LMFDB - Embedded newform 364.2.bq.a.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [364,2,Mod(121,364)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(364, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("364.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 364 = 2^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	364.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.90655463357$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 188 x^{14} - 49 x^{13} + 1116 x^{12} - x^{11} + 4649 x^{10} + \cdots + 16 $ x^18 - x^17 + 17x^16 - 6x^15 + 188x^14 - 49x^13 + 1116x^12 - x^11 + 4649x^10 + 106x^9 + 9589x^8 + 3532x^7 + 12349x^6 + 753x^5 + 2622x^4 - 883x^3 + 541x^2 - 92*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$0.893365 + 1.54735i$ of defining polynomial
Character	$\chi$	$=$	364.361
Dual form			364.2.bq.a.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.78673 q^{3} +(1.22316 - 0.706193i) q^{5} +(-0.507200 + 2.59668i) q^{7} +0.192402 q^{9} +1.67026i q^{11} +(2.45155 - 2.64384i) q^{13} +(-2.18546 + 1.26178i) q^{15} +(3.38930 + 5.87045i) q^{17} +5.66799i q^{19} +(0.906229 - 4.63956i) q^{21} +(0.576127 - 0.997882i) q^{23} +(-1.50258 + 2.60255i) q^{25} +5.01642 q^{27} +(1.79209 + 3.10400i) q^{29} +(4.45548 + 2.57238i) q^{31} -2.98431i q^{33} +(1.21337 + 3.53434i) q^{35} +(-4.91950 - 2.84027i) q^{37} +(-4.38026 + 4.72383i) q^{39} +(6.63082 - 3.82831i) q^{41} +(-2.20385 + 3.81717i) q^{43} +(0.235339 - 0.135873i) q^{45} +(-10.1613 + 5.86665i) q^{47} +(-6.48550 - 2.63407i) q^{49} +(-6.05577 - 10.4889i) q^{51} +(1.58494 - 2.74520i) q^{53} +(1.17953 + 2.04300i) q^{55} -10.1272i q^{57} +(6.77778 - 3.91315i) q^{59} +4.00570 q^{61} +(-0.0975863 + 0.499606i) q^{63} +(1.13158 - 4.96511i) q^{65} -13.7239i q^{67} +(-1.02938 + 1.78294i) q^{69} +(-2.78064 - 1.60540i) q^{71} +(-10.5543 - 6.09350i) q^{73} +(2.68471 - 4.65006i) q^{75} +(-4.33714 - 0.847158i) q^{77} +(-5.73321 - 9.93021i) q^{79} -9.54019 q^{81} +6.72074i q^{83} +(8.29133 + 4.78700i) q^{85} +(-3.20199 - 5.54600i) q^{87} +(6.22521 + 3.59413i) q^{89} +(5.62178 + 7.70685i) q^{91} +(-7.96075 - 4.59614i) q^{93} +(4.00269 + 6.93286i) q^{95} +(2.06757 + 1.19371i) q^{97} +0.321362i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} + q^{7} + 12 q^{9} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 7 q^{21} - 6 q^{23} + 5 q^{25} - 20 q^{27} + 2 q^{29} + 9 q^{31} + 3 q^{35} + 18 q^{37} + 11 q^{39} - 9 q^{41} - 14 q^{43} + 30 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) $ 18 * q - 2 * q^3 + q^7 + 12 * q^9 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 7 * q^21 - 6 * q^23 + 5 * q^25 - 20 * q^27 + 2 * q^29 + 9 * q^31 + 3 * q^35 + 18 * q^37 + 11 * q^39 - 9 * q^41 - 14 * q^43 + 30 * q^45 + 36 * q^47 - 11 * q^49 + 2 * q^51 - 13 * q^53 - q^55 - 42 * q^61 - 32 * q^63 + 30 * q^65 - q^69 - 45 * q^71 - 33 * q^73 + 25 * q^75 - 9 * q^77 - 14 * q^79 + 2 * q^81 - 30 * q^85 + 2 * q^87 - 9 * q^89 + 21 * q^93 + 30 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/364\mathbb{Z}\right)^\times$.

$n$	$157$	$183$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.78673			−1.03157			−0.515784	−	0.856718i	$-0.672499\pi$
$3$	−1.78673			−1.03157			−0.515784	+	0.856718i	$0.672499\pi$
$4$		0			0
$5$	1.22316	−	0.706193i	0.547015	−	0.315819i	−0.200902	−	0.979611i	$-0.564387\pi$
$5$	1.22316	−	0.706193i	0.547015	−	0.315819i	0.747917	+	0.663792i	$0.231054\pi$
$6$		0			0
$7$	−0.507200	+	2.59668i	−0.191704	+	0.981453i
$7$	−0.507200	+	2.59668i	−0.191704	+	0.981453i
$8$		0			0
$9$	0.192402			0.0641340
$10$		0			0
$11$			1.67026i			0.503604i	0.967779	+	0.251802i	$0.0810231\pi$
$11$			1.67026i			0.503604i	−0.967779	+	0.251802i	$0.918977\pi$
$12$		0			0
$13$	2.45155	−	2.64384i	0.679938	−	0.733270i
$13$	2.45155	−	2.64384i	0.679938	−	0.733270i
$14$		0			0
$15$	−2.18546	+	1.26178i	−0.564283	+	0.325789i
$16$		0			0
$17$	3.38930	+	5.87045i	0.822027	+	1.42379i	0.904170	+	0.427172i	$0.140490\pi$
$17$	3.38930	+	5.87045i	0.822027	+	1.42379i	−0.0821435	+	0.996621i	$0.526177\pi$
$18$		0			0
$19$			5.66799i			1.30033i	0.759795	+	0.650163i	$0.225299\pi$
$19$			5.66799i			1.30033i	−0.759795	+	0.650163i	$0.774701\pi$
$20$		0			0
$21$	0.906229	−	4.63956i	0.197755	−	1.01244i
$22$		0			0
$23$	0.576127	−	0.997882i	0.120131	−	0.208073i	−0.799688	−	0.600415i	$-0.795002\pi$
$23$	0.576127	−	0.997882i	0.120131	−	0.208073i	0.919819	+	0.392343i	$0.128335\pi$
$24$		0			0
$25$	−1.50258	+	2.60255i	−0.300517	+	0.520510i
$26$		0			0
$27$	5.01642			0.965410
$28$		0			0
$29$	1.79209	+	3.10400i	0.332784	+	0.576398i	0.983057	−	0.183303i	$-0.0586788\pi$
$29$	1.79209	+	3.10400i	0.332784	+	0.576398i	−0.650273	+	0.759701i	$0.725345\pi$
$30$		0			0
$31$	4.45548	+	2.57238i	0.800229	+	0.462012i	0.843551	−	0.537049i	$-0.180461\pi$
$31$	4.45548	+	2.57238i	0.800229	+	0.462012i	−0.0433224	+	0.999061i	$0.513794\pi$
$32$		0			0
$33$		−	2.98431i		−	0.519502i
$34$		0			0
$35$	1.21337	+	3.53434i	0.205097	+	0.597413i
$36$		0			0
$37$	−4.91950	−	2.84027i	−0.808761	−	0.466938i	0.0377646	−	0.999287i	$-0.487976\pi$
$37$	−4.91950	−	2.84027i	−0.808761	−	0.466938i	−0.846525	+	0.532348i	$0.821310\pi$
$38$		0			0
$39$	−4.38026	+	4.72383i	−0.701403	+	0.756418i
$40$		0			0
$41$	6.63082	−	3.82831i	1.03556	−	0.597881i	0.116987	−	0.993133i	$-0.462676\pi$
$41$	6.63082	−	3.82831i	1.03556	−	0.597881i	0.918572	+	0.395253i	$0.129343\pi$
$42$		0			0
$43$	−2.20385	+	3.81717i	−0.336083	+	0.582113i	−0.983692	−	0.179860i	$-0.942436\pi$
$43$	−2.20385	+	3.81717i	−0.336083	+	0.582113i	0.647609	+	0.761973i	$0.275769\pi$
$44$		0			0
$45$	0.235339	−	0.135873i	0.0350822	−	0.0202547i
$46$		0			0
$47$	−10.1613	+	5.86665i	−1.48218	+	0.855739i	−0.999796	−	0.0202189i	$-0.993564\pi$
$47$	−10.1613	+	5.86665i	−1.48218	+	0.855739i	−0.482388	+	0.875958i	$0.660230\pi$
$48$		0			0
$49$	−6.48550	−	2.63407i	−0.926499	−	0.376296i
$50$		0			0
$51$	−6.05577	−	10.4889i	−0.847977	−	1.46874i
$52$		0			0
$53$	1.58494	−	2.74520i	0.217708	−	0.377082i	−0.736399	−	0.676548i	$-0.763475\pi$
$53$	1.58494	−	2.74520i	0.217708	−	0.377082i	0.954107	+	0.299466i	$0.0968085\pi$
$54$		0			0
$55$	1.17953	+	2.04300i	0.159048	+	0.275478i
$56$		0			0
$57$		−	10.1272i		−	1.34137i
$58$		0			0
$59$	6.77778	−	3.91315i	0.882391	−	0.509449i	0.0109453	−	0.999940i	$-0.496516\pi$
$59$	6.77778	−	3.91315i	0.882391	−	0.509449i	0.871446	+	0.490491i	$0.163183\pi$
$60$		0			0
$61$	4.00570			0.512877			0.256439	−	0.966561i	$-0.417451\pi$
$61$	4.00570			0.512877			0.256439	+	0.966561i	$0.417451\pi$
$62$		0			0
$63$	−0.0975863	+	0.499606i	−0.0122947	+	0.0629445i
$64$		0			0
$65$	1.13158	−	4.96511i	0.140356	−	0.615846i
$66$		0			0
$67$		−	13.7239i		−	1.67664i	−0.545175	−	0.838322i	$-0.683537\pi$
$67$		−	13.7239i		−	1.67664i	0.545175	−	0.838322i	$-0.316463\pi$
$68$		0			0
$69$	−1.02938	+	1.78294i	−0.123923	+	0.214641i
$70$		0			0
$71$	−2.78064	−	1.60540i	−0.330001	−	0.190526i	0.325841	−	0.945425i	$-0.394353\pi$
$71$	−2.78064	−	1.60540i	−0.330001	−	0.190526i	−0.655841	+	0.754899i	$0.727686\pi$
$72$		0			0
$73$	−10.5543	−	6.09350i	−1.23528	−	0.713190i	−0.267156	−	0.963653i	$-0.586084\pi$
$73$	−10.5543	−	6.09350i	−1.23528	−	0.713190i	−0.968126	+	0.250463i	$0.919417\pi$
$74$		0			0
$75$	2.68471	−	4.65006i	0.310004	−	0.536942i
$76$		0			0
$77$	−4.33714	−	0.847158i	−0.494263	−	0.0965426i
$78$		0			0
$79$	−5.73321	−	9.93021i	−0.645037	−	1.11724i	−0.984293	−	0.176542i	$-0.943509\pi$
$79$	−5.73321	−	9.93021i	−0.645037	−	1.11724i	0.339256	−	0.940694i	$-0.389825\pi$
$80$		0			0
$81$	−9.54019			−1.06002
$82$		0			0
$83$			6.72074i			0.737697i	0.929490	+	0.368848i	$0.120248\pi$
$83$			6.72074i			0.737697i	−0.929490	+	0.368848i	$0.879752\pi$
$84$		0			0
$85$	8.29133	+	4.78700i	0.899321	+	0.519223i
$86$		0			0
$87$	−3.20199	−	5.54600i	−0.343289	−	0.594594i
$88$		0			0
$89$	6.22521	+	3.59413i	0.659871	+	0.380977i	0.792228	−	0.610225i	$-0.208921\pi$
$89$	6.22521	+	3.59413i	0.659871	+	0.380977i	−0.132357	+	0.991202i	$0.542254\pi$
$90$		0			0
$91$	5.62178	+	7.70685i	0.589323	+	0.807898i
$92$		0			0
$93$	−7.96075	−	4.59614i	−0.825491	−	0.476597i
$94$		0			0
$95$	4.00269	+	6.93286i	0.410667	+	0.711297i
$96$		0			0
$97$	2.06757	+	1.19371i	0.209930	+	0.121203i	0.601279	−	0.799039i	$-0.294658\pi$
$97$	2.06757	+	1.19371i	0.209930	+	0.121203i	−0.391349	+	0.920242i	$0.627991\pi$
$98$		0			0
$99$			0.321362i			0.0322981i
$100$		0			0
$101$	9.95283			0.990344			0.495172	−	0.868795i	$-0.335105\pi$
$101$	9.95283			0.990344			0.495172	+	0.868795i	$0.335105\pi$
$102$		0			0
$103$	−7.36258	−	12.7524i	−0.725456	−	1.25653i	−0.958786	−	0.284130i	$-0.908295\pi$
$103$	−7.36258	−	12.7524i	−0.725456	−	1.25653i	0.233330	−	0.972398i	$-0.425038\pi$
$104$		0			0
$105$	−2.16796	−	6.31491i	−0.211571	−	0.616272i
$106$		0			0
$107$	−0.521717	+	0.903640i	−0.0504362	+	0.0873581i	−0.890141	−	0.455685i	$-0.849395\pi$
$107$	−0.521717	+	0.903640i	−0.0504362	+	0.0873581i	0.839705	+	0.543043i	$0.182728\pi$
$108$		0			0
$109$	10.2335	+	5.90829i	0.980188	+	0.565912i	0.902327	−	0.431052i	$-0.141858\pi$
$109$	10.2335	+	5.90829i	0.980188	+	0.565912i	0.0778611	+	0.996964i	$0.475191\pi$
$110$		0			0
$111$	8.78981	+	5.07480i	0.834292	+	0.481679i
$112$		0			0
$113$	−7.69833	+	13.3339i	−0.724198	+	1.25435i	0.235105	+	0.971970i	$0.424457\pi$
$113$	−7.69833	+	13.3339i	−0.724198	+	1.25435i	−0.959303	+	0.282378i	$0.908877\pi$
$114$		0			0
$115$		−	1.62743i		−	0.151758i
$116$		0			0
$117$	0.471683	−	0.508680i	0.0436071	−	0.0470275i
$118$		0			0
$119$	−16.9627	+	5.82345i	−1.55497	+	0.533835i
$120$		0			0
$121$	8.21022			0.746383
$122$		0			0
$123$	−11.8475	+	6.84015i	−1.06825	+	0.616755i
$124$		0			0
$125$			11.3064i			1.01127i
$126$		0			0
$127$	−0.493081	−	0.854041i	−0.0437538	−	0.0757839i	0.843319	−	0.537413i	$-0.180598\pi$
$127$	−0.493081	−	0.854041i	−0.0437538	−	0.0757839i	−0.887073	+	0.461629i	$0.847265\pi$
$128$		0			0
$129$	3.93767	−	6.82025i	0.346693	−	0.600490i
$130$		0			0
$131$	6.30826	+	10.9262i	0.551155	+	0.954629i	0.998192	+	0.0601131i	$0.0191461\pi$
$131$	6.30826	+	10.9262i	0.551155	+	0.954629i	−0.447036	+	0.894516i	$0.647521\pi$
$132$		0			0
$133$	−14.7179	−	2.87480i	−1.27621	−	0.249277i
$134$		0			0
$135$	6.13589	−	3.54256i	0.528093	−	0.304895i
$136$		0			0
$137$	−16.0896	+	9.28931i	−1.37462	+	0.793639i	−0.991506	−	0.130060i	$-0.958483\pi$
$137$	−16.0896	+	9.28931i	−1.37462	+	0.793639i	−0.383118	+	0.923700i	$0.625150\pi$
$138$		0			0
$139$	4.75252	−	8.23161i	0.403104	−	0.698196i	−0.590995	−	0.806675i	$-0.701265\pi$
$139$	4.75252	−	8.23161i	0.403104	−	0.698196i	0.994099	+	0.108479i	$0.0345981\pi$
$140$		0			0
$141$	18.1556	−	10.4821i	1.52897	−	0.882753i
$142$		0			0
$143$	4.41591	+	4.09474i	0.369277	+	0.342419i
$144$		0			0
$145$	4.38404	+	2.53113i	0.364075	+	0.210199i
$146$		0			0
$147$	11.5878	+	4.70638i	0.955748	+	0.388175i
$148$		0			0
$149$		−	1.88358i		−	0.154309i	−0.997019	−	0.0771545i	$-0.975417\pi$
$149$		−	1.88358i		−	0.154309i	0.997019	−	0.0771545i	$-0.0245835\pi$
$150$		0			0
$151$	−1.44355	−	0.833432i	−0.117474	−	0.0678238i	0.440112	−	0.897943i	$-0.354939\pi$
$151$	−1.44355	−	0.833432i	−0.117474	−	0.0678238i	−0.557586	+	0.830119i	$0.688272\pi$
$152$		0			0
$153$	0.652109	+	1.12949i	0.0527199	+	0.0913135i
$154$		0			0
$155$	7.26637			0.583649
$156$		0			0
$157$	4.81241	−	8.33535i	0.384072	−	0.665233i	−0.607568	−	0.794268i	$-0.707855\pi$
$157$	4.81241	−	8.33535i	0.384072	−	0.665233i	0.991640	+	0.129035i	$0.0411880\pi$
$158$		0			0
$159$	−2.83186	+	4.90492i	−0.224581	+	0.388986i
$160$		0			0
$161$	2.29897	+	2.00214i	0.181184	+	0.157791i
$162$		0			0
$163$		−	2.81545i		−	0.220523i	−0.993903	−	0.110262i	$-0.964831\pi$
$163$		−	2.81545i		−	0.220523i	0.993903	−	0.110262i	$-0.0351688\pi$
$164$		0			0
$165$	−2.10750	−	3.65029i	−0.164068	−	0.284175i
$166$		0			0
$167$	3.82773	−	2.20994i	0.296198	−	0.171010i	−0.344535	−	0.938773i	$-0.611964\pi$
$167$	3.82773	−	2.20994i	0.296198	−	0.171010i	0.640734	+	0.767763i	$0.278630\pi$
$168$		0			0
$169$	−0.979788	−	12.9630i	−0.0753683	−	0.997156i
$170$		0			0
$171$			1.09053i			0.0833950i
$172$		0			0
$173$	18.5093			1.40723			0.703617	−	0.710580i	$-0.251567\pi$
$173$	18.5093			1.40723			0.703617	+	0.710580i	$0.251567\pi$
$174$		0			0
$175$	−5.99588	−	5.22174i	−0.453246	−	0.394727i
$176$		0			0
$177$	−12.1101	+	6.99174i	−0.910247	+	0.525532i
$178$		0			0
$179$	−5.98312			−0.447200			−0.223600	−	0.974681i	$-0.571781\pi$
$179$	−5.98312			−0.447200			−0.223600	+	0.974681i	$0.571781\pi$
$180$		0			0
$181$	−2.08148			−0.154715			−0.0773575	−	0.997003i	$-0.524648\pi$
$181$	−2.08148			−0.154715			−0.0773575	+	0.997003i	$0.524648\pi$
$182$		0			0
$183$	−7.15710			−0.529068
$184$		0			0
$185$	−8.02312			−0.589872
$186$		0			0
$187$	−9.80520	+	5.66103i	−0.717027	+	0.413976i
$188$		0			0
$189$	−2.54433	+	13.0260i	−0.185073	+	0.947504i
$190$		0			0
$191$	26.0882			1.88768			0.943838	−	0.330408i	$-0.107186\pi$
$191$	26.0882			1.88768			0.943838	+	0.330408i	$0.107186\pi$
$192$		0			0
$193$			13.4469i			0.967930i	0.875087	+	0.483965i	$0.160804\pi$
$193$			13.4469i			0.967930i	−0.875087	+	0.483965i	$0.839196\pi$
$194$		0			0
$195$	−2.02183	+	8.87131i	−0.144786	+	0.635288i
$196$		0			0
$197$	4.44601	−	2.56691i	0.316765	−	0.182885i	−0.333184	−	0.942862i	$-0.608123\pi$
$197$	4.44601	−	2.56691i	0.316765	−	0.182885i	0.649950	+	0.759977i	$0.274790\pi$
$198$		0			0
$199$	−9.31361	−	16.1316i	−0.660224	−	1.14354i	−0.980556	−	0.196237i	$-0.937128\pi$
$199$	−9.31361	−	16.1316i	−0.660224	−	1.14354i	0.320332	−	0.947305i	$-0.396206\pi$
$200$		0			0
$201$			24.5209i			1.72957i
$202$		0			0
$203$	−8.96904	+	3.07915i	−0.629503	+	0.216114i
$204$		0			0
$205$	5.40704	−	9.36527i	0.377644	−	0.654099i
$206$		0			0
$207$	0.110848	−	0.191994i	0.00770447	−	0.0133445i
$208$		0			0
$209$	−9.46703			−0.654848
$210$		0			0
$211$	0.720035	+	1.24714i	0.0495692	+	0.0858564i	0.889745	−	0.456457i	$-0.150882\pi$
$211$	0.720035	+	1.24714i	0.0495692	+	0.0858564i	−0.840176	+	0.542314i	$0.817548\pi$
$212$		0			0
$213$	4.96824	+	2.86842i	0.340418	+	0.196541i
$214$		0			0
$215$			6.22536i			0.424566i
$216$		0			0
$217$	−8.93946	+	10.2648i	−0.606850	+	0.696817i
$218$		0			0
$219$	18.8576	+	10.8874i	1.27428	+	0.735705i
$220$		0			0
$221$	23.8296	+	5.43092i	1.60295	+	0.365323i
$222$		0			0
$223$	0.263960	−	0.152397i	0.0176761	−	0.0102053i	−0.491136	−	0.871083i	$-0.663418\pi$
$223$	0.263960	−	0.152397i	0.0176761	−	0.0102053i	0.508812	+	0.860878i	$0.330085\pi$
$224$		0			0
$225$	−0.289100	+	0.500736i	−0.0192733	+	0.0333824i
$226$		0			0
$227$	2.18239	−	1.26001i	0.144851	−	0.0836295i	−0.425823	−	0.904806i	$-0.640015\pi$
$227$	2.18239	−	1.26001i	0.144851	−	0.0836295i	0.570674	+	0.821177i	$0.306682\pi$
$228$		0			0
$229$	−6.36123	+	3.67266i	−0.420362	+	0.242696i	−0.695232	−	0.718785i	$-0.744698\pi$
$229$	−6.36123	+	3.67266i	−0.420362	+	0.242696i	0.274870	+	0.961481i	$0.411365\pi$
$230$		0			0
$231$	7.74930	+	1.51364i	0.509866	+	0.0995904i
$232$		0			0
$233$	−12.2428	−	21.2052i	−0.802053	−	1.38920i	−0.918262	−	0.395973i	$-0.870408\pi$
$233$	−12.2428	−	21.2052i	−0.802053	−	1.38920i	0.116209	−	0.993225i	$-0.462926\pi$
$234$		0			0
$235$	−8.28597	+	14.3517i	−0.540517	+	0.936203i
$236$		0			0
$237$	10.2437	+	17.7426i	0.665400	+	1.15251i
$238$		0			0
$239$		−	1.44381i		−	0.0933922i	−0.998909	−	0.0466961i	$-0.985131\pi$
$239$		−	1.44381i		−	0.0933922i	0.998909	−	0.0466961i	$-0.0148692\pi$
$240$		0			0
$241$	−9.51138	+	5.49140i	−0.612682	+	0.353732i	−0.774014	−	0.633168i	$-0.781754\pi$
$241$	−9.51138	+	5.49140i	−0.612682	+	0.353732i	0.161333	+	0.986900i	$0.448421\pi$
$242$		0			0
$243$	1.99648			0.128074
$244$		0			0
$245$	−9.79297	+	1.35811i	−0.625650	+	0.0867666i
$246$		0			0
$247$	14.9853	+	13.8954i	0.953489	+	0.884141i
$248$		0			0
$249$		−	12.0081i		−	0.760985i
$250$		0			0
$251$	8.01603	−	13.8842i	0.505967	−	0.876361i	−0.494009	−	0.869457i	$-0.664469\pi$
$251$	8.01603	−	13.8842i	0.505967	−	0.876361i	0.999976	−	0.00690401i	$-0.00219763\pi$
$252$		0			0
$253$	1.66673	+	0.962284i	0.104786	+	0.0604983i
$254$		0			0
$255$	−14.8144	−	8.55308i	−0.927712	−	0.535615i
$256$		0			0
$257$	13.7003	−	23.7296i	0.854600	−	1.48021i	−0.0224155	−	0.999749i	$-0.507136\pi$
$257$	13.7003	−	23.7296i	0.854600	−	1.48021i	0.877016	−	0.480462i	$-0.159531\pi$
$258$		0			0
$259$	9.87045	−	11.3338i	0.613320	−	0.704247i
$260$		0			0
$261$	0.344802	+	0.597215i	0.0213427	+	0.0369667i
$262$		0			0
$263$	20.2007			1.24563			0.622814	−	0.782370i	$-0.285989\pi$
$263$	20.2007			1.24563			0.622814	+	0.782370i	$0.285989\pi$
$264$		0			0
$265$		−	4.47709i		−	0.275026i
$266$		0			0
$267$	−11.1228	−	6.42174i	−0.680703	−	0.393004i
$268$		0			0
$269$	4.54691	+	7.87548i	0.277230	+	0.480176i	0.970695	−	0.240314i	$-0.0772503\pi$
$269$	4.54691	+	7.87548i	0.277230	+	0.480176i	−0.693465	+	0.720490i	$0.743917\pi$
$270$		0			0
$271$	1.56769	+	0.905105i	0.0952303	+	0.0549812i	0.546859	−	0.837225i	$-0.315823\pi$
$271$	1.56769	+	0.905105i	0.0952303	+	0.0549812i	−0.451629	+	0.892206i	$0.649157\pi$
$272$		0			0
$273$	−10.0446	−	13.7701i	−0.607927	−	0.833402i
$274$		0			0
$275$	−4.34695	−	2.50971i	−0.262131	−	0.151341i
$276$		0			0
$277$	4.04743	+	7.01035i	0.243186	+	0.421211i	0.961620	−	0.274384i	$-0.0884740\pi$
$277$	4.04743	+	7.01035i	0.243186	+	0.421211i	−0.718434	+	0.695595i	$0.755141\pi$
$278$		0			0
$279$	0.857244	+	0.494930i	0.0513218	+	0.0296307i
$280$		0			0
$281$			16.0935i			0.960059i	0.877252	+	0.480030i	$0.159374\pi$
$281$			16.0935i			0.960059i	−0.877252	+	0.480030i	$0.840626\pi$
$282$		0			0
$283$	11.1911			0.665242			0.332621	−	0.943061i	$-0.392067\pi$
$283$	11.1911			0.665242			0.332621	+	0.943061i	$0.392067\pi$
$284$		0			0
$285$	−7.15173	−	12.3872i	−0.423632	−	0.733752i
$286$		0			0
$287$	6.57773	+	19.1598i	0.388271	+	1.13097i
$288$		0			0
$289$	−14.4748	+	25.0710i	−0.851457	+	1.47477i
$290$		0			0
$291$	−3.69419	−	2.13284i	−0.216557	−	0.125029i
$292$		0			0
$293$	−12.9552	−	7.47966i	−0.756848	−	0.436967i	0.0713148	−	0.997454i	$-0.477281\pi$
$293$	−12.9552	−	7.47966i	−0.756848	−	0.436967i	−0.828163	+	0.560487i	$0.810614\pi$
$294$		0			0
$295$	5.52688	−	9.57283i	0.321787	−	0.557352i
$296$		0			0
$297$			8.37874i			0.486184i
$298$		0			0
$299$	−1.22583	−	3.96955i	−0.0708918	−	0.229565i
$300$		0			0
$301$	−8.79418	−	7.65875i	−0.506888	−	0.441443i
$302$		0			0
$303$	−17.7830			−1.02161
$304$		0			0
$305$	4.89962	−	2.82880i	0.280551	−	0.161976i
$306$		0			0
$307$		−	10.4783i		−	0.598030i	−0.954248	−	0.299015i	$-0.903342\pi$
$307$		−	10.4783i		−	0.598030i	0.954248	−	0.299015i	$-0.0966581\pi$
$308$		0			0
$309$	13.1549	+	22.7850i	0.748358	+	1.29619i
$310$		0			0
$311$	4.83914	−	8.38164i	0.274403	−	0.475279i	−0.695582	−	0.718447i	$-0.744853\pi$
$311$	4.83914	−	8.38164i	0.274403	−	0.475279i	0.969984	+	0.243168i	$0.0781866\pi$
$312$		0			0
$313$	−15.7678	−	27.3106i	−0.891247	−	1.54368i	−0.838382	−	0.545083i	$-0.816498\pi$
$313$	−15.7678	−	27.3106i	−0.891247	−	1.54368i	−0.0528647	−	0.998602i	$-0.516835\pi$
$314$		0			0
$315$	0.233454	+	0.680014i	0.0131537	+	0.0383144i
$316$		0			0
$317$	1.93778	−	1.11878i	0.108836	−	0.0628367i	−0.444594	−	0.895732i	$-0.646652\pi$
$317$	1.93778	−	1.11878i	0.108836	−	0.0628367i	0.553430	+	0.832896i	$0.313319\pi$
$318$		0			0
$319$	−5.18450	+	2.99327i	−0.290276	+	0.167591i
$320$		0			0
$321$	0.932166	−	1.61456i	0.0520284	−	0.0901159i
$322$		0			0
$323$	−33.2736	+	19.2105i	−1.85139	+	1.06890i
$324$		0			0
$325$	3.19707	+	10.3529i	0.177342	+	0.574275i
$326$		0			0
$327$	−18.2844	−	10.5565i	−1.01113	−	0.583777i
$328$		0			0
$329$	−10.0800	−	29.3613i	−0.555727	−	1.61874i
$330$		0			0
$331$		−	21.0554i		−	1.15731i	−0.815572	−	0.578656i	$-0.803577\pi$
$331$		−	21.0554i		−	1.15731i	0.815572	−	0.578656i	$-0.196423\pi$
$332$		0			0
$333$	−0.946521	−	0.546474i	−0.0518690	−	0.0299466i
$334$		0			0
$335$	−9.69174	−	16.7866i	−0.529516	−	0.917149i
$336$		0			0
$337$	24.6487			1.34270			0.671349	−	0.741141i	$-0.265715\pi$
$337$	24.6487			1.34270			0.671349	+	0.741141i	$0.265715\pi$
$338$		0			0
$339$	13.7548	−	23.8241i	0.747060	−	1.29395i
$340$		0			0
$341$	−4.29655	+	7.44184i	−0.232671	+	0.402998i
$342$		0			0
$343$	10.1293	−	15.5048i	0.546930	−	0.837178i
$344$		0			0
$345$			2.90777i			0.156549i
$346$		0			0
$347$	−16.8055	−	29.1080i	−0.902167	−	1.56260i	−0.824676	−	0.565606i	$-0.808642\pi$
$347$	−16.8055	−	29.1080i	−0.902167	−	1.56260i	−0.0774912	−	0.996993i	$-0.524691\pi$
$348$		0			0
$349$	−2.46776	+	1.42476i	−0.132096	+	0.0762658i	−0.564592	−	0.825370i	$-0.690966\pi$
$349$	−2.46776	+	1.42476i	−0.132096	+	0.0762658i	0.432496	+	0.901636i	$0.357633\pi$
$350$		0			0
$351$	12.2980	−	13.2626i	0.656419	−	0.707906i
$352$		0			0
$353$			28.5979i			1.52211i	0.648685	+	0.761057i	$0.275319\pi$
$353$			28.5979i			1.52211i	−0.648685	+	0.761057i	$0.724681\pi$
$354$		0			0
$355$	−4.53489			−0.240687
$356$		0			0
$357$	30.3078	−	10.4049i	1.60406	−	0.550687i
$358$		0			0
$359$	−2.32566	+	1.34272i	−0.122743	+	0.0708660i	−0.560115	−	0.828415i	$-0.689243\pi$
$359$	−2.32566	+	1.34272i	−0.122743	+	0.0708660i	0.437371	+	0.899281i	$0.355910\pi$
$360$		0			0
$361$	−13.1261			−0.690846
$362$		0			0
$363$	−14.6694			−0.769946
$364$		0			0
$365$	−17.2127			−0.900956
$366$		0			0
$367$	1.13963			0.0594884			0.0297442	−	0.999558i	$-0.490531\pi$
$367$	1.13963			0.0594884			0.0297442	+	0.999558i	$0.490531\pi$
$368$		0			0
$369$	1.27578	−	0.736573i	0.0664146	−	0.0383445i
$370$		0			0
$371$	6.32452	+	5.50795i	0.328353	+	0.285958i
$372$		0			0
$373$	−23.0729			−1.19467			−0.597334	−	0.801993i	$-0.703773\pi$
$373$	−23.0729			−1.19467			−0.597334	+	0.801993i	$0.703773\pi$
$374$		0			0
$375$		−	20.2014i		−	1.04320i
$376$		0			0
$377$	12.5999	+	2.87160i	0.648927	+	0.147895i
$378$		0			0
$379$	−15.5083	+	8.95374i	−0.796609	+	0.459923i	−0.842284	−	0.539034i	$-0.818789\pi$
$379$	−15.5083	+	8.95374i	−0.796609	+	0.459923i	0.0456749	+	0.998956i	$0.485456\pi$
$380$		0			0
$381$	0.881002	+	1.52594i	0.0451351	+	0.0781763i
$382$		0			0
$383$			35.3019i			1.80384i	0.431899	+	0.901922i	$0.357844\pi$
$383$			35.3019i			1.80384i	−0.431899	+	0.901922i	$0.642156\pi$
$384$		0			0
$385$	−5.90328	+	2.02665i	−0.300859	+	0.103287i
$386$		0			0
$387$	−0.424024	+	0.734431i	−0.0215544	+	0.0373332i
$388$		0			0
$389$	15.9362	−	27.6023i	0.807999	−	1.39949i	−0.106249	−	0.994340i	$-0.533884\pi$
$389$	15.9362	−	27.6023i	0.807999	−	1.39949i	0.914248	−	0.405155i	$-0.132782\pi$
$390$		0			0
$391$	7.81068			0.395003
$392$		0			0
$393$	−11.2712	−	19.5222i	−0.568555	−	0.984765i
$394$		0			0
$395$	−14.0253	−	8.09750i	−0.705689	−	0.407430i
$396$		0			0
$397$			8.89935i			0.446646i	0.974745	+	0.223323i	$0.0716904\pi$
$397$			8.89935i			0.446646i	−0.974745	+	0.223323i	$0.928310\pi$
$398$		0			0
$399$	26.2970	+	5.13650i	1.31650	+	0.257146i
$400$		0			0
$401$	−7.84908	−	4.53167i	−0.391964	−	0.226301i	0.291047	−	0.956709i	$-0.405997\pi$
$401$	−7.84908	−	4.53167i	−0.391964	−	0.226301i	−0.683011	+	0.730408i	$0.739330\pi$
$402$		0			0
$403$	17.7238	−	5.47328i	0.882886	−	0.272644i
$404$		0			0
$405$	−11.6692	+	6.73721i	−0.579847	+	0.334775i
$406$		0			0
$407$	4.74401	−	8.21686i	0.235152	−	0.407295i
$408$		0			0
$409$	−10.2498	+	5.91773i	−0.506820	+	0.292613i	−0.731526	−	0.681814i	$-0.761191\pi$
$409$	−10.2498	+	5.91773i	−0.506820	+	0.292613i	0.224705	+	0.974427i	$0.427858\pi$
$410$		0			0
$411$	28.7477	−	16.5975i	1.41802	−	0.818694i
$412$		0			0
$413$	6.72351	+	19.5845i	0.330842	+	0.963689i
$414$		0			0
$415$	4.74614	+	8.22055i	0.232979	+	0.403531i
$416$		0			0
$417$	−8.49147	+	14.7077i	−0.415829	+	0.720237i
$418$		0			0
$419$	−8.87793	−	15.3770i	−0.433715	−	0.751217i	0.563475	−	0.826133i	$-0.309464\pi$
$419$	−8.87793	−	15.3770i	−0.433715	−	0.751217i	−0.997190	+	0.0749167i	$0.976131\pi$
$420$		0			0
$421$		−	22.6045i		−	1.10168i	−0.834612	−	0.550838i	$-0.814308\pi$
$421$		−	22.6045i		−	1.10168i	0.834612	−	0.550838i	$-0.185692\pi$
$422$		0			0
$423$	−1.95506	+	1.12875i	−0.0950583	+	0.0548819i
$424$		0			0
$425$	−20.3709			−0.988131
$426$		0			0
$427$	−2.03169	+	10.4015i	−0.0983204	+	0.503365i
$428$		0			0
$429$	−7.89004	−	7.31619i	−0.380935	−	0.353229i
$430$		0			0
$431$		−	21.0750i		−	1.01515i	−0.861609	−	0.507573i	$-0.830543\pi$
$431$		−	21.0750i		−	1.01515i	0.861609	−	0.507573i	$-0.169457\pi$
$432$		0			0
$433$	−12.8663	+	22.2851i	−0.618316	+	1.07095i	0.371477	+	0.928442i	$0.378851\pi$
$433$	−12.8663	+	22.2851i	−0.618316	+	1.07095i	−0.989793	+	0.142512i	$0.954482\pi$
$434$		0			0
$435$	−7.83310	−	4.52244i	−0.375568	−	0.216834i
$436$		0			0
$437$	5.65598	+	3.26548i	0.270562	+	0.156209i
$438$		0			0
$439$	15.8732	−	27.4931i	0.757585	−	1.31218i	−0.186494	−	0.982456i	$-0.559712\pi$
$439$	15.8732	−	27.4931i	0.757585	−	1.31218i	0.944079	−	0.329720i	$-0.106954\pi$
$440$		0			0
$441$	−1.24782	−	0.506801i	−0.0594201	−	0.0241334i
$442$		0			0
$443$	9.91818	+	17.1788i	0.471227	+	0.816189i	0.999458	−	0.0329114i	$-0.0104779\pi$
$443$	9.91818	+	17.1788i	0.471227	+	0.816189i	−0.528231	+	0.849101i	$0.677145\pi$
$444$		0			0
$445$	10.1526			0.481279
$446$		0			0
$447$			3.36545i			0.159180i
$448$		0			0
$449$	−15.2765	−	8.81989i	−0.720942	−	0.416236i	0.0941570	−	0.995557i	$-0.469984\pi$
$449$	−15.2765	−	8.81989i	−0.720942	−	0.416236i	−0.815099	+	0.579321i	$0.803318\pi$
$450$		0			0
$451$	6.39428	+	11.0752i	0.301095	+	0.521512i
$452$		0			0
$453$	2.57923	+	1.48912i	0.121183	+	0.0699649i
$454$		0			0
$455$	12.3189	+	5.45666i	0.577518	+	0.255812i
$456$		0			0
$457$	23.1212	+	13.3490i	1.08156	+	0.624441i	0.931318	−	0.364207i	$-0.118660\pi$
$457$	23.1212	+	13.3490i	1.08156	+	0.624441i	0.150246	+	0.988649i	$0.451993\pi$
$458$		0			0
$459$	17.0022	+	29.4486i	0.793593	+	1.37454i
$460$		0			0
$461$	3.64848	+	2.10645i	0.169927	+	0.0981071i	0.582551	−	0.812794i	$-0.302055\pi$
$461$	3.64848	+	2.10645i	0.169927	+	0.0981071i	−0.412625	+	0.910901i	$0.635388\pi$
$462$		0			0
$463$			34.4422i			1.60067i	0.599556	+	0.800333i	$0.295344\pi$
$463$			34.4422i			1.60067i	−0.599556	+	0.800333i	$0.704656\pi$
$464$		0			0
$465$	−12.9830			−0.602074
$466$		0			0
$467$	−13.4413	−	23.2810i	−0.621988	−	1.07732i	−0.989115	−	0.147144i	$-0.952992\pi$
$467$	−13.4413	−	23.2810i	−0.621988	−	1.07732i	0.367127	−	0.930171i	$-0.380342\pi$
$468$		0			0
$469$	35.6367	+	6.96078i	1.64555	+	0.321419i
$470$		0			0
$471$	−8.59848	+	14.8930i	−0.396197	+	0.686234i
$472$		0			0
$473$	−6.37568	−	3.68100i	−0.293154	−	0.169253i
$474$		0			0
$475$	−14.7512	−	8.51662i	−0.676833	−	0.390770i
$476$		0			0
$477$	0.304946	−	0.528181i	0.0139625	−	0.0241838i
$478$		0			0
$479$			35.5745i			1.62544i	0.582654	+	0.812720i	$0.302014\pi$
$479$			35.5745i			1.62544i	−0.582654	+	0.812720i	$0.697986\pi$
$480$		0			0
$481$	−19.5696	+	6.04329i	−0.892299	+	0.275550i
$482$		0			0
$483$	−4.10763	−	3.57729i	−0.186904	−	0.162772i
$484$		0			0
$485$	3.37197			0.153113
$486$		0			0
$487$	21.6293	−	12.4877i	0.980117	−	0.565871i	0.0778114	−	0.996968i	$-0.475207\pi$
$487$	21.6293	−	12.4877i	0.980117	−	0.565871i	0.902305	+	0.431097i	$0.141873\pi$
$488$		0			0
$489$			5.03045i			0.227485i
$490$		0			0
$491$	18.6406	+	32.2865i	0.841240	+	1.45707i	0.888847	+	0.458205i	$0.151507\pi$
$491$	18.6406	+	32.2865i	0.841240	+	1.45707i	−0.0476065	+	0.998866i	$0.515159\pi$
$492$		0			0
$493$	−12.1479	+	21.0408i	−0.547114	+	0.947629i
$494$		0			0
$495$	0.226944	+	0.393078i	0.0102004	+	0.0176675i
$496$		0			0
$497$	5.57905	−	6.40616i	0.250255	−	0.287356i
$498$		0			0
$499$	−2.60298	+	1.50283i	−0.116525	+	0.0672759i	−0.557130	−	0.830425i	$-0.688097\pi$
$499$	−2.60298	+	1.50283i	−0.116525	+	0.0672759i	0.440605	+	0.897701i	$0.354764\pi$
$500$		0			0
$501$	−6.83911	+	3.94856i	−0.305549	+	0.176409i
$502$		0			0
$503$	6.70811	−	11.6188i	0.299100	−	0.518056i	−0.676831	−	0.736139i	$-0.736647\pi$
$503$	6.70811	−	11.6188i	0.299100	−	0.518056i	0.975930	+	0.218083i	$0.0699804\pi$
$504$		0			0
$505$	12.1739	−	7.02862i	0.541733	−	0.312769i
$506$		0			0
$507$	1.75062	+	23.1614i	0.0777476	+	1.02863i
$508$		0			0
$509$	36.1416	+	20.8664i	1.60195	+	0.924886i	0.991097	+	0.133143i	$0.0425068\pi$
$509$	36.1416	+	20.8664i	1.60195	+	0.924886i	0.610853	+	0.791744i	$0.290827\pi$
$510$		0			0
$511$	21.1760	−	24.3154i	0.936771	−	1.07565i
$512$		0			0
$513$			28.4330i			1.25535i
$514$		0			0
$515$	−18.0112	−	10.3988i	−0.793670	−	0.458226i
$516$		0			0
$517$	−9.79886	−	16.9721i	−0.430953	−	0.746433i
$518$		0			0
$519$	−33.0710			−1.45166
$520$		0			0
$521$	−10.2284	+	17.7161i	−0.448115	+	0.776158i	−0.998263	−	0.0589091i	$-0.981238\pi$
$521$	−10.2284	+	17.7161i	−0.448115	+	0.776158i	0.550148	+	0.835067i	$0.314571\pi$
$522$		0			0
$523$	1.30125	−	2.25383i	0.0568996	−	0.0985529i	−0.836173	−	0.548466i	$-0.815212\pi$
$523$	1.30125	−	2.25383i	0.0568996	−	0.0985529i	0.893072	+	0.449913i	$0.148545\pi$
$524$		0			0
$525$	10.7130	+	9.32984i	0.467555	+	0.407188i
$526$		0			0
$527$			34.8742i			1.51915i
$528$		0			0
$529$	10.8362	+	18.7688i	0.471137	+	0.816034i
$530$		0			0
$531$	1.30406	−	0.752898i	0.0565913	−	0.0326730i
$532$		0			0
$533$	6.13437	−	26.9161i	0.265709	−	1.16587i
$534$		0			0
$535$			1.47373i			0.0637149i
$536$		0			0
$537$	10.6902			0.461317
$538$		0			0
$539$	4.39960	−	10.8325i	0.189504	−	0.466588i
$540$		0			0
$541$	−12.7573	+	7.36542i	−0.548478	+	0.316664i	−0.748508	−	0.663126i	$-0.769229\pi$
$541$	−12.7573	+	7.36542i	−0.548478	+	0.316664i	0.200030	+	0.979790i	$0.435896\pi$
$542$		0			0
$543$	3.71904			0.159599
$544$		0			0
$545$	16.6896			0.714903
$546$		0			0
$547$	−0.154082			−0.00658808			−0.00329404	−	0.999995i	$-0.501049\pi$
$547$	−0.154082			−0.00658808			−0.00329404	+	0.999995i	$0.501049\pi$
$548$		0			0
$549$	0.770704			0.0328929
$550$		0			0
$551$	−17.5934	+	10.1576i	−0.749505	+	0.432727i
$552$		0			0
$553$	28.6935	−	9.85071i	1.22017	−	0.418895i
$554$		0			0
$555$	14.3352			0.608493
$556$		0			0
$557$		−	26.9944i		−	1.14379i	−0.820326	−	0.571896i	$-0.806208\pi$
$557$		−	26.9944i		−	1.14379i	0.820326	−	0.571896i	$-0.193792\pi$
$558$		0			0
$559$	4.68915	+	15.1846i	0.198330	+	0.642241i
$560$		0			0
$561$	17.5192	−	10.1147i	0.739663	−	0.427044i
$562$		0			0
$563$	−20.2361	−	35.0500i	−0.852852	−	1.47718i	−0.878624	−	0.477515i	$-0.841538\pi$
$563$	−20.2361	−	35.0500i	−0.852852	−	1.47718i	0.0257722	−	0.999668i	$-0.491796\pi$
$564$		0			0
$565$			21.7460i			0.914862i
$566$		0			0
$567$	4.83878	−	24.7728i	0.203210	−	1.04036i
$568$		0			0
$569$	−2.74231	+	4.74982i	−0.114964	+	0.199123i	−0.917765	−	0.397124i	$-0.870008\pi$
$569$	−2.74231	+	4.74982i	−0.114964	+	0.199123i	0.802802	+	0.596246i	$0.203342\pi$
$570$		0			0
$571$	−9.73251	+	16.8572i	−0.407293	+	0.705452i	−0.994585	−	0.103923i	$-0.966860\pi$
$571$	−9.73251	+	16.8572i	−0.407293	+	0.705452i	0.587293	+	0.809375i	$0.300194\pi$
$572$		0			0
$573$	−46.6126			−1.94727
$574$		0			0
$575$	1.73136	+	2.99880i	0.0722026	+	0.125059i
$576$		0			0
$577$	25.1822	+	14.5389i	1.04835	+	0.605264i	0.922186	−	0.386746i	$-0.126401\pi$
$577$	25.1822	+	14.5389i	1.04835	+	0.605264i	0.126161	+	0.992010i	$0.459734\pi$
$578$		0			0
$579$		−	24.0260i		−	0.998486i
$580$		0			0
$581$	−17.4516	−	3.40876i	−0.724015	−	0.141419i
$582$		0			0
$583$	4.58520	+	2.64727i	0.189900	+	0.109639i
$584$		0			0
$585$	0.217719	−	0.955297i	0.00900156	−	0.0394967i
$586$		0			0
$587$	21.2641	−	12.2768i	0.877662	−	0.506718i	0.00777502	−	0.999970i	$-0.497525\pi$
$587$	21.2641	−	12.2768i	0.877662	−	0.506718i	0.869887	+	0.493252i	$0.164192\pi$
$588$		0			0
$589$	−14.5802	+	25.2536i	−0.600766	+	1.04056i
$590$		0			0
$591$	−7.94382	+	4.58637i	−0.326765	+	0.188658i
$592$		0			0
$593$	23.0759	−	13.3229i	0.947612	−	0.547104i	0.0552739	−	0.998471i	$-0.482397\pi$
$593$	23.0759	−	13.3229i	0.947612	−	0.547104i	0.892338	+	0.451367i	$0.149063\pi$
$594$		0			0
$595$	−16.6357	+	19.1020i	−0.681996	+	0.783104i
$596$		0			0
$597$	16.6409	+	28.8229i	0.681067	+	1.17964i
$598$		0			0
$599$	−1.09700	+	1.90005i	−0.0448220	+	0.0776340i	−0.887566	−	0.460680i	$-0.847605\pi$
$599$	−1.09700	+	1.90005i	−0.0448220	+	0.0776340i	0.842744	+	0.538315i	$0.180939\pi$
$600$		0			0
$601$	−2.47046	−	4.27896i	−0.100772	−	0.174542i	0.811231	−	0.584726i	$-0.198798\pi$
$601$	−2.47046	−	4.27896i	−0.100772	−	0.174542i	−0.912003	+	0.410184i	$0.865465\pi$
$602$		0			0
$603$		−	2.64051i		−	0.107530i
$604$		0			0
$605$	10.0424	−	5.79800i	0.408283	−	0.235722i
$606$		0			0
$607$	8.16315			0.331332			0.165666	−	0.986182i	$-0.447023\pi$
$607$	8.16315			0.331332			0.165666	+	0.986182i	$0.447023\pi$
$608$		0			0
$609$	16.0252	−	5.50160i	0.649376	−	0.222936i
$610$		0			0
$611$	−9.40055	+	41.2474i	−0.380306	+	1.66869i
$612$		0			0
$613$		−	20.8841i		−	0.843503i	−0.906712	−	0.421751i	$-0.861416\pi$
$613$		−	20.8841i		−	0.843503i	0.906712	−	0.421751i	$-0.138584\pi$
$614$		0			0
$615$	−9.66092	+	16.7332i	−0.389566	+	0.674748i
$616$		0			0
$617$	−32.3343	−	18.6682i	−1.30173	−	0.751555i	−0.321030	−	0.947069i	$-0.604029\pi$
$617$	−32.3343	−	18.6682i	−1.30173	−	0.751555i	−0.980701	+	0.195514i	$0.937362\pi$
$618$		0			0
$619$	−11.5619	−	6.67527i	−0.464712	−	0.268302i	0.249311	−	0.968423i	$-0.419796\pi$
$619$	−11.5619	−	6.67527i	−0.464712	−	0.268302i	−0.714024	+	0.700122i	$0.753129\pi$
$620$		0			0
$621$	2.89009	−	5.00579i	0.115976	−	0.200875i
$622$		0			0
$623$	−12.4902	+	14.3419i	−0.500411	+	0.574598i
$624$		0			0
$625$	0.471566	+	0.816776i	0.0188626	+	0.0326710i
$626$		0			0
$627$	16.9150			0.675521
$628$		0			0
$629$		−	38.5062i		−	1.53534i
$630$		0			0
$631$	37.7929	+	21.8198i	1.50451	+	0.868631i	0.999986	+	0.00523510i	$0.00166639\pi$
$631$	37.7929	+	21.8198i	1.50451	+	0.868631i	0.504527	+	0.863396i	$0.331667\pi$
$632$		0			0
$633$	−1.28651	−	2.22830i	−0.0511341	−	0.0885668i
$634$		0			0
$635$	−1.20623	−	0.696420i	−0.0478680	−	0.0276366i
$636$		0			0
$637$	−22.8636	+	10.6891i	−0.905889	+	0.423516i
$638$		0			0
$639$	−0.535000	−	0.308882i	−0.0211643	−	0.0122192i
$640$		0			0
$641$	−13.0431	−	22.5914i	−0.515173	−	0.892306i	−0.999845	−	0.0176101i	$-0.994394\pi$
$641$	−13.0431	−	22.5914i	−0.515173	−	0.892306i	0.484672	−	0.874696i	$-0.338939\pi$
$642$		0			0
$643$	−38.2452	−	22.0809i	−1.50825	−	0.870786i	−0.999954	−	0.00960062i	$-0.996944\pi$
$643$	−38.2452	−	22.0809i	−1.50825	−	0.870786i	−0.508291	−	0.861185i	$-0.669723\pi$
$644$		0			0
$645$		−	11.1230i		−	0.437969i
$646$		0			0
$647$	−15.5207			−0.610182			−0.305091	−	0.952323i	$-0.598687\pi$
$647$	−15.5207			−0.610182			−0.305091	+	0.952323i	$0.598687\pi$
$648$		0			0
$649$	6.53600	+	11.3207i	0.256560	+	0.444375i
$650$		0			0
$651$	15.9724	−	18.3403i	0.626007	−	0.718815i
$652$		0			0
$653$	19.1084	−	33.0967i	0.747769	−	1.29517i	−0.201121	−	0.979566i	$-0.564458\pi$
$653$	19.1084	−	33.0967i	0.747769	−	1.29517i	0.948890	−	0.315608i	$-0.102208\pi$
$654$		0			0
$655$	15.4320	+	8.90970i	0.602980	+	0.348131i
$656$		0			0
$657$	−2.03066	−	1.17240i	−0.0792236	−	0.0457397i
$658$		0			0
$659$	−10.2159	+	17.6944i	−0.397955	+	0.689277i	−0.993473	−	0.114064i	$-0.963613\pi$
$659$	−10.2159	+	17.6944i	−0.397955	+	0.689277i	0.595519	+	0.803341i	$0.296946\pi$
$660$		0			0
$661$		−	8.65534i		−	0.336654i	−0.985731	−	0.168327i	$-0.946164\pi$
$661$		−	8.65534i		−	0.336654i	0.985731	−	0.168327i	$-0.0538364\pi$
$662$		0			0
$663$	−42.5770	−	9.70359i	−1.65355	−	0.376856i
$664$		0			0
$665$	−20.0326	+	6.87736i	−0.776831	+	0.266693i
$666$		0			0
$667$	4.12990			0.159910
$668$		0			0
$669$	−0.471625	+	0.272293i	−0.0182341	+	0.0105275i
$670$		0			0
$671$			6.69058i			0.258287i
$672$		0			0
$673$	−13.0726	−	22.6424i	−0.503912	−	0.872801i	−0.999990	−	0.00452265i	$-0.998560\pi$
$673$	−13.0726	−	22.6424i	−0.503912	−	0.872801i	0.496078	−	0.868278i	$-0.334773\pi$
$674$		0			0
$675$	−7.53759	+	13.0555i	−0.290122	+	0.502506i
$676$		0			0
$677$	−0.159898	−	0.276952i	−0.00614539	−	0.0106441i	0.862936	−	0.505313i	$-0.168623\pi$
$677$	−0.159898	−	0.276952i	−0.00614539	−	0.0106441i	−0.869082	+	0.494668i	$0.835289\pi$
$678$		0			0
$679$	−4.14836	+	4.76337i	−0.159200	+	0.182801i
$680$		0			0
$681$	−3.89935	+	2.25129i	−0.149423	+	0.0862696i
$682$		0			0
$683$	−4.50473	+	2.60081i	−0.172369	+	0.0995170i	−0.583702	−	0.811968i	$-0.698396\pi$
$683$	−4.50473	+	2.60081i	−0.172369	+	0.0995170i	0.411334	+	0.911485i	$0.365063\pi$
$684$		0			0
$685$	−13.1201	+	22.7247i	−0.501293	+	0.868265i
$686$		0			0
$687$	11.3658	−	6.56204i	0.433632	−	0.250357i
$688$		0			0
$689$	−3.37230	−	10.9203i	−0.128474	−	0.416031i
$690$		0			0
$691$	−5.48965	−	3.16945i	−0.208836	−	0.120572i	0.391934	−	0.919993i	$-0.371806\pi$
$691$	−5.48965	−	3.16945i	−0.208836	−	0.120572i	−0.600770	+	0.799422i	$0.705139\pi$
$692$		0			0
$693$	−0.834474	−	0.162995i	−0.0316991	−	0.00619166i
$694$		0			0
$695$		−	13.4248i		−	0.509231i
$696$		0			0
$697$	44.9477	+	25.9506i	1.70252	+	0.982948i
$698$		0			0
$699$	21.8746	+	37.8879i	0.827373	+	1.43305i
$700$		0			0
$701$	39.6964			1.49931			0.749655	−	0.661828i	$-0.230219\pi$
$701$	39.6964			1.49931			0.749655	+	0.661828i	$0.230219\pi$
$702$		0			0
$703$	16.0986	−	27.8837i	0.607172	−	1.05165i
$704$		0			0
$705$	14.8048	−	25.6426i	0.557581	−	0.965758i
$706$		0			0
$707$	−5.04808	+	25.8443i	−0.189853	+	0.971976i
$708$		0			0
$709$		−	30.3877i		−	1.14123i	−0.821217	−	0.570617i	$-0.806704\pi$
$709$		−	30.3877i		−	1.14123i	0.821217	−	0.570617i	$-0.193296\pi$
$710$		0			0
$711$	−1.10308	−	1.91059i	−0.0413688	−	0.0716528i
$712$		0			0
$713$	5.13385	−	2.96403i	0.192264	−	0.111004i
$714$		0			0
$715$	8.29305	+	1.89004i	0.310142	+	0.0706836i
$716$		0			0
$717$			2.57969i			0.0963404i
$718$		0			0
$719$	22.2790			0.830865			0.415432	−	0.909624i	$-0.363630\pi$
$719$	22.2790			0.830865			0.415432	+	0.909624i	$0.363630\pi$
$720$		0			0
$721$	36.8481	−	12.6503i	1.37229	−	0.471120i
$722$		0			0
$723$	16.9943	−	9.81164i	0.632023	−	0.364899i
$724$		0			0
$725$	−10.7711			−0.400028
$726$		0			0
$727$	−39.0166			−1.44705			−0.723523	−	0.690300i	$-0.757478\pi$
$727$	−39.0166			−1.44705			−0.723523	+	0.690300i	$0.757478\pi$
$728$		0			0
$729$	25.0534			0.927903
$730$		0			0
$731$	−29.8780			−1.10508
$732$		0			0
$733$	−30.9728	+	17.8821i	−1.14400	+	0.660491i	−0.947419	−	0.319995i	$-0.896319\pi$
$733$	−30.9728	+	17.8821i	−1.14400	+	0.660491i	−0.196586	+	0.980487i	$0.562985\pi$
$734$		0			0
$735$	17.4974	−	2.42658i	0.645401	−	0.0895057i
$736$		0			0
$737$	22.9226			0.844364
$738$		0			0
$739$		−	19.6281i		−	0.722030i	−0.932560	−	0.361015i	$-0.882430\pi$
$739$		−	19.6281i		−	0.722030i	0.932560	−	0.361015i	$-0.117570\pi$
$740$		0			0
$741$	−26.7746	−	24.8273i	−0.983589	−	0.912052i
$742$		0			0
$743$	−20.5695	+	11.8758i	−0.754621	+	0.435681i	−0.827361	−	0.561670i	$-0.810159\pi$
$743$	−20.5695	+	11.8758i	−0.754621	+	0.435681i	0.0727399	+	0.997351i	$0.476826\pi$
$744$		0			0
$745$	−1.33017	−	2.30392i	−0.0487337	−	0.0844092i
$746$		0			0
$747$			1.29308i			0.0473114i
$748$		0			0
$749$	−2.08185	−	1.81306i	−0.0760691	−	0.0662477i
$750$		0			0
$751$	−8.26053	+	14.3077i	−0.301431	+	0.522094i	−0.976460	−	0.215697i	$-0.930798\pi$
$751$	−8.26053	+	14.3077i	−0.301431	+	0.522094i	0.675029	+	0.737791i	$0.264131\pi$
$752$		0			0
$753$	−14.3225	+	24.8072i	−0.521940	+	0.904026i
$754$		0			0
$755$	−2.35426			−0.0856801
$756$		0			0
$757$	−5.76790	−	9.99030i	−0.209638	−	0.363104i	0.741963	−	0.670441i	$-0.233895\pi$
$757$	−5.76790	−	9.99030i	−0.209638	−	0.363104i	−0.951601	+	0.307338i	$0.900562\pi$
$758$		0			0
$759$	−2.97799	−	1.71934i	−0.108094	−	0.0624082i
$760$		0			0
$761$		−	12.1906i		−	0.441909i	−0.975284	−	0.220954i	$-0.929083\pi$
$761$		−	12.1906i		−	0.441909i	0.975284	−	0.220954i	$-0.0709172\pi$
$762$		0			0
$763$	−20.5324	+	23.5763i	−0.743321	+	0.853521i
$764$		0			0
$765$	1.59527	+	0.921029i	0.0576771	+	0.0332999i
$766$		0			0
$767$	6.27032	−	27.5127i	0.226408	−	0.993424i
$768$		0			0
$769$	12.3254	−	7.11605i	0.444464	−	0.256611i	−0.261026	−	0.965332i	$-0.584061\pi$
$769$	12.3254	−	7.11605i	0.444464	−	0.256611i	0.705489	+	0.708721i	$0.250727\pi$
$770$		0			0
$771$	−24.4787	+	42.3983i	−0.881579	+	1.52694i
$772$		0			0
$773$	40.0536	−	23.1250i	1.44063	−	0.831748i	0.442738	−	0.896651i	$-0.354007\pi$
$773$	40.0536	−	23.1250i	1.44063	−	0.831748i	0.997892	+	0.0649035i	$0.0206740\pi$
$774$		0			0
$775$	−13.3895	+	7.73042i	−0.480964	+	0.277685i
$776$		0			0
$777$	−17.6358	+	20.2504i	−0.632682	+	0.726479i
$778$		0			0
$779$	21.6988	+	37.5834i	0.777440	+	1.34656i
$780$		0			0
$781$	2.68144	−	4.64440i	0.0959496	−	0.166190i
$782$		0			0
$783$	8.98989	+	15.5710i	0.321273	+	0.556460i
$784$		0			0
$785$		−	13.5940i		−	0.485189i
$786$		0			0
$787$	27.3472	−	15.7889i	0.974822	−	0.562814i	0.0741191	−	0.997249i	$-0.476385\pi$
$787$	27.3472	−	15.7889i	0.974822	−	0.562814i	0.900703	+	0.434436i	$0.143052\pi$
$788$		0			0
$789$	−36.0932			−1.28495
$790$		0			0
$791$	−30.7193	−	26.7531i	−1.09225	−	0.951229i
$792$		0			0
$793$	9.82018	−	10.5904i	0.348725	−	0.376077i
$794$		0			0
$795$			7.99935i			0.283708i
$796$		0			0
$797$	−2.40382	+	4.16354i	−0.0851477	+	0.147480i	−0.905454	−	0.424444i	$-0.860470\pi$
$797$	−2.40382	+	4.16354i	−0.0851477	+	0.147480i	0.820306	+	0.571924i	$0.193803\pi$
$798$		0			0
$799$	−68.8797	−	39.7677i	−2.43679	−	1.40688i
$800$		0			0
$801$	1.19774	+	0.691517i	0.0423202	+	0.0244336i
$802$		0			0
$803$	10.1778	−	17.6284i	0.359165	−	0.622092i
$804$		0			0
$805$	4.22591	+	0.825431i	0.148944	+	0.0290926i
$806$		0			0
$807$	−8.12410	−	14.0713i	−0.285982	−	0.495335i
$808$		0			0
$809$	−1.51624			−0.0533082			−0.0266541	−	0.999645i	$-0.508485\pi$
$809$	−1.51624			−0.0533082			−0.0266541	+	0.999645i	$0.508485\pi$
$810$		0			0
$811$			44.4771i			1.56180i	0.624654	+	0.780901i	$0.285240\pi$
$811$			44.4771i			1.56180i	−0.624654	+	0.780901i	$0.714760\pi$
$812$		0			0
$813$	−2.80104	−	1.61718i	−0.0982366	−	0.0567169i
$814$		0			0
$815$	−1.98825	−	3.44375i	−0.0696454	−	0.120629i
$816$		0			0
$817$	−21.6357	−	12.4914i	−0.756937	−	0.437018i
$818$		0			0
$819$	1.08164	+	1.48281i	0.0377956	+	0.0518137i
$820$		0			0
$821$	10.8647	+	6.27272i	0.379179	+	0.218919i	0.677461	−	0.735559i	$-0.263080\pi$
$821$	10.8647	+	6.27272i	0.379179	+	0.218919i	−0.298282	+	0.954478i	$0.596414\pi$
$822$		0			0
$823$	19.3302	+	33.4809i	0.673808	+	1.16707i	0.976816	+	0.214082i	$0.0686760\pi$
$823$	19.3302	+	33.4809i	0.673808	+	1.16707i	−0.303007	+	0.952988i	$0.597991\pi$
$824$		0			0
$825$	7.76682	+	4.48418i	0.270406	+	0.156119i
$826$		0			0
$827$		−	10.4039i		−	0.361780i	−0.983503	−	0.180890i	$-0.942102\pi$
$827$		−	10.4039i		−	0.361780i	0.983503	−	0.180890i	$-0.0578977\pi$
$828$		0			0
$829$	−17.9274			−0.622645			−0.311323	−	0.950304i	$-0.600772\pi$
$829$	−17.9274			−0.622645			−0.311323	+	0.950304i	$0.600772\pi$
$830$		0			0
$831$	−7.23166	−	12.5256i	−0.250864	−	0.434508i
$832$		0			0
$833$	−6.51813	−	47.0004i	−0.225840	−	1.62847i
$834$		0			0
$835$	3.12129	−	5.40622i	0.108017	−	0.187090i
$836$		0			0
$837$	22.3506	+	12.9041i	0.772549	+	0.446031i
$838$		0			0
$839$	−8.61866	−	4.97598i	−0.297549	−	0.171790i	0.343792	−	0.939046i	$-0.388288\pi$
$839$	−8.61866	−	4.97598i	−0.297549	−	0.171790i	−0.641341	+	0.767256i	$0.721622\pi$
$840$		0			0
$841$	8.07680	−	13.9894i	0.278510	−	0.482394i
$842$		0			0
$843$		−	28.7548i		−	0.990367i
$844$		0			0
$845$	−10.3528	−	15.1640i	−0.356148	−	0.521656i
$846$		0			0
$847$	−4.16422	+	21.3193i	−0.143084	+	0.732540i
$848$		0			0
$849$	−19.9955			−0.686242
$850$		0			0
$851$	−5.66851	+	3.27272i	−0.194314	+	0.112187i
$852$		0			0
$853$		−	21.5922i		−	0.739302i	−0.929171	−	0.369651i	$-0.879477\pi$
$853$		−	21.5922i		−	0.739302i	0.929171	−	0.369651i	$-0.120523\pi$
$854$		0			0
$855$	0.770125	+	1.33390i	0.0263377	+	0.0456183i
$856$		0			0
$857$	1.98635	−	3.44046i	0.0678524	−	0.117524i	−0.830103	−	0.557610i	$-0.811719\pi$
$857$	1.98635	−	3.44046i	0.0678524	−	0.117524i	0.897956	+	0.440086i	$0.145052\pi$
$858$		0			0
$859$	24.9020	+	43.1315i	0.849644	+	1.47163i	0.881527	+	0.472134i	$0.156516\pi$
$859$	24.9020	+	43.1315i	0.849644	+	1.47163i	−0.0318828	+	0.999492i	$0.510150\pi$
$860$		0			0
$861$	−11.7526	−	34.2334i	−0.400528	−	1.16667i
$862$		0			0
$863$	−9.81070	+	5.66421i	−0.333960	+	0.192812i	−0.657598	−	0.753369i	$-0.728427\pi$
$863$	−9.81070	+	5.66421i	−0.333960	+	0.192812i	0.323638	+	0.946181i	$0.395094\pi$
$864$		0			0
$865$	22.6398	−	13.0711i	0.769777	−	0.444431i
$866$		0			0
$867$	25.8625	−	44.7951i	0.878336	−	1.52132i
$868$		0			0
$869$	16.5861	−	9.57598i	0.562644	−	0.324843i
$870$		0			0
$871$	−36.2839	−	33.6449i	−1.22943	−	1.14001i
$872$		0			0
$873$	0.397805	+	0.229673i	0.0134636	+	0.00777324i
$874$		0			0
$875$	−29.3591	−	5.73460i	−0.992517	−	0.193865i
$876$		0			0
$877$			5.21814i			0.176204i	0.996111	+	0.0881019i	$0.0280801\pi$
$877$			5.21814i			0.176204i	−0.996111	+	0.0881019i	$0.971920\pi$
$878$		0			0
$879$	23.1474	+	13.3641i	0.780741	+	0.450761i
$880$		0			0
$881$	−16.4160	−	28.4334i	−0.553070	−	0.957946i	−0.998051	−	0.0624056i	$-0.980123\pi$
$881$	−16.4160	−	28.4334i	−0.553070	−	0.957946i	0.444981	−	0.895540i	$-0.353211\pi$
$882$		0			0
$883$	45.6813			1.53730			0.768648	−	0.639672i	$-0.220930\pi$
$883$	45.6813			1.53730			0.768648	+	0.639672i	$0.220930\pi$
$884$		0			0
$885$	−9.87504	+	17.1041i	−0.331946	+	0.574947i
$886$		0			0
$887$	3.32423	−	5.75774i	0.111617	−	0.193326i	−0.804805	−	0.593539i	$-0.797730\pi$
$887$	3.32423	−	5.75774i	0.111617	−	0.193326i	0.916422	+	0.400213i	$0.131064\pi$
$888$		0			0
$889$	2.46776	−	0.847203i	0.0827660	−	0.0284143i
$890$		0			0
$891$		−	15.9346i		−	0.533830i
$892$		0			0
$893$	−33.2521	−	57.5943i	−1.11274	−	1.92732i
$894$		0			0
$895$	−7.31833	+	4.22524i	−0.244625	+	0.141234i
$896$		0			0
$897$	2.19023	+	7.09251i	0.0731298	+	0.236812i
$898$		0			0
$899$			18.4398i			0.615000i
$900$		0			0
$901$	21.4874			0.715848
$902$		0			0
$903$	15.7128	+	13.6841i	0.522890	+	0.455379i
$904$		0			0
$905$	−2.54598	+	1.46992i	−0.0846314	+	0.0488619i
$906$		0			0
$907$	−24.7179			−0.820744			−0.410372	−	0.911918i	$-0.634601\pi$
$907$	−24.7179			−0.820744			−0.410372	+	0.911918i	$0.634601\pi$
$908$		0			0
$909$	1.91494			0.0635147
$910$		0			0
$911$	−14.4092			−0.477397			−0.238698	−	0.971094i	$-0.576721\pi$
$911$	−14.4092			−0.477397			−0.238698	+	0.971094i	$0.576721\pi$
$912$		0			0
$913$	−11.2254			−0.371507
$914$		0			0
$915$	−8.75429	+	5.05429i	−0.289408	+	0.167090i
$916$		0			0
$917$	−31.5715	+	10.8388i	−1.04258	+	0.357927i
$918$		0			0
$919$	−3.73332			−0.123151			−0.0615754	−	0.998102i	$-0.519612\pi$
$919$	−3.73332			−0.123151			−0.0615754	+	0.998102i	$0.519612\pi$
$920$		0			0
$921$			18.7220i			0.616909i
$922$		0			0
$923$	−11.0613	+	3.41583i	−0.364087	+	0.112434i
$924$		0			0
$925$	14.7839	−	8.53550i	0.486092	−	0.280645i
$926$		0			0
$927$	−1.41657	−	2.45358i	−0.0465264	−	0.0805861i
$928$		0			0
$929$			25.4504i			0.834999i	0.908677	+	0.417500i	$0.137093\pi$
$929$			25.4504i			0.834999i	−0.908677	+	0.417500i	$0.862907\pi$
$930$		0			0
$931$	14.9299	−	36.7597i	0.489307	−	1.20475i
$932$		0			0
$933$	−8.64624	+	14.9757i	−0.283065	+	0.490283i
$934$		0			0
$935$	−7.99556	+	13.8487i	−0.261483	+	0.452901i
$936$		0			0
$937$	25.0364			0.817905			0.408952	−	0.912556i	$-0.365894\pi$
$937$	25.0364			0.817905			0.408952	+	0.912556i	$0.365894\pi$
$938$		0			0
$939$	28.1727	+	48.7966i	0.919382	+	1.59242i
$940$		0			0
$941$	−10.7221	−	6.19042i	−0.349531	−	0.201802i	0.314948	−	0.949109i	$-0.398013\pi$
$941$	−10.7221	−	6.19042i	−0.349531	−	0.201802i	−0.664479	+	0.747307i	$0.731346\pi$
$942$		0			0
$943$		−	8.82236i		−	0.287296i
$944$		0			0
$945$	6.08677	+	17.7297i	0.198002	+	0.576748i
$946$		0			0
$947$	−17.5614	−	10.1391i	−0.570669	−	0.329476i	0.186747	−	0.982408i	$-0.440205\pi$
$947$	−17.5614	−	10.1391i	−0.570669	−	0.329476i	−0.757417	+	0.652932i	$0.773539\pi$
$948$		0			0
$949$	−41.9846	+	12.9652i	−1.36288	+	0.420869i
$950$		0			0
$951$	−3.46228	+	1.99895i	−0.112272	+	0.0648204i
$952$		0			0
$953$	−0.542566	+	0.939751i	−0.0175754	+	0.0304415i	−0.874679	−	0.484702i	$-0.838928\pi$
$953$	−0.542566	+	0.939751i	−0.0175754	+	0.0304415i	0.857104	+	0.515144i	$0.172261\pi$
$954$		0			0
$955$	31.9101	−	18.4233i	1.03259	−	0.596164i
$956$		0			0
$957$	9.26329	−	5.34816i	0.299440	−	0.172882i
$958$		0			0
$959$	−15.9607	−	46.4910i	−0.515399	−	1.50127i
$960$		0			0
$961$	−2.26577	−	3.92443i	−0.0730893	−	0.126594i
$962$		0			0
$963$	−0.100379	+	0.173862i	−0.00323468	+	0.00560262i
$964$		0			0
$965$	9.49611	+	16.4477i	0.305691	+	0.529472i
$966$		0			0
$967$		−	6.19597i		−	0.199249i	−0.995025	−	0.0996245i	$-0.968236\pi$
$967$		−	6.19597i		−	0.199249i	0.995025	−	0.0996245i	$-0.0317642\pi$
$968$		0			0
$969$	59.4509	−	34.3240i	1.90984	−	1.10265i
$970$		0			0
$971$	43.0247			1.38073			0.690364	−	0.723462i	$-0.257450\pi$
$971$	43.0247			1.38073			0.690364	+	0.723462i	$0.257450\pi$
$972$		0			0
$973$	18.9644	+	16.5159i	0.607970	+	0.529474i
$974$		0			0
$975$	−5.71230	−	18.4978i	−0.182940	−	0.592404i
$976$		0			0
$977$		−	57.4675i		−	1.83855i	−0.393616	−	0.919275i	$-0.628776\pi$
$977$		−	57.4675i		−	1.83855i	0.393616	−	0.919275i	$-0.371224\pi$
$978$		0			0
$979$	−6.00315	+	10.3978i	−0.191861	+	0.332314i
$980$		0			0
$981$	1.96894	+	1.13677i	0.0628634	+	0.0362942i
$982$		0			0
$983$	4.43890	+	2.56280i	0.141579	+	0.0817406i	0.569116	−	0.822257i	$-0.307285\pi$
$983$	4.43890	+	2.56280i	0.141579	+	0.0817406i	−0.427537	+	0.903998i	$0.640619\pi$
$984$		0			0
$985$	3.62546	−	6.27949i	0.115517	−	0.200081i
$986$		0			0
$987$	18.0102	+	52.4607i	0.573271	+	1.66984i
$988$		0			0
$989$	2.53939	+	4.39835i	0.0807479	+	0.139859i
$990$		0			0
$991$	35.5383			1.12891			0.564456	−	0.825463i	$-0.309086\pi$
$991$	35.5383			1.12891			0.564456	+	0.825463i	$0.309086\pi$
$992$		0			0
$993$			37.6204i			1.19385i
$994$		0			0
$995$	−22.7841	−	13.1544i	−0.722305	−	0.417023i
$996$		0			0
$997$	20.5543	+	35.6011i	0.650961	+	1.12750i	0.982890	+	0.184193i	$0.0589673\pi$
$997$	20.5543	+	35.6011i	0.650961	+	1.12750i	−0.331929	+	0.943304i	$0.607699\pi$
$998$		0			0
$999$	−24.6783	−	14.2480i	−0.780786	−	0.450787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	364.2.bq.a.361.3	yes	18
3.2	odd	2		3276.2.fe.i.361.3		18
7.2	even	3		364.2.bb.a.205.7	✓	18
7.3	odd	6		2548.2.u.d.1765.3		18
7.4	even	3		2548.2.u.e.1765.7		18
7.5	odd	6		2548.2.bb.f.569.3		18
7.6	odd	2		2548.2.bq.f.361.7		18
13.4	even	6		364.2.bb.a.277.7	yes	18
21.2	odd	6		3276.2.hi.i.1297.7		18
39.17	odd	6		3276.2.hi.i.1369.7		18
91.4	even	6		2548.2.u.e.589.7		18
91.17	odd	6		2548.2.u.d.589.3		18
91.30	even	6	inner	364.2.bq.a.121.3	yes	18
91.69	odd	6		2548.2.bb.f.1733.3		18
91.82	odd	6		2548.2.bq.f.1941.7		18
273.212	odd	6		3276.2.fe.i.2305.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.7	✓	18	7.2	even	3
364.2.bb.a.277.7	yes	18	13.4	even	6
364.2.bq.a.121.3	yes	18	91.30	even	6	inner
364.2.bq.a.361.3	yes	18	1.1	even	1	trivial
2548.2.u.d.589.3		18	91.17	odd	6
2548.2.u.d.1765.3		18	7.3	odd	6
2548.2.u.e.589.7		18	91.4	even	6
2548.2.u.e.1765.7		18	7.4	even	3
2548.2.bb.f.569.3		18	7.5	odd	6
2548.2.bb.f.1733.3		18	91.69	odd	6
2548.2.bq.f.361.7		18	7.6	odd	2
2548.2.bq.f.1941.7		18	91.82	odd	6
3276.2.fe.i.361.3		18	3.2	odd	2
3276.2.fe.i.2305.3		18	273.212	odd	6
3276.2.hi.i.1297.7		18	21.2	odd	6
3276.2.hi.i.1369.7		18	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.78673 q^{3} +(1.22316 - 0.706193i) q^{5} +(-0.507200 + 2.59668i) q^{7} +0.192402 q^{9} +1.67026i q^{11} +(2.45155 - 2.64384i) q^{13} +(-2.18546 + 1.26178i) q^{15} +(3.38930 + 5.87045i) q^{17} +5.66799i q^{19} +(0.906229 - 4.63956i) q^{21} +(0.576127 - 0.997882i) q^{23} +(-1.50258 + 2.60255i) q^{25} +5.01642 q^{27} +(1.79209 + 3.10400i) q^{29} +(4.45548 + 2.57238i) q^{31} -2.98431i q^{33} +(1.21337 + 3.53434i) q^{35} +(-4.91950 - 2.84027i) q^{37} +(-4.38026 + 4.72383i) q^{39} +(6.63082 - 3.82831i) q^{41} +(-2.20385 + 3.81717i) q^{43} +(0.235339 - 0.135873i) q^{45} +(-10.1613 + 5.86665i) q^{47} +(-6.48550 - 2.63407i) q^{49} +(-6.05577 - 10.4889i) q^{51} +(1.58494 - 2.74520i) q^{53} +(1.17953 + 2.04300i) q^{55} -10.1272i q^{57} +(6.77778 - 3.91315i) q^{59} +4.00570 q^{61} +(-0.0975863 + 0.499606i) q^{63} +(1.13158 - 4.96511i) q^{65} -13.7239i q^{67} +(-1.02938 + 1.78294i) q^{69} +(-2.78064 - 1.60540i) q^{71} +(-10.5543 - 6.09350i) q^{73} +(2.68471 - 4.65006i) q^{75} +(-4.33714 - 0.847158i) q^{77} +(-5.73321 - 9.93021i) q^{79} -9.54019 q^{81} +6.72074i q^{83} +(8.29133 + 4.78700i) q^{85} +(-3.20199 - 5.54600i) q^{87} +(6.22521 + 3.59413i) q^{89} +(5.62178 + 7.70685i) q^{91} +(-7.96075 - 4.59614i) q^{93} +(4.00269 + 6.93286i) q^{95} +(2.06757 + 1.19371i) q^{97} +0.321362i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} + q^{7} + 12 q^{9} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 7 q^{21} - 6 q^{23} + 5 q^{25} - 20 q^{27} + 2 q^{29} + 9 q^{31} + 3 q^{35} + 18 q^{37} + 11 q^{39} - 9 q^{41} - 14 q^{43} + 30 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) \) 18 * q - 2 * q^3 + q^7 + 12 * q^9 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 7 * q^21 - 6 * q^23 + 5 * q^25 - 20 * q^27 + 2 * q^29 + 9 * q^31 + 3 * q^35 + 18 * q^37 + 11 * q^39 - 9 * q^41 - 14 * q^43 + 30 * q^45 + 36 * q^47 - 11 * q^49 + 2 * q^51 - 13 * q^53 - q^55 - 42 * q^61 - 32 * q^63 + 30 * q^65 - q^69 - 45 * q^71 - 33 * q^73 + 25 * q^75 - 9 * q^77 - 14 * q^79 + 2 * q^81 - 30 * q^85 + 2 * q^87 - 9 * q^89 + 21 * q^93 + 30 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

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