LMFDB - Embedded newform 252.2.w.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$1.68124 + 0.416458i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +O(q^{10})$	\(q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +(0.229685 - 0.132608i) q^{11} +(1.13823 - 0.657156i) q^{13} +(1.19992 - 0.169570i) q^{15} +(-1.86392 + 3.22840i) q^{17} +(-0.382449 + 0.220807i) q^{19} +(3.88637 + 2.42819i) q^{21} +(-4.29949 - 2.48231i) q^{23} +(2.25524 + 3.90619i) q^{25} +(-4.74208 + 2.12432i) q^{27} +(-0.273287 - 0.157782i) q^{29} -5.60632i q^{31} +(0.426051 + 0.171758i) q^{33} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(2.11134 + 0.851166i) q^{39} +(-5.39354 - 9.34189i) q^{41} +(3.73131 - 6.46283i) q^{43} +(1.51209 + 1.45576i) q^{45} -7.00570 q^{47} +(5.36869 - 4.49190i) q^{49} +(-6.39328 + 0.903488i) q^{51} +(8.51919 + 4.91856i) q^{53} -0.185561i q^{55} +(-0.709419 - 0.285995i) q^{57} -13.4636 q^{59} +5.65207i q^{61} +(0.836106 + 7.89309i) q^{63} -0.919566i q^{65} -5.94120 q^{67} +(-1.20324 - 8.51439i) q^{69} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(-2.92105 + 7.24575i) q^{75} +(0.451424 - 0.537212i) q^{77} +1.39672 q^{79} +(-7.95938 - 4.20099i) q^{81} +(-3.72399 + 6.45014i) q^{83} +(1.30410 + 2.25877i) q^{85} +(-0.0764809 - 0.541196i) q^{87} +(5.59261 + 9.68668i) q^{89} +(2.23708 - 2.66221i) q^{91} +(7.64736 - 5.98417i) q^{93} +0.308978i q^{95} +(-9.18225 - 5.30138i) q^{97} +(0.220477 + 0.764493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.06740	+	1.36406i	0.616262	+	0.787541i
$3$	1.06740	+	1.36406i	0.616262	+	0.787541i
$4$		0			0
$5$	0.349828	−	0.605920i	0.156448	−	0.270975i	−0.777137	−	0.629331i	$-0.783329\pi$
$5$	0.349828	−	0.605920i	0.156448	−	0.270975i	0.933585	+	0.358355i	$0.116662\pi$
$6$		0			0
$7$	2.48683	−	0.903137i	0.939935	−	0.341354i
$7$	2.48683	−	0.903137i	0.939935	−	0.341354i
$8$		0			0
$9$	−0.721326	+	2.91199i	−0.240442	+	0.970663i
$10$		0			0
$11$	0.229685	−	0.132608i	0.0692525	−	0.0399829i	−0.464974	−	0.885324i	$-0.653936\pi$
$11$	0.229685	−	0.132608i	0.0692525	−	0.0399829i	0.534226	+	0.845341i	$0.320603\pi$
$12$		0			0
$13$	1.13823	−	0.657156i	0.315688	−	0.182262i	−0.333781	−	0.942651i	$-0.608325\pi$
$13$	1.13823	−	0.657156i	0.315688	−	0.182262i	0.649469	+	0.760388i	$0.274991\pi$
$14$		0			0
$15$	1.19992	−	0.169570i	0.309817	−	0.0437829i
$16$		0			0
$17$	−1.86392	+	3.22840i	−0.452067	+	0.783003i	−0.998514	−	0.0544906i	$-0.982646\pi$
$17$	−1.86392	+	3.22840i	−0.452067	+	0.783003i	0.546447	+	0.837493i	$0.315980\pi$
$18$		0			0
$19$	−0.382449	+	0.220807i	−0.0877398	+	0.0506566i	−0.543228	−	0.839585i	$-0.682798\pi$
$19$	−0.382449	+	0.220807i	−0.0877398	+	0.0506566i	0.455488	+	0.890242i	$0.349465\pi$
$20$		0			0
$21$	3.88637	+	2.42819i	0.848076	+	0.529874i
$22$		0			0
$23$	−4.29949	−	2.48231i	−0.896507	−	0.517598i	−0.0204414	−	0.999791i	$-0.506507\pi$
$23$	−4.29949	−	2.48231i	−0.896507	−	0.517598i	−0.876065	+	0.482193i	$0.839840\pi$
$24$		0			0
$25$	2.25524	+	3.90619i	0.451048	+	0.781238i
$26$		0			0
$27$	−4.74208	+	2.12432i	−0.912613	+	0.408825i
$28$		0			0
$29$	−0.273287	−	0.157782i	−0.0507480	−	0.0292994i	0.474411	−	0.880303i	$-0.342661\pi$
$29$	−0.273287	−	0.157782i	−0.0507480	−	0.0292994i	−0.525159	+	0.851004i	$0.675994\pi$
$30$		0			0
$31$		−	5.60632i		−	1.00692i	−0.864017	−	0.503462i	$-0.832059\pi$
$31$		−	5.60632i		−	1.00692i	0.864017	−	0.503462i	$-0.167941\pi$
$32$		0			0
$33$	0.426051	+	0.171758i	0.0741659	+	0.0298992i
$34$		0			0
$35$	0.322736	−	1.82276i	0.0545523	−	0.308103i
$36$		0			0
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	0.835719	−	0.549157i	$-0.185051\pi$
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	−0.893444	+	0.449175i	$0.851718\pi$
$38$		0			0
$39$	2.11134	+	0.851166i	0.338085	+	0.136296i
$40$		0			0
$41$	−5.39354	−	9.34189i	−0.842330	−	1.45896i	−0.887920	−	0.459998i	$-0.847850\pi$
$41$	−5.39354	−	9.34189i	−0.842330	−	1.45896i	0.0455900	−	0.998960i	$-0.485483\pi$
$42$		0			0
$43$	3.73131	−	6.46283i	0.569020	−	0.985572i	−0.427643	−	0.903948i	$-0.640656\pi$
$43$	3.73131	−	6.46283i	0.569020	−	0.985572i	0.996663	−	0.0816240i	$-0.0260106\pi$
$44$		0			0
$45$	1.51209	+	1.45576i	0.225409	+	0.217012i
$46$		0			0
$47$	−7.00570			−1.02189			−0.510943	−	0.859614i	$-0.670704\pi$
$47$	−7.00570			−1.02189			−0.510943	+	0.859614i	$0.670704\pi$
$48$		0			0
$49$	5.36869	−	4.49190i	0.766955	−	0.641700i
$50$		0			0
$51$	−6.39328	+	0.903488i	−0.895239	+	0.126514i
$52$		0			0
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.953727	−	0.300672i	$-0.0972111\pi$
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.216474	+	0.976288i	$0.430544\pi$
$54$		0			0
$55$		−	0.185561i		−	0.0250210i
$56$		0			0
$57$	−0.709419	−	0.285995i	−0.0939648	−	0.0378809i
$58$		0			0
$59$	−13.4636			−1.75282			−0.876408	−	0.481570i	$-0.840067\pi$
$59$	−13.4636			−1.75282			−0.876408	+	0.481570i	$0.840067\pi$
$60$		0			0
$61$			5.65207i			0.723674i	0.932241	+	0.361837i	$0.117850\pi$
$61$			5.65207i			0.723674i	−0.932241	+	0.361837i	$0.882150\pi$
$62$		0			0
$63$	0.836106	+	7.89309i	0.105340	+	0.994436i
$64$		0			0
$65$		−	0.919566i		−	0.114058i
$66$		0			0
$67$	−5.94120			−0.725833			−0.362916	−	0.931822i	$-0.618219\pi$
$67$	−5.94120			−0.725833			−0.362916	+	0.931822i	$0.618219\pi$
$68$		0			0
$69$	−1.20324	−	8.51439i	−0.144853	−	1.02501i
$70$		0			0
$71$		−	13.4323i		−	1.59412i	−0.603900	−	0.797060i	$-0.706387\pi$
$71$		−	13.4323i		−	1.59412i	0.603900	−	0.797060i	$-0.293613\pi$
$72$		0			0
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	0.0566194	−	0.998396i	$-0.481968\pi$
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	−0.836326	+	0.548232i	$0.815301\pi$
$74$		0			0
$75$	−2.92105	+	7.24575i	−0.337293	+	0.836667i
$76$		0			0
$77$	0.451424	−	0.537212i	0.0514445	−	0.0612210i
$78$		0			0
$79$	1.39672			0.157143			0.0785716	−	0.996908i	$-0.474964\pi$
$79$	1.39672			0.157143			0.0785716	+	0.996908i	$0.474964\pi$
$80$		0			0
$81$	−7.95938	−	4.20099i	−0.884375	−	0.466777i
$82$		0			0
$83$	−3.72399	+	6.45014i	−0.408761	+	0.707995i	−0.994751	−	0.102323i	$-0.967372\pi$
$83$	−3.72399	+	6.45014i	−0.408761	+	0.707995i	0.585990	+	0.810318i	$0.300706\pi$
$84$		0			0
$85$	1.30410	+	2.25877i	0.141450	+	0.244998i
$86$		0			0
$87$	−0.0764809	−	0.541196i	−0.00819961	−	0.0580223i
$88$		0			0
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	0.993851	+	0.110724i	$0.0353168\pi$
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	−0.401036	+	0.916062i	$0.631350\pi$
$90$		0			0
$91$	2.23708	−	2.66221i	0.234510	−	0.279076i
$92$		0			0
$93$	7.64736	−	5.98417i	0.792995	−	0.620529i
$94$		0			0
$95$			0.308978i			0.0317004i
$96$		0			0
$97$	−9.18225	−	5.30138i	−0.932316	−	0.538273i	−0.0447729	−	0.998997i	$-0.514256\pi$
$97$	−9.18225	−	5.30138i	−0.932316	−	0.538273i	−0.887543	+	0.460724i	$0.847590\pi$
$98$		0			0
$99$	0.220477	+	0.764493i	0.0221588	+	0.0768345i
$100$		0			0
$101$	8.75357	+	15.1616i	0.871013	+	1.50864i	0.860950	+	0.508690i	$0.169870\pi$
$101$	8.75357	+	15.1616i	0.871013	+	1.50864i	0.0100634	+	0.999949i	$0.496797\pi$
$102$		0			0
$103$	7.39775	+	4.27110i	0.728922	+	0.420844i	0.818028	−	0.575179i	$-0.195067\pi$
$103$	7.39775	+	4.27110i	0.728922	+	0.420844i	−0.0891054	+	0.996022i	$0.528401\pi$
$104$		0			0
$105$	2.83085	−	1.50538i	0.276263	−	0.146910i
$106$		0			0
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.00882940	−	0.999961i	$-0.497189\pi$
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.870406	+	0.492334i	$0.163856\pi$
$108$		0			0
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	0.292268	+	0.956337i	$0.405590\pi$
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	−0.974346	+	0.225057i	$0.927743\pi$
$110$		0			0
$111$	0.454785	−	1.12811i	0.0431663	−	0.107075i
$112$		0			0
$113$	13.3783	−	7.72396i	1.25852	−	0.726609i	0.285737	−	0.958308i	$-0.407762\pi$
$113$	13.3783	−	7.72396i	1.25852	−	0.726609i	0.972788	+	0.231699i	$0.0744284\pi$
$114$		0			0
$115$	−3.00817	+	1.73677i	−0.280513	+	0.161954i
$116$		0			0
$117$	1.09260	+	3.78853i	0.101011	+	0.350250i
$118$		0			0
$119$	−1.71957	+	9.71188i	−0.157633	+	0.890286i
$120$		0			0
$121$	−5.46483	+	9.46536i	−0.496803	+	0.860488i
$122$		0			0
$123$	6.98586	−	17.3286i	0.629894	−	1.56247i
$124$		0			0
$125$	6.65406			0.595157
$126$		0			0
$127$	21.8304			1.93713			0.968566	−	0.248758i	$-0.0800225\pi$
$127$	21.8304			1.93713			0.968566	+	0.248758i	$0.0800225\pi$
$128$		0			0
$129$	12.7985	−	1.80866i	1.12684	−	0.159244i
$130$		0			0
$131$	2.60461	−	4.51132i	0.227566	−	0.394156i	−0.729520	−	0.683959i	$-0.760257\pi$
$131$	2.60461	−	4.51132i	0.227566	−	0.394156i	0.957086	+	0.289803i	$0.0935899\pi$
$132$		0			0
$133$	−0.751668	+	0.894514i	−0.0651779	+	0.0775642i
$134$		0			0
$135$	−0.371744	+	3.61646i	−0.0319947	+	0.311255i
$136$		0			0
$137$	−2.33589	+	1.34863i	−0.199568	+	0.115221i	−0.596454	−	0.802647i	$-0.703424\pi$
$137$	−2.33589	+	1.34863i	−0.199568	+	0.115221i	0.396886	+	0.917868i	$0.370091\pi$
$138$		0			0
$139$	−10.1448	+	5.85710i	−0.860470	+	0.496793i	−0.864170	−	0.503200i	$-0.832156\pi$
$139$	−10.1448	+	5.85710i	−0.860470	+	0.496793i	0.00369951	+	0.999993i	$0.498822\pi$
$140$		0			0
$141$	−7.47787	−	9.55621i	−0.629750	−	0.804778i
$142$		0			0
$143$	0.174289	−	0.301877i	0.0145748	−	0.0252442i
$144$		0			0
$145$	−0.191206	+	0.110393i	−0.0158788	+	0.00916765i
$146$		0			0
$147$	11.8578	+	2.52858i	0.978011	+	0.208553i
$148$		0			0
$149$	16.3055	+	9.41399i	1.33580	+	0.771224i	0.986182	−	0.165668i	$-0.0529781\pi$
$149$	16.3055	+	9.41399i	1.33580	+	0.771224i	0.349618	+	0.936892i	$0.386311\pi$
$150$		0			0
$151$	−5.00143	−	8.66273i	−0.407010	−	0.704963i	0.587543	−	0.809193i	$-0.300095\pi$
$151$	−5.00143	−	8.66273i	−0.407010	−	0.704963i	−0.994553	+	0.104230i	$0.966762\pi$
$152$		0			0
$153$	−8.05659	−	7.75645i	−0.651336	−	0.627072i
$154$		0			0
$155$	−3.39698	−	1.96125i	−0.272852	−	0.157531i
$156$		0			0
$157$		−	0.252063i		−	0.0201168i	−0.999949	−	0.0100584i	$-0.996798\pi$
$157$		−	0.252063i		−	0.0201168i	0.999949	−	0.0100584i	$-0.00320175\pi$
$158$		0			0
$159$	2.38415	+	16.8708i	0.189075	+	1.33794i
$160$		0			0
$161$	−12.9340	−	2.29007i	−1.01934	−	0.180483i
$162$		0			0
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	0.983796	−	0.179289i	$-0.0573797\pi$
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	−0.647167	+	0.762348i	$0.724046\pi$
$164$		0			0
$165$	0.253116	−	0.198067i	0.0197050	−	0.0154195i
$166$		0			0
$167$	2.24437	+	3.88736i	0.173674	+	0.300813i	0.939702	−	0.341995i	$-0.111103\pi$
$167$	2.24437	+	3.88736i	0.173674	+	0.300813i	−0.766027	+	0.642808i	$0.777769\pi$
$168$		0			0
$169$	−5.63629	+	9.76234i	−0.433561	+	0.750949i
$170$		0			0
$171$	−0.367117	−	1.27296i	−0.0280742	−	0.0973457i
$172$		0			0
$173$	−7.12145			−0.541434			−0.270717	−	0.962659i	$-0.587261\pi$
$173$	−7.12145			−0.541434			−0.270717	+	0.962659i	$0.587261\pi$
$174$		0			0
$175$	9.13624	+	7.67726i	0.690634	+	0.580346i
$176$		0			0
$177$	−14.3710	−	18.3652i	−1.08019	−	1.38041i
$178$		0			0
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.975470	+	0.220134i	$0.0706494\pi$
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.678376	+	0.734715i	$0.262684\pi$
$180$		0			0
$181$		−	0.943175i		−	0.0701057i	−0.999385	−	0.0350528i	$-0.988840\pi$
$181$		−	0.943175i		−	0.0701057i	0.999385	−	0.0350528i	$-0.0111599\pi$
$182$		0			0
$183$	−7.70977	+	6.03301i	−0.569923	+	0.445973i
$184$		0			0
$185$	−0.491332			−0.0361234
$186$		0			0
$187$			0.988686i			0.0722999i
$188$		0			0
$189$	−9.87421	+	9.56557i	−0.718243	+	0.695793i
$190$		0			0
$191$		−	2.97235i		−	0.215072i	−0.994201	−	0.107536i	$-0.965704\pi$
$191$		−	2.97235i		−	0.215072i	0.994201	−	0.107536i	$-0.0342960\pi$
$192$		0			0
$193$	−18.5144			−1.33270			−0.666348	−	0.745641i	$-0.732144\pi$
$193$	−18.5144			−1.33270			−0.666348	+	0.745641i	$0.732144\pi$
$194$		0			0
$195$	1.25434	−	0.981542i	0.0898255	−	0.0702897i
$196$		0			0
$197$		−	14.1774i		−	1.01010i	−0.863091	−	0.505048i	$-0.831475\pi$
$197$		−	14.1774i		−	1.01010i	0.863091	−	0.505048i	$-0.168525\pi$
$198$		0			0
$199$	−20.5293	−	11.8526i	−1.45529	−	0.840209i	−0.456512	−	0.889717i	$-0.650901\pi$
$199$	−20.5293	−	11.8526i	−1.45529	−	0.840209i	−0.998774	+	0.0495081i	$0.984235\pi$
$200$		0			0
$201$	−6.34162	−	8.10416i	−0.447303	−	0.571623i
$202$		0			0
$203$	−0.822117	−	0.145563i	−0.0577013	−	0.0102165i
$204$		0			0
$205$	−7.54725			−0.527123
$206$		0			0
$207$	10.3298	−	10.7295i	0.717972	−	0.745754i
$208$		0			0
$209$	−0.0585617	+	0.101432i	−0.00405080	+	0.00701619i
$210$		0			0
$211$	3.04004	+	5.26550i	0.209285	+	0.362492i	0.951489	−	0.307681i	$-0.0995531\pi$
$211$	3.04004	+	5.26550i	0.209285	+	0.362492i	−0.742205	+	0.670173i	$0.766220\pi$
$212$		0			0
$213$	18.3225	−	14.3376i	1.25544	−	0.982396i
$214$		0			0
$215$	−2.61063	−	4.52175i	−0.178044	−	0.308381i
$216$		0			0
$217$	−5.06327	−	13.9420i	−0.343717	−	0.946444i
$218$		0			0
$219$	−1.86435	−	13.1926i	−0.125981	−	0.891470i
$220$		0			0
$221$			4.89954i			0.329579i
$222$		0			0
$223$	0.796137	+	0.459650i	0.0533133	+	0.0307804i	0.526420	−	0.850225i	$-0.323534\pi$
$223$	0.796137	+	0.459650i	0.0533133	+	0.0307804i	−0.473106	+	0.881005i	$0.656867\pi$
$224$		0			0
$225$	−13.0016	+	3.74960i	−0.866771	+	0.249973i
$226$		0			0
$227$	5.00297	+	8.66540i	0.332059	+	0.575143i	0.982915	−	0.184058i	$-0.0589234\pi$
$227$	5.00297	+	8.66540i	0.332059	+	0.575143i	−0.650857	+	0.759201i	$0.725590\pi$
$228$		0			0
$229$	−2.38179	−	1.37513i	−0.157393	−	0.0908710i	0.419235	−	0.907878i	$-0.362298\pi$
$229$	−2.38179	−	1.37513i	−0.157393	−	0.0908710i	−0.576628	+	0.817007i	$0.695632\pi$
$230$		0			0
$231$	1.21464	+	0.0423515i	0.0799173	+	0.00278652i
$232$		0			0
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	−0.670803	−	0.741636i	$-0.734050\pi$
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	0.306874	+	0.951750i	$0.400717\pi$
$234$		0			0
$235$	−2.45079	+	4.24489i	−0.159872	+	0.276906i
$236$		0			0
$237$	1.49085	+	1.90521i	0.0968414	+	0.123757i
$238$		0			0
$239$	−11.4288	+	6.59844i	−0.739270	+	0.426818i	−0.821804	−	0.569770i	$-0.807032\pi$
$239$	−11.4288	+	6.59844i	−0.739270	+	0.426818i	0.0825337	+	0.996588i	$0.473699\pi$
$240$		0			0
$241$	−2.20722	+	1.27434i	−0.142180	+	0.0820874i	−0.569402	−	0.822059i	$-0.692825\pi$
$241$	−2.20722	+	1.27434i	−0.142180	+	0.0820874i	0.427223	+	0.904146i	$0.359492\pi$
$242$		0			0
$243$	−2.76541	−	15.3412i	−0.177401	−	0.984139i
$244$		0			0
$245$	−0.843615	−	4.82439i	−0.0538966	−	0.308219i
$246$		0			0
$247$	−0.290209	+	0.502657i	−0.0184656	+	0.0319833i
$248$		0			0
$249$	−12.7734	+	1.80511i	−0.809479	+	0.114394i
$250$		0			0
$251$	18.7893			1.18597			0.592986	−	0.805213i	$-0.297949\pi$
$251$	18.7893			1.18597			0.592986	+	0.805213i	$0.297949\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$	−1.68911	+	4.18988i	−0.105776	+	0.262380i
$256$		0			0
$257$	7.19727	−	12.4660i	0.448953	−	0.777610i	−0.549365	−	0.835583i	$-0.685130\pi$
$257$	7.19727	−	12.4660i	0.448953	−	0.777610i	0.998318	+	0.0579725i	$0.0184636\pi$
$258$		0			0
$259$	−1.42244	−	1.19529i	−0.0883863	−	0.0742718i
$260$		0			0
$261$	0.656589	−	0.681995i	0.0406418	−	0.0422145i
$262$		0			0
$263$	6.79810	−	3.92488i	0.419189	−	0.242019i	−0.275542	−	0.961289i	$-0.588857\pi$
$263$	6.79810	−	3.92488i	0.419189	−	0.242019i	0.694730	+	0.719271i	$0.255524\pi$
$264$		0			0
$265$	5.96050	−	3.44130i	0.366151	−	0.211397i
$266$		0			0
$267$	−7.24369	+	17.9682i	−0.443307	+	1.09964i
$268$		0			0
$269$	−7.72267	+	13.3760i	−0.470859	+	0.815552i	−0.999444	−	0.0333281i	$-0.989389\pi$
$269$	−7.72267	+	13.3760i	−0.470859	+	0.815552i	0.528585	+	0.848880i	$0.322723\pi$
$270$		0			0
$271$	10.9476	−	6.32057i	0.665016	−	0.383947i	−0.129169	−	0.991623i	$-0.541231\pi$
$271$	10.9476	−	6.32057i	0.665016	−	0.383947i	0.794186	+	0.607675i	$0.207898\pi$
$272$		0			0
$273$	6.01928	+	0.209878i	0.364303	+	0.0127024i
$274$		0			0
$275$	1.03599	+	0.598128i	0.0624724	+	0.0360685i
$276$		0			0
$277$	5.94531	+	10.2976i	0.357219	+	0.618722i	0.987495	−	0.157649i	$-0.0503915\pi$
$277$	5.94531	+	10.2976i	0.357219	+	0.618722i	−0.630276	+	0.776371i	$0.717058\pi$
$278$		0			0
$279$	16.3255	+	4.04399i	0.977385	+	0.242107i
$280$		0			0
$281$	−2.75411	−	1.59009i	−0.164297	−	0.0948568i	0.415597	−	0.909549i	$-0.363573\pi$
$281$	−2.75411	−	1.59009i	−0.164297	−	0.0948568i	−0.579894	+	0.814692i	$0.696906\pi$
$282$		0			0
$283$		−	18.4978i		−	1.09958i	−0.835303	−	0.549789i	$-0.814708\pi$
$283$		−	18.4978i		−	1.09958i	0.835303	−	0.549789i	$-0.185292\pi$
$284$		0			0
$285$	−0.421464	+	0.329802i	−0.0249654	+	0.0195358i
$286$		0			0
$287$	−21.8499	−	18.3606i	−1.28976	−	1.08379i
$288$		0			0
$289$	1.55161	+	2.68746i	0.0912711	+	0.158086i
$290$		0			0
$291$	−2.56971	−	18.1838i	−0.150639	−	1.06595i
$292$		0			0
$293$	−1.42975	−	2.47639i	−0.0835266	−	0.144672i	0.821236	−	0.570589i	$-0.193285\pi$
$293$	−1.42975	−	2.47639i	−0.0835266	−	0.144672i	−0.904762	+	0.425917i	$0.859952\pi$
$294$		0			0
$295$	−4.70995	+	8.15788i	−0.274224	+	0.474970i
$296$		0			0
$297$	−0.807479	+	1.11676i	−0.0468547	+	0.0648011i
$298$		0			0
$299$	−6.52507			−0.377355
$300$		0			0
$301$	3.44234	−	19.4419i	0.198413	−	1.12061i
$302$		0			0
$303$	−11.3379	+	28.1239i	−0.651343	+	1.61568i
$304$		0			0
$305$	3.42470	+	1.97725i	0.196098	+	0.113217i
$306$		0			0
$307$			21.6746i			1.23704i	0.785771	+	0.618518i	$0.212266\pi$
$307$			21.6746i			1.23704i	−0.785771	+	0.618518i	$0.787734\pi$
$308$		0			0
$309$	2.07031	+	14.6499i	0.117776	+	0.833406i
$310$		0			0
$311$	−23.6925			−1.34348			−0.671738	−	0.740789i	$-0.734452\pi$
$311$	−23.6925			−1.34348			−0.671738	+	0.740789i	$0.734452\pi$
$312$		0			0
$313$		−	27.2836i		−	1.54216i	−0.636737	−	0.771081i	$-0.719716\pi$
$313$		−	27.2836i		−	1.54216i	0.636737	−	0.771081i	$-0.280284\pi$
$314$		0			0
$315$	5.07507	+	2.25461i	0.285948	+	0.127033i
$316$		0			0
$317$		−	24.5544i		−	1.37911i	−0.724232	−	0.689556i	$-0.757806\pi$
$317$		−	24.5544i		−	1.37911i	0.724232	−	0.689556i	$-0.242194\pi$
$318$		0			0
$319$	−0.0836929			−0.00468590
$320$		0			0
$321$	16.8705	+	6.80115i	0.941617	+	0.379603i
$322$		0			0
$323$		−	1.64626i		−	0.0916006i
$324$		0			0
$325$	5.13396	+	2.96409i	0.284781	+	0.164418i
$326$		0			0
$327$	−24.4255	+	3.45178i	−1.35074	+	0.190884i
$328$		0			0
$329$	−17.4220	+	6.32711i	−0.960507	+	0.348825i
$330$		0			0
$331$	16.3116			0.896566			0.448283	−	0.893892i	$-0.352036\pi$
$331$	16.3116			0.896566			0.448283	+	0.893892i	$0.352036\pi$
$332$		0			0
$333$	2.02424	−	0.583784i	0.110928	−	0.0319912i
$334$		0			0
$335$	−2.07840	+	3.59989i	−0.113555	+	0.196683i
$336$		0			0
$337$	13.6580	+	23.6563i	0.743998	+	1.28864i	0.950661	+	0.310230i	$0.100406\pi$
$337$	13.6580	+	23.6563i	0.743998	+	1.28864i	−0.206663	+	0.978412i	$0.566261\pi$
$338$		0			0
$339$	24.8159	+	10.0043i	1.34782	+	0.543358i
$340$		0			0
$341$	−0.743445	−	1.28768i	−0.0402598	−	0.0697320i
$342$		0			0
$343$	9.29424	−	16.0193i	0.501842	−	0.864960i
$344$		0			0
$345$	−5.57996	−	2.24950i	−0.300415	−	0.121109i
$346$		0			0
$347$			6.21213i			0.333485i	0.986001	+	0.166742i	$0.0533248\pi$
$347$			6.21213i			0.333485i	−0.986001	+	0.166742i	$0.946675\pi$
$348$		0			0
$349$	24.6529	+	14.2334i	1.31964	+	0.761896i	0.983671	−	0.179977i	$-0.0576023\pi$
$349$	24.6529	+	14.2334i	1.31964	+	0.761896i	0.335971	+	0.941872i	$0.390936\pi$
$350$		0			0
$351$	−4.00155	+	5.53424i	−0.213587	+	0.295396i
$352$		0			0
$353$	1.49346	+	2.58674i	0.0794887	+	0.137678i	0.903029	−	0.429579i	$-0.141338\pi$
$353$	1.49346	+	2.58674i	0.0794887	+	0.137678i	−0.823541	+	0.567257i	$0.808005\pi$
$354$		0			0
$355$	−8.13889	−	4.69899i	−0.431968	−	0.249397i
$356$		0			0
$357$	−15.0831	+	8.02083i	−0.798280	+	0.424508i
$358$		0			0
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.994777	−	0.102070i	$-0.967454\pi$
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.408994	+	0.912537i	$0.634120\pi$
$360$		0			0
$361$	−9.40249	+	16.2856i	−0.494868	+	0.857136i
$362$		0			0
$363$	−18.7445	+	2.64894i	−0.983830	+	0.139033i
$364$		0			0
$365$	−4.66098	+	2.69102i	−0.243967	+	0.140854i
$366$		0			0
$367$	16.4877	−	9.51918i	0.860651	−	0.496897i	−0.00357920	−	0.999994i	$-0.501139\pi$
$367$	16.4877	−	9.51918i	0.860651	−	0.496897i	0.864230	+	0.503096i	$0.167806\pi$
$368$		0			0
$369$	31.0940	−	8.96739i	1.61869	−	0.466824i
$370$		0			0
$371$	25.6280	+	4.53764i	1.33054	+	0.235583i
$372$		0			0
$373$	−2.05869	+	3.56576i	−0.106595	+	0.184628i	−0.914389	−	0.404837i	$-0.867328\pi$
$373$	−2.05869	+	3.56576i	−0.106595	+	0.184628i	0.807794	+	0.589465i	$0.200661\pi$
$374$		0			0
$375$	7.10253	+	9.07655i	0.366773	+	0.468711i
$376$		0			0
$377$	−0.414750			−0.0213607
$378$		0			0
$379$	−11.2436			−0.577546			−0.288773	−	0.957398i	$-0.593247\pi$
$379$	−11.2436			−0.577546			−0.288773	+	0.957398i	$0.593247\pi$
$380$		0			0
$381$	23.3017	+	29.7779i	1.19378	+	1.52557i
$382$		0			0
$383$	15.8046	−	27.3745i	0.807580	−	1.39877i	−0.106956	−	0.994264i	$-0.534110\pi$
$383$	15.8046	−	27.3745i	0.807580	−	1.39877i	0.914536	−	0.404505i	$-0.132556\pi$
$384$		0			0
$385$	−0.167586	−	0.461458i	−0.00854100	−	0.0235181i
$386$		0			0
$387$	16.1282	+	15.5274i	0.819842	+	0.789300i
$388$		0			0
$389$	18.4018	−	10.6243i	0.933007	−	0.538672i	0.0452458	−	0.998976i	$-0.485593\pi$
$389$	18.4018	−	10.6243i	0.933007	−	0.538672i	0.887761	+	0.460304i	$0.152260\pi$
$390$		0			0
$391$	16.0278	−	9.25367i	0.810562	−	0.467978i
$392$		0			0
$393$	8.93387	−	1.26252i	0.450654	−	0.0636857i
$394$		0			0
$395$	0.488611	−	0.846300i	0.0245847	−	0.0425820i
$396$		0			0
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.119118	−	0.992880i	$-0.461993\pi$
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.919419	+	0.393281i	$0.128660\pi$
$398$		0			0
$399$	−2.02250	−	0.0705196i	−0.101252	−	0.00353040i
$400$		0			0
$401$	22.0121	+	12.7087i	1.09923	+	0.634642i	0.936019	−	0.351948i	$-0.114481\pi$
$401$	22.0121	+	12.7087i	1.09923	+	0.634642i	0.163213	+	0.986591i	$0.447814\pi$
$402$		0			0
$403$	−3.68423	−	6.38127i	−0.183524	−	0.317874i
$404$		0			0
$405$	−5.32987	+	3.35312i	−0.264844	+	0.166618i
$406$		0			0
$407$	−0.161295	−	0.0931240i	−0.00799512	−	0.00461598i
$408$		0			0
$409$		−	22.3817i		−	1.10670i	−0.832948	−	0.553351i	$-0.813349\pi$
$409$		−	22.3817i		−	1.10670i	0.832948	−	0.553351i	$-0.186651\pi$
$410$		0			0
$411$	−4.33293	−	1.74678i	−0.213728	−	0.0861621i
$412$		0			0
$413$	−33.4818	+	12.1595i	−1.64753	+	0.598330i
$414$		0			0
$415$	2.60551	+	4.51288i	0.127900	+	0.221528i
$416$		0			0
$417$	−18.8180	−	7.58627i	−0.921520	−	0.371501i
$418$		0			0
$419$	7.04181	+	12.1968i	0.344015	+	0.595851i	0.985174	−	0.171556i	$-0.0548796\pi$
$419$	7.04181	+	12.1968i	0.344015	+	0.595851i	−0.641159	+	0.767408i	$0.721546\pi$
$420$		0			0
$421$	8.07639	−	13.9887i	0.393619	−	0.681768i	−0.599305	−	0.800521i	$-0.704556\pi$
$421$	8.07639	−	13.9887i	0.393619	−	0.681768i	0.992924	+	0.118753i	$0.0378896\pi$
$422$		0			0
$423$	5.05340	−	20.4005i	0.245705	−	0.991908i
$424$		0			0
$425$	−16.8143			−0.815616
$426$		0			0
$427$	5.10459	+	14.0558i	0.247029	+	0.680206i
$428$		0			0
$429$	0.597815	−	0.0844822i	0.0288628	−	0.00407884i
$430$		0			0
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	0.317497	−	0.948259i	$-0.397158\pi$
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	−0.662468	+	0.749090i	$0.730491\pi$
$432$		0			0
$433$		−	4.35102i		−	0.209097i	−0.994520	−	0.104548i	$-0.966660\pi$
$433$		−	4.35102i		−	0.209097i	0.994520	−	0.104548i	$-0.0333397\pi$
$434$		0			0
$435$	−0.354676	−	0.142984i	−0.0170054	−	0.00685556i
$436$		0			0
$437$	2.19245			0.104879
$438$		0			0
$439$			20.8077i			0.993098i	0.868009	+	0.496549i	$0.165400\pi$
$439$			20.8077i			0.993098i	−0.868009	+	0.496549i	$0.834600\pi$
$440$		0			0
$441$	9.20780	+	18.8737i	0.438467	+	0.898747i
$442$		0			0
$443$		−	30.9376i		−	1.46989i	−0.678127	−	0.734945i	$-0.737208\pi$
$443$		−	30.9376i		−	1.46989i	0.678127	−	0.734945i	$-0.262792\pi$
$444$		0			0
$445$	7.82580			0.370978
$446$		0			0
$447$	4.56320	+	32.2902i	0.215832	+	1.52727i
$448$		0			0
$449$			20.9215i			0.987346i	0.869648	+	0.493673i	$0.164346\pi$
$449$			20.9215i			0.987346i	−0.869648	+	0.493673i	$0.835654\pi$
$450$		0			0
$451$	−2.47763	−	1.43046i	−0.116667	−	0.0673577i
$452$		0			0
$453$	6.47798	−	16.0688i	0.304362	−	0.754979i
$454$		0			0
$455$	−0.830494	−	2.28681i	−0.0389342	−	0.107207i
$456$		0			0
$457$	2.30115			0.107643			0.0538217	−	0.998551i	$-0.482860\pi$
$457$	2.30115			0.107643			0.0538217	+	0.998551i	$0.482860\pi$
$458$		0			0
$459$	1.98069	−	19.2689i	0.0924509	−	0.899395i
$460$		0			0
$461$	8.92497	−	15.4585i	0.415677	−	0.719974i	−0.579822	−	0.814743i	$-0.696878\pi$
$461$	8.92497	−	15.4585i	0.415677	−	0.719974i	0.995499	+	0.0947688i	$0.0302112\pi$
$462$		0			0
$463$	−6.24034	−	10.8086i	−0.290013	−	0.502318i	0.683799	−	0.729670i	$-0.260326\pi$
$463$	−6.24034	−	10.8086i	−0.290013	−	0.502318i	−0.973813	+	0.227353i	$0.926993\pi$
$464$		0			0
$465$	−0.950665	−	6.72712i	−0.0440860	−	0.311963i
$466$		0			0
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	0.804365	−	0.594136i	$-0.202506\pi$
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	−0.916719	+	0.399533i	$0.869172\pi$
$468$		0			0
$469$	−14.7748	+	5.36571i	−0.682236	+	0.247766i
$470$		0			0
$471$	0.343830	−	0.269052i	0.0158428	−	0.0123972i
$472$		0			0
$473$		−	1.97921i		−	0.0910044i
$474$		0			0
$475$	−1.72503	−	0.995945i	−0.0791497	−	0.0456971i
$476$		0			0
$477$	−20.4679	+	21.2599i	−0.937161	+	0.973425i
$478$		0			0
$479$	4.40542	+	7.63041i	0.201289	+	0.348642i	0.948944	−	0.315445i	$-0.102154\pi$
$479$	4.40542	+	7.63041i	0.201289	+	0.348642i	−0.747655	+	0.664087i	$0.768820\pi$
$480$		0			0
$481$	−0.799318	−	0.461486i	−0.0364458	−	0.0210420i
$482$		0			0
$483$	−10.6819	−	20.0872i	−0.486044	−	0.913999i
$484$		0			0
$485$	−6.42441	+	3.70914i	−0.291718	+	0.168423i
$486$		0			0
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	−0.740857	−	0.671663i	$-0.765580\pi$
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	0.952106	+	0.305770i	$0.0989137\pi$
$488$		0			0
$489$	−5.56662	+	13.8082i	−0.251731	+	0.624427i
$490$		0			0
$491$	−26.9192	+	15.5418i	−1.21485	+	0.701391i	−0.963811	−	0.266587i	$-0.914104\pi$
$491$	−26.9192	+	15.5418i	−1.21485	+	0.701391i	−0.251034	+	0.967978i	$0.580771\pi$
$492$		0			0
$493$	1.01877	−	0.588186i	0.0458830	−	0.0264906i
$494$		0			0
$495$	0.540350	+	0.133850i	0.0242869	+	0.00601610i
$496$		0			0
$497$	−12.1312	−	33.4039i	−0.544159	−	1.49837i
$498$		0			0
$499$	11.1694	−	19.3459i	0.500010	−	0.866043i	−0.499990	−	0.866031i	$-0.666663\pi$
$499$	11.1694	−	19.3459i	0.500010	−	0.866043i	1.00000		1.16519e-5i	$-3.70891e-6\pi$
$500$		0			0
$501$	−2.90697	+	7.21081i	−0.129874	+	0.322155i
$502$		0			0
$503$	−12.2396			−0.545738			−0.272869	−	0.962051i	$-0.587973\pi$
$503$	−12.2396			−0.545738			−0.272869	+	0.962051i	$0.587973\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$	−19.3326	+	2.73205i	−0.858591	+	0.121335i
$508$		0			0
$509$	−7.05496	+	12.2195i	−0.312706	+	0.541622i	−0.978947	−	0.204114i	$-0.934569\pi$
$509$	−7.05496	+	12.2195i	−0.312706	+	0.541622i	0.666242	+	0.745736i	$0.267902\pi$
$510$		0			0
$511$	−20.0405	−	3.54834i	−0.886539	−	0.156969i
$512$		0			0
$513$	1.34454	−	1.85953i	0.0593627	−	0.0821000i
$514$		0			0
$515$	5.17588	−	2.98830i	0.228077	−	0.131680i
$516$		0			0
$517$	−1.60910	+	0.929015i	−0.0707682	+	0.0408580i
$518$		0			0
$519$	−7.60141	−	9.71409i	−0.333665	−	0.426401i
$520$		0			0
$521$	2.81632	−	4.87800i	0.123385	−	0.213709i	−0.797715	−	0.603034i	$-0.793958\pi$
$521$	2.81632	−	4.87800i	0.123385	−	0.213709i	0.921101	+	0.389325i	$0.127292\pi$
$522$		0			0
$523$	−33.2293	+	19.1849i	−1.45302	+	0.838899i	−0.998651	−	0.0519176i	$-0.983467\pi$
$523$	−33.2293	+	19.1849i	−1.45302	+	0.838899i	−0.454364	+	0.890816i	$0.650133\pi$
$524$		0			0
$525$	−0.720262	+	20.6571i	−0.0314348	+	0.901549i
$526$		0			0
$527$	18.0995	+	10.4497i	0.788425	+	0.455197i
$528$		0			0
$529$	0.823769	+	1.42681i	0.0358161	+	0.0620352i
$530$		0			0
$531$	9.71167	−	39.2060i	0.421451	−	1.70139i
$532$		0			0
$533$	−12.2782	−	7.08880i	−0.531826	−	0.307050i
$534$		0			0
$535$		−	7.34769i		−	0.317668i
$536$		0			0
$537$	6.19236	+	43.8185i	0.267220	+	1.89091i
$538$		0			0
$539$	0.637441	−	1.74365i	0.0274565	−	0.0751045i
$540$		0			0
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	0.788555	−	0.614965i	$-0.210830\pi$
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	−0.926852	+	0.375426i	$0.877496\pi$
$542$		0			0
$543$	1.28655	−	1.00674i	0.0552111	−	0.0432035i
$544$		0			0
$545$	4.98232	+	8.62963i	0.213419	+	0.369653i
$546$		0			0
$547$	−6.52889	+	11.3084i	−0.279155	+	0.483511i	−0.971175	−	0.238368i	$-0.923388\pi$
$547$	−6.52889	+	11.3084i	−0.279155	+	0.483511i	0.692020	+	0.721878i	$0.256721\pi$
$548$		0			0
$549$	−16.4588	−	4.07699i	−0.702444	−	0.174002i
$550$		0			0
$551$	0.139357			0.00593683
$552$		0			0
$553$	3.47341	−	1.26143i	0.147704	−	0.0536414i
$554$		0			0
$555$	−0.524446	−	0.670206i	−0.0222615	−	0.0284487i
$556$		0			0
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.150712	−	0.988578i	$-0.548157\pi$
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.931489	+	0.363769i	$0.881490\pi$
$558$		0			0
$559$		−	9.80822i		−	0.414844i
$560$		0			0
$561$	−1.34863	+	1.05532i	−0.0569391	+	0.0445557i
$562$		0			0
$563$	−10.5187			−0.443310			−0.221655	−	0.975125i	$-0.571146\pi$
$563$	−10.5187			−0.443310			−0.221655	+	0.975125i	$0.571146\pi$
$564$		0			0
$565$		−	10.8082i		−	0.454706i
$566$		0			0
$567$	−23.5877	−	3.25876i	−0.990591	−	0.136855i
$568$		0			0
$569$		−	26.3334i		−	1.10395i	−0.833859	−	0.551977i	$-0.813874\pi$
$569$		−	26.3334i		−	1.10395i	0.833859	−	0.551977i	$-0.186126\pi$
$570$		0			0
$571$	−44.0590			−1.84381			−0.921906	−	0.387413i	$-0.873369\pi$
$571$	−44.0590			−1.84381			−0.921906	+	0.387413i	$0.873369\pi$
$572$		0			0
$573$	4.05447	−	3.17268i	0.169378	−	0.132540i
$574$		0			0
$575$		−	22.3929i		−	0.933847i
$576$		0			0
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	0.731170	−	0.682195i	$-0.238974\pi$
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	−0.225213	+	0.974310i	$0.572308\pi$
$578$		0			0
$579$	−19.7622	−	25.2548i	−0.821290	−	1.04955i
$580$		0			0
$581$	−3.43559	+	19.4037i	−0.142532	+	0.805001i
$582$		0			0
$583$	2.60897			0.108052
$584$		0			0
$585$	2.67777	+	0.663307i	0.110712	+	0.0274244i
$586$		0			0
$587$	1.52469	−	2.64085i	0.0629308	−	0.108999i	−0.832843	−	0.553509i	$-0.813289\pi$
$587$	1.52469	−	2.64085i	0.0629308	−	0.108999i	0.895774	+	0.444509i	$0.146622\pi$
$588$		0			0
$589$	1.23791	+	2.14413i	0.0510073	+	0.0883473i
$590$		0			0
$591$	19.3388	−	15.1329i	0.795493	−	0.622484i
$592$		0			0
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	0.998522	+	0.0543552i	$0.0173103\pi$
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	−0.452188	+	0.891923i	$0.649356\pi$
$594$		0			0
$595$	5.28306	+	4.43941i	0.216585	+	0.181998i
$596$		0			0
$597$	−5.74526	−	40.6547i	−0.235138	−	1.66389i
$598$		0			0
$599$			4.46099i			0.182271i	0.995838	+	0.0911356i	$0.0290497\pi$
$599$			4.46099i			0.182271i	−0.995838	+	0.0911356i	$0.970950\pi$
$600$		0			0
$601$	5.25019	+	3.03120i	0.214160	+	0.123645i	0.603243	−	0.797557i	$-0.293875\pi$
$601$	5.25019	+	3.03120i	0.214160	+	0.123645i	−0.389083	+	0.921203i	$0.627208\pi$
$602$		0			0
$603$	4.28554	−	17.3007i	0.174521	−	0.704539i
$604$		0			0
$605$	3.82350	+	6.62250i	0.155447	+	0.269243i
$606$		0			0
$607$	39.2581	+	22.6657i	1.59344	+	0.919971i	0.992711	+	0.120516i	$0.0384548\pi$
$607$	39.2581	+	22.6657i	1.59344	+	0.919971i	0.600725	+	0.799455i	$0.294879\pi$
$608$		0			0
$609$	−0.678969	−	1.27679i	−0.0275132	−	0.0517382i
$610$		0			0
$611$	−7.97409	+	4.60384i	−0.322597	+	0.186251i
$612$		0			0
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	−0.305781	−	0.952102i	$-0.598917\pi$
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	0.977435	−	0.211237i	$-0.0677492\pi$
$614$		0			0
$615$	−8.05591	−	10.2949i	−0.324846	−	0.415131i
$616$		0			0
$617$	31.3001	−	18.0711i	1.26010	−	0.727516i	0.287002	−	0.957930i	$-0.407341\pi$
$617$	31.3001	−	18.0711i	1.26010	−	0.727516i	0.973093	+	0.230414i	$0.0740079\pi$
$618$		0			0
$619$	−22.9031	+	13.2231i	−0.920554	+	0.531482i	−0.883812	−	0.467843i	$-0.845031\pi$
$619$	−22.9031	+	13.2231i	−0.920554	+	0.531482i	−0.0367423	+	0.999325i	$0.511698\pi$
$620$		0			0
$621$	25.6617	+	2.63783i	1.02977	+	0.105852i
$622$		0			0
$623$	22.6563	+	19.0383i	0.907705	+	0.762752i
$624$		0			0
$625$	−8.94843	+	15.4991i	−0.357937	+	0.619965i
$626$		0			0
$627$	−0.200868	+	0.0283863i	−0.00802189	+	0.00113364i
$628$		0			0
$629$	2.61787			0.104381
$630$		0			0
$631$	−32.0484			−1.27583			−0.637914	−	0.770107i	$-0.720203\pi$
$631$	−32.0484			−1.27583			−0.637914	+	0.770107i	$0.720203\pi$
$632$		0			0
$633$	−3.93754	+	9.76717i	−0.156503	+	0.388210i
$634$		0			0
$635$	7.63687	−	13.2274i	0.303060	−	0.524915i
$636$		0			0
$637$	3.15891	−	8.64088i	0.125161	−	0.342364i
$638$		0			0
$639$	39.1147	+	9.68907i	1.54735	+	0.383294i
$640$		0			0
$641$	−21.1444	+	12.2077i	−0.835153	+	0.482176i	−0.855614	−	0.517615i	$-0.826820\pi$
$641$	−21.1444	+	12.2077i	−0.835153	+	0.482176i	0.0204610	+	0.999791i	$0.493487\pi$
$642$		0			0
$643$	−31.9014	+	18.4183i	−1.25807	+	0.726346i	−0.972699	−	0.232071i	$-0.925450\pi$
$643$	−31.9014	+	18.4183i	−1.25807	+	0.726346i	−0.285370	+	0.958418i	$0.592116\pi$
$644$		0			0
$645$	3.38136	−	8.38757i	0.133141	−	0.330260i
$646$		0			0
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	−0.477389	−	0.878692i	$-0.658417\pi$
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	0.999664	−	0.0259155i	$-0.00825009\pi$
$648$		0			0
$649$	−3.09239	+	1.78539i	−0.121387	+	0.0700827i
$650$		0			0
$651$	13.6132	−	21.7883i	0.533543	−	0.853949i
$652$		0			0
$653$	26.2767	+	15.1709i	1.02829	+	0.593683i	0.916494	−	0.400049i	$-0.131007\pi$
$653$	26.2767	+	15.1709i	1.02829	+	0.593683i	0.111794	+	0.993731i	$0.464340\pi$
$654$		0			0
$655$	−1.82233	−	3.15637i	−0.0712044	−	0.123330i
$656$		0			0
$657$	16.0055	−	16.6248i	0.624432	−	0.648595i
$658$		0			0
$659$	40.9873	+	23.6640i	1.59664	+	0.921820i	0.992129	+	0.125223i	$0.0399647\pi$
$659$	40.9873	+	23.6640i	1.59664	+	0.921820i	0.604511	+	0.796597i	$0.293369\pi$
$660$		0			0
$661$			35.1245i			1.36618i	0.730332	+	0.683092i	$0.239365\pi$
$661$			35.1245i			1.36618i	−0.730332	+	0.683092i	$0.760635\pi$
$662$		0			0
$663$	−6.68328	+	5.22976i	−0.259557	+	0.203107i
$664$		0			0
$665$	0.279049	+	0.768376i	0.0108211	+	0.0297963i
$666$		0			0
$667$	0.783329	+	1.35677i	0.0303306	+	0.0525342i
$668$		0			0
$669$	0.222804	+	1.57661i	0.00861409	+	0.0609552i
$670$		0			0
$671$	0.749513	+	1.29819i	0.0289346	+	0.0501162i
$672$		0			0
$673$	−2.54758	+	4.41254i	−0.0982020	+	0.170091i	−0.910940	−	0.412538i	$-0.864642\pi$
$673$	−2.54758	+	4.41254i	−0.0982020	+	0.170091i	0.812738	+	0.582629i	$0.197976\pi$
$674$		0			0
$675$	−18.9925	−	13.7326i	−0.731022	−	0.528568i
$676$		0			0
$677$	−16.8414			−0.647269			−0.323635	−	0.946182i	$-0.604905\pi$
$677$	−16.8414			−0.647269			−0.323635	+	0.946182i	$0.604905\pi$
$678$		0			0
$679$	−27.6226	−	4.89081i	−1.06006	−	0.187692i
$680$		0			0
$681$	−6.47998	+	16.0738i	−0.248313	+	0.615949i
$682$		0			0
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	0.770169	−	0.637840i	$-0.220172\pi$
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	−0.167301	+	0.985906i	$0.553505\pi$
$684$		0			0
$685$			1.88715i			0.0721042i
$686$		0			0
$687$	−0.666559	−	4.71672i	−0.0254308	−	0.179954i
$688$		0			0
$689$	12.9290			0.492557
$690$		0			0
$691$			3.52652i			0.134155i	0.997748	+	0.0670775i	$0.0213675\pi$
$691$			3.52652i			0.134155i	−0.997748	+	0.0670775i	$0.978633\pi$
$692$		0			0
$693$	1.23873	+	1.70205i	0.0470555	+	0.0646554i
$694$		0			0
$695$			8.19591i			0.310888i
$696$		0			0
$697$	40.2125			1.52316
$698$		0			0
$699$	−10.3044	−	4.15412i	−0.389749	−	0.157123i
$700$		0			0
$701$		−	13.3502i		−	0.504229i	−0.967697	−	0.252114i	$-0.918874\pi$
$701$		−	13.3502i		−	0.504229i	0.967697	−	0.252114i	$-0.0811259\pi$
$702$		0			0
$703$	0.268574	+	0.155061i	0.0101295	+	0.00584824i
$704$		0			0
$705$	−8.40626	+	1.18796i	−0.316598	+	0.0447411i
$706$		0			0
$707$	35.4617	+	29.7988i	1.33368	+	1.12070i
$708$		0			0
$709$	−42.2894			−1.58821			−0.794107	−	0.607779i	$-0.792061\pi$
$709$	−42.2894			−1.58821			−0.794107	+	0.607779i	$0.792061\pi$
$710$		0			0
$711$	−1.00749	+	4.06723i	−0.0377838	+	0.152533i
$712$		0			0
$713$	−13.9166	+	24.1043i	−0.521182	+	0.902715i
$714$		0			0
$715$	−0.121942	−	0.211210i	−0.00456038	−	0.00789881i
$716$		0			0
$717$	−21.1998	−	8.54648i	−0.791721	−	0.319174i
$718$		0			0
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	0.996861	+	0.0791697i	$0.0252269\pi$
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	−0.429868	+	0.902892i	$0.641440\pi$
$720$		0			0
$721$	22.2544	+	3.94032i	0.828796	+	0.146745i
$722$		0			0
$723$	−4.09426	−	1.65056i	−0.152267	−	0.0613849i
$724$		0			0
$725$		−	1.42335i		−	0.0528617i
$726$		0			0
$727$	−11.3671	−	6.56280i	−0.421583	−	0.243401i	0.274171	−	0.961681i	$-0.411596\pi$
$727$	−11.3671	−	6.56280i	−0.421583	−	0.243401i	−0.695754	+	0.718280i	$0.744930\pi$
$728$		0			0
$729$	17.9746	−	20.1473i	0.665724	−	0.746198i
$730$		0			0
$731$	13.9097	+	24.0924i	0.514470	+	0.891089i
$732$		0			0
$733$	−32.7001	−	18.8794i	−1.20781	−	0.697327i	−0.245527	−	0.969390i	$-0.578961\pi$
$733$	−32.7001	−	18.8794i	−1.20781	−	0.697327i	−0.962280	+	0.272063i	$0.912294\pi$
$734$		0			0
$735$	5.68029	−	6.30028i	0.209521	−	0.232389i
$736$		0			0
$737$	−1.36460	+	0.787853i	−0.0502657	+	0.0290209i
$738$		0			0
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	−0.999802	−	0.0198820i	$-0.993671\pi$
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	0.517119	+	0.855913i	$0.327004\pi$
$740$		0			0
$741$	−0.995424	+	0.140672i	−0.0365678	+	0.00516770i
$742$		0			0
$743$	−8.78379	+	5.07132i	−0.322246	+	0.186049i	−0.652393	−	0.757881i	$-0.726235\pi$
$743$	−8.78379	+	5.07132i	−0.322246	+	0.186049i	0.330147	+	0.943929i	$0.392902\pi$
$744$		0			0
$745$	11.4082	−	6.58655i	0.417966	−	0.241313i
$746$		0			0
$747$	−16.0965	−	15.4969i	−0.588941	−	0.567001i
$748$		0			0
$749$	17.8752	−	21.2721i	0.653144	−	0.777267i
$750$		0			0
$751$	−3.95369	+	6.84798i	−0.144272	+	0.249886i	−0.929101	−	0.369826i	$-0.879417\pi$
$751$	−3.95369	+	6.84798i	−0.144272	+	0.249886i	0.784829	+	0.619712i	$0.212751\pi$
$752$		0			0
$753$	20.0557	+	25.6298i	0.730870	+	0.934002i
$754$		0			0
$755$	−6.99855			−0.254703
$756$		0			0
$757$	29.8903			1.08638			0.543191	−	0.839609i	$-0.317216\pi$
$757$	29.8903			1.08638			0.543191	+	0.839609i	$0.317216\pi$
$758$		0			0
$759$	−1.40545	−	1.79606i	−0.0510144	−	0.0651930i
$760$		0			0
$761$	−3.05687	+	5.29465i	−0.110811	+	0.191931i	−0.916098	−	0.400955i	$-0.868678\pi$
$761$	−3.05687	+	5.29465i	−0.110811	+	0.191931i	0.805286	+	0.592886i	$0.202012\pi$
$762$		0			0
$763$	−6.56961	+	37.1042i	−0.237836	+	1.34326i
$764$		0			0
$765$	−7.51820	+	2.16822i	−0.271821	+	0.0783922i
$766$		0			0
$767$	−15.3247	+	8.84771i	−0.553342	+	0.319472i
$768$		0			0
$769$	−9.79863	+	5.65724i	−0.353348	+	0.204005i	−0.666159	−	0.745810i	$-0.732063\pi$
$769$	−9.79863	+	5.65724i	−0.353348	+	0.204005i	0.312811	+	0.949815i	$0.398729\pi$
$770$		0			0
$771$	24.6868	−	3.48870i	0.889073	−	0.125642i
$772$		0			0
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	−0.280569	−	0.959834i	$-0.590523\pi$
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	0.971525	−	0.236937i	$-0.0761437\pi$
$774$		0			0
$775$	21.8994	−	12.6436i	0.786648	−	0.454172i
$776$		0			0
$777$	0.112139	−	3.21615i	0.00402297	−	0.115379i
$778$		0			0
$779$	4.12551	+	2.38186i	0.147812	+	0.0853391i
$780$		0			0
$781$	−1.78124	−	3.08519i	−0.0637376	−	0.110397i
$782$		0			0
$783$	1.63112	+	0.167667i	0.0582916	+	0.00599193i
$784$		0			0
$785$	−0.152730	−	0.0881788i	−0.00545117	−	0.00314723i
$786$		0			0
$787$			47.6600i			1.69889i	0.527674	+	0.849447i	$0.323064\pi$
$787$			47.6600i			1.69889i	−0.527674	+	0.849447i	$0.676936\pi$
$788$		0			0
$789$	12.6100	+	5.08361i	0.448930	+	0.180981i
$790$		0			0
$791$	26.2938	−	31.2906i	0.934900	−	1.11257i
$792$		0			0
$793$	3.71430	+	6.43335i	0.131898	+	0.228455i
$794$		0			0
$795$	11.0564	+	4.45726i	0.392129	+	0.158083i
$796$		0			0
$797$	−15.1359	−	26.2161i	−0.536139	−	0.928621i	−0.999107	−	0.0422457i	$-0.986549\pi$
$797$	−15.1359	−	26.2161i	−0.536139	−	0.928621i	0.462968	−	0.886375i	$-0.346785\pi$
$798$		0			0
$799$	13.0581	−	22.6172i	0.461961	−	0.800140i
$800$		0			0
$801$	−32.2416	+	9.29836i	−1.13920	+	0.328541i
$802$		0			0
$803$	−2.04016			−0.0719955
$804$		0			0
$805$	−5.91227	+	7.03583i	−0.208380	+	0.247981i
$806$		0			0
$807$	−26.4889	+	3.74337i	−0.932454	+	0.131773i
$808$		0			0
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	0.503851	−	0.863790i	$-0.331916\pi$
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	−0.496139	+	0.868243i	$0.665249\pi$
$810$		0			0
$811$		−	22.0629i		−	0.774735i	−0.921925	−	0.387367i	$-0.873385\pi$
$811$		−	22.0629i		−	0.774735i	0.921925	−	0.387367i	$-0.126615\pi$
$812$		0			0
$813$	20.3070	+	8.18657i	0.712199	+	0.287116i
$814$		0			0
$815$	6.01395			0.210660
$816$		0			0
$817$			3.29560i			0.115298i
$818$		0			0
$819$	6.13868	+	8.43469i	0.214503	+	0.294732i
$820$		0			0
$821$			27.9976i			0.977124i	0.872529	+	0.488562i	$0.162478\pi$
$821$			27.9976i			0.977124i	−0.872529	+	0.488562i	$0.837522\pi$
$822$		0			0
$823$	48.9542			1.70643			0.853217	−	0.521556i	$-0.174648\pi$
$823$	48.9542			1.70643			0.853217	+	0.521556i	$0.174648\pi$
$824$		0			0
$825$	0.289928	+	2.05159i	0.0100940	+	0.0714272i
$826$		0			0
$827$			0.641658i			0.0223126i	0.999938	+	0.0111563i	$0.00355124\pi$
$827$			0.641658i			0.0223126i	−0.999938	+	0.0111563i	$0.996449\pi$
$828$		0			0
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	0.656925	−	0.753956i	$-0.271857\pi$
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	−0.324483	+	0.945892i	$0.605190\pi$
$830$		0			0
$831$	−7.70053	+	19.1014i	−0.267128	+	0.662620i
$832$		0			0
$833$	4.49487	+	25.7048i	0.155738	+	0.890620i
$834$		0			0
$835$	3.14057			0.108684
$836$		0			0
$837$	11.9096	+	26.5856i	0.411656	+	0.918932i
$838$		0			0
$839$	−4.62330	+	8.00780i	−0.159614	+	0.276460i	−0.934730	−	0.355360i	$-0.884358\pi$
$839$	−4.62330	+	8.00780i	−0.159614	+	0.276460i	0.775115	+	0.631820i	$0.217692\pi$
$840$		0			0
$841$	−14.4502	−	25.0285i	−0.498283	−	0.863052i
$842$		0			0
$843$	−0.770756	−	5.45404i	−0.0265462	−	0.187847i
$844$		0			0
$845$	3.94346	+	6.83028i	0.135659	+	0.234969i
$846$		0			0
$847$	−5.04161	+	28.4743i	−0.173232	+	0.978388i
$848$		0			0
$849$	25.2321	−	19.7445i	0.865963	−	0.677629i
$850$		0			0
$851$			3.48640i			0.119512i
$852$		0			0
$853$	−34.3256	−	19.8179i	−1.17529	−	0.678551i	−0.220366	−	0.975417i	$-0.570725\pi$
$853$	−34.3256	−	19.8179i	−1.17529	−	0.678551i	−0.954919	+	0.296866i	$0.904059\pi$
$854$		0			0
$855$	−0.899740	−	0.222874i	−0.0307705	−	0.00762212i
$856$		0			0
$857$	−11.9260	−	20.6565i	−0.407385	−	0.705612i	0.587211	−	0.809434i	$-0.300226\pi$
$857$	−11.9260	−	20.6565i	−0.407385	−	0.705612i	−0.994596	+	0.103822i	$0.966893\pi$
$858$		0			0
$859$	−9.62480	−	5.55688i	−0.328394	−	0.189598i	0.326734	−	0.945116i	$-0.394052\pi$
$859$	−9.62480	−	5.55688i	−0.328394	−	0.189598i	−0.655128	+	0.755518i	$0.727385\pi$
$860$		0			0
$861$	1.72255	−	49.4026i	0.0587043	−	1.68364i
$862$		0			0
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.983731	−	0.179646i	$-0.942505\pi$
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.336287	+	0.941759i	$0.609171\pi$
$864$		0			0
$865$	−2.49128	+	4.31503i	−0.0847061	+	0.146715i
$866$		0			0
$867$	−2.00968	+	4.98508i	−0.0682525	+	0.169302i
$868$		0			0
$869$	0.320805	−	0.185217i	0.0108826	−	0.00628305i
$870$		0			0
$871$	−6.76244	+	3.90429i	−0.229136	+	0.132292i
$872$		0			0
$873$	22.0610	−	22.9146i	0.746650	−	0.775542i
$874$		0			0
$875$	16.5476	−	6.00953i	0.559409	−	0.203159i
$876$		0			0
$877$	−1.84096	+	3.18863i	−0.0621647	+	0.107672i	−0.895433	−	0.445197i	$-0.853134\pi$
$877$	−1.84096	+	3.18863i	−0.0621647	+	0.107672i	0.833268	+	0.552869i	$0.186467\pi$
$878$		0			0
$879$	1.85184	−	4.59355i	0.0624611	−	0.154937i
$880$		0			0
$881$	17.3992			0.586194			0.293097	−	0.956083i	$-0.405314\pi$
$881$	17.3992			0.586194			0.293097	+	0.956083i	$0.405314\pi$
$882$		0			0
$883$	−2.02834			−0.0682592			−0.0341296	−	0.999417i	$-0.510866\pi$
$883$	−2.02834			−0.0682592			−0.0341296	+	0.999417i	$0.510866\pi$
$884$		0			0
$885$	−16.1552	+	2.28303i	−0.543052	+	0.0767433i
$886$		0			0
$887$	23.1890	−	40.1645i	0.778610	−	1.34859i	−0.154132	−	0.988050i	$-0.549258\pi$
$887$	23.1890	−	40.1645i	0.778610	−	1.34859i	0.932743	−	0.360542i	$-0.117408\pi$
$888$		0			0
$889$	54.2885	−	19.7158i	1.82078	−	0.661247i
$890$		0			0
$891$	−2.38523	+	0.0905779i	−0.0799083	+	0.00303447i
$892$		0			0
$893$	2.67932	−	1.54691i	0.0896601	−	0.0517653i
$894$		0			0
$895$	15.4812	−	8.93810i	0.517481	−	0.298768i
$896$		0			0
$897$	−6.96484	−	8.90060i	−0.232549	−	0.297182i
$898$		0			0
$899$	−0.884576	+	1.53213i	−0.0295023	+	0.0510994i
$900$		0			0
$901$	−31.7582	+	18.3356i	−1.05802	+	0.610847i
$902$		0			0
$903$	30.1942	−	16.0566i	1.00480	−	0.534331i
$904$		0			0
$905$	−0.571488	−	0.329949i	−0.0189969	−	0.0109679i
$906$		0			0
$907$	−8.01957	−	13.8903i	−0.266285	−	0.461220i	0.701614	−	0.712557i	$-0.252463\pi$
$907$	−8.01957	−	13.8903i	−0.266285	−	0.461220i	−0.967900	+	0.251337i	$0.919130\pi$
$908$		0			0
$909$	−50.4647	+	14.5538i	−1.67381	+	0.482720i
$910$		0			0
$911$	17.7833	+	10.2672i	0.589187	+	0.340167i	0.764776	−	0.644296i	$-0.222850\pi$
$911$	17.7833	+	10.2672i	0.589187	+	0.340167i	−0.175589	+	0.984464i	$0.556183\pi$
$912$		0			0
$913$			1.97533i			0.0653739i
$914$		0			0
$915$	0.958424	+	6.78202i	0.0316845	+	0.224207i
$916$		0			0
$917$	2.40290	−	13.5712i	0.0793507	−	0.448161i
$918$		0			0
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	−0.994987	−	0.100001i	$-0.968115\pi$
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	0.410890	−	0.911685i	$-0.365218\pi$
$920$		0			0
$921$	−29.5655	+	23.1354i	−0.974216	+	0.762338i
$922$		0			0
$923$	−8.82712	−	15.2890i	−0.290548	−	0.503244i
$924$		0			0
$925$	1.58374	−	2.74311i	0.0520730	−	0.0901930i
$926$		0			0
$927$	−17.7736	+	18.4613i	−0.583761	+	0.606350i
$928$		0			0
$929$	−39.7251			−1.30334			−0.651670	−	0.758503i	$-0.725931\pi$
$929$	−39.7251			−1.30334			−0.651670	+	0.758503i	$0.725931\pi$
$930$		0			0
$931$	−1.06141	+	2.90337i	−0.0347861	+	0.0951540i
$932$		0			0
$933$	−25.2893	−	32.3180i	−0.827933	−	1.05804i
$934$		0			0
$935$	0.599064	+	0.345870i	0.0195915	+	0.0113112i
$936$		0			0
$937$		−	23.2142i		−	0.758376i	−0.925320	−	0.379188i	$-0.876203\pi$
$937$		−	23.2142i		−	0.758376i	0.925320	−	0.379188i	$-0.123797\pi$
$938$		0			0
$939$	37.2165	−	29.1225i	1.21452	−	0.950376i
$940$		0			0
$941$	−35.9232			−1.17106			−0.585531	−	0.810650i	$-0.699114\pi$
$941$	−35.9232			−1.17106			−0.585531	+	0.810650i	$0.699114\pi$
$942$		0			0
$943$			53.5539i			1.74395i
$944$		0			0
$945$	2.34169	+	9.32928i	0.0761753	+	0.303481i
$946$		0			0
$947$		−	30.8726i		−	1.00322i	−0.865093	−	0.501612i	$-0.832740\pi$
$947$		−	30.8726i		−	1.00322i	0.865093	−	0.501612i	$-0.167260\pi$
$948$		0			0
$949$	−10.1102			−0.328192
$950$		0			0
$951$	33.4937	−	26.2093i	1.08611	−	0.849894i
$952$		0			0
$953$			30.4640i			0.986826i	0.869795	+	0.493413i	$0.164251\pi$
$953$			30.4640i			0.986826i	−0.869795	+	0.493413i	$0.835749\pi$
$954$		0			0
$955$	−1.80100	−	1.03981i	−0.0582791	−	0.0336475i
$956$		0			0
$957$	−0.0893336	−	0.114162i	−0.00288774	−	0.00369034i
$958$		0			0
$959$	−4.59098	+	5.46344i	−0.148250	+	0.176424i
$960$		0			0
$961$	−0.430813			−0.0138972
$962$		0			0
$963$	8.73029	+	30.2719i	0.281330	+	0.975497i
$964$		0			0
$965$	−6.47686	+	11.2182i	−0.208497	+	0.361128i
$966$		0			0
$967$	−6.75865	−	11.7063i	−0.217343	−	0.376450i	0.736652	−	0.676272i	$-0.236406\pi$
$967$	−6.75865	−	11.7063i	−0.217343	−	0.376450i	−0.953995	+	0.299823i	$0.903072\pi$
$968$		0			0
$969$	2.24561	−	1.75722i	0.0721393	−	0.0564500i
$970$		0			0
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	0.999207	+	0.0398238i	$0.0126797\pi$
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	−0.465115	+	0.885250i	$0.653987\pi$
$972$		0			0
$973$	−19.9387	+	23.7278i	−0.639204	+	0.760677i
$974$		0			0
$975$	1.43677	+	10.1669i	0.0460134	+	0.325601i
$976$		0			0
$977$		−	44.9325i		−	1.43752i	−0.695260	−	0.718758i	$-0.744711\pi$
$977$		−	44.9325i		−	1.43752i	0.695260	−	0.718758i	$-0.255289\pi$
$978$		0			0
$979$	2.56907	+	1.48325i	0.0821079	+	0.0474050i
$980$		0			0
$981$	−30.7802	−	29.6335i	−0.982736	−	0.946125i
$982$		0			0
$983$	−13.4474	−	23.2916i	−0.428907	−	0.742888i	0.567870	−	0.823118i	$-0.307768\pi$
$983$	−13.4474	−	23.2916i	−0.428907	−	0.742888i	−0.996776	+	0.0802305i	$0.974434\pi$
$984$		0			0
$985$	−8.59035	−	4.95964i	−0.273711	−	0.158027i
$986$		0			0
$987$	−27.2268	−	17.0112i	−0.866638	−	0.541471i
$988$		0			0
$989$	−32.0855	+	18.5246i	−1.02026	+	0.589048i
$990$		0			0
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	−0.434346	−	0.900746i	$-0.643020\pi$
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	0.997242	−	0.0742186i	$-0.0236463\pi$
$992$		0			0
$993$	17.4109	+	22.2500i	0.552520	+	0.706082i
$994$		0			0
$995$	−14.3635	+	8.29275i	−0.455352	+	0.262898i
$996$		0			0
$997$	−28.1418	+	16.2477i	−0.891259	+	0.514568i	−0.874354	−	0.485289i	$-0.838714\pi$
$997$	−28.1418	+	16.2477i	−0.891259	+	0.514568i	−0.0169046	+	0.999857i	$0.505381\pi$
$998$		0			0
$999$	2.95699	+	2.13806i	0.0935550	+	0.0676453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.w.a.101.6	yes	16
3.2	odd	2		756.2.w.a.521.4		16
4.3	odd	2		1008.2.ca.d.353.3		16
7.2	even	3		1764.2.bm.a.1685.1		16
7.3	odd	6		1764.2.x.b.1469.3		16
7.4	even	3		1764.2.x.a.1469.6		16
7.5	odd	6		252.2.bm.a.173.8	yes	16
7.6	odd	2		1764.2.w.b.1109.3		16
9.2	odd	6		2268.2.t.a.1781.4		16
9.4	even	3		756.2.bm.a.17.4		16
9.5	odd	6		252.2.bm.a.185.8	yes	16
9.7	even	3		2268.2.t.b.1781.5		16
12.11	even	2		3024.2.ca.d.2033.4		16
21.2	odd	6		5292.2.bm.a.4625.5		16
21.5	even	6		756.2.bm.a.89.4		16
21.11	odd	6		5292.2.x.a.4409.4		16
21.17	even	6		5292.2.x.b.4409.5		16
21.20	even	2		5292.2.w.b.521.5		16
28.19	even	6		1008.2.df.d.929.1		16
36.23	even	6		1008.2.df.d.689.1		16
36.31	odd	6		3024.2.df.d.17.4		16
63.4	even	3		5292.2.x.b.881.5		16
63.5	even	6	inner	252.2.w.a.5.6	✓	16
63.13	odd	6		5292.2.bm.a.2285.5		16
63.23	odd	6		1764.2.w.b.509.3		16
63.31	odd	6		5292.2.x.a.881.4		16
63.32	odd	6		1764.2.x.b.293.3		16
63.40	odd	6		756.2.w.a.341.4		16
63.41	even	6		1764.2.bm.a.1697.1		16
63.47	even	6		2268.2.t.b.2105.5		16
63.58	even	3		5292.2.w.b.1097.5		16
63.59	even	6		1764.2.x.a.293.6		16
63.61	odd	6		2268.2.t.a.2105.4		16
84.47	odd	6		3024.2.df.d.1601.4		16
252.103	even	6		3024.2.ca.d.2609.4		16
252.131	odd	6		1008.2.ca.d.257.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	63.5	even	6	inner
252.2.w.a.101.6	yes	16	1.1	even	1	trivial
252.2.bm.a.173.8	yes	16	7.5	odd	6
252.2.bm.a.185.8	yes	16	9.5	odd	6
756.2.w.a.341.4		16	63.40	odd	6
756.2.w.a.521.4		16	3.2	odd	2
756.2.bm.a.17.4		16	9.4	even	3
756.2.bm.a.89.4		16	21.5	even	6
1008.2.ca.d.257.3		16	252.131	odd	6
1008.2.ca.d.353.3		16	4.3	odd	2
1008.2.df.d.689.1		16	36.23	even	6
1008.2.df.d.929.1		16	28.19	even	6
1764.2.w.b.509.3		16	63.23	odd	6
1764.2.w.b.1109.3		16	7.6	odd	2
1764.2.x.a.293.6		16	63.59	even	6
1764.2.x.a.1469.6		16	7.4	even	3
1764.2.x.b.293.3		16	63.32	odd	6
1764.2.x.b.1469.3		16	7.3	odd	6
1764.2.bm.a.1685.1		16	7.2	even	3
1764.2.bm.a.1697.1		16	63.41	even	6
2268.2.t.a.1781.4		16	9.2	odd	6
2268.2.t.a.2105.4		16	63.61	odd	6
2268.2.t.b.1781.5		16	9.7	even	3
2268.2.t.b.2105.5		16	63.47	even	6
3024.2.ca.d.2033.4		16	12.11	even	2
3024.2.ca.d.2609.4		16	252.103	even	6
3024.2.df.d.17.4		16	36.31	odd	6
3024.2.df.d.1601.4		16	84.47	odd	6
5292.2.w.b.521.5		16	21.20	even	2
5292.2.w.b.1097.5		16	63.58	even	3
5292.2.x.a.881.4		16	63.31	odd	6
5292.2.x.a.4409.4		16	21.11	odd	6
5292.2.x.b.881.5		16	63.4	even	3
5292.2.x.b.4409.5		16	21.17	even	6
5292.2.bm.a.2285.5		16	63.13	odd	6
5292.2.bm.a.4625.5		16	21.2	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +O(q^{10})\)	\(q+(1.06740 + 1.36406i) q^{3} +(0.349828 - 0.605920i) q^{5} +(2.48683 - 0.903137i) q^{7} +(-0.721326 + 2.91199i) q^{9} +(0.229685 - 0.132608i) q^{11} +(1.13823 - 0.657156i) q^{13} +(1.19992 - 0.169570i) q^{15} +(-1.86392 + 3.22840i) q^{17} +(-0.382449 + 0.220807i) q^{19} +(3.88637 + 2.42819i) q^{21} +(-4.29949 - 2.48231i) q^{23} +(2.25524 + 3.90619i) q^{25} +(-4.74208 + 2.12432i) q^{27} +(-0.273287 - 0.157782i) q^{29} -5.60632i q^{31} +(0.426051 + 0.171758i) q^{33} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(2.11134 + 0.851166i) q^{39} +(-5.39354 - 9.34189i) q^{41} +(3.73131 - 6.46283i) q^{43} +(1.51209 + 1.45576i) q^{45} -7.00570 q^{47} +(5.36869 - 4.49190i) q^{49} +(-6.39328 + 0.903488i) q^{51} +(8.51919 + 4.91856i) q^{53} -0.185561i q^{55} +(-0.709419 - 0.285995i) q^{57} -13.4636 q^{59} +5.65207i q^{61} +(0.836106 + 7.89309i) q^{63} -0.919566i q^{65} -5.94120 q^{67} +(-1.20324 - 8.51439i) q^{69} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(-2.92105 + 7.24575i) q^{75} +(0.451424 - 0.537212i) q^{77} +1.39672 q^{79} +(-7.95938 - 4.20099i) q^{81} +(-3.72399 + 6.45014i) q^{83} +(1.30410 + 2.25877i) q^{85} +(-0.0764809 - 0.541196i) q^{87} +(5.59261 + 9.68668i) q^{89} +(2.23708 - 2.66221i) q^{91} +(7.64736 - 5.98417i) q^{93} +0.308978i q^{95} +(-9.18225 - 5.30138i) q^{97} +(0.220477 + 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

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