LMFDB - Embedded newform 405.2.f.a.242.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(242,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("405.242");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			242.8
Root			$0.601150 + 2.24352i$ of defining polynomial
Character	$\chi$	$=$	405.242
Dual form			405.2.f.a.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64237 - 1.64237i) q^{2} -3.39477i q^{4} +(-0.394116 - 2.20106i) q^{5} +(-0.550102 - 0.550102i) q^{7} +(-2.29074 - 2.29074i) q^{8} +(-4.26225 - 2.96768i) q^{10} -0.254252i q^{11} +(-2.71215 + 2.71215i) q^{13} -1.80695 q^{14} -0.734947 q^{16} +(3.93311 - 3.93311i) q^{17} +0.440377i q^{19} +(-7.47211 + 1.33793i) q^{20} +(-0.417576 - 0.417576i) q^{22} +(2.50550 + 2.50550i) q^{23} +(-4.68935 + 1.73495i) q^{25} +8.90871i q^{26} +(-1.86747 + 1.86747i) q^{28} +5.52530 q^{29} +0.194366 q^{31} +(3.37442 - 3.37442i) q^{32} -12.9193i q^{34} +(-0.994005 + 1.42761i) q^{35} +(-0.123005 - 0.123005i) q^{37} +(0.723262 + 0.723262i) q^{38} +(-4.13924 + 5.94488i) q^{40} +4.48282i q^{41} +(-0.977199 + 0.977199i) q^{43} -0.863127 q^{44} +8.22993 q^{46} +(-3.05520 + 3.05520i) q^{47} -6.39477i q^{49} +(-4.85222 + 10.5511i) q^{50} +(9.20713 + 9.20713i) q^{52} +(0.938022 + 0.938022i) q^{53} +(-0.559623 + 0.100205i) q^{55} +2.52028i q^{56} +(9.07460 - 9.07460i) q^{58} +8.04558 q^{59} +2.88371 q^{61} +(0.319221 - 0.319221i) q^{62} -12.5540i q^{64} +(7.03850 + 4.90070i) q^{65} +(9.49217 + 9.49217i) q^{67} +(-13.3520 - 13.3520i) q^{68} +(0.712146 + 3.97720i) q^{70} -2.15986i q^{71} +(-9.18432 + 9.18432i) q^{73} -0.404041 q^{74} +1.49498 q^{76} +(-0.139864 + 0.139864i) q^{77} +13.8251i q^{79} +(0.289654 + 1.61766i) q^{80} +(7.36245 + 7.36245i) q^{82} +(-3.80803 - 3.80803i) q^{83} +(-10.2071 - 7.10692i) q^{85} +3.20985i q^{86} +(-0.582424 + 0.582424i) q^{88} +0.285526 q^{89} +2.98392 q^{91} +(8.50561 - 8.50561i) q^{92} +10.0356i q^{94} +(0.969296 - 0.173559i) q^{95} +(-6.39477 - 6.39477i) q^{97} +(-10.5026 - 10.5026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70}+ \cdots - 56 q^{97}+O(q^{100}) $ 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.64237	−	1.64237i	1.16133	−	1.16133i	0.177149	−	0.984184i	$-0.443313\pi$
$2$	1.64237	−	1.64237i	1.16133	−	1.16133i	0.984184	−	0.177149i	$-0.0566873\pi$
$3$		0			0
$3$		0			0
$4$		−	3.39477i		−	1.69739i
$5$	−0.394116	−	2.20106i	−0.176254	−	0.984345i
$5$	−0.394116	−	2.20106i	−0.176254	−	0.984345i
$6$		0			0
$7$	−0.550102	−	0.550102i	−0.207919	−	0.207919i	0.595463	−	0.803382i	$-0.296968\pi$
$7$	−0.550102	−	0.550102i	−0.207919	−	0.207919i	−0.803382	+	0.595463i	$0.796968\pi$
$8$	−2.29074	−	2.29074i	−0.809899	−	0.809899i
$9$		0			0
$10$	−4.26225	−	2.96768i	−1.34784	−	0.938462i
$11$		−	0.254252i		−	0.0766597i	−0.999265	−	0.0383299i	$-0.987796\pi$
$11$		−	0.254252i		−	0.0766597i	0.999265	−	0.0383299i	$-0.0122038\pi$
$12$		0			0
$13$	−2.71215	+	2.71215i	−0.752214	+	0.752214i	−0.974892	−	0.222678i	$-0.928520\pi$
$13$	−2.71215	+	2.71215i	−0.752214	+	0.752214i	0.222678	+	0.974892i	$0.428520\pi$
$14$	−1.80695			−0.482927
$15$		0			0
$16$	−0.734947			−0.183737
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	−0.0450642	−	0.998984i	$-0.514349\pi$
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	0.998984	+	0.0450642i	$0.0143492\pi$
$18$		0			0
$19$			0.440377i			0.101029i	0.998723	+	0.0505147i	$0.0160862\pi$
$19$			0.440377i			0.101029i	−0.998723	+	0.0505147i	$0.983914\pi$
$20$	−7.47211	+	1.33793i	−1.67081	+	0.299171i
$21$		0			0
$22$	−0.417576	−	0.417576i	−0.0890275	−	0.0890275i
$23$	2.50550	+	2.50550i	0.522433	+	0.522433i	0.918305	−	0.395873i	$-0.129558\pi$
$23$	2.50550	+	2.50550i	0.522433	+	0.522433i	−0.395873	+	0.918305i	$0.629558\pi$
$24$		0			0
$25$	−4.68935	+	1.73495i	−0.937869	+	0.346989i
$26$			8.90871i			1.74714i
$27$		0			0
$28$	−1.86747	+	1.86747i	−0.352919	+	0.352919i
$29$	5.52530			1.02602			0.513011	−	0.858382i	$-0.328530\pi$
$29$	5.52530			1.02602			0.513011	+	0.858382i	$0.328530\pi$
$30$		0			0
$31$	0.194366			0.0349091			0.0174546	−	0.999848i	$-0.494444\pi$
$31$	0.194366			0.0349091			0.0174546	+	0.999848i	$0.494444\pi$
$32$	3.37442	−	3.37442i	0.596519	−	0.596519i
$33$		0			0
$34$		−	12.9193i		−	2.21564i
$35$	−0.994005	+	1.42761i	−0.168018	+	0.241311i
$36$		0			0
$37$	−0.123005	−	0.123005i	−0.0202220	−	0.0202220i	0.696924	−	0.717145i	$-0.254552\pi$
$37$	−0.123005	−	0.123005i	−0.0202220	−	0.0202220i	−0.717145	+	0.696924i	$0.754552\pi$
$38$	0.723262	+	0.723262i	0.117329	+	0.117329i
$39$		0			0
$40$	−4.13924	+	5.94488i	−0.654472	+	0.939968i
$41$			4.48282i			0.700098i	0.936731	+	0.350049i	$0.113835\pi$
$41$			4.48282i			0.700098i	−0.936731	+	0.350049i	$0.886165\pi$
$42$		0			0
$43$	−0.977199	+	0.977199i	−0.149021	+	0.149021i	−0.777681	−	0.628659i	$-0.783604\pi$
$43$	−0.977199	+	0.977199i	−0.149021	+	0.149021i	0.628659	+	0.777681i	$0.283604\pi$
$44$	−0.863127			−0.130121
$45$		0			0
$46$	8.22993			1.21344
$47$	−3.05520	+	3.05520i	−0.445647	+	0.445647i	−0.893905	−	0.448257i	$-0.852045\pi$
$47$	−3.05520	+	3.05520i	−0.445647	+	0.445647i	0.448257	+	0.893905i	$0.352045\pi$
$48$		0			0
$49$		−	6.39477i		−	0.913539i
$50$	−4.85222	+	10.5511i	−0.686208	+	1.49215i
$51$		0			0
$52$	9.20713	+	9.20713i	1.27680	+	1.27680i
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	0.768589	−	0.639742i	$-0.220959\pi$
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	−0.639742	+	0.768589i	$0.720959\pi$
$54$		0			0
$55$	−0.559623	+	0.100205i	−0.0754596	+	0.0135116i
$56$			2.52028i			0.336787i
$57$		0			0
$58$	9.07460	−	9.07460i	1.19155	−	1.19155i
$59$	8.04558			1.04745			0.523723	−	0.851889i	$-0.324543\pi$
$59$	8.04558			1.04745			0.523723	+	0.851889i	$0.324543\pi$
$60$		0			0
$61$	2.88371			0.369221			0.184611	−	0.982812i	$-0.440898\pi$
$61$	2.88371			0.369221			0.184611	+	0.982812i	$0.440898\pi$
$62$	0.319221	−	0.319221i	0.0405411	−	0.0405411i
$63$		0			0
$64$		−	12.5540i		−	1.56925i
$65$	7.03850	+	4.90070i	0.873019	+	0.607857i
$66$		0			0
$67$	9.49217	+	9.49217i	1.15965	+	1.15965i	0.984550	+	0.175104i	$0.0560261\pi$
$67$	9.49217	+	9.49217i	1.15965	+	1.15965i	0.175104	+	0.984550i	$0.443974\pi$
$68$	−13.3520	−	13.3520i	−1.61917	−	1.61917i
$69$		0			0
$70$	0.712146	+	3.97720i	0.0851177	+	0.475366i
$71$		−	2.15986i		−	0.256328i	−0.991753	−	0.128164i	$-0.959092\pi$
$71$		−	2.15986i		−	0.256328i	0.991753	−	0.128164i	$-0.0409085\pi$
$72$		0			0
$73$	−9.18432	+	9.18432i	−1.07494	+	1.07494i	−0.0779897	+	0.996954i	$0.524850\pi$
$73$	−9.18432	+	9.18432i	−1.07494	+	1.07494i	−0.996954	+	0.0779897i	$0.975150\pi$
$74$	−0.404041			−0.0469689
$75$		0			0
$76$	1.49498			0.171486
$77$	−0.139864	+	0.139864i	−0.0159390	+	0.0159390i
$78$		0			0
$79$			13.8251i			1.55545i	0.628607	+	0.777723i	$0.283625\pi$
$79$			13.8251i			1.55545i	−0.628607	+	0.777723i	$0.716375\pi$
$80$	0.289654	+	1.61766i	0.0323843	+	0.180860i
$81$		0			0
$82$	7.36245	+	7.36245i	0.813047	+	0.813047i
$83$	−3.80803	−	3.80803i	−0.417986	−	0.417986i	0.466523	−	0.884509i	$-0.345506\pi$
$83$	−3.80803	−	3.80803i	−0.417986	−	0.417986i	−0.884509	+	0.466523i	$0.845506\pi$
$84$		0			0
$85$	−10.2071	−	7.10692i	−1.10712	−	0.770854i
$86$			3.20985i			0.346127i
$87$		0			0
$88$	−0.582424	+	0.582424i	−0.0620866	+	0.0620866i
$89$	0.285526			0.0302657			0.0151328	−	0.999885i	$-0.495183\pi$
$89$	0.285526			0.0302657			0.0151328	+	0.999885i	$0.495183\pi$
$90$		0			0
$91$	2.98392			0.312799
$92$	8.50561	−	8.50561i	0.886771	−	0.886771i
$93$		0			0
$94$			10.0356i			1.03509i
$95$	0.969296	−	0.173559i	0.0994477	−	0.0178068i
$96$		0			0
$97$	−6.39477	−	6.39477i	−0.649291	−	0.649291i	0.303531	−	0.952822i	$-0.401835\pi$
$97$	−6.39477	−	6.39477i	−0.649291	−	0.649291i	−0.952822	+	0.303531i	$0.901835\pi$
$98$	−10.5026	−	10.5026i	−1.06092	−	1.06092i
$99$		0			0
$100$	5.88975	+	15.9193i	0.588975	+	1.59193i
$101$		−	13.1570i		−	1.30917i	−0.755990	−	0.654583i	$-0.772844\pi$
$101$		−	13.1570i		−	1.30917i	0.755990	−	0.654583i	$-0.227156\pi$
$102$		0			0
$103$	−11.5724	+	11.5724i	−1.14026	+	1.14026i	−0.151859	+	0.988402i	$0.548526\pi$
$103$	−11.5724	+	11.5724i	−1.14026	+	1.14026i	−0.988402	+	0.151859i	$0.951474\pi$
$104$	12.4256			1.21843
$105$		0			0
$106$	3.08116			0.299269
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$108$		0			0
$109$			8.81907i			0.844713i	0.906430	+	0.422357i	$0.138797\pi$
$109$			8.81907i			0.844713i	−0.906430	+	0.422357i	$0.861203\pi$
$110$	−0.754537	+	1.08368i	−0.0719423	+	0.103325i
$111$		0			0
$112$	0.404296	+	0.404296i	0.0382024	+	0.0382024i
$113$	−9.52338	−	9.52338i	−0.895884	−	0.895884i	0.0991847	−	0.995069i	$-0.468377\pi$
$113$	−9.52338	−	9.52338i	−0.895884	−	0.895884i	−0.995069	+	0.0991847i	$0.968377\pi$
$114$		0			0
$115$	4.52730	−	6.50222i	0.422173	−	0.606335i
$116$		−	18.7571i		−	1.74156i
$117$		0			0
$118$	13.2138	−	13.2138i	1.21643	−	1.21643i
$119$	−4.32723			−0.396676
$120$		0			0
$121$	10.9354			0.994123
$122$	4.73613	−	4.73613i	0.428789	−	0.428789i
$123$		0			0
$124$		−	0.659828i		−	0.0592543i
$125$	5.66687	+	9.63777i	0.506860	+	0.862028i
$126$		0			0
$127$	−6.72167	−	6.72167i	−0.596452	−	0.596452i	0.342915	−	0.939366i	$-0.388586\pi$
$127$	−6.72167	−	6.72167i	−0.596452	−	0.596452i	−0.939366	+	0.342915i	$0.888586\pi$
$128$	−13.8695	−	13.8695i	−1.22590	−	1.22590i
$129$		0			0
$130$	19.6086	−	3.51106i	1.71979	−	0.307941i
$131$		−	13.4502i		−	1.17515i	−0.809171	−	0.587573i	$-0.800084\pi$
$131$		−	13.4502i		−	1.17515i	0.809171	−	0.587573i	$-0.199916\pi$
$132$		0			0
$133$	0.242252	−	0.242252i	0.0210059	−	0.0210059i
$134$	31.1794			2.69349
$135$		0			0
$136$	−18.0195			−1.54516
$137$	−6.92241	+	6.92241i	−0.591421	+	0.591421i	−0.938015	−	0.346594i	$-0.887338\pi$
$137$	−6.92241	+	6.92241i	−0.591421	+	0.591421i	0.346594	+	0.938015i	$0.387338\pi$
$138$		0			0
$139$			7.90880i			0.670815i	0.942073	+	0.335408i	$0.108874\pi$
$139$			7.90880i			0.670815i	−0.942073	+	0.335408i	$0.891126\pi$
$140$	4.84643	+	3.37442i	0.409598	+	0.285191i
$141$		0			0
$142$	−3.54730	−	3.54730i	−0.297683	−	0.297683i
$143$	0.689567	+	0.689567i	0.0576645	+	0.0576645i
$144$		0			0
$145$	−2.17761	−	12.1615i	−0.180841	−	1.00996i
$146$			30.1682i			2.49674i
$147$		0			0
$148$	−0.417576	+	0.417576i	−0.0343245	+	0.0343245i
$149$	−9.13510			−0.748377			−0.374188	−	0.927353i	$-0.622079\pi$
$149$	−9.13510			−0.748377			−0.374188	+	0.927353i	$0.622079\pi$
$150$		0			0
$151$	14.6998			1.19625			0.598127	−	0.801401i	$-0.295912\pi$
$151$	14.6998			1.19625			0.598127	+	0.801401i	$0.295912\pi$
$152$	1.00879	−	1.00879i	0.0818235	−	0.0818235i
$153$		0			0
$154$			0.459419i			0.0370210i
$155$	−0.0766026	−	0.427811i	−0.00615287	−	0.0343626i
$156$		0			0
$157$	−11.9739	−	11.9739i	−0.955619	−	0.955619i	0.0434369	−	0.999056i	$-0.486169\pi$
$157$	−11.9739	−	11.9739i	−0.955619	−	0.955619i	−0.999056	+	0.0434369i	$0.986169\pi$
$158$	22.7060	+	22.7060i	1.80639	+	1.80639i
$159$		0			0
$160$	−8.75723	−	6.09740i	−0.692320	−	0.482042i
$161$		−	2.75656i		−	0.217248i
$162$		0			0
$163$	9.74771	−	9.74771i	0.763499	−	0.763499i	−0.213454	−	0.976953i	$-0.568471\pi$
$163$	9.74771	−	9.74771i	0.763499	−	0.763499i	0.976953	+	0.213454i	$0.0684713\pi$
$164$	15.2181			1.18834
$165$		0			0
$166$	−12.5084			−0.970841
$167$	−13.9502	+	13.9502i	−1.07950	+	1.07950i	−0.0829458	+	0.996554i	$0.526433\pi$
$167$	−13.9502	+	13.9502i	−1.07950	+	1.07950i	−0.996554	+	0.0829458i	$0.973567\pi$
$168$		0			0
$169$		−	1.71147i		−	0.131652i
$170$	−28.4361	+	5.09169i	−2.18095	+	0.390515i
$171$		0			0
$172$	3.31737	+	3.31737i	0.252947	+	0.252947i
$173$	−7.33975	−	7.33975i	−0.558031	−	0.558031i	0.370716	−	0.928746i	$-0.379112\pi$
$173$	−7.33975	−	7.33975i	−0.558031	−	0.558031i	−0.928746	+	0.370716i	$0.879112\pi$
$174$		0			0
$175$	3.53402	+	1.62522i	0.267147	+	0.122855i
$176$			0.186861i			0.0140852i
$177$		0			0
$178$	0.468940	−	0.468940i	0.0351485	−	0.0351485i
$179$	−15.1015			−1.12874			−0.564370	−	0.825522i	$-0.690881\pi$
$179$	−15.1015			−1.12874			−0.564370	+	0.825522i	$0.690881\pi$
$180$		0			0
$181$	−7.82954			−0.581965			−0.290983	−	0.956728i	$-0.593982\pi$
$181$	−7.82954			−0.581965			−0.290983	+	0.956728i	$0.593982\pi$
$182$	4.90070	−	4.90070i	0.363264	−	0.363264i
$183$		0			0
$184$		−	11.4789i		−	0.846235i
$185$	−0.222264	+	0.319221i	−0.0163412	+	0.0234696i
$186$		0			0
$187$	−1.00000	−	1.00000i	−0.0731272	−	0.0731272i
$188$	10.3717	+	10.3717i	0.756436	+	0.756436i
$189$		0			0
$190$	1.30690	−	1.87699i	0.0948122	−	0.136171i
$191$			11.4726i			0.830129i	0.909792	+	0.415065i	$0.136241\pi$
$191$			11.4726i			0.830129i	−0.909792	+	0.415065i	$0.863759\pi$
$192$		0			0
$193$	3.90208	−	3.90208i	0.280878	−	0.280878i	−0.552581	−	0.833459i	$-0.686357\pi$
$193$	3.90208	−	3.90208i	0.280878	−	0.280878i	0.833459	+	0.552581i	$0.186357\pi$
$194$	−21.0052			−1.50809
$195$		0			0
$196$	−21.7088			−1.55063
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	−0.785000	−	0.619496i	$-0.787337\pi$
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	0.619496	+	0.785000i	$0.287337\pi$
$198$		0			0
$199$			17.1978i			1.21912i	0.792741	+	0.609558i	$0.208653\pi$
$199$			17.1978i			1.21912i	−0.792741	+	0.609558i	$0.791347\pi$
$200$	14.7164	+	6.76776i	1.04061	+	0.478553i
$201$		0			0
$202$	−21.6086	−	21.6086i	−1.52038	−	1.52038i
$203$	−3.03948	−	3.03948i	−0.213330	−	0.213330i
$204$		0			0
$205$	9.86695	−	1.76675i	0.689138	−	0.123395i
$206$			38.0123i			2.64844i
$207$		0			0
$208$	1.99328	−	1.99328i	0.138209	−	0.138209i
$209$	0.111966			0.00774488
$210$		0			0
$211$	4.54958			0.313206			0.156603	−	0.987662i	$-0.449946\pi$
$211$	4.54958			0.313206			0.156603	+	0.987662i	$0.449946\pi$
$212$	3.18437	−	3.18437i	0.218704	−	0.218704i
$213$		0			0
$214$			19.0976i			1.30548i
$215$	2.53601	+	1.76575i	0.172954	+	0.120423i
$216$		0			0
$217$	−0.106921	−	0.106921i	−0.00725827	−	0.00725827i
$218$	14.4842	+	14.4842i	0.980993	+	0.980993i
$219$		0			0
$220$	0.340172	+	1.89980i	0.0229344	+	0.128084i
$221$			21.3344i			1.43510i
$222$		0			0
$223$	−12.9516	+	12.9516i	−0.867303	+	0.867303i	−0.992173	−	0.124870i	$-0.960149\pi$
$223$	−12.9516	+	12.9516i	−0.867303	+	0.867303i	0.124870	+	0.992173i	$0.460149\pi$
$224$	−3.71256			−0.248056
$225$		0			0
$226$	−31.2819			−2.08084
$227$	7.97652	−	7.97652i	0.529420	−	0.529420i	−0.390979	−	0.920400i	$-0.627864\pi$
$227$	7.97652	−	7.97652i	0.529420	−	0.529420i	0.920400	+	0.390979i	$0.127864\pi$
$228$		0			0
$229$			4.87767i			0.322325i	0.986928	+	0.161163i	$0.0515244\pi$
$229$			4.87767i			0.322325i	−0.986928	+	0.161163i	$0.948476\pi$
$230$	−3.24355	−	18.1146i	−0.213873	−	1.19444i
$231$		0			0
$232$	−12.6570	−	12.6570i	−0.830974	−	0.830974i
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	0.398943	−	0.916976i	$-0.369377\pi$
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	−0.916976	+	0.398943i	$0.869377\pi$
$234$		0			0
$235$	7.92879	+	5.52058i	0.517217	+	0.360123i
$236$		−	27.3129i		−	1.77792i
$237$		0			0
$238$	−7.10692	+	7.10692i	−0.460673	+	0.460673i
$239$	22.2724			1.44068			0.720340	−	0.693621i	$-0.243986\pi$
$239$	22.2724			1.44068			0.720340	+	0.693621i	$0.243986\pi$
$240$		0			0
$241$	−28.9492			−1.86478			−0.932392	−	0.361449i	$-0.882282\pi$
$241$	−28.9492			−1.86478			−0.932392	+	0.361449i	$0.882282\pi$
$242$	17.9599	−	17.9599i	1.15451	−	1.15451i
$243$		0			0
$244$		−	9.78955i		−	0.626712i
$245$	−14.0753	+	2.52028i	−0.899238	+	0.161015i
$246$		0			0
$247$	−1.19437	−	1.19437i	−0.0759957	−	0.0759957i
$248$	−0.445241	−	0.445241i	−0.0282729	−	0.0282729i
$249$		0			0
$250$	25.1359	+	6.52169i	1.58974	+	0.412468i
$251$		−	20.4218i		−	1.28901i	−0.764599	−	0.644507i	$-0.777063\pi$
$251$		−	20.4218i		−	1.28901i	0.764599	−	0.644507i	$-0.222937\pi$
$252$		0			0
$253$	0.637027	−	0.637027i	0.0400496	−	0.0400496i
$254$	−22.0790			−1.38536
$255$		0			0
$256$	−20.4498			−1.27811
$257$	5.19206	−	5.19206i	0.323872	−	0.323872i	−0.526378	−	0.850250i	$-0.676450\pi$
$257$	5.19206	−	5.19206i	0.323872	−	0.323872i	0.850250	+	0.526378i	$0.176450\pi$
$258$		0			0
$259$			0.135331i			0.00840907i
$260$	16.6368	−	23.8941i	1.03177	−	1.48185i
$261$		0			0
$262$	−22.0902	−	22.0902i	−1.36473	−	1.36473i
$263$	10.3290	+	10.3290i	0.636916	+	0.636916i	0.949794	−	0.312877i	$-0.101293\pi$
$263$	10.3290	+	10.3290i	0.636916	+	0.636916i	−0.312877	+	0.949794i	$0.601293\pi$
$264$		0			0
$265$	1.69495	−	2.43433i	0.104120	−	0.149540i
$266$		−	0.795737i		−	0.0487897i
$267$		0			0
$268$	32.2238	−	32.2238i	1.96838	−	1.96838i
$269$	−3.76010			−0.229257			−0.114629	−	0.993408i	$-0.536568\pi$
$269$	−3.76010			−0.229257			−0.114629	+	0.993408i	$0.536568\pi$
$270$		0			0
$271$	14.0785			0.855209			0.427604	−	0.903966i	$-0.359358\pi$
$271$	14.0785			0.855209			0.427604	+	0.903966i	$0.359358\pi$
$272$	−2.89063	+	2.89063i	−0.175270	+	0.175270i
$273$		0			0
$274$			22.7383i			1.37367i
$275$	0.441113	+	1.19227i	0.0266001	+	0.0718968i
$276$		0			0
$277$	1.47926	+	1.47926i	0.0888802	+	0.0888802i	0.750149	−	0.661269i	$-0.229982\pi$
$277$	1.47926	+	1.47926i	0.0888802	+	0.0888802i	−0.661269	+	0.750149i	$0.729982\pi$
$278$	12.9892	+	12.9892i	0.779040	+	0.779040i
$279$		0			0
$280$	5.54730	−	0.993284i	0.331514	−	0.0593600i
$281$			9.26846i			0.552910i	0.961027	+	0.276455i	$0.0891596\pi$
$281$			9.26846i			0.552910i	−0.961027	+	0.276455i	$0.910840\pi$
$282$		0			0
$283$	22.7744	−	22.7744i	1.35380	−	1.35380i	0.472431	−	0.881368i	$-0.343377\pi$
$283$	22.7744	−	22.7744i	1.35380	−	1.35380i	0.881368	−	0.472431i	$-0.156623\pi$
$284$	−7.33224			−0.435089
$285$		0			0
$286$	2.26505			0.133935
$287$	2.46601	−	2.46601i	0.145564	−	0.145564i
$288$		0			0
$289$		−	13.9387i		−	0.819926i
$290$	−23.5502	−	16.3973i	−1.38292	−	0.962883i
$291$		0			0
$292$	31.1787	+	31.1787i	1.82460	+	1.82460i
$293$	−4.67039	−	4.67039i	−0.272847	−	0.272847i	0.557398	−	0.830245i	$-0.311800\pi$
$293$	−4.67039	−	4.67039i	−0.272847	−	0.272847i	−0.830245	+	0.557398i	$0.811800\pi$
$294$		0			0
$295$	−3.17089	−	17.7088i	−0.184616	−	1.03105i
$296$			0.563547i			0.0327555i
$297$		0			0
$298$	−15.0032	+	15.0032i	−0.869114	+	0.869114i
$299$	−13.5906			−0.785962
$300$		0			0
$301$	1.07512			0.0619688
$302$	24.1426	−	24.1426i	1.38925	−	1.38925i
$303$		0			0
$304$		−	0.323653i		−	0.0185628i
$305$	−1.13652	−	6.34723i	−0.0650767	−	0.363441i
$306$		0			0
$307$	5.82120	+	5.82120i	0.332233	+	0.332233i	0.853434	−	0.521201i	$-0.174516\pi$
$307$	5.82120	+	5.82120i	0.332233	+	0.332233i	−0.521201	+	0.853434i	$0.674516\pi$
$308$	0.474808	+	0.474808i	0.0270547	+	0.0270547i
$309$		0			0
$310$	−0.828435	−	0.576815i	−0.0470520	−	0.0327609i
$311$		−	11.5317i		−	0.653905i	−0.945041	−	0.326953i	$-0.893978\pi$
$311$		−	11.5317i		−	0.653905i	0.945041	−	0.326953i	$-0.106022\pi$
$312$		0			0
$313$	4.70919	−	4.70919i	0.266179	−	0.266179i	−0.561379	−	0.827559i	$-0.689729\pi$
$313$	4.70919	−	4.70919i	0.266179	−	0.266179i	0.827559	+	0.561379i	$0.189729\pi$
$314$	−39.3311			−2.21958
$315$		0			0
$316$	46.9331			2.64020
$317$	−1.41863	+	1.41863i	−0.0796780	+	0.0796780i	−0.745823	−	0.666145i	$-0.767943\pi$
$317$	−1.41863	+	1.41863i	−0.0796780	+	0.0796780i	0.666145	+	0.745823i	$0.267943\pi$
$318$		0			0
$319$		−	1.40482i		−	0.0786546i
$320$	−27.6322	+	4.94774i	−1.54468	+	0.276587i
$321$		0			0
$322$	−4.52730	−	4.52730i	−0.252297	−	0.252297i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$		0			0
$325$	8.01276	−	17.4236i	0.444468	−	0.966488i
$326$		−	32.0187i		−	1.77335i
$327$		0			0
$328$	10.2690	−	10.2690i	0.567009	−	0.567009i
$329$	3.36135			0.185317
$330$		0			0
$331$	23.5400			1.29387			0.646937	−	0.762543i	$-0.276050\pi$
$331$	23.5400			1.29387			0.646937	+	0.762543i	$0.276050\pi$
$332$	−12.9274	+	12.9274i	−0.709484	+	0.709484i
$333$		0			0
$334$			45.8229i			2.50732i
$335$	17.1518	−	24.6339i	0.937105	−	1.34589i
$336$		0			0
$337$	−8.05608	−	8.05608i	−0.438842	−	0.438842i	0.452780	−	0.891622i	$-0.350432\pi$
$337$	−8.05608	−	8.05608i	−0.438842	−	0.438842i	−0.891622	+	0.452780i	$0.850432\pi$
$338$	−2.81088	−	2.81088i	−0.152892	−	0.152892i
$339$		0			0
$340$	−24.1264	+	34.6509i	−1.30844	+	1.87921i
$341$		−	0.0494178i		−	0.00267612i
$342$		0			0
$343$	−7.36850	+	7.36850i	−0.397861	+	0.397861i
$344$	4.47702			0.241385
$345$		0			0
$346$	−24.1092			−1.29612
$347$	−10.1044	+	10.1044i	−0.542430	+	0.542430i	−0.924241	−	0.381810i	$-0.875301\pi$
$347$	−10.1044	+	10.1044i	−0.542430	+	0.542430i	0.381810	+	0.924241i	$0.375301\pi$
$348$		0			0
$349$		−	17.5645i		−	0.940206i	−0.882612	−	0.470103i	$-0.844217\pi$
$349$		−	17.5645i		−	0.940206i	0.882612	−	0.470103i	$-0.155783\pi$
$350$	8.47339	−	3.13496i	0.452922	−	0.167570i
$351$		0			0
$352$	−0.857952	−	0.857952i	−0.0457290	−	0.0457290i
$353$	12.3253	+	12.3253i	0.656008	+	0.656008i	0.954433	−	0.298425i	$-0.0964613\pi$
$353$	12.3253	+	12.3253i	0.656008	+	0.656008i	−0.298425	+	0.954433i	$0.596461\pi$
$354$		0			0
$355$	−4.75399	+	0.851236i	−0.252316	+	0.0451789i
$356$		−	0.969296i		−	0.0513726i
$357$		0			0
$358$	−24.8023	+	24.8023i	−1.31084	+	1.31084i
$359$	34.0577			1.79750			0.898748	−	0.438465i	$-0.144478\pi$
$359$	34.0577			1.79750			0.898748	+	0.438465i	$0.144478\pi$
$360$		0			0
$361$	18.8061			0.989793
$362$	−12.8590	+	12.8590i	−0.675855	+	0.675855i
$363$		0			0
$364$		−	10.1297i		−	0.530942i
$365$	23.8350	+	16.5956i	1.24758	+	0.868652i
$366$		0			0
$367$	9.98059	+	9.98059i	0.520983	+	0.520983i	0.917868	−	0.396886i	$-0.129909\pi$
$367$	9.98059	+	9.98059i	0.520983	+	0.520983i	−0.396886	+	0.917868i	$0.629909\pi$
$368$	−1.84141	−	1.84141i	−0.0959901	−	0.0959901i
$369$		0			0
$370$	0.159239	+	0.889320i	0.00827845	+	0.0462336i
$371$		−	1.03202i		−	0.0535796i
$372$		0			0
$373$	−15.2239	+	15.2239i	−0.788263	+	0.788263i	−0.981209	−	0.192946i	$-0.938196\pi$
$373$	−15.2239	+	15.2239i	−0.788263	+	0.788263i	0.192946	+	0.981209i	$0.438196\pi$
$374$	−3.28475			−0.169850
$375$		0			0
$376$	13.9973			0.721858
$377$	−14.9854	+	14.9854i	−0.771788	+	0.771788i
$378$		0			0
$379$		−	9.52893i		−	0.489468i	−0.969590	−	0.244734i	$-0.921299\pi$
$379$		−	9.52893i		−	0.489468i	0.969590	−	0.244734i	$-0.0787007\pi$
$380$	−0.589195	−	3.29054i	−0.0302251	−	0.168801i
$381$		0			0
$382$	18.8423	+	18.8423i	0.964056	+	0.964056i
$383$	7.04088	+	7.04088i	0.359772	+	0.359772i	0.863729	−	0.503957i	$-0.168123\pi$
$383$	7.04088	+	7.04088i	0.359772	+	0.359772i	−0.503957	+	0.863729i	$0.668123\pi$
$384$		0			0
$385$	0.362973	+	0.252727i	0.0184988	+	0.0128802i
$386$		−	12.8173i		−	0.652385i
$387$		0			0
$388$	−21.7088	+	21.7088i	−1.10210	+	1.10210i
$389$	29.1344			1.47717			0.738587	−	0.674158i	$-0.235493\pi$
$389$	29.1344			1.47717			0.738587	+	0.674158i	$0.235493\pi$
$390$		0			0
$391$	19.7088			0.996718
$392$	−14.6488	+	14.6488i	−0.739874	+	0.739874i
$393$		0			0
$394$			7.63031i			0.384409i
$395$	30.4299	−	5.44870i	1.53110	−	0.274154i
$396$		0			0
$397$	−18.9354	−	18.9354i	−0.950338	−	0.950338i	0.0484856	−	0.998824i	$-0.484561\pi$
$397$	−18.9354	−	18.9354i	−0.950338	−	0.950338i	−0.998824	+	0.0484856i	$0.984561\pi$
$398$	28.2451	+	28.2451i	1.41580	+	1.41580i
$399$		0			0
$400$	3.44642	−	1.27509i	0.172321	−	0.0637547i
$401$		−	24.4907i		−	1.22301i	−0.791242	−	0.611503i	$-0.790565\pi$
$401$		−	24.4907i		−	1.22301i	0.791242	−	0.611503i	$-0.209435\pi$
$402$		0			0
$403$	−0.527148	+	0.527148i	−0.0262591	+	0.0262591i
$404$	−44.6649			−2.22216
$405$		0			0
$406$	−9.98392			−0.495493
$407$	−0.0312743	+	0.0312743i	−0.00155021	+	0.00155021i
$408$		0			0
$409$			14.1623i			0.700282i	0.936697	+	0.350141i	$0.113866\pi$
$409$			14.1623i			0.700282i	−0.936697	+	0.350141i	$0.886134\pi$
$410$	13.3036	−	19.1069i	0.657016	−	0.943621i
$411$		0			0
$412$	39.2856	+	39.2856i	1.93546	+	1.93546i
$413$	−4.42589	−	4.42589i	−0.217784	−	0.217784i
$414$		0			0
$415$	−6.88091	+	9.88252i	−0.337770	+	0.485114i
$416$			18.3039i			0.897420i
$417$		0			0
$418$	0.183891	−	0.183891i	0.00899438	−	0.00899438i
$419$	−27.7616			−1.35624			−0.678120	−	0.734951i	$-0.737205\pi$
$419$	−27.7616			−1.35624			−0.678120	+	0.734951i	$0.737205\pi$
$420$		0			0
$421$	0.859803			0.0419042			0.0209521	−	0.999780i	$-0.493330\pi$
$421$	0.859803			0.0419042			0.0209521	+	0.999780i	$0.493330\pi$
$422$	7.47211	−	7.47211i	0.363737	−	0.363737i
$423$		0			0
$424$		−	4.29753i		−	0.208706i
$425$	−11.6200	+	25.2675i	−0.563652	+	1.22565i
$426$		0			0
$427$	−1.58634	−	1.58634i	−0.0767682	−	0.0767682i
$428$	19.7373	+	19.7373i	0.954037	+	0.954037i
$429$		0			0
$430$	7.06508	−	1.26505i	0.340708	−	0.0610063i
$431$			25.5770i			1.23200i	0.787746	+	0.616000i	$0.211248\pi$
$431$			25.5770i			1.23200i	−0.787746	+	0.616000i	$0.788752\pi$
$432$		0			0
$433$	6.30733	−	6.30733i	0.303111	−	0.303111i	−0.539119	−	0.842230i	$-0.681243\pi$
$433$	6.30733	−	6.30733i	0.303111	−	0.303111i	0.842230	+	0.539119i	$0.181243\pi$
$434$	−0.351208			−0.0168585
$435$		0			0
$436$	29.9387			1.43381
$437$	−1.10336	+	1.10336i	−0.0527810	+	0.0527810i
$438$		0			0
$439$			14.3952i			0.687046i	0.939144	+	0.343523i	$0.111620\pi$
$439$			14.3952i			0.687046i	−0.939144	+	0.343523i	$0.888380\pi$
$440$	1.51149	+	1.05241i	0.0720577	+	0.0501716i
$441$		0			0
$442$	35.0390	+	35.0390i	1.66663	+	1.66663i
$443$	−15.5005	−	15.5005i	−0.736452	−	0.736452i	0.235437	−	0.971890i	$-0.424348\pi$
$443$	−15.5005	−	15.5005i	−0.736452	−	0.736452i	−0.971890	+	0.235437i	$0.924348\pi$
$444$		0			0
$445$	−0.112530	−	0.628460i	−0.00533445	−	0.0297919i
$446$			42.5427i			2.01445i
$447$		0			0
$448$	−6.90599	+	6.90599i	−0.326277	+	0.326277i
$449$	23.6447			1.11586			0.557931	−	0.829888i	$-0.311596\pi$
$449$	23.6447			1.11586			0.557931	+	0.829888i	$0.311596\pi$
$450$		0			0
$451$	1.13976			0.0536693
$452$	−32.3297	+	32.3297i	−1.52066	+	1.52066i
$453$		0			0
$454$		−	26.2008i		−	1.22967i
$455$	−1.17601	−	6.56778i	−0.0551321	−	0.307902i
$456$		0			0
$457$	−4.03328	−	4.03328i	−0.188669	−	0.188669i	0.606452	−	0.795120i	$-0.292592\pi$
$457$	−4.03328	−	4.03328i	−0.188669	−	0.188669i	−0.795120	+	0.606452i	$0.792592\pi$
$458$	8.01095	+	8.01095i	0.374327	+	0.374327i
$459$		0			0
$460$	−22.0736	−	15.3692i	−1.02919	−	0.716591i
$461$		−	32.2095i		−	1.50015i	−0.661355	−	0.750073i	$-0.730018\pi$
$461$		−	32.2095i		−	1.50015i	0.661355	−	0.750073i	$-0.269982\pi$
$462$		0			0
$463$	−4.52074	+	4.52074i	−0.210097	+	0.210097i	−0.804308	−	0.594212i	$-0.797464\pi$
$463$	−4.52074	+	4.52074i	−0.210097	+	0.210097i	0.594212	+	0.804308i	$0.297464\pi$
$464$	−4.06080			−0.188518
$465$		0			0
$466$	−25.9739			−1.20322
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	−0.938233	−	0.346003i	$-0.887539\pi$
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	0.346003	+	0.938233i	$0.387539\pi$
$468$		0			0
$469$		−	10.4433i		−	0.482228i
$470$	22.0889	−	3.95517i	1.01888	−	0.182439i
$471$		0			0
$472$	−18.4303	−	18.4303i	−0.848325	−	0.848325i
$473$	0.248454	+	0.248454i	0.0114239	+	0.0114239i
$474$		0			0
$475$	−0.764030	−	2.06508i	−0.0350561	−	0.0947523i
$476$			14.6900i			0.673314i
$477$		0			0
$478$	36.5795	−	36.5795i	1.67311	−	1.67311i
$479$	3.52331			0.160984			0.0804921	−	0.996755i	$-0.474351\pi$
$479$	3.52331			0.160984			0.0804921	+	0.996755i	$0.474351\pi$
$480$		0			0
$481$	0.667217			0.0304225
$482$	−47.5454	+	47.5454i	−2.16563	+	2.16563i
$483$		0			0
$484$		−	37.1231i		−	1.68741i
$485$	−11.5550	+	16.5956i	−0.524686	+	0.753566i
$486$		0			0
$487$	29.3442	+	29.3442i	1.32971	+	1.32971i	0.905616	+	0.424098i	$0.139409\pi$
$487$	29.3442	+	29.3442i	1.32971	+	1.32971i	0.424098	+	0.905616i	$0.360591\pi$
$488$	−6.60583	−	6.60583i	−0.299032	−	0.299032i
$489$		0			0
$490$	−18.9776	+	27.2561i	−0.857322	+	1.23131i
$491$		−	20.6692i		−	0.932789i	−0.884577	−	0.466395i	$-0.845553\pi$
$491$		−	20.6692i		−	0.932789i	0.884577	−	0.466395i	$-0.154447\pi$
$492$		0			0
$493$	21.7316	−	21.7316i	0.978743	−	0.978743i
$494$	−3.92319			−0.176513
$495$		0			0
$496$	−0.142849			−0.00641409
$497$	−1.18814	+	1.18814i	−0.0532956	+	0.0532956i
$498$		0			0
$499$		−	26.1761i		−	1.17180i	−0.810383	−	0.585901i	$-0.800741\pi$
$499$		−	26.1761i		−	1.17180i	0.810383	−	0.585901i	$-0.199259\pi$
$500$	32.7181	−	19.2378i	1.46320	−	0.860338i
$501$		0			0
$502$	−33.5402	−	33.5402i	−1.49697	−	1.49697i
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	0.541233	−	0.840873i	$-0.317958\pi$
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	−0.840873	+	0.541233i	$0.817958\pi$
$504$		0			0
$505$	−28.9593	+	5.18536i	−1.28867	+	0.230746i
$506$		−	2.09247i		−	0.0930217i
$507$		0			0
$508$	−22.8185	+	22.8185i	−1.01241	+	1.01241i
$509$	23.9352			1.06091			0.530454	−	0.847714i	$-0.322022\pi$
$509$	23.9352			1.06091			0.530454	+	0.847714i	$0.322022\pi$
$510$		0			0
$511$	10.1046			0.447003
$512$	−5.84717	+	5.84717i	−0.258411	+	0.258411i
$513$		0			0
$514$		−	17.0546i		−	0.752246i
$515$	30.0324	+	20.9107i	1.32339	+	0.921434i
$516$		0			0
$517$	0.776790	+	0.776790i	0.0341632	+	0.0341632i
$518$	0.222264	+	0.222264i	0.00976573	+	0.00976573i
$519$		0			0
$520$	−4.89714	−	27.3496i	−0.214754	−	1.19936i
$521$		−	3.23141i		−	0.141571i	−0.997492	−	0.0707853i	$-0.977449\pi$
$521$		−	3.23141i		−	0.141571i	0.997492	−	0.0707853i	$-0.0225505\pi$
$522$		0			0
$523$	−8.67002	+	8.67002i	−0.379114	+	0.379114i	−0.870782	−	0.491669i	$-0.836387\pi$
$523$	−8.67002	+	8.67002i	−0.379114	+	0.379114i	0.491669	+	0.870782i	$0.336387\pi$
$524$	−45.6602			−1.99468
$525$		0			0
$526$	33.9283			1.47934
$527$	0.764462	−	0.764462i	0.0333005	−	0.0333005i
$528$		0			0
$529$		−	10.4449i		−	0.454128i
$530$	−1.21434	−	6.78183i	−0.0527474	−	0.294584i
$531$		0			0
$532$	−0.822392	−	0.822392i	−0.0356552	−	0.0356552i
$533$	−12.1581	−	12.1581i	−0.526624	−	0.526624i
$534$		0			0
$535$	15.0884	+	10.5056i	0.652328	+	0.454197i
$536$		−	43.4882i		−	1.87840i
$537$		0			0
$538$	−6.17548	+	6.17548i	−0.266244	+	0.266244i
$539$	−1.62588			−0.0700317
$540$		0			0
$541$	−11.1502			−0.479386			−0.239693	−	0.970849i	$-0.577047\pi$
$541$	−11.1502			−0.479386			−0.239693	+	0.970849i	$0.577047\pi$
$542$	23.1222	−	23.1222i	0.993182	−	0.993182i
$543$		0			0
$544$		−	26.5440i		−	1.13806i
$545$	19.4113	−	3.47573i	0.831489	−	0.148884i
$546$		0			0
$547$	9.68543	+	9.68543i	0.414119	+	0.414119i	0.883171	−	0.469052i	$-0.155404\pi$
$547$	9.68543	+	9.68543i	0.414119	+	0.414119i	−0.469052	+	0.883171i	$0.655404\pi$
$548$	23.5000	+	23.5000i	1.00387	+	1.00387i
$549$		0			0
$550$	2.68263	+	1.23369i	0.114388	+	0.0526045i
$551$			2.43321i			0.103658i
$552$		0			0
$553$	7.60523	−	7.60523i	0.323407	−	0.323407i
$554$	4.85900			0.206439
$555$		0			0
$556$	26.8486			1.13863
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	−0.408721	−	0.912659i	$-0.634025\pi$
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	0.912659	+	0.408721i	$0.134025\pi$
$558$		0			0
$559$		−	5.30061i		−	0.224192i
$560$	0.730541	−	1.04922i	0.0308710	−	0.0443376i
$561$		0			0
$562$	15.2223	+	15.2223i	0.642112	+	0.642112i
$563$	17.4218	+	17.4218i	0.734242	+	0.734242i	0.971457	−	0.237215i	$-0.0762346\pi$
$563$	17.4218	+	17.4218i	0.734242	+	0.734242i	−0.237215	+	0.971457i	$0.576235\pi$
$564$		0			0
$565$	−17.2082	+	24.7149i	−0.723956	+	1.03976i
$566$		−	74.8082i		−	3.14442i
$567$		0			0
$568$	−4.94768	+	4.94768i	−0.207600	+	0.207600i
$569$	−12.4971			−0.523907			−0.261953	−	0.965081i	$-0.584367\pi$
$569$	−12.4971			−0.523907			−0.261953	+	0.965081i	$0.584367\pi$
$570$		0			0
$571$	−27.4131			−1.14720			−0.573601	−	0.819135i	$-0.694454\pi$
$571$	−27.4131			−1.14720			−0.573601	+	0.819135i	$0.694454\pi$
$572$	2.34093	−	2.34093i	0.0978790	−	0.0978790i
$573$		0			0
$574$		−	8.10020i		−	0.338096i
$575$	−16.0961	−	7.40224i	−0.671252	−	0.308695i
$576$		0			0
$577$	−11.1638	−	11.1638i	−0.464755	−	0.464755i	0.435455	−	0.900210i	$-0.356587\pi$
$577$	−11.1638	−	11.1638i	−0.464755	−	0.464755i	−0.900210	+	0.435455i	$0.856587\pi$
$578$	−22.8926	−	22.8926i	−0.952207	−	0.952207i
$579$		0			0
$580$	−41.2856	+	7.39249i	−1.71429	+	0.306956i
$581$			4.18961i			0.173814i
$582$		0			0
$583$	0.238494	−	0.238494i	0.00987739	−	0.00987739i
$584$	42.0778			1.74119
$585$		0			0
$586$	−15.3410			−0.633733
$587$	−13.0202	+	13.0202i	−0.537403	+	0.537403i	−0.922765	−	0.385363i	$-0.874076\pi$
$587$	−13.0202	+	13.0202i	−0.537403	+	0.537403i	0.385363	+	0.922765i	$0.374076\pi$
$588$		0			0
$589$			0.0855941i			0.00352684i
$590$	−34.2923	−	23.8767i	−1.41179	−	0.982988i
$591$		0			0
$592$	0.0904025	+	0.0904025i	0.00371552	+	0.00371552i
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	0.342377	−	0.939563i	$-0.388768\pi$
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	−0.939563	+	0.342377i	$0.888768\pi$
$594$		0			0
$595$	1.70543	+	9.52450i	0.0699158	+	0.390466i
$596$			31.0116i			1.27029i
$597$		0			0
$598$	−22.3208	+	22.3208i	−0.912764	+	0.912764i
$599$	−35.3945			−1.44618			−0.723089	−	0.690755i	$-0.757279\pi$
$599$	−35.3945			−1.44618			−0.723089	+	0.690755i	$0.757279\pi$
$600$		0			0
$601$	−14.6347			−0.596964			−0.298482	−	0.954415i	$-0.596480\pi$
$601$	−14.6347			−0.596964			−0.298482	+	0.954415i	$0.596480\pi$
$602$	1.76575	−	1.76575i	0.0719664	−	0.0719664i
$603$		0			0
$604$		−	49.9026i		−	2.03051i
$605$	−4.30980	−	24.0694i	−0.175218	−	0.978560i
$606$		0			0
$607$	5.52612	+	5.52612i	0.224298	+	0.224298i	0.810306	−	0.586007i	$-0.199301\pi$
$607$	5.52612	+	5.52612i	0.224298	+	0.224298i	−0.586007	+	0.810306i	$0.699301\pi$
$608$	1.48602	+	1.48602i	0.0602660	+	0.0602660i
$609$		0			0
$610$	−12.2911	−	8.55793i	−0.497652	−	0.346500i
$611$		−	16.5723i		−	0.670444i
$612$		0			0
$613$	3.49830	−	3.49830i	0.141295	−	0.141295i	−0.632921	−	0.774216i	$-0.718144\pi$
$613$	3.49830	−	3.49830i	0.141295	−	0.141295i	0.774216	+	0.632921i	$0.218144\pi$
$614$	19.1212			0.771667
$615$		0			0
$616$	0.640786			0.0258180
$617$	17.5004	−	17.5004i	0.704541	−	0.704541i	−0.260841	−	0.965382i	$-0.584000\pi$
$617$	17.5004	−	17.5004i	0.704541	−	0.704541i	0.965382	+	0.260841i	$0.0839997\pi$
$618$		0			0
$619$		−	17.8236i		−	0.716392i	−0.933646	−	0.358196i	$-0.883392\pi$
$619$		−	17.8236i		−	0.716392i	0.933646	−	0.358196i	$-0.116608\pi$
$620$	−1.45232	+	0.260049i	−0.0583267	+	0.0104438i
$621$		0			0
$622$	−18.9394	−	18.9394i	−0.759402	−	0.759402i
$623$	−0.157068	−	0.157068i	−0.00629281	−	0.00629281i
$624$		0			0
$625$	18.9799	−	16.2715i	0.759197	−	0.650861i
$626$		−	15.4685i		−	0.618245i
$627$		0			0
$628$	−40.6486	+	40.6486i	−1.62206	+	1.62206i
$629$	−0.967588			−0.0385803
$630$		0			0
$631$	−29.9153			−1.19091			−0.595454	−	0.803389i	$-0.703028\pi$
$631$	−29.9153			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$632$	31.6697	−	31.6697i	1.25975	−	1.25975i
$633$		0			0
$634$			4.65983i			0.185065i
$635$	−12.1457	+	17.4439i	−0.481987	+	0.692241i
$636$		0			0
$637$	17.3436	+	17.3436i	0.687177	+	0.687177i
$638$	−2.30723	−	2.30723i	−0.0913441	−	0.0913441i
$639$		0			0
$640$	−25.0615	+	35.9939i	−0.990642	+	1.42278i
$641$		−	15.8660i		−	0.626668i	−0.949643	−	0.313334i	$-0.898554\pi$
$641$		−	15.8660i		−	0.626668i	0.949643	−	0.313334i	$-0.101446\pi$
$642$		0			0
$643$	16.4395	−	16.4395i	0.648310	−	0.648310i	−0.304274	−	0.952584i	$-0.598414\pi$
$643$	16.4395	−	16.4395i	0.648310	−	0.648310i	0.952584	+	0.304274i	$0.0984139\pi$
$644$	−9.35791			−0.368753
$645$		0			0
$646$	5.68935			0.223844
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	−0.860212	−	0.509937i	$-0.829669\pi$
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	0.509937	+	0.860212i	$0.329669\pi$
$648$		0			0
$649$		−	2.04560i		−	0.0802969i
$650$	−15.4561	−	41.7760i	−0.606240	−	1.63859i
$651$		0			0
$652$	−33.0913	−	33.0913i	−1.29595	−	1.29595i
$653$	−10.2796	−	10.2796i	−0.402273	−	0.402273i	0.476760	−	0.879033i	$-0.341811\pi$
$653$	−10.2796	−	10.2796i	−0.402273	−	0.402273i	−0.879033	+	0.476760i	$0.841811\pi$
$654$		0			0
$655$	−29.6046	+	5.30092i	−1.15675	+	0.207124i
$656$		−	3.29463i		−	0.128634i
$657$		0			0
$658$	5.52058	−	5.52058i	0.215215	−	0.215215i
$659$	9.01471			0.351163			0.175582	−	0.984465i	$-0.443819\pi$
$659$	9.01471			0.351163			0.175582	+	0.984465i	$0.443819\pi$
$660$		0			0
$661$	−30.0068			−1.16713			−0.583564	−	0.812067i	$-0.698342\pi$
$661$	−30.0068			−1.16713			−0.583564	+	0.812067i	$0.698342\pi$
$662$	38.6614	−	38.6614i	1.50262	−	1.50262i
$663$		0			0
$664$			17.4464i			0.677052i
$665$	−0.628687	−	0.437737i	−0.0243795	−	0.0169747i
$666$		0			0
$667$	13.8436	+	13.8436i	0.536028	+	0.536028i
$668$	47.3578	+	47.3578i	1.83233	+	1.83233i
$669$		0			0
$670$	−12.2883	−	68.6277i	−0.474738	−	2.65132i
$671$		−	0.733188i		−	0.0283044i
$672$		0			0
$673$	−19.2396	+	19.2396i	−0.741632	+	0.741632i	−0.972892	−	0.231260i	$-0.925715\pi$
$673$	−19.2396	+	19.2396i	−0.741632	+	0.741632i	0.231260	+	0.972892i	$0.425715\pi$
$674$	−26.4622			−1.01928
$675$		0			0
$676$	−5.81007			−0.223464
$677$	−12.2708	+	12.2708i	−0.471604	+	0.471604i	−0.902433	−	0.430829i	$-0.858221\pi$
$677$	−12.2708	+	12.2708i	−0.471604	+	0.471604i	0.430829	+	0.902433i	$0.358221\pi$
$678$		0			0
$679$			7.03556i			0.270000i
$680$	7.10176	+	39.6620i	0.272340	+	1.52097i
$681$		0			0
$682$	−0.0811624	−	0.0811624i	−0.00310787	−	0.00310787i
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.998569	+	0.0534806i	$0.0170315\pi$
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.0534806	+	0.998569i	$0.482968\pi$
$684$		0			0
$685$	17.9649	+	12.5084i	0.686403	+	0.477922i
$686$			24.2036i			0.924099i
$687$		0			0
$688$	0.718190	−	0.718190i	0.0273807	−	0.0273807i
$689$	−5.08810			−0.193841
$690$		0			0
$691$	18.1502			0.690468			0.345234	−	0.938517i	$-0.387800\pi$
$691$	18.1502			0.690468			0.345234	+	0.938517i	$0.387800\pi$
$692$	−24.9168	+	24.9168i	−0.947195	+	0.947195i
$693$		0			0
$694$			33.1902i			1.25988i
$695$	17.4077	−	3.11698i	0.660314	−	0.118234i
$696$		0			0
$697$	17.6314	+	17.6314i	0.667838	+	0.667838i
$698$	−28.8474	−	28.8474i	−1.09189	−	1.09189i
$699$		0			0
$700$	5.51726	−	11.9972i	0.208533	−	0.453451i
$701$			5.23510i			0.197727i	0.995101	+	0.0988635i	$0.0315207\pi$
$701$			5.23510i			0.197727i	−0.995101	+	0.0988635i	$0.968479\pi$
$702$		0			0
$703$	0.0541687	−	0.0541687i	0.00204301	−	0.00204301i
$704$	−3.19188			−0.120298
$705$		0			0
$706$	40.4854			1.52369
$707$	−7.23767	+	7.23767i	−0.272201	+	0.272201i
$708$		0			0
$709$		−	16.9944i		−	0.638238i	−0.947715	−	0.319119i	$-0.896613\pi$
$709$		−	16.9944i		−	0.638238i	0.947715	−	0.319119i	$-0.103387\pi$
$710$	−6.40977	+	9.20587i	−0.240555	+	0.345490i
$711$		0			0
$712$	−0.654066	−	0.654066i	−0.0245121	−	0.0245121i
$713$	0.486983	+	0.486983i	0.0182377	+	0.0182377i
$714$		0			0
$715$	1.24601	−	1.78955i	0.0465982	−	0.0669254i
$716$			51.2662i			1.91591i
$717$		0			0
$718$	55.9354	−	55.9354i	2.08749	−	2.08749i
$719$	−49.3502			−1.84045			−0.920225	−	0.391389i	$-0.871995\pi$
$719$	−49.3502			−1.84045			−0.920225	+	0.391389i	$0.871995\pi$
$720$		0			0
$721$	12.7320			0.474164
$722$	30.8866	−	30.8866i	1.14948	−	1.14948i
$723$		0			0
$724$			26.5795i			0.987821i
$725$	−25.9100	+	9.58610i	−0.962275	+	0.356019i
$726$		0			0
$727$	−27.7441	−	27.7441i	−1.02897	−	1.02897i	−0.999568	−	0.0294042i	$-0.990639\pi$
$727$	−27.7441	−	27.7441i	−1.02897	−	1.02897i	−0.0294042	−	0.999568i	$-0.509361\pi$
$728$	−6.83537	−	6.83537i	−0.253336	−	0.253336i
$729$		0			0
$730$	66.4020	−	11.8898i	2.45765	−	0.440060i
$731$			7.68687i			0.284309i
$732$		0			0
$733$	−5.36126	+	5.36126i	−0.198023	+	0.198023i	−0.799152	−	0.601129i	$-0.794718\pi$
$733$	−5.36126	+	5.36126i	−0.198023	+	0.198023i	0.601129	+	0.799152i	$0.294718\pi$
$734$	32.7837			1.21007
$735$		0			0
$736$	16.9092			0.623283
$737$	2.41340	−	2.41340i	0.0888987	−	0.0888987i
$738$		0			0
$739$		−	43.8329i		−	1.61242i	−0.591629	−	0.806210i	$-0.701515\pi$
$739$		−	43.8329i		−	1.61242i	0.591629	−	0.806210i	$-0.298485\pi$
$740$	1.08368	+	0.754537i	0.0398370	+	0.0277373i
$741$		0			0
$742$	−1.69495	−	1.69495i	−0.0622237	−	0.0622237i
$743$	6.60225	+	6.60225i	0.242213	+	0.242213i	0.817765	−	0.575552i	$-0.195213\pi$
$743$	6.60225	+	6.60225i	0.242213	+	0.242213i	−0.575552	+	0.817765i	$0.695213\pi$
$744$		0			0
$745$	3.60029	+	20.1069i	0.131904	+	0.736661i
$746$			50.0066i			1.83087i
$747$		0			0
$748$	−3.39477	+	3.39477i	−0.124125	+	0.124125i
$749$	6.39660			0.233727
$750$		0			0
$751$	−47.3926			−1.72938			−0.864689	−	0.502307i	$-0.832485\pi$
$751$	−47.3926			−1.72938			−0.864689	+	0.502307i	$0.832485\pi$
$752$	2.24541	−	2.24541i	0.0818817	−	0.0818817i
$753$		0			0
$754$			49.2233i			1.79261i
$755$	−5.79343	−	32.3552i	−0.210845	−	1.17753i
$756$		0			0
$757$	1.37906	+	1.37906i	0.0501227	+	0.0501227i	0.731724	−	0.681601i	$-0.238716\pi$
$757$	1.37906	+	1.37906i	0.0501227	+	0.0501227i	−0.681601	+	0.731724i	$0.738716\pi$
$758$	−15.6501	−	15.6501i	−0.568435	−	0.568435i
$759$		0			0
$760$	−2.61798	−	1.82283i	−0.0949643	−	0.0661208i
$761$			48.3288i			1.75192i	0.482386	+	0.875958i	$0.339770\pi$
$761$			48.3288i			1.75192i	−0.482386	+	0.875958i	$0.660230\pi$
$762$		0			0
$763$	4.85139	−	4.85139i	0.175632	−	0.175632i
$764$	38.9469			1.40905
$765$		0			0
$766$	23.1275			0.835631
$767$	−21.8208	+	21.8208i	−0.787903	+	0.787903i
$768$		0			0
$769$			29.7383i			1.07239i	0.844094	+	0.536196i	$0.180139\pi$
$769$			29.7383i			1.07239i	−0.844094	+	0.536196i	$0.819861\pi$
$770$	1.01121	−	0.181064i	0.0364414	−	0.00652510i
$771$		0			0
$772$	−13.2467	−	13.2467i	−0.476759	−	0.476759i
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	0.914139	−	0.405401i	$-0.132868\pi$
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	−0.405401	+	0.914139i	$0.632868\pi$
$774$		0			0
$775$	−0.911448	+	0.337214i	−0.0327402	+	0.0121131i
$776$			29.2975i			1.05172i
$777$		0			0
$778$	47.8496	−	47.8496i	1.71549	−	1.71549i
$779$	−1.97413			−0.0707304
$780$		0			0
$781$	−0.549148			−0.0196501
$782$	32.3692	−	32.3692i	1.15752	−	1.15752i
$783$		0			0
$784$			4.69982i			0.167851i
$785$	−21.6361	+	31.0743i	−0.772227	+	1.10909i
$786$		0			0
$787$	1.27473	+	1.27473i	0.0454391	+	0.0454391i	0.729461	−	0.684022i	$-0.239771\pi$
$787$	1.27473	+	1.27473i	0.0454391	+	0.0454391i	−0.684022	+	0.729461i	$0.739771\pi$
$788$	7.88591	+	7.88591i	0.280924	+	0.280924i
$789$		0			0
$790$	41.0285	−	58.9261i	1.45973	−	2.09649i
$791$			10.4777i			0.372543i
$792$		0			0
$793$	−7.82105	+	7.82105i	−0.277733	+	0.277733i
$794$	−62.1978			−2.20732
$795$		0			0
$796$	58.3825			2.06931
$797$	5.01455	−	5.01455i	0.177624	−	0.177624i	−0.612695	−	0.790319i	$-0.709915\pi$
$797$	5.01455	−	5.01455i	0.177624	−	0.177624i	0.790319	+	0.612695i	$0.209915\pi$
$798$		0			0
$799$			24.0329i			0.850223i
$800$	−9.96939	+	21.6783i	−0.352471	+	0.766443i
$801$		0			0
$802$	−40.2228	−	40.2228i	−1.42032	−	1.42032i
$803$	2.33513	+	2.33513i	0.0824049	+	0.0824049i
$804$		0			0
$805$	−6.06736	+	1.08640i	−0.213846	+	0.0382907i
$806$			1.73155i			0.0609912i
$807$		0			0
$808$	−30.1392	+	30.1392i	−1.06029	+	1.06029i
$809$	24.7868			0.871457			0.435728	−	0.900078i	$-0.356491\pi$
$809$	24.7868			0.871457			0.435728	+	0.900078i	$0.356491\pi$
$810$		0			0
$811$	−5.24853			−0.184301			−0.0921505	−	0.995745i	$-0.529374\pi$
$811$	−5.24853			−0.184301			−0.0921505	+	0.995745i	$0.529374\pi$
$812$	−10.3183	+	10.3183i	−0.362103	+	0.362103i
$813$		0			0
$814$			0.102728i			0.00360062i
$815$	−25.2970	−	17.6136i	−0.886116	−	0.616977i
$816$		0			0
$817$	−0.430336	−	0.430336i	−0.0150555	−	0.0150555i
$818$	23.2598	+	23.2598i	0.813260	+	0.813260i
$819$		0			0
$820$	−5.99772	−	33.4961i	−0.209449	−	1.16973i
$821$			27.2060i			0.949497i	0.880122	+	0.474748i	$0.157461\pi$
$821$			27.2060i			0.949497i	−0.880122	+	0.474748i	$0.842539\pi$
$822$		0			0
$823$	−23.7962	+	23.7962i	−0.829483	+	0.829483i	−0.987445	−	0.157962i	$-0.949508\pi$
$823$	−23.7962	+	23.7962i	−0.829483	+	0.829483i	0.157962	+	0.987445i	$0.449508\pi$
$824$	53.0186			1.84699
$825$		0			0
$826$	−14.5379			−0.505839
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	−0.530353	−	0.847777i	$-0.677941\pi$
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	0.847777	+	0.530353i	$0.177941\pi$
$828$		0			0
$829$			44.3456i			1.54019i	0.637931	+	0.770093i	$0.279790\pi$
$829$			44.3456i			1.54019i	−0.637931	+	0.770093i	$0.720210\pi$
$830$	4.92976	+	27.5318i	0.171115	+	0.955642i
$831$		0			0
$832$	34.0483	+	34.0483i	1.18041	+	1.18041i
$833$	−25.1514	−	25.1514i	−0.871443	−	0.871443i
$834$		0			0
$835$	36.2033	+	25.2073i	1.25287	+	0.872334i
$836$		−	0.380101i		−	0.0131461i
$837$		0			0
$838$	−45.5948	+	45.5948i	−1.57505	+	1.57505i
$839$	−47.9321			−1.65480			−0.827399	−	0.561614i	$-0.810181\pi$
$839$	−47.9321			−1.65480			−0.827399	+	0.561614i	$0.810181\pi$
$840$		0			0
$841$	1.52893			0.0527217
$842$	1.41212	−	1.41212i	0.0486648	−	0.0486648i
$843$		0			0
$844$		−	15.4448i		−	0.531632i
$845$	−3.76706	+	0.674519i	−0.129591	+	0.0232042i
$846$		0			0
$847$	−6.01556	−	6.01556i	−0.206697	−	0.206697i
$848$	−0.689396	−	0.689396i	−0.0236740	−	0.0236740i
$849$		0			0
$850$	22.4143	+	60.5829i	0.768802	+	2.07798i
$851$		−	0.616380i		−	0.0211292i
$852$		0			0
$853$	4.10088	−	4.10088i	0.140411	−	0.140411i	−0.633407	−	0.773819i	$-0.718344\pi$
$853$	4.10088	−	4.10088i	0.140411	−	0.140411i	0.773819	+	0.633407i	$0.218344\pi$
$854$	−5.21071			−0.178307
$855$		0			0
$856$	26.6368			0.910427
$857$	22.5011	−	22.5011i	0.768623	−	0.768623i	−0.209241	−	0.977864i	$-0.567099\pi$
$857$	22.5011	−	22.5011i	0.768623	−	0.768623i	0.977864	+	0.209241i	$0.0670993\pi$
$858$		0			0
$859$			11.9151i			0.406540i	0.979123	+	0.203270i	$0.0651568\pi$
$859$			11.9151i			0.406540i	−0.979123	+	0.203270i	$0.934843\pi$
$860$	5.99431	−	8.60917i	0.204404	−	0.293570i
$861$		0			0
$862$	42.0069	+	42.0069i	1.43076	+	1.43076i
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	0.442267	−	0.896884i	$-0.354174\pi$
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	−0.896884	+	0.442267i	$0.854174\pi$
$864$		0			0
$865$	−13.2625	+	19.0480i	−0.450940	+	0.647650i
$866$		−	20.7180i		−	0.704025i
$867$		0			0
$868$	−0.362973	+	0.362973i	−0.0123201	+	0.0123201i
$869$	3.51506			0.119240
$870$		0			0
$871$	−51.4883			−1.74462
$872$	20.2022	−	20.2022i	0.684132	−	0.684132i
$873$		0			0
$874$			3.62427i			0.122593i
$875$	2.18440	−	8.41912i	0.0738462	−	0.284618i
$876$		0			0
$877$	4.73028	+	4.73028i	0.159730	+	0.159730i	0.782447	−	0.622717i	$-0.213971\pi$
$877$	4.73028	+	4.73028i	0.159730	+	0.159730i	−0.622717	+	0.782447i	$0.713971\pi$
$878$	23.6423	+	23.6423i	0.797889	+	0.797889i
$879$		0			0
$880$	0.411294	−	0.0736451i	0.0138647	−	0.00248257i
$881$			13.4495i			0.453126i	0.973996	+	0.226563i	$0.0727490\pi$
$881$			13.4495i			0.453126i	−0.973996	+	0.226563i	$0.927251\pi$
$882$		0			0
$883$	32.5618	−	32.5618i	1.09579	−	1.09579i	0.100896	−	0.994897i	$-0.467829\pi$
$883$	32.5618	−	32.5618i	1.09579	−	1.09579i	0.994897	−	0.100896i	$-0.0321708\pi$
$884$	72.4253			2.43593
$885$		0			0
$886$	−50.9153			−1.71053
$887$	18.6289	−	18.6289i	0.625496	−	0.625496i	−0.321435	−	0.946932i	$-0.604165\pi$
$887$	18.6289	−	18.6289i	0.625496	−	0.625496i	0.946932	+	0.321435i	$0.104165\pi$
$888$		0			0
$889$			7.39521i			0.248027i
$890$	−1.21698	−	0.847349i	−0.0407933	−	0.0284032i
$891$		0			0
$892$	43.9677	+	43.9677i	1.47215	+	1.47215i
$893$	−1.34544	−	1.34544i	−0.0450234	−	0.0450234i
$894$		0			0
$895$	5.95175	+	33.2394i	0.198945	+	1.11107i
$896$			15.2593i			0.509778i
$897$		0			0
$898$	38.8334	−	38.8334i	1.29589	−	1.29589i
$899$	1.07393			0.0358175
$900$		0			0
$901$	7.37869			0.245820
$902$	1.87192	−	1.87192i	0.0623280	−	0.0623280i
$903$		0			0
$904$			43.6312i			1.45115i
$905$	3.08575	+	17.2333i	0.102574	+	0.572854i
$906$		0			0
$907$	−33.2566	−	33.2566i	−1.10427	−	1.10427i	−0.993890	−	0.110379i	$-0.964794\pi$
$907$	−33.2566	−	33.2566i	−1.10427	−	1.10427i	−0.110379	−	0.993890i	$-0.535206\pi$
$908$	−27.0785	−	27.0785i	−0.898632	−	0.898632i
$909$		0			0
$910$	−12.7182	−	8.85530i	−0.421604	−	0.293550i
$911$		−	22.0158i		−	0.729417i	−0.931122	−	0.364709i	$-0.881169\pi$
$911$		−	22.0158i		−	0.729417i	0.931122	−	0.364709i	$-0.118831\pi$
$912$		0			0
$913$	−0.968198	+	0.968198i	−0.0320427	+	0.0320427i
$914$	−13.2483			−0.438214
$915$		0			0
$916$	16.5586			0.547111
$917$	−7.39896	+	7.39896i	−0.244335	+	0.244335i
$918$		0			0
$919$			28.3896i			0.936486i	0.883600	+	0.468243i	$0.155113\pi$
$919$			28.3896i			0.936486i	−0.883600	+	0.468243i	$0.844887\pi$
$920$	−25.2658	+	4.52402i	−0.832987	+	0.149152i
$921$		0			0
$922$	−52.9000	−	52.9000i	−1.74217	−	1.74217i
$923$	5.85786	+	5.85786i	0.192814	+	0.192814i
$924$		0			0
$925$	0.790223	+	0.363407i	0.0259824	+	0.0119488i
$926$			14.8495i			0.487984i
$927$		0			0
$928$	18.6447	−	18.6447i	0.612042	−	0.612042i
$929$	37.8405			1.24151			0.620753	−	0.784006i	$-0.286827\pi$
$929$	37.8405			1.24151			0.620753	+	0.784006i	$0.286827\pi$
$930$		0			0
$931$	2.81611			0.0922943
$932$	−26.8439	+	26.8439i	−0.879302	+	0.879302i
$933$		0			0
$934$			42.0388i			1.37555i
$935$	−1.80695	+	2.59518i	−0.0590934	+	0.0848714i
$936$		0			0
$937$	36.4371	+	36.4371i	1.19035	+	1.19035i	0.976969	+	0.213379i	$0.0684470\pi$
$937$	36.4371	+	36.4371i	1.19035	+	1.19035i	0.213379	+	0.976969i	$0.431553\pi$
$938$	−17.1518	−	17.1518i	−0.560028	−	0.560028i
$939$		0			0
$940$	18.7411	−	26.9165i	0.611269	−	0.877918i
$941$		−	31.2566i		−	1.01893i	−0.860490	−	0.509467i	$-0.829842\pi$
$941$		−	31.2566i		−	1.01893i	0.860490	−	0.509467i	$-0.170158\pi$
$942$		0			0
$943$	−11.2317	+	11.2317i	−0.365754	+	0.365754i
$944$	−5.91308			−0.192454
$945$		0			0
$946$	0.816109			0.0265340
$947$	−10.6342	+	10.6342i	−0.345565	+	0.345565i	−0.858455	−	0.512890i	$-0.828575\pi$
$947$	−10.6342	+	10.6342i	−0.345565	+	0.345565i	0.512890	+	0.858455i	$0.328575\pi$
$948$		0			0
$949$		−	49.8185i		−	1.61718i
$950$	−4.64645	−	2.13681i	−0.150751	−	0.0693271i
$951$		0			0
$952$	9.91256	+	9.91256i	0.321268	+	0.321268i
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.972544	−	0.232720i	$-0.925237\pi$
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.232720	−	0.972544i	$-0.574763\pi$
$954$		0			0
$955$	25.2519	−	4.52154i	0.817133	−	0.146314i
$956$		−	75.6097i		−	2.44539i
$957$		0			0
$958$	5.78659	−	5.78659i	0.186956	−	0.186956i
$959$	7.61606			0.245935
$960$		0			0
$961$	−30.9622			−0.998781
$962$	1.09582	−	1.09582i	0.0353306	−	0.0353306i
$963$		0			0
$964$			98.2761i			3.16526i
$965$	−10.1266	−	7.05085i	−0.325987	−	0.226975i
$966$		0			0
$967$	−13.9248	−	13.9248i	−0.447791	−	0.447791i	0.446828	−	0.894620i	$-0.352553\pi$
$967$	−13.9248	−	13.9248i	−0.447791	−	0.447791i	−0.894620	+	0.446828i	$0.852553\pi$
$968$	−25.0501	−	25.0501i	−0.805139	−	0.805139i
$969$		0			0
$970$	8.27849	+	46.2338i	0.265806	+	1.48448i
$971$			6.75294i			0.216712i	0.994112	+	0.108356i	$0.0345586\pi$
$971$			6.75294i			0.216712i	−0.994112	+	0.108356i	$0.965441\pi$
$972$		0			0
$973$	4.35065	−	4.35065i	0.139475	−	0.139475i
$974$	96.3883			3.08848
$975$		0			0
$976$	−2.11937			−0.0678395
$977$	−20.9616	+	20.9616i	−0.670622	+	0.670622i	−0.957859	−	0.287238i	$-0.907263\pi$
$977$	−20.9616	+	20.9616i	−0.670622	+	0.670622i	0.287238	+	0.957859i	$0.407263\pi$
$978$		0			0
$979$		−	0.0725954i		−	0.00232016i
$980$	8.55579	+	47.7825i	0.273305	+	1.52635i
$981$		0			0
$982$	−33.9466	−	33.9466i	−1.08328	−	1.08328i
$983$	−12.5020	−	12.5020i	−0.398752	−	0.398752i	0.479040	−	0.877793i	$-0.340985\pi$
$983$	−12.5020	−	12.5020i	−0.398752	−	0.398752i	−0.877793	+	0.479040i	$0.840985\pi$
$984$		0			0
$985$	6.02848	+	4.19745i	0.192083	+	0.133742i
$986$		−	71.3828i		−	2.27329i
$987$		0			0
$988$	−4.05460	+	4.05460i	−0.128994	+	0.128994i
$989$	−4.89674			−0.155707
$990$		0			0
$991$	−61.9280			−1.96721			−0.983603	−	0.180345i	$-0.942279\pi$
$991$	−61.9280			−1.96721			−0.983603	+	0.180345i	$0.942279\pi$
$992$	0.655872	−	0.655872i	0.0208240	−	0.0208240i
$993$		0			0
$994$			3.90275i			0.123788i
$995$	37.8533	−	6.77791i	1.20003	−	0.214874i
$996$		0			0
$997$	17.7693	+	17.7693i	0.562760	+	0.562760i	0.930091	−	0.367330i	$-0.119728\pi$
$997$	17.7693	+	17.7693i	0.562760	+	0.562760i	−0.367330	+	0.930091i	$0.619728\pi$
$998$	−42.9908	−	42.9908i	−1.36085	−	1.36085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.f.a.242.8		16
3.2	odd	2	inner	405.2.f.a.242.1		16
5.3	odd	4	inner	405.2.f.a.323.1		16
9.2	odd	6		135.2.m.a.17.4		16
9.4	even	3		135.2.m.a.62.4		16
9.5	odd	6		45.2.l.a.2.1	✓	16
9.7	even	3		45.2.l.a.32.1	yes	16
15.8	even	4	inner	405.2.f.a.323.8		16
36.7	odd	6		720.2.cu.c.257.2		16
36.23	even	6		720.2.cu.c.497.4		16
45.2	even	12		675.2.q.a.368.1		16
45.4	even	6		675.2.q.a.332.1		16
45.7	odd	12		225.2.p.b.68.4		16
45.13	odd	12		135.2.m.a.8.4		16
45.14	odd	6		225.2.p.b.182.4		16
45.22	odd	12		675.2.q.a.143.1		16
45.23	even	12		45.2.l.a.38.1	yes	16
45.29	odd	6		675.2.q.a.557.1		16
45.32	even	12		225.2.p.b.218.4		16
45.34	even	6		225.2.p.b.32.4		16
45.38	even	12		135.2.m.a.98.4		16
45.43	odd	12		45.2.l.a.23.1	yes	16
180.23	odd	12		720.2.cu.c.353.2		16
180.43	even	12		720.2.cu.c.113.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.1	✓	16	9.5	odd	6
45.2.l.a.23.1	yes	16	45.43	odd	12
45.2.l.a.32.1	yes	16	9.7	even	3
45.2.l.a.38.1	yes	16	45.23	even	12
135.2.m.a.8.4		16	45.13	odd	12
135.2.m.a.17.4		16	9.2	odd	6
135.2.m.a.62.4		16	9.4	even	3
135.2.m.a.98.4		16	45.38	even	12
225.2.p.b.32.4		16	45.34	even	6
225.2.p.b.68.4		16	45.7	odd	12
225.2.p.b.182.4		16	45.14	odd	6
225.2.p.b.218.4		16	45.32	even	12
405.2.f.a.242.1		16	3.2	odd	2	inner
405.2.f.a.242.8		16	1.1	even	1	trivial
405.2.f.a.323.1		16	5.3	odd	4	inner
405.2.f.a.323.8		16	15.8	even	4	inner
675.2.q.a.143.1		16	45.22	odd	12
675.2.q.a.332.1		16	45.4	even	6
675.2.q.a.368.1		16	45.2	even	12
675.2.q.a.557.1		16	45.29	odd	6
720.2.cu.c.113.4		16	180.43	even	12
720.2.cu.c.257.2		16	36.7	odd	6
720.2.cu.c.353.2		16	180.23	odd	12
720.2.cu.c.497.4		16	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64237 - 1.64237i) q^{2} -3.39477i q^{4} +(-0.394116 - 2.20106i) q^{5} +(-0.550102 - 0.550102i) q^{7} +(-2.29074 - 2.29074i) q^{8} +(-4.26225 - 2.96768i) q^{10} -0.254252i q^{11} +(-2.71215 + 2.71215i) q^{13} -1.80695 q^{14} -0.734947 q^{16} +(3.93311 - 3.93311i) q^{17} +0.440377i q^{19} +(-7.47211 + 1.33793i) q^{20} +(-0.417576 - 0.417576i) q^{22} +(2.50550 + 2.50550i) q^{23} +(-4.68935 + 1.73495i) q^{25} +8.90871i q^{26} +(-1.86747 + 1.86747i) q^{28} +5.52530 q^{29} +0.194366 q^{31} +(3.37442 - 3.37442i) q^{32} -12.9193i q^{34} +(-0.994005 + 1.42761i) q^{35} +(-0.123005 - 0.123005i) q^{37} +(0.723262 + 0.723262i) q^{38} +(-4.13924 + 5.94488i) q^{40} +4.48282i q^{41} +(-0.977199 + 0.977199i) q^{43} -0.863127 q^{44} +8.22993 q^{46} +(-3.05520 + 3.05520i) q^{47} -6.39477i q^{49} +(-4.85222 + 10.5511i) q^{50} +(9.20713 + 9.20713i) q^{52} +(0.938022 + 0.938022i) q^{53} +(-0.559623 + 0.100205i) q^{55} +2.52028i q^{56} +(9.07460 - 9.07460i) q^{58} +8.04558 q^{59} +2.88371 q^{61} +(0.319221 - 0.319221i) q^{62} -12.5540i q^{64} +(7.03850 + 4.90070i) q^{65} +(9.49217 + 9.49217i) q^{67} +(-13.3520 - 13.3520i) q^{68} +(0.712146 + 3.97720i) q^{70} -2.15986i q^{71} +(-9.18432 + 9.18432i) q^{73} -0.404041 q^{74} +1.49498 q^{76} +(-0.139864 + 0.139864i) q^{77} +13.8251i q^{79} +(0.289654 + 1.61766i) q^{80} +(7.36245 + 7.36245i) q^{82} +(-3.80803 - 3.80803i) q^{83} +(-10.2071 - 7.10692i) q^{85} +3.20985i q^{86} +(-0.582424 + 0.582424i) q^{88} +0.285526 q^{89} +2.98392 q^{91} +(8.50561 - 8.50561i) q^{92} +10.0356i q^{94} +(0.969296 - 0.173559i) q^{95} +(-6.39477 - 6.39477i) q^{97} +(-10.5026 - 10.5026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70}+ \cdots - 56 q^{97}+O(q^{100}) \) 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Introduction

L-functions

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Varieties

Fields

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