LMFDB - Embedded newform 504.2.t.c.193.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (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			193.9
Character	$\chi$	$=$	504.193
Dual form			504.2.t.c.457.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13766 + 1.30604i) q^{3} +3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} +O(q^{10})$	\(q+(1.13766 + 1.30604i) q^{3} +3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} -2.28279 q^{11} +(-0.675051 + 1.16922i) q^{13} +(3.63481 + 4.17279i) q^{15} +(2.21425 - 3.83519i) q^{17} +(-3.69214 - 6.39497i) q^{19} +(3.51548 + 2.93962i) q^{21} -6.46959 q^{23} +5.20800 q^{25} +(-4.34921 + 2.84330i) q^{27} +(-1.06167 - 1.83887i) q^{29} +(0.316154 + 0.547595i) q^{31} +(-2.59702 - 2.98141i) q^{33} +(8.34818 - 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(-2.29503 + 0.448529i) q^{39} +(-5.05124 + 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(-1.31468 + 9.49440i) q^{45} +(-3.26587 + 5.65664i) q^{47} +(6.65440 - 2.17232i) q^{49} +(7.52795 - 1.47123i) q^{51} +(2.39950 - 4.15606i) q^{53} -7.29349 q^{55} +(4.15170 - 12.0974i) q^{57} +(-3.10191 - 5.37267i) q^{59} +(4.45546 - 7.71709i) q^{61} +(0.160142 + 7.93564i) q^{63} +(-2.15679 + 3.73566i) q^{65} +(1.50785 + 2.61167i) q^{67} +(-7.36017 - 8.44954i) q^{69} -15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(5.92492 + 6.80186i) q^{75} +(-5.96467 + 0.948938i) q^{77} +(0.938050 - 1.62475i) q^{79} +(-8.66137 - 2.44554i) q^{81} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(1.19382 - 3.47859i) q^{87} +(2.65390 + 4.59668i) q^{89} +(-1.27780 + 3.33566i) q^{91} +(-0.355506 + 1.03588i) q^{93} +(-11.7964 - 20.4319i) q^{95} +(7.44539 + 12.8958i) q^{97} +(0.939319 - 6.78363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.13766	+	1.30604i	0.656826	+	0.754042i
$3$	1.13766	+	1.30604i	0.656826	+	0.754042i
$4$		0			0
$5$	3.19500			1.42885			0.714423	−	0.699714i	$-0.246689\pi$
$5$	3.19500			1.42885			0.714423	+	0.699714i	$0.246689\pi$
$6$		0			0
$7$	2.61289	−	0.415693i	0.987580	−	0.157117i
$7$	2.61289	−	0.415693i	0.987580	−	0.157117i
$8$		0			0
$9$	−0.411479	+	2.97165i	−0.137160	+	0.990549i
$10$		0			0
$11$	−2.28279			−0.688286			−0.344143	−	0.938917i	$-0.611830\pi$
$11$	−2.28279			−0.688286			−0.344143	+	0.938917i	$0.611830\pi$
$12$		0			0
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	−0.944324	−	0.329017i	$-0.893283\pi$
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	0.757099	+	0.653300i	$0.226616\pi$
$14$		0			0
$15$	3.63481	+	4.17279i	0.938503	+	1.07741i
$16$		0			0
$17$	2.21425	−	3.83519i	0.537033	−	0.930169i	−0.462028	−	0.886865i	$-0.652878\pi$
$17$	2.21425	−	3.83519i	0.537033	−	0.930169i	0.999062	−	0.0433042i	$-0.0137885\pi$
$18$		0			0
$19$	−3.69214	−	6.39497i	−0.847034	−	1.46711i	−0.883843	−	0.467784i	$-0.845052\pi$
$19$	−3.69214	−	6.39497i	−0.847034	−	1.46711i	0.0368084	−	0.999322i	$-0.488281\pi$
$20$		0			0
$21$	3.51548	+	2.93962i	0.767141	+	0.641479i
$22$		0			0
$23$	−6.46959			−1.34900			−0.674501	−	0.738274i	$-0.735641\pi$
$23$	−6.46959			−1.34900			−0.674501	+	0.738274i	$0.735641\pi$
$24$		0			0
$25$	5.20800			1.04160
$26$		0			0
$27$	−4.34921	+	2.84330i	−0.837006	+	0.547194i
$28$		0			0
$29$	−1.06167	−	1.83887i	−0.197148	−	0.341470i	0.750455	−	0.660922i	$-0.229834\pi$
$29$	−1.06167	−	1.83887i	−0.197148	−	0.341470i	−0.947602	+	0.319452i	$0.896501\pi$
$30$		0			0
$31$	0.316154	+	0.547595i	0.0567830	+	0.0983510i	0.893020	−	0.450018i	$-0.148582\pi$
$31$	0.316154	+	0.547595i	0.0567830	+	0.0983510i	−0.836237	+	0.548369i	$0.815249\pi$
$32$		0			0
$33$	−2.59702	−	2.98141i	−0.452084	−	0.518997i
$34$		0			0
$35$	8.34818	−	1.32814i	1.41110	−	0.224496i
$36$		0			0
$37$	1.92885	+	3.34087i	0.317102	+	0.549236i	0.979882	−	0.199578i	$-0.0639570\pi$
$37$	1.92885	+	3.34087i	0.317102	+	0.549236i	−0.662780	+	0.748814i	$0.730624\pi$
$38$		0			0
$39$	−2.29503	+	0.448529i	−0.367498	+	0.0718222i
$40$		0			0
$41$	−5.05124	+	8.74900i	−0.788871	+	1.36636i	0.137788	+	0.990462i	$0.456001\pi$
$41$	−5.05124	+	8.74900i	−0.788871	+	1.36636i	−0.926659	+	0.375903i	$0.877333\pi$
$42$		0			0
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	0.983680	+	0.179929i	$0.0575867\pi$
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	−0.336017	+	0.941856i	$0.609080\pi$
$44$		0			0
$45$	−1.31468	+	9.49440i	−0.195980	+	1.41534i
$46$		0			0
$47$	−3.26587	+	5.65664i	−0.476375	+	0.825106i	−0.999634	−	0.0270678i	$-0.991383\pi$
$47$	−3.26587	+	5.65664i	−0.476375	+	0.825106i	0.523258	+	0.852174i	$0.324716\pi$
$48$		0			0
$49$	6.65440	−	2.17232i	0.950628	−	0.310332i
$50$		0			0
$51$	7.52795	−	1.47123i	1.05412	−	0.206013i
$52$		0			0
$53$	2.39950	−	4.15606i	0.329597	−	0.570879i	−0.652835	−	0.757500i	$-0.726420\pi$
$53$	2.39950	−	4.15606i	0.329597	−	0.570879i	0.982432	+	0.186621i	$0.0597538\pi$
$54$		0			0
$55$	−7.29349			−0.983454
$56$		0			0
$57$	4.15170	−	12.0974i	0.549906	−	1.60233i
$58$		0			0
$59$	−3.10191	−	5.37267i	−0.403835	−	0.699463i	0.590350	−	0.807147i	$-0.298990\pi$
$59$	−3.10191	−	5.37267i	−0.403835	−	0.699463i	−0.994185	+	0.107685i	$0.965656\pi$
$60$		0			0
$61$	4.45546	−	7.71709i	0.570464	−	0.988072i	−0.426055	−	0.904697i	$-0.640097\pi$
$61$	4.45546	−	7.71709i	0.570464	−	0.988072i	0.996518	−	0.0833747i	$-0.0265698\pi$
$62$		0			0
$63$	0.160142	+	7.93564i	0.0201760	+	0.999796i
$64$		0			0
$65$	−2.15679	+	3.73566i	−0.267516	+	0.463352i
$66$		0			0
$67$	1.50785	+	2.61167i	0.184213	+	0.319067i	0.943311	−	0.331910i	$-0.107693\pi$
$67$	1.50785	+	2.61167i	0.184213	+	0.319067i	−0.759098	+	0.650976i	$0.774360\pi$
$68$		0			0
$69$	−7.36017	−	8.44954i	−0.886060	−	1.01721i
$70$		0			0
$71$	−15.3791			−1.82516			−0.912580	−	0.408899i	$-0.865913\pi$
$71$	−15.3791			−1.82516			−0.912580	+	0.408899i	$0.865913\pi$
$72$		0			0
$73$	4.36577	−	7.56173i	0.510974	−	0.885033i	−0.488945	−	0.872315i	$-0.662618\pi$
$73$	4.36577	−	7.56173i	0.510974	−	0.885033i	0.999919	−	0.0127186i	$-0.00404857\pi$
$74$		0			0
$75$	5.92492	+	6.80186i	0.684150	+	0.785411i
$76$		0			0
$77$	−5.96467	+	0.948938i	−0.679737	+	0.108142i
$78$		0			0
$79$	0.938050	−	1.62475i	0.105539	−	0.182799i	−0.808419	−	0.588607i	$-0.799677\pi$
$79$	0.938050	−	1.62475i	0.105539	−	0.182799i	0.913958	+	0.405808i	$0.133010\pi$
$80$		0			0
$81$	−8.66137	−	2.44554i	−0.962374	−	0.271727i
$82$		0			0
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	0.652956	−	0.757396i	$-0.273529\pi$
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	−0.982402	+	0.186779i	$0.940195\pi$
$84$		0			0
$85$	7.07451	−	12.2534i	0.767338	−	1.32907i
$86$		0			0
$87$	1.19382	−	3.47859i	0.127991	−	0.372944i
$88$		0			0
$89$	2.65390	+	4.59668i	0.281313	+	0.487248i	0.971708	−	0.236184i	$-0.0758969\pi$
$89$	2.65390	+	4.59668i	0.281313	+	0.487248i	−0.690396	+	0.723432i	$0.742564\pi$
$90$		0			0
$91$	−1.27780	+	3.33566i	−0.133949	+	0.349673i
$92$		0			0
$93$	−0.355506	+	1.03588i	−0.0368643	+	0.107416i
$94$		0			0
$95$	−11.7964	−	20.4319i	−1.21028	−	2.09627i
$96$		0			0
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	0.944893	+	0.327378i	$0.106165\pi$
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	−0.188929	+	0.981991i	$0.560502\pi$
$98$		0			0
$99$	0.939319	−	6.78363i	0.0944051	−	0.681781i
$100$		0			0
$101$	−14.0060			−1.39365			−0.696824	−	0.717242i	$-0.745404\pi$
$101$	−14.0060			−1.39365			−0.696824	+	0.717242i	$0.745404\pi$
$102$		0			0
$103$	16.0611			1.58255			0.791274	−	0.611462i	$-0.209418\pi$
$103$	16.0611			1.58255			0.791274	+	0.611462i	$0.209418\pi$
$104$		0			0
$105$	11.2320	+	9.39209i	1.09613	+	0.916574i
$106$		0			0
$107$	1.26820	+	2.19658i	0.122601	+	0.212352i	0.920793	−	0.390052i	$-0.127543\pi$
$107$	1.26820	+	2.19658i	0.122601	+	0.212352i	−0.798191	+	0.602404i	$0.794210\pi$
$108$		0			0
$109$	8.10946	−	14.0460i	0.776746	−	1.34536i	−0.157062	−	0.987589i	$-0.550202\pi$
$109$	8.10946	−	14.0460i	0.776746	−	1.34536i	0.933808	−	0.357775i	$-0.116464\pi$
$110$		0			0
$111$	−2.16894	+	6.31992i	−0.205867	+	0.599860i
$112$		0			0
$113$	1.61499	−	2.79725i	0.151926	−	0.263143i	−0.780010	−	0.625767i	$-0.784786\pi$
$113$	1.61499	−	2.79725i	0.151926	−	0.263143i	0.931935	+	0.362625i	$0.118119\pi$
$114$		0			0
$115$	−20.6703			−1.92752
$116$		0			0
$117$	−3.19675	−	2.48712i	−0.295539	−	0.229935i
$118$		0			0
$119$	4.19132	−	10.9414i	0.384218	−	1.00299i
$120$		0			0
$121$	−5.78889			−0.526263
$122$		0			0
$123$	−17.1731	+	3.35623i	−1.54845	+	0.302621i
$124$		0			0
$125$	0.664575			0.0594414
$126$		0			0
$127$	−12.6429			−1.12187			−0.560936	−	0.827859i	$-0.689559\pi$
$127$	−12.6429			−1.12187			−0.560936	+	0.827859i	$0.689559\pi$
$128$		0			0
$129$	−4.77564	+	13.9154i	−0.420472	+	1.22518i
$130$		0			0
$131$	19.0686			1.66603			0.833015	−	0.553250i	$-0.186613\pi$
$131$	19.0686			1.66603			0.833015	+	0.553250i	$0.186613\pi$
$132$		0			0
$133$	−12.3055	−	15.1746i	−1.06702	−	1.31580i
$134$		0			0
$135$	−13.8957	+	9.08434i	−1.19595	+	0.781856i
$136$		0			0
$137$	6.76473			0.577949			0.288975	−	0.957337i	$-0.406686\pi$
$137$	6.76473			0.577949			0.288975	+	0.957337i	$0.406686\pi$
$138$		0			0
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	0.440263	+	0.897869i	$0.354885\pi$
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	−0.997709	+	0.0676550i	$0.978448\pi$
$140$		0			0
$141$	−11.1032	+	2.16996i	−0.935061	+	0.182744i
$142$		0			0
$143$	1.54100	−	2.66908i	0.128865	−	0.223200i
$144$		0			0
$145$	−3.39204	−	5.87518i	−0.281693	−	0.487907i
$146$		0			0
$147$	10.4076	+	6.21956i	0.858400	+	0.512980i
$148$		0			0
$149$	0.280514			0.0229806			0.0114903	−	0.999934i	$-0.496342\pi$
$149$	0.280514			0.0229806			0.0114903	+	0.999934i	$0.496342\pi$
$150$		0			0
$151$	8.85798			0.720852			0.360426	−	0.932788i	$-0.382631\pi$
$151$	8.85798			0.720852			0.360426	+	0.932788i	$0.382631\pi$
$152$		0			0
$153$	10.4857	+	8.15806i	0.847719	+	0.659540i
$154$		0			0
$155$	1.01011	+	1.74956i	0.0811341	+	0.140528i
$156$		0			0
$157$	0.964471	+	1.67051i	0.0769731	+	0.133321i	0.901943	−	0.431856i	$-0.142141\pi$
$157$	0.964471	+	1.67051i	0.0769731	+	0.133321i	−0.824969	+	0.565177i	$0.808808\pi$
$158$		0			0
$159$	8.15779	−	1.59432i	0.646955	−	0.126438i
$160$		0			0
$161$	−16.9043	+	2.68936i	−1.33225	+	0.211952i
$162$		0			0
$163$	−12.1983	−	21.1281i	−0.955446	−	1.65488i	−0.733345	−	0.679856i	$-0.762042\pi$
$163$	−12.1983	−	21.1281i	−0.955446	−	1.65488i	−0.222100	−	0.975024i	$-0.571291\pi$
$164$		0			0
$165$	−8.29748	−	9.52559i	−0.645958	−	0.741566i
$166$		0			0
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	−0.739438	−	0.673224i	$-0.764909\pi$
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	0.952749	+	0.303760i	$0.0982421\pi$
$168$		0			0
$169$	5.58861	+	9.67976i	0.429893	+	0.744597i
$170$		0			0
$171$	20.5228	−	8.34033i	1.56942	−	0.637801i
$172$		0			0
$173$	−6.30260	+	10.9164i	−0.479178	+	0.829960i	−0.999715	−	0.0238790i	$-0.992398\pi$
$173$	−6.30260	+	10.9164i	−0.479178	+	0.829960i	0.520537	+	0.853839i	$0.325732\pi$
$174$		0			0
$175$	13.6079	−	2.16493i	1.02866	−	0.163653i
$176$		0			0
$177$	3.48801	−	10.1635i	0.262175	−	0.763934i
$178$		0			0
$179$	5.10472	−	8.84164i	0.381545	−	0.660855i	−0.609738	−	0.792603i	$-0.708725\pi$
$179$	5.10472	−	8.84164i	0.381545	−	0.660855i	0.991283	+	0.131747i	$0.0420588\pi$
$180$		0			0
$181$	−16.2398			−1.20710			−0.603548	−	0.797327i	$-0.706247\pi$
$181$	−16.2398			−1.20710			−0.603548	+	0.797327i	$0.706247\pi$
$182$		0			0
$183$	15.1476	−	2.96038i	1.11974	−	0.218837i
$184$		0			0
$185$	6.16268	+	10.6741i	0.453089	+	0.784774i
$186$		0			0
$187$	−5.05465	+	8.75491i	−0.369632	+	0.640222i
$188$		0			0
$189$	−10.1821	+	9.23718i	−0.740637	+	0.671906i
$190$		0			0
$191$	1.97060	−	3.41318i	0.142587	−	0.246969i	−0.785883	−	0.618375i	$-0.787791\pi$
$191$	1.97060	−	3.41318i	0.142587	−	0.246969i	0.928470	+	0.371407i	$0.121124\pi$
$192$		0			0
$193$	2.87056	+	4.97196i	0.206627	+	0.357889i	0.950650	−	0.310265i	$-0.100418\pi$
$193$	2.87056	+	4.97196i	0.206627	+	0.357889i	−0.744023	+	0.668154i	$0.767085\pi$
$194$		0			0
$195$	−7.33260	+	1.43305i	−0.525098	+	0.102623i
$196$		0			0
$197$	−7.67480			−0.546807			−0.273403	−	0.961899i	$-0.588149\pi$
$197$	−7.67480			−0.546807			−0.273403	+	0.961899i	$0.588149\pi$
$198$		0			0
$199$	−2.26928	+	3.93050i	−0.160865	+	0.278626i	−0.935179	−	0.354175i	$-0.884762\pi$
$199$	−2.26928	+	3.93050i	−0.160865	+	0.278626i	0.774314	+	0.632801i	$0.218095\pi$
$200$		0			0
$201$	−1.69553	+	4.94049i	−0.119594	+	0.348476i
$202$		0			0
$203$	−3.53844	−	4.36344i	−0.248350	−	0.306253i
$204$		0			0
$205$	−16.1387	+	27.9530i	−1.12718	+	1.95232i
$206$		0			0
$207$	2.66210	−	19.2253i	0.185029	−	1.33625i
$208$		0			0
$209$	8.42836	+	14.5983i	0.583002	+	1.00979i
$210$		0			0
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	−0.298257	−	0.954486i	$-0.596405\pi$
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$212$		0			0
$213$	−17.4961	−	20.0857i	−1.19881	−	1.37625i
$214$		0			0
$215$	13.5692	+	23.5025i	0.925410	+	1.60286i
$216$		0			0
$217$	1.05371	+	1.29938i	0.0715304	+	0.0882079i
$218$		0			0
$219$	14.8427	−	2.90078i	1.00297	−	0.196016i
$220$		0			0
$221$	2.98946	+	5.17789i	0.201093	+	0.348303i
$222$		0			0
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	0.998005	−	0.0631368i	$-0.0201105\pi$
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	−0.553681	+	0.832729i	$0.686777\pi$
$224$		0			0
$225$	−2.14299	+	15.4764i	−0.142866	+	1.03176i
$226$		0			0
$227$	22.0610			1.46424			0.732118	−	0.681177i	$-0.238532\pi$
$227$	22.0610			1.46424			0.732118	+	0.681177i	$0.238532\pi$
$228$		0			0
$229$	−17.8472			−1.17938			−0.589688	−	0.807631i	$-0.700749\pi$
$229$	−17.8472			−1.17938			−0.589688	+	0.807631i	$0.700749\pi$
$230$		0			0
$231$	−8.02509	−	6.71053i	−0.528012	−	0.441520i
$232$		0			0
$233$	−7.84409	−	13.5864i	−0.513883	−	0.890072i	−0.999870	−	0.0161061i	$-0.994873\pi$
$233$	−7.84409	−	13.5864i	−0.513883	−	0.890072i	0.485987	−	0.873966i	$-0.338460\pi$
$234$		0			0
$235$	−10.4344	+	18.0730i	−0.680667	+	1.17895i
$236$		0			0
$237$	3.18917	−	0.623276i	0.207159	−	0.0404861i
$238$		0			0
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	−0.868087	−	0.496412i	$-0.834650\pi$
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	0.863949	+	0.503579i	$0.167984\pi$
$240$		0			0
$241$	15.0869			0.971830			0.485915	−	0.874006i	$-0.338486\pi$
$241$	15.0869			0.971830			0.485915	+	0.874006i	$0.338486\pi$
$242$		0			0
$243$	−6.65968	−	14.0943i	−0.427219	−	0.904148i
$244$		0			0
$245$	21.2608	−	6.94056i	1.35830	−	0.443416i
$246$		0			0
$247$	9.96952			0.634345
$248$		0			0
$249$	3.37498	−	9.83413i	0.213881	−	0.623212i
$250$		0			0
$251$	12.3738			0.781030			0.390515	−	0.920596i	$-0.372297\pi$
$251$	12.3738			0.781030			0.390515	+	0.920596i	$0.372297\pi$
$252$		0			0
$253$	14.7687			0.928499
$254$		0			0
$255$	24.0518	−	4.70057i	1.50618	−	0.294361i
$256$		0			0
$257$	22.0867			1.37773			0.688865	−	0.724890i	$-0.258109\pi$
$257$	22.0867			1.37773			0.688865	+	0.724890i	$0.258109\pi$
$258$		0			0
$259$	6.42866	+	7.92752i	0.399458	+	0.492592i
$260$		0			0
$261$	5.90133	−	2.39826i	0.365283	−	0.148448i
$262$		0			0
$263$	−7.79357			−0.480572			−0.240286	−	0.970702i	$-0.577241\pi$
$263$	−7.79357			−0.480572			−0.240286	+	0.970702i	$0.577241\pi$
$264$		0			0
$265$	7.66641	−	13.2786i	0.470944	−	0.815698i
$266$		0			0
$267$	−2.98423	+	8.69554i	−0.182632	+	0.532158i
$268$		0			0
$269$	−3.85738	+	6.68119i	−0.235189	+	0.407359i	−0.959328	−	0.282295i	$-0.908904\pi$
$269$	−3.85738	+	6.68119i	−0.235189	+	0.407359i	0.724139	+	0.689654i	$0.242238\pi$
$270$		0			0
$271$	12.5744	+	21.7795i	0.763839	+	1.32301i	0.940858	+	0.338801i	$0.110021\pi$
$271$	12.5744	+	21.7795i	0.763839	+	1.32301i	−0.177019	+	0.984207i	$0.556645\pi$
$272$		0			0
$273$	−5.81020	+	2.12598i	−0.351649	+	0.128670i
$274$		0			0
$275$	−11.8888			−0.716919
$276$		0			0
$277$	−7.96273			−0.478434			−0.239217	−	0.970966i	$-0.576891\pi$
$277$	−7.96273			−0.478434			−0.239217	+	0.970966i	$0.576891\pi$
$278$		0			0
$279$	−1.75735	+	0.714175i	−0.105210	+	0.0427565i
$280$		0			0
$281$	13.3385	+	23.1030i	0.795710	+	1.37821i	0.922388	+	0.386266i	$0.126235\pi$
$281$	13.3385	+	23.1030i	0.795710	+	1.37821i	−0.126678	+	0.991944i	$0.540431\pi$
$282$		0			0
$283$	−7.21996	−	12.5053i	−0.429182	−	0.743365i	0.567619	−	0.823292i	$-0.307865\pi$
$283$	−7.21996	−	12.5053i	−0.429182	−	0.743365i	−0.996801	+	0.0799265i	$0.974531\pi$
$284$		0			0
$285$	13.2647	−	38.6510i	0.785732	−	2.28949i
$286$		0			0
$287$	−9.56144	+	24.9600i	−0.564394	+	1.47334i
$288$		0			0
$289$	−1.30577	−	2.26166i	−0.0768099	−	0.133039i
$290$		0			0
$291$	−8.37213	+	24.3949i	−0.490783	+	1.43006i
$292$		0			0
$293$	−8.27703	+	14.3362i	−0.483549	+	0.837532i	−0.999822	−	0.0188927i	$-0.993986\pi$
$293$	−8.27703	+	14.3362i	−0.483549	+	0.837532i	0.516272	+	0.856424i	$0.327319\pi$
$294$		0			0
$295$	−9.91061	−	17.1657i	−0.577018	−	0.999424i
$296$		0			0
$297$	9.92831	−	6.49065i	0.576099	−	0.376626i
$298$		0			0
$299$	4.36730	−	7.56439i	0.252568	−	0.437460i
$300$		0			0
$301$	14.1548	+	17.4551i	0.815870	+	1.00609i
$302$		0			0
$303$	−15.9340	−	18.2924i	−0.915384	−	1.05087i
$304$		0			0
$305$	14.2352	−	24.6561i	0.815105	−	1.41180i
$306$		0			0
$307$	10.9233			0.623425			0.311713	−	0.950176i	$-0.399097\pi$
$307$	10.9233			0.623425			0.311713	+	0.950176i	$0.399097\pi$
$308$		0			0
$309$	18.2720	+	20.9764i	1.03946	+	1.19331i
$310$		0			0
$311$	2.62680	+	4.54975i	0.148952	+	0.257992i	0.930840	−	0.365426i	$-0.119077\pi$
$311$	2.62680	+	4.54975i	0.148952	+	0.257992i	−0.781888	+	0.623418i	$0.785743\pi$
$312$		0			0
$313$	−10.7592	+	18.6354i	−0.608145	+	1.05334i	0.383401	+	0.923582i	$0.374753\pi$
$313$	−10.7592	+	18.6354i	−0.608145	+	1.05334i	−0.991546	+	0.129756i	$0.958581\pi$
$314$		0			0
$315$	0.511654	+	25.3543i	0.0288284	+	1.42856i
$316$		0			0
$317$	8.76613	−	15.1834i	0.492355	−	0.852784i	−0.507606	−	0.861589i	$-0.669470\pi$
$317$	8.76613	−	15.1834i	0.492355	−	0.852784i	0.999961	+	0.00880525i	$0.00280283\pi$
$318$		0			0
$319$	2.42357	+	4.19774i	0.135694	+	0.235029i
$320$		0			0
$321$	−1.42605	+	4.15527i	−0.0795945	+	0.231925i
$322$		0			0
$323$	−32.7012			−1.81954
$324$		0			0
$325$	−3.51567	+	6.08932i	−0.195014	+	0.337774i
$326$		0			0
$327$	27.5704	−	5.38823i	1.52465	−	0.297970i
$328$		0			0
$329$	−6.18192	+	16.1378i	−0.340820	+	0.889705i
$330$		0			0
$331$	−3.13795	+	5.43508i	−0.172477	+	0.298739i	−0.939285	−	0.343137i	$-0.888510\pi$
$331$	−3.13795	+	5.43508i	−0.172477	+	0.298739i	0.766808	+	0.641876i	$0.221844\pi$
$332$		0			0
$333$	−10.7216	+	4.35717i	−0.587539	+	0.238772i
$334$		0			0
$335$	4.81757	+	8.34428i	0.263212	+	0.455897i
$336$		0			0
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	−0.211876	−	0.977297i	$-0.567957\pi$
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	0.952302	−	0.305159i	$-0.0987095\pi$
$338$		0			0
$339$	5.49062	−	1.07306i	0.298210	−	0.0582807i
$340$		0			0
$341$	−0.721712	−	1.25004i	−0.0390829	−	0.0676936i
$342$		0			0
$343$	16.4842	−	8.44222i	0.890063	−	0.455837i
$344$		0			0
$345$	−23.5157	−	26.9963i	−1.26604	−	1.45343i
$346$		0			0
$347$	9.59040	+	16.6111i	0.514840	+	0.891728i	0.999852	+	0.0172210i	$0.00548188\pi$
$347$	9.59040	+	16.6111i	0.514840	+	0.891728i	−0.485012	+	0.874507i	$0.661185\pi$
$348$		0			0
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	0.998859	+	0.0477584i	$0.0152078\pi$
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	−0.458069	+	0.888916i	$0.651459\pi$
$350$		0			0
$351$	−0.388515	−	7.00457i	−0.0207374	−	0.373876i
$352$		0			0
$353$	−28.4999			−1.51690			−0.758448	−	0.651733i	$-0.774042\pi$
$353$	−28.4999			−1.51690			−0.758448	+	0.651733i	$0.774042\pi$
$354$		0			0
$355$	−49.1361			−2.60787
$356$		0			0
$357$	19.0581	−	6.97348i	1.00866	−	0.369076i
$358$		0			0
$359$	15.4572	+	26.7727i	0.815802	+	1.41301i	0.908751	+	0.417339i	$0.137037\pi$
$359$	15.4572	+	26.7727i	0.815802	+	1.41301i	−0.0929489	+	0.995671i	$0.529629\pi$
$360$		0			0
$361$	−17.7638	+	30.7677i	−0.934934	+	1.61935i
$362$		0			0
$363$	−6.58576	−	7.56052i	−0.345663	−	0.396824i
$364$		0			0
$365$	13.9486	−	24.1597i	0.730103	−	1.26458i
$366$		0			0
$367$	−6.83095			−0.356573			−0.178286	−	0.983979i	$-0.557055\pi$
$367$	−6.83095			−0.356573			−0.178286	+	0.983979i	$0.557055\pi$
$368$		0			0
$369$	−23.9205	−	18.6105i	−1.24525	−	0.968825i
$370$		0			0
$371$	4.54199	−	11.8568i	0.235809	−	0.615574i
$372$		0			0
$373$	6.76490			0.350273			0.175137	−	0.984544i	$-0.443963\pi$
$373$	6.76490			0.350273			0.175137	+	0.984544i	$0.443963\pi$
$374$		0			0
$375$	0.756057	+	0.867961i	0.0390426	+	0.0448213i
$376$		0			0
$377$	2.86673			0.147644
$378$		0			0
$379$	−7.62967			−0.391910			−0.195955	−	0.980613i	$-0.562781\pi$
$379$	−7.62967			−0.391910			−0.195955	+	0.980613i	$0.562781\pi$
$380$		0			0
$381$	−14.3832	−	16.5121i	−0.736874	−	0.845939i
$382$		0			0
$383$	−6.42264			−0.328181			−0.164091	−	0.986445i	$-0.552469\pi$
$383$	−6.42264			−0.328181			−0.164091	+	0.986445i	$0.552469\pi$
$384$		0			0
$385$	−19.0571	+	3.03185i	−0.971240	+	0.154518i
$386$		0			0
$387$	−23.6071	+	9.59375i	−1.20002	+	0.487678i
$388$		0			0
$389$	−15.8535			−0.803804			−0.401902	−	0.915683i	$-0.631651\pi$
$389$	−15.8535			−0.803804			−0.401902	+	0.915683i	$0.631651\pi$
$390$		0			0
$391$	−14.3253	+	24.8121i	−0.724460	+	1.25480i
$392$		0			0
$393$	21.6935	+	24.9043i	1.09429	+	1.25626i
$394$		0			0
$395$	2.99707	−	5.19107i	0.150799	−	0.261191i
$396$		0			0
$397$	−8.56287	−	14.8313i	−0.429758	−	0.744363i	0.567093	−	0.823654i	$-0.308068\pi$
$397$	−8.56287	−	14.8313i	−0.429758	−	0.744363i	−0.996852	+	0.0792903i	$0.974735\pi$
$398$		0			0
$399$	5.81916	−	33.3349i	0.291323	−	1.66883i
$400$		0			0
$401$	23.7691			1.18697			0.593486	−	0.804844i	$-0.297751\pi$
$401$	23.7691			1.18697			0.593486	+	0.804844i	$0.297751\pi$
$402$		0			0
$403$	−0.853681			−0.0425249
$404$		0			0
$405$	−27.6730	−	7.81350i	−1.37508	−	0.388256i
$406$		0			0
$407$	−4.40316	−	7.62649i	−0.218256	−	0.378031i
$408$		0			0
$409$	−7.55946	−	13.0934i	−0.373791	−	0.647425i	0.616354	−	0.787469i	$-0.288609\pi$
$409$	−7.55946	−	13.0934i	−0.373791	−	0.647425i	−0.990145	+	0.140044i	$0.955276\pi$
$410$		0			0
$411$	7.69593	+	8.83500i	0.379612	+	0.435798i
$412$		0			0
$413$	−10.3383	−	12.7488i	−0.508717	−	0.627326i
$414$		0			0
$415$	−9.58945	−	16.6094i	−0.470728	−	0.815324i
$416$		0			0
$417$	−22.3440	+	4.36681i	−1.09419	+	0.213843i
$418$		0			0
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	−0.788681	−	0.614803i	$-0.789236\pi$
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	0.926775	+	0.375616i	$0.122569\pi$
$420$		0			0
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	−0.991300	−	0.131625i	$-0.957981\pi$
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	0.381660	−	0.924303i	$-0.375353\pi$
$422$		0			0
$423$	−15.4657	−	12.0326i	−0.751969	−	0.585045i
$424$		0			0
$425$	11.5318	−	19.9737i	0.559375	−	0.968865i
$426$		0			0
$427$	8.43370	−	22.0160i	0.408135	−	1.06543i
$428$		0			0
$429$	5.23905	−	1.02390i	0.252944	−	0.0494342i
$430$		0			0
$431$	10.4514	−	18.1024i	0.503428	−	0.871962i	−0.496564	−	0.868000i	$-0.665405\pi$
$431$	10.4514	−	18.1024i	0.503428	−	0.871962i	0.999992	−	0.00396247i	$-0.00126130\pi$
$432$		0			0
$433$	−21.2708			−1.02221			−0.511104	−	0.859519i	$-0.670763\pi$
$433$	−21.2708			−1.02221			−0.511104	+	0.859519i	$0.670763\pi$
$434$		0			0
$435$	3.81425	−	11.1141i	0.182879	−	0.532879i
$436$		0			0
$437$	23.8866	+	41.3728i	1.14265	+	1.97913i
$438$		0			0
$439$	−8.59087	+	14.8798i	−0.410020	+	0.710176i	−0.994891	−	0.100951i	$-0.967812\pi$
$439$	−8.59087	+	14.8798i	−0.410020	+	0.710176i	0.584871	+	0.811126i	$0.301145\pi$
$440$		0			0
$441$	3.71722	+	20.6684i	0.177011	+	0.984209i
$442$		0			0
$443$	6.37181	−	11.0363i	0.302734	−	0.524350i	−0.674020	−	0.738713i	$-0.735434\pi$
$443$	6.37181	−	11.0363i	0.302734	−	0.524350i	0.976754	+	0.214363i	$0.0687674\pi$
$444$		0			0
$445$	8.47919	+	14.6864i	0.401952	+	0.696202i
$446$		0			0
$447$	0.319128	+	0.366362i	0.0150942	+	0.0173283i
$448$		0			0
$449$	31.5913			1.49088			0.745442	−	0.666570i	$-0.232238\pi$
$449$	31.5913			1.49088			0.745442	+	0.666570i	$0.232238\pi$
$450$		0			0
$451$	11.5309	−	19.9721i	0.542969	−	0.940449i
$452$		0			0
$453$	10.0773	+	11.5689i	0.473474	+	0.543553i
$454$		0			0
$455$	−4.08256	+	10.6574i	−0.191393	+	0.499628i
$456$		0			0
$457$	3.65243	−	6.32619i	0.170853	−	0.295927i	−0.767865	−	0.640612i	$-0.778681\pi$
$457$	3.65243	−	6.32619i	0.170853	−	0.295927i	0.938718	+	0.344685i	$0.112014\pi$
$458$		0			0
$459$	1.27437	+	22.9758i	0.0594827	+	1.07242i
$460$		0			0
$461$	−13.3651	−	23.1491i	−0.622477	−	1.07816i	−0.989023	−	0.147761i	$-0.952793\pi$
$461$	−13.3651	−	23.1491i	−0.622477	−	1.07816i	0.366546	−	0.930400i	$-0.380540\pi$
$462$		0			0
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	−0.903942	−	0.427654i	$-0.859340\pi$
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	0.822331	+	0.569010i	$0.192673\pi$
$464$		0			0
$465$	−1.13584	+	3.30965i	−0.0526734	+	0.153481i
$466$		0			0
$467$	−7.80239	−	13.5141i	−0.361052	−	0.625360i	0.627083	−	0.778953i	$-0.284249\pi$
$467$	−7.80239	−	13.5141i	−0.361052	−	0.625360i	−0.988134	+	0.153593i	$0.950915\pi$
$468$		0			0
$469$	5.02550	+	6.19721i	0.232056	+	0.286161i
$470$		0			0
$471$	−1.08452	+	3.16010i	−0.0499720	+	0.145610i
$472$		0			0
$473$	−9.69501	−	16.7922i	−0.445777	−	0.772108i
$474$		0			0
$475$	−19.2287	−	33.3050i	−0.882272	−	1.52814i
$476$		0			0
$477$	11.3630	+	8.84061i	0.520276	+	0.404784i
$478$		0			0
$479$	−17.0889			−0.780811			−0.390405	−	0.920643i	$-0.627665\pi$
$479$	−17.0889			−0.780811			−0.390405	+	0.920643i	$0.627665\pi$
$480$		0			0
$481$	−5.20830			−0.237478
$482$		0			0
$483$	−22.7437	−	19.0182i	−1.03488	−	0.865356i
$484$		0			0
$485$	23.7880	+	41.2020i	1.08016	+	1.87089i
$486$		0			0
$487$	−12.9335	+	22.4014i	−0.586072	+	1.01511i	0.408669	+	0.912683i	$0.365993\pi$
$487$	−12.9335	+	22.4014i	−0.586072	+	1.01511i	−0.994741	+	0.102423i	$0.967340\pi$
$488$		0			0
$489$	13.7167	−	39.9680i	0.620289	−	1.80741i
$490$		0			0
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	−0.984269	−	0.176679i	$-0.943465\pi$
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	0.645143	+	0.764062i	$0.276798\pi$
$492$		0			0
$493$	−9.40321			−0.423499
$494$		0			0
$495$	3.00112	−	21.6737i	0.134890	−	0.974160i
$496$		0			0
$497$	−40.1838	+	6.39297i	−1.80249	+	0.286764i
$498$		0			0
$499$	15.2419			0.682321			0.341160	−	0.940005i	$-0.389180\pi$
$499$	15.2419			0.682321			0.341160	+	0.940005i	$0.389180\pi$
$500$		0			0
$501$	9.37176	−	1.83157i	0.418699	−	0.0818287i
$502$		0			0
$503$	18.6284			0.830599			0.415299	−	0.909685i	$-0.363677\pi$
$503$	18.6284			0.830599			0.415299	+	0.909685i	$0.363677\pi$
$504$		0			0
$505$	−44.7491			−1.99131
$506$		0			0
$507$	−6.28424	+	18.3112i	−0.279093	+	0.813228i
$508$		0			0
$509$	−7.44665			−0.330067			−0.165034	−	0.986288i	$-0.552773\pi$
$509$	−7.44665			−0.330067			−0.165034	+	0.986288i	$0.552773\pi$
$510$		0			0
$511$	8.26391	−	21.5728i	0.365574	−	0.954324i
$512$		0			0
$513$	34.2407	+	17.3152i	1.51176	+	0.764485i
$514$		0			0
$515$	51.3152			2.26122
$516$		0			0
$517$	7.45527	−	12.9129i	0.327882	−	0.567909i
$518$		0			0
$519$	−21.4275	+	4.18768i	−0.940561	+	0.183819i
$520$		0			0
$521$	−11.3853	+	19.7200i	−0.498800	+	0.863947i	−0.999999	−	0.00138491i	$-0.999559\pi$
$521$	−11.3853	+	19.7200i	−0.498800	+	0.863947i	0.501199	+	0.865332i	$0.332893\pi$
$522$		0			0
$523$	16.5092	+	28.5949i	0.721899	+	1.25037i	0.960238	+	0.279184i	$0.0900639\pi$
$523$	16.5092	+	28.5949i	0.721899	+	1.25037i	−0.238339	+	0.971182i	$0.576603\pi$
$524$		0			0
$525$	18.3086	+	15.3096i	0.799055	+	0.668165i
$526$		0			0
$527$	2.80017			0.121977
$528$		0			0
$529$	18.8556			0.819808
$530$		0			0
$531$	17.2421	−	7.00705i	0.748242	−	0.304080i
$532$		0			0
$533$	−6.81969	−	11.8120i	−0.295393	−	0.511636i
$534$		0			0
$535$	4.05189	+	7.01808i	0.175179	+	0.303418i
$536$		0			0
$537$	17.3550	−	3.39177i	0.748921	−	0.146366i
$538$		0			0
$539$	−15.1906	+	4.95894i	−0.654304	+	0.213597i
$540$		0			0
$541$	8.53464	+	14.7824i	0.366933	+	0.635546i	0.989084	−	0.147351i	$-0.0470745\pi$
$541$	8.53464	+	14.7824i	0.366933	+	0.635546i	−0.622151	+	0.782897i	$0.713741\pi$
$542$		0			0
$543$	−18.4753	−	21.2098i	−0.792852	−	0.910201i
$544$		0			0
$545$	25.9097	−	44.8769i	1.10985	−	1.92232i
$546$		0			0
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	0.968678	+	0.248319i	$0.0798782\pi$
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	−0.269288	+	0.963060i	$0.586788\pi$
$548$		0			0
$549$	21.0991	+	16.4155i	0.900489	+	0.700596i
$550$		0			0
$551$	−7.83968	+	13.5787i	−0.333981	+	0.578473i
$552$		0			0
$553$	1.77563	−	4.63524i	0.0755073	−	0.197110i
$554$		0			0
$555$	−6.92976	+	20.1921i	−0.294152	+	0.857108i
$556$		0			0
$557$	17.0783	−	29.5806i	0.723633	−	1.25337i	−0.235902	−	0.971777i	$-0.575804\pi$
$557$	17.0783	−	29.5806i	0.723633	−	1.25337i	0.959534	−	0.281592i	$-0.0908623\pi$
$558$		0			0
$559$	−11.4678			−0.485036
$560$		0			0
$561$	−17.1847	+	3.35850i	−0.725539	+	0.141796i
$562$		0			0
$563$	4.83537	+	8.37510i	0.203786	+	0.352969i	0.949745	−	0.313023i	$-0.101342\pi$
$563$	4.83537	+	8.37510i	0.203786	+	0.352969i	−0.745959	+	0.665992i	$0.768009\pi$
$564$		0			0
$565$	5.15989	−	8.93720i	0.217078	−	0.375991i
$566$		0			0
$567$	−23.6478	−	2.78947i	−0.993115	−	0.117147i
$568$		0			0
$569$	−5.56369	+	9.63659i	−0.233242	+	0.403987i	−0.958760	−	0.284216i	$-0.908267\pi$
$569$	−5.56369	+	9.63659i	−0.233242	+	0.403987i	0.725518	+	0.688203i	$0.241600\pi$
$570$		0			0
$571$	−0.364653	−	0.631597i	−0.0152602	−	0.0264315i	0.858294	−	0.513158i	$-0.171524\pi$
$571$	−0.364653	−	0.631597i	−0.0152602	−	0.0264315i	−0.873555	+	0.486726i	$0.838191\pi$
$572$		0			0
$573$	6.69960	−	1.30934i	0.279880	−	0.0546984i
$574$		0			0
$575$	−33.6937			−1.40512
$576$		0			0
$577$	9.49359	−	16.4434i	0.395223	−	0.684547i	−0.597906	−	0.801566i	$-0.704001\pi$
$577$	9.49359	−	16.4434i	0.395223	−	0.684547i	0.993130	+	0.117019i	$0.0373338\pi$
$578$		0			0
$579$	−3.22786	+	9.40544i	−0.134145	+	0.390877i
$580$		0			0
$581$	−10.0033	−	12.3356i	−0.415008	−	0.511769i
$582$		0			0
$583$	−5.47755	+	9.48740i	−0.226857	+	0.392928i
$584$		0			0
$585$	−10.2136	−	7.94635i	−0.422280	−	0.328541i
$586$		0			0
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	0.837829	−	0.545933i	$-0.183825\pi$
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	−0.891706	+	0.452615i	$0.850491\pi$
$588$		0			0
$589$	2.33457	−	4.04359i	0.0961942	−	0.166613i
$590$		0			0
$591$	−8.73128	−	10.0236i	−0.359157	−	0.412315i
$592$		0			0
$593$	−7.92622	−	13.7286i	−0.325491	−	0.563767i	0.656121	−	0.754656i	$-0.272196\pi$
$593$	−7.92622	−	13.7286i	−0.325491	−	0.563767i	−0.981612	+	0.190889i	$0.938863\pi$
$594$		0			0
$595$	13.3913	−	34.9576i	0.548988	−	1.43312i
$596$		0			0
$597$	−7.71505	+	1.50779i	−0.315756	+	0.0617098i
$598$		0			0
$599$	−7.93051	−	13.7360i	−0.324032	−	0.561239i	0.657284	−	0.753643i	$-0.271705\pi$
$599$	−7.93051	−	13.7360i	−0.324032	−	0.561239i	−0.981316	+	0.192403i	$0.938372\pi$
$600$		0			0
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	0.882537	−	0.470244i	$-0.155834\pi$
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	−0.848511	+	0.529177i	$0.822501\pi$
$602$		0			0
$603$	−8.38142	+	3.40615i	−0.341318	+	0.138709i
$604$		0			0
$605$	−18.4955			−0.751949
$606$		0			0
$607$	−36.5110			−1.48194			−0.740968	−	0.671541i	$-0.765633\pi$
$607$	−36.5110			−1.48194			−0.740968	+	0.671541i	$0.765633\pi$
$608$		0			0
$609$	1.67330	−	9.58543i	0.0678054	−	0.388421i
$610$		0			0
$611$	−4.40925	−	7.63705i	−0.178379	−	0.308962i
$612$		0			0
$613$	18.2957	−	31.6891i	0.738958	−	1.27991i	−0.214007	−	0.976832i	$-0.568652\pi$
$613$	18.2957	−	31.6891i	0.738958	−	1.27991i	0.952965	−	0.303080i	$-0.0980150\pi$
$614$		0			0
$615$	−54.8680	+	10.7232i	−2.21249	+	0.432399i
$616$		0			0
$617$	−5.10936	+	8.84967i	−0.205695	+	0.356274i	−0.950354	−	0.311171i	$-0.899279\pi$
$617$	−5.10936	+	8.84967i	−0.205695	+	0.356274i	0.744659	+	0.667445i	$0.232612\pi$
$618$		0			0
$619$	−24.7329			−0.994098			−0.497049	−	0.867723i	$-0.665583\pi$
$619$	−24.7329			−0.994098			−0.497049	+	0.867723i	$0.665583\pi$
$620$		0			0
$621$	28.1376	−	18.3950i	1.12912	−	0.738166i
$622$		0			0
$623$	8.84515	+	10.9074i	0.354374	+	0.436997i
$624$		0			0
$625$	−23.9167			−0.956668
$626$		0			0
$627$	−9.47745	+	27.6157i	−0.378493	+	1.10286i
$628$		0			0
$629$	17.0838			0.681177
$630$		0			0
$631$	42.1420			1.67765			0.838823	−	0.544404i	$-0.183244\pi$
$631$	42.1420			1.67765			0.838823	+	0.544404i	$0.183244\pi$
$632$		0			0
$633$	33.4571	−	6.53871i	1.32980	−	0.259890i
$634$		0			0
$635$	−40.3939			−1.60298
$636$		0			0
$637$	−1.95213	+	9.24690i	−0.0773463	+	0.366375i
$638$		0			0
$639$	6.32817	−	45.7012i	0.250338	−	1.80791i
$640$		0			0
$641$	−2.33038			−0.0920444			−0.0460222	−	0.998940i	$-0.514654\pi$
$641$	−2.33038			−0.0920444			−0.0460222	+	0.998940i	$0.514654\pi$
$642$		0			0
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	−0.332085	−	0.943250i	$-0.607752\pi$
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	0.982920	−	0.184031i	$-0.0589147\pi$
$644$		0			0
$645$	−15.2582	+	44.4596i	−0.600789	+	1.75060i
$646$		0			0
$647$	−10.4187	+	18.0458i	−0.409603	+	0.709452i	−0.994845	−	0.101406i	$-0.967666\pi$
$647$	−10.4187	+	18.0458i	−0.409603	+	0.709452i	0.585243	+	0.810858i	$0.300999\pi$
$648$		0			0
$649$	7.08101	+	12.2647i	0.277954	+	0.481430i
$650$		0			0
$651$	−0.498289	+	2.85443i	−0.0195295	+	0.111874i
$652$		0			0
$653$	−48.8352			−1.91107			−0.955534	−	0.294882i	$-0.904720\pi$
$653$	−48.8352			−1.91107			−0.955534	+	0.294882i	$0.904720\pi$
$654$		0			0
$655$	60.9241			2.38050
$656$		0			0
$657$	20.6744	+	16.0850i	0.806584	+	0.627536i
$658$		0			0
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	0.871287	−	0.490773i	$-0.163286\pi$
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	−0.860666	+	0.509170i	$0.829952\pi$
$660$		0			0
$661$	23.2125	+	40.2052i	0.902861	+	1.56380i	0.823763	+	0.566934i	$0.191871\pi$
$661$	23.2125	+	40.2052i	0.902861	+	1.56380i	0.0790978	+	0.996867i	$0.474796\pi$
$662$		0			0
$663$	−3.36156	+	9.79501i	−0.130552	+	0.380407i
$664$		0			0
$665$	−39.3160	−	48.4827i	−1.52461	−	1.88008i
$666$		0			0
$667$	6.86858	+	11.8967i	0.265953	+	0.460643i
$668$		0			0
$669$	−7.46107	+	21.7403i	−0.288462	+	0.840527i
$670$		0			0
$671$	−10.1709	+	17.6165i	−0.392642	+	0.680076i
$672$		0			0
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	−0.981975	−	0.189013i	$-0.939471\pi$
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	0.327298	−	0.944921i	$-0.393862\pi$
$674$		0			0
$675$	−22.6507	+	14.8079i	−0.871826	+	0.569958i
$676$		0			0
$677$	−15.6425	+	27.0936i	−0.601191	+	1.04129i	0.391450	+	0.920199i	$0.371974\pi$
$677$	−15.6425	+	27.0936i	−0.601191	+	1.04129i	−0.992641	+	0.121094i	$0.961360\pi$
$678$		0			0
$679$	24.8147	+	30.6003i	0.952300	+	1.17433i
$680$		0			0
$681$	25.0978	+	28.8125i	0.961749	+	1.10410i
$682$		0			0
$683$	0.289712	−	0.501795i	0.0110855	−	0.0192007i	−0.860429	−	0.509570i	$-0.829805\pi$
$683$	0.289712	−	0.501795i	0.0110855	−	0.0192007i	0.871515	+	0.490369i	$0.163138\pi$
$684$		0			0
$685$	21.6133			0.825801
$686$		0			0
$687$	−20.3040	−	23.3091i	−0.774644	−	0.889299i
$688$		0			0
$689$	3.23957	+	5.61111i	0.123418	+	0.213766i
$690$		0			0
$691$	−1.10782	+	1.91881i	−0.0421436	+	0.0729948i	−0.886328	−	0.463058i	$-0.846752\pi$
$691$	−1.10782	+	1.91881i	−0.0421436	+	0.0729948i	0.844184	+	0.536053i	$0.180085\pi$
$692$		0			0
$693$	−0.365570	−	18.1154i	−0.0138869	−	0.688146i
$694$		0			0
$695$	−20.9981	+	36.3698i	−0.796504	+	1.37958i
$696$		0			0
$697$	22.3694	+	38.7449i	0.847300	+	1.46757i
$698$		0			0
$699$	8.82046	−	25.7013i	0.333620	−	0.972112i
$700$		0			0
$701$	4.74299			0.179140			0.0895702	−	0.995981i	$-0.471451\pi$
$701$	4.74299			0.179140			0.0895702	+	0.995981i	$0.471451\pi$
$702$		0			0
$703$	14.2432	−	24.6699i	0.537192	−	0.930444i
$704$		0			0
$705$	−35.4748	+	6.93303i	−1.33606	+	0.261113i
$706$		0			0
$707$	−36.5961	+	5.82219i	−1.37634	+	0.218966i
$708$		0			0
$709$	11.6883	−	20.2446i	0.438962	−	0.760304i	−0.558648	−	0.829405i	$-0.688680\pi$
$709$	11.6883	−	20.2446i	0.438962	−	0.760304i	0.997610	+	0.0691011i	$0.0220131\pi$
$710$		0			0
$711$	4.44220	+	3.45611i	0.166595	+	0.129614i
$712$		0			0
$713$	−2.04539	−	3.54272i	−0.0766004	−	0.132676i
$714$		0			0
$715$	4.92348	−	8.52771i	0.184128	−	0.318918i
$716$		0			0
$717$	−0.217469	+	0.0425012i	−0.00812154	+	0.00158723i
$718$		0			0
$719$	13.0256	+	22.5610i	0.485772	+	0.841382i	0.999866	−	0.0163516i	$-0.00520511\pi$
$719$	13.0256	+	22.5610i	0.485772	+	0.841382i	−0.514094	+	0.857734i	$0.671872\pi$
$720$		0			0
$721$	41.9659	−	6.67649i	1.56289	−	0.248645i
$722$		0			0
$723$	17.1637	+	19.7040i	0.638323	+	0.732801i
$724$		0			0
$725$	−5.52919	−	9.57684i	−0.205349	−	0.355675i
$726$		0			0
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	0.953274	−	0.302108i	$-0.0976905\pi$
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	−0.738270	+	0.674505i	$0.764357\pi$
$728$		0			0
$729$	10.8313	−	24.7322i	0.401158	−	0.916009i
$730$		0			0
$731$	37.6157			1.39127
$732$		0			0
$733$	−35.3487			−1.30563			−0.652816	−	0.757516i	$-0.726413\pi$
$733$	−35.3487			−1.30563			−0.652816	+	0.757516i	$0.726413\pi$
$734$		0			0
$735$	33.2521	+	19.8715i	1.22652	+	0.732970i
$736$		0			0
$737$	−3.44210	−	5.96189i	−0.126791	−	0.219609i
$738$		0			0
$739$	4.66968	−	8.08812i	0.171777	−	0.297526i	−0.767264	−	0.641331i	$-0.778383\pi$
$739$	4.66968	−	8.08812i	0.171777	−	0.297526i	0.939041	+	0.343805i	$0.111716\pi$
$740$		0			0
$741$	11.3419	+	13.0206i	0.416654	+	0.478323i
$742$		0			0
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	0.462326	+	0.886710i	$0.347015\pi$
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	−0.999076	+	0.0429687i	$0.986318\pi$
$744$		0			0
$745$	0.896240			0.0328357
$746$		0			0
$747$	16.6833	−	6.77999i	0.610411	−	0.248067i
$748$		0			0
$749$	4.22677	+	5.21225i	0.154443	+	0.190452i
$750$		0			0
$751$	26.6213			0.971424			0.485712	−	0.874119i	$-0.338560\pi$
$751$	26.6213			0.971424			0.485712	+	0.874119i	$0.338560\pi$
$752$		0			0
$753$	14.0772	+	16.1607i	0.513001	+	0.588930i
$754$		0			0
$755$	28.3012			1.02999
$756$		0			0
$757$	−35.3183			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$757$	−35.3183			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$758$		0			0
$759$	16.8017	+	19.2885i	0.609862	+	0.700128i
$760$		0			0
$761$	31.5648			1.14422			0.572112	−	0.820175i	$-0.306124\pi$
$761$	31.5648			1.14422			0.572112	+	0.820175i	$0.306124\pi$
$762$		0			0
$763$	15.3503	−	40.0717i	0.555719	−	1.45069i
$764$		0			0
$765$	33.5018	+	26.0650i	1.21126	+	0.942381i
$766$		0			0
$767$	8.37580			0.302433
$768$		0			0
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	0.0119829	+	0.999928i	$0.496186\pi$
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	−0.871955	+	0.489587i	$0.837148\pi$
$770$		0			0
$771$	25.1270	+	28.8461i	0.904928	+	1.03887i
$772$		0			0
$773$	20.7219	−	35.8914i	0.745314	−	1.29092i	−0.204733	−	0.978818i	$-0.565633\pi$
$773$	20.7219	−	35.8914i	0.745314	−	1.29092i	0.950048	−	0.312105i	$-0.101034\pi$
$774$		0			0
$775$	1.64653	+	2.85188i	0.0591452	+	0.102442i
$776$		0			0
$777$	−3.04006	+	17.4149i	−0.109062	+	0.624755i
$778$		0			0
$779$	74.5995			2.67280
$780$		0			0
$781$	35.1071			1.25623
$782$		0			0
$783$	9.84590	+	4.97898i	0.351864	+	0.177934i
$784$		0			0
$785$	3.08148	+	5.33728i	0.109983	+	0.190496i
$786$		0			0
$787$	13.1589	+	22.7918i	0.469063	+	0.812440i	0.999375	−	0.0353624i	$-0.0112585\pi$
$787$	13.1589	+	22.7918i	0.469063	+	0.812440i	−0.530312	+	0.847803i	$0.677925\pi$
$788$		0			0
$789$	−8.86640	−	10.1787i	−0.315652	−	0.362372i
$790$		0			0
$791$	3.05700	−	7.98024i	0.108694	−	0.283745i
$792$		0			0
$793$	6.01533	+	10.4189i	0.213611	+	0.369984i
$794$		0			0
$795$	26.0641	−	5.09385i	0.924399	−	0.180660i
$796$		0			0
$797$	8.42109	−	14.5858i	0.298290	−	0.516654i	−0.677455	−	0.735565i	$-0.736917\pi$
$797$	8.42109	−	14.5858i	0.298290	−	0.516654i	0.975745	+	0.218911i	$0.0702503\pi$
$798$		0			0
$799$	14.4629	+	25.0504i	0.511659	+	0.886220i
$800$		0			0
$801$	−14.7517	+	5.99500i	−0.521227	+	0.211823i
$802$		0			0
$803$	−9.96611	+	17.2618i	−0.351696	+	0.609156i
$804$		0			0
$805$	−54.0093	+	8.59251i	−1.90358	+	0.302846i
$806$		0			0
$807$	−13.1143	+	2.56299i	−0.461644	+	0.0902216i
$808$		0			0
$809$	−11.8734	+	20.5653i	−0.417445	+	0.723036i	−0.995682	−	0.0928330i	$-0.970408\pi$
$809$	−11.8734	+	20.5653i	−0.417445	+	0.723036i	0.578237	+	0.815869i	$0.303741\pi$
$810$		0			0
$811$	21.9596			0.771107			0.385553	−	0.922686i	$-0.374011\pi$
$811$	21.9596			0.771107			0.385553	+	0.922686i	$0.374011\pi$
$812$		0			0
$813$	−14.1395	+	41.2002i	−0.495895	+	1.44495i
$814$		0			0
$815$	−38.9736	−	67.5042i	−1.36518	−	2.36457i
$816$		0			0
$817$	31.3611	−	54.3190i	1.09718	−	1.90038i
$818$		0			0
$819$	−9.38663	−	5.16972i	−0.327995	−	0.180645i
$820$		0			0
$821$	10.6104	−	18.3777i	0.370305	−	0.641387i	−0.619307	−	0.785149i	$-0.712587\pi$
$821$	10.6104	−	18.3777i	0.370305	−	0.641387i	0.989612	+	0.143762i	$0.0459199\pi$
$822$		0			0
$823$	−6.53927	−	11.3264i	−0.227945	−	0.394812i	0.729254	−	0.684243i	$-0.239867\pi$
$823$	−6.53927	−	11.3264i	−0.227945	−	0.394812i	−0.957199	+	0.289431i	$0.906534\pi$
$824$		0			0
$825$	−13.5253	−	15.5272i	−0.470891	−	0.540587i
$826$		0			0
$827$	−25.8079			−0.897427			−0.448714	−	0.893676i	$-0.648118\pi$
$827$	−25.8079			−0.897427			−0.448714	+	0.893676i	$0.648118\pi$
$828$		0			0
$829$	−6.21392	+	10.7628i	−0.215818	+	0.373808i	−0.953525	−	0.301313i	$-0.902575\pi$
$829$	−6.21392	+	10.7628i	−0.215818	+	0.373808i	0.737707	+	0.675121i	$0.235909\pi$
$830$		0			0
$831$	−9.05885	−	10.3996i	−0.314248	−	0.360760i
$832$		0			0
$833$	6.40322	−	30.3309i	0.221858	−	1.05090i
$834$		0			0
$835$	8.80725	−	15.2546i	0.304788	−	0.527908i
$836$		0			0
$837$	−2.93200	−	1.48268i	−0.101345	−	0.0512491i
$838$		0			0
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	0.874396	−	0.485213i	$-0.161258\pi$
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	−0.857405	+	0.514643i	$0.827925\pi$
$840$		0			0
$841$	12.2457	−	21.2102i	0.422266	−	0.731386i
$842$		0			0
$843$	−14.9988	+	43.7039i	−0.516586	+	1.50524i
$844$		0			0
$845$	17.8556	+	30.9268i	0.614251	+	1.06391i
$846$		0			0
$847$	−15.1257	+	2.40640i	−0.519727	+	0.0826849i
$848$		0			0
$849$	8.11864	−	23.6563i	0.278631	−	0.811883i
$850$		0			0
$851$	−12.4789	−	21.6141i	−0.427771	−	0.740921i
$852$		0			0
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	0.774936	−	0.632040i	$-0.217782\pi$
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	−0.934830	+	0.355095i	$0.884449\pi$
$854$		0			0
$855$	65.5704	−	26.6473i	2.24246	−	0.911319i
$856$		0			0
$857$	−11.5798			−0.395559			−0.197779	−	0.980247i	$-0.563373\pi$
$857$	−11.5798			−0.395559			−0.197779	+	0.980247i	$0.563373\pi$
$858$		0			0
$859$	−53.6428			−1.83027			−0.915134	−	0.403150i	$-0.867915\pi$
$859$	−53.6428			−1.83027			−0.915134	+	0.403150i	$0.867915\pi$
$860$		0			0
$861$	−43.4763	+	15.9082i	−1.48167	+	0.542150i
$862$		0			0
$863$	−4.80485	−	8.32225i	−0.163559	−	0.283293i	0.772584	−	0.634913i	$-0.218964\pi$
$863$	−4.80485	−	8.32225i	−0.163559	−	0.283293i	−0.936143	+	0.351620i	$0.885631\pi$
$864$		0			0
$865$	−20.1368	+	34.8779i	−0.684671	+	1.18588i
$866$		0			0
$867$	1.46830	−	4.27837i	0.0498661	−	0.145301i
$868$		0			0
$869$	−2.14137	+	3.70896i	−0.0726409	+	0.125818i
$870$		0			0
$871$	−4.07150			−0.137958
$872$		0			0
$873$	−41.3854	+	16.8187i	−1.40068	+	0.569227i
$874$		0			0
$875$	1.73646	−	0.276259i	0.0587031	−	0.00933926i
$876$		0			0
$877$	−1.06483			−0.0359568			−0.0179784	−	0.999838i	$-0.505723\pi$
$877$	−1.06483			−0.0359568			−0.0179784	+	0.999838i	$0.505723\pi$
$878$		0			0
$879$	−28.1401	+	5.49957i	−0.949142	+	0.185496i
$880$		0			0
$881$	−20.7526			−0.699171			−0.349586	−	0.936904i	$-0.613678\pi$
$881$	−20.7526			−0.699171			−0.349586	+	0.936904i	$0.613678\pi$
$882$		0			0
$883$	−8.80560			−0.296332			−0.148166	−	0.988963i	$-0.547337\pi$
$883$	−8.80560			−0.296332			−0.148166	+	0.988963i	$0.547337\pi$
$884$		0			0
$885$	11.1442	−	32.4723i	0.374608	−	1.09154i
$886$		0			0
$887$	20.0149			0.672033			0.336017	−	0.941856i	$-0.390920\pi$
$887$	20.0149			0.672033			0.336017	+	0.941856i	$0.390920\pi$
$888$		0			0
$889$	−33.0344	+	5.25554i	−1.10794	+	0.176265i
$890$		0			0
$891$	19.7720	+	5.58265i	0.662389	+	0.187026i
$892$		0			0
$893$	48.2321			1.61403
$894$		0			0
$895$	16.3096	−	28.2490i	0.545169	−	0.944260i
$896$		0			0
$897$	14.8479	−	2.90180i	0.495756	−	0.0968883i
$898$		0			0
$899$	0.671304	−	1.16273i	0.0223892	−	0.0387793i
$900$		0			0
$901$	−10.6262	−	18.4051i	−0.354009	−	0.613162i
$902$		0			0
$903$	−6.69369	+	38.3446i	−0.222752	+	1.27603i
$904$		0			0
$905$	−51.8861			−1.72475
$906$		0			0
$907$	25.0615			0.832152			0.416076	−	0.909330i	$-0.363405\pi$
$907$	25.0615			0.832152			0.416076	+	0.909330i	$0.363405\pi$
$908$		0			0
$909$	5.76317	−	41.6208i	0.191152	−	1.38048i
$910$		0			0
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	0.935266	−	0.353946i	$-0.115160\pi$
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	−0.774159	+	0.632991i	$0.781827\pi$
$912$		0			0
$913$	6.85154	+	11.8672i	0.226753	+	0.392748i
$914$		0			0
$915$	48.3966	−	9.45840i	1.59994	−	0.312685i
$916$		0			0
$917$	49.8241	−	7.92668i	1.64534	−	0.261762i
$918$		0			0
$919$	−23.2582	−	40.2844i	−0.767217	−	1.32886i	−0.939066	−	0.343736i	$-0.888308\pi$
$919$	−23.2582	−	40.2844i	−0.767217	−	1.32886i	0.171849	−	0.985123i	$-0.445026\pi$
$920$		0			0
$921$	12.4269	+	14.2663i	0.409482	+	0.470089i
$922$		0			0
$923$	10.3817	−	17.9815i	0.341716	−	0.591870i
$924$		0			0
$925$	10.0455	+	17.3993i	0.330293	+	0.572085i
$926$		0			0
$927$	−6.60881	+	47.7279i	−0.217062	+	1.56759i
$928$		0			0
$929$	−17.2340	+	29.8501i	−0.565429	+	0.979351i	0.431581	+	0.902074i	$0.357956\pi$
$929$	−17.2340	+	29.8501i	−0.565429	+	0.979351i	−0.997010	+	0.0772768i	$0.975377\pi$
$930$		0			0
$931$	−38.4609	−	34.5342i	−1.26050	−	1.13181i
$932$		0			0
$933$	−2.95376	+	8.60675i	−0.0967017	+	0.281772i
$934$		0			0
$935$	−16.1496	+	27.9719i	−0.528148	+	0.914779i
$936$		0			0
$937$	27.1376			0.886547			0.443274	−	0.896386i	$-0.353817\pi$
$937$	27.1376			0.886547			0.443274	+	0.896386i	$0.353817\pi$
$938$		0			0
$939$	−36.5789	+	7.14880i	−1.19371	+	0.233292i
$940$		0			0
$941$	5.01950	+	8.69403i	0.163631	+	0.283417i	0.936168	−	0.351552i	$-0.114346\pi$
$941$	5.01950	+	8.69403i	0.163631	+	0.283417i	−0.772537	+	0.634969i	$0.781013\pi$
$942$		0			0
$943$	32.6794	−	56.6025i	1.06419	−	1.84323i
$944$		0			0
$945$	−32.5317	+	29.5127i	−1.05826	+	0.960050i
$946$		0			0
$947$	8.54883	−	14.8070i	0.277800	−	0.481163i	−0.693038	−	0.720901i	$-0.743728\pi$
$947$	8.54883	−	14.8070i	0.277800	−	0.481163i	0.970838	+	0.239738i	$0.0770615\pi$
$948$		0			0
$949$	5.89423	+	10.2091i	0.191335	+	0.331401i
$950$		0			0
$951$	29.8029	−	5.82455i	0.966427	−	0.188874i
$952$		0			0
$953$	−2.79843			−0.0906500			−0.0453250	−	0.998972i	$-0.514432\pi$
$953$	−2.79843			−0.0906500			−0.0453250	+	0.998972i	$0.514432\pi$
$954$		0			0
$955$	6.29605	−	10.9051i	0.203736	−	0.352880i
$956$		0			0
$957$	−2.72523	+	7.94087i	−0.0880943	+	0.256692i
$958$		0			0
$959$	17.6755	−	2.81205i	0.570771	−	0.0908058i
$960$		0			0
$961$	15.3001	−	26.5005i	0.493551	−	0.854856i
$962$		0			0
$963$	−7.04931	+	2.86479i	−0.227161	+	0.0923166i
$964$		0			0
$965$	9.17143	+	15.8854i	0.295239	+	0.511369i
$966$		0			0
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	−0.774816	−	0.632186i	$-0.782158\pi$
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	0.934898	+	0.354917i	$0.115491\pi$
$968$		0			0
$969$	−37.2027	−	42.7091i	−1.19512	−	1.37201i
$970$		0			0
$971$	−1.13634	−	1.96819i	−0.0364668	−	0.0631623i	0.847216	−	0.531249i	$-0.178277\pi$
$971$	−1.13634	−	1.96819i	−0.0364668	−	0.0631623i	−0.883683	+	0.468086i	$0.844944\pi$
$972$		0			0
$973$	−12.4404	+	32.4755i	−0.398822	+	1.04112i
$974$		0			0
$975$	−11.9525	+	2.33594i	−0.382787	+	0.0748100i
$976$		0			0
$977$	−8.42330	−	14.5896i	−0.269485	−	0.466762i	0.699244	−	0.714883i	$-0.253520\pi$
$977$	−8.42330	−	14.5896i	−0.269485	−	0.466762i	−0.968729	+	0.248121i	$0.920187\pi$
$978$		0			0
$979$	−6.05828	−	10.4932i	−0.193623	−	0.335366i
$980$		0			0
$981$	38.4029	+	29.8781i	1.22611	+	0.953934i
$982$		0			0
$983$	−21.5322			−0.686772			−0.343386	−	0.939194i	$-0.611574\pi$
$983$	−21.5322			−0.686772			−0.343386	+	0.939194i	$0.611574\pi$
$984$		0			0
$985$	−24.5210			−0.781303
$986$		0			0
$987$	−28.1095	+	10.2854i	−0.894735	+	0.327388i
$988$		0			0
$989$	−27.4764	−	47.5905i	−0.873699	−	1.51329i
$990$		0			0
$991$	−16.8227	+	29.1378i	−0.534392	+	0.925594i	0.464801	+	0.885415i	$0.346126\pi$
$991$	−16.8227	+	29.1378i	−0.534392	+	0.925594i	−0.999193	+	0.0401785i	$0.987207\pi$
$992$		0			0
$993$	−10.6683	+	2.08497i	−0.338549	+	0.0661645i
$994$		0			0
$995$	−7.25033	+	12.5579i	−0.229851	+	0.398113i
$996$		0			0
$997$	13.9881			0.443008			0.221504	−	0.975159i	$-0.428903\pi$
$997$	13.9881			0.443008			0.221504	+	0.975159i	$0.428903\pi$
$998$		0			0
$999$	−17.8881	−	9.04584i	−0.565954	−	0.286198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.193.9	yes	22
3.2	odd	2		1512.2.t.c.361.2		22
4.3	odd	2		1008.2.t.l.193.3		22
7.2	even	3		504.2.q.c.121.2	yes	22
9.2	odd	6		1512.2.q.d.1369.10		22
9.7	even	3		504.2.q.c.25.2	✓	22
12.11	even	2		3024.2.t.k.1873.2		22
21.2	odd	6		1512.2.q.d.793.10		22
28.23	odd	6		1008.2.q.l.625.10		22
36.7	odd	6		1008.2.q.l.529.10		22
36.11	even	6		3024.2.q.l.2881.10		22
63.2	odd	6		1512.2.t.c.289.2		22
63.16	even	3	inner	504.2.t.c.457.9	yes	22
84.23	even	6		3024.2.q.l.2305.10		22
252.79	odd	6		1008.2.t.l.961.3		22
252.191	even	6		3024.2.t.k.289.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.2	✓	22	9.7	even	3
504.2.q.c.121.2	yes	22	7.2	even	3
504.2.t.c.193.9	yes	22	1.1	even	1	trivial
504.2.t.c.457.9	yes	22	63.16	even	3	inner
1008.2.q.l.529.10		22	36.7	odd	6
1008.2.q.l.625.10		22	28.23	odd	6
1008.2.t.l.193.3		22	4.3	odd	2
1008.2.t.l.961.3		22	252.79	odd	6
1512.2.q.d.793.10		22	21.2	odd	6
1512.2.q.d.1369.10		22	9.2	odd	6
1512.2.t.c.289.2		22	63.2	odd	6
1512.2.t.c.361.2		22	3.2	odd	2
3024.2.q.l.2305.10		22	84.23	even	6
3024.2.q.l.2881.10		22	36.11	even	6
3024.2.t.k.289.2		22	252.191	even	6
3024.2.t.k.1873.2		22	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.13766 + 1.30604i) q^{3} +3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} +O(q^{10})\)	\(q+(1.13766 + 1.30604i) q^{3} +3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} -2.28279 q^{11} +(-0.675051 + 1.16922i) q^{13} +(3.63481 + 4.17279i) q^{15} +(2.21425 - 3.83519i) q^{17} +(-3.69214 - 6.39497i) q^{19} +(3.51548 + 2.93962i) q^{21} -6.46959 q^{23} +5.20800 q^{25} +(-4.34921 + 2.84330i) q^{27} +(-1.06167 - 1.83887i) q^{29} +(0.316154 + 0.547595i) q^{31} +(-2.59702 - 2.98141i) q^{33} +(8.34818 - 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(-2.29503 + 0.448529i) q^{39} +(-5.05124 + 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(-1.31468 + 9.49440i) q^{45} +(-3.26587 + 5.65664i) q^{47} +(6.65440 - 2.17232i) q^{49} +(7.52795 - 1.47123i) q^{51} +(2.39950 - 4.15606i) q^{53} -7.29349 q^{55} +(4.15170 - 12.0974i) q^{57} +(-3.10191 - 5.37267i) q^{59} +(4.45546 - 7.71709i) q^{61} +(0.160142 + 7.93564i) q^{63} +(-2.15679 + 3.73566i) q^{65} +(1.50785 + 2.61167i) q^{67} +(-7.36017 - 8.44954i) q^{69} -15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(5.92492 + 6.80186i) q^{75} +(-5.96467 + 0.948938i) q^{77} +(0.938050 - 1.62475i) q^{79} +(-8.66137 - 2.44554i) q^{81} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(1.19382 - 3.47859i) q^{87} +(2.65390 + 4.59668i) q^{89} +(-1.27780 + 3.33566i) q^{91} +(-0.355506 + 1.03588i) q^{93} +(-11.7964 - 20.4319i) q^{95} +(7.44539 + 12.8958i) q^{97} +(0.939319 - 6.78363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

L-functions

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