LMFDB - Embedded newform 28.5.h.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,5,Mod(5,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("28.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	28.h (of order $6$, degree $2$, 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:	$2.89435896635$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$3.17656i$ of defining polynomial
Character	$\chi$	$=$	28.17
Dual form			28.5.h.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.81152 - 4.50998i) q^{3} +(-26.9260 + 15.5457i) q^{5} +(-48.6720 - 5.65972i) q^{7} +(0.179888 + 0.311574i) q^{9} +(72.8605 - 126.198i) q^{11} +209.930i q^{13} +280.444 q^{15} +(-162.074 - 93.5735i) q^{17} +(153.531 - 88.6415i) q^{19} +(354.677 + 263.721i) q^{21} +(-166.842 - 288.979i) q^{23} +(170.838 - 295.901i) q^{25} +727.372i q^{27} -1387.57 q^{29} +(-1345.74 - 776.966i) q^{31} +(-1138.30 + 657.199i) q^{33} +(1398.53 - 604.248i) q^{35} +(1138.99 + 1972.78i) q^{37} +(946.779 - 1639.87i) q^{39} -781.977i q^{41} +837.131 q^{43} +(-9.68729 - 5.59296i) q^{45} +(-1296.36 + 748.454i) q^{47} +(2336.94 + 550.940i) q^{49} +(844.030 + 1461.90i) q^{51} +(2233.55 - 3868.63i) q^{53} +4530.67i q^{55} -1599.09 q^{57} +(-3815.50 - 2202.88i) q^{59} +(2257.75 - 1303.51i) q^{61} +(-6.99207 - 16.1831i) q^{63} +(-3263.51 - 5652.56i) q^{65} +(-2887.15 + 5000.70i) q^{67} +3009.82i q^{69} +1149.20 q^{71} +(-3194.47 - 1844.33i) q^{73} +(-2669.01 + 1540.96i) q^{75} +(-4260.52 + 5729.95i) q^{77} +(-1349.16 - 2336.81i) q^{79} +(3295.01 - 5707.12i) q^{81} -2689.70i q^{83} +5818.67 q^{85} +(10839.1 + 6257.93i) q^{87} +(5037.61 - 2908.47i) q^{89} +(1188.14 - 10217.7i) q^{91} +(7008.21 + 12138.6i) q^{93} +(-2755.99 + 4773.51i) q^{95} -7890.42i q^{97} +52.4268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} - 27 q^{5} + 66 q^{7} + 90 q^{9} + 135 q^{11} - 486 q^{15} - 1107 q^{17} - 747 q^{19} + 2169 q^{21} + 243 q^{23} + 1878 q^{25} - 540 q^{29} - 5355 q^{31} - 1863 q^{33} + 6021 q^{35} + 2355 q^{37}+ \cdots + 8100 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 - 27 * q^5 + 66 * q^7 + 90 * q^9 + 135 * q^11 - 486 * q^15 - 1107 * q^17 - 747 * q^19 + 2169 * q^21 + 243 * q^23 + 1878 * q^25 - 540 * q^29 - 5355 * q^31 - 1863 * q^33 + 6021 * q^35 + 2355 * q^37 + 6588 * q^39 - 948 * q^43 - 14418 * q^45 - 9747 * q^47 + 8430 * q^49 - 891 * q^51 + 6291 * q^53 - 6894 * q^57 - 2943 * q^59 + 4041 * q^61 + 15138 * q^63 + 7668 * q^65 + 1659 * q^67 + 2268 * q^71 - 8703 * q^73 - 3438 * q^75 - 10665 * q^77 - 7773 * q^79 - 7479 * q^81 - 702 * q^85 + 40014 * q^87 + 14985 * q^89 - 20952 * q^91 + 1449 * q^93 - 20655 * q^95 + 8100 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−7.81152	−	4.50998i	−0.867947	−	0.501109i	−0.00128125	−	0.999999i	$-0.500408\pi$
$3$	−7.81152	−	4.50998i	−0.867947	−	0.501109i	−0.866665	+	0.498890i	$0.833741\pi$
$4$		0			0
$5$	−26.9260	+	15.5457i	−1.07704	+	0.621829i	−0.930096	−	0.367317i	$-0.880277\pi$
$5$	−26.9260	+	15.5457i	−1.07704	+	0.621829i	−0.146943	+	0.989145i	$0.546943\pi$
$6$		0			0
$7$	−48.6720	−	5.65972i	−0.993307	−	0.115505i
$7$	−48.6720	−	5.65972i	−0.993307	−	0.115505i
$8$		0			0
$9$	0.179888	+	0.311574i	0.00222083	+	0.00384660i
$10$		0			0
$11$	72.8605	−	126.198i	0.602153	−	1.04296i	−0.390341	−	0.920670i	$-0.627643\pi$
$11$	72.8605	−	126.198i	0.602153	−	1.04296i	0.992494	−	0.122290i	$-0.0390236\pi$
$12$		0			0
$13$			209.930i			1.24219i	0.783736	+	0.621094i	$0.213311\pi$
$13$			209.930i			1.24219i	−0.783736	+	0.621094i	$0.786689\pi$
$14$		0			0
$15$	280.444			1.24642
$16$		0			0
$17$	−162.074	−	93.5735i	−0.560810	−	0.323784i	0.192661	−	0.981265i	$-0.438288\pi$
$17$	−162.074	−	93.5735i	−0.560810	−	0.323784i	−0.753470	+	0.657482i	$0.771622\pi$
$18$		0			0
$19$	153.531	−	88.6415i	0.425295	−	0.245544i	−0.272045	−	0.962284i	$-0.587700\pi$
$19$	153.531	−	88.6415i	0.425295	−	0.245544i	0.697340	+	0.716740i	$0.254367\pi$
$20$		0			0
$21$	354.677	+	263.721i	0.804257	+	0.598007i
$22$		0			0
$23$	−166.842	−	288.979i	−0.315392	−	0.546275i	0.664129	−	0.747618i	$-0.268803\pi$
$23$	−166.842	−	288.979i	−0.315392	−	0.546275i	−0.979521	+	0.201343i	$0.935469\pi$
$24$		0			0
$25$	170.838	−	295.901i	0.273341	−	0.473441i
$26$		0			0
$27$			727.372i			0.997767i
$28$		0			0
$29$	−1387.57			−1.64991			−0.824954	−	0.565199i	$-0.808799\pi$
$29$	−1387.57			−1.64991			−0.824954	+	0.565199i	$0.808799\pi$
$30$		0			0
$31$	−1345.74	−	776.966i	−1.40036	−	0.808497i	−0.405930	−	0.913904i	$-0.633052\pi$
$31$	−1345.74	−	776.966i	−1.40036	−	0.808497i	−0.994429	+	0.105407i	$0.966385\pi$
$32$		0			0
$33$	−1138.30	+	657.199i	−1.04527	+	0.603489i
$34$		0			0
$35$	1398.53	−	604.248i	1.14165	−	0.493264i
$36$		0			0
$37$	1138.99	+	1972.78i	0.831985	+	1.44104i	0.896462	+	0.443122i	$0.146129\pi$
$37$	1138.99	+	1972.78i	0.831985	+	1.44104i	−0.0644762	+	0.997919i	$0.520538\pi$
$38$		0			0
$39$	946.779	−	1639.87i	0.622471	−	1.07815i
$40$		0			0
$41$		−	781.977i		−	0.465185i	−0.972574	−	0.232593i	$-0.925279\pi$
$41$		−	781.977i		−	0.465185i	0.972574	−	0.232593i	$-0.0747209\pi$
$42$		0			0
$43$	837.131			0.452748			0.226374	−	0.974040i	$-0.427313\pi$
$43$	837.131			0.452748			0.226374	+	0.974040i	$0.427313\pi$
$44$		0			0
$45$	−9.68729	−	5.59296i	−0.00478385	−	0.00276196i
$46$		0			0
$47$	−1296.36	+	748.454i	−0.586854	+	0.338820i	−0.763853	−	0.645391i	$-0.776695\pi$
$47$	−1296.36	+	748.454i	−0.586854	+	0.338820i	0.176999	+	0.984211i	$0.443361\pi$
$48$		0			0
$49$	2336.94	+	550.940i	0.973317	+	0.229463i
$50$		0			0
$51$	844.030	+	1461.90i	0.324502	+	0.562054i
$52$		0			0
$53$	2233.55	−	3868.63i	0.795141	−	1.37723i	−0.127608	−	0.991825i	$-0.540730\pi$
$53$	2233.55	−	3868.63i	0.795141	−	1.37723i	0.922749	−	0.385400i	$-0.125937\pi$
$54$		0			0
$55$			4530.67i			1.49774i
$56$		0			0
$57$	−1599.09			−0.492178
$58$		0			0
$59$	−3815.50	−	2202.88i	−1.09609	−	0.632829i	−0.160900	−	0.986971i	$-0.551440\pi$
$59$	−3815.50	−	2202.88i	−1.09609	−	0.632829i	−0.935192	+	0.354142i	$0.884773\pi$
$60$		0			0
$61$	2257.75	−	1303.51i	0.606758	−	0.350312i	−0.164938	−	0.986304i	$-0.552742\pi$
$61$	2257.75	−	1303.51i	0.606758	−	0.350312i	0.771695	+	0.635992i	$0.219409\pi$
$62$		0			0
$63$	−6.99207	−	16.1831i	−0.00176167	−	0.00407737i
$64$		0			0
$65$	−3263.51	−	5652.56i	−0.772427	−	1.33788i
$66$		0			0
$67$	−2887.15	+	5000.70i	−0.643162	+	1.11399i	0.341561	+	0.939860i	$0.389044\pi$
$67$	−2887.15	+	5000.70i	−0.643162	+	1.11399i	−0.984723	+	0.174129i	$0.944289\pi$
$68$		0			0
$69$			3009.82i			0.632183i
$70$		0			0
$71$	1149.20			0.227971			0.113986	−	0.993482i	$-0.463638\pi$
$71$	1149.20			0.227971			0.113986	+	0.993482i	$0.463638\pi$
$72$		0			0
$73$	−3194.47	−	1844.33i	−0.599450	−	0.346093i	0.169375	−	0.985552i	$-0.445825\pi$
$73$	−3194.47	−	1844.33i	−0.599450	−	0.346093i	−0.768825	+	0.639459i	$0.779158\pi$
$74$		0			0
$75$	−2669.01	+	1540.96i	−0.474491	+	0.273948i
$76$		0			0
$77$	−4260.52	+	5729.95i	−0.718589	+	0.966428i
$78$		0			0
$79$	−1349.16	−	2336.81i	−0.216177	−	0.374429i	0.737459	−	0.675392i	$-0.236025\pi$
$79$	−1349.16	−	2336.81i	−0.216177	−	0.374429i	−0.953636	+	0.300963i	$0.902692\pi$
$80$		0			0
$81$	3295.01	−	5707.12i	0.502211	−	0.869855i
$82$		0			0
$83$		−	2689.70i		−	0.390433i	−0.980760	−	0.195217i	$-0.937459\pi$
$83$		−	2689.70i		−	0.390433i	0.980760	−	0.195217i	$-0.0625410\pi$
$84$		0			0
$85$	5818.67			0.805352
$86$		0			0
$87$	10839.1	+	6257.93i	1.43203	+	0.826784i
$88$		0			0
$89$	5037.61	−	2908.47i	0.635982	−	0.367184i	−0.147083	−	0.989124i	$-0.546988\pi$
$89$	5037.61	−	2908.47i	0.635982	−	0.367184i	0.783065	+	0.621940i	$0.213655\pi$
$90$		0			0
$91$	1188.14	−	10217.7i	0.143478	−	1.23387i
$92$		0			0
$93$	7008.21	+	12138.6i	0.810291	+	1.40347i
$94$		0			0
$95$	−2755.99	+	4773.51i	−0.305373	+	0.528921i
$96$		0			0
$97$		−	7890.42i		−	0.838604i	−0.907847	−	0.419302i	$-0.862275\pi$
$97$		−	7890.42i		−	0.838604i	0.907847	−	0.419302i	$-0.137725\pi$
$98$		0			0
$99$	52.4268			0.00534913
$100$		0			0
$101$	6860.28	+	3960.78i	0.672510	+	0.388274i	0.797027	−	0.603944i	$-0.206405\pi$
$101$	6860.28	+	3960.78i	0.672510	+	0.388274i	−0.124517	+	0.992217i	$0.539738\pi$
$102$		0			0
$103$	−1479.71	+	854.312i	−0.139477	+	0.0805271i	−0.568115	−	0.822949i	$-0.692327\pi$
$103$	−1479.71	+	854.312i	−0.139477	+	0.0805271i	0.428638	+	0.903476i	$0.358994\pi$
$104$		0			0
$105$	−13649.8	−	1587.23i	−1.23807	−	0.143967i
$106$		0			0
$107$	−2674.96	−	4633.17i	−0.233641	−	0.404679i	0.725236	−	0.688501i	$-0.241731\pi$
$107$	−2674.96	−	4633.17i	−0.233641	−	0.404679i	−0.958877	+	0.283822i	$0.908397\pi$
$108$		0			0
$109$	−10512.9	+	18208.9i	−0.884851	+	1.53261i	−0.0389661	+	0.999241i	$0.512406\pi$
$109$	−10512.9	+	18208.9i	−0.884851	+	1.53261i	−0.845885	+	0.533366i	$0.820927\pi$
$110$		0			0
$111$		−	20547.3i		−	1.66766i
$112$		0			0
$113$	−9886.76			−0.774278			−0.387139	−	0.922021i	$-0.626537\pi$
$113$	−9886.76			−0.774278			−0.387139	+	0.922021i	$0.626537\pi$
$114$		0			0
$115$	8984.78	+	5187.36i	0.679378	+	0.392239i
$116$		0			0
$117$	−65.4087	+	37.7637i	−0.00477819	+	0.00275869i
$118$		0			0
$119$	7358.87	+	5471.71i	0.519658	+	0.386393i
$120$		0			0
$121$	−3296.81	−	5710.24i	−0.225177	−	0.390017i
$122$		0			0
$123$	−3526.70	+	6108.43i	−0.233109	+	0.403756i
$124$		0			0
$125$		−	8808.92i		−	0.563771i
$126$		0			0
$127$	−12148.0			−0.753178			−0.376589	−	0.926380i	$-0.622903\pi$
$127$	−12148.0			−0.753178			−0.376589	+	0.926380i	$0.622903\pi$
$128$		0			0
$129$	−6539.27	−	3775.45i	−0.392961	−	0.226876i
$130$		0			0
$131$	4869.90	−	2811.64i	0.283777	−	0.163839i	−0.351355	−	0.936242i	$-0.614279\pi$
$131$	4869.90	−	2811.64i	0.283777	−	0.163839i	0.635132	+	0.772404i	$0.280946\pi$
$132$		0			0
$133$	−7974.38	+	3445.41i	−0.450810	+	0.194777i
$134$		0			0
$135$	−11307.5	−	19585.2i	−0.620440	−	1.07463i
$136$		0			0
$137$	−14897.8	+	25803.8i	−0.793748	+	1.37481i	0.129884	+	0.991529i	$0.458540\pi$
$137$	−14897.8	+	25803.8i	−0.793748	+	1.37481i	−0.923631	+	0.383282i	$0.874794\pi$
$138$		0			0
$139$			15694.4i			0.812298i	0.913807	+	0.406149i	$0.133129\pi$
$139$			15694.4i			0.812298i	−0.913807	+	0.406149i	$0.866871\pi$
$140$		0			0
$141$	13502.1			0.679144
$142$		0			0
$143$	26492.7	+	15295.6i	1.29555	+	0.747987i
$144$		0			0
$145$	37361.7	−	21570.8i	1.77702	−	1.02596i
$146$		0			0
$147$	−15770.3	−	14843.2i	−0.729802	−	0.686900i
$148$		0			0
$149$	13728.4	+	23778.3i	0.618369	+	1.07105i	0.989783	+	0.142580i	$0.0455397\pi$
$149$	13728.4	+	23778.3i	0.618369	+	1.07105i	−0.371414	+	0.928467i	$0.621127\pi$
$150$		0			0
$151$	14971.0	−	25930.6i	0.656596	−	1.13726i	−0.324896	−	0.945750i	$-0.605329\pi$
$151$	14971.0	−	25930.6i	0.656596	−	1.13726i	0.981491	−	0.191507i	$-0.0613375\pi$
$152$		0			0
$153$		−	67.3308i		−	0.00287628i
$154$		0			0
$155$	48314.0			2.01099
$156$		0			0
$157$	−13415.4	−	7745.40i	−0.544258	−	0.314228i	0.202545	−	0.979273i	$-0.435079\pi$
$157$	−13415.4	−	7745.40i	−0.544258	−	0.314228i	−0.746803	+	0.665045i	$0.768412\pi$
$158$		0			0
$159$	−34894.9	+	20146.6i	−1.38028	+	0.796905i
$160$		0			0
$161$	6485.01	+	15009.5i	0.250184	+	0.579048i
$162$		0			0
$163$	−13669.3	−	23675.9i	−0.514482	−	0.891108i	−0.999859	−	0.0168034i	$-0.994651\pi$
$163$	−13669.3	−	23675.9i	−0.514482	−	0.891108i	0.485377	−	0.874305i	$-0.338682\pi$
$164$		0			0
$165$	20433.3	−	35391.5i	0.750533	−	1.29996i
$166$		0			0
$167$			19753.9i			0.708306i	0.935188	+	0.354153i	$0.115231\pi$
$167$			19753.9i			0.708306i	−0.935188	+	0.354153i	$0.884769\pi$
$168$		0			0
$169$	−15509.5			−0.543029
$170$		0			0
$171$	55.2368	+	31.8910i	0.00188902	+	0.00109063i
$172$		0			0
$173$	−19872.6	+	11473.4i	−0.663991	+	0.383355i	−0.793796	−	0.608184i	$-0.791898\pi$
$173$	−19872.6	+	11473.4i	−0.663991	+	0.383355i	0.129805	+	0.991540i	$0.458565\pi$
$174$		0			0
$175$	−9989.77	+	13435.2i	−0.326196	+	0.438700i
$176$		0			0
$177$	19869.9	+	34415.6i	0.634233	+	1.09852i
$178$		0			0
$179$	−7039.56	+	12192.9i	−0.219705	+	0.380540i	−0.954718	−	0.297513i	$-0.903843\pi$
$179$	−7039.56	+	12192.9i	−0.219705	+	0.380540i	0.735013	+	0.678053i	$0.237176\pi$
$180$		0			0
$181$		−	12131.5i		−	0.370304i	−0.982710	−	0.185152i	$-0.940722\pi$
$181$		−	12131.5i		−	0.370304i	0.982710	−	0.185152i	$-0.0592778\pi$
$182$		0			0
$183$	−23515.2			−0.702178
$184$		0			0
$185$	−61336.7	−	35412.8i	−1.79216	−	1.03470i
$186$		0			0
$187$	−23617.6	+	13635.6i	−0.675387	+	0.389935i
$188$		0			0
$189$	4116.72	−	35402.7i	0.115247	−	0.991089i
$190$		0			0
$191$	−15002.6	−	25985.3i	−0.411245	−	0.712298i	0.583781	−	0.811911i	$-0.301573\pi$
$191$	−15002.6	−	25985.3i	−0.411245	−	0.712298i	−0.995026	+	0.0996136i	$0.968239\pi$
$192$		0			0
$193$	9352.36	−	16198.8i	0.251077	−	0.434878i	−0.712746	−	0.701422i	$-0.752549\pi$
$193$	9352.36	−	16198.8i	0.251077	−	0.434878i	0.963823	+	0.266545i	$0.0858820\pi$
$194$		0			0
$195$			58873.4i			1.54828i
$196$		0			0
$197$	−10271.9			−0.264678			−0.132339	−	0.991205i	$-0.542249\pi$
$197$	−10271.9			−0.264678			−0.132339	+	0.991205i	$0.542249\pi$
$198$		0			0
$199$	6225.42	+	3594.25i	0.157204	+	0.0907616i	0.576538	−	0.817070i	$-0.304403\pi$
$199$	6225.42	+	3594.25i	0.157204	+	0.0907616i	−0.419335	+	0.907832i	$0.637737\pi$
$200$		0			0
$201$	45106.1	−	26042.0i	1.11646	−	0.644589i
$202$		0			0
$203$	67536.0	+	7853.28i	1.63887	+	0.190572i
$204$		0			0
$205$	12156.4	+	21055.5i	0.289266	+	0.501023i
$206$		0			0
$207$	60.0257	−	103.968i	0.00140087	−	0.00242637i
$208$		0			0
$209$		−	25833.8i		−	0.591421i
$210$		0			0
$211$	−62160.8			−1.39621			−0.698107	−	0.715993i	$-0.745974\pi$
$211$	−62160.8			−1.39621			−0.698107	+	0.715993i	$0.745974\pi$
$212$		0			0
$213$	−8977.02	−	5182.89i	−0.197867	−	0.114238i
$214$		0			0
$215$	−22540.6	+	13013.8i	−0.487627	+	0.281532i
$216$		0			0
$217$	61102.7	+	45433.1i	1.29760	+	0.964834i
$218$		0			0
$219$	16635.8	+	28814.0i	0.346860	+	0.600780i
$220$		0			0
$221$	19643.9	−	34024.1i	0.402200	−	0.696631i
$222$		0			0
$223$			7060.74i			0.141984i	0.997477	+	0.0709921i	$0.0226165\pi$
$223$			7060.74i			0.141984i	−0.997477	+	0.0709921i	$0.977383\pi$
$224$		0			0
$225$	122.927			0.00242818
$226$		0			0
$227$	−33869.7	−	19554.7i	−0.657294	−	0.379489i	0.133951	−	0.990988i	$-0.457234\pi$
$227$	−33869.7	−	19554.7i	−0.657294	−	0.379489i	−0.791245	+	0.611499i	$0.790567\pi$
$228$		0			0
$229$	313.976	−	181.274i	0.00598723	−	0.00345673i	−0.497003	−	0.867749i	$-0.665566\pi$
$229$	313.976	−	181.274i	0.00598723	−	0.00345673i	0.502991	+	0.864292i	$0.332233\pi$
$230$		0			0
$231$	59123.1	−	25544.8i	1.10798	−	0.478716i
$232$		0			0
$233$	−3438.16	−	5955.07i	−0.0633307	−	0.109692i	0.832622	−	0.553842i	$-0.186839\pi$
$233$	−3438.16	−	5955.07i	−0.0633307	−	0.109692i	−0.895952	+	0.444150i	$0.853506\pi$
$234$		0			0
$235$	23270.5	−	40305.7i	0.421376	−	0.729845i
$236$		0			0
$237$			24338.7i			0.433313i
$238$		0			0
$239$	90119.7			1.57770			0.788849	−	0.614587i	$-0.210677\pi$
$239$	90119.7			1.57770			0.788849	+	0.614587i	$0.210677\pi$
$240$		0			0
$241$	37564.8	+	21688.1i	0.646766	+	0.373411i	0.787216	−	0.616677i	$-0.211522\pi$
$241$	37564.8	+	21688.1i	0.646766	+	0.373411i	−0.140450	+	0.990088i	$0.544855\pi$
$242$		0			0
$243$	−454.272	+	262.274i	−0.00769314	+	0.00444164i
$244$		0			0
$245$	−71489.0	+	21494.7i	−1.19099	+	0.358096i
$246$		0			0
$247$	18608.5	+	32230.8i	0.305012	+	0.528296i
$248$		0			0
$249$	−12130.5	+	21010.6i	−0.195650	+	0.338875i
$250$		0			0
$251$		−	57720.4i		−	0.916183i	−0.888905	−	0.458091i	$-0.848533\pi$
$251$		−	57720.4i		−	0.916183i	0.888905	−	0.458091i	$-0.151467\pi$
$252$		0			0
$253$	−48624.9			−0.759657
$254$		0			0
$255$	−45452.6	−	26242.1i	−0.699002	−	0.403569i
$256$		0			0
$257$	−58712.4	+	33897.6i	−0.888921	+	0.513219i	−0.873589	−	0.486664i	$-0.838214\pi$
$257$	−58712.4	+	33897.6i	−0.888921	+	0.513219i	−0.0153317	+	0.999882i	$0.504880\pi$
$258$		0			0
$259$	−44271.5	−	102466.i	−0.659970	−	1.52749i
$260$		0			0
$261$	−249.607	−	432.332i	−0.00366417	−	0.00634653i
$262$		0			0
$263$	3383.74	−	5860.80i	0.0489198	−	0.0847317i	−0.840529	−	0.541767i	$-0.817755\pi$
$263$	3383.74	−	5860.80i	0.0489198	−	0.0847317i	0.889448	+	0.457036i	$0.151089\pi$
$264$		0			0
$265$			138889.i			1.97777i
$266$		0			0
$267$	−52468.5			−0.735998
$268$		0			0
$269$	−72784.4	−	42022.1i	−1.00585	−	0.580728i	−0.0958768	−	0.995393i	$-0.530565\pi$
$269$	−72784.4	−	42022.1i	−1.00585	−	0.580728i	−0.909974	+	0.414665i	$0.863899\pi$
$270$		0			0
$271$	−33737.9	+	19478.6i	−0.459388	+	0.265228i	−0.711787	−	0.702396i	$-0.752114\pi$
$271$	−33737.9	+	19478.6i	−0.459388	+	0.265228i	0.252399	+	0.967623i	$0.418780\pi$
$272$		0			0
$273$	−55362.9	+	74457.3i	−0.742837	+	0.999038i
$274$		0			0
$275$	−24894.7	−	43119.0i	−0.329187	−	0.570168i
$276$		0			0
$277$	35691.1	−	61818.9i	0.465158	−	0.805678i	−0.534050	−	0.845453i	$-0.679331\pi$
$277$	35691.1	−	61818.9i	0.465158	−	0.805678i	0.999209	+	0.0397747i	$0.0126640\pi$
$278$		0			0
$279$		−	559.066i		−	0.00718216i
$280$		0			0
$281$	57835.9			0.732462			0.366231	−	0.930524i	$-0.380648\pi$
$281$	57835.9			0.732462			0.366231	+	0.930524i	$0.380648\pi$
$282$		0			0
$283$	87465.4	+	50498.2i	1.09210	+	0.630526i	0.934135	−	0.356919i	$-0.116173\pi$
$283$	87465.4	+	50498.2i	1.09210	+	0.630526i	0.157967	+	0.987444i	$0.449506\pi$
$284$		0			0
$285$	43056.9	−	24858.9i	0.530094	−	0.306050i
$286$		0			0
$287$	−4425.77	+	38060.4i	−0.0537310	+	0.462072i
$288$		0			0
$289$	−24248.5	−	41999.6i	−0.290328	−	0.502863i
$290$		0			0
$291$	−35585.7	+	61636.2i	−0.420232	+	0.727863i
$292$		0			0
$293$		−	133132.i		−	1.55077i	−0.631487	−	0.775387i	$-0.717555\pi$
$293$		−	133132.i		−	1.55077i	0.631487	−	0.775387i	$-0.282445\pi$
$294$		0			0
$295$	136981.			1.57404
$296$		0			0
$297$	91793.0	+	52996.7i	1.04063	+	0.600808i
$298$		0			0
$299$	60665.3	−	35025.1i	0.678575	−	0.391776i
$300$		0			0
$301$	−40744.9	−	4737.93i	−0.449718	−	0.0522945i
$302$		0			0
$303$	−35726.1	−	61879.5i	−0.389135	−	0.674002i
$304$		0			0
$305$	−40528.0	+	70196.5i	−0.435668	+	0.754599i
$306$		0			0
$307$			7667.32i			0.0813517i	0.999172	+	0.0406758i	$0.0129511\pi$
$307$			7667.32i			0.0813517i	−0.999172	+	0.0406758i	$0.987049\pi$
$308$		0			0
$309$	15411.7			0.161411
$310$		0			0
$311$	−1424.80	−	822.609i	−0.0147310	−	0.00850497i	0.492616	−	0.870247i	$-0.336041\pi$
$311$	−1424.80	−	822.609i	−0.0147310	−	0.00850497i	−0.507347	+	0.861742i	$0.669374\pi$
$312$		0			0
$313$	97074.6	−	56046.0i	0.990871	−	0.572079i	0.0853362	−	0.996352i	$-0.472804\pi$
$313$	97074.6	−	56046.0i	0.990871	−	0.572079i	0.905534	+	0.424273i	$0.139470\pi$
$314$		0			0
$315$	439.846	+	327.048i	0.00443281	+	0.00329603i
$316$		0			0
$317$	−1681.22	−	2911.96i	−0.0167304	−	0.0289779i	0.857539	−	0.514419i	$-0.171992\pi$
$317$	−1681.22	−	2911.96i	−0.0167304	−	0.0289779i	−0.874269	+	0.485441i	$0.838659\pi$
$318$		0			0
$319$	−101099.	+	175109.i	−0.993498	+	1.72079i
$320$		0			0
$321$			48256.1i			0.468319i
$322$		0			0
$323$	−33178.0			−0.318013
$324$		0			0
$325$	62118.3	+	35864.0i	0.588103	+	0.339541i
$326$		0			0
$327$	164244.	−	94826.1i	1.53601	−	0.886814i
$328$		0			0
$329$	67332.5	−	29091.7i	0.622061	−	0.268768i
$330$		0			0
$331$	43484.9	+	75318.1i	0.396902	+	0.687454i	0.993342	−	0.115204i	$-0.0367520\pi$
$331$	43484.9	+	75318.1i	0.396902	+	0.687454i	−0.596440	+	0.802658i	$0.703419\pi$
$332$		0			0
$333$	−409.780	+	709.759i	−0.00369540	+	0.00640063i
$334$		0			0
$335$		−	179531.i		−	1.59975i
$336$		0			0
$337$	−112228.			−0.988195			−0.494098	−	0.869406i	$-0.664502\pi$
$337$	−112228.			−0.988195			−0.494098	+	0.869406i	$0.664502\pi$
$338$		0			0
$339$	77230.6	+	44589.1i	0.672032	+	0.387998i
$340$		0			0
$341$	−196103.	+	113220.i	−1.68646	+	0.973678i
$342$		0			0
$343$	−110625.	−	40041.8i	−0.940299	−	0.340350i
$344$		0			0
$345$	−46789.8	−	81042.4i	−0.393109	−	0.680885i
$346$		0			0
$347$	17145.7	−	29697.3i	0.142396	−	0.246637i	−0.786003	−	0.618223i	$-0.787853\pi$
$347$	17145.7	−	29697.3i	0.142396	−	0.246637i	0.928398	+	0.371587i	$0.121186\pi$
$348$		0			0
$349$		−	133358.i		−	1.09488i	−0.836844	−	0.547441i	$-0.815602\pi$
$349$		−	133358.i		−	1.09488i	0.836844	−	0.547441i	$-0.184398\pi$
$350$		0			0
$351$	−152697.			−1.23941
$352$		0			0
$353$	131657.	+	76012.1i	1.05656	+	0.610005i	0.924479	−	0.381234i	$-0.124501\pi$
$353$	131657.	+	76012.1i	1.05656	+	0.610005i	0.132081	+	0.991239i	$0.457834\pi$
$354$		0			0
$355$	−30943.4	+	17865.2i	−0.245534	+	0.141759i
$356$		0			0
$357$	−32806.7	−	75930.7i	−0.257410	−	0.595773i
$358$		0			0
$359$	40660.5	+	70426.0i	0.315488	+	0.546442i	0.979541	−	0.201244i	$-0.0644983\pi$
$359$	40660.5	+	70426.0i	0.315488	+	0.546442i	−0.664053	+	0.747686i	$0.731165\pi$
$360$		0			0
$361$	−49445.9	+	85642.8i	−0.379416	+	0.657168i
$362$		0			0
$363$			59474.2i			0.451352i
$364$		0			0
$365$	114686.			0.860841
$366$		0			0
$367$	−175518.	−	101336.i	−1.30314	−	0.752368i	−0.322198	−	0.946672i	$-0.604422\pi$
$367$	−175518.	−	101336.i	−1.30314	−	0.752368i	−0.980941	+	0.194305i	$0.937755\pi$
$368$		0			0
$369$	243.644	−	140.668i	0.00178938	−	0.00103310i
$370$		0			0
$371$	−130607.	+	175653.i	−0.948895	+	1.27616i
$372$		0			0
$373$	38371.1	+	66460.8i	0.275795	+	0.477692i	0.970335	−	0.241762i	$-0.0777254\pi$
$373$	38371.1	+	66460.8i	0.275795	+	0.477692i	−0.694540	+	0.719454i	$0.744392\pi$
$374$		0			0
$375$	−39728.1	+	68811.1i	−0.282511	+	0.489323i
$376$		0			0
$377$		−	291293.i		−	2.04950i
$378$		0			0
$379$	13185.2			0.0917926			0.0458963	−	0.998946i	$-0.485386\pi$
$379$	13185.2			0.0917926			0.0458963	+	0.998946i	$0.485386\pi$
$380$		0			0
$381$	94894.4	+	54787.3i	0.653718	+	0.377424i
$382$		0			0
$383$	−228538.	+	131947.i	−1.55798	+	0.899499i	−0.560528	+	0.828135i	$0.689402\pi$
$383$	−228538.	+	131947.i	−1.55798	+	0.899499i	−0.997450	+	0.0713639i	$0.977265\pi$
$384$		0			0
$385$	25642.4	−	220517.i	0.172996	−	1.48772i
$386$		0			0
$387$	150.590	+	260.829i	0.00100548	+	0.00174154i
$388$		0			0
$389$	−50770.5	+	87937.0i	−0.335515	+	0.581129i	−0.983584	−	0.180453i	$-0.942244\pi$
$389$	−50770.5	+	87937.0i	−0.335515	+	0.581129i	0.648069	+	0.761582i	$0.275577\pi$
$390$		0			0
$391$			62448.1i			0.408475i
$392$		0			0
$393$	−50721.7			−0.328405
$394$		0			0
$395$	72654.8	+	41947.3i	0.465661	+	0.268850i
$396$		0			0
$397$	186579.	−	107722.i	1.18381	−	0.683473i	0.226917	−	0.973914i	$-0.427135\pi$
$397$	186579.	−	107722.i	1.18381	−	0.683473i	0.956893	+	0.290441i	$0.0938019\pi$
$398$		0			0
$399$	77830.8	+	9050.38i	0.488884	+	0.0568488i
$400$		0			0
$401$	−1625.64	−	2815.69i	−0.0101096	−	0.0175104i	0.860926	−	0.508730i	$-0.169885\pi$
$401$	−1625.64	−	2815.69i	−0.0101096	−	0.0175104i	−0.871036	+	0.491219i	$0.836551\pi$
$402$		0			0
$403$	163108.	−	282512.i	1.00431	−	1.73951i
$404$		0			0
$405$			204893.i			1.24916i
$406$		0			0
$407$	331949.			2.00393
$408$		0			0
$409$	−128989.	−	74472.0i	−0.771094	−	0.445191i	0.0621707	−	0.998066i	$-0.480198\pi$
$409$	−128989.	−	74472.0i	−0.771094	−	0.445191i	−0.833265	+	0.552874i	$0.813531\pi$
$410$		0			0
$411$	232750.	−	134378.i	1.37786	−	0.795508i
$412$		0			0
$413$	173240.	+	128813.i	1.01566	+	0.755197i
$414$		0			0
$415$	41813.2	+	72422.6i	0.242783	+	0.420512i
$416$		0			0
$417$	70781.5	−	122597.i	0.407050	−	0.705031i
$418$		0			0
$419$			286696.i			1.63303i	0.577324	+	0.816515i	$0.304097\pi$
$419$			286696.i			1.63303i	−0.577324	+	0.816515i	$0.695903\pi$
$420$		0			0
$421$	−5357.63			−0.0302280			−0.0151140	−	0.999886i	$-0.504811\pi$
$421$	−5357.63			−0.0302280			−0.0151140	+	0.999886i	$0.504811\pi$
$422$		0			0
$423$	−466.398	−	269.275i	−0.00260661	−	0.00150493i
$424$		0			0
$425$	−55376.9	+	31971.9i	−0.306585	+	0.177007i
$426$		0			0
$427$	−117267.	+	50666.3i	−0.643159	+	0.277884i
$428$		0			0
$429$	−137966.	−	238964.i	−0.749646	−	1.29843i
$430$		0			0
$431$	27144.6	−	47015.8i	0.146126	−	0.253098i	−0.783666	−	0.621182i	$-0.786653\pi$
$431$	27144.6	−	47015.8i	0.146126	−	0.253098i	0.929793	+	0.368084i	$0.119986\pi$
$432$		0			0
$433$			206336.i			1.10052i	0.834992	+	0.550262i	$0.185472\pi$
$433$			206336.i			1.10052i	−0.834992	+	0.550262i	$0.814528\pi$
$434$		0			0
$435$	−389136.			−2.05647
$436$		0			0
$437$	−51231.1	−	29578.3i	−0.268269	−	0.154885i
$438$		0			0
$439$	63763.3	−	36813.8i	0.330858	−	0.191021i	−0.325364	−	0.945589i	$-0.605487\pi$
$439$	63763.3	−	36813.8i	0.330858	−	0.191021i	0.656222	+	0.754568i	$0.272153\pi$
$440$		0			0
$441$	248.727	+	827.236i	0.00127893	+	0.00425356i
$442$		0			0
$443$	−72316.4	−	125256.i	−0.368493	−	0.638249i	0.620837	−	0.783940i	$-0.286793\pi$
$443$	−72316.4	−	125256.i	−0.368493	−	0.638249i	−0.989330	+	0.145691i	$0.953460\pi$
$444$		0			0
$445$	−90428.4	+	156627.i	−0.456651	+	0.790943i
$446$		0			0
$447$		−	247660.i		−	1.23948i
$448$		0			0
$449$	305112.			1.51345			0.756723	−	0.653735i	$-0.226799\pi$
$449$	305112.			1.51345			0.756723	+	0.653735i	$0.226799\pi$
$450$		0			0
$451$	−98684.0	−	56975.2i	−0.485170	−	0.280113i
$452$		0			0
$453$	−233893.	+	135038.i	−1.13978	+	0.658052i
$454$		0			0
$455$	126850.	+	293592.i	0.612726	+	1.41815i
$456$		0			0
$457$	−17887.3	−	30981.7i	−0.0856470	−	0.148345i	0.820020	−	0.572335i	$-0.193962\pi$
$457$	−17887.3	−	30981.7i	−0.0856470	−	0.148345i	−0.905667	+	0.423990i	$0.860629\pi$
$458$		0			0
$459$	68062.7	−	117888.i	0.323061	−	0.559557i
$460$		0			0
$461$			332913.i			1.56649i	0.621710	+	0.783247i	$0.286438\pi$
$461$			332913.i			1.56649i	−0.621710	+	0.783247i	$0.713562\pi$
$462$		0			0
$463$	−45033.5			−0.210075			−0.105037	−	0.994468i	$-0.533496\pi$
$463$	−45033.5			−0.210075			−0.105037	+	0.994468i	$0.533496\pi$
$464$		0			0
$465$	−377405.	−	217895.i	−1.74543	−	1.00772i
$466$		0			0
$467$	94249.4	−	54414.9i	0.432160	−	0.249508i	−0.268106	−	0.963389i	$-0.586398\pi$
$467$	94249.4	−	54414.9i	0.432160	−	0.249508i	0.700266	+	0.713882i	$0.253065\pi$
$468$		0			0
$469$	168826.	−	227054.i	0.767528	−	1.03224i
$470$		0			0
$471$	69863.2	+	121007.i	0.314925	+	0.545466i
$472$		0			0
$473$	60993.8	−	105644.i	0.272624	−	0.472198i
$474$		0			0
$475$		−	60573.4i		−	0.268470i
$476$		0			0
$477$	1607.15			0.00706351
$478$		0			0
$479$	−330760.	−	190965.i	−1.44159	−	0.832304i	−0.443636	−	0.896207i	$-0.646312\pi$
$479$	−330760.	−	190965.i	−1.44159	−	0.832304i	−0.997956	+	0.0639035i	$0.979645\pi$
$480$		0			0
$481$	−414146.	+	239107.i	−1.79004	+	1.03348i
$482$		0			0
$483$	17034.8	−	146494.i	0.0730200	−	0.627952i
$484$		0			0
$485$	122662.	+	212457.i	0.521468	+	0.903209i
$486$		0			0
$487$	135129.	−	234050.i	0.569756	−	0.986847i	−0.426833	−	0.904330i	$-0.640371\pi$
$487$	135129.	−	234050.i	0.569756	−	0.986847i	0.996590	−	0.0825166i	$-0.0262958\pi$
$488$		0			0
$489$			246593.i			1.03125i
$490$		0			0
$491$	−240609.			−0.998040			−0.499020	−	0.866590i	$-0.666307\pi$
$491$	−240609.			−0.998040			−0.499020	+	0.866590i	$0.666307\pi$
$492$		0			0
$493$	224890.	+	129840.i	0.925285	+	0.534214i
$494$		0			0
$495$	−1411.64	+	815.012i	−0.00576122	+	0.00332624i
$496$		0			0
$497$	−55934.1	−	6504.17i	−0.226445	−	0.0263317i
$498$		0			0
$499$	93314.5	+	161626.i	0.374756	+	0.649096i	0.990290	−	0.139014i	$-0.0443933\pi$
$499$	93314.5	+	161626.i	0.374756	+	0.649096i	−0.615535	+	0.788110i	$0.711060\pi$
$500$		0			0
$501$	89089.9	−	154308.i	0.354938	−	0.614772i
$502$		0			0
$503$		−	349740.i		−	1.38232i	−0.722700	−	0.691162i	$-0.757099\pi$
$503$		−	349740.i		−	1.38232i	0.722700	−	0.691162i	$-0.242901\pi$
$504$		0			0
$505$	−246293.			−0.965759
$506$		0			0
$507$	121152.	+	69947.4i	0.471320	+	0.272117i
$508$		0			0
$509$	−109504.	+	63222.4i	−0.422665	+	0.244025i	−0.696217	−	0.717832i	$-0.745135\pi$
$509$	−109504.	+	63222.4i	−0.422665	+	0.244025i	0.273552	+	0.961857i	$0.411801\pi$
$510$		0			0
$511$	145043.	+	107847.i	0.555463	+	0.413015i
$512$		0			0
$513$	64475.3	+	111675.i	0.244996	+	0.424345i
$514$		0			0
$515$	26561.8	−	46006.3i	0.100148	−	0.173462i
$516$		0			0
$517$			218131.i			0.816087i
$518$		0			0
$519$	206980.			0.768411
$520$		0			0
$521$	127740.	+	73751.0i	0.470601	+	0.271702i	0.716491	−	0.697596i	$-0.245747\pi$
$521$	127740.	+	73751.0i	0.470601	+	0.271702i	−0.245890	+	0.969298i	$0.579080\pi$
$522$		0			0
$523$	222222.	−	128300.i	0.812426	−	0.469054i	−0.0353716	−	0.999374i	$-0.511261\pi$
$523$	222222.	−	128300.i	0.812426	−	0.469054i	0.847798	+	0.530320i	$0.177928\pi$
$524$		0			0
$525$	138628.	−	59895.6i	0.502958	−	0.217308i
$526$		0			0
$527$	145407.	+	251852.i	0.523557	+	0.906827i
$528$		0			0
$529$	84247.8	−	145921.i	0.301056	−	0.521444i
$530$		0			0
$531$		−	1585.08i		−	0.00562163i
$532$		0			0
$533$	164160.			0.577847
$534$		0			0
$535$	144052.	+	83168.3i	0.503281	+	0.290570i
$536$		0			0
$537$	109979.	−	63496.6i	0.381384	−	0.220192i
$538$		0			0
$539$	239798.	−	254775.i	0.825407	−	0.876959i
$540$		0			0
$541$	−198343.	−	343541.i	−0.677678	−	1.17377i	−0.975678	−	0.219207i	$-0.929653\pi$
$541$	−198343.	−	343541.i	−0.677678	−	1.17377i	0.298001	−	0.954566i	$-0.403680\pi$
$542$		0			0
$543$	−54713.1	+	94765.8i	−0.185563	+	0.321405i
$544$		0			0
$545$		−	653723.i		−	2.20090i
$546$		0			0
$547$	−266914.			−0.892065			−0.446032	−	0.895017i	$-0.647163\pi$
$547$	−266914.			−0.892065			−0.446032	+	0.895017i	$0.647163\pi$
$548$		0			0
$549$	812.281	+	468.971i	0.00269502	+	0.00155597i
$550$		0			0
$551$	−213036.	+	122997.i	−0.701698	+	0.405125i
$552$		0			0
$553$	52440.6	+	121373.i	0.171482	+	0.396892i
$554$		0			0
$555$	319422.	+	553255.i	1.03700	+	1.79614i
$556$		0			0
$557$	−205639.	+	356177.i	−0.662819	+	1.14804i	0.317052	+	0.948408i	$0.397307\pi$
$557$	−205639.	+	356177.i	−0.662819	+	1.14804i	−0.979872	+	0.199629i	$0.936026\pi$
$558$		0			0
$559$			175739.i			0.562398i
$560$		0			0
$561$	245986.			0.781599
$562$		0			0
$563$	−490992.	−	283475.i	−1.54902	−	0.894329i	−0.998217	−	0.0596957i	$-0.980987\pi$
$563$	−490992.	−	283475.i	−1.54902	−	0.894329i	−0.550806	−	0.834633i	$-0.685680\pi$
$564$		0			0
$565$	266211.	−	153697.i	0.833928	−	0.481468i
$566$		0			0
$567$	−192675.	+	259128.i	−0.599322	+	0.806025i
$568$		0			0
$569$	−298656.	−	517288.i	−0.922459	−	1.59775i	−0.795597	−	0.605826i	$-0.792843\pi$
$569$	−298656.	−	517288.i	−0.922459	−	1.59775i	−0.126863	−	0.991920i	$-0.540491\pi$
$570$		0			0
$571$	−124106.	+	214958.i	−0.380645	+	0.659296i	−0.991155	−	0.132713i	$-0.957631\pi$
$571$	−124106.	+	214958.i	−0.380645	+	0.659296i	0.610510	+	0.792009i	$0.290965\pi$
$572$		0			0
$573$			270647.i			0.824315i
$574$		0			0
$575$	−114012.			−0.344839
$576$		0			0
$577$	52929.2	+	30558.7i	0.158980	+	0.0917873i	0.577379	−	0.816476i	$-0.304075\pi$
$577$	52929.2	+	30558.7i	0.158980	+	0.0917873i	−0.418399	+	0.908263i	$0.637409\pi$
$578$		0			0
$579$	−146112.	+	84357.9i	−0.435842	+	0.251634i
$580$		0			0
$581$	−15222.9	+	130913.i	−0.0450968	+	0.387820i
$582$		0			0
$583$	−325475.	−	563740.i	−0.957593	−	1.65860i
$584$		0			0
$585$	1174.13	−	2033.65i	0.00343087	−	0.00594244i
$586$		0			0
$587$			199552.i			0.579136i	0.957157	+	0.289568i	$0.0935117\pi$
$587$			199552.i			0.579136i	−0.957157	+	0.289568i	$0.906488\pi$
$588$		0			0
$589$	−275486.			−0.794087
$590$		0			0
$591$	80239.1	+	46326.0i	0.229726	+	0.132633i
$592$		0			0
$593$	135567.	−	78269.4i	0.385517	−	0.222578i	−0.294699	−	0.955590i	$-0.595219\pi$
$593$	135567.	−	78269.4i	0.385517	−	0.222578i	0.680216	+	0.733012i	$0.261886\pi$
$594$		0			0
$595$	−283206.	−	32932.0i	−0.799961	−	0.0930218i
$596$		0			0
$597$	−32420.0	−	56153.1i	−0.0909629	−	0.157552i
$598$		0			0
$599$	−146312.	+	253420.i	−0.407781	+	0.706297i	−0.994641	−	0.103392i	$-0.967031\pi$
$599$	−146312.	+	253420.i	−0.407781	+	0.706297i	0.586860	+	0.809688i	$0.300364\pi$
$600$		0			0
$601$		−	71047.1i		−	0.196697i	−0.995152	−	0.0983485i	$-0.968644\pi$
$601$		−	71047.1i		−	0.196697i	0.995152	−	0.0983485i	$-0.0313560\pi$
$602$		0			0
$603$	−2077.45			−0.00571342
$604$		0			0
$605$	177540.	+	102503.i	0.485048	+	0.280043i
$606$		0			0
$607$	138904.	−	80196.3i	0.376997	−	0.217659i	−0.299514	−	0.954092i	$-0.596825\pi$
$607$	138904.	−	80196.3i	0.376997	−	0.217659i	0.676511	+	0.736433i	$0.263491\pi$
$608$		0			0
$609$	−492141.	−	365932.i	−1.32695	−	0.986657i
$610$		0			0
$611$	−157123.	−	272144.i	−0.420878	−	0.728982i
$612$		0			0
$613$	33763.5	−	58480.1i	0.0898517	−	0.155628i	−0.817597	−	0.575791i	$-0.804694\pi$
$613$	33763.5	−	58480.1i	0.0898517	−	0.155628i	0.907448	+	0.420164i	$0.138027\pi$
$614$		0			0
$615$		−	219300.i		−	0.579815i
$616$		0			0
$617$	−18373.7			−0.0482644			−0.0241322	−	0.999709i	$-0.507682\pi$
$617$	−18373.7			−0.0482644			−0.0241322	+	0.999709i	$0.507682\pi$
$618$		0			0
$619$	511947.	+	295573.i	1.33612	+	0.771407i	0.986229	−	0.165385i	$-0.0528868\pi$
$619$	511947.	+	295573.i	1.33612	+	0.771407i	0.349887	+	0.936792i	$0.386220\pi$
$620$		0			0
$621$	210195.	−	121356.i	0.545055	−	0.314687i
$622$		0			0
$623$	−261652.	+	113050.i	−0.674137	+	0.291268i
$624$		0			0
$625$	243715.	+	422127.i	0.623910	+	1.08064i
$626$		0			0
$627$	−116510.	+	201802.i	−0.296366	+	0.513322i
$628$		0			0
$629$		−	426316.i		−	1.07753i
$630$		0			0
$631$	729341.			1.83177			0.915887	−	0.401436i	$-0.131489\pi$
$631$	729341.			1.83177			0.915887	+	0.401436i	$0.131489\pi$
$632$		0			0
$633$	485571.	+	280344.i	1.21184	+	0.699656i
$634$		0			0
$635$	327097.	−	188849.i	0.811202	−	0.468348i
$636$		0			0
$637$	−115659.	+	490592.i	−0.285036	+	1.20904i
$638$		0			0
$639$	206.727	+	358.062i	0.000506286	+	0.000876914i
$640$		0			0
$641$	116758.	−	202231.i	0.284165	−	0.492188i	−0.688242	−	0.725482i	$-0.741617\pi$
$641$	116758.	−	202231.i	0.284165	−	0.492188i	0.972406	+	0.233294i	$0.0749504\pi$
$642$		0			0
$643$			382516.i			0.925184i	0.886571	+	0.462592i	$0.153080\pi$
$643$			382516.i			0.925184i	−0.886571	+	0.462592i	$0.846920\pi$
$644$		0			0
$645$	234768.			0.564313
$646$		0			0
$647$	−436213.	−	251848.i	−1.04205	−	0.601631i	−0.121640	−	0.992574i	$-0.538815\pi$
$647$	−436213.	−	251848.i	−1.04205	−	0.601631i	−0.920415	+	0.390944i	$0.872149\pi$
$648$		0			0
$649$	−555998.	+	321006.i	−1.32003	+	0.762120i
$650$		0			0
$651$	−272403.	−	630474.i	−0.642761	−	1.48766i
$652$		0			0
$653$	−120715.	−	209084.i	−0.283096	−	0.490337i	0.689049	−	0.724714i	$-0.258028\pi$
$653$	−120715.	−	209084.i	−0.283096	−	0.490337i	−0.972146	+	0.234377i	$0.924695\pi$
$654$		0			0
$655$	−87417.8	+	151412.i	−0.203759	+	0.352921i
$656$		0			0
$657$		−	1327.09i		−	0.00307446i
$658$		0			0
$659$	652340.			1.50211			0.751057	−	0.660237i	$-0.229544\pi$
$659$	652340.			1.50211			0.751057	+	0.660237i	$0.229544\pi$
$660$		0			0
$661$	−13430.3	−	7753.99i	−0.0307385	−	0.0177469i	0.484552	−	0.874762i	$-0.338983\pi$
$661$	−13430.3	−	7753.99i	−0.0307385	−	0.0177469i	−0.515291	+	0.857016i	$0.672316\pi$
$662$		0			0
$663$	−306897.	+	177187.i	−0.698176	+	0.403092i
$664$		0			0
$665$	161156.	−	216738.i	0.364422	−	0.490109i
$666$		0			0
$667$	231506.	+	400980.i	0.520368	+	0.901303i
$668$		0			0
$669$	31843.8	−	55155.1i	0.0711496	−	0.123235i
$670$		0			0
$671$		−	379898.i		−	0.843765i
$672$		0			0
$673$	62603.2			0.138219			0.0691093	−	0.997609i	$-0.477984\pi$
$673$	62603.2			0.138219			0.0691093	+	0.997609i	$0.477984\pi$
$674$		0			0
$675$	215230.	+	124263.i	0.472384	+	0.272731i
$676$		0			0
$677$	340591.	−	196640.i	0.743115	−	0.429038i	−0.0800858	−	0.996788i	$-0.525519\pi$
$677$	340591.	−	196640.i	0.743115	−	0.429038i	0.823201	+	0.567750i	$0.192186\pi$
$678$		0			0
$679$	−44657.6	+	384043.i	−0.0968626	+	0.832991i
$680$		0			0
$681$	176383.	+	305504.i	0.380331	+	0.658752i
$682$		0			0
$683$	−220205.	+	381407.i	−0.472048	+	0.817611i	−0.999488	−	0.0319809i	$-0.989818\pi$
$683$	−220205.	+	381407.i	−0.472048	+	0.817611i	0.527440	+	0.849592i	$0.323152\pi$
$684$		0			0
$685$		−	926391.i		−	1.97430i
$686$		0			0
$687$	−3270.17			−0.00692879
$688$		0			0
$689$	812139.	+	468889.i	1.71077	+	0.987714i
$690$		0			0
$691$	808775.	−	466947.i	1.69384	−	0.977938i	0.742470	−	0.669879i	$-0.233654\pi$
$691$	808775.	−	466947.i	1.69384	−	0.977938i	0.951367	−	0.308059i	$-0.0996794\pi$
$692$		0			0
$693$	−2551.72	−	296.721i	−0.00531333	−	0.000617849i
$694$		0			0
$695$	−243981.	−	422587.i	−0.505110	−	0.874876i
$696$		0			0
$697$	−73172.3	+	126738.i	−0.150619	+	0.260881i
$698$		0			0
$699$			62024.1i			0.126942i
$700$		0			0
$701$	−903363.			−1.83834			−0.919171	−	0.393860i	$-0.871140\pi$
$701$	−903363.			−1.83834			−0.919171	+	0.393860i	$0.871140\pi$
$702$		0			0
$703$	349741.	+	201923.i	0.707678	+	0.408578i
$704$		0			0
$705$	−363556.	+	209899.i	−0.731464	+	0.422311i
$706$		0			0
$707$	−311487.	−	231607.i	−0.623162	−	0.463353i
$708$		0			0
$709$	−88591.0	−	153444.i	−0.176237	−	0.305251i	0.764352	−	0.644800i	$-0.223059\pi$
$709$	−88591.0	−	153444.i	−0.176237	−	0.305251i	−0.940589	+	0.339548i	$0.889726\pi$
$710$		0			0
$711$	485.394	−	840.727i	0.000960185	−	0.00166309i
$712$		0			0
$713$			518523.i			1.01997i
$714$		0			0
$715$	−951123.			−1.86048
$716$		0			0
$717$	−703972.	−	406438.i	−1.36936	−	0.790599i
$718$		0			0
$719$	−580300.	+	335036.i	−1.12252	+	0.648088i	−0.942043	−	0.335491i	$-0.891098\pi$
$719$	−580300.	+	335036.i	−1.12252	+	0.648088i	−0.180478	+	0.983579i	$0.557764\pi$
$720$		0			0
$721$	76855.7	−	33206.3i	0.147845	−	0.0638779i
$722$		0			0
$723$	−195626.	−	338834.i	−0.374239	−	0.648201i
$724$		0			0
$725$	−237051.	+	410584.i	−0.450988	+	0.781135i
$726$		0			0
$727$		−	465279.i		−	0.880329i	−0.897917	−	0.440164i	$-0.854920\pi$
$727$		−	465279.i		−	0.880329i	0.897917	−	0.440164i	$-0.145080\pi$
$728$		0			0
$729$	−529060.			−0.995519
$730$		0			0
$731$	−135677.	−	78333.3i	−0.253906	−	0.146592i
$732$		0			0
$733$	162756.	−	93967.1i	0.302920	−	0.174891i	−0.340834	−	0.940124i	$-0.610709\pi$
$733$	162756.	−	93967.1i	0.302920	−	0.174891i	0.643754	+	0.765232i	$0.277376\pi$
$734$		0			0
$735$	655378.	+	154508.i	1.21316	+	0.286006i
$736$		0			0
$737$	420719.	+	728707.i	0.774564	+	1.34158i
$738$		0			0
$739$	−108230.	+	187460.i	−0.198180	+	0.343258i	−0.947938	−	0.318454i	$-0.896836\pi$
$739$	−108230.	+	187460.i	−0.198180	+	0.343258i	0.749758	+	0.661712i	$0.230170\pi$
$740$		0			0
$741$		−	335696.i		−	0.611377i
$742$		0			0
$743$	202338.			0.366521			0.183261	−	0.983064i	$-0.441335\pi$
$743$	202338.			0.366521			0.183261	+	0.983064i	$0.441335\pi$
$744$		0			0
$745$	−739302.	−	426836.i	−1.33202	−	0.769039i
$746$		0			0
$747$	838.040	−	483.843i	0.00150184	−	0.000867088i
$748$		0			0
$749$	103973.	+	240645.i	0.185335	+	0.428957i
$750$		0			0
$751$	−250793.	−	434385.i	−0.444667	−	0.770185i	0.553362	−	0.832941i	$-0.313345\pi$
$751$	−250793.	−	434385.i	−0.444667	−	0.770185i	−0.998029	+	0.0627553i	$0.980011\pi$
$752$		0			0
$753$	−260318.	+	450884.i	−0.459108	+	0.795198i
$754$		0			0
$755$			930942.i			1.63316i
$756$		0			0
$757$	−21535.3			−0.0375802			−0.0187901	−	0.999823i	$-0.505981\pi$
$757$	−21535.3			−0.0375802			−0.0187901	+	0.999823i	$0.505981\pi$
$758$		0			0
$759$	379834.	+	219297.i	0.659341	+	0.380671i
$760$		0			0
$761$	700732.	−	404568.i	1.20999	−	0.698589i	0.247235	−	0.968956i	$-0.420478\pi$
$761$	700732.	−	404568.i	1.20999	−	0.698589i	0.962758	+	0.270366i	$0.0871448\pi$
$762$		0			0
$763$	614742.	−	826764.i	1.05595	−	1.42014i
$764$		0			0
$765$	1046.71	+	1812.95i	0.00178855	+	0.00309786i
$766$		0			0
$767$	462449.	−	800986.i	0.786092	−	1.36155i
$768$		0			0
$769$			356884.i			0.603496i	0.953388	+	0.301748i	$0.0975702\pi$
$769$			356884.i			0.603496i	−0.953388	+	0.301748i	$0.902430\pi$
$770$		0			0
$771$	611510.			1.02871
$772$		0			0
$773$	−169520.	−	97872.5i	−0.283702	−	0.163795i	0.351396	−	0.936227i	$-0.385707\pi$
$773$	−169520.	−	97872.5i	−0.283702	−	0.163795i	−0.635098	+	0.772431i	$0.719040\pi$
$774$		0			0
$775$	−459810.	+	265471.i	−0.765552	+	0.441992i
$776$		0			0
$777$	−116292.	+	1.00008e6i	−0.192623	+	1.65650i
$778$		0			0
$779$	−69315.6	−	120058.i	−0.114224	−	0.197841i
$780$		0			0
$781$	83731.5	−	145027.i	0.137274	−	0.237765i
$782$		0			0
$783$		−	1.00928e6i		−	1.64622i
$784$		0			0
$785$	481631.			0.781583
$786$		0			0
$787$	−388287.	−	224177.i	−0.626907	−	0.361945i	0.152646	−	0.988281i	$-0.451220\pi$
$787$	−388287.	−	224177.i	−0.626907	−	0.361945i	−0.779553	+	0.626336i	$0.784554\pi$
$788$		0			0
$789$	−52864.3	+	30521.2i	−0.0849196	+	0.0490284i
$790$		0			0
$791$	481209.	+	55956.3i	0.769096	+	0.0894327i
$792$		0			0
$793$	273645.	+	473968.i	0.435153	+	0.753707i
$794$		0			0
$795$	626385.	−	1.08493e6i	0.991077	−	1.71660i
$796$		0			0
$797$			536814.i			0.845099i	0.906340	+	0.422549i	$0.138865\pi$
$797$			536814.i			0.845099i	−0.906340	+	0.422549i	$0.861135\pi$
$798$		0			0
$799$	280142.			0.438818
$800$		0			0
$801$	1812.41	+	1046.39i	0.00282482	+	0.00163091i
$802$		0			0
$803$	−465501.	+	268757.i	−0.721921	+	0.416801i
$804$		0			0
$805$	−407948.	−	303331.i	−0.629526	−	0.468085i
$806$		0			0
$807$	379038.	+	656513.i	0.582017	+	1.00808i
$808$		0			0
$809$	186264.	−	322619.i	0.284598	−	0.492938i	−0.687914	−	0.725793i	$-0.741473\pi$
$809$	186264.	−	322619.i	0.284598	−	0.492938i	0.972512	+	0.232854i	$0.0748066\pi$
$810$		0			0
$811$			559118.i			0.850084i	0.905174	+	0.425042i	$0.139741\pi$
$811$			559118.i			0.850084i	−0.905174	+	0.425042i	$0.860259\pi$
$812$		0			0
$813$	351392.			0.531632
$814$		0			0
$815$	736116.	+	424997.i	1.10823	+	0.639839i
$816$		0			0
$817$	128526.	−	74204.5i	0.192552	−	0.111170i
$818$		0			0
$819$	3397.31	−	1467.84i	0.00506486	−	0.00218832i
$820$		0			0
$821$	171900.	+	297739.i	0.255029	+	0.441722i	0.964903	−	0.262606i	$-0.0845818\pi$
$821$	171900.	+	297739.i	0.255029	+	0.441722i	−0.709875	+	0.704328i	$0.751248\pi$
$822$		0			0
$823$	−25861.2	+	44793.0i	−0.0381812	+	0.0661318i	−0.884485	−	0.466570i	$-0.845490\pi$
$823$	−25861.2	+	44793.0i	−0.0381812	+	0.0661318i	0.846303	+	0.532701i	$0.178823\pi$
$824$		0			0
$825$			449099.i			0.659834i
$826$		0			0
$827$	−1.27662e6			−1.86659			−0.933297	−	0.359105i	$-0.883082\pi$
$827$	−1.27662e6			−1.86659			−0.933297	+	0.359105i	$0.883082\pi$
$828$		0			0
$829$	−453405.	−	261774.i	−0.659747	−	0.380905i	0.132434	−	0.991192i	$-0.457721\pi$
$829$	−453405.	−	261774.i	−0.659747	−	0.380905i	−0.792181	+	0.610287i	$0.791054\pi$
$830$		0			0
$831$	−557604.	+	321933.i	−0.807465	+	0.466190i
$832$		0			0
$833$	−327203.	−	307968.i	−0.471550	−	0.443829i
$834$		0			0
$835$	−307089.	−	531894.i	−0.440445	−	0.762873i
$836$		0			0
$837$	565143.	−	978857.i	0.806692	−	1.39723i
$838$		0			0
$839$			1.14150e6i			1.62163i	0.585303	+	0.810815i	$0.300976\pi$
$839$			1.14150e6i			1.62163i	−0.585303	+	0.810815i	$0.699024\pi$
$840$		0			0
$841$	1.21808e6			1.72220
$842$		0			0
$843$	−451787.	−	260839.i	−0.635738	−	0.367044i
$844$		0			0
$845$	417607.	−	241106.i	0.584864	−	0.337671i
$846$		0			0
$847$	128144.	+	296588.i	0.178621	+	0.413416i
$848$		0			0
$849$	−455492.	−	788935.i	−0.631924	−	1.09453i
$850$		0			0
$851$	380063.	−	658288.i	0.524803	−	0.908985i
$852$		0			0
$853$			587560.i			0.807521i	0.914865	+	0.403761i	$0.132297\pi$
$853$			587560.i			0.807521i	−0.914865	+	0.403761i	$0.867703\pi$
$854$		0			0
$855$	−1983.07			−0.00271273
$856$		0			0
$857$	−1.05627e6	−	609838.i	−1.43818	−	0.830334i	−0.440457	−	0.897774i	$-0.645184\pi$
$857$	−1.05627e6	−	609838.i	−1.43818	−	0.830334i	−0.997723	+	0.0674398i	$0.978517\pi$
$858$		0			0
$859$	−724073.	+	418044.i	−0.981287	+	0.566546i	−0.902658	−	0.430358i	$-0.858387\pi$
$859$	−724073.	+	418044.i	−0.981287	+	0.566546i	−0.0786283	+	0.996904i	$0.525054\pi$
$860$		0			0
$861$	206224.	−	277349.i	0.278184	−	0.374129i
$862$		0			0
$863$	383588.	+	664393.i	0.515042	+	0.892079i	0.999848	+	0.0174573i	$0.00555712\pi$
$863$	383588.	+	664393.i	0.515042	+	0.892079i	−0.484805	+	0.874622i	$0.661110\pi$
$864$		0			0
$865$	356726.	−	617867.i	0.476762	−	0.825777i
$866$		0			0
$867$			437441.i			0.581945i
$868$		0			0
$869$	−393202.			−0.520686
$870$		0			0
$871$	−1.04979e6	−	606099.i	−1.38378	−	0.798928i
$872$		0			0
$873$	2458.45	−	1419.39i	0.00322577	−	0.00186240i
$874$		0			0
$875$	−49856.1	+	428748.i	−0.0651181	+	0.559998i
$876$		0			0
$877$	246604.	+	427131.i	0.320628	+	0.555343i	0.980618	−	0.195931i	$-0.0627729\pi$
$877$	246604.	+	427131.i	0.320628	+	0.555343i	−0.659990	+	0.751274i	$0.729440\pi$
$878$		0			0
$879$	−600425.	+	1.03997e6i	−0.777107	+	1.34599i
$880$		0			0
$881$		−	549789.i		−	0.708344i	−0.935180	−	0.354172i	$-0.884763\pi$
$881$		−	549789.i		−	0.708344i	0.935180	−	0.354172i	$-0.115237\pi$
$882$		0			0
$883$	177926.			0.228202			0.114101	−	0.993469i	$-0.463601\pi$
$883$	177926.			0.228202			0.114101	+	0.993469i	$0.463601\pi$
$884$		0			0
$885$	−1.07003e6	−	617783.i	−1.36619	−	0.788768i
$886$		0			0
$887$	−23246.4	+	13421.3i	−0.0295467	+	0.0170588i	−0.514701	−	0.857370i	$-0.672097\pi$
$887$	−23246.4	+	13421.3i	−0.0295467	+	0.0170588i	0.485154	+	0.874429i	$0.338764\pi$
$888$		0			0
$889$	591268.	+	68754.4i	0.748137	+	0.0869955i
$890$		0			0
$891$	−480152.	−	831647.i	−0.604816	−	1.04757i
$892$		0			0
$893$	−132688.	+	229823.i	−0.166391	+	0.288197i
$894$		0			0
$895$		−	437740.i		−	0.546475i
$896$		0			0
$897$	−631851.			−0.785290
$898$		0			0
$899$	1.86732e6	+	1.07810e6i	2.31046	+	1.33395i
$900$		0			0
$901$	−724002.	+	418002.i	−0.891846	+	0.514908i
$902$		0			0
$903$	296912.	+	220769.i	0.364126	+	0.270747i
$904$		0			0
$905$	188594.	+	326654.i	0.230266	+	0.398832i
$906$		0			0
$907$	−614619.	+	1.06455e6i	−0.747122	+	1.29405i	0.202074	+	0.979370i	$0.435232\pi$
$907$	−614619.	+	1.06455e6i	−0.747122	+	1.29405i	−0.949197	+	0.314684i	$0.898102\pi$
$908$		0			0
$909$			2849.98i			0.00344917i
$910$		0			0
$911$	−701772.			−0.845589			−0.422794	−	0.906226i	$-0.638951\pi$
$911$	−701772.			−0.845589			−0.422794	+	0.906226i	$0.638951\pi$
$912$		0			0
$913$	−339435.	−	195973.i	−0.407206	−	0.235101i
$914$		0			0
$915$	633170.	−	365561.i	0.756273	−	0.436634i
$916$		0			0
$917$	−252941.	+	109286.i	−0.300802	+	0.129965i
$918$		0			0
$919$	−755117.	−	1.30790e6i	−0.894094	−	1.54862i	−0.834922	−	0.550369i	$-0.814487\pi$
$919$	−755117.	−	1.30790e6i	−0.894094	−	1.54862i	−0.0591725	−	0.998248i	$-0.518846\pi$
$920$		0			0
$921$	34579.5	−	59893.4i	0.0407661	−	0.0706089i
$922$		0			0
$923$			241252.i			0.283183i
$924$		0			0
$925$	778331.			0.909664
$926$		0			0
$927$	−532.363	−	307.360i	−0.000619510	−	0.000357675i
$928$		0			0
$929$	803655.	−	463990.i	0.931190	−	0.537623i	0.0440021	−	0.999031i	$-0.485989\pi$
$929$	803655.	−	463990.i	0.931190	−	0.537623i	0.887188	+	0.461409i	$0.152656\pi$
$930$		0			0
$931$	407629.	−	122563.i	0.470290	−	0.141403i
$932$		0			0
$933$	7419.91	+	12851.7i	0.00852384	+	0.0147637i
$934$		0			0
$935$	423951.	−	734305.i	0.484945	−	0.839949i
$936$		0			0
$937$		−	902133.i		−	1.02752i	−0.857933	−	0.513761i	$-0.828252\pi$
$937$		−	902133.i		−	1.02752i	0.857933	−	0.513761i	$-0.171748\pi$
$938$		0			0
$939$	−1.01107e6			−1.14670
$940$		0			0
$941$	760903.	+	439308.i	0.859310	+	0.496123i	0.863781	−	0.503867i	$-0.168090\pi$
$941$	760903.	+	439308.i	0.859310	+	0.496123i	−0.00447086	+	0.999990i	$0.501423\pi$
$942$		0			0
$943$	−225975.	+	130467.i	−0.254119	+	0.146716i
$944$		0			0
$945$	439513.	+	1.01725e6i	0.492162	+	1.13910i
$946$		0			0
$947$	721180.	+	1.24912e6i	0.804162	+	1.39285i	0.916855	+	0.399220i	$0.130719\pi$
$947$	721180.	+	1.24912e6i	0.804162	+	1.39285i	−0.112693	+	0.993630i	$0.535948\pi$
$948$		0			0
$949$	387179.	−	670614.i	0.429912	−	0.744629i
$950$		0			0
$951$			30329.1i			0.0335350i
$952$		0			0
$953$	−524371.			−0.577368			−0.288684	−	0.957424i	$-0.593218\pi$
$953$	−524371.			−0.577368			−0.288684	+	0.957424i	$0.593218\pi$
$954$		0			0
$955$	807921.	+	466453.i	0.885854	+	0.511448i
$956$		0			0
$957$	1.57948e6	−	911912.i	1.72461	−	0.995702i
$958$		0			0
$959$	871151.	−	1.17161e6i	0.947232	−	1.27393i
$960$		0			0
$961$	745592.	+	1.29140e6i	0.807336	+	1.39835i
$962$		0			0
$963$	962.384	−	1666.90i	0.00103776	−	0.00179745i
$964$		0			0
$965$			581556.i			0.624507i
$966$		0			0
$967$	1.40754e6			1.50525			0.752624	−	0.658450i	$-0.228788\pi$
$967$	1.40754e6			1.50525			0.752624	+	0.658450i	$0.228788\pi$
$968$		0			0
$969$	259170.	+	149632.i	0.276018	+	0.159359i
$970$		0			0
$971$	−324836.	+	187544.i	−0.344529	+	0.198914i	−0.662273	−	0.749262i	$-0.730408\pi$
$971$	−324836.	+	187544.i	−0.344529	+	0.198914i	0.317744	+	0.948177i	$0.397075\pi$
$972$		0			0
$973$	88826.0	−	763879.i	0.0938241	−	0.806861i
$974$		0			0
$975$	−323492.	−	560305.i	−0.340294	−	0.589407i
$976$		0			0
$977$	−649690.	+	1.12530e6i	−0.680640	+	1.17890i	0.294146	+	0.955760i	$0.404965\pi$
$977$	−649690.	+	1.12530e6i	−0.680640	+	1.17890i	−0.974786	+	0.223142i	$0.928369\pi$
$978$		0			0
$979$		−	847650.i		−	0.884405i
$980$		0			0
$981$	−7564.57			−0.00786043
$982$		0			0
$983$	−693008.	−	400108.i	−0.717185	−	0.414067i	0.0965310	−	0.995330i	$-0.469225\pi$
$983$	−693008.	−	400108.i	−0.717185	−	0.414067i	−0.813716	+	0.581263i	$0.802559\pi$
$984$		0			0
$985$	276581.	−	159684.i	0.285068	−	0.164584i
$986$		0			0
$987$	−657173.	−	76417.9i	−0.674598	−	0.0784442i
$988$		0			0
$989$	−139669.	−	241914.i	−0.142793	−	0.247325i
$990$		0			0
$991$	−461620.	+	799550.i	−0.470043	+	0.814138i	−0.999413	−	0.0342525i	$-0.989095\pi$
$991$	−461620.	+	799550.i	−0.470043	+	0.814138i	0.529370	+	0.848391i	$0.322428\pi$
$992$		0			0
$993$		−	784465.i		−	0.795564i
$994$		0			0
$995$	−223501.			−0.225752
$996$		0			0
$997$	610224.	+	352313.i	0.613902	+	0.354436i	0.774491	−	0.632585i	$-0.218006\pi$
$997$	610224.	+	352313.i	0.613902	+	0.354436i	−0.160589	+	0.987021i	$0.551339\pi$
$998$		0			0
$999$	−1.43495e6	+	828468.i	−1.43782	+	0.830127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.5.h.a.17.1	yes	6
3.2	odd	2		252.5.z.f.73.3		6
4.3	odd	2		112.5.s.c.17.3		6
5.2	odd	4		700.5.o.a.549.2		12
5.3	odd	4		700.5.o.a.549.5		12
5.4	even	2		700.5.s.a.101.3		6
7.2	even	3		196.5.h.c.117.3		6
7.3	odd	6		196.5.b.a.97.2		6
7.4	even	3		196.5.b.a.97.5		6
7.5	odd	6	inner	28.5.h.a.5.1	✓	6
7.6	odd	2		196.5.h.c.129.3		6
21.5	even	6		252.5.z.f.145.3		6
28.3	even	6		784.5.c.e.97.5		6
28.11	odd	6		784.5.c.e.97.2		6
28.19	even	6		112.5.s.c.33.3		6
35.12	even	12		700.5.o.a.649.5		12
35.19	odd	6		700.5.s.a.201.3		6
35.33	even	12		700.5.o.a.649.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.5.h.a.5.1	✓	6	7.5	odd	6	inner
28.5.h.a.17.1	yes	6	1.1	even	1	trivial
112.5.s.c.17.3		6	4.3	odd	2
112.5.s.c.33.3		6	28.19	even	6
196.5.b.a.97.2		6	7.3	odd	6
196.5.b.a.97.5		6	7.4	even	3
196.5.h.c.117.3		6	7.2	even	3
196.5.h.c.129.3		6	7.6	odd	2
252.5.z.f.73.3		6	3.2	odd	2
252.5.z.f.145.3		6	21.5	even	6
700.5.o.a.549.2		12	5.2	odd	4
700.5.o.a.549.5		12	5.3	odd	4
700.5.o.a.649.2		12	35.33	even	12
700.5.o.a.649.5		12	35.12	even	12
700.5.s.a.101.3		6	5.4	even	2
700.5.s.a.201.3		6	35.19	odd	6
784.5.c.e.97.2		6	28.11	odd	6
784.5.c.e.97.5		6	28.3	even	6

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	28.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.81152 - 4.50998i) q^{3} +(-26.9260 + 15.5457i) q^{5} +(-48.6720 - 5.65972i) q^{7} +(0.179888 + 0.311574i) q^{9} +(72.8605 - 126.198i) q^{11} +209.930i q^{13} +280.444 q^{15} +(-162.074 - 93.5735i) q^{17} +(153.531 - 88.6415i) q^{19} +(354.677 + 263.721i) q^{21} +(-166.842 - 288.979i) q^{23} +(170.838 - 295.901i) q^{25} +727.372i q^{27} -1387.57 q^{29} +(-1345.74 - 776.966i) q^{31} +(-1138.30 + 657.199i) q^{33} +(1398.53 - 604.248i) q^{35} +(1138.99 + 1972.78i) q^{37} +(946.779 - 1639.87i) q^{39} -781.977i q^{41} +837.131 q^{43} +(-9.68729 - 5.59296i) q^{45} +(-1296.36 + 748.454i) q^{47} +(2336.94 + 550.940i) q^{49} +(844.030 + 1461.90i) q^{51} +(2233.55 - 3868.63i) q^{53} +4530.67i q^{55} -1599.09 q^{57} +(-3815.50 - 2202.88i) q^{59} +(2257.75 - 1303.51i) q^{61} +(-6.99207 - 16.1831i) q^{63} +(-3263.51 - 5652.56i) q^{65} +(-2887.15 + 5000.70i) q^{67} +3009.82i q^{69} +1149.20 q^{71} +(-3194.47 - 1844.33i) q^{73} +(-2669.01 + 1540.96i) q^{75} +(-4260.52 + 5729.95i) q^{77} +(-1349.16 - 2336.81i) q^{79} +(3295.01 - 5707.12i) q^{81} -2689.70i q^{83} +5818.67 q^{85} +(10839.1 + 6257.93i) q^{87} +(5037.61 - 2908.47i) q^{89} +(1188.14 - 10217.7i) q^{91} +(7008.21 + 12138.6i) q^{93} +(-2755.99 + 4773.51i) q^{95} -7890.42i q^{97} +52.4268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} - 27 q^{5} + 66 q^{7} + 90 q^{9} + 135 q^{11} - 486 q^{15} - 1107 q^{17} - 747 q^{19} + 2169 q^{21} + 243 q^{23} + 1878 q^{25} - 540 q^{29} - 5355 q^{31} - 1863 q^{33} + 6021 q^{35} + 2355 q^{37}+ \cdots + 8100 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 - 27 * q^5 + 66 * q^7 + 90 * q^9 + 135 * q^11 - 486 * q^15 - 1107 * q^17 - 747 * q^19 + 2169 * q^21 + 243 * q^23 + 1878 * q^25 - 540 * q^29 - 5355 * q^31 - 1863 * q^33 + 6021 * q^35 + 2355 * q^37 + 6588 * q^39 - 948 * q^43 - 14418 * q^45 - 9747 * q^47 + 8430 * q^49 - 891 * q^51 + 6291 * q^53 - 6894 * q^57 - 2943 * q^59 + 4041 * q^61 + 15138 * q^63 + 7668 * q^65 + 1659 * q^67 + 2268 * q^71 - 8703 * q^73 - 3438 * q^75 - 10665 * q^77 - 7773 * q^79 - 7479 * q^81 - 702 * q^85 + 40014 * q^87 + 14985 * q^89 - 20952 * q^91 + 1449 * q^93 - 20655 * q^95 + 8100 * q^99

Introduction

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