LMFDB - Embedded newform 403.2.c.b.311.15

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			311.15
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.475674i q^{2} +0.345654 q^{3} +1.77373 q^{4} -0.161594i q^{5} -0.164419i q^{6} -4.07996i q^{7} -1.79507i q^{8} -2.88052 q^{9} +O(q^{10})$	\(q-0.475674i q^{2} +0.345654 q^{3} +1.77373 q^{4} -0.161594i q^{5} -0.164419i q^{6} -4.07996i q^{7} -1.79507i q^{8} -2.88052 q^{9} -0.0768661 q^{10} -3.77693i q^{11} +0.613099 q^{12} +(-3.57244 + 0.487542i) q^{13} -1.94073 q^{14} -0.0558557i q^{15} +2.69360 q^{16} +1.83266 q^{17} +1.37019i q^{18} +6.07852i q^{19} -0.286625i q^{20} -1.41025i q^{21} -1.79659 q^{22} +8.58551 q^{23} -0.620472i q^{24} +4.97389 q^{25} +(0.231911 + 1.69931i) q^{26} -2.03263 q^{27} -7.23676i q^{28} -5.21592 q^{29} -0.0265691 q^{30} +1.00000i q^{31} -4.87141i q^{32} -1.30551i q^{33} -0.871748i q^{34} -0.659297 q^{35} -5.10928 q^{36} +11.7559i q^{37} +2.89139 q^{38} +(-1.23483 + 0.168521i) q^{39} -0.290072 q^{40} -4.76311i q^{41} -0.670821 q^{42} +6.24514 q^{43} -6.69927i q^{44} +0.465476i q^{45} -4.08390i q^{46} +4.70897i q^{47} +0.931056 q^{48} -9.64605 q^{49} -2.36595i q^{50} +0.633467 q^{51} +(-6.33655 + 0.864769i) q^{52} +6.16063 q^{53} +0.966867i q^{54} -0.610330 q^{55} -7.32379 q^{56} +2.10107i q^{57} +2.48107i q^{58} -7.98069i q^{59} -0.0990732i q^{60} -4.52134 q^{61} +0.475674 q^{62} +11.7524i q^{63} +3.07001 q^{64} +(0.0787839 + 0.577285i) q^{65} -0.620998 q^{66} +7.69808i q^{67} +3.25065 q^{68} +2.96762 q^{69} +0.313610i q^{70} -7.77152i q^{71} +5.17073i q^{72} -4.96395i q^{73} +5.59197 q^{74} +1.71925 q^{75} +10.7817i q^{76} -15.4097 q^{77} +(0.0801609 + 0.587375i) q^{78} +8.26843 q^{79} -0.435271i q^{80} +7.93898 q^{81} -2.26569 q^{82} +12.1642i q^{83} -2.50142i q^{84} -0.296147i q^{85} -2.97065i q^{86} -1.80290 q^{87} -6.77984 q^{88} +3.17056i q^{89} +0.221415 q^{90} +(1.98915 + 14.5754i) q^{91} +15.2284 q^{92} +0.345654i q^{93} +2.23993 q^{94} +0.982253 q^{95} -1.68382i q^{96} +0.366185i q^{97} +4.58837i q^{98} +10.8795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.475674i		−	0.336352i	−0.985757	−	0.168176i	$-0.946212\pi$
$2$		−	0.475674i		−	0.336352i	0.985757	−	0.168176i	$-0.0537877\pi$
$3$	0.345654			0.199564			0.0997818	−	0.995009i	$-0.468186\pi$
$3$	0.345654			0.199564			0.0997818	+	0.995009i	$0.468186\pi$
$4$	1.77373			0.886867
$5$		−	0.161594i		−	0.0722671i	−0.999347	−	0.0361336i	$-0.988496\pi$
$5$		−	0.161594i		−	0.0722671i	0.999347	−	0.0361336i	$-0.0115042\pi$
$6$		−	0.164419i		−	0.0671236i
$7$		−	4.07996i		−	1.54208i	−0.636787	−	0.771039i	$-0.719737\pi$
$7$		−	4.07996i		−	1.54208i	0.636787	−	0.771039i	$-0.280263\pi$
$8$		−	1.79507i		−	0.634652i
$9$	−2.88052			−0.960174
$10$	−0.0768661			−0.0243072
$11$		−	3.77693i		−	1.13879i	−0.822065	−	0.569394i	$-0.807178\pi$
$11$		−	3.77693i		−	1.13879i	0.822065	−	0.569394i	$-0.192822\pi$
$12$	0.613099			0.176986
$13$	−3.57244	+	0.487542i	−0.990816	+	0.135220i
$13$	−3.57244	+	0.487542i	−0.990816	+	0.135220i
$14$	−1.94073			−0.518681
$15$		−	0.0558557i		−	0.0144219i
$16$	2.69360			0.673401
$17$	1.83266			0.444485			0.222243	−	0.974991i	$-0.428662\pi$
$17$	1.83266			0.444485			0.222243	+	0.974991i	$0.428662\pi$
$18$			1.37019i			0.322957i
$19$			6.07852i			1.39451i	0.716825	+	0.697254i	$0.245595\pi$
$19$			6.07852i			1.39451i	−0.716825	+	0.697254i	$0.754405\pi$
$20$		−	0.286625i		−	0.0640913i
$21$		−	1.41025i		−	0.307743i
$22$	−1.79659			−0.383033
$23$	8.58551			1.79020			0.895102	−	0.445862i	$-0.147103\pi$
$23$	8.58551			1.79020			0.895102	+	0.445862i	$0.147103\pi$
$24$		−	0.620472i		−	0.126653i
$25$	4.97389			0.994777
$26$	0.231911	+	1.69931i	0.0454814	+	0.333263i
$27$	−2.03263			−0.391179
$28$		−	7.23676i		−	1.36762i
$29$	−5.21592			−0.968571			−0.484286	−	0.874910i	$-0.660920\pi$
$29$	−5.21592			−0.968571			−0.484286	+	0.874910i	$0.660920\pi$
$30$	−0.0265691			−0.00485083
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$		−	4.87141i		−	0.861151i
$33$		−	1.30551i		−	0.227261i
$34$		−	0.871748i		−	0.149504i
$35$	−0.659297			−0.111442
$36$	−5.10928			−0.851547
$37$			11.7559i			1.93266i	0.257313	+	0.966328i	$0.417163\pi$
$37$			11.7559i			1.93266i	−0.257313	+	0.966328i	$0.582837\pi$
$38$	2.89139			0.469045
$39$	−1.23483	+	0.168521i	−0.197731	+	0.0269849i
$40$	−0.290072			−0.0458644
$41$		−	4.76311i		−	0.743873i	−0.928258	−	0.371937i	$-0.878694\pi$
$41$		−	4.76311i		−	0.743873i	0.928258	−	0.371937i	$-0.121306\pi$
$42$	−0.670821			−0.103510
$43$	6.24514			0.952374			0.476187	−	0.879344i	$-0.342018\pi$
$43$	6.24514			0.952374			0.476187	+	0.879344i	$0.342018\pi$
$44$		−	6.69927i		−	1.00995i
$45$			0.465476i			0.0693890i
$46$		−	4.08390i		−	0.602138i
$47$			4.70897i			0.686874i	0.939176	+	0.343437i	$0.111591\pi$
$47$			4.70897i			0.686874i	−0.939176	+	0.343437i	$0.888409\pi$
$48$	0.931056			0.134386
$49$	−9.64605			−1.37801
$50$		−	2.36595i		−	0.334595i
$51$	0.633467			0.0887031
$52$	−6.33655	+	0.864769i	−0.878722	+	0.119922i
$53$	6.16063			0.846227			0.423113	−	0.906077i	$-0.360937\pi$
$53$	6.16063			0.846227			0.423113	+	0.906077i	$0.360937\pi$
$54$			0.966867i			0.131574i
$55$	−0.610330			−0.0822969
$56$	−7.32379			−0.978683
$57$			2.10107i			0.278293i
$58$			2.48107i			0.325781i
$59$		−	7.98069i		−	1.03900i	−0.854471	−	0.519499i	$-0.826119\pi$
$59$		−	7.98069i		−	1.03900i	0.854471	−	0.519499i	$-0.173881\pi$
$60$		−	0.0990732i		−	0.0127903i
$61$	−4.52134			−0.578899			−0.289449	−	0.957193i	$-0.593472\pi$
$61$	−4.52134			−0.578899			−0.289449	+	0.957193i	$0.593472\pi$
$62$	0.475674			0.0604106
$63$			11.7524i			1.48066i
$64$	3.07001			0.383751
$65$	0.0787839	+	0.577285i	0.00977194	+	0.0716034i
$66$	−0.620998			−0.0764395
$67$			7.69808i			0.940470i	0.882541	+	0.470235i	$0.155831\pi$
$67$			7.69808i			0.940470i	−0.882541	+	0.470235i	$0.844169\pi$
$68$	3.25065			0.394199
$69$	2.96762			0.357259
$70$			0.313610i			0.0374836i
$71$		−	7.77152i		−	0.922310i	−0.887320	−	0.461155i	$-0.847435\pi$
$71$		−	7.77152i		−	0.922310i	0.887320	−	0.461155i	$-0.152565\pi$
$72$			5.17073i			0.609376i
$73$		−	4.96395i		−	0.580986i	−0.956877	−	0.290493i	$-0.906181\pi$
$73$		−	4.96395i		−	0.580986i	0.956877	−	0.290493i	$-0.0938194\pi$
$74$	5.59197			0.650053
$75$	1.71925			0.198521
$76$			10.7817i			1.23674i
$77$	−15.4097			−1.75610
$78$	0.0801609	+	0.587375i	0.00907644	+	0.0665071i
$79$	8.26843			0.930271			0.465135	−	0.885240i	$-0.346006\pi$
$79$	8.26843			0.930271			0.465135	+	0.885240i	$0.346006\pi$
$80$		−	0.435271i		−	0.0486648i
$81$	7.93898			0.882109
$82$	−2.26569			−0.250203
$83$			12.1642i			1.33520i	0.744522	+	0.667598i	$0.232678\pi$
$83$			12.1642i			1.33520i	−0.744522	+	0.667598i	$0.767322\pi$
$84$		−	2.50142i		−	0.272927i
$85$		−	0.296147i		−	0.0321217i
$86$		−	2.97065i		−	0.320333i
$87$	−1.80290			−0.193292
$88$	−6.77984			−0.722733
$89$			3.17056i			0.336079i	0.985780	+	0.168040i	$0.0537436\pi$
$89$			3.17056i			0.336079i	−0.985780	+	0.168040i	$0.946256\pi$
$90$	0.221415			0.0233391
$91$	1.98915	+	14.5754i	0.208519	+	1.52792i
$92$	15.2284			1.58767
$93$			0.345654i			0.0358427i
$94$	2.23993			0.231031
$95$	0.982253			0.100777
$96$		−	1.68382i		−	0.171854i
$97$			0.366185i			0.0371804i	0.999827	+	0.0185902i	$0.00591779\pi$
$97$			0.366185i			0.0371804i	−0.999827	+	0.0185902i	$0.994082\pi$
$98$			4.58837i			0.463495i
$99$			10.8795i			1.09343i
$100$	8.82236			0.882236
$101$	4.41069			0.438880			0.219440	−	0.975626i	$-0.429577\pi$
$101$	4.41069			0.438880			0.219440	+	0.975626i	$0.429577\pi$
$102$		−	0.301323i		−	0.0298355i
$103$	−5.82239			−0.573697			−0.286849	−	0.957976i	$-0.592608\pi$
$103$	−5.82239			−0.573697			−0.286849	+	0.957976i	$0.592608\pi$
$104$	0.875169	+	6.41276i	0.0858174	+	0.628823i
$105$	−0.227889			−0.0222397
$106$		−	2.93045i		−	0.284630i
$107$	−16.7531			−1.61958			−0.809790	−	0.586720i	$-0.800419\pi$
$107$	−16.7531			−1.61958			−0.809790	+	0.586720i	$0.800419\pi$
$108$	−3.60534			−0.346924
$109$			7.98649i			0.764967i	0.923962	+	0.382484i	$0.124931\pi$
$109$			7.98649i			0.764967i	−0.923962	+	0.382484i	$0.875069\pi$
$110$			0.290318i			0.0276807i
$111$			4.06347i			0.385688i
$112$		−	10.9898i		−	1.03844i
$113$	−8.73574			−0.821789			−0.410895	−	0.911683i	$-0.634784\pi$
$113$	−8.73574			−0.821789			−0.410895	+	0.911683i	$0.634784\pi$
$114$	0.999421			0.0936044
$115$		−	1.38737i		−	0.129373i
$116$	−9.25165			−0.858994
$117$	10.2905	−	1.40437i	0.951356	−	0.129834i
$118$	−3.79620			−0.349469
$119$		−	7.47717i		−	0.685431i
$120$	−0.100265			−0.00915287
$121$	−3.26520			−0.296837
$122$			2.15068i			0.194714i
$123$		−	1.64639i		−	0.148450i
$124$			1.77373i			0.159286i
$125$		−	1.61172i		−	0.144157i
$126$	5.59031			0.498024
$127$	10.6754			0.947291			0.473646	−	0.880715i	$-0.342938\pi$
$127$	10.6754			0.947291			0.473646	+	0.880715i	$0.342938\pi$
$128$		−	11.2031i		−	0.990227i
$129$	2.15866			0.190059
$130$	0.274599	−	0.0374754i	0.0240839	−	0.00328681i
$131$	−19.6250			−1.71464			−0.857322	−	0.514780i	$-0.827873\pi$
$131$	−19.6250			−1.71464			−0.857322	+	0.514780i	$0.827873\pi$
$132$		−	2.31563i		−	0.201550i
$133$	24.8001			2.15044
$134$	3.66177			0.316329
$135$			0.328461i			0.0282694i
$136$		−	3.28974i		−	0.282093i
$137$			2.38607i			0.203856i	0.994792	+	0.101928i	$0.0325012\pi$
$137$			2.38607i			0.203856i	−0.994792	+	0.101928i	$0.967499\pi$
$138$		−	1.41162i		−	0.120165i
$139$	−16.6882			−1.41547			−0.707735	−	0.706478i	$-0.750283\pi$
$139$	−16.6882			−1.41547			−0.707735	+	0.706478i	$0.750283\pi$
$140$	−1.16942			−0.0988339
$141$			1.62768i			0.137075i
$142$	−3.69671			−0.310221
$143$	1.84141	+	13.4928i	0.153986	+	1.12833i
$144$	−7.75899			−0.646582
$145$			0.842862i			0.0699959i
$146$	−2.36122			−0.195416
$147$	−3.33420			−0.275000
$148$			20.8518i			1.71401i
$149$		−	17.0531i		−	1.39705i	−0.715588	−	0.698523i	$-0.753841\pi$
$149$		−	17.0531i		−	1.39705i	0.715588	−	0.698523i	$-0.246159\pi$
$150$		−	0.817800i		−	0.0667731i
$151$			14.6889i			1.19537i	0.801733	+	0.597683i	$0.203912\pi$
$151$			14.6889i			1.19537i	−0.801733	+	0.597683i	$0.796088\pi$
$152$	10.9113			0.885026
$153$	−5.27902			−0.426783
$154$			7.32999i			0.590668i
$155$	0.161594			0.0129796
$156$	−2.19026	+	0.298911i	−0.175361	+	0.0239321i
$157$	3.04722			0.243195			0.121597	−	0.992580i	$-0.461198\pi$
$157$	3.04722			0.243195			0.121597	+	0.992580i	$0.461198\pi$
$158$		−	3.93307i		−	0.312898i
$159$	2.12945			0.168876
$160$	−0.787191			−0.0622329
$161$		−	35.0285i		−	2.76063i
$162$		−	3.77636i		−	0.296699i
$163$		−	13.4400i		−	1.05270i	−0.850267	−	0.526351i	$-0.823560\pi$
$163$		−	13.4400i		−	1.05270i	0.850267	−	0.526351i	$-0.176440\pi$
$164$		−	8.44850i		−	0.659717i
$165$	−0.210963			−0.0164235
$166$	5.78620			0.449096
$167$			18.9746i			1.46830i	0.678990	+	0.734148i	$0.262418\pi$
$167$			18.9746i			1.46830i	−0.678990	+	0.734148i	$0.737582\pi$
$168$	−2.53150			−0.195309
$169$	12.5246	−	3.48342i	0.963431	−	0.267956i
$170$	−0.140869			−0.0108042
$171$		−	17.5093i		−	1.33897i
$172$	11.0772			0.844630
$173$	−4.56058			−0.346735			−0.173367	−	0.984857i	$-0.555465\pi$
$173$	−4.56058			−0.346735			−0.173367	+	0.984857i	$0.555465\pi$
$174$			0.857594i			0.0650140i
$175$		−	20.2932i		−	1.53403i
$176$		−	10.1736i		−	0.766861i
$177$		−	2.75856i		−	0.207346i
$178$	1.50815			0.113041
$179$	3.85639			0.288240			0.144120	−	0.989560i	$-0.453965\pi$
$179$	3.85639			0.288240			0.144120	+	0.989560i	$0.453965\pi$
$180$			0.825631i			0.0615389i
$181$	8.51055			0.632584			0.316292	−	0.948662i	$-0.397562\pi$
$181$	8.51055			0.632584			0.316292	+	0.948662i	$0.397562\pi$
$182$	6.93313	−	0.946185i	0.513918	−	0.0701359i
$183$	−1.56282			−0.115527
$184$		−	15.4116i		−	1.13616i
$185$	1.89968			0.139667
$186$	0.164419			0.0120558
$187$		−	6.92183i		−	0.506174i
$188$			8.35246i			0.609166i
$189$			8.29304i			0.603230i
$190$		−	0.467232i		−	0.0338965i
$191$	8.46629			0.612599			0.306300	−	0.951935i	$-0.400909\pi$
$191$	8.46629			0.612599			0.306300	+	0.951935i	$0.400909\pi$
$192$	1.06116			0.0765827
$193$		−	1.35305i		−	0.0973950i	−0.998814	−	0.0486975i	$-0.984493\pi$
$193$		−	1.35305i		−	0.0973950i	0.998814	−	0.0486975i	$-0.0155070\pi$
$194$	0.174184			0.0125057
$195$	0.0272320	+	0.199541i	0.00195012	+	0.0142894i
$196$	−17.1095			−1.22211
$197$		−	4.99593i		−	0.355946i	−0.984035	−	0.177973i	$-0.943046\pi$
$197$		−	4.99593i		−	0.355946i	0.984035	−	0.177973i	$-0.0569539\pi$
$198$	5.17511			0.367779
$199$	−18.1523			−1.28678			−0.643390	−	0.765539i	$-0.722472\pi$
$199$	−18.1523			−1.28678			−0.643390	+	0.765539i	$0.722472\pi$
$200$		−	8.92845i		−	0.631337i
$201$			2.66087i			0.187684i
$202$		−	2.09805i		−	0.147618i
$203$			21.2807i			1.49361i
$204$	1.12360			0.0786679
$205$	−0.769691			−0.0537576
$206$			2.76956i			0.192964i
$207$	−24.7308			−1.71891
$208$	−9.62273	+	1.31324i	−0.667216	+	0.0910571i
$209$	22.9581			1.58805
$210$			0.108401i			0.00748036i
$211$	−17.5202			−1.20614			−0.603069	−	0.797689i	$-0.706056\pi$
$211$	−17.5202			−1.20614			−0.603069	+	0.797689i	$0.706056\pi$
$212$	10.9273			0.750491
$213$		−	2.68626i		−	0.184060i
$214$			7.96899i			0.544749i
$215$		−	1.00918i		−	0.0688254i
$216$			3.64870i			0.248263i
$217$	4.07996			0.276966
$218$	3.79896			0.257298
$219$		−	1.71581i		−	0.115944i
$220$	−1.08256			−0.0729864
$221$	−6.54706	+	0.893498i	−0.440403	+	0.0601032i
$222$	1.93289			0.129727
$223$			14.9046i			0.998084i	0.866578	+	0.499042i	$0.166315\pi$
$223$			14.9046i			0.998084i	−0.866578	+	0.499042i	$0.833685\pi$
$224$	−19.8751			−1.32796
$225$	−14.3274			−0.955160
$226$			4.15536i			0.276410i
$227$		−	23.7120i		−	1.57382i	−0.617068	−	0.786910i	$-0.711680\pi$
$227$		−	23.7120i		−	1.57382i	0.617068	−	0.786910i	$-0.288320\pi$
$228$			3.72673i			0.246809i
$229$		−	13.5862i		−	0.897804i	−0.893581	−	0.448902i	$-0.851815\pi$
$229$		−	13.5862i		−	0.897804i	0.893581	−	0.448902i	$-0.148185\pi$
$230$	−0.659935			−0.0435148
$231$	−5.32643			−0.350454
$232$			9.36291i			0.614705i
$233$	−12.3027			−0.805980			−0.402990	−	0.915204i	$-0.632029\pi$
$233$	−12.3027			−0.805980			−0.402990	+	0.915204i	$0.632029\pi$
$234$	−0.668024	−	4.89491i	−0.0436701	−	0.319990i
$235$	0.760942			0.0496384
$236$		−	14.1556i		−	0.921453i
$237$	2.85802			0.185648
$238$	−3.55669			−0.230546
$239$			21.8890i			1.41588i	0.706273	+	0.707940i	$0.250375\pi$
$239$			21.8890i			1.41588i	−0.706273	+	0.707940i	$0.749625\pi$
$240$		−	0.150453i		−	0.00971171i
$241$		−	7.21497i		−	0.464757i	−0.972625	−	0.232379i	$-0.925349\pi$
$241$		−	7.21497i		−	0.464757i	0.972625	−	0.232379i	$-0.0746509\pi$
$242$			1.55317i			0.0998416i
$243$	8.84203			0.567216
$244$	−8.01967			−0.513406
$245$			1.55875i			0.0995846i
$246$	−0.783144			−0.0499315
$247$	−2.96353	−	21.7151i	−0.188565	−	1.38170i
$248$	1.79507			0.113987
$249$			4.20462i			0.266457i
$250$	−0.766654			−0.0484874
$251$	13.8037			0.871280			0.435640	−	0.900121i	$-0.356522\pi$
$251$	13.8037			0.871280			0.435640	+	0.900121i	$0.356522\pi$
$252$			20.8457i			1.31315i
$253$		−	32.4269i		−	2.03866i
$254$		−	5.07802i		−	0.318623i
$255$		−	0.102365i		−	0.00641032i
$256$	0.810980			0.0506863
$257$	10.4274			0.650446			0.325223	−	0.945637i	$-0.394561\pi$
$257$	10.4274			0.650446			0.325223	+	0.945637i	$0.394561\pi$
$258$		−	1.02682i		−	0.0639268i
$259$	47.9635			2.98031
$260$	0.139742	+	1.02395i	0.00866641	+	0.0635027i
$261$	15.0246			0.929997
$262$			9.33509i			0.576724i
$263$	21.8967			1.35021			0.675105	−	0.737721i	$-0.264098\pi$
$263$	21.8967			1.35021			0.675105	+	0.737721i	$0.264098\pi$
$264$	−2.34348			−0.144231
$265$		−	0.995521i		−	0.0611544i
$266$		−	11.7967i		−	0.723305i
$267$			1.09592i			0.0670692i
$268$			13.6543i			0.834072i
$269$	−4.19670			−0.255877			−0.127939	−	0.991782i	$-0.540836\pi$
$269$	−4.19670			−0.255877			−0.127939	+	0.991782i	$0.540836\pi$
$270$	0.156240			0.00950847
$271$		−	4.89966i		−	0.297633i	−0.988865	−	0.148817i	$-0.952454\pi$
$271$		−	4.89966i		−	0.297633i	0.988865	−	0.148817i	$-0.0475464\pi$
$272$	4.93646			0.299317
$273$	0.687558	+	5.03805i	0.0416129	+	0.304916i
$274$	1.13499			0.0685674
$275$		−	18.7860i		−	1.13284i
$276$	5.26377			0.316842
$277$	−15.9569			−0.958760			−0.479380	−	0.877608i	$-0.659138\pi$
$277$	−15.9569			−0.958760			−0.479380	+	0.877608i	$0.659138\pi$
$278$			7.93811i			0.476096i
$279$		−	2.88052i		−	0.172452i
$280$			1.18348i			0.0707266i
$281$			8.30204i			0.495258i	0.968855	+	0.247629i	$0.0796514\pi$
$281$			8.30204i			0.495258i	−0.968855	+	0.247629i	$0.920349\pi$
$282$	0.774242			0.0461055
$283$	21.4803			1.27687			0.638436	−	0.769675i	$-0.279582\pi$
$283$	21.4803			1.27687			0.638436	+	0.769675i	$0.279582\pi$
$284$		−	13.7846i		−	0.817967i
$285$	0.339520			0.0201114
$286$	6.41819	−	0.875910i	0.379515	−	0.0517937i
$287$	−19.4333			−1.14711
$288$			14.0322i			0.826855i
$289$	−13.6414			−0.802433
$290$	0.400927			0.0235432
$291$			0.126573i			0.00741986i
$292$		−	8.80473i		−	0.515258i
$293$		−	25.3620i		−	1.48166i	−0.671690	−	0.740832i	$-0.734431\pi$
$293$		−	25.3620i		−	1.48166i	0.671690	−	0.740832i	$-0.265569\pi$
$294$			1.58599i			0.0924968i
$295$	−1.28963			−0.0750854
$296$	21.1026			1.22656
$297$			7.67710i			0.445470i
$298$	−8.11171			−0.469899
$299$	−30.6712	+	4.18579i	−1.77376	+	0.242071i
$300$	3.04949			0.176062
$301$		−	25.4799i		−	1.46864i
$302$	6.98712			0.402064
$303$	1.52457			0.0875845
$304$			16.3731i			0.939063i
$305$			0.730623i			0.0418354i
$306$			2.51109i			0.143549i
$307$			24.5792i			1.40281i	0.712765	+	0.701403i	$0.247443\pi$
$307$			24.5792i			1.40281i	−0.712765	+	0.701403i	$0.752557\pi$
$308$	−27.3327			−1.55743
$309$	−2.01253			−0.114489
$310$		−	0.0768661i		−	0.00436570i
$311$	11.9767			0.679138			0.339569	−	0.940581i	$-0.389719\pi$
$311$	11.9767			0.679138			0.339569	+	0.940581i	$0.389719\pi$
$312$	0.302506	+	2.21660i	0.0171260	+	0.125490i
$313$	4.14553			0.234319			0.117160	−	0.993113i	$-0.462621\pi$
$313$	4.14553			0.234319			0.117160	+	0.993113i	$0.462621\pi$
$314$		−	1.44948i		−	0.0817990i
$315$	1.89912			0.107003
$316$	14.6660			0.825027
$317$			31.3673i			1.76176i	0.473335	+	0.880882i	$0.343050\pi$
$317$			31.3673i			1.76176i	−0.473335	+	0.880882i	$0.656950\pi$
$318$		−	1.01292i		−	0.0568018i
$319$			19.7002i			1.10300i
$320$		−	0.496095i		−	0.0277326i
$321$	−5.79077			−0.323209
$322$	−16.6621			−0.928545
$323$			11.1399i			0.619838i
$324$	14.0816			0.782314
$325$	−17.7689	+	2.42498i	−0.985641	+	0.134514i
$326$	−6.39305			−0.354078
$327$			2.76056i			0.152660i
$328$	−8.55010			−0.472100
$329$	19.2124			1.05921
$330$			0.100350i			0.00552406i
$331$			0.485651i			0.0266938i	0.999911	+	0.0133469i	$0.00424858\pi$
$331$			0.485651i			0.0266938i	−0.999911	+	0.0133469i	$0.995751\pi$
$332$			21.5761i			1.18414i
$333$		−	33.8631i		−	1.85569i
$334$	9.02569			0.493864
$335$	1.24396			0.0679650
$336$		−	3.79867i		−	0.207234i
$337$	−10.4733			−0.570518			−0.285259	−	0.958451i	$-0.592080\pi$
$337$	−10.4733			−0.570518			−0.285259	+	0.958451i	$0.592080\pi$
$338$	−1.65697	−	5.95762i	−0.0901274	−	0.324052i
$339$	−3.01955			−0.163999
$340$		−	0.525286i		−	0.0284877i
$341$	3.77693			0.204532
$342$	−8.32871			−0.450365
$343$			10.7958i			0.582917i
$344$		−	11.2104i		−	0.604426i
$345$		−	0.479550i		−	0.0258181i
$346$			2.16935i			0.116625i
$347$	16.0801			0.863225			0.431613	−	0.902059i	$-0.357945\pi$
$347$	16.0801			0.863225			0.431613	+	0.902059i	$0.357945\pi$
$348$	−3.19787			−0.171424
$349$			27.1125i			1.45130i	0.688064	+	0.725650i	$0.258461\pi$
$349$			27.1125i			1.45130i	−0.688064	+	0.725650i	$0.741539\pi$
$350$	−9.65296			−0.515972
$351$	7.26144	−	0.990991i	0.387587	−	0.0528952i
$352$	−18.3990			−0.980668
$353$		−	2.27544i		−	0.121109i	−0.998165	−	0.0605547i	$-0.980713\pi$
$353$		−	2.27544i		−	0.121109i	0.998165	−	0.0605547i	$-0.0192869\pi$
$354$	−1.31217			−0.0697413
$355$	−1.25583			−0.0666527
$356$			5.62374i			0.298058i
$357$		−	2.58452i		−	0.136787i
$358$		−	1.83438i		−	0.0969502i
$359$			2.58251i			0.136300i	0.997675	+	0.0681498i	$0.0217096\pi$
$359$			2.58251i			0.136300i	−0.997675	+	0.0681498i	$0.978290\pi$
$360$	0.835560			0.0440379
$361$	−17.9484			−0.944650
$362$		−	4.04824i		−	0.212771i
$363$	−1.12863			−0.0592378
$364$	3.52822	+	25.8529i	0.184929	+	1.35506i
$365$	−0.802146			−0.0419862
$366$			0.743393i			0.0388578i
$367$	−15.6380			−0.816296			−0.408148	−	0.912916i	$-0.633825\pi$
$367$	−15.6380			−0.816296			−0.408148	+	0.912916i	$0.633825\pi$
$368$	23.1260			1.20552
$369$			13.7203i			0.714248i
$370$		−	0.903629i		−	0.0469774i
$371$		−	25.1351i		−	1.30495i
$372$			0.613099i			0.0317877i
$373$	−28.3986			−1.47042			−0.735211	−	0.677839i	$-0.762917\pi$
$373$	−28.3986			−1.47042			−0.735211	+	0.677839i	$0.762917\pi$
$374$	−3.29253			−0.170253
$375$		−	0.557099i		−	0.0287685i
$376$	8.45291			0.435926
$377$	18.6335	−	2.54298i	0.959676	−	0.130970i
$378$	3.94478			0.202897
$379$		−	3.66801i		−	0.188413i	−0.995553	−	0.0942066i	$-0.969969\pi$
$379$		−	3.66801i		−	0.188413i	0.995553	−	0.0942066i	$-0.0300314\pi$
$380$	1.74226			0.0893758
$381$	3.69001			0.189045
$382$		−	4.02719i		−	0.206049i
$383$			27.7530i			1.41811i	0.705153	+	0.709056i	$0.250878\pi$
$383$			27.7530i			1.41811i	−0.705153	+	0.709056i	$0.749122\pi$
$384$		−	3.87241i		−	0.197613i
$385$			2.49012i			0.126908i
$386$	−0.643612			−0.0327590
$387$	−17.9893			−0.914446
$388$			0.649514i			0.0329741i
$389$	7.80800			0.395881			0.197941	−	0.980214i	$-0.436575\pi$
$389$	7.80800			0.395881			0.197941	+	0.980214i	$0.436575\pi$
$390$	0.0949164	−	0.0129535i	0.00480628	−	0.000655928i
$391$	15.7343			0.795719
$392$			17.3153i			0.874554i
$393$	−6.78347			−0.342181
$394$	−2.37643			−0.119723
$395$		−	1.33613i		−	0.0672280i
$396$			19.2974i			0.969731i
$397$			32.5182i			1.63204i	0.578024	+	0.816020i	$0.303824\pi$
$397$			32.5182i			1.63204i	−0.578024	+	0.816020i	$0.696176\pi$
$398$			8.63455i			0.432811i
$399$	8.57226			0.429150
$400$	13.3977			0.669884
$401$		−	18.4545i		−	0.921574i	−0.887511	−	0.460787i	$-0.847567\pi$
$401$		−	18.4545i		−	0.921574i	0.887511	−	0.460787i	$-0.152433\pi$
$402$	1.26571			0.0631277
$403$	−0.487542	−	3.57244i	−0.0242862	−	0.177956i
$404$	7.82340			0.389228
$405$		−	1.28289i		−	0.0637475i
$406$	10.1227			0.502380
$407$	44.4012			2.20088
$408$		−	1.13711i		−	0.0562956i
$409$		−	20.3559i		−	1.00653i	−0.864132	−	0.503266i	$-0.832132\pi$
$409$		−	20.3559i		−	1.00653i	0.864132	−	0.503266i	$-0.167868\pi$
$410$			0.366122i			0.0180815i
$411$			0.824757i			0.0406823i
$412$	−10.3274			−0.508793
$413$	−32.5609			−1.60222
$414$			11.7638i			0.578158i
$415$	1.96567			0.0964908
$416$	2.37501	+	17.4028i	0.116445	+	0.853242i
$417$	−5.76833			−0.282477
$418$		−	10.9206i		−	0.534143i
$419$	−32.6649			−1.59578			−0.797891	−	0.602801i	$-0.794051\pi$
$419$	−32.6649			−1.59578			−0.797891	+	0.602801i	$0.794051\pi$
$420$	−0.404215			−0.0197237
$421$			10.0153i			0.488114i	0.969761	+	0.244057i	$0.0784783\pi$
$421$			10.0153i			0.488114i	−0.969761	+	0.244057i	$0.921522\pi$
$422$			8.33388i			0.405687i
$423$		−	13.5643i		−	0.659519i
$424$		−	11.0587i		−	0.537059i
$425$	9.11544			0.442164
$426$	−1.27778			−0.0619088
$427$			18.4469i			0.892708i
$428$	−29.7155			−1.43635
$429$	0.636492	+	4.66386i	0.0307301	+	0.225173i
$430$	−0.480039			−0.0231495
$431$		−	15.7075i		−	0.756604i	−0.925682	−	0.378302i	$-0.876508\pi$
$431$		−	15.7075i		−	0.756604i	0.925682	−	0.378302i	$-0.123492\pi$
$432$	−5.47510			−0.263421
$433$	23.0783			1.10907			0.554537	−	0.832159i	$-0.312895\pi$
$433$	23.0783			1.10907			0.554537	+	0.832159i	$0.312895\pi$
$434$		−	1.94073i		−	0.0931579i
$435$			0.291339i			0.0139686i
$436$			14.1659i			0.678424i
$437$			52.1872i			2.49645i
$438$	−0.816166			−0.0389979
$439$	−9.91131			−0.473041			−0.236520	−	0.971627i	$-0.576007\pi$
$439$	−9.91131			−0.473041			−0.236520	+	0.971627i	$0.576007\pi$
$440$			1.09558i			0.0522298i
$441$	27.7857			1.32313
$442$	0.425013	+	3.11426i	0.0202158	+	0.148130i
$443$	−10.2386			−0.486452			−0.243226	−	0.969970i	$-0.578206\pi$
$443$	−10.2386			−0.486452			−0.243226	+	0.969970i	$0.578206\pi$
$444$			7.20752i			0.342054i
$445$	0.512345			0.0242875
$446$	7.08971			0.335708
$447$		−	5.89448i		−	0.278799i
$448$		−	12.5255i		−	0.591774i
$449$		−	37.8155i		−	1.78462i	−0.451421	−	0.892311i	$-0.649083\pi$
$449$		−	37.8155i		−	1.78462i	0.451421	−	0.892311i	$-0.350917\pi$
$450$			6.81516i			0.321270i
$451$	−17.9899			−0.847113
$452$	−15.4949			−0.728818
$453$			5.07728i			0.238552i
$454$	−11.2792			−0.529357
$455$	2.35530	−	0.321435i	0.110418	−	0.0150691i
$456$	3.77155			0.176619
$457$		−	5.76721i		−	0.269779i	−0.990861	−	0.134889i	$-0.956932\pi$
$457$		−	5.76721i		−	0.269779i	0.990861	−	0.134889i	$-0.0430679\pi$
$458$	−6.46261			−0.301978
$459$	−3.72512			−0.173874
$460$		−	2.46082i		−	0.114737i
$461$		−	19.4478i		−	0.905775i	−0.891568	−	0.452888i	$-0.850394\pi$
$461$		−	19.4478i		−	0.905775i	0.891568	−	0.452888i	$-0.149606\pi$
$462$			2.53364i			0.117876i
$463$		−	17.5592i		−	0.816046i	−0.912972	−	0.408023i	$-0.866218\pi$
$463$		−	17.5592i		−	0.816046i	0.912972	−	0.408023i	$-0.133782\pi$
$464$	−14.0496			−0.652237
$465$	0.0558557			0.00259025
$466$			5.85209i			0.271093i
$467$	21.5159			0.995637			0.497818	−	0.867281i	$-0.334135\pi$
$467$	21.5159			0.995637			0.497818	+	0.867281i	$0.334135\pi$
$468$	18.2526	−	2.49099i	0.843726	−	0.115146i
$469$	31.4078			1.45028
$470$		−	0.361960i		−	0.0166960i
$471$	1.05328			0.0485328
$472$	−14.3259			−0.659401
$473$		−	23.5874i		−	1.08455i
$474$		−	1.35948i		−	0.0624432i
$475$			30.2339i			1.38722i
$476$		−	13.2625i		−	0.607887i
$477$	−17.7458			−0.812525
$478$	10.4120			0.476234
$479$			40.4137i			1.84655i	0.384139	+	0.923275i	$0.374498\pi$
$479$			40.4137i			1.84655i	−0.384139	+	0.923275i	$0.625502\pi$
$480$	−0.272096			−0.0124194
$481$	−5.73148	−	41.9972i	−0.261333	−	1.91491i
$482$	−3.43197			−0.156322
$483$		−	12.1078i		−	0.550922i
$484$	−5.79160			−0.263255
$485$	0.0591733			0.00268692
$486$		−	4.20592i		−	0.190784i
$487$			0.476889i			0.0216099i	0.999942	+	0.0108050i	$0.00343939\pi$
$487$			0.476889i			0.0216099i	−0.999942	+	0.0108050i	$0.996561\pi$
$488$			8.11611i			0.367399i
$489$		−	4.64559i		−	0.210081i
$490$	0.741454			0.0334955
$491$	−5.42032			−0.244616			−0.122308	−	0.992492i	$-0.539030\pi$
$491$	−5.42032			−0.244616			−0.122308	+	0.992492i	$0.539030\pi$
$492$		−	2.92026i		−	0.131655i
$493$	−9.55900			−0.430516
$494$	−10.3293	+	1.40967i	−0.464737	+	0.0634242i
$495$	1.75807			0.0790194
$496$			2.69360i			0.120946i
$497$	−31.7075			−1.42227
$498$	2.00002			0.0896232
$499$		−	12.7183i		−	0.569350i	−0.958624	−	0.284675i	$-0.908114\pi$
$499$		−	12.7183i		−	0.569350i	0.958624	−	0.284675i	$-0.0918856\pi$
$500$		−	2.85877i		−	0.127848i
$501$			6.55864i			0.293018i
$502$		−	6.56604i		−	0.293057i
$503$	3.19745			0.142567			0.0712835	−	0.997456i	$-0.477290\pi$
$503$	3.19745			0.142567			0.0712835	+	0.997456i	$0.477290\pi$
$504$	21.0964			0.939706
$505$		−	0.712742i		−	0.0317166i
$506$	−15.4246			−0.685708
$507$	4.32918	−	1.20406i	0.192266	−	0.0534742i
$508$	18.9354			0.840122
$509$			29.0567i			1.28791i	0.765061	+	0.643957i	$0.222709\pi$
$509$			29.0567i			1.28791i	−0.765061	+	0.643957i	$0.777291\pi$
$510$	−0.0486921			−0.00215612
$511$	−20.2527			−0.895927
$512$		−	22.7920i		−	1.00728i
$513$		−	12.3554i		−	0.545503i
$514$		−	4.96006i		−	0.218779i
$515$			0.940864i			0.0414594i
$516$	3.82889			0.168557
$517$	17.7855			0.782203
$518$		−	22.8150i		−	1.00243i
$519$	−1.57639			−0.0691956
$520$	1.03626	−	0.141422i	0.0454432	−	0.00620178i
$521$	−32.5948			−1.42800			−0.714001	−	0.700145i	$-0.753119\pi$
$521$	−32.5948			−1.42800			−0.714001	+	0.700145i	$0.753119\pi$
$522$		−	7.14679i		−	0.312806i
$523$	24.3813			1.06612			0.533059	−	0.846078i	$-0.321042\pi$
$523$	24.3813			1.06612			0.533059	+	0.846078i	$0.321042\pi$
$524$	−34.8095			−1.52066
$525$		−	7.01445i		−	0.306136i
$526$		−	10.4157i		−	0.454146i
$527$			1.83266i			0.0798319i
$528$		−	3.51653i		−	0.153037i
$529$	50.7110			2.20483
$530$	−0.473543			−0.0205694
$531$			22.9886i			0.997619i
$532$	43.9888			1.90716
$533$	2.32221	+	17.0159i	0.100586	+	0.737041i
$534$	0.521300			0.0225588
$535$			2.70720i			0.117042i
$536$	13.8186			0.596871
$537$	1.33298			0.0575223
$538$			1.99626i			0.0860649i
$539$			36.4325i			1.56926i
$540$			0.582603i			0.0250712i
$541$		−	36.9850i		−	1.59011i	−0.606537	−	0.795055i	$-0.707442\pi$
$541$		−	36.9850i		−	1.59011i	0.606537	−	0.795055i	$-0.292558\pi$
$542$	−2.33064			−0.100110
$543$	2.94171			0.126241
$544$		−	8.92763i		−	0.382769i
$545$	1.29057			0.0552820
$546$	2.39647	−	0.327053i	0.102559	−	0.0139966i
$547$	10.3345			0.441872			0.220936	−	0.975288i	$-0.429089\pi$
$547$	10.3345			0.441872			0.220936	+	0.975288i	$0.429089\pi$
$548$			4.23226i			0.180793i
$549$	13.0238			0.555844
$550$	−8.93602			−0.381033
$551$		−	31.7050i		−	1.35068i
$552$		−	5.32707i		−	0.226735i
$553$		−	33.7348i		−	1.43455i
$554$			7.59029i			0.322481i
$555$	0.656634			0.0278726
$556$	−29.6004			−1.25533
$557$		−	5.13754i		−	0.217685i	−0.994059	−	0.108842i	$-0.965286\pi$
$557$		−	5.13754i		−	0.217685i	0.994059	−	0.108842i	$-0.0347143\pi$
$558$	−1.37019			−0.0580047
$559$	−22.3104	+	3.04476i	−0.943627	+	0.128780i
$560$	−1.77589			−0.0750449
$561$		−	2.39256i		−	0.101014i
$562$	3.94906			0.166581
$563$	−5.84576			−0.246370			−0.123185	−	0.992384i	$-0.539311\pi$
$563$	−5.84576			−0.246370			−0.123185	+	0.992384i	$0.539311\pi$
$564$			2.88706i			0.121567i
$565$			1.41164i			0.0593883i
$566$		−	10.2176i		−	0.429478i
$567$		−	32.3907i		−	1.36028i
$568$	−13.9504			−0.585346
$569$	−19.4506			−0.815413			−0.407706	−	0.913113i	$-0.633671\pi$
$569$	−19.4506			−0.815413			−0.407706	+	0.913113i	$0.633671\pi$
$570$		−	0.161501i		−	0.00676452i
$571$	4.61628			0.193185			0.0965927	−	0.995324i	$-0.469206\pi$
$571$	4.61628			0.193185			0.0965927	+	0.995324i	$0.469206\pi$
$572$	3.26617	+	23.9327i	0.136566	+	1.00068i
$573$	2.92641			0.122253
$574$			9.24390i			0.385833i
$575$	42.7034			1.78085
$576$	−8.84323			−0.368468
$577$		−	26.1386i		−	1.08817i	−0.839032	−	0.544083i	$-0.816878\pi$
$577$		−	26.1386i		−	1.08817i	0.839032	−	0.544083i	$-0.183122\pi$
$578$			6.48883i			0.269900i
$579$		−	0.467689i		−	0.0194365i
$580$			1.49501i			0.0620770i
$581$	49.6295			2.05898
$582$	0.0602076			0.00249568
$583$		−	23.2683i		−	0.963673i
$584$	−8.91062			−0.368724
$585$	−0.226939	−	1.66288i	−0.00938276	−	0.0687517i
$586$	−12.0640			−0.498361
$587$			19.2852i			0.795983i	0.917389	+	0.397992i	$0.130293\pi$
$587$			19.2852i			0.795983i	−0.917389	+	0.397992i	$0.869707\pi$
$588$	−5.91398			−0.243889
$589$	−6.07852			−0.250461
$590$			0.613445i			0.0252551i
$591$		−	1.72687i		−	0.0710338i
$592$			31.6657i			1.30145i
$593$		−	16.2964i		−	0.669214i	−0.942358	−	0.334607i	$-0.891397\pi$
$593$		−	16.2964i		−	0.669214i	0.942358	−	0.334607i	$-0.108603\pi$
$594$	3.65179			0.149835
$595$	−1.20827			−0.0495341
$596$		−	30.2477i		−	1.23899i
$597$	−6.27441			−0.256794
$598$	1.99107	+	14.5895i	0.0814210	+	0.596608i
$599$	−24.5049			−1.00124			−0.500622	−	0.865666i	$-0.666895\pi$
$599$	−24.5049			−1.00124			−0.500622	+	0.865666i	$0.666895\pi$
$600$		−	3.08616i		−	0.125992i
$601$	−6.30942			−0.257367			−0.128683	−	0.991686i	$-0.541075\pi$
$601$	−6.30942			−0.257367			−0.128683	+	0.991686i	$0.541075\pi$
$602$	−12.1201			−0.493979
$603$		−	22.1745i		−	0.903015i
$604$			26.0542i			1.06013i
$605$			0.527638i			0.0214515i
$606$		−	0.725200i		−	0.0294592i
$607$	1.35917			0.0551672			0.0275836	−	0.999620i	$-0.491219\pi$
$607$	1.35917			0.0551672			0.0275836	+	0.999620i	$0.491219\pi$
$608$	29.6109			1.20088
$609$			7.35577i			0.298071i
$610$	0.347538			0.0140714
$611$	−2.29582	−	16.8225i	−0.0928789	−	0.680565i
$612$	−9.36358			−0.378500
$613$			29.2724i			1.18230i	0.806562	+	0.591150i	$0.201326\pi$
$613$			29.2724i			1.18230i	−0.806562	+	0.591150i	$0.798674\pi$
$614$	11.6917			0.471837
$615$	−0.266047			−0.0107281
$616$			27.6615i			1.11451i
$617$		−	19.6789i		−	0.792241i	−0.918198	−	0.396121i	$-0.870356\pi$
$617$		−	19.6789i		−	0.792241i	0.918198	−	0.396121i	$-0.129644\pi$
$618$			0.957309i			0.0385086i
$619$			20.4145i			0.820528i	0.911967	+	0.410264i	$0.134563\pi$
$619$			20.4145i			0.820528i	−0.911967	+	0.410264i	$0.865437\pi$
$620$	0.286625			0.0115111
$621$	−17.4512			−0.700291
$622$		−	5.69701i		−	0.228429i
$623$	12.9358			0.518261
$624$	−3.32614	+	0.453928i	−0.133152	+	0.0181717i
$625$	24.6090			0.984360
$626$		−	1.97192i		−	0.0788137i
$627$	7.93558			0.316916
$628$	5.40496			0.215681
$629$			21.5445i			0.859037i
$630$		−	0.903362i		−	0.0359908i
$631$		−	23.8412i		−	0.949104i	−0.880228	−	0.474552i	$-0.842610\pi$
$631$		−	23.8412i		−	0.949104i	0.880228	−	0.474552i	$-0.157390\pi$
$632$		−	14.8424i		−	0.590398i
$633$	−6.05592			−0.240701
$634$	14.9206			0.592573
$635$		−	1.72509i		−	0.0684580i
$636$	3.77707			0.149771
$637$	34.4599	−	4.70285i	1.36535	−	0.186334i
$638$	9.37084			0.370995
$639$			22.3860i			0.885578i
$640$	−1.81036			−0.0715608
$641$	14.6516			0.578705			0.289352	−	0.957223i	$-0.406560\pi$
$641$	14.6516			0.578705			0.289352	+	0.957223i	$0.406560\pi$
$642$			2.75452i			0.108712i
$643$			41.7544i			1.64663i	0.567582	+	0.823317i	$0.307879\pi$
$643$			41.7544i			1.64663i	−0.567582	+	0.823317i	$0.692121\pi$
$644$		−	62.1313i		−	2.44832i
$645$		−	0.348827i		−	0.0137350i
$646$	5.29893			0.208484
$647$	48.8162			1.91916			0.959582	−	0.281430i	$-0.0908087\pi$
$647$	48.8162			1.91916			0.959582	+	0.281430i	$0.0908087\pi$
$648$		−	14.2510i		−	0.559832i
$649$	−30.1425			−1.18320
$650$	1.15350	+	8.45219i	0.0452439	+	0.331522i
$651$	1.41025			0.0552722
$652$		−	23.8390i		−	0.933607i
$653$	−22.5149			−0.881076			−0.440538	−	0.897734i	$-0.645212\pi$
$653$	−22.5149			−0.881076			−0.440538	+	0.897734i	$0.645212\pi$
$654$	1.31313			0.0513474
$655$			3.17129i			0.123912i
$656$		−	12.8299i		−	0.500925i
$657$			14.2988i			0.557848i
$658$		−	9.13883i		−	0.356269i
$659$	5.23972			0.204110			0.102055	−	0.994779i	$-0.467458\pi$
$659$	5.23972			0.204110			0.102055	+	0.994779i	$0.467458\pi$
$660$	−0.374193			−0.0145654
$661$		−	24.7912i		−	0.964266i	−0.876098	−	0.482133i	$-0.839862\pi$
$661$		−	24.7912i		−	0.964266i	0.876098	−	0.482133i	$-0.160138\pi$
$662$	0.231012			0.00897852
$663$	−2.26302	+	0.308841i	−0.0878884	+	0.0119944i
$664$	21.8356			0.847385
$665$		−	4.00755i		−	0.155406i
$666$	−16.1078			−0.624164
$667$	−44.7813			−1.73394
$668$			33.6558i			1.30218i
$669$			5.15183i			0.199181i
$670$		−	0.591721i		−	0.0228602i
$671$			17.0768i			0.659243i
$672$	−6.86993			−0.265013
$673$	−26.8313			−1.03427			−0.517135	−	0.855904i	$-0.673001\pi$
$673$	−26.8313			−1.03427			−0.517135	+	0.855904i	$0.673001\pi$
$674$			4.98188i			0.191895i
$675$	−10.1101			−0.389137
$676$	22.2153	−	6.17867i	0.854436	−	0.237641i
$677$	−8.48908			−0.326262			−0.163131	−	0.986604i	$-0.552159\pi$
$677$	−8.48908			−0.326262			−0.163131	+	0.986604i	$0.552159\pi$
$678$			1.43632i			0.0551615i
$679$	1.49402			0.0573351
$680$	−0.531604			−0.0203861
$681$		−	8.19615i		−	0.314077i
$682$		−	1.79659i		−	0.0687948i
$683$			33.5723i			1.28461i	0.766449	+	0.642305i	$0.222022\pi$
$683$			33.5723i			1.28461i	−0.766449	+	0.642305i	$0.777978\pi$
$684$		−	31.0569i		−	1.18749i
$685$	0.385576			0.0147321
$686$	5.13526			0.196065
$687$		−	4.69614i		−	0.179169i
$688$	16.8219			0.641330
$689$	−22.0084	+	3.00356i	−0.838455	+	0.114427i
$690$	−0.228109			−0.00868397
$691$		−	39.7800i		−	1.51330i	−0.653818	−	0.756652i	$-0.726834\pi$
$691$		−	39.7800i		−	1.51330i	0.653818	−	0.756652i	$-0.273166\pi$
$692$	−8.08927			−0.307508
$693$	44.3880			1.68616
$694$		−	7.64888i		−	0.290348i
$695$			2.69671i			0.102292i
$696$			3.23633i			0.122673i
$697$		−	8.72916i		−	0.330641i
$698$	12.8967			0.488148
$699$	−4.25250			−0.160844
$700$		−	35.9948i		−	1.36048i
$701$	−5.79116			−0.218729			−0.109365	−	0.994002i	$-0.534882\pi$
$701$	−5.79116			−0.218729			−0.109365	+	0.994002i	$0.534882\pi$
$702$	−0.471388	−	3.45407i	−0.0177914	−	0.130366i
$703$	−71.4584			−2.69510
$704$		−	11.5952i		−	0.437011i
$705$	0.263023			0.00990602
$706$	−1.08237			−0.0407354
$707$		−	17.9954i		−	0.676788i
$708$		−	4.89295i		−	0.183888i
$709$			11.9447i			0.448594i	0.974521	+	0.224297i	$0.0720086\pi$
$709$			11.9447i			0.448594i	−0.974521	+	0.224297i	$0.927991\pi$
$710$			0.597366i			0.0224188i
$711$	−23.8174			−0.893222
$712$	5.69137			0.213293
$713$			8.58551i			0.321530i
$714$	−1.22939			−0.0460086
$715$	2.18037	−	0.297561i	0.0815410	−	0.0111282i
$716$	6.84021			0.255631
$717$			7.56601i			0.282558i
$718$	1.22843			0.0458446
$719$	−39.8697			−1.48689			−0.743445	−	0.668797i	$-0.766809\pi$
$719$	−39.8697			−1.48689			−0.743445	+	0.668797i	$0.766809\pi$
$720$			1.25381i			0.0467266i
$721$			23.7551i			0.884686i
$722$			8.53756i			0.317735i
$723$		−	2.49389i		−	0.0927486i
$724$	15.0955			0.561018
$725$	−25.9434			−0.963513
$726$			0.536860i			0.0199248i
$727$	−45.0588			−1.67114			−0.835569	−	0.549385i	$-0.814862\pi$
$727$	−45.0588			−1.67114			−0.835569	+	0.549385i	$0.814862\pi$
$728$	26.1638	−	3.57065i	0.969694	−	0.132337i
$729$	−20.7607			−0.768913
$730$			0.381559i			0.0141221i
$731$	11.4452			0.423316
$732$	−2.77203			−0.102457
$733$		−	28.3348i		−	1.04657i	−0.852158	−	0.523285i	$-0.824706\pi$
$733$		−	28.3348i		−	1.04657i	0.852158	−	0.523285i	$-0.175294\pi$
$734$			7.43857i			0.274563i
$735$			0.538787i			0.0198735i
$736$		−	41.8235i		−	1.54164i
$737$	29.0751			1.07100
$738$	6.52636			0.240239
$739$			2.93397i			0.107928i	0.998543	+	0.0539639i	$0.0171856\pi$
$739$			2.93397i			0.107928i	−0.998543	+	0.0539639i	$0.982814\pi$
$740$	3.36953			0.123867
$741$	−1.02436	−	7.50592i	−0.0376307	−	0.275737i
$742$	−11.9561			−0.438922
$743$			0.923703i			0.0338874i	0.999856	+	0.0169437i	$0.00539360\pi$
$743$			0.923703i			0.0338874i	−0.999856	+	0.0169437i	$0.994606\pi$
$744$	0.620472			0.0227476
$745$	−2.75568			−0.100960
$746$			13.5084i			0.494579i
$747$		−	35.0393i		−	1.28202i
$748$		−	12.2775i		−	0.448909i
$749$			68.3518i			2.49752i
$750$	−0.264997			−0.00967633
$751$	28.7114			1.04769			0.523847	−	0.851812i	$-0.324496\pi$
$751$	28.7114			1.04769			0.523847	+	0.851812i	$0.324496\pi$
$752$			12.6841i			0.462542i
$753$	4.77130			0.173876
$754$	−1.20963	−	8.86348i	−0.0440520	−	0.322789i
$755$	2.37364			0.0863856
$756$			14.7096i			0.534985i
$757$	−5.59884			−0.203493			−0.101747	−	0.994810i	$-0.532443\pi$
$757$	−5.59884			−0.203493			−0.101747	+	0.994810i	$0.532443\pi$
$758$	−1.74478			−0.0633731
$759$		−	11.2085i		−	0.406843i
$760$		−	1.76321i		−	0.0639583i
$761$			15.3752i			0.557351i	0.960385	+	0.278676i	$0.0898955\pi$
$761$			15.3752i			0.557351i	−0.960385	+	0.278676i	$0.910105\pi$
$762$		−	1.75524i		−	0.0635856i
$763$	32.5845			1.17964
$764$	15.0170			0.543294
$765$			0.853059i			0.0308424i
$766$	13.2014			0.476985
$767$	3.89092	+	28.5105i	0.140493	+	1.02946i
$768$	0.280319			0.0101151
$769$			15.2197i			0.548838i	0.961610	+	0.274419i	$0.0884855\pi$
$769$			15.2197i			0.548838i	−0.961610	+	0.274419i	$0.911515\pi$
$770$	1.18448			0.0426859
$771$	3.60429			0.129805
$772$		−	2.39996i		−	0.0863764i
$773$			22.8328i			0.821239i	0.911807	+	0.410620i	$0.134688\pi$
$773$			22.8328i			0.821239i	−0.911807	+	0.410620i	$0.865312\pi$
$774$			8.55702i			0.307576i
$775$			4.97389i			0.178667i
$776$	0.657325			0.0235966
$777$	16.5788			0.594761
$778$		−	3.71406i		−	0.133155i
$779$	28.9526			1.03734
$780$	0.0483023	+	0.353933i	0.00172950	+	0.0126728i
$781$	−29.3525			−1.05031
$782$		−	7.48440i		−	0.267642i
$783$	10.6020			0.378885
$784$	−25.9826			−0.927951
$785$		−	0.492413i		−	0.0175750i
$786$			3.22672i			0.115093i
$787$		−	45.5221i		−	1.62269i	−0.584570	−	0.811343i	$-0.698737\pi$
$787$		−	45.5221i		−	1.62269i	0.584570	−	0.811343i	$-0.301263\pi$
$788$		−	8.86146i		−	0.315677i
$789$	7.56870			0.269453
$790$	−0.635562			−0.0226123
$791$			35.6414i			1.26726i
$792$	19.5295			0.693950
$793$	16.1522	−	2.20434i	0.573582	−	0.0782785i
$794$	15.4680			0.548940
$795$		−	0.344106i		−	0.0122042i
$796$	−32.1973			−1.14120
$797$	−32.8209			−1.16258			−0.581288	−	0.813698i	$-0.697451\pi$
$797$	−32.8209			−1.16258			−0.581288	+	0.813698i	$0.697451\pi$
$798$		−	4.07760i		−	0.144345i
$799$			8.62994i			0.305305i
$800$		−	24.2298i		−	0.856654i
$801$		−	9.13288i		−	0.322695i
$802$	−8.77832			−0.309973
$803$	−18.7485			−0.661620
$804$			4.71968i			0.166450i
$805$	−5.66041			−0.199503
$806$	−1.69931	+	0.231911i	−0.0598558	+	0.00816870i
$807$	−1.45061			−0.0510638
$808$		−	7.91748i		−	0.278536i
$809$	−23.3816			−0.822055			−0.411027	−	0.911623i	$-0.634830\pi$
$809$	−23.3816			−0.822055			−0.411027	+	0.911623i	$0.634830\pi$
$810$	−0.610238			−0.0214416
$811$			20.9233i			0.734717i	0.930079	+	0.367358i	$0.119738\pi$
$811$			20.9233i			0.734717i	−0.930079	+	0.367358i	$0.880262\pi$
$812$			37.7463i			1.32464i
$813$		−	1.69359i		−	0.0593968i
$814$		−	21.1205i		−	0.740272i
$815$	−2.17183			−0.0760757
$816$	1.70631			0.0597327
$817$			37.9612i			1.32809i
$818$	−9.68274			−0.338549
$819$	−5.72979	−	41.9847i	−0.200215	−	1.46707i
$820$	−1.36523			−0.0476758
$821$			33.5027i			1.16925i	0.811303	+	0.584626i	$0.198759\pi$
$821$			33.5027i			1.16925i	−0.811303	+	0.584626i	$0.801241\pi$
$822$	0.392315			0.0136836
$823$	30.7439			1.07167			0.535833	−	0.844324i	$-0.319998\pi$
$823$	30.7439			1.07167			0.535833	+	0.844324i	$0.319998\pi$
$824$			10.4516i			0.364098i
$825$		−	6.49347i		−	0.226074i
$826$			15.4883i			0.538909i
$827$			38.4208i			1.33602i	0.744151	+	0.668012i	$0.232854\pi$
$827$			38.4208i			1.33602i	−0.744151	+	0.668012i	$0.767146\pi$
$828$	−43.8658			−1.52444
$829$	40.4200			1.40385			0.701923	−	0.712253i	$-0.252325\pi$
$829$	40.4200			1.40385			0.701923	+	0.712253i	$0.252325\pi$
$830$		−	0.935016i		−	0.0324549i
$831$	−5.51559			−0.191334
$832$	−10.9674	+	1.49676i	−0.380227	+	0.0518907i
$833$	−17.6779			−0.612504
$834$			2.74384i			0.0950115i
$835$	3.06618			0.106109
$836$	40.7216			1.40839
$837$		−	2.03263i		−	0.0702579i
$838$			15.5378i			0.536745i
$839$			10.2387i			0.353478i	0.984258	+	0.176739i	$0.0565549\pi$
$839$			10.2387i			0.353478i	−0.984258	+	0.176739i	$0.943445\pi$
$840$			0.409076i			0.0141145i
$841$	−1.79422			−0.0618695
$842$	4.76399			0.164178
$843$			2.86964i			0.0988355i
$844$	−31.0761			−1.06968
$845$	−0.562901	−	2.02390i	−0.0193644	−	0.0696244i
$846$	−6.45218			−0.221830
$847$			13.3219i			0.457746i
$848$	16.5943			0.569850
$849$	7.42476			0.254817
$850$		−	4.33598i		−	0.148723i
$851$			100.930i			3.45985i
$852$		−	4.76471i		−	0.163236i
$853$			39.8271i			1.36365i	0.731514	+	0.681826i	$0.238814\pi$
$853$			39.8271i			1.36365i	−0.731514	+	0.681826i	$0.761186\pi$
$854$	8.77470			0.300264
$855$	−2.82940			−0.0967635
$856$			30.0729i			1.02787i
$857$	17.2714			0.589981			0.294990	−	0.955500i	$-0.404684\pi$
$857$	17.2714			0.589981			0.294990	+	0.955500i	$0.404684\pi$
$858$	2.21847	−	0.302762i	0.0757375	−	0.0103361i
$859$	20.0471			0.683999			0.342000	−	0.939700i	$-0.388896\pi$
$859$	20.0471			0.683999			0.342000	+	0.939700i	$0.388896\pi$
$860$		−	1.79001i		−	0.0610390i
$861$	−6.71720			−0.228922
$862$	−7.47165			−0.254485
$863$			17.6248i			0.599957i	0.953946	+	0.299978i	$0.0969795\pi$
$863$			17.6248i			0.599957i	−0.953946	+	0.299978i	$0.903021\pi$
$864$			9.90176i			0.336865i
$865$			0.736964i			0.0250575i
$866$		−	10.9778i		−	0.373039i
$867$	−4.71519			−0.160136
$868$	7.23676			0.245632
$869$		−	31.2293i		−	1.05938i
$870$	0.138582			0.00469838
$871$	−3.75313	−	27.5009i	−0.127170	−	0.931832i
$872$	14.3363			0.485488
$873$		−	1.05480i		−	0.0356997i
$874$	24.8241			0.839686
$875$	−6.57576			−0.222301
$876$		−	3.04339i		−	0.102827i
$877$			21.4082i			0.722902i	0.932391	+	0.361451i	$0.117719\pi$
$877$			21.4082i			0.722902i	−0.932391	+	0.361451i	$0.882281\pi$
$878$			4.71455i			0.159108i
$879$		−	8.76649i		−	0.295686i
$880$	−1.64399			−0.0554188
$881$	−30.4594			−1.02620			−0.513102	−	0.858328i	$-0.671504\pi$
$881$	−30.4594			−1.02620			−0.513102	+	0.858328i	$0.671504\pi$
$882$		−	13.2169i		−	0.445036i
$883$	25.8122			0.868651			0.434326	−	0.900756i	$-0.356987\pi$
$883$	25.8122			0.868651			0.434326	+	0.900756i	$0.356987\pi$
$884$	−11.6127	+	1.58483i	−0.390579	+	0.0533035i
$885$	−0.445767			−0.0149843
$886$			4.87025i			0.163619i
$887$	17.1989			0.577484			0.288742	−	0.957407i	$-0.406763\pi$
$887$	17.1989			0.577484			0.288742	+	0.957407i	$0.406763\pi$
$888$	7.29420			0.244777
$889$		−	43.5553i		−	1.46080i
$890$		−	0.243709i		−	0.00816914i
$891$		−	29.9850i		−	1.00453i
$892$			26.4368i			0.885168i
$893$	−28.6235			−0.957851
$894$	−2.80385			−0.0937747
$895$		−	0.623170i		−	0.0208303i
$896$	−45.7083			−1.52701
$897$	−10.6016	+	1.44684i	−0.353978	+	0.0483085i
$898$	−17.9878			−0.600261
$899$		−	5.21592i		−	0.173961i
$900$	−25.4130			−0.847100
$901$	11.2903			0.376135
$902$			8.55734i			0.284928i
$903$		−	8.80723i		−	0.293086i
$904$			15.6812i			0.521550i
$905$		−	1.37525i		−	0.0457150i
$906$	2.41513			0.0802373
$907$	−19.7028			−0.654220			−0.327110	−	0.944986i	$-0.606075\pi$
$907$	−19.7028			−0.654220			−0.327110	+	0.944986i	$0.606075\pi$
$908$		−	42.0588i		−	1.39577i
$909$	−12.7051			−0.421402
$910$	−0.152898	−	1.12035i	−0.00506852	−	0.0371393i
$911$	−21.7935			−0.722050			−0.361025	−	0.932556i	$-0.617573\pi$
$911$	−21.7935			−0.722050			−0.361025	+	0.932556i	$0.617573\pi$
$912$			5.65944i			0.187403i
$913$	45.9434			1.52051
$914$	−2.74331			−0.0907406
$915$			0.252543i			0.00834881i
$916$		−	24.0984i		−	0.796233i
$917$			80.0692i			2.64412i
$918$			1.77194i			0.0584827i
$919$	−17.9983			−0.593709			−0.296855	−	0.954923i	$-0.595938\pi$
$919$	−17.9983			−0.593709			−0.296855	+	0.954923i	$0.595938\pi$
$920$	−2.49042			−0.0821067
$921$			8.49589i			0.279949i
$922$	−9.25081			−0.304659
$923$	3.78894	+	27.7633i	0.124714	+	0.913839i
$924$	−9.44768			−0.310806
$925$			58.4725i			1.92256i
$926$	−8.35246			−0.274479
$927$	16.7715			0.550849
$928$			25.4089i			0.834087i
$929$			41.5350i			1.36272i	0.731949	+	0.681360i	$0.238611\pi$
$929$			41.5350i			1.36272i	−0.731949	+	0.681360i	$0.761389\pi$
$930$		−	0.0265691i		−	0.000871235i
$931$		−	58.6337i		−	1.92164i
$932$	−21.8218			−0.714797
$933$	4.13981			0.135531
$934$		−	10.2345i		−	0.334884i
$935$	−1.11853			−0.0365798
$936$	−2.52094	−	18.4721i	−0.0823997	−	0.603779i
$937$	32.8134			1.07197			0.535983	−	0.844229i	$-0.319941\pi$
$937$	32.8134			1.07197			0.535983	+	0.844229i	$0.319941\pi$
$938$		−	14.9399i		−	0.487804i
$939$	1.43292			0.0467616
$940$	1.34971			0.0440227
$941$		−	47.4967i		−	1.54835i	−0.632972	−	0.774174i	$-0.718165\pi$
$941$		−	47.4967i		−	1.54835i	0.632972	−	0.774174i	$-0.281835\pi$
$942$		−	0.501019i		−	0.0163241i
$943$		−	40.8938i		−	1.33168i
$944$		−	21.4968i		−	0.699662i
$945$	1.34011			0.0435937
$946$	−11.2199			−0.364791
$947$		−	32.9725i		−	1.07146i	−0.844388	−	0.535731i	$-0.820036\pi$
$947$		−	32.9725i		−	1.07146i	0.844388	−	0.535731i	$-0.179964\pi$
$948$	5.06937			0.164645
$949$	2.42013	+	17.7334i	0.0785608	+	0.575650i
$950$	14.3814			0.466596
$951$			10.8423i			0.351584i
$952$	−13.4220			−0.435010
$953$	−8.49881			−0.275304			−0.137652	−	0.990481i	$-0.543955\pi$
$953$	−8.49881			−0.275304			−0.137652	+	0.990481i	$0.543955\pi$
$954$			8.44122i			0.273295i
$955$		−	1.36810i		−	0.0442708i
$956$			38.8252i			1.25570i
$957$			6.80944i			0.220118i
$958$	19.2237			0.621091
$959$	9.73508			0.314362
$960$		−	0.171478i		−	0.00553441i
$961$	−1.00000			−0.0322581
$962$	−19.9769	+	2.72632i	−0.644082	+	0.0878999i
$963$	48.2576			1.55508
$964$		−	12.7974i		−	0.412178i
$965$	−0.218646			−0.00703846
$966$	−5.75934			−0.185304
$967$			10.3380i			0.332448i	0.986088	+	0.166224i	$0.0531575\pi$
$967$			10.3380i			0.332448i	−0.986088	+	0.166224i	$0.946842\pi$
$968$			5.86125i			0.188388i
$969$			3.85054i			0.123697i
$970$		−	0.0281472i		−	0.000903751i
$971$	−42.4243			−1.36146			−0.680730	−	0.732534i	$-0.738337\pi$
$971$	−42.4243			−1.36146			−0.680730	+	0.732534i	$0.738337\pi$
$972$	15.6834			0.503046
$973$			68.0870i			2.18277i
$974$	0.226844			0.00726853
$975$	−6.14190	+	0.838204i	−0.196698	+	0.0268440i
$976$	−12.1787			−0.389831
$977$			9.45047i			0.302347i	0.988507	+	0.151174i	$0.0483053\pi$
$977$			9.45047i			0.302347i	−0.988507	+	0.151174i	$0.951695\pi$
$978$	−2.20979			−0.0706612
$979$	11.9750			0.382723
$980$			2.76480i			0.0883183i
$981$		−	23.0053i		−	0.734502i
$982$			2.57830i			0.0822770i
$983$			47.9698i			1.53000i	0.644031	+	0.765000i	$0.277261\pi$
$983$			47.9698i			1.53000i	−0.644031	+	0.765000i	$0.722739\pi$
$984$	−2.95538			−0.0942140
$985$	−0.807314			−0.0257232
$986$			4.54696i			0.144805i
$987$	6.64085			0.211381
$988$	−5.25651	−	38.5168i	−0.167232	−	1.22538i
$989$	53.6177			1.70494
$990$		−	0.836267i		−	0.0265783i
$991$	−12.1349			−0.385477			−0.192739	−	0.981250i	$-0.561737\pi$
$991$	−12.1349			−0.385477			−0.192739	+	0.981250i	$0.561737\pi$
$992$	4.87141			0.154667
$993$			0.167868i			0.00532711i
$994$			15.0824i			0.478385i
$995$			2.93330i			0.0929918i
$996$			7.45787i			0.236312i
$997$	15.1463			0.479688			0.239844	−	0.970811i	$-0.422904\pi$
$997$	15.1463			0.479688			0.239844	+	0.970811i	$0.422904\pi$
$998$	−6.04976			−0.191502
$999$		−	23.8954i		−	0.756015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.15	✓	32
13.5	odd	4		5239.2.a.k.1.9		16
13.8	odd	4		5239.2.a.l.1.8		16
13.12	even	2	inner	403.2.c.b.311.18	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.15	✓	32	1.1	even	1	trivial
403.2.c.b.311.18	yes	32	13.12	even	2	inner
5239.2.a.k.1.9		16	13.5	odd	4
5239.2.a.l.1.8		16	13.8	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)

\(f(q)\)	\(=\)	\(q-0.475674i q^{2} +0.345654 q^{3} +1.77373 q^{4} -0.161594i q^{5} -0.164419i q^{6} -4.07996i q^{7} -1.79507i q^{8} -2.88052 q^{9} +O(q^{10})\)	\(q-0.475674i q^{2} +0.345654 q^{3} +1.77373 q^{4} -0.161594i q^{5} -0.164419i q^{6} -4.07996i q^{7} -1.79507i q^{8} -2.88052 q^{9} -0.0768661 q^{10} -3.77693i q^{11} +0.613099 q^{12} +(-3.57244 + 0.487542i) q^{13} -1.94073 q^{14} -0.0558557i q^{15} +2.69360 q^{16} +1.83266 q^{17} +1.37019i q^{18} +6.07852i q^{19} -0.286625i q^{20} -1.41025i q^{21} -1.79659 q^{22} +8.58551 q^{23} -0.620472i q^{24} +4.97389 q^{25} +(0.231911 + 1.69931i) q^{26} -2.03263 q^{27} -7.23676i q^{28} -5.21592 q^{29} -0.0265691 q^{30} +1.00000i q^{31} -4.87141i q^{32} -1.30551i q^{33} -0.871748i q^{34} -0.659297 q^{35} -5.10928 q^{36} +11.7559i q^{37} +2.89139 q^{38} +(-1.23483 + 0.168521i) q^{39} -0.290072 q^{40} -4.76311i q^{41} -0.670821 q^{42} +6.24514 q^{43} -6.69927i q^{44} +0.465476i q^{45} -4.08390i q^{46} +4.70897i q^{47} +0.931056 q^{48} -9.64605 q^{49} -2.36595i q^{50} +0.633467 q^{51} +(-6.33655 + 0.864769i) q^{52} +6.16063 q^{53} +0.966867i q^{54} -0.610330 q^{55} -7.32379 q^{56} +2.10107i q^{57} +2.48107i q^{58} -7.98069i q^{59} -0.0990732i q^{60} -4.52134 q^{61} +0.475674 q^{62} +11.7524i q^{63} +3.07001 q^{64} +(0.0787839 + 0.577285i) q^{65} -0.620998 q^{66} +7.69808i q^{67} +3.25065 q^{68} +2.96762 q^{69} +0.313610i q^{70} -7.77152i q^{71} +5.17073i q^{72} -4.96395i q^{73} +5.59197 q^{74} +1.71925 q^{75} +10.7817i q^{76} -15.4097 q^{77} +(0.0801609 + 0.587375i) q^{78} +8.26843 q^{79} -0.435271i q^{80} +7.93898 q^{81} -2.26569 q^{82} +12.1642i q^{83} -2.50142i q^{84} -0.296147i q^{85} -2.97065i q^{86} -1.80290 q^{87} -6.77984 q^{88} +3.17056i q^{89} +0.221415 q^{90} +(1.98915 + 14.5754i) q^{91} +15.2284 q^{92} +0.345654i q^{93} +2.23993 q^{94} +0.982253 q^{95} -1.68382i q^{96} +0.366185i q^{97} +4.58837i q^{98} +10.8795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 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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