LMFDB - Embedded newform 403.2.c.b.311.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.10
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +O(q^{10})$	\(q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +3.76969 q^{10} -0.0546038i q^{11} +0.206658 q^{12} +(-1.72882 + 3.16404i) q^{13} -7.19586 q^{14} -7.30664i q^{15} -4.14259 q^{16} -5.08006 q^{17} -6.90098i q^{18} -1.17518i q^{19} -0.193789i q^{20} +13.9475i q^{21} -0.0786376 q^{22} -7.81207 q^{23} +7.74242i q^{24} -1.85165 q^{25} +(4.55670 + 2.48976i) q^{26} -5.00174 q^{27} +0.369920i q^{28} -7.02474 q^{29} -10.5227 q^{30} -1.00000i q^{31} +0.418588i q^{32} +0.152420i q^{33} +7.31605i q^{34} +13.0789 q^{35} -0.354761 q^{36} -6.75099i q^{37} -1.69243 q^{38} +(4.82581 - 8.83208i) q^{39} +7.26030 q^{40} +1.55918i q^{41} +20.0864 q^{42} -3.02644 q^{43} +0.00404255i q^{44} +12.5430i q^{45} +11.2506i q^{46} -0.191499i q^{47} +11.5636 q^{48} -17.9661 q^{49} +2.66666i q^{50} +14.1804 q^{51} +(0.127992 - 0.234248i) q^{52} +8.59226 q^{53} +7.20326i q^{54} +0.142929 q^{55} -13.8590 q^{56} +3.28038i q^{57} +10.1167i q^{58} +2.91407i q^{59} +0.540942i q^{60} +5.96368 q^{61} -1.44015 q^{62} -23.9430i q^{63} -7.68234 q^{64} +(-8.28210 - 4.52530i) q^{65} +0.219508 q^{66} -1.50321i q^{67} +0.376098 q^{68} +21.8065 q^{69} -18.8357i q^{70} -1.44037i q^{71} -13.2911i q^{72} -13.9550i q^{73} -9.72244 q^{74} +5.16869 q^{75} +0.0870034i q^{76} -0.272833 q^{77} +(-12.7195 - 6.94989i) q^{78} +1.10819 q^{79} -10.8435i q^{80} -0.413740 q^{81} +2.24545 q^{82} -1.74923i q^{83} -1.03259i q^{84} -13.2974i q^{85} +4.35854i q^{86} +19.6088 q^{87} -0.151453 q^{88} -2.35995i q^{89} +18.0638 q^{90} +(15.8095 + 8.63823i) q^{91} +0.578360 q^{92} +2.79139i q^{93} -0.275787 q^{94} +3.07611 q^{95} -1.16844i q^{96} +12.1357i q^{97} +25.8738i q^{98} -0.261653i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.44015i		−	1.01834i	−0.860666	−	0.509170i	$-0.829952\pi$
$2$		−	1.44015i		−	1.01834i	0.860666	−	0.509170i	$-0.170048\pi$
$3$	−2.79139			−1.61161			−0.805804	−	0.592182i	$-0.798267\pi$
$3$	−2.79139			−1.61161			−0.805804	+	0.592182i	$0.798267\pi$
$4$	−0.0740342			−0.0370171
$5$			2.61757i			1.17061i	0.810813	+	0.585306i	$0.199025\pi$
$5$			2.61757i			1.17061i	−0.810813	+	0.585306i	$0.800975\pi$
$6$			4.02002i			1.64117i
$7$		−	4.99660i		−	1.88854i	−0.329173	−	0.944269i	$-0.606770\pi$
$7$		−	4.99660i		−	1.88854i	0.329173	−	0.944269i	$-0.393230\pi$
$8$		−	2.77368i		−	0.980644i
$9$	4.79185			1.59728
$10$	3.76969			1.19208
$11$		−	0.0546038i		−	0.0164637i	−0.999966	−	0.00823183i	$-0.997380\pi$
$11$		−	0.0546038i		−	0.0164637i	0.999966	−	0.00823183i	$-0.00262030\pi$
$12$	0.206658			0.0596571
$13$	−1.72882	+	3.16404i	−0.479489	+	0.877548i
$13$	−1.72882	+	3.16404i	−0.479489	+	0.877548i
$14$	−7.19586			−1.92318
$15$		−	7.30664i		−	1.88657i
$16$	−4.14259			−1.03565
$17$	−5.08006			−1.23209			−0.616047	−	0.787709i	$-0.711267\pi$
$17$	−5.08006			−1.23209			−0.616047	+	0.787709i	$0.711267\pi$
$18$		−	6.90098i		−	1.62658i
$19$		−	1.17518i		−	0.269604i	−0.990873	−	0.134802i	$-0.956960\pi$
$19$		−	1.17518i		−	0.269604i	0.990873	−	0.134802i	$-0.0430399\pi$
$20$		−	0.193789i		−	0.0433326i
$21$			13.9475i			3.04359i
$22$	−0.0786376			−0.0167656
$23$	−7.81207			−1.62893			−0.814464	−	0.580213i	$-0.802969\pi$
$23$	−7.81207			−1.62893			−0.814464	+	0.580213i	$0.802969\pi$
$24$			7.74242i			1.58041i
$25$	−1.85165			−0.370331
$26$	4.55670	+	2.48976i	0.893643	+	0.488283i
$27$	−5.00174			−0.962586
$28$			0.369920i			0.0699082i
$29$	−7.02474			−1.30446			−0.652231	−	0.758020i	$-0.726167\pi$
$29$	−7.02474			−1.30446			−0.652231	+	0.758020i	$0.726167\pi$
$30$	−10.5227			−1.92117
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$			0.418588i			0.0739966i
$33$			0.152420i			0.0265330i
$34$			7.31605i			1.25469i
$35$	13.0789			2.21075
$36$	−0.354761			−0.0591268
$37$		−	6.75099i		−	1.10986i	−0.831899	−	0.554928i	$-0.812746\pi$
$37$		−	6.75099i		−	1.10986i	0.831899	−	0.554928i	$-0.187254\pi$
$38$	−1.69243			−0.274549
$39$	4.82581	−	8.83208i	0.772748	−	1.41426i
$40$	7.26030			1.14795
$41$			1.55918i			0.243503i	0.992561	+	0.121751i	$0.0388511\pi$
$41$			1.55918i			0.243503i	−0.992561	+	0.121751i	$0.961149\pi$
$42$	20.0864			3.09941
$43$	−3.02644			−0.461528			−0.230764	−	0.973010i	$-0.574123\pi$
$43$	−3.02644			−0.461528			−0.230764	+	0.973010i	$0.574123\pi$
$44$			0.00404255i			0.000609437i
$45$			12.5430i			1.86980i
$46$			11.2506i			1.65880i
$47$		−	0.191499i		−	0.0279330i	−0.999902	−	0.0139665i	$-0.995554\pi$
$47$		−	0.191499i		−	0.0279330i	0.999902	−	0.0139665i	$-0.00444582\pi$
$48$	11.5636			1.66906
$49$	−17.9661			−2.56658
$50$			2.66666i			0.377123i
$51$	14.1804			1.98565
$52$	0.127992	−	0.234248i	0.0177493	−	0.0324843i
$53$	8.59226			1.18024			0.590119	−	0.807317i	$-0.299081\pi$
$53$	8.59226			1.18024			0.590119	+	0.807317i	$0.299081\pi$
$54$			7.20326i			0.980240i
$55$	0.142929			0.0192725
$56$	−13.8590			−1.85199
$57$			3.28038i			0.434497i
$58$			10.1167i			1.32839i
$59$			2.91407i			0.379379i	0.981844	+	0.189690i	$0.0607482\pi$
$59$			2.91407i			0.379379i	−0.981844	+	0.189690i	$0.939252\pi$
$60$			0.540942i			0.0698353i
$61$	5.96368			0.763571			0.381786	−	0.924251i	$-0.375309\pi$
$61$	5.96368			0.763571			0.381786	+	0.924251i	$0.375309\pi$
$62$	−1.44015			−0.182899
$63$		−	23.9430i		−	3.01653i
$64$	−7.68234			−0.960293
$65$	−8.28210	−	4.52530i	−1.02727	−	0.561295i
$66$	0.219508			0.0270196
$67$		−	1.50321i		−	0.183646i	−0.995775	−	0.0918231i	$-0.970731\pi$
$67$		−	1.50321i		−	0.183646i	0.995775	−	0.0918231i	$-0.0292694\pi$
$68$	0.376098			0.0456086
$69$	21.8065			2.62520
$70$		−	18.8357i		−	2.25129i
$71$		−	1.44037i		−	0.170940i	−0.996341	−	0.0854701i	$-0.972761\pi$
$71$		−	1.44037i		−	0.170940i	0.996341	−	0.0854701i	$-0.0272392\pi$
$72$		−	13.2911i		−	1.56637i
$73$		−	13.9550i		−	1.63331i	−0.577124	−	0.816656i	$-0.695825\pi$
$73$		−	13.9550i		−	1.63331i	0.577124	−	0.816656i	$-0.304175\pi$
$74$	−9.72244			−1.13021
$75$	5.16869			0.596829
$76$			0.0870034i			0.00997997i
$77$	−0.272833			−0.0310922
$78$	−12.7195	−	6.94989i	−1.44020	−	0.786920i
$79$	1.10819			0.124681			0.0623404	−	0.998055i	$-0.480144\pi$
$79$	1.10819			0.124681			0.0623404	+	0.998055i	$0.480144\pi$
$80$		−	10.8435i		−	1.21234i
$81$	−0.413740			−0.0459711
$82$	2.24545			0.247969
$83$		−	1.74923i		−	0.192003i	−0.995381	−	0.0960015i	$-0.969395\pi$
$83$		−	1.74923i		−	0.192003i	0.995381	−	0.0960015i	$-0.0306054\pi$
$84$		−	1.03259i		−	0.112665i
$85$		−	13.2974i		−	1.44230i
$86$			4.35854i			0.469993i
$87$	19.6088			2.10228
$88$	−0.151453			−0.0161450
$89$		−	2.35995i		−	0.250154i	−0.992147	−	0.125077i	$-0.960082\pi$
$89$		−	2.35995i		−	0.250154i	0.992147	−	0.125077i	$-0.0399179\pi$
$90$	18.0638			1.90409
$91$	15.8095	+	8.63823i	1.65728	+	0.905533i
$92$	0.578360			0.0602982
$93$			2.79139i			0.289453i
$94$	−0.275787			−0.0284453
$95$	3.07611			0.315602
$96$		−	1.16844i		−	0.119254i
$97$			12.1357i			1.23220i	0.787670	+	0.616098i	$0.211287\pi$
$97$			12.1357i			1.23220i	−0.787670	+	0.616098i	$0.788713\pi$
$98$			25.8738i			2.61365i
$99$		−	0.261653i		−	0.0262971i
$100$	0.137086			0.0137086
$101$	11.6128			1.15552			0.577758	−	0.816208i	$-0.303928\pi$
$101$	11.6128			1.15552			0.577758	+	0.816208i	$0.303928\pi$
$102$		−	20.4219i		−	2.02207i
$103$	−12.7238			−1.25371			−0.626857	−	0.779134i	$-0.715659\pi$
$103$	−12.7238			−1.25371			−0.626857	+	0.779134i	$0.715659\pi$
$104$	8.77605	+	4.79520i	0.860563	+	0.470208i
$105$	−36.5084			−3.56286
$106$		−	12.3741i		−	1.20188i
$107$	−2.95463			−0.285635			−0.142817	−	0.989749i	$-0.545616\pi$
$107$	−2.95463			−0.285635			−0.142817	+	0.989749i	$0.545616\pi$
$108$	0.370300			0.0356321
$109$		−	19.9084i		−	1.90688i	−0.301587	−	0.953439i	$-0.597516\pi$
$109$		−	19.9084i		−	1.90688i	0.301587	−	0.953439i	$-0.402484\pi$
$110$		−	0.205839i		−	0.0196260i
$111$			18.8446i			1.78865i
$112$			20.6989i			1.95586i
$113$	0.926163			0.0871261			0.0435630	−	0.999051i	$-0.486129\pi$
$113$	0.926163			0.0871261			0.0435630	+	0.999051i	$0.486129\pi$
$114$	4.72424			0.442465
$115$		−	20.4486i		−	1.90684i
$116$	0.520071			0.0482874
$117$	−8.28425	+	15.1616i	−0.765879	+	1.40169i
$118$	4.19670			0.386337
$119$			25.3830i			2.32686i
$120$	−20.2663			−1.85005
$121$	10.9970			0.999729
$122$		−	8.58860i		−	0.777575i
$123$		−	4.35227i		−	0.392431i
$124$			0.0740342i			0.00664847i
$125$			8.24100i			0.737098i
$126$	−34.4815			−3.07185
$127$	16.3194			1.44812			0.724058	−	0.689739i	$-0.242275\pi$
$127$	16.3194			1.44812			0.724058	+	0.689739i	$0.242275\pi$
$128$			11.9009i			1.05190i
$129$	8.44798			0.743803
$130$	−6.51712	+	11.9275i	−0.571589	+	1.04611i
$131$	15.1689			1.32532			0.662658	−	0.748922i	$-0.269428\pi$
$131$	15.1689			1.32532			0.662658	+	0.748922i	$0.269428\pi$
$132$		−	0.0112843i		−	0.000982174i
$133$	−5.87190			−0.509158
$134$	−2.16485			−0.187014
$135$		−	13.0924i		−	1.12681i
$136$			14.0905i			1.20825i
$137$			11.4877i			0.981463i	0.871311	+	0.490732i	$0.163270\pi$
$137$			11.4877i			0.981463i	−0.871311	+	0.490732i	$0.836730\pi$
$138$		−	31.4047i		−	2.67334i
$139$	−6.64791			−0.563869			−0.281934	−	0.959434i	$-0.590976\pi$
$139$	−6.64791			−0.563869			−0.281934	+	0.959434i	$0.590976\pi$
$140$	−0.968289			−0.0818354
$141$			0.534548i			0.0450170i
$142$	−2.07435			−0.174075
$143$	0.172769	+	0.0944001i	0.0144476	+	0.00789413i
$144$	−19.8506			−1.65422
$145$		−	18.3877i		−	1.52702i
$146$	−20.0973			−1.66327
$147$	50.1502			4.13632
$148$			0.499804i			0.0410836i
$149$			1.35792i			0.111245i	0.998452	+	0.0556224i	$0.0177143\pi$
$149$			1.35792i			0.111245i	−0.998452	+	0.0556224i	$0.982286\pi$
$150$		−	7.44369i		−	0.607775i
$151$		−	12.4451i		−	1.01277i	−0.862308	−	0.506384i	$-0.830982\pi$
$151$		−	12.4451i		−	1.01277i	0.862308	−	0.506384i	$-0.169018\pi$
$152$	−3.25957			−0.264386
$153$	−24.3429			−1.96800
$154$			0.392921i			0.0316625i
$155$	2.61757			0.210248
$156$	−0.357275	+	0.653876i	−0.0286049	+	0.0523520i
$157$	15.5894			1.24417			0.622086	−	0.782949i	$-0.286286\pi$
$157$	15.5894			1.24417			0.622086	+	0.782949i	$0.286286\pi$
$158$		−	1.59596i		−	0.126968i
$159$	−23.9843			−1.90208
$160$	−1.09568			−0.0866213
$161$			39.0338i			3.07630i
$162$			0.595848i			0.0468143i
$163$			2.52440i			0.197726i	0.995101	+	0.0988632i	$0.0315206\pi$
$163$			2.52440i			0.197726i	−0.995101	+	0.0988632i	$0.968479\pi$
$164$		−	0.115433i		−	0.00901377i
$165$	−0.398970			−0.0310598
$166$	−2.51916			−0.195524
$167$		−	9.92382i		−	0.767928i	−0.923348	−	0.383964i	$-0.874559\pi$
$167$		−	9.92382i		−	0.767928i	0.923348	−	0.383964i	$-0.125441\pi$
$168$	38.6858			2.98468
$169$	−7.02236	−	10.9401i	−0.540181	−	0.841549i
$170$	−19.1502			−1.46876
$171$		−	5.63127i		−	0.430634i
$172$	0.224060			0.0170844
$173$	−20.3536			−1.54745			−0.773726	−	0.633520i	$-0.781609\pi$
$173$	−20.3536			−1.54745			−0.773726	+	0.633520i	$0.781609\pi$
$174$		−	28.2396i		−	2.14084i
$175$			9.25199i			0.699385i
$176$			0.226201i			0.0170505i
$177$		−	8.13429i		−	0.611411i
$178$	−3.39869			−0.254742
$179$	4.85781			0.363090			0.181545	−	0.983383i	$-0.441890\pi$
$179$	4.85781			0.363090			0.181545	+	0.983383i	$0.441890\pi$
$180$		−	0.928610i		−	0.0692145i
$181$	6.82673			0.507427			0.253713	−	0.967279i	$-0.418348\pi$
$181$	6.82673			0.507427			0.253713	+	0.967279i	$0.418348\pi$
$182$	12.4404	−	22.7680i	0.922141	−	1.68768i
$183$	−16.6469			−1.23058
$184$			21.6682i			1.59740i
$185$	17.6712			1.29921
$186$	4.02002			0.294762
$187$			0.277390i			0.0202848i
$188$			0.0141775i			0.00103400i
$189$			24.9917i			1.81788i
$190$		−	4.43006i		−	0.321390i
$191$	−13.8071			−0.999043			−0.499522	−	0.866301i	$-0.666491\pi$
$191$	−13.8071			−0.999043			−0.499522	+	0.866301i	$0.666491\pi$
$192$	21.4444			1.54762
$193$		−	8.92165i		−	0.642194i	−0.947046	−	0.321097i	$-0.895948\pi$
$193$		−	8.92165i		−	0.642194i	0.947046	−	0.321097i	$-0.104052\pi$
$194$	17.4773			1.25479
$195$	23.1185	+	12.6319i	1.65555	+	0.904588i
$196$	1.33010			0.0950073
$197$			8.13765i			0.579783i	0.957059	+	0.289892i	$0.0936193\pi$
$197$			8.13765i			0.579783i	−0.957059	+	0.289892i	$0.906381\pi$
$198$	−0.376820			−0.0267794
$199$	12.4940			0.885678			0.442839	−	0.896601i	$-0.353971\pi$
$199$	12.4940			0.885678			0.442839	+	0.896601i	$0.353971\pi$
$200$			5.13590i			0.363163i
$201$			4.19604i			0.295966i
$202$		−	16.7242i		−	1.17671i
$203$			35.0999i			2.46353i
$204$	−1.04984			−0.0735032
$205$	−4.08126			−0.285047
$206$			18.3242i			1.27671i
$207$	−37.4342			−2.60186
$208$	7.16179	−	13.1073i	0.496581	−	0.908830i
$209$	−0.0641691			−0.00443867
$210$			52.5776i			3.62820i
$211$	−20.8611			−1.43614			−0.718068	−	0.695973i	$-0.754973\pi$
$211$	−20.8611			−1.43614			−0.718068	+	0.695973i	$0.754973\pi$
$212$	−0.636121			−0.0436890
$213$			4.02063i			0.275489i
$214$			4.25511i			0.290873i
$215$		−	7.92192i		−	0.540270i
$216$			13.8732i			0.943954i
$217$	−4.99660			−0.339192
$218$	−28.6711			−1.94185
$219$			38.9539i			2.63226i
$220$	−0.0105816			−0.000713414
$221$	8.78251	−	16.0735i	0.590775	−	1.08122i
$222$	27.1391			1.82146
$223$		−	18.6577i		−	1.24941i	−0.780859	−	0.624707i	$-0.785218\pi$
$223$		−	18.6577i		−	1.24941i	0.780859	−	0.624707i	$-0.214782\pi$
$224$	2.09152			0.139746
$225$	−8.87285			−0.591523
$226$		−	1.33381i		−	0.0887240i
$227$		−	27.9915i		−	1.85786i	−0.370251	−	0.928932i	$-0.620728\pi$
$227$		−	27.9915i		−	1.85786i	0.370251	−	0.928932i	$-0.379272\pi$
$228$		−	0.242860i		−	0.0160838i
$229$			9.20943i			0.608576i	0.952580	+	0.304288i	$0.0984186\pi$
$229$			9.20943i			0.608576i	−0.952580	+	0.304288i	$0.901581\pi$
$230$	−29.4491			−1.94181
$231$	0.761584			0.0501085
$232$			19.4844i			1.27921i
$233$	19.5339			1.27971			0.639854	−	0.768497i	$-0.278995\pi$
$233$	19.5339			1.27971			0.639854	+	0.768497i	$0.278995\pi$
$234$	21.8350	+	11.9306i	1.42740	+	0.779925i
$235$	0.501261			0.0326987
$236$		−	0.215741i		−	0.0140435i
$237$	−3.09338			−0.200937
$238$	36.5554			2.36953
$239$		−	16.9297i		−	1.09509i	−0.836776	−	0.547546i	$-0.815562\pi$
$239$		−	16.9297i		−	1.09509i	0.836776	−	0.547546i	$-0.184438\pi$
$240$			30.2684i			1.95382i
$241$		−	14.6063i		−	0.940875i	−0.882433	−	0.470438i	$-0.844096\pi$
$241$		−	14.6063i		−	0.940875i	0.882433	−	0.470438i	$-0.155904\pi$
$242$		−	15.8374i		−	1.01806i
$243$	16.1601			1.03667
$244$	−0.441516			−0.0282652
$245$		−	47.0273i		−	3.00447i
$246$	−6.26793			−0.399629
$247$	3.71832	+	2.03167i	0.236591	+	0.129272i
$248$	−2.77368			−0.176129
$249$			4.88278i			0.309434i
$250$	11.8683			0.750616
$251$	−28.9232			−1.82561			−0.912807	−	0.408391i	$-0.866090\pi$
$251$	−28.9232			−1.82561			−0.912807	+	0.408391i	$0.866090\pi$
$252$			1.77260i			0.111663i
$253$			0.426568i			0.0268181i
$254$		−	23.5025i		−	1.47468i
$255$			37.1182i			2.32443i
$256$	1.77442			0.110901
$257$	−19.4544			−1.21353			−0.606767	−	0.794880i	$-0.707534\pi$
$257$	−19.4544			−1.21353			−0.606767	+	0.794880i	$0.707534\pi$
$258$		−	12.1664i		−	0.757445i
$259$	−33.7320			−2.09601
$260$	0.613159	+	0.335027i	0.0380265	+	0.0207775i
$261$	−33.6615			−2.08359
$262$		−	21.8456i		−	1.34962i
$263$	20.2310			1.24750			0.623750	−	0.781624i	$-0.285608\pi$
$263$	20.2310			1.24750			0.623750	+	0.781624i	$0.285608\pi$
$264$	0.422765			0.0260194
$265$			22.4908i			1.38160i
$266$			8.45642i			0.518496i
$267$			6.58754i			0.403151i
$268$			0.111289i			0.00679805i
$269$	−8.30420			−0.506316			−0.253158	−	0.967425i	$-0.581469\pi$
$269$	−8.30420			−0.506316			−0.253158	+	0.967425i	$0.581469\pi$
$270$	−18.8550			−1.14748
$271$			14.7486i			0.895912i	0.894056	+	0.447956i	$0.147848\pi$
$271$			14.7486i			0.895912i	−0.894056	+	0.447956i	$0.852152\pi$
$272$	21.0446			1.27601
$273$	−44.1304	−	24.1127i	−2.67089	−	1.45936i
$274$	16.5441			0.999464
$275$			0.101107i			0.00609700i
$276$	−1.61443			−0.0971772
$277$	−15.4228			−0.926664			−0.463332	−	0.886185i	$-0.653346\pi$
$277$	−15.4228			−0.926664			−0.463332	+	0.886185i	$0.653346\pi$
$278$			9.57400i			0.574210i
$279$		−	4.79185i		−	0.286880i
$280$		−	36.2768i		−	2.16795i
$281$		−	17.2595i		−	1.02962i	−0.857306	−	0.514808i	$-0.827863\pi$
$281$		−	17.2595i		−	1.02962i	0.857306	−	0.514808i	$-0.172137\pi$
$282$	0.769829			0.0458427
$283$	12.2230			0.726583			0.363291	−	0.931676i	$-0.381653\pi$
$283$	12.2230			0.726583			0.363291	+	0.931676i	$0.381653\pi$
$284$			0.106636i			0.00632771i
$285$	−8.58661			−0.508627
$286$	0.135950	−	0.248813i	0.00803891	−	0.0147126i
$287$	7.79060			0.459865
$288$			2.00581i			0.118194i
$289$	8.80698			0.518057
$290$	−26.4811			−1.55502
$291$		−	33.8755i		−	1.98582i
$292$			1.03315i			0.0604605i
$293$			11.5516i			0.674850i	0.941352	+	0.337425i	$0.109556\pi$
$293$			11.5516i			0.674850i	−0.941352	+	0.337425i	$0.890444\pi$
$294$		−	72.2239i		−	4.21218i
$295$	−7.62776			−0.444106
$296$	−18.7251			−1.08837
$297$			0.273114i			0.0158477i
$298$	1.95560			0.113285
$299$	13.5057	−	24.7177i	0.781053	−	1.42946i
$300$	−0.382660			−0.0220929
$301$			15.1219i			0.871614i
$302$	−17.9228			−1.03134
$303$	−32.4158			−1.86224
$304$			4.86828i			0.279215i
$305$			15.6103i			0.893845i
$306$			35.0574i			2.00410i
$307$			22.1226i			1.26260i	0.775537	+	0.631302i	$0.217479\pi$
$307$			22.1226i			1.26260i	−0.775537	+	0.631302i	$0.782521\pi$
$308$	0.0201990			0.00115095
$309$	35.5171			2.02050
$310$		−	3.76969i		−	0.214104i
$311$	−17.1273			−0.971203			−0.485601	−	0.874180i	$-0.661399\pi$
$311$	−17.1273			−0.971203			−0.485601	+	0.874180i	$0.661399\pi$
$312$	−24.4974	−	13.3853i	−1.38689	−	0.757791i
$313$	−28.9822			−1.63817			−0.819086	−	0.573670i	$-0.805519\pi$
$313$	−28.9822			−1.63817			−0.819086	+	0.573670i	$0.805519\pi$
$314$		−	22.4511i		−	1.26699i
$315$	62.6723			3.53118
$316$	−0.0820438			−0.00461532
$317$			6.22426i			0.349590i	0.984605	+	0.174795i	$0.0559262\pi$
$317$			6.22426i			0.349590i	−0.984605	+	0.174795i	$0.944074\pi$
$318$			34.5410i			1.93697i
$319$			0.383577i			0.0214762i
$320$		−	20.1090i		−	1.12413i
$321$	8.24751			0.460331
$322$	56.2146			3.13272
$323$			5.96997i			0.332178i
$324$	0.0306309			0.00170172
$325$	3.20118	−	5.85872i	0.177569	−	0.324983i
$326$	3.63552			0.201353
$327$			55.5720i			3.07314i
$328$	4.32467			0.238790
$329$	−0.956844			−0.0527525
$330$			0.574577i			0.0316294i
$331$			5.28437i			0.290455i	0.989398	+	0.145228i	$0.0463915\pi$
$331$			5.28437i			0.290455i	−0.989398	+	0.145228i	$0.953609\pi$
$332$			0.129503i			0.00710740i
$333$		−	32.3497i		−	1.77275i
$334$	−14.2918			−0.782012
$335$	3.93475			0.214978
$336$		−	57.7786i		−	3.15208i
$337$	−7.23845			−0.394304			−0.197152	−	0.980373i	$-0.563169\pi$
$337$	−7.23845			−0.394304			−0.197152	+	0.980373i	$0.563169\pi$
$338$	−15.7554	+	10.1133i	−0.856983	+	0.550089i
$339$	−2.58528			−0.140413
$340$			0.984462i			0.0533899i
$341$	−0.0546038			−0.00295696
$342$	−8.10988			−0.438532
$343$			54.7930i			2.95855i
$344$			8.39439i			0.452595i
$345$			57.0800i			3.07308i
$346$			29.3122i			1.57583i
$347$	33.0880			1.77626			0.888128	−	0.459597i	$-0.152006\pi$
$347$	33.0880			1.77626			0.888128	+	0.459597i	$0.152006\pi$
$348$	−1.45172			−0.0778204
$349$			6.94086i			0.371536i	0.982594	+	0.185768i	$0.0594772\pi$
$349$			6.94086i			0.371536i	−0.982594	+	0.185768i	$0.940523\pi$
$350$	13.3243			0.712211
$351$	8.64711	−	15.8257i	0.461549	−	0.844715i
$352$	0.0228565			0.00121825
$353$			30.0813i			1.60107i	0.599288	+	0.800534i	$0.295450\pi$
$353$			30.0813i			1.60107i	−0.599288	+	0.800534i	$0.704550\pi$
$354$	−11.7146			−0.622624
$355$	3.77026			0.200105
$356$			0.174717i			0.00925999i
$357$		−	70.8539i		−	3.74999i
$358$		−	6.99598i		−	0.369749i
$359$			3.73997i			0.197388i	0.995118	+	0.0986940i	$0.0314665\pi$
$359$			3.73997i			0.197388i	−0.995118	+	0.0986940i	$0.968534\pi$
$360$	34.7902			1.83361
$361$	17.6190			0.927314
$362$		−	9.83152i		−	0.516733i
$363$	−30.6969			−1.61117
$364$	−1.17044	−	0.639525i	−0.0613478	−	0.0335202i
$365$	36.5282			1.91197
$366$			23.9741i			1.25315i
$367$	4.57778			0.238958			0.119479	−	0.992837i	$-0.461878\pi$
$367$	4.57778			0.238958			0.119479	+	0.992837i	$0.461878\pi$
$368$	32.3622			1.68700
$369$			7.47135i			0.388943i
$370$		−	25.4491i		−	1.32304i
$371$		−	42.9321i		−	2.22892i
$372$		−	0.206658i		−	0.0107147i
$373$	−11.9473			−0.618607			−0.309303	−	0.950963i	$-0.600096\pi$
$373$	−11.9473			−0.618607			−0.309303	+	0.950963i	$0.600096\pi$
$374$	0.399484			0.0206568
$375$		−	23.0038i		−	1.18791i
$376$	−0.531157			−0.0273923
$377$	12.1445	−	22.2266i	0.625475	−	1.14473i
$378$	35.9919			1.85122
$379$		−	0.620093i		−	0.0318521i	−0.999873	−	0.0159260i	$-0.994930\pi$
$379$		−	0.620093i		−	0.0318521i	0.999873	−	0.0159260i	$-0.00506963\pi$
$380$	−0.227737			−0.0116827
$381$	−45.5539			−2.33380
$382$			19.8842i			1.01737i
$383$		−	27.8945i		−	1.42534i	−0.701498	−	0.712671i	$-0.747485\pi$
$383$		−	27.8945i		−	1.42534i	0.701498	−	0.712671i	$-0.252515\pi$
$384$		−	33.2201i		−	1.69525i
$385$		−	0.714160i		−	0.0363969i
$386$	−12.8485			−0.653972
$387$	−14.5023			−0.737191
$388$		−	0.898459i		−	0.0456123i
$389$	12.8614			0.652097			0.326048	−	0.945353i	$-0.394283\pi$
$389$	12.8614			0.652097			0.326048	+	0.945353i	$0.394283\pi$
$390$	18.1918	−	33.2942i	0.921178	−	1.68592i
$391$	39.6858			2.00699
$392$			49.8321i			2.51690i
$393$	−42.3424			−2.13589
$394$	11.7194			0.590417
$395$			2.90075i			0.145953i
$396$			0.0193713i			0.000973443i
$397$			24.6396i			1.23663i	0.785931	+	0.618314i	$0.212184\pi$
$397$			24.6396i			1.23663i	−0.785931	+	0.618314i	$0.787816\pi$
$398$		−	17.9933i		−	0.901922i
$399$	16.3907			0.820564
$400$	7.67064			0.383532
$401$		−	20.3020i		−	1.01383i	−0.861995	−	0.506917i	$-0.830785\pi$
$401$		−	20.3020i		−	1.01383i	0.861995	−	0.506917i	$-0.169215\pi$
$402$	6.04293			0.301394
$403$	3.16404	+	1.72882i	0.157612	+	0.0861187i
$404$	−0.859744			−0.0427739
$405$		−	1.08299i		−	0.0538143i
$406$	50.5491			2.50871
$407$	−0.368629			−0.0182723
$408$		−	39.3319i		−	1.94722i
$409$			7.67595i			0.379551i	0.981827	+	0.189776i	$0.0607761\pi$
$409$			7.67595i			0.379551i	−0.981827	+	0.189776i	$0.939224\pi$
$410$			5.87762i			0.290275i
$411$		−	32.0667i		−	1.58174i
$412$	0.941997			0.0464089
$413$	14.5604			0.716472
$414$			53.9110i			2.64958i
$415$	4.57873			0.224761
$416$	−1.32443	−	0.723664i	−0.0649356	−	0.0354805i
$417$	18.5569			0.908736
$418$			0.0924132i			0.00452008i
$419$	−24.4074			−1.19238			−0.596189	−	0.802844i	$-0.703319\pi$
$419$	−24.4074			−1.19238			−0.596189	+	0.802844i	$0.703319\pi$
$420$	2.70287			0.131887
$421$		−	7.83588i		−	0.381898i	−0.981600	−	0.190949i	$-0.938844\pi$
$421$		−	7.83588i		−	0.381898i	0.981600	−	0.190949i	$-0.0611564\pi$
$422$			30.0431i			1.46248i
$423$		−	0.917633i		−	0.0446169i
$424$		−	23.8322i		−	1.15739i
$425$	9.40651			0.456283
$426$	5.79031			0.280541
$427$		−	29.7982i		−	1.44203i
$428$	0.218744			0.0105734
$429$	−0.482265	−	0.263507i	−0.0232840	−	0.0127223i
$430$	−11.4088			−0.550179
$431$		−	7.77841i		−	0.374673i	−0.982296	−	0.187337i	$-0.940015\pi$
$431$		−	7.77841i		−	0.374673i	0.982296	−	0.187337i	$-0.0599855\pi$
$432$	20.7202			0.996899
$433$	26.6655			1.28146			0.640732	−	0.767765i	$-0.278631\pi$
$433$	26.6655			1.28146			0.640732	+	0.767765i	$0.278631\pi$
$434$			7.19586i			0.345413i
$435$			51.3273i			2.46096i
$436$			1.47390i			0.0705871i
$437$			9.18057i			0.439166i
$438$	56.0995			2.68054
$439$	14.4283			0.688626			0.344313	−	0.938855i	$-0.388112\pi$
$439$	14.4283			0.688626			0.344313	+	0.938855i	$0.388112\pi$
$440$		−	0.396439i		−	0.0188995i
$441$	−86.0906			−4.09955
$442$	−23.1483	−	12.6481i	−1.10105	−	0.601610i
$443$	5.19341			0.246746			0.123373	−	0.992360i	$-0.460629\pi$
$443$	5.19341			0.246746			0.123373	+	0.992360i	$0.460629\pi$
$444$		−	1.39515i		−	0.0662108i
$445$	6.17733			0.292834
$446$	−26.8699			−1.27233
$447$		−	3.79047i		−	0.179283i
$448$			38.3856i			1.81355i
$449$		−	14.9729i		−	0.706615i	−0.935507	−	0.353308i	$-0.885057\pi$
$449$		−	14.9729i		−	0.706615i	0.935507	−	0.353308i	$-0.114943\pi$
$450$			12.7782i			0.602372i
$451$	0.0851371			0.00400895
$452$	−0.0685677			−0.00322516
$453$			34.7391i			1.63218i
$454$	−40.3120			−1.89194
$455$	−22.6112	+	41.3824i	−1.06003	+	1.94004i
$456$	9.09872			0.426087
$457$			42.0543i			1.96722i	0.180316	+	0.983609i	$0.442288\pi$
$457$			42.0543i			1.96722i	−0.180316	+	0.983609i	$0.557712\pi$
$458$	13.2630			0.619738
$459$	25.4091			1.18600
$460$			1.51390i			0.0705858i
$461$			9.31370i			0.433782i	0.976196	+	0.216891i	$0.0695917\pi$
$461$			9.31370i			0.433782i	−0.976196	+	0.216891i	$0.930408\pi$
$462$		−	1.09680i		−	0.0510275i
$463$		−	10.3203i		−	0.479625i	−0.970819	−	0.239813i	$-0.922914\pi$
$463$		−	10.3203i		−	0.479625i	0.970819	−	0.239813i	$-0.0770860\pi$
$464$	29.1006			1.35096
$465$	−7.30664			−0.338838
$466$		−	28.1318i		−	1.30318i
$467$	−0.661824			−0.0306255			−0.0153128	−	0.999883i	$-0.504874\pi$
$467$	−0.661824			−0.0306255			−0.0153128	+	0.999883i	$0.504874\pi$
$468$	0.613318	−	1.12248i	0.0283506	−	0.0518866i
$469$	−7.51094			−0.346823
$470$		−	0.721891i		−	0.0332984i
$471$	−43.5161			−2.00512
$472$	8.08269			0.372036
$473$			0.165255i			0.00759844i
$474$			4.45493i			0.204622i
$475$			2.17602i			0.0998428i
$476$		−	1.87921i		−	0.0861336i
$477$	41.1728			1.88517
$478$	−24.3813			−1.11518
$479$			3.63440i			0.166060i	0.996547	+	0.0830300i	$0.0264597\pi$
$479$			3.63440i			0.166060i	−0.996547	+	0.0830300i	$0.973540\pi$
$480$	3.05847			0.139600
$481$	21.3604	+	11.6712i	0.973952	+	0.532163i
$482$	−21.0353			−0.958131
$483$		−	108.959i		−	4.95778i
$484$	−0.814156			−0.0370071
$485$	−31.7661			−1.44242
$486$		−	23.2730i		−	1.05569i
$487$		−	31.1232i		−	1.41033i	−0.709045	−	0.705163i	$-0.750874\pi$
$487$		−	31.1232i		−	1.41033i	0.709045	−	0.705163i	$-0.249126\pi$
$488$		−	16.5413i		−	0.748792i
$489$		−	7.04659i		−	0.318658i
$490$	−67.7265			−3.05957
$491$	17.9607			0.810555			0.405277	−	0.914194i	$-0.367175\pi$
$491$	17.9607			0.810555			0.405277	+	0.914194i	$0.367175\pi$
$492$			0.322217i			0.0145267i
$493$	35.6861			1.60722
$494$	2.92591	−	5.35493i	0.131643	−	0.240930i
$495$	0.684894			0.0307837
$496$			4.14259i			0.186008i
$497$	−7.19695			−0.322827
$498$	7.03194			0.315109
$499$			8.12403i			0.363681i	0.983328	+	0.181841i	$0.0582055\pi$
$499$			8.12403i			0.363681i	−0.983328	+	0.181841i	$0.941794\pi$
$500$		−	0.610116i		−	0.0272852i
$501$			27.7012i			1.23760i
$502$			41.6537i			1.85910i
$503$	−38.6811			−1.72471			−0.862354	−	0.506307i	$-0.831010\pi$
$503$	−38.6811			−1.72471			−0.862354	+	0.506307i	$0.831010\pi$
$504$	−66.4102			−2.95814
$505$			30.3973i			1.35266i
$506$	0.614323			0.0273100
$507$	19.6021	+	30.5382i	0.870561	+	1.35625i
$508$	−1.20820			−0.0536051
$509$		−	16.1272i		−	0.714826i	−0.933946	−	0.357413i	$-0.883659\pi$
$509$		−	16.1272i		−	0.714826i	0.933946	−	0.357413i	$-0.116341\pi$
$510$	53.4558			2.36706
$511$	−69.7278			−3.08458
$512$			21.2464i			0.938967i
$513$			5.87794i			0.259517i
$514$			28.0173i			1.23579i
$515$		−	33.3054i		−	1.46761i
$516$	−0.625439			−0.0275334
$517$	−0.0104566			−0.000459879
$518$			48.5792i			2.13445i
$519$	56.8147			2.49389
$520$	−12.5517	+	22.9719i	−0.550431	+	1.00738i
$521$	5.58342			0.244614			0.122307	−	0.992492i	$-0.460971\pi$
$521$	5.58342			0.244614			0.122307	+	0.992492i	$0.460971\pi$
$522$			48.4776i			2.12181i
$523$	−24.8140			−1.08504			−0.542520	−	0.840043i	$-0.682530\pi$
$523$	−24.8140			−1.08504			−0.542520	+	0.840043i	$0.682530\pi$
$524$	−1.12302			−0.0490594
$525$		−	25.8259i		−	1.12713i
$526$		−	29.1358i		−	1.27038i
$527$			5.08006i			0.221291i
$528$		−	0.631414i		−	0.0274788i
$529$	38.0284			1.65341
$530$	32.3901			1.40694
$531$			13.9638i			0.605976i
$532$	0.434721			0.0188476
$533$	−4.93331	−	2.69554i	−0.213686	−	0.116757i
$534$	9.48705			0.410545
$535$		−	7.73394i		−	0.334367i
$536$	−4.16942			−0.180092
$537$	−13.5600			−0.585159
$538$			11.9593i			0.515602i
$539$			0.981014i			0.0422553i
$540$			0.969285i			0.0417114i
$541$		−	30.2928i		−	1.30239i	−0.758911	−	0.651195i	$-0.774268\pi$
$541$		−	30.2928i		−	1.30239i	0.758911	−	0.651195i	$-0.225732\pi$
$542$	21.2402			0.912344
$543$	−19.0560			−0.817773
$544$		−	2.12645i		−	0.0911709i
$545$	52.1115			2.23221
$546$	−34.7259	+	63.5544i	−1.48613	+	2.71988i
$547$	−0.782832			−0.0334715			−0.0167357	−	0.999860i	$-0.505327\pi$
$547$	−0.782832			−0.0334715			−0.0167357	+	0.999860i	$0.505327\pi$
$548$		−	0.850485i		−	0.0363309i
$549$	28.5770			1.21964
$550$	0.145610			0.00620882
$551$			8.25532i			0.351688i
$552$		−	60.4843i		−	2.57438i
$553$		−	5.53717i		−	0.235465i
$554$			22.2111i			0.943659i
$555$	−49.3271			−2.09382
$556$	0.492173			0.0208728
$557$		−	12.1105i		−	0.513140i	−0.966526	−	0.256570i	$-0.917408\pi$
$557$		−	12.1105i		−	0.513140i	0.966526	−	0.256570i	$-0.0825924\pi$
$558$	−6.90098			−0.292142
$559$	5.23218	−	9.57580i	0.221298	−	0.405013i
$560$	−54.1807			−2.28955
$561$		−	0.774304i		−	0.0326911i
$562$	−24.8563			−1.04850
$563$	11.9218			0.502446			0.251223	−	0.967929i	$-0.419167\pi$
$563$	11.9218			0.502446			0.251223	+	0.967929i	$0.419167\pi$
$564$		−	0.0395748i		−	0.00166640i
$565$			2.42429i			0.101991i
$566$		−	17.6030i		−	0.739908i
$567$			2.06730i			0.0868183i
$568$	−3.99512			−0.167632
$569$	−14.4513			−0.605831			−0.302916	−	0.953017i	$-0.597960\pi$
$569$	−14.4513			−0.605831			−0.302916	+	0.953017i	$0.597960\pi$
$570$			12.3660i			0.517955i
$571$	−22.3002			−0.933233			−0.466616	−	0.884460i	$-0.654527\pi$
$571$	−22.3002			−0.933233			−0.466616	+	0.884460i	$0.654527\pi$
$572$	−0.0127908	−	0.00698884i	−0.000534810	−	0.000292218i
$573$	38.5408			1.61007
$574$		−	11.2196i		−	0.468299i
$575$	14.4653			0.603243
$576$	−36.8126			−1.53386
$577$		−	34.1283i		−	1.42078i	−0.703808	−	0.710390i	$-0.748519\pi$
$577$		−	34.1283i		−	1.42078i	0.703808	−	0.710390i	$-0.251481\pi$
$578$		−	12.6834i		−	0.527559i
$579$			24.9038i			1.03497i
$580$			1.36132i			0.0565258i
$581$	−8.74022			−0.362605
$582$	−48.7858			−2.02224
$583$		−	0.469169i		−	0.0194310i
$584$	−38.7068			−1.60170
$585$	−39.6865	−	21.6846i	−1.64084	−	0.896546i
$586$	16.6360			0.687227
$587$		−	17.1675i		−	0.708579i	−0.935136	−	0.354290i	$-0.884723\pi$
$587$		−	17.1675i		−	0.708579i	0.935136	−	0.354290i	$-0.115277\pi$
$588$	−3.71283			−0.153115
$589$	−1.17518			−0.0484224
$590$			10.9851i			0.452251i
$591$		−	22.7153i		−	0.934384i
$592$			27.9666i			1.14942i
$593$		−	23.3023i		−	0.956909i	−0.878112	−	0.478455i	$-0.841197\pi$
$593$		−	23.3023i		−	0.956909i	0.878112	−	0.478455i	$-0.158803\pi$
$594$	0.393325			0.0161383
$595$	−66.4418			−2.72385
$596$		−	0.100532i		−	0.00411796i
$597$	−34.8757			−1.42737
$598$	−35.5973	−	19.4502i	−1.45568	−	0.795378i
$599$	−12.7509			−0.520986			−0.260493	−	0.965476i	$-0.583885\pi$
$599$	−12.7509			−0.520986			−0.260493	+	0.965476i	$0.583885\pi$
$600$		−	14.3363i		−	0.585277i
$601$	21.0313			0.857886			0.428943	−	0.903332i	$-0.358886\pi$
$601$	21.0313			0.857886			0.428943	+	0.903332i	$0.358886\pi$
$602$	21.7779			0.887600
$603$		−	7.20315i		−	0.293335i
$604$			0.921363i			0.0374897i
$605$			28.7854i			1.17029i
$606$			46.6837i			1.89639i
$607$	−28.5285			−1.15793			−0.578967	−	0.815351i	$-0.696544\pi$
$607$	−28.5285			−1.15793			−0.578967	+	0.815351i	$0.696544\pi$
$608$	0.491915			0.0199498
$609$		−	97.9773i		−	3.97024i
$610$	22.4812			0.910238
$611$	0.605911	+	0.331067i	0.0245125	+	0.0133935i
$612$	1.80220			0.0728498
$613$			20.0076i			0.808099i	0.914737	+	0.404050i	$0.132398\pi$
$613$			20.0076i			0.808099i	−0.914737	+	0.404050i	$0.867602\pi$
$614$	31.8599			1.28576
$615$	11.3924			0.459385
$616$			0.756753i			0.0304904i
$617$			5.04682i			0.203177i	0.994826	+	0.101589i	$0.0323926\pi$
$617$			5.04682i			0.203177i	−0.994826	+	0.101589i	$0.967607\pi$
$618$		−	51.1500i		−	2.05755i
$619$		−	27.5782i		−	1.10846i	−0.832363	−	0.554231i	$-0.813013\pi$
$619$		−	27.5782i		−	1.10846i	0.832363	−	0.554231i	$-0.186987\pi$
$620$	−0.193789			−0.00778277
$621$	39.0740			1.56798
$622$			24.6660i			0.989015i
$623$	−11.7917			−0.472426
$624$	−19.9913	+	36.5876i	−0.800294	+	1.46468i
$625$	−30.8296			−1.23319
$626$			41.7388i			1.66822i
$627$	0.179121			0.00715340
$628$	−1.15415			−0.0460556
$629$			34.2954i			1.36745i
$630$		−	90.2576i		−	3.59595i
$631$			46.3626i			1.84566i	0.385202	+	0.922832i	$0.374132\pi$
$631$			46.3626i			1.84566i	−0.385202	+	0.922832i	$0.625868\pi$
$632$		−	3.07376i		−	0.122268i
$633$	58.2314			2.31449
$634$	8.96388			0.356001
$635$			42.7172i			1.69518i
$636$	1.77566			0.0704095
$637$	31.0601	−	56.8454i	1.23065	−	2.25230i
$638$	0.552409			0.0218701
$639$		−	6.90202i		−	0.273040i
$640$	−31.1514			−1.23137
$641$	16.3261			0.644843			0.322422	−	0.946596i	$-0.395503\pi$
$641$	16.3261			0.644843			0.322422	+	0.946596i	$0.395503\pi$
$642$		−	11.8777i		−	0.468774i
$643$		−	6.80196i		−	0.268243i	−0.990965	−	0.134122i	$-0.957179\pi$
$643$		−	6.80196i		−	0.268243i	0.990965	−	0.134122i	$-0.0428213\pi$
$644$		−	2.88984i		−	0.113876i
$645$			22.1131i			0.870704i
$646$	8.59766			0.338270
$647$	−12.7863			−0.502681			−0.251340	−	0.967899i	$-0.580871\pi$
$647$	−12.7863			−0.502681			−0.251340	+	0.967899i	$0.580871\pi$
$648$			1.14758i			0.0450813i
$649$	0.159119			0.00624597
$650$	−8.43744	−	4.61018i	−0.330944	−	0.180826i
$651$	13.9475			0.546644
$652$		−	0.186892i		−	0.00731926i
$653$	31.3311			1.22608			0.613041	−	0.790051i	$-0.289946\pi$
$653$	31.3311			1.22608			0.613041	+	0.790051i	$0.289946\pi$
$654$	80.0321			3.12950
$655$			39.7057i			1.55143i
$656$		−	6.45904i		−	0.252183i
$657$		−	66.8704i		−	2.60886i
$658$			1.37800i			0.0537200i
$659$	−18.7431			−0.730127			−0.365064	−	0.930983i	$-0.618953\pi$
$659$	−18.7431			−0.730127			−0.365064	+	0.930983i	$0.618953\pi$
$660$	0.0295374			0.00114974
$661$			13.7249i			0.533836i	0.963719	+	0.266918i	$0.0860053\pi$
$661$			13.7249i			0.533836i	−0.963719	+	0.266918i	$0.913995\pi$
$662$	7.61029			0.295782
$663$	−24.5154	+	44.8675i	−0.952099	+	1.74251i
$664$	−4.85181			−0.188287
$665$		−	15.3701i		−	0.596026i
$666$	−46.5885			−1.80527
$667$	54.8778			2.12488
$668$			0.734702i			0.0284265i
$669$			52.0810i			2.01357i
$670$		−	5.66663i		−	0.218921i
$671$		−	0.325639i		−	0.0125712i
$672$	−5.83824			−0.225215
$673$	15.0786			0.581237			0.290619	−	0.956839i	$-0.406139\pi$
$673$	15.0786			0.581237			0.290619	+	0.956839i	$0.406139\pi$
$674$			10.4245i			0.401535i
$675$	9.26150			0.356475
$676$	0.519895	+	0.809944i	0.0199960	+	0.0311517i
$677$	−26.8652			−1.03251			−0.516257	−	0.856434i	$-0.672675\pi$
$677$	−26.8652			−1.03251			−0.516257	+	0.856434i	$0.672675\pi$
$678$			3.72319i			0.142988i
$679$	60.6374			2.32705
$680$	−36.8827			−1.41439
$681$			78.1352i			2.99415i
$682$			0.0786376i			0.00301119i
$683$		−	10.6702i		−	0.408285i	−0.978941	−	0.204143i	$-0.934559\pi$
$683$		−	10.6702i		−	0.408285i	0.978941	−	0.204143i	$-0.0654406\pi$
$684$			0.416907i			0.0159408i
$685$	−30.0699			−1.14891
$686$	78.9102			3.01281
$687$		−	25.7071i		−	0.980787i
$688$	12.5373			0.477980
$689$	−14.8545	+	27.1863i	−0.565910	+	1.03571i
$690$	82.2038			3.12945
$691$			0.654117i			0.0248838i	0.999923	+	0.0124419i	$0.00396048\pi$
$691$			0.654117i			0.0248838i	−0.999923	+	0.0124419i	$0.996040\pi$
$692$	1.50686			0.0572822
$693$	−1.30738			−0.0496631
$694$		−	47.6517i		−	1.80883i
$695$		−	17.4014i		−	0.660071i
$696$		−	54.3885i		−	2.06159i
$697$		−	7.92072i		−	0.300019i
$698$	9.99588			0.378350
$699$	−54.5267			−2.06239
$700$		−	0.684964i		−	0.0258892i
$701$	20.2045			0.763112			0.381556	−	0.924346i	$-0.375388\pi$
$701$	20.2045			0.763112			0.381556	+	0.924346i	$0.375388\pi$
$702$	−22.7914	−	12.4531i	−0.860208	−	0.470014i
$703$	−7.93361			−0.299222
$704$			0.419485i			0.0158099i
$705$	−1.39921			−0.0526974
$706$	43.3216			1.63043
$707$		−	58.0246i		−	2.18224i
$708$			0.602216i			0.0226327i
$709$			48.7025i			1.82906i	0.404518	+	0.914530i	$0.367439\pi$
$709$			48.7025i			1.82906i	−0.404518	+	0.914530i	$0.632561\pi$
$710$		−	5.42974i		−	0.203775i
$711$	5.31026			0.199150
$712$	−6.54575			−0.245313
$713$			7.81207i			0.292564i
$714$	−102.040			−3.81876
$715$	−0.247099	+	0.452234i	−0.00924096	+	0.0169126i
$716$	−0.359644			−0.0134405
$717$			47.2574i			1.76486i
$718$	5.38612			0.201008
$719$	16.7247			0.623725			0.311862	−	0.950127i	$-0.399047\pi$
$719$	16.7247			0.623725			0.311862	+	0.950127i	$0.399047\pi$
$720$		−	51.9604i		−	1.93645i
$721$			63.5758i			2.36769i
$722$		−	25.3740i		−	0.944321i
$723$			40.7719i			1.51632i
$724$	−0.505411			−0.0187835
$725$	13.0074			0.483083
$726$			44.2082i			1.64072i
$727$	−20.1667			−0.747940			−0.373970	−	0.927441i	$-0.622004\pi$
$727$	−20.1667			−0.747940			−0.373970	+	0.927441i	$0.622004\pi$
$728$	23.9597	−	43.8505i	0.888006	−	1.62521i
$729$	−43.8680			−1.62474
$730$		−	52.6062i		−	1.94704i
$731$	15.3745			0.568647
$732$	1.23244			0.0455524
$733$		−	6.69141i		−	0.247153i	−0.992335	−	0.123576i	$-0.960564\pi$
$733$		−	6.69141i		−	0.247153i	0.992335	−	0.123576i	$-0.0394364\pi$
$734$		−	6.59270i		−	0.243341i
$735$			131.272i			4.84203i
$736$		−	3.27004i		−	0.120535i
$737$	−0.0820809			−0.00302349
$738$	10.7599			0.396076
$739$		−	14.7948i		−	0.544235i	−0.962264	−	0.272118i	$-0.912276\pi$
$739$		−	14.7948i		−	0.544235i	0.962264	−	0.272118i	$-0.0877240\pi$
$740$	−1.30827			−0.0480930
$741$	−10.3793	−	5.67118i	−0.381292	−	0.208336i
$742$	−61.8287			−2.26980
$743$		−	12.2435i		−	0.449170i	−0.974455	−	0.224585i	$-0.927897\pi$
$743$		−	12.2435i		−	0.449170i	0.974455	−	0.224585i	$-0.0721026\pi$
$744$	7.74242			0.283851
$745$	−3.55444			−0.130224
$746$			17.2059i			0.629952i
$747$		−	8.38205i		−	0.306683i
$748$		−	0.0205364i		−	0.000750884i
$749$			14.7631i			0.539432i
$750$	−33.1290			−1.20970
$751$	22.4866			0.820548			0.410274	−	0.911962i	$-0.365433\pi$
$751$	22.4866			0.820548			0.410274	+	0.911962i	$0.365433\pi$
$752$			0.793301i			0.0289287i
$753$	80.7358			2.94218
$754$	−32.0096	−	17.4899i	−1.16572	−	0.636946i
$755$	32.5759			1.18556
$756$		−	1.85024i		−	0.0672927i
$757$	3.82393			0.138983			0.0694915	−	0.997583i	$-0.477862\pi$
$757$	3.82393			0.138983			0.0694915	+	0.997583i	$0.477862\pi$
$758$	−0.893028			−0.0324362
$759$		−	1.19072i		−	0.0432203i
$760$		−	8.53214i		−	0.309493i
$761$		−	33.7254i		−	1.22254i	−0.791420	−	0.611272i	$-0.790658\pi$
$761$		−	33.7254i		−	1.22254i	0.791420	−	0.611272i	$-0.209342\pi$
$762$			65.6045i			2.37660i
$763$	−99.4743			−3.60121
$764$	1.02219			0.0369817
$765$		−	63.7190i		−	2.30377i
$766$	−40.1723			−1.45148
$767$	−9.22024	−	5.03790i	−0.332923	−	0.181908i
$768$	−4.95308			−0.178729
$769$			12.5287i			0.451795i	0.974151	+	0.225897i	$0.0725314\pi$
$769$			12.5287i			0.451795i	−0.974151	+	0.225897i	$0.927469\pi$
$770$	−1.02850			−0.0370645
$771$	54.3048			1.95574
$772$			0.660507i			0.0237722i
$773$			23.6248i			0.849723i	0.905258	+	0.424862i	$0.139677\pi$
$773$			23.6248i			0.849723i	−0.905258	+	0.424862i	$0.860323\pi$
$774$			20.8854i			0.750711i
$775$			1.85165i			0.0665134i
$776$	33.6606			1.20835
$777$	94.1592			3.37794
$778$		−	18.5223i		−	0.664056i
$779$	1.83231			0.0656494
$780$	−1.71156	−	0.935191i	−0.0612838	−	0.0334852i
$781$	−0.0786495			−0.00281430
$782$		−	57.1535i		−	2.04380i
$783$	35.1359			1.25566
$784$	74.4260			2.65807
$785$			40.8063i			1.45644i
$786$			60.9794i			2.17506i
$787$		−	1.20685i		−	0.0430194i	−0.999769	−	0.0215097i	$-0.993153\pi$
$787$		−	1.20685i		−	0.0430194i	0.999769	−	0.0215097i	$-0.00684729\pi$
$788$		−	0.602464i		−	0.0214619i
$789$	−56.4727			−2.01048
$790$	4.17752			0.148630
$791$		−	4.62767i		−	0.164541i
$792$	−0.725742			−0.0257881
$793$	−10.3101	+	18.8694i	−0.366124	+	0.670070i
$794$	35.4848			1.25931
$795$		−	62.7806i		−	2.22660i
$796$	−0.924985			−0.0327852
$797$	−28.1207			−0.996085			−0.498042	−	0.867153i	$-0.665948\pi$
$797$	−28.1207			−0.996085			−0.498042	+	0.867153i	$0.665948\pi$
$798$		−	23.6051i		−	0.835613i
$799$			0.972825i			0.0344161i
$800$		−	0.775081i		−	0.0274032i
$801$		−	11.3085i		−	0.399567i
$802$	−29.2380			−1.03243
$803$	−0.761997			−0.0268903
$804$		−	0.310650i		−	0.0109558i
$805$	−102.174			−3.60115
$806$	2.48976	−	4.55670i	0.0876981	−	0.160503i
$807$	23.1802			0.815983
$808$		−	32.2102i		−	1.13315i
$809$	−32.4182			−1.13976			−0.569881	−	0.821727i	$-0.693011\pi$
$809$	−32.4182			−1.13976			−0.569881	+	0.821727i	$0.693011\pi$
$810$	−1.55967			−0.0548013
$811$			15.1013i			0.530279i	0.964210	+	0.265139i	$0.0854180\pi$
$811$			15.1013i			0.530279i	−0.964210	+	0.265139i	$0.914582\pi$
$812$		−	2.59859i		−	0.0911926i
$813$		−	41.1690i		−	1.44386i
$814$			0.530882i			0.0186074i
$815$	−6.60779			−0.231461
$816$	−58.7436			−2.05644
$817$			3.55661i			0.124430i
$818$	11.0545			0.386513
$819$	75.7566	+	41.3931i	2.64715	+	1.44639i
$820$	0.302153			0.0105516
$821$			7.53751i			0.263061i	0.991312	+	0.131531i	$0.0419891\pi$
$821$			7.53751i			0.263061i	−0.991312	+	0.131531i	$0.958011\pi$
$822$	−46.1809			−1.61074
$823$	−20.7098			−0.721897			−0.360949	−	0.932586i	$-0.617547\pi$
$823$	−20.7098			−0.721897			−0.360949	+	0.932586i	$0.617547\pi$
$824$			35.2918i			1.22945i
$825$		−	0.282230i		−	0.00982598i
$826$		−	20.9692i		−	0.729613i
$827$			22.6064i			0.786101i	0.919517	+	0.393051i	$0.128580\pi$
$827$			22.6064i			0.786101i	−0.919517	+	0.393051i	$0.871420\pi$
$828$	2.77141			0.0963133
$829$	50.3014			1.74704			0.873520	−	0.486789i	$-0.161832\pi$
$829$	50.3014			1.74704			0.873520	+	0.486789i	$0.161832\pi$
$830$		−	6.59406i		−	0.228883i
$831$	43.0509			1.49342
$832$	13.2814	−	24.3073i	0.460450	−	0.842703i
$833$	91.2686			3.16227
$834$		−	26.7247i		−	0.925402i
$835$	25.9763			0.898945
$836$	0.00475071			0.000164307
$837$			5.00174i			0.172885i
$838$			35.1503i			1.21425i
$839$		−	27.1797i		−	0.938346i	−0.883106	−	0.469173i	$-0.844552\pi$
$839$		−	27.1797i		−	0.938346i	0.883106	−	0.469173i	$-0.155448\pi$
$840$			101.263i			3.49389i
$841$	20.3470			0.701620
$842$	−11.2849			−0.388902
$843$			48.1779i			1.65934i
$844$	1.54443			0.0531616
$845$	28.6365	−	18.3815i	0.985126	−	0.632342i
$846$	−1.32153			−0.0454351
$847$		−	54.9478i		−	1.88803i
$848$	−35.5942			−1.22231
$849$	−34.1192			−1.17097
$850$		−	13.5468i		−	0.464651i
$851$			52.7392i			1.80788i
$852$		−	0.297664i		−	0.0101978i
$853$			7.69689i			0.263536i	0.991281	+	0.131768i	$0.0420655\pi$
$853$			7.69689i			0.263536i	−0.991281	+	0.131768i	$0.957935\pi$
$854$	−42.9138			−1.46848
$855$	14.7402			0.504105
$856$			8.19520i			0.280106i
$857$	−53.2084			−1.81756			−0.908782	−	0.417272i	$-0.862986\pi$
$857$	−53.2084			−1.81756			−0.908782	+	0.417272i	$0.862986\pi$
$858$	−0.379490	+	0.694534i	−0.0129556	+	0.0237110i
$859$	−28.0111			−0.955728			−0.477864	−	0.878434i	$-0.658589\pi$
$859$	−28.0111			−0.955728			−0.477864	+	0.878434i	$0.658589\pi$
$860$			0.586493i			0.0199992i
$861$	−21.7466			−0.741122
$862$	−11.2021			−0.381545
$863$			19.3779i			0.659630i	0.944046	+	0.329815i	$0.106986\pi$
$863$			19.3779i			0.659630i	−0.944046	+	0.329815i	$0.893014\pi$
$864$		−	2.09367i		−	0.0712281i
$865$		−	53.2768i		−	1.81146i
$866$		−	38.4024i		−	1.30497i
$867$	−24.5837			−0.834906
$868$	0.369920			0.0125559
$869$		−	0.0605112i		−	0.00205270i
$870$	73.9190			2.50609
$871$	4.75622	+	2.59878i	0.161158	+	0.0880563i
$872$	−55.2195			−1.86997
$873$			58.1525i			1.96817i
$874$	13.2214			0.447221
$875$	41.1770			1.39204
$876$		−	2.88392i		−	0.0974387i
$877$			6.54713i			0.221081i	0.993872	+	0.110540i	$0.0352582\pi$
$877$			6.54713i			0.221081i	−0.993872	+	0.110540i	$0.964742\pi$
$878$		−	20.7790i		−	0.701256i
$879$		−	32.2449i		−	1.08759i
$880$	−0.592096			−0.0199595
$881$	−50.1477			−1.68952			−0.844760	−	0.535145i	$-0.820257\pi$
$881$	−50.1477			−1.68952			−0.844760	+	0.535145i	$0.820257\pi$
$882$			123.983i			4.17474i
$883$	−6.21470			−0.209141			−0.104571	−	0.994517i	$-0.533347\pi$
$883$	−6.21470			−0.209141			−0.104571	+	0.994517i	$0.533347\pi$
$884$	−0.650206	+	1.18999i	−0.0218688	+	0.0400237i
$885$	21.2920			0.715724
$886$		−	7.47929i		−	0.251272i
$887$	−0.519213			−0.0174335			−0.00871673	−	0.999962i	$-0.502775\pi$
$887$	−0.519213			−0.0174335			−0.00871673	+	0.999962i	$0.502775\pi$
$888$	52.2690			1.75403
$889$		−	81.5418i		−	2.73482i
$890$		−	8.89629i		−	0.298204i
$891$			0.0225918i			0.000756853i
$892$			1.38131i			0.0462497i
$893$	−0.225045			−0.00753085
$894$	−5.45885			−0.182571
$895$			12.7156i			0.425037i
$896$	59.4641			1.98656
$897$	−37.6996	+	68.9968i	−1.25875	+	2.30374i
$898$	−21.5632			−0.719575
$899$			7.02474i			0.234288i
$900$	0.656894			0.0218965
$901$	−43.6492			−1.45416
$902$		−	0.122610i		−	0.00408247i
$903$		−	42.2112i		−	1.40470i
$904$		−	2.56888i		−	0.0854397i
$905$			17.8694i			0.593999i
$906$	50.0295			1.66212
$907$	−32.5497			−1.08079			−0.540397	−	0.841410i	$-0.681726\pi$
$907$	−32.5497			−1.08079			−0.540397	+	0.841410i	$0.681726\pi$
$908$			2.07233i			0.0687727i
$909$	55.6468			1.84569
$910$	59.5968	+	32.5635i	1.97562	+	1.07947i
$911$	12.1736			0.403331			0.201665	−	0.979454i	$-0.435365\pi$
$911$	12.1736			0.403331			0.201665	+	0.979454i	$0.435365\pi$
$912$		−	13.5892i		−	0.449985i
$913$	−0.0955146			−0.00316107
$914$	60.5645			2.00330
$915$		−	43.5745i		−	1.44053i
$916$		−	0.681813i		−	0.0225277i
$917$		−	75.7932i		−	2.50291i
$918$		−	36.5930i		−	1.20775i
$919$	33.3627			1.10053			0.550266	−	0.834989i	$-0.314526\pi$
$919$	33.3627			1.10053			0.550266	+	0.834989i	$0.314526\pi$
$920$	−56.7179			−1.86993
$921$		−	61.7528i		−	2.03482i
$922$	13.4131			0.441738
$923$	4.55739	+	2.49014i	0.150008	+	0.0819639i
$924$	−0.0563833			−0.00185487
$925$			12.5005i			0.411014i
$926$	−14.8628			−0.488422
$927$	−60.9706			−2.00254
$928$		−	2.94047i		−	0.0965258i
$929$		−	4.29919i		−	0.141052i	−0.997510	−	0.0705259i	$-0.977532\pi$
$929$		−	4.29919i		−	0.141052i	0.997510	−	0.0705259i	$-0.0224678\pi$
$930$			10.5227i			0.345052i
$931$			21.1133i			0.691961i
$932$	−1.44618			−0.0473711
$933$	47.8091			1.56520
$934$			0.953126i			0.0311872i
$935$	−0.726087			−0.0237456
$936$	42.0535	+	22.9779i	1.37456	+	0.751055i
$937$	48.4050			1.58132			0.790662	−	0.612253i	$-0.209737\pi$
$937$	48.4050			1.58132			0.790662	+	0.612253i	$0.209737\pi$
$938$			10.8169i			0.353184i
$939$	80.9006			2.64009
$940$	−0.0371105			−0.00121041
$941$		−	31.2320i		−	1.01813i	−0.860727	−	0.509067i	$-0.829990\pi$
$941$		−	31.2320i		−	1.01813i	0.860727	−	0.509067i	$-0.170010\pi$
$942$			62.6698i			2.04189i
$943$		−	12.1804i		−	0.396649i
$944$		−	12.0718i		−	0.392903i
$945$	−65.4175			−2.12803
$946$	0.237992			0.00773780
$947$		−	27.4625i		−	0.892410i	−0.894931	−	0.446205i	$-0.852775\pi$
$947$		−	27.4625i		−	0.892410i	0.894931	−	0.446205i	$-0.147225\pi$
$948$	0.229016			0.00743809
$949$	44.1543	+	24.1257i	1.43331	+	0.783155i
$950$	3.13380			0.101674
$951$		−	17.3743i		−	0.563401i
$952$	70.4044			2.28182
$953$	−39.5670			−1.28170			−0.640850	−	0.767666i	$-0.721418\pi$
$953$	−39.5670			−1.28170			−0.640850	+	0.767666i	$0.721418\pi$
$954$		−	59.2950i		−	1.91975i
$955$		−	36.1409i		−	1.16949i
$956$			1.25338i			0.0405371i
$957$		−	1.07071i		−	0.0346112i
$958$	5.23409			0.169106
$959$	57.3997			1.85353
$960$			56.1322i			1.81166i
$961$	−1.00000			−0.0322581
$962$	16.8084	−	30.7622i	0.541923	−	0.991814i
$963$	−14.1581			−0.456239
$964$			1.08137i			0.0348285i
$965$	23.3530			0.751760
$966$	−156.917			−5.04871
$967$			0.618915i			0.0199030i	0.999950	+	0.00995149i	$0.00316771\pi$
$967$			0.618915i			0.0199030i	−0.999950	+	0.00995149i	$0.996832\pi$
$968$		−	30.5022i		−	0.980379i
$969$		−	16.6645i		−	0.535341i
$970$			45.7479i			1.46888i
$971$	9.35978			0.300370			0.150185	−	0.988658i	$-0.452013\pi$
$971$	9.35978			0.300370			0.150185	+	0.988658i	$0.452013\pi$
$972$	−1.19640			−0.0383746
$973$			33.2170i			1.06489i
$974$	−44.8221			−1.43619
$975$	−8.93573	+	16.3540i	−0.286173	+	0.523746i
$976$	−24.7051			−0.790790
$977$		−	21.1557i		−	0.676830i	−0.940997	−	0.338415i	$-0.890109\pi$
$977$		−	21.1557i		−	0.676830i	0.940997	−	0.338415i	$-0.109891\pi$
$978$	−10.1481			−0.324502
$979$	−0.128862			−0.00411846
$980$			3.48163i			0.111217i
$981$		−	95.3979i		−	3.04582i
$982$		−	25.8661i		−	0.825421i
$983$			18.5493i			0.591630i	0.955245	+	0.295815i	$0.0955912\pi$
$983$			18.5493i			0.591630i	−0.955245	+	0.295815i	$0.904409\pi$
$984$	−12.0718			−0.384836
$985$	−21.3008			−0.678701
$986$		−	51.3933i		−	1.63670i
$987$	2.67092			0.0850164
$988$	−0.275283	−	0.150413i	−0.00875790	−	0.00478528i
$989$	23.6428			0.751797
$990$		−	0.986350i		−	0.0313483i
$991$	−32.6306			−1.03654			−0.518272	−	0.855216i	$-0.673425\pi$
$991$	−32.6306			−1.03654			−0.518272	+	0.855216i	$0.673425\pi$
$992$	0.418588			0.0132902
$993$		−	14.7507i		−	0.468100i
$994$			10.3647i			0.328748i
$995$			32.7039i			1.03678i
$996$		−	0.361493i		−	0.0114543i
$997$	−12.4748			−0.395082			−0.197541	−	0.980295i	$-0.563296\pi$
$997$	−12.4748			−0.395082			−0.197541	+	0.980295i	$0.563296\pi$
$998$	11.6998			0.370351
$999$			33.7667i			1.06833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.10	✓	32
13.5	odd	4		5239.2.a.l.1.4		16
13.8	odd	4		5239.2.a.k.1.13		16
13.12	even	2	inner	403.2.c.b.311.23	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.10	✓	32	1.1	even	1	trivial
403.2.c.b.311.23	yes	32	13.12	even	2	inner
5239.2.a.k.1.13		16	13.8	odd	4
5239.2.a.l.1.4		16	13.5	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +O(q^{10})\)	\(q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +3.76969 q^{10} -0.0546038i q^{11} +0.206658 q^{12} +(-1.72882 + 3.16404i) q^{13} -7.19586 q^{14} -7.30664i q^{15} -4.14259 q^{16} -5.08006 q^{17} -6.90098i q^{18} -1.17518i q^{19} -0.193789i q^{20} +13.9475i q^{21} -0.0786376 q^{22} -7.81207 q^{23} +7.74242i q^{24} -1.85165 q^{25} +(4.55670 + 2.48976i) q^{26} -5.00174 q^{27} +0.369920i q^{28} -7.02474 q^{29} -10.5227 q^{30} -1.00000i q^{31} +0.418588i q^{32} +0.152420i q^{33} +7.31605i q^{34} +13.0789 q^{35} -0.354761 q^{36} -6.75099i q^{37} -1.69243 q^{38} +(4.82581 - 8.83208i) q^{39} +7.26030 q^{40} +1.55918i q^{41} +20.0864 q^{42} -3.02644 q^{43} +0.00404255i q^{44} +12.5430i q^{45} +11.2506i q^{46} -0.191499i q^{47} +11.5636 q^{48} -17.9661 q^{49} +2.66666i q^{50} +14.1804 q^{51} +(0.127992 - 0.234248i) q^{52} +8.59226 q^{53} +7.20326i q^{54} +0.142929 q^{55} -13.8590 q^{56} +3.28038i q^{57} +10.1167i q^{58} +2.91407i q^{59} +0.540942i q^{60} +5.96368 q^{61} -1.44015 q^{62} -23.9430i q^{63} -7.68234 q^{64} +(-8.28210 - 4.52530i) q^{65} +0.219508 q^{66} -1.50321i q^{67} +0.376098 q^{68} +21.8065 q^{69} -18.8357i q^{70} -1.44037i q^{71} -13.2911i q^{72} -13.9550i q^{73} -9.72244 q^{74} +5.16869 q^{75} +0.0870034i q^{76} -0.272833 q^{77} +(-12.7195 - 6.94989i) q^{78} +1.10819 q^{79} -10.8435i q^{80} -0.413740 q^{81} +2.24545 q^{82} -1.74923i q^{83} -1.03259i q^{84} -13.2974i q^{85} +4.35854i q^{86} +19.6088 q^{87} -0.151453 q^{88} -2.35995i q^{89} +18.0638 q^{90} +(15.8095 + 8.63823i) q^{91} +0.578360 q^{92} +2.79139i q^{93} -0.275787 q^{94} +3.07611 q^{95} -1.16844i q^{96} +12.1357i q^{97} +25.8738i q^{98} -0.261653i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

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