LMFDB - Embedded newform 633.2.d.a.632.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(632,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("633.632");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			632.50
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34820 q^{2} +(-0.793870 + 1.53941i) q^{3} -0.182353 q^{4} -1.28346i q^{5} +(-1.07030 + 2.07543i) q^{6} -2.59500i q^{7} -2.94225 q^{8} +(-1.73954 - 2.44418i) q^{9} +O(q^{10})$	\(q+1.34820 q^{2} +(-0.793870 + 1.53941i) q^{3} -0.182353 q^{4} -1.28346i q^{5} +(-1.07030 + 2.07543i) q^{6} -2.59500i q^{7} -2.94225 q^{8} +(-1.73954 - 2.44418i) q^{9} -1.73036i q^{10} +4.75091i q^{11} +(0.144764 - 0.280715i) q^{12} -6.72460 q^{13} -3.49858i q^{14} +(1.97577 + 1.01890i) q^{15} -3.60204 q^{16} -4.43143 q^{17} +(-2.34525 - 3.29524i) q^{18} -6.32695 q^{19} +0.234043i q^{20} +(3.99476 + 2.06009i) q^{21} +6.40519i q^{22} +6.19362 q^{23} +(2.33576 - 4.52932i) q^{24} +3.35273 q^{25} -9.06611 q^{26} +(5.14355 - 0.737505i) q^{27} +0.473206i q^{28} +0.966780 q^{29} +(2.66373 + 1.37368i) q^{30} -10.2081i q^{31} +1.02823 q^{32} +(-7.31358 - 3.77161i) q^{33} -5.97446 q^{34} -3.33058 q^{35} +(0.317211 + 0.445703i) q^{36} -0.457033 q^{37} -8.53001 q^{38} +(5.33845 - 10.3519i) q^{39} +3.77627i q^{40} -6.08630 q^{41} +(5.38574 + 2.77742i) q^{42} -3.88186 q^{43} -0.866343i q^{44} +(-3.13700 + 2.23263i) q^{45} +8.35025 q^{46} +4.10698i q^{47} +(2.85955 - 5.54500i) q^{48} +0.265981 q^{49} +4.52015 q^{50} +(3.51798 - 6.82177i) q^{51} +1.22625 q^{52} +11.6850i q^{53} +(6.93454 - 0.994306i) q^{54} +6.09761 q^{55} +7.63514i q^{56} +(5.02278 - 9.73975i) q^{57} +1.30341 q^{58} -9.40621i q^{59} +(-0.360287 - 0.185800i) q^{60} +7.82516i q^{61} -13.7626i q^{62} +(-6.34263 + 4.51411i) q^{63} +8.59034 q^{64} +8.63076i q^{65} +(-9.86018 - 5.08488i) q^{66} -4.40747i q^{67} +0.808084 q^{68} +(-4.91693 + 9.53450i) q^{69} -4.49029 q^{70} +1.64430i q^{71} +(5.11817 + 7.19138i) q^{72} +0.568453 q^{73} -0.616173 q^{74} +(-2.66163 + 5.16121i) q^{75} +1.15374 q^{76} +12.3286 q^{77} +(7.19731 - 13.9564i) q^{78} -12.3033 q^{79} +4.62308i q^{80} +(-2.94799 + 8.50349i) q^{81} -8.20556 q^{82} -0.218874i q^{83} +(-0.728456 - 0.375664i) q^{84} +5.68756i q^{85} -5.23352 q^{86} +(-0.767497 + 1.48827i) q^{87} -13.9784i q^{88} +1.91360 q^{89} +(-4.22931 + 3.01004i) q^{90} +17.4503i q^{91} -1.12942 q^{92} +(15.7144 + 8.10391i) q^{93} +5.53704i q^{94} +8.12040i q^{95} +(-0.816277 + 1.58286i) q^{96} -9.85223i q^{97} +0.358596 q^{98} +(11.6121 - 8.26441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.34820			0.953322			0.476661	−	0.879087i	$-0.341847\pi$
$2$	1.34820			0.953322			0.476661	+	0.879087i	$0.341847\pi$
$3$	−0.793870	+	1.53941i	−0.458341	+	0.888777i
$3$	−0.793870	+	1.53941i	−0.458341	+	0.888777i
$4$	−0.182353			−0.0911765
$5$		−	1.28346i		−	0.573981i	−0.957933	−	0.286991i	$-0.907345\pi$
$5$		−	1.28346i		−	0.573981i	0.957933	−	0.286991i	$-0.0926549\pi$
$6$	−1.07030	+	2.07543i	−0.436947	+	0.847291i
$7$		−	2.59500i		−	0.980817i	−0.871493	−	0.490409i	$-0.836848\pi$
$7$		−	2.59500i		−	0.980817i	0.871493	−	0.490409i	$-0.163152\pi$
$8$	−2.94225			−1.04024
$9$	−1.73954	−	2.44418i	−0.579847	−	0.814725i
$10$		−	1.73036i		−	0.547189i
$11$			4.75091i			1.43245i	0.697867	+	0.716227i	$0.254132\pi$
$11$			4.75091i			1.43245i	−0.697867	+	0.716227i	$0.745868\pi$
$12$	0.144764	−	0.280715i	0.0417899	−	0.0810355i
$13$	−6.72460			−1.86507			−0.932534	−	0.361083i	$-0.882407\pi$
$13$	−6.72460			−1.86507			−0.932534	+	0.361083i	$0.882407\pi$
$14$		−	3.49858i		−	0.935035i
$15$	1.97577	+	1.01890i	0.510141	+	0.263079i
$16$	−3.60204			−0.900510
$17$	−4.43143			−1.07478			−0.537389	−	0.843334i	$-0.680589\pi$
$17$	−4.43143			−1.07478			−0.537389	+	0.843334i	$0.680589\pi$
$18$	−2.34525	−	3.29524i	−0.552781	−	0.776696i
$19$	−6.32695			−1.45150			−0.725752	−	0.687957i	$-0.758508\pi$
$19$	−6.32695			−1.45150			−0.725752	+	0.687957i	$0.758508\pi$
$20$			0.234043i			0.0523336i
$21$	3.99476	+	2.06009i	0.871727	+	0.449549i
$22$			6.40519i			1.36559i
$23$	6.19362			1.29146			0.645730	−	0.763566i	$-0.276553\pi$
$23$	6.19362			1.29146			0.645730	+	0.763566i	$0.276553\pi$
$24$	2.33576	−	4.52932i	0.476786	−	0.924543i
$25$	3.35273			0.670546
$26$	−9.06611			−1.77801
$27$	5.14355	−	0.737505i	0.989876	−	0.141933i
$28$			0.473206i			0.0894275i
$29$	0.966780			0.179526			0.0897632	−	0.995963i	$-0.471389\pi$
$29$	0.966780			0.179526			0.0897632	+	0.995963i	$0.471389\pi$
$30$	2.66373	+	1.37368i	0.486329	+	0.250799i
$31$		−	10.2081i		−	1.83343i	−0.399541	−	0.916715i	$-0.630830\pi$
$31$		−	10.2081i		−	1.83343i	0.399541	−	0.916715i	$-0.369170\pi$
$32$	1.02823			0.181766
$33$	−7.31358	−	3.77161i	−1.27313	−	0.656552i
$34$	−5.97446			−1.02461
$35$	−3.33058			−0.562971
$36$	0.317211	+	0.445703i	0.0528684	+	0.0742838i
$37$	−0.457033			−0.0751358			−0.0375679	−	0.999294i	$-0.511961\pi$
$37$	−0.457033			−0.0751358			−0.0375679	+	0.999294i	$0.511961\pi$
$38$	−8.53001			−1.38375
$39$	5.33845	−	10.3519i	0.854836	−	1.65763i
$40$			3.77627i			0.597080i
$41$	−6.08630			−0.950520			−0.475260	−	0.879845i	$-0.657646\pi$
$41$	−6.08630			−0.950520			−0.475260	+	0.879845i	$0.657646\pi$
$42$	5.38574	+	2.77742i	0.831037	+	0.428565i
$43$	−3.88186			−0.591977			−0.295989	−	0.955191i	$-0.595649\pi$
$43$	−3.88186			−0.591977			−0.295989	+	0.955191i	$0.595649\pi$
$44$		−	0.866343i		−	0.130606i
$45$	−3.13700	+	2.23263i	−0.467637	+	0.332822i
$46$	8.35025			1.23118
$47$			4.10698i			0.599065i	0.954086	+	0.299533i	$0.0968307\pi$
$47$			4.10698i			0.599065i	−0.954086	+	0.299533i	$0.903169\pi$
$48$	2.85955	−	5.54500i	0.412741	−	0.800352i
$49$	0.265981			0.0379973
$50$	4.52015			0.639246
$51$	3.51798	−	6.82177i	0.492615	−	0.955238i
$52$	1.22625			0.170050
$53$			11.6850i			1.60506i	0.596614	+	0.802529i	$0.296513\pi$
$53$			11.6850i			1.60506i	−0.596614	+	0.802529i	$0.703487\pi$
$54$	6.93454	−	0.994306i	0.943671	−	0.135308i
$55$	6.09761			0.822202
$56$			7.63514i			1.02029i
$57$	5.02278	−	9.73975i	0.665283	−	1.29006i
$58$	1.30341			0.171147
$59$		−	9.40621i		−	1.22458i	−0.790632	−	0.612292i	$-0.790248\pi$
$59$		−	9.40621i		−	1.22458i	0.790632	−	0.612292i	$-0.209752\pi$
$60$	−0.360287	−	0.185800i	−0.0465129	−	0.0239866i
$61$			7.82516i			1.00191i	0.865473	+	0.500955i	$0.167018\pi$
$61$			7.82516i			1.00191i	−0.865473	+	0.500955i	$0.832982\pi$
$62$		−	13.7626i		−	1.74785i
$63$	−6.34263	+	4.51411i	−0.799097	+	0.568724i
$64$	8.59034			1.07379
$65$			8.63076i			1.07051i
$66$	−9.86018	−	5.08488i	−1.21370	−	0.625906i
$67$		−	4.40747i		−	0.538458i	−0.963076	−	0.269229i	$-0.913231\pi$
$67$		−	4.40747i		−	0.538458i	0.963076	−	0.269229i	$-0.0867688\pi$
$68$	0.808084			0.0979945
$69$	−4.91693	+	9.53450i	−0.591928	+	1.14782i
$70$	−4.49029			−0.536693
$71$			1.64430i			0.195142i	0.995229	+	0.0975712i	$0.0311074\pi$
$71$			1.64430i			0.195142i	−0.995229	+	0.0975712i	$0.968893\pi$
$72$	5.11817	+	7.19138i	0.603182	+	0.847512i
$73$	0.568453			0.0665324			0.0332662	−	0.999447i	$-0.489409\pi$
$73$	0.568453			0.0665324			0.0332662	+	0.999447i	$0.489409\pi$
$74$	−0.616173			−0.0716286
$75$	−2.66163	+	5.16121i	−0.307338	+	0.595965i
$76$	1.15374			0.132343
$77$	12.3286			1.40498
$78$	7.19731	−	13.9564i	0.814935	−	1.58025i
$79$	−12.3033			−1.38423			−0.692113	−	0.721789i	$-0.743320\pi$
$79$	−12.3033			−1.38423			−0.692113	+	0.721789i	$0.743320\pi$
$80$			4.62308i			0.516876i
$81$	−2.94799	+	8.50349i	−0.327554	+	0.944832i
$82$	−8.20556			−0.906152
$83$		−	0.218874i		−	0.0240245i	−0.999928	−	0.0120123i	$-0.996176\pi$
$83$		−	0.218874i		−	0.0240245i	0.999928	−	0.0120123i	$-0.00382371\pi$
$84$	−0.728456	−	0.375664i	−0.0794810	−	0.0409883i
$85$			5.68756i			0.616903i
$86$	−5.23352			−0.564345
$87$	−0.767497	+	1.48827i	−0.0822843	+	0.159559i
$88$		−	13.9784i		−	1.49010i
$89$	1.91360			0.202841			0.101421	−	0.994844i	$-0.467661\pi$
$89$	1.91360			0.202841			0.101421	+	0.994844i	$0.467661\pi$
$90$	−4.22931	+	3.01004i	−0.445809	+	0.317286i
$91$			17.4503i			1.82929i
$92$	−1.12942			−0.117751
$93$	15.7144	+	8.10391i	1.62951	+	0.840336i
$94$			5.53704i			0.571102i
$95$			8.12040i			0.833136i
$96$	−0.816277	+	1.58286i	−0.0833109	+	0.161550i
$97$		−	9.85223i		−	1.00034i	−0.865927	−	0.500171i	$-0.833270\pi$
$97$		−	9.85223i		−	1.00034i	0.865927	−	0.500171i	$-0.166730\pi$
$98$	0.358596			0.0362237
$99$	11.6121	−	8.26441i	1.16706	−	0.830605i
$100$	−0.611380			−0.0611380
$101$			7.14225i			0.710681i	0.934737	+	0.355340i	$0.115635\pi$
$101$			7.14225i			0.710681i	−0.934737	+	0.355340i	$0.884365\pi$
$102$	4.74294	−	9.19711i	0.469621	−	0.910650i
$103$	−0.502325			−0.0494956			−0.0247478	−	0.999694i	$-0.507878\pi$
$103$	−0.502325			−0.0494956			−0.0247478	+	0.999694i	$0.507878\pi$
$104$	19.7854			1.94012
$105$	2.64405	−	5.12712i	0.258032	−	0.500355i
$106$			15.7537i			1.53014i
$107$			7.90302i			0.764014i	0.924159	+	0.382007i	$0.124767\pi$
$107$			7.90302i			0.764014i	−0.924159	+	0.382007i	$0.875233\pi$
$108$	−0.937941	+	0.134486i	−0.0902534	+	0.0129409i
$109$	−6.65713			−0.637637			−0.318819	−	0.947816i	$-0.603286\pi$
$109$	−6.65713			−0.637637			−0.318819	+	0.947816i	$0.603286\pi$
$110$	8.22081			0.783823
$111$	0.362825	−	0.703560i	0.0344378	−	0.0667789i
$112$			9.34729i			0.883236i
$113$		−	14.9150i		−	1.40308i	−0.712629	−	0.701541i	$-0.752496\pi$
$113$		−	14.9150i		−	1.40308i	0.712629	−	0.701541i	$-0.247504\pi$
$114$	6.77172	−	13.1311i	0.634229	−	1.22984i
$115$		−	7.94927i		−	0.741273i
$116$	−0.176295			−0.0163686
$117$	11.6977	+	16.4361i	1.08145	+	1.51952i
$118$		−	12.6815i		−	1.16742i
$119$			11.4995i			1.05416i
$120$	−5.81321	−	2.99786i	−0.530671	−	0.273666i
$121$	−11.5712			−1.05192
$122$			10.5499i			0.955143i
$123$	4.83173	−	9.36929i	0.435662	−	0.844800i
$124$			1.86148i			0.167166i
$125$		−	10.7204i		−	0.958862i
$126$	−8.55115	+	6.08593i	−0.761797	+	0.542178i
$127$			9.58452i			0.850489i	0.905079	+	0.425244i	$0.139812\pi$
$127$			9.58452i			0.850489i	−0.905079	+	0.425244i	$0.860188\pi$
$128$	9.52506			0.841904
$129$	3.08169	−	5.97575i	0.271327	−	0.526136i
$130$			11.6360i			1.02054i
$131$	4.47676			0.391136			0.195568	−	0.980690i	$-0.437345\pi$
$131$	4.47676			0.391136			0.195568	+	0.980690i	$0.437345\pi$
$132$	1.33365	+	0.687763i	0.116080	+	0.0598621i
$133$			16.4184i			1.42366i
$134$		−	5.94215i		−	0.513324i
$135$	−0.946559	−	6.60154i	−0.0814668	−	0.568170i
$136$	13.0384			1.11803
$137$		−	6.95548i		−	0.594247i	−0.954839	−	0.297124i	$-0.903973\pi$
$137$		−	6.95548i		−	0.594247i	0.954839	−	0.297124i	$-0.0960273\pi$
$138$	−6.62901	+	12.8544i	−0.564299	+	1.09424i
$139$	−13.1752			−1.11751			−0.558753	−	0.829334i	$-0.688720\pi$
$139$	−13.1752			−1.11751			−0.558753	+	0.829334i	$0.688720\pi$
$140$	0.607341			0.0513297
$141$	−6.32232	−	3.26041i	−0.532435	−	0.274576i
$142$			2.21685i			0.186034i
$143$		−	31.9480i		−	2.67162i
$144$	6.26590	+	8.80402i	0.522159	+	0.733668i
$145$		−	1.24082i		−	0.103045i
$146$	0.766390			0.0634269
$147$	−0.211154	+	0.409453i	−0.0174157	+	0.0337711i
$148$	0.0833413			0.00685062
$149$	−22.6884			−1.85871			−0.929353	−	0.369192i	$-0.879634\pi$
$149$	−22.6884			−1.85871			−0.929353	+	0.369192i	$0.879634\pi$
$150$	−3.58841	+	6.95835i	−0.292993	+	0.568147i
$151$	−7.26914			−0.591554			−0.295777	−	0.955257i	$-0.595579\pi$
$151$	−7.26914			−0.591554			−0.295777	+	0.955257i	$0.595579\pi$
$152$	18.6155			1.50992
$153$	7.70865	+	10.8312i	0.623208	+	0.875649i
$154$	16.6215			1.33939
$155$	−13.1017			−1.05235
$156$	−0.973482	+	1.88770i	−0.0779410	+	0.151137i
$157$			21.5233i			1.71775i	0.512188	+	0.858873i	$0.328835\pi$
$157$			21.5233i			1.71775i	−0.512188	+	0.858873i	$0.671165\pi$
$158$	−16.5873			−1.31961
$159$	−17.9879	−	9.27636i	−1.42654	−	0.735663i
$160$		−	1.31969i		−	0.104330i
$161$		−	16.0724i		−	1.26669i
$162$	−3.97448	+	11.4644i	−0.312265	+	0.900730i
$163$	−2.01926			−0.158161			−0.0790804	−	0.996868i	$-0.525198\pi$
$163$	−2.01926			−0.158161			−0.0790804	+	0.996868i	$0.525198\pi$
$164$	1.10985			0.0866651
$165$	−4.84071	+	9.38670i	−0.376849	+	0.730754i
$166$		−	0.295086i		−	0.0229031i
$167$	0.980410			0.0758664			0.0379332	−	0.999280i	$-0.487923\pi$
$167$	0.980410			0.0758664			0.0379332	+	0.999280i	$0.487923\pi$
$168$	−11.7536	−	6.06130i	−0.906808	−	0.467640i
$169$	32.2202			2.47848
$170$			7.66798i			0.588107i
$171$	11.0060	+	15.4642i	0.841650	+	1.18258i
$172$	0.707868			0.0539744
$173$		−	11.1444i		−	0.847290i	−0.905828	−	0.423645i	$-0.860750\pi$
$173$		−	11.1444i		−	0.847290i	0.905828	−	0.423645i	$-0.139250\pi$
$174$	−1.03474	+	2.00648i	−0.0784435	+	0.152111i
$175$		−	8.70032i		−	0.657683i
$176$		−	17.1130i		−	1.28994i
$177$	14.4800	+	7.46730i	1.08838	+	0.561277i
$178$	2.57992			0.193373
$179$		−	4.06908i		−	0.304137i	−0.988370	−	0.152069i	$-0.951407\pi$
$179$		−	4.06908i		−	0.304137i	0.988370	−	0.152069i	$-0.0485935\pi$
$180$	0.572042	−	0.407127i	0.0426375	−	0.0303455i
$181$		−	22.4435i		−	1.66821i	−0.551606	−	0.834105i	$-0.685985\pi$
$181$		−	22.4435i		−	1.66821i	0.551606	−	0.834105i	$-0.314015\pi$
$182$			23.5265i			1.74390i
$183$	−12.0461	−	6.21216i	−0.890474	−	0.459216i
$184$	−18.2232			−1.34343
$185$			0.586584i			0.0431265i
$186$	21.1862	+	10.9257i	1.55345	+	0.801111i
$187$		−	21.0533i		−	1.53957i
$188$		−	0.748921i		−	0.0546206i
$189$	−1.91383	−	13.3475i	−0.139210	−	0.970888i
$190$			10.9479i			0.794247i
$191$	−8.18924			−0.592553			−0.296276	−	0.955102i	$-0.595745\pi$
$191$	−8.18924			−0.592553			−0.296276	+	0.955102i	$0.595745\pi$
$192$	−6.81961	+	13.2240i	−0.492163	+	0.954361i
$193$	−7.60825			−0.547654			−0.273827	−	0.961779i	$-0.588290\pi$
$193$	−7.60825			−0.547654			−0.273827	+	0.961779i	$0.588290\pi$
$194$		−	13.2828i		−	0.953648i
$195$	−13.2862	−	6.85169i	−0.951447	−	0.490660i
$196$	−0.0485025			−0.00346446
$197$	19.7770			1.40905			0.704526	−	0.709678i	$-0.251160\pi$
$197$	19.7770			1.40905			0.704526	+	0.709678i	$0.251160\pi$
$198$	15.6554	−	11.1421i	1.11258	−	0.791834i
$199$	−6.76023			−0.479220			−0.239610	−	0.970869i	$-0.577020\pi$
$199$	−6.76023			−0.479220			−0.239610	+	0.970869i	$0.577020\pi$
$200$	−9.86457			−0.697530
$201$	6.78488	+	3.49895i	0.478569	+	0.246797i
$202$			9.62920i			0.677508i
$203$		−	2.50879i		−	0.176083i
$204$	−0.641513	+	1.24397i	−0.0449149	+	0.0870952i
$205$			7.81153i			0.545581i
$206$	−0.677235			−0.0471852
$207$	−10.7741	−	15.1383i	−0.748849	−	1.05218i
$208$	24.2223			1.67951
$209$		−	30.0588i		−	2.07921i
$210$	3.56471	−	6.91238i	0.245988	−	0.477000i
$211$	−12.0190	−	8.15740i	−0.827423	−	0.561579i
$211$	−12.0190	−	8.15740i	−0.827423	−	0.561579i
$212$		−	2.13079i		−	0.146343i
$213$	−2.53124	−	1.30536i	−0.173438	−	0.0894417i
$214$			10.6549i			0.728351i
$215$			4.98221i			0.339784i
$216$	−15.1336	+	2.16993i	−1.02971	+	0.147645i
$217$	−26.4900			−1.79826
$218$	−8.97515			−0.607874
$219$	−0.451278	+	0.875081i	−0.0304945	+	0.0591325i
$220$	−1.11192			−0.0749655
$221$	29.7996			2.00453
$222$	0.489161	−	0.948540i	0.0328303	−	0.0636618i
$223$		−	2.50656i		−	0.167852i	−0.996472	−	0.0839260i	$-0.973254\pi$
$223$		−	2.50656i		−	0.167852i	0.996472	−	0.0839260i	$-0.0267459\pi$
$224$		−	2.66824i		−	0.178279i
$225$	−5.83221	−	8.19465i	−0.388814	−	0.546310i
$226$		−	20.1084i		−	1.33759i
$227$		−	10.0017i		−	0.663835i	−0.943308	−	0.331917i	$-0.892304\pi$
$227$		−	10.0017i		−	0.663835i	0.943308	−	0.331917i	$-0.107696\pi$
$228$	−0.915918	+	1.77607i	−0.0606582	+	0.117623i
$229$		−	1.38853i		−	0.0917569i	−0.998947	−	0.0458785i	$-0.985391\pi$
$229$		−	1.38853i		−	0.0917569i	0.998947	−	0.0458785i	$-0.0146087\pi$
$230$		−	10.7172i		−	0.706672i
$231$	−9.78731	+	18.9787i	−0.643958	+	1.24871i
$232$	−2.84451			−0.186751
$233$	15.2444			0.998696			0.499348	−	0.866402i	$-0.333573\pi$
$233$	15.2444			0.998696			0.499348	+	0.866402i	$0.333573\pi$
$234$	15.7709	+	22.1592i	1.03097	+	1.44859i
$235$	5.27115			0.343852
$236$			1.71525i			0.111653i
$237$	9.76720	−	18.9397i	0.634448	−	1.23027i
$238$			15.5037i			1.00496i
$239$	5.86280			0.379233			0.189617	−	0.981858i	$-0.439276\pi$
$239$	5.86280			0.379233			0.189617	+	0.981858i	$0.439276\pi$
$240$	−7.11680	−	3.67012i	−0.459387	−	0.236905i
$241$	23.7016			1.52675			0.763376	−	0.645955i	$-0.223541\pi$
$241$	23.7016			1.52675			0.763376	+	0.645955i	$0.223541\pi$
$242$	−15.6003			−1.00282
$243$	−10.7500	−	11.2888i	−0.689613	−	0.724178i
$244$		−	1.42694i		−	0.0913506i
$245$		−	0.341377i		−	0.0218097i
$246$	6.51414	−	12.6317i	0.415327	−	0.805367i
$247$	42.5462			2.70715
$248$			30.0348i			1.90721i
$249$	0.336935	+	0.173757i	0.0213524	+	0.0110114i
$250$		−	14.4533i		−	0.914104i
$251$	−4.63768			−0.292728			−0.146364	−	0.989231i	$-0.546757\pi$
$251$	−4.63768			−0.292728			−0.146364	+	0.989231i	$0.546757\pi$
$252$	1.15660	−	0.823161i	0.0728588	−	0.0518543i
$253$			29.4253i			1.84996i
$254$			12.9219i			0.810790i
$255$	−8.75547	−	4.51518i	−0.548289	−	0.282752i
$256$	−4.33898			−0.271186
$257$			24.1300i			1.50519i	0.658484	+	0.752595i	$0.271198\pi$
$257$			24.1300i			1.50519i	−0.658484	+	0.752595i	$0.728802\pi$
$258$	4.15474	−	8.05652i	0.258663	−	0.501577i
$259$			1.18600i			0.0736945i
$260$		−	1.57384i		−	0.0976056i
$261$	−1.68175	−	2.36298i	−0.104098	−	0.146265i
$262$	6.03557			0.372879
$263$		−	5.40571i		−	0.333330i	−0.986014	−	0.166665i	$-0.946700\pi$
$263$		−	5.40571i		−	0.333330i	0.986014	−	0.166665i	$-0.0532999\pi$
$264$	21.5184	+	11.0970i	1.32437	+	0.682974i
$265$	14.9972			0.921273
$266$			22.1354i			1.35721i
$267$	−1.51915	+	2.94581i	−0.0929703	+	0.180280i
$268$			0.803715i			0.0490947i
$269$			21.0439i			1.28307i	0.767093	+	0.641536i	$0.221702\pi$
$269$			21.0439i			1.28307i	−0.767093	+	0.641536i	$0.778298\pi$
$270$	−1.27615	−	8.90021i	−0.0776642	−	0.541650i
$271$		−	28.6781i		−	1.74207i	−0.491221	−	0.871035i	$-0.663449\pi$
$271$		−	28.6781i		−	1.74207i	0.491221	−	0.871035i	$-0.336551\pi$
$272$	15.9622			0.967850
$273$	−26.8631	−	13.8533i	−1.62583	−	0.838438i
$274$		−	9.37739i		−	0.566509i
$275$			15.9285i			0.960526i
$276$	0.896616	−	1.73864i	0.0539699	−	0.104654i
$277$	−22.4494			−1.34885			−0.674426	−	0.738342i	$-0.735609\pi$
$277$	−22.4494			−1.34885			−0.674426	+	0.738342i	$0.735609\pi$
$278$	−17.7628			−1.06534
$279$	−24.9504	+	17.7574i	−1.49374	+	1.06311i
$280$	9.79940			0.585626
$281$			8.89731i			0.530769i	0.964143	+	0.265385i	$0.0854989\pi$
$281$			8.89731i			0.530769i	−0.964143	+	0.265385i	$0.914501\pi$
$282$	−8.52375	−	4.39569i	−0.507582	−	0.261759i
$283$		−	2.37606i		−	0.141242i	−0.997503	−	0.0706212i	$-0.977502\pi$
$283$		−	2.37606i		−	0.141242i	0.997503	−	0.0706212i	$-0.0224982\pi$
$284$		−	0.299843i		−	0.0177924i
$285$	−12.5006	−	6.44654i	−0.740471	−	0.381860i
$286$		−	43.0723i		−	2.54692i
$287$			15.7939i			0.932287i
$288$	−1.78864	−	2.51316i	−0.105397	−	0.148090i
$289$	2.63754			0.155150
$290$		−	1.67288i		−	0.0982349i
$291$	15.1666	+	7.82138i	0.889080	+	0.458498i
$292$	−0.103659			−0.00606619
$293$		−	17.6596i		−	1.03168i	−0.856684	−	0.515842i	$-0.827479\pi$
$293$		−	17.6596i		−	1.03168i	0.856684	−	0.515842i	$-0.172521\pi$
$294$	−0.284679	+	0.552025i	−0.0166028	+	0.0321948i
$295$	−12.0725			−0.702888
$296$	1.34471			0.0781595
$297$	3.50382	+	24.4365i	0.203312	+	1.41795i
$298$	−30.5885			−1.77195
$299$	−41.6496			−2.40866
$300$	0.485356	−	0.941162i	0.0280220	−	0.0543380i
$301$			10.0734i			0.580622i
$302$	−9.80027			−0.563942
$303$	−10.9948	−	5.67002i	−0.631636	−	0.325734i
$304$	22.7900			1.30709
$305$	10.0433			0.575077
$306$	10.3928	+	14.6026i	0.594118	+	0.834776i
$307$	−13.3186			−0.760131			−0.380066	−	0.924960i	$-0.624099\pi$
$307$	−13.3186			−0.760131			−0.380066	+	0.924960i	$0.624099\pi$
$308$	−2.24816			−0.128101
$309$	0.398781	−	0.773282i	0.0226858	−	0.0439905i
$310$	−17.6637			−1.00323
$311$		−	2.91169i		−	0.165107i	−0.996587	−	0.0825534i	$-0.973692\pi$
$311$		−	2.91169i		−	0.165107i	0.996587	−	0.0825534i	$-0.0263075\pi$
$312$	−15.7071	+	30.4578i	−0.889238	+	1.72434i
$313$			23.0656i			1.30375i	0.758328	+	0.651874i	$0.226017\pi$
$313$			23.0656i			1.30375i	−0.758328	+	0.651874i	$0.773983\pi$
$314$			29.0177i			1.63757i
$315$	5.79368	+	8.14052i	0.326437	+	0.458666i
$316$	2.24354			0.126209
$317$	−24.1284			−1.35519			−0.677594	−	0.735436i	$-0.736977\pi$
$317$	−24.1284			−1.35519			−0.677594	+	0.735436i	$0.736977\pi$
$318$	−24.2514	−	12.5064i	−1.35995	−	0.701324i
$319$			4.59308i			0.257163i
$320$		−	11.0254i		−	0.616337i
$321$	−12.1660	−	6.27397i	−0.679038	−	0.350179i
$322$		−	21.6689i		−	1.20756i
$323$	28.0374			1.56004
$324$	0.537574	−	1.55064i	0.0298652	−	0.0861465i
$325$	−22.5457			−1.25061
$326$	−2.72237			−0.150778
$327$	5.28489	−	10.2480i	0.292255	−	0.566717i
$328$	17.9074			0.988772
$329$	10.6576			0.587573
$330$	−6.52625	+	12.6552i	−0.359258	+	0.696644i
$331$	12.0940			0.664745			0.332372	−	0.943148i	$-0.392151\pi$
$331$	12.0940			0.664745			0.332372	+	0.943148i	$0.392151\pi$
$332$			0.0399122i			0.00219047i
$333$	0.795028	+	1.11707i	0.0435673	+	0.0612150i
$334$	1.32179			0.0723251
$335$	−5.65681			−0.309065
$336$	−14.3893	−	7.42053i	−0.785000	−	0.404823i
$337$	−13.5089			−0.735876			−0.367938	−	0.929850i	$-0.619936\pi$
$337$	−13.5089			−0.735876			−0.367938	+	0.929850i	$0.619936\pi$
$338$	43.4393			2.36279
$339$	22.9602	+	11.8405i	1.24703	+	0.643090i
$340$		−	1.03714i		−	0.0562470i
$341$	48.4978			2.62631
$342$	14.8383	+	20.8488i	0.802364	+	1.12738i
$343$		−	18.8552i		−	1.01809i
$344$	11.4214			0.615800
$345$	12.2372	+	6.31068i	0.658826	+	0.339756i
$346$		−	15.0248i		−	0.807740i
$347$		−	18.2638i		−	0.980451i	−0.871596	−	0.490226i	$-0.836914\pi$
$347$		−	18.2638i		−	0.980451i	0.871596	−	0.490226i	$-0.163086\pi$
$348$	0.139955	−	0.271390i	0.00750239	−	0.0145480i
$349$			2.99438i			0.160285i	0.996783	+	0.0801426i	$0.0255376\pi$
$349$			2.99438i			0.160285i	−0.996783	+	0.0801426i	$0.974462\pi$
$350$		−	11.7298i		−	0.626984i
$351$	−34.5883	+	4.95942i	−1.84619	+	0.264714i
$352$			4.88501i			0.260372i
$353$	−1.11299			−0.0592386			−0.0296193	−	0.999561i	$-0.509429\pi$
$353$	−1.11299			−0.0592386			−0.0296193	+	0.999561i	$0.509429\pi$
$354$	19.5219	+	10.0674i	1.03758	+	0.535078i
$355$	2.11039			0.112008
$356$	−0.348950			−0.0184943
$357$	−17.7025	−	9.12914i	−0.936914	−	0.483165i
$358$		−	5.48594i		−	0.289941i
$359$			19.7396i			1.04181i	0.853613	+	0.520907i	$0.174406\pi$
$359$			19.7396i			1.04181i	−0.853613	+	0.520907i	$0.825594\pi$
$360$	9.22985	−	6.56897i	0.486456	−	0.346215i
$361$	21.0304			1.10686
$362$		−	30.2583i		−	1.59034i
$363$	9.18600	−	17.8127i	0.482140	−	0.934926i
$364$		−	3.18212i		−	0.166788i
$365$		−	0.729588i		−	0.0381884i
$366$	−16.2406	−	8.37524i	−0.848909	−	0.437781i
$367$			3.65952i			0.191026i	0.995428	+	0.0955128i	$0.0304491\pi$
$367$			3.65952i			0.191026i	−0.995428	+	0.0955128i	$0.969551\pi$
$368$	−22.3097			−1.16297
$369$	10.5874	+	14.8760i	0.551157	+	0.774413i
$370$			0.790834i			0.0411135i
$371$	30.3225			1.57427
$372$	−2.86557	−	1.47777i	−0.148573	−	0.0766189i
$373$		−	0.674316i		−	0.0349148i	−0.999848	−	0.0174574i	$-0.994443\pi$
$373$		−	0.674316i		−	0.0349148i	0.999848	−	0.0174574i	$-0.00555714\pi$
$374$		−	28.3841i		−	1.46771i
$375$	16.5031	+	8.51060i	0.852214	+	0.439486i
$376$		−	12.0838i		−	0.623173i
$377$	−6.50120			−0.334829
$378$	−2.58022	−	17.9951i	−0.132712	−	0.925569i
$379$		−	32.2518i		−	1.65666i	−0.560239	−	0.828331i	$-0.689291\pi$
$379$		−	32.2518i		−	1.65666i	0.560239	−	0.828331i	$-0.310709\pi$
$380$		−	1.48078i		−	0.0759624i
$381$	−14.7545	−	7.60886i	−0.755894	−	0.389814i
$382$	−11.0408			−0.564894
$383$			16.7702i			0.856918i	0.903561	+	0.428459i	$0.140943\pi$
$383$			16.7702i			0.856918i	−0.903561	+	0.428459i	$0.859057\pi$
$384$	−7.56165	+	14.6629i	−0.385879	+	0.748264i
$385$		−	15.8233i		−	0.806430i
$386$	−10.2575			−0.522091
$387$	6.75265	+	9.48794i	0.343257	+	0.482299i
$388$			1.79658i			0.0912076i
$389$			29.9738i			1.51973i	0.650080	+	0.759866i	$0.274735\pi$
$389$			29.9738i			1.51973i	−0.650080	+	0.759866i	$0.725265\pi$
$390$	−17.9125	−	9.23746i	−0.907036	−	0.467757i
$391$	−27.4466			−1.38803
$392$	−0.782584			−0.0395264
$393$	−3.55396	+	6.89155i	−0.179274	+	0.347633i
$394$	26.6634			1.34328
$395$			15.7908i			0.794520i
$396$	−2.11749	+	1.50704i	−0.106408	+	0.0757316i
$397$			33.6619i			1.68944i	0.535208	+	0.844720i	$0.320233\pi$
$397$			33.6619i			1.68944i	−0.535208	+	0.844720i	$0.679767\pi$
$398$	−9.11416			−0.456851
$399$	−25.2746	−	13.0341i	−1.26531	−	0.652521i
$400$	−12.0767			−0.603833
$401$	−10.8161			−0.540130			−0.270065	−	0.962842i	$-0.587045\pi$
$401$	−10.8161			−0.540130			−0.270065	+	0.962842i	$0.587045\pi$
$402$	9.14739	+	4.71730i	0.456230	+	0.235277i
$403$			68.6454i			3.41947i
$404$		−	1.30241i		−	0.0647974i
$405$	10.9139	+	3.78363i	0.542316	+	0.188010i
$406$		−	3.38236i		−	0.167864i
$407$		−	2.17132i		−	0.107629i
$408$	−10.3508	+	20.0713i	−0.512439	+	0.993680i
$409$		−	18.9663i		−	0.937823i	−0.883245	−	0.468911i	$-0.844646\pi$
$409$		−	18.9663i		−	0.937823i	0.883245	−	0.468911i	$-0.155354\pi$
$410$			10.5315i			0.520114i
$411$	10.7073	+	5.52175i	0.528153	+	0.272368i
$412$	0.0916004			0.00451283
$413$	−24.4091			−1.20109
$414$	−14.5256	−	20.4095i	−0.713895	−	1.00307i
$415$	−0.280916			−0.0137896
$416$	−6.91440			−0.339006
$417$	10.4594	−	20.2820i	0.512198	−	0.993212i
$418$		−	40.5253i		−	1.98216i
$419$			0.0197728i			0.000965962i	1.00000		0.000482981i	$0.000153738\pi$
$419$			0.0197728i			0.000965962i	−1.00000		0.000482981i	$0.999846\pi$
$420$	−0.482150	+	0.934944i	−0.0235265	+	0.0456206i
$421$		−	11.6691i		−	0.568719i	−0.958718	−	0.284359i	$-0.908219\pi$
$421$		−	11.6691i		−	0.568719i	0.958718	−	0.284359i	$-0.0917809\pi$
$422$	−16.2041	−	10.9978i	−0.788801	−	0.535366i
$423$	10.0382	−	7.14427i	0.488073	−	0.347366i
$424$		−	34.3802i		−	1.66965i
$425$	−14.8574			−0.720688
$426$	−3.41263	−	1.75989i	−0.165342	−	0.0852668i
$427$	20.3063			0.982690
$428$		−	1.44114i		−	0.0696601i
$429$	49.1809	+	25.3625i	2.37448	+	1.22451i
$430$			6.71702i			0.323924i
$431$		−	27.8342i		−	1.34072i	−0.742034	−	0.670362i	$-0.766139\pi$
$431$		−	27.8342i		−	1.34072i	0.742034	−	0.670362i	$-0.233861\pi$
$432$	−18.5273	+	2.65652i	−0.891394	+	0.127812i
$433$	8.24486			0.396223			0.198111	−	0.980180i	$-0.436519\pi$
$433$	8.24486			0.396223			0.198111	+	0.980180i	$0.436519\pi$
$434$	−35.7139			−1.71432
$435$	1.91013	+	0.985052i	0.0915838	+	0.0472296i
$436$	1.21395			0.0581375
$437$	−39.1868			−1.87456
$438$	−0.608413	+	1.17978i	−0.0290711	+	0.0563723i
$439$		−	4.45379i		−	0.212568i	−0.994336	−	0.106284i	$-0.966105\pi$
$439$		−	4.45379i		−	0.212568i	0.994336	−	0.106284i	$-0.0338952\pi$
$440$	−17.9407			−0.855290
$441$	−0.462686	−	0.650105i	−0.0220326	−	0.0309574i
$442$	40.1758			1.91097
$443$			26.2249i			1.24598i	0.782228	+	0.622992i	$0.214083\pi$
$443$			26.2249i			1.24598i	−0.782228	+	0.622992i	$0.785917\pi$
$444$	−0.0661622	+	0.128296i	−0.00313992	+	0.00608867i
$445$		−	2.45603i		−	0.116427i
$446$		−	3.37935i		−	0.160017i
$447$	18.0116	−	34.9267i	0.851921	−	1.65197i
$448$		−	22.2919i		−	1.05319i
$449$	−33.6525			−1.58816			−0.794080	−	0.607814i	$-0.792047\pi$
$449$	−33.6525			−1.58816			−0.794080	+	0.607814i	$0.792047\pi$
$450$	−7.86300	−	11.0480i	−0.370665	−	0.520810i
$451$		−	28.9155i		−	1.36158i
$452$			2.71979i			0.127928i
$453$	5.77075	−	11.1902i	0.271133	−	0.525760i
$454$		−	13.4843i		−	0.632849i
$455$	22.3968			1.04998
$456$	−14.7783	+	28.6568i	−0.692056	+	1.34198i
$457$			6.22888i			0.291375i	0.989331	+	0.145687i	$0.0465393\pi$
$457$			6.22888i			0.291375i	−0.989331	+	0.145687i	$0.953461\pi$
$458$		−	1.87202i		−	0.0874740i
$459$	−22.7933	+	3.26820i	−1.06390	+	0.152547i
$460$			1.44957i			0.0675867i
$461$	−7.12742			−0.331957			−0.165978	−	0.986129i	$-0.553078\pi$
$461$	−7.12742			−0.331957			−0.165978	+	0.986129i	$0.553078\pi$
$462$	−13.1953	+	25.5872i	−0.613899	+	1.19042i
$463$			22.2470i			1.03391i	0.856014	+	0.516953i	$0.172934\pi$
$463$			22.2470i			1.03391i	−0.856014	+	0.516953i	$0.827066\pi$
$464$	−3.48238			−0.161665
$465$	10.4011	−	20.1689i	0.482337	−	0.935308i
$466$	20.5526			0.952079
$467$		−	22.0501i		−	1.02036i	−0.860068	−	0.510179i	$-0.829579\pi$
$467$		−	22.0501i		−	1.02036i	0.860068	−	0.510179i	$-0.170421\pi$
$468$	−2.13311	−	2.99717i	−0.0986032	−	0.138544i
$469$	−11.4374			−0.528129
$470$	7.10658			0.327802
$471$	−33.1331	−	17.0867i	−1.52669	−	0.787313i
$472$			27.6754i			1.27386i
$473$		−	18.4424i		−	0.847981i
$474$	13.1681	−	25.5346i	0.604833	−	1.17284i
$475$	−21.2126			−0.973299
$476$		−	2.09698i		−	0.0961147i
$477$	28.5602	−	20.3265i	1.30768	−	0.930688i
$478$	7.90424			0.361531
$479$	−24.5814			−1.12315			−0.561576	−	0.827425i	$-0.689805\pi$
$479$	−24.5814			−1.12315			−0.561576	+	0.827425i	$0.689805\pi$
$480$	2.03153	+	1.04766i	0.0927264	+	0.0478189i
$481$	3.07336			0.140133
$482$	31.9545			1.45549
$483$	24.7420	+	12.7594i	1.12580	+	0.580574i
$484$	2.11004			0.0959108
$485$	−12.6449			−0.574178
$486$	−14.4932	−	15.2196i	−0.657424	−	0.690375i
$487$	42.1017			1.90781			0.953905	−	0.300109i	$-0.0970230\pi$
$487$	42.1017			1.90781			0.953905	+	0.300109i	$0.0970230\pi$
$488$		−	23.0236i		−	1.04223i
$489$	1.60303	−	3.10846i	0.0724915	−	0.140570i
$490$		−	0.460244i		−	0.0207917i
$491$		−	38.3282i		−	1.72973i	−0.502006	−	0.864864i	$-0.667404\pi$
$491$		−	38.3282i		−	1.72973i	0.502006	−	0.864864i	$-0.332596\pi$
$492$	−0.881080	+	1.70852i	−0.0397221	+	0.0770259i
$493$	−4.28421			−0.192951
$494$	57.3609			2.58079
$495$	−10.6071	−	14.9036i	−0.476752	−	0.669868i
$496$			36.7700i			1.65102i
$497$	4.26695			0.191399
$498$	0.454257	+	0.234260i	0.0203557	+	0.0104974i
$499$			6.25687i			0.280096i	0.990145	+	0.140048i	$0.0447257\pi$
$499$			6.25687i			0.280096i	−0.990145	+	0.140048i	$0.955274\pi$
$500$			1.95490i			0.0874256i
$501$	−0.778318	+	1.50925i	−0.0347727	+	0.0674283i
$502$	−6.25253			−0.279064
$503$			2.94307i			0.131225i	0.997845	+	0.0656124i	$0.0209001\pi$
$503$			2.94307i			0.131225i	−0.997845	+	0.0656124i	$0.979100\pi$
$504$	18.6616	−	13.2816i	0.831255	−	0.591612i
$505$	9.16681			0.407918
$506$			39.6713i			1.76360i
$507$	−25.5786	+	49.5999i	−1.13599	+	2.20281i
$508$		−	1.74777i		−	0.0775445i
$509$			13.3964i			0.593786i	0.954911	+	0.296893i	$0.0959504\pi$
$509$			13.3964i			0.593786i	−0.954911	+	0.296893i	$0.904050\pi$
$510$	−11.8041	−	6.08738i	−0.522696	−	0.269554i
$511$		−	1.47514i		−	0.0652562i
$512$	−24.8999			−1.10043
$513$	−32.5430	+	4.66616i	−1.43681	+	0.206016i
$514$			32.5321i			1.43493i
$515$			0.644715i			0.0284095i
$516$	−0.561955	+	1.08970i	−0.0247387	+	0.0479712i
$517$	−19.5119			−0.858133
$518$			1.59897i			0.0702546i
$519$	17.1557	+	8.84716i	0.753051	+	0.388347i
$520$		−	25.3939i		−	1.11359i
$521$		−	13.1718i		−	0.577069i	−0.957470	−	0.288534i	$-0.906832\pi$
$521$		−	13.1718i		−	0.577069i	0.957470	−	0.288534i	$-0.0931680\pi$
$522$	−2.26734	−	3.18577i	−0.0992389	−	0.139437i
$523$	6.05354			0.264703			0.132351	−	0.991203i	$-0.457747\pi$
$523$	6.05354			0.264703			0.132351	+	0.991203i	$0.457747\pi$
$524$	−0.816350			−0.0356624
$525$	13.3933	+	6.90692i	0.584533	+	0.301443i
$526$		−	7.28799i		−	0.317771i
$527$			45.2365i			1.97053i
$528$	26.3438	+	13.5855i	1.14647	+	0.591232i
$529$	15.3609			0.667867
$530$	20.2193			0.878270
$531$	−22.9904	+	16.3625i	−0.997699	+	0.710072i
$532$		−	2.99395i		−	0.129804i
$533$	40.9279			1.77278
$534$	−2.04812	+	3.97154i	−0.0886307	+	0.171865i
$535$	10.1432			0.438530
$536$			12.9679i			0.560127i
$537$	6.26396	+	3.23032i	0.270310	+	0.139398i
$538$			28.3715i			1.22318i
$539$			1.26365i			0.0544294i
$540$	0.172608	+	1.20381i	0.00742786	+	0.0518038i
$541$	−29.3473			−1.26174			−0.630871	−	0.775888i	$-0.717302\pi$
$541$	−29.3473			−1.26174			−0.630871	+	0.775888i	$0.717302\pi$
$542$		−	38.6638i		−	1.66075i
$543$	34.5496	+	17.8172i	1.48267	+	0.764609i
$544$	−4.55650			−0.195359
$545$			8.54417i			0.365992i
$546$	−36.2169	−	18.6770i	−1.54994	−	0.799302i
$547$	26.2283			1.12144			0.560721	−	0.828005i	$-0.310524\pi$
$547$	26.2283			1.12144			0.560721	+	0.828005i	$0.310524\pi$
$548$			1.26835i			0.0541814i
$549$	19.1261	−	13.6122i	0.816281	−	0.580955i
$550$			21.4748i			0.915691i
$551$	−6.11677			−0.260583
$552$	14.4668	−	28.0529i	0.615749	−	1.19401i
$553$			31.9270i			1.35767i
$554$	−30.2663			−1.28589
$555$	−0.902991	−	0.465671i	−0.0383299	−	0.0197667i
$556$	2.40254			0.101890
$557$	43.0626			1.82462			0.912310	−	0.409500i	$-0.134297\pi$
$557$	43.0626			1.82462			0.912310	+	0.409500i	$0.134297\pi$
$558$	−33.6382	+	23.9406i	−1.42402	+	1.01349i
$559$	26.1039			1.10408
$560$	11.9969			0.506961
$561$	32.4096	+	16.7136i	1.36833	+	0.705648i
$562$			11.9954i			0.505994i
$563$	−43.1095			−1.81685			−0.908425	−	0.418048i	$-0.862714\pi$
$563$	−43.1095			−1.81685			−0.908425	+	0.418048i	$0.862714\pi$
$564$	1.15289	+	0.594545i	0.0485455	+	0.0250349i
$565$	−19.1428			−0.805343
$566$		−	3.20341i		−	0.134650i
$567$	22.0666	+	7.65002i	0.926708	+	0.321271i
$568$		−	4.83794i		−	0.202995i
$569$	−29.8330			−1.25066			−0.625331	−	0.780359i	$-0.715036\pi$
$569$	−29.8330			−1.25066			−0.625331	+	0.780359i	$0.715036\pi$
$570$	−16.8533	−	8.69123i	−0.705908	−	0.364036i
$571$		−	16.6931i		−	0.698586i	−0.937014	−	0.349293i	$-0.886422\pi$
$571$		−	16.6931i		−	0.698586i	0.937014	−	0.349293i	$-0.113578\pi$
$572$			5.82580i			0.243589i
$573$	6.50119	−	12.6066i	0.271591	−	0.526647i
$574$			21.2934i			0.888770i
$575$	20.7655			0.865982
$576$	−14.9433	−	20.9963i	−0.622636	−	0.874845i
$577$			5.28095i			0.219849i	0.993940	+	0.109924i	$0.0350609\pi$
$577$			5.28095i			0.219849i	−0.993940	+	0.109924i	$0.964939\pi$
$578$	3.55594			0.147908
$579$	6.03996	−	11.7122i	0.251012	−	0.486742i
$580$			0.226268i			0.00939526i
$581$	−0.567977			−0.0235636
$582$	20.4476	+	10.5448i	0.847580	+	0.437096i
$583$	−55.5144			−2.29917
$584$	−1.67253			−0.0692099
$585$	21.0951	−	15.0136i	0.872174	−	0.620734i
$586$		−	23.8087i		−	0.983528i
$587$	−15.3009			−0.631535			−0.315768	−	0.948837i	$-0.602262\pi$
$587$	−15.3009			−0.631535			−0.315768	+	0.948837i	$0.602262\pi$
$588$	0.0385046	−	0.0746650i	0.00158790	−	0.00307913i
$589$			64.5863i			2.66123i
$590$	−16.2762			−0.670079
$591$	−15.7003	+	30.4448i	−0.645826	+	1.25233i
$592$	1.64625			0.0676606
$593$			17.7062i			0.727108i	0.931573	+	0.363554i	$0.118437\pi$
$593$			17.7062i			0.727108i	−0.931573	+	0.363554i	$0.881563\pi$
$594$	4.72386	+	32.9454i	0.193822	+	1.35177i
$595$	14.7592			0.605069
$596$	4.13730			0.169470
$597$	5.36674	−	10.4067i	0.219646	−	0.425920i
$598$	−56.1520			−2.29623
$599$	43.3788			1.77241			0.886204	−	0.463296i	$-0.153333\pi$
$599$	43.3788			1.77241			0.886204	+	0.463296i	$0.153333\pi$
$600$	7.83118	−	15.1856i	0.319707	−	0.619948i
$601$	46.1583			1.88284			0.941418	−	0.337241i	$-0.109494\pi$
$601$	46.1583			1.88284			0.941418	+	0.337241i	$0.109494\pi$
$602$			13.5810i			0.553520i
$603$	−10.7726	+	7.66698i	−0.438695	+	0.312223i
$604$	1.32555			0.0539358
$605$			14.8511i			0.603785i
$606$	−14.8232	−	7.64433i	−0.602153	−	0.310530i
$607$	24.5729			0.997384			0.498692	−	0.866779i	$-0.333814\pi$
$607$	24.5729			0.997384			0.498692	+	0.866779i	$0.333814\pi$
$608$	−6.50553			−0.263834
$609$	3.86205	+	1.99165i	0.156498	+	0.0807059i
$610$	13.5404			0.548234
$611$		−	27.6178i		−	1.11730i
$612$	−1.40570	−	1.97510i	−0.0568219	−	0.0798386i
$613$		−	12.0265i		−	0.485744i	−0.970058	−	0.242872i	$-0.921910\pi$
$613$		−	12.0265i		−	0.485744i	0.970058	−	0.242872i	$-0.0780895\pi$
$614$	−17.9561			−0.724650
$615$	−12.0251	−	6.20133i	−0.484899	−	0.250062i
$616$	−36.2739			−1.46152
$617$	−3.85405			−0.155158			−0.0775791	−	0.996986i	$-0.524719\pi$
$617$	−3.85405			−0.155158			−0.0775791	+	0.996986i	$0.524719\pi$
$618$	0.537637	−	1.04254i	0.0216269	−	0.0419371i
$619$		−	34.1827i		−	1.37392i	−0.726696	−	0.686959i	$-0.758945\pi$
$619$		−	34.1827i		−	1.37392i	0.726696	−	0.686959i	$-0.241055\pi$
$620$	2.38914			0.0959500
$621$	31.8572	−	4.56783i	1.27838	−	0.183301i
$622$		−	3.92555i		−	0.157400i
$623$		−	4.96579i		−	0.198950i
$624$	−19.2293	+	37.2879i	−0.769789	+	1.49271i
$625$	3.00442			0.120177
$626$			31.0971i			1.24289i
$627$	46.2727	+	23.8628i	1.84795	+	0.952987i
$628$		−	3.92484i		−	0.156618i
$629$	2.02531			0.0807544
$630$	7.81105	+	10.9751i	0.311200	+	0.437257i
$631$	0.0878589			0.00349761			0.00174880	−	0.999998i	$-0.499443\pi$
$631$	0.0878589			0.00349761			0.00174880	+	0.999998i	$0.499443\pi$
$632$	36.1993			1.43993
$633$	22.0991	−	12.0262i	0.878360	−	0.478000i
$634$	−32.5300			−1.29193
$635$	12.3014			0.488165
$636$	3.28016	+	1.69157i	0.130067	+	0.0670752i
$637$	−1.78862			−0.0708675
$638$			6.19240i			0.245160i
$639$	4.01895	−	2.86033i	0.158987	−	0.113153i
$640$		−	12.2250i		−	0.483237i
$641$	10.9975			0.434375			0.217188	−	0.976130i	$-0.430312\pi$
$641$	10.9975			0.434375			0.217188	+	0.976130i	$0.430312\pi$
$642$	−16.4022	−	8.45857i	−0.647342	−	0.333833i
$643$			4.62653i			0.182453i	0.995830	+	0.0912264i	$0.0290787\pi$
$643$			4.62653i			0.182453i	−0.995830	+	0.0912264i	$0.970921\pi$
$644$			2.93086i			0.115492i
$645$	−7.66965	−	3.95523i	−0.301992	−	0.155737i
$646$	37.8001			1.48723
$647$		−	5.85772i		−	0.230291i	−0.993349	−	0.115145i	$-0.963267\pi$
$647$		−	5.85772i		−	0.230291i	0.993349	−	0.115145i	$-0.0367334\pi$
$648$	8.67372	−	25.0194i	0.340736	−	0.982855i
$649$	44.6881			1.75416
$650$	−30.3962			−1.19224
$651$	21.0296	−	40.7789i	0.824216	−	1.59825i
$652$	0.368218			0.0144205
$653$		−	1.50673i		−	0.0589631i	−0.999565	−	0.0294815i	$-0.990614\pi$
$653$		−	1.50673i		−	0.0589631i	0.999565	−	0.0294815i	$-0.00938562\pi$
$654$	7.12510	−	13.8164i	0.278613	−	0.540264i
$655$		−	5.74574i		−	0.224505i
$656$	21.9231			0.855953
$657$	−0.988849	−	1.38940i	−0.0385787	−	0.0542056i
$658$	14.3686			0.560147
$659$	1.15558			0.0450151			0.0225075	−	0.999747i	$-0.492835\pi$
$659$	1.15558			0.0450151			0.0225075	+	0.999747i	$0.492835\pi$
$660$	0.882717	−	1.71169i	0.0343597	−	0.0666275i
$661$			28.6849i			1.11571i	0.829937	+	0.557857i	$0.188376\pi$
$661$			28.6849i			1.11571i	−0.829937	+	0.557857i	$0.811624\pi$
$662$	16.3051			0.633716
$663$	−23.6570	+	45.8736i	−0.918760	+	1.78158i
$664$			0.643981i			0.0249913i
$665$	21.0724			0.817154
$666$	1.07186	+	1.50603i	0.0415337	+	0.0583576i
$667$	5.98787			0.231851
$668$	−0.178781			−0.00691723
$669$	3.85862	+	1.98988i	0.149183	+	0.0769334i
$670$	−7.62652			−0.294638
$671$	−37.1767			−1.43519
$672$	4.10751	+	2.11824i	0.158451	+	0.0817128i
$673$			6.71033i			0.258664i	0.991601	+	0.129332i	$0.0412833\pi$
$673$			6.71033i			0.258664i	−0.991601	+	0.129332i	$0.958717\pi$
$674$	−18.2127			−0.701527
$675$	17.2449	−	2.47265i	0.663757	−	0.0951725i
$676$	−5.87544			−0.225979
$677$			42.0418i			1.61580i	0.589321	+	0.807899i	$0.299395\pi$
$677$			42.0418i			1.61580i	−0.589321	+	0.807899i	$0.700605\pi$
$678$	30.9550	+	15.9634i	1.18882	+	0.613072i
$679$	−25.5665			−0.981153
$680$		−	16.7342i		−	0.641729i
$681$	15.3967	+	7.94003i	0.590001	+	0.304263i
$682$	65.3849			2.50372
$683$	13.8291			0.529156			0.264578	−	0.964364i	$-0.414767\pi$
$683$	13.8291			0.529156			0.264578	+	0.964364i	$0.414767\pi$
$684$	−2.00698	−	2.81994i	−0.0767387	−	0.107823i
$685$	−8.92709			−0.341087
$686$		−	25.4206i		−	0.970564i
$687$	2.13752	+	1.10232i	0.0815514	+	0.0420560i
$688$	13.9826			0.533082
$689$		−	78.5768i		−	2.99354i
$690$	16.4982	+	8.50807i	0.628074	+	0.323897i
$691$	−20.5121			−0.780317			−0.390159	−	0.920748i	$-0.627580\pi$
$691$	−20.5121			−0.780317			−0.390159	+	0.920748i	$0.627580\pi$
$692$			2.03221i			0.0772529i
$693$	−21.4461	−	30.1333i	−0.814672	−	1.14467i
$694$		−	24.6233i		−	0.934686i
$695$			16.9098i			0.641427i
$696$	2.25817	−	4.37885i	0.0855957	−	0.165980i
$697$	26.9710			1.02160
$698$			4.03702i			0.152804i
$699$	−12.1021	+	23.4674i	−0.457743	+	0.887617i
$700$			1.58653i			0.0599652i
$701$	19.8043			0.747999			0.373999	−	0.927429i	$-0.377986\pi$
$701$	19.8043			0.747999			0.373999	+	0.927429i	$0.377986\pi$
$702$	−46.6320	+	6.68630i	−1.76001	+	0.252358i
$703$	2.89163			0.109060
$704$			40.8119i			1.53816i
$705$	−4.18461	+	8.11445i	−0.157601	+	0.305608i
$706$	−1.50054			−0.0564734
$707$	18.5341			0.697048
$708$	−2.64047	−	1.36168i	−0.0992348	−	0.0511752i
$709$	5.89064			0.221227			0.110614	−	0.993863i	$-0.464718\pi$
$709$	5.89064			0.221227			0.110614	+	0.993863i	$0.464718\pi$
$710$	2.84524			0.106780
$711$	21.4021	+	30.0714i	0.802640	+	1.12776i
$712$	−5.63029			−0.211004
$713$		−	63.2252i		−	2.36780i
$714$	−23.8665	−	12.3079i	−0.893181	−	0.460612i
$715$	−41.0040			−1.53346
$716$			0.742008i			0.0277301i
$717$	−4.65430	+	9.02523i	−0.173818	+	0.337053i
$718$			26.6129i			0.993185i
$719$	−29.0762			−1.08436			−0.542179	−	0.840263i	$-0.682401\pi$
$719$	−29.0762			−1.08436			−0.542179	+	0.840263i	$0.682401\pi$
$720$	11.2996	−	8.04204i	0.421112	−	0.299709i
$721$			1.30353i			0.0485461i
$722$	28.3532			1.05520
$723$	−18.8159	+	36.4863i	−0.699773	+	1.35694i
$724$			4.09263i			0.152101i
$725$	3.24135			0.120381
$726$	12.3846	−	24.0151i	0.459635	−	0.891286i
$727$			31.2137i			1.15765i	0.815451	+	0.578826i	$0.196489\pi$
$727$			31.2137i			1.15765i	−0.815451	+	0.578826i	$0.803511\pi$
$728$		−	51.3432i		−	1.90291i
$729$	25.9122	−	7.58679i	0.959710	−	0.280992i
$730$		−	0.983631i		−	0.0364058i
$731$	17.2022			0.636245
$732$	2.19664	+	1.13281i	0.0811903	+	0.0418697i
$733$	−9.80481			−0.362149			−0.181074	−	0.983469i	$-0.557957\pi$
$733$	−9.80481			−0.362149			−0.181074	+	0.983469i	$0.557957\pi$
$734$			4.93378i			0.182109i
$735$	0.525517	+	0.271008i	0.0193840	+	0.00999630i
$736$	6.36844			0.234744
$737$	20.9395			0.771316
$738$	14.2739	+	20.0558i	0.525430	+	0.738265i
$739$		−	30.9787i		−	1.13957i	−0.821794	−	0.569785i	$-0.807026\pi$
$739$		−	30.9787i		−	1.13957i	0.821794	−	0.569785i	$-0.192974\pi$
$740$		−	0.106965i		−	0.00393213i
$741$	−33.7761	+	65.4959i	−1.24080	+	2.40605i
$742$	40.8809			1.50078
$743$	1.89005			0.0693391			0.0346696	−	0.999399i	$-0.488962\pi$
$743$	1.89005			0.0693391			0.0346696	+	0.999399i	$0.488962\pi$
$744$	−46.2358	−	23.8437i	−1.69509	−	0.874154i
$745$			29.1197i			1.06686i
$746$		−	0.909114i		−	0.0332850i
$747$	−0.534965	+	0.380740i	−0.0195734	+	0.0139305i
$748$			3.83914i			0.140373i
$749$	20.5083			0.749358
$750$	22.2494	+	11.4740i	0.812435	+	0.418971i
$751$		−	31.6598i		−	1.15528i	−0.816290	−	0.577642i	$-0.803973\pi$
$751$		−	31.6598i		−	1.15528i	0.816290	−	0.577642i	$-0.196027\pi$
$752$		−	14.7935i		−	0.539464i
$753$	3.68171	−	7.13927i	0.134169	−	0.260170i
$754$	−8.76493			−0.319200
$755$			9.32966i			0.339541i
$756$	0.348992	+	2.43396i	0.0126927	+	0.0885221i
$757$		−	8.27548i		−	0.300777i	−0.988627	−	0.150389i	$-0.951947\pi$
$757$		−	8.27548i		−	0.300777i	0.988627	−	0.150389i	$-0.0480525\pi$
$758$		−	43.4819i		−	1.57933i
$759$	−45.2976	−	23.3599i	−1.64420	−	0.847910i
$760$		−	23.8923i		−	0.866663i
$761$	−36.3757			−1.31862			−0.659309	−	0.751872i	$-0.729151\pi$
$761$	−36.3757			−1.31862			−0.659309	+	0.751872i	$0.729151\pi$
$762$	−19.8920	−	10.2583i	−0.720611	−	0.371618i
$763$			17.2752i			0.625406i
$764$	1.49333			0.0540269
$765$	13.9014	−	9.89376i	0.502606	−	0.357710i
$766$			22.6096i			0.816919i
$767$			63.2529i			2.28393i
$768$	3.44459	−	6.67946i	0.124296	−	0.241024i
$769$	−36.1533			−1.30372			−0.651862	−	0.758338i	$-0.726012\pi$
$769$	−36.1533			−1.30372			−0.651862	+	0.758338i	$0.726012\pi$
$770$		−	21.3330i		−	0.768788i
$771$	−37.1459	−	19.1561i	−1.33778	−	0.689890i
$772$	1.38739			0.0499332
$773$	19.9411			0.717233			0.358616	−	0.933485i	$-0.383249\pi$
$773$	19.9411			0.717233			0.358616	+	0.933485i	$0.383249\pi$
$774$	9.10394	+	12.7916i	0.327234	+	0.459786i
$775$		−	34.2250i		−	1.22940i
$776$			28.9877i			1.04060i
$777$	−1.82574	−	0.941530i	−0.0654979	−	0.0337772i
$778$			40.4107i			1.44879i
$779$	38.5077			1.37968
$780$	2.42278	+	1.24943i	0.0867496	+	0.0447367i
$781$	−7.81192			−0.279532
$782$	−37.0035			−1.32324
$783$	4.97268	−	0.713005i	0.177709	−	0.0254807i
$784$	−0.958075			−0.0342170
$785$	27.6243			0.985954
$786$	−4.79146	+	9.29120i	−0.170906	+	0.331406i
$787$	−6.92225			−0.246752			−0.123376	−	0.992360i	$-0.539372\pi$
$787$	−6.92225			−0.246752			−0.123376	+	0.992360i	$0.539372\pi$
$788$	−3.60639			−0.128472
$789$	8.32158	+	4.29143i	0.296256	+	0.152779i
$790$			21.2891i			0.757434i
$791$	−38.7043			−1.37617
$792$	−34.1656	+	24.3160i	−1.21402	+	0.864031i
$793$		−	52.6211i		−	1.86863i
$794$			45.3830i			1.61058i
$795$	−11.9058	+	23.0868i	−0.422257	+	0.818806i
$796$	1.23275			0.0436936
$797$	−8.12779			−0.287901			−0.143951	−	0.989585i	$-0.545981\pi$
$797$	−8.12779			−0.287901			−0.143951	+	0.989585i	$0.545981\pi$
$798$	−34.0753	−	17.5726i	−1.20625	−	0.622063i
$799$		−	18.1998i		−	0.643863i
$800$	3.44736			0.121883
$801$	−3.32879	−	4.67717i	−0.117617	−	0.165260i
$802$	−14.5823			−0.514918
$803$			2.70067i			0.0953047i
$804$	−1.23724	−	0.638045i	−0.0436342	−	0.0225021i
$805$	−20.6283			−0.727054
$806$			92.5478i			3.25986i
$807$	−32.3952	−	16.7061i	−1.14036	−	0.588084i
$808$		−	21.0143i		−	0.739281i
$809$			38.3793i			1.34934i	0.738118	+	0.674672i	$0.235715\pi$
$809$			38.3793i			1.34934i	−0.738118	+	0.674672i	$0.764285\pi$
$810$	14.7141	+	5.10109i	0.517002	+	0.179234i
$811$	36.0339			1.26532			0.632660	−	0.774429i	$-0.281963\pi$
$811$	36.0339			1.26532			0.632660	+	0.774429i	$0.281963\pi$
$812$			0.457486i			0.0160546i
$813$	44.1472	+	22.7667i	1.54831	+	0.798462i
$814$		−	2.92738i		−	0.102605i
$815$			2.59164i			0.0907813i
$816$	−12.6719	+	24.5723i	−0.443605	+	0.860202i
$817$	24.5603			0.859257
$818$		−	25.5704i		−	0.894047i
$819$	42.6516	−	30.3556i	1.49037	−	1.06071i
$820$		−	1.42446i		−	0.0497441i
$821$			11.3312i			0.395463i	0.980256	+	0.197732i	$0.0633574\pi$
$821$			11.3312i			0.395463i	−0.980256	+	0.197732i	$0.936643\pi$
$822$	14.4356	+	7.44443i	0.503500	+	0.259654i
$823$		−	17.0572i		−	0.594576i	−0.954788	−	0.297288i	$-0.903918\pi$
$823$		−	17.0572i		−	0.594576i	0.954788	−	0.297288i	$-0.0960821\pi$
$824$	1.47797			0.0514874
$825$	−24.5205	−	12.6452i	−0.853693	−	0.440248i
$826$	−32.9084			−1.14503
$827$			18.2519i			0.634680i	0.948312	+	0.317340i	$0.102790\pi$
$827$			18.2519i			0.634680i	−0.948312	+	0.317340i	$0.897210\pi$
$828$	1.96468	+	2.76051i	0.0682774	+	0.0959344i
$829$	17.1596			0.595978			0.297989	−	0.954569i	$-0.403684\pi$
$829$	17.1596			0.595978			0.297989	+	0.954569i	$0.403684\pi$
$830$	−0.378731			−0.0131459
$831$	17.8219	−	34.5587i	0.618234	−	1.19883i
$832$	−57.7665			−2.00269
$833$	−1.17868			−0.0408387
$834$	14.1014	−	27.3442i	0.488290	−	0.946852i
$835$		−	1.25832i		−	0.0435459i
$836$			5.48131i			0.189575i
$837$	−7.52853	−	52.5059i	−0.260224	−	1.81487i
$838$			0.0266577i			0.000920873i
$839$	−43.3650			−1.49713			−0.748563	−	0.663064i	$-0.769256\pi$
$839$	−43.3650			−1.49713			−0.748563	+	0.663064i	$0.769256\pi$
$840$	−7.77945	+	15.0853i	−0.268416	+	0.520491i
$841$	−28.0653			−0.967770
$842$		−	15.7323i		−	0.542173i
$843$	−13.6966	−	7.06331i	−0.471735	−	0.243273i
$844$	2.19170	+	1.48753i	0.0754415	+	0.0512028i
$845$		−	41.3533i		−	1.42260i
$846$	13.5335	−	9.63192i	0.465291	−	0.331152i
$847$			30.0272i			1.03175i
$848$		−	42.0898i		−	1.44537i
$849$	3.65773	+	1.88629i	0.125533	+	0.0647372i
$850$	−20.0307			−0.687048
$851$	−2.83069			−0.0970348
$852$	0.461580	+	0.238036i	0.0158135	+	0.00815498i
$853$	35.4618			1.21419			0.607094	−	0.794630i	$-0.292335\pi$
$853$	35.4618			1.21419			0.607094	+	0.794630i	$0.292335\pi$
$854$	27.3770			0.936821
$855$	19.8477	−	14.1258i	0.678776	−	0.483091i
$856$		−	23.2527i		−	0.794760i
$857$			42.2903i			1.44461i	0.691575	+	0.722305i	$0.256917\pi$
$857$			42.2903i			1.44461i	−0.691575	+	0.722305i	$0.743083\pi$
$858$	66.3057	+	34.1938i	2.26364	+	1.16736i
$859$			13.9750i			0.476820i	0.971165	+	0.238410i	$0.0766262\pi$
$859$			13.9750i			0.476820i	−0.971165	+	0.238410i	$0.923374\pi$
$860$		−	0.908521i		−	0.0309803i
$861$	−24.3133	−	12.5383i	−0.828595	−	0.427305i
$862$		−	37.5261i		−	1.27814i
$863$			36.2987i			1.23562i	0.786326	+	0.617812i	$0.211981\pi$
$863$			36.2987i			1.23562i	−0.786326	+	0.617812i	$0.788019\pi$
$864$	5.28873	−	0.758321i	0.179926	−	0.0257986i
$865$	−14.3033			−0.486328
$866$	11.1157			0.377728
$867$	−2.09387	+	4.06025i	−0.0711114	+	0.137893i
$868$	4.83054			0.163959
$869$		−	58.4518i		−	1.98284i
$870$	2.57524	+	1.32805i	0.0873089	+	0.0450251i
$871$			29.6384i			1.00426i
$872$	19.5870			0.663298
$873$	−24.0806	+	17.1384i	−0.815004	+	0.580046i
$874$	−52.8316			−1.78706
$875$	−27.8194			−0.940468
$876$	0.0822918	−	0.159574i	0.00278038	−	0.00539149i
$877$			30.5831i			1.03272i	0.856372	+	0.516359i	$0.172713\pi$
$877$			30.5831i			1.03272i	−0.856372	+	0.516359i	$0.827287\pi$
$878$		−	6.00460i		−	0.202646i
$879$	27.1853	+	14.0194i	0.916937	+	0.472863i
$880$	−21.9638			−0.740401
$881$			9.41800i			0.317300i	0.987335	+	0.158650i	$0.0507142\pi$
$881$			9.41800i			0.317300i	−0.987335	+	0.158650i	$0.949286\pi$
$882$	−0.623793	−	0.876472i	−0.0210042	−	0.0295124i
$883$		−	44.7957i		−	1.50749i	−0.657165	−	0.753747i	$-0.728244\pi$
$883$		−	44.7957i		−	1.50749i	0.657165	−	0.753747i	$-0.271756\pi$
$884$	−5.43404			−0.182766
$885$	9.58399	−	18.5845i	0.322162	−	0.624711i
$886$			35.3565i			1.18782i
$887$		−	39.3694i		−	1.32190i	−0.750432	−	0.660948i	$-0.770155\pi$
$887$		−	39.3694i		−	1.32190i	0.750432	−	0.660948i	$-0.229845\pi$
$888$	−1.06752	+	2.07005i	−0.0358237	+	0.0694663i
$889$	24.8718			0.834174
$890$		−	3.31122i		−	0.110992i
$891$	−40.3993	−	14.0056i	−1.35343	−	0.469206i
$892$			0.457079i			0.0153041i
$893$		−	25.9847i		−	0.869545i
$894$	24.2833	−	47.0882i	0.812155	−	1.57486i
$895$	−5.22250			−0.174569
$896$		−	24.7175i		−	0.825754i
$897$	33.0643	−	64.1156i	1.10399	−	2.14076i
$898$	−45.3703			−1.51403
$899$		−	9.86899i		−	0.329149i
$900$	1.06352	+	1.49432i	0.0354507	+	0.0498106i
$901$		−	51.7812i		−	1.72508i
$902$		−	38.9839i		−	1.29802i
$903$	−15.5071	−	7.99698i	−0.516043	−	0.266123i
$904$			43.8836i			1.45955i
$905$	−28.8053			−0.957521
$906$	7.78013	−	15.0866i	0.258478	−	0.501218i
$907$			39.7977i			1.32146i	0.750624	+	0.660730i	$0.229753\pi$
$907$			39.7977i			1.32146i	−0.750624	+	0.660730i	$0.770247\pi$
$908$			1.82384i			0.0605261i
$909$	17.4569	−	12.4243i	0.579010	−	0.412086i
$910$	30.1954			1.00097
$911$	−5.35642			−0.177466			−0.0887331	−	0.996055i	$-0.528282\pi$
$911$	−5.35642			−0.177466			−0.0887331	+	0.996055i	$0.528282\pi$
$912$	−18.0923	+	35.0830i	−0.599094	+	1.16171i
$913$	1.03985			0.0344140
$914$			8.39778i			0.277774i
$915$	−7.97307	+	15.4607i	−0.263581	+	0.511115i
$916$			0.253203i			0.00836607i
$917$		−	11.6172i		−	0.383633i
$918$	−30.7299	+	4.40619i	−1.01424	+	0.145426i
$919$			22.9673i			0.757620i	0.925474	+	0.378810i	$0.123667\pi$
$919$			22.9673i			0.757620i	−0.925474	+	0.378810i	$0.876333\pi$
$920$			23.3888i			0.771104i
$921$	10.5732	−	20.5027i	0.348399	−	0.675587i
$922$	−9.60919			−0.316462
$923$		−	11.0572i		−	0.363954i
$924$	1.78474	−	3.46083i	0.0587138	−	0.113853i
$925$	−1.53231			−0.0503820
$926$			29.9935i			0.985646i
$927$	0.873816	+	1.22777i	0.0286999	+	0.0403253i
$928$	0.994067			0.0326318
$929$	33.5778			1.10165			0.550825	−	0.834620i	$-0.314313\pi$
$929$	33.5778			1.10165			0.550825	+	0.834620i	$0.314313\pi$
$930$	14.0227	−	27.1917i	0.459823	−	0.891650i
$931$	−1.68285			−0.0551532
$932$	−2.77987			−0.0910576
$933$	4.48227	+	2.31150i	0.146743	+	0.0756752i
$934$		−	29.7280i		−	0.972730i
$935$	−27.0211			−0.883685
$936$	−34.4176	−	48.3591i	−1.12498	−	1.58067i
$937$	−37.4331			−1.22289			−0.611443	−	0.791289i	$-0.709411\pi$
$937$	−37.4331			−1.22289			−0.611443	+	0.791289i	$0.709411\pi$
$938$	−15.4199			−0.503477
$939$	−35.5074	−	18.3111i	−1.15874	−	0.597561i
$940$	−0.961210			−0.0313512
$941$	29.9196			0.975352			0.487676	−	0.873025i	$-0.337845\pi$
$941$	29.9196			0.975352			0.487676	+	0.873025i	$0.337845\pi$
$942$	−44.6701	−	23.0363i	−1.45543	−	0.750563i
$943$	−37.6962			−1.22756
$944$			33.8816i			1.10275i
$945$	−17.1310	+	2.45632i	−0.557271	+	0.0799041i
$946$		−	24.8640i		−	0.808399i
$947$		−	34.5594i		−	1.12303i	−0.827466	−	0.561515i	$-0.810219\pi$
$947$		−	34.5594i		−	1.12303i	0.827466	−	0.561515i	$-0.189781\pi$
$948$	−1.78108	+	3.45372i	−0.0578467	+	0.112172i
$949$	−3.82262			−0.124087
$950$	−28.5988			−0.927868
$951$	19.1548	−	37.1435i	0.621138	−	1.20446i
$952$		−	33.8346i		−	1.09658i
$953$		−	16.7854i		−	0.543731i	−0.962335	−	0.271866i	$-0.912359\pi$
$953$		−	16.7854i		−	0.543731i	0.962335	−	0.271866i	$-0.0876406\pi$
$954$	38.5049	−	27.4043i	1.24664	−	0.887246i
$955$			10.5106i			0.340114i
$956$	−1.06910			−0.0345771
$957$	−7.07062	−	3.64631i	−0.228561	−	0.117868i
$958$	−33.1407			−1.07073
$959$	−18.0495			−0.582848
$960$	16.9725	+	8.75270i	0.547785	+	0.282492i
$961$	−73.2055			−2.36147
$962$	4.14351			0.133592
$963$	19.3164	−	13.7476i	0.622461	−	0.443011i
$964$	−4.32205			−0.139204
$965$			9.76489i			0.314343i
$966$	33.3572	+	17.2023i	1.07325	+	0.553474i
$967$	27.4381			0.882349			0.441174	−	0.897421i	$-0.354562\pi$
$967$	27.4381			0.882349			0.441174	+	0.897421i	$0.354562\pi$
$968$	34.0453			1.09426
$969$	−22.2581	+	43.1610i	−0.715032	+	1.38653i
$970$	−17.0479			−0.547376
$971$	−27.1508			−0.871311			−0.435655	−	0.900114i	$-0.643483\pi$
$971$	−27.1508			−0.871311			−0.435655	+	0.900114i	$0.643483\pi$
$972$	1.96030	+	2.05855i	0.0628765	+	0.0660280i
$973$			34.1896i			1.09607i
$974$	56.7616			1.81876
$975$	17.8984	−	34.7070i	0.573207	−	1.11151i
$976$		−	28.1866i		−	0.902230i
$977$	31.2464			0.999661			0.499830	−	0.866123i	$-0.333396\pi$
$977$	31.2464			0.999661			0.499830	+	0.866123i	$0.333396\pi$
$978$	2.16121	−	4.19083i	0.0691078	−	0.134008i
$979$			9.09134i			0.290561i
$980$			0.0622510i			0.00198854i
$981$	11.5804	+	16.2712i	0.369732	+	0.519499i
$982$		−	51.6742i		−	1.64899i
$983$			43.5390i			1.38868i	0.719647	+	0.694340i	$0.244304\pi$
$983$			43.5390i			1.38868i	−0.719647	+	0.694340i	$0.755696\pi$
$984$	−14.2162	+	27.5668i	−0.453195	+	0.878797i
$985$		−	25.3830i		−	0.808769i
$986$	−5.77598			−0.183945
$987$	−8.46076	+	16.4064i	−0.269309	+	0.522222i
$988$	−7.75843			−0.246828
$989$	−24.0427			−0.764515
$990$	−14.3004	−	20.0931i	−0.454498	−	0.638601i
$991$		−	12.6996i		−	0.403415i	−0.979446	−	0.201708i	$-0.935351\pi$
$991$		−	12.6996i		−	0.403415i	0.979446	−	0.201708i	$-0.0646491\pi$
$992$		−	10.4962i		−	0.333256i
$993$	−9.60104	+	18.6175i	−0.304680	+	0.590810i
$994$	5.75271			0.182465
$995$			8.67650i			0.275063i
$996$	−0.0614412	−	0.0316851i	−0.00194684	−	0.00100398i
$997$		−	51.4797i		−	1.63038i	−0.579196	−	0.815188i	$-0.696633\pi$
$997$		−	51.4797i		−	1.63038i	0.579196	−	0.815188i	$-0.303367\pi$
$998$			8.43553i			0.267022i
$999$	−2.35077	+	0.337064i	−0.0743751	+	0.0106642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.d.a.632.50	yes	68
3.2	odd	2	inner	633.2.d.a.632.20	yes	68
211.210	odd	2	inner	633.2.d.a.632.19	✓	68
633.632	even	2	inner	633.2.d.a.632.49	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.d.a.632.19	✓	68	211.210	odd	2	inner
633.2.d.a.632.20	yes	68	3.2	odd	2	inner
633.2.d.a.632.49	yes	68	633.632	even	2	inner
633.2.d.a.632.50	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.34820 q^{2} +(-0.793870 + 1.53941i) q^{3} -0.182353 q^{4} -1.28346i q^{5} +(-1.07030 + 2.07543i) q^{6} -2.59500i q^{7} -2.94225 q^{8} +(-1.73954 - 2.44418i) q^{9} +O(q^{10})\)	\(q+1.34820 q^{2} +(-0.793870 + 1.53941i) q^{3} -0.182353 q^{4} -1.28346i q^{5} +(-1.07030 + 2.07543i) q^{6} -2.59500i q^{7} -2.94225 q^{8} +(-1.73954 - 2.44418i) q^{9} -1.73036i q^{10} +4.75091i q^{11} +(0.144764 - 0.280715i) q^{12} -6.72460 q^{13} -3.49858i q^{14} +(1.97577 + 1.01890i) q^{15} -3.60204 q^{16} -4.43143 q^{17} +(-2.34525 - 3.29524i) q^{18} -6.32695 q^{19} +0.234043i q^{20} +(3.99476 + 2.06009i) q^{21} +6.40519i q^{22} +6.19362 q^{23} +(2.33576 - 4.52932i) q^{24} +3.35273 q^{25} -9.06611 q^{26} +(5.14355 - 0.737505i) q^{27} +0.473206i q^{28} +0.966780 q^{29} +(2.66373 + 1.37368i) q^{30} -10.2081i q^{31} +1.02823 q^{32} +(-7.31358 - 3.77161i) q^{33} -5.97446 q^{34} -3.33058 q^{35} +(0.317211 + 0.445703i) q^{36} -0.457033 q^{37} -8.53001 q^{38} +(5.33845 - 10.3519i) q^{39} +3.77627i q^{40} -6.08630 q^{41} +(5.38574 + 2.77742i) q^{42} -3.88186 q^{43} -0.866343i q^{44} +(-3.13700 + 2.23263i) q^{45} +8.35025 q^{46} +4.10698i q^{47} +(2.85955 - 5.54500i) q^{48} +0.265981 q^{49} +4.52015 q^{50} +(3.51798 - 6.82177i) q^{51} +1.22625 q^{52} +11.6850i q^{53} +(6.93454 - 0.994306i) q^{54} +6.09761 q^{55} +7.63514i q^{56} +(5.02278 - 9.73975i) q^{57} +1.30341 q^{58} -9.40621i q^{59} +(-0.360287 - 0.185800i) q^{60} +7.82516i q^{61} -13.7626i q^{62} +(-6.34263 + 4.51411i) q^{63} +8.59034 q^{64} +8.63076i q^{65} +(-9.86018 - 5.08488i) q^{66} -4.40747i q^{67} +0.808084 q^{68} +(-4.91693 + 9.53450i) q^{69} -4.49029 q^{70} +1.64430i q^{71} +(5.11817 + 7.19138i) q^{72} +0.568453 q^{73} -0.616173 q^{74} +(-2.66163 + 5.16121i) q^{75} +1.15374 q^{76} +12.3286 q^{77} +(7.19731 - 13.9564i) q^{78} -12.3033 q^{79} +4.62308i q^{80} +(-2.94799 + 8.50349i) q^{81} -8.20556 q^{82} -0.218874i q^{83} +(-0.728456 - 0.375664i) q^{84} +5.68756i q^{85} -5.23352 q^{86} +(-0.767497 + 1.48827i) q^{87} -13.9784i q^{88} +1.91360 q^{89} +(-4.22931 + 3.01004i) q^{90} +17.4503i q^{91} -1.12942 q^{92} +(15.7144 + 8.10391i) q^{93} +5.53704i q^{94} +8.12040i q^{95} +(-0.816277 + 1.58286i) q^{96} -9.85223i q^{97} +0.358596 q^{98} +(11.6121 - 8.26441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

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