LMFDB - Embedded newform 1035.2.j.b.323.12

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			323.12
Character	$\chi$	$=$	1035.323
Dual form			1035.2.j.b.737.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0986143 + 0.0986143i) q^{2} -1.98055i q^{4} +(1.99036 - 1.01906i) q^{5} +(0.908571 - 0.908571i) q^{7} +(0.392539 - 0.392539i) q^{8} +O(q^{10})$	\(q+(0.0986143 + 0.0986143i) q^{2} -1.98055i q^{4} +(1.99036 - 1.01906i) q^{5} +(0.908571 - 0.908571i) q^{7} +(0.392539 - 0.392539i) q^{8} +(0.296772 + 0.0957835i) q^{10} -3.38524i q^{11} +(0.942974 + 0.942974i) q^{13} +0.179196 q^{14} -3.88368 q^{16} +(5.15629 + 5.15629i) q^{17} -4.57037i q^{19} +(-2.01830 - 3.94200i) q^{20} +(0.333833 - 0.333833i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(2.92303 - 4.05659i) q^{25} +0.185982i q^{26} +(-1.79947 - 1.79947i) q^{28} +4.70684 q^{29} -6.77058 q^{31} +(-1.16807 - 1.16807i) q^{32} +1.01697i q^{34} +(0.882490 - 2.73427i) q^{35} +(-8.21967 + 8.21967i) q^{37} +(0.450704 - 0.450704i) q^{38} +(0.381271 - 1.18131i) q^{40} -0.370746i q^{41} +(0.155875 + 0.155875i) q^{43} -6.70464 q^{44} -0.139462 q^{46} +(-6.67121 - 6.67121i) q^{47} +5.34900i q^{49} +(0.688290 - 0.111785i) q^{50} +(1.86761 - 1.86761i) q^{52} +(7.54852 - 7.54852i) q^{53} +(-3.44977 - 6.73783i) q^{55} -0.713300i q^{56} +(0.464162 + 0.464162i) q^{58} +12.8662 q^{59} -9.21336 q^{61} +(-0.667676 - 0.667676i) q^{62} +7.53699i q^{64} +(2.83780 + 0.915905i) q^{65} +(0.394099 - 0.394099i) q^{67} +(10.2123 - 10.2123i) q^{68} +(0.356664 - 0.182612i) q^{70} +6.01714i q^{71} +(-0.849714 - 0.849714i) q^{73} -1.62115 q^{74} -9.05184 q^{76} +(-3.07573 - 3.07573i) q^{77} -13.3138i q^{79} +(-7.72991 + 3.95771i) q^{80} +(0.0365608 - 0.0365608i) q^{82} +(1.16003 - 1.16003i) q^{83} +(15.5174 + 5.00827i) q^{85} +0.0307430i q^{86} +(-1.32884 - 1.32884i) q^{88} -8.53947 q^{89} +1.71352 q^{91} +(1.40046 + 1.40046i) q^{92} -1.31575i q^{94} +(-4.65748 - 9.09665i) q^{95} +(9.92587 - 9.92587i) q^{97} +(-0.527488 + 0.527488i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.0986143	+	0.0986143i	0.0697309	+	0.0697309i	0.741112	−	0.671381i	$-0.234299\pi$
$2$	0.0986143	+	0.0986143i	0.0697309	+	0.0697309i	−0.671381	+	0.741112i	$0.734299\pi$
$3$		0			0
$3$		0			0
$4$		−	1.98055i		−	0.990275i
$5$	1.99036	−	1.01906i	0.890114	−	0.455738i
$5$	1.99036	−	1.01906i	0.890114	−	0.455738i
$6$		0			0
$7$	0.908571	−	0.908571i	0.343408	−	0.343408i	−0.514239	−	0.857647i	$-0.671926\pi$
$7$	0.908571	−	0.908571i	0.343408	−	0.343408i	0.857647	+	0.514239i	$0.171926\pi$
$8$	0.392539	−	0.392539i	0.138784	−	0.138784i
$9$		0			0
$10$	0.296772	+	0.0957835i	0.0938474	+	0.0302894i
$11$		−	3.38524i		−	1.02069i	−0.859970	−	0.510344i	$-0.829518\pi$
$11$		−	3.38524i		−	1.02069i	0.859970	−	0.510344i	$-0.170482\pi$
$12$		0			0
$13$	0.942974	+	0.942974i	0.261534	+	0.261534i	0.825677	−	0.564143i	$-0.190793\pi$
$13$	0.942974	+	0.942974i	0.261534	+	0.261534i	−0.564143	+	0.825677i	$0.690793\pi$
$14$	0.179196			0.0478922
$15$		0			0
$16$	−3.88368			−0.970920
$17$	5.15629	+	5.15629i	1.25058	+	1.25058i	0.955459	+	0.295124i	$0.0953610\pi$
$17$	5.15629	+	5.15629i	1.25058	+	1.25058i	0.295124	+	0.955459i	$0.404639\pi$
$18$		0			0
$19$		−	4.57037i		−	1.04851i	−0.851560	−	0.524257i	$-0.824343\pi$
$19$		−	4.57037i		−	1.04851i	0.851560	−	0.524257i	$-0.175657\pi$
$20$	−2.01830	−	3.94200i	−0.451306	−	0.881458i
$21$		0			0
$22$	0.333833	−	0.333833i	0.0711735	−	0.0711735i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	2.92303	−	4.05659i	0.584606	−	0.811318i
$26$			0.185982i			0.0364740i
$27$		0			0
$28$	−1.79947	−	1.79947i	−0.340068	−	0.340068i
$29$	4.70684			0.874038			0.437019	−	0.899452i	$-0.356034\pi$
$29$	4.70684			0.874038			0.437019	+	0.899452i	$0.356034\pi$
$30$		0			0
$31$	−6.77058			−1.21603			−0.608016	−	0.793925i	$-0.708034\pi$
$31$	−6.77058			−1.21603			−0.608016	+	0.793925i	$0.708034\pi$
$32$	−1.16807	−	1.16807i	−0.206487	−	0.206487i
$33$		0			0
$34$			1.01697i			0.174408i
$35$	0.882490	−	2.73427i	0.149168	−	0.462176i
$36$		0			0
$37$	−8.21967	+	8.21967i	−1.35130	+	1.35130i	−0.467101	+	0.884204i	$0.654701\pi$
$37$	−8.21967	+	8.21967i	−1.35130	+	1.35130i	−0.884204	+	0.467101i	$0.845299\pi$
$38$	0.450704	−	0.450704i	0.0731138	−	0.0731138i
$39$		0			0
$40$	0.381271	−	1.18131i	0.0602843	−	0.186782i
$41$		−	0.370746i		−	0.0579008i	−0.999581	−	0.0289504i	$-0.990784\pi$
$41$		−	0.370746i		−	0.0579008i	0.999581	−	0.0289504i	$-0.00921648\pi$
$42$		0			0
$43$	0.155875	+	0.155875i	0.0237707	+	0.0237707i	0.718892	−	0.695122i	$-0.244649\pi$
$43$	0.155875	+	0.155875i	0.0237707	+	0.0237707i	−0.695122	+	0.718892i	$0.744649\pi$
$44$	−6.70464			−1.01076
$45$		0			0
$46$	−0.139462			−0.0205625
$47$	−6.67121	−	6.67121i	−0.973096	−	0.973096i	0.0265515	−	0.999647i	$-0.491547\pi$
$47$	−6.67121	−	6.67121i	−0.973096	−	0.973096i	−0.999647	+	0.0265515i	$0.991547\pi$
$48$		0			0
$49$			5.34900i			0.764142i
$50$	0.688290	−	0.111785i	0.0973389	−	0.0158088i
$51$		0			0
$52$	1.86761	−	1.86761i	0.258991	−	0.258991i
$53$	7.54852	−	7.54852i	1.03687	−	1.03687i	0.0375753	−	0.999294i	$-0.488037\pi$
$53$	7.54852	−	7.54852i	1.03687	−	1.03687i	0.999294	−	0.0375753i	$-0.0119634\pi$
$54$		0			0
$55$	−3.44977	−	6.73783i	−0.465167	−	0.908529i
$56$		−	0.713300i		−	0.0953187i
$57$		0			0
$58$	0.464162	+	0.464162i	0.0609474	+	0.0609474i
$59$	12.8662			1.67504			0.837519	−	0.546408i	$-0.184005\pi$
$59$	12.8662			1.67504			0.837519	+	0.546408i	$0.184005\pi$
$60$		0			0
$61$	−9.21336			−1.17965			−0.589825	−	0.807531i	$-0.700803\pi$
$61$	−9.21336			−1.17965			−0.589825	+	0.807531i	$0.700803\pi$
$62$	−0.667676	−	0.667676i	−0.0847949	−	0.0847949i
$63$		0			0
$64$			7.53699i			0.942123i
$65$	2.83780	+	0.915905i	0.351986	+	0.113604i
$66$		0			0
$67$	0.394099	−	0.394099i	0.0481468	−	0.0481468i	−0.682623	−	0.730770i	$-0.739161\pi$
$67$	0.394099	−	0.394099i	0.0481468	−	0.0481468i	0.730770	+	0.682623i	$0.239161\pi$
$68$	10.2123	−	10.2123i	1.23842	−	1.23842i
$69$		0			0
$70$	0.356664	−	0.182612i	0.0426295	−	0.0218263i
$71$			6.01714i			0.714103i	0.934085	+	0.357052i	$0.116218\pi$
$71$			6.01714i			0.714103i	−0.934085	+	0.357052i	$0.883782\pi$
$72$		0			0
$73$	−0.849714	−	0.849714i	−0.0994516	−	0.0994516i	0.655630	−	0.755082i	$-0.272403\pi$
$73$	−0.849714	−	0.849714i	−0.0994516	−	0.0994516i	−0.755082	+	0.655630i	$0.772403\pi$
$74$	−1.62115			−0.188455
$75$		0			0
$76$	−9.05184			−1.03832
$77$	−3.07573	−	3.07573i	−0.350512	−	0.350512i
$78$		0			0
$79$		−	13.3138i		−	1.49792i	−0.662615	−	0.748960i	$-0.730553\pi$
$79$		−	13.3138i		−	1.49792i	0.662615	−	0.748960i	$-0.269447\pi$
$80$	−7.72991	+	3.95771i	−0.864230	+	0.442485i
$81$		0			0
$82$	0.0365608	−	0.0365608i	0.00403747	−	0.00403747i
$83$	1.16003	−	1.16003i	0.127330	−	0.127330i	−0.640570	−	0.767900i	$-0.721302\pi$
$83$	1.16003	−	1.16003i	0.127330	−	0.127330i	0.767900	+	0.640570i	$0.221302\pi$
$84$		0			0
$85$	15.5174	+	5.00827i	1.68310	+	0.543223i
$86$			0.0307430i			0.00331511i
$87$		0			0
$88$	−1.32884	−	1.32884i	−0.141655	−	0.141655i
$89$	−8.53947			−0.905182			−0.452591	−	0.891718i	$-0.649500\pi$
$89$	−8.53947			−0.905182			−0.452591	+	0.891718i	$0.649500\pi$
$90$		0			0
$91$	1.71352			0.179626
$92$	1.40046	+	1.40046i	0.146008	+	0.146008i
$93$		0			0
$94$		−	1.31575i		−	0.135710i
$95$	−4.65748	−	9.09665i	−0.477848	−	0.933297i
$96$		0			0
$97$	9.92587	−	9.92587i	1.00782	−	1.00782i	0.00785052	−	0.999969i	$-0.497501\pi$
$97$	9.92587	−	9.92587i	1.00782	−	1.00782i	0.999969	−	0.00785052i	$-0.00249893\pi$
$98$	−0.527488	+	0.527488i	−0.0532843	+	0.0532843i
$99$		0			0
$100$	−8.03428	−	5.78921i	−0.803428	−	0.578921i
$101$			18.2115i			1.81211i	0.423156	+	0.906057i	$0.360922\pi$
$101$			18.2115i			1.81211i	−0.423156	+	0.906057i	$0.639078\pi$
$102$		0			0
$103$	6.28732	+	6.28732i	0.619508	+	0.619508i	0.945405	−	0.325898i	$-0.105666\pi$
$103$	6.28732	+	6.28732i	0.619508	+	0.619508i	−0.325898	+	0.945405i	$0.605666\pi$
$104$	0.740309			0.0725933
$105$		0			0
$106$	1.48878			0.144604
$107$	0.912430	+	0.912430i	0.0882079	+	0.0882079i	0.749834	−	0.661626i	$-0.230133\pi$
$107$	0.912430	+	0.912430i	0.0882079	+	0.0882079i	−0.661626	+	0.749834i	$0.730133\pi$
$108$		0			0
$109$		−	7.59639i		−	0.727602i	−0.931477	−	0.363801i	$-0.881479\pi$
$109$		−	7.59639i		−	0.727602i	0.931477	−	0.363801i	$-0.118521\pi$
$110$	0.324250	−	1.00464i	0.0309161	−	0.0957890i
$111$		0			0
$112$	−3.52860	+	3.52860i	−0.333421	+	0.333421i
$113$	0.256845	−	0.256845i	0.0241619	−	0.0241619i	−0.694923	−	0.719085i	$-0.744561\pi$
$113$	0.256845	−	0.256845i	0.0241619	−	0.0241619i	0.719085	+	0.694923i	$0.244561\pi$
$114$		0			0
$115$	−0.686809	+	2.12798i	−0.0640452	+	0.198435i
$116$		−	9.32213i		−	0.865538i
$117$		0			0
$118$	1.26879	+	1.26879i	0.116802	+	0.116802i
$119$	9.36971			0.858920
$120$		0			0
$121$	−0.459864			−0.0418058
$122$	−0.908569	−	0.908569i	−0.0822580	−	0.0822580i
$123$		0			0
$124$			13.4095i			1.20421i
$125$	1.68396	−	11.0528i	0.150618	−	0.988592i
$126$		0			0
$127$	7.40871	−	7.40871i	0.657416	−	0.657416i	−0.297352	−	0.954768i	$-0.596103\pi$
$127$	7.40871	−	7.40871i	0.657416	−	0.657416i	0.954768	+	0.297352i	$0.0961033\pi$
$128$	−3.07938	+	3.07938i	−0.272182	+	0.272182i
$129$		0			0
$130$	0.189527	+	0.370169i	0.0166226	+	0.0324660i
$131$			10.9489i			0.956609i	0.878194	+	0.478305i	$0.158748\pi$
$131$			10.9489i			0.956609i	−0.878194	+	0.478305i	$0.841252\pi$
$132$		0			0
$133$	−4.15250	−	4.15250i	−0.360068	−	0.360068i
$134$	0.0777276			0.00671464
$135$		0			0
$136$	4.04809			0.347121
$137$	10.8655	+	10.8655i	0.928300	+	0.928300i	0.997596	−	0.0692961i	$-0.0220753\pi$
$137$	10.8655	+	10.8655i	0.928300	+	0.928300i	−0.0692961	+	0.997596i	$0.522075\pi$
$138$		0			0
$139$			9.57586i			0.812214i	0.913826	+	0.406107i	$0.133114\pi$
$139$			9.57586i			0.812214i	−0.913826	+	0.406107i	$0.866886\pi$
$140$	−5.41536	−	1.74782i	−0.457681	−	0.147717i
$141$		0			0
$142$	−0.593376	+	0.593376i	−0.0497950	+	0.0497950i
$143$	3.19220	−	3.19220i	0.266945	−	0.266945i
$144$		0			0
$145$	9.36828	−	4.79656i	0.777994	−	0.398332i
$146$		−	0.167588i		−	0.0138697i
$147$		0			0
$148$	16.2795	+	16.2795i	1.33816	+	1.33816i
$149$	13.2969			1.08932			0.544662	−	0.838655i	$-0.316658\pi$
$149$	13.2969			1.08932			0.544662	+	0.838655i	$0.316658\pi$
$150$		0			0
$151$	−5.46366			−0.444626			−0.222313	−	0.974975i	$-0.571361\pi$
$151$	−5.46366			−0.444626			−0.222313	+	0.974975i	$0.571361\pi$
$152$	−1.79405	−	1.79405i	−0.145517	−	0.145517i
$153$		0			0
$154$		−	0.606623i		−	0.0488831i
$155$	−13.4759	+	6.89963i	−1.08241	+	0.554192i
$156$		0			0
$157$	−6.58335	+	6.58335i	−0.525409	+	0.525409i	−0.919200	−	0.393791i	$-0.871163\pi$
$157$	−6.58335	+	6.58335i	−0.525409	+	0.525409i	0.393791	+	0.919200i	$0.371163\pi$
$158$	1.31293	−	1.31293i	0.104451	−	0.104451i
$159$		0			0
$160$	−3.51519	−	1.13453i	−0.277901	−	0.0896929i
$161$			1.28491i			0.101265i
$162$		0			0
$163$	14.5001	+	14.5001i	1.13574	+	1.13574i	0.989206	+	0.146531i	$0.0468109\pi$
$163$	14.5001	+	14.5001i	1.13574	+	1.13574i	0.146531	+	0.989206i	$0.453189\pi$
$164$	−0.734281			−0.0573377
$165$		0			0
$166$	0.228791			0.0177576
$167$	1.05953	+	1.05953i	0.0819891	+	0.0819891i	0.746912	−	0.664923i	$-0.231536\pi$
$167$	1.05953	+	1.05953i	0.0819891	+	0.0819891i	−0.664923	+	0.746912i	$0.731536\pi$
$168$		0			0
$169$		−	11.2216i		−	0.863200i
$170$	1.03635	+	2.02413i	0.0794846	+	0.155243i
$171$		0			0
$172$	0.308719	−	0.308719i	0.0235396	−	0.0235396i
$173$	−11.9696	+	11.9696i	−0.910033	+	0.910033i	−0.996274	−	0.0862416i	$-0.972514\pi$
$173$	−11.9696	+	11.9696i	−0.910033	+	0.910033i	0.0862416	+	0.996274i	$0.472514\pi$
$174$		0			0
$175$	−1.02992	−	6.34148i	−0.0778545	−	0.479371i
$176$			13.1472i			0.991007i
$177$		0			0
$178$	−0.842114	−	0.842114i	−0.0631191	−	0.0631191i
$179$	−2.53263			−0.189298			−0.0946488	−	0.995511i	$-0.530173\pi$
$179$	−2.53263			−0.189298			−0.0946488	+	0.995511i	$0.530173\pi$
$180$		0			0
$181$	−23.7079			−1.76220			−0.881098	−	0.472934i	$-0.843195\pi$
$181$	−23.7079			−1.76220			−0.881098	+	0.472934i	$0.843195\pi$
$182$	0.168977	+	0.168977i	0.0125254	+	0.0125254i
$183$		0			0
$184$			0.555134i			0.0409250i
$185$	−7.98371	+	24.7364i	−0.586974	+	1.81866i
$186$		0			0
$187$	17.4553	−	17.4553i	1.27646	−	1.27646i
$188$	−13.2127	+	13.2127i	−0.963633	+	0.963633i
$189$		0			0
$190$	0.437766	−	1.35635i	0.0317589	−	0.0984003i
$191$		−	1.44945i		−	0.104879i	−0.998624	−	0.0524393i	$-0.983300\pi$
$191$		−	1.44945i		−	0.104879i	0.998624	−	0.0524393i	$-0.0166996\pi$
$192$		0			0
$193$	1.53918	+	1.53918i	0.110793	+	0.110793i	0.760330	−	0.649537i	$-0.225037\pi$
$193$	1.53918	+	1.53918i	0.110793	+	0.110793i	−0.649537	+	0.760330i	$0.725037\pi$
$194$	1.95767			0.140552
$195$		0			0
$196$	10.5940			0.756711
$197$	−4.61500	−	4.61500i	−0.328805	−	0.328805i	0.523327	−	0.852132i	$-0.324691\pi$
$197$	−4.61500	−	4.61500i	−0.328805	−	0.328805i	−0.852132	+	0.523327i	$0.824691\pi$
$198$		0			0
$199$			6.73779i			0.477629i	0.971065	+	0.238815i	$0.0767588\pi$
$199$			6.73779i			0.477629i	−0.971065	+	0.238815i	$0.923241\pi$
$200$	−0.444966	−	2.73977i	−0.0314639	−	0.193731i
$201$		0			0
$202$	−1.79592	+	1.79592i	−0.126360	+	0.126360i
$203$	4.27650	−	4.27650i	0.300151	−	0.300151i
$204$		0			0
$205$	−0.377813	−	0.737916i	−0.0263876	−	0.0515383i
$206$			1.24004i			0.0863976i
$207$		0			0
$208$	−3.66221	−	3.66221i	−0.253929	−	0.253929i
$209$	−15.4718			−1.07021
$210$		0			0
$211$	−22.8822			−1.57528			−0.787639	−	0.616137i	$-0.788697\pi$
$211$	−22.8822			−1.57528			−0.787639	+	0.616137i	$0.788697\pi$
$212$	−14.9502	−	14.9502i	−1.02679	−	1.02679i
$213$		0			0
$214$			0.179957i			0.0123016i
$215$	0.469093	+	0.151401i	0.0319919	+	0.0103254i
$216$		0			0
$217$	−6.15155	+	6.15155i	−0.417595	+	0.417595i
$218$	0.749113	−	0.749113i	0.0507363	−	0.0507363i
$219$		0			0
$220$	−13.3446	+	6.83244i	−0.899694	+	0.460643i
$221$			9.72449i			0.654140i
$222$		0			0
$223$	15.7903	+	15.7903i	1.05740	+	1.05740i	0.998249	+	0.0591508i	$0.0188393\pi$
$223$	15.7903	+	15.7903i	1.05740	+	1.05740i	0.0591508	+	0.998249i	$0.481161\pi$
$224$	−2.12254			−0.141818
$225$		0			0
$226$	0.0506571			0.00336966
$227$	11.8493	+	11.8493i	0.786464	+	0.786464i	0.980913	−	0.194449i	$-0.0622919\pi$
$227$	11.8493	+	11.8493i	0.786464	+	0.786464i	−0.194449	+	0.980913i	$0.562292\pi$
$228$		0			0
$229$			26.6447i			1.76073i	0.474294	+	0.880366i	$0.342703\pi$
$229$			26.6447i			1.76073i	−0.474294	+	0.880366i	$0.657297\pi$
$230$	−0.277578	+	0.142120i	−0.0183030	+	0.00937112i
$231$		0			0
$232$	1.84762	−	1.84762i	0.121302	−	0.121302i
$233$	−0.349706	+	0.349706i	−0.0229100	+	0.0229100i	−0.718469	−	0.695559i	$-0.755157\pi$
$233$	−0.349706	+	0.349706i	−0.0229100	+	0.0229100i	0.695559	+	0.718469i	$0.255157\pi$
$234$		0			0
$235$	−20.0764	−	6.47971i	−1.30964	−	0.422690i
$236$		−	25.4822i		−	1.65875i
$237$		0			0
$238$	0.923987	+	0.923987i	0.0598932	+	0.0598932i
$239$	−4.07502			−0.263591			−0.131795	−	0.991277i	$-0.542074\pi$
$239$	−4.07502			−0.263591			−0.131795	+	0.991277i	$0.542074\pi$
$240$		0			0
$241$	16.0988			1.03702			0.518508	−	0.855073i	$-0.326488\pi$
$241$	16.0988			1.03702			0.518508	+	0.855073i	$0.326488\pi$
$242$	−0.0453492	−	0.0453492i	−0.00291516	−	0.00291516i
$243$		0			0
$244$			18.2475i			1.16818i
$245$	5.45095	+	10.6464i	0.348249	+	0.680174i
$246$		0			0
$247$	4.30974	−	4.30974i	0.274222	−	0.274222i
$248$	−2.65772	+	2.65772i	−0.168765	+	0.168765i
$249$		0			0
$250$	1.25603	−	0.923902i	0.0794381	−	0.0584327i
$251$			29.1511i			1.84000i	0.391916	+	0.920001i	$0.371812\pi$
$251$			29.1511i			1.84000i	−0.391916	+	0.920001i	$0.628188\pi$
$252$		0			0
$253$	2.39373	+	2.39373i	0.150492	+	0.150492i
$254$	1.46121			0.0916844
$255$		0			0
$256$	14.4666			0.904164
$257$	−1.80883	−	1.80883i	−0.112832	−	0.112832i	0.648437	−	0.761268i	$-0.275423\pi$
$257$	−1.80883	−	1.80883i	−0.112832	−	0.112832i	−0.761268	+	0.648437i	$0.775423\pi$
$258$		0			0
$259$			14.9363i			0.928097i
$260$	1.81400	−	5.62041i	0.112499	−	0.348563i
$261$		0			0
$262$	−1.07972	+	1.07972i	−0.0667052	+	0.0667052i
$263$	11.2056	−	11.2056i	0.690964	−	0.690964i	−0.271480	−	0.962444i	$-0.587513\pi$
$263$	11.2056	−	11.2056i	0.690964	−	0.690964i	0.962444	+	0.271480i	$0.0875131\pi$
$264$		0			0
$265$	7.33183	−	22.7166i	0.450391	−	1.39547i
$266$		−	0.818992i		−	0.0502157i
$267$		0			0
$268$	−0.780533	−	0.780533i	−0.0476786	−	0.0476786i
$269$	−4.83700			−0.294917			−0.147459	−	0.989068i	$-0.547109\pi$
$269$	−4.83700			−0.294917			−0.147459	+	0.989068i	$0.547109\pi$
$270$		0			0
$271$	5.57013			0.338361			0.169181	−	0.985585i	$-0.445888\pi$
$271$	5.57013			0.338361			0.169181	+	0.985585i	$0.445888\pi$
$272$	−20.0254	−	20.0254i	−1.21422	−	1.21422i
$273$		0			0
$274$			2.14298i			0.129462i
$275$	−13.7325	−	9.89516i	−0.828103	−	0.596701i
$276$		0			0
$277$	19.5409	−	19.5409i	1.17410	−	1.17410i	0.192874	−	0.981224i	$-0.438219\pi$
$277$	19.5409	−	19.5409i	1.17410	−	1.17410i	0.981224	−	0.192874i	$-0.0617809\pi$
$278$	−0.944317	+	0.944317i	−0.0566364	+	0.0566364i
$279$		0			0
$280$	−0.726896	−	1.41972i	−0.0434403	−	0.0848445i
$281$		−	6.92795i		−	0.413287i	−0.978416	−	0.206644i	$-0.933746\pi$
$281$		−	6.92795i		−	0.413287i	0.978416	−	0.206644i	$-0.0662540\pi$
$282$		0			0
$283$	−13.1884	−	13.1884i	−0.783969	−	0.783969i	0.196529	−	0.980498i	$-0.437033\pi$
$283$	−13.1884	−	13.1884i	−0.783969	−	0.783969i	−0.980498	+	0.196529i	$0.937033\pi$
$284$	11.9172			0.707159
$285$		0			0
$286$	0.629592			0.0372286
$287$	−0.336849	−	0.336849i	−0.0198836	−	0.0198836i
$288$		0			0
$289$			36.1746i			2.12792i
$290$	1.39686	+	0.450838i	0.0820262	+	0.0264741i
$291$		0			0
$292$	−1.68290	+	1.68290i	−0.0984844	+	0.0984844i
$293$	−21.8606	+	21.8606i	−1.27711	+	1.27711i	−0.334833	+	0.942278i	$0.608680\pi$
$293$	−21.8606	+	21.8606i	−1.27711	+	1.27711i	−0.942278	+	0.334833i	$0.891320\pi$
$294$		0			0
$295$	25.6083	−	13.1115i	1.49097	−	0.763378i
$296$			6.45308i			0.375078i
$297$		0			0
$298$	1.31127	+	1.31127i	0.0759596	+	0.0759596i
$299$	−1.33357			−0.0771222
$300$		0			0
$301$	0.283247			0.0163261
$302$	−0.538795	−	0.538795i	−0.0310042	−	0.0310042i
$303$		0			0
$304$			17.7498i			1.01802i
$305$	−18.3379	+	9.38898i	−1.05002	+	0.537611i
$306$		0			0
$307$	9.52145	−	9.52145i	0.543418	−	0.543418i	−0.381111	−	0.924529i	$-0.624458\pi$
$307$	9.52145	−	9.52145i	0.543418	−	0.543418i	0.924529	+	0.381111i	$0.124458\pi$
$308$	−6.09165	+	6.09165i	−0.347104	+	0.347104i
$309$		0			0
$310$	−2.00932	−	0.648510i	−0.114121	−	0.0368329i
$311$		−	6.11034i		−	0.346486i	−0.984879	−	0.173243i	$-0.944575\pi$
$311$		−	6.11034i		−	0.346486i	0.984879	−	0.173243i	$-0.0554245\pi$
$312$		0			0
$313$	−2.25776	−	2.25776i	−0.127616	−	0.127616i	0.640414	−	0.768030i	$-0.278763\pi$
$313$	−2.25776	−	2.25776i	−0.127616	−	0.127616i	−0.768030	+	0.640414i	$0.778763\pi$
$314$	−1.29843			−0.0732744
$315$		0			0
$316$	−26.3687			−1.48335
$317$	−6.17604	−	6.17604i	−0.346881	−	0.346881i	0.512066	−	0.858946i	$-0.328880\pi$
$317$	−6.17604	−	6.17604i	−0.346881	−	0.346881i	−0.858946	+	0.512066i	$0.828880\pi$
$318$		0			0
$319$		−	15.9338i		−	0.892121i
$320$	7.68065	+	15.0013i	0.429361	+	0.838597i
$321$		0			0
$322$	−0.126711	+	0.126711i	−0.00706132	+	0.00706132i
$323$	23.5661	−	23.5661i	1.31125	−	1.31125i
$324$		0			0
$325$	6.58160	−	1.06892i	0.365081	−	0.0592928i
$326$			2.85984i			0.158392i
$327$		0			0
$328$	−0.145532	−	0.145532i	−0.00803568	−	0.00803568i
$329$	−12.1225			−0.668337
$330$		0			0
$331$	7.56813			0.415982			0.207991	−	0.978131i	$-0.433308\pi$
$331$	7.56813			0.415982			0.207991	+	0.978131i	$0.433308\pi$
$332$	−2.29750	−	2.29750i	−0.126092	−	0.126092i
$333$		0			0
$334$			0.208970i			0.0114343i
$335$	0.382786	−	1.18601i	0.0209138	−	0.0647985i
$336$		0			0
$337$	−7.69294	+	7.69294i	−0.419061	+	0.419061i	−0.884880	−	0.465819i	$-0.845760\pi$
$337$	−7.69294	+	7.69294i	−0.419061	+	0.419061i	0.465819	+	0.884880i	$0.345760\pi$
$338$	1.10661	−	1.10661i	0.0601917	−	0.0601917i
$339$		0			0
$340$	9.91913	−	30.7330i	0.537941	−	1.66673i
$341$			22.9201i			1.24119i
$342$		0			0
$343$	11.2199	+	11.2199i	0.605820	+	0.605820i
$344$	0.122374			0.00659798
$345$		0			0
$346$	−2.36075			−0.126915
$347$	−9.93312	−	9.93312i	−0.533238	−	0.533238i	0.388296	−	0.921535i	$-0.373064\pi$
$347$	−9.93312	−	9.93312i	−0.533238	−	0.533238i	−0.921535	+	0.388296i	$0.873064\pi$
$348$		0			0
$349$		−	15.2116i		−	0.814258i	−0.913371	−	0.407129i	$-0.866530\pi$
$349$		−	15.2116i		−	0.814258i	0.913371	−	0.407129i	$-0.133470\pi$
$350$	0.523796	−	0.726925i	0.0279981	−	0.0388558i
$351$		0			0
$352$	−3.95418	+	3.95418i	−0.210759	+	0.210759i
$353$	−0.0288653	+	0.0288653i	−0.00153634	+	0.00153634i	−0.707875	−	0.706338i	$-0.750346\pi$
$353$	−0.0288653	+	0.0288653i	−0.00153634	+	0.00153634i	0.706338	+	0.707875i	$0.250346\pi$
$354$		0			0
$355$	6.13183	+	11.9762i	0.325444	+	0.635633i
$356$			16.9128i			0.896379i
$357$		0			0
$358$	−0.249754	−	0.249754i	−0.0131999	−	0.0131999i
$359$	37.4002			1.97391			0.986955	−	0.160999i	$-0.0514716\pi$
$359$	37.4002			1.97391			0.986955	+	0.160999i	$0.0514716\pi$
$360$		0			0
$361$	−1.88824			−0.0993813
$362$	−2.33794	−	2.33794i	−0.122879	−	0.122879i
$363$		0			0
$364$		−	3.39371i		−	0.177879i
$365$	−2.55714	−	0.825323i	−0.133847	−	0.0431994i
$366$		0			0
$367$	−0.147719	+	0.147719i	−0.00771087	+	0.00771087i	−0.710952	−	0.703241i	$-0.751736\pi$
$367$	−0.147719	+	0.147719i	−0.00771087	+	0.00771087i	0.703241	+	0.710952i	$0.251736\pi$
$368$	2.74618	−	2.74618i	0.143154	−	0.143154i
$369$		0			0
$370$	−3.22667	+	1.65205i	−0.167747	+	0.0858862i
$371$		−	13.7167i		−	0.712137i
$372$		0			0
$373$	19.8863	+	19.8863i	1.02967	+	1.02967i	0.999546	+	0.0301276i	$0.00959137\pi$
$373$	19.8863	+	19.8863i	1.02967	+	1.02967i	0.0301276	+	0.999546i	$0.490409\pi$
$374$	3.44268			0.178017
$375$		0			0
$376$	−5.23742			−0.270100
$377$	4.43843	+	4.43843i	0.228591	+	0.228591i
$378$		0			0
$379$			15.8484i			0.814078i	0.913411	+	0.407039i	$0.133439\pi$
$379$			15.8484i			0.814078i	−0.913411	+	0.407039i	$0.866561\pi$
$380$	−18.0164	+	9.22438i	−0.924221	+	0.473201i
$381$		0			0
$382$	0.142937	−	0.142937i	0.00731328	−	0.00731328i
$383$	2.11982	−	2.11982i	0.108318	−	0.108318i	−0.650871	−	0.759189i	$-0.725596\pi$
$383$	2.11982	−	2.11982i	0.108318	−	0.108318i	0.759189	+	0.650871i	$0.225596\pi$
$384$		0			0
$385$	−9.25616	−	2.98744i	−0.471738	−	0.152254i
$386$			0.303570i			0.0154513i
$387$		0			0
$388$	−19.6587	−	19.6587i	−0.998019	−	0.998019i
$389$	9.05218			0.458964			0.229482	−	0.973313i	$-0.426297\pi$
$389$	9.05218			0.458964			0.229482	+	0.973313i	$0.426297\pi$
$390$		0			0
$391$	−7.29209			−0.368777
$392$	2.09969	+	2.09969i	0.106050	+	0.106050i
$393$		0			0
$394$		−	0.910209i		−	0.0458557i
$395$	−13.5676	−	26.4992i	−0.682659	−	1.33332i
$396$		0			0
$397$	7.71651	−	7.71651i	0.387280	−	0.387280i	−0.486436	−	0.873716i	$-0.661703\pi$
$397$	7.71651	−	7.71651i	0.387280	−	0.387280i	0.873716	+	0.486436i	$0.161703\pi$
$398$	−0.664443	+	0.664443i	−0.0333055	+	0.0333055i
$399$		0			0
$400$	−11.3521	+	15.7545i	−0.567606	+	0.787725i
$401$		−	2.72279i		−	0.135970i	−0.997686	−	0.0679848i	$-0.978343\pi$
$401$		−	2.72279i		−	0.135970i	0.997686	−	0.0679848i	$-0.0216569\pi$
$402$		0			0
$403$	−6.38448	−	6.38448i	−0.318034	−	0.318034i
$404$	36.0688			1.79449
$405$		0			0
$406$	0.843448			0.0418596
$407$	27.8256	+	27.8256i	1.37926	+	1.37926i
$408$		0			0
$409$		−	22.9180i		−	1.13322i	−0.823985	−	0.566612i	$-0.808254\pi$
$409$		−	22.9180i		−	1.13322i	0.823985	−	0.566612i	$-0.191746\pi$
$410$	0.0355113	−	0.110027i	0.00175378	−	0.00543384i
$411$		0			0
$412$	12.4523	−	12.4523i	0.613483	−	0.613483i
$413$	11.6899	−	11.6899i	0.575221	−	0.575221i
$414$		0			0
$415$	1.12673	−	3.49101i	0.0553090	−	0.171367i
$416$		−	2.20291i		−	0.108007i
$417$		0			0
$418$	−1.52574	−	1.52574i	−0.0746264	−	0.0746264i
$419$	27.7004			1.35325			0.676627	−	0.736326i	$-0.263441\pi$
$419$	27.7004			1.35325			0.676627	+	0.736326i	$0.263441\pi$
$420$		0			0
$421$	−0.00816555			−0.000397964			−0.000198982	−	1.00000i	$-0.500063\pi$
$421$	−0.00816555			−0.000397964			−0.000198982		1.00000i	$0.500063\pi$
$422$	−2.25652	−	2.25652i	−0.109845	−	0.109845i
$423$		0			0
$424$		−	5.92618i		−	0.287801i
$425$	35.9889	−	5.84495i	1.74572	−	0.283522i
$426$		0			0
$427$	−8.37099	+	8.37099i	−0.405101	+	0.405101i
$428$	1.80711	−	1.80711i	0.0873501	−	0.0873501i
$429$		0			0
$430$	0.0313290	+	0.0611896i	0.00151082	+	0.00295082i
$431$			4.72091i			0.227398i	0.993515	+	0.113699i	$0.0362700\pi$
$431$			4.72091i			0.227398i	−0.993515	+	0.113699i	$0.963730\pi$
$432$		0			0
$433$	1.57796	+	1.57796i	0.0758319	+	0.0758319i	0.744005	−	0.668174i	$-0.232924\pi$
$433$	1.57796	+	1.57796i	0.0758319	+	0.0758319i	−0.668174	+	0.744005i	$0.732924\pi$
$434$	−1.21326			−0.0582385
$435$		0			0
$436$	−15.0450			−0.720526
$437$	3.23174	+	3.23174i	0.154595	+	0.154595i
$438$		0			0
$439$		−	34.7552i		−	1.65878i	−0.558673	−	0.829388i	$-0.688689\pi$
$439$		−	34.7552i		−	1.65878i	0.558673	−	0.829388i	$-0.311311\pi$
$440$	−3.99903	−	1.29070i	−0.190646	−	0.0615315i
$441$		0			0
$442$	−0.958974	+	0.958974i	−0.0456137	+	0.0456137i
$443$	0.522128	−	0.522128i	0.0248071	−	0.0248071i	−0.694594	−	0.719402i	$-0.744416\pi$
$443$	0.522128	−	0.522128i	0.0248071	−	0.0248071i	0.719402	+	0.694594i	$0.244416\pi$
$444$		0			0
$445$	−16.9966	+	8.70224i	−0.805715	+	0.412526i
$446$			3.11431i			0.147467i
$447$		0			0
$448$	6.84789	+	6.84789i	0.323532	+	0.323532i
$449$	−29.0525			−1.37107			−0.685535	−	0.728039i	$-0.740432\pi$
$449$	−29.0525			−1.37107			−0.685535	+	0.728039i	$0.740432\pi$
$450$		0			0
$451$	−1.25506			−0.0590987
$452$	−0.508694	−	0.508694i	−0.0239269	−	0.0239269i
$453$		0			0
$454$			2.33701i			0.109682i
$455$	3.41051	−	1.74618i	0.159887	−	0.0818622i
$456$		0			0
$457$	−3.93063	+	3.93063i	−0.183867	+	0.183867i	−0.793039	−	0.609171i	$-0.791502\pi$
$457$	−3.93063	+	3.93063i	−0.183867	+	0.183867i	0.609171	+	0.793039i	$0.291502\pi$
$458$	−2.62755	+	2.62755i	−0.122777	+	0.122777i
$459$		0			0
$460$	4.21457	+	1.36026i	0.196505	+	0.0634224i
$461$			7.42840i			0.345975i	0.984924	+	0.172988i	$0.0553420\pi$
$461$			7.42840i			0.345975i	−0.984924	+	0.172988i	$0.944658\pi$
$462$		0			0
$463$	−20.1880	−	20.1880i	−0.938217	−	0.938217i	0.0599822	−	0.998199i	$-0.480896\pi$
$463$	−20.1880	−	20.1880i	−0.938217	−	0.938217i	−0.998199	+	0.0599822i	$0.980896\pi$
$464$	−18.2799			−0.848621
$465$		0			0
$466$	−0.0689721			−0.00319507
$467$	7.15372	+	7.15372i	0.331035	+	0.331035i	0.852979	−	0.521945i	$-0.174793\pi$
$467$	7.15372	+	7.15372i	0.331035	+	0.331035i	−0.521945	+	0.852979i	$0.674793\pi$
$468$		0			0
$469$		−	0.716134i		−	0.0330680i
$470$	−1.34083	−	2.61882i	−0.0618480	−	0.120797i
$471$		0			0
$472$	5.05049	−	5.05049i	0.232468	−	0.232468i
$473$	0.527675	−	0.527675i	0.0242625	−	0.0242625i
$474$		0			0
$475$	−18.5401	−	13.3593i	−0.850678	−	0.612967i
$476$		−	18.5572i		−	0.850567i
$477$		0			0
$478$	−0.401855	−	0.401855i	−0.0183804	−	0.0183804i
$479$	−18.4867			−0.844681			−0.422340	−	0.906437i	$-0.638791\pi$
$479$	−18.4867			−0.844681			−0.422340	+	0.906437i	$0.638791\pi$
$480$		0			0
$481$	−15.5019			−0.706824
$482$	1.58757	+	1.58757i	0.0723120	+	0.0723120i
$483$		0			0
$484$			0.910784i			0.0413993i
$485$	9.64094	−	29.8711i	0.437773	−	1.35638i
$486$		0			0
$487$	−11.7367	+	11.7367i	−0.531841	+	0.531841i	−0.921120	−	0.389279i	$-0.872724\pi$
$487$	−11.7367	+	11.7367i	−0.531841	+	0.531841i	0.389279	+	0.921120i	$0.372724\pi$
$488$	−3.61661	+	3.61661i	−0.163716	+	0.163716i
$489$		0			0
$490$	−0.512346	+	1.58743i	−0.0231454	+	0.0717128i
$491$		−	11.5097i		−	0.519424i	−0.965686	−	0.259712i	$-0.916372\pi$
$491$		−	11.5097i		−	0.519424i	0.965686	−	0.259712i	$-0.0836276\pi$
$492$		0			0
$493$	24.2698	+	24.2698i	1.09306	+	1.09306i
$494$	0.850004			0.0382435
$495$		0			0
$496$	26.2948			1.18067
$497$	5.46700	+	5.46700i	0.245228	+	0.245228i
$498$		0			0
$499$			7.57451i			0.339081i	0.985523	+	0.169541i	$0.0542284\pi$
$499$			7.57451i			0.339081i	−0.985523	+	0.169541i	$0.945772\pi$
$500$	−21.8906	−	3.33516i	−0.978978	−	0.149153i
$501$		0			0
$502$	−2.87472	+	2.87472i	−0.128305	+	0.128305i
$503$	8.96796	−	8.96796i	0.399861	−	0.399861i	−0.478323	−	0.878184i	$-0.658755\pi$
$503$	8.96796	−	8.96796i	0.399861	−	0.399861i	0.878184	+	0.478323i	$0.158755\pi$
$504$		0			0
$505$	18.5586	+	36.2474i	0.825849	+	1.61299i
$506$			0.472112i			0.0209879i
$507$		0			0
$508$	−14.6733	−	14.6733i	−0.651023	−	0.651023i
$509$	9.77001			0.433048			0.216524	−	0.976277i	$-0.430528\pi$
$509$	9.77001			0.433048			0.216524	+	0.976277i	$0.430528\pi$
$510$		0			0
$511$	−1.54405			−0.0683048
$512$	7.58539	+	7.58539i	0.335230	+	0.335230i
$513$		0			0
$514$		−	0.356753i		−	0.0157357i
$515$	18.9211	+	6.10683i	0.833765	+	0.269099i
$516$		0			0
$517$	−22.5837	+	22.5837i	−0.993228	+	0.993228i
$518$	−1.47293	+	1.47293i	−0.0647170	+	0.0647170i
$519$		0			0
$520$	1.47348	−	0.754420i	0.0646163	−	0.0330835i
$521$		−	0.273332i		−	0.0119749i	−0.999982	−	0.00598744i	$-0.998094\pi$
$521$		−	0.273332i		−	0.0119749i	0.999982	−	0.00598744i	$-0.00190587\pi$
$522$		0			0
$523$	−24.1923	−	24.1923i	−1.05786	−	1.05786i	−0.998220	−	0.0596368i	$-0.981006\pi$
$523$	−24.1923	−	24.1923i	−1.05786	−	1.05786i	−0.0596368	−	0.998220i	$-0.518994\pi$
$524$	21.6848			0.947306
$525$		0			0
$526$	2.21006			0.0963630
$527$	−34.9110	−	34.9110i	−1.52075	−	1.52075i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	2.96321	−	1.51716i	0.128714	−	0.0659013i
$531$		0			0
$532$	−8.22424	+	8.22424i	−0.356566	+	0.356566i
$533$	0.349604	−	0.349604i	0.0151430	−	0.0151430i
$534$		0			0
$535$	2.74588	+	0.886238i	0.118715	+	0.0383154i
$536$		−	0.309399i		−	0.0133640i
$537$		0			0
$538$	−0.476998	−	0.476998i	−0.0205648	−	0.0205648i
$539$	18.1076			0.779952
$540$		0			0
$541$	4.21519			0.181225			0.0906125	−	0.995886i	$-0.471118\pi$
$541$	4.21519			0.181225			0.0906125	+	0.995886i	$0.471118\pi$
$542$	0.549295	+	0.549295i	0.0235942	+	0.0235942i
$543$		0			0
$544$		−	12.0458i		−	0.516458i
$545$	−7.74118	−	15.1195i	−0.331596	−	0.647649i
$546$		0			0
$547$	−22.2779	+	22.2779i	−0.952533	+	0.952533i	−0.998923	−	0.0463908i	$-0.985228\pi$
$547$	−22.2779	+	22.2779i	−0.952533	+	0.952533i	0.0463908	+	0.998923i	$0.485228\pi$
$548$	21.5196	−	21.5196i	0.919272	−	0.919272i
$549$		0			0
$550$	−0.378420	−	2.33003i	−0.0161359	−	0.0993528i
$551$		−	21.5120i		−	0.916441i
$552$		0			0
$553$	−12.0965	−	12.0965i	−0.514397	−	0.514397i
$554$	3.85402			0.163742
$555$		0			0
$556$	18.9655			0.804315
$557$	9.26448	+	9.26448i	0.392549	+	0.392549i	0.875595	−	0.483046i	$-0.160470\pi$
$557$	9.26448	+	9.26448i	0.392549	+	0.392549i	−0.483046	+	0.875595i	$0.660470\pi$
$558$		0			0
$559$			0.293972i			0.0124337i
$560$	−3.42731	+	10.6190i	−0.144830	+	0.448736i
$561$		0			0
$562$	0.683195	−	0.683195i	0.0288189	−	0.0288189i
$563$	19.3446	−	19.3446i	0.815276	−	0.815276i	−0.170144	−	0.985419i	$-0.554423\pi$
$563$	19.3446	−	19.3446i	0.815276	−	0.815276i	0.985419	+	0.170144i	$0.0544232\pi$
$564$		0			0
$565$	0.249472	−	0.772952i	0.0104954	−	0.0325183i
$566$		−	2.60113i		−	0.109334i
$567$		0			0
$568$	2.36196	+	2.36196i	0.0991058	+	0.0991058i
$569$	12.0693			0.505972			0.252986	−	0.967470i	$-0.418587\pi$
$569$	12.0693			0.505972			0.252986	+	0.967470i	$0.418587\pi$
$570$		0			0
$571$	−38.3625			−1.60542			−0.802709	−	0.596370i	$-0.796609\pi$
$571$	−38.3625			−1.60542			−0.802709	+	0.596370i	$0.796609\pi$
$572$	−6.32230	−	6.32230i	−0.264349	−	0.264349i
$573$		0			0
$574$		−	0.0664363i		−	0.00277300i
$575$	0.801547	+	4.93533i	0.0334268	+	0.205818i
$576$		0			0
$577$	25.5389	−	25.5389i	1.06320	−	1.06320i	0.0653368	−	0.997863i	$-0.479188\pi$
$577$	25.5389	−	25.5389i	1.06320	−	1.06320i	0.997863	−	0.0653368i	$-0.0208122\pi$
$578$	−3.56733	+	3.56733i	−0.148381	+	0.148381i
$579$		0			0
$580$	−9.49982	−	18.5544i	−0.394459	−	0.770428i
$581$		−	2.10794i		−	0.0874521i
$582$		0			0
$583$	−25.5536	−	25.5536i	−1.05832	−	1.05832i
$584$	−0.667093			−0.0276045
$585$		0			0
$586$	−4.31154			−0.178108
$587$	−23.1975	−	23.1975i	−0.957462	−	0.957462i	0.0416694	−	0.999131i	$-0.486732\pi$
$587$	−23.1975	−	23.1975i	−0.957462	−	0.957462i	−0.999131	+	0.0416694i	$0.986732\pi$
$588$		0			0
$589$			30.9440i			1.27503i
$590$	3.81833	+	1.23237i	0.157198	+	0.0507359i
$591$		0			0
$592$	31.9226	−	31.9226i	1.31201	−	1.31201i
$593$	−2.14843	+	2.14843i	−0.0882256	+	0.0882256i	−0.749842	−	0.661617i	$-0.769871\pi$
$593$	−2.14843	+	2.14843i	−0.0882256	+	0.0882256i	0.661617	+	0.749842i	$0.269871\pi$
$594$		0			0
$595$	18.6490	−	9.54830i	0.764536	−	0.391442i
$596$		−	26.3352i		−	1.07873i
$597$		0			0
$598$	−0.131509	−	0.131509i	−0.00537779	−	0.00537779i
$599$	−33.4811			−1.36800			−0.684001	−	0.729481i	$-0.739762\pi$
$599$	−33.4811			−1.36800			−0.684001	+	0.729481i	$0.739762\pi$
$600$		0			0
$601$	1.18166			0.0482009			0.0241004	−	0.999710i	$-0.492328\pi$
$601$	1.18166			0.0482009			0.0241004	+	0.999710i	$0.492328\pi$
$602$	0.0279322	+	0.0279322i	0.00113843	+	0.00113843i
$603$		0			0
$604$			10.8211i			0.440302i
$605$	−0.915293	+	0.468630i	−0.0372119	+	0.0190525i
$606$		0			0
$607$	−29.0454	+	29.0454i	−1.17891	+	1.17891i	−0.198894	+	0.980021i	$0.563735\pi$
$607$	−29.0454	+	29.0454i	−1.17891	+	1.17891i	−0.980021	+	0.198894i	$0.936265\pi$
$608$	−5.33848	+	5.33848i	−0.216504	+	0.216504i
$609$		0			0
$610$	−2.73426	−	0.882488i	−0.110707	−	0.0357309i
$611$		−	12.5816i		−	0.508995i
$612$		0			0
$613$	15.5615	+	15.5615i	0.628523	+	0.628523i	0.947696	−	0.319173i	$-0.103405\pi$
$613$	15.5615	+	15.5615i	0.628523	+	0.628523i	−0.319173	+	0.947696i	$0.603405\pi$
$614$	1.87790			0.0757860
$615$		0			0
$616$	−2.41469			−0.0972907
$617$	16.1580	+	16.1580i	0.650497	+	0.650497i	0.953113	−	0.302616i	$-0.0978600\pi$
$617$	16.1580	+	16.1580i	0.650497	+	0.650497i	−0.302616	+	0.953113i	$0.597860\pi$
$618$		0			0
$619$		−	32.8174i		−	1.31904i	−0.751686	−	0.659522i	$-0.770759\pi$
$619$		−	32.8174i		−	1.31904i	0.751686	−	0.659522i	$-0.229241\pi$
$620$	13.6651	+	26.6896i	0.548803	+	1.07188i
$621$		0			0
$622$	0.602567	−	0.602567i	0.0241607	−	0.0241607i
$623$	−7.75871	+	7.75871i	−0.310846	+	0.310846i
$624$		0			0
$625$	−7.91180	−	23.7150i	−0.316472	−	0.948602i
$626$		−	0.445295i		−	0.0177976i
$627$		0			0
$628$	13.0387	+	13.0387i	0.520299	+	0.520299i
$629$	−84.7659			−3.37984
$630$		0			0
$631$	−22.6792			−0.902843			−0.451422	−	0.892311i	$-0.649083\pi$
$631$	−22.6792			−0.902843			−0.451422	+	0.892311i	$0.649083\pi$
$632$	−5.22619	−	5.22619i	−0.207887	−	0.207887i
$633$		0			0
$634$		−	1.21809i		−	0.0483766i
$635$	7.19603	−	22.2959i	0.285566	−	0.884785i
$636$		0			0
$637$	−5.04397	+	5.04397i	−0.199849	+	0.199849i
$638$	1.57130	−	1.57130i	0.0622084	−	0.0622084i
$639$		0			0
$640$	−2.99099	+	9.26715i	−0.118229	+	0.366316i
$641$		−	21.6571i		−	0.855405i	−0.903920	−	0.427702i	$-0.859323\pi$
$641$		−	21.6571i		−	0.855405i	0.903920	−	0.427702i	$-0.140677\pi$
$642$		0			0
$643$	11.8113	+	11.8113i	0.465791	+	0.465791i	0.900548	−	0.434757i	$-0.143166\pi$
$643$	11.8113	+	11.8113i	0.465791	+	0.465791i	−0.434757	+	0.900548i	$0.643166\pi$
$644$	2.54484			0.100281
$645$		0			0
$646$	4.64791			0.182870
$647$	−2.75857	−	2.75857i	−0.108451	−	0.108451i	0.650799	−	0.759250i	$-0.274434\pi$
$647$	−2.75857	−	2.75857i	−0.108451	−	0.108451i	−0.759250	+	0.650799i	$0.774434\pi$
$648$		0			0
$649$		−	43.5552i		−	1.70969i
$650$	0.754450	+	0.543629i	0.0295920	+	0.0213229i
$651$		0			0
$652$	28.7182	−	28.7182i	1.12469	−	1.12469i
$653$	26.8749	−	26.8749i	1.05170	−	1.05170i	0.0531090	−	0.998589i	$-0.483087\pi$
$653$	26.8749	−	26.8749i	1.05170	−	1.05170i	0.998589	−	0.0531090i	$-0.0169131\pi$
$654$		0			0
$655$	11.1576	+	21.7922i	0.435963	+	0.851491i
$656$			1.43986i			0.0562170i
$657$		0			0
$658$	−1.19546	−	1.19546i	−0.0466037	−	0.0466037i
$659$	−28.9666			−1.12838			−0.564189	−	0.825646i	$-0.690811\pi$
$659$	−28.9666			−1.12838			−0.564189	+	0.825646i	$0.690811\pi$
$660$		0			0
$661$	14.7479			0.573626			0.286813	−	0.957987i	$-0.407404\pi$
$661$	14.7479			0.573626			0.286813	+	0.957987i	$0.407404\pi$
$662$	0.746326	+	0.746326i	0.0290068	+	0.0290068i
$663$		0			0
$664$		−	0.910715i		−	0.0353426i
$665$	−12.4966	−	4.03330i	−0.484598	−	0.156405i
$666$		0			0
$667$	−3.32824	+	3.32824i	−0.128870	+	0.128870i
$668$	2.09846	−	2.09846i	0.0811918	−	0.0811918i
$669$		0			0
$670$	0.154706	−	0.0792092i	0.00597680	−	0.00306012i
$671$			31.1895i			1.20406i
$672$		0			0
$673$	−0.931311	−	0.931311i	−0.0358994	−	0.0358994i	0.688929	−	0.724829i	$-0.258081\pi$
$673$	−0.931311	−	0.931311i	−0.0358994	−	0.0358994i	−0.724829	+	0.688929i	$0.758081\pi$
$674$	−1.51727			−0.0584430
$675$		0			0
$676$	−22.2249			−0.854806
$677$	−12.9667	−	12.9667i	−0.498350	−	0.498350i	0.412574	−	0.910924i	$-0.364630\pi$
$677$	−12.9667	−	12.9667i	−0.498350	−	0.498350i	−0.910924	+	0.412574i	$0.864630\pi$
$678$		0			0
$679$		−	18.0367i		−	0.692186i
$680$	8.05714	−	4.12525i	0.308977	−	0.158196i
$681$		0			0
$682$	−2.26025	+	2.26025i	−0.0865493	+	0.0865493i
$683$	23.4849	−	23.4849i	0.898626	−	0.898626i	−0.0966884	−	0.995315i	$-0.530825\pi$
$683$	23.4849	−	23.4849i	0.898626	−	0.898626i	0.995315	+	0.0966884i	$0.0308250\pi$
$684$		0			0
$685$	32.6987	+	10.5536i	1.24935	+	0.403231i
$686$			2.21289i			0.0844887i
$687$		0			0
$688$	−0.605369	−	0.605369i	−0.0230795	−	0.0230795i
$689$	14.2361			0.542353
$690$		0			0
$691$	−7.30940			−0.278063			−0.139031	−	0.990288i	$-0.544399\pi$
$691$	−7.30940			−0.278063			−0.139031	+	0.990288i	$0.544399\pi$
$692$	23.7064	+	23.7064i	0.901183	+	0.901183i
$693$		0			0
$694$		−	1.95910i		−	0.0743663i
$695$	9.75839	+	19.0594i	0.370157	+	0.722963i
$696$		0			0
$697$	1.91167	−	1.91167i	0.0724097	−	0.0724097i
$698$	1.50008	−	1.50008i	0.0567789	−	0.0567789i
$699$		0			0
$700$	−12.5596	+	2.03981i	−0.474709	+	0.0770974i
$701$			6.64763i			0.251077i	0.992089	+	0.125539i	$0.0400659\pi$
$701$			6.64763i			0.251077i	−0.992089	+	0.125539i	$0.959934\pi$
$702$		0			0
$703$	37.5669	+	37.5669i	1.41686	+	1.41686i
$704$	25.5145			0.961615
$705$		0			0
$706$	−0.00569306			−0.000214261
$707$	16.5465	+	16.5465i	0.622294	+	0.622294i
$708$		0			0
$709$		−	15.1224i		−	0.567933i	−0.958834	−	0.283966i	$-0.908350\pi$
$709$		−	15.1224i		−	0.567933i	0.958834	−	0.283966i	$-0.0916504\pi$
$710$	−0.576343	+	1.78572i	−0.0216298	+	0.0670167i
$711$		0			0
$712$	−3.35208	+	3.35208i	−0.125624	+	0.125624i
$713$	4.78752	−	4.78752i	0.179294	−	0.179294i
$714$		0			0
$715$	3.10056	−	9.60665i	0.115954	−	0.359268i
$716$			5.01600i			0.187457i
$717$		0			0
$718$	3.68820	+	3.68820i	0.137642	+	0.137642i
$719$	13.2160			0.492874			0.246437	−	0.969159i	$-0.420740\pi$
$719$	13.2160			0.492874			0.246437	+	0.969159i	$0.420740\pi$
$720$		0			0
$721$	11.4249			0.425487
$722$	−0.186208	−	0.186208i	−0.00692994	−	0.00692994i
$723$		0			0
$724$			46.9547i			1.74506i
$725$	13.7582	−	19.0937i	0.510968	−	0.709122i
$726$		0			0
$727$	−23.5095	+	23.5095i	−0.871919	+	0.871919i	−0.992681	−	0.120762i	$-0.961466\pi$
$727$	−23.5095	+	23.5095i	−0.871919	+	0.871919i	0.120762	+	0.992681i	$0.461466\pi$
$728$	0.672623	−	0.672623i	0.0249291	−	0.0249291i
$729$		0			0
$730$	−0.170782	−	0.333560i	−0.00632094	−	0.0123456i
$731$			1.60747i			0.0594546i
$732$		0			0
$733$	14.3962	+	14.3962i	0.531737	+	0.531737i	0.921089	−	0.389352i	$-0.127301\pi$
$733$	14.3962	+	14.3962i	0.531737	+	0.531737i	−0.389352	+	0.921089i	$0.627301\pi$
$734$	−0.0291344			−0.00107537
$735$		0			0
$736$	1.65189			0.0608896
$737$	−1.33412	−	1.33412i	−0.0491429	−	0.0491429i
$738$		0			0
$739$		−	11.5824i		−	0.426067i	−0.977045	−	0.213034i	$-0.931666\pi$
$739$		−	11.5824i		−	0.426067i	0.977045	−	0.213034i	$-0.0683344\pi$
$740$	48.9917	+	15.8121i	1.80097	+	0.581266i
$741$		0			0
$742$	1.35267	−	1.35267i	0.0496580	−	0.0496580i
$743$	−1.84796	+	1.84796i	−0.0677951	+	0.0677951i	−0.740191	−	0.672396i	$-0.765265\pi$
$743$	−1.84796	+	1.84796i	−0.0677951	+	0.0677951i	0.672396	+	0.740191i	$0.265265\pi$
$744$		0			0
$745$	26.4656	−	13.5504i	0.969623	−	0.496447i
$746$			3.92215i			0.143600i
$747$		0			0
$748$	−34.5711	−	34.5711i	−1.26404	−	1.26404i
$749$	1.65801			0.0605825
$750$		0			0
$751$	18.0547			0.658826			0.329413	−	0.944186i	$-0.393149\pi$
$751$	18.0547			0.658826			0.329413	+	0.944186i	$0.393149\pi$
$752$	25.9088	+	25.9088i	0.944799	+	0.944799i
$753$		0			0
$754$			0.875385i			0.0318796i
$755$	−10.8746	+	5.56780i	−0.395768	+	0.202633i
$756$		0			0
$757$	−22.9333	+	22.9333i	−0.833523	+	0.833523i	−0.987997	−	0.154473i	$-0.950632\pi$
$757$	−22.9333	+	22.9333i	−0.833523	+	0.833523i	0.154473	+	0.987997i	$0.450632\pi$
$758$	−1.56288	+	1.56288i	−0.0567664	+	0.0567664i
$759$		0			0
$760$	−5.39904	−	1.74255i	−0.195844	−	0.0632089i
$761$			27.9786i			1.01422i	0.861881	+	0.507111i	$0.169287\pi$
$761$			27.9786i			1.01422i	−0.861881	+	0.507111i	$0.830713\pi$
$762$		0			0
$763$	−6.90186	−	6.90186i	−0.249864	−	0.249864i
$764$	−2.87071			−0.103859
$765$		0			0
$766$	0.418090			0.0151062
$767$	12.1325	+	12.1325i	0.438079	+	0.438079i
$768$		0			0
$769$			8.62217i			0.310923i	0.987842	+	0.155462i	$0.0496865\pi$
$769$			8.62217i			0.310923i	−0.987842	+	0.155462i	$0.950313\pi$
$770$	−0.618186	−	1.20739i	−0.0222779	−	0.0435115i
$771$		0			0
$772$	3.04842	−	3.04842i	0.109715	−	0.109715i
$773$	−30.3771	+	30.3771i	−1.09259	+	1.09259i	−0.0973371	+	0.995251i	$0.531033\pi$
$773$	−30.3771	+	30.3771i	−1.09259	+	1.09259i	−0.995251	+	0.0973371i	$0.968967\pi$
$774$		0			0
$775$	−19.7906	+	27.4654i	−0.710899	+	0.986588i
$776$		−	7.79259i		−	0.279738i
$777$		0			0
$778$	0.892674	+	0.892674i	0.0320039	+	0.0320039i
$779$	−1.69444			−0.0607098
$780$		0			0
$781$	20.3695			0.728877
$782$	−0.719104	−	0.719104i	−0.0257151	−	0.0257151i
$783$		0			0
$784$		−	20.7738i		−	0.741921i
$785$	−6.39437	+	19.8121i	−0.228225	+	0.707122i
$786$		0			0
$787$	13.9212	−	13.9212i	0.496236	−	0.496236i	−0.414028	−	0.910264i	$-0.635879\pi$
$787$	13.9212	−	13.9212i	0.496236	−	0.496236i	0.910264	+	0.414028i	$0.135879\pi$
$788$	−9.14023	+	9.14023i	−0.325607	+	0.325607i
$789$		0			0
$790$	1.27524	−	3.95116i	0.0453711	−	0.140576i
$791$		−	0.466723i		−	0.0165948i
$792$		0			0
$793$	−8.68796	−	8.68796i	−0.308518	−	0.308518i
$794$	1.52192			0.0540108
$795$		0			0
$796$	13.3445			0.472984
$797$	−26.9916	−	26.9916i	−0.956092	−	0.956092i	0.0429842	−	0.999076i	$-0.486313\pi$
$797$	−26.9916	−	26.9916i	−0.956092	−	0.956092i	−0.999076	+	0.0429842i	$0.986313\pi$
$798$		0			0
$799$		−	68.7973i		−	2.43387i
$800$	−8.15265	+	1.32407i	−0.288240	+	0.0468130i
$801$		0			0
$802$	0.268506	−	0.268506i	0.00948127	−	0.00948127i
$803$	−2.87649	+	2.87649i	−0.101509	+	0.101509i
$804$		0			0
$805$	1.30941	+	2.55743i	0.0461505	+	0.0901377i
$806$		−	1.25920i		−	0.0443535i
$807$		0			0
$808$	7.14873	+	7.14873i	0.251492	+	0.251492i
$809$	−26.3651			−0.926949			−0.463474	−	0.886110i	$-0.653397\pi$
$809$	−26.3651			−0.926949			−0.463474	+	0.886110i	$0.653397\pi$
$810$		0			0
$811$	−50.3009			−1.76630			−0.883152	−	0.469087i	$-0.844583\pi$
$811$	−50.3009			−1.76630			−0.883152	+	0.469087i	$0.844583\pi$
$812$	−8.46982	−	8.46982i	−0.297232	−	0.297232i
$813$		0			0
$814$			5.48800i			0.192354i
$815$	43.6369	+	14.0839i	1.52853	+	0.493337i
$816$		0			0
$817$	0.712407	−	0.712407i	0.0249239	−	0.0249239i
$818$	2.26005	−	2.26005i	0.0790206	−	0.0790206i
$819$		0			0
$820$	−1.46148	+	0.748277i	−0.0510371	+	0.0261310i
$821$		−	35.3593i		−	1.23405i	−0.786945	−	0.617024i	$-0.788338\pi$
$821$		−	35.3593i		−	1.23405i	0.786945	−	0.617024i	$-0.211662\pi$
$822$		0			0
$823$	−32.8329	−	32.8329i	−1.14448	−	1.14448i	−0.987620	−	0.156863i	$-0.949862\pi$
$823$	−32.8329	−	32.8329i	−1.14448	−	1.14448i	−0.156863	−	0.987620i	$-0.550138\pi$
$824$	4.93604			0.171955
$825$		0			0
$826$	2.30558			0.0802213
$827$	14.7979	+	14.7979i	0.514575	+	0.514575i	0.915925	−	0.401350i	$-0.131459\pi$
$827$	14.7979	+	14.7979i	0.514575	+	0.514575i	−0.401350	+	0.915925i	$0.631459\pi$
$828$		0			0
$829$		−	9.60372i		−	0.333551i	−0.985995	−	0.166776i	$-0.946664\pi$
$829$		−	9.60372i		−	0.333551i	0.985995	−	0.166776i	$-0.0533355\pi$
$830$	0.455376	−	0.233152i	0.0158063	−	0.00809283i
$831$		0			0
$832$	−7.10718	+	7.10718i	−0.246397	+	0.246397i
$833$	−27.5810	+	27.5810i	−0.955624	+	0.955624i
$834$		0			0
$835$	3.18858	+	1.02912i	0.110345	+	0.0356141i
$836$			30.6427i			1.05980i
$837$		0			0
$838$	2.73166	+	2.73166i	0.0943636	+	0.0943636i
$839$	−15.4142			−0.532157			−0.266079	−	0.963951i	$-0.585728\pi$
$839$	−15.4142			−0.532157			−0.266079	+	0.963951i	$0.585728\pi$
$840$		0			0
$841$	−6.84566			−0.236057
$842$	−0.000805240	0	0.000805240i	−2.77504e−5	0	2.77504e-5i
$843$		0			0
$844$			45.3194i			1.55996i
$845$	−11.4355	−	22.3350i	−0.393393	−	0.768346i
$846$		0			0
$847$	−0.417819	+	0.417819i	−0.0143564	+	0.0143564i
$848$	−29.3160	+	29.3160i	−1.00672	+	1.00672i
$849$		0			0
$850$	4.12542	+	2.97262i	0.141501	+	0.101960i
$851$		−	11.6244i		−	0.398478i
$852$		0			0
$853$	−10.6045	−	10.6045i	−0.363091	−	0.363091i	0.501859	−	0.864950i	$-0.332650\pi$
$853$	−10.6045	−	10.6045i	−0.363091	−	0.363091i	−0.864950	+	0.501859i	$0.832650\pi$
$854$	−1.65100			−0.0564960
$855$		0			0
$856$	0.716329			0.0244836
$857$	12.3027	+	12.3027i	0.420253	+	0.420253i	0.885291	−	0.465038i	$-0.153959\pi$
$857$	12.3027	+	12.3027i	0.420253	+	0.420253i	−0.465038	+	0.885291i	$0.653959\pi$
$858$		0			0
$859$		−	35.4895i		−	1.21089i	−0.795889	−	0.605443i	$-0.792996\pi$
$859$		−	35.4895i		−	1.21089i	0.795889	−	0.605443i	$-0.207004\pi$
$860$	0.299857	−	0.929063i	0.0102250	−	0.0316808i
$861$		0			0
$862$	−0.465549	+	0.465549i	−0.0158567	+	0.0158567i
$863$	−23.0493	+	23.0493i	−0.784606	+	0.784606i	−0.980604	−	0.195998i	$-0.937205\pi$
$863$	−23.0493	+	23.0493i	−0.784606	+	0.784606i	0.195998	+	0.980604i	$0.437205\pi$
$864$		0			0
$865$	−11.6260	+	36.0215i	−0.395296	+	1.22477i
$866$			0.311219i			0.0105757i
$867$		0			0
$868$	12.1835	+	12.1835i	0.413534	+	0.413534i
$869$	−45.0705			−1.52891
$870$		0			0
$871$	0.743250			0.0251841
$872$	−2.98188	−	2.98188i	−0.100979	−	0.100979i
$873$		0			0
$874$			0.637391i			0.0215601i
$875$	−8.51226	−	11.5722i	−0.287767	−	0.391213i
$876$		0			0
$877$	−32.4685	+	32.4685i	−1.09638	+	1.09638i	−0.101555	+	0.994830i	$0.532382\pi$
$877$	−32.4685	+	32.4685i	−1.09638	+	1.09638i	−0.994830	+	0.101555i	$0.967618\pi$
$878$	3.42736	−	3.42736i	0.115668	−	0.115668i
$879$		0			0
$880$	13.3978	+	26.1676i	0.451640	+	0.882110i
$881$			29.2721i			0.986203i	0.869972	+	0.493101i	$0.164137\pi$
$881$			29.2721i			0.986203i	−0.869972	+	0.493101i	$0.835863\pi$
$882$		0			0
$883$	8.91932	+	8.91932i	0.300159	+	0.300159i	0.841076	−	0.540917i	$-0.181923\pi$
$883$	8.91932	+	8.91932i	0.300159	+	0.300159i	−0.540917	+	0.841076i	$0.681923\pi$
$884$	19.2598			0.647779
$885$		0			0
$886$	0.102979			0.00345963
$887$	39.2579	+	39.2579i	1.31815	+	1.31815i	0.915239	+	0.402911i	$0.132002\pi$
$887$	39.2579	+	39.2579i	1.31815	+	1.31815i	0.402911	+	0.915239i	$0.367998\pi$
$888$		0			0
$889$		−	13.4627i		−	0.451524i
$890$	−2.53427	−	0.817940i	−0.0849489	−	0.0274174i
$891$		0			0
$892$	31.2736	−	31.2736i	1.04712	−	1.04712i
$893$	−30.4899	+	30.4899i	−1.02030	+	1.02030i
$894$		0			0
$895$	−5.04083	+	2.58091i	−0.168497	+	0.0862701i
$896$			5.59568i			0.186939i
$897$		0			0
$898$	−2.86499	−	2.86499i	−0.0956059	−	0.0956059i
$899$	−31.8680			−1.06286
$900$		0			0
$901$	77.8447			2.59338
$902$	−0.123767	−	0.123767i	−0.00412100	−	0.00412100i
$903$		0			0
$904$		−	0.201643i		−	0.00670655i
$905$	−47.1872	+	24.1598i	−1.56856	+	0.803100i
$906$		0			0
$907$	−19.2956	+	19.2956i	−0.640698	+	0.640698i	−0.950727	−	0.310029i	$-0.899661\pi$
$907$	−19.2956	+	19.2956i	−0.640698	+	0.640698i	0.310029	+	0.950727i	$0.399661\pi$
$908$	23.4681	−	23.4681i	0.778815	−	0.778815i
$909$		0			0
$910$	0.508524	+	0.164127i	0.0168574	+	0.00544075i
$911$		−	20.7610i		−	0.687844i	−0.938998	−	0.343922i	$-0.888244\pi$
$911$		−	20.7610i		−	0.687844i	0.938998	−	0.343922i	$-0.111756\pi$
$912$		0			0
$913$	−3.92698	−	3.92698i	−0.129964	−	0.129964i
$914$	−0.775233			−0.0256424
$915$		0			0
$916$	52.7712			1.74361
$917$	9.94785	+	9.94785i	0.328507	+	0.328507i
$918$		0			0
$919$			50.0209i			1.65004i	0.565104	+	0.825019i	$0.308836\pi$
$919$			50.0209i			1.65004i	−0.565104	+	0.825019i	$0.691164\pi$
$920$	0.565716	+	1.10491i	0.0186511	+	0.0364280i
$921$		0			0
$922$	−0.732547	+	0.732547i	−0.0241251	+	0.0241251i
$923$	−5.67401	+	5.67401i	−0.186762	+	0.186762i
$924$		0			0
$925$	9.31747	+	57.3701i	0.306357	+	1.88632i
$926$		−	3.98166i		−	0.130845i
$927$		0			0
$928$	−5.49789	−	5.49789i	−0.180477	−	0.180477i
$929$	10.7628			0.353115			0.176557	−	0.984290i	$-0.443504\pi$
$929$	10.7628			0.353115			0.176557	+	0.984290i	$0.443504\pi$
$930$		0			0
$931$	24.4469			0.801214
$932$	0.692611	+	0.692611i	0.0226872	+	0.0226872i
$933$		0			0
$934$			1.41092i			0.0461667i
$935$	16.9542	−	52.5302i	0.554462	−	1.71792i
$936$		0			0
$937$	−2.93668	+	2.93668i	−0.0959371	+	0.0959371i	−0.753446	−	0.657509i	$-0.771610\pi$
$937$	−2.93668	+	2.93668i	−0.0959371	+	0.0959371i	0.657509	+	0.753446i	$0.271610\pi$
$938$	0.0706210	−	0.0706210i	0.00230586	−	0.00230586i
$939$		0			0
$940$	−12.8334	+	39.7624i	−0.418579	+	1.29691i
$941$		−	36.9829i		−	1.20561i	−0.797889	−	0.602804i	$-0.794050\pi$
$941$		−	36.9829i		−	1.20561i	0.797889	−	0.602804i	$-0.205950\pi$
$942$		0			0
$943$	0.262157	+	0.262157i	0.00853700	+	0.00853700i
$944$	−49.9683			−1.62633
$945$		0			0
$946$	0.104073			0.00338369
$947$	−26.8975	−	26.8975i	−0.874051	−	0.874051i	0.118860	−	0.992911i	$-0.462076\pi$
$947$	−26.8975	−	26.8975i	−0.874051	−	0.874051i	−0.992911	+	0.118860i	$0.962076\pi$
$948$		0			0
$949$		−	1.60252i		−	0.0520199i
$950$	−0.510899	−	3.14574i	−0.0165757	−	0.102061i
$951$		0			0
$952$	3.67798	−	3.67798i	0.119204	−	0.119204i
$953$	−32.3527	+	32.3527i	−1.04801	+	1.04801i	−0.0492172	+	0.998788i	$0.515673\pi$
$953$	−32.3527	+	32.3527i	−1.04801	+	1.04801i	−0.998788	+	0.0492172i	$0.984327\pi$
$954$		0			0
$955$	−1.47708	−	2.88492i	−0.0477972	−	0.0933539i
$956$			8.07078i			0.261028i
$957$		0			0
$958$	−1.82306	−	1.82306i	−0.0589003	−	0.0589003i
$959$	19.7441			0.637571
$960$		0			0
$961$	14.8407			0.478734
$962$	−1.52871	−	1.52871i	−0.0492875	−	0.0492875i
$963$		0			0
$964$		−	31.8845i		−	1.02693i
$965$	4.63203	+	1.49500i	0.149110	+	0.0481256i
$966$		0			0
$967$	−18.4591	+	18.4591i	−0.593604	+	0.593604i	−0.938603	−	0.344999i	$-0.887879\pi$
$967$	−18.4591	+	18.4591i	−0.593604	+	0.593604i	0.344999	+	0.938603i	$0.387879\pi$
$968$	−0.180515	+	0.180515i	−0.00580196	+	0.00580196i
$969$		0			0
$970$	3.89645	−	1.99498i	0.125108	−	0.0640550i
$971$			19.3265i			0.620217i	0.950701	+	0.310108i	$0.100365\pi$
$971$			19.3265i			0.620217i	−0.950701	+	0.310108i	$0.899635\pi$
$972$		0			0
$973$	8.70035	+	8.70035i	0.278920	+	0.278920i
$974$	−2.31481			−0.0741714
$975$		0			0
$976$	35.7817			1.14535
$977$	26.3332	+	26.3332i	0.842474	+	0.842474i	0.989180	−	0.146706i	$-0.0468672\pi$
$977$	26.3332	+	26.3332i	0.842474	+	0.842474i	−0.146706	+	0.989180i	$0.546867\pi$
$978$		0			0
$979$			28.9082i			0.923909i
$980$	21.0857	−	10.7959i	0.673559	−	0.344862i
$981$		0			0
$982$	1.13502	−	1.13502i	0.0362199	−	0.0362199i
$983$	−11.7245	+	11.7245i	−0.373952	+	0.373952i	−0.868914	−	0.494962i	$-0.835182\pi$
$983$	−11.7245	+	11.7245i	−0.373952	+	0.373952i	0.494962	+	0.868914i	$0.335182\pi$
$984$		0			0
$985$	−13.8884	−	4.48252i	−0.442523	−	0.142825i
$986$			4.78670i			0.152440i
$987$		0			0
$988$	−8.53565	−	8.53565i	−0.271555	−	0.271555i
$989$	−0.220441			−0.00700961
$990$		0			0
$991$	−27.6194			−0.877358			−0.438679	−	0.898644i	$-0.644554\pi$
$991$	−27.6194			−0.877358			−0.438679	+	0.898644i	$0.644554\pi$
$992$	7.90848	+	7.90848i	0.251094	+	0.251094i
$993$		0			0
$994$			1.07825i			0.0342000i
$995$	6.86622	+	13.4106i	0.217674	+	0.425145i
$996$		0			0
$997$	34.8619	−	34.8619i	1.10409	−	1.10409i	0.110176	−	0.993912i	$-0.464858\pi$
$997$	34.8619	−	34.8619i	1.10409	−	1.10409i	0.993912	−	0.110176i	$-0.0351416\pi$
$998$	−0.746955	+	0.746955i	−0.0236444	+	0.0236444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.323.12	yes	44
3.2	odd	2	inner	1035.2.j.b.323.11	✓	44
5.2	odd	4	inner	1035.2.j.b.737.11	yes	44
15.2	even	4	inner	1035.2.j.b.737.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.11	✓	44	3.2	odd	2	inner
1035.2.j.b.323.12	yes	44	1.1	even	1	trivial
1035.2.j.b.737.11	yes	44	5.2	odd	4	inner
1035.2.j.b.737.12	yes	44	15.2	even	4	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)

\(f(q)\)	\(=\)	\(q+(0.0986143 + 0.0986143i) q^{2} -1.98055i q^{4} +(1.99036 - 1.01906i) q^{5} +(0.908571 - 0.908571i) q^{7} +(0.392539 - 0.392539i) q^{8} +O(q^{10})\)	\(q+(0.0986143 + 0.0986143i) q^{2} -1.98055i q^{4} +(1.99036 - 1.01906i) q^{5} +(0.908571 - 0.908571i) q^{7} +(0.392539 - 0.392539i) q^{8} +(0.296772 + 0.0957835i) q^{10} -3.38524i q^{11} +(0.942974 + 0.942974i) q^{13} +0.179196 q^{14} -3.88368 q^{16} +(5.15629 + 5.15629i) q^{17} -4.57037i q^{19} +(-2.01830 - 3.94200i) q^{20} +(0.333833 - 0.333833i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(2.92303 - 4.05659i) q^{25} +0.185982i q^{26} +(-1.79947 - 1.79947i) q^{28} +4.70684 q^{29} -6.77058 q^{31} +(-1.16807 - 1.16807i) q^{32} +1.01697i q^{34} +(0.882490 - 2.73427i) q^{35} +(-8.21967 + 8.21967i) q^{37} +(0.450704 - 0.450704i) q^{38} +(0.381271 - 1.18131i) q^{40} -0.370746i q^{41} +(0.155875 + 0.155875i) q^{43} -6.70464 q^{44} -0.139462 q^{46} +(-6.67121 - 6.67121i) q^{47} +5.34900i q^{49} +(0.688290 - 0.111785i) q^{50} +(1.86761 - 1.86761i) q^{52} +(7.54852 - 7.54852i) q^{53} +(-3.44977 - 6.73783i) q^{55} -0.713300i q^{56} +(0.464162 + 0.464162i) q^{58} +12.8662 q^{59} -9.21336 q^{61} +(-0.667676 - 0.667676i) q^{62} +7.53699i q^{64} +(2.83780 + 0.915905i) q^{65} +(0.394099 - 0.394099i) q^{67} +(10.2123 - 10.2123i) q^{68} +(0.356664 - 0.182612i) q^{70} +6.01714i q^{71} +(-0.849714 - 0.849714i) q^{73} -1.62115 q^{74} -9.05184 q^{76} +(-3.07573 - 3.07573i) q^{77} -13.3138i q^{79} +(-7.72991 + 3.95771i) q^{80} +(0.0365608 - 0.0365608i) q^{82} +(1.16003 - 1.16003i) q^{83} +(15.5174 + 5.00827i) q^{85} +0.0307430i q^{86} +(-1.32884 - 1.32884i) q^{88} -8.53947 q^{89} +1.71352 q^{91} +(1.40046 + 1.40046i) q^{92} -1.31575i q^{94} +(-4.65748 - 9.09665i) q^{95} +(9.92587 - 9.92587i) q^{97} +(-0.527488 + 0.527488i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 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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