LMFDB - Embedded newform 128.3.h.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	128.47
Dual form			128.3.h.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +O(q^{10})$	\(q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +20.3488 q^{15} -3.67152i q^{17} +(1.65751 + 0.686564i) q^{19} +(11.7458 - 4.86528i) q^{21} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(-27.1564 + 11.2485i) q^{27} +(-38.8592 - 16.0960i) q^{29} -4.11293i q^{31} +39.0124 q^{33} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(12.7544 + 12.7544i) q^{39} +(21.1187 + 21.1187i) q^{41} +(0.102495 + 0.247444i) q^{43} +(9.58403 - 23.1379i) q^{45} +39.3838 q^{47} -22.0079i q^{49} +(8.30063 + 3.43823i) q^{51} +(22.6154 - 9.36759i) q^{53} +(-93.7406 + 93.7406i) q^{55} +(-3.10439 + 3.10439i) q^{57} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} -15.6472i q^{63} -61.2936 q^{65} +(-3.67448 + 8.87098i) q^{67} +(11.0124 + 26.5863i) q^{69} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-41.3427 - 99.8102i) q^{75} +(-31.6965 + 76.5221i) q^{77} -2.76556 q^{79} -44.8236i q^{81} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(72.7802 - 72.7802i) q^{87} +(72.4200 - 72.4200i) q^{89} +(-35.3801 + 14.6549i) q^{91} +(9.29858 + 3.85160i) q^{93} -14.9187i q^{95} +66.0511 q^{97} +(18.3743 - 44.3596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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
$3$	−0.936461	+	2.26082i	−0.312154	+	0.753605i	0.687471	+	0.726212i	$0.258721\pi$
$3$	−0.936461	+	2.26082i	−0.312154	+	0.753605i	−0.999625	+	0.0273938i	$0.991279\pi$
$4$		0			0
$5$	−3.18221	−	7.68254i	−0.636442	−	1.53651i	−0.831387	−	0.555693i	$-0.812453\pi$
$5$	−3.18221	−	7.68254i	−0.636442	−	1.53651i	0.194945	−	0.980814i	$-0.437547\pi$
$6$		0			0
$7$	−3.67370	−	3.67370i	−0.524814	−	0.524814i	0.394208	−	0.919021i	$-0.371019\pi$
$7$	−3.67370	−	3.67370i	−0.524814	−	0.524814i	−0.919021	+	0.394208i	$0.871019\pi$
$8$		0			0
$9$	2.12963	+	2.12963i	0.236625	+	0.236625i
$10$		0			0
$11$	−6.10089	−	14.7288i	−0.554626	−	1.33899i	−0.913971	−	0.405781i	$-0.867000\pi$
$11$	−6.10089	−	14.7288i	−0.554626	−	1.33899i	0.359345	−	0.933205i	$-0.383000\pi$
$12$		0			0
$13$	2.82075	−	6.80990i	0.216981	−	0.523839i	−0.777484	−	0.628902i	$-0.783505\pi$
$13$	2.82075	−	6.80990i	0.216981	−	0.523839i	0.994466	+	0.105063i	$0.0335046\pi$
$14$		0			0
$15$	20.3488			1.35659
$16$		0			0
$17$		−	3.67152i		−	0.215972i	−0.994152	−	0.107986i	$-0.965560\pi$
$17$		−	3.67152i		−	0.215972i	0.994152	−	0.107986i	$-0.0344401\pi$
$18$		0			0
$19$	1.65751	+	0.686564i	0.0872375	+	0.0361349i	0.425875	−	0.904782i	$-0.359966\pi$
$19$	1.65751	+	0.686564i	0.0872375	+	0.0361349i	−0.338638	+	0.940917i	$0.609966\pi$
$20$		0			0
$21$	11.7458	−	4.86528i	0.559325	−	0.231680i
$22$		0			0
$23$	8.31529	−	8.31529i	0.361534	−	0.361534i	−0.502843	−	0.864378i	$-0.667713\pi$
$23$	8.31529	−	8.31529i	0.361534	−	0.361534i	0.864378	+	0.502843i	$0.167713\pi$
$24$		0			0
$25$	−31.2172	+	31.2172i	−1.24869	+	1.24869i
$26$		0			0
$27$	−27.1564	+	11.2485i	−1.00579	+	0.416612i
$28$		0			0
$29$	−38.8592	−	16.0960i	−1.33997	−	0.555035i	−0.406489	−	0.913656i	$-0.633247\pi$
$29$	−38.8592	−	16.0960i	−1.33997	−	0.555035i	−0.933483	+	0.358621i	$0.883247\pi$
$30$		0			0
$31$		−	4.11293i		−	0.132675i	−0.997797	−	0.0663376i	$-0.978869\pi$
$31$		−	4.11293i		−	0.132675i	0.997797	−	0.0663376i	$-0.0211314\pi$
$32$		0			0
$33$	39.0124			1.18220
$34$		0			0
$35$	−16.5328	+	39.9138i	−0.472367	+	1.14039i
$36$		0			0
$37$	19.8759	+	47.9847i	0.537186	+	1.29688i	0.926679	+	0.375853i	$0.122650\pi$
$37$	19.8759	+	47.9847i	0.537186	+	1.29688i	−0.389493	+	0.921030i	$0.627350\pi$
$38$		0			0
$39$	12.7544	+	12.7544i	0.327036	+	0.327036i
$40$		0			0
$41$	21.1187	+	21.1187i	0.515091	+	0.515091i	0.916082	−	0.400991i	$-0.131334\pi$
$41$	21.1187	+	21.1187i	0.515091	+	0.515091i	−0.400991	+	0.916082i	$0.631334\pi$
$42$		0			0
$43$	0.102495	+	0.247444i	0.00238360	+	0.00575451i	0.925067	−	0.379804i	$-0.124009\pi$
$43$	0.102495	+	0.247444i	0.00238360	+	0.00575451i	−0.922683	+	0.385559i	$0.874009\pi$
$44$		0			0
$45$	9.58403	−	23.1379i	0.212978	−	0.514175i
$46$		0			0
$47$	39.3838			0.837952			0.418976	−	0.907997i	$-0.362389\pi$
$47$	39.3838			0.837952			0.418976	+	0.907997i	$0.362389\pi$
$48$		0			0
$49$		−	22.0079i		−	0.449141i
$50$		0			0
$51$	8.30063	+	3.43823i	0.162757	+	0.0674163i
$52$		0			0
$53$	22.6154	−	9.36759i	0.426705	−	0.176747i	−0.158987	−	0.987281i	$-0.550823\pi$
$53$	22.6154	−	9.36759i	0.426705	−	0.176747i	0.585692	+	0.810534i	$0.300823\pi$
$54$		0			0
$55$	−93.7406	+	93.7406i	−1.70437	+	1.70437i
$56$		0			0
$57$	−3.10439	+	3.10439i	−0.0544630	+	0.0544630i
$58$		0			0
$59$	101.380	−	41.9931i	1.71831	−	0.711747i	0.718441	−	0.695588i	$-0.244856\pi$
$59$	101.380	−	41.9931i	1.71831	−	0.711747i	0.999869	−	0.0161592i	$-0.00514387\pi$
$60$		0			0
$61$	−14.0475	−	5.81867i	−0.230287	−	0.0953880i	0.264556	−	0.964370i	$-0.414775\pi$
$61$	−14.0475	−	5.81867i	−0.230287	−	0.0953880i	−0.494843	+	0.868982i	$0.664775\pi$
$62$		0			0
$63$		−	15.6472i		−	0.248369i
$64$		0			0
$65$	−61.2936			−0.942978
$66$		0			0
$67$	−3.67448	+	8.87098i	−0.0548430	+	0.132403i	−0.948926	−	0.315498i	$-0.897828\pi$
$67$	−3.67448	+	8.87098i	−0.0548430	+	0.132403i	0.894083	+	0.447901i	$0.147828\pi$
$68$		0			0
$69$	11.0124	+	26.5863i	0.159600	+	0.385309i
$70$		0			0
$71$	−75.7712	−	75.7712i	−1.06720	−	1.06720i	−0.997573	−	0.0696271i	$-0.977819\pi$
$71$	−75.7712	−	75.7712i	−1.06720	−	1.06720i	−0.0696271	−	0.997573i	$-0.522181\pi$
$72$		0			0
$73$	−29.0378	−	29.0378i	−0.397779	−	0.397779i	0.479670	−	0.877449i	$-0.340756\pi$
$73$	−29.0378	−	29.0378i	−0.397779	−	0.397779i	−0.877449	+	0.479670i	$0.840756\pi$
$74$		0			0
$75$	−41.3427	−	99.8102i	−0.551237	−	1.33080i
$76$		0			0
$77$	−31.6965	+	76.5221i	−0.411643	+	0.993793i
$78$		0			0
$79$	−2.76556			−0.0350072			−0.0175036	−	0.999847i	$-0.505572\pi$
$79$	−2.76556			−0.0350072			−0.0175036	+	0.999847i	$0.505572\pi$
$80$		0			0
$81$		−	44.8236i		−	0.553378i
$82$		0			0
$83$	79.1972	+	32.8045i	0.954183	+	0.395235i	0.804801	−	0.593544i	$-0.202272\pi$
$83$	79.1972	+	32.8045i	0.954183	+	0.395235i	0.149381	+	0.988780i	$0.452272\pi$
$84$		0			0
$85$	−28.2066	+	11.6835i	−0.331842	+	0.137453i
$86$		0			0
$87$	72.7802	−	72.7802i	0.836554	−	0.836554i
$88$		0			0
$89$	72.4200	−	72.4200i	0.813708	−	0.813708i	−0.171480	−	0.985188i	$-0.554855\pi$
$89$	72.4200	−	72.4200i	0.813708	−	0.813708i	0.985188	+	0.171480i	$0.0548548\pi$
$90$		0			0
$91$	−35.3801	+	14.6549i	−0.388792	+	0.161043i
$92$		0			0
$93$	9.29858	+	3.85160i	0.0999847	+	0.0414150i
$94$		0			0
$95$		−	14.9187i		−	0.157039i
$96$		0			0
$97$	66.0511			0.680940			0.340470	−	0.940255i	$-0.389414\pi$
$97$	66.0511			0.680940			0.340470	+	0.940255i	$0.389414\pi$
$98$		0			0
$99$	18.3743	−	44.3596i	0.185599	−	0.448077i
$100$		0			0
$101$	−7.51179	−	18.1351i	−0.0743742	−	0.179555i	0.882320	−	0.470650i	$-0.155981\pi$
$101$	−7.51179	−	18.1351i	−0.0743742	−	0.179555i	−0.956694	+	0.291095i	$0.905981\pi$
$102$		0			0
$103$	−0.589180	−	0.589180i	−0.00572020	−	0.00572020i	0.704241	−	0.709961i	$-0.251288\pi$
$103$	−0.589180	−	0.589180i	−0.00572020	−	0.00572020i	−0.709961	+	0.704241i	$0.751288\pi$
$104$		0			0
$105$	−74.7554	−	74.7554i	−0.711956	−	0.711956i
$106$		0			0
$107$	55.4567	+	133.884i	0.518287	+	1.25126i	0.938955	+	0.344041i	$0.111796\pi$
$107$	55.4567	+	133.884i	0.518287	+	1.25126i	−0.420668	+	0.907215i	$0.638204\pi$
$108$		0			0
$109$	29.4015	−	70.9815i	0.269739	−	0.651207i	−0.729732	−	0.683733i	$-0.760355\pi$
$109$	29.4015	−	70.9815i	0.269739	−	0.651207i	0.999471	+	0.0325264i	$0.0103553\pi$
$110$		0			0
$111$	−127.098			−1.14502
$112$		0			0
$113$		−	134.274i		−	1.18826i	−0.804368	−	0.594131i	$-0.797496\pi$
$113$		−	134.274i		−	1.18826i	0.804368	−	0.594131i	$-0.202504\pi$
$114$		0			0
$115$	−90.3436	−	37.4215i	−0.785596	−	0.325405i
$116$		0			0
$117$	20.5097	−	8.49541i	0.175297	−	0.0726103i
$118$		0			0
$119$	−13.4880	+	13.4880i	−0.113345	+	0.113345i
$120$		0			0
$121$	−94.1580	+	94.1580i	−0.778166	+	0.778166i
$122$		0			0
$123$	−67.5224	+	27.9687i	−0.548963	+	0.227388i
$124$		0			0
$125$	147.104	+	60.9325i	1.17683	+	0.487460i
$126$		0			0
$127$			95.5030i			0.751992i	0.926621	+	0.375996i	$0.122699\pi$
$127$			95.5030i			0.751992i	−0.926621	+	0.375996i	$0.877301\pi$
$128$		0			0
$129$	−0.655407			−0.00508068
$130$		0			0
$131$	67.1188	−	162.039i	0.512357	−	1.23694i	−0.430151	−	0.902757i	$-0.641540\pi$
$131$	67.1188	−	162.039i	0.512357	−	1.23694i	0.942508	−	0.334183i	$-0.108460\pi$
$132$		0			0
$133$	−3.56697	−	8.61142i	−0.0268193	−	0.0647475i
$134$		0			0
$135$	172.835	+	172.835i	1.28026	+	1.28026i
$136$		0			0
$137$	88.7244	+	88.7244i	0.647624	+	0.647624i	0.952418	−	0.304794i	$-0.0985878\pi$
$137$	88.7244	+	88.7244i	0.647624	+	0.647624i	−0.304794	+	0.952418i	$0.598588\pi$
$138$		0			0
$139$	27.6838	+	66.8346i	0.199164	+	0.480824i	0.991633	−	0.129087i	$-0.0412048\pi$
$139$	27.6838	+	66.8346i	0.199164	+	0.480824i	−0.792469	+	0.609912i	$0.791205\pi$
$140$		0			0
$141$	−36.8813	+	89.0394i	−0.261570	+	0.631485i
$142$		0			0
$143$	−117.511			−0.821756
$144$		0			0
$145$			349.758i			2.41213i
$146$		0			0
$147$	49.7558	+	20.6095i	0.338475	+	0.140201i
$148$		0			0
$149$	−100.536	+	41.6433i	−0.674737	+	0.279485i	−0.693625	−	0.720336i	$-0.743987\pi$
$149$	−100.536	+	41.6433i	−0.674737	+	0.279485i	0.0188878	+	0.999822i	$0.493987\pi$
$150$		0			0
$151$	134.706	−	134.706i	0.892096	−	0.892096i	−0.102624	−	0.994720i	$-0.532724\pi$
$151$	134.706	−	134.706i	0.892096	−	0.892096i	0.994720	+	0.102624i	$0.0327239\pi$
$152$		0			0
$153$	7.81897	−	7.81897i	0.0511044	−	0.0511044i
$154$		0			0
$155$	−31.5977	+	13.0882i	−0.203856	+	0.0844401i
$156$		0			0
$157$	−56.0501	−	23.2167i	−0.357007	−	0.147877i	0.196969	−	0.980410i	$-0.436890\pi$
$157$	−56.0501	−	23.2167i	−0.357007	−	0.147877i	−0.553976	+	0.832533i	$0.686890\pi$
$158$		0			0
$159$			59.9015i			0.376739i
$160$		0			0
$161$	−61.0957			−0.379476
$162$		0			0
$163$	−85.7621	+	207.048i	−0.526148	+	1.27023i	0.407881	+	0.913035i	$0.366268\pi$
$163$	−85.7621	+	207.048i	−0.526148	+	1.27023i	−0.934029	+	0.357198i	$0.883732\pi$
$164$		0			0
$165$	−124.146	−	299.715i	−0.752399	−	1.81645i
$166$		0			0
$167$	−72.6395	−	72.6395i	−0.434967	−	0.434967i	0.455347	−	0.890314i	$-0.349515\pi$
$167$	−72.6395	−	72.6395i	−0.434967	−	0.434967i	−0.890314	+	0.455347i	$0.849515\pi$
$168$		0			0
$169$	81.0829	+	81.0829i	0.479781	+	0.479781i
$170$		0			0
$171$	2.06776	+	4.99201i	0.0120922	+	0.0291930i
$172$		0			0
$173$	−4.05480	+	9.78916i	−0.0234382	+	0.0565847i	−0.935165	−	0.354212i	$-0.884749\pi$
$173$	−4.05480	+	9.78916i	−0.0234382	+	0.0565847i	0.911727	+	0.410796i	$0.134749\pi$
$174$		0			0
$175$	229.365			1.31066
$176$		0			0
$177$			268.527i			1.51710i
$178$		0			0
$179$	−214.146	−	88.7024i	−1.19635	−	0.495544i	−0.306531	−	0.951861i	$-0.599168\pi$
$179$	−214.146	−	88.7024i	−1.19635	−	0.495544i	−0.889817	+	0.456317i	$0.849168\pi$
$180$		0			0
$181$	−98.2125	+	40.6810i	−0.542611	+	0.224757i	−0.637116	−	0.770768i	$-0.719873\pi$
$181$	−98.2125	+	40.6810i	−0.542611	+	0.224757i	0.0945057	+	0.995524i	$0.469873\pi$
$182$		0			0
$183$	26.3099	−	26.3099i	0.143770	−	0.143770i
$184$		0			0
$185$	305.395	−	305.395i	1.65078	−	1.65078i
$186$		0			0
$187$	−54.0772	+	22.3995i	−0.289183	+	0.119783i
$188$		0			0
$189$	141.088	+	58.4405i	0.746497	+	0.309209i
$190$		0			0
$191$		−	181.842i		−	0.952052i	−0.879431	−	0.476026i	$-0.842077\pi$
$191$		−	181.842i		−	0.952052i	0.879431	−	0.476026i	$-0.157923\pi$
$192$		0			0
$193$	−221.267			−1.14646			−0.573230	−	0.819394i	$-0.694310\pi$
$193$	−221.267			−1.14646			−0.573230	+	0.819394i	$0.694310\pi$
$194$		0			0
$195$	57.3990	−	138.574i	0.294354	−	0.710633i
$196$		0			0
$197$	−15.4361	−	37.2660i	−0.0783556	−	0.189167i	0.879847	−	0.475256i	$-0.157645\pi$
$197$	−15.4361	−	37.2660i	−0.0783556	−	0.189167i	−0.958203	+	0.286089i	$0.907645\pi$
$198$		0			0
$199$	135.618	+	135.618i	0.681498	+	0.681498i	0.960338	−	0.278840i	$-0.0899498\pi$
$199$	135.618	+	135.618i	0.681498	+	0.681498i	−0.278840	+	0.960338i	$0.589950\pi$
$200$		0			0
$201$	−16.6146	−	16.6146i	−0.0826599	−	0.0826599i
$202$		0			0
$203$	83.6250	+	201.889i	0.411946	+	0.994526i
$204$		0			0
$205$	95.0411	−	229.450i	0.463615	−	1.11927i
$206$		0			0
$207$	35.4170			0.171096
$208$		0			0
$209$		−	28.6019i		−	0.136851i
$210$		0			0
$211$	−138.015	−	57.1678i	−0.654100	−	0.270937i	0.0308532	−	0.999524i	$-0.490178\pi$
$211$	−138.015	−	57.1678i	−0.654100	−	0.270937i	−0.684954	+	0.728587i	$0.740178\pi$
$212$		0			0
$213$	242.262	−	100.348i	1.13738	−	0.471118i
$214$		0			0
$215$	1.57484	−	1.57484i	0.00732483	−	0.00732483i
$216$		0			0
$217$	−15.1097	+	15.1097i	−0.0696298	+	0.0696298i
$218$		0			0
$219$	92.8420	−	38.4564i	0.423936	−	0.175600i
$220$		0			0
$221$	−25.0027	−	10.3564i	−0.113134	−	0.0468618i
$222$		0			0
$223$			30.6228i			0.137322i	0.997640	+	0.0686609i	$0.0218727\pi$
$223$			30.6228i			0.137322i	−0.997640	+	0.0686609i	$0.978127\pi$
$224$		0			0
$225$	−132.962			−0.590944
$226$		0			0
$227$	−8.41171	+	20.3077i	−0.0370560	+	0.0894611i	−0.941324	−	0.337504i	$-0.890417\pi$
$227$	−8.41171	+	20.3077i	−0.0370560	+	0.0894611i	0.904268	+	0.426965i	$0.140417\pi$
$228$		0			0
$229$	76.6532	+	185.057i	0.334730	+	0.808110i	0.998204	+	0.0599101i	$0.0190814\pi$
$229$	76.6532	+	185.057i	0.334730	+	0.808110i	−0.663474	+	0.748199i	$0.730919\pi$
$230$		0			0
$231$	−143.320	−	143.320i	−0.620432	−	0.620432i
$232$		0			0
$233$	−127.558	−	127.558i	−0.547461	−	0.547461i	0.378245	−	0.925706i	$-0.376528\pi$
$233$	−127.558	−	127.558i	−0.547461	−	0.547461i	−0.925706	+	0.378245i	$0.876528\pi$
$234$		0			0
$235$	−125.327	−	302.567i	−0.533308	−	1.28752i
$236$		0			0
$237$	2.58984	−	6.25243i	0.0109276	−	0.0263816i
$238$		0			0
$239$	−397.241			−1.66210			−0.831048	−	0.556200i	$-0.812259\pi$
$239$	−397.241			−1.66210			−0.831048	+	0.556200i	$0.812259\pi$
$240$		0			0
$241$		−	401.128i		−	1.66443i	−0.554451	−	0.832216i	$-0.687072\pi$
$241$		−	401.128i		−	1.66443i	0.554451	−	0.832216i	$-0.312928\pi$
$242$		0			0
$243$	−143.069	−	59.2612i	−0.588763	−	0.243873i
$244$		0			0
$245$	−169.077	+	70.0338i	−0.690109	+	0.285852i
$246$		0			0
$247$	9.35087	−	9.35087i	0.0378578	−	0.0378578i
$248$		0			0
$249$	−148.330	+	148.330i	−0.595703	+	0.595703i
$250$		0			0
$251$	−220.193	+	91.2070i	−0.877264	+	0.363375i	−0.775435	−	0.631427i	$-0.782469\pi$
$251$	−220.193	+	91.2070i	−0.877264	+	0.363375i	−0.101829	+	0.994802i	$0.532469\pi$
$252$		0			0
$253$	−173.205	−	71.7440i	−0.684606	−	0.283573i
$254$		0			0
$255$		−	74.7111i		−	0.292985i
$256$		0			0
$257$	436.624			1.69893			0.849463	−	0.527648i	$-0.176926\pi$
$257$	436.624			1.69893			0.849463	+	0.527648i	$0.176926\pi$
$258$		0			0
$259$	103.263	−	249.299i	0.398699	−	0.962545i
$260$		0			0
$261$	−48.4771	−	117.034i	−0.185736	−	0.448407i
$262$		0			0
$263$	324.662	+	324.662i	1.23445	+	1.23445i	0.962235	+	0.272219i	$0.0877576\pi$
$263$	324.662	+	324.662i	1.23445	+	1.23445i	0.272219	+	0.962235i	$0.412242\pi$
$264$		0			0
$265$	−143.934	−	143.934i	−0.543146	−	0.543146i
$266$		0			0
$267$	95.9098	+	231.547i	0.359213	+	0.867217i
$268$		0			0
$269$	−98.7998	+	238.524i	−0.367286	+	0.886706i	0.626907	+	0.779094i	$0.284320\pi$
$269$	−98.7998	+	238.524i	−0.367286	+	0.886706i	−0.994193	+	0.107612i	$0.965680\pi$
$270$		0			0
$271$	91.7678			0.338627			0.169313	−	0.985562i	$-0.445845\pi$
$271$	91.7678			0.338627			0.169313	+	0.985562i	$0.445845\pi$
$272$		0			0
$273$		−	93.7117i		−	0.343266i
$274$		0			0
$275$	650.247	+	269.341i	2.36453	+	0.979422i
$276$		0			0
$277$	42.7749	−	17.7179i	0.154422	−	0.0639636i	−0.304134	−	0.952629i	$-0.598367\pi$
$277$	42.7749	−	17.7179i	0.154422	−	0.0639636i	0.458556	+	0.888666i	$0.348367\pi$
$278$		0			0
$279$	8.75902	−	8.75902i	0.0313943	−	0.0313943i
$280$		0			0
$281$	−167.424	+	167.424i	−0.595813	+	0.595813i	−0.939196	−	0.343382i	$-0.888427\pi$
$281$	−167.424	+	167.424i	−0.595813	+	0.595813i	0.343382	+	0.939196i	$0.388427\pi$
$282$		0			0
$283$	494.380	−	204.779i	1.74693	−	0.723601i	0.748775	−	0.662824i	$-0.230642\pi$
$283$	494.380	−	204.779i	1.74693	−	0.723601i	0.998151	−	0.0607762i	$-0.0193576\pi$
$284$		0			0
$285$	33.7284	+	13.9708i	0.118345	+	0.0490202i
$286$		0			0
$287$		−	155.168i		−	0.540653i
$288$		0			0
$289$	275.520			0.953356
$290$		0			0
$291$	−61.8543	+	149.329i	−0.212558	+	0.513160i
$292$		0			0
$293$	146.767	+	354.328i	0.500913	+	1.20931i	0.948987	+	0.315314i	$0.102110\pi$
$293$	146.767	+	354.328i	0.500913	+	1.20931i	−0.448075	+	0.893996i	$0.647890\pi$
$294$		0			0
$295$	−645.227	−	645.227i	−2.18721	−	2.18721i
$296$		0			0
$297$	331.356	+	331.356i	1.11568	+	1.11568i
$298$		0			0
$299$	−33.1709	−	80.0817i	−0.110940	−	0.267832i
$300$		0			0
$301$	0.532500	−	1.28557i	0.00176910	−	0.00427099i
$302$		0			0
$303$	48.0346			0.158530
$304$		0			0
$305$			126.437i			0.414547i
$306$		0			0
$307$	53.4306	+	22.1317i	0.174041	+	0.0720902i	0.468003	−	0.883727i	$-0.344974\pi$
$307$	53.4306	+	22.1317i	0.174041	+	0.0720902i	−0.293962	+	0.955817i	$0.594974\pi$
$308$		0			0
$309$	1.88377	−	0.780284i	0.00609635	−	0.00252519i
$310$		0			0
$311$	−274.515	+	274.515i	−0.882685	+	0.882685i	−0.993807	−	0.111122i	$-0.964556\pi$
$311$	−274.515	+	274.515i	−0.882685	+	0.882685i	0.111122	+	0.993807i	$0.464556\pi$
$312$		0			0
$313$	−78.4013	+	78.4013i	−0.250483	+	0.250483i	−0.821169	−	0.570685i	$-0.806678\pi$
$313$	−78.4013	+	78.4013i	−0.250483	+	0.250483i	0.570685	+	0.821169i	$0.306678\pi$
$314$		0			0
$315$	−120.210	+	49.7928i	−0.381620	+	0.158072i
$316$		0			0
$317$	−136.520	−	56.5483i	−0.430661	−	0.178386i	0.156814	−	0.987628i	$-0.449878\pi$
$317$	−136.520	−	56.5483i	−0.430661	−	0.178386i	−0.587475	+	0.809243i	$0.699878\pi$
$318$		0			0
$319$			670.551i			2.10204i
$320$		0			0
$321$	−354.621			−1.10474
$322$		0			0
$323$	2.52073	−	6.08558i	0.00780412	−	0.0188408i
$324$		0			0
$325$	124.530	+	300.643i	0.383170	+	0.925054i
$326$		0			0
$327$	132.943	+	132.943i	0.406553	+	0.406553i
$328$		0			0
$329$	−144.684	−	144.684i	−0.439769	−	0.439769i
$330$		0			0
$331$	−143.690	−	346.898i	−0.434109	−	1.04803i	−0.977949	−	0.208843i	$-0.933030\pi$
$331$	−143.690	−	346.898i	−0.434109	−	1.04803i	0.543841	−	0.839189i	$-0.316970\pi$
$332$		0			0
$333$	−59.8612	+	144.518i	−0.179763	+	0.433987i
$334$		0			0
$335$	79.8446			0.238342
$336$		0			0
$337$		−	479.136i		−	1.42177i	−0.703310	−	0.710884i	$-0.748295\pi$
$337$		−	479.136i		−	1.42177i	0.703310	−	0.710884i	$-0.251705\pi$
$338$		0			0
$339$	303.568	+	125.742i	0.895481	+	0.370920i
$340$		0			0
$341$	−60.5787	+	25.0925i	−0.177650	+	0.0735851i
$342$		0			0
$343$	−260.861	+	260.861i	−0.760529	+	0.760529i
$344$		0			0
$345$	169.206	−	169.206i	0.490453	−	0.490453i
$346$		0			0
$347$	−172.145	+	71.3048i	−0.496095	+	0.205489i	−0.616680	−	0.787214i	$-0.711523\pi$
$347$	−172.145	+	71.3048i	−0.496095	+	0.205489i	0.120585	+	0.992703i	$0.461523\pi$
$348$		0			0
$349$	388.120	+	160.765i	1.11209	+	0.460644i	0.861658	−	0.507490i	$-0.169427\pi$
$349$	388.120	+	160.765i	1.11209	+	0.460644i	0.250434	+	0.968134i	$0.419427\pi$
$350$		0			0
$351$			216.662i			0.617269i
$352$		0			0
$353$	−165.952			−0.470120			−0.235060	−	0.971981i	$-0.575529\pi$
$353$	−165.952			−0.470120			−0.235060	+	0.971981i	$0.575529\pi$
$354$		0			0
$355$	−340.995	+	823.235i	−0.960550	+	2.31897i
$356$		0			0
$357$	−17.8630	−	43.1250i	−0.0500363	−	0.120798i
$358$		0			0
$359$	−100.971	−	100.971i	−0.281257	−	0.281257i	0.552353	−	0.833610i	$-0.313730\pi$
$359$	−100.971	−	100.971i	−0.281257	−	0.281257i	−0.833610	+	0.552353i	$0.813730\pi$
$360$		0			0
$361$	−252.990	−	252.990i	−0.700802	−	0.700802i
$362$		0			0
$363$	−124.699	−	301.049i	−0.343523	−	0.829337i
$364$		0			0
$365$	−130.680	+	315.489i	−0.358027	+	0.864353i
$366$		0			0
$367$	651.959			1.77645			0.888227	−	0.459405i	$-0.151937\pi$
$367$	651.959			1.77645			0.888227	+	0.459405i	$0.151937\pi$
$368$		0			0
$369$			89.9501i			0.243767i
$370$		0			0
$371$	−117.496	−	48.6683i	−0.316700	−	0.131181i
$372$		0			0
$373$	605.919	−	250.980i	1.62445	−	0.672868i	0.629854	−	0.776713i	$-0.283115\pi$
$373$	605.919	−	250.980i	1.62445	−	0.672868i	0.994593	+	0.103845i	$0.0331146\pi$
$374$		0			0
$375$	−275.515	+	275.515i	−0.734705	+	0.734705i
$376$		0			0
$377$	−219.224	+	219.224i	−0.581497	+	0.581497i
$378$		0			0
$379$	431.591	−	178.771i	1.13876	−	0.471691i	0.268011	−	0.963416i	$-0.413634\pi$
$379$	431.591	−	178.771i	1.13876	−	0.471691i	0.870750	+	0.491725i	$0.163634\pi$
$380$		0			0
$381$	−215.915	−	89.4348i	−0.566705	−	0.234737i
$382$		0			0
$383$		−	583.987i		−	1.52477i	−0.647124	−	0.762385i	$-0.724028\pi$
$383$		−	583.987i		−	1.52477i	0.647124	−	0.762385i	$-0.275972\pi$
$384$		0			0
$385$	688.749			1.78896
$386$		0			0
$387$	−0.308688	+	0.745239i	−0.000797644	+	0.00192568i
$388$		0			0
$389$	−57.9070	−	139.800i	−0.148861	−	0.359383i	0.831806	−	0.555067i	$-0.187307\pi$
$389$	−57.9070	−	139.800i	−0.148861	−	0.359383i	−0.980667	+	0.195684i	$0.937307\pi$
$390$		0			0
$391$	−30.5297	−	30.5297i	−0.0780812	−	0.0780812i
$392$		0			0
$393$	303.487	+	303.487i	0.772231	+	0.772231i
$394$		0			0
$395$	8.80061	+	21.2466i	0.0222800	+	0.0537888i
$396$		0			0
$397$	216.482	−	522.634i	0.545295	−	1.31646i	−0.375649	−	0.926762i	$-0.622580\pi$
$397$	216.482	−	522.634i	0.545295	−	1.31646i	0.920944	−	0.389696i	$-0.127420\pi$
$398$		0			0
$399$	22.8092			0.0571658
$400$		0			0
$401$		−	271.900i		−	0.678055i	−0.940776	−	0.339028i	$-0.889902\pi$
$401$		−	271.900i		−	0.678055i	0.940776	−	0.339028i	$-0.110098\pi$
$402$		0			0
$403$	−28.0087	−	11.6016i	−0.0695004	−	0.0287880i
$404$		0			0
$405$	−344.359	+	142.638i	−0.850269	+	0.352193i
$406$		0			0
$407$	585.498	−	585.498i	1.43857	−	1.43857i
$408$		0			0
$409$	−181.723	+	181.723i	−0.444310	+	0.444310i	−0.893458	−	0.449147i	$-0.851728\pi$
$409$	−181.723	+	181.723i	−0.444310	+	0.444310i	0.449147	+	0.893458i	$0.351728\pi$
$410$		0			0
$411$	−283.677	+	117.503i	−0.690211	+	0.285895i
$412$		0			0
$413$	−526.710	−	218.171i	−1.27533	−	0.528258i
$414$		0			0
$415$		−	712.826i		−	1.71765i
$416$		0			0
$417$	−177.026			−0.424522
$418$		0			0
$419$	84.5458	−	204.112i	0.201780	−	0.487140i	−0.790304	−	0.612715i	$-0.790077\pi$
$419$	84.5458	−	204.112i	0.201780	−	0.487140i	0.992084	+	0.125575i	$0.0400775\pi$
$420$		0			0
$421$	13.1417	+	31.7269i	0.0312155	+	0.0753608i	0.938719	−	0.344685i	$-0.112014\pi$
$421$	13.1417	+	31.7269i	0.0312155	+	0.0753608i	−0.907503	+	0.420045i	$0.862014\pi$
$422$		0			0
$423$	83.8728	+	83.8728i	0.198281	+	0.198281i
$424$		0			0
$425$	114.615	+	114.615i	0.269682	+	0.269682i
$426$		0			0
$427$	30.2302	+	72.9823i	0.0707968	+	0.170919i
$428$		0			0
$429$	110.045	−	265.671i	0.256514	−	0.619280i
$430$		0			0
$431$	−18.4839			−0.0428861			−0.0214431	−	0.999770i	$-0.506826\pi$
$431$	−18.4839			−0.0428861			−0.0214431	+	0.999770i	$0.506826\pi$
$432$		0			0
$433$			370.297i			0.855190i	0.903970	+	0.427595i	$0.140639\pi$
$433$			370.297i			0.855190i	−0.903970	+	0.427595i	$0.859361\pi$
$434$		0			0
$435$	−790.739	−	327.535i	−1.81779	−	0.752954i
$436$		0			0
$437$	19.4917	−	8.07372i	0.0446034	−	0.0184753i
$438$		0			0
$439$	1.47108	−	1.47108i	0.00335099	−	0.00335099i	−0.705429	−	0.708780i	$-0.749246\pi$
$439$	1.47108	−	1.47108i	0.00335099	−	0.00335099i	0.708780	+	0.705429i	$0.249246\pi$
$440$		0			0
$441$	46.8687	−	46.8687i	0.106278	−	0.106278i
$442$		0			0
$443$	−15.4970	+	6.41908i	−0.0349820	+	0.0144900i	−0.400106	−	0.916469i	$-0.631027\pi$
$443$	−15.4970	+	6.41908i	−0.0349820	+	0.0144900i	0.365124	+	0.930959i	$0.381027\pi$
$444$		0			0
$445$	−786.825	−	325.914i	−1.76815	−	0.732390i
$446$		0			0
$447$		−	266.290i		−	0.595728i
$448$		0			0
$449$	−349.645			−0.778719			−0.389359	−	0.921086i	$-0.627304\pi$
$449$	−349.645			−0.778719			−0.389359	+	0.921086i	$0.627304\pi$
$450$		0			0
$451$	182.211	−	439.897i	0.404016	−	0.975382i
$452$		0			0
$453$	178.399	+	430.694i	0.393817	+	0.950759i
$454$		0			0
$455$	225.174	+	225.174i	0.494888	+	0.494888i
$456$		0			0
$457$	167.442	+	167.442i	0.366393	+	0.366393i	0.866160	−	0.499767i	$-0.166581\pi$
$457$	167.442	+	167.442i	0.366393	+	0.366393i	−0.499767	+	0.866160i	$0.666581\pi$
$458$		0			0
$459$	41.2992	+	99.7051i	0.0899764	+	0.217222i
$460$		0			0
$461$	299.864	−	723.935i	0.650463	−	1.57036i	−0.161644	−	0.986849i	$-0.551680\pi$
$461$	299.864	−	723.935i	0.650463	−	1.57036i	0.812107	−	0.583508i	$-0.198320\pi$
$462$		0			0
$463$	70.4485			0.152157			0.0760783	−	0.997102i	$-0.475760\pi$
$463$	70.4485			0.152157			0.0760783	+	0.997102i	$0.475760\pi$
$464$		0			0
$465$		−	83.6933i		−	0.179986i
$466$		0			0
$467$	89.8391	+	37.2126i	0.192375	+	0.0796843i	0.476791	−	0.879017i	$-0.341800\pi$
$467$	89.8391	+	37.2126i	0.192375	+	0.0796843i	−0.284416	+	0.958701i	$0.591800\pi$
$468$		0			0
$469$	46.0882	−	19.0904i	0.0982691	−	0.0407044i
$470$		0			0
$471$	104.977	−	104.977i	0.222882	−	0.222882i
$472$		0			0
$473$	3.01925	−	3.01925i	0.00638320	−	0.00638320i
$474$		0			0
$475$	−73.1756	+	30.3103i	−0.154054	+	0.0638112i
$476$		0			0
$477$	68.1118	+	28.2128i	0.142792	+	0.0591464i
$478$		0			0
$479$			900.546i			1.88005i	0.341101	+	0.940027i	$0.389200\pi$
$479$			900.546i			1.88005i	−0.341101	+	0.940027i	$0.610800\pi$
$480$		0			0
$481$	382.836			0.795917
$482$		0			0
$483$	57.2137	−	138.126i	0.118455	−	0.285976i
$484$		0			0
$485$	−210.189	−	507.440i	−0.433379	−	1.04627i
$486$		0			0
$487$	175.466	+	175.466i	0.360301	+	0.360301i	0.863924	−	0.503623i	$-0.168000\pi$
$487$	175.466	+	175.466i	0.360301	+	0.360301i	−0.503623	+	0.863924i	$0.668000\pi$
$488$		0			0
$489$	−387.785	−	387.785i	−0.793015	−	0.793015i
$490$		0			0
$491$	111.990	+	270.368i	0.228086	+	0.550648i	0.995944	−	0.0899713i	$-0.0286775\pi$
$491$	111.990	+	270.368i	0.228086	+	0.550648i	−0.767858	+	0.640620i	$0.778678\pi$
$492$		0			0
$493$	−59.0968	+	142.672i	−0.119872	+	0.289396i
$494$		0			0
$495$	−399.265			−0.806596
$496$		0			0
$497$			556.721i			1.12016i
$498$		0			0
$499$	−96.4128	−	39.9355i	−0.193212	−	0.0800310i	0.283980	−	0.958830i	$-0.408345\pi$
$499$	−96.4128	−	39.9355i	−0.193212	−	0.0800310i	−0.477192	+	0.878799i	$0.658345\pi$
$500$		0			0
$501$	232.249	−	96.2005i	0.463570	−	0.192017i
$502$		0			0
$503$	−491.151	+	491.151i	−0.976442	+	0.976442i	−0.999729	−	0.0232864i	$-0.992587\pi$
$503$	−491.151	+	491.151i	−0.976442	+	0.976442i	0.0232864	+	0.999729i	$0.492587\pi$
$504$		0			0
$505$	−115.419	+	115.419i	−0.228553	+	0.228553i
$506$		0			0
$507$	−259.245	+	107.383i	−0.511331	+	0.211800i
$508$		0			0
$509$	891.336	+	369.204i	1.75115	+	0.725351i	0.997695	+	0.0678534i	$0.0216150\pi$
$509$	891.336	+	369.204i	1.75115	+	0.725351i	0.753457	+	0.657498i	$0.228385\pi$
$510$		0			0
$511$			213.352i			0.417519i
$512$		0			0
$513$	−52.7348			−0.102797
$514$		0			0
$515$	−2.65150	+	6.40130i	−0.00514855	+	0.0124297i
$516$		0			0
$517$	−240.276	−	580.077i	−0.464750	−	1.12201i
$518$		0			0
$519$	−18.3343	−	18.3343i	−0.0353263	−	0.0353263i
$520$		0			0
$521$	285.723	+	285.723i	0.548413	+	0.548413i	0.925982	−	0.377569i	$-0.123240\pi$
$521$	285.723	+	285.723i	0.548413	+	0.548413i	−0.377569	+	0.925982i	$0.623240\pi$
$522$		0			0
$523$	−260.696	−	629.375i	−0.498462	−	1.20339i	−0.950312	−	0.311300i	$-0.899236\pi$
$523$	−260.696	−	629.375i	−0.498462	−	1.20339i	0.451849	−	0.892094i	$-0.350764\pi$
$524$		0			0
$525$	−214.792	+	518.553i	−0.409127	+	0.987720i
$526$		0			0
$527$	−15.1007			−0.0286541
$528$		0			0
$529$			390.712i			0.738586i
$530$		0			0
$531$	305.332	+	126.473i	0.575013	+	0.238178i
$532$		0			0
$533$	203.387	−	84.2457i	0.381589	−	0.158059i
$534$		0			0
$535$	852.096	−	852.096i	1.59270	−	1.59270i
$536$		0			0
$537$	401.079	−	401.079i	0.746889	−	0.746889i
$538$		0			0
$539$	−324.151	+	134.268i	−0.601393	+	0.249105i
$540$		0			0
$541$	355.077	+	147.078i	0.656335	+	0.271863i	0.685895	−	0.727700i	$-0.259411\pi$
$541$	355.077	+	147.078i	0.656335	+	0.271863i	−0.0295603	+	0.999563i	$0.509411\pi$
$542$		0			0
$543$		−	260.137i		−	0.479073i
$544$		0			0
$545$	−638.880			−1.17226
$546$		0			0
$547$	−404.897	+	977.508i	−0.740214	+	1.78704i	−0.135204	+	0.990818i	$0.543169\pi$
$547$	−404.897	+	977.508i	−0.740214	+	1.78704i	−0.605010	+	0.796218i	$0.706831\pi$
$548$		0			0
$549$	−17.5244	−	42.3076i	−0.0319205	−	0.0770630i
$550$		0			0
$551$	−53.3586	−	53.3586i	−0.0968396	−	0.0968396i
$552$		0			0
$553$	10.1598	+	10.1598i	0.0183722	+	0.0183722i
$554$		0			0
$555$	404.451	+	976.431i	0.728741	+	1.75934i
$556$		0			0
$557$	−296.952	+	716.907i	−0.533128	+	1.28709i	0.396313	+	0.918115i	$0.370289\pi$
$557$	−296.952	+	716.907i	−0.533128	+	1.28709i	−0.929441	+	0.368970i	$0.879711\pi$
$558$		0			0
$559$	1.97418			0.00353163
$560$		0			0
$561$		−	143.235i		−	0.255321i
$562$		0			0
$563$	44.6869	+	18.5099i	0.0793728	+	0.0328773i	0.422017	−	0.906588i	$-0.361322\pi$
$563$	44.6869	+	18.5099i	0.0793728	+	0.0328773i	−0.342644	+	0.939465i	$0.611322\pi$
$564$		0			0
$565$	−1031.56	+	427.287i	−1.82577	+	0.756260i
$566$		0			0
$567$	−164.668	+	164.668i	−0.290420	+	0.290420i
$568$		0			0
$569$	487.094	−	487.094i	0.856053	−	0.856053i	−0.134818	−	0.990870i	$-0.543045\pi$
$569$	487.094	−	487.094i	0.856053	−	0.856053i	0.990870	+	0.134818i	$0.0430449\pi$
$570$		0			0
$571$	252.561	−	104.614i	0.442313	−	0.183212i	−0.150401	−	0.988625i	$-0.548056\pi$
$571$	252.561	−	104.614i	0.442313	−	0.183212i	0.592714	+	0.805413i	$0.298056\pi$
$572$		0			0
$573$	411.111	+	170.288i	0.717472	+	0.297187i
$574$		0			0
$575$			519.161i			0.902889i
$576$		0			0
$577$	460.004			0.797234			0.398617	−	0.917118i	$-0.369490\pi$
$577$	460.004			0.797234			0.398617	+	0.917118i	$0.369490\pi$
$578$		0			0
$579$	207.208	−	500.244i	0.357872	−	0.863979i
$580$		0			0
$581$	−170.432	−	411.460i	−0.293343	−	0.708193i
$582$		0			0
$583$	−275.947	−	275.947i	−0.473323	−	0.473323i
$584$		0			0
$585$	−130.533	−	130.533i	−0.223133	−	0.223133i
$586$		0			0
$587$	−68.3015	−	164.895i	−0.116357	−	0.280911i	0.854962	−	0.518690i	$-0.173580\pi$
$587$	−68.3015	−	164.895i	−0.116357	−	0.280911i	−0.971319	+	0.237780i	$0.923580\pi$
$588$		0			0
$589$	2.82379	−	6.81723i	0.00479421	−	0.0115742i
$590$		0			0
$591$	98.7067			0.167016
$592$		0			0
$593$			167.545i			0.282538i	0.989971	+	0.141269i	$0.0451182\pi$
$593$			167.545i			0.282538i	−0.989971	+	0.141269i	$0.954882\pi$
$594$		0			0
$595$	146.544	+	60.7006i	0.246293	+	0.102018i
$596$		0			0
$597$	−433.609	+	179.607i	−0.726313	+	0.300848i
$598$		0			0
$599$	316.998	−	316.998i	0.529213	−	0.529213i	−0.391125	−	0.920338i	$-0.627914\pi$
$599$	316.998	−	316.998i	0.529213	−	0.529213i	0.920338	+	0.391125i	$0.127914\pi$
$600$		0			0
$601$	−224.198	+	224.198i	−0.373042	+	0.373042i	−0.868584	−	0.495542i	$-0.834970\pi$
$601$	−224.198	+	224.198i	−0.373042	+	0.373042i	0.495542	+	0.868584i	$0.334970\pi$
$602$		0			0
$603$	−26.7172	+	11.0666i	−0.0443071	+	0.0183526i
$604$		0			0
$605$	1023.00	+	423.742i	1.69091	+	0.700400i
$606$		0			0
$607$			89.2468i			0.147029i	0.997294	+	0.0735146i	$0.0234216\pi$
$607$			89.2468i			0.147029i	−0.997294	+	0.0735146i	$0.976578\pi$
$608$		0			0
$609$	−534.745			−0.878070
$610$		0			0
$611$	111.092	−	268.200i	0.181820	−	0.438952i
$612$		0			0
$613$	202.134	+	487.995i	0.329746	+	0.796076i	0.998611	+	0.0526926i	$0.0167803\pi$
$613$	202.134	+	487.995i	0.329746	+	0.796076i	−0.668865	+	0.743384i	$0.733220\pi$
$614$		0			0
$615$	429.741	+	429.741i	0.698766	+	0.698766i
$616$		0			0
$617$	380.984	+	380.984i	0.617479	+	0.617479i	0.944884	−	0.327405i	$-0.106174\pi$
$617$	380.984	+	380.984i	0.617479	+	0.617479i	−0.327405	+	0.944884i	$0.606174\pi$
$618$		0			0
$619$	371.320	+	896.447i	0.599871	+	1.44822i	0.873712	+	0.486443i	$0.161706\pi$
$619$	371.320	+	896.447i	0.599871	+	1.44822i	−0.273841	+	0.961775i	$0.588294\pi$
$620$		0			0
$621$	−132.278	+	319.348i	−0.213008	+	0.514248i
$622$		0			0
$623$	−532.098			−0.854090
$624$		0			0
$625$		−	220.337i		−	0.352539i
$626$		0			0
$627$	64.6636	+	26.7845i	0.103132	+	0.0427186i
$628$		0			0
$629$	176.177	−	72.9747i	0.280090	−	0.116017i
$630$		0			0
$631$	−384.726	+	384.726i	−0.609708	+	0.609708i	−0.942870	−	0.333162i	$-0.891885\pi$
$631$	−384.726	+	384.726i	−0.609708	+	0.609708i	0.333162	+	0.942870i	$0.391885\pi$
$632$		0			0
$633$	258.492	−	258.492i	0.408360	−	0.408360i
$634$		0			0
$635$	733.706	−	303.911i	1.15544	−	0.478600i
$636$		0			0
$637$	−149.872	−	62.0789i	−0.235277	−	0.0974551i
$638$		0			0
$639$		−	322.729i		−	0.505053i
$640$		0			0
$641$	−407.931			−0.636398			−0.318199	−	0.948024i	$-0.603078\pi$
$641$	−407.931			−0.636398			−0.318199	+	0.948024i	$0.603078\pi$
$642$		0			0
$643$	319.302	−	770.863i	0.496582	−	1.19885i	−0.454732	−	0.890629i	$-0.650265\pi$
$643$	319.302	−	770.863i	0.496582	−	1.19885i	0.951313	−	0.308226i	$-0.0997352\pi$
$644$		0			0
$645$	2.08564	+	5.03519i	0.00323356	+	0.00780650i
$646$		0			0
$647$	48.6565	+	48.6565i	0.0752033	+	0.0752033i	0.743708	−	0.668505i	$-0.233065\pi$
$647$	48.6565	+	48.6565i	0.0752033	+	0.0752033i	−0.668505	+	0.743708i	$0.733065\pi$
$648$		0			0
$649$	−1237.02	−	1237.02i	−1.90604	−	1.90604i
$650$		0			0
$651$	−20.0106	−	48.3098i	−0.0307382	−	0.0742085i
$652$		0			0
$653$	−290.106	+	700.378i	−0.444267	+	1.07255i	0.530170	+	0.847892i	$0.322128\pi$
$653$	−290.106	+	700.378i	−0.444267	+	1.07255i	−0.974436	+	0.224663i	$0.927872\pi$
$654$		0			0
$655$	−1458.46			−2.22665
$656$		0			0
$657$		−	123.680i		−	0.188249i
$658$		0			0
$659$	−818.045	−	338.845i	−1.24134	−	0.514181i	−0.337209	−	0.941430i	$-0.609483\pi$
$659$	−818.045	−	338.845i	−1.24134	−	0.514181i	−0.904134	+	0.427248i	$0.859483\pi$
$660$		0			0
$661$	−35.2123	+	14.5854i	−0.0532712	+	0.0220657i	−0.409160	−	0.912463i	$-0.634178\pi$
$661$	−35.2123	+	14.5854i	−0.0532712	+	0.0220657i	0.355889	+	0.934528i	$0.384178\pi$
$662$		0			0
$663$	46.8281	−	46.8281i	0.0706306	−	0.0706306i
$664$		0			0
$665$	−54.8067	+	54.8067i	−0.0824161	+	0.0824161i
$666$		0			0
$667$	−456.969	+	189.283i	−0.685110	+	0.283782i
$668$		0			0
$669$	−69.2325	−	28.6770i	−0.103487	−	0.0428655i
$670$		0			0
$671$			242.402i			0.361256i
$672$		0			0
$673$	114.199			0.169687			0.0848434	−	0.996394i	$-0.472961\pi$
$673$	114.199			0.169687			0.0848434	+	0.996394i	$0.472961\pi$
$674$		0			0
$675$	496.599	−	1198.90i	0.735702	−	1.77614i
$676$		0			0
$677$	−212.733	−	513.583i	−0.314229	−	0.758617i	−0.999539	−	0.0303647i	$-0.990333\pi$
$677$	−212.733	−	513.583i	−0.314229	−	0.758617i	0.685310	−	0.728252i	$-0.259667\pi$
$678$		0			0
$679$	−242.652	−	242.652i	−0.357366	−	0.357366i
$680$		0			0
$681$	−38.0347	−	38.0347i	−0.0558512	−	0.0558512i
$682$		0			0
$683$	−363.453	−	877.454i	−0.532142	−	1.28471i	−0.930102	−	0.367302i	$-0.880281\pi$
$683$	−363.453	−	877.454i	−0.532142	−	1.28471i	0.397959	−	0.917403i	$-0.369719\pi$
$684$		0			0
$685$	399.289	−	963.969i	0.582904	−	1.40725i
$686$		0			0
$687$	−490.163			−0.713483
$688$		0			0
$689$		−	180.432i		−	0.261875i
$690$		0			0
$691$	682.306	+	282.620i	0.987418	+	0.409002i	0.817168	−	0.576399i	$-0.195543\pi$
$691$	682.306	+	282.620i	0.987418	+	0.409002i	0.170249	+	0.985401i	$0.445543\pi$
$692$		0			0
$693$	−230.465	+	95.4619i	−0.332562	+	0.137752i
$694$		0			0
$695$	425.364	−	425.364i	0.612034	−	0.612034i
$696$		0			0
$697$	77.5377	−	77.5377i	0.111245	−	0.111245i
$698$		0			0
$699$	407.840	−	168.933i	0.583462	−	0.241678i
$700$		0			0
$701$	−565.621	−	234.288i	−0.806878	−	0.334220i	−0.0591703	−	0.998248i	$-0.518846\pi$
$701$	−565.621	−	234.288i	−0.806878	−	0.334220i	−0.747708	+	0.664028i	$0.768846\pi$
$702$		0			0
$703$			93.1812i			0.132548i
$704$		0			0
$705$	801.413			1.13676
$706$		0			0
$707$	−39.0267	+	94.2188i	−0.0552004	+	0.133266i
$708$		0			0
$709$	447.695	+	1080.83i	0.631446	+	1.52444i	0.837806	+	0.545968i	$0.183838\pi$
$709$	447.695	+	1080.83i	0.631446	+	1.52444i	−0.206360	+	0.978476i	$0.566162\pi$
$710$		0			0
$711$	−5.88963	−	5.88963i	−0.00828358	−	0.00828358i
$712$		0			0
$713$	−34.2002	−	34.2002i	−0.0479666	−	0.0479666i
$714$		0			0
$715$	373.945	+	902.783i	0.523000	+	1.26263i
$716$		0			0
$717$	372.001	−	898.089i	0.518829	−	1.25257i
$718$		0			0
$719$	−122.001			−0.169681			−0.0848406	−	0.996395i	$-0.527038\pi$
$719$	−122.001			−0.169681			−0.0848406	+	0.996395i	$0.527038\pi$
$720$		0			0
$721$			4.32894i			0.00600408i
$722$		0			0
$723$	906.877	+	375.641i	1.25433	+	0.519559i
$724$		0			0
$725$	1715.55	−	710.604i	2.36628	−	0.980144i
$726$		0			0
$727$	−438.189	+	438.189i	−0.602736	+	0.602736i	−0.941038	−	0.338301i	$-0.890148\pi$
$727$	−438.189	+	438.189i	−0.602736	+	0.602736i	0.338301	+	0.941038i	$0.390148\pi$
$728$		0			0
$729$	553.213	−	553.213i	0.758866	−	0.758866i
$730$		0			0
$731$	0.908495	−	0.376311i	0.00124281	−	0.000514789i
$732$		0			0
$733$	−629.241	−	260.640i	−0.858446	−	0.355580i	−0.0903463	−	0.995910i	$-0.528797\pi$
$733$	−629.241	−	260.640i	−0.858446	−	0.355580i	−0.768099	+	0.640331i	$0.778797\pi$
$734$		0			0
$735$		−	447.835i		−	0.609299i
$736$		0			0
$737$	153.077			0.207703
$738$		0			0
$739$	−55.5902	+	134.207i	−0.0752235	+	0.181606i	−0.957018	−	0.290028i	$-0.906335\pi$
$739$	−55.5902	+	134.207i	−0.0752235	+	0.181606i	0.881795	+	0.471633i	$0.156335\pi$
$740$		0			0
$741$	12.3839	+	29.8973i	0.0167124	+	0.0403473i
$742$		0			0
$743$	180.295	+	180.295i	0.242658	+	0.242658i	0.817949	−	0.575291i	$-0.195111\pi$
$743$	180.295	+	180.295i	0.242658	+	0.242658i	−0.575291	+	0.817949i	$0.695111\pi$
$744$		0			0
$745$	639.853	+	639.853i	0.858863	+	0.858863i
$746$		0			0
$747$	98.7991	+	238.522i	0.132261	+	0.319307i
$748$		0			0
$749$	288.119	−	695.581i	0.384672	−	0.928680i
$750$		0			0
$751$	264.213			0.351815			0.175908	−	0.984407i	$-0.443714\pi$
$751$	264.213			0.351815			0.175908	+	0.984407i	$0.443714\pi$
$752$		0			0
$753$		−	583.228i		−	0.774539i
$754$		0			0
$755$	−1463.55	−	606.223i	−1.93848	−	0.802945i
$756$		0			0
$757$	−691.098	+	286.262i	−0.912944	+	0.378154i	−0.789183	−	0.614158i	$-0.789496\pi$
$757$	−691.098	+	286.262i	−0.912944	+	0.378154i	−0.123761	+	0.992312i	$0.539496\pi$
$758$		0			0
$759$	324.400	−	324.400i	0.427404	−	0.427404i
$760$		0			0
$761$	287.342	−	287.342i	0.377585	−	0.377585i	−0.492645	−	0.870230i	$-0.663970\pi$
$761$	287.342	−	287.342i	0.377585	−	0.377585i	0.870230	+	0.492645i	$0.163970\pi$
$762$		0			0
$763$	−368.777	+	152.752i	−0.483325	+	0.200200i
$764$		0			0
$765$	−84.9511	−	35.1879i	−0.111047	−	0.0459973i
$766$		0			0
$767$		−	808.842i		−	1.05455i
$768$		0			0
$769$	−1240.31			−1.61289			−0.806446	−	0.591308i	$-0.798612\pi$
$769$	−1240.31			−1.61289			−0.806446	+	0.591308i	$0.798612\pi$
$770$		0			0
$771$	−408.881	+	987.127i	−0.530326	+	1.28032i
$772$		0			0
$773$	−318.633	−	769.248i	−0.412203	−	0.995146i	−0.984545	−	0.175131i	$-0.943965\pi$
$773$	−318.633	−	769.248i	−0.412203	−	0.995146i	0.572342	−	0.820015i	$-0.306035\pi$
$774$		0			0
$775$	128.394	+	128.394i	0.165670	+	0.165670i
$776$		0			0
$777$	466.918	+	466.918i	0.600924	+	0.600924i
$778$		0			0
$779$	20.5052	+	49.5039i	0.0263224	+	0.0635480i
$780$		0			0
$781$	−653.751	+	1578.29i	−0.837069	+	2.02086i
$782$		0			0
$783$	1236.33			1.57897
$784$		0			0
$785$			504.487i			0.642659i
$786$		0			0
$787$	−584.664	−	242.176i	−0.742902	−	0.307720i	−0.0210600	−	0.999778i	$-0.506704\pi$
$787$	−584.664	−	242.176i	−0.742902	−	0.307720i	−0.721842	+	0.692058i	$0.756704\pi$
$788$		0			0
$789$	−1038.03	+	429.967i	−1.31563	+	0.544952i
$790$		0			0
$791$	−493.280	+	493.280i	−0.623616	+	0.623616i
$792$		0			0
$793$	−79.2491	+	79.2491i	−0.0999358	+	0.0999358i
$794$		0			0
$795$	460.196	−	190.619i	0.578863	−	0.239773i
$796$		0			0
$797$	−651.965	−	270.053i	−0.818024	−	0.338837i	−0.0658733	−	0.997828i	$-0.520983\pi$
$797$	−651.965	−	270.053i	−0.818024	−	0.338837i	−0.752150	+	0.658991i	$0.770983\pi$
$798$		0			0
$799$		−	144.598i		−	0.180974i
$800$		0			0
$801$	308.455			0.385088
$802$		0			0
$803$	−250.537	+	604.850i	−0.312002	+	0.753238i
$804$		0			0
$805$	194.419	+	469.370i	0.241515	+	0.583068i
$806$		0			0
$807$	−446.737	−	446.737i	−0.553577	−	0.553577i
$808$		0			0
$809$	−734.385	−	734.385i	−0.907769	−	0.907769i	0.0883227	−	0.996092i	$-0.471849\pi$
$809$	−734.385	−	734.385i	−0.907769	−	0.907769i	−0.996092	+	0.0883227i	$0.971849\pi$
$810$		0			0
$811$	−430.173	−	1038.53i	−0.530423	−	1.28055i	−0.931243	−	0.364398i	$-0.881275\pi$
$811$	−430.173	−	1038.53i	−0.530423	−	1.28055i	0.400820	−	0.916157i	$-0.368725\pi$
$812$		0			0
$813$	−85.9370	+	207.470i	−0.105704	+	0.255191i
$814$		0			0
$815$	1863.57			2.28658
$816$		0			0
$817$			0.480510i			0.000588140i
$818$		0			0
$819$	−106.556	−	44.1370i	−0.130105	−	0.0538913i
$820$		0			0
$821$	30.8969	−	12.7979i	0.0376333	−	0.0155882i	−0.363787	−	0.931482i	$-0.618517\pi$
$821$	30.8969	−	12.7979i	0.0376333	−	0.0155882i	0.401421	+	0.915894i	$0.368517\pi$
$822$		0			0
$823$	−581.324	+	581.324i	−0.706348	+	0.706348i	−0.965765	−	0.259417i	$-0.916470\pi$
$823$	−581.324	+	581.324i	−0.706348	+	0.706348i	0.259417	+	0.965765i	$0.416470\pi$
$824$		0			0
$825$	−1217.86	+	1217.86i	−1.47620	+	1.47620i
$826$		0			0
$827$	−625.862	+	259.241i	−0.756786	+	0.313471i	−0.727507	−	0.686100i	$-0.759321\pi$
$827$	−625.862	+	259.241i	−0.756786	+	0.313471i	−0.0292791	+	0.999571i	$0.509321\pi$
$828$		0			0
$829$	1209.84	+	501.131i	1.45939	+	0.604500i	0.964412	−	0.264403i	$-0.0851750\pi$
$829$	1209.84	+	501.131i	1.45939	+	0.604500i	0.494981	+	0.868904i	$0.335175\pi$
$830$		0			0
$831$			113.298i			0.136340i
$832$		0			0
$833$	−80.8024			−0.0970017
$834$		0			0
$835$	−326.901	+	789.210i	−0.391499	+	0.945162i
$836$		0			0
$837$	46.2644	+	111.692i	0.0552741	+	0.133444i
$838$		0			0
$839$	92.2651	+	92.2651i	0.109970	+	0.109970i	0.759951	−	0.649981i	$-0.225223\pi$
$839$	92.2651	+	92.2651i	0.109970	+	0.109970i	−0.649981	+	0.759951i	$0.725223\pi$
$840$		0			0
$841$	656.279	+	656.279i	0.780355	+	0.780355i
$842$		0			0
$843$	−221.728	−	535.300i	−0.263023	−	0.634994i
$844$		0			0
$845$	364.900	−	880.946i	0.431834	−	1.04254i
$846$		0			0
$847$	691.816			0.816784
$848$		0			0
$849$			1309.47i			1.54237i
$850$		0			0
$851$	564.280	+	233.733i	0.663079	+	0.274656i
$852$		0			0
$853$	404.566	−	167.577i	0.474286	−	0.196456i	−0.132719	−	0.991154i	$-0.542371\pi$
$853$	404.566	−	167.577i	0.474286	−	0.196456i	0.607005	+	0.794698i	$0.292371\pi$
$854$		0			0
$855$	31.7713	−	31.7713i	0.0371594	−	0.0371594i
$856$		0			0
$857$	−870.817	+	870.817i	−1.01612	+	1.01612i	−0.0162551	+	0.999868i	$0.505174\pi$
$857$	−870.817	+	870.817i	−1.01612	+	1.01612i	−0.999868	+	0.0162551i	$0.994826\pi$
$858$		0			0
$859$	1000.98	−	414.619i	1.16528	−	0.482677i	0.285653	−	0.958333i	$-0.407789\pi$
$859$	1000.98	−	414.619i	1.16528	−	0.482677i	0.879631	+	0.475657i	$0.157789\pi$
$860$		0			0
$861$	350.805	+	145.308i	0.407439	+	0.168767i
$862$		0			0
$863$			130.559i			0.151285i	0.997135	+	0.0756423i	$0.0241007\pi$
$863$			130.559i			0.151285i	−0.997135	+	0.0756423i	$0.975899\pi$
$864$		0			0
$865$	88.1088			0.101860
$866$		0			0
$867$	−258.014	+	622.900i	−0.297594	+	0.718455i
$868$		0			0
$869$	16.8724	+	40.7336i	0.0194159	+	0.0468741i
$870$		0			0
$871$	50.0457	+	50.0457i	0.0574577	+	0.0574577i
$872$		0			0
$873$	140.664	+	140.664i	0.161128	+	0.161128i
$874$		0			0
$875$	−316.568	−	764.264i	−0.361792	−	0.873444i
$876$		0			0
$877$	−251.771	+	607.829i	−0.287082	+	0.693077i	−0.999966	−	0.00820433i	$-0.997388\pi$
$877$	−251.771	+	607.829i	−0.287082	+	0.693077i	0.712884	+	0.701282i	$0.247388\pi$
$878$		0			0
$879$	−938.512			−1.06770
$880$		0			0
$881$			349.331i			0.396516i	0.980150	+	0.198258i	$0.0635284\pi$
$881$			349.331i			0.396516i	−0.980150	+	0.198258i	$0.936472\pi$
$882$		0			0
$883$	1394.24	+	577.514i	1.57898	+	0.654036i	0.988252	−	0.152832i	$-0.0488395\pi$
$883$	1394.24	+	577.514i	1.57898	+	0.654036i	0.590731	+	0.806869i	$0.298839\pi$
$884$		0			0
$885$	2062.97	−	854.510i	2.33104	−	0.965548i
$886$		0			0
$887$	980.070	−	980.070i	1.10493	−	1.10493i	0.111120	−	0.993807i	$-0.464556\pi$
$887$	980.070	−	980.070i	1.10493	−	1.10493i	0.993807	−	0.111120i	$-0.0354439\pi$
$888$		0			0
$889$	350.849	−	350.849i	0.394656	−	0.394656i
$890$		0			0
$891$	−660.200	+	273.464i	−0.740965	+	0.306918i
$892$		0			0
$893$	65.2790	+	27.0395i	0.0731008	+	0.0302793i
$894$		0			0
$895$			1927.46i			2.15358i
$896$		0			0
$897$	212.113			0.236470
$898$		0			0
$899$	−66.2018	+	159.825i	−0.0736393	+	0.177781i
$900$		0			0
$901$	−34.3933	−	83.0327i	−0.0381723	−	0.0921561i
$902$		0			0
$903$	2.40777	+	2.40777i	0.00266641	+	0.00266641i
$904$		0			0
$905$	625.066	+	625.066i	0.690681	+	0.690681i
$906$		0			0
$907$	−64.9162	−	156.722i	−0.0715725	−	0.172791i	0.884045	−	0.467402i	$-0.154810\pi$
$907$	−64.9162	−	156.722i	−0.0715725	−	0.172791i	−0.955617	+	0.294611i	$0.904810\pi$
$908$		0			0
$909$	22.6236	−	54.6183i	0.0248885	−	0.0600861i
$910$		0			0
$911$	989.468			1.08613			0.543067	−	0.839689i	$-0.317263\pi$
$911$	989.468			1.08613			0.543067	+	0.839689i	$0.317263\pi$
$912$		0			0
$913$		−	1366.62i		−	1.49684i
$914$		0			0
$915$	−285.850	−	118.403i	−0.312405	−	0.129402i
$916$		0			0
$917$	−841.857	+	348.708i	−0.918055	+	0.380271i
$918$		0			0
$919$	−594.043	+	594.043i	−0.646402	+	0.646402i	−0.952122	−	0.305720i	$-0.901103\pi$
$919$	−594.043	+	594.043i	−0.646402	+	0.646402i	0.305720	+	0.952122i	$0.401103\pi$
$920$		0			0
$921$	−100.071	+	100.071i	−0.108655	+	0.108655i
$922$		0			0
$923$	−729.727	+	302.263i	−0.790603	+	0.327478i
$924$		0			0
$925$	−2118.42	−	877.478i	−2.29018	−	0.948625i
$926$		0			0
$927$		−	2.50947i		−	0.00270709i
$928$		0			0
$929$	1637.29			1.76242			0.881209	−	0.472726i	$-0.156730\pi$
$929$	1637.29			1.76242			0.881209	+	0.472726i	$0.156730\pi$
$930$		0			0
$931$	15.1098	−	36.4784i	0.0162297	−	0.0391819i
$932$		0			0
$933$	−363.556	−	877.701i	−0.389663	−	0.940730i
$934$		0			0
$935$	344.170	+	344.170i	0.368096	+	0.368096i
$936$		0			0
$937$	−407.126	−	407.126i	−0.434500	−	0.434500i	0.455656	−	0.890156i	$-0.349405\pi$
$937$	−407.126	−	407.126i	−0.434500	−	0.434500i	−0.890156	+	0.455656i	$0.849405\pi$
$938$		0			0
$939$	−103.831	−	250.671i	−0.110576	−	0.266955i
$940$		0			0
$941$	510.935	−	1233.51i	0.542970	−	1.31085i	−0.379648	−	0.925131i	$-0.623955\pi$
$941$	510.935	−	1233.51i	0.542970	−	1.31085i	0.922618	−	0.385715i	$-0.126045\pi$
$942$		0			0
$943$	351.217			0.372446
$944$		0			0
$945$		−	1269.88i		−	1.34379i
$946$		0			0
$947$	627.458	+	259.902i	0.662574	+	0.274447i	0.688521	−	0.725216i	$-0.258260\pi$
$947$	627.458	+	259.902i	0.662574	+	0.274447i	−0.0259471	+	0.999663i	$0.508260\pi$
$948$		0			0
$949$	−279.654	+	115.836i	−0.294682	+	0.122061i
$950$		0			0
$951$	255.691	−	255.691i	0.268865	−	0.268865i
$952$		0			0
$953$	−1189.93	+	1189.93i	−1.24862	+	1.24862i	−0.292290	+	0.956330i	$0.594417\pi$
$953$	−1189.93	+	1189.93i	−1.24862	+	1.24862i	−0.956330	+	0.292290i	$0.905583\pi$
$954$		0			0
$955$	−1397.01	+	578.660i	−1.46284	+	0.605926i
$956$		0			0
$957$	−1515.99	−	627.945i	−1.58411	−	0.656159i
$958$		0			0
$959$		−	651.893i		−	0.679764i
$960$		0			0
$961$	944.084			0.982397
$962$		0			0
$963$	−167.022	+	403.226i	−0.173439	+	0.418719i
$964$		0			0
$965$	704.118	+	1699.89i	0.729656	+	1.76155i
$966$		0			0
$967$	−633.832	−	633.832i	−0.655462	−	0.655462i	0.298841	−	0.954303i	$-0.403400\pi$
$967$	−633.832	−	633.832i	−0.655462	−	0.655462i	−0.954303	+	0.298841i	$0.903400\pi$
$968$		0			0
$969$	11.3978	+	11.3978i	0.0117625	+	0.0117625i
$970$		0			0
$971$	399.517	+	964.518i	0.411449	+	0.993325i	0.984749	+	0.173980i	$0.0556627\pi$
$971$	399.517	+	964.518i	0.411449	+	0.993325i	−0.573301	+	0.819345i	$0.694337\pi$
$972$		0			0
$973$	143.828	−	347.232i	0.147819	−	0.356867i
$974$		0			0
$975$	−796.316			−0.816734
$976$		0			0
$977$		−	122.057i		−	0.124931i	−0.998047	−	0.0624653i	$-0.980104\pi$
$977$		−	122.057i		−	0.124931i	0.998047	−	0.0624653i	$-0.0198963\pi$
$978$		0			0
$979$	−1508.49	−	624.837i	−1.54085	−	0.638240i
$980$		0			0
$981$	213.779	−	88.5500i	0.217919	−	0.0902650i
$982$		0			0
$983$	−1257.94	+	1257.94i	−1.27970	+	1.27970i	−0.338864	+	0.940835i	$0.610043\pi$
$983$	−1257.94	+	1257.94i	−1.27970	+	1.27970i	−0.940835	+	0.338864i	$0.889957\pi$
$984$		0			0
$985$	−237.176	+	237.176i	−0.240788	+	0.240788i
$986$		0			0
$987$	462.595	−	191.613i	0.468688	−	0.194137i
$988$		0			0
$989$	2.90984	+	1.20530i	0.00294220	+	0.00121870i
$990$		0			0
$991$		−	1409.81i		−	1.42261i	−0.702884	−	0.711304i	$-0.748105\pi$
$991$		−	1409.81i		−	1.42261i	0.702884	−	0.711304i	$-0.251895\pi$
$992$		0			0
$993$	918.834			0.925311
$994$		0			0
$995$	610.326	−	1473.46i	0.613393	−	1.48086i
$996$		0			0
$997$	−60.9825	−	147.225i	−0.0611660	−	0.147668i	0.890341	−	0.455293i	$-0.150466\pi$
$997$	−60.9825	−	147.225i	−0.0611660	−	0.147668i	−0.951508	+	0.307625i	$0.900466\pi$
$998$		0			0
$999$	−1079.51	−	1079.51i	−1.08059	−	1.08059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.47.2		28
4.3	odd	2		32.3.h.a.3.3	✓	28
8.3	odd	2		256.3.h.b.95.2		28
8.5	even	2		256.3.h.a.95.6		28
12.11	even	2		288.3.u.a.163.5		28
32.5	even	8		256.3.h.b.159.2		28
32.11	odd	8	inner	128.3.h.a.79.2		28
32.21	even	8		32.3.h.a.11.3	yes	28
32.27	odd	8		256.3.h.a.159.6		28
96.53	odd	8		288.3.u.a.235.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.3	✓	28	4.3	odd	2
32.3.h.a.11.3	yes	28	32.21	even	8
128.3.h.a.47.2		28	1.1	even	1	trivial
128.3.h.a.79.2		28	32.11	odd	8	inner
256.3.h.a.95.6		28	8.5	even	2
256.3.h.a.159.6		28	32.27	odd	8
256.3.h.b.95.2		28	8.3	odd	2
256.3.h.b.159.2		28	32.5	even	8
288.3.u.a.163.5		28	12.11	even	2
288.3.u.a.235.5		28	96.53	odd	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +O(q^{10})\)	\(q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +20.3488 q^{15} -3.67152i q^{17} +(1.65751 + 0.686564i) q^{19} +(11.7458 - 4.86528i) q^{21} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(-27.1564 + 11.2485i) q^{27} +(-38.8592 - 16.0960i) q^{29} -4.11293i q^{31} +39.0124 q^{33} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(12.7544 + 12.7544i) q^{39} +(21.1187 + 21.1187i) q^{41} +(0.102495 + 0.247444i) q^{43} +(9.58403 - 23.1379i) q^{45} +39.3838 q^{47} -22.0079i q^{49} +(8.30063 + 3.43823i) q^{51} +(22.6154 - 9.36759i) q^{53} +(-93.7406 + 93.7406i) q^{55} +(-3.10439 + 3.10439i) q^{57} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} -15.6472i q^{63} -61.2936 q^{65} +(-3.67448 + 8.87098i) q^{67} +(11.0124 + 26.5863i) q^{69} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-41.3427 - 99.8102i) q^{75} +(-31.6965 + 76.5221i) q^{77} -2.76556 q^{79} -44.8236i q^{81} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(72.7802 - 72.7802i) q^{87} +(72.4200 - 72.4200i) q^{89} +(-35.3801 + 14.6549i) q^{91} +(9.29858 + 3.85160i) q^{93} -14.9187i q^{95} +66.0511 q^{97} +(18.3743 - 44.3596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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