LMFDB - Embedded newform 1920.2.s.e.481.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(481,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1920.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.s (of order $4$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
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} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			481.6
Root			$1.19834 + 0.750988i$ of defining polynomial
Character	$\chi$	$=$	1920.481
Dual form			1920.2.s.e.1441.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -3.79862i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -3.79862i q^{7} -1.00000i q^{9} +(-3.08662 - 3.08662i) q^{11} +(-1.54638 + 1.54638i) q^{13} +1.00000 q^{15} +4.32428 q^{17} +(5.37165 - 5.37165i) q^{19} +(-2.68603 - 2.68603i) q^{21} +3.91059i q^{23} +1.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-1.84243 + 1.84243i) q^{29} -9.52790 q^{31} -4.36514 q^{33} +(2.68603 - 2.68603i) q^{35} +(-4.55033 - 4.55033i) q^{37} +2.18691i q^{39} -0.580195i q^{41} +(-0.994741 - 0.994741i) q^{43} +(0.707107 - 0.707107i) q^{45} +2.22461 q^{47} -7.42948 q^{49} +(3.05773 - 3.05773i) q^{51} +(-4.80257 - 4.80257i) q^{53} -4.36514i q^{55} -7.59666i q^{57} +(-7.26404 - 7.26404i) q^{59} +(-0.301222 + 0.301222i) q^{61} -3.79862 q^{63} -2.18691 q^{65} +(-6.97711 + 6.97711i) q^{67} +(2.76520 + 2.76520i) q^{69} -0.585051i q^{71} -11.9999i q^{73} +(0.707107 + 0.707107i) q^{75} +(-11.7249 + 11.7249i) q^{77} +12.6436 q^{79} -1.00000 q^{81} +(11.1632 - 11.1632i) q^{83} +(3.05773 + 3.05773i) q^{85} +2.60559i q^{87} +12.9706i q^{89} +(5.87409 + 5.87409i) q^{91} +(-6.73724 + 6.73724i) q^{93} +7.59666 q^{95} -6.78553 q^{97} +(-3.08662 + 3.08662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 8 q^{11} + 20 q^{15} - 24 q^{17} + 4 q^{19} - 16 q^{29} + 16 q^{33} - 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} + 16 q^{53} + 16 q^{59} + 4 q^{61} - 8 q^{63} + 8 q^{67} + 4 q^{69} + 40 q^{77} + 56 q^{79} - 20 q^{81} + 48 q^{83} - 4 q^{85} + 8 q^{91} - 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 8 * q^11 + 20 * q^15 - 24 * q^17 + 4 * q^19 - 16 * q^29 + 16 * q^33 - 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 + 16 * q^53 + 16 * q^59 + 4 * q^61 - 8 * q^63 + 8 * q^67 + 4 * q^69 + 40 * q^77 + 56 * q^79 - 20 * q^81 + 48 * q^83 - 4 * q^85 + 8 * q^91 - 16 * q^93 + 56 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	3.79862i		−	1.43574i	−0.696176	−	0.717871i	$-0.745117\pi$
$7$		−	3.79862i		−	1.43574i	0.696176	−	0.717871i	$-0.254883\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.08662	−	3.08662i	−0.930650	−	0.930650i	0.0670964	−	0.997746i	$-0.478626\pi$
$11$	−3.08662	−	3.08662i	−0.930650	−	0.930650i	−0.997746	+	0.0670964i	$0.978626\pi$
$12$		0			0
$13$	−1.54638	+	1.54638i	−0.428888	+	0.428888i	−0.888249	−	0.459361i	$-0.848078\pi$
$13$	−1.54638	+	1.54638i	−0.428888	+	0.428888i	0.459361	+	0.888249i	$0.348078\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	4.32428			1.04879			0.524396	−	0.851474i	$-0.324291\pi$
$17$	4.32428			1.04879			0.524396	+	0.851474i	$0.324291\pi$
$18$		0			0
$19$	5.37165	−	5.37165i	1.23234	−	1.23234i	0.269279	−	0.963062i	$-0.413215\pi$
$19$	5.37165	−	5.37165i	1.23234	−	1.23234i	0.963062	−	0.269279i	$-0.0867853\pi$
$20$		0			0
$21$	−2.68603	−	2.68603i	−0.586139	−	0.586139i
$22$		0			0
$23$			3.91059i			0.815414i	0.913113	+	0.407707i	$0.133671\pi$
$23$			3.91059i			0.815414i	−0.913113	+	0.407707i	$0.866329\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−1.84243	+	1.84243i	−0.342131	+	0.342131i	−0.857168	−	0.515037i	$-0.827778\pi$
$29$	−1.84243	+	1.84243i	−0.342131	+	0.342131i	0.515037	+	0.857168i	$0.327778\pi$
$30$		0			0
$31$	−9.52790			−1.71126			−0.855630	−	0.517587i	$-0.826830\pi$
$31$	−9.52790			−1.71126			−0.855630	+	0.517587i	$0.826830\pi$
$32$		0			0
$33$	−4.36514			−0.759873
$34$		0			0
$35$	2.68603	−	2.68603i	0.454021	−	0.454021i
$36$		0			0
$37$	−4.55033	−	4.55033i	−0.748070	−	0.748070i	0.226047	−	0.974116i	$-0.427420\pi$
$37$	−4.55033	−	4.55033i	−0.748070	−	0.748070i	−0.974116	+	0.226047i	$0.927420\pi$
$38$		0			0
$39$			2.18691i			0.350186i
$40$		0			0
$41$		−	0.580195i		−	0.0906112i	−0.998973	−	0.0453056i	$-0.985574\pi$
$41$		−	0.580195i		−	0.0906112i	0.998973	−	0.0453056i	$-0.0144262\pi$
$42$		0			0
$43$	−0.994741	−	0.994741i	−0.151697	−	0.151697i	0.627179	−	0.778875i	$-0.284210\pi$
$43$	−0.994741	−	0.994741i	−0.151697	−	0.151697i	−0.778875	+	0.627179i	$0.784210\pi$
$44$		0			0
$45$	0.707107	−	0.707107i	0.105409	−	0.105409i
$46$		0			0
$47$	2.22461			0.324492			0.162246	−	0.986750i	$-0.448126\pi$
$47$	2.22461			0.324492			0.162246	+	0.986750i	$0.448126\pi$
$48$		0			0
$49$	−7.42948			−1.06135
$50$		0			0
$51$	3.05773	−	3.05773i	0.428168	−	0.428168i
$52$		0			0
$53$	−4.80257	−	4.80257i	−0.659684	−	0.659684i	0.295622	−	0.955305i	$-0.404473\pi$
$53$	−4.80257	−	4.80257i	−0.659684	−	0.659684i	−0.955305	+	0.295622i	$0.904473\pi$
$54$		0			0
$55$		−	4.36514i		−	0.588595i
$56$		0			0
$57$		−	7.59666i		−	1.00620i
$58$		0			0
$59$	−7.26404	−	7.26404i	−0.945698	−	0.945698i	0.0529020	−	0.998600i	$-0.483153\pi$
$59$	−7.26404	−	7.26404i	−0.945698	−	0.945698i	−0.998600	+	0.0529020i	$0.983153\pi$
$60$		0			0
$61$	−0.301222	+	0.301222i	−0.0385676	+	0.0385676i	−0.726128	−	0.687560i	$-0.758682\pi$
$61$	−0.301222	+	0.301222i	−0.0385676	+	0.0385676i	0.687560	+	0.726128i	$0.258682\pi$
$62$		0			0
$63$	−3.79862			−0.478581
$64$		0			0
$65$	−2.18691			−0.271253
$66$		0			0
$67$	−6.97711	+	6.97711i	−0.852389	+	0.852389i	−0.990427	−	0.138038i	$-0.955921\pi$
$67$	−6.97711	+	6.97711i	−0.852389	+	0.852389i	0.138038	+	0.990427i	$0.455921\pi$
$68$		0			0
$69$	2.76520	+	2.76520i	0.332891	+	0.332891i
$70$		0			0
$71$		−	0.585051i		−	0.0694327i	−0.999397	−	0.0347164i	$-0.988947\pi$
$71$		−	0.585051i		−	0.0694327i	0.999397	−	0.0347164i	$-0.0110528\pi$
$72$		0			0
$73$		−	11.9999i		−	1.40448i	−0.711939	−	0.702241i	$-0.752183\pi$
$73$		−	11.9999i		−	1.40448i	0.711939	−	0.702241i	$-0.247817\pi$
$74$		0			0
$75$	0.707107	+	0.707107i	0.0816497	+	0.0816497i
$76$		0			0
$77$	−11.7249	+	11.7249i	−1.33617	+	1.33617i
$78$		0			0
$79$	12.6436			1.42252			0.711260	−	0.702929i	$-0.248125\pi$
$79$	12.6436			1.42252			0.711260	+	0.702929i	$0.248125\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	11.1632	−	11.1632i	1.22532	−	1.22532i	0.259610	−	0.965713i	$-0.416406\pi$
$83$	11.1632	−	11.1632i	1.22532	−	1.22532i	0.965713	−	0.259610i	$-0.0835941\pi$
$84$		0			0
$85$	3.05773	+	3.05773i	0.331657	+	0.331657i
$86$		0			0
$87$			2.60559i			0.279349i
$88$		0			0
$89$			12.9706i			1.37488i	0.726241	+	0.687440i	$0.241266\pi$
$89$			12.9706i			1.37488i	−0.726241	+	0.687440i	$0.758734\pi$
$90$		0			0
$91$	5.87409	+	5.87409i	0.615772	+	0.615772i
$92$		0			0
$93$	−6.73724	+	6.73724i	−0.698619	+	0.698619i
$94$		0			0
$95$	7.59666			0.779401
$96$		0			0
$97$	−6.78553			−0.688966			−0.344483	−	0.938793i	$-0.611946\pi$
$97$	−6.78553			−0.688966			−0.344483	+	0.938793i	$0.611946\pi$
$98$		0			0
$99$	−3.08662	+	3.08662i	−0.310217	+	0.310217i
$100$		0			0
$101$	6.19304	+	6.19304i	0.616231	+	0.616231i	0.944562	−	0.328332i	$-0.106486\pi$
$101$	6.19304	+	6.19304i	0.616231	+	0.616231i	−0.328332	+	0.944562i	$0.606486\pi$
$102$		0			0
$103$		−	11.3519i		−	1.11854i	−0.828987	−	0.559269i	$-0.811082\pi$
$103$		−	11.3519i		−	1.11854i	0.828987	−	0.559269i	$-0.188918\pi$
$104$		0			0
$105$		−	3.79862i		−	0.370707i
$106$		0			0
$107$	8.58488	+	8.58488i	0.829932	+	0.829932i	0.987507	−	0.157575i	$-0.0503677\pi$
$107$	8.58488	+	8.58488i	0.829932	+	0.829932i	−0.157575	+	0.987507i	$0.550368\pi$
$108$		0			0
$109$	10.6624	−	10.6624i	1.02127	−	1.02127i	0.0215039	−	0.999769i	$-0.493155\pi$
$109$	10.6624	−	10.6624i	1.02127	−	1.02127i	0.999769	−	0.0215039i	$-0.00684543\pi$
$110$		0			0
$111$	−6.43514			−0.610797
$112$		0			0
$113$	−3.11152			−0.292707			−0.146354	−	0.989232i	$-0.546754\pi$
$113$	−3.11152			−0.292707			−0.146354	+	0.989232i	$0.546754\pi$
$114$		0			0
$115$	−2.76520	+	2.76520i	−0.257856	+	0.257856i
$116$		0			0
$117$	1.54638	+	1.54638i	0.142963	+	0.142963i
$118$		0			0
$119$		−	16.4263i		−	1.50579i
$120$		0			0
$121$			8.05441i			0.732219i
$122$		0			0
$123$	−0.410260	−	0.410260i	−0.0369919	−	0.0369919i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−7.16390			−0.635693			−0.317846	−	0.948142i	$-0.602960\pi$
$127$	−7.16390			−0.635693			−0.317846	+	0.948142i	$0.602960\pi$
$128$		0			0
$129$	−1.40678			−0.123860
$130$		0			0
$131$	6.55090	−	6.55090i	0.572355	−	0.572355i	−0.360431	−	0.932786i	$-0.617370\pi$
$131$	6.55090	−	6.55090i	0.572355	−	0.572355i	0.932786	+	0.360431i	$0.117370\pi$
$132$		0			0
$133$	−20.4048	−	20.4048i	−1.76932	−	1.76932i
$134$		0			0
$135$		−	1.00000i		−	0.0860663i
$136$		0			0
$137$		−	11.0502i		−	0.944082i	−0.881577	−	0.472041i	$-0.843518\pi$
$137$		−	11.0502i		−	0.944082i	0.881577	−	0.472041i	$-0.156482\pi$
$138$		0			0
$139$	5.17171	+	5.17171i	0.438659	+	0.438659i	0.891561	−	0.452902i	$-0.149611\pi$
$139$	5.17171	+	5.17171i	0.438659	+	0.438659i	−0.452902	+	0.891561i	$0.649611\pi$
$140$		0			0
$141$	1.57304	−	1.57304i	0.132473	−	0.132473i
$142$		0			0
$143$	9.54615			0.798289
$144$		0			0
$145$	−2.60559			−0.216383
$146$		0			0
$147$	−5.25343	+	5.25343i	−0.433296	+	0.433296i
$148$		0			0
$149$	5.80335	+	5.80335i	0.475429	+	0.475429i	0.903666	−	0.428237i	$-0.140865\pi$
$149$	5.80335	+	5.80335i	0.475429	+	0.475429i	−0.428237	+	0.903666i	$0.640865\pi$
$150$		0			0
$151$		−	13.2591i		−	1.07901i	−0.841982	−	0.539505i	$-0.818611\pi$
$151$		−	13.2591i		−	1.07901i	0.841982	−	0.539505i	$-0.181389\pi$
$152$		0			0
$153$		−	4.32428i		−	0.349597i
$154$		0			0
$155$	−6.73724	−	6.73724i	−0.541148	−	0.541148i
$156$		0			0
$157$	−6.83329	+	6.83329i	−0.545356	+	0.545356i	−0.925094	−	0.379738i	$-0.876014\pi$
$157$	−6.83329	+	6.83329i	−0.545356	+	0.545356i	0.379738	+	0.925094i	$0.376014\pi$
$158$		0			0
$159$	−6.79186			−0.538629
$160$		0			0
$161$	14.8548			1.17072
$162$		0			0
$163$	7.11541	−	7.11541i	0.557322	−	0.557322i	−0.371222	−	0.928544i	$-0.621061\pi$
$163$	7.11541	−	7.11541i	0.557322	−	0.557322i	0.928544	+	0.371222i	$0.121061\pi$
$164$		0			0
$165$	−3.08662	−	3.08662i	−0.240293	−	0.240293i
$166$		0			0
$167$		−	6.14029i		−	0.475150i	−0.971369	−	0.237575i	$-0.923648\pi$
$167$		−	6.14029i		−	0.475150i	0.971369	−	0.237575i	$-0.0763525\pi$
$168$		0			0
$169$			8.21743i			0.632110i
$170$		0			0
$171$	−5.37165	−	5.37165i	−0.410780	−	0.410780i
$172$		0			0
$173$	7.29269	−	7.29269i	0.554453	−	0.554453i	−0.373270	−	0.927723i	$-0.621763\pi$
$173$	7.29269	−	7.29269i	0.554453	−	0.554453i	0.927723	+	0.373270i	$0.121763\pi$
$174$		0			0
$175$	3.79862			0.287148
$176$		0			0
$177$	−10.2729			−0.772159
$178$		0			0
$179$	−6.22897	+	6.22897i	−0.465575	+	0.465575i	−0.900478	−	0.434902i	$-0.856783\pi$
$179$	−6.22897	+	6.22897i	−0.465575	+	0.465575i	0.434902	+	0.900478i	$0.356783\pi$
$180$		0			0
$181$	1.27302	+	1.27302i	0.0946227	+	0.0946227i	0.752834	−	0.658211i	$-0.228686\pi$
$181$	1.27302	+	1.27302i	0.0946227	+	0.0946227i	−0.658211	+	0.752834i	$0.728686\pi$
$182$		0			0
$183$			0.425993i			0.0314903i
$184$		0			0
$185$		−	6.43514i		−	0.473121i
$186$		0			0
$187$	−13.3474	−	13.3474i	−0.976058	−	0.976058i
$188$		0			0
$189$	−2.68603	+	2.68603i	−0.195380	+	0.195380i
$190$		0			0
$191$	9.63638			0.697264			0.348632	−	0.937260i	$-0.386646\pi$
$191$	9.63638			0.697264			0.348632	+	0.937260i	$0.386646\pi$
$192$		0			0
$193$	−3.64530			−0.262394			−0.131197	−	0.991356i	$-0.541882\pi$
$193$	−3.64530			−0.262394			−0.131197	+	0.991356i	$0.541882\pi$
$194$		0			0
$195$	−1.54638	+	1.54638i	−0.110738	+	0.110738i
$196$		0			0
$197$	7.55422	+	7.55422i	0.538216	+	0.538216i	0.923005	−	0.384789i	$-0.125726\pi$
$197$	7.55422	+	7.55422i	0.538216	+	0.538216i	−0.384789	+	0.923005i	$0.625726\pi$
$198$		0			0
$199$			23.7442i			1.68318i	0.540116	+	0.841591i	$0.318380\pi$
$199$			23.7442i			1.68318i	−0.540116	+	0.841591i	$0.681620\pi$
$200$		0			0
$201$			9.86712i			0.695973i
$202$		0			0
$203$	6.99870	+	6.99870i	0.491212	+	0.491212i
$204$		0			0
$205$	0.410260	−	0.410260i	0.0286538	−	0.0286538i
$206$		0			0
$207$	3.91059			0.271805
$208$		0			0
$209$	−33.1605			−2.29376
$210$		0			0
$211$	−14.5856	+	14.5856i	−1.00412	+	1.00412i	−0.00412399	+	0.999991i	$0.501313\pi$
$211$	−14.5856	+	14.5856i	−1.00412	+	1.00412i	−0.999991	+	0.00412399i	$0.998687\pi$
$212$		0			0
$213$	−0.413693	−	0.413693i	−0.0283458	−	0.0283458i
$214$		0			0
$215$		−	1.40678i		−	0.0959413i
$216$		0			0
$217$			36.1928i			2.45693i
$218$		0			0
$219$	−8.48521	−	8.48521i	−0.573377	−	0.573377i
$220$		0			0
$221$	−6.68697	+	6.68697i	−0.449814	+	0.449814i
$222$		0			0
$223$	−13.6893			−0.916702			−0.458351	−	0.888771i	$-0.651560\pi$
$223$	−13.6893			−0.916702			−0.458351	+	0.888771i	$0.651560\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	11.9490	−	11.9490i	0.793085	−	0.793085i	−0.188910	−	0.981994i	$-0.560495\pi$
$227$	11.9490	−	11.9490i	0.793085	−	0.793085i	0.981994	+	0.188910i	$0.0604953\pi$
$228$		0			0
$229$	−9.40821	−	9.40821i	−0.621712	−	0.621712i	0.324257	−	0.945969i	$-0.394886\pi$
$229$	−9.40821	−	9.40821i	−0.621712	−	0.621712i	−0.945969	+	0.324257i	$0.894886\pi$
$230$		0			0
$231$			16.5815i			1.09098i
$232$		0			0
$233$			11.8223i			0.774505i	0.921974	+	0.387253i	$0.126576\pi$
$233$			11.8223i			0.774505i	−0.921974	+	0.387253i	$0.873424\pi$
$234$		0			0
$235$	1.57304	+	1.57304i	0.102614	+	0.102614i
$236$		0			0
$237$	8.94040	−	8.94040i	0.580741	−	0.580741i
$238$		0			0
$239$	11.2115			0.725213			0.362607	−	0.931942i	$-0.381887\pi$
$239$	11.2115			0.725213			0.362607	+	0.931942i	$0.381887\pi$
$240$		0			0
$241$	7.89997			0.508881			0.254441	−	0.967088i	$-0.418109\pi$
$241$	7.89997			0.508881			0.254441	+	0.967088i	$0.418109\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−5.25343	−	5.25343i	−0.335630	−	0.335630i
$246$		0			0
$247$			16.6132i			1.05707i
$248$		0			0
$249$		−	15.7872i		−	1.00047i
$250$		0			0
$251$	5.34286	+	5.34286i	0.337238	+	0.337238i	0.855327	−	0.518089i	$-0.173356\pi$
$251$	5.34286	+	5.34286i	0.337238	+	0.337238i	−0.518089	+	0.855327i	$0.673356\pi$
$252$		0			0
$253$	12.0705	−	12.0705i	0.758865	−	0.758865i
$254$		0			0
$255$	4.32428			0.270797
$256$		0			0
$257$	15.5250			0.968420			0.484210	−	0.874952i	$-0.339107\pi$
$257$	15.5250			0.968420			0.484210	+	0.874952i	$0.339107\pi$
$258$		0			0
$259$	−17.2850	+	17.2850i	−1.07404	+	1.07404i
$260$		0			0
$261$	1.84243	+	1.84243i	0.114044	+	0.114044i
$262$		0			0
$263$		−	14.3705i		−	0.886126i	−0.896491	−	0.443063i	$-0.853892\pi$
$263$		−	14.3705i		−	0.886126i	0.896491	−	0.443063i	$-0.146108\pi$
$264$		0			0
$265$		−	6.79186i		−	0.417221i
$266$		0			0
$267$	9.17160	+	9.17160i	0.561293	+	0.561293i
$268$		0			0
$269$	19.0607	−	19.0607i	1.16215	−	1.16215i	0.178145	−	0.984004i	$-0.442990\pi$
$269$	19.0607	−	19.0607i	1.16215	−	1.16215i	0.984004	−	0.178145i	$-0.0570098\pi$
$270$		0			0
$271$	−4.66889			−0.283615			−0.141808	−	0.989894i	$-0.545291\pi$
$271$	−4.66889			−0.283615			−0.141808	+	0.989894i	$0.545291\pi$
$272$		0			0
$273$	8.30722			0.502776
$274$		0			0
$275$	3.08662	−	3.08662i	0.186130	−	0.186130i
$276$		0			0
$277$	6.24572	+	6.24572i	0.375269	+	0.375269i	0.869392	−	0.494123i	$-0.164511\pi$
$277$	6.24572	+	6.24572i	0.375269	+	0.375269i	−0.494123	+	0.869392i	$0.664511\pi$
$278$		0			0
$279$			9.52790i			0.570420i
$280$		0			0
$281$			29.7389i			1.77407i	0.461699	+	0.887037i	$0.347240\pi$
$281$			29.7389i			1.77407i	−0.461699	+	0.887037i	$0.652760\pi$
$282$		0			0
$283$	9.49040	+	9.49040i	0.564146	+	0.564146i	0.930482	−	0.366337i	$-0.119388\pi$
$283$	9.49040	+	9.49040i	0.564146	+	0.564146i	−0.366337	+	0.930482i	$0.619388\pi$
$284$		0			0
$285$	5.37165	−	5.37165i	0.318189	−	0.318189i
$286$		0			0
$287$	−2.20394			−0.130094
$288$		0			0
$289$	1.69940			0.0999648
$290$		0			0
$291$	−4.79809	+	4.79809i	−0.281269	+	0.281269i
$292$		0			0
$293$	1.72797	+	1.72797i	0.100949	+	0.100949i	0.755777	−	0.654829i	$-0.227259\pi$
$293$	1.72797	+	1.72797i	0.100949	+	0.100949i	−0.654829	+	0.755777i	$0.727259\pi$
$294$		0			0
$295$		−	10.2729i		−	0.598112i
$296$		0			0
$297$			4.36514i			0.253291i
$298$		0			0
$299$	−6.04724	−	6.04724i	−0.349721	−	0.349721i
$300$		0			0
$301$	−3.77864	+	3.77864i	−0.217797	+	0.217797i
$302$		0			0
$303$	8.75828			0.503150
$304$		0			0
$305$	−0.425993			−0.0243923
$306$		0			0
$307$	−17.5875	+	17.5875i	−1.00377	+	1.00377i	−0.00377977	+	0.999993i	$0.501203\pi$
$307$	−17.5875	+	17.5875i	−1.00377	+	1.00377i	−0.999993	+	0.00377977i	$0.998797\pi$
$308$		0			0
$309$	−8.02701	−	8.02701i	−0.456641	−	0.456641i
$310$		0			0
$311$			1.71809i			0.0974241i	0.998813	+	0.0487120i	$0.0155117\pi$
$311$			1.71809i			0.0974241i	−0.998813	+	0.0487120i	$0.984488\pi$
$312$		0			0
$313$		−	16.4421i		−	0.929363i	−0.885478	−	0.464682i	$-0.846169\pi$
$313$		−	16.4421i		−	0.929363i	0.885478	−	0.464682i	$-0.153831\pi$
$314$		0			0
$315$	−2.68603	−	2.68603i	−0.151340	−	0.151340i
$316$		0			0
$317$	7.96065	−	7.96065i	0.447114	−	0.447114i	−0.447280	−	0.894394i	$-0.647607\pi$
$317$	7.96065	−	7.96065i	0.447114	−	0.447114i	0.894394	+	0.447280i	$0.147607\pi$
$318$		0			0
$319$	11.3738			0.636809
$320$		0			0
$321$	12.1409			0.677637
$322$		0			0
$323$	23.2285	−	23.2285i	1.29247	−	1.29247i
$324$		0			0
$325$	−1.54638	−	1.54638i	−0.0857776	−	0.0857776i
$326$		0			0
$327$		−	15.0789i		−	0.833866i
$328$		0			0
$329$		−	8.45043i		−	0.465887i
$330$		0			0
$331$	−9.02535	−	9.02535i	−0.496078	−	0.496078i	0.414137	−	0.910215i	$-0.364084\pi$
$331$	−9.02535	−	9.02535i	−0.496078	−	0.496078i	−0.910215	+	0.414137i	$0.864084\pi$
$332$		0			0
$333$	−4.55033	+	4.55033i	−0.249357	+	0.249357i
$334$		0			0
$335$	−9.86712			−0.539098
$336$		0			0
$337$	7.44173			0.405377			0.202688	−	0.979243i	$-0.435032\pi$
$337$	7.44173			0.405377			0.202688	+	0.979243i	$0.435032\pi$
$338$		0			0
$339$	−2.20018	+	2.20018i	−0.119497	+	0.119497i
$340$		0			0
$341$	29.4090	+	29.4090i	1.59258	+	1.59258i
$342$		0			0
$343$			1.63142i			0.0880882i
$344$		0			0
$345$			3.91059i			0.210539i
$346$		0			0
$347$	0.659315	+	0.659315i	0.0353939	+	0.0353939i	0.724582	−	0.689188i	$-0.242033\pi$
$347$	0.659315	+	0.659315i	0.0353939	+	0.0353939i	−0.689188	+	0.724582i	$0.742033\pi$
$348$		0			0
$349$	−8.04705	+	8.04705i	−0.430749	+	0.430749i	−0.888883	−	0.458134i	$-0.848518\pi$
$349$	−8.04705	+	8.04705i	−0.430749	+	0.430749i	0.458134	+	0.888883i	$0.348518\pi$
$350$		0			0
$351$	2.18691			0.116729
$352$		0			0
$353$	18.3339			0.975815			0.487907	−	0.872895i	$-0.337760\pi$
$353$	18.3339			0.975815			0.487907	+	0.872895i	$0.337760\pi$
$354$		0			0
$355$	0.413693	−	0.413693i	0.0219566	−	0.0219566i
$356$		0			0
$357$	−11.6151	−	11.6151i	−0.614738	−	0.614738i
$358$		0			0
$359$			11.8783i			0.626912i	0.949603	+	0.313456i	$0.101487\pi$
$359$			11.8783i			0.626912i	−0.949603	+	0.313456i	$0.898513\pi$
$360$		0			0
$361$		−	38.7093i		−	2.03733i
$362$		0			0
$363$	5.69533	+	5.69533i	0.298927	+	0.298927i
$364$		0			0
$365$	8.48521	−	8.48521i	0.444136	−	0.444136i
$366$		0			0
$367$	−24.0792			−1.25692			−0.628462	−	0.777841i	$-0.716315\pi$
$367$	−24.0792			−1.25692			−0.628462	+	0.777841i	$0.716315\pi$
$368$		0			0
$369$	−0.580195			−0.0302037
$370$		0			0
$371$	−18.2431	+	18.2431i	−0.947135	+	0.947135i
$372$		0			0
$373$	−5.50986	−	5.50986i	−0.285290	−	0.285290i	0.549925	−	0.835214i	$-0.314656\pi$
$373$	−5.50986	−	5.50986i	−0.285290	−	0.285290i	−0.835214	+	0.549925i	$0.814656\pi$
$374$		0			0
$375$			1.00000i			0.0516398i
$376$		0			0
$377$		−	5.69820i		−	0.293472i
$378$		0			0
$379$	4.41212	+	4.41212i	0.226635	+	0.226635i	0.811285	−	0.584650i	$-0.198768\pi$
$379$	4.41212	+	4.41212i	0.226635	+	0.226635i	−0.584650	+	0.811285i	$0.698768\pi$
$380$		0			0
$381$	−5.06564	+	5.06564i	−0.259521	+	0.259521i
$382$		0			0
$383$	12.4394			0.635625			0.317812	−	0.948154i	$-0.397052\pi$
$383$	12.4394			0.635625			0.317812	+	0.948154i	$0.397052\pi$
$384$		0			0
$385$	−16.5815			−0.845070
$386$		0			0
$387$	−0.994741	+	0.994741i	−0.0505655	+	0.0505655i
$388$		0			0
$389$	22.7006	+	22.7006i	1.15097	+	1.15097i	0.986359	+	0.164609i	$0.0526363\pi$
$389$	22.7006	+	22.7006i	1.15097	+	1.15097i	0.164609	+	0.986359i	$0.447364\pi$
$390$		0			0
$391$			16.9105i			0.855199i
$392$		0			0
$393$		−	9.26437i		−	0.467326i
$394$		0			0
$395$	8.94040	+	8.94040i	0.449840	+	0.449840i
$396$		0			0
$397$	23.2641	−	23.2641i	1.16759	−	1.16759i	0.184819	−	0.982773i	$-0.440830\pi$
$397$	23.2641	−	23.2641i	1.16759	−	1.16759i	0.982773	−	0.184819i	$-0.0591698\pi$
$398$		0			0
$399$	−28.8568			−1.44465
$400$		0			0
$401$	31.5965			1.57786			0.788928	−	0.614486i	$-0.210636\pi$
$401$	31.5965			1.57786			0.788928	+	0.614486i	$0.210636\pi$
$402$		0			0
$403$	14.7337	−	14.7337i	0.733939	−	0.733939i
$404$		0			0
$405$	−0.707107	−	0.707107i	−0.0351364	−	0.0351364i
$406$		0			0
$407$			28.0903i			1.39238i
$408$		0			0
$409$		−	14.4988i		−	0.716917i	−0.933546	−	0.358459i	$-0.883302\pi$
$409$		−	14.4988i		−	0.716917i	0.933546	−	0.358459i	$-0.116698\pi$
$410$		0			0
$411$	−7.81367	−	7.81367i	−0.385420	−	0.385420i
$412$		0			0
$413$	−27.5933	+	27.5933i	−1.35778	+	1.35778i
$414$		0			0
$415$	15.7872			0.774963
$416$		0			0
$417$	7.31391			0.358164
$418$		0			0
$419$	−24.0709	+	24.0709i	−1.17594	+	1.17594i	−0.195169	+	0.980770i	$0.562525\pi$
$419$	−24.0709	+	24.0709i	−1.17594	+	1.17594i	−0.980770	+	0.195169i	$0.937475\pi$
$420$		0			0
$421$	20.1095	+	20.1095i	0.980079	+	0.980079i	0.999805	−	0.0197268i	$-0.00627965\pi$
$421$	20.1095	+	20.1095i	0.980079	+	0.980079i	−0.0197268	+	0.999805i	$0.506280\pi$
$422$		0			0
$423$		−	2.22461i		−	0.108164i
$424$		0			0
$425$			4.32428i			0.209758i
$426$		0			0
$427$	1.14423	+	1.14423i	0.0553730	+	0.0553730i
$428$		0			0
$429$	6.75015	−	6.75015i	0.325900	−	0.325900i
$430$		0			0
$431$	−29.9026			−1.44036			−0.720180	−	0.693787i	$-0.755941\pi$
$431$	−29.9026			−1.44036			−0.720180	+	0.693787i	$0.755941\pi$
$432$		0			0
$433$	17.7487			0.852950			0.426475	−	0.904499i	$-0.359755\pi$
$433$	17.7487			0.852950			0.426475	+	0.904499i	$0.359755\pi$
$434$		0			0
$435$	−1.84243	+	1.84243i	−0.0883379	+	0.0883379i
$436$		0			0
$437$	21.0063	+	21.0063i	1.00487	+	1.00487i
$438$		0			0
$439$		−	15.1376i		−	0.722478i	−0.932473	−	0.361239i	$-0.882354\pi$
$439$		−	15.1376i		−	0.722478i	0.932473	−	0.361239i	$-0.117646\pi$
$440$		0			0
$441$			7.42948i			0.353785i
$442$		0			0
$443$	16.4687	+	16.4687i	0.782451	+	0.782451i	0.980244	−	0.197793i	$-0.0633773\pi$
$443$	16.4687	+	16.4687i	0.782451	+	0.782451i	−0.197793	+	0.980244i	$0.563377\pi$
$444$		0			0
$445$	−9.17160	+	9.17160i	−0.434775	+	0.434775i
$446$		0			0
$447$	8.20718			0.388186
$448$		0			0
$449$	35.6078			1.68044			0.840218	−	0.542249i	$-0.182427\pi$
$449$	35.6078			1.68044			0.840218	+	0.542249i	$0.182427\pi$
$450$		0			0
$451$	−1.79084	+	1.79084i	−0.0843273	+	0.0843273i
$452$		0			0
$453$	−9.37560	−	9.37560i	−0.440504	−	0.440504i
$454$		0			0
$455$			8.30722i			0.389449i
$456$		0			0
$457$		−	1.98064i		−	0.0926502i	−0.998926	−	0.0463251i	$-0.985249\pi$
$457$		−	1.98064i		−	0.0926502i	0.998926	−	0.0463251i	$-0.0147510\pi$
$458$		0			0
$459$	−3.05773	−	3.05773i	−0.142723	−	0.142723i
$460$		0			0
$461$	4.13532	−	4.13532i	0.192601	−	0.192601i	−0.604218	−	0.796819i	$-0.706514\pi$
$461$	4.13532	−	4.13532i	0.192601	−	0.192601i	0.796819	+	0.604218i	$0.206514\pi$
$462$		0			0
$463$	23.4228			1.08855			0.544274	−	0.838907i	$-0.316805\pi$
$463$	23.4228			1.08855			0.544274	+	0.838907i	$0.316805\pi$
$464$		0			0
$465$	−9.52790			−0.441846
$466$		0			0
$467$	4.20786	−	4.20786i	0.194717	−	0.194717i	−0.603014	−	0.797731i	$-0.706034\pi$
$467$	4.20786	−	4.20786i	0.194717	−	0.194717i	0.797731	+	0.603014i	$0.206034\pi$
$468$		0			0
$469$	26.5033	+	26.5033i	1.22381	+	1.22381i
$470$		0			0
$471$			9.66373i			0.445281i
$472$		0			0
$473$			6.14077i			0.282353i
$474$		0			0
$475$	5.37165	+	5.37165i	0.246468	+	0.246468i
$476$		0			0
$477$	−4.80257	+	4.80257i	−0.219895	+	0.219895i
$478$		0			0
$479$	5.52216			0.252314			0.126157	−	0.992010i	$-0.459736\pi$
$479$	5.52216			0.252314			0.126157	+	0.992010i	$0.459736\pi$
$480$		0			0
$481$	14.0731			0.641676
$482$		0			0
$483$	10.5039	−	10.5039i	0.477946	−	0.477946i
$484$		0			0
$485$	−4.79809	−	4.79809i	−0.217870	−	0.217870i
$486$		0			0
$487$			28.0612i			1.27158i	0.771864	+	0.635788i	$0.219325\pi$
$487$			28.0612i			1.27158i	−0.771864	+	0.635788i	$0.780675\pi$
$488$		0			0
$489$		−	10.0627i		−	0.455051i
$490$		0			0
$491$	1.27407	+	1.27407i	0.0574979	+	0.0574979i	0.735271	−	0.677773i	$-0.237055\pi$
$491$	1.27407	+	1.27407i	0.0574979	+	0.0574979i	−0.677773	+	0.735271i	$0.737055\pi$
$492$		0			0
$493$	−7.96720	+	7.96720i	−0.358825	+	0.358825i
$494$		0			0
$495$	−4.36514			−0.196198
$496$		0			0
$497$	−2.22238			−0.0996875
$498$		0			0
$499$	26.3351	−	26.3351i	1.17892	−	1.17892i	0.198901	−	0.980020i	$-0.436263\pi$
$499$	26.3351	−	26.3351i	1.17892	−	1.17892i	0.980020	−	0.198901i	$-0.0637373\pi$
$500$		0			0
$501$	−4.34184	−	4.34184i	−0.193979	−	0.193979i
$502$		0			0
$503$		−	33.2293i		−	1.48162i	−0.671715	−	0.740810i	$-0.734442\pi$
$503$		−	33.2293i		−	1.48162i	0.671715	−	0.740810i	$-0.265558\pi$
$504$		0			0
$505$			8.75828i			0.389739i
$506$		0			0
$507$	5.81060	+	5.81060i	0.258058	+	0.258058i
$508$		0			0
$509$	5.03424	−	5.03424i	0.223139	−	0.223139i	−0.586680	−	0.809819i	$-0.699565\pi$
$509$	5.03424	−	5.03424i	0.223139	−	0.223139i	0.809819	+	0.586680i	$0.199565\pi$
$510$		0			0
$511$	−45.5830			−2.01647
$512$		0			0
$513$	−7.59666			−0.335401
$514$		0			0
$515$	8.02701	−	8.02701i	0.353713	−	0.353713i
$516$		0			0
$517$	−6.86651	−	6.86651i	−0.301989	−	0.301989i
$518$		0			0
$519$		−	10.3134i		−	0.452709i
$520$		0			0
$521$			29.6023i			1.29690i	0.761257	+	0.648450i	$0.224582\pi$
$521$			29.6023i			1.29690i	−0.761257	+	0.648450i	$0.775418\pi$
$522$		0			0
$523$	−6.90122	−	6.90122i	−0.301769	−	0.301769i	0.539937	−	0.841706i	$-0.318448\pi$
$523$	−6.90122	−	6.90122i	−0.301769	−	0.301769i	−0.841706	+	0.539937i	$0.818448\pi$
$524$		0			0
$525$	2.68603	−	2.68603i	0.117228	−	0.117228i
$526$		0			0
$527$	−41.2013			−1.79476
$528$		0			0
$529$	7.70731			0.335100
$530$		0			0
$531$	−7.26404	+	7.26404i	−0.315233	+	0.315233i
$532$		0			0
$533$	0.897200	+	0.897200i	0.0388621	+	0.0388621i
$534$		0			0
$535$			12.1409i			0.524895i
$536$		0			0
$537$			8.80909i			0.380140i
$538$		0			0
$539$	22.9319	+	22.9319i	0.987749	+	0.987749i
$540$		0			0
$541$	7.18248	−	7.18248i	0.308799	−	0.308799i	−0.535645	−	0.844443i	$-0.679931\pi$
$541$	7.18248	−	7.18248i	0.308799	−	0.308799i	0.844443	+	0.535645i	$0.179931\pi$
$542$		0			0
$543$	1.80032			0.0772591
$544$		0			0
$545$	15.0789			0.645910
$546$		0			0
$547$	14.9525	−	14.9525i	0.639323	−	0.639323i	−0.311066	−	0.950388i	$-0.600686\pi$
$547$	14.9525	−	14.9525i	0.639323	−	0.639323i	0.950388	+	0.311066i	$0.100686\pi$
$548$		0			0
$549$	0.301222	+	0.301222i	0.0128559	+	0.0128559i
$550$		0			0
$551$			19.7938i			0.843245i
$552$		0			0
$553$		−	48.0283i		−	2.04237i
$554$		0			0
$555$	−4.55033	−	4.55033i	−0.193151	−	0.193151i
$556$		0			0
$557$	−24.8706	+	24.8706i	−1.05380	+	1.05380i	−0.0553344	+	0.998468i	$0.517622\pi$
$557$	−24.8706	+	24.8706i	−1.05380	+	1.05380i	−0.998468	+	0.0553344i	$0.982378\pi$
$558$		0			0
$559$	3.07649			0.130122
$560$		0			0
$561$	−18.8761			−0.796948
$562$		0			0
$563$	−11.1111	+	11.1111i	−0.468277	+	0.468277i	−0.901356	−	0.433079i	$-0.857427\pi$
$563$	−11.1111	+	11.1111i	−0.468277	+	0.468277i	0.433079	+	0.901356i	$0.357427\pi$
$564$		0			0
$565$	−2.20018	−	2.20018i	−0.0925621	−	0.0925621i
$566$		0			0
$567$			3.79862i			0.159527i
$568$		0			0
$569$			12.9347i			0.542250i	0.962544	+	0.271125i	$0.0873956\pi$
$569$			12.9347i			0.542250i	−0.962544	+	0.271125i	$0.912604\pi$
$570$		0			0
$571$	14.5979	+	14.5979i	0.610903	+	0.610903i	0.943181	−	0.332278i	$-0.107817\pi$
$571$	14.5979	+	14.5979i	0.610903	+	0.610903i	−0.332278	+	0.943181i	$0.607817\pi$
$572$		0			0
$573$	6.81395	−	6.81395i	0.284657	−	0.284657i
$574$		0			0
$575$	−3.91059			−0.163083
$576$		0			0
$577$	15.7906			0.657373			0.328687	−	0.944439i	$-0.393394\pi$
$577$	15.7906			0.657373			0.328687	+	0.944439i	$0.393394\pi$
$578$		0			0
$579$	−2.57761	+	2.57761i	−0.107122	+	0.107122i
$580$		0			0
$581$	−42.4048	−	42.4048i	−1.75925	−	1.75925i
$582$		0			0
$583$			29.6474i			1.22787i
$584$		0			0
$585$			2.18691i			0.0904175i
$586$		0			0
$587$	−13.9365	−	13.9365i	−0.575221	−	0.575221i	0.358362	−	0.933583i	$-0.383335\pi$
$587$	−13.9365	−	13.9365i	−0.575221	−	0.575221i	−0.933583	+	0.358362i	$0.883335\pi$
$588$		0			0
$589$	−51.1805	+	51.1805i	−2.10886	+	2.10886i
$590$		0			0
$591$	10.6833			0.439452
$592$		0			0
$593$	−47.4176			−1.94721			−0.973604	−	0.228242i	$-0.926702\pi$
$593$	−47.4176			−1.94721			−0.973604	+	0.228242i	$0.926702\pi$
$594$		0			0
$595$	11.6151	−	11.6151i	0.476174	−	0.476174i
$596$		0			0
$597$	16.7897	+	16.7897i	0.687156	+	0.687156i
$598$		0			0
$599$		−	23.5791i		−	0.963415i	−0.876332	−	0.481707i	$-0.840017\pi$
$599$		−	23.5791i		−	0.963415i	0.876332	−	0.481707i	$-0.159983\pi$
$600$		0			0
$601$		−	3.86582i		−	0.157690i	−0.996887	−	0.0788450i	$-0.974877\pi$
$601$		−	3.86582i		−	0.157690i	0.996887	−	0.0788450i	$-0.0251232\pi$
$602$		0			0
$603$	6.97711	+	6.97711i	0.284130	+	0.284130i
$604$		0			0
$605$	−5.69533	+	5.69533i	−0.231548	+	0.231548i
$606$		0			0
$607$	32.4306			1.31632			0.658159	−	0.752879i	$-0.271335\pi$
$607$	32.4306			1.31632			0.658159	+	0.752879i	$0.271335\pi$
$608$		0			0
$609$	9.89765			0.401073
$610$		0			0
$611$	−3.44008	+	3.44008i	−0.139171	+	0.139171i
$612$		0			0
$613$	−21.7952	−	21.7952i	−0.880298	−	0.880298i	0.113267	−	0.993565i	$-0.463869\pi$
$613$	−21.7952	−	21.7952i	−0.880298	−	0.880298i	−0.993565	+	0.113267i	$0.963869\pi$
$614$		0			0
$615$		−	0.580195i		−	0.0233957i
$616$		0			0
$617$			1.49837i			0.0603219i	0.999545	+	0.0301610i	$0.00960199\pi$
$617$			1.49837i			0.0603219i	−0.999545	+	0.0301610i	$0.990398\pi$
$618$		0			0
$619$	−16.7004	−	16.7004i	−0.671246	−	0.671246i	0.286757	−	0.958003i	$-0.407423\pi$
$619$	−16.7004	−	16.7004i	−0.671246	−	0.671246i	−0.958003	+	0.286757i	$0.907423\pi$
$620$		0			0
$621$	2.76520	−	2.76520i	0.110964	−	0.110964i
$622$		0			0
$623$	49.2703			1.97397
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−23.4480	+	23.4480i	−0.936422	+	0.936422i
$628$		0			0
$629$	−19.6769	−	19.6769i	−0.784570	−	0.784570i
$630$		0			0
$631$			28.6304i			1.13976i	0.821729	+	0.569878i	$0.193010\pi$
$631$			28.6304i			1.13976i	−0.821729	+	0.569878i	$0.806990\pi$
$632$		0			0
$633$			20.6272i			0.819857i
$634$		0			0
$635$	−5.06564	−	5.06564i	−0.201024	−	0.201024i
$636$		0			0
$637$	11.4888	−	11.4888i	0.455202	−	0.455202i
$638$		0			0
$639$	−0.585051			−0.0231442
$640$		0			0
$641$	−47.4097			−1.87257			−0.936286	−	0.351239i	$-0.885760\pi$
$641$	−47.4097			−1.87257			−0.936286	+	0.351239i	$0.885760\pi$
$642$		0			0
$643$	−22.0744	+	22.0744i	−0.870528	+	0.870528i	−0.992530	−	0.122002i	$-0.961069\pi$
$643$	−22.0744	+	22.0744i	−0.870528	+	0.870528i	0.122002	+	0.992530i	$0.461069\pi$
$644$		0			0
$645$	−0.994741	−	0.994741i	−0.0391679	−	0.0391679i
$646$		0			0
$647$			28.8171i			1.13292i	0.824090	+	0.566459i	$0.191687\pi$
$647$			28.8171i			1.13292i	−0.824090	+	0.566459i	$0.808313\pi$
$648$		0			0
$649$			44.8426i			1.76023i
$650$		0			0
$651$	25.5922	+	25.5922i	1.00304	+	1.00304i
$652$		0			0
$653$	25.1198	−	25.1198i	0.983015	−	0.983015i	−0.0168430	−	0.999858i	$-0.505362\pi$
$653$	25.1198	−	25.1198i	0.983015	−	0.983015i	0.999858	+	0.0168430i	$0.00536155\pi$
$654$		0			0
$655$	9.26437			0.361989
$656$		0			0
$657$	−11.9999			−0.468161
$658$		0			0
$659$	−11.3103	+	11.3103i	−0.440585	+	0.440585i	−0.892209	−	0.451623i	$-0.850845\pi$
$659$	−11.3103	+	11.3103i	−0.440585	+	0.440585i	0.451623	+	0.892209i	$0.350845\pi$
$660$		0			0
$661$	19.4036	+	19.4036i	0.754713	+	0.754713i	0.975355	−	0.220642i	$-0.0708153\pi$
$661$	19.4036	+	19.4036i	0.754713	+	0.754713i	−0.220642	+	0.975355i	$0.570815\pi$
$662$		0			0
$663$			9.45680i			0.367272i
$664$		0			0
$665$		−	28.8568i		−	1.11902i
$666$		0			0
$667$	−7.20500	−	7.20500i	−0.278979	−	0.278979i
$668$		0			0
$669$	−9.67978	+	9.67978i	−0.374242	+	0.374242i
$670$		0			0
$671$	1.85952			0.0717858
$672$		0			0
$673$	−6.76645			−0.260827			−0.130414	−	0.991460i	$-0.541631\pi$
$673$	−6.76645			−0.260827			−0.130414	+	0.991460i	$0.541631\pi$
$674$		0			0
$675$	0.707107	−	0.707107i	0.0272166	−	0.0272166i
$676$		0			0
$677$	2.12216	+	2.12216i	0.0815613	+	0.0815613i	0.746710	−	0.665149i	$-0.231632\pi$
$677$	2.12216	+	2.12216i	0.0815613	+	0.0815613i	−0.665149	+	0.746710i	$0.731632\pi$
$678$		0			0
$679$			25.7756i			0.989177i
$680$		0			0
$681$		−	16.8985i		−	0.647551i
$682$		0			0
$683$	−16.9525	−	16.9525i	−0.648669	−	0.648669i	0.304002	−	0.952671i	$-0.401677\pi$
$683$	−16.9525	−	16.9525i	−0.648669	−	0.648669i	−0.952671	+	0.304002i	$0.901677\pi$
$684$		0			0
$685$	7.81367	−	7.81367i	0.298545	−	0.298545i
$686$		0			0
$687$	−13.3052			−0.507626
$688$		0			0
$689$	14.8532			0.565861
$690$		0			0
$691$	−18.4439	+	18.4439i	−0.701640	+	0.701640i	−0.964763	−	0.263122i	$-0.915248\pi$
$691$	−18.4439	+	18.4439i	−0.701640	+	0.701640i	0.263122	+	0.964763i	$0.415248\pi$
$692$		0			0
$693$	11.7249	+	11.7249i	0.445391	+	0.445391i
$694$		0			0
$695$			7.31391i			0.277432i
$696$		0			0
$697$		−	2.50893i		−	0.0950323i
$698$		0			0
$699$	8.35964	+	8.35964i	0.316190	+	0.316190i
$700$		0			0
$701$	−6.59102	+	6.59102i	−0.248940	+	0.248940i	−0.820535	−	0.571596i	$-0.806325\pi$
$701$	−6.59102	+	6.59102i	−0.248940	+	0.248940i	0.571596	+	0.820535i	$0.306325\pi$
$702$		0			0
$703$	−48.8856			−1.84375
$704$		0			0
$705$	2.22461			0.0837836
$706$		0			0
$707$	23.5250	−	23.5250i	0.884748	−	0.884748i
$708$		0			0
$709$	12.7715	+	12.7715i	0.479642	+	0.479642i	0.905017	−	0.425375i	$-0.139858\pi$
$709$	12.7715	+	12.7715i	0.479642	+	0.479642i	−0.425375	+	0.905017i	$0.639858\pi$
$710$		0			0
$711$		−	12.6436i		−	0.474173i
$712$		0			0
$713$		−	37.2597i		−	1.39539i
$714$		0			0
$715$	6.75015	+	6.75015i	0.252441	+	0.252441i
$716$		0			0
$717$	7.92775	−	7.92775i	0.296067	−	0.296067i
$718$		0			0
$719$	17.1105			0.638115			0.319057	−	0.947735i	$-0.396634\pi$
$719$	17.1105			0.638115			0.319057	+	0.947735i	$0.396634\pi$
$720$		0			0
$721$	−43.1215			−1.60593
$722$		0			0
$723$	5.58612	−	5.58612i	0.207750	−	0.207750i
$724$		0			0
$725$	−1.84243	−	1.84243i	−0.0684263	−	0.0684263i
$726$		0			0
$727$		−	43.9133i		−	1.62865i	−0.580407	−	0.814327i	$-0.697107\pi$
$727$		−	43.9133i		−	1.62865i	0.580407	−	0.814327i	$-0.302893\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−4.30154	−	4.30154i	−0.159098	−	0.159098i
$732$		0			0
$733$	16.5301	−	16.5301i	0.610553	−	0.610553i	−0.332537	−	0.943090i	$-0.607905\pi$
$733$	16.5301	−	16.5301i	0.610553	−	0.610553i	0.943090	+	0.332537i	$0.107905\pi$
$734$		0			0
$735$	−7.42948			−0.274040
$736$		0			0
$737$	43.0713			1.58655
$738$		0			0
$739$	17.2689	−	17.2689i	0.635246	−	0.635246i	−0.314133	−	0.949379i	$-0.601714\pi$
$739$	17.2689	−	17.2689i	0.635246	−	0.635246i	0.949379	+	0.314133i	$0.101714\pi$
$740$		0			0
$741$	11.7473	+	11.7473i	0.431548	+	0.431548i
$742$		0			0
$743$		−	20.9862i		−	0.769909i	−0.922936	−	0.384955i	$-0.874217\pi$
$743$		−	20.9862i		−	0.769909i	0.922936	−	0.384955i	$-0.125783\pi$
$744$		0			0
$745$			8.20718i			0.300688i
$746$		0			0
$747$	−11.1632	−	11.1632i	−0.408441	−	0.408441i
$748$		0			0
$749$	32.6107	−	32.6107i	1.19157	−	1.19157i
$750$		0			0
$751$	−1.64813			−0.0601413			−0.0300706	−	0.999548i	$-0.509573\pi$
$751$	−1.64813			−0.0601413			−0.0300706	+	0.999548i	$0.509573\pi$
$752$		0			0
$753$	7.55594			0.275354
$754$		0			0
$755$	9.37560	−	9.37560i	0.341213	−	0.341213i
$756$		0			0
$757$	−2.50864	−	2.50864i	−0.0911779	−	0.0911779i	0.660047	−	0.751225i	$-0.270536\pi$
$757$	−2.50864	−	2.50864i	−0.0911779	−	0.0911779i	−0.751225	+	0.660047i	$0.770536\pi$
$758$		0			0
$759$		−	17.0702i		−	0.619611i
$760$		0			0
$761$			19.9555i			0.723387i	0.932297	+	0.361693i	$0.117801\pi$
$761$			19.9555i			0.723387i	−0.932297	+	0.361693i	$0.882199\pi$
$762$		0			0
$763$	−40.5024	−	40.5024i	−1.46628	−	1.46628i
$764$		0			0
$765$	3.05773	−	3.05773i	0.110552	−	0.110552i
$766$		0			0
$767$	22.4659			0.811197
$768$		0			0
$769$	28.8082			1.03885			0.519426	−	0.854516i	$-0.326146\pi$
$769$	28.8082			1.03885			0.519426	+	0.854516i	$0.326146\pi$
$770$		0			0
$771$	10.9778	−	10.9778i	0.395356	−	0.395356i
$772$		0			0
$773$	−33.6461	−	33.6461i	−1.21017	−	1.21017i	−0.970972	−	0.239195i	$-0.923116\pi$
$773$	−33.6461	−	33.6461i	−1.21017	−	1.21017i	−0.239195	−	0.970972i	$-0.576884\pi$
$774$		0			0
$775$		−	9.52790i		−	0.342252i
$776$		0			0
$777$			24.4446i			0.876946i
$778$		0			0
$779$	−3.11660	−	3.11660i	−0.111664	−	0.111664i
$780$		0			0
$781$	−1.80583	+	1.80583i	−0.0646176	+	0.0646176i
$782$		0			0
$783$	2.60559			0.0931164
$784$		0			0
$785$	−9.66373			−0.344913
$786$		0			0
$787$	11.0029	−	11.0029i	0.392211	−	0.392211i	−0.483264	−	0.875475i	$-0.660549\pi$
$787$	11.0029	−	11.0029i	0.392211	−	0.392211i	0.875475	+	0.483264i	$0.160549\pi$
$788$		0			0
$789$	−10.1615	−	10.1615i	−0.361759	−	0.361759i
$790$		0			0
$791$			11.8195i			0.420252i
$792$		0			0
$793$		−	0.931607i		−	0.0330823i
$794$		0			0
$795$	−4.80257	−	4.80257i	−0.170330	−	0.170330i
$796$		0			0
$797$	−13.3729	+	13.3729i	−0.473692	+	0.473692i	−0.903107	−	0.429415i	$-0.858720\pi$
$797$	−13.3729	+	13.3729i	−0.473692	+	0.473692i	0.429415	+	0.903107i	$0.358720\pi$
$798$		0			0
$799$	9.61983			0.340325
$800$		0			0
$801$	12.9706			0.458293
$802$		0			0
$803$	−37.0391	+	37.0391i	−1.30708	+	1.30708i
$804$		0			0
$805$	10.5039	+	10.5039i	0.370215	+	0.370215i
$806$		0			0
$807$		−	26.9559i		−	0.948891i
$808$		0			0
$809$		−	20.9970i		−	0.738214i	−0.929387	−	0.369107i	$-0.879664\pi$
$809$		−	20.9970i		−	0.738214i	0.929387	−	0.369107i	$-0.120336\pi$
$810$		0			0
$811$	−26.7257	−	26.7257i	−0.938468	−	0.938468i	0.0597459	−	0.998214i	$-0.480971\pi$
$811$	−26.7257	−	26.7257i	−0.938468	−	0.938468i	−0.998214	+	0.0597459i	$0.980971\pi$
$812$		0			0
$813$	−3.30141	+	3.30141i	−0.115785	+	0.115785i
$814$		0			0
$815$	10.0627			0.352481
$816$		0			0
$817$	−10.6868			−0.373884
$818$		0			0
$819$	5.87409	−	5.87409i	0.205257	−	0.205257i
$820$		0			0
$821$	9.81609	+	9.81609i	0.342584	+	0.342584i	0.857338	−	0.514754i	$-0.172117\pi$
$821$	9.81609	+	9.81609i	0.342584	+	0.342584i	−0.514754	+	0.857338i	$0.672117\pi$
$822$		0			0
$823$		−	23.7241i		−	0.826969i	−0.910511	−	0.413484i	$-0.864312\pi$
$823$		−	23.7241i		−	0.826969i	0.910511	−	0.413484i	$-0.135688\pi$
$824$		0			0
$825$		−	4.36514i		−	0.151975i
$826$		0			0
$827$	−13.8903	−	13.8903i	−0.483014	−	0.483014i	0.423079	−	0.906093i	$-0.360949\pi$
$827$	−13.8903	−	13.8903i	−0.483014	−	0.483014i	−0.906093	+	0.423079i	$0.860949\pi$
$828$		0			0
$829$	−34.7927	+	34.7927i	−1.20840	+	1.20840i	−0.236856	+	0.971545i	$0.576117\pi$
$829$	−34.7927	+	34.7927i	−1.20840	+	1.20840i	−0.971545	+	0.236856i	$0.923883\pi$
$830$		0			0
$831$	8.83278			0.306406
$832$		0			0
$833$	−32.1271			−1.11314
$834$		0			0
$835$	4.34184	−	4.34184i	0.150256	−	0.150256i
$836$		0			0
$837$	6.73724	+	6.73724i	0.232873	+	0.232873i
$838$		0			0
$839$		−	41.9136i		−	1.44702i	−0.690314	−	0.723510i	$-0.742528\pi$
$839$		−	41.9136i		−	1.44702i	0.690314	−	0.723510i	$-0.257472\pi$
$840$		0			0
$841$			22.2109i			0.765892i
$842$		0			0
$843$	21.0286	+	21.0286i	0.724262	+	0.724262i
$844$		0			0
$845$	−5.81060	+	5.81060i	−0.199891	+	0.199891i
$846$		0			0
$847$	30.5956			1.05128
$848$		0			0
$849$	13.4215			0.460623
$850$		0			0
$851$	17.7945	−	17.7945i	0.609987	−	0.609987i
$852$		0			0
$853$	17.8552	+	17.8552i	0.611349	+	0.611349i	0.943297	−	0.331949i	$-0.107706\pi$
$853$	17.8552	+	17.8552i	0.611349	+	0.611349i	−0.331949	+	0.943297i	$0.607706\pi$
$854$		0			0
$855$		−	7.59666i		−	0.259800i
$856$		0			0
$857$			37.8604i			1.29328i	0.762793	+	0.646642i	$0.223827\pi$
$857$			37.8604i			1.29328i	−0.762793	+	0.646642i	$0.776173\pi$
$858$		0			0
$859$	33.0486	+	33.0486i	1.12760	+	1.12760i	0.990566	+	0.137036i	$0.0437576\pi$
$859$	33.0486	+	33.0486i	1.12760	+	1.12760i	0.137036	+	0.990566i	$0.456242\pi$
$860$		0			0
$861$	−1.55842	+	1.55842i	−0.0531108	+	0.0531108i
$862$		0			0
$863$	7.90340			0.269035			0.134518	−	0.990911i	$-0.457052\pi$
$863$	7.90340			0.269035			0.134518	+	0.990911i	$0.457052\pi$
$864$		0			0
$865$	10.3134			0.350667
$866$		0			0
$867$	1.20166	−	1.20166i	0.0408104	−	0.0408104i
$868$		0			0
$869$	−39.0260	−	39.0260i	−1.32387	−	1.32387i
$870$		0			0
$871$		−	21.5785i		−	0.731159i
$872$		0			0
$873$			6.78553i			0.229655i
$874$		0			0
$875$	2.68603	+	2.68603i	0.0908043	+	0.0908043i
$876$		0			0
$877$	23.4020	−	23.4020i	0.790229	−	0.790229i	−0.191302	−	0.981531i	$-0.561271\pi$
$877$	23.4020	−	23.4020i	0.790229	−	0.790229i	0.981531	+	0.191302i	$0.0612711\pi$
$878$		0			0
$879$	2.44371			0.0824243
$880$		0			0
$881$	4.99400			0.168252			0.0841261	−	0.996455i	$-0.473190\pi$
$881$	4.99400			0.168252			0.0841261	+	0.996455i	$0.473190\pi$
$882$		0			0
$883$	22.8573	−	22.8573i	0.769209	−	0.769209i	−0.208758	−	0.977967i	$-0.566942\pi$
$883$	22.8573	−	22.8573i	0.769209	−	0.769209i	0.977967	+	0.208758i	$0.0669423\pi$
$884$		0			0
$885$	−7.26404	−	7.26404i	−0.244178	−	0.244178i
$886$		0			0
$887$		−	20.5245i		−	0.689146i	−0.938760	−	0.344573i	$-0.888024\pi$
$887$		−	20.5245i		−	0.689146i	0.938760	−	0.344573i	$-0.111976\pi$
$888$		0			0
$889$			27.2129i			0.912691i
$890$		0			0
$891$	3.08662	+	3.08662i	0.103406	+	0.103406i
$892$		0			0
$893$	11.9498	−	11.9498i	0.399885	−	0.399885i
$894$		0			0
$895$	−8.80909			−0.294456
$896$		0			0
$897$	−8.55210			−0.285546
$898$		0			0
$899$	17.5545	−	17.5545i	0.585476	−	0.585476i
$900$		0			0
$901$	−20.7677	−	20.7677i	−0.691871	−	0.691871i
$902$		0			0
$903$			5.34380i			0.177831i
$904$		0			0
$905$			1.80032i			0.0598446i
$906$		0			0
$907$	12.1526	+	12.1526i	0.403521	+	0.403521i	0.879472	−	0.475951i	$-0.157896\pi$
$907$	12.1526	+	12.1526i	0.403521	+	0.403521i	−0.475951	+	0.879472i	$0.657896\pi$
$908$		0			0
$909$	6.19304	−	6.19304i	0.205410	−	0.205410i
$910$		0			0
$911$	26.1222			0.865468			0.432734	−	0.901522i	$-0.357549\pi$
$911$	26.1222			0.865468			0.432734	+	0.901522i	$0.357549\pi$
$912$		0			0
$913$	−68.9132			−2.28070
$914$		0			0
$915$	−0.301222	+	0.301222i	−0.00995810	+	0.00995810i
$916$		0			0
$917$	−24.8843	−	24.8843i	−0.821753	−	0.821753i
$918$		0			0
$919$		−	12.3754i		−	0.408228i	−0.978947	−	0.204114i	$-0.934569\pi$
$919$		−	12.3754i		−	0.408228i	0.978947	−	0.204114i	$-0.0654313\pi$
$920$		0			0
$921$			24.8725i			0.819577i
$922$		0			0
$923$	0.904709	+	0.904709i	0.0297789	+	0.0297789i
$924$		0			0
$925$	4.55033	−	4.55033i	0.149614	−	0.149614i
$926$		0			0
$927$	−11.3519			−0.372846
$928$		0			0
$929$	−14.1300			−0.463591			−0.231795	−	0.972765i	$-0.574460\pi$
$929$	−14.1300			−0.463591			−0.231795	+	0.972765i	$0.574460\pi$
$930$		0			0
$931$	−39.9085	+	39.9085i	−1.30795	+	1.30795i
$932$		0			0
$933$	1.21487	+	1.21487i	0.0397732	+	0.0397732i
$934$		0			0
$935$		−	18.8761i		−	0.617314i
$936$		0			0
$937$		−	39.1538i		−	1.27910i	−0.768750	−	0.639549i	$-0.779121\pi$
$937$		−	39.1538i		−	1.27910i	0.768750	−	0.639549i	$-0.220879\pi$
$938$		0			0
$939$	−11.6263	−	11.6263i	−0.379411	−	0.379411i
$940$		0			0
$941$	17.1373	−	17.1373i	0.558661	−	0.558661i	−0.370265	−	0.928926i	$-0.620733\pi$
$941$	17.1373	−	17.1373i	0.558661	−	0.558661i	0.928926	+	0.370265i	$0.120733\pi$
$942$		0			0
$943$	2.26890			0.0738856
$944$		0			0
$945$	−3.79862			−0.123569
$946$		0			0
$947$	−21.7252	+	21.7252i	−0.705973	+	0.705973i	−0.965686	−	0.259713i	$-0.916372\pi$
$947$	−21.7252	+	21.7252i	−0.705973	+	0.705973i	0.259713	+	0.965686i	$0.416372\pi$
$948$		0			0
$949$	18.5564	+	18.5564i	0.602365	+	0.602365i
$950$		0			0
$951$		−	11.2581i		−	0.365067i
$952$		0			0
$953$			6.05956i			0.196288i	0.995172	+	0.0981442i	$0.0312906\pi$
$953$			6.05956i			0.196288i	−0.995172	+	0.0981442i	$0.968709\pi$
$954$		0			0
$955$	6.81395	+	6.81395i	0.220494	+	0.220494i
$956$		0			0
$957$	8.04247	−	8.04247i	0.259976	−	0.259976i
$958$		0			0
$959$	−41.9754			−1.35546
$960$		0			0
$961$	59.7808			1.92841
$962$		0			0
$963$	8.58488	−	8.58488i	0.276644	−	0.276644i
$964$		0			0
$965$	−2.57761	−	2.57761i	−0.0829763	−	0.0829763i
$966$		0			0
$967$		−	32.6389i		−	1.04959i	−0.851227	−	0.524797i	$-0.824141\pi$
$967$		−	32.6389i		−	1.04959i	0.851227	−	0.524797i	$-0.175859\pi$
$968$		0			0
$969$		−	32.8501i		−	1.05530i
$970$		0			0
$971$	4.73662	+	4.73662i	0.152005	+	0.152005i	0.779013	−	0.627008i	$-0.215721\pi$
$971$	4.73662	+	4.73662i	0.152005	+	0.152005i	−0.627008	+	0.779013i	$0.715721\pi$
$972$		0			0
$973$	19.6453	−	19.6453i	0.629801	−	0.629801i
$974$		0			0
$975$	−2.18691			−0.0700371
$976$		0			0
$977$	−31.9605			−1.02251			−0.511254	−	0.859430i	$-0.670819\pi$
$977$	−31.9605			−1.02251			−0.511254	+	0.859430i	$0.670819\pi$
$978$		0			0
$979$	40.0353	−	40.0353i	1.27953	−	1.27953i
$980$		0			0
$981$	−10.6624	−	10.6624i	−0.340424	−	0.340424i
$982$		0			0
$983$			36.1044i			1.15155i	0.817607	+	0.575776i	$0.195300\pi$
$983$			36.1044i			1.15155i	−0.817607	+	0.575776i	$0.804700\pi$
$984$		0			0
$985$			10.6833i			0.340398i
$986$		0			0
$987$	−5.97536	−	5.97536i	−0.190198	−	0.190198i
$988$		0			0
$989$	3.89002	−	3.89002i	0.123695	−	0.123695i
$990$		0			0
$991$	19.3054			0.613255			0.306628	−	0.951830i	$-0.400799\pi$
$991$	19.3054			0.613255			0.306628	+	0.951830i	$0.400799\pi$
$992$		0			0
$993$	−12.7638			−0.405046
$994$		0			0
$995$	−16.7897	+	16.7897i	−0.532269	+	0.532269i
$996$		0			0
$997$	6.99944	+	6.99944i	0.221674	+	0.221674i	0.809203	−	0.587529i	$-0.199899\pi$
$997$	6.99944	+	6.99944i	0.221674	+	0.221674i	−0.587529	+	0.809203i	$0.699899\pi$
$998$		0			0
$999$			6.43514i			0.203599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.s.e.481.6		20
4.3	odd	2		1920.2.s.f.481.5		20
8.3	odd	2		960.2.s.c.241.10		20
8.5	even	2		240.2.s.c.181.9	yes	20
16.3	odd	4		1920.2.s.f.1441.1		20
16.5	even	4		240.2.s.c.61.9	✓	20
16.11	odd	4		960.2.s.c.721.6		20
16.13	even	4	inner	1920.2.s.e.1441.10		20
24.5	odd	2		720.2.t.d.181.2		20
24.11	even	2		2880.2.t.d.2161.10		20
48.5	odd	4		720.2.t.d.541.2		20
48.11	even	4		2880.2.t.d.721.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.9	✓	20	16.5	even	4
240.2.s.c.181.9	yes	20	8.5	even	2
720.2.t.d.181.2		20	24.5	odd	2
720.2.t.d.541.2		20	48.5	odd	4
960.2.s.c.241.10		20	8.3	odd	2
960.2.s.c.721.6		20	16.11	odd	4
1920.2.s.e.481.6		20	1.1	even	1	trivial
1920.2.s.e.1441.10		20	16.13	even	4	inner
1920.2.s.f.481.5		20	4.3	odd	2
1920.2.s.f.1441.1		20	16.3	odd	4
2880.2.t.d.721.6		20	48.11	even	4
2880.2.t.d.2161.10		20	24.11	even	2

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -3.79862i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -3.79862i q^{7} -1.00000i q^{9} +(-3.08662 - 3.08662i) q^{11} +(-1.54638 + 1.54638i) q^{13} +1.00000 q^{15} +4.32428 q^{17} +(5.37165 - 5.37165i) q^{19} +(-2.68603 - 2.68603i) q^{21} +3.91059i q^{23} +1.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-1.84243 + 1.84243i) q^{29} -9.52790 q^{31} -4.36514 q^{33} +(2.68603 - 2.68603i) q^{35} +(-4.55033 - 4.55033i) q^{37} +2.18691i q^{39} -0.580195i q^{41} +(-0.994741 - 0.994741i) q^{43} +(0.707107 - 0.707107i) q^{45} +2.22461 q^{47} -7.42948 q^{49} +(3.05773 - 3.05773i) q^{51} +(-4.80257 - 4.80257i) q^{53} -4.36514i q^{55} -7.59666i q^{57} +(-7.26404 - 7.26404i) q^{59} +(-0.301222 + 0.301222i) q^{61} -3.79862 q^{63} -2.18691 q^{65} +(-6.97711 + 6.97711i) q^{67} +(2.76520 + 2.76520i) q^{69} -0.585051i q^{71} -11.9999i q^{73} +(0.707107 + 0.707107i) q^{75} +(-11.7249 + 11.7249i) q^{77} +12.6436 q^{79} -1.00000 q^{81} +(11.1632 - 11.1632i) q^{83} +(3.05773 + 3.05773i) q^{85} +2.60559i q^{87} +12.9706i q^{89} +(5.87409 + 5.87409i) q^{91} +(-6.73724 + 6.73724i) q^{93} +7.59666 q^{95} -6.78553 q^{97} +(-3.08662 + 3.08662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 8 q^{11} + 20 q^{15} - 24 q^{17} + 4 q^{19} - 16 q^{29} + 16 q^{33} - 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} + 16 q^{53} + 16 q^{59} + 4 q^{61} - 8 q^{63} + 8 q^{67} + 4 q^{69} + 40 q^{77} + 56 q^{79} - 20 q^{81} + 48 q^{83} - 4 q^{85} + 8 q^{91} - 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 8 * q^11 + 20 * q^15 - 24 * q^17 + 4 * q^19 - 16 * q^29 + 16 * q^33 - 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 + 16 * q^53 + 16 * q^59 + 4 * q^61 - 8 * q^63 + 8 * q^67 + 4 * q^69 + 40 * q^77 + 56 * q^79 - 20 * q^81 + 48 * q^83 - 4 * q^85 + 8 * q^91 - 16 * q^93 + 56 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more