LMFDB - Embedded newform 450.2.l.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.1
Root			$-0.0566033 - 1.17421i$ of defining polynomial
Character	$\chi$	$=$	450.109
Dual form			450.2.l.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.87020 + 1.22570i) q^{5} -3.26086i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.87020 + 1.22570i) q^{5} -3.26086i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.107666 - 2.23347i) q^{10} +(1.44726 + 1.05149i) q^{11} +(3.38313 + 4.65648i) q^{13} +(2.63809 + 1.91668i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(6.26221 + 2.03472i) q^{17} +(-1.21533 + 3.74041i) q^{19} +(1.74363 + 1.39991i) q^{20} +(-1.70135 + 0.552802i) q^{22} +(-4.91598 + 6.76626i) q^{23} +(1.99532 - 4.58462i) q^{25} -5.75573 q^{26} +(-3.10126 + 1.00766i) q^{28} +(-0.442669 - 1.36239i) q^{29} +(1.99827 - 6.15005i) q^{31} -1.00000i q^{32} +(-5.32696 + 3.87026i) q^{34} +(3.99683 + 6.09846i) q^{35} +(6.56303 + 9.03323i) q^{37} +(-2.31170 - 3.18178i) q^{38} +(-2.15743 + 0.587785i) q^{40} +(3.18453 - 2.31370i) q^{41} +2.18577i q^{43} +(0.552802 - 1.70135i) q^{44} +(-2.58448 - 7.95422i) q^{46} +(-6.88191 + 2.23607i) q^{47} -3.63318 q^{49} +(2.53621 + 4.30902i) q^{50} +(3.38313 - 4.65648i) q^{52} +(1.47281 - 0.478544i) q^{53} +(-3.99548 - 0.192604i) q^{55} +(1.00766 - 3.10126i) q^{56} +(1.36239 + 0.442669i) q^{58} +(8.85810 - 6.43579i) q^{59} +(0.637605 + 0.463247i) q^{61} +(3.80094 + 5.23154i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-12.0346 - 4.56186i) q^{65} +(7.46309 + 2.42490i) q^{67} -6.58448i q^{68} +(-7.28304 - 0.351083i) q^{70} +(-2.12853 - 6.55093i) q^{71} +(-7.26733 + 10.0026i) q^{73} -11.1657 q^{74} +3.93290 q^{76} +(3.42877 - 4.71929i) q^{77} +(1.18285 + 3.64043i) q^{79} +(0.792578 - 2.09089i) q^{80} +3.93630i q^{82} +(-6.37438 - 2.07116i) q^{83} +(-14.2056 + 3.87026i) q^{85} +(-1.76833 - 1.28477i) q^{86} +(1.05149 + 1.44726i) q^{88} +(1.29271 + 0.939207i) q^{89} +(15.1841 - 11.0319i) q^{91} +(7.95422 + 2.58448i) q^{92} +(2.23607 - 6.88191i) q^{94} +(-2.31170 - 8.48495i) q^{95} +(8.68131 - 2.82073i) q^{97} +(2.13553 - 2.93930i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.87020	+	1.22570i	−0.836380	+	0.548150i
$5$	−1.87020	+	1.22570i	−0.836380	+	0.548150i
$6$		0			0
$7$		−	3.26086i		−	1.23249i	−0.787555	−	0.616244i	$-0.788654\pi$
$7$		−	3.26086i		−	1.23249i	0.787555	−	0.616244i	$-0.211346\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	0.107666	−	2.23347i	0.0340469	−	0.706287i
$11$	1.44726	+	1.05149i	0.436364	+	0.317037i	0.784189	−	0.620523i	$-0.213080\pi$
$11$	1.44726	+	1.05149i	0.436364	+	0.317037i	−0.347825	+	0.937560i	$0.613080\pi$
$12$		0			0
$13$	3.38313	+	4.65648i	0.938312	+	1.29148i	0.956528	+	0.291641i	$0.0942013\pi$
$13$	3.38313	+	4.65648i	0.938312	+	1.29148i	−0.0182161	+	0.999834i	$0.505799\pi$
$14$	2.63809	+	1.91668i	0.705059	+	0.512255i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	6.26221	+	2.03472i	1.51881	+	0.493491i	0.945438	−	0.325803i	$-0.105635\pi$
$17$	6.26221	+	2.03472i	1.51881	+	0.493491i	0.573373	+	0.819295i	$0.305635\pi$
$18$		0			0
$19$	−1.21533	+	3.74041i	−0.278816	+	0.858108i	0.709368	+	0.704838i	$0.248980\pi$
$19$	−1.21533	+	3.74041i	−0.278816	+	0.858108i	−0.988184	+	0.153270i	$0.951020\pi$
$20$	1.74363	+	1.39991i	0.389889	+	0.313029i
$21$		0			0
$22$	−1.70135	+	0.552802i	−0.362729	+	0.117858i
$23$	−4.91598	+	6.76626i	−1.02505	+	1.41086i	−0.116452	+	0.993196i	$0.537152\pi$
$23$	−4.91598	+	6.76626i	−1.02505	+	1.41086i	−0.908600	+	0.417667i	$0.862848\pi$
$24$		0			0
$25$	1.99532	−	4.58462i	0.399064	−	0.916923i
$26$	−5.75573			−1.12879
$27$		0			0
$28$	−3.10126	+	1.00766i	−0.586083	+	0.190430i
$29$	−0.442669	−	1.36239i	−0.0822015	−	0.252990i	0.901506	−	0.432767i	$-0.142463\pi$
$29$	−0.442669	−	1.36239i	−0.0822015	−	0.252990i	−0.983708	+	0.179776i	$0.942463\pi$
$30$		0			0
$31$	1.99827	−	6.15005i	0.358900	−	1.10458i	−0.594813	−	0.803864i	$-0.702774\pi$
$31$	1.99827	−	6.15005i	0.358900	−	1.10458i	0.953713	−	0.300717i	$-0.0972261\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.32696	+	3.87026i	−0.913566	+	0.663744i
$35$	3.99683	+	6.09846i	0.675588	+	1.03083i
$36$		0			0
$37$	6.56303	+	9.03323i	1.07895	+	1.48505i	0.860666	+	0.509170i	$0.170047\pi$
$37$	6.56303	+	9.03323i	1.07895	+	1.48505i	0.218289	+	0.975884i	$0.429953\pi$
$38$	−2.31170	−	3.18178i	−0.375007	−	0.516153i
$39$		0			0
$40$	−2.15743	+	0.587785i	−0.341120	+	0.0929370i
$41$	3.18453	−	2.31370i	0.497340	−	0.361339i	−0.310660	−	0.950521i	$-0.600550\pi$
$41$	3.18453	−	2.31370i	0.497340	−	0.361339i	0.808000	+	0.589182i	$0.200550\pi$
$42$		0			0
$43$			2.18577i			0.333327i	0.986014	+	0.166664i	$0.0532994\pi$
$43$			2.18577i			0.333327i	−0.986014	+	0.166664i	$0.946701\pi$
$44$	0.552802	−	1.70135i	0.0833381	−	0.256488i
$45$		0			0
$46$	−2.58448	−	7.95422i	−0.381061	−	1.17279i
$47$	−6.88191	+	2.23607i	−1.00383	+	0.326164i	−0.764395	−	0.644748i	$-0.776962\pi$
$47$	−6.88191	+	2.23607i	−1.00383	+	0.326164i	−0.239435	+	0.970912i	$0.576962\pi$
$48$		0			0
$49$	−3.63318			−0.519026
$50$	2.53621	+	4.30902i	0.358675	+	0.609387i
$51$		0			0
$52$	3.38313	−	4.65648i	0.469156	−	0.645738i
$53$	1.47281	−	0.478544i	0.202306	−	0.0657330i	−0.206111	−	0.978529i	$-0.566081\pi$
$53$	1.47281	−	0.478544i	0.202306	−	0.0657330i	0.408417	+	0.912795i	$0.366081\pi$
$54$		0			0
$55$	−3.99548	−	0.192604i	−0.538750	−	0.0259707i
$56$	1.00766	−	3.10126i	0.134654	−	0.414423i
$57$		0			0
$58$	1.36239	+	0.442669i	0.178891	+	0.0581253i
$59$	8.85810	−	6.43579i	1.15323	−	0.837868i	0.164320	−	0.986407i	$-0.447457\pi$
$59$	8.85810	−	6.43579i	1.15323	−	0.837868i	0.988907	+	0.148539i	$0.0474570\pi$
$60$		0			0
$61$	0.637605	+	0.463247i	0.0816370	+	0.0593128i	0.627855	−	0.778330i	$-0.283933\pi$
$61$	0.637605	+	0.463247i	0.0816370	+	0.0593128i	−0.546218	+	0.837643i	$0.683933\pi$
$62$	3.80094	+	5.23154i	0.482720	+	0.664407i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−12.0346	−	4.56186i	−1.49271	−	0.565829i
$66$		0			0
$67$	7.46309	+	2.42490i	0.911762	+	0.296249i	0.727083	−	0.686550i	$-0.240876\pi$
$67$	7.46309	+	2.42490i	0.911762	+	0.296249i	0.184679	+	0.982799i	$0.440876\pi$
$68$		−	6.58448i		−	0.798486i
$69$		0			0
$70$	−7.28304	−	0.351083i	−0.870489	−	0.0419624i
$71$	−2.12853	−	6.55093i	−0.252610	−	0.777452i	−0.994291	−	0.106700i	$-0.965971\pi$
$71$	−2.12853	−	6.55093i	−0.252610	−	0.777452i	0.741682	−	0.670752i	$-0.234029\pi$
$72$		0			0
$73$	−7.26733	+	10.0026i	−0.850577	+	1.17072i	0.133159	+	0.991095i	$0.457488\pi$
$73$	−7.26733	+	10.0026i	−0.850577	+	1.17072i	−0.983735	+	0.179624i	$0.942512\pi$
$74$	−11.1657			−1.29798
$75$		0			0
$76$	3.93290			0.451134
$77$	3.42877	−	4.71929i	0.390744	−	0.537813i
$78$		0			0
$79$	1.18285	+	3.64043i	0.133081	+	0.409580i	0.995287	−	0.0969777i	$-0.0309176\pi$
$79$	1.18285	+	3.64043i	0.133081	+	0.409580i	−0.862206	+	0.506558i	$0.830918\pi$
$80$	0.792578	−	2.09089i	0.0886129	−	0.233769i
$81$		0			0
$82$			3.93630i			0.434691i
$83$	−6.37438	−	2.07116i	−0.699679	−	0.227339i	−0.0624883	−	0.998046i	$-0.519904\pi$
$83$	−6.37438	−	2.07116i	−0.699679	−	0.227339i	−0.637191	+	0.770706i	$0.719904\pi$
$84$		0			0
$85$	−14.2056	+	3.87026i	−1.54081	+	0.419789i
$86$	−1.76833	−	1.28477i	−0.190684	−	0.138540i
$87$		0			0
$88$	1.05149	+	1.44726i	0.112090	+	0.154278i
$89$	1.29271	+	0.939207i	0.137027	+	0.0995557i	0.654187	−	0.756333i	$-0.273011\pi$
$89$	1.29271	+	0.939207i	0.137027	+	0.0995557i	−0.517160	+	0.855889i	$0.673011\pi$
$90$		0			0
$91$	15.1841	−	11.0319i	1.59173	−	1.15646i
$92$	7.95422	+	2.58448i	0.829285	+	0.269451i
$93$		0			0
$94$	2.23607	−	6.88191i	0.230633	−	0.709815i
$95$	−2.31170	−	8.48495i	−0.237175	−	0.870538i
$96$		0			0
$97$	8.68131	−	2.82073i	0.881454	−	0.286402i	0.166893	−	0.985975i	$-0.446627\pi$
$97$	8.68131	−	2.82073i	0.881454	−	0.286402i	0.714561	+	0.699573i	$0.246627\pi$
$98$	2.13553	−	2.93930i	0.215721	−	0.296915i
$99$		0			0
$100$	−4.97682	−	0.480938i	−0.497682	−	0.0480938i
$101$	−4.57572			−0.455302			−0.227651	−	0.973743i	$-0.573104\pi$
$101$	−4.57572			−0.455302			−0.227651	+	0.973743i	$0.573104\pi$
$102$		0			0
$103$	4.54128	−	1.47555i	0.447466	−	0.145390i	−0.0766118	−	0.997061i	$-0.524410\pi$
$103$	4.54128	−	1.47555i	0.447466	−	0.145390i	0.524078	+	0.851671i	$0.324410\pi$
$104$	1.77862	+	5.47402i	0.174408	+	0.536772i
$105$		0			0
$106$	−0.478544	+	1.47281i	−0.0464803	+	0.143052i
$107$		−	9.80214i		−	0.947609i	−0.880630	−	0.473804i	$-0.842880\pi$
$107$		−	9.80214i		−	0.947609i	0.880630	−	0.473804i	$-0.157120\pi$
$108$		0			0
$109$	−7.36472	+	5.35079i	−0.705413	+	0.512512i	−0.881691	−	0.471828i	$-0.843594\pi$
$109$	−7.36472	+	5.35079i	−0.705413	+	0.512512i	0.176278	+	0.984340i	$0.443594\pi$
$110$	2.50430	−	3.11920i	0.238776	−	0.297404i
$111$		0			0
$112$	1.91668	+	2.63809i	0.181110	+	0.249276i
$113$	2.67031	+	3.67537i	0.251202	+	0.345750i	0.915932	−	0.401334i	$-0.131453\pi$
$113$	2.67031	+	3.67537i	0.251202	+	0.345750i	−0.664730	+	0.747084i	$0.731453\pi$
$114$		0			0
$115$	0.900470	−	18.6798i	0.0839692	−	1.74190i
$116$	−1.15892	+	0.842006i	−0.107603	+	0.0781783i
$117$		0			0
$118$			10.9492i			1.00796i
$119$	6.63492	−	20.4202i	0.608222	−	1.87191i
$120$		0			0
$121$	−2.41027	−	7.41806i	−0.219116	−	0.674369i
$122$	−0.749550	+	0.243544i	−0.0678611	+	0.0220494i
$123$		0			0
$124$	−6.46655			−0.580713
$125$	1.88771	+	11.0198i	0.168842	+	0.985643i
$126$		0			0
$127$	6.88140	−	9.47144i	0.610626	−	0.840454i	−0.386003	−	0.922498i	$-0.626145\pi$
$127$	6.88140	−	9.47144i	0.610626	−	0.840454i	0.996629	+	0.0820432i	$0.0261446\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	10.7644	−	7.05479i	0.944098	−	0.618746i
$131$	0.164308	−	0.505688i	0.0143557	−	0.0441822i	−0.943622	−	0.331025i	$-0.892606\pi$
$131$	0.164308	−	0.505688i	0.0143557	−	0.0441822i	0.957978	+	0.286843i	$0.0926057\pi$
$132$		0			0
$133$	12.1969	+	3.96302i	1.05761	+	0.343638i
$134$	−6.34848	+	4.61244i	−0.548425	+	0.398454i
$135$		0			0
$136$	5.32696	+	3.87026i	0.456783	+	0.331872i
$137$	−11.7483	−	16.1701i	−1.00372	−	1.38151i	−0.923013	−	0.384770i	$-0.874281\pi$
$137$	−11.7483	−	16.1701i	−1.00372	−	1.38151i	−0.0807113	−	0.996738i	$-0.525719\pi$
$138$		0			0
$139$	−16.8021	−	12.2075i	−1.42514	−	1.03542i	−0.990896	−	0.134628i	$-0.957016\pi$
$139$	−16.8021	−	12.2075i	−1.42514	−	1.03542i	−0.434243	−	0.900796i	$-0.642984\pi$
$140$	4.56489	−	5.68574i	0.385804	−	0.480533i
$141$		0			0
$142$	6.55093	+	2.12853i	0.549742	+	0.178622i
$143$			10.2965i			0.861033i
$144$		0			0
$145$	2.49777	+	2.00538i	0.207428	+	0.166537i
$146$	−3.82066	−	11.7588i	−0.316200	−	0.973164i
$147$		0			0
$148$	6.56303	−	9.03323i	0.539477	−	0.742527i
$149$	−3.80700			−0.311882			−0.155941	−	0.987766i	$-0.549841\pi$
$149$	−3.80700			−0.311882			−0.155941	+	0.987766i	$0.549841\pi$
$150$		0			0
$151$	−14.9802			−1.21907			−0.609534	−	0.792760i	$-0.708643\pi$
$151$	−14.9802			−1.21907			−0.609534	+	0.792760i	$0.708643\pi$
$152$	−2.31170	+	3.18178i	−0.187503	+	0.258076i
$153$		0			0
$154$	1.80261	+	5.54786i	0.145258	+	0.447059i
$155$	3.80094	+	13.9511i	0.305299	+	1.12058i
$156$		0			0
$157$			0.333474i			0.0266141i	0.999911	+	0.0133071i	$0.00423589\pi$
$157$			0.333474i			0.0266141i	−0.999911	+	0.0133071i	$0.995764\pi$
$158$	−3.64043	−	1.18285i	−0.289617	−	0.0941023i
$159$		0			0
$160$	1.22570	+	1.87020i	0.0969001	+	0.147853i
$161$	22.0638	+	16.0303i	1.73887	+	1.26336i
$162$		0			0
$163$	−1.13075	−	1.55635i	−0.0885674	−	0.121903i	0.762434	−	0.647066i	$-0.224004\pi$
$163$	−1.13075	−	1.55635i	−0.0885674	−	0.121903i	−0.851001	+	0.525163i	$0.824004\pi$
$164$	−3.18453	−	2.31370i	−0.248670	−	0.180669i
$165$		0			0
$166$	5.42237	−	3.93958i	0.420858	−	0.305771i
$167$	1.34265	+	0.436254i	0.103898	+	0.0337584i	0.360504	−	0.932757i	$-0.382605\pi$
$167$	1.34265	+	0.436254i	0.103898	+	0.0337584i	−0.256607	+	0.966516i	$0.582605\pi$
$168$		0			0
$169$	−6.22001	+	19.1432i	−0.478462	+	1.47256i
$170$	5.21871	−	13.7674i	0.400257	−	1.05591i
$171$		0			0
$172$	2.07879	−	0.675441i	0.158507	−	0.0515019i
$173$	7.78821	−	10.7195i	0.592126	−	0.814992i	−0.402833	−	0.915274i	$-0.631974\pi$
$173$	7.78821	−	10.7195i	0.592126	−	0.814992i	0.994959	+	0.100282i	$0.0319744\pi$
$174$		0			0
$175$	−14.9498	−	6.50645i	−1.13010	−	0.491841i
$176$	−1.78891			−0.134844
$177$		0			0
$178$	−1.51967	+	0.493770i	−0.113904	+	0.0370096i
$179$	7.39730	+	22.7665i	0.552900	+	1.70165i	0.701425	+	0.712743i	$0.252547\pi$
$179$	7.39730	+	22.7665i	0.552900	+	1.70165i	−0.148525	+	0.988909i	$0.547453\pi$
$180$		0			0
$181$	−3.36799	+	10.3656i	−0.250340	+	0.770468i	0.744372	+	0.667766i	$0.232749\pi$
$181$	−3.36799	+	10.3656i	−0.250340	+	0.770468i	−0.994712	+	0.102703i	$0.967251\pi$
$182$			18.7686i			1.39122i
$183$		0			0
$184$	−6.76626	+	4.91598i	−0.498815	+	0.362411i
$185$	−23.3462	−	8.84968i	−1.71645	−	0.650641i
$186$		0			0
$187$	6.92354	+	9.52943i	0.506299	+	0.696861i
$188$	4.25325	+	5.85410i	0.310200	+	0.426954i
$189$		0			0
$190$	8.22325	+	3.11713i	0.596577	+	0.226140i
$191$	−4.22273	+	3.06799i	−0.305546	+	0.221992i	−0.729983	−	0.683465i	$-0.760472\pi$
$191$	−4.22273	+	3.06799i	−0.305546	+	0.221992i	0.424437	+	0.905458i	$0.360472\pi$
$192$		0			0
$193$			5.70634i			0.410751i	0.978683	+	0.205376i	$0.0658416\pi$
$193$			5.70634i			0.410751i	−0.978683	+	0.205376i	$0.934158\pi$
$194$	−2.82073	+	8.68131i	−0.202517	+	0.623282i
$195$		0			0
$196$	1.12271	+	3.45536i	0.0801939	+	0.246811i
$197$	−17.0025	+	5.52445i	−1.21138	+	0.393600i	−0.843935	−	0.536446i	$-0.819767\pi$
$197$	−17.0025	+	5.52445i	−1.21138	+	0.393600i	−0.367443	+	0.930046i	$0.619767\pi$
$198$		0			0
$199$	−11.6446			−0.825461			−0.412730	−	0.910853i	$-0.635425\pi$
$199$	−11.6446			−0.825461			−0.412730	+	0.910853i	$0.635425\pi$
$200$	3.31439	−	3.74364i	0.234362	−	0.264715i
$201$		0			0
$202$	2.68954	−	3.70184i	0.189236	−	0.260460i
$203$	−4.44257	+	1.44348i	−0.311807	+	0.101312i
$204$		0			0
$205$	−3.11982	+	8.23036i	−0.217898	+	0.574833i
$206$	−1.47555	+	4.54128i	−0.102807	+	0.316406i
$207$		0			0
$208$	−5.47402	−	1.77862i	−0.379555	−	0.123325i
$209$	−5.69191	+	4.13541i	−0.393717	+	0.286052i
$210$		0			0
$211$	4.96645	+	3.60834i	0.341904	+	0.248408i	0.745465	−	0.666545i	$-0.232228\pi$
$211$	4.96645	+	3.60834i	0.341904	+	0.248408i	−0.403561	+	0.914953i	$0.632228\pi$
$212$	−0.910244	−	1.25284i	−0.0625158	−	0.0860457i
$213$		0			0
$214$	7.93010	+	5.76156i	0.542091	+	0.393852i
$215$	−2.67910	−	4.08784i	−0.182713	−	0.278788i
$216$		0			0
$217$	−20.0544	−	6.51608i	−1.36138	−	0.442340i
$218$		−	9.10330i		−	0.616553i
$219$		0			0
$220$	1.05149	+	3.85944i	0.0708916	+	0.260204i
$221$	11.7113	+	36.0436i	0.787785	+	2.42455i
$222$		0			0
$223$	−4.32111	+	5.94750i	−0.289363	+	0.398274i	−0.928807	−	0.370563i	$-0.879165\pi$
$223$	−4.32111	+	5.94750i	−0.289363	+	0.398274i	0.639444	+	0.768838i	$0.279165\pi$
$224$	−3.26086			−0.217875
$225$		0			0
$226$	−4.54301			−0.302196
$227$	9.42691	−	12.9750i	0.625686	−	0.861183i	−0.372065	−	0.928207i	$-0.621350\pi$
$227$	9.42691	−	12.9750i	0.625686	−	0.861183i	0.997751	+	0.0670236i	$0.0213503\pi$
$228$		0			0
$229$	−3.53767	−	10.8878i	−0.233776	−	0.719488i	−0.997281	−	0.0736867i	$-0.976524\pi$
$229$	−3.53767	−	10.8878i	−0.233776	−	0.719488i	0.763506	−	0.645801i	$-0.223476\pi$
$230$	14.5830	+	11.7082i	0.961574	+	0.772016i
$231$		0			0
$232$		−	1.43251i		−	0.0940487i
$233$	8.93253	+	2.90235i	0.585189	+	0.190140i	0.586624	−	0.809859i	$-0.300457\pi$
$233$	8.93253	+	2.90235i	0.585189	+	0.190140i	−0.00143462	+	0.999999i	$0.500457\pi$
$234$		0			0
$235$	10.1298	−	12.6171i	0.660797	−	0.823046i
$236$	−8.85810	−	6.43579i	−0.576613	−	0.418934i
$237$		0			0
$238$	12.6204	+	17.3704i	0.818057	+	1.12596i
$239$	7.21159	+	5.23952i	0.466479	+	0.338917i	0.796067	−	0.605208i	$-0.206910\pi$
$239$	7.21159	+	5.23952i	0.466479	+	0.338917i	−0.329589	+	0.944125i	$0.606910\pi$
$240$		0			0
$241$	7.06186	−	5.13074i	0.454894	−	0.330500i	−0.336631	−	0.941637i	$-0.609287\pi$
$241$	7.06186	−	5.13074i	0.454894	−	0.330500i	0.791525	+	0.611137i	$0.209287\pi$
$242$	7.41806	+	2.41027i	0.476851	+	0.154938i
$243$		0			0
$244$	0.243544	−	0.749550i	0.0155913	−	0.0479850i
$245$	6.79478	−	4.45319i	0.434103	−	0.284504i
$246$		0			0
$247$	−21.5288	+	6.99512i	−1.36984	+	0.445089i
$248$	3.80094	−	5.23154i	0.241360	−	0.332203i
$249$		0			0
$250$	−10.0248	−	4.95010i	−0.634024	−	0.313072i
$251$	12.6654			0.799434			0.399717	−	0.916639i	$-0.369108\pi$
$251$	12.6654			0.799434			0.399717	+	0.916639i	$0.369108\pi$
$252$		0			0
$253$	−14.2294	+	4.62340i	−0.894592	+	0.290670i
$254$	3.61777	+	11.1343i	0.226999	+	0.698631i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$			23.3320i			1.45541i	0.685889	+	0.727706i	$0.259413\pi$
$257$			23.3320i			1.45541i	−0.685889	+	0.727706i	$0.740587\pi$
$258$		0			0
$259$	29.4561	−	21.4011i	1.83031	−	1.32980i
$260$	−0.619695	+	12.8553i	−0.0384319	+	0.797250i
$261$		0			0
$262$	0.312532	+	0.430164i	0.0193083	+	0.0265756i
$263$	16.9057	+	23.2687i	1.04245	+	1.43481i	0.895176	+	0.445713i	$0.147050\pi$
$263$	16.9057	+	23.2687i	1.04245	+	1.43481i	0.147274	+	0.989096i	$0.452950\pi$
$264$		0			0
$265$	−2.16790	+	2.70019i	−0.133173	+	0.165872i
$266$	−10.3753	+	7.53811i	−0.636152	+	0.462191i
$267$		0			0
$268$		−	7.84716i		−	0.479341i
$269$	8.10976	−	24.9593i	0.494461	−	1.52179i	−0.323335	−	0.946284i	$-0.604804\pi$
$269$	8.10976	−	24.9593i	0.494461	−	1.52179i	0.817796	−	0.575508i	$-0.195196\pi$
$270$		0			0
$271$	−4.54474	−	13.9873i	−0.276073	−	0.849666i	−0.988933	−	0.148360i	$-0.952601\pi$
$271$	−4.54474	−	13.9873i	−0.276073	−	0.849666i	0.712860	−	0.701306i	$-0.247399\pi$
$272$	−6.26221	+	2.03472i	−0.379703	+	0.123373i
$273$		0			0
$274$	19.9874			1.20748
$275$	7.70843	−	4.53705i	0.464836	−	0.273594i
$276$		0			0
$277$	3.80958	−	5.24344i	0.228895	−	0.315048i	−0.679085	−	0.734059i	$-0.737623\pi$
$277$	3.80958	−	5.24344i	0.228895	−	0.315048i	0.907981	+	0.419012i	$0.137623\pi$
$278$	19.7521	−	6.41785i	1.18465	−	0.384917i
$279$		0			0
$280$	1.91668	+	7.03507i	0.114544	+	0.420426i
$281$	4.22790	−	13.0121i	0.252215	−	0.776239i	−0.742150	−	0.670234i	$-0.766194\pi$
$281$	4.22790	−	13.0121i	0.252215	−	0.776239i	0.994366	−	0.106005i	$-0.0338061\pi$
$282$		0			0
$283$	−5.07176	−	1.64792i	−0.301485	−	0.0979584i	0.154368	−	0.988013i	$-0.450666\pi$
$283$	−5.07176	−	1.64792i	−0.301485	−	0.0979584i	−0.455853	+	0.890055i	$0.650666\pi$
$284$	−5.57255	+	4.04870i	−0.330670	+	0.240246i
$285$		0			0
$286$	−8.33001	−	6.05210i	−0.492564	−	0.357868i
$287$	−7.54463	−	10.3843i	−0.445346	−	0.612966i
$288$		0			0
$289$	21.3220	+	15.4913i	1.25423	+	0.911254i
$290$	−3.09053	+	0.842006i	−0.181482	+	0.0494443i
$291$		0			0
$292$	11.7588	+	3.82066i	0.688131	+	0.223587i
$293$			5.03444i			0.294115i	0.989128	+	0.147058i	$0.0469803\pi$
$293$			5.03444i			0.294115i	−0.989128	+	0.147058i	$0.953020\pi$
$294$		0			0
$295$	−8.67811	+	22.8936i	−0.505259	+	1.33292i
$296$	3.45039	+	10.6192i	0.200550	+	0.617228i
$297$		0			0
$298$	2.23770	−	3.07993i	0.129626	−	0.178415i
$299$	−48.1384			−2.78391
$300$		0			0
$301$	7.12749			0.410822
$302$	8.80511	−	12.1192i	0.506677	−	0.697382i
$303$		0			0
$304$	−1.21533	−	3.74041i	−0.0697041	−	0.214527i
$305$	−1.76025	−	0.0848540i	−0.100792	−	0.00485873i
$306$		0			0
$307$		−	16.3668i		−	0.934103i	−0.884230	−	0.467052i	$-0.845316\pi$
$307$		−	16.3668i		−	0.934103i	0.884230	−	0.467052i	$-0.154684\pi$
$308$	−5.54786	−	1.80261i	−0.316119	−	0.102713i
$309$		0			0
$310$	−13.5208	−	5.12524i	−0.767932	−	0.291094i
$311$	−16.7904	−	12.1989i	−0.952096	−	0.691738i	−0.000794562	−	1.00000i	$-0.500253\pi$
$311$	−16.7904	−	12.1989i	−0.952096	−	0.691738i	−0.951302	+	0.308261i	$0.900253\pi$
$312$		0			0
$313$	−17.5274	−	24.1244i	−0.990707	−	1.36359i	−0.930857	−	0.365384i	$-0.880938\pi$
$313$	−17.5274	−	24.1244i	−0.990707	−	1.36359i	−0.0598502	−	0.998207i	$-0.519062\pi$
$314$	−0.269786	−	0.196011i	−0.0152249	−	0.0110615i
$315$		0			0
$316$	3.09673	−	2.24991i	0.174205	−	0.126567i
$317$	−23.6062	−	7.67013i	−1.32586	−	0.430797i	−0.441355	−	0.897332i	$-0.645502\pi$
$317$	−23.6062	−	7.67013i	−1.32586	−	0.430797i	−0.884503	+	0.466535i	$0.845502\pi$
$318$		0			0
$319$	0.791893	−	2.43720i	0.0443375	−	0.136457i
$320$	−2.23347	−	0.107666i	−0.124855	−	0.00601870i
$321$		0			0
$322$	−25.9376	+	8.42762i	−1.44544	+	0.469653i
$323$	−15.2213	+	20.9504i	−0.846938	+	1.16571i
$324$		0			0
$325$	28.0986	−	6.21919i	1.55863	−	0.344978i
$326$	1.92375			0.106547
$327$		0			0
$328$	3.74364	−	1.21638i	0.206708	−	0.0671635i
$329$	7.29149	+	22.4409i	0.401993	+	1.23721i
$330$		0			0
$331$	0.629410	−	1.93712i	0.0345955	−	0.106474i	−0.932268	−	0.361769i	$-0.882173\pi$
$331$	0.629410	−	1.93712i	0.0345955	−	0.106474i	0.966863	+	0.255295i	$0.0821727\pi$
$332$			6.70242i			0.367843i
$333$		0			0
$334$	−1.14213	+	0.829805i	−0.0624945	+	0.0454049i
$335$	−16.9297	+	4.61244i	−0.924968	+	0.252005i
$336$		0			0
$337$	14.8274	+	20.4082i	0.807700	+	1.11170i	0.991674	+	0.128773i	$0.0411038\pi$
$337$	14.8274	+	20.4082i	0.807700	+	1.11170i	−0.183974	+	0.982931i	$0.558896\pi$
$338$	−11.8312	−	16.2842i	−0.643531	−	0.885744i
$339$		0			0
$340$	8.07060	+	12.3143i	0.437690	+	0.667838i
$341$	9.35874	−	6.79953i	0.506804	−	0.368215i
$342$		0			0
$343$		−	10.9787i		−	0.592795i
$344$	−0.675441	+	2.07879i	−0.0364173	+	0.112081i
$345$		0			0
$346$	4.09450	+	12.6016i	0.220122	+	0.677465i
$347$	19.2892	−	6.26743i	1.03550	−	0.336453i	0.258535	−	0.966002i	$-0.416760\pi$
$347$	19.2892	−	6.26743i	1.03550	−	0.336453i	0.776961	+	0.629549i	$0.216760\pi$
$348$		0			0
$349$	1.40434			0.0751724			0.0375862	−	0.999293i	$-0.488033\pi$
$349$	1.40434			0.0751724			0.0375862	+	0.999293i	$0.488033\pi$
$350$	14.0511	−	8.27022i	0.751062	−	0.442062i
$351$		0			0
$352$	1.05149	−	1.44726i	0.0560448	−	0.0771390i
$353$	3.65495	−	1.18756i	0.194533	−	0.0632077i	−0.210130	−	0.977673i	$-0.567389\pi$
$353$	3.65495	−	1.18756i	0.194533	−	0.0632077i	0.404663	+	0.914466i	$0.367389\pi$
$354$		0			0
$355$	12.0103	+	9.64264i	0.637438	+	0.511778i
$356$	0.493770	−	1.51967i	0.0261698	−	0.0805423i
$357$		0			0
$358$	−22.7665	−	7.39730i	−1.20325	−	0.390959i
$359$	19.8653	−	14.4330i	1.04845	−	0.761744i	0.0765337	−	0.997067i	$-0.475615\pi$
$359$	19.8653	−	14.4330i	1.04845	−	0.761744i	0.971917	+	0.235323i	$0.0756147\pi$
$360$		0			0
$361$	2.85771	+	2.07625i	0.150406	+	0.109276i
$362$	−6.40629	−	8.81750i	−0.336707	−	0.463438i
$363$		0			0
$364$	−15.1841	−	11.0319i	−0.795864	−	0.578229i
$365$	1.33117	−	27.6145i	0.0696767	−	1.44541i
$366$		0			0
$367$	0.243387	+	0.0790811i	0.0127047	+	0.00412800i	0.315362	−	0.948971i	$-0.397874\pi$
$367$	0.243387	+	0.0790811i	0.0127047	+	0.00412800i	−0.302658	+	0.953099i	$0.597874\pi$
$368$		−	8.36356i		−	0.435981i
$369$		0			0
$370$	20.8821	−	13.6858i	1.08561	−	0.711490i
$371$	−1.56046	−	4.80261i	−0.0810152	−	0.249339i
$372$		0			0
$373$	6.79290	−	9.34963i	0.351723	−	0.484105i	−0.596096	−	0.802913i	$-0.703282\pi$
$373$	6.79290	−	9.34963i	0.351723	−	0.484105i	0.947819	+	0.318808i	$0.103282\pi$
$374$	−11.7790			−0.609079
$375$		0			0
$376$	−7.23607			−0.373172
$377$	4.84636	−	6.67044i	0.249600	−	0.343545i
$378$		0			0
$379$	3.86925	+	11.9083i	0.198750	+	0.611689i	0.999912	+	0.0132423i	$0.00421528\pi$
$379$	3.86925	+	11.9083i	0.198750	+	0.611689i	−0.801162	+	0.598447i	$0.795785\pi$
$380$	−7.35531	+	4.82055i	−0.377320	+	0.247289i
$381$		0			0
$382$		−	5.21958i		−	0.267057i
$383$	0.620541	+	0.201626i	0.0317082	+	0.0103026i	0.324828	−	0.945773i	$-0.394694\pi$
$383$	0.620541	+	0.201626i	0.0317082	+	0.0103026i	−0.293120	+	0.956076i	$0.594694\pi$
$384$		0			0
$385$	−0.628054	+	13.0287i	−0.0320086	+	0.664003i
$386$	−4.61653	−	3.35410i	−0.234975	−	0.170719i
$387$		0			0
$388$	−5.36535	−	7.38477i	−0.272384	−	0.374905i
$389$	27.5315	+	20.0028i	1.39590	+	1.01418i	0.995188	+	0.0979818i	$0.0312387\pi$
$389$	27.5315	+	20.0028i	1.39590	+	1.01418i	0.400716	+	0.916202i	$0.368761\pi$
$390$		0			0
$391$	−44.5523	+	32.3692i	−2.25311	+	1.63698i
$392$	−3.45536	−	1.12271i	−0.174522	−	0.0567056i
$393$		0			0
$394$	5.52445	−	17.0025i	0.278318	−	0.856573i
$395$	−6.67424	−	5.35853i	−0.335817	−	0.269617i
$396$		0			0
$397$	−28.2990	+	9.19490i	−1.42029	+	0.461479i	−0.915693	−	0.401879i	$-0.868357\pi$
$397$	−28.2990	+	9.19490i	−1.42029	+	0.461479i	−0.504592	+	0.863358i	$0.668357\pi$
$398$	6.84450	−	9.42064i	0.343084	−	0.472214i
$399$		0			0
$400$	1.08052	+	4.88185i	0.0540261	+	0.244093i
$401$	17.3426			0.866050			0.433025	−	0.901382i	$-0.357446\pi$
$401$	17.3426			0.866050			0.433025	+	0.901382i	$0.357446\pi$
$402$		0			0
$403$	35.3980	−	11.5015i	1.76330	−	0.572931i
$404$	1.41398	+	4.35177i	0.0703480	+	0.216509i
$405$		0			0
$406$	1.44348	−	4.44257i	0.0716387	−	0.220481i
$407$			19.9744i			0.990093i
$408$		0			0
$409$	6.90864	−	5.01942i	0.341610	−	0.248195i	−0.403731	−	0.914878i	$-0.632287\pi$
$409$	6.90864	−	5.01942i	0.341610	−	0.248195i	0.745341	+	0.666683i	$0.232287\pi$
$410$	−4.82472	−	7.36167i	−0.238276	−	0.363567i
$411$		0			0
$412$	−2.80667	−	3.86304i	−0.138275	−	0.190319i
$413$	−20.9862	−	28.8850i	−1.03266	−	1.42134i
$414$		0			0
$415$	14.4600	−	3.93958i	0.709814	−	0.193387i
$416$	4.65648	−	3.38313i	0.228303	−	0.165872i
$417$		0			0
$418$		−	7.03558i		−	0.344122i
$419$	11.2825	−	34.7240i	0.551186	−	1.69638i	−0.154623	−	0.987974i	$-0.549416\pi$
$419$	11.2825	−	34.7240i	0.551186	−	1.69638i	0.705809	−	0.708402i	$-0.250584\pi$
$420$		0			0
$421$	−0.826416	−	2.54345i	−0.0402770	−	0.123960i	0.928896	−	0.370340i	$-0.120759\pi$
$421$	−0.826416	−	2.54345i	−0.0402770	−	0.123960i	−0.969173	+	0.246380i	$0.920759\pi$
$422$	−5.83841	+	1.89701i	−0.284209	+	0.0923452i
$423$		0			0
$424$	1.54860			0.0752067
$425$	21.8235	−	24.6499i	1.05860	−	1.19570i
$426$		0			0
$427$	1.51058	−	2.07914i	0.0731022	−	0.100617i
$428$	−9.32239	+	3.02903i	−0.450615	+	0.146414i
$429$		0			0
$430$	4.88187	+	0.235333i	0.235425	+	0.0113488i
$431$	−2.67910	+	8.24543i	−0.129048	+	0.397168i	−0.994617	−	0.103621i	$-0.966957\pi$
$431$	−2.67910	+	8.24543i	−0.129048	+	0.397168i	0.865569	+	0.500790i	$0.166957\pi$
$432$		0			0
$433$	18.9977	+	6.17274i	0.912973	+	0.296643i	0.727581	−	0.686022i	$-0.240644\pi$
$433$	18.9977	+	6.17274i	0.912973	+	0.296643i	0.185392	+	0.982665i	$0.440644\pi$
$434$	17.0593	−	12.3943i	0.818873	−	0.594946i
$435$		0			0
$436$	7.36472	+	5.35079i	0.352706	+	0.256256i
$437$	−19.3340	−	26.6110i	−0.924872	−	1.27298i
$438$		0			0
$439$	14.7988	+	10.7520i	0.706310	+	0.513164i	0.881981	−	0.471285i	$-0.156210\pi$
$439$	14.7988	+	10.7520i	0.706310	+	0.513164i	−0.175671	+	0.984449i	$0.556210\pi$
$440$	−3.74041	−	1.41785i	−0.178317	−	0.0675932i
$441$		0			0
$442$	−36.0436	−	11.7113i	−1.71442	−	0.557048i
$443$		−	12.0428i		−	0.572170i	−0.958204	−	0.286085i	$-0.907646\pi$
$443$		−	12.0428i		−	0.572170i	0.958204	−	0.286085i	$-0.0923540\pi$
$444$		0			0
$445$	−3.56881	−	0.172036i	−0.169178	−	0.00815531i
$446$	−2.27174	−	6.99171i	−0.107570	−	0.331067i
$447$		0			0
$448$	1.91668	−	2.63809i	0.0905548	−	0.124638i
$449$	−35.7261			−1.68602			−0.843010	−	0.537898i	$-0.819218\pi$
$449$	−35.7261			−1.68602			−0.843010	+	0.537898i	$0.819218\pi$
$450$		0			0
$451$	7.04167			0.331579
$452$	2.67031	−	3.67537i	0.125601	−	0.172875i
$453$		0			0
$454$	4.95602	+	15.2531i	0.232598	+	0.715862i
$455$	−14.8756	+	39.2431i	−0.697377	+	1.83974i
$456$		0			0
$457$		−	4.79597i		−	0.224346i	−0.993689	−	0.112173i	$-0.964219\pi$
$457$		−	4.79597i		−	0.224346i	0.993689	−	0.112173i	$-0.0357811\pi$
$458$	10.8878	+	3.53767i	0.508755	+	0.165304i
$459$		0			0
$460$	−18.0438	+	4.91598i	−0.841297	+	0.229209i
$461$	0.416802	+	0.302824i	0.0194124	+	0.0141039i	0.597449	−	0.801907i	$-0.296181\pi$
$461$	0.416802	+	0.302824i	0.0194124	+	0.0141039i	−0.578037	+	0.816011i	$0.696181\pi$
$462$		0			0
$463$	−13.2736	−	18.2695i	−0.616876	−	0.849057i	0.380245	−	0.924886i	$-0.375840\pi$
$463$	−13.2736	−	18.2695i	−0.616876	−	0.849057i	−0.997121	+	0.0758291i	$0.975840\pi$
$464$	1.15892	+	0.842006i	0.0538016	+	0.0390892i
$465$		0			0
$466$	−7.59846	+	5.52061i	−0.351992	+	0.255737i
$467$	37.5947	+	12.2153i	1.73968	+	0.565255i	0.994791	−	0.101936i	$-0.0325036\pi$
$467$	37.5947	+	12.2153i	1.73968	+	0.565255i	0.744886	+	0.667191i	$0.232504\pi$
$468$		0			0
$469$	7.90726	−	24.3361i	0.365124	−	1.12373i
$470$	4.25325	+	15.6113i	0.196188	+	0.720096i
$471$		0			0
$472$	10.4133	−	3.38349i	0.479312	−	0.155738i
$473$	−2.29833	+	3.16337i	−0.105677	+	0.145452i
$474$		0			0
$475$	14.7233	+	13.0351i	0.675554	+	0.598093i
$476$	−21.4710			−0.984124
$477$		0			0
$478$	−8.47773	+	2.75458i	−0.387762	+	0.125992i
$479$	−10.0117	−	30.8129i	−0.457447	−	1.40788i	−0.868238	−	0.496148i	$-0.834747\pi$
$479$	−10.0117	−	30.8129i	−0.457447	−	1.40788i	0.410791	−	0.911730i	$-0.365253\pi$
$480$		0			0
$481$	−19.8595	+	61.1212i	−0.905514	+	2.78689i
$482$			8.72894i			0.397592i
$483$		0			0
$484$	−6.31018	+	4.58462i	−0.286826	+	0.208392i
$485$	−12.7785	+	15.9160i	−0.580240	+	0.722709i
$486$		0			0
$487$	−21.5148	−	29.6125i	−0.974928	−	1.34187i	−0.939518	−	0.342500i	$-0.888726\pi$
$487$	−21.5148	−	29.6125i	−0.974928	−	1.34187i	−0.0354097	−	0.999373i	$-0.511274\pi$
$488$	0.463247	+	0.637605i	0.0209702	+	0.0288630i
$489$		0			0
$490$	−0.391169	+	8.11461i	−0.0176712	+	0.366581i
$491$	−15.3601	+	11.1597i	−0.693190	+	0.503632i	−0.877707	−	0.479197i	$-0.840928\pi$
$491$	−15.3601	+	11.1597i	−0.693190	+	0.503632i	0.184517	+	0.982829i	$0.440928\pi$
$492$		0			0
$493$		−	9.43231i		−	0.424810i
$494$	6.99512	−	21.5288i	0.314725	−	0.968624i
$495$		0			0
$496$	1.99827	+	6.15005i	0.0897251	+	0.276145i
$497$	−21.3616	+	6.94082i	−0.958200	+	0.311338i
$498$		0			0
$499$	15.2476			0.682578			0.341289	−	0.939958i	$-0.389137\pi$
$499$	15.2476			0.682578			0.341289	+	0.939958i	$0.389137\pi$
$500$	9.89714	−	5.20063i	0.442614	−	0.232579i
$501$		0			0
$502$	−7.44455	+	10.2465i	−0.332266	+	0.457325i
$503$	−9.83195	+	3.19460i	−0.438385	+	0.142440i	−0.519890	−	0.854233i	$-0.674027\pi$
$503$	−9.83195	+	3.19460i	−0.438385	+	0.142440i	0.0815053	+	0.996673i	$0.474027\pi$
$504$		0			0
$505$	8.55753	−	5.60846i	0.380805	−	0.249573i
$506$	4.62340	−	14.2294i	0.205535	−	0.632572i
$507$		0			0
$508$	−11.1343	−	3.61777i	−0.494007	−	0.160512i
$509$	11.0094	−	7.99881i	0.487984	−	0.354541i	−0.316424	−	0.948618i	$-0.602482\pi$
$509$	11.0094	−	7.99881i	0.487984	−	0.354541i	0.804409	+	0.594077i	$0.202482\pi$
$510$		0			0
$511$	32.6171	+	23.6977i	1.44290	+	1.04833i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	−18.8760	−	13.7142i	−0.832585	−	0.604908i
$515$	−6.68454	+	8.32583i	−0.294556	+	0.366880i
$516$		0			0
$517$	−12.3111	−	4.00012i	−0.541441	−	0.175925i
$518$			36.4097i			1.59975i
$519$		0			0
$520$	−10.0359	−	8.05748i	−0.440103	−	0.353344i
$521$	−12.9865	−	39.9683i	−0.568948	−	1.75104i	−0.655919	−	0.754832i	$-0.727719\pi$
$521$	−12.9865	−	39.9683i	−0.568948	−	1.75104i	0.0869703	−	0.996211i	$-0.472281\pi$
$522$		0			0
$523$	−18.9423	+	26.0718i	−0.828287	+	1.14004i	0.159952	+	0.987125i	$0.448866\pi$
$523$	−18.9423	+	26.0718i	−0.828287	+	1.14004i	−0.988239	+	0.152915i	$0.951134\pi$
$524$	−0.531712			−0.0232279
$525$		0			0
$526$	−28.7617			−1.25407
$527$	25.0272	−	34.4470i	1.09020	−	1.50054i
$528$		0			0
$529$	−14.5081	−	44.6513i	−0.630786	−	1.94136i
$530$	−0.910244	−	3.34100i	−0.0395385	−	0.145124i
$531$		0			0
$532$		−	12.8246i		−	0.556017i
$533$	21.5474	+	7.00116i	0.933320	+	0.303254i
$534$		0			0
$535$	12.0145	+	18.3320i	0.519432	+	0.792561i
$536$	6.34848	+	4.61244i	0.274213	+	0.199227i
$537$		0			0
$538$	15.4257	+	21.2316i	0.665048	+	0.915360i
$539$	−5.25814	−	3.82026i	−0.226484	−	0.164550i
$540$		0			0
$541$	16.1531	−	11.7359i	0.694476	−	0.504566i	−0.183653	−	0.982991i	$-0.558792\pi$
$541$	16.1531	−	11.7359i	0.694476	−	0.504566i	0.878128	+	0.478425i	$0.158792\pi$
$542$	13.9873	+	4.54474i	0.600804	+	0.195213i
$543$		0			0
$544$	2.03472	−	6.26221i	0.0872378	−	0.268490i
$545$	7.21507	−	19.0340i	0.309060	−	0.815327i
$546$		0			0
$547$	−0.331447	+	0.107694i	−0.0141717	+	0.00460465i	−0.316094	−	0.948728i	$-0.602372\pi$
$547$	−0.331447	+	0.107694i	−0.0141717	+	0.00460465i	0.301923	+	0.953332i	$0.402372\pi$
$548$	−11.7483	+	16.1701i	−0.501862	+	0.690754i
$549$		0			0
$550$	−0.860353	+	8.90306i	−0.0366856	+	0.379628i
$551$	5.63390			0.240012
$552$		0			0
$553$	11.8709	−	3.85709i	0.504803	−	0.164020i
$554$	2.00281	+	6.16403i	0.0850914	+	0.261885i
$555$		0			0
$556$	−6.41785	+	19.7521i	−0.272177	+	0.837676i
$557$			21.1297i			0.895294i	0.894210	+	0.447647i	$0.147738\pi$
$557$			21.1297i			0.895294i	−0.894210	+	0.447647i	$0.852262\pi$
$558$		0			0
$559$	−10.1780	+	7.39476i	−0.430484	+	0.312765i
$560$	−6.81809	−	2.58448i	−0.288117	−	0.109214i
$561$		0			0
$562$	8.04194	+	11.0688i	0.339229	+	0.466908i
$563$	−17.9593	−	24.7188i	−0.756893	−	1.04177i	−0.997466	−	0.0711432i	$-0.977335\pi$
$563$	−17.9593	−	24.7188i	−0.756893	−	1.04177i	0.240573	−	0.970631i	$-0.422665\pi$
$564$		0			0
$565$	−9.49893	−	3.60069i	−0.399623	−	0.151482i
$566$	4.31430	−	3.13452i	0.181344	−	0.131754i
$567$		0			0
$568$		−	6.88806i		−	0.289016i
$569$	−7.63431	+	23.4960i	−0.320047	+	0.985003i	0.653580	+	0.756857i	$0.273266\pi$
$569$	−7.63431	+	23.4960i	−0.320047	+	0.985003i	−0.973627	+	0.228146i	$0.926734\pi$
$570$		0			0
$571$	10.9666	+	33.7519i	0.458940	+	1.41247i	0.866447	+	0.499269i	$0.166398\pi$
$571$	10.9666	+	33.7519i	0.458940	+	1.41247i	−0.407507	+	0.913202i	$0.633602\pi$
$572$	9.79251	−	3.18178i	0.409445	−	0.133037i
$573$		0			0
$574$	12.8357			0.535752
$575$	21.2118	+	36.0387i	0.884592	+	1.50292i
$576$		0			0
$577$	−3.35546	+	4.61840i	−0.139690	+	0.192266i	−0.873130	−	0.487488i	$-0.837913\pi$
$577$	−3.35546	+	4.61840i	−0.139690	+	0.192266i	0.733440	+	0.679754i	$0.237913\pi$
$578$	−25.0655	+	8.14427i	−1.04259	+	0.338757i
$579$		0			0
$580$	1.13537	−	2.99521i	0.0471438	−	0.124369i
$581$	−6.75376	+	20.7859i	−0.280193	+	0.862346i
$582$		0			0
$583$	2.63471	+	0.856070i	0.109119	+	0.0354548i
$584$	−10.0026	+	7.26733i	−0.413911	+	0.300724i
$585$		0			0
$586$	−4.07295	−	2.95917i	−0.168252	−	0.122242i
$587$	11.2569	+	15.4938i	0.464624	+	0.639499i	0.975460	−	0.220179i	$-0.0706641\pi$
$587$	11.2569	+	15.4938i	0.464624	+	0.639499i	−0.510836	+	0.859678i	$0.670664\pi$
$588$		0			0
$589$	20.5751	+	14.9487i	0.847783	+	0.615950i
$590$	−13.4205	−	20.4773i	−0.552511	−	0.843035i
$591$		0			0
$592$	−10.6192	−	3.45039i	−0.436446	−	0.141810i
$593$		−	10.9253i		−	0.448648i	−0.974515	−	0.224324i	$-0.927983\pi$
$593$		−	10.9253i		−	0.448648i	0.974515	−	0.224324i	$-0.0720174\pi$
$594$		0			0
$595$	12.6204	+	46.3223i	0.517384	+	1.89903i
$596$	1.17643	+	3.62067i	0.0481884	+	0.148309i
$597$		0			0
$598$	28.2950	−	38.9447i	1.15707	−	1.59257i
$599$	17.5722			0.717981			0.358991	−	0.933341i	$-0.383121\pi$
$599$	17.5722			0.717981			0.358991	+	0.933341i	$0.383121\pi$
$600$		0			0
$601$	−16.9235			−0.690325			−0.345163	−	0.938543i	$-0.612176\pi$
$601$	−16.9235			−0.690325			−0.345163	+	0.938543i	$0.612176\pi$
$602$	−4.18943	+	5.76626i	−0.170749	+	0.235015i
$603$		0			0
$604$	4.62912	+	14.2470i	0.188356	+	0.579701i
$605$	13.6000	+	10.9190i	0.552920	+	0.443921i
$606$		0			0
$607$			35.3264i			1.43386i	0.697147	+	0.716928i	$0.254452\pi$
$607$			35.3264i			1.43386i	−0.697147	+	0.716928i	$0.745548\pi$
$608$	3.74041	+	1.21533i	0.151694	+	0.0492882i
$609$		0			0
$610$	1.10330	−	1.37420i	0.0446713	−	0.0556397i
$611$	−33.6946	−	24.4806i	−1.36314	−	0.990378i
$612$		0			0
$613$	−22.9273	−	31.5567i	−0.926024	−	1.27456i	−0.961390	−	0.275188i	$-0.911260\pi$
$613$	−22.9273	−	31.5567i	−0.926024	−	1.27456i	0.0353661	−	0.999374i	$-0.488740\pi$
$614$	13.2410	+	9.62017i	0.534364	+	0.388238i
$615$		0			0
$616$	4.71929	−	3.42877i	0.190146	−	0.138149i
$617$	19.8036	+	6.43456i	0.797261	+	0.259046i	0.679193	−	0.733960i	$-0.262330\pi$
$617$	19.8036	+	6.43456i	0.797261	+	0.259046i	0.118068	+	0.993006i	$0.462330\pi$
$618$		0			0
$619$	−2.20465	+	6.78522i	−0.0886124	+	0.272721i	−0.985536	−	0.169464i	$-0.945796\pi$
$619$	−2.20465	+	6.78522i	−0.0886124	+	0.272721i	0.896924	+	0.442185i	$0.145796\pi$
$620$	12.0938	−	7.92604i	0.485697	−	0.318318i
$621$		0			0
$622$	19.7383	−	6.41336i	0.791434	−	0.257152i
$623$	3.06262	−	4.21533i	0.122701	−	0.168884i
$624$		0			0
$625$	−17.0374	−	18.2955i	−0.681496	−	0.731822i
$626$	29.8194			1.19182
$627$		0			0
$628$	0.317153	−	0.103049i	0.0126558	−	0.00411211i
$629$	22.7190	+	69.9219i	0.905866	+	2.78797i
$630$		0			0
$631$	11.2234	−	34.5422i	0.446798	−	1.37510i	−0.433701	−	0.901057i	$-0.642793\pi$
$631$	11.2234	−	34.5422i	0.446798	−	1.37510i	0.880499	−	0.474047i	$-0.157207\pi$
$632$			3.82777i			0.152261i
$633$		0			0
$634$	20.0807	−	14.5895i	0.797505	−	0.579421i
$635$	−1.26048	+	26.1480i	−0.0500207	+	1.03765i
$636$		0			0
$637$	−12.2915	−	16.9178i	−0.487008	−	0.670309i
$638$	1.50627	+	2.07320i	0.0596338	+	0.0820789i
$639$		0			0
$640$	1.39991	−	1.74363i	0.0553362	−	0.0689232i
$641$	−0.245277	+	0.178204i	−0.00968787	+	0.00703865i	−0.592619	−	0.805483i	$-0.701906\pi$
$641$	−0.245277	+	0.178204i	−0.00968787	+	0.00703865i	0.582931	+	0.812522i	$0.301906\pi$
$642$		0			0
$643$		−	45.5553i		−	1.79652i	−0.439461	−	0.898262i	$-0.644830\pi$
$643$		−	45.5553i		−	1.79652i	0.439461	−	0.898262i	$-0.355170\pi$
$644$	8.42762	−	25.9376i	0.332095	−	1.02208i
$645$		0			0
$646$	−8.00233	−	24.6286i	−0.314847	−	0.969001i
$647$	−24.4716	+	7.95130i	−0.962078	+	0.312598i	−0.747614	−	0.664134i	$-0.768800\pi$
$647$	−24.4716	+	7.95130i	−0.962078	+	0.312598i	−0.214464	+	0.976732i	$0.568800\pi$
$648$		0			0
$649$	19.5871			0.768862
$650$	−11.4845	+	26.3878i	−0.450460	+	1.03501i
$651$		0			0
$652$	−1.13075	+	1.55635i	−0.0442837	+	0.0609513i
$653$	−3.37510	+	1.09664i	−0.132078	+	0.0429148i	−0.374310	−	0.927304i	$-0.622120\pi$
$653$	−3.37510	+	1.09664i	−0.132078	+	0.0429148i	0.242232	+	0.970218i	$0.422120\pi$
$654$		0			0
$655$	0.312532	+	1.14713i	0.0122116	+	0.0448221i
$656$	−1.21638	+	3.74364i	−0.0474918	+	0.146165i
$657$		0			0
$658$	−22.4409	−	7.29149i	−0.874838	−	0.284252i
$659$	7.87551	−	5.72189i	0.306786	−	0.222893i	−0.423730	−	0.905789i	$-0.639279\pi$
$659$	7.87551	−	5.72189i	0.306786	−	0.222893i	0.730516	+	0.682895i	$0.239279\pi$
$660$		0			0
$661$	−27.8343	−	20.2228i	−1.08263	−	0.786575i	−0.104488	−	0.994526i	$-0.533320\pi$
$661$	−27.8343	−	20.2228i	−1.08263	−	0.786575i	−0.978139	+	0.207952i	$0.933320\pi$
$662$	1.19721	+	1.64782i	0.0465308	+	0.0640442i
$663$		0			0
$664$	−5.42237	−	3.93958i	−0.210429	−	0.152885i
$665$	−27.6682	+	7.53811i	−1.07293	+	0.292316i
$666$		0			0
$667$	11.3945	+	3.70229i	0.441196	+	0.143353i
$668$		−	1.41175i		−	0.0546222i
$669$		0			0
$670$	6.21948	−	16.4075i	0.240280	−	0.633879i
$671$	0.435677	+	1.34088i	0.0168191	+	0.0517639i
$672$		0			0
$673$	11.6142	−	15.9856i	0.447696	−	0.616200i	−0.524205	−	0.851592i	$-0.675637\pi$
$673$	11.6142	−	15.9856i	0.447696	−	0.616200i	0.971901	+	0.235392i	$0.0756374\pi$
$674$	−25.2259			−0.971665
$675$		0			0
$676$	20.1284			0.774169
$677$	−12.1757	+	16.7585i	−0.467952	+	0.644081i	−0.976134	−	0.217169i	$-0.930318\pi$
$677$	−12.1757	+	16.7585i	−0.467952	+	0.644081i	0.508182	+	0.861250i	$0.330318\pi$
$678$		0			0
$679$	−9.19799	−	28.3085i	−0.352987	−	1.08638i
$680$	−14.7063	−	0.708924i	−0.563960	−	0.0271860i
$681$		0			0
$682$			11.5680i			0.442963i
$683$	−23.7317	−	7.71091i	−0.908069	−	0.295050i	−0.182506	−	0.983205i	$-0.558421\pi$
$683$	−23.7317	−	7.71091i	−0.908069	−	0.295050i	−0.725564	+	0.688155i	$0.758421\pi$
$684$		0			0
$685$	41.7914	+	15.8416i	1.59677	+	0.605275i
$686$	8.88197	+	6.45313i	0.339115	+	0.246382i
$687$		0			0
$688$	−1.28477	−	1.76833i	−0.0489812	−	0.0674169i
$689$	7.21103	+	5.23912i	0.274718	+	0.199594i
$690$		0			0
$691$	−3.52642	+	2.56210i	−0.134152	+	0.0974668i	−0.652837	−	0.757498i	$-0.726421\pi$
$691$	−3.52642	+	2.56210i	−0.134152	+	0.0974668i	0.518686	+	0.854965i	$0.326421\pi$
$692$	−12.6016	−	4.09450i	−0.479040	−	0.155650i
$693$		0			0
$694$	−6.26743	+	19.2892i	−0.237908	+	0.732206i
$695$	46.3861	+	2.23607i	1.75953	+	0.0848189i
$696$		0			0
$697$	24.6499	−	8.00925i	0.933683	−	0.303372i
$698$	−0.825448	+	1.13613i	−0.0312437	+	0.0430032i
$699$		0			0
$700$	−1.56827	+	16.2287i	−0.0592750	+	0.613386i
$701$	−1.08146			−0.0408460			−0.0204230	−	0.999791i	$-0.506501\pi$
$701$	−1.08146			−0.0408460			−0.0204230	+	0.999791i	$0.506501\pi$
$702$		0			0
$703$	−41.7642	+	13.5700i	−1.57517	+	0.511803i
$704$	0.552802	+	1.70135i	0.0208345	+	0.0641221i
$705$		0			0
$706$	−1.18756	+	3.65495i	−0.0446946	+	0.137556i
$707$			14.9208i			0.561154i
$708$		0			0
$709$	12.0706	−	8.76980i	0.453321	−	0.329357i	−0.337585	−	0.941295i	$-0.609610\pi$
$709$	12.0706	−	8.76980i	0.453321	−	0.329357i	0.790906	+	0.611938i	$0.209610\pi$
$710$	−14.8605	+	4.04870i	−0.557705	+	0.151945i
$711$		0			0
$712$	0.939207	+	1.29271i	0.0351983	+	0.0484463i
$713$	31.7894	+	43.7543i	1.19052	+	1.63861i
$714$		0			0
$715$	−12.6204	−	19.2565i	−0.471975	−	0.720151i
$716$	19.3664	−	14.0705i	0.723756	−	0.525839i
$717$		0			0
$718$			24.5549i			0.916380i
$719$	12.4072	−	38.1853i	0.462709	−	1.42407i	−0.399132	−	0.916893i	$-0.630689\pi$
$719$	12.4072	−	38.1853i	0.462709	−	1.42407i	0.861841	−	0.507178i	$-0.169311\pi$
$720$		0			0
$721$	−4.81156	−	14.8085i	−0.179192	−	0.551496i
$722$	−3.35944	+	1.09155i	−0.125026	+	0.0406233i
$723$		0			0
$724$	10.8990			0.405059
$725$	−7.12932	−	0.688947i	−0.264776	−	0.0255868i
$726$		0			0
$727$	−22.3143	+	30.7130i	−0.827592	+	1.13908i	0.160774	+	0.986991i	$0.448601\pi$
$727$	−22.3143	+	30.7130i	−0.827592	+	1.13908i	−0.988366	+	0.152092i	$0.951399\pi$
$728$	17.8500	−	5.79981i	0.661565	−	0.214955i
$729$		0			0
$730$	21.5582	+	17.3083i	0.797903	+	0.640610i
$731$	−4.44743	+	13.6878i	−0.164494	+	0.506261i
$732$		0			0
$733$	23.0797	+	7.49904i	0.852468	+	0.276984i	0.702479	−	0.711704i	$-0.252076\pi$
$733$	23.0797	+	7.49904i	0.852468	+	0.276984i	0.149988	+	0.988688i	$0.452076\pi$
$734$	−0.207037	+	0.150421i	−0.00764187	+	0.00555215i
$735$		0			0
$736$	6.76626	+	4.91598i	0.249408	+	0.181205i
$737$	8.25123	+	11.3568i	0.303938	+	0.418335i
$738$		0			0
$739$	30.7190	+	22.3186i	1.13002	+	0.821004i	0.985697	−	0.168527i	$-0.0539011\pi$
$739$	30.7190	+	22.3186i	1.13002	+	0.821004i	0.144318	+	0.989531i	$0.453901\pi$
$740$	−1.20216	+	24.9383i	−0.0441924	+	0.916749i
$741$		0			0
$742$	4.80261	+	1.56046i	0.176309	+	0.0572864i
$743$			27.7086i			1.01653i	0.861201	+	0.508265i	$0.169713\pi$
$743$			27.7086i			1.01653i	−0.861201	+	0.508265i	$0.830287\pi$
$744$		0			0
$745$	7.11986	−	4.66624i	0.260852	−	0.170958i
$746$	3.57124	+	10.9911i	0.130752	+	0.402415i
$747$		0			0
$748$	6.92354	−	9.52943i	0.253150	−	0.348430i
$749$	−31.9634			−1.16792
$750$		0			0
$751$	−16.1379			−0.588882			−0.294441	−	0.955670i	$-0.595133\pi$
$751$	−16.1379			−0.588882			−0.294441	+	0.955670i	$0.595133\pi$
$752$	4.25325	−	5.85410i	0.155100	−	0.213477i
$753$		0			0
$754$	2.54788	+	7.84157i	0.0927883	+	0.285573i
$755$	28.0159	−	18.3612i	1.01960	−	0.668231i
$756$		0			0
$757$		−	10.6556i		−	0.387283i	−0.981072	−	0.193641i	$-0.937970\pi$
$757$		−	10.6556i		−	0.387283i	0.981072	−	0.193641i	$-0.0620298\pi$
$758$	−11.9083	−	3.86925i	−0.432530	−	0.140537i
$759$		0			0
$760$	0.423439	−	8.78402i	0.0153597	−	0.318630i
$761$	−1.57163	−	1.14185i	−0.0569714	−	0.0413922i	0.558935	−	0.829211i	$-0.311210\pi$
$761$	−1.57163	−	1.14185i	−0.0569714	−	0.0413922i	−0.615906	+	0.787819i	$0.711210\pi$
$762$		0			0
$763$	17.4481	+	24.0153i	0.631665	+	0.869412i
$764$	4.22273	+	3.06799i	0.152773	+	0.110996i
$765$		0			0
$766$	−0.527864	+	0.383516i	−0.0190725	+	0.0138570i
$767$	59.9362	+	19.4745i	2.16417	+	0.703182i
$768$		0			0
$769$	2.82372	−	8.69051i	0.101826	−	0.313388i	−0.887147	−	0.461488i	$-0.847316\pi$
$769$	2.82372	−	8.69051i	0.101826	−	0.313388i	0.988972	+	0.148100i	$0.0473158\pi$
$770$	−10.1713	−	8.16617i	−0.366547	−	0.294288i
$771$		0			0
$772$	5.42705	−	1.76336i	0.195324	−	0.0634646i
$773$	24.7553	−	34.0728i	0.890387	−	1.22551i	−0.0830472	−	0.996546i	$-0.526465\pi$
$773$	24.7553	−	34.0728i	0.890387	−	1.22551i	0.973434	−	0.228967i	$-0.0735348\pi$
$774$		0			0
$775$	−24.2084	−	21.4326i	−0.869592	−	0.769883i
$776$	9.12807			0.327679
$777$		0			0
$778$	−32.3653	+	10.5161i	−1.16035	+	0.377021i
$779$	4.78391	+	14.7233i	0.171401	+	0.527519i
$780$		0			0
$781$	3.80773	−	11.7190i	0.136251	−	0.419339i
$782$		−	55.0697i		−	1.96929i
$783$		0			0
$784$	2.93930	−	2.13553i	0.104975	−	0.0762689i
$785$	−0.408739	−	0.623664i	−0.0145885	−	0.0222595i
$786$		0			0
$787$	−2.06835	−	2.84684i	−0.0737287	−	0.101479i	0.770560	−	0.637368i	$-0.219977\pi$
$787$	−2.06835	−	2.84684i	−0.0737287	−	0.101479i	−0.844289	+	0.535889i	$0.819977\pi$
$788$	10.5081	+	14.4632i	0.374336	+	0.515230i
$789$		0			0
$790$	8.25816	−	2.24991i	0.293812	−	0.0800482i
$791$	11.9849	−	8.70751i	0.426132	−	0.309603i
$792$		0			0
$793$			4.53622i			0.161086i
$794$	9.19490	−	28.2990i	0.326315	−	1.00429i
$795$		0			0
$796$	3.59837	+	11.0746i	0.127541	+	0.392530i
$797$	−31.5697	+	10.2576i	−1.11826	+	0.363344i	−0.809102	−	0.587668i	$-0.800046\pi$
$797$	−31.5697	+	10.2576i	−1.11826	+	0.363344i	−0.309155	+	0.951012i	$0.600046\pi$
$798$		0			0
$799$	−47.6458			−1.68559
$800$	−4.58462	−	1.99532i	−0.162091	−	0.0705452i
$801$		0			0
$802$	−10.1937	+	14.0305i	−0.359954	+	0.495434i
$803$	−21.0354	+	6.83481i	−0.742322	+	0.241195i
$804$		0			0
$805$	−60.9121	−	2.93630i	−2.14687	−	0.103491i
$806$	−11.5015	+	35.3980i	−0.405123	+	1.24684i
$807$		0			0
$808$	−4.35177	−	1.41398i	−0.153095	−	0.0497435i
$809$	−6.07490	+	4.41367i	−0.213582	+	0.155176i	−0.689433	−	0.724350i	$-0.742140\pi$
$809$	−6.07490	+	4.41367i	−0.213582	+	0.155176i	0.475851	+	0.879526i	$0.342140\pi$
$810$		0			0
$811$	−30.5051	−	22.1632i	−1.07118	−	0.778256i	−0.0950543	−	0.995472i	$-0.530302\pi$
$811$	−30.5051	−	22.1632i	−1.07118	−	0.778256i	−0.976124	+	0.217216i	$0.930302\pi$
$812$	2.74566	+	3.77908i	0.0963538	+	0.132620i
$813$		0			0
$814$	−16.1596	−	11.7406i	−0.566394	−	0.411509i
$815$	4.02235	+	1.52472i	0.140897	+	0.0534087i
$816$		0			0
$817$	−8.17568	−	2.65644i	−0.286031	−	0.0929371i
$818$			8.53955i			0.298579i
$819$		0			0
$820$	8.79162	+	0.423805i	0.307017	+	0.0147999i
$821$	−1.20526	−	3.70942i	−0.0420640	−	0.129460i	0.927819	−	0.373030i	$-0.121681\pi$
$821$	−1.20526	−	3.70942i	−0.0420640	−	0.129460i	−0.969883	+	0.243571i	$0.921681\pi$
$822$		0			0
$823$	−25.3684	+	34.9166i	−0.884286	+	1.21711i	0.0909296	+	0.995857i	$0.471016\pi$
$823$	−25.3684	+	34.9166i	−0.884286	+	1.21711i	−0.975215	+	0.221258i	$0.928984\pi$
$824$	4.77499			0.166345
$825$		0			0
$826$	35.7038			1.24229
$827$	−1.65632	+	2.27973i	−0.0575960	+	0.0792741i	−0.836843	−	0.547442i	$-0.815602\pi$
$827$	−1.65632	+	2.27973i	−0.0575960	+	0.0792741i	0.779247	+	0.626716i	$0.215602\pi$
$828$		0			0
$829$	13.4671	+	41.4475i	0.467732	+	1.43953i	0.855514	+	0.517780i	$0.173241\pi$
$829$	13.4671	+	41.4475i	0.467732	+	1.43953i	−0.387782	+	0.921751i	$0.626759\pi$
$830$	−5.31219	+	14.0140i	−0.184389	+	0.486434i
$831$		0			0
$832$			5.75573i			0.199544i
$833$	−22.7517	−	7.39249i	−0.788301	−	0.256135i
$834$		0			0
$835$	−3.04575	+	0.829805i	−0.105403	+	0.0287166i
$836$	5.69191	+	4.13541i	0.196859	+	0.143026i
$837$		0			0
$838$	21.4606	+	29.5380i	0.741344	+	1.02037i
$839$	−26.3904	−	19.1737i	−0.911098	−	0.661951i	0.0301946	−	0.999544i	$-0.490387\pi$
$839$	−26.3904	−	19.1737i	−0.911098	−	0.661951i	−0.941292	+	0.337593i	$0.890387\pi$
$840$		0			0
$841$	21.8013	−	15.8396i	0.751770	−	0.546193i
$842$	2.54345	+	0.826416i	0.0876530	+	0.0284802i
$843$		0			0
$844$	1.89701	−	5.83841i	0.0652979	−	0.200966i
$845$	−11.8312	−	43.4256i	−0.407004	−	1.49389i
$846$		0			0
$847$	−24.1892	+	7.85956i	−0.831152	+	0.270058i
$848$	−0.910244	+	1.25284i	−0.0312579	+	0.0430228i
$849$		0			0
$850$	7.11468	+	32.1445i	0.244031	+	1.10255i
$851$	−93.3849			−3.20119
$852$		0			0
$853$	−2.97505	+	0.966652i	−0.101864	+	0.0330975i	−0.359505	−	0.933143i	$-0.617055\pi$
$853$	−2.97505	+	0.966652i	−0.101864	+	0.0330975i	0.257642	+	0.966241i	$0.417055\pi$
$854$	0.794161	+	2.44417i	0.0271756	+	0.0836379i
$855$		0			0
$856$	3.02903	−	9.32239i	0.103530	−	0.318633i
$857$		−	26.4837i		−	0.904666i	−0.891849	−	0.452333i	$-0.850592\pi$
$857$		−	26.4837i		−	0.904666i	0.891849	−	0.452333i	$-0.149408\pi$
$858$		0			0
$859$	0.278666	−	0.202463i	0.00950797	−	0.00690795i	−0.583021	−	0.812457i	$-0.698130\pi$
$859$	0.278666	−	0.202463i	0.00950797	−	0.00690795i	0.592529	+	0.805549i	$0.298130\pi$
$860$	−3.05988	+	3.81119i	−0.104341	+	0.129960i
$861$		0			0
$862$	−5.09595	−	7.01398i	−0.173569	−	0.238897i
$863$	−12.3485	−	16.9962i	−0.420347	−	0.578558i	0.545357	−	0.838204i	$-0.316394\pi$
$863$	−12.3485	−	16.9962i	−0.420347	−	0.578558i	−0.965704	+	0.259646i	$0.916394\pi$
$864$		0			0
$865$	−1.42658	+	29.5937i	−0.0485052	+	1.00622i
$866$	−16.1604	+	11.7413i	−0.549154	+	0.398984i
$867$		0			0
$868$			21.0865i			0.715721i
$869$	−2.11600	+	6.51239i	−0.0717805	+	0.220918i
$870$		0			0
$871$	13.9571	+	42.9555i	0.472918	+	1.45549i
$872$	−8.65775	+	2.81307i	−0.293188	+	0.0952627i
$873$		0			0
$874$	32.8930			1.11262
$875$	35.9341	−	6.15555i	1.21479	−	0.208095i
$876$		0			0
$877$	28.6819	−	39.4773i	0.968519	−	1.33305i	0.0257283	−	0.999669i	$-0.491810\pi$
$877$	28.6819	−	39.4773i	0.968519	−	1.33305i	0.942791	−	0.333384i	$-0.108190\pi$
$878$	−17.3971	+	5.65265i	−0.587123	+	0.190768i
$879$		0			0
$880$	3.34562	−	2.19266i	0.112781	−	0.0739146i
$881$	0.690898	−	2.12637i	0.0232769	−	0.0716391i	−0.938743	−	0.344617i	$-0.888009\pi$
$881$	0.690898	−	2.12637i	0.0232769	−	0.0716391i	0.962020	+	0.272978i	$0.0880087\pi$
$882$		0			0
$883$	10.1665	+	3.30330i	0.342130	+	0.111165i	0.475042	−	0.879963i	$-0.342433\pi$
$883$	10.1665	+	3.30330i	0.342130	+	0.111165i	−0.132912	+	0.991128i	$0.542433\pi$
$884$	30.6605	−	22.2762i	1.03122	−	0.749228i
$885$		0			0
$886$	9.74282	+	7.07858i	0.327317	+	0.237809i
$887$	−15.3734	−	21.1596i	−0.516187	−	0.710470i	0.468761	−	0.883325i	$-0.344701\pi$
$887$	−15.3734	−	21.1596i	−0.516187	−	0.710470i	−0.984947	+	0.172855i	$0.944701\pi$
$888$		0			0
$889$	−30.8850	−	22.4393i	−1.03585	−	0.752589i
$890$	2.23687	−	2.78611i	0.0749802	−	0.0933906i
$891$		0			0
$892$	6.99171	+	2.27174i	0.234100	+	0.0760636i
$893$		−	28.4587i		−	0.952334i
$894$		0			0
$895$	−41.7394	−	33.5112i	−1.39519	−	1.12016i
$896$	1.00766	+	3.10126i	0.0336636	+	0.103606i
$897$		0			0
$898$	20.9993	−	28.9030i	0.700755	−	0.964507i
$899$	−9.26337			−0.308951
$900$		0			0
$901$	10.1967			0.339702
$902$	−4.13899	+	5.69683i	−0.137813	+	0.189684i
$903$		0			0
$904$	1.40387	+	4.32066i	0.0466919	+	0.143703i
$905$	−6.40629	−	23.5139i	−0.212952	−	0.781629i
$906$		0			0
$907$		−	9.59794i		−	0.318694i	−0.987223	−	0.159347i	$-0.949061\pi$
$907$		−	9.59794i		−	0.318694i	0.987223	−	0.159347i	$-0.0509389\pi$
$908$	−15.2531	−	4.95602i	−0.506191	−	0.164471i
$909$		0			0
$910$	−23.0047	−	35.1011i	−0.762597	−	1.16359i
$911$	34.8520	+	25.3215i	1.15470	+	0.838937i	0.989098	−	0.147256i	$-0.0470440\pi$
$911$	34.8520	+	25.3215i	1.15470	+	0.838937i	0.165600	+	0.986193i	$0.447044\pi$
$912$		0			0
$913$	−7.04755	−	9.70011i	−0.233240	−	0.321027i
$914$	3.88002	+	2.81900i	0.128340	+	0.0932442i
$915$		0			0
$916$	−9.26174	+	6.72905i	−0.306016	+	0.222334i
$917$	−1.64898	−	0.535785i	−0.0544540	−	0.0176932i
$918$		0			0
$919$	−10.3901	+	31.9774i	−0.342737	+	1.05484i	0.620047	+	0.784565i	$0.287114\pi$
$919$	−10.3901	+	31.9774i	−0.342737	+	1.05484i	−0.962784	+	0.270272i	$0.912886\pi$
$920$	6.62877	−	17.4873i	0.218544	−	0.576539i
$921$		0			0
$922$	−0.489980	+	0.159204i	−0.0161366	+	0.00524311i
$923$	23.3032	−	32.0741i	0.767034	−	1.05573i
$924$		0			0
$925$	54.5092	−	12.0648i	1.79225	−	0.396687i
$926$	22.5824			0.742103
$927$		0			0
$928$	−1.36239	+	0.442669i	−0.0447228	+	0.0145313i
$929$	7.76297	+	23.8920i	0.254695	+	0.783870i	0.993890	+	0.110378i	$0.0352063\pi$
$929$	7.76297	+	23.8920i	0.254695	+	0.783870i	−0.739195	+	0.673492i	$0.764794\pi$
$930$		0			0
$931$	4.41552	−	13.5896i	0.144713	−	0.445380i
$932$		−	9.39222i		−	0.307652i
$933$		0			0
$934$	−31.9800	+	23.2348i	−1.04642	+	0.760267i
$935$	−24.6286	−	9.33579i	−0.805443	−	0.305313i
$936$		0			0
$937$	−21.9522	−	30.2146i	−0.717146	−	0.987066i	−0.999614	−	0.0277897i	$-0.991153\pi$
$937$	−21.9522	−	30.2146i	−0.717146	−	0.987066i	0.282468	−	0.959277i	$-0.408847\pi$
$938$	15.0405	+	20.7015i	0.491090	+	0.675928i
$939$		0			0
$940$	−15.1298	−	5.73515i	−0.493480	−	0.187060i
$941$	45.5557	−	33.0981i	1.48507	−	1.07897i	0.509194	−	0.860652i	$-0.329943\pi$
$941$	45.5557	−	33.0981i	1.48507	−	1.07897i	0.975878	−	0.218317i	$-0.0700566\pi$
$942$		0			0
$943$			32.9215i			1.07207i
$944$	−3.38349	+	10.4133i	−0.110123	+	0.338925i
$945$		0			0
$946$	−1.20830	−	3.71877i	−0.0392853	−	0.120908i
$947$	−1.00257	+	0.325756i	−0.0325793	+	0.0105856i	−0.325261	−	0.945624i	$-0.605452\pi$
$947$	−1.00257	+	0.325756i	−0.0325793	+	0.0105856i	0.292682	+	0.956210i	$0.405452\pi$
$948$		0			0
$949$	−71.1633			−2.31006
$950$	−19.1998	+	4.24958i	−0.622924	+	0.137875i
$951$		0			0
$952$	12.6204	−	17.3704i	0.409028	−	0.562979i
$953$	45.6210	−	14.8232i	1.47781	−	0.480169i	0.544351	−	0.838857i	$-0.316776\pi$
$953$	45.6210	−	14.8232i	1.47781	−	0.480169i	0.933457	+	0.358688i	$0.116776\pi$
$954$		0			0
$955$	4.13693	−	10.9136i	0.133868	−	0.353155i
$956$	2.75458	−	8.47773i	0.0890895	−	0.274189i
$957$		0			0
$958$	30.8129	+	10.0117i	0.995520	+	0.323464i
$959$	−52.7285	+	38.3095i	−1.70269	+	1.23708i
$960$		0			0
$961$	−8.75049	−	6.35761i	−0.282274	−	0.205084i
$962$	−37.7750	−	51.9928i	−1.21791	−	1.67632i
$963$		0			0
$964$	−7.06186	−	5.13074i	−0.227447	−	0.165250i
$965$	−6.99426	−	10.6720i	−0.225153	−	0.343544i
$966$		0			0
$967$	39.7284	+	12.9085i	1.27758	+	0.415111i	0.867727	−	0.497041i	$-0.165580\pi$
$967$	39.7284	+	12.9085i	1.27758	+	0.415111i	0.409853	+	0.912152i	$0.365580\pi$
$968$		−	7.79981i		−	0.250696i
$969$		0			0
$970$	−5.36535	−	19.6932i	−0.172271	−	0.632310i
$971$	−5.52977	−	17.0189i	−0.177459	−	0.546162i	0.822278	−	0.569085i	$-0.192703\pi$
$971$	−5.52977	−	17.0189i	−0.177459	−	0.546162i	−0.999737	+	0.0229233i	$0.992703\pi$
$972$		0			0
$973$	−39.8068	+	54.7894i	−1.27615	+	1.75647i
$974$	36.6031			1.17284
$975$		0			0
$976$	−0.788124			−0.0252272
$977$	−10.0952	+	13.8949i	−0.322976	+	0.444538i	−0.939373	−	0.342898i	$-0.888592\pi$
$977$	−10.0952	+	13.8949i	−0.322976	+	0.444538i	0.616397	+	0.787435i	$0.288592\pi$
$978$		0			0
$979$	0.883309	+	2.71854i	0.0282307	+	0.0868851i
$980$	−6.33494	−	5.08611i	−0.202362	−	0.162470i
$981$		0			0
$982$		−	18.9861i		−	0.605870i
$983$	14.6491	+	4.75978i	0.467234	+	0.151813i	0.533166	−	0.846011i	$-0.321002\pi$
$983$	14.6491	+	4.75978i	0.467234	+	0.151813i	−0.0659323	+	0.997824i	$0.521002\pi$
$984$		0			0
$985$	25.0268	−	31.1718i	0.797420	−	0.993216i
$986$	7.63090	+	5.54417i	0.243017	+	0.176562i
$987$		0			0
$988$	13.3055	+	18.3135i	0.423304	+	0.582629i
$989$	−14.7895	−	10.7452i	−0.470279	−	0.341678i
$990$		0			0
$991$	−5.05504	+	3.67270i	−0.160579	+	0.116667i	−0.665173	−	0.746689i	$-0.731642\pi$
$991$	−5.05504	+	3.67270i	−0.160579	+	0.116667i	0.504594	+	0.863357i	$0.331642\pi$
$992$	−6.15005	−	1.99827i	−0.195264	−	0.0634452i
$993$		0			0
$994$	6.94082	−	21.3616i	0.220149	−	0.677550i
$995$	21.7777	−	14.2727i	0.690399	−	0.452476i
$996$		0			0
$997$	8.04054	−	2.61253i	0.254646	−	0.0827397i	−0.178912	−	0.983865i	$-0.557258\pi$
$997$	8.04054	−	2.61253i	0.254646	−	0.0827397i	0.433559	+	0.901125i	$0.357258\pi$
$998$	−8.96234	+	12.3356i	−0.283698	+	0.390477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.d.109.1	✓	16
3.2	odd	2	inner	450.2.l.d.109.4	yes	16
25.14	even	10	inner	450.2.l.d.289.1	yes	16
75.14	odd	10	inner	450.2.l.d.289.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.l.d.109.1	✓	16	1.1	even	1	trivial
450.2.l.d.109.4	yes	16	3.2	odd	2	inner
450.2.l.d.289.1	yes	16	25.14	even	10	inner
450.2.l.d.289.4	yes	16	75.14	odd	10	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.87020 + 1.22570i) q^{5} -3.26086i q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-1.87020 + 1.22570i) q^{5} -3.26086i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.107666 - 2.23347i) q^{10} +(1.44726 + 1.05149i) q^{11} +(3.38313 + 4.65648i) q^{13} +(2.63809 + 1.91668i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(6.26221 + 2.03472i) q^{17} +(-1.21533 + 3.74041i) q^{19} +(1.74363 + 1.39991i) q^{20} +(-1.70135 + 0.552802i) q^{22} +(-4.91598 + 6.76626i) q^{23} +(1.99532 - 4.58462i) q^{25} -5.75573 q^{26} +(-3.10126 + 1.00766i) q^{28} +(-0.442669 - 1.36239i) q^{29} +(1.99827 - 6.15005i) q^{31} -1.00000i q^{32} +(-5.32696 + 3.87026i) q^{34} +(3.99683 + 6.09846i) q^{35} +(6.56303 + 9.03323i) q^{37} +(-2.31170 - 3.18178i) q^{38} +(-2.15743 + 0.587785i) q^{40} +(3.18453 - 2.31370i) q^{41} +2.18577i q^{43} +(0.552802 - 1.70135i) q^{44} +(-2.58448 - 7.95422i) q^{46} +(-6.88191 + 2.23607i) q^{47} -3.63318 q^{49} +(2.53621 + 4.30902i) q^{50} +(3.38313 - 4.65648i) q^{52} +(1.47281 - 0.478544i) q^{53} +(-3.99548 - 0.192604i) q^{55} +(1.00766 - 3.10126i) q^{56} +(1.36239 + 0.442669i) q^{58} +(8.85810 - 6.43579i) q^{59} +(0.637605 + 0.463247i) q^{61} +(3.80094 + 5.23154i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-12.0346 - 4.56186i) q^{65} +(7.46309 + 2.42490i) q^{67} -6.58448i q^{68} +(-7.28304 - 0.351083i) q^{70} +(-2.12853 - 6.55093i) q^{71} +(-7.26733 + 10.0026i) q^{73} -11.1657 q^{74} +3.93290 q^{76} +(3.42877 - 4.71929i) q^{77} +(1.18285 + 3.64043i) q^{79} +(0.792578 - 2.09089i) q^{80} +3.93630i q^{82} +(-6.37438 - 2.07116i) q^{83} +(-14.2056 + 3.87026i) q^{85} +(-1.76833 - 1.28477i) q^{86} +(1.05149 + 1.44726i) q^{88} +(1.29271 + 0.939207i) q^{89} +(15.1841 - 11.0319i) q^{91} +(7.95422 + 2.58448i) q^{92} +(2.23607 - 6.88191i) q^{94} +(-2.31170 - 8.48495i) q^{95} +(8.68131 - 2.82073i) q^{97} +(2.13553 - 2.93930i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more