LMFDB - Embedded newform 256.3.h.a.95.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, 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("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.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:	$6.97549476762$
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			95.6
Character	$\chi$	$=$	256.95
Dual form			256.3.h.a.159.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.936461 - 2.26082i) q^{3} +(3.18221 + 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +O(q^{10})$	\(q+(0.936461 - 2.26082i) q^{3} +(3.18221 + 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +(6.10089 + 14.7288i) q^{11} +(-2.82075 + 6.80990i) q^{13} +20.3488 q^{15} -3.67152i q^{17} +(-1.65751 - 0.686564i) q^{19} +(-11.7458 + 4.86528i) q^{21} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(27.1564 - 11.2485i) q^{27} +(38.8592 + 16.0960i) q^{29} -4.11293i q^{31} +39.0124 q^{33} +(16.5328 - 39.9138i) q^{35} +(-19.8759 - 47.9847i) q^{37} +(12.7544 + 12.7544i) q^{39} +(21.1187 + 21.1187i) q^{41} +(-0.102495 - 0.247444i) q^{43} +(-9.58403 + 23.1379i) q^{45} +39.3838 q^{47} -22.0079i q^{49} +(-8.30063 - 3.43823i) q^{51} +(-22.6154 + 9.36759i) q^{53} +(-93.7406 + 93.7406i) q^{55} +(-3.10439 + 3.10439i) q^{57} +(-101.380 + 41.9931i) q^{59} +(14.0475 + 5.81867i) q^{61} -15.6472i q^{63} -61.2936 q^{65} +(3.67448 - 8.87098i) q^{67} +(-11.0124 - 26.5863i) q^{69} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(41.3427 + 99.8102i) q^{75} +(31.6965 - 76.5221i) q^{77} -2.76556 q^{79} -44.8236i q^{81} +(-79.1972 - 32.8045i) q^{83} +(28.2066 - 11.6835i) q^{85} +(72.7802 - 72.7802i) q^{87} +(72.4200 - 72.4200i) q^{89} +(35.3801 - 14.6549i) q^{91} +(-9.29858 - 3.85160i) q^{93} -14.9187i q^{95} +66.0511 q^{97} +(-18.3743 + 44.3596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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	$-0.741279\pi$
$3$	0.936461	−	2.26082i	0.312154	−	0.753605i	0.999625	−	0.0273938i	$-0.00872079\pi$
$4$		0			0
$5$	3.18221	+	7.68254i	0.636442	+	1.53651i	0.831387	+	0.555693i	$0.187547\pi$
$5$	3.18221	+	7.68254i	0.636442	+	1.53651i	−0.194945	+	0.980814i	$0.562453\pi$
$6$		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	$0.133000\pi$
$11$	6.10089	+	14.7288i	0.554626	+	1.33899i	−0.359345	+	0.933205i	$0.617000\pi$
$12$		0			0
$13$	−2.82075	+	6.80990i	−0.216981	+	0.523839i	−0.994466	−	0.105063i	$-0.966495\pi$
$13$	−2.82075	+	6.80990i	−0.216981	+	0.523839i	0.777484	+	0.628902i	$0.216495\pi$
$14$		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	0.338638	−	0.940917i	$-0.390034\pi$
$19$	−1.65751	−	0.686564i	−0.0872375	−	0.0361349i	−0.425875	+	0.904782i	$0.640034\pi$
$20$		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	0.933483	−	0.358621i	$-0.116753\pi$
$29$	38.8592	+	16.0960i	1.33997	+	0.555035i	0.406489	+	0.913656i	$0.366753\pi$
$30$		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	$-0.877350\pi$
$37$	−19.8759	−	47.9847i	−0.537186	−	1.29688i	0.389493	−	0.921030i	$-0.372650\pi$
$38$		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	0.922683	−	0.385559i	$-0.125991\pi$
$43$	−0.102495	−	0.247444i	−0.00238360	−	0.00575451i	−0.925067	+	0.379804i	$0.875991\pi$
$44$		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	−0.585692	−	0.810534i	$-0.699177\pi$
$53$	−22.6154	+	9.36759i	−0.426705	+	0.176747i	0.158987	+	0.987281i	$0.449177\pi$
$54$		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	$0.755144\pi$
$59$	−101.380	+	41.9931i	−1.71831	+	0.711747i	−0.999869	+	0.0161592i	$0.994856\pi$
$60$		0			0
$61$	14.0475	+	5.81867i	0.230287	+	0.0953880i	0.494843	−	0.868982i	$-0.335225\pi$
$61$	14.0475	+	5.81867i	0.230287	+	0.0953880i	−0.264556	+	0.964370i	$0.585225\pi$
$62$		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	−0.894083	−	0.447901i	$-0.852172\pi$
$67$	3.67448	−	8.87098i	0.0548430	−	0.132403i	0.948926	+	0.315498i	$0.102172\pi$
$68$		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	−0.149381	−	0.988780i	$-0.547728\pi$
$83$	−79.1972	−	32.8045i	−0.954183	−	0.395235i	−0.804801	+	0.593544i	$0.797728\pi$
$84$		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	0.956694	−	0.291095i	$-0.0940195\pi$
$101$	7.51179	+	18.1351i	0.0743742	+	0.179555i	−0.882320	+	0.470650i	$0.844019\pi$
$102$		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	$-0.888204\pi$
$107$	−55.4567	−	133.884i	−0.518287	−	1.25126i	0.420668	−	0.907215i	$-0.361796\pi$
$108$		0			0
$109$	−29.4015	+	70.9815i	−0.269739	+	0.651207i	−0.999471	−	0.0325264i	$-0.989645\pi$
$109$	−29.4015	+	70.9815i	−0.269739	+	0.651207i	0.729732	+	0.683733i	$0.239645\pi$
$110$		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	$0.358460\pi$
$131$	−67.1188	+	162.039i	−0.512357	+	1.23694i	−0.942508	+	0.334183i	$0.891540\pi$
$132$		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	0.792469	−	0.609912i	$-0.208795\pi$
$139$	−27.6838	−	66.8346i	−0.199164	−	0.480824i	−0.991633	+	0.129087i	$0.958795\pi$
$140$		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	−0.0188878	−	0.999822i	$-0.506013\pi$
$149$	100.536	−	41.6433i	0.674737	−	0.279485i	0.693625	+	0.720336i	$0.256013\pi$
$150$		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	0.553976	−	0.832533i	$-0.313110\pi$
$157$	56.0501	+	23.2167i	0.357007	+	0.147877i	−0.196969	+	0.980410i	$0.563110\pi$
$158$		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	$-0.633732\pi$
$163$	85.7621	−	207.048i	0.526148	−	1.27023i	0.934029	−	0.357198i	$-0.116268\pi$
$164$		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	−0.911727	−	0.410796i	$-0.865251\pi$
$173$	4.05480	−	9.78916i	0.0234382	−	0.0565847i	0.935165	+	0.354212i	$0.115251\pi$
$174$		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	0.889817	−	0.456317i	$-0.150832\pi$
$179$	214.146	+	88.7024i	1.19635	+	0.495544i	0.306531	+	0.951861i	$0.400832\pi$
$180$		0			0
$181$	98.2125	−	40.6810i	0.542611	−	0.224757i	−0.0945057	−	0.995524i	$-0.530127\pi$
$181$	98.2125	−	40.6810i	0.542611	−	0.224757i	0.637116	+	0.770768i	$0.280127\pi$
$182$		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	0.958203	−	0.286089i	$-0.0923553\pi$
$197$	15.4361	+	37.2660i	0.0783556	+	0.189167i	−0.879847	+	0.475256i	$0.842355\pi$
$198$		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	0.684954	−	0.728587i	$-0.259822\pi$
$211$	138.015	+	57.1678i	0.654100	+	0.270937i	−0.0308532	+	0.999524i	$0.509822\pi$
$212$		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	−0.904268	−	0.426965i	$-0.859583\pi$
$227$	8.41171	−	20.3077i	0.0370560	−	0.0894611i	0.941324	+	0.337504i	$0.109583\pi$
$228$		0			0
$229$	−76.6532	−	185.057i	−0.334730	−	0.808110i	−0.998204	−	0.0599101i	$-0.980919\pi$
$229$	−76.6532	−	185.057i	−0.334730	−	0.808110i	0.663474	−	0.748199i	$-0.269081\pi$
$230$		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	0.101829	−	0.994802i	$-0.467531\pi$
$251$	220.193	−	91.2070i	0.877264	−	0.363375i	0.775435	+	0.631427i	$0.217531\pi$
$252$		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	$-0.715680\pi$
$269$	98.7998	−	238.524i	0.367286	−	0.886706i	0.994193	−	0.107612i	$-0.0343205\pi$
$270$		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	−0.458556	−	0.888666i	$-0.651633\pi$
$277$	−42.7749	+	17.7179i	−0.154422	+	0.0639636i	0.304134	+	0.952629i	$0.401633\pi$
$278$		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	$0.769358\pi$
$283$	−494.380	+	204.779i	−1.74693	+	0.723601i	−0.998151	+	0.0607762i	$0.980642\pi$
$284$		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	$-0.897890\pi$
$293$	−146.767	−	354.328i	−0.500913	−	1.20931i	0.448075	−	0.893996i	$-0.352110\pi$
$294$		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	0.293962	−	0.955817i	$-0.405026\pi$
$307$	−53.4306	−	22.1317i	−0.174041	−	0.0720902i	−0.468003	+	0.883727i	$0.655026\pi$
$308$		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	0.587475	−	0.809243i	$-0.300122\pi$
$317$	136.520	+	56.5483i	0.430661	+	0.178386i	−0.156814	+	0.987628i	$0.550122\pi$
$318$		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	$0.0669696\pi$
$331$	143.690	+	346.898i	0.434109	+	1.04803i	−0.543841	+	0.839189i	$0.683030\pi$
$332$		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	−0.120585	−	0.992703i	$-0.538477\pi$
$347$	172.145	−	71.3048i	0.496095	−	0.205489i	0.616680	+	0.787214i	$0.288477\pi$
$348$		0			0
$349$	−388.120	−	160.765i	−1.11209	−	0.460644i	−0.250434	−	0.968134i	$-0.580573\pi$
$349$	−388.120	−	160.765i	−1.11209	−	0.460644i	−0.861658	+	0.507490i	$0.830573\pi$
$350$		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	−0.994593	−	0.103845i	$-0.966885\pi$
$373$	−605.919	+	250.980i	−1.62445	+	0.672868i	−0.629854	+	0.776713i	$0.716885\pi$
$374$		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	−0.870750	−	0.491725i	$-0.836366\pi$
$379$	−431.591	+	178.771i	−1.13876	+	0.471691i	−0.268011	+	0.963416i	$0.586366\pi$
$380$		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	0.980667	−	0.195684i	$-0.0626927\pi$
$389$	57.9070	+	139.800i	0.148861	+	0.359383i	−0.831806	+	0.555067i	$0.812693\pi$
$390$		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	$0.377420\pi$
$397$	−216.482	+	522.634i	−0.545295	+	1.31646i	−0.920944	+	0.389696i	$0.872580\pi$
$398$		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	−0.992084	−	0.125575i	$-0.959923\pi$
$419$	−84.5458	+	204.112i	−0.201780	+	0.487140i	0.790304	+	0.612715i	$0.209923\pi$
$420$		0			0
$421$	−13.1417	−	31.7269i	−0.0312155	−	0.0753608i	0.907503	−	0.420045i	$-0.137986\pi$
$421$	−13.1417	−	31.7269i	−0.0312155	−	0.0753608i	−0.938719	+	0.344685i	$0.887986\pi$
$422$		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	−0.365124	−	0.930959i	$-0.618973\pi$
$443$	15.4970	−	6.41908i	0.0349820	−	0.0144900i	0.400106	+	0.916469i	$0.368973\pi$
$444$		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	$0.448320\pi$
$461$	−299.864	+	723.935i	−0.650463	+	1.57036i	−0.812107	+	0.583508i	$0.801680\pi$
$462$		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	0.284416	−	0.958701i	$-0.408200\pi$
$467$	−89.8391	−	37.2126i	−0.192375	−	0.0796843i	−0.476791	+	0.879017i	$0.658200\pi$
$468$		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	0.767858	−	0.640620i	$-0.221322\pi$
$491$	−111.990	−	270.368i	−0.228086	−	0.550648i	−0.995944	+	0.0899713i	$0.971322\pi$
$492$		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	0.477192	−	0.878799i	$-0.341655\pi$
$499$	96.4128	+	39.9355i	0.193212	+	0.0800310i	−0.283980	+	0.958830i	$0.591655\pi$
$500$		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	$-0.978385\pi$
$509$	−891.336	−	369.204i	−1.75115	−	0.725351i	−0.753457	−	0.657498i	$-0.771615\pi$
$510$		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	$0.100764\pi$
$523$	260.696	+	629.375i	0.498462	+	1.20339i	−0.451849	+	0.892094i	$0.649236\pi$
$524$		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	0.0295603	−	0.999563i	$-0.490589\pi$
$541$	−355.077	−	147.078i	−0.656335	−	0.271863i	−0.685895	+	0.727700i	$0.740589\pi$
$542$		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	$-0.456831\pi$
$547$	404.897	−	977.508i	0.740214	−	1.78704i	0.605010	−	0.796218i	$-0.293169\pi$
$548$		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	$-0.629711\pi$
$557$	296.952	−	716.907i	0.533128	−	1.28709i	0.929441	−	0.368970i	$-0.120289\pi$
$558$		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	0.342644	−	0.939465i	$-0.388678\pi$
$563$	−44.6869	−	18.5099i	−0.0793728	−	0.0328773i	−0.422017	+	0.906588i	$0.638678\pi$
$564$		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	−0.592714	−	0.805413i	$-0.701944\pi$
$571$	−252.561	+	104.614i	−0.442313	+	0.183212i	0.150401	+	0.988625i	$0.451944\pi$
$572$		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	0.971319	−	0.237780i	$-0.0764197\pi$
$587$	68.3015	+	164.895i	0.116357	+	0.280911i	−0.854962	+	0.518690i	$0.826420\pi$
$588$		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	$-0.983220\pi$
$613$	−202.134	−	487.995i	−0.329746	−	0.796076i	0.668865	−	0.743384i	$-0.266780\pi$
$614$		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	$-0.838294\pi$
$619$	−371.320	−	896.447i	−0.599871	−	1.44822i	0.273841	−	0.961775i	$-0.411706\pi$
$620$		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	$0.349735\pi$
$643$	−319.302	+	770.863i	−0.496582	+	1.19885i	−0.951313	+	0.308226i	$0.900265\pi$
$644$		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	$-0.677872\pi$
$653$	290.106	−	700.378i	0.444267	−	1.07255i	0.974436	−	0.224663i	$-0.0721282\pi$
$654$		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	0.904134	−	0.427248i	$-0.140517\pi$
$659$	818.045	+	338.845i	1.24134	+	0.514181i	0.337209	+	0.941430i	$0.390517\pi$
$660$		0			0
$661$	35.2123	−	14.5854i	0.0532712	−	0.0220657i	−0.355889	−	0.934528i	$-0.615822\pi$
$661$	35.2123	−	14.5854i	0.0532712	−	0.0220657i	0.409160	+	0.912463i	$0.365822\pi$
$662$		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	$0.00966689\pi$
$677$	212.733	+	513.583i	0.314229	+	0.758617i	−0.685310	+	0.728252i	$0.740333\pi$
$678$		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	$0.119719\pi$
$683$	363.453	+	877.454i	0.532142	+	1.28471i	−0.397959	+	0.917403i	$0.630281\pi$
$684$		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	−0.170249	−	0.985401i	$-0.554457\pi$
$691$	−682.306	−	282.620i	−0.987418	−	0.409002i	−0.817168	+	0.576399i	$0.804457\pi$
$692$		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	0.747708	−	0.664028i	$-0.231154\pi$
$701$	565.621	+	234.288i	0.806878	+	0.334220i	0.0591703	+	0.998248i	$0.481154\pi$
$702$		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	$-0.816162\pi$
$709$	−447.695	−	1080.83i	−0.631446	−	1.52444i	0.206360	−	0.978476i	$-0.433838\pi$
$710$		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	0.768099	−	0.640331i	$-0.221203\pi$
$733$	629.241	+	260.640i	0.858446	+	0.355580i	0.0903463	+	0.995910i	$0.471203\pi$
$734$		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	−0.881795	−	0.471633i	$-0.843665\pi$
$739$	55.5902	−	134.207i	0.0752235	−	0.181606i	0.957018	+	0.290028i	$0.0936646\pi$
$740$		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	0.123761	−	0.992312i	$-0.460504\pi$
$757$	691.098	−	286.262i	0.912944	−	0.378154i	0.789183	+	0.614158i	$0.210504\pi$
$758$		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	$0.0560350\pi$
$773$	318.633	+	769.248i	0.412203	+	0.995146i	−0.572342	+	0.820015i	$0.693965\pi$
$774$		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	0.721842	−	0.692058i	$-0.243296\pi$
$787$	584.664	+	242.176i	0.742902	+	0.307720i	0.0210600	+	0.999778i	$0.493296\pi$
$788$		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	0.752150	−	0.658991i	$-0.229017\pi$
$797$	651.965	+	270.053i	0.818024	+	0.338837i	0.0658733	+	0.997828i	$0.479017\pi$
$798$		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	$0.118725\pi$
$811$	430.173	+	1038.53i	0.530423	+	1.28055i	−0.400820	+	0.916157i	$0.631275\pi$
$812$		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	−0.401421	−	0.915894i	$-0.631483\pi$
$821$	−30.8969	+	12.7979i	−0.0376333	+	0.0155882i	0.363787	+	0.931482i	$0.381483\pi$
$822$		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	0.0292791	−	0.999571i	$-0.490679\pi$
$827$	625.862	−	259.241i	0.756786	−	0.313471i	0.727507	+	0.686100i	$0.240679\pi$
$828$		0			0
$829$	−1209.84	−	501.131i	−1.45939	−	0.604500i	−0.494981	−	0.868904i	$-0.664825\pi$
$829$	−1209.84	−	501.131i	−1.45939	−	0.604500i	−0.964412	+	0.264403i	$0.914825\pi$
$830$		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	−0.607005	−	0.794698i	$-0.707629\pi$
$853$	−404.566	+	167.577i	−0.474286	+	0.196456i	0.132719	+	0.991154i	$0.457629\pi$
$854$		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	−0.879631	−	0.475657i	$-0.842211\pi$
$859$	−1000.98	+	414.619i	−1.16528	+	0.482677i	−0.285653	+	0.958333i	$0.592211\pi$
$860$		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	−0.712884	−	0.701282i	$-0.752612\pi$
$877$	251.771	−	607.829i	0.287082	−	0.693077i	0.999966	+	0.00820433i	$0.00261155\pi$
$878$		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	−0.590731	−	0.806869i	$-0.701161\pi$
$883$	−1394.24	−	577.514i	−1.57898	−	0.654036i	−0.988252	+	0.152832i	$0.951161\pi$
$884$		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	0.955617	−	0.294611i	$-0.0951900\pi$
$907$	64.9162	+	156.722i	0.0715725	+	0.172791i	−0.884045	+	0.467402i	$0.845190\pi$
$908$		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	$0.376045\pi$
$941$	−510.935	+	1233.51i	−0.542970	+	1.31085i	−0.922618	+	0.385715i	$0.873955\pi$
$942$		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	0.0259471	−	0.999663i	$-0.491740\pi$
$947$	−627.458	−	259.902i	−0.662574	−	0.274447i	−0.688521	+	0.725216i	$0.741740\pi$
$948$		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	$-0.944337\pi$
$971$	−399.517	−	964.518i	−0.411449	−	0.993325i	0.573301	−	0.819345i	$-0.305663\pi$
$972$		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	0.951508	−	0.307625i	$-0.0995344\pi$
$997$	60.9825	+	147.225i	0.0611660	+	0.147668i	−0.890341	+	0.455293i	$0.849534\pi$
$998$		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	256.3.h.a.95.6		28
4.3	odd	2		256.3.h.b.95.2		28
8.3	odd	2		32.3.h.a.3.3	✓	28
8.5	even	2		128.3.h.a.47.2		28
24.11	even	2		288.3.u.a.163.5		28
32.5	even	8		32.3.h.a.11.3	yes	28
32.11	odd	8	inner	256.3.h.a.159.6		28
32.21	even	8		256.3.h.b.159.2		28
32.27	odd	8		128.3.h.a.79.2		28
96.5	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	8.3	odd	2
32.3.h.a.11.3	yes	28	32.5	even	8
128.3.h.a.47.2		28	8.5	even	2
128.3.h.a.79.2		28	32.27	odd	8
256.3.h.a.95.6		28	1.1	even	1	trivial
256.3.h.a.159.6		28	32.11	odd	8	inner
256.3.h.b.95.2		28	4.3	odd	2
256.3.h.b.159.2		28	32.21	even	8
288.3.u.a.163.5		28	24.11	even	2
288.3.u.a.235.5		28	96.5	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.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

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