LMFDB - Embedded newform 2548.2.bq.f.361.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(361,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("2548.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.3458824350$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.7
Root			$0.893365 + 1.54735i$ of defining polynomial
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.f.1941.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.78673 q^{3} +(-1.22316 + 0.706193i) q^{5} +0.192402 q^{9} +1.67026i q^{11} +(-2.45155 + 2.64384i) q^{13} +(-2.18546 + 1.26178i) q^{15} +(-3.38930 - 5.87045i) q^{17} -5.66799i q^{19} +(0.576127 - 0.997882i) q^{23} +(-1.50258 + 2.60255i) q^{25} -5.01642 q^{27} +(1.79209 + 3.10400i) q^{29} +(-4.45548 - 2.57238i) q^{31} +2.98431i q^{33} +(-4.91950 - 2.84027i) q^{37} +(-4.38026 + 4.72383i) q^{39} +(-6.63082 + 3.82831i) q^{41} +(-2.20385 + 3.81717i) q^{43} +(-0.235339 + 0.135873i) q^{45} +(10.1613 - 5.86665i) q^{47} +(-6.05577 - 10.4889i) q^{51} +(1.58494 - 2.74520i) q^{53} +(-1.17953 - 2.04300i) q^{55} -10.1272i q^{57} +(-6.77778 + 3.91315i) q^{59} -4.00570 q^{61} +(1.13158 - 4.96511i) q^{65} -13.7239i q^{67} +(1.02938 - 1.78294i) q^{69} +(-2.78064 - 1.60540i) q^{71} +(10.5543 + 6.09350i) q^{73} +(-2.68471 + 4.65006i) q^{75} +(-5.73321 - 9.93021i) q^{79} -9.54019 q^{81} -6.72074i q^{83} +(8.29133 + 4.78700i) q^{85} +(3.20199 + 5.54600i) q^{87} +(-6.22521 - 3.59413i) q^{89} +(-7.96075 - 4.59614i) q^{93} +(4.00269 + 6.93286i) q^{95} +(-2.06757 - 1.19371i) q^{97} +0.321362i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{3} + 12 q^{9} + 4 q^{13} + 6 q^{15} + 10 q^{17} - 6 q^{23} + 5 q^{25} + 20 q^{27} + 2 q^{29} - 9 q^{31} + 18 q^{37} + 11 q^{39} + 9 q^{41} - 14 q^{43} - 30 q^{45} - 36 q^{47} + 2 q^{51} - 13 q^{53}+ \cdots + 18 q^{97}+O(q^{100}) $ 18 * q + 2 * q^3 + 12 * q^9 + 4 * q^13 + 6 * q^15 + 10 * q^17 - 6 * q^23 + 5 * q^25 + 20 * q^27 + 2 * q^29 - 9 * q^31 + 18 * q^37 + 11 * q^39 + 9 * q^41 - 14 * q^43 - 30 * q^45 - 36 * q^47 + 2 * q^51 - 13 * q^53 + q^55 + 42 * q^61 + 30 * q^65 + q^69 - 45 * q^71 + 33 * q^73 - 25 * q^75 - 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 $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.78673			1.03157			0.515784	−	0.856718i	$-0.327501\pi$
$3$	1.78673			1.03157			0.515784	+	0.856718i	$0.327501\pi$
$4$		0			0
$5$	−1.22316	+	0.706193i	−0.547015	+	0.315819i	−0.747917	−	0.663792i	$-0.768946\pi$
$5$	−1.22316	+	0.706193i	−0.547015	+	0.315819i	0.200902	+	0.979611i	$0.435613\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		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	$-0.859510\pi$
$17$	−3.38930	−	5.87045i	−0.822027	−	1.42379i	0.0821435	−	0.996621i	$-0.473823\pi$
$18$		0			0
$19$		−	5.66799i		−	1.30033i	−0.759795	−	0.650163i	$-0.774701\pi$
$19$		−	5.66799i		−	1.30033i	0.759795	−	0.650163i	$-0.225299\pi$
$20$		0			0
$21$		0			0
$22$		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	0.0433224	−	0.999061i	$-0.486206\pi$
$31$	−4.45548	−	2.57238i	−0.800229	−	0.462012i	−0.843551	+	0.537049i	$0.819539\pi$
$32$		0			0
$33$			2.98431i			0.519502i
$34$		0			0
$35$		0			0
$36$		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	−0.918572	−	0.395253i	$-0.870657\pi$
$41$	−6.63082	+	3.82831i	−1.03556	+	0.597881i	−0.116987	+	0.993133i	$0.537324\pi$
$42$		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	0.482388	−	0.875958i	$-0.339770\pi$
$47$	10.1613	−	5.86665i	1.48218	−	0.855739i	0.999796	+	0.0202189i	$0.00643631\pi$
$48$		0			0
$49$		0			0
$50$		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	−0.871446	−	0.490491i	$-0.836817\pi$
$59$	−6.77778	+	3.91315i	−0.882391	+	0.509449i	−0.0109453	+	0.999940i	$0.503484\pi$
$60$		0			0
$61$	−4.00570			−0.512877			−0.256439	−	0.966561i	$-0.582549\pi$
$61$	−4.00570			−0.512877			−0.256439	+	0.966561i	$0.582549\pi$
$62$		0			0
$63$		0			0
$64$		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	0.968126	−	0.250463i	$-0.0805828\pi$
$73$	10.5543	+	6.09350i	1.23528	+	0.713190i	0.267156	+	0.963653i	$0.413916\pi$
$74$		0			0
$75$	−2.68471	+	4.65006i	−0.310004	+	0.536942i
$76$		0			0
$77$		0			0
$78$		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	$-0.879752\pi$
$83$		−	6.72074i		−	0.737697i	0.929490	−	0.368848i	$-0.120248\pi$
$84$		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	0.132357	−	0.991202i	$-0.457746\pi$
$89$	−6.22521	−	3.59413i	−0.659871	−	0.380977i	−0.792228	+	0.610225i	$0.791079\pi$
$90$		0			0
$91$		0			0
$92$		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	0.391349	−	0.920242i	$-0.372009\pi$
$97$	−2.06757	−	1.19371i	−0.209930	−	0.121203i	−0.601279	+	0.799039i	$0.705342\pi$
$98$		0			0
$99$			0.321362i			0.0322981i
$100$		0			0
$101$	−9.95283			−0.990344			−0.495172	−	0.868795i	$-0.664895\pi$
$101$	−9.95283			−0.990344			−0.495172	+	0.868795i	$0.664895\pi$
$102$		0			0
$103$	7.36258	+	12.7524i	0.725456	+	1.25653i	0.958786	+	0.284130i	$0.0917046\pi$
$103$	7.36258	+	12.7524i	0.725456	+	1.25653i	−0.233330	+	0.972398i	$0.574962\pi$
$104$		0			0
$105$		0			0
$106$		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
$119$		0			0
$120$		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	$-0.980854\pi$
$131$	−6.30826	−	10.9262i	−0.551155	−	0.954629i	0.447036	−	0.894516i	$-0.352479\pi$
$132$		0			0
$133$		0			0
$134$		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	−0.994099	−	0.108479i	$-0.965402\pi$
$139$	−4.75252	+	8.23161i	−0.403104	+	0.698196i	0.590995	+	0.806675i	$0.298735\pi$
$140$		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
$147$		0			0
$148$		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	−0.991640	−	0.129035i	$-0.958812\pi$
$157$	−4.81241	+	8.33535i	−0.384072	+	0.665233i	0.607568	+	0.794268i	$0.292145\pi$
$158$		0			0
$159$	2.83186	−	4.90492i	0.224581	−	0.388986i
$160$		0			0
$161$		0			0
$162$		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	−0.640734	−	0.767763i	$-0.721370\pi$
$167$	−3.82773	+	2.20994i	−0.296198	+	0.171010i	0.344535	+	0.938773i	$0.388036\pi$
$168$		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	$-0.748433\pi$
$173$	−18.5093			−1.40723			−0.703617	+	0.710580i	$0.748433\pi$
$174$		0			0
$175$		0			0
$176$		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	$-0.475352\pi$
$181$	2.08148			0.154715			0.0773575	+	0.997003i	$0.475352\pi$
$182$		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
$189$		0			0
$190$		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	$0.0628722\pi$
$199$	9.31361	+	16.1316i	0.660224	+	1.14354i	−0.320332	+	0.947305i	$0.603794\pi$
$200$		0			0
$201$		−	24.5209i		−	1.72957i
$202$		0			0
$203$		0			0
$204$		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
$217$		0			0
$218$		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	−0.508812	−	0.860878i	$-0.669915\pi$
$223$	−0.263960	+	0.152397i	−0.0176761	+	0.0102053i	0.491136	+	0.871083i	$0.336582\pi$
$224$		0			0
$225$	−0.289100	+	0.500736i	−0.0192733	+	0.0333824i
$226$		0			0
$227$	−2.18239	+	1.26001i	−0.144851	+	0.0836295i	−0.570674	−	0.821177i	$-0.693318\pi$
$227$	−2.18239	+	1.26001i	−0.144851	+	0.0836295i	0.425823	+	0.904806i	$0.359985\pi$
$228$		0			0
$229$	6.36123	−	3.67266i	0.420362	−	0.242696i	−0.274870	−	0.961481i	$-0.588635\pi$
$229$	6.36123	−	3.67266i	0.420362	−	0.242696i	0.695232	+	0.718785i	$0.255302\pi$
$230$		0			0
$231$		0			0
$232$		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	−0.161333	−	0.986900i	$-0.551579\pi$
$241$	9.51138	−	5.49140i	0.612682	−	0.353732i	0.774014	+	0.633168i	$0.218246\pi$
$242$		0			0
$243$	−1.99648			−0.128074
$244$		0			0
$245$		0			0
$246$		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	$0.335531\pi$
$251$	−8.01603	+	13.8842i	−0.505967	+	0.876361i	−0.999976	+	0.00690401i	$0.997802\pi$
$252$		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	$0.492864\pi$
$257$	−13.7003	+	23.7296i	−0.854600	+	1.48021i	−0.877016	+	0.480462i	$0.840469\pi$
$258$		0			0
$259$		0			0
$260$		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	0.693465	−	0.720490i	$-0.256083\pi$
$269$	−4.54691	−	7.87548i	−0.277230	−	0.480176i	−0.970695	+	0.240314i	$0.922750\pi$
$270$		0			0
$271$	−1.56769	−	0.905105i	−0.0952303	−	0.0549812i	0.451629	−	0.892206i	$-0.350843\pi$
$271$	−1.56769	−	0.905105i	−0.0952303	−	0.0549812i	−0.546859	+	0.837225i	$0.684177\pi$
$272$		0			0
$273$		0			0
$274$		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	$-0.607933\pi$
$283$	−11.1911			−0.665242			−0.332621	+	0.943061i	$0.607933\pi$
$284$		0			0
$285$	7.15173	+	12.3872i	0.423632	+	0.733752i
$286$		0			0
$287$		0			0
$288$		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	0.828163	−	0.560487i	$-0.189386\pi$
$293$	12.9552	+	7.47966i	0.756848	+	0.436967i	−0.0713148	+	0.997454i	$0.522719\pi$
$294$		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
$301$		0			0
$302$		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	$0.0966581\pi$
$307$			10.4783i			0.598030i	−0.954248	+	0.299015i	$0.903342\pi$
$308$		0			0
$309$	13.1549	+	22.7850i	0.748358	+	1.29619i
$310$		0			0
$311$	−4.83914	+	8.38164i	−0.274403	+	0.475279i	−0.969984	−	0.243168i	$-0.921813\pi$
$311$	−4.83914	+	8.38164i	−0.274403	+	0.475279i	0.695582	+	0.718447i	$0.255147\pi$
$312$		0			0
$313$	15.7678	+	27.3106i	0.891247	+	1.54368i	0.838382	+	0.545083i	$0.183502\pi$
$313$	15.7678	+	27.3106i	0.891247	+	1.54368i	0.0528647	+	0.998602i	$0.483165\pi$
$314$		0			0
$315$		0			0
$316$		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
$329$		0			0
$330$		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
$343$		0			0
$344$		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	−0.432496	−	0.901636i	$-0.642367\pi$
$349$	2.46776	−	1.42476i	0.132096	−	0.0762658i	0.564592	+	0.825370i	$0.309034\pi$
$350$		0			0
$351$	12.2980	−	13.2626i	0.656419	−	0.707906i
$352$		0			0
$353$		−	28.5979i		−	1.52211i	−0.648685	−	0.761057i	$-0.724681\pi$
$353$		−	28.5979i		−	1.52211i	0.648685	−	0.761057i	$-0.275319\pi$
$354$		0			0
$355$	4.53489			0.240687
$356$		0			0
$357$		0			0
$358$		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	$-0.509469\pi$
$367$	−1.13963			−0.0594884			−0.0297442	+	0.999558i	$0.509469\pi$
$368$		0			0
$369$	−1.27578	+	0.736573i	−0.0664146	+	0.0383445i
$370$		0			0
$371$		0			0
$372$		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	$-0.642156\pi$
$383$		−	35.3019i		−	1.80384i	0.431899	−	0.901922i	$-0.357844\pi$
$384$		0			0
$385$		0			0
$386$		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	$-0.928310\pi$
$397$		−	8.89935i		−	0.446646i	0.974745	−	0.223323i	$-0.0716904\pi$
$398$		0			0
$399$		0			0
$400$		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	−0.224705	−	0.974427i	$-0.572142\pi$
$409$	10.2498	−	5.91773i	0.506820	−	0.292613i	0.731526	+	0.681814i	$0.238809\pi$
$410$		0			0
$411$	−28.7477	+	16.5975i	−1.41802	+	0.818694i
$412$		0			0
$413$		0			0
$414$		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	0.997190	−	0.0749167i	$-0.0238691\pi$
$419$	8.87793	+	15.3770i	0.433715	+	0.751217i	−0.563475	+	0.826133i	$0.690536\pi$
$420$		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
$427$		0			0
$428$		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	$-0.621149\pi$
$433$	12.8663	−	22.2851i	0.618316	−	1.07095i	0.989793	−	0.142512i	$-0.0455181\pi$
$434$		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	$0.440288\pi$
$439$	−15.8732	+	27.4931i	−0.757585	+	1.31218i	−0.944079	+	0.329720i	$0.893046\pi$
$440$		0			0
$441$		0			0
$442$		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
$455$		0			0
$456$		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	0.412625	−	0.910901i	$-0.364612\pi$
$461$	−3.64848	−	2.10645i	−0.169927	−	0.0981071i	−0.582551	+	0.812794i	$0.697945\pi$
$462$		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	$0.0470082\pi$
$467$	13.4413	+	23.2810i	0.621988	+	1.07732i	−0.367127	+	0.930171i	$0.619658\pi$
$468$		0			0
$469$		0			0
$470$		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	$-0.697986\pi$
$479$		−	35.5745i		−	1.62544i	0.582654	−	0.812720i	$-0.302014\pi$
$480$		0			0
$481$	19.5696	−	6.04329i	0.892299	−	0.275550i
$482$		0			0
$483$		0			0
$484$		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
$497$		0			0
$498$		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	−0.975930	−	0.218083i	$-0.930020\pi$
$503$	−6.70811	+	11.6188i	−0.299100	+	0.518056i	0.676831	+	0.736139i	$0.263353\pi$
$504$		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	$-0.957493\pi$
$509$	−36.1416	−	20.8664i	−1.60195	−	0.924886i	−0.610853	−	0.791744i	$-0.709173\pi$
$510$		0			0
$511$		0			0
$512$		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	−0.550148	−	0.835067i	$-0.685429\pi$
$521$	10.2284	−	17.7161i	0.448115	−	0.776158i	0.998263	+	0.0589091i	$0.0187622\pi$
$522$		0			0
$523$	−1.30125	+	2.25383i	−0.0568996	+	0.0985529i	−0.893072	−	0.449913i	$-0.851455\pi$
$523$	−1.30125	+	2.25383i	−0.0568996	+	0.0985529i	0.836173	+	0.548466i	$0.184788\pi$
$524$		0			0
$525$		0			0
$526$		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
$539$		0			0
$540$		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
$553$		0			0
$554$		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	$0.158462\pi$
$563$	20.2361	+	35.0500i	0.852852	+	1.47718i	−0.0257722	+	0.999668i	$0.508204\pi$
$564$		0			0
$565$		−	21.7460i		−	0.914862i
$566$		0			0
$567$		0			0
$568$		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	−0.126161	−	0.992010i	$-0.540266\pi$
$577$	−25.1822	−	14.5389i	−1.04835	−	0.605264i	−0.922186	+	0.386746i	$0.873599\pi$
$578$		0			0
$579$			24.0260i			0.998486i
$580$		0			0
$581$		0			0
$582$		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	−0.869887	−	0.493252i	$-0.835808\pi$
$587$	−21.2641	+	12.2768i	−0.877662	+	0.506718i	−0.00777502	+	0.999970i	$0.502475\pi$
$588$		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	−0.892338	−	0.451367i	$-0.850937\pi$
$593$	−23.0759	+	13.3229i	−0.947612	+	0.547104i	−0.0552739	+	0.998471i	$0.517603\pi$
$594$		0			0
$595$		0			0
$596$		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	0.912003	−	0.410184i	$-0.134535\pi$
$601$	2.47046	+	4.27896i	0.100772	+	0.174542i	−0.811231	+	0.584726i	$0.801202\pi$
$602$		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	$-0.552977\pi$
$607$	−8.16315			−0.331332			−0.165666	+	0.986182i	$0.552977\pi$
$608$		0			0
$609$		0			0
$610$		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	0.714024	−	0.700122i	$-0.246871\pi$
$619$	11.5619	+	6.67527i	0.464712	+	0.268302i	−0.249311	+	0.968423i	$0.580204\pi$
$620$		0			0
$621$	−2.89009	+	5.00579i	−0.115976	+	0.200875i
$622$		0			0
$623$		0			0
$624$		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
$637$		0			0
$638$		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	$0.00305602\pi$
$643$	38.2452	+	22.0809i	1.50825	+	0.870786i	0.508291	+	0.861185i	$0.330277\pi$
$644$		0			0
$645$		−	11.1230i		−	0.437969i
$646$		0			0
$647$	15.5207			0.610182			0.305091	−	0.952323i	$-0.401313\pi$
$647$	15.5207			0.610182			0.305091	+	0.952323i	$0.401313\pi$
$648$		0			0
$649$	−6.53600	−	11.3207i	−0.256560	−	0.444375i
$650$		0			0
$651$		0			0
$652$		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	$0.0538364\pi$
$661$			8.65534i			0.336654i	−0.985731	+	0.168327i	$0.946164\pi$
$662$		0			0
$663$	42.5770	+	9.70359i	1.65355	+	0.376856i
$664$		0			0
$665$		0			0
$666$		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	0.869082	−	0.494668i	$-0.164711\pi$
$677$	0.159898	+	0.276952i	0.00614539	+	0.0106441i	−0.862936	+	0.505313i	$0.831377\pi$
$678$		0			0
$679$		0			0
$680$		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	0.600770	−	0.799422i	$-0.294861\pi$
$691$	5.48965	+	3.16945i	0.208836	+	0.120572i	−0.391934	+	0.919993i	$0.628194\pi$
$692$		0			0
$693$		0			0
$694$		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
$707$		0			0
$708$		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	$-0.636370\pi$
$719$	−22.2790			−0.830865			−0.415432	+	0.909624i	$0.636370\pi$
$720$		0			0
$721$		0			0
$722$		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	$-0.242522\pi$
$727$	39.0166			1.44705			0.723523	+	0.690300i	$0.242522\pi$
$728$		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	0.196586	−	0.980487i	$-0.437015\pi$
$733$	30.9728	−	17.8821i	1.14400	−	0.660491i	0.947419	+	0.319995i	$0.103681\pi$
$734$		0			0
$735$		0			0
$736$		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
$749$		0			0
$750$		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	$0.0709172\pi$
$761$			12.1906i			0.441909i	−0.975284	+	0.220954i	$0.929083\pi$
$762$		0			0
$763$		0			0
$764$		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	−0.705489	−	0.708721i	$-0.749273\pi$
$769$	−12.3254	+	7.11605i	−0.444464	+	0.256611i	0.261026	+	0.965332i	$0.415939\pi$
$770$		0			0
$771$	−24.4787	+	42.3983i	−0.881579	+	1.52694i
$772$		0			0
$773$	−40.0536	+	23.1250i	−1.44063	+	0.831748i	−0.997892	−	0.0649035i	$-0.979326\pi$
$773$	−40.0536	+	23.1250i	−1.44063	+	0.831748i	−0.442738	+	0.896651i	$0.645993\pi$
$774$		0			0
$775$	13.3895	−	7.73042i	0.480964	−	0.277685i
$776$		0			0
$777$		0			0
$778$		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	−0.900703	−	0.434436i	$-0.856948\pi$
$787$	−27.3472	+	15.7889i	−0.974822	+	0.562814i	−0.0741191	+	0.997249i	$0.523615\pi$
$788$		0			0
$789$	36.0932			1.28495
$790$		0			0
$791$		0			0
$792$		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	−0.820306	−	0.571924i	$-0.806197\pi$
$797$	2.40382	−	4.16354i	0.0851477	−	0.147480i	0.905454	+	0.424444i	$0.139530\pi$
$798$		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
$805$		0			0
$806$		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	$-0.714760\pi$
$811$		−	44.4771i		−	1.56180i	0.624654	−	0.780901i	$-0.285240\pi$
$812$		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
$819$		0			0
$820$		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	$-0.399228\pi$
$829$	17.9274			0.622645			0.311323	+	0.950304i	$0.399228\pi$
$830$		0			0
$831$	7.23166	+	12.5256i	0.250864	+	0.434508i
$832$		0			0
$833$		0			0
$834$		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	0.641341	−	0.767256i	$-0.278378\pi$
$839$	8.61866	+	4.97598i	0.297549	+	0.171790i	−0.343792	+	0.939046i	$0.611712\pi$
$840$		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
$847$		0			0
$848$		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	$0.120523\pi$
$853$			21.5922i			0.739302i	−0.929171	+	0.369651i	$0.879477\pi$
$854$		0			0
$855$	0.770125	+	1.33390i	0.0263377	+	0.0456183i
$856$		0			0
$857$	−1.98635	+	3.44046i	−0.0678524	+	0.117524i	−0.897956	−	0.440086i	$-0.854948\pi$
$857$	−1.98635	+	3.44046i	−0.0678524	+	0.117524i	0.830103	+	0.557610i	$0.188281\pi$
$858$		0			0
$859$	−24.9020	−	43.1315i	−0.849644	−	1.47163i	−0.881527	−	0.472134i	$-0.843484\pi$
$859$	−24.9020	−	43.1315i	−0.849644	−	1.47163i	0.0318828	−	0.999492i	$-0.489850\pi$
$860$		0			0
$861$		0			0
$862$		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
$875$		0			0
$876$		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	$0.0198772\pi$
$881$	16.4160	+	28.4334i	0.553070	+	0.957946i	−0.444981	+	0.895540i	$0.646789\pi$
$882$		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	−0.916422	−	0.400213i	$-0.868936\pi$
$887$	−3.32423	+	5.75774i	−0.111617	+	0.193326i	0.804805	+	0.593539i	$0.202270\pi$
$888$		0			0
$889$		0			0
$890$		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
$903$		0			0
$904$		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
$917$		0			0
$918$		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	$-0.862907\pi$
$929$		−	25.4504i		−	0.834999i	0.908677	−	0.417500i	$-0.137093\pi$
$930$		0			0
$931$		0			0
$932$		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	$-0.634106\pi$
$937$	−25.0364			−0.817905			−0.408952	+	0.912556i	$0.634106\pi$
$938$		0			0
$939$	28.1727	+	48.7966i	0.919382	+	1.59242i
$940$		0			0
$941$	10.7221	+	6.19042i	0.349531	+	0.201802i	0.664479	−	0.747307i	$-0.268654\pi$
$941$	10.7221	+	6.19042i	0.349531	+	0.201802i	−0.314948	+	0.949109i	$0.601987\pi$
$942$		0			0
$943$			8.82236i			0.287296i
$944$		0			0
$945$		0			0
$946$		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
$959$		0			0
$960$		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	$-0.742550\pi$
$971$	−43.0247			−1.38073			−0.690364	+	0.723462i	$0.742550\pi$
$972$		0			0
$973$		0			0
$974$		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	0.427537	−	0.903998i	$-0.359381\pi$
$983$	−4.43890	−	2.56280i	−0.141579	−	0.0817406i	−0.569116	+	0.822257i	$0.692715\pi$
$984$		0			0
$985$	−3.62546	+	6.27949i	−0.115517	+	0.200081i
$986$		0			0
$987$		0			0
$988$		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	$-0.941033\pi$
$997$	−20.5543	−	35.6011i	−0.650961	−	1.12750i	0.331929	−	0.943304i	$-0.392301\pi$
$998$		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	2548.2.bq.f.361.7		18
7.2	even	3		2548.2.bb.f.569.3		18
7.3	odd	6		2548.2.u.e.1765.7		18
7.4	even	3		2548.2.u.d.1765.3		18
7.5	odd	6		364.2.bb.a.205.7	✓	18
7.6	odd	2		364.2.bq.a.361.3	yes	18
13.4	even	6		2548.2.bb.f.1733.3		18
21.5	even	6		3276.2.hi.i.1297.7		18
21.20	even	2		3276.2.fe.i.361.3		18
91.4	even	6		2548.2.u.d.589.3		18
91.17	odd	6		2548.2.u.e.589.7		18
91.30	even	6	inner	2548.2.bq.f.1941.7		18
91.69	odd	6		364.2.bb.a.277.7	yes	18
91.82	odd	6		364.2.bq.a.121.3	yes	18
273.173	even	6		3276.2.fe.i.2305.3		18
273.251	even	6		3276.2.hi.i.1369.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.7	✓	18	7.5	odd	6
364.2.bb.a.277.7	yes	18	91.69	odd	6
364.2.bq.a.121.3	yes	18	91.82	odd	6
364.2.bq.a.361.3	yes	18	7.6	odd	2
2548.2.u.d.589.3		18	91.4	even	6
2548.2.u.d.1765.3		18	7.4	even	3
2548.2.u.e.589.7		18	91.17	odd	6
2548.2.u.e.1765.7		18	7.3	odd	6
2548.2.bb.f.569.3		18	7.2	even	3
2548.2.bb.f.1733.3		18	13.4	even	6
2548.2.bq.f.361.7		18	1.1	even	1	trivial
2548.2.bq.f.1941.7		18	91.30	even	6	inner
3276.2.fe.i.361.3		18	21.20	even	2
3276.2.fe.i.2305.3		18	273.173	even	6
3276.2.hi.i.1297.7		18	21.5	even	6
3276.2.hi.i.1369.7		18	273.251	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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

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

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Database

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