LMFDB - Embedded newform 731.2.d.d.560.19

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			560.19
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.366222 q^{2} -1.80029i q^{3} -1.86588 q^{4} +2.01471i q^{5} -0.659307i q^{6} +2.54407i q^{7} -1.41577 q^{8} -0.241043 q^{9} +O(q^{10})$	\(q+0.366222 q^{2} -1.80029i q^{3} -1.86588 q^{4} +2.01471i q^{5} -0.659307i q^{6} +2.54407i q^{7} -1.41577 q^{8} -0.241043 q^{9} +0.737831i q^{10} -5.65625i q^{11} +3.35913i q^{12} -0.166551 q^{13} +0.931697i q^{14} +3.62706 q^{15} +3.21327 q^{16} +(-1.56250 - 3.81557i) q^{17} -0.0882754 q^{18} +8.12788 q^{19} -3.75920i q^{20} +4.58007 q^{21} -2.07145i q^{22} -8.66228i q^{23} +2.54880i q^{24} +0.940958 q^{25} -0.0609948 q^{26} -4.96692i q^{27} -4.74694i q^{28} +3.73355i q^{29} +1.32831 q^{30} +10.1265i q^{31} +4.00832 q^{32} -10.1829 q^{33} +(-0.572221 - 1.39735i) q^{34} -5.12556 q^{35} +0.449758 q^{36} -7.40785i q^{37} +2.97661 q^{38} +0.299841i q^{39} -2.85237i q^{40} -5.10638i q^{41} +1.67732 q^{42} -1.00000 q^{43} +10.5539i q^{44} -0.485631i q^{45} -3.17232i q^{46} +7.92510 q^{47} -5.78483i q^{48} +0.527690 q^{49} +0.344600 q^{50} +(-6.86914 + 2.81294i) q^{51} +0.310765 q^{52} -12.8298 q^{53} -1.81900i q^{54} +11.3957 q^{55} -3.60183i q^{56} -14.6325i q^{57} +1.36731i q^{58} +6.96375 q^{59} -6.76765 q^{60} +0.320356i q^{61} +3.70854i q^{62} -0.613232i q^{63} -4.95861 q^{64} -0.335552i q^{65} -3.72920 q^{66} -2.61335 q^{67} +(2.91543 + 7.11941i) q^{68} -15.5946 q^{69} -1.87710 q^{70} -1.24894i q^{71} +0.341262 q^{72} -3.36816i q^{73} -2.71292i q^{74} -1.69400i q^{75} -15.1657 q^{76} +14.3899 q^{77} +0.109808i q^{78} +0.324716i q^{79} +6.47381i q^{80} -9.66503 q^{81} -1.87007i q^{82} -8.16612 q^{83} -8.54586 q^{84} +(7.68726 - 3.14797i) q^{85} -0.366222 q^{86} +6.72148 q^{87} +8.00796i q^{88} +9.69705 q^{89} -0.177849i q^{90} -0.423719i q^{91} +16.1628i q^{92} +18.2306 q^{93} +2.90235 q^{94} +16.3753i q^{95} -7.21613i q^{96} +0.511176i q^{97} +0.193252 q^{98} +1.36340i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.366222			0.258958			0.129479	−	0.991582i	$-0.458669\pi$
$2$	0.366222			0.258958			0.129479	+	0.991582i	$0.458669\pi$
$3$		−	1.80029i		−	1.03940i	−0.854350	−	0.519699i	$-0.826044\pi$
$3$		−	1.80029i		−	1.03940i	0.854350	−	0.519699i	$-0.173956\pi$
$4$	−1.86588			−0.932941
$5$			2.01471i			0.901004i	0.892775	+	0.450502i	$0.148755\pi$
$5$			2.01471i			0.901004i	−0.892775	+	0.450502i	$0.851245\pi$
$6$		−	0.659307i		−	0.269161i
$7$			2.54407i			0.961569i	0.876839	+	0.480785i	$0.159648\pi$
$7$			2.54407i			0.961569i	−0.876839	+	0.480785i	$0.840352\pi$
$8$	−1.41577			−0.500551
$9$	−0.241043			−0.0803477
$10$			0.737831i			0.233323i
$11$		−	5.65625i		−	1.70542i	−0.522382	−	0.852712i	$-0.674957\pi$
$11$		−	5.65625i		−	1.70542i	0.522382	−	0.852712i	$-0.325043\pi$
$12$			3.35913i			0.969696i
$13$	−0.166551			−0.0461930			−0.0230965	−	0.999733i	$-0.507353\pi$
$13$	−0.166551			−0.0461930			−0.0230965	+	0.999733i	$0.507353\pi$
$14$			0.931697i			0.249006i
$15$	3.62706			0.936502
$16$	3.21327			0.803319
$17$	−1.56250	−	3.81557i	−0.378961	−	0.925413i
$17$	−1.56250	−	3.81557i	−0.378961	−	0.925413i
$18$	−0.0882754			−0.0208067
$19$	8.12788			1.86466			0.932332	−	0.361604i	$-0.117771\pi$
$19$	8.12788			1.86466			0.932332	+	0.361604i	$0.117771\pi$
$20$		−	3.75920i		−	0.840583i
$21$	4.58007			0.999453
$22$		−	2.07145i		−	0.441634i
$23$		−	8.66228i		−	1.80621i	−0.429420	−	0.903105i	$-0.641282\pi$
$23$		−	8.66228i		−	1.80621i	0.429420	−	0.903105i	$-0.358718\pi$
$24$			2.54880i			0.520272i
$25$	0.940958			0.188192
$26$	−0.0609948			−0.0119621
$27$		−	4.96692i		−	0.955885i
$28$		−	4.74694i		−	0.897087i
$29$			3.73355i			0.693304i	0.937994	+	0.346652i	$0.112681\pi$
$29$			3.73355i			0.693304i	−0.937994	+	0.346652i	$0.887319\pi$
$30$	1.32831			0.242515
$31$			10.1265i			1.81877i	0.415957	+	0.909384i	$0.363447\pi$
$31$			10.1265i			1.81877i	−0.415957	+	0.909384i	$0.636553\pi$
$32$	4.00832			0.708577
$33$	−10.1829			−1.77261
$34$	−0.572221	−	1.39735i	−0.0981351	−	0.239643i
$35$	−5.12556			−0.866378
$36$	0.449758			0.0749596
$37$		−	7.40785i		−	1.21784i	−0.793231	−	0.608921i	$-0.791603\pi$
$37$		−	7.40785i		−	1.21784i	0.793231	−	0.608921i	$-0.208397\pi$
$38$	2.97661			0.482870
$39$			0.299841i			0.0480129i
$40$		−	2.85237i		−	0.450999i
$41$		−	5.10638i		−	0.797483i	−0.917063	−	0.398741i	$-0.869447\pi$
$41$		−	5.10638i		−	0.797483i	0.917063	−	0.398741i	$-0.130553\pi$
$42$	1.67732			0.258817
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$			10.5539i			1.59106i
$45$		−	0.485631i		−	0.0723936i
$46$		−	3.17232i		−	0.467733i
$47$	7.92510			1.15599			0.577997	−	0.816039i	$-0.303834\pi$
$47$	7.92510			1.15599			0.577997	+	0.816039i	$0.303834\pi$
$48$		−	5.78483i		−	0.834968i
$49$	0.527690			0.0753843
$50$	0.344600			0.0487338
$51$	−6.86914	+	2.81294i	−0.961872	+	0.393891i
$52$	0.310765			0.0430953
$53$	−12.8298			−1.76231			−0.881156	−	0.472825i	$-0.843234\pi$
$53$	−12.8298			−1.76231			−0.881156	+	0.472825i	$0.843234\pi$
$54$		−	1.81900i		−	0.247534i
$55$	11.3957			1.53659
$56$		−	3.60183i		−	0.481315i
$57$		−	14.6325i		−	1.93813i
$58$			1.36731i			0.179537i
$59$	6.96375			0.906603			0.453301	−	0.891357i	$-0.350246\pi$
$59$	6.96375			0.906603			0.453301	+	0.891357i	$0.350246\pi$
$60$	−6.76765			−0.873700
$61$			0.320356i			0.0410173i	0.999790	+	0.0205087i	$0.00652857\pi$
$61$			0.320356i			0.0410173i	−0.999790	+	0.0205087i	$0.993471\pi$
$62$			3.70854i			0.470985i
$63$		−	0.613232i		−	0.0772599i
$64$	−4.95861			−0.619827
$65$		−	0.335552i		−	0.0416201i
$66$	−3.72920			−0.459033
$67$	−2.61335			−0.319271			−0.159636	−	0.987176i	$-0.551032\pi$
$67$	−2.61335			−0.319271			−0.159636	+	0.987176i	$0.551032\pi$
$68$	2.91543	+	7.11941i	0.353548	+	0.863355i
$69$	−15.5946			−1.87737
$70$	−1.87710			−0.224356
$71$		−	1.24894i		−	0.148222i	−0.997250	−	0.0741111i	$-0.976388\pi$
$71$		−	1.24894i		−	0.148222i	0.997250	−	0.0741111i	$-0.0236120\pi$
$72$	0.341262			0.0402181
$73$		−	3.36816i		−	0.394214i	−0.980382	−	0.197107i	$-0.936845\pi$
$73$		−	3.36816i		−	0.394214i	0.980382	−	0.197107i	$-0.0631546\pi$
$74$		−	2.71292i		−	0.315371i
$75$		−	1.69400i		−	0.195606i
$76$	−15.1657			−1.73962
$77$	14.3899			1.63988
$78$			0.109808i			0.0124333i
$79$			0.324716i			0.0365334i	0.999833	+	0.0182667i	$0.00581480\pi$
$79$			0.324716i			0.0365334i	−0.999833	+	0.0182667i	$0.994185\pi$
$80$			6.47381i			0.723793i
$81$	−9.66503			−1.07389
$82$		−	1.87007i		−	0.206515i
$83$	−8.16612			−0.896348			−0.448174	−	0.893946i	$-0.647926\pi$
$83$	−8.16612			−0.896348			−0.448174	+	0.893946i	$0.647926\pi$
$84$	−8.54586			−0.932430
$85$	7.68726	−	3.14797i	0.833801	−	0.341445i
$86$	−0.366222			−0.0394908
$87$	6.72148			0.720618
$88$			8.00796i			0.853651i
$89$	9.69705			1.02789			0.513943	−	0.857825i	$-0.328184\pi$
$89$	9.69705			1.02789			0.513943	+	0.857825i	$0.328184\pi$
$90$		−	0.177849i		−	0.0187469i
$91$		−	0.423719i		−	0.0444178i
$92$			16.1628i			1.68509i
$93$	18.2306			1.89042
$94$	2.90235			0.299355
$95$			16.3753i			1.68007i
$96$		−	7.21613i		−	0.736494i
$97$			0.511176i			0.0519020i	0.999663	+	0.0259510i	$0.00826139\pi$
$97$			0.511176i			0.0519020i	−0.999663	+	0.0259510i	$0.991739\pi$
$98$	0.193252			0.0195214
$99$			1.36340i			0.137027i
$100$	−1.75571			−0.175571
$101$	8.47209			0.843004			0.421502	−	0.906827i	$-0.361503\pi$
$101$	8.47209			0.843004			0.421502	+	0.906827i	$0.361503\pi$
$102$	−2.51563	+	1.03016i	−0.249085	+	0.102001i
$103$	2.04848			0.201842			0.100921	−	0.994894i	$-0.467821\pi$
$103$	2.04848			0.201842			0.100921	+	0.994894i	$0.467821\pi$
$104$	0.235799			0.0231220
$105$			9.22750i			0.900511i
$106$	−4.69857			−0.456366
$107$			5.70671i			0.551688i	0.961202	+	0.275844i	$0.0889573\pi$
$107$			5.70671i			0.551688i	−0.961202	+	0.275844i	$0.911043\pi$
$108$			9.26769i			0.891783i
$109$			4.16541i			0.398974i	0.979901	+	0.199487i	$0.0639275\pi$
$109$			4.16541i			0.398974i	−0.979901	+	0.199487i	$0.936072\pi$
$110$	4.17335			0.397914
$111$	−13.3363			−1.26582
$112$			8.17481i			0.772447i
$113$			1.62816i			0.153165i	0.997063	+	0.0765823i	$0.0244008\pi$
$113$			1.62816i			0.153165i	−0.997063	+	0.0765823i	$0.975599\pi$
$114$		−	5.35876i		−	0.501894i
$115$	17.4519			1.62740
$116$		−	6.96637i		−	0.646811i
$117$	0.0401461			0.00371150
$118$	2.55028			0.234772
$119$	9.70710	−	3.97510i	0.889849	−	0.364397i
$120$	−5.13509			−0.468767
$121$	−20.9931			−1.90847
$122$			0.117321i			0.0106218i
$123$	−9.19297			−0.828902
$124$		−	18.8948i		−	1.69680i
$125$			11.9693i			1.07057i
$126$		−	0.224579i		−	0.0200071i
$127$	8.94806			0.794012			0.397006	−	0.917816i	$-0.370049\pi$
$127$	8.94806			0.794012			0.397006	+	0.917816i	$0.370049\pi$
$128$	−9.83259			−0.869087
$129$			1.80029i			0.158507i
$130$		−	0.122887i		−	0.0107779i
$131$			6.31234i			0.551511i	0.961228	+	0.275756i	$0.0889281\pi$
$131$			6.31234i			0.551511i	−0.961228	+	0.275756i	$0.911072\pi$
$132$	19.0001			1.65374
$133$			20.6779i			1.79300i
$134$	−0.957066			−0.0826779
$135$	10.0069			0.861256
$136$	2.21214	+	5.40199i	0.189689	+	0.463216i
$137$	19.4123			1.65850			0.829252	−	0.558875i	$-0.188767\pi$
$137$	19.4123			1.65850			0.829252	+	0.558875i	$0.188767\pi$
$138$	−5.71109			−0.486161
$139$			0.283489i			0.0240452i	0.999928	+	0.0120226i	$0.00382700\pi$
$139$			0.283489i			0.0240452i	−0.999928	+	0.0120226i	$0.996173\pi$
$140$	9.56369			0.808279
$141$		−	14.2675i		−	1.20154i
$142$		−	0.457391i		−	0.0383834i
$143$			0.942056i			0.0787786i
$144$	−0.774538			−0.0645448
$145$	−7.52202			−0.624669
$146$		−	1.23350i		−	0.102085i
$147$		−	0.949995i		−	0.0783543i
$148$			13.8222i			1.13617i
$149$	−22.8925			−1.87543			−0.937714	−	0.347408i	$-0.887062\pi$
$149$	−22.8925			−1.87543			−0.937714	+	0.347408i	$0.887062\pi$
$150$		−	0.620379i		−	0.0506538i
$151$	3.12202			0.254067			0.127033	−	0.991898i	$-0.459454\pi$
$151$	3.12202			0.254067			0.127033	+	0.991898i	$0.459454\pi$
$152$	−11.5072			−0.933359
$153$	0.376629	+	0.919718i	0.0304486	+	0.0743548i
$154$	5.26991			0.424661
$155$	−20.4019			−1.63872
$156$		−	0.559467i		−	0.0447932i
$157$	1.06533			0.0850225			0.0425112	−	0.999096i	$-0.486464\pi$
$157$	1.06533			0.0850225			0.0425112	+	0.999096i	$0.486464\pi$
$158$			0.118918i			0.00946064i
$159$			23.0974i			1.83174i
$160$			8.07558i			0.638431i
$161$	22.0375			1.73680
$162$	−3.53955			−0.278093
$163$			5.41259i			0.423947i	0.977275	+	0.211973i	$0.0679891\pi$
$163$			5.41259i			0.423947i	−0.977275	+	0.211973i	$0.932011\pi$
$164$			9.52790i			0.744004i
$165$		−	20.5155i		−	1.59713i
$166$	−2.99062			−0.232117
$167$		−	14.2600i		−	1.10347i	−0.834019	−	0.551736i	$-0.813965\pi$
$167$		−	14.2600i		−	1.10347i	0.834019	−	0.551736i	$-0.186035\pi$
$168$	−6.48434			−0.500277
$169$	−12.9723			−0.997866
$170$	2.81525	−	1.15286i	0.215920	−	0.0884201i
$171$	−1.95917			−0.149821
$172$	1.86588			0.142272
$173$		−	16.7180i		−	1.27104i	−0.772083	−	0.635522i	$-0.780785\pi$
$173$		−	16.7180i		−	1.27104i	0.772083	−	0.635522i	$-0.219215\pi$
$174$	2.46156			0.186610
$175$			2.39387i			0.180959i
$176$		−	18.1751i		−	1.37000i
$177$		−	12.5368i		−	0.942321i
$178$	3.55128			0.266180
$179$	−8.57287			−0.640766			−0.320383	−	0.947288i	$-0.603812\pi$
$179$	−8.57287			−0.640766			−0.320383	+	0.947288i	$0.603812\pi$
$180$			0.906130i			0.0675390i
$181$		−	19.8607i		−	1.47624i	−0.674671	−	0.738119i	$-0.735714\pi$
$181$		−	19.8607i		−	1.47624i	0.674671	−	0.738119i	$-0.264286\pi$
$182$		−	0.155175i		−	0.0115024i
$183$	0.576733			0.0426333
$184$			12.2638i			0.904100i
$185$	14.9246			1.09728
$186$	6.67645			0.489541
$187$	−21.5818	+	8.83786i	−1.57822	+	0.646289i
$188$	−14.7873			−1.07847
$189$	12.6362			0.919149
$190$			5.99700i			0.435068i
$191$	6.63966			0.480429			0.240215	−	0.970720i	$-0.422782\pi$
$191$	6.63966			0.480429			0.240215	+	0.970720i	$0.422782\pi$
$192$			8.92694i			0.644246i
$193$		−	1.32214i		−	0.0951694i	−0.998867	−	0.0475847i	$-0.984848\pi$
$193$		−	1.32214i		−	0.0951694i	0.998867	−	0.0475847i	$-0.0151524\pi$
$194$			0.187204i			0.0134405i
$195$	−0.604091			−0.0432598
$196$	−0.984607			−0.0703291
$197$			8.26886i			0.589132i	0.955631	+	0.294566i	$0.0951751\pi$
$197$			8.26886i			0.589132i	−0.955631	+	0.294566i	$0.904825\pi$
$198$			0.499308i			0.0354843i
$199$			23.7804i			1.68575i	0.538113	+	0.842873i	$0.319137\pi$
$199$			23.7804i			1.68575i	−0.538113	+	0.842873i	$0.680863\pi$
$200$	−1.33218			−0.0941995
$201$			4.70478i			0.331850i
$202$	3.10267			0.218303
$203$	−9.49844			−0.666660
$204$	12.8170	−	5.24862i	0.897369	−	0.367477i
$205$	10.2879			0.718535
$206$	0.750198			0.0522688
$207$			2.08798i			0.145125i
$208$	−0.535175			−0.0371077
$209$		−	45.9733i		−	3.18004i
$210$			3.37932i			0.233195i
$211$		−	2.07545i		−	0.142880i	−0.997445	−	0.0714398i	$-0.977241\pi$
$211$		−	2.07545i		−	0.142880i	0.997445	−	0.0714398i	$-0.0227594\pi$
$212$	23.9389			1.64413
$213$	−2.24846			−0.154062
$214$			2.08992i			0.142864i
$215$		−	2.01471i		−	0.137402i
$216$			7.03203i			0.478469i
$217$	−25.7625			−1.74887
$218$			1.52547i			0.103318i
$219$	−6.06367			−0.409745
$220$	−21.2630			−1.43355
$221$	0.260236	+	0.635489i	0.0175053	+	0.0427476i
$222$	−4.88404			−0.327795
$223$	23.9342			1.60275			0.801376	−	0.598162i	$-0.204102\pi$
$223$	23.9342			1.60275			0.801376	+	0.598162i	$0.204102\pi$
$224$			10.1975i			0.681346i
$225$	−0.226811			−0.0151208
$226$			0.596270i			0.0396633i
$227$			9.21030i			0.611309i	0.952142	+	0.305655i	$0.0988753\pi$
$227$			9.21030i			0.611309i	−0.952142	+	0.305655i	$0.901125\pi$
$228$			27.3026i			1.80816i
$229$	−13.5778			−0.897246			−0.448623	−	0.893721i	$-0.648085\pi$
$229$	−13.5778			−0.897246			−0.448623	+	0.893721i	$0.648085\pi$
$230$	6.39129			0.421429
$231$		−	25.9060i		−	1.70449i
$232$		−	5.28586i		−	0.347034i
$233$		−	3.57576i		−	0.234256i	−0.993117	−	0.117128i	$-0.962631\pi$
$233$		−	3.57576i		−	0.234256i	0.993117	−	0.117128i	$-0.0373688\pi$
$234$	0.0147024			0.000961125
$235$			15.9668i			1.04156i
$236$	−12.9935			−0.845806
$237$	0.584583			0.0379728
$238$	3.55496	−	1.45577i	0.230434	−	0.0943637i
$239$	−10.9641			−0.709209			−0.354604	−	0.935016i	$-0.615384\pi$
$239$	−10.9641			−0.709209			−0.354604	+	0.935016i	$0.615384\pi$
$240$	11.6547			0.752309
$241$		−	13.5154i		−	0.870603i	−0.900285	−	0.435301i	$-0.856642\pi$
$241$		−	13.5154i		−	0.870603i	0.900285	−	0.435301i	$-0.143358\pi$
$242$	−7.68816			−0.494214
$243$			2.49909i			0.160316i
$244$		−	0.597745i		−	0.0382667i
$245$			1.06314i			0.0679216i
$246$	−3.36667			−0.214651
$247$	−1.35371			−0.0861344
$248$		−	14.3368i		−	0.910387i
$249$			14.7014i			0.931662i
$250$			4.38342i			0.277232i
$251$	−22.8328			−1.44119			−0.720596	−	0.693355i	$-0.756132\pi$
$251$	−22.8328			−1.44119			−0.720596	+	0.693355i	$0.756132\pi$
$252$			1.14422i			0.0720789i
$253$	−48.9960			−3.08035
$254$	3.27698			0.205616
$255$	−5.66726	−	13.8393i	−0.354897	−	0.866651i
$256$	6.31631			0.394769
$257$	−14.4086			−0.898785			−0.449393	−	0.893334i	$-0.648360\pi$
$257$	−14.4086			−0.898785			−0.449393	+	0.893334i	$0.648360\pi$
$258$			0.659307i			0.0410466i
$259$	18.8461			1.17104
$260$			0.626100i			0.0388291i
$261$		−	0.899948i		−	0.0557054i
$262$			2.31172i			0.142819i
$263$	16.5843			1.02263			0.511317	−	0.859392i	$-0.329158\pi$
$263$	16.5843			1.02263			0.511317	+	0.859392i	$0.329158\pi$
$264$	14.4166			0.887283
$265$		−	25.8483i		−	1.58785i
$266$			7.57272i			0.464313i
$267$		−	17.4575i		−	1.06838i
$268$	4.87619			0.297861
$269$			27.9932i			1.70678i	0.521277	+	0.853388i	$0.325456\pi$
$269$			27.9932i			1.70678i	−0.521277	+	0.853388i	$0.674544\pi$
$270$	3.66475			0.223029
$271$	−20.3717			−1.23749			−0.618746	−	0.785591i	$-0.712359\pi$
$271$	−20.3717			−1.23749			−0.618746	+	0.785591i	$0.712359\pi$
$272$	−5.02073	−	12.2605i	−0.304426	−	0.743401i
$273$	−0.762817			−0.0461678
$274$	7.10921			0.429483
$275$		−	5.32229i		−	0.320946i
$276$	29.0977			1.75147
$277$		−	3.02471i		−	0.181737i	−0.995863	−	0.0908685i	$-0.971036\pi$
$277$		−	3.02471i		−	0.181737i	0.995863	−	0.0908685i	$-0.0289643\pi$
$278$			0.103820i			0.00622670i
$279$		−	2.44092i		−	0.146134i
$280$	7.25663			0.433667
$281$	−23.2817			−1.38887			−0.694436	−	0.719555i	$-0.744346\pi$
$281$	−23.2817			−1.38887			−0.694436	+	0.719555i	$0.744346\pi$
$282$		−	5.22507i		−	0.311148i
$283$			9.67434i			0.575080i	0.957769	+	0.287540i	$0.0928374\pi$
$283$			9.67434i			0.575080i	−0.957769	+	0.287540i	$0.907163\pi$
$284$			2.33038i			0.138283i
$285$	29.4803			1.74626
$286$			0.345002i			0.0204004i
$287$	12.9910			0.766835
$288$	−0.966178			−0.0569326
$289$	−12.1172	+	11.9236i	−0.712777	+	0.701390i
$290$	−2.75473			−0.161763
$291$	0.920264			0.0539468
$292$			6.28459i			0.367778i
$293$	−7.02277			−0.410274			−0.205137	−	0.978733i	$-0.565764\pi$
$293$	−7.02277			−0.410274			−0.205137	+	0.978733i	$0.565764\pi$
$294$		−	0.347910i		−	0.0202905i
$295$			14.0299i			0.816853i
$296$			10.4878i			0.609592i
$297$	−28.0941			−1.63019
$298$	−8.38376			−0.485658
$299$			1.44271i			0.0834343i
$300$			3.16080i			0.182489i
$301$		−	2.54407i		−	0.146638i
$302$	1.14336			0.0657927
$303$		−	15.2522i		−	0.876217i
$304$	26.1171			1.49792
$305$	−0.645422			−0.0369568
$306$	0.137930	+	0.336821i	0.00788493	+	0.0192548i
$307$	−13.8911			−0.792809			−0.396405	−	0.918076i	$-0.629742\pi$
$307$	−13.8911			−0.792809			−0.396405	+	0.918076i	$0.629742\pi$
$308$	−26.8499			−1.52991
$309$		−	3.68785i		−	0.209794i
$310$	−7.47162			−0.424360
$311$			16.2493i			0.921416i	0.887552	+	0.460708i	$0.152404\pi$
$311$			16.2493i			0.921416i	−0.887552	+	0.460708i	$0.847596\pi$
$312$		−	0.424506i		−	0.0240329i
$313$			27.9056i			1.57732i	0.614832	+	0.788658i	$0.289224\pi$
$313$			27.9056i			1.57732i	−0.614832	+	0.788658i	$0.710776\pi$
$314$	0.390147			0.0220173
$315$	1.23548			0.0696115
$316$		−	0.605882i		−	0.0340835i
$317$		−	23.1235i		−	1.29875i	−0.760469	−	0.649374i	$-0.775031\pi$
$317$		−	23.1235i		−	1.29875i	0.760469	−	0.649374i	$-0.224969\pi$
$318$			8.45879i			0.474345i
$319$	21.1179			1.18238
$320$		−	9.99015i		−	0.558466i
$321$	10.2737			0.573423
$322$	8.07061			0.449758
$323$	−12.6998	−	31.0125i	−0.706634	−	1.72558i
$324$	18.0338			1.00188
$325$	−0.156718			−0.00869313
$326$			1.98221i			0.109785i
$327$	7.49894			0.414692
$328$			7.22948i			0.399181i
$329$			20.1620i			1.11157i
$330$		−	7.51325i		−	0.413591i
$331$	19.2410			1.05758			0.528790	−	0.848753i	$-0.322646\pi$
$331$	19.2410			1.05758			0.528790	+	0.848753i	$0.322646\pi$
$332$	15.2370			0.836239
$333$			1.78561i			0.0978509i
$334$		−	5.22234i		−	0.285753i
$335$		−	5.26513i		−	0.287665i
$336$	14.7170			0.802879
$337$		−	3.78320i		−	0.206084i	−0.994677	−	0.103042i	$-0.967142\pi$
$337$		−	3.78320i		−	0.206084i	0.994677	−	0.103042i	$-0.0328576\pi$
$338$	−4.75073			−0.258406
$339$	2.93116			0.159199
$340$	−14.3435	+	5.87374i	−0.777886	+	0.318548i
$341$	57.2779			3.10177
$342$	−0.717492			−0.0387975
$343$			19.1510i			1.03406i
$344$	1.41577			0.0763333
$345$		−	31.4186i		−	1.69152i
$346$		−	6.12249i		−	0.329147i
$347$		−	6.53427i		−	0.350778i	−0.984499	−	0.175389i	$-0.943882\pi$
$347$		−	6.53427i		−	0.350778i	0.984499	−	0.175389i	$-0.0561183\pi$
$348$	−12.5415			−0.672294
$349$	18.5188			0.991287			0.495644	−	0.868526i	$-0.334932\pi$
$349$	18.5188			0.991287			0.495644	+	0.868526i	$0.334932\pi$
$350$			0.876687i			0.0468609i
$351$			0.827247i			0.0441552i
$352$		−	22.6720i		−	1.20842i
$353$	23.2176			1.23575			0.617875	−	0.786277i	$-0.287994\pi$
$353$	23.2176			1.23575			0.617875	+	0.786277i	$0.287994\pi$
$354$		−	4.59124i		−	0.244022i
$355$	2.51625			0.133549
$356$	−18.0935			−0.958956
$357$	−7.15634	−	17.4756i	−0.378754	−	0.924907i
$358$	−3.13958			−0.165932
$359$	21.1815			1.11792			0.558958	−	0.829196i	$-0.311201\pi$
$359$	21.1815			1.11792			0.558958	+	0.829196i	$0.311201\pi$
$360$			0.687543i			0.0362367i
$361$	47.0624			2.47697
$362$		−	7.27345i		−	0.382284i
$363$			37.7937i			1.98366i
$364$			0.790609i			0.0414392i
$365$	6.78586			0.355188
$366$	0.211213			0.0110403
$367$			10.2872i			0.536987i	0.963282	+	0.268493i	$0.0865258\pi$
$367$			10.2872i			0.536987i	−0.963282	+	0.268493i	$0.913474\pi$
$368$		−	27.8343i		−	1.45096i
$369$			1.23086i			0.0640759i
$370$	5.46574			0.284150
$371$		−	32.6400i		−	1.69459i
$372$	−34.0161			−1.76365
$373$	11.7319			0.607456			0.303728	−	0.952759i	$-0.401769\pi$
$373$	11.7319			0.607456			0.303728	+	0.952759i	$0.401769\pi$
$374$	−7.90375	+	3.23662i	−0.408693	+	0.167362i
$375$	21.5482			1.11274
$376$	−11.2201			−0.578635
$377$		−	0.621828i		−	0.0320258i
$378$	4.62767			0.238021
$379$		−	9.67131i		−	0.496782i	−0.968660	−	0.248391i	$-0.920098\pi$
$379$		−	9.67131i		−	0.496782i	0.968660	−	0.248391i	$-0.0799017\pi$
$380$		−	30.5543i		−	1.56740i
$381$		−	16.1091i		−	0.825294i
$382$	2.43159			0.124411
$383$	3.85968			0.197220			0.0986102	−	0.995126i	$-0.468560\pi$
$383$	3.85968			0.197220			0.0986102	+	0.995126i	$0.468560\pi$
$384$			17.7015i			0.903327i
$385$			28.9914i			1.47754i
$386$		−	0.484196i		−	0.0246449i
$387$	0.241043			0.0122529
$388$		−	0.953793i		−	0.0484215i
$389$	−6.63240			−0.336276			−0.168138	−	0.985763i	$-0.553775\pi$
$389$	−6.63240			−0.336276			−0.168138	+	0.985763i	$0.553775\pi$
$390$	−0.221232			−0.0112025
$391$	−33.0516	+	13.5348i	−1.67149	+	0.684483i
$392$	−0.747089			−0.0377337
$393$	11.3640			0.573240
$394$			3.02824i			0.152561i
$395$	−0.654208			−0.0329168
$396$		−	2.54394i		−	0.127838i
$397$		−	15.8984i		−	0.797917i	−0.916969	−	0.398959i	$-0.869372\pi$
$397$		−	15.8984i		−	0.797917i	0.916969	−	0.398959i	$-0.130628\pi$
$398$			8.70890i			0.436538i
$399$	37.2263			1.86364
$400$	3.02356			0.151178
$401$			22.7671i			1.13693i	0.822706	+	0.568467i	$0.192463\pi$
$401$			22.7671i			1.13693i	−0.822706	+	0.568467i	$0.807537\pi$
$402$			1.72300i			0.0859353i
$403$		−	1.68658i		−	0.0840144i
$404$	−15.8079			−0.786473
$405$		−	19.4722i		−	0.967581i
$406$	−3.47854			−0.172637
$407$	−41.9006			−2.07694
$408$	9.72514	−	3.98249i	0.481466	−	0.197163i
$409$	−36.9885			−1.82897			−0.914483	−	0.404624i	$-0.867402\pi$
$409$	−36.9885			−1.82897			−0.914483	+	0.404624i	$0.867402\pi$
$410$	3.76765			0.186071
$411$		−	34.9477i		−	1.72384i
$412$	−3.82221			−0.188307
$413$			17.7163i			0.871761i
$414$			0.764666i			0.0375813i
$415$		−	16.4523i		−	0.807613i
$416$	−0.667591			−0.0327313
$417$	0.510362			0.0249925
$418$		−	16.8365i		−	0.823498i
$419$		−	13.6620i		−	0.667432i	−0.942674	−	0.333716i	$-0.891697\pi$
$419$		−	13.6620i		−	0.667432i	0.942674	−	0.333716i	$-0.108303\pi$
$420$		−	17.2174i		−	0.840124i
$421$	26.8860			1.31035			0.655173	−	0.755479i	$-0.272596\pi$
$421$	26.8860			1.31035			0.655173	+	0.755479i	$0.272596\pi$
$422$		−	0.760075i		−	0.0369999i
$423$	−1.91029			−0.0928816
$424$	18.1641			0.882127
$425$	−1.47024	−	3.59029i	−0.0713172	−	0.174155i
$426$	−0.823436			−0.0398956
$427$	−0.815008			−0.0394410
$428$		−	10.6480i		−	0.514692i
$429$	1.69597			0.0818823
$430$		−	0.737831i		−	0.0355814i
$431$			25.5671i			1.23153i	0.787931	+	0.615763i	$0.211152\pi$
$431$			25.5671i			1.23153i	−0.787931	+	0.615763i	$0.788848\pi$
$432$		−	15.9601i		−	0.767880i
$433$	−5.17819			−0.248848			−0.124424	−	0.992229i	$-0.539708\pi$
$433$	−5.17819			−0.248848			−0.124424	+	0.992229i	$0.539708\pi$
$434$	−9.43480			−0.452885
$435$			13.5418i			0.649280i
$436$		−	7.77216i		−	0.372219i
$437$		−	70.4059i		−	3.36797i
$438$	−2.22065			−0.106107
$439$			33.7623i			1.61139i	0.592333	+	0.805693i	$0.298207\pi$
$439$			33.7623i			1.61139i	−0.592333	+	0.805693i	$0.701793\pi$
$440$	−16.1337			−0.769144
$441$	−0.127196			−0.00605696
$442$	0.0953042	+	0.232730i	0.00453316	+	0.0110699i
$443$	19.6727			0.934678			0.467339	−	0.884078i	$-0.345213\pi$
$443$	19.6727			0.934678			0.467339	+	0.884078i	$0.345213\pi$
$444$	24.8839			1.18094
$445$			19.5367i			0.926129i
$446$	8.76523			0.415046
$447$			41.2132i			1.94932i
$448$		−	12.6151i		−	0.596006i
$449$			9.06524i			0.427815i	0.976854	+	0.213908i	$0.0686192\pi$
$449$			9.06524i			0.427815i	−0.976854	+	0.213908i	$0.931381\pi$
$450$	−0.0830634			−0.00391565
$451$	−28.8830			−1.36005
$452$		−	3.03796i		−	0.142894i
$453$		−	5.62055i		−	0.264076i
$454$			3.37302i			0.158304i
$455$	0.853669			0.0400206
$456$			20.7163i			0.970132i
$457$	−3.83988			−0.179622			−0.0898110	−	0.995959i	$-0.528626\pi$
$457$	−3.83988			−0.179622			−0.0898110	+	0.995959i	$0.528626\pi$
$458$	−4.97249			−0.232349
$459$	−18.9517	+	7.76079i	−0.884588	+	0.362243i
$460$	−32.5633			−1.51827
$461$	6.71439			0.312720			0.156360	−	0.987700i	$-0.450024\pi$
$461$	6.71439			0.312720			0.156360	+	0.987700i	$0.450024\pi$
$462$		−	9.48736i		−	0.441392i
$463$	5.09331			0.236706			0.118353	−	0.992972i	$-0.462239\pi$
$463$	5.09331			0.236706			0.118353	+	0.992972i	$0.462239\pi$
$464$			11.9969i			0.556944i
$465$			36.7293i			1.70328i
$466$		−	1.30952i		−	0.0606625i
$467$	−21.6422			−1.00148			−0.500740	−	0.865598i	$-0.666939\pi$
$467$	−21.6422			−1.00148			−0.500740	+	0.865598i	$0.666939\pi$
$468$	−0.0749078			−0.00346261
$469$		−	6.64855i		−	0.307001i
$470$			5.84738i			0.269720i
$471$		−	1.91790i		−	0.0883722i
$472$	−9.85908			−0.453801
$473$			5.65625i			0.260075i
$474$	0.214088			0.00983337
$475$	7.64799			0.350914
$476$	−18.1123	+	7.41707i	−0.830176	+	0.339961i
$477$	3.09254			0.141598
$478$	−4.01530			−0.183656
$479$		−	21.9373i		−	1.00234i	−0.865348	−	0.501171i	$-0.832903\pi$
$479$		−	21.9373i		−	1.00234i	0.865348	−	0.501171i	$-0.167097\pi$
$480$	14.5384			0.663584
$481$			1.23379i			0.0562558i
$482$		−	4.94964i		−	0.225450i
$483$		−	39.6738i		−	1.80522i
$484$	39.1707			1.78049
$485$	−1.02987			−0.0467639
$486$			0.915221i			0.0415153i
$487$		−	9.88385i		−	0.447880i	−0.974603	−	0.223940i	$-0.928108\pi$
$487$		−	9.88385i		−	0.447880i	0.974603	−	0.223940i	$-0.0718920\pi$
$488$		−	0.453551i		−	0.0205313i
$489$	9.74424			0.440650
$490$			0.389346i			0.0175889i
$491$	20.1895			0.911138			0.455569	−	0.890201i	$-0.349436\pi$
$491$	20.1895			0.911138			0.455569	+	0.890201i	$0.349436\pi$
$492$	17.1530			0.773316
$493$	14.2457	−	5.83366i	0.641592	−	0.262735i
$494$	−0.495759			−0.0223052
$495$	−2.74685			−0.123462
$496$			32.5391i			1.46105i
$497$	3.17740			0.142526
$498$			5.38398i			0.241262i
$499$		−	2.67217i		−	0.119623i	−0.998210	−	0.0598113i	$-0.980950\pi$
$499$		−	2.67217i		−	0.119623i	0.998210	−	0.0598113i	$-0.0190499\pi$
$500$		−	22.3333i		−	0.998774i
$501$	−25.6721			−1.14695
$502$	−8.36187			−0.373209
$503$		−	3.97904i		−	0.177417i	−0.996058	−	0.0887084i	$-0.971726\pi$
$503$		−	3.97904i		−	0.177417i	0.996058	−	0.0887084i	$-0.0282739\pi$
$504$			0.868196i			0.0386725i
$505$			17.0688i			0.759550i
$506$	−17.9434			−0.797683
$507$			23.3538i			1.03718i
$508$	−16.6960			−0.740766
$509$	18.1742			0.805555			0.402778	−	0.915298i	$-0.368045\pi$
$509$	18.1742			0.805555			0.402778	+	0.915298i	$0.368045\pi$
$510$	−2.07548	−	5.06826i	−0.0919037	−	0.224426i
$511$	8.56886			0.379064
$512$	21.9784			0.971315
$513$		−	40.3705i		−	1.78240i
$514$	−5.27676			−0.232748
$515$			4.12708i			0.181861i
$516$		−	3.35913i		−	0.147877i
$517$		−	44.8263i		−	1.97146i
$518$	6.90187			0.303251
$519$	−30.0972			−1.32112
$520$			0.475065i			0.0208330i
$521$			13.1804i			0.577444i	0.957413	+	0.288722i	$0.0932304\pi$
$521$			13.1804i			0.577444i	−0.957413	+	0.288722i	$0.906770\pi$
$522$		−	0.329581i		−	0.0144254i
$523$	−7.46932			−0.326611			−0.163305	−	0.986576i	$-0.552216\pi$
$523$	−7.46932			−0.326611			−0.163305	+	0.986576i	$0.552216\pi$
$524$		−	11.7781i		−	0.514527i
$525$	4.30965			0.188089
$526$	6.07356			0.264820
$527$	38.6383	−	15.8226i	1.68311	−	0.689242i
$528$	−32.7204			−1.42397
$529$	−52.0350			−2.26239
$530$		−	9.46624i		−	0.411187i
$531$	−1.67856			−0.0728435
$532$		−	38.5825i		−	1.67277i
$533$			0.850475i			0.0368381i
$534$		−	6.39333i		−	0.276666i
$535$	−11.4973			−0.497073
$536$	3.69990			0.159812
$537$			15.4336i			0.666011i
$538$			10.2517i			0.441984i
$539$		−	2.98475i		−	0.128562i
$540$	−18.6717			−0.803501
$541$			44.0525i			1.89396i	0.321286	+	0.946982i	$0.395885\pi$
$541$			44.0525i			1.89396i	−0.321286	+	0.946982i	$0.604115\pi$
$542$	−7.46057			−0.320459
$543$	−35.7551			−1.53440
$544$	−6.26298	−	15.2940i	−0.268523	−	0.655726i
$545$	−8.39207			−0.359477
$546$	−0.279361			−0.0119555
$547$			28.7810i			1.23059i	0.788299	+	0.615293i	$0.210962\pi$
$547$			28.7810i			1.23059i	−0.788299	+	0.615293i	$0.789038\pi$
$548$	−36.2210			−1.54728
$549$		−	0.0772195i		−	0.00329565i
$550$		−	1.94914i		−	0.0831117i
$551$			30.3459i			1.29278i
$552$	22.0784			0.939720
$553$	−0.826102			−0.0351294
$554$		−	1.10772i		−	0.0470623i
$555$		−	26.8687i		−	1.14051i
$556$		−	0.528956i		−	0.0224327i
$557$	29.5881			1.25369			0.626844	−	0.779145i	$-0.284346\pi$
$557$	29.5881			1.25369			0.626844	+	0.779145i	$0.284346\pi$
$558$		−	0.893919i		−	0.0378426i
$559$	0.166551			0.00704437
$560$	−16.4698			−0.695978
$561$	15.9107	+	38.8536i	0.671751	+	1.64040i
$562$	−8.52629			−0.359660
$563$	−4.98730			−0.210190			−0.105095	−	0.994462i	$-0.533515\pi$
$563$	−4.98730			−0.210190			−0.105095	+	0.994462i	$0.533515\pi$
$564$			26.6214i			1.12096i
$565$	−3.28027			−0.138002
$566$			3.54296i			0.148922i
$567$		−	24.5885i		−	1.03262i
$568$			1.76822i			0.0741928i
$569$	4.29287			0.179967			0.0899833	−	0.995943i	$-0.471319\pi$
$569$	4.29287			0.179967			0.0899833	+	0.995943i	$0.471319\pi$
$570$	10.7963			0.452209
$571$			30.5455i			1.27829i	0.769087	+	0.639144i	$0.220711\pi$
$571$			30.5455i			1.27829i	−0.769087	+	0.639144i	$0.779289\pi$
$572$		−	1.75776i		−	0.0734958i
$573$		−	11.9533i		−	0.499357i
$574$	4.75760			0.198578
$575$		−	8.15083i		−	0.339913i
$576$	1.19524			0.0498017
$577$	6.17414			0.257033			0.128516	−	0.991707i	$-0.458979\pi$
$577$	6.17414			0.257033			0.128516	+	0.991707i	$0.458979\pi$
$578$	−4.43760	+	4.36670i	−0.184580	+	0.181631i
$579$	−2.38023			−0.0989188
$580$	14.0352			0.582779
$581$		−	20.7752i		−	0.861901i
$582$	0.337021			0.0139700
$583$			72.5687i			3.00549i
$584$			4.76855i			0.197324i
$585$			0.0808825i			0.00334408i
$586$	−2.57190			−0.106244
$587$	−13.9516			−0.575842			−0.287921	−	0.957654i	$-0.592964\pi$
$587$	−13.9516			−0.575842			−0.287921	+	0.957654i	$0.592964\pi$
$588$			1.77258i			0.0730999i
$589$			82.3068i			3.39139i
$590$			5.13807i			0.211531i
$591$	14.8863			0.612342
$592$		−	23.8034i		−	0.978316i
$593$	13.3026			0.546271			0.273135	−	0.961976i	$-0.411939\pi$
$593$	13.3026			0.546271			0.273135	+	0.961976i	$0.411939\pi$
$594$	−10.2887			−0.422151
$595$	8.00867	+	19.5570i	0.328323	+	0.801757i
$596$	42.7147			1.74966
$597$	42.8116			1.75216
$598$			0.528354i			0.0216060i
$599$	−18.1851			−0.743025			−0.371512	−	0.928428i	$-0.621161\pi$
$599$	−18.1851			−0.743025			−0.371512	+	0.928428i	$0.621161\pi$
$600$			2.39831i			0.0979107i
$601$		−	36.8462i		−	1.50299i	−0.659739	−	0.751494i	$-0.729333\pi$
$601$		−	36.8462i		−	1.50299i	0.659739	−	0.751494i	$-0.270667\pi$
$602$		−	0.931697i		−	0.0379731i
$603$	0.629929			0.0256527
$604$	−5.82533			−0.237029
$605$		−	42.2950i		−	1.71954i
$606$		−	5.58570i		−	0.226904i
$607$			48.8196i			1.98153i	0.135606	+	0.990763i	$0.456702\pi$
$607$			48.8196i			1.98153i	−0.135606	+	0.990763i	$0.543298\pi$
$608$	32.5791			1.32126
$609$			17.0999i			0.692924i
$610$	−0.236368			−0.00957027
$611$	−1.31994			−0.0533989
$612$	−0.702745	−	1.71608i	−0.0284068	−	0.0693686i
$613$	28.0305			1.13214			0.566071	−	0.824356i	$-0.308463\pi$
$613$	28.0305			1.13214			0.566071	+	0.824356i	$0.308463\pi$
$614$	−5.08725			−0.205305
$615$		−	18.5211i		−	0.746844i
$616$	−20.3728			−0.820845
$617$			30.5759i			1.23094i	0.788160	+	0.615470i	$0.211034\pi$
$617$			30.5759i			1.23094i	−0.788160	+	0.615470i	$0.788966\pi$
$618$		−	1.35057i		−	0.0543280i
$619$		−	13.8133i		−	0.555203i	−0.960696	−	0.277602i	$-0.910460\pi$
$619$		−	13.8133i		−	0.555203i	0.960696	−	0.277602i	$-0.0895395\pi$
$620$	38.0675			1.52883
$621$	−43.0248			−1.72653
$622$			5.95087i			0.238608i
$623$			24.6700i			0.988383i
$624$			0.963470i			0.0385697i
$625$	−19.4098			−0.776392
$626$			10.2197i			0.408459i
$627$	−82.7653			−3.30533
$628$	−1.98778			−0.0793209
$629$	−28.2652	+	11.5747i	−1.12701	+	0.461515i
$630$	0.452461			0.0180265
$631$	−3.80772			−0.151583			−0.0757915	−	0.997124i	$-0.524148\pi$
$631$	−3.80772			−0.151583			−0.0757915	+	0.997124i	$0.524148\pi$
$632$		−	0.459724i		−	0.0182869i
$633$	−3.73640			−0.148509
$634$		−	8.46836i		−	0.336322i
$635$			18.0277i			0.715408i
$636$		−	43.0970i		−	1.70891i
$637$	−0.0878875			−0.00348223
$638$	7.73385			0.306186
$639$			0.301049i			0.0119093i
$640$		−	19.8098i		−	0.783051i
$641$		−	5.40845i		−	0.213621i	−0.994279	−	0.106811i	$-0.965936\pi$
$641$		−	5.40845i		−	0.213621i	0.994279	−	0.106811i	$-0.0340638\pi$
$642$	3.76247			0.148493
$643$		−	17.2012i		−	0.678351i	−0.940723	−	0.339175i	$-0.889852\pi$
$643$		−	17.2012i		−	0.678351i	0.940723	−	0.339175i	$-0.110148\pi$
$644$	−41.1193			−1.62033
$645$	−3.62706			−0.142815
$646$	−4.65094	−	11.3575i	−0.182989	−	0.446854i
$647$	37.9802			1.49316			0.746579	−	0.665297i	$-0.231695\pi$
$647$	37.9802			1.49316			0.746579	+	0.665297i	$0.231695\pi$
$648$	13.6835			0.537538
$649$		−	39.3887i		−	1.54614i
$650$	−0.0573935			−0.00225116
$651$			46.3800i			1.81777i
$652$		−	10.0993i		−	0.395517i
$653$			20.0335i			0.783973i	0.919971	+	0.391987i	$0.128212\pi$
$653$			20.0335i			0.783973i	−0.919971	+	0.391987i	$0.871788\pi$
$654$	2.74628			0.107388
$655$	−12.7175			−0.496914
$656$		−	16.4082i		−	0.640633i
$657$			0.811873i			0.0316742i
$658$			7.38379i			0.287850i
$659$	40.1976			1.56588			0.782938	−	0.622099i	$-0.213720\pi$
$659$	40.1976			1.56588			0.782938	+	0.622099i	$0.213720\pi$
$660$			38.2795i			1.49003i
$661$	4.55180			0.177044			0.0885222	−	0.996074i	$-0.471786\pi$
$661$	4.55180			0.177044			0.0885222	+	0.996074i	$0.471786\pi$
$662$	7.04648			0.273869
$663$	1.14406	−	0.468500i	0.0444318	−	0.0181950i
$664$	11.5614			0.448668
$665$	−41.6599			−1.61550
$666$			0.653931i			0.0253393i
$667$	32.3411			1.25225
$668$			26.6075i			1.02947i
$669$		−	43.0885i		−	1.66590i
$670$		−	1.92821i		−	0.0744932i
$671$	1.81201			0.0699519
$672$	18.3584			0.708190
$673$		−	49.0009i		−	1.88885i	−0.328733	−	0.944423i	$-0.606622\pi$
$673$		−	49.0009i		−	1.88885i	0.328733	−	0.944423i	$-0.393378\pi$
$674$		−	1.38549i		−	0.0533672i
$675$		−	4.67366i		−	0.179889i
$676$	24.2047			0.930950
$677$		−	28.5671i		−	1.09792i	−0.835847	−	0.548962i	$-0.815023\pi$
$677$		−	28.5671i		−	1.09792i	0.835847	−	0.548962i	$-0.184977\pi$
$678$	1.07346			0.0412259
$679$	−1.30047			−0.0499074
$680$	−10.8834	+	4.45681i	−0.417360	+	0.170911i
$681$	16.5812			0.635394
$682$	20.9764			0.803229
$683$			33.5607i			1.28417i	0.766635	+	0.642083i	$0.221929\pi$
$683$			33.5607i			1.28417i	−0.766635	+	0.642083i	$0.778071\pi$
$684$	3.65558			0.139775
$685$			39.1101i			1.49432i
$686$			7.01352i			0.267778i
$687$			24.4440i			0.932595i
$688$	−3.21327			−0.122505
$689$	2.13682			0.0814065
$690$		−	11.5062i		−	0.438033i
$691$		−	27.8189i		−	1.05828i	−0.848535	−	0.529140i	$-0.822515\pi$
$691$		−	27.8189i		−	1.05828i	0.848535	−	0.529140i	$-0.177485\pi$
$692$			31.1937i			1.18581i
$693$	−3.46859			−0.131761
$694$		−	2.39300i		−	0.0908369i
$695$	−0.571146			−0.0216648
$696$	−9.51609			−0.360706
$697$	−19.4838	+	7.97870i	−0.738001	+	0.302215i
$698$	6.78199			0.256702
$699$	−6.43741			−0.243485
$700$		−	4.46667i		−	0.168824i
$701$	−6.74018			−0.254573			−0.127287	−	0.991866i	$-0.540627\pi$
$701$	−6.74018			−0.254573			−0.127287	+	0.991866i	$0.540627\pi$
$702$			0.302957i			0.0114344i
$703$		−	60.2101i		−	2.27087i
$704$			28.0471i			1.05707i
$705$	28.7448			1.08259
$706$	8.50281			0.320008
$707$			21.5536i			0.810607i
$708$			23.3921i			0.879129i
$709$			27.0676i			1.01654i	0.861196	+	0.508272i	$0.169716\pi$
$709$			27.0676i			1.01654i	−0.861196	+	0.508272i	$0.830284\pi$
$710$	0.921508			0.0345836
$711$		−	0.0782706i		−	0.00293538i
$712$	−13.7288			−0.514509
$713$	87.7183			3.28508
$714$	−2.62081	−	6.39996i	−0.0980814	−	0.239512i
$715$	−1.89797			−0.0709799
$716$	15.9960			0.597797
$717$			19.7386i			0.737150i
$718$	7.75713			0.289494
$719$			7.72596i			0.288130i	0.989568	+	0.144065i	$0.0460174\pi$
$719$			7.72596i			0.288130i	−0.989568	+	0.144065i	$0.953983\pi$
$720$		−	1.56047i		−	0.0581552i
$721$			5.21147i			0.194085i
$722$	17.2353			0.641432
$723$	−24.3316			−0.904903
$724$			37.0578i			1.37724i
$725$			3.51312i			0.130474i
$726$			13.8409i			0.513685i
$727$	−10.9077			−0.404544			−0.202272	−	0.979329i	$-0.564832\pi$
$727$	−10.9077			−0.404544			−0.202272	+	0.979329i	$0.564832\pi$
$728$			0.599889i			0.0222334i
$729$	−24.4960			−0.907259
$730$	2.48514			0.0919790
$731$	1.56250	+	3.81557i	0.0577910	+	0.141124i
$732$	−1.07611			−0.0397743
$733$	−36.5674			−1.35065			−0.675324	−	0.737521i	$-0.735996\pi$
$733$	−36.5674			−1.35065			−0.675324	+	0.737521i	$0.735996\pi$
$734$			3.76740i			0.139057i
$735$	1.91396			0.0705975
$736$		−	34.7212i		−	1.27984i
$737$			14.7817i			0.544492i
$738$			0.450768i			0.0165930i
$739$	−32.2995			−1.18816			−0.594078	−	0.804408i	$-0.702483\pi$
$739$	−32.2995			−1.18816			−0.594078	+	0.804408i	$0.702483\pi$
$740$	−27.8476			−1.02370
$741$			2.43707i			0.0895279i
$742$		−	11.9535i		−	0.438827i
$743$			21.7251i			0.797018i	0.917164	+	0.398509i	$0.130472\pi$
$743$			21.7251i			0.797018i	−0.917164	+	0.398509i	$0.869528\pi$
$744$	−25.8104			−0.946254
$745$		−	46.1217i		−	1.68977i
$746$	4.29649			0.157306
$747$	1.96839			0.0720195
$748$	40.2691	−	16.4904i	1.47239	−	0.602949i
$749$	−14.5183			−0.530486
$750$	7.89143			0.288154
$751$			5.82756i			0.212651i	0.994331	+	0.106325i	$0.0339085\pi$
$751$			5.82756i			0.212651i	−0.994331	+	0.106325i	$0.966092\pi$
$752$	25.4655			0.928632
$753$			41.1056i			1.49797i
$754$		−	0.227727i		−	0.00829335i
$755$			6.28996i			0.228915i
$756$	−23.5777			−0.857512
$757$	−37.6987			−1.37018			−0.685091	−	0.728458i	$-0.740237\pi$
$757$	−37.6987			−1.37018			−0.685091	+	0.728458i	$0.740237\pi$
$758$		−	3.54185i		−	0.128646i
$759$			88.2070i			3.20171i
$760$		−	23.1837i		−	0.840961i
$761$	17.7359			0.642924			0.321462	−	0.946922i	$-0.395826\pi$
$761$	17.7359			0.642924			0.321462	+	0.946922i	$0.395826\pi$
$762$		−	5.89951i		−	0.213717i
$763$	−10.5971			−0.383641
$764$	−12.3888			−0.448212
$765$	−1.85296	+	0.758797i	−0.0669940	+	0.0274344i
$766$	1.41350			0.0510719
$767$	−1.15982			−0.0418787
$768$		−	11.3712i		−	0.410322i
$769$	27.1080			0.977539			0.488770	−	0.872413i	$-0.337446\pi$
$769$	27.1080			0.977539			0.488770	+	0.872413i	$0.337446\pi$
$770$			10.6173i			0.382622i
$771$			25.9397i			0.934195i
$772$			2.46695i			0.0887874i
$773$	−27.2536			−0.980242			−0.490121	−	0.871654i	$-0.663047\pi$
$773$	−27.2536			−0.980242			−0.490121	+	0.871654i	$0.663047\pi$
$774$	0.0882754			0.00317299
$775$			9.52858i			0.342277i
$776$		−	0.723708i		−	0.0259796i
$777$		−	33.9285i		−	1.21718i
$778$	−2.42893			−0.0870814
$779$		−	41.5041i		−	1.48704i
$780$	1.12716			0.0403589
$781$	−7.06433			−0.252782
$782$	−12.1042	+	4.95674i	−0.432846	+	0.177253i
$783$	18.5443			0.662718
$784$	1.69561			0.0605576
$785$			2.14633i			0.0766056i
$786$	4.16177			0.148445
$787$		−	18.5974i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$787$		−	18.5974i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$788$		−	15.4287i		−	0.549625i
$789$		−	29.8566i		−	1.06292i
$790$	−0.239586			−0.00852407
$791$	−4.14217			−0.147278
$792$		−	1.93026i		−	0.0685890i
$793$		−	0.0533556i		−	0.00189471i
$794$		−	5.82235i		−	0.206627i
$795$	−46.5345			−1.65041
$796$		−	44.3713i		−	1.57270i
$797$	−26.5081			−0.938965			−0.469482	−	0.882942i	$-0.655559\pi$
$797$	−26.5081			−0.938965			−0.469482	+	0.882942i	$0.655559\pi$
$798$	13.6331			0.482606
$799$	−12.3829	−	30.2388i	−0.438077	−	1.06977i
$800$	3.77166			0.133348
$801$	−2.33741			−0.0825883
$802$			8.33782i			0.294419i
$803$	−19.0512			−0.672301
$804$		−	8.77856i		−	0.309596i
$805$			44.3990i			1.56486i
$806$		−	0.617663i		−	0.0217562i
$807$	50.3959			1.77402
$808$	−11.9945			−0.421967
$809$		−	24.7691i		−	0.870834i	−0.900229	−	0.435417i	$-0.856601\pi$
$809$		−	24.7691i		−	0.870834i	0.900229	−	0.435417i	$-0.143399\pi$
$810$		−	7.13115i		−	0.250563i
$811$		−	5.36090i		−	0.188247i	−0.995561	−	0.0941233i	$-0.969995\pi$
$811$		−	5.36090i		−	0.188247i	0.995561	−	0.0941233i	$-0.0300048\pi$
$812$	17.7230			0.621954
$813$			36.6750i			1.28625i
$814$	−15.3449			−0.537840
$815$	−10.9048			−0.381978
$816$	−22.0724	+	9.03876i	−0.772690	+	0.316420i
$817$	−8.12788			−0.284359
$818$	−13.5460			−0.473626
$819$			0.102135i			0.00356887i
$820$	−19.1959			−0.670351
$821$		−	14.6483i		−	0.511228i	−0.966779	−	0.255614i	$-0.917722\pi$
$821$		−	14.6483i		−	0.511228i	0.966779	−	0.255614i	$-0.0822776\pi$
$822$		−	12.7986i		−	0.446404i
$823$			43.1091i			1.50269i	0.659910	+	0.751345i	$0.270594\pi$
$823$			43.1091i			1.50269i	−0.659910	+	0.751345i	$0.729406\pi$
$824$	−2.90018			−0.101032
$825$	−9.58166			−0.333591
$826$			6.48810i			0.225750i
$827$			8.72324i			0.303337i	0.988431	+	0.151668i	$0.0484646\pi$
$827$			8.72324i			0.303337i	−0.988431	+	0.151668i	$0.951535\pi$
$828$		−	3.89593i		−	0.135393i
$829$	−12.5501			−0.435883			−0.217942	−	0.975962i	$-0.569934\pi$
$829$	−12.5501			−0.435883			−0.217942	+	0.975962i	$0.569934\pi$
$830$		−	6.02521i		−	0.209138i
$831$	−5.44535			−0.188897
$832$	0.825863			0.0286317
$833$	−0.824514	−	2.01344i	−0.0285677	−	0.0697616i
$834$	0.186906			0.00647202
$835$	28.7297			0.994233
$836$			85.7807i			2.96679i
$837$	50.2974			1.73853
$838$		−	5.00333i		−	0.172837i
$839$			13.6554i			0.471435i	0.971822	+	0.235718i	$0.0757441\pi$
$839$			13.6554i			0.471435i	−0.971822	+	0.235718i	$0.924256\pi$
$840$		−	13.0640i		−	0.450752i
$841$	15.0606			0.519330
$842$	9.84627			0.339325
$843$			41.9138i			1.44359i
$844$			3.87254i			0.133298i
$845$		−	26.1353i		−	0.899082i
$846$	−0.699592			−0.0240525
$847$		−	53.4081i		−	1.83512i
$848$	−41.2258			−1.41570
$849$	17.4166			0.597737
$850$	−0.538436	−	1.31485i	−0.0184682	−	0.0450988i
$851$	−64.1688			−2.19968
$852$	4.19536			0.143731
$853$		−	16.7821i		−	0.574608i	−0.957839	−	0.287304i	$-0.907241\pi$
$853$		−	16.7821i		−	0.574608i	0.957839	−	0.287304i	$-0.0927590\pi$
$854$	−0.298474			−0.0102136
$855$		−	3.94715i		−	0.134990i
$856$		−	8.07940i		−	0.276148i
$857$			34.4911i			1.17819i	0.808062	+	0.589097i	$0.200517\pi$
$857$			34.4911i			1.17819i	−0.808062	+	0.589097i	$0.799483\pi$
$858$	0.621103			0.0212041
$859$	9.41156			0.321118			0.160559	−	0.987026i	$-0.448670\pi$
$859$	9.41156			0.321118			0.160559	+	0.987026i	$0.448670\pi$
$860$			3.75920i			0.128188i
$861$		−	23.3876i		−	0.797047i
$862$			9.36326i			0.318914i
$863$	−7.78571			−0.265029			−0.132514	−	0.991181i	$-0.542305\pi$
$863$	−7.78571			−0.265029			−0.132514	+	0.991181i	$0.542305\pi$
$864$		−	19.9090i		−	0.677318i
$865$	33.6818			1.14522
$866$	−1.89637			−0.0644412
$867$	21.4660	+	21.8145i	0.729024	+	0.740859i
$868$	48.0698			1.63159
$869$	1.83668			0.0623050
$870$			4.95931i			0.168137i
$871$	0.435256			0.0147481
$872$		−	5.89727i		−	0.199707i
$873$		−	0.123215i		−	0.00417021i
$874$		−	25.7842i		−	0.872165i
$875$	−30.4507			−1.02942
$876$	11.3141			0.382268
$877$		−	28.2707i		−	0.954633i	−0.878731	−	0.477317i	$-0.841609\pi$
$877$		−	28.2707i		−	0.954633i	0.878731	−	0.477317i	$-0.158391\pi$
$878$			12.3645i			0.417282i
$879$			12.6430i			0.426438i
$880$	36.6175			1.23437
$881$		−	10.3653i		−	0.349217i	−0.984638	−	0.174608i	$-0.944134\pi$
$881$		−	10.3653i		−	0.349217i	0.984638	−	0.174608i	$-0.0558660\pi$
$882$	−0.0465821			−0.00156850
$883$	−1.04337			−0.0351121			−0.0175560	−	0.999846i	$-0.505589\pi$
$883$	−1.04337			−0.0351121			−0.0175560	+	0.999846i	$0.505589\pi$
$884$	−0.485569	−	1.18575i	−0.0163314	−	0.0398810i
$885$	25.2579			0.849035
$886$	7.20458			0.242043
$887$		−	29.8347i		−	1.00175i	−0.865520	−	0.500875i	$-0.833012\pi$
$887$		−	29.8347i		−	1.00175i	0.865520	−	0.500875i	$-0.166988\pi$
$888$	18.8811			0.633609
$889$			22.7645i			0.763497i
$890$			7.15478i			0.239829i
$891$			54.6678i			1.83144i
$892$	−44.6583			−1.49527
$893$	64.4143			2.15554
$894$			15.0932i			0.504792i
$895$		−	17.2718i		−	0.577333i
$896$		−	25.0148i		−	0.835687i
$897$	2.59730			0.0867214
$898$			3.31990i			0.110786i
$899$	−37.8077			−1.26096
$900$	0.423203			0.0141068
$901$	20.0465	+	48.9532i	0.667847	+	1.63087i
$902$	−10.5776			−0.352195
$903$	−4.58007			−0.152415
$904$		−	2.30511i		−	0.0766667i
$905$	40.0136			1.33010
$906$		−	2.05837i		−	0.0683848i
$907$		−	18.6307i		−	0.618621i	−0.950961	−	0.309310i	$-0.899902\pi$
$907$		−	18.6307i		−	0.618621i	0.950961	−	0.309310i	$-0.100098\pi$
$908$		−	17.1853i		−	0.570315i
$909$	−2.04214			−0.0677335
$910$	0.312633			0.0103637
$911$		−	30.6611i		−	1.01585i	−0.861402	−	0.507924i	$-0.830413\pi$
$911$		−	30.6611i		−	1.01585i	0.861402	−	0.507924i	$-0.169587\pi$
$912$		−	47.0184i		−	1.55693i
$913$			46.1896i			1.52865i
$914$	−1.40625			−0.0465146
$915$			1.16195i			0.0384128i
$916$	25.3345			0.837077
$917$	−16.0590			−0.530317
$918$	−6.94052	+	2.84218i	−0.229071	+	0.0938058i
$919$	−30.8093			−1.01630			−0.508152	−	0.861268i	$-0.669671\pi$
$919$	−30.8093			−1.01630			−0.508152	+	0.861268i	$0.669671\pi$
$920$	−24.7080			−0.814598
$921$			25.0081i			0.824044i
$922$	2.45896			0.0809815
$923$			0.208013i			0.00684683i
$924$			48.3375i			1.59019i
$925$		−	6.97047i		−	0.229188i
$926$	1.86528			0.0612971
$927$	−0.493771			−0.0162176
$928$			14.9653i			0.491259i
$929$			24.6735i			0.809510i	0.914425	+	0.404755i	$0.132643\pi$
$929$			24.6735i			0.809510i	−0.914425	+	0.404755i	$0.867357\pi$
$930$			13.4511i			0.441079i
$931$	4.28900			0.140566
$932$			6.67194i			0.218547i
$933$	29.2535			0.957717
$934$	−7.92585			−0.259342
$935$	−17.8057	−	43.4811i	−0.582309	−	1.42198i
$936$	−0.0568377			−0.00185780
$937$	49.4019			1.61389			0.806945	−	0.590627i	$-0.201120\pi$
$937$	49.4019			1.61389			0.806945	+	0.590627i	$0.201120\pi$
$938$		−	2.43485i		−	0.0795006i
$939$	50.2381			1.63946
$940$		−	29.7921i		−	0.971710i
$941$		−	3.34488i		−	0.109040i	−0.998513	−	0.0545200i	$-0.982637\pi$
$941$		−	3.34488i		−	0.109040i	0.998513	−	0.0545200i	$-0.0173629\pi$
$942$		−	0.702378i		−	0.0228847i
$943$	−44.2329			−1.44042
$944$	22.3764			0.728291
$945$			25.4583i			0.828157i
$946$			2.07145i			0.0673485i
$947$			30.6725i			0.996723i	0.866969	+	0.498361i	$0.166065\pi$
$947$			30.6725i			0.996723i	−0.866969	+	0.498361i	$0.833935\pi$
$948$	−1.09076			−0.0354263
$949$			0.560972i			0.0182099i
$950$	2.80087			0.0908721
$951$	−41.6291			−1.34992
$952$	−13.7430	+	5.62784i	−0.445415	+	0.182399i
$953$	−12.3425			−0.399814			−0.199907	−	0.979815i	$-0.564064\pi$
$953$	−12.3425			−0.399814			−0.199907	+	0.979815i	$0.564064\pi$
$954$	1.13256			0.0366679
$955$			13.3770i			0.432869i
$956$	20.4577			0.661650
$957$		−	38.0184i		−	1.22896i
$958$		−	8.03394i		−	0.259565i
$959$			49.3863i			1.59477i
$960$	−17.9852			−0.580469
$961$	−71.5455			−2.30792
$962$			0.451840i			0.0145679i
$963$		−	1.37556i		−	0.0443269i
$964$			25.2181i			0.812221i
$965$	2.66371			0.0857480
$966$		−	14.5294i		−	0.467477i
$967$	23.5652			0.757807			0.378903	−	0.925436i	$-0.376301\pi$
$967$	23.5652			0.757807			0.378903	+	0.925436i	$0.376301\pi$
$968$	29.7215			0.955286
$969$	−55.8315	+	22.8633i	−1.79357	+	0.734474i
$970$	−0.377161			−0.0121099
$971$	48.2500			1.54842			0.774208	−	0.632931i	$-0.218148\pi$
$971$	48.2500			1.54842			0.774208	+	0.632931i	$0.218148\pi$
$972$		−	4.66300i		−	0.149566i
$973$	−0.721216			−0.0231211
$974$		−	3.61969i		−	0.115982i
$975$			0.282137i			0.00903562i
$976$			1.02939i			0.0329500i
$977$	1.92571			0.0616088			0.0308044	−	0.999525i	$-0.490193\pi$
$977$	1.92571			0.0616088			0.0308044	+	0.999525i	$0.490193\pi$
$978$	3.56856			0.114110
$979$		−	54.8489i		−	1.75298i
$980$		−	1.98369i		−	0.0633668i
$981$		−	1.00404i		−	0.0320566i
$982$	7.39384			0.235947
$983$		−	32.5788i		−	1.03910i	−0.854439	−	0.519552i	$-0.826099\pi$
$983$		−	32.5788i		−	1.03910i	0.854439	−	0.519552i	$-0.173901\pi$
$984$	13.0152			0.414908
$985$	−16.6593			−0.530810
$986$	5.21708	−	2.13642i	0.166146	−	0.0680374i
$987$	36.2975			1.15536
$988$	2.52586			0.0803583
$989$			8.66228i			0.275444i
$990$	−1.00596			−0.0319715
$991$		−	13.8700i		−	0.440596i	−0.975433	−	0.220298i	$-0.929297\pi$
$991$		−	13.8700i		−	0.440596i	0.975433	−	0.220298i	$-0.0707030\pi$
$992$			40.5901i			1.28874i
$993$		−	34.6394i		−	1.09925i
$994$	1.16364			0.0369083
$995$	−47.9105			−1.51886
$996$		−	27.4310i		−	0.869185i
$997$			15.7140i			0.497667i	0.968546	+	0.248833i	$0.0800472\pi$
$997$			15.7140i			0.497667i	−0.968546	+	0.248833i	$0.919953\pi$
$998$		−	0.978607i		−	0.0309773i
$999$	−36.7942			−1.16412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.19	✓	34
17.16	even	2	inner	731.2.d.d.560.20	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.19	✓	34	1.1	even	1	trivial
731.2.d.d.560.20	yes	34	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q+0.366222 q^{2} -1.80029i q^{3} -1.86588 q^{4} +2.01471i q^{5} -0.659307i q^{6} +2.54407i q^{7} -1.41577 q^{8} -0.241043 q^{9} +O(q^{10})\)	\(q+0.366222 q^{2} -1.80029i q^{3} -1.86588 q^{4} +2.01471i q^{5} -0.659307i q^{6} +2.54407i q^{7} -1.41577 q^{8} -0.241043 q^{9} +0.737831i q^{10} -5.65625i q^{11} +3.35913i q^{12} -0.166551 q^{13} +0.931697i q^{14} +3.62706 q^{15} +3.21327 q^{16} +(-1.56250 - 3.81557i) q^{17} -0.0882754 q^{18} +8.12788 q^{19} -3.75920i q^{20} +4.58007 q^{21} -2.07145i q^{22} -8.66228i q^{23} +2.54880i q^{24} +0.940958 q^{25} -0.0609948 q^{26} -4.96692i q^{27} -4.74694i q^{28} +3.73355i q^{29} +1.32831 q^{30} +10.1265i q^{31} +4.00832 q^{32} -10.1829 q^{33} +(-0.572221 - 1.39735i) q^{34} -5.12556 q^{35} +0.449758 q^{36} -7.40785i q^{37} +2.97661 q^{38} +0.299841i q^{39} -2.85237i q^{40} -5.10638i q^{41} +1.67732 q^{42} -1.00000 q^{43} +10.5539i q^{44} -0.485631i q^{45} -3.17232i q^{46} +7.92510 q^{47} -5.78483i q^{48} +0.527690 q^{49} +0.344600 q^{50} +(-6.86914 + 2.81294i) q^{51} +0.310765 q^{52} -12.8298 q^{53} -1.81900i q^{54} +11.3957 q^{55} -3.60183i q^{56} -14.6325i q^{57} +1.36731i q^{58} +6.96375 q^{59} -6.76765 q^{60} +0.320356i q^{61} +3.70854i q^{62} -0.613232i q^{63} -4.95861 q^{64} -0.335552i q^{65} -3.72920 q^{66} -2.61335 q^{67} +(2.91543 + 7.11941i) q^{68} -15.5946 q^{69} -1.87710 q^{70} -1.24894i q^{71} +0.341262 q^{72} -3.36816i q^{73} -2.71292i q^{74} -1.69400i q^{75} -15.1657 q^{76} +14.3899 q^{77} +0.109808i q^{78} +0.324716i q^{79} +6.47381i q^{80} -9.66503 q^{81} -1.87007i q^{82} -8.16612 q^{83} -8.54586 q^{84} +(7.68726 - 3.14797i) q^{85} -0.366222 q^{86} +6.72148 q^{87} +8.00796i q^{88} +9.69705 q^{89} -0.177849i q^{90} -0.423719i q^{91} +16.1628i q^{92} +18.2306 q^{93} +2.90235 q^{94} +16.3753i q^{95} -7.21613i q^{96} +0.511176i q^{97} +0.193252 q^{98} +1.36340i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 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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