LMFDB - Embedded newform 828.2.q.c.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(73,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("828.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.q (of order $11$, degree $10$, 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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			325.1
Root			$2.31834 + 1.48991i$ of defining polynomial
Character	$\chi$	$=$	828.325
Dual form			828.2.q.c.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.735636 + 0.848969i) q^{5} +(0.891451 - 0.572901i) q^{7} +O(q^{10})$	$q+(-0.735636 + 0.848969i) q^{5} +(0.891451 - 0.572901i) q^{7} +(-0.347809 + 2.41907i) q^{11} +(1.00126 + 0.643468i) q^{13} +(0.810376 + 0.237948i) q^{17} +(1.83256 - 0.538087i) q^{19} +(0.265350 + 4.78849i) q^{23} +(0.531986 + 3.70004i) q^{25} +(0.551701 + 0.161994i) q^{29} +(0.110721 + 0.242445i) q^{31} +(-0.169408 + 1.17826i) q^{35} +(5.68252 + 6.55798i) q^{37} +(3.19380 - 3.68585i) q^{41} +(-1.36978 + 2.99940i) q^{43} -0.561056 q^{47} +(-2.44144 + 5.34600i) q^{49} +(5.21451 - 3.35116i) q^{53} +(-1.79785 - 2.07483i) q^{55} +(1.23668 + 0.794765i) q^{59} +(3.69276 + 8.08602i) q^{61} +(-1.28285 + 0.376677i) q^{65} +(0.709022 + 4.93135i) q^{67} +(0.0399653 + 0.277964i) q^{71} +(-4.93870 + 1.45013i) q^{73} +(1.07583 + 2.35574i) q^{77} +(-4.92920 - 3.16780i) q^{79} +(-3.38585 - 3.90747i) q^{83} +(-0.798152 + 0.512941i) q^{85} +(5.04667 - 11.0507i) q^{89} +1.26121 q^{91} +(-0.891275 + 1.95162i) q^{95} +(2.64165 - 3.04863i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^5	$ 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) $ 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.735636	+	0.848969i	−0.328986	+	0.379671i	−0.896012	−	0.444030i	$-0.853549\pi$
$5$	−0.735636	+	0.848969i	−0.328986	+	0.379671i	0.567026	+	0.823700i	$0.308094\pi$
$6$		0			0
$7$	0.891451	−	0.572901i	0.336937	−	0.216536i	−0.361221	−	0.932480i	$-0.617640\pi$
$7$	0.891451	−	0.572901i	0.336937	−	0.216536i	0.698157	+	0.715944i	$0.254004\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.347809	+	2.41907i	−0.104868	+	0.729376i	0.867756	+	0.496991i	$0.165562\pi$
$11$	−0.347809	+	2.41907i	−0.104868	+	0.729376i	−0.972624	+	0.232385i	$0.925347\pi$
$12$		0			0
$13$	1.00126	+	0.643468i	0.277699	+	0.178466i	0.672075	−	0.740483i	$-0.265403\pi$
$13$	1.00126	+	0.643468i	0.277699	+	0.178466i	−0.394377	+	0.918949i	$0.629039\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.810376	+	0.237948i	0.196545	+	0.0577108i	0.378523	−	0.925592i	$-0.376432\pi$
$17$	0.810376	+	0.237948i	0.196545	+	0.0577108i	−0.181978	+	0.983303i	$0.558250\pi$
$18$		0			0
$19$	1.83256	−	0.538087i	0.420417	−	0.123446i	−0.0646796	−	0.997906i	$-0.520603\pi$
$19$	1.83256	−	0.538087i	0.420417	−	0.123446i	0.485097	+	0.874460i	$0.338784\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.265350	+	4.78849i	0.0553292	+	0.998468i
$23$	0.265350	+	4.78849i	0.0553292	+	0.998468i
$24$		0			0
$25$	0.531986	+	3.70004i	0.106397	+	0.740009i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.551701	+	0.161994i	0.102448	+	0.0300815i	0.332555	−	0.943084i	$-0.392089\pi$
$29$	0.551701	+	0.161994i	0.102448	+	0.0300815i	−0.230107	+	0.973165i	$0.573908\pi$
$30$		0			0
$31$	0.110721	+	0.242445i	0.0198861	+	0.0435444i	0.919314	−	0.393524i	$-0.128744\pi$
$31$	0.110721	+	0.242445i	0.0198861	+	0.0435444i	−0.899428	+	0.437068i	$0.856017\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.169408	+	1.17826i	−0.0286352	+	0.199162i
$36$		0			0
$37$	5.68252	+	6.55798i	0.934201	+	1.07812i	0.996788	+	0.0800854i	$0.0255193\pi$
$37$	5.68252	+	6.55798i	0.934201	+	1.07812i	−0.0625874	+	0.998039i	$0.519935\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.19380	−	3.68585i	0.498788	−	0.575632i	−0.449404	−	0.893328i	$-0.648364\pi$
$41$	3.19380	−	3.68585i	0.498788	−	0.575632i	0.948193	+	0.317696i	$0.102909\pi$
$42$		0			0
$43$	−1.36978	+	2.99940i	−0.208889	+	0.457404i	−0.984857	−	0.173369i	$-0.944535\pi$
$43$	−1.36978	+	2.99940i	−0.208889	+	0.457404i	0.775968	+	0.630773i	$0.217262\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.561056			−0.0818384			−0.0409192	−	0.999162i	$-0.513029\pi$
$47$	−0.561056			−0.0818384			−0.0409192	+	0.999162i	$0.513029\pi$
$48$		0			0
$49$	−2.44144	+	5.34600i	−0.348777	+	0.763714i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.21451	−	3.35116i	0.716268	−	0.460318i	−0.131069	−	0.991373i	$-0.541841\pi$
$53$	5.21451	−	3.35116i	0.716268	−	0.460318i	0.847337	+	0.531056i	$0.178204\pi$
$54$		0			0
$55$	−1.79785	−	2.07483i	−0.242422	−	0.279770i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.23668	+	0.794765i	0.161002	+	0.103470i	0.618661	−	0.785658i	$-0.287676\pi$
$59$	1.23668	+	0.794765i	0.161002	+	0.103470i	−0.457659	+	0.889128i	$0.651312\pi$
$60$		0			0
$61$	3.69276	+	8.08602i	0.472810	+	1.03531i	0.984378	+	0.176067i	$0.0563374\pi$
$61$	3.69276	+	8.08602i	0.472810	+	1.03531i	−0.511568	+	0.859243i	$0.670935\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.28285	+	0.376677i	−0.159117	+	0.0467211i
$66$		0			0
$67$	0.709022	+	4.93135i	0.0866208	+	0.602461i	0.986182	+	0.165666i	$0.0529773\pi$
$67$	0.709022	+	4.93135i	0.0866208	+	0.602461i	−0.899561	+	0.436795i	$0.856114\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.0399653	+	0.277964i	0.00474300	+	0.0329883i	0.992056	−	0.125801i	$-0.0401501\pi$
$71$	0.0399653	+	0.277964i	0.00474300	+	0.0329883i	−0.987313	+	0.158789i	$0.949241\pi$
$72$		0			0
$73$	−4.93870	+	1.45013i	−0.578031	+	0.169725i	−0.557663	−	0.830067i	$-0.688302\pi$
$73$	−4.93870	+	1.45013i	−0.578031	+	0.169725i	−0.0203679	+	0.999793i	$0.506484\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.07583	+	2.35574i	0.122602	+	0.268461i
$78$		0			0
$79$	−4.92920	−	3.16780i	−0.554578	−	0.356406i	0.233139	−	0.972444i	$-0.425100\pi$
$79$	−4.92920	−	3.16780i	−0.554578	−	0.356406i	−0.787716	+	0.616038i	$0.788737\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.38585	−	3.90747i	−0.371645	−	0.428901i	0.538863	−	0.842394i	$-0.318854\pi$
$83$	−3.38585	−	3.90747i	−0.371645	−	0.428901i	−0.910507	+	0.413493i	$0.864309\pi$
$84$		0			0
$85$	−0.798152	+	0.512941i	−0.0865718	+	0.0556363i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.04667	−	11.0507i	0.534946	−	1.17137i	−0.428519	−	0.903533i	$-0.640964\pi$
$89$	5.04667	−	11.0507i	0.534946	−	1.17137i	0.963465	−	0.267835i	$-0.0863083\pi$
$90$		0			0
$91$	1.26121			0.132211
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.891275	+	1.95162i	−0.0914429	+	0.200232i
$96$		0			0
$97$	2.64165	−	3.04863i	0.268219	−	0.309542i	−0.605622	−	0.795752i	$-0.707076\pi$
$97$	2.64165	−	3.04863i	0.268219	−	0.309542i	0.873842	+	0.486211i	$0.161621\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.90660	+	9.12470i	0.786736	+	0.907942i	0.997576	−	0.0695785i	$-0.0221654\pi$
$101$	7.90660	+	9.12470i	0.786736	+	0.907942i	−0.210840	+	0.977521i	$0.567620\pi$
$102$		0			0
$103$	2.41213	−	16.7767i	0.237674	−	1.65306i	−0.425770	−	0.904831i	$-0.639997\pi$
$103$	2.41213	−	16.7767i	0.237674	−	1.65306i	0.663444	−	0.748226i	$-0.269094\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.19217	−	11.3693i	−0.501946	−	1.09911i	−0.975832	−	0.218522i	$-0.929876\pi$
$107$	−5.19217	−	11.3693i	−0.501946	−	1.09911i	0.473886	−	0.880586i	$-0.342851\pi$
$108$		0			0
$109$	0.535214	+	0.157153i	0.0512642	+	0.0150525i	0.307264	−	0.951624i	$-0.400586\pi$
$109$	0.535214	+	0.157153i	0.0512642	+	0.0150525i	−0.256000	+	0.966677i	$0.582405\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.19921	+	8.34069i	0.112812	+	0.784626i	0.965162	+	0.261654i	$0.0842679\pi$
$113$	1.19921	+	8.34069i	0.112812	+	0.784626i	−0.852350	+	0.522973i	$0.824823\pi$
$114$		0			0
$115$	−4.26048	−	3.29731i	−0.397292	−	0.307476i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.858731	−	0.252146i	0.0787197	−	0.0231142i
$120$		0			0
$121$	4.82351	+	1.41631i	0.438501	+	0.128756i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.25767	−	5.30688i	−0.738588	−	0.474662i
$126$		0			0
$127$	2.07067	−	14.4018i	0.183742	−	1.27796i	−0.664074	−	0.747667i	$-0.731174\pi$
$127$	2.07067	−	14.4018i	0.183742	−	1.27796i	0.847817	−	0.530290i	$-0.177917\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.54743	+	5.49310i	−0.746793	+	0.479935i	−0.857863	−	0.513878i	$-0.828208\pi$
$131$	−8.54743	+	5.49310i	−0.746793	+	0.479935i	0.111070	+	0.993813i	$0.464572\pi$
$132$		0			0
$133$	1.32536	−	1.52955i	0.114924	−	0.132629i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.5603			−0.902226			−0.451113	−	0.892467i	$-0.648973\pi$
$137$	−10.5603			−0.902226			−0.451113	+	0.892467i	$0.648973\pi$
$138$		0			0
$139$	−6.20115			−0.525975			−0.262987	−	0.964799i	$-0.584708\pi$
$139$	−6.20115			−0.525975			−0.262987	+	0.964799i	$0.584708\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.90484	+	2.19830i	−0.159291	+	0.183831i
$144$		0			0
$145$	−0.543379	+	0.349208i	−0.0451252	+	0.0290002i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.91401	+	13.3122i	−0.156802	+	1.09058i	0.747677	+	0.664062i	$0.231169\pi$
$149$	−1.91401	+	13.3122i	−0.156802	+	1.09058i	−0.904479	+	0.426518i	$0.859740\pi$
$150$		0			0
$151$	−15.3689	−	9.87699i	−1.25070	−	0.803778i	−0.263720	−	0.964599i	$-0.584949\pi$
$151$	−15.3689	−	9.87699i	−1.25070	−	0.803778i	−0.986984	+	0.160821i	$0.948586\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.287279	−	0.0843527i	−0.0230748	−	0.00677537i
$156$		0			0
$157$	18.1248	−	5.32192i	1.44652	−	0.424735i	0.538127	−	0.842864i	$-0.319132\pi$
$157$	18.1248	−	5.32192i	1.44652	−	0.424735i	0.908388	+	0.418129i	$0.137314\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.97987	+	4.11668i	0.234847	+	0.324440i
$162$		0			0
$163$	0.0147334	+	0.102473i	0.00115401	+	0.00802632i	0.990390	−	0.138301i	$-0.0441640\pi$
$163$	0.0147334	+	0.102473i	0.00115401	+	0.00802632i	−0.989236	+	0.146327i	$0.953255\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.4318	−	4.82480i	−1.27153	−	0.373355i	−0.424755	−	0.905308i	$-0.639640\pi$
$167$	−16.4318	−	4.82480i	−1.27153	−	0.373355i	−0.846774	+	0.531954i	$0.821458\pi$
$168$		0			0
$169$	−4.81193	−	10.5367i	−0.370149	−	0.810512i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.42048	+	9.87965i	−0.107997	+	0.751136i	0.861805	+	0.507240i	$0.169334\pi$
$173$	−1.42048	+	9.87965i	−0.107997	+	0.751136i	−0.969802	+	0.243895i	$0.921575\pi$
$174$		0			0
$175$	2.59400	+	2.99363i	0.196088	+	0.226297i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.7566	−	19.3381i	1.25245	−	1.44540i	0.405177	−	0.914238i	$-0.367210\pi$
$179$	16.7566	−	19.3381i	1.25245	−	1.44540i	0.847270	−	0.531163i	$-0.178245\pi$
$180$		0			0
$181$	0.409057	−	0.895711i	0.0304050	−	0.0665776i	−0.893820	−	0.448426i	$-0.851985\pi$
$181$	0.409057	−	0.895711i	0.0304050	−	0.0665776i	0.924225	+	0.381848i	$0.124712\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.74779			−0.716672
$186$		0			0
$187$	−0.857468	+	1.87759i	−0.0627043	+	0.137303i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.90200	−	2.50766i	0.282339	−	0.181448i	−0.391805	−	0.920048i	$-0.628149\pi$
$191$	3.90200	−	2.50766i	0.282339	−	0.181448i	0.674144	+	0.738600i	$0.264513\pi$
$192$		0			0
$193$	−11.2976	−	13.0381i	−0.813220	−	0.938506i	0.185808	−	0.982586i	$-0.440510\pi$
$193$	−11.2976	−	13.0381i	−0.813220	−	0.938506i	−0.999028	+	0.0440804i	$0.985964\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.22558	+	0.787630i	0.0873187	+	0.0561163i	0.583572	−	0.812062i	$-0.301655\pi$
$197$	1.22558	+	0.787630i	0.0873187	+	0.0561163i	−0.496253	+	0.868178i	$0.665291\pi$
$198$		0			0
$199$	−3.02962	−	6.63394i	−0.214764	−	0.470268i	0.771334	−	0.636430i	$-0.219590\pi$
$199$	−3.02962	−	6.63394i	−0.214764	−	0.470268i	−0.986098	+	0.166162i	$0.946862\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.584621	−	0.171660i	0.0410323	−	0.0120482i
$204$		0			0
$205$	0.779693	+	5.42288i	0.0544561	+	0.378750i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.664288	+	4.62023i	0.0459498	+	0.319588i
$210$		0			0
$211$	−23.9625	+	7.03603i	−1.64965	+	0.484380i	−0.968758	−	0.248007i	$-0.920224\pi$
$211$	−23.9625	+	7.03603i	−1.64965	+	0.484380i	−0.680889	+	0.732387i	$0.738406\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.53874	−	3.36937i	−0.104941	−	0.229789i
$216$		0			0
$217$	0.237599	+	0.152696i	0.0161293	+	0.0103657i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.658282	+	0.759698i	0.0442809	+	0.0511028i
$222$		0			0
$223$	−5.31965	+	3.41873i	−0.356230	+	0.228935i	−0.706499	−	0.707714i	$-0.749727\pi$
$223$	−5.31965	+	3.41873i	−0.356230	+	0.228935i	0.350269	+	0.936649i	$0.386090\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.3131	−	22.5824i	0.684502	−	1.49885i	−0.173300	−	0.984869i	$-0.555443\pi$
$227$	10.3131	−	22.5824i	0.684502	−	1.49885i	0.857802	−	0.513980i	$-0.171830\pi$
$228$		0			0
$229$	8.33079			0.550514			0.275257	−	0.961371i	$-0.411237\pi$
$229$	8.33079			0.550514			0.275257	+	0.961371i	$0.411237\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.86217	−	21.5951i	0.646092	−	1.41474i	−0.248841	−	0.968544i	$-0.580050\pi$
$233$	9.86217	−	21.5951i	0.646092	−	1.41474i	0.894933	−	0.446200i	$-0.147223\pi$
$234$		0			0
$235$	0.412733	−	0.476319i	0.0269237	−	0.0310716i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.9798	+	18.4417i	1.03365	+	1.19289i	0.980945	+	0.194283i	$0.0622381\pi$
$239$	15.9798	+	18.4417i	1.03365	+	1.19289i	0.0527025	+	0.998610i	$0.483216\pi$
$240$		0			0
$241$	1.73814	−	12.0890i	0.111963	−	0.778721i	−0.854043	−	0.520202i	$-0.825856\pi$
$241$	1.73814	−	12.0890i	0.111963	−	0.778721i	0.966006	−	0.258519i	$-0.0832344\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.74258	−	6.00541i	−0.175217	−	0.383672i
$246$		0			0
$247$	2.18110	+	0.640429i	0.138780	+	0.0407495i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.55527	−	24.7275i	−0.224407	−	1.56078i	−0.721083	−	0.692848i	$-0.756356\pi$
$251$	−3.55527	−	24.7275i	−0.224407	−	1.56078i	0.496677	−	0.867936i	$-0.334553\pi$
$252$		0			0
$253$	−11.6760	−	1.02358i	−0.734061	−	0.0643520i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.3823	+	3.34213i	−0.710005	+	0.208476i	−0.616742	−	0.787165i	$-0.711548\pi$
$257$	−11.3823	+	3.34213i	−0.710005	+	0.208476i	−0.0932631	+	0.995642i	$0.529730\pi$
$258$		0			0
$259$	8.82276	+	2.59060i	0.548219	+	0.160972i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.82837	−	5.03099i	−0.482718	−	0.310224i	0.276553	−	0.960999i	$-0.410808\pi$
$263$	−7.82837	−	5.03099i	−0.482718	−	0.310224i	−0.759271	+	0.650775i	$0.774444\pi$
$264$		0			0
$265$	−0.990948	+	6.89220i	−0.0608735	+	0.423384i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.4123	−	6.69157i	0.634848	−	0.407992i	−0.183253	−	0.983066i	$-0.558663\pi$
$269$	10.4123	−	6.69157i	0.634848	−	0.407992i	0.818102	+	0.575073i	$0.195027\pi$
$270$		0			0
$271$	−8.32197	+	9.60406i	−0.505523	+	0.583405i	−0.949947	−	0.312412i	$-0.898863\pi$
$271$	−8.32197	+	9.60406i	−0.505523	+	0.583405i	0.444423	+	0.895817i	$0.353409\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.13568			−0.550902
$276$		0			0
$277$	19.8326			1.19163			0.595813	−	0.803123i	$-0.296830\pi$
$277$	19.8326			1.19163			0.595813	+	0.803123i	$0.296830\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.05300	+	10.4477i	−0.540056	+	0.623258i	−0.958537	−	0.284967i	$-0.908017\pi$
$281$	−9.05300	+	10.4477i	−0.540056	+	0.623258i	0.418481	+	0.908226i	$0.362563\pi$
$282$		0			0
$283$	−6.02597	+	3.87266i	−0.358207	+	0.230206i	−0.707349	−	0.706864i	$-0.750109\pi$
$283$	−6.02597	+	3.87266i	−0.358207	+	0.230206i	0.349143	+	0.937070i	$0.386473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.735495	−	5.11548i	0.0434149	−	0.301957i
$288$		0			0
$289$	−13.7012	−	8.80524i	−0.805954	−	0.517955i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	17.4859	+	5.13434i	1.02154	+	0.299951i	0.749266	−	0.662269i	$-0.230406\pi$
$293$	17.4859	+	5.13434i	1.02154	+	0.299951i	0.272274	+	0.962220i	$0.412224\pi$
$294$		0			0
$295$	−1.58448	+	0.465244i	−0.0922518	+	0.0270876i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.81556	+	4.96525i	−0.162828	+	0.287148i
$300$		0			0
$301$	0.497267	+	3.45857i	0.0286620	+	0.199348i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.58131	−	2.81333i	−0.548624	−	0.161091i
$306$		0			0
$307$	6.61813	+	14.4917i	0.377717	+	0.827085i	0.999052	+	0.0435395i	$0.0138634\pi$
$307$	6.61813	+	14.4917i	0.377717	+	0.827085i	−0.621335	+	0.783545i	$0.713409\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.14594	+	28.8357i	−0.235095	+	1.63512i	0.440432	+	0.897786i	$0.354825\pi$
$311$	−4.14594	+	28.8357i	−0.235095	+	1.63512i	−0.675527	+	0.737335i	$0.736084\pi$
$312$		0			0
$313$	11.6702	+	13.4682i	0.659640	+	0.761266i	0.982718	−	0.185107i	$-0.0592631\pi$
$313$	11.6702	+	13.4682i	0.659640	+	0.761266i	−0.323078	+	0.946372i	$0.604718\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.6720	−	18.0865i	0.880227	−	1.01584i	−0.119508	−	0.992833i	$-0.538132\pi$
$317$	15.6720	−	18.0865i	0.880227	−	1.01584i	0.999735	−	0.0230031i	$-0.00732276\pi$
$318$		0			0
$319$	−0.583761	+	1.27826i	−0.0326843	+	0.0715687i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.61310			0.0897551
$324$		0			0
$325$	−1.84821	+	4.04701i	−0.102520	+	0.224488i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.500154	+	0.321429i	−0.0275744	+	0.0177210i
$330$		0			0
$331$	4.23218	+	4.88419i	0.232621	+	0.268459i	0.860044	−	0.510219i	$-0.170436\pi$
$331$	4.23218	+	4.88419i	0.232621	+	0.268459i	−0.627423	+	0.778679i	$0.715890\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.70815	−	3.02574i	−0.257234	−	0.165314i
$336$		0			0
$337$	−3.48662	−	7.63463i	−0.189928	−	0.415885i	0.790581	−	0.612357i	$-0.209779\pi$
$337$	−3.48662	−	7.63463i	−0.189928	−	0.415885i	−0.980509	+	0.196473i	$0.937051\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.625001	+	0.183517i	−0.0338457	+	0.00993799i
$342$		0			0
$343$	1.94195	+	13.5066i	0.104856	+	0.729287i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.15938	+	15.0188i	0.115922	+	0.806253i	0.961972	+	0.273149i	$0.0880653\pi$
$347$	2.15938	+	15.0188i	0.115922	+	0.806253i	−0.846050	+	0.533104i	$0.821026\pi$
$348$		0			0
$349$	−5.81125	+	1.70634i	−0.311069	+	0.0913382i	−0.433541	−	0.901134i	$-0.642736\pi$
$349$	−5.81125	+	1.70634i	−0.311069	+	0.0913382i	0.122472	+	0.992472i	$0.460918\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.6513	+	29.8922i	0.726585	+	1.59100i	0.804440	+	0.594034i	$0.202466\pi$
$353$	13.6513	+	29.8922i	0.726585	+	1.59100i	−0.0778551	+	0.996965i	$0.524807\pi$
$354$		0			0
$355$	−0.265383	−	0.170551i	−0.0140851	−	0.00905193i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.97285	+	3.43085i	0.156901	+	0.181073i	0.828757	−	0.559608i	$-0.189048\pi$
$359$	2.97285	+	3.43085i	0.156901	+	0.181073i	−0.671856	+	0.740681i	$0.734503\pi$
$360$		0			0
$361$	−12.9151	+	8.30003i	−0.679742	+	0.436843i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.40197	−	5.25957i	0.125725	−	0.275299i
$366$		0			0
$367$	31.9179			1.66610			0.833050	−	0.553198i	$-0.186593\pi$
$367$	31.9179			1.66610			0.833050	+	0.553198i	$0.186593\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.72860	−	5.97479i	0.141662	−	0.310196i
$372$		0			0
$373$	1.47685	−	1.70437i	0.0764683	−	0.0882491i	−0.716226	−	0.697868i	$-0.754132\pi$
$373$	1.47685	−	1.70437i	0.0764683	−	0.0882491i	0.792695	+	0.609619i	$0.208678\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.448156	+	0.517200i	0.0230812	+	0.0266371i
$378$		0			0
$379$	3.66978	−	25.5239i	0.188504	−	1.31107i	−0.647380	−	0.762167i	$-0.724135\pi$
$379$	3.66978	−	25.5239i	0.188504	−	1.31107i	0.835884	−	0.548906i	$-0.184955\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.68120	+	10.2504i	0.239198	+	0.523771i	0.990717	−	0.135941i	$-0.0434056\pi$
$383$	4.68120	+	10.2504i	0.239198	+	0.523771i	−0.751519	+	0.659712i	$0.770678\pi$
$384$		0			0
$385$	−2.79137	−	0.819620i	−0.142261	−	0.0417717i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.09611	+	28.4891i	0.207681	+	1.44445i	0.780697	+	0.624910i	$0.214864\pi$
$389$	4.09611	+	28.4891i	0.207681	+	1.44445i	−0.573016	+	0.819544i	$0.694227\pi$
$390$		0			0
$391$	−0.924377	+	3.94361i	−0.0467477	+	0.199437i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.31546	−	1.85439i	0.317765	−	0.0933043i
$396$		0			0
$397$	32.8529	+	9.64649i	1.64884	+	0.484143i	0.968554	−	0.248803i	$-0.0800372\pi$
$397$	32.8529	+	9.64649i	1.64884	+	0.484143i	0.680287	+	0.732946i	$0.261855\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−23.7957	−	15.2926i	−1.18830	−	0.763674i	−0.211406	−	0.977398i	$-0.567804\pi$
$401$	−23.7957	−	15.2926i	−1.18830	−	0.763674i	−0.976894	+	0.213724i	$0.931441\pi$
$402$		0			0
$403$	−0.0451457	+	0.313995i	−0.00224887	+	0.0156412i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.8406	+	11.4655i	−0.884327	+	0.568322i
$408$		0			0
$409$	−1.46621	+	1.69210i	−0.0724996	+	0.0836690i	−0.790841	−	0.612022i	$-0.790356\pi$
$409$	−1.46621	+	1.69210i	−0.0724996	+	0.0836690i	0.718341	+	0.695691i	$0.244902\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.55776			0.0766523
$414$		0			0
$415$	5.80807			0.285107
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.4966	+	16.7300i	−0.708205	+	0.817312i	−0.989836	−	0.142211i	$-0.954579\pi$
$419$	−14.4966	+	16.7300i	−0.708205	+	0.817312i	0.281632	+	0.959523i	$0.409124\pi$
$420$		0			0
$421$	−6.06100	+	3.89517i	−0.295395	+	0.189839i	−0.679941	−	0.733267i	$-0.737994\pi$
$421$	−6.06100	+	3.89517i	−0.295395	+	0.189839i	0.384546	+	0.923106i	$0.374358\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.449309	+	3.12501i	−0.0217947	+	0.151585i
$426$		0			0
$427$	7.92440	+	5.09271i	0.383489	+	0.246453i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.4454	+	3.65430i	0.599475	+	0.176022i	0.567370	−	0.823463i	$-0.307961\pi$
$431$	12.4454	+	3.65430i	0.599475	+	0.176022i	0.0321045	+	0.999485i	$0.489779\pi$
$432$		0			0
$433$	14.3167	−	4.20377i	0.688019	−	0.202020i	0.0810071	−	0.996714i	$-0.474186\pi$
$433$	14.3167	−	4.20377i	0.688019	−	0.202020i	0.607012	+	0.794693i	$0.292368\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.06289	+	8.63239i	0.146518	+	0.412943i
$438$		0			0
$439$	−0.0758913	−	0.527836i	−0.00362210	−	0.0251922i	0.987930	−	0.154899i	$-0.0495054\pi$
$439$	−0.0758913	−	0.527836i	−0.00362210	−	0.0251922i	−0.991552	+	0.129707i	$0.958596\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.4315	−	5.41197i	−0.875705	−	0.257130i	−0.187165	−	0.982328i	$-0.559930\pi$
$443$	−18.4315	−	5.41197i	−0.875705	−	0.257130i	−0.688540	+	0.725198i	$0.741748\pi$
$444$		0			0
$445$	5.66916	+	12.4137i	0.268744	+	0.588467i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.820060	+	5.70365i	−0.0387010	+	0.269172i	−0.999979	−	0.00640731i	$-0.997960\pi$
$449$	−0.820060	+	5.70365i	−0.0387010	+	0.269172i	0.961278	+	0.275579i	$0.0888696\pi$
$450$		0			0
$451$	7.80547	+	9.00799i	0.367545	+	0.424170i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.927795	+	1.07073i	−0.0434957	+	0.0501967i
$456$		0			0
$457$	5.55155	−	12.1562i	0.259690	−	0.568643i	−0.734210	−	0.678922i	$-0.762447\pi$
$457$	5.55155	−	12.1562i	0.259690	−	0.568643i	0.993901	+	0.110279i	$0.0351746\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.9200			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$461$	−22.9200			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$462$		0			0
$463$	5.01092	−	10.9724i	0.232877	−	0.509930i	−0.756730	−	0.653728i	$-0.773204\pi$
$463$	5.01092	−	10.9724i	0.232877	−	0.509930i	0.989607	+	0.143798i	$0.0459314\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.16270	−	3.96053i	0.285176	−	0.183271i	−0.390230	−	0.920717i	$-0.627605\pi$
$467$	6.16270	−	3.96053i	0.285176	−	0.183271i	0.675406	+	0.737446i	$0.263968\pi$
$468$		0			0
$469$	3.45723	+	3.98986i	0.159640	+	0.184235i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.77933	−	4.35681i	−0.311714	−	0.200326i
$474$		0			0
$475$	2.96584	+	6.49428i	0.136082	+	0.297978i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	32.9833	−	9.68478i	1.50705	−	0.442509i	0.579111	−	0.815248i	$-0.303400\pi$
$479$	32.9833	−	9.68478i	1.50705	−	0.442509i	0.927936	+	0.372739i	$0.121581\pi$
$480$		0			0
$481$	1.46981	+	10.2227i	0.0670175	+	0.466117i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.644898	+	4.48537i	0.0292833	+	0.203670i
$486$		0			0
$487$	−10.9571	+	3.21729i	−0.496513	+	0.145789i	−0.520395	−	0.853925i	$-0.674215\pi$
$487$	−10.9571	+	3.21729i	−0.496513	+	0.145789i	0.0238826	+	0.999715i	$0.492397\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.4308	+	35.9785i	0.741514	+	1.62369i	0.781048	+	0.624471i	$0.214685\pi$
$491$	16.4308	+	35.9785i	0.741514	+	1.62369i	−0.0395346	+	0.999218i	$0.512588\pi$
$492$		0			0
$493$	0.408539	+	0.262552i	0.0183997	+	0.0118248i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.194873	+	0.224896i	0.00874125	+	0.0100879i
$498$		0			0
$499$	10.3299	−	6.63865i	0.462432	−	0.297187i	−0.288604	−	0.957449i	$-0.593191\pi$
$499$	10.3299	−	6.63865i	0.462432	−	0.297187i	0.751036	+	0.660262i	$0.229555\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.5877	−	23.1839i	0.472084	−	1.03372i	−0.512480	−	0.858699i	$-0.671273\pi$
$503$	10.5877	−	23.1839i	0.472084	−	1.03372i	0.984565	−	0.175022i	$-0.0559995\pi$
$504$		0			0
$505$	−13.5630			−0.603544
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.83427	−	21.5340i	0.435896	−	0.954480i	−0.556437	−	0.830890i	$-0.687832\pi$
$509$	9.83427	−	21.5340i	0.435896	−	0.954480i	0.992333	−	0.123590i	$-0.0394408\pi$
$510$		0			0
$511$	−3.57183	+	4.12211i	−0.158008	+	0.182351i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.4685	+	14.3894i	0.549426	+	0.634071i
$516$		0			0
$517$	0.195140	−	1.35723i	0.00858227	−	0.0596910i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.40596	−	20.5962i	−0.412083	−	0.902335i	−0.995901	−	0.0904506i	$-0.971169\pi$
$521$	−9.40596	−	20.5962i	−0.412083	−	0.902335i	0.583818	−	0.811884i	$-0.301558\pi$
$522$		0			0
$523$	8.76777	+	2.57445i	0.383388	+	0.112573i	0.467747	−	0.883863i	$-0.345066\pi$
$523$	8.76777	+	2.57445i	0.383388	+	0.112573i	−0.0843587	+	0.996435i	$0.526884\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.0320363	+	0.222818i	0.00139552	+	0.00970609i
$528$		0			0
$529$	−22.8592	+	2.54125i	−0.993877	+	0.110489i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.56954	−	1.63536i	0.241244	−	0.0708355i
$534$		0			0
$535$	13.4717	+	3.95565i	0.582432	+	0.171018i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.0832	−	7.76538i	−0.520459	−	0.334479i
$540$		0			0
$541$	−4.81852	+	33.5135i	−0.207164	+	1.44086i	0.575188	+	0.818021i	$0.304929\pi$
$541$	−4.81852	+	33.5135i	−0.207164	+	1.44086i	−0.782352	+	0.622837i	$0.785980\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.527141	+	0.338773i	−0.0225802	+	0.0145114i
$546$		0			0
$547$	7.24934	−	8.36618i	0.309959	−	0.357712i	−0.579301	−	0.815114i	$-0.696674\pi$
$547$	7.24934	−	8.36618i	0.309959	−	0.357712i	0.889260	+	0.457402i	$0.151220\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.09819			0.0467845
$552$		0			0
$553$	−6.20897			−0.264032
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.0341	−	11.5799i	0.425157	−	0.490658i	−0.502244	−	0.864726i	$-0.667492\pi$
$557$	10.0341	−	11.5799i	0.425157	−	0.490658i	0.927401	+	0.374068i	$0.122037\pi$
$558$		0			0
$559$	−3.30152	+	2.12176i	−0.139639	+	0.0897408i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.138018	−	0.959933i	0.00581675	−	0.0404564i	−0.986706	−	0.162513i	$-0.948040\pi$
$563$	0.138018	−	0.959933i	0.00581675	−	0.0404564i	0.992523	+	0.122057i	$0.0389491\pi$
$564$		0			0
$565$	−7.96317	−	5.11762i	−0.335013	−	0.215300i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.53852	+	0.745376i	0.106420	+	0.0312478i	0.334509	−	0.942393i	$-0.391430\pi$
$569$	2.53852	+	0.745376i	0.106420	+	0.0312478i	−0.228089	+	0.973640i	$0.573248\pi$
$570$		0			0
$571$	−24.9891	+	7.33747i	−1.04576	+	0.307063i	−0.759104	−	0.650970i	$-0.774363\pi$
$571$	−24.9891	+	7.33747i	−1.04576	+	0.307063i	−0.286658	+	0.958033i	$0.592544\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−17.5764	+	3.52921i	−0.732988	+	0.147178i
$576$		0			0
$577$	−3.37205	−	23.4531i	−0.140380	−	0.976366i	−0.931250	−	0.364381i	$-0.881280\pi$
$577$	−3.37205	−	23.4531i	−0.140380	−	0.976366i	0.790870	−	0.611985i	$-0.209629\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.25691	−	1.54357i	−0.218093	−	0.0640380i
$582$		0			0
$583$	6.29303	+	13.7798i	0.260631	+	0.570702i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.32866	+	16.1962i	−0.0961139	+	0.668487i	0.883623	+	0.468199i	$0.155097\pi$
$587$	−2.32866	+	16.1962i	−0.0961139	+	0.668487i	−0.979737	+	0.200288i	$0.935812\pi$
$588$		0			0
$589$	0.333359	+	0.384717i	0.0137358	+	0.0158520i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	29.5422	−	34.0936i	1.21315	−	1.40006i	0.321763	−	0.946820i	$-0.395724\pi$
$593$	29.5422	−	34.0936i	1.21315	−	1.40006i	0.891391	−	0.453235i	$-0.149730\pi$
$594$		0			0
$595$	−0.417649	+	0.914524i	−0.0171219	+	0.0374918i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.5788			0.513957			0.256978	−	0.966417i	$-0.417273\pi$
$599$	12.5788			0.513957			0.256978	+	0.966417i	$0.417273\pi$
$600$		0			0
$601$	−13.2373	+	28.9856i	−0.539959	+	1.18235i	0.421356	+	0.906895i	$0.361554\pi$
$601$	−13.2373	+	28.9856i	−0.539959	+	1.18235i	−0.961315	+	0.275451i	$0.911173\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.75075	+	3.05312i	−0.193146	+	0.124127i
$606$		0			0
$607$	13.8020	+	15.9283i	0.560205	+	0.646511i	0.963230	−	0.268678i	$-0.0865866\pi$
$607$	13.8020	+	15.9283i	0.560205	+	0.646511i	−0.403025	+	0.915189i	$0.632041\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.561761	−	0.361022i	−0.0227264	−	0.0146054i
$612$		0			0
$613$	−2.06471	−	4.52108i	−0.0833927	−	0.182605i	0.863342	−	0.504619i	$-0.168367\pi$
$613$	−2.06471	−	4.52108i	−0.0833927	−	0.182605i	−0.946735	+	0.322015i	$0.895640\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.41675	−	1.59050i	0.218070	−	0.0640312i	−0.170872	−	0.985293i	$-0.554659\pi$
$617$	5.41675	−	1.59050i	0.218070	−	0.0640312i	0.388943	+	0.921262i	$0.372840\pi$
$618$		0			0
$619$	−0.298014	−	2.07273i	−0.0119782	−	0.0833101i	0.982955	−	0.183844i	$-0.0588541\pi$
$619$	−0.298014	−	2.07273i	−0.0119782	−	0.0833101i	−0.994934	+	0.100534i	$0.967945\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.83208	−	12.7424i	−0.0734005	−	0.510512i
$624$		0			0
$625$	−7.35334	+	2.15914i	−0.294134	+	0.0863655i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.04452	+	6.66657i	0.121393	+	0.265814i
$630$		0			0
$631$	−18.4937	−	11.8852i	−0.736223	−	0.473142i	0.118023	−	0.993011i	$-0.462344\pi$
$631$	−18.4937	−	11.8852i	−0.736223	−	0.473142i	−0.854246	+	0.519869i	$0.825981\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.7035	+	12.3524i	0.424754	+	0.490192i
$636$		0			0
$637$	−5.88448	+	3.78173i	−0.233152	+	0.149838i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.85869	−	4.06996i	0.0734138	−	0.160754i	−0.869367	−	0.494167i	$-0.835473\pi$
$641$	1.85869	−	4.06996i	0.0734138	−	0.160754i	0.942781	+	0.333413i	$0.108200\pi$
$642$		0			0
$643$	15.7233			0.620067			0.310034	−	0.950726i	$-0.399660\pi$
$643$	15.7233			0.620067			0.310034	+	0.950726i	$0.399660\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.14760	−	20.0305i	0.359629	−	0.787478i	−0.640185	−	0.768221i	$-0.721142\pi$
$647$	9.14760	−	20.0305i	0.359629	−	0.787478i	0.999815	−	0.0192578i	$-0.00613033\pi$
$648$		0			0
$649$	−2.35272	+	2.71518i	−0.0923523	+	0.106580i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.14529	−	4.78391i	−0.162218	−	0.187209i	0.668822	−	0.743423i	$-0.266799\pi$
$653$	−4.14529	−	4.78391i	−0.162218	−	0.187209i	−0.831039	+	0.556214i	$0.812254\pi$
$654$		0			0
$655$	1.62433	−	11.2974i	0.0634676	−	0.441427i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.00751	+	4.39583i	0.0782014	+	0.171237i	0.944694	−	0.327952i	$-0.106358\pi$
$659$	2.00751	+	4.39583i	0.0782014	+	0.171237i	−0.866493	+	0.499189i	$0.833631\pi$
$660$		0			0
$661$	−5.68540	−	1.66938i	−0.221136	−	0.0649315i	0.169288	−	0.985567i	$-0.445853\pi$
$661$	−5.68540	−	1.66938i	−0.221136	−	0.0649315i	−0.390424	+	0.920635i	$0.627672\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.323557	+	2.25039i	0.0125470	+	0.0872662i
$666$		0			0
$667$	−0.629312	+	2.68480i	−0.0243671	+	0.103956i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−20.8450	+	6.12065i	−0.804712	+	0.236285i
$672$		0			0
$673$	−48.3632	−	14.2007i	−1.86426	−	0.547397i	−0.998932	−	0.0461990i	$-0.985289\pi$
$673$	−48.3632	−	14.2007i	−1.86426	−	0.547397i	−0.865332	−	0.501198i	$-0.832893\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−34.9502	−	22.4611i	−1.34324	−	0.863251i	−0.346058	−	0.938213i	$-0.612480\pi$
$677$	−34.9502	−	22.4611i	−1.34324	−	0.863251i	−0.997186	+	0.0749627i	$0.976116\pi$
$678$		0			0
$679$	0.608342	−	4.23111i	0.0233460	−	0.162375i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−36.5235	+	23.4722i	−1.39753	+	0.898140i	−0.999812	−	0.0193668i	$-0.993835\pi$
$683$	−36.5235	+	23.4722i	−1.39753	+	0.898140i	−0.397720	+	0.917507i	$0.630199\pi$
$684$		0			0
$685$	7.76852	−	8.96535i	0.296820	−	0.342548i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.37743			0.281058
$690$		0			0
$691$	−16.4600			−0.626168			−0.313084	−	0.949725i	$-0.601362\pi$
$691$	−16.4600			−0.626168			−0.313084	+	0.949725i	$0.601362\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.56179	−	5.26459i	0.173039	−	0.199697i
$696$		0			0
$697$	3.46522	−	2.22696i	0.131255	−	0.0843522i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.43218	−	9.96101i	0.0540926	−	0.376222i	−0.944736	−	0.327832i	$-0.893682\pi$
$701$	1.43218	−	9.96101i	0.0540926	−	0.376222i	0.998829	−	0.0483898i	$-0.0154090\pi$
$702$		0			0
$703$	13.9423	+	8.96017i	0.525844	+	0.337939i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.2759	+	3.60453i	0.461683	+	0.135562i
$708$		0			0
$709$	33.0074	−	9.69186i	1.23962	−	0.363985i	0.404748	−	0.914428i	$-0.367359\pi$
$709$	33.0074	−	9.69186i	1.23962	−	0.363985i	0.834873	+	0.550443i	$0.185541\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.13157	+	0.594519i	−0.0423775	+	0.0222649i
$714$		0			0
$715$	−0.465022	−	3.23430i	−0.0173908	−	0.120956i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.8137	−	4.05608i	−0.515165	−	0.151266i	0.0138079	−	0.999905i	$-0.495605\pi$
$719$	−13.8137	−	4.05608i	−0.515165	−	0.151266i	−0.528973	+	0.848638i	$0.677423\pi$
$720$		0			0
$721$	−7.46109	−	16.3375i	−0.277866	−	0.608441i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.305888	+	2.12750i	−0.0113604	+	0.0790132i
$726$		0			0
$727$	2.20780	+	2.54794i	0.0818827	+	0.0944977i	0.795213	−	0.606331i	$-0.207359\pi$
$727$	2.20780	+	2.54794i	0.0818827	+	0.0944977i	−0.713330	+	0.700829i	$0.752814\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.82374	+	2.10471i	−0.0674534	+	0.0778453i
$732$		0			0
$733$	7.38377	−	16.1682i	0.272726	−	0.597186i	−0.722865	−	0.690989i	$-0.757175\pi$
$733$	7.38377	−	16.1682i	0.272726	−	0.597186i	0.995591	+	0.0938032i	$0.0299024\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.1759			−0.448504
$738$		0			0
$739$	13.4290	−	29.4055i	0.493995	−	1.08170i	−0.484380	−	0.874858i	$-0.660955\pi$
$739$	13.4290	−	29.4055i	0.493995	−	1.08170i	0.978375	−	0.206840i	$-0.0663181\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.89559	+	3.78886i	−0.216288	+	0.139000i	−0.644299	−	0.764774i	$-0.722851\pi$
$743$	−5.89559	+	3.78886i	−0.216288	+	0.139000i	0.428011	+	0.903774i	$0.359214\pi$
$744$		0			0
$745$	−9.89365	−	11.4179i	−0.362475	−	0.418319i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.1420	−	7.16054i	−0.407121	−	0.261641i
$750$		0			0
$751$	−1.51872	−	3.32554i	−0.0554190	−	0.121351i	0.879897	−	0.475165i	$-0.157612\pi$
$751$	−1.51872	−	3.32554i	−0.0554190	−	0.121351i	−0.935316	+	0.353815i	$0.884884\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	19.6912	−	5.78185i	0.716635	−	0.210423i
$756$		0			0
$757$	−6.00136	−	41.7404i	−0.218123	−	1.51708i	−0.744958	−	0.667112i	$-0.767530\pi$
$757$	−6.00136	−	41.7404i	−0.218123	−	1.51708i	0.526835	−	0.849968i	$-0.323379\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.33621	−	30.1590i	−0.157187	−	1.09326i	−0.903785	−	0.427986i	$-0.859223\pi$
$761$	−4.33621	−	30.1590i	−0.157187	−	1.09326i	0.746598	−	0.665276i	$-0.231686\pi$
$762$		0			0
$763$	0.567150	−	0.166530i	0.0205322	−	0.00602880i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.726826	+	1.59153i	0.0262442	+	0.0574667i
$768$		0			0
$769$	−36.2713	−	23.3102i	−1.30798	−	0.840586i	−0.313921	−	0.949449i	$-0.601643\pi$
$769$	−36.2713	−	23.3102i	−1.30798	−	0.840586i	−0.994057	+	0.108863i	$0.965279\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	27.4944	+	31.7302i	0.988903	+	1.14126i	0.989973	+	0.141256i	$0.0451140\pi$
$773$	27.4944	+	31.7302i	0.988903	+	1.14126i	−0.00106970	+	0.999999i	$0.500340\pi$
$774$		0			0
$775$	−0.838156	+	0.538650i	−0.0301074	+	0.0193489i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.86952	−	8.47306i	0.138640	−	0.303579i
$780$		0			0
$781$	−0.686315			−0.0245583
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.81510	+	19.3024i	−0.314624	+	0.688931i
$786$		0			0
$787$	27.2807	−	31.4836i	0.972451	−	1.12227i	−0.0200212	−	0.999800i	$-0.506373\pi$
$787$	27.2807	−	31.4836i	0.972451	−	1.12227i	0.992472	−	0.122469i	$-0.0390812\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.84743	+	6.74829i	0.207911	+	0.239942i
$792$		0			0
$793$	−1.50570	+	10.4724i	−0.0534689	+	0.371884i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.8644	−	28.1691i	−0.455680	−	0.997800i	−0.988451	−	0.151541i	$-0.951577\pi$
$797$	−12.8644	−	28.1691i	−0.455680	−	0.997800i	0.532771	−	0.846260i	$-0.321151\pi$
$798$		0			0
$799$	−0.454666	−	0.133502i	−0.0160849	−	0.00472296i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.79024	−	12.4514i	−0.0631763	−	0.439401i
$804$		0			0
$805$	−5.68704	−	0.498558i	−0.200442	−	0.0175719i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−53.0442	+	15.5752i	−1.86493	+	0.547594i	−0.866070	+	0.499922i	$0.833362\pi$
$809$	−53.0442	+	15.5752i	−1.86493	+	0.547594i	−0.998863	+	0.0476716i	$0.984820\pi$
$810$		0			0
$811$	−29.6152	−	8.69581i	−1.03993	−	0.305351i	−0.283188	−	0.959064i	$-0.591392\pi$
$811$	−29.6152	−	8.69581i	−1.03993	−	0.305351i	−0.756743	+	0.653713i	$0.773210\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.0978350	−	0.0628747i	−0.00342701	−	0.00220241i
$816$		0			0
$817$	−0.896261	+	6.23363i	−0.0313562	+	0.218087i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.317226	−	0.203869i	0.0110713	−	0.00711506i	−0.535093	−	0.844793i	$-0.679724\pi$
$821$	0.317226	−	0.203869i	0.0110713	−	0.00711506i	0.546165	+	0.837678i	$0.316087\pi$
$822$		0			0
$823$	2.87193	−	3.31438i	0.100109	−	0.115532i	−0.703484	−	0.710711i	$-0.748373\pi$
$823$	2.87193	−	3.31438i	0.100109	−	0.115532i	0.803593	+	0.595179i	$0.202919\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	37.5607			1.30611			0.653056	−	0.757309i	$-0.273487\pi$
$827$	37.5607			1.30611			0.653056	+	0.757309i	$0.273487\pi$
$828$		0			0
$829$	18.6526			0.647832			0.323916	−	0.946086i	$-0.395000\pi$
$829$	18.6526			0.647832			0.323916	+	0.946086i	$0.395000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.25055	+	3.75133i	−0.112625	+	0.129976i
$834$		0			0
$835$	16.1839	−	10.4008i	0.560067	−	0.359933i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.98323	−	34.6591i	0.172040	−	1.19657i	−0.702525	−	0.711659i	$-0.747944\pi$
$839$	4.98323	−	34.6591i	0.172040	−	1.19657i	0.874565	−	0.484908i	$-0.161147\pi$
$840$		0			0
$841$	−24.1182	−	15.4998i	−0.831663	−	0.534477i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.4851	+	3.66597i	0.429502	+	0.126113i
$846$		0			0
$847$	5.11133	−	1.50082i	0.175627	−	0.0515688i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−29.8949	+	28.9508i	−1.02478	+	0.992421i
$852$		0			0
$853$	−5.23460	−	36.4075i	−0.179229	−	1.24657i	−0.858551	−	0.512728i	$-0.828635\pi$
$853$	−5.23460	−	36.4075i	−0.179229	−	1.24657i	0.679322	−	0.733840i	$-0.262274\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.9111	+	8.48905i	0.987583	+	0.289981i	0.735351	−	0.677686i	$-0.237017\pi$
$857$	28.9111	+	8.48905i	0.987583	+	0.289981i	0.252232	+	0.967667i	$0.418835\pi$
$858$		0			0
$859$	5.89911	+	12.9172i	0.201275	+	0.440731i	0.983173	−	0.182675i	$-0.0584757\pi$
$859$	5.89911	+	12.9172i	0.201275	+	0.440731i	−0.781898	+	0.623406i	$0.785748\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.61465	+	11.2302i	−0.0549634	+	0.382279i	0.943709	+	0.330776i	$0.107310\pi$
$863$	−1.61465	+	11.2302i	−0.0549634	+	0.382279i	−0.998673	+	0.0515033i	$0.983599\pi$
$864$		0			0
$865$	−7.34256	−	8.47377i	−0.249655	−	0.288117i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.37754	−	10.8223i	0.318111	−	0.367120i
$870$		0			0
$871$	−2.46326	+	5.39378i	−0.0834643	+	0.182761i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.4016			−0.351639
$876$		0			0
$877$	10.0433	−	21.9917i	0.339138	−	0.742608i	−0.660831	−	0.750535i	$-0.729796\pi$
$877$	10.0433	−	21.9917i	0.339138	−	0.742608i	0.999969	+	0.00792694i	$0.00252325\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−28.9136	+	18.5817i	−0.974125	+	0.626032i	−0.927873	−	0.372897i	$-0.878364\pi$
$881$	−28.9136	+	18.5817i	−0.974125	+	0.626032i	−0.0462528	+	0.998930i	$0.514728\pi$
$882$		0			0
$883$	11.4383	+	13.2005i	0.384930	+	0.444233i	0.914837	−	0.403823i	$-0.132319\pi$
$883$	11.4383	+	13.2005i	0.384930	+	0.444233i	−0.529907	+	0.848056i	$0.677773\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.1796	−	16.8246i	−0.879025	−	0.564915i	0.0214758	−	0.999769i	$-0.493164\pi$
$887$	−26.1796	−	16.8246i	−0.879025	−	0.564915i	−0.900501	+	0.434854i	$0.856800\pi$
$888$		0			0
$889$	−6.40492	−	14.0248i	−0.214814	−	0.470377i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.02817	+	0.301897i	−0.0344063	+	0.0101026i
$894$		0			0
$895$	4.09073	+	28.4517i	0.136738	+	0.951034i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.0218102	+	0.151693i	0.000727411	+	0.00505926i
$900$		0			0
$901$	5.02312	−	1.47492i	0.167344	−	0.0491367i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.459513	+	1.00619i	0.0152747	+	0.0334470i
$906$		0			0
$907$	−30.4322	−	19.5576i	−1.01049	−	0.649400i	−0.0729669	−	0.997334i	$-0.523247\pi$
$907$	−30.4322	−	19.5576i	−1.01049	−	0.649400i	−0.937519	+	0.347935i	$0.886883\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.76824	+	8.96503i	0.257373	+	0.297025i	0.869700	−	0.493580i	$-0.164312\pi$
$911$	7.76824	+	8.96503i	0.257373	+	0.297025i	−0.612327	+	0.790604i	$0.709766\pi$
$912$		0			0
$913$	10.6301	−	6.83153i	0.351804	−	0.226091i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.47262	+	9.79366i	−0.147699	+	0.323415i
$918$		0			0
$919$	8.62999			0.284677			0.142338	−	0.989818i	$-0.454538\pi$
$919$	8.62999			0.284677			0.142338	+	0.989818i	$0.454538\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.138846	+	0.304030i	−0.00457017	+	0.0100073i
$924$		0			0
$925$	−21.2418	+	24.5143i	−0.698425	+	0.806026i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.92062	+	9.14089i	0.259867	+	0.299903i	0.870658	−	0.491890i	$-0.163694\pi$
$929$	7.92062	+	9.14089i	0.259867	+	0.299903i	−0.610790	+	0.791792i	$0.709148\pi$
$930$		0			0
$931$	−1.59746	+	11.1105i	−0.0523545	+	0.364134i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.963234	−	2.10919i	−0.0315011	−	0.0689779i
$936$		0			0
$937$	15.7156	+	4.61451i	0.513405	+	0.150749i	0.528165	−	0.849142i	$-0.322880\pi$
$937$	15.7156	+	4.61451i	0.513405	+	0.150749i	−0.0147599	+	0.999891i	$0.504698\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.06149	+	28.2483i	0.132401	+	0.920867i	0.942412	+	0.334453i	$0.108552\pi$
$941$	4.06149	+	28.2483i	0.132401	+	0.920867i	−0.810012	+	0.586414i	$0.800539\pi$
$942$		0			0
$943$	18.4971	+	14.3154i	0.602348	+	0.466175i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.35603	−	0.985419i	0.109056	−	0.0320218i	−0.226749	−	0.973953i	$-0.572810\pi$
$947$	3.35603	−	0.985419i	0.109056	−	0.0320218i	0.335805	+	0.941931i	$0.390992\pi$
$948$		0			0
$949$	−5.87802	−	1.72594i	−0.190809	−	0.0560265i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−32.2661	−	20.7362i	−1.04520	−	0.671710i	−0.0989337	−	0.995094i	$-0.531543\pi$
$953$	−32.2661	−	20.7362i	−1.04520	−	0.671710i	−0.946268	+	0.323384i	$0.895180\pi$
$954$		0			0
$955$	−0.741522	+	5.15740i	−0.0239951	+	0.166890i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.41397	+	6.04999i	−0.303993	+	0.195364i
$960$		0			0
$961$	20.2542	−	23.3745i	0.653360	−	0.754018i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.3799			0.623861
$966$		0			0
$967$	−55.1290			−1.77283			−0.886415	−	0.462892i	$-0.846812\pi$
$967$	−55.1290			−1.77283			−0.886415	+	0.462892i	$0.846812\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.79907	−	2.07624i	0.0577350	−	0.0666297i	−0.726147	−	0.687539i	$-0.758691\pi$
$971$	1.79907	−	2.07624i	0.0577350	−	0.0666297i	0.783882	+	0.620909i	$0.213236\pi$
$972$		0			0
$973$	−5.52802	+	3.55264i	−0.177220	+	0.113893i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.75026	−	46.9491i	0.215960	−	1.50203i	−0.536784	−	0.843720i	$-0.680361\pi$
$977$	6.75026	−	46.9491i	0.215960	−	1.50203i	0.752744	−	0.658314i	$-0.228730\pi$
$978$		0			0
$979$	24.9770	+	16.0518i	0.798269	+	0.513016i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.1583	−	6.50627i	−0.706741	−	0.207518i	−0.0914405	−	0.995811i	$-0.529147\pi$
$983$	−22.1583	−	6.50627i	−0.706741	−	0.207518i	−0.615300	+	0.788293i	$0.710965\pi$
$984$		0			0
$985$	−1.57025	+	0.461068i	−0.0500324	+	0.0146908i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−14.7261	−	5.76328i	−0.468261	−	0.183262i
$990$		0			0
$991$	5.83205	+	40.5628i	0.185261	+	1.28852i	0.844080	+	0.536218i	$0.180147\pi$
$991$	5.83205	+	40.5628i	0.185261	+	1.28852i	−0.658819	+	0.752302i	$0.728944\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.86071	+	2.30811i	0.249201	+	0.0731721i
$996$		0			0
$997$	5.74303	+	12.5755i	0.181884	+	0.398269i	0.978509	−	0.206204i	$-0.0661110\pi$
$997$	5.74303	+	12.5755i	0.181884	+	0.398269i	−0.796626	+	0.604473i	$0.793384\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.q.c.325.1		20
3.2	odd	2		276.2.i.a.49.2	✓	20
23.8	even	11	inner	828.2.q.c.721.1		20
69.8	odd	22		276.2.i.a.169.2	yes	20
69.56	even	22		6348.2.a.t.1.6		10
69.59	odd	22		6348.2.a.s.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.49.2	✓	20	3.2	odd	2
276.2.i.a.169.2	yes	20	69.8	odd	22
828.2.q.c.325.1		20	1.1	even	1	trivial
828.2.q.c.721.1		20	23.8	even	11	inner
6348.2.a.s.1.5		10	69.59	odd	22
6348.2.a.t.1.6		10	69.56	even	22

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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.735636 + 0.848969i) q^{5} +(0.891451 - 0.572901i) q^{7} +O(q^{10})\)	\(q+(-0.735636 + 0.848969i) q^{5} +(0.891451 - 0.572901i) q^{7} +(-0.347809 + 2.41907i) q^{11} +(1.00126 + 0.643468i) q^{13} +(0.810376 + 0.237948i) q^{17} +(1.83256 - 0.538087i) q^{19} +(0.265350 + 4.78849i) q^{23} +(0.531986 + 3.70004i) q^{25} +(0.551701 + 0.161994i) q^{29} +(0.110721 + 0.242445i) q^{31} +(-0.169408 + 1.17826i) q^{35} +(5.68252 + 6.55798i) q^{37} +(3.19380 - 3.68585i) q^{41} +(-1.36978 + 2.99940i) q^{43} -0.561056 q^{47} +(-2.44144 + 5.34600i) q^{49} +(5.21451 - 3.35116i) q^{53} +(-1.79785 - 2.07483i) q^{55} +(1.23668 + 0.794765i) q^{59} +(3.69276 + 8.08602i) q^{61} +(-1.28285 + 0.376677i) q^{65} +(0.709022 + 4.93135i) q^{67} +(0.0399653 + 0.277964i) q^{71} +(-4.93870 + 1.45013i) q^{73} +(1.07583 + 2.35574i) q^{77} +(-4.92920 - 3.16780i) q^{79} +(-3.38585 - 3.90747i) q^{83} +(-0.798152 + 0.512941i) q^{85} +(5.04667 - 11.0507i) q^{89} +1.26121 q^{91} +(-0.891275 + 1.95162i) q^{95} +(2.64165 - 3.04863i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^5	\( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

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