LMFDB - Embedded newform 403.2.c.b.311.8

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			311.8
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +O(q^{10})$	\(q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +1.03155 q^{10} +2.69554i q^{11} -0.655040 q^{12} +(-3.22749 + 1.60727i) q^{13} +1.71676 q^{14} +2.07594i q^{15} -4.38931 q^{16} -4.04263 q^{17} -8.91428i q^{18} -5.06961i q^{19} -0.151346i q^{20} +3.45488i q^{21} +4.01494 q^{22} -1.01940 q^{23} -7.95365i q^{24} +4.52036 q^{25} +(2.39399 + 4.80726i) q^{26} +8.94703 q^{27} -0.251878i q^{28} -8.56509 q^{29} +3.09205 q^{30} +1.00000i q^{31} +1.23085i q^{32} +8.07982i q^{33} +6.02139i q^{34} -0.798246 q^{35} -1.30787 q^{36} +5.88104i q^{37} -7.55104 q^{38} +(-9.67431 + 4.81776i) q^{39} +1.83768 q^{40} -11.8895i q^{41} +5.14596 q^{42} -3.63935 q^{43} -0.589058i q^{44} +4.14488i q^{45} +1.51836i q^{46} -0.848777i q^{47} -13.1568 q^{48} +5.67152 q^{49} -6.73295i q^{50} -12.1177 q^{51} +(0.705305 - 0.351239i) q^{52} +1.67652 q^{53} -13.3264i q^{54} -1.86683 q^{55} +3.05836 q^{56} -15.1960i q^{57} +12.7575i q^{58} +1.68042i q^{59} -0.453656i q^{60} +2.00772 q^{61} +1.48947 q^{62} +6.89813i q^{63} -6.94529 q^{64} +(-1.11314 - 2.23524i) q^{65} +12.0347 q^{66} -8.32497i q^{67} +0.883439 q^{68} -3.05562 q^{69} +1.18897i q^{70} -5.15229i q^{71} -15.8805i q^{72} +14.8210i q^{73} +8.75965 q^{74} +13.5497 q^{75} +1.10786i q^{76} -3.10687 q^{77} +(7.17593 + 14.4096i) q^{78} +0.873238 q^{79} -3.03987i q^{80} +8.86392 q^{81} -17.7091 q^{82} +10.8692i q^{83} -0.754998i q^{84} -2.79977i q^{85} +5.42072i q^{86} -25.6736 q^{87} +7.15249 q^{88} -3.90690i q^{89} +6.17370 q^{90} +(-1.85254 - 3.71999i) q^{91} +0.222769 q^{92} +2.99747i q^{93} -1.26423 q^{94} +3.51102 q^{95} +3.68945i q^{96} +10.3729i q^{97} -8.44757i q^{98} +16.1324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.48947i		−	1.05322i	−0.850108	−	0.526608i	$-0.823463\pi$
$2$		−	1.48947i		−	1.05322i	0.850108	−	0.526608i	$-0.176537\pi$
$3$	2.99747			1.73059			0.865296	−	0.501261i	$-0.167130\pi$
$3$	2.99747			1.73059			0.865296	+	0.501261i	$0.167130\pi$
$4$	−0.218531			−0.109265
$5$			0.692562i			0.309723i	0.987936	+	0.154862i	$0.0494932\pi$
$5$			0.692562i			0.309723i	−0.987936	+	0.154862i	$0.950507\pi$
$6$		−	4.46466i		−	1.82269i
$7$			1.15260i			0.435641i	0.975989	+	0.217821i	$0.0698947\pi$
$7$			1.15260i			0.435641i	−0.975989	+	0.217821i	$0.930105\pi$
$8$		−	2.65345i		−	0.938137i
$9$	5.98485			1.99495
$10$	1.03155			0.326206
$11$			2.69554i			0.812736i	0.913709	+	0.406368i	$0.133205\pi$
$11$			2.69554i			0.812736i	−0.913709	+	0.406368i	$0.866795\pi$
$12$	−0.655040			−0.189094
$13$	−3.22749	+	1.60727i	−0.895144	+	0.445777i
$13$	−3.22749	+	1.60727i	−0.895144	+	0.445777i
$14$	1.71676			0.458824
$15$			2.07594i			0.536005i
$16$	−4.38931			−1.09733
$17$	−4.04263			−0.980482			−0.490241	−	0.871587i	$-0.663091\pi$
$17$	−4.04263			−0.980482			−0.490241	+	0.871587i	$0.663091\pi$
$18$		−	8.91428i		−	2.10112i
$19$		−	5.06961i		−	1.16305i	−0.813530	−	0.581524i	$-0.802457\pi$
$19$		−	5.06961i		−	1.16305i	0.813530	−	0.581524i	$-0.197543\pi$
$20$		−	0.151346i		−	0.0338420i
$21$			3.45488i			0.753917i
$22$	4.01494			0.855987
$23$	−1.01940			−0.212559			−0.106279	−	0.994336i	$-0.533894\pi$
$23$	−1.01940			−0.212559			−0.106279	+	0.994336i	$0.533894\pi$
$24$		−	7.95365i		−	1.62353i
$25$	4.52036			0.904071
$26$	2.39399	+	4.80726i	0.469500	+	0.942780i
$27$	8.94703			1.72186
$28$		−	0.251878i		−	0.0476005i
$29$	−8.56509			−1.59050			−0.795249	−	0.606283i	$-0.792660\pi$
$29$	−8.56509			−1.59050			−0.795249	+	0.606283i	$0.792660\pi$
$30$	3.09205			0.564529
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$			1.23085i			0.217586i
$33$			8.07982i			1.40652i
$34$			6.02139i			1.03266i
$35$	−0.798246			−0.134928
$36$	−1.30787			−0.217979
$37$			5.88104i			0.966837i	0.875389	+	0.483418i	$0.160605\pi$
$37$			5.88104i			0.966837i	−0.875389	+	0.483418i	$0.839395\pi$
$38$	−7.55104			−1.22494
$39$	−9.67431	+	4.81776i	−1.54913	+	0.771459i
$40$	1.83768			0.290563
$41$		−	11.8895i		−	1.85683i	−0.371551	−	0.928413i	$-0.621174\pi$
$41$		−	11.8895i		−	1.85683i	0.371551	−	0.928413i	$-0.378826\pi$
$42$	5.14596			0.794038
$43$	−3.63935			−0.554996			−0.277498	−	0.960726i	$-0.589505\pi$
$43$	−3.63935			−0.554996			−0.277498	+	0.960726i	$0.589505\pi$
$44$		−	0.589058i		−	0.0888039i
$45$			4.14488i			0.617883i
$46$			1.51836i			0.223871i
$47$		−	0.848777i		−	0.123807i	−0.998082	−	0.0619034i	$-0.980283\pi$
$47$		−	0.848777i		−	0.123807i	0.998082	−	0.0619034i	$-0.0197171\pi$
$48$	−13.1568			−1.89903
$49$	5.67152			0.810217
$50$		−	6.73295i		−	0.952183i
$51$	−12.1177			−1.69681
$52$	0.705305	−	0.351239i	0.0978082	−	0.0487080i
$53$	1.67652			0.230287			0.115144	−	0.993349i	$-0.463267\pi$
$53$	1.67652			0.230287			0.115144	+	0.993349i	$0.463267\pi$
$54$		−	13.3264i		−	1.81349i
$55$	−1.86683			−0.251723
$56$	3.05836			0.408691
$57$		−	15.1960i		−	2.01276i
$58$			12.7575i			1.67514i
$59$			1.68042i			0.218772i	0.993999	+	0.109386i	$0.0348885\pi$
$59$			1.68042i			0.218772i	−0.993999	+	0.109386i	$0.965111\pi$
$60$		−	0.453656i		−	0.0585668i
$61$	2.00772			0.257062			0.128531	−	0.991705i	$-0.458974\pi$
$61$	2.00772			0.257062			0.128531	+	0.991705i	$0.458974\pi$
$62$	1.48947			0.189163
$63$			6.89813i			0.869083i
$64$	−6.94529			−0.868161
$65$	−1.11314	−	2.23524i	−0.138068	−	0.277247i
$66$	12.0347			1.48137
$67$		−	8.32497i		−	1.01706i	−0.861045	−	0.508529i	$-0.830190\pi$
$67$		−	8.32497i		−	1.01706i	0.861045	−	0.508529i	$-0.169810\pi$
$68$	0.883439			0.107133
$69$	−3.05562			−0.367853
$70$			1.18897i			0.142109i
$71$		−	5.15229i		−	0.611465i	−0.952117	−	0.305732i	$-0.901099\pi$
$71$		−	5.15229i		−	0.611465i	0.952117	−	0.305732i	$-0.0989013\pi$
$72$		−	15.8805i		−	1.87154i
$73$			14.8210i			1.73466i	0.497730	+	0.867332i	$0.334167\pi$
$73$			14.8210i			1.73466i	−0.497730	+	0.867332i	$0.665833\pi$
$74$	8.75965			1.01829
$75$	13.5497			1.56458
$76$			1.10786i			0.127081i
$77$	−3.10687			−0.354061
$78$	7.17593	+	14.4096i	0.812514	+	1.63157i
$79$	0.873238			0.0982470			0.0491235	−	0.998793i	$-0.484357\pi$
$79$	0.873238			0.0982470			0.0491235	+	0.998793i	$0.484357\pi$
$80$		−	3.03987i		−	0.339868i
$81$	8.86392			0.984880
$82$	−17.7091			−1.95564
$83$			10.8692i			1.19305i	0.802596	+	0.596523i	$0.203452\pi$
$83$			10.8692i			1.19305i	−0.802596	+	0.596523i	$0.796548\pi$
$84$		−	0.754998i		−	0.0823770i
$85$		−	2.79977i		−	0.303678i
$86$			5.42072i			0.584531i
$87$	−25.6736			−2.75250
$88$	7.15249			0.762457
$89$		−	3.90690i		−	0.414131i	−0.978327	−	0.207065i	$-0.933609\pi$
$89$		−	3.90690i		−	0.414131i	0.978327	−	0.207065i	$-0.0663913\pi$
$90$	6.17370			0.650765
$91$	−1.85254	−	3.71999i	−0.194199	−	0.389961i
$92$	0.222769			0.0232253
$93$			2.99747i			0.310824i
$94$	−1.26423			−0.130395
$95$	3.51102			0.360223
$96$			3.68945i			0.376553i
$97$			10.3729i			1.05321i	0.850110	+	0.526606i	$0.176536\pi$
$97$			10.3729i			1.05321i	−0.850110	+	0.526606i	$0.823464\pi$
$98$		−	8.44757i		−	0.853334i
$99$			16.1324i			1.62137i
$100$	−0.987837			−0.0987837
$101$	−1.55946			−0.155172			−0.0775862	−	0.996986i	$-0.524721\pi$
$101$	−1.55946			−0.155172			−0.0775862	+	0.996986i	$0.524721\pi$
$102$			18.0490i			1.78711i
$103$	18.4902			1.82189			0.910947	−	0.412523i	$-0.135352\pi$
$103$	18.4902			1.82189			0.910947	+	0.412523i	$0.135352\pi$
$104$	4.26482	+	8.56398i	0.418200	+	0.839767i
$105$	−2.39272			−0.233506
$106$		−	2.49713i		−	0.242543i
$107$	15.4750			1.49602			0.748010	−	0.663687i	$-0.231009\pi$
$107$	15.4750			1.49602			0.748010	+	0.663687i	$0.231009\pi$
$108$	−1.95520			−0.188139
$109$			11.0776i			1.06104i	0.847673	+	0.530518i	$0.178003\pi$
$109$			11.0776i			1.06104i	−0.847673	+	0.530518i	$0.821997\pi$
$110$			2.78059i			0.265119i
$111$			17.6283i			1.67320i
$112$		−	5.05910i		−	0.478040i
$113$	1.83667			0.172780			0.0863898	−	0.996261i	$-0.472467\pi$
$113$	1.83667			0.172780			0.0863898	+	0.996261i	$0.472467\pi$
$114$	−22.6341			−2.11987
$115$		−	0.705996i		−	0.0658344i
$116$	1.87174			0.173786
$117$	−19.3160	+	9.61930i	−1.78577	+	0.889304i
$118$	2.50294			0.230415
$119$		−	4.65953i		−	0.427138i
$120$	5.50840			0.502846
$121$	3.73406			0.339460
$122$		−	2.99045i		−	0.270743i
$123$		−	35.6384i		−	3.21341i
$124$		−	0.218531i		−	0.0196246i
$125$			6.59344i			0.589735i
$126$	10.2746			0.915333
$127$	14.4471			1.28198			0.640988	−	0.767551i	$-0.278525\pi$
$127$	14.4471			1.28198			0.640988	+	0.767551i	$0.278525\pi$
$128$			12.8065i			1.13195i
$129$	−10.9089			−0.960472
$130$	−3.32932	+	1.65799i	−0.292001	+	0.145415i
$131$	−6.01302			−0.525360			−0.262680	−	0.964883i	$-0.584606\pi$
$131$	−6.01302			−0.525360			−0.262680	+	0.964883i	$0.584606\pi$
$132$		−	1.76569i		−	0.153683i
$133$	5.84322			0.506671
$134$	−12.3998			−1.07118
$135$			6.19637i			0.533299i
$136$			10.7269i			0.919826i
$137$		−	16.9039i		−	1.44420i	−0.691791	−	0.722098i	$-0.743178\pi$
$137$		−	16.9039i		−	1.44420i	0.691791	−	0.722098i	$-0.256822\pi$
$138$			4.55126i			0.387429i
$139$	−0.0379050			−0.00321506			−0.00160753	−	0.999999i	$-0.500512\pi$
$139$	−0.0379050			−0.00321506			−0.00160753	+	0.999999i	$0.500512\pi$
$140$	0.174441			0.0147430
$141$		−	2.54419i		−	0.214259i
$142$	−7.67421			−0.644005
$143$	−4.33247	−	8.69982i	−0.362299	−	0.727516i
$144$	−26.2694			−2.18911
$145$		−	5.93186i		−	0.492614i
$146$	22.0754			1.82698
$147$	17.0002			1.40216
$148$		−	1.28519i		−	0.105642i
$149$			16.6078i			1.36056i	0.732952	+	0.680281i	$0.238142\pi$
$149$			16.6078i			1.36056i	−0.732952	+	0.680281i	$0.761858\pi$
$150$		−	20.1819i		−	1.64784i
$151$			3.90890i			0.318102i	0.987270	+	0.159051i	$0.0508434\pi$
$151$			3.90890i			0.318102i	−0.987270	+	0.159051i	$0.949157\pi$
$152$	−13.4519			−1.09110
$153$	−24.1945			−1.95601
$154$			4.62761i			0.372903i
$155$	−0.692562			−0.0556279
$156$	2.11413	−	1.05283i	0.169266	−	0.0842937i
$157$	4.63903			0.370235			0.185117	−	0.982716i	$-0.440733\pi$
$157$	4.63903			0.370235			0.185117	+	0.982716i	$0.440733\pi$
$158$		−	1.30066i		−	0.103475i
$159$	5.02532			0.398534
$160$	−0.852441			−0.0673914
$161$		−	1.17495i		−	0.0925994i
$162$		−	13.2026i		−	1.03729i
$163$			14.1214i			1.10607i	0.833158	+	0.553035i	$0.186531\pi$
$163$			14.1214i			1.10607i	−0.833158	+	0.553035i	$0.813469\pi$
$164$			2.59822i			0.202887i
$165$	−5.59578			−0.435631
$166$	16.1893			1.25654
$167$		−	10.5161i		−	0.813759i	−0.913482	−	0.406879i	$-0.866617\pi$
$167$		−	10.5161i		−	0.813759i	0.913482	−	0.406879i	$-0.133383\pi$
$168$	9.16736			0.707277
$169$	7.83335	−	10.3749i	0.602565	−	0.798070i
$170$	−4.17019			−0.319839
$171$		−	30.3409i		−	2.32022i
$172$	0.795310			0.0606418
$173$	20.5134			1.55960			0.779801	−	0.626028i	$-0.215320\pi$
$173$	20.5134			1.55960			0.779801	+	0.626028i	$0.215320\pi$
$174$			38.2402i			2.89898i
$175$			5.21015i			0.393851i
$176$		−	11.8316i		−	0.891837i
$177$			5.03702i			0.378606i
$178$	−5.81923			−0.436170
$179$	−10.7116			−0.800620			−0.400310	−	0.916380i	$-0.631098\pi$
$179$	−10.7116			−0.800620			−0.400310	+	0.916380i	$0.631098\pi$
$180$		−	0.905785i		−	0.0675132i
$181$	−23.9491			−1.78012			−0.890061	−	0.455842i	$-0.849338\pi$
$181$	−23.9491			−1.78012			−0.890061	+	0.455842i	$0.849338\pi$
$182$	−5.54083	+	2.75931i	−0.410714	+	0.204534i
$183$	6.01810			0.444871
$184$			2.70492i			0.199409i
$185$	−4.07299			−0.299452
$186$	4.46466			0.327365
$187$		−	10.8971i		−	0.796873i
$188$			0.185484i			0.0135278i
$189$			10.3123i			0.750111i
$190$		−	5.22957i		−	0.379393i
$191$	−3.30915			−0.239442			−0.119721	−	0.992808i	$-0.538200\pi$
$191$	−3.30915			−0.239442			−0.119721	+	0.992808i	$0.538200\pi$
$192$	−20.8183			−1.50243
$193$		−	9.66509i		−	0.695709i	−0.937549	−	0.347854i	$-0.886910\pi$
$193$		−	9.66509i		−	0.695709i	0.937549	−	0.347854i	$-0.113090\pi$
$194$	15.4502			1.10926
$195$	−3.33660	−	6.70006i	−0.238939	−	0.479801i
$196$	−1.23940			−0.0885286
$197$		−	26.5454i		−	1.89128i	−0.325212	−	0.945641i	$-0.605436\pi$
$197$		−	26.5454i		−	1.89128i	0.325212	−	0.945641i	$-0.394564\pi$
$198$	24.0288			1.70765
$199$	−6.60253			−0.468041			−0.234021	−	0.972232i	$-0.575188\pi$
$199$	−6.60253			−0.468041			−0.234021	+	0.972232i	$0.575188\pi$
$200$		−	11.9945i		−	0.848143i
$201$		−	24.9539i		−	1.76011i
$202$			2.32278i			0.163430i
$203$		−	9.87211i		−	0.692886i
$204$	2.64808			0.185403
$205$	8.23421			0.575102
$206$		−	27.5407i		−	1.91885i
$207$	−6.10094			−0.424045
$208$	14.1664	−	7.05481i	0.982265	−	0.489163i
$209$	13.6653			0.945250
$210$			3.56390i			0.245932i
$211$	−18.1733			−1.25110			−0.625551	−	0.780183i	$-0.715126\pi$
$211$	−18.1733			−1.25110			−0.625551	+	0.780183i	$0.715126\pi$
$212$	−0.366371			−0.0251624
$213$		−	15.4439i		−	1.05820i
$214$		−	23.0495i		−	1.57563i
$215$		−	2.52048i		−	0.171895i
$216$		−	23.7405i		−	1.61534i
$217$	−1.15260			−0.0782434
$218$	16.4997			1.11750
$219$			44.4255i			3.00200i
$220$	0.407960			0.0275046
$221$	13.0475	−	6.49761i	0.877672	−	0.437076i
$222$	26.2568			1.76224
$223$		−	3.90568i		−	0.261544i	−0.991412	−	0.130772i	$-0.958254\pi$
$223$		−	3.90568i		−	0.261544i	0.991412	−	0.130772i	$-0.0417456\pi$
$224$	−1.41868			−0.0947894
$225$	27.0537			1.80358
$226$		−	2.73568i		−	0.181974i
$227$		−	16.9202i		−	1.12303i	−0.827466	−	0.561515i	$-0.810219\pi$
$227$		−	16.9202i		−	1.12303i	0.827466	−	0.561515i	$-0.189781\pi$
$228$			3.32080i			0.219925i
$229$		−	11.5304i		−	0.761949i	−0.924585	−	0.380975i	$-0.875589\pi$
$229$		−	11.5304i		−	0.761949i	0.924585	−	0.380975i	$-0.124411\pi$
$230$	−1.05156			−0.0693379
$231$	−9.31278			−0.612736
$232$			22.7271i			1.49210i
$233$	0.108649			0.00711784			0.00355892	−	0.999994i	$-0.498867\pi$
$233$	0.108649			0.00711784			0.00355892	+	0.999994i	$0.498867\pi$
$234$	14.3277	+	28.7707i	0.936630	+	1.88080i
$235$	0.587831			0.0383459
$236$		−	0.367224i		−	0.0239042i
$237$	2.61751			0.170026
$238$	−6.94024			−0.449869
$239$			15.8424i			1.02476i	0.858760	+	0.512378i	$0.171235\pi$
$239$			15.8424i			1.02476i	−0.858760	+	0.512378i	$0.828765\pi$
$240$		−	9.11193i		−	0.588172i
$241$		−	4.44336i		−	0.286222i	−0.989707	−	0.143111i	$-0.954289\pi$
$241$		−	4.44336i		−	0.286222i	0.989707	−	0.143111i	$-0.0457106\pi$
$242$		−	5.56178i		−	0.357525i
$243$	−0.271696			−0.0174293
$244$	−0.438749			−0.0280880
$245$			3.92788i			0.250943i
$246$	−53.0825			−3.38442
$247$	8.14824	+	16.3621i	0.518460	+	1.04109i
$248$	2.65345			0.168494
$249$			32.5801i			2.06468i
$250$	9.82075			0.621119
$251$	8.24869			0.520653			0.260326	−	0.965521i	$-0.416170\pi$
$251$	8.24869			0.520653			0.260326	+	0.965521i	$0.416170\pi$
$252$		−	1.50745i		−	0.0949606i
$253$		−	2.74783i		−	0.172754i
$254$		−	21.5186i		−	1.35020i
$255$		−	8.39225i		−	0.525543i
$256$	5.18440			0.324025
$257$	−8.29303			−0.517305			−0.258652	−	0.965970i	$-0.583278\pi$
$257$	−8.29303			−0.517305			−0.258652	+	0.965970i	$0.583278\pi$
$258$			16.2485i			1.01159i
$259$	−6.77847			−0.421194
$260$	0.243255	+	0.488468i	0.0150860	+	0.0302935i
$261$	−51.2608			−3.17297
$262$			8.95624i			0.553318i
$263$	−19.7412			−1.21729			−0.608646	−	0.793442i	$-0.708287\pi$
$263$	−19.7412			−1.21729			−0.608646	+	0.793442i	$0.708287\pi$
$264$	21.4394			1.31950
$265$			1.16109i			0.0713254i
$266$		−	8.70331i		−	0.533634i
$267$		−	11.7108i		−	0.716692i
$268$			1.81926i			0.111129i
$269$	−28.8863			−1.76123			−0.880614	−	0.473834i	$-0.842870\pi$
$269$	−28.8863			−1.76123			−0.880614	+	0.473834i	$0.842870\pi$
$270$	9.22933			0.561679
$271$			0.993095i			0.0603262i	0.999545	+	0.0301631i	$0.00960268\pi$
$271$			0.993095i			0.0603262i	−0.999545	+	0.0301631i	$0.990397\pi$
$272$	17.7443			1.07591
$273$	−5.55294	−	11.1506i	−0.336079	−	0.674864i
$274$	−25.1779			−1.52105
$275$			12.1848i			0.734772i
$276$	0.667746			0.0401936
$277$	1.99748			0.120017			0.0600085	−	0.998198i	$-0.480887\pi$
$277$	1.99748			0.120017			0.0600085	+	0.998198i	$0.480887\pi$
$278$			0.0564585i			0.00338616i
$279$			5.98485i			0.358304i
$280$			2.11811i			0.126581i
$281$		−	9.22146i		−	0.550106i	−0.961429	−	0.275053i	$-0.911305\pi$
$281$		−	9.22146i		−	0.550106i	0.961429	−	0.275053i	$-0.0886955\pi$
$282$	−3.78950			−0.225661
$283$	−6.66812			−0.396379			−0.198189	−	0.980164i	$-0.563506\pi$
$283$	−6.66812			−0.396379			−0.198189	+	0.980164i	$0.563506\pi$
$284$			1.12593i			0.0668119i
$285$	10.5242			0.623399
$286$	−12.9582	+	6.45310i	−0.766232	+	0.381580i
$287$	13.7038			0.808909
$288$			7.36647i			0.434073i
$289$	−0.657150			−0.0386559
$290$	−8.83535			−0.518829
$291$			31.0926i			1.82268i
$292$		−	3.23884i		−	0.189539i
$293$			20.6409i			1.20585i	0.797797	+	0.602926i	$0.205999\pi$
$293$			20.6409i			1.20585i	−0.797797	+	0.602926i	$0.794001\pi$
$294$		−	25.3214i		−	1.47677i
$295$	−1.16380			−0.0677589
$296$	15.6050			0.907025
$297$			24.1171i			1.39941i
$298$	24.7368			1.43297
$299$	3.29009	−	1.63845i	0.190271	−	0.0947539i
$300$	−2.96102			−0.170954
$301$		−	4.19471i		−	0.241779i
$302$	5.82220			0.335030
$303$	−4.67445			−0.268540
$304$			22.2520i			1.27624i
$305$			1.39047i			0.0796182i
$306$			36.0371i			2.06011i
$307$			3.05469i			0.174340i	0.996193	+	0.0871702i	$0.0277824\pi$
$307$			3.05469i			0.174340i	−0.996193	+	0.0871702i	$0.972218\pi$
$308$	0.678947			0.0386866
$309$	55.4239			3.15296
$310$			1.03155i			0.0585883i
$311$	−22.9204			−1.29969			−0.649847	−	0.760065i	$-0.725167\pi$
$311$	−22.9204			−1.29969			−0.649847	+	0.760065i	$0.725167\pi$
$312$	12.7837	+	25.6703i	0.723734	+	1.45330i
$313$	10.3566			0.585391			0.292695	−	0.956206i	$-0.405448\pi$
$313$	10.3566			0.585391			0.292695	+	0.956206i	$0.405448\pi$
$314$		−	6.90971i		−	0.389937i
$315$	−4.77739			−0.269175
$316$	−0.190829			−0.0107350
$317$		−	9.04755i		−	0.508161i	−0.967183	−	0.254080i	$-0.918227\pi$
$317$		−	9.04755i		−	0.508161i	0.967183	−	0.254080i	$-0.0817728\pi$
$318$		−	7.48508i		−	0.419742i
$319$		−	23.0876i		−	1.29265i
$320$		−	4.81005i		−	0.268890i
$321$	46.3858			2.58900
$322$	−1.75006			−0.0975272
$323$			20.4945i			1.14035i
$324$	−1.93704			−0.107613
$325$	−14.5894	+	7.26545i	−0.809274	+	0.403015i
$326$	21.0334			1.16493
$327$			33.2047i			1.83622i
$328$	−31.5482			−1.74196
$329$	0.978299			0.0539354
$330$			8.33476i			0.458813i
$331$		−	32.1476i		−	1.76699i	−0.468438	−	0.883496i	$-0.655183\pi$
$331$		−	32.1476i		−	1.76699i	0.468438	−	0.883496i	$-0.344817\pi$
$332$		−	2.37525i		−	0.130359i
$333$			35.1972i			1.92879i
$334$	−15.6634			−0.857064
$335$	5.76556			0.315006
$336$		−	15.1645i		−	0.827293i
$337$	31.7351			1.72872			0.864361	−	0.502871i	$-0.167723\pi$
$337$	31.7351			1.72872			0.864361	+	0.502871i	$0.167723\pi$
$338$	−15.4531	−	11.6676i	−0.840540	−	0.634632i
$339$	5.50538			0.299011
$340$			0.611836i			0.0331815i
$341$	−2.69554			−0.145972
$342$	−45.1919			−2.44370
$343$			14.6052i			0.788605i
$344$			9.65684i			0.520662i
$345$		−	2.11620i		−	0.113933i
$346$		−	30.5541i		−	1.64260i
$347$	−1.57708			−0.0846622			−0.0423311	−	0.999104i	$-0.513478\pi$
$347$	−1.57708			−0.0846622			−0.0423311	+	0.999104i	$0.513478\pi$
$348$	5.61048			0.300753
$349$		−	33.0608i		−	1.76970i	−0.465872	−	0.884852i	$-0.654259\pi$
$349$		−	33.0608i		−	1.76970i	0.465872	−	0.884852i	$-0.345741\pi$
$350$	7.76039			0.414810
$351$	−28.8764	+	14.3803i	−1.54131	+	0.767564i
$352$	−3.31781			−0.176840
$353$			4.70845i			0.250605i	0.992119	+	0.125303i	$0.0399902\pi$
$353$			4.70845i			0.250605i	−0.992119	+	0.125303i	$0.960010\pi$
$354$	7.50251			0.398754
$355$	3.56829			0.189385
$356$			0.853778i			0.0452502i
$357$		−	13.9668i		−	0.739202i
$358$			15.9546i			0.843226i
$359$			27.2147i			1.43634i	0.695868	+	0.718169i	$0.255020\pi$
$359$			27.2147i			1.43634i	−0.695868	+	0.718169i	$0.744980\pi$
$360$	10.9982			0.579659
$361$	−6.70090			−0.352679
$362$			35.6715i			1.87485i
$363$	11.1928			0.587467
$364$	0.404837	+	0.812933i	0.0212192	+	0.0426093i
$365$	−10.2644			−0.537266
$366$		−	8.96379i		−	0.468545i
$367$	4.82539			0.251883			0.125942	−	0.992038i	$-0.459805\pi$
$367$	4.82539			0.251883			0.125942	+	0.992038i	$0.459805\pi$
$368$	4.47444			0.233246
$369$		−	71.1568i		−	3.70428i
$370$			6.06660i			0.315388i
$371$			1.93235i			0.100323i
$372$		−	0.655040i		−	0.0339623i
$373$	17.5308			0.907710			0.453855	−	0.891076i	$-0.350048\pi$
$373$	17.5308			0.907710			0.453855	+	0.891076i	$0.350048\pi$
$374$	−16.2309			−0.839280
$375$			19.7637i			1.02059i
$376$	−2.25219			−0.116148
$377$	27.6437	−	13.7664i	1.42372	−	0.709008i
$378$	15.3599			0.790030
$379$			33.9284i			1.74279i	0.490586	+	0.871393i	$0.336783\pi$
$379$			33.9284i			1.74279i	−0.490586	+	0.871393i	$0.663217\pi$
$380$	−0.767265			−0.0393599
$381$	43.3049			2.21858
$382$			4.92889i			0.252184i
$383$		−	6.07830i		−	0.310587i	−0.987868	−	0.155293i	$-0.950368\pi$
$383$		−	6.07830i		−	0.310587i	0.987868	−	0.155293i	$-0.0496323\pi$
$384$			38.3872i			1.95894i
$385$		−	2.15170i		−	0.109661i
$386$	−14.3959			−0.732732
$387$	−21.7810			−1.10719
$388$		−	2.26680i		−	0.115080i
$389$	15.9014			0.806232			0.403116	−	0.915149i	$-0.367927\pi$
$389$	15.9014			0.806232			0.403116	+	0.915149i	$0.367927\pi$
$390$	−9.97956	+	4.96978i	−0.505335	+	0.251654i
$391$	4.12104			0.208410
$392$		−	15.0491i		−	0.760094i
$393$	−18.0239			−0.909185
$394$	−39.5387			−1.99193
$395$			0.604772i			0.0304294i
$396$		−	3.52543i		−	0.177159i
$397$		−	26.8597i		−	1.34805i	−0.738709	−	0.674024i	$-0.764564\pi$
$397$		−	26.8597i		−	1.34805i	0.738709	−	0.674024i	$-0.235436\pi$
$398$			9.83430i			0.492949i
$399$	17.5149			0.876841
$400$	−19.8412			−0.992062
$401$		−	29.4467i		−	1.47050i	−0.677797	−	0.735249i	$-0.737065\pi$
$401$		−	29.4467i		−	1.47050i	0.677797	−	0.735249i	$-0.262935\pi$
$402$	−37.1682			−1.85378
$403$	−1.60727	−	3.22749i	−0.0800640	−	0.160773i
$404$	0.340791			0.0169550
$405$			6.13882i			0.305040i
$406$	−14.7042			−0.729759
$407$	−15.8526			−0.785783
$408$			32.1537i			1.59184i
$409$		−	38.4627i		−	1.90186i	−0.309408	−	0.950930i	$-0.600131\pi$
$409$		−	38.4627i		−	1.90186i	0.309408	−	0.950930i	$-0.399869\pi$
$410$		−	12.2646i		−	0.605707i
$411$		−	50.6690i		−	2.49932i
$412$	−4.04068			−0.199070
$413$	−1.93685			−0.0953062
$414$			9.08719i			0.446611i
$415$	−7.52757			−0.369514
$416$	−1.97831	−	3.97256i	−0.0969949	−	0.194771i
$417$	−0.113619			−0.00556396
$418$		−	20.3541i		−	0.995554i
$419$	6.73204			0.328882			0.164441	−	0.986387i	$-0.447418\pi$
$419$	6.73204			0.328882			0.164441	+	0.986387i	$0.447418\pi$
$420$	0.522883			0.0255141
$421$		−	0.815884i		−	0.0397637i	−0.999802	−	0.0198819i	$-0.993671\pi$
$421$		−	0.815884i		−	0.0397637i	0.999802	−	0.0198819i	$-0.00632901\pi$
$422$			27.0686i			1.31768i
$423$		−	5.07981i		−	0.246989i
$424$		−	4.44856i		−	0.216041i
$425$	−18.2741			−0.886425
$426$	−23.0032			−1.11451
$427$			2.31410i			0.111987i
$428$	−3.38175			−0.163463
$429$	−12.9865	−	26.0775i	−0.626993	−	1.25903i
$430$	−3.75418			−0.181043
$431$			35.7637i			1.72268i	0.508032	+	0.861338i	$0.330373\pi$
$431$			35.7637i			1.72268i	−0.508032	+	0.861338i	$0.669627\pi$
$432$	−39.2712			−1.88944
$433$	−25.8780			−1.24362			−0.621808	−	0.783170i	$-0.713601\pi$
$433$	−25.8780			−1.24362			−0.621808	+	0.783170i	$0.713601\pi$
$434$			1.71676i			0.0824073i
$435$		−	17.7806i		−	0.852515i
$436$		−	2.42078i		−	0.115935i
$437$			5.16794i			0.247216i
$438$	66.1706			3.16175
$439$	−24.4490			−1.16689			−0.583444	−	0.812153i	$-0.698295\pi$
$439$	−24.4490			−1.16689			−0.583444	+	0.812153i	$0.698295\pi$
$440$			4.95354i			0.236151i
$441$	33.9432			1.61634
$442$	−9.67802	−	19.4340i	−0.460336	−	0.924379i
$443$	15.4138			0.732330			0.366165	−	0.930550i	$-0.380671\pi$
$443$	15.4138			0.732330			0.366165	+	0.930550i	$0.380671\pi$
$444$		−	3.85232i		−	0.182823i
$445$	2.70577			0.128266
$446$	−5.81741			−0.275462
$447$			49.7814i			2.35458i
$448$		−	8.00513i		−	0.378207i
$449$			1.20092i			0.0566750i	0.999598	+	0.0283375i	$0.00902131\pi$
$449$			1.20092i			0.0566750i	−0.999598	+	0.0283375i	$0.990979\pi$
$450$		−	40.2957i		−	1.89956i
$451$	32.0486			1.50911
$452$	−0.401369			−0.0188788
$453$			11.7168i			0.550504i
$454$	−25.2021			−1.18279
$455$	2.57633	−	1.28300i	0.120780	−	0.0601479i
$456$	−40.3219			−1.88824
$457$			4.20576i			0.196737i	0.995150	+	0.0983686i	$0.0313624\pi$
$457$			4.20576i			0.196737i	−0.995150	+	0.0983686i	$0.968638\pi$
$458$	−17.1742			−0.802498
$459$	−36.1695			−1.68825
$460$			0.154282i			0.00719342i
$461$			14.1239i			0.657814i	0.944362	+	0.328907i	$0.106680\pi$
$461$			14.1239i			0.657814i	−0.944362	+	0.328907i	$0.893320\pi$
$462$			13.8711i			0.645344i
$463$			21.9558i			1.02037i	0.860064	+	0.510186i	$0.170423\pi$
$463$			21.9558i			1.02037i	−0.860064	+	0.510186i	$0.829577\pi$
$464$	37.5948			1.74530
$465$	−2.07594			−0.0962693
$466$		−	0.161830i		−	0.00749663i
$467$	−0.918022			−0.0424810			−0.0212405	−	0.999774i	$-0.506762\pi$
$467$	−0.918022			−0.0424810			−0.0212405	+	0.999774i	$0.506762\pi$
$468$	4.22115	−	2.10211i	0.195123	−	0.0971701i
$469$	9.59535			0.443072
$470$		−	0.875559i		−	0.0403865i
$471$	13.9054			0.640726
$472$	4.45892			0.205238
$473$		−	9.81002i		−	0.451065i
$474$		−	3.89871i		−	0.179074i
$475$		−	22.9164i		−	1.05148i
$476$			1.01825i			0.0466714i
$477$	10.0337			0.459412
$478$	23.5968			1.07929
$479$			4.85495i			0.221828i	0.993830	+	0.110914i	$0.0353778\pi$
$479$			4.85495i			0.221828i	−0.993830	+	0.110914i	$0.964622\pi$
$480$	−2.55517			−0.116627
$481$	−9.45243	−	18.9810i	−0.430994	−	0.865458i
$482$	−6.61826			−0.301454
$483$		−	3.52190i		−	0.160252i
$484$	−0.816007			−0.0370912
$485$	−7.18390			−0.326204
$486$			0.404684i			0.0183568i
$487$			39.7612i			1.80175i	0.434075	+	0.900877i	$0.357075\pi$
$487$			39.7612i			1.80175i	−0.434075	+	0.900877i	$0.642925\pi$
$488$		−	5.32739i		−	0.241160i
$489$			42.3284i			1.91416i
$490$	5.85047			0.264297
$491$	6.08825			0.274759			0.137379	−	0.990519i	$-0.456132\pi$
$491$	6.08825			0.274759			0.137379	+	0.990519i	$0.456132\pi$
$492$			7.78809i			0.351114i
$493$	34.6255			1.55945
$494$	24.3709	−	12.1366i	1.09650	−	0.546051i
$495$	−11.1727			−0.502176
$496$		−	4.38931i		−	0.197086i
$497$	5.93852			0.266379
$498$	48.5271			2.17455
$499$			26.0135i			1.16453i	0.813001	+	0.582263i	$0.197832\pi$
$499$			26.0135i			1.16453i	−0.813001	+	0.582263i	$0.802168\pi$
$500$		−	1.44087i		−	0.0644376i
$501$		−	31.5217i		−	1.40829i
$502$		−	12.2862i		−	0.548360i
$503$	−26.6423			−1.18792			−0.593962	−	0.804493i	$-0.702437\pi$
$503$	−26.6423			−1.18792			−0.593962	+	0.804493i	$0.702437\pi$
$504$	18.3039			0.815318
$505$		−	1.08003i		−	0.0480605i
$506$	−4.09281			−0.181948
$507$	23.4803	−	31.0985i	1.04279	−	1.38113i
$508$	−3.15714			−0.140075
$509$		−	33.0607i		−	1.46539i	−0.680558	−	0.732694i	$-0.738262\pi$
$509$		−	33.0607i		−	1.46539i	0.680558	−	0.732694i	$-0.261738\pi$
$510$	−12.5000			−0.553511
$511$	−17.0826			−0.755691
$512$			17.8910i			0.790679i
$513$		−	45.3579i		−	2.00260i
$514$			12.3522i			0.544834i
$515$			12.8056i			0.564283i
$516$	2.38392			0.104946
$517$	2.28791			0.100622
$518$			10.0964i			0.443608i
$519$	61.4883			2.69904
$520$	−5.93109	+	2.95365i	−0.260095	+	0.129526i
$521$	25.8957			1.13451			0.567255	−	0.823543i	$-0.308006\pi$
$521$	25.8957			1.13451			0.567255	+	0.823543i	$0.308006\pi$
$522$			76.3516i			3.34182i
$523$	−25.9541			−1.13489			−0.567447	−	0.823410i	$-0.692069\pi$
$523$	−25.9541			−1.13489			−0.567447	+	0.823410i	$0.692069\pi$
$524$	1.31403			0.0574037
$525$			15.6173i			0.681595i
$526$			29.4039i			1.28207i
$527$		−	4.04263i		−	0.176100i
$528$		−	35.4648i		−	1.54341i
$529$	−21.9608			−0.954819
$530$	1.72942			0.0751211
$531$			10.0571i			0.436440i
$532$	−1.27692			−0.0553616
$533$	19.1096	+	38.3732i	0.827731	+	1.66213i
$534$	−17.4430			−0.754832
$535$			10.7174i			0.463352i
$536$	−22.0899			−0.954139
$537$	−32.1077			−1.38555
$538$			43.0254i			1.85496i
$539$			15.2878i			0.658493i
$540$		−	1.35410i		−	0.0582711i
$541$		−	28.6632i		−	1.23233i	−0.787618	−	0.616164i	$-0.788686\pi$
$541$		−	28.6632i		−	1.23233i	0.787618	−	0.616164i	$-0.211314\pi$
$542$	1.47919			0.0635366
$543$	−71.7868			−3.08067
$544$		−	4.97588i		−	0.213339i
$545$	−7.67189			−0.328628
$546$	−16.6085	+	8.27096i	−0.710778	+	0.353964i
$547$	12.0729			0.516198			0.258099	−	0.966119i	$-0.416904\pi$
$547$	12.0729			0.516198			0.258099	+	0.966119i	$0.416904\pi$
$548$			3.69402i			0.157801i
$549$	12.0159			0.512827
$550$	18.1489			0.773874
$551$			43.4216i			1.84982i
$552$			8.10793i			0.345096i
$553$			1.00649i			0.0428004i
$554$		−	2.97520i		−	0.126404i
$555$	−12.2087			−0.518229
$556$	0.00828341			0.000351295
$557$		−	2.10575i		−	0.0892234i	−0.999004	−	0.0446117i	$-0.985795\pi$
$557$		−	2.10575i		−	0.0892234i	0.999004	−	0.0446117i	$-0.0142051\pi$
$558$	8.91428			0.377372
$559$	11.7460	−	5.84943i	0.496801	−	0.247405i
$560$	3.50374			0.148060
$561$		−	32.6637i		−	1.37906i
$562$	−13.7351			−0.579381
$563$	22.0349			0.928662			0.464331	−	0.885662i	$-0.346295\pi$
$563$	22.0349			0.928662			0.464331	+	0.885662i	$0.346295\pi$
$564$			0.555983i			0.0234111i
$565$			1.27201i			0.0535139i
$566$			9.93199i			0.417473i
$567$			10.2165i			0.429054i
$568$	−13.6714			−0.573638
$569$	36.0563			1.51156			0.755780	−	0.654826i	$-0.227258\pi$
$569$	36.0563			1.51156			0.755780	+	0.654826i	$0.227258\pi$
$570$		−	15.6755i		−	0.656574i
$571$	34.7416			1.45389			0.726945	−	0.686695i	$-0.240939\pi$
$571$	34.7416			1.45389			0.726945	+	0.686695i	$0.240939\pi$
$572$	0.946778	+	1.90118i	0.0395868	+	0.0794923i
$573$	−9.91909			−0.414376
$574$		−	20.4114i		−	0.851957i
$575$	−4.60804			−0.192168
$576$	−41.5666			−1.73194
$577$			11.2505i			0.468364i	0.972193	+	0.234182i	$0.0752411\pi$
$577$			11.2505i			0.468364i	−0.972193	+	0.234182i	$0.924759\pi$
$578$			0.978807i			0.0407130i
$579$		−	28.9709i		−	1.20399i
$580$			1.29629i			0.0538257i
$581$	−12.5278			−0.519740
$582$	46.3116			1.91968
$583$			4.51912i			0.187163i
$584$	39.3267			1.62735
$585$	−6.66196	−	13.3776i	−0.275438	−	0.553094i
$586$	30.7440			1.27002
$587$		−	16.1947i		−	0.668426i	−0.942498	−	0.334213i	$-0.891529\pi$
$587$		−	16.1947i		−	0.668426i	0.942498	−	0.334213i	$-0.108471\pi$
$588$	−3.71507			−0.153207
$589$	5.06961			0.208889
$590$			1.73344i			0.0713648i
$591$		−	79.5692i		−	3.27304i
$592$		−	25.8137i		−	1.06094i
$593$			23.3449i			0.958660i	0.877635	+	0.479330i	$0.159120\pi$
$593$			23.3449i			0.958660i	−0.877635	+	0.479330i	$0.840880\pi$
$594$	35.9217			1.47389
$595$	3.22701			0.132295
$596$		−	3.62931i		−	0.148662i
$597$	−19.7909			−0.809989
$598$	−2.44043	−	4.90050i	−0.0997964	−	0.200396i
$599$	−40.5953			−1.65868			−0.829340	−	0.558744i	$-0.811284\pi$
$599$	−40.5953			−1.65868			−0.829340	+	0.558744i	$0.811284\pi$
$600$		−	35.9534i		−	1.46779i
$601$	−39.5067			−1.61151			−0.805755	−	0.592249i	$-0.798240\pi$
$601$	−39.5067			−1.61151			−0.805755	+	0.592249i	$0.798240\pi$
$602$	−6.24791			−0.254646
$603$		−	49.8237i		−	2.02898i
$604$		−	0.854214i		−	0.0347575i
$605$			2.58607i			0.105139i
$606$			6.96247i			0.282831i
$607$	1.07768			0.0437419			0.0218709	−	0.999761i	$-0.493038\pi$
$607$	1.07768			0.0437419			0.0218709	+	0.999761i	$0.493038\pi$
$608$	6.23993			0.253063
$609$		−	29.5914i		−	1.19910i
$610$	2.07107			0.0838553
$611$	1.36422	+	2.73942i	0.0551903	+	0.110825i
$612$	5.28725			0.213724
$613$			19.5448i			0.789406i	0.918809	+	0.394703i	$0.129152\pi$
$613$			19.5448i			0.789406i	−0.918809	+	0.394703i	$0.870848\pi$
$614$	4.54988			0.183618
$615$	24.6818			0.995267
$616$			8.24394i			0.332158i
$617$			25.7573i			1.03695i	0.855093	+	0.518474i	$0.173500\pi$
$617$			25.7573i			1.03695i	−0.855093	+	0.518474i	$0.826500\pi$
$618$		−	82.5525i		−	3.32075i
$619$			23.1573i			0.930770i	0.885108	+	0.465385i	$0.154084\pi$
$619$			23.1573i			0.930770i	−0.885108	+	0.465385i	$0.845916\pi$
$620$	0.151346			0.00607821
$621$	−9.12057			−0.365996
$622$			34.1393i			1.36886i
$623$	4.50309			0.180412
$624$	42.4635	−	21.1466i	1.69990	−	0.846542i
$625$	18.0354			0.721417
$626$		−	15.4259i		−	0.616543i
$627$	40.9615			1.63584
$628$	−1.01377			−0.0404538
$629$		−	23.7749i		−	0.947966i
$630$			7.11579i			0.283500i
$631$		−	42.2030i		−	1.68008i	−0.542528	−	0.840038i	$-0.682533\pi$
$631$		−	42.2030i		−	1.68008i	0.542528	−	0.840038i	$-0.317467\pi$
$632$		−	2.31709i		−	0.0921691i
$633$	−54.4740			−2.16515
$634$	−13.4761			−0.535203
$635$			10.0055i			0.397058i
$636$	−1.09819			−0.0435459
$637$	−18.3048	+	9.11568i	−0.725261	+	0.361176i
$638$	−34.3883			−1.36145
$639$		−	30.8357i		−	1.21984i
$640$	−8.86932			−0.350591
$641$	35.9647			1.42052			0.710260	−	0.703939i	$-0.248577\pi$
$641$	35.9647			1.42052			0.710260	+	0.703939i	$0.248577\pi$
$642$		−	69.0904i		−	2.72678i
$643$			11.9104i			0.469701i	0.972032	+	0.234850i	$0.0754600\pi$
$643$			11.9104i			0.469701i	−0.972032	+	0.234850i	$0.924540\pi$
$644$			0.256764i			0.0101179i
$645$		−	7.55507i		−	0.297481i
$646$	30.5261			1.20103
$647$	3.70864			0.145802			0.0729009	−	0.997339i	$-0.476774\pi$
$647$	3.70864			0.145802			0.0729009	+	0.997339i	$0.476774\pi$
$648$		−	23.5200i		−	0.923952i
$649$	−4.52965			−0.177804
$650$	10.8217	+	21.7305i	0.424462	+	0.852341i
$651$	−3.45488			−0.135408
$652$		−	3.08595i		−	0.120855i
$653$	−13.2111			−0.516991			−0.258496	−	0.966012i	$-0.583227\pi$
$653$	−13.2111			−0.516991			−0.258496	+	0.966012i	$0.583227\pi$
$654$	49.4575			1.93394
$655$		−	4.16439i		−	0.162716i
$656$			52.1866i			2.03754i
$657$			88.7014i			3.46057i
$658$		−	1.45715i		−	0.0568056i
$659$	−37.0706			−1.44407			−0.722033	−	0.691858i	$-0.756792\pi$
$659$	−37.0706			−1.44407			−0.722033	+	0.691858i	$0.756792\pi$
$660$	1.22285			0.0475993
$661$		−	1.86574i		−	0.0725687i	−0.999342	−	0.0362844i	$-0.988448\pi$
$661$		−	1.86574i		−	0.0725687i	0.999342	−	0.0362844i	$-0.0115522\pi$
$662$	−47.8830			−1.86103
$663$	39.1097	−	19.4764i	1.51889	−	0.756401i
$664$	28.8408			1.11924
$665$			4.04679i			0.156928i
$666$	52.4252			2.03144
$667$	8.73123			0.338074
$668$			2.29809i			0.0889156i
$669$		−	11.7072i		−	0.452626i
$670$		−	8.58765i		−	0.331770i
$671$			5.41190i			0.208924i
$672$	−4.25245			−0.164042
$673$	38.8121			1.49610			0.748048	−	0.663645i	$-0.230991\pi$
$673$	38.8121			1.49610			0.748048	+	0.663645i	$0.230991\pi$
$674$		−	47.2686i		−	1.82072i
$675$	40.4438			1.55668
$676$	−1.71183	+	2.26724i	−0.0658395	+	0.0872014i
$677$	−18.1456			−0.697394			−0.348697	−	0.937236i	$-0.613376\pi$
$677$	−18.1456			−0.697394			−0.348697	+	0.937236i	$0.613376\pi$
$678$		−	8.20012i		−	0.314924i
$679$	−11.9558			−0.458822
$680$	−7.42906			−0.284891
$681$		−	50.7178i		−	1.94351i
$682$			4.01494i			0.153740i
$683$			23.3612i			0.893891i	0.894561	+	0.446946i	$0.147488\pi$
$683$			23.3612i			0.893891i	−0.894561	+	0.446946i	$0.852512\pi$
$684$			6.63041i			0.253520i
$685$	11.7070			0.447301
$686$	21.7540			0.830572
$687$		−	34.5620i		−	1.31862i
$688$	15.9742			0.609012
$689$	−5.41094	+	2.69462i	−0.206140	+	0.102657i
$690$	−3.15203			−0.119996
$691$		−	9.52166i		−	0.362221i	−0.983463	−	0.181111i	$-0.942031\pi$
$691$		−	9.52166i		−	0.362221i	0.983463	−	0.181111i	$-0.0579692\pi$
$692$	−4.48280			−0.170410
$693$	−18.5942			−0.706335
$694$			2.34902i			0.0891676i
$695$		−	0.0262516i		−	0.000995780i
$696$			68.1238i			2.58222i
$697$			48.0648i			1.82058i
$698$	−49.2432			−1.86388
$699$	0.325673			0.0123181
$700$		−	1.13858i		−	0.0430342i
$701$	7.92968			0.299500			0.149750	−	0.988724i	$-0.452153\pi$
$701$	7.92968			0.299500			0.149750	+	0.988724i	$0.452153\pi$
$702$	21.4191	+	43.0106i	0.808412	+	1.62333i
$703$	29.8145			1.12448
$704$		−	18.7213i		−	0.705586i
$705$	1.76201			0.0663611
$706$	7.01310			0.263942
$707$		−	1.79743i		−	0.0675994i
$708$		−	1.10074i		−	0.0413685i
$709$		−	0.516551i		−	0.0193995i	−0.999953	−	0.00969973i	$-0.996912\pi$
$709$		−	0.516551i		−	0.0193995i	0.999953	−	0.00969973i	$-0.00308757\pi$
$710$		−	5.31487i		−	0.199463i
$711$	5.22620			0.195998
$712$	−10.3668			−0.388511
$713$		−	1.01940i		−	0.0381767i
$714$	−20.8032			−0.778540
$715$	6.02517	−	3.00051i	0.225329	−	0.112213i
$716$	2.34081			0.0874800
$717$			47.4871i			1.77344i
$718$	40.5356			1.51278
$719$	−25.0988			−0.936026			−0.468013	−	0.883722i	$-0.655030\pi$
$719$	−25.0988			−0.936026			−0.468013	+	0.883722i	$0.655030\pi$
$720$		−	18.1932i		−	0.678019i
$721$			21.3118i			0.793692i
$722$			9.98081i			0.371447i
$723$		−	13.3188i		−	0.495333i
$724$	5.23361			0.194506
$725$	−38.7173			−1.43792
$726$		−	16.6713i		−	0.618730i
$727$	24.2348			0.898819			0.449409	−	0.893326i	$-0.351634\pi$
$727$	24.2348			0.898819			0.449409	+	0.893326i	$0.351634\pi$
$728$	−9.87082	+	4.91562i	−0.365837	+	0.182185i
$729$	−27.4062			−1.01504
$730$			15.2886i			0.565857i
$731$	14.7126			0.544163
$732$	−1.31514			−0.0486089
$733$		−	47.9992i		−	1.77289i	−0.462834	−	0.886445i	$-0.653167\pi$
$733$		−	47.9992i		−	1.77289i	0.462834	−	0.886445i	$-0.346833\pi$
$734$		−	7.18729i		−	0.265288i
$735$			11.7737i			0.434280i
$736$		−	1.25473i		−	0.0462498i
$737$	22.4403			0.826599
$738$	−105.986			−3.90141
$739$			13.4514i			0.494817i	0.968911	+	0.247409i	$0.0795790\pi$
$739$			13.4514i			0.494817i	−0.968911	+	0.247409i	$0.920421\pi$
$740$	0.890072			0.0327197
$741$	24.4241	+	49.0449i	0.897243	+	1.80171i
$742$	2.87818			0.105661
$743$		−	17.9897i		−	0.659977i	−0.943985	−	0.329989i	$-0.892955\pi$
$743$		−	17.9897i		−	0.659977i	0.943985	−	0.329989i	$-0.107045\pi$
$744$	7.95365			0.291595
$745$	−11.5019			−0.421397
$746$		−	26.1116i		−	0.956015i
$747$			65.0504i			2.38007i
$748$			2.38134i			0.0870706i
$749$			17.8364i			0.651728i
$750$	29.4375			1.07490
$751$	5.17026			0.188666			0.0943328	−	0.995541i	$-0.469928\pi$
$751$	5.17026			0.188666			0.0943328	+	0.995541i	$0.469928\pi$
$752$			3.72554i			0.135857i
$753$	24.7252			0.901038
$754$	−20.5047	−	41.1746i	−0.746739	−	1.49949i
$755$	−2.70716			−0.0985235
$756$		−	2.25356i		−	0.0819612i
$757$	16.2563			0.590845			0.295422	−	0.955367i	$-0.404540\pi$
$757$	16.2563			0.590845			0.295422	+	0.955367i	$0.404540\pi$
$758$	50.5355			1.83553
$759$		−	8.23654i		−	0.298967i
$760$		−	9.31631i		−	0.337938i
$761$			26.5204i			0.961365i	0.876895	+	0.480682i	$0.159611\pi$
$761$			26.5204i			0.961365i	−0.876895	+	0.480682i	$0.840389\pi$
$762$		−	64.5015i		−	2.33664i
$763$	−12.7680			−0.462231
$764$	0.723150			0.0261627
$765$		−	16.7562i		−	0.605823i
$766$	−9.05347			−0.327115
$767$	−2.70090	−	5.42354i	−0.0975237	−	0.195833i
$768$	15.5401			0.560755
$769$			0.983871i			0.0354793i	0.999843	+	0.0177397i	$0.00564700\pi$
$769$			0.983871i			0.0354793i	−0.999843	+	0.0177397i	$0.994353\pi$
$770$	−3.20491			−0.115497
$771$	−24.8581			−0.895244
$772$			2.11212i			0.0760168i
$773$			27.6879i			0.995866i	0.867215	+	0.497933i	$0.165907\pi$
$773$			27.6879i			0.995866i	−0.867215	+	0.497933i	$0.834093\pi$
$774$			32.4422i			1.16611i
$775$			4.52036i			0.162376i
$776$	27.5241			0.988056
$777$	−20.3183			−0.728915
$778$		−	23.6847i		−	0.849137i
$779$	−60.2750			−2.15958
$780$	0.729149	+	1.46417i	0.0261077	+	0.0524257i
$781$	13.8882			0.496960
$782$		−	6.13818i		−	0.219501i
$783$	−76.6321			−2.73861
$784$	−24.8940			−0.889072
$785$			3.21282i			0.114670i
$786$			26.8461i			0.957569i
$787$		−	50.0529i		−	1.78419i	−0.451846	−	0.892096i	$-0.649234\pi$
$787$		−	50.0529i		−	1.78419i	0.451846	−	0.892096i	$-0.350766\pi$
$788$			5.80099i			0.206652i
$789$	−59.1736			−2.10664
$790$	0.900791			0.0320487
$791$			2.11695i			0.0752699i
$792$	42.8066			1.52107
$793$	−6.47990	+	3.22696i	−0.230108	+	0.114593i
$794$	−40.0068			−1.41979
$795$			3.48035i			0.123435i
$796$	1.44286			0.0511407
$797$	−33.6343			−1.19139			−0.595694	−	0.803212i	$-0.703123\pi$
$797$	−33.6343			−1.19139			−0.595694	+	0.803212i	$0.703123\pi$
$798$		−	26.0880i		−	0.923504i
$799$			3.43129i			0.121390i
$800$			5.56389i			0.196713i
$801$		−	23.3823i		−	0.826171i
$802$	−43.8601			−1.54875
$803$	−39.9505			−1.40982
$804$			5.45319i			0.192319i
$805$	0.813729			0.0286802
$806$	−4.80726	+	2.39399i	−0.169328	+	0.0843247i
$807$	−86.5859			−3.04797
$808$			4.13796i			0.145573i
$809$	20.5333			0.721913			0.360956	−	0.932583i	$-0.382450\pi$
$809$	20.5333			0.721913			0.360956	+	0.932583i	$0.382450\pi$
$810$	9.14361			0.321274
$811$			21.2908i			0.747622i	0.927505	+	0.373811i	$0.121949\pi$
$811$			21.2908i			0.747622i	−0.927505	+	0.373811i	$0.878051\pi$
$812$			2.15736i			0.0757084i
$813$			2.97678i			0.104400i
$814$			23.6120i			0.827600i
$815$	−9.77993			−0.342576
$816$	53.1882			1.86196
$817$			18.4501i			0.645487i
$818$	−57.2892			−2.00307
$819$	−11.0872	−	22.2636i	−0.387417	−	0.777954i
$820$	−1.79943			−0.0628387
$821$		−	18.4733i		−	0.644723i	−0.946617	−	0.322362i	$-0.895523\pi$
$821$		−	18.4733i		−	0.644723i	0.946617	−	0.322362i	$-0.104477\pi$
$822$	−75.4701			−2.63232
$823$	19.9508			0.695442			0.347721	−	0.937598i	$-0.386956\pi$
$823$	19.9508			0.695442			0.347721	+	0.937598i	$0.386956\pi$
$824$		−	49.0629i		−	1.70919i
$825$			36.5237i			1.27159i
$826$			2.88489i			0.100378i
$827$			44.1949i			1.53681i	0.639966	+	0.768403i	$0.278948\pi$
$827$			44.1949i			1.53681i	−0.639966	+	0.768403i	$0.721052\pi$
$828$	1.33324			0.0463334
$829$	−8.44679			−0.293369			−0.146685	−	0.989183i	$-0.546860\pi$
$829$	−8.44679			−0.293369			−0.146685	+	0.989183i	$0.546860\pi$
$830$			11.2121i			0.389178i
$831$	5.98740			0.207701
$832$	22.4158	−	11.1630i	0.777129	−	0.387007i
$833$	−22.9278			−0.794403
$834$			0.169233i			0.00586006i
$835$	7.28304			0.252040
$836$	−2.98629			−0.103283
$837$			8.94703i			0.309254i
$838$		−	10.0272i		−	0.346384i
$839$			39.8660i			1.37633i	0.725556	+	0.688163i	$0.241583\pi$
$839$			39.8660i			1.37633i	−0.725556	+	0.688163i	$0.758417\pi$
$840$			6.34897i			0.219060i
$841$	44.3608			1.52968
$842$	−1.21524			−0.0418798
$843$		−	27.6411i		−	0.952010i
$844$	3.97142			0.136702
$845$	7.18527	+	5.42508i	0.247181	+	0.186628i
$846$	−7.56624			−0.260133
$847$			4.30387i			0.147883i
$848$	−7.35875			−0.252700
$849$	−19.9875			−0.685970
$850$			27.2188i			0.933598i
$851$		−	5.99511i		−	0.205510i
$852$			3.37496i			0.115624i
$853$			9.26849i			0.317347i	0.987331	+	0.158674i	$0.0507217\pi$
$853$			9.26849i			0.317347i	−0.987331	+	0.158674i	$0.949278\pi$
$854$	3.44678			0.117947
$855$	21.0129			0.718627
$856$		−	41.0620i		−	1.40347i
$857$	−37.4028			−1.27766			−0.638828	−	0.769350i	$-0.720580\pi$
$857$	−37.4028			−1.27766			−0.638828	+	0.769350i	$0.720580\pi$
$858$	−38.8417	+	19.3430i	−1.32604	+	0.660359i
$859$	−23.2534			−0.793395			−0.396698	−	0.917949i	$-0.629844\pi$
$859$	−23.2534			−0.793395			−0.396698	+	0.917949i	$0.629844\pi$
$860$			0.550802i			0.0187822i
$861$	41.0768			1.39989
$862$	53.2691			1.81435
$863$			22.9063i			0.779741i	0.920870	+	0.389871i	$0.127480\pi$
$863$			22.9063i			0.779741i	−0.920870	+	0.389871i	$0.872520\pi$
$864$			11.0125i			0.374652i
$865$			14.2068i			0.483045i
$866$			38.5445i			1.30980i
$867$	−1.96979			−0.0668976
$868$	0.251878			0.00854930
$869$			2.35385i			0.0798489i
$870$	−26.4837			−0.897883
$871$	13.3805	+	26.8687i	0.453381	+	0.910413i
$872$	29.3937			0.995398
$873$			62.0805i			2.10111i
$874$	7.69751			0.260372
$875$	−7.59959			−0.256913
$876$		−	9.70834i		−	0.328014i
$877$			20.8719i			0.704795i	0.935850	+	0.352397i	$0.114633\pi$
$877$			20.8719i			0.704795i	−0.935850	+	0.352397i	$0.885367\pi$
$878$			36.4162i			1.22899i
$879$			61.8705i			2.08684i
$880$	8.19409			0.276223
$881$	−24.7872			−0.835102			−0.417551	−	0.908653i	$-0.637112\pi$
$881$	−24.7872			−0.835102			−0.417551	+	0.908653i	$0.637112\pi$
$882$		−	50.5575i		−	1.70236i
$883$	−42.9772			−1.44630			−0.723148	−	0.690693i	$-0.757306\pi$
$883$	−42.9772			−1.44630			−0.723148	+	0.690693i	$0.757306\pi$
$884$	−2.85129	+	1.41993i	−0.0958991	+	0.0477573i
$885$	−3.48845			−0.117263
$886$		−	22.9584i		−	0.771302i
$887$	20.4768			0.687544			0.343772	−	0.939053i	$-0.388295\pi$
$887$	20.4768			0.687544			0.343772	+	0.939053i	$0.388295\pi$
$888$	46.7757			1.56969
$889$			16.6517i			0.558481i
$890$		−	4.03018i		−	0.135092i
$891$			23.8931i			0.800448i
$892$			0.853512i			0.0285777i
$893$	−4.30297			−0.143993
$894$	74.1480			2.47988
$895$		−	7.41843i		−	0.247971i
$896$	−14.7608			−0.493123
$897$	9.86196	−	4.91121i	0.329281	−	0.163981i
$898$	1.78874			0.0596910
$899$		−	8.56509i		−	0.285662i
$900$	−5.91206			−0.197069
$901$	−6.77754			−0.225793
$902$		−	47.7355i		−	1.58942i
$903$		−	12.5735i		−	0.418421i
$904$		−	4.87352i		−	0.162091i
$905$		−	16.5862i		−	0.551345i
$906$	17.4519			0.579800
$907$	−38.8180			−1.28893			−0.644466	−	0.764633i	$-0.722920\pi$
$907$	−38.8180			−1.28893			−0.644466	+	0.764633i	$0.722920\pi$
$908$			3.69757i			0.122708i
$909$	−9.33316			−0.309561
$910$	−1.91099	−	3.83737i	−0.0633488	−	0.127208i
$911$	14.2402			0.471799			0.235900	−	0.971777i	$-0.424196\pi$
$911$	14.2402			0.471799			0.235900	+	0.971777i	$0.424196\pi$
$912$			66.7000i			2.20866i
$913$	−29.2983			−0.969632
$914$	6.26437			0.207207
$915$			4.16791i			0.137787i
$916$			2.51974i			0.0832546i
$917$		−	6.93060i		−	0.228869i
$918$			53.8735i			1.77809i
$919$	53.7283			1.77233			0.886166	−	0.463367i	$-0.153359\pi$
$919$	53.7283			1.77233			0.886166	+	0.463367i	$0.153359\pi$
$920$	−1.87332			−0.0617617
$921$			9.15636i			0.301712i
$922$	21.0371			0.692821
$923$	8.28114	+	16.6290i	0.272577	+	0.547349i
$924$	2.03513			0.0669508
$925$			26.5844i			0.874090i
$926$	32.7025			1.07467
$927$	110.661			3.63459
$928$		−	10.5424i		−	0.346070i
$929$		−	29.9480i		−	0.982562i	−0.871001	−	0.491281i	$-0.836529\pi$
$929$		−	29.9480i		−	0.982562i	0.871001	−	0.491281i	$-0.163471\pi$
$930$			3.09205i			0.101392i
$931$		−	28.7524i		−	0.942320i
$932$	−0.0237432			−0.000777734
$933$	−68.7032			−2.24924
$934$			1.36737i			0.0447417i
$935$	7.54690			0.246810
$936$	25.5243	+	51.2542i	0.834289	+	1.67529i
$937$	−32.2927			−1.05496			−0.527479	−	0.849568i	$-0.676863\pi$
$937$	−32.2927			−1.05496			−0.527479	+	0.849568i	$0.676863\pi$
$938$		−	14.2920i		−	0.466651i
$939$	31.0437			1.01307
$940$	−0.128459			−0.00418987
$941$			10.7946i			0.351894i	0.984400	+	0.175947i	$0.0562987\pi$
$941$			10.7946i			0.351894i	−0.984400	+	0.175947i	$0.943701\pi$
$942$		−	20.7117i		−	0.674823i
$943$			12.1201i			0.394685i
$944$		−	7.37589i		−	0.240065i
$945$	−7.14193			−0.232327
$946$	−14.6118			−0.475069
$947$			55.7380i			1.81124i	0.424090	+	0.905620i	$0.360594\pi$
$947$			55.7380i			1.81124i	−0.424090	+	0.905620i	$0.639406\pi$
$948$	−0.572006			−0.0185779
$949$	−23.8214	−	47.8345i	−0.773274	−	1.55277i
$950$	−34.1334			−1.10743
$951$		−	27.1198i		−	0.879419i
$952$	−12.3638			−0.400714
$953$	42.0978			1.36368			0.681841	−	0.731500i	$-0.261180\pi$
$953$	42.0978			1.36368			0.681841	+	0.731500i	$0.261180\pi$
$954$		−	14.9449i		−	0.483861i
$955$		−	2.29179i		−	0.0741606i
$956$		−	3.46204i		−	0.111970i
$957$		−	69.2044i		−	2.23706i
$958$	7.23131			0.233633
$959$	19.4834			0.629151
$960$		−	14.4180i		−	0.465339i
$961$	−1.00000			−0.0322581
$962$	−28.2717	+	14.0791i	−0.911515	+	0.453930i
$963$	92.6153			2.98449
$964$			0.971010i			0.0312741i
$965$	6.69368			0.215477
$966$	−5.24577			−0.168780
$967$		−	46.8530i		−	1.50669i	−0.657625	−	0.753345i	$-0.728439\pi$
$967$		−	46.8530i		−	1.50669i	0.657625	−	0.753345i	$-0.271561\pi$
$968$		−	9.90814i		−	0.318460i
$969$			61.4318i			1.97348i
$970$			10.7002i			0.343564i
$971$	43.0627			1.38195			0.690975	−	0.722879i	$-0.257182\pi$
$971$	43.0627			1.38195			0.690975	+	0.722879i	$0.257182\pi$
$972$	0.0593739			0.00190442
$973$		−	0.0436892i		−	0.00140061i
$974$	59.2233			1.89764
$975$	−43.7313	+	21.7780i	−1.40052	+	0.697454i
$976$	−8.81251			−0.282081
$977$			11.4541i			0.366448i	0.983071	+	0.183224i	$0.0586533\pi$
$977$			11.4541i			0.366448i	−0.983071	+	0.183224i	$0.941347\pi$
$978$	63.0471			2.01602
$979$	10.5312			0.336579
$980$		−	0.858362i		−	0.0274194i
$981$			66.2975i			2.11672i
$982$		−	9.06828i		−	0.289380i
$983$			7.93525i			0.253095i	0.991961	+	0.126548i	$0.0403896\pi$
$983$			7.93525i			0.253095i	−0.991961	+	0.126548i	$0.959610\pi$
$984$	−94.5648			−3.01462
$985$	18.3843			0.585774
$986$		−	51.5737i		−	1.64244i
$987$	2.93243			0.0933401
$988$	−1.78064	−	3.57562i	−0.0566497	−	0.113756i
$989$	3.70994			0.117969
$990$			16.6414i			0.528900i
$991$	20.2465			0.643150			0.321575	−	0.946884i	$-0.395788\pi$
$991$	20.2465			0.643150			0.321575	+	0.946884i	$0.395788\pi$
$992$	−1.23085			−0.0390796
$993$		−	96.3617i		−	3.05795i
$994$		−	8.84527i		−	0.280555i
$995$		−	4.57266i		−	0.144963i
$996$		−	7.11974i		−	0.225598i
$997$	−18.4051			−0.582896			−0.291448	−	0.956587i	$-0.594137\pi$
$997$	−18.4051			−0.582896			−0.291448	+	0.956587i	$0.594137\pi$
$998$	38.7465			1.22650
$999$			52.6178i			1.66475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.8	✓	32
13.5	odd	4		5239.2.a.k.1.5		16
13.8	odd	4		5239.2.a.l.1.12		16
13.12	even	2	inner	403.2.c.b.311.25	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.8	✓	32	1.1	even	1	trivial
403.2.c.b.311.25	yes	32	13.12	even	2	inner
5239.2.a.k.1.5		16	13.5	odd	4
5239.2.a.l.1.12		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)

\(f(q)\)	\(=\)	\(q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +O(q^{10})\)	\(q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +1.03155 q^{10} +2.69554i q^{11} -0.655040 q^{12} +(-3.22749 + 1.60727i) q^{13} +1.71676 q^{14} +2.07594i q^{15} -4.38931 q^{16} -4.04263 q^{17} -8.91428i q^{18} -5.06961i q^{19} -0.151346i q^{20} +3.45488i q^{21} +4.01494 q^{22} -1.01940 q^{23} -7.95365i q^{24} +4.52036 q^{25} +(2.39399 + 4.80726i) q^{26} +8.94703 q^{27} -0.251878i q^{28} -8.56509 q^{29} +3.09205 q^{30} +1.00000i q^{31} +1.23085i q^{32} +8.07982i q^{33} +6.02139i q^{34} -0.798246 q^{35} -1.30787 q^{36} +5.88104i q^{37} -7.55104 q^{38} +(-9.67431 + 4.81776i) q^{39} +1.83768 q^{40} -11.8895i q^{41} +5.14596 q^{42} -3.63935 q^{43} -0.589058i q^{44} +4.14488i q^{45} +1.51836i q^{46} -0.848777i q^{47} -13.1568 q^{48} +5.67152 q^{49} -6.73295i q^{50} -12.1177 q^{51} +(0.705305 - 0.351239i) q^{52} +1.67652 q^{53} -13.3264i q^{54} -1.86683 q^{55} +3.05836 q^{56} -15.1960i q^{57} +12.7575i q^{58} +1.68042i q^{59} -0.453656i q^{60} +2.00772 q^{61} +1.48947 q^{62} +6.89813i q^{63} -6.94529 q^{64} +(-1.11314 - 2.23524i) q^{65} +12.0347 q^{66} -8.32497i q^{67} +0.883439 q^{68} -3.05562 q^{69} +1.18897i q^{70} -5.15229i q^{71} -15.8805i q^{72} +14.8210i q^{73} +8.75965 q^{74} +13.5497 q^{75} +1.10786i q^{76} -3.10687 q^{77} +(7.17593 + 14.4096i) q^{78} +0.873238 q^{79} -3.03987i q^{80} +8.86392 q^{81} -17.7091 q^{82} +10.8692i q^{83} -0.754998i q^{84} -2.79977i q^{85} +5.42072i q^{86} -25.6736 q^{87} +7.15249 q^{88} -3.90690i q^{89} +6.17370 q^{90} +(-1.85254 - 3.71999i) q^{91} +0.222769 q^{92} +2.99747i q^{93} -1.26423 q^{94} +3.51102 q^{95} +3.68945i q^{96} +10.3729i q^{97} -8.44757i q^{98} +16.1324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 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

Modular forms

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