LMFDB - Embedded newform 1008.2.cz.h.607.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.3
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.h.367.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43691 + 0.967101i) q^{3} +(1.73177 - 0.999840i) q^{5} +(-2.38101 + 1.15360i) q^{7} +(1.12943 - 2.77928i) q^{9} +O(q^{10})$	\(q+(-1.43691 + 0.967101i) q^{3} +(1.73177 - 0.999840i) q^{5} +(-2.38101 + 1.15360i) q^{7} +(1.12943 - 2.77928i) q^{9} +(-1.17995 - 0.681244i) q^{11} +(1.71030 + 0.987444i) q^{13} +(-1.52146 + 3.11148i) q^{15} +(0.868852 - 0.501632i) q^{17} +(0.774396 - 1.34129i) q^{19} +(2.30566 - 3.96030i) q^{21} +(7.59639 - 4.38578i) q^{23} +(-0.500642 + 0.867137i) q^{25} +(1.06494 + 5.08585i) q^{27} +(0.854529 + 1.48009i) q^{29} +0.522244 q^{31} +(2.35431 - 0.162242i) q^{33} +(-2.96996 + 4.37840i) q^{35} +(1.53855 - 2.66485i) q^{37} +(-3.41251 + 0.235165i) q^{39} +(-0.386794 - 0.223316i) q^{41} +(5.49888 - 3.17478i) q^{43} +(-0.822910 - 5.94233i) q^{45} +1.63949 q^{47} +(4.33842 - 5.49346i) q^{49} +(-0.763335 + 1.56107i) q^{51} +(1.24313 + 2.15316i) q^{53} -2.72454 q^{55} +(0.184426 + 2.67624i) q^{57} +12.6284 q^{59} +10.5433i q^{61} +(0.516980 + 7.92040i) q^{63} +3.94914 q^{65} +6.50486i q^{67} +(-6.67385 + 13.6484i) q^{69} +1.57299i q^{71} +(13.6347 - 7.87199i) q^{73} +(-0.119230 - 1.73017i) q^{75} +(3.59535 + 0.260861i) q^{77} -5.95935i q^{79} +(-6.44876 - 6.27801i) q^{81} +(4.80565 + 8.32363i) q^{83} +(1.00310 - 1.73743i) q^{85} +(-2.65928 - 1.30034i) q^{87} +(-1.10887 - 0.640207i) q^{89} +(-5.21136 - 0.378111i) q^{91} +(-0.750419 + 0.505063i) q^{93} -3.09709i q^{95} +(8.31781 - 4.80229i) q^{97} +(-3.22604 + 2.50999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.43691	+	0.967101i	−0.829602	+	0.558356i
$3$	−1.43691	+	0.967101i	−0.829602	+	0.558356i
$4$		0			0
$5$	1.73177	−	0.999840i	0.774472	−	0.447142i	−0.0599953	−	0.998199i	$-0.519109\pi$
$5$	1.73177	−	0.999840i	0.774472	−	0.447142i	0.834468	+	0.551057i	$0.185775\pi$
$6$		0			0
$7$	−2.38101	+	1.15360i	−0.899937	+	0.436019i
$7$	−2.38101	+	1.15360i	−0.899937	+	0.436019i
$8$		0			0
$9$	1.12943	−	2.77928i	0.376478	−	0.926426i
$10$		0			0
$11$	−1.17995	−	0.681244i	−0.355768	−	0.205403i	0.311455	−	0.950261i	$-0.399184\pi$
$11$	−1.17995	−	0.681244i	−0.355768	−	0.205403i	−0.667223	+	0.744858i	$0.732517\pi$
$12$		0			0
$13$	1.71030	+	0.987444i	0.474353	+	0.273868i	0.718060	−	0.695981i	$-0.245030\pi$
$13$	1.71030	+	0.987444i	0.474353	+	0.273868i	−0.243707	+	0.969849i	$0.578364\pi$
$14$		0			0
$15$	−1.52146	+	3.11148i	−0.392839	+	0.803381i
$16$		0			0
$17$	0.868852	−	0.501632i	0.210728	−	0.121664i	−0.390922	−	0.920424i	$-0.627844\pi$
$17$	0.868852	−	0.501632i	0.210728	−	0.121664i	0.601649	+	0.798760i	$0.294510\pi$
$18$		0			0
$19$	0.774396	−	1.34129i	0.177659	−	0.307714i	−0.763420	−	0.645903i	$-0.776481\pi$
$19$	0.774396	−	1.34129i	0.177659	−	0.307714i	0.941078	+	0.338189i	$0.109814\pi$
$20$		0			0
$21$	2.30566	−	3.96030i	0.503135	−	0.864208i
$22$		0			0
$23$	7.59639	−	4.38578i	1.58396	−	0.914498i	0.589682	−	0.807635i	$-0.299253\pi$
$23$	7.59639	−	4.38578i	1.58396	−	0.914498i	0.994274	−	0.106862i	$-0.0340804\pi$
$24$		0			0
$25$	−0.500642	+	0.867137i	−0.100128	+	0.173427i
$26$		0			0
$27$	1.06494	+	5.08585i	0.204949	+	0.978773i
$28$		0			0
$29$	0.854529	+	1.48009i	0.158682	+	0.274846i	0.934394	−	0.356242i	$-0.115942\pi$
$29$	0.854529	+	1.48009i	0.158682	+	0.274846i	−0.775712	+	0.631088i	$0.782609\pi$
$30$		0			0
$31$	0.522244			0.0937979			0.0468989	−	0.998900i	$-0.485066\pi$
$31$	0.522244			0.0937979			0.0468989	+	0.998900i	$0.485066\pi$
$32$		0			0
$33$	2.35431	−	0.162242i	0.409833	−	0.0282427i
$34$		0			0
$35$	−2.96996	+	4.37840i	−0.502014	+	0.740085i
$36$		0			0
$37$	1.53855	−	2.66485i	0.252936	−	0.438099i	−0.711397	−	0.702791i	$-0.751937\pi$
$37$	1.53855	−	2.66485i	0.252936	−	0.438099i	0.964333	+	0.264692i	$0.0852703\pi$
$38$		0			0
$39$	−3.41251	+	0.235165i	−0.546439	+	0.0376565i
$40$		0			0
$41$	−0.386794	−	0.223316i	−0.0604071	−	0.0348761i	0.469492	−	0.882937i	$-0.344437\pi$
$41$	−0.386794	−	0.223316i	−0.0604071	−	0.0348761i	−0.529899	+	0.848061i	$0.677770\pi$
$42$		0			0
$43$	5.49888	−	3.17478i	0.838572	−	0.484150i	−0.0182067	−	0.999834i	$-0.505796\pi$
$43$	5.49888	−	3.17478i	0.838572	−	0.484150i	0.856779	+	0.515685i	$0.172462\pi$
$44$		0			0
$45$	−0.822910	−	5.94233i	−0.122672	−	0.885830i
$46$		0			0
$47$	1.63949			0.239144			0.119572	−	0.992826i	$-0.461848\pi$
$47$	1.63949			0.239144			0.119572	+	0.992826i	$0.461848\pi$
$48$		0			0
$49$	4.33842	−	5.49346i	0.619774	−	0.784780i
$50$		0			0
$51$	−0.763335	+	1.56107i	−0.106888	+	0.218593i
$52$		0			0
$53$	1.24313	+	2.15316i	0.170757	+	0.295760i	0.938685	−	0.344777i	$-0.112045\pi$
$53$	1.24313	+	2.15316i	0.170757	+	0.295760i	−0.767928	+	0.640537i	$0.778712\pi$
$54$		0			0
$55$	−2.72454			−0.367377
$56$		0			0
$57$	0.184426	+	2.67624i	0.0244279	+	0.354476i
$58$		0			0
$59$	12.6284			1.64408			0.822040	−	0.569430i	$-0.192836\pi$
$59$	12.6284			1.64408			0.822040	+	0.569430i	$0.192836\pi$
$60$		0			0
$61$			10.5433i			1.34994i	0.737847	+	0.674968i	$0.235843\pi$
$61$			10.5433i			1.34994i	−0.737847	+	0.674968i	$0.764157\pi$
$62$		0			0
$63$	0.516980	+	7.92040i	0.0651333	+	0.997877i
$64$		0			0
$65$	3.94914			0.489831
$66$		0			0
$67$			6.50486i			0.794695i	0.917668	+	0.397347i	$0.130069\pi$
$67$			6.50486i			0.794695i	−0.917668	+	0.397347i	$0.869931\pi$
$68$		0			0
$69$	−6.67385	+	13.6484i	−0.803438	+	1.64308i
$70$		0			0
$71$			1.57299i			0.186679i	0.995634	+	0.0933396i	$0.0297542\pi$
$71$			1.57299i			0.186679i	−0.995634	+	0.0933396i	$0.970246\pi$
$72$		0			0
$73$	13.6347	−	7.87199i	1.59582	−	0.921346i	0.603538	−	0.797334i	$-0.293757\pi$
$73$	13.6347	−	7.87199i	1.59582	−	0.921346i	0.992281	−	0.124012i	$-0.0395760\pi$
$74$		0			0
$75$	−0.119230	−	1.73017i	−0.0137675	−	0.199783i
$76$		0			0
$77$	3.59535	+	0.260861i	0.409728	+	0.0297279i
$78$		0			0
$79$		−	5.95935i		−	0.670479i	−0.942133	−	0.335240i	$-0.891183\pi$
$79$		−	5.95935i		−	0.670479i	0.942133	−	0.335240i	$-0.108817\pi$
$80$		0			0
$81$	−6.44876	−	6.27801i	−0.716529	−	0.697557i
$82$		0			0
$83$	4.80565	+	8.32363i	0.527489	+	0.913637i	0.999487	+	0.0320377i	$0.0101997\pi$
$83$	4.80565	+	8.32363i	0.527489	+	0.913637i	−0.471998	+	0.881600i	$0.656467\pi$
$84$		0			0
$85$	1.00310	−	1.73743i	0.108802	−	0.188450i
$86$		0			0
$87$	−2.65928	−	1.30034i	−0.285105	−	0.139411i
$88$		0			0
$89$	−1.10887	−	0.640207i	−0.117540	−	0.0678618i	0.440077	−	0.897960i	$-0.354951\pi$
$89$	−1.10887	−	0.640207i	−0.117540	−	0.0678618i	−0.557617	+	0.830098i	$0.688284\pi$
$90$		0			0
$91$	−5.21136	−	0.378111i	−0.546299	−	0.0396368i
$92$		0			0
$93$	−0.750419	+	0.505063i	−0.0778149	+	0.0523726i
$94$		0			0
$95$		−	3.09709i		−	0.317754i
$96$		0			0
$97$	8.31781	−	4.80229i	0.844546	−	0.487599i	−0.0142608	−	0.999898i	$-0.504540\pi$
$97$	8.31781	−	4.80229i	0.844546	−	0.487599i	0.858807	+	0.512299i	$0.171206\pi$
$98$		0			0
$99$	−3.22604	+	2.50999i	−0.324229	+	0.252263i
$100$		0			0
$101$	9.76069	+	5.63534i	0.971225	+	0.560737i	0.899610	−	0.436695i	$-0.143851\pi$
$101$	9.76069	+	5.63534i	0.971225	+	0.560737i	0.0716156	+	0.997432i	$0.477185\pi$
$102$		0			0
$103$	−4.80600	−	8.32424i	−0.473550	−	0.820212i	0.525992	−	0.850490i	$-0.323694\pi$
$103$	−4.80600	−	8.32424i	−0.473550	−	0.820212i	−0.999542	+	0.0302775i	$0.990361\pi$
$104$		0			0
$105$	0.0332122	−	9.16362i	0.00324117	−	0.894278i
$106$		0			0
$107$	11.0876	+	6.40144i	1.07188	+	0.618850i	0.928695	−	0.370845i	$-0.120932\pi$
$107$	11.0876	+	6.40144i	1.07188	+	0.618850i	0.143186	+	0.989696i	$0.454265\pi$
$108$		0			0
$109$	−7.28182	−	12.6125i	−0.697472	−	1.20806i	−0.969340	−	0.245722i	$-0.920975\pi$
$109$	−7.28182	−	12.6125i	−0.697472	−	1.20806i	0.271869	−	0.962334i	$-0.412358\pi$
$110$		0			0
$111$	0.366414	+	5.31709i	0.0347785	+	0.504676i
$112$		0			0
$113$	−9.07922	+	15.7257i	−0.854101	+	1.47935i	0.0233754	+	0.999727i	$0.492559\pi$
$113$	−9.07922	+	15.7257i	−0.854101	+	1.47935i	−0.877476	+	0.479620i	$0.840775\pi$
$114$		0			0
$115$	8.77014	−	15.1903i	0.817820	−	1.41651i
$116$		0			0
$117$	4.67605	−	3.63815i	0.432301	−	0.336348i
$118$		0			0
$119$	−1.49006	+	2.19670i	−0.136594	+	0.201371i
$120$		0			0
$121$	−4.57181	−	7.91861i	−0.415619	−	0.719874i
$122$		0			0
$123$	0.771759	−	0.0531839i	0.0695871	−	0.00479543i
$124$		0			0
$125$			12.0006i			1.07337i
$126$		0			0
$127$		−	13.2304i		−	1.17401i	−0.809585	−	0.587003i	$-0.800308\pi$
$127$		−	13.2304i		−	1.17401i	0.809585	−	0.587003i	$-0.199692\pi$
$128$		0			0
$129$	−4.83108	+	9.87986i	−0.425353	+	0.869873i
$130$		0			0
$131$	4.27126	+	7.39804i	0.373182	+	0.646370i	0.990053	−	0.140694i	$-0.0449334\pi$
$131$	4.27126	+	7.39804i	0.373182	+	0.646370i	−0.616871	+	0.787064i	$0.711600\pi$
$132$		0			0
$133$	−0.296530	+	4.08697i	−0.0257125	+	0.354386i
$134$		0			0
$135$	6.92928	+	7.74277i	0.596377	+	0.666391i
$136$		0			0
$137$	1.92756	−	3.33864i	0.164683	−	0.285239i	−0.771860	−	0.635793i	$-0.780673\pi$
$137$	1.92756	−	3.33864i	0.164683	−	0.285239i	0.936543	+	0.350554i	$0.114007\pi$
$138$		0			0
$139$	−7.59749	+	13.1592i	−0.644410	+	1.11615i	0.340027	+	0.940416i	$0.389564\pi$
$139$	−7.59749	+	13.1592i	−0.644410	+	1.11615i	−0.984437	+	0.175736i	$0.943770\pi$
$140$		0			0
$141$	−2.35580	+	1.58555i	−0.198394	+	0.133527i
$142$		0			0
$143$	−1.34538	−	2.33027i	−0.112506	−	0.194867i
$144$		0			0
$145$	2.95970	+	1.70878i	0.245790	+	0.141907i
$146$		0			0
$147$	−0.921198	+	12.0893i	−0.0759792	+	0.997109i
$148$		0			0
$149$	−5.77752	−	10.0070i	−0.473313	−	0.819802i	0.526221	−	0.850348i	$-0.323609\pi$
$149$	−5.77752	−	10.0070i	−0.473313	−	0.819802i	−0.999533	+	0.0305463i	$0.990275\pi$
$150$		0			0
$151$	−19.6224	−	11.3290i	−1.59685	−	0.921941i	−0.992089	−	0.125533i	$-0.959936\pi$
$151$	−19.6224	−	11.3290i	−1.59685	−	0.921941i	−0.604759	−	0.796408i	$-0.706731\pi$
$152$		0			0
$153$	−0.412864	−	2.98134i	−0.0333781	−	0.241027i
$154$		0			0
$155$	0.904409	−	0.522161i	0.0726439	−	0.0419409i
$156$		0			0
$157$			14.6276i			1.16741i	0.811965	+	0.583706i	$0.198398\pi$
$157$			14.6276i			1.16741i	−0.811965	+	0.583706i	$0.801602\pi$
$158$		0			0
$159$	−3.86859	−	1.89168i	−0.306800	−	0.150020i
$160$		0			0
$161$	−13.0276	+	19.2058i	−1.02672	+	1.51363i
$162$		0			0
$163$	−10.4437	−	6.02970i	−0.818017	−	0.472282i	0.0317152	−	0.999497i	$-0.489903\pi$
$163$	−10.4437	−	6.02970i	−0.818017	−	0.472282i	−0.849732	+	0.527215i	$0.823236\pi$
$164$		0			0
$165$	3.91492	−	2.63490i	0.304776	−	0.205127i
$166$		0			0
$167$	11.0887	−	19.2062i	0.858069	−	1.48622i	−0.0156998	−	0.999877i	$-0.504998\pi$
$167$	11.0887	−	19.2062i	0.858069	−	1.48622i	0.873769	−	0.486342i	$-0.161669\pi$
$168$		0			0
$169$	−4.54991	−	7.88067i	−0.349993	−	0.606206i
$170$		0			0
$171$	−2.85320	−	3.66716i	−0.218189	−	0.280435i
$172$		0			0
$173$		−	14.9706i		−	1.13819i	−0.822270	−	0.569097i	$-0.807293\pi$
$173$		−	14.9706i		−	1.13819i	0.822270	−	0.569097i	$-0.192707\pi$
$174$		0			0
$175$	0.191705	−	2.64220i	0.0144915	−	0.199732i
$176$		0			0
$177$	−18.1459	+	12.2129i	−1.36393	+	0.917982i
$178$		0			0
$179$	−12.1951	+	7.04084i	−0.911505	+	0.526257i	−0.880915	−	0.473275i	$-0.843072\pi$
$179$	−12.1951	+	7.04084i	−0.911505	+	0.526257i	−0.0305897	+	0.999532i	$0.509739\pi$
$180$		0			0
$181$			4.70875i			0.349999i	0.984569	+	0.174999i	$0.0559924\pi$
$181$			4.70875i			0.349999i	−0.984569	+	0.174999i	$0.944008\pi$
$182$		0			0
$183$	−10.1965	−	15.1499i	−0.753745	−	1.11991i
$184$		0			0
$185$		−	6.15322i		−	0.452394i
$186$		0			0
$187$	−1.36693			−0.0999601
$188$		0			0
$189$	−8.40268	−	10.8809i	−0.611205	−	0.791472i
$190$		0			0
$191$			8.63432i			0.624758i	0.949958	+	0.312379i	$0.101126\pi$
$191$			8.63432i			0.624758i	−0.949958	+	0.312379i	$0.898874\pi$
$192$		0			0
$193$	10.9280			0.786613			0.393307	−	0.919407i	$-0.371331\pi$
$193$	10.9280			0.786613			0.393307	+	0.919407i	$0.371331\pi$
$194$		0			0
$195$	−5.67457	+	3.81922i	−0.406364	+	0.273500i
$196$		0			0
$197$	−19.7147			−1.40461			−0.702305	−	0.711876i	$-0.747846\pi$
$197$	−19.7147			−1.40461			−0.702305	+	0.711876i	$0.747846\pi$
$198$		0			0
$199$	−13.3575	−	23.1359i	−0.946889	−	1.64006i	−0.751924	−	0.659249i	$-0.770874\pi$
$199$	−13.3575	−	23.1359i	−0.946889	−	1.64006i	−0.194965	−	0.980810i	$-0.562459\pi$
$200$		0			0
$201$	−6.29085	−	9.34691i	−0.443722	−	0.659280i
$202$		0			0
$203$	−3.74207	−	2.53832i	−0.262642	−	0.178155i
$204$		0			0
$205$	−0.893120			−0.0623782
$206$		0			0
$207$	−3.60968	−	26.0659i	−0.250890	−	1.81171i
$208$		0			0
$209$	−1.82749	+	1.05510i	−0.126410	+	0.0729831i
$210$		0			0
$211$	−6.27293	−	3.62168i	−0.431846	−	0.249327i	0.268286	−	0.963339i	$-0.413543\pi$
$211$	−6.27293	−	3.62168i	−0.431846	−	0.249327i	−0.700133	+	0.714012i	$0.746876\pi$
$212$		0			0
$213$	−1.52124	−	2.26024i	−0.104233	−	0.154869i
$214$		0			0
$215$	6.34854	−	10.9960i	0.432967	−	0.749921i
$216$		0			0
$217$	−1.24347	+	0.602460i	−0.0844122	+	0.0408977i
$218$		0			0
$219$	−11.9788	+	24.4975i	−0.809455	+	1.65538i
$220$		0			0
$221$	1.98133			0.133279
$222$		0			0
$223$	9.80779	+	16.9876i	0.656778	+	1.13757i	0.981445	+	0.191744i	$0.0614145\pi$
$223$	9.80779	+	16.9876i	0.656778	+	1.13757i	−0.324667	+	0.945828i	$0.605252\pi$
$224$		0			0
$225$	1.84457	+	2.37079i	0.122971	+	0.158053i
$226$		0			0
$227$	10.3892	−	17.9947i	0.689557	−	1.19435i	−0.282424	−	0.959290i	$-0.591139\pi$
$227$	10.3892	−	17.9947i	0.689557	−	1.19435i	0.971981	−	0.235058i	$-0.0755281\pi$
$228$		0			0
$229$	−19.1630	+	11.0638i	−1.26633	+	0.731113i	−0.974291	−	0.225294i	$-0.927666\pi$
$229$	−19.1630	+	11.0638i	−1.26633	+	0.731113i	−0.292035	+	0.956408i	$0.594332\pi$
$230$		0			0
$231$	−5.41848	+	3.10223i	−0.356510	+	0.204112i
$232$		0			0
$233$	−1.95965	+	3.39421i	−0.128381	+	0.222362i	−0.923049	−	0.384681i	$-0.874311\pi$
$233$	−1.95965	+	3.39421i	−0.128381	+	0.222362i	0.794669	+	0.607043i	$0.207645\pi$
$234$		0			0
$235$	2.83922	−	1.63922i	0.185210	−	0.106931i
$236$		0			0
$237$	5.76329	+	8.56306i	0.374366	+	0.556231i
$238$		0			0
$239$	7.38657	+	4.26464i	0.477798	+	0.275857i	0.719498	−	0.694494i	$-0.244372\pi$
$239$	7.38657	+	4.26464i	0.477798	+	0.275857i	−0.241701	+	0.970351i	$0.577705\pi$
$240$		0			0
$241$	2.09775	+	1.21114i	0.135128	+	0.0780161i	0.566040	−	0.824378i	$-0.308475\pi$
$241$	2.09775	+	1.21114i	0.135128	+	0.0780161i	−0.430912	+	0.902394i	$0.641808\pi$
$242$		0			0
$243$	15.3378	+	2.78435i	0.983919	+	0.178616i
$244$		0			0
$245$	2.02058	−	13.8512i	0.129090	−	0.884918i
$246$		0			0
$247$	2.64890	−	1.52934i	0.168546	−	0.0973099i
$248$		0			0
$249$	−14.9551	−	7.31278i	−0.947740	−	0.463429i
$250$		0			0
$251$	1.09792			0.0693002			0.0346501	−	0.999400i	$-0.488968\pi$
$251$	1.09792			0.0693002			0.0346501	+	0.999400i	$0.488968\pi$
$252$		0			0
$253$	−11.9511			−0.751361
$254$		0			0
$255$	0.238894	+	3.46663i	0.0149601	+	0.217089i
$256$		0			0
$257$	−18.2289	+	10.5245i	−1.13709	+	0.656498i	−0.945708	−	0.325018i	$-0.894629\pi$
$257$	−18.2289	+	10.5245i	−1.13709	+	0.656498i	−0.191380	+	0.981516i	$0.561296\pi$
$258$		0			0
$259$	−0.589140	+	8.11991i	−0.0366074	+	0.504547i
$260$		0			0
$261$	5.07871	−	0.703314i	0.314364	−	0.0435340i
$262$		0			0
$263$	−21.1850	−	12.2312i	−1.30632	−	0.754206i	−0.324843	−	0.945768i	$-0.605311\pi$
$263$	−21.1850	−	12.2312i	−1.30632	−	0.754206i	−0.981481	+	0.191562i	$0.938645\pi$
$264$		0			0
$265$	4.30564	+	2.48586i	0.264493	+	0.152705i
$266$		0			0
$267$	2.21249	−	0.152469i	0.135402	−	0.00933093i
$268$		0			0
$269$	−9.79690	+	5.65624i	−0.597327	+	0.344867i	−0.767989	−	0.640462i	$-0.778743\pi$
$269$	−9.79690	+	5.65624i	−0.597327	+	0.344867i	0.170662	+	0.985330i	$0.445409\pi$
$270$		0			0
$271$	−0.480849	+	0.832856i	−0.0292095	+	0.0505924i	−0.880261	−	0.474490i	$-0.842632\pi$
$271$	−0.480849	+	0.832856i	−0.0292095	+	0.0505924i	0.851051	+	0.525083i	$0.175966\pi$
$272$		0			0
$273$	7.85394	−	4.49660i	0.475342	−	0.272147i
$274$		0			0
$275$	1.18146	−	0.682118i	0.0712449	−	0.0411333i
$276$		0			0
$277$	12.5249	−	21.6938i	0.752549	−	1.30345i	−0.194034	−	0.980995i	$-0.562157\pi$
$277$	12.5249	−	21.6938i	0.752549	−	1.30345i	0.946583	−	0.322459i	$-0.104509\pi$
$278$		0			0
$279$	0.589840	−	1.45146i	0.0353128	−	0.0868967i
$280$		0			0
$281$	11.0324	+	19.1087i	0.658139	+	1.13993i	0.981097	+	0.193517i	$0.0619896\pi$
$281$	11.0324	+	19.1087i	0.658139	+	1.13993i	−0.322958	+	0.946413i	$0.604677\pi$
$282$		0			0
$283$	5.26865			0.313189			0.156594	−	0.987663i	$-0.449948\pi$
$283$	5.26865			0.313189			0.156594	+	0.987663i	$0.449948\pi$
$284$		0			0
$285$	2.99519	+	4.45024i	0.177420	+	0.263609i
$286$		0			0
$287$	1.17858	+	0.0855118i	0.0695693	+	0.00504760i
$288$		0			0
$289$	−7.99673	+	13.8507i	−0.470396	+	0.814750i
$290$		0			0
$291$	−7.30767	+	14.9446i	−0.428383	+	0.876070i
$292$		0			0
$293$	−12.1084	−	6.99080i	−0.707381	−	0.408407i	0.102709	−	0.994711i	$-0.467249\pi$
$293$	−12.1084	−	6.99080i	−0.707381	−	0.408407i	−0.810091	+	0.586305i	$0.800582\pi$
$294$		0			0
$295$	21.8696	−	12.6264i	1.27329	−	0.735137i
$296$		0			0
$297$	2.20812	−	6.72653i	0.128128	−	0.390313i
$298$		0			0
$299$	17.3228			1.00181
$300$		0			0
$301$	−9.43047	+	13.9027i	−0.543563	+	0.801338i
$302$		0			0
$303$	−19.4752	+	1.34209i	−1.11882	+	0.0771008i
$304$		0			0
$305$	10.5416	+	18.2587i	0.603613	+	1.04549i
$306$		0			0
$307$	16.2755			0.928893			0.464446	−	0.885601i	$-0.346253\pi$
$307$	16.2755			0.928893			0.464446	+	0.885601i	$0.346253\pi$
$308$		0			0
$309$	14.9562	+	7.31332i	0.850828	+	0.416040i
$310$		0			0
$311$	6.38973			0.362329			0.181164	−	0.983453i	$-0.442013\pi$
$311$	6.38973			0.362329			0.181164	+	0.983453i	$0.442013\pi$
$312$		0			0
$313$			25.6429i			1.44942i	0.689053	+	0.724711i	$0.258027\pi$
$313$			25.6429i			1.44942i	−0.689053	+	0.724711i	$0.741973\pi$
$314$		0			0
$315$	8.81442	+	13.1994i	0.496636	+	0.743704i
$316$		0			0
$317$	29.3042			1.64589			0.822945	−	0.568122i	$-0.192330\pi$
$317$	29.3042			1.64589			0.822945	+	0.568122i	$0.192330\pi$
$318$		0			0
$319$		−	2.32857i		−	0.130375i
$320$		0			0
$321$	−22.1228	+	1.52454i	−1.23477	+	0.0850913i
$322$		0			0
$323$		−	1.55385i		−	0.0864583i
$324$		0			0
$325$	−1.71250	+	0.988711i	−0.0949923	+	0.0548438i
$326$		0			0
$327$	22.6609	+	11.0808i	1.25315	+	0.612768i
$328$		0			0
$329$	−3.90363	+	1.89131i	−0.215214	+	0.104271i
$330$		0			0
$331$		−	0.133691i		−	0.00734833i	−0.999993	−	0.00367417i	$-0.998830\pi$
$331$		−	0.133691i		−	0.00734833i	0.999993	−	0.00367417i	$-0.00116953\pi$
$332$		0			0
$333$	−5.66867	−	7.28583i	−0.310641	−	0.399261i
$334$		0			0
$335$	6.50381	+	11.2649i	0.355341	+	0.615469i
$336$		0			0
$337$	9.96606	−	17.2617i	0.542886	−	0.940306i	−0.455851	−	0.890056i	$-0.650665\pi$
$337$	9.96606	−	17.2617i	0.542886	−	0.940306i	0.998737	−	0.0502498i	$-0.0160017\pi$
$338$		0			0
$339$	−2.16226	−	31.3769i	−0.117438	−	1.70416i
$340$		0			0
$341$	−0.616222	−	0.355776i	−0.0333703	−	0.0192663i
$342$		0			0
$343$	−3.99257	+	18.0848i	−0.215579	+	0.976486i
$344$		0			0
$345$	2.08866	+	30.3088i	0.112449	+	1.63177i
$346$		0			0
$347$		−	5.55582i		−	0.298252i	−0.988818	−	0.149126i	$-0.952354\pi$
$347$		−	5.55582i		−	0.298252i	0.988818	−	0.149126i	$-0.0476460\pi$
$348$		0			0
$349$	0.710293	−	0.410088i	0.0380211	−	0.0219515i	−0.480869	−	0.876792i	$-0.659679\pi$
$349$	0.710293	−	0.410088i	0.0380211	−	0.0219515i	0.518890	+	0.854841i	$0.326345\pi$
$350$		0			0
$351$	−3.20062	+	9.74992i	−0.170836	+	0.520412i
$352$		0			0
$353$	18.5479	+	10.7086i	0.987203	+	0.569962i	0.904437	−	0.426607i	$-0.140291\pi$
$353$	18.5479	+	10.7086i	0.987203	+	0.569962i	0.0827662	+	0.996569i	$0.473625\pi$
$354$		0			0
$355$	1.57273	+	2.72406i	0.0834721	+	0.144578i
$356$		0			0
$357$	0.0166629	−	4.59750i	0.000881897	−	0.243326i
$358$		0			0
$359$	−5.64573	−	3.25956i	−0.297970	−	0.172033i	0.343560	−	0.939131i	$-0.388367\pi$
$359$	−5.64573	−	3.25956i	−0.297970	−	0.172033i	−0.641531	+	0.767097i	$0.721700\pi$
$360$		0			0
$361$	8.30062	+	14.3771i	0.436875	+	0.756689i
$362$		0			0
$363$	14.2274	+	6.95695i	0.746744	+	0.365145i
$364$		0			0
$365$	15.7414	−	27.2650i	0.823945	−	1.42711i
$366$		0			0
$367$	−6.58460	+	11.4049i	−0.343713	+	0.595329i	−0.985119	−	0.171873i	$-0.945018\pi$
$367$	−6.58460	+	11.4049i	−0.343713	+	0.595329i	0.641406	+	0.767202i	$0.278351\pi$
$368$		0			0
$369$	−1.05752	+	0.822789i	−0.0550520	+	0.0428327i
$370$		0			0
$371$	−5.44379	−	3.69263i	−0.282628	−	0.191712i
$372$		0			0
$373$	−14.7435	−	25.5364i	−0.763388	−	1.32223i	−0.941095	−	0.338143i	$-0.890201\pi$
$373$	−14.7435	−	25.5364i	−0.763388	−	1.32223i	0.177707	−	0.984083i	$-0.443132\pi$
$374$		0			0
$375$	−11.6058	−	17.2439i	−0.599322	−	0.890469i
$376$		0			0
$377$			3.37520i			0.173832i
$378$		0			0
$379$			25.2566i			1.29735i	0.761067	+	0.648673i	$0.224676\pi$
$379$			25.2566i			1.29735i	−0.761067	+	0.648673i	$0.775324\pi$
$380$		0			0
$381$	12.7951	+	19.0109i	0.655513	+	0.973957i
$382$		0			0
$383$	2.61272	+	4.52537i	0.133504	+	0.231236i	0.925025	−	0.379906i	$-0.124044\pi$
$383$	2.61272	+	4.52537i	0.133504	+	0.231236i	−0.791521	+	0.611142i	$0.790710\pi$
$384$		0			0
$385$	6.48715	−	3.14302i	0.330616	−	0.160183i
$386$		0			0
$387$	−2.61298	−	18.8686i	−0.132825	−	0.959146i
$388$		0			0
$389$	12.9830	−	22.4872i	0.658264	−	1.14015i	−0.322801	−	0.946467i	$-0.604625\pi$
$389$	12.9830	−	22.4872i	0.658264	−	1.14015i	0.981065	−	0.193679i	$-0.0620421\pi$
$390$		0			0
$391$	4.40009	−	7.62118i	0.222522	−	0.385420i
$392$		0			0
$393$	−13.2921	−	6.49960i	−0.670497	−	0.327861i
$394$		0			0
$395$	−5.95839	−	10.3202i	−0.299799	−	0.519268i
$396$		0			0
$397$	12.5913	+	7.26961i	0.631941	+	0.364851i	0.781503	−	0.623901i	$-0.214453\pi$
$397$	12.5913	+	7.26961i	0.631941	+	0.364851i	−0.149562	+	0.988752i	$0.547786\pi$
$398$		0			0
$399$	−3.52643	−	6.15940i	−0.176542	−	0.308355i
$400$		0			0
$401$	−6.86138	−	11.8843i	−0.342641	−	0.593471i	0.642281	−	0.766469i	$-0.277988\pi$
$401$	−6.86138	−	11.8843i	−0.342641	−	0.593471i	−0.984922	+	0.172998i	$0.944655\pi$
$402$		0			0
$403$	0.893196	+	0.515687i	0.0444933	+	0.0256882i
$404$		0			0
$405$	−17.4448	−	4.42437i	−0.866839	−	0.219848i
$406$		0			0
$407$	−3.63082	+	2.09626i	−0.179973	+	0.103908i
$408$		0			0
$409$		−	10.0019i		−	0.494561i	−0.968944	−	0.247281i	$-0.920463\pi$
$409$		−	10.0019i		−	0.494561i	0.968944	−	0.247281i	$-0.0795370\pi$
$410$		0			0
$411$	0.459059	+	6.66147i	0.0226437	+	0.328586i
$412$		0			0
$413$	−30.0684	+	14.5681i	−1.47957	+	0.716851i
$414$		0			0
$415$	16.6446	+	9.60976i	0.817051	+	0.471725i
$416$		0			0
$417$	−1.80938	−	26.2562i	−0.0886058	−	1.28577i
$418$		0			0
$419$	−3.51452	+	6.08732i	−0.171695	+	0.297385i	−0.939013	−	0.343882i	$-0.888258\pi$
$419$	−3.51452	+	6.08732i	−0.171695	+	0.297385i	0.767317	+	0.641268i	$0.221591\pi$
$420$		0			0
$421$	−3.01107	−	5.21533i	−0.146751	−	0.254179i	0.783274	−	0.621676i	$-0.213548\pi$
$421$	−3.01107	−	5.21533i	−0.146751	−	0.254179i	−0.930025	+	0.367497i	$0.880215\pi$
$422$		0			0
$423$	1.85169	−	4.55658i	0.0900322	−	0.221549i
$424$		0			0
$425$			1.00455i			0.0487279i
$426$		0			0
$427$	−12.1628	−	25.1038i	−0.588598	−	1.21486i
$428$		0			0
$429$	4.18679	+	2.04727i	0.202140	+	0.0988431i
$430$		0			0
$431$	−14.3683	+	8.29555i	−0.692097	+	0.399582i	−0.804397	−	0.594092i	$-0.797512\pi$
$431$	−14.3683	+	8.29555i	−0.692097	+	0.399582i	0.112300	+	0.993674i	$0.464178\pi$
$432$		0			0
$433$		−	6.42380i		−	0.308708i	−0.988016	−	0.154354i	$-0.950670\pi$
$433$		−	6.42380i		−	0.308708i	0.988016	−	0.154354i	$-0.0493297\pi$
$434$		0			0
$435$	−5.90540	+	0.406956i	−0.283142	+	0.0195121i
$436$		0			0
$437$		−	13.5853i		−	0.649873i
$438$		0			0
$439$	4.46311			0.213013			0.106506	−	0.994312i	$-0.466034\pi$
$439$	4.46311			0.213013			0.106506	+	0.994312i	$0.466034\pi$
$440$		0			0
$441$	−10.3679	−	18.2622i	−0.493709	−	0.869627i
$442$		0			0
$443$			27.5435i			1.30863i	0.756222	+	0.654315i	$0.227043\pi$
$443$			27.5435i			1.30863i	−0.756222	+	0.654315i	$0.772957\pi$
$444$		0			0
$445$	−2.56042			−0.121375
$446$		0			0
$447$	17.9795	+	8.79167i	0.850402	+	0.415832i
$448$		0			0
$449$	38.3329			1.80904			0.904520	−	0.426432i	$-0.140229\pi$
$449$	38.3329			1.80904			0.904520	+	0.426432i	$0.140229\pi$
$450$		0			0
$451$	0.304265	+	0.527003i	0.0143273	+	0.0248156i
$452$		0			0
$453$	39.1520	−	2.69806i	1.83952	−	0.126766i
$454$		0			0
$455$	−9.40295	+	4.55573i	−0.440817	+	0.213576i
$456$		0			0
$457$	−34.3165			−1.60526			−0.802629	−	0.596478i	$-0.796566\pi$
$457$	−34.3165			−1.60526			−0.802629	+	0.596478i	$0.796566\pi$
$458$		0			0
$459$	3.47651	+	3.88464i	0.162269	+	0.181320i
$460$		0			0
$461$	−13.9331	+	8.04429i	−0.648930	+	0.374660i	−0.788046	−	0.615616i	$-0.788907\pi$
$461$	−13.9331	+	8.04429i	−0.648930	+	0.374660i	0.139116	+	0.990276i	$0.455574\pi$
$462$		0			0
$463$	15.7583	+	9.09805i	0.732349	+	0.422822i	0.819281	−	0.573392i	$-0.194373\pi$
$463$	15.7583	+	9.09805i	0.732349	+	0.422822i	−0.0869318	+	0.996214i	$0.527706\pi$
$464$		0			0
$465$	−0.794574	+	1.62495i	−0.0368475	+	0.0753554i
$466$		0			0
$467$	7.08122	−	12.2650i	0.327680	−	0.567558i	−0.654371	−	0.756173i	$-0.727067\pi$
$467$	7.08122	−	12.2650i	0.327680	−	0.567558i	0.982051	+	0.188615i	$0.0603999\pi$
$468$		0			0
$469$	−7.50399	−	15.4881i	−0.346502	−	0.715175i
$470$		0			0
$471$	−14.1464	−	21.0186i	−0.651831	−	0.968486i
$472$		0			0
$473$	−8.65120			−0.397783
$474$		0			0
$475$	0.775389	+	1.34301i	0.0355773	+	0.0616217i
$476$		0			0
$477$	7.38827	−	1.02315i	0.338286	−	0.0468467i
$478$		0			0
$479$	−16.8982	+	29.2685i	−0.772096	+	1.33731i	0.164316	+	0.986408i	$0.447458\pi$
$479$	−16.8982	+	29.2685i	−0.772096	+	1.33731i	−0.936412	+	0.350902i	$0.885875\pi$
$480$		0			0
$481$	5.26278	−	3.03847i	0.239962	−	0.138542i
$482$		0			0
$483$	0.145684	−	40.1960i	0.00662887	−	1.82898i
$484$		0			0
$485$	9.60304	−	16.6330i	0.436052	−	0.755264i
$486$		0			0
$487$	−9.41218	+	5.43412i	−0.426506	+	0.246244i	−0.697857	−	0.716237i	$-0.745863\pi$
$487$	−9.41218	+	5.43412i	−0.426506	+	0.246244i	0.271351	+	0.962481i	$0.412530\pi$
$488$		0			0
$489$	20.8381	−	1.43600i	0.942330	−	0.0649384i
$490$		0			0
$491$	−29.3930	−	16.9701i	−1.32649	−	0.765848i	−0.341733	−	0.939797i	$-0.611014\pi$
$491$	−29.3930	−	16.9701i	−1.32649	−	0.765848i	−0.984755	+	0.173949i	$0.944347\pi$
$492$		0			0
$493$	1.48492	+	0.857318i	0.0668774	+	0.0386117i
$494$		0			0
$495$	−3.07718	+	7.57224i	−0.138309	+	0.340347i
$496$		0			0
$497$	−1.81460	−	3.74530i	−0.0813958	−	0.168000i
$498$		0			0
$499$	2.57367	−	1.48591i	0.115213	−	0.0665185i	−0.441286	−	0.897367i	$-0.645478\pi$
$499$	2.57367	−	1.48591i	0.115213	−	0.0665185i	0.556499	+	0.830848i	$0.312144\pi$
$500$		0			0
$501$	2.64083	+	38.3215i	0.117984	+	1.71208i
$502$		0			0
$503$	−26.0651			−1.16219			−0.581093	−	0.813837i	$-0.697375\pi$
$503$	−26.0651			−1.16219			−0.581093	+	0.813837i	$0.697375\pi$
$504$		0			0
$505$	22.5377			1.00292
$506$		0			0
$507$	14.1592	+	6.92362i	0.628833	+	0.307489i
$508$		0			0
$509$	15.3806	−	8.87997i	0.681731	−	0.393598i	−0.118776	−	0.992921i	$-0.537897\pi$
$509$	15.3806	−	8.87997i	0.681731	−	0.393598i	0.800507	+	0.599323i	$0.204564\pi$
$510$		0			0
$511$	−23.3832	+	34.4722i	−1.03441	+	1.52496i
$512$		0			0
$513$	7.64630	+	2.51006i	0.337593	+	0.110822i
$514$		0			0
$515$	−16.6458	−	9.61047i	−0.733502	−	0.423488i
$516$		0			0
$517$	−1.93451	−	1.11689i	−0.0850796	−	0.0491207i
$518$		0			0
$519$	14.4781	+	21.5115i	0.635518	+	0.944248i
$520$		0			0
$521$	24.9679	−	14.4152i	1.09387	−	0.631543i	0.159262	−	0.987236i	$-0.449088\pi$
$521$	24.9679	−	14.4152i	1.09387	−	0.631543i	0.934603	+	0.355693i	$0.115755\pi$
$522$		0			0
$523$	−6.32766	+	10.9598i	−0.276689	+	0.479240i	−0.970560	−	0.240860i	$-0.922571\pi$
$523$	−6.32766	+	10.9598i	−0.276689	+	0.479240i	0.693871	+	0.720100i	$0.255904\pi$
$524$		0			0
$525$	2.27981	+	3.98201i	0.0994991	+	0.173789i
$526$		0			0
$527$	0.453753	−	0.261974i	0.0197658	−	0.0114118i
$528$		0			0
$529$	26.9701	−	46.7135i	1.17261	−	2.03102i
$530$		0			0
$531$	14.2629	−	35.0979i	0.618959	−	1.52312i
$532$		0			0
$533$	−0.441024	−	0.763876i	−0.0191029	−	0.0330871i
$534$		0			0
$535$	25.6016			1.10686
$536$		0			0
$537$	10.7141	−	21.9110i	0.462347	−	0.945528i
$538$		0			0
$539$	−8.86150	+	3.52648i	−0.381692	+	0.151896i
$540$		0			0
$541$	−7.29665	+	12.6382i	−0.313708	+	0.543358i	−0.979162	−	0.203081i	$-0.934905\pi$
$541$	−7.29665	+	12.6382i	−0.313708	+	0.543358i	0.665454	+	0.746439i	$0.268238\pi$
$542$		0			0
$543$	−4.55384	−	6.76606i	−0.195424	−	0.290360i
$544$		0			0
$545$	−25.2209	−	14.5613i	−1.08035	−	0.623738i
$546$		0			0
$547$	−5.61933	+	3.24432i	−0.240265	+	0.138717i	−0.615299	−	0.788294i	$-0.710965\pi$
$547$	−5.61933	+	3.24432i	−0.240265	+	0.138717i	0.375033	+	0.927011i	$0.377631\pi$
$548$		0			0
$549$	29.3029	+	11.9080i	1.25062	+	0.508221i
$550$		0			0
$551$	2.64698			0.112765
$552$		0			0
$553$	6.87470	+	14.1893i	0.292342	+	0.603389i
$554$		0			0
$555$	5.95078	+	8.84164i	0.252597	+	0.375307i
$556$		0			0
$557$	18.2102	+	31.5410i	0.771590	+	1.33643i	0.936691	+	0.350157i	$0.113872\pi$
$557$	18.2102	+	31.5410i	0.771590	+	1.33643i	−0.165101	+	0.986277i	$0.552795\pi$
$558$		0			0
$559$	12.5397			0.530372
$560$		0			0
$561$	1.96416	−	1.32196i	0.0829271	−	0.0558133i
$562$		0			0
$563$	7.55398			0.318362			0.159181	−	0.987249i	$-0.449115\pi$
$563$	7.55398			0.318362			0.159181	+	0.987249i	$0.449115\pi$
$564$		0			0
$565$			36.3110i			1.52762i
$566$		0			0
$567$	22.5969	+	7.50873i	0.948980	+	0.315337i
$568$		0			0
$569$	23.8329			0.999127			0.499564	−	0.866277i	$-0.333494\pi$
$569$	23.8329			0.999127			0.499564	+	0.866277i	$0.333494\pi$
$570$		0			0
$571$			19.1328i			0.800682i	0.916366	+	0.400341i	$0.131108\pi$
$571$			19.1328i			0.800682i	−0.916366	+	0.400341i	$0.868892\pi$
$572$		0			0
$573$	−8.35026	−	12.4068i	−0.348837	−	0.518300i
$574$		0			0
$575$			8.78281i			0.366268i
$576$		0			0
$577$	0.278675	−	0.160893i	0.0116014	−	0.00669808i	−0.494188	−	0.869355i	$-0.664535\pi$
$577$	0.278675	−	0.160893i	0.0116014	−	0.00669808i	0.505789	+	0.862657i	$0.331201\pi$
$578$		0			0
$579$	−15.7025	+	10.5685i	−0.652575	+	0.439210i
$580$		0			0
$581$	−21.0444	−	14.2749i	−0.873070	−	0.592221i
$582$		0			0
$583$		−	3.38750i		−	0.140296i
$584$		0			0
$585$	4.46029	−	10.9758i	0.184410	−	0.453792i
$586$		0			0
$587$	22.9285	+	39.7134i	0.946362	+	1.63915i	0.753001	+	0.658019i	$0.228605\pi$
$587$	22.9285	+	39.7134i	0.946362	+	1.63915i	0.193360	+	0.981128i	$0.438061\pi$
$588$		0			0
$589$	0.404424	−	0.700483i	0.0166640	−	0.0288629i
$590$		0			0
$591$	28.3282	−	19.0661i	1.16527	−	0.784273i
$592$		0			0
$593$	−24.8195	−	14.3295i	−1.01921	−	0.588443i	−0.105338	−	0.994437i	$-0.533592\pi$
$593$	−24.8195	−	14.3295i	−1.01921	−	0.588443i	−0.913876	+	0.405993i	$0.866926\pi$
$594$		0			0
$595$	−0.384107	+	5.29401i	−0.0157468	+	0.217033i
$596$		0			0
$597$	41.5683	+	20.3262i	1.70128	+	0.831895i
$598$		0			0
$599$			24.4551i			0.999208i	0.866254	+	0.499604i	$0.166521\pi$
$599$			24.4551i			0.999208i	−0.866254	+	0.499604i	$0.833479\pi$
$600$		0			0
$601$	−6.86788	+	3.96517i	−0.280147	+	0.161743i	−0.633490	−	0.773751i	$-0.718378\pi$
$601$	−6.86788	+	3.96517i	−0.280147	+	0.161743i	0.353343	+	0.935494i	$0.385045\pi$
$602$		0			0
$603$	18.0788	+	7.34680i	0.736226	+	0.299185i
$604$		0			0
$605$	−15.8347	−	9.14216i	−0.643772	−	0.371682i
$606$		0			0
$607$	−2.45236	−	4.24762i	−0.0995384	−	0.172406i	0.811955	−	0.583720i	$-0.198403\pi$
$607$	−2.45236	−	4.24762i	−0.0995384	−	0.172406i	−0.911494	+	0.411314i	$0.865070\pi$
$608$		0			0
$609$	7.83184	+	0.0283853i	0.317362	+	0.00115023i
$610$		0			0
$611$	2.80402	+	1.61890i	0.113438	+	0.0654937i
$612$		0			0
$613$	9.53276	+	16.5112i	0.385025	+	0.666882i	0.991773	−	0.128012i	$-0.0408596\pi$
$613$	9.53276	+	16.5112i	0.385025	+	0.666882i	−0.606748	+	0.794894i	$0.707526\pi$
$614$		0			0
$615$	1.28334	−	0.863737i	0.0517491	−	0.0348292i
$616$		0			0
$617$	21.2636	−	36.8296i	0.856040	−	1.48270i	−0.0196377	−	0.999807i	$-0.506251\pi$
$617$	21.2636	−	36.8296i	0.856040	−	1.48270i	0.875677	−	0.482897i	$-0.160415\pi$
$618$		0			0
$619$	−6.26243	+	10.8468i	−0.251708	+	0.435971i	−0.963996	−	0.265916i	$-0.914326\pi$
$619$	−6.26243	+	10.8468i	−0.251708	+	0.435971i	0.712288	+	0.701887i	$0.247659\pi$
$620$		0			0
$621$	30.3951	+	33.9635i	1.21972	+	1.36291i
$622$		0			0
$623$	3.37877	+	0.245147i	0.135368	+	0.00982161i
$624$		0			0
$625$	9.49551	+	16.4467i	0.379820	+	0.657868i
$626$		0			0
$627$	1.60556	−	3.28346i	0.0641197	−	0.131129i
$628$		0			0
$629$		−	3.08715i		−	0.123093i
$630$		0			0
$631$			17.8526i			0.710700i	0.934733	+	0.355350i	$0.115638\pi$
$631$			17.8526i			0.710700i	−0.934733	+	0.355350i	$0.884362\pi$
$632$		0			0
$633$	12.5162	−	0.862522i	0.497474	−	0.0342822i
$634$		0			0
$635$	−13.2283	−	22.9120i	−0.524947	−	0.909235i
$636$		0			0
$637$	12.8445	−	5.11154i	0.508918	−	0.202526i
$638$		0			0
$639$	4.37177	+	1.77658i	0.172944	+	0.0702806i
$640$		0			0
$641$	−19.5722	+	33.9000i	−0.773054	+	1.33897i	0.162827	+	0.986655i	$0.447939\pi$
$641$	−19.5722	+	33.9000i	−0.773054	+	1.33897i	−0.935882	+	0.352315i	$0.885395\pi$
$642$		0			0
$643$	2.93372	−	5.08136i	0.115695	−	0.200389i	−0.802363	−	0.596837i	$-0.796424\pi$
$643$	2.93372	−	5.08136i	0.115695	−	0.200389i	0.918057	+	0.396448i	$0.129757\pi$
$644$		0			0
$645$	1.51194	+	21.9400i	0.0595326	+	0.863886i
$646$		0			0
$647$	−19.5795	−	33.9127i	−0.769750	−	1.33325i	−0.937699	−	0.347450i	$-0.887048\pi$
$647$	−19.5795	−	33.9127i	−0.769750	−	1.33325i	0.167949	−	0.985796i	$-0.446286\pi$
$648$		0			0
$649$	−14.9009	−	8.60303i	−0.584911	−	0.337698i
$650$		0			0
$651$	1.20412	−	2.06824i	0.0471930	−	0.0810608i
$652$		0			0
$653$	−13.6261	−	23.6011i	−0.533231	−	0.923584i	−0.999247	−	0.0388072i	$-0.987644\pi$
$653$	−13.6261	−	23.6011i	−0.533231	−	0.923584i	0.466015	−	0.884777i	$-0.345689\pi$
$654$		0			0
$655$	14.7937	+	8.54115i	0.578038	+	0.333730i
$656$		0			0
$657$	−6.47898	−	46.7854i	−0.252769	−	1.82527i
$658$		0			0
$659$	18.1766	−	10.4943i	0.708061	−	0.408799i	−0.102282	−	0.994755i	$-0.532614\pi$
$659$	18.1766	−	10.4943i	0.708061	−	0.408799i	0.810343	+	0.585956i	$0.199281\pi$
$660$		0			0
$661$			2.10749i			0.0819720i	0.999160	+	0.0409860i	$0.0130499\pi$
$661$			2.10749i			0.0819720i	−0.999160	+	0.0409860i	$0.986950\pi$
$662$		0			0
$663$	−2.84700	+	1.91615i	−0.110568	+	0.0744171i
$664$		0			0
$665$	3.57279	+	7.37419i	0.138547	+	0.285959i
$666$		0			0
$667$	12.9827	+	7.49555i	0.502691	+	0.290229i
$668$		0			0
$669$	−30.5216	−	14.9245i	−1.18003	−	0.577016i
$670$		0			0
$671$	7.18258	−	12.4406i	0.277281	−	0.480264i
$672$		0			0
$673$	3.40292	+	5.89403i	0.131173	+	0.227198i	0.924129	−	0.382081i	$-0.124792\pi$
$673$	3.40292	+	5.89403i	0.131173	+	0.227198i	−0.792956	+	0.609279i	$0.791459\pi$
$674$		0			0
$675$	−4.94329	−	1.62274i	−0.190267	−	0.0624592i
$676$		0			0
$677$		−	43.3463i		−	1.66593i	−0.553323	−	0.832967i	$-0.686640\pi$
$677$		−	43.3463i		−	1.66593i	0.553323	−	0.832967i	$-0.313360\pi$
$678$		0			0
$679$	−14.2649	+	21.0297i	−0.547436	+	0.807047i
$680$		0			0
$681$	2.47425	+	35.9042i	0.0948134	+	1.37585i
$682$		0			0
$683$	−25.2674	+	14.5882i	−0.966832	+	0.558201i	−0.898269	−	0.439446i	$-0.855175\pi$
$683$	−25.2674	+	14.5882i	−0.966832	+	0.558201i	−0.0685629	+	0.997647i	$0.521841\pi$
$684$		0			0
$685$		−	7.70901i		−	0.294546i
$686$		0			0
$687$	16.8358	−	34.4302i	0.642324	−	1.31359i
$688$		0			0
$689$			4.91008i			0.187059i
$690$		0			0
$691$	−47.1974			−1.79547			−0.897736	−	0.440533i	$-0.854790\pi$
$691$	−47.1974			−1.79547			−0.897736	+	0.440533i	$0.854790\pi$
$692$		0			0
$693$	4.78571	−	9.69785i	0.181794	−	0.368391i
$694$		0			0
$695$			30.3851i			1.15257i
$696$		0			0
$697$	−0.448089			−0.0169726
$698$		0			0
$699$	−0.466700	−	6.77236i	−0.0176522	−	0.256154i
$700$		0			0
$701$	14.7459			0.556946			0.278473	−	0.960444i	$-0.410172\pi$
$701$	14.7459			0.556946			0.278473	+	0.960444i	$0.410172\pi$
$702$		0			0
$703$	−2.38290	−	4.12730i	−0.0898726	−	0.155664i
$704$		0			0
$705$	−2.49441	+	5.10123i	−0.0939450	+	0.192123i
$706$		0			0
$707$	−29.7412	−	2.15788i	−1.11853	−	0.0811553i
$708$		0			0
$709$	−29.3420			−1.10196			−0.550981	−	0.834518i	$-0.685746\pi$
$709$	−29.3420			−1.10196			−0.550981	+	0.834518i	$0.685746\pi$
$710$		0			0
$711$	−16.5627	−	6.73068i	−0.621149	−	0.252420i
$712$		0			0
$713$	3.96717	−	2.29045i	0.148572	−	0.0857779i
$714$		0			0
$715$	−4.65978	−	2.69033i	−0.174266	−	0.100613i
$716$		0			0
$717$	−14.7382	+	1.01565i	−0.550408	+	0.0379300i
$718$		0			0
$719$	19.0100	−	32.9262i	0.708952	−	1.22794i	−0.256294	−	0.966599i	$-0.582502\pi$
$719$	19.0100	−	32.9262i	0.708952	−	1.22794i	0.965246	−	0.261342i	$-0.0841651\pi$
$720$		0			0
$721$	21.0460	+	14.2759i	0.783793	+	0.531663i
$722$		0			0
$723$	−4.18557	+	0.288438i	−0.155663	+	0.0107271i
$724$		0			0
$725$	−1.71125			−0.0635543
$726$		0			0
$727$	1.33619	+	2.31435i	0.0495565	+	0.0858343i	0.889740	−	0.456469i	$-0.150886\pi$
$727$	1.33619	+	2.31435i	0.0495565	+	0.0858343i	−0.840183	+	0.542303i	$0.817553\pi$
$728$		0			0
$729$	−24.7318	+	10.8323i	−0.915992	+	0.401197i
$730$		0			0
$731$	3.18514	−	5.51683i	0.117807	−	0.204047i
$732$		0			0
$733$	−2.84392	+	1.64194i	−0.105042	+	0.0606463i	−0.551601	−	0.834108i	$-0.685983\pi$
$733$	−2.84392	+	1.64194i	−0.105042	+	0.0606463i	0.446558	+	0.894754i	$0.352650\pi$
$734$		0			0
$735$	10.4921	+	21.8570i	0.387006	+	0.806207i
$736$		0			0
$737$	4.43139	−	7.67540i	0.163232	−	0.282727i
$738$		0			0
$739$	22.7991	−	13.1631i	0.838680	−	0.484212i	−0.0181356	−	0.999836i	$-0.505773\pi$
$739$	22.7991	−	13.1631i	0.838680	−	0.484212i	0.856815	+	0.515624i	$0.172440\pi$
$740$		0			0
$741$	−2.32721	+	4.75929i	−0.0854922	+	0.174837i
$742$		0			0
$743$	21.0356	+	12.1449i	0.771720	+	0.445553i	0.833488	−	0.552538i	$-0.186341\pi$
$743$	21.0356	+	12.1449i	0.771720	+	0.445553i	−0.0617681	+	0.998091i	$0.519674\pi$
$744$		0			0
$745$	−20.0107	−	11.5532i	−0.733135	−	0.423276i
$746$		0			0
$747$	28.5613	−	3.95525i	1.04500	−	0.144715i
$748$		0			0
$749$	−33.7844	−	2.45123i	−1.23446	−	0.0895660i
$750$		0			0
$751$	8.11887	−	4.68743i	0.296262	−	0.171047i	−0.344501	−	0.938786i	$-0.611952\pi$
$751$	8.11887	−	4.68743i	0.296262	−	0.171047i	0.640762	+	0.767739i	$0.278618\pi$
$752$		0			0
$753$	−1.57762	+	1.06180i	−0.0574915	+	0.0386941i
$754$		0			0
$755$	−45.3087			−1.64895
$756$		0			0
$757$	−50.8723			−1.84899			−0.924493	−	0.381200i	$-0.875511\pi$
$757$	−50.8723			−1.84899			−0.924493	+	0.381200i	$0.875511\pi$
$758$		0			0
$759$	17.1727	−	11.5579i	0.623330	−	0.419527i
$760$		0			0
$761$	−36.6769	+	21.1754i	−1.32954	+	0.767608i	−0.985228	−	0.171249i	$-0.945220\pi$
$761$	−36.6769	+	21.1754i	−1.32954	+	0.767608i	−0.344308	+	0.938857i	$0.611886\pi$
$762$		0			0
$763$	31.8878	+	21.6301i	1.15442	+	0.783064i
$764$		0			0
$765$	−3.69585	−	4.75021i	−0.133624	−	0.171744i
$766$		0			0
$767$	21.5984	+	12.4699i	0.779874	+	0.450260i
$768$		0			0
$769$	−3.61419	−	2.08665i	−0.130331	−	0.0752467i	0.433417	−	0.901194i	$-0.357308\pi$
$769$	−3.61419	−	2.08665i	−0.130331	−	0.0752467i	−0.563748	+	0.825947i	$0.690641\pi$
$770$		0			0
$771$	16.0151	−	32.7519i	0.576770	−	1.17953i
$772$		0			0
$773$	−4.51890	+	2.60899i	−0.162534	+	0.0938389i	−0.579061	−	0.815285i	$-0.696581\pi$
$773$	−4.51890	+	2.60899i	−0.162534	+	0.0938389i	0.416527	+	0.909123i	$0.363247\pi$
$774$		0			0
$775$	−0.261457	+	0.452857i	−0.00939182	+	0.0162671i
$776$		0			0
$777$	−7.00623	−	12.2374i	−0.251347	−	0.439013i
$778$		0			0
$779$	−0.599064	+	0.345870i	−0.0214637	+	0.0123921i
$780$		0			0
$781$	1.07159	−	1.85604i	0.0383444	−	0.0664145i
$782$		0			0
$783$	−6.61748	+	5.92222i	−0.236490	+	0.211643i
$784$		0			0
$785$	14.6253	+	25.3317i	0.521998	+	0.904128i
$786$		0			0
$787$	29.5860			1.05463			0.527314	−	0.849670i	$-0.323199\pi$
$787$	29.5860			1.05463			0.527314	+	0.849670i	$0.323199\pi$
$788$		0			0
$789$	42.2698	−	2.91292i	1.50484	−	0.103703i
$790$		0			0
$791$	3.47660	−	47.9168i	0.123614	−	1.70372i
$792$		0			0
$793$	−10.4110	+	18.0323i	−0.369704	+	0.640346i
$794$		0			0
$795$	−8.59090	+	0.592021i	−0.304688	+	0.0209968i
$796$		0			0
$797$	41.7053	+	24.0785i	1.47728	+	0.852906i	0.999671	−	0.0256682i	$-0.00817133\pi$
$797$	41.7053	+	24.0785i	1.47728	+	0.852906i	0.477606	+	0.878574i	$0.341505\pi$
$798$		0			0
$799$	1.42447	−	0.822418i	0.0503941	−	0.0290951i
$800$		0			0
$801$	−3.03171	+	2.35879i	−0.107120	+	0.0833437i
$802$		0			0
$803$	−21.4510			−0.756988
$804$		0			0
$805$	−3.35825	+	46.2856i	−0.118363	+	1.63135i
$806$		0			0
$807$	8.60713	−	17.6021i	0.302985	−	0.619624i
$808$		0			0
$809$	−2.61482	−	4.52900i	−0.0919321	−	0.159231i	0.816392	−	0.577498i	$-0.195971\pi$
$809$	−2.61482	−	4.52900i	−0.0919321	−	0.159231i	−0.908324	+	0.418267i	$0.862638\pi$
$810$		0			0
$811$	28.4364			0.998538			0.499269	−	0.866447i	$-0.333602\pi$
$811$	28.4364			0.998538			0.499269	+	0.866447i	$0.333602\pi$
$812$		0			0
$813$	−0.114517	−	1.66177i	−0.00401628	−	0.0582808i
$814$		0			0
$815$	−24.1149			−0.844709
$816$		0			0
$817$		−	9.83415i		−	0.344053i
$818$		0			0
$819$	−6.93676	+	14.0568i	−0.242390	+	0.491183i
$820$		0			0
$821$	5.16817			0.180370			0.0901851	−	0.995925i	$-0.471254\pi$
$821$	5.16817			0.180370			0.0901851	+	0.995925i	$0.471254\pi$
$822$		0			0
$823$			17.1504i			0.597825i	0.954281	+	0.298912i	$0.0966238\pi$
$823$			17.1504i			0.597825i	−0.954281	+	0.298912i	$0.903376\pi$
$824$		0			0
$825$	−1.03798	+	2.12274i	−0.0361379	+	0.0739042i
$826$		0			0
$827$			46.7499i			1.62565i	0.582505	+	0.812827i	$0.302073\pi$
$827$			46.7499i			1.62565i	−0.582505	+	0.812827i	$0.697927\pi$
$828$		0			0
$829$	−31.5449	+	18.2124i	−1.09560	+	0.632544i	−0.935062	−	0.354485i	$-0.884656\pi$
$829$	−31.5449	+	18.2124i	−1.09560	+	0.632544i	−0.160538	+	0.987030i	$0.551323\pi$
$830$		0			0
$831$	2.98288	+	43.2849i	0.103475	+	1.50154i
$832$		0			0
$833$	1.01375	−	6.94929i	0.0351243	−	0.240779i
$834$		0			0
$835$		−	44.3477i		−	1.53471i
$836$		0			0
$837$	0.556162	+	2.65606i	0.0192238	+	0.0918068i
$838$		0			0
$839$	−5.36691	−	9.29577i	−0.185286	−	0.320925i	0.758387	−	0.651805i	$-0.225988\pi$
$839$	−5.36691	−	9.29577i	−0.185286	−	0.320925i	−0.943673	+	0.330880i	$0.892655\pi$
$840$		0			0
$841$	13.0396	−	22.5852i	0.449640	−	0.778799i
$842$		0			0
$843$	−34.3327	−	16.7881i	−1.18248	−	0.578212i
$844$		0			0
$845$	−15.7588	−	9.09836i	−0.542120	−	0.312993i
$846$		0			0
$847$	20.0204	+	13.5803i	0.687910	+	0.466623i
$848$		0			0
$849$	−7.57058	+	5.09531i	−0.259822	+	0.174871i
$850$		0			0
$851$		−	26.9910i		−	0.925239i
$852$		0			0
$853$	−29.2849	+	16.9076i	−1.00269	+	0.578906i	−0.909044	−	0.416699i	$-0.863187\pi$
$853$	−29.2849	+	16.9076i	−1.00269	+	0.578906i	−0.0936502	+	0.995605i	$0.529854\pi$
$854$		0			0
$855$	−8.60766	−	3.49795i	−0.294376	−	0.119627i
$856$		0			0
$857$	26.5914	+	15.3526i	0.908347	+	0.524434i	0.879899	−	0.475161i	$-0.157610\pi$
$857$	26.5914	+	15.3526i	0.908347	+	0.524434i	0.0284478	+	0.999595i	$0.490944\pi$
$858$		0			0
$859$	−12.9394	−	22.4117i	−0.441487	−	0.764679i	0.556313	−	0.830973i	$-0.312216\pi$
$859$	−12.9394	−	22.4117i	−0.441487	−	0.764679i	−0.997800	+	0.0662945i	$0.978882\pi$
$860$		0			0
$861$	−1.77621	+	1.01693i	−0.0605332	+	0.0346569i
$862$		0			0
$863$	−24.1208	−	13.9262i	−0.821083	−	0.474052i	0.0297071	−	0.999559i	$-0.490543\pi$
$863$	−24.1208	−	13.9262i	−0.821083	−	0.474052i	−0.850790	+	0.525506i	$0.823876\pi$
$864$		0			0
$865$	−14.9682	−	25.9257i	−0.508935	−	0.881500i
$866$		0			0
$867$	−1.90446	−	27.6359i	−0.0646790	−	0.938566i
$868$		0			0
$869$	−4.05977	+	7.03173i	−0.137718	+	0.238535i
$870$		0			0
$871$	−6.42318	+	11.1253i	−0.217641	+	0.376966i
$872$		0			0
$873$	−3.95249	−	28.5414i	−0.133771	−	0.965979i
$874$		0			0
$875$	−13.8439	−	28.5736i	−0.468010	−	0.965966i
$876$		0			0
$877$	−9.25496	−	16.0301i	−0.312518	−	0.541297i	0.666389	−	0.745604i	$-0.267839\pi$
$877$	−9.25496	−	16.0301i	−0.312518	−	0.541297i	−0.978907	+	0.204307i	$0.934506\pi$
$878$		0			0
$879$	24.1595	−	1.66490i	0.814881	−	0.0561555i
$880$		0			0
$881$			37.6194i			1.26743i	0.773567	+	0.633714i	$0.218470\pi$
$881$			37.6194i			1.26743i	−0.773567	+	0.633714i	$0.781530\pi$
$882$		0			0
$883$			15.2541i			0.513340i	0.966499	+	0.256670i	$0.0826254\pi$
$883$			15.2541i			0.513340i	−0.966499	+	0.256670i	$0.917375\pi$
$884$		0			0
$885$	−19.2136	+	39.2931i	−0.645859	+	1.32082i
$886$		0			0
$887$	8.98340	+	15.5597i	0.301633	+	0.522444i	0.976506	−	0.215490i	$-0.0691349\pi$
$887$	8.98340	+	15.5597i	0.301633	+	0.522444i	−0.674873	+	0.737934i	$0.735802\pi$
$888$		0			0
$889$	15.2625	+	31.5017i	0.511889	+	1.05653i
$890$		0			0
$891$	3.33235	+	11.8009i	0.111638	+	0.395345i
$892$		0			0
$893$	1.26961	−	2.19903i	0.0424859	−	0.0735877i
$894$		0			0
$895$	−14.0794	+	24.3863i	−0.470623	+	0.815144i
$896$		0			0
$897$	−24.8914	+	16.7529i	−0.831099	+	0.559364i
$898$		0			0
$899$	0.446273	+	0.772968i	0.0148840	+	0.0257799i
$900$		0			0
$901$	2.16019	+	1.24719i	0.0719664	+	0.0415498i
$902$		0			0
$903$	0.105458	−	29.0972i	0.00350943	−	0.968293i
$904$		0			0
$905$	4.70800	+	8.15449i	0.156499	+	0.271064i
$906$		0			0
$907$	15.6153	+	9.01551i	0.518498	+	0.299355i	0.736320	−	0.676633i	$-0.236562\pi$
$907$	15.6153	+	9.01551i	0.518498	+	0.299355i	−0.217822	+	0.975989i	$0.569895\pi$
$908$		0			0
$909$	26.6862	−	20.7629i	0.885126	−	0.688663i
$910$		0			0
$911$	7.79715	−	4.50169i	0.258331	−	0.149148i	−0.365242	−	0.930913i	$-0.619014\pi$
$911$	7.79715	−	4.50169i	0.258331	−	0.149148i	0.623573	+	0.781765i	$0.285680\pi$
$912$		0			0
$913$		−	13.0953i		−	0.433390i
$914$		0			0
$915$	−32.8054	−	16.0413i	−1.08451	−	0.530308i
$916$		0			0
$917$	−18.7043	−	12.6875i	−0.617670	−	0.418978i
$918$		0			0
$919$	20.9938	+	12.1208i	0.692522	+	0.399828i	0.804556	−	0.593876i	$-0.202403\pi$
$919$	20.9938	+	12.1208i	0.692522	+	0.399828i	−0.112034	+	0.993704i	$0.535737\pi$
$920$		0			0
$921$	−23.3865	+	15.7401i	−0.770611	+	0.518653i
$922$		0			0
$923$	−1.55324	+	2.69028i	−0.0511254	+	0.0885518i
$924$		0			0
$925$	1.54053	+	2.66827i	0.0506522	+	0.0877322i
$926$		0			0
$927$	−28.5634	+	3.95554i	−0.938147	+	0.129917i
$928$		0			0
$929$		−	45.8160i		−	1.50317i	−0.659635	−	0.751586i	$-0.729289\pi$
$929$		−	45.8160i		−	1.50317i	0.659635	−	0.751586i	$-0.270711\pi$
$930$		0			0
$931$	−4.00869	−	10.0732i	−0.131379	−	0.330136i
$932$		0			0
$933$	−9.18149	+	6.17952i	−0.300588	+	0.202308i
$934$		0			0
$935$	−2.36722	+	1.36671i	−0.0774164	+	0.0446964i
$936$		0			0
$937$			16.0236i			0.523467i	0.965140	+	0.261733i	$0.0842941\pi$
$937$			16.0236i			0.523467i	−0.965140	+	0.261733i	$0.915706\pi$
$938$		0			0
$939$	−24.7993	−	36.8466i	−0.809293	−	1.20244i
$940$		0			0
$941$			7.92698i			0.258412i	0.991618	+	0.129206i	$0.0412428\pi$
$941$			7.92698i			0.258412i	−0.991618	+	0.129206i	$0.958757\pi$
$942$		0			0
$943$	−3.91765			−0.127576
$944$		0			0
$945$	−25.4307	−	10.4420i	−0.827262	−	0.339678i
$946$		0			0
$947$		−	15.3073i		−	0.497421i	−0.968578	−	0.248711i	$-0.919993\pi$
$947$		−	15.3073i		−	0.497421i	0.968578	−	0.248711i	$-0.0800068\pi$
$948$		0			0
$949$	31.0926			1.00931
$950$		0			0
$951$	−42.1076	+	28.3401i	−1.36543	+	0.918992i
$952$		0			0
$953$	−36.5759			−1.18481			−0.592405	−	0.805640i	$-0.701821\pi$
$953$	−36.5759			−1.18481			−0.592405	+	0.805640i	$0.701821\pi$
$954$		0			0
$955$	8.63294	+	14.9527i	0.279355	+	0.483858i
$956$		0			0
$957$	2.25196	+	3.34595i	0.0727956	+	0.108159i
$958$		0			0
$959$	−0.738099	+	10.1730i	−0.0238345	+	0.328502i
$960$		0			0
$961$	−30.7273			−0.991202
$962$		0			0
$963$	30.3141	−	23.5856i	0.976858	−	0.760034i
$964$		0			0
$965$	18.9248	−	10.9262i	0.609210	−	0.351728i
$966$		0			0
$967$	−27.8653	−	16.0880i	−0.896088	−	0.517357i	−0.0201591	−	0.999797i	$-0.506417\pi$
$967$	−27.8653	−	16.0880i	−0.896088	−	0.517357i	−0.875929	+	0.482440i	$0.839751\pi$
$968$		0			0
$969$	1.50273	+	2.23274i	0.0482745	+	0.0717260i
$970$		0			0
$971$	24.1287	−	41.7921i	0.774326	−	1.34117i	−0.160846	−	0.986979i	$-0.551422\pi$
$971$	24.1287	−	41.7921i	0.774326	−	1.34117i	0.935172	−	0.354193i	$-0.115244\pi$
$972$		0			0
$973$	2.90922	−	40.0967i	0.0932653	−	1.28544i
$974$		0			0
$975$	1.50453	−	3.07685i	0.0481834	−	0.0985380i
$976$		0			0
$977$	2.60494			0.0833394			0.0416697	−	0.999131i	$-0.486732\pi$
$977$	2.60494			0.0833394			0.0416697	+	0.999131i	$0.486732\pi$
$978$		0			0
$979$	0.872274	+	1.51082i	0.0278780	+	0.0482861i
$980$		0			0
$981$	−43.2779	+	5.99324i	−1.38176	+	0.191350i
$982$		0			0
$983$	−19.9000	+	34.4678i	−0.634711	+	1.09935i	0.351865	+	0.936051i	$0.385547\pi$
$983$	−19.9000	+	34.4678i	−0.634711	+	1.09935i	−0.986576	+	0.163301i	$0.947786\pi$
$984$		0			0
$985$	−34.1413	+	19.7115i	−1.08783	+	0.628060i
$986$		0			0
$987$	3.78009	−	6.49285i	0.120322	−	0.206670i
$988$		0			0
$989$	27.8478	−	48.2337i	0.885507	−	1.53374i
$990$		0			0
$991$	9.30303	−	5.37111i	0.295521	−	0.170619i	−0.344908	−	0.938636i	$-0.612090\pi$
$991$	9.30303	−	5.37111i	0.295521	−	0.170619i	0.640429	+	0.768018i	$0.278757\pi$
$992$		0			0
$993$	0.129293	+	0.192103i	0.00410298	+	0.00609619i
$994$		0			0
$995$	−46.2644	−	26.7107i	−1.46668	−	0.846787i
$996$		0			0
$997$	−20.6620	−	11.9292i	−0.654373	−	0.377803i	0.135756	−	0.990742i	$-0.456654\pi$
$997$	−20.6620	−	11.9292i	−0.654373	−	0.377803i	−0.790130	+	0.612940i	$0.789987\pi$
$998$		0			0
$999$	15.1915	+	4.98693i	0.480638	+	0.157779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.h.607.3	yes	24
3.2	odd	2		3024.2.cz.g.1279.4		24
4.3	odd	2		1008.2.cz.g.607.10	yes	24
7.3	odd	6		1008.2.bf.h.31.2	yes	24
9.2	odd	6		3024.2.bf.h.2287.4		24
9.7	even	3		1008.2.bf.g.943.11	yes	24
12.11	even	2		3024.2.cz.h.1279.4		24
21.17	even	6		3024.2.bf.g.1711.9		24
28.3	even	6		1008.2.bf.g.31.11	✓	24
36.7	odd	6		1008.2.bf.h.943.2	yes	24
36.11	even	6		3024.2.bf.g.2287.4		24
63.38	even	6		3024.2.cz.h.2719.4		24
63.52	odd	6		1008.2.cz.g.367.10	yes	24
84.59	odd	6		3024.2.bf.h.1711.9		24
252.115	even	6	inner	1008.2.cz.h.367.3	yes	24
252.227	odd	6		3024.2.cz.g.2719.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.11	✓	24	28.3	even	6
1008.2.bf.g.943.11	yes	24	9.7	even	3
1008.2.bf.h.31.2	yes	24	7.3	odd	6
1008.2.bf.h.943.2	yes	24	36.7	odd	6
1008.2.cz.g.367.10	yes	24	63.52	odd	6
1008.2.cz.g.607.10	yes	24	4.3	odd	2
1008.2.cz.h.367.3	yes	24	252.115	even	6	inner
1008.2.cz.h.607.3	yes	24	1.1	even	1	trivial
3024.2.bf.g.1711.9		24	21.17	even	6
3024.2.bf.g.2287.4		24	36.11	even	6
3024.2.bf.h.1711.9		24	84.59	odd	6
3024.2.bf.h.2287.4		24	9.2	odd	6
3024.2.cz.g.1279.4		24	3.2	odd	2
3024.2.cz.g.2719.4		24	252.227	odd	6
3024.2.cz.h.1279.4		24	12.11	even	2
3024.2.cz.h.2719.4		24	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43691 + 0.967101i) q^{3} +(1.73177 - 0.999840i) q^{5} +(-2.38101 + 1.15360i) q^{7} +(1.12943 - 2.77928i) q^{9} +O(q^{10})\)	\(q+(-1.43691 + 0.967101i) q^{3} +(1.73177 - 0.999840i) q^{5} +(-2.38101 + 1.15360i) q^{7} +(1.12943 - 2.77928i) q^{9} +(-1.17995 - 0.681244i) q^{11} +(1.71030 + 0.987444i) q^{13} +(-1.52146 + 3.11148i) q^{15} +(0.868852 - 0.501632i) q^{17} +(0.774396 - 1.34129i) q^{19} +(2.30566 - 3.96030i) q^{21} +(7.59639 - 4.38578i) q^{23} +(-0.500642 + 0.867137i) q^{25} +(1.06494 + 5.08585i) q^{27} +(0.854529 + 1.48009i) q^{29} +0.522244 q^{31} +(2.35431 - 0.162242i) q^{33} +(-2.96996 + 4.37840i) q^{35} +(1.53855 - 2.66485i) q^{37} +(-3.41251 + 0.235165i) q^{39} +(-0.386794 - 0.223316i) q^{41} +(5.49888 - 3.17478i) q^{43} +(-0.822910 - 5.94233i) q^{45} +1.63949 q^{47} +(4.33842 - 5.49346i) q^{49} +(-0.763335 + 1.56107i) q^{51} +(1.24313 + 2.15316i) q^{53} -2.72454 q^{55} +(0.184426 + 2.67624i) q^{57} +12.6284 q^{59} +10.5433i q^{61} +(0.516980 + 7.92040i) q^{63} +3.94914 q^{65} +6.50486i q^{67} +(-6.67385 + 13.6484i) q^{69} +1.57299i q^{71} +(13.6347 - 7.87199i) q^{73} +(-0.119230 - 1.73017i) q^{75} +(3.59535 + 0.260861i) q^{77} -5.95935i q^{79} +(-6.44876 - 6.27801i) q^{81} +(4.80565 + 8.32363i) q^{83} +(1.00310 - 1.73743i) q^{85} +(-2.65928 - 1.30034i) q^{87} +(-1.10887 - 0.640207i) q^{89} +(-5.21136 - 0.378111i) q^{91} +(-0.750419 + 0.505063i) q^{93} -3.09709i q^{95} +(8.31781 - 4.80229i) q^{97} +(-3.22604 + 2.50999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Introduction

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