LMFDB - Embedded newform 605.2.j.f.124.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.3
Root			$-0.492303 + 0.159959i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.f.444.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.304260 + 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(3.18230 + 1.03399i) q^{7} +(1.83730 - 0.596975i) q^{8} +(0.592242 - 0.430289i) q^{9} +O(q^{10})$	\(q+(0.304260 + 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(3.18230 + 1.03399i) q^{7} +(1.83730 - 0.596975i) q^{8} +(0.592242 - 0.430289i) q^{9} +(0.732051 - 0.896575i) q^{10} -3.34607i q^{12} +(-2.49376 - 3.43237i) q^{13} +(0.535233 + 1.64728i) q^{14} +(-2.33805 - 3.63233i) q^{15} +(-1.99350 - 1.44836i) q^{16} +(-2.27103 + 3.12580i) q^{17} +(0.360391 + 0.117098i) q^{18} +(1.29668 + 3.99078i) q^{19} +(-3.86682 - 0.218323i) q^{20} +6.46410 q^{21} +3.48477i q^{23} +(3.01929 - 2.19364i) q^{24} +(-4.35019 + 2.46492i) q^{25} +(0.678648 - 2.08867i) q^{26} +(-2.57529 + 3.54458i) q^{27} +(3.40654 - 4.68870i) q^{28} +(-2.14093 + 6.58911i) q^{29} +(0.809764 - 2.08429i) q^{30} +(7.06438 - 5.13257i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(0.421768 - 7.47013i) q^{35} +(-0.391818 - 1.20589i) q^{36} +(-1.70539 - 0.554114i) q^{37} +(-1.27672 + 1.75726i) q^{38} +(-6.63083 - 4.81758i) q^{39} +(-2.33805 - 3.63233i) q^{40} +(0.535233 + 1.64728i) q^{41} +(1.96677 + 2.70702i) q^{42} -6.45189i q^{43} +(-1.26795 - 1.03528i) q^{45} +(-1.45934 + 1.06028i) q^{46} +(10.8919 - 3.53899i) q^{47} +(-4.52729 - 1.47101i) q^{48} +(3.39476 + 2.46644i) q^{49} +(-2.35584 - 1.07179i) q^{50} +(-2.30653 + 7.09878i) q^{51} +(-6.98881 + 2.27080i) q^{52} +(-1.27672 - 1.75726i) q^{53} -2.26795 q^{54} +6.46410 q^{56} +(4.76479 + 6.55817i) q^{57} +(-3.41078 + 1.10823i) q^{58} +(0.391818 - 1.20589i) q^{59} +(-7.23485 + 1.90727i) q^{60} +(9.49143 + 6.89593i) q^{61} +(4.29882 + 1.39677i) q^{62} +(2.32960 - 0.756934i) q^{63} +(-1.83481 + 1.33307i) q^{64} +(-6.00000 + 7.34847i) q^{65} -2.20925i q^{67} +(3.93354 + 5.41405i) q^{68} +(2.08032 + 6.40256i) q^{69} +(3.25665 - 2.09624i) q^{70} +(6.63083 + 4.81758i) q^{71} +(0.831254 - 1.14412i) q^{72} +(-4.65921 - 1.51387i) q^{73} +(-0.286831 - 0.882774i) q^{74} +(-6.52111 + 7.12576i) q^{75} +7.26795 q^{76} -4.24264i q^{78} +(1.18448 - 0.860577i) q^{79} +(-1.99534 + 5.13591i) q^{80} +(-3.29420 + 10.1385i) q^{81} +(-0.526994 + 0.725345i) q^{82} +(-5.81878 + 8.00886i) q^{83} +(3.45980 - 10.6482i) q^{84} +(8.05309 + 3.12869i) q^{85} +(2.70191 - 1.96305i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(0.0477646 - 0.845982i) q^{90} +(-4.38685 - 13.5013i) q^{91} +(5.74038 + 1.86516i) q^{92} +(9.91537 - 13.6473i) q^{93} +(4.79602 + 3.48451i) q^{94} +(7.88973 - 5.07844i) q^{95} +(-3.06798 - 9.44228i) q^{96} +(-5.37331 - 7.39573i) q^{97} +2.17209i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^6 - 4 * q^9	$ 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) $ 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.304260	+	0.418778i	0.215144	+	0.296121i	0.902925	−	0.429797i	$-0.141415\pi$
$2$	0.304260	+	0.418778i	0.215144	+	0.296121i	−0.687781	+	0.725918i	$0.741415\pi$
$3$	1.83730	−	0.596975i	1.06077	−	0.344664i	0.273881	−	0.961764i	$-0.411693\pi$
$3$	1.83730	−	0.596975i	1.06077	−	0.344664i	0.786885	+	0.617100i	$0.211693\pi$
$4$	0.535233	−	1.64728i	0.267617	−	0.823639i
$5$	−0.570005	−	2.16220i	−0.254914	−	0.966964i
$5$	−0.570005	−	2.16220i	−0.254914	−	0.966964i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	3.18230	+	1.03399i	1.20280	+	0.390812i	0.840789	−	0.541364i	$-0.182092\pi$
$7$	3.18230	+	1.03399i	1.20280	+	0.390812i	0.362007	+	0.932175i	$0.382092\pi$
$8$	1.83730	−	0.596975i	0.649584	−	0.211063i
$9$	0.592242	−	0.430289i	0.197414	−	0.143430i
$10$	0.732051	−	0.896575i	0.231495	−	0.283522i
$11$		0			0
$11$		0			0
$12$		−	3.34607i		−	0.965926i
$13$	−2.49376	−	3.43237i	−0.691645	−	0.951968i	−1.00000		0.000696272i	$-0.999778\pi$
$13$	−2.49376	−	3.43237i	−0.691645	−	0.951968i	0.308355	−	0.951271i	$-0.400222\pi$
$14$	0.535233	+	1.64728i	0.143047	+	0.440254i
$15$	−2.33805	−	3.63233i	−0.603681	−	0.937862i
$16$	−1.99350	−	1.44836i	−0.498375	−	0.362091i
$17$	−2.27103	+	3.12580i	−0.550805	+	0.758118i	−0.990121	−	0.140214i	$-0.955221\pi$
$17$	−2.27103	+	3.12580i	−0.550805	+	0.758118i	0.439316	+	0.898333i	$0.355221\pi$
$18$	0.360391	+	0.117098i	0.0849449	+	0.0276003i
$19$	1.29668	+	3.99078i	0.297479	+	0.915547i	0.982377	+	0.186908i	$0.0598467\pi$
$19$	1.29668	+	3.99078i	0.297479	+	0.915547i	−0.684898	+	0.728639i	$0.740153\pi$
$20$	−3.86682	−	0.218323i	−0.864648	−	0.0488185i
$21$	6.46410			1.41058
$22$		0			0
$23$			3.48477i			0.726624i	0.931668	+	0.363312i	$0.118354\pi$
$23$			3.48477i			0.726624i	−0.931668	+	0.363312i	$0.881646\pi$
$24$	3.01929	−	2.19364i	0.616311	−	0.447776i
$25$	−4.35019	+	2.46492i	−0.870038	+	0.492985i
$26$	0.678648	−	2.08867i	0.133094	−	0.409621i
$27$	−2.57529	+	3.54458i	−0.495614	+	0.682155i
$28$	3.40654	−	4.68870i	0.643776	−	0.886081i
$29$	−2.14093	+	6.58911i	−0.397561	+	1.22357i	0.529388	+	0.848380i	$0.322422\pi$
$29$	−2.14093	+	6.58911i	−0.397561	+	1.22357i	−0.926949	+	0.375188i	$0.877578\pi$
$30$	0.809764	−	2.08429i	0.147842	−	0.380538i
$31$	7.06438	−	5.13257i	1.26880	−	0.921837i	0.269646	−	0.962960i	$-0.413093\pi$
$31$	7.06438	−	5.13257i	1.26880	−	0.921837i	0.999154	+	0.0411227i	$0.0130935\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	0.421768	−	7.47013i	0.0712918	−	1.26268i
$36$	−0.391818	−	1.20589i	−0.0653030	−	0.200982i
$37$	−1.70539	−	0.554114i	−0.280364	−	0.0910958i	0.165460	−	0.986217i	$-0.447089\pi$
$37$	−1.70539	−	0.554114i	−0.280364	−	0.0910958i	−0.445824	+	0.895121i	$0.647089\pi$
$38$	−1.27672	+	1.75726i	−0.207112	+	0.285065i
$39$	−6.63083	−	4.81758i	−1.06178	−	0.771430i
$40$	−2.33805	−	3.63233i	−0.369678	−	0.574321i
$41$	0.535233	+	1.64728i	0.0835894	+	0.257262i	0.984112	−	0.177547i	$-0.0568161\pi$
$41$	0.535233	+	1.64728i	0.0835894	+	0.257262i	−0.900523	+	0.434808i	$0.856816\pi$
$42$	1.96677	+	2.70702i	0.303479	+	0.417703i
$43$		−	6.45189i		−	0.983905i	−0.870622	−	0.491952i	$-0.836283\pi$
$43$		−	6.45189i		−	0.983905i	0.870622	−	0.491952i	$-0.163717\pi$
$44$		0			0
$45$	−1.26795	−	1.03528i	−0.189015	−	0.154330i
$46$	−1.45934	+	1.06028i	−0.215168	+	0.156329i
$47$	10.8919	−	3.53899i	1.58875	−	0.516215i	0.624455	−	0.781061i	$-0.285321\pi$
$47$	10.8919	−	3.53899i	1.58875	−	0.516215i	0.964291	+	0.264846i	$0.0853213\pi$
$48$	−4.52729	−	1.47101i	−0.653459	−	0.212322i
$49$	3.39476	+	2.46644i	0.484966	+	0.352348i
$50$	−2.35584	−	1.07179i	−0.333167	−	0.151573i
$51$	−2.30653	+	7.09878i	−0.322979	+	0.994028i
$52$	−6.98881	+	2.27080i	−0.969174	+	0.314904i
$53$	−1.27672	−	1.75726i	−0.175371	−	0.241378i	0.712279	−	0.701897i	$-0.247663\pi$
$53$	−1.27672	−	1.75726i	−0.175371	−	0.241378i	−0.887650	+	0.460519i	$0.847663\pi$
$54$	−2.26795			−0.308629
$55$		0			0
$56$	6.46410			0.863802
$57$	4.76479	+	6.55817i	0.631112	+	0.868651i
$58$	−3.41078	+	1.10823i	−0.447857	+	0.145517i
$59$	0.391818	−	1.20589i	0.0510103	−	0.156994i	−0.922306	−	0.386459i	$-0.873698\pi$
$59$	0.391818	−	1.20589i	0.0510103	−	0.156994i	0.973317	+	0.229466i	$0.0736979\pi$
$60$	−7.23485	+	1.90727i	−0.934015	+	0.246228i
$61$	9.49143	+	6.89593i	1.21525	+	0.882933i	0.995697	−	0.0926671i	$-0.0295392\pi$
$61$	9.49143	+	6.89593i	1.21525	+	0.882933i	0.219556	+	0.975600i	$0.429539\pi$
$62$	4.29882	+	1.39677i	0.545950	+	0.177390i
$63$	2.32960	−	0.756934i	0.293502	−	0.0953647i
$64$	−1.83481	+	1.33307i	−0.229351	+	0.166633i
$65$	−6.00000	+	7.34847i	−0.744208	+	0.911465i
$66$		0			0
$67$		−	2.20925i		−	0.269903i	−0.990852	−	0.134952i	$-0.956912\pi$
$67$		−	2.20925i		−	0.269903i	0.990852	−	0.134952i	$-0.0430879\pi$
$68$	3.93354	+	5.41405i	0.477011	+	0.656550i
$69$	2.08032	+	6.40256i	0.250441	+	0.770778i
$70$	3.25665	−	2.09624i	0.389245	−	0.250548i
$71$	6.63083	+	4.81758i	0.786934	+	0.571741i	0.907052	−	0.421018i	$-0.138327\pi$
$71$	6.63083	+	4.81758i	0.786934	+	0.571741i	−0.120118	+	0.992760i	$0.538327\pi$
$72$	0.831254	−	1.14412i	0.0979642	−	0.134836i
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	0.0233860	−	0.999727i	$-0.492555\pi$
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	−0.568705	+	0.822542i	$0.692555\pi$
$74$	−0.286831	−	0.882774i	−0.0333434	−	0.102620i
$75$	−6.52111	+	7.12576i	−0.752992	+	0.822812i
$76$	7.26795			0.833691
$77$		0			0
$78$		−	4.24264i		−	0.480384i
$79$	1.18448	−	0.860577i	0.133265	−	0.0968225i	−0.519156	−	0.854680i	$-0.673754\pi$
$79$	1.18448	−	0.860577i	0.133265	−	0.0968225i	0.652421	+	0.757857i	$0.273754\pi$
$80$	−1.99534	+	5.13591i	−0.223086	+	0.574213i
$81$	−3.29420	+	10.1385i	−0.366022	+	1.12650i
$82$	−0.526994	+	0.725345i	−0.0581967	+	0.0801009i
$83$	−5.81878	+	8.00886i	−0.638694	+	0.879087i	−0.998545	−	0.0539231i	$-0.982827\pi$
$83$	−5.81878	+	8.00886i	−0.638694	+	0.879087i	0.359851	+	0.933010i	$0.382827\pi$
$84$	3.45980	−	10.6482i	0.377495	−	1.16181i
$85$	8.05309	+	3.12869i	0.873481	+	0.339354i
$86$	2.70191	−	1.96305i	0.291355	−	0.211681i
$87$			13.3843i			1.43494i
$88$		0			0
$89$	−0.464102			−0.0491947			−0.0245973	−	0.999697i	$-0.507830\pi$
$89$	−0.464102			−0.0491947			−0.0245973	+	0.999697i	$0.507830\pi$
$90$	0.0477646	−	0.845982i	0.00503483	−	0.0891744i
$91$	−4.38685	−	13.5013i	−0.459867	−	1.41533i
$92$	5.74038	+	1.86516i	0.598476	+	0.194457i
$93$	9.91537	−	13.6473i	1.02818	−	1.41516i
$94$	4.79602	+	3.48451i	0.494671	+	0.359400i
$95$	7.88973	−	5.07844i	0.809469	−	0.521037i
$96$	−3.06798	−	9.44228i	−0.313125	−	0.963699i
$97$	−5.37331	−	7.39573i	−0.545577	−	0.750922i	0.443827	−	0.896113i	$-0.353621\pi$
$97$	−5.37331	−	7.39573i	−0.545577	−	0.750922i	−0.989404	+	0.145190i	$0.953621\pi$
$98$			2.17209i			0.219414i
$99$		0			0
$100$	1.73205	+	8.48528i	0.173205	+	0.848528i
$101$	−15.6887	+	11.3985i	−1.56108	+	1.13419i	−0.625971	+	0.779847i	$0.715297\pi$
$101$	−15.6887	+	11.3985i	−1.56108	+	1.13419i	−0.935114	+	0.354348i	$0.884703\pi$
$102$	−3.67460	+	1.19395i	−0.363840	+	0.118219i
$103$	4.03499	+	1.31105i	0.397579	+	0.129181i	0.500981	−	0.865458i	$-0.332973\pi$
$103$	4.03499	+	1.31105i	0.397579	+	0.129181i	−0.103401	+	0.994640i	$0.532973\pi$
$104$	−6.63083	−	4.81758i	−0.650206	−	0.472402i
$105$	−3.68457	−	13.9767i	−0.359577	−	1.36398i
$106$	0.347445	−	1.06933i	0.0337468	−	0.103862i
$107$	2.82191	−	0.916893i	0.272804	−	0.0886394i	−0.169420	−	0.985544i	$-0.554190\pi$
$107$	2.82191	−	0.916893i	0.272804	−	0.0886394i	0.442224	+	0.896905i	$0.354190\pi$
$108$	4.46053	+	6.13939i	0.429215	+	0.590763i
$109$	−9.19615			−0.880832			−0.440416	−	0.897794i	$-0.645169\pi$
$109$	−9.19615			−0.880832			−0.440416	+	0.897794i	$0.645169\pi$
$110$		0			0
$111$	−3.46410			−0.328798
$112$	−4.84632	−	6.67038i	−0.457934	−	0.630292i
$113$	−2.68999	+	0.874032i	−0.253053	+	0.0822220i	−0.432797	−	0.901492i	$-0.642473\pi$
$113$	−2.68999	+	0.874032i	−0.253053	+	0.0822220i	0.179743	+	0.983714i	$0.442473\pi$
$114$	−1.29668	+	3.99078i	−0.121445	+	0.373771i
$115$	7.53475	−	1.98633i	0.702619	−	0.185226i
$116$	9.70820	+	7.05342i	0.901384	+	0.654894i
$117$	−2.95382	−	0.959754i	−0.273081	−	0.0887293i
$118$	0.624215	−	0.202820i	0.0574637	−	0.0186711i
$119$	−10.4591	+	7.59901i	−0.958787	+	0.696600i
$120$	−6.46410	−	5.27792i	−0.590089	−	0.481806i
$121$		0			0
$122$			6.07296i			0.549820i
$123$	1.96677	+	2.70702i	0.177337	+	0.244084i
$124$	−4.67368	−	14.3841i	−0.419709	−	1.29173i
$125$	7.80928	+	8.00095i	0.698483	+	0.715626i
$126$	1.02579	+	0.745282i	0.0913849	+	0.0663950i
$127$	0.526994	−	0.725345i	0.0467631	−	0.0643639i	−0.784995	−	0.619502i	$-0.787335\pi$
$127$	0.526994	−	0.725345i	0.0467631	−	0.0643639i	0.831758	+	0.555138i	$0.187335\pi$
$128$	−10.8919	−	3.53899i	−0.962716	−	0.312805i
$129$	−3.85162	−	11.8541i	−0.339116	−	1.04369i
$130$	−4.90294	−	0.276823i	−0.430016	−	0.0242789i
$131$	−3.12436			−0.272976			−0.136488	−	0.990642i	$-0.543582\pi$
$131$	−3.12436			−0.272976			−0.136488	+	0.990642i	$0.543582\pi$
$132$		0			0
$133$			14.0406i			1.21747i
$134$	0.925187	−	0.672187i	0.0799239	−	0.0580681i
$135$	9.13200	+	3.54785i	0.785958	+	0.305350i
$136$	−2.30653	+	7.09878i	−0.197784	+	0.608716i
$137$	5.21026	−	7.17130i	0.445142	−	0.612686i	−0.526203	−	0.850359i	$-0.676385\pi$
$137$	5.21026	−	7.17130i	0.445142	−	0.612686i	0.971345	+	0.237673i	$0.0763847\pi$
$138$	−2.04829	+	2.81923i	−0.174362	+	0.239989i
$139$	4.50808	−	13.8744i	0.382370	−	1.17682i	−0.555999	−	0.831183i	$-0.687664\pi$
$139$	4.50808	−	13.8744i	0.382370	−	1.17682i	0.938370	−	0.345633i	$-0.112336\pi$
$140$	−12.0796	−	4.69303i	−1.02092	−	0.396634i
$141$	17.8990	−	13.0044i	1.50737	−	1.09517i
$142$			4.24264i			0.356034i
$143$		0			0
$144$	−1.80385			−0.150321
$145$	15.4673	+	0.873292i	1.28449	+	0.0725230i
$146$	−0.783636	−	2.41178i	−0.0648542	−	0.199601i
$147$	7.70959	+	2.50500i	0.635876	+	0.206609i
$148$	−1.82556	+	2.51267i	−0.150060	+	0.206540i
$149$	−8.30695	−	6.03535i	−0.680531	−	0.494435i	0.193002	−	0.981198i	$-0.438177\pi$
$149$	−8.30695	−	6.03535i	−0.680531	−	0.494435i	−0.873534	+	0.486763i	$0.838177\pi$
$150$	−4.96822	−	0.562811i	−0.405654	−	0.0459534i
$151$	1.29668	+	3.99078i	0.105523	+	0.324765i	0.989853	−	0.142097i	$-0.0453845\pi$
$151$	1.29668	+	3.99078i	0.105523	+	0.324765i	−0.884330	+	0.466862i	$0.845384\pi$
$152$	4.76479	+	6.55817i	0.386475	+	0.531938i
$153$			2.82843i			0.228665i
$154$		0			0
$155$	−15.1244	−	12.3490i	−1.21482	−	0.991894i
$156$	−11.4849	+	8.34429i	−0.919530	+	0.668078i
$157$	−20.7992	+	6.75806i	−1.65995	+	0.539352i	−0.980863	−	0.194701i	$-0.937626\pi$
$157$	−20.7992	+	6.75806i	−1.65995	+	0.539352i	−0.679092	+	0.734053i	$0.737626\pi$
$158$	0.720782	+	0.234196i	0.0573423	+	0.0186316i
$159$	−3.39476	−	2.46644i	−0.269222	−	0.195601i
$160$	−11.1120	+	2.92938i	−0.878480	+	0.231588i
$161$	−3.60322	+	11.0896i	−0.283973	+	0.873980i
$162$	−5.24808	+	1.70520i	−0.412328	+	0.133973i
$163$	3.02076	+	4.15771i	0.236604	+	0.325657i	0.910763	−	0.412928i	$-0.135494\pi$
$163$	3.02076	+	4.15771i	0.236604	+	0.325657i	−0.674160	+	0.738586i	$0.735494\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	−5.12436			−0.397727
$167$	0.304260	+	0.418778i	0.0235443	+	0.0324060i	0.820627	−	0.571464i	$-0.193624\pi$
$167$	0.304260	+	0.418778i	0.0235443	+	0.0324060i	−0.797083	+	0.603870i	$0.793624\pi$
$168$	11.8765	−	3.85891i	0.916291	−	0.297721i
$169$	−1.54508	+	4.75528i	−0.118853	+	0.365791i
$170$	1.14001	+	4.32439i	0.0874347	+	0.331666i
$171$	2.48514	+	1.80556i	0.190043	+	0.138074i
$172$	−10.6281	−	3.45327i	−0.810382	−	0.263309i
$173$	−20.7026	+	6.72668i	−1.57399	+	0.511420i	−0.960499	−	0.278282i	$-0.910235\pi$
$173$	−20.7026	+	6.72668i	−1.57399	+	0.511420i	−0.613490	+	0.789702i	$0.710235\pi$
$174$	−5.60503	+	4.07230i	−0.424917	+	0.308720i
$175$	−16.3923	+	3.34607i	−1.23914	+	0.252939i
$176$		0			0
$177$		−	2.44949i		−	0.184115i
$178$	−0.141208	−	0.194356i	−0.0105840	−	0.0145676i
$179$	4.77867	+	14.7072i	0.357175	+	1.09927i	0.954738	+	0.297449i	$0.0961357\pi$
$179$	4.77867	+	14.7072i	0.357175	+	1.09927i	−0.597563	+	0.801822i	$0.703864\pi$
$180$	−2.38404	+	1.53455i	−0.177696	+	0.114379i
$181$	14.0707	+	10.2229i	1.04586	+	0.759865i	0.971422	−	0.237360i	$-0.0762821\pi$
$181$	14.0707	+	10.2229i	1.04586	+	0.759865i	0.0744429	+	0.997225i	$0.476282\pi$
$182$	4.31932	−	5.94504i	0.320169	−	0.440675i
$183$	21.5553	+	7.00374i	1.59341	+	0.517731i
$184$	2.08032	+	6.40256i	0.153363	+	0.472003i
$185$	−0.226025	+	4.00323i	−0.0166177	+	0.294323i
$186$	8.73205			0.640265
$187$		0			0
$188$		−	19.8362i		−	1.44670i
$189$	−11.8604	+	8.61708i	−0.862717	+	0.626800i
$190$	4.52727	+	1.75888i	0.328443	+	0.127602i
$191$	−2.24592	+	6.91223i	−0.162509	+	0.500151i	−0.998844	−	0.0480672i	$-0.984694\pi$
$191$	−2.24592	+	6.91223i	−0.162509	+	0.500151i	0.836335	+	0.548219i	$0.184694\pi$
$192$	−2.57529	+	3.54458i	−0.185855	+	0.255808i
$193$	8.92106	−	12.2788i	0.642152	−	0.883846i	−0.356576	−	0.934266i	$-0.616056\pi$
$193$	8.92106	−	12.2788i	0.642152	−	0.883846i	0.998728	+	0.0504200i	$0.0160560\pi$
$194$	1.46228	−	4.50045i	0.104986	−	0.323113i
$195$	−6.63695	+	17.0832i	−0.475282	+	1.22335i
$196$	5.87989	−	4.27199i	0.419992	−	0.305142i
$197$		−	17.2480i		−	1.22887i	−0.788969	−	0.614433i	$-0.789385\pi$
$197$		−	17.2480i		−	1.22887i	0.788969	−	0.614433i	$-0.210615\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	−6.52111	+	7.12576i	−0.461112	+	0.503867i
$201$	−1.31887	−	4.05906i	−0.0930258	−	0.286304i
$202$	−9.54689	−	3.10197i	−0.671717	−	0.218254i
$203$	−13.6262	+	18.7548i	−0.956369	+	1.31633i
$204$	10.4591	+	7.59901i	0.732286	+	0.532037i
$205$	3.25665	−	2.09624i	0.227455	−	0.146407i
$206$	0.678648	+	2.08867i	0.0472837	+	0.145524i
$207$	1.49946	+	2.06382i	0.104219	+	0.143446i
$208$			10.4543i			0.724875i
$209$		0			0
$210$	4.73205	−	5.79555i	0.326543	−	0.399931i
$211$	10.6178	−	7.71430i	0.730961	−	0.531074i	−0.158906	−	0.987294i	$-0.550797\pi$
$211$	10.6178	−	7.71430i	0.730961	−	0.531074i	0.889867	+	0.456219i	$0.150797\pi$
$212$	−3.57803	+	1.16257i	−0.245740	+	0.0798459i
$213$	15.0588	+	4.89290i	1.03181	+	0.335256i
$214$	1.24257	+	0.902778i	0.0849402	+	0.0617127i
$215$	−13.9503	+	3.67761i	−0.951400	+	0.250811i
$216$	−2.61555	+	8.04984i	−0.177966	+	0.547722i
$217$	27.7880	−	9.02886i	1.88637	−	0.612919i
$218$	−2.79802	−	3.85115i	−0.189506	−	0.260833i
$219$	−9.46410			−0.639525
$220$		0			0
$221$	16.3923			1.10267
$222$	−1.05399	−	1.45069i	−0.0707390	−	0.0973639i
$223$	−1.47691	+	0.479877i	−0.0989012	+	0.0321349i	−0.358050	−	0.933703i	$-0.616558\pi$
$223$	−1.47691	+	0.479877i	−0.0989012	+	0.0321349i	0.259148	+	0.965838i	$0.416558\pi$
$224$	5.31390	−	16.3545i	0.355050	−	1.09273i
$225$	−1.51573	+	3.33167i	−0.101049	+	0.222111i
$226$	−1.18448	−	0.860577i	−0.0787906	−	0.0572448i
$227$	−19.1291	−	6.21543i	−1.26964	−	0.412533i	−0.404723	−	0.914439i	$-0.632632\pi$
$227$	−19.1291	−	6.21543i	−1.26964	−	0.412533i	−0.864922	+	0.501907i	$0.832632\pi$
$228$	13.3534	−	4.33878i	0.884351	−	0.287343i
$229$	−3.29415	+	2.39334i	−0.217684	+	0.158156i	−0.691283	−	0.722584i	$-0.742954\pi$
$229$	−3.29415	+	2.39334i	−0.217684	+	0.158156i	0.473600	+	0.880740i	$0.342954\pi$
$230$	3.12436	+	2.55103i	0.206014	+	0.168210i
$231$		0			0
$232$			13.3843i			0.878720i
$233$	−0.994306	−	1.36855i	−0.0651392	−	0.0896564i	0.775204	−	0.631710i	$-0.217647\pi$
$233$	−0.994306	−	1.36855i	−0.0651392	−	0.0896564i	−0.840344	+	0.542054i	$0.817647\pi$
$234$	−0.496805	−	1.52901i	−0.0324772	−	0.0999544i
$235$	−13.8604	−	21.5332i	−0.904154	−	1.40467i
$236$	−1.77672	−	1.29087i	−0.115655	−	0.0840282i
$237$	1.66251	−	2.28825i	0.107991	−	0.148638i
$238$	−6.36459	−	2.06798i	−0.412555	−	0.134047i
$239$	−1.74911	−	5.38322i	−0.113141	−	0.348212i	0.878414	−	0.477901i	$-0.158602\pi$
$239$	−1.74911	−	5.38322i	−0.113141	−	0.348212i	−0.991555	+	0.129689i	$0.958602\pi$
$240$	−0.600028	+	10.6274i	−0.0387316	+	0.685995i
$241$	14.1244			0.909830			0.454915	−	0.890535i	$-0.349670\pi$
$241$	14.1244			0.909830			0.454915	+	0.890535i	$0.349670\pi$
$242$		0			0
$243$			7.45001i			0.477918i
$244$	16.4396	−	11.9441i	1.05244	−	0.764642i
$245$	3.39789	−	8.74602i	0.217083	−	0.558762i
$246$	−0.535233	+	1.64728i	−0.0341252	+	0.105027i
$247$	10.4642	−	14.4027i	0.665821	−	0.916424i
$248$	9.91537	−	13.6473i	0.629626	−	0.866606i
$249$	−5.90975	+	18.1883i	−0.374515	+	1.15264i
$250$	−0.974569	+	5.70472i	−0.0616371	+	0.360798i
$251$	3.07738	−	2.23585i	0.194242	−	0.141125i	−0.486413	−	0.873729i	$-0.661695\pi$
$251$	3.07738	−	2.23585i	0.194242	−	0.141125i	0.680656	+	0.732604i	$0.261695\pi$
$252$		−	4.24264i		−	0.267261i
$253$		0			0
$254$	0.464102			0.0291203
$255$	16.6637	+	0.940842i	1.04352	+	0.0589178i
$256$	−0.430246	−	1.32416i	−0.0268904	−	0.0827600i
$257$	−14.0742	−	4.57298i	−0.877924	−	0.285255i	−0.164829	−	0.986322i	$-0.552707\pi$
$257$	−14.0742	−	4.57298i	−0.877924	−	0.285255i	−0.713095	+	0.701068i	$0.752707\pi$
$258$	3.79233	−	5.21969i	0.236100	−	0.324964i
$259$	−4.85410	−	3.52671i	−0.301619	−	0.219139i
$260$	8.89357	+	13.8168i	0.551556	+	0.856882i
$261$	1.56727	+	4.82357i	0.0970117	+	0.298571i
$262$	−0.950617	−	1.30841i	−0.0587293	−	0.0808339i
$263$		−	6.79367i		−	0.418915i	−0.977818	−	0.209458i	$-0.932830\pi$
$263$		−	6.79367i		−	0.418915i	0.977818	−	0.209458i	$-0.0671699\pi$
$264$		0			0
$265$	−3.07180	+	3.76217i	−0.188699	+	0.231108i
$266$	−5.87989	+	4.27199i	−0.360519	+	0.261933i
$267$	−0.852694	+	0.277057i	−0.0521840	+	0.0169556i
$268$	−3.63925	−	1.18247i	−0.222303	−	0.0722306i
$269$	−13.1610	−	9.56206i	−0.802443	−	0.583009i	0.109187	−	0.994021i	$-0.465175\pi$
$269$	−13.1610	−	9.56206i	−0.802443	−	0.583009i	−0.911630	+	0.411012i	$0.865175\pi$
$270$	1.29274	+	4.90375i	0.0786737	+	0.298433i
$271$	3.54260	−	10.9030i	0.215198	−	0.662311i	−0.783942	−	0.620834i	$-0.786794\pi$
$271$	3.54260	−	10.9030i	0.215198	−	0.662311i	0.999139	−	0.0414762i	$-0.0132061\pi$
$272$	9.05459	−	2.94201i	0.549015	−	0.178386i
$273$	−16.1199	−	22.1872i	−0.975622	−	1.34283i
$274$	4.58846			0.277199
$275$		0			0
$276$	11.6603			0.701865
$277$	−18.3313	−	25.2308i	−1.10142	−	1.51597i	−0.833489	−	0.552536i	$-0.813660\pi$
$277$	−18.3313	−	25.2308i	−1.10142	−	1.51597i	−0.267930	−	0.963438i	$-0.586340\pi$
$278$	7.18194	−	2.33355i	0.430744	−	0.139957i
$279$	1.97533	−	6.07944i	0.118260	−	0.363967i
$280$	−3.68457	−	13.9767i	−0.220195	−	0.835265i
$281$	14.0126	+	10.1807i	0.835921	+	0.607332i	0.921228	−	0.389023i	$-0.127187\pi$
$281$	14.0126	+	10.1807i	0.835921	+	0.607332i	−0.0853074	+	0.996355i	$0.527187\pi$
$282$	10.8919	+	3.53899i	0.648603	+	0.210744i
$283$	7.67425	−	2.49351i	0.456187	−	0.148224i	−0.0719049	−	0.997411i	$-0.522908\pi$
$283$	7.67425	−	2.49351i	0.456187	−	0.148224i	0.528091	+	0.849187i	$0.322908\pi$
$284$	11.4849	−	8.34429i	0.681505	−	0.495142i
$285$	11.4641	−	14.0406i	0.679075	−	0.831693i
$286$		0			0
$287$			5.79555i			0.342101i
$288$	−2.21135	−	3.04366i	−0.130305	−	0.179349i
$289$	0.640220	+	1.97040i	0.0376600	+	0.115906i
$290$	4.34037	+	6.74307i	0.254875	+	0.395967i
$291$	−14.2874	−	10.3804i	−0.837545	−	0.608512i
$292$	−4.98752	+	6.86474i	−0.291873	+	0.401728i
$293$	14.3380	+	4.65870i	0.837635	+	0.272164i	0.696258	−	0.717792i	$-0.254847\pi$
$293$	14.3380	+	4.65870i	0.837635	+	0.272164i	0.141377	+	0.989956i	$0.454847\pi$
$294$	1.29668	+	3.99078i	0.0756241	+	0.232747i
$295$	−2.83071	−	0.159824i	−0.164810	−	0.00930529i
$296$	−3.46410			−0.201347
$297$		0			0
$298$		−	5.31508i		−	0.307894i
$299$	11.9610	−	8.69018i	0.691723	−	0.502566i
$300$	8.24780	+	14.5560i	0.476187	+	0.840392i
$301$	6.67120	−	20.5318i	0.384522	−	1.18344i
$302$	−1.27672	+	1.75726i	−0.0734671	+	0.101119i
$303$	−22.0202	+	30.3082i	−1.26503	+	1.74116i
$304$	3.19516	−	9.83368i	0.183255	−	0.564000i
$305$	9.50019	−	24.4530i	0.543979	−	1.40018i
$306$	−1.18448	+	0.860577i	−0.0677124	+	0.0491959i
$307$			7.82894i			0.446821i	0.974724	+	0.223411i	$0.0717191\pi$
$307$			7.82894i			0.446821i	−0.974724	+	0.223411i	$0.928281\pi$
$308$		0			0
$309$	8.19615			0.466263
$310$	0.569746	−	10.0911i	0.0323594	−	0.573133i
$311$	3.10641	+	9.56055i	0.176148	+	0.542129i	0.999684	−	0.0251354i	$-0.00800169\pi$
$311$	3.10641	+	9.56055i	0.176148	+	0.542129i	−0.823536	+	0.567265i	$0.808002\pi$
$312$	−15.0588	−	4.89290i	−0.852536	−	0.277006i
$313$	−10.0784	+	13.8718i	−0.569666	+	0.784078i	−0.992515	−	0.122122i	$-0.961030\pi$
$313$	−10.0784	+	13.8718i	−0.569666	+	0.784078i	0.422849	+	0.906200i	$0.361030\pi$
$314$	−9.15848	−	6.65403i	−0.516843	−	0.375509i
$315$	−2.96452	−	4.60560i	−0.167032	−	0.259496i
$316$	−0.783636	−	2.41178i	−0.0440830	−	0.135673i
$317$	−7.42160	−	10.2150i	−0.416839	−	0.573729i	0.548031	−	0.836458i	$-0.315378\pi$
$317$	−7.42160	−	10.2150i	−0.416839	−	0.573729i	−0.964870	+	0.262729i	$0.915378\pi$
$318$		−	2.17209i		−	0.121805i
$319$		0			0
$320$	3.92820	+	3.20736i	0.219593	+	0.179297i
$321$	4.63733	−	3.36921i	0.258830	−	0.188051i
$322$	−5.74038	+	1.86516i	−0.319899	+	0.103941i
$323$	−15.4192	−	5.01000i	−0.857946	−	0.278764i
$324$	14.9378	+	10.8529i	0.829876	+	0.602940i
$325$	19.3089	+	8.78452i	1.07106	+	0.487277i
$326$	−0.822064	+	2.53005i	−0.0455299	+	0.140127i
$327$	−16.8961	+	5.48987i	−0.934356	+	0.303591i
$328$	1.96677	+	2.70702i	0.108597	+	0.149470i
$329$	38.3205			2.11268
$330$		0			0
$331$	−18.1962			−1.00015			−0.500075	−	0.865982i	$-0.666694\pi$
$331$	−18.1962			−1.00015			−0.500075	+	0.865982i	$0.666694\pi$
$332$	10.0784	+	13.8718i	0.553125	+	0.761311i
$333$	−1.24843	+	0.405640i	−0.0684136	+	0.0222289i
$334$	−0.0828009	+	0.254835i	−0.00453066	+	0.0139439i
$335$	−4.77684	+	1.25928i	−0.260987	+	0.0688021i
$336$	−12.8862	−	9.36236i	−0.702999	−	0.510759i
$337$	16.7642	+	5.44701i	0.913203	+	0.296718i	0.727676	−	0.685921i	$-0.240601\pi$
$337$	16.7642	+	5.44701i	0.913203	+	0.296718i	0.185527	+	0.982639i	$0.440601\pi$
$338$	−2.46152	+	0.799795i	−0.133889	+	0.0435031i
$339$	−4.42055	+	3.21172i	−0.240091	+	0.174437i
$340$	9.46410	−	11.5911i	0.513263	−	0.628616i
$341$		0			0
$342$			1.59008i			0.0859816i
$343$	−5.51452	−	7.59008i	−0.297756	−	0.409826i
$344$	−3.85162	−	11.8541i	−0.207665	−	0.639128i
$345$	12.6578	−	8.14755i	0.681473	−	0.438649i
$346$	−9.11596	−	6.62313i	−0.490077	−	0.356062i
$347$	2.57529	−	3.54458i	0.138249	−	0.190283i	−0.734279	−	0.678848i	$-0.762479\pi$
$347$	2.57529	−	3.54458i	0.138249	−	0.190283i	0.872527	+	0.488565i	$0.162479\pi$
$348$	22.0476	+	7.16370i	1.18188	+	0.384015i
$349$	2.26216	+	6.96222i	0.121091	+	0.372679i	0.993169	−	0.116688i	$-0.0372278\pi$
$349$	2.26216	+	6.96222i	0.121091	+	0.372679i	−0.872078	+	0.489367i	$0.837228\pi$
$350$	−6.38878	−	5.84666i	−0.341495	−	0.312517i
$351$	18.5885			0.992178
$352$		0			0
$353$		−	13.0053i		−	0.692204i	−0.938197	−	0.346102i	$-0.887505\pi$
$353$		−	13.0053i		−	0.692204i	0.938197	−	0.346102i	$-0.112495\pi$
$354$	1.02579	−	0.745282i	0.0545203	−	0.0396113i
$355$	6.63695	−	17.0832i	0.352253	−	0.906682i
$356$	−0.248403	+	0.764504i	−0.0131653	+	0.0405187i
$357$	−14.6802	+	20.2055i	−0.776956	+	1.06939i
$358$	−4.70511	+	6.47603i	−0.248673	+	0.342269i
$359$	−11.0196	+	33.9149i	−0.581594	+	1.78996i	0.0309462	+	0.999521i	$0.490148\pi$
$359$	−11.0196	+	33.9149i	−0.581594	+	1.78996i	−0.612540	+	0.790440i	$0.709852\pi$
$360$	−2.94764	−	1.14518i	−0.155354	−	0.0603562i
$361$	1.12640	−	0.818376i	0.0592841	−	0.0430724i
$362$			9.00292i			0.473183i
$363$		0			0
$364$	−24.5885			−1.28879
$365$	−0.617511	+	10.9370i	−0.0323220	+	0.572470i
$366$	3.62540	+	11.1578i	0.189503	+	0.583230i
$367$	16.0787	+	5.22430i	0.839304	+	0.272706i	0.696959	−	0.717111i	$-0.254536\pi$
$367$	16.0787	+	5.22430i	0.839304	+	0.272706i	0.142345	+	0.989817i	$0.454536\pi$
$368$	5.04720	−	6.94688i	0.263104	−	0.362131i
$369$	1.02579	+	0.745282i	0.0534006	+	0.0387978i
$370$	−1.74524	+	1.12337i	−0.0907305	+	0.0584012i
$371$	−2.24592	−	6.91223i	−0.116602	−	0.358865i
$372$	−17.1739	−	23.6379i	−0.890426	−	1.22557i
$373$			0.175865i			0.00910597i	0.999990	+	0.00455298i	$0.00144926\pi$
$373$			0.175865i			0.00910597i	−0.999990	+	0.00455298i	$0.998551\pi$
$374$		0			0
$375$	19.1244	+	10.0382i	0.987577	+	0.518370i
$376$	17.8990	−	13.0044i	0.923069	−	0.670649i
$377$	27.9552	−	9.08321i	1.43977	−	0.467809i
$378$	−7.21729	−	2.34504i	−0.371217	−	0.120616i
$379$	1.18448	+	0.860577i	0.0608428	+	0.0442049i	0.617791	−	0.786342i	$-0.288028\pi$
$379$	1.18448	+	0.860577i	0.0608428	+	0.0442049i	−0.556948	+	0.830547i	$0.688028\pi$
$380$	−4.14276	−	15.7147i	−0.212519	−	0.806149i
$381$	0.535233	−	1.64728i	0.0274208	−	0.0843926i
$382$	−3.57803	+	1.16257i	−0.183068	+	0.0594824i
$383$	22.6069	+	31.1157i	1.15516	+	1.58994i	0.727684	+	0.685913i	$0.240597\pi$
$383$	22.6069	+	31.1157i	1.15516	+	1.58994i	0.427475	+	0.904027i	$0.359403\pi$
$384$	−22.1244			−1.12903
$385$		0			0
$386$	7.85641			0.399881
$387$	−2.77618	−	3.82108i	−0.141121	−	0.194236i
$388$	−15.0588	+	4.89290i	−0.764494	+	0.248399i
$389$	−1.89253	+	5.82461i	−0.0959551	+	0.295319i	−0.987501	−	0.157610i	$-0.949621\pi$
$389$	−1.89253	+	5.82461i	−0.0959551	+	0.295319i	0.891546	+	0.452929i	$0.149621\pi$
$390$	−9.17342	+	2.41832i	−0.464514	+	0.122457i
$391$	−10.8927	−	7.91400i	−0.550867	−	0.400228i
$392$	7.70959	+	2.50500i	0.389393	+	0.126522i
$393$	−5.74038	+	1.86516i	−0.289564	+	0.0940850i
$394$	7.22307	−	5.24787i	0.363893	−	0.264384i
$395$	−2.53590	−	2.07055i	−0.127595	−	0.104181i
$396$		0			0
$397$		−	32.9802i		−	1.65523i	−0.561298	−	0.827614i	$-0.689698\pi$
$397$		−	32.9802i		−	1.65523i	0.561298	−	0.827614i	$-0.310302\pi$
$398$	0.608520	+	0.837556i	0.0305024	+	0.0419829i
$399$	8.38189	+	25.7968i	0.419619	+	1.29146i
$400$	12.2422	+	1.38682i	0.612110	+	0.0693412i
$401$	−1.87733	−	1.36396i	−0.0937494	−	0.0681129i	0.539923	−	0.841714i	$-0.318453\pi$
$401$	−1.87733	−	1.36396i	−0.0937494	−	0.0681129i	−0.633673	+	0.773601i	$0.718453\pi$
$402$	1.29857	−	1.78732i	0.0647666	−	0.0891436i
$403$	−35.2337	−	11.4481i	−1.75512	−	0.570272i
$404$	10.3794	+	31.9445i	0.516395	+	1.58930i
$405$	23.7991	+	1.34371i	1.18259	+	0.0667696i
$406$	−12.0000			−0.595550
$407$		0			0
$408$			14.4195i			0.713873i
$409$	−21.1350	+	15.3555i	−1.04506	+	0.759281i	−0.971267	−	0.237992i	$-0.923511\pi$
$409$	−21.1350	+	15.3555i	−1.04506	+	0.759281i	−0.0737938	+	0.997274i	$0.523511\pi$
$410$	1.86873	+	0.726014i	0.0922899	+	0.0358553i
$411$	5.29172	−	16.2862i	0.261021	−	0.803340i
$412$	4.31932	−	5.94504i	0.212798	−	0.292891i
$413$	2.49376	−	3.43237i	0.122710	−	0.168896i
$414$	−0.408059	+	1.25588i	−0.0200550	+	0.0617230i
$415$	20.6335	+	8.01625i	1.01286	+	0.393502i
$416$	−17.6397	+	12.8160i	−0.864857	+	0.628355i
$417$		−	28.1827i		−	1.38011i
$418$		0			0
$419$	12.3397			0.602836			0.301418	−	0.953492i	$-0.402540\pi$
$419$	12.3397			0.602836			0.301418	+	0.953492i	$0.402540\pi$
$420$	−24.9955	−	1.41126i	−1.21966	−	0.0688626i
$421$	−5.26953	−	16.2179i	−0.256821	−	0.790414i	−0.993465	−	0.114134i	$-0.963591\pi$
$421$	−5.26953	−	16.2179i	−0.256821	−	0.790414i	0.736644	−	0.676281i	$-0.236409\pi$
$422$	6.46116	+	2.09936i	0.314524	+	0.102195i
$423$	4.92784	−	6.78259i	0.239600	−	0.329781i
$424$	−3.39476	−	2.46644i	−0.164864	−	0.119781i
$425$	2.17454	−	19.1957i	0.105481	−	0.931130i
$426$	2.53275	+	7.79500i	0.122712	+	0.377669i
$427$	23.0742	+	31.7589i	1.11664	+	1.53692i
$428$		−	5.13922i		−	0.248413i
$429$		0			0
$430$	−5.78461	−	4.72311i	−0.278959	−	0.227769i
$431$	4.10317	−	2.98113i	0.197643	−	0.143596i	−0.484562	−	0.874757i	$-0.661021\pi$
$431$	4.10317	−	2.98113i	0.197643	−	0.143596i	0.682205	+	0.731161i	$0.261021\pi$
$432$	10.2677	−	3.33617i	0.494004	−	0.160512i
$433$	−27.3310	−	8.88039i	−1.31345	−	0.426764i	−0.433206	−	0.901295i	$-0.642618\pi$
$433$	−27.3310	−	8.88039i	−1.31345	−	0.426764i	−0.880239	+	0.474531i	$0.842618\pi$
$434$	12.2359	+	8.88987i	0.587340	+	0.426728i
$435$	28.9394	−	7.62909i	1.38754	−	0.365787i
$436$	−4.92209	+	15.1486i	−0.235725	+	0.725487i
$437$	−13.9069	+	4.51863i	−0.665259	+	0.216156i
$438$	−2.87955	−	3.96336i	−0.137590	−	0.189377i
$439$	−28.2487			−1.34824			−0.674119	−	0.738623i	$-0.735476\pi$
$439$	−28.2487			−1.34824			−0.674119	+	0.738623i	$0.735476\pi$
$440$		0			0
$441$	3.07180			0.146276
$442$	4.98752	+	6.86474i	0.237232	+	0.326522i
$443$	−26.2145	+	8.51761i	−1.24549	+	0.404684i	−0.856302	−	0.516475i	$-0.827244\pi$
$443$	−26.2145	+	8.51761i	−1.24549	+	0.404684i	−0.389187	+	0.921159i	$0.627244\pi$
$444$	−1.85410	+	5.70634i	−0.0879918	+	0.270811i
$445$	0.264540	+	1.00348i	0.0125404	+	0.0475695i
$446$	−0.650326	−	0.472490i	−0.0307938	−	0.0223730i
$447$	−18.8653	−	6.12971i	−0.892298	−	0.289925i
$448$	−7.21729	+	2.34504i	−0.340985	+	0.110793i
$449$	27.9246	−	20.2884i	1.31784	−	0.957468i	0.317885	−	0.948129i	$-0.397027\pi$
$449$	27.9246	−	20.2884i	1.31784	−	0.957468i	0.999956	−	0.00933886i	$-0.00297270\pi$
$450$	−1.85641	+	0.378937i	−0.0875118	+	0.0178633i
$451$		0			0
$452$			4.89898i			0.230429i
$453$	4.76479	+	6.55817i	0.223869	+	0.308130i
$454$	−3.21734	−	9.90197i	−0.150997	−	0.464722i
$455$	−26.6920	+	17.1811i	−1.25134	+	0.805461i
$456$	12.6694	+	9.20487i	0.593300	+	0.431057i
$457$	12.4688	−	17.1618i	0.583266	−	0.802797i	−0.410782	−	0.911733i	$-0.634744\pi$
$457$	12.4688	−	17.1618i	0.583266	−	0.802797i	0.994049	+	0.108936i	$0.0347444\pi$
$458$	−2.00456	−	0.651320i	−0.0936668	−	0.0304342i
$459$	−5.23110	−	16.0997i	−0.244167	−	0.751469i
$460$	0.760805	−	13.4750i	0.0354727	−	0.628274i
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$		−	20.3166i		−	0.944194i	−0.881547	−	0.472097i	$-0.843497\pi$
$463$		−	20.3166i		−	0.944194i	0.881547	−	0.472097i	$-0.156503\pi$
$464$	13.8114	−	10.0346i	0.641177	−	0.465842i
$465$	−35.1600	−	13.6599i	−1.63051	−	0.633464i
$466$	0.270589	−	0.832787i	0.0125348	−	0.0385781i
$467$	0.363941	−	0.500922i	0.0168412	−	0.0231799i	−0.800513	−	0.599315i	$-0.795440\pi$
$467$	0.363941	−	0.500922i	0.0168412	−	0.0231799i	0.817355	+	0.576135i	$0.195440\pi$
$468$	−3.16196	+	4.35207i	−0.146162	+	0.201174i
$469$	2.28435	−	7.03050i	0.105481	−	0.324638i
$470$	4.80044	−	12.3561i	0.221428	−	0.569945i
$471$	−34.1799	+	24.8332i	−1.57493	+	1.14425i
$472$		−	2.44949i		−	0.112747i
$473$		0			0
$474$	1.46410			0.0672484
$475$	−15.4778	−	14.1644i	−0.710169	−	0.649908i
$476$	6.91960	+	21.2963i	0.317159	+	0.976116i
$477$	−1.51226	−	0.491361i	−0.0692414	−	0.0224979i
$478$	1.72219	−	2.37039i	0.0787711	−	0.108419i
$479$	2.05158	+	1.49056i	0.0937393	+	0.0681056i	0.633668	−	0.773605i	$-0.281549\pi$
$479$	2.05158	+	1.49056i	0.0937393	+	0.0681056i	−0.539928	+	0.841711i	$0.681549\pi$
$480$	−18.6673	+	12.0157i	−0.852042	+	0.548440i
$481$	2.35091	+	7.23535i	0.107192	+	0.329903i
$482$	4.29748	+	5.91497i	0.195745	+	0.269419i
$483$			22.5259i			1.02496i
$484$		0			0
$485$	−12.9282	+	15.8338i	−0.587039	+	0.718974i
$486$	−3.11990	+	2.26674i	−0.141521	+	0.102821i
$487$	12.1050	−	3.93314i	0.548529	−	0.178228i	−0.0216245	−	0.999766i	$-0.506884\pi$
$487$	12.1050	−	3.93314i	0.548529	−	0.178228i	0.570153	+	0.821538i	$0.306884\pi$
$488$	21.5553	+	7.00374i	0.975762	+	0.317044i
$489$	8.03209	+	5.83565i	0.363223	+	0.263897i
$490$	4.69648	−	1.23810i	0.212165	−	0.0559317i
$491$	12.2719	−	37.7691i	0.553825	−	1.70450i	−0.145203	−	0.989402i	$-0.546383\pi$
$491$	12.2719	−	37.7691i	0.553825	−	1.70450i	0.699027	−	0.715095i	$-0.253617\pi$
$492$	5.51190	−	1.79092i	0.248496	−	0.0807411i
$493$	−15.7341	−	21.6562i	−0.708630	−	0.975346i
$494$	9.21539			0.414620
$495$		0			0
$496$	−21.5167			−0.966127
$497$	16.1199	+	22.1872i	0.723078	+	0.995231i
$498$	−9.41498	+	3.05911i	−0.421895	+	0.137082i
$499$	−5.44108	+	16.7459i	−0.243576	+	0.749650i	0.752291	+	0.658831i	$0.228949\pi$
$499$	−5.44108	+	16.7459i	−0.243576	+	0.749650i	−0.995867	+	0.0908194i	$0.971051\pi$
$500$	17.3596	−	8.58168i	0.776344	−	0.383785i
$501$	0.809017	+	0.587785i	0.0361442	+	0.0262603i
$502$	1.87265	+	0.608460i	0.0835803	+	0.0271569i
$503$	7.02416	−	2.28229i	0.313192	−	0.101762i	−0.148204	−	0.988957i	$-0.547349\pi$
$503$	7.02416	−	2.28229i	0.313192	−	0.101762i	0.461395	+	0.887195i	$0.347349\pi$
$504$	3.82831	−	2.78143i	0.170526	−	0.123895i
$505$	33.5885	+	27.4249i	1.49467	+	1.22039i
$506$		0			0
$507$			9.65926i			0.428983i
$508$	−0.912780	−	1.25633i	−0.0404981	−	0.0557408i
$509$	2.49432	+	7.67673i	0.110559	+	0.340265i	0.990995	−	0.133900i	$-0.0427500\pi$
$509$	2.49432	+	7.67673i	0.110559	+	0.340265i	−0.880436	+	0.474165i	$0.842750\pi$
$510$	4.67609	+	7.26465i	0.207061	+	0.321684i
$511$	−13.2617	−	9.63516i	−0.586661	−	0.426234i
$512$	−13.0395	+	17.9473i	−0.576270	+	0.793167i
$513$	−17.4850	−	5.68121i	−0.771980	−	0.250831i
$514$	−2.36715	−	7.28533i	−0.104410	−	0.321342i
$515$	0.534780	−	9.47175i	0.0235652	−	0.417375i
$516$	−21.5885			−0.950379
$517$		0			0
$518$		−	3.10583i		−	0.136462i
$519$	−34.0212	+	24.7179i	−1.49337	+	1.08499i
$520$	−6.63695	+	17.0832i	−0.291049	+	0.749148i
$521$	−2.85801	+	8.79605i	−0.125212	+	0.385362i	−0.993940	−	0.109928i	$-0.964938\pi$
$521$	−2.85801	+	8.79605i	−0.125212	+	0.385362i	0.868728	+	0.495290i	$0.164938\pi$
$522$	−1.54315	+	2.12396i	−0.0675416	+	0.0929631i
$523$	15.0659	−	20.7365i	0.658788	−	0.906743i	−0.340653	−	0.940189i	$-0.610648\pi$
$523$	15.0659	−	20.7365i	0.658788	−	0.906743i	0.999441	+	0.0334458i	$0.0106481\pi$
$524$	−1.67226	+	5.14668i	−0.0730530	+	0.224834i
$525$	−28.1201	+	15.9335i	−1.22726	+	0.695396i
$526$	2.84504	−	2.06704i	0.124050	−	0.0901273i
$527$			33.7381i			1.46965i
$528$		0			0
$529$	10.8564			0.472018
$530$	−2.51014	−	0.141724i	−0.109033	−	0.00615609i
$531$	−0.286831	−	0.882774i	−0.0124474	−	0.0383091i
$532$	23.1288	+	7.51499i	1.00276	+	0.325816i
$533$	4.31932	−	5.94504i	0.187091	−	0.257508i
$534$	−0.375466	−	0.272792i	−0.0162480	−	0.0118049i
$535$	−3.59100	−	5.57888i	−0.155253	−	0.241196i
$536$	−1.31887	−	4.05906i	−0.0569665	−	0.175325i
$537$	17.5597	+	24.1689i	0.757757	+	1.04296i
$538$		−	8.42091i		−	0.363051i
$539$		0			0
$540$	10.7321	−	13.1440i	0.461834	−	0.565629i
$541$	2.10967	−	1.53276i	0.0907018	−	0.0658987i	−0.541510	−	0.840694i	$-0.682147\pi$
$541$	2.10967	−	1.53276i	0.0907018	−	0.0658987i	0.632212	+	0.774796i	$0.282147\pi$
$542$	5.64381	−	1.83379i	0.242423	−	0.0787678i
$543$	31.9549	+	10.3828i	1.37132	+	0.445567i
$544$	16.0642	+	11.6713i	0.688746	+	0.500403i
$545$	5.24185	+	19.8839i	0.224536	+	0.851732i
$546$	4.38685	−	13.5013i	0.187740	−	0.577804i
$547$	−27.3310	+	8.88039i	−1.16859	+	0.379698i	−0.828116	−	0.560556i	$-0.810587\pi$
$547$	−27.3310	+	8.88039i	−1.16859	+	0.379698i	−0.340474	+	0.940254i	$0.610587\pi$
$548$	−9.02443	−	12.4211i	−0.385505	−	0.530601i
$549$	8.58846			0.366546
$550$		0			0
$551$	−29.0718			−1.23850
$552$	7.64434	+	10.5215i	0.325365	+	0.447826i
$553$	4.65921	−	1.51387i	0.198130	−	0.0643762i
$554$	4.98864	−	15.3535i	0.211947	−	0.652306i
$555$	1.97455	+	7.49007i	0.0838152	+	0.317936i
$556$	−20.4422	−	14.8521i	−0.866942	−	0.629871i
$557$	35.7614	+	11.6196i	1.51526	+	0.492337i	0.944425	−	0.328728i	$-0.106620\pi$
$557$	35.7614	+	11.6196i	1.51526	+	0.492337i	0.570834	+	0.821065i	$0.306620\pi$
$558$	3.14695	−	1.02251i	0.133221	−	0.0432862i
$559$	−22.1453	+	16.0895i	−0.936645	+	0.680513i
$560$	−11.6603	+	14.2808i	−0.492736	+	0.603475i
$561$		0			0
$562$			8.96575i			0.378198i
$563$	−9.38837	−	12.9220i	−0.395673	−	0.544597i	0.563979	−	0.825789i	$-0.309270\pi$
$563$	−9.38837	−	12.9220i	−0.395673	−	0.544597i	−0.959651	+	0.281193i	$0.909270\pi$
$564$	−11.8417	−	36.4450i	−0.498625	−	1.53461i
$565$	3.42314	+	5.31809i	0.144013	+	0.223734i
$566$	3.37919	+	2.45513i	0.142038	+	0.103197i
$567$	−20.9662	+	28.8576i	−0.880499	+	1.21190i
$568$	15.0588	+	4.89290i	0.631853	+	0.205301i
$569$	−9.30894	−	28.6500i	−0.390251	−	1.20107i	−0.932599	−	0.360915i	$-0.882464\pi$
$569$	−9.30894	−	28.6500i	−0.390251	−	1.20107i	0.542348	−	0.840154i	$-0.317536\pi$
$570$	9.36796	+	0.528920i	0.392381	+	0.0221540i
$571$	−19.7128			−0.824956			−0.412478	−	0.910968i	$-0.635337\pi$
$571$	−19.7128			−0.824956			−0.412478	+	0.910968i	$0.635337\pi$
$572$		0			0
$573$			14.0406i			0.586554i
$574$	−2.42705	+	1.76336i	−0.101303	+	0.0736010i
$575$	−8.58968	−	15.1594i	−0.358215	−	0.632190i
$576$	−0.513047	+	1.57900i	−0.0213769	+	0.0657915i
$577$	2.21135	−	3.04366i	0.0920596	−	0.126709i	−0.760503	−	0.649335i	$-0.775047\pi$
$577$	2.21135	−	3.04366i	0.0920596	−	0.126709i	0.852562	+	0.522626i	$0.175047\pi$
$578$	−0.630365	+	0.867623i	−0.0262197	+	0.0360884i
$579$	9.06054	−	27.8855i	0.376543	−	1.15888i
$580$	9.71717	−	25.0115i	0.403483	−	1.03855i
$581$	−26.7982	+	19.4700i	−1.11178	+	0.807752i
$582$		−	9.14162i		−	0.378932i
$583$		0			0
$584$	−9.46410			−0.391627
$585$	−0.391486	+	6.93380i	−0.0161860	+	0.286677i
$586$	2.41152	+	7.42190i	0.0996190	+	0.306596i
$587$	19.3930	+	6.30115i	0.800433	+	0.260076i	0.680540	−	0.732711i	$-0.261745\pi$
$587$	19.3930	+	6.30115i	0.800433	+	0.260076i	0.119892	+	0.992787i	$0.461745\pi$
$588$	8.25286	−	11.3591i	0.340342	−	0.468441i
$589$	29.6432	+	21.5370i	1.22143	+	0.887419i
$590$	−0.794342	−	1.23407i	−0.0327025	−	0.0508058i
$591$	−10.2966	−	31.6897i	−0.423546	−	1.30354i
$592$	2.59713	+	3.57465i	0.106741	+	0.146917i
$593$			0.859411i			0.0352918i	0.999844	+	0.0176459i	$0.00561715\pi$
$593$			0.859411i			0.0352918i	−0.999844	+	0.0176459i	$0.994383\pi$
$594$		0			0
$595$	22.3923	+	18.2832i	0.917995	+	0.749540i
$596$	−14.3881	+	10.4535i	−0.589358	+	0.428193i
$597$	3.67460	−	1.19395i	0.150391	−	0.0488651i
$598$	7.27851	+	2.36493i	0.297640	+	0.0967092i
$599$	−31.1025	−	22.5973i	−1.27082	−	0.923302i	−0.271581	−	0.962416i	$-0.587546\pi$
$599$	−31.1025	−	22.5973i	−1.27082	−	0.923302i	−0.999235	+	0.0391140i	$0.987546\pi$
$600$	−7.72733	+	16.9851i	−0.315467	+	0.693414i
$601$	6.18034	−	19.0211i	0.252101	−	0.775888i	−0.742286	−	0.670084i	$-0.766258\pi$
$601$	6.18034	−	19.0211i	0.252101	−	0.775888i	0.994387	−	0.105804i	$-0.0337418\pi$
$602$	10.6281	−	3.45327i	0.433168	−	0.140745i
$603$	−0.950617	−	1.30841i	−0.0387121	−	0.0532826i
$604$	7.26795			0.295729
$605$		0			0
$606$	−19.3923			−0.787759
$607$	21.3899	+	29.4406i	0.868188	+	1.19496i	0.979555	+	0.201179i	$0.0644772\pi$
$607$	21.3899	+	29.4406i	0.868188	+	1.19496i	−0.111367	+	0.993779i	$0.535523\pi$
$608$	20.5095	−	6.66393i	0.831769	−	0.270258i
$609$	−13.8392	+	42.5927i	−0.560793	+	1.72594i
$610$	13.1309	−	3.46161i	0.531656	−	0.140157i
$611$	−39.3089	−	28.5596i	−1.59027	−	1.15540i
$612$	4.65921	+	1.51387i	0.188337	+	0.0611945i
$613$	−1.70539	+	0.554114i	−0.0688800	+	0.0223805i	−0.343254	−	0.939243i	$-0.611529\pi$
$613$	−1.70539	+	0.554114i	−0.0688800	+	0.0223805i	0.274374	+	0.961623i	$0.411529\pi$
$614$	−3.27859	+	2.38203i	−0.132313	+	0.0961311i
$615$	4.73205	−	5.79555i	0.190815	−	0.233699i
$616$		0			0
$617$		−	13.0053i		−	0.523575i	−0.965126	−	0.261787i	$-0.915688\pi$
$617$		−	13.0053i		−	0.523575i	0.965126	−	0.261787i	$-0.0843119\pi$
$618$	2.49376	+	3.43237i	0.100314	+	0.138070i
$619$	−3.95066	−	12.1589i	−0.158790	−	0.488707i	0.839735	−	0.542997i	$-0.182710\pi$
$619$	−3.95066	−	12.1589i	−0.158790	−	0.488707i	−0.998525	+	0.0542900i	$0.982710\pi$
$620$	−28.4373	+	18.3044i	−1.14207	+	0.735124i
$621$	−12.3520	−	8.97428i	−0.495670	−	0.360125i
$622$	−3.05859	+	4.20979i	−0.122638	+	0.168797i
$623$	−1.47691	−	0.479877i	−0.0591711	−	0.0192259i
$624$	6.24095	+	19.2077i	0.249838	+	0.768923i
$625$	12.8483	−	21.4458i	0.513932	−	0.857831i
$626$	−8.87564			−0.354742
$627$		0			0
$628$			37.8792i			1.51154i
$629$	5.60503	−	4.07230i	0.223487	−	0.162373i
$630$	1.02674	−	2.64278i	0.0409063	−	0.105291i
$631$	−4.73430	+	14.5707i	−0.188469	+	0.580049i	−0.999991	−	0.00427343i	$-0.998640\pi$
$631$	−4.73430	+	14.5707i	−0.188469	+	0.580049i	0.811521	+	0.584323i	$0.198640\pi$
$632$	1.66251	−	2.28825i	0.0661310	−	0.0910215i
$633$	14.9029	−	20.5121i	0.592337	−	0.815281i
$634$	2.01970	−	6.21601i	0.0802127	−	0.246869i
$635$	−1.86873	−	0.726014i	−0.0741582	−	0.0288110i
$636$	−5.87989	+	4.27199i	−0.233153	+	0.169396i
$637$		−	17.8028i		−	0.705371i
$638$		0			0
$639$	6.00000			0.237356
$640$	−1.44356	+	25.5676i	−0.0570619	+	1.01065i
$641$	−2.42776	−	7.47189i	−0.0958909	−	0.295122i	0.891594	−	0.452836i	$-0.149588\pi$
$641$	−2.42776	−	7.47189i	−0.0958909	−	0.295122i	−0.987485	+	0.157714i	$0.949588\pi$
$642$	2.82191	+	0.916893i	0.111372	+	0.0361869i
$643$	−6.18272	+	8.50978i	−0.243823	+	0.335593i	−0.913336	−	0.407207i	$-0.866503\pi$
$643$	−6.18272	+	8.50978i	−0.243823	+	0.335593i	0.669513	+	0.742800i	$0.266503\pi$
$644$	16.3390	+	11.8710i	0.643848	+	0.467783i
$645$	−23.4354	+	15.0848i	−0.922767	+	0.593965i
$646$	−2.59336	−	7.98156i	−0.102035	−	0.314030i
$647$	−21.9606	−	30.2261i	−0.863358	−	1.18831i	−0.980758	−	0.195226i	$-0.937456\pi$
$647$	−21.9606	−	30.2261i	−0.863358	−	1.18831i	0.117400	−	0.993085i	$-0.462544\pi$
$648$			20.5940i			0.809010i
$649$		0			0
$650$	2.19615	+	10.7589i	0.0861402	+	0.421999i
$651$	45.6649	−	33.1775i	1.78975	−	1.30033i
$652$	8.46572	−	2.75068i	0.331543	−	0.107725i
$653$	11.5514	+	3.75329i	0.452043	+	0.146878i	0.526185	−	0.850370i	$-0.323622\pi$
$653$	11.5514	+	3.75329i	0.452043	+	0.146878i	−0.0741421	+	0.997248i	$0.523622\pi$
$654$	−7.43984	−	5.40536i	−0.290921	−	0.211366i
$655$	1.78090	+	6.75547i	0.0695854	+	0.263958i
$656$	1.31887	−	4.05906i	0.0514932	−	0.158480i
$657$	−3.41078	+	1.10823i	−0.133067	+	0.0432361i
$658$	11.6594	+	16.0478i	0.454531	+	0.625608i
$659$	23.3205			0.908438			0.454219	−	0.890890i	$-0.349918\pi$
$659$	23.3205			0.908438			0.454219	+	0.890890i	$0.349918\pi$
$660$		0			0
$661$	29.5885			1.15086			0.575429	−	0.817852i	$-0.304835\pi$
$661$	29.5885			1.15086			0.575429	+	0.817852i	$0.304835\pi$
$662$	−5.53636	−	7.62015i	−0.215177	−	0.296165i
$663$	30.1176	−	9.78580i	1.16967	−	0.380049i
$664$	−5.90975	+	18.1883i	−0.229343	+	0.705845i
$665$	30.3585	−	8.00321i	1.17725	−	0.310351i
$666$	−0.549721	−	0.399395i	−0.0213012	−	0.0154763i
$667$	−22.9615	−	7.46065i	−0.889073	−	0.288877i
$668$	0.852694	−	0.277057i	0.0329917	−	0.0107197i
$669$	−2.42705	+	1.76336i	−0.0938352	+	0.0681753i
$670$	−1.98076	−	1.61729i	−0.0765235	−	0.0624812i
$671$		0			0
$672$		−	33.2204i		−	1.28151i
$673$	23.9870	+	33.0153i	0.924631	+	1.27265i	0.961917	+	0.273341i	$0.0881286\pi$
$673$	23.9870	+	33.0153i	0.924631	+	1.27265i	−0.0372864	+	0.999305i	$0.511871\pi$
$674$	2.81958	+	8.67778i	0.108606	+	0.334256i
$675$	2.46587	−	21.7675i	0.0949113	−	0.837831i
$676$	7.00629	+	5.09037i	0.269473	+	0.195783i
$677$	−11.9637	+	16.4666i	−0.459801	+	0.632861i	−0.974467	−	0.224529i	$-0.927916\pi$
$677$	−11.9637	+	16.4666i	−0.459801	+	0.632861i	0.514667	+	0.857390i	$0.327916\pi$
$678$	−2.68999	−	0.874032i	−0.103309	−	0.0335670i
$679$	−9.45235	−	29.0914i	−0.362748	−	1.11642i
$680$	16.6637	+	0.940842i	0.639024	+	0.0360796i
$681$	−38.8564			−1.48898
$682$		0			0
$683$			29.8372i			1.14169i	0.821058	+	0.570844i	$0.193384\pi$
$683$			29.8372i			1.14169i	−0.821058	+	0.570844i	$0.806616\pi$
$684$	4.30438	−	3.12732i	0.164582	−	0.119576i
$685$	−18.4756	−	7.17792i	−0.705918	−	0.274254i
$686$	1.50071	−	4.61872i	0.0572975	−	0.176343i
$687$	−4.62358	+	6.36381i	−0.176401	+	0.242795i
$688$	−9.34468	+	12.8619i	−0.356263	+	0.490353i
$689$	−2.84771	+	8.76436i	−0.108489	+	0.333895i
$690$	7.26328	+	2.82184i	0.276508	+	0.107426i
$691$	−30.6690	+	22.2823i	−1.16670	+	0.847660i	−0.990611	−	0.136714i	$-0.956346\pi$
$691$	−30.6690	+	22.2823i	−1.16670	+	0.847660i	−0.176093	+	0.984374i	$0.556346\pi$
$692$			37.7033i			1.43326i
$693$		0			0
$694$	2.26795			0.0860902
$695$	−32.5689	−	1.83886i	−1.23541	−	0.0697519i
$696$	7.99007	+	24.5909i	0.302863	+	0.932116i
$697$	−6.36459	−	2.06798i	−0.241076	−	0.0783304i
$698$	−2.22734	+	3.06567i	−0.0843060	+	0.116037i
$699$	−2.64383	−	1.92085i	−0.0999987	−	0.0726533i
$700$	−3.26180	+	28.7936i	−0.123285	+	1.08830i
$701$	11.6983	+	36.0036i	0.441838	+	1.35984i	0.885915	+	0.463848i	$0.153532\pi$
$701$	11.6983	+	36.0036i	0.441838	+	1.35984i	−0.444077	+	0.895989i	$0.646468\pi$
$702$	5.65572	+	7.78444i	0.213462	+	0.293805i
$703$		−	7.52433i		−	0.283786i
$704$		0			0
$705$	−38.3205	−	31.2886i	−1.44323	−	1.17840i
$706$	5.44634	−	3.95700i	0.204976	−	0.148924i
$707$	−61.7121	+	20.0515i	−2.32092	+	0.754113i
$708$	−4.03499	−	1.31105i	−0.151644	−	0.0492722i
$709$	2.10967	+	1.53276i	0.0792303	+	0.0575642i	0.626695	−	0.779264i	$-0.284407\pi$
$709$	2.10967	+	1.53276i	0.0792303	+	0.0575642i	−0.547465	+	0.836829i	$0.684407\pi$
$710$	9.17342	−	2.41832i	0.344272	−	0.0907581i
$711$	0.331203	−	1.01934i	0.0124211	−	0.0382282i
$712$	−0.852694	+	0.277057i	−0.0319561	+	0.0103832i
$713$	17.8858	+	24.6177i	0.669829	+	0.921940i
$714$	−12.9282			−0.483826
$715$		0			0
$716$	26.7846			1.00099
$717$	−6.42730	−	8.84642i	−0.240032	−	0.330375i
$718$	−17.5557	+	5.70418i	−0.655171	+	0.212878i
$719$	15.5115	−	47.7394i	0.578480	−	1.78038i	−0.0455311	−	0.998963i	$-0.514498\pi$
$719$	15.5115	−	47.7394i	0.578480	−	1.78038i	0.624011	−	0.781415i	$-0.285502\pi$
$720$	1.02820	+	3.90027i	0.0383188	+	0.145355i
$721$	11.4849	+	8.34429i	0.427721	+	0.310758i
$722$	0.685436	+	0.222712i	0.0255093	+	0.00828847i
$723$	25.9507	−	8.43189i	0.965116	−	0.313585i
$724$	24.3711	−	17.7067i	0.905745	−	0.658063i
$725$	−6.92820	−	33.9411i	−0.257307	−	1.26054i
$726$		0			0
$727$			8.24504i			0.305792i	0.988242	+	0.152896i	$0.0488599\pi$
$727$			8.24504i			0.305792i	−0.988242	+	0.152896i	$0.951140\pi$
$728$	−16.1199	−	22.1872i	−0.597444	−	0.822312i
$729$	−5.43513	−	16.7276i	−0.201301	−	0.619541i
$730$	−4.76807	+	3.06910i	−0.176474	+	0.113593i
$731$	20.1673	+	14.6524i	0.745916	+	0.541940i
$732$	23.0742	−	31.7589i	0.852848	−	1.17384i
$733$	−8.86146	−	2.87926i	−0.327305	−	0.106348i	0.140755	−	0.990044i	$-0.455047\pi$
$733$	−8.86146	−	2.87926i	−0.327305	−	0.106348i	−0.468060	+	0.883697i	$0.655047\pi$
$734$	2.70430	+	8.32297i	0.0998174	+	0.307206i
$735$	1.02180	−	18.0975i	0.0376895	−	0.667537i
$736$	17.9090			0.660133
$737$		0			0
$738$			0.656339i			0.0241602i
$739$	−31.4936	+	22.8814i	−1.15851	+	0.841707i	−0.989589	−	0.143923i	$-0.954028\pi$
$739$	−31.4936	+	22.8814i	−1.15851	+	0.841707i	−0.168921	+	0.985630i	$0.554028\pi$
$740$	6.47346	+	2.51499i	0.237969	+	0.0924528i
$741$	10.6278	−	32.7090i	0.390422	−	1.20160i
$742$	2.21135	−	3.04366i	0.0811811	−	0.111736i
$743$	25.5083	−	35.1092i	0.935809	−	1.28803i	−0.0217414	−	0.999764i	$-0.506921\pi$
$743$	25.5083	−	35.1092i	0.935809	−	1.28803i	0.957550	−	0.288267i	$-0.0930789\pi$
$744$	10.0704	−	30.9935i	0.369198	−	1.13628i
$745$	−8.31461	+	21.4014i	−0.304624	+	0.784088i
$746$	−0.0736486	+	0.0535088i	−0.00269647	+	0.00195910i
$747$			7.24693i			0.265151i
$748$		0			0
$749$	9.92820			0.362769
$750$	1.61500	+	11.0631i	0.0589715	+	0.403967i
$751$	15.0309	+	46.2604i	0.548485	+	1.68806i	0.712556	+	0.701616i	$0.247538\pi$
$751$	15.0309	+	46.2604i	0.548485	+	1.68806i	−0.164070	+	0.986449i	$0.552462\pi$
$752$	−26.8387	−	8.72043i	−0.978707	−	0.318001i
$753$	4.31932	−	5.94504i	0.157405	−	0.216649i
$754$	12.3095	+	8.94338i	0.448286	+	0.325699i
$755$	7.88973	−	5.07844i	0.287137	−	0.184824i
$756$	7.84665	+	24.1495i	0.285380	+	0.878309i
$757$	−29.2569	−	40.2687i	−1.06336	−	1.46359i	−0.876621	−	0.481182i	$-0.840207\pi$
$757$	−29.2569	−	40.2687i	−1.06336	−	1.46359i	−0.186741	−	0.982409i	$-0.559793\pi$
$758$			0.757875i			0.0275273i
$759$		0			0
$760$	11.4641	−	14.0406i	0.415847	−	0.509306i
$761$	16.0642	−	11.6713i	0.582326	−	0.423084i	−0.257236	−	0.966349i	$-0.582812\pi$
$761$	16.0642	−	11.6713i	0.582326	−	0.423084i	0.839562	+	0.543264i	$0.182812\pi$
$762$	0.852694	−	0.277057i	0.0308898	−	0.0100367i
$763$	−29.2649	−	9.50874i	−1.05946	−	0.344239i
$764$	10.1843	+	7.39931i	0.368454	+	0.267698i
$765$	6.11562	−	1.61222i	0.221111	−	0.0582898i
$766$	−6.15221	+	18.9346i	−0.222288	+	0.684133i
$767$	−5.11616	+	1.66234i	−0.184734	+	0.0600237i
$768$	−1.58098	−	2.17603i	−0.0570488	−	0.0785209i
$769$	9.85641			0.355431			0.177716	−	0.984082i	$-0.443129\pi$
$769$	9.85641			0.355431			0.177716	+	0.984082i	$0.443129\pi$
$770$		0			0
$771$	−28.5885			−1.02959
$772$	−15.4517	−	21.2675i	−0.556120	−	0.765433i
$773$	11.4549	−	3.72192i	0.412004	−	0.133868i	−0.0956791	−	0.995412i	$-0.530502\pi$
$773$	11.4549	−	3.72192i	0.412004	−	0.133868i	0.507683	+	0.861544i	$0.330502\pi$
$774$	0.755504	−	2.32520i	0.0271560	−	0.0835777i
$775$	−18.0800	+	39.7408i	−0.649452	+	1.42753i
$776$	−14.2874	−	10.3804i	−0.512889	−	0.372636i
$777$	−11.0238	−	3.58185i	−0.395477	−	0.128498i
$778$	−3.01504	+	0.979646i	−0.108094	+	0.0351220i
$779$	−5.87989	+	4.27199i	−0.210669	+	0.153060i
$780$	24.5885	+	20.0764i	0.880408	+	0.718850i
$781$		0			0
$782$		−	6.96953i		−	0.249230i
$783$	−17.8421	−	24.5576i	−0.637625	−	0.877616i
$784$	−3.19516	−	9.83368i	−0.114113	−	0.351203i
$785$	26.4679	+	41.1198i	0.944679	+	1.46763i
$786$	−2.52766	−	1.83645i	−0.0901585	−	0.0655040i
$787$	10.2196	−	14.0661i	0.364290	−	0.501403i	−0.587048	−	0.809552i	$-0.699710\pi$
$787$	10.2196	−	14.0661i	0.364290	−	0.501403i	0.951338	+	0.308150i	$0.0997098\pi$
$788$	−28.4122	−	9.23168i	−1.01214	−	0.328865i
$789$	−4.05565	−	12.4820i	−0.144385	−	0.444371i
$790$	0.0955293	−	1.69196i	0.00339878	−	0.0601974i
$791$	−9.46410			−0.336505
$792$		0			0
$793$		−	49.7749i		−	1.76756i
$794$	13.8114	−	10.0346i	0.490147	−	0.356113i
$795$	−3.39789	+	8.74602i	−0.120511	+	0.310189i
$796$	1.07047	−	3.29456i	0.0379417	−	0.116772i
$797$	−21.2705	+	29.2763i	−0.753440	+	1.03702i	0.244292	+	0.969702i	$0.421445\pi$
$797$	−21.2705	+	29.2763i	−0.753440	+	1.03702i	−0.997731	+	0.0673193i	$0.978555\pi$
$798$	−8.25286	+	11.3591i	−0.292148	+	0.402107i
$799$	−13.6736	+	42.0830i	−0.483737	+	1.48879i
$800$	12.6678	+	22.3566i	0.447874	+	0.790424i
$801$	−0.274860	+	0.199698i	−0.00971171	+	0.00705597i
$802$		−	1.20118i		−	0.0424153i
$803$		0			0
$804$	−7.39230			−0.260706
$805$	26.0317	+	1.46976i	0.917496	+	0.0518023i
$806$	−5.92599	−	18.2383i	−0.208734	−	0.642418i
$807$	−29.8891	−	9.71156i	−1.05215	−	0.341863i
$808$	−22.0202	+	30.3082i	−0.774669	+	1.06624i
$809$	−11.7598	−	8.54399i	−0.413452	−	0.300391i	0.361546	−	0.932354i	$-0.382249\pi$
$809$	−11.7598	−	8.54399i	−0.413452	−	0.300391i	−0.774998	+	0.631964i	$0.782249\pi$
$810$	6.67841	+	10.3754i	0.234655	+	0.364554i
$811$	5.86538	+	18.0518i	0.205961	+	0.633884i	0.999673	+	0.0255890i	$0.00814611\pi$
$811$	5.86538	+	18.0518i	0.205961	+	0.633884i	−0.793711	+	0.608295i	$0.791854\pi$
$812$	23.6012	+	32.4843i	0.828240	+	1.13997i
$813$		−	22.1469i		−	0.776727i
$814$		0			0
$815$	7.26795	−	8.90138i	0.254585	−	0.311802i
$816$	14.8797	−	10.8107i	0.520893	−	0.378451i
$817$	25.7481	−	8.36606i	0.900811	−	0.292691i
$818$	−12.8611	−	4.17882i	−0.449678	−	0.146109i
$819$	−8.40755	−	6.10844i	−0.293784	−	0.213446i
$820$	−1.71001	−	6.48659i	−0.0597163	−	0.226522i
$821$	9.02211	−	27.7672i	0.314874	−	0.969082i	−0.660933	−	0.750445i	$-0.729839\pi$
$821$	9.02211	−	27.7672i	0.314874	−	0.969082i	0.975806	−	0.218636i	$-0.0701609\pi$
$822$	8.43037	−	2.73919i	0.294043	−	0.0955404i
$823$	3.97137	+	5.46612i	0.138433	+	0.190537i	0.872605	−	0.488427i	$-0.162429\pi$
$823$	3.97137	+	5.46612i	0.138433	+	0.190537i	−0.734171	+	0.678964i	$0.762429\pi$
$824$	8.19615			0.285526
$825$		0			0
$826$	2.19615			0.0764139
$827$	−20.0316	−	27.5712i	−0.696568	−	0.958743i	−0.999983	−	0.00588462i	$-0.998127\pi$
$827$	−20.0316	−	27.5712i	−0.696568	−	0.958743i	0.303415	−	0.952858i	$-0.401873\pi$
$828$	4.20225	−	1.36539i	0.146038	−	0.0474507i
$829$	3.08423	−	9.49227i	0.107120	−	0.329680i	−0.883103	−	0.469180i	$-0.844550\pi$
$829$	3.08423	−	9.49227i	0.107120	−	0.329680i	0.990222	+	0.139500i	$0.0445495\pi$
$830$	2.92091	+	11.0799i	0.101386	+	0.384588i
$831$	−48.7422	−	35.4133i	−1.69085	−	1.22847i
$832$	9.15115	+	2.97339i	0.317259	+	0.103084i
$833$	−15.4192	+	5.01000i	−0.534243	+	0.173586i
$834$	11.8023	−	8.57488i	0.408681	−	0.296924i
$835$	0.732051	−	0.896575i	0.0253337	−	0.0310273i
$836$		0			0
$837$			38.2581i			1.32239i
$838$	3.75449	+	5.16761i	0.129697	+	0.178512i
$839$	11.9851	+	36.8864i	0.413772	+	1.27346i	0.913345	+	0.407187i	$0.133490\pi$
$839$	11.9851	+	36.8864i	0.413772	+	1.27346i	−0.499573	+	0.866272i	$0.666510\pi$
$840$	−15.1134	−	23.4797i	−0.521461	−	0.810127i
$841$	−15.3713	−	11.1679i	−0.530046	−	0.385101i
$842$	5.18841	−	7.14124i	0.178804	−	0.246103i
$843$	31.8230	+	10.3399i	1.09604	+	0.356125i
$844$	−7.02459	−	21.6195i	−0.241796	−	0.744173i
$845$	11.1626	+	0.630244i	0.384004	+	0.0216811i
$846$	4.33975			0.149204
$847$		0			0
$848$			5.35225i			0.183797i
$849$	12.6113	−	9.16267i	0.432820	−	0.314462i
$850$	8.70038	−	4.92985i	0.298421	−	0.169092i
$851$	1.93096	−	5.94288i	0.0661924	−	0.203719i
$852$	16.1199	−	22.1872i	0.552260	−	0.760120i
$853$	−27.2523	+	37.5096i	−0.933102	+	1.28430i	0.0255350	+	0.999674i	$0.491871\pi$
$853$	−27.2523	+	37.5096i	−0.933102	+	1.28430i	−0.958637	+	0.284631i	$0.908129\pi$
$854$	−6.27938	+	19.3260i	−0.214876	+	0.661320i
$855$	2.48743	−	6.40253i	0.0850683	−	0.218962i
$856$	4.63733	−	3.36921i	0.158501	−	0.115157i
$857$		−	29.3195i		−	1.00154i	−0.865581	−	0.500768i	$-0.833051\pi$
$857$		−	29.3195i		−	1.00154i	0.865581	−	0.500768i	$-0.166949\pi$
$858$		0			0
$859$	22.1962			0.757323			0.378661	−	0.925535i	$-0.376384\pi$
$859$	22.1962			0.757323			0.378661	+	0.925535i	$0.376384\pi$
$860$	−1.40860	+	24.9483i	−0.0480328	+	0.850731i
$861$	3.45980	+	10.6482i	0.117910	+	0.362889i
$862$	2.49686	+	0.811279i	0.0850434	+	0.0276323i
$863$	10.0566	−	13.8417i	0.342330	−	0.471176i	−0.602790	−	0.797900i	$-0.705944\pi$
$863$	10.0566	−	13.8417i	0.342330	−	0.471176i	0.945120	+	0.326723i	$0.105944\pi$
$864$	18.2164	+	13.2350i	0.619733	+	0.450263i
$865$	26.3450	+	40.9289i	0.895757	+	1.39162i
$866$	−4.59683	−	14.1476i	−0.156207	−	0.480754i
$867$	2.35255	+	3.23801i	0.0798969	+	0.109969i
$868$		−	50.6071i		−	1.71772i
$869$		0			0
$870$	12.0000	+	9.79796i	0.406838	+	0.332182i
$871$	−7.58297	+	5.50935i	−0.256939	+	0.186677i
$872$	−16.8961	+	5.48987i	−0.572174	+	0.185911i
$873$	−6.36459	−	2.06798i	−0.215409	−	0.0699906i
$874$	−6.12363	−	4.44908i	−0.207135	−	0.150492i
$875$	16.5785	+	33.5361i	0.560457	+	1.13373i
$876$	−5.06550	+	15.5900i	−0.171147	+	0.526738i
$877$	11.3135	−	3.67598i	0.382030	−	0.124129i	−0.111705	−	0.993741i	$-0.535631\pi$
$877$	11.3135	−	3.67598i	0.382030	−	0.124129i	0.493735	+	0.869612i	$0.335631\pi$
$878$	−8.59495	−	11.8299i	−0.290066	−	0.399241i
$879$	29.1244			0.982340
$880$		0			0
$881$	−26.9090			−0.906586			−0.453293	−	0.891362i	$-0.649751\pi$
$881$	−26.9090			−0.906586			−0.453293	+	0.891362i	$0.649751\pi$
$882$	0.934625	+	1.28640i	0.0314705	+	0.0433154i
$883$	20.5095	−	6.66393i	0.690199	−	0.224259i	0.0571437	−	0.998366i	$-0.481801\pi$
$883$	20.5095	−	6.66393i	0.690199	−	0.224259i	0.633055	+	0.774107i	$0.281801\pi$
$884$	8.77370	−	27.0027i	0.295092	−	0.908199i
$885$	−5.29628	+	1.39622i	−0.178032	+	0.0469334i
$886$	−11.5430	−	8.38649i	−0.387795	−	0.281750i
$887$	−14.9269	−	4.85004i	−0.501196	−	0.162848i	0.0474989	−	0.998871i	$-0.484875\pi$
$887$	−14.9269	−	4.85004i	−0.501196	−	0.162848i	−0.548694	+	0.836023i	$0.684875\pi$
$888$	−6.36459	+	2.06798i	−0.213582	+	0.0693969i
$889$	2.42705	−	1.76336i	0.0814007	−	0.0591411i
$890$	−0.339746	+	0.416102i	−0.0113883	+	0.0139478i
$891$		0			0
$892$			2.68973i			0.0900587i
$893$	28.2466	+	38.8782i	0.945238	+	1.30101i
$894$	−3.17297	−	9.76540i	−0.106120	−	0.326604i
$895$	29.0761	−	18.7156i	0.971906	−	0.625594i
$896$	−31.0019	−	22.5242i	−1.03570	−	0.752482i
$897$	16.7881	−	23.1069i	0.560539	−	0.771516i
$898$	16.9927	+	5.52125i	0.567052	+	0.184246i
$899$	18.6947	+	57.5365i	0.623504	+	1.91895i
$900$	4.67691	+	4.28005i	0.155897	+	0.142668i
$901$	8.39230			0.279588
$902$		0			0
$903$		−	41.7057i		−	1.38788i
$904$	−4.42055	+	3.21172i	−0.147025	+	0.106820i
$905$	14.0837	−	36.2507i	0.468157	−	1.20501i
$906$	−1.29668	+	3.99078i	−0.0430794	+	0.132585i
$907$	17.7009	−	24.3632i	0.587749	−	0.808967i	−0.406769	−	0.913531i	$-0.633345\pi$
$907$	17.7009	−	24.3632i	0.587749	−	0.808967i	0.994518	+	0.104564i	$0.0333446\pi$
$908$	−20.4771	+	28.1843i	−0.679556	+	0.935329i
$909$	−4.38685	+	13.5013i	−0.145503	+	0.447811i
$910$	−15.3164	−	5.95053i	−0.507733	−	0.197258i
$911$	24.4717	−	17.7797i	0.810784	−	0.589069i	−0.103274	−	0.994653i	$-0.532932\pi$
$911$	24.4717	−	17.7797i	0.810784	−	0.589069i	0.914058	+	0.405584i	$0.132932\pi$
$912$		−	19.9749i		−	0.661434i
$913$		0			0
$914$	10.9808			0.363211
$915$	2.85685	−	50.5990i	0.0944444	−	1.67275i
$916$	2.17936	+	6.70738i	0.0720081	+	0.221618i
$917$	−9.94263	−	3.23056i	−0.328335	−	0.106682i
$918$	5.15058	−	7.08916i	0.169994	−	0.233977i
$919$	−15.3558	−	11.1566i	−0.506540	−	0.368023i	0.304970	−	0.952362i	$-0.401354\pi$
$919$	−15.3558	−	11.1566i	−0.506540	−	0.368023i	−0.811509	+	0.584339i	$0.801354\pi$
$920$	12.6578	−	8.14755i	0.417315	−	0.268617i
$921$	4.67368	+	14.3841i	0.154003	+	0.473973i
$922$	−10.0406	−	13.8197i	−0.330669	−	0.455127i
$923$		−	34.7733i		−	1.14458i
$924$		0			0
$925$	8.78461	−	1.79315i	0.288836	−	0.0589584i
$926$	8.50816	−	6.18154i	0.279595	−	0.203138i
$927$	2.95382	−	0.959754i	0.0970161	−	0.0315225i
$928$	33.8629	+	11.0027i	1.11160	+	0.361182i
$929$	−35.4806	−	25.7781i	−1.16408	−	0.845754i	−0.173792	−	0.984782i	$-0.555602\pi$
$929$	−35.4806	−	25.7781i	−1.16408	−	0.845754i	−0.990288	+	0.139029i	$0.955602\pi$
$930$	−4.97731	−	18.8804i	−0.163212	−	0.619113i
$931$	−5.44108	+	16.7459i	−0.178324	+	0.548825i
$932$	−2.78656	+	0.905408i	−0.0912768	+	0.0296576i
$933$	11.4148	+	15.7112i	0.373704	+	0.514360i
$934$	0.320508			0.0104873
$935$		0			0
$936$	−6.00000			−0.196116
$937$	−18.3313	−	25.2308i	−0.598857	−	0.824255i	0.396746	−	0.917928i	$-0.370139\pi$
$937$	−18.3313	−	25.2308i	−0.598857	−	0.824255i	−0.995603	+	0.0936728i	$0.970139\pi$
$938$	3.63925	−	1.18247i	0.118826	−	0.0386089i
$939$	−10.2360	+	31.5031i	−0.334039	+	1.02807i
$940$	−42.8897	+	11.3067i	−1.39891	+	0.368784i
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	0.883843	−	0.467784i	$-0.154947\pi$
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	−0.171766	+	0.985138i	$0.554947\pi$
$942$	−20.7992	−	6.75806i	−0.677674	−	0.220190i
$943$	−5.74038	+	1.86516i	−0.186932	+	0.0607380i
$944$	−2.52766	+	1.83645i	−0.0822682	+	0.0597714i
$945$	25.3923	+	20.7327i	0.826012	+	0.674436i
$946$		0			0
$947$			19.9749i			0.649096i	0.945869	+	0.324548i	$0.105212\pi$
$947$			19.9749i			0.649096i	−0.945869	+	0.324548i	$0.894788\pi$
$948$	−2.87955	−	3.96336i	−0.0935234	−	0.128724i
$949$	6.42280	+	19.7673i	0.208493	+	0.641675i
$950$	1.22248	−	10.7914i	0.0396624	−	0.350120i
$951$	−19.7338	−	14.3374i	−0.639912	−	0.464923i
$952$	−14.6802	+	20.2055i	−0.475787	+	0.654864i
$953$	15.8761	+	5.15847i	0.514279	+	0.167099i	0.554647	−	0.832086i	$-0.312853\pi$
$953$	15.8761	+	5.15847i	0.514279	+	0.167099i	−0.0403686	+	0.999185i	$0.512853\pi$
$954$	−0.254347	−	0.782801i	−0.00823480	−	0.0253441i
$955$	16.2258	+	0.916117i	0.525054	+	0.0296448i
$956$	−9.80385			−0.317079
$957$		0			0
$958$			1.31268i			0.0424107i
$959$	23.9956	−	17.4339i	0.774860	−	0.562969i
$960$	9.13200	+	3.54785i	0.294734	+	0.114506i
$961$	13.9826	−	43.0341i	0.451052	−	1.38820i
$962$	−2.31472	+	3.18594i	−0.0746295	+	0.102719i
$963$	1.27672	−	1.75726i	0.0411418	−	0.0566268i
$964$	7.55982	−	23.2667i	0.243486	−	0.749371i
$965$	−31.6342	−	12.2901i	−1.01834	−	0.395633i
$966$	−9.43334	+	6.85373i	−0.303513	+	0.220515i
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		0			0
$969$	−31.3205			−1.00616
$970$	−10.5644	−	0.596470i	−0.339201	−	0.0191515i
$971$	−7.70324	−	23.7081i	−0.247209	−	0.760830i	−0.995265	−	0.0971952i	$-0.969013\pi$
$971$	−7.70324	−	23.7081i	−0.247209	−	0.760830i	0.748057	−	0.663635i	$-0.230987\pi$
$972$	12.2722	+	3.98749i	0.393632	+	0.127899i
$973$	28.6921	−	39.4913i	0.919827	−	1.26603i
$974$	5.33017	+	3.87260i	0.170790	+	0.124086i
$975$	40.7203	+	4.61289i	1.30409	+	0.147731i
$976$	−8.93336	−	27.4941i	−0.285950	−	0.880063i
$977$	−17.1142	−	23.5557i	−0.547533	−	0.753614i	0.442142	−	0.896945i	$-0.354219\pi$
$977$	−17.1142	−	23.5557i	−0.547533	−	0.753614i	−0.989675	+	0.143331i	$0.954219\pi$
$978$			5.13922i			0.164334i
$979$		0			0
$980$	−12.5885	−	10.2784i	−0.402124	−	0.328332i
$981$	−5.44634	+	3.95700i	−0.173888	+	0.126337i
$982$	19.5507	−	6.35242i	0.623889	−	0.202714i
$983$	−53.2817	−	17.3123i	−1.69942	−	0.552176i	−0.710906	−	0.703287i	$-0.751715\pi$
$983$	−53.2817	−	17.3123i	−1.69942	−	0.552176i	−0.988517	+	0.151112i	$0.951715\pi$
$984$	5.22957	+	3.79950i	0.166713	+	0.121124i
$985$	−37.2935	+	9.83142i	−1.18827	+	0.313255i
$986$	4.28187	−	13.1782i	0.136362	−	0.419680i
$987$	70.4063	−	22.8764i	2.24106	−	0.728163i
$988$	−18.1245	−	24.9463i	−0.576618	−	0.793647i
$989$	22.4833			0.714929
$990$		0			0
$991$	19.9090			0.632429			0.316215	−	0.948688i	$-0.397588\pi$
$991$	19.9090			0.632429			0.316215	+	0.948688i	$0.397588\pi$
$992$	−26.3774	−	36.3054i	−0.837483	−	1.15270i
$993$	−33.4318	+	10.8626i	−1.06093	+	0.344716i
$994$	−4.38685	+	13.5013i	−0.139143	+	0.428237i
$995$	−1.14001	−	4.32439i	−0.0361407	−	0.137092i
$996$	26.7982	+	19.4700i	0.849132	+	0.616931i
$997$	32.4472	+	10.5427i	1.02761	+	0.333892i	0.773846	−	0.633374i	$-0.218330\pi$
$997$	32.4472	+	10.5427i	1.02761	+	0.333892i	0.253767	+	0.967265i	$0.418330\pi$
$998$	−8.66832	+	2.81651i	−0.274391	+	0.0891550i
$999$	6.35597	−	4.61788i	0.201094	−	0.146103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.f.124.3		16
5.4	even	2	inner	605.2.j.f.124.2		16
11.2	odd	10		605.2.b.e.364.3	yes	4
11.3	even	5	inner	605.2.j.f.269.3		16
11.4	even	5	inner	605.2.j.f.444.2		16
11.5	even	5	inner	605.2.j.f.9.2		16
11.6	odd	10		605.2.j.e.9.3		16
11.7	odd	10		605.2.j.e.444.3		16
11.8	odd	10		605.2.j.e.269.2		16
11.9	even	5		605.2.b.d.364.2	✓	4
11.10	odd	2		605.2.j.e.124.2		16
55.2	even	20		3025.2.a.z.1.2		4
55.4	even	10	inner	605.2.j.f.444.3		16
55.9	even	10		605.2.b.d.364.3	yes	4
55.13	even	20		3025.2.a.z.1.3		4
55.14	even	10	inner	605.2.j.f.269.2		16
55.19	odd	10		605.2.j.e.269.3		16
55.24	odd	10		605.2.b.e.364.2	yes	4
55.29	odd	10		605.2.j.e.444.2		16
55.39	odd	10		605.2.j.e.9.2		16
55.42	odd	20		3025.2.a.y.1.3		4
55.49	even	10	inner	605.2.j.f.9.3		16
55.53	odd	20		3025.2.a.y.1.2		4
55.54	odd	2		605.2.j.e.124.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.2	✓	4	11.9	even	5
605.2.b.d.364.3	yes	4	55.9	even	10
605.2.b.e.364.2	yes	4	55.24	odd	10
605.2.b.e.364.3	yes	4	11.2	odd	10
605.2.j.e.9.2		16	55.39	odd	10
605.2.j.e.9.3		16	11.6	odd	10
605.2.j.e.124.2		16	11.10	odd	2
605.2.j.e.124.3		16	55.54	odd	2
605.2.j.e.269.2		16	11.8	odd	10
605.2.j.e.269.3		16	55.19	odd	10
605.2.j.e.444.2		16	55.29	odd	10
605.2.j.e.444.3		16	11.7	odd	10
605.2.j.f.9.2		16	11.5	even	5	inner
605.2.j.f.9.3		16	55.49	even	10	inner
605.2.j.f.124.2		16	5.4	even	2	inner
605.2.j.f.124.3		16	1.1	even	1	trivial
605.2.j.f.269.2		16	55.14	even	10	inner
605.2.j.f.269.3		16	11.3	even	5	inner
605.2.j.f.444.2		16	11.4	even	5	inner
605.2.j.f.444.3		16	55.4	even	10	inner
3025.2.a.y.1.2		4	55.53	odd	20
3025.2.a.y.1.3		4	55.42	odd	20
3025.2.a.z.1.2		4	55.2	even	20
3025.2.a.z.1.3		4	55.13	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.304260 + 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(3.18230 + 1.03399i) q^{7} +(1.83730 - 0.596975i) q^{8} +(0.592242 - 0.430289i) q^{9} +O(q^{10})\)	\(q+(0.304260 + 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(3.18230 + 1.03399i) q^{7} +(1.83730 - 0.596975i) q^{8} +(0.592242 - 0.430289i) q^{9} +(0.732051 - 0.896575i) q^{10} -3.34607i q^{12} +(-2.49376 - 3.43237i) q^{13} +(0.535233 + 1.64728i) q^{14} +(-2.33805 - 3.63233i) q^{15} +(-1.99350 - 1.44836i) q^{16} +(-2.27103 + 3.12580i) q^{17} +(0.360391 + 0.117098i) q^{18} +(1.29668 + 3.99078i) q^{19} +(-3.86682 - 0.218323i) q^{20} +6.46410 q^{21} +3.48477i q^{23} +(3.01929 - 2.19364i) q^{24} +(-4.35019 + 2.46492i) q^{25} +(0.678648 - 2.08867i) q^{26} +(-2.57529 + 3.54458i) q^{27} +(3.40654 - 4.68870i) q^{28} +(-2.14093 + 6.58911i) q^{29} +(0.809764 - 2.08429i) q^{30} +(7.06438 - 5.13257i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(0.421768 - 7.47013i) q^{35} +(-0.391818 - 1.20589i) q^{36} +(-1.70539 - 0.554114i) q^{37} +(-1.27672 + 1.75726i) q^{38} +(-6.63083 - 4.81758i) q^{39} +(-2.33805 - 3.63233i) q^{40} +(0.535233 + 1.64728i) q^{41} +(1.96677 + 2.70702i) q^{42} -6.45189i q^{43} +(-1.26795 - 1.03528i) q^{45} +(-1.45934 + 1.06028i) q^{46} +(10.8919 - 3.53899i) q^{47} +(-4.52729 - 1.47101i) q^{48} +(3.39476 + 2.46644i) q^{49} +(-2.35584 - 1.07179i) q^{50} +(-2.30653 + 7.09878i) q^{51} +(-6.98881 + 2.27080i) q^{52} +(-1.27672 - 1.75726i) q^{53} -2.26795 q^{54} +6.46410 q^{56} +(4.76479 + 6.55817i) q^{57} +(-3.41078 + 1.10823i) q^{58} +(0.391818 - 1.20589i) q^{59} +(-7.23485 + 1.90727i) q^{60} +(9.49143 + 6.89593i) q^{61} +(4.29882 + 1.39677i) q^{62} +(2.32960 - 0.756934i) q^{63} +(-1.83481 + 1.33307i) q^{64} +(-6.00000 + 7.34847i) q^{65} -2.20925i q^{67} +(3.93354 + 5.41405i) q^{68} +(2.08032 + 6.40256i) q^{69} +(3.25665 - 2.09624i) q^{70} +(6.63083 + 4.81758i) q^{71} +(0.831254 - 1.14412i) q^{72} +(-4.65921 - 1.51387i) q^{73} +(-0.286831 - 0.882774i) q^{74} +(-6.52111 + 7.12576i) q^{75} +7.26795 q^{76} -4.24264i q^{78} +(1.18448 - 0.860577i) q^{79} +(-1.99534 + 5.13591i) q^{80} +(-3.29420 + 10.1385i) q^{81} +(-0.526994 + 0.725345i) q^{82} +(-5.81878 + 8.00886i) q^{83} +(3.45980 - 10.6482i) q^{84} +(8.05309 + 3.12869i) q^{85} +(2.70191 - 1.96305i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(0.0477646 - 0.845982i) q^{90} +(-4.38685 - 13.5013i) q^{91} +(5.74038 + 1.86516i) q^{92} +(9.91537 - 13.6473i) q^{93} +(4.79602 + 3.48451i) q^{94} +(7.88973 - 5.07844i) q^{95} +(-3.06798 - 9.44228i) q^{96} +(-5.37331 - 7.39573i) q^{97} +2.17209i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^6 - 4 * q^9	\( 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) \) 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

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