LMFDB - Embedded newform 633.2.d.a.632.1

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			632.1
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69215 q^{2} +(-0.336216 - 1.69911i) q^{3} +5.24765 q^{4} +2.13595i q^{5} +(0.905142 + 4.57424i) q^{6} +2.13995i q^{7} -8.74315 q^{8} +(-2.77392 + 1.14253i) q^{9} +O(q^{10})$	\(q-2.69215 q^{2} +(-0.336216 - 1.69911i) q^{3} +5.24765 q^{4} +2.13595i q^{5} +(0.905142 + 4.57424i) q^{6} +2.13995i q^{7} -8.74315 q^{8} +(-2.77392 + 1.14253i) q^{9} -5.75028i q^{10} -5.34816i q^{11} +(-1.76434 - 8.91631i) q^{12} -2.31513 q^{13} -5.76105i q^{14} +(3.62920 - 0.718139i) q^{15} +13.0425 q^{16} +3.95708 q^{17} +(7.46779 - 3.07586i) q^{18} -3.06546 q^{19} +11.2087i q^{20} +(3.63599 - 0.719484i) q^{21} +14.3980i q^{22} -3.62517 q^{23} +(2.93959 + 14.8555i) q^{24} +0.437736 q^{25} +6.23267 q^{26} +(2.87392 + 4.32904i) q^{27} +11.2297i q^{28} +7.38829 q^{29} +(-9.77033 + 1.93333i) q^{30} -4.50630i q^{31} -17.6261 q^{32} +(-9.08709 + 1.79814i) q^{33} -10.6530 q^{34} -4.57081 q^{35} +(-14.5566 + 5.99561i) q^{36} +1.56258 q^{37} +8.25268 q^{38} +(0.778384 + 3.93365i) q^{39} -18.6749i q^{40} +7.77584 q^{41} +(-9.78863 + 1.93695i) q^{42} +11.6018 q^{43} -28.0653i q^{44} +(-2.44039 - 5.92494i) q^{45} +9.75949 q^{46} +4.24446i q^{47} +(-4.38511 - 22.1607i) q^{48} +2.42063 q^{49} -1.17845 q^{50} +(-1.33043 - 6.72349i) q^{51} -12.1490 q^{52} +13.3224i q^{53} +(-7.73701 - 11.6544i) q^{54} +11.4234 q^{55} -18.7099i q^{56} +(1.03066 + 5.20855i) q^{57} -19.8904 q^{58} -4.60711i q^{59} +(19.0448 - 3.76854i) q^{60} +2.70933i q^{61} +12.1316i q^{62} +(-2.44496 - 5.93603i) q^{63} +21.3670 q^{64} -4.94499i q^{65} +(24.4638 - 4.84085i) q^{66} +0.247622i q^{67} +20.7654 q^{68} +(1.21884 + 6.15955i) q^{69} +12.3053 q^{70} -10.6508i q^{71} +(24.2528 - 9.98933i) q^{72} +14.4052 q^{73} -4.20669 q^{74} +(-0.147174 - 0.743759i) q^{75} -16.0865 q^{76} +11.4448 q^{77} +(-2.09552 - 10.5900i) q^{78} -0.894007 q^{79} +27.8582i q^{80} +(6.38924 - 6.33858i) q^{81} -20.9337 q^{82} -6.62938i q^{83} +(19.0804 - 3.77560i) q^{84} +8.45210i q^{85} -31.2339 q^{86} +(-2.48406 - 12.5535i) q^{87} +46.7598i q^{88} +7.62948 q^{89} +(6.56988 + 15.9508i) q^{90} -4.95425i q^{91} -19.0236 q^{92} +(-7.65668 + 1.51509i) q^{93} -11.4267i q^{94} -6.54767i q^{95} +(5.92618 + 29.9486i) q^{96} -16.5837i q^{97} -6.51670 q^{98} +(6.11045 + 14.8354i) 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 $

$2$	−2.69215			−1.90363			−0.951817	−	0.306665i	$-0.900787\pi$
$2$	−2.69215			−1.90363			−0.951817	+	0.306665i	$0.900787\pi$
$3$	−0.336216	−	1.69911i	−0.194114	−	0.980979i
$3$	−0.336216	−	1.69911i	−0.194114	−	0.980979i
$4$	5.24765			2.62383
$5$			2.13595i			0.955224i	0.878571	+	0.477612i	$0.158498\pi$
$5$			2.13595i			0.955224i	−0.878571	+	0.477612i	$0.841502\pi$
$6$	0.905142	+	4.57424i	0.369523	+	1.86743i
$7$			2.13995i			0.808823i	0.914577	+	0.404412i	$0.132524\pi$
$7$			2.13995i			0.808823i	−0.914577	+	0.404412i	$0.867476\pi$
$8$	−8.74315			−3.09117
$9$	−2.77392	+	1.14253i	−0.924639	+	0.380844i
$10$		−	5.75028i		−	1.81840i
$11$		−	5.34816i		−	1.61253i	−0.591553	−	0.806266i	$-0.701485\pi$
$11$		−	5.34816i		−	1.61253i	0.591553	−	0.806266i	$-0.298515\pi$
$12$	−1.76434	−	8.91631i	−0.509322	−	2.57392i
$13$	−2.31513			−0.642102			−0.321051	−	0.947062i	$-0.604036\pi$
$13$	−2.31513			−0.642102			−0.321051	+	0.947062i	$0.604036\pi$
$14$		−	5.76105i		−	1.53970i
$15$	3.62920	−	0.718139i	0.937055	−	0.185423i
$16$	13.0425			3.26064
$17$	3.95708			0.959732			0.479866	−	0.877342i	$-0.340685\pi$
$17$	3.95708			0.959732			0.479866	+	0.877342i	$0.340685\pi$
$18$	7.46779	−	3.07586i	1.76018	−	0.724988i
$19$	−3.06546			−0.703266			−0.351633	−	0.936138i	$-0.614373\pi$
$19$	−3.06546			−0.703266			−0.351633	+	0.936138i	$0.614373\pi$
$20$			11.2087i			2.50634i
$21$	3.63599	−	0.719484i	0.793439	−	0.157004i
$22$			14.3980i			3.06967i
$23$	−3.62517			−0.755900			−0.377950	−	0.925826i	$-0.623371\pi$
$23$	−3.62517			−0.755900			−0.377950	+	0.925826i	$0.623371\pi$
$24$	2.93959	+	14.8555i	0.600040	+	3.03237i
$25$	0.437736			0.0875471
$26$	6.23267			1.22233
$27$	2.87392	+	4.32904i	0.553086	+	0.833124i
$28$			11.2297i			2.12221i
$29$	7.38829			1.37197			0.685986	−	0.727615i	$-0.259371\pi$
$29$	7.38829			1.37197			0.685986	+	0.727615i	$0.259371\pi$
$30$	−9.77033	+	1.93333i	−1.78381	+	0.352977i
$31$		−	4.50630i		−	0.809356i	−0.914459	−	0.404678i	$-0.867384\pi$
$31$		−	4.50630i		−	0.809356i	0.914459	−	0.404678i	$-0.132616\pi$
$32$	−17.6261			−3.11589
$33$	−9.08709	+	1.79814i	−1.58186	+	0.313015i
$34$	−10.6530			−1.82698
$35$	−4.57081			−0.772608
$36$	−14.5566	+	5.99561i	−2.42609	+	0.999268i
$37$	1.56258			0.256886			0.128443	−	0.991717i	$-0.459002\pi$
$37$	1.56258			0.256886			0.128443	+	0.991717i	$0.459002\pi$
$38$	8.25268			1.33876
$39$	0.778384	+	3.93365i	0.124641	+	0.629888i
$40$		−	18.6749i		−	2.95276i
$41$	7.77584			1.21438			0.607191	−	0.794556i	$-0.292296\pi$
$41$	7.77584			1.21438			0.607191	+	0.794556i	$0.292296\pi$
$42$	−9.78863	+	1.93695i	−1.51042	+	0.298879i
$43$	11.6018			1.76926			0.884632	−	0.466289i	$-0.154409\pi$
$43$	11.6018			1.76926			0.884632	+	0.466289i	$0.154409\pi$
$44$		−	28.0653i		−	4.23100i
$45$	−2.44039	−	5.92494i	−0.363791	−	0.883238i
$46$	9.75949			1.43896
$47$			4.24446i			0.619118i	0.950880	+	0.309559i	$0.100181\pi$
$47$			4.24446i			0.619118i	−0.950880	+	0.309559i	$0.899819\pi$
$48$	−4.38511	−	22.1607i	−0.632936	−	3.19861i
$49$	2.42063			0.345805
$50$	−1.17845			−0.166658
$51$	−1.33043	−	6.72349i	−0.186298	−	0.941477i
$52$	−12.1490			−1.68476
$53$			13.3224i			1.82998i	0.403480	+	0.914989i	$0.367801\pi$
$53$			13.3224i			1.82998i	−0.403480	+	0.914989i	$0.632199\pi$
$54$	−7.73701	−	11.6544i	−1.05287	−	1.58596i
$55$	11.4234			1.54033
$56$		−	18.7099i		−	2.50021i
$57$	1.03066	+	5.20855i	0.136514	+	0.689889i
$58$	−19.8904			−2.61173
$59$		−	4.60711i		−	0.599795i	−0.953971	−	0.299898i	$-0.903047\pi$
$59$		−	4.60711i		−	0.599795i	0.953971	−	0.299898i	$-0.0969525\pi$
$60$	19.0448	−	3.76854i	2.45867	−	0.486517i
$61$			2.70933i			0.346894i	0.984843	+	0.173447i	$0.0554906\pi$
$61$			2.70933i			0.346894i	−0.984843	+	0.173447i	$0.944509\pi$
$62$			12.1316i			1.54072i
$63$	−2.44496	−	5.93603i	−0.308036	−	0.747870i
$64$	21.3670			2.67088
$65$		−	4.94499i		−	0.613351i
$66$	24.4638	−	4.84085i	3.01128	−	0.595867i
$67$			0.247622i			0.0302518i	0.999886	+	0.0151259i	$0.00481490\pi$
$67$			0.247622i			0.0302518i	−0.999886	+	0.0151259i	$0.995185\pi$
$68$	20.7654			2.51817
$69$	1.21884	+	6.15955i	0.146731	+	0.741522i
$70$	12.3053			1.47076
$71$		−	10.6508i		−	1.26402i	−0.774962	−	0.632008i	$-0.782231\pi$
$71$		−	10.6508i		−	1.26402i	0.774962	−	0.632008i	$-0.217769\pi$
$72$	24.2528	−	9.98933i	2.85822	−	1.17725i
$73$	14.4052			1.68600			0.843001	−	0.537912i	$-0.180787\pi$
$73$	14.4052			1.68600			0.843001	+	0.537912i	$0.180787\pi$
$74$	−4.20669			−0.489018
$75$	−0.147174	−	0.743759i	−0.0169941	−	0.0858819i
$76$	−16.0865			−1.84525
$77$	11.4448			1.30425
$78$	−2.09552	−	10.5900i	−0.237271	−	1.19908i
$79$	−0.894007			−0.100584			−0.0502918	−	0.998735i	$-0.516015\pi$
$79$	−0.894007			−0.100584			−0.0502918	+	0.998735i	$0.516015\pi$
$80$			27.8582i			3.11464i
$81$	6.38924	−	6.33858i	0.709916	−	0.704287i
$82$	−20.9337			−2.31174
$83$		−	6.62938i		−	0.727669i	−0.931464	−	0.363834i	$-0.881467\pi$
$83$		−	6.62938i		−	0.727669i	0.931464	−	0.363834i	$-0.118533\pi$
$84$	19.0804	−	3.77560i	2.08185	−	0.411952i
$85$			8.45210i			0.916759i
$86$	−31.2339			−3.36803
$87$	−2.48406	−	12.5535i	−0.266319	−	1.34587i
$88$			46.7598i			4.98461i
$89$	7.62948			0.808723			0.404362	−	0.914599i	$-0.367494\pi$
$89$	7.62948			0.808723			0.404362	+	0.914599i	$0.367494\pi$
$90$	6.56988	+	15.9508i	0.692526	+	1.68136i
$91$		−	4.95425i		−	0.519347i
$92$	−19.0236			−1.98335
$93$	−7.65668	+	1.51509i	−0.793961	+	0.157108i
$94$		−	11.4267i		−	1.17857i
$95$		−	6.54767i		−	0.671776i
$96$	5.92618	+	29.9486i	0.604838	+	3.05662i
$97$		−	16.5837i		−	1.68382i	−0.539617	−	0.841910i	$-0.681431\pi$
$97$		−	16.5837i		−	1.68382i	0.539617	−	0.841910i	$-0.318569\pi$
$98$	−6.51670			−0.658286
$99$	6.11045	+	14.8354i	0.614123	+	1.49101i
$100$	2.29708			0.229708
$101$			1.24337i			0.123720i	0.998085	+	0.0618598i	$0.0197032\pi$
$101$			1.24337i			0.123720i	−0.998085	+	0.0618598i	$0.980297\pi$
$102$	3.58172	+	18.1006i	0.354643	+	1.79223i
$103$	−11.6594			−1.14883			−0.574416	−	0.818563i	$-0.694771\pi$
$103$	−11.6594			−1.14883			−0.574416	+	0.818563i	$0.694771\pi$
$104$	20.2415			1.98485
$105$	1.53678	+	7.76628i	0.149974	+	0.757912i
$106$		−	35.8659i		−	3.48361i
$107$			11.2021i			1.08294i	0.840719	+	0.541472i	$0.182133\pi$
$107$			11.2021i			1.08294i	−0.840719	+	0.541472i	$0.817867\pi$
$108$	15.0813	+	22.7173i	1.45120	+	2.18597i
$109$	10.1935			0.976363			0.488181	−	0.872742i	$-0.337660\pi$
$109$	10.1935			0.976363			0.488181	+	0.872742i	$0.337660\pi$
$110$	−30.7534			−2.93222
$111$	−0.525364	−	2.65499i	−0.0498653	−	0.252000i
$112$			27.9103i			2.63728i
$113$		−	14.7011i		−	1.38296i	−0.722393	−	0.691482i	$-0.756958\pi$
$113$		−	14.7011i		−	1.38296i	0.722393	−	0.691482i	$-0.243042\pi$
$114$	−2.77468	−	14.0222i	−0.259873	−	1.31330i
$115$		−	7.74317i		−	0.722054i
$116$	38.7712			3.59981
$117$	6.42198	−	2.64511i	0.593712	−	0.244541i
$118$			12.4030i			1.14179i
$119$			8.46793i			0.776254i
$120$	−31.7306	+	6.27880i	−2.89660	+	0.573173i
$121$	−17.6028			−1.60026
$122$		−	7.29392i		−	0.660360i
$123$	−2.61436	−	13.2120i	−0.235729	−	1.19128i
$124$		−	23.6475i		−	2.12361i
$125$			11.6147i			1.03885i
$126$	6.58218	+	15.9807i	0.586387	+	1.42367i
$127$		−	8.48535i		−	0.752953i	−0.926426	−	0.376476i	$-0.877136\pi$
$127$		−	8.48535i		−	0.752953i	0.926426	−	0.376476i	$-0.122864\pi$
$128$	−22.2709			−1.96849
$129$	−3.90072	−	19.7128i	−0.343440	−	1.73561i
$130$			13.3126i			1.16760i
$131$	9.77584			0.854119			0.427059	−	0.904224i	$-0.359549\pi$
$131$	9.77584			0.854119			0.427059	+	0.904224i	$0.359549\pi$
$132$	−47.6859	+	9.43600i	−4.15052	+	0.821298i
$133$		−	6.55993i		−	0.568818i
$134$		−	0.666633i		−	0.0575884i
$135$	−9.24660	+	6.13853i	−0.795820	+	0.528321i
$136$	−34.5973			−2.96670
$137$			2.54568i			0.217492i	0.994070	+	0.108746i	$0.0346835\pi$
$137$			2.54568i			0.217492i	−0.994070	+	0.108746i	$0.965316\pi$
$138$	−3.28129	−	16.5824i	−0.279322	−	1.41159i
$139$	10.1344			0.859589			0.429795	−	0.902927i	$-0.358586\pi$
$139$	10.1344			0.859589			0.429795	+	0.902927i	$0.358586\pi$
$140$	−23.9860			−2.02719
$141$	7.21179	−	1.42705i	0.607342	−	0.120180i
$142$			28.6735i			2.40622i
$143$			12.3817i			1.03541i
$144$	−36.1789	+	14.9015i	−3.01491	+	1.24179i
$145$			15.7810i			1.31054i
$146$	−38.7809			−3.20953
$147$	−0.813855	−	4.11291i	−0.0671256	−	0.339227i
$148$	8.19987			0.674025
$149$	−12.9344			−1.05963			−0.529813	−	0.848115i	$-0.677738\pi$
$149$	−12.9344			−1.05963			−0.529813	+	0.848115i	$0.677738\pi$
$150$	0.396213	+	2.00231i	0.0323506	+	0.163488i
$151$	−7.86111			−0.639728			−0.319864	−	0.947463i	$-0.603637\pi$
$151$	−7.86111			−0.639728			−0.319864	+	0.947463i	$0.603637\pi$
$152$	26.8018			2.17391
$153$	−10.9766	+	4.52109i	−0.887406	+	0.365508i
$154$	−30.8110			−2.48282
$155$	9.62522			0.773116
$156$	4.08469	+	20.6424i	0.327037	+	1.65272i
$157$			20.7378i			1.65506i	0.561422	+	0.827530i	$0.310255\pi$
$157$			20.7378i			1.65506i	−0.561422	+	0.827530i	$0.689745\pi$
$158$	2.40680			0.191475
$159$	22.6362	−	4.47921i	1.79517	−	0.355225i
$160$		−	37.6485i		−	2.97637i
$161$		−	7.75767i		−	0.611390i
$162$	−17.2008	+	17.0644i	−1.35142	+	1.34070i
$163$	−9.49896			−0.744016			−0.372008	−	0.928230i	$-0.621331\pi$
$163$	−9.49896			−0.744016			−0.372008	+	0.928230i	$0.621331\pi$
$164$	40.8049			3.18633
$165$	−3.84072	−	19.4095i	−0.299000	−	1.51103i
$166$			17.8473i			1.38522i
$167$	1.95044			0.150930			0.0754649	−	0.997148i	$-0.475956\pi$
$167$	1.95044			0.150930			0.0754649	+	0.997148i	$0.475956\pi$
$168$	−31.7900	+	6.29055i	−2.45266	+	0.485327i
$169$	−7.64017			−0.587705
$170$		−	22.7543i		−	1.74518i
$171$	8.50335	−	3.50239i	0.650267	−	0.267835i
$172$	60.8824			4.64224
$173$		−	7.91665i		−	0.601892i	−0.953641	−	0.300946i	$-0.902698\pi$
$173$		−	7.91665i		−	0.601892i	0.953641	−	0.300946i	$-0.0973023\pi$
$174$	6.68745	+	33.7958i	0.506975	+	2.56205i
$175$			0.936730i			0.0708102i
$176$		−	69.7536i		−	5.25788i
$177$	−7.82797	+	1.54898i	−0.588387	+	0.116429i
$178$	−20.5397			−1.53951
$179$			17.0377i			1.27346i	0.771088	+	0.636728i	$0.219713\pi$
$179$			17.0377i			1.27346i	−0.771088	+	0.636728i	$0.780287\pi$
$180$	−12.8063	−	31.0920i	−0.954525	−	2.31746i
$181$			20.7572i			1.54287i	0.636306	+	0.771437i	$0.280462\pi$
$181$			20.7572i			1.54287i	−0.636306	+	0.771437i	$0.719538\pi$
$182$			13.3376i			0.988647i
$183$	4.60344	−	0.910920i	0.340296	−	0.0673371i
$184$	31.6954			2.33662
$185$			3.33758i			0.245384i
$186$	20.6129	−	4.07884i	1.51141	−	0.299075i
$187$		−	21.1631i		−	1.54760i
$188$			22.2734i			1.62446i
$189$	−9.26391	+	6.15003i	−0.673851	+	0.447349i
$190$			17.6273i			1.27882i
$191$	−10.3643			−0.749937			−0.374968	−	0.927038i	$-0.622346\pi$
$191$	−10.3643			−0.749937			−0.374968	+	0.927038i	$0.622346\pi$
$192$	−7.18393	−	36.3048i	−0.518456	−	2.62008i
$193$	−24.7954			−1.78481			−0.892406	−	0.451234i	$-0.850984\pi$
$193$	−24.7954			−1.78481			−0.892406	+	0.451234i	$0.850984\pi$
$194$			44.6458i			3.20538i
$195$	−8.40207	+	1.66259i	−0.601684	+	0.119060i
$196$	12.7026			0.907331
$197$	6.35379			0.452689			0.226344	−	0.974047i	$-0.427323\pi$
$197$	6.35379			0.452689			0.226344	+	0.974047i	$0.427323\pi$
$198$	−16.4502	−	39.9390i	−1.16907	−	2.83834i
$199$	26.6434			1.88870			0.944351	−	0.328939i	$-0.106691\pi$
$199$	26.6434			1.88870			0.944351	+	0.328939i	$0.106691\pi$
$200$	−3.82719			−0.270623
$201$	0.420735	−	0.0832543i	0.0296764	−	0.00587230i
$202$		−	3.34732i		−	0.235517i
$203$			15.8105i			1.10968i
$204$	−6.98164	−	35.2825i	−0.488813	−	2.47027i
$205$			16.6088i			1.16001i
$206$	31.3888			2.18696
$207$	10.0559	−	4.14187i	0.698935	−	0.287880i
$208$	−30.1952			−2.09366
$209$			16.3946i			1.13404i
$210$	−4.13723	−	20.9080i	−0.285496	−	1.44279i
$211$	9.31046	−	11.1497i	0.640959	−	0.767575i
$211$	9.31046	−	11.1497i	0.640959	−	0.767575i
$212$			69.9115i			4.80154i
$213$	−18.0968	+	3.58096i	−1.23997	+	0.245363i
$214$		−	30.1576i		−	2.06153i
$215$			24.7809i			1.69004i
$216$	−25.1271	−	37.8495i	−1.70968	−	2.57533i
$217$	9.64324			0.654626
$218$	−27.4425			−1.85864
$219$	−4.84326	−	24.4760i	−0.327277	−	1.65393i
$220$	59.9459			4.04156
$221$	−9.16115			−0.616246
$222$	1.41436	+	7.14761i	0.0949254	+	0.479716i
$223$		−	18.4179i		−	1.23335i	−0.787216	−	0.616677i	$-0.788478\pi$
$223$		−	18.4179i		−	1.23335i	0.787216	−	0.616677i	$-0.211522\pi$
$224$		−	37.7190i		−	2.52020i
$225$	−1.21424	+	0.500127i	−0.0809495	+	0.0333418i
$226$			39.5776i			2.63266i
$227$		−	9.64075i		−	0.639879i	−0.947438	−	0.319939i	$-0.896337\pi$
$227$		−	9.64075i		−	0.639879i	0.947438	−	0.319939i	$-0.103663\pi$
$228$	5.40853	+	27.3326i	0.358189	+	1.81015i
$229$		−	15.5256i		−	1.02596i	−0.858400	−	0.512982i	$-0.828541\pi$
$229$		−	15.5256i		−	1.02596i	0.858400	−	0.512982i	$-0.171459\pi$
$230$			20.8457i			1.37453i
$231$	−3.84792	−	19.4459i	−0.253174	−	1.27945i
$232$	−64.5970			−4.24100
$233$	3.82396			0.250516			0.125258	−	0.992124i	$-0.460024\pi$
$233$	3.82396			0.250516			0.125258	+	0.992124i	$0.460024\pi$
$234$	−17.2889	+	7.12103i	−1.13021	+	0.465516i
$235$	−9.06594			−0.591397
$236$		−	24.1765i		−	1.57376i
$237$	0.300579	+	1.51901i	0.0195247	+	0.0986705i
$238$		−	22.7969i		−	1.47770i
$239$	25.8792			1.67398			0.836992	−	0.547215i	$-0.184312\pi$
$239$	25.8792			1.67398			0.836992	+	0.547215i	$0.184312\pi$
$240$	47.3340	−	9.36635i	3.05539	−	0.604596i
$241$	10.7420			0.691951			0.345975	−	0.938244i	$-0.387548\pi$
$241$	10.7420			0.691951			0.345975	+	0.938244i	$0.387548\pi$
$242$	47.3894			3.04631
$243$	−12.9181	−	8.72486i	−0.828695	−	0.559700i
$244$			14.2176i			0.910190i
$245$			5.17034i			0.330321i
$246$	7.03824	+	35.5686i	0.448742	+	2.26777i
$247$	7.09695			0.451568
$248$			39.3993i			2.50186i
$249$	−11.2640	+	2.22890i	−0.713828	+	0.141251i
$250$		−	31.2685i		−	1.97759i
$251$	−6.90438			−0.435801			−0.217900	−	0.975971i	$-0.569921\pi$
$251$	−6.90438			−0.435801			−0.217900	+	0.975971i	$0.569921\pi$
$252$	−12.8303	−	31.1502i	−0.808232	−	1.96228i
$253$			19.3880i			1.21891i
$254$			22.8438i			1.43335i
$255$	14.3610	−	2.84173i	0.899322	−	0.177956i
$256$	17.2225			1.07641
$257$		−	19.9475i		−	1.24429i	−0.782902	−	0.622145i	$-0.786262\pi$
$257$		−	19.9475i		−	1.24429i	0.782902	−	0.622145i	$-0.213738\pi$
$258$	10.5013	+	53.0696i	0.653784	+	3.30397i
$259$			3.34383i			0.207776i
$260$		−	25.9496i		−	1.60933i
$261$	−20.4945	+	8.44136i	−1.26858	+	0.522507i
$262$	−26.3180			−1.62593
$263$			16.2815i			1.00396i	0.864879	+	0.501980i	$0.167395\pi$
$263$			16.2815i			1.00396i	−0.864879	+	0.501980i	$0.832605\pi$
$264$	79.4498	−	15.7214i	4.88980	−	0.967584i
$265$	−28.4560			−1.74804
$266$			17.6603i			1.08282i
$267$	−2.56515	−	12.9633i	−0.156985	−	0.793340i
$268$			1.29943i			0.0793754i
$269$		−	0.0225528i		−	0.00137507i	−1.00000		0.000687533i	$-0.999781\pi$
$269$		−	0.0225528i		−	0.00137507i	1.00000		0.000687533i	$-0.000218849\pi$
$270$	24.8932	−	16.5258i	1.51495	−	1.00573i
$271$		−	7.36861i		−	0.447611i	−0.974634	−	0.223806i	$-0.928152\pi$
$271$		−	7.36861i		−	0.447611i	0.974634	−	0.223806i	$-0.0718481\pi$
$272$	51.6104			3.12934
$273$	−8.41780	+	1.66570i	−0.509468	+	0.100813i
$274$		−	6.85334i		−	0.414026i
$275$		−	2.34108i		−	0.141173i
$276$	6.39605	+	32.3232i	0.384997	+	1.94563i
$277$	17.6424			1.06003			0.530014	−	0.847989i	$-0.322187\pi$
$277$	17.6424			1.06003			0.530014	+	0.847989i	$0.322187\pi$
$278$	−27.2833			−1.63634
$279$	5.14860	+	12.5001i	0.308238	+	0.748362i
$280$	39.9633			2.38826
$281$		−	12.2130i		−	0.728568i	−0.931288	−	0.364284i	$-0.881314\pi$
$281$		−	12.2130i		−	0.728568i	0.931288	−	0.364284i	$-0.118686\pi$
$282$	−19.4152	+	3.84184i	−1.15616	+	0.228778i
$283$			33.2242i			1.97498i	0.157695	+	0.987488i	$0.449594\pi$
$283$			33.2242i			1.97498i	−0.157695	+	0.987488i	$0.550406\pi$
$284$		−	55.8916i		−	3.31656i
$285$	−11.1252	+	2.20143i	−0.658998	+	0.130401i
$286$		−	33.3333i		−	1.97104i
$287$			16.6399i			0.982221i
$288$	48.8934	−	20.1384i	2.88107	−	1.18667i
$289$	−1.34153			−0.0789136
$290$		−	42.4847i		−	2.49479i
$291$	−28.1775	+	5.57571i	−1.65179	+	0.326854i
$292$	75.5935			4.42377
$293$		−	12.3539i		−	0.721720i	−0.932620	−	0.360860i	$-0.882483\pi$
$293$		−	12.3539i		−	0.721720i	0.932620	−	0.360860i	$-0.117517\pi$
$294$	2.19102	+	11.0726i	0.127783	+	0.645764i
$295$	9.84055			0.572939
$296$	−13.6619			−0.794080
$297$	23.1524	−	15.3702i	1.34344	−	0.891868i
$298$	34.8212			2.01714
$299$	8.39274			0.485365
$300$	−0.772316	−	3.90299i	−0.0445897	−	0.225339i
$301$			24.8273i			1.43102i
$302$	21.1633			1.21781
$303$	2.11261	−	0.418039i	0.121366	−	0.0240157i
$304$	−39.9814			−2.29309
$305$	−5.78699			−0.331362
$306$	29.5506	−	12.1714i	1.68930	−	0.695795i
$307$	3.54176			0.202139			0.101069	−	0.994879i	$-0.467774\pi$
$307$	3.54176			0.202139			0.101069	+	0.994879i	$0.467774\pi$
$308$	60.0582			3.42213
$309$	3.92007	+	19.8105i	0.223005	+	1.12698i
$310$	−25.9125			−1.47173
$311$		−	2.02911i		−	0.115060i	−0.998344	−	0.0575302i	$-0.981677\pi$
$311$		−	2.02911i		−	0.115060i	0.998344	−	0.0575302i	$-0.0183226\pi$
$312$	−6.80553	−	34.3925i	−0.385287	−	1.94709i
$313$		−	8.25448i		−	0.466571i	−0.972408	−	0.233285i	$-0.925052\pi$
$313$		−	8.25448i		−	0.466571i	0.972408	−	0.233285i	$-0.0749476\pi$
$314$		−	55.8293i		−	3.15063i
$315$	12.6790	−	5.22229i	0.714383	−	0.294243i
$316$	−4.69144			−0.263914
$317$	−5.29001			−0.297117			−0.148558	−	0.988904i	$-0.547463\pi$
$317$	−5.29001			−0.297117			−0.148558	+	0.988904i	$0.547463\pi$
$318$	−60.9400	+	12.0587i	−3.41735	+	0.676218i
$319$		−	39.5138i		−	2.21235i
$320$			45.6388i			2.55129i
$321$	19.0335	−	3.76631i	1.06234	−	0.210215i
$322$			20.8848i			1.16386i
$323$	−12.1303			−0.674947
$324$	33.5285	−	33.2627i	1.86269	−	1.84793i
$325$	−1.01342			−0.0562142
$326$	25.5726			1.41633
$327$	−3.42722	−	17.3199i	−0.189526	−	0.957791i
$328$	−67.9854			−3.75386
$329$	−9.08291			−0.500757
$330$	10.3398	+	52.2533i	0.569187	+	2.87645i
$331$	−2.60067			−0.142946			−0.0714730	−	0.997443i	$-0.522770\pi$
$331$	−2.60067			−0.142946			−0.0714730	+	0.997443i	$0.522770\pi$
$332$		−	34.7887i		−	1.90928i
$333$	−4.33447	+	1.78530i	−0.237527	+	0.0978337i
$334$	−5.25088			−0.287315
$335$	−0.528906			−0.0288972
$336$	47.4226	−	9.38390i	2.58711	−	0.511933i
$337$	13.3858			0.729170			0.364585	−	0.931170i	$-0.381211\pi$
$337$	13.3858			0.729170			0.364585	+	0.931170i	$0.381211\pi$
$338$	20.5685			1.11878
$339$	−24.9787	+	4.94275i	−1.35666	+	0.268453i
$340$			44.3537i			2.40542i
$341$	−24.1004			−1.30511
$342$	−22.8922	+	9.42895i	−1.23787	+	0.509859i
$343$			20.1596i			1.08852i
$344$	−101.437			−5.46910
$345$	−13.1565	+	2.60338i	−0.708320	+	0.140161i
$346$			21.3128i			1.14578i
$347$		−	0.422009i		−	0.0226546i	−0.999936	−	0.0113273i	$-0.996394\pi$
$347$		−	0.422009i		−	0.0226546i	0.999936	−	0.0113273i	$-0.00360567\pi$
$348$	−13.0355	−	65.8763i	−0.698775	−	3.53134i
$349$			17.7958i			0.952586i	0.879287	+	0.476293i	$0.158020\pi$
$349$			17.7958i			0.952586i	−0.879287	+	0.476293i	$0.841980\pi$
$350$		−	2.52182i		−	0.134797i
$351$	−6.65349	−	10.0223i	−0.355137	−	0.534951i
$352$			94.2674i			5.02447i
$353$	−19.5583			−1.04098			−0.520491	−	0.853867i	$-0.674251\pi$
$353$	−19.5583			−1.04098			−0.520491	+	0.853867i	$0.674251\pi$
$354$	21.0740	−	4.17009i	1.12007	−	0.221638i
$355$	22.7495			1.20742
$356$	40.0368			2.12195
$357$	14.3879	−	2.84705i	0.761489	−	0.150682i
$358$		−	45.8680i		−	2.42420i
$359$			15.0964i			0.796755i	0.917222	+	0.398377i	$0.130427\pi$
$359$			15.0964i			0.796755i	−0.917222	+	0.398377i	$0.869573\pi$
$360$	21.3367	+	51.8026i	1.12454	+	2.73024i
$361$	−9.60293			−0.505417
$362$		−	55.8815i		−	2.93707i
$363$	5.91835	+	29.9091i	0.310633	+	1.56982i
$364$		−	25.9982i		−	1.36268i
$365$			30.7687i			1.61051i
$366$	−12.3931	+	2.45233i	−0.647799	+	0.128185i
$367$			24.8617i			1.29777i	0.760887	+	0.648884i	$0.224764\pi$
$367$			24.8617i			1.29777i	−0.760887	+	0.648884i	$0.775236\pi$
$368$	−47.2814			−2.46472
$369$	−21.5695	+	8.88415i	−1.12287	+	0.462490i
$370$		−	8.98526i		−	0.467122i
$371$	−28.5093			−1.48013
$372$	−40.1796	+	7.95066i	−2.08322	+	0.412223i
$373$		−	20.6292i		−	1.06814i	−0.845440	−	0.534070i	$-0.820662\pi$
$373$		−	20.6292i		−	1.06814i	0.845440	−	0.534070i	$-0.179338\pi$
$374$			56.9742i			2.94606i
$375$	19.7346	−	3.90505i	1.01909	−	0.201656i
$376$		−	37.1100i		−	1.91380i
$377$	−17.1049			−0.880945
$378$	24.9398	−	16.5568i	1.28277	−	0.851589i
$379$		−	13.8194i		−	0.709854i	−0.934894	−	0.354927i	$-0.884506\pi$
$379$		−	13.8194i		−	0.709854i	0.934894	−	0.354927i	$-0.115494\pi$
$380$		−	34.3599i		−	1.76262i
$381$	−14.4175	+	2.85291i	−0.738631	+	0.146159i
$382$	27.9023			1.42761
$383$			10.4266i			0.532776i	0.963866	+	0.266388i	$0.0858302\pi$
$383$			10.4266i			0.532776i	−0.963866	+	0.266388i	$0.914170\pi$
$384$	7.48783	+	37.8406i	0.382112	+	1.93105i
$385$			24.4454i			1.24585i
$386$	66.7528			3.39763
$387$	−32.1826	+	13.2555i	−1.63593	+	0.673814i
$388$		−	87.0255i		−	4.41805i
$389$		−	0.919823i		−	0.0466369i	−0.999728	−	0.0233184i	$-0.992577\pi$
$389$		−	0.919823i		−	0.0466369i	0.999728	−	0.0233184i	$-0.00742316\pi$
$390$	22.6196	−	4.47592i	1.14539	−	0.226647i
$391$	−14.3451			−0.725462
$392$	−21.1640			−1.06894
$393$	−3.28679	−	16.6102i	−0.165797	−	0.837873i
$394$	−17.1053			−0.861754
$395$		−	1.90955i		−	0.0960799i
$396$	32.0655	+	77.8508i	1.61135	+	3.91215i
$397$		−	7.50366i		−	0.376598i	−0.982112	−	0.188299i	$-0.939703\pi$
$397$		−	7.50366i		−	0.376598i	0.982112	−	0.188299i	$-0.0602974\pi$
$398$	−71.7280			−3.59540
$399$	−11.1460	+	2.20555i	−0.557998	+	0.110416i
$400$	5.70919			0.285459
$401$	14.6505			0.731610			0.365805	−	0.930692i	$-0.380794\pi$
$401$	14.6505			0.731610			0.365805	+	0.930692i	$0.380794\pi$
$402$	−1.13268	+	0.224133i	−0.0564930	+	0.0111787i
$403$			10.4327i			0.519689i
$404$			6.52475i			0.324619i
$405$	13.5389	+	13.6471i	0.672752	+	0.678128i
$406$		−	42.5643i		−	2.11243i
$407$		−	8.35693i		−	0.414237i
$408$	11.6322	+	58.7845i	0.575878	+	2.91027i
$409$		−	12.6013i		−	0.623097i	−0.950230	−	0.311548i	$-0.899152\pi$
$409$		−	12.6013i		−	0.623097i	0.950230	−	0.311548i	$-0.100848\pi$
$410$		−	44.7132i		−	2.20823i
$411$	4.32538	−	0.855898i	0.213355	−	0.0422183i
$412$	−61.1844			−3.01434
$413$	9.85898			0.485128
$414$	−27.0720	+	11.1505i	−1.33052	+	0.548019i
$415$	14.1600			0.695087
$416$	40.8068			2.00072
$417$	−3.40735	−	17.2194i	−0.166859	−	0.843239i
$418$		−	44.1367i		−	2.15879i
$419$		−	7.75794i		−	0.379000i	−0.981881	−	0.189500i	$-0.939313\pi$
$419$		−	7.75794i		−	0.379000i	0.981881	−	0.189500i	$-0.0606867\pi$
$420$	8.06447	+	40.7548i	0.393506	+	1.98863i
$421$			27.6294i			1.34658i	0.739380	+	0.673288i	$0.235119\pi$
$421$			27.6294i			1.34658i	−0.739380	+	0.673288i	$0.764881\pi$
$422$	−25.0651	+	30.0166i	−1.22015	+	1.46118i
$423$	−4.84943	−	11.7738i	−0.235787	−	0.572461i
$424$		−	116.480i		−	5.65677i
$425$	1.73215			0.0840218
$426$	48.7192	−	9.64047i	2.36045	−	0.467082i
$427$	−5.79782			−0.280576
$428$			58.7845i			2.84145i
$429$	21.0378	−	4.16292i	1.01571	−	0.200988i
$430$		−	66.7138i		−	3.21723i
$431$			4.49504i			0.216518i	0.994123	+	0.108259i	$0.0345277\pi$
$431$			4.49504i			0.216518i	−0.994123	+	0.108259i	$0.965472\pi$
$432$	37.4832	+	56.4617i	1.80341	+	2.71652i
$433$	−11.8406			−0.569025			−0.284512	−	0.958672i	$-0.591832\pi$
$433$	−11.8406			−0.569025			−0.284512	+	0.958672i	$0.591832\pi$
$434$	−25.9610			−1.24617
$435$	26.8136	−	5.30582i	1.28561	−	0.254395i
$436$	53.4921			2.56181
$437$	11.1128			0.531599
$438$	13.0388	+	65.8929i	0.623016	+	3.14848i
$439$			9.59107i			0.457757i	0.973455	+	0.228878i	$0.0735058\pi$
$439$			9.59107i			0.457757i	−0.973455	+	0.228878i	$0.926494\pi$
$440$	−99.8764			−4.76142
$441$	−6.71464	+	2.76565i	−0.319745	+	0.131698i
$442$	24.6632			1.17311
$443$		−	10.2125i		−	0.485211i	−0.970125	−	0.242605i	$-0.921998\pi$
$443$		−	10.2125i		−	0.485211i	0.970125	−	0.242605i	$-0.0780020\pi$
$444$	−2.75693	−	13.9324i	−0.130838	−	0.661204i
$445$			16.2962i			0.772512i
$446$			49.5837i			2.34786i
$447$	4.34874	+	21.9769i	0.205688	+	1.03947i
$448$			45.7243i			2.16027i
$449$	−14.8845			−0.702442			−0.351221	−	0.936293i	$-0.614233\pi$
$449$	−14.8845			−0.702442			−0.351221	+	0.936293i	$0.614233\pi$
$450$	3.26892	−	1.34641i	0.154098	−	0.0634706i
$451$		−	41.5865i		−	1.95823i
$452$		−	77.1463i		−	3.62866i
$453$	2.64303	+	13.3568i	0.124180	+	0.627560i
$454$			25.9543i			1.21810i
$455$	10.5820			0.496093
$456$	−9.01120	−	45.5391i	−0.421988	−	2.13256i
$457$		−	3.17914i		−	0.148714i	−0.997232	−	0.0743570i	$-0.976310\pi$
$457$		−	3.17914i		−	0.148714i	0.997232	−	0.0743570i	$-0.0236904\pi$
$458$			41.7973i			1.95306i
$459$	11.3723	+	17.1304i	0.530814	+	0.799577i
$460$		−	40.6334i		−	1.89454i
$461$	−16.9857			−0.791104			−0.395552	−	0.918444i	$-0.629447\pi$
$461$	−16.9857			−0.791104			−0.395552	+	0.918444i	$0.629447\pi$
$462$	10.3592	+	52.3512i	0.481951	+	2.43560i
$463$		−	39.2860i		−	1.82578i	−0.408211	−	0.912888i	$-0.633847\pi$
$463$		−	39.2860i		−	1.82578i	0.408211	−	0.912888i	$-0.366153\pi$
$464$	96.3621			4.47350
$465$	−3.23615	−	16.3543i	−0.150073	−	0.758411i
$466$	−10.2947			−0.476891
$467$		−	26.3667i		−	1.22011i	−0.792360	−	0.610053i	$-0.791148\pi$
$467$		−	26.3667i		−	1.22011i	0.792360	−	0.610053i	$-0.208852\pi$
$468$	33.7003	−	13.8806i	1.55780	−	0.641632i
$469$	−0.529897			−0.0244684
$470$	24.4068			1.12580
$471$	35.2358	−	6.97239i	1.62358	−	0.321271i
$472$			40.2807i			1.85407i
$473$		−	62.0486i		−	2.85300i
$474$	−0.809204	−	4.08940i	−0.0371680	−	0.187833i
$475$	−1.34186			−0.0615689
$476$			44.4368i			2.03676i
$477$	−15.2213	−	36.9553i	−0.696936	−	1.69207i
$478$	−69.6705			−3.18666
$479$	−18.3147			−0.836821			−0.418411	−	0.908258i	$-0.637413\pi$
$479$	−18.3147			−0.836821			−0.418411	+	0.908258i	$0.637413\pi$
$480$	−63.9687	+	12.6580i	−2.91976	+	0.577756i
$481$	−3.61757			−0.164947
$482$	−28.9189			−1.31722
$483$	−13.1811	+	2.60825i	−0.599761	+	0.118680i
$484$	−92.3736			−4.19880
$485$	35.4219			1.60843
$486$	34.7774	+	23.4886i	1.57753	+	1.06546i
$487$	−23.9354			−1.08462			−0.542309	−	0.840179i	$-0.682450\pi$
$487$	−23.9354			−1.08462			−0.542309	+	0.840179i	$0.682450\pi$
$488$		−	23.6881i		−	1.07231i
$489$	3.19370	+	16.1397i	0.144424	+	0.729864i
$490$		−	13.9193i		−	0.628810i
$491$			9.65789i			0.435854i	0.975965	+	0.217927i	$0.0699295\pi$
$491$			9.65789i			0.435854i	−0.975965	+	0.217927i	$0.930070\pi$
$492$	−13.7193	−	69.3318i	−0.618512	−	3.12572i
$493$	29.2360			1.31673
$494$	−19.1060			−0.859621
$495$	−31.6875	+	13.0516i	−1.42425	+	0.586625i
$496$		−	58.7736i		−	2.63901i
$497$	22.7921			1.02237
$498$	30.3244	−	6.00053i	1.35887	−	0.268890i
$499$			34.7806i			1.55700i	0.627647	+	0.778498i	$0.284018\pi$
$499$			34.7806i			1.55700i	−0.627647	+	0.778498i	$0.715982\pi$
$500$			60.9499i			2.72576i
$501$	−0.655770	−	3.31401i	−0.0292976	−	0.148059i
$502$	18.5876			0.829606
$503$		−	2.00523i		−	0.0894089i	−0.999000	−	0.0447045i	$-0.985765\pi$
$503$		−	2.00523i		−	0.0894089i	0.999000	−	0.0447045i	$-0.0142346\pi$
$504$	21.3766	+	51.8996i	0.952191	+	2.31179i
$505$	−2.65576			−0.118180
$506$		−	52.1953i		−	2.32037i
$507$	2.56875	+	12.9815i	0.114082	+	0.576527i
$508$		−	44.5281i		−	1.97562i
$509$			40.8841i			1.81216i	0.423110	+	0.906078i	$0.360938\pi$
$509$			40.8841i			1.81216i	−0.423110	+	0.906078i	$0.639062\pi$
$510$	−38.6620	+	7.65036i	−1.71198	+	0.338763i
$511$			30.8264i			1.36368i
$512$	−1.82364			−0.0805942
$513$	−8.80989	−	13.2705i	−0.388966	−	0.585908i
$514$			53.7015i			2.36867i
$515$		−	24.9038i		−	1.09739i
$516$	−20.4696	−	103.446i	−0.901126	−	4.55394i
$517$	22.7001			0.998348
$518$		−	9.00209i		−	0.395529i
$519$	−13.4512	+	2.66170i	−0.590443	+	0.116836i
$520$			43.2348i			1.89597i
$521$			21.0579i			0.922565i	0.887253	+	0.461282i	$0.152610\pi$
$521$			21.0579i			0.922565i	−0.887253	+	0.461282i	$0.847390\pi$
$522$	55.1742	−	22.7254i	2.41491	−	0.994663i
$523$	18.6625			0.816055			0.408027	−	0.912970i	$-0.366217\pi$
$523$	18.6625			0.816055			0.408027	+	0.912970i	$0.366217\pi$
$524$	51.3002			2.24106
$525$	1.59160	−	0.314944i	0.0694633	−	0.0137453i
$526$		−	43.8322i		−	1.91117i
$527$		−	17.8318i		−	0.776765i
$528$	−118.519	+	23.4523i	−5.15787	+	1.02063i
$529$	−9.85814			−0.428615
$530$	76.6077			3.32763
$531$	5.26378	+	12.7798i	0.228428	+	0.554594i
$532$		−	34.4242i		−	1.49248i
$533$	−18.0021			−0.779757
$534$	6.90576	+	34.8991i	0.298842	+	1.51023i
$535$	−23.9270			−1.03445
$536$		−	2.16499i		−	0.0935134i
$537$	28.9488	−	5.72834i	1.24923	−	0.247196i
$538$			0.0607154i			0.00261762i
$539$		−	12.9459i		−	0.557621i
$540$	−48.5229	+	32.2129i	−2.08809	+	1.38622i
$541$	−5.15254			−0.221525			−0.110762	−	0.993847i	$-0.535329\pi$
$541$	−5.15254			−0.221525			−0.110762	+	0.993847i	$0.535329\pi$
$542$			19.8374i			0.852089i
$543$	35.2687	−	6.97891i	1.51353	−	0.299494i
$544$	−69.7480			−2.99042
$545$			21.7728i			0.932645i
$546$	22.6619	−	4.48430i	0.969842	−	0.191910i
$547$	−12.9459			−0.553527			−0.276764	−	0.960938i	$-0.589262\pi$
$547$	−12.9459			−0.553527			−0.276764	+	0.960938i	$0.589262\pi$
$548$			13.3588i			0.570662i
$549$	−3.09550	−	7.51546i	−0.132113	−	0.320752i
$550$			6.30253i			0.268741i
$551$	−22.6485			−0.964860
$552$	−10.6565	−	53.8539i	−0.453571	−	2.29217i
$553$		−	1.91313i		−	0.0813544i
$554$	−47.4959			−2.01791
$555$	5.67091	−	1.12215i	0.240717	−	0.0476325i
$556$	53.1818			2.25541
$557$	−28.2310			−1.19619			−0.598093	−	0.801426i	$-0.704075\pi$
$557$	−28.2310			−1.19619			−0.598093	+	0.801426i	$0.704075\pi$
$558$	−13.8608	−	33.6521i	−0.586773	−	1.42461i
$559$	−26.8598			−1.13605
$560$	−59.6150			−2.51919
$561$	−35.9583	+	7.11537i	−1.51816	+	0.300411i
$562$			32.8792i			1.38693i
$563$	−32.5829			−1.37320			−0.686602	−	0.727033i	$-0.740898\pi$
$563$	−32.5829			−1.37320			−0.686602	+	0.727033i	$0.740898\pi$
$564$	37.8449	−	7.48869i	1.59356	−	0.315331i
$565$	31.4008			1.32104
$566$		−	89.4445i		−	3.75963i
$567$	13.5642	+	13.6726i	0.569644	+	0.574196i
$568$			93.1214i			3.90729i
$569$	20.4531			0.857440			0.428720	−	0.903437i	$-0.358965\pi$
$569$	20.4531			0.857440			0.428720	+	0.903437i	$0.358965\pi$
$570$	29.9506	−	5.92657i	1.25449	−	0.248237i
$571$			9.75810i			0.408364i	0.978933	+	0.204182i	$0.0654534\pi$
$571$			9.75810i			0.408364i	−0.978933	+	0.204182i	$0.934547\pi$
$572$			64.9748i			2.71673i
$573$	3.48465	+	17.6101i	0.145573	+	0.735672i
$574$		−	44.7970i		−	1.86979i
$575$	−1.58687			−0.0661769
$576$	−59.2704	+	24.4125i	−2.46960	+	1.01719i
$577$			33.2172i			1.38285i	0.722449	+	0.691424i	$0.243016\pi$
$577$			33.2172i			1.38285i	−0.722449	+	0.691424i	$0.756984\pi$
$578$	3.61160			0.150223
$579$	8.33660	+	42.1300i	0.346457	+	1.75086i
$580$			82.8131i			3.43863i
$581$	14.1865			0.588555
$582$	75.8579	−	15.0106i	3.14441	−	0.622210i
$583$	71.2506			2.95090
$584$	−125.947			−5.21172
$585$	5.64981	+	13.7170i	0.233591	+	0.567128i
$586$			33.2584i			1.37389i
$587$	30.5854			1.26239			0.631197	−	0.775623i	$-0.282564\pi$
$587$	30.5854			1.26239			0.631197	+	0.775623i	$0.282564\pi$
$588$	−4.27083	−	21.5831i	−0.176126	−	0.890073i
$589$			13.8139i			0.569192i
$590$	−26.4922			−1.09067
$591$	−2.13624	−	10.7958i	−0.0878733	−	0.444078i
$592$	20.3800			0.837613
$593$			26.0426i			1.06944i	0.845029	+	0.534721i	$0.179583\pi$
$593$			26.0426i			1.06944i	−0.845029	+	0.534721i	$0.820417\pi$
$594$	−62.3297	+	41.3788i	−2.55742	+	1.69779i
$595$	−18.0870			−0.741497
$596$	−67.8751			−2.78027
$597$	−8.95794	−	45.2700i	−0.366624	−	1.85278i
$598$	−22.5945			−0.923958
$599$	1.79150			0.0731986			0.0365993	−	0.999330i	$-0.488347\pi$
$599$	1.79150			0.0731986			0.0365993	+	0.999330i	$0.488347\pi$
$600$	1.28676	+	6.50280i	0.0525318	+	0.265476i
$601$	−8.50229			−0.346815			−0.173408	−	0.984850i	$-0.555478\pi$
$601$	−8.50229			−0.346815			−0.173408	+	0.984850i	$0.555478\pi$
$602$		−	66.8388i		−	2.72415i
$603$	−0.282916	−	0.686882i	−0.0115212	−	0.0279720i
$604$	−41.2524			−1.67853
$605$		−	37.5987i		−	1.52861i
$606$	−5.68745	+	1.12542i	−0.231037	+	0.0457172i
$607$	−0.269222			−0.0109274			−0.00546370	−	0.999985i	$-0.501739\pi$
$607$	−0.269222			−0.0109274			−0.00546370	+	0.999985i	$0.501739\pi$
$608$	54.0323			2.19130
$609$	26.8638	−	5.31575i	1.08858	−	0.215405i
$610$	15.5794			0.630792
$611$		−	9.82648i		−	0.397537i
$612$	−57.6014	+	23.7251i	−2.32840	+	0.959030i
$613$			21.6528i			0.874547i	0.899329	+	0.437273i	$0.144056\pi$
$613$			21.6528i			0.874547i	−0.899329	+	0.437273i	$0.855944\pi$
$614$	−9.53494			−0.384799
$615$	28.2201	−	5.58413i	1.13794	−	0.225174i
$616$	−100.063			−4.03167
$617$	14.3558			0.577944			0.288972	−	0.957337i	$-0.406686\pi$
$617$	14.3558			0.577944			0.288972	+	0.957337i	$0.406686\pi$
$618$	−10.5534	−	53.3328i	−0.424520	−	2.14536i
$619$		−	8.73850i		−	0.351230i	−0.984459	−	0.175615i	$-0.943809\pi$
$619$		−	8.73850i		−	0.351230i	0.984459	−	0.175615i	$-0.0561914\pi$
$620$	50.5098			2.02852
$621$	−10.4184	−	15.6935i	−0.418078	−	0.629759i
$622$			5.46267i			0.219033i
$623$			16.3267i			0.654114i
$624$	10.1521	+	51.3048i	0.406409	+	2.05384i
$625$	−22.6197			−0.904788
$626$			22.2223i			0.888180i
$627$	27.8562	−	5.51212i	1.11247	−	0.220133i
$628$			108.825i			4.34259i
$629$	6.18325			0.246542
$630$	−34.1338	+	14.0592i	−1.35993	+	0.560131i
$631$	−1.76315			−0.0701899			−0.0350950	−	0.999384i	$-0.511173\pi$
$631$	−1.76315			−0.0701899			−0.0350950	+	0.999384i	$0.511173\pi$
$632$	7.81644			0.310921
$633$	−22.0748	−	12.0708i	−0.877394	−	0.479770i
$634$	14.2415			0.565602
$635$	18.1242			0.719238
$636$	118.787	−	23.5054i	4.71021	−	0.932048i
$637$	−5.60408			−0.222042
$638$			106.377i			4.21150i
$639$	12.1689	+	29.5444i	0.481393	+	1.16876i
$640$		−	47.5695i		−	1.88035i
$641$	14.5596			0.575069			0.287535	−	0.957770i	$-0.407164\pi$
$641$	14.5596			0.575069			0.287535	+	0.957770i	$0.407164\pi$
$642$	−51.2409	+	10.1395i	−2.02232	+	0.400172i
$643$			2.44682i			0.0964931i	0.998835	+	0.0482465i	$0.0153633\pi$
$643$			2.44682i			0.0964931i	−0.998835	+	0.0482465i	$0.984637\pi$
$644$		−	40.7095i		−	1.60418i
$645$	42.1054	−	8.33173i	1.65790	−	0.328062i
$646$	32.6565			1.28485
$647$		−	22.7311i		−	0.893653i	−0.894621	−	0.446826i	$-0.852554\pi$
$647$		−	22.7311i		−	0.893653i	0.894621	−	0.446826i	$-0.147446\pi$
$648$	−55.8621	+	55.4192i	−2.19447	+	2.17707i
$649$	−24.6396			−0.967189
$650$	2.72826			0.107011
$651$	−3.24221	−	16.3849i	−0.127072	−	0.642174i
$652$	−49.8472			−1.95217
$653$		−	35.9421i		−	1.40652i	−0.710930	−	0.703262i	$-0.751726\pi$
$653$		−	35.9421i		−	1.40652i	0.710930	−	0.703262i	$-0.248274\pi$
$654$	9.22659	+	46.6276i	0.360788	+	1.82329i
$655$			20.8807i			0.815875i
$656$	101.417			3.95966
$657$	−39.9589	+	16.4584i	−1.55894	+	0.642104i
$658$	24.4525			0.953259
$659$	18.4243			0.717709			0.358855	−	0.933393i	$-0.383167\pi$
$659$	18.4243			0.717709			0.358855	+	0.933393i	$0.383167\pi$
$660$	−20.1548	−	101.854i	−0.784524	−	3.96468i
$661$		−	11.1715i		−	0.434519i	−0.976114	−	0.217260i	$-0.930288\pi$
$661$		−	11.1715i		−	0.434519i	0.976114	−	0.217260i	$-0.0697119\pi$
$662$	7.00140			0.272117
$663$	3.08012	+	15.5658i	0.119622	+	0.604524i
$664$			57.9617i			2.24935i
$665$	14.0116			0.543348
$666$	11.6690	−	4.80628i	0.452165	−	0.186240i
$667$	−26.7838			−1.03707
$668$	10.2353			0.396014
$669$	−31.2940	+	6.19239i	−1.20989	+	0.239412i
$670$	1.42389			0.0550098
$671$	14.4899			0.559378
$672$	−64.0885	+	12.6817i	−2.47227	+	0.489208i
$673$			9.29195i			0.358178i	0.983833	+	0.179089i	$0.0573150\pi$
$673$			9.29195i			0.358178i	−0.983833	+	0.179089i	$0.942685\pi$
$674$	−36.0365			−1.38807
$675$	1.25802	+	1.89498i	0.0484211	+	0.0729376i
$676$	−40.0929			−1.54204
$677$		−	31.9496i		−	1.22792i	−0.789337	−	0.613961i	$-0.789575\pi$
$677$		−	31.9496i		−	1.22792i	0.789337	−	0.613961i	$-0.210425\pi$
$678$	67.2464	−	13.3066i	2.58258	−	0.511037i
$679$	35.4882			1.36191
$680$		−	73.8980i		−	2.83386i
$681$	−16.3806	+	3.24137i	−0.627708	+	0.124210i
$682$	64.8819			2.48446
$683$	49.0349			1.87627			0.938134	−	0.346272i	$-0.112553\pi$
$683$	49.0349			1.87627			0.938134	+	0.346272i	$0.112553\pi$
$684$	44.6226	−	18.3793i	1.70619	−	0.702751i
$685$	−5.43744			−0.207754
$686$		−	54.2727i		−	2.07214i
$687$	−26.3797	+	5.21997i	−1.00645	+	0.199154i
$688$	151.318			5.76893
$689$		−	30.8432i		−	1.17503i
$690$	35.4191	−	7.00867i	1.34838	−	0.266815i
$691$	17.3750			0.660977			0.330488	−	0.943810i	$-0.392787\pi$
$691$	17.3750			0.660977			0.330488	+	0.943810i	$0.392787\pi$
$692$		−	41.5438i		−	1.57926i
$693$	−31.7469	+	13.0760i	−1.20596	+	0.496717i
$694$			1.13611i			0.0431261i
$695$			21.6465i			0.821100i
$696$	21.7185	+	109.757i	0.823238	+	4.16033i
$697$	30.7696			1.16548
$698$		−	47.9088i		−	1.81338i
$699$	−1.28567	−	6.49731i	−0.0486287	−	0.245751i
$700$			4.91563i			0.185794i
$701$	−40.6360			−1.53480			−0.767400	−	0.641169i	$-0.778450\pi$
$701$	−40.6360			−1.53480			−0.767400	+	0.641169i	$0.778450\pi$
$702$	17.9122	+	26.9815i	0.676052	+	1.01835i
$703$	−4.79003			−0.180659
$704$		−	114.274i		−	4.30688i
$705$	3.04811	+	15.4040i	0.114799	+	0.580148i
$706$	52.6538			1.98165
$707$	−2.66074			−0.100067
$708$	−41.0785	+	8.12853i	−1.54382	+	0.305489i
$709$	−27.6409			−1.03808			−0.519038	−	0.854751i	$-0.673710\pi$
$709$	−27.6409			−1.03808			−0.519038	+	0.854751i	$0.673710\pi$
$710$	−61.2450			−2.29848
$711$	2.47990	−	1.02143i	0.0930036	−	0.0383067i
$712$	−66.7057			−2.49990
$713$			16.3361i			0.611792i
$714$	−38.7344	+	7.66468i	−1.44960	+	0.286844i
$715$	−26.4466			−0.989048
$716$			89.4079i			3.34133i
$717$	−8.70099	−	43.9714i	−0.324944	−	1.64214i
$718$		−	40.6416i		−	1.51673i
$719$	17.0774			0.636881			0.318441	−	0.947943i	$-0.396841\pi$
$719$	17.0774			0.636881			0.318441	+	0.947943i	$0.396841\pi$
$720$	−31.8288	−	77.2763i	−1.18619	−	2.87992i
$721$		−	24.9504i		−	0.929203i
$722$	25.8525			0.962130
$723$	−3.61162	−	18.2517i	−0.134317	−	0.678789i
$724$			108.927i			4.04823i
$725$	3.23412			0.120112
$726$	−15.9331	−	80.5196i	−0.591332	−	2.98836i
$727$		−	32.5486i		−	1.20716i	−0.797303	−	0.603580i	$-0.793741\pi$
$727$		−	32.5486i		−	1.20716i	0.797303	−	0.603580i	$-0.206259\pi$
$728$			43.3158i			1.60539i
$729$	−10.4812	+	24.8826i	−0.388193	+	0.921578i
$730$		−	82.8339i		−	3.06582i
$731$	45.9094			1.69802
$732$	24.1572	−	4.78019i	0.892878	−	0.176681i
$733$	16.8055			0.620725			0.310362	−	0.950618i	$-0.399550\pi$
$733$	16.8055			0.620725			0.310362	+	0.950618i	$0.399550\pi$
$734$		−	66.9313i		−	2.47048i
$735$	8.78495	−	1.73835i	0.324038	−	0.0641200i
$736$	63.8977			2.35530
$737$	1.32432			0.0487820
$738$	58.0684	−	23.9174i	2.13753	−	0.880413i
$739$			29.3115i			1.07824i	0.842229	+	0.539120i	$0.181243\pi$
$739$			29.3115i			1.07824i	−0.842229	+	0.539120i	$0.818757\pi$
$740$			17.5145i			0.643845i
$741$	−2.38611	−	12.0585i	−0.0876558	−	0.442979i
$742$	76.7512			2.81762
$743$	−24.8539			−0.911802			−0.455901	−	0.890031i	$-0.650683\pi$
$743$	−24.8539			−0.911802			−0.455901	+	0.890031i	$0.650683\pi$
$744$	66.9435	−	13.2467i	2.45427	−	0.485646i
$745$		−	27.6271i		−	1.01218i
$746$			55.5368i			2.03335i
$747$	7.57428	+	18.3893i	0.277128	+	0.672831i
$748$		−	111.057i		−	4.06063i
$749$	−23.9718			−0.875910
$750$	−53.1285	+	10.5130i	−1.93998	+	0.383879i
$751$		−	20.9092i		−	0.762989i	−0.924371	−	0.381495i	$-0.875409\pi$
$751$		−	20.9092i		−	0.762989i	0.924371	−	0.381495i	$-0.124591\pi$
$752$			55.3586i			2.01872i
$753$	2.32136	+	11.7313i	0.0845952	+	0.427511i
$754$	46.0488			1.67700
$755$		−	16.7909i		−	0.611083i
$756$	−48.6138	+	32.2732i	−1.76807	+	1.17376i
$757$		−	16.6277i		−	0.604344i	−0.953253	−	0.302172i	$-0.902288\pi$
$757$		−	16.6277i		−	0.604344i	0.953253	−	0.302172i	$-0.0977117\pi$
$758$			37.2038i			1.35130i
$759$	32.9423	−	6.51855i	1.19573	−	0.236608i
$760$			57.2472i			2.07658i
$761$	54.5969			1.97914			0.989569	−	0.144063i	$-0.0460168\pi$
$761$	54.5969			1.97914			0.989569	+	0.144063i	$0.0460168\pi$
$762$	38.8140	−	7.68044i	1.40608	−	0.278233i
$763$			21.8136i			0.789705i
$764$	−54.3884			−1.96770
$765$	−9.65680	−	23.4454i	−0.349142	−	0.847672i
$766$		−	28.0700i		−	1.01421i
$767$			10.6661i			0.385130i
$768$	−5.79047	−	29.2628i	−0.208946	−	1.05593i
$769$	−37.8773			−1.36589			−0.682946	−	0.730469i	$-0.739301\pi$
$769$	−37.8773			−1.36589			−0.682946	+	0.730469i	$0.739301\pi$
$770$		−	65.8107i		−	2.37165i
$771$	−33.8929	+	6.70665i	−1.22062	+	0.241534i
$772$	−130.118			−4.68303
$773$	33.9282			1.22031			0.610157	−	0.792281i	$-0.291106\pi$
$773$	33.9282			1.22031			0.610157	+	0.792281i	$0.291106\pi$
$774$	86.6402	−	35.6857i	3.11422	−	1.28270i
$775$		−	1.97257i		−	0.0708568i
$776$			144.994i			5.20498i
$777$	5.68153	−	1.12425i	0.203824	−	0.0403322i
$778$			2.47630i			0.0887796i
$779$	−23.8366			−0.854033
$780$	−44.0911	+	8.72467i	−1.57871	+	0.312393i
$781$	−56.9621			−2.03826
$782$	38.6191			1.38102
$783$	21.2333	+	31.9842i	0.758818	+	1.14302i
$784$	31.5712			1.12754
$785$	−44.2949			−1.58095
$786$	8.84852	+	44.7170i	0.315616	+	1.59500i
$787$	20.4237			0.728027			0.364014	−	0.931394i	$-0.381406\pi$
$787$	20.4237			0.728027			0.364014	+	0.931394i	$0.381406\pi$
$788$	33.3425			1.18778
$789$	27.6640	−	5.47410i	0.984864	−	0.194883i
$790$			5.14079i			0.182901i
$791$	31.4596			1.11857
$792$	−53.4246	−	129.708i	−1.89836	−	4.60897i
$793$		−	6.27246i		−	0.222741i
$794$			20.2010i			0.716905i
$795$	9.56736	+	48.3497i	0.339319	+	1.71479i
$796$	139.815			4.95562
$797$	−46.2901			−1.63968			−0.819839	−	0.572593i	$-0.805937\pi$
$797$	−46.2901			−1.63968			−0.819839	+	0.572593i	$0.805937\pi$
$798$	30.0067	−	5.93767i	1.06222	−	0.210191i
$799$			16.7957i			0.594188i
$800$	−7.71558			−0.272787
$801$	−21.1635	+	8.71692i	−0.747777	+	0.307997i
$802$	−39.4412			−1.39272
$803$		−	77.0414i		−	2.71873i
$804$	2.20787	−	0.436889i	0.0778656	−	0.0154079i
$805$	16.5700			0.584014
$806$		−	28.0863i		−	0.989298i
$807$	−0.0383195	+	0.00758260i	−0.00134891	+	0.000266920i
$808$		−	10.8709i		−	0.382438i
$809$		−	20.7719i		−	0.730302i	−0.930948	−	0.365151i	$-0.881017\pi$
$809$		−	20.7719i		−	0.730302i	0.930948	−	0.365151i	$-0.118983\pi$
$810$	−36.4486	−	36.7399i	−1.28067	−	1.29091i
$811$	34.0589			1.19597			0.597985	−	0.801508i	$-0.295968\pi$
$811$	34.0589			1.19597			0.597985	+	0.801508i	$0.295968\pi$
$812$			82.9682i			2.91161i
$813$	−12.5201	+	2.47744i	−0.439097	+	0.0868878i
$814$			22.4981i			0.788557i
$815$		−	20.2893i		−	0.710702i
$816$	−17.3522	−	87.6914i	−0.607449	−	3.06981i
$817$	−35.5650			−1.24426
$818$			33.9247i			1.18615i
$819$	5.66039	+	13.7427i	0.197790	+	0.480209i
$820$			87.1571i			3.04366i
$821$		−	22.4789i		−	0.784520i	−0.919854	−	0.392260i	$-0.871693\pi$
$821$		−	22.4789i		−	0.784520i	0.919854	−	0.392260i	$-0.128307\pi$
$822$	−11.6446	+	2.30420i	−0.406150	+	0.0803683i
$823$		−	19.5070i		−	0.679973i	−0.940430	−	0.339986i	$-0.889578\pi$
$823$		−	19.5070i		−	0.679973i	0.940430	−	0.339986i	$-0.110422\pi$
$824$	101.940			3.55124
$825$	−3.97774	+	0.787108i	−0.138487	+	0.0274036i
$826$	−26.5418			−0.923508
$827$		−	8.32038i		−	0.289328i	−0.989481	−	0.144664i	$-0.953790\pi$
$827$		−	8.32038i		−	0.289328i	0.989481	−	0.144664i	$-0.0462101\pi$
$828$	52.7700	−	21.7351i	1.83388	−	0.755347i
$829$	22.0060			0.764298			0.382149	−	0.924101i	$-0.375184\pi$
$829$	22.0060			0.764298			0.382149	+	0.924101i	$0.375184\pi$
$830$	−38.1208			−1.32319
$831$	−5.93165	−	29.9763i	−0.205767	−	1.03986i
$832$	−49.4675			−1.71498
$833$	9.57863			0.331880
$834$	9.17308	+	46.3572i	0.317638	+	1.60522i
$835$			4.16604i			0.144172i
$836$			86.0332i			2.97552i
$837$	19.5080	−	12.9507i	0.674294	−	0.447643i
$838$			20.8855i			0.721478i
$839$	−42.5965			−1.47060			−0.735298	−	0.677744i	$-0.762958\pi$
$839$	−42.5965			−1.47060			−0.735298	+	0.677744i	$0.762958\pi$
$840$	−13.4363	−	67.9018i	−0.463596	−	2.34284i
$841$	25.5868			0.882305
$842$		−	74.3825i		−	2.56339i
$843$	−20.7512	+	4.10621i	−0.714710	+	0.141425i
$844$	48.8581	−	58.5096i	1.68176	−	2.01398i
$845$		−	16.3190i		−	0.561390i
$846$	13.0554	+	31.6967i	0.448853	+	1.08976i
$847$		−	37.6691i		−	1.29433i
$848$			173.758i			5.96689i
$849$	56.4515	−	11.1705i	1.93741	−	0.383371i
$850$	−4.66321			−0.159947
$851$	−5.66462			−0.194181
$852$	−94.9657	+	18.7916i	−3.25347	+	0.643791i
$853$	4.42585			0.151538			0.0757692	−	0.997125i	$-0.475859\pi$
$853$	4.42585			0.151538			0.0757692	+	0.997125i	$0.475859\pi$
$854$	15.6086			0.534115
$855$	7.48092	+	18.1627i	0.255842	+	0.621151i
$856$		−	97.9413i		−	3.34756i
$857$		−	32.3831i		−	1.10619i	−0.833119	−	0.553093i	$-0.813447\pi$
$857$		−	32.3831i		−	1.10619i	0.833119	−	0.553093i	$-0.186553\pi$
$858$	−56.6369	+	11.2072i	−1.93355	+	0.382607i
$859$		−	30.5434i		−	1.04213i	−0.853518	−	0.521064i	$-0.825535\pi$
$859$		−	30.5434i		−	1.04213i	0.853518	−	0.521064i	$-0.174465\pi$
$860$			130.042i			4.43438i
$861$	28.2729	−	5.59459i	0.963538	−	0.190663i
$862$		−	12.1013i		−	0.412172i
$863$			28.2825i			0.962746i	0.876516	+	0.481373i	$0.159862\pi$
$863$			28.2825i			0.962746i	−0.876516	+	0.481373i	$0.840138\pi$
$864$	−50.6560	−	76.3042i	−1.72335	−	2.59592i
$865$	16.9095			0.574941
$866$	31.8767			1.08321
$867$	0.451044	+	2.27940i	0.0153183	+	0.0774126i
$868$	50.6044			1.71762
$869$			4.78130i			0.162194i
$870$	−72.1860	+	14.2840i	−2.44734	+	0.484274i
$871$		−	0.573276i		−	0.0194247i
$872$	−89.1236			−3.01810
$873$	18.9474	+	46.0019i	0.641273	+	1.55693i
$874$	−29.9174			−1.01197
$875$	−24.8548			−0.840247
$876$	−25.4157	−	128.441i	−0.858718	−	4.33963i
$877$			39.9204i			1.34802i	0.738724	+	0.674009i	$0.235429\pi$
$877$			39.9204i			1.34802i	−0.738724	+	0.674009i	$0.764571\pi$
$878$		−	25.8206i		−	0.871402i
$879$	−20.9905	+	4.15356i	−0.707992	+	0.140096i
$880$	148.990			5.02245
$881$			25.3843i			0.855220i	0.903963	+	0.427610i	$0.140644\pi$
$881$			25.3843i			0.855220i	−0.903963	+	0.427610i	$0.859356\pi$
$882$	18.0768	−	7.44553i	0.608677	−	0.250704i
$883$			26.0218i			0.875702i	0.899048	+	0.437851i	$0.144260\pi$
$883$			26.0218i			0.875702i	−0.899048	+	0.437851i	$0.855740\pi$
$884$	−48.0745			−1.61692
$885$	−3.30855	−	16.7201i	−0.111216	−	0.562041i
$886$			27.4936i			0.923664i
$887$		−	19.5373i		−	0.655999i	−0.944678	−	0.327999i	$-0.893626\pi$
$887$		−	19.5373i		−	0.655999i	0.944678	−	0.327999i	$-0.106374\pi$
$888$	4.59334	+	23.2130i	0.154142	+	0.778976i
$889$	18.1582			0.609006
$890$		−	43.8716i		−	1.47058i
$891$	−33.8998	−	34.1707i	−1.13568	−	1.14476i
$892$		−	96.6507i		−	3.23611i
$893$		−	13.0112i		−	0.435405i
$894$	−11.7074	−	59.1649i	−0.391556	−	1.97877i
$895$	−36.3916			−1.21644
$896$		−	47.6585i		−	1.59216i
$897$	−2.82177	−	14.2602i	−0.0942163	−	0.476133i
$898$	40.0712			1.33719
$899$		−	33.2939i		−	1.11041i
$900$	−6.37192	+	2.62449i	−0.212397	+	0.0874831i
$901$			52.7179i			1.75629i
$902$			111.957i			3.72776i
$903$	42.1842	−	8.34734i	1.40380	−	0.277782i
$904$			128.534i			4.27498i
$905$	−44.3364			−1.47379
$906$	−7.11542	−	35.9586i	−0.236394	−	1.19464i
$907$			22.3484i			0.742068i	0.928619	+	0.371034i	$0.120997\pi$
$907$			22.3484i			0.742068i	−0.928619	+	0.371034i	$0.879003\pi$
$908$		−	50.5913i		−	1.67893i
$909$	−1.42059	−	3.44900i	−0.0471179	−	0.114396i
$910$	−28.4883			−0.944379
$911$	−12.4799			−0.413477			−0.206739	−	0.978396i	$-0.566285\pi$
$911$	−12.4799			−0.413477			−0.206739	+	0.978396i	$0.566285\pi$
$912$	13.4424	+	67.9327i	0.445122	+	2.24948i
$913$	−35.4550			−1.17339
$914$			8.55872i			0.283097i
$915$	1.94568	+	9.83270i	0.0643221	+	0.325059i
$916$		−	81.4731i		−	2.69195i
$917$			20.9198i			0.690831i
$918$	−30.6159	−	46.1174i	−1.01048	−	1.52210i
$919$		−	21.5535i		−	0.710984i	−0.934679	−	0.355492i	$-0.884313\pi$
$919$		−	21.5535i		−	0.710984i	0.934679	−	0.355492i	$-0.115687\pi$
$920$			67.6997i			2.23199i
$921$	−1.19080	−	6.01782i	−0.0392380	−	0.198294i
$922$	45.7281			1.50597
$923$			24.6580i			0.811626i
$924$	−20.1925	−	102.045i	−0.664285	−	3.35704i
$925$	0.683996			0.0224897
$926$			105.764i			3.47561i
$927$	32.3422	−	13.3212i	1.06226	−	0.437526i
$928$	−130.227			−4.27491
$929$	0.124011			0.00406867			0.00203433	−	0.999998i	$-0.499352\pi$
$929$	0.124011			0.00406867			0.00203433	+	0.999998i	$0.499352\pi$
$930$	8.71219	+	44.0281i	0.285684	+	1.44374i
$931$	−7.42036			−0.243193
$932$	20.0668			0.657310
$933$	−3.44768	+	0.682220i	−0.112872	+	0.0223349i
$934$			70.9831i			2.32264i
$935$	45.2032			1.47830
$936$	−56.1484	+	23.1266i	−1.83527	+	0.755917i
$937$	35.9844			1.17556			0.587780	−	0.809021i	$-0.300002\pi$
$937$	35.9844			1.17556			0.587780	+	0.809021i	$0.300002\pi$
$938$	1.42656			0.0465788
$939$	−14.0252	+	2.77529i	−0.457696	+	0.0905681i
$940$	−47.5749			−1.55172
$941$	51.9947			1.69498			0.847489	−	0.530812i	$-0.178113\pi$
$941$	51.9947			1.69498			0.847489	+	0.530812i	$0.178113\pi$
$942$	−94.8598	+	18.7707i	−3.09070	+	0.611582i
$943$	−28.1888			−0.917952
$944$		−	60.0885i		−	1.95571i
$945$	−13.1361	−	19.7872i	−0.427318	−	0.643678i
$946$			167.044i			5.43106i
$947$			37.1697i			1.20785i	0.797040	+	0.603926i	$0.206398\pi$
$947$			37.1697i			1.20785i	−0.797040	+	0.603926i	$0.793602\pi$
$948$	1.57734	+	7.97125i	0.0512295	+	0.258894i
$949$	−33.3499			−1.08258
$950$	3.61249			0.117205
$951$	1.77859	+	8.98829i	0.0576746	+	0.291465i
$952$		−	74.0364i		−	2.39953i
$953$			39.5998i			1.28276i	0.767222	+	0.641382i	$0.221638\pi$
$953$			39.5998i			1.28276i	−0.767222	+	0.641382i	$0.778362\pi$
$954$	40.9780	+	99.4892i	1.32671	+	3.22108i
$955$		−	22.1377i		−	0.716358i
$956$	135.805			4.39224
$957$	−67.1381	+	13.2852i	−2.17027	+	0.429448i
$958$	49.3059			1.59300
$959$	−5.44762			−0.175913
$960$	77.5452	−	15.3445i	2.50276	−	0.495241i
$961$	10.6932			0.344943
$962$	9.73904			0.313999
$963$	−12.7987	−	31.0736i	−0.412433	−	1.00133i
$964$	56.3701			1.81556
$965$		−	52.9616i		−	1.70489i
$966$	35.4854	−	7.02179i	1.14173	−	0.225922i
$967$	27.6755			0.889983			0.444992	−	0.895535i	$-0.353207\pi$
$967$	27.6755			0.889983			0.444992	+	0.895535i	$0.353207\pi$
$968$	153.904			4.94667
$969$	4.07839	+	20.6106i	0.131017	+	0.662109i
$970$	−95.3610			−3.06186
$971$	−11.6774			−0.374745			−0.187373	−	0.982289i	$-0.559997\pi$
$971$	−11.6774			−0.374745			−0.187373	+	0.982289i	$0.559997\pi$
$972$	−67.7896	−	45.7850i	−2.17435	−	1.46856i
$973$			21.6871i			0.695256i
$974$	64.4376			2.06472
$975$	0.340726	+	1.72190i	0.0109120	+	0.0551449i
$976$			35.3366i			1.13110i
$977$	−24.4707			−0.782886			−0.391443	−	0.920202i	$-0.628024\pi$
$977$	−24.4707			−0.782886			−0.391443	+	0.920202i	$0.628024\pi$
$978$	−8.59791	−	43.4505i	−0.274931	−	1.38939i
$979$		−	40.8037i		−	1.30409i
$980$			27.1321i			0.866704i
$981$	−28.2760	+	11.6464i	−0.902783	+	0.371842i
$982$		−	26.0005i		−	0.829708i
$983$			10.8033i			0.344571i	0.985047	+	0.172285i	$0.0551151\pi$
$983$			10.8033i			0.344571i	−0.985047	+	0.172285i	$0.944885\pi$
$984$	22.8578	+	115.514i	0.728679	+	3.68246i
$985$			13.5713i			0.432419i
$986$	−78.7077			−2.50656
$987$	3.05382	+	15.4328i	0.0972041	+	0.491232i
$988$	37.2423			1.18484
$989$	−42.0587			−1.33739
$990$	85.3075	−	35.1368i	2.71125	−	1.11672i
$991$			27.5383i			0.874784i	0.899271	+	0.437392i	$0.144098\pi$
$991$			27.5383i			0.874784i	−0.899271	+	0.437392i	$0.855902\pi$
$992$			79.4287i			2.52186i
$993$	0.874388	+	4.41882i	0.0277479	+	0.140227i
$994$	−61.3597			−1.94621
$995$			56.9089i			1.80413i
$996$	−59.1096	+	11.6965i	−1.87296	+	0.370618i
$997$			12.3927i			0.392480i	0.980556	+	0.196240i	$0.0628732\pi$
$997$			12.3927i			0.392480i	−0.980556	+	0.196240i	$0.937127\pi$
$998$		−	93.6346i		−	2.96395i
$999$	4.49072	+	6.76447i	0.142080	+	0.214018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.d.a.632.1	✓	68
3.2	odd	2	inner	633.2.d.a.632.67	yes	68
211.210	odd	2	inner	633.2.d.a.632.68	yes	68
633.632	even	2	inner	633.2.d.a.632.2	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.d.a.632.1	✓	68	1.1	even	1	trivial
633.2.d.a.632.2	yes	68	633.632	even	2	inner
633.2.d.a.632.67	yes	68	3.2	odd	2	inner
633.2.d.a.632.68	yes	68	211.210	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)

\(f(q)\)	\(=\)	\(q-2.69215 q^{2} +(-0.336216 - 1.69911i) q^{3} +5.24765 q^{4} +2.13595i q^{5} +(0.905142 + 4.57424i) q^{6} +2.13995i q^{7} -8.74315 q^{8} +(-2.77392 + 1.14253i) q^{9} +O(q^{10})\)	\(q-2.69215 q^{2} +(-0.336216 - 1.69911i) q^{3} +5.24765 q^{4} +2.13595i q^{5} +(0.905142 + 4.57424i) q^{6} +2.13995i q^{7} -8.74315 q^{8} +(-2.77392 + 1.14253i) q^{9} -5.75028i q^{10} -5.34816i q^{11} +(-1.76434 - 8.91631i) q^{12} -2.31513 q^{13} -5.76105i q^{14} +(3.62920 - 0.718139i) q^{15} +13.0425 q^{16} +3.95708 q^{17} +(7.46779 - 3.07586i) q^{18} -3.06546 q^{19} +11.2087i q^{20} +(3.63599 - 0.719484i) q^{21} +14.3980i q^{22} -3.62517 q^{23} +(2.93959 + 14.8555i) q^{24} +0.437736 q^{25} +6.23267 q^{26} +(2.87392 + 4.32904i) q^{27} +11.2297i q^{28} +7.38829 q^{29} +(-9.77033 + 1.93333i) q^{30} -4.50630i q^{31} -17.6261 q^{32} +(-9.08709 + 1.79814i) q^{33} -10.6530 q^{34} -4.57081 q^{35} +(-14.5566 + 5.99561i) q^{36} +1.56258 q^{37} +8.25268 q^{38} +(0.778384 + 3.93365i) q^{39} -18.6749i q^{40} +7.77584 q^{41} +(-9.78863 + 1.93695i) q^{42} +11.6018 q^{43} -28.0653i q^{44} +(-2.44039 - 5.92494i) q^{45} +9.75949 q^{46} +4.24446i q^{47} +(-4.38511 - 22.1607i) q^{48} +2.42063 q^{49} -1.17845 q^{50} +(-1.33043 - 6.72349i) q^{51} -12.1490 q^{52} +13.3224i q^{53} +(-7.73701 - 11.6544i) q^{54} +11.4234 q^{55} -18.7099i q^{56} +(1.03066 + 5.20855i) q^{57} -19.8904 q^{58} -4.60711i q^{59} +(19.0448 - 3.76854i) q^{60} +2.70933i q^{61} +12.1316i q^{62} +(-2.44496 - 5.93603i) q^{63} +21.3670 q^{64} -4.94499i q^{65} +(24.4638 - 4.84085i) q^{66} +0.247622i q^{67} +20.7654 q^{68} +(1.21884 + 6.15955i) q^{69} +12.3053 q^{70} -10.6508i q^{71} +(24.2528 - 9.98933i) q^{72} +14.4052 q^{73} -4.20669 q^{74} +(-0.147174 - 0.743759i) q^{75} -16.0865 q^{76} +11.4448 q^{77} +(-2.09552 - 10.5900i) q^{78} -0.894007 q^{79} +27.8582i q^{80} +(6.38924 - 6.33858i) q^{81} -20.9337 q^{82} -6.62938i q^{83} +(19.0804 - 3.77560i) q^{84} +8.45210i q^{85} -31.2339 q^{86} +(-2.48406 - 12.5535i) q^{87} +46.7598i q^{88} +7.62948 q^{89} +(6.56988 + 15.9508i) q^{90} -4.95425i q^{91} -19.0236 q^{92} +(-7.65668 + 1.51509i) q^{93} -11.4267i q^{94} -6.54767i q^{95} +(5.92618 + 29.9486i) q^{96} -16.5837i q^{97} -6.51670 q^{98} +(6.11045 + 14.8354i) 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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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