LMFDB - Embedded newform 675.2.ba.c.443.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [288] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.12
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.c.32.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0304268 - 0.347779i) q^{2} +(-1.64956 - 0.528165i) q^{3} +(1.84959 - 0.326133i) q^{4} +(-0.133494 + 0.589753i) q^{6} +(0.696364 + 0.994510i) q^{7} +(-0.350411 - 1.30775i) q^{8} +(2.44208 + 1.74248i) q^{9} +(-0.626120 - 1.72025i) q^{11} +(-3.22326 - 0.438914i) q^{12} +(0.347377 + 0.0303916i) q^{13} +(0.324682 - 0.272441i) q^{14} +(3.08557 - 1.12306i) q^{16} +(0.515030 - 1.92212i) q^{17} +(0.531693 - 0.902324i) q^{18} +(4.81794 + 2.78164i) q^{19} +(-0.623426 - 2.00830i) q^{21} +(-0.579217 + 0.270093i) q^{22} +(2.41651 + 1.69206i) q^{23} +(-0.112685 + 2.34229i) q^{24} -0.121735i q^{26} +(-3.10804 - 4.16414i) q^{27} +(1.61233 + 1.61233i) q^{28} +(1.34520 + 1.12876i) q^{29} +(-0.372471 - 2.11239i) q^{31} +(-1.62881 - 3.49300i) q^{32} +(0.124245 + 3.16835i) q^{33} +(-0.684143 - 0.120633i) q^{34} +(5.08513 + 2.42643i) q^{36} +(-1.61707 - 0.433293i) q^{37} +(0.820803 - 1.76022i) q^{38} +(-0.556967 - 0.233605i) q^{39} +(-7.15599 - 8.52817i) q^{41} +(-0.679476 + 0.277921i) q^{42} +(3.99477 + 1.86279i) q^{43} +(-1.71910 - 2.97756i) q^{44} +(0.514936 - 0.891896i) q^{46} +(9.15123 - 6.40776i) q^{47} +(-5.68299 + 0.222855i) q^{48} +(1.89001 - 5.19277i) q^{49} +(-1.86477 + 2.89862i) q^{51} +(0.652418 - 0.0570792i) q^{52} +(5.25853 - 5.25853i) q^{53} +(-1.35364 + 1.20761i) q^{54} +(1.05656 - 1.25916i) q^{56} +(-6.47831 - 7.13315i) q^{57} +(0.351629 - 0.502179i) q^{58} +(5.35536 + 1.94919i) q^{59} +(1.30500 - 7.40100i) q^{61} +(-0.723312 + 0.193811i) q^{62} +(-0.0323344 + 3.64208i) q^{63} +(4.52212 - 2.61085i) q^{64} +(1.09811 - 0.139612i) q^{66} +(-0.854027 + 9.76158i) q^{67} +(0.325729 - 3.72310i) q^{68} +(-3.09249 - 4.06746i) q^{69} +(-13.6425 + 7.87649i) q^{71} +(1.42299 - 3.80422i) q^{72} +(11.5895 - 3.10541i) q^{73} +(-0.101488 + 0.575568i) q^{74} +(9.81841 + 3.57361i) q^{76} +(1.27480 - 1.82060i) q^{77} +(-0.0642964 + 0.200810i) q^{78} +(-9.65809 + 11.5101i) q^{79} +(2.92754 + 8.51055i) q^{81} +(-2.74819 + 2.74819i) q^{82} +(-12.8776 + 1.12664i) q^{83} +(-1.80806 - 3.51121i) q^{84} +(0.526293 - 1.44598i) q^{86} +(-1.62282 - 2.57244i) q^{87} +(-2.03026 + 1.42160i) q^{88} +(1.27248 - 2.20400i) q^{89} +(0.211676 + 0.366634i) q^{91} +(5.02139 + 2.34151i) q^{92} +(-0.501277 + 3.68124i) q^{93} +(-2.50693 - 2.98764i) q^{94} +(0.841940 + 6.62218i) q^{96} +(-2.57343 + 5.51873i) q^{97} +(-1.86344 - 0.499308i) q^{98} +(1.46846 - 5.29200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0304268	−	0.347779i	−0.0215150	−	0.245917i	−0.999335	−	0.0364693i	$-0.988389\pi$
$2$	−0.0304268	−	0.347779i	−0.0215150	−	0.245917i	0.977820	−	0.209448i	$-0.0671667\pi$
$3$	−1.64956	−	0.528165i	−0.952373	−	0.304936i
$3$	−1.64956	−	0.528165i	−0.952373	−	0.304936i
$4$	1.84959	−	0.326133i	0.924795	−	0.163066i
$5$		0			0
$5$		0			0
$6$	−0.133494	+	0.589753i	−0.0544988	+	0.240765i
$7$	0.696364	+	0.994510i	0.263201	+	0.375890i	0.928900	−	0.370330i	$-0.120756\pi$
$7$	0.696364	+	0.994510i	0.263201	+	0.375890i	−0.665699	+	0.746220i	$0.731867\pi$
$8$	−0.350411	−	1.30775i	−0.123889	−	0.462360i
$9$	2.44208	+	1.74248i	0.814028	+	0.580826i
$10$		0			0
$11$	−0.626120	−	1.72025i	−0.188782	−	0.518675i	0.808807	−	0.588075i	$-0.200114\pi$
$11$	−0.626120	−	1.72025i	−0.188782	−	0.518675i	−0.997589	+	0.0693995i	$0.977892\pi$
$12$	−3.22326	−	0.438914i	−0.930475	−	0.126704i
$13$	0.347377	+	0.0303916i	0.0963452	+	0.00842911i	0.135226	−	0.990815i	$-0.456824\pi$
$13$	0.347377	+	0.0303916i	0.0963452	+	0.00842911i	−0.0388812	+	0.999244i	$0.512379\pi$
$14$	0.324682	−	0.272441i	0.0867749	−	0.0728128i
$15$		0			0
$16$	3.08557	−	1.12306i	0.771393	−	0.280764i
$17$	0.515030	−	1.92212i	0.124913	−	0.466182i	−0.874924	−	0.484261i	$-0.839088\pi$
$17$	0.515030	−	1.92212i	0.124913	−	0.466182i	0.999837	+	0.0180793i	$0.00575515\pi$
$18$	0.531693	−	0.902324i	0.125321	−	0.212680i
$19$	4.81794	+	2.78164i	1.10531	+	0.638152i	0.937611	−	0.347685i	$-0.113032\pi$
$19$	4.81794	+	2.78164i	1.10531	+	0.638152i	0.167701	+	0.985838i	$0.446366\pi$
$20$		0			0
$21$	−0.623426	−	2.00830i	−0.136043	−	0.438246i
$22$	−0.579217	+	0.270093i	−0.123489	+	0.0575841i
$23$	2.41651	+	1.69206i	0.503877	+	0.352818i	0.797713	−	0.603037i	$-0.206043\pi$
$23$	2.41651	+	1.69206i	0.503877	+	0.352818i	−0.293836	+	0.955856i	$0.594932\pi$
$24$	−0.112685	+	2.34229i	−0.0230018	+	0.478117i
$25$		0			0
$26$		−	0.121735i		−	0.0238743i
$27$	−3.10804	−	4.16414i	−0.598143	−	0.801389i
$28$	1.61233	+	1.61233i	0.304702	+	0.304702i
$29$	1.34520	+	1.12876i	0.249798	+	0.209605i	0.759085	−	0.650991i	$-0.225647\pi$
$29$	1.34520	+	1.12876i	0.249798	+	0.209605i	−0.509287	+	0.860597i	$0.670091\pi$
$30$		0			0
$31$	−0.372471	−	2.11239i	−0.0668978	−	0.379396i	−0.999814	−	0.0193020i	$-0.993856\pi$
$31$	−0.372471	−	2.11239i	−0.0668978	−	0.379396i	0.932916	−	0.360094i	$-0.117256\pi$
$32$	−1.62881	−	3.49300i	−0.287936	−	0.617481i
$33$	0.124245	+	3.16835i	0.0216283	+	0.551539i
$34$	−0.684143	−	0.120633i	−0.117330	−	0.0206884i
$35$		0			0
$36$	5.08513	+	2.42643i	0.847522	+	0.404405i
$37$	−1.61707	−	0.433293i	−0.265845	−	0.0712329i	0.123434	−	0.992353i	$-0.460609\pi$
$37$	−1.61707	−	0.433293i	−0.265845	−	0.0712329i	−0.389279	+	0.921120i	$0.627276\pi$
$38$	0.820803	−	1.76022i	0.133152	−	0.285545i
$39$	−0.556967	−	0.233605i	−0.0891862	−	0.0374068i
$40$		0			0
$41$	−7.15599	−	8.52817i	−1.11758	−	1.33188i	−0.937405	−	0.348242i	$-0.886779\pi$
$41$	−7.15599	−	8.52817i	−1.11758	−	1.33188i	−0.180172	−	0.983635i	$-0.557666\pi$
$42$	−0.679476	+	0.277921i	−0.104845	+	0.0428841i
$43$	3.99477	+	1.86279i	0.609197	+	0.284073i	0.702634	−	0.711552i	$-0.252007\pi$
$43$	3.99477	+	1.86279i	0.609197	+	0.284073i	−0.0934362	+	0.995625i	$0.529785\pi$
$44$	−1.71910	−	2.97756i	−0.259163	−	0.448884i
$45$		0			0
$46$	0.514936	−	0.891896i	0.0759232	−	0.131503i
$47$	9.15123	−	6.40776i	1.33484	−	0.934668i	0.334874	−	0.942263i	$-0.391306\pi$
$47$	9.15123	−	6.40776i	1.33484	−	0.934668i	0.999971	+	0.00759474i	$0.00241751\pi$
$48$	−5.68299	+	0.222855i	−0.820269	+	0.0321664i
$49$	1.89001	−	5.19277i	0.270002	−	0.741824i
$50$		0			0
$51$	−1.86477	+	2.89862i	−0.261119	+	0.405888i
$52$	0.652418	−	0.0570792i	0.0904741	−	0.00791545i
$53$	5.25853	−	5.25853i	0.722314	−	0.722314i	−0.246762	−	0.969076i	$-0.579367\pi$
$53$	5.25853	−	5.25853i	0.722314	−	0.722314i	0.969076	+	0.246762i	$0.0793666\pi$
$54$	−1.35364	+	1.20761i	−0.184206	+	0.164335i
$55$		0			0
$56$	1.05656	−	1.25916i	0.141189	−	0.168262i
$57$	−6.47831	−	7.13315i	−0.858074	−	0.944809i
$58$	0.351629	−	0.502179i	0.0461712	−	0.0659393i
$59$	5.35536	+	1.94919i	0.697209	+	0.253763i	0.666219	−	0.745756i	$-0.267912\pi$
$59$	5.35536	+	1.94919i	0.697209	+	0.253763i	0.0309902	+	0.999520i	$0.490134\pi$
$60$		0			0
$61$	1.30500	−	7.40100i	0.167088	−	0.947602i	−0.779798	−	0.626031i	$-0.784678\pi$
$61$	1.30500	−	7.40100i	0.167088	−	0.947602i	0.946886	−	0.321570i	$-0.104211\pi$
$62$	−0.723312	+	0.193811i	−0.0918608	+	0.0246140i
$63$	−0.0323344	+	3.64208i	−0.00407376	+	0.458858i
$64$	4.52212	−	2.61085i	0.565265	−	0.326356i
$65$		0			0
$66$	1.09811	−	0.139612i	0.135167	−	0.0171851i
$67$	−0.854027	+	9.76158i	−0.104336	+	1.19257i	0.745861	+	0.666102i	$0.232038\pi$
$67$	−0.854027	+	9.76158i	−0.104336	+	1.19257i	−0.850197	+	0.526465i	$0.823517\pi$
$68$	0.325729	−	3.72310i	0.0395004	−	0.451492i
$69$	−3.09249	−	4.06746i	−0.372291	−	0.489665i
$70$		0			0
$71$	−13.6425	+	7.87649i	−1.61906	+	0.934767i	−0.631901	+	0.775049i	$0.717725\pi$
$71$	−13.6425	+	7.87649i	−1.61906	+	0.934767i	−0.987163	+	0.159718i	$0.948942\pi$
$72$	1.42299	−	3.80422i	0.167702	−	0.448332i
$73$	11.5895	−	3.10541i	1.35645	−	0.363460i	0.493940	−	0.869496i	$-0.335556\pi$
$73$	11.5895	−	3.10541i	1.35645	−	0.363460i	0.862513	+	0.506036i	$0.168890\pi$
$74$	−0.101488	+	0.575568i	−0.0117978	+	0.0669084i
$75$		0			0
$76$	9.81841	+	3.57361i	1.12625	+	0.409921i
$77$	1.27480	−	1.82060i	0.145277	−	0.207477i
$78$	−0.0642964	+	0.200810i	−0.00728013	+	0.0227372i
$79$	−9.65809	+	11.5101i	−1.08662	+	1.29498i	−0.133946	+	0.990989i	$0.542765\pi$
$79$	−9.65809	+	11.5101i	−1.08662	+	1.29498i	−0.952674	+	0.303995i	$0.901679\pi$
$80$		0			0
$81$	2.92754	+	8.51055i	0.325282	+	0.945617i
$82$	−2.74819	+	2.74819i	−0.303487	+	0.303487i
$83$	−12.8776	+	1.12664i	−1.41350	+	0.123665i	−0.768174	−	0.640241i	$-0.778834\pi$
$83$	−12.8776	+	1.12664i	−1.41350	+	0.123665i	−0.645327	+	0.763906i	$0.723279\pi$
$84$	−1.80806	−	3.51121i	−0.197275	−	0.383104i
$85$		0			0
$86$	0.526293	−	1.44598i	0.0567517	−	0.155924i
$87$	−1.62282	−	2.57244i	−0.173985	−	0.275795i
$88$	−2.03026	+	1.42160i	−0.216426	+	0.151543i
$89$	1.27248	−	2.20400i	0.134883	−	0.233623i	−0.790670	−	0.612243i	$-0.790268\pi$
$89$	1.27248	−	2.20400i	0.134883	−	0.233623i	0.925553	+	0.378619i	$0.123601\pi$
$90$		0			0
$91$	0.211676	+	0.366634i	0.0221897	+	0.0384337i
$92$	5.02139	+	2.34151i	0.523516	+	0.244119i
$93$	−0.501277	+	3.68124i	−0.0519801	+	0.381726i
$94$	−2.50693	−	2.98764i	−0.258570	−	0.308152i
$95$		0			0
$96$	0.841940	+	6.62218i	0.0859301	+	0.675874i
$97$	−2.57343	+	5.51873i	−0.261292	+	0.560342i	−0.992561	−	0.121746i	$-0.961151\pi$
$97$	−2.57343	+	5.51873i	−0.261292	+	0.560342i	0.731269	+	0.682089i	$0.238928\pi$
$98$	−1.86344	−	0.499308i	−0.188236	−	0.0504378i
$99$	1.46846	−	5.29200i	0.147586	−	0.531866i
$100$		0			0
$101$	6.16986	+	1.08791i	0.613924	+	0.108251i	0.471959	−	0.881620i	$-0.343547\pi$
$101$	6.16986	+	1.08791i	0.613924	+	0.108251i	0.141965	+	0.989872i	$0.454658\pi$
$102$	1.06482	+	0.560332i	0.105433	+	0.0554811i
$103$	−6.03233	−	12.9364i	−0.594383	−	1.27466i	−0.941556	−	0.336858i	$-0.890636\pi$
$103$	−6.03233	−	12.9364i	−0.594383	−	1.27466i	0.347172	−	0.937801i	$-0.387142\pi$
$104$	−0.0819802	−	0.464933i	−0.00803882	−	0.0455904i
$105$		0			0
$106$	−1.98881	−	1.66881i	−0.193170	−	0.162089i
$107$	12.7480	+	12.7480i	1.23240	+	1.23240i	0.963041	+	0.269355i	$0.0868104\pi$
$107$	12.7480	+	12.7480i	1.23240	+	1.23240i	0.269355	+	0.963041i	$0.413190\pi$
$108$	−7.10667	−	6.68832i	−0.683839	−	0.643584i
$109$			9.14545i			0.875976i	0.898981	+	0.437988i	$0.144309\pi$
$109$			9.14545i			0.875976i	−0.898981	+	0.437988i	$0.855691\pi$
$110$		0			0
$111$	2.43860	+	1.56882i	0.231462	+	0.148906i
$112$	3.26557	+	2.28658i	0.308567	+	0.216061i
$113$	−11.0711	+	5.16253i	−1.04148	+	0.485650i	−0.866633	−	0.498946i	$-0.833721\pi$
$113$	−11.0711	+	5.16253i	−1.04148	+	0.485650i	−0.174846	+	0.984596i	$0.555943\pi$
$114$	−2.28365	+	2.47006i	−0.213883	+	0.231343i
$115$		0			0
$116$	2.85620	+	1.64903i	0.265192	+	0.153108i
$117$	0.795368	+	0.679516i	0.0735318	+	0.0628213i
$118$	0.514943	−	1.92179i	0.0474043	−	0.176915i
$119$	2.27021	−	0.826290i	0.208110	−	0.0757459i
$120$		0			0
$121$	5.85925	−	4.91650i	0.532659	−	0.446954i
$122$	−2.61362	−	0.228662i	−0.236626	−	0.0207021i
$123$	7.29993	+	17.8473i	0.658213	+	1.60923i
$124$	−1.37784	−	3.78558i	−0.123734	−	0.339955i
$125$		0			0
$126$	1.26762	−	0.0995713i	0.112929	−	0.00887051i
$127$	1.77940	+	6.64080i	0.157896	+	0.589276i	0.998840	+	0.0481536i	$0.0153337\pi$
$127$	1.77940	+	6.64080i	0.157896	+	0.589276i	−0.840944	+	0.541122i	$0.818000\pi$
$128$	−5.46683	−	7.80744i	−0.483204	−	0.690087i
$129$	−5.60575	−	5.18269i	−0.493559	−	0.456310i
$130$		0			0
$131$	−18.1487	+	3.20011i	−1.58566	+	0.279595i	−0.895837	−	0.444384i	$-0.853423\pi$
$131$	−18.1487	+	3.20011i	−1.58566	+	0.279595i	−0.689823	+	0.723978i	$0.742312\pi$
$132$	1.26310	+	5.81963i	0.109939	+	0.506534i
$133$	0.588670	+	6.72853i	0.0510442	+	0.583438i
$134$	3.42086			0.295517
$135$		0			0
$136$	−2.69412			−0.231019
$137$	0.0433972	+	0.496033i	0.00370768	+	0.0423789i	0.997823	−	0.0659466i	$-0.0210067\pi$
$137$	0.0433972	+	0.496033i	0.00370768	+	0.0423789i	−0.994115	+	0.108325i	$0.965451\pi$
$138$	−1.32049	+	1.19926i	−0.112407	+	0.102088i
$139$	−1.39820	+	0.246540i	−0.118594	+	0.0209113i	−0.232630	−	0.972565i	$-0.574733\pi$
$139$	−1.39820	+	0.246540i	−0.118594	+	0.0209113i	0.114036	+	0.993477i	$0.463622\pi$
$140$		0			0
$141$	−18.4798	+	5.73661i	−1.55628	+	0.483110i
$142$	3.15438	+	4.50492i	0.264709	+	0.378044i
$143$	−0.165219	−	0.616605i	−0.0138163	−	0.0515631i
$144$	9.49212	+	2.63394i	0.791010	+	0.219495i
$145$		0			0
$146$	−1.43263	−	3.93611i	−0.118565	−	0.325755i
$147$	−5.86032	+	7.56753i	−0.483351	+	0.624159i
$148$	−3.13223	−	0.274035i	−0.257468	−	0.0225255i
$149$	−12.3163	+	10.3346i	−1.00899	+	0.846644i	−0.988204	−	0.153140i	$-0.951061\pi$
$149$	−12.3163	+	10.3346i	−1.00899	+	0.846644i	−0.0207862	+	0.999784i	$0.506617\pi$
$150$		0			0
$151$	−0.578102	+	0.210412i	−0.0470453	+	0.0171231i	−0.365436	−	0.930837i	$-0.619080\pi$
$151$	−0.578102	+	0.210412i	−0.0470453	+	0.0171231i	0.318390	+	0.947960i	$0.396858\pi$
$152$	1.94943	−	7.27539i	0.158120	−	0.590112i
$153$	4.60699	−	3.79654i	0.372453	−	0.306932i
$154$	−0.671956	−	0.387954i	−0.0541478	−	0.0312622i
$155$		0			0
$156$	−1.10635	−	0.250429i	−0.0885787	−	0.0200504i
$157$	−7.55527	+	3.52308i	−0.602976	+	0.281172i	−0.700038	−	0.714106i	$-0.746833\pi$
$157$	−7.55527	+	3.52308i	−0.602976	+	0.281172i	0.0970614	+	0.995278i	$0.469056\pi$
$158$	4.29683	+	3.00867i	0.341837	+	0.239357i
$159$	−11.4516	+	5.89687i	−0.908172	+	0.467652i
$160$		0			0
$161$			3.58153i			0.282264i
$162$	2.87072	−	1.27709i	0.225545	−	0.100337i
$163$	12.1060	+	12.1060i	0.948215	+	0.948215i	0.998724	−	0.0505083i	$-0.0160841\pi$
$163$	12.1060	+	12.1060i	0.948215	+	0.948215i	−0.0505083	+	0.998724i	$0.516084\pi$
$164$	−16.0170	−	13.4398i	−1.25071	−	1.04947i
$165$		0			0
$166$	0.783648	+	4.44429i	0.0608228	+	0.344943i
$167$	7.59058	+	16.2781i	0.587377	+	1.25963i	0.945397	+	0.325920i	$0.105674\pi$
$167$	7.59058	+	16.2781i	0.587377	+	1.25963i	−0.358020	+	0.933714i	$0.616548\pi$
$168$	−2.40790	+	1.51902i	−0.185773	+	0.117195i
$169$	−12.6828	−	2.23631i	−0.975596	−	0.172024i
$170$		0			0
$171$	6.91887	+	15.1882i	0.529099	+	1.16147i
$172$	7.99621	+	2.14258i	0.609706	+	0.163370i
$173$	−3.14693	+	6.74861i	−0.239257	+	0.513088i	−0.988869	−	0.148790i	$-0.952462\pi$
$173$	−3.14693	+	6.74861i	−0.239257	+	0.513088i	0.749612	+	0.661877i	$0.230240\pi$
$174$	−0.845266	+	0.642654i	−0.0640794	+	0.0487195i
$175$		0			0
$176$	−3.86388	−	4.60479i	−0.291251	−	0.347099i
$177$	−7.80449	−	6.04382i	−0.586621	−	0.454282i
$178$	−0.805223	−	0.375482i	−0.0603540	−	0.0281435i
$179$	1.32416	+	2.29350i	0.0989720	+	0.171425i	0.911259	−	0.411833i	$-0.135111\pi$
$179$	1.32416	+	2.29350i	0.0989720	+	0.171425i	−0.812287	+	0.583257i	$0.801778\pi$
$180$		0			0
$181$	−4.01126	+	6.94770i	−0.298155	+	0.516419i	−0.975714	−	0.219049i	$-0.929704\pi$
$181$	−4.01126	+	6.94770i	−0.298155	+	0.516419i	0.677559	+	0.735468i	$0.263038\pi$
$182$	0.121067	−	0.0847721i	0.00897409	−	0.00628373i
$183$	−6.06162	+	11.5191i	−0.448088	+	0.851519i
$184$	1.36602	−	3.75311i	0.100704	−	0.276683i
$185$		0			0
$186$	1.29551	+	0.0623259i	0.0949914	+	0.00456996i
$187$	−3.62899	+	0.317496i	−0.265378	+	0.0232176i
$188$	14.8363	−	14.8363i	1.08205	−	1.08205i
$189$	1.97695	−	5.99074i	0.143802	−	0.435762i
$190$		0			0
$191$	7.76324	−	9.25187i	0.561728	−	0.669442i	−0.408183	−	0.912900i	$-0.633838\pi$
$191$	7.76324	−	9.25187i	0.561728	−	0.669442i	0.969911	+	0.243458i	$0.0782820\pi$
$192$	−8.83846	+	1.91832i	−0.637861	+	0.138443i
$193$	4.46264	−	6.37332i	0.321228	−	0.458761i	−0.625767	−	0.780010i	$-0.715214\pi$
$193$	4.46264	−	6.37332i	0.321228	−	0.458761i	0.946995	+	0.321249i	$0.104103\pi$
$194$	1.99760	+	0.727068i	0.143420	+	0.0522004i
$195$		0			0
$196$	1.80222	−	10.2209i	0.128730	−	0.730063i
$197$	−0.538437	+	0.144274i	−0.0383620	+	0.0102791i	−0.277949	−	0.960596i	$-0.589655\pi$
$197$	−0.538437	+	0.144274i	−0.0383620	+	0.0102791i	0.239587	+	0.970875i	$0.422988\pi$
$198$	−1.88513	−	0.349683i	−0.133970	−	0.0248509i
$199$	−2.90871	+	1.67935i	−0.206193	+	0.119046i	−0.599541	−	0.800344i	$-0.704650\pi$
$199$	−2.90871	+	1.67935i	−0.206193	+	0.119046i	0.393348	+	0.919390i	$0.371317\pi$
$200$		0			0
$201$	6.56449	−	15.6512i	0.463023	−	1.10395i
$202$	0.190625	−	2.17885i	0.0134123	−	0.153304i
$203$	−0.185812	+	2.12385i	−0.0130415	+	0.149065i
$204$	−2.50372	+	5.96943i	−0.175295	+	0.417943i
$205$		0			0
$206$	−4.31546	+	2.49153i	−0.300672	+	0.173593i
$207$	2.95294	+	8.34286i	0.205244	+	0.579869i
$208$	1.10599	−	0.296349i	0.0766865	−	0.0205481i
$209$	1.76851	−	10.0297i	0.122330	−	0.693770i
$210$		0			0
$211$	12.2782	+	4.46890i	0.845267	+	0.307652i	0.728109	−	0.685461i	$-0.240399\pi$
$211$	12.2782	+	4.46890i	0.845267	+	0.307652i	0.117158	+	0.993113i	$0.462622\pi$
$212$	8.01114	−	11.4411i	0.550208	−	0.785778i
$213$	26.6641	−	5.78724i	1.82700	−	0.396535i
$214$	4.04561	−	4.82137i	0.276552	−	0.329582i
$215$		0			0
$216$	−4.35657	+	5.52370i	−0.296427	+	0.375841i
$217$	1.84142	−	1.84142i	0.125004	−	0.125004i
$218$	3.18060	−	0.278266i	0.215417	−	0.0188466i
$219$	−20.7578	−	0.998640i	−1.40268	−	0.0674818i
$220$		0			0
$221$	0.237326	−	0.652047i	0.0159643	−	0.0438615i
$222$	0.471406	−	0.895830i	0.0316387	−	0.0601242i
$223$	−13.0904	+	9.16597i	−0.876595	+	0.613799i	−0.922862	−	0.385131i	$-0.874156\pi$
$223$	−13.0904	+	9.16597i	−0.876595	+	0.613799i	0.0462669	+	0.998929i	$0.485268\pi$
$224$	2.33958	−	4.05227i	0.156320	−	0.270753i
$225$		0			0
$226$	2.13228	+	3.69321i	0.141837	+	0.245669i
$227$	−8.41164	−	3.92241i	−0.558300	−	0.260340i	0.122922	−	0.992416i	$-0.460774\pi$
$227$	−8.41164	−	3.92241i	−0.558300	−	0.260340i	−0.681222	+	0.732077i	$0.738551\pi$
$228$	−14.3086	−	11.0806i	−0.947609	−	0.733832i
$229$	4.29414	+	5.11756i	0.283765	+	0.338178i	0.889032	−	0.457844i	$-0.151378\pi$
$229$	4.29414	+	5.11756i	0.283765	+	0.338178i	−0.605268	+	0.796022i	$0.706934\pi$
$230$		0			0
$231$	−3.06444	+	2.32989i	−0.201625	+	0.153295i
$232$	1.00476	−	2.15472i	0.0659659	−	0.141464i
$233$	5.37169	+	1.43934i	0.351911	+	0.0942942i	0.430444	−	0.902617i	$-0.358357\pi$
$233$	5.37169	+	1.43934i	0.351911	+	0.0942942i	−0.0785332	+	0.996911i	$0.525024\pi$
$234$	0.212121	−	0.297288i	0.0138668	−	0.0194343i
$235$		0			0
$236$	10.5409	+	1.85865i	0.686156	+	0.120988i
$237$	22.0108	−	13.8855i	1.42975	−	0.901957i
$238$	−0.356442	−	0.764392i	−0.0231047	−	0.0495482i
$239$	−1.28207	−	7.27098i	−0.0829302	−	0.470320i	−0.997784	−	0.0665354i	$-0.978805\pi$
$239$	−1.28207	−	7.27098i	−0.0829302	−	0.470320i	0.914854	−	0.403785i	$-0.132306\pi$
$240$		0			0
$241$	−11.5447	−	9.68711i	−0.743656	−	0.624002i	0.190161	−	0.981753i	$-0.439099\pi$
$241$	−11.5447	−	9.68711i	−0.743656	−	0.624002i	−0.933817	+	0.357751i	$0.883544\pi$
$242$	−1.88813	−	1.88813i	−0.121374	−	0.121374i
$243$	−0.334171	−	15.5849i	−0.0214371	−	0.999770i
$244$		−	14.1144i		−	0.903584i
$245$		0			0
$246$	5.98479	−	3.08180i	0.381577	−	0.196488i
$247$	1.58911	+	1.11270i	0.101112	+	0.0707997i
$248$	−2.63196	+	1.22730i	−0.167130	+	0.0779339i
$249$	21.8374	+	4.94304i	1.38389	+	0.313252i
$250$		0			0
$251$	24.4606	+	14.1224i	1.54394	+	0.891395i	0.998584	+	0.0531910i	$0.0169392\pi$
$251$	24.4606	+	14.1224i	1.54394	+	0.891395i	0.545357	+	0.838204i	$0.316394\pi$
$252$	1.12799	+	6.74689i	0.0710570	+	0.425014i
$253$	1.39774	−	5.21643i	0.0878751	−	0.327954i
$254$	2.25539	−	0.820896i	0.141516	−	0.0515076i
$255$		0			0
$256$	5.45117	−	4.57408i	0.340698	−	0.285880i
$257$	−20.1058	−	1.75903i	−1.25417	−	0.109725i	−0.559362	−	0.828924i	$-0.688954\pi$
$257$	−20.1058	−	1.75903i	−1.25417	−	0.109725i	−0.694805	+	0.719198i	$0.744509\pi$
$258$	−1.63187	+	2.10726i	−0.101596	+	0.131192i
$259$	−0.695156	−	1.90992i	−0.0431949	−	0.118677i
$260$		0			0
$261$	1.31826	+	5.10051i	0.0815982	+	0.315714i
$262$	1.66514	+	6.21438i	0.102872	+	0.383925i
$263$	−7.28196	−	10.3997i	−0.449025	−	0.641274i	0.529279	−	0.848448i	$-0.322462\pi$
$263$	−7.28196	−	10.3997i	−0.449025	−	0.641274i	−0.978304	+	0.207174i	$0.933573\pi$
$264$	4.09987	−	1.27270i	0.252330	−	0.0783296i
$265$		0			0
$266$	2.32213	−	0.409455i	0.142379	−	0.0251053i
$267$	−3.26310	+	2.96354i	−0.199699	+	0.181366i
$268$	1.60397	+	18.3334i	0.0979780	+	1.11989i
$269$	19.2549			1.17399			0.586995	−	0.809591i	$-0.300311\pi$
$269$	19.2549			1.17399			0.586995	+	0.809591i	$0.300311\pi$
$270$		0			0
$271$	−21.6954			−1.31790			−0.658952	−	0.752185i	$-0.729000\pi$
$271$	−21.6954			−1.31790			−0.658952	+	0.752185i	$0.729000\pi$
$272$	−0.569484	−	6.50923i	−0.0345301	−	0.394680i
$273$	−0.155529	−	0.716584i	−0.00941304	−	0.0433696i
$274$	0.171189	−	0.0301853i	0.0103419	−	0.00182356i
$275$		0			0
$276$	−7.04636	−	6.51458i	−0.424141	−	0.392132i
$277$	−14.8367	−	21.1890i	−0.891452	−	1.27312i	−0.961282	−	0.275566i	$-0.911135\pi$
$277$	−14.8367	−	21.1890i	−0.891452	−	1.27312i	0.0698305	−	0.997559i	$-0.477754\pi$
$278$	0.128284	+	0.478764i	0.00769399	+	0.0287143i
$279$	2.77119	−	5.80765i	0.165907	−	0.347695i
$280$		0			0
$281$	1.44986	+	3.98347i	0.0864916	+	0.237634i	0.975396	−	0.220458i	$-0.0707553\pi$
$281$	1.44986	+	3.98347i	0.0864916	+	0.237634i	−0.888905	+	0.458092i	$0.848533\pi$
$282$	2.55736	+	6.25236i	0.152288	+	0.372323i
$283$	−14.2374	−	1.24561i	−0.846327	−	0.0740440i	−0.344262	−	0.938874i	$-0.611871\pi$
$283$	−14.2374	−	1.24561i	−0.846327	−	0.0740440i	−0.502065	+	0.864830i	$0.667426\pi$
$284$	−22.6642	+	19.0175i	−1.34487	+	1.12848i
$285$		0			0
$286$	−0.209415	+	0.0762210i	−0.0123830	+	0.00450704i
$287$	3.49819	−	13.0554i	0.206491	−	0.770636i
$288$	2.10878	−	11.3684i	0.124261	−	0.669887i
$289$	11.2932	+	6.52011i	0.664303	+	0.383536i
$290$		0			0
$291$	7.15982	−	7.74428i	0.419716	−	0.453977i
$292$	20.4231	−	9.52346i	1.19517	−	0.557318i
$293$	23.5035	+	16.4573i	1.37309	+	0.961447i	0.999426	+	0.0338821i	$0.0107871\pi$
$293$	23.5035	+	16.4573i	1.37309	+	0.961447i	0.373663	+	0.927565i	$0.378102\pi$
$294$	2.81014	+	1.80784i	0.163891	+	0.105436i
$295$		0			0
$296$			2.26656i			0.131741i
$297$	−5.21736	+	7.95386i	−0.302742	+	0.461530i
$298$	3.96891	+	3.96891i	0.229913	+	0.229913i
$299$	0.788016	+	0.661224i	0.0455722	+	0.0382396i
$300$		0			0
$301$	0.929248	+	5.27003i	0.0535609	+	0.303759i
$302$	0.0907668	+	0.194650i	0.00522304	+	0.0112008i
$303$	−9.60295	−	5.05328i	−0.551675	−	0.290303i
$304$	17.9901	+	3.17213i	1.03180	+	0.181934i
$305$		0			0
$306$	−1.46053	−	1.48670i	−0.0834932	−	0.0849890i
$307$	−2.18762	−	0.586171i	−0.124854	−	0.0334545i	0.195851	−	0.980634i	$-0.437253\pi$
$307$	−2.18762	−	0.586171i	−0.124854	−	0.0334545i	−0.320705	+	0.947179i	$0.603920\pi$
$308$	1.76410	−	3.78312i	0.100519	−	0.215564i
$309$	3.11814	+	24.5254i	0.177385	+	1.39520i
$310$		0			0
$311$	−7.85950	−	9.36659i	−0.445672	−	0.531131i	0.495704	−	0.868492i	$-0.334910\pi$
$311$	−7.85950	−	9.36659i	−0.445672	−	0.531131i	−0.941375	+	0.337361i	$0.890466\pi$
$312$	−0.110330	+	0.810233i	−0.00624622	+	0.0458704i
$313$	−15.3315	−	7.14921i	−0.866590	−	0.404097i	−0.0621042	−	0.998070i	$-0.519781\pi$
$313$	−15.3315	−	7.14921i	−0.866590	−	0.404097i	−0.804486	+	0.593972i	$0.797559\pi$
$314$	1.45514	+	2.52037i	0.0821181	+	0.142233i
$315$		0			0
$316$	−14.1097	+	24.4387i	−0.793733	+	1.37479i
$317$	−10.2285	+	7.16210i	−0.574492	+	0.402264i	−0.824401	−	0.566006i	$-0.808488\pi$
$317$	−10.2285	+	7.16210i	−0.574492	+	0.402264i	0.249909	+	0.968269i	$0.419599\pi$
$318$	2.39925	+	3.80321i	0.134543	+	0.213274i
$319$	1.09949	−	3.02083i	0.0615597	−	0.169134i
$320$		0			0
$321$	−14.2955	−	27.7616i	−0.797898	−	1.54950i
$322$	1.24558	−	0.108974i	0.0694136	−	0.00607290i
$323$	7.82802	−	7.82802i	0.435563	−	0.435563i
$324$	8.19032	+	14.7863i	0.455018	+	0.821460i
$325$		0			0
$326$	3.84187	−	4.57856i	0.212782	−	0.253583i
$327$	4.83031	−	15.0860i	0.267117	−	0.834255i
$328$	−8.64519	+	12.3466i	−0.477351	+	0.681728i
$329$	12.7452	+	4.63886i	0.702664	+	0.255749i
$330$		0			0
$331$	3.65344	−	20.7197i	0.200811	−	1.13886i	−0.703086	−	0.711105i	$-0.748195\pi$
$331$	3.65344	−	20.7197i	0.200811	−	1.13886i	0.903897	−	0.427751i	$-0.140694\pi$
$332$	−23.4509	+	6.28364i	−1.28703	+	0.344860i
$333$	−3.19402	−	3.87585i	−0.175031	−	0.212395i
$334$	5.43022	−	3.13514i	0.297128	−	0.171547i
$335$		0			0
$336$	−4.17906	−	5.49660i	−0.227986	−	0.299864i
$337$	2.73757	−	31.2906i	0.149125	−	1.70451i	−0.441255	−	0.897382i	$-0.645467\pi$
$337$	2.73757	−	31.2906i	0.149125	−	1.70451i	0.590380	−	0.807125i	$-0.298978\pi$
$338$	−0.391848	+	4.47884i	−0.0213137	+	0.243617i
$339$	20.9891	−	2.66853i	1.13997	−	0.144935i
$340$		0			0
$341$	−3.40063	+	1.96335i	−0.184154	+	0.106322i
$342$	5.07161	−	2.86837i	0.274241	−	0.155104i
$343$	14.6893	−	3.93599i	0.793149	−	0.212524i
$344$	1.03626	−	5.87691i	0.0558713	−	0.316862i
$345$		0			0
$346$	2.44278	+	0.889099i	0.131325	+	0.0477983i
$347$	−3.47900	+	4.96853i	−0.186763	+	0.266725i	−0.901604	−	0.432562i	$-0.857610\pi$
$347$	−3.47900	+	4.96853i	−0.186763	+	0.266725i	0.714842	+	0.699286i	$0.246499\pi$
$348$	−3.84051	−	4.22871i	−0.205873	−	0.226683i
$349$	−6.64292	+	7.91672i	−0.355587	+	0.423772i	−0.913951	−	0.405824i	$-0.866985\pi$
$349$	−6.64292	+	7.91672i	−0.355587	+	0.423772i	0.558364	+	0.829596i	$0.311429\pi$
$350$		0			0
$351$	−0.953109	−	1.54099i	−0.0508732	−	0.0822518i
$352$	−4.98900	+	4.98900i	−0.265915	+	0.265915i
$353$	−13.4872	+	1.17998i	−0.717851	+	0.0628039i	−0.440228	−	0.897886i	$-0.645102\pi$
$353$	−13.4872	+	1.17998i	−0.717851	+	0.0628039i	−0.277624	+	0.960690i	$0.589547\pi$
$354$	−1.86445	+	2.89813i	−0.0990945	+	0.154034i
$355$		0			0
$356$	1.63477	−	4.49149i	0.0866426	−	0.238049i
$357$	−4.18126	+	0.163966i	−0.221296	+	0.00867799i
$358$	0.757344	−	0.530298i	0.0400269	−	0.0280271i
$359$	−4.91852	+	8.51912i	−0.259589	+	0.449622i	−0.966132	−	0.258049i	$-0.916921\pi$
$359$	−4.91852	+	8.51912i	−0.259589	+	0.449622i	0.706543	+	0.707670i	$0.250254\pi$
$360$		0			0
$361$	5.97506	+	10.3491i	0.314477	+	0.544690i
$362$	2.53832	+	1.18364i	0.133411	+	0.0622106i
$363$	−12.2619	+	5.01539i	−0.643583	+	0.263240i
$364$	0.511086	+	0.609088i	0.0267882	+	0.0319249i
$365$		0			0
$366$	4.19055	+	1.75762i	0.219044	+	0.0918721i
$367$	−2.65847	+	5.70110i	−0.138771	+	0.297595i	−0.963395	−	0.268086i	$-0.913609\pi$
$367$	−2.65847	+	5.70110i	−0.138771	+	0.297595i	0.824624	+	0.565681i	$0.191387\pi$
$368$	9.35658	+	2.50709i	0.487746	+	0.130691i
$369$	−2.61536	−	33.2957i	−0.136150	−	1.73330i
$370$		0			0
$371$	8.89150	+	1.56781i	0.461624	+	0.0813967i
$372$	0.273413	+	6.97226i	0.0141758	+	0.361495i
$373$	−9.46829	−	20.3048i	−0.490249	−	1.05134i	−0.983409	−	0.181404i	$-0.941936\pi$
$373$	−9.46829	−	20.3048i	−0.490249	−	1.05134i	0.493159	−	0.869939i	$-0.335842\pi$
$374$	0.220837	+	1.25243i	0.0114192	+	0.0647615i
$375$		0			0
$376$	−11.5865	−	9.72219i	−0.597526	−	0.501383i
$377$	0.432989	+	0.432989i	0.0223000	+	0.0223000i
$378$	−2.14361	−	0.505265i	−0.110255	−	0.0259880i
$379$			19.0825i			0.980201i	0.871666	+	0.490101i	$0.163040\pi$
$379$			19.0825i			0.980201i	−0.871666	+	0.490101i	$0.836960\pi$
$380$		0			0
$381$	0.572220	−	11.8942i	0.0293157	−	0.609358i
$382$	−3.45382	−	2.41839i	−0.176713	−	0.123736i
$383$	−33.8190	+	15.7700i	−1.72807	+	0.805811i	−0.736467	+	0.676473i	$0.763507\pi$
$383$	−33.8190	+	15.7700i	−1.72807	+	0.805811i	−0.991601	+	0.129338i	$0.958715\pi$
$384$	4.89423	+	15.7662i	0.249758	+	0.804566i
$385$		0			0
$386$	−2.35229	−	1.35810i	−0.119729	−	0.0691253i
$387$	6.50969	+	11.5099i	0.330906	+	0.585081i
$388$	−2.95995	+	11.0467i	−0.150269	+	0.560810i
$389$	15.5765	−	5.66936i	0.789757	−	0.287448i	0.0845222	−	0.996422i	$-0.473064\pi$
$389$	15.5765	−	5.66936i	0.789757	−	0.287448i	0.705235	+	0.708973i	$0.250841\pi$
$390$		0			0
$391$	4.49691	−	3.77335i	0.227418	−	0.190827i
$392$	−7.45313	−	0.652064i	−0.376440	−	0.0329342i
$393$	31.6275	+	4.30675i	1.59540	+	0.217247i
$394$	0.0665583	+	0.182867i	0.00335316	+	0.00921273i
$395$		0			0
$396$	0.990160	−	10.2669i	0.0497574	−	0.515933i
$397$	−5.85505	−	21.8514i	−0.293857	−	1.09669i	−0.942121	−	0.335273i	$-0.891171\pi$
$397$	−5.85505	−	21.8514i	−0.293857	−	1.09669i	0.648264	−	0.761415i	$-0.275495\pi$
$398$	0.672545	+	0.960494i	0.0337116	+	0.0481452i
$399$	2.58273	−	11.4100i	0.129298	−	0.571215i
$400$		0			0
$401$	16.6110	−	2.92896i	0.829512	−	0.146265i	0.257259	−	0.966342i	$-0.417181\pi$
$401$	16.6110	−	2.92896i	0.829512	−	0.146265i	0.572253	+	0.820077i	$0.306069\pi$
$402$	−5.64291	−	1.80678i	−0.281443	−	0.0901139i
$403$	−0.0651892	−	0.745116i	−0.00324731	−	0.0371169i
$404$	11.7665			0.585406
$405$		0			0
$406$	0.744283			0.0369382
$407$	0.267108	+	3.05306i	0.0132401	+	0.151335i
$408$	4.44411	+	1.42294i	0.220016	+	0.0704461i
$409$	18.0511	−	3.18290i	0.892572	−	0.157384i	0.291492	−	0.956573i	$-0.405848\pi$
$409$	18.0511	−	3.18290i	0.892572	−	0.157384i	0.601080	+	0.799189i	$0.294737\pi$
$410$		0			0
$411$	0.190401	−	0.841156i	0.00939178	−	0.0414911i
$412$	−15.3763	−	21.9597i	−0.757537	−	1.08187i
$413$	1.79079	+	6.68331i	0.0881189	+	0.328864i
$414$	2.81163	−	1.28082i	0.138184	−	0.0629488i
$415$		0			0
$416$	−0.459655	−	1.26289i	−0.0225364	−	0.0619183i
$417$	2.43663	+	0.331798i	0.119322	+	0.0162482i
$418$	−3.54194	−	0.309879i	−0.173242	−	0.0151567i
$419$	−15.7554	+	13.2204i	−0.769702	+	0.645857i	−0.940633	−	0.339426i	$-0.889767\pi$
$419$	−15.7554	+	13.2204i	−0.769702	+	0.645857i	0.170930	+	0.985283i	$0.445323\pi$
$420$		0			0
$421$	−20.2545	+	7.37202i	−0.987143	+	0.359290i	−0.784613	−	0.619986i	$-0.787138\pi$
$421$	−20.2545	+	7.37202i	−0.987143	+	0.359290i	−0.202529	+	0.979276i	$0.564916\pi$
$422$	1.18061	−	4.40608i	0.0574710	−	0.214485i
$423$	33.5135	+	0.297533i	1.62948	+	0.0144666i
$424$	−8.71949	−	5.03420i	−0.423456	−	0.244482i
$425$		0			0
$426$	−2.82399	−	9.09715i	−0.136823	−	0.440758i
$427$	8.26913	−	3.85596i	0.400171	−	0.186603i
$428$	27.7361	+	19.4210i	1.34068	+	0.938752i
$429$	−0.0531312	+	1.10439i	−0.00256520	+	0.0533204i
$430$		0			0
$431$			12.5960i			0.606728i	0.952875	+	0.303364i	$0.0981099\pi$
$431$			12.5960i			0.606728i	−0.952875	+	0.303364i	$0.901890\pi$
$432$	−14.2666	−	9.35825i	−0.686404	−	0.450249i
$433$	−21.2452	−	21.2452i	−1.02098	−	1.02098i	−0.999775	−	0.0212037i	$-0.993250\pi$
$433$	−21.2452	−	21.2452i	−1.02098	−	1.02098i	−0.0212037	−	0.999775i	$-0.506750\pi$
$434$	−0.696435	−	0.584379i	−0.0334300	−	0.0280511i
$435$		0			0
$436$	2.98263	+	16.9153i	0.142842	+	0.810098i
$437$	6.93591	+	14.8741i	0.331789	+	0.711525i
$438$	0.284285	+	7.24951i	0.0135837	+	0.346395i
$439$	−18.8946	−	3.33163i	−0.901790	−	0.159010i	−0.296517	−	0.955028i	$-0.595825\pi$
$439$	−18.8946	−	3.33163i	−0.901790	−	0.159010i	−0.605273	+	0.796018i	$0.706936\pi$
$440$		0			0
$441$	13.6639	−	9.38786i	0.650660	−	0.447041i
$442$	−0.233990	−	0.0626973i	−0.0111298	−	0.00298221i
$443$	−4.83128	+	10.3607i	−0.229541	+	0.492252i	−0.987018	−	0.160610i	$-0.948654\pi$
$443$	−4.83128	+	10.3607i	−0.229541	+	0.492252i	0.757477	+	0.652862i	$0.226432\pi$
$444$	5.02206	+	2.10637i	0.238337	+	0.0999640i
$445$		0			0
$446$	3.58603	+	4.27367i	0.169804	+	0.202364i
$447$	25.7748	−	10.5425i	1.21911	−	0.498643i
$448$	5.74556	+	2.67920i	0.271452	+	0.126580i
$449$	16.0515	+	27.8021i	0.757519	+	1.31206i	0.944112	+	0.329625i	$0.106922\pi$
$449$	16.0515	+	27.8021i	0.757519	+	1.31206i	−0.186593	+	0.982437i	$0.559744\pi$
$450$		0			0
$451$	−10.1901	+	17.6497i	−0.479832	+	0.831094i
$452$	−18.7933	+	13.1592i	−0.883962	+	0.618957i
$453$	1.06475	−	0.0417534i	0.0500261	−	0.00196175i
$454$	−1.10820	+	3.04474i	−0.0520102	+	0.142897i
$455$		0			0
$456$	−7.05831	+	10.9716i	−0.330536	+	0.513790i
$457$	3.80025	−	0.332479i	0.177768	−	0.0155527i	0.00207595	−	0.999998i	$-0.499339\pi$
$457$	3.80025	−	0.332479i	0.177768	−	0.0155527i	0.175692	+	0.984445i	$0.443784\pi$
$458$	1.64912	−	1.64912i	0.0770585	−	0.0770585i
$459$	−9.60470	+	3.82936i	−0.448309	+	0.178739i
$460$		0			0
$461$	19.3941	−	23.1130i	0.903273	−	1.07648i	−0.0934525	−	0.995624i	$-0.529790\pi$
$461$	19.3941	−	23.1130i	0.903273	−	1.07648i	0.996726	−	0.0808555i	$-0.0257652\pi$
$462$	0.903527	+	0.994857i	0.0420359	+	0.0462849i
$463$	19.6216	−	28.0226i	0.911895	−	1.30232i	−0.0410431	−	0.999157i	$-0.513068\pi$
$463$	19.6216	−	28.0226i	0.911895	−	1.30232i	0.952938	−	0.303164i	$-0.0980430\pi$
$464$	5.41838	+	1.97213i	0.251542	+	0.0915538i
$465$		0			0
$466$	0.337129	−	1.91196i	0.0156172	−	0.0885696i
$467$	3.57267	−	0.957293i	0.165323	−	0.0442982i	−0.175208	−	0.984531i	$-0.556060\pi$
$467$	3.57267	−	0.957293i	0.165323	−	0.0442982i	0.340531	+	0.940233i	$0.389393\pi$
$468$	1.69272	+	0.997432i	0.0782459	+	0.0461063i
$469$	−10.3027	+	5.94827i	−0.475734	+	0.274665i
$470$		0			0
$471$	14.3236	−	1.82110i	0.659998	−	0.0839116i
$472$	0.672482	−	7.68650i	0.0309535	−	0.353800i
$473$	0.703264	−	8.03835i	0.0323361	−	0.369604i
$474$	−5.49879	−	7.23241i	−0.252568	−	0.332196i
$475$		0			0
$476$	3.92948	−	2.26869i	0.180108	−	0.103985i
$477$	22.0046	−	3.67889i	1.00752	−	0.168445i
$478$	−2.48969	+	0.667110i	−0.113876	+	0.0305129i
$479$	2.01746	−	11.4416i	0.0921799	−	0.522778i	−0.903395	−	0.428809i	$-0.858933\pi$
$479$	2.01746	−	11.4416i	0.0921799	−	0.522778i	0.995575	−	0.0939694i	$-0.0299556\pi$
$480$		0			0
$481$	−0.548566	−	0.199662i	−0.0250124	−	0.00910379i
$482$	−3.01771	+	4.30974i	−0.137453	+	0.196303i
$483$	1.89164	−	5.90794i	0.0860726	−	0.268821i
$484$	9.23379	−	11.0044i	0.419718	−	0.500200i
$485$		0			0
$486$	−5.40993	+	0.590415i	−0.245399	+	0.0267818i
$487$	8.89951	−	8.89951i	0.403275	−	0.403275i	−0.476110	−	0.879386i	$-0.657954\pi$
$487$	8.89951	−	8.89951i	0.403275	−	0.403275i	0.879386	+	0.476110i	$0.157954\pi$
$488$	−10.1360	+	0.886781i	−0.458833	+	0.0401427i
$489$	−13.5756	−	26.3635i	−0.613909	−	1.19220i
$490$		0			0
$491$	−9.12806	+	25.0791i	−0.411943	+	1.13181i	0.544212	+	0.838947i	$0.316829\pi$
$491$	−9.12806	+	25.0791i	−0.411943	+	1.13181i	−0.956156	+	0.292858i	$0.905394\pi$
$492$	19.3225	+	30.6294i	0.871124	+	1.38088i
$493$	2.86243	−	2.00429i	0.128917	−	0.0902688i
$494$	0.338624	−	0.586515i	0.0152354	−	0.0263885i
$495$		0			0
$496$	−3.52162	−	6.09962i	−0.158125	−	0.273881i
$497$	−17.3334	−	8.08268i	−0.777508	−	0.362558i
$498$	1.05464	−	7.74500i	0.0472598	−	0.347062i
$499$	−19.0750	−	22.7327i	−0.853916	−	1.01766i	−0.999599	−	0.0283261i	$-0.990982\pi$
$499$	−19.0750	−	22.7327i	−0.853916	−	1.01766i	0.145683	−	0.989331i	$-0.453462\pi$
$500$		0			0
$501$	−3.92360	−	30.8607i	−0.175294	−	1.37875i
$502$	4.16721	−	8.93660i	0.185991	−	0.398860i
$503$	−3.32076	−	0.889794i	−0.148065	−	0.0396740i	0.184025	−	0.982922i	$-0.441087\pi$
$503$	−3.32076	−	0.889794i	−0.148065	−	0.0396740i	−0.332090	+	0.943248i	$0.607754\pi$
$504$	4.77426	−	1.23394i	0.212662	−	0.0549639i
$505$		0			0
$506$	−1.85670	−	0.327386i	−0.0825402	−	0.0145541i
$507$	19.7398	+	10.3875i	0.876675	+	0.461326i
$508$	5.45694	+	11.7024i	0.242113	+	0.519212i
$509$	−6.07079	−	34.4292i	−0.269083	−	1.52605i	−0.757151	−	0.653240i	$-0.773409\pi$
$509$	−6.07079	−	34.4292i	−0.269083	−	1.52605i	0.488068	−	0.872806i	$-0.337702\pi$
$510$		0			0
$511$	11.1589	+	9.36342i	0.493640	+	0.414213i
$512$	−15.2357	−	15.2357i	−0.673328	−	0.673328i
$513$	−3.39122	−	28.7081i	−0.149726	−	1.26749i
$514$			7.04591i			0.310782i
$515$		0			0
$516$	−12.0586	−	7.75763i	−0.530850	−	0.341511i
$517$	−16.7527	−	11.7304i	−0.736784	−	0.515902i
$518$	−0.643081	+	0.299874i	−0.0282554	+	0.0131757i
$519$	8.75543	−	9.47013i	0.384321	−	0.415693i
$520$		0			0
$521$	20.9011	+	12.0673i	0.915696	+	0.528677i	0.882259	−	0.470764i	$-0.156022\pi$
$521$	20.9011	+	12.0673i	0.915696	+	0.528677i	0.0334362	+	0.999441i	$0.489355\pi$
$522$	1.73374	−	0.613656i	0.0758839	−	0.0268590i
$523$	3.50904	−	13.0959i	0.153440	−	0.572645i	−0.845794	−	0.533509i	$-0.820873\pi$
$523$	3.50904	−	13.0959i	0.153440	−	0.572645i	0.999234	−	0.0391356i	$-0.0124604\pi$
$524$	−32.5240	+	11.8378i	−1.42082	+	0.517135i
$525$		0			0
$526$	−3.39524	+	2.84894i	−0.148040	+	0.124220i
$527$	−4.25209	−	0.372010i	−0.185224	−	0.0162050i
$528$	3.94160	+	9.63663i	0.171536	+	0.419380i
$529$	−4.89001	−	13.4352i	−0.212609	−	0.584139i
$530$		0			0
$531$	9.68182	+	14.0917i	0.420155	+	0.611527i
$532$	3.28319	+	12.2530i	0.142344	+	0.531237i
$533$	−2.22664	−	3.17998i	−0.0964466	−	0.137740i
$534$	1.12995	+	1.04467i	0.0488975	+	0.0452073i
$535$		0			0
$536$	13.0650	−	2.30371i	0.564321	−	0.0995050i
$537$	−0.972922	−	4.48264i	−0.0419847	−	0.193440i
$538$	−0.585863	−	6.69645i	−0.0252584	−	0.288704i
$539$	−10.1162			−0.435737
$540$		0			0
$541$	−4.99037			−0.214553			−0.107276	−	0.994229i	$-0.534213\pi$
$541$	−4.99037			−0.214553			−0.107276	+	0.994229i	$0.534213\pi$
$542$	0.660122	+	7.54523i	0.0283547	+	0.324095i
$543$	10.2863	−	9.34203i	0.441429	−	0.400905i
$544$	−7.55283	+	1.33177i	−0.323825	+	0.0570991i
$545$		0			0
$546$	−0.244481	+	0.0758931i	−0.0104628	+	0.00324792i
$547$	14.9768	+	21.3890i	0.640360	+	0.914528i	0.999826	−	0.0186294i	$-0.00593027\pi$
$547$	14.9768	+	21.3890i	0.640360	+	0.914528i	−0.359467	+	0.933158i	$0.617041\pi$
$548$	0.242040	+	0.903304i	0.0103394	+	0.0385872i
$549$	16.0830	−	15.7999i	0.686406	−	0.674325i
$550$		0			0
$551$	3.34131	+	9.18018i	0.142345	+	0.391089i
$552$	−4.23559	+	5.46948i	−0.180279	+	0.232797i
$553$	−18.1724	−	1.58988i	−0.772770	−	0.0676086i
$554$	−6.91767	+	5.80462i	−0.293904	+	0.246615i
$555$		0			0
$556$	−2.50569	+	0.911998i	−0.106265	+	0.0386773i
$557$	−11.5718	+	43.1866i	−0.490313	+	1.82987i	0.0645241	+	0.997916i	$0.479447\pi$
$557$	−11.5718	+	43.1866i	−0.490313	+	1.82987i	−0.554838	+	0.831959i	$0.687220\pi$
$558$	−2.10410	−	0.787053i	−0.0890737	−	0.0333186i
$559$	1.33108	+	0.768500i	0.0562987	+	0.0325041i
$560$		0			0
$561$	6.15392	+	1.39298i	0.259819	+	0.0588117i
$562$	1.34125	−	0.625436i	0.0565773	−	0.0263824i
$563$	29.7327	+	20.8190i	1.25308	+	0.877418i	0.996033	−	0.0889809i	$-0.0283610\pi$
$563$	29.7327	+	20.8190i	1.25308	+	0.877418i	0.257049	+	0.966398i	$0.417250\pi$
$564$	−32.3093	+	16.6373i	−1.36047	+	0.700556i
$565$		0			0
$566$			4.98938i			0.209719i
$567$	−6.42520	+	8.83791i	−0.269833	+	0.371157i
$568$	15.0810	+	15.0810i	0.632783	+	0.632783i
$569$	15.5547	+	13.0520i	0.652088	+	0.547167i	0.907704	−	0.419612i	$-0.137834\pi$
$569$	15.5547	+	13.0520i	0.652088	+	0.547167i	−0.255616	+	0.966778i	$0.582278\pi$
$570$		0			0
$571$	0.319709	+	1.81316i	0.0133794	+	0.0758784i	0.990766	−	0.135580i	$-0.0432898\pi$
$571$	0.319709	+	1.81316i	0.0133794	+	0.0758784i	−0.977387	+	0.211458i	$0.932179\pi$
$572$	−0.506682	−	1.08658i	−0.0211855	−	0.0454324i
$573$	−17.6924	+	11.1612i	−0.739112	+	0.466267i
$574$	−4.64684	−	0.819363i	−0.193955	−	0.0341996i
$575$		0			0
$576$	15.5927	+	1.50379i	0.649698	+	0.0626579i
$577$	−8.77425	−	2.35105i	−0.365277	−	0.0978756i	0.0715120	−	0.997440i	$-0.477218\pi$
$577$	−8.77425	−	2.35105i	−0.365277	−	0.0978756i	−0.436789	+	0.899564i	$0.643884\pi$
$578$	1.92394	−	4.12591i	0.0800255	−	0.171615i
$579$	−10.7276	+	8.15614i	−0.445822	+	0.338958i
$580$		0			0
$581$	−10.0880	−	12.0224i	−0.418519	−	0.498771i
$582$	−2.91115	−	2.25440i	−0.120671	−	0.0934481i
$583$	−12.3385	−	5.75351i	−0.511006	−	0.238286i
$584$	−8.12220	−	14.0681i	−0.336099	−	0.582140i
$585$		0			0
$586$	5.00838	−	8.67477i	0.206894	−	0.358351i
$587$	8.92820	−	6.25159i	0.368506	−	0.258031i	−0.374625	−	0.927176i	$-0.622229\pi$
$587$	8.92820	−	6.25159i	0.368506	−	0.258031i	0.743131	+	0.669145i	$0.233340\pi$
$588$	−8.37118	+	15.9081i	−0.345222	+	0.656038i
$589$	4.08136	−	11.2135i	0.168170	−	0.462042i
$590$		0			0
$591$	0.964383	+	0.0463957i	0.0396694	+	0.00190846i
$592$	−5.47620	+	0.479106i	−0.225071	+	0.0196911i
$593$	−14.2644	+	14.2644i	−0.585769	+	0.585769i	−0.936483	−	0.350714i	$-0.885939\pi$
$593$	−14.2644	+	14.2644i	−0.585769	+	0.585769i	0.350714	+	0.936483i	$0.385939\pi$
$594$	2.92494	+	1.57248i	0.120012	+	0.0645196i
$595$		0			0
$596$	−19.4097	+	23.1315i	−0.795051	+	0.947505i
$597$	5.68507	−	1.23390i	0.232674	−	0.0505001i
$598$	0.205983	−	0.294175i	0.00842328	−	0.0120297i
$599$	29.1082	+	10.5945i	1.18933	+	0.432880i	0.859488	−	0.511157i	$-0.170783\pi$
$599$	29.1082	+	10.5945i	1.18933	+	0.432880i	0.329841	+	0.944037i	$0.393005\pi$
$600$		0			0
$601$	−6.41218	+	36.3653i	−0.261558	+	1.48337i	0.517101	+	0.855925i	$0.327011\pi$
$601$	−6.41218	+	36.3653i	−0.261558	+	1.48337i	−0.778659	+	0.627447i	$0.784100\pi$
$602$	1.80453	−	0.483523i	0.0735472	−	0.0197069i
$603$	−19.0949	+	22.3505i	−0.777606	+	0.910181i
$604$	−1.00063	+	0.577714i	−0.0407151	+	0.0235069i
$605$		0			0
$606$	−1.46524	+	3.49346i	−0.0595213	+	0.141912i
$607$	−2.05629	+	23.5036i	−0.0834624	+	0.953980i	0.832846	+	0.553506i	$0.186710\pi$
$607$	−2.05629	+	23.5036i	−0.0834624	+	0.953980i	−0.916308	+	0.400474i	$0.868845\pi$
$608$	1.86874	−	21.3598i	0.0757876	−	0.866256i
$609$	1.42825	−	3.40527i	0.0578756	−	0.137988i
$610$		0			0
$611$	3.37367	−	1.94779i	0.136484	−	0.0787992i
$612$	7.28287	−	8.52454i	0.294393	−	0.344584i
$613$	−17.3022	+	4.63610i	−0.698828	+	0.187251i	−0.590706	−	0.806887i	$-0.701151\pi$
$613$	−17.3022	+	4.63610i	−0.698828	+	0.187251i	−0.108123	+	0.994138i	$0.534484\pi$
$614$	−0.137296	+	0.778644i	−0.00554081	+	0.0314235i
$615$		0			0
$616$	−2.82760	−	1.02916i	−0.113927	−	0.0414661i
$617$	2.01607	−	2.87925i	0.0811641	−	0.115914i	−0.776517	−	0.630096i	$-0.783015\pi$
$617$	2.01607	−	2.87925i	0.0811641	−	0.115914i	0.857681	+	0.514182i	$0.171904\pi$
$618$	8.43454	−	1.83065i	0.339287	−	0.0736396i
$619$	−15.8282	+	18.8633i	−0.636188	+	0.758180i	−0.983763	−	0.179473i	$-0.942561\pi$
$619$	−15.8282	+	18.8633i	−0.636188	+	0.758180i	0.347575	+	0.937652i	$0.387005\pi$
$620$		0			0
$621$	−0.464642	−	15.3217i	−0.0186455	−	0.614837i
$622$	−3.01837	+	3.01837i	−0.121026	+	0.121026i
$623$	3.07801	−	0.269291i	0.123318	−	0.0107889i
$624$	−1.98091	−	0.0953002i	−0.0793000	−	0.00381506i
$625$		0			0
$626$	−2.01986	+	5.54952i	−0.0807299	+	0.221803i
$627$	−8.21460	+	15.6105i	−0.328060	+	0.623425i
$628$	−12.8252	+	8.98028i	−0.511780	+	0.358352i
$629$	−1.66568	+	2.88504i	−0.0664150	+	0.115034i
$630$		0			0
$631$	−3.43649	−	5.95218i	−0.136805	−	0.236953i	0.789481	−	0.613775i	$-0.210350\pi$
$631$	−3.43649	−	5.95218i	−0.136805	−	0.236953i	−0.926285	+	0.376823i	$0.877017\pi$
$632$	18.4366	+	8.59713i	0.733368	+	0.341975i
$633$	−17.8933	−	13.8566i	−0.711195	−	0.550752i
$634$	2.80205	+	3.33936i	0.111284	+	0.132623i
$635$		0			0
$636$	−19.2576	+	14.6415i	−0.763615	+	0.580575i
$637$	0.814364	−	1.74641i	0.0322663	−	0.0691953i
$638$	−1.08404	−	0.290466i	−0.0429174	−	0.0114997i
$639$	−47.0407	−	4.53668i	−1.86090	−	0.179468i
$640$		0			0
$641$	11.3164	+	1.99539i	0.446972	+	0.0788133i	0.392604	−	0.919708i	$-0.371574\pi$
$641$	11.3164	+	1.99539i	0.446972	+	0.0788133i	0.0543684	+	0.998521i	$0.482685\pi$
$642$	−9.21995	+	5.81638i	−0.363882	+	0.229554i
$643$	3.99541	+	8.56819i	0.157564	+	0.337896i	0.969203	−	0.246262i	$-0.0792024\pi$
$643$	3.99541	+	8.56819i	0.157564	+	0.337896i	−0.811640	+	0.584158i	$0.801425\pi$
$644$	1.16805	+	6.62436i	0.0460278	+	0.261037i
$645$		0			0
$646$	−2.96061	−	2.48424i	−0.116484	−	0.0977413i
$647$	19.8792	+	19.8792i	0.781533	+	0.781533i	0.980090	−	0.198556i	$-0.0636252\pi$
$647$	19.8792	+	19.8792i	0.781533	+	0.781533i	−0.198556	+	0.980090i	$0.563625\pi$
$648$	10.1038	−	6.81068i	0.396916	−	0.267549i
$649$		−	10.4330i		−	0.409531i
$650$		0			0
$651$	−4.01010	+	2.06495i	−0.157168	+	0.0809319i
$652$	26.3393	+	18.4430i	1.03153	+	0.722283i
$653$	−32.5186	+	15.1637i	−1.27255	+	0.593400i	−0.937233	−	0.348705i	$-0.886622\pi$
$653$	−32.5186	+	15.1637i	−1.27255	+	0.593400i	−0.335318	+	0.942105i	$0.608844\pi$
$654$	−5.39356	−	1.22087i	−0.210905	−	0.0477396i
$655$		0			0
$656$	−31.6579	−	18.2777i	−1.23603	−	0.713625i
$657$	33.7137	+	12.6109i	1.31530	+	0.491996i
$658$	1.22551	−	4.57365i	0.0477752	−	0.178300i
$659$	−24.5585	+	8.93857i	−0.956664	+	0.348197i	−0.772725	−	0.634741i	$-0.781107\pi$
$659$	−24.5585	+	8.93857i	−0.956664	+	0.348197i	−0.183939	+	0.982938i	$0.558885\pi$
$660$		0			0
$661$	−12.4073	+	10.4109i	−0.482587	+	0.404939i	−0.851361	−	0.524581i	$-0.824222\pi$
$661$	−12.4073	+	10.4109i	−0.482587	+	0.404939i	0.368774	+	0.929519i	$0.379778\pi$
$662$	−7.31703	−	0.640157i	−0.284385	−	0.0248804i
$663$	−0.735871	+	0.950243i	−0.0285789	+	0.0369044i
$664$	5.98582	+	16.4459i	0.232295	+	0.638225i
$665$		0			0
$666$	−1.25076	+	1.22874i	−0.0484659	+	0.0476129i
$667$	1.34077	+	5.00382i	0.0519148	+	0.193749i
$668$	19.3483	+	27.6322i	0.748607	+	1.06912i
$669$	26.4345	−	8.20592i	1.02201	−	0.317259i
$670$		0			0
$671$	−13.5487	+	2.38900i	−0.523041	+	0.0922262i
$672$	−5.99953	+	5.44876i	−0.231437	+	0.210191i
$673$	1.72224	+	19.6853i	0.0663875	+	0.758813i	0.954310	+	0.298819i	$0.0965927\pi$
$673$	1.72224	+	19.6853i	0.0663875	+	0.758813i	−0.887922	+	0.459994i	$0.847852\pi$
$674$	−10.9655			−0.422376
$675$		0			0
$676$	−24.1872			−0.930278
$677$	−1.03213	−	11.7973i	−0.0396679	−	0.453407i	−0.989890	−	0.141834i	$-0.954700\pi$
$677$	−1.03213	−	11.7973i	−0.0396679	−	0.453407i	0.950222	−	0.311572i	$-0.100856\pi$
$678$	−1.56669	−	7.21836i	−0.0601683	−	0.277220i
$679$	−7.28048	+	1.28374i	−0.279399	+	0.0492656i
$680$		0			0
$681$	11.8038	+	10.9130i	0.452323	+	0.418187i
$682$	0.786284	+	1.12293i	0.0301084	+	0.0429992i
$683$	−3.04307	−	11.3569i	−0.116440	−	0.434559i	0.882951	−	0.469466i	$-0.155553\pi$
$683$	−3.04307	−	11.3569i	−0.116440	−	0.434559i	−0.999391	+	0.0349062i	$0.988887\pi$
$684$	17.7504	+	25.8354i	0.678705	+	0.987842i
$685$		0			0
$686$	−1.81581	−	4.98889i	−0.0693278	−	0.190477i
$687$	−4.38052	−	10.7097i	−0.167127	−	0.408601i
$688$	14.4182	+	1.26143i	0.549688	+	0.0480915i
$689$	1.98651	−	1.66688i	0.0756799	−	0.0635030i
$690$		0			0
$691$	5.29511	−	1.92726i	0.201435	−	0.0733165i	−0.239332	−	0.970938i	$-0.576929\pi$
$691$	5.29511	−	1.92726i	0.201435	−	0.0733165i	0.440768	+	0.897621i	$0.354706\pi$
$692$	−3.61959	+	13.5085i	−0.137596	+	0.513516i
$693$	6.28553	−	2.22475i	0.238767	−	0.0845114i
$694$	1.83381	+	1.05875i	0.0696104	+	0.0401896i
$695$		0			0
$696$	−2.79546	+	3.02366i	−0.105962	+	0.114611i
$697$	−20.0777	+	9.36238i	−0.760497	+	0.354625i
$698$	2.95540	+	2.06939i	0.111863	+	0.0783276i
$699$	−8.10070	−	5.21141i	−0.306397	−	0.197114i
$700$		0			0
$701$			21.8407i			0.824911i	0.910978	+	0.412455i	$0.135329\pi$
$701$			21.8407i			0.824911i	−0.910978	+	0.412455i	$0.864671\pi$
$702$	−0.506924	+	0.378359i	−0.0191326	+	0.0142802i
$703$	−6.58570	−	6.58570i	−0.248384	−	0.248384i
$704$	−7.32271	−	6.14448i	−0.275985	−	0.231579i
$705$		0			0
$706$	0.820744	+	4.65467i	0.0308891	+	0.175181i
$707$	3.21453	+	6.89357i	0.120895	+	0.259260i
$708$	−16.4062	−	8.63330i	−0.616583	−	0.324459i
$709$	17.5327	+	3.09148i	0.658453	+	0.116103i	0.492884	−	0.870095i	$-0.335943\pi$
$709$	17.5327	+	3.09148i	0.658453	+	0.116103i	0.165569	+	0.986198i	$0.447054\pi$
$710$		0			0
$711$	−43.6419	+	11.2795i	−1.63670	+	0.423015i
$712$	−3.32817	−	0.891781i	−0.124729	−	0.0334209i
$713$	2.67420	−	5.73485i	0.100150	−	0.214772i
$714$	0.184246	+	1.44917i	0.00689524	+	0.0542338i
$715$		0			0
$716$	3.19713	+	3.81019i	0.119482	+	0.142394i
$717$	−1.72543	+	12.6710i	−0.0644373	+	0.473209i
$718$	3.11243	+	1.45135i	0.116155	+	0.0541639i
$719$	−12.2911	−	21.2888i	−0.458381	−	0.793939i	0.540495	−	0.841347i	$-0.318237\pi$
$719$	−12.2911	−	21.2888i	−0.458381	−	0.793939i	−0.998876	+	0.0474084i	$0.984904\pi$
$720$		0			0
$721$	8.66466	−	15.0076i	0.322689	−	0.558914i
$722$	3.41741	−	2.39289i	0.127183	−	0.0890543i
$723$	13.9272	+	22.0769i	0.517957	+	0.821050i
$724$	−5.15331	+	14.1586i	−0.191521	+	0.526201i
$725$		0			0
$726$	2.11734	+	4.11183i	0.0785819	+	0.152604i
$727$	32.6578	−	2.85719i	1.21121	−	0.105967i	0.536404	−	0.843962i	$-0.319782\pi$
$727$	32.6578	−	2.85719i	1.21121	−	0.105967i	0.674807	+	0.737994i	$0.264227\pi$
$728$	0.405292	−	0.405292i	0.0150211	−	0.0150211i
$729$	−7.68015	+	25.8847i	−0.284450	+	0.958691i
$730$		0			0
$731$	5.63793	−	6.71903i	0.208526	−	0.248512i
$732$	−7.45475	+	23.2826i	−0.275536	+	0.860549i
$733$	−17.8772	+	25.5313i	−0.660311	+	0.943022i	0.339686	+	0.940539i	$0.389679\pi$
$733$	−17.8772	+	25.5313i	−0.660311	+	0.943022i	−0.999997	+	0.00248290i	$0.999210\pi$
$734$	2.06361	+	0.751094i	0.0761694	+	0.0277234i
$735$		0			0
$736$	1.97432	−	11.1969i	0.0727742	−	0.412723i
$737$	17.3271	−	4.64278i	0.638251	−	0.171019i
$738$	−11.5000	+	1.92265i	−0.423320	+	0.0707736i
$739$	9.53500	−	5.50503i	0.350751	−	0.202506i	−0.314265	−	0.949335i	$-0.601758\pi$
$739$	9.53500	−	5.50503i	0.350751	−	0.202506i	0.665016	+	0.746829i	$0.268425\pi$
$740$		0			0
$741$	−2.03363	−	2.67478i	−0.0747073	−	0.0982606i
$742$	0.274713	−	3.13998i	0.0100850	−	0.115272i
$743$	4.37657	−	50.0244i	0.160561	−	1.83522i	−0.307532	−	0.951538i	$-0.599503\pi$
$743$	4.37657	−	50.0244i	0.160561	−	1.83522i	0.468092	−	0.883679i	$-0.344941\pi$
$744$	4.98979	−	0.634398i	0.182935	−	0.0232582i
$745$		0			0
$746$	−6.77350	+	3.91068i	−0.247996	+	0.143180i
$747$	−33.4113	−	19.6876i	−1.22246	−	0.720331i
$748$	−6.60861	+	1.77077i	−0.241635	+	0.0647458i
$749$	−3.80077	+	21.5553i	−0.138877	+	0.787612i
$750$		0			0
$751$	−11.3558	−	4.13319i	−0.414380	−	0.150822i	0.126413	−	0.991978i	$-0.459654\pi$
$751$	−11.3558	−	4.13319i	−0.414380	−	0.150822i	−0.540793	+	0.841156i	$0.681876\pi$
$752$	21.0405	−	30.0490i	0.767268	−	1.09577i
$753$	−32.8903	−	36.2149i	−1.19859	−	1.31974i
$754$	0.137410	−	0.163759i	0.00500418	−	0.00596375i
$755$		0			0
$756$	1.70278	−	11.7252i	0.0619296	−	0.426440i
$757$	14.6269	−	14.6269i	0.531625	−	0.531625i	−0.389431	−	0.921056i	$-0.627328\pi$
$757$	14.6269	−	14.6269i	0.531625	−	0.531625i	0.921056	+	0.389431i	$0.127328\pi$
$758$	6.63649	−	0.580618i	0.241048	−	0.0210890i
$759$	−5.06079	+	7.86657i	−0.183695	+	0.285538i
$760$		0			0
$761$	7.74333	−	21.2746i	0.280695	−	0.771204i	−0.716585	−	0.697500i	$-0.754296\pi$
$761$	7.74333	−	21.2746i	0.280695	−	0.771204i	0.997280	−	0.0737041i	$-0.0234820\pi$
$762$	−4.15397	+	0.162895i	−0.150482	+	0.00590108i
$763$	−9.09525	+	6.36856i	−0.329270	+	0.230557i
$764$	11.3415	−	19.6440i	0.410320	−	0.710696i
$765$		0			0
$766$	6.51349	+	11.2817i	0.235342	+	0.407625i
$767$	1.80109	+	0.839864i	0.0650337	+	0.0303257i
$768$	−11.4079	+	4.66609i	−0.411647	+	0.168373i
$769$	−13.7049	−	16.3329i	−0.494213	−	0.588980i	0.460071	−	0.887882i	$-0.347824\pi$
$769$	−13.7049	−	16.3329i	−0.494213	−	0.588980i	−0.954284	+	0.298902i	$0.903380\pi$
$770$		0			0
$771$	32.2367	+	13.5208i	1.16098	+	0.486940i
$772$	6.17552	−	13.2434i	0.222262	−	0.476642i
$773$	15.8037	+	4.23460i	0.568421	+	0.152308i	0.531572	−	0.847013i	$-0.321601\pi$
$773$	15.8037	+	4.23460i	0.568421	+	0.152308i	0.0368487	+	0.999321i	$0.488268\pi$
$774$	3.80484	−	2.61415i	0.136762	−	0.0939635i
$775$		0			0
$776$	8.11889	+	1.43158i	0.291451	+	0.0513907i
$777$	0.137944	+	3.51769i	0.00494872	+	0.126196i
$778$	−2.44563	−	5.24467i	−0.0876800	−	0.188030i
$779$	−10.7548	−	60.9936i	−0.385332	−	2.18532i
$780$		0			0
$781$	22.0914	+	18.5368i	0.790491	+	0.663301i
$782$	−1.44912	−	1.44912i	−0.0518204	−	0.0518204i
$783$	0.519367	−	9.10985i	0.0185607	−	0.325559i
$784$		−	18.1452i		−	0.648044i
$785$		0			0
$786$	0.535476	−	11.1304i	0.0190998	−	0.397010i
$787$	−10.1336	−	7.09564i	−0.361225	−	0.252932i	0.378848	−	0.925459i	$-0.376320\pi$
$787$	−10.1336	−	7.09564i	−0.361225	−	0.252932i	−0.740073	+	0.672527i	$0.765209\pi$
$788$	−0.948835	+	0.442449i	−0.0338009	+	0.0157616i
$789$	6.51925	+	21.0010i	0.232091	+	0.747656i
$790$		0			0
$791$	−12.8437	−	7.41530i	−0.456669	−	0.263658i
$792$	−7.43518	−	0.0660097i	−0.264198	−	0.00234555i
$793$	0.678255	−	2.53128i	0.0240855	−	0.0898884i
$794$	−7.42130	+	2.70113i	−0.263372	+	0.0958596i
$795$		0			0
$796$	−4.83224	+	4.05473i	−0.171274	+	0.143716i
$797$	−51.3006	−	4.48822i	−1.81716	−	0.158981i	−0.872839	−	0.488009i	$-0.837723\pi$
$797$	−51.3006	−	4.48822i	−1.81716	−	0.158981i	−0.944320	+	0.329028i	$0.893279\pi$
$798$	−4.04675	−	0.551050i	−0.143253	−	0.0195070i
$799$	−7.60331	−	20.8899i	−0.268986	−	0.739033i
$800$		0			0
$801$	6.94792	−	3.16508i	0.245493	−	0.111833i
$802$	−1.52405	−	5.68784i	−0.0538161	−	0.200844i
$803$	−12.5985	−	17.9926i	−0.444592	−	0.634943i
$804$	7.03725	−	31.0892i	0.248185	−	1.09643i
$805$		0			0
$806$	−0.257153	+	0.0453429i	−0.00905781	+	0.00159714i
$807$	−31.7620	−	10.1697i	−1.11808	−	0.357992i
$808$	−0.739267	−	8.44986i	−0.0260073	−	0.297265i
$809$	−29.5460			−1.03878			−0.519391	−	0.854537i	$-0.673841\pi$
$809$	−29.5460			−1.03878			−0.519391	+	0.854537i	$0.673841\pi$
$810$		0			0
$811$	51.8564			1.82093			0.910463	−	0.413591i	$-0.135726\pi$
$811$	51.8564			1.82093			0.910463	+	0.413591i	$0.135726\pi$
$812$	0.348979	+	3.98885i	0.0122468	+	0.139981i
$813$	35.7879	+	11.4588i	1.25514	+	0.401877i
$814$	1.05367	−	0.185790i	0.0369309	−	0.00651192i
$815$		0			0
$816$	−2.49855	+	11.0381i	−0.0874669	+	0.386412i
$817$	14.0650	+	20.0869i	0.492071	+	0.702751i
$818$	−1.65619	−	6.18097i	−0.0579072	−	0.216113i
$819$	−0.121921	+	1.26419i	−0.00426025	+	0.0441744i
$820$		0			0
$821$	9.08233	+	24.9535i	0.316976	+	0.870883i	0.991202	+	0.132358i	$0.0422550\pi$
$821$	9.08233	+	24.9535i	0.316976	+	0.870883i	−0.674226	+	0.738525i	$0.735523\pi$
$822$	−0.298330	−	0.0406239i	−0.0104054	−	0.00141692i
$823$	23.5911	+	2.06396i	0.822335	+	0.0719450i	0.490553	−	0.871411i	$-0.336795\pi$
$823$	23.5911	+	2.06396i	0.822335	+	0.0719450i	0.331782	+	0.943356i	$0.392350\pi$
$824$	−14.8038	+	12.4218i	−0.515714	+	0.432735i
$825$		0			0
$826$	2.26983	−	0.826151i	0.0789775	−	0.0287455i
$827$	2.87604	−	10.7335i	0.100010	−	0.373241i	−0.897722	−	0.440563i	$-0.854779\pi$
$827$	2.87604	−	10.7335i	0.100010	−	0.373241i	0.997731	+	0.0673219i	$0.0214454\pi$
$828$	8.18261	+	14.4678i	0.284365	+	0.502792i
$829$	22.4115	+	12.9393i	0.778382	+	0.449399i	0.835857	−	0.548948i	$-0.184971\pi$
$829$	22.4115	+	12.9393i	0.778382	+	0.449399i	−0.0574744	+	0.998347i	$0.518305\pi$
$830$		0			0
$831$	13.2827	+	42.7888i	0.460772	+	1.48433i
$832$	1.65023	−	0.769515i	0.0572115	−	0.0266781i
$833$	−9.00769	−	6.30725i	−0.312098	−	0.218533i
$834$	0.0412538	−	0.857504i	0.00142850	−	0.0296929i
$835$		0			0
$836$		−	19.1276i		−	0.661543i
$837$	−7.63863	+	8.11642i	−0.264030	+	0.280544i
$838$	5.07716	+	5.07716i	0.175387	+	0.175387i
$839$	7.70983	+	6.46931i	0.266173	+	0.223346i	0.766099	−	0.642722i	$-0.222195\pi$
$839$	7.70983	+	6.46931i	0.266173	+	0.223346i	−0.499926	+	0.866068i	$0.666640\pi$
$840$		0			0
$841$	−4.50032	−	25.5226i	−0.155184	−	0.880090i
$842$	3.18012	+	6.81978i	0.109594	+	0.235025i
$843$	−0.287705	−	7.33673i	−0.00990910	−	0.252690i
$844$	24.1671	+	4.26131i	0.831866	+	0.146680i
$845$		0			0
$846$	−0.916230	−	11.6643i	−0.0315006	−	0.401028i
$847$	8.96968	+	2.40342i	0.308202	+	0.0825824i
$848$	10.3199	−	22.1312i	0.354388	−	0.759988i
$849$	22.8276	+	9.57442i	0.783440	+	0.328593i
$850$		0			0
$851$	−3.17451	−	3.78323i	−0.108821	−	0.129688i
$852$	47.4303	−	19.4001i	1.62494	−	0.664636i
$853$	18.6740	+	8.70782i	0.639385	+	0.298150i	0.715145	−	0.698976i	$-0.246361\pi$
$853$	18.6740	+	8.70782i	0.639385	+	0.298150i	−0.0757601	+	0.997126i	$0.524138\pi$
$854$	−1.59263	−	2.75851i	−0.0544985	−	0.0943942i
$855$		0			0
$856$	12.2042	−	21.1382i	0.417130	−	0.722490i
$857$	21.1722	−	14.8249i	0.723228	−	0.506409i	−0.153048	−	0.988219i	$-0.548909\pi$
$857$	21.1722	−	14.8249i	0.723228	−	0.506409i	0.876276	+	0.481809i	$0.160020\pi$
$858$	0.385700	−	0.0151250i	0.0131676	−	0.000516359i
$859$	7.25364	−	19.9292i	0.247491	−	0.679976i	−0.752285	−	0.658837i	$-0.771049\pi$
$859$	7.25364	−	19.9292i	0.247491	−	0.679976i	0.999777	−	0.0211390i	$-0.00672924\pi$
$860$		0			0
$861$	−12.6659	+	19.6880i	−0.431652	+	0.670966i
$862$	4.38063	−	0.383256i	0.149205	−	0.0130537i
$863$	−27.3490	+	27.3490i	−0.930969	+	0.930969i	−0.997767	−	0.0667973i	$-0.978722\pi$
$863$	−27.3490	+	27.3490i	−0.930969	+	0.930969i	0.0667973	+	0.997767i	$0.478722\pi$
$864$	−9.48292	+	17.6390i	−0.322616	+	0.600090i
$865$		0			0
$866$	−6.74222	+	8.03506i	−0.229110	+	0.273043i
$867$	−15.1850	−	16.7199i	−0.515710	−	0.567839i
$868$	2.80532	−	4.00642i	0.0952188	−	0.135987i
$869$	25.8473	+	9.40766i	0.876810	+	0.319133i
$870$		0			0
$871$	−0.593339	+	3.36500i	−0.0201045	+	0.114019i
$872$	11.9600	−	3.20467i	0.405016	−	0.108524i
$873$	−15.9008	+	8.99306i	−0.538160	+	0.304369i
$874$	4.96187	−	2.86474i	0.167838	−	0.0969011i
$875$		0			0
$876$	−38.7191	+	4.92272i	−1.30820	+	0.166323i
$877$	−3.06431	+	35.0252i	−0.103474	+	1.18272i	0.749948	+	0.661497i	$0.230079\pi$
$877$	−3.06431	+	35.0252i	−0.103474	+	1.18272i	−0.853422	+	0.521221i	$0.825477\pi$
$878$	−0.583770	+	6.67252i	−0.0197013	+	0.225187i
$879$	−30.0782	−	39.5610i	−1.01451	−	1.33436i
$880$		0			0
$881$	30.8912	−	17.8350i	1.04075	−	0.600877i	0.120704	−	0.992689i	$-0.461485\pi$
$881$	30.8912	−	17.8350i	1.04075	−	0.600877i	0.920046	+	0.391811i	$0.128151\pi$
$882$	−3.68065	−	4.46636i	−0.123934	−	0.150390i
$883$	33.6176	−	9.00780i	1.13132	−	0.303137i	0.355865	−	0.934537i	$-0.384186\pi$
$883$	33.6176	−	9.00780i	1.13132	−	0.303137i	0.775457	+	0.631401i	$0.217520\pi$
$884$	0.226302	−	1.28342i	0.00761135	−	0.0431661i
$885$		0			0
$886$	3.75024	+	1.36498i	0.125992	+	0.0458572i
$887$	28.6614	−	40.9327i	0.962355	−	1.37439i	0.0353349	−	0.999376i	$-0.488750\pi$
$887$	28.6614	−	40.9327i	0.962355	−	1.37439i	0.927021	−	0.375010i	$-0.122361\pi$
$888$	1.19712	−	3.73882i	0.0401726	−	0.125467i
$889$	−5.36524	+	6.39404i	−0.179944	+	0.214449i
$890$		0			0
$891$	12.8073	−	10.3647i	0.429060	−	0.347232i
$892$	−21.2225	+	21.2225i	−0.710581	+	0.710581i
$893$	61.9142	−	5.41679i	2.07188	−	0.181266i
$894$	−4.45070	−	8.64318i	−0.148854	−	0.289071i
$895$		0			0
$896$	3.95768	−	10.8736i	0.132217	−	0.363263i
$897$	−0.950643	−	1.50693i	−0.0317410	−	0.0503149i
$898$	9.18060	−	6.42832i	0.306361	−	0.214516i
$899$	1.88333	−	3.26202i	0.0628126	−	0.108795i
$900$		0			0
$901$	−7.39920	−	12.8158i	−0.246503	−	0.426956i
$902$	6.44827	+	3.00688i	0.214704	+	0.100118i
$903$	1.25060	−	9.18401i	0.0416172	−	0.305625i
$904$	10.6307	+	12.6692i	0.353573	+	0.421372i
$905$		0			0
$906$	−0.0469177	−	0.369026i	−0.00155874	−	0.0122601i
$907$	−21.8442	+	46.8450i	−0.725325	+	1.55546i	0.102662	+	0.994716i	$0.467264\pi$
$907$	−21.8442	+	46.8450i	−0.725325	+	1.55546i	−0.827987	+	0.560747i	$0.810514\pi$
$908$	−16.8373	−	4.51155i	−0.558766	−	0.149721i
$909$	13.1717	+	13.4076i	0.436876	+	0.444703i
$910$		0			0
$911$	−57.8699	−	10.2040i	−1.91731	−	0.338074i	−0.918906	−	0.394476i	$-0.870926\pi$
$911$	−57.8699	−	10.2040i	−1.91731	−	0.338074i	−0.998408	+	0.0564017i	$0.982037\pi$
$912$	−28.0002	−	14.7343i	−0.927180	−	0.487902i
$913$	10.0010	+	21.4473i	0.330986	+	0.709802i
$914$	−0.231259	−	1.31153i	−0.00764935	−	0.0433816i
$915$		0			0
$916$	9.61141	+	8.06493i	0.317570	+	0.266473i
$917$	−15.8206	−	15.8206i	−0.522443	−	0.522443i
$918$	1.62401	+	3.22380i	0.0536004	+	0.106401i
$919$			31.9476i			1.05385i	0.849911	+	0.526927i	$0.176656\pi$
$919$			31.9476i			1.05385i	−0.849911	+	0.526927i	$0.823344\pi$
$920$		0			0
$921$	3.29901	+	2.12235i	0.108706	+	0.0699337i
$922$	−8.62832	−	6.04162i	−0.284159	−	0.198970i
$923$	−4.97847	+	2.32150i	−0.163868	+	0.0764130i
$924$	−4.90810	+	5.30875i	−0.161465	+	0.174645i
$925$		0			0
$926$	−10.3427	−	5.97137i	−0.339883	−	0.196231i
$927$	7.80990	−	42.1029i	0.256511	−	1.38284i
$928$	1.75167	−	6.53733i	0.0575014	−	0.214598i
$929$	42.9561	−	15.6347i	1.40934	−	0.512959i	0.478407	−	0.878138i	$-0.341215\pi$
$929$	42.9561	−	15.6347i	1.40934	−	0.512959i	0.930937	+	0.365179i	$0.118992\pi$
$930$		0			0
$931$	23.5504	−	19.7611i	0.771833	−	0.647645i
$932$	10.4048	+	0.910305i	0.340822	+	0.0298180i
$933$	8.01760	+	19.6019i	0.262484	+	0.641736i
$934$	−0.441631	−	1.21337i	−0.0144506	−	0.0397028i
$935$		0			0
$936$	0.609933	−	1.27825i	0.0199363	−	0.0417810i
$937$	−11.4496	−	42.7303i	−0.374041	−	1.39594i	−0.854741	−	0.519054i	$-0.826284\pi$
$937$	−11.4496	−	42.7303i	−0.374041	−	1.39594i	0.480701	−	0.876885i	$-0.340382\pi$
$938$	2.38216	+	3.40208i	0.0777804	+	0.111082i
$939$	21.5143	+	19.8906i	0.702093	+	0.649106i
$940$		0			0
$941$	2.76151	−	0.486928i	0.0900225	−	0.0158734i	−0.128455	−	0.991715i	$-0.541002\pi$
$941$	2.76151	−	0.486928i	0.0900225	−	0.0158734i	0.218478	+	0.975842i	$0.429891\pi$
$942$	−1.06916	−	4.92605i	−0.0348351	−	0.160499i
$943$	−2.86234	−	32.7167i	−0.0932107	−	1.06540i
$944$	18.7134			0.609070
$945$		0			0
$946$	−2.81697			−0.0915876
$947$	−2.83159	−	32.3652i	−0.0920142	−	1.05173i	−0.892099	−	0.451840i	$-0.850768\pi$
$947$	−2.83159	−	32.3652i	−0.0920142	−	1.05173i	0.800085	−	0.599887i	$-0.204788\pi$
$948$	36.1825	−	32.8608i	1.17515	−	1.06727i
$949$	4.12032	−	0.726524i	0.133751	−	0.0235840i
$950$		0			0
$951$	20.6553	−	6.41194i	0.669795	−	0.207921i
$952$	−1.87609	−	2.67933i	−0.0608044	−	0.0868376i
$953$	−2.39049	−	8.92145i	−0.0774357	−	0.288994i	0.916339	−	0.400404i	$-0.131130\pi$
$953$	−2.39049	−	8.92145i	−0.0774357	−	0.288994i	−0.993775	+	0.111410i	$0.964463\pi$
$954$	−1.94897	−	7.54082i	−0.0631003	−	0.244143i
$955$		0			0
$956$	−4.74261	−	13.0302i	−0.153387	−	0.421427i
$957$	−3.40917	+	4.40232i	−0.110203	+	0.142307i
$958$	−4.04053	−	0.353500i	−0.130543	−	0.0114211i
$959$	−0.463089	+	0.388578i	−0.0149539	+	0.0125478i
$960$		0			0
$961$	24.8070	−	9.02902i	0.800226	−	0.291259i
$962$	−0.0527471	+	0.196855i	−0.00170064	+	0.00634686i
$963$	8.91857	+	53.3448i	0.287397	+	1.71901i
$964$	−24.5122	−	14.1521i	−0.789484	−	0.455809i
$965$		0			0
$966$	−2.11222	−	0.478114i	−0.0679595	−	0.0153831i
$967$	−36.6740	+	17.1014i	−1.17936	+	0.549943i	−0.910610	−	0.413267i	$-0.864387\pi$
$967$	−36.6740	+	17.1014i	−1.17936	+	0.549943i	−0.268747	+	0.963211i	$0.586610\pi$
$968$	−8.48270	−	5.93965i	−0.272644	−	0.190908i
$969$	−17.0473	+	8.77829i	−0.547637	+	0.281999i
$970$		0			0
$971$		−	12.5885i		−	0.403983i	−0.979387	−	0.201991i	$-0.935259\pi$
$971$		−	12.5885i		−	0.403983i	0.979387	−	0.201991i	$-0.0647413\pi$
$972$	−5.70082	−	28.7167i	−0.182854	−	0.921087i
$973$	−1.21884	−	1.21884i	−0.0390743	−	0.0390743i
$974$	−3.36585	−	2.82428i	−0.107849	−	0.0904959i
$975$		0			0
$976$	−4.28508	−	24.3019i	−0.137162	−	0.777885i
$977$	13.8598	+	29.7224i	0.443414	+	0.950905i	0.993289	+	0.115658i	$0.0368976\pi$
$977$	13.8598	+	29.7224i	0.443414	+	0.950905i	−0.549875	+	0.835247i	$0.685325\pi$
$978$	−8.75563	+	5.52347i	−0.279974	+	0.176621i
$979$	−4.58816	−	0.809016i	−0.146638	−	0.0258563i
$980$		0			0
$981$	−15.9358	+	22.3340i	−0.508789	+	0.713068i
$982$	8.99974	+	2.41147i	0.287193	+	0.0769532i
$983$	−6.35642	+	13.6314i	−0.202738	+	0.434774i	−0.981220	−	0.192894i	$-0.938213\pi$
$983$	−6.35642	+	13.6314i	−0.202738	+	0.434774i	0.778481	+	0.627668i	$0.215990\pi$
$984$	20.7818	−	15.8004i	0.662499	−	0.503697i
$985$		0			0
$986$	−0.784146	−	0.934509i	−0.0249723	−	0.0297608i
$987$	−18.5738	−	14.3836i	−0.591211	−	0.457836i
$988$	3.30209	+	1.53979i	0.105053	+	0.0489872i
$989$	6.50145	+	11.2608i	0.206734	+	0.358074i
$990$		0			0
$991$	26.1024	−	45.2106i	0.829169	−	1.43616i	−0.0695216	−	0.997580i	$-0.522147\pi$
$991$	26.1024	−	45.2106i	0.829169	−	1.43616i	0.898691	−	0.438583i	$-0.144519\pi$
$992$	−6.77188	+	4.74172i	−0.215008	+	0.150550i
$993$	−16.9700	+	32.2487i	−0.538525	+	1.02338i
$994$	−2.28359	+	6.27412i	−0.0724311	+	0.199003i
$995$		0			0
$996$	42.0024	+	2.02070i	1.33090	+	0.0640283i
$997$	−9.37125	+	0.819878i	−0.296791	+	0.0259658i	−0.234579	−	0.972097i	$-0.575371\pi$
$997$	−9.37125	+	0.819878i	−0.296791	+	0.0259658i	−0.0622119	+	0.998063i	$0.519815\pi$
$998$	−7.32559	+	7.32559i	−0.231887	+	0.231887i
$999$	3.22163	+	8.08041i	0.101928	+	0.255653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.443.12	yes	288
5.2	odd	4	inner	675.2.ba.c.632.13	yes	288
5.3	odd	4	inner	675.2.ba.c.632.12	yes	288
5.4	even	2	inner	675.2.ba.c.443.13	yes	288
27.5	odd	18	inner	675.2.ba.c.518.13	yes	288
135.32	even	36	inner	675.2.ba.c.32.12	✓	288
135.59	odd	18	inner	675.2.ba.c.518.12	yes	288
135.113	even	36	inner	675.2.ba.c.32.13	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.12	✓	288	135.32	even	36	inner
675.2.ba.c.32.13	yes	288	135.113	even	36	inner
675.2.ba.c.443.12	yes	288	1.1	even	1	trivial
675.2.ba.c.443.13	yes	288	5.4	even	2	inner
675.2.ba.c.518.12	yes	288	135.59	odd	18	inner
675.2.ba.c.518.13	yes	288	27.5	odd	18	inner
675.2.ba.c.632.12	yes	288	5.3	odd	4	inner
675.2.ba.c.632.13	yes	288	5.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0304268 - 0.347779i) q^{2} +(-1.64956 - 0.528165i) q^{3} +(1.84959 - 0.326133i) q^{4} +(-0.133494 + 0.589753i) q^{6} +(0.696364 + 0.994510i) q^{7} +(-0.350411 - 1.30775i) q^{8} +(2.44208 + 1.74248i) q^{9} +(-0.626120 - 1.72025i) q^{11} +(-3.22326 - 0.438914i) q^{12} +(0.347377 + 0.0303916i) q^{13} +(0.324682 - 0.272441i) q^{14} +(3.08557 - 1.12306i) q^{16} +(0.515030 - 1.92212i) q^{17} +(0.531693 - 0.902324i) q^{18} +(4.81794 + 2.78164i) q^{19} +(-0.623426 - 2.00830i) q^{21} +(-0.579217 + 0.270093i) q^{22} +(2.41651 + 1.69206i) q^{23} +(-0.112685 + 2.34229i) q^{24} -0.121735i q^{26} +(-3.10804 - 4.16414i) q^{27} +(1.61233 + 1.61233i) q^{28} +(1.34520 + 1.12876i) q^{29} +(-0.372471 - 2.11239i) q^{31} +(-1.62881 - 3.49300i) q^{32} +(0.124245 + 3.16835i) q^{33} +(-0.684143 - 0.120633i) q^{34} +(5.08513 + 2.42643i) q^{36} +(-1.61707 - 0.433293i) q^{37} +(0.820803 - 1.76022i) q^{38} +(-0.556967 - 0.233605i) q^{39} +(-7.15599 - 8.52817i) q^{41} +(-0.679476 + 0.277921i) q^{42} +(3.99477 + 1.86279i) q^{43} +(-1.71910 - 2.97756i) q^{44} +(0.514936 - 0.891896i) q^{46} +(9.15123 - 6.40776i) q^{47} +(-5.68299 + 0.222855i) q^{48} +(1.89001 - 5.19277i) q^{49} +(-1.86477 + 2.89862i) q^{51} +(0.652418 - 0.0570792i) q^{52} +(5.25853 - 5.25853i) q^{53} +(-1.35364 + 1.20761i) q^{54} +(1.05656 - 1.25916i) q^{56} +(-6.47831 - 7.13315i) q^{57} +(0.351629 - 0.502179i) q^{58} +(5.35536 + 1.94919i) q^{59} +(1.30500 - 7.40100i) q^{61} +(-0.723312 + 0.193811i) q^{62} +(-0.0323344 + 3.64208i) q^{63} +(4.52212 - 2.61085i) q^{64} +(1.09811 - 0.139612i) q^{66} +(-0.854027 + 9.76158i) q^{67} +(0.325729 - 3.72310i) q^{68} +(-3.09249 - 4.06746i) q^{69} +(-13.6425 + 7.87649i) q^{71} +(1.42299 - 3.80422i) q^{72} +(11.5895 - 3.10541i) q^{73} +(-0.101488 + 0.575568i) q^{74} +(9.81841 + 3.57361i) q^{76} +(1.27480 - 1.82060i) q^{77} +(-0.0642964 + 0.200810i) q^{78} +(-9.65809 + 11.5101i) q^{79} +(2.92754 + 8.51055i) q^{81} +(-2.74819 + 2.74819i) q^{82} +(-12.8776 + 1.12664i) q^{83} +(-1.80806 - 3.51121i) q^{84} +(0.526293 - 1.44598i) q^{86} +(-1.62282 - 2.57244i) q^{87} +(-2.03026 + 1.42160i) q^{88} +(1.27248 - 2.20400i) q^{89} +(0.211676 + 0.366634i) q^{91} +(5.02139 + 2.34151i) q^{92} +(-0.501277 + 3.68124i) q^{93} +(-2.50693 - 2.98764i) q^{94} +(0.841940 + 6.62218i) q^{96} +(-2.57343 + 5.51873i) q^{97} +(-1.86344 - 0.499308i) q^{98} +(1.46846 - 5.29200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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