LMFDB - Embedded newform 1008.2.t.l.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, 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("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.l.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13766 - 1.30604i) q^{3} +3.19500 q^{5} +(-2.61289 + 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} +O(q^{10})$	\(q+(-1.13766 - 1.30604i) q^{3} +3.19500 q^{5} +(-2.61289 + 0.415693i) q^{7} +(-0.411479 + 2.97165i) q^{9} +2.28279 q^{11} +(-0.675051 + 1.16922i) q^{13} +(-3.63481 - 4.17279i) q^{15} +(2.21425 - 3.83519i) q^{17} +(3.69214 + 6.39497i) q^{19} +(3.51548 + 2.93962i) q^{21} +6.46959 q^{23} +5.20800 q^{25} +(4.34921 - 2.84330i) q^{27} +(-1.06167 - 1.83887i) q^{29} +(-0.316154 - 0.547595i) q^{31} +(-2.59702 - 2.98141i) q^{33} +(-8.34818 + 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(2.29503 - 0.448529i) q^{39} +(-5.05124 + 8.74900i) q^{41} +(-4.24701 - 7.35603i) q^{43} +(-1.31468 + 9.49440i) q^{45} +(3.26587 - 5.65664i) q^{47} +(6.65440 - 2.17232i) q^{49} +(-7.52795 + 1.47123i) q^{51} +(2.39950 - 4.15606i) q^{53} +7.29349 q^{55} +(4.15170 - 12.0974i) q^{57} +(3.10191 + 5.37267i) q^{59} +(4.45546 - 7.71709i) q^{61} +(-0.160142 - 7.93564i) q^{63} +(-2.15679 + 3.73566i) q^{65} +(-1.50785 - 2.61167i) q^{67} +(-7.36017 - 8.44954i) q^{69} +15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(-5.92492 - 6.80186i) q^{75} +(-5.96467 + 0.948938i) q^{77} +(-0.938050 + 1.62475i) q^{79} +(-8.66137 - 2.44554i) q^{81} +(3.00140 + 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-1.19382 + 3.47859i) q^{87} +(2.65390 + 4.59668i) q^{89} +(1.27780 - 3.33566i) q^{91} +(-0.355506 + 1.03588i) q^{93} +(11.7964 + 20.4319i) q^{95} +(7.44539 + 12.8958i) q^{97} +(-0.939319 + 6.78363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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	$-0.388170\pi$
$11$	2.28279			0.688286			0.344143	+	0.938917i	$0.388170\pi$
$12$		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	$0.154948\pi$
$19$	3.69214	+	6.39497i	0.847034	+	1.46711i	−0.0368084	+	0.999322i	$0.511719\pi$
$20$		0			0
$21$	3.51548	+	2.93962i	0.767141	+	0.641479i
$22$		0			0
$23$	6.46959			1.34900			0.674501	−	0.738274i	$-0.264359\pi$
$23$	6.46959			1.34900			0.674501	+	0.738274i	$0.264359\pi$
$24$		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	0.836237	−	0.548369i	$-0.184751\pi$
$31$	−0.316154	−	0.547595i	−0.0567830	−	0.0983510i	−0.893020	+	0.450018i	$0.851418\pi$
$32$		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	$-0.942413\pi$
$43$	−4.24701	−	7.35603i	−0.647663	−	1.12178i	0.336017	−	0.941856i	$-0.390920\pi$
$44$		0			0
$45$	−1.31468	+	9.49440i	−0.195980	+	1.41534i
$46$		0			0
$47$	3.26587	−	5.65664i	0.476375	−	0.825106i	−0.523258	−	0.852174i	$-0.675284\pi$
$47$	3.26587	−	5.65664i	0.476375	−	0.825106i	0.999634	+	0.0270678i	$0.00861699\pi$
$48$		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	0.994185	−	0.107685i	$-0.0343437\pi$
$59$	3.10191	+	5.37267i	0.403835	+	0.699463i	−0.590350	+	0.807147i	$0.701010\pi$
$60$		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	0.759098	−	0.650976i	$-0.225640\pi$
$67$	−1.50785	−	2.61167i	−0.184213	−	0.319067i	−0.943311	+	0.331910i	$0.892307\pi$
$68$		0			0
$69$	−7.36017	−	8.44954i	−0.886060	−	1.01721i
$70$		0			0
$71$	15.3791			1.82516			0.912580	−	0.408899i	$-0.134087\pi$
$71$	15.3791			1.82516			0.912580	+	0.408899i	$0.134087\pi$
$72$		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	−0.913958	−	0.405808i	$-0.866990\pi$
$79$	−0.938050	+	1.62475i	−0.105539	+	0.182799i	0.808419	+	0.588607i	$0.200323\pi$
$80$		0			0
$81$	−8.66137	−	2.44554i	−0.962374	−	0.271727i
$82$		0			0
$83$	3.00140	+	5.19857i	0.329446	+	0.570617i	0.982402	−	0.186779i	$-0.0598047\pi$
$83$	3.00140	+	5.19857i	0.329446	+	0.570617i	−0.652956	+	0.757396i	$0.726471\pi$
$84$		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	$-0.790582\pi$
$103$	−16.0611			−1.58255			−0.791274	+	0.611462i	$0.790582\pi$
$104$		0			0
$105$	11.2320	+	9.39209i	1.09613	+	0.916574i
$106$		0			0
$107$	−1.26820	−	2.19658i	−0.122601	−	0.212352i	0.798191	−	0.602404i	$-0.205790\pi$
$107$	−1.26820	−	2.19658i	−0.122601	−	0.212352i	−0.920793	+	0.390052i	$0.872457\pi$
$108$		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	$-0.310441\pi$
$127$	12.6429			1.12187			0.560936	+	0.827859i	$0.310441\pi$
$128$		0			0
$129$	−4.77564	+	13.9154i	−0.420472	+	1.22518i
$130$		0			0
$131$	−19.0686			−1.66603			−0.833015	−	0.553250i	$-0.813387\pi$
$131$	−19.0686			−1.66603			−0.833015	+	0.553250i	$0.813387\pi$
$132$		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	$-0.645115\pi$
$139$	6.57218	−	11.3834i	0.557445	−	0.965524i	0.997709	−	0.0676550i	$-0.0215517\pi$
$140$		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	$-0.617369\pi$
$151$	−8.85798			−0.720852			−0.360426	+	0.932788i	$0.617369\pi$
$152$		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	$0.237958\pi$
$163$	12.1983	+	21.1281i	0.955446	+	1.65488i	0.222100	+	0.975024i	$0.428709\pi$
$164$		0			0
$165$	−8.29748	−	9.52559i	−0.645958	−	0.741566i
$166$		0			0
$167$	−2.75658	+	4.77453i	−0.213310	+	0.369464i	−0.952749	−	0.303760i	$-0.901758\pi$
$167$	−2.75658	+	4.77453i	−0.213310	+	0.369464i	0.739438	+	0.673224i	$0.235091\pi$
$168$		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	−0.991283	−	0.131747i	$-0.957941\pi$
$179$	−5.10472	+	8.84164i	−0.381545	+	0.660855i	0.609738	+	0.792603i	$0.291275\pi$
$180$		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	−0.928470	−	0.371407i	$-0.878876\pi$
$191$	−1.97060	+	3.41318i	−0.142587	+	0.246969i	0.785883	+	0.618375i	$0.212209\pi$
$192$		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	−0.774314	−	0.632801i	$-0.781905\pi$
$199$	2.26928	−	3.93050i	0.160865	−	0.278626i	0.935179	+	0.354175i	$0.115238\pi$
$200$		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	$0.403595\pi$
$211$	−9.84097	+	17.0451i	−0.677480	+	1.17343i	−0.975737	+	0.218944i	$0.929739\pi$
$212$		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	0.553681	−	0.832729i	$-0.313223\pi$
$223$	−6.63518	−	11.4925i	−0.444324	−	0.769592i	−0.998005	+	0.0631368i	$0.979890\pi$
$224$		0			0
$225$	−2.14299	+	15.4764i	−0.142866	+	1.03176i
$226$		0			0
$227$	−22.0610			−1.46424			−0.732118	−	0.681177i	$-0.761468\pi$
$227$	−22.0610			−1.46424			−0.732118	+	0.681177i	$0.761468\pi$
$228$		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	−0.863949	−	0.503579i	$-0.832016\pi$
$239$	0.0639656	−	0.110792i	0.00413759	−	0.00716652i	0.868087	+	0.496412i	$0.165350\pi$
$240$		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	$-0.627703\pi$
$251$	−12.3738			−0.781030			−0.390515	+	0.920596i	$0.627703\pi$
$252$		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	$-0.422759\pi$
$263$	7.79357			0.480572			0.240286	+	0.970702i	$0.422759\pi$
$264$		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	$-0.889979\pi$
$271$	−12.5744	−	21.7795i	−0.763839	−	1.32301i	0.177019	−	0.984207i	$-0.443355\pi$
$272$		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	0.996801	−	0.0799265i	$-0.0254686\pi$
$283$	7.21996	+	12.5053i	0.429182	+	0.743365i	−0.567619	+	0.823292i	$0.692135\pi$
$284$		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	$-0.600903\pi$
$307$	−10.9233			−0.623425			−0.311713	+	0.950176i	$0.600903\pi$
$308$		0			0
$309$	18.2720	+	20.9764i	1.03946	+	1.19331i
$310$		0			0
$311$	−2.62680	−	4.54975i	−0.148952	−	0.257992i	0.781888	−	0.623418i	$-0.214257\pi$
$311$	−2.62680	−	4.54975i	−0.148952	−	0.257992i	−0.930840	+	0.365426i	$0.880923\pi$
$312$		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	−0.766808	−	0.641876i	$-0.778156\pi$
$331$	3.13795	−	5.43508i	0.172477	−	0.298739i	0.939285	+	0.343137i	$0.111490\pi$
$332$		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	$-0.994518\pi$
$347$	−9.59040	−	16.6111i	−0.514840	−	0.891728i	0.485012	−	0.874507i	$-0.338815\pi$
$348$		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	$-0.862963\pi$
$359$	−15.4572	−	26.7727i	−0.815802	−	1.41301i	0.0929489	−	0.995671i	$-0.470371\pi$
$360$		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	$-0.442945\pi$
$367$	6.83095			0.356573			0.178286	+	0.983979i	$0.442945\pi$
$368$		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	$-0.437219\pi$
$379$	7.62967			0.391910			0.195955	+	0.980613i	$0.437219\pi$
$380$		0			0
$381$	−14.3832	−	16.5121i	−0.736874	−	0.845939i
$382$		0			0
$383$	6.42264			0.328181			0.164091	−	0.986445i	$-0.447531\pi$
$383$	6.42264			0.328181			0.164091	+	0.986445i	$0.447531\pi$
$384$		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	−0.926775	−	0.375616i	$-0.877431\pi$
$419$	−2.82673	+	4.89604i	−0.138095	+	0.239187i	0.788681	+	0.614803i	$0.210764\pi$
$420$		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	$0.334595\pi$
$431$	−10.4514	+	18.1024i	−0.503428	+	0.871962i	−0.999992	+	0.00396247i	$0.998739\pi$
$432$		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	−0.584871	−	0.811126i	$-0.698855\pi$
$439$	8.59087	−	14.8798i	0.410020	−	0.710176i	0.994891	+	0.100951i	$0.0321884\pi$
$440$		0			0
$441$	3.71722	+	20.6684i	0.177011	+	0.984209i
$442$		0			0
$443$	−6.37181	+	11.0363i	−0.302734	+	0.524350i	−0.976754	−	0.214363i	$-0.931233\pi$
$443$	−6.37181	+	11.0363i	−0.302734	+	0.524350i	0.674020	+	0.738713i	$0.264566\pi$
$444$		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	−0.822331	−	0.569010i	$-0.807327\pi$
$463$	1.75608	−	3.04161i	0.0816117	−	0.141356i	0.903942	+	0.427654i	$0.140660\pi$
$464$		0			0
$465$	−1.13584	+	3.30965i	−0.0526734	+	0.153481i
$466$		0			0
$467$	7.80239	+	13.5141i	0.361052	+	0.625360i	0.988134	−	0.153593i	$-0.0490845\pi$
$467$	7.80239	+	13.5141i	0.361052	+	0.625360i	−0.627083	+	0.778953i	$0.715751\pi$
$468$		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	$-0.372335\pi$
$479$	17.0889			0.780811			0.390405	+	0.920643i	$0.372335\pi$
$480$		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	$-0.634007\pi$
$487$	12.9335	−	22.4014i	0.586072	−	1.01511i	0.994741	−	0.102423i	$-0.0326597\pi$
$488$		0			0
$489$	13.7167	−	39.9680i	0.620289	−	1.80741i
$490$		0			0
$491$	7.51452	−	13.0155i	0.339126	−	0.587383i	−0.645143	−	0.764062i	$-0.723202\pi$
$491$	7.51452	−	13.0155i	0.339126	−	0.587383i	0.984269	+	0.176679i	$0.0565355\pi$
$492$		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	$-0.610820\pi$
$499$	−15.2419			−0.682321			−0.341160	+	0.940005i	$0.610820\pi$
$500$		0			0
$501$	9.37176	−	1.83157i	0.418699	−	0.0818287i
$502$		0			0
$503$	−18.6284			−0.830599			−0.415299	−	0.909685i	$-0.636323\pi$
$503$	−18.6284			−0.830599			−0.415299	+	0.909685i	$0.636323\pi$
$504$		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	$-0.909936\pi$
$523$	−16.5092	−	28.5949i	−0.721899	−	1.25037i	0.238339	−	0.971182i	$-0.423397\pi$
$524$		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	$-0.920122\pi$
$547$	−16.3574	−	28.3318i	−0.699390	−	1.21138i	0.269288	−	0.963060i	$-0.413212\pi$
$548$		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	0.745959	−	0.665992i	$-0.231991\pi$
$563$	−4.83537	−	8.37510i	−0.203786	−	0.352969i	−0.949745	+	0.313023i	$0.898658\pi$
$564$		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	0.873555	−	0.486726i	$-0.161809\pi$
$571$	0.364653	+	0.631597i	0.0152602	+	0.0264315i	−0.858294	+	0.513158i	$0.828476\pi$
$572$		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	0.891706	−	0.452615i	$-0.149509\pi$
$587$	1.30535	+	2.26093i	0.0538775	+	0.0933185i	−0.837829	+	0.545933i	$0.816175\pi$
$588$		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	0.981316	−	0.192403i	$-0.0616282\pi$
$599$	7.93051	+	13.7360i	0.324032	+	0.561239i	−0.657284	+	0.753643i	$0.728295\pi$
$600$		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	$-0.234367\pi$
$607$	36.5110			1.48194			0.740968	+	0.671541i	$0.234367\pi$
$608$		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	$-0.334417\pi$
$619$	24.7329			0.994098			0.497049	+	0.867723i	$0.334417\pi$
$620$		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	$-0.816756\pi$
$631$	−42.1420			−1.67765			−0.838823	+	0.544404i	$0.816756\pi$
$632$		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	$0.392248\pi$
$643$	−16.5035	+	28.5850i	−0.650836	+	1.12728i	−0.982920	+	0.184031i	$0.941085\pi$
$644$		0			0
$645$	−15.2582	+	44.4596i	−0.600789	+	1.75060i
$646$		0			0
$647$	10.4187	−	18.0458i	0.409603	−	0.709452i	−0.585243	−	0.810858i	$-0.699001\pi$
$647$	10.4187	−	18.0458i	0.409603	−	0.709452i	0.994845	+	0.101406i	$0.0323341\pi$
$648$		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	0.860666	−	0.509170i	$-0.170048\pi$
$659$	−0.272662	−	0.472265i	−0.0106214	−	0.0183968i	−0.871287	+	0.490773i	$0.836714\pi$
$660$		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	−0.871515	−	0.490369i	$-0.836862\pi$
$683$	−0.289712	+	0.501795i	−0.0110855	+	0.0192007i	0.860429	+	0.509570i	$0.170195\pi$
$684$		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	−0.844184	−	0.536053i	$-0.819915\pi$
$691$	1.10782	−	1.91881i	0.0421436	−	0.0729948i	0.886328	+	0.463058i	$0.153248\pi$
$692$		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	0.514094	−	0.857734i	$-0.328128\pi$
$719$	−13.0256	−	22.5610i	−0.485772	−	0.841382i	−0.999866	+	0.0163516i	$0.994795\pi$
$720$		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	0.738270	−	0.674505i	$-0.235643\pi$
$727$	−5.79712	−	10.0409i	−0.215003	−	0.372396i	−0.953274	+	0.302108i	$0.902310\pi$
$728$		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	−0.939041	−	0.343805i	$-0.888284\pi$
$739$	−4.66968	+	8.08812i	−0.171777	+	0.297526i	0.767264	+	0.641331i	$0.221617\pi$
$740$		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	$-0.652985\pi$
$743$	14.6308	−	25.3412i	0.536750	−	0.929679i	0.999076	−	0.0429687i	$-0.0136816\pi$
$744$		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	$-0.661440\pi$
$751$	−26.6213			−0.971424			−0.485712	+	0.874119i	$0.661440\pi$
$752$		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	0.530312	−	0.847803i	$-0.322075\pi$
$787$	−13.1589	−	22.7918i	−0.469063	−	0.812440i	−0.999375	+	0.0353624i	$0.988741\pi$
$788$		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	$-0.625989\pi$
$811$	−21.9596			−0.771107			−0.385553	+	0.922686i	$0.625989\pi$
$812$		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	0.957199	−	0.289431i	$-0.0934661\pi$
$823$	6.53927	+	11.3264i	0.227945	+	0.394812i	−0.729254	+	0.684243i	$0.760133\pi$
$824$		0			0
$825$	−13.5253	−	15.5272i	−0.470891	−	0.540587i
$826$		0			0
$827$	25.8079			0.897427			0.448714	−	0.893676i	$-0.351882\pi$
$827$	25.8079			0.897427			0.448714	+	0.893676i	$0.351882\pi$
$828$		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	0.857405	−	0.514643i	$-0.172075\pi$
$839$	−0.492155	−	0.852437i	−0.0169911	−	0.0294294i	−0.874396	+	0.485213i	$0.838742\pi$
$840$		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	$-0.132085\pi$
$859$	53.6428			1.83027			0.915134	+	0.403150i	$0.132085\pi$
$860$		0			0
$861$	−43.4763	+	15.9082i	−1.48167	+	0.542150i
$862$		0			0
$863$	4.80485	+	8.32225i	0.163559	+	0.283293i	0.936143	−	0.351620i	$-0.114369\pi$
$863$	4.80485	+	8.32225i	0.163559	+	0.283293i	−0.772584	+	0.634913i	$0.781036\pi$
$864$		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	$-0.452663\pi$
$883$	8.80560			0.296332			0.148166	+	0.988963i	$0.452663\pi$
$884$		0			0
$885$	11.1442	−	32.4723i	0.374608	−	1.09154i
$886$		0			0
$887$	−20.0149			−0.672033			−0.336017	−	0.941856i	$-0.609080\pi$
$887$	−20.0149			−0.672033			−0.336017	+	0.941856i	$0.609080\pi$
$888$		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	$-0.636595\pi$
$907$	−25.0615			−0.832152			−0.416076	+	0.909330i	$0.636595\pi$
$908$		0			0
$909$	5.76317	−	41.6208i	0.191152	−	1.38048i
$910$		0			0
$911$	−4.86265	−	8.42236i	−0.161107	−	0.279045i	0.774159	−	0.632991i	$-0.218173\pi$
$911$	−4.86265	−	8.42236i	−0.161107	−	0.279045i	−0.935266	+	0.353946i	$0.884840\pi$
$912$		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	$0.111692\pi$
$919$	23.2582	+	40.2844i	0.767217	+	1.32886i	−0.171849	+	0.985123i	$0.554974\pi$
$920$		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	−0.970838	−	0.239738i	$-0.922938\pi$
$947$	−8.54883	+	14.8070i	−0.277800	+	0.481163i	0.693038	+	0.720901i	$0.256272\pi$
$948$		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	−0.934898	−	0.354917i	$-0.884509\pi$
$967$	−4.97799	+	8.62213i	−0.160081	+	0.277269i	0.774816	+	0.632186i	$0.217842\pi$
$968$		0			0
$969$	−37.2027	−	42.7091i	−1.19512	−	1.37201i
$970$		0			0
$971$	1.13634	+	1.96819i	0.0364668	+	0.0631623i	0.883683	−	0.468086i	$-0.155056\pi$
$971$	1.13634	+	1.96819i	0.0364668	+	0.0631623i	−0.847216	+	0.531249i	$0.821723\pi$
$972$		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	$-0.388426\pi$
$983$	21.5322			0.686772			0.343386	+	0.939194i	$0.388426\pi$
$984$		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	$-0.653874\pi$
$991$	16.8227	−	29.1378i	0.534392	−	0.925594i	0.999193	−	0.0401785i	$-0.0127927\pi$
$992$		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	1008.2.t.l.193.3		22
3.2	odd	2		3024.2.t.k.1873.2		22
4.3	odd	2		504.2.t.c.193.9	yes	22
7.2	even	3		1008.2.q.l.625.10		22
9.2	odd	6		3024.2.q.l.2881.10		22
9.7	even	3		1008.2.q.l.529.10		22
12.11	even	2		1512.2.t.c.361.2		22
21.2	odd	6		3024.2.q.l.2305.10		22
28.23	odd	6		504.2.q.c.121.2	yes	22
36.7	odd	6		504.2.q.c.25.2	✓	22
36.11	even	6		1512.2.q.d.1369.10		22
63.2	odd	6		3024.2.t.k.289.2		22
63.16	even	3	inner	1008.2.t.l.961.3		22
84.23	even	6		1512.2.q.d.793.10		22
252.79	odd	6		504.2.t.c.457.9	yes	22
252.191	even	6		1512.2.t.c.289.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.2	✓	22	36.7	odd	6
504.2.q.c.121.2	yes	22	28.23	odd	6
504.2.t.c.193.9	yes	22	4.3	odd	2
504.2.t.c.457.9	yes	22	252.79	odd	6
1008.2.q.l.529.10		22	9.7	even	3
1008.2.q.l.625.10		22	7.2	even	3
1008.2.t.l.193.3		22	1.1	even	1	trivial
1008.2.t.l.961.3		22	63.16	even	3	inner
1512.2.q.d.793.10		22	84.23	even	6
1512.2.q.d.1369.10		22	36.11	even	6
1512.2.t.c.289.2		22	252.191	even	6
1512.2.t.c.361.2		22	12.11	even	2
3024.2.q.l.2305.10		22	21.2	odd	6
3024.2.q.l.2881.10		22	9.2	odd	6
3024.2.t.k.289.2		22	63.2	odd	6
3024.2.t.k.1873.2		22	3.2	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not 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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