LMFDB - Embedded newform 784.2.bg.e.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(65,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 20]))

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

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

chi := DirichletCharacter("784.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bg (of order $21$, degree $12$, 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:	$84$
Relative dimension:	$7$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	784.193
Dual form			784.2.bg.e.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167965 - 2.24134i) q^{3} +(1.72106 + 1.17340i) q^{5} +(-2.19081 - 1.48335i) q^{7} +(-2.02891 - 0.305809i) q^{9} +O(q^{10})$	\(q+(0.167965 - 2.24134i) q^{3} +(1.72106 + 1.17340i) q^{5} +(-2.19081 - 1.48335i) q^{7} +(-2.02891 - 0.305809i) q^{9} +(-3.20409 + 0.482939i) q^{11} +(-2.26376 - 2.83867i) q^{13} +(2.91907 - 3.66040i) q^{15} +(-3.38373 - 1.04374i) q^{17} +(-1.35571 - 2.34817i) q^{19} +(-3.69268 + 4.66121i) q^{21} +(0.439482 - 0.135562i) q^{23} +(-0.241514 - 0.615368i) q^{25} +(0.474224 - 2.07771i) q^{27} +(-0.802873 - 3.51761i) q^{29} +(1.87491 - 3.24745i) q^{31} +(0.544255 + 7.26258i) q^{33} +(-2.02996 - 5.12365i) q^{35} +(6.25512 - 5.80390i) q^{37} +(-6.74265 + 4.59706i) q^{39} +(-7.91173 + 3.81009i) q^{41} +(9.23205 + 4.44592i) q^{43} +(-3.13305 - 2.90704i) q^{45} +(0.153488 - 0.391081i) q^{47} +(2.59932 + 6.49950i) q^{49} +(-2.90773 + 7.40879i) q^{51} +(3.48193 + 3.23076i) q^{53} +(-6.08113 - 2.92852i) q^{55} +(-5.49076 + 2.64421i) q^{57} +(-5.32195 + 3.62845i) q^{59} +(5.97036 - 5.53968i) q^{61} +(3.99134 + 3.67956i) q^{63} +(-0.565182 - 7.54183i) q^{65} +(-7.97896 + 13.8200i) q^{67} +(-0.230024 - 1.00780i) q^{69} +(0.653752 - 2.86427i) q^{71} +(-4.67536 - 11.9126i) q^{73} +(-1.41982 + 0.437955i) q^{75} +(7.73594 + 3.69477i) q^{77} +(-4.83228 - 8.36976i) q^{79} +(-10.4592 - 3.22624i) q^{81} +(-2.56908 + 3.22153i) q^{83} +(-4.59889 - 5.76683i) q^{85} +(-8.01903 + 1.20867i) q^{87} +(12.7736 + 1.92531i) q^{89} +(0.748728 + 9.57694i) q^{91} +(-6.96372 - 4.74778i) q^{93} +(0.422071 - 5.63214i) q^{95} +6.30931 q^{97} +6.64850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 10 q^{3} - q^{5} + 4 q^{7} - 11 q^{9}+O(q^{10}) $ 84 * q - 10 * q^3 - q^5 + 4 * q^7 - 11 * q^9	$ 84 q - 10 q^{3} - q^{5} + 4 q^{7} - 11 q^{9} - q^{11} + 10 q^{13} - 9 q^{15} + 3 q^{17} + 23 q^{19} - 10 q^{21} + q^{23} + 6 q^{25} + 32 q^{27} - 13 q^{29} + 29 q^{31} + 11 q^{33} - 30 q^{35} + 48 q^{37} - 51 q^{39} + 20 q^{41} + 14 q^{43} + 22 q^{45} + 34 q^{47} - 2 q^{49} - 3 q^{51} - 40 q^{53} + 9 q^{55} - 10 q^{57} - 38 q^{59} + 10 q^{61} - 9 q^{63} - 2 q^{65} + 37 q^{67} - 87 q^{69} - 5 q^{71} + 21 q^{73} + 12 q^{75} + 71 q^{77} - 19 q^{79} - 70 q^{81} + 55 q^{83} + 29 q^{85} + 165 q^{87} - 65 q^{89} + 15 q^{91} - 120 q^{93} - 7 q^{95} + 170 q^{97} - 110 q^{99}+O(q^{100}) $ 84 * q - 10 * q^3 - q^5 + 4 * q^7 - 11 * q^9 - q^11 + 10 * q^13 - 9 * q^15 + 3 * q^17 + 23 * q^19 - 10 * q^21 + q^23 + 6 * q^25 + 32 * q^27 - 13 * q^29 + 29 * q^31 + 11 * q^33 - 30 * q^35 + 48 * q^37 - 51 * q^39 + 20 * q^41 + 14 * q^43 + 22 * q^45 + 34 * q^47 - 2 * q^49 - 3 * q^51 - 40 * q^53 + 9 * q^55 - 10 * q^57 - 38 * q^59 + 10 * q^61 - 9 * q^63 - 2 * q^65 + 37 * q^67 - 87 * q^69 - 5 * q^71 + 21 * q^73 + 12 * q^75 + 71 * q^77 - 19 * q^79 - 70 * q^81 + 55 * q^83 + 29 * q^85 + 165 * q^87 - 65 * q^89 + 15 * q^91 - 120 * q^93 - 7 * q^95 + 170 * q^97 - 110 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{21}\right)$

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			0
$2$		0			0
$3$	0.167965	−	2.24134i	0.0969748	−	1.29404i	−0.710315	−	0.703884i	$-0.751447\pi$
$3$	0.167965	−	2.24134i	0.0969748	−	1.29404i	0.807290	−	0.590155i	$-0.200933\pi$
$4$		0			0
$5$	1.72106	+	1.17340i	0.769683	+	0.524761i	0.883325	−	0.468761i	$-0.155299\pi$
$5$	1.72106	+	1.17340i	0.769683	+	0.524761i	−0.113642	+	0.993522i	$0.536252\pi$
$6$		0			0
$7$	−2.19081	−	1.48335i	−0.828049	−	0.560655i
$7$	−2.19081	−	1.48335i	−0.828049	−	0.560655i
$8$		0			0
$9$	−2.02891	−	0.305809i	−0.676303	−	0.101936i
$10$		0			0
$11$	−3.20409	+	0.482939i	−0.966070	+	0.145612i	−0.613085	−	0.790017i	$-0.710072\pi$
$11$	−3.20409	+	0.482939i	−0.966070	+	0.145612i	−0.352986	+	0.935629i	$0.614834\pi$
$12$		0			0
$13$	−2.26376	−	2.83867i	−0.627854	−	0.787304i	0.361572	−	0.932344i	$-0.382240\pi$
$13$	−2.26376	−	2.83867i	−0.627854	−	0.787304i	−0.989426	+	0.145040i	$0.953669\pi$
$14$		0			0
$15$	2.91907	−	3.66040i	0.753702	−	0.945112i
$16$		0			0
$17$	−3.38373	−	1.04374i	−0.820676	−	0.253145i	−0.144142	−	0.989557i	$-0.546042\pi$
$17$	−3.38373	−	1.04374i	−0.820676	−	0.253145i	−0.676533	+	0.736412i	$0.736518\pi$
$18$		0			0
$19$	−1.35571	−	2.34817i	−0.311022	−	0.538706i	0.667562	−	0.744554i	$-0.267338\pi$
$19$	−1.35571	−	2.34817i	−0.311022	−	0.538706i	−0.978584	+	0.205848i	$0.934005\pi$
$20$		0			0
$21$	−3.69268	+	4.66121i	−0.805810	+	1.01716i
$22$		0			0
$23$	0.439482	−	0.135562i	0.0916383	−	0.0282667i	−0.248597	−	0.968607i	$-0.579969\pi$
$23$	0.439482	−	0.135562i	0.0916383	−	0.0282667i	0.340235	+	0.940340i	$0.389493\pi$
$24$		0			0
$25$	−0.241514	−	0.615368i	−0.0483028	−	0.123074i
$26$		0			0
$27$	0.474224	−	2.07771i	0.0912644	−	0.399856i
$28$		0			0
$29$	−0.802873	−	3.51761i	−0.149090	−	0.653205i	−0.993139	−	0.116939i	$-0.962692\pi$
$29$	−0.802873	−	3.51761i	−0.149090	−	0.653205i	0.844049	−	0.536265i	$-0.180165\pi$
$30$		0			0
$31$	1.87491	−	3.24745i	0.336744	−	0.583259i	−0.647074	−	0.762427i	$-0.724007\pi$
$31$	1.87491	−	3.24745i	0.336744	−	0.583259i	0.983818	+	0.179169i	$0.0573408\pi$
$32$		0			0
$33$	0.544255	+	7.26258i	0.0947427	+	1.26425i
$34$		0			0
$35$	−2.02996	−	5.12365i	−0.343126	−	0.866055i
$36$		0			0
$37$	6.25512	−	5.80390i	1.02833	−	0.954155i	0.0293666	−	0.999569i	$-0.490651\pi$
$37$	6.25512	−	5.80390i	1.02833	−	0.954155i	0.998968	+	0.0454133i	$0.0144605\pi$
$38$		0			0
$39$	−6.74265	+	4.59706i	−1.07969	+	0.736119i
$40$		0			0
$41$	−7.91173	+	3.81009i	−1.23561	+	0.595036i	−0.933616	−	0.358275i	$-0.883365\pi$
$41$	−7.91173	+	3.81009i	−1.23561	+	0.595036i	−0.301989	+	0.953311i	$0.597651\pi$
$42$		0			0
$43$	9.23205	+	4.44592i	1.40787	+	0.677997i	0.974742	−	0.223334i	$-0.0716939\pi$
$43$	9.23205	+	4.44592i	1.40787	+	0.677997i	0.433132	+	0.901330i	$0.357408\pi$
$44$		0			0
$45$	−3.13305	−	2.90704i	−0.467047	−	0.433356i
$46$		0			0
$47$	0.153488	−	0.391081i	0.0223885	−	0.0570450i	−0.919242	−	0.393692i	$-0.871198\pi$
$47$	0.153488	−	0.391081i	0.0223885	−	0.0570450i	0.941631	+	0.336647i	$0.109293\pi$
$48$		0			0
$49$	2.59932	+	6.49950i	0.371332	+	0.928500i
$50$		0			0
$51$	−2.90773	+	7.40879i	−0.407164	+	1.03744i
$52$		0			0
$53$	3.48193	+	3.23076i	0.478279	+	0.443778i	0.882102	−	0.471059i	$-0.156128\pi$
$53$	3.48193	+	3.23076i	0.478279	+	0.443778i	−0.403822	+	0.914837i	$0.632319\pi$
$54$		0			0
$55$	−6.08113	−	2.92852i	−0.819980	−	0.394881i
$56$		0			0
$57$	−5.49076	+	2.64421i	−0.727268	+	0.350234i
$58$		0			0
$59$	−5.32195	+	3.62845i	−0.692859	+	0.472383i	−0.857842	−	0.513913i	$-0.828195\pi$
$59$	−5.32195	+	3.62845i	−0.692859	+	0.472383i	0.164983	+	0.986296i	$0.447243\pi$
$60$		0			0
$61$	5.97036	−	5.53968i	0.764426	−	0.709284i	−0.198187	−	0.980164i	$-0.563505\pi$
$61$	5.97036	−	5.53968i	0.764426	−	0.709284i	0.962613	+	0.270880i	$0.0873148\pi$
$62$		0			0
$63$	3.99134	+	3.67956i	0.502861	+	0.463581i
$64$		0			0
$65$	−0.565182	−	7.54183i	−0.0701022	−	0.935448i
$66$		0			0
$67$	−7.97896	+	13.8200i	−0.974785	+	1.68838i	−0.294141	+	0.955762i	$0.595034\pi$
$67$	−7.97896	+	13.8200i	−0.974785	+	1.68838i	−0.680643	+	0.732615i	$0.738300\pi$
$68$		0			0
$69$	−0.230024	−	1.00780i	−0.0276916	−	0.121325i
$70$		0			0
$71$	0.653752	−	2.86427i	0.0775861	−	0.339927i	−0.921205	−	0.389077i	$-0.872794\pi$
$71$	0.653752	−	2.86427i	0.0775861	−	0.339927i	0.998791	+	0.0491499i	$0.0156512\pi$
$72$		0			0
$73$	−4.67536	−	11.9126i	−0.547209	−	1.39427i	−0.890477	−	0.455029i	$-0.849629\pi$
$73$	−4.67536	−	11.9126i	−0.547209	−	1.39427i	0.343267	−	0.939238i	$-0.388466\pi$
$74$		0			0
$75$	−1.41982	+	0.437955i	−0.163946	+	0.0505707i
$76$		0			0
$77$	7.73594	+	3.69477i	0.881592	+	0.421059i
$78$		0			0
$79$	−4.83228	−	8.36976i	−0.543674	−	0.941671i	−0.998689	−	0.0511873i	$-0.983699\pi$
$79$	−4.83228	−	8.36976i	−0.543674	−	0.941671i	0.455015	−	0.890484i	$-0.349634\pi$
$80$		0			0
$81$	−10.4592	−	3.22624i	−1.16213	−	0.358471i
$82$		0			0
$83$	−2.56908	+	3.22153i	−0.281993	+	0.353609i	−0.902574	−	0.430534i	$-0.858325\pi$
$83$	−2.56908	+	3.22153i	−0.281993	+	0.353609i	0.620581	+	0.784142i	$0.286897\pi$
$84$		0			0
$85$	−4.59889	−	5.76683i	−0.498820	−	0.625500i
$86$		0			0
$87$	−8.01903	+	1.20867i	−0.859730	+	0.129583i
$88$		0			0
$89$	12.7736	+	1.92531i	1.35400	+	0.204083i	0.785633	−	0.618693i	$-0.212338\pi$
$89$	12.7736	+	1.92531i	1.35400	+	0.204083i	0.568366	+	0.822776i	$0.307576\pi$
$90$		0			0
$91$	0.748728	+	9.57694i	0.0784881	+	1.00394i
$92$		0			0
$93$	−6.96372	−	4.74778i	−0.722104	−	0.492322i
$94$		0			0
$95$	0.422071	−	5.63214i	0.0433035	−	0.577846i
$96$		0			0
$97$	6.30931			0.640613			0.320307	−	0.947314i	$-0.396214\pi$
$97$	6.30931			0.640613			0.320307	+	0.947314i	$0.396214\pi$
$98$		0			0
$99$	6.64850			0.668199
$100$		0			0
$101$	−0.798075	+	10.6496i	−0.0794114	+	1.05967i	0.805096	+	0.593145i	$0.202114\pi$
$101$	−0.798075	+	10.6496i	−0.0794114	+	1.05967i	−0.884507	+	0.466527i	$0.845505\pi$
$102$		0			0
$103$	6.43246	+	4.38558i	0.633810	+	0.432124i	0.837142	−	0.546986i	$-0.184225\pi$
$103$	6.43246	+	4.38558i	0.633810	+	0.432124i	−0.203332	+	0.979110i	$0.565177\pi$
$104$		0			0
$105$	−11.8248	+	3.68924i	−1.15398	+	0.360033i
$106$		0			0
$107$	19.2035	+	2.89446i	1.85647	+	0.279818i	0.979607	−	0.200924i	$-0.0643943\pi$
$107$	19.2035	+	2.89446i	1.85647	+	0.279818i	0.876862	+	0.480741i	$0.159632\pi$
$108$		0			0
$109$	5.94650	−	0.896291i	0.569572	−	0.0858491i	0.142059	−	0.989858i	$-0.454628\pi$
$109$	5.94650	−	0.896291i	0.569572	−	0.0858491i	0.427513	+	0.904009i	$0.359390\pi$
$110$		0			0
$111$	−11.9579	−	14.9947i	−1.13499	−	1.42323i
$112$		0			0
$113$	−2.69499	+	3.37941i	−0.253523	+	0.317908i	−0.892264	−	0.451514i	$-0.850884\pi$
$113$	−2.69499	+	3.37941i	−0.253523	+	0.317908i	0.638741	+	0.769422i	$0.279456\pi$
$114$		0			0
$115$	0.915446	+	0.282378i	0.0853657	+	0.0263318i
$116$		0			0
$117$	3.72487	+	6.45167i	0.344365	+	0.596457i
$118$		0			0
$119$	5.86488	+	7.30592i	0.537633	+	0.669732i
$120$		0			0
$121$	−0.478321	+	0.147542i	−0.0434837	+	0.0134129i
$122$		0			0
$123$	7.21082	+	18.3729i	0.650177	+	1.65663i
$124$		0			0
$125$	2.62398	−	11.4964i	0.234696	−	1.02827i
$126$		0			0
$127$	1.13972	+	4.99342i	0.101133	+	0.443094i	0.999988	+	0.00484782i	$0.00154312\pi$
$127$	1.13972	+	4.99342i	0.101133	+	0.443094i	−0.898855	+	0.438246i	$0.855600\pi$
$128$		0			0
$129$	11.5155	−	19.9454i	1.01388	−	1.75610i
$130$		0			0
$131$	−1.16379	−	15.5297i	−0.101681	−	1.35684i	−0.781705	−	0.623649i	$-0.785650\pi$
$131$	−1.16379	−	15.5297i	−0.101681	−	1.35684i	0.680024	−	0.733190i	$-0.261969\pi$
$132$		0			0
$133$	−0.513046	+	7.15540i	−0.0444867	+	0.620452i
$134$		0			0
$135$	3.25416	−	3.01942i	0.280073	−	0.259870i
$136$		0			0
$137$	5.09645	−	3.47470i	0.435419	−	0.296864i	−0.325703	−	0.945472i	$-0.605601\pi$
$137$	5.09645	−	3.47470i	0.435419	−	0.296864i	0.761122	+	0.648608i	$0.224649\pi$
$138$		0			0
$139$	13.9779	−	6.73140i	1.18559	−	0.570950i	0.266055	−	0.963958i	$-0.414280\pi$
$139$	13.9779	−	6.73140i	1.18559	−	0.570950i	0.919535	+	0.393008i	$0.128565\pi$
$140$		0			0
$141$	−0.850766	−	0.409707i	−0.0716474	−	0.0345036i
$142$		0			0
$143$	8.62420	+	8.00209i	0.721192	+	0.669168i
$144$		0			0
$145$	2.74578	−	6.99613i	0.228025	−	0.580997i
$146$		0			0
$147$	15.0042	−	4.73428i	1.23753	−	0.390476i
$148$		0			0
$149$	−5.07168	+	12.9224i	−0.415488	+	1.05865i	0.557986	+	0.829850i	$0.311574\pi$
$149$	−5.07168	+	12.9224i	−0.415488	+	1.05865i	−0.973474	+	0.228796i	$0.926521\pi$
$150$		0			0
$151$	−16.9323	−	15.7109i	−1.37793	−	1.27853i	−0.921286	−	0.388887i	$-0.872860\pi$
$151$	−16.9323	−	15.7109i	−1.37793	−	1.27853i	−0.456647	−	0.889648i	$-0.650950\pi$
$152$		0			0
$153$	6.54610	+	3.15243i	0.529220	+	0.254859i
$154$		0			0
$155$	7.03741	−	3.38904i	0.565258	−	0.272214i
$156$		0			0
$157$	17.0788	−	11.6441i	1.36304	−	0.929304i	0.363042	−	0.931773i	$-0.381738\pi$
$157$	17.0788	−	11.6441i	1.36304	−	0.929304i	0.999997	+	0.00246905i	$0.000785923\pi$
$158$		0			0
$159$	7.82607	−	7.26153i	0.620648	−	0.575877i
$160$		0			0
$161$	−1.16391	−	0.354916i	−0.0917289	−	0.0279713i
$162$		0			0
$163$	1.17042	+	15.6182i	0.0916743	+	1.22331i	0.833425	+	0.552633i	$0.186377\pi$
$163$	1.17042	+	15.6182i	0.0916743	+	1.22331i	−0.741751	+	0.670676i	$0.766004\pi$
$164$		0			0
$165$	−7.58523	+	13.1380i	−0.590509	+	1.02279i
$166$		0			0
$167$	−5.38695	−	23.6018i	−0.416855	−	1.82636i	−0.549876	−	0.835246i	$-0.685325\pi$
$167$	−5.38695	−	23.6018i	−0.416855	−	1.82636i	0.133021	−	0.991113i	$-0.457532\pi$
$168$		0			0
$169$	−0.0406392	+	0.178052i	−0.00312609	+	0.0136963i
$170$		0			0
$171$	2.03253	+	5.17880i	0.155431	+	0.396033i
$172$		0			0
$173$	6.00249	−	1.85152i	0.456361	−	0.140769i	−0.0580480	−	0.998314i	$-0.518488\pi$
$173$	6.00249	−	1.85152i	0.456361	−	0.140769i	0.514409	+	0.857545i	$0.328011\pi$
$174$		0			0
$175$	−0.383697	+	1.70641i	−0.0290047	+	0.128992i
$176$		0			0
$177$	7.23868	+	12.5378i	0.544093	+	0.942396i
$178$		0			0
$179$	−4.12217	−	1.27152i	−0.308106	−	0.0950380i	0.136847	−	0.990592i	$-0.456303\pi$
$179$	−4.12217	−	1.27152i	−0.308106	−	0.0950380i	−0.444952	+	0.895554i	$0.646779\pi$
$180$		0			0
$181$	−9.17957	+	11.5108i	−0.682312	+	0.855592i	−0.995565	−	0.0940775i	$-0.970010\pi$
$181$	−9.17957	+	11.5108i	−0.682312	+	0.855592i	0.313253	+	0.949670i	$0.398581\pi$
$182$		0			0
$183$	−11.4135	−	14.3121i	−0.843711	−	1.05798i
$184$		0			0
$185$	17.5758	−	2.64912i	1.29220	−	0.194767i
$186$		0			0
$187$	11.3459	+	1.71011i	0.829691	+	0.125056i
$188$		0			0
$189$	−4.12092	+	3.84843i	−0.299753	+	0.279932i
$190$		0			0
$191$	14.8799	+	10.1450i	1.07667	+	0.734064i	0.965674	−	0.259756i	$-0.0836421\pi$
$191$	14.8799	+	10.1450i	1.07667	+	0.734064i	0.111000	+	0.993820i	$0.464595\pi$
$192$		0			0
$193$	−0.0292430	+	0.390221i	−0.00210496	+	0.0280887i	−0.998157	−	0.0606783i	$-0.980674\pi$
$193$	−0.0292430	+	0.390221i	−0.00210496	+	0.0280887i	0.996052	+	0.0887670i	$0.0282927\pi$
$194$		0			0
$195$	−16.9987			−1.21731
$196$		0			0
$197$	15.5843			1.11034			0.555168	−	0.831738i	$-0.312654\pi$
$197$	15.5843			1.11034			0.555168	+	0.831738i	$0.312654\pi$
$198$		0			0
$199$	−0.277087	+	3.69746i	−0.0196422	+	0.262106i	0.978734	+	0.205135i	$0.0657634\pi$
$199$	−0.277087	+	3.69746i	−0.0196422	+	0.262106i	−0.998376	+	0.0569712i	$0.981856\pi$
$200$		0			0
$201$	29.6351	+	20.2048i	2.09030	+	1.42514i
$202$		0			0
$203$	−3.45892	+	8.89738i	−0.242769	+	0.624474i
$204$		0			0
$205$	−18.0874	−	2.72623i	−1.26328	−	0.190408i
$206$		0			0
$207$	−0.933125	+	0.140646i	−0.0648566	+	0.00977557i
$208$		0			0
$209$	5.47786	+	6.86901i	0.378911	+	0.475140i
$210$		0			0
$211$	−3.14905	+	3.94878i	−0.216789	+	0.271845i	−0.878320	−	0.478073i	$-0.841336\pi$
$211$	−3.14905	+	3.94878i	−0.216789	+	0.271845i	0.661531	+	0.749918i	$0.269907\pi$
$212$		0			0
$213$	−6.31001	−	1.94638i	−0.432355	−	0.133364i
$214$		0			0
$215$	10.6721	+	18.4846i	0.727831	+	1.26064i
$216$		0			0
$217$	−8.92470	+	4.33339i	−0.605848	+	0.294169i
$218$		0			0
$219$	−27.4856	+	8.47817i	−1.85730	+	0.572902i
$220$		0			0
$221$	4.69712	+	11.9681i	0.315962	+	0.805059i
$222$		0			0
$223$	2.14652	−	9.40450i	0.143741	−	0.629772i	−0.850805	−	0.525481i	$-0.823885\pi$
$223$	2.14652	−	9.40450i	0.143741	−	0.629772i	0.994547	−	0.104291i	$-0.0332574\pi$
$224$		0			0
$225$	0.301825	+	1.32238i	0.0201217	+	0.0881589i
$226$		0			0
$227$	10.8360	−	18.7685i	0.719209	−	1.24571i	−0.242104	−	0.970250i	$-0.577837\pi$
$227$	10.8360	−	18.7685i	0.719209	−	1.24571i	0.961313	−	0.275457i	$-0.0888292\pi$
$228$		0			0
$229$	−1.99012	−	26.5563i	−0.131511	−	1.75489i	−0.539577	−	0.841936i	$-0.681416\pi$
$229$	−1.99012	−	26.5563i	−0.131511	−	1.75489i	0.408066	−	0.912952i	$-0.366203\pi$
$230$		0			0
$231$	9.58062	−	16.7183i	0.630359	−	1.09998i
$232$		0			0
$233$	−18.5474	+	17.2095i	−1.21508	+	1.12743i	−0.226935	+	0.973910i	$0.572871\pi$
$233$	−18.5474	+	17.2095i	−1.21508	+	1.12743i	−0.988145	+	0.153520i	$0.950939\pi$
$234$		0			0
$235$	0.723058	−	0.492973i	0.0471671	−	0.0321580i
$236$		0			0
$237$	−19.5711	+	9.42496i	−1.27128	+	0.612217i
$238$		0			0
$239$	−1.42808	−	0.687728i	−0.0923749	−	0.0444854i	0.387126	−	0.922027i	$-0.373468\pi$
$239$	−1.42808	−	0.687728i	−0.0923749	−	0.0444854i	−0.479501	+	0.877541i	$0.659182\pi$
$240$		0			0
$241$	−8.70358	−	8.07574i	−0.560647	−	0.520204i	0.348152	−	0.937438i	$-0.386809\pi$
$241$	−8.70358	−	8.07574i	−0.560647	−	0.520204i	−0.908799	+	0.417234i	$0.863000\pi$
$242$		0			0
$243$	−6.65211	+	16.9493i	−0.426733	+	1.08730i
$244$		0			0
$245$	−3.15293	+	14.2361i	−0.201433	+	0.909512i
$246$		0			0
$247$	−3.59665	+	9.16410i	−0.228849	+	0.583098i
$248$		0			0
$249$	6.78903	+	6.29930i	0.430237	+	0.399202i
$250$		0			0
$251$	4.87091	+	2.34571i	0.307449	+	0.148060i	0.581246	−	0.813728i	$-0.302565\pi$
$251$	4.87091	+	2.34571i	0.307449	+	0.148060i	−0.273797	+	0.961788i	$0.588280\pi$
$252$		0			0
$253$	−1.34267	+	0.646597i	−0.0844131	+	0.0406512i
$254$		0			0
$255$	−13.6979	+	9.33906i	−0.857795	+	0.584835i
$256$		0			0
$257$	−4.50157	+	4.17684i	−0.280800	+	0.260544i	−0.807981	−	0.589209i	$-0.799440\pi$
$257$	−4.50157	+	4.17684i	−0.280800	+	0.260544i	0.527181	+	0.849753i	$0.323249\pi$
$258$		0			0
$259$	−22.3130	+	3.43670i	−1.38646	+	0.213546i
$260$		0			0
$261$	0.553238	+	7.38244i	0.0342445	+	0.456962i
$262$		0			0
$263$	4.53008	−	7.84633i	0.279337	−	0.483826i	−0.691883	−	0.722009i	$-0.743219\pi$
$263$	4.53008	−	7.84633i	0.279337	−	0.483826i	0.971220	+	0.238184i	$0.0765520\pi$
$264$		0			0
$265$	2.20165	+	9.64604i	0.135246	+	0.592551i
$266$		0			0
$267$	6.46080	−	28.3066i	0.395395	−	1.73234i
$268$		0			0
$269$	8.45733	+	21.5489i	0.515653	+	1.31386i	0.917347	+	0.398088i	$0.130326\pi$
$269$	8.45733	+	21.5489i	0.515653	+	1.31386i	−0.401695	+	0.915774i	$0.631579\pi$
$270$		0			0
$271$	−15.8734	+	4.89630i	−0.964242	+	0.297429i	−0.736610	−	0.676318i	$-0.763575\pi$
$271$	−15.8734	+	4.89630i	−0.964242	+	0.297429i	−0.227632	+	0.973747i	$0.573098\pi$
$272$		0			0
$273$	21.5910	−	0.0695616i	1.30674	−	0.00421006i
$274$		0			0
$275$	1.07102	+	1.85506i	0.0645849	+	0.111864i
$276$		0			0
$277$	−22.2757	−	6.87113i	−1.33842	−	0.412846i	−0.458803	−	0.888538i	$-0.651722\pi$
$277$	−22.2757	−	6.87113i	−1.33842	−	0.412846i	−0.879612	+	0.475692i	$0.842198\pi$
$278$		0			0
$279$	−4.79713	+	6.01541i	−0.287196	+	0.360133i
$280$		0			0
$281$	−14.8220	−	18.5862i	−0.884207	−	1.10876i	−0.993396	−	0.114740i	$-0.963397\pi$
$281$	−14.8220	−	18.5862i	−0.884207	−	1.10876i	0.109188	−	0.994021i	$-0.465175\pi$
$282$		0			0
$283$	16.0390	−	2.41749i	0.953419	−	0.143705i	0.346130	−	0.938186i	$-0.387495\pi$
$283$	16.0390	−	2.41749i	0.953419	−	0.143705i	0.607288	+	0.794482i	$0.292257\pi$
$284$		0			0
$285$	−12.5527	−	1.89201i	−0.743556	−	0.112073i
$286$		0			0
$287$	22.9848	+	3.38871i	1.35675	+	0.200029i
$288$		0			0
$289$	−3.68582	−	2.51295i	−0.216813	−	0.147820i
$290$		0			0
$291$	1.05975	−	14.1413i	0.0621234	−	0.828979i
$292$		0			0
$293$	−6.55955			−0.383213			−0.191607	−	0.981472i	$-0.561370\pi$
$293$	−6.55955			−0.383213			−0.191607	+	0.981472i	$0.561370\pi$
$294$		0			0
$295$	−13.4171			−0.781171
$296$		0			0
$297$	−0.516049	+	6.88620i	−0.0299442	+	0.399578i
$298$		0			0
$299$	−1.37970	−	0.940662i	−0.0797900	−	0.0543999i
$300$		0			0
$301$	−13.6308	−	23.4346i	−0.785667	−	1.35075i
$302$		0			0
$303$	23.7353	+	3.57752i	1.36356	+	0.205523i
$304$		0			0
$305$	16.7757	−	2.52852i	0.960571	−	0.144783i
$306$		0			0
$307$	9.33283	+	11.7030i	0.532653	+	0.667925i	0.973242	−	0.229784i	$-0.0738018\pi$
$307$	9.33283	+	11.7030i	0.532653	+	0.667925i	−0.440589	+	0.897709i	$0.645230\pi$
$308$		0			0
$309$	10.9100	−	13.6807i	0.620649	−	0.778269i
$310$		0			0
$311$	17.6386	+	5.44078i	1.00019	+	0.308518i	0.751262	−	0.660004i	$-0.229445\pi$
$311$	17.6386	+	5.44078i	1.00019	+	0.308518i	0.248929	+	0.968522i	$0.419922\pi$
$312$		0			0
$313$	−9.57570	−	16.5856i	−0.541251	−	0.937474i	−0.998833	−	0.0483062i	$-0.984618\pi$
$313$	−9.57570	−	16.5856i	−0.541251	−	0.937474i	0.457582	−	0.889167i	$-0.348716\pi$
$314$		0			0
$315$	2.55174	+	11.0162i	0.143774	+	0.620692i
$316$		0			0
$317$	14.0307	−	4.32788i	0.788040	−	0.243078i	0.125489	−	0.992095i	$-0.459950\pi$
$317$	14.0307	−	4.32788i	0.788040	−	0.243078i	0.662551	+	0.749017i	$0.269474\pi$
$318$		0			0
$319$	4.27127	+	10.8830i	0.239145	+	0.609332i
$320$		0			0
$321$	9.71298	−	42.5554i	0.542126	−	2.37521i
$322$		0			0
$323$	2.13649	+	9.36058i	0.118878	+	0.520837i
$324$		0			0
$325$	−1.20009	+	2.07862i	−0.0665692	+	0.115301i
$326$		0			0
$327$	−1.01009	−	13.4787i	−0.0558580	−	0.745374i
$328$		0			0
$329$	−0.916375	+	0.629108i	−0.0505214	+	0.0346839i
$330$		0			0
$331$	−13.3796	+	12.4145i	−0.735412	+	0.682362i	−0.956119	−	0.292978i	$-0.905354\pi$
$331$	−13.3796	+	12.4145i	−0.735412	+	0.682362i	0.220708	+	0.975340i	$0.429163\pi$
$332$		0			0
$333$	−14.4659	+	9.86271i	−0.792729	+	0.540473i
$334$		0			0
$335$	−29.9487	+	14.4225i	−1.63627	+	0.787986i
$336$		0			0
$337$	−5.39950	−	2.60026i	−0.294130	−	0.141645i	0.281000	−	0.959708i	$-0.409334\pi$
$337$	−5.39950	−	2.60026i	−0.294130	−	0.141645i	−0.575129	+	0.818063i	$0.695048\pi$
$338$		0			0
$339$	7.12174	+	6.60801i	0.386800	+	0.358898i
$340$		0			0
$341$	−4.43908	+	11.3106i	−0.240390	+	0.612503i
$342$		0			0
$343$	3.94644	−	18.0949i	0.213088	−	0.977033i
$344$		0			0
$345$	0.786668	−	2.00440i	0.0423528	−	0.107913i
$346$		0			0
$347$	7.15404	+	6.63798i	0.384049	+	0.356345i	0.848446	−	0.529282i	$-0.177539\pi$
$347$	7.15404	+	6.63798i	0.384049	+	0.356345i	−0.464397	+	0.885627i	$0.653729\pi$
$348$		0			0
$349$	−4.59361	−	2.21217i	−0.245890	−	0.118415i	0.306880	−	0.951748i	$-0.400715\pi$
$349$	−4.59361	−	2.21217i	−0.245890	−	0.118415i	−0.552770	+	0.833334i	$0.686429\pi$
$350$		0			0
$351$	−6.97145	+	3.35727i	−0.372109	+	0.179198i
$352$		0			0
$353$	7.10674	−	4.84529i	0.378254	−	0.257889i	−0.359237	−	0.933246i	$-0.616963\pi$
$353$	7.10674	−	4.84529i	0.378254	−	0.257889i	0.737491	+	0.675357i	$0.236011\pi$
$354$		0			0
$355$	4.48609	−	4.16249i	0.238097	−	0.220922i
$356$		0			0
$357$	17.3602	−	11.9181i	0.918797	−	0.630771i
$358$		0			0
$359$	0.549849	+	7.33723i	0.0290199	+	0.387244i	0.992736	+	0.120314i	$0.0383902\pi$
$359$	0.549849	+	7.33723i	0.0290199	+	0.387244i	−0.963716	+	0.266930i	$0.913991\pi$
$360$		0			0
$361$	5.82408	−	10.0876i	0.306530	−	0.530926i
$362$		0			0
$363$	0.250352	+	1.09686i	0.0131401	+	0.0575703i
$364$		0			0
$365$	5.93170	−	25.9885i	0.310479	−	1.36030i
$366$		0			0
$367$	−6.56179	−	16.7192i	−0.342523	−	0.872733i	−0.993520	−	0.113654i	$-0.963745\pi$
$367$	−6.56179	−	16.7192i	−0.342523	−	0.872733i	0.650998	−	0.759080i	$-0.274351\pi$
$368$		0			0
$369$	17.2173	−	5.31085i	0.896299	−	0.276472i
$370$		0			0
$371$	−2.83589	−	12.2429i	−0.147232	−	0.635620i
$372$		0			0
$373$	13.8055	+	23.9119i	0.714824	+	1.23811i	0.963027	+	0.269403i	$0.0868265\pi$
$373$	13.8055	+	23.9119i	0.714824	+	1.23811i	−0.248204	+	0.968708i	$0.579840\pi$
$374$		0			0
$375$	−25.3266	−	7.81224i	−1.30786	−	0.403422i
$376$		0			0
$377$	−8.16782	+	10.2421i	−0.420664	+	0.527496i
$378$		0			0
$379$	−17.5144	−	21.9624i	−0.899655	−	1.12813i	−0.991206	−	0.132331i	$-0.957754\pi$
$379$	−17.5144	−	21.9624i	−0.899655	−	1.12813i	0.0915507	−	0.995800i	$-0.470818\pi$
$380$		0			0
$381$	11.3834	−	1.71577i	0.583189	−	0.0879016i
$382$		0			0
$383$	4.76080	+	0.717575i	0.243265	+	0.0366664i	0.269543	−	0.962988i	$-0.413127\pi$
$383$	4.76080	+	0.717575i	0.243265	+	0.0366664i	−0.0262777	+	0.999655i	$0.508365\pi$
$384$		0			0
$385$	8.97859	+	15.4363i	0.457591	+	0.786707i
$386$		0			0
$387$	−17.3714	−	11.8436i	−0.883037	−	0.602044i
$388$		0			0
$389$	2.29375	−	30.6080i	0.116298	−	1.55188i	−0.568213	−	0.822882i	$-0.692365\pi$
$389$	2.29375	−	30.6080i	0.116298	−	1.55188i	0.684510	−	0.729003i	$-0.260016\pi$
$390$		0			0
$391$	−1.62858			−0.0823609
$392$		0			0
$393$	−35.0029			−1.76566
$394$		0			0
$395$	1.50442	−	20.0751i	0.0756956	−	1.01009i
$396$		0			0
$397$	1.55504	+	1.06021i	0.0780454	+	0.0532104i	0.601714	−	0.798712i	$-0.294485\pi$
$397$	1.55504	+	1.06021i	0.0780454	+	0.0532104i	−0.523669	+	0.851922i	$0.675437\pi$
$398$		0			0
$399$	15.9515	+	2.35177i	0.798575	+	0.117736i
$400$		0			0
$401$	−21.2248	−	3.19913i	−1.05992	−	0.159757i	−0.404130	−	0.914702i	$-0.632426\pi$
$401$	−21.2248	−	3.19913i	−1.05992	−	0.159757i	−0.655788	+	0.754945i	$0.727664\pi$
$402$		0			0
$403$	−13.4628	+	2.02919i	−0.670628	+	0.101081i
$404$		0			0
$405$	−14.2153	−	17.8254i	−0.706364	−	0.885752i
$406$		0			0
$407$	−17.2390	+	21.6171i	−0.854508	+	1.07152i
$408$		0			0
$409$	5.16087	+	1.59192i	0.255189	+	0.0787153i	0.419710	−	0.907658i	$-0.362132\pi$
$409$	5.16087	+	1.59192i	0.255189	+	0.0787153i	−0.164521	+	0.986374i	$0.552608\pi$
$410$		0			0
$411$	−6.93197	−	12.0065i	−0.341929	−	0.592238i
$412$		0			0
$413$	17.0417	−	0.0549047i	0.838566	−	0.00270168i
$414$		0			0
$415$	−8.20170	+	2.52989i	−0.402606	+	0.124187i
$416$		0			0
$417$	−12.7396	−	32.4599i	−0.623860	−	1.58957i
$418$		0			0
$419$	−3.07146	+	13.4570i	−0.150051	+	0.657415i	0.842818	+	0.538199i	$0.180895\pi$
$419$	−3.07146	+	13.4570i	−0.150051	+	0.657415i	−0.992868	+	0.119216i	$0.961962\pi$
$420$		0			0
$421$	1.11575	+	4.88843i	0.0543784	+	0.238247i	0.994812	−	0.101730i	$-0.0324377\pi$
$421$	1.11575	+	4.88843i	0.0543784	+	0.238247i	−0.940434	+	0.339977i	$0.889581\pi$
$422$		0			0
$423$	−0.431009	+	0.746530i	−0.0209564	+	0.0362975i
$424$		0			0
$425$	0.174933	+	2.33432i	0.00848550	+	0.113231i
$426$		0			0
$427$	−21.2973	+	3.28025i	−1.03065	+	0.158743i
$428$		0			0
$429$	19.3840	−	17.9857i	0.935867	−	0.868358i
$430$		0			0
$431$	11.3062	−	7.70846i	0.544602	−	0.371304i	−0.259547	−	0.965730i	$-0.583573\pi$
$431$	11.3062	−	7.70846i	0.544602	−	0.371304i	0.804150	+	0.594427i	$0.202621\pi$
$432$		0			0
$433$	−28.3186	+	13.6375i	−1.36091	+	0.655378i	−0.964838	−	0.262844i	$-0.915340\pi$
$433$	−28.3186	+	13.6375i	−1.36091	+	0.655378i	−0.396068	+	0.918221i	$0.629625\pi$
$434$		0			0
$435$	−15.2195	−	7.32934i	−0.729721	−	0.351415i
$436$		0			0
$437$	−0.914134	−	0.848193i	−0.0437290	−	0.0405746i
$438$		0			0
$439$	−1.31777	+	3.35761i	−0.0628935	+	0.160250i	−0.958866	−	0.283860i	$-0.908385\pi$
$439$	−1.31777	+	3.35761i	−0.0628935	+	0.160250i	0.895972	+	0.444110i	$0.146480\pi$
$440$		0			0
$441$	−3.28618	−	13.9818i	−0.156485	−	0.665799i
$442$		0			0
$443$	−7.96533	+	20.2953i	−0.378444	+	0.964260i	0.607067	+	0.794651i	$0.292346\pi$
$443$	−7.96533	+	20.2953i	−0.378444	+	0.964260i	−0.985511	+	0.169610i	$0.945749\pi$
$444$		0			0
$445$	19.7250	+	18.3022i	0.935056	+	0.867605i
$446$		0			0
$447$	28.1117	+	13.5379i	1.32964	+	0.640320i
$448$		0			0
$449$	−3.87521	+	1.86620i	−0.182883	+	0.0880717i	−0.523085	−	0.852281i	$-0.675219\pi$
$449$	−3.87521	+	1.86620i	−0.182883	+	0.0880717i	0.340202	+	0.940352i	$0.389505\pi$
$450$		0			0
$451$	23.5099	−	16.0288i	1.10704	−	0.754765i
$452$		0			0
$453$	−38.0575	+	35.3122i	−1.78810	+	1.65911i
$454$		0			0
$455$	−9.94899	+	17.3611i	−0.466416	+	0.813901i
$456$		0			0
$457$	0.139107	+	1.85625i	0.00650713	+	0.0868316i	0.999512	−	0.0312434i	$-0.00994671\pi$
$457$	0.139107	+	1.85625i	0.00650713	+	0.0868316i	−0.993005	+	0.118075i	$0.962328\pi$
$458$		0			0
$459$	−3.77324	+	6.53545i	−0.176120	+	0.305049i
$460$		0			0
$461$	−4.43162	−	19.4162i	−0.206401	−	0.904303i	−0.966939	−	0.255009i	$-0.917922\pi$
$461$	−4.43162	−	19.4162i	−0.206401	−	0.904303i	0.760537	−	0.649294i	$-0.224936\pi$
$462$		0			0
$463$	2.64798	−	11.6016i	0.123062	−	0.539171i	−0.875383	−	0.483430i	$-0.839391\pi$
$463$	2.64798	−	11.6016i	0.123062	−	0.539171i	0.998445	−	0.0557409i	$-0.0177521\pi$
$464$		0			0
$465$	−6.41395	−	16.3425i	−0.297440	−	0.757864i
$466$		0			0
$467$	5.95999	−	1.83841i	0.275796	−	0.0850717i	−0.153772	−	0.988106i	$-0.549142\pi$
$467$	5.95999	−	1.83841i	0.275796	−	0.0850717i	0.429568	+	0.903035i	$0.358666\pi$
$468$		0			0
$469$	37.9803	−	18.4413i	1.75377	−	0.851541i
$470$		0			0
$471$	−23.2299	−	40.2353i	−1.07038	−	1.85394i
$472$		0			0
$473$	−31.7275	−	9.78662i	−1.45883	−	0.449989i
$474$		0			0
$475$	−1.11756	+	1.40138i	−0.0512773	+	0.0642997i
$476$		0			0
$477$	−6.07652	−	7.61971i	−0.278225	−	0.348883i
$478$		0			0
$479$	−12.7347	+	1.91945i	−0.581864	+	0.0877019i	−0.433377	−	0.901213i	$-0.642678\pi$
$479$	−12.7347	+	1.91945i	−0.581864	+	0.0877019i	−0.148487	+	0.988914i	$0.547440\pi$
$480$		0			0
$481$	−30.6354	−	4.61755i	−1.39685	−	0.210542i
$482$		0			0
$483$	−0.990984	+	2.54910i	−0.0450913	+	0.115988i
$484$		0			0
$485$	10.8587	+	7.40336i	0.493069	+	0.336169i
$486$		0			0
$487$	1.44341	−	19.2610i	0.0654073	−	0.872799i	−0.863941	−	0.503594i	$-0.832011\pi$
$487$	1.44341	−	19.2610i	0.0654073	−	0.872799i	0.929348	−	0.369205i	$-0.120370\pi$
$488$		0			0
$489$	35.2022			1.59190
$490$		0			0
$491$	19.6858			0.888409			0.444204	−	0.895925i	$-0.353486\pi$
$491$	19.6858			0.888409			0.444204	+	0.895925i	$0.353486\pi$
$492$		0			0
$493$	−0.954780	+	12.7407i	−0.0430011	+	0.573810i
$494$		0			0
$495$	11.4425	+	7.80136i	0.514302	+	0.350645i
$496$		0			0
$497$	−5.68098	+	5.30534i	−0.254827	+	0.237977i
$498$		0			0
$499$	−6.32413	−	0.953209i	−0.283107	−	0.0426715i	0.00595385	−	0.999982i	$-0.498105\pi$
$499$	−6.32413	−	0.953209i	−0.283107	−	0.0426715i	−0.289061	+	0.957311i	$0.593343\pi$
$500$		0			0
$501$	−53.8044	+	8.10972i	−2.40381	+	0.362315i
$502$		0			0
$503$	22.6243	+	28.3700i	1.00877	+	1.26496i	0.963984	+	0.265960i	$0.0856890\pi$
$503$	22.6243	+	28.3700i	1.00877	+	1.26496i	0.0447853	+	0.998997i	$0.485740\pi$
$504$		0			0
$505$	−13.8698	+	17.3921i	−0.617196	+	0.773940i
$506$		0			0
$507$	0.392250	+	0.120993i	0.0174204	+	0.00537349i
$508$		0			0
$509$	0.605617	+	1.04896i	0.0268435	+	0.0464943i	0.879135	−	0.476573i	$-0.158121\pi$
$509$	0.605617	+	1.04896i	0.0268435	+	0.0464943i	−0.852292	+	0.523067i	$0.824788\pi$
$510$		0			0
$511$	−7.42780	+	33.0335i	−0.328587	+	1.46132i
$512$		0			0
$513$	−5.52172	+	1.70323i	−0.243790	+	0.0751992i
$514$		0			0
$515$	5.92464	+	15.0957i	0.261071	+	0.665197i
$516$		0			0
$517$	−0.302921	+	1.32719i	−0.0133225	+	0.0583695i
$518$		0			0
$519$	−3.14168	−	13.7646i	−0.137905	−	0.604200i
$520$		0			0
$521$	−19.4894	+	33.7567i	−0.853847	+	1.47891i	0.0238632	+	0.999715i	$0.492403\pi$
$521$	−19.4894	+	33.7567i	−0.853847	+	1.47891i	−0.877710	+	0.479192i	$0.840930\pi$
$522$		0			0
$523$	−1.26003	−	16.8139i	−0.0550971	−	0.735220i	−0.954521	−	0.298143i	$-0.903633\pi$
$523$	−1.26003	−	16.8139i	−0.0550971	−	0.735220i	0.899424	−	0.437077i	$-0.143986\pi$
$524$		0			0
$525$	3.76020	+	1.14661i	0.164108	+	0.0500423i
$526$		0			0
$527$	−9.73371	+	9.03156i	−0.424007	+	0.393421i
$528$		0			0
$529$	−18.8287	+	12.8372i	−0.818640	+	0.558139i
$530$		0			0
$531$	11.9074	−	5.73429i	0.516736	−	0.248847i
$532$		0			0
$533$	28.7258	+	13.8336i	1.24425	+	0.599201i
$534$		0			0
$535$	29.6540	+	27.5149i	1.28206	+	1.18957i
$536$		0			0
$537$	−3.54230	+	9.02563i	−0.152861	+	0.389485i
$538$		0			0
$539$	−11.4673	−	19.5697i	−0.493933	−	0.842926i
$540$		0			0
$541$	−6.85433	+	17.4645i	−0.294691	+	0.750859i	0.704464	+	0.709740i	$0.251188\pi$
$541$	−6.85433	+	17.4645i	−0.294691	+	0.750859i	−0.999154	+	0.0411192i	$0.986908\pi$
$542$		0			0
$543$	24.2578	+	22.5080i	1.04100	+	0.965910i
$544$		0			0
$545$	11.2860	+	5.43506i	0.483440	+	0.232813i
$546$		0			0
$547$	6.75602	−	3.25353i	0.288867	−	0.139111i	−0.283839	−	0.958872i	$-0.591608\pi$
$547$	6.75602	−	3.25353i	0.288867	−	0.139111i	0.572706	+	0.819761i	$0.305894\pi$
$548$		0			0
$549$	−13.8074	+	9.41372i	−0.589285	+	0.401768i
$550$		0			0
$551$	−7.17148	+	6.65416i	−0.305515	+	0.283477i
$552$		0			0
$553$	−1.82869	+	25.5045i	−0.0777638	+	1.08456i
$554$		0			0
$555$	−2.98547	−	39.8383i	−0.126726	−	1.69104i
$556$		0			0
$557$	16.4056	−	28.4153i	0.695128	−	1.20400i	−0.275010	−	0.961441i	$-0.588681\pi$
$557$	16.4056	−	28.4153i	0.695128	−	1.20400i	0.970138	−	0.242555i	$-0.0779855\pi$
$558$		0			0
$559$	−8.27867	−	36.2712i	−0.350150	−	1.53411i
$560$		0			0
$561$	5.73866	−	25.1427i	0.242286	−	1.06153i
$562$		0			0
$563$	−13.2861	−	33.8525i	−0.559943	−	1.42671i	−0.878009	−	0.478643i	$-0.841129\pi$
$563$	−13.2861	−	33.8525i	−0.559943	−	1.42671i	0.318066	−	0.948068i	$-0.396967\pi$
$564$		0			0
$565$	−8.60365	+	2.65387i	−0.361958	+	0.111649i
$566$		0			0
$567$	18.1285	+	22.5828i	0.761326	+	0.948389i
$568$		0			0
$569$	21.7850	+	37.7327i	0.913273	+	1.58184i	0.809410	+	0.587244i	$0.199787\pi$
$569$	21.7850	+	37.7327i	0.913273	+	1.58184i	0.103863	+	0.994592i	$0.466880\pi$
$570$		0			0
$571$	−29.3174	−	9.04321i	−1.22689	−	0.378447i	−0.387449	−	0.921891i	$-0.626644\pi$
$571$	−29.3174	−	9.04321i	−1.22689	−	0.378447i	−0.839445	+	0.543445i	$0.817120\pi$
$572$		0			0
$573$	25.2377	−	31.6470i	1.05432	−	1.32207i
$574$		0			0
$575$	−0.189562	−	0.237703i	−0.00790527	−	0.00991290i
$576$		0			0
$577$	12.5340	−	1.88919i	0.521796	−	0.0786481i	0.117137	−	0.993116i	$-0.462628\pi$
$577$	12.5340	−	1.88919i	0.521796	−	0.0786481i	0.404659	+	0.914468i	$0.367390\pi$
$578$		0			0
$579$	0.869706	+	0.131087i	0.0361437	+	0.00544779i
$580$		0			0
$581$	10.4070	−	3.24690i	0.431757	−	0.134704i
$582$		0			0
$583$	−12.7167	−	8.67008i	−0.526671	−	0.359078i
$584$		0			0
$585$	−1.15965	+	15.4745i	−0.0479458	+	0.639792i
$586$		0			0
$587$	−16.0746			−0.663469			−0.331735	−	0.943373i	$-0.607634\pi$
$587$	−16.0746			−0.663469			−0.331735	+	0.943373i	$0.607634\pi$
$588$		0			0
$589$	−10.1674			−0.418940
$590$		0			0
$591$	2.61762	−	34.9297i	0.107675	−	1.43682i
$592$		0			0
$593$	9.93446	+	6.77320i	0.407959	+	0.278142i	0.749863	−	0.661593i	$-0.230119\pi$
$593$	9.93446	+	6.77320i	0.407959	+	0.278142i	−0.341904	+	0.939735i	$0.611072\pi$
$594$		0			0
$595$	1.52106	+	19.4558i	0.0623575	+	0.797611i
$596$		0			0
$597$	8.24074	+	1.24209i	0.337271	+	0.0508354i
$598$		0			0
$599$	−10.4581	+	1.57630i	−0.427306	+	0.0644060i	−0.359175	−	0.933270i	$-0.616942\pi$
$599$	−10.4581	+	1.57630i	−0.427306	+	0.0644060i	−0.0681314	+	0.997676i	$0.521704\pi$
$600$		0			0
$601$	0.238914	+	0.299588i	0.00974549	+	0.0122205i	0.786680	−	0.617361i	$-0.211798\pi$
$601$	0.238914	+	0.299588i	0.00974549	+	0.0122205i	−0.776935	+	0.629581i	$0.783227\pi$
$602$		0			0
$603$	20.4148	−	25.5994i	0.831356	−	1.04249i
$604$		0			0
$605$	−0.996347	−	0.307332i	−0.0405073	−	0.0124948i
$606$		0			0
$607$	13.2672	+	22.9794i	0.538499	+	0.932707i	0.998985	+	0.0450402i	$0.0143416\pi$
$607$	13.2672	+	22.9794i	0.538499	+	0.932707i	−0.460487	+	0.887667i	$0.652325\pi$
$608$		0			0
$609$	19.3611	+	9.24708i	0.784551	+	0.374711i
$610$		0			0
$611$	−1.45761	+	0.449613i	−0.0589685	+	0.0181894i
$612$		0			0
$613$	17.9805	+	45.8136i	0.726227	+	1.85039i	0.465756	+	0.884913i	$0.345782\pi$
$613$	17.9805	+	45.8136i	0.726227	+	1.85039i	0.260471	+	0.965482i	$0.416122\pi$
$614$		0			0
$615$	−9.14847	+	40.0821i	−0.368902	+	1.61626i
$616$		0			0
$617$	7.10315	+	31.1209i	0.285962	+	1.25288i	0.890013	+	0.455936i	$0.150695\pi$
$617$	7.10315	+	31.1209i	0.285962	+	1.25288i	−0.604051	+	0.796946i	$0.706447\pi$
$618$		0			0
$619$	8.37986	−	14.5143i	0.336815	−	0.583381i	−0.647017	−	0.762476i	$-0.723984\pi$
$619$	8.37986	−	14.5143i	0.336815	−	0.583381i	0.983832	+	0.179095i	$0.0573170\pi$
$620$		0			0
$621$	−0.0732462	−	0.977403i	−0.00293927	−	0.0392218i
$622$		0			0
$623$	−25.1287	−	23.1658i	−1.00676	−	0.928117i
$624$		0			0
$625$	15.5830	−	14.4589i	0.623319	−	0.578355i
$626$		0			0
$627$	16.3159	−	11.1240i	0.651594	−	0.444249i
$628$		0			0
$629$	−27.2234	+	13.1101i	−1.08547	+	0.522734i
$630$		0			0
$631$	40.0297	+	19.2773i	1.59356	+	0.767417i	0.999320	−	0.0368732i	$-0.0117398\pi$
$631$	40.0297	+	19.2773i	1.59356	+	0.767417i	0.594237	+	0.804290i	$0.297454\pi$
$632$		0			0
$633$	8.32164	+	7.72135i	0.330755	+	0.306896i
$634$		0			0
$635$	−3.89776	+	9.93134i	−0.154678	+	0.394113i
$636$		0			0
$637$	12.5657	−	22.0919i	0.497870	−	0.875314i
$638$		0			0
$639$	−2.20232	+	5.61143i	−0.0871225	+	0.221985i
$640$		0			0
$641$	−2.48163	−	2.30261i	−0.0980183	−	0.0909477i	0.629642	−	0.776886i	$-0.283202\pi$
$641$	−2.48163	−	2.30261i	−0.0980183	−	0.0909477i	−0.727660	+	0.685938i	$0.759392\pi$
$642$		0			0
$643$	21.2342	+	10.2259i	0.837397	+	0.403269i	0.802884	−	0.596135i	$-0.203298\pi$
$643$	21.2342	+	10.2259i	0.837397	+	0.403269i	0.0345126	+	0.999404i	$0.489012\pi$
$644$		0			0
$645$	43.2229	−	20.8151i	1.70190	−	0.819592i
$646$		0			0
$647$	−9.92934	+	6.76971i	−0.390363	+	0.266145i	−0.742558	−	0.669782i	$-0.766388\pi$
$647$	−9.92934	+	6.76971i	−0.390363	+	0.266145i	0.352195	+	0.935927i	$0.385435\pi$
$648$		0			0
$649$	15.2997	−	14.1961i	0.600566	−	0.557244i
$650$		0			0
$651$	8.21356	+	20.7312i	0.321915	+	0.812518i
$652$		0			0
$653$	2.94871	+	39.3478i	0.115392	+	1.53980i	0.691471	+	0.722404i	$0.256963\pi$
$653$	2.94871	+	39.3478i	0.115392	+	1.53980i	−0.576079	+	0.817394i	$0.695418\pi$
$654$		0			0
$655$	16.2197	−	28.0933i	0.633754	−	1.09769i
$656$		0			0
$657$	5.84289	+	25.5994i	0.227953	+	0.998727i
$658$		0			0
$659$	−6.44941	+	28.2567i	−0.251233	+	1.10073i	0.679110	+	0.734036i	$0.262366\pi$
$659$	−6.44941	+	28.2567i	−0.251233	+	1.10073i	−0.930343	+	0.366689i	$0.880491\pi$
$660$		0			0
$661$	3.91515	+	9.97565i	0.152282	+	0.388008i	0.986574	−	0.163315i	$-0.0522186\pi$
$661$	3.91515	+	9.97565i	0.152282	+	0.388008i	−0.834292	+	0.551323i	$0.814123\pi$
$662$		0			0
$663$	27.6135	−	8.51763i	1.07242	−	0.330797i
$664$		0			0
$665$	−9.27914	+	11.7129i	−0.359830	+	0.454206i
$666$		0			0
$667$	−0.829703	−	1.43709i	−0.0321262	−	0.0556443i
$668$		0			0
$669$	−20.7182	−	6.39071i	−0.801011	−	0.247079i
$670$		0			0
$671$	−16.4543	+	20.6330i	−0.635210	+	0.796528i
$672$		0			0
$673$	7.38722	+	9.26328i	0.284756	+	0.357073i	0.903552	−	0.428479i	$-0.140950\pi$
$673$	7.38722	+	9.26328i	0.284756	+	0.357073i	−0.618795	+	0.785552i	$0.712379\pi$
$674$		0			0
$675$	−1.39309	+	0.209974i	−0.0536200	+	0.00808192i
$676$		0			0
$677$	−29.2222	−	4.40454i	−1.12310	−	0.169280i	−0.438873	−	0.898549i	$-0.644622\pi$
$677$	−29.2222	−	4.40454i	−1.12310	−	0.169280i	−0.684227	+	0.729269i	$0.739860\pi$
$678$		0			0
$679$	−13.8225	−	9.35894i	−0.530459	−	0.359163i
$680$		0			0
$681$	−40.2465	−	27.4396i	−1.54225	−	1.05149i
$682$		0			0
$683$	2.54144	−	33.9132i	0.0972456	−	1.29765i	−0.708636	−	0.705575i	$-0.750689\pi$
$683$	2.54144	−	33.9132i	0.0972456	−	1.29765i	0.805881	−	0.592077i	$-0.201692\pi$
$684$		0			0
$685$	12.8485			0.490918
$686$		0			0
$687$	−59.8560			−2.28365
$688$		0			0
$689$	1.28879	−	17.1977i	0.0490989	−	0.655179i
$690$		0			0
$691$	−9.73189	−	6.63509i	−0.370219	−	0.252411i	0.363891	−	0.931441i	$-0.381448\pi$
$691$	−9.73189	−	6.63509i	−0.370219	−	0.252411i	−0.734110	+	0.679031i	$0.762400\pi$
$692$		0			0
$693$	−14.5656	−	9.86208i	−0.553302	−	0.374629i
$694$		0			0
$695$	31.9555	+	4.81652i	1.21214	+	0.182701i
$696$		0			0
$697$	30.7479	−	4.63451i	1.16466	−	0.175544i
$698$		0			0
$699$	35.4570	+	44.4617i	1.34111	+	1.68169i
$700$		0			0
$701$	13.9858	−	17.5376i	0.528235	−	0.662385i	−0.444100	−	0.895977i	$-0.646476\pi$
$701$	13.9858	−	17.5376i	0.528235	−	0.662385i	0.972335	+	0.233592i	$0.0750479\pi$
$702$		0			0
$703$	−22.1087	−	6.81962i	−0.833844	−	0.257207i
$704$		0			0
$705$	−0.983471	−	1.70342i	−0.0370397	−	0.0641546i
$706$		0			0
$707$	17.5455	−	22.1474i	0.659867	−	0.832938i
$708$		0			0
$709$	7.94878	−	2.45187i	0.298523	−	0.0920821i	−0.141876	−	0.989884i	$-0.545313\pi$
$709$	7.94878	−	2.45187i	0.298523	−	0.0920821i	0.440399	+	0.897802i	$0.354837\pi$
$710$		0			0
$711$	7.24471	+	18.4592i	0.271698	+	0.692275i
$712$		0			0
$713$	0.383760	−	1.68136i	0.0143719	−	0.0629675i
$714$		0			0
$715$	5.45314	+	23.8918i	0.203936	+	0.893501i
$716$		0			0
$717$	−1.78130	+	3.08531i	−0.0665239	+	0.115223i
$718$		0			0
$719$	−1.07948	−	14.4046i	−0.0402577	−	0.537202i	−0.980477	−	0.196633i	$-0.936999\pi$
$719$	−1.07948	−	14.4046i	−0.0402577	−	0.537202i	0.940220	−	0.340569i	$-0.110620\pi$
$720$		0			0
$721$	−7.58696	−	19.1496i	−0.282553	−	0.713169i
$722$		0			0
$723$	−19.5624	+	18.1513i	−0.727533	+	0.675052i
$724$		0			0
$725$	−1.97072	+	1.34362i	−0.0731908	+	0.0499007i
$726$		0			0
$727$	−5.78517	+	2.78599i	−0.214560	+	0.103327i	−0.538077	−	0.842896i	$-0.680849\pi$
$727$	−5.78517	+	2.78599i	−0.214560	+	0.103327i	0.323517	+	0.946222i	$0.395135\pi$
$728$		0			0
$729$	7.28721	+	3.50934i	0.269897	+	0.129975i
$730$		0			0
$731$	−26.5984	−	24.6797i	−0.983777	−	0.912811i
$732$		0			0
$733$	5.64411	−	14.3810i	0.208470	−	0.531173i	−0.787948	−	0.615742i	$-0.788856\pi$
$733$	5.64411	−	14.3810i	0.208470	−	0.531173i	0.996418	+	0.0845694i	$0.0269515\pi$
$734$		0			0
$735$	31.3784	+	9.45797i	1.15741	+	0.348862i
$736$		0			0
$737$	18.8911	−	48.1338i	0.695863	−	1.77303i
$738$		0			0
$739$	23.9645	+	22.2358i	0.881547	+	0.817956i	0.984255	−	0.176756i	$-0.0565602\pi$
$739$	23.9645	+	22.2358i	0.881547	+	0.817956i	−0.102708	+	0.994712i	$0.532751\pi$
$740$		0			0
$741$	19.9358	+	9.60056i	0.732359	+	0.352686i
$742$		0			0
$743$	−1.38535	+	0.667150i	−0.0508236	+	0.0244754i	−0.459123	−	0.888373i	$-0.651836\pi$
$743$	−1.38535	+	0.667150i	−0.0508236	+	0.0244754i	0.408299	+	0.912848i	$0.366122\pi$
$744$		0			0
$745$	−23.8919	+	16.2892i	−0.875331	+	0.596790i
$746$		0			0
$747$	6.19760	−	5.75054i	0.226758	−	0.210401i
$748$		0			0
$749$	−37.7777	−	34.8268i	−1.38037	−	1.27254i
$750$		0			0
$751$	−2.03443	−	27.1475i	−0.0742373	−	0.990628i	−0.902612	−	0.430454i	$-0.858353\pi$
$751$	−2.03443	−	27.1475i	−0.0742373	−	0.990628i	0.828375	−	0.560174i	$-0.189266\pi$
$752$		0			0
$753$	6.07568	−	10.5234i	0.221410	−	0.383493i
$754$		0			0
$755$	−10.7064	−	46.9079i	−0.389646	−	1.70715i
$756$		0			0
$757$	−1.55929	+	6.83168i	−0.0566732	+	0.248302i	−0.995327	−	0.0965585i	$-0.969217\pi$
$757$	−1.55929	+	6.83168i	−0.0566732	+	0.248302i	0.938654	+	0.344860i	$0.112074\pi$
$758$		0			0
$759$	1.22372	+	3.11799i	0.0444183	+	0.113176i
$760$		0			0
$761$	32.4548	−	10.0110i	1.17649	−	0.362898i	0.355957	−	0.934502i	$-0.384155\pi$
$761$	32.4548	−	10.0110i	1.17649	−	0.362898i	0.820529	+	0.571604i	$0.193679\pi$
$762$		0			0
$763$	−14.3572	−	6.85717i	−0.519765	−	0.248246i
$764$		0			0
$765$	7.56718	+	13.1067i	0.273592	+	0.473875i
$766$		0			0
$767$	22.3476	+	6.89331i	0.806924	+	0.248903i
$768$		0			0
$769$	−14.0080	+	17.5655i	−0.505141	+	0.633427i	−0.967380	−	0.253328i	$-0.918475\pi$
$769$	−14.0080	+	17.5655i	−0.505141	+	0.633427i	0.462239	+	0.886755i	$0.347046\pi$
$770$		0			0
$771$	8.60562	+	10.7911i	0.309924	+	0.388632i
$772$		0			0
$773$	−6.87676	+	1.03650i	−0.247340	+	0.0372805i	−0.271542	−	0.962427i	$-0.587534\pi$
$773$	−6.87676	+	1.03650i	−0.247340	+	0.0372805i	0.0242021	+	0.999707i	$0.492295\pi$
$774$		0			0
$775$	−2.45119	−	0.369458i	−0.0880495	−	0.0132713i
$776$		0			0
$777$	3.95501	+	50.5884i	0.141885	+	1.81485i
$778$		0			0
$779$	19.6728	+	13.4127i	0.704850	+	0.480559i
$780$		0			0
$781$	−0.711411	+	9.49312i	−0.0254563	+	0.339691i
$782$		0			0
$783$	−7.68932			−0.274794
$784$		0			0
$785$	43.0570			1.53677
$786$		0			0
$787$	−2.52913	+	33.7489i	−0.0901539	+	1.20302i	0.750285	+	0.661114i	$0.229916\pi$
$787$	−2.52913	+	33.7489i	−0.0901539	+	1.20302i	−0.840439	+	0.541906i	$0.817703\pi$
$788$		0			0
$789$	−16.8254	−	11.4714i	−0.599001	−	0.408392i
$790$		0			0
$791$	10.9171	−	3.40603i	0.388166	−	0.121104i
$792$		0			0
$793$	−29.2408	−	4.40734i	−1.03837	−	0.156509i
$794$		0			0
$795$	21.9899	−	3.31444i	0.779900	−	0.117551i
$796$		0			0
$797$	−29.4140	−	36.8840i	−1.04190	−	1.30650i	−0.950513	−	0.310683i	$-0.899442\pi$
$797$	−29.4140	−	36.8840i	−1.04190	−	1.30650i	−0.0913848	−	0.995816i	$-0.529129\pi$
$798$		0			0
$799$	−0.927550	+	1.16311i	−0.0328144	+	0.0411479i
$800$		0			0
$801$	−25.3277	−	7.81256i	−0.894910	−	0.276043i
$802$		0			0
$803$	20.7334	+	35.9112i	0.731664	+	1.26728i
$804$		0			0
$805$	−1.58670	−	1.97657i	−0.0559240	−	0.0696648i
$806$		0			0
$807$	49.7191	−	15.3363i	1.75019	−	0.539863i
$808$		0			0
$809$	19.7045	+	50.2062i	0.692772	+	1.76516i	0.642330	+	0.766428i	$0.277968\pi$
$809$	19.7045	+	50.2062i	0.692772	+	1.76516i	0.0504424	+	0.998727i	$0.483937\pi$
$810$		0			0
$811$	10.5183	−	46.0836i	0.369347	−	1.61821i	−0.359230	−	0.933249i	$-0.616961\pi$
$811$	10.5183	−	46.0836i	0.369347	−	1.61821i	0.728577	−	0.684964i	$-0.240182\pi$
$812$		0			0
$813$	8.30811	+	36.4002i	0.291378	+	1.27661i
$814$		0			0
$815$	−16.3120	+	28.2532i	−0.571385	+	0.989667i
$816$		0			0
$817$	−2.07626	−	27.7058i	−0.0726392	−	0.969303i
$818$		0			0
$819$	1.40961	−	19.6597i	0.0492558	−	0.686966i
$820$		0			0
$821$	23.1623	−	21.4915i	0.808370	−	0.750058i	−0.163255	−	0.986584i	$-0.552199\pi$
$821$	23.1623	−	21.4915i	0.808370	−	0.750058i	0.971625	+	0.236526i	$0.0760089\pi$
$822$		0			0
$823$	12.5700	−	8.57008i	0.438162	−	0.298734i	−0.324075	−	0.946031i	$-0.605053\pi$
$823$	12.5700	−	8.57008i	0.438162	−	0.298734i	0.762238	+	0.647297i	$0.224101\pi$
$824$		0			0
$825$	4.33772	−	2.08893i	0.151020	−	0.0727274i
$826$		0			0
$827$	−44.9707	−	21.6568i	−1.56379	−	0.753079i	−0.566317	−	0.824187i	$-0.691632\pi$
$827$	−44.9707	−	21.6568i	−1.56379	−	0.753079i	−0.997469	+	0.0711080i	$0.977347\pi$
$828$		0			0
$829$	23.1925	+	21.5195i	0.805509	+	0.747403i	0.971070	−	0.238796i	$-0.0767528\pi$
$829$	23.1925	+	21.5195i	0.805509	+	0.747403i	−0.165560	+	0.986200i	$0.552943\pi$
$830$		0			0
$831$	−19.1421	+	48.7733i	−0.664032	+	1.69193i
$832$		0			0
$833$	−2.01159	−	24.7056i	−0.0696976	−	0.855998i
$834$		0			0
$835$	18.4231	−	46.9412i	0.637557	−	1.62447i
$836$		0			0
$837$	−5.85812	−	5.43554i	−0.202486	−	0.187880i
$838$		0			0
$839$	36.5402	+	17.5968i	1.26151	+	0.607511i	0.940573	−	0.339590i	$-0.110288\pi$
$839$	36.5402	+	17.5968i	1.26151	+	0.607511i	0.320935	+	0.947101i	$0.396003\pi$
$840$		0			0
$841$	14.3991	−	6.93424i	0.496520	−	0.239112i
$842$		0			0
$843$	−44.1476	+	30.0994i	−1.52053	+	1.03668i
$844$		0			0
$845$	−0.278869	+	0.258753i	−0.00959340	+	0.00890137i
$846$		0			0
$847$	1.26677	+	0.386281i	0.0435267	+	0.0132728i
$848$		0			0
$849$	−2.72442	−	36.3549i	−0.0935020	−	1.24770i
$850$		0			0
$851$	1.96222	−	3.39867i	0.0672641	−	0.116505i
$852$		0			0
$853$	−1.93037	−	8.45752i	−0.0660948	−	0.289580i	0.931069	−	0.364843i	$-0.118877\pi$
$853$	−1.93037	−	8.45752i	−0.0660948	−	0.289580i	−0.997164	+	0.0752632i	$0.976020\pi$
$854$		0			0
$855$	−2.57870	+	11.2980i	−0.0881897	+	0.386384i
$856$		0			0
$857$	−18.7196	−	47.6968i	−0.639450	−	1.62929i	−0.770145	−	0.637869i	$-0.779816\pi$
$857$	−18.7196	−	47.6968i	−0.639450	−	1.62929i	0.130695	−	0.991423i	$-0.458279\pi$
$858$		0			0
$859$	0.237939	−	0.0733946i	0.00811839	−	0.00250419i	−0.290693	−	0.956816i	$-0.593886\pi$
$859$	0.237939	−	0.0733946i	0.00811839	−	0.00250419i	0.298812	+	0.954312i	$0.403410\pi$
$860$		0			0
$861$	11.4559	−	50.9477i	0.390416	−	1.73629i
$862$		0			0
$863$	4.90348	+	8.49307i	0.166916	+	0.289107i	0.937334	−	0.348432i	$-0.113286\pi$
$863$	4.90348	+	8.49307i	0.166916	+	0.289107i	−0.770418	+	0.637539i	$0.779952\pi$
$864$		0			0
$865$	12.5032	+	3.85674i	0.425123	+	0.131133i
$866$		0			0
$867$	−6.25146	+	7.83909i	−0.212311	+	0.266229i
$868$		0			0
$869$	19.5252	+	24.4838i	0.662346	+	0.830555i
$870$		0			0
$871$	57.2927	−	8.63548i	1.94129	−	0.292602i
$872$		0			0
$873$	−12.8010	−	1.92944i	−0.433249	−	0.0653017i
$874$		0			0
$875$	−22.8019	+	21.2942i	−0.770845	+	0.719875i
$876$		0			0
$877$	38.0851	+	25.9660i	1.28604	+	0.876809i	0.996760	−	0.0804347i	$-0.0256308\pi$
$877$	38.0851	+	25.9660i	1.28604	+	0.876809i	0.289283	+	0.957244i	$0.406583\pi$
$878$		0			0
$879$	−1.10178	+	14.7022i	−0.0371620	+	0.495893i
$880$		0			0
$881$	18.9168			0.637325			0.318662	−	0.947868i	$-0.396766\pi$
$881$	18.9168			0.637325			0.318662	+	0.947868i	$0.396766\pi$
$882$		0			0
$883$	11.3676			0.382549			0.191274	−	0.981537i	$-0.438738\pi$
$883$	11.3676			0.382549			0.191274	+	0.981537i	$0.438738\pi$
$884$		0			0
$885$	−2.25360	+	30.0722i	−0.0757539	+	1.01087i
$886$		0			0
$887$	41.8981	+	28.5656i	1.40680	+	0.959140i	0.998937	+	0.0460965i	$0.0146782\pi$
$887$	41.8981	+	28.5656i	1.40680	+	0.959140i	0.407863	+	0.913043i	$0.366274\pi$
$888$		0			0
$889$	4.91011	−	12.6302i	0.164680	−	0.423605i
$890$		0			0
$891$	35.0704	+	5.28601i	1.17490	+	0.177088i
$892$		0			0
$893$	−1.12641	+	0.169779i	−0.0376938	+	0.00568143i
$894$		0			0
$895$	−5.60252	−	7.02534i	−0.187272	−	0.234831i
$896$		0			0
$897$	−2.34009	+	2.93437i	−0.0781332	+	0.0979759i
$898$		0			0
$899$	−12.9286	−	3.98794i	−0.431192	−	0.133005i
$900$		0			0
$901$	−8.40983	−	14.5662i	−0.280172	−	0.485272i
$902$		0			0
$903$	−54.8144	+	26.6151i	−1.82411	+	0.885696i
$904$		0			0
$905$	−29.3054	+	9.03953i	−0.974146	+	0.300484i
$906$		0			0
$907$	−3.74735	−	9.54810i	−0.124429	−	0.317040i	0.855063	−	0.518525i	$-0.173519\pi$
$907$	−3.74735	−	9.54810i	−0.124429	−	0.317040i	−0.979492	+	0.201485i	$0.935423\pi$
$908$		0			0
$909$	4.87595	−	21.3629i	0.161725	−	0.708564i
$910$		0			0
$911$	7.05674	+	30.9176i	0.233800	+	1.02435i	0.946456	+	0.322832i	$0.104635\pi$
$911$	7.05674	+	30.9176i	0.233800	+	1.02435i	−0.712656	+	0.701514i	$0.752508\pi$
$912$		0			0
$913$	6.67578	−	11.5628i	0.220936	−	0.382672i
$914$		0			0
$915$	−2.84956	−	38.0247i	−0.0942034	−	1.25706i
$916$		0			0
$917$	−20.4864	+	35.7490i	−0.676522	+	1.18054i
$918$		0			0
$919$	−11.7991	+	10.9480i	−0.389216	+	0.361140i	−0.850374	−	0.526178i	$-0.823625\pi$
$919$	−11.7991	+	10.9480i	−0.389216	+	0.361140i	0.461158	+	0.887318i	$0.347434\pi$
$920$		0			0
$921$	27.7980	−	18.9524i	0.915976	−	0.624502i
$922$		0			0
$923$	−9.61065	+	4.62825i	−0.316339	+	0.152341i
$924$		0			0
$925$	−5.08224	−	2.44748i	−0.167103	−	0.0804725i
$926$		0			0
$927$	−11.7097	−	10.8650i	−0.384598	−	0.356855i
$928$		0			0
$929$	5.12039	−	13.0465i	0.167995	−	0.428043i	−0.821939	−	0.569575i	$-0.807108\pi$
$929$	5.12039	−	13.0465i	0.167995	−	0.428043i	0.989934	+	0.141532i	$0.0452029\pi$
$930$		0			0
$931$	11.7380	−	14.9151i	0.384697	−	0.488823i
$932$		0			0
$933$	15.1573	−	38.6202i	0.496228	−	1.26437i
$934$		0			0
$935$	17.5203	+	16.2565i	0.572975	+	0.531643i
$936$		0			0
$937$	−35.4962	−	17.0941i	−1.15961	−	0.558438i	−0.247703	−	0.968836i	$-0.579676\pi$
$937$	−35.4962	−	17.0941i	−1.15961	−	0.558438i	−0.911907	+	0.410398i	$0.865390\pi$
$938$		0			0
$939$	−38.7824	+	18.6766i	−1.26562	+	0.609488i
$940$		0			0
$941$	−15.2928	+	10.4264i	−0.498530	+	0.339892i	−0.786338	−	0.617796i	$-0.788026\pi$
$941$	−15.2928	+	10.4264i	−0.498530	+	0.339892i	0.287808	+	0.957688i	$0.407073\pi$
$942$		0			0
$943$	−2.96056	+	2.74700i	−0.0964091	+	0.0894546i
$944$		0			0
$945$	−11.6081	+	1.78791i	−0.377612	+	0.0581607i
$946$		0			0
$947$	−2.70954	−	36.1562i	−0.0880481	−	1.17492i	−0.849819	−	0.527074i	$-0.823289\pi$
$947$	−2.70954	−	36.1562i	−0.0880481	−	1.17492i	0.761771	−	0.647846i	$-0.224330\pi$
$948$		0			0
$949$	−23.2321	+	40.2391i	−0.754144	+	1.30622i
$950$		0			0
$951$	−7.34360	−	32.1744i	−0.238133	−	1.04333i
$952$		0			0
$953$	−6.47297	+	28.3599i	−0.209680	+	0.918669i	0.755100	+	0.655610i	$0.227588\pi$
$953$	−6.47297	+	28.3599i	−0.209680	+	0.918669i	−0.964780	+	0.263059i	$0.915269\pi$
$954$		0			0
$955$	13.7052	+	34.9203i	0.443490	+	1.12999i
$956$		0			0
$957$	25.1100	−	7.74541i	0.811691	−	0.250374i
$958$		0			0
$959$	−16.3196	+	0.0525783i	−0.526987	+	0.00169784i
$960$		0			0
$961$	8.46939	+	14.6694i	0.273206	+	0.473207i
$962$		0			0
$963$	−38.0769	−	11.7452i	−1.22701	−	0.378483i
$964$		0			0
$965$	−0.508215	+	0.637281i	−0.0163600	+	0.0205148i
$966$		0			0
$967$	6.56259	+	8.22923i	0.211039	+	0.264634i	0.876073	−	0.482179i	$-0.160154\pi$
$967$	6.56259	+	8.22923i	0.211039	+	0.264634i	−0.665034	+	0.746813i	$0.731583\pi$
$968$		0			0
$969$	21.3391	−	3.21635i	0.685511	−	0.103324i
$970$		0			0
$971$	−19.7059	−	2.97018i	−0.632391	−	0.0953176i	−0.174979	−	0.984572i	$-0.555986\pi$
$971$	−19.7059	−	2.97018i	−0.632391	−	0.0953176i	−0.457413	+	0.889255i	$0.651224\pi$
$972$		0			0
$973$	−40.6080	−	5.98694i	−1.30183	−	0.191932i
$974$		0			0
$975$	4.45733	+	3.03896i	0.142749	+	0.0973245i
$976$		0			0
$977$	4.13415	−	55.1664i	0.132263	−	1.76493i	−0.398271	−	0.917268i	$-0.630390\pi$
$977$	4.13415	−	55.1664i	0.132263	−	1.76493i	0.530535	−	0.847663i	$-0.321991\pi$
$978$		0			0
$979$	−41.8576			−1.33778
$980$		0			0
$981$	−12.3390			−0.393954
$982$		0			0
$983$	−3.51151	+	46.8578i	−0.112000	+	1.49453i	0.604310	+	0.796750i	$0.293449\pi$
$983$	−3.51151	+	46.8578i	−0.112000	+	1.49453i	−0.716309	+	0.697783i	$0.754170\pi$
$984$		0			0
$985$	26.8216	+	18.2866i	0.854607	+	0.582661i
$986$		0			0
$987$	1.25613	+	2.15958i	0.0399830	+	0.0687401i
$988$		0			0
$989$	4.66002	+	0.702385i	0.148180	+	0.0223345i
$990$		0			0
$991$	0.912026	−	0.137466i	0.0289715	−	0.00436675i	−0.134541	−	0.990908i	$-0.542956\pi$
$991$	0.912026	−	0.137466i	0.0289715	−	0.00436675i	0.163512	+	0.986541i	$0.447718\pi$
$992$		0			0
$993$	25.5778	+	32.0736i	0.811687	+	1.01782i
$994$		0			0
$995$	−4.81550	+	6.03844i	−0.152661	+	0.191431i
$996$		0			0
$997$	−25.2117	−	7.77677i	−0.798462	−	0.246293i	−0.131433	−	0.991325i	$-0.541958\pi$
$997$	−25.2117	−	7.77677i	−0.798462	−	0.246293i	−0.667029	+	0.745032i	$0.732434\pi$
$998$		0			0
$999$	−9.09250	−	15.7487i	−0.287674	−	0.498266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bg.e.193.6		84
4.3	odd	2		392.2.y.b.193.2	yes	84
49.16	even	21	inner	784.2.bg.e.65.6		84
196.163	odd	42		392.2.y.b.65.2	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.y.b.65.2	✓	84	196.163	odd	42
392.2.y.b.193.2	yes	84	4.3	odd	2
784.2.bg.e.65.6		84	49.16	even	21	inner
784.2.bg.e.193.6		84	1.1	even	1	trivial

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.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.167965 - 2.24134i) q^{3} +(1.72106 + 1.17340i) q^{5} +(-2.19081 - 1.48335i) q^{7} +(-2.02891 - 0.305809i) q^{9} +O(q^{10})\)	\(q+(0.167965 - 2.24134i) q^{3} +(1.72106 + 1.17340i) q^{5} +(-2.19081 - 1.48335i) q^{7} +(-2.02891 - 0.305809i) q^{9} +(-3.20409 + 0.482939i) q^{11} +(-2.26376 - 2.83867i) q^{13} +(2.91907 - 3.66040i) q^{15} +(-3.38373 - 1.04374i) q^{17} +(-1.35571 - 2.34817i) q^{19} +(-3.69268 + 4.66121i) q^{21} +(0.439482 - 0.135562i) q^{23} +(-0.241514 - 0.615368i) q^{25} +(0.474224 - 2.07771i) q^{27} +(-0.802873 - 3.51761i) q^{29} +(1.87491 - 3.24745i) q^{31} +(0.544255 + 7.26258i) q^{33} +(-2.02996 - 5.12365i) q^{35} +(6.25512 - 5.80390i) q^{37} +(-6.74265 + 4.59706i) q^{39} +(-7.91173 + 3.81009i) q^{41} +(9.23205 + 4.44592i) q^{43} +(-3.13305 - 2.90704i) q^{45} +(0.153488 - 0.391081i) q^{47} +(2.59932 + 6.49950i) q^{49} +(-2.90773 + 7.40879i) q^{51} +(3.48193 + 3.23076i) q^{53} +(-6.08113 - 2.92852i) q^{55} +(-5.49076 + 2.64421i) q^{57} +(-5.32195 + 3.62845i) q^{59} +(5.97036 - 5.53968i) q^{61} +(3.99134 + 3.67956i) q^{63} +(-0.565182 - 7.54183i) q^{65} +(-7.97896 + 13.8200i) q^{67} +(-0.230024 - 1.00780i) q^{69} +(0.653752 - 2.86427i) q^{71} +(-4.67536 - 11.9126i) q^{73} +(-1.41982 + 0.437955i) q^{75} +(7.73594 + 3.69477i) q^{77} +(-4.83228 - 8.36976i) q^{79} +(-10.4592 - 3.22624i) q^{81} +(-2.56908 + 3.22153i) q^{83} +(-4.59889 - 5.76683i) q^{85} +(-8.01903 + 1.20867i) q^{87} +(12.7736 + 1.92531i) q^{89} +(0.748728 + 9.57694i) q^{91} +(-6.96372 - 4.74778i) q^{93} +(0.422071 - 5.63214i) q^{95} +6.30931 q^{97} +6.64850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 10 q^{3} - q^{5} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) 84 * q - 10 * q^3 - q^5 + 4 * q^7 - 11 * q^9	\( 84 q - 10 q^{3} - q^{5} + 4 q^{7} - 11 q^{9} - q^{11} + 10 q^{13} - 9 q^{15} + 3 q^{17} + 23 q^{19} - 10 q^{21} + q^{23} + 6 q^{25} + 32 q^{27} - 13 q^{29} + 29 q^{31} + 11 q^{33} - 30 q^{35} + 48 q^{37} - 51 q^{39} + 20 q^{41} + 14 q^{43} + 22 q^{45} + 34 q^{47} - 2 q^{49} - 3 q^{51} - 40 q^{53} + 9 q^{55} - 10 q^{57} - 38 q^{59} + 10 q^{61} - 9 q^{63} - 2 q^{65} + 37 q^{67} - 87 q^{69} - 5 q^{71} + 21 q^{73} + 12 q^{75} + 71 q^{77} - 19 q^{79} - 70 q^{81} + 55 q^{83} + 29 q^{85} + 165 q^{87} - 65 q^{89} + 15 q^{91} - 120 q^{93} - 7 q^{95} + 170 q^{97} - 110 q^{99}+O(q^{100}) \) 84 * q - 10 * q^3 - q^5 + 4 * q^7 - 11 * q^9 - q^11 + 10 * q^13 - 9 * q^15 + 3 * q^17 + 23 * q^19 - 10 * q^21 + q^23 + 6 * q^25 + 32 * q^27 - 13 * q^29 + 29 * q^31 + 11 * q^33 - 30 * q^35 + 48 * q^37 - 51 * q^39 + 20 * q^41 + 14 * q^43 + 22 * q^45 + 34 * q^47 - 2 * q^49 - 3 * q^51 - 40 * q^53 + 9 * q^55 - 10 * q^57 - 38 * q^59 + 10 * q^61 - 9 * q^63 - 2 * q^65 + 37 * q^67 - 87 * q^69 - 5 * q^71 + 21 * q^73 + 12 * q^75 + 71 * q^77 - 19 * q^79 - 70 * q^81 + 55 * q^83 + 29 * q^85 + 165 * q^87 - 65 * q^89 + 15 * q^91 - 120 * q^93 - 7 * q^95 + 170 * q^97 - 110 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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