LMFDB - Embedded newform 1148.2.n.d.365.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			365.2
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.d.953.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40864 q^{3} +(1.08800 - 3.34852i) q^{5} +(-0.809017 - 0.587785i) q^{7} +2.80153 q^{9} +O(q^{10})$	\(q-2.40864 q^{3} +(1.08800 - 3.34852i) q^{5} +(-0.809017 - 0.587785i) q^{7} +2.80153 q^{9} +(-1.11153 - 3.42095i) q^{11} +(4.63256 - 3.36575i) q^{13} +(-2.62060 + 8.06537i) q^{15} +(0.00444489 + 0.0136800i) q^{17} +(0.791999 + 0.575421i) q^{19} +(1.94863 + 1.41576i) q^{21} +(2.12614 - 1.54473i) q^{23} +(-5.98375 - 4.34745i) q^{25} +0.478035 q^{27} +(-0.429188 + 1.32090i) q^{29} +(-1.33388 - 4.10527i) q^{31} +(2.67728 + 8.23982i) q^{33} +(-2.84842 + 2.06950i) q^{35} +(1.05003 - 3.23167i) q^{37} +(-11.1582 + 8.10688i) q^{39} +(4.18618 + 4.84519i) q^{41} +(-9.78452 + 7.10887i) q^{43} +(3.04807 - 9.38099i) q^{45} +(-6.98521 + 5.07505i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.0107061 - 0.0329501i) q^{51} +(3.40301 - 10.4734i) q^{53} -12.6645 q^{55} +(-1.90764 - 1.38598i) q^{57} +(4.98665 - 3.62301i) q^{59} +(0.0940089 + 0.0683015i) q^{61} +(-2.26649 - 1.64670i) q^{63} +(-6.23006 - 19.1742i) q^{65} +(-0.918740 + 2.82759i) q^{67} +(-5.12109 + 3.72069i) q^{69} +(-3.84048 - 11.8198i) q^{71} -3.56684 q^{73} +(14.4127 + 10.4714i) q^{75} +(-1.11153 + 3.42095i) q^{77} -11.0514 q^{79} -9.55601 q^{81} +6.79567 q^{83} +0.0506437 q^{85} +(1.03376 - 3.18158i) q^{87} +(-11.2473 - 8.17166i) q^{89} -5.72616 q^{91} +(3.21284 + 9.88811i) q^{93} +(2.78850 - 2.02597i) q^{95} +(-4.29833 + 13.2289i) q^{97} +(-3.11400 - 9.58390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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			0
$2$		0			0
$3$	−2.40864			−1.39063			−0.695314	−	0.718706i	$-0.744735\pi$
$3$	−2.40864			−1.39063			−0.695314	+	0.718706i	$0.744735\pi$
$4$		0			0
$5$	1.08800	−	3.34852i	0.486568	−	1.49750i	−0.343128	−	0.939289i	$-0.611487\pi$
$5$	1.08800	−	3.34852i	0.486568	−	1.49750i	0.829697	−	0.558215i	$-0.188513\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	2.80153			0.933844
$10$		0			0
$11$	−1.11153	−	3.42095i	−0.335140	−	1.03145i	−0.966653	−	0.256090i	$-0.917566\pi$
$11$	−1.11153	−	3.42095i	−0.335140	−	1.03145i	0.631513	−	0.775365i	$-0.282434\pi$
$12$		0			0
$13$	4.63256	−	3.36575i	1.28484	−	0.933492i	0.285154	−	0.958482i	$-0.407955\pi$
$13$	4.63256	−	3.36575i	1.28484	−	0.933492i	0.999688	+	0.0249898i	$0.00795532\pi$
$14$		0			0
$15$	−2.62060	+	8.06537i	−0.676635	+	2.08247i
$16$		0			0
$17$	0.00444489	+	0.0136800i	0.00107804	+	0.00331788i	0.951594	−	0.307358i	$-0.0994448\pi$
$17$	0.00444489	+	0.0136800i	0.00107804	+	0.00331788i	−0.950516	+	0.310675i	$0.899445\pi$
$18$		0			0
$19$	0.791999	+	0.575421i	0.181697	+	0.132011i	0.674916	−	0.737895i	$-0.264180\pi$
$19$	0.791999	+	0.575421i	0.181697	+	0.132011i	−0.493219	+	0.869905i	$0.664180\pi$
$20$		0			0
$21$	1.94863	+	1.41576i	0.425226	+	0.308944i
$22$		0			0
$23$	2.12614	−	1.54473i	0.443330	−	0.322098i	−0.343627	−	0.939106i	$-0.611655\pi$
$23$	2.12614	−	1.54473i	0.443330	−	0.322098i	0.786957	+	0.617008i	$0.211655\pi$
$24$		0			0
$25$	−5.98375	−	4.34745i	−1.19675	−	0.869490i
$26$		0			0
$27$	0.478035			0.0919979
$28$		0			0
$29$	−0.429188	+	1.32090i	−0.0796982	+	0.245286i	−0.982965	−	0.183794i	$-0.941162\pi$
$29$	−0.429188	+	1.32090i	−0.0796982	+	0.245286i	0.903267	+	0.429080i	$0.141162\pi$
$30$		0			0
$31$	−1.33388	−	4.10527i	−0.239573	−	0.737329i	−0.996482	−	0.0838087i	$-0.973292\pi$
$31$	−1.33388	−	4.10527i	−0.239573	−	0.737329i	0.756909	−	0.653520i	$-0.226708\pi$
$32$		0			0
$33$	2.67728	+	8.23982i	0.466055	+	1.43437i
$34$		0			0
$35$	−2.84842	+	2.06950i	−0.481471	+	0.349809i
$36$		0			0
$37$	1.05003	−	3.23167i	0.172625	−	0.531284i	−0.826892	−	0.562360i	$-0.809893\pi$
$37$	1.05003	−	3.23167i	0.172625	−	0.531284i	0.999517	+	0.0310762i	$0.00989346\pi$
$38$		0			0
$39$	−11.1582	+	8.10688i	−1.78674	+	1.29814i
$40$		0			0
$41$	4.18618	+	4.84519i	0.653772	+	0.756692i
$41$	4.18618	+	4.84519i	0.653772	+	0.756692i
$42$		0			0
$43$	−9.78452	+	7.10887i	−1.49213	+	1.08409i	−0.518736	+	0.854934i	$0.673597\pi$
$43$	−9.78452	+	7.10887i	−1.49213	+	1.08409i	−0.973389	+	0.229158i	$0.926403\pi$
$44$		0			0
$45$	3.04807	−	9.38099i	0.454379	−	1.39843i
$46$		0			0
$47$	−6.98521	+	5.07505i	−1.01890	+	0.740272i	−0.966056	−	0.258331i	$-0.916827\pi$
$47$	−6.98521	+	5.07505i	−1.01890	+	0.740272i	−0.0528404	+	0.998603i	$0.516827\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	−0.0107061	−	0.0329501i	−0.00149916	−	0.00461394i
$52$		0			0
$53$	3.40301	−	10.4734i	0.467439	−	1.43863i	−0.388450	−	0.921470i	$-0.626989\pi$
$53$	3.40301	−	10.4734i	0.467439	−	1.43863i	0.855889	−	0.517159i	$-0.173011\pi$
$54$		0			0
$55$	−12.6645			−1.70768
$56$		0			0
$57$	−1.90764	−	1.38598i	−0.252673	−	0.183578i
$58$		0			0
$59$	4.98665	−	3.62301i	0.649207	−	0.471676i	−0.213794	−	0.976879i	$-0.568582\pi$
$59$	4.98665	−	3.62301i	0.649207	−	0.471676i	0.863001	+	0.505202i	$0.168582\pi$
$60$		0			0
$61$	0.0940089	+	0.0683015i	0.0120366	+	0.00874511i	0.593787	−	0.804622i	$-0.297632\pi$
$61$	0.0940089	+	0.0683015i	0.0120366	+	0.00874511i	−0.581751	+	0.813367i	$0.697632\pi$
$62$		0			0
$63$	−2.26649	−	1.64670i	−0.285551	−	0.207465i
$64$		0			0
$65$	−6.23006	−	19.1742i	−0.772744	−	2.37826i
$66$		0			0
$67$	−0.918740	+	2.82759i	−0.112242	+	0.345445i	−0.991362	−	0.131156i	$-0.958131\pi$
$67$	−0.918740	+	2.82759i	−0.112242	+	0.345445i	0.879120	+	0.476601i	$0.158131\pi$
$68$		0			0
$69$	−5.12109	+	3.72069i	−0.616507	+	0.447918i
$70$		0			0
$71$	−3.84048	−	11.8198i	−0.455781	−	1.40275i	−0.870216	−	0.492670i	$-0.836021\pi$
$71$	−3.84048	−	11.8198i	−0.455781	−	1.40275i	0.414436	−	0.910079i	$-0.363979\pi$
$72$		0			0
$73$	−3.56684			−0.417467			−0.208733	−	0.977973i	$-0.566934\pi$
$73$	−3.56684			−0.417467			−0.208733	+	0.977973i	$0.566934\pi$
$74$		0			0
$75$	14.4127	+	10.4714i	1.66423	+	1.20914i
$76$		0			0
$77$	−1.11153	+	3.42095i	−0.126671	+	0.389853i
$78$		0			0
$79$	−11.0514			−1.24337			−0.621687	−	0.783265i	$-0.713553\pi$
$79$	−11.0514			−1.24337			−0.621687	+	0.783265i	$0.713553\pi$
$80$		0			0
$81$	−9.55601			−1.06178
$82$		0			0
$83$	6.79567			0.745922			0.372961	−	0.927847i	$-0.378343\pi$
$83$	6.79567			0.745922			0.372961	+	0.927847i	$0.378343\pi$
$84$		0			0
$85$	0.0506437			0.00549308
$86$		0			0
$87$	1.03376	−	3.18158i	0.110830	−	0.341101i
$88$		0			0
$89$	−11.2473	−	8.17166i	−1.19221	−	0.866194i	−0.198718	−	0.980057i	$-0.563678\pi$
$89$	−11.2473	−	8.17166i	−1.19221	−	0.866194i	−0.993497	+	0.113862i	$0.963678\pi$
$90$		0			0
$91$	−5.72616			−0.600265
$92$		0			0
$93$	3.21284	+	9.88811i	0.333156	+	1.02535i
$94$		0			0
$95$	2.78850	−	2.02597i	0.286094	−	0.207860i
$96$		0			0
$97$	−4.29833	+	13.2289i	−0.436429	+	1.34319i	0.455186	+	0.890396i	$0.349573\pi$
$97$	−4.29833	+	13.2289i	−0.436429	+	1.34319i	−0.891615	+	0.452794i	$0.850427\pi$
$98$		0			0
$99$	−3.11400	−	9.58390i	−0.312969	−	0.963218i
$100$		0			0
$101$	−5.89446	−	4.28258i	−0.586521	−	0.426132i	0.254548	−	0.967060i	$-0.418073\pi$
$101$	−5.89446	−	4.28258i	−0.586521	−	0.426132i	−0.841069	+	0.540928i	$0.818073\pi$
$102$		0			0
$103$	7.06618	+	5.13388i	0.696251	+	0.505856i	0.878709	−	0.477357i	$-0.158405\pi$
$103$	7.06618	+	5.13388i	0.696251	+	0.505856i	−0.182458	+	0.983214i	$0.558405\pi$
$104$		0			0
$105$	6.86081	−	4.98467i	0.669547	−	0.486454i
$106$		0			0
$107$	−2.09424	−	1.52156i	−0.202458	−	0.147094i	0.481937	−	0.876206i	$-0.339934\pi$
$107$	−2.09424	−	1.52156i	−0.202458	−	0.147094i	−0.684395	+	0.729112i	$0.739934\pi$
$108$		0			0
$109$	−14.0889			−1.34948			−0.674738	−	0.738057i	$-0.735743\pi$
$109$	−14.0889			−1.34948			−0.674738	+	0.738057i	$0.735743\pi$
$110$		0			0
$111$	−2.52915	+	7.78393i	−0.240057	+	0.738818i
$112$		0			0
$113$	3.55234	+	10.9330i	0.334176	+	1.02849i	0.967127	+	0.254295i	$0.0818435\pi$
$113$	3.55234	+	10.9330i	0.334176	+	1.02849i	−0.632951	+	0.774192i	$0.718157\pi$
$114$		0			0
$115$	−2.85932	−	8.80007i	−0.266633	−	0.820611i
$116$		0			0
$117$	12.9783	−	9.42927i	1.19984	−	0.871736i
$118$		0			0
$119$	0.00444489	−	0.0136800i	0.000407463	−	0.00125404i
$120$		0			0
$121$	−1.56820	+	1.13936i	−0.142563	+	0.103578i
$122$		0			0
$123$	−10.0830	−	11.6703i	−0.909153	−	1.05228i
$124$		0			0
$125$	−6.82573	+	4.95918i	−0.610512	+	0.443563i
$126$		0			0
$127$	3.35312	−	10.3199i	0.297542	−	0.915739i	−0.684814	−	0.728718i	$-0.740117\pi$
$127$	3.35312	−	10.3199i	0.297542	−	0.915739i	0.982356	−	0.187021i	$-0.0598834\pi$
$128$		0			0
$129$	23.5674	−	17.1227i	2.07499	−	1.50757i
$130$		0			0
$131$	6.79305	+	20.9069i	0.593512	+	1.82664i	0.561999	+	0.827138i	$0.310033\pi$
$131$	6.79305	+	20.9069i	0.593512	+	1.82664i	0.0315129	+	0.999503i	$0.489967\pi$
$132$		0			0
$133$	−0.302517	−	0.931050i	−0.0262315	−	0.0807323i
$134$		0			0
$135$	0.520102	−	1.60071i	0.0447633	−	0.137767i
$136$		0			0
$137$	4.53609			0.387545			0.193772	−	0.981047i	$-0.437928\pi$
$137$	4.53609			0.387545			0.193772	+	0.981047i	$0.437928\pi$
$138$		0			0
$139$	9.43531	+	6.85515i	0.800292	+	0.581446i	0.911000	−	0.412407i	$-0.135312\pi$
$139$	9.43531	+	6.85515i	0.800292	+	0.581446i	−0.110708	+	0.993853i	$0.535312\pi$
$140$		0			0
$141$	16.8248	−	12.2240i	1.41691	−	1.02944i
$142$		0			0
$143$	−16.6633	−	12.1066i	−1.39346	−	1.01241i
$144$		0			0
$145$	3.95612	+	2.87429i	0.328538	+	0.238696i
$146$		0			0
$147$	−0.744310	−	2.29075i	−0.0613896	−	0.188938i
$148$		0			0
$149$	1.20046	−	3.69462i	0.0983451	−	0.302675i	−0.889766	−	0.456417i	$-0.849132\pi$
$149$	1.20046	−	3.69462i	0.0983451	−	0.302675i	0.988111	+	0.153742i	$0.0491325\pi$
$150$		0			0
$151$	8.53886	−	6.20385i	0.694883	−	0.504862i	−0.183379	−	0.983042i	$-0.558704\pi$
$151$	8.53886	−	6.20385i	0.694883	−	0.504862i	0.878262	+	0.478181i	$0.158704\pi$
$152$		0			0
$153$	0.0124525	+	0.0383249i	0.00100673	+	0.00309838i
$154$		0			0
$155$	−15.1978			−1.22072
$156$		0			0
$157$	−3.50414	−	2.54591i	−0.279661	−	0.203185i	0.439109	−	0.898434i	$-0.355294\pi$
$157$	−3.50414	−	2.54591i	−0.279661	−	0.203185i	−0.718769	+	0.695249i	$0.755294\pi$
$158$		0			0
$159$	−8.19661	+	25.2266i	−0.650033	+	2.00060i
$160$		0			0
$161$	−2.62805			−0.207119
$162$		0			0
$163$	−5.82104			−0.455939			−0.227970	−	0.973668i	$-0.573209\pi$
$163$	−5.82104			−0.455939			−0.227970	+	0.973668i	$0.573209\pi$
$164$		0			0
$165$	30.5041			2.37474
$166$		0			0
$167$	2.06967			0.160156			0.0800781	−	0.996789i	$-0.474483\pi$
$167$	2.06967			0.160156			0.0800781	+	0.996789i	$0.474483\pi$
$168$		0			0
$169$	6.11511	−	18.8204i	0.470393	−	1.44772i
$170$		0			0
$171$	2.21881	+	1.61206i	0.169677	+	0.123277i
$172$		0			0
$173$	19.3266			1.46938			0.734688	−	0.678406i	$-0.237329\pi$
$173$	19.3266			1.46938			0.734688	+	0.678406i	$0.237329\pi$
$174$		0			0
$175$	2.28559	+	7.03432i	0.172774	+	0.531745i
$176$		0			0
$177$	−12.0110	+	8.72653i	−0.902805	+	0.655926i
$178$		0			0
$179$	0.907714	−	2.79366i	0.0678457	−	0.208808i	−0.911386	−	0.411553i	$-0.864986\pi$
$179$	0.907714	−	2.79366i	0.0678457	−	0.208808i	0.979231	+	0.202746i	$0.0649864\pi$
$180$		0			0
$181$	0.288806	+	0.888854i	0.0214668	+	0.0660680i	0.961216	−	0.275797i	$-0.0889416\pi$
$181$	0.288806	+	0.888854i	0.0214668	+	0.0660680i	−0.939749	+	0.341865i	$0.888942\pi$
$182$		0			0
$183$	−0.226433	−	0.164513i	−0.0167384	−	0.0121612i
$184$		0			0
$185$	−9.67888	−	7.03212i	−0.711606	−	0.517012i
$186$		0			0
$187$	0.0418578	−	0.0304115i	0.00306095	−	0.00222391i
$188$		0			0
$189$	−0.386739	−	0.280982i	−0.0281311	−	0.0204384i
$190$		0			0
$191$	21.7167			1.57136			0.785682	−	0.618631i	$-0.212312\pi$
$191$	21.7167			1.57136			0.785682	+	0.618631i	$0.212312\pi$
$192$		0			0
$193$	−7.14252	+	21.9824i	−0.514130	+	1.58233i	0.270729	+	0.962656i	$0.412735\pi$
$193$	−7.14252	+	21.9824i	−0.514130	+	1.58233i	−0.784859	+	0.619674i	$0.787265\pi$
$194$		0			0
$195$	15.0060	+	46.1836i	1.07460	+	3.30728i
$196$		0			0
$197$	3.61240	+	11.1178i	0.257373	+	0.792112i	0.993353	+	0.115109i	$0.0367217\pi$
$197$	3.61240	+	11.1178i	0.257373	+	0.792112i	−0.735980	+	0.677003i	$0.763278\pi$
$198$		0			0
$199$	−4.57434	+	3.32345i	−0.324266	+	0.235593i	−0.737994	−	0.674808i	$-0.764227\pi$
$199$	−4.57434	+	3.32345i	−0.324266	+	0.235593i	0.413728	+	0.910401i	$0.364227\pi$
$200$		0			0
$201$	2.21291	−	6.81064i	0.156087	−	0.480386i
$202$		0			0
$203$	1.12363	−	0.816364i	0.0788632	−	0.0572975i
$204$		0			0
$205$	20.7788	−	8.74594i	1.45125	−	0.610843i
$206$		0			0
$207$	5.95644	−	4.32761i	0.414001	−	0.300789i
$208$		0			0
$209$	1.08815	−	3.34899i	0.0752690	−	0.231654i
$210$		0			0
$211$	−10.4414	+	7.58611i	−0.718815	+	0.522249i	−0.886005	−	0.463675i	$-0.846530\pi$
$211$	−10.4414	+	7.58611i	−0.718815	+	0.522249i	0.167191	+	0.985925i	$0.446530\pi$
$212$		0			0
$213$	9.25031	+	28.4695i	0.633821	+	1.95070i
$214$		0			0
$215$	13.1586	+	40.4981i	0.897411	+	2.76195i
$216$		0			0
$217$	−1.33388	+	4.10527i	−0.0905499	+	0.278684i
$218$		0			0
$219$	8.59122			0.580541
$220$		0			0
$221$	0.0666347	+	0.0484129i	0.00448233	+	0.00325660i
$222$		0			0
$223$	11.3439	−	8.24183i	0.759644	−	0.551914i	−0.139157	−	0.990270i	$-0.544439\pi$
$223$	11.3439	−	8.24183i	0.759644	−	0.551914i	0.898801	+	0.438356i	$0.144439\pi$
$224$		0			0
$225$	−16.7637	−	12.1795i	−1.11758	−	0.811968i
$226$		0			0
$227$	13.1202	+	9.53240i	0.870820	+	0.632688i	0.930807	−	0.365512i	$-0.119106\pi$
$227$	13.1202	+	9.53240i	0.870820	+	0.632688i	−0.0599871	+	0.998199i	$0.519106\pi$
$228$		0			0
$229$	−1.48190	−	4.56081i	−0.0979266	−	0.301387i	0.890079	−	0.455807i	$-0.150649\pi$
$229$	−1.48190	−	4.56081i	−0.0979266	−	0.301387i	−0.988005	+	0.154420i	$0.950649\pi$
$230$		0			0
$231$	2.67728	−	8.23982i	0.176152	−	0.542141i
$232$		0			0
$233$	−15.5956	+	11.3309i	−1.02170	+	0.742309i	−0.966631	−	0.256173i	$-0.917538\pi$
$233$	−15.5956	+	11.3309i	−1.02170	+	0.742309i	−0.0550700	+	0.998482i	$0.517538\pi$
$234$		0			0
$235$	9.39399	+	28.9117i	0.612797	+	1.88599i
$236$		0			0
$237$	26.6187			1.72907
$238$		0			0
$239$	−3.36644	−	2.44586i	−0.217757	−	0.158210i	0.473560	−	0.880762i	$-0.342969\pi$
$239$	−3.36644	−	2.44586i	−0.217757	−	0.158210i	−0.691316	+	0.722552i	$0.742969\pi$
$240$		0			0
$241$	−0.810559	+	2.49464i	−0.0522127	+	0.160694i	−0.973763	−	0.227565i	$-0.926924\pi$
$241$	−0.810559	+	2.49464i	−0.0522127	+	0.160694i	0.921550	+	0.388259i	$0.126924\pi$
$242$		0			0
$243$	21.5829			1.38454
$244$		0			0
$245$	3.52084			0.224938
$246$		0			0
$247$	5.60571			0.356683
$248$		0			0
$249$	−16.3683			−1.03730
$250$		0			0
$251$	7.29213	−	22.4429i	0.460275	−	1.41658i	−0.404553	−	0.914515i	$-0.632573\pi$
$251$	7.29213	−	22.4429i	0.460275	−	1.41658i	0.864828	−	0.502068i	$-0.167427\pi$
$252$		0			0
$253$	−7.64771	−	5.55638i	−0.480807	−	0.349327i
$254$		0			0
$255$	−0.121982			−0.00763883
$256$		0			0
$257$	3.88856	+	11.9678i	0.242562	+	0.746529i	0.996028	+	0.0890419i	$0.0283805\pi$
$257$	3.88856	+	11.9678i	0.242562	+	0.746529i	−0.753466	+	0.657487i	$0.771619\pi$
$258$		0			0
$259$	−2.74903	+	1.99728i	−0.170816	+	0.124105i
$260$		0			0
$261$	−1.20238	+	3.70056i	−0.0744257	+	0.229059i
$262$		0			0
$263$	−9.41298	−	28.9702i	−0.580429	−	1.78638i	−0.616899	−	0.787042i	$-0.711611\pi$
$263$	−9.41298	−	28.9702i	−0.580429	−	1.78638i	0.0364703	−	0.999335i	$-0.488389\pi$
$264$		0			0
$265$	−31.3678	−	22.7901i	−1.92691	−	1.39998i
$266$		0			0
$267$	27.0907	+	19.6826i	1.65793	+	1.20455i
$268$		0			0
$269$	−3.12793	+	2.27257i	−0.190713	+	0.138561i	−0.679045	−	0.734097i	$-0.737606\pi$
$269$	−3.12793	+	2.27257i	−0.190713	+	0.138561i	0.488332	+	0.872658i	$0.337606\pi$
$270$		0			0
$271$	−2.03026	−	1.47507i	−0.123329	−	0.0896041i	0.524411	−	0.851466i	$-0.324286\pi$
$271$	−2.03026	−	1.47507i	−0.123329	−	0.0896041i	−0.647740	+	0.761861i	$0.724286\pi$
$272$		0			0
$273$	13.7922			0.834745
$274$		0			0
$275$	−8.22126	+	25.3024i	−0.495761	+	1.52579i
$276$		0			0
$277$	0.957618	+	2.94725i	0.0575377	+	0.177083i	0.975695	−	0.219133i	$-0.0703230\pi$
$277$	0.957618	+	2.94725i	0.0575377	+	0.177083i	−0.918157	+	0.396216i	$0.870323\pi$
$278$		0			0
$279$	−3.73692	−	11.5011i	−0.223724	−	0.688550i
$280$		0			0
$281$	−6.79314	+	4.93551i	−0.405245	+	0.294428i	−0.771674	−	0.636018i	$-0.780580\pi$
$281$	−6.79314	+	4.93551i	−0.405245	+	0.294428i	0.366429	+	0.930446i	$0.380580\pi$
$282$		0			0
$283$	−7.85095	+	24.1627i	−0.466690	+	1.43633i	0.390154	+	0.920750i	$0.372422\pi$
$283$	−7.85095	+	24.1627i	−0.466690	+	1.43633i	−0.856844	+	0.515576i	$0.827578\pi$
$284$		0			0
$285$	−6.71649	+	4.87981i	−0.397850	+	0.289055i
$286$		0			0
$287$	−0.538759	−	6.38042i	−0.0318020	−	0.376624i
$288$		0			0
$289$	13.7531	−	9.99223i	0.809007	−	0.587778i
$290$		0			0
$291$	10.3531	−	31.8636i	0.606910	−	1.86788i
$292$		0			0
$293$	25.3373	−	18.4087i	1.48022	−	1.07545i	0.502739	−	0.864438i	$-0.332326\pi$
$293$	25.3373	−	18.4087i	1.48022	−	1.07545i	0.977485	−	0.211007i	$-0.0676743\pi$
$294$		0			0
$295$	−6.70626	−	20.6397i	−0.390453	−	1.20169i
$296$		0			0
$297$	−0.531352	−	1.63533i	−0.0308322	−	0.0948917i
$298$		0			0
$299$	4.65028	−	14.3121i	0.268933	−	0.827690i
$300$		0			0
$301$	12.0943			0.697106
$302$		0			0
$303$	14.1976	+	10.3152i	0.815632	+	0.592591i
$304$		0			0
$305$	0.330990	−	0.240479i	0.0189525	−	0.0137698i
$306$		0			0
$307$	9.28729	+	6.74761i	0.530054	+	0.385107i	0.820378	−	0.571822i	$-0.193763\pi$
$307$	9.28729	+	6.74761i	0.530054	+	0.385107i	−0.290324	+	0.956928i	$0.593763\pi$
$308$		0			0
$309$	−17.0199	−	12.3657i	−0.968226	−	0.703457i
$310$		0			0
$311$	−10.6608	−	32.8105i	−0.604517	−	1.86051i	−0.500078	−	0.865980i	$-0.666695\pi$
$311$	−10.6608	−	32.8105i	−0.604517	−	1.86051i	−0.104439	−	0.994531i	$-0.533305\pi$
$312$		0			0
$313$	8.13686	−	25.0427i	0.459923	−	1.41550i	−0.405335	−	0.914168i	$-0.632845\pi$
$313$	8.13686	−	25.0427i	0.459923	−	1.41550i	0.865257	−	0.501328i	$-0.167155\pi$
$314$		0			0
$315$	−7.97994	+	5.79777i	−0.449619	+	0.326667i
$316$		0			0
$317$	9.69893	+	29.8502i	0.544746	+	1.67656i	0.721593	+	0.692318i	$0.243410\pi$
$317$	9.69893	+	29.8502i	0.544746	+	1.67656i	−0.176847	+	0.984238i	$0.556590\pi$
$318$		0			0
$319$	4.99580			0.279711
$320$		0			0
$321$	5.04427	+	3.66488i	0.281544	+	0.204554i
$322$		0			0
$323$	−0.00435139	+	0.0133922i	−0.000242118	+	0.000745162i
$324$		0			0
$325$	−42.3525			−2.34930
$326$		0			0
$327$	33.9351			1.87662
$328$		0			0
$329$	8.63419			0.476018
$330$		0			0
$331$	−35.1463			−1.93182			−0.965908	−	0.258886i	$-0.916645\pi$
$331$	−35.1463			−1.93182			−0.965908	+	0.258886i	$0.916645\pi$
$332$		0			0
$333$	2.94171	−	9.05364i	0.161205	−	0.496137i
$334$		0			0
$335$	8.46865	+	6.15284i	0.462692	+	0.336165i
$336$		0			0
$337$	16.2977			0.887794			0.443897	−	0.896078i	$-0.353596\pi$
$337$	16.2977			0.887794			0.443897	+	0.896078i	$0.353596\pi$
$338$		0			0
$339$	−8.55629	−	26.3336i	−0.464714	−	1.43024i
$340$		0			0
$341$	−12.5613	+	9.12630i	−0.680231	+	0.494217i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	6.88706	+	21.1962i	0.370787	+	1.14116i
$346$		0			0
$347$	21.1156	+	15.3414i	1.13355	+	0.823569i	0.986207	−	0.165517i	$-0.0529294\pi$
$347$	21.1156	+	15.3414i	1.13355	+	0.823569i	0.147338	+	0.989086i	$0.452929\pi$
$348$		0			0
$349$	−26.6203	−	19.3408i	−1.42495	−	1.03529i	−0.990929	−	0.134388i	$-0.957093\pi$
$349$	−26.6203	−	19.3408i	−1.42495	−	1.03529i	−0.434024	−	0.900901i	$-0.642907\pi$
$350$		0			0
$351$	2.21453	−	1.60895i	0.118203	−	0.0858793i
$352$		0			0
$353$	0.221365	+	0.160831i	0.0117821	+	0.00856017i	0.593661	−	0.804715i	$-0.297682\pi$
$353$	0.221365	+	0.160831i	0.0117821	+	0.00856017i	−0.581879	+	0.813276i	$0.697682\pi$
$354$		0			0
$355$	−43.7572			−2.32239
$356$		0			0
$357$	−0.0107061	+	0.0329501i	−0.000566629	+	0.00174390i
$358$		0			0
$359$	−4.22302	−	12.9971i	−0.222882	−	0.685961i	−0.998500	−	0.0547577i	$-0.982561\pi$
$359$	−4.22302	−	12.9971i	−0.222882	−	0.685961i	0.775617	−	0.631203i	$-0.217439\pi$
$360$		0			0
$361$	−5.57517	−	17.1586i	−0.293430	−	0.903085i
$362$		0			0
$363$	3.77721	−	2.74431i	0.198252	−	0.144039i
$364$		0			0
$365$	−3.88072	+	11.9436i	−0.203126	+	0.625158i
$366$		0			0
$367$	−3.83092	+	2.78333i	−0.199973	+	0.145289i	−0.683265	−	0.730170i	$-0.739441\pi$
$367$	−3.83092	+	2.78333i	−0.199973	+	0.145289i	0.483293	+	0.875459i	$0.339441\pi$
$368$		0			0
$369$	11.7277	+	13.5740i	0.610521	+	0.706632i
$370$		0			0
$371$	−8.90919	+	6.47290i	−0.462542	+	0.336056i
$372$		0			0
$373$	8.45885	−	26.0337i	0.437983	−	1.34797i	−0.452016	−	0.892010i	$-0.649295\pi$
$373$	8.45885	−	26.0337i	0.437983	−	1.34797i	0.889999	−	0.455963i	$-0.150705\pi$
$374$		0			0
$375$	16.4407	−	11.9449i	0.848995	−	0.616831i
$376$		0			0
$377$	2.45760	+	7.56371i	0.126573	+	0.389551i
$378$		0			0
$379$	−3.83842	−	11.8134i	−0.197166	−	0.606815i	−0.999944	−	0.0105374i	$-0.996646\pi$
$379$	−3.83842	−	11.8134i	−0.197166	−	0.606815i	0.802778	−	0.596278i	$-0.203354\pi$
$380$		0			0
$381$	−8.07646	+	24.8568i	−0.413770	+	1.27345i
$382$		0			0
$383$	−11.5989			−0.592678			−0.296339	−	0.955083i	$-0.595766\pi$
$383$	−11.5989			−0.592678			−0.296339	+	0.955083i	$0.595766\pi$
$384$		0			0
$385$	10.2458	+	7.44398i	0.522172	+	0.379380i
$386$		0			0
$387$	−27.4117	+	19.9157i	−1.39341	+	1.01237i
$388$		0			0
$389$	9.30596	+	6.76118i	0.471831	+	0.342805i	0.798154	−	0.602453i	$-0.205810\pi$
$389$	9.30596	+	6.76118i	0.471831	+	0.342805i	−0.326324	+	0.945258i	$0.605810\pi$
$390$		0			0
$391$	0.0305823	+	0.0222193i	0.00154661	+	0.00112368i
$392$		0			0
$393$	−16.3620	−	50.3571i	−0.825354	−	2.54018i
$394$		0			0
$395$	−12.0239	+	37.0057i	−0.604987	+	1.86196i
$396$		0			0
$397$	−26.1531	+	19.0013i	−1.31258	+	0.953649i	−0.312592	+	0.949888i	$0.601197\pi$
$397$	−26.1531	+	19.0013i	−1.31258	+	0.953649i	−0.999993	+	0.00376095i	$0.998803\pi$
$398$		0			0
$399$	0.728653	+	2.24256i	0.0364783	+	0.112269i
$400$		0			0
$401$	−0.233353			−0.0116531			−0.00582656	−	0.999983i	$-0.501855\pi$
$401$	−0.233353			−0.0116531			−0.00582656	+	0.999983i	$0.501855\pi$
$402$		0			0
$403$	−19.9966	−	14.5284i	−0.996103	−	0.723711i
$404$		0			0
$405$	−10.3969	+	31.9985i	−0.516628	+	1.59002i
$406$		0			0
$407$	−12.2225			−0.605849
$408$		0			0
$409$	−0.858414			−0.0424459			−0.0212229	−	0.999775i	$-0.506756\pi$
$409$	−0.858414			−0.0424459			−0.0212229	+	0.999775i	$0.506756\pi$
$410$		0			0
$411$	−10.9258			−0.538930
$412$		0			0
$413$	−6.16384			−0.303303
$414$		0			0
$415$	7.39369	−	22.7554i	0.362942	−	1.11702i
$416$		0			0
$417$	−22.7262	−	16.5116i	−1.11291	−	0.808575i
$418$		0			0
$419$	34.2207			1.67179			0.835895	−	0.548889i	$-0.184949\pi$
$419$	34.2207			1.67179			0.835895	+	0.548889i	$0.184949\pi$
$420$		0			0
$421$	−10.4646	−	32.2069i	−0.510016	−	1.56967i	−0.792172	−	0.610298i	$-0.791050\pi$
$421$	−10.4646	−	32.2069i	−0.510016	−	1.56967i	0.282156	−	0.959368i	$-0.408950\pi$
$422$		0			0
$423$	−19.5693	+	14.2179i	−0.951491	+	0.691299i
$424$		0			0
$425$	0.0328759	−	0.101181i	0.00159471	−	0.00490802i
$426$		0			0
$427$	−0.0359082	−	0.110514i	−0.00173772	−	0.00534815i
$428$		0			0
$429$	40.1359	+	29.1604i	1.93778	+	1.40788i
$430$		0			0
$431$	−18.4082	−	13.3743i	−0.886690	−	0.644218i	0.0483230	−	0.998832i	$-0.484612\pi$
$431$	−18.4082	−	13.3743i	−0.886690	−	0.644218i	−0.935013	+	0.354614i	$0.884612\pi$
$432$		0			0
$433$	7.92753	−	5.75969i	0.380973	−	0.276793i	−0.380774	−	0.924668i	$-0.624342\pi$
$433$	7.92753	−	5.75969i	0.380973	−	0.276793i	0.761746	+	0.647875i	$0.224342\pi$
$434$		0			0
$435$	−9.52885	−	6.92311i	−0.456873	−	0.331938i
$436$		0			0
$437$	2.57277			0.123072
$438$		0			0
$439$	5.65255	−	17.3968i	0.269781	−	0.830302i	−0.720772	−	0.693172i	$-0.756212\pi$
$439$	5.65255	−	17.3968i	0.269781	−	0.830302i	0.990553	−	0.137129i	$-0.0437876\pi$
$440$		0			0
$441$	0.865721	+	2.66442i	0.0412248	+	0.126877i
$442$		0			0
$443$	−6.83871	−	21.0474i	−0.324917	−	0.999992i	−0.971478	−	0.237130i	$-0.923793\pi$
$443$	−6.83871	−	21.0474i	−0.324917	−	0.999992i	0.646561	−	0.762862i	$-0.276207\pi$
$444$		0			0
$445$	−39.6001	+	28.7711i	−1.87722	+	1.36388i
$446$		0			0
$447$	−2.89146	+	8.89900i	−0.136761	+	0.420908i
$448$		0			0
$449$	26.4638	−	19.2271i	1.24890	−	0.907381i	0.250745	−	0.968053i	$-0.419324\pi$
$449$	26.4638	−	19.2271i	1.24890	−	0.907381i	0.998158	+	0.0606719i	$0.0193243\pi$
$450$		0			0
$451$	11.9221	−	19.7063i	0.561388	−	0.927934i
$452$		0			0
$453$	−20.5670	+	14.9428i	−0.966323	+	0.702075i
$454$		0			0
$455$	−6.23006	+	19.1742i	−0.292070	+	0.898898i
$456$		0			0
$457$	−15.9331	+	11.5761i	−0.745320	+	0.541507i	−0.894373	−	0.447322i	$-0.852378\pi$
$457$	−15.9331	+	11.5761i	−0.745320	+	0.541507i	0.149052	+	0.988829i	$0.452378\pi$
$458$		0			0
$459$	0.00212482	+	0.00653951i	9.91779e−5	+	0.000305238i
$460$		0			0
$461$	−0.390516	−	1.20188i	−0.0181881	−	0.0559773i	0.941551	−	0.336872i	$-0.109369\pi$
$461$	−0.390516	−	1.20188i	−0.0181881	−	0.0559773i	−0.959739	+	0.280894i	$0.909369\pi$
$462$		0			0
$463$	10.1499	−	31.2383i	0.471707	−	1.45176i	−0.378641	−	0.925544i	$-0.623608\pi$
$463$	10.1499	−	31.2383i	0.471707	−	1.45176i	0.850348	−	0.526221i	$-0.176392\pi$
$464$		0			0
$465$	36.6061			1.69757
$466$		0			0
$467$	−3.75519	−	2.72831i	−0.173769	−	0.126251i	0.497501	−	0.867463i	$-0.334251\pi$
$467$	−3.75519	−	2.72831i	−0.173769	−	0.126251i	−0.671270	+	0.741212i	$0.734251\pi$
$468$		0			0
$469$	2.40529	−	1.74755i	0.111066	−	0.0806942i
$470$		0			0
$471$	8.44020	+	6.13216i	0.388904	+	0.282555i
$472$		0			0
$473$	35.1949	+	25.5706i	1.61826	+	1.17574i
$474$		0			0
$475$	−2.23751	−	6.88635i	−0.102664	−	0.315967i
$476$		0			0
$477$	9.53364	−	29.3415i	0.436515	−	1.34346i
$478$		0			0
$479$	0.797282	−	0.579259i	0.0364287	−	0.0264670i	−0.569422	−	0.822045i	$-0.692833\pi$
$479$	0.797282	−	0.579259i	0.0364287	−	0.0264670i	0.605851	+	0.795578i	$0.292833\pi$
$480$		0			0
$481$	−6.01267	−	18.5051i	−0.274154	−	0.843759i
$482$		0			0
$483$	6.33002			0.288026
$484$		0			0
$485$	39.6206	+	28.7861i	1.79908	+	1.30711i
$486$		0			0
$487$	−1.17484	+	3.61580i	−0.0532373	+	0.163848i	−0.974140	−	0.225945i	$-0.927453\pi$
$487$	−1.17484	+	3.61580i	−0.0532373	+	0.163848i	0.920903	+	0.389792i	$0.127453\pi$
$488$		0			0
$489$	14.0208			0.634041
$490$		0			0
$491$	12.1843			0.549870			0.274935	−	0.961463i	$-0.411344\pi$
$491$	12.1843			0.549870			0.274935	+	0.961463i	$0.411344\pi$
$492$		0			0
$493$	−0.0199776			−0.000899747
$494$		0			0
$495$	−35.4799			−1.59470
$496$		0			0
$497$	−3.84048	+	11.8198i	−0.172269	+	0.530189i
$498$		0			0
$499$	−1.13431	−	0.824127i	−0.0507789	−	0.0368930i	0.562106	−	0.827065i	$-0.309991\pi$
$499$	−1.13431	−	0.824127i	−0.0507789	−	0.0368930i	−0.612885	+	0.790172i	$0.709991\pi$
$500$		0			0
$501$	−4.98510			−0.222718
$502$		0			0
$503$	−3.95955	−	12.1862i	−0.176548	−	0.543358i	0.823153	−	0.567819i	$-0.192213\pi$
$503$	−3.95955	−	12.1862i	−0.176548	−	0.543358i	−0.999701	+	0.0244618i	$0.992213\pi$
$504$		0			0
$505$	−20.7535	+	15.0783i	−0.923517	+	0.670974i
$506$		0			0
$507$	−14.7291	+	45.3315i	−0.654142	+	2.01324i
$508$		0			0
$509$	0.154918	+	0.476789i	0.00686663	+	0.0211333i	0.954431	−	0.298431i	$-0.0964634\pi$
$509$	0.154918	+	0.476789i	0.00686663	+	0.0211333i	−0.947565	+	0.319565i	$0.896463\pi$
$510$		0			0
$511$	2.88563	+	2.09654i	0.127653	+	0.0927453i
$512$		0			0
$513$	0.378603	+	0.275071i	0.0167157	+	0.0121447i
$514$		0			0
$515$	24.8789	−	18.0756i	1.09630	−	0.796505i
$516$		0			0
$517$	25.1258	+	18.2549i	1.10503	+	0.802851i
$518$		0			0
$519$	−46.5508			−2.04335
$520$		0			0
$521$	5.29612	−	16.2998i	0.232027	−	0.714107i	−0.765475	−	0.643466i	$-0.777496\pi$
$521$	5.29612	−	16.2998i	0.232027	−	0.714107i	0.997502	−	0.0706404i	$-0.0225043\pi$
$522$		0			0
$523$	−1.38259	−	4.25519i	−0.0604566	−	0.186066i	0.916267	−	0.400568i	$-0.131187\pi$
$523$	−1.38259	−	4.25519i	−0.0604566	−	0.186066i	−0.976724	+	0.214502i	$0.931187\pi$
$524$		0			0
$525$	−5.50515	−	16.9431i	−0.240265	−	0.739459i
$526$		0			0
$527$	0.0502310	−	0.0364950i	0.00218810	−	0.00158975i
$528$		0			0
$529$	−4.97312	+	15.3057i	−0.216223	+	0.665465i
$530$		0			0
$531$	13.9703	−	10.1500i	0.606258	−	0.440472i
$532$		0			0
$533$	35.7005	+	8.35600i	1.54636	+	0.361938i
$534$		0			0
$535$	−7.37350	+	5.35716i	−0.318784	+	0.231610i
$536$		0			0
$537$	−2.18635	+	6.72890i	−0.0943481	+	0.290374i
$538$		0			0
$539$	2.91003	−	2.11426i	0.125344	−	0.0910677i
$540$		0			0
$541$	−1.74850	−	5.38132i	−0.0751737	−	0.231361i	0.906408	−	0.422403i	$-0.138813\pi$
$541$	−1.74850	−	5.38132i	−0.0751737	−	0.231361i	−0.981582	+	0.191042i	$0.938813\pi$
$542$		0			0
$543$	−0.695629	−	2.14093i	−0.0298523	−	0.0918759i
$544$		0			0
$545$	−15.3288	+	47.1771i	−0.656612	+	2.02084i
$546$		0			0
$547$	32.0605			1.37081			0.685403	−	0.728164i	$-0.259626\pi$
$547$	32.0605			1.37081			0.685403	+	0.728164i	$0.259626\pi$
$548$		0			0
$549$	0.263369	+	0.191349i	0.0112403	+	0.00816657i
$550$		0			0
$551$	−1.09999	+	0.799191i	−0.0468612	+	0.0340467i
$552$		0			0
$553$	8.94073	+	6.49582i	0.380199	+	0.276231i
$554$		0			0
$555$	23.3129	+	16.9378i	0.989578	+	0.718971i
$556$		0			0
$557$	7.26395	+	22.3562i	0.307784	+	0.947261i	0.978624	+	0.205659i	$0.0659336\pi$
$557$	7.26395	+	22.3562i	0.307784	+	0.947261i	−0.670840	+	0.741602i	$0.734066\pi$
$558$		0			0
$559$	−21.4007	+	65.8646i	−0.905153	+	2.78577i
$560$		0			0
$561$	−0.100820	+	0.0732503i	−0.00425664	+	0.00309263i
$562$		0			0
$563$	−7.37107	−	22.6858i	−0.310654	−	0.956093i	−0.977507	−	0.210904i	$-0.932359\pi$
$563$	−7.37107	−	22.6858i	−0.310654	−	0.956093i	0.666853	−	0.745189i	$-0.267641\pi$
$564$		0			0
$565$	40.4742			1.70276
$566$		0			0
$567$	7.73098	+	5.61688i	0.324670	+	0.235887i
$568$		0			0
$569$	−6.19946	+	19.0800i	−0.259895	+	0.799874i	0.732931	+	0.680303i	$0.238152\pi$
$569$	−6.19946	+	19.0800i	−0.259895	+	0.799874i	−0.992826	+	0.119571i	$0.961848\pi$
$570$		0			0
$571$	2.33766			0.0978282			0.0489141	−	0.998803i	$-0.484424\pi$
$571$	2.33766			0.0978282			0.0489141	+	0.998803i	$0.484424\pi$
$572$		0			0
$573$	−52.3076			−2.18518
$574$		0			0
$575$	−19.4379			−0.810616
$576$		0			0
$577$	35.0323			1.45841			0.729206	−	0.684294i	$-0.239890\pi$
$577$	35.0323			1.45841			0.729206	+	0.684294i	$0.239890\pi$
$578$		0			0
$579$	17.2037	−	52.9477i	0.714963	−	2.20043i
$580$		0			0
$581$	−5.49781	−	3.99440i	−0.228088	−	0.165715i
$582$		0			0
$583$	−39.6114			−1.64054
$584$		0			0
$585$	−17.4537	−	53.7170i	−0.721623	−	2.22093i
$586$		0			0
$587$	4.67158	−	3.39410i	0.192817	−	0.140090i	−0.487188	−	0.873297i	$-0.661978\pi$
$587$	4.67158	−	3.39410i	0.192817	−	0.140090i	0.680005	+	0.733207i	$0.261978\pi$
$588$		0			0
$589$	1.30582	−	4.01892i	0.0538056	−	0.165597i
$590$		0			0
$591$	−8.70096	−	26.7788i	−0.357910	−	1.10153i
$592$		0			0
$593$	−13.0588	−	9.48774i	−0.536259	−	0.389615i	0.286435	−	0.958100i	$-0.407530\pi$
$593$	−13.0588	−	9.48774i	−0.536259	−	0.389615i	−0.822694	+	0.568485i	$0.807530\pi$
$594$		0			0
$595$	−0.0409716	−	0.0297676i	−0.00167967	−	0.00122035i
$596$		0			0
$597$	11.0179	−	8.00499i	0.450933	−	0.327622i
$598$		0			0
$599$	16.5345	+	12.0130i	0.675583	+	0.490840i	0.871889	−	0.489703i	$-0.162895\pi$
$599$	16.5345	+	12.0130i	0.675583	+	0.490840i	−0.196307	+	0.980543i	$0.562895\pi$
$600$		0			0
$601$	−30.4745			−1.24308			−0.621541	−	0.783382i	$-0.713493\pi$
$601$	−30.4745			−1.24308			−0.621541	+	0.783382i	$0.713493\pi$
$602$		0			0
$603$	−2.57388	+	7.92159i	−0.104817	+	0.322592i
$604$		0			0
$605$	2.10898	+	6.49076i	0.0857420	+	0.263887i
$606$		0			0
$607$	0.257493	+	0.792483i	0.0104513	+	0.0321659i	0.956146	−	0.292890i	$-0.0946169\pi$
$607$	0.257493	+	0.792483i	0.0104513	+	0.0321659i	−0.945695	+	0.325056i	$0.894617\pi$
$608$		0			0
$609$	−2.70641	+	1.96632i	−0.109669	+	0.0796795i
$610$		0			0
$611$	−15.2780	+	47.0210i	−0.618083	+	1.90226i
$612$		0			0
$613$	−11.5118	+	8.36381i	−0.464957	+	0.337811i	−0.795473	−	0.605989i	$-0.792777\pi$
$613$	−11.5118	+	8.36381i	−0.464957	+	0.337811i	0.330515	+	0.943801i	$0.392777\pi$
$614$		0			0
$615$	−50.0485	+	21.0658i	−2.01815	+	0.849455i
$616$		0			0
$617$	−17.4145	+	12.6524i	−0.701080	+	0.509364i	−0.880284	−	0.474448i	$-0.842648\pi$
$617$	−17.4145	+	12.6524i	−0.701080	+	0.509364i	0.179204	+	0.983812i	$0.442648\pi$
$618$		0			0
$619$	−1.36389	+	4.19761i	−0.0548192	+	0.168716i	−0.974717	−	0.223441i	$-0.928271\pi$
$619$	−1.36389	+	4.19761i	−0.0548192	+	0.168716i	0.919898	+	0.392157i	$0.128271\pi$
$620$		0			0
$621$	1.01637	−	0.738435i	0.0407854	−	0.0296324i
$622$		0			0
$623$	4.29610	+	13.2220i	0.172119	+	0.529729i
$624$		0			0
$625$	−2.24842	−	6.91992i	−0.0899367	−	0.276797i
$626$		0			0
$627$	−2.62096	+	8.06649i	−0.104671	+	0.322145i
$628$		0			0
$629$	0.0488765			0.00194883
$630$		0			0
$631$	4.59650	+	3.33955i	0.182984	+	0.132946i	0.675506	−	0.737354i	$-0.263925\pi$
$631$	4.59650	+	3.33955i	0.182984	+	0.132946i	−0.492523	+	0.870300i	$0.663925\pi$
$632$		0			0
$633$	25.1495	−	18.2722i	0.999603	−	0.726254i
$634$		0			0
$635$	−30.9080	−	22.4560i	−1.22655	−	0.891139i
$636$		0			0
$637$	4.63256	+	3.36575i	0.183549	+	0.133356i
$638$		0			0
$639$	−10.7592	−	33.1135i	−0.425628	−	1.30995i
$640$		0			0
$641$	−6.21895	+	19.1400i	−0.245634	+	0.755983i	0.749898	+	0.661554i	$0.230103\pi$
$641$	−6.21895	+	19.1400i	−0.245634	+	0.755983i	−0.995532	+	0.0944294i	$0.969897\pi$
$642$		0			0
$643$	28.1879	−	20.4797i	1.11162	−	0.807640i	0.128702	−	0.991683i	$-0.458919\pi$
$643$	28.1879	−	20.4797i	1.11162	−	0.807640i	0.982918	+	0.184044i	$0.0589188\pi$
$644$		0			0
$645$	−31.6944	−	97.5452i	−1.24796	−	3.84084i
$646$		0			0
$647$	31.0472			1.22059			0.610296	−	0.792173i	$-0.291050\pi$
$647$	31.0472			1.22059			0.610296	+	0.792173i	$0.291050\pi$
$648$		0			0
$649$	−17.9370	−	13.0320i	−0.704088	−	0.511550i
$650$		0			0
$651$	3.21284	−	9.88811i	0.125921	−	0.387546i
$652$		0			0
$653$	−6.98379			−0.273297			−0.136648	−	0.990620i	$-0.543633\pi$
$653$	−6.98379			−0.273297			−0.136648	+	0.990620i	$0.543633\pi$
$654$		0			0
$655$	77.3979			3.02419
$656$		0			0
$657$	−9.99262			−0.389849
$658$		0			0
$659$	−43.3158			−1.68735			−0.843673	−	0.536858i	$-0.819611\pi$
$659$	−43.3158			−1.68735			−0.843673	+	0.536858i	$0.819611\pi$
$660$		0			0
$661$	−4.20100	+	12.9294i	−0.163400	+	0.502894i	−0.998915	−	0.0465742i	$-0.985170\pi$
$661$	−4.20100	+	12.9294i	−0.163400	+	0.502894i	0.835515	+	0.549468i	$0.185170\pi$
$662$		0			0
$663$	−0.160499	−	0.116609i	−0.00623325	−	0.00452872i
$664$		0			0
$665$	−3.44678			−0.133660
$666$		0			0
$667$	1.12793	+	3.47140i	0.0436735	+	0.134413i
$668$		0			0
$669$	−27.3234	+	19.8516i	−1.05638	+	0.767506i
$670$		0			0
$671$	0.129162	−	0.397519i	0.00498624	−	0.0153461i
$672$		0			0
$673$	−7.79981	−	24.0053i	−0.300661	−	0.925338i	−0.981261	−	0.192683i	$-0.938281\pi$
$673$	−7.79981	−	24.0053i	−0.300661	−	0.925338i	0.680600	−	0.732655i	$-0.261719\pi$
$674$		0			0
$675$	−2.86044	−	2.07823i	−0.110099	−	0.0799913i
$676$		0			0
$677$	1.09234	+	0.793635i	0.0419822	+	0.0305019i	0.608578	−	0.793494i	$-0.291740\pi$
$677$	1.09234	+	0.793635i	0.0419822	+	0.0305019i	−0.566596	+	0.823996i	$0.691740\pi$
$678$		0			0
$679$	11.2532	−	8.17590i	0.431857	−	0.313762i
$680$		0			0
$681$	−31.6019	−	22.9601i	−1.21099	−	0.879833i
$682$		0			0
$683$	8.59772			0.328983			0.164491	−	0.986379i	$-0.447402\pi$
$683$	8.59772			0.328983			0.164491	+	0.986379i	$0.447402\pi$
$684$		0			0
$685$	4.93527	−	15.1892i	0.188567	−	0.580349i
$686$		0			0
$687$	3.56936	+	10.9853i	0.136179	+	0.419117i
$688$		0			0
$689$	−19.4862	−	59.9723i	−0.742364	−	2.28476i
$690$		0			0
$691$	27.8956	−	20.2674i	1.06120	−	0.771007i	0.0868903	−	0.996218i	$-0.472307\pi$
$691$	27.8956	−	20.2674i	1.06120	−	0.771007i	0.974310	+	0.225211i	$0.0723070\pi$
$692$		0			0
$693$	−3.11400	+	9.58390i	−0.118291	+	0.364062i
$694$		0			0
$695$	33.2202	−	24.1359i	1.26011	−	0.915527i
$696$		0			0
$697$	−0.0476750	+	0.0788032i	−0.00180582	+	0.00298488i
$698$		0			0
$699$	37.5641	−	27.2919i	1.42081	−	1.03228i
$700$		0			0
$701$	3.30315	−	10.1660i	0.124758	−	0.383966i	−0.869099	−	0.494639i	$-0.835300\pi$
$701$	3.30315	−	10.1660i	0.124758	−	0.383966i	0.993857	+	0.110672i	$0.0353004\pi$
$702$		0			0
$703$	2.69120	−	1.95527i	0.101500	−	0.0737444i
$704$		0			0
$705$	−22.6267	−	69.6379i	−0.852172	−	2.62271i
$706$		0			0
$707$	2.25148	+	6.92935i	0.0846758	+	0.260605i
$708$		0			0
$709$	9.38502	−	28.8841i	0.352462	−	1.08477i	−0.605005	−	0.796222i	$-0.706829\pi$
$709$	9.38502	−	28.8841i	0.352462	−	1.08477i	0.957467	−	0.288544i	$-0.0931712\pi$
$710$		0			0
$711$	−30.9607			−1.16112
$712$		0			0
$713$	−9.17755	−	6.66788i	−0.343702	−	0.249714i
$714$		0			0
$715$	−58.6689	+	42.6254i	−2.19409	+	1.59410i
$716$		0			0
$717$	8.10853	+	5.89119i	0.302818	+	0.220011i
$718$		0			0
$719$	15.5047	+	11.2648i	0.578227	+	0.420106i	0.838084	−	0.545541i	$-0.183676\pi$
$719$	15.5047	+	11.2648i	0.578227	+	0.420106i	−0.259858	+	0.965647i	$0.583676\pi$
$720$		0			0
$721$	−2.69904	−	8.30679i	−0.100518	−	0.309361i
$722$		0			0
$723$	1.95234	−	6.00869i	0.0726084	−	0.223466i
$724$		0			0
$725$	8.31071	−	6.03809i	0.308652	−	0.224249i
$726$		0			0
$727$	1.52792	+	4.70245i	0.0566674	+	0.174404i	0.975384	−	0.220513i	$-0.0707732\pi$
$727$	1.52792	+	4.70245i	0.0566674	+	0.174404i	−0.918717	+	0.394917i	$0.870773\pi$
$728$		0			0
$729$	−23.3172			−0.863602
$730$		0			0
$731$	−0.140740	−	0.102254i	−0.00520547	−	0.00378199i
$732$		0			0
$733$	−12.5344	+	38.5769i	−0.462969	+	1.42487i	0.398550	+	0.917147i	$0.369514\pi$
$733$	−12.5344	+	38.5769i	−0.462969	+	1.42487i	−0.861519	+	0.507725i	$0.830486\pi$
$734$		0			0
$735$	−8.48043			−0.312805
$736$		0			0
$737$	10.6943			0.393928
$738$		0			0
$739$	−27.0875			−0.996430			−0.498215	−	0.867053i	$-0.666011\pi$
$739$	−27.0875			−0.996430			−0.498215	+	0.867053i	$0.666011\pi$
$740$		0			0
$741$	−13.5021			−0.496013
$742$		0			0
$743$	−10.7108	+	32.9644i	−0.392941	+	1.20935i	0.537613	+	0.843192i	$0.319326\pi$
$743$	−10.7108	+	32.9644i	−0.392941	+	1.20935i	−0.930554	+	0.366156i	$0.880674\pi$
$744$		0			0
$745$	−11.0654	−	8.03949i	−0.405405	−	0.294544i
$746$		0			0
$747$	19.0383			0.696575
$748$		0			0
$749$	0.799930	+	2.46193i	0.0292288	+	0.0899570i
$750$		0			0
$751$	−39.3662	+	28.6012i	−1.43649	+	1.04367i	−0.447732	+	0.894168i	$0.647768\pi$
$751$	−39.3662	+	28.6012i	−1.43649	+	1.04367i	−0.988761	+	0.149505i	$0.952232\pi$
$752$		0			0
$753$	−17.5641	+	54.0568i	−0.640072	+	1.96994i
$754$		0			0
$755$	−11.4834	−	35.3423i	−0.417924	−	1.28624i
$756$		0			0
$757$	37.3023	+	27.1017i	1.35577	+	0.985027i	0.998701	+	0.0509507i	$0.0162251\pi$
$757$	37.3023	+	27.1017i	1.35577	+	0.985027i	0.357073	+	0.934077i	$0.383775\pi$
$758$		0			0
$759$	18.4206	+	13.3833i	0.668624	+	0.485784i
$760$		0			0
$761$	34.6357	−	25.1643i	1.25554	−	0.912205i	0.257013	−	0.966408i	$-0.417262\pi$
$761$	34.6357	−	25.1643i	1.25554	−	0.912205i	0.998530	+	0.0542027i	$0.0172617\pi$
$762$		0			0
$763$	11.3982	+	8.28127i	0.412642	+	0.299802i
$764$		0			0
$765$	0.141880			0.00512968
$766$		0			0
$767$	10.9068	−	33.5677i	0.393822	−	1.21206i
$768$		0			0
$769$	11.6002	+	35.7016i	0.418312	+	1.28743i	0.909255	+	0.416240i	$0.136653\pi$
$769$	11.6002	+	35.7016i	0.418312	+	1.28743i	−0.490942	+	0.871192i	$0.663347\pi$
$770$		0			0
$771$	−9.36614	−	28.8260i	−0.337313	−	1.03814i
$772$		0			0
$773$	3.17239	−	2.30488i	0.114103	−	0.0829006i	−0.529270	−	0.848453i	$-0.677534\pi$
$773$	3.17239	−	2.30488i	0.114103	−	0.0829006i	0.643373	+	0.765553i	$0.277534\pi$
$774$		0			0
$775$	−9.86583	+	30.3639i	−0.354391	+	1.09070i
$776$		0			0
$777$	6.62141	−	4.81073i	0.237542	−	0.172584i
$778$		0			0
$779$	0.527426	+	6.24620i	0.0188970	+	0.223793i
$780$		0			0
$781$	−36.1660	+	26.2761i	−1.29412	+	0.940234i
$782$		0			0
$783$	−0.205167	+	0.631439i	−0.00733207	+	0.0225658i
$784$		0			0
$785$	−12.3375	+	8.96373i	−0.440345	+	0.319929i
$786$		0			0
$787$	−9.58791	−	29.5086i	−0.341772	−	1.05187i	−0.963289	−	0.268466i	$-0.913483\pi$
$787$	−9.58791	−	29.5086i	−0.341772	−	1.05187i	0.621517	−	0.783401i	$-0.286517\pi$
$788$		0			0
$789$	22.6724	+	69.7786i	0.807160	+	2.48418i
$790$		0			0
$791$	3.55234	−	10.9330i	0.126307	−	0.388732i
$792$		0			0
$793$	0.665388			0.0236286
$794$		0			0
$795$	75.5537	+	54.8930i	2.67961	+	1.94685i
$796$		0			0
$797$	20.3060	−	14.7532i	0.719274	−	0.522583i	−0.166878	−	0.985978i	$-0.553369\pi$
$797$	20.3060	−	14.7532i	0.719274	−	0.522583i	0.886152	+	0.463394i	$0.153369\pi$
$798$		0			0
$799$	−0.100475	−	0.0729994i	−0.00355455	−	0.00258253i
$800$		0			0
$801$	−31.5098	−	22.8932i	−1.11334	−	0.808891i
$802$		0			0
$803$	3.96466	+	12.2020i	0.139910	+	0.430598i
$804$		0			0
$805$	−2.85932	+	8.80007i	−0.100778	+	0.310162i
$806$		0			0
$807$	7.53404	−	5.47380i	0.265211	−	0.192687i
$808$		0			0
$809$	14.9371	+	45.9717i	0.525160	+	1.61628i	0.763998	+	0.645218i	$0.223234\pi$
$809$	14.9371	+	45.9717i	0.525160	+	1.61628i	−0.238838	+	0.971059i	$0.576766\pi$
$810$		0			0
$811$	16.0854			0.564833			0.282417	−	0.959292i	$-0.408864\pi$
$811$	16.0854			0.564833			0.282417	+	0.959292i	$0.408864\pi$
$812$		0			0
$813$	4.89016	+	3.55291i	0.171505	+	0.124606i
$814$		0			0
$815$	−6.33329	+	19.4919i	−0.221846	+	0.682770i
$816$		0			0
$817$	−11.8399			−0.414226
$818$		0			0
$819$	−16.0420			−0.560554
$820$		0			0
$821$	−17.7590			−0.619794			−0.309897	−	0.950770i	$-0.600295\pi$
$821$	−17.7590			−0.619794			−0.309897	+	0.950770i	$0.600295\pi$
$822$		0			0
$823$	−8.04496			−0.280430			−0.140215	−	0.990121i	$-0.544779\pi$
$823$	−8.04496			−0.280430			−0.140215	+	0.990121i	$0.544779\pi$
$824$		0			0
$825$	19.8020	−	60.9444i	0.689418	−	2.12181i
$826$		0			0
$827$	9.14448	+	6.64385i	0.317985	+	0.231029i	0.735315	−	0.677726i	$-0.237034\pi$
$827$	9.14448	+	6.64385i	0.317985	+	0.231029i	−0.417330	+	0.908755i	$0.637034\pi$
$828$		0			0
$829$	6.41898			0.222940			0.111470	−	0.993768i	$-0.464444\pi$
$829$	6.41898			0.222940			0.111470	+	0.993768i	$0.464444\pi$
$830$		0			0
$831$	−2.30656	−	7.09885i	−0.0800135	−	0.246256i
$832$		0			0
$833$	−0.0116369	+	0.00845469i	−0.000403194	+	0.000292938i
$834$		0			0
$835$	2.25181	−	6.93034i	0.0779269	−	0.239834i
$836$		0			0
$837$	−0.637644	−	1.96247i	−0.0220402	−	0.0678327i
$838$		0			0
$839$	7.31503	+	5.31468i	0.252543	+	0.183483i	0.706853	−	0.707360i	$-0.250114\pi$
$839$	7.31503	+	5.31468i	0.252543	+	0.183483i	−0.454310	+	0.890844i	$0.650114\pi$
$840$		0			0
$841$	21.9009	+	15.9119i	0.755204	+	0.548688i
$842$		0			0
$843$	16.3622	−	11.8878i	0.563545	−	0.409439i
$844$		0			0
$845$	−56.3672	−	40.9532i	−1.93909	−	1.40883i
$846$		0			0
$847$	1.93840			0.0666041
$848$		0			0
$849$	18.9101	−	58.1993i	0.648993	−	1.99739i
$850$		0			0
$851$	−2.75954	−	8.49300i	−0.0945959	−	0.291136i
$852$		0			0
$853$	−8.58767	−	26.4301i	−0.294036	−	0.904950i	−0.983544	−	0.180671i	$-0.942173\pi$
$853$	−8.58767	−	26.4301i	−0.294036	−	0.904950i	0.689507	−	0.724279i	$-0.257827\pi$
$854$		0			0
$855$	7.81208	−	5.67581i	0.267167	−	0.194109i
$856$		0			0
$857$	−6.08534	+	18.7287i	−0.207871	+	0.639762i	0.791712	+	0.610894i	$0.209190\pi$
$857$	−6.08534	+	18.7287i	−0.207871	+	0.639762i	−0.999583	+	0.0288672i	$0.990810\pi$
$858$		0			0
$859$	44.5413	−	32.3611i	1.51973	−	1.10415i	0.558108	−	0.829768i	$-0.311527\pi$
$859$	44.5413	−	32.3611i	1.51973	−	1.10415i	0.961621	−	0.274380i	$-0.0884726\pi$
$860$		0			0
$861$	1.29768	+	15.3681i	0.0442247	+	0.523744i
$862$		0			0
$863$	−18.9014	+	13.7327i	−0.643410	+	0.467465i	−0.861020	−	0.508571i	$-0.830174\pi$
$863$	−18.9014	+	13.7327i	−0.643410	+	0.467465i	0.217610	+	0.976036i	$0.430174\pi$
$864$		0			0
$865$	21.0273	−	64.7155i	0.714951	−	2.20039i
$866$		0			0
$867$	−33.1263	+	24.0677i	−1.12503	+	0.817380i
$868$		0			0
$869$	12.2840	+	37.8061i	0.416705	+	1.28248i
$870$		0			0
$871$	5.26085	+	16.1912i	0.178257	+	0.548619i
$872$		0			0
$873$	−12.0419	+	37.0612i	−0.407557	+	1.25433i
$874$		0			0
$875$	8.43707			0.285225
$876$		0			0
$877$	26.9653	+	19.5914i	0.910553	+	0.661555i	0.941155	−	0.337976i	$-0.109742\pi$
$877$	26.9653	+	19.5914i	0.910553	+	0.661555i	−0.0306020	+	0.999532i	$0.509742\pi$
$878$		0			0
$879$	−61.0285	+	44.3398i	−2.05844	+	1.49554i
$880$		0			0
$881$	−14.0567	−	10.2128i	−0.473581	−	0.344077i	0.325254	−	0.945627i	$-0.394550\pi$
$881$	−14.0567	−	10.2128i	−0.473581	−	0.344077i	−0.798835	+	0.601550i	$0.794550\pi$
$882$		0			0
$883$	−38.6076	−	28.0501i	−1.29925	−	0.943960i	−0.299302	−	0.954158i	$-0.596754\pi$
$883$	−38.6076	−	28.0501i	−1.29925	−	0.943960i	−0.999948	+	0.0101979i	$0.996754\pi$
$884$		0			0
$885$	16.1529	+	49.7136i	0.542975	+	1.67111i
$886$		0			0
$887$	13.9884	−	43.0518i	0.469683	−	1.44554i	−0.383312	−	0.923619i	$-0.625217\pi$
$887$	13.9884	−	43.0518i	0.469683	−	1.44554i	0.852996	−	0.521918i	$-0.174783\pi$
$888$		0			0
$889$	−8.77859	+	6.37802i	−0.294425	+	0.213912i
$890$		0			0
$891$	10.6218	+	32.6906i	0.355845	+	1.09518i
$892$		0			0
$893$	−8.45256			−0.282854
$894$		0			0
$895$	−8.36702	−	6.07899i	−0.279679	−	0.203198i
$896$		0			0
$897$	−11.2008	+	34.4727i	−0.373985	+	1.15101i
$898$		0			0
$899$	5.99516			0.199950
$900$		0			0
$901$	0.158402			0.00527712
$902$		0			0
$903$	−29.1309			−0.969414
$904$		0			0
$905$	3.29056			0.109382
$906$		0			0
$907$	−4.83422	+	14.8782i	−0.160518	+	0.494023i	−0.998678	−	0.0514010i	$-0.983631\pi$
$907$	−4.83422	+	14.8782i	−0.160518	+	0.494023i	0.838160	+	0.545424i	$0.183631\pi$
$908$		0			0
$909$	−16.5135	−	11.9978i	−0.547719	−	0.397941i
$910$		0			0
$911$	−27.6460			−0.915953			−0.457976	−	0.888964i	$-0.651426\pi$
$911$	−27.6460			−0.915953			−0.457976	+	0.888964i	$0.651426\pi$
$912$		0			0
$913$	−7.55362	−	23.2476i	−0.249988	−	0.769385i
$914$		0			0
$915$	−0.797236	+	0.579226i	−0.0263558	+	0.0191486i
$916$		0			0
$917$	6.79305	−	20.9069i	0.224326	−	0.690406i
$918$		0			0
$919$	−8.95359	−	27.5563i	−0.295352	−	0.908999i	−0.983103	−	0.183053i	$-0.941402\pi$
$919$	−8.95359	−	27.5563i	−0.295352	−	0.908999i	0.687752	−	0.725946i	$-0.258598\pi$
$920$		0			0
$921$	−22.3697	−	16.2525i	−0.737107	−	0.535540i
$922$		0			0
$923$	−57.5737	−	41.8297i	−1.89506	−	1.37684i
$924$		0			0
$925$	−20.3327	+	14.7726i	−0.668535	+	0.485719i
$926$		0			0
$927$	19.7961	+	14.3827i	0.650190	+	0.472391i
$928$		0			0
$929$	8.92739			0.292898			0.146449	−	0.989218i	$-0.453216\pi$
$929$	8.92739			0.292898			0.146449	+	0.989218i	$0.453216\pi$
$930$		0			0
$931$	−0.302517	+	0.931050i	−0.00991458	+	0.0305139i
$932$		0			0
$933$	25.6779	+	79.0285i	0.840658	+	2.58728i
$934$		0			0
$935$	−0.0562922	−	0.173249i	−0.00184095	−	0.00566586i
$936$		0			0
$937$	−40.3543	+	29.3191i	−1.31832	+	0.957814i	−0.318366	+	0.947968i	$0.603134\pi$
$937$	−40.3543	+	29.3191i	−1.31832	+	0.957814i	−0.999952	+	0.00984596i	$0.996866\pi$
$938$		0			0
$939$	−19.5987	+	60.3187i	−0.639581	+	1.96843i
$940$		0			0
$941$	16.3100	−	11.8499i	0.531691	−	0.386296i	−0.289299	−	0.957239i	$-0.593422\pi$
$941$	16.3100	−	11.8499i	0.531691	−	0.386296i	0.820990	+	0.570943i	$0.193422\pi$
$942$		0			0
$943$	16.3849	+	3.83502i	0.533566	+	0.124886i
$944$		0			0
$945$	−1.36165	+	0.989293i	−0.0442943	+	0.0321817i
$946$		0			0
$947$	7.22387	−	22.2328i	0.234744	−	0.722468i	−0.762411	−	0.647093i	$-0.775984\pi$
$947$	7.22387	−	22.2328i	0.234744	−	0.722468i	0.997155	−	0.0753754i	$-0.0240155\pi$
$948$		0			0
$949$	−16.5236	+	12.0051i	−0.536379	+	0.389702i
$950$		0			0
$951$	−23.3612	−	71.8984i	−0.757539	−	2.33146i
$952$		0			0
$953$	12.1037	+	37.2513i	0.392077	+	1.20669i	0.931215	+	0.364471i	$0.118750\pi$
$953$	12.1037	+	37.2513i	0.392077	+	1.20669i	−0.539138	+	0.842217i	$0.681250\pi$
$954$		0			0
$955$	23.6277	−	72.7187i	0.764575	−	2.35312i
$956$		0			0
$957$	−12.0331			−0.388974
$958$		0			0
$959$	−3.66978	−	2.66625i	−0.118503	−	0.0860977i
$960$		0			0
$961$	10.0055	−	7.26943i	0.322758	−	0.234498i
$962$		0			0
$963$	−5.86709	−	4.26269i	−0.189064	−	0.137363i
$964$		0			0
$965$	65.8375	+	47.8337i	2.11938	+	1.53982i
$966$		0			0
$967$	9.10899	+	28.0346i	0.292925	+	0.901531i	0.983910	+	0.178662i	$0.0571770\pi$
$967$	9.10899	+	28.0346i	0.292925	+	0.901531i	−0.690985	+	0.722869i	$0.742823\pi$
$968$		0			0
$969$	0.0104809	−	0.0322570i	0.000336696	−	0.00103624i
$970$		0			0
$971$	32.3011	−	23.4681i	1.03659	−	0.753128i	0.0669739	−	0.997755i	$-0.478666\pi$
$971$	32.3011	−	23.4681i	1.03659	−	0.753128i	0.969617	+	0.244627i	$0.0786656\pi$
$972$		0			0
$973$	−3.60397	−	11.0919i	−0.115538	−	0.355589i
$974$		0			0
$975$	102.012			3.26699
$976$		0			0
$977$	−44.9792	−	32.6793i	−1.43901	−	1.04550i	−0.988248	−	0.152862i	$-0.951151\pi$
$977$	−44.9792	−	32.6793i	−1.43901	−	1.04550i	−0.450765	−	0.892643i	$-0.648849\pi$
$978$		0			0
$979$	−15.4531	+	47.5596i	−0.493882	+	1.52001i
$980$		0			0
$981$	−39.4706			−1.26020
$982$		0			0
$983$	−10.6485			−0.339636			−0.169818	−	0.985475i	$-0.554318\pi$
$983$	−10.6485			−0.339636			−0.169818	+	0.985475i	$0.554318\pi$
$984$		0			0
$985$	41.1585			1.31142
$986$		0			0
$987$	−20.7966			−0.661964
$988$		0			0
$989$	−9.82195	+	30.2288i	−0.312320	+	0.961221i
$990$		0			0
$991$	28.0499	+	20.3794i	0.891033	+	0.647373i	0.936147	−	0.351608i	$-0.114365\pi$
$991$	28.0499	+	20.3794i	0.891033	+	0.647373i	−0.0451142	+	0.998982i	$0.514365\pi$
$992$		0			0
$993$	84.6547			2.68644
$994$		0			0
$995$	6.15176	+	18.9332i	0.195024	+	0.600222i
$996$		0			0
$997$	38.5067	−	27.9768i	1.21952	−	0.886033i	0.223460	−	0.974713i	$-0.428265\pi$
$997$	38.5067	−	27.9768i	1.21952	−	0.886033i	0.996060	+	0.0886801i	$0.0282649\pi$
$998$		0			0
$999$	0.501954	−	1.54485i	0.0158811	−	0.0488770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.365.2	✓	24
41.10	even	5	inner	1148.2.n.d.953.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.365.2	✓	24	1.1	even	1	trivial
1148.2.n.d.953.2	yes	24	41.10	even	5	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.40864 q^{3} +(1.08800 - 3.34852i) q^{5} +(-0.809017 - 0.587785i) q^{7} +2.80153 q^{9} +O(q^{10})\)	\(q-2.40864 q^{3} +(1.08800 - 3.34852i) q^{5} +(-0.809017 - 0.587785i) q^{7} +2.80153 q^{9} +(-1.11153 - 3.42095i) q^{11} +(4.63256 - 3.36575i) q^{13} +(-2.62060 + 8.06537i) q^{15} +(0.00444489 + 0.0136800i) q^{17} +(0.791999 + 0.575421i) q^{19} +(1.94863 + 1.41576i) q^{21} +(2.12614 - 1.54473i) q^{23} +(-5.98375 - 4.34745i) q^{25} +0.478035 q^{27} +(-0.429188 + 1.32090i) q^{29} +(-1.33388 - 4.10527i) q^{31} +(2.67728 + 8.23982i) q^{33} +(-2.84842 + 2.06950i) q^{35} +(1.05003 - 3.23167i) q^{37} +(-11.1582 + 8.10688i) q^{39} +(4.18618 + 4.84519i) q^{41} +(-9.78452 + 7.10887i) q^{43} +(3.04807 - 9.38099i) q^{45} +(-6.98521 + 5.07505i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.0107061 - 0.0329501i) q^{51} +(3.40301 - 10.4734i) q^{53} -12.6645 q^{55} +(-1.90764 - 1.38598i) q^{57} +(4.98665 - 3.62301i) q^{59} +(0.0940089 + 0.0683015i) q^{61} +(-2.26649 - 1.64670i) q^{63} +(-6.23006 - 19.1742i) q^{65} +(-0.918740 + 2.82759i) q^{67} +(-5.12109 + 3.72069i) q^{69} +(-3.84048 - 11.8198i) q^{71} -3.56684 q^{73} +(14.4127 + 10.4714i) q^{75} +(-1.11153 + 3.42095i) q^{77} -11.0514 q^{79} -9.55601 q^{81} +6.79567 q^{83} +0.0506437 q^{85} +(1.03376 - 3.18158i) q^{87} +(-11.2473 - 8.17166i) q^{89} -5.72616 q^{91} +(3.21284 + 9.88811i) q^{93} +(2.78850 - 2.02597i) q^{95} +(-4.29833 + 13.2289i) q^{97} +(-3.11400 - 9.58390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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