LMFDB - Embedded newform 504.2.q.c.25.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.7
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.748111 + 1.56216i) q^{3} +(2.11148 - 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(-1.88066 + 2.33733i) q^{9} +O(q^{10})$	\(q+(0.748111 + 1.56216i) q^{3} +(2.11148 - 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(-1.88066 + 2.33733i) q^{9} +(-0.964575 - 1.67069i) q^{11} +(-0.291529 - 0.504943i) q^{13} +(7.29273 + 0.562477i) q^{15} +(3.61082 - 6.25412i) q^{17} +(2.10268 + 3.64194i) q^{19} +(-0.670409 + 4.53327i) q^{21} +(-0.639939 + 1.10841i) q^{23} +(-6.41671 - 11.1141i) q^{25} +(-5.05822 - 1.18930i) q^{27} +(-4.20305 + 7.27990i) q^{29} -0.952121 q^{31} +(1.88827 - 2.75668i) q^{33} +(10.0423 - 4.89755i) q^{35} +(3.03329 + 5.25381i) q^{37} +(0.570704 - 0.833168i) q^{39} +(1.31299 + 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(4.57709 + 11.8132i) q^{45} +5.76401 q^{47} +(2.62182 + 6.49046i) q^{49} +(12.4712 + 0.961885i) q^{51} +(-0.962456 + 1.66702i) q^{53} -8.14673 q^{55} +(-4.11625 + 6.00929i) q^{57} -4.55229 q^{59} -10.5802 q^{61} +(-7.58322 + 2.34411i) q^{63} -2.46223 q^{65} -4.86383 q^{67} +(-2.21025 - 0.170473i) q^{69} +11.5443 q^{71} +(0.446138 - 0.772734i) q^{73} +(12.5615 - 18.3384i) q^{75} +(0.356209 - 5.09160i) q^{77} -11.8704 q^{79} +(-1.92623 - 8.79145i) q^{81} +(-5.24250 + 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-14.5167 - 1.11965i) q^{87} +(3.87906 + 6.71874i) q^{89} +(0.107659 - 1.53887i) q^{91} +(-0.712292 - 1.48736i) q^{93} +17.7591 q^{95} +(-1.98651 + 3.44073i) q^{97} +(5.71900 + 0.887474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.748111	+	1.56216i	0.431922	+	0.901911i
$3$	0.748111	+	1.56216i	0.431922	+	0.901911i
$4$		0			0
$5$	2.11148	−	3.65719i	0.944283	−	1.63555i	0.187103	−	0.982340i	$-0.440090\pi$
$5$	2.11148	−	3.65719i	0.944283	−	1.63555i	0.757180	−	0.653206i	$-0.226577\pi$
$6$		0			0
$7$	2.19338	+	1.47956i	0.829019	+	0.559220i
$7$	2.19338	+	1.47956i	0.829019	+	0.559220i
$8$		0			0
$9$	−1.88066	+	2.33733i	−0.626887	+	0.779110i
$10$		0			0
$11$	−0.964575	−	1.67069i	−0.290830	−	0.503733i	0.683176	−	0.730254i	$-0.260598\pi$
$11$	−0.964575	−	1.67069i	−0.290830	−	0.503733i	−0.974006	+	0.226521i	$0.927265\pi$
$12$		0			0
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	0.822762	−	0.568386i	$-0.192432\pi$
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	−0.903618	+	0.428340i	$0.859099\pi$
$14$		0			0
$15$	7.29273	+	0.562477i	1.88297	+	0.145231i
$16$		0			0
$17$	3.61082	−	6.25412i	0.875753	−	1.51685i	0.0197936	−	0.999804i	$-0.493699\pi$
$17$	3.61082	−	6.25412i	0.875753	−	1.51685i	0.855959	−	0.517044i	$-0.172968\pi$
$18$		0			0
$19$	2.10268	+	3.64194i	0.482387	+	0.835519i	0.999796	−	0.0202194i	$-0.00643646\pi$
$19$	2.10268	+	3.64194i	0.482387	+	0.835519i	−0.517408	+	0.855739i	$0.673103\pi$
$20$		0			0
$21$	−0.670409	+	4.53327i	−0.146295	+	0.989241i
$22$		0			0
$23$	−0.639939	+	1.10841i	−0.133437	+	0.231119i	−0.924999	−	0.379969i	$-0.875935\pi$
$23$	−0.639939	+	1.10841i	−0.133437	+	0.231119i	0.791563	+	0.611088i	$0.209268\pi$
$24$		0			0
$25$	−6.41671	−	11.1141i	−1.28334	−	2.22281i
$26$		0			0
$27$	−5.05822	−	1.18930i	−0.973454	−	0.228881i
$28$		0			0
$29$	−4.20305	+	7.27990i	−0.780487	+	1.35184i	0.151171	+	0.988508i	$0.451695\pi$
$29$	−4.20305	+	7.27990i	−0.780487	+	1.35184i	−0.931658	+	0.363335i	$0.881638\pi$
$30$		0			0
$31$	−0.952121			−0.171006			−0.0855030	−	0.996338i	$-0.527250\pi$
$31$	−0.952121			−0.171006			−0.0855030	+	0.996338i	$0.527250\pi$
$32$		0			0
$33$	1.88827	−	2.75668i	0.328706	−	0.479876i
$34$		0			0
$35$	10.0423	−	4.89755i	1.69746	−	0.827837i
$36$		0			0
$37$	3.03329	+	5.25381i	0.498669	+	0.863721i	0.999999	−	0.00153588i	$-0.000488885\pi$
$37$	3.03329	+	5.25381i	0.498669	+	0.863721i	−0.501330	+	0.865256i	$0.667156\pi$
$38$		0			0
$39$	0.570704	−	0.833168i	0.0913858	−	0.133414i
$40$		0			0
$41$	1.31299	+	2.27416i	0.205054	+	0.355164i	0.950150	−	0.311794i	$-0.100930\pi$
$41$	1.31299	+	2.27416i	0.205054	+	0.355164i	−0.745096	+	0.666957i	$0.767596\pi$
$42$		0			0
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	−0.830324	−	0.557281i	$-0.811845\pi$
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	0.897782	+	0.440441i	$0.145178\pi$
$44$		0			0
$45$	4.57709	+	11.8132i	0.682313	+	1.76100i
$46$		0			0
$47$	5.76401			0.840767			0.420384	−	0.907346i	$-0.361895\pi$
$47$	5.76401			0.840767			0.420384	+	0.907346i	$0.361895\pi$
$48$		0			0
$49$	2.62182	+	6.49046i	0.374545	+	0.927209i
$50$		0			0
$51$	12.4712	+	0.961885i	1.74632	+	0.134691i
$52$		0			0
$53$	−0.962456	+	1.66702i	−0.132204	+	0.228983i	−0.924526	−	0.381120i	$-0.875539\pi$
$53$	−0.962456	+	1.66702i	−0.132204	+	0.228983i	0.792322	+	0.610103i	$0.208872\pi$
$54$		0			0
$55$	−8.14673			−1.09850
$56$		0			0
$57$	−4.11625	+	6.00929i	−0.545210	+	0.795950i
$58$		0			0
$59$	−4.55229			−0.592657			−0.296329	−	0.955086i	$-0.595762\pi$
$59$	−4.55229			−0.592657			−0.296329	+	0.955086i	$0.595762\pi$
$60$		0			0
$61$	−10.5802			−1.35465			−0.677325	−	0.735684i	$-0.736861\pi$
$61$	−10.5802			−1.35465			−0.677325	+	0.735684i	$0.736861\pi$
$62$		0			0
$63$	−7.58322	+	2.34411i	−0.955395	+	0.295330i
$64$		0			0
$65$	−2.46223			−0.305403
$66$		0			0
$67$	−4.86383			−0.594211			−0.297106	−	0.954845i	$-0.596021\pi$
$67$	−4.86383			−0.594211			−0.297106	+	0.954845i	$0.596021\pi$
$68$		0			0
$69$	−2.21025	−	0.170473i	−0.266083	−	0.0205226i
$70$		0			0
$71$	11.5443			1.37005			0.685027	−	0.728518i	$-0.259791\pi$
$71$	11.5443			1.37005			0.685027	+	0.728518i	$0.259791\pi$
$72$		0			0
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	−0.838736	−	0.544539i	$-0.816705\pi$
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	0.890952	+	0.454097i	$0.150038\pi$
$74$		0			0
$75$	12.5615	−	18.3384i	1.45048	−	2.11754i
$76$		0			0
$77$	0.356209	−	5.09160i	0.0405937	−	0.580242i
$78$		0			0
$79$	−11.8704			−1.33553			−0.667763	−	0.744374i	$-0.732748\pi$
$79$	−11.8704			−1.33553			−0.667763	+	0.744374i	$0.732748\pi$
$80$		0			0
$81$	−1.92623	−	8.79145i	−0.214026	−	0.976828i
$82$		0			0
$83$	−5.24250	+	9.08028i	−0.575439	+	0.996690i	0.420555	+	0.907267i	$0.361836\pi$
$83$	−5.24250	+	9.08028i	−0.575439	+	0.996690i	−0.995994	+	0.0894227i	$0.971498\pi$
$84$		0			0
$85$	−15.2484	−	26.4109i	−1.65392	−	2.86467i
$86$		0			0
$87$	−14.5167	−	1.11965i	−1.55635	−	0.120039i
$88$		0			0
$89$	3.87906	+	6.71874i	0.411180	+	0.712185i	0.995019	−	0.0996849i	$-0.0317835\pi$
$89$	3.87906	+	6.71874i	0.411180	+	0.712185i	−0.583839	+	0.811869i	$0.698450\pi$
$90$		0			0
$91$	0.107659	−	1.53887i	0.0112857	−	0.161317i
$92$		0			0
$93$	−0.712292	−	1.48736i	−0.0738613	−	0.154232i
$94$		0			0
$95$	17.7591			1.82204
$96$		0			0
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	−0.949076	−	0.315047i	$-0.897980\pi$
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	0.747377	+	0.664400i	$0.231313\pi$
$98$		0			0
$99$	5.71900	+	0.887474i	0.574781	+	0.0891945i
$100$		0			0
$101$	−8.38533	−	14.5238i	−0.834372	−	1.44517i	−0.894541	−	0.446986i	$-0.852497\pi$
$101$	−8.38533	−	14.5238i	−0.834372	−	1.44517i	0.0601687	−	0.998188i	$-0.480836\pi$
$102$		0			0
$103$	−5.80569	+	10.0558i	−0.572052	+	0.990823i	0.424303	+	0.905520i	$0.360519\pi$
$103$	−5.80569	+	10.0558i	−0.572052	+	0.990823i	−0.996355	+	0.0853025i	$0.972814\pi$
$104$		0			0
$105$	15.1635	+	12.0237i	1.47981	+	1.17340i
$106$		0			0
$107$	−10.2454	−	17.7455i	−0.990460	−	1.71553i	−0.614570	−	0.788862i	$-0.710671\pi$
$107$	−10.2454	−	17.7455i	−0.990460	−	1.71553i	−0.375890	−	0.926664i	$-0.622663\pi$
$108$		0			0
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	−0.723172	−	0.690668i	$-0.757317\pi$
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	0.959722	+	0.280951i	$0.0906500\pi$
$110$		0			0
$111$	−5.93803	+	8.66890i	−0.563613	+	0.822815i
$112$		0			0
$113$	−7.42131	−	12.8541i	−0.698138	−	1.20921i	−0.969111	−	0.246623i	$-0.920679\pi$
$113$	−7.42131	−	12.8541i	−0.698138	−	1.20921i	0.270974	−	0.962587i	$-0.412654\pi$
$114$		0			0
$115$	2.70244	+	4.68076i	0.252004	+	0.436484i
$116$		0			0
$117$	1.72849	+	0.268227i	0.159799	+	0.0247976i
$118$		0			0
$119$	17.1732	−	8.37524i	1.57427	−	0.767757i
$120$		0			0
$121$	3.63919	−	6.30326i	0.330836	−	0.573024i
$122$		0			0
$123$	−2.57033	+	3.75241i	−0.231759	+	0.338343i
$124$		0			0
$125$	−33.0802			−2.95879
$126$		0			0
$127$	−8.53648			−0.757490			−0.378745	−	0.925501i	$-0.623644\pi$
$127$	−8.53648			−0.757490			−0.378745	+	0.925501i	$0.623644\pi$
$128$		0			0
$129$	1.52781	+	0.117837i	0.134516	+	0.0103750i
$130$		0			0
$131$	1.17342	−	2.03243i	0.102522	−	0.177574i	−0.810201	−	0.586152i	$-0.800642\pi$
$131$	1.17342	−	2.03243i	0.102522	−	0.177574i	0.912723	+	0.408578i	$0.133975\pi$
$132$		0			0
$133$	−0.776499	+	11.0992i	−0.0673310	+	0.962422i
$134$		0			0
$135$	−15.0298	+	15.9877i	−1.29356	+	1.37600i
$136$		0			0
$137$	−0.641815	−	1.11166i	−0.0548340	−	0.0949752i	0.837305	−	0.546735i	$-0.184130\pi$
$137$	−0.641815	−	1.11166i	−0.0548340	−	0.0949752i	−0.892139	+	0.451760i	$0.850796\pi$
$138$		0			0
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	0.890757	−	0.454481i	$-0.150175\pi$
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	−0.838970	+	0.544177i	$0.816842\pi$
$140$		0			0
$141$	4.31212	+	9.00428i	0.363146	+	0.758297i
$142$		0			0
$143$	−0.562403	+	0.974111i	−0.0470305	+	0.0814593i
$144$		0			0
$145$	17.7493	+	30.7427i	1.47400	+	2.55305i
$146$		0			0
$147$	−8.17770	+	8.95127i	−0.674485	+	0.738288i
$148$		0			0
$149$	−3.14729	+	5.45127i	−0.257836	+	0.446585i	−0.965662	−	0.259802i	$-0.916343\pi$
$149$	−3.14729	+	5.45127i	−0.257836	+	0.446585i	0.707826	+	0.706387i	$0.249676\pi$
$150$		0			0
$151$	−1.17726	−	2.03908i	−0.0958044	−	0.165938i	0.814140	−	0.580669i	$-0.197209\pi$
$151$	−1.17726	−	2.03908i	−0.0958044	−	0.165938i	−0.909944	+	0.414731i	$0.863876\pi$
$152$		0			0
$153$	7.82723	+	20.2016i	0.632794	+	1.63320i
$154$		0			0
$155$	−2.01039	+	3.48209i	−0.161478	+	0.279688i
$156$		0			0
$157$	−2.88873			−0.230546			−0.115273	−	0.993334i	$-0.536774\pi$
$157$	−2.88873			−0.230546			−0.115273	+	0.993334i	$0.536774\pi$
$158$		0			0
$159$	−3.32417	−	0.256388i	−0.263624	−	0.0203329i
$160$		0			0
$161$	−3.04358	+	1.48433i	−0.239868	+	0.116982i
$162$		0			0
$163$	2.60538	+	4.51265i	0.204069	+	0.353458i	0.949836	−	0.312749i	$-0.101250\pi$
$163$	2.60538	+	4.51265i	0.204069	+	0.353458i	−0.745767	+	0.666207i	$0.767917\pi$
$164$		0			0
$165$	−6.09465	−	12.7265i	−0.474468	−	0.990753i
$166$		0			0
$167$	10.5400	+	18.2558i	0.815610	+	1.41268i	0.908889	+	0.417039i	$0.136932\pi$
$167$	10.5400	+	18.2558i	0.815610	+	1.41268i	−0.0932784	+	0.995640i	$0.529735\pi$
$168$		0			0
$169$	6.33002	−	10.9639i	0.486925	−	0.843378i
$170$		0			0
$171$	−12.4669	−	1.93461i	−0.953364	−	0.147943i
$172$		0			0
$173$	−4.07305			−0.309669			−0.154834	−	0.987940i	$-0.549484\pi$
$173$	−4.07305			−0.309669			−0.154834	+	0.987940i	$0.549484\pi$
$174$		0			0
$175$	2.36963	−	33.8712i	0.179127	−	2.56042i
$176$		0			0
$177$	−3.40562	−	7.11138i	−0.255982	−	0.534524i
$178$		0			0
$179$	−3.11088	+	5.38821i	−0.232518	+	0.402733i	−0.958549	−	0.284929i	$-0.908030\pi$
$179$	−3.11088	+	5.38821i	−0.232518	+	0.402733i	0.726030	+	0.687663i	$0.241363\pi$
$180$		0			0
$181$	18.2396			1.35574			0.677868	−	0.735184i	$-0.262904\pi$
$181$	18.2396			1.35574			0.677868	+	0.735184i	$0.262904\pi$
$182$		0			0
$183$	−7.91513	−	16.5279i	−0.585103	−	1.22177i
$184$		0			0
$185$	25.6189			1.88354
$186$		0			0
$187$	−13.9316			−1.01878
$188$		0			0
$189$	−9.33495	−	10.0925i	−0.679017	−	0.734122i
$190$		0			0
$191$	−7.38597			−0.534430			−0.267215	−	0.963637i	$-0.586103\pi$
$191$	−7.38597			−0.534430			−0.267215	+	0.963637i	$0.586103\pi$
$192$		0			0
$193$	19.5182			1.40495			0.702474	−	0.711709i	$-0.252079\pi$
$193$	19.5182			1.40495			0.702474	+	0.711709i	$0.252079\pi$
$194$		0			0
$195$	−1.84202	−	3.84639i	−0.131910	−	0.275446i
$196$		0			0
$197$	7.77564			0.553992			0.276996	−	0.960871i	$-0.410661\pi$
$197$	7.77564			0.553992			0.276996	+	0.960871i	$0.410661\pi$
$198$		0			0
$199$	−3.85734	+	6.68110i	−0.273439	+	0.473611i	−0.969740	−	0.244139i	$-0.921495\pi$
$199$	−3.85734	+	6.68110i	−0.273439	+	0.473611i	0.696301	+	0.717750i	$0.254828\pi$
$200$		0			0
$201$	−3.63868	−	7.59806i	−0.256653	−	0.535926i
$202$		0			0
$203$	−19.9899	+	9.74891i	−1.40302	+	0.684240i
$204$		0			0
$205$	11.0894			0.774515
$206$		0			0
$207$	−1.38721	−	3.58029i	−0.0964176	−	0.248847i
$208$		0			0
$209$	4.05638	−	7.02585i	0.280586	−	0.485989i
$210$		0			0
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	0.912933	+	0.408109i	$0.133812\pi$
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	−0.103034	+	0.994678i	$0.532855\pi$
$212$		0			0
$213$	8.63640	+	18.0339i	0.591756	+	1.23567i
$214$		0			0
$215$	−1.86802	−	3.23551i	−0.127398	−	0.220660i
$216$		0			0
$217$	−2.08836	−	1.40872i	−0.141767	−	0.0956301i
$218$		0			0
$219$	1.54089	+	0.118847i	0.104124	+	0.00803090i
$220$		0			0
$221$	−4.21064			−0.283238
$222$		0			0
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	−0.981208	−	0.192952i	$-0.938194\pi$
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	0.657705	+	0.753275i	$0.271527\pi$
$224$		0			0
$225$	38.0449	+	5.90381i	2.53633	+	0.393587i
$226$		0			0
$227$	−8.98592	−	15.5641i	−0.596417	−	1.03302i	−0.993345	−	0.115175i	$-0.963257\pi$
$227$	−8.98592	−	15.5641i	−0.596417	−	1.03302i	0.396929	−	0.917850i	$-0.370076\pi$
$228$		0			0
$229$	3.95834	−	6.85604i	0.261574	−	0.453060i	−0.705086	−	0.709122i	$-0.749092\pi$
$229$	3.95834	−	6.85604i	0.261574	−	0.453060i	0.966660	+	0.256062i	$0.0824250\pi$
$230$		0			0
$231$	8.22036	−	3.25263i	0.540860	−	0.214007i
$232$		0			0
$233$	3.27796	+	5.67759i	0.214746	+	0.371951i	0.953194	−	0.302359i	$-0.0977742\pi$
$233$	3.27796	+	5.67759i	0.214746	+	0.371951i	−0.738448	+	0.674311i	$0.764441\pi$
$234$		0			0
$235$	12.1706	−	21.0801i	0.793922	−	1.37511i
$236$		0			0
$237$	−8.88038	−	18.5434i	−0.576843	−	1.20452i
$238$		0			0
$239$	−8.01922	−	13.8897i	−0.518720	−	0.898450i	−0.999763	−	0.0217529i	$-0.993075\pi$
$239$	−8.01922	−	13.8897i	−0.518720	−	0.898450i	0.481043	−	0.876697i	$-0.340258\pi$
$240$		0			0
$241$	−5.58957	−	9.68142i	−0.360056	−	0.623635i	0.627914	−	0.778283i	$-0.283909\pi$
$241$	−5.58957	−	9.68142i	−0.360056	−	0.623635i	−0.987970	+	0.154648i	$0.950576\pi$
$242$		0			0
$243$	12.2926	−	9.58606i	0.788569	−	0.614946i
$244$		0			0
$245$	29.2728	+	4.11599i	1.87017	+	0.262961i
$246$		0			0
$247$	1.22598	−	2.12347i	0.0780075	−	0.135113i
$248$		0			0
$249$	−18.1068	−	1.39655i	−1.14747	−	0.0885026i
$250$		0			0
$251$	14.6169			0.922613			0.461307	−	0.887241i	$-0.347381\pi$
$251$	14.6169			0.922613			0.461307	+	0.887241i	$0.347381\pi$
$252$		0			0
$253$	2.46908			0.155230
$254$		0			0
$255$	29.8505	−	43.5786i	1.86931	−	2.72900i
$256$		0			0
$257$	−7.45936	+	12.9200i	−0.465302	+	0.805927i	−0.999215	−	0.0396123i	$-0.987388\pi$
$257$	−7.45936	+	12.9200i	−0.465302	+	0.805927i	0.533913	+	0.845540i	$0.320721\pi$
$258$		0			0
$259$	−1.12016	+	16.0115i	−0.0696037	+	0.994907i
$260$		0			0
$261$	−9.11102	−	23.5149i	−0.563958	−	1.45554i
$262$		0			0
$263$	11.1057	+	19.2357i	0.684808	+	1.18612i	0.973497	+	0.228699i	$0.0734472\pi$
$263$	11.1057	+	19.2357i	0.684808	+	1.18612i	−0.288689	+	0.957423i	$0.593219\pi$
$264$		0			0
$265$	4.06442	+	7.03978i	0.249675	+	0.432450i
$266$		0			0
$267$	−7.59374	+	11.0861i	−0.464729	+	0.678456i
$268$		0			0
$269$	−4.73590	+	8.20281i	−0.288753	+	0.500134i	−0.973512	−	0.228635i	$-0.926574\pi$
$269$	−4.73590	+	8.20281i	−0.288753	+	0.500134i	0.684760	+	0.728769i	$0.259907\pi$
$270$		0			0
$271$	8.78188	+	15.2107i	0.533461	+	0.923982i	0.999236	+	0.0390786i	$0.0124423\pi$
$271$	8.78188	+	15.2107i	0.533461	+	0.923982i	−0.465775	+	0.884903i	$0.654224\pi$
$272$		0			0
$273$	2.48449	−	0.983062i	0.150368	−	0.0594976i
$274$		0			0
$275$	−12.3788	+	21.4407i	−0.746469	+	1.29292i
$276$		0			0
$277$	−6.77651	−	11.7373i	−0.407161	−	0.705224i	0.587409	−	0.809290i	$-0.300148\pi$
$277$	−6.77651	−	11.7373i	−0.407161	−	0.705224i	−0.994570	+	0.104066i	$0.966815\pi$
$278$		0			0
$279$	1.79062	−	2.22542i	0.107201	−	0.133233i
$280$		0			0
$281$	6.14196	−	10.6382i	0.366398	−	0.634621i	−0.622601	−	0.782539i	$-0.713924\pi$
$281$	6.14196	−	10.6382i	0.366398	−	0.634621i	0.989000	+	0.147919i	$0.0472574\pi$
$282$		0			0
$283$	14.0483			0.835084			0.417542	−	0.908658i	$-0.362892\pi$
$283$	14.0483			0.835084			0.417542	+	0.908658i	$0.362892\pi$
$284$		0			0
$285$	13.2857	+	27.7424i	0.786980	+	1.64332i
$286$		0			0
$287$	−0.484873	+	6.93072i	−0.0286212	+	0.409108i
$288$		0			0
$289$	−17.5760	−	30.4426i	−1.03388	−	1.79074i
$290$		0			0
$291$	−6.86109	−	0.529185i	−0.402204	−	0.0310214i
$292$		0			0
$293$	4.05863	+	7.02975i	0.237108	+	0.410682i	0.959883	−	0.280401i	$-0.0904673\pi$
$293$	4.05863	+	7.02975i	0.237108	+	0.410682i	−0.722776	+	0.691083i	$0.757134\pi$
$294$		0			0
$295$	−9.61207	+	16.6486i	−0.559636	+	0.969319i
$296$		0			0
$297$	2.89207	+	9.59790i	0.167815	+	0.556926i
$298$		0			0
$299$	0.746244			0.0431564
$300$		0			0
$301$	2.10383	−	1.02602i	0.121263	−	0.0591390i
$302$		0			0
$303$	16.4153	−	23.9646i	0.943035	−	1.37673i
$304$		0			0
$305$	−22.3398	+	38.6937i	−1.27917	+	2.21559i
$306$		0			0
$307$	6.61556			0.377570			0.188785	−	0.982018i	$-0.439545\pi$
$307$	6.61556			0.377570			0.188785	+	0.982018i	$0.439545\pi$
$308$		0			0
$309$	−20.0519	−	1.54658i	−1.14072	−	0.0879816i
$310$		0			0
$311$	−8.35961			−0.474030			−0.237015	−	0.971506i	$-0.576169\pi$
$311$	−8.35961			−0.474030			−0.237015	+	0.971506i	$0.576169\pi$
$312$		0			0
$313$	26.1083			1.47573			0.737864	−	0.674949i	$-0.235834\pi$
$313$	26.1083			1.47573			0.737864	+	0.674949i	$0.235834\pi$
$314$		0			0
$315$	−7.43897	+	32.6828i	−0.419138	+	1.84147i
$316$		0			0
$317$	11.2148			0.629887			0.314943	−	0.949110i	$-0.398014\pi$
$317$	11.2148			0.629887			0.314943	+	0.949110i	$0.398014\pi$
$318$		0			0
$319$	16.2166			0.907957
$320$		0			0
$321$	20.0566	−	29.2805i	1.11945	−	1.63428i
$322$		0			0
$323$	30.3696			1.68981
$324$		0			0
$325$	−3.74132	+	6.48015i	−0.207531	+	0.359454i
$326$		0			0
$327$	8.52980	+	0.657890i	0.471699	+	0.0363814i
$328$		0			0
$329$	12.6427	+	8.52819i	0.697012	+	0.470174i
$330$		0			0
$331$	−18.2329			−1.00217			−0.501086	−	0.865398i	$-0.667066\pi$
$331$	−18.2329			−1.00217			−0.501086	+	0.865398i	$0.667066\pi$
$332$		0			0
$333$	−17.9845	−	2.79083i	−0.985543	−	0.152937i
$334$		0			0
$335$	−10.2699	+	17.7880i	−0.561104	+	0.971860i
$336$		0			0
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	0.964007	−	0.265876i	$-0.0856612\pi$
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	−0.712259	+	0.701917i	$0.752328\pi$
$338$		0			0
$339$	14.5281	−	21.2095i	0.789059	−	1.15194i
$340$		0			0
$341$	0.918392	+	1.59070i	0.0497337	+	0.0861413i
$342$		0			0
$343$	−3.85237	+	18.1152i	−0.208009	+	0.978127i
$344$		0			0
$345$	−5.29036	+	7.72336i	−0.284823	+	0.415812i
$346$		0			0
$347$	−31.6649			−1.69986			−0.849931	−	0.526894i	$-0.823356\pi$
$347$	−31.6649			−1.69986			−0.849931	+	0.526894i	$0.823356\pi$
$348$		0			0
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.294296	+	0.955714i	$0.595085\pi$
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.680525	+	0.732725i	$0.738248\pi$
$350$		0			0
$351$	0.874088	+	2.90083i	0.0466554	+	0.154835i
$352$		0			0
$353$	−3.59888	−	6.23345i	−0.191549	−	0.331773i	0.754215	−	0.656628i	$-0.228018\pi$
$353$	−3.59888	−	6.23345i	−0.191549	−	0.331773i	−0.945764	+	0.324855i	$0.894684\pi$
$354$		0			0
$355$	24.3755	−	42.2196i	1.29372	−	2.24079i
$356$		0			0
$357$	25.9309	+	20.5617i	1.37241	+	1.08824i
$358$		0			0
$359$	−7.39891	−	12.8153i	−0.390499	−	0.676365i	0.602016	−	0.798484i	$-0.294364\pi$
$359$	−7.39891	−	12.8153i	−0.390499	−	0.676365i	−0.992515	+	0.122119i	$0.961031\pi$
$360$		0			0
$361$	0.657495	−	1.13881i	0.0346050	−	0.0599376i
$362$		0			0
$363$	12.5692	+	0.969442i	0.659712	+	0.0508825i
$364$		0			0
$365$	−1.88402	−	3.26323i	−0.0986144	−	0.170805i
$366$		0			0
$367$	−2.09550	−	3.62951i	−0.109384	−	0.189459i	0.806137	−	0.591729i	$-0.201555\pi$
$367$	−2.09550	−	3.62951i	−0.109384	−	0.189459i	−0.915521	+	0.402270i	$0.868221\pi$
$368$		0			0
$369$	−7.78474	−	1.20804i	−0.405257	−	0.0628878i
$370$		0			0
$371$	−4.57749	+	2.23240i	−0.237651	+	0.115901i
$372$		0			0
$373$	−8.70875	+	15.0840i	−0.450922	+	0.781020i	−0.998444	−	0.0557718i	$-0.982238\pi$
$373$	−8.70875	+	15.0840i	−0.450922	+	0.781020i	0.547522	+	0.836792i	$0.315571\pi$
$374$		0			0
$375$	−24.7477	−	51.6765i	−1.27796	−	2.66856i
$376$		0			0
$377$	4.90125			0.252427
$378$		0			0
$379$	−11.1732			−0.573927			−0.286964	−	0.957941i	$-0.592646\pi$
$379$	−11.1732			−0.573927			−0.286964	+	0.957941i	$0.592646\pi$
$380$		0			0
$381$	−6.38624	−	13.3353i	−0.327177	−	0.683189i
$382$		0			0
$383$	12.5508	−	21.7386i	0.641316	−	1.11079i	−0.343823	−	0.939035i	$-0.611722\pi$
$383$	12.5508	−	21.7386i	0.641316	−	1.11079i	0.985139	−	0.171758i	$-0.0549448\pi$
$384$		0			0
$385$	−17.8689	−	12.0536i	−0.910681	−	0.614306i
$386$		0			0
$387$	0.958888	+	2.47482i	0.0487430	+	0.125802i
$388$		0			0
$389$	−0.732011	−	1.26788i	−0.0371144	−	0.0642841i	0.846872	−	0.531798i	$-0.178483\pi$
$389$	−0.732011	−	1.26788i	−0.0371144	−	0.0642841i	−0.883986	+	0.467513i	$0.845150\pi$
$390$		0			0
$391$	4.62141	+	8.00452i	0.233715	+	0.404806i
$392$		0			0
$393$	4.05282	+	0.312587i	0.204438	+	0.0157679i
$394$		0			0
$395$	−25.0641	+	43.4124i	−1.26111	+	2.18431i
$396$		0			0
$397$	−1.49591	−	2.59100i	−0.0750778	−	0.130039i	0.826042	−	0.563608i	$-0.190587\pi$
$397$	−1.49591	−	2.59100i	−0.0750778	−	0.130039i	−0.901120	+	0.433570i	$0.857254\pi$
$398$		0			0
$399$	−17.9196	+	7.09042i	−0.897101	+	0.354965i
$400$		0			0
$401$	13.1685	−	22.8086i	0.657605	−	1.13901i	−0.323629	−	0.946184i	$-0.604903\pi$
$401$	13.1685	−	22.8086i	0.657605	−	1.13901i	0.981234	−	0.192821i	$-0.0617637\pi$
$402$		0			0
$403$	0.277571	+	0.480767i	0.0138268	+	0.0239487i
$404$		0			0
$405$	−36.2192	−	11.5184i	−1.79975	−	0.572353i
$406$		0			0
$407$	5.85166	−	10.1354i	0.290056	−	0.502392i
$408$		0			0
$409$	3.00784			0.148728			0.0743642	−	0.997231i	$-0.476307\pi$
$409$	3.00784			0.148728			0.0743642	+	0.997231i	$0.476307\pi$
$410$		0			0
$411$	1.25643	−	1.83426i	0.0619752	−	0.0904773i
$412$		0			0
$413$	−9.98489	−	6.73537i	−0.491324	−	0.331426i
$414$		0			0
$415$	22.1389	+	38.3457i	1.08676	+	1.88232i
$416$		0			0
$417$	−1.19523	+	1.74491i	−0.0585308	+	0.0854488i
$418$		0			0
$419$	−17.2414	−	29.8630i	−0.842297	−	1.45890i	−0.887948	−	0.459944i	$-0.847869\pi$
$419$	−17.2414	−	29.8630i	−0.842297	−	1.45890i	0.0456508	−	0.998957i	$-0.485464\pi$
$420$		0			0
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	−0.519132	−	0.854694i	$-0.673745\pi$
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	0.999753	+	0.0222349i	$0.00707818\pi$
$422$		0			0
$423$	−10.8401	+	13.4724i	−0.527066	+	0.655051i
$424$		0			0
$425$	−92.6783			−4.49556
$426$		0			0
$427$	−23.2063	−	15.6540i	−1.12303	−	0.757548i
$428$		0			0
$429$	−1.94245	−	0.149818i	−0.0937825	−	0.00723330i
$430$		0			0
$431$	10.4257	−	18.0578i	0.502188	−	0.869816i	−0.497808	−	0.867287i	$-0.665862\pi$
$431$	10.4257	−	18.0578i	0.502188	−	0.869816i	0.999997	−	0.00252883i	$-0.000804953\pi$
$432$		0			0
$433$	15.6324			0.751247			0.375624	−	0.926772i	$-0.377429\pi$
$433$	15.6324			0.751247			0.375624	+	0.926772i	$0.377429\pi$
$434$		0			0
$435$	−34.7465	+	50.7262i	−1.66597	+	2.43213i
$436$		0			0
$437$	−5.38235			−0.257473
$438$		0			0
$439$	35.6989			1.70382			0.851909	−	0.523690i	$-0.175445\pi$
$439$	35.6989			1.70382			0.851909	+	0.523690i	$0.175445\pi$
$440$		0			0
$441$	−20.1011	−	6.07829i	−0.957195	−	0.289443i
$442$		0			0
$443$	18.1157			0.860705			0.430352	−	0.902661i	$-0.358389\pi$
$443$	18.1157			0.860705			0.430352	+	0.902661i	$0.358389\pi$
$444$		0			0
$445$	32.7623			1.55308
$446$		0			0
$447$	−10.8703	−	0.838406i	−0.514146	−	0.0396552i
$448$		0			0
$449$	17.4189			0.822051			0.411025	−	0.911624i	$-0.365171\pi$
$449$	17.4189			0.822051			0.411025	+	0.911624i	$0.365171\pi$
$450$		0			0
$451$	2.53294	−	4.38719i	0.119272	−	0.206585i
$452$		0			0
$453$	2.30464	−	3.36453i	0.108281	−	0.158079i
$454$		0			0
$455$	−5.40061	−	3.64302i	−0.253185	−	0.170787i
$456$		0			0
$457$	15.3584			0.718434			0.359217	−	0.933254i	$-0.383044\pi$
$457$	15.3584			0.718434			0.359217	+	0.933254i	$0.383044\pi$
$458$		0			0
$459$	−25.7023	+	27.3404i	−1.19968	+	1.27614i
$460$		0			0
$461$	−6.15140	+	10.6545i	−0.286499	+	0.496231i	−0.972972	−	0.230924i	$-0.925825\pi$
$461$	−6.15140	+	10.6545i	−0.286499	+	0.496231i	0.686472	+	0.727156i	$0.259158\pi$
$462$		0			0
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	0.996610	−	0.0822677i	$-0.0262162\pi$
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	−0.569551	+	0.821956i	$0.692883\pi$
$464$		0			0
$465$	−6.94356	−	0.535546i	−0.322000	−	0.0248353i
$466$		0			0
$467$	−11.1020	−	19.2292i	−0.513738	−	0.889820i	−0.999873	−	0.0159363i	$-0.994927\pi$
$467$	−11.1020	−	19.2292i	−0.513738	−	0.889820i	0.486135	−	0.873884i	$-0.338406\pi$
$468$		0			0
$469$	−10.6682	−	7.19631i	−0.492612	−	0.332295i
$470$		0			0
$471$	−2.16109	−	4.51265i	−0.0995779	−	0.207932i
$472$		0			0
$473$	−1.70672			−0.0784749
$474$		0			0
$475$	26.9845	−	46.7386i	1.23814	−	2.14451i
$476$		0			0
$477$	−2.08633	−	5.38468i	−0.0955266	−	0.246548i
$478$		0			0
$479$	17.2969	+	29.9591i	0.790317	+	1.36887i	0.925771	+	0.378085i	$0.123417\pi$
$479$	17.2969	+	29.9591i	0.790317	+	1.36887i	−0.135454	+	0.990784i	$0.543249\pi$
$480$		0			0
$481$	1.76858	−	3.06328i	0.0806405	−	0.139673i
$482$		0			0
$483$	−4.59569	−	3.64411i	−0.209111	−	0.165813i
$484$		0			0
$485$	8.38895	+	14.5301i	0.380922	+	0.659777i
$486$		0			0
$487$	6.79789	−	11.7743i	0.308042	−	0.533544i	−0.669892	−	0.742458i	$-0.733660\pi$
$487$	6.79789	−	11.7743i	0.308042	−	0.533544i	0.977934	+	0.208915i	$0.0669931\pi$
$488$		0			0
$489$	−5.10035	+	7.44597i	−0.230646	+	0.336718i
$490$		0			0
$491$	−7.01841	−	12.1563i	−0.316737	−	0.548604i	0.663069	−	0.748559i	$-0.269254\pi$
$491$	−7.01841	−	12.1563i	−0.316737	−	0.548604i	−0.979805	+	0.199955i	$0.935920\pi$
$492$		0			0
$493$	30.3529	+	52.5728i	1.36703	+	2.36776i
$494$		0			0
$495$	15.3212	−	19.0416i	0.688638	−	0.855856i
$496$		0			0
$497$	25.3210	+	17.0804i	1.13580	+	0.766161i
$498$		0			0
$499$	15.1408	−	26.2246i	0.677794	−	1.17397i	−0.297849	−	0.954613i	$-0.596269\pi$
$499$	15.1408	−	26.2246i	0.677794	−	1.17397i	0.975644	−	0.219362i	$-0.0703974\pi$
$500$		0			0
$501$	−20.6334	+	30.1225i	−0.921830	+	1.34577i
$502$		0			0
$503$	−35.5942			−1.58707			−0.793533	−	0.608527i	$-0.791761\pi$
$503$	−35.5942			−1.58707			−0.793533	+	0.608527i	$0.791761\pi$
$504$		0			0
$505$	−70.8219			−3.15153
$506$		0			0
$507$	21.8629	+	1.68625i	0.970966	+	0.0748891i
$508$		0			0
$509$	3.23675	−	5.60621i	0.143466	−	0.248491i	−0.785333	−	0.619073i	$-0.787508\pi$
$509$	3.23675	−	5.60621i	0.143466	−	0.248491i	0.928800	+	0.370582i	$0.120842\pi$
$510$		0			0
$511$	2.12185	−	1.03481i	0.0938653	−	0.0457773i
$512$		0			0
$513$	−6.30443	−	20.9225i	−0.278347	−	0.923749i
$514$		0			0
$515$	24.5172	+	42.4651i	1.08036	+	1.87123i
$516$		0			0
$517$	−5.55982	−	9.62989i	−0.244521	−	0.423522i
$518$		0			0
$519$	−3.04710	−	6.36274i	−0.133753	−	0.279293i
$520$		0			0
$521$	6.18988	−	10.7212i	0.271184	−	0.469704i	−0.697982	−	0.716116i	$-0.745918\pi$
$521$	6.18988	−	10.7212i	0.271184	−	0.469704i	0.969165	+	0.246412i	$0.0792516\pi$
$522$		0			0
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	0.999793	−	0.0203585i	$-0.00648074\pi$
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	−0.517527	+	0.855667i	$0.673147\pi$
$524$		0			0
$525$	54.6849	−	21.6377i	2.38664	−	0.944347i
$526$		0			0
$527$	−3.43794	+	5.95469i	−0.149759	+	0.259390i
$528$		0			0
$529$	10.6810	+	18.5000i	0.464389	+	0.804346i
$530$		0			0
$531$	8.56131	−	10.6402i	0.371529	−	0.461746i
$532$		0			0
$533$	0.765547	−	1.32597i	0.0331595	−	0.0574340i
$534$		0			0
$535$	−86.5319			−3.74110
$536$		0			0
$537$	−10.7445	−	0.828706i	−0.463659	−	0.0357613i
$538$		0			0
$539$	8.31462	−	10.6408i	0.358136	−	0.458331i
$540$		0			0
$541$	7.24989	+	12.5572i	0.311697	+	0.539875i	0.978730	−	0.205153i	$-0.0657693\pi$
$541$	7.24989	+	12.5572i	0.311697	+	0.539875i	−0.667033	+	0.745028i	$0.732436\pi$
$542$		0			0
$543$	13.6452	+	28.4930i	0.585572	+	1.22275i
$544$		0			0
$545$	−10.4293	−	18.0640i	−0.446740	−	0.773777i
$546$		0			0
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	0.469042	+	0.883176i	$0.344599\pi$
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	−0.999374	+	0.0353858i	$0.988734\pi$
$548$		0			0
$549$	19.8977	−	24.7293i	0.849212	−	1.05542i
$550$		0			0
$551$	−35.3506			−1.50599
$552$		0			0
$553$	−26.0363	−	17.5630i	−1.10718	−	0.746853i
$554$		0			0
$555$	19.1658	+	40.0207i	0.813542	+	1.69879i
$556$		0			0
$557$	9.02336	−	15.6289i	0.382332	−	0.662219i	−0.609063	−	0.793122i	$-0.708454\pi$
$557$	9.02336	−	15.6289i	0.382332	−	0.662219i	0.991395	+	0.130903i	$0.0417877\pi$
$558$		0			0
$559$	−0.515831			−0.0218173
$560$		0			0
$561$	−10.4224	−	21.7634i	−0.440034	−	0.918850i
$562$		0			0
$563$	19.0350			0.802228			0.401114	−	0.916028i	$-0.368623\pi$
$563$	19.0350			0.802228			0.401114	+	0.916028i	$0.368623\pi$
$564$		0			0
$565$	−62.6798			−2.63696
$566$		0			0
$567$	8.78250	−	22.1330i	0.368830	−	0.929497i
$568$		0			0
$569$	9.36036			0.392407			0.196203	−	0.980563i	$-0.437139\pi$
$569$	9.36036			0.392407			0.196203	+	0.980563i	$0.437139\pi$
$570$		0			0
$571$	35.3611			1.47981			0.739907	−	0.672709i	$-0.234869\pi$
$571$	35.3611			1.47981			0.739907	+	0.672709i	$0.234869\pi$
$572$		0			0
$573$	−5.52552	−	11.5380i	−0.230832	−	0.482008i
$574$		0			0
$575$	16.4252			0.684979
$576$		0			0
$577$	14.0160	−	24.2764i	0.583493	−	1.01064i	−0.411568	−	0.911379i	$-0.635019\pi$
$577$	14.0160	−	24.2764i	0.583493	−	1.01064i	0.995061	−	0.0992610i	$-0.0316479\pi$
$578$		0			0
$579$	14.6018	+	30.4904i	0.606828	+	1.26714i
$580$		0			0
$581$	−24.9336	+	12.1599i	−1.03442	+	0.504478i
$582$		0			0
$583$	3.71344			0.153795
$584$		0			0
$585$	4.63063	−	5.75506i	0.191453	−	0.237942i
$586$		0			0
$587$	13.7305	−	23.7819i	0.566718	−	0.981585i	−0.430169	−	0.902748i	$-0.641546\pi$
$587$	13.7305	−	23.7819i	0.566718	−	0.981585i	0.996888	−	0.0788364i	$-0.0251205\pi$
$588$		0			0
$589$	−2.00200	−	3.46757i	−0.0824912	−	0.142879i
$590$		0			0
$591$	5.81704	+	12.1468i	0.239281	+	0.499651i
$592$		0			0
$593$	−11.1267	−	19.2719i	−0.456917	−	0.791404i	0.541879	−	0.840457i	$-0.317713\pi$
$593$	−11.1267	−	19.2719i	−0.456917	−	0.791404i	−0.998796	+	0.0490525i	$0.984380\pi$
$594$		0			0
$595$	5.63108	−	80.4900i	0.230852	−	3.29977i
$596$		0			0
$597$	−13.3226	−	1.02755i	−0.545259	−	0.0420550i
$598$		0			0
$599$	6.74118			0.275437			0.137719	−	0.990471i	$-0.456023\pi$
$599$	6.74118			0.275437			0.137719	+	0.990471i	$0.456023\pi$
$600$		0			0
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	−0.771747	−	0.635929i	$-0.780617\pi$
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	0.936605	+	0.350388i	$0.113950\pi$
$602$		0			0
$603$	9.14721	−	11.3684i	0.372503	−	0.462956i
$604$		0			0
$605$	−15.3682	−	26.6185i	−0.624805	−	1.08219i
$606$		0			0
$607$	−15.8020	+	27.3698i	−0.641382	+	1.11091i	0.343742	+	0.939064i	$0.388305\pi$
$607$	−15.8020	+	27.3698i	−0.641382	+	1.11091i	−0.985124	+	0.171843i	$0.945028\pi$
$608$		0			0
$609$	−30.1840	−	23.9341i	−1.22312	−	0.969858i
$610$		0			0
$611$	−1.68038	−	2.91050i	−0.0679808	−	0.117746i
$612$		0			0
$613$	−3.10601	+	5.37977i	−0.125451	+	0.217287i	−0.921909	−	0.387407i	$-0.873371\pi$
$613$	−3.10601	+	5.37977i	−0.125451	+	0.217287i	0.796458	+	0.604693i	$0.206704\pi$
$614$		0			0
$615$	8.29608	+	17.3233i	0.334530	+	0.698544i
$616$		0			0
$617$	−0.309009	−	0.535218i	−0.0124402	−	0.0215471i	0.859738	−	0.510735i	$-0.170627\pi$
$617$	−0.309009	−	0.535218i	−0.0124402	−	0.0215471i	−0.872178	+	0.489188i	$0.837293\pi$
$618$		0			0
$619$	−20.0103	−	34.6589i	−0.804283	−	1.39306i	−0.916774	−	0.399406i	$-0.869217\pi$
$619$	−20.0103	−	34.6589i	−0.804283	−	1.39306i	0.112492	−	0.993653i	$-0.464117\pi$
$620$		0			0
$621$	4.55518	−	4.84549i	0.182793	−	0.194443i
$622$		0			0
$623$	−1.43250	+	20.4760i	−0.0573920	+	0.820355i
$624$		0			0
$625$	−37.7647	+	65.4105i	−1.51059	+	2.61642i
$626$		0			0
$627$	14.0101	+	1.08058i	0.559509	+	0.0431541i
$628$		0			0
$629$	43.8106			1.74684
$630$		0			0
$631$	5.20154			0.207070			0.103535	−	0.994626i	$-0.466985\pi$
$631$	5.20154			0.207070			0.103535	+	0.994626i	$0.466985\pi$
$632$		0			0
$633$	−23.0304	+	33.6219i	−0.915376	+	1.33635i
$634$		0			0
$635$	−18.0246	+	31.2196i	−0.715285	+	1.23891i
$636$		0			0
$637$	2.51298	−	3.21603i	0.0995678	−	0.127424i
$638$		0			0
$639$	−21.7109	+	26.9828i	−0.858868	+	1.06742i
$640$		0			0
$641$	0.137294	+	0.237799i	0.00542277	+	0.00939251i	0.868724	−	0.495296i	$-0.164941\pi$
$641$	0.137294	+	0.237799i	0.00542277	+	0.00939251i	−0.863301	+	0.504689i	$0.831607\pi$
$642$		0			0
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	0.998002	−	0.0631900i	$-0.0201274\pi$
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	−0.553725	+	0.832700i	$0.686794\pi$
$644$		0			0
$645$	3.65689	−	5.33867i	0.143990	−	0.210210i
$646$		0			0
$647$	12.2737	−	21.2586i	0.482528	−	0.835763i	−0.517271	−	0.855822i	$-0.673052\pi$
$647$	12.2737	−	21.2586i	0.482528	−	0.835763i	0.999799	+	0.0200588i	$0.00638534\pi$
$648$		0			0
$649$	4.39102	+	7.60547i	0.172363	+	0.298541i
$650$		0			0
$651$	0.638311	−	4.31623i	0.0250174	−	0.169166i
$652$		0			0
$653$	−16.5154	+	28.6055i	−0.646298	+	1.11942i	0.337703	+	0.941253i	$0.390350\pi$
$653$	−16.5154	+	28.6055i	−0.646298	+	1.11942i	−0.984000	+	0.178167i	$0.942983\pi$
$654$		0			0
$655$	−4.95532	−	8.58286i	−0.193620	−	0.335360i
$656$		0			0
$657$	0.967101	+	2.49602i	0.0377302	+	0.0973791i
$658$		0			0
$659$	21.3813	−	37.0335i	0.832897	−	1.44262i	−0.0628336	−	0.998024i	$-0.520014\pi$
$659$	21.3813	−	37.0335i	0.832897	−	1.44262i	0.895731	−	0.444596i	$-0.146653\pi$
$660$		0			0
$661$	−19.1083			−0.743227			−0.371614	−	0.928387i	$-0.621195\pi$
$661$	−19.1083			−0.743227			−0.371614	+	0.928387i	$0.621195\pi$
$662$		0			0
$663$	−3.15002	−	6.57767i	−0.122337	−	0.255456i
$664$		0			0
$665$	38.9523	+	26.2756i	1.51051	+	1.01892i
$666$		0			0
$667$	−5.37940	−	9.31739i	−0.208291	−	0.360771i
$668$		0			0
$669$	−16.6853	−	1.28691i	−0.645090	−	0.0497548i
$670$		0			0
$671$	10.2054	+	17.6762i	0.393973	+	0.682382i
$672$		0			0
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	−0.999999	−	0.00162995i	$-0.999481\pi$
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	0.501411	+	0.865209i	$0.332815\pi$
$674$		0			0
$675$	19.2391	+	63.8487i	0.740515	+	2.45754i
$676$		0			0
$677$	1.89337			0.0727682			0.0363841	−	0.999338i	$-0.488416\pi$
$677$	1.89337			0.0727682			0.0363841	+	0.999338i	$0.488416\pi$
$678$		0			0
$679$	−9.44792	+	4.60767i	−0.362578	+	0.176826i
$680$		0			0
$681$	17.5910	−	25.6811i	0.674090	−	0.984101i
$682$		0			0
$683$	−6.39573	+	11.0777i	−0.244726	+	0.423878i	−0.962055	−	0.272857i	$-0.912031\pi$
$683$	−6.39573	+	11.0777i	−0.244726	+	0.423878i	0.717329	+	0.696735i	$0.245365\pi$
$684$		0			0
$685$	−5.42072			−0.207115
$686$		0			0
$687$	13.6715	+	1.05446i	0.521599	+	0.0402301i
$688$		0			0
$689$	1.12234			0.0427576
$690$		0			0
$691$	−36.0698			−1.37216			−0.686079	−	0.727527i	$-0.740670\pi$
$691$	−36.0698			−1.37216			−0.686079	+	0.727527i	$0.740670\pi$
$692$		0			0
$693$	11.2309	+	10.4082i	0.426625	+	0.395373i
$694$		0			0
$695$	5.15669			0.195604
$696$		0			0
$697$	18.9638			0.718306
$698$		0			0
$699$	−6.41700	+	9.36815i	−0.242713	+	0.354336i
$700$		0			0
$701$	−20.2524			−0.764922			−0.382461	−	0.923972i	$-0.624923\pi$
$701$	−20.2524			−0.764922			−0.382461	+	0.923972i	$0.624923\pi$
$702$		0			0
$703$	−12.7560	+	22.0941i	−0.481103	+	0.833296i
$704$		0			0
$705$	42.0354	+	3.24212i	1.58314	+	0.122105i
$706$		0			0
$707$	3.09663	−	44.2628i	0.116461	−	1.66468i
$708$		0			0
$709$	−6.76636			−0.254116			−0.127058	−	0.991895i	$-0.540553\pi$
$709$	−6.76636			−0.254116			−0.127058	+	0.991895i	$0.540553\pi$
$710$		0			0
$711$	22.3242	−	27.7451i	0.837223	−	1.04052i
$712$		0			0
$713$	0.609300	−	1.05534i	0.0228185	−	0.0395227i
$714$		0			0
$715$	2.37501	+	4.11364i	0.0888203	+	0.153841i
$716$		0			0
$717$	15.6986	−	22.9183i	0.586275	−	0.855900i
$718$		0			0
$719$	6.43767	+	11.1504i	0.240084	+	0.415839i	0.960738	−	0.277457i	$-0.0894915\pi$
$719$	6.43767	+	11.1504i	0.240084	+	0.415839i	−0.720654	+	0.693295i	$0.756158\pi$
$720$		0			0
$721$	−27.6121	+	13.4662i	−1.02833	+	0.501508i
$722$		0			0
$723$	10.9423	−	15.9745i	0.406947	−	0.594100i
$724$		0			0
$725$	107.879			4.00653
$726$		0			0
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	−0.466613	−	0.884461i	$-0.654526\pi$
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	0.999273	−	0.0381316i	$-0.0121406\pi$
$728$		0			0
$729$	24.1711	+	12.0315i	0.895227	+	0.445611i
$730$		0			0
$731$	−3.19449	−	5.53301i	−0.118152	−	0.204646i
$732$		0			0
$733$	−2.33025	+	4.03611i	−0.0860697	+	0.149077i	−0.905847	−	0.423606i	$-0.860764\pi$
$733$	−2.33025	+	4.03611i	−0.0860697	+	0.149077i	0.819777	+	0.572683i	$0.194097\pi$
$734$		0			0
$735$	15.4695	+	48.8079i	0.570600	+	1.80031i
$736$		0			0
$737$	4.69153	+	8.12596i	0.172815	+	0.299324i
$738$		0			0
$739$	9.46395	−	16.3920i	0.348137	−	0.602991i	−0.637782	−	0.770217i	$-0.720148\pi$
$739$	9.46395	−	16.3920i	0.348137	−	0.602991i	0.985919	+	0.167227i	$0.0534811\pi$
$740$		0			0
$741$	4.23436	+	0.326589i	0.155553	+	0.0119976i
$742$		0			0
$743$	6.64732	+	11.5135i	0.243867	+	0.422389i	0.961812	−	0.273710i	$-0.0882507\pi$
$743$	6.64732	+	11.5135i	0.243867	+	0.422389i	−0.717946	+	0.696099i	$0.754917\pi$
$744$		0			0
$745$	13.2909	+	23.0205i	0.486941	+	0.843406i
$746$		0			0
$747$	−11.3643	−	29.3304i	−0.415796	−	1.07314i
$748$		0			0
$749$	3.78353	−	54.0814i	0.138247	−	1.97609i
$750$		0			0
$751$	7.61766	−	13.1942i	0.277972	−	0.481462i	−0.692908	−	0.721026i	$-0.743671\pi$
$751$	7.61766	−	13.1942i	0.277972	−	0.481462i	0.970881	+	0.239563i	$0.0770043\pi$
$752$		0			0
$753$	10.9351	+	22.8339i	0.398497	+	0.832115i
$754$		0			0
$755$	−9.94308			−0.361866
$756$		0			0
$757$	15.6279			0.568004			0.284002	−	0.958824i	$-0.408338\pi$
$757$	15.6279			0.568004			0.284002	+	0.958824i	$0.408338\pi$
$758$		0			0
$759$	1.84714	+	3.85708i	0.0670471	+	0.140003i
$760$		0			0
$761$	−3.54797	+	6.14527i	−0.128614	+	0.222766i	−0.923140	−	0.384464i	$-0.874386\pi$
$761$	−3.54797	+	6.14527i	−0.128614	+	0.222766i	0.794526	+	0.607230i	$0.207719\pi$
$762$		0			0
$763$	11.7458	−	5.72832i	0.425226	−	0.207379i
$764$		0			0
$765$	90.4081	+	14.0295i	3.26871	+	0.507239i
$766$		0			0
$767$	1.32712	+	2.29865i	0.0479197	+	0.0829994i
$768$		0			0
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	0.950492	−	0.310748i	$-0.100579\pi$
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	−0.744362	+	0.667777i	$0.767246\pi$
$770$		0			0
$771$	−25.7635	−	1.98710i	−0.927849	−	0.0715635i
$772$		0			0
$773$	7.40125	−	12.8193i	0.266204	−	0.461080i	−0.701674	−	0.712498i	$-0.747564\pi$
$773$	7.40125	−	12.8193i	0.266204	−	0.461080i	0.967878	+	0.251418i	$0.0808970\pi$
$774$		0			0
$775$	6.10949	+	10.5819i	0.219459	+	0.380114i
$776$		0			0
$777$	−25.8505	+	10.2285i	−0.927381	+	0.366946i
$778$		0			0
$779$	−5.52157	+	9.56364i	−0.197831	+	0.342653i
$780$		0			0
$781$	−11.1353	−	19.2869i	−0.398453	−	0.690141i
$782$		0			0
$783$	29.9179	−	31.8246i	1.06918	−	1.13732i
$784$		0			0
$785$	−6.09951	+	10.5647i	−0.217701	+	0.377069i
$786$		0			0
$787$	−19.7177			−0.702861			−0.351431	−	0.936214i	$-0.614305\pi$
$787$	−19.7177			−0.702861			−0.351431	+	0.936214i	$0.614305\pi$
$788$		0			0
$789$	−21.7408	+	31.7393i	−0.773993	+	1.12995i
$790$		0			0
$791$	2.74062	−	39.1741i	0.0974452	−	1.39287i
$792$		0			0
$793$	3.08442	+	5.34238i	0.109531	+	0.189713i
$794$		0			0
$795$	−7.95659	+	11.6158i	−0.282191	+	0.411969i
$796$		0			0
$797$	22.2215	+	38.4887i	0.787125	+	1.36334i	0.927722	+	0.373273i	$0.121764\pi$
$797$	22.2215	+	38.4887i	0.787125	+	1.36334i	−0.140597	+	0.990067i	$0.544902\pi$
$798$		0			0
$799$	20.8128	−	36.0488i	0.736304	−	1.27532i
$800$		0			0
$801$	−22.9991	−	3.56900i	−0.812634	−	0.126104i
$802$		0			0
$803$	−1.72133			−0.0607446
$804$		0			0
$805$	−0.997986	+	14.2651i	−0.0351744	+	0.502779i
$806$		0			0
$807$	−16.3570	−	1.26159i	−0.575795	−	0.0444102i
$808$		0			0
$809$	−5.34657	+	9.26053i	−0.187975	+	0.325583i	−0.944575	−	0.328296i	$-0.893526\pi$
$809$	−5.34657	+	9.26053i	−0.187975	+	0.325583i	0.756600	+	0.653878i	$0.226859\pi$
$810$		0			0
$811$	−13.1292			−0.461030			−0.230515	−	0.973069i	$-0.574041\pi$
$811$	−13.1292			−0.461030			−0.230515	+	0.973069i	$0.574041\pi$
$812$		0			0
$813$	−17.1916	+	25.0979i	−0.602936	+	0.880222i
$814$		0			0
$815$	22.0048			0.770796
$816$		0			0
$817$	3.72047			0.130163
$818$		0			0
$819$	3.39437	+	3.14572i	0.118609	+	0.109920i
$820$		0			0
$821$	2.62808			0.0917205			0.0458602	−	0.998948i	$-0.485397\pi$
$821$	2.62808			0.0917205			0.0458602	+	0.998948i	$0.485397\pi$
$822$		0			0
$823$	−46.3921			−1.61713			−0.808563	−	0.588410i	$-0.799754\pi$
$823$	−46.3921			−1.61713			−0.808563	+	0.588410i	$0.799754\pi$
$824$		0			0
$825$	−42.7544	−	3.29758i	−1.48852	−	0.114807i
$826$		0			0
$827$	−15.2072			−0.528807			−0.264404	−	0.964412i	$-0.585175\pi$
$827$	−15.2072			−0.528807			−0.264404	+	0.964412i	$0.585175\pi$
$828$		0			0
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	−0.317311	−	0.948322i	$-0.602780\pi$
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	0.979926	−	0.199361i	$-0.0638867\pi$
$830$		0			0
$831$	13.2658	−	19.3667i	0.460187	−	0.671825i
$832$		0			0
$833$	50.0591	+	7.03871i	1.73444	+	0.243877i
$834$		0			0
$835$	89.0201			3.08067
$836$		0			0
$837$	4.81604	+	1.13236i	0.166467	+	0.0391400i
$838$		0			0
$839$	−5.52298	+	9.56608i	−0.190674	+	0.330258i	−0.945474	−	0.325698i	$-0.894401\pi$
$839$	−5.52298	+	9.56608i	−0.190674	+	0.330258i	0.754800	+	0.655955i	$0.227734\pi$
$840$		0			0
$841$	−20.8313	−	36.0808i	−0.718320	−	1.24417i
$842$		0			0
$843$	21.2134	+	1.63615i	0.730627	+	0.0563521i
$844$		0			0
$845$	−26.7314	−	46.3002i	−0.919590	−	1.59278i
$846$		0			0
$847$	17.3082	−	8.44105i	0.594716	−	0.290038i
$848$		0			0
$849$	10.5097	+	21.9456i	0.360691	+	0.753172i
$850$		0			0
$851$	−7.76448			−0.266163
$852$		0			0
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	−0.170881	−	0.985292i	$-0.554661\pi$
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	0.938728	−	0.344659i	$-0.112005\pi$
$854$		0			0
$855$	−33.3988	+	41.5088i	−1.14221	+	1.41957i
$856$		0			0
$857$	−3.04764	−	5.27866i	−0.104105	−	0.180316i	0.809267	−	0.587441i	$-0.199865\pi$
$857$	−3.04764	−	5.27866i	−0.104105	−	0.180316i	−0.913372	+	0.407125i	$0.866531\pi$
$858$		0			0
$859$	−15.1068	+	26.1658i	−0.515438	+	0.892765i	0.484401	+	0.874846i	$0.339038\pi$
$859$	−15.1068	+	26.1658i	−0.515438	+	0.892765i	−0.999839	+	0.0179194i	$0.994296\pi$
$860$		0			0
$861$	−11.1896	+	4.42750i	−0.381341	+	0.150889i
$862$		0			0
$863$	−21.3315	−	36.9472i	−0.726131	−	1.25770i	−0.958507	−	0.285070i	$-0.907983\pi$
$863$	−21.3315	−	36.9472i	−0.726131	−	1.25770i	0.232375	−	0.972626i	$-0.425350\pi$
$864$		0			0
$865$	−8.60018	+	14.8959i	−0.292415	+	0.506477i
$866$		0			0
$867$	34.4073	−	50.2310i	1.16853	−	1.70593i
$868$		0			0
$869$	11.4499	+	19.8318i	0.388411	+	0.672748i
$870$		0			0
$871$	1.41795	+	2.45596i	0.0480453	+	0.0832170i
$872$		0			0
$873$	−4.30618	−	11.1140i	−0.145742	−	0.376151i
$874$		0			0
$875$	−72.5575	−	48.9441i	−2.45289	−	1.65461i
$876$		0			0
$877$	−10.3375	+	17.9051i	−0.349074	+	0.604613i	−0.986085	−	0.166241i	$-0.946837\pi$
$877$	−10.3375	+	17.9051i	−0.349074	+	0.604613i	0.637012	+	0.770854i	$0.280170\pi$
$878$		0			0
$879$	−7.94526	+	11.5992i	−0.267987	+	0.391233i
$880$		0			0
$881$	5.40674			0.182158			0.0910789	−	0.995844i	$-0.470968\pi$
$881$	5.40674			0.182158			0.0910789	+	0.995844i	$0.470968\pi$
$882$		0			0
$883$	−3.16348			−0.106460			−0.0532299	−	0.998582i	$-0.516952\pi$
$883$	−3.16348			−0.106460			−0.0532299	+	0.998582i	$0.516952\pi$
$884$		0			0
$885$	−33.1986	−	2.56056i	−1.11596	−	0.0860721i
$886$		0			0
$887$	5.04317	−	8.73502i	0.169333	−	0.293293i	−0.768853	−	0.639426i	$-0.779172\pi$
$887$	5.04317	−	8.73502i	0.169333	−	0.293293i	0.938186	+	0.346133i	$0.112505\pi$
$888$		0			0
$889$	−18.7237	−	12.6302i	−0.627974	−	0.423604i
$890$		0			0
$891$	−12.8298	+	11.6982i	−0.429815	+	0.391903i
$892$		0			0
$893$	12.1199	+	20.9922i	0.405575	+	0.702477i
$894$		0			0
$895$	13.1371	+	22.7542i	0.439126	+	0.760589i
$896$		0			0
$897$	0.558273	+	1.16575i	0.0186402	+	0.0389232i
$898$		0			0
$899$	4.00181	−	6.93135i	0.133468	−	0.231173i
$900$		0			0
$901$	6.95051	+	12.0386i	0.231555	+	0.401065i
$902$		0			0
$903$	3.17671	+	2.51894i	0.105714	+	0.0838250i
$904$		0			0
$905$	38.5125	−	66.7056i	1.28020	−	2.21737i
$906$		0			0
$907$	11.9318	+	20.6665i	0.396190	+	0.686221i	0.993252	−	0.115974i	$-0.0369988\pi$
$907$	11.9318	+	20.6665i	0.396190	+	0.686221i	−0.597062	+	0.802195i	$0.703666\pi$
$908$		0			0
$909$	49.7170	+	7.71508i	1.64901	+	0.255893i
$910$		0			0
$911$	9.67946	−	16.7653i	0.320695	−	0.555460i	−0.659937	−	0.751321i	$-0.729417\pi$
$911$	9.67946	−	16.7653i	0.320695	−	0.555460i	0.980632	+	0.195862i	$0.0627503\pi$
$912$		0			0
$913$	20.2271			0.669420
$914$		0			0
$915$	−77.1582	−	5.95109i	−2.55077	−	0.196737i
$916$		0			0
$917$	5.58085	−	2.72174i	0.184296	−	0.0898796i
$918$		0			0
$919$	−25.2052	−	43.6567i	−0.831444	−	1.44010i	−0.896893	−	0.442247i	$-0.854182\pi$
$919$	−25.2052	−	43.6567i	−0.831444	−	1.44010i	0.0654498	−	0.997856i	$-0.479152\pi$
$920$		0			0
$921$	4.94917	+	10.3345i	0.163081	+	0.340534i
$922$		0			0
$923$	−3.36549	−	5.82920i	−0.110777	−	0.191871i
$924$		0			0
$925$	38.9274	−	67.4243i	1.27993	−	2.21690i
$926$		0			0
$927$	−12.5851	−	32.4813i	−0.413349	−	1.06682i
$928$		0			0
$929$	42.2929			1.38759			0.693793	−	0.720175i	$-0.255938\pi$
$929$	42.2929			1.38759			0.693793	+	0.720175i	$0.255938\pi$
$930$		0			0
$931$	−18.1251	+	23.1959i	−0.594025	+	0.760214i
$932$		0			0
$933$	−6.25391	−	13.0590i	−0.204744	−	0.427533i
$934$		0			0
$935$	−29.4164	+	50.9506i	−0.962018	+	1.66626i
$936$		0			0
$937$	20.6771			0.675490			0.337745	−	0.941238i	$-0.390336\pi$
$937$	20.6771			0.675490			0.337745	+	0.941238i	$0.390336\pi$
$938$		0			0
$939$	19.5319	+	40.7852i	0.637400	+	1.33098i
$940$		0			0
$941$	−34.3292			−1.11910			−0.559550	−	0.828796i	$-0.689026\pi$
$941$	−34.3292			−1.11910			−0.559550	+	0.828796i	$0.689026\pi$
$942$		0			0
$943$	−3.36092			−0.109447
$944$		0			0
$945$	−56.6208	+	12.8295i	−1.84188	+	0.417345i
$946$		0			0
$947$	−27.7300			−0.901103			−0.450551	−	0.892751i	$-0.648773\pi$
$947$	−27.7300			−0.901103			−0.450551	+	0.892751i	$0.648773\pi$
$948$		0			0
$949$	−0.520249			−0.0168880
$950$		0			0
$951$	8.38992	+	17.5193i	0.272062	+	0.568102i
$952$		0			0
$953$	−22.8102			−0.738894			−0.369447	−	0.929252i	$-0.620453\pi$
$953$	−22.8102			−0.738894			−0.369447	+	0.929252i	$0.620453\pi$
$954$		0			0
$955$	−15.5953	+	27.0119i	−0.504653	+	0.874085i
$956$		0			0
$957$	12.1318	+	25.3329i	0.392167	+	0.818896i
$958$		0			0
$959$	0.237016	−	3.38789i	0.00765366	−	0.109401i
$960$		0			0
$961$	−30.0935			−0.970757
$962$		0			0
$963$	60.7453	+	9.42646i	1.95749	+	0.303763i
$964$		0			0
$965$	41.2123	−	71.3817i	1.32667	−	2.29786i
$966$		0			0
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	0.986169	−	0.165744i	$-0.0530024\pi$
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	−0.636623	+	0.771175i	$0.719669\pi$
$968$		0			0
$969$	22.7198	+	47.4420i	0.729865	+	1.52406i
$970$		0			0
$971$	−19.7959	−	34.2875i	−0.635281	−	1.10034i	−0.986455	−	0.164029i	$-0.947551\pi$
$971$	−19.7959	−	34.2875i	−0.635281	−	1.10034i	0.351174	−	0.936310i	$-0.385782\pi$
$972$		0			0
$973$	−0.225472	+	3.22287i	−0.00722829	+	0.103320i
$974$		0			0
$975$	−12.9219	−	0.996647i	−0.413833	−	0.0319183i
$976$		0			0
$977$	−45.7447			−1.46350			−0.731752	−	0.681571i	$-0.761297\pi$
$977$	−45.7447			−1.46350			−0.731752	+	0.681571i	$0.761297\pi$
$978$		0			0
$979$	7.48329	−	12.9614i	0.239167	−	0.414250i
$980$		0			0
$981$	5.35351	+	13.8170i	0.170924	+	0.441144i
$982$		0			0
$983$	−7.52490	−	13.0335i	−0.240007	−	0.415704i	0.720709	−	0.693238i	$-0.243816\pi$
$983$	−7.52490	−	13.0335i	−0.240007	−	0.415704i	−0.960716	+	0.277534i	$0.910483\pi$
$984$		0			0
$985$	16.4181	−	28.4370i	0.523125	−	0.906079i
$986$		0			0
$987$	−3.86424	+	26.1298i	−0.123000	+	0.831721i
$988$		0			0
$989$	0.566154	+	0.980607i	0.0180026	+	0.0311815i
$990$		0			0
$991$	−11.3516	+	19.6616i	−0.360596	+	0.624570i	−0.988059	−	0.154076i	$-0.950760\pi$
$991$	−11.3516	+	19.6616i	−0.360596	+	0.624570i	0.627463	+	0.778646i	$0.284093\pi$
$992$		0			0
$993$	−13.6402	−	28.4826i	−0.432860	−	0.903869i
$994$		0			0
$995$	16.2894	+	28.2140i	0.516408	+	0.894445i
$996$		0			0
$997$	27.7676	+	48.0949i	0.879408	+	1.52318i	0.851992	+	0.523556i	$0.175395\pi$
$997$	27.7676	+	48.0949i	0.879408	+	1.52318i	0.0274166	+	0.999624i	$0.491272\pi$
$998$		0			0
$999$	−9.09467	−	30.1824i	−0.287743	−	0.954929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.25.7	✓	22
3.2	odd	2		1512.2.q.d.1369.1		22
4.3	odd	2		1008.2.q.l.529.5		22
7.2	even	3		504.2.t.c.457.1	yes	22
9.4	even	3		504.2.t.c.193.1	yes	22
9.5	odd	6		1512.2.t.c.361.11		22
12.11	even	2		3024.2.q.l.2881.1		22
21.2	odd	6		1512.2.t.c.289.11		22
28.23	odd	6		1008.2.t.l.961.11		22
36.23	even	6		3024.2.t.k.1873.11		22
36.31	odd	6		1008.2.t.l.193.11		22
63.23	odd	6		1512.2.q.d.793.1		22
63.58	even	3	inner	504.2.q.c.121.7	yes	22
84.23	even	6		3024.2.t.k.289.11		22
252.23	even	6		3024.2.q.l.2305.1		22
252.247	odd	6		1008.2.q.l.625.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.7	✓	22	1.1	even	1	trivial
504.2.q.c.121.7	yes	22	63.58	even	3	inner
504.2.t.c.193.1	yes	22	9.4	even	3
504.2.t.c.457.1	yes	22	7.2	even	3
1008.2.q.l.529.5		22	4.3	odd	2
1008.2.q.l.625.5		22	252.247	odd	6
1008.2.t.l.193.11		22	36.31	odd	6
1008.2.t.l.961.11		22	28.23	odd	6
1512.2.q.d.793.1		22	63.23	odd	6
1512.2.q.d.1369.1		22	3.2	odd	2
1512.2.t.c.289.11		22	21.2	odd	6
1512.2.t.c.361.11		22	9.5	odd	6
3024.2.q.l.2305.1		22	252.23	even	6
3024.2.q.l.2881.1		22	12.11	even	2
3024.2.t.k.289.11		22	84.23	even	6
3024.2.t.k.1873.11		22	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.748111 + 1.56216i) q^{3} +(2.11148 - 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(-1.88066 + 2.33733i) q^{9} +O(q^{10})\)	\(q+(0.748111 + 1.56216i) q^{3} +(2.11148 - 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(-1.88066 + 2.33733i) q^{9} +(-0.964575 - 1.67069i) q^{11} +(-0.291529 - 0.504943i) q^{13} +(7.29273 + 0.562477i) q^{15} +(3.61082 - 6.25412i) q^{17} +(2.10268 + 3.64194i) q^{19} +(-0.670409 + 4.53327i) q^{21} +(-0.639939 + 1.10841i) q^{23} +(-6.41671 - 11.1141i) q^{25} +(-5.05822 - 1.18930i) q^{27} +(-4.20305 + 7.27990i) q^{29} -0.952121 q^{31} +(1.88827 - 2.75668i) q^{33} +(10.0423 - 4.89755i) q^{35} +(3.03329 + 5.25381i) q^{37} +(0.570704 - 0.833168i) q^{39} +(1.31299 + 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(4.57709 + 11.8132i) q^{45} +5.76401 q^{47} +(2.62182 + 6.49046i) q^{49} +(12.4712 + 0.961885i) q^{51} +(-0.962456 + 1.66702i) q^{53} -8.14673 q^{55} +(-4.11625 + 6.00929i) q^{57} -4.55229 q^{59} -10.5802 q^{61} +(-7.58322 + 2.34411i) q^{63} -2.46223 q^{65} -4.86383 q^{67} +(-2.21025 - 0.170473i) q^{69} +11.5443 q^{71} +(0.446138 - 0.772734i) q^{73} +(12.5615 - 18.3384i) q^{75} +(0.356209 - 5.09160i) q^{77} -11.8704 q^{79} +(-1.92623 - 8.79145i) q^{81} +(-5.24250 + 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-14.5167 - 1.11965i) q^{87} +(3.87906 + 6.71874i) q^{89} +(0.107659 - 1.53887i) q^{91} +(-0.712292 - 1.48736i) q^{93} +17.7591 q^{95} +(-1.98651 + 3.44073i) q^{97} +(5.71900 + 0.887474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more