LMFDB - Embedded newform 201.2.d.a.200.20

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			200.20
Root			$0.362922 - 1.69360i$ of defining polynomial
Character	$\chi$	$=$	201.200
Dual form			201.2.d.a.200.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.50456 q^{2} +(0.362922 + 1.69360i) q^{3} +4.27284 q^{4} -2.28042 q^{5} +(0.908961 + 4.24173i) q^{6} -3.79080i q^{7} +5.69246 q^{8} +(-2.73658 + 1.22929i) q^{9} +O(q^{10})$	\(q+2.50456 q^{2} +(0.362922 + 1.69360i) q^{3} +4.27284 q^{4} -2.28042 q^{5} +(0.908961 + 4.24173i) q^{6} -3.79080i q^{7} +5.69246 q^{8} +(-2.73658 + 1.22929i) q^{9} -5.71146 q^{10} -3.32556 q^{11} +(1.55071 + 7.23648i) q^{12} -0.642388i q^{13} -9.49429i q^{14} +(-0.827614 - 3.86212i) q^{15} +5.71146 q^{16} +6.62832i q^{17} +(-6.85393 + 3.07884i) q^{18} +7.09076 q^{19} -9.74386 q^{20} +(6.42010 - 1.37576i) q^{21} -8.32906 q^{22} -4.00860i q^{23} +(2.06592 + 9.64076i) q^{24} +0.200315 q^{25} -1.60890i q^{26} +(-3.07509 - 4.18853i) q^{27} -16.1975i q^{28} -5.77864i q^{29} +(-2.07281 - 9.67293i) q^{30} +6.65258i q^{31} +2.91978 q^{32} +(-1.20692 - 5.63217i) q^{33} +16.6010i q^{34} +8.64461i q^{35} +(-11.6929 + 5.25256i) q^{36} +2.27593 q^{37} +17.7592 q^{38} +(1.08795 - 0.233137i) q^{39} -12.9812 q^{40} +3.28305 q^{41} +(16.0795 - 3.44569i) q^{42} +1.72449i q^{43} -14.2096 q^{44} +(6.24054 - 2.80330i) q^{45} -10.0398i q^{46} +3.84745i q^{47} +(2.07281 + 9.67293i) q^{48} -7.37014 q^{49} +0.501701 q^{50} +(-11.2257 + 2.40556i) q^{51} -2.74482i q^{52} +1.46035 q^{53} +(-7.70176 - 10.4904i) q^{54} +7.58366 q^{55} -21.5790i q^{56} +(2.57339 + 12.0089i) q^{57} -14.4730i q^{58} +6.37672i q^{59} +(-3.53626 - 16.5022i) q^{60} -8.90249i q^{61} +16.6618i q^{62} +(4.65999 + 10.3738i) q^{63} -4.11014 q^{64} +1.46491i q^{65} +(-3.02280 - 14.1061i) q^{66} +(2.41692 + 7.82039i) q^{67} +28.3217i q^{68} +(6.78897 - 1.45481i) q^{69} +21.6510i q^{70} +4.06748i q^{71} +(-15.5778 + 6.99769i) q^{72} -12.2408 q^{73} +5.70020 q^{74} +(0.0726986 + 0.339253i) q^{75} +30.2976 q^{76} +12.6065i q^{77} +(2.72484 - 0.583905i) q^{78} +0.616736i q^{79} -13.0245 q^{80} +(5.97769 - 6.72809i) q^{81} +8.22260 q^{82} -13.9103i q^{83} +(27.4320 - 5.87841i) q^{84} -15.1154i q^{85} +4.31909i q^{86} +(9.78672 - 2.09720i) q^{87} -18.9306 q^{88} +1.85514i q^{89} +(15.6298 - 7.02104i) q^{90} -2.43516 q^{91} -17.1281i q^{92} +(-11.2668 + 2.41437i) q^{93} +9.63619i q^{94} -16.1699 q^{95} +(1.05965 + 4.94494i) q^{96} +3.55200i q^{97} -18.4590 q^{98} +(9.10063 - 4.08807i) 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 $

$2$	2.50456			1.77099			0.885497	−	0.464646i	$-0.153818\pi$
$2$	2.50456			1.77099			0.885497	+	0.464646i	$0.153818\pi$
$3$	0.362922	+	1.69360i	0.209533	+	0.977802i
$3$	0.362922	+	1.69360i	0.209533	+	0.977802i
$4$	4.27284			2.13642
$5$	−2.28042			−1.01983			−0.509917	−	0.860223i	$-0.670324\pi$
$5$	−2.28042			−1.01983			−0.509917	+	0.860223i	$0.670324\pi$
$6$	0.908961	+	4.24173i	0.371082	+	1.73168i
$7$		−	3.79080i		−	1.43279i	−0.697697	−	0.716393i	$-0.745792\pi$
$7$		−	3.79080i		−	1.43279i	0.697697	−	0.716393i	$-0.254208\pi$
$8$	5.69246			2.01259
$9$	−2.73658	+	1.22929i	−0.912192	+	0.409764i
$10$	−5.71146			−1.80612
$11$	−3.32556			−1.00269			−0.501346	−	0.865247i	$-0.667162\pi$
$11$	−3.32556			−1.00269			−0.501346	+	0.865247i	$0.667162\pi$
$12$	1.55071	+	7.23648i	0.447650	+	2.08899i
$13$		−	0.642388i		−	0.178166i	−0.996024	−	0.0890831i	$-0.971606\pi$
$13$		−	0.642388i		−	0.178166i	0.996024	−	0.0890831i	$-0.0283937\pi$
$14$		−	9.49429i		−	2.53746i
$15$	−0.827614	−	3.86212i	−0.213689	−	0.997196i
$16$	5.71146			1.42786
$17$			6.62832i			1.60760i	0.594897	+	0.803802i	$0.297193\pi$
$17$			6.62832i			1.60760i	−0.594897	+	0.803802i	$0.702807\pi$
$18$	−6.85393	+	3.07884i	−1.61549	+	0.725689i
$19$	7.09076			1.62673			0.813366	−	0.581753i	$-0.197633\pi$
$19$	7.09076			1.62673			0.813366	+	0.581753i	$0.197633\pi$
$20$	−9.74386			−2.17879
$21$	6.42010	−	1.37576i	1.40098	−	0.300216i
$22$	−8.32906			−1.77576
$23$		−	4.00860i		−	0.835850i	−0.908482	−	0.417925i	$-0.862757\pi$
$23$		−	4.00860i		−	0.835850i	0.908482	−	0.417925i	$-0.137243\pi$
$24$	2.06592	+	9.64076i	0.421704	+	1.96791i
$25$	0.200315			0.0400629
$26$		−	1.60890i		−	0.315531i
$27$	−3.07509	−	4.18853i	−0.591802	−	0.806084i
$28$		−	16.1975i		−	3.06103i
$29$		−	5.77864i		−	1.07307i	−0.843879	−	0.536533i	$-0.819734\pi$
$29$		−	5.77864i		−	1.07307i	0.843879	−	0.536533i	$-0.180266\pi$
$30$	−2.07281	−	9.67293i	−0.378442	−	1.76603i
$31$			6.65258i			1.19484i	0.801929	+	0.597419i	$0.203807\pi$
$31$			6.65258i			1.19484i	−0.801929	+	0.597419i	$0.796193\pi$
$32$	2.91978			0.516149
$33$	−1.20692	−	5.63217i	−0.210097	−	0.980434i
$34$			16.6010i			2.84706i
$35$			8.64461i			1.46121i
$36$	−11.6929	+	5.25256i	−1.94882	+	0.875426i
$37$	2.27593			0.374160			0.187080	−	0.982345i	$-0.440098\pi$
$37$	2.27593			0.374160			0.187080	+	0.982345i	$0.440098\pi$
$38$	17.7592			2.88093
$39$	1.08795	−	0.233137i	0.174211	−	0.0373317i
$40$	−12.9812			−2.05251
$41$	3.28305			0.512726			0.256363	−	0.966581i	$-0.417476\pi$
$41$	3.28305			0.512726			0.256363	+	0.966581i	$0.417476\pi$
$42$	16.0795	−	3.44569i	2.48113	−	0.531681i
$43$			1.72449i			0.262982i	0.991317	+	0.131491i	$0.0419764\pi$
$43$			1.72449i			0.262982i	−0.991317	+	0.131491i	$0.958024\pi$
$44$	−14.2096			−2.14217
$45$	6.24054	−	2.80330i	0.930285	−	0.417891i
$46$		−	10.0398i		−	1.48029i
$47$			3.84745i			0.561209i	0.959824	+	0.280604i	$0.0905349\pi$
$47$			3.84745i			0.561209i	−0.959824	+	0.280604i	$0.909465\pi$
$48$	2.07281	+	9.67293i	0.299185	+	1.39617i
$49$	−7.37014			−1.05288
$50$	0.501701			0.0709512
$51$	−11.2257	+	2.40556i	−1.57192	+	0.336846i
$52$		−	2.74482i		−	0.380638i
$53$	1.46035			0.200595			0.100297	−	0.994958i	$-0.468021\pi$
$53$	1.46035			0.200595			0.100297	+	0.994958i	$0.468021\pi$
$54$	−7.70176	−	10.4904i	−1.04808	−	1.42757i
$55$	7.58366			1.02258
$56$		−	21.5790i		−	2.88361i
$57$	2.57339	+	12.0089i	0.340854	+	1.59062i
$58$		−	14.4730i		−	1.90039i
$59$			6.37672i			0.830178i	0.909781	+	0.415089i	$0.136249\pi$
$59$			6.37672i			0.830178i	−0.909781	+	0.415089i	$0.863751\pi$
$60$	−3.53626	−	16.5022i	−0.456529	−	2.13043i
$61$		−	8.90249i		−	1.13985i	−0.821698	−	0.569923i	$-0.806973\pi$
$61$		−	8.90249i		−	1.13985i	0.821698	−	0.569923i	$-0.193027\pi$
$62$			16.6618i			2.11605i
$63$	4.65999	+	10.3738i	0.587104	+	1.30698i
$64$	−4.11014			−0.513768
$65$			1.46491i			0.181700i
$66$	−3.02280	−	14.1061i	−0.372081	−	1.73634i
$67$	2.41692	+	7.82039i	0.295274	+	0.955413i
$67$	2.41692	+	7.82039i	0.295274	+	0.955413i
$68$			28.3217i			3.43451i
$69$	6.78897	−	1.45481i	0.817296	−	0.175138i
$70$			21.6510i			2.58779i
$71$			4.06748i			0.482721i	0.970435	+	0.241361i	$0.0775937\pi$
$71$			4.06748i			0.482721i	−0.970435	+	0.241361i	$0.922406\pi$
$72$	−15.5778	+	6.99769i	−1.83587	+	0.824686i
$73$	−12.2408			−1.43268			−0.716341	−	0.697751i	$-0.754184\pi$
$73$	−12.2408			−1.43268			−0.716341	+	0.697751i	$0.754184\pi$
$74$	5.70020			0.662635
$75$	0.0726986	+	0.339253i	0.00839451	+	0.0391736i
$76$	30.2976			3.47538
$77$			12.6065i			1.43664i
$78$	2.72484	−	0.583905i	0.308527	−	0.0661142i
$79$			0.616736i			0.0693882i	0.999398	+	0.0346941i	$0.0110457\pi$
$79$			0.616736i			0.0693882i	−0.999398	+	0.0346941i	$0.988954\pi$
$80$	−13.0245			−1.45619
$81$	5.97769	−	6.72809i	0.664188	−	0.747566i
$82$	8.22260			0.908034
$83$		−	13.9103i		−	1.52685i	−0.645896	−	0.763426i	$-0.723516\pi$
$83$		−	13.9103i		−	1.52685i	0.645896	−	0.763426i	$-0.276484\pi$
$84$	27.4320	−	5.87841i	2.99308	−	0.641387i
$85$		−	15.1154i		−	1.63949i
$86$			4.31909i			0.465739i
$87$	9.78672	−	2.09720i	1.04925	−	0.224843i
$88$	−18.9306			−2.01801
$89$			1.85514i			0.196645i	0.995155	+	0.0983225i	$0.0313477\pi$
$89$			1.85514i			0.196645i	−0.995155	+	0.0983225i	$0.968652\pi$
$90$	15.6298	−	7.02104i	1.64753	−	0.740082i
$91$	−2.43516			−0.255274
$92$		−	17.1281i		−	1.78573i
$93$	−11.2668	+	2.41437i	−1.16831	+	0.250358i
$94$			9.63619i			0.993897i
$95$	−16.1699			−1.65900
$96$	1.05965	+	4.94494i	0.108150	+	0.504691i
$97$			3.55200i			0.360651i	0.983607	+	0.180326i	$0.0577151\pi$
$97$			3.55200i			0.360651i	−0.983607	+	0.180326i	$0.942285\pi$
$98$	−18.4590			−1.86464
$99$	9.10063	−	4.08807i	0.914648	−	0.410867i
$100$	0.855912			0.0855912
$101$	−9.53612			−0.948879			−0.474440	−	0.880288i	$-0.657349\pi$
$101$	−9.53612			−0.948879			−0.474440	+	0.880288i	$0.657349\pi$
$102$	−28.1156	+	6.02488i	−2.78386	+	0.596552i
$103$	13.4883			1.32904			0.664521	−	0.747270i	$-0.268636\pi$
$103$	13.4883			1.32904			0.664521	+	0.747270i	$0.268636\pi$
$104$		−	3.65677i		−	0.358575i
$105$	−14.6405	+	3.13732i	−1.42877	+	0.306171i
$106$	3.65754			0.355252
$107$		−	9.37985i		−	0.906784i	−0.891311	−	0.453392i	$-0.850214\pi$
$107$		−	9.37985i		−	0.906784i	0.891311	−	0.453392i	$-0.149786\pi$
$108$	−13.1394	−	17.8969i	−1.26434	−	1.72213i
$109$		−	15.2545i		−	1.46112i	−0.682851	−	0.730558i	$-0.739260\pi$
$109$		−	15.2545i		−	1.46112i	0.682851	−	0.730558i	$-0.260740\pi$
$110$	18.9938			1.81098
$111$	0.825984	+	3.85451i	0.0783989	+	0.365854i
$112$		−	21.6510i		−	2.04582i
$113$	6.65189			0.625757			0.312878	−	0.949793i	$-0.398707\pi$
$113$	6.65189			0.625757			0.312878	+	0.949793i	$0.398707\pi$
$114$	6.44522	+	30.0771i	0.603650	+	2.81698i
$115$			9.14128i			0.852429i
$116$		−	24.6912i		−	2.29252i
$117$	0.789681	+	1.75794i	0.0730060	+	0.162522i
$118$			15.9709i			1.47024i
$119$	25.1266			2.30335
$120$	−4.71116	−	21.9850i	−0.430068	−	2.00695i
$121$	0.0593167			0.00539243
$122$		−	22.2968i		−	2.01866i
$123$	1.19149	+	5.56017i	0.107433	+	0.501344i
$124$			28.4254i			2.55267i
$125$	10.9453			0.978977
$126$	11.6712	+	25.9818i	1.03976	+	2.31465i
$127$	−3.67347			−0.325967			−0.162984	−	0.986629i	$-0.552112\pi$
$127$	−3.67347			−0.325967			−0.162984	+	0.986629i	$0.552112\pi$
$128$	−16.1337			−1.42603
$129$	−2.92060	+	0.625854i	−0.257144	+	0.0551034i
$130$			3.66897i			0.321790i
$131$			3.00313i			0.262385i	0.991357	+	0.131192i	$0.0418806\pi$
$131$			3.00313i			0.262385i	−0.991357	+	0.131192i	$0.958119\pi$
$132$	−5.15696	−	24.0653i	−0.448856	−	2.09462i
$133$		−	26.8796i		−	2.33076i
$134$	6.05334	+	19.5867i	0.522929	+	1.69203i
$135$	7.01250	+	9.55161i	0.603540	+	0.822072i
$136$			37.7315i			3.23545i
$137$	14.9061			1.27352			0.636758	−	0.771064i	$-0.280275\pi$
$137$	14.9061			1.27352			0.636758	+	0.771064i	$0.280275\pi$
$138$	17.0034	−	3.64366i	1.44743	−	0.310169i
$139$			7.41193i			0.628672i	0.949312	+	0.314336i	$0.101782\pi$
$139$			7.41193i			0.628672i	−0.949312	+	0.314336i	$0.898218\pi$
$140$			36.9370i			3.12175i
$141$	−6.51605	+	1.39633i	−0.548751	+	0.117592i
$142$			10.1873i			0.854896i
$143$			2.13630i			0.178646i
$144$	−15.6298	+	7.02104i	−1.30249	+	0.585087i
$145$			13.1777i			1.09435i
$146$	−30.6579			−2.53727
$147$	−2.67479	−	12.4821i	−0.220613	−	1.02951i
$148$	9.72466			0.799362
$149$		−	13.6469i		−	1.11800i	−0.829169	−	0.558998i	$-0.811186\pi$
$149$		−	13.6469i		−	1.11800i	0.829169	−	0.558998i	$-0.188814\pi$
$150$	0.182078	+	0.849681i	0.0148666	+	0.0693762i
$151$	−5.76883			−0.469461			−0.234730	−	0.972061i	$-0.575421\pi$
$151$	−5.76883			−0.469461			−0.234730	+	0.972061i	$0.575421\pi$
$152$	40.3639			3.27394
$153$	−8.14813	−	18.1389i	−0.658738	−	1.46644i
$154$			31.5738i			2.54429i
$155$		−	15.1707i		−	1.21854i
$156$	4.64863	−	0.996154i	0.372188	−	0.0797562i
$157$	−15.6023			−1.24520			−0.622598	−	0.782542i	$-0.713923\pi$
$157$	−15.6023			−1.24520			−0.622598	+	0.782542i	$0.713923\pi$
$158$			1.54465i			0.122886i
$159$	0.529993	+	2.47325i	0.0420312	+	0.196142i
$160$	−6.65832			−0.526386
$161$	−15.1958			−1.19759
$162$	14.9715	−	16.8509i	1.17627	−	1.32393i
$163$	1.04302			0.0816958			0.0408479	−	0.999165i	$-0.486994\pi$
$163$	1.04302			0.0816958			0.0408479	+	0.999165i	$0.486994\pi$
$164$	14.0279			1.09540
$165$	2.75228	+	12.8437i	0.214265	+	0.999881i
$166$		−	34.8392i		−	2.70404i
$167$			17.2185i			1.33241i	0.745768	+	0.666205i	$0.232083\pi$
$167$			17.2185i			1.33241i	−0.745768	+	0.666205i	$0.767917\pi$
$168$	36.5462	−	7.83148i	2.81960	−	0.604212i
$169$	12.5873			0.968257
$170$		−	37.8574i		−	2.90353i
$171$	−19.4044	+	8.71660i	−1.48389	+	0.666575i
$172$			7.36845i			0.561839i
$173$		−	7.53153i		−	0.572611i	−0.958138	−	0.286306i	$-0.907573\pi$
$173$		−	7.53153i		−	0.572611i	0.958138	−	0.286306i	$-0.0924273\pi$
$174$	24.5114	−	5.25256i	1.85821	−	0.398195i
$175$		−	0.759352i		−	0.0574016i
$176$	−18.9938			−1.43171
$177$	−10.7996	+	2.31425i	−0.811749	+	0.173950i
$178$			4.64633i			0.348257i
$179$	20.1193			1.50379			0.751895	−	0.659283i	$-0.229140\pi$
$179$	20.1193			1.50379			0.751895	+	0.659283i	$0.229140\pi$
$180$	26.6648	−	11.9780i	1.98748	−	0.892790i
$181$	1.69322			0.125856			0.0629280	−	0.998018i	$-0.479956\pi$
$181$	1.69322			0.125856			0.0629280	+	0.998018i	$0.479956\pi$
$182$	−6.09901			−0.452089
$183$	15.0773	−	3.23091i	1.11454	−	0.238836i
$184$		−	22.8188i		−	1.68222i
$185$	−5.19007			−0.381581
$186$	−28.2185	+	6.04693i	−2.06908	+	0.443383i
$187$		−	22.0428i		−	1.61193i
$188$			16.4395i			1.19898i
$189$	−15.8779	+	11.6571i	−1.15495	+	0.847926i
$190$	−40.4985			−2.93807
$191$	−0.993418			−0.0718812			−0.0359406	−	0.999354i	$-0.511443\pi$
$191$	−0.993418			−0.0718812			−0.0359406	+	0.999354i	$0.511443\pi$
$192$	−1.49166	−	6.96095i	−0.107651	−	0.502363i
$193$	−14.1028			−1.01514			−0.507571	−	0.861610i	$-0.669457\pi$
$193$	−14.1028			−1.01514			−0.507571	+	0.861610i	$0.669457\pi$
$194$			8.89621i			0.638711i
$195$	−2.48098	+	0.531649i	−0.177667	+	0.0380722i
$196$	−31.4914			−2.24939
$197$	−10.3052			−0.734213			−0.367106	−	0.930179i	$-0.619651\pi$
$197$	−10.3052			−0.734213			−0.367106	+	0.930179i	$0.619651\pi$
$198$	22.7931	−	10.2388i	1.61984	−	0.727643i
$199$	5.03684			0.357052			0.178526	−	0.983935i	$-0.442867\pi$
$199$	5.03684			0.357052			0.178526	+	0.983935i	$0.442867\pi$
$200$	1.14028			0.0806302
$201$	−12.3675	+	6.93150i	−0.872334	+	0.488910i
$202$	−23.8838			−1.68046
$203$	−21.9056			−1.53748
$204$	−47.9657	+	10.2786i	−3.35827	+	0.719644i
$205$	−7.48672			−0.522895
$206$	33.7823			2.35372
$207$	4.92773	+	10.9698i	0.342501	+	0.762456i
$208$		−	3.66897i		−	0.254397i
$209$	−23.5807			−1.63111
$210$	−36.6681	+	7.85761i	−2.53034	+	0.542227i
$211$	−3.86760			−0.266257			−0.133128	−	0.991099i	$-0.542502\pi$
$211$	−3.86760			−0.266257			−0.133128	+	0.991099i	$0.542502\pi$
$212$	6.23984			0.428554
$213$	−6.88869	+	1.47618i	−0.472006	+	0.101146i
$214$		−	23.4924i		−	1.60591i
$215$		−	3.93256i		−	0.268198i
$216$	−17.5048	−	23.8431i	−1.19105	−	1.62231i
$217$	25.2186			1.71195
$218$		−	38.2059i		−	2.58763i
$219$	−4.44247	−	20.7311i	−0.300194	−	1.40088i
$220$	32.4037			2.18466
$221$	4.25795			0.286421
$222$	2.06873	+	9.65387i	0.138844	+	0.647925i
$223$	0.688187			0.0460844			0.0230422	−	0.999734i	$-0.492665\pi$
$223$	0.688187			0.0460844			0.0230422	+	0.999734i	$0.492665\pi$
$224$		−	11.0683i		−	0.739531i
$225$	−0.548176	+	0.246245i	−0.0365451	+	0.0164163i
$226$	16.6601			1.10821
$227$		−	27.5016i		−	1.82534i	−0.408692	−	0.912672i	$-0.634015\pi$
$227$		−	27.5016i		−	1.82534i	0.408692	−	0.912672i	$-0.365985\pi$
$228$	10.9957	+	51.3122i	0.728207	+	3.39823i
$229$			20.9485i			1.38432i	0.721745	+	0.692159i	$0.243340\pi$
$229$			20.9485i			1.38432i	−0.721745	+	0.692159i	$0.756660\pi$
$230$			22.8949i			1.50965i
$231$	−21.3504	+	4.57518i	−1.40475	+	0.301025i
$232$		−	32.8947i		−	2.15964i
$233$	−27.8137			−1.82214			−0.911069	−	0.412253i	$-0.864742\pi$
$233$	−27.8137			−1.82214			−0.911069	+	0.412253i	$0.864742\pi$
$234$	1.97781	+	4.40288i	0.129293	+	0.287825i
$235$		−	8.77381i		−	0.572340i
$236$			27.2467i			1.77361i
$237$	−1.04451	+	0.223827i	−0.0678479	+	0.0145391i
$238$	62.9312			4.07922
$239$	−0.389883			−0.0252194			−0.0126097	−	0.999920i	$-0.504014\pi$
$239$	−0.389883			−0.0252194			−0.0126097	+	0.999920i	$0.504014\pi$
$240$	−4.72688	−	22.0583i	−0.305119	−	1.42386i
$241$	−17.0093			−1.09566			−0.547832	−	0.836588i	$-0.684547\pi$
$241$	−17.0093			−1.09566			−0.547832	+	0.836588i	$0.684547\pi$
$242$	0.148563			0.00954996
$243$	13.5641	+	7.68205i	0.870140	+	0.492804i
$244$		−	38.0389i		−	2.43519i
$245$	16.8070			1.07376
$246$	2.98416	+	13.9258i	0.190263	+	0.887877i
$247$		−	4.55501i		−	0.289829i
$248$			37.8695i			2.40472i
$249$	23.5585	−	5.04834i	1.49296	−	0.319926i
$250$	27.4132			1.73376
$251$	−10.9321			−0.690031			−0.345016	−	0.938597i	$-0.612126\pi$
$251$	−10.9321			−0.690031			−0.345016	+	0.938597i	$0.612126\pi$
$252$	19.9114	+	44.3256i	1.25430	+	2.79225i
$253$			13.3308i			0.838101i
$254$	−9.20043			−0.577286
$255$	25.5994	−	5.48569i	1.60310	−	0.343527i
$256$	−32.1875			−2.01172
$257$		−	23.8590i		−	1.48829i	−0.668020	−	0.744143i	$-0.732858\pi$
$257$		−	23.8590i		−	1.48829i	0.668020	−	0.744143i	$-0.267142\pi$
$258$	−7.31481	+	1.56749i	−0.455400	+	0.0975878i
$259$		−	8.62757i		−	0.536091i
$260$			6.25933i			0.388187i
$261$	7.10363	+	15.8137i	0.439704	+	0.978842i
$262$			7.52154i			0.464682i
$263$			12.8212i			0.790587i	0.918555	+	0.395294i	$0.129357\pi$
$263$			12.8212i			0.790587i	−0.918555	+	0.395294i	$0.870643\pi$
$264$	−6.87033	−	32.0609i	−0.422839	−	1.97321i
$265$	−3.33021			−0.204573
$266$		−	67.3217i		−	4.12776i
$267$	−3.14188	+	0.673273i	−0.192280	+	0.0412036i
$268$	10.3271	+	33.4152i	0.630829	+	2.04116i
$269$			12.6656i			0.772235i	0.922450	+	0.386117i	$0.126184\pi$
$269$			12.6656i			0.772235i	−0.922450	+	0.386117i	$0.873816\pi$
$270$	17.5633	+	23.9226i	1.06887	+	1.45588i
$271$			10.5222i			0.639180i	0.947556	+	0.319590i	$0.103545\pi$
$271$			10.5222i			0.639180i	−0.947556	+	0.319590i	$0.896455\pi$
$272$			37.8574i			2.29544i
$273$	−0.883773	−	4.12419i	−0.0534884	−	0.249608i
$274$	37.3333			2.25539
$275$	−0.666157			−0.0401708
$276$	29.0081	−	6.21615i	1.74608	−	0.374169i
$277$	10.5955			0.636625			0.318312	−	0.947986i	$-0.396884\pi$
$277$	10.5955			0.636625			0.318312	+	0.947986i	$0.396884\pi$
$278$			18.5636i			1.11337i
$279$	−8.17795	−	18.2053i	−0.489601	−	1.08992i
$280$			49.2091i			2.94081i
$281$	20.0851			1.19818			0.599089	−	0.800683i	$-0.295530\pi$
$281$	20.0851			1.19818			0.599089	+	0.800683i	$0.295530\pi$
$282$	−16.3199	+	3.49718i	−0.971834	+	0.208254i
$283$	11.8682			0.705490			0.352745	−	0.935719i	$-0.385248\pi$
$283$	11.8682			0.705490			0.352745	+	0.935719i	$0.385248\pi$
$284$			17.3797i			1.03129i
$285$	−5.86841	−	27.3854i	−0.347615	−	1.62217i
$286$			5.35049i			0.316381i
$287$		−	12.4454i		−	0.734626i
$288$	−7.99019	+	3.58926i	−0.470827	+	0.211499i
$289$	−26.9346			−1.58439
$290$			33.0044i			1.93809i
$291$	−6.01568	+	1.28910i	−0.352645	+	0.0755684i
$292$	−52.3031			−3.06081
$293$		−	0.0262169i		−	0.00153160i	−1.00000		0.000765802i	$-0.999756\pi$
$293$		−	0.0262169i		−	0.00153160i	1.00000		0.000765802i	$-0.000243763\pi$
$294$	−6.69917	−	31.2622i	−0.390704	−	1.82325i
$295$		−	14.5416i		−	0.846644i
$296$	12.9556			0.753030
$297$	10.2264	+	13.9292i	0.593395	+	0.808254i
$298$		−	34.1795i		−	1.97996i
$299$	−2.57507			−0.148920
$300$	0.310629	+	1.44957i	0.0179342	+	0.0836912i
$301$	6.53718			0.376797
$302$	−14.4484			−0.831412
$303$	−3.46087	−	16.1504i	−0.198822	−	0.927816i
$304$	40.4985			2.32275
$305$			20.3014i			1.16246i
$306$	−20.4075	−	45.4300i	−1.16662	−	2.59706i
$307$	−20.5808			−1.17461			−0.587304	−	0.809367i	$-0.699811\pi$
$307$	−20.5808			−1.17461			−0.587304	+	0.809367i	$0.699811\pi$
$308$			53.8655i			3.06927i
$309$	4.89520	+	22.8438i	0.278478	+	1.29954i
$310$		−	37.9959i		−	2.15802i
$311$	29.9008			1.69552			0.847761	−	0.530379i	$-0.177950\pi$
$311$	29.9008			1.69552			0.847761	+	0.530379i	$0.177950\pi$
$312$	6.19311	−	1.32712i	0.350616	−	0.0751334i
$313$			18.2037i			1.02893i	0.857510	+	0.514467i	$0.172010\pi$
$313$			18.2037i			1.02893i	−0.857510	+	0.514467i	$0.827990\pi$
$314$	−39.0769			−2.20523
$315$	−10.6267	−	23.6566i	−0.598749	−	1.33290i
$316$			2.63521i			0.148242i
$317$		−	14.4179i		−	0.809789i	−0.914363	−	0.404895i	$-0.867308\pi$
$317$		−	14.4179i		−	0.809789i	0.914363	−	0.404895i	$-0.132692\pi$
$318$	1.32740	+	6.19441i	0.0744370	+	0.347366i
$319$			19.2172i			1.07596i
$320$	9.37285			0.523958
$321$	15.8857	−	3.40415i	0.886655	−	0.190001i
$322$	−38.0588			−2.12093
$323$			46.9998i			2.61514i
$324$	25.5417	−	28.7480i	1.41898	−	1.59711i
$325$		−	0.128680i		−	0.00713786i
$326$	2.61231			0.144683
$327$	25.8351	−	5.53619i	1.42868	−	0.306152i
$328$	18.6886			1.03191
$329$	14.5849			0.804092
$330$	6.89325	+	32.1679i	0.379461	+	1.77078i
$331$			28.8976i			1.58836i	0.607686	+	0.794178i	$0.292098\pi$
$331$			28.8976i			1.58836i	−0.607686	+	0.794178i	$0.707902\pi$
$332$		−	59.4363i		−	3.26199i
$333$	−6.22824	+	2.79777i	−0.341306	+	0.153317i
$334$			43.1249i			2.35969i
$335$	−5.51160	−	17.8338i	−0.301131	−	0.974363i
$336$	36.6681	−	7.85761i	2.00041	−	0.428668i
$337$		−	9.68749i		−	0.527711i	−0.964562	−	0.263856i	$-0.915006\pi$
$337$		−	9.68749i		−	0.527711i	0.964562	−	0.263856i	$-0.0849943\pi$
$338$	31.5258			1.71478
$339$	2.41412	+	11.2656i	0.131117	+	0.611866i
$340$		−	64.5854i		−	3.50264i
$341$		−	22.1235i		−	1.19806i
$342$	−48.5995	+	21.8313i	−2.62796	+	1.18050i
$343$			1.40314i			0.0757622i
$344$			9.81658i			0.529274i
$345$	−15.4817	+	3.31757i	−0.833506	+	0.178612i
$346$		−	18.8632i		−	1.01409i
$347$	24.1144			1.29453			0.647265	−	0.762265i	$-0.275913\pi$
$347$	24.1144			1.29453			0.647265	+	0.762265i	$0.275913\pi$
$348$	41.8170	−	8.96097i	2.24163	−	0.480358i
$349$	3.99596			0.213899			0.106949	−	0.994264i	$-0.465892\pi$
$349$	3.99596			0.213899			0.106949	+	0.994264i	$0.465892\pi$
$350$		−	1.90185i		−	0.101658i
$351$	−2.69066	+	1.97540i	−0.143617	+	0.105439i
$352$	−9.70988			−0.517538
$353$	−12.0605			−0.641917			−0.320958	−	0.947093i	$-0.604005\pi$
$353$	−12.0605			−0.641917			−0.320958	+	0.947093i	$0.604005\pi$
$354$	−27.0483	+	5.79618i	−1.43760	+	0.308064i
$355$		−	9.27557i		−	0.492296i
$356$			7.92673i			0.420116i
$357$	9.11900	+	42.5545i	0.482629	+	2.25222i
$358$	50.3901			2.66320
$359$			20.2456i			1.06852i	0.845319	+	0.534262i	$0.179411\pi$
$359$			20.2456i			1.06852i	−0.845319	+	0.534262i	$0.820589\pi$
$360$	35.5240	−	15.9577i	1.87228	−	0.841043i
$361$	31.2788			1.64626
$362$	4.24077			0.222890
$363$	0.0215273	+	0.100459i	0.00112989	+	0.00527273i
$364$	−10.4050			−0.545372
$365$	27.9142			1.46110
$366$	37.7620	−	8.09201i	1.97385	−	0.422976i
$367$			5.72356i			0.298768i	0.988779	+	0.149384i	$0.0477290\pi$
$367$			5.72356i			0.298768i	−0.988779	+	0.149384i	$0.952271\pi$
$368$		−	22.8949i		−	1.19348i
$369$	−8.98430	+	4.03582i	−0.467704	+	0.210096i
$370$	−12.9989			−0.675778
$371$		−	5.53589i		−	0.287409i
$372$	−48.1413	+	10.3162i	−2.49601	+	0.534870i
$373$		−	23.0024i		−	1.19102i	−0.803349	−	0.595509i	$-0.796950\pi$
$373$		−	23.0024i		−	1.19102i	0.803349	−	0.595509i	$-0.203050\pi$
$374$		−	55.2077i		−	2.85472i
$375$	3.97229	+	18.5370i	0.205128	+	0.957245i
$376$			21.9015i			1.12948i
$377$	−3.71213			−0.191184
$378$	−39.7671	+	29.1958i	−2.04540	+	1.50167i
$379$			6.92189i			0.355554i	0.984071	+	0.177777i	$0.0568905\pi$
$379$			6.92189i			0.355554i	−0.984071	+	0.177777i	$0.943109\pi$
$380$	−69.0914			−3.54431
$381$	−1.33318	−	6.22139i	−0.0683009	−	0.318731i
$382$	−2.48808			−0.127301
$383$	−24.2988			−1.24161			−0.620806	−	0.783965i	$-0.713194\pi$
$383$	−24.2988			−1.24161			−0.620806	+	0.783965i	$0.713194\pi$
$384$	−5.85526	−	27.3240i	−0.298800	−	1.39437i
$385$		−	28.7481i		−	1.46514i
$386$	−35.3214			−1.79781
$387$	−2.11990	−	4.71919i	−0.107760	−	0.239890i
$388$			15.1771i			0.770502i
$389$			19.0497i			0.965858i	0.875659	+	0.482929i	$0.160427\pi$
$389$			19.0497i			0.965858i	−0.875659	+	0.482929i	$0.839573\pi$
$390$	−6.21377	+	1.33155i	−0.314647	+	0.0674256i
$391$	26.5703			1.34372
$392$	−41.9542			−2.11901
$393$	−5.08611	+	1.08990i	−0.256560	+	0.0549783i
$394$	−25.8099			−1.30029
$395$		−	1.40642i		−	0.0707645i
$396$	38.8855	−	17.4677i	1.95407	−	0.877783i
$397$	2.97569			0.149346			0.0746729	−	0.997208i	$-0.476209\pi$
$397$	2.97569			0.149346			0.0746729	+	0.997208i	$0.476209\pi$
$398$	12.6151			0.632337
$399$	45.5234	−	9.75521i	2.27902	−	0.488371i
$400$	1.14409			0.0572044
$401$	13.5663			0.677470			0.338735	−	0.940882i	$-0.390001\pi$
$401$	13.5663			0.677470			0.338735	+	0.940882i	$0.390001\pi$
$402$	−30.9751	+	17.3604i	−1.54490	+	0.865857i
$403$	4.27353			0.212880
$404$	−40.7463			−2.02720
$405$	−13.6316	+	15.3429i	−0.677362	+	0.762394i
$406$	−54.8641			−2.72286
$407$	−7.56872			−0.375167
$408$	−63.9021	+	13.6936i	−3.16362	+	0.677933i
$409$		−	0.807186i		−	0.0399128i	−0.999801	−	0.0199564i	$-0.993647\pi$
$409$		−	0.807186i		−	0.0399128i	0.999801	−	0.0199564i	$-0.00635274\pi$
$410$	−18.7510			−0.926044
$411$	5.40976	+	25.2450i	0.266844	+	1.24525i
$412$	57.6333			2.83939
$413$	24.1728			1.18947
$414$	12.3418	+	27.4746i	0.606567	+	1.35030i
$415$			31.7213i			1.55714i
$416$		−	1.87563i		−	0.0919603i
$417$	−12.5529	+	2.68995i	−0.614716	+	0.131728i
$418$	−59.0594			−2.88869
$419$			0.0609183i			0.00297606i	0.999999	+	0.00148803i	$0.000473654\pi$
$419$			0.0609183i			0.00297606i	−0.999999	+	0.00148803i	$0.999526\pi$
$420$	−62.5566	+	13.4052i	−3.05245	+	0.654109i
$421$	9.58973			0.467375			0.233687	−	0.972312i	$-0.424921\pi$
$421$	9.58973			0.467375			0.233687	+	0.972312i	$0.424921\pi$
$422$	−9.68665			−0.471539
$423$	−4.72964	−	10.5288i	−0.229963	−	0.511930i
$424$	8.31299			0.403714
$425$			1.32775i			0.0644053i
$426$	−17.2532	+	3.69718i	−0.835919	+	0.179129i
$427$	−33.7475			−1.63316
$428$		−	40.0786i		−	1.93727i
$429$	−3.61803	+	0.775308i	−0.174680	+	0.0374322i
$430$		−	9.84933i		−	0.474977i
$431$			0.500789i			0.0241222i	0.999927	+	0.0120611i	$0.00383926\pi$
$431$			0.500789i			0.0241222i	−0.999927	+	0.0120611i	$0.996161\pi$
$432$	−17.5633	−	23.9226i	−0.845012	−	1.15098i
$433$		−	3.88698i		−	0.186796i	−0.995629	−	0.0933981i	$-0.970227\pi$
$433$		−	3.88698i		−	0.186796i	0.995629	−	0.0933981i	$-0.0297729\pi$
$434$	63.1615			3.03185
$435$	−22.3178	+	4.78249i	−1.07006	+	0.229303i
$436$		−	65.1800i		−	3.12156i
$437$		−	28.4240i		−	1.35970i
$438$	−11.1264	−	51.9223i	−0.531642	−	2.48095i
$439$	−25.8449			−1.23351			−0.616755	−	0.787155i	$-0.711553\pi$
$439$	−25.8449			−1.23351			−0.616755	+	0.787155i	$0.711553\pi$
$440$	43.1697			2.05803
$441$	20.1690	−	9.06005i	0.960426	−	0.431431i
$442$	10.6643			0.507249
$443$	0.892276			0.0423933			0.0211967	−	0.999775i	$-0.493252\pi$
$443$	0.892276			0.0423933			0.0211967	+	0.999775i	$0.493252\pi$
$444$	3.52929	+	16.4697i	0.167493	+	0.781618i
$445$		−	4.23051i		−	0.200545i
$446$	1.72361			0.0816152
$447$	23.1124	−	4.95275i	1.09318	−	0.234257i
$448$			15.5807i			0.736120i
$449$		−	14.0303i		−	0.662130i	−0.943608	−	0.331065i	$-0.892592\pi$
$449$		−	14.0303i		−	0.662130i	0.943608	−	0.331065i	$-0.107408\pi$
$450$	−1.37294	+	0.616736i	−0.0647211	+	0.0290732i
$451$	−10.9180			−0.514106
$452$	28.4224			1.33688
$453$	−2.09364	−	9.77010i	−0.0983676	−	0.459039i
$454$		−	68.8795i		−	3.23267i
$455$	5.55319			0.260338
$456$	14.6489	+	68.3603i	0.685999	+	3.20127i
$457$	6.57517			0.307574			0.153787	−	0.988104i	$-0.450853\pi$
$457$	6.57517			0.307574			0.153787	+	0.988104i	$0.450853\pi$
$458$			52.4669i			2.45162i
$459$	27.7629	−	20.3827i	1.29586	−	0.951383i
$460$			39.0592i			1.82114i
$461$			22.9451i			1.06866i	0.845276	+	0.534330i	$0.179436\pi$
$461$			22.9451i			1.06866i	−0.845276	+	0.534330i	$0.820564\pi$
$462$	−53.4734	+	11.4588i	−2.48781	+	0.533113i
$463$		−	11.9996i		−	0.557668i	−0.960339	−	0.278834i	$-0.910052\pi$
$463$		−	11.9996i		−	0.557668i	0.960339	−	0.278834i	$-0.0899480\pi$
$464$		−	33.0044i		−	1.53219i
$465$	25.6931	−	5.50577i	1.19149	−	0.255324i
$466$	−69.6613			−3.22700
$467$		−	13.9254i		−	0.644391i	−0.946673	−	0.322195i	$-0.895579\pi$
$467$		−	13.9254i		−	0.644391i	0.946673	−	0.322195i	$-0.104421\pi$
$468$	3.37418	+	7.51140i	0.155971	+	0.347214i
$469$	29.6455	−	9.16207i	1.36890	−	0.423065i
$470$		−	21.9746i		−	1.01361i
$471$	−5.66241	−	26.4240i	−0.260910	−	1.21756i
$472$			36.2992i			1.67081i
$473$		−	5.73488i		−	0.263690i
$474$	−2.61603	+	0.560589i	−0.120158	+	0.0257487i
$475$	1.42038			0.0651716
$476$	107.362			4.92093
$477$	−3.99636	+	1.79519i	−0.182981	+	0.0821963i
$478$	−0.976487			−0.0446635
$479$			28.2608i			1.29127i	0.763646	+	0.645635i	$0.223407\pi$
$479$			28.2608i			1.29127i	−0.763646	+	0.645635i	$0.776593\pi$
$480$	−2.41645	−	11.2765i	−0.110295	−	0.514701i
$481$		−	1.46203i		−	0.0666627i
$482$	−42.6009			−1.94042
$483$	−5.51488	−	25.7356i	−0.250936	−	1.17101i
$484$	0.253451			0.0115205
$485$		−	8.10006i		−	0.367805i
$486$	33.9723	+	19.2402i	1.54101	+	0.872753i
$487$			19.6516i			0.890498i	0.895407	+	0.445249i	$0.146885\pi$
$487$			19.6516i			0.890498i	−0.895407	+	0.445249i	$0.853115\pi$
$488$		−	50.6771i		−	2.29404i
$489$	0.378536	+	1.76646i	0.0171180	+	0.0798823i
$490$	42.0942			1.90162
$491$			6.08065i			0.274416i	0.990542	+	0.137208i	$0.0438128\pi$
$491$			6.08065i			0.274416i	−0.990542	+	0.137208i	$0.956187\pi$
$492$	5.09104	+	23.7577i	0.229522	+	1.07108i
$493$	38.3027			1.72507
$494$		−	11.4083i		−	0.513285i
$495$	−20.7533	+	9.32252i	−0.932790	+	0.419016i
$496$			37.9959i			1.70607i
$497$	15.4190			0.691637
$498$	59.0037	−	12.6439i	2.64402	−	0.566587i
$499$			33.0747i			1.48063i	0.672263	+	0.740313i	$0.265323\pi$
$499$			33.0747i			1.48063i	−0.672263	+	0.740313i	$0.734677\pi$
$500$	46.7675			2.09150
$501$	−29.1613	+	6.24899i	−1.30283	+	0.279184i
$502$	−27.3803			−1.22204
$503$	−27.5056			−1.22641			−0.613206	−	0.789923i	$-0.710121\pi$
$503$	−27.5056			−1.22641			−0.613206	+	0.789923i	$0.710121\pi$
$504$	26.5268	+	59.0525i	1.18160	+	2.63041i
$505$	21.7464			0.967700
$506$			33.3878i			1.48427i
$507$	4.56822	+	21.3179i	0.202882	+	0.946763i
$508$	−15.6961			−0.696402
$509$		−	26.5494i		−	1.17678i	−0.808576	−	0.588392i	$-0.799761\pi$
$509$		−	26.5494i		−	1.17678i	0.808576	−	0.588392i	$-0.200239\pi$
$510$	64.1153	−	13.7393i	2.83907	−	0.608385i
$511$			46.4025i			2.05273i
$512$	−48.3483			−2.13671
$513$	−21.8047	−	29.6999i	−0.962703	−	1.31128i
$514$		−	59.7565i		−	2.63575i
$515$	−30.7590			−1.35540
$516$	−12.4792	+	2.67417i	−0.549367	+	0.117724i
$517$		−	12.7949i		−	0.562720i
$518$		−	21.6083i		−	0.949414i
$519$	12.7554	−	2.73336i	0.559900	−	0.119981i
$520$			8.33896i			0.365688i
$521$	−19.0527			−0.834715			−0.417358	−	0.908742i	$-0.637044\pi$
$521$	−19.0527			−0.834715			−0.417358	+	0.908742i	$0.637044\pi$
$522$	17.7915	+	39.6064i	0.778712	+	1.73352i
$523$	−30.2265			−1.32171			−0.660856	−	0.750513i	$-0.729807\pi$
$523$	−30.2265			−1.32171			−0.660856	+	0.750513i	$0.729807\pi$
$524$			12.8319i			0.560564i
$525$	1.28604	−	0.275586i	0.0561274	−	0.0120275i
$526$			32.1114i			1.40013i
$527$	−44.0954			−1.92083
$528$	−6.89325	−	32.1679i	−0.299990	−	1.39993i
$529$	6.93116			0.301355
$530$	−8.34072			−0.362298
$531$	−7.83884	−	17.4504i	−0.340177	−	0.757281i
$532$		−	114.852i		−	4.97948i
$533$		−	2.10899i		−	0.0913504i
$534$	−7.86903	+	1.68625i	−0.340526	+	0.0729714i
$535$			21.3900i			0.924770i
$536$	13.7582	+	44.5173i	0.594266	+	1.92285i
$537$	7.30175	+	34.0742i	0.315094	+	1.47041i
$538$			31.7218i			1.36762i
$539$	24.5098			1.05571
$540$	29.9633	+	40.8125i	1.28941	+	1.75629i
$541$		−	5.76630i		−	0.247913i	−0.992288	−	0.123956i	$-0.960442\pi$
$541$		−	5.76630i		−	0.247913i	0.992288	−	0.123956i	$-0.0395583\pi$
$542$			26.3536i			1.13198i
$543$	0.614506	+	2.86764i	0.0263710	+	0.123062i
$544$			19.3532i			0.829763i
$545$			34.7867i			1.49010i
$546$	−2.21347	−	10.3293i	−0.0947276	−	0.442053i
$547$		−	20.0366i		−	0.856703i	−0.903612	−	0.428351i	$-0.859095\pi$
$547$		−	20.0366i		−	0.856703i	0.903612	−	0.428351i	$-0.140905\pi$
$548$	63.6914			2.72076
$549$	10.9437	+	24.3623i	0.467068	+	1.03976i
$550$	−1.66843			−0.0711422
$551$		−	40.9749i		−	1.74559i
$552$	38.6459	−	8.28144i	1.64488	−	0.352481i
$553$	2.33792			0.0994185
$554$	26.5372			1.12746
$555$	−1.88359	−	8.78991i	−0.0799539	−	0.373111i
$556$			31.6700i			1.34311i
$557$			6.58474i			0.279005i	0.990222	+	0.139502i	$0.0445503\pi$
$557$			6.58474i			0.279005i	−0.990222	+	0.139502i	$0.955450\pi$
$558$	−20.4822	−	45.5963i	−0.867081	−	1.93024i
$559$	1.10779			0.0468545
$560$			49.3733i			2.08640i
$561$	37.3318	−	7.99983i	1.57615	−	0.337753i
$562$	50.3044			2.12196
$563$	22.9566			0.967504			0.483752	−	0.875205i	$-0.339274\pi$
$563$	22.9566			0.967504			0.483752	+	0.875205i	$0.339274\pi$
$564$	−27.8420	+	5.96627i	−1.17236	+	0.251225i
$565$	−15.1691			−0.638168
$566$	29.7246			1.24942
$567$	−25.5048	−	22.6602i	−1.07110	−	0.951639i
$568$			23.1540i			0.971519i
$569$			11.3646i			0.476427i	0.971213	+	0.238214i	$0.0765618\pi$
$569$			11.3646i			0.476427i	−0.971213	+	0.238214i	$0.923438\pi$
$570$	−14.6978	−	68.5884i	−0.615624	−	2.87285i
$571$	17.8939			0.748837			0.374419	−	0.927260i	$-0.377842\pi$
$571$	17.8939			0.748837			0.374419	+	0.927260i	$0.377842\pi$
$572$			9.12804i			0.381662i
$573$	−0.360533	−	1.68246i	−0.0150615	−	0.0702856i
$574$		−	31.1702i		−	1.30102i
$575$		−	0.802981i		−	0.0334866i
$576$	11.2477	−	5.05256i	0.468655	−	0.210523i
$577$			18.2091i			0.758054i	0.925386	+	0.379027i	$0.123741\pi$
$577$			18.2091i			0.758054i	−0.925386	+	0.379027i	$0.876259\pi$
$578$	−67.4595			−2.80595
$579$	−5.11822	−	23.8846i	−0.212706	−	0.992608i
$580$			56.3063i			2.33799i
$581$	−52.7310			−2.18765
$582$	−15.0666	+	3.22863i	−0.624533	+	0.133831i
$583$	−4.85647			−0.201135
$584$	−69.6805			−2.88340
$585$	−1.80080	−	4.00885i	−0.0744541	−	0.165745i
$586$		−	0.0656618i		−	0.00271246i
$587$	9.60136			0.396291			0.198145	−	0.980173i	$-0.436508\pi$
$587$	9.60136			0.396291			0.198145	+	0.980173i	$0.436508\pi$
$588$	−11.4289	−	53.3339i	−0.471321	−	2.19945i
$589$			47.1718i			1.94368i
$590$		−	36.4203i		−	1.49940i
$591$	−3.73997	−	17.4528i	−0.153842	−	0.717914i
$592$	12.9989			0.534249
$593$	−11.2316			−0.461226			−0.230613	−	0.973046i	$-0.574073\pi$
$593$	−11.2316			−0.461226			−0.230613	+	0.973046i	$0.574073\pi$
$594$	25.6126	+	34.8866i	1.05090	+	1.43141i
$595$	−57.2992			−2.34904
$596$		−	58.3109i		−	2.38851i
$597$	1.82798	+	8.53040i	0.0748142	+	0.349126i
$598$	−6.44943			−0.263737
$599$	10.8447			0.443100			0.221550	−	0.975149i	$-0.428888\pi$
$599$	10.8447			0.443100			0.221550	+	0.975149i	$0.428888\pi$
$600$	0.413834	+	1.93119i	0.0168947	+	0.0788403i
$601$	17.5002			0.713850			0.356925	−	0.934133i	$-0.383825\pi$
$601$	17.5002			0.713850			0.356925	+	0.934133i	$0.383825\pi$
$602$	16.3728			0.667305
$603$	−16.2276	−	18.4300i	−0.660840	−	0.750527i
$604$	−24.6493			−1.00296
$605$	−0.135267			−0.00549939
$606$	−8.66796	−	40.4497i	−0.352112	−	1.64316i
$607$	39.8577			1.61777			0.808887	−	0.587965i	$-0.200071\pi$
$607$	39.8577			1.61777			0.808887	+	0.587965i	$0.200071\pi$
$608$	20.7034			0.839635
$609$	−7.95004	−	37.0995i	−0.322152	−	1.50335i
$610$			50.8462i			2.05870i
$611$	2.47156			0.0999884
$612$	−34.8156	−	77.5045i	−1.40734	−	3.13294i
$613$	−26.9806			−1.08973			−0.544867	−	0.838522i	$-0.683420\pi$
$613$	−26.9806			−1.08973			−0.544867	+	0.838522i	$0.683420\pi$
$614$	−51.5459			−2.08022
$615$	−2.71710	−	12.6795i	−0.109564	−	0.511288i
$616$			71.7620i			2.89137i
$617$			14.7709i			0.594653i	0.954776	+	0.297327i	$0.0960950\pi$
$617$			14.7709i			0.594653i	−0.954776	+	0.297327i	$0.903905\pi$
$618$	12.2603	+	57.2138i	0.493183	+	2.30147i
$619$	14.8997			0.598871			0.299436	−	0.954117i	$-0.403202\pi$
$619$	14.8997			0.598871			0.299436	+	0.954117i	$0.403202\pi$
$620$		−	64.8218i		−	2.60331i
$621$	−16.7901	+	12.3268i	−0.673765	+	0.494658i
$622$	74.8885			3.00276
$623$	7.03248			0.281750
$624$	6.21377	−	1.33155i	0.248750	−	0.0533046i
$625$	−25.9614			−1.03846
$626$			45.5923i			1.82224i
$627$	−8.55796	−	39.9363i	−0.341772	−	1.59490i
$628$	−66.6659			−2.66026
$629$			15.0856i			0.601501i
$630$	−26.6153	−	59.2495i	−1.06038	−	2.36056i
$631$		−	14.8748i		−	0.592157i	−0.955164	−	0.296078i	$-0.904321\pi$
$631$		−	14.8748i		−	0.592157i	0.955164	−	0.296078i	$-0.0956789\pi$
$632$			3.51075i			0.139650i
$633$	−1.40364	−	6.55017i	−0.0557895	−	0.260346i
$634$		−	36.1105i		−	1.43413i
$635$	8.37704			0.332433
$636$	2.26457	+	10.5678i	0.0897962	+	0.419040i
$637$			4.73449i			0.187587i
$638$			48.1306i			1.90551i
$639$	−5.00012	−	11.1310i	−0.197802	−	0.440334i
$640$	36.7915			1.45431
$641$	−18.8228			−0.743456			−0.371728	−	0.928342i	$-0.621235\pi$
$641$	−18.8228			−0.743456			−0.371728	+	0.928342i	$0.621235\pi$
$642$	39.7868	−	8.52591i	1.57026	−	0.336491i
$643$	−41.1209			−1.62165			−0.810824	−	0.585290i	$-0.800981\pi$
$643$	−41.1209			−1.62165			−0.810824	+	0.585290i	$0.800981\pi$
$644$	−64.9291			−2.55856
$645$	6.66018	−	1.42721i	0.262244	−	0.0561964i
$646$			117.714i			4.63140i
$647$	9.74294			0.383034			0.191517	−	0.981489i	$-0.438659\pi$
$647$	9.74294			0.383034			0.191517	+	0.981489i	$0.438659\pi$
$648$	34.0278	−	38.2994i	1.33674	−	1.50454i
$649$		−	21.2061i		−	0.832413i
$650$		−	0.322286i		−	0.0126411i
$651$	9.15237	+	42.7102i	0.358710	+	1.67395i
$652$	4.45666			0.174536
$653$	−9.21343			−0.360549			−0.180275	−	0.983616i	$-0.557699\pi$
$653$	−9.21343			−0.360549			−0.180275	+	0.983616i	$0.557699\pi$
$654$	64.7055	−	13.8657i	2.53019	−	0.542194i
$655$		−	6.84840i		−	0.267589i
$656$	18.7510			0.732102
$657$	33.4980	−	15.0475i	1.30688	−	0.587060i
$658$	36.5288			1.42404
$659$			25.3068i			0.985813i	0.870082	+	0.492906i	$0.164066\pi$
$659$			25.3068i			0.985813i	−0.870082	+	0.492906i	$0.835934\pi$
$660$	11.7600	+	54.8790i	0.457759	+	2.13616i
$661$		−	5.99797i		−	0.233294i	−0.993173	−	0.116647i	$-0.962785\pi$
$661$		−	5.99797i		−	0.233294i	0.993173	−	0.116647i	$-0.0372146\pi$
$662$			72.3758i			2.81297i
$663$	1.54530	+	7.21127i	0.0600146	+	0.280063i
$664$		−	79.1837i		−	3.07292i
$665$			61.2968i			2.37699i
$666$	−15.5990	+	7.00720i	−0.604450	+	0.271524i
$667$	−23.1642			−0.896923
$668$			73.5720i			2.84659i
$669$	0.249758	+	1.16551i	0.00965621	+	0.0450614i
$670$	−13.8042	−	44.6658i	−0.533301	−	1.72559i
$671$			29.6057i			1.14292i
$672$	18.7453	−	4.01692i	0.723114	−	0.154956i
$673$		−	9.52121i		−	0.367016i	−0.983018	−	0.183508i	$-0.941255\pi$
$673$		−	9.52121i		−	0.367016i	0.983018	−	0.183508i	$-0.0587453\pi$
$674$		−	24.2629i		−	0.934573i
$675$	−0.615986	−	0.839025i	−0.0237093	−	0.0322941i
$676$	53.7836			2.06860
$677$	−24.7739			−0.952137			−0.476068	−	0.879408i	$-0.657939\pi$
$677$	−24.7739			−0.952137			−0.476068	+	0.879408i	$0.657939\pi$
$678$	6.04630	+	28.2155i	0.232207	+	1.08361i
$679$	13.4649			0.516736
$680$		−	86.0436i		−	3.29962i
$681$	46.5767	−	9.98093i	1.78482	−	0.382470i
$682$		−	55.4097i		−	2.12175i
$683$	−50.2944			−1.92446			−0.962231	−	0.272233i	$-0.912238\pi$
$683$	−50.2944			−1.92446			−0.962231	+	0.272233i	$0.912238\pi$
$684$	−82.9118	+	37.2446i	−3.17021	+	1.42408i
$685$	−33.9922			−1.29878
$686$			3.51424i			0.134174i
$687$	−35.4785	+	7.60268i	−1.35359	+	0.290060i
$688$			9.84933i			0.375502i
$689$		−	0.938111i		−	0.0357392i
$690$	−38.7749	+	8.30907i	−1.47613	+	0.316321i
$691$	37.5188			1.42728			0.713642	−	0.700511i	$-0.247044\pi$
$691$	37.5188			1.42728			0.713642	+	0.700511i	$0.247044\pi$
$692$		−	32.1810i		−	1.22334i
$693$	−15.4971	−	34.4986i	−0.588685	−	1.31050i
$694$	60.3961			2.29261
$695$		−	16.9023i		−	0.641141i
$696$	55.7105	−	11.9382i	2.11170	−	0.452516i
$697$			21.7611i			0.824260i
$698$	10.0081			0.378813
$699$	−10.0942	−	47.1054i	−0.381798	−	1.78169i
$700$		−	3.24459i		−	0.122634i
$701$	35.1034			1.32584			0.662919	−	0.748691i	$-0.269317\pi$
$701$	35.1034			1.32584			0.662919	+	0.748691i	$0.269317\pi$
$702$	−6.73893	+	4.94752i	−0.254345	+	0.186732i
$703$	16.1380			0.608658
$704$	13.6685			0.515151
$705$	14.8593	−	3.18421i	0.559635	−	0.119924i
$706$	−30.2063			−1.13683
$707$			36.1495i			1.35954i
$708$	−46.1450	+	9.88841i	−1.73424	+	0.371629i
$709$	−17.9249			−0.673183			−0.336592	−	0.941651i	$-0.609274\pi$
$709$	−17.9249			−0.673183			−0.336592	+	0.941651i	$0.609274\pi$
$710$		−	23.2312i		−	0.871853i
$711$	−0.758148	−	1.68774i	−0.0284328	−	0.0632954i
$712$			10.5603i			0.395765i
$713$	26.6675			0.998706
$714$	22.8391	+	106.580i	0.854732	+	3.98867i
$715$		−	4.87165i		−	0.182189i
$716$	85.9666			3.21272
$717$	−0.141497	−	0.660307i	−0.00528431	−	0.0246596i
$718$			50.7065i			1.89235i
$719$			36.3629i			1.35611i	0.735012	+	0.678054i	$0.237176\pi$
$719$			36.3629i			1.35611i	−0.735012	+	0.678054i	$0.762824\pi$
$720$	35.6426	−	16.0109i	1.32832	−	0.596692i
$721$		−	51.1314i		−	1.90423i
$722$	78.3398			2.91551
$723$	−6.17305	−	28.8070i	−0.229578	−	1.07134i
$724$	7.23485			0.268881
$725$		−	1.15755i		−	0.0429902i
$726$	0.0539166	+	0.251606i	0.00200103	+	0.00933797i
$727$		−	40.3875i		−	1.49789i	−0.662633	−	0.748944i	$-0.730561\pi$
$727$		−	40.3875i		−	1.49789i	0.662633	−	0.748944i	$-0.269439\pi$
$728$	−13.8621			−0.513762
$729$	−8.08761	+	25.7603i	−0.299541	+	0.954083i
$730$	69.9130			2.58759
$731$	−11.4305			−0.422771
$732$	64.4227	−	13.8051i	2.38113	−	0.510253i
$733$		−	47.3781i		−	1.74995i	−0.484168	−	0.874975i	$-0.660877\pi$
$733$		−	47.3781i		−	1.74995i	0.484168	−	0.874975i	$-0.339123\pi$
$734$			14.3350i			0.529115i
$735$	6.09964	+	28.4644i	0.224988	+	1.04993i
$736$		−	11.7042i		−	0.431423i
$737$	−8.03761	−	26.0071i	−0.296069	−	0.957985i
$738$	−22.5018	+	10.1080i	−0.828301	+	0.372079i
$739$		−	13.6714i		−	0.502910i	−0.967869	−	0.251455i	$-0.919091\pi$
$739$		−	13.6714i		−	0.502910i	0.967869	−	0.251455i	$-0.0809090\pi$
$740$	−22.1763			−0.815217
$741$	7.71438	−	1.65311i	0.283395	−	0.0607287i
$742$		−	13.8650i		−	0.509000i
$743$		−	29.5301i		−	1.08335i	−0.840587	−	0.541676i	$-0.817790\pi$
$743$		−	29.5301i		−	1.08335i	0.840587	−	0.541676i	$-0.182210\pi$
$744$	−64.1359	+	13.7437i	−2.35134	+	0.503868i
$745$			31.1206i			1.14017i
$746$		−	57.6109i		−	2.10929i
$747$	17.0998	+	38.0665i	0.625648	+	1.39278i
$748$		−	94.1855i		−	3.44376i
$749$	−35.5571			−1.29923
$750$	9.94885	+	46.4270i	0.363281	+	1.69528i
$751$	12.0295			0.438963			0.219481	−	0.975617i	$-0.429563\pi$
$751$	12.0295			0.438963			0.219481	+	0.975617i	$0.429563\pi$
$752$			21.9746i			0.801330i
$753$	−3.96752	−	18.5147i	−0.144584	−	0.674714i
$754$	−9.29725			−0.338586
$755$	13.1554			0.478772
$756$	−67.8436	+	49.8087i	−2.46745	+	1.81152i
$757$		−	17.0764i		−	0.620653i	−0.950630	−	0.310326i	$-0.899562\pi$
$757$		−	17.0764i		−	0.620653i	0.950630	−	0.310326i	$-0.100438\pi$
$758$			17.3363i			0.629683i
$759$	−22.5771	+	4.83804i	−0.819496	+	0.175610i
$760$	−92.0466			−3.33888
$761$		−	42.8974i		−	1.55503i	−0.628864	−	0.777515i	$-0.716480\pi$
$761$		−	42.8974i		−	1.55503i	0.628864	−	0.777515i	$-0.283520\pi$
$762$	−3.33904	−	15.5819i	−0.120961	−	0.564471i
$763$	−57.8267			−2.09347
$764$	−4.24471			−0.153568
$765$	18.5812	+	41.3643i	0.671803	+	1.49553i
$766$	−60.8579			−2.19889
$767$	4.09632			0.147910
$768$	−11.6816	−	54.5128i	−0.421522	−	1.96706i
$769$			37.4031i			1.34879i	0.738371	+	0.674395i	$0.235596\pi$
$769$			37.4031i			1.34879i	−0.738371	+	0.674395i	$0.764404\pi$
$770$		−	72.0015i		−	2.59475i
$771$	40.4077	−	8.65897i	1.45525	−	0.311845i
$772$	−60.2590			−2.16877
$773$			25.2597i			0.908529i	0.890867	+	0.454264i	$0.150098\pi$
$773$			25.2597i			0.908529i	−0.890867	+	0.454264i	$0.849902\pi$
$774$	−5.30941	−	11.8195i	−0.190843	−	0.424843i
$775$			1.33261i			0.0478687i
$776$			20.2196i			0.725843i
$777$	14.6117	−	3.13114i	0.524191	−	0.112329i
$778$			47.7112i			1.71053i
$779$	23.2793			0.834067
$780$	−10.6008	+	2.27165i	−0.379570	+	0.0813381i
$781$		−	13.5266i		−	0.484021i
$782$	66.5469			2.37971
$783$	−24.2040	+	17.7699i	−0.864981	+	0.635043i
$784$	−42.0942			−1.50337
$785$	35.5797			1.26989
$786$	−12.7385	+	2.72973i	−0.454367	+	0.0973663i
$787$			44.1882i			1.57514i	0.616225	+	0.787570i	$0.288661\pi$
$787$			44.1882i			1.57514i	−0.616225	+	0.787570i	$0.711339\pi$
$788$	−44.0323			−1.56858
$789$	−21.7140	+	4.65308i	−0.773038	+	0.165654i
$790$		−	3.52246i		−	0.125324i
$791$		−	25.2159i		−	0.896576i
$792$	51.8050	−	23.2712i	1.84081	−	0.826906i
$793$	−5.71885			−0.203082
$794$	7.45281			0.264490
$795$	−1.20861	−	5.64005i	−0.0428649	−	0.200032i
$796$	21.5216			0.762813
$797$		−	35.1721i		−	1.24586i	−0.782278	−	0.622930i	$-0.785942\pi$
$797$		−	35.1721i		−	1.24586i	0.782278	−	0.622930i	$-0.214058\pi$
$798$	114.016	−	24.4325i	4.03613	−	0.864902i
$799$	−25.5022			−0.902201
$800$	0.584874			0.0206784
$801$	−2.28051	−	5.07674i	−0.0805779	−	0.179378i
$802$	33.9777			1.19980
$803$	40.7076			1.43654
$804$	−52.8442	+	29.6172i	−1.86367	+	1.04452i
$805$	34.6527			1.22135
$806$	10.7033			0.377009
$807$	−21.4505	+	4.59662i	−0.755092	+	0.161809i
$808$	−54.2840			−1.90970
$809$	29.0877			1.02267			0.511335	−	0.859381i	$-0.329151\pi$
$809$	29.0877			1.02267			0.511335	+	0.859381i	$0.329151\pi$
$810$	−34.1413	+	38.4272i	−1.19960	+	1.35019i
$811$		−	15.3903i		−	0.540425i	−0.962801	−	0.270213i	$-0.912906\pi$
$811$		−	15.3903i		−	0.540425i	0.962801	−	0.270213i	$-0.0870940\pi$
$812$	−93.5992			−3.28469
$813$	−17.8205	+	3.81875i	−0.624991	+	0.133929i
$814$	−18.9563			−0.664419
$815$	−2.37853			−0.0833162
$816$	−64.1153	+	13.7393i	−2.24448	+	0.480971i
$817$			12.2279i			0.427801i
$818$		−	2.02165i		−	0.0706853i
$819$	6.66400	−	2.99352i	0.232859	−	0.104602i
$820$	−31.9895			−1.11712
$821$			53.7596i			1.87622i	0.346336	+	0.938111i	$0.387426\pi$
$821$			53.7596i			1.87622i	−0.346336	+	0.938111i	$0.612574\pi$
$822$	13.5491	+	63.2278i	0.472579	+	2.20532i
$823$	−14.3455			−0.500051			−0.250026	−	0.968239i	$-0.580439\pi$
$823$	−14.3455			−0.500051			−0.250026	+	0.968239i	$0.580439\pi$
$824$	76.7816			2.67481
$825$	−0.241763	−	1.12821i	−0.00841711	−	0.0392791i
$826$	60.5424			2.10654
$827$		−	16.2924i		−	0.566544i	−0.959040	−	0.283272i	$-0.908580\pi$
$827$		−	16.2924i		−	0.566544i	0.959040	−	0.283272i	$-0.0914199\pi$
$828$	21.0554	+	46.8723i	0.731725	+	1.62892i
$829$	34.7314			1.20627			0.603137	−	0.797638i	$-0.293917\pi$
$829$	34.7314			1.20627			0.603137	+	0.797638i	$0.293917\pi$
$830$			79.4479i			2.75768i
$831$	3.84536	+	17.9446i	0.133394	+	0.622492i
$832$			2.64030i			0.0915361i
$833$		−	48.8517i		−	1.69261i
$834$	−31.4394	+	6.73716i	−1.08866	+	0.233289i
$835$		−	39.2655i		−	1.35884i
$836$	−100.756			−3.48474
$837$	27.8645	−	20.4573i	0.963139	−	0.707107i
$838$			0.152574i			0.00527058i
$839$		−	8.31696i		−	0.287133i	−0.989641	−	0.143567i	$-0.954143\pi$
$839$		−	8.31696i		−	0.287133i	0.989641	−	0.143567i	$-0.0458572\pi$
$840$	−83.3406	+	17.8591i	−2.87552	+	0.616196i
$841$	−4.39267			−0.151472
$842$	24.0181			0.827718
$843$	7.28933	+	34.0162i	0.251058	+	1.17158i
$844$	−16.5256			−0.568835
$845$	−28.7044			−0.987462
$846$	−11.8457	−	26.3702i	−0.407263	−	0.906625i
$847$		−	0.224858i		−	0.00772620i
$848$	8.34072			0.286422
$849$	4.30722	+	20.1000i	0.147824	+	0.689830i
$850$			3.32543i			0.114061i
$851$		−	9.12327i		−	0.312742i
$852$	−29.4343	+	6.30747i	−1.00840	+	0.216090i
$853$	3.26257			0.111708			0.0558542	−	0.998439i	$-0.482212\pi$
$853$	3.26257			0.111708			0.0558542	+	0.998439i	$0.482212\pi$
$854$	−84.5228			−2.89231
$855$	44.2502	−	19.8775i	1.51332	−	0.679797i
$856$		−	53.3944i		−	1.82498i
$857$	3.88776			0.132803			0.0664016	−	0.997793i	$-0.478848\pi$
$857$	3.88776			0.132803			0.0664016	+	0.997793i	$0.478848\pi$
$858$	−9.06159	+	1.94181i	−0.309358	+	0.0662923i
$859$	36.2780			1.23779			0.618895	−	0.785474i	$-0.287581\pi$
$859$	36.2780			1.23779			0.618895	+	0.785474i	$0.287581\pi$
$860$		−	16.8032i		−	0.572983i
$861$	21.0775	−	4.51669i	0.718319	−	0.153929i
$862$			1.25426i			0.0427202i
$863$			18.0830i			0.615551i	0.951459	+	0.307775i	$0.0995846\pi$
$863$			18.0830i			0.615551i	−0.951459	+	0.307775i	$0.900415\pi$
$864$	−8.97859	−	12.2296i	−0.305458	−	0.416059i
$865$			17.1750i			0.583969i
$866$		−	9.73517i		−	0.330815i
$867$	−9.77517	−	45.6166i	−0.331982	−	1.54922i
$868$	107.755			3.65744
$869$		−	2.05099i		−	0.0695751i
$870$	−55.8964	+	11.9780i	−1.89506	+	0.406093i
$871$	5.02372	−	1.55260i	0.170222	−	0.0526079i
$872$		−	86.8357i		−	2.94063i
$873$	−4.36644	−	9.72032i	−0.147782	−	0.328983i
$874$		−	71.1897i		−	2.40803i
$875$		−	41.4914i		−	1.40267i
$876$	−18.9819	−	88.5806i	−0.641340	−	2.99286i
$877$	−31.1390			−1.05149			−0.525745	−	0.850642i	$-0.676213\pi$
$877$	−31.1390			−1.05149			−0.525745	+	0.850642i	$0.676213\pi$
$878$	−64.7302			−2.18454
$879$	0.0444009	−	0.00951467i	0.00149761	−	0.000320922i
$880$	43.3137			1.46011
$881$			34.3904i			1.15864i	0.815100	+	0.579321i	$0.196682\pi$
$881$			34.3904i			1.15864i	−0.815100	+	0.579321i	$0.803318\pi$
$882$	50.5144	−	22.6915i	1.70091	−	0.764061i
$883$			23.5451i			0.792356i	0.918174	+	0.396178i	$0.129664\pi$
$883$			23.5451i			0.792356i	−0.918174	+	0.396178i	$0.870336\pi$
$884$	18.1935			0.611914
$885$	24.6277	−	5.27746i	0.827850	−	0.177400i
$886$	2.23476			0.0750783
$887$			2.37660i			0.0797985i	0.999204	+	0.0398993i	$0.0127037\pi$
$887$			2.37660i			0.0797985i	−0.999204	+	0.0398993i	$0.987296\pi$
$888$	4.70188	+	21.9417i	0.157785	+	0.736314i
$889$			13.9254i			0.467042i
$890$		−	10.5956i		−	0.355165i
$891$	−19.8791	+	22.3746i	−0.665976	+	0.749579i
$892$	2.94051			0.0984555
$893$			27.2814i			0.912936i
$894$	57.8864	−	12.4045i	1.93601	−	0.414868i
$895$	−45.8805			−1.53362
$896$			61.1595i			2.04319i
$897$	−0.934550	−	4.36115i	−0.0312037	−	0.145614i
$898$		−	35.1397i		−	1.17263i
$899$	38.4429			1.28214
$900$	−2.34227	+	1.05216i	−0.0780756	+	0.0350721i
$901$			9.67967i			0.322477i
$902$	−27.3447			−0.910479
$903$	2.37249	+	11.0714i	0.0789514	+	0.368433i
$904$	37.8656			1.25939
$905$	−3.86125			−0.128352
$906$	−5.24364	−	24.4698i	−0.174208	−	0.812956i
$907$	28.9175			0.960189			0.480094	−	0.877217i	$-0.340602\pi$
$907$	28.9175			0.960189			0.480094	+	0.877217i	$0.340602\pi$
$908$		−	117.510i		−	3.89970i
$909$	26.0963	−	11.7227i	0.865560	−	0.388816i
$910$	13.9083			0.461056
$911$		−	42.8181i		−	1.41863i	−0.704893	−	0.709313i	$-0.749005\pi$
$911$		−	42.8181i		−	1.41863i	0.704893	−	0.709313i	$-0.250995\pi$
$912$	14.6978	+	68.5884i	0.486693	+	2.27119i
$913$			46.2594i			1.53096i
$914$	16.4679			0.544711
$915$	−34.3825	+	7.36783i	−1.13665	+	0.243573i
$916$			89.5096i			2.95748i
$917$	11.3843			0.375942
$918$	69.5340	−	51.0498i	2.29497	−	1.68489i
$919$			2.19036i			0.0722533i	0.999347	+	0.0361267i	$0.0115020\pi$
$919$			2.19036i			0.0722533i	−0.999347	+	0.0361267i	$0.988498\pi$
$920$			52.0364i			1.71559i
$921$	−7.46922	−	34.8557i	−0.246119	−	1.14853i
$922$			57.4675i			1.89259i
$923$	2.61290			0.0860046
$924$	−91.2268	+	19.5490i	−3.00114	+	0.643114i
$925$	0.455901			0.0149899
$926$		−	30.0537i		−	0.987627i
$927$	−36.9117	+	16.5810i	−1.21234	+	0.544593i
$928$		−	16.8723i		−	0.553862i
$929$	−47.2048			−1.54874			−0.774370	−	0.632733i	$-0.781933\pi$
$929$	−47.2048			−1.54874			−0.774370	+	0.632733i	$0.781933\pi$
$930$	64.3499	−	13.7895i	2.11012	−	0.452177i
$931$	−52.2599			−1.71275
$932$	−118.844			−3.89285
$933$	10.8517	+	50.6401i	0.355268	+	1.65788i
$934$		−	34.8770i		−	1.14121i
$935$			50.2669i			1.64390i
$936$	4.49523	+	10.0070i	0.146931	+	0.327090i
$937$		−	11.9835i		−	0.391485i	−0.980655	−	0.195742i	$-0.937288\pi$
$937$		−	11.9835i		−	0.391485i	0.980655	−	0.195742i	$-0.0627116\pi$
$938$	74.2490	−	22.9470i	2.42432	−	0.749245i
$939$	−30.8298	+	6.60652i	−1.00609	+	0.215596i
$940$		−	37.4890i		−	1.22276i
$941$	−4.33529			−0.141326			−0.0706632	−	0.997500i	$-0.522512\pi$
$941$	−4.33529			−0.141326			−0.0706632	+	0.997500i	$0.522512\pi$
$942$	−14.1819	−	66.1806i	−0.462070	−	2.15628i
$943$		−	13.1604i		−	0.428562i
$944$			36.4203i			1.18538i
$945$	36.2082	−	26.5830i	1.17785	−	0.864744i
$946$		−	14.3634i		−	0.466993i
$947$		−	1.87045i		−	0.0607816i	−0.999538	−	0.0303908i	$-0.990325\pi$
$947$		−	1.87045i		−	0.0607816i	0.999538	−	0.0303908i	$-0.00967518\pi$
$948$	−4.46300	+	0.956376i	−0.144951	+	0.0310617i
$949$			7.86336i			0.255255i
$950$	3.55744			0.115419
$951$	24.4182	−	5.23257i	0.791813	−	0.169678i
$952$	143.032			4.63570
$953$			23.5124i			0.761641i	0.924649	+	0.380820i	$0.124358\pi$
$953$			23.5124i			0.761641i	−0.924649	+	0.380820i	$0.875642\pi$
$954$	−10.0091	+	4.49618i	−0.324058	+	0.145569i
$955$	2.26541			0.0733070
$956$	−1.66591			−0.0538793
$957$	−32.5463	+	6.97434i	−1.05207	+	0.225448i
$958$			70.7810i			2.28683i
$959$		−	56.5061i		−	1.82468i
$960$	3.40161	+	15.8739i	0.109787	+	0.512327i
$961$	−13.2568			−0.427639
$962$		−	3.66174i		−	0.118059i
$963$	11.5306	+	25.6687i	0.371567	+	0.827161i
$964$	−72.6779			−2.34080
$965$	32.1603			1.03528
$966$	−13.8124	−	64.4564i	−0.444406	−	2.07385i
$967$	16.5695			0.532838			0.266419	−	0.963857i	$-0.414159\pi$
$967$	16.5695			0.532838			0.266419	+	0.963857i	$0.414159\pi$
$968$	0.337658			0.0108527
$969$	−79.5990	+	17.0573i	−2.55709	+	0.547958i
$970$		−	20.2871i		−	0.651380i
$971$			29.7699i			0.955361i	0.878534	+	0.477680i	$0.158522\pi$
$971$			29.7699i			0.955361i	−0.878534	+	0.477680i	$0.841478\pi$
$972$	57.9574	+	32.8242i	1.85898	+	1.05284i
$973$	28.0971			0.900752
$974$			49.2186i			1.57707i
$975$	0.217932	−	0.0467007i	0.00697941	−	0.00149562i
$976$		−	50.8462i		−	1.62755i
$977$			1.53083i			0.0489754i	0.999700	+	0.0244877i	$0.00779546\pi$
$977$			1.53083i			0.0489754i	−0.999700	+	0.0244877i	$0.992205\pi$
$978$	0.948066	+	4.42422i	0.0303158	+	0.141471i
$979$		−	6.16939i		−	0.197174i
$980$	71.8136			2.29400
$981$	18.7522	+	41.7451i	0.598712	+	1.33282i
$982$			15.2294i			0.485988i
$983$	3.58107			0.114218			0.0571091	−	0.998368i	$-0.481812\pi$
$983$	3.58107			0.114218			0.0571091	+	0.998368i	$0.481812\pi$
$984$	6.78251	+	31.6511i	0.216218	+	1.00900i
$985$	23.5001			0.748776
$986$	95.9315			3.05508
$987$	5.29319	+	24.7010i	0.168484	+	0.786243i
$988$		−	19.4628i		−	0.619195i
$989$	6.91277			0.219813
$990$	−51.9779	+	23.3489i	−1.65196	+	0.742075i
$991$			9.01459i			0.286358i	0.989697	+	0.143179i	$0.0457324\pi$
$991$			9.01459i			0.286358i	−0.989697	+	0.143179i	$0.954268\pi$
$992$			19.4241i			0.616714i
$993$	−48.9410	+	10.4876i	−1.55310	+	0.332813i
$994$	38.6178			1.22488
$995$	−11.4861			−0.364134
$996$	100.661	−	21.5707i	3.18958	−	0.683495i
$997$	16.7935			0.531856			0.265928	−	0.963993i	$-0.414322\pi$
$997$	16.7935			0.531856			0.265928	+	0.963993i	$0.414322\pi$
$998$			82.8376i			2.62218i
$999$	−6.99868	−	9.53279i	−0.221429	−	0.301604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.d.a.200.20	yes	20
3.2	odd	2	inner	201.2.d.a.200.2	yes	20
67.66	odd	2	inner	201.2.d.a.200.1	✓	20
201.200	even	2	inner	201.2.d.a.200.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.d.a.200.1	✓	20	67.66	odd	2	inner
201.2.d.a.200.2	yes	20	3.2	odd	2	inner
201.2.d.a.200.19	yes	20	201.200	even	2	inner
201.2.d.a.200.20	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.50456 q^{2} +(0.362922 + 1.69360i) q^{3} +4.27284 q^{4} -2.28042 q^{5} +(0.908961 + 4.24173i) q^{6} -3.79080i q^{7} +5.69246 q^{8} +(-2.73658 + 1.22929i) q^{9} +O(q^{10})\)	\(q+2.50456 q^{2} +(0.362922 + 1.69360i) q^{3} +4.27284 q^{4} -2.28042 q^{5} +(0.908961 + 4.24173i) q^{6} -3.79080i q^{7} +5.69246 q^{8} +(-2.73658 + 1.22929i) q^{9} -5.71146 q^{10} -3.32556 q^{11} +(1.55071 + 7.23648i) q^{12} -0.642388i q^{13} -9.49429i q^{14} +(-0.827614 - 3.86212i) q^{15} +5.71146 q^{16} +6.62832i q^{17} +(-6.85393 + 3.07884i) q^{18} +7.09076 q^{19} -9.74386 q^{20} +(6.42010 - 1.37576i) q^{21} -8.32906 q^{22} -4.00860i q^{23} +(2.06592 + 9.64076i) q^{24} +0.200315 q^{25} -1.60890i q^{26} +(-3.07509 - 4.18853i) q^{27} -16.1975i q^{28} -5.77864i q^{29} +(-2.07281 - 9.67293i) q^{30} +6.65258i q^{31} +2.91978 q^{32} +(-1.20692 - 5.63217i) q^{33} +16.6010i q^{34} +8.64461i q^{35} +(-11.6929 + 5.25256i) q^{36} +2.27593 q^{37} +17.7592 q^{38} +(1.08795 - 0.233137i) q^{39} -12.9812 q^{40} +3.28305 q^{41} +(16.0795 - 3.44569i) q^{42} +1.72449i q^{43} -14.2096 q^{44} +(6.24054 - 2.80330i) q^{45} -10.0398i q^{46} +3.84745i q^{47} +(2.07281 + 9.67293i) q^{48} -7.37014 q^{49} +0.501701 q^{50} +(-11.2257 + 2.40556i) q^{51} -2.74482i q^{52} +1.46035 q^{53} +(-7.70176 - 10.4904i) q^{54} +7.58366 q^{55} -21.5790i q^{56} +(2.57339 + 12.0089i) q^{57} -14.4730i q^{58} +6.37672i q^{59} +(-3.53626 - 16.5022i) q^{60} -8.90249i q^{61} +16.6618i q^{62} +(4.65999 + 10.3738i) q^{63} -4.11014 q^{64} +1.46491i q^{65} +(-3.02280 - 14.1061i) q^{66} +(2.41692 + 7.82039i) q^{67} +28.3217i q^{68} +(6.78897 - 1.45481i) q^{69} +21.6510i q^{70} +4.06748i q^{71} +(-15.5778 + 6.99769i) q^{72} -12.2408 q^{73} +5.70020 q^{74} +(0.0726986 + 0.339253i) q^{75} +30.2976 q^{76} +12.6065i q^{77} +(2.72484 - 0.583905i) q^{78} +0.616736i q^{79} -13.0245 q^{80} +(5.97769 - 6.72809i) q^{81} +8.22260 q^{82} -13.9103i q^{83} +(27.4320 - 5.87841i) q^{84} -15.1154i q^{85} +4.31909i q^{86} +(9.78672 - 2.09720i) q^{87} -18.9306 q^{88} +1.85514i q^{89} +(15.6298 - 7.02104i) q^{90} -2.43516 q^{91} -17.1281i q^{92} +(-11.2668 + 2.41437i) q^{93} +9.63619i q^{94} -16.1699 q^{95} +(1.05965 + 4.94494i) q^{96} +3.55200i q^{97} -18.4590 q^{98} +(9.10063 - 4.08807i) 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

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