LMFDB - Embedded newform 201.2.d.a.200.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.200");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 7 x^{18} + 32 x^{16} + 128 x^{14} + 423 x^{12} + 1186 x^{10} + 3807 x^{8} + 10368 x^{6} + \cdots + 59049 $ x^20 + 7x^18 + 32x^16 + 128x^14 + 423x^12 + 1186x^10 + 3807x^8 + 10368x^6 + 23328x^4 + 45927*x^2 + 59049
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.8
Root			$1.58783 - 0.691953i$ of defining polynomial
Character	$\chi$	$=$	201.200
Dual form			201.2.d.a.200.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.758634 q^{2} +(1.58783 + 0.691953i) q^{3} -1.42447 q^{4} +1.15744 q^{5} +(-1.20458 - 0.524939i) q^{6} -4.81799i q^{7} +2.59792 q^{8} +(2.04240 + 2.19741i) q^{9} +O(q^{10})$	\(q-0.758634 q^{2} +(1.58783 + 0.691953i) q^{3} -1.42447 q^{4} +1.15744 q^{5} +(-1.20458 - 0.524939i) q^{6} -4.81799i q^{7} +2.59792 q^{8} +(2.04240 + 2.19741i) q^{9} -0.878075 q^{10} +4.12483 q^{11} +(-2.26182 - 0.985670i) q^{12} +3.26028i q^{13} +3.65509i q^{14} +(1.83782 + 0.800896i) q^{15} +0.878075 q^{16} +4.51999i q^{17} +(-1.54944 - 1.66703i) q^{18} -2.83364 q^{19} -1.64875 q^{20} +(3.33382 - 7.65014i) q^{21} -3.12924 q^{22} -4.65183i q^{23} +(4.12506 + 1.79764i) q^{24} -3.66033 q^{25} -2.47336i q^{26} +(1.72248 + 4.90235i) q^{27} +6.86310i q^{28} -2.59854i q^{29} +(-1.39423 - 0.607587i) q^{30} -4.91295i q^{31} -5.86198 q^{32} +(6.54953 + 2.85419i) q^{33} -3.42902i q^{34} -5.57654i q^{35} +(-2.90935 - 3.13015i) q^{36} +2.03607 q^{37} +2.14969 q^{38} +(-2.25597 + 5.17677i) q^{39} +3.00695 q^{40} -3.18530 q^{41} +(-2.52915 + 5.80366i) q^{42} -4.89176i q^{43} -5.87572 q^{44} +(2.36396 + 2.54337i) q^{45} +3.52904i q^{46} +9.17850i q^{47} +(1.39423 + 0.607587i) q^{48} -16.2130 q^{49} +2.77685 q^{50} +(-3.12762 + 7.17697i) q^{51} -4.64419i q^{52} -8.07074 q^{53} +(-1.30673 - 3.71909i) q^{54} +4.77426 q^{55} -12.5168i q^{56} +(-4.49933 - 1.96074i) q^{57} +1.97134i q^{58} +7.67711i q^{59} +(-2.61793 - 1.14086i) q^{60} -1.31014i q^{61} +3.72713i q^{62} +(10.5871 - 9.84026i) q^{63} +2.69095 q^{64} +3.77359i q^{65} +(-4.96870 - 2.16529i) q^{66} +(-7.63852 + 2.94161i) q^{67} -6.43861i q^{68} +(3.21885 - 7.38632i) q^{69} +4.23055i q^{70} +6.86818i q^{71} +(5.30600 + 5.70869i) q^{72} +1.65301 q^{73} -1.54463 q^{74} +(-5.81197 - 2.53278i) q^{75} +4.03644 q^{76} -19.8734i q^{77} +(1.71145 - 3.92728i) q^{78} +6.10187i q^{79} +1.01632 q^{80} +(-0.657196 + 8.97597i) q^{81} +2.41648 q^{82} +11.5731i q^{83} +(-4.74894 + 10.8974i) q^{84} +5.23162i q^{85} +3.71105i q^{86} +(1.79807 - 4.12603i) q^{87} +10.7160 q^{88} -5.56987i q^{89} +(-1.79338 - 1.92949i) q^{90} +15.7080 q^{91} +6.62642i q^{92} +(3.39953 - 7.80092i) q^{93} -6.96312i q^{94} -3.27977 q^{95} +(-9.30783 - 4.05622i) q^{96} +11.5124i q^{97} +12.2997 q^{98} +(8.42457 + 9.06394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.758634			−0.536435			−0.268218	−	0.963358i	$-0.586435\pi$
$2$	−0.758634			−0.536435			−0.268218	+	0.963358i	$0.586435\pi$
$3$	1.58783	+	0.691953i	0.916733	+	0.399499i
$3$	1.58783	+	0.691953i	0.916733	+	0.399499i
$4$	−1.42447			−0.712237
$5$	1.15744			0.517624			0.258812	−	0.965928i	$-0.416669\pi$
$5$	1.15744			0.517624			0.258812	+	0.965928i	$0.416669\pi$
$6$	−1.20458	−	0.524939i	−0.491768	−	0.214306i
$7$		−	4.81799i		−	1.82103i	−0.413479	−	0.910514i	$-0.635686\pi$
$7$		−	4.81799i		−	1.82103i	0.413479	−	0.910514i	$-0.364314\pi$
$8$	2.59792			0.918505
$9$	2.04240	+	2.19741i	0.680800	+	0.732469i
$10$	−0.878075			−0.277672
$11$	4.12483			1.24368			0.621842	−	0.783143i	$-0.286385\pi$
$11$	4.12483			1.24368			0.621842	+	0.783143i	$0.286385\pi$
$12$	−2.26182	−	0.985670i	−0.652932	−	0.284538i
$13$			3.26028i			0.904240i	0.891957	+	0.452120i	$0.149332\pi$
$13$			3.26028i			0.904240i	−0.891957	+	0.452120i	$0.850668\pi$
$14$			3.65509i			0.976864i
$15$	1.83782	+	0.800896i	0.474523	+	0.206790i
$16$	0.878075			0.219519
$17$			4.51999i			1.09626i	0.836394	+	0.548129i	$0.184660\pi$
$17$			4.51999i			1.09626i	−0.836394	+	0.548129i	$0.815340\pi$
$18$	−1.54944	−	1.66703i	−0.365205	−	0.392922i
$19$	−2.83364			−0.650081			−0.325040	−	0.945700i	$-0.605378\pi$
$19$	−2.83364			−0.650081			−0.325040	+	0.945700i	$0.605378\pi$
$20$	−1.64875			−0.368671
$21$	3.33382	−	7.65014i	0.727500	−	1.66940i
$22$	−3.12924			−0.667156
$23$		−	4.65183i		−	0.969975i	−0.874521	−	0.484987i	$-0.838824\pi$
$23$		−	4.65183i		−	0.969975i	0.874521	−	0.484987i	$-0.161176\pi$
$24$	4.12506	+	1.79764i	0.842024	+	0.366942i
$25$	−3.66033			−0.732066
$26$		−	2.47336i		−	0.485066i
$27$	1.72248	+	4.90235i	0.331491	+	0.943458i
$28$			6.86310i			1.29700i
$29$		−	2.59854i		−	0.482536i	−0.970458	−	0.241268i	$-0.922437\pi$
$29$		−	2.59854i		−	0.482536i	0.970458	−	0.241268i	$-0.0775633\pi$
$30$	−1.39423	−	0.607587i	−0.254551	−	0.110930i
$31$		−	4.91295i		−	0.882391i	−0.897411	−	0.441196i	$-0.854554\pi$
$31$		−	4.91295i		−	0.882391i	0.897411	−	0.441196i	$-0.145446\pi$
$32$	−5.86198			−1.03626
$33$	6.54953	+	2.85419i	1.14013	+	0.496851i
$34$		−	3.42902i		−	0.588072i
$35$		−	5.57654i		−	0.942607i
$36$	−2.90935	−	3.13015i	−0.484891	−	0.521692i
$37$	2.03607			0.334728			0.167364	−	0.985895i	$-0.446474\pi$
$37$	2.03607			0.334728			0.167364	+	0.985895i	$0.446474\pi$
$38$	2.14969			0.348726
$39$	−2.25597	+	5.17677i	−0.361244	+	0.828947i
$40$	3.00695			0.475440
$41$	−3.18530			−0.497460			−0.248730	−	0.968573i	$-0.580013\pi$
$41$	−3.18530			−0.497460			−0.248730	+	0.968573i	$0.580013\pi$
$42$	−2.52915	+	5.80366i	−0.390256	+	0.895524i
$43$		−	4.89176i		−	0.745986i	−0.927834	−	0.372993i	$-0.878332\pi$
$43$		−	4.89176i		−	0.745986i	0.927834	−	0.372993i	$-0.121668\pi$
$44$	−5.87572			−0.885798
$45$	2.36396	+	2.54337i	0.352398	+	0.379143i
$46$			3.52904i			0.520329i
$47$			9.17850i			1.33882i	0.742893	+	0.669411i	$0.233453\pi$
$47$			9.17850i			1.33882i	−0.742893	+	0.669411i	$0.766547\pi$
$48$	1.39423	+	0.607587i	0.201240	+	0.0876976i
$49$	−16.2130			−2.31614
$50$	2.77685			0.392706
$51$	−3.12762	+	7.17697i	−0.437955	+	1.00498i
$52$		−	4.64419i		−	0.644033i
$53$	−8.07074			−1.10860			−0.554301	−	0.832316i	$-0.687014\pi$
$53$	−8.07074			−1.10860			−0.554301	+	0.832316i	$0.687014\pi$
$54$	−1.30673	−	3.71909i	−0.177824	−	0.506104i
$55$	4.77426			0.643761
$56$		−	12.5168i		−	1.67262i
$57$	−4.49933	−	1.96074i	−0.595951	−	0.259707i
$58$			1.97134i			0.258850i
$59$			7.67711i			0.999475i	0.866177	+	0.499737i	$0.166570\pi$
$59$			7.67711i			0.999475i	−0.866177	+	0.499737i	$0.833430\pi$
$60$	−2.61793	−	1.14086i	−0.337973	−	0.147284i
$61$		−	1.31014i		−	0.167746i	−0.996476	−	0.0838728i	$-0.973271\pi$
$61$		−	1.31014i		−	0.167746i	0.996476	−	0.0838728i	$-0.0267289\pi$
$62$			3.72713i			0.473346i
$63$	10.5871	−	9.84026i	1.33385	−	1.23976i
$64$	2.69095			0.336369
$65$			3.77359i			0.468056i
$66$	−4.96870	−	2.16529i	−0.611605	−	0.266529i
$67$	−7.63852	+	2.94161i	−0.933193	+	0.359375i
$67$	−7.63852	+	2.94161i	−0.933193	+	0.359375i
$68$		−	6.43861i		−	0.780796i
$69$	3.21885	−	7.38632i	0.387504	−	0.889208i
$70$			4.23055i			0.505648i
$71$			6.86818i			0.815103i	0.913182	+	0.407551i	$0.133617\pi$
$71$			6.86818i			0.815103i	−0.913182	+	0.407551i	$0.866383\pi$
$72$	5.30600	+	5.70869i	0.625318	+	0.672776i
$73$	1.65301			0.193470			0.0967352	−	0.995310i	$-0.469160\pi$
$73$	1.65301			0.193470			0.0967352	+	0.995310i	$0.469160\pi$
$74$	−1.54463			−0.179560
$75$	−5.81197	−	2.53278i	−0.671109	−	0.292460i
$76$	4.03644			0.463012
$77$		−	19.8734i		−	2.26478i
$78$	1.71145	−	3.92728i	0.193784	−	0.444677i
$79$			6.10187i			0.686514i	0.939242	+	0.343257i	$0.111530\pi$
$79$			6.10187i			0.686514i	−0.939242	+	0.343257i	$0.888470\pi$
$80$	1.01632			0.113628
$81$	−0.657196	+	8.97597i	−0.0730217	+	0.997330i
$82$	2.41648			0.266855
$83$			11.5731i			1.27032i	0.772382	+	0.635159i	$0.219065\pi$
$83$			11.5731i			1.27032i	−0.772382	+	0.635159i	$0.780935\pi$
$84$	−4.74894	+	10.8974i	−0.518152	+	1.18901i
$85$			5.23162i			0.567449i
$86$			3.71105i			0.400173i
$87$	1.79807	−	4.12603i	0.192773	−	0.442357i
$88$	10.7160			1.14233
$89$		−	5.56987i		−	0.590405i	−0.955435	−	0.295202i	$-0.904613\pi$
$89$		−	5.56987i		−	0.590405i	0.955435	−	0.295202i	$-0.0953871\pi$
$90$	−1.79338	−	1.92949i	−0.189039	−	0.203386i
$91$	15.7080			1.64665
$92$			6.62642i			0.690852i
$93$	3.39953	−	7.80092i	0.352515	−	0.808918i
$94$		−	6.96312i		−	0.718191i
$95$	−3.27977			−0.336497
$96$	−9.30783	−	4.05622i	−0.949976	−	0.413986i
$97$			11.5124i			1.16890i	0.811429	+	0.584451i	$0.198690\pi$
$97$			11.5124i			1.16890i	−0.811429	+	0.584451i	$0.801310\pi$
$98$	12.2997			1.24246
$99$	8.42457	+	9.06394i	0.846701	+	0.910960i
$100$	5.21404			0.521404
$101$	17.3147			1.72287			0.861437	−	0.507864i	$-0.169565\pi$
$101$	17.3147			1.72287			0.861437	+	0.507864i	$0.169565\pi$
$102$	2.37272	−	5.44469i	0.234934	−	0.539105i
$103$	−9.61484			−0.947378			−0.473689	−	0.880692i	$-0.657078\pi$
$103$	−9.61484			−0.947378			−0.473689	+	0.880692i	$0.657078\pi$
$104$			8.46997i			0.830549i
$105$	3.85871	−	8.85459i	0.376571	−	0.864120i
$106$	6.12274			0.594693
$107$		−	19.8203i		−	1.91610i	−0.286606	−	0.958049i	$-0.592527\pi$
$107$		−	19.8203i		−	1.91610i	0.286606	−	0.958049i	$-0.407473\pi$
$108$	−2.45363	−	6.98327i	−0.236101	−	0.671966i
$109$		−	14.2590i		−	1.36576i	−0.730530	−	0.682881i	$-0.760727\pi$
$109$		−	14.2590i		−	1.36576i	0.730530	−	0.682881i	$-0.239273\pi$
$110$	−3.62191			−0.345336
$111$	3.23293	+	1.40887i	0.306857	+	0.133724i
$112$		−	4.23055i		−	0.399750i
$113$	−0.668111			−0.0628506			−0.0314253	−	0.999506i	$-0.510005\pi$
$113$	−0.668111			−0.0628506			−0.0314253	+	0.999506i	$0.510005\pi$
$114$	3.41335	+	1.48749i	0.319689	+	0.139316i
$115$		−	5.38423i		−	0.502082i
$116$			3.70155i			0.343680i
$117$	−7.16417	+	6.65881i	−0.662328	+	0.615607i
$118$		−	5.82412i		−	0.536154i
$119$	21.7772			1.99632
$120$	4.77451	+	2.08067i	0.435852	+	0.189938i
$121$	6.01426			0.546751
$122$			0.993913i			0.0899847i
$123$	−5.05771	−	2.20408i	−0.456039	−	0.198735i
$124$			6.99837i			0.628472i
$125$	−10.0238			−0.896558
$126$	−8.03172	+	7.46516i	−0.715522	+	0.665049i
$127$	9.74513			0.864740			0.432370	−	0.901696i	$-0.357677\pi$
$127$	9.74513			0.864740			0.432370	+	0.901696i	$0.357677\pi$
$128$	9.68252			0.855822
$129$	3.38487	−	7.76727i	0.298021	−	0.683870i
$130$		−	2.86277i		−	0.251082i
$131$			12.1432i			1.06095i	0.847700	+	0.530476i	$0.177987\pi$
$131$			12.1432i			1.06095i	−0.847700	+	0.530476i	$0.822013\pi$
$132$	−9.32964	−	4.06572i	−0.812041	−	0.353876i
$133$			13.6524i			1.18382i
$134$	5.79484	−	2.23160i	0.500598	−	0.192781i
$135$	1.99367	+	5.67419i	0.171588	+	0.488356i
$136$			11.7426i			1.00692i
$137$	−15.6350			−1.33579			−0.667895	−	0.744255i	$-0.732805\pi$
$137$	−15.6350			−1.33579			−0.667895	+	0.744255i	$0.732805\pi$
$138$	−2.44193	+	5.60351i	−0.207871	+	0.477003i
$139$		−	22.5484i		−	1.91253i	−0.292507	−	0.956263i	$-0.594489\pi$
$139$		−	22.5484i		−	1.91253i	0.292507	−	0.956263i	$-0.405511\pi$
$140$			7.94364i			0.671360i
$141$	−6.35109	+	14.5739i	−0.534858	+	1.22734i
$142$		−	5.21043i		−	0.437250i
$143$			13.4481i			1.12459i
$144$	1.79338	+	1.92949i	0.149448	+	0.160791i
$145$		−	3.00766i		−	0.249772i
$146$	−1.25403			−0.103784
$147$	−25.7435	−	11.2186i	−2.12328	−	0.925297i
$148$	−2.90033			−0.238406
$149$			0.303481i			0.0248622i	0.999923	+	0.0124311i	$0.00395704\pi$
$149$			0.303481i			0.0248622i	−0.999923	+	0.0124311i	$0.996043\pi$
$150$	4.40916	+	1.92145i	0.360007	+	0.156886i
$151$	−12.6440			−1.02895			−0.514476	−	0.857505i	$-0.672013\pi$
$151$	−12.6440			−1.02895			−0.514476	+	0.857505i	$0.672013\pi$
$152$	−7.36157			−0.597102
$153$	−9.93225	+	9.23163i	−0.802975	+	0.746333i
$154$			15.0766i			1.21491i
$155$		−	5.68645i		−	0.456747i
$156$	3.21356	−	7.37418i	0.257291	−	0.590407i
$157$	−18.2548			−1.45689			−0.728445	−	0.685104i	$-0.759757\pi$
$157$	−18.2548			−1.45689			−0.728445	+	0.685104i	$0.759757\pi$
$158$		−	4.62909i		−	0.368270i
$159$	−12.8150	−	5.58458i	−1.01629	−	0.442886i
$160$	−6.78491			−0.536394
$161$	−22.4125			−1.76635
$162$	0.498571	−	6.80948i	0.0391714	−	0.535003i
$163$	9.33212			0.730948			0.365474	−	0.930822i	$-0.380907\pi$
$163$	9.33212			0.730948			0.365474	+	0.930822i	$0.380907\pi$
$164$	4.53738			0.354310
$165$	7.58070	+	3.30356i	0.590157	+	0.257182i
$166$		−	8.77978i		−	0.681443i
$167$		−	5.25688i		−	0.406790i	−0.979097	−	0.203395i	$-0.934803\pi$
$167$		−	5.25688i		−	0.406790i	0.979097	−	0.203395i	$-0.0651975\pi$
$168$	8.66101	−	19.8745i	0.668212	−	1.53335i
$169$	2.37054			0.182349
$170$		−	3.96889i		−	0.304400i
$171$	−5.78742	−	6.22665i	−0.442575	−	0.476164i
$172$			6.96818i			0.531319i
$173$		−	3.77167i		−	0.286755i	−0.989668	−	0.143378i	$-0.954204\pi$
$173$		−	3.77167i		−	0.286755i	0.989668	−	0.143378i	$-0.0457963\pi$
$174$	−1.36407	+	3.13015i	−0.103410	+	0.237296i
$175$			17.6354i			1.33311i
$176$	3.62191			0.273012
$177$	−5.31220	+	12.1899i	−0.399290	+	0.916252i
$178$			4.22549i			0.316714i
$179$	2.73551			0.204461			0.102231	−	0.994761i	$-0.467402\pi$
$179$	2.73551			0.204461			0.102231	+	0.994761i	$0.467402\pi$
$180$	−3.36740	−	3.62297i	−0.250991	−	0.270040i
$181$	4.94757			0.367750			0.183875	−	0.982950i	$-0.441136\pi$
$181$	4.94757			0.367750			0.183875	+	0.982950i	$0.441136\pi$
$182$	−11.9166			−0.883319
$183$	0.906553	−	2.08027i	0.0670143	−	0.153778i
$184$		−	12.0851i		−	0.890926i
$185$	2.35664			0.173263
$186$	−2.57900	+	5.91804i	−0.189101	+	0.433932i
$187$			18.6442i			1.36340i
$188$		−	13.0745i		−	0.953558i
$189$	23.6195	−	8.29889i	1.71806	−	0.603655i
$190$	2.48815			0.180509
$191$	7.64457			0.553142			0.276571	−	0.960994i	$-0.410802\pi$
$191$	7.64457			0.553142			0.276571	+	0.960994i	$0.410802\pi$
$192$	4.27277	+	1.86201i	0.308361	+	0.134379i
$193$	14.8242			1.06707			0.533535	−	0.845778i	$-0.320863\pi$
$193$	14.8242			1.06707			0.533535	+	0.845778i	$0.320863\pi$
$194$		−	8.73366i		−	0.627040i
$195$	−2.61115	+	5.99182i	−0.186988	+	0.429083i
$196$	23.0950			1.64964
$197$	12.9008			0.919147			0.459574	−	0.888140i	$-0.348002\pi$
$197$	12.9008			0.919147			0.459574	+	0.888140i	$0.348002\pi$
$198$	−6.39116	−	6.87622i	−0.454200	−	0.488671i
$199$	2.41103			0.170913			0.0854567	−	0.996342i	$-0.472765\pi$
$199$	2.41103			0.170913			0.0854567	+	0.996342i	$0.472765\pi$
$200$	−9.50925			−0.672406
$201$	−14.1641	−	0.614727i	−0.999060	−	0.0433595i
$202$	−13.1355			−0.924211
$203$	−12.5197			−0.878712
$204$	4.45522	−	10.2234i	0.311927	−	0.715782i
$205$	−3.68680			−0.257497
$206$	7.29415			0.508207
$207$	10.2220	−	9.50091i	0.710476	−	0.660359i
$208$			2.86277i			0.198498i
$209$	−11.6883			−0.808495
$210$	−2.92735	+	6.71740i	−0.202006	+	0.463544i
$211$	24.3266			1.67471			0.837354	−	0.546660i	$-0.184101\pi$
$211$	24.3266			1.67471			0.837354	+	0.546660i	$0.184101\pi$
$212$	11.4966			0.789587
$213$	−4.75246	+	10.9055i	−0.325633	+	0.747232i
$214$			15.0363i			1.02786i
$215$		−	5.66193i		−	0.386140i
$216$	4.47487	+	12.7359i	0.304476	+	0.866571i
$217$	−23.6705			−1.60686
$218$			10.8173i			0.732643i
$219$	2.62470	+	1.14381i	0.177361	+	0.0772913i
$220$	−6.80081			−0.458510
$221$	−14.7364			−0.991281
$222$	−2.45261	−	1.06881i	−0.164609	−	0.0717341i
$223$	4.23865			0.283841			0.141920	−	0.989878i	$-0.454672\pi$
$223$	4.23865			0.283841			0.141920	+	0.989878i	$0.454672\pi$
$224$			28.2430i			1.88706i
$225$	−7.47586	−	8.04323i	−0.498391	−	0.536215i
$226$	0.506852			0.0337153
$227$		−	13.8151i		−	0.916938i	−0.888710	−	0.458469i	$-0.848398\pi$
$227$		−	13.8151i		−	0.916938i	0.888710	−	0.458469i	$-0.151602\pi$
$228$	6.40918	+	2.79303i	0.424458	+	0.184973i
$229$		−	11.3573i		−	0.750514i	−0.926921	−	0.375257i	$-0.877554\pi$
$229$		−	11.3573i		−	0.750514i	0.926921	−	0.375257i	$-0.122446\pi$
$230$			4.08466i			0.269335i
$231$	13.7515	−	31.5556i	0.904780	−	2.07620i
$232$		−	6.75080i		−	0.443212i
$233$	−12.0774			−0.791220			−0.395610	−	0.918419i	$-0.629467\pi$
$233$	−12.0774			−0.791220			−0.395610	+	0.918419i	$0.629467\pi$
$234$	5.43499	−	5.05160i	0.355296	−	0.330233i
$235$			10.6236i			0.693006i
$236$		−	10.9358i		−	0.711863i
$237$	−4.22221	+	9.68872i	−0.274262	+	0.629350i
$238$	−16.5210			−1.07089
$239$	15.1469			0.979770			0.489885	−	0.871787i	$-0.337039\pi$
$239$	15.1469			0.979770			0.489885	+	0.871787i	$0.337039\pi$
$240$	1.61374	+	0.703247i	0.104167	+	0.0453944i
$241$	3.55906			0.229259			0.114630	−	0.993408i	$-0.463432\pi$
$241$	3.55906			0.229259			0.114630	+	0.993408i	$0.463432\pi$
$242$	−4.56262			−0.293297
$243$	−7.25447	+	13.7976i	−0.465374	+	0.885114i
$244$			1.86625i			0.119475i
$245$	−18.7656			−1.19889
$246$	3.83695	+	1.67209i	0.244635	+	0.106609i
$247$		−	9.23846i		−	0.587829i
$248$		−	12.7635i		−	0.810481i
$249$	−8.00808	+	18.3762i	−0.507491	+	1.16454i
$250$	7.60442			0.480946
$251$	30.2834			1.91147			0.955736	−	0.294225i	$-0.0950614\pi$
$251$	30.2834			1.91147			0.955736	+	0.294225i	$0.0950614\pi$
$252$	−15.0810	+	14.0172i	−0.950015	+	0.883000i
$253$		−	19.1880i		−	1.20634i
$254$	−7.39299			−0.463877
$255$	−3.62004	+	8.30692i	−0.226696	+	0.520200i
$256$	−12.7274			−0.795462
$257$			17.4692i			1.08970i	0.838533	+	0.544851i	$0.183414\pi$
$257$			17.4692i			1.08970i	−0.838533	+	0.544851i	$0.816586\pi$
$258$	−2.56788	+	5.89252i	−0.159869	+	0.366852i
$259$		−	9.80977i		−	0.609549i
$260$		−	5.37538i		−	0.333367i
$261$	5.71004	−	5.30726i	0.353443	−	0.328511i
$262$		−	9.21221i		−	0.569132i
$263$		−	27.0698i		−	1.66920i	−0.550859	−	0.834598i	$-0.685700\pi$
$263$		−	27.0698i		−	1.66920i	0.550859	−	0.834598i	$-0.314300\pi$
$264$	17.0152	+	7.41497i	1.04721	+	0.456360i
$265$	−9.34142			−0.573839
$266$		−	10.3572i		−	0.635040i
$267$	3.85409	−	8.84400i	0.235866	−	0.541244i
$268$	10.8809	−	4.19025i	0.664655	−	0.255960i
$269$			24.4769i			1.49238i	0.665733	+	0.746190i	$0.268119\pi$
$269$			24.4769i			1.49238i	−0.665733	+	0.746190i	$0.731881\pi$
$270$	−1.51247	−	4.30463i	−0.0920458	−	0.261972i
$271$			5.13812i			0.312118i	0.987748	+	0.156059i	$0.0498791\pi$
$271$			5.13812i			0.312118i	−0.987748	+	0.156059i	$0.950121\pi$
$272$			3.96889i			0.240649i
$273$	24.9416	+	10.8692i	1.50954	+	0.657834i
$274$	11.8613			0.716565
$275$	−15.0982			−0.910459
$276$	−4.58517	+	10.5216i	−0.275995	+	0.633327i
$277$	−14.2399			−0.855593			−0.427797	−	0.903875i	$-0.640710\pi$
$277$	−14.2399			−0.855593			−0.427797	+	0.903875i	$0.640710\pi$
$278$			17.1060i			1.02595i
$279$	10.7957	−	10.0342i	0.646324	−	0.600732i
$280$		−	14.4874i		−	0.865789i
$281$	19.5713			1.16752			0.583762	−	0.811925i	$-0.301580\pi$
$281$	19.5713			1.16752			0.583762	+	0.811925i	$0.301580\pi$
$282$	4.81815	−	11.0562i	0.286917	−	0.658390i
$283$	−29.1908			−1.73521			−0.867607	−	0.497251i	$-0.834343\pi$
$283$	−29.1908			−1.73521			−0.867607	+	0.497251i	$0.834343\pi$
$284$		−	9.78354i		−	0.580546i
$285$	−5.20771	−	2.26945i	−0.308478	−	0.134430i
$286$		−	10.2022i		−	0.603270i
$287$			15.3467i			0.905889i
$288$	−11.9725	−	12.8812i	−0.705488	−	0.759030i
$289$	−3.43029			−0.201782
$290$			2.28171i			0.133987i
$291$	−7.96601	+	18.2796i	−0.466976	+	1.07157i
$292$	−2.35467			−0.137797
$293$			5.73291i			0.334920i	0.985879	+	0.167460i	$0.0535566\pi$
$293$			5.73291i			0.334920i	−0.985879	+	0.167460i	$0.946443\pi$
$294$	19.5299	+	8.51084i	1.13900	+	0.496362i
$295$			8.88581i			0.517352i
$296$	5.28956			0.307449
$297$	7.10495	+	20.2214i	0.412271	+	1.17336i
$298$		−	0.230231i		−	0.0133369i
$299$	15.1663			0.877090
$300$	8.27901	+	3.60787i	0.477989	+	0.208301i
$301$	−23.5684			−1.35846
$302$	9.59214			0.551966
$303$	27.4927	+	11.9809i	1.57942	+	0.688288i
$304$	−2.48815			−0.142705
$305$		−	1.51641i		−	0.0868291i
$306$	7.53495	−	7.00343i	0.430744	−	0.400359i
$307$	14.1006			0.804761			0.402381	−	0.915472i	$-0.368183\pi$
$307$	14.1006			0.804761			0.402381	+	0.915472i	$0.368183\pi$
$308$			28.3091i			1.61306i
$309$	−15.2667	−	6.65302i	−0.868493	−	0.378477i
$310$			4.31394i			0.245015i
$311$	−0.918663			−0.0520926			−0.0260463	−	0.999661i	$-0.508292\pi$
$311$	−0.918663			−0.0520926			−0.0260463	+	0.999661i	$0.508292\pi$
$312$	−5.86082	+	13.4489i	−0.331804	+	0.761392i
$313$		−	16.0015i		−	0.904460i	−0.891901	−	0.452230i	$-0.850629\pi$
$313$		−	16.0015i		−	0.904460i	0.891901	−	0.452230i	$-0.149371\pi$
$314$	13.8487			0.781527
$315$	12.2539	−	11.3895i	0.690431	−	0.641727i
$316$		−	8.69196i		−	0.488961i
$317$			7.86411i			0.441692i	0.975309	+	0.220846i	$0.0708819\pi$
$317$			7.86411i			0.441692i	−0.975309	+	0.220846i	$0.929118\pi$
$318$	9.72187	+	4.23665i	0.545175	+	0.237580i
$319$		−	10.7185i		−	0.600123i
$320$	3.11462			0.174113
$321$	13.7147	−	31.4712i	0.765480	−	1.75655i
$322$	17.0029			0.947533
$323$		−	12.8080i		−	0.712656i
$324$	0.936158	−	12.7860i	0.0520088	−	0.710336i
$325$		−	11.9337i		−	0.661963i
$326$	−7.07967			−0.392106
$327$	9.86655	−	22.6408i	0.545621	−	1.25204i
$328$	−8.27517			−0.456920
$329$	44.2219			2.43803
$330$	−5.75098	−	2.50620i	−0.316581	−	0.137962i
$331$			3.51798i			0.193365i	0.995315	+	0.0966827i	$0.0308232\pi$
$331$			3.51798i			0.193365i	−0.995315	+	0.0966827i	$0.969177\pi$
$332$		−	16.4856i		−	0.904767i
$333$	4.15848	+	4.47408i	0.227883	+	0.245178i
$334$			3.98805i			0.218216i
$335$	−8.84114	+	3.40474i	−0.483043	+	0.186021i
$336$	2.92735	−	6.71740i	0.159700	−	0.366464i
$337$			25.6874i			1.39928i	0.714494	+	0.699642i	$0.246657\pi$
$337$			25.6874i			1.39928i	−0.714494	+	0.699642i	$0.753343\pi$
$338$	−1.79838			−0.0978187
$339$	−1.06085	−	0.462301i	−0.0576172	−	0.0251088i
$340$		−	7.45231i		−	0.404158i
$341$		−	20.2651i		−	1.09742i
$342$	4.39054	+	4.72375i	0.237413	+	0.255431i
$343$			44.3881i			2.39673i
$344$		−	12.7084i		−	0.685192i
$345$	3.72564	−	8.54923i	0.200581	−	0.460275i
$346$			2.86132i			0.153826i
$347$	−30.2457			−1.62367			−0.811836	−	0.583886i	$-0.801532\pi$
$347$	−30.2457			−1.62367			−0.811836	+	0.583886i	$0.801532\pi$
$348$	−2.56130	+	5.87743i	−0.137300	+	0.315063i
$349$	−2.14630			−0.114889			−0.0574443	−	0.998349i	$-0.518295\pi$
$349$	−2.14630			−0.114889			−0.0574443	+	0.998349i	$0.518295\pi$
$350$		−	13.3788i		−	0.715128i
$351$	−15.9831	+	5.61578i	−0.853113	+	0.299748i
$352$	−24.1797			−1.28878
$353$	−13.4536			−0.716063			−0.358031	−	0.933710i	$-0.616552\pi$
$353$	−13.4536			−0.716063			−0.358031	+	0.933710i	$0.616552\pi$
$354$	4.03002	−	9.24770i	0.214193	−	0.491510i
$355$			7.94952i			0.421917i
$356$			7.93413i			0.420508i
$357$	34.5785	+	15.0688i	1.83009	+	0.797527i
$358$	−2.07525			−0.109680
$359$		−	17.9586i		−	0.947820i	−0.880573	−	0.473910i	$-0.842842\pi$
$359$		−	17.9586i		−	0.947820i	0.880573	−	0.473910i	$-0.157158\pi$
$360$	6.14139	+	6.60748i	0.323680	+	0.348245i
$361$	−10.9705			−0.577395
$362$	−3.75339			−0.197274
$363$	9.54962	+	4.16159i	0.501225	+	0.218427i
$364$	−22.3757			−1.17280
$365$	1.91327			0.100145
$366$	−0.687742	+	1.57816i	−0.0359488	+	0.0824920i
$367$		−	19.4619i		−	1.01590i	−0.861386	−	0.507951i	$-0.830403\pi$
$367$		−	19.4619i		−	1.01590i	0.861386	−	0.507951i	$-0.169597\pi$
$368$		−	4.08466i		−	0.212928i
$369$	−6.50566	−	6.99940i	−0.338671	−	0.364374i
$370$	−1.78782			−0.0929446
$371$			38.8847i			2.01879i
$372$	−4.84254	+	11.1122i	−0.251074	+	0.576141i
$373$		−	8.59845i		−	0.445211i	−0.974909	−	0.222605i	$-0.928544\pi$
$373$		−	8.59845i		−	0.445211i	0.974909	−	0.222605i	$-0.0714561\pi$
$374$		−	14.1441i		−	0.731376i
$375$	−15.9161	−	6.93602i	−0.821905	−	0.358175i
$376$			23.8450i			1.22971i
$377$	8.47197			0.436329
$378$	−17.9185	+	6.29582i	−0.921630	+	0.323822i
$379$			1.08642i			0.0558057i	0.999611	+	0.0279028i	$0.00888290\pi$
$379$			1.08642i			0.0558057i	−0.999611	+	0.0279028i	$0.991117\pi$
$380$	4.67195			0.239666
$381$	15.4736	+	6.74318i	0.792736	+	0.345463i
$382$	−5.79943			−0.296725
$383$	−19.0065			−0.971187			−0.485593	−	0.874185i	$-0.661396\pi$
$383$	−19.0065			−0.971187			−0.485593	+	0.874185i	$0.661396\pi$
$384$	15.3742	+	6.69985i	0.784561	+	0.341900i
$385$		−	23.0023i		−	1.17231i
$386$	−11.2462			−0.572414
$387$	10.7492	−	9.99093i	0.546412	−	0.507868i
$388$		−	16.3990i		−	0.832535i
$389$			14.0181i			0.710748i	0.934724	+	0.355374i	$0.115646\pi$
$389$			14.0181i			0.710748i	−0.934724	+	0.355374i	$0.884354\pi$
$390$	1.98091	−	4.54560i	0.100307	−	0.230175i
$391$	21.0262			1.06334
$392$	−42.1201			−2.12739
$393$	−8.40250	+	19.2812i	−0.423850	+	0.972610i
$394$	−9.78702			−0.493063
$395$			7.06256i			0.355356i
$396$	−12.0006	−	12.9113i	−0.603052	−	0.648820i
$397$	30.4547			1.52848			0.764240	−	0.644932i	$-0.223114\pi$
$397$	30.4547			1.52848			0.764240	+	0.644932i	$0.223114\pi$
$398$	−1.82909			−0.0916840
$399$	−9.44684	+	21.6777i	−0.472934	+	1.08524i
$400$	−3.21404			−0.160702
$401$	1.34123			0.0669778			0.0334889	−	0.999439i	$-0.489338\pi$
$401$	1.34123			0.0669778			0.0334889	+	0.999439i	$0.489338\pi$
$402$	10.7454	+	0.466353i	0.535931	+	0.0232596i
$403$	16.0176			0.797894
$404$	−24.6643			−1.22710
$405$	−0.760666	+	10.3892i	−0.0377978	+	0.516242i
$406$	9.49789			0.471372
$407$	8.39846			0.416296
$408$	−8.12532	+	18.6452i	−0.402263	+	0.923075i
$409$		−	6.86816i		−	0.339609i	−0.985478	−	0.169804i	$-0.945686\pi$
$409$		−	6.86816i		−	0.339609i	0.985478	−	0.169804i	$-0.0543136\pi$
$410$	2.79693			0.138131
$411$	−24.8257	−	10.8187i	−1.22456	−	0.533648i
$412$	13.6961			0.674758
$413$	36.9882			1.82007
$414$	−7.75474	+	7.20772i	−0.381125	+	0.354240i
$415$			13.3952i			0.657547i
$416$		−	19.1117i		−	0.937030i
$417$	15.6024	−	35.8029i	0.764053	−	1.75328i
$418$	8.86713			0.433706
$419$		−	20.8056i		−	1.01642i	−0.861233	−	0.508210i	$-0.830307\pi$
$419$		−	20.8056i		−	1.01642i	0.861233	−	0.508210i	$-0.169693\pi$
$420$	−5.49663	+	12.6131i	−0.268208	+	0.615458i
$421$	−12.6110			−0.614622			−0.307311	−	0.951609i	$-0.599429\pi$
$421$	−12.6110			−0.614622			−0.307311	+	0.951609i	$0.599429\pi$
$422$	−18.4550			−0.898373
$423$	−20.1689	+	18.7462i	−0.980645	+	0.911470i
$424$	−20.9672			−1.01826
$425$		−	16.5446i		−	0.802533i
$426$	3.60538	−	8.27328i	0.174681	−	0.400842i
$427$	−6.31221			−0.305469
$428$			28.2335i			1.36472i
$429$	−9.30548	+	21.3533i	−0.449273	+	1.03095i
$430$			4.29533i			0.207139i
$431$			25.3275i			1.21998i	0.792408	+	0.609991i	$0.208827\pi$
$431$			25.3275i			1.21998i	−0.792408	+	0.609991i	$0.791173\pi$
$432$	1.51247	+	4.30463i	0.0727686	+	0.207107i
$433$		−	21.8609i		−	1.05057i	−0.850927	−	0.525284i	$-0.823959\pi$
$433$		−	21.8609i		−	1.05057i	0.850927	−	0.525284i	$-0.176041\pi$
$434$	17.9573			0.861976
$435$	2.08116	−	4.77564i	0.0997839	−	0.228975i
$436$			20.3115i			0.972746i
$437$			13.1816i			0.630562i
$438$	−1.99119	−	0.867731i	−0.0951426	−	0.0414618i
$439$	31.1141			1.48500			0.742499	−	0.669848i	$-0.233641\pi$
$439$	31.1141			1.48500			0.742499	+	0.669848i	$0.233641\pi$
$440$	12.4032			0.591297
$441$	−33.1134	−	35.6265i	−1.57683	−	1.69650i
$442$	11.1796			0.531758
$443$	−10.1923			−0.484251			−0.242126	−	0.970245i	$-0.577845\pi$
$443$	−10.1923			−0.484251			−0.242126	+	0.970245i	$0.577845\pi$
$444$	−4.60523	−	2.00689i	−0.218555	−	0.0952430i
$445$		−	6.44680i		−	0.305608i
$446$	−3.21558			−0.152262
$447$	−0.209995	+	0.481876i	−0.00993242	+	0.0227920i
$448$		−	12.9650i		−	0.612537i
$449$		−	11.9715i		−	0.564971i	−0.959272	−	0.282485i	$-0.908841\pi$
$449$		−	11.9715i		−	0.564971i	0.959272	−	0.282485i	$-0.0911589\pi$
$450$	5.67144	+	6.10187i	0.267354	+	0.287645i
$451$	−13.1388			−0.618684
$452$	0.951706			0.0447645
$453$	−20.0765	−	8.74903i	−0.943274	−	0.411066i
$454$			10.4806i			0.491878i
$455$	18.1811			0.852343
$456$	−11.6889	−	5.09386i	−0.547384	−	0.238542i
$457$	−14.9452			−0.699108			−0.349554	−	0.936916i	$-0.613667\pi$
$457$	−14.9452			−0.699108			−0.349554	+	0.936916i	$0.613667\pi$
$458$			8.61607i			0.402603i
$459$	−22.1586	+	7.78559i	−1.03427	+	0.363400i
$460$			7.66970i			0.357601i
$461$		−	26.4931i		−	1.23391i	−0.786999	−	0.616954i	$-0.788366\pi$
$461$		−	26.4931i		−	1.23391i	0.786999	−	0.616954i	$-0.211634\pi$
$462$	−10.4323	+	23.9391i	−0.485356	+	1.11375i
$463$		−	28.1127i		−	1.30651i	−0.757139	−	0.653254i	$-0.773403\pi$
$463$		−	28.1127i		−	1.30651i	0.757139	−	0.653254i	$-0.226597\pi$
$464$		−	2.28171i		−	0.105926i
$465$	3.93476	−	9.02911i	0.182470	−	0.418715i
$466$	9.16236			0.424438
$467$		−	8.22235i		−	0.380485i	−0.981737	−	0.190243i	$-0.939073\pi$
$467$		−	8.22235i		−	0.380485i	0.981737	−	0.190243i	$-0.0609274\pi$
$468$	10.2052	−	9.48530i	0.471735	−	0.438458i
$469$	14.1726	+	36.8023i	0.654431	+	1.69937i
$470$		−	8.05941i		−	0.371753i
$471$	−28.9855	−	12.6315i	−1.33558	−	0.582027i
$472$			19.9445i			0.918022i
$473$		−	20.1777i		−	0.927771i
$474$	3.20311	−	7.35020i	0.147124	−	0.337606i
$475$	10.3720			0.475902
$476$	−31.0211			−1.42185
$477$	−16.4837	−	17.7347i	−0.754736	−	0.812016i
$478$	−11.4909			−0.525583
$479$			14.3670i			0.656444i	0.944601	+	0.328222i	$0.106449\pi$
$479$			14.3670i			0.656444i	−0.944601	+	0.328222i	$0.893551\pi$
$480$	−10.7733	−	4.69484i	−0.491730	−	0.214289i
$481$			6.63817i			0.302675i
$482$	−2.70002			−0.122983
$483$	−35.5872	−	15.5084i	−1.61927	−	0.705656i
$484$	−8.56716			−0.389416
$485$			13.3249i			0.605052i
$486$	5.50349	−	10.4673i	0.249643	−	0.474806i
$487$			17.6219i			0.798526i	0.916836	+	0.399263i	$0.130734\pi$
$487$			17.6219i			0.798526i	−0.916836	+	0.399263i	$0.869266\pi$
$488$		−	3.40363i		−	0.154075i
$489$	14.8178	+	6.45739i	0.670085	+	0.292013i
$490$	14.2362			0.643127
$491$			10.9975i			0.496311i	0.968720	+	0.248156i	$0.0798244\pi$
$491$			10.9975i			0.496311i	−0.968720	+	0.248156i	$0.920176\pi$
$492$	7.20458	+	3.13965i	0.324808	+	0.141547i
$493$	11.7454			0.528984
$494$			7.00861i			0.315332i
$495$	9.75095	+	10.4910i	0.438272	+	0.471535i
$496$		−	4.31394i		−	0.193701i
$497$	33.0908			1.48432
$498$	6.07520	−	13.9408i	0.272236	−	0.624702i
$499$		−	0.0397963i		−	0.00178153i	−1.00000		0.000890763i	$-0.999716\pi$
$499$		−	0.0397963i		−	0.00178153i	1.00000		0.000890763i	$-0.000283539\pi$
$500$	14.2787			0.638562
$501$	3.63752	−	8.34703i	0.162512	−	0.372918i
$502$	−22.9740			−1.02538
$503$	29.8766			1.33213			0.666067	−	0.745892i	$-0.267977\pi$
$503$	29.8766			1.33213			0.666067	+	0.745892i	$0.267977\pi$
$504$	27.5044	−	25.5642i	1.22514	−	1.13872i
$505$	20.0407			0.891801
$506$			14.5567i			0.647125i
$507$	3.76402	+	1.64031i	0.167166	+	0.0728485i
$508$	−13.8817			−0.615900
$509$			23.4973i			1.04150i	0.853710	+	0.520749i	$0.174347\pi$
$509$			23.4973i			1.04150i	−0.853710	+	0.520749i	$0.825653\pi$
$510$	2.74629	−	6.30192i	0.121608	−	0.279054i
$511$		−	7.96419i		−	0.352315i
$512$	−9.70961			−0.429108
$513$	−4.88088	−	13.8915i	−0.215496	−	0.613324i
$514$		−	13.2528i		−	0.584554i
$515$	−11.1286			−0.490386
$516$	−4.82166	+	11.0643i	−0.212262	+	0.487078i
$517$			37.8598i			1.66507i
$518$			7.44202i			0.326984i
$519$	2.60982	−	5.98877i	0.114558	−	0.262878i
$520$			9.80350i			0.429912i
$521$	−4.89841			−0.214603			−0.107302	−	0.994227i	$-0.534221\pi$
$521$	−4.89841			−0.214603			−0.107302	+	0.994227i	$0.534221\pi$
$522$	−4.33184	+	4.02627i	−0.189599	+	0.176225i
$523$	9.40151			0.411099			0.205550	−	0.978647i	$-0.434102\pi$
$523$	9.40151			0.411099			0.205550	+	0.978647i	$0.434102\pi$
$524$		−	17.2976i		−	0.755649i
$525$	−12.2029	+	28.0020i	−0.532577	+	1.22211i
$526$			20.5361i			0.895416i
$527$	22.2065			0.967329
$528$	5.75098	+	2.50620i	0.250279	+	0.109068i
$529$	1.36043			0.0591492
$530$	7.08672			0.307827
$531$	−16.8697	+	15.6797i	−0.732084	+	0.680443i
$532$		−	19.4475i		−	0.843157i
$533$		−	10.3850i		−	0.449824i
$534$	−2.92384	+	6.70936i	−0.126527	+	0.290342i
$535$		−	22.9408i		−	0.991818i
$536$	−19.8443	+	7.64207i	−0.857142	+	0.330087i
$537$	4.34352	+	1.89284i	0.187437	+	0.0816822i
$538$		−	18.5690i		−	0.800566i
$539$	−66.8759			−2.88055
$540$	−2.83993	−	8.08274i	−0.122211	−	0.347826i
$541$			12.4235i			0.534129i	0.963679	+	0.267064i	$0.0860537\pi$
$541$			12.4235i			0.534129i	−0.963679	+	0.267064i	$0.913946\pi$
$542$		−	3.89795i		−	0.167431i
$543$	7.85589	+	3.42348i	0.337128	+	0.146916i
$544$		−	26.4961i		−	1.13601i
$545$		−	16.5039i		−	0.706951i
$546$	−18.9216	−	8.24575i	−0.809769	−	0.352886i
$547$			9.50576i			0.406437i	0.979133	+	0.203219i	$0.0651402\pi$
$547$			9.50576i			0.406437i	−0.979133	+	0.203219i	$0.934860\pi$
$548$	22.2717			0.951400
$549$	2.87890	−	2.67582i	0.122868	−	0.114201i
$550$	11.4540			0.488402
$551$			7.36331i			0.313688i
$552$	8.36233	−	19.1891i	0.355924	−	0.816742i
$553$	29.3987			1.25016
$554$	10.8029			0.458971
$555$	3.74193	+	1.63068i	0.158836	+	0.0692186i
$556$			32.1196i			1.36217i
$557$		−	28.6546i		−	1.21413i	−0.794651	−	0.607067i	$-0.792346\pi$
$557$		−	28.6546i		−	1.21413i	0.794651	−	0.607067i	$-0.207654\pi$
$558$	−8.19002	+	7.61229i	−0.346711	+	0.322254i
$559$	15.9485			0.674551
$560$		−	4.89662i		−	0.206920i
$561$	−12.9009	+	29.6038i	−0.544677	+	1.24987i
$562$	−14.8474			−0.626301
$563$	−34.9225			−1.47181			−0.735904	−	0.677086i	$-0.763242\pi$
$563$	−34.9225			−1.47181			−0.735904	+	0.677086i	$0.763242\pi$
$564$	9.04697	−	20.7601i	0.380946	−	0.874159i
$565$	−0.773299			−0.0325329
$566$	22.1451			0.930830
$567$	43.2461	+	3.16636i	1.81617	+	0.132975i
$568$			17.8430i			0.748676i
$569$			10.5705i			0.443140i	0.975144	+	0.221570i	$0.0711181\pi$
$569$			10.5705i			0.443140i	−0.975144	+	0.221570i	$0.928882\pi$
$570$	3.95075	+	1.72168i	0.165479	+	0.0721133i
$571$	−6.10345			−0.255421			−0.127711	−	0.991811i	$-0.540763\pi$
$571$	−6.10345			−0.255421			−0.127711	+	0.991811i	$0.540763\pi$
$572$		−	19.1565i		−	0.800974i
$573$	12.1383	+	5.28969i	0.507083	+	0.220980i
$574$		−	11.6426i		−	0.485951i
$575$			17.0272i			0.710085i
$576$	5.49600	+	5.91312i	0.229000	+	0.246380i
$577$		−	25.9099i		−	1.07864i	−0.842100	−	0.539321i	$-0.818681\pi$
$577$		−	25.9099i		−	1.07864i	0.842100	−	0.539321i	$-0.181319\pi$
$578$	2.60234			0.108243
$579$	23.5383	+	10.2577i	0.978219	+	0.426294i
$580$			4.28433i			0.177897i
$581$	55.7593			2.31328
$582$	6.04329	−	13.8676i	0.250502	−	0.574829i
$583$	−33.2905			−1.37875
$584$	4.29440			0.177704
$585$	−8.29211	+	7.70719i	−0.342837	+	0.318653i
$586$		−	4.34918i		−	0.179663i
$587$	−22.6962			−0.936771			−0.468386	−	0.883524i	$-0.655164\pi$
$587$	−22.6962			−0.936771			−0.468386	+	0.883524i	$0.655164\pi$
$588$	36.6709	+	15.9807i	1.51228	+	0.659031i
$589$			13.9215i			0.573626i
$590$		−	6.74108i		−	0.277526i
$591$	20.4843	+	8.92678i	0.842613	+	0.367199i
$592$	1.78782			0.0734791
$593$	−10.7989			−0.443459			−0.221730	−	0.975108i	$-0.571170\pi$
$593$	−10.7989			−0.443459			−0.221730	+	0.975108i	$0.571170\pi$
$594$	−5.39006	−	15.3406i	−0.221157	−	0.629434i
$595$	25.2059			1.03334
$596$		−	0.432301i		−	0.0177078i
$597$	3.82830	+	1.66832i	0.156682	+	0.0682798i
$598$	−11.5057			−0.470502
$599$	18.0014			0.735518			0.367759	−	0.929921i	$-0.380125\pi$
$599$	18.0014			0.735518			0.367759	+	0.929921i	$0.380125\pi$
$600$	−15.0991	−	6.57996i	−0.616417	−	0.268626i
$601$	32.1152			1.31001			0.655003	−	0.755626i	$-0.272667\pi$
$601$	32.1152			1.31001			0.655003	+	0.755626i	$0.272667\pi$
$602$	17.8798			0.728727
$603$	−22.0648	−	10.7770i	−0.898549	−	0.438873i
$604$	18.0110			0.732857
$605$	6.96116			0.283011
$606$	−20.8569	−	9.08916i	−0.847255	−	0.369222i
$607$	−9.00471			−0.365490			−0.182745	−	0.983160i	$-0.558498\pi$
$607$	−9.00471			−0.365490			−0.182745	+	0.983160i	$0.558498\pi$
$608$	16.6107			0.673654
$609$	−19.8792	−	8.66306i	−0.805545	−	0.351045i
$610$			1.15040i			0.0465782i
$611$	−29.9245			−1.21062
$612$	14.1482	−	13.1502i	0.571909	−	0.531566i
$613$	−6.69654			−0.270471			−0.135235	−	0.990814i	$-0.543179\pi$
$613$	−6.69654			−0.270471			−0.135235	+	0.990814i	$0.543179\pi$
$614$	−10.6972			−0.431703
$615$	−5.85401	−	2.55109i	−0.236056	−	0.102870i
$616$		−	51.6296i		−	2.08021i
$617$			42.2544i			1.70110i	0.525895	+	0.850550i	$0.323731\pi$
$617$			42.2544i			1.70110i	−0.525895	+	0.850550i	$0.676269\pi$
$618$	11.5819	+	5.04721i	0.465891	+	0.203028i
$619$	−11.7324			−0.471564			−0.235782	−	0.971806i	$-0.575765\pi$
$619$	−11.7324			−0.471564			−0.235782	+	0.971806i	$0.575765\pi$
$620$			8.10020i			0.325312i
$621$	22.8049	−	8.01269i	0.915131	−	0.321538i
$622$	0.696929			0.0279443
$623$	−26.8355			−1.07514
$624$	−1.98091	+	4.54560i	−0.0792997	+	0.181969i
$625$	6.69964			0.267986
$626$			12.1393i			0.485185i
$627$	−18.5590	−	8.08775i	−0.741175	−	0.322993i
$628$	26.0035			1.03765
$629$			9.20302i			0.366949i
$630$	−9.29625	+	8.64049i	−0.370371	+	0.344245i
$631$		−	14.6750i		−	0.584203i	−0.956387	−	0.292102i	$-0.905645\pi$
$631$		−	14.6750i		−	0.584203i	0.956387	−	0.292102i	$-0.0943545\pi$
$632$			15.8522i			0.630566i
$633$	38.6264	+	16.8328i	1.53526	+	0.669045i
$634$		−	5.96598i		−	0.236939i
$635$	11.2794			0.447610
$636$	18.2546	+	7.95509i	0.723841	+	0.315440i
$637$		−	52.8590i		−	2.09435i
$638$			8.13145i			0.321927i
$639$	−15.0922	+	14.0276i	−0.597037	+	0.554922i
$640$	11.2070			0.442994
$641$	−10.4157			−0.411396			−0.205698	−	0.978615i	$-0.565947\pi$
$641$	−10.4157			−0.411396			−0.205698	+	0.978615i	$0.565947\pi$
$642$	−10.4044	+	23.8751i	−0.410630	+	0.942276i
$643$	28.7349			1.13319			0.566596	−	0.823996i	$-0.308260\pi$
$643$	28.7349			1.13319			0.566596	+	0.823996i	$0.308260\pi$
$644$	31.9260			1.25806
$645$	3.91779	−	8.99017i	0.154263	−	0.353988i
$646$			9.71659i			0.382294i
$647$	11.9282			0.468948			0.234474	−	0.972122i	$-0.424663\pi$
$647$	11.9282			0.468948			0.234474	+	0.972122i	$0.424663\pi$
$648$	−1.70734	+	23.3189i	−0.0670708	+	0.916052i
$649$			31.6668i			1.24303i
$650$			9.05332i			0.355100i
$651$	−37.5847	−	16.3789i	−1.47306	−	0.641939i
$652$	−13.2934			−0.520608
$653$	5.77574			0.226022			0.113011	−	0.993594i	$-0.463950\pi$
$653$	5.77574			0.226022			0.113011	+	0.993594i	$0.463950\pi$
$654$	−7.48510	+	17.1761i	−0.292691	+	0.671638i
$655$			14.0550i			0.549174i
$656$	−2.79693			−0.109202
$657$	3.37611	+	3.63234i	0.131715	+	0.141711i
$658$	−33.5482			−1.30785
$659$		−	10.4692i		−	0.407823i	−0.978989	−	0.203911i	$-0.934635\pi$
$659$		−	10.4692i		−	0.407823i	0.978989	−	0.203911i	$-0.0653655\pi$
$660$	−10.7985	−	4.70584i	−0.420332	−	0.183175i
$661$		−	4.00272i		−	0.155688i	−0.996966	−	0.0778439i	$-0.975196\pi$
$661$		−	4.00272i		−	0.155688i	0.996966	−	0.0778439i	$-0.0248036\pi$
$662$		−	2.66886i		−	0.103728i
$663$	−23.3990	−	10.1969i	−0.908740	−	0.396016i
$664$			30.0661i			1.16679i
$665$			15.8019i			0.612771i
$666$	−3.15476	−	3.39419i	−0.122245	−	0.131522i
$667$	−12.0880			−0.468048
$668$			7.48829i			0.289731i
$669$	6.73025	+	2.93295i	0.260206	+	0.113394i
$670$	6.70719	−	2.58295i	0.259121	−	0.0997882i
$671$		−	5.40409i		−	0.208623i
$672$	−19.5428	+	44.8450i	−0.753880	+	1.72993i
$673$			10.3909i			0.400541i	0.979741	+	0.200270i	$0.0641821\pi$
$673$			10.3909i			0.400541i	−0.979741	+	0.200270i	$0.935818\pi$
$674$		−	19.4874i		−	0.750625i
$675$	−6.30484	−	17.9442i	−0.242674	−	0.690673i
$676$	−3.37678			−0.129876
$677$	15.8805			0.610337			0.305169	−	0.952298i	$-0.401287\pi$
$677$	15.8805			0.610337			0.305169	+	0.952298i	$0.401287\pi$
$678$	0.804793	+	0.350718i	0.0309079	+	0.0134692i
$679$	55.4663			2.12860
$680$			13.5914i			0.521205i
$681$	9.55938	−	21.9360i	0.366316	−	0.840588i
$682$			15.3738i			0.588693i
$683$	−14.9946			−0.573753			−0.286877	−	0.957968i	$-0.592617\pi$
$683$	−14.9946			−0.573753			−0.286877	+	0.957968i	$0.592617\pi$
$684$	8.24403	+	8.86971i	0.315219	+	0.339142i
$685$	−18.0966			−0.691437
$686$		−	33.6743i		−	1.28569i
$687$	7.85875	−	18.0335i	0.299830	−	0.688022i
$688$		−	4.29533i		−	0.163758i
$689$		−	26.3129i		−	1.00244i
$690$	−2.82639	+	6.48574i	−0.107599	+	0.246908i
$691$	10.9971			0.418349			0.209174	−	0.977878i	$-0.432922\pi$
$691$	10.9971			0.418349			0.209174	+	0.977878i	$0.432922\pi$
$692$			5.37265i			0.204238i
$693$	43.6699	−	40.5894i	1.65888	−	1.54187i
$694$	22.9454			0.870995
$695$		−	26.0984i		−	0.989969i
$696$	4.67124	−	10.7191i	0.177063	−	0.406307i
$697$		−	14.3975i		−	0.545345i
$698$	1.62825			0.0616303
$699$	−19.1769	−	8.35703i	−0.725338	−	0.316092i
$700$		−	25.1212i		−	0.949492i
$701$	−8.45832			−0.319466			−0.159733	−	0.987160i	$-0.551063\pi$
$701$	−8.45832			−0.319466			−0.159733	+	0.987160i	$0.551063\pi$
$702$	12.1253	−	4.26032i	0.457640	−	0.160795i
$703$	−5.76949			−0.217600
$704$	11.0997			0.418337
$705$	−7.35102	+	16.8684i	−0.276855	+	0.635302i
$706$	10.2064			0.384121
$707$		−	83.4219i		−	3.13740i
$708$	7.56710	−	17.3643i	0.284389	−	0.652589i
$709$	−21.2193			−0.796906			−0.398453	−	0.917189i	$-0.630453\pi$
$709$	−21.2193			−0.796906			−0.398453	+	0.917189i	$0.630453\pi$
$710$		−	6.03078i		−	0.226331i
$711$	−13.4083	+	12.4625i	−0.502850	+	0.467379i
$712$		−	14.4701i		−	0.542289i
$713$	−22.8542			−0.855897
$714$	−26.2325	−	11.4317i	−0.981725	−	0.427822i
$715$			15.5654i			0.582114i
$716$	−3.89666			−0.145625
$717$	24.0506	+	10.4809i	0.898188	+	0.391417i
$718$			13.6240i			0.508444i
$719$		−	21.9798i		−	0.819709i	−0.912151	−	0.409855i	$-0.865579\pi$
$719$		−	21.9798i		−	0.819709i	0.912151	−	0.409855i	$-0.134421\pi$
$720$	2.07574	+	2.23327i	0.0773581	+	0.0832291i
$721$			46.3242i			1.72520i
$722$	8.32260			0.309735
$723$	5.65117	+	2.46270i	0.210169	+	0.0915889i
$724$	−7.04768			−0.261925
$725$			9.51150i			0.353248i
$726$	−7.24467	−	3.15712i	−0.268875	−	0.117172i
$727$			28.3674i			1.05209i	0.850457	+	0.526045i	$0.176326\pi$
$727$			28.3674i			1.05209i	−0.850457	+	0.526045i	$0.823674\pi$
$728$	40.8082			1.51245
$729$	−21.0661	+	16.8884i	−0.780227	+	0.625497i
$730$	−1.45147			−0.0537213
$731$	22.1107			0.817793
$732$	−1.29136	+	2.96329i	−0.0477301	+	0.109526i
$733$		−	12.3363i		−	0.455653i	−0.973702	−	0.227827i	$-0.926838\pi$
$733$		−	12.3363i		−	0.455653i	0.973702	−	0.227827i	$-0.0731620\pi$
$734$			14.7644i			0.544965i
$735$	−29.7966	−	12.9849i	−1.09906	−	0.478956i
$736$			27.2690i			1.00515i
$737$	−31.5076	+	12.1336i	−1.16060	+	0.446949i
$738$	4.93542	+	5.30999i	0.181675	+	0.195463i
$739$			23.3385i			0.858521i	0.903181	+	0.429260i	$0.141226\pi$
$739$			23.3385i			0.858521i	−0.903181	+	0.429260i	$0.858774\pi$
$740$	−3.35697			−0.123405
$741$	6.39259	−	14.6691i	0.234837	−	0.538883i
$742$		−	29.4993i		−	1.08295i
$743$			13.0138i			0.477430i	0.971090	+	0.238715i	$0.0767262\pi$
$743$			13.0138i			0.477430i	−0.971090	+	0.238715i	$0.923274\pi$
$744$	8.83172	−	20.2662i	0.323787	−	0.742995i
$745$			0.351262i			0.0128692i
$746$			6.52308i			0.238827i
$747$	−25.4309	+	23.6370i	−0.930468	+	0.864833i
$748$		−	26.5582i		−	0.971063i
$749$	−95.4938			−3.48927
$750$	12.0745	+	5.26190i	0.440899	+	0.192138i
$751$	1.90373			0.0694682			0.0347341	−	0.999397i	$-0.488942\pi$
$751$	1.90373			0.0694682			0.0347341	+	0.999397i	$0.488942\pi$
$752$			8.05941i			0.293896i
$753$	48.0849	+	20.9547i	1.75231	+	0.763632i
$754$	−6.42713			−0.234062
$755$	−14.6347			−0.532610
$756$	−33.6453	+	11.8215i	−1.22367	+	0.429946i
$757$		−	45.1621i		−	1.64144i	−0.571328	−	0.820722i	$-0.693572\pi$
$757$		−	45.1621i		−	1.64144i	0.571328	−	0.820722i	$-0.306428\pi$
$758$		−	0.824195i		−	0.0299361i
$759$	13.2772	−	30.4673i	0.481933	−	1.10589i
$760$	−8.52059			−0.309074
$761$			46.7374i			1.69423i	0.531410	+	0.847115i	$0.321663\pi$
$761$			46.7374i			1.69423i	−0.531410	+	0.847115i	$0.678337\pi$
$762$	−11.7388	−	5.11560i	−0.425252	−	0.185319i
$763$	−68.6995			−2.48709
$764$	−10.8895			−0.393968
$765$	−11.4960	+	10.6851i	−0.415639	+	0.386320i
$766$	14.4190			0.520979
$767$	−25.0296			−0.903765
$768$	−20.2089	−	8.80676i	−0.729227	−	0.317787i
$769$			10.2376i			0.369179i	0.982816	+	0.184589i	$0.0590955\pi$
$769$			10.2376i			0.369179i	−0.982816	+	0.184589i	$0.940904\pi$
$770$			17.4503i			0.628866i
$771$	−12.0879	+	27.7382i	−0.435335	+	0.998966i
$772$	−21.1167			−0.760007
$773$		−	20.7981i		−	0.748056i	−0.927417	−	0.374028i	$-0.877976\pi$
$773$		−	20.7981i		−	0.748056i	0.927417	−	0.374028i	$-0.122024\pi$
$774$	−8.15470	+	7.57946i	−0.293115	+	0.272438i
$775$			17.9830i			0.645968i
$776$			29.9082i			1.07364i
$777$	6.78790	−	15.5762i	0.243515	−	0.558794i
$778$		−	10.6346i		−	0.381270i
$779$	9.02599			0.323389
$780$	3.71951	−	8.53519i	0.133180	−	0.305609i
$781$			28.3301i			1.01373i
$782$	−15.9512			−0.570415
$783$	12.7389	−	4.47593i	0.455253	−	0.159957i
$784$	−14.2362			−0.508437
$785$	−21.1288			−0.754121
$786$	6.37442	−	14.6274i	0.227368	−	0.521743i
$787$			15.9717i			0.569329i	0.958627	+	0.284664i	$0.0918822\pi$
$787$			15.9717i			0.569329i	−0.958627	+	0.284664i	$0.908118\pi$
$788$	−18.3769			−0.654651
$789$	18.7311	−	42.9822i	0.666843	−	1.53021i
$790$		−	5.35790i		−	0.190626i
$791$			3.21895i			0.114453i
$792$	21.8864	+	23.5474i	0.777699	+	0.836721i
$793$	4.27141			0.151682
$794$	−23.1040			−0.819931
$795$	−14.8326	−	6.46382i	−0.526057	−	0.229248i
$796$	−3.43445			−0.121731
$797$			27.2509i			0.965275i	0.875820	+	0.482638i	$0.160321\pi$
$797$			27.2509i			0.965275i	−0.875820	+	0.482638i	$0.839679\pi$
$798$	7.16670	−	16.4455i	0.253698	−	0.582163i
$799$	−41.4867			−1.46769
$800$	21.4568			0.758612
$801$	12.2393	−	11.3759i	0.432453	−	0.401948i
$802$	−1.01750			−0.0359292
$803$	6.81840			0.240616
$804$	20.1764	+	0.875663i	0.711567	+	0.0308822i
$805$	−25.9411			−0.914305
$806$	−12.1515			−0.428019
$807$	−16.9368	+	38.8651i	−0.596205	+	1.36811i
$808$	44.9822			1.58247
$809$	31.7333			1.11568			0.557842	−	0.829947i	$-0.311630\pi$
$809$	31.7333			1.11568			0.557842	+	0.829947i	$0.311630\pi$
$810$	0.577067	−	7.88158i	0.0202761	−	0.276930i
$811$			13.7313i			0.482170i	0.970504	+	0.241085i	$0.0775032\pi$
$811$			13.7313i			0.482170i	−0.970504	+	0.241085i	$0.922497\pi$
$812$	17.8340			0.625851
$813$	−3.55534	+	8.15845i	−0.124691	+	0.286129i
$814$	−6.37136			−0.223316
$815$	10.8014			0.378356
$816$	−2.74629	+	6.30192i	−0.0961392	+	0.220611i
$817$			13.8615i			0.484951i
$818$			5.21042i			0.182178i
$819$	32.0821	+	34.5169i	1.12104	+	1.20612i
$820$	5.25175			0.183399
$821$			15.7639i			0.550164i	0.961421	+	0.275082i	$0.0887051\pi$
$821$			15.7639i			0.550164i	−0.961421	+	0.275082i	$0.911295\pi$
$822$	18.8337	+	8.20744i	0.656899	+	0.286267i
$823$	49.9092			1.73973			0.869863	−	0.493293i	$-0.164207\pi$
$823$	49.9092			1.73973			0.869863	+	0.493293i	$0.164207\pi$
$824$	−24.9786			−0.870171
$825$	−23.9734	−	10.4473i	−0.834648	−	0.363728i
$826$	−28.0605			−0.976351
$827$		−	29.1324i		−	1.01303i	−0.862230	−	0.506516i	$-0.830933\pi$
$827$		−	29.1324i		−	1.01303i	0.862230	−	0.506516i	$-0.169067\pi$
$828$	−14.5609	+	13.5338i	−0.506028	+	0.470332i
$829$	−16.7842			−0.582939			−0.291470	−	0.956580i	$-0.594144\pi$
$829$	−16.7842			−0.582939			−0.291470	+	0.956580i	$0.594144\pi$
$830$		−	10.1621i		−	0.352731i
$831$	−22.6105	−	9.85335i	−0.784351	−	0.341809i
$832$			8.77327i			0.304158i
$833$		−	73.2825i		−	2.53909i
$834$	−11.8365	+	27.1613i	−0.409865	+	0.940520i
$835$		−	6.08453i		−	0.210564i
$836$	16.6497			0.575840
$837$	24.0850	−	8.46246i	0.832499	−	0.292505i
$838$			15.7838i			0.545243i
$839$			1.40933i			0.0486553i	0.999704	+	0.0243277i	$0.00774450\pi$
$839$			1.40933i			0.0486553i	−0.999704	+	0.0243277i	$0.992255\pi$
$840$	10.0246	−	23.0035i	0.345882	−	0.793698i
$841$	22.2476			0.767159
$842$	9.56713			0.329705
$843$	31.0758	+	13.5424i	1.07031	+	0.466425i
$844$	−34.6525			−1.19279
$845$	2.74377			0.0943884
$846$	15.3008	−	14.2215i	0.526053	−	0.488945i
$847$		−	28.9766i		−	0.995649i
$848$	−7.08672			−0.243359
$849$	−46.3500	−	20.1987i	−1.59073	−	0.693217i
$850$			12.5513i			0.430507i
$851$		−	9.47147i		−	0.324678i
$852$	6.76975	−	15.5346i	0.231928	−	0.532206i
$853$	−29.1498			−0.998070			−0.499035	−	0.866582i	$-0.666312\pi$
$853$	−29.1498			−0.998070			−0.499035	+	0.866582i	$0.666312\pi$
$854$	4.78866			0.163865
$855$	−6.69861	−	7.20699i	−0.229087	−	0.246474i
$856$		−	51.4915i		−	1.75994i
$857$	49.7984			1.70108			0.850540	−	0.525910i	$-0.176275\pi$
$857$	49.7984			1.70108			0.850540	+	0.525910i	$0.176275\pi$
$858$	7.05946	−	16.1994i	0.241006	−	0.553037i
$859$	−13.2906			−0.453470			−0.226735	−	0.973957i	$-0.572805\pi$
$859$	−13.2906			−0.453470			−0.226735	+	0.973957i	$0.572805\pi$
$860$			8.06527i			0.275023i
$861$	−10.6192	+	24.3680i	−0.361902	+	0.830459i
$862$		−	19.2143i		−	0.654442i
$863$			25.0799i			0.853729i	0.904316	+	0.426864i	$0.140382\pi$
$863$			25.0799i			0.853729i	−0.904316	+	0.426864i	$0.859618\pi$
$864$	−10.0972	−	28.7375i	−0.343512	−	0.977670i
$865$		−	4.36549i		−	0.148431i
$866$			16.5844i			0.563562i
$867$	−5.44672	−	2.37360i	−0.184980	−	0.0806118i
$868$	33.7180			1.14446
$869$			25.1692i			0.853807i
$870$	−1.57884	+	3.62297i	−0.0535276	+	0.122830i
$871$	−9.59048	−	24.9037i	−0.324961	−	0.843831i
$872$		−	37.0437i		−	1.25446i
$873$	−25.2973	+	23.5128i	−0.856185	+	0.795789i
$874$		−	10.0000i		−	0.338256i
$875$			48.2947i			1.63266i
$876$	−3.73882	−	1.62932i	−0.126323	−	0.0550498i
$877$	−9.91626			−0.334848			−0.167424	−	0.985885i	$-0.553545\pi$
$877$	−9.91626			−0.334848			−0.167424	+	0.985885i	$0.553545\pi$
$878$	−23.6043			−0.796605
$879$	−3.96691	+	9.10288i	−0.133800	+	0.307033i
$880$	4.19216			0.141318
$881$		−	29.4625i		−	0.992615i	−0.868147	−	0.496308i	$-0.834689\pi$
$881$		−	29.4625i		−	0.992615i	0.868147	−	0.496308i	$-0.165311\pi$
$882$	25.1210	+	27.0275i	0.845867	+	0.910064i
$883$			31.5231i			1.06084i	0.847736	+	0.530419i	$0.177965\pi$
$883$			31.5231i			1.06084i	−0.847736	+	0.530419i	$0.822035\pi$
$884$	20.9917			0.706027
$885$	−6.14857	+	14.1091i	−0.206682	+	0.474274i
$886$	7.73224			0.259770
$887$		−	6.31449i		−	0.212020i	−0.994365	−	0.106010i	$-0.966192\pi$
$887$		−	6.31449i		−	0.212020i	0.994365	−	0.106010i	$-0.0338075\pi$
$888$	8.39891	+	3.66013i	0.281849	+	0.122826i
$889$		−	46.9519i		−	1.57472i
$890$			4.89076i			0.163939i
$891$	−2.71082	+	37.0244i	−0.0908160	+	1.24036i
$892$	−6.03785			−0.202162
$893$		−	26.0085i		−	0.870342i
$894$	0.159309	−	0.365568i	0.00532810	−	0.0122264i
$895$	3.16619			0.105834
$896$		−	46.6503i		−	1.55848i
$897$	24.0815	+	10.4944i	0.804058	+	0.350397i
$898$			9.08200i			0.303070i
$899$	−12.7665			−0.425786
$900$	10.6492	+	11.4574i	0.354972	+	0.381912i
$901$		−	36.4797i		−	1.21531i
$902$	9.96757			0.331884
$903$	−37.4226	−	16.3082i	−1.24535	−	0.542705i
$904$	−1.73570			−0.0577285
$905$	5.72652			0.190356
$906$	15.2307	+	6.63732i	0.506006	+	0.220510i
$907$	−12.7175			−0.422278			−0.211139	−	0.977456i	$-0.567717\pi$
$907$	−12.7175			−0.422278			−0.211139	+	0.977456i	$0.567717\pi$
$908$			19.6792i			0.653077i
$909$	35.3635	+	38.0474i	1.17293	+	1.26195i
$910$	−13.7928			−0.457227
$911$		−	45.9331i		−	1.52183i	−0.648851	−	0.760915i	$-0.724750\pi$
$911$		−	45.9331i		−	1.52183i	0.648851	−	0.760915i	$-0.275250\pi$
$912$	−3.95075	−	1.72168i	−0.130822	−	0.0570105i
$913$			47.7373i			1.57987i
$914$	11.3380			0.375026
$915$	1.04928	−	2.40779i	0.0346882	−	0.0795992i
$916$			16.1782i			0.534544i
$917$	58.5055			1.93202
$918$	16.8103	−	5.90641i	0.554821	−	0.194941i
$919$		−	44.5893i		−	1.47087i	−0.677597	−	0.735433i	$-0.736979\pi$
$919$		−	44.5893i		−	1.47087i	0.677597	−	0.735433i	$-0.263021\pi$
$920$		−	13.9878i		−	0.461165i
$921$	22.3893	+	9.75693i	0.737752	+	0.321502i
$922$			20.0986i			0.661912i
$923$	−22.3922			−0.737049
$924$	−19.5886	+	44.9501i	−0.644418	+	1.47875i
$925$	−7.45269			−0.245043
$926$			21.3273i			0.700857i
$927$	−19.6374	−	21.1277i	−0.644975	−	0.693925i
$928$			15.2326i			0.500034i
$929$	−12.1575			−0.398876			−0.199438	−	0.979910i	$-0.563912\pi$
$929$	−12.1575			−0.398876			−0.199438	+	0.979910i	$0.563912\pi$
$930$	−2.98504	+	6.84979i	−0.0978834	+	0.224614i
$931$	45.9417			1.50568
$932$	17.2040			0.563536
$933$	−1.45868	−	0.635672i	−0.0477550	−	0.0208110i
$934$			6.23776i			0.204106i
$935$			21.5796i			0.705728i
$936$	−18.6120	+	17.2991i	−0.608351	+	0.565438i
$937$		−	35.0548i		−	1.14519i	−0.819838	−	0.572596i	$-0.805937\pi$
$937$		−	35.0548i		−	1.14519i	0.819838	−	0.572596i	$-0.194063\pi$
$938$	−10.7518	−	27.9195i	−0.351060	−	0.911603i
$939$	11.0723	−	25.4077i	0.361331	−	0.829149i
$940$		−	15.1330i		−	0.493584i
$941$	−15.5515			−0.506965			−0.253482	−	0.967340i	$-0.581576\pi$
$941$	−15.5515			−0.506965			−0.253482	+	0.967340i	$0.581576\pi$
$942$	21.9894	+	9.58265i	0.716452	+	0.312220i
$943$			14.8175i			0.482524i
$944$			6.74108i			0.219403i
$945$	27.3382	−	9.60548i	0.889311	−	0.312466i
$946$			15.3075i			0.497689i
$947$			36.5281i			1.18700i	0.804833	+	0.593502i	$0.202255\pi$
$947$			36.5281i			1.18700i	−0.804833	+	0.593502i	$0.797745\pi$
$948$	6.01443	−	13.8013i	0.195340	−	0.448247i
$949$			5.38929i			0.174944i
$950$	−7.86858			−0.255291
$951$	−5.44160	+	12.4869i	−0.176456	+	0.404914i
$952$	56.5756			1.83363
$953$			25.0488i			0.811410i	0.914004	+	0.405705i	$0.132974\pi$
$953$			25.0488i			0.811410i	−0.914004	+	0.405705i	$0.867026\pi$
$954$	12.5051	+	13.4542i	0.404867	+	0.435594i
$955$	8.84815			0.286319
$956$	−21.5763			−0.697828
$957$	7.41673	−	17.0192i	0.239749	−	0.550153i
$958$		−	10.8993i		−	0.352140i
$959$			75.3294i			2.43251i
$960$	4.94548	+	2.15517i	0.159615	+	0.0695579i
$961$	6.86295			0.221385
$962$		−	5.03595i		−	0.162365i
$963$	43.5532	−	40.4809i	1.40348	−	1.30448i
$964$	−5.06979			−0.163287
$965$	17.1582			0.552341
$966$	26.9976	+	11.7652i	0.868635	+	0.378539i
$967$	27.9900			0.900099			0.450050	−	0.893004i	$-0.351406\pi$
$967$	27.9900			0.900099			0.450050	+	0.893004i	$0.351406\pi$
$968$	15.6246			0.502193
$969$	8.86254	−	20.3369i	0.284706	−	0.653316i
$970$		−	10.1087i		−	0.324571i
$971$		−	8.05839i		−	0.258606i	−0.991605	−	0.129303i	$-0.958726\pi$
$971$		−	8.05839i		−	0.258606i	0.991605	−	0.129303i	$-0.0412740\pi$
$972$	10.3338	−	19.6543i	0.331457	−	0.630411i
$973$	−108.638			−3.48276
$974$		−	13.3686i		−	0.428358i
$975$	8.25757	−	18.9487i	0.264454	−	0.606844i
$976$		−	1.15040i		−	0.0368233i
$977$			26.5054i			0.847982i	0.905666	+	0.423991i	$0.139371\pi$
$977$			26.5054i			0.847982i	−0.905666	+	0.423991i	$0.860629\pi$
$978$	−11.2413	−	4.89880i	−0.359457	−	0.156646i
$979$		−	22.9748i		−	0.734277i
$980$	26.7311			0.853894
$981$	31.3328	−	29.1225i	1.00038	−	0.929811i
$982$		−	8.34309i		−	0.266239i
$983$	56.1623			1.79130			0.895649	−	0.444762i	$-0.146712\pi$
$983$	56.1623			1.79130			0.895649	+	0.444762i	$0.146712\pi$
$984$	−13.1395	−	5.72603i	−0.418874	−	0.182539i
$985$	14.9320			0.475772
$986$	−8.91043			−0.283766
$987$	70.2168	+	30.5995i	2.23502	+	0.973992i
$988$			13.1600i			0.418674i
$989$	−22.7556			−0.723588
$990$	−7.39740	−	7.95882i	−0.235105	−	0.252948i
$991$		−	35.1209i		−	1.11565i	−0.829958	−	0.557826i	$-0.811636\pi$
$991$		−	35.1209i		−	1.11565i	0.829958	−	0.557826i	$-0.188364\pi$
$992$			28.7996i			0.914389i
$993$	−2.43427	+	5.58594i	−0.0772494	+	0.177265i
$994$	−25.1038			−0.796244
$995$	2.79063			0.0884688
$996$	11.4073	−	26.1764i	0.361454	−	0.829431i
$997$	9.73924			0.308445			0.154222	−	0.988036i	$-0.450713\pi$
$997$	9.73924			0.308445			0.154222	+	0.988036i	$0.450713\pi$
$998$			0.0301908i			0.000955673i
$999$	3.50709	+	9.98154i	0.110960	+	0.315802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.d.a.200.8	yes	20
3.2	odd	2	inner	201.2.d.a.200.14	yes	20
67.66	odd	2	inner	201.2.d.a.200.13	yes	20
201.200	even	2	inner	201.2.d.a.200.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.d.a.200.7	✓	20	201.200	even	2	inner
201.2.d.a.200.8	yes	20	1.1	even	1	trivial
201.2.d.a.200.13	yes	20	67.66	odd	2	inner
201.2.d.a.200.14	yes	20	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.758634 q^{2} +(1.58783 + 0.691953i) q^{3} -1.42447 q^{4} +1.15744 q^{5} +(-1.20458 - 0.524939i) q^{6} -4.81799i q^{7} +2.59792 q^{8} +(2.04240 + 2.19741i) q^{9} +O(q^{10})\)	\(q-0.758634 q^{2} +(1.58783 + 0.691953i) q^{3} -1.42447 q^{4} +1.15744 q^{5} +(-1.20458 - 0.524939i) q^{6} -4.81799i q^{7} +2.59792 q^{8} +(2.04240 + 2.19741i) q^{9} -0.878075 q^{10} +4.12483 q^{11} +(-2.26182 - 0.985670i) q^{12} +3.26028i q^{13} +3.65509i q^{14} +(1.83782 + 0.800896i) q^{15} +0.878075 q^{16} +4.51999i q^{17} +(-1.54944 - 1.66703i) q^{18} -2.83364 q^{19} -1.64875 q^{20} +(3.33382 - 7.65014i) q^{21} -3.12924 q^{22} -4.65183i q^{23} +(4.12506 + 1.79764i) q^{24} -3.66033 q^{25} -2.47336i q^{26} +(1.72248 + 4.90235i) q^{27} +6.86310i q^{28} -2.59854i q^{29} +(-1.39423 - 0.607587i) q^{30} -4.91295i q^{31} -5.86198 q^{32} +(6.54953 + 2.85419i) q^{33} -3.42902i q^{34} -5.57654i q^{35} +(-2.90935 - 3.13015i) q^{36} +2.03607 q^{37} +2.14969 q^{38} +(-2.25597 + 5.17677i) q^{39} +3.00695 q^{40} -3.18530 q^{41} +(-2.52915 + 5.80366i) q^{42} -4.89176i q^{43} -5.87572 q^{44} +(2.36396 + 2.54337i) q^{45} +3.52904i q^{46} +9.17850i q^{47} +(1.39423 + 0.607587i) q^{48} -16.2130 q^{49} +2.77685 q^{50} +(-3.12762 + 7.17697i) q^{51} -4.64419i q^{52} -8.07074 q^{53} +(-1.30673 - 3.71909i) q^{54} +4.77426 q^{55} -12.5168i q^{56} +(-4.49933 - 1.96074i) q^{57} +1.97134i q^{58} +7.67711i q^{59} +(-2.61793 - 1.14086i) q^{60} -1.31014i q^{61} +3.72713i q^{62} +(10.5871 - 9.84026i) q^{63} +2.69095 q^{64} +3.77359i q^{65} +(-4.96870 - 2.16529i) q^{66} +(-7.63852 + 2.94161i) q^{67} -6.43861i q^{68} +(3.21885 - 7.38632i) q^{69} +4.23055i q^{70} +6.86818i q^{71} +(5.30600 + 5.70869i) q^{72} +1.65301 q^{73} -1.54463 q^{74} +(-5.81197 - 2.53278i) q^{75} +4.03644 q^{76} -19.8734i q^{77} +(1.71145 - 3.92728i) q^{78} +6.10187i q^{79} +1.01632 q^{80} +(-0.657196 + 8.97597i) q^{81} +2.41648 q^{82} +11.5731i q^{83} +(-4.74894 + 10.8974i) q^{84} +5.23162i q^{85} +3.71105i q^{86} +(1.79807 - 4.12603i) q^{87} +10.7160 q^{88} -5.56987i q^{89} +(-1.79338 - 1.92949i) q^{90} +15.7080 q^{91} +6.62642i q^{92} +(3.39953 - 7.80092i) q^{93} -6.96312i q^{94} -3.27977 q^{95} +(-9.30783 - 4.05622i) q^{96} +11.5124i q^{97} +12.2997 q^{98} +(8.42457 + 9.06394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

Introduction

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