.956676	−	0.291153i	$-0.905961\pi$
$643$		−	14.7658i		−	0.582306i	0.956676	−	0.291153i	$-0.0940389\pi$
$644$	0.545072			0.0214789
$645$	0.792872			0.0312193
$646$	−0.812958	+	6.84768i	−0.0319854	+	0.269418i
$647$	18.2678			0.718182			0.359091	−	0.933303i	$-0.383087\pi$
$647$	18.2678			0.718182			0.359091	+	0.933303i	$0.383087\pi$
$648$	8.62567			0.338848
$649$		−	22.8754i		−	0.897939i
$650$	−1.94826			−0.0764171
$651$			0.644453i			0.0252581i
$652$			10.7969i			0.422838i
$653$			31.0460i			1.21492i	0.794349	+	0.607462i	$0.207812\pi$
$653$			31.0460i			1.21492i	−0.794349	+	0.607462i	$0.792188\pi$
$654$	−3.01765			−0.117999
$655$	−5.34454			−0.208828
$656$			3.93822i			0.153761i
$657$		−	18.3700i		−	0.716682i
$658$		−	0.584309i		−	0.0227787i
$659$	−40.7371			−1.58689			−0.793445	−	0.608642i	$-0.791715\pi$
$659$	−40.7371			−1.58689			−0.793445	+	0.608642i	$0.791715\pi$
$660$		−	3.50675i		−	0.136500i
$661$	−10.6276			−0.413367			−0.206684	−	0.978408i	$-0.566267\pi$
$661$	−10.6276			−0.413367			−0.206684	+	0.978408i	$0.566267\pi$
$662$	6.29598			0.244700
$663$	−4.59189	−	0.545149i	−0.178334	−	0.0211718i
$664$	−0.821128			−0.0318660
$665$	−2.69597			−0.104545
$666$		−	9.31348i		−	0.360890i
$667$	6.60807			0.255866
$668$			11.2708i			0.436080i
$669$		−	10.3420i		−	0.399846i
$670$		−	1.14857i		−	0.0443731i
$671$	10.8773			0.419913
$672$	−0.699337			−0.0269775
$673$		−	33.7198i		−	1.29980i	−0.760018	−	0.649902i	$-0.774810\pi$
$673$		−	33.7198i		−	1.29980i	0.760018	−	0.649902i	$-0.225190\pi$
$674$		−	9.22073i		−	0.355169i
$675$			8.12433i			0.312705i
$676$	15.8821			0.610850
$677$			49.5263i			1.90345i	0.306952	+	0.951725i	$0.400691\pi$
$677$			49.5263i			1.90345i	−0.306952	+	0.951725i	$0.599309\pi$
$678$	0.0637739			0.00244922
$679$	1.77272			0.0680308
$680$	−8.09235	−	0.960725i	−0.310327	−	0.0368421i
$681$	−0.198822			−0.00761887
$682$	−2.70755			−0.103677
$683$		−	36.4052i		−	1.39301i	−0.717553	−	0.696504i	$-0.754738\pi$
$683$		−	36.4052i		−	1.39301i	0.717553	−	0.696504i	$-0.245262\pi$
$684$	25.6095			0.979202
$685$		−	1.53321i		−	0.0585809i
$686$			1.66699i			0.0636461i
$687$			6.80387i			0.259584i
$688$	−3.33569			−0.127172
$689$	−5.71942			−0.217893
$690$		−	0.215039i		−	0.00818640i
$691$		−	23.7189i		−	0.902311i	−0.892445	−	0.451155i	$-0.851012\pi$
$691$		−	23.7189i		−	0.902311i	0.892445	−	0.451155i	$-0.148988\pi$
$692$		−	25.9530i		−	0.986585i
$693$	−2.28518			−0.0868068
$694$		−	8.43072i		−	0.320026i
$695$	−14.5396			−0.551517
$696$	−5.59800			−0.212192
$697$	−4.83391	−	0.573883i	−0.183097	−	0.0217374i
$698$	6.05909			0.229340
$699$	−0.370707			−0.0140214
$700$			1.82877i			0.0691209i
$701$	−21.3279			−0.805545			−0.402773	−	0.915300i	$-0.631953\pi$
$701$	−21.3279			−0.805545			−0.402773	+	0.915300i	$0.631953\pi$
$702$		−	2.15705i		−	0.0814126i
$703$		−	50.6456i		−	1.91014i
$704$			12.6973i			0.478546i
$705$	3.85524			0.145197
$706$	−5.43094			−0.204396
$707$			3.33485i			0.125420i
$708$		−	9.64855i		−	0.362615i
$709$			12.2532i			0.460177i	0.973170	+	0.230089i	$0.0739016\pi$
$709$			12.2532i			0.460177i	−0.973170	+	0.230089i	$0.926098\pi$
$710$	1.44550			0.0542488
$711$		−	6.62332i		−	0.248394i
$712$	0.260150			0.00974953
$713$	2.77673			0.103990
$714$	0.0305972	−	0.257725i	0.00114507	−	0.00964512i
$715$	7.59533			0.284049
$716$	15.0224			0.561415
$717$			9.07707i			0.338989i
$718$	−0.932792			−0.0348115
$719$		−	41.7135i		−	1.55565i	−0.628481	−	0.777825i	$-0.716323\pi$
$719$		−	41.7135i		−	1.55565i	0.628481	−	0.777825i	$-0.283677\pi$
$720$			13.7618i			0.512873i
$721$			2.70743i			0.100830i
$722$	−1.94451			−0.0723672
$723$	11.3938			0.423741
$724$			35.3350i			1.31322i
$725$			22.1707i			0.823398i
$726$		−	0.969054i		−	0.0359650i
$727$	−9.32450			−0.345826			−0.172913	−	0.984937i	$-0.555318\pi$
$727$	−9.32450			−0.345826			−0.172913	+	0.984937i	$0.555318\pi$
$728$		−	1.00013i		−	0.0370672i
$729$	13.2920			0.492297
$730$	−3.42690			−0.126835
$731$	0.486082	−	4.09435i	0.0179784	−	0.151435i
$732$	4.58790			0.169574
$733$	17.4957			0.646218			0.323109	−	0.946362i	$-0.395272\pi$
$733$	17.4957			0.646218			0.323109	+	0.946362i	$0.395272\pi$
$734$			4.01136i			0.148062i
$735$	−5.44863			−0.200976
$736$			3.01321i			0.111068i
$737$		−	5.29412i		−	0.195011i
$738$		−	1.08096i		−	0.0397907i
$739$	50.9090			1.87272			0.936359	−	0.351045i	$-0.114173\pi$
$739$	50.9090			1.87272			0.936359	+	0.351045i	$0.114173\pi$
$740$	29.0569			1.06815
$741$		−	5.58383i		−	0.205127i
$742$		−	0.321009i		−	0.0117846i
$743$		−	44.5156i		−	1.63312i	−0.577261	−	0.816560i	$-0.695878\pi$
$743$		−	44.5156i		−	1.63312i	0.577261	−	0.816560i	$-0.304122\pi$
$744$	−2.35230			−0.0862395
$745$			12.1983i			0.446909i
$746$	−4.81091			−0.176140
$747$	−1.71400			−0.0627121
$748$	−18.1087	−	2.14987i	−0.662119	−	0.0786069i
$749$	1.94138			0.0709365
$750$	2.05317			0.0749712
$751$		−	22.8841i		−	0.835051i	−0.908665	−	0.417526i	$-0.862897\pi$
$751$		−	22.8841i		−	0.835051i	0.908665	−	0.417526i	$-0.137103\pi$
$752$	−16.2194			−0.591460
$753$			15.3192i			0.558264i
$754$		−	5.88643i		−	0.214371i
$755$		−	8.27917i		−	0.301310i
$756$	−2.02475			−0.0736394
$757$	−18.3817			−0.668094			−0.334047	−	0.942556i	$-0.608414\pi$
$757$	−18.3817			−0.668094			−0.334047	+	0.942556i	$0.608414\pi$
$758$			10.4381i			0.379130i
$759$		−	0.991182i		−	0.0359776i
$760$		−	9.84047i		−	0.356952i
$761$	37.7127			1.36708			0.683542	−	0.729911i	$-0.260439\pi$
$761$	37.7127			1.36708			0.683542	+	0.729911i	$0.260439\pi$
$762$		−	3.51426i		−	0.127308i
$763$	−6.13510			−0.222106
$764$	−23.2175			−0.839979
$765$	−16.8918	−	2.00539i	−0.610724	−	0.0725052i
$766$	12.2624			0.443058
$767$	20.8980			0.754582
$768$			4.04218i			0.145860i
$769$	2.06121			0.0743293			0.0371646	−	0.999309i	$-0.488167\pi$
$769$	2.06121			0.0743293			0.0371646	+	0.999309i	$0.488167\pi$
$770$			0.426297i			0.0153627i
$771$		−	7.34412i		−	0.264492i
$772$			33.0785i			1.19052i
$773$	37.2235			1.33884			0.669419	−	0.742885i	$-0.266543\pi$
$773$	37.2235			1.33884			0.669419	+	0.742885i	$0.266543\pi$
$774$	0.915581			0.0329099
$775$			9.31620i			0.334648i
$776$			6.47056i			0.232280i
$777$			1.90614i			0.0683825i
$778$	5.04640			0.180922
$779$		−	5.87814i		−	0.210606i
$780$	3.20361			0.114708
$781$	6.66277			0.238413
$782$	−1.11045	−	0.131833i	−0.0397097	−	0.00471434i
$783$	−24.5466			−0.877224
$784$	22.9230			0.818677
$785$			8.95990i			0.319793i
$786$	0.621290			0.0221607
$787$			18.5994i			0.662997i	0.943456	+	0.331499i	$0.107554\pi$
$787$			18.5994i			0.662997i	−0.943456	+	0.331499i	$0.892446\pi$
$788$			20.3651i			0.725478i
$789$			6.47755i			0.230607i
$790$	−1.23557			−0.0439596
$791$	0.129657			0.00461008
$792$		−	8.34108i		−	0.296387i
$793$			9.93702i			0.352874i
$794$		−	8.46395i		−	0.300374i
$795$	2.11800			0.0751178
$796$			21.4894i			0.761671i
$797$	9.48292			0.335902			0.167951	−	0.985795i	$-0.446285\pi$
$797$	9.48292			0.335902			0.167951	+	0.985795i	$0.446285\pi$
$798$	0.313400			0.0110942
$799$	2.36351	−	19.9083i	0.0836151	−	0.704304i
$800$	−10.1096			−0.357428
$801$	0.543031			0.0191870
$802$		−	7.64065i		−	0.269801i
$803$	−15.7956			−0.557416
$804$		−	2.23299i		−	0.0787515i
$805$		−	0.437191i		−	0.0154089i
$806$		−	2.47350i		−	0.0871252i
$807$	−5.36523			−0.188865
$808$	−12.1724			−0.428225
$809$		−	12.0761i		−	0.424572i	−0.977208	−	0.212286i	$-0.931909\pi$
$809$		−	12.0761i		−	0.424572i	0.977208	−	0.212286i	$-0.0680909\pi$
$810$		−	3.35881i		−	0.118017i
$811$			38.5146i			1.35243i	0.736703	+	0.676216i	$0.236381\pi$
$811$			38.5146i			1.35243i	−0.736703	+	0.676216i	$0.763619\pi$
$812$	−5.52539			−0.193903
$813$		−	1.50161i		−	0.0526639i
$814$	−8.00830			−0.280691
$815$	8.65993			0.303344
$816$	−7.15400	−	0.849323i	−0.250440	−	0.0297323i
$817$	4.97882			0.174187
$818$	3.46094			0.121009
$819$		−	2.08764i		−	0.0729481i
$820$	3.37247			0.117772
$821$		−	33.0334i		−	1.15287i	−0.817142	−	0.576436i	$-0.804443\pi$
$821$		−	33.0334i		−	1.15287i	0.817142	−	0.576436i	$-0.195557\pi$
$822$			0.178232i			0.00621655i
$823$			26.8364i			0.935459i	0.883872	+	0.467729i	$0.154928\pi$
$823$			26.8364i			0.935459i	−0.883872	+	0.467729i	$0.845072\pi$
$824$	−9.88230			−0.344266
$825$	3.32551			0.115779
$826$			1.17292i			0.0408113i
$827$		−	47.5210i		−	1.65247i	−0.563327	−	0.826234i	$-0.690479\pi$
$827$		−	47.5210i		−	1.65247i	0.563327	−	0.826234i	$-0.309521\pi$
$828$			4.15295i			0.144325i
$829$	−15.3817			−0.534228			−0.267114	−	0.963665i	$-0.586070\pi$
$829$	−15.3817			−0.534228			−0.267114	+	0.963665i	$0.586070\pi$
$830$			0.319745i			0.0110985i
$831$	9.69402			0.336282
$832$	−11.5997			−0.402146
$833$	−3.34037	+	28.1365i	−0.115737	+	0.974872i
$834$	1.69019			0.0585265
$835$	9.04005			0.312844
$836$		−	22.0206i		−	0.761597i
$837$	−10.3146			−0.356524
$838$		−	9.41932i		−	0.325385i
$839$			50.4231i			1.74080i	0.492347	+	0.870399i	$0.336139\pi$
$839$			50.4231i			1.74080i	−0.492347	+	0.870399i	$0.663861\pi$
$840$			0.370365i			0.0127788i
$841$	−37.9859			−1.30986
$842$	−6.58941			−0.227086
$843$			2.24671i			0.0773809i
$844$			10.1881i			0.350689i
$845$		−	12.7387i		−	0.438224i
$846$	4.45190			0.153059
$847$		−	1.97016i		−	0.0676954i
$848$	−8.91065			−0.305993
$849$	13.3774			0.459111
$850$	0.442312	−	3.72567i	0.0151712	−	0.127789i
$851$	8.21294			0.281536
$852$	2.81027			0.0962783
$853$			46.0255i			1.57588i	0.615751	+	0.787941i	$0.288853\pi$
$853$			46.0255i			1.57588i	−0.615751	+	0.787941i	$0.711147\pi$
$854$	−0.557727			−0.0190850
$855$		−	20.5408i		−	0.702480i
$856$			7.08618i			0.242201i
$857$		−	36.6695i		−	1.25261i	−0.779580	−	0.626303i	$-0.784567\pi$
$857$		−	36.6695i		−	1.25261i	0.779580	−	0.626303i	$-0.215433\pi$
$858$	−0.882939			−0.0301430
$859$	−46.2784			−1.57900			−0.789499	−	0.613752i	$-0.789659\pi$
$859$	−46.2784			−1.57900			−0.789499	+	0.613752i	$0.789659\pi$
$860$			2.85650i			0.0974058i
$861$			0.221235i			0.00753966i
$862$			2.24133i			0.0763402i
$863$	34.8942			1.18781			0.593906	−	0.804535i	$-0.297585\pi$
$863$	34.8942			1.18781			0.593906	+	0.804535i	$0.297585\pi$
$864$		−	11.1930i		−	0.380793i
$865$	−20.8163			−0.707777
$866$	−9.27418			−0.315150
$867$	2.08498	−	8.65732i	0.0708097	−	0.294018i
$868$	−2.32179			−0.0788066
$869$	−5.69513			−0.193194
$870$			2.17985i			0.0739038i
$871$	4.83648			0.163878
$872$		−	22.3936i		−	0.758342i
$873$			13.5065i			0.457126i
$874$		−	1.35033i		−	0.0456757i
$875$	4.17425			0.141115
$876$	−6.66239			−0.225101
$877$			16.8350i			0.568476i	0.958754	+	0.284238i	$0.0917406\pi$
$877$			16.8350i			0.568476i	−0.958754	+	0.284238i	$0.908259\pi$
$878$			4.99562i			0.168594i
$879$		−	5.09311i		−	0.171786i
$880$	11.8333			0.398899
$881$		−	46.2930i		−	1.55965i	−0.625996	−	0.779826i	$-0.715308\pi$
$881$		−	46.2930i		−	1.55965i	0.625996	−	0.779826i	$-0.284692\pi$
$882$	−6.29190			−0.211859
$883$	−13.4947			−0.454133			−0.227066	−	0.973879i	$-0.572913\pi$
$883$	−13.4947			−0.454133			−0.227066	+	0.973879i	$0.572913\pi$
$884$	1.96402	−	16.5433i	0.0660573	−	0.556412i
$885$	−7.73889			−0.260140
$886$	−11.5638			−0.388494
$887$			21.3741i			0.717673i	0.933400	+	0.358836i	$0.116826\pi$
$887$			21.3741i			0.717673i	−0.933400	+	0.358836i	$0.883174\pi$
$888$	−6.95756			−0.233480
$889$		−	7.14475i		−	0.239627i
$890$		−	0.101302i		−	0.00339564i
$891$		−	15.4818i		−	0.518660i
$892$	37.2595			1.24754
$893$	24.2089			0.810120
$894$		−	1.41802i		−	0.0474256i
$895$		−	12.0492i		−	0.402759i
$896$		−	3.32121i		−	0.110954i
$897$	0.905501			0.0302338
$898$			11.1724i			0.372827i
$899$	−28.1477			−0.938778
$900$	−13.9335			−0.464451
$901$	1.29847	−	10.9373i	0.0432584	−	0.364373i
$902$	−0.929476			−0.0309482
$903$	−0.187387			−0.00623586
$904$			0.473258i			0.0157403i
$905$	28.3414			0.942101
$906$			0.962433i			0.0319747i
$907$		−	7.99322i		−	0.265411i	−0.991156	−	0.132705i	$-0.957634\pi$
$907$		−	7.99322i		−	0.265411i	0.991156	−	0.132705i	$-0.0423664\pi$
$908$		−	0.716300i		−	0.0237713i
$909$	−25.4085			−0.842745
$910$	−0.389447			−0.0129100
$911$			0.539948i			0.0178893i	0.999960	+	0.00894463i	$0.00284720\pi$
$911$			0.539948i			0.0178893i	−0.999960	+	0.00894463i	$0.997153\pi$
$912$		−	8.69942i		−	0.288066i
$913$			1.47380i			0.0487758i
$914$	0.665213			0.0220033
$915$		−	3.67985i		−	0.121652i
$916$	−24.5125			−0.809915
$917$	1.26313			0.0417122
$918$	4.12493	+	0.489712i	0.136143	+	0.0161629i
$919$	8.64047			0.285023			0.142511	−	0.989793i	$-0.454482\pi$
$919$	8.64047			0.285023			0.142511	+	0.989793i	$0.454482\pi$
$920$	1.59578			0.0526112
$921$		−	5.18550i		−	0.170868i
$922$	6.54115			0.215421
$923$			6.08682i			0.200350i
$924$			0.828785i			0.0272650i
$925$			27.5551i			0.906008i
$926$	−4.24283			−0.139428
$927$	−20.6281			−0.677516
$928$		−	30.5448i		−	1.00268i
$929$			32.6656i			1.07172i	0.844306	+	0.535862i	$0.180013\pi$
$929$			32.6656i			1.07172i	−0.844306	+	0.535862i	$0.819987\pi$
$930$			0.915980i			0.0300362i
$931$	−34.2146			−1.12134
$932$		−	1.33556i		−	0.0437476i
$933$	−7.39258			−0.242022
$934$	−3.25947			−0.106653
$935$	−1.72436	+	14.5246i	−0.0563926	+	0.475005i
$936$	7.62005			0.249069
$937$	−2.84579			−0.0929678			−0.0464839	−	0.998919i	$-0.514802\pi$
$937$	−2.84579			−0.0929678			−0.0464839	+	0.998919i	$0.514802\pi$
$938$			0.271453i			0.00886326i
$939$	7.88349			0.257268
$940$			13.8894i			0.453021i
$941$		−	44.5611i		−	1.45265i	−0.687350	−	0.726326i	$-0.741226\pi$
$941$		−	44.5611i		−	1.45265i	0.687350	−	0.726326i	$-0.258774\pi$
$942$		−	1.04157i		−	0.0339361i
$943$	0.953227			0.0310414
$944$	32.5583			1.05968
$945$			1.62401i			0.0528289i
$946$		−	0.787272i		−	0.0255964i
$947$			49.5587i			1.61044i	0.592975	+	0.805221i	$0.297953\pi$
$947$			49.5587i			1.61044i	−0.592975	+	0.805221i	$0.702047\pi$
$948$	−2.40213			−0.0780176
$949$		−	14.4302i		−	0.468424i
$950$	4.53050			0.146989
$951$	−12.4738			−0.404491
$952$	1.91255	+	0.227058i	0.0619860	+	0.00735898i
$953$	26.9765			0.873853			0.436927	−	0.899497i	$-0.356067\pi$
$953$	26.9765			0.873853			0.436927	+	0.899497i	$0.356067\pi$
$954$	2.44580			0.0791856
$955$			18.6222i			0.602601i
$956$	−32.7022			−1.05766
$957$			10.0476i			0.324793i
$958$			10.0831i			0.325772i
$959$			0.362359i			0.0117012i
$960$	4.29556			0.138639
$961$	19.1722			0.618459
$962$		−	7.31603i		−	0.235878i
$963$			14.7915i			0.476650i
$964$			41.0488i			1.32209i
$965$	26.5315			0.854081
$966$			0.0508223i			0.00163518i
$967$	−40.1870			−1.29233			−0.646164	−	0.763199i	$-0.723628\pi$
$967$	−40.1870			−1.29233			−0.646164	+	0.763199i	$0.723628\pi$
$968$	7.19122			0.231135
$969$	10.6780	+	1.26769i	0.343026	+	0.0407241i
$970$	2.51962			0.0809001
$971$	−55.8227			−1.79144			−0.895718	−	0.444623i	$-0.853338\pi$
$971$	−55.8227			−1.79144			−0.895718	+	0.444623i	$0.853338\pi$
$972$		−	23.5097i		−	0.754075i
$973$	3.43628			0.110162
$974$		−	11.5755i		−	0.370903i
$975$			3.03804i			0.0972951i
$976$			15.4815i			0.495551i
$977$	44.8797			1.43583			0.717915	−	0.696131i	$-0.245097\pi$
$977$	44.8797			1.43583			0.717915	+	0.696131i	$0.245097\pi$
$978$	−1.00670			−0.0321906
$979$		−	0.466931i		−	0.0149232i
$980$		−	19.6299i		−	0.627055i
$981$		−	46.7438i		−	1.49242i
$982$	6.90721			0.220418
$983$			26.8024i			0.854863i	0.904048	+	0.427431i	$0.140581\pi$
$983$			26.8024i			0.854863i	−0.904048	+	0.427431i	$0.859419\pi$
$984$	−0.807523			−0.0257429
$985$	16.3344			0.520458
$986$	11.2566	+	1.33639i	0.358484	+	0.0425593i
$987$	−0.911147			−0.0290021
$988$	20.1170			0.640008
$989$			0.807389i			0.0256735i
$990$	−3.24799			−0.103228
$991$		−	2.27629i		−	0.0723088i	−0.999346	−	0.0361544i	$-0.988489\pi$
$991$		−	2.27629i		−	0.0723088i	0.999346	−	0.0361544i	$-0.0115108\pi$
$992$		−	12.8350i		−	0.407513i
$993$		−	9.81769i		−	0.311555i
$994$	−0.341630			−0.0108358
$995$	17.2362			0.546423
$996$			0.621632i			0.0196972i
$997$			54.1854i			1.71607i	0.513591	+	0.858035i	$0.328315\pi$
$997$			54.1854i			1.71607i	−0.513591	+	0.858035i	$0.671685\pi$
$998$			12.7235i			0.402756i
$999$	−30.5081			−0.965234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.18	yes	34
17.16	even	2	inner	731.2.d.d.560.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.17	✓	34	17.16	even	2	inner
731.2.d.d.560.18	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)

\(f(q)\)	\(=\)	\(q-0.335917 q^{2} +0.523814i q^{3} -1.88716 q^{4} +1.51365i q^{5} -0.175958i q^{6} -0.357736i q^{7} +1.30576 q^{8} +2.72562 q^{9} +O(q^{10})\)	\(q-0.335917 q^{2} +0.523814i q^{3} -1.88716 q^{4} +1.51365i q^{5} -0.175958i q^{6} -0.357736i q^{7} +1.30576 q^{8} +2.72562 q^{9} -0.508460i q^{10} -2.34365i q^{11} -0.988522i q^{12} +2.14106 q^{13} +0.120169i q^{14} -0.792872 q^{15} +3.33569 q^{16} +(-0.486082 + 4.09435i) q^{17} -0.915581 q^{18} -4.97882 q^{19} -2.85650i q^{20} +0.187387 q^{21} +0.787272i q^{22} -0.807389i q^{23} +0.683977i q^{24} +2.70887 q^{25} -0.719217 q^{26} +2.99916i q^{27} +0.675105i q^{28} +8.18449i q^{29} +0.266339 q^{30} +3.43915i q^{31} -3.73204 q^{32} +1.22764 q^{33} +(0.163283 - 1.37536i) q^{34} +0.541487 q^{35} -5.14368 q^{36} +10.1722i q^{37} +1.67247 q^{38} +1.12152i q^{39} +1.97647i q^{40} +1.18063i q^{41} -0.0629465 q^{42} -1.00000 q^{43} +4.42284i q^{44} +4.12563i q^{45} +0.271216i q^{46} -4.86238 q^{47} +1.74728i q^{48} +6.87203 q^{49} -0.909953 q^{50} +(-2.14468 - 0.254617i) q^{51} -4.04052 q^{52} -2.67131 q^{53} -1.00747i q^{54} +3.54747 q^{55} -0.467118i q^{56} -2.60798i q^{57} -2.74931i q^{58} +9.76059 q^{59} +1.49628 q^{60} +4.64117i q^{61} -1.15527i q^{62} -0.975051i q^{63} -5.41773 q^{64} +3.24081i q^{65} -0.412384 q^{66} +2.25892 q^{67} +(0.917314 - 7.72670i) q^{68} +0.422922 q^{69} -0.181894 q^{70} +2.84290i q^{71} +3.55901 q^{72} -6.73975i q^{73} -3.41702i q^{74} +1.41894i q^{75} +9.39583 q^{76} -0.838408 q^{77} -0.376736i q^{78} -2.43002i q^{79} +5.04907i q^{80} +6.60585 q^{81} -0.396593i q^{82} -0.628850 q^{83} -0.353630 q^{84} +(-6.19741 - 0.735758i) q^{85} +0.335917 q^{86} -4.28715 q^{87} -3.06025i q^{88} +0.199232 q^{89} -1.38587i q^{90} -0.765933i q^{91} +1.52367i q^{92} -1.80148 q^{93} +1.63335 q^{94} -7.53619i q^{95} -1.95490i q^{96} +4.95539i q^{97} -2.30843 q^{98} -6.38790i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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