LMFDB - Embedded newform 633.2.d.a.632.20

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			632.20
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.19

$q$-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	$-0.658153\pi$
$2$	−1.34820			−0.953322			−0.476661	+	0.879087i	$0.658153\pi$
$3$	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	$0.0926549\pi$
$5$			1.28346i			0.573981i	−0.957933	+	0.286991i	$0.907345\pi$
$6$	−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	$-0.745868\pi$
$11$		−	4.75091i		−	1.43245i	0.697867	−	0.716227i	$-0.254132\pi$
$12$	−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	$-0.319411\pi$
$17$	4.43143			1.07478			0.537389	+	0.843334i	$0.319411\pi$
$18$	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	$-0.723447\pi$
$23$	−6.19362			−1.29146			−0.645730	+	0.763566i	$0.723447\pi$
$24$	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	$-0.528611\pi$
$29$	−0.966780			−0.179526			−0.0897632	+	0.995963i	$0.528611\pi$
$30$	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	$-0.342354\pi$
$41$	6.08630			0.950520			0.475260	+	0.879845i	$0.342354\pi$
$42$	−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	$-0.903169\pi$
$47$		−	4.10698i		−	0.599065i	0.954086	−	0.299533i	$-0.0968307\pi$
$48$	−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	$-0.703487\pi$
$53$		−	11.6850i		−	1.60506i	0.596614	−	0.802529i	$-0.296513\pi$
$54$	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	$0.209752\pi$
$59$			9.40621i			1.22458i	−0.790632	+	0.612292i	$0.790248\pi$
$60$	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	$-0.968893\pi$
$71$		−	1.64430i		−	0.195142i	0.995229	−	0.0975712i	$-0.0311074\pi$
$72$	−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	$0.00382371\pi$
$83$			0.218874i			0.0240245i	−0.999928	+	0.0120123i	$0.996176\pi$
$84$	−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	$-0.532339\pi$
$89$	−1.91360			−0.202841			−0.101421	+	0.994844i	$0.532339\pi$
$90$	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	$-0.884365\pi$
$101$		−	7.14225i		−	0.710681i	0.934737	−	0.355340i	$-0.115635\pi$
$102$	−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	$-0.875233\pi$
$107$		−	7.90302i		−	0.764014i	0.924159	−	0.382007i	$-0.124767\pi$
$108$	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	$0.247504\pi$
$113$			14.9150i			1.40308i	−0.712629	+	0.701541i	$0.752496\pi$
$114$	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	$-0.562655\pi$
$131$	−4.47676			−0.391136			−0.195568	+	0.980690i	$0.562655\pi$
$132$	−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	$0.0960273\pi$
$137$			6.95548i			0.594247i	−0.954839	+	0.297124i	$0.903973\pi$
$138$	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	$-0.120366\pi$
$149$	22.6884			1.85871			0.929353	+	0.369192i	$0.120366\pi$
$150$	−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	$-0.512077\pi$
$167$	−0.980410			−0.0758664			−0.0379332	+	0.999280i	$0.512077\pi$
$168$	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	$0.139250\pi$
$173$			11.1444i			0.847290i	−0.905828	+	0.423645i	$0.860750\pi$
$174$	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	$0.0485935\pi$
$179$			4.06908i			0.304137i	−0.988370	+	0.152069i	$0.951407\pi$
$180$	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	$-0.404255\pi$
$191$	8.18924			0.592553			0.296276	+	0.955102i	$0.404255\pi$
$192$	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	$-0.748840\pi$
$197$	−19.7770			−1.40905			−0.704526	+	0.709678i	$0.748840\pi$
$198$	−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	$0.107696\pi$
$227$			10.0017i			0.663835i	−0.943308	+	0.331917i	$0.892304\pi$
$228$	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	$-0.666427\pi$
$233$	−15.2444			−0.998696			−0.499348	+	0.866402i	$0.666427\pi$
$234$	−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	$-0.560724\pi$
$239$	−5.86280			−0.379233			−0.189617	+	0.981858i	$0.560724\pi$
$240$	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	$-0.453243\pi$
$251$	4.63768			0.292728			0.146364	+	0.989231i	$0.453243\pi$
$252$	−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	$-0.728802\pi$
$257$		−	24.1300i		−	1.50519i	0.658484	−	0.752595i	$-0.271198\pi$
$258$	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	$0.0532999\pi$
$263$			5.40571i			0.333330i	−0.986014	+	0.166665i	$0.946700\pi$
$264$	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	$-0.778298\pi$
$269$		−	21.0439i		−	1.28307i	0.767093	−	0.641536i	$-0.221702\pi$
$270$	−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	$-0.914501\pi$
$281$		−	8.89731i		−	0.530769i	0.964143	−	0.265385i	$-0.0854989\pi$
$282$	−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	$0.172521\pi$
$293$			17.6596i			1.03168i	−0.856684	+	0.515842i	$0.827479\pi$
$294$	−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	$0.0263075\pi$
$311$			2.91169i			0.165107i	−0.996587	+	0.0825534i	$0.973692\pi$
$312$	−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	$-0.263023\pi$
$317$	24.1284			1.35519			0.677594	+	0.735436i	$0.263023\pi$
$318$	−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	$0.163086\pi$
$347$			18.2638i			0.980451i	−0.871596	+	0.490226i	$0.836914\pi$
$348$	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	$-0.490571\pi$
$353$	1.11299			0.0592386			0.0296193	+	0.999561i	$0.490571\pi$
$354$	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	$-0.825594\pi$
$359$		−	19.7396i		−	1.04181i	0.853613	−	0.520907i	$-0.174406\pi$
$360$	−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	$-0.859057\pi$
$383$		−	16.7702i		−	0.856918i	0.903561	−	0.428459i	$-0.140943\pi$
$384$	−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	$-0.725265\pi$
$389$		−	29.9738i		−	1.51973i	0.650080	−	0.759866i	$-0.274735\pi$
$390$	−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	$-0.412955\pi$
$401$	10.8161			0.540130			0.270065	+	0.962842i	$0.412955\pi$
$402$	−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	$-0.999846\pi$
$419$		−	0.0197728i		−	0.000965962i	1.00000		0.000482981i	$-0.000153738\pi$
$420$	−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	$0.233861\pi$
$431$			27.8342i			1.34072i	−0.742034	+	0.670362i	$0.766139\pi$
$432$	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	$-0.785917\pi$
$443$		−	26.2249i		−	1.24598i	0.782228	−	0.622992i	$-0.214083\pi$
$444$	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	$-0.207953\pi$
$449$	33.6525			1.58816			0.794080	+	0.607814i	$0.207953\pi$
$450$	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	$-0.446922\pi$
$461$	7.12742			0.331957			0.165978	+	0.986129i	$0.446922\pi$
$462$	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	$0.170421\pi$
$467$			22.0501i			1.02036i	−0.860068	+	0.510179i	$0.829579\pi$
$468$	−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	$-0.310195\pi$
$479$	24.5814			1.12315			0.561576	+	0.827425i	$0.310195\pi$
$480$	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	$0.332596\pi$
$491$			38.3282i			1.72973i	−0.502006	+	0.864864i	$0.667404\pi$
$492$	−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	$-0.979100\pi$
$503$		−	2.94307i		−	0.131225i	0.997845	−	0.0656124i	$-0.0209001\pi$
$504$	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	$-0.904050\pi$
$509$		−	13.3964i		−	0.593786i	0.954911	−	0.296893i	$-0.0959504\pi$
$510$	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	$0.0931680\pi$
$521$			13.1718i			0.577069i	−0.957470	+	0.288534i	$0.906832\pi$
$522$	−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	$-0.865703\pi$
$557$	−43.0626			−1.82462			−0.912310	+	0.409500i	$0.865703\pi$
$558$	−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	$-0.137286\pi$
$563$	43.1095			1.81685			0.908425	+	0.418048i	$0.137286\pi$
$564$	−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	$-0.284964\pi$
$569$	29.8330			1.25066			0.625331	+	0.780359i	$0.284964\pi$
$570$	−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	$-0.397738\pi$
$587$	15.3009			0.631535			0.315768	+	0.948837i	$0.397738\pi$
$588$	−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	$-0.881563\pi$
$593$		−	17.7062i		−	0.727108i	0.931573	−	0.363554i	$-0.118437\pi$
$594$	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	$-0.846667\pi$
$599$	−43.3788			−1.77241			−0.886204	+	0.463296i	$0.846667\pi$
$600$	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	$-0.475281\pi$
$617$	3.85405			0.155158			0.0775791	+	0.996986i	$0.475281\pi$
$618$	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
$633$	3.01602	−	24.9781i	0.119876	−	0.992789i
$634$	−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	$-0.569688\pi$
$641$	−10.9975			−0.434375			−0.217188	+	0.976130i	$0.569688\pi$
$642$	−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	$0.0367334\pi$
$647$			5.85772i			0.230291i	−0.993349	+	0.115145i	$0.963267\pi$
$648$	−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	$0.00938562\pi$
$653$			1.50673i			0.0589631i	−0.999565	+	0.0294815i	$0.990614\pi$
$654$	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	$-0.507165\pi$
$659$	−1.15558			−0.0450151			−0.0225075	+	0.999747i	$0.507165\pi$
$660$	−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	$-0.700605\pi$
$677$		−	42.0418i		−	1.61580i	0.589321	−	0.807899i	$-0.299395\pi$
$678$	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	$-0.585233\pi$
$683$	−13.8291			−0.529156			−0.264578	+	0.964364i	$0.585233\pi$
$684$	−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	$-0.622014\pi$
$701$	−19.8043			−0.747999			−0.373999	+	0.927429i	$0.622014\pi$
$702$	−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	$-0.317599\pi$
$719$	29.0762			1.08436			0.542179	+	0.840263i	$0.317599\pi$
$720$	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	$-0.511038\pi$
$743$	−1.89005			−0.0693391			−0.0346696	+	0.999399i	$0.511038\pi$
$744$	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	$-0.270849\pi$
$761$	36.3757			1.31862			0.659309	+	0.751872i	$0.270849\pi$
$762$	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	$-0.616751\pi$
$773$	−19.9411			−0.717233			−0.358616	+	0.933485i	$0.616751\pi$
$774$	−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	$-0.454019\pi$
$797$	8.12779			0.287901			0.143951	+	0.989585i	$0.454019\pi$
$798$	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	$-0.764285\pi$
$809$		−	38.3793i		−	1.34934i	0.738118	−	0.674672i	$-0.235715\pi$
$810$	−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	$-0.936643\pi$
$821$		−	11.3312i		−	0.395463i	0.980256	−	0.197732i	$-0.0633574\pi$
$822$	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	$-0.897210\pi$
$827$		−	18.2519i		−	0.634680i	0.948312	−	0.317340i	$-0.102790\pi$
$828$	−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	$-0.230744\pi$
$839$	43.3650			1.49713			0.748563	+	0.663064i	$0.230744\pi$
$840$	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	$-0.743083\pi$
$857$		−	42.2903i		−	1.44461i	0.691575	−	0.722305i	$-0.256917\pi$
$858$	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	$-0.788019\pi$
$863$		−	36.2987i		−	1.23562i	0.786326	−	0.617812i	$-0.211981\pi$
$864$	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	$-0.949286\pi$
$881$		−	9.41800i		−	0.317300i	0.987335	−	0.158650i	$-0.0507142\pi$
$882$	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	$0.229845\pi$
$887$			39.3694i			1.32190i	−0.750432	+	0.660948i	$0.770155\pi$
$888$	−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	$-0.471718\pi$
$911$	5.35642			0.177466			0.0887331	+	0.996055i	$0.471718\pi$
$912$	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	$-0.685687\pi$
$929$	−33.5778			−1.10165			−0.550825	+	0.834620i	$0.685687\pi$
$930$	−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	$-0.662155\pi$
$941$	−29.9196			−0.975352			−0.487676	+	0.873025i	$0.662155\pi$
$942$	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	$0.189781\pi$
$947$			34.5594i			1.12303i	−0.827466	+	0.561515i	$0.810219\pi$
$948$	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	$0.0876406\pi$
$953$			16.7854i			0.543731i	−0.962335	+	0.271866i	$0.912359\pi$
$954$	−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	$-0.356517\pi$
$971$	27.1508			0.871311			0.435655	+	0.900114i	$0.356517\pi$
$972$	−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	$-0.666604\pi$
$977$	−31.2464			−0.999661			−0.499830	+	0.866123i	$0.666604\pi$
$978$	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	$-0.755696\pi$
$983$		−	43.5390i		−	1.38868i	0.719647	−	0.694340i	$-0.244304\pi$
$984$	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.632.20	yes	68
3.2	odd	2	inner	633.2.d.a.632.50	yes	68
211.210	odd	2	inner	633.2.d.a.632.49	yes	68
633.632	even	2	inner	633.2.d.a.632.19	✓	68

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
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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