LMFDB - Embedded newform 867.2.h.j.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	16.0.1963501163244660295991296.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1889x^{8} + 65536 $ x^16 + 1889*x^8 + 65536
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			757.1
Root			$-0.980264 - 2.36657i$ of defining polynomial
Character	$\chi$	$=$	867.757
Dual form			867.2.h.j.733.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81129 + 1.81129i) q^{2} +(-0.923880 - 0.382683i) q^{3} -4.56155i q^{4} +(-1.36295 + 3.29045i) q^{5} +(2.36657 - 0.980264i) q^{6} +(4.63972 + 4.63972i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-1.81129 + 1.81129i) q^{2} +(-0.923880 - 0.382683i) q^{3} -4.56155i q^{4} +(-1.36295 + 3.29045i) q^{5} +(2.36657 - 0.980264i) q^{6} +(4.63972 + 4.63972i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-3.49126 - 8.42865i) q^{10} +(-1.44269 + 0.597580i) q^{11} +(-1.74563 + 4.21433i) q^{12} +0.438447i q^{13} +(2.51840 - 2.51840i) q^{15} -7.68466 q^{16} -2.56155 q^{18} +(-3.31255 + 3.31255i) q^{19} +(15.0095 + 6.21716i) q^{20} +(1.53073 - 3.69552i) q^{22} +(-2.25283 + 0.933153i) q^{23} +(-2.51100 - 6.06208i) q^{24} +(-5.43387 - 5.43387i) q^{25} +(-0.794156 - 0.794156i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(-3.15569 + 7.61851i) q^{29} +9.12311i q^{30} +(-2.88537 - 1.19516i) q^{31} +(4.63972 - 4.63972i) q^{32} +1.56155 q^{33} +(3.22550 - 3.22550i) q^{36} +(-4.73313 - 1.96053i) q^{37} -12.0000i q^{38} +(0.167786 - 0.405072i) q^{39} +(-21.5904 + 8.94305i) q^{40} +(1.36295 + 3.29045i) q^{41} +(3.31255 + 3.31255i) q^{43} +(2.72589 + 6.58089i) q^{44} +(-3.29045 + 1.36295i) q^{45} +(2.39032 - 5.77075i) q^{46} -11.1231i q^{47} +(7.09970 + 2.94079i) q^{48} +(4.94975 - 4.94975i) q^{49} +19.6847 q^{50} +2.00000 q^{52} +(8.65938 - 8.65938i) q^{53} +(2.36657 + 0.980264i) q^{54} -5.56155i q^{55} +(4.32806 - 1.79274i) q^{57} +(-8.08346 - 19.5152i) q^{58} +(-5.03680 - 5.03680i) q^{59} +(-11.4878 - 11.4878i) q^{60} +(3.49126 + 8.42865i) q^{61} +(7.39104 - 3.06147i) q^{62} +1.43845i q^{64} +(-1.44269 - 0.597580i) q^{65} +(-2.82843 + 2.82843i) q^{66} -4.00000 q^{67} +2.43845 q^{69} +(-5.77075 - 2.39032i) q^{71} +6.56155i q^{72} +(4.68642 - 11.3140i) q^{73} +(12.1242 - 5.02200i) q^{74} +(2.94079 + 7.09970i) q^{75} +(15.1104 + 15.1104i) q^{76} +(0.429794 + 1.03761i) q^{78} +(8.65612 - 3.58548i) q^{79} +(10.4738 - 25.2860i) q^{80} +1.00000i q^{81} +(-8.42865 - 3.49126i) q^{82} +(0.620058 - 0.620058i) q^{83} -12.0000 q^{86} +(5.83095 - 5.83095i) q^{87} +(-9.46626 - 3.92106i) q^{88} +1.12311i q^{89} +(3.49126 - 8.42865i) q^{90} +(4.25663 + 10.2764i) q^{92} +(2.20837 + 2.20837i) q^{93} +(20.1472 + 20.1472i) q^{94} +(-6.38494 - 15.4146i) q^{95} +(-6.06208 + 2.51100i) q^{96} +(-1.10094 + 2.65790i) q^{97} +17.9309i q^{98} +(-1.44269 - 0.597580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) $ 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.81129	+	1.81129i	−1.28078	+	1.28078i	−0.340550	+	0.940226i	$0.610613\pi$
$2$	−1.81129	+	1.81129i	−1.28078	+	1.28078i	−0.940226	+	0.340550i	$0.889387\pi$
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$		−	4.56155i		−	2.28078i
$5$	−1.36295	+	3.29045i	−0.609529	+	1.47153i	0.253986	+	0.967208i	$0.418258\pi$
$5$	−1.36295	+	3.29045i	−0.609529	+	1.47153i	−0.863514	+	0.504324i	$0.831742\pi$
$6$	2.36657	−	0.980264i	0.966147	−	0.400191i
$7$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$7$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$8$	4.63972	+	4.63972i	1.64039	+	1.64039i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	−3.49126	−	8.42865i	−1.10403	−	2.66537i
$11$	−1.44269	+	0.597580i	−0.434986	+	0.180177i	−0.589421	−	0.807826i	$-0.700644\pi$
$11$	−1.44269	+	0.597580i	−0.434986	+	0.180177i	0.154435	+	0.988003i	$0.450644\pi$
$12$	−1.74563	+	4.21433i	−0.503920	+	1.21657i
$13$			0.438447i			0.121603i	0.998150	+	0.0608017i	$0.0193657\pi$
$13$			0.438447i			0.121603i	−0.998150	+	0.0608017i	$0.980634\pi$
$14$		0			0
$15$	2.51840	−	2.51840i	0.650248	−	0.650248i
$16$	−7.68466			−1.92116
$17$		0			0
$17$		0			0
$18$	−2.56155			−0.603764
$19$	−3.31255	+	3.31255i	−0.759952	+	0.759952i	−0.976313	−	0.216361i	$-0.930581\pi$
$19$	−3.31255	+	3.31255i	−0.759952	+	0.759952i	0.216361	+	0.976313i	$0.430581\pi$
$20$	15.0095	+	6.21716i	3.35624	+	1.39020i
$21$		0			0
$22$	1.53073	−	3.69552i	0.326354	−	0.787887i
$23$	−2.25283	+	0.933153i	−0.469748	+	0.194576i	−0.604984	−	0.796237i	$-0.706821\pi$
$23$	−2.25283	+	0.933153i	−0.469748	+	0.194576i	0.135236	+	0.990813i	$0.456821\pi$
$24$	−2.51100	−	6.06208i	−0.512555	−	1.23742i
$25$	−5.43387	−	5.43387i	−1.08677	−	1.08677i
$26$	−0.794156	−	0.794156i	−0.155747	−	0.155747i
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$		0			0
$29$	−3.15569	+	7.61851i	−0.585997	+	1.41472i	0.301303	+	0.953528i	$0.402578\pi$
$29$	−3.15569	+	7.61851i	−0.585997	+	1.41472i	−0.887300	+	0.461193i	$0.847422\pi$
$30$			9.12311i			1.66564i
$31$	−2.88537	−	1.19516i	−0.518228	−	0.214657i	0.108210	−	0.994128i	$-0.465488\pi$
$31$	−2.88537	−	1.19516i	−0.518228	−	0.214657i	−0.626439	+	0.779471i	$0.715488\pi$
$32$	4.63972	−	4.63972i	0.820194	−	0.820194i
$33$	1.56155			0.271831
$34$		0			0
$35$		0			0
$36$	3.22550	−	3.22550i	0.537584	−	0.537584i
$37$	−4.73313	−	1.96053i	−0.778122	−	0.322309i	−0.0419647	−	0.999119i	$-0.513362\pi$
$37$	−4.73313	−	1.96053i	−0.778122	−	0.322309i	−0.736157	+	0.676810i	$0.763362\pi$
$38$		−	12.0000i		−	1.94666i
$39$	0.167786	−	0.405072i	0.0268673	−	0.0648635i
$40$	−21.5904	+	8.94305i	−3.41375	+	1.41402i
$41$	1.36295	+	3.29045i	0.212857	+	0.513881i	0.993860	−	0.110646i	$-0.0352918\pi$
$41$	1.36295	+	3.29045i	0.212857	+	0.513881i	−0.781003	+	0.624527i	$0.785292\pi$
$42$		0			0
$43$	3.31255	+	3.31255i	0.505160	+	0.505160i	0.913037	−	0.407877i	$-0.133731\pi$
$43$	3.31255	+	3.31255i	0.505160	+	0.505160i	−0.407877	+	0.913037i	$0.633731\pi$
$44$	2.72589	+	6.58089i	0.410944	+	0.992107i
$45$	−3.29045	+	1.36295i	−0.490511	+	0.203176i
$46$	2.39032	−	5.77075i	0.352434	−	0.850850i
$47$		−	11.1231i		−	1.62247i	−0.584719	−	0.811236i	$-0.698795\pi$
$47$		−	11.1231i		−	1.62247i	0.584719	−	0.811236i	$-0.301205\pi$
$48$	7.09970	+	2.94079i	1.02475	+	0.424467i
$49$	4.94975	−	4.94975i	0.707107	−	0.707107i
$50$	19.6847			2.78383
$51$		0			0
$52$	2.00000			0.277350
$53$	8.65938	−	8.65938i	1.18946	−	1.18946i	0.212240	−	0.977218i	$-0.431924\pi$
$53$	8.65938	−	8.65938i	1.18946	−	1.18946i	0.977218	−	0.212240i	$-0.0680757\pi$
$54$	2.36657	+	0.980264i	0.322049	+	0.133397i
$55$		−	5.56155i		−	0.749920i
$56$		0			0
$57$	4.32806	−	1.79274i	0.573266	−	0.237454i
$58$	−8.08346	−	19.5152i	−1.06141	−	2.56247i
$59$	−5.03680	−	5.03680i	−0.655735	−	0.655735i	0.298633	−	0.954368i	$-0.403469\pi$
$59$	−5.03680	−	5.03680i	−0.655735	−	0.655735i	−0.954368	+	0.298633i	$0.903469\pi$
$60$	−11.4878	−	11.4878i	−1.48307	−	1.48307i
$61$	3.49126	+	8.42865i	0.447010	+	1.07918i	0.973436	+	0.228957i	$0.0735316\pi$
$61$	3.49126	+	8.42865i	0.447010	+	1.07918i	−0.526426	+	0.850221i	$0.676468\pi$
$62$	7.39104	−	3.06147i	0.938663	−	0.388807i
$63$		0			0
$64$			1.43845i			0.179806i
$65$	−1.44269	−	0.597580i	−0.178943	−	0.0741207i
$66$	−2.82843	+	2.82843i	−0.348155	+	0.348155i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	2.43845			0.293555
$70$		0			0
$71$	−5.77075	−	2.39032i	−0.684862	−	0.283679i	0.0129959	−	0.999916i	$-0.495863\pi$
$71$	−5.77075	−	2.39032i	−0.684862	−	0.283679i	−0.697858	+	0.716237i	$0.745863\pi$
$72$			6.56155i			0.773286i
$73$	4.68642	−	11.3140i	0.548504	−	1.32421i	−0.370087	−	0.928997i	$-0.620672\pi$
$73$	4.68642	−	11.3140i	0.548504	−	1.32421i	0.918591	−	0.395209i	$-0.129328\pi$
$74$	12.1242	−	5.02200i	1.40941	−	0.583795i
$75$	2.94079	+	7.09970i	0.339573	+	0.819803i
$76$	15.1104	+	15.1104i	1.73328	+	1.73328i
$77$		0			0
$78$	0.429794	+	1.03761i	0.0486646	+	0.117487i
$79$	8.65612	−	3.58548i	0.973890	−	0.403398i	0.161731	−	0.986835i	$-0.448292\pi$
$79$	8.65612	−	3.58548i	0.973890	−	0.403398i	0.812159	+	0.583437i	$0.198292\pi$
$80$	10.4738	−	25.2860i	1.17100	−	2.82706i
$81$			1.00000i			0.111111i
$82$	−8.42865	−	3.49126i	−0.930789	−	0.385545i
$83$	0.620058	−	0.620058i	0.0680602	−	0.0680602i	−0.672257	−	0.740318i	$-0.734675\pi$
$83$	0.620058	−	0.620058i	0.0680602	−	0.0680602i	0.740318	+	0.672257i	$0.234675\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$	5.83095	−	5.83095i	0.625144	−	0.625144i
$88$	−9.46626	−	3.92106i	−1.00911	−	0.417986i
$89$			1.12311i			0.119049i	0.998227	+	0.0595245i	$0.0189584\pi$
$89$			1.12311i			0.119049i	−0.998227	+	0.0595245i	$0.981042\pi$
$90$	3.49126	−	8.42865i	0.368011	−	0.888458i
$91$		0			0
$92$	4.25663	+	10.2764i	0.443784	+	1.07139i
$93$	2.20837	+	2.20837i	0.228997	+	0.228997i
$94$	20.1472	+	20.1472i	2.07802	+	2.07802i
$95$	−6.38494	−	15.4146i	−0.655081	−	1.58151i
$96$	−6.06208	+	2.51100i	−0.618709	+	0.256278i
$97$	−1.10094	+	2.65790i	−0.111784	+	0.269869i	−0.969864	−	0.243645i	$-0.921657\pi$
$97$	−1.10094	+	2.65790i	−0.111784	+	0.269869i	0.858081	+	0.513514i	$0.171657\pi$
$98$			17.9309i			1.81129i
$99$	−1.44269	−	0.597580i	−0.144995	−	0.0600591i
$100$	−24.7869	+	24.7869i	−2.47869	+	2.47869i
$101$	−10.8769			−1.08229			−0.541146	−	0.840929i	$-0.682009\pi$
$101$	−10.8769			−1.08229			−0.541146	+	0.840929i	$0.682009\pi$
$102$		0			0
$103$	16.6847			1.64399			0.821994	−	0.569496i	$-0.192862\pi$
$103$	16.6847			1.64399			0.821994	+	0.569496i	$0.192862\pi$
$104$	−2.03427	+	2.03427i	−0.199477	+	0.199477i
$105$		0			0
$106$			31.3693i			3.04686i
$107$	1.79274	−	4.32806i	0.173311	−	0.418409i	−0.813226	−	0.581948i	$-0.802291\pi$
$107$	1.79274	−	4.32806i	0.173311	−	0.418409i	0.986537	+	0.163538i	$0.0522908\pi$
$108$	−4.21433	+	1.74563i	−0.405524	+	0.167973i
$109$	2.63167	+	6.35342i	0.252069	+	0.608547i	0.998371	−	0.0570599i	$-0.0181726\pi$
$109$	2.63167	+	6.35342i	0.252069	+	0.608547i	−0.746302	+	0.665607i	$0.768173\pi$
$110$	10.0736	+	10.0736i	0.960479	+	0.960479i
$111$	3.62258	+	3.62258i	0.343840	+	0.343840i
$112$		0			0
$113$	0.405072	−	0.167786i	0.0381060	−	0.0157840i	−0.363549	−	0.931575i	$-0.618435\pi$
$113$	0.405072	−	0.167786i	0.0381060	−	0.0157840i	0.401655	+	0.915791i	$0.368435\pi$
$114$	−4.59220	+	11.0866i	−0.430099	+	1.03835i
$115$		−	8.68466i		−	0.809849i
$116$	34.7522	+	14.3948i	3.22666	+	1.33653i
$117$	−0.310029	+	0.310029i	−0.0286622	+	0.0286622i
$118$	18.2462			1.67970
$119$		0			0
$120$	23.3693			2.13332
$121$	−6.05393	+	6.05393i	−0.550357	+	0.550357i
$122$	−21.5904	−	8.94305i	−1.95471	−	0.809666i
$123$		−	3.56155i		−	0.321134i
$124$	−5.45179	+	13.1618i	−0.489585	+	1.18196i
$125$	8.83372	−	3.65905i	0.790112	−	0.327275i
$126$		0			0
$127$	−14.0062	−	14.0062i	−1.24285	−	1.24285i	−0.958814	−	0.284036i	$-0.908326\pi$
$127$	−14.0062	−	14.0062i	−1.24285	−	1.24285i	−0.284036	−	0.958814i	$-0.591674\pi$
$128$	6.67399	+	6.67399i	0.589903	+	0.589903i
$129$	−1.79274	−	4.32806i	−0.157842	−	0.381064i
$130$	3.69552	−	1.53073i	0.324118	−	0.134254i
$131$	5.52535	−	13.3394i	0.482752	−	1.16547i	−0.475544	−	0.879692i	$-0.657749\pi$
$131$	5.52535	−	13.3394i	0.482752	−	1.16547i	0.958297	−	0.285776i	$-0.0922512\pi$
$132$		−	7.12311i		−	0.619987i
$133$		0			0
$134$	7.24517	−	7.24517i	0.625887	−	0.625887i
$135$	3.56155			0.306530
$136$		0			0
$137$	0.246211			0.0210352			0.0105176	−	0.999945i	$-0.496652\pi$
$137$	0.246211			0.0210352			0.0105176	+	0.999945i	$0.496652\pi$
$138$	−4.41674	+	4.41674i	−0.375978	+	0.375978i
$139$	−0.810145	−	0.335573i	−0.0687156	−	0.0284629i	0.348061	−	0.937472i	$-0.386840\pi$
$139$	−0.810145	−	0.335573i	−0.0687156	−	0.0284629i	−0.416777	+	0.909009i	$0.636840\pi$
$140$		0			0
$141$	−4.25663	+	10.2764i	−0.358473	+	0.865430i
$142$	14.7821	−	6.12293i	1.24048	−	0.513825i
$143$	−0.262007	−	0.632542i	−0.0219102	−	0.0528958i
$144$	−5.43387	−	5.43387i	−0.452823	−	0.452823i
$145$	−20.7672	−	20.7672i	−1.72463	−	1.72463i
$146$	12.0045	+	28.9815i	0.993501	+	2.39852i
$147$	−6.46716	+	2.67878i	−0.533402	+	0.220942i
$148$	−8.94305	+	21.5904i	−0.735114	+	1.77472i
$149$			12.2462i			1.00325i	0.865086	+	0.501624i	$0.167264\pi$
$149$			12.2462i			1.00325i	−0.865086	+	0.501624i	$0.832736\pi$
$150$	−18.1863	−	7.53299i	−1.48490	−	0.615066i
$151$	−5.65685	+	5.65685i	−0.460348	+	0.460348i	−0.898770	−	0.438421i	$-0.855538\pi$
$151$	−5.65685	+	5.65685i	−0.460348	+	0.460348i	0.438421	+	0.898770i	$0.355538\pi$
$152$	−30.7386			−2.49323
$153$		0			0
$154$		0			0
$155$	7.86522	−	7.86522i	0.631750	−	0.631750i
$156$	−1.84776	−	0.765367i	−0.147939	−	0.0612784i
$157$		−	6.68466i		−	0.533494i	−0.963767	−	0.266747i	$-0.914051\pi$
$157$		−	6.68466i		−	0.533494i	0.963767	−	0.266747i	$-0.0859488\pi$
$158$	−9.18440	+	22.1731i	−0.730672	+	1.76400i
$159$	−11.3140	+	4.68642i	−0.897260	+	0.371657i
$160$	8.94305	+	21.5904i	0.707010	+	1.70687i
$161$		0			0
$162$	−1.81129	−	1.81129i	−0.142308	−	0.142308i
$163$	−5.78736	−	13.9719i	−0.453301	−	1.09437i	−0.971059	−	0.238839i	$-0.923233\pi$
$163$	−5.78736	−	13.9719i	−0.453301	−	1.09437i	0.517758	−	0.855527i	$-0.326767\pi$
$164$	15.0095	−	6.21716i	1.17205	−	0.485478i
$165$	−2.12831	+	5.13820i	−0.165689	+	0.400009i
$166$			2.24621i			0.174340i
$167$	−18.3000	−	7.58010i	−1.41610	−	0.586566i	−0.462219	−	0.886766i	$-0.652947\pi$
$167$	−18.3000	−	7.58010i	−1.41610	−	0.586566i	−0.953876	+	0.300200i	$0.902947\pi$
$168$		0			0
$169$	12.8078			0.985213
$170$		0			0
$171$	−4.68466			−0.358245
$172$	15.1104	−	15.1104i	1.15216	−	1.15216i
$173$	1.67016	+	0.691801i	0.126980	+	0.0525967i	0.445269	−	0.895397i	$-0.353108\pi$
$173$	1.67016	+	0.691801i	0.126980	+	0.0525967i	−0.318289	+	0.947994i	$0.603108\pi$
$174$			21.1231i			1.60134i
$175$		0			0
$176$	11.0866	−	4.59220i	0.835680	−	0.346150i
$177$	2.72589	+	6.58089i	0.204891	+	0.494650i
$178$	−2.03427	−	2.03427i	−0.152475	−	0.152475i
$179$	−0.620058	−	0.620058i	−0.0463453	−	0.0463453i	0.683554	−	0.729900i	$-0.260433\pi$
$179$	−0.620058	−	0.620058i	−0.0463453	−	0.0463453i	−0.729900	+	0.683554i	$0.760433\pi$
$180$	6.21716	+	15.0095i	0.463399	+	1.11875i
$181$	−5.54328	+	2.29610i	−0.412029	+	0.170668i	−0.579062	−	0.815283i	$-0.696581\pi$
$181$	−5.54328	+	2.29610i	−0.412029	+	0.170668i	0.167034	+	0.985951i	$0.446581\pi$
$182$		0			0
$183$		−	9.12311i		−	0.674399i
$184$	−14.7821	−	6.12293i	−1.08975	−	0.451389i
$185$	12.9020	−	12.9020i	0.948575	−	0.948575i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−50.7386			−3.70050
$189$		0			0
$190$	39.4853	+	16.3554i	2.86457	+	1.18654i
$191$			4.87689i			0.352880i	0.984311	+	0.176440i	$0.0564581\pi$
$191$			4.87689i			0.352880i	−0.984311	+	0.176440i	$0.943542\pi$
$192$	0.550470	−	1.32895i	0.0397267	−	0.0959088i
$193$	−7.16357	+	2.96725i	−0.515645	+	0.213587i	−0.625303	−	0.780382i	$-0.715024\pi$
$193$	−7.16357	+	2.96725i	−0.515645	+	0.213587i	0.109658	+	0.993969i	$0.465024\pi$
$194$	−2.82012	−	6.80836i	−0.202472	−	0.488812i
$195$	1.10418	+	1.10418i	0.0790723	+	0.0790723i
$196$	−22.5785	−	22.5785i	−1.61275	−	1.61275i
$197$	−3.41770	−	8.25105i	−0.243501	−	0.587863i	0.754125	−	0.656731i	$-0.228061\pi$
$197$	−3.41770	−	8.25105i	−0.243501	−	0.587863i	−0.997626	+	0.0688681i	$0.978061\pi$
$198$	3.69552	−	1.53073i	0.262629	−	0.108785i
$199$	6.12293	−	14.7821i	0.434043	−	1.04787i	−0.543928	−	0.839132i	$-0.683063\pi$
$199$	6.12293	−	14.7821i	0.434043	−	1.04787i	0.977971	−	0.208741i	$-0.0669366\pi$
$200$		−	50.4233i		−	3.56547i
$201$	3.69552	+	1.53073i	0.260662	+	0.107970i
$202$	19.7012	−	19.7012i	1.38617	−	1.38617i
$203$		0			0
$204$		0			0
$205$	−12.6847			−0.885935
$206$	−30.2208	+	30.2208i	−2.10558	+	2.10558i
$207$	−2.25283	−	0.933153i	−0.156583	−	0.0648586i
$208$		−	3.36932i		−	0.233620i
$209$	2.79946	−	6.75849i	0.193643	−	0.467495i
$210$		0			0
$211$	−5.11622	−	12.3516i	−0.352215	−	0.850322i	−0.996346	−	0.0854069i	$-0.972781\pi$
$211$	−5.11622	−	12.3516i	−0.352215	−	0.850322i	0.644131	−	0.764915i	$-0.277219\pi$
$212$	−39.5002	−	39.5002i	−2.71289	−	2.71289i
$213$	4.41674	+	4.41674i	0.302630	+	0.302630i
$214$	4.59220	+	11.0866i	0.313916	+	0.757861i
$215$	−15.4146	+	6.38494i	−1.05127	+	0.435449i
$216$	2.51100	−	6.06208i	0.170852	−	0.412473i
$217$		0			0
$218$	−16.2746	−	6.74117i	−1.10226	−	0.456570i
$219$	−8.65938	+	8.65938i	−0.585147	+	0.585147i
$220$	−25.3693			−1.71040
$221$		0			0
$222$	−13.1231			−0.880765
$223$	−10.5577	+	10.5577i	−0.706997	+	0.706997i	−0.965903	−	0.258905i	$-0.916638\pi$
$223$	−10.5577	+	10.5577i	−0.706997	+	0.706997i	0.258905	+	0.965903i	$0.416638\pi$
$224$		0			0
$225$		−	7.68466i		−	0.512311i
$226$	−0.429794	+	1.03761i	−0.0285895	+	0.0690211i
$227$	−12.9842	+	5.37822i	−0.861790	+	0.356965i	−0.769407	−	0.638758i	$-0.779448\pi$
$227$	−12.9842	+	5.37822i	−0.861790	+	0.356965i	−0.0923829	+	0.995724i	$0.529448\pi$
$228$	−8.17768	−	19.7427i	−0.541580	−	1.30749i
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	0.552892	−	0.833253i	$-0.313524\pi$
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	−0.833253	+	0.552892i	$0.813524\pi$
$230$	15.7304	+	15.7304i	1.03723	+	1.03723i
$231$		0			0
$232$	−49.9892	+	20.7062i	−3.28195	+	1.35943i
$233$	−1.36295	+	3.29045i	−0.0892896	+	0.215564i	−0.962216	−	0.272288i	$-0.912220\pi$
$233$	−1.36295	+	3.29045i	−0.0892896	+	0.215564i	0.872926	+	0.487852i	$0.162220\pi$
$234$		−	1.12311i		−	0.0734197i
$235$	36.6000	+	15.1602i	2.38752	+	0.988943i
$236$	−22.9756	+	22.9756i	−1.49558	+	1.49558i
$237$	−9.36932			−0.608603
$238$		0			0
$239$	−6.24621			−0.404034			−0.202017	−	0.979382i	$-0.564750\pi$
$239$	−6.24621			−0.404034			−0.202017	+	0.979382i	$0.564750\pi$
$240$	−19.3530	+	19.3530i	−1.24923	+	1.24923i
$241$	3.11284	+	1.28938i	0.200516	+	0.0830564i	0.480681	−	0.876895i	$-0.340389\pi$
$241$	3.11284	+	1.28938i	0.200516	+	0.0830564i	−0.280166	+	0.959952i	$0.590389\pi$
$242$		−	21.9309i		−	1.40977i
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$	38.4477	−	15.9256i	2.46136	−	1.01953i
$245$	9.54063	+	23.0331i	0.609529	+	1.47153i
$246$	6.45101	+	6.45101i	0.411301	+	0.411301i
$247$	−1.45238	−	1.45238i	−0.0924127	−	0.0924127i
$248$	−7.84211	−	18.9325i	−0.497975	−	1.20222i
$249$	−0.810145	+	0.335573i	−0.0513408	+	0.0212661i
$250$	−9.37284	+	22.6280i	−0.592791	+	1.43112i
$251$			8.49242i			0.536037i	0.963414	+	0.268018i	$0.0863688\pi$
$251$			8.49242i			0.536037i	−0.963414	+	0.268018i	$0.913631\pi$
$252$		0			0
$253$	2.69250	−	2.69250i	0.169276	−	0.169276i
$254$	50.7386			3.18363
$255$		0			0
$256$	−27.0540			−1.69087
$257$	−10.8677	+	10.8677i	−0.677912	+	0.677912i	−0.959527	−	0.281616i	$-0.909130\pi$
$257$	−10.8677	+	10.8677i	−0.677912	+	0.677912i	0.281616	+	0.959527i	$0.409130\pi$
$258$	11.0866	+	4.59220i	0.690219	+	0.285898i
$259$		0			0
$260$	−2.72589	+	6.58089i	−0.169053	+	0.408130i
$261$	−7.61851	+	3.15569i	−0.471574	+	0.195332i
$262$	14.1535	+	34.1695i	0.874405	+	2.11100i
$263$	14.4903	+	14.4903i	0.893512	+	0.893512i	0.994852	−	0.101340i	$-0.0323129\pi$
$263$	14.4903	+	14.4903i	0.893512	+	0.893512i	−0.101340	+	0.994852i	$0.532313\pi$
$264$	7.24517	+	7.24517i	0.445909	+	0.445909i
$265$	16.6909	+	40.2955i	1.02532	+	2.47533i
$266$		0			0
$267$	0.429794	−	1.03761i	0.0263030	−	0.0635010i
$268$			18.2462i			1.11456i
$269$	−15.1871	−	6.29072i	−0.925977	−	0.383552i	−0.131826	−	0.991273i	$-0.542084\pi$
$269$	−15.1871	−	6.29072i	−0.925977	−	0.383552i	−0.794151	+	0.607721i	$0.792084\pi$
$270$	−6.45101	+	6.45101i	−0.392596	+	0.392596i
$271$	−19.8078			−1.20324			−0.601618	−	0.798784i	$-0.705477\pi$
$271$	−19.8078			−1.20324			−0.601618	+	0.798784i	$0.705477\pi$
$272$		0			0
$273$		0			0
$274$	−0.445960	+	0.445960i	−0.0269414	+	0.0269414i
$275$	11.0866	+	4.59220i	0.668544	+	0.276920i
$276$		−	11.1231i		−	0.669532i
$277$	−2.29610	+	5.54328i	−0.137959	+	0.333063i	−0.977726	−	0.209884i	$-0.932691\pi$
$277$	−2.29610	+	5.54328i	−0.137959	+	0.333063i	0.839767	+	0.542947i	$0.182691\pi$
$278$	2.07523	−	0.859588i	0.124464	−	0.0515547i
$279$	−1.19516	−	2.88537i	−0.0715524	−	0.172743i
$280$		0			0
$281$	−7.69113	−	7.69113i	−0.458814	−	0.458814i	0.439452	−	0.898266i	$-0.355173\pi$
$281$	−7.69113	−	7.69113i	−0.458814	−	0.458814i	−0.898266	+	0.439452i	$0.855173\pi$
$282$	−10.9036	−	26.3236i	−0.649299	−	1.56755i
$283$	−19.7427	+	8.17768i	−1.17358	+	0.486113i	−0.882375	−	0.470548i	$-0.844056\pi$
$283$	−19.7427	+	8.17768i	−1.17358	+	0.486113i	−0.291206	+	0.956660i	$0.594056\pi$
$284$	−10.9036	+	26.3236i	−0.647008	+	1.56202i
$285$			16.6847i			0.988314i
$286$	1.62029	+	0.671146i	0.0958097	+	0.0396857i
$287$		0			0
$288$	6.56155			0.386643
$289$		0			0
$290$	75.2311			4.41772
$291$	2.03427	−	2.03427i	0.119251	−	0.119251i
$292$	−51.6095	−	21.3774i	−3.02022	−	1.25102i
$293$		−	1.12311i		−	0.0656125i	−0.999462	−	0.0328063i	$-0.989556\pi$
$293$		−	1.12311i		−	0.0656125i	0.999462	−	0.0328063i	$-0.0104444\pi$
$294$	6.86185	−	16.5660i	0.400191	−	0.966147i
$295$	23.4382	−	9.70842i	1.36462	−	0.565246i
$296$	−12.8641	−	31.0567i	−0.747711	−	1.80513i
$297$	1.10418	+	1.10418i	0.0640713	+	0.0640713i
$298$	−22.1815	−	22.1815i	−1.28494	−	1.28494i
$299$	−0.409138	−	0.987748i	−0.0236611	−	0.0571229i
$300$	32.3857	−	13.4146i	1.86979	−	0.774491i
$301$		0			0
$302$		−	20.4924i		−	1.17921i
$303$	10.0489	+	4.16241i	0.577297	+	0.239124i
$304$	25.4558	−	25.4558i	1.45999	−	1.45999i
$305$	−32.4924			−1.86051
$306$		0			0
$307$	32.4924			1.85444			0.927220	−	0.374516i	$-0.122191\pi$
$307$	32.4924			1.85444			0.927220	+	0.374516i	$0.122191\pi$
$308$		0			0
$309$	−15.4146	−	6.38494i	−0.876907	−	0.363227i
$310$			28.4924i			1.61826i
$311$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$311$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$312$	2.65790	−	1.10094i	0.150474	−	0.0623284i
$313$	−12.8641	−	31.0567i	−0.727122	−	1.75543i	−0.651955	−	0.758257i	$-0.726051\pi$
$313$	−12.8641	−	31.0567i	−0.727122	−	1.75543i	−0.0751670	−	0.997171i	$-0.523949\pi$
$314$	12.1079	+	12.1079i	0.683286	+	0.683286i
$315$		0			0
$316$	−16.3554	−	39.4853i	−0.920061	−	2.22122i
$317$	16.6298	−	6.88830i	0.934024	−	0.386886i	0.136821	−	0.990596i	$-0.456312\pi$
$317$	16.6298	−	6.88830i	0.934024	−	0.386886i	0.797204	+	0.603710i	$0.206312\pi$
$318$	12.0045	−	28.9815i	0.673180	−	1.62520i
$319$		−	12.8769i		−	0.720968i
$320$	−4.73313	−	1.96053i	−0.264590	−	0.109597i
$321$	−3.31255	+	3.31255i	−0.184889	+	0.184889i
$322$		0			0
$323$		0			0
$324$	4.56155			0.253420
$325$	2.38247	−	2.38247i	0.132155	−	0.132155i
$326$	35.7898	+	14.8246i	1.98222	+	0.821061i
$327$		−	6.87689i		−	0.380293i
$328$	−8.94305	+	21.5904i	−0.493797	+	1.19213i
$329$		0			0
$330$	−5.45179	−	13.1618i	−0.300111	−	0.724532i
$331$	24.6999	+	24.6999i	1.35763	+	1.35763i	0.876835	+	0.480792i	$0.159651\pi$
$331$	24.6999	+	24.6999i	1.35763	+	1.35763i	0.480792	+	0.876835i	$0.340349\pi$
$332$	−2.82843	−	2.82843i	−0.155230	−	0.155230i
$333$	−1.96053	−	4.73313i	−0.107436	−	0.259374i
$334$	46.8764	−	19.4168i	2.56496	−	1.06244i
$335$	5.45179	−	13.1618i	0.297863	−	0.719105i
$336$		0			0
$337$	15.4645	+	6.40560i	0.842404	+	0.348935i	0.761801	−	0.647811i	$-0.224315\pi$
$337$	15.4645	+	6.40560i	0.842404	+	0.348935i	0.0806030	+	0.996746i	$0.474315\pi$
$338$	−23.1986	+	23.1986i	−1.26184	+	1.26184i
$339$	−0.438447			−0.0238132
$340$		0			0
$341$	4.87689			0.264099
$342$	8.48528	−	8.48528i	0.458831	−	0.458831i
$343$		0			0
$344$			30.7386i			1.65732i
$345$	−3.32347	+	8.02358i	−0.178930	+	0.431975i
$346$	−4.27819	+	1.77209i	−0.229997	+	0.0952679i
$347$	3.24991	+	7.84598i	0.174464	+	0.421194i	0.986789	−	0.162012i	$-0.0517982\pi$
$347$	3.24991	+	7.84598i	0.174464	+	0.421194i	−0.812325	+	0.583206i	$0.801798\pi$
$348$	−26.5982	−	26.5982i	−1.42581	−	1.42581i
$349$	8.17525	+	8.17525i	0.437611	+	0.437611i	0.891207	−	0.453596i	$-0.149859\pi$
$349$	8.17525	+	8.17525i	0.437611	+	0.437611i	−0.453596	+	0.891207i	$0.649859\pi$
$350$		0			0
$351$	0.405072	−	0.167786i	0.0216212	−	0.00895578i
$352$	−3.92106	+	9.46626i	−0.208993	+	0.504554i
$353$		−	10.4924i		−	0.558455i	−0.960225	−	0.279228i	$-0.909922\pi$
$353$		−	10.4924i		−	0.558455i	0.960225	−	0.279228i	$-0.0900784\pi$
$354$	−16.8573	−	6.98252i	−0.895955	−	0.371117i
$355$	15.7304	−	15.7304i	0.834885	−	0.834885i
$356$	5.12311			0.271524
$357$		0			0
$358$	2.24621			0.118716
$359$	10.0736	−	10.0736i	0.531664	−	0.531664i	−0.389403	−	0.921067i	$-0.627319\pi$
$359$	10.0736	−	10.0736i	0.531664	−	0.531664i	0.921067	+	0.389403i	$0.127319\pi$
$360$	−21.5904	−	8.94305i	−1.13792	−	0.471340i
$361$		−	2.94602i		−	0.155054i
$362$	5.88158	−	14.1994i	0.309129	−	0.746304i
$363$	7.90984	−	3.27636i	0.415159	−	0.171965i
$364$		0			0
$365$	30.8408	+	30.8408i	1.61428	+	1.61428i
$366$	16.5246	+	16.5246i	0.863755	+	0.863755i
$367$	−0.671146	−	1.62029i	−0.0350335	−	0.0845784i	0.905394	−	0.424572i	$-0.139575\pi$
$367$	−0.671146	−	1.62029i	−0.0350335	−	0.0845784i	−0.940428	+	0.339993i	$0.889575\pi$
$368$	17.3122	−	7.17096i	0.902463	−	0.373812i
$369$	−1.36295	+	3.29045i	−0.0709522	+	0.171294i
$370$			46.7386i			2.42983i
$371$		0			0
$372$	10.0736	−	10.0736i	0.522291	−	0.522291i
$373$	0.246211			0.0127483			0.00637417	−	0.999980i	$-0.497971\pi$
$373$	0.246211			0.0127483			0.00637417	+	0.999980i	$0.497971\pi$
$374$		0			0
$375$	−9.56155			−0.493756
$376$	51.6081	−	51.6081i	2.66148	−	2.66148i
$377$	−3.34031	−	1.38360i	−0.172035	−	0.0712592i
$378$		0			0
$379$	4.59220	−	11.0866i	0.235886	−	0.569478i	−0.760964	−	0.648794i	$-0.775274\pi$
$379$	4.59220	−	11.0866i	0.235886	−	0.569478i	0.996850	+	0.0793161i	$0.0252736\pi$
$380$	−70.3146	+	29.1253i	−3.60706	+	1.49409i
$381$	7.58010	+	18.3000i	0.388340	+	0.937537i
$382$	−8.83348	−	8.83348i	−0.451960	−	0.451960i
$383$	4.41674	+	4.41674i	0.225685	+	0.225685i	0.810887	−	0.585202i	$-0.198985\pi$
$383$	4.41674	+	4.41674i	0.225685	+	0.225685i	−0.585202	+	0.810887i	$0.698985\pi$
$384$	−3.61194	−	8.71999i	−0.184321	−	0.444990i
$385$		0			0
$386$	7.60076	−	18.3499i	0.386868	−	0.933983i
$387$			4.68466i			0.238135i
$388$	12.1242	+	5.02200i	0.615511	+	0.254953i
$389$	−25.3581	+	25.3581i	−1.28571	+	1.28571i	−0.348336	+	0.937370i	$0.613253\pi$
$389$	−25.3581	+	25.3581i	−1.28571	+	1.28571i	−0.937370	+	0.348336i	$0.886747\pi$
$390$	−4.00000			−0.202548
$391$		0			0
$392$	45.9309			2.31986
$393$	−10.2095	+	10.2095i	−0.515002	+	0.515002i
$394$	21.1355	+	8.75461i	1.06479	+	0.441051i
$395$			33.3693i			1.67899i
$396$	−2.72589	+	6.58089i	−0.136981	+	0.330702i
$397$	−17.8949	+	7.41232i	−0.898120	+	0.372014i	−0.783497	−	0.621396i	$-0.786566\pi$
$397$	−17.8949	+	7.41232i	−0.898120	+	0.372014i	−0.114623	+	0.993409i	$0.536566\pi$
$398$	15.6842	+	37.8651i	0.786179	+	1.89800i
$399$		0			0
$400$	41.7575	+	41.7575i	2.08787	+	2.08787i
$401$	14.9924	+	36.1949i	0.748686	+	1.80749i	0.566178	+	0.824283i	$0.308421\pi$
$401$	14.9924	+	36.1949i	0.748686	+	1.80749i	0.182507	+	0.983204i	$0.441579\pi$
$402$	−9.46626	+	3.92106i	−0.472134	+	0.195564i
$403$	0.524015	−	1.26508i	0.0261030	−	0.0630183i
$404$			49.6155i			2.46846i
$405$	−3.29045	−	1.36295i	−0.163504	−	0.0677254i
$406$		0			0
$407$	8.00000			0.396545
$408$		0			0
$409$	−14.6847			−0.726110			−0.363055	−	0.931768i	$-0.618266\pi$
$409$	−14.6847			−0.726110			−0.363055	+	0.931768i	$0.618266\pi$
$410$	22.9756	−	22.9756i	1.13468	−	1.13468i
$411$	−0.227470	−	0.0942210i	−0.0112202	−	0.00464758i
$412$		−	76.1080i		−	3.74957i
$413$		0			0
$414$	5.77075	−	2.39032i	0.283617	−	0.117478i
$415$	1.19516	+	2.88537i	0.0586681	+	0.141637i
$416$	2.03427	+	2.03427i	0.0997384	+	0.0997384i
$417$	0.620058	+	0.620058i	0.0303644	+	0.0303644i
$418$	7.17096	+	17.3122i	0.350743	+	0.846769i
$419$	0.454939	−	0.188442i	0.0222252	−	0.00920599i	−0.371543	−	0.928416i	$-0.621171\pi$
$419$	0.454939	−	0.188442i	0.0222252	−	0.00920599i	0.393768	+	0.919210i	$0.371171\pi$
$420$		0			0
$421$			24.4384i			1.19106i	0.803334	+	0.595529i	$0.203057\pi$
$421$			24.4384i			1.19106i	−0.803334	+	0.595529i	$0.796943\pi$
$422$	31.6394	+	13.1055i	1.54018	+	0.637964i
$423$	7.86522	−	7.86522i	0.382420	−	0.382420i
$424$	80.3542			3.90234
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	−19.7427	−	8.17768i	−0.954298	−	0.395283i
$429$			0.684658i			0.0330556i
$430$	16.3554	−	39.4853i	0.788726	−	1.90415i
$431$	−22.1731	+	9.18440i	−1.06804	+	0.442397i	−0.846299	−	0.532708i	$-0.821174\pi$
$431$	−22.1731	+	9.18440i	−1.06804	+	0.442397i	−0.221742	+	0.975105i	$0.571174\pi$
$432$	2.94079	+	7.09970i	0.141489	+	0.341584i
$433$	−18.8689	−	18.8689i	−0.906782	−	0.906782i	0.0892295	−	0.996011i	$-0.471560\pi$
$433$	−18.8689	−	18.8689i	−0.906782	−	0.906782i	−0.996011	+	0.0892295i	$0.971560\pi$
$434$		0			0
$435$	11.2392	+	27.1337i	0.538876	+	1.30096i
$436$	28.9815	−	12.0045i	1.38796	−	0.574912i
$437$	4.37150	−	10.5537i	0.209117	−	0.504854i
$438$		−	31.3693i		−	1.49888i
$439$	20.5528	+	8.51326i	0.980933	+	0.406316i	0.814771	−	0.579783i	$-0.196863\pi$
$439$	20.5528	+	8.51326i	0.980933	+	0.406316i	0.166162	+	0.986099i	$0.446863\pi$
$440$	25.8040	−	25.8040i	1.23016	−	1.23016i
$441$	7.00000			0.333333
$442$		0			0
$443$	−31.1231			−1.47870			−0.739352	−	0.673319i	$-0.764868\pi$
$443$	−31.1231			−1.47870			−0.739352	+	0.673319i	$0.764868\pi$
$444$	16.5246	−	16.5246i	0.784223	−	0.784223i
$445$	−3.69552	−	1.53073i	−0.175184	−	0.0725637i
$446$		−	38.2462i		−	1.81101i
$447$	4.68642	−	11.3140i	0.221660	−	0.535135i
$448$		0			0
$449$	−14.0593	−	33.9421i	−0.663498	−	1.60183i	−0.792284	−	0.610153i	$-0.791108\pi$
$449$	−14.0593	−	33.9421i	−0.663498	−	1.60183i	0.128786	−	0.991672i	$-0.458892\pi$
$450$	13.9192	+	13.9192i	0.656155	+	0.656155i
$451$	−3.93261	−	3.93261i	−0.185179	−	0.185179i
$452$	−0.765367	−	1.84776i	−0.0359998	−	0.0869113i
$453$	7.39104	−	3.06147i	0.347261	−	0.143840i
$454$	13.7766	−	33.2597i	0.646568	−	1.56095i
$455$		0			0
$456$	28.3988	+	11.7632i	1.32990	+	0.550861i
$457$	−9.76356	+	9.76356i	−0.456720	+	0.456720i	−0.897577	−	0.440857i	$-0.854675\pi$
$457$	−9.76356	+	9.76356i	−0.456720	+	0.456720i	0.440857	+	0.897577i	$0.354675\pi$
$458$	15.3693			0.718161
$459$		0			0
$460$	−39.6155			−1.84708
$461$	−5.83095	+	5.83095i	−0.271575	+	0.271575i	−0.829734	−	0.558159i	$-0.811508\pi$
$461$	−5.83095	+	5.83095i	−0.271575	+	0.271575i	0.558159	+	0.829734i	$0.311508\pi$
$462$		0			0
$463$			40.9848i			1.90473i	0.304965	+	0.952364i	$0.401355\pi$
$463$			40.9848i			1.90473i	−0.304965	+	0.952364i	$0.598645\pi$
$464$	24.2504	−	58.5456i	1.12580	−	2.71791i
$465$	−10.2764	+	4.25663i	−0.476557	+	0.197396i
$466$	−3.49126	−	8.42865i	−0.161730	−	0.390450i
$467$	−15.1104	−	15.1104i	−0.699225	−	0.699225i	0.265018	−	0.964243i	$-0.414622\pi$
$467$	−15.1104	−	15.1104i	−0.699225	−	0.699225i	−0.964243	+	0.265018i	$0.914622\pi$
$468$	1.41421	+	1.41421i	0.0653720	+	0.0653720i
$469$		0			0
$470$	−93.7528	+	38.8337i	−4.32449	+	1.79126i
$471$	−2.55811	+	6.17582i	−0.117871	+	0.284567i
$472$		−	46.7386i		−	2.15132i
$473$	−6.75849	−	2.79946i	−0.310756	−	0.128719i
$474$	16.9706	−	16.9706i	0.779484	−	0.779484i
$475$	36.0000			1.65179
$476$		0			0
$477$	12.2462			0.560715
$478$	11.3137	−	11.3137i	0.517477	−	0.517477i
$479$	22.4504	+	9.29928i	1.02579	+	0.424895i	0.831190	−	0.555988i	$-0.187660\pi$
$479$	22.4504	+	9.29928i	1.02579	+	0.424895i	0.194597	+	0.980883i	$0.437660\pi$
$480$		−	23.3693i		−	1.06666i
$481$	0.859588	−	2.07523i	0.0391938	−	0.0946223i
$482$	−7.97371	+	3.30282i	−0.363193	+	0.150439i
$483$		0			0
$484$	27.6153	+	27.6153i	1.25524	+	1.25524i
$485$	−7.24517	−	7.24517i	−0.328986	−	0.328986i
$486$	0.980264	+	2.36657i	0.0444657	+	0.107350i
$487$	−16.0472	+	6.64695i	−0.727166	+	0.301202i	−0.715387	−	0.698729i	$-0.753750\pi$
$487$	−16.0472	+	6.64695i	−0.727166	+	0.301202i	−0.0117792	+	0.999931i	$0.503750\pi$
$488$	−22.9081	+	55.3050i	−1.03700	+	2.50354i
$489$			15.1231i			0.683890i
$490$	−59.0006	−	24.4388i	−2.66537	−	1.10403i
$491$	15.1104	−	15.1104i	0.681922	−	0.681922i	−0.278511	−	0.960433i	$-0.589841\pi$
$491$	15.1104	−	15.1104i	0.681922	−	0.681922i	0.960433	+	0.278511i	$0.0898408\pi$
$492$	−16.2462			−0.732436
$493$		0			0
$494$	5.26137			0.236720
$495$	3.93261	−	3.93261i	0.176758	−	0.176758i
$496$	22.1731	+	9.18440i	0.995602	+	0.412392i
$497$		0			0
$498$	0.859588	−	2.07523i	0.0385191	−	0.0929932i
$499$	12.3516	−	5.11622i	0.552935	−	0.229033i	−0.0886797	−	0.996060i	$-0.528265\pi$
$499$	12.3516	−	5.11622i	0.552935	−	0.229033i	0.641615	+	0.767027i	$0.278265\pi$
$500$	−16.6909	−	40.2955i	−0.746442	−	1.80207i
$501$	14.0062	+	14.0062i	0.625751	+	0.625751i
$502$	−15.3823	−	15.3823i	−0.686543	−	0.686543i
$503$	−11.3127	−	27.3113i	−0.504409	−	1.21775i	−0.947060	−	0.321057i	$-0.895962\pi$
$503$	−11.3127	−	27.3113i	−0.504409	−	1.21775i	0.442651	−	0.896694i	$-0.354038\pi$
$504$		0			0
$505$	14.8246	−	35.7898i	0.659688	−	1.59263i
$506$			9.75379i			0.433609i
$507$	−11.8328	−	4.90132i	−0.525514	−	0.217675i
$508$	−63.8900	+	63.8900i	−2.83466	+	2.83466i
$509$	−25.1231			−1.11356			−0.556781	−	0.830659i	$-0.687964\pi$
$509$	−25.1231			−1.11356			−0.556781	+	0.830659i	$0.687964\pi$
$510$		0			0
$511$		0			0
$512$	35.6547	−	35.6547i	1.57573	−	1.57573i
$513$	4.32806	+	1.79274i	0.191089	+	0.0791515i
$514$		−	39.3693i		−	1.73651i
$515$	−22.7403	+	54.9000i	−1.00206	+	2.41918i
$516$	−19.7427	+	8.17768i	−0.869123	+	0.360002i
$517$	6.64695	+	16.0472i	0.292333	+	0.705753i
$518$		0			0
$519$	−1.27828	−	1.27828i	−0.0561104	−	0.0561104i
$520$	−3.92106	−	9.46626i	−0.171950	−	0.415123i
$521$	32.8546	−	13.6088i	1.43939	−	0.596213i	0.479736	−	0.877413i	$-0.340732\pi$
$521$	32.8546	−	13.6088i	1.43939	−	0.596213i	0.959649	+	0.281200i	$0.0907323\pi$
$522$	8.08346	−	19.5152i	0.353804	−	0.854157i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−60.8483	−	25.2042i	−2.65817	−	1.10105i
$525$		0			0
$526$	−52.4924			−2.28878
$527$		0			0
$528$	−12.0000			−0.522233
$529$	−12.0590	+	12.0590i	−0.524304	+	0.524304i
$530$	−103.219	−	42.7547i	−4.48355	−	1.85715i
$531$		−	7.12311i		−	0.309116i
$532$		0			0
$533$	−1.44269	+	0.597580i	−0.0624897	+	0.0258841i
$534$	1.10094	+	2.65790i	0.0476423	+	0.115019i
$535$	11.7978	+	11.7978i	0.510065	+	0.510065i
$536$	−18.5589	−	18.5589i	−0.801621	−	0.801621i
$537$	0.335573	+	0.810145i	0.0144810	+	0.0349603i
$538$	38.9027	−	16.1140i	1.67721	−	0.694725i
$539$	−4.18306	+	10.0988i	−0.180177	+	0.434986i
$540$		−	16.2462i		−	0.699126i
$541$	−31.5116	−	13.0525i	−1.35479	−	0.561173i	−0.417169	−	0.908829i	$-0.636978\pi$
$541$	−31.5116	−	13.0525i	−1.35479	−	0.561173i	−0.937622	+	0.347656i	$0.886978\pi$
$542$	35.8776	−	35.8776i	1.54108	−	1.54108i
$543$	6.00000			0.257485
$544$		0			0
$545$	−24.4924			−1.04914
$546$		0			0
$547$	25.8686	+	10.7151i	1.10606	+	0.458146i	0.859580	−	0.511001i	$-0.170725\pi$
$547$	25.8686	+	10.7151i	1.10606	+	0.458146i	0.246483	+	0.969147i	$0.420725\pi$
$548$		−	1.12311i		−	0.0479767i
$549$	−3.49126	+	8.42865i	−0.149003	+	0.359726i
$550$	−28.3988	+	11.7632i	−1.21093	+	0.501583i
$551$	−14.7833	−	35.6901i	−0.629791	−	1.52045i
$552$	11.3137	+	11.3137i	0.481543	+	0.481543i
$553$		0			0
$554$	−5.88158	−	14.1994i	−0.249885	−	0.603275i
$555$	−16.8573	+	6.98252i	−0.715553	+	0.296392i
$556$	−1.53073	+	3.69552i	−0.0649176	+	0.156725i
$557$			26.4924i			1.12252i	0.827640	+	0.561260i	$0.189683\pi$
$557$			26.4924i			1.12252i	−0.827640	+	0.561260i	$0.810317\pi$
$558$	7.39104	+	3.06147i	0.312888	+	0.129602i
$559$	−1.45238	+	1.45238i	−0.0614291	+	0.0614291i
$560$		0			0
$561$		0			0
$562$	27.8617			1.17528
$563$	22.0074	−	22.0074i	0.927500	−	0.927500i	−0.0700443	−	0.997544i	$-0.522314\pi$
$563$	22.0074	−	22.0074i	0.927500	−	0.927500i	0.997544	+	0.0700443i	$0.0223141\pi$
$564$	46.8764	+	19.4168i	1.97385	+	0.817596i
$565$			1.56155i			0.0656950i
$566$	20.9476	−	50.5719i	0.880492	−	2.12570i
$567$		0			0
$568$	−15.6842	−	37.8651i	−0.658095	−	1.58878i
$569$	−14.9363	−	14.9363i	−0.626162	−	0.626162i	0.320938	−	0.947100i	$-0.396002\pi$
$569$	−14.9363	−	14.9363i	−0.626162	−	0.626162i	−0.947100	+	0.320938i	$0.896002\pi$
$570$	−30.2208	−	30.2208i	−1.26581	−	1.26581i
$571$	−11.7632	−	28.3988i	−0.492273	−	1.18845i	−0.953560	−	0.301202i	$-0.902612\pi$
$571$	−11.7632	−	28.3988i	−0.492273	−	1.18845i	0.461287	−	0.887251i	$-0.347388\pi$
$572$	−2.88537	+	1.19516i	−0.120644	+	0.0499722i
$573$	1.86631	−	4.50566i	0.0779661	−	0.188227i
$574$		0			0
$575$	17.3122	+	7.17096i	0.721970	+	0.299050i
$576$	−1.01714	+	1.01714i	−0.0423807	+	0.0423807i
$577$	3.94602			0.164275			0.0821376	−	0.996621i	$-0.473825\pi$
$577$	3.94602			0.164275			0.0821376	+	0.996621i	$0.473825\pi$
$578$		0			0
$579$	7.75379			0.322236
$580$	−94.7309	+	94.7309i	−3.93349	+	3.93349i
$581$		0			0
$582$			7.36932i			0.305468i
$583$	−7.31810	+	17.6674i	−0.303085	+	0.731711i
$584$	74.2376	−	30.7502i	3.07197	−	1.27245i
$585$	−0.597580	−	1.44269i	−0.0247069	−	0.0596478i
$586$	2.03427	+	2.03427i	0.0840350	+	0.0840350i
$587$	−20.4954	−	20.4954i	−0.845935	−	0.845935i	0.143688	−	0.989623i	$-0.454104\pi$
$587$	−20.4954	−	20.4954i	−0.845935	−	0.845935i	−0.989623	+	0.143688i	$0.954104\pi$
$588$	12.2194	+	29.5003i	0.503920	+	1.21657i
$589$	13.5170	−	5.59892i	0.556958	−	0.230699i
$590$	−24.8686	+	60.0382i	−1.02383	+	2.47173i
$591$			8.93087i			0.367367i
$592$	36.3725	+	15.0660i	1.49490	+	0.619208i
$593$	−19.6249	+	19.6249i	−0.805898	+	0.805898i	−0.984010	−	0.178112i	$-0.943001\pi$
$593$	−19.6249	+	19.6249i	−0.805898	+	0.805898i	0.178112	+	0.984010i	$0.443001\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	55.8617			2.28819
$597$	−11.3137	+	11.3137i	−0.463039	+	0.463039i
$598$	2.53017	+	1.04803i	0.103466	+	0.0428571i
$599$			0.384472i			0.0157091i	0.999969	+	0.00785455i	$0.00250021\pi$
$599$			0.384472i			0.0157091i	−0.999969	+	0.00785455i	$0.997500\pi$
$600$	−19.2962	+	46.5850i	−0.787762	+	1.90183i
$601$	−28.6263	+	11.8574i	−1.16769	+	0.483673i	−0.880428	−	0.474179i	$-0.842745\pi$
$601$	−28.6263	+	11.8574i	−1.16769	+	0.483673i	−0.287261	+	0.957852i	$0.592745\pi$
$602$		0			0
$603$	−2.82843	−	2.82843i	−0.115182	−	0.115182i
$604$	25.8040	+	25.8040i	1.04995	+	1.04995i
$605$	−11.6689	−	28.1713i	−0.474410	−	1.14533i
$606$	−25.7409	+	10.6622i	−1.04565	+	0.433123i
$607$	−3.58548	+	8.65612i	−0.145530	+	0.351341i	−0.979790	−	0.200031i	$-0.935896\pi$
$607$	−3.58548	+	8.65612i	−0.145530	+	0.351341i	0.834259	+	0.551372i	$0.185896\pi$
$608$			30.7386i			1.24662i
$609$		0			0
$610$	58.8532	−	58.8532i	2.38290	−	2.38290i
$611$	4.87689			0.197298
$612$		0			0
$613$	14.6847			0.593108			0.296554	−	0.955016i	$-0.404163\pi$
$613$	14.6847			0.593108			0.296554	+	0.955016i	$0.404163\pi$
$614$	−58.8532	+	58.8532i	−2.37512	+	2.37512i
$615$	11.7191	+	4.85421i	0.472560	+	0.195741i
$616$		0			0
$617$	16.9323	−	40.8782i	0.681668	−	1.64569i	−0.0792574	−	0.996854i	$-0.525255\pi$
$617$	16.9323	−	40.8782i	0.681668	−	1.64569i	0.760926	−	0.648839i	$-0.224745\pi$
$618$	39.4853	−	16.3554i	1.58833	−	0.657909i
$619$	−2.05475	−	4.96060i	−0.0825873	−	0.199383i	0.877191	−	0.480141i	$-0.159414\pi$
$619$	−2.05475	−	4.96060i	−0.0825873	−	0.199383i	−0.959779	+	0.280757i	$0.909414\pi$
$620$	−35.8776	−	35.8776i	−1.44088	−	1.44088i
$621$	1.72424	+	1.72424i	0.0691915	+	0.0691915i
$622$		0			0
$623$		0			0
$624$	−1.28938	+	3.11284i	−0.0516166	+	0.124613i
$625$		−	4.36932i		−	0.174773i
$626$	79.5534	+	32.9521i	3.17959	+	1.31703i
$627$	−5.17273	+	5.17273i	−0.206579	+	0.206579i
$628$	−30.4924			−1.21678
$629$		0			0
$630$		0			0
$631$	−0.484127	+	0.484127i	−0.0192728	+	0.0192728i	−0.716678	−	0.697405i	$-0.754338\pi$
$631$	−0.484127	+	0.484127i	−0.0192728	+	0.0192728i	0.697405	+	0.716678i	$0.254338\pi$
$632$	56.7976	+	23.5263i	2.25929	+	0.935827i
$633$			13.3693i			0.531383i
$634$	−17.6447	+	42.5982i	−0.700762	+	1.69179i
$635$	65.1764	−	26.9969i	2.58645	−	1.07134i
$636$	21.3774	+	51.6095i	0.847668	+	2.04645i
$637$	2.17020	+	2.17020i	0.0859866	+	0.0859866i
$638$	23.3238	+	23.3238i	0.923398	+	0.923398i
$639$	−2.39032	−	5.77075i	−0.0945597	−	0.228287i
$640$	−31.0567	+	12.8641i	−1.22762	+	0.508498i
$641$	−11.0714	+	26.7286i	−0.437293	+	1.05572i	0.539587	+	0.841930i	$0.318580\pi$
$641$	−11.0714	+	26.7286i	−0.437293	+	1.05572i	−0.976880	+	0.213788i	$0.931420\pi$
$642$		−	12.0000i		−	0.473602i
$643$	12.7068	+	5.26335i	0.501109	+	0.207566i	0.618896	−	0.785473i	$-0.287580\pi$
$643$	12.7068	+	5.26335i	0.501109	+	0.207566i	−0.117787	+	0.993039i	$0.537580\pi$
$644$		0			0
$645$	16.6847			0.656958
$646$		0			0
$647$	−9.36932			−0.368346			−0.184173	−	0.982894i	$-0.558961\pi$
$647$	−9.36932			−0.368346			−0.184173	+	0.982894i	$0.558961\pi$
$648$	−4.63972	+	4.63972i	−0.182265	+	0.182265i
$649$	10.2764	+	4.25663i	0.403384	+	0.167087i
$650$			8.63068i			0.338523i
$651$		0			0
$652$	−63.7337	+	26.3994i	−2.49600	+	1.03388i
$653$	12.6021	+	30.4242i	0.493158	+	1.19059i	0.953104	+	0.302642i	$0.0978688\pi$
$653$	12.6021	+	30.4242i	0.493158	+	1.19059i	−0.459946	+	0.887947i	$0.652131\pi$
$654$	12.4561	+	12.4561i	0.487070	+	0.487070i
$655$	36.3618	+	36.3618i	1.42077	+	1.42077i
$656$	−10.4738	−	25.2860i	−0.408933	−	0.987251i
$657$	11.3140	−	4.68642i	0.441402	−	0.182835i
$658$		0			0
$659$		−	9.86174i		−	0.384159i	−0.981379	−	0.192079i	$-0.938477\pi$
$659$		−	9.86174i		−	0.384159i	0.981379	−	0.192079i	$-0.0615231\pi$
$660$	23.4382	+	9.70842i	0.912330	+	0.377900i
$661$	−9.41537	+	9.41537i	−0.366215	+	0.366215i	−0.866095	−	0.499880i	$-0.833378\pi$
$661$	−9.41537	+	9.41537i	−0.366215	+	0.366215i	0.499880	+	0.866095i	$0.333378\pi$
$662$	−89.4773			−3.47763
$663$		0			0
$664$	5.75379			0.223290
$665$		0			0
$666$	12.1242	+	5.02200i	0.469802	+	0.194598i
$667$		−	20.1080i		−	0.778583i
$668$	−34.5770	+	83.4764i	−1.33783	+	3.22980i
$669$	13.7943	−	5.71380i	0.533319	−	0.220908i
$670$	13.9650	+	33.7146i	0.539517	+	1.30251i
$671$	−10.0736	−	10.0736i	−0.388887	−	0.388887i
$672$		0			0
$673$	−0.282663	−	0.682409i	−0.0108959	−	0.0263049i	0.918338	−	0.395797i	$-0.129532\pi$
$673$	−0.282663	−	0.682409i	−0.0108959	−	0.0263049i	−0.929234	+	0.369492i	$0.879532\pi$
$674$	−39.6131	+	16.4083i	−1.52584	+	0.632023i
$675$	−2.94079	+	7.09970i	−0.113191	+	0.273268i
$676$		−	58.4233i		−	2.24705i
$677$	1.21522	+	0.503359i	0.0467046	+	0.0193457i	0.405913	−	0.913912i	$-0.366953\pi$
$677$	1.21522	+	0.503359i	0.0467046	+	0.0193457i	−0.359209	+	0.933257i	$0.616953\pi$
$678$	0.794156	−	0.794156i	0.0304994	−	0.0304994i
$679$		0			0
$680$		0			0
$681$	14.0540			0.538550
$682$	−8.83348	+	8.83348i	−0.338251	+	0.338251i
$683$	−8.83372	−	3.65905i	−0.338013	−	0.140010i	0.207219	−	0.978294i	$-0.433559\pi$
$683$	−8.83372	−	3.65905i	−0.338013	−	0.140010i	−0.545232	+	0.838285i	$0.683559\pi$
$684$			21.3693i			0.817076i
$685$	−0.335573	+	0.810145i	−0.0128216	+	0.0309540i
$686$		0			0
$687$	2.29610	+	5.54328i	0.0876017	+	0.211489i
$688$	−25.4558	−	25.4558i	−0.970495	−	0.970495i
$689$	3.79668	+	3.79668i	0.144642	+	0.144642i
$690$	−8.51326	−	20.5528i	−0.324094	−	0.782432i
$691$	26.7785	−	11.0920i	1.01870	−	0.421960i	0.190080	−	0.981769i	$-0.439125\pi$
$691$	26.7785	−	11.0920i	1.01870	−	0.421960i	0.828622	+	0.559808i	$0.189125\pi$
$692$	3.15569	−	7.61851i	0.119961	−	0.289612i
$693$		0			0
$694$	−20.0979	−	8.32481i	−0.762905	−	0.316006i
$695$	2.20837	−	2.20837i	0.0837682	−	0.0837682i
$696$	54.1080			2.05096
$697$		0			0
$698$	−29.6155			−1.12096
$699$	2.51840	−	2.51840i	0.0952546	−	0.0952546i
$700$		0			0
$701$		−	15.3693i		−	0.580491i	−0.956952	−	0.290246i	$-0.906263\pi$
$701$		−	15.3693i		−	0.580491i	0.956952	−	0.290246i	$-0.0937370\pi$
$702$	−0.429794	+	1.03761i	−0.0162215	+	0.0391622i
$703$	22.1731	−	9.18440i	0.836275	−	0.346396i
$704$	−0.859588	−	2.07523i	−0.0323969	−	0.0782131i
$705$	−28.0124	−	28.0124i	−1.05501	−	1.05501i
$706$	19.0048	+	19.0048i	0.715256	+	0.715256i
$707$		0			0
$708$	30.0191	−	12.4343i	1.12819	−	0.467310i
$709$	−17.1207	+	41.3331i	−0.642983	+	1.55230i	0.179654	+	0.983730i	$0.442502\pi$
$709$	−17.1207	+	41.3331i	−0.642983	+	1.55230i	−0.822637	+	0.568568i	$0.807498\pi$
$710$			56.9848i			2.13860i
$711$	8.65612	+	3.58548i	0.324630	+	0.134466i
$712$	−5.21089	+	5.21089i	−0.195287	+	0.195287i
$713$	7.61553			0.285204
$714$		0			0
$715$	2.43845			0.0911928
$716$	−2.82843	+	2.82843i	−0.105703	+	0.105703i
$717$	5.77075	+	2.39032i	0.215512	+	0.0892682i
$718$			36.4924i			1.36189i
$719$	4.51864	−	10.9090i	0.168517	−	0.406835i	−0.816949	−	0.576710i	$-0.804336\pi$
$719$	4.51864	−	10.9090i	0.168517	−	0.406835i	0.985466	+	0.169875i	$0.0543363\pi$
$720$	25.2860	−	10.4738i	0.942352	−	0.390335i
$721$		0			0
$722$	5.33611	+	5.33611i	0.198589	+	0.198589i
$723$	−2.38247	−	2.38247i	−0.0886049	−	0.0886049i
$724$	10.4738	+	25.2860i	0.389255	+	0.939745i
$725$	58.5456	−	24.2504i	2.17433	−	0.900637i
$726$	−8.39258	+	20.2615i	−0.311478	+	0.751974i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	−111.723			−4.13507
$731$		0			0
$732$	−41.6155			−1.53815
$733$	−8.31118	+	8.31118i	−0.306981	+	0.306981i	−0.843737	−	0.536757i	$-0.819649\pi$
$733$	−8.31118	+	8.31118i	−0.306981	+	0.306981i	0.536757	+	0.843737i	$0.319649\pi$
$734$	4.15046	+	1.71918i	0.153196	+	0.0634559i
$735$		−	24.9309i		−	0.919589i
$736$	−6.12293	+	14.7821i	−0.225694	+	0.544874i
$737$	5.77075	−	2.39032i	0.212568	−	0.0880486i
$738$	−3.49126	−	8.42865i	−0.128515	−	0.310263i
$739$	14.6263	+	14.6263i	0.538036	+	0.538036i	0.922952	−	0.384916i	$-0.125770\pi$
$739$	14.6263	+	14.6263i	0.538036	+	0.538036i	−0.384916	+	0.922952i	$0.625770\pi$
$740$	−58.8532	−	58.8532i	−2.16349	−	2.16349i
$741$	0.786022	+	1.89763i	0.0288753	+	0.0697110i
$742$		0			0
$743$	10.9036	−	26.3236i	0.400013	−	0.965718i	−0.587648	−	0.809116i	$-0.699946\pi$
$743$	10.9036	−	26.3236i	0.400013	−	0.965718i	0.987662	−	0.156602i	$-0.0500538\pi$
$744$			20.4924i			0.751289i
$745$	−40.2955	−	16.6909i	−1.47631	−	0.611509i
$746$	−0.445960	+	0.445960i	−0.0163278	+	0.0163278i
$747$	0.876894			0.0320839
$748$		0			0
$749$		0			0
$750$	17.3188	−	17.3188i	0.632392	−	0.632392i
$751$	−23.4382	−	9.70842i	−0.855272	−	0.354265i	−0.0884152	−	0.996084i	$-0.528180\pi$
$751$	−23.4382	−	9.70842i	−0.855272	−	0.354265i	−0.766857	+	0.641819i	$0.778180\pi$
$752$			85.4773i			3.11704i
$753$	3.24991	−	7.84598i	0.118433	−	0.285923i
$754$	8.55639	−	3.54417i	0.311605	−	0.129071i
$755$	−10.9036	−	26.3236i	−0.396822	−	0.958013i
$756$		0			0
$757$	11.3519	+	11.3519i	0.412591	+	0.412591i	0.882640	−	0.470049i	$-0.155764\pi$
$757$	11.3519	+	11.3519i	0.412591	+	0.412591i	−0.470049	+	0.882640i	$0.655764\pi$
$758$	11.7632	+	28.3988i	0.427257	+	1.03149i
$759$	−3.51792	+	1.45717i	−0.127692	+	0.0528919i
$760$	41.8951	−	101.144i	1.51970	−	3.66887i
$761$		−	15.7538i		−	0.571074i	−0.958368	−	0.285537i	$-0.907828\pi$
$761$		−	15.7538i		−	0.571074i	0.958368	−	0.285537i	$-0.0921720\pi$
$762$	−46.8764	−	19.4168i	−1.69815	−	0.703398i
$763$		0			0
$764$	22.2462			0.804840
$765$		0			0
$766$	−16.0000			−0.578103
$767$	2.20837	−	2.20837i	0.0797396	−	0.0797396i
$768$	24.9946	+	10.3531i	0.901915	+	0.373586i
$769$		−	40.5464i		−	1.46214i	−0.682302	−	0.731070i	$-0.739021\pi$
$769$		−	40.5464i		−	1.46214i	0.682302	−	0.731070i	$-0.260979\pi$
$770$		0			0
$771$	14.1994	−	5.88158i	0.511379	−	0.211820i
$772$	13.5353	+	32.6770i	0.487144	+	1.17607i
$773$	6.10281	+	6.10281i	0.219503	+	0.219503i	0.808289	−	0.588786i	$-0.200394\pi$
$773$	6.10281	+	6.10281i	0.219503	+	0.219503i	−0.588786	+	0.808289i	$0.700394\pi$
$774$	−8.48528	−	8.48528i	−0.304997	−	0.304997i
$775$	9.18440	+	22.1731i	0.329913	+	0.796482i
$776$	−17.4400	+	7.22387i	−0.626059	+	0.259322i
$777$		0			0
$778$		−	91.8617i		−	3.29340i
$779$	−15.4146	−	6.38494i	−0.552286	−	0.228764i
$780$	5.03680	−	5.03680i	0.180346	−	0.180346i
$781$	9.75379			0.349018
$782$		0			0
$783$	8.24621			0.294696
$784$	−38.0371	+	38.0371i	−1.35847	+	1.35847i
$785$	21.9955	+	9.11084i	0.785053	+	0.325180i
$786$		−	36.9848i		−	1.31921i
$787$	3.92106	−	9.46626i	0.139771	−	0.337436i	−0.838458	−	0.544966i	$-0.816543\pi$
$787$	3.92106	−	9.46626i	0.139771	−	0.337436i	0.978229	+	0.207530i	$0.0665425\pi$
$788$	−37.6376	+	15.5900i	−1.34078	+	0.555371i
$789$	−7.84211	−	18.9325i	−0.279187	−	0.674016i
$790$	−60.4416	−	60.4416i	−2.15041	−	2.15041i
$791$		0			0
$792$	−3.92106	−	9.46626i	−0.139329	−	0.336369i
$793$	−3.69552	+	1.53073i	−0.131232	+	0.0543579i
$794$	18.9870	−	45.8388i	0.673825	−	1.62676i
$795$		−	43.6155i		−	1.54688i
$796$	−67.4292	−	27.9301i	−2.38996	−	0.989956i
$797$	6.79921	−	6.79921i	0.240840	−	0.240840i	−0.576357	−	0.817198i	$-0.695526\pi$
$797$	6.79921	−	6.79921i	0.240840	−	0.240840i	0.817198	+	0.576357i	$0.195526\pi$
$798$		0			0
$799$		0			0
$800$	−50.4233			−1.78273
$801$	−0.794156	+	0.794156i	−0.0280601	+	0.0280601i
$802$	−92.7152	−	38.4039i	−3.27389	−	1.35609i
$803$			19.1231i			0.674840i
$804$	6.98252	−	16.8573i	0.246255	−	0.594511i
$805$		0			0
$806$	1.34229	+	3.24058i	0.0472802	+	0.114145i
$807$	11.6237	+	11.6237i	0.409175	+	0.409175i
$808$	−50.4657	−	50.4657i	−1.77538	−	1.77538i
$809$	6.10228	+	14.7322i	0.214545	+	0.517957i	0.994111	−	0.108362i	$-0.0345607\pi$
$809$	6.10228	+	14.7322i	0.214545	+	0.517957i	−0.779567	+	0.626319i	$0.784561\pi$
$810$	8.42865	−	3.49126i	0.296153	−	0.122670i
$811$	−17.3621	+	41.9158i	−0.609665	+	1.47186i	0.253700	+	0.967283i	$0.418352\pi$
$811$	−17.3621	+	41.9158i	−0.609665	+	1.47186i	−0.863365	+	0.504579i	$0.831648\pi$
$812$		0			0
$813$	18.3000	+	7.58010i	0.641809	+	0.265846i
$814$	−14.4903	+	14.4903i	−0.507886	+	0.507886i
$815$	53.8617			1.88669
$816$		0			0
$817$	−21.9460			−0.767794
$818$	26.5982	−	26.5982i	0.929984	−	0.929984i
$819$		0			0
$820$			57.8617i			2.02062i
$821$	4.75999	−	11.4916i	0.166125	−	0.401061i	−0.818792	−	0.574091i	$-0.805356\pi$
$821$	4.75999	−	11.4916i	0.166125	−	0.401061i	0.984917	+	0.173030i	$0.0553557\pi$
$822$	0.582675	−	0.241352i	0.0203231	−	0.00841812i
$823$	−1.34229	−	3.24058i	−0.0467894	−	0.112959i	0.898757	−	0.438447i	$-0.144471\pi$
$823$	−1.34229	−	3.24058i	−0.0467894	−	0.112959i	−0.945546	+	0.325488i	$0.894471\pi$
$824$	77.4121	+	77.4121i	2.69678	+	2.69678i
$825$	−8.48528	−	8.48528i	−0.295420	−	0.295420i
$826$		0			0
$827$	−43.8134	+	18.1481i	−1.52354	+	0.631072i	−0.978297	−	0.207206i	$-0.933563\pi$
$827$	−43.8134	+	18.1481i	−1.52354	+	0.631072i	−0.545244	+	0.838277i	$0.683563\pi$
$828$	−4.25663	+	10.2764i	−0.147928	+	0.357130i
$829$			17.5076i			0.608063i	0.952662	+	0.304032i	$0.0983329\pi$
$829$			17.5076i			0.608063i	−0.952662	+	0.304032i	$0.901667\pi$
$830$	−7.39104	−	3.06147i	−0.256547	−	0.106265i
$831$	4.24264	−	4.24264i	0.147176	−	0.147176i
$832$	−0.630683			−0.0218650
$833$		0			0
$834$	−2.24621			−0.0777799
$835$	49.8838	−	49.8838i	1.72630	−	1.72630i
$836$	−30.8292	−	12.7699i	−1.06625	−	0.441656i
$837$			3.12311i			0.107950i
$838$	−0.482704	+	1.16535i	−0.0166747	+	0.0402564i
$839$	−24.0707	+	9.97042i	−0.831014	+	0.344217i	−0.757304	−	0.653062i	$-0.773484\pi$
$839$	−24.0707	+	9.97042i	−0.831014	+	0.344217i	−0.0737100	+	0.997280i	$0.523484\pi$
$840$		0			0
$841$	−27.5772	−	27.5772i	−0.950937	−	0.950937i
$842$	−44.2651	−	44.2651i	−1.52548	−	1.52548i
$843$	4.16241	+	10.0489i	0.143361	+	0.346104i
$844$	−56.3427	+	23.3379i	−1.93939	+	0.803323i
$845$	−17.4563	+	42.1433i	−0.600515	+	1.44977i
$846$			28.4924i			0.979590i
$847$		0			0
$848$	−66.5444	+	66.5444i	−2.28514	+	2.28514i
$849$	21.3693			0.733393
$850$		0			0
$851$	12.4924			0.428235
$852$	20.1472	−	20.1472i	0.690231	−	0.690231i
$853$	−26.5510	−	10.9978i	−0.909090	−	0.376557i	−0.121382	−	0.992606i	$-0.538733\pi$
$853$	−26.5510	−	10.9978i	−0.909090	−	0.376557i	−0.787708	+	0.616048i	$0.788733\pi$
$854$		0			0
$855$	6.38494	−	15.4146i	0.218360	−	0.527169i
$856$	28.3988	−	11.7632i	0.970651	−	0.402057i
$857$	2.29610	+	5.54328i	0.0784333	+	0.189355i	0.958232	−	0.285991i	$-0.0923229\pi$
$857$	2.29610	+	5.54328i	0.0784333	+	0.189355i	−0.879799	+	0.475346i	$0.842323\pi$
$858$	−1.24012	−	1.24012i	−0.0423369	−	0.0423369i
$859$	8.48528	+	8.48528i	0.289514	+	0.289514i	0.836888	−	0.547374i	$-0.184372\pi$
$859$	8.48528	+	8.48528i	0.289514	+	0.289514i	−0.547374	+	0.836888i	$0.684372\pi$
$860$	29.1253	+	70.3146i	0.993163	+	2.39771i
$861$		0			0
$862$	23.5263	−	56.7976i	0.801310	−	1.93453i
$863$		−	9.75379i		−	0.332023i	−0.986124	−	0.166011i	$-0.946911\pi$
$863$		−	9.75379i		−	0.332023i	0.986124	−	0.166011i	$-0.0530889\pi$
$864$	−6.06208	−	2.51100i	−0.206236	−	0.0854259i
$865$	−4.55267	+	4.55267i	−0.154795	+	0.154795i
$866$	68.3542			2.32277
$867$		0			0
$868$		0			0
$869$	−10.3455	+	10.3455i	−0.350946	+	0.350946i
$870$	−69.5044	−	28.7897i	−2.35642	−	0.976062i
$871$		−	1.75379i		−	0.0594249i
$872$	−17.2679	+	41.6883i	−0.584764	+	1.41174i
$873$	−2.65790	+	1.10094i	−0.0899564	+	0.0372612i
$874$	11.1978	+	27.0340i	0.378773	+	0.914438i
$875$		0			0
$876$	39.5002	+	39.5002i	1.33459	+	1.33459i
$877$	−13.0112	−	31.4119i	−0.439358	−	1.06070i	−0.976171	−	0.217003i	$-0.930372\pi$
$877$	−13.0112	−	31.4119i	−0.439358	−	1.06070i	0.536813	−	0.843701i	$-0.319628\pi$
$878$	−52.6471	+	21.8072i	−1.77675	+	0.735956i
$879$	−0.429794	+	1.03761i	−0.0144966	+	0.0349979i
$880$			42.7386i			1.44072i
$881$	−37.1827	−	15.4016i	−1.25272	−	0.518892i	−0.345049	−	0.938585i	$-0.612138\pi$
$881$	−37.1827	−	15.4016i	−1.25272	−	0.518892i	−0.907666	+	0.419693i	$0.862138\pi$
$882$	−12.6790	+	12.6790i	−0.426925	+	0.426925i
$883$	23.4233			0.788257			0.394128	−	0.919055i	$-0.371047\pi$
$883$	23.4233			0.788257			0.394128	+	0.919055i	$0.371047\pi$
$884$		0			0
$885$	−25.3693			−0.852780
$886$	56.3730	−	56.3730i	1.89389	−	1.89389i
$887$	17.0349	+	7.05609i	0.571976	+	0.236920i	0.649875	−	0.760041i	$-0.274821\pi$
$887$	17.0349	+	7.05609i	0.571976	+	0.236920i	−0.0778990	+	0.996961i	$0.524821\pi$
$888$			33.6155i			1.12806i
$889$		0			0
$890$	9.46626	−	3.92106i	0.317310	−	0.131434i
$891$	−0.597580	−	1.44269i	−0.0200197	−	0.0483318i
$892$	48.1596	+	48.1596i	1.61250	+	1.61250i
$893$	36.8459	+	36.8459i	1.23300	+	1.23300i
$894$	12.0045	+	28.9815i	0.401491	+	0.969285i
$895$	2.88537	−	1.19516i	0.0964474	−	0.0399498i
$896$		0			0
$897$			1.06913i			0.0356972i
$898$	86.9444	+	36.0136i	2.90137	+	1.20179i
$899$	18.2107	−	18.2107i	0.607360	−	0.607360i
$900$	−35.0540			−1.16847
$901$		0			0
$902$	14.2462			0.474347
$903$		0			0
$904$	2.65790	+	1.10094i	0.0884006	+	0.0366167i
$905$		−	21.3693i		−	0.710340i
$906$	−7.84211	+	18.9325i	−0.260537	+	0.628991i
$907$	−9.11106	+	3.77392i	−0.302528	+	0.125311i	−0.528783	−	0.848757i	$-0.677352\pi$
$907$	−9.11106	+	3.77392i	−0.302528	+	0.125311i	0.226256	+	0.974068i	$0.427352\pi$
$908$	24.5331	+	59.2280i	0.814158	+	1.96555i
$909$	−7.69113	−	7.69113i	−0.255099	−	0.255099i
$910$		0			0
$911$	9.29928	+	22.4504i	0.308099	+	0.743816i	0.999767	+	0.0216007i	$0.00687624\pi$
$911$	9.29928	+	22.4504i	0.308099	+	0.743816i	−0.691668	+	0.722216i	$0.743124\pi$
$912$	−33.2597	+	13.7766i	−1.10134	+	0.456189i
$913$	−0.524015	+	1.26508i	−0.0173424	+	0.0418682i
$914$		−	35.3693i		−	1.16991i
$915$	30.0191	+	12.4343i	0.992400	+	0.411066i
$916$	−19.3530	+	19.3530i	−0.639442	+	0.639442i
$917$		0			0
$918$		0			0
$919$	−16.6847			−0.550376			−0.275188	−	0.961390i	$-0.588740\pi$
$919$	−16.6847			−0.550376			−0.275188	+	0.961390i	$0.588740\pi$
$920$	40.2944	−	40.2944i	1.32847	−	1.32847i
$921$	−30.0191	−	12.4343i	−0.989162	−	0.409725i
$922$		−	21.1231i		−	0.695652i
$923$	1.04803	−	2.53017i	0.0344963	−	0.0832815i
$924$		0			0
$925$	15.0660	+	36.3725i	0.495367	+	1.19592i
$926$	−74.2355	−	74.2355i	−2.43953	−	2.43953i
$927$	11.7978	+	11.7978i	0.387492	+	0.387492i
$928$	20.7062	+	49.9892i	0.679715	+	1.64098i
$929$	−2.83551	+	1.17451i	−0.0930300	+	0.0385343i	−0.428713	−	0.903441i	$-0.641033\pi$
$929$	−2.83551	+	1.17451i	−0.0930300	+	0.0385343i	0.335683	+	0.941975i	$0.391033\pi$
$930$	10.9036	−	26.3236i	0.357542	−	0.863184i
$931$			32.7926i			1.07473i
$932$	15.0095	+	6.21716i	0.491654	+	0.203650i
$933$		0			0
$934$	54.7386			1.79110
$935$		0			0
$936$	−2.87689			−0.0940342
$937$	−15.5563	+	15.5563i	−0.508204	+	0.508204i	−0.913975	−	0.405771i	$-0.867003\pi$
$937$	−15.5563	+	15.5563i	−0.508204	+	0.508204i	0.405771	+	0.913975i	$0.367003\pi$
$938$		0			0
$939$			33.6155i			1.09700i
$940$	69.1541	−	166.953i	2.25556	−	5.44540i
$941$	27.7164	−	11.4805i	0.903528	−	0.374254i	0.117953	−	0.993019i	$-0.462367\pi$
$941$	27.7164	−	11.4805i	0.903528	−	0.374254i	0.785576	+	0.618766i	$0.212367\pi$
$942$	−6.55273	−	15.8197i	−0.213499	−	0.515433i
$943$	−6.14098	−	6.14098i	−0.199978	−	0.199978i
$944$	38.7061	+	38.7061i	1.25977	+	1.25977i
$945$		0			0
$946$	17.3122	−	7.17096i	0.562869	−	0.233148i
$947$	4.59220	−	11.0866i	0.149226	−	0.360265i	−0.831536	−	0.555471i	$-0.812538\pi$
$947$	4.59220	−	11.0866i	0.149226	−	0.360265i	0.980762	+	0.195207i	$0.0625378\pi$
$948$			42.7386i			1.38809i
$949$	4.96060	+	2.05475i	0.161028	+	0.0667000i
$950$	−65.2065	+	65.2065i	−2.11558	+	2.11558i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	36.3542			1.17763			0.588813	−	0.808269i	$-0.299595\pi$
$953$	36.3542			1.17763			0.588813	+	0.808269i	$0.299595\pi$
$954$	−22.1815	+	22.1815i	−0.718151	+	0.718151i
$955$	−16.0472	−	6.64695i	−0.519274	−	0.215090i
$956$			28.4924i			0.921511i
$957$	−4.92777	+	11.8967i	−0.159292	+	0.384566i
$958$	−57.5080	+	23.8206i	−1.85800	+	0.769608i
$959$		0			0
$960$	3.62258	+	3.62258i	0.116918	+	0.116918i
$961$	−15.0233	−	15.0233i	−0.484624	−	0.484624i
$962$	2.20188	+	5.31581i	0.0709914	+	0.171389i
$963$	4.32806	−	1.79274i	0.139470	−	0.0577703i
$964$	5.88158	−	14.1994i	0.189433	−	0.457332i
$965$		−	27.6155i		−	0.888975i
$966$		0			0
$967$	−30.0085	+	30.0085i	−0.965009	+	0.965009i	−0.999408	−	0.0343994i	$-0.989048\pi$
$967$	−30.0085	+	30.0085i	−0.965009	+	0.965009i	0.0343994	+	0.999408i	$0.489048\pi$
$968$	−56.1771			−1.80560
$969$		0			0
$970$	26.2462			0.842715
$971$	−30.8408	+	30.8408i	−0.989730	+	0.989730i	−0.999948	−	0.0102183i	$-0.996747\pi$
$971$	−30.8408	+	30.8408i	−0.989730	+	0.989730i	0.0102183	+	0.999948i	$0.496747\pi$
$972$	−4.21433	−	1.74563i	−0.135175	−	0.0559911i
$973$		0			0
$974$	17.0265	−	41.1056i	0.545565	−	1.31711i
$975$	−3.11284	+	1.28938i	−0.0996908	+	0.0412933i
$976$	−26.8292	−	64.7713i	−0.858780	−	2.07328i
$977$	−5.83095	−	5.83095i	−0.186549	−	0.186549i	0.607654	−	0.794202i	$-0.292111\pi$
$977$	−5.83095	−	5.83095i	−0.186549	−	0.186549i	−0.794202	+	0.607654i	$0.792111\pi$
$978$	−27.3924	−	27.3924i	−0.875911	−	0.875911i
$979$	−0.671146	−	1.62029i	−0.0214499	−	0.0517847i
$980$	105.067	−	43.5201i	3.35624	−	1.39020i
$981$	−2.63167	+	6.35342i	−0.0840229	+	0.202849i
$982$			54.7386i			1.74678i
$983$	−28.5764	−	11.8367i	−0.911446	−	0.377533i	−0.122836	−	0.992427i	$-0.539199\pi$
$983$	−28.5764	−	11.8367i	−0.911446	−	0.377533i	−0.788610	+	0.614894i	$0.789199\pi$
$984$	16.5246	−	16.5246i	0.526785	−	0.526785i
$985$	31.8078			1.01348
$986$		0			0
$987$		0			0
$988$	−6.62511	+	6.62511i	−0.210773	+	0.210773i
$989$	−10.5537	−	4.37150i	−0.335590	−	0.139006i
$990$			14.2462i			0.452774i
$991$	−16.3554	+	39.4853i	−0.519545	+	1.25429i	0.418638	+	0.908153i	$0.362508\pi$
$991$	−16.3554	+	39.4853i	−0.519545	+	1.25429i	−0.938183	+	0.346140i	$0.887492\pi$
$992$	−18.9325	+	7.84211i	−0.601108	+	0.248987i
$993$	−13.3675	−	32.2719i	−0.424204	−	1.02412i
$994$		0			0
$995$	40.2944	+	40.2944i	1.27742	+	1.27742i
$996$	1.53073	+	3.69552i	0.0485032	+	0.117097i
$997$	9.23880	−	3.82683i	0.292596	−	0.121197i	−0.231557	−	0.972821i	$-0.574382\pi$
$997$	9.23880	−	3.82683i	0.292596	−	0.121197i	0.524153	+	0.851624i	$0.324382\pi$
$998$	−13.1055	+	31.6394i	−0.414846	+	1.00153i
$999$			5.12311i			0.162088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.j.757.1		16
17.2	even	8	inner	867.2.h.j.733.1		16
17.3	odd	16		867.2.e.f.829.3		8
17.4	even	4	inner	867.2.h.j.688.3		16
17.5	odd	16		867.2.e.f.616.2		8
17.6	odd	16		51.2.a.b.1.1	✓	2
17.7	odd	16		867.2.d.c.577.4		4
17.8	even	8	inner	867.2.h.j.712.4		16
17.9	even	8	inner	867.2.h.j.712.3		16
17.10	odd	16		867.2.d.c.577.3		4
17.11	odd	16		867.2.a.f.1.1		2
17.12	odd	16		867.2.e.f.616.1		8
17.13	even	4	inner	867.2.h.j.688.4		16
17.14	odd	16		867.2.e.f.829.4		8
17.15	even	8	inner	867.2.h.j.733.2		16
17.16	even	2	inner	867.2.h.j.757.2		16
51.11	even	16		2601.2.a.t.1.2		2
51.23	even	16		153.2.a.e.1.2		2
68.23	even	16		816.2.a.m.1.2		2
85.23	even	16		1275.2.b.d.1174.4		4
85.57	even	16		1275.2.b.d.1174.1		4
85.74	odd	16		1275.2.a.n.1.2		2
119.6	even	16		2499.2.a.o.1.1		2
136.91	even	16		3264.2.a.bg.1.1		2
136.125	odd	16		3264.2.a.bl.1.1		2
187.142	even	16		6171.2.a.p.1.2		2
204.23	odd	16		2448.2.a.v.1.1		2
221.142	odd	16		8619.2.a.q.1.2		2
255.74	even	16		3825.2.a.s.1.1		2
357.125	odd	16		7497.2.a.v.1.2		2
408.125	even	16		9792.2.a.cy.1.2		2
408.227	odd	16		9792.2.a.cz.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.1	✓	2	17.6	odd	16
153.2.a.e.1.2		2	51.23	even	16
816.2.a.m.1.2		2	68.23	even	16
867.2.a.f.1.1		2	17.11	odd	16
867.2.d.c.577.3		4	17.10	odd	16
867.2.d.c.577.4		4	17.7	odd	16
867.2.e.f.616.1		8	17.12	odd	16
867.2.e.f.616.2		8	17.5	odd	16
867.2.e.f.829.3		8	17.3	odd	16
867.2.e.f.829.4		8	17.14	odd	16
867.2.h.j.688.3		16	17.4	even	4	inner
867.2.h.j.688.4		16	17.13	even	4	inner
867.2.h.j.712.3		16	17.9	even	8	inner
867.2.h.j.712.4		16	17.8	even	8	inner
867.2.h.j.733.1		16	17.2	even	8	inner
867.2.h.j.733.2		16	17.15	even	8	inner
867.2.h.j.757.1		16	1.1	even	1	trivial
867.2.h.j.757.2		16	17.16	even	2	inner
1275.2.a.n.1.2		2	85.74	odd	16
1275.2.b.d.1174.1		4	85.57	even	16
1275.2.b.d.1174.4		4	85.23	even	16
2448.2.a.v.1.1		2	204.23	odd	16
2499.2.a.o.1.1		2	119.6	even	16
2601.2.a.t.1.2		2	51.11	even	16
3264.2.a.bg.1.1		2	136.91	even	16
3264.2.a.bl.1.1		2	136.125	odd	16
3825.2.a.s.1.1		2	255.74	even	16
6171.2.a.p.1.2		2	187.142	even	16
7497.2.a.v.1.2		2	357.125	odd	16
8619.2.a.q.1.2		2	221.142	odd	16
9792.2.a.cy.1.2		2	408.125	even	16
9792.2.a.cz.1.2		2	408.227	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81129 + 1.81129i) q^{2} +(-0.923880 - 0.382683i) q^{3} -4.56155i q^{4} +(-1.36295 + 3.29045i) q^{5} +(2.36657 - 0.980264i) q^{6} +(4.63972 + 4.63972i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-1.81129 + 1.81129i) q^{2} +(-0.923880 - 0.382683i) q^{3} -4.56155i q^{4} +(-1.36295 + 3.29045i) q^{5} +(2.36657 - 0.980264i) q^{6} +(4.63972 + 4.63972i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-3.49126 - 8.42865i) q^{10} +(-1.44269 + 0.597580i) q^{11} +(-1.74563 + 4.21433i) q^{12} +0.438447i q^{13} +(2.51840 - 2.51840i) q^{15} -7.68466 q^{16} -2.56155 q^{18} +(-3.31255 + 3.31255i) q^{19} +(15.0095 + 6.21716i) q^{20} +(1.53073 - 3.69552i) q^{22} +(-2.25283 + 0.933153i) q^{23} +(-2.51100 - 6.06208i) q^{24} +(-5.43387 - 5.43387i) q^{25} +(-0.794156 - 0.794156i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(-3.15569 + 7.61851i) q^{29} +9.12311i q^{30} +(-2.88537 - 1.19516i) q^{31} +(4.63972 - 4.63972i) q^{32} +1.56155 q^{33} +(3.22550 - 3.22550i) q^{36} +(-4.73313 - 1.96053i) q^{37} -12.0000i q^{38} +(0.167786 - 0.405072i) q^{39} +(-21.5904 + 8.94305i) q^{40} +(1.36295 + 3.29045i) q^{41} +(3.31255 + 3.31255i) q^{43} +(2.72589 + 6.58089i) q^{44} +(-3.29045 + 1.36295i) q^{45} +(2.39032 - 5.77075i) q^{46} -11.1231i q^{47} +(7.09970 + 2.94079i) q^{48} +(4.94975 - 4.94975i) q^{49} +19.6847 q^{50} +2.00000 q^{52} +(8.65938 - 8.65938i) q^{53} +(2.36657 + 0.980264i) q^{54} -5.56155i q^{55} +(4.32806 - 1.79274i) q^{57} +(-8.08346 - 19.5152i) q^{58} +(-5.03680 - 5.03680i) q^{59} +(-11.4878 - 11.4878i) q^{60} +(3.49126 + 8.42865i) q^{61} +(7.39104 - 3.06147i) q^{62} +1.43845i q^{64} +(-1.44269 - 0.597580i) q^{65} +(-2.82843 + 2.82843i) q^{66} -4.00000 q^{67} +2.43845 q^{69} +(-5.77075 - 2.39032i) q^{71} +6.56155i q^{72} +(4.68642 - 11.3140i) q^{73} +(12.1242 - 5.02200i) q^{74} +(2.94079 + 7.09970i) q^{75} +(15.1104 + 15.1104i) q^{76} +(0.429794 + 1.03761i) q^{78} +(8.65612 - 3.58548i) q^{79} +(10.4738 - 25.2860i) q^{80} +1.00000i q^{81} +(-8.42865 - 3.49126i) q^{82} +(0.620058 - 0.620058i) q^{83} -12.0000 q^{86} +(5.83095 - 5.83095i) q^{87} +(-9.46626 - 3.92106i) q^{88} +1.12311i q^{89} +(3.49126 - 8.42865i) q^{90} +(4.25663 + 10.2764i) q^{92} +(2.20837 + 2.20837i) q^{93} +(20.1472 + 20.1472i) q^{94} +(-6.38494 - 15.4146i) q^{95} +(-6.06208 + 2.51100i) q^{96} +(-1.10094 + 2.65790i) q^{97} +17.9309i q^{98} +(-1.44269 - 0.597580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) \) 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

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