LMFDB - Embedded newform 784.2.x.n.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Character	$\chi$	$=$	784.557
Dual form			784.2.x.n.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08279 + 0.909711i) q^{2} +(1.23755 - 0.331601i) q^{3} +(0.344852 - 1.97004i) q^{4} +(3.17421 + 0.850527i) q^{5} +(-1.03834 + 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} +(-1.17650 + 0.679252i) q^{9} +O(q^{10})$	\(q+(-1.08279 + 0.909711i) q^{2} +(1.23755 - 0.331601i) q^{3} +(0.344852 - 1.97004i) q^{4} +(3.17421 + 0.850527i) q^{5} +(-1.03834 + 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} +(-1.17650 + 0.679252i) q^{9} +(-4.21072 + 1.96667i) q^{10} +(0.110070 + 0.410787i) q^{11} +(-0.226497 - 2.55239i) q^{12} +(3.70160 + 3.70160i) q^{13} +4.21029 q^{15} +(-3.76215 - 1.35875i) q^{16} +(-1.35248 + 2.34256i) q^{17} +(0.655973 - 1.80576i) q^{18} +(-0.914248 + 3.41202i) q^{19} +(2.77021 - 5.96003i) q^{20} +(-0.492880 - 0.344662i) q^{22} +(-4.36053 + 2.51755i) q^{23} +(2.56718 + 2.55764i) q^{24} +(5.02207 + 2.89950i) q^{25} +(-7.37543 - 0.640655i) q^{26} +(-3.94859 + 3.94859i) q^{27} +(0.464798 + 0.464798i) q^{29} +(-4.55884 + 3.83014i) q^{30} +(3.87569 - 6.71289i) q^{31} +(5.30968 - 1.95124i) q^{32} +(0.272435 + 0.471871i) q^{33} +(-0.666608 - 3.76685i) q^{34} +(0.932439 + 2.55200i) q^{36} +(5.24218 + 1.40464i) q^{37} +(-2.11402 - 4.52619i) q^{38} +(5.80838 + 3.35347i) q^{39} +(2.42236 + 8.97352i) q^{40} -10.5868i q^{41} +(8.35006 - 8.35006i) q^{43} +(0.847226 - 0.0751823i) q^{44} +(-4.31217 + 1.15544i) q^{45} +(2.43127 - 6.69279i) q^{46} +(-5.11933 - 8.86694i) q^{47} +(-5.10643 - 0.433986i) q^{48} +(-8.07554 + 1.42910i) q^{50} +(-0.896966 + 3.34752i) q^{51} +(8.56882 - 6.01581i) q^{52} +(3.30284 + 12.3264i) q^{53} +(0.683403 - 7.86756i) q^{54} +1.39754i q^{55} +4.52572i q^{57} +(-0.926108 - 0.0804449i) q^{58} +(2.63392 + 9.82994i) q^{59} +(1.45192 - 8.29445i) q^{60} +(1.84061 - 6.86924i) q^{61} +(1.91025 + 10.7944i) q^{62} +(-3.97418 + 6.94305i) q^{64} +(8.60134 + 14.8980i) q^{65} +(-0.724255 - 0.263098i) q^{66} +(-0.243592 + 0.0652703i) q^{67} +(4.14854 + 3.47228i) q^{68} +(-4.56156 + 4.56156i) q^{69} -6.38433i q^{71} +(-3.33121 - 1.91502i) q^{72} +(-1.22356 - 0.706421i) q^{73} +(-6.95397 + 3.24795i) q^{74} +(7.17656 + 1.92295i) q^{75} +(6.40655 + 2.97775i) q^{76} +(-9.33992 + 1.65286i) q^{78} +(-4.14366 - 7.17702i) q^{79} +(-10.7862 - 7.51276i) q^{80} +(-1.53948 + 2.66646i) q^{81} +(9.63096 + 11.4633i) q^{82} +(-2.84836 - 2.84836i) q^{83} +(-6.28545 + 6.28545i) q^{85} +(-1.44519 + 16.6375i) q^{86} +(0.729339 + 0.421084i) q^{87} +(-0.848971 + 0.852137i) q^{88} +(-0.471871 + 0.272435i) q^{89} +(3.61804 - 5.17393i) q^{90} +(3.45595 + 9.45861i) q^{92} +(2.57037 - 9.59274i) q^{93} +(13.6095 + 4.94389i) q^{94} +(-5.80403 + 10.0529i) q^{95} +(5.92397 - 4.17546i) q^{96} -3.67469 q^{97} +(-0.408525 - 0.408525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4}+O(q^{10}) $ 40 * q + 8 * q^4	$ 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.08279	+	0.909711i	−0.765645	+	0.643263i
$2$	−1.08279	+	0.909711i	−0.765645	+	0.643263i
$3$	1.23755	−	0.331601i	0.714502	−	0.191450i	0.116785	−	0.993157i	$-0.462741\pi$
$3$	1.23755	−	0.331601i	0.714502	−	0.191450i	0.597717	+	0.801707i	$0.296075\pi$
$4$	0.344852	−	1.97004i	0.172426	−	0.985022i
$5$	3.17421	+	0.850527i	1.41955	+	0.380367i	0.885324	−	0.464975i	$-0.153937\pi$
$5$	3.17421	+	0.850527i	1.41955	+	0.380367i	0.534225	+	0.845342i	$0.320603\pi$
$6$	−1.03834	+	1.48487i	−0.423902	+	0.606195i
$7$		0			0
$7$		0			0
$8$	1.41877	+	2.44685i	0.501611	+	0.865093i
$9$	−1.17650	+	0.679252i	−0.392166	+	0.226417i
$10$	−4.21072	+	1.96667i	−1.33155	+	0.621917i
$11$	0.110070	+	0.410787i	0.0331874	+	0.123857i	0.980532	−	0.196358i	$-0.0629115\pi$
$11$	0.110070	+	0.410787i	0.0331874	+	0.123857i	−0.947345	+	0.320215i	$0.896245\pi$
$12$	−0.226497	−	2.55239i	−0.0653841	−	0.736811i
$13$	3.70160	+	3.70160i	1.02664	+	1.02664i	0.999635	+	0.0270035i	$0.00859654\pi$
$13$	3.70160	+	3.70160i	1.02664	+	1.02664i	0.0270035	+	0.999635i	$0.491403\pi$
$14$		0			0
$15$	4.21029			1.08709
$16$	−3.76215	−	1.35875i	−0.940539	−	0.339687i
$17$	−1.35248	+	2.34256i	−0.328024	+	0.568154i	−0.982120	−	0.188258i	$-0.939716\pi$
$17$	−1.35248	+	2.34256i	−0.328024	+	0.568154i	0.654096	+	0.756412i	$0.273049\pi$
$18$	0.655973	−	1.80576i	0.154614	−	0.425621i
$19$	−0.914248	+	3.41202i	−0.209743	+	0.782771i	0.778208	+	0.628006i	$0.216129\pi$
$19$	−0.914248	+	3.41202i	−0.209743	+	0.782771i	−0.987951	+	0.154765i	$0.950538\pi$
$20$	2.77021	−	5.96003i	0.619437	−	1.33270i
$21$		0			0
$22$	−0.492880	−	0.344662i	−0.105082	−	0.0734823i
$23$	−4.36053	+	2.51755i	−0.909232	+	0.524946i	−0.880184	−	0.474632i	$-0.842581\pi$
$23$	−4.36053	+	2.51755i	−0.909232	+	0.524946i	−0.0290483	+	0.999578i	$0.509248\pi$
$24$	2.56718	+	2.55764i	0.524024	+	0.522077i
$25$	5.02207	+	2.89950i	1.00441	+	0.579899i
$26$	−7.37543	−	0.640655i	−1.44644	−	0.125643i
$27$	−3.94859	+	3.94859i	−0.759907	+	0.759907i
$28$		0			0
$29$	0.464798	+	0.464798i	0.0863108	+	0.0863108i	0.748944	−	0.662633i	$-0.230561\pi$
$29$	0.464798	+	0.464798i	0.0863108	+	0.0863108i	−0.662633	+	0.748944i	$0.730561\pi$
$30$	−4.55884	+	3.83014i	−0.832326	+	0.699285i
$31$	3.87569	−	6.71289i	0.696094	−	1.20567i	−0.273716	−	0.961811i	$-0.588253\pi$
$31$	3.87569	−	6.71289i	0.696094	−	1.20567i	0.969810	−	0.243860i	$-0.0784138\pi$
$32$	5.30968	−	1.95124i	0.938627	−	0.344934i
$33$	0.272435	+	0.471871i	0.0474248	+	0.0821422i
$34$	−0.666608	−	3.76685i	−0.114322	−	0.646010i
$35$		0			0
$36$	0.932439	+	2.55200i	0.155406	+	0.425333i
$37$	5.24218	+	1.40464i	0.861809	+	0.230921i	0.662543	−	0.749024i	$-0.269477\pi$
$37$	5.24218	+	1.40464i	0.861809	+	0.230921i	0.199267	+	0.979945i	$0.436144\pi$
$38$	−2.11402	−	4.52619i	−0.342939	−	0.734245i
$39$	5.80838	+	3.35347i	0.930085	+	0.536985i
$40$	2.42236	+	8.97352i	0.383009	+	1.41884i
$41$		−	10.5868i		−	1.65339i	−0.562653	−	0.826693i	$-0.690219\pi$
$41$		−	10.5868i		−	1.65339i	0.562653	−	0.826693i	$-0.309781\pi$
$42$		0			0
$43$	8.35006	−	8.35006i	1.27337	−	1.27337i	0.329065	−	0.944307i	$-0.393267\pi$
$43$	8.35006	−	8.35006i	1.27337	−	1.27337i	0.944307	−	0.329065i	$-0.106733\pi$
$44$	0.847226	−	0.0751823i	0.127724	−	0.0113342i
$45$	−4.31217	+	1.15544i	−0.642821	+	0.172243i
$46$	2.43127	−	6.69279i	0.358472	−	0.986798i
$47$	−5.11933	−	8.86694i	−0.746731	−	1.29338i	−0.949382	−	0.314125i	$-0.898289\pi$
$47$	−5.11933	−	8.86694i	−0.746731	−	1.29338i	0.202651	−	0.979251i	$-0.435044\pi$
$48$	−5.10643	−	0.433986i	−0.737049	−	0.0626404i
$49$		0			0
$50$	−8.07554	+	1.42910i	−1.14205	+	0.202106i
$51$	−0.896966	+	3.34752i	−0.125600	+	0.468747i
$52$	8.56882	−	6.01581i	1.18828	−	0.834243i
$53$	3.30284	+	12.3264i	0.453680	+	1.69316i	0.691941	+	0.721954i	$0.256756\pi$
$53$	3.30284	+	12.3264i	0.453680	+	1.69316i	−0.238261	+	0.971201i	$0.576577\pi$
$54$	0.683403	−	7.86756i	0.0929994	−	1.07064i
$55$			1.39754i			0.188444i
$56$		0			0
$57$			4.52572i			0.599446i
$58$	−0.926108	−	0.0804449i	−0.121604	−	0.0105629i
$59$	2.63392	+	9.82994i	0.342908	+	1.27975i	0.895037	+	0.445991i	$0.147149\pi$
$59$	2.63392	+	9.82994i	0.342908	+	1.27975i	−0.552130	+	0.833758i	$0.686185\pi$
$60$	1.45192	−	8.29445i	0.187443	−	1.07081i
$61$	1.84061	−	6.86924i	0.235666	−	0.879516i	−0.742182	−	0.670198i	$-0.766209\pi$
$61$	1.84061	−	6.86924i	0.235666	−	0.879516i	0.977848	−	0.209318i	$-0.0671244\pi$
$62$	1.91025	+	10.7944i	0.242602	+	1.37089i
$63$		0			0
$64$	−3.97418	+	6.94305i	−0.496772	+	0.867881i
$65$	8.60134	+	14.8980i	1.06686	+	1.84786i
$66$	−0.724255	−	0.263098i	−0.0891496	−	0.0323852i
$67$	−0.243592	+	0.0652703i	−0.0297595	+	0.00797403i	−0.273668	−	0.961824i	$-0.588237\pi$
$67$	−0.243592	+	0.0652703i	−0.0297595	+	0.00797403i	0.243909	+	0.969798i	$0.421570\pi$
$68$	4.14854	+	3.47228i	0.503085	+	0.421075i
$69$	−4.56156	+	4.56156i	−0.549147	+	0.549147i
$70$		0			0
$71$		−	6.38433i		−	0.757680i	−0.925462	−	0.378840i	$-0.876323\pi$
$71$		−	6.38433i		−	0.757680i	0.925462	−	0.378840i	$-0.123677\pi$
$72$	−3.33121	−	1.91502i	−0.392587	−	0.225687i
$73$	−1.22356	−	0.706421i	−0.143206	−	0.0826803i	0.426685	−	0.904400i	$-0.359681\pi$
$73$	−1.22356	−	0.706421i	−0.143206	−	0.0826803i	−0.569891	+	0.821720i	$0.693015\pi$
$74$	−6.95397	+	3.24795i	−0.808383	+	0.377566i
$75$	7.17656	+	1.92295i	0.828678	+	0.222044i
$76$	6.40655	+	2.97775i	0.734882	+	0.341571i
$77$		0			0
$78$	−9.33992	+	1.65286i	−1.05754	+	0.187149i
$79$	−4.14366	−	7.17702i	−0.466198	−	0.807478i	0.533057	−	0.846079i	$-0.321043\pi$
$79$	−4.14366	−	7.17702i	−0.466198	−	0.807478i	−0.999255	+	0.0386013i	$0.987710\pi$
$80$	−10.7862	−	7.51276i	−1.20594	−	0.839952i
$81$	−1.53948	+	2.66646i	−0.171053	+	0.296273i
$82$	9.63096	+	11.4633i	1.06356	+	1.26591i
$83$	−2.84836	−	2.84836i	−0.312648	−	0.312648i	0.533286	−	0.845935i	$-0.320957\pi$
$83$	−2.84836	−	2.84836i	−0.312648	−	0.312648i	−0.845935	+	0.533286i	$0.820957\pi$
$84$		0			0
$85$	−6.28545	+	6.28545i	−0.681753	+	0.681753i
$86$	−1.44519	+	16.6375i	−0.155839	+	1.79406i
$87$	0.729339	+	0.421084i	0.0781934	+	0.0451450i
$88$	−0.848971	+	0.852137i	−0.0905006	+	0.0908382i
$89$	−0.471871	+	0.272435i	−0.0500182	+	0.0288780i	−0.524801	−	0.851225i	$-0.675860\pi$
$89$	−0.471871	+	0.272435i	−0.0500182	+	0.0288780i	0.474782	+	0.880103i	$0.342527\pi$
$90$	3.61804	−	5.17393i	0.381375	−	0.545380i
$91$		0			0
$92$	3.45595	+	9.45861i	0.360308	+	0.986129i
$93$	2.57037	−	9.59274i	0.266535	−	0.994721i
$94$	13.6095	+	4.94389i	1.40371	+	0.509923i
$95$	−5.80403	+	10.0529i	−0.595481	+	1.03140i
$96$	5.92397	−	4.17546i	0.604613	−	0.426156i
$97$	−3.67469			−0.373108			−0.186554	−	0.982445i	$-0.559732\pi$
$97$	−3.67469			−0.373108			−0.186554	+	0.982445i	$0.559732\pi$
$98$		0			0
$99$	−0.408525	−	0.408525i	−0.0410583	−	0.0410583i
$100$	7.44401	−	8.89382i	0.744401	−	0.889382i
$101$	−1.01856	−	3.80130i	−0.101350	−	0.378244i	0.896555	−	0.442931i	$-0.146062\pi$
$101$	−1.01856	−	3.80130i	−0.101350	−	0.378244i	−0.997906	+	0.0646878i	$0.979395\pi$
$102$	−2.07406	−	4.44063i	−0.205362	−	0.439688i
$103$	−12.0052	+	6.93123i	−1.18291	+	0.682955i	−0.956686	−	0.291120i	$-0.905972\pi$
$103$	−12.0052	+	6.93123i	−1.18291	+	0.682955i	−0.226226	+	0.974075i	$0.572639\pi$
$104$	−3.80555	+	14.3090i	−0.373165	+	1.40311i
$105$		0			0
$106$	−14.7897	−	10.3422i	−1.43650	−	1.00452i
$107$	9.44326	+	2.53031i	0.912914	+	0.244615i	0.684554	−	0.728962i	$-0.259997\pi$
$107$	9.44326	+	2.53031i	0.912914	+	0.244615i	0.228360	+	0.973577i	$0.426664\pi$
$108$	6.41723	+	9.14059i	0.617498	+	0.879553i
$109$	−14.3947	+	3.85705i	−1.37876	+	0.369438i	−0.870672	−	0.491865i	$-0.836315\pi$
$109$	−14.3947	+	3.85705i	−1.37876	+	0.369438i	−0.508091	+	0.861303i	$0.669649\pi$
$110$	−1.27136	−	1.51324i	−0.121219	−	0.144282i
$111$	6.95325			0.659974
$112$		0			0
$113$	0.0535041			0.00503324			0.00251662	−	0.999997i	$-0.499199\pi$
$113$	0.0535041			0.00503324			0.00251662	+	0.999997i	$0.499199\pi$
$114$	−4.11710	−	4.90039i	−0.385602	−	0.458963i
$115$	−15.9825	+	4.28249i	−1.49037	+	0.399344i
$116$	1.07596	−	0.755386i	0.0999002	−	0.0701358i
$117$	−6.86924	−	1.84061i	−0.635062	−	0.170164i
$118$	−11.7944	−	8.24761i	−1.08576	−	0.759254i
$119$		0			0
$120$	5.97343	+	10.3020i	0.545297	+	0.940435i
$121$	9.36965	−	5.40957i	0.851786	−	0.491779i
$122$	4.25604	+	9.11234i	0.385324	+	0.824993i
$123$	−3.51061	−	13.1018i	−0.316541	−	1.18135i
$124$	−11.8882	−	9.95023i	−1.06759	−	0.893557i
$125$	1.85660	+	1.85660i	0.166060	+	0.166060i
$126$		0			0
$127$	5.69350			0.505216			0.252608	−	0.967569i	$-0.418712\pi$
$127$	5.69350			0.505216			0.252608	+	0.967569i	$0.418712\pi$
$128$	−2.01298	−	11.1332i	−0.177924	−	0.984044i
$129$	7.56475	−	13.1025i	0.666039	−	1.15361i
$130$	−22.8662	−	8.30657i	−2.00550	−	0.728534i
$131$	−0.677104	+	2.52699i	−0.0591589	+	0.220784i	−0.989176	−	0.146731i	$-0.953125\pi$
$131$	−0.677104	+	2.52699i	−0.0591589	+	0.220784i	0.930018	+	0.367515i	$0.119791\pi$
$132$	1.02356	−	0.373983i	0.0890892	−	0.0325511i
$133$		0			0
$134$	0.204381	−	0.292272i	0.0176558	−	0.0252485i
$135$	−15.8920	+	9.17527i	−1.36777	+	0.789682i
$136$	−7.65075	+	0.0142423i	−0.656046	+	0.00122127i
$137$	11.8037	+	6.81486i	1.00846	+	0.582232i	0.910739	−	0.412982i	$-0.135513\pi$
$137$	11.8037	+	6.81486i	1.00846	+	0.582232i	0.0977169	+	0.995214i	$0.468846\pi$
$138$	0.789492	−	9.08889i	0.0672060	−	0.773698i
$139$	14.5483	−	14.5483i	1.23397	−	1.23397i	0.271549	−	0.962425i	$-0.412464\pi$
$139$	14.5483	−	14.5483i	1.23397	−	1.23397i	0.962425	−	0.271549i	$-0.0875359\pi$
$140$		0			0
$141$	−9.27573	−	9.27573i	−0.781157	−	0.781157i
$142$	5.80789	+	6.91286i	0.487387	+	0.580114i
$143$	−1.11313	+	1.92800i	−0.0930849	+	0.161228i
$144$	5.34910	−	0.956886i	0.445758	−	0.0797405i
$145$	1.08004	+	1.87069i	0.0896926	+	0.155352i
$146$	1.96749	−	0.348180i	0.162831	−	0.0288156i
$147$		0			0
$148$	4.57497	−	9.84294i	0.376061	−	0.809085i
$149$	6.66184	+	1.78503i	0.545759	+	0.146236i	0.521156	−	0.853462i	$-0.325501\pi$
$149$	6.66184	+	1.78503i	0.545759	+	0.146236i	0.0246034	+	0.999697i	$0.492168\pi$
$150$	−9.52001	+	4.44645i	−0.777306	+	0.363051i
$151$	0.116037	+	0.0669937i	0.00944292	+	0.00545187i	0.504714	−	0.863287i	$-0.331598\pi$
$151$	0.116037	+	0.0669937i	0.00944292	+	0.00545187i	−0.495271	+	0.868738i	$0.664931\pi$
$152$	−9.64582	+	2.60384i	−0.782379	+	0.211200i
$153$		−	3.67469i		−	0.297081i
$154$		0			0
$155$	18.0117	−	18.0117i	1.44674	−	1.44674i
$156$	8.60952	−	10.2863i	0.689313	−	0.823565i
$157$	3.58877	−	0.961608i	0.286415	−	0.0767446i	−0.112751	−	0.993623i	$-0.535966\pi$
$157$	3.58877	−	0.961608i	0.286415	−	0.0767446i	0.399166	+	0.916879i	$0.369300\pi$
$158$	11.0157	+	4.00165i	0.876363	+	0.318354i
$159$	8.17487	+	14.1593i	0.648310	+	1.12291i
$160$	18.5136	−	1.67763i	1.46363	−	0.132628i
$161$		0			0
$162$	−0.758778	−	4.28768i	−0.0596152	−	0.336872i
$163$	4.89083	−	18.2528i	0.383079	−	1.42967i	−0.458093	−	0.888904i	$-0.651467\pi$
$163$	4.89083	−	18.2528i	0.383079	−	1.42967i	0.841172	−	0.540767i	$-0.181866\pi$
$164$	−20.8565	−	3.65089i	−1.62862	−	0.285087i
$165$	0.463426	+	1.72953i	0.0360777	+	0.134644i
$166$	5.67535	+	0.492981i	0.440493	+	0.0382627i
$167$		−	4.72699i		−	0.365785i	−0.983133	−	0.182893i	$-0.941454\pi$
$167$		−	4.72699i		−	0.365785i	0.983133	−	0.182893i	$-0.0585461\pi$
$168$		0			0
$169$			14.4037i			1.10797i
$170$	1.08786	−	12.5237i	0.0834347	−	0.960527i
$171$	−1.24201	−	4.63524i	−0.0949788	−	0.354466i
$172$	−13.5705	−	19.3295i	−1.03474	−	1.47386i
$173$	−3.84658	+	14.3556i	−0.292450	+	1.09144i	0.650772	+	0.759274i	$0.274446\pi$
$173$	−3.84658	+	14.3556i	−0.292450	+	1.09144i	−0.943222	+	0.332164i	$0.892221\pi$
$174$	−1.17278	+	0.207544i	−0.0889085	+	0.0157339i
$175$		0			0
$176$	0.144055	−	1.69500i	0.0108586	−	0.127765i
$177$	6.51924	+	11.2917i	0.490016	+	0.848733i
$178$	0.263098	−	0.724255i	0.0197201	−	0.0542852i
$179$	−10.8194	+	2.89905i	−0.808681	+	0.216685i	−0.639392	−	0.768881i	$-0.720814\pi$
$179$	−10.8194	+	2.89905i	−0.808681	+	0.216685i	−0.169289	+	0.985566i	$0.554147\pi$
$180$	0.789215	+	8.89363i	0.0588246	+	0.662892i
$181$	−1.84499	+	1.84499i	−0.137137	+	0.137137i	−0.772343	−	0.635206i	$-0.780915\pi$
$181$	−1.84499	+	1.84499i	−0.137137	+	0.137137i	0.635206	+	0.772343i	$0.280915\pi$
$182$		0			0
$183$		−	9.11140i		−	0.673534i
$184$	−12.3467	−	7.09774i	−0.910208	−	0.523252i
$185$	15.4451	+	8.91723i	1.13555	+	0.655607i
$186$	5.94346	+	12.7252i	0.435796	+	0.933055i
$187$	−1.11116	−	0.297734i	−0.0812560	−	0.0217725i
$188$	−19.2337	+	7.02753i	−1.40276	+	0.512535i
$189$		0			0
$190$	−2.86069	−	16.1651i	−0.207536	−	1.17274i
$191$	−10.7344	−	18.5925i	−0.776713	−	1.34531i	−0.933827	−	0.357726i	$-0.883552\pi$
$191$	−10.7344	−	18.5925i	−0.776713	−	1.34531i	0.157114	−	0.987580i	$-0.449781\pi$
$192$	−2.61593	+	9.91023i	−0.188789	+	0.715209i
$193$	6.36523	−	11.0249i	0.458179	−	0.793590i	−0.540686	−	0.841225i	$-0.681835\pi$
$193$	6.36523	−	11.0249i	0.458179	−	0.793590i	0.998865	+	0.0476350i	$0.0151684\pi$
$194$	3.97890	−	3.34290i	0.285668	−	0.240007i
$195$	15.5848	+	15.5848i	1.11605	+	1.11605i
$196$		0			0
$197$	−4.30651	+	4.30651i	−0.306826	+	0.306826i	−0.843677	−	0.536851i	$-0.819614\pi$
$197$	−4.30651	+	4.30651i	−0.306826	+	0.306826i	0.536851	+	0.843677i	$0.319614\pi$
$198$	0.813985	+	0.0707055i	0.0578474	+	0.00502482i
$199$	−5.07795	−	2.93176i	−0.359967	−	0.207827i	0.309100	−	0.951030i	$-0.399972\pi$
$199$	−5.07795	−	2.93176i	−0.359967	−	0.207827i	−0.669066	+	0.743203i	$0.733306\pi$
$200$	0.0305332	+	16.4020i	0.00215902	+	1.15980i
$201$	−0.279814	+	0.161551i	−0.0197366	+	0.0113949i
$202$	4.56096	+	3.18941i	0.320908	+	0.224406i
$203$		0			0
$204$	6.28545	+	2.92146i	0.440070	+	0.204543i
$205$	9.00439	−	33.6048i	0.628894	−	2.34706i
$206$	6.69370	−	18.4263i	0.466372	−	1.28382i
$207$	3.42010	−	5.92379i	0.237713	−	0.411732i
$208$	−8.89645	−	18.9555i	−0.616858	−	1.31433i
$209$	−1.50224			−0.103912
$210$		0			0
$211$	−1.72014	−	1.72014i	−0.118420	−	0.118420i	0.645414	−	0.763833i	$-0.276685\pi$
$211$	−1.72014	−	1.72014i	−0.118420	−	0.118420i	−0.763833	+	0.645414i	$0.776685\pi$
$212$	25.4225	−	2.25597i	1.74602	−	0.154941i
$213$	−2.11705	−	7.90094i	−0.145058	−	0.541364i
$214$	−12.5269	+	5.85085i	−0.856320	+	0.399956i
$215$	33.6068	−	19.4029i	2.29196	−	1.32327i
$216$	−15.2638	−	4.05948i	−1.03857	−	0.276212i
$217$		0			0
$218$	12.0776	−	17.2714i	0.817998	−	1.16977i
$219$	−1.74847	−	0.468500i	−0.118150	−	0.0316583i
$220$	2.75322	+	0.481944i	0.185622	+	0.0324927i
$221$	−13.6775	+	3.66489i	−0.920051	+	0.246527i
$222$	−7.52889	+	6.32545i	−0.505306	+	0.424537i
$223$	−27.1830			−1.82031			−0.910154	−	0.414270i	$-0.864037\pi$
$223$	−27.1830			−1.82031			−0.910154	+	0.414270i	$0.864037\pi$
$224$		0			0
$225$	−7.87795			−0.525197
$226$	−0.0579335	+	0.0486733i	−0.00385368	+	0.00323770i
$227$	20.6177	−	5.52450i	1.36844	−	0.366674i	0.501534	−	0.865138i	$-0.332769\pi$
$227$	20.6177	−	5.52450i	1.36844	−	0.366674i	0.866910	+	0.498464i	$0.166102\pi$
$228$	8.91587	+	1.56070i	0.590468	+	0.103360i
$229$	−2.75965	−	0.739446i	−0.182363	−	0.0488639i	0.166482	−	0.986045i	$-0.446759\pi$
$229$	−2.75965	−	0.739446i	−0.182363	−	0.0488639i	−0.348845	+	0.937181i	$0.613426\pi$
$230$	13.4098	−	19.1764i	0.884213	−	1.26446i
$231$		0			0
$232$	−0.477850	+	1.79673i	−0.0313724	+	0.117961i
$233$	−14.3933	+	8.31000i	−0.942939	+	0.544406i	−0.890880	−	0.454238i	$-0.849912\pi$
$233$	−14.3933	+	8.31000i	−0.942939	+	0.544406i	−0.0520584	+	0.998644i	$0.516578\pi$
$234$	9.11234	−	4.25604i	0.595692	−	0.278226i
$235$	−8.70825	−	32.4996i	−0.568064	−	2.12004i
$236$	20.2737	−	1.79908i	1.31971	−	0.117110i
$237$	−7.50790	−	7.50790i	−0.487691	−	0.487691i
$238$		0			0
$239$	−2.17404			−0.140627			−0.0703135	−	0.997525i	$-0.522400\pi$
$239$	−2.17404			−0.140627			−0.0703135	+	0.997525i	$0.522400\pi$
$240$	−15.8397	−	5.72071i	−1.02245	−	0.369270i
$241$	−6.91869	+	11.9835i	−0.445672	+	0.771927i	−0.998099	−	0.0616347i	$-0.980369\pi$
$241$	−6.91869	+	11.9835i	−0.445672	+	0.771927i	0.552427	+	0.833562i	$0.313702\pi$
$242$	−5.22418	+	14.3811i	−0.335823	+	0.924451i
$243$	3.31487	−	12.3713i	0.212649	−	0.793617i
$244$	−12.8980	−	5.99495i	−0.825709	−	0.383787i
$245$		0			0
$246$	15.7201	+	10.9928i	1.00227	+	0.700874i
$247$	−16.0141	+	9.24575i	−1.01895	+	0.588293i
$248$	21.9242	−	0.0408130i	1.39219	−	0.00259163i
$249$	−4.46952	−	2.58048i	−0.283244	−	0.163531i
$250$	−3.69928	−	0.321332i	−0.233963	−	0.0203228i
$251$	−9.65581	+	9.65581i	−0.609469	+	0.609469i	−0.942807	−	0.333338i	$-0.891825\pi$
$251$	−9.65581	+	9.65581i	−0.609469	+	0.609469i	0.333338	+	0.942807i	$0.391825\pi$
$252$		0			0
$253$	−1.51414	−	1.51414i	−0.0951931	−	0.0951931i
$254$	−6.16484	+	5.17944i	−0.386817	+	0.324987i
$255$	−5.69431	+	9.86284i	−0.356592	+	0.617635i
$256$	12.3076	+	10.2236i	0.769226	+	0.638977i
$257$	−8.38205	−	14.5181i	−0.522858	−	0.905617i	−0.999646	−	0.0265986i	$-0.991532\pi$
$257$	−8.38205	−	14.5181i	−0.522858	−	0.905617i	0.476788	−	0.879018i	$-0.341801\pi$
$258$	3.72851	+	21.0690i	0.232127	+	1.31170i
$259$		0			0
$260$	32.3158	−	11.8074i	2.00414	−	0.732266i
$261$	−0.862548	−	0.231119i	−0.0533904	−	0.0143059i
$262$	−1.56567	−	3.35216i	−0.0967274	−	0.207097i
$263$	9.07855	+	5.24150i	0.559808	+	0.323205i	0.753068	−	0.657942i	$-0.228573\pi$
$263$	9.07855	+	5.24150i	0.559808	+	0.323205i	−0.193261	+	0.981147i	$0.561906\pi$
$264$	−0.768076	+	1.33609i	−0.0472718	+	0.0822303i
$265$			41.9356i			2.57608i
$266$		0			0
$267$	−0.493626	+	0.493626i	−0.0302094	+	0.0302094i
$268$	0.0445823	+	0.502396i	0.00272330	+	0.0306887i
$269$	−6.33256	+	1.69680i	−0.386103	+	0.103456i	−0.446649	−	0.894709i	$-0.647383\pi$
$269$	−6.33256	+	1.69680i	−0.386103	+	0.103456i	0.0605458	+	0.998165i	$0.480716\pi$
$270$	8.86083	−	24.3920i	0.539253	−	1.48445i
$271$	−4.32258	−	7.48692i	−0.262578	−	0.454798i	0.704348	−	0.709854i	$-0.251239\pi$
$271$	−4.32258	−	7.48692i	−0.262578	−	0.454798i	−0.966926	+	0.255056i	$0.917906\pi$
$272$	8.27117	−	6.97539i	0.501513	−	0.422945i
$273$		0			0
$274$	−18.9804	+	3.35890i	−1.14665	+	0.202919i
$275$	−0.638295	+	2.38215i	−0.0384906	+	0.143649i
$276$	7.41341	+	10.5595i	0.446235	+	0.635609i
$277$	−2.90888	−	10.8561i	−0.174778	−	0.652279i	−0.996589	−	0.0825201i	$-0.973703\pi$
$277$	−2.90888	−	10.8561i	−0.174778	−	0.652279i	0.821812	−	0.569759i	$-0.192964\pi$
$278$	−2.51795	+	28.9875i	−0.151017	+	1.73856i
$279$			10.5303i			0.630431i
$280$		0			0
$281$			9.46552i			0.564666i	0.959317	+	0.282333i	$0.0911083\pi$
$281$			9.46552i			0.564666i	−0.959317	+	0.282333i	$0.908892\pi$
$282$	18.4819	+	1.60540i	1.10058	+	0.0956001i
$283$	−2.50560	−	9.35103i	−0.148942	−	0.555861i	−0.999548	−	0.0300568i	$-0.990431\pi$
$283$	−2.50560	−	9.35103i	−0.148942	−	0.555861i	0.850606	−	0.525804i	$-0.176235\pi$
$284$	−12.5774	−	2.20165i	−0.746332	−	0.130644i
$285$	−3.84925	+	14.3656i	−0.228010	+	0.850943i
$286$	−0.548641	−	3.10024i	−0.0324418	−	0.183321i
$287$		0			0
$288$	−4.92144	+	5.90224i	−0.289999	+	0.347793i
$289$	4.84161	+	8.38592i	0.284801	+	0.493289i
$290$	−2.87124	−	1.04303i	−0.168605	−	0.0612487i
$291$	−4.54762	+	1.21853i	−0.266586	+	0.0714316i
$292$	−1.81363	+	2.16685i	−0.106134	+	0.126805i
$293$	20.0723	−	20.0723i	1.17264	−	1.17264i	0.191059	−	0.981578i	$-0.438808\pi$
$293$	20.0723	−	20.0723i	1.17264	−	1.17264i	0.981578	−	0.191059i	$-0.0611923\pi$
$294$		0			0
$295$			33.4425i			1.94710i
$296$	4.00051	+	14.8197i	0.232525	+	0.861378i
$297$	−2.05665	−	1.18741i	−0.119339	−	0.0689004i
$298$	−8.83721	+	4.12754i	−0.511926	+	0.239102i
$299$	−25.4599	−	6.82195i	−1.47238	−	0.394524i
$300$	6.26315	−	13.4750i	0.361603	−	0.777980i
$301$		0			0
$302$	−0.186588	+	0.0330198i	−0.0107369	+	0.00190008i
$303$	−2.52103	−	4.36656i	−0.144830	−	0.250852i
$304$	8.07561	−	11.5943i	0.463168	−	0.664980i
$305$	11.6849	−	20.2389i	0.669078	−	1.15888i
$306$	3.34290	+	3.97890i	0.191101	+	0.227459i
$307$	−18.4969	−	18.4969i	−1.05568	−	1.05568i	−0.998356	−	0.0573195i	$-0.981745\pi$
$307$	−18.4969	−	18.4969i	−1.05568	−	1.05568i	−0.0573195	−	0.998356i	$-0.518255\pi$
$308$		0			0
$309$	−12.5587	+	12.5587i	−0.714441	+	0.714441i
$310$	−3.11738	+	35.8883i	−0.177055	+	2.03832i
$311$	−4.30392	−	2.48487i	−0.244053	−	0.140904i	0.372985	−	0.927837i	$-0.378334\pi$
$311$	−4.30392	−	2.48487i	−0.244053	−	0.140904i	−0.617038	+	0.786933i	$0.711668\pi$
$312$	0.0353138	+	18.9701i	0.00199925	+	1.07397i
$313$	16.3888	−	9.46210i	0.926351	−	0.534829i	0.0406956	−	0.999172i	$-0.487043\pi$
$313$	16.3888	−	9.46210i	0.926351	−	0.534829i	0.885656	+	0.464342i	$0.153709\pi$
$314$	−3.01108	+	4.30596i	−0.169925	+	0.242999i
$315$		0			0
$316$	−15.5680	+	5.68818i	−0.875768	+	0.319985i
$317$	−0.850424	+	3.17383i	−0.0477646	+	0.178260i	−0.985687	−	0.168585i	$-0.946080\pi$
$317$	−0.850424	+	3.17383i	−0.0477646	+	0.178260i	0.937923	+	0.346845i	$0.112747\pi$
$318$	−21.7325	−	7.89472i	−1.21870	−	0.442714i
$319$	−0.139772	+	0.242093i	−0.00782576	+	0.0135546i
$320$	−18.5201	+	18.6585i	−1.03531	+	1.04304i
$321$	12.5256			0.699110
$322$		0			0
$323$	−6.75636	−	6.75636i	−0.375934	−	0.375934i
$324$	4.72215	+	3.95238i	0.262341	+	0.219576i
$325$	7.85694	+	29.3225i	0.435824	+	1.62652i
$326$	11.3091	+	24.2132i	0.626352	+	1.34104i
$327$	−16.5352	+	9.54661i	−0.914399	+	0.527929i
$328$	25.9044	−	15.0203i	1.43033	−	0.829357i
$329$		0			0
$330$	−2.07516	−	1.45113i	−0.114234	−	0.0798819i
$331$	26.6522	+	7.14145i	1.46494	+	0.392530i	0.901193	−	0.433418i	$-0.142693\pi$
$331$	26.6522	+	7.14145i	1.46494	+	0.392530i	0.563747	+	0.825947i	$0.309359\pi$
$332$	−6.59366	+	4.62914i	−0.361874	+	0.254057i
$333$	−7.12152	+	1.90821i	−0.390257	+	0.104569i
$334$	4.30019	+	5.11832i	0.235296	+	0.280062i
$335$	−0.828726			−0.0452781
$336$		0			0
$337$	4.93980			0.269088			0.134544	−	0.990908i	$-0.457043\pi$
$337$	4.93980			0.269088			0.134544	+	0.990908i	$0.457043\pi$
$338$	−13.1032	−	15.5961i	−0.712719	−	0.848316i
$339$	0.0662141	−	0.0177420i	0.00359626	−	0.000963614i
$340$	10.2151	+	14.5502i	0.553990	+	0.789094i
$341$	3.18416	+	0.853194i	0.172432	+	0.0462031i
$342$	5.56156	+	3.88910i	0.300735	+	0.210299i
$343$		0			0
$344$	32.2782	+	8.58454i	1.74032	+	0.462848i
$345$	−18.3591	+	10.5996i	−0.988419	+	0.570664i
$346$	−8.89445	−	19.0433i	−0.478168	−	1.02378i
$347$	−1.94457	−	7.25722i	−0.104390	−	0.389588i	0.893885	−	0.448296i	$-0.147969\pi$
$347$	−1.94457	−	7.25722i	−0.104390	−	0.389588i	−0.998275	+	0.0587074i	$0.981302\pi$
$348$	1.08107	−	1.29162i	0.0579514	−	0.0692381i
$349$	−10.1009	−	10.1009i	−0.540687	−	0.540687i	0.383043	−	0.923730i	$-0.374876\pi$
$349$	−10.1009	−	10.1009i	−0.540687	−	0.540687i	−0.923730	+	0.383043i	$0.874876\pi$
$350$		0			0
$351$	−29.2322			−1.56030
$352$	1.38598	+	1.96637i	0.0738730	+	0.104808i
$353$	−12.0953	+	20.9496i	−0.643766	+	1.11504i	0.340819	+	0.940129i	$0.389296\pi$
$353$	−12.0953	+	20.9496i	−0.643766	+	1.11504i	−0.984585	+	0.174906i	$0.944038\pi$
$354$	−17.3311	−	6.29583i	−0.921137	−	0.334619i
$355$	5.43004	−	20.2652i	0.288196	−	1.07556i
$356$	0.373983	+	1.02356i	0.0198211	+	0.0542484i
$357$		0			0
$358$	9.07781	−	12.9816i	0.479777	−	0.686099i
$359$	−17.4845	+	10.0947i	−0.922796	+	0.532777i	−0.884526	−	0.466491i	$-0.845518\pi$
$359$	−17.4845	+	10.0947i	−0.922796	+	0.532777i	−0.0382701	+	0.999267i	$0.512185\pi$
$360$	−8.94518	−	8.91194i	−0.471453	−	0.469701i
$361$	5.64845	+	3.26114i	0.297287	+	0.171639i
$362$	0.319323	−	3.67615i	0.0167832	−	0.193214i
$363$	9.80162	−	9.80162i	0.514451	−	0.514451i
$364$		0			0
$365$	−3.28299	−	3.28299i	−0.171840	−	0.171840i
$366$	8.28874	+	9.86570i	0.433259	+	0.515688i
$367$	3.22474	−	5.58542i	0.168330	−	0.291557i	−0.769503	−	0.638644i	$-0.779496\pi$
$367$	3.22474	−	5.58542i	0.168330	−	0.291557i	0.937833	+	0.347087i	$0.112829\pi$
$368$	19.8257	−	3.54656i	1.03349	−	0.184877i
$369$	7.19113	+	12.4554i	0.374355	+	0.648402i
$370$	−24.8358	+	4.39512i	−1.29115	+	0.228491i
$371$		0			0
$372$	−18.0117	−	8.37181i	−0.933865	−	0.434058i
$373$	−23.5392	−	6.30730i	−1.21881	−	0.326580i	−0.408598	−	0.912714i	$-0.633982\pi$
$373$	−23.5392	−	6.30730i	−1.21881	−	0.326580i	−0.810214	+	0.586134i	$0.800649\pi$
$374$	1.47400	−	0.688451i	0.0762187	−	0.0355990i
$375$	2.91330	+	1.68199i	0.150442	+	0.0868578i
$376$	14.4329	−	25.1064i	0.744322	−	1.29476i
$377$			3.44099i			0.177220i
$378$		0			0
$379$	−17.7287	+	17.7287i	−0.910663	+	0.910663i	−0.996324	−	0.0856617i	$-0.972700\pi$
$379$	−17.7287	+	17.7287i	−0.910663	+	0.910663i	0.0856617	+	0.996324i	$0.472700\pi$
$380$	17.8031	+	14.9009i	0.913278	+	0.764402i
$381$	7.04601	−	1.88797i	0.360978	−	0.0967237i
$382$	28.5368	+	10.3665i	1.46007	+	0.530397i
$383$	10.8136	+	18.7298i	0.552551	+	0.957047i	0.998090	+	0.0617841i	$0.0196790\pi$
$383$	10.8136	+	18.7298i	0.552551	+	0.957047i	−0.445538	+	0.895263i	$0.646988\pi$
$384$	−6.18295	−	13.1104i	−0.315522	−	0.669037i
$385$		0			0
$386$	3.13729	+	17.7281i	0.159684	+	0.902338i
$387$	−4.15204	+	15.4956i	−0.211060	+	0.787687i
$388$	−1.26722	+	7.23930i	−0.0643335	+	0.367520i
$389$	1.31022	+	4.88980i	0.0664307	+	0.247923i	0.991154	−	0.132718i	$-0.0423703\pi$
$389$	1.31022	+	4.88980i	0.0664307	+	0.247923i	−0.924723	+	0.380640i	$0.875704\pi$
$390$	−31.0527	−	2.69734i	−1.57241	−	0.136585i
$391$		−	13.6197i		−	0.688778i
$392$		0			0
$393$			3.35181i			0.169076i
$394$	0.745350	−	8.58072i	0.0375502	−	0.432290i
$395$	−7.04858	−	26.3056i	−0.354652	−	1.32358i
$396$	−0.945693	+	0.663932i	−0.0475228	+	0.0333638i
$397$	4.18982	−	15.6366i	0.210281	−	0.784779i	−0.777494	−	0.628891i	$-0.783509\pi$
$397$	4.18982	−	15.6366i	0.210281	−	0.784779i	0.987775	−	0.155889i	$-0.0498241\pi$
$398$	8.16539	−	1.44500i	0.409294	−	0.0724315i
$399$		0			0
$400$	−14.9541	−	17.7321i	−0.747707	−	0.886604i
$401$	10.8910	+	18.8637i	0.543868	+	0.942007i	0.998677	+	0.0514182i	$0.0163742\pi$
$401$	10.8910	+	18.8637i	0.543868	+	0.942007i	−0.454809	+	0.890589i	$0.650293\pi$
$402$	0.156014	−	0.429475i	0.00778129	−	0.0214203i
$403$	39.1947	−	10.5022i	1.95243	−	0.523151i
$404$	−7.83999	+	0.695715i	−0.390054	+	0.0346131i
$405$	−7.15452	+	7.15452i	−0.355511	+	0.355511i
$406$		0			0
$407$			2.30803i			0.114405i
$408$	−9.46348	+	2.55462i	−0.468512	+	0.126473i
$409$	−10.1896	−	5.88299i	−0.503845	−	0.290895i	0.226455	−	0.974022i	$-0.427286\pi$
$409$	−10.1896	−	5.88299i	−0.503845	−	0.290895i	−0.730300	+	0.683127i	$0.760620\pi$
$410$	20.8209	+	44.5782i	1.02827	+	2.20156i
$411$	16.8675	+	4.51963i	0.832012	+	0.222937i
$412$	9.51481	+	26.0411i	0.468761	+	1.28295i
$413$		0			0
$414$	1.68570	+	9.52550i	0.0828475	+	0.468153i
$415$	−6.61869	−	11.4639i	−0.324898	−	0.562741i
$416$	26.8770	+	12.4316i	1.31775	+	0.609508i
$417$	13.1801	−	22.8286i	0.645432	−	1.11792i
$418$	1.62661	−	1.36661i	0.0795600	−	0.0668430i
$419$	9.80162	+	9.80162i	0.478840	+	0.478840i	0.904761	−	0.425920i	$-0.140050\pi$
$419$	9.80162	+	9.80162i	0.478840	+	0.478840i	−0.425920	+	0.904761i	$0.640050\pi$
$420$		0			0
$421$	−15.0848	+	15.0848i	−0.735188	+	0.735188i	−0.971642	−	0.236455i	$-0.924014\pi$
$421$	−15.0848	+	15.0848i	−0.735188	+	0.735188i	0.236455	+	0.971642i	$0.424014\pi$
$422$	3.42738	+	0.297714i	0.166842	+	0.0144925i
$423$	12.0458	+	6.95463i	0.585685	+	0.338145i
$424$	−25.4748	+	25.5698i	−1.23717	+	1.24178i
$425$	−13.5845	+	7.84300i	−0.658944	+	0.380441i
$426$	9.47989	+	6.62912i	0.459302	+	0.321182i
$427$		0			0
$428$	8.24135	−	17.7311i	0.398361	−	0.857063i
$429$	−0.738233	+	2.75512i	−0.0356422	+	0.133019i
$430$	−18.7379	+	51.5816i	−0.903623	+	2.48749i
$431$	−2.24452	+	3.88762i	−0.108115	+	0.187260i	−0.915006	−	0.403439i	$-0.867815\pi$
$431$	−2.24452	+	3.88762i	−0.108115	+	0.187260i	0.806892	+	0.590699i	$0.201148\pi$
$432$	20.2204	−	9.49008i	0.972852	−	0.456592i
$433$	24.0001			1.15337			0.576685	−	0.816966i	$-0.304346\pi$
$433$	24.0001			1.15337			0.576685	+	0.816966i	$0.304346\pi$
$434$		0			0
$435$	1.95693	+	1.95693i	0.0938277	+	0.0938277i
$436$	2.63452	+	29.6883i	0.126171	+	1.42181i
$437$	−4.60333	−	17.1799i	−0.220207	−	0.821824i
$438$	2.31941	−	1.08331i	0.110826	−	0.0517627i
$439$	−12.5085	+	7.22181i	−0.597000	+	0.344678i	−0.767861	−	0.640617i	$-0.778679\pi$
$439$	−12.5085	+	7.22181i	−0.597000	+	0.344678i	0.170860	+	0.985295i	$0.445345\pi$
$440$	−3.41958	+	1.98279i	−0.163022	+	0.0945258i
$441$		0			0
$442$	11.4759	−	16.4109i	0.545851	−	0.780587i
$443$	7.15743	+	1.91783i	0.340060	+	0.0911187i	0.424808	−	0.905284i	$-0.360342\pi$
$443$	7.15743	+	1.91783i	0.340060	+	0.0911187i	−0.0847478	+	0.996402i	$0.527008\pi$
$444$	2.39784	−	13.6982i	0.113797	−	0.650089i
$445$	−1.72953	+	0.463426i	−0.0819876	+	0.0219685i
$446$	29.4334	−	24.7287i	1.39371	−	1.17094i
$447$	8.83630			0.417943
$448$		0			0
$449$	19.7284			0.931041			0.465520	−	0.885037i	$-0.345867\pi$
$449$	19.7284			0.931041			0.465520	+	0.885037i	$0.345867\pi$
$450$	8.53014	−	7.16666i	0.402114	−	0.337840i
$451$	4.34893	−	1.16529i	0.204783	−	0.0548715i
$452$	0.0184510	−	0.105405i	0.000867861	−	0.00495786i
$453$	0.165817	+	0.0444304i	0.00779074	+	0.00208752i
$454$	−17.2989	+	24.7380i	−0.811876	+	1.16101i
$455$		0			0
$456$	−11.0738	+	6.42096i	−0.518577	+	0.300689i
$457$	−1.10811	+	0.639767i	−0.0518351	+	0.0299270i	−0.525694	−	0.850674i	$-0.676194\pi$
$457$	−1.10811	+	0.639767i	−0.0518351	+	0.0299270i	0.473858	+	0.880601i	$0.342861\pi$
$458$	3.66079	−	1.70982i	0.171058	−	0.0798947i
$459$	−3.90943	−	14.5902i	−0.182477	−	0.681012i
$460$	2.92511	+	32.9630i	0.136384	+	1.53691i
$461$	6.44148	+	6.44148i	0.300009	+	0.300009i	0.841017	−	0.541008i	$-0.181957\pi$
$461$	6.44148	+	6.44148i	0.300009	+	0.300009i	−0.541008	+	0.841017i	$0.681957\pi$
$462$		0			0
$463$	12.5243			0.582055			0.291028	−	0.956715i	$-0.406003\pi$
$463$	12.5243			0.582055			0.291028	+	0.956715i	$0.406003\pi$
$464$	−1.11710	−	2.38018i	−0.0518600	−	0.110497i
$465$	16.3178	−	28.2632i	0.756718	−	1.31067i
$466$	8.02521	−	22.0917i	0.371761	−	1.02338i
$467$	−9.53643	+	35.5905i	−0.441294	+	1.64693i	0.284247	+	0.958751i	$0.408256\pi$
$467$	−9.53643	+	35.5905i	−0.441294	+	1.64693i	−0.725541	+	0.688179i	$0.758410\pi$
$468$	−5.99495	+	12.8980i	−0.277117	+	0.596209i
$469$		0			0
$470$	38.9944	+	27.2682i	1.79868	+	1.25779i
$471$	4.12242	−	2.38008i	0.189951	−	0.109668i
$472$	−20.3155	+	20.3913i	−0.935096	+	0.938584i
$473$	4.34918	+	2.51100i	0.199976	+	0.115456i
$474$	14.9595	+	1.29943i	0.687111	+	0.0596848i
$475$	−14.4846	+	14.4846i	−0.664597	+	0.664597i
$476$		0			0
$477$	−12.2585	−	12.2585i	−0.561277	−	0.561277i
$478$	2.35402	−	1.97775i	0.107670	−	0.0904601i
$479$	−8.42003	+	14.5839i	−0.384721	+	0.666357i	−0.991730	−	0.128338i	$-0.959036\pi$
$479$	−8.42003	+	14.5839i	−0.384721	+	0.666357i	0.607009	+	0.794695i	$0.292369\pi$
$480$	22.3553	−	8.21528i	1.02037	−	0.374975i
$481$	14.2050	+	24.6039i	0.647694	+	1.12184i
$482$	−3.41008	−	19.2696i	−0.155325	−	0.877707i
$483$		0			0
$484$	−7.42596	−	20.3241i	−0.337543	−	0.923824i
$485$	−11.6642	−	3.12542i	−0.529645	−	0.141918i
$486$	7.66498	+	16.4110i	0.347690	+	0.744418i
$487$	20.4526	+	11.8083i	0.926795	+	0.535086i	0.885797	−	0.464074i	$-0.153613\pi$
$487$	20.4526	+	11.8083i	0.926795	+	0.535086i	0.0409987	+	0.999159i	$0.486946\pi$
$488$	19.4194	−	5.24219i	0.879076	−	0.237303i
$489$		−	24.2106i		−	1.09484i
$490$		0			0
$491$	−3.03082	+	3.03082i	−0.136779	+	0.136779i	−0.772181	−	0.635402i	$-0.780834\pi$
$491$	−3.03082	+	3.03082i	−0.136779	+	0.136779i	0.635402	+	0.772181i	$0.280834\pi$
$492$	−27.0217	+	2.39789i	−1.21823	+	0.108105i
$493$	−1.71744	+	0.460188i	−0.0773498	+	0.0207258i
$494$	8.92889	−	24.5794i	0.401730	−	1.10588i
$495$	−0.949282	−	1.64420i	−0.0426670	−	0.0739015i
$496$	−23.7021	+	19.9889i	−1.06425	+	0.897526i
$497$		0			0
$498$	7.18702	−	1.27186i	0.322058	−	0.0569936i
$499$	−2.55853	+	9.54857i	−0.114536	+	0.427453i	−0.999252	−	0.0386774i	$-0.987686\pi$
$499$	−2.55853	+	9.54857i	−0.114536	+	0.427453i	0.884716	+	0.466130i	$0.154352\pi$
$500$	4.29785	−	3.01734i	0.192206	−	0.134940i
$501$	−1.56748	−	5.84990i	−0.0700296	−	0.261354i
$502$	1.67118	−	19.2392i	0.0745884	−	0.858686i
$503$			23.6060i			1.05254i	0.850318	+	0.526269i	$0.176410\pi$
$503$			23.6060i			1.05254i	−0.850318	+	0.526269i	$0.823590\pi$
$504$		0			0
$505$		−	12.9324i		−	0.575486i
$506$	3.01692	+	0.262060i	0.134118	+	0.0116500i
$507$	4.77628	+	17.8253i	0.212122	+	0.791650i
$508$	1.96341	−	11.2164i	0.0871124	−	0.497649i
$509$	4.25539	−	15.8813i	0.188617	−	0.703928i	−0.805210	−	0.592989i	$-0.797948\pi$
$509$	4.25539	−	15.8813i	0.188617	−	0.703928i	0.993827	−	0.110939i	$-0.0353857\pi$
$510$	−2.80661	−	15.8595i	−0.124279	−	0.702272i
$511$		0			0
$512$	−22.6271	+	0.126366i	−0.999984	+	0.00558463i
$513$	−9.86268	−	17.0827i	−0.435448	−	0.754218i
$514$	22.2833	+	8.09480i	0.982874	+	0.357046i
$515$	−44.0023	+	11.7904i	−1.93898	+	0.519547i
$516$	−23.2039	−	19.4213i	−1.02149	−	0.854976i
$517$	3.07894	−	3.07894i	0.135411	−	0.135411i
$518$		0			0
$519$			19.0414i			0.835824i
$520$	−24.2498	+	42.1830i	−1.06342	+	1.84985i
$521$	−38.6498	−	22.3144i	−1.69328	−	0.977614i	−0.951842	−	0.306588i	$-0.900813\pi$
$521$	−38.6498	−	22.3144i	−1.69328	−	0.977614i	−0.741434	−	0.671026i	$-0.765854\pi$
$522$	1.14421	−	0.534417i	0.0500806	−	0.0233908i
$523$	−14.4133	−	3.86203i	−0.630250	−	0.168875i	−0.0704666	−	0.997514i	$-0.522449\pi$
$523$	−14.4133	−	3.86203i	−0.630250	−	0.168875i	−0.559783	+	0.828639i	$0.689115\pi$
$524$	4.74478	+	2.20536i	0.207277	+	0.0963417i
$525$		0			0
$526$	−14.5984	+	2.58343i	−0.636520	+	0.112643i
$527$	10.4836	+	18.1581i	0.456671	+	0.790977i
$528$	−0.383789	−	2.14542i	−0.0167023	−	0.0933675i
$529$	1.17612	−	2.03710i	0.0511357	−	0.0885696i
$530$	−38.1493	−	45.4073i	−1.65710	−	1.97237i
$531$	−9.77581	−	9.77581i	−0.424234	−	0.424234i
$532$		0			0
$533$	39.1882	−	39.1882i	1.69743	−	1.69743i
$534$	0.0854343	−	0.983548i	0.00369710	−	0.0425623i
$535$	27.8228	+	16.0635i	1.20288	+	0.694485i
$536$	−0.505308	−	0.503430i	−0.0218260	−	0.0217449i
$537$	−12.4283	+	7.17546i	−0.536319	+	0.309644i
$538$	5.31320	−	7.59807i	0.229068	−	0.327576i
$539$		0			0
$540$	12.5953	+	34.4721i	0.542016	+	1.48344i
$541$	8.17870	−	30.5233i	0.351630	−	1.31230i	−0.533043	−	0.846088i	$-0.678952\pi$
$541$	8.17870	−	30.5233i	0.351630	−	1.31230i	0.884673	−	0.466212i	$-0.154382\pi$
$542$	11.4914	+	4.17444i	0.493596	+	0.179308i
$543$	−1.67148	+	2.89508i	−0.0717299	+	0.124240i
$544$	−2.61032	+	15.0772i	−0.111916	+	0.646431i
$545$	−48.9723			−2.09774
$546$		0			0
$547$	13.2104	+	13.2104i	0.564836	+	0.564836i	0.930677	−	0.365841i	$-0.119219\pi$
$547$	13.2104	+	13.2104i	0.564836	+	0.564836i	−0.365841	+	0.930677i	$0.619219\pi$
$548$	17.4961	−	20.9037i	0.747396	−	0.892960i
$549$	2.50047	+	9.33189i	0.106718	+	0.398275i
$550$	−1.47593	−	3.16002i	−0.0629339	−	0.134744i
$551$	−2.01084	+	1.16096i	−0.0856646	+	0.0494585i
$552$	−17.6333	−	4.68966i	−0.750522	−	0.199605i
$553$		0			0
$554$	13.0256	+	9.10858i	0.553405	+	0.386987i
$555$	22.0711	+	5.91393i	0.936865	+	0.251032i
$556$	−23.6439	−	33.6779i	−1.00272	−	1.42826i
$557$	12.6326	−	3.38489i	0.535260	−	0.143423i	0.0189440	−	0.999821i	$-0.493970\pi$
$557$	12.6326	−	3.38489i	0.535260	−	0.143423i	0.516316	+	0.856398i	$0.327303\pi$
$558$	−9.57951	−	11.4020i	−0.405533	−	0.482687i
$559$	61.8171			2.61459
$560$		0			0
$561$	−1.47385			−0.0622259
$562$	−8.61089	−	10.2491i	−0.363228	−	0.432334i
$563$	6.41791	−	1.71967i	0.270483	−	0.0724756i	−0.121028	−	0.992649i	$-0.538619\pi$
$563$	6.41791	−	1.71967i	0.270483	−	0.0724756i	0.391511	+	0.920173i	$0.371953\pi$
$564$	−21.4724	+	15.0749i	−0.904149	+	0.634766i
$565$	0.169833	+	0.0455066i	0.00714493	+	0.00191448i
$566$	11.2198	+	7.84579i	0.471602	+	0.329783i
$567$		0			0
$568$	15.6215	−	9.05790i	0.655464	−	0.380061i
$569$	−37.3188	+	21.5460i	−1.56448	+	0.903256i	−0.567691	+	0.823242i	$0.692163\pi$
$569$	−37.3188	+	21.5460i	−1.56448	+	0.903256i	−0.996794	+	0.0800139i	$0.974504\pi$
$570$	−8.90062	−	19.0566i	−0.372806	−	0.798191i
$571$	6.10236	+	22.7743i	0.255376	+	0.953075i	0.967881	+	0.251408i	$0.0808937\pi$
$571$	6.10236	+	22.7743i	0.255376	+	0.953075i	−0.712505	+	0.701667i	$0.752440\pi$
$572$	3.41439	+	2.85780i	0.142763	+	0.119491i
$573$	−19.4497	−	19.4497i	−0.812521	−	0.812521i
$574$		0			0
$575$	−29.1985			−1.21766
$576$	−0.0404627	−	10.8680i	−0.00168595	−	0.452831i
$577$	16.6532	−	28.8442i	0.693283	−	1.20080i	−0.277473	−	0.960733i	$-0.589497\pi$
$577$	16.6532	−	28.8442i	0.693283	−	1.20080i	0.970756	−	0.240068i	$-0.0771696\pi$
$578$	−12.8712	−	4.67569i	−0.535371	−	0.194483i
$579$	4.22144	−	15.7546i	0.175437	−	0.654740i
$580$	4.05779	−	1.48262i	0.168491	−	0.0615625i
$581$		0			0
$582$	3.81559	−	5.45643i	0.158161	−	0.226176i
$583$	−4.69996	+	2.71352i	−0.194653	+	0.112383i
$584$	−0.00743898	−	3.99611i	−0.000307827	−	0.165360i
$585$	−20.2389	−	11.6849i	−0.836776	−	0.483113i
$586$	−3.47402	+	39.9941i	−0.143510	+	1.65214i
$587$	−9.82134	+	9.82134i	−0.405370	+	0.405370i	−0.880121	−	0.474750i	$-0.842538\pi$
$587$	−9.82134	+	9.82134i	−0.405370	+	0.405370i	0.474750	+	0.880121i	$0.342538\pi$
$588$		0			0
$589$	19.3612	+	19.3612i	0.797763	+	0.797763i
$590$	−30.4230	−	36.2111i	−1.25250	−	1.49079i
$591$	−3.90149	+	6.75758i	−0.160486	+	0.277970i
$592$	−17.8133	−	12.4073i	−0.732124	−	0.509935i
$593$	−14.2045	−	24.6029i	−0.583307	−	1.01032i	−0.995084	−	0.0990333i	$-0.968425\pi$
$593$	−14.2045	−	24.6029i	−0.583307	−	1.01032i	0.411777	−	0.911285i	$-0.364908\pi$
$594$	3.30711	−	0.585249i	0.135692	−	0.0240131i
$595$		0			0
$596$	5.81395	−	12.5086i	0.238148	−	0.512370i
$597$	−7.25641	−	1.94435i	−0.296985	−	0.0795769i
$598$	33.7736	−	15.7744i	1.38111	−	0.645064i
$599$	−1.92076	−	1.10895i	−0.0784803	−	0.0453106i	0.460246	−	0.887791i	$-0.347761\pi$
$599$	−1.92076	−	1.10895i	−0.0784803	−	0.0453106i	−0.538727	+	0.842481i	$0.681094\pi$
$600$	5.47671	+	20.2882i	0.223586	+	0.828263i
$601$		−	41.6237i		−	1.69787i	−0.528501	−	0.848933i	$-0.677246\pi$
$601$		−	41.6237i		−	1.69787i	0.528501	−	0.848933i	$-0.322754\pi$
$602$		0			0
$603$	0.242251	−	0.242251i	0.00986521	−	0.00986521i
$604$	0.171996	−	0.205494i	0.00699842	−	0.00836145i
$605$	34.3422	−	9.20196i	1.39621	−	0.374113i
$606$	6.70205	+	2.43464i	0.272252	+	0.0989003i
$607$	−3.58511	−	6.20960i	−0.145515	−	0.252040i	0.784050	−	0.620698i	$-0.213151\pi$
$607$	−3.58511	−	6.20960i	−0.145515	−	0.252040i	−0.929565	+	0.368658i	$0.879817\pi$
$608$	1.80331	+	19.9006i	0.0731340	+	0.807077i
$609$		0			0
$610$	5.75927	+	32.5443i	0.233186	+	1.31768i
$611$	13.8721	−	51.7716i	0.561207	−	2.09445i
$612$	−7.23930	−	1.26722i	−0.292631	−	0.0512244i
$613$	−6.61205	−	24.6765i	−0.267058	−	0.996674i	−0.960979	−	0.276623i	$-0.910785\pi$
$613$	−6.61205	−	24.6765i	−0.267058	−	0.996674i	0.693920	−	0.720052i	$-0.255882\pi$
$614$	36.8551	+	3.20136i	1.48735	+	0.129196i
$615$		−	44.5736i		−	1.79738i
$616$		0			0
$617$		−	17.1272i		−	0.689513i	−0.938692	−	0.344757i	$-0.887961\pi$
$617$		−	17.1272i		−	0.689513i	0.938692	−	0.344757i	$-0.112039\pi$
$618$	2.17360	−	25.0232i	0.0874351	−	1.00658i
$619$	2.45015	+	9.14409i	0.0984799	+	0.367532i	0.997524	−	0.0703260i	$-0.0224040\pi$
$619$	2.45015	+	9.14409i	0.0984799	+	0.367532i	−0.899044	+	0.437858i	$0.855737\pi$
$620$	−29.2726	−	41.6953i	−1.17561	−	1.67452i
$621$	7.27716	−	27.1587i	0.292022	−	1.08984i
$622$	6.92074	−	1.22474i	0.277496	−	0.0491077i
$623$		0			0
$624$	−17.2955	−	20.5084i	−0.692374	−	0.820993i
$625$	−10.1833	−	17.6380i	−0.407333	−	0.705521i
$626$	−9.13783	+	25.1545i	−0.365221	+	1.00538i
$627$	−1.85911	+	0.498146i	−0.0742456	+	0.0198940i
$628$	−0.656817	−	7.40165i	−0.0262099	−	0.295358i
$629$	−10.3804	+	10.3804i	−0.413893	+	0.413893i
$630$		0			0
$631$			18.0767i			0.719622i	0.933025	+	0.359811i	$0.117159\pi$
$631$			18.0767i			0.719622i	−0.933025	+	0.359811i	$0.882841\pi$
$632$	11.6822	−	20.3215i	0.464694	−	0.808344i
$633$	−2.69917	−	1.55837i	−0.107282	−	0.0619395i
$634$	−1.96644	−	4.21022i	−0.0780972	−	0.167209i
$635$	18.0723	+	4.84247i	0.717179	+	0.192168i
$636$	30.7136	−	11.2220i	1.21787	−	0.444982i
$637$		0			0
$638$	−0.0688910	−	0.389288i	−0.00272742	−	0.0154120i
$639$	4.33656	+	7.51115i	0.171552	+	0.297136i
$640$	3.07945	−	37.0512i	0.121726	−	1.46458i
$641$	−8.50035	+	14.7230i	−0.335744	+	0.581525i	−0.983627	−	0.180214i	$-0.942321\pi$
$641$	−8.50035	+	14.7230i	−0.335744	+	0.581525i	0.647884	+	0.761739i	$0.275654\pi$
$642$	−13.5625	+	11.3947i	−0.535270	+	0.449711i
$643$	−5.91368	−	5.91368i	−0.233213	−	0.233213i	0.580820	−	0.814032i	$-0.302732\pi$
$643$	−5.91368	−	5.91368i	−0.233213	−	0.233213i	−0.814032	+	0.580820i	$0.802732\pi$
$644$		0			0
$645$	35.1561	−	35.1561i	1.38427	−	1.38427i
$646$	13.4620	+	1.16936i	0.529656	+	0.0460077i
$647$	−33.8617	−	19.5501i	−1.33124	−	0.768592i	−0.345751	−	0.938326i	$-0.612376\pi$
$647$	−33.8617	−	19.5501i	−1.33124	−	0.768592i	−0.985490	+	0.169734i	$0.945709\pi$
$648$	−8.70859	+	0.0162115i	−0.342106	+	0.000636849i
$649$	−3.74809	+	2.16396i	−0.147126	+	0.0849430i
$650$	−35.1824	−	24.6024i	−1.37997	−	0.964987i
$651$		0			0
$652$	−34.2723	−	15.9297i	−1.34221	−	0.623854i
$653$	−5.56236	+	20.7590i	−0.217672	+	0.812362i	0.767537	+	0.641005i	$0.221482\pi$
$653$	−5.56236	+	20.7590i	−0.217672	+	0.812362i	−0.985209	+	0.171358i	$0.945185\pi$
$654$	9.21944	−	25.3792i	0.360509	−	0.992405i
$655$	−4.29854	+	7.44529i	−0.167958	+	0.290912i
$656$	−14.3848	+	39.8293i	−0.561633	+	1.55507i
$657$	1.91935			0.0748810
$658$		0			0
$659$	−6.07124	−	6.07124i	−0.236502	−	0.236502i	0.578898	−	0.815400i	$-0.303483\pi$
$659$	−6.07124	−	6.07124i	−0.236502	−	0.236502i	−0.815400	+	0.578898i	$0.803483\pi$
$660$	3.56707	−	0.316539i	0.138848	−	0.0123213i
$661$	−2.82377	−	10.5385i	−0.109832	−	0.409899i	0.889016	−	0.457875i	$-0.151389\pi$
$661$	−2.82377	−	10.5385i	−0.109832	−	0.409899i	−0.998848	+	0.0479766i	$0.984723\pi$
$662$	−35.3553	+	16.5132i	−1.37412	+	0.641803i
$663$	−15.7114	+	9.07098i	−0.610180	+	0.352288i
$664$	2.92835	−	11.0107i	0.113642	−	0.427298i
$665$		0			0
$666$	5.97517	−	8.54470i	0.231533	−	0.331100i
$667$	−3.19691	−	0.856610i	−0.123785	−	0.0331681i
$668$	−9.31238	−	1.63011i	−0.360307	−	0.0630709i
$669$	−33.6404	+	9.01392i	−1.30061	+	0.348498i
$670$	0.897333	−	0.753901i	0.0346670	−	0.0291257i
$671$	3.02439			0.116755
$672$		0			0
$673$	36.3104			1.39966			0.699831	−	0.714308i	$-0.253259\pi$
$673$	36.3104			1.39966			0.699831	+	0.714308i	$0.253259\pi$
$674$	−5.34875	+	4.49379i	−0.206026	+	0.173094i
$675$	−31.2791	+	8.38120i	−1.20393	+	0.322593i
$676$	28.3759	+	4.96713i	1.09138	+	0.191044i
$677$	32.6507	+	8.74872i	1.25487	+	0.336241i	0.824215	−	0.566277i	$-0.191617\pi$
$677$	32.6507	+	8.74872i	1.25487	+	0.336241i	0.430652	+	0.902518i	$0.358284\pi$
$678$	−0.0555556	+	0.0794465i	−0.00213360	+	0.00305113i
$679$		0			0
$680$	−24.2972	−	6.46196i	−0.931755	−	0.247805i
$681$	23.6836	−	13.6737i	0.907556	−	0.523978i
$682$	−4.22393	+	1.97284i	−0.161743	+	0.0755440i
$683$	3.33399	+	12.4426i	0.127572	+	0.476104i	0.999918	−	0.0127838i	$-0.00406932\pi$
$683$	3.33399	+	12.4426i	0.127572	+	0.476104i	−0.872347	+	0.488888i	$0.837403\pi$
$684$	−9.55994	+	0.848343i	−0.365533	+	0.0324372i
$685$	31.6711	+	31.6711i	1.21009	+	1.21009i
$686$		0			0
$687$	−3.66041			−0.139653
$688$	−42.7598	+	20.0686i	−1.63020	+	0.765108i
$689$	−33.4015	+	57.8530i	−1.27249	+	2.20402i
$690$	10.2364	−	28.1785i	0.389691	−	1.07274i
$691$	−10.6306	+	39.6740i	−0.404408	+	1.50927i	0.400738	+	0.916193i	$0.368754\pi$
$691$	−10.6306	+	39.6740i	−0.404408	+	1.50927i	−0.805145	+	0.593077i	$0.797913\pi$
$692$	26.9547	+	12.5285i	1.02466	+	0.476262i
$693$		0			0
$694$	8.70753	+	6.08903i	0.330533	+	0.231136i
$695$	58.5532	−	33.8057i	2.22105	−	1.28232i
$696$	0.00443424	+	2.38201i	0.000168079	+	0.0902898i
$697$	24.8003	+	14.3185i	0.939378	+	0.542350i
$698$	20.1259	+	1.74821i	0.761778	+	0.0661707i
$699$	−15.0569	+	15.0569i	−0.569505	+	0.569505i
$700$		0			0
$701$	−13.5706	−	13.5706i	−0.512556	−	0.512556i	0.402753	−	0.915309i	$-0.368054\pi$
$701$	−13.5706	−	13.5706i	−0.512556	−	0.512556i	−0.915309	+	0.402753i	$0.868054\pi$
$702$	31.6522	−	26.5929i	1.19464	−	1.00368i
$703$	−9.58530	+	16.6022i	−0.361517	+	0.626165i
$704$	−3.28955	−	0.868319i	−0.123980	−	0.0327260i
$705$	−21.5538	−	37.3323i	−0.811765	−	1.40602i
$706$	−5.96151	−	33.6871i	−0.224364	−	1.26783i
$707$		0			0
$708$	24.4933	−	8.94925i	0.920513	−	0.336334i
$709$	−15.8360	−	4.24324i	−0.594733	−	0.159358i	−0.0511177	−	0.998693i	$-0.516278\pi$
$709$	−15.8360	−	4.24324i	−0.594733	−	0.159358i	−0.543616	+	0.839334i	$0.682945\pi$
$710$	12.5559	+	26.8826i	0.471214	+	1.00889i
$711$	9.75001	+	5.62917i	0.365654	+	0.211110i
$712$	−1.33609	−	0.768076i	−0.0500719	−	0.0287849i
$713$			39.0290i			1.46165i
$714$		0			0
$715$	−5.17313	+	5.17313i	−0.193464	+	0.193464i
$716$	1.98017	+	22.3145i	0.0740025	+	0.833931i
$717$	−2.69049	+	0.720914i	−0.100478	+	0.0269230i
$718$	9.74873	−	26.8362i	0.363819	−	1.00152i
$719$	−20.4180	−	35.3651i	−0.761464	−	1.31889i	−0.942096	−	0.335344i	$-0.891148\pi$
$719$	−20.4180	−	35.3651i	−0.761464	−	1.31889i	0.180632	−	0.983551i	$-0.442186\pi$
$720$	17.7930	+	1.51220i	0.663106	+	0.0563562i
$721$		0			0
$722$	−9.08276	+	1.60735i	−0.338025	+	0.0598193i
$723$	−4.58850	+	17.1245i	−0.170648	+	0.636867i
$724$	2.99847	+	4.27097i	0.111437	+	0.158729i
$725$	0.986570	+	3.68193i	0.0366403	+	0.136743i
$726$	−1.69642	+	19.5297i	−0.0629599	+	0.724815i
$727$			29.6262i			1.09878i	0.835567	+	0.549388i	$0.185139\pi$
$727$			29.6262i			1.09878i	−0.835567	+	0.549388i	$0.814861\pi$
$728$		0			0
$729$		−	25.6462i		−	0.949859i
$730$	6.54135	+	0.568205i	0.242106	+	0.0210302i
$731$	8.26724	+	30.8538i	0.305775	+	1.14117i
$732$	−17.9499	−	3.14208i	−0.663446	−	0.116135i
$733$	3.10596	−	11.5916i	0.114721	−	0.428146i	−0.884545	−	0.466456i	$-0.845531\pi$
$733$	3.10596	−	11.5916i	0.114721	−	0.428146i	0.999266	+	0.0383098i	$0.0121974\pi$
$734$	1.58941	+	8.98140i	0.0586662	+	0.331510i
$735$		0			0
$736$	−18.2406	+	21.8758i	−0.672358	+	0.806353i
$737$	−0.0536243	−	0.0928801i	−0.00197528	−	0.00342128i
$738$	−19.1173	−	6.94469i	−0.703716	−	0.255637i
$739$	29.6977	−	7.95747i	1.09245	−	0.292720i	0.332762	−	0.943011i	$-0.392019\pi$
$739$	29.6977	−	7.95747i	1.09245	−	0.292720i	0.759686	+	0.650290i	$0.225353\pi$
$740$	22.8936	−	27.3524i	0.841586	−	1.00549i
$741$	−16.7524	+	16.7524i	−0.615415	+	0.615415i
$742$		0			0
$743$		−	33.3740i		−	1.22437i	−0.790714	−	0.612186i	$-0.790290\pi$
$743$		−	33.3740i		−	1.22437i	0.790714	−	0.612186i	$-0.209710\pi$
$744$	27.1188	−	7.32059i	0.994223	−	0.268386i
$745$	19.6278	+	11.3321i	0.719109	+	0.415178i
$746$	31.2257	−	14.5844i	1.14325	−	0.533972i
$747$	5.28585	+	1.41634i	0.193399	+	0.0518211i
$748$	−0.969735	+	2.08636i	−0.0354570	+	0.0762849i
$749$		0			0
$750$	−4.68461	+	0.829020i	−0.171058	+	0.0302715i
$751$	22.4412	+	38.8692i	0.818889	+	1.41836i	0.906501	+	0.422203i	$0.138743\pi$
$751$	22.4412	+	38.8692i	0.818889	+	1.41836i	−0.0876116	+	0.996155i	$0.527923\pi$
$752$	7.21178	+	40.3147i	0.262987	+	1.47012i
$753$	−8.74770	+	15.1515i	−0.318784	+	0.552150i
$754$	−3.13031	−	3.72586i	−0.113999	−	0.135688i
$755$	0.311344	+	0.311344i	0.0113310	+	0.0113310i
$756$		0			0
$757$	1.21561	−	1.21561i	0.0441819	−	0.0441819i	−0.684671	−	0.728853i	$-0.740054\pi$
$757$	1.21561	−	1.21561i	0.0441819	−	0.0441819i	0.728853	+	0.684671i	$0.240054\pi$
$758$	3.06840	−	35.3244i	0.111449	−	1.28304i
$759$	−2.37592	−	1.37174i	−0.0862404	−	0.0497909i
$760$	−32.8325	+	0.0611194i	−1.19096	+	0.00221704i
$761$	−1.13480	+	0.655177i	−0.0411364	+	0.0237501i	−0.520427	−	0.853906i	$-0.674227\pi$
$761$	−1.13480	+	0.655177i	−0.0411364	+	0.0237501i	0.479291	+	0.877656i	$0.340894\pi$
$762$	−5.91181	+	8.45410i	−0.214162	+	0.306260i
$763$		0			0
$764$	−40.3298	+	14.7356i	−1.45908	+	0.533114i
$765$	3.12542	−	11.6642i	0.113000	−	0.421721i
$766$	−28.7475	−	10.4431i	−1.03869	−	0.377323i
$767$	−26.6368	+	46.1362i	−0.961798	+	1.66588i
$768$	18.6215	+	8.57106i	0.671945	+	0.309282i
$769$	−12.6459			−0.456022			−0.228011	−	0.973659i	$-0.573222\pi$
$769$	−12.6459			−0.456022			−0.228011	+	0.973659i	$0.573222\pi$
$770$		0			0
$771$	−15.1875	−	15.1875i	−0.546963	−	0.546963i
$772$	−19.5245	−	16.3417i	−0.702702	−	0.588152i
$773$	−4.26539	−	15.9187i	−0.153415	−	0.572554i	−0.999236	−	0.0390865i	$-0.987555\pi$
$773$	−4.26539	−	15.9187i	−0.153415	−	0.572554i	0.845820	−	0.533468i	$-0.179111\pi$
$774$	−9.60077	−	20.5556i	−0.345092	−	0.738856i
$775$	38.9280	−	22.4751i	1.39834	−	0.807329i
$776$	−5.21354	−	8.99142i	−0.187155	−	0.322773i
$777$		0			0
$778$	−5.86699	−	4.10269i	−0.210342	−	0.147088i
$779$	36.1225	+	9.67900i	1.29422	+	0.346786i
$780$	36.0772	−	25.3283i	1.29177	−	0.906899i
$781$	2.62260	−	0.702723i	0.0938439	−	0.0251454i
$782$	12.3900	+	14.7472i	0.443066	+	0.527360i
$783$	−3.67059			−0.131176
$784$		0			0
$785$	12.2094			0.435771
$786$	−3.04918	−	3.62929i	−0.108761	−	0.129453i
$787$	18.7439	−	5.02241i	0.668147	−	0.179029i	0.0912269	−	0.995830i	$-0.470921\pi$
$787$	18.7439	−	5.02241i	0.668147	−	0.179029i	0.576920	+	0.816801i	$0.304254\pi$
$788$	6.99892	+	9.96913i	0.249326	+	0.355136i
$789$	12.9733	+	3.47618i	0.461861	+	0.123755i
$790$	31.5626	+	22.0712i	1.12295	+	0.785259i
$791$		0			0
$792$	0.419997	−	1.57920i	0.0149239	−	0.0561145i
$793$	32.2404	−	18.6140i	1.14489	−	0.661002i
$794$	9.68812	+	20.7426i	0.343819	+	0.736129i
$795$	13.9059	+	51.8975i	0.493191	+	1.84061i
$796$	−7.52684	+	8.99277i	−0.266782	+	0.318740i
$797$	13.4205	+	13.4205i	0.475377	+	0.475377i	0.903650	−	0.428272i	$-0.140878\pi$
$797$	13.4205	+	13.4205i	0.475377	+	0.475377i	−0.428272	+	0.903650i	$0.640878\pi$
$798$		0			0
$799$	27.6951			0.979782
$800$	32.3232	+	5.59611i	1.14280	+	0.197852i
$801$	0.370104	−	0.641038i	0.0130770	−	0.0226500i
$802$	−28.9531	−	10.5177i	−1.02237	−	0.371393i
$803$	0.155511	−	0.580377i	0.00548788	−	0.0204810i
$804$	0.221768	+	0.606958i	0.00782116	+	0.0214058i
$805$		0			0
$806$	−32.8855	+	47.0274i	−1.15834	+	1.65647i
$807$	−7.27421	+	4.19977i	−0.256064	+	0.147839i
$808$	7.85613	−	7.88543i	0.276378	−	0.277409i
$809$	−19.3727	−	11.1848i	−0.681109	−	0.393238i	0.119164	−	0.992875i	$-0.461979\pi$
$809$	−19.3727	−	11.1848i	−0.681109	−	0.393238i	−0.800273	+	0.599636i	$0.795312\pi$
$810$	1.23827	−	14.2554i	0.0435084	−	0.500882i
$811$	−5.78629	+	5.78629i	−0.203184	+	0.203184i	−0.801363	−	0.598179i	$-0.795891\pi$
$811$	−5.78629	+	5.78629i	−0.203184	+	0.203184i	0.598179	+	0.801363i	$0.295891\pi$
$812$		0			0
$813$	−7.83209	−	7.83209i	−0.274683	−	0.274683i
$814$	−2.09964	−	2.49910i	−0.0735923	−	0.0875934i
$815$	31.0490	−	53.7785i	1.08760	−	1.88378i
$816$	7.92296	−	11.3751i	0.277359	−	0.398210i
$817$	20.8565	+	36.1246i	0.729678	+	1.26384i
$818$	16.3850	−	2.89961i	0.572889	−	0.101382i
$819$		0			0
$820$	−63.0978	−	29.3277i	−2.20347	−	1.02417i
$821$	28.0902	+	7.52676i	0.980356	+	0.262686i	0.713195	−	0.700966i	$-0.247248\pi$
$821$	28.0902	+	7.52676i	0.980356	+	0.262686i	0.267162	+	0.963652i	$0.413914\pi$
$822$	−22.3754	+	10.4507i	−0.780433	+	0.364512i
$823$	−14.5994	−	8.42898i	−0.508904	−	0.293816i	0.223479	−	0.974709i	$-0.428259\pi$
$823$	−14.5994	−	8.42898i	−0.508904	−	0.293816i	−0.732383	+	0.680893i	$0.761592\pi$
$824$	−33.9924	−	19.5412i	−1.18418	−	0.680751i
$825$			3.15970i			0.110006i
$826$		0			0
$827$	−26.8509	+	26.8509i	−0.933697	+	0.933697i	−0.997935	−	0.0642374i	$-0.979539\pi$
$827$	−26.8509	+	26.8509i	−0.933697	+	0.933697i	0.0642374	+	0.997935i	$0.479539\pi$
$828$	−10.4907	−	8.78058i	−0.364577	−	0.305146i
$829$	−9.73516	+	2.60853i	−0.338116	+	0.0905979i	−0.423882	−	0.905717i	$-0.639333\pi$
$829$	−9.73516	+	2.60853i	−0.338116	+	0.0905979i	0.0857661	+	0.996315i	$0.472666\pi$
$830$	17.5955	+	6.39186i	0.610747	+	0.221865i
$831$	−7.19979	−	12.4704i	−0.249758	−	0.432593i
$832$	−40.4112	+	10.9896i	−1.40101	+	0.380995i
$833$		0			0
$834$	6.49619	+	36.7085i	0.224945	+	1.27111i
$835$	4.02043	−	15.0044i	0.139133	−	0.519250i
$836$	−0.518051	+	2.95949i	−0.0179172	+	0.102356i
$837$	11.2030	+	41.8100i	0.387231	+	1.44516i
$838$	−19.5297	−	1.69642i	−0.674642	−	0.0586017i
$839$		−	10.3160i		−	0.356150i	−0.984017	−	0.178075i	$-0.943013\pi$
$839$		−	10.3160i		−	0.356150i	0.984017	−	0.178075i	$-0.0569869\pi$
$840$		0			0
$841$		−	28.5679i		−	0.985101i
$842$	2.61080	−	30.0564i	0.0899742	−	1.03581i
$843$	3.13878	+	11.7141i	0.108105	+	0.403455i
$844$	−3.98195	+	2.79557i	−0.137065	+	0.0962273i
$845$	−12.2507	+	45.7203i	−0.421437	+	1.57282i
$846$	−19.3697	+	3.42779i	−0.665944	+	0.117850i
$847$		0			0
$848$	4.32261	−	50.8614i	0.148439	−	1.74659i
$849$	−6.20163	−	10.7415i	−0.212839	−	0.368648i
$850$	7.57422	−	20.8502i	0.259794	−	0.715157i
$851$	−26.3949	+	7.07249i	−0.904806	+	0.242442i
$852$	−16.2953	+	1.44603i	−0.558267	+	0.0495402i
$853$	1.19902	−	1.19902i	0.0410536	−	0.0410536i	−0.686282	−	0.727336i	$-0.740758\pi$
$853$	1.19902	−	1.19902i	0.0410536	−	0.0410536i	0.727336	+	0.686282i	$0.240758\pi$
$854$		0			0
$855$		−	15.7696i		−	0.539308i
$856$	7.20651	+	26.6962i	0.246314	+	0.912457i
$857$	20.1302	+	11.6222i	0.687635	+	0.397006i	0.802725	−	0.596349i	$-0.203383\pi$
$857$	20.1302	+	11.6222i	0.687635	+	0.397006i	−0.115091	+	0.993355i	$0.536716\pi$
$858$	−1.70702	−	3.65479i	−0.0582766	−	0.124772i
$859$	30.1679	+	8.08347i	1.02932	+	0.275804i	0.733679	−	0.679496i	$-0.237802\pi$
$859$	30.1679	+	8.08347i	1.02932	+	0.275804i	0.295637	+	0.955300i	$0.404468\pi$
$860$	−26.6352	−	72.8980i	−0.908252	−	2.48580i
$861$		0			0
$862$	−1.10628	−	6.25132i	−0.0376799	−	0.212921i
$863$	−16.3316	−	28.2872i	−0.555936	−	0.962909i	−0.997830	−	0.0658417i	$-0.979027\pi$
$863$	−16.3316	−	28.2872i	−0.555936	−	0.962909i	0.441894	−	0.897067i	$-0.354307\pi$
$864$	−13.2611	+	28.6704i	−0.451152	+	0.975387i
$865$	−24.4197	+	42.2961i	−0.830294	+	1.43811i
$866$	−25.9870	+	21.8331i	−0.883073	+	0.741920i
$867$	8.77254	+	8.77254i	0.297931	+	0.297931i
$868$		0			0
$869$	2.49213	−	2.49213i	0.0845398	−	0.0845398i
$870$	−3.89918	−	0.338696i	−0.132195	−	0.0114829i
$871$	−1.14328	−	0.660076i	−0.0387387	−	0.0223658i
$872$	−29.8604	−	29.7495i	−1.01120	−	1.00744i
$873$	4.32326	−	2.49604i	0.146320	−	0.0844781i
$874$	20.6131	+	14.4144i	0.697250	+	0.487575i
$875$		0			0
$876$	−1.52593	+	3.28299i	−0.0515563	+	0.110922i
$877$	−6.87485	+	25.6573i	−0.232147	+	0.866386i	0.747267	+	0.664524i	$0.231366\pi$
$877$	−6.87485	+	25.6573i	−0.232147	+	0.866386i	−0.979414	+	0.201861i	$0.935301\pi$
$878$	6.97432	−	19.1988i	0.235372	−	0.647929i
$879$	18.1846	−	31.4966i	0.613350	−	1.06235i
$880$	1.89890	−	5.25776i	0.0640120	−	0.177239i
$881$	37.5249			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$881$	37.5249			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$882$		0			0
$883$	20.1752	+	20.1752i	0.678950	+	0.678950i	0.959763	−	0.280812i	$-0.0906039\pi$
$883$	20.1752	+	20.1752i	0.678950	+	0.678950i	−0.280812	+	0.959763i	$0.590604\pi$
$884$	2.50327	+	28.2092i	0.0841940	+	0.948778i
$885$	11.0896	+	41.3869i	0.372772	+	1.39120i
$886$	−9.49463	+	4.43460i	−0.318978	+	0.148983i
$887$	8.10455	−	4.67916i	0.272124	−	0.157111i	−0.357728	−	0.933826i	$-0.616449\pi$
$887$	8.10455	−	4.67916i	0.272124	−	0.157111i	0.629853	+	0.776715i	$0.283115\pi$
$888$	9.86508	+	17.0136i	0.331050	+	0.570939i
$889$		0			0
$890$	1.45113	−	2.07516i	0.0486419	−	0.0695597i
$891$	−1.26480	−	0.338901i	−0.0423722	−	0.0113536i
$892$	−9.37410	+	53.5517i	−0.313868	+	1.79304i
$893$	34.9345	−	9.36067i	1.16904	−	0.313243i
$894$	−9.56782	+	8.03848i	−0.319996	+	0.268847i
$895$	−36.8088			−1.23038
$896$		0			0
$897$	−33.7701			−1.12755
$898$	−21.3616	+	17.9471i	−0.712847	+	0.598904i
$899$	4.92155	−	1.31872i	0.164143	−	0.0439819i
$900$	−2.71673	+	15.5199i	−0.0905575	+	0.517331i
$901$	−33.3422	−	8.93402i	−1.11079	−	0.297635i
$902$	−3.64888	+	5.21804i	−0.121495	+	0.173742i
$903$		0			0
$904$	0.0759100	+	0.130917i	0.00252473	+	0.00435422i
$905$	−7.42561	+	4.28718i	−0.246836	+	0.142511i
$906$	−0.219963	+	0.102737i	−0.00730777	+	0.00341319i
$907$	3.05723	+	11.4097i	0.101514	+	0.378854i	0.997926	−	0.0643663i	$-0.0205026\pi$
$907$	3.05723	+	11.4097i	0.101514	+	0.378854i	−0.896413	+	0.443220i	$0.853836\pi$
$908$	−3.77346	−	42.5229i	−0.125227	−	1.41117i
$909$	3.78037	+	3.78037i	0.125387	+	0.125387i
$910$		0			0
$911$	−29.8691			−0.989608			−0.494804	−	0.869004i	$-0.664760\pi$
$911$	−29.8691			−0.989608			−0.494804	+	0.869004i	$0.664760\pi$
$912$	6.14931	−	17.0265i	0.203624	−	0.563802i
$913$	0.856550	−	1.48359i	0.0283477	−	0.0490996i
$914$	0.617842	−	1.70079i	0.0204364	−	0.0562571i
$915$	7.74949	−	28.9215i	0.256190	−	0.956115i
$916$	−2.40841	+	5.18163i	−0.0795761	+	0.171206i
$917$		0			0
$918$	17.5059	+	12.2416i	0.577782	+	0.404033i
$919$	41.8441	−	24.1587i	1.38031	−	0.796923i	0.388115	−	0.921611i	$-0.373126\pi$
$919$	41.8441	−	24.1587i	1.38031	−	0.796923i	0.992196	+	0.124688i	$0.0397930\pi$
$920$	−33.1541	−	33.0309i	−1.09306	−	1.08900i
$921$	−29.0245	−	16.7573i	−0.956391	−	0.552172i
$922$	−12.8346	−	1.11486i	−0.422686	−	0.0367159i
$923$	23.6322	−	23.6322i	0.777864	−	0.777864i
$924$		0			0
$925$	22.2539	+	22.2539i	0.731703	+	0.731703i
$926$	−13.5612	+	11.3935i	−0.445648	+	0.374414i
$927$	9.41610	−	16.3092i	0.309265	−	0.535663i
$928$	3.37486	+	1.56099i	0.110785	+	0.0512421i
$929$	21.9366	+	37.9953i	0.719716	+	1.24658i	0.961112	+	0.276158i	$0.0890613\pi$
$929$	21.9366	+	37.9953i	0.719716	+	1.24658i	−0.241396	+	0.970427i	$0.577605\pi$
$930$	8.04269	+	45.4474i	0.263730	+	1.49028i
$931$		0			0
$932$	11.4075	+	31.2212i	0.373665	+	1.02269i
$933$	−6.15032	−	1.64797i	−0.201352	−	0.0539522i
$934$	−22.0511	−	47.2123i	−0.721534	−	1.54483i
$935$	−3.27382	−	1.89014i	−0.107065	−	0.0618142i
$936$	−5.24219	−	19.4194i	−0.171346	−	0.634744i
$937$		−	53.2767i		−	1.74047i	−0.492634	−	0.870237i	$-0.663966\pi$
$937$		−	53.2767i		−	1.74047i	0.492634	−	0.870237i	$-0.336034\pi$
$938$		0			0
$939$	17.1444	−	17.1444i	0.559486	−	0.559486i
$940$	−67.0288	+	5.94809i	−2.18624	+	0.194005i
$941$	−18.8605	+	5.05364i	−0.614833	+	0.164744i	−0.552778	−	0.833329i	$-0.686432\pi$
$941$	−18.8605	+	5.05364i	−0.614833	+	0.164744i	−0.0620554	+	0.998073i	$0.519766\pi$
$942$	−2.29851	+	6.32733i	−0.0748896	+	0.206156i
$943$	26.6529	+	46.1642i	0.867938	+	1.50331i
$944$	3.44717	−	40.5606i	0.112196	−	1.32013i
$945$		0			0
$946$	−6.99352	+	1.23762i	−0.227379	+	0.0402386i
$947$	−11.4471	+	42.7212i	−0.371981	+	1.38825i	0.485724	+	0.874112i	$0.338556\pi$
$947$	−11.4471	+	42.7212i	−0.371981	+	1.38825i	−0.857706	+	0.514141i	$0.828111\pi$
$948$	−17.3800	+	12.2018i	−0.564477	+	0.396296i
$949$	−1.91423	−	7.14400i	−0.0621385	−	0.231904i
$950$	2.50692	−	28.8604i	0.0813351	−	0.936356i
$951$			4.20978i			0.136511i
$952$		0			0
$953$			10.3382i			0.334886i	0.985882	+	0.167443i	$0.0535511\pi$
$953$			10.3382i			0.334886i	−0.985882	+	0.167443i	$0.946449\pi$
$954$	24.4250	+	2.12164i	0.790788	+	0.0686906i
$955$	−18.2598	−	68.1463i	−0.590872	−	2.20516i
$956$	−0.749721	+	4.28296i	−0.0242477	+	0.138521i
$957$	−0.0926975	+	0.345952i	−0.00299648	+	0.0111830i
$958$	−4.15006	−	23.4511i	−0.134082	−	0.757670i
$959$		0			0
$960$	−16.7324	+	29.2322i	−0.540037	+	0.943466i
$961$	−14.5419	−	25.1874i	−0.469095	−	0.812496i
$962$	−37.7634	−	13.7182i	−1.21754	−	0.442293i
$963$	−12.8287	+	3.43744i	−0.413399	+	0.110770i
$964$	21.2222	+	17.7627i	0.683520	+	0.572097i
$965$	29.5815	−	29.5815i	0.952263	−	0.952263i
$966$		0			0
$967$			37.2109i			1.19662i	0.801264	+	0.598311i	$0.204161\pi$
$967$			37.2109i			1.19662i	−0.801264	+	0.598311i	$0.795839\pi$
$968$	26.5298	+	15.2512i	0.852700	+	0.490193i
$969$	−10.6018	−	6.12093i	−0.340578	−	0.196633i
$970$	15.4731	−	7.22691i	0.496811	−	0.232042i
$971$	−32.2822	−	8.64999i	−1.03598	−	0.277591i	−0.299536	−	0.954085i	$-0.596832\pi$
$971$	−32.2822	−	8.64999i	−1.03598	−	0.277591i	−0.736448	+	0.676494i	$0.763499\pi$
$972$	−23.2288	−	10.7967i	−0.745064	−	0.346304i
$973$		0			0
$974$	−32.8879	+	5.82007i	−1.05380	+	0.186487i
$975$	19.4467	+	33.6828i	0.622794	+	1.07871i
$976$	−16.2582	+	23.3422i	−0.520413	+	0.747167i
$977$	18.9263	−	32.7812i	0.605505	−	1.04876i	−0.386467	−	0.922303i	$-0.626305\pi$
$977$	18.9263	−	32.7812i	0.605505	−	1.04876i	0.991972	−	0.126461i	$-0.0403620\pi$
$978$	22.0247	+	26.2150i	0.704272	+	0.838262i
$979$	−0.163851	−	0.163851i	−0.00523672	−	0.00523672i
$980$		0			0
$981$	14.3154	−	14.3154i	0.457057	−	0.457057i
$982$	0.524559	−	6.03890i	0.0167394	−	0.192709i
$983$	−1.29314	−	0.746595i	−0.0412448	−	0.0238127i	0.479236	−	0.877686i	$-0.340914\pi$
$983$	−1.29314	−	0.746595i	−0.0412448	−	0.0238127i	−0.520481	+	0.853873i	$0.674247\pi$
$984$	27.0774	−	27.1784i	0.863195	−	0.866414i
$985$	−17.3326	+	10.0070i	−0.552262	+	0.318848i
$986$	1.44099	−	2.06066i	0.0458904	−	0.0656248i
$987$		0			0
$988$	12.6921	+	34.7369i	0.403788	+	1.10513i
$989$	−15.3889	+	57.4323i	−0.489340	+	1.82624i
$990$	2.52362	+	0.916749i	0.0802059	+	0.0291362i
$991$	−16.9352	+	29.3327i	−0.537966	+	0.931784i	0.461048	+	0.887375i	$0.347474\pi$
$991$	−16.9352	+	29.3327i	−0.537966	+	0.931784i	−0.999013	+	0.0444085i	$0.985860\pi$
$992$	7.48018	−	43.2057i	0.237496	−	1.37178i
$993$	35.3517			1.12185
$994$		0			0
$995$	−13.6249	−	13.6249i	−0.431940	−	0.431940i
$996$	−6.62498	+	7.91527i	−0.209920	+	0.250805i
$997$	0.0415223	+	0.154963i	0.00131502	+	0.00490774i	0.966580	−	0.256364i	$-0.0825247\pi$
$997$	0.0415223	+	0.154963i	0.00131502	+	0.00490774i	−0.965265	+	0.261272i	$0.915858\pi$
$998$	−5.91610	−	12.6666i	−0.187271	−	0.400954i
$999$	−26.2456	+	15.1529i	−0.830373	+	0.479416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.n.557.4		40
7.2	even	3	inner	784.2.x.n.765.9		40
7.3	odd	6		784.2.m.i.589.6	yes	20
7.4	even	3		784.2.m.i.589.5	yes	20
7.5	odd	6	inner	784.2.x.n.765.10		40
7.6	odd	2	inner	784.2.x.n.557.3		40
16.5	even	4	inner	784.2.x.n.165.9		40
112.5	odd	12	inner	784.2.x.n.373.3		40
112.37	even	12	inner	784.2.x.n.373.4		40
112.53	even	12		784.2.m.i.197.5	✓	20
112.69	odd	4	inner	784.2.x.n.165.10		40
112.101	odd	12		784.2.m.i.197.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.5	✓	20	112.53	even	12
784.2.m.i.197.6	yes	20	112.101	odd	12
784.2.m.i.589.5	yes	20	7.4	even	3
784.2.m.i.589.6	yes	20	7.3	odd	6
784.2.x.n.165.9		40	16.5	even	4	inner
784.2.x.n.165.10		40	112.69	odd	4	inner
784.2.x.n.373.3		40	112.5	odd	12	inner
784.2.x.n.373.4		40	112.37	even	12	inner
784.2.x.n.557.3		40	7.6	odd	2	inner
784.2.x.n.557.4		40	1.1	even	1	trivial
784.2.x.n.765.9		40	7.2	even	3	inner
784.2.x.n.765.10		40	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08279 + 0.909711i) q^{2} +(1.23755 - 0.331601i) q^{3} +(0.344852 - 1.97004i) q^{4} +(3.17421 + 0.850527i) q^{5} +(-1.03834 + 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} +(-1.17650 + 0.679252i) q^{9} +O(q^{10})\)	\(q+(-1.08279 + 0.909711i) q^{2} +(1.23755 - 0.331601i) q^{3} +(0.344852 - 1.97004i) q^{4} +(3.17421 + 0.850527i) q^{5} +(-1.03834 + 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} +(-1.17650 + 0.679252i) q^{9} +(-4.21072 + 1.96667i) q^{10} +(0.110070 + 0.410787i) q^{11} +(-0.226497 - 2.55239i) q^{12} +(3.70160 + 3.70160i) q^{13} +4.21029 q^{15} +(-3.76215 - 1.35875i) q^{16} +(-1.35248 + 2.34256i) q^{17} +(0.655973 - 1.80576i) q^{18} +(-0.914248 + 3.41202i) q^{19} +(2.77021 - 5.96003i) q^{20} +(-0.492880 - 0.344662i) q^{22} +(-4.36053 + 2.51755i) q^{23} +(2.56718 + 2.55764i) q^{24} +(5.02207 + 2.89950i) q^{25} +(-7.37543 - 0.640655i) q^{26} +(-3.94859 + 3.94859i) q^{27} +(0.464798 + 0.464798i) q^{29} +(-4.55884 + 3.83014i) q^{30} +(3.87569 - 6.71289i) q^{31} +(5.30968 - 1.95124i) q^{32} +(0.272435 + 0.471871i) q^{33} +(-0.666608 - 3.76685i) q^{34} +(0.932439 + 2.55200i) q^{36} +(5.24218 + 1.40464i) q^{37} +(-2.11402 - 4.52619i) q^{38} +(5.80838 + 3.35347i) q^{39} +(2.42236 + 8.97352i) q^{40} -10.5868i q^{41} +(8.35006 - 8.35006i) q^{43} +(0.847226 - 0.0751823i) q^{44} +(-4.31217 + 1.15544i) q^{45} +(2.43127 - 6.69279i) q^{46} +(-5.11933 - 8.86694i) q^{47} +(-5.10643 - 0.433986i) q^{48} +(-8.07554 + 1.42910i) q^{50} +(-0.896966 + 3.34752i) q^{51} +(8.56882 - 6.01581i) q^{52} +(3.30284 + 12.3264i) q^{53} +(0.683403 - 7.86756i) q^{54} +1.39754i q^{55} +4.52572i q^{57} +(-0.926108 - 0.0804449i) q^{58} +(2.63392 + 9.82994i) q^{59} +(1.45192 - 8.29445i) q^{60} +(1.84061 - 6.86924i) q^{61} +(1.91025 + 10.7944i) q^{62} +(-3.97418 + 6.94305i) q^{64} +(8.60134 + 14.8980i) q^{65} +(-0.724255 - 0.263098i) q^{66} +(-0.243592 + 0.0652703i) q^{67} +(4.14854 + 3.47228i) q^{68} +(-4.56156 + 4.56156i) q^{69} -6.38433i q^{71} +(-3.33121 - 1.91502i) q^{72} +(-1.22356 - 0.706421i) q^{73} +(-6.95397 + 3.24795i) q^{74} +(7.17656 + 1.92295i) q^{75} +(6.40655 + 2.97775i) q^{76} +(-9.33992 + 1.65286i) q^{78} +(-4.14366 - 7.17702i) q^{79} +(-10.7862 - 7.51276i) q^{80} +(-1.53948 + 2.66646i) q^{81} +(9.63096 + 11.4633i) q^{82} +(-2.84836 - 2.84836i) q^{83} +(-6.28545 + 6.28545i) q^{85} +(-1.44519 + 16.6375i) q^{86} +(0.729339 + 0.421084i) q^{87} +(-0.848971 + 0.852137i) q^{88} +(-0.471871 + 0.272435i) q^{89} +(3.61804 - 5.17393i) q^{90} +(3.45595 + 9.45861i) q^{92} +(2.57037 - 9.59274i) q^{93} +(13.6095 + 4.94389i) q^{94} +(-5.80403 + 10.0529i) q^{95} +(5.92397 - 4.17546i) q^{96} -3.67469 q^{97} +(-0.408525 - 0.408525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4}+O(q^{10}) \) 40 * q + 8 * q^4	\( 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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