LMFDB - Embedded newform 405.2.j.f.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(109,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("405.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			379.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	405.379
Dual form			405.2.j.f.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-1.67303 - 1.48356i) q^{5} +(-2.59808 - 1.50000i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(-1.67303 - 1.48356i) q^{5} +(-2.59808 - 1.50000i) q^{7} -2.82843i q^{8} +(-1.00000 - 3.00000i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-2.59808 + 1.50000i) q^{13} +(-2.12132 - 3.67423i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.82843i q^{17} -1.00000 q^{19} +(5.19615 - 3.00000i) q^{22} +(6.12372 - 3.53553i) q^{23} +(0.598076 + 4.96410i) q^{25} -4.24264 q^{26} +(2.12132 - 3.67423i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.00000 + 3.46410i) q^{34} +(2.12132 + 6.36396i) q^{35} +9.00000i q^{37} +(-1.22474 - 0.707107i) q^{38} +(-4.19615 + 4.73205i) q^{40} +(-2.12132 - 3.67423i) q^{41} +(5.19615 + 3.00000i) q^{43} +10.0000 q^{46} +(-2.44949 - 1.41421i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-2.77766 + 6.50266i) q^{50} -9.89949i q^{53} +(-9.00000 + 3.00000i) q^{55} +(-4.24264 + 7.34847i) q^{56} +(5.19615 - 3.00000i) q^{58} +(4.24264 + 7.34847i) q^{59} +(6.50000 - 11.2583i) q^{61} -2.82843i q^{62} -8.00000 q^{64} +(6.57201 + 1.34486i) q^{65} +(-2.59808 + 1.50000i) q^{67} +(-1.90192 + 9.29423i) q^{70} +12.7279 q^{71} -9.00000i q^{73} +(-6.36396 + 11.0227i) q^{74} +(-11.0227 + 6.36396i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-8.48528 + 2.82843i) q^{80} -6.00000i q^{82} +(1.22474 + 0.707107i) q^{83} +(4.19615 - 4.73205i) q^{85} +(4.24264 + 7.34847i) q^{86} +(-10.3923 - 6.00000i) q^{88} +9.00000 q^{91} +(-2.00000 - 3.46410i) q^{94} +(1.67303 + 1.48356i) q^{95} +(-2.59808 - 1.50000i) q^{97} +2.82843i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{10} + 16 q^{16} - 8 q^{19} - 16 q^{25} - 8 q^{31} - 16 q^{34} + 8 q^{40} + 80 q^{46} + 8 q^{49} - 72 q^{55} + 52 q^{61} - 64 q^{64} - 36 q^{70} - 20 q^{79} - 8 q^{85} + 72 q^{91} - 16 q^{94}+O(q^{100}) $ 8 * q - 8 * q^10 + 16 * q^16 - 8 * q^19 - 16 * q^25 - 8 * q^31 - 16 * q^34 + 8 * q^40 + 80 * q^46 + 8 * q^49 - 72 * q^55 + 52 * q^61 - 64 * q^64 - 36 * q^70 - 20 * q^79 - 8 * q^85 + 72 * q^91 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	1.22474	+	0.707107i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.67303	−	1.48356i	−0.748203	−	0.663470i
$5$	−1.67303	−	1.48356i	−0.748203	−	0.663470i
$6$		0			0
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	−1.00000	−	3.00000i	−0.316228	−	0.948683i
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$		0			0
$13$	−2.59808	+	1.50000i	−0.720577	+	0.416025i	−0.814965	−	0.579510i	$-0.803244\pi$
$13$	−2.59808	+	1.50000i	−0.720577	+	0.416025i	0.0943882	+	0.995535i	$0.469911\pi$
$14$	−2.12132	−	3.67423i	−0.566947	−	0.981981i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$		0			0
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$		0			0
$22$	5.19615	−	3.00000i	1.10782	−	0.639602i
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.300610	−	0.953747i	$-0.402810\pi$
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.976274	+	0.216537i	$0.0694763\pi$
$24$		0			0
$25$	0.598076	+	4.96410i	0.119615	+	0.992820i
$26$	−4.24264			−0.832050
$27$		0			0
$28$		0			0
$29$	2.12132	−	3.67423i	0.393919	−	0.682288i	−0.599043	−	0.800717i	$-0.704452\pi$
$29$	2.12132	−	3.67423i	0.393919	−	0.682288i	0.992963	+	0.118428i	$0.0377856\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$		0			0
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	2.12132	+	6.36396i	0.358569	+	1.07571i
$36$		0			0
$37$			9.00000i			1.47959i	0.672832	+	0.739795i	$0.265078\pi$
$37$			9.00000i			1.47959i	−0.672832	+	0.739795i	$0.734922\pi$
$38$	−1.22474	−	0.707107i	−0.198680	−	0.114708i
$39$		0			0
$40$	−4.19615	+	4.73205i	−0.663470	+	0.748203i
$41$	−2.12132	−	3.67423i	−0.331295	−	0.573819i	0.651471	−	0.758673i	$-0.274152\pi$
$41$	−2.12132	−	3.67423i	−0.331295	−	0.573819i	−0.982766	+	0.184854i	$0.940819\pi$
$42$		0			0
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	0.840809	−	0.541332i	$-0.182080\pi$
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	−0.0484030	+	0.998828i	$0.515413\pi$
$44$		0			0
$45$		0			0
$46$	10.0000			1.47442
$47$	−2.44949	−	1.41421i	−0.357295	−	0.206284i	0.310599	−	0.950541i	$-0.399470\pi$
$47$	−2.44949	−	1.41421i	−0.357295	−	0.206284i	−0.667893	+	0.744257i	$0.732804\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$	−2.77766	+	6.50266i	−0.392820	+	0.919615i
$51$		0			0
$52$		0			0
$53$		−	9.89949i		−	1.35980i	−0.733305	−	0.679900i	$-0.762023\pi$
$53$		−	9.89949i		−	1.35980i	0.733305	−	0.679900i	$-0.237977\pi$
$54$		0			0
$55$	−9.00000	+	3.00000i	−1.21356	+	0.404520i
$56$	−4.24264	+	7.34847i	−0.566947	+	0.981981i
$57$		0			0
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	0.998105	+	0.0615367i	$0.0196001\pi$
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	−0.445760	+	0.895152i	$0.647067\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		−	2.82843i		−	0.359211i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	6.57201	+	1.34486i	0.815158	+	0.166810i
$66$		0			0
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$		0			0
$69$		0			0
$70$	−1.90192	+	9.29423i	−0.227323	+	1.11087i
$71$	12.7279			1.51053			0.755263	−	0.655422i	$-0.227509\pi$
$71$	12.7279			1.51053			0.755263	+	0.655422i	$0.227509\pi$
$72$		0			0
$73$		−	9.00000i		−	1.05337i	−0.850060	−	0.526685i	$-0.823435\pi$
$73$		−	9.00000i		−	1.05337i	0.850060	−	0.526685i	$-0.176565\pi$
$74$	−6.36396	+	11.0227i	−0.739795	+	1.28136i
$75$		0			0
$76$		0			0
$77$	−11.0227	+	6.36396i	−1.25615	+	0.725241i
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−8.48528	+	2.82843i	−0.948683	+	0.316228i
$81$		0			0
$82$		−	6.00000i		−	0.662589i
$83$	1.22474	+	0.707107i	0.134433	+	0.0776151i	0.565708	−	0.824605i	$-0.308603\pi$
$83$	1.22474	+	0.707107i	0.134433	+	0.0776151i	−0.431275	+	0.902220i	$0.641936\pi$
$84$		0			0
$85$	4.19615	−	4.73205i	0.455137	−	0.513263i
$86$	4.24264	+	7.34847i	0.457496	+	0.792406i
$87$		0			0
$88$	−10.3923	−	6.00000i	−1.10782	−	0.639602i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	9.00000			0.943456
$92$		0			0
$93$		0			0
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	1.67303	+	1.48356i	0.171650	+	0.152210i
$96$		0			0
$97$	−2.59808	−	1.50000i	−0.263795	−	0.152302i	0.362270	−	0.932073i	$-0.382002\pi$
$97$	−2.59808	−	1.50000i	−0.263795	−	0.152302i	−0.626064	+	0.779771i	$0.715335\pi$
$98$			2.82843i			0.285714i
$99$		0			0
$100$		0			0
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	−0.996150	−	0.0876610i	$-0.972061\pi$
$101$	−4.24264	+	7.34847i	−0.422159	+	0.731200i	0.573992	+	0.818861i	$0.305394\pi$
$102$		0			0
$103$	−2.59808	+	1.50000i	−0.255996	+	0.147799i	−0.622507	−	0.782614i	$-0.713886\pi$
$103$	−2.59808	+	1.50000i	−0.255996	+	0.147799i	0.366511	+	0.930414i	$0.380552\pi$
$104$	4.24264	+	7.34847i	0.416025	+	0.720577i
$105$		0			0
$106$	7.00000	−	12.1244i	0.679900	−	1.17762i
$107$			7.07107i			0.683586i	0.939775	+	0.341793i	$0.111034\pi$
$107$			7.07107i			0.683586i	−0.939775	+	0.341793i	$0.888966\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	−13.1440	−	2.68973i	−1.25323	−	0.256455i
$111$		0			0
$112$	−10.3923	+	6.00000i	−0.981981	+	0.566947i
$113$	−1.22474	+	0.707107i	−0.115214	+	0.0665190i	−0.556500	−	0.830848i	$-0.687856\pi$
$113$	−1.22474	+	0.707107i	−0.115214	+	0.0665190i	0.441285	+	0.897367i	$0.354523\pi$
$114$		0			0
$115$	−15.4904	−	3.16987i	−1.44449	−	0.295592i
$116$		0			0
$117$		0			0
$118$			12.0000i			1.10469i
$119$	4.24264	−	7.34847i	0.388922	−	0.673633i
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	15.9217	−	9.19239i	1.44148	−	0.832240i
$123$		0			0
$124$		0			0
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$		0			0
$127$		−	18.0000i		−	1.59724i	−0.601834	−	0.798621i	$-0.705563\pi$
$127$		−	18.0000i		−	1.59724i	0.601834	−	0.798621i	$-0.294437\pi$
$128$	−9.79796	−	5.65685i	−0.866025	−	0.500000i
$129$		0			0
$130$	7.09808	+	6.29423i	0.622542	+	0.552040i
$131$	4.24264	+	7.34847i	0.370681	+	0.642039i	0.989671	−	0.143361i	$-0.0457909\pi$
$131$	4.24264	+	7.34847i	0.370681	+	0.642039i	−0.618989	+	0.785399i	$0.712458\pi$
$132$		0			0
$133$	2.59808	+	1.50000i	0.225282	+	0.130066i
$134$	−4.24264			−0.366508
$135$		0			0
$136$	8.00000			0.685994
$137$	1.22474	+	0.707107i	0.104637	+	0.0604122i	0.551405	−	0.834238i	$-0.314092\pi$
$137$	1.22474	+	0.707107i	0.104637	+	0.0604122i	−0.446768	+	0.894650i	$0.647425\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		0			0
$141$		0			0
$142$	15.5885	+	9.00000i	1.30815	+	0.755263i
$143$			12.7279i			1.06436i
$144$		0			0
$145$	−9.00000	+	3.00000i	−0.747409	+	0.249136i
$146$	6.36396	−	11.0227i	0.526685	−	0.912245i
$147$		0			0
$148$		0			0
$149$	−8.48528	−	14.6969i	−0.695141	−	1.20402i	−0.970133	−	0.242574i	$-0.922008\pi$
$149$	−8.48528	−	14.6969i	−0.695141	−	1.20402i	0.274992	−	0.961447i	$-0.411325\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$			2.82843i			0.229416i
$153$		0			0
$154$	−18.0000			−1.45048
$155$	−0.896575	+	4.38134i	−0.0720147	+	0.351918i
$156$		0			0
$157$	5.19615	−	3.00000i	0.414698	−	0.239426i	−0.278108	−	0.960550i	$-0.589707\pi$
$157$	5.19615	−	3.00000i	0.414698	−	0.239426i	0.692806	+	0.721124i	$0.256374\pi$
$158$	−6.12372	+	3.53553i	−0.487177	+	0.281272i
$159$		0			0
$160$		0			0
$161$	−21.2132			−1.67183
$162$		0			0
$163$			9.00000i			0.704934i	0.935824	+	0.352467i	$0.114657\pi$
$163$			9.00000i			0.704934i	−0.935824	+	0.352467i	$0.885343\pi$
$164$		0			0
$165$		0			0
$166$	1.00000	+	1.73205i	0.0776151	+	0.134433i
$167$	−4.89898	+	2.82843i	−0.379094	+	0.218870i	−0.677424	−	0.735593i	$-0.736904\pi$
$167$	−4.89898	+	2.82843i	−0.379094	+	0.218870i	0.298330	+	0.954463i	$0.403570\pi$
$168$		0			0
$169$	−2.00000	+	3.46410i	−0.153846	+	0.266469i
$170$	8.48528	−	2.82843i	0.650791	−	0.216930i
$171$		0			0
$172$		0			0
$173$	12.2474	+	7.07107i	0.931156	+	0.537603i	0.887177	−	0.461429i	$-0.152663\pi$
$173$	12.2474	+	7.07107i	0.931156	+	0.537603i	0.0439792	+	0.999032i	$0.485996\pi$
$174$		0			0
$175$	5.89230	−	13.7942i	0.445416	−	1.04275i
$176$	−8.48528	−	14.6969i	−0.639602	−	1.10782i
$177$		0			0
$178$		0			0
$179$	12.7279			0.951330			0.475665	−	0.879627i	$-0.342208\pi$
$179$	12.7279			0.951330			0.475665	+	0.879627i	$0.342208\pi$
$180$		0			0
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$	11.0227	+	6.36396i	0.817057	+	0.471728i
$183$		0			0
$184$	−10.0000	−	17.3205i	−0.737210	−	1.27688i
$185$	13.3521	−	15.0573i	0.981664	−	1.10703i
$186$		0			0
$187$	10.3923	+	6.00000i	0.759961	+	0.438763i
$188$		0			0
$189$		0			0
$190$	1.00000	+	3.00000i	0.0725476	+	0.217643i
$191$	8.48528	−	14.6969i	0.613973	−	1.06343i	−0.376590	−	0.926380i	$-0.622904\pi$
$191$	8.48528	−	14.6969i	0.613973	−	1.06343i	0.990564	−	0.137053i	$-0.0437631\pi$
$192$		0			0
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	−0.590584	−	0.806976i	$-0.701102\pi$
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	0.403570	+	0.914949i	$0.367769\pi$
$194$	−2.12132	−	3.67423i	−0.152302	−	0.263795i
$195$		0			0
$196$		0			0
$197$		−	22.6274i		−	1.61214i	−0.591822	−	0.806068i	$-0.701591\pi$
$197$		−	22.6274i		−	1.61214i	0.591822	−	0.806068i	$-0.298409\pi$
$198$		0			0
$199$	11.0000			0.779769			0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000			0.779769			0.389885	+	0.920864i	$0.372515\pi$
$200$	14.0406	−	1.69161i	0.992820	−	0.119615i
$201$		0			0
$202$	−10.3923	+	6.00000i	−0.731200	+	0.422159i
$203$	−11.0227	+	6.36396i	−0.773642	+	0.446663i
$204$		0			0
$205$	−1.90192	+	9.29423i	−0.132836	+	0.649137i
$206$	−4.24264			−0.295599
$207$		0			0
$208$			12.0000i			0.832050i
$209$	−2.12132	+	3.67423i	−0.146735	+	0.254152i
$210$		0			0
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	0.960985	−	0.276600i	$-0.0892077\pi$
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	−0.720035	+	0.693938i	$0.755874\pi$
$212$		0			0
$213$		0			0
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$	−4.24264	−	12.7279i	−0.289346	−	0.868037i
$216$		0			0
$217$			6.00000i			0.407307i
$218$	9.79796	+	5.65685i	0.663602	+	0.383131i
$219$		0			0
$220$		0			0
$221$	−4.24264	−	7.34847i	−0.285391	−	0.494312i
$222$		0			0
$223$	5.19615	+	3.00000i	0.347960	+	0.200895i	0.663786	−	0.747922i	$-0.268948\pi$
$223$	5.19615	+	3.00000i	0.347960	+	0.200895i	−0.315826	+	0.948817i	$0.602282\pi$
$224$		0			0
$225$		0			0
$226$	−2.00000			−0.133038
$227$	−20.8207	−	12.0208i	−1.38192	−	0.797850i	−0.389530	−	0.921014i	$-0.627362\pi$
$227$	−20.8207	−	12.0208i	−1.38192	−	0.797850i	−0.992386	+	0.123164i	$0.960696\pi$
$228$		0			0
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$	−16.7303	−	14.8356i	−1.10317	−	0.978233i
$231$		0			0
$232$	−10.3923	−	6.00000i	−0.682288	−	0.393919i
$233$			19.7990i			1.29707i	0.761183	+	0.648537i	$0.224619\pi$
$233$			19.7990i			1.29707i	−0.761183	+	0.648537i	$0.775381\pi$
$234$		0			0
$235$	2.00000	+	6.00000i	0.130466	+	0.391397i
$236$		0			0
$237$		0			0
$238$	10.3923	−	6.00000i	0.673633	−	0.388922i
$239$	−2.12132	−	3.67423i	−0.137217	−	0.237666i	0.789225	−	0.614104i	$-0.210482\pi$
$239$	−2.12132	−	3.67423i	−0.137217	−	0.237666i	−0.926442	+	0.376437i	$0.877149\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$		−	9.89949i		−	0.636364i
$243$		0			0
$244$		0			0
$245$	0.896575	−	4.38134i	0.0572801	−	0.279914i
$246$		0			0
$247$	2.59808	−	1.50000i	0.165312	−	0.0954427i
$248$	−4.89898	+	2.82843i	−0.311086	+	0.179605i
$249$		0			0
$250$	14.2942	−	6.75833i	0.904046	−	0.427434i
$251$	12.7279			0.803379			0.401690	−	0.915776i	$-0.368423\pi$
$251$	12.7279			0.803379			0.401690	+	0.915776i	$0.368423\pi$
$252$		0			0
$253$		−	30.0000i		−	1.88608i
$254$	12.7279	−	22.0454i	0.798621	−	1.38325i
$255$		0			0
$256$		0			0
$257$	17.1464	−	9.89949i	1.06956	−	0.617514i	0.141502	−	0.989938i	$-0.454807\pi$
$257$	17.1464	−	9.89949i	1.06956	−	0.617514i	0.928063	+	0.372424i	$0.121473\pi$
$258$		0			0
$259$	13.5000	−	23.3827i	0.838849	−	1.45293i
$260$		0			0
$261$		0			0
$262$			12.0000i			0.741362i
$263$	−2.44949	−	1.41421i	−0.151042	−	0.0872041i	0.422574	−	0.906328i	$-0.361127\pi$
$263$	−2.44949	−	1.41421i	−0.151042	−	0.0872041i	−0.573616	+	0.819124i	$0.694460\pi$
$264$		0			0
$265$	−14.6865	+	16.5622i	−0.902187	+	1.01741i
$266$	2.12132	+	3.67423i	0.130066	+	0.225282i
$267$		0			0
$268$		0			0
$269$	−25.4558			−1.55207			−0.776035	−	0.630690i	$-0.782772\pi$
$269$	−25.4558			−1.55207			−0.776035	+	0.630690i	$0.782772\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	9.79796	+	5.65685i	0.594089	+	0.342997i
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	19.5080	+	8.33298i	1.17638	+	0.502497i
$276$		0			0
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	0.154172	−	0.988044i	$-0.450729\pi$
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	−0.778585	+	0.627539i	$0.784062\pi$
$278$			18.3848i			1.10265i
$279$		0			0
$280$	18.0000	−	6.00000i	1.07571	−	0.358569i
$281$	−4.24264	+	7.34847i	−0.253095	+	0.438373i	−0.964376	−	0.264534i	$-0.914782\pi$
$281$	−4.24264	+	7.34847i	−0.253095	+	0.438373i	0.711282	+	0.702907i	$0.248115\pi$
$282$		0			0
$283$	5.19615	−	3.00000i	0.308879	−	0.178331i	−0.337546	−	0.941309i	$-0.609597\pi$
$283$	5.19615	−	3.00000i	0.308879	−	0.178331i	0.646425	+	0.762978i	$0.276263\pi$
$284$		0			0
$285$		0			0
$286$	−9.00000	+	15.5885i	−0.532181	+	0.921765i
$287$			12.7279i			0.751305i
$288$		0			0
$289$	9.00000			0.529412
$290$	−13.1440	−	2.68973i	−0.771844	−	0.157946i
$291$		0			0
$292$		0			0
$293$	6.12372	−	3.53553i	0.357752	−	0.206548i	−0.310342	−	0.950625i	$-0.600444\pi$
$293$	6.12372	−	3.53553i	0.357752	−	0.206548i	0.668094	+	0.744077i	$0.267110\pi$
$294$		0			0
$295$	3.80385	−	18.5885i	0.221469	−	1.08226i
$296$	25.4558			1.47959
$297$		0			0
$298$		−	24.0000i		−	1.39028i
$299$	−10.6066	+	18.3712i	−0.613396	+	1.06243i
$300$		0			0
$301$	−9.00000	−	15.5885i	−0.518751	−	0.898504i
$302$	1.22474	−	0.707107i	0.0704761	−	0.0406894i
$303$		0			0
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−27.5772	+	9.19239i	−1.57906	+	0.526355i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−4.19615	+	4.73205i	−0.238325	+	0.268762i
$311$	4.24264	+	7.34847i	0.240578	+	0.416693i	0.960879	−	0.276968i	$-0.0893297\pi$
$311$	4.24264	+	7.34847i	0.240578	+	0.416693i	−0.720301	+	0.693662i	$0.755996\pi$
$312$		0			0
$313$	−18.1865	−	10.5000i	−1.02796	−	0.593495i	−0.111563	−	0.993757i	$-0.535586\pi$
$313$	−18.1865	−	10.5000i	−1.02796	−	0.593495i	−0.916401	+	0.400262i	$0.868919\pi$
$314$	8.48528			0.478852
$315$		0			0
$316$		0			0
$317$	−9.79796	−	5.65685i	−0.550308	−	0.317721i	0.198938	−	0.980012i	$-0.436251\pi$
$317$	−9.79796	−	5.65685i	−0.550308	−	0.317721i	−0.749246	+	0.662291i	$0.769584\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	13.3843	+	11.8685i	0.748203	+	0.663470i
$321$		0			0
$322$	−25.9808	−	15.0000i	−1.44785	−	0.835917i
$323$		−	2.82843i		−	0.157378i
$324$		0			0
$325$	−9.00000	−	12.0000i	−0.499230	−	0.665640i
$326$	−6.36396	+	11.0227i	−0.352467	+	0.610491i
$327$		0			0
$328$	−10.3923	+	6.00000i	−0.573819	+	0.331295i
$329$	4.24264	+	7.34847i	0.233904	+	0.405134i
$330$		0			0
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$		0			0
$333$		0			0
$334$	−8.00000			−0.437741
$335$	6.57201	+	1.34486i	0.359067	+	0.0734777i
$336$		0			0
$337$	28.5788	−	16.5000i	1.55679	−	0.898812i	0.559227	−	0.829014i	$-0.311098\pi$
$337$	28.5788	−	16.5000i	1.55679	−	0.898812i	0.997561	−	0.0697980i	$-0.0222355\pi$
$338$	−4.89898	+	2.82843i	−0.266469	+	0.153846i
$339$		0			0
$340$		0			0
$341$	−8.48528			−0.459504
$342$		0			0
$343$			15.0000i			0.809924i
$344$	8.48528	−	14.6969i	0.457496	−	0.792406i
$345$		0			0
$346$	10.0000	+	17.3205i	0.537603	+	0.931156i
$347$	−23.2702	+	13.4350i	−1.24921	+	0.721230i	−0.970951	−	0.239277i	$-0.923090\pi$
$347$	−23.2702	+	13.4350i	−1.24921	+	0.721230i	−0.278256	+	0.960507i	$0.589756\pi$
$348$		0			0
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$	16.9706	−	12.7279i	0.907115	−	0.680336i
$351$		0			0
$352$		0			0
$353$	−24.4949	−	14.1421i	−1.30373	−	0.752710i	−0.322690	−	0.946505i	$-0.604587\pi$
$353$	−24.4949	−	14.1421i	−1.30373	−	0.752710i	−0.981042	+	0.193795i	$0.937920\pi$
$354$		0			0
$355$	−21.2942	−	18.8827i	−1.13018	−	1.00219i
$356$		0			0
$357$		0			0
$358$	15.5885	+	9.00000i	0.823876	+	0.475665i
$359$	12.7279			0.671754			0.335877	−	0.941906i	$-0.390967\pi$
$359$	12.7279			0.671754			0.335877	+	0.941906i	$0.390967\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	−1.22474	−	0.707107i	−0.0643712	−	0.0371647i
$363$		0			0
$364$		0			0
$365$	−13.3521	+	15.0573i	−0.698880	+	0.788135i
$366$		0			0
$367$	12.9904	+	7.50000i	0.678092	+	0.391497i	0.799136	−	0.601150i	$-0.205291\pi$
$367$	12.9904	+	7.50000i	0.678092	+	0.391497i	−0.121044	+	0.992647i	$0.538624\pi$
$368$		−	28.2843i		−	1.47442i
$369$		0			0
$370$	27.0000	−	9.00000i	1.40366	−	0.467888i
$371$	−14.8492	+	25.7196i	−0.770934	+	1.33530i
$372$		0			0
$373$	−18.1865	+	10.5000i	−0.941663	+	0.543669i	−0.890481	−	0.455020i	$-0.849632\pi$
$373$	−18.1865	+	10.5000i	−0.941663	+	0.543669i	−0.0511818	+	0.998689i	$0.516299\pi$
$374$	8.48528	+	14.6969i	0.438763	+	0.759961i
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$			12.7279i			0.655521i
$378$		0			0
$379$	35.0000			1.79783			0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000			1.79783			0.898915	+	0.438124i	$0.144357\pi$
$380$		0			0
$381$		0			0
$382$	20.7846	−	12.0000i	1.06343	−	0.613973i
$383$	−4.89898	+	2.82843i	−0.250326	+	0.144526i	−0.619914	−	0.784670i	$-0.712832\pi$
$383$	−4.89898	+	2.82843i	−0.250326	+	0.144526i	0.369587	+	0.929196i	$0.379499\pi$
$384$		0			0
$385$	27.8827	+	5.70577i	1.42103	+	0.290793i
$386$	−4.24264			−0.215945
$387$		0			0
$388$		0			0
$389$	−16.9706	+	29.3939i	−0.860442	+	1.49033i	0.0110615	+	0.999939i	$0.496479\pi$
$389$	−16.9706	+	29.3939i	−0.860442	+	1.49033i	−0.871503	+	0.490390i	$0.836854\pi$
$390$		0			0
$391$	10.0000	+	17.3205i	0.505722	+	0.875936i
$392$	4.89898	−	2.82843i	0.247436	−	0.142857i
$393$		0			0
$394$	16.0000	−	27.7128i	0.806068	−	1.39615i
$395$	10.6066	−	3.53553i	0.533676	−	0.177892i
$396$		0			0
$397$			36.0000i			1.80679i	0.428811	+	0.903394i	$0.358933\pi$
$397$			36.0000i			1.80679i	−0.428811	+	0.903394i	$0.641067\pi$
$398$	13.4722	+	7.77817i	0.675300	+	0.389885i
$399$		0			0
$400$	18.3923	+	7.85641i	0.919615	+	0.392820i
$401$	−2.12132	−	3.67423i	−0.105934	−	0.183483i	0.808186	−	0.588928i	$-0.200450\pi$
$401$	−2.12132	−	3.67423i	−0.105934	−	0.183483i	−0.914119	+	0.405445i	$0.867116\pi$
$402$		0			0
$403$	5.19615	+	3.00000i	0.258839	+	0.149441i
$404$		0			0
$405$		0			0
$406$	−18.0000			−0.893325
$407$	33.0681	+	19.0919i	1.63913	+	0.946350i
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$	−8.90138	+	10.0382i	−0.439608	+	0.495751i
$411$		0			0
$412$		0			0
$413$		−	25.4558i		−	1.25260i
$414$		0			0
$415$	−1.00000	−	3.00000i	−0.0490881	−	0.147264i
$416$		0			0
$417$		0			0
$418$	−5.19615	+	3.00000i	−0.254152	+	0.146735i
$419$	16.9706	+	29.3939i	0.829066	+	1.43598i	0.898772	+	0.438417i	$0.144461\pi$
$419$	16.9706	+	29.3939i	0.829066	+	1.43598i	−0.0697053	+	0.997568i	$0.522206\pi$
$420$		0			0
$421$	−11.5000	+	19.9186i	−0.560476	+	0.970772i	0.436979	+	0.899472i	$0.356048\pi$
$421$	−11.5000	+	19.9186i	−0.560476	+	0.970772i	−0.997455	+	0.0713008i	$0.977285\pi$
$422$			9.89949i			0.481900i
$423$		0			0
$424$	−28.0000			−1.35980
$425$	−14.0406	+	1.69161i	−0.681069	+	0.0820554i
$426$		0			0
$427$	−33.7750	+	19.5000i	−1.63449	+	0.943671i
$428$		0			0
$429$		0			0
$430$	3.80385	−	18.5885i	0.183438	−	0.896415i
$431$	−12.7279			−0.613082			−0.306541	−	0.951857i	$-0.599172\pi$
$431$	−12.7279			−0.613082			−0.306541	+	0.951857i	$0.599172\pi$
$432$		0			0
$433$			36.0000i			1.73005i	0.501729	+	0.865025i	$0.332697\pi$
$433$			36.0000i			1.73005i	−0.501729	+	0.865025i	$0.667303\pi$
$434$	−4.24264	+	7.34847i	−0.203653	+	0.352738i
$435$		0			0
$436$		0			0
$437$	−6.12372	+	3.53553i	−0.292937	+	0.169128i
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$	8.48528	+	25.4558i	0.404520	+	1.21356i
$441$		0			0
$442$		−	12.0000i		−	0.570782i
$443$	12.2474	+	7.07107i	0.581894	+	0.335957i	0.761886	−	0.647712i	$-0.224274\pi$
$443$	12.2474	+	7.07107i	0.581894	+	0.335957i	−0.179992	+	0.983668i	$0.557607\pi$
$444$		0			0
$445$		0			0
$446$	4.24264	+	7.34847i	0.200895	+	0.347960i
$447$		0			0
$448$	20.7846	+	12.0000i	0.981981	+	0.566947i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$		0			0
$453$		0			0
$454$	−17.0000	−	29.4449i	−0.797850	−	1.38192i
$455$	−15.0573	−	13.3521i	−0.705897	−	0.625955i
$456$		0			0
$457$	−10.3923	−	6.00000i	−0.486132	−	0.280668i	0.236837	−	0.971549i	$-0.423889\pi$
$457$	−10.3923	−	6.00000i	−0.486132	−	0.280668i	−0.722968	+	0.690881i	$0.757223\pi$
$458$			22.6274i			1.05731i
$459$		0			0
$460$		0			0
$461$	8.48528	−	14.6969i	0.395199	−	0.684505i	−0.597928	−	0.801550i	$-0.704009\pi$
$461$	8.48528	−	14.6969i	0.395199	−	0.684505i	0.993127	+	0.117045i	$0.0373423\pi$
$462$		0			0
$463$	12.9904	−	7.50000i	0.603714	−	0.348555i	−0.166787	−	0.985993i	$-0.553339\pi$
$463$	12.9904	−	7.50000i	0.603714	−	0.348555i	0.770501	+	0.637438i	$0.220006\pi$
$464$	−8.48528	−	14.6969i	−0.393919	−	0.682288i
$465$		0			0
$466$	−14.0000	+	24.2487i	−0.648537	+	1.12330i
$467$		−	22.6274i		−	1.04707i	−0.852004	−	0.523536i	$-0.824613\pi$
$467$		−	22.6274i		−	1.04707i	0.852004	−	0.523536i	$-0.175387\pi$
$468$		0			0
$469$	9.00000			0.415581
$470$	−1.79315	+	8.76268i	−0.0827119	+	0.404192i
$471$		0			0
$472$	20.7846	−	12.0000i	0.956689	−	0.552345i
$473$	22.0454	−	12.7279i	1.01365	−	0.585230i
$474$		0			0
$475$	−0.598076	−	4.96410i	−0.0274416	−	0.227769i
$476$		0			0
$477$		0			0
$478$		−	6.00000i		−	0.274434i
$479$	2.12132	−	3.67423i	0.0969256	−	0.167880i	−0.813485	−	0.581586i	$-0.802432\pi$
$479$	2.12132	−	3.67423i	0.0969256	−	0.167880i	0.910411	+	0.413706i	$0.135766\pi$
$480$		0			0
$481$	−13.5000	−	23.3827i	−0.615547	−	1.06616i
$482$	−6.12372	+	3.53553i	−0.278928	+	0.161039i
$483$		0			0
$484$		0			0
$485$	2.12132	+	6.36396i	0.0963242	+	0.288973i
$486$		0			0
$487$		−	9.00000i		−	0.407829i	−0.978989	−	0.203914i	$-0.934634\pi$
$487$		−	9.00000i		−	0.407829i	0.978989	−	0.203914i	$-0.0653664\pi$
$488$	−31.8434	−	18.3848i	−1.44148	−	0.832240i
$489$		0			0
$490$	4.19615	−	4.73205i	0.189563	−	0.213772i
$491$	10.6066	+	18.3712i	0.478669	+	0.829079i	0.999701	−	0.0244579i	$-0.00778598\pi$
$491$	10.6066	+	18.3712i	0.478669	+	0.829079i	−0.521032	+	0.853537i	$0.674453\pi$
$492$		0			0
$493$	10.3923	+	6.00000i	0.468046	+	0.270226i
$494$	4.24264			0.190885
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−33.0681	−	19.0919i	−1.48331	−	0.856388i
$498$		0			0
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$		0			0
$501$		0			0
$502$	15.5885	+	9.00000i	0.695747	+	0.401690i
$503$		−	35.3553i		−	1.57642i	−0.615409	−	0.788208i	$-0.711009\pi$
$503$		−	35.3553i		−	1.57642i	0.615409	−	0.788208i	$-0.288991\pi$
$504$		0			0
$505$	18.0000	−	6.00000i	0.800989	−	0.266996i
$506$	21.2132	−	36.7423i	0.943042	−	1.63340i
$507$		0			0
$508$		0			0
$509$	−14.8492	−	25.7196i	−0.658181	−	1.14000i	−0.981086	−	0.193572i	$-0.937993\pi$
$509$	−14.8492	−	25.7196i	−0.658181	−	1.14000i	0.322905	−	0.946431i	$-0.395341\pi$
$510$		0			0
$511$	−13.5000	+	23.3827i	−0.597205	+	1.03439i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	28.0000			1.23503
$515$	6.57201	+	1.34486i	0.289597	+	0.0592618i
$516$		0			0
$517$	−10.3923	+	6.00000i	−0.457053	+	0.263880i
$518$	33.0681	−	19.0919i	1.45293	−	0.838849i
$519$		0			0
$520$	3.80385	−	18.5885i	0.166810	−	0.815158i
$521$	−12.7279			−0.557620			−0.278810	−	0.960346i	$-0.589940\pi$
$521$	−12.7279			−0.557620			−0.278810	+	0.960346i	$0.589940\pi$
$522$		0			0
$523$			9.00000i			0.393543i	0.980449	+	0.196771i	$0.0630456\pi$
$523$			9.00000i			0.393543i	−0.980449	+	0.196771i	$0.936954\pi$
$524$		0			0
$525$		0			0
$526$	−2.00000	−	3.46410i	−0.0872041	−	0.151042i
$527$	4.89898	−	2.82843i	0.213403	−	0.123208i
$528$		0			0
$529$	13.5000	−	23.3827i	0.586957	−	1.01664i
$530$	−29.6985	+	9.89949i	−1.29002	+	0.430007i
$531$		0			0
$532$		0			0
$533$	11.0227	+	6.36396i	0.477446	+	0.275654i
$534$		0			0
$535$	10.4904	−	11.8301i	0.453539	−	0.511461i
$536$	4.24264	+	7.34847i	0.183254	+	0.317406i
$537$		0			0
$538$	−31.1769	−	18.0000i	−1.34413	−	0.776035i
$539$	8.48528			0.365487
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	−23.2702	−	13.4350i	−0.999539	−	0.577084i
$543$		0			0
$544$		0			0
$545$	−13.3843	−	11.8685i	−0.573319	−	0.508391i
$546$		0			0
$547$	−2.59808	−	1.50000i	−0.111086	−	0.0641354i	0.443428	−	0.896310i	$-0.353762\pi$
$547$	−2.59808	−	1.50000i	−0.111086	−	0.0641354i	−0.554513	+	0.832175i	$0.687096\pi$
$548$		0			0
$549$		0			0
$550$	18.0000	+	24.0000i	0.767523	+	1.02336i
$551$	−2.12132	+	3.67423i	−0.0903713	+	0.156528i
$552$		0			0
$553$	12.9904	−	7.50000i	0.552407	−	0.318932i
$554$	−8.48528	−	14.6969i	−0.360505	−	0.624413i
$555$		0			0
$556$		0			0
$557$			19.7990i			0.838910i	0.907776	+	0.419455i	$0.137779\pi$
$557$			19.7990i			0.838910i	−0.907776	+	0.419455i	$0.862221\pi$
$558$		0			0
$559$	−18.0000			−0.761319
$560$	26.2880	+	5.37945i	1.11087	+	0.227323i
$561$		0			0
$562$	−10.3923	+	6.00000i	−0.438373	+	0.253095i
$563$	9.79796	−	5.65685i	0.412935	−	0.238408i	−0.279115	−	0.960258i	$-0.590041\pi$
$563$	9.79796	−	5.65685i	0.412935	−	0.238408i	0.692050	+	0.721850i	$0.256708\pi$
$564$		0			0
$565$	3.09808	+	0.633975i	0.130337	+	0.0266715i
$566$	8.48528			0.356663
$567$		0			0
$568$		−	36.0000i		−	1.51053i
$569$	21.2132	−	36.7423i	0.889304	−	1.54032i	0.0486037	−	0.998818i	$-0.484523\pi$
$569$	21.2132	−	36.7423i	0.889304	−	1.54032i	0.840700	−	0.541501i	$-0.182144\pi$
$570$		0			0
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	0.999638	+	0.0268925i	$0.00856117\pi$
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	−0.476530	+	0.879158i	$0.658105\pi$
$572$		0			0
$573$		0			0
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$	21.2132	+	28.2843i	0.884652	+	1.17954i
$576$		0			0
$577$		−	45.0000i		−	1.87337i	−0.350167	−	0.936687i	$-0.613875\pi$
$577$		−	45.0000i		−	1.87337i	0.350167	−	0.936687i	$-0.386125\pi$
$578$	11.0227	+	6.36396i	0.458484	+	0.264706i
$579$		0			0
$580$		0			0
$581$	−2.12132	−	3.67423i	−0.0880072	−	0.152433i
$582$		0			0
$583$	−36.3731	−	21.0000i	−1.50642	−	0.869731i
$584$	−25.4558			−1.05337
$585$		0			0
$586$	10.0000			0.413096
$587$	23.2702	+	13.4350i	0.960462	+	0.554523i	0.896315	−	0.443417i	$-0.146234\pi$
$587$	23.2702	+	13.4350i	0.960462	+	0.554523i	0.0641468	+	0.997940i	$0.479567\pi$
$588$		0			0
$589$	1.00000	+	1.73205i	0.0412043	+	0.0713679i
$590$	17.8028	−	20.0764i	0.732928	−	0.826532i
$591$		0			0
$592$	31.1769	+	18.0000i	1.28136	+	0.739795i
$593$		−	9.89949i		−	0.406524i	−0.979124	−	0.203262i	$-0.934846\pi$
$593$		−	9.89949i		−	0.406524i	0.979124	−	0.203262i	$-0.0651542\pi$
$594$		0			0
$595$	−18.0000	+	6.00000i	−0.737928	+	0.245976i
$596$		0			0
$597$		0			0
$598$	−25.9808	+	15.0000i	−1.06243	+	0.613396i
$599$	−14.8492	−	25.7196i	−0.606724	−	1.05088i	−0.991777	−	0.127982i	$-0.959150\pi$
$599$	−14.8492	−	25.7196i	−0.606724	−	1.05088i	0.385053	−	0.922894i	$-0.374183\pi$
$600$		0			0
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	−0.0929227	−	0.995673i	$-0.529621\pi$
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	0.908740	−	0.417363i	$-0.137046\pi$
$602$		−	25.4558i		−	1.03750i
$603$		0			0
$604$		0			0
$605$	−3.13801	+	15.3347i	−0.127578	+	0.623444i
$606$		0			0
$607$	−33.7750	+	19.5000i	−1.37088	+	0.791481i	−0.991039	−	0.133570i	$-0.957356\pi$
$607$	−33.7750	+	19.5000i	−1.37088	+	0.791481i	−0.379845	+	0.925050i	$0.624023\pi$
$608$		0			0
$609$		0			0
$610$	−40.2750	−	8.24167i	−1.63069	−	0.333695i
$611$	8.48528			0.343278
$612$		0			0
$613$		−	9.00000i		−	0.363507i	−0.983344	−	0.181753i	$-0.941823\pi$
$613$		−	9.00000i		−	0.363507i	0.983344	−	0.181753i	$-0.0581772\pi$
$614$		0			0
$615$		0			0
$616$	18.0000	+	31.1769i	0.725241	+	1.25615i
$617$	6.12372	−	3.53553i	0.246532	−	0.142335i	−0.371643	−	0.928376i	$-0.621206\pi$
$617$	6.12372	−	3.53553i	0.246532	−	0.142335i	0.618175	+	0.786040i	$0.287872\pi$
$618$		0			0
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	−0.609488	−	0.792796i	$-0.708625\pi$
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	0.991325	+	0.131434i	$0.0419582\pi$
$620$		0			0
$621$		0			0
$622$			12.0000i			0.481156i
$623$		0			0
$624$		0			0
$625$	−24.2846	+	5.93782i	−0.971384	+	0.237513i
$626$	−14.8492	−	25.7196i	−0.593495	−	1.02796i
$627$		0			0
$628$		0			0
$629$	−25.4558			−1.01499
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	12.2474	+	7.07107i	0.487177	+	0.281272i
$633$		0			0
$634$	−8.00000	−	13.8564i	−0.317721	−	0.550308i
$635$	−26.7042	+	30.1146i	−1.05972	+	1.19506i
$636$		0			0
$637$	−5.19615	−	3.00000i	−0.205879	−	0.118864i
$638$		−	25.4558i		−	1.00781i
$639$		0			0
$640$	8.00000	+	24.0000i	0.316228	+	0.948683i
$641$	8.48528	−	14.6969i	0.335148	−	0.580494i	−0.648365	−	0.761330i	$-0.724547\pi$
$641$	8.48528	−	14.6969i	0.335148	−	0.580494i	0.983513	+	0.180836i	$0.0578802\pi$
$642$		0			0
$643$	36.3731	−	21.0000i	1.43441	−	0.828159i	0.436960	−	0.899481i	$-0.356055\pi$
$643$	36.3731	−	21.0000i	1.43441	−	0.828159i	0.997453	+	0.0713216i	$0.0227217\pi$
$644$		0			0
$645$		0			0
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$		−	9.89949i		−	0.389189i	−0.980884	−	0.194595i	$-0.937661\pi$
$647$		−	9.89949i		−	0.389189i	0.980884	−	0.194595i	$-0.0623391\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$	−2.53742	−	21.0609i	−0.0995259	−	0.826076i
$651$		0			0
$652$		0			0
$653$	−4.89898	+	2.82843i	−0.191712	+	0.110685i	−0.592784	−	0.805362i	$-0.701971\pi$
$653$	−4.89898	+	2.82843i	−0.191712	+	0.110685i	0.401072	+	0.916047i	$0.368638\pi$
$654$		0			0
$655$	3.80385	−	18.5885i	0.148629	−	0.726311i
$656$	−16.9706			−0.662589
$657$		0			0
$658$			12.0000i			0.467809i
$659$	8.48528	−	14.6969i	0.330540	−	0.572511i	−0.652078	−	0.758152i	$-0.726103\pi$
$659$	8.48528	−	14.6969i	0.330540	−	0.572511i	0.982618	+	0.185640i	$0.0594359\pi$
$660$		0			0
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$662$	−20.8207	+	12.0208i	−0.809218	+	0.467202i
$663$		0			0
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$	−2.12132	−	6.36396i	−0.0822613	−	0.246784i
$666$		0			0
$667$		−	30.0000i		−	1.16160i
$668$		0			0
$669$		0			0
$670$	7.09808	+	6.29423i	0.274223	+	0.243167i
$671$	−27.5772	−	47.7650i	−1.06460	−	1.84395i
$672$		0			0
$673$	12.9904	+	7.50000i	0.500742	+	0.289104i	0.729020	−	0.684492i	$-0.239976\pi$
$673$	12.9904	+	7.50000i	0.500742	+	0.289104i	−0.228278	+	0.973596i	$0.573309\pi$
$674$	46.6690			1.79762
$675$		0			0
$676$		0			0
$677$	41.6413	+	24.0416i	1.60041	+	0.923995i	0.991405	+	0.130825i	$0.0417627\pi$
$677$	41.6413	+	24.0416i	1.60041	+	0.923995i	0.609001	+	0.793170i	$0.291571\pi$
$678$		0			0
$679$	4.50000	+	7.79423i	0.172694	+	0.299115i
$680$	−13.3843	−	11.8685i	−0.513263	−	0.455137i
$681$		0			0
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$			15.5563i			0.595247i	0.954683	+	0.297624i	$0.0961940\pi$
$683$			15.5563i			0.595247i	−0.954683	+	0.297624i	$0.903806\pi$
$684$		0			0
$685$	−1.00000	−	3.00000i	−0.0382080	−	0.114624i
$686$	−10.6066	+	18.3712i	−0.404962	+	0.701415i
$687$		0			0
$688$	20.7846	−	12.0000i	0.792406	−	0.457496i
$689$	14.8492	+	25.7196i	0.565711	+	0.979840i
$690$		0			0
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$		0			0
$693$		0			0
$694$	−38.0000			−1.44246
$695$	5.82774	−	28.4787i	0.221059	−	1.08026i
$696$		0			0
$697$	10.3923	−	6.00000i	0.393637	−	0.227266i
$698$	−6.12372	+	3.53553i	−0.231786	+	0.133822i
$699$		0			0
$700$		0			0
$701$	38.1838			1.44218			0.721090	−	0.692841i	$-0.243641\pi$
$701$	38.1838			1.44218			0.721090	+	0.692841i	$0.243641\pi$
$702$		0			0
$703$		−	9.00000i		−	0.339441i
$704$	−16.9706	+	29.3939i	−0.639602	+	1.10782i
$705$		0			0
$706$	−20.0000	−	34.6410i	−0.752710	−	1.30373i
$707$	22.0454	−	12.7279i	0.829103	−	0.478683i
$708$		0			0
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$	−12.7279	−	38.1838i	−0.477670	−	1.43301i
$711$		0			0
$712$		0			0
$713$	−12.2474	−	7.07107i	−0.458671	−	0.264814i
$714$		0			0
$715$	18.8827	−	21.2942i	0.706172	−	0.796359i
$716$		0			0
$717$		0			0
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$	−12.7279			−0.474671			−0.237336	−	0.971428i	$-0.576274\pi$
$719$	−12.7279			−0.474671			−0.237336	+	0.971428i	$0.576274\pi$
$720$		0			0
$721$	9.00000			0.335178
$722$	−22.0454	−	12.7279i	−0.820445	−	0.473684i
$723$		0			0
$724$		0			0
$725$	19.5080	+	8.33298i	0.724508	+	0.309479i
$726$		0			0
$727$	36.3731	+	21.0000i	1.34900	+	0.778847i	0.988108	−	0.153760i	$-0.0491382\pi$
$727$	36.3731	+	21.0000i	1.34900	+	0.778847i	0.360894	+	0.932607i	$0.382472\pi$
$728$		−	25.4558i		−	0.943456i
$729$		0			0
$730$	−27.0000	+	9.00000i	−0.999315	+	0.333105i
$731$	−8.48528	+	14.6969i	−0.313839	+	0.543586i
$732$		0			0
$733$	20.7846	−	12.0000i	0.767697	−	0.443230i	−0.0643554	−	0.997927i	$-0.520499\pi$
$733$	20.7846	−	12.0000i	0.767697	−	0.443230i	0.832052	+	0.554697i	$0.187166\pi$
$734$	10.6066	+	18.3712i	0.391497	+	0.678092i
$735$		0			0
$736$		0			0
$737$			12.7279i			0.468839i
$738$		0			0
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$		0			0
$741$		0			0
$742$	−36.3731	+	21.0000i	−1.33530	+	0.770934i
$743$	−12.2474	+	7.07107i	−0.449315	+	0.259412i	−0.707541	−	0.706672i	$-0.750196\pi$
$743$	−12.2474	+	7.07107i	−0.449315	+	0.259412i	0.258226	+	0.966085i	$0.416862\pi$
$744$		0			0
$745$	−7.60770	+	37.1769i	−0.278724	+	1.36206i
$746$	−29.6985			−1.08734
$747$		0			0
$748$		0			0
$749$	10.6066	−	18.3712i	0.387557	−	0.671268i
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	−9.79796	+	5.65685i	−0.357295	+	0.206284i
$753$		0			0
$754$	−9.00000	+	15.5885i	−0.327761	+	0.567698i
$755$	−2.12132	+	0.707107i	−0.0772028	+	0.0257343i
$756$		0			0
$757$			27.0000i			0.981332i	0.871348	+	0.490666i	$0.163246\pi$
$757$			27.0000i			0.981332i	−0.871348	+	0.490666i	$0.836754\pi$
$758$	42.8661	+	24.7487i	1.55697	+	0.898915i
$759$		0			0
$760$	4.19615	−	4.73205i	0.152210	−	0.171650i
$761$	−2.12132	−	3.67423i	−0.0768978	−	0.133191i	0.825012	−	0.565115i	$-0.191168\pi$
$761$	−2.12132	−	3.67423i	−0.0768978	−	0.133191i	−0.901910	+	0.431924i	$0.857835\pi$
$762$		0			0
$763$	−20.7846	−	12.0000i	−0.752453	−	0.434429i
$764$		0			0
$765$		0			0
$766$	−8.00000			−0.289052
$767$	−22.0454	−	12.7279i	−0.796014	−	0.459579i
$768$		0			0
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	0.749654	−	0.661830i	$-0.230220\pi$
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	−0.947989	+	0.318304i	$0.896887\pi$
$770$	30.1146	+	26.7042i	1.08525	+	0.962351i
$771$		0			0
$772$		0			0
$773$			41.0122i			1.47511i	0.675289	+	0.737553i	$0.264019\pi$
$773$			41.0122i			1.47511i	−0.675289	+	0.737553i	$0.735981\pi$
$774$		0			0
$775$	8.00000	−	6.00000i	0.287368	−	0.215526i
$776$	−4.24264	+	7.34847i	−0.152302	+	0.263795i
$777$		0			0
$778$	−41.5692	+	24.0000i	−1.49033	+	0.860442i
$779$	2.12132	+	3.67423i	0.0760042	+	0.131643i
$780$		0			0
$781$	27.0000	−	46.7654i	0.966136	−	1.67340i
$782$			28.2843i			1.01144i
$783$		0			0
$784$	8.00000			0.285714
$785$	−13.1440	−	2.68973i	−0.469130	−	0.0960005i
$786$		0			0
$787$	12.9904	−	7.50000i	0.463057	−	0.267346i	−0.250272	−	0.968176i	$-0.580520\pi$
$787$	12.9904	−	7.50000i	0.463057	−	0.267346i	0.713329	+	0.700830i	$0.247187\pi$
$788$		0			0
$789$		0			0
$790$	15.4904	+	3.16987i	0.551123	+	0.112779i
$791$	4.24264			0.150851
$792$		0			0
$793$			39.0000i			1.38493i
$794$	−25.4558	+	44.0908i	−0.903394	+	1.56472i
$795$		0			0
$796$		0			0
$797$	17.1464	−	9.89949i	0.607358	−	0.350658i	−0.164573	−	0.986365i	$-0.552625\pi$
$797$	17.1464	−	9.89949i	0.607358	−	0.350658i	0.771931	+	0.635707i	$0.219291\pi$
$798$		0			0
$799$	4.00000	−	6.92820i	0.141510	−	0.245102i
$800$		0			0
$801$		0			0
$802$		−	6.00000i		−	0.211867i
$803$	−33.0681	−	19.0919i	−1.16695	−	0.673738i
$804$		0			0
$805$	35.4904	+	31.4711i	1.25087	+	1.10921i
$806$	4.24264	+	7.34847i	0.149441	+	0.258839i
$807$		0			0
$808$	20.7846	+	12.0000i	0.731200	+	0.422159i
$809$	25.4558			0.894980			0.447490	−	0.894289i	$-0.352318\pi$
$809$	25.4558			0.894980			0.447490	+	0.894289i	$0.352318\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$	27.0000	+	46.7654i	0.946350	+	1.63913i
$815$	13.3521	−	15.0573i	0.467703	−	0.527434i
$816$		0			0
$817$	−5.19615	−	3.00000i	−0.181790	−	0.104957i
$818$			35.3553i			1.23617i
$819$		0			0
$820$		0			0
$821$	−4.24264	+	7.34847i	−0.148069	+	0.256463i	−0.930514	−	0.366257i	$-0.880639\pi$
$821$	−4.24264	+	7.34847i	−0.148069	+	0.256463i	0.782445	+	0.622720i	$0.213972\pi$
$822$		0			0
$823$	−33.7750	+	19.5000i	−1.17732	+	0.679727i	−0.955394	−	0.295336i	$-0.904569\pi$
$823$	−33.7750	+	19.5000i	−1.17732	+	0.679727i	−0.221929	+	0.975063i	$0.571235\pi$
$824$	4.24264	+	7.34847i	0.147799	+	0.255996i
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$			2.82843i			0.0983540i	0.998790	+	0.0491770i	$0.0156598\pi$
$827$			2.82843i			0.0983540i	−0.998790	+	0.0491770i	$0.984340\pi$
$828$		0			0
$829$	−7.00000			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$830$	0.896575	−	4.38134i	0.0311206	−	0.152079i
$831$		0			0
$832$	20.7846	−	12.0000i	0.720577	−	0.416025i
$833$	−4.89898	+	2.82843i	−0.169740	+	0.0979992i
$834$		0			0
$835$	12.3923	+	2.53590i	0.428853	+	0.0877584i
$836$		0			0
$837$		0			0
$838$			48.0000i			1.65813i
$839$	21.2132	−	36.7423i	0.732361	−	1.26849i	−0.223510	−	0.974702i	$-0.571752\pi$
$839$	21.2132	−	36.7423i	0.732361	−	1.26849i	0.955871	−	0.293785i	$-0.0949150\pi$
$840$		0			0
$841$	5.50000	+	9.52628i	0.189655	+	0.328492i
$842$	−28.1691	+	16.2635i	−0.970772	+	0.560476i
$843$		0			0
$844$		0			0
$845$	8.48528	−	2.82843i	0.291903	−	0.0973009i
$846$		0			0
$847$			21.0000i			0.721569i
$848$	−34.2929	−	19.7990i	−1.17762	−	0.679900i
$849$		0			0
$850$	−18.3923	−	7.85641i	−0.630851	−	0.269473i
$851$	31.8198	+	55.1135i	1.09077	+	1.88927i
$852$		0			0
$853$	28.5788	+	16.5000i	0.978521	+	0.564949i	0.901823	−	0.432105i	$-0.142229\pi$
$853$	28.5788	+	16.5000i	0.978521	+	0.564949i	0.0766976	+	0.997054i	$0.475562\pi$
$854$	−55.1543			−1.88734
$855$		0			0
$856$	20.0000			0.683586
$857$	23.2702	+	13.4350i	0.794893	+	0.458932i	0.841682	−	0.539973i	$-0.181566\pi$
$857$	23.2702	+	13.4350i	0.794893	+	0.458932i	−0.0467891	+	0.998905i	$0.514899\pi$
$858$		0			0
$859$	−23.5000	−	40.7032i	−0.801810	−	1.38878i	−0.918424	−	0.395598i	$-0.870537\pi$
$859$	−23.5000	−	40.7032i	−0.801810	−	1.38878i	0.116614	−	0.993177i	$-0.462796\pi$
$860$		0			0
$861$		0			0
$862$	−15.5885	−	9.00000i	−0.530945	−	0.306541i
$863$			28.2843i			0.962808i	0.876499	+	0.481404i	$0.159873\pi$
$863$			28.2843i			0.962808i	−0.876499	+	0.481404i	$0.840127\pi$
$864$		0			0
$865$	−10.0000	−	30.0000i	−0.340010	−	1.02003i
$866$	−25.4558	+	44.0908i	−0.865025	+	1.49827i
$867$		0			0
$868$		0			0
$869$	10.6066	+	18.3712i	0.359804	+	0.623199i
$870$		0			0
$871$	4.50000	−	7.79423i	0.152477	−	0.264097i
$872$		−	22.6274i		−	0.766261i
$873$		0			0
$874$	−10.0000			−0.338255
$875$	−30.3226	+	14.3366i	−1.02509	+	0.484665i
$876$		0			0
$877$	12.9904	−	7.50000i	0.438654	−	0.253257i	−0.264373	−	0.964421i	$-0.585165\pi$
$877$	12.9904	−	7.50000i	0.438654	−	0.253257i	0.703027	+	0.711164i	$0.251832\pi$
$878$	−17.1464	+	9.89949i	−0.578664	+	0.334092i
$879$		0			0
$880$	−7.60770	+	37.1769i	−0.256455	+	1.25323i
$881$	38.1838			1.28644			0.643222	−	0.765680i	$-0.277597\pi$
$881$	38.1838			1.28644			0.643222	+	0.765680i	$0.277597\pi$
$882$		0			0
$883$		−	27.0000i		−	0.908622i	−0.890843	−	0.454311i	$-0.849885\pi$
$883$		−	27.0000i		−	0.908622i	0.890843	−	0.454311i	$-0.150115\pi$
$884$		0			0
$885$		0			0
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	39.1918	−	22.6274i	1.31593	−	0.759754i	0.332861	−	0.942976i	$-0.391986\pi$
$887$	39.1918	−	22.6274i	1.31593	−	0.759754i	0.983072	+	0.183221i	$0.0586525\pi$
$888$		0			0
$889$	−27.0000	+	46.7654i	−0.905551	+	1.56846i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.44949	+	1.41421i	0.0819690	+	0.0473249i
$894$		0			0
$895$	−21.2942	−	18.8827i	−0.711788	−	0.631179i
$896$	16.9706	+	29.3939i	0.566947	+	0.981981i
$897$		0			0
$898$		0			0
$899$	−8.48528			−0.283000
$900$		0			0
$901$	28.0000			0.932815
$902$	−22.0454	−	12.7279i	−0.734032	−	0.423793i
$903$		0			0
$904$	2.00000	+	3.46410i	0.0665190	+	0.115214i
$905$	1.67303	+	1.48356i	0.0556135	+	0.0493153i
$906$		0			0
$907$	−2.59808	−	1.50000i	−0.0862677	−	0.0498067i	0.456246	−	0.889854i	$-0.349194\pi$
$907$	−2.59808	−	1.50000i	−0.0862677	−	0.0498067i	−0.542513	+	0.840047i	$0.682527\pi$
$908$		0			0
$909$		0			0
$910$	−9.00000	−	27.0000i	−0.298347	−	0.895041i
$911$	21.2132	−	36.7423i	0.702825	−	1.21733i	−0.264646	−	0.964346i	$-0.585255\pi$
$911$	21.2132	−	36.7423i	0.702825	−	1.21733i	0.967471	−	0.252983i	$-0.0814115\pi$
$912$		0			0
$913$	5.19615	−	3.00000i	0.171968	−	0.0992855i
$914$	−8.48528	−	14.6969i	−0.280668	−	0.486132i
$915$		0			0
$916$		0			0
$917$		−	25.4558i		−	0.840626i
$918$		0			0
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$	−8.96575	+	43.8134i	−0.295592	+	1.44449i
$921$		0			0
$922$	20.7846	−	12.0000i	0.684505	−	0.395199i
$923$	−33.0681	+	19.0919i	−1.08845	+	0.628417i
$924$		0			0
$925$	−44.6769	+	5.38269i	−1.46897	+	0.176982i
$926$	21.2132			0.697109
$927$		0			0
$928$		0			0
$929$	−23.3345	+	40.4166i	−0.765581	+	1.32603i	0.174358	+	0.984682i	$0.444215\pi$
$929$	−23.3345	+	40.4166i	−0.765581	+	1.32603i	−0.939939	+	0.341343i	$0.889118\pi$
$930$		0			0
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$		0			0
$933$		0			0
$934$	16.0000	−	27.7128i	0.523536	−	0.906791i
$935$	−8.48528	−	25.4558i	−0.277498	−	0.832495i
$936$		0			0
$937$		−	9.00000i		−	0.294017i	−0.989135	−	0.147009i	$-0.953036\pi$
$937$		−	9.00000i		−	0.294017i	0.989135	−	0.147009i	$-0.0469645\pi$
$938$	11.0227	+	6.36396i	0.359904	+	0.207791i
$939$		0			0
$940$		0			0
$941$	10.6066	+	18.3712i	0.345765	+	0.598883i	0.985493	−	0.169719i	$-0.0542860\pi$
$941$	10.6066	+	18.3712i	0.345765	+	0.598883i	−0.639727	+	0.768602i	$0.720953\pi$
$942$		0			0
$943$	−25.9808	−	15.0000i	−0.846050	−	0.488467i
$944$	33.9411			1.10469
$945$		0			0
$946$	36.0000			1.17046
$947$	−31.8434	−	18.3848i	−1.03477	−	0.597425i	−0.116423	−	0.993200i	$-0.537143\pi$
$947$	−31.8434	−	18.3848i	−1.03477	−	0.597425i	−0.918348	+	0.395775i	$0.870476\pi$
$948$		0			0
$949$	13.5000	+	23.3827i	0.438229	+	0.759034i
$950$	2.77766	−	6.50266i	0.0901192	−	0.210974i
$951$		0			0
$952$	−20.7846	−	12.0000i	−0.673633	−	0.388922i
$953$		−	5.65685i		−	0.183243i	−0.995794	−	0.0916217i	$-0.970795\pi$
$953$		−	5.65685i		−	0.183243i	0.995794	−	0.0916217i	$-0.0292051\pi$
$954$		0			0
$955$	−36.0000	+	12.0000i	−1.16493	+	0.388311i
$956$		0			0
$957$		0			0
$958$	5.19615	−	3.00000i	0.167880	−	0.0969256i
$959$	−2.12132	−	3.67423i	−0.0685010	−	0.118647i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		−	38.1838i		−	1.23109i
$963$		0			0
$964$		0			0
$965$	6.57201	+	1.34486i	0.211561	+	0.0432927i
$966$		0			0
$967$	28.5788	−	16.5000i	0.919033	−	0.530604i	0.0357069	−	0.999362i	$-0.488632\pi$
$967$	28.5788	−	16.5000i	0.919033	−	0.530604i	0.883327	+	0.468758i	$0.155298\pi$
$968$	−17.1464	+	9.89949i	−0.551107	+	0.318182i
$969$		0			0
$970$	−1.90192	+	9.29423i	−0.0610671	+	0.298420i
$971$	−25.4558			−0.816917			−0.408458	−	0.912777i	$-0.633934\pi$
$971$	−25.4558			−0.816917			−0.408458	+	0.912777i	$0.633934\pi$
$972$		0			0
$973$		−	39.0000i		−	1.25028i
$974$	6.36396	−	11.0227i	0.203914	−	0.353190i
$975$		0			0
$976$	−26.0000	−	45.0333i	−0.832240	−	1.44148i
$977$	−1.22474	+	0.707107i	−0.0391831	+	0.0226224i	−0.519464	−	0.854493i	$-0.673868\pi$
$977$	−1.22474	+	0.707107i	−0.0391831	+	0.0226224i	0.480281	+	0.877115i	$0.340535\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$			30.0000i			0.957338i
$983$	45.3156	+	26.1630i	1.44534	+	0.834469i	0.998199	−	0.0599939i	$-0.0191081\pi$
$983$	45.3156	+	26.1630i	1.44534	+	0.834469i	0.447143	+	0.894462i	$0.352441\pi$
$984$		0			0
$985$	−33.5692	+	37.8564i	−1.06960	+	1.20621i
$986$	8.48528	+	14.6969i	0.270226	+	0.468046i
$987$		0			0
$988$		0			0
$989$	42.4264			1.34908
$990$		0			0
$991$	53.0000			1.68360			0.841800	−	0.539789i	$-0.181496\pi$
$991$	53.0000			1.68360			0.841800	+	0.539789i	$0.181496\pi$
$992$		0			0
$993$		0			0
$994$	−27.0000	−	46.7654i	−0.856388	−	1.48331i
$995$	−18.4034	−	16.3192i	−0.583426	−	0.517354i
$996$		0			0
$997$	−41.5692	−	24.0000i	−1.31651	−	0.760088i	−0.333345	−	0.942805i	$-0.608177\pi$
$997$	−41.5692	−	24.0000i	−1.31651	−	0.760088i	−0.983165	+	0.182717i	$0.941511\pi$
$998$			22.6274i			0.716258i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.j.f.379.3		8
3.2	odd	2	inner	405.2.j.f.379.2		8
5.4	even	2	inner	405.2.j.f.379.1		8
9.2	odd	6		135.2.b.b.109.3	yes	4
9.4	even	3	inner	405.2.j.f.109.1		8
9.5	odd	6	inner	405.2.j.f.109.4		8
9.7	even	3		135.2.b.b.109.2	yes	4
15.14	odd	2	inner	405.2.j.f.379.4		8
36.7	odd	6		2160.2.f.k.1729.3		4
36.11	even	6		2160.2.f.k.1729.2		4
45.2	even	12		675.2.a.l.1.1		2
45.4	even	6	inner	405.2.j.f.109.3		8
45.7	odd	12		675.2.a.l.1.2		2
45.14	odd	6	inner	405.2.j.f.109.2		8
45.29	odd	6		135.2.b.b.109.1	✓	4
45.34	even	6		135.2.b.b.109.4	yes	4
45.38	even	12		675.2.a.m.1.2		2
45.43	odd	12		675.2.a.m.1.1		2
180.79	odd	6		2160.2.f.k.1729.4		4
180.119	even	6		2160.2.f.k.1729.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.b.b.109.1	✓	4	45.29	odd	6
135.2.b.b.109.2	yes	4	9.7	even	3
135.2.b.b.109.3	yes	4	9.2	odd	6
135.2.b.b.109.4	yes	4	45.34	even	6
405.2.j.f.109.1		8	9.4	even	3	inner
405.2.j.f.109.2		8	45.14	odd	6	inner
405.2.j.f.109.3		8	45.4	even	6	inner
405.2.j.f.109.4		8	9.5	odd	6	inner
405.2.j.f.379.1		8	5.4	even	2	inner
405.2.j.f.379.2		8	3.2	odd	2	inner
405.2.j.f.379.3		8	1.1	even	1	trivial
405.2.j.f.379.4		8	15.14	odd	2	inner
675.2.a.l.1.1		2	45.2	even	12
675.2.a.l.1.2		2	45.7	odd	12
675.2.a.m.1.1		2	45.43	odd	12
675.2.a.m.1.2		2	45.38	even	12
2160.2.f.k.1729.1		4	180.119	even	6
2160.2.f.k.1729.2		4	36.11	even	6
2160.2.f.k.1729.3		4	36.7	odd	6
2160.2.f.k.1729.4		4	180.79	odd	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-1.67303 - 1.48356i) q^{5} +(-2.59808 - 1.50000i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(-1.67303 - 1.48356i) q^{5} +(-2.59808 - 1.50000i) q^{7} -2.82843i q^{8} +(-1.00000 - 3.00000i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-2.59808 + 1.50000i) q^{13} +(-2.12132 - 3.67423i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.82843i q^{17} -1.00000 q^{19} +(5.19615 - 3.00000i) q^{22} +(6.12372 - 3.53553i) q^{23} +(0.598076 + 4.96410i) q^{25} -4.24264 q^{26} +(2.12132 - 3.67423i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.00000 + 3.46410i) q^{34} +(2.12132 + 6.36396i) q^{35} +9.00000i q^{37} +(-1.22474 - 0.707107i) q^{38} +(-4.19615 + 4.73205i) q^{40} +(-2.12132 - 3.67423i) q^{41} +(5.19615 + 3.00000i) q^{43} +10.0000 q^{46} +(-2.44949 - 1.41421i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-2.77766 + 6.50266i) q^{50} -9.89949i q^{53} +(-9.00000 + 3.00000i) q^{55} +(-4.24264 + 7.34847i) q^{56} +(5.19615 - 3.00000i) q^{58} +(4.24264 + 7.34847i) q^{59} +(6.50000 - 11.2583i) q^{61} -2.82843i q^{62} -8.00000 q^{64} +(6.57201 + 1.34486i) q^{65} +(-2.59808 + 1.50000i) q^{67} +(-1.90192 + 9.29423i) q^{70} +12.7279 q^{71} -9.00000i q^{73} +(-6.36396 + 11.0227i) q^{74} +(-11.0227 + 6.36396i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-8.48528 + 2.82843i) q^{80} -6.00000i q^{82} +(1.22474 + 0.707107i) q^{83} +(4.19615 - 4.73205i) q^{85} +(4.24264 + 7.34847i) q^{86} +(-10.3923 - 6.00000i) q^{88} +9.00000 q^{91} +(-2.00000 - 3.46410i) q^{94} +(1.67303 + 1.48356i) q^{95} +(-2.59808 - 1.50000i) q^{97} +2.82843i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{10} + 16 q^{16} - 8 q^{19} - 16 q^{25} - 8 q^{31} - 16 q^{34} + 8 q^{40} + 80 q^{46} + 8 q^{49} - 72 q^{55} + 52 q^{61} - 64 q^{64} - 36 q^{70} - 20 q^{79} - 8 q^{85} + 72 q^{91} - 16 q^{94}+O(q^{100}) \) 8 * q - 8 * q^10 + 16 * q^16 - 8 * q^19 - 16 * q^25 - 8 * q^31 - 16 * q^34 + 8 * q^40 + 80 * q^46 + 8 * q^49 - 72 * q^55 + 52 * q^61 - 64 * q^64 - 36 * q^70 - 20 * q^79 - 8 * q^85 + 72 * q^91 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more