LMFDB - Embedded newform 1035.2.j.b.737.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, 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:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.1
Character	$\chi$	$=$	1035.737
Dual form			1035.2.j.b.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79212 + 1.79212i) q^{2} -4.42339i q^{4} +(-0.646671 + 2.14052i) q^{5} +(-0.345144 - 0.345144i) q^{7} +(4.34301 + 4.34301i) q^{8} +O(q^{10})$	\(q+(-1.79212 + 1.79212i) q^{2} -4.42339i q^{4} +(-0.646671 + 2.14052i) q^{5} +(-0.345144 - 0.345144i) q^{7} +(4.34301 + 4.34301i) q^{8} +(-2.67715 - 4.99498i) q^{10} +0.0944405i q^{11} +(-0.829331 + 0.829331i) q^{13} +1.23708 q^{14} -6.71961 q^{16} +(-1.32819 + 1.32819i) q^{17} -0.316758i q^{19} +(9.46835 + 2.86048i) q^{20} +(-0.169249 - 0.169249i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-4.16363 - 2.76842i) q^{25} -2.97252i q^{26} +(-1.52671 + 1.52671i) q^{28} -4.62862 q^{29} -6.04848 q^{31} +(3.35634 - 3.35634i) q^{32} -4.76055i q^{34} +(0.961982 - 0.515593i) q^{35} +(6.84163 + 6.84163i) q^{37} +(0.567669 + 0.567669i) q^{38} +(-12.1048 + 6.48779i) q^{40} -8.77308i q^{41} +(-1.95972 + 1.95972i) q^{43} +0.417748 q^{44} -2.53444 q^{46} +(-4.30574 + 4.30574i) q^{47} -6.76175i q^{49} +(12.4231 - 2.50039i) q^{50} +(3.66845 + 3.66845i) q^{52} +(-2.54424 - 2.54424i) q^{53} +(-0.202152 - 0.0610719i) q^{55} -2.99793i q^{56} +(8.29504 - 8.29504i) q^{58} -9.28606 q^{59} -2.16719 q^{61} +(10.8396 - 10.8396i) q^{62} -1.40931i q^{64} +(-1.23889 - 2.31150i) q^{65} +(-5.18450 - 5.18450i) q^{67} +(5.87511 + 5.87511i) q^{68} +(-0.799983 + 2.64799i) q^{70} -9.33930i q^{71} +(5.77659 - 5.77659i) q^{73} -24.5220 q^{74} -1.40114 q^{76} +(0.0325956 - 0.0325956i) q^{77} -15.8795i q^{79} +(4.34538 - 14.3835i) q^{80} +(15.7224 + 15.7224i) q^{82} +(-4.23833 - 4.23833i) q^{83} +(-1.98411 - 3.70192i) q^{85} -7.02409i q^{86} +(-0.410156 + 0.410156i) q^{88} +9.90441 q^{89} +0.572477 q^{91} +(3.12781 - 3.12781i) q^{92} -15.4328i q^{94} +(0.678026 + 0.204838i) q^{95} +(3.36974 + 3.36974i) q^{97} +(12.1179 + 12.1179i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.79212	+	1.79212i	−1.26722	+	1.26722i	−0.319703	+	0.947518i	$0.603583\pi$
$2$	−1.79212	+	1.79212i	−1.26722	+	1.26722i	−0.947518	+	0.319703i	$0.896417\pi$
$3$		0			0
$3$		0			0
$4$		−	4.42339i		−	2.21170i
$5$	−0.646671	+	2.14052i	−0.289200	+	0.957269i
$5$	−0.646671	+	2.14052i	−0.289200	+	0.957269i
$6$		0			0
$7$	−0.345144	−	0.345144i	−0.130452	−	0.130452i	0.638866	−	0.769318i	$-0.279404\pi$
$7$	−0.345144	−	0.345144i	−0.130452	−	0.130452i	−0.769318	+	0.638866i	$0.779404\pi$
$8$	4.34301	+	4.34301i	1.53549	+	1.53549i
$9$		0			0
$10$	−2.67715	−	4.99498i	−0.846591	−	1.57955i
$11$			0.0944405i			0.0284749i	0.999899	+	0.0142374i	$0.00453207\pi$
$11$			0.0944405i			0.0284749i	−0.999899	+	0.0142374i	$0.995468\pi$
$12$		0			0
$13$	−0.829331	+	0.829331i	−0.230015	+	0.230015i	−0.812699	−	0.582684i	$-0.802003\pi$
$13$	−0.829331	+	0.829331i	−0.230015	+	0.230015i	0.582684	+	0.812699i	$0.302003\pi$
$14$	1.23708			0.330623
$15$		0			0
$16$	−6.71961			−1.67990
$17$	−1.32819	+	1.32819i	−0.322133	+	0.322133i	−0.849585	−	0.527452i	$-0.823148\pi$
$17$	−1.32819	+	1.32819i	−0.322133	+	0.322133i	0.527452	+	0.849585i	$0.323148\pi$
$18$		0			0
$19$		−	0.316758i		−	0.0726693i	−0.999340	−	0.0363346i	$-0.988432\pi$
$19$		−	0.316758i		−	0.0726693i	0.999340	−	0.0363346i	$-0.0115682\pi$
$20$	9.46835	+	2.86048i	2.11719	+	0.639622i
$21$		0			0
$22$	−0.169249	−	0.169249i	−0.0360840	−	0.0360840i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−4.16363	−	2.76842i	−0.832727	−	0.553684i
$26$		−	2.97252i		−	0.582959i
$27$		0			0
$28$	−1.52671	+	1.52671i	−0.288521	+	0.288521i
$29$	−4.62862			−0.859513			−0.429757	−	0.902945i	$-0.641401\pi$
$29$	−4.62862			−0.859513			−0.429757	+	0.902945i	$0.641401\pi$
$30$		0			0
$31$	−6.04848			−1.08634			−0.543170	−	0.839623i	$-0.682776\pi$
$31$	−6.04848			−1.08634			−0.543170	+	0.839623i	$0.682776\pi$
$32$	3.35634	−	3.35634i	0.593322	−	0.593322i
$33$		0			0
$34$		−	4.76055i		−	0.816428i
$35$	0.961982	−	0.515593i	0.162605	−	0.0871510i
$36$		0			0
$37$	6.84163	+	6.84163i	1.12476	+	1.12476i	0.991016	+	0.133740i	$0.0426988\pi$
$37$	6.84163	+	6.84163i	1.12476	+	1.12476i	0.133740	+	0.991016i	$0.457301\pi$
$38$	0.567669	+	0.567669i	0.0920880	+	0.0920880i
$39$		0			0
$40$	−12.1048	+	6.48779i	−1.91394	+	1.02581i
$41$		−	8.77308i		−	1.37012i	−0.728484	−	0.685062i	$-0.759775\pi$
$41$		−	8.77308i		−	1.37012i	0.728484	−	0.685062i	$-0.240225\pi$
$42$		0			0
$43$	−1.95972	+	1.95972i	−0.298854	+	0.298854i	−0.840565	−	0.541711i	$-0.817777\pi$
$43$	−1.95972	+	1.95972i	−0.298854	+	0.298854i	0.541711	+	0.840565i	$0.317777\pi$
$44$	0.417748			0.0629778
$45$		0			0
$46$	−2.53444			−0.373683
$47$	−4.30574	+	4.30574i	−0.628057	+	0.628057i	−0.947579	−	0.319522i	$-0.896478\pi$
$47$	−4.30574	+	4.30574i	−0.628057	+	0.628057i	0.319522	+	0.947579i	$0.396478\pi$
$48$		0			0
$49$		−	6.76175i		−	0.965964i
$50$	12.4231	−	2.50039i	1.75689	−	0.353609i
$51$		0			0
$52$	3.66845	+	3.66845i	0.508723	+	0.508723i
$53$	−2.54424	−	2.54424i	−0.349478	−	0.349478i	0.510437	−	0.859915i	$-0.329484\pi$
$53$	−2.54424	−	2.54424i	−0.349478	−	0.349478i	−0.859915	+	0.510437i	$0.829484\pi$
$54$		0			0
$55$	−0.202152	−	0.0610719i	−0.0272581	−	0.00823494i
$56$		−	2.99793i		−	0.400615i
$57$		0			0
$58$	8.29504	−	8.29504i	1.08919	−	1.08919i
$59$	−9.28606			−1.20894			−0.604471	−	0.796627i	$-0.706615\pi$
$59$	−9.28606			−1.20894			−0.604471	+	0.796627i	$0.706615\pi$
$60$		0			0
$61$	−2.16719			−0.277481			−0.138740	−	0.990329i	$-0.544305\pi$
$61$	−2.16719			−0.277481			−0.138740	+	0.990329i	$0.544305\pi$
$62$	10.8396	−	10.8396i	1.37663	−	1.37663i
$63$		0			0
$64$		−	1.40931i		−	0.176163i
$65$	−1.23889	−	2.31150i	−0.153666	−	0.286706i
$66$		0			0
$67$	−5.18450	−	5.18450i	−0.633388	−	0.633388i	0.315528	−	0.948916i	$-0.397818\pi$
$67$	−5.18450	−	5.18450i	−0.633388	−	0.633388i	−0.948916	+	0.315528i	$0.897818\pi$
$68$	5.87511	+	5.87511i	0.712461	+	0.712461i
$69$		0			0
$70$	−0.799983	+	2.64799i	−0.0956163	+	0.316495i
$71$		−	9.33930i		−	1.10837i	−0.832393	−	0.554185i	$-0.813030\pi$
$71$		−	9.33930i		−	1.10837i	0.832393	−	0.554185i	$-0.186970\pi$
$72$		0			0
$73$	5.77659	−	5.77659i	0.676099	−	0.676099i	−0.283016	−	0.959115i	$-0.591335\pi$
$73$	5.77659	−	5.77659i	0.676099	−	0.676099i	0.959115	+	0.283016i	$0.0913351\pi$
$74$	−24.5220			−2.85063
$75$		0			0
$76$	−1.40114			−0.160722
$77$	0.0325956	−	0.0325956i	0.00371461	−	0.00371461i
$78$		0			0
$79$		−	15.8795i		−	1.78658i	−0.449477	−	0.893292i	$-0.648390\pi$
$79$		−	15.8795i		−	1.78658i	0.449477	−	0.893292i	$-0.351610\pi$
$80$	4.34538	−	14.3835i	0.485828	−	1.60812i
$81$		0			0
$82$	15.7224	+	15.7224i	1.73625	+	1.73625i
$83$	−4.23833	−	4.23833i	−0.465217	−	0.465217i	0.435144	−	0.900361i	$-0.356697\pi$
$83$	−4.23833	−	4.23833i	−0.465217	−	0.465217i	−0.900361	+	0.435144i	$0.856697\pi$
$84$		0			0
$85$	−1.98411	−	3.70192i	−0.215207	−	0.401529i
$86$		−	7.02409i		−	0.757427i
$87$		0			0
$88$	−0.410156	+	0.410156i	−0.0437228	+	0.0437228i
$89$	9.90441			1.04987			0.524933	−	0.851144i	$-0.324090\pi$
$89$	9.90441			1.04987			0.524933	+	0.851144i	$0.324090\pi$
$90$		0			0
$91$	0.572477			0.0600119
$92$	3.12781	−	3.12781i	0.326097	−	0.326097i
$93$		0			0
$94$		−	15.4328i		−	1.59177i
$95$	0.678026	+	0.204838i	0.0695640	+	0.0210159i
$96$		0			0
$97$	3.36974	+	3.36974i	0.342146	+	0.342146i	0.857173	−	0.515028i	$-0.172218\pi$
$97$	3.36974	+	3.36974i	0.342146	+	0.342146i	−0.515028	+	0.857173i	$0.672218\pi$
$98$	12.1179	+	12.1179i	1.22409	+	1.22409i
$99$		0			0
$100$	−12.2458	+	18.4174i	−1.22458	+	1.84174i
$101$			2.85067i			0.283652i	0.989892	+	0.141826i	$0.0452974\pi$
$101$			2.85067i			0.283652i	−0.989892	+	0.141826i	$0.954703\pi$
$102$		0			0
$103$	1.34043	−	1.34043i	0.132076	−	0.132076i	−0.637978	−	0.770054i	$-0.720229\pi$
$103$	1.34043	−	1.34043i	0.132076	−	0.132076i	0.770054	+	0.637978i	$0.220229\pi$
$104$	−7.20358			−0.706369
$105$		0			0
$106$	9.11915			0.885730
$107$	−0.792532	+	0.792532i	−0.0766169	+	0.0766169i	−0.744377	−	0.667760i	$-0.767253\pi$
$107$	−0.792532	+	0.792532i	−0.0766169	+	0.0766169i	0.667760	+	0.744377i	$0.267253\pi$
$108$		0			0
$109$			20.4923i			1.96280i	0.191965	+	0.981402i	$0.438514\pi$
$109$			20.4923i			1.96280i	−0.191965	+	0.981402i	$0.561486\pi$
$110$	0.471728	−	0.252832i	0.0449775	−	0.0241066i
$111$		0			0
$112$	2.31924	+	2.31924i	0.219147	+	0.219147i
$113$	−1.92173	−	1.92173i	−0.180781	−	0.180781i	0.610915	−	0.791696i	$-0.290802\pi$
$113$	−1.92173	−	1.92173i	−0.180781	−	0.180781i	−0.791696	+	0.610915i	$0.790802\pi$
$114$		0			0
$115$	−1.97084	+	1.05631i	−0.183782	+	0.0985014i
$116$			20.4742i			1.90098i
$117$		0			0
$118$	16.6417	−	16.6417i	1.53200	−	1.53200i
$119$	0.916834			0.0840460
$120$		0			0
$121$	10.9911			0.999189
$122$	3.88387	−	3.88387i	0.351629	−	0.351629i
$123$		0			0
$124$			26.7548i			2.40265i
$125$	8.61835	−	7.12208i	0.770849	−	0.637018i
$126$		0			0
$127$	−1.71591	−	1.71591i	−0.152262	−	0.152262i	0.626866	−	0.779127i	$-0.284338\pi$
$127$	−1.71591	−	1.71591i	−0.152262	−	0.152262i	−0.779127	+	0.626866i	$0.784338\pi$
$128$	9.23832	+	9.23832i	0.816560	+	0.816560i
$129$		0			0
$130$	6.36273	+	1.92224i	0.558049	+	0.168592i
$131$		−	4.46157i		−	0.389809i	−0.980822	−	0.194905i	$-0.937560\pi$
$131$		−	4.46157i		−	0.389809i	0.980822	−	0.194905i	$-0.0624397\pi$
$132$		0			0
$133$	−0.109327	+	0.109327i	−0.00947987	+	0.00947987i
$134$	18.5825			1.60528
$135$		0			0
$136$	−11.5367			−0.989263
$137$	0.192274	−	0.192274i	0.0164270	−	0.0164270i	−0.698846	−	0.715273i	$-0.746303\pi$
$137$	0.192274	−	0.192274i	0.0164270	−	0.0164270i	0.715273	+	0.698846i	$0.246303\pi$
$138$		0			0
$139$		−	8.75684i		−	0.742745i	−0.928484	−	0.371373i	$-0.878887\pi$
$139$		−	8.75684i		−	0.742745i	0.928484	−	0.371373i	$-0.121113\pi$
$140$	−2.28067	−	4.25522i	−0.192752	−	0.359632i
$141$		0			0
$142$	16.7371	+	16.7371i	1.40455	+	1.40455i
$143$	−0.0783224	−	0.0783224i	−0.00654965	−	0.00654965i
$144$		0			0
$145$	2.99319	−	9.90764i	0.248571	−	0.822785i
$146$			20.7047i			1.71353i
$147$		0			0
$148$	30.2632	−	30.2632i	2.48762	−	2.48762i
$149$	−16.1940			−1.32666			−0.663332	−	0.748325i	$-0.730858\pi$
$149$	−16.1940			−1.32666			−0.663332	+	0.748325i	$0.730858\pi$
$150$		0			0
$151$	5.40549			0.439892			0.219946	−	0.975512i	$-0.429412\pi$
$151$	5.40549			0.439892			0.219946	+	0.975512i	$0.429412\pi$
$152$	1.37568	−	1.37568i	0.111583	−	0.111583i
$153$		0			0
$154$			0.116830i			0.00941447i
$155$	3.91138	−	12.9469i	0.314169	−	1.03992i
$156$		0			0
$157$	−12.6177	−	12.6177i	−1.00700	−	1.00700i	−0.999975	−	0.00702952i	$-0.997762\pi$
$157$	−12.6177	−	12.6177i	−1.00700	−	1.00700i	−0.00702952	−	0.999975i	$-0.502238\pi$
$158$	28.4580	+	28.4580i	2.26400	+	2.26400i
$159$		0			0
$160$	5.01385	+	9.35474i	0.396380	+	0.739557i
$161$		−	0.488107i		−	0.0384683i
$162$		0			0
$163$	12.2199	−	12.2199i	0.957140	−	0.957140i	−0.0419788	−	0.999119i	$-0.513366\pi$
$163$	12.2199	−	12.2199i	0.957140	−	0.957140i	0.999119	+	0.0419788i	$0.0133662\pi$
$164$	−38.8068			−3.03030
$165$		0			0
$166$	15.1912			1.17906
$167$	−8.23072	+	8.23072i	−0.636912	+	0.636912i	−0.949792	−	0.312881i	$-0.898706\pi$
$167$	−8.23072	+	8.23072i	−0.636912	+	0.636912i	0.312881	+	0.949792i	$0.398706\pi$
$168$		0			0
$169$			11.6244i			0.894186i
$170$	10.1901	+	3.07851i	0.781541	+	0.236111i
$171$		0			0
$172$	8.66859	+	8.66859i	0.660974	+	0.660974i
$173$	−12.5493	−	12.5493i	−0.954102	−	0.954102i	0.0448896	−	0.998992i	$-0.485706\pi$
$173$	−12.5493	−	12.5493i	−0.954102	−	0.954102i	−0.998992	+	0.0448896i	$0.985706\pi$
$174$		0			0
$175$	0.481550	+	2.39256i	0.0364017	+	0.180860i
$176$		−	0.634604i		−	0.0478351i
$177$		0			0
$178$	−17.7499	+	17.7499i	−1.33041	+	1.33041i
$179$	−8.73199			−0.652660			−0.326330	−	0.945256i	$-0.605812\pi$
$179$	−8.73199			−0.652660			−0.326330	+	0.945256i	$0.605812\pi$
$180$		0			0
$181$	−0.0190328			−0.00141470			−0.000707348	−	1.00000i	$-0.500225\pi$
$181$	−0.0190328			−0.00141470			−0.000707348		1.00000i	$0.500225\pi$
$182$	−1.02595	+	1.02595i	−0.0760483	+	0.0760483i
$183$		0			0
$184$			6.14195i			0.452790i
$185$	−19.0689	+	10.2203i	−1.40197	+	0.751415i
$186$		0			0
$187$	−0.125435	−	0.125435i	−0.00917272	−	0.00917272i
$188$	19.0460	+	19.0460i	1.38907	+	1.38907i
$189$		0			0
$190$	−1.58220	+	0.848010i	−0.114785	+	0.0615211i
$191$		−	9.20696i		−	0.666192i	−0.942893	−	0.333096i	$-0.891907\pi$
$191$		−	9.20696i		−	0.666192i	0.942893	−	0.333096i	$-0.108093\pi$
$192$		0			0
$193$	−3.78477	+	3.78477i	−0.272434	+	0.272434i	−0.830079	−	0.557646i	$-0.811705\pi$
$193$	−3.78477	+	3.78477i	−0.272434	+	0.272434i	0.557646	+	0.830079i	$0.311705\pi$
$194$	−12.0780			−0.867148
$195$		0			0
$196$	−29.9099			−2.13642
$197$	−11.5764	+	11.5764i	−0.824783	+	0.824783i	−0.986790	−	0.162006i	$-0.948203\pi$
$197$	−11.5764	+	11.5764i	−0.824783	+	0.824783i	0.162006	+	0.986790i	$0.448203\pi$
$198$		0			0
$199$			10.3454i			0.733365i	0.930346	+	0.366683i	$0.119507\pi$
$199$			10.3454i			0.733365i	−0.930346	+	0.366683i	$0.880493\pi$
$200$	−6.05943	−	30.1060i	−0.428466	−	2.12881i
$201$		0			0
$202$	−5.10875	−	5.10875i	−0.359450	−	0.359450i
$203$	1.59754	+	1.59754i	0.112125	+	0.112125i
$204$		0			0
$205$	18.7789	+	5.67329i	1.31158	+	0.396240i
$206$			4.80441i			0.334739i
$207$		0			0
$208$	5.57278	−	5.57278i	0.386403	−	0.386403i
$209$	0.0299148			0.00206925
$210$		0			0
$211$	−25.6256			−1.76414			−0.882070	−	0.471118i	$-0.843851\pi$
$211$	−25.6256			−1.76414			−0.882070	+	0.471118i	$0.843851\pi$
$212$	−11.2542	+	11.2542i	−0.772938	+	0.772938i
$213$		0			0
$214$		−	2.84062i		−	0.194181i
$215$	−2.92751	−	5.46210i	−0.199655	−	0.372512i
$216$		0			0
$217$	2.08760	+	2.08760i	0.141715	+	0.141715i
$218$	−36.7246	−	36.7246i	−2.48731	−	2.48731i
$219$		0			0
$220$	−0.270145	+	0.894196i	−0.0182132	+	0.0602867i
$221$		−	2.20302i		−	0.148191i
$222$		0			0
$223$	−1.35128	+	1.35128i	−0.0904884	+	0.0904884i	−0.750902	−	0.660414i	$-0.770381\pi$
$223$	−1.35128	+	1.35128i	−0.0904884	+	0.0904884i	0.660414	+	0.750902i	$0.270381\pi$
$224$	−2.31684			−0.154800
$225$		0			0
$226$	6.88795			0.458180
$227$	15.0940	−	15.0940i	1.00182	−	1.00182i	0.00182308	−	0.999998i	$-0.499420\pi$
$227$	15.0940	−	15.0940i	1.00182	−	1.00182i	0.999998	−	0.00182308i	$-0.000580303\pi$
$228$		0			0
$229$			9.85946i			0.651531i	0.945451	+	0.325766i	$0.105622\pi$
$229$			9.85946i			0.651531i	−0.945451	+	0.325766i	$0.894378\pi$
$230$	1.63895	−	5.42502i	0.108069	−	0.357715i
$231$		0			0
$232$	−20.1021	−	20.1021i	−1.31977	−	1.31977i
$233$	−12.5373	−	12.5373i	−0.821343	−	0.821343i	0.164957	−	0.986301i	$-0.447251\pi$
$233$	−12.5373	−	12.5373i	−0.821343	−	0.821343i	−0.986301	+	0.164957i	$0.947251\pi$
$234$		0			0
$235$	−6.43212	−	12.0009i	−0.419585	−	0.782853i
$236$			41.0759i			2.67381i
$237$		0			0
$238$	−1.64308	+	1.64308i	−0.106505	+	0.106505i
$239$	27.1404			1.75556			0.877782	−	0.479060i	$-0.159022\pi$
$239$	27.1404			1.75556			0.877782	+	0.479060i	$0.159022\pi$
$240$		0			0
$241$	−24.1442			−1.55526			−0.777632	−	0.628720i	$-0.783579\pi$
$241$	−24.1442			−1.55526			−0.777632	+	0.628720i	$0.783579\pi$
$242$	−19.6973	+	19.6973i	−1.26619	+	1.26619i
$243$		0			0
$244$			9.58635i			0.613703i
$245$	14.4736	+	4.37263i	0.924688	+	0.279357i
$246$		0			0
$247$	0.262697	+	0.262697i	0.0167150	+	0.0167150i
$248$	−26.2686	−	26.2686i	−1.66806	−	1.66806i
$249$		0			0
$250$	−2.68151	+	28.2087i	−0.169594	+	1.78408i
$251$		−	3.70131i		−	0.233625i	−0.993154	−	0.116812i	$-0.962732\pi$
$251$		−	3.70131i		−	0.233625i	0.993154	−	0.116812i	$-0.0372676\pi$
$252$		0			0
$253$	−0.0667796	+	0.0667796i	−0.00419839	+	0.00419839i
$254$	6.15022			0.385899
$255$		0			0
$256$	−30.2938			−1.89336
$257$	−17.1989	+	17.1989i	−1.07284	+	1.07284i	−0.0757080	+	0.997130i	$0.524122\pi$
$257$	−17.1989	+	17.1989i	−1.07284	+	1.07284i	−0.997130	+	0.0757080i	$0.975878\pi$
$258$		0			0
$259$		−	4.72270i		−	0.293454i
$260$	−10.2247	+	5.48011i	−0.634107	+	0.339862i
$261$		0			0
$262$	7.99567	+	7.99567i	0.493974	+	0.493974i
$263$	−11.6977	−	11.6977i	−0.721314	−	0.721314i	0.247559	−	0.968873i	$-0.420372\pi$
$263$	−11.6977	−	11.6977i	−0.721314	−	0.721314i	−0.968873	+	0.247559i	$0.920372\pi$
$264$		0			0
$265$	7.09126	−	3.80070i	0.435613	−	0.233475i
$266$		−	0.391855i		−	0.0240262i
$267$		0			0
$268$	−22.9331	+	22.9331i	−1.40086	+	1.40086i
$269$	7.31662			0.446102			0.223051	−	0.974807i	$-0.428398\pi$
$269$	7.31662			0.446102			0.223051	+	0.974807i	$0.428398\pi$
$270$		0			0
$271$	−26.6266			−1.61745			−0.808725	−	0.588187i	$-0.799842\pi$
$271$	−26.6266			−1.61745			−0.808725	+	0.588187i	$0.799842\pi$
$272$	8.92493	−	8.92493i	0.541153	−	0.541153i
$273$		0			0
$274$			0.689155i			0.0416334i
$275$	0.261451	−	0.393216i	0.0157661	−	0.0237118i
$276$		0			0
$277$	−0.930920	−	0.930920i	−0.0559335	−	0.0559335i	0.678587	−	0.734520i	$-0.262593\pi$
$277$	−0.930920	−	0.930920i	−0.0559335	−	0.0559335i	−0.734520	+	0.678587i	$0.762593\pi$
$278$	15.6933	+	15.6933i	0.941222	+	0.941222i
$279$		0			0
$280$	6.41712	+	1.93867i	0.383496	+	0.115858i
$281$		−	29.1290i		−	1.73769i	−0.495085	−	0.868845i	$-0.664863\pi$
$281$		−	29.1290i		−	1.73769i	0.495085	−	0.868845i	$-0.335137\pi$
$282$		0			0
$283$	−18.6893	+	18.6893i	−1.11096	+	1.11096i	−0.117941	+	0.993021i	$0.537629\pi$
$283$	−18.6893	+	18.6893i	−1.11096	+	1.11096i	−0.993021	+	0.117941i	$0.962371\pi$
$284$	−41.3114			−2.45138
$285$		0			0
$286$	0.280726			0.0165997
$287$	−3.02798	+	3.02798i	−0.178736	+	0.178736i
$288$		0			0
$289$			13.4718i			0.792460i
$290$	12.3915	+	23.1199i	0.727656	+	1.35764i
$291$		0			0
$292$	−25.5521	−	25.5521i	−1.49532	−	1.49532i
$293$	12.2105	+	12.2105i	0.713343	+	0.713343i	0.967233	−	0.253890i	$-0.0817101\pi$
$293$	12.2105	+	12.2105i	0.713343	+	0.713343i	−0.253890	+	0.967233i	$0.581710\pi$
$294$		0			0
$295$	6.00502	−	19.8770i	0.349626	−	1.15728i
$296$			59.4265i			3.45410i
$297$		0			0
$298$	29.0216	−	29.0216i	1.68118	−	1.68118i
$299$	−1.17285			−0.0678277
$300$		0			0
$301$	1.35277			0.0779723
$302$	−9.68729	+	9.68729i	−0.557441	+	0.557441i
$303$		0			0
$304$			2.12849i			0.122077i
$305$	1.40146	−	4.63892i	0.0802474	−	0.265624i
$306$		0			0
$307$	15.4101	+	15.4101i	0.879503	+	0.879503i	0.993483	−	0.113980i	$-0.0363600\pi$
$307$	15.4101	+	15.4101i	0.879503	+	0.879503i	−0.113980	+	0.993483i	$0.536360\pi$
$308$	−0.144183	−	0.144183i	−0.00821560	−	0.00821560i
$309$		0			0
$310$	16.1927	+	30.2120i	0.919685	+	1.71593i
$311$			24.9914i			1.41713i	0.705646	+	0.708565i	$0.250657\pi$
$311$			24.9914i			1.41713i	−0.705646	+	0.708565i	$0.749343\pi$
$312$		0			0
$313$	−16.9952	+	16.9952i	−0.960623	+	0.960623i	−0.999254	−	0.0386305i	$-0.987700\pi$
$313$	−16.9952	+	16.9952i	−0.960623	+	0.960623i	0.0386305	+	0.999254i	$0.487700\pi$
$314$	45.2250			2.55219
$315$		0			0
$316$	−70.2413			−3.95138
$317$	−9.66829	+	9.66829i	−0.543025	+	0.543025i	−0.924415	−	0.381389i	$-0.875446\pi$
$317$	−9.66829	+	9.66829i	−0.543025	+	0.543025i	0.381389	+	0.924415i	$0.375446\pi$
$318$		0			0
$319$		−	0.437129i		−	0.0244745i
$320$	3.01665	+	0.911358i	0.168636	+	0.0509465i
$321$		0			0
$322$	0.874747	+	0.874747i	0.0487478	+	0.0487478i
$323$	0.420715	+	0.420715i	0.0234092	+	0.0234092i
$324$		0			0
$325$	5.74896	−	1.15709i	0.318895	−	0.0641840i
$326$			43.7992i			2.42581i
$327$		0			0
$328$	38.1016	−	38.1016i	2.10381	−	2.10381i
$329$	2.97220			0.163863
$330$		0			0
$331$	−16.8804			−0.927832			−0.463916	−	0.885879i	$-0.653556\pi$
$331$	−16.8804			−0.927832			−0.463916	+	0.885879i	$0.653556\pi$
$332$	−18.7478	+	18.7478i	−1.02892	+	1.02892i
$333$		0			0
$334$		−	29.5009i		−	1.61422i
$335$	14.4502	−	7.74486i	0.789498	−	0.423147i
$336$		0			0
$337$	17.5498	+	17.5498i	0.955997	+	0.955997i	0.999072	−	0.0430746i	$-0.0137153\pi$
$337$	17.5498	+	17.5498i	0.955997	+	0.955997i	−0.0430746	+	0.999072i	$0.513715\pi$
$338$	−20.8324	−	20.8324i	−1.13313	−	1.13313i
$339$		0			0
$340$	−16.3750	+	8.77651i	−0.888061	+	0.475973i
$341$		−	0.571222i		−	0.0309334i
$342$		0			0
$343$	−4.74979	+	4.74979i	−0.256464	+	0.256464i
$344$	−17.0221			−0.917772
$345$		0			0
$346$	44.9796			2.41812
$347$	−19.8111	+	19.8111i	−1.06352	+	1.06352i	−0.0656760	+	0.997841i	$0.520920\pi$
$347$	−19.8111	+	19.8111i	−1.06352	+	1.06352i	−0.997841	+	0.0656760i	$0.979080\pi$
$348$		0			0
$349$			3.30027i			0.176660i	0.996091	+	0.0883298i	$0.0281529\pi$
$349$			3.30027i			0.176660i	−0.996091	+	0.0883298i	$0.971847\pi$
$350$	−5.15075	−	3.42476i	−0.275319	−	0.183061i
$351$		0			0
$352$	0.316974	+	0.316974i	0.0168948	+	0.0168948i
$353$	−8.34743	−	8.34743i	−0.444289	−	0.444289i	0.449162	−	0.893451i	$-0.351723\pi$
$353$	−8.34743	−	8.34743i	−0.444289	−	0.444289i	−0.893451	+	0.449162i	$0.851723\pi$
$354$		0			0
$355$	19.9909	+	6.03945i	1.06101	+	0.320541i
$356$		−	43.8111i		−	2.32198i
$357$		0			0
$358$	15.6488	−	15.6488i	0.827064	−	0.827064i
$359$	33.6482			1.77588			0.887941	−	0.459957i	$-0.152135\pi$
$359$	33.6482			1.77588			0.887941	+	0.459957i	$0.152135\pi$
$360$		0			0
$361$	18.8997			0.994719
$362$	0.0341091	−	0.0341091i	0.00179273	−	0.00179273i
$363$		0			0
$364$		−	2.53229i		−	0.132728i
$365$	8.62934	+	16.1004i	0.451680	+	0.842736i
$366$		0			0
$367$	−19.9796	−	19.9796i	−1.04292	−	1.04292i	−0.999036	−	0.0438879i	$-0.986026\pi$
$367$	−19.9796	−	19.9796i	−1.04292	−	1.04292i	−0.0438879	−	0.999036i	$-0.513974\pi$
$368$	−4.75148	−	4.75148i	−0.247688	−	0.247688i
$369$		0			0
$370$	15.8577	−	52.4899i	0.824402	−	2.72882i
$371$			1.75626i			0.0911802i
$372$		0			0
$373$	−3.88059	+	3.88059i	−0.200929	+	0.200929i	−0.800398	−	0.599469i	$-0.795379\pi$
$373$	−3.88059	+	3.88059i	−0.200929	+	0.200929i	0.599469	+	0.800398i	$0.295379\pi$
$374$	0.449589			0.0232477
$375$		0			0
$376$	−37.3998			−1.92875
$377$	3.83866	−	3.83866i	0.197701	−	0.197701i
$378$		0			0
$379$		−	6.13747i		−	0.315261i	−0.987498	−	0.157630i	$-0.949615\pi$
$379$		−	6.13747i		−	0.315261i	0.987498	−	0.157630i	$-0.0503854\pi$
$380$	0.906079	−	2.99918i	0.0464809	−	0.153854i
$381$		0			0
$382$	16.5000	+	16.5000i	0.844213	+	0.844213i
$383$	−12.1692	−	12.1692i	−0.621817	−	0.621817i	0.324178	−	0.945996i	$-0.394912\pi$
$383$	−12.1692	−	12.1692i	−0.621817	−	0.621817i	−0.945996	+	0.324178i	$0.894912\pi$
$384$		0			0
$385$	0.0486928	+	0.0908501i	0.00248162	+	0.00463015i
$386$		−	13.5655i		−	0.690467i
$387$		0			0
$388$	14.9057	−	14.9057i	0.756722	−	0.756722i
$389$	15.9745			0.809940			0.404970	−	0.914330i	$-0.367282\pi$
$389$	15.9745			0.809940			0.404970	+	0.914330i	$0.367282\pi$
$390$		0			0
$391$	−1.87834			−0.0949920
$392$	29.3664	−	29.3664i	1.48323	−	1.48323i
$393$		0			0
$394$		−	41.4926i		−	2.09036i
$395$	33.9904	+	10.2688i	1.71024	+	0.516680i
$396$		0			0
$397$	−8.69924	−	8.69924i	−0.436602	−	0.436602i	0.454265	−	0.890867i	$-0.349902\pi$
$397$	−8.69924	−	8.69924i	−0.436602	−	0.436602i	−0.890867	+	0.454265i	$0.849902\pi$
$398$	−18.5402	−	18.5402i	−0.929336	−	0.929336i
$399$		0			0
$400$	27.9780	+	18.6027i	1.39890	+	0.930136i
$401$			0.266455i			0.0133061i	0.999978	+	0.00665305i	$0.00211775\pi$
$401$			0.266455i			0.0133061i	−0.999978	+	0.00665305i	$0.997882\pi$
$402$		0			0
$403$	5.01619	−	5.01619i	0.249874	−	0.249874i
$404$	12.6096			0.627353
$405$		0			0
$406$	−5.72597			−0.284175
$407$	−0.646127	+	0.646127i	−0.0320273	+	0.0320273i
$408$		0			0
$409$		−	15.5804i		−	0.770400i	−0.922833	−	0.385200i	$-0.874133\pi$
$409$		−	15.5804i		−	0.770400i	0.922833	−	0.385200i	$-0.125867\pi$
$410$	−43.8213	+	23.4869i	−2.16418	+	1.15993i
$411$		0			0
$412$	−5.92923	−	5.92923i	−0.292112	−	0.292112i
$413$	3.20503	+	3.20503i	0.157709	+	0.157709i
$414$		0			0
$415$	11.8130	−	6.33141i	0.579878	−	0.310797i
$416$			5.56703i			0.272946i
$417$		0			0
$418$	−0.0536109	+	0.0536109i	−0.00262220	+	0.00262220i
$419$	33.3970			1.63155			0.815774	−	0.578371i	$-0.196311\pi$
$419$	33.3970			1.63155			0.815774	+	0.578371i	$0.196311\pi$
$420$		0			0
$421$	4.09270			0.199466			0.0997330	−	0.995014i	$-0.468201\pi$
$421$	4.09270			0.199466			0.0997330	+	0.995014i	$0.468201\pi$
$422$	45.9242	−	45.9242i	2.23556	−	2.23556i
$423$		0			0
$424$		−	22.0993i		−	1.07324i
$425$	9.20709	−	1.85311i	0.446609	−	0.0898890i
$426$		0			0
$427$	0.747994	+	0.747994i	0.0361980	+	0.0361980i
$428$	3.50568	+	3.50568i	0.169453	+	0.169453i
$429$		0			0
$430$	15.0352	+	4.54227i	0.725061	+	0.219048i
$431$		−	24.7647i		−	1.19288i	−0.802659	−	0.596438i	$-0.796582\pi$
$431$		−	24.7647i		−	1.19288i	0.802659	−	0.596438i	$-0.203418\pi$
$432$		0			0
$433$	−23.6661	+	23.6661i	−1.13732	+	1.13732i	−0.148390	+	0.988929i	$0.547409\pi$
$433$	−23.6661	+	23.6661i	−1.13732	+	1.13732i	−0.988929	+	0.148390i	$0.952591\pi$
$434$	−7.48246			−0.359169
$435$		0			0
$436$	90.6453			4.34112
$437$	0.223982	−	0.223982i	0.0107145	−	0.0107145i
$438$		0			0
$439$			32.0016i			1.52735i	0.645599	+	0.763676i	$0.276608\pi$
$439$			32.0016i			1.52735i	−0.645599	+	0.763676i	$0.723392\pi$
$440$	−0.612711	−	1.14318i	−0.0292098	−	0.0544991i
$441$		0			0
$442$	3.94807	+	3.94807i	0.187791	+	0.187791i
$443$	13.2627	+	13.2627i	0.630129	+	0.630129i	0.948100	−	0.317972i	$-0.103002\pi$
$443$	13.2627	+	13.2627i	0.630129	+	0.630129i	−0.317972	+	0.948100i	$0.603002\pi$
$444$		0			0
$445$	−6.40489	+	21.2006i	−0.303621	+	1.00500i
$446$		−	4.84332i		−	0.229338i
$447$		0			0
$448$	−0.486414	+	0.486414i	−0.0229809	+	0.0229809i
$449$	−2.04296			−0.0964130			−0.0482065	−	0.998837i	$-0.515351\pi$
$449$	−2.04296			−0.0964130			−0.0482065	+	0.998837i	$0.515351\pi$
$450$		0			0
$451$	0.828534			0.0390142
$452$	−8.50057	+	8.50057i	−0.399833	+	0.399833i
$453$		0			0
$454$			54.1004i			2.53906i
$455$	−0.370204	+	1.22540i	−0.0173554	+	0.0574475i
$456$		0			0
$457$	9.93931	+	9.93931i	0.464941	+	0.464941i	0.900271	−	0.435330i	$-0.143368\pi$
$457$	9.93931	+	9.93931i	0.464941	+	0.464941i	−0.435330	+	0.900271i	$0.643368\pi$
$458$	−17.6693	−	17.6693i	−0.825634	−	0.825634i
$459$		0			0
$460$	4.67247	+	8.71780i	0.217855	+	0.406469i
$461$			14.3885i			0.670139i	0.942193	+	0.335069i	$0.108760\pi$
$461$			14.3885i			0.670139i	−0.942193	+	0.335069i	$0.891240\pi$
$462$		0			0
$463$	9.95221	−	9.95221i	0.462518	−	0.462518i	−0.436962	−	0.899480i	$-0.643946\pi$
$463$	9.95221	−	9.95221i	0.462518	−	0.462518i	0.899480	+	0.436962i	$0.143946\pi$
$464$	31.1025			1.44390
$465$		0			0
$466$	44.9366			2.08165
$467$	−3.78951	+	3.78951i	−0.175358	+	0.175358i	−0.789329	−	0.613971i	$-0.789571\pi$
$467$	−3.78951	+	3.78951i	−0.175358	+	0.175358i	0.613971	+	0.789329i	$0.289571\pi$
$468$		0			0
$469$			3.57880i			0.165254i
$470$	33.0342	+	9.97995i	1.52375	+	0.460341i
$471$		0			0
$472$	−40.3294	−	40.3294i	−1.85631	−	1.85631i
$473$	−0.185077	−	0.185077i	−0.00850983	−	0.00850983i
$474$		0			0
$475$	−0.876919	+	1.31886i	−0.0402358	+	0.0605136i
$476$		−	4.05552i		−	0.185884i
$477$		0			0
$478$	−48.6388	+	48.6388i	−2.22469	+	2.22469i
$479$	−10.7935			−0.493168			−0.246584	−	0.969121i	$-0.579308\pi$
$479$	−10.7935			−0.493168			−0.246584	+	0.969121i	$0.579308\pi$
$480$		0			0
$481$	−11.3479			−0.517422
$482$	43.2693	−	43.2693i	1.97086	−	1.97086i
$483$		0			0
$484$		−	48.6179i		−	2.20990i
$485$	−9.39211	+	5.03388i	−0.426474	+	0.228577i
$486$		0			0
$487$	26.3689	+	26.3689i	1.19489	+	1.19489i	0.975677	+	0.219214i	$0.0703492\pi$
$487$	26.3689	+	26.3689i	1.19489	+	1.19489i	0.219214	+	0.975677i	$0.429651\pi$
$488$	−9.41214	−	9.41214i	−0.426068	−	0.426068i
$489$		0			0
$490$	−33.7748	+	18.1023i	−1.52579	+	0.817776i
$491$			4.70672i			0.212411i	0.994344	+	0.106206i	$0.0338702\pi$
$491$			4.70672i			0.212411i	−0.994344	+	0.106206i	$0.966130\pi$
$492$		0			0
$493$	6.14769	−	6.14769i	0.276878	−	0.276878i
$494$	−0.941570			−0.0423632
$495$		0			0
$496$	40.6435			1.82495
$497$	−3.22340	+	3.22340i	−0.144589	+	0.144589i
$498$		0			0
$499$			40.8405i			1.82827i	0.405407	+	0.914136i	$0.367130\pi$
$499$			40.8405i			1.82827i	−0.405407	+	0.914136i	$0.632870\pi$
$500$	−31.5037	−	38.1224i	−1.40889	−	1.70488i
$501$		0			0
$502$	6.63320	+	6.63320i	0.296054	+	0.296054i
$503$	10.1545	+	10.1545i	0.452766	+	0.452766i	0.896272	−	0.443506i	$-0.146265\pi$
$503$	10.1545	+	10.1545i	0.452766	+	0.452766i	−0.443506	+	0.896272i	$0.646265\pi$
$504$		0			0
$505$	−6.10191	−	1.84345i	−0.271532	−	0.0820322i
$506$		−	0.239354i		−	0.0106406i
$507$		0			0
$508$	−7.59012	+	7.59012i	−0.336757	+	0.336757i
$509$	35.8608			1.58950			0.794751	−	0.606935i	$-0.207601\pi$
$509$	35.8608			1.58950			0.794751	+	0.606935i	$0.207601\pi$
$510$		0			0
$511$	−3.98751			−0.176397
$512$	35.8134	−	35.8134i	1.58274	−	1.58274i
$513$		0			0
$514$		−	61.6450i		−	2.71905i
$515$	2.00239	+	3.73602i	0.0882360	+	0.164629i
$516$		0			0
$517$	−0.406636	−	0.406636i	−0.0178839	−	0.0178839i
$518$	8.46364	+	8.46364i	0.371871	+	0.371871i
$519$		0			0
$520$	4.65835	−	15.4194i	0.204282	−	0.676185i
$521$			1.28945i			0.0564920i	0.999601	+	0.0282460i	$0.00899218\pi$
$521$			1.28945i			0.0564920i	−0.999601	+	0.0282460i	$0.991008\pi$
$522$		0			0
$523$	−9.76891	+	9.76891i	−0.427165	+	0.427165i	−0.887661	−	0.460497i	$-0.847671\pi$
$523$	−9.76891	+	9.76891i	−0.427165	+	0.427165i	0.460497	+	0.887661i	$0.347671\pi$
$524$	−19.7353			−0.862139
$525$		0			0
$526$	41.9276			1.82813
$527$	8.03354	−	8.03354i	0.349946	−	0.349946i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−5.89709	+	19.5197i	−0.256153	+	0.847882i
$531$		0			0
$532$	0.483597	+	0.483597i	0.0209666	+	0.0209666i
$533$	7.27578	+	7.27578i	0.315149	+	0.315149i
$534$		0			0
$535$	−1.18392	−	2.20894i	−0.0511854	−	0.0955006i
$536$		−	45.0327i		−	1.94512i
$537$		0			0
$538$	−13.1123	+	13.1123i	−0.565310	+	0.565310i
$539$	0.638583			0.0275057
$540$		0			0
$541$	−6.43591			−0.276701			−0.138351	−	0.990383i	$-0.544180\pi$
$541$	−6.43591			−0.276701			−0.138351	+	0.990383i	$0.544180\pi$
$542$	47.7180	−	47.7180i	2.04967	−	2.04967i
$543$		0			0
$544$			8.91571i			0.382258i
$545$	−43.8641	−	13.2518i	−1.87893	−	0.567643i
$546$		0			0
$547$	−8.70091	−	8.70091i	−0.372024	−	0.372024i	0.496190	−	0.868214i	$-0.334732\pi$
$547$	−8.70091	−	8.70091i	−0.372024	−	0.372024i	−0.868214	+	0.496190i	$0.834732\pi$
$548$	−0.850502	−	0.850502i	−0.0363316	−	0.0363316i
$549$		0			0
$550$	0.236138	+	1.17324i	0.0100690	+	0.0500272i
$551$			1.46615i			0.0624602i
$552$		0			0
$553$	−5.48072	+	5.48072i	−0.233064	+	0.233064i
$554$	3.33664			0.141760
$555$		0			0
$556$	−38.7349			−1.64273
$557$	−1.55440	+	1.55440i	−0.0658622	+	0.0658622i	−0.739271	−	0.673408i	$-0.764830\pi$
$557$	−1.55440	+	1.55440i	−0.0658622	+	0.0658622i	0.673408	+	0.739271i	$0.264830\pi$
$558$		0			0
$559$		−	3.25050i		−	0.137482i
$560$	−6.46415	+	3.46458i	−0.273160	+	0.146405i
$561$		0			0
$562$	52.2027	+	52.2027i	2.20204	+	2.20204i
$563$	−21.0632	−	21.0632i	−0.887707	−	0.887707i	0.106595	−	0.994303i	$-0.466005\pi$
$563$	−21.0632	−	21.0632i	−0.887707	−	0.887707i	−0.994303	+	0.106595i	$0.966005\pi$
$564$		0			0
$565$	5.35623	−	2.87077i	0.225338	−	0.120774i
$566$		−	66.9868i		−	2.81567i
$567$		0			0
$568$	40.5607	−	40.5607i	1.70189	−	1.70189i
$569$	−8.85122			−0.371062			−0.185531	−	0.982638i	$-0.559401\pi$
$569$	−8.85122			−0.371062			−0.185531	+	0.982638i	$0.559401\pi$
$570$		0			0
$571$	39.7197			1.66222			0.831108	−	0.556111i	$-0.187707\pi$
$571$	39.7197			1.66222			0.831108	+	0.556111i	$0.187707\pi$
$572$	−0.346451	+	0.346451i	−0.0144858	+	0.0144858i
$573$		0			0
$574$		−	10.8530i		−	0.452995i
$575$	−0.986565	−	4.90170i	−0.0411426	−	0.204415i
$576$		0			0
$577$	6.27513	+	6.27513i	0.261237	+	0.261237i	0.825556	−	0.564320i	$-0.190861\pi$
$577$	6.27513	+	6.27513i	0.261237	+	0.261237i	−0.564320	+	0.825556i	$0.690861\pi$
$578$	−24.1431	−	24.1431i	−1.00422	−	1.00422i
$579$		0			0
$580$	−43.8254	−	13.2401i	−1.81975	−	0.549764i
$581$			2.92567i			0.121377i
$582$		0			0
$583$	0.240279	−	0.240279i	0.00995134	−	0.00995134i
$584$	50.1756			2.07628
$585$		0			0
$586$	−43.7653			−1.80793
$587$	30.2135	−	30.2135i	1.24704	−	1.24704i	0.290024	−	0.957019i	$-0.406337\pi$
$587$	30.2135	−	30.2135i	1.24704	−	1.24704i	0.957019	−	0.290024i	$-0.0936634\pi$
$588$		0			0
$589$			1.91591i			0.0789435i
$590$	24.8602	+	46.3836i	1.02348	+	1.90958i
$591$		0			0
$592$	−45.9731	−	45.9731i	−1.88948	−	1.88948i
$593$	−29.4511	−	29.4511i	−1.20941	−	1.20941i	−0.971217	−	0.238196i	$-0.923444\pi$
$593$	−29.4511	−	29.4511i	−1.20941	−	1.20941i	−0.238196	−	0.971217i	$-0.576556\pi$
$594$		0			0
$595$	−0.592890	+	1.96250i	−0.0243061	+	0.0804546i
$596$			71.6324i			2.93418i
$597$		0			0
$598$	2.10189	−	2.10189i	0.0859526	−	0.0859526i
$599$	−3.22513			−0.131775			−0.0658877	−	0.997827i	$-0.520988\pi$
$599$	−3.22513			−0.131775			−0.0658877	+	0.997827i	$0.520988\pi$
$600$		0			0
$601$	−16.9745			−0.692402			−0.346201	−	0.938160i	$-0.612529\pi$
$601$	−16.9745			−0.692402			−0.346201	+	0.938160i	$0.612529\pi$
$602$	−2.42432	+	2.42432i	−0.0988081	+	0.0988081i
$603$		0			0
$604$		−	23.9106i		−	0.972908i
$605$	−7.10761	+	23.5266i	−0.288965	+	0.956493i
$606$		0			0
$607$	−17.2933	−	17.2933i	−0.701915	−	0.701915i	0.262906	−	0.964821i	$-0.415319\pi$
$607$	−17.2933	−	17.2933i	−0.701915	−	0.701915i	−0.964821	+	0.262906i	$0.915319\pi$
$608$	−1.06315	−	1.06315i	−0.0431163	−	0.0431163i
$609$		0			0
$610$	5.80191	+	10.8251i	0.234913	+	0.438295i
$611$		−	7.14176i		−	0.288925i
$612$		0			0
$613$	−18.2273	+	18.2273i	−0.736193	+	0.736193i	−0.971839	−	0.235646i	$-0.924279\pi$
$613$	−18.2273	+	18.2273i	−0.736193	+	0.736193i	0.235646	+	0.971839i	$0.424279\pi$
$614$	−55.2337			−2.22905
$615$		0			0
$616$	0.283126			0.0114075
$617$	−31.0949	+	31.0949i	−1.25183	+	1.25183i	−0.296938	+	0.954897i	$0.595965\pi$
$617$	−31.0949	+	31.0949i	−1.25183	+	1.25183i	−0.954897	+	0.296938i	$0.904035\pi$
$618$		0			0
$619$		−	27.7742i		−	1.11634i	−0.829726	−	0.558170i	$-0.811504\pi$
$619$		−	27.7742i		−	1.11634i	0.829726	−	0.558170i	$-0.188496\pi$
$620$	−57.2692	−	17.3016i	−2.29998	−	0.694847i
$621$		0			0
$622$	−44.7875	−	44.7875i	−1.79582	−	1.79582i
$623$	−3.41845	−	3.41845i	−0.136957	−	0.136957i
$624$		0			0
$625$	9.67170	+	23.0534i	0.386868	+	0.922135i
$626$		−	60.9147i		−	2.43464i
$627$		0			0
$628$	−55.8132	+	55.8132i	−2.22719	+	2.22719i
$629$	−18.1740			−0.724644
$630$		0			0
$631$	−30.9859			−1.23353			−0.616764	−	0.787148i	$-0.711557\pi$
$631$	−30.9859			−1.23353			−0.616764	+	0.787148i	$0.711557\pi$
$632$	68.9649	−	68.9649i	2.74327	−	2.74327i
$633$		0			0
$634$		−	34.6535i		−	1.37627i
$635$	4.78255	−	2.56330i	0.189790	−	0.101721i
$636$		0			0
$637$	5.60773	+	5.60773i	0.222186	+	0.222186i
$638$	0.783389	+	0.783389i	0.0310147	+	0.0310147i
$639$		0			0
$640$	−25.7489	+	13.8006i	−1.01782	+	0.545518i
$641$			18.6196i			0.735430i	0.929939	+	0.367715i	$0.119860\pi$
$641$			18.6196i			0.735430i	−0.929939	+	0.367715i	$0.880140\pi$
$642$		0			0
$643$	−4.17084	+	4.17084i	−0.164482	+	0.164482i	−0.784549	−	0.620067i	$-0.787105\pi$
$643$	−4.17084	+	4.17084i	−0.164482	+	0.164482i	0.620067	+	0.784549i	$0.287105\pi$
$644$	−2.15909			−0.0850801
$645$		0			0
$646$	−1.50794			−0.0593293
$647$	17.6451	−	17.6451i	0.693702	−	0.693702i	−0.269342	−	0.963044i	$-0.586806\pi$
$647$	17.6451	−	17.6451i	0.693702	−	0.693702i	0.963044	+	0.269342i	$0.0868064\pi$
$648$		0			0
$649$		−	0.876980i		−	0.0344245i
$650$	−8.22919	+	12.3765i	−0.322775	+	0.485446i
$651$		0			0
$652$	−54.0536	−	54.0536i	−2.11690	−	2.11690i
$653$	21.0461	+	21.0461i	0.823598	+	0.823598i	0.986622	−	0.163024i	$-0.0521248\pi$
$653$	21.0461	+	21.0461i	0.823598	+	0.823598i	−0.163024	+	0.986622i	$0.552125\pi$
$654$		0			0
$655$	9.55007	+	2.88517i	0.373152	+	0.112733i
$656$			58.9517i			2.30168i
$657$		0			0
$658$	−5.32654	+	5.32654i	−0.207650	+	0.207650i
$659$	0.731375			0.0284903			0.0142452	−	0.999899i	$-0.495465\pi$
$659$	0.731375			0.0284903			0.0142452	+	0.999899i	$0.495465\pi$
$660$		0			0
$661$	26.4957			1.03056			0.515282	−	0.857020i	$-0.327687\pi$
$661$	26.4957			1.03056			0.515282	+	0.857020i	$0.327687\pi$
$662$	30.2518	−	30.2518i	1.17577	−	1.17577i
$663$		0			0
$664$		−	36.8142i		−	1.42867i
$665$	−0.163318	−	0.304715i	−0.00633320	−	0.0118164i
$666$		0			0
$667$	−3.27293	−	3.27293i	−0.126728	−	0.126728i
$668$	36.4077	+	36.4077i	1.40866	+	1.40866i
$669$		0			0
$670$	−12.0168	+	39.7762i	−0.464248	+	1.53669i
$671$		−	0.204671i		−	0.00790123i
$672$		0			0
$673$	31.3051	−	31.3051i	1.20672	−	1.20672i	0.234643	−	0.972082i	$-0.424608\pi$
$673$	31.3051	−	31.3051i	1.20672	−	1.20672i	0.972082	−	0.234643i	$-0.0753920\pi$
$674$	−62.9026			−2.42292
$675$		0			0
$676$	51.4194			1.97767
$677$	−19.9605	+	19.9605i	−0.767145	+	0.767145i	−0.977603	−	0.210458i	$-0.932504\pi$
$677$	−19.9605	+	19.9605i	−0.767145	+	0.767145i	0.210458	+	0.977603i	$0.432504\pi$
$678$		0			0
$679$		−	2.32609i		−	0.0892673i
$680$	7.46044	−	24.6945i	0.286095	−	0.946991i
$681$		0			0
$682$	1.02370	+	1.02370i	0.0391995	+	0.0391995i
$683$	5.19418	+	5.19418i	0.198750	+	0.198750i	0.799464	−	0.600714i	$-0.205117\pi$
$683$	5.19418	+	5.19418i	0.198750	+	0.198750i	−0.600714	+	0.799464i	$0.705117\pi$
$684$		0			0
$685$	0.287227	+	0.535903i	0.0109744	+	0.0204758i
$686$		−	17.0244i		−	0.649994i
$687$		0			0
$688$	13.1685	−	13.1685i	0.502045	−	0.502045i
$689$	4.22002			0.160770
$690$		0			0
$691$	−3.99236			−0.151876			−0.0759382	−	0.997113i	$-0.524195\pi$
$691$	−3.99236			−0.151876			−0.0759382	+	0.997113i	$0.524195\pi$
$692$	−55.5103	+	55.5103i	−2.11018	+	2.11018i
$693$		0			0
$694$		−	71.0079i		−	2.69542i
$695$	18.7442	+	5.66279i	0.711007	+	0.214802i
$696$		0			0
$697$	11.6523	+	11.6523i	0.441363	+	0.441363i
$698$	−5.91449	−	5.91449i	−0.223867	−	0.223867i
$699$		0			0
$700$	10.5832	−	2.13008i	0.400008	−	0.0805096i
$701$			28.4253i			1.07361i	0.843707	+	0.536804i	$0.180368\pi$
$701$			28.4253i			1.07361i	−0.843707	+	0.536804i	$0.819632\pi$
$702$		0			0
$703$	2.16714	−	2.16714i	0.0817353	−	0.0817353i
$704$	0.133096			0.00501624
$705$		0			0
$706$	29.9192			1.12602
$707$	0.983892	−	0.983892i	0.0370031	−	0.0370031i
$708$		0			0
$709$			6.74285i			0.253233i	0.991952	+	0.126617i	$0.0404118\pi$
$709$			6.74285i			0.253233i	−0.991952	+	0.126617i	$0.959588\pi$
$710$	−46.6496	+	25.0027i	−1.75073	+	0.938336i
$711$		0			0
$712$	43.0150	+	43.0150i	1.61205	+	1.61205i
$713$	−4.27692	−	4.27692i	−0.160172	−	0.160172i
$714$		0			0
$715$	0.218299	−	0.117002i	0.00816393	−	0.00437562i
$716$			38.6250i			1.44349i
$717$		0			0
$718$	−60.3016	+	60.3016i	−2.25043	+	2.25043i
$719$	15.6422			0.583354			0.291677	−	0.956517i	$-0.405787\pi$
$719$	15.6422			0.583354			0.291677	+	0.956517i	$0.405787\pi$
$720$		0			0
$721$	−0.925281			−0.0344593
$722$	−33.8705	+	33.8705i	−1.26053	+	1.26053i
$723$		0			0
$724$			0.0841895i			0.00312888i
$725$	19.2719	+	12.8140i	0.715740	+	0.475899i
$726$		0			0
$727$	17.3397	+	17.3397i	0.643093	+	0.643093i	0.951315	−	0.308222i	$-0.0997339\pi$
$727$	17.3397	+	17.3397i	0.643093	+	0.643093i	−0.308222	+	0.951315i	$0.599734\pi$
$728$	2.48627	+	2.48627i	0.0921475	+	0.0921475i
$729$		0			0
$730$	−44.3188	−	13.3891i	−1.64031	−	0.495553i
$731$		−	5.20575i		−	0.192542i
$732$		0			0
$733$	24.1866	−	24.1866i	0.893352	−	0.893352i	−0.101485	−	0.994837i	$-0.532359\pi$
$733$	24.1866	−	24.1866i	0.893352	−	0.893352i	0.994837	+	0.101485i	$0.0323594\pi$
$734$	71.6116			2.64323
$735$		0			0
$736$	4.74658			0.174961
$737$	0.489627	−	0.489627i	0.0180357	−	0.0180357i
$738$		0			0
$739$		−	19.1846i		−	0.705716i	−0.935677	−	0.352858i	$-0.885210\pi$
$739$		−	19.1846i		−	0.705716i	0.935677	−	0.352858i	$-0.114790\pi$
$740$	45.2086	+	84.3493i	1.66190	+	3.10074i
$741$		0			0
$742$	−3.14742	−	3.14742i	−0.115545	−	0.115545i
$743$	−4.92023	−	4.92023i	−0.180506	−	0.180506i	0.611070	−	0.791576i	$-0.290739\pi$
$743$	−4.92023	−	4.92023i	−0.180506	−	0.180506i	−0.791576	+	0.611070i	$0.790739\pi$
$744$		0			0
$745$	10.4722	−	34.6636i	0.383671	−	1.26997i
$746$		−	13.9090i		−	0.509244i
$747$		0			0
$748$	−0.554848	+	0.554848i	−0.0202873	+	0.0202873i
$749$	0.547075			0.0199897
$750$		0			0
$751$	−23.0185			−0.839956			−0.419978	−	0.907534i	$-0.637962\pi$
$751$	−23.0185			−0.839956			−0.419978	+	0.907534i	$0.637962\pi$
$752$	28.9329	−	28.9329i	1.05507	−	1.05507i
$753$		0			0
$754$			13.7587i			0.501061i
$755$	−3.49557	+	11.5705i	−0.127217	+	0.421095i
$756$		0			0
$757$	−6.52034	−	6.52034i	−0.236986	−	0.236986i	0.578615	−	0.815601i	$-0.303593\pi$
$757$	−6.52034	−	6.52034i	−0.236986	−	0.236986i	−0.815601	+	0.578615i	$0.803593\pi$
$758$	10.9991	+	10.9991i	0.399505	+	0.399505i
$759$		0			0
$760$	2.05506	+	3.83429i	0.0745449	+	0.139084i
$761$			21.4235i			0.776601i	0.921533	+	0.388300i	$0.126938\pi$
$761$			21.4235i			0.776601i	−0.921533	+	0.388300i	$0.873062\pi$
$762$		0			0
$763$	7.07279	−	7.07279i	0.256052	−	0.256052i
$764$	−40.7260			−1.47342
$765$		0			0
$766$	43.6174			1.57596
$767$	7.70121	−	7.70121i	0.278075	−	0.278075i
$768$		0			0
$769$		−	19.4517i		−	0.701445i	−0.936479	−	0.350723i	$-0.885936\pi$
$769$		−	19.4517i		−	0.701445i	0.936479	−	0.350723i	$-0.114064\pi$
$770$	−0.250078	−	0.0755509i	−0.00901218	−	0.00272266i
$771$		0			0
$772$	16.7415	+	16.7415i	0.602540	+	0.602540i
$773$	−3.65076	−	3.65076i	−0.131309	−	0.131309i	0.638398	−	0.769707i	$-0.279597\pi$
$773$	−3.65076	−	3.65076i	−0.131309	−	0.131309i	−0.769707	+	0.638398i	$0.779597\pi$
$774$		0			0
$775$	25.1837	+	16.7447i	0.904624	+	0.601489i
$776$			29.2697i			1.05072i
$777$		0			0
$778$	−28.6283	+	28.6283i	−1.02637	+	1.02637i
$779$	−2.77894			−0.0995660
$780$		0			0
$781$	0.882008			0.0315607
$782$	3.36622	−	3.36622i	0.120376	−	0.120376i
$783$		0			0
$784$			45.4364i			1.62273i
$785$	35.1680	−	18.8490i	1.25520	−	0.672748i
$786$		0			0
$787$	−30.9134	−	30.9134i	−1.10194	−	1.10194i	−0.994176	−	0.107768i	$-0.965630\pi$
$787$	−30.9134	−	30.9134i	−1.10194	−	1.10194i	−0.107768	−	0.994176i	$-0.534370\pi$
$788$	51.2069	+	51.2069i	1.82417	+	1.82417i
$789$		0			0
$790$	−79.3178	+	42.5119i	−2.82200	+	1.51250i
$791$			1.32655i			0.0471666i
$792$		0			0
$793$	1.79732	−	1.79732i	0.0638247	−	0.0638247i
$794$	31.1802			1.10654
$795$		0			0
$796$	45.7617			1.62198
$797$	−34.3416	+	34.3416i	−1.21644	+	1.21644i	−0.247575	+	0.968869i	$0.579634\pi$
$797$	−34.3416	+	34.3416i	−1.21644	+	1.21644i	−0.968869	+	0.247575i	$0.920366\pi$
$798$		0			0
$799$		−	11.4377i		−	0.404636i
$800$	−23.2663	+	4.68281i	−0.822588	+	0.165562i
$801$		0			0
$802$	−0.477519	−	0.477519i	−0.0168618	−	0.0168618i
$803$	0.545544	+	0.545544i	0.0192518	+	0.0192518i
$804$		0			0
$805$	1.04480	+	0.315645i	0.0368245	+	0.0111250i
$806$			17.9792i			0.633292i
$807$		0			0
$808$	−12.3805	+	12.3805i	−0.435544	+	0.435544i
$809$	−26.9595			−0.947844			−0.473922	−	0.880567i	$-0.657162\pi$
$809$	−26.9595			−0.947844			−0.473922	+	0.880567i	$0.657162\pi$
$810$		0			0
$811$	7.17135			0.251820			0.125910	−	0.992042i	$-0.459815\pi$
$811$	7.17135			0.251820			0.125910	+	0.992042i	$0.459815\pi$
$812$	7.06655	−	7.06655i	0.247987	−	0.247987i
$813$		0			0
$814$		−	2.31588i		−	0.0811714i
$815$	18.2547	+	34.0593i	0.639435	+	1.19304i
$816$		0			0
$817$	0.620755	+	0.620755i	0.0217175	+	0.0217175i
$818$	27.9219	+	27.9219i	0.976266	+	0.976266i
$819$		0			0
$820$	25.0952	−	83.0666i	0.876362	−	2.90081i
$821$			37.6285i			1.31324i	0.754221	+	0.656621i	$0.228015\pi$
$821$			37.6285i			1.31324i	−0.754221	+	0.656621i	$0.771985\pi$
$822$		0			0
$823$	8.39144	−	8.39144i	0.292507	−	0.292507i	−0.545563	−	0.838070i	$-0.683684\pi$
$823$	8.39144	−	8.39144i	0.292507	−	0.292507i	0.838070	+	0.545563i	$0.183684\pi$
$824$	11.6430			0.405602
$825$		0			0
$826$	−11.4876			−0.399704
$827$	22.6642	−	22.6642i	0.788111	−	0.788111i	−0.193073	−	0.981184i	$-0.561845\pi$
$827$	22.6642	−	22.6642i	0.788111	−	0.788111i	0.981184	+	0.193073i	$0.0618455\pi$
$828$		0			0
$829$			21.2872i			0.739334i	0.929164	+	0.369667i	$0.120528\pi$
$829$			21.2872i			0.739334i	−0.929164	+	0.369667i	$0.879472\pi$
$830$	−9.82369	+	32.5170i	−0.340985	+	1.12868i
$831$		0			0
$832$	1.16878	+	1.16878i	0.0405202	+	0.0405202i
$833$	8.98089	+	8.98089i	0.311169	+	0.311169i
$834$		0			0
$835$	−12.2954	−	22.9406i	−0.425501	−	0.793891i
$836$		−	0.132325i		−	0.00457655i
$837$		0			0
$838$	−59.8514	+	59.8514i	−2.06753	+	2.06753i
$839$	15.9644			0.551153			0.275576	−	0.961279i	$-0.411131\pi$
$839$	15.9644			0.551153			0.275576	+	0.961279i	$0.411131\pi$
$840$		0			0
$841$	−7.57588			−0.261237
$842$	−7.33461	+	7.33461i	−0.252767	+	0.252767i
$843$		0			0
$844$			113.352i			3.90174i
$845$	−24.8823	−	7.51717i	−0.855977	−	0.258599i
$846$		0			0
$847$	−3.79351	−	3.79351i	−0.130346	−	0.130346i
$848$	17.0963	+	17.0963i	0.587089	+	0.587089i
$849$		0			0
$850$	−13.1792	+	19.8212i	−0.452043	+	0.679862i
$851$			9.67552i			0.331673i
$852$		0			0
$853$	−28.6451	+	28.6451i	−0.980790	+	0.980790i	−0.999819	−	0.0190293i	$-0.993942\pi$
$853$	−28.6451	+	28.6451i	−0.980790	+	0.980790i	0.0190293	+	0.999819i	$0.493942\pi$
$854$	−2.68099			−0.0917416
$855$		0			0
$856$	−6.88395			−0.235289
$857$	12.3396	−	12.3396i	0.421512	−	0.421512i	−0.464212	−	0.885724i	$-0.653662\pi$
$857$	12.3396	−	12.3396i	0.421512	−	0.421512i	0.885724	+	0.464212i	$0.153662\pi$
$858$		0			0
$859$		−	17.4472i		−	0.595290i	−0.954677	−	0.297645i	$-0.903799\pi$
$859$		−	17.4472i		−	0.595290i	0.954677	−	0.297645i	$-0.0962012\pi$
$860$	−24.1610	+	12.9495i	−0.823883	+	0.441576i
$861$		0			0
$862$	44.3814	+	44.3814i	1.51164	+	1.51164i
$863$	3.42850	+	3.42850i	0.116707	+	0.116707i	0.763049	−	0.646341i	$-0.223702\pi$
$863$	3.42850	+	3.42850i	0.116707	+	0.116707i	−0.646341	+	0.763049i	$0.723702\pi$
$864$		0			0
$865$	34.9771	−	18.7467i	1.18926	−	0.637406i
$866$		−	84.8249i		−	2.88247i
$867$		0			0
$868$	9.23427	−	9.23427i	0.313431	−	0.313431i
$869$	1.49967			0.0508728
$870$		0			0
$871$	8.59933			0.291377
$872$	−88.9982	+	88.9982i	−3.01386	+	3.01386i
$873$		0			0
$874$			0.802805i			0.0271553i
$875$	−5.43272	−	0.516431i	−0.183659	−	0.0174586i
$876$		0			0
$877$	−3.41921	−	3.41921i	−0.115459	−	0.115459i	0.647017	−	0.762476i	$-0.276016\pi$
$877$	−3.41921	−	3.41921i	−0.115459	−	0.115459i	−0.762476	+	0.647017i	$0.776016\pi$
$878$	−57.3507	−	57.3507i	−1.93549	−	1.93549i
$879$		0			0
$880$	1.35838	+	0.410380i	0.0457910	+	0.0138339i
$881$		−	53.8030i		−	1.81267i	−0.422561	−	0.906334i	$-0.638869\pi$
$881$		−	53.8030i		−	1.81267i	0.422561	−	0.906334i	$-0.361131\pi$
$882$		0			0
$883$	14.5823	−	14.5823i	0.490732	−	0.490732i	−0.417805	−	0.908537i	$-0.637200\pi$
$883$	14.5823	−	14.5823i	0.490732	−	0.490732i	0.908537	+	0.417805i	$0.137200\pi$
$884$	−9.74481			−0.327753
$885$		0			0
$886$	−47.5366			−1.59702
$887$	−12.4623	+	12.4623i	−0.418442	+	0.418442i	−0.884666	−	0.466225i	$-0.845614\pi$
$887$	−12.4623	+	12.4623i	−0.418442	+	0.418442i	0.466225	+	0.884666i	$0.345614\pi$
$888$		0			0
$889$			1.18447i			0.0397258i
$890$	−26.5156	−	49.4723i	−0.888806	−	1.65832i
$891$		0			0
$892$	5.97724	+	5.97724i	0.200133	+	0.200133i
$893$	1.36388	+	1.36388i	0.0456404	+	0.0456404i
$894$		0			0
$895$	5.64672	−	18.6910i	0.188749	−	0.624771i
$896$		−	6.37711i		−	0.213044i
$897$		0			0
$898$	3.66122	−	3.66122i	0.122177	−	0.122177i
$899$	27.9961			0.933723
$900$		0			0
$901$	6.75846			0.225157
$902$	−1.48483	+	1.48483i	−0.0494396	+	0.0494396i
$903$		0			0
$904$		−	16.6922i		−	0.555174i
$905$	0.0123079	−	0.0407400i	0.000409130	−	0.00135424i
$906$		0			0
$907$	30.5342	+	30.5342i	1.01387	+	1.01387i	0.999902	+	0.0139686i	$0.00444648\pi$
$907$	30.5342	+	30.5342i	1.01387	+	1.01387i	0.0139686	+	0.999902i	$0.495554\pi$
$908$	−66.7665	−	66.7665i	−2.21572	−	2.21572i
$909$		0			0
$910$	−1.53261	−	2.85951i	−0.0508055	−	0.0947918i
$911$		−	2.96535i		−	0.0982464i	−0.998793	−	0.0491232i	$-0.984357\pi$
$911$		−	2.96535i		−	0.0982464i	0.998793	−	0.0491232i	$-0.0156427\pi$
$912$		0			0
$913$	0.400270	−	0.400270i	0.0132470	−	0.0132470i
$914$	−35.6249			−1.17837
$915$		0			0
$916$	43.6123			1.44099
$917$	−1.53988	+	1.53988i	−0.0508515	+	0.0508515i
$918$		0			0
$919$		−	38.4804i		−	1.26935i	−0.772778	−	0.634676i	$-0.781134\pi$
$919$		−	38.4804i		−	1.26935i	0.772778	−	0.634676i	$-0.218866\pi$
$920$	−13.1469	−	3.97182i	−0.433442	−	0.130947i
$921$		0			0
$922$	−25.7859	−	25.7859i	−0.849213	−	0.849213i
$923$	7.74536	+	7.74536i	0.254942	+	0.254942i
$924$		0			0
$925$	−9.54553	−	47.4265i	−0.313855	−	1.55938i
$926$			35.6711i			1.17223i
$927$		0			0
$928$	−15.5352	+	15.5352i	−0.509968	+	0.509968i
$929$	16.5260			0.542201			0.271101	−	0.962551i	$-0.412612\pi$
$929$	16.5260			0.542201			0.271101	+	0.962551i	$0.412612\pi$
$930$		0			0
$931$	−2.14184			−0.0701959
$932$	−55.4572	+	55.4572i	−1.81656	+	1.81656i
$933$		0			0
$934$		−	13.5825i		−	0.444433i
$935$	0.349611	−	0.187381i	0.0114335	−	0.00612801i
$936$		0			0
$937$	−28.3632	−	28.3632i	−0.926585	−	0.926585i	0.0708982	−	0.997484i	$-0.477413\pi$
$937$	−28.3632	−	28.3632i	−0.926585	−	0.926585i	−0.997484	+	0.0708982i	$0.977413\pi$
$938$	−6.41364	−	6.41364i	−0.209413	−	0.209413i
$939$		0			0
$940$	−53.0847	+	28.4518i	−1.73143	+	0.927995i
$941$		−	20.5082i		−	0.668548i	−0.942476	−	0.334274i	$-0.891509\pi$
$941$		−	20.5082i		−	0.668548i	0.942476	−	0.334274i	$-0.108491\pi$
$942$		0			0
$943$	6.20350	−	6.20350i	0.202014	−	0.202014i
$944$	62.3987			2.03091
$945$		0			0
$946$	0.663359			0.0215677
$947$	−39.5888	+	39.5888i	−1.28646	+	1.28646i	−0.349541	+	0.936921i	$0.613662\pi$
$947$	−39.5888	+	39.5888i	−1.28646	+	1.28646i	−0.936921	+	0.349541i	$0.886338\pi$
$948$		0			0
$949$			9.58140i			0.311025i
$950$	−0.792019	−	3.93511i	−0.0256965	−	0.127672i
$951$		0			0
$952$	3.98182	+	3.98182i	0.129052	+	0.129052i
$953$	−9.98868	−	9.98868i	−0.323565	−	0.323565i	0.526568	−	0.850133i	$-0.323479\pi$
$953$	−9.98868	−	9.98868i	−0.323565	−	0.323565i	−0.850133	+	0.526568i	$0.823479\pi$
$954$		0			0
$955$	19.7077	+	5.95387i	0.637725	+	0.192663i
$956$		−	120.052i		−	3.88277i
$957$		0			0
$958$	19.3433	−	19.3433i	0.624953	−	0.624953i
$959$	−0.132724			−0.00428589
$960$		0			0
$961$	5.58415			0.180134
$962$	20.3369	−	20.3369i	0.655687	−	0.655687i
$963$		0			0
$964$			106.799i			3.43977i
$965$	−5.65387	−	10.5489i	−0.182004	−	0.339580i
$966$		0			0
$967$	0.467483	+	0.467483i	0.0150332	+	0.0150332i	0.714583	−	0.699550i	$-0.246616\pi$
$967$	0.467483	+	0.467483i	0.0150332	+	0.0150332i	−0.699550	+	0.714583i	$0.746616\pi$
$968$	47.7344	+	47.7344i	1.53424	+	1.53424i
$969$		0			0
$970$	7.81047	−	25.8531i	0.250779	−	0.830094i
$971$		−	33.8862i		−	1.08746i	−0.839260	−	0.543730i	$-0.817012\pi$
$971$		−	33.8862i		−	1.08746i	0.839260	−	0.543730i	$-0.182988\pi$
$972$		0			0
$973$	−3.02237	+	3.02237i	−0.0968928	+	0.0968928i
$974$	−94.5126			−3.02838
$975$		0			0
$976$	14.5627			0.466141
$977$	−28.7652	+	28.7652i	−0.920280	+	0.920280i	−0.997049	−	0.0767686i	$-0.975540\pi$
$977$	−28.7652	+	28.7652i	−0.920280	+	0.920280i	0.0767686	+	0.997049i	$0.475540\pi$
$978$		0			0
$979$			0.935378i			0.0298948i
$980$	19.3418	−	64.0226i	0.617852	−	2.04513i
$981$		0			0
$982$	−8.43502	−	8.43502i	−0.269172	−	0.269172i
$983$	−14.6013	−	14.6013i	−0.465709	−	0.465709i	0.434812	−	0.900521i	$-0.356815\pi$
$983$	−14.6013	−	14.6013i	−0.465709	−	0.465709i	−0.900521	+	0.434812i	$0.856815\pi$
$984$		0			0
$985$	−17.2934	−	32.2656i	−0.551012	−	1.02807i
$986$			22.0348i			0.701731i
$987$		0			0
$988$	1.16201	−	1.16201i	0.0369685	−	0.0369685i
$989$	−2.77146			−0.0881272
$990$		0			0
$991$	25.1852			0.800035			0.400018	−	0.916507i	$-0.369004\pi$
$991$	25.1852			0.800035			0.400018	+	0.916507i	$0.369004\pi$
$992$	−20.3007	+	20.3007i	−0.644549	+	0.644549i
$993$		0			0
$994$		−	11.5535i		−	0.366453i
$995$	−22.1445	−	6.69006i	−0.702028	−	0.212089i
$996$		0			0
$997$	−3.08183	−	3.08183i	−0.0976026	−	0.0976026i	0.656619	−	0.754222i	$-0.271986\pi$
$997$	−3.08183	−	3.08183i	−0.0976026	−	0.0976026i	−0.754222	+	0.656619i	$0.771986\pi$
$998$	−73.1911	−	73.1911i	−2.31682	−	2.31682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.737.1	yes	44
3.2	odd	2	inner	1035.2.j.b.737.22	yes	44
5.3	odd	4	inner	1035.2.j.b.323.22	yes	44
15.8	even	4	inner	1035.2.j.b.323.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.1	✓	44	15.8	even	4	inner
1035.2.j.b.323.22	yes	44	5.3	odd	4	inner
1035.2.j.b.737.1	yes	44	1.1	even	1	trivial
1035.2.j.b.737.22	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79212 + 1.79212i) q^{2} -4.42339i q^{4} +(-0.646671 + 2.14052i) q^{5} +(-0.345144 - 0.345144i) q^{7} +(4.34301 + 4.34301i) q^{8} +O(q^{10})\)	\(q+(-1.79212 + 1.79212i) q^{2} -4.42339i q^{4} +(-0.646671 + 2.14052i) q^{5} +(-0.345144 - 0.345144i) q^{7} +(4.34301 + 4.34301i) q^{8} +(-2.67715 - 4.99498i) q^{10} +0.0944405i q^{11} +(-0.829331 + 0.829331i) q^{13} +1.23708 q^{14} -6.71961 q^{16} +(-1.32819 + 1.32819i) q^{17} -0.316758i q^{19} +(9.46835 + 2.86048i) q^{20} +(-0.169249 - 0.169249i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-4.16363 - 2.76842i) q^{25} -2.97252i q^{26} +(-1.52671 + 1.52671i) q^{28} -4.62862 q^{29} -6.04848 q^{31} +(3.35634 - 3.35634i) q^{32} -4.76055i q^{34} +(0.961982 - 0.515593i) q^{35} +(6.84163 + 6.84163i) q^{37} +(0.567669 + 0.567669i) q^{38} +(-12.1048 + 6.48779i) q^{40} -8.77308i q^{41} +(-1.95972 + 1.95972i) q^{43} +0.417748 q^{44} -2.53444 q^{46} +(-4.30574 + 4.30574i) q^{47} -6.76175i q^{49} +(12.4231 - 2.50039i) q^{50} +(3.66845 + 3.66845i) q^{52} +(-2.54424 - 2.54424i) q^{53} +(-0.202152 - 0.0610719i) q^{55} -2.99793i q^{56} +(8.29504 - 8.29504i) q^{58} -9.28606 q^{59} -2.16719 q^{61} +(10.8396 - 10.8396i) q^{62} -1.40931i q^{64} +(-1.23889 - 2.31150i) q^{65} +(-5.18450 - 5.18450i) q^{67} +(5.87511 + 5.87511i) q^{68} +(-0.799983 + 2.64799i) q^{70} -9.33930i q^{71} +(5.77659 - 5.77659i) q^{73} -24.5220 q^{74} -1.40114 q^{76} +(0.0325956 - 0.0325956i) q^{77} -15.8795i q^{79} +(4.34538 - 14.3835i) q^{80} +(15.7224 + 15.7224i) q^{82} +(-4.23833 - 4.23833i) q^{83} +(-1.98411 - 3.70192i) q^{85} -7.02409i q^{86} +(-0.410156 + 0.410156i) q^{88} +9.90441 q^{89} +0.572477 q^{91} +(3.12781 - 3.12781i) q^{92} -15.4328i q^{94} +(0.678026 + 0.204838i) q^{95} +(3.36974 + 3.36974i) q^{97} +(12.1179 + 12.1179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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