LMFDB - Embedded newform 731.2.d.d.560.10

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			560.10
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52896 q^{2} +1.41141i q^{3} +0.337716 q^{4} -1.28480i q^{5} -2.15799i q^{6} +2.51989i q^{7} +2.54156 q^{8} +1.00791 q^{9} +O(q^{10})$	\(q-1.52896 q^{2} +1.41141i q^{3} +0.337716 q^{4} -1.28480i q^{5} -2.15799i q^{6} +2.51989i q^{7} +2.54156 q^{8} +1.00791 q^{9} +1.96441i q^{10} -5.00231i q^{11} +0.476657i q^{12} -0.374993 q^{13} -3.85282i q^{14} +1.81338 q^{15} -4.56138 q^{16} +(-3.99839 - 1.00641i) q^{17} -1.54106 q^{18} +1.22867 q^{19} -0.433897i q^{20} -3.55661 q^{21} +7.64832i q^{22} -5.61391i q^{23} +3.58720i q^{24} +3.34929 q^{25} +0.573349 q^{26} +5.65682i q^{27} +0.851009i q^{28} -0.871819i q^{29} -2.77259 q^{30} -7.21032i q^{31} +1.89103 q^{32} +7.06033 q^{33} +(6.11338 + 1.53875i) q^{34} +3.23756 q^{35} +0.340388 q^{36} +2.29851i q^{37} -1.87859 q^{38} -0.529270i q^{39} -3.26540i q^{40} -4.11822i q^{41} +5.43792 q^{42} -1.00000 q^{43} -1.68936i q^{44} -1.29496i q^{45} +8.58343i q^{46} +10.6603 q^{47} -6.43799i q^{48} +0.650132 q^{49} -5.12093 q^{50} +(1.42045 - 5.64339i) q^{51} -0.126641 q^{52} +7.42508 q^{53} -8.64905i q^{54} -6.42697 q^{55} +6.40447i q^{56} +1.73417i q^{57} +1.33298i q^{58} +3.05139 q^{59} +0.612409 q^{60} -1.29356i q^{61} +11.0243i q^{62} +2.53983i q^{63} +6.23145 q^{64} +0.481791i q^{65} -10.7950 q^{66} +7.23387 q^{67} +(-1.35032 - 0.339879i) q^{68} +7.92355 q^{69} -4.95010 q^{70} +0.777920i q^{71} +2.56167 q^{72} +11.2786i q^{73} -3.51433i q^{74} +4.72723i q^{75} +0.414943 q^{76} +12.6053 q^{77} +0.809232i q^{78} -6.45681i q^{79} +5.86046i q^{80} -4.96038 q^{81} +6.29659i q^{82} -5.26052 q^{83} -1.20113 q^{84} +(-1.29303 + 5.13714i) q^{85} +1.52896 q^{86} +1.23050 q^{87} -12.7137i q^{88} +4.39100 q^{89} +1.97995i q^{90} -0.944942i q^{91} -1.89591i q^{92} +10.1767 q^{93} -16.2992 q^{94} -1.57860i q^{95} +2.66903i q^{96} -8.20733i q^{97} -0.994026 q^{98} -5.04188i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.52896			−1.08114			−0.540569	−	0.841300i	$-0.681791\pi$
$2$	−1.52896			−1.08114			−0.540569	+	0.841300i	$0.681791\pi$
$3$			1.41141i			0.814880i	0.913232	+	0.407440i	$0.133578\pi$
$3$			1.41141i			0.814880i	−0.913232	+	0.407440i	$0.866422\pi$
$4$	0.337716			0.168858
$5$		−	1.28480i		−	0.574580i	−0.957844	−	0.287290i	$-0.907246\pi$
$5$		−	1.28480i		−	0.574580i	0.957844	−	0.287290i	$-0.0927543\pi$
$6$		−	2.15799i		−	0.880997i
$7$			2.51989i			0.952431i	0.879329	+	0.476215i	$0.157992\pi$
$7$			2.51989i			0.952431i	−0.879329	+	0.476215i	$0.842008\pi$
$8$	2.54156			0.898579
$9$	1.00791			0.335970
$10$			1.96441i			0.621200i
$11$		−	5.00231i		−	1.50825i	−0.656729	−	0.754126i	$-0.728061\pi$
$11$		−	5.00231i		−	1.50825i	0.656729	−	0.754126i	$-0.271939\pi$
$12$			0.476657i			0.137599i
$13$	−0.374993			−0.104004			−0.0520022	−	0.998647i	$-0.516560\pi$
$13$	−0.374993			−0.104004			−0.0520022	+	0.998647i	$0.516560\pi$
$14$		−	3.85282i		−	1.02971i
$15$	1.81338			0.468214
$16$	−4.56138			−1.14034
$17$	−3.99839	−	1.00641i	−0.969753	−	0.244089i
$17$	−3.99839	−	1.00641i	−0.969753	−	0.244089i
$18$	−1.54106			−0.363230
$19$	1.22867			0.281877			0.140939	−	0.990018i	$-0.454988\pi$
$19$	1.22867			0.281877			0.140939	+	0.990018i	$0.454988\pi$
$20$		−	0.433897i		−	0.0970224i
$21$	−3.55661			−0.776117
$22$			7.64832i			1.63063i
$23$		−	5.61391i		−	1.17058i	−0.810824	−	0.585290i	$-0.800981\pi$
$23$		−	5.61391i		−	1.17058i	0.810824	−	0.585290i	$-0.199019\pi$
$24$			3.58720i			0.732234i
$25$	3.34929			0.669858
$26$	0.573349			0.112443
$27$			5.65682i			1.08866i
$28$			0.851009i			0.160825i
$29$		−	0.871819i		−	0.161893i	−0.996718	−	0.0809463i	$-0.974206\pi$
$29$		−	0.871819i		−	0.161893i	0.996718	−	0.0809463i	$-0.0257942\pi$
$30$	−2.77259			−0.506203
$31$		−	7.21032i		−	1.29501i	−0.762061	−	0.647506i	$-0.775812\pi$
$31$		−	7.21032i		−	1.29501i	0.762061	−	0.647506i	$-0.224188\pi$
$32$	1.89103			0.334291
$33$	7.06033			1.22905
$34$	6.11338	+	1.53875i	1.04844	+	0.263894i
$35$	3.23756			0.547248
$36$	0.340388			0.0567313
$37$			2.29851i			0.377873i	0.981989	+	0.188936i	$0.0605040\pi$
$37$			2.29851i			0.377873i	−0.981989	+	0.188936i	$0.939496\pi$
$38$	−1.87859			−0.304748
$39$		−	0.529270i		−	0.0847510i
$40$		−	3.26540i		−	0.516305i
$41$		−	4.11822i		−	0.643158i	−0.946883	−	0.321579i	$-0.895786\pi$
$41$		−	4.11822i		−	0.643158i	0.946883	−	0.321579i	$-0.104214\pi$
$42$	5.43792			0.839089
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$		−	1.68936i		−	0.254680i
$45$		−	1.29496i		−	0.193042i
$46$			8.58343i			1.26556i
$47$	10.6603			1.55497			0.777485	−	0.628902i	$-0.216495\pi$
$47$	10.6603			1.55497			0.777485	+	0.628902i	$0.216495\pi$
$48$		−	6.43799i		−	0.929244i
$49$	0.650132			0.0928760
$50$	−5.12093			−0.724208
$51$	1.42045	−	5.64339i	0.198903	−	0.790232i
$52$	−0.126641			−0.0175620
$53$	7.42508			1.01991			0.509957	−	0.860200i	$-0.329661\pi$
$53$	7.42508			1.01991			0.509957	+	0.860200i	$0.329661\pi$
$54$		−	8.64905i		−	1.17699i
$55$	−6.42697			−0.866612
$56$			6.40447i			0.855834i
$57$			1.73417i			0.229696i
$58$			1.33298i			0.175028i
$59$	3.05139			0.397257			0.198629	−	0.980075i	$-0.436351\pi$
$59$	3.05139			0.397257			0.198629	+	0.980075i	$0.436351\pi$
$60$	0.612409			0.0790616
$61$		−	1.29356i		−	0.165623i	−0.996565	−	0.0828117i	$-0.973610\pi$
$61$		−	1.29356i		−	0.165623i	0.996565	−	0.0828117i	$-0.0263900\pi$
$62$			11.0243i			1.40009i
$63$			2.53983i			0.319989i
$64$	6.23145			0.778931
$65$			0.481791i			0.0597588i
$66$	−10.7950			−1.32877
$67$	7.23387			0.883757			0.441879	−	0.897075i	$-0.354312\pi$
$67$	7.23387			0.883757			0.441879	+	0.897075i	$0.354312\pi$
$68$	−1.35032	−	0.339879i	−0.163750	−	0.0412164i
$69$	7.92355			0.953883
$70$	−4.95010			−0.591650
$71$			0.777920i			0.0923221i	0.998934	+	0.0461610i	$0.0146987\pi$
$71$			0.777920i			0.0923221i	−0.998934	+	0.0461610i	$0.985301\pi$
$72$	2.56167			0.301896
$73$			11.2786i			1.32006i	0.751240	+	0.660029i	$0.229456\pi$
$73$			11.2786i			1.32006i	−0.751240	+	0.660029i	$0.770544\pi$
$74$		−	3.51433i		−	0.408532i
$75$			4.72723i			0.545854i
$76$	0.414943			0.0475972
$77$	12.6053			1.43651
$78$			0.809232i			0.0916275i
$79$		−	6.45681i		−	0.726448i	−0.931702	−	0.363224i	$-0.881676\pi$
$79$		−	6.45681i		−	0.726448i	0.931702	−	0.363224i	$-0.118324\pi$
$80$			5.86046i			0.655219i
$81$	−4.96038			−0.551153
$82$			6.29659i			0.695342i
$83$	−5.26052			−0.577417			−0.288708	−	0.957417i	$-0.593226\pi$
$83$	−5.26052			−0.577417			−0.288708	+	0.957417i	$0.593226\pi$
$84$	−1.20113			−0.131053
$85$	−1.29303	+	5.13714i	−0.140249	+	0.557201i
$86$	1.52896			0.164872
$87$	1.23050			0.131923
$88$		−	12.7137i		−	1.35528i
$89$	4.39100			0.465445			0.232723	−	0.972543i	$-0.425237\pi$
$89$	4.39100			0.465445			0.232723	+	0.972543i	$0.425237\pi$
$90$			1.97995i			0.208705i
$91$		−	0.944942i		−	0.0990569i
$92$		−	1.89591i		−	0.197662i
$93$	10.1767			1.05528
$94$	−16.2992			−1.68114
$95$		−	1.57860i		−	0.161961i
$96$			2.66903i			0.272407i
$97$		−	8.20733i		−	0.833328i	−0.909061	−	0.416664i	$-0.863199\pi$
$97$		−	8.20733i		−	0.833328i	0.909061	−	0.416664i	$-0.136801\pi$
$98$	−0.994026			−0.100412
$99$		−	5.04188i		−	0.506728i
$100$	1.13111			0.113111
$101$	13.1554			1.30902			0.654508	−	0.756055i	$-0.272876\pi$
$101$	13.1554			1.30902			0.654508	+	0.756055i	$0.272876\pi$
$102$	−2.17182	+	8.62851i	−0.215042	+	0.854350i
$103$	4.12395			0.406345			0.203172	−	0.979143i	$-0.434875\pi$
$103$	4.12395			0.406345			0.203172	+	0.979143i	$0.434875\pi$
$104$	−0.953069			−0.0934561
$105$			4.56954i			0.445941i
$106$	−11.3526			−1.10267
$107$		−	4.80517i		−	0.464533i	−0.972652	−	0.232267i	$-0.925386\pi$
$107$		−	4.80517i		−	0.464533i	0.972652	−	0.232267i	$-0.0746142\pi$
$108$			1.91040i			0.183828i
$109$		−	3.83757i		−	0.367573i	−0.982966	−	0.183786i	$-0.941165\pi$
$109$		−	3.83757i		−	0.367573i	0.982966	−	0.183786i	$-0.0588355\pi$
$110$	9.82657			0.936926
$111$	−3.24415			−0.307921
$112$		−	11.4942i		−	1.08610i
$113$			10.6566i			1.00249i	0.865307	+	0.501243i	$0.167124\pi$
$113$			10.6566i			1.00249i	−0.865307	+	0.501243i	$0.832876\pi$
$114$		−	2.65147i		−	0.248333i
$115$	−7.21275			−0.672592
$116$		−	0.294427i		−	0.0273369i
$117$	−0.377960			−0.0349424
$118$	−4.66545			−0.429490
$119$	2.53604	−	10.0755i	0.232478	−	0.923622i
$120$	4.60883			0.420727
$121$	−14.0231			−1.27483
$122$			1.97780i			0.179062i
$123$	5.81252			0.524097
$124$		−	2.43504i		−	0.218673i
$125$		−	10.7272i		−	0.959467i
$126$		−	3.88330i		−	0.345952i
$127$	−17.2660			−1.53211			−0.766053	−	0.642778i	$-0.777782\pi$
$127$	−17.2660			−1.53211			−0.766053	+	0.642778i	$0.777782\pi$
$128$	−13.3097			−1.17642
$129$		−	1.41141i		−	0.124268i
$130$		−	0.736638i		−	0.0646075i
$131$		−	6.56738i		−	0.573795i	−0.957961	−	0.286897i	$-0.907376\pi$
$131$		−	6.56738i		−	0.573795i	0.957961	−	0.286897i	$-0.0926238\pi$
$132$	2.38438			0.207534
$133$			3.09613i			0.268468i
$134$	−11.0603			−0.955463
$135$	7.26788			0.625520
$136$	−10.1622	−	2.55784i	−0.871399	−	0.219333i
$137$	6.70043			0.572456			0.286228	−	0.958161i	$-0.407598\pi$
$137$	6.70043			0.572456			0.286228	+	0.958161i	$0.407598\pi$
$138$	−12.1148			−1.03128
$139$		−	5.33613i		−	0.452604i	−0.974057	−	0.226302i	$-0.927336\pi$
$139$		−	5.33613i		−	0.452604i	0.974057	−	0.226302i	$-0.0726637\pi$
$140$	1.09338			0.0924071
$141$			15.0461i			1.26711i
$142$		−	1.18941i		−	0.0998129i
$143$			1.87583i			0.156865i
$144$	−4.59747			−0.383122
$145$	−1.12011			−0.0930203
$146$		−	17.2445i		−	1.42716i
$147$			0.917606i			0.0756828i
$148$			0.776244i			0.0638068i
$149$	21.6939			1.77723			0.888616	−	0.458651i	$-0.151667\pi$
$149$	21.6939			1.77723			0.888616	+	0.458651i	$0.151667\pi$
$150$		−	7.22775i		−	0.590143i
$151$	−14.1113			−1.14836			−0.574179	−	0.818730i	$-0.694679\pi$
$151$	−14.1113			−1.14836			−0.574179	+	0.818730i	$0.694679\pi$
$152$	3.12275			0.253289
$153$	−4.03003	−	1.01437i	−0.325808	−	0.0820067i
$154$	−19.2730			−1.55306
$155$	−9.26382			−0.744088
$156$		−	0.178743i		−	0.0143109i
$157$	−3.02465			−0.241393			−0.120697	−	0.992689i	$-0.538513\pi$
$157$	−3.02465			−0.241393			−0.120697	+	0.992689i	$0.538513\pi$
$158$			9.87220i			0.785390i
$159$			10.4799i			0.831107i
$160$		−	2.42960i		−	0.192077i
$161$	14.1465			1.11490
$162$	7.58422			0.595873
$163$		−	6.91278i		−	0.541451i	−0.962657	−	0.270725i	$-0.912736\pi$
$163$		−	6.91278i		−	0.541451i	0.962657	−	0.270725i	$-0.0872635\pi$
$164$		−	1.39079i		−	0.108602i
$165$		−	9.07111i		−	0.706185i
$166$	8.04311			0.624267
$167$		−	3.88093i		−	0.300315i	−0.988662	−	0.150158i	$-0.952022\pi$
$167$		−	3.88093i		−	0.300315i	0.988662	−	0.150158i	$-0.0479781\pi$
$168$	−9.03936			−0.697402
$169$	−12.8594			−0.989183
$170$	1.97699	−	7.85447i	0.151628	−	0.602410i
$171$	1.23839			0.0947024
$172$	−0.337716			−0.0257506
$173$			14.1722i			1.07750i	0.842467	+	0.538748i	$0.181102\pi$
$173$			14.1722i			1.07750i	−0.842467	+	0.538748i	$0.818898\pi$
$174$	−1.88138			−0.142627
$175$			8.43986i			0.637993i
$176$			22.8174i			1.71993i
$177$			4.30678i			0.323717i
$178$	−6.71366			−0.503210
$179$	−19.8258			−1.48185			−0.740927	−	0.671586i	$-0.765613\pi$
$179$	−19.8258			−1.48185			−0.740927	+	0.671586i	$0.765613\pi$
$180$		−	0.437330i		−	0.0325967i
$181$			14.9159i			1.10869i	0.832286	+	0.554347i	$0.187032\pi$
$181$			14.9159i			1.10869i	−0.832286	+	0.554347i	$0.812968\pi$
$182$			1.44478i			0.107094i
$183$	1.82575			0.134963
$184$		−	14.2681i		−	1.05186i
$185$	2.95313			0.217118
$186$	−15.5598			−1.14090
$187$	−5.03435	+	20.0012i	−0.368148	+	1.46263i
$188$	3.60016			0.262569
$189$	−14.2546			−1.03687
$190$			2.41361i			0.175102i
$191$	−18.3407			−1.32708			−0.663542	−	0.748139i	$-0.730948\pi$
$191$	−18.3407			−1.32708			−0.663542	+	0.748139i	$0.730948\pi$
$192$			8.79515i			0.634735i
$193$			9.19570i			0.661921i	0.943645	+	0.330960i	$0.107373\pi$
$193$			9.19570i			0.661921i	−0.943645	+	0.330960i	$0.892627\pi$
$194$			12.5487i			0.900942i
$195$	−0.680006			−0.0486963
$196$	0.219560			0.0156829
$197$		−	6.10699i		−	0.435105i	−0.976049	−	0.217552i	$-0.930193\pi$
$197$		−	6.10699i		−	0.435105i	0.976049	−	0.217552i	$-0.0698073\pi$
$198$			7.70883i			0.547843i
$199$			7.64933i			0.542247i	0.962545	+	0.271123i	$0.0873951\pi$
$199$			7.64933i			0.542247i	−0.962545	+	0.271123i	$0.912605\pi$
$200$	8.51243			0.601920
$201$			10.2100i			0.720156i
$202$	−20.1141			−1.41523
$203$	2.19689			0.154192
$204$	0.479710	−	1.90586i	0.0335864	−	0.133437i
$205$	−5.29109			−0.369546
$206$	−6.30535			−0.439315
$207$		−	5.65832i		−	0.393280i
$208$	1.71048			0.118601
$209$		−	6.14621i		−	0.425142i
$210$		−	6.98663i		−	0.482124i
$211$		−	14.0216i		−	0.965290i	−0.875816	−	0.482645i	$-0.839676\pi$
$211$		−	14.0216i		−	0.965290i	0.875816	−	0.482645i	$-0.160324\pi$
$212$	2.50757			0.172221
$213$	−1.09797			−0.0752314
$214$			7.34691i			0.502224i
$215$			1.28480i			0.0876226i
$216$			14.3772i			0.978243i
$217$	18.1692			1.23341
$218$			5.86749i			0.397397i
$219$	−15.9187			−1.07569
$220$	−2.17049			−0.146334
$221$	1.49937	+	0.377395i	0.100858	+	0.0253863i
$222$	4.96017			0.332905
$223$	−2.04250			−0.136776			−0.0683881	−	0.997659i	$-0.521786\pi$
$223$	−2.04250			−0.136776			−0.0683881	+	0.997659i	$0.521786\pi$
$224$			4.76521i			0.318389i
$225$	3.37579			0.225052
$226$		−	16.2935i		−	1.08382i
$227$		−	3.86486i		−	0.256520i	−0.991741	−	0.128260i	$-0.959061\pi$
$227$		−	3.86486i		−	0.256520i	0.991741	−	0.128260i	$-0.0409392\pi$
$228$			0.585656i			0.0387860i
$229$	12.5052			0.826368			0.413184	−	0.910648i	$-0.364417\pi$
$229$	12.5052			0.826368			0.413184	+	0.910648i	$0.364417\pi$
$230$	11.0280			0.727164
$231$			17.7913i			1.17058i
$232$		−	2.21578i		−	0.145473i
$233$		−	5.41182i		−	0.354540i	−0.984162	−	0.177270i	$-0.943273\pi$
$233$		−	5.41182i		−	0.354540i	0.984162	−	0.177270i	$-0.0567266\pi$
$234$	0.577885			0.0377775
$235$		−	13.6964i		−	0.893454i
$236$	1.03050			0.0670801
$237$	9.11323			0.591968
$238$	−3.87749	+	15.4051i	−0.251341	+	0.998562i
$239$	−14.2558			−0.922133			−0.461067	−	0.887366i	$-0.652533\pi$
$239$	−14.2558			−0.922133			−0.461067	+	0.887366i	$0.652533\pi$
$240$	−8.27153			−0.533925
$241$			26.2241i			1.68924i	0.535366	+	0.844620i	$0.320174\pi$
$241$			26.2241i			1.68924i	−0.535366	+	0.844620i	$0.679826\pi$
$242$	21.4407			1.37826
$243$			9.96931i			0.639532i
$244$		−	0.436856i		−	0.0279668i
$245$		−	0.835290i		−	0.0533647i
$246$	−8.88710			−0.566621
$247$	−0.460744			−0.0293164
$248$		−	18.3255i		−	1.16367i
$249$		−	7.42476i		−	0.470525i
$250$			16.4014i			1.03732i
$251$	−0.642515			−0.0405552			−0.0202776	−	0.999794i	$-0.506455\pi$
$251$	−0.642515			−0.0405552			−0.0202776	+	0.999794i	$0.506455\pi$
$252$			0.857741i			0.0540326i
$253$	−28.0825			−1.76553
$254$	26.3989			1.65642
$255$	−7.25062	−	1.82500i	−0.454052	−	0.114286i
$256$	7.88709			0.492943
$257$	6.39189			0.398715			0.199357	−	0.979927i	$-0.436115\pi$
$257$	6.39189			0.398715			0.199357	+	0.979927i	$0.436115\pi$
$258$			2.15799i			0.134351i
$259$	−5.79200			−0.359898
$260$			0.162708i			0.0100907i
$261$		−	0.878716i		−	0.0543912i
$262$			10.0413i			0.620351i
$263$	6.96317			0.429367			0.214684	−	0.976684i	$-0.431128\pi$
$263$	6.96317			0.429367			0.214684	+	0.976684i	$0.431128\pi$
$264$	17.9443			1.10439
$265$		−	9.53974i		−	0.586022i
$266$		−	4.73385i		−	0.290251i
$267$			6.19752i			0.379282i
$268$	2.44299			0.149229
$269$		−	18.3997i		−	1.12185i	−0.827867	−	0.560924i	$-0.810446\pi$
$269$		−	18.3997i		−	1.12185i	0.827867	−	0.560924i	$-0.189554\pi$
$270$	−11.1123			−0.676273
$271$	22.2418			1.35109			0.675547	−	0.737317i	$-0.263908\pi$
$271$	22.2418			1.35109			0.675547	+	0.737317i	$0.263908\pi$
$272$	18.2382	+	4.59060i	1.10585	+	0.278346i
$273$	1.33370			0.0807195
$274$	−10.2447			−0.618904
$275$		−	16.7542i		−	1.01031i
$276$	2.67591			0.161071
$277$		−	32.9210i		−	1.97803i	−0.147805	−	0.989017i	$-0.547221\pi$
$277$		−	32.9210i		−	1.97803i	0.147805	−	0.989017i	$-0.452779\pi$
$278$			8.15872i			0.489328i
$279$		−	7.26736i		−	0.435086i
$280$	8.22847			0.491745
$281$	−27.8601			−1.66199			−0.830997	−	0.556277i	$-0.812229\pi$
$281$	−27.8601			−1.66199			−0.830997	+	0.556277i	$0.812229\pi$
$282$		−	23.0049i		−	1.36992i
$283$		−	30.8571i		−	1.83426i	−0.398584	−	0.917132i	$-0.630498\pi$
$283$		−	30.8571i		−	1.83426i	0.398584	−	0.917132i	$-0.369502\pi$
$284$			0.262716i			0.0155893i
$285$	2.22806			0.131979
$286$		−	2.86807i		−	0.169592i
$287$	10.3775			0.612564
$288$	1.90600			0.112312
$289$	14.9743	+	8.04801i	0.880841	+	0.473412i
$290$	1.71261			0.100568
$291$	11.5839			0.679062
$292$			3.80895i			0.222902i
$293$	9.29885			0.543245			0.271622	−	0.962404i	$-0.412440\pi$
$293$	9.29885			0.543245			0.271622	+	0.962404i	$0.412440\pi$
$294$		−	1.40298i		−	0.0818235i
$295$		−	3.92043i		−	0.228256i
$296$			5.84181i			0.339548i
$297$	28.2972			1.64197
$298$	−33.1691			−1.92143
$299$			2.10518i			0.121745i
$300$			1.59646i			0.0921718i
$301$		−	2.51989i		−	0.145244i
$302$	21.5755			1.24153
$303$			18.5678i			1.06669i
$304$	−5.60445			−0.321437
$305$	−1.66197			−0.0951638
$306$	6.16174	+	1.55093i	0.352243	+	0.0886605i
$307$	17.5766			1.00315			0.501574	−	0.865115i	$-0.332755\pi$
$307$	17.5766			1.00315			0.501574	+	0.865115i	$0.332755\pi$
$308$	4.25701			0.242565
$309$			5.82060i			0.331122i
$310$	14.1640			0.804461
$311$		−	7.29330i		−	0.413565i	−0.978387	−	0.206783i	$-0.933701\pi$
$311$		−	7.29330i		−	0.413565i	0.978387	−	0.206783i	$-0.0662993\pi$
$312$		−	1.34517i		−	0.0761555i
$313$		−	23.0816i		−	1.30465i	−0.757939	−	0.652326i	$-0.773793\pi$
$313$		−	23.0816i		−	1.30465i	0.757939	−	0.652326i	$-0.226207\pi$
$314$	4.62456			0.260979
$315$	3.26317			0.183859
$316$		−	2.18057i		−	0.122667i
$317$			12.3680i			0.694656i	0.937744	+	0.347328i	$0.112911\pi$
$317$			12.3680i			0.694656i	−0.937744	+	0.347328i	$0.887089\pi$
$318$		−	16.0233i		−	0.898541i
$319$	−4.36111			−0.244175
$320$		−	8.00616i		−	0.447558i
$321$	6.78208			0.378539
$322$	−21.6293			−1.20536
$323$	−4.91272	−	1.23654i	−0.273351	−	0.0688031i
$324$	−1.67520			−0.0930667
$325$	−1.25596			−0.0696681
$326$			10.5694i			0.585383i
$327$	5.41640			0.299528
$328$		−	10.4667i		−	0.577928i
$329$			26.8629i			1.48100i
$330$			13.8694i			0.763483i
$331$	10.5726			0.581120			0.290560	−	0.956857i	$-0.406158\pi$
$331$	10.5726			0.581120			0.290560	+	0.956857i	$0.406158\pi$
$332$	−1.77656			−0.0975014
$333$			2.31669i			0.126954i
$334$			5.93378i			0.324682i
$335$		−	9.29407i		−	0.507789i
$336$	16.2231			0.885041
$337$			7.31016i			0.398210i	0.979978	+	0.199105i	$0.0638035\pi$
$337$			7.31016i			0.398210i	−0.979978	+	0.199105i	$0.936197\pi$
$338$	19.6615			1.06944
$339$	−15.0408			−0.816906
$340$	−0.436677	+	1.73489i	−0.0236821	+	0.0940878i
$341$	−36.0682			−1.95320
$342$	−1.89345			−0.102386
$343$			19.2775i			1.04089i
$344$	−2.54156			−0.137032
$345$		−	10.1802i		−	0.548082i
$346$		−	21.6688i		−	1.16492i
$347$		−	11.8624i		−	0.636808i	−0.947955	−	0.318404i	$-0.896853\pi$
$347$		−	11.8624i		−	0.636808i	0.947955	−	0.318404i	$-0.103147\pi$
$348$	0.415559			0.0222763
$349$	−18.3753			−0.983608			−0.491804	−	0.870706i	$-0.663662\pi$
$349$	−18.3753			−0.983608			−0.491804	+	0.870706i	$0.663662\pi$
$350$		−	12.9042i		−	0.689758i
$351$		−	2.12127i		−	0.113225i
$352$		−	9.45954i		−	0.504195i
$353$	−5.80227			−0.308824			−0.154412	−	0.988007i	$-0.549348\pi$
$353$	−5.80227			−0.308824			−0.154412	+	0.988007i	$0.549348\pi$
$354$		−	6.58488i		−	0.349983i
$355$	0.999471			0.0530464
$356$	1.48291			0.0785941
$357$	14.2207	+	3.57939i	0.752641	+	0.189442i
$358$	30.3129			1.60209
$359$	−11.0355			−0.582431			−0.291216	−	0.956657i	$-0.594060\pi$
$359$	−11.0355			−0.582431			−0.291216	+	0.956657i	$0.594060\pi$
$360$		−	3.29124i		−	0.173463i
$361$	−17.4904			−0.920545
$362$		−	22.8059i		−	1.19865i
$363$		−	19.7924i		−	1.03883i
$364$		−	0.319122i		−	0.0167265i
$365$	14.4907			0.758478
$366$	−2.79149			−0.145914
$367$			25.0407i			1.30711i	0.756878	+	0.653557i	$0.226724\pi$
$367$			25.0407i			1.30711i	−0.756878	+	0.653557i	$0.773276\pi$
$368$			25.6072i			1.33487i
$369$		−	4.15080i		−	0.216082i
$370$	−4.51521			−0.234735
$371$			18.7104i			0.971397i
$372$	3.43685			0.178192
$373$	12.7689			0.661149			0.330574	−	0.943780i	$-0.392758\pi$
$373$	12.7689			0.661149			0.330574	+	0.943780i	$0.392758\pi$
$374$	7.69731	−	30.5810i	0.398019	−	1.58131i
$375$	15.1405			0.781850
$376$	27.0939			1.39726
$377$			0.326926i			0.0168375i
$378$	21.7947			1.12100
$379$			18.8958i			0.970613i	0.874344	+	0.485307i	$0.161292\pi$
$379$			18.8958i			0.970613i	−0.874344	+	0.485307i	$0.838708\pi$
$380$		−	0.533118i		−	0.0273484i
$381$		−	24.3694i		−	1.24848i
$382$	28.0421			1.43476
$383$	1.53620			0.0784961			0.0392481	−	0.999229i	$-0.487504\pi$
$383$	1.53620			0.0784961			0.0392481	+	0.999229i	$0.487504\pi$
$384$		−	18.7855i		−	0.958643i
$385$		−	16.1953i		−	0.825388i
$386$		−	14.0598i		−	0.715627i
$387$	−1.00791			−0.0512350
$388$		−	2.77175i		−	0.140714i
$389$	30.6871			1.55590			0.777950	−	0.628327i	$-0.216260\pi$
$389$	30.6871			1.55590			0.777950	+	0.628327i	$0.216260\pi$
$390$	1.03970			0.0526473
$391$	−5.64987	+	22.4466i	−0.285726	+	1.13517i
$392$	1.65235			0.0834564
$393$	9.26929			0.467574
$394$			9.33734i			0.470408i
$395$	−8.29571			−0.417403
$396$		−	1.70272i		−	0.0855651i
$397$			14.9630i			0.750973i	0.926828	+	0.375486i	$0.122524\pi$
$397$			14.9630i			0.750973i	−0.926828	+	0.375486i	$0.877476\pi$
$398$		−	11.6955i		−	0.586243i
$399$	−4.36992			−0.218770
$400$	−15.2774			−0.763869
$401$			32.8928i			1.64259i	0.570505	+	0.821294i	$0.306748\pi$
$401$			32.8928i			1.64259i	−0.570505	+	0.821294i	$0.693252\pi$
$402$		−	15.6106i		−	0.778588i
$403$			2.70382i			0.134687i
$404$	4.44280			0.221038
$405$			6.37310i			0.316682i
$406$	−3.35896			−0.166702
$407$	11.4979			0.569928
$408$	3.61018	−	14.3430i	0.178730	−	0.710086i
$409$	23.0558			1.14003			0.570017	−	0.821633i	$-0.306937\pi$
$409$	23.0558			1.14003			0.570017	+	0.821633i	$0.306937\pi$
$410$	8.08986			0.399530
$411$			9.45708i			0.466483i
$412$	1.39272			0.0686146
$413$			7.68918i			0.378360i
$414$			8.65134i			0.425190i
$415$			6.75871i			0.331772i
$416$	−0.709124			−0.0347677
$417$	7.53148			0.368818
$418$			9.39730i			0.459637i
$419$			4.83507i			0.236209i	0.993001	+	0.118104i	$0.0376818\pi$
$419$			4.83507i			0.236209i	−0.993001	+	0.118104i	$0.962318\pi$
$420$			1.54321i			0.0753007i
$421$	−5.35660			−0.261065			−0.130532	−	0.991444i	$-0.541669\pi$
$421$	−5.35660			−0.261065			−0.130532	+	0.991444i	$0.541669\pi$
$422$			21.4385i			1.04361i
$423$	10.7447			0.522424
$424$	18.8713			0.916472
$425$	−13.3918	−	3.37074i	−0.649597	−	0.163505i
$426$	1.67875			0.0813355
$427$	3.25963			0.157745
$428$		−	1.62278i		−	0.0784401i
$429$	−2.64757			−0.127826
$430$		−	1.96441i		−	0.0947321i
$431$		−	25.3061i		−	1.21895i	−0.792805	−	0.609475i	$-0.791380\pi$
$431$		−	25.3061i		−	1.21895i	0.792805	−	0.609475i	$-0.208620\pi$
$432$		−	25.8029i		−	1.24144i
$433$	0.746176			0.0358589			0.0179295	−	0.999839i	$-0.494293\pi$
$433$	0.746176			0.0358589			0.0179295	+	0.999839i	$0.494293\pi$
$434$	−27.7800			−1.33348
$435$		−	1.58094i		−	0.0758004i
$436$		−	1.29601i		−	0.0620676i
$437$		−	6.89766i		−	0.329960i
$438$	24.3391			1.16297
$439$			27.7636i			1.32508i	0.749025	+	0.662541i	$0.230522\pi$
$439$			27.7636i			1.32508i	−0.749025	+	0.662541i	$0.769478\pi$
$440$	−16.3345			−0.778719
$441$	0.655276			0.0312036
$442$	−2.29247	−	0.577021i	−0.109042	−	0.0274461i
$443$	−12.7205			−0.604369			−0.302184	−	0.953249i	$-0.597716\pi$
$443$	−12.7205			−0.604369			−0.302184	+	0.953249i	$0.597716\pi$
$444$	−1.09560			−0.0519949
$445$		−	5.64156i		−	0.267435i
$446$	3.12291			0.147874
$447$			30.6191i			1.44823i
$448$			15.7026i			0.741877i
$449$		−	14.2889i		−	0.674335i	−0.941445	−	0.337167i	$-0.890531\pi$
$449$		−	14.2889i		−	0.674335i	0.941445	−	0.337167i	$-0.109469\pi$
$450$	−5.16144			−0.243313
$451$	−20.6006			−0.970045
$452$			3.59889i			0.169278i
$453$		−	19.9168i		−	0.935775i
$454$			5.90922i			0.277333i
$455$	−1.21406			−0.0569161
$456$			4.40750i			0.206400i
$457$	−39.5933			−1.85210			−0.926049	−	0.377404i	$-0.876817\pi$
$457$	−39.5933			−1.85210			−0.926049	+	0.377404i	$0.876817\pi$
$458$	−19.1200			−0.893417
$459$	5.69305	−	22.6182i	0.265729	−	1.05573i
$460$	−2.43586			−0.113573
$461$	−30.6210			−1.42616			−0.713081	−	0.701082i	$-0.752701\pi$
$461$	−30.6210			−1.42616			−0.713081	+	0.701082i	$0.752701\pi$
$462$		−	27.2021i		−	1.26556i
$463$	19.7870			0.919581			0.459791	−	0.888027i	$-0.347924\pi$
$463$	19.7870			0.919581			0.459791	+	0.888027i	$0.347924\pi$
$464$			3.97670i			0.184614i
$465$		−	13.0751i		−	0.606342i
$466$			8.27445i			0.383306i
$467$	33.9296			1.57008			0.785038	−	0.619447i	$-0.212643\pi$
$467$	33.9296			1.57008			0.785038	+	0.619447i	$0.212643\pi$
$468$	−0.127643			−0.00590030
$469$			18.2286i			0.841718i
$470$			20.9412i			0.965947i
$471$		−	4.26903i		−	0.196707i
$472$	7.75531			0.356967
$473$			5.00231i			0.230006i
$474$	−13.9338			−0.639999
$475$	4.11518			0.188818
$476$	0.856460	−	3.40267i	0.0392558	−	0.155961i
$477$	7.48382			0.342661
$478$	21.7966			0.996953
$479$		−	4.35145i		−	0.198823i	−0.995046	−	0.0994114i	$-0.968304\pi$
$479$		−	4.35145i		−	0.198823i	0.995046	−	0.0994114i	$-0.0316960\pi$
$480$	3.42917			0.156520
$481$		−	0.861925i		−	0.0393004i
$482$		−	40.0955i		−	1.82630i
$483$			19.9665i			0.908507i
$484$	−4.73582			−0.215265
$485$	−10.5448			−0.478814
$486$		−	15.2427i		−	0.691422i
$487$		−	14.7387i		−	0.667875i	−0.942595	−	0.333937i	$-0.891623\pi$
$487$		−	14.7387i		−	0.667875i	0.942595	−	0.333937i	$-0.108377\pi$
$488$		−	3.28766i		−	0.148826i
$489$	9.75679			0.441217
$490$			1.27712i			0.0576946i
$491$	−39.9397			−1.80245			−0.901226	−	0.433349i	$-0.857332\pi$
$491$	−39.9397			−1.80245			−0.901226	+	0.433349i	$0.857332\pi$
$492$	1.96298			0.0884979
$493$	−0.877403	+	3.48587i	−0.0395162	+	0.156996i
$494$	0.704459			0.0316951
$495$	−6.47781			−0.291156
$496$			32.8890i			1.47676i
$497$	−1.96028			−0.0879304
$498$			11.3522i			0.508702i
$499$			32.1440i			1.43896i	0.694511	+	0.719482i	$0.255621\pi$
$499$			32.1440i			1.43896i	−0.694511	+	0.719482i	$0.744379\pi$
$500$		−	3.62274i		−	0.162014i
$501$	5.47760			0.244721
$502$	0.982378			0.0438457
$503$			29.2668i			1.30494i	0.757813	+	0.652471i	$0.226268\pi$
$503$			29.2668i			1.30494i	−0.757813	+	0.652471i	$0.773732\pi$
$504$			6.45514i			0.287535i
$505$		−	16.9021i		−	0.752134i
$506$	42.9370			1.90878
$507$		−	18.1499i		−	0.806066i
$508$	−5.83099			−0.258708
$509$	39.8613			1.76682			0.883410	−	0.468602i	$-0.155242\pi$
$509$	39.8613			1.76682			0.883410	+	0.468602i	$0.155242\pi$
$510$	11.0859	+	2.79035i	0.490892	+	0.123559i
$511$	−28.4208			−1.25726
$512$	14.5604			0.643483
$513$			6.95039i			0.306867i
$514$	−9.77293			−0.431066
$515$		−	5.29845i		−	0.233478i
$516$		−	0.476657i		−	0.0209837i
$517$		−	53.3263i		−	2.34529i
$518$	8.85574			0.389099
$519$	−20.0029			−0.878030
$520$			1.22450i			0.0536980i
$521$			23.8789i			1.04615i	0.852285	+	0.523077i	$0.175216\pi$
$521$			23.8789i			1.04615i	−0.852285	+	0.523077i	$0.824784\pi$
$522$			1.34352i			0.0588043i
$523$	−24.7628			−1.08280			−0.541400	−	0.840765i	$-0.682106\pi$
$523$	−24.7628			−1.08280			−0.541400	+	0.840765i	$0.682106\pi$
$524$		−	2.21791i		−	0.0968898i
$525$	−11.9121			−0.519888
$526$	−10.6464			−0.464205
$527$	−7.25650	+	28.8297i	−0.316098	+	1.25584i
$528$	−32.2048			−1.40154
$529$	−8.51595			−0.370259
$530$			14.5859i			0.633570i
$531$	3.07553			0.133467
$532$			1.04561i			0.0453330i
$533$			1.54430i			0.0668912i
$534$		−	9.47575i		−	0.410056i
$535$	−6.17368			−0.266912
$536$	18.3853			0.794126
$537$		−	27.9825i		−	1.20753i
$538$			28.1323i			1.21287i
$539$		−	3.25216i		−	0.140081i
$540$	2.45448			0.105624
$541$		−	23.9865i		−	1.03126i	−0.856811	−	0.515630i	$-0.827558\pi$
$541$		−	23.9865i		−	1.03126i	0.856811	−	0.515630i	$-0.172442\pi$
$542$	−34.0068			−1.46072
$543$	−21.0526			−0.903452
$544$	−7.56110	−	1.90315i	−0.324179	−	0.0815968i
$545$	−4.93051			−0.211200
$546$	−2.03918			−0.0872688
$547$		−	10.2012i		−	0.436172i	−0.975930	−	0.218086i	$-0.930019\pi$
$547$		−	10.2012i		−	0.436172i	0.975930	−	0.218086i	$-0.0699813\pi$
$548$	2.26284			0.0966638
$549$		−	1.30379i		−	0.0556445i
$550$			25.6165i			1.09229i
$551$		−	1.07118i		−	0.0456338i
$552$	20.1382			0.857139
$553$	16.2705			0.691891
$554$			50.3349i			2.13853i
$555$			4.16808i			0.176925i
$556$		−	1.80210i		−	0.0764259i
$557$	25.4771			1.07950			0.539749	−	0.841826i	$-0.318519\pi$
$557$	25.4771			1.07950			0.539749	+	0.841826i	$0.318519\pi$
$558$			11.1115i			0.470387i
$559$	0.374993			0.0158605
$560$	−14.7677			−0.624051
$561$	−28.2300	−	7.10555i	−1.19187	−	0.299997i
$562$	42.5969			1.79684
$563$	−31.9238			−1.34543			−0.672714	−	0.739903i	$-0.734871\pi$
$563$	−31.9238			−1.34543			−0.672714	+	0.739903i	$0.734871\pi$
$564$			5.08132i			0.213962i
$565$	13.6916			0.576008
$566$			47.1792i			1.98309i
$567$		−	12.4996i		−	0.524935i
$568$			1.97713i			0.0829587i
$569$	−2.00012			−0.0838496			−0.0419248	−	0.999121i	$-0.513349\pi$
$569$	−2.00012			−0.0838496			−0.0419248	+	0.999121i	$0.513349\pi$
$570$	−3.40661			−0.142687
$571$			11.9955i			0.501996i	0.967988	+	0.250998i	$0.0807587\pi$
$571$			11.9955i			0.501996i	−0.967988	+	0.250998i	$0.919241\pi$
$572$			0.633498i			0.0264879i
$573$		−	25.8863i		−	1.08141i
$574$	−15.8668			−0.662265
$575$		−	18.8026i		−	0.784123i
$576$	6.28074			0.261698
$577$	8.26848			0.344221			0.172111	−	0.985078i	$-0.444941\pi$
$577$	8.26848			0.344221			0.172111	+	0.985078i	$0.444941\pi$
$578$	−22.8951	−	12.3051i	−0.952310	−	0.511824i
$579$	−12.9789			−0.539386
$580$	−0.378280			−0.0157072
$581$		−	13.2559i		−	0.549949i
$582$	−17.7114			−0.734160
$583$		−	37.1425i		−	1.53829i
$584$			28.6652i			1.18618i
$585$			0.485602i			0.0200772i
$586$	−14.2176			−0.587322
$587$	−9.36104			−0.386371			−0.193186	−	0.981162i	$-0.561882\pi$
$587$	−9.36104			−0.386371			−0.193186	+	0.981162i	$0.561882\pi$
$588$			0.309890i			0.0127796i
$589$		−	8.85913i		−	0.365034i
$590$			5.99417i			0.246776i
$591$	8.61949			0.354558
$592$		−	10.4844i		−	0.430905i
$593$	−31.1857			−1.28064			−0.640322	−	0.768106i	$-0.721199\pi$
$593$	−31.1857			−1.28064			−0.640322	+	0.768106i	$0.721199\pi$
$594$	−43.2652			−1.77519
$595$	−12.9450	−	3.25830i	−0.530695	−	0.133577i
$596$	7.32637			0.300100
$597$	−10.7964			−0.441866
$598$		−	3.21873i		−	0.131624i
$599$	−20.2213			−0.826222			−0.413111	−	0.910681i	$-0.635558\pi$
$599$	−20.2213			−0.826222			−0.413111	+	0.910681i	$0.635558\pi$
$600$			12.0146i			0.490493i
$601$		−	10.2780i		−	0.419248i	−0.977782	−	0.209624i	$-0.932776\pi$
$601$		−	10.2780i		−	0.419248i	0.977782	−	0.209624i	$-0.0672239\pi$
$602$			3.85282i			0.157029i
$603$	7.29110			0.296916
$604$	−4.76560			−0.193909
$605$			18.0169i			0.732490i
$606$		−	28.3894i		−	1.15324i
$607$			8.86711i			0.359905i	0.983675	+	0.179952i	$0.0575944\pi$
$607$			8.86711i			0.359905i	−0.983675	+	0.179952i	$0.942406\pi$
$608$	2.32346			0.0942289
$609$			3.10072i			0.125648i
$610$	2.54108			0.102885
$611$	−3.99755			−0.161723
$612$	−1.36100	−	0.342568i	−0.0550153	−	0.0138475i
$613$	5.36906			0.216854			0.108427	−	0.994104i	$-0.465419\pi$
$613$	5.36906			0.216854			0.108427	+	0.994104i	$0.465419\pi$
$614$	−26.8738			−1.08454
$615$		−	7.46792i		−	0.301136i
$616$	32.0372			1.29081
$617$		−	48.4228i		−	1.94943i	−0.223453	−	0.974715i	$-0.571733\pi$
$617$		−	48.4228i		−	1.94943i	0.223453	−	0.974715i	$-0.428267\pi$
$618$		−	8.89946i		−	0.357989i
$619$			21.0092i			0.844432i	0.906495	+	0.422216i	$0.138748\pi$
$619$			21.0092i			0.844432i	−0.906495	+	0.422216i	$0.861252\pi$
$620$	−3.12854			−0.125645
$621$	31.7569			1.27436
$622$			11.1512i			0.447121i
$623$			11.0649i			0.443304i
$624$			2.41420i			0.0966454i
$625$	2.96418			0.118567
$626$			35.2909i			1.41051i
$627$	8.67484			0.346440
$628$	−1.02147			−0.0407612
$629$	2.31323	−	9.19035i	0.0922346	−	0.366443i
$630$	−4.98926			−0.198777
$631$	−45.1534			−1.79753			−0.898765	−	0.438431i	$-0.855534\pi$
$631$	−45.1534			−1.79753			−0.898765	+	0.438431i	$0.855534\pi$
$632$		−	16.4104i		−	0.652771i
$633$	19.7903			0.786595
$634$		−	18.9102i		−	0.751018i
$635$			22.1833i			0.880317i
$636$			3.53922i			0.140339i
$637$	−0.243795			−0.00965951
$638$	6.66795			0.263987
$639$			0.784074i			0.0310175i
$640$			17.1003i			0.675948i
$641$			31.1611i			1.23079i	0.788219	+	0.615395i	$0.211003\pi$
$641$			31.1611i			1.23079i	−0.788219	+	0.615395i	$0.788997\pi$
$642$	−10.3695			−0.409253
$643$			30.3485i			1.19683i	0.801186	+	0.598415i	$0.204203\pi$
$643$			30.3485i			1.19683i	−0.801186	+	0.598415i	$0.795797\pi$
$644$	4.77748			0.188259
$645$	−1.81338			−0.0714019
$646$	7.51135	+	1.89063i	0.295530	+	0.0743856i
$647$	−17.8213			−0.700627			−0.350314	−	0.936632i	$-0.613925\pi$
$647$	−17.8213			−0.700627			−0.350314	+	0.936632i	$0.613925\pi$
$648$	−12.6071			−0.495255
$649$		−	15.2640i		−	0.599164i
$650$	1.92031			0.0753208
$651$			25.6443i			1.00508i
$652$		−	2.33456i		−	0.0914283i
$653$			30.8799i			1.20843i	0.796823	+	0.604213i	$0.206512\pi$
$653$			30.8799i			1.20843i	−0.796823	+	0.604213i	$0.793488\pi$
$654$	−8.28146			−0.323831
$655$	−8.43777			−0.329691
$656$			18.7848i			0.733422i
$657$			11.3678i			0.443500i
$658$		−	41.0723i		−	1.60116i
$659$	16.7016			0.650602			0.325301	−	0.945611i	$-0.394534\pi$
$659$	16.7016			0.650602			0.325301	+	0.945611i	$0.394534\pi$
$660$		−	3.06346i		−	0.119245i
$661$	−22.2204			−0.864274			−0.432137	−	0.901808i	$-0.642240\pi$
$661$	−22.2204			−0.864274			−0.432137	+	0.901808i	$0.642240\pi$
$662$	−16.1650			−0.628271
$663$	−0.532660	+	2.11623i	−0.0206868	+	0.0821876i
$664$	−13.3699			−0.518854
$665$	3.97791			0.154257
$666$		−	3.54213i		−	0.137255i
$667$	−4.89431			−0.189508
$668$		−	1.31065i		−	0.0507106i
$669$		−	2.88282i		−	0.111456i
$670$			14.2103i			0.548990i
$671$	−6.47078			−0.249802
$672$	−6.72568			−0.259449
$673$			19.2616i			0.742479i	0.928537	+	0.371240i	$0.121067\pi$
$673$			19.2616i			0.742479i	−0.928537	+	0.371240i	$0.878933\pi$
$674$		−	11.1769i		−	0.430520i
$675$			18.9463i			0.729245i
$676$	−4.34282			−0.167031
$677$		−	40.5824i		−	1.55971i	−0.625960	−	0.779855i	$-0.715293\pi$
$677$		−	40.5824i		−	1.55971i	0.625960	−	0.779855i	$-0.284707\pi$
$678$	22.9968			0.883187
$679$	20.6816			0.793687
$680$	−3.28632	+	13.0564i	−0.126025	+	0.500689i
$681$	5.45492			0.209033
$682$	55.1469			2.11168
$683$			3.79985i			0.145397i	0.997354	+	0.0726986i	$0.0231611\pi$
$683$			3.79985i			0.145397i	−0.997354	+	0.0726986i	$0.976839\pi$
$684$	0.418225			0.0159913
$685$		−	8.60871i		−	0.328922i
$686$		−	29.4745i		−	1.12534i
$687$			17.6500i			0.673391i
$688$	4.56138			0.173901
$689$	−2.78435			−0.106075
$690$			15.5651i			0.592552i
$691$		−	44.5379i		−	1.69430i	−0.531352	−	0.847151i	$-0.678316\pi$
$691$		−	44.5379i		−	1.69430i	0.531352	−	0.847151i	$-0.321684\pi$
$692$			4.78619i			0.181944i
$693$	12.7050			0.482624
$694$			18.1372i			0.688477i
$695$	−6.85586			−0.260057
$696$	3.12739			0.118543
$697$	−4.14460	+	16.4663i	−0.156988	+	0.623705i
$698$	28.0951			1.06341
$699$	7.63831			0.288907
$700$			2.85027i			0.107730i
$701$	33.4278			1.26255			0.631275	−	0.775559i	$-0.282532\pi$
$701$	33.4278			1.26255			0.631275	+	0.775559i	$0.282532\pi$
$702$			3.24333i			0.122412i
$703$			2.82412i			0.106514i
$704$		−	31.1716i		−	1.17482i
$705$	19.3313			0.728058
$706$	8.87144			0.333881
$707$			33.1503i			1.24675i
$708$			1.45447i			0.0546622i
$709$			19.7158i			0.740442i	0.928944	+	0.370221i	$0.120718\pi$
$709$			19.7158i			0.740442i	−0.928944	+	0.370221i	$0.879282\pi$
$710$	−1.52815			−0.0573505
$711$		−	6.50789i		−	0.244065i
$712$	11.1600			0.418239
$713$	−40.4781			−1.51592
$714$	−21.7429	−	5.47275i	−0.813709	−	0.204812i
$715$	2.41007			0.0901314
$716$	−6.69550			−0.250223
$717$		−	20.1209i		−	0.751428i
$718$	16.8728			0.629688
$719$		−	42.6170i		−	1.58935i	−0.607038	−	0.794673i	$-0.707642\pi$
$719$		−	42.6170i		−	1.58935i	0.607038	−	0.794673i	$-0.292358\pi$
$720$			5.90682i			0.220134i
$721$			10.3919i			0.387015i
$722$	26.7420			0.995236
$723$	−37.0130			−1.37653
$724$			5.03735i			0.187212i
$725$		−	2.91997i		−	0.108445i
$726$			30.2617i			1.12312i
$727$	−12.9988			−0.482099			−0.241049	−	0.970513i	$-0.577492\pi$
$727$	−12.9988			−0.482099			−0.241049	+	0.970513i	$0.577492\pi$
$728$		−	2.40163i		−	0.0890104i
$729$	−28.9520			−1.07230
$730$	−22.1557			−0.820019
$731$	3.99839	+	1.00641i	0.147886	+	0.0372232i
$732$	0.616584			0.0227896
$733$	49.3002			1.82094			0.910472	−	0.413571i	$-0.135719\pi$
$733$	49.3002			1.82094			0.910472	+	0.413571i	$0.135719\pi$
$734$		−	38.2862i		−	1.41317i
$735$	1.17894			0.0434858
$736$		−	10.6161i		−	0.391314i
$737$		−	36.1860i		−	1.33293i
$738$			6.34641i			0.233615i
$739$	1.57221			0.0578347			0.0289174	−	0.999582i	$-0.490794\pi$
$739$	1.57221			0.0578347			0.0289174	+	0.999582i	$0.490794\pi$
$740$	0.997318			0.0366621
$741$		−	0.650300i		−	0.0238894i
$742$		−	28.6075i		−	1.05021i
$743$			10.0841i			0.369949i	0.982743	+	0.184975i	$0.0592203\pi$
$743$			10.0841i			0.369949i	−0.982743	+	0.184975i	$0.940780\pi$
$744$	25.8648			0.948251
$745$		−	27.8723i		−	1.02116i
$746$	−19.5231			−0.714792
$747$	−5.30213			−0.193995
$748$	−1.70018	+	6.75472i	−0.0621647	+	0.246977i
$749$	12.1085			0.442436
$750$	−23.1492			−0.845288
$751$		−	25.7112i		−	0.938215i	−0.883141	−	0.469108i	$-0.844576\pi$
$751$		−	25.7112i		−	0.938215i	0.883141	−	0.469108i	$-0.155424\pi$
$752$	−48.6258			−1.77320
$753$		−	0.906854i		−	0.0330476i
$754$		−	0.499856i		−	0.0182037i
$755$			18.1302i			0.659824i
$756$	−4.81400			−0.175084
$757$	1.64432			0.0597636			0.0298818	−	0.999553i	$-0.490487\pi$
$757$	1.64432			0.0597636			0.0298818	+	0.999553i	$0.490487\pi$
$758$		−	28.8909i		−	1.04937i
$759$		−	39.6360i		−	1.43870i
$760$		−	4.01211i		−	0.145535i
$761$	−50.3613			−1.82560			−0.912798	−	0.408412i	$-0.866083\pi$
$761$	−50.3613			−1.82560			−0.912798	+	0.408412i	$0.866083\pi$
$762$			37.2598i			1.34978i
$763$	9.67028			0.350088
$764$	−6.19394			−0.224089
$765$	−1.30326	+	5.17778i	−0.0471194	+	0.187203i
$766$	−2.34879			−0.0848651
$767$	−1.14425			−0.0413165
$768$			11.1319i			0.401689i
$769$	−45.7188			−1.64866			−0.824331	−	0.566108i	$-0.808448\pi$
$769$	−45.7188			−1.64866			−0.824331	+	0.566108i	$0.808448\pi$
$770$			24.7619i			0.892357i
$771$			9.02159i			0.324905i
$772$			3.10553i			0.111771i
$773$	−6.91786			−0.248818			−0.124409	−	0.992231i	$-0.539704\pi$
$773$	−6.91786			−0.248818			−0.124409	+	0.992231i	$0.539704\pi$
$774$	1.54106			0.0553921
$775$		−	24.1494i		−	0.867474i
$776$		−	20.8595i		−	0.748811i
$777$		−	8.17491i		−	0.293273i
$778$	−46.9194			−1.68214
$779$		−	5.05995i		−	0.181292i
$780$	−0.229649			−0.00822275
$781$	3.89139			0.139245
$782$	8.63841	−	34.3199i	0.308909	−	1.22728i
$783$	4.93172			0.176245
$784$	−2.96550			−0.105911
$785$			3.88607i			0.138700i
$786$	−14.1724			−0.505511
$787$			45.4650i			1.62065i	0.585980	+	0.810326i	$0.300710\pi$
$787$			45.4650i			1.62065i	−0.585980	+	0.810326i	$0.699290\pi$
$788$		−	2.06243i		−	0.0734709i
$789$			9.82791i			0.349883i
$790$	12.6838			0.451269
$791$	−26.8534			−0.954798
$792$		−	12.8143i		−	0.455335i
$793$			0.485076i			0.0172255i
$794$		−	22.8779i		−	0.811905i
$795$	13.4645			0.477537
$796$			2.58330i			0.0915627i
$797$	27.9740			0.990890			0.495445	−	0.868639i	$-0.335005\pi$
$797$	27.9740			0.990890			0.495445	+	0.868639i	$0.335005\pi$
$798$	6.68143			0.236520
$799$	−42.6242	−	10.7286i	−1.50794	−	0.379551i
$800$	6.33362			0.223927
$801$	4.42574			0.156376
$802$		−	50.2918i		−	1.77586i
$803$	56.4189			1.99098
$804$			3.44807i			0.121604i
$805$		−	18.1754i		−	0.640597i
$806$		−	4.13403i		−	0.145615i
$807$	25.9695			0.914171
$808$	33.4354			1.17625
$809$			21.2461i			0.746973i	0.927636	+	0.373487i	$0.121838\pi$
$809$			21.2461i			0.746973i	−0.927636	+	0.373487i	$0.878162\pi$
$810$		−	9.74420i		−	0.342376i
$811$			47.5943i			1.67126i	0.549292	+	0.835631i	$0.314898\pi$
$811$			47.5943i			1.67126i	−0.549292	+	0.835631i	$0.685102\pi$
$812$	0.741925			0.0260365
$813$			31.3924i			1.10098i
$814$	−17.5798			−0.616170
$815$	−8.88154			−0.311107
$816$	−6.47923	+	25.7416i	−0.226818	+	0.901137i
$817$	−1.22867			−0.0429859
$818$	−35.2513			−1.23253
$819$		−	0.952418i		−	0.0332802i
$820$	−1.78689			−0.0624008
$821$		−	35.7790i		−	1.24870i	−0.781146	−	0.624348i	$-0.785365\pi$
$821$		−	35.7790i		−	1.24870i	0.781146	−	0.624348i	$-0.214635\pi$
$822$		−	14.4595i		−	0.504332i
$823$		−	21.0343i		−	0.733211i	−0.930377	−	0.366605i	$-0.880520\pi$
$823$		−	21.0343i		−	0.733211i	0.930377	−	0.366605i	$-0.119480\pi$
$824$	10.4813			0.365133
$825$	23.6471			0.823286
$826$		−	11.7564i		−	0.409059i
$827$			15.6794i			0.545228i	0.962124	+	0.272614i	$0.0878882\pi$
$827$			15.6794i			0.545228i	−0.962124	+	0.272614i	$0.912112\pi$
$828$		−	1.91091i		−	0.0664085i
$829$	−15.4192			−0.535532			−0.267766	−	0.963484i	$-0.586285\pi$
$829$	−15.4192			−0.535532			−0.267766	+	0.963484i	$0.586285\pi$
$830$		−	10.3338i		−	0.358691i
$831$	46.4652			1.61186
$832$	−2.33675			−0.0810121
$833$	−2.59948	−	0.654296i	−0.0900668	−	0.0226700i
$834$	−11.5153			−0.398743
$835$	−4.98622			−0.172555
$836$		−	2.07567i		−	0.0717886i
$837$	40.7875			1.40982
$838$		−	7.39263i		−	0.255374i
$839$		−	34.3683i		−	1.18653i	−0.805009	−	0.593263i	$-0.797839\pi$
$839$		−	34.3683i		−	1.18653i	0.805009	−	0.593263i	$-0.202161\pi$
$840$			11.6138i			0.400713i
$841$	28.2399			0.973791
$842$	8.19002			0.282247
$843$		−	39.3221i		−	1.35433i
$844$		−	4.73533i		−	0.162997i
$845$			16.5217i			0.568365i
$846$	−16.4282			−0.564812
$847$		−	35.3367i		−	1.21418i
$848$	−33.8686			−1.16305
$849$	43.5521			1.49470
$850$	20.4755	+	5.15373i	0.702303	+	0.176771i
$851$	12.9036			0.442331
$852$	−0.370801			−0.0127034
$853$			31.7789i			1.08809i	0.839056	+	0.544045i	$0.183108\pi$
$853$			31.7789i			1.08809i	−0.839056	+	0.544045i	$0.816892\pi$
$854$	−4.98385			−0.170544
$855$		−	1.59109i		−	0.0544141i
$856$		−	12.2126i		−	0.417420i
$857$			39.0745i			1.33476i	0.744718	+	0.667379i	$0.232584\pi$
$857$			39.0745i			1.33476i	−0.744718	+	0.667379i	$0.767416\pi$
$858$	4.04803			0.138197
$859$	25.6728			0.875945			0.437973	−	0.898988i	$-0.355697\pi$
$859$	25.6728			0.875945			0.437973	+	0.898988i	$0.355697\pi$
$860$			0.433897i			0.0147958i
$861$			14.6469i			0.499166i
$862$			38.6919i			1.31785i
$863$	−36.2707			−1.23467			−0.617334	−	0.786701i	$-0.711787\pi$
$863$	−36.2707			−1.23467			−0.617334	+	0.786701i	$0.711787\pi$
$864$			10.6972i			0.363928i
$865$	18.2085			0.619107
$866$	−1.14087			−0.0387684
$867$	−11.3591	+	21.1349i	−0.385774	+	0.717780i
$868$	6.13604			0.208271
$869$	−32.2990			−1.09567
$870$			2.41720i			0.0819506i
$871$	−2.71265			−0.0919146
$872$		−	9.75344i		−	0.330293i
$873$		−	8.27226i		−	0.279974i
$874$			10.5462i			0.356732i
$875$	27.0313			0.913826
$876$	−5.37601			−0.181639
$877$			12.2913i			0.415046i	0.978230	+	0.207523i	$0.0665402\pi$
$877$			12.2913i			0.415046i	−0.978230	+	0.207523i	$0.933460\pi$
$878$		−	42.4494i		−	1.43260i
$879$			13.1245i			0.442679i
$880$	29.3158			0.988236
$881$			39.1962i			1.32055i	0.751022	+	0.660277i	$0.229561\pi$
$881$			39.1962i			1.32055i	−0.751022	+	0.660277i	$0.770439\pi$
$882$	−1.00189			−0.0337354
$883$	−7.37264			−0.248109			−0.124055	−	0.992275i	$-0.539590\pi$
$883$	−7.37264			−0.248109			−0.124055	+	0.992275i	$0.539590\pi$
$884$	0.506361	+	0.127452i	0.0170308	+	0.00428668i
$885$	5.53334			0.186001
$886$	19.4491			0.653406
$887$			8.16060i			0.274006i	0.990571	+	0.137003i	$0.0437470\pi$
$887$			8.16060i			0.274006i	−0.990571	+	0.137003i	$0.956253\pi$
$888$	−8.24521			−0.276691
$889$		−	43.5084i		−	1.45922i
$890$			8.62571i			0.289134i
$891$			24.8134i			0.831279i
$892$	−0.689786			−0.0230958
$893$	13.0981			0.438310
$894$		−	46.8153i		−	1.56574i
$895$			25.4722i			0.851443i
$896$		−	33.5390i		−	1.12046i
$897$	−2.97127			−0.0992079
$898$			21.8471i			0.729048i
$899$	−6.28609			−0.209653
$900$	1.14006			0.0380019
$901$	−29.6884	−	7.47264i	−0.989064	−	0.248950i
$902$	31.4975			1.04875
$903$	3.55661			0.118357
$904$			27.0844i			0.900812i
$905$	19.1640			0.637033
$906$			30.4520i			1.01170i
$907$			47.5787i			1.57982i	0.613221	+	0.789912i	$0.289874\pi$
$907$			47.5787i			1.57982i	−0.613221	+	0.789912i	$0.710126\pi$
$908$		−	1.30523i		−	0.0433155i
$909$	13.2595			0.439791
$910$	1.85625			0.0615341
$911$		−	35.1884i		−	1.16584i	−0.812528	−	0.582922i	$-0.801910\pi$
$911$		−	35.1884i		−	1.16584i	0.812528	−	0.582922i	$-0.198090\pi$
$912$		−	7.91019i		−	0.261933i
$913$			26.3147i			0.870890i
$914$	60.5366			2.00237
$915$		−	2.34572i		−	0.0775471i
$916$	4.22321			0.139539
$917$	16.5491			0.546499
$918$	−8.70445	+	34.5823i	−0.287290	+	1.14139i
$919$	49.9985			1.64930			0.824649	−	0.565644i	$-0.191372\pi$
$919$	49.9985			1.64930			0.824649	+	0.565644i	$0.191372\pi$
$920$	−18.3317			−0.604377
$921$			24.8078i			0.817445i
$922$	46.8182			1.54188
$923$		−	0.291714i		−	0.00960190i
$924$			6.00840i			0.197662i
$925$			7.69838i			0.253121i
$926$	−30.2536			−0.994194
$927$	4.15657			0.136520
$928$		−	1.64864i		−	0.0541192i
$929$			37.2556i			1.22232i	0.791509	+	0.611158i	$0.209296\pi$
$929$			37.2556i			1.22232i	−0.791509	+	0.611158i	$0.790704\pi$
$930$			19.9913i			0.655539i
$931$	0.798800			0.0261796
$932$		−	1.82766i		−	0.0598669i
$933$	10.2939			0.337006
$934$	−51.8770			−1.69747
$935$	25.6975	+	6.46813i	0.840399	+	0.211531i
$936$	−0.960608			−0.0313985
$937$	9.65076			0.315277			0.157638	−	0.987497i	$-0.449612\pi$
$937$	9.65076			0.315277			0.157638	+	0.987497i	$0.449612\pi$
$938$		−	27.8708i		−	0.910012i
$939$	32.5777			1.06313
$940$		−	4.62549i		−	0.150867i
$941$			29.2622i			0.953919i	0.878925	+	0.476960i	$0.158261\pi$
$941$			29.2622i			0.953919i	−0.878925	+	0.476960i	$0.841739\pi$
$942$			6.52717i			0.212667i
$943$	−23.1193			−0.752869
$944$	−13.9186			−0.453010
$945$			18.3143i			0.595764i
$946$		−	7.64832i		−	0.248668i
$947$			48.1728i			1.56541i	0.622395	+	0.782703i	$0.286160\pi$
$947$			48.1728i			1.56541i	−0.622395	+	0.782703i	$0.713840\pi$
$948$	3.07768			0.0999585
$949$		−	4.22938i		−	0.137292i
$950$	−6.29195			−0.204138
$951$	−17.4564			−0.566061
$952$	6.44550	−	25.6076i	0.208900	−	0.829947i
$953$	−37.3514			−1.20993			−0.604966	−	0.796251i	$-0.706813\pi$
$953$	−37.3514			−1.20993			−0.604966	+	0.796251i	$0.706813\pi$
$954$	−11.4425			−0.370463
$955$			23.5641i			0.762516i
$956$	−4.81442			−0.155710
$957$		−	6.15533i		−	0.198973i
$958$			6.65319i			0.214955i
$959$			16.8844i			0.545225i
$960$	11.3000			0.364706
$961$	−20.9887			−0.677054
$962$			1.31785i			0.0424891i
$963$		−	4.84318i		−	0.156069i
$964$			8.85629i			0.285242i
$965$	11.8146			0.380326
$966$		−	30.5280i		−	0.982221i
$967$	54.6794			1.75837			0.879186	−	0.476479i	$-0.158087\pi$
$967$	54.6794			1.75837			0.879186	+	0.476479i	$0.158087\pi$
$968$	−35.6406			−1.14553
$969$	1.74527	−	6.93388i	0.0560663	−	0.222748i
$970$	16.1225			0.517663
$971$	−12.4575			−0.399779			−0.199889	−	0.979818i	$-0.564058\pi$
$971$	−12.4575			−0.399779			−0.199889	+	0.979818i	$0.564058\pi$
$972$			3.36680i			0.107990i
$973$	13.4465			0.431074
$974$			22.5349i			0.722064i
$975$		−	1.77268i		−	0.0567712i
$976$			5.90042i			0.188868i
$977$	−17.0254			−0.544691			−0.272345	−	0.962200i	$-0.587799\pi$
$977$	−17.0254			−0.544691			−0.272345	+	0.962200i	$0.587799\pi$
$978$	−14.9177			−0.477017
$979$		−	21.9651i		−	0.702009i
$980$		−	0.282091i		−	0.00901106i
$981$		−	3.86793i		−	0.123494i
$982$	61.0661			1.94870
$983$		−	14.8743i		−	0.474416i	−0.971459	−	0.237208i	$-0.923768\pi$
$983$		−	14.8743i		−	0.474416i	0.971459	−	0.237208i	$-0.0762322\pi$
$984$	14.7729			0.470942
$985$	−7.84626			−0.250003
$986$	1.34151	−	5.32976i	0.0427225	−	0.169734i
$987$	−37.9147			−1.20684
$988$	−0.155601			−0.00495031
$989$			5.61391i			0.178512i
$990$	9.90431			0.314780
$991$		−	19.4290i		−	0.617182i	−0.951195	−	0.308591i	$-0.900142\pi$
$991$		−	19.4290i		−	0.617182i	0.951195	−	0.308591i	$-0.0998575\pi$
$992$		−	13.6350i		−	0.432910i
$993$			14.9223i			0.473543i
$994$	2.99718			0.0950648
$995$	9.82786			0.311564
$996$		−	2.50746i		−	0.0794520i
$997$			47.2677i			1.49698i	0.663144	+	0.748492i	$0.269222\pi$
$997$			47.2677i			1.49698i	−0.663144	+	0.748492i	$0.730778\pi$
$998$		−	49.1469i		−	1.55572i
$999$	−13.0023			−0.411373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.10	yes	34
17.16	even	2	inner	731.2.d.d.560.9	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.9	✓	34	17.16	even	2	inner
731.2.d.d.560.10	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)

\(f(q)\)	\(=\)	\(q-1.52896 q^{2} +1.41141i q^{3} +0.337716 q^{4} -1.28480i q^{5} -2.15799i q^{6} +2.51989i q^{7} +2.54156 q^{8} +1.00791 q^{9} +O(q^{10})\)	\(q-1.52896 q^{2} +1.41141i q^{3} +0.337716 q^{4} -1.28480i q^{5} -2.15799i q^{6} +2.51989i q^{7} +2.54156 q^{8} +1.00791 q^{9} +1.96441i q^{10} -5.00231i q^{11} +0.476657i q^{12} -0.374993 q^{13} -3.85282i q^{14} +1.81338 q^{15} -4.56138 q^{16} +(-3.99839 - 1.00641i) q^{17} -1.54106 q^{18} +1.22867 q^{19} -0.433897i q^{20} -3.55661 q^{21} +7.64832i q^{22} -5.61391i q^{23} +3.58720i q^{24} +3.34929 q^{25} +0.573349 q^{26} +5.65682i q^{27} +0.851009i q^{28} -0.871819i q^{29} -2.77259 q^{30} -7.21032i q^{31} +1.89103 q^{32} +7.06033 q^{33} +(6.11338 + 1.53875i) q^{34} +3.23756 q^{35} +0.340388 q^{36} +2.29851i q^{37} -1.87859 q^{38} -0.529270i q^{39} -3.26540i q^{40} -4.11822i q^{41} +5.43792 q^{42} -1.00000 q^{43} -1.68936i q^{44} -1.29496i q^{45} +8.58343i q^{46} +10.6603 q^{47} -6.43799i q^{48} +0.650132 q^{49} -5.12093 q^{50} +(1.42045 - 5.64339i) q^{51} -0.126641 q^{52} +7.42508 q^{53} -8.64905i q^{54} -6.42697 q^{55} +6.40447i q^{56} +1.73417i q^{57} +1.33298i q^{58} +3.05139 q^{59} +0.612409 q^{60} -1.29356i q^{61} +11.0243i q^{62} +2.53983i q^{63} +6.23145 q^{64} +0.481791i q^{65} -10.7950 q^{66} +7.23387 q^{67} +(-1.35032 - 0.339879i) q^{68} +7.92355 q^{69} -4.95010 q^{70} +0.777920i q^{71} +2.56167 q^{72} +11.2786i q^{73} -3.51433i q^{74} +4.72723i q^{75} +0.414943 q^{76} +12.6053 q^{77} +0.809232i q^{78} -6.45681i q^{79} +5.86046i q^{80} -4.96038 q^{81} +6.29659i q^{82} -5.26052 q^{83} -1.20113 q^{84} +(-1.29303 + 5.13714i) q^{85} +1.52896 q^{86} +1.23050 q^{87} -12.7137i q^{88} +4.39100 q^{89} +1.97995i q^{90} -0.944942i q^{91} -1.89591i q^{92} +10.1767 q^{93} -16.2992 q^{94} -1.57860i q^{95} +2.66903i q^{96} -8.20733i q^{97} -0.994026 q^{98} -5.04188i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 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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Database

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