LMFDB - Embedded newform 1040.2.dh.c.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1040.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.513226913958144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6x^{10} + 28x^{8} - 46x^{6} + 58x^{4} - 8x^{2} + 1 $ x^12 - 6x^10 + 28x^8 - 46x^6 + 58x^4 - 8*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.4
Root			$1.75675 - 1.01426i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.c.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +O(q^{10})$	\(q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-3.51351 - 0.809492i) q^{13} +(-0.511544 - 0.0999188i) q^{15} +(-3.31164 + 1.91198i) q^{17} +(-1.14207 - 1.97813i) q^{19} +1.00000 q^{21} +(-4.97295 - 2.87113i) q^{23} +(3.94567 - 3.07111i) q^{25} -1.38589i q^{27} +(-1.14207 + 1.97813i) q^{29} +6.22982 q^{31} +(-0.201864 + 0.116546i) q^{33} +(-6.30021 + 7.23421i) q^{35} +(-5.82679 - 3.36410i) q^{37} +(-0.614908 - 0.572894i) q^{39} +(-1.33076 + 2.30494i) q^{41} +(-5.97130 + 3.44753i) q^{43} +(4.96711 + 4.32581i) q^{45} -6.60840i q^{47} +(5.70265 - 9.87728i) q^{49} -0.891336 q^{51} -5.04299i q^{53} +(0.428666 - 2.19459i) q^{55} -0.532418i q^{57} +(-5.56058 - 9.63120i) q^{59} +(-2.08774 - 3.61607i) q^{61} +(-10.9442 - 6.31866i) q^{63} +(8.01848 - 0.839022i) q^{65} +(3.76176 + 2.17185i) q^{67} +(-0.669240 - 1.15916i) q^{69} +(-3.37189 - 5.84028i) q^{71} -13.5697i q^{73} +(1.15442 - 0.160094i) q^{75} +4.29014i q^{77} +11.4053 q^{79} +(-4.25698 + 7.37331i) q^{81} +10.0324i q^{83} +(5.61560 - 6.44811i) q^{85} +(-0.461087 + 0.266209i) q^{87} +(-5.56058 + 9.63120i) q^{89} +(-14.7904 + 4.52915i) q^{91} +(1.25758 + 0.726062i) q^{93} +(3.85162 + 3.35434i) q^{95} +(-12.8538 + 7.42115i) q^{97} +2.94567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^9	$ 12 q + 4 q^{9} - 6 q^{11} - 10 q^{15} - 10 q^{19} + 12 q^{21} + 4 q^{25} - 10 q^{29} + 24 q^{31} + 6 q^{35} + 18 q^{39} + 2 q^{41} + 12 q^{45} - 4 q^{49} + 76 q^{51} + 2 q^{59} + 22 q^{61} - 40 q^{65} - 26 q^{69} + 14 q^{71} + 8 q^{75} - 8 q^{79} - 22 q^{81} + 14 q^{85} + 2 q^{89} - 58 q^{91} + 20 q^{95} - 8 q^{99}+O(q^{100}) $ 12 * q + 4 * q^9 - 6 * q^11 - 10 * q^15 - 10 * q^19 + 12 * q^21 + 4 * q^25 - 10 * q^29 + 24 * q^31 + 6 * q^35 + 18 * q^39 + 2 * q^41 + 12 * q^45 - 4 * q^49 + 76 * q^51 + 2 * q^59 + 22 * q^61 - 40 * q^65 - 26 * q^69 + 14 * q^71 + 8 * q^75 - 8 * q^79 - 22 * q^81 + 14 * q^85 + 2 * q^89 - 58 * q^91 + 20 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.201864	+	0.116546i	0.116546	+	0.0672881i	0.557140	−	0.830419i	$-0.311899\pi$
$3$	0.201864	+	0.116546i	0.116546	+	0.0672881i	−0.440594	+	0.897707i	$0.645232\pi$
$4$		0			0
$5$	−2.11491	+	0.726062i	−0.945815	+	0.324705i
$5$	−2.11491	+	0.726062i	−0.945815	+	0.324705i
$6$		0			0
$7$	3.71537	−	2.14507i	1.40428	−	0.810760i	0.409450	−	0.912333i	$-0.365721\pi$
$7$	3.71537	−	2.14507i	1.40428	−	0.810760i	0.994828	+	0.101573i	$0.0323874\pi$
$8$		0			0
$9$	−1.47283	−	2.55102i	−0.490945	−	0.850341i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	−3.51351	−	0.809492i	−0.974471	−	0.224513i
$13$	−3.51351	−	0.809492i	−0.974471	−	0.224513i
$14$		0			0
$15$	−0.511544	−	0.0999188i	−0.132080	−	0.0257989i
$16$		0			0
$17$	−3.31164	+	1.91198i	−0.803191	+	0.463723i	−0.844586	−	0.535420i	$-0.820153\pi$
$17$	−3.31164	+	1.91198i	−0.803191	+	0.463723i	0.0413947	+	0.999143i	$0.486820\pi$
$18$		0			0
$19$	−1.14207	−	1.97813i	−0.262010	−	0.453814i	0.704766	−	0.709440i	$-0.251052\pi$
$19$	−1.14207	−	1.97813i	−0.262010	−	0.453814i	−0.966776	+	0.255626i	$0.917719\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$		0			0
$23$	−4.97295	−	2.87113i	−1.03693	−	0.598672i	−0.117968	−	0.993017i	$-0.537638\pi$
$23$	−4.97295	−	2.87113i	−1.03693	−	0.598672i	−0.918962	+	0.394345i	$0.870972\pi$
$24$		0			0
$25$	3.94567	−	3.07111i	0.789134	−	0.614222i
$26$		0			0
$27$		−	1.38589i		−	0.266715i
$28$		0			0
$29$	−1.14207	+	1.97813i	−0.212078	+	0.367329i	−0.952365	−	0.304962i	$-0.901356\pi$
$29$	−1.14207	+	1.97813i	−0.212078	+	0.367329i	0.740287	+	0.672291i	$0.234690\pi$
$30$		0			0
$31$	6.22982			1.11891			0.559454	−	0.828861i	$-0.311011\pi$
$31$	6.22982			1.11891			0.559454	+	0.828861i	$0.311011\pi$
$32$		0			0
$33$	−0.201864	+	0.116546i	−0.0351400	+	0.0202881i
$34$		0			0
$35$	−6.30021	+	7.23421i	−1.06493	+	1.22281i
$36$		0			0
$37$	−5.82679	−	3.36410i	−0.957919	−	0.553055i	−0.0623871	−	0.998052i	$-0.519871\pi$
$37$	−5.82679	−	3.36410i	−0.957919	−	0.553055i	−0.895532	+	0.444997i	$0.853205\pi$
$38$		0			0
$39$	−0.614908	−	0.572894i	−0.0984640	−	0.0917364i
$40$		0			0
$41$	−1.33076	+	2.30494i	−0.207830	+	0.359972i	−0.951031	−	0.309097i	$-0.899973\pi$
$41$	−1.33076	+	2.30494i	−0.207830	+	0.359972i	0.743201	+	0.669068i	$0.233307\pi$
$42$		0			0
$43$	−5.97130	+	3.44753i	−0.910615	+	0.525744i	−0.880629	−	0.473807i	$-0.842880\pi$
$43$	−5.97130	+	3.44753i	−0.910615	+	0.525744i	−0.0299858	+	0.999550i	$0.509546\pi$
$44$		0			0
$45$	4.96711	+	4.32581i	0.740453	+	0.644854i
$46$		0			0
$47$		−	6.60840i		−	0.963934i	−0.876189	−	0.481967i	$-0.839922\pi$
$47$		−	6.60840i		−	0.963934i	0.876189	−	0.481967i	$-0.160078\pi$
$48$		0			0
$49$	5.70265	−	9.87728i	0.814664	−	1.41104i
$50$		0			0
$51$	−0.891336			−0.124812
$52$		0			0
$53$		−	5.04299i		−	0.692707i	−0.938104	−	0.346354i	$-0.887420\pi$
$53$		−	5.04299i		−	0.692707i	0.938104	−	0.346354i	$-0.112580\pi$
$54$		0			0
$55$	0.428666	−	2.19459i	0.0578013	−	0.295919i
$56$		0			0
$57$		−	0.532418i		−	0.0705205i
$58$		0			0
$59$	−5.56058	−	9.63120i	−0.723925	−	1.25388i	−0.959415	−	0.281998i	$-0.909003\pi$
$59$	−5.56058	−	9.63120i	−0.723925	−	1.25388i	0.235490	−	0.971877i	$-0.424331\pi$
$60$		0			0
$61$	−2.08774	−	3.61607i	−0.267308	−	0.462991i	0.700858	−	0.713301i	$-0.252801\pi$
$61$	−2.08774	−	3.61607i	−0.267308	−	0.462991i	−0.968166	+	0.250310i	$0.919467\pi$
$62$		0			0
$63$	−10.9442	−	6.31866i	−1.37885	−	0.796077i
$64$		0			0
$65$	8.01848	−	0.839022i	0.994570	−	0.104068i
$66$		0			0
$67$	3.76176	+	2.17185i	0.459572	+	0.265334i	0.711864	−	0.702317i	$-0.247851\pi$
$67$	3.76176	+	2.17185i	0.459572	+	0.265334i	−0.252292	+	0.967651i	$0.581184\pi$
$68$		0			0
$69$	−0.669240	−	1.15916i	−0.0805670	−	0.139546i
$70$		0			0
$71$	−3.37189	−	5.84028i	−0.400170	−	0.693114i	0.593577	−	0.804778i	$-0.297715\pi$
$71$	−3.37189	−	5.84028i	−0.400170	−	0.693114i	−0.993746	+	0.111664i	$0.964382\pi$
$72$		0			0
$73$		−	13.5697i		−	1.58821i	−0.607779	−	0.794106i	$-0.707939\pi$
$73$		−	13.5697i		−	1.58821i	0.607779	−	0.794106i	$-0.292061\pi$
$74$		0			0
$75$	1.15442	−	0.160094i	0.133300	−	0.0184860i
$76$		0			0
$77$			4.29014i			0.488907i
$78$		0			0
$79$	11.4053			1.28320			0.641598	−	0.767041i	$-0.278272\pi$
$79$	11.4053			1.28320			0.641598	+	0.767041i	$0.278272\pi$
$80$		0			0
$81$	−4.25698	+	7.37331i	−0.472998	+	0.819256i
$82$		0			0
$83$			10.0324i			1.10120i	0.834769	+	0.550600i	$0.185601\pi$
$83$			10.0324i			1.10120i	−0.834769	+	0.550600i	$0.814399\pi$
$84$		0			0
$85$	5.61560	−	6.44811i	0.609098	−	0.699396i
$86$		0			0
$87$	−0.461087	+	0.266209i	−0.0494338	+	0.0285406i
$88$		0			0
$89$	−5.56058	+	9.63120i	−0.589420	+	1.02091i	0.404889	+	0.914366i	$0.367310\pi$
$89$	−5.56058	+	9.63120i	−0.589420	+	1.02091i	−0.994309	+	0.106539i	$0.966023\pi$
$90$		0			0
$91$	−14.7904	+	4.52915i	−1.55045	+	0.474784i
$92$		0			0
$93$	1.25758	+	0.726062i	0.130405	+	0.0752891i
$94$		0			0
$95$	3.85162	+	3.35434i	0.395168	+	0.344149i
$96$		0			0
$97$	−12.8538	+	7.42115i	−1.30511	+	0.753503i	−0.981275	−	0.192611i	$-0.938304\pi$
$97$	−12.8538	+	7.42115i	−1.30511	+	0.753503i	−0.323831	+	0.946115i	$0.604971\pi$
$98$		0			0
$99$	2.94567			0.296051
$100$		0			0
$101$	9.48680	−	16.4316i	0.943972	−	1.63501i	0.186174	−	0.982517i	$-0.440391\pi$
$101$	9.48680	−	16.4316i	0.943972	−	1.63501i	0.757797	−	0.652490i	$-0.226275\pi$
$102$		0			0
$103$		−	17.9796i		−	1.77159i	−0.464080	−	0.885793i	$-0.653615\pi$
$103$		−	17.9796i		−	1.77159i	0.464080	−	0.885793i	$-0.346385\pi$
$104$		0			0
$105$	−2.11491	+	0.726062i	−0.206394	+	0.0708564i
$106$		0			0
$107$	3.97459	+	2.29473i	0.384238	+	0.221840i	0.679661	−	0.733527i	$-0.262127\pi$
$107$	3.97459	+	2.29473i	0.384238	+	0.221840i	−0.295422	+	0.955367i	$0.595460\pi$
$108$		0			0
$109$	0.147558			0.0141335			0.00706676	−	0.999975i	$-0.497751\pi$
$109$	0.147558			0.0141335			0.00706676	+	0.999975i	$0.497751\pi$
$110$		0			0
$111$	−0.784147	−	1.35818i	−0.0744280	−	0.128913i
$112$		0			0
$113$	−13.9503	+	8.05419i	−1.31233	+	0.757675i	−0.982482	−	0.186359i	$-0.940331\pi$
$113$	−13.9503	+	8.05419i	−1.31233	+	0.757675i	−0.329849	+	0.944034i	$0.606998\pi$
$114$		0			0
$115$	12.6019	+	2.46151i	1.17514	+	0.229537i
$116$		0			0
$117$	3.10978	+	10.1553i	0.287499	+	0.938856i
$118$		0			0
$119$	−8.20265	+	14.2074i	−0.751936	+	1.30239i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	−0.537266	+	0.310190i	−0.0484436	+	0.0279689i
$124$		0			0
$125$	−6.11491	+	9.35991i	−0.546934	+	0.837176i
$126$		0			0
$127$	8.98829	+	5.18939i	0.797582	+	0.460484i	0.842625	−	0.538501i	$-0.181009\pi$
$127$	8.98829	+	5.18939i	0.797582	+	0.460484i	−0.0450429	+	0.998985i	$0.514342\pi$
$128$		0			0
$129$	−1.60719			−0.141505
$130$		0			0
$131$	17.6351			1.54079			0.770393	−	0.637569i	$-0.220060\pi$
$131$	17.6351			1.54079			0.770393	+	0.637569i	$0.220060\pi$
$132$		0			0
$133$	−8.48645	−	4.89966i	−0.735869	−	0.424854i
$134$		0			0
$135$	1.00624	+	2.93103i	0.0866036	+	0.252263i
$136$		0			0
$137$	5.56757	−	3.21444i	0.475670	−	0.274628i	−0.242940	−	0.970041i	$-0.578112\pi$
$137$	5.56757	−	3.21444i	0.475670	−	0.274628i	0.718610	+	0.695413i	$0.244779\pi$
$138$		0			0
$139$	7.48680	+	12.9675i	0.635022	+	1.09989i	0.986511	+	0.163698i	$0.0523422\pi$
$139$	7.48680	+	12.9675i	0.635022	+	1.09989i	−0.351489	+	0.936192i	$0.614324\pi$
$140$		0			0
$141$	0.770185	−	1.33400i	0.0648613	−	0.112343i
$142$		0			0
$143$	2.45779	−	2.63804i	0.205531	−	0.220604i
$144$		0			0
$145$	0.979135	−	5.01278i	0.0813128	−	0.416289i
$146$		0			0
$147$	2.30232	−	1.32925i	0.189892	−	0.109634i
$148$		0			0
$149$	7.84472	+	13.5875i	0.642665	+	1.11313i	0.984836	+	0.173490i	$0.0555045\pi$
$149$	7.84472	+	13.5875i	0.642665	+	1.11313i	−0.342171	+	0.939638i	$0.611162\pi$
$150$		0			0
$151$	1.17548			0.0956594			0.0478297	−	0.998856i	$-0.484770\pi$
$151$	1.17548			0.0956594			0.0478297	+	0.998856i	$0.484770\pi$
$152$		0			0
$153$	9.75500	+	5.63205i	0.788645	+	0.455324i
$154$		0			0
$155$	−13.1755	+	4.52323i	−1.05828	+	0.363315i
$156$		0			0
$157$		−	5.45560i		−	0.435405i	−0.976015	−	0.217702i	$-0.930144\pi$
$157$		−	5.45560i		−	0.435405i	0.976015	−	0.217702i	$-0.0698562\pi$
$158$		0			0
$159$	0.587741	−	1.01800i	0.0466109	−	0.0807325i
$160$		0			0
$161$	−24.6351			−1.94152
$162$		0			0
$163$	4.02098	−	2.32152i	0.314948	−	0.181835i	−0.334191	−	0.942506i	$-0.608463\pi$
$163$	4.02098	−	2.32152i	0.314948	−	0.181835i	0.649138	+	0.760670i	$0.275130\pi$
$164$		0			0
$165$	0.342304	−	0.393051i	0.0266483	−	0.0305989i
$166$		0			0
$167$	−2.76341	−	1.59545i	−0.213839	−	0.123460i	0.389255	−	0.921130i	$-0.372732\pi$
$167$	−2.76341	−	1.59545i	−0.213839	−	0.123460i	−0.603094	+	0.797670i	$0.706066\pi$
$168$		0			0
$169$	11.6894	+	5.68831i	0.899188	+	0.437562i
$170$		0			0
$171$	−3.36417	+	5.82691i	−0.257264	+	0.445595i
$172$		0			0
$173$	−3.00603	+	1.73553i	−0.228544	+	0.131950i	−0.609900	−	0.792478i	$-0.708790\pi$
$173$	−3.00603	+	1.73553i	−0.228544	+	0.131950i	0.381356	+	0.924428i	$0.375457\pi$
$174$		0			0
$175$	8.07187	−	19.8740i	0.610176	−	1.50234i
$176$		0			0
$177$		−	2.59226i		−	0.194846i
$178$		0			0
$179$	−2.56058	+	4.43505i	−0.191386	+	0.331491i	−0.945710	−	0.325012i	$-0.894632\pi$
$179$	−2.56058	+	4.43505i	−0.191386	+	0.331491i	0.754324	+	0.656503i	$0.227965\pi$
$180$		0			0
$181$	−4.14756			−0.308286			−0.154143	−	0.988049i	$-0.549262\pi$
$181$	−4.14756			−0.308286			−0.154143	+	0.988049i	$0.549262\pi$
$182$		0			0
$183$		−	0.973274i		−	0.0719465i
$184$		0			0
$185$	14.7657	+	2.88415i	1.08559	+	0.212047i
$186$		0			0
$187$		−	3.82395i		−	0.279635i
$188$		0			0
$189$	−2.97283	−	5.14910i	−0.216242	−	0.374542i
$190$		0			0
$191$	−0.404539	−	0.700683i	−0.0292714	−	0.0506996i	0.851019	−	0.525136i	$-0.175985\pi$
$191$	−0.404539	−	0.700683i	−0.0292714	−	0.0506996i	−0.880290	+	0.474436i	$0.842652\pi$
$192$		0			0
$193$	−8.34195	−	4.81623i	−0.600466	−	0.346679i	0.168759	−	0.985657i	$-0.446024\pi$
$193$	−8.34195	−	4.81623i	−0.600466	−	0.346679i	−0.769225	+	0.638978i	$0.779358\pi$
$194$		0			0
$195$	1.71643	+	0.765156i	0.122916	+	0.0547940i
$196$		0			0
$197$	14.0650	+	8.12043i	1.00209	+	0.578556i	0.908866	−	0.417089i	$-0.136950\pi$
$197$	14.0650	+	8.12043i	1.00209	+	0.578556i	0.0932234	+	0.995645i	$0.470283\pi$
$198$		0			0
$199$	−2.06829	−	3.58239i	−0.146618	−	0.253949i	0.783358	−	0.621571i	$-0.213505\pi$
$199$	−2.06829	−	3.58239i	−0.146618	−	0.253949i	−0.929975	+	0.367622i	$0.880172\pi$
$200$		0			0
$201$	0.506243	+	0.876839i	0.0357076	+	0.0618474i
$202$		0			0
$203$			9.79931i			0.687777i
$204$		0			0
$205$	1.14090	−	5.84096i	0.0796841	−	0.407950i
$206$		0			0
$207$			16.9148i			1.17566i
$208$		0			0
$209$	2.28415			0.157998
$210$		0			0
$211$	4.80359	−	8.32007i	0.330693	−	0.572777i	−0.651955	−	0.758258i	$-0.726051\pi$
$211$	4.80359	−	8.32007i	0.330693	−	0.572777i	0.982648	+	0.185481i	$0.0593842\pi$
$212$		0			0
$213$		−	1.57192i		−	0.107707i
$214$		0			0
$215$	10.1256	−	11.6267i	0.690562	−	0.792937i
$216$		0			0
$217$	23.1461	−	13.3634i	1.57126	−	0.907166i
$218$		0			0
$219$	1.58150	−	2.73924i	0.106868	−	0.185100i
$220$		0			0
$221$	13.1832	−	4.03700i	0.886798	−	0.271558i
$222$		0			0
$223$	−13.0447	−	7.53136i	−0.873538	−	0.504337i	−0.00501557	−	0.999987i	$-0.501597\pi$
$223$	−13.0447	−	7.53136i	−0.873538	−	0.504337i	−0.868522	+	0.495650i	$0.834930\pi$
$224$		0			0
$225$	−13.6458	−	5.54226i	−0.909719	−	0.369484i
$226$		0			0
$227$	−17.4174	+	10.0559i	−1.15603	+	0.667436i	−0.950350	−	0.311183i	$-0.899275\pi$
$227$	−17.4174	+	10.0559i	−1.15603	+	0.667436i	−0.205683	+	0.978619i	$0.565941\pi$
$228$		0			0
$229$	−12.5683			−0.830536			−0.415268	−	0.909699i	$-0.636312\pi$
$229$	−12.5683			−0.830536			−0.415268	+	0.909699i	$0.636312\pi$
$230$		0			0
$231$	−0.500000	+	0.866025i	−0.0328976	+	0.0569803i
$232$		0			0
$233$		−	11.3712i		−	0.744954i	−0.928041	−	0.372477i	$-0.878508\pi$
$233$		−	11.3712i		−	0.744954i	0.928041	−	0.372477i	$-0.121492\pi$
$234$		0			0
$235$	4.79811	+	13.9762i	0.312994	+	0.911704i
$236$		0			0
$237$	2.30232	+	1.32925i	0.149552	+	0.0863438i
$238$		0			0
$239$	18.3510			1.18703			0.593513	−	0.804825i	$-0.297741\pi$
$239$	18.3510			1.18703			0.593513	+	0.804825i	$0.297741\pi$
$240$		0			0
$241$	0.688687	+	1.19284i	0.0443622	+	0.0768376i	0.887354	−	0.461089i	$-0.152541\pi$
$241$	0.688687	+	1.19284i	0.0443622	+	0.0768376i	−0.842992	+	0.537927i	$0.819208\pi$
$242$		0			0
$243$	−5.31932	+	3.07111i	−0.341234	+	0.197012i
$244$		0			0
$245$	−4.88906	+	25.0300i	−0.312351	+	1.59911i
$246$		0			0
$247$	2.41140	+	7.87467i	0.153434	+	0.501053i
$248$		0			0
$249$	−1.16924	+	2.02518i	−0.0740976	+	0.128341i
$250$		0			0
$251$	−12.6149	−	21.8497i	−0.796246	−	1.37914i	−0.922045	−	0.387083i	$-0.873483\pi$
$251$	−12.6149	−	21.8497i	−0.796246	−	1.37914i	0.125799	−	0.992056i	$-0.459851\pi$
$252$		0			0
$253$	4.97295	−	2.87113i	0.312646	−	0.180507i
$254$		0			0
$255$	1.88509	−	0.647165i	0.118049	−	0.0405270i
$256$		0			0
$257$	26.3596	+	15.2187i	1.64427	+	0.949318i	0.979292	+	0.202451i	$0.0648907\pi$
$257$	26.3596	+	15.2187i	1.64427	+	0.949318i	0.664974	+	0.746866i	$0.268443\pi$
$258$		0			0
$259$	−28.8649			−1.79358
$260$		0			0
$261$	6.72834			0.416474
$262$		0			0
$263$	2.80980	+	1.62224i	0.173260	+	0.100032i	0.584122	−	0.811666i	$-0.301439\pi$
$263$	2.80980	+	1.62224i	0.173260	+	0.100032i	−0.410862	+	0.911697i	$0.634772\pi$
$264$		0			0
$265$	3.66152	+	10.6654i	0.224925	+	0.655173i
$266$		0			0
$267$	−2.24496	+	1.29613i	−0.137389	+	0.0793218i
$268$		0			0
$269$	−0.554332	−	0.960132i	−0.0337982	−	0.0585403i	0.848632	−	0.528984i	$-0.177427\pi$
$269$	−0.554332	−	0.960132i	−0.0337982	−	0.0585403i	−0.882430	+	0.470444i	$0.844094\pi$
$270$		0			0
$271$	−15.0877	+	26.1327i	−0.916515	+	1.58745i	−0.111847	+	0.993725i	$0.535677\pi$
$271$	−15.0877	+	26.1327i	−0.916515	+	1.58745i	−0.804668	+	0.593725i	$0.797657\pi$
$272$		0			0
$273$	−3.51351	−	0.809492i	−0.212647	−	0.0489927i
$274$		0			0
$275$	0.686824	+	4.95260i	0.0414170	+	0.298653i
$276$		0			0
$277$	22.4941	−	12.9870i	1.35154	−	0.780311i	0.363073	−	0.931761i	$-0.381727\pi$
$277$	22.4941	−	12.9870i	1.35154	−	0.780311i	0.988465	+	0.151449i	$0.0483941\pi$
$278$		0			0
$279$	−9.17548	−	15.8924i	−0.549322	−	0.951453i
$280$		0			0
$281$	17.7827			1.06083			0.530413	−	0.847740i	$-0.322037\pi$
$281$	17.7827			1.06083			0.530413	+	0.847740i	$0.322037\pi$
$282$		0			0
$283$	−6.37503	−	3.68062i	−0.378956	−	0.218790i	0.298408	−	0.954438i	$-0.403544\pi$
$283$	−6.37503	−	3.68062i	−0.378956	−	0.218790i	−0.677364	+	0.735648i	$0.736878\pi$
$284$		0			0
$285$	0.386568	+	1.12601i	0.0228983	+	0.0666994i
$286$		0			0
$287$			11.4183i			0.674001i
$288$		0			0
$289$	−1.18869	+	2.05887i	−0.0699227	+	0.121110i
$290$		0			0
$291$	−3.45963			−0.202807
$292$		0			0
$293$	−14.5449	+	8.39750i	−0.849722	+	0.490587i	−0.860557	−	0.509354i	$-0.829884\pi$
$293$	−14.5449	+	8.39750i	−0.849722	+	0.490587i	0.0108351	+	0.999941i	$0.496551\pi$
$294$		0			0
$295$	18.7530	+	16.3318i	1.09184	+	0.950873i
$296$		0			0
$297$	1.20022	+	0.692946i	0.0696437	+	0.0402088i
$298$		0			0
$299$	15.1483	+	14.1133i	0.876050	+	0.816193i
$300$		0			0
$301$	−14.7904	+	25.6177i	−0.852504	+	1.47658i
$302$		0			0
$303$	3.83009	−	2.21130i	0.220033	−	0.127036i
$304$		0			0
$305$	7.04087	+	6.13183i	0.403159	+	0.351108i
$306$		0			0
$307$			3.12468i			0.178335i	0.996017	+	0.0891674i	$0.0284206\pi$
$307$			3.12468i			0.178335i	−0.996017	+	0.0891674i	$0.971579\pi$
$308$		0			0
$309$	2.09546	−	3.62944i	0.119207	−	0.206472i
$310$		0			0
$311$	18.6072			1.05512			0.527558	−	0.849519i	$-0.323108\pi$
$311$	18.6072			1.05512			0.527558	+	0.849519i	$0.323108\pi$
$312$		0			0
$313$			17.5732i			0.993295i	0.867952	+	0.496647i	$0.165436\pi$
$313$			17.5732i			0.993295i	−0.867952	+	0.496647i	$0.834564\pi$
$314$		0			0
$315$	27.7338	+	5.41719i	1.56262	+	0.305224i
$316$		0			0
$317$		−	22.2633i		−	1.25043i	−0.780453	−	0.625215i	$-0.785011\pi$
$317$		−	22.2633i		−	1.25043i	0.780453	−	0.625215i	$-0.214989\pi$
$318$		0			0
$319$	−1.14207	−	1.97813i	−0.0639438	−	0.110754i
$320$		0			0
$321$	0.534885	+	0.926448i	0.0298544	+	0.0517093i
$322$		0			0
$323$	7.56428	+	4.36724i	0.420888	+	0.243000i
$324$		0			0
$325$	−16.3492	+	7.59637i	−0.906888	+	0.421371i
$326$		0			0
$327$	0.0297867	+	0.0171974i	0.00164721	+	0.000951017i
$328$		0			0
$329$	−14.1755	−	24.5527i	−0.781520	−	1.35363i
$330$		0			0
$331$	14.2026	+	24.5997i	0.780648	+	1.35212i	0.931565	+	0.363576i	$0.118444\pi$
$331$	14.2026	+	24.5997i	0.780648	+	1.35212i	−0.150916	+	0.988547i	$0.548222\pi$
$332$		0			0
$333$			19.8190i			1.08608i
$334$		0			0
$335$	−9.53268	−	1.86200i	−0.520826	−	0.101732i
$336$		0			0
$337$			8.87960i			0.483703i	0.970313	+	0.241851i	$0.0777547\pi$
$337$			8.87960i			0.483703i	−0.970313	+	0.241851i	$0.922245\pi$
$338$		0			0
$339$	−3.75475			−0.203930
$340$		0			0
$341$	−3.11491	+	5.39518i	−0.168682	+	0.292165i
$342$		0			0
$343$		−	18.8993i		−	1.02047i
$344$		0			0
$345$	2.25700	+	1.96560i	0.121513	+	0.105824i
$346$		0			0
$347$	14.9652	−	8.64018i	0.803376	−	0.463829i	−0.0412745	−	0.999148i	$-0.513142\pi$
$347$	14.9652	−	8.64018i	0.803376	−	0.463829i	0.844650	+	0.535319i	$0.179808\pi$
$348$		0			0
$349$	−5.37189	+	9.30438i	−0.287551	+	0.498052i	−0.973225	−	0.229857i	$-0.926174\pi$
$349$	−5.37189	+	9.30438i	−0.287551	+	0.498052i	0.685674	+	0.727909i	$0.259508\pi$
$350$		0			0
$351$	−1.12187	+	4.86934i	−0.0598809	+	0.259906i
$352$		0			0
$353$	−27.8598	−	16.0849i	−1.48283	−	0.856111i	−0.483017	−	0.875611i	$-0.660459\pi$
$353$	−27.8598	−	16.0849i	−1.48283	−	0.856111i	−0.999810	+	0.0195003i	$0.993792\pi$
$354$		0			0
$355$	11.3716	+	9.90346i	0.603544	+	0.525621i
$356$		0			0
$357$	−3.31164	+	1.91198i	−0.175271	+	0.101193i
$358$		0			0
$359$	−13.8913			−0.733157			−0.366578	−	0.930387i	$-0.619471\pi$
$359$	−13.8913			−0.733157			−0.366578	+	0.930387i	$0.619471\pi$
$360$		0			0
$361$	6.89134	−	11.9361i	0.362702	−	0.628218i
$362$		0			0
$363$			2.33093i			0.122342i
$364$		0			0
$365$	9.85244	+	28.6987i	0.515700	+	1.50216i
$366$		0			0
$367$	−15.6282	−	9.02293i	−0.815784	−	0.470993i	0.0331762	−	0.999450i	$-0.489438\pi$
$367$	−15.6282	−	9.02293i	−0.815784	−	0.470993i	−0.848961	+	0.528456i	$0.822771\pi$
$368$		0			0
$369$	7.83996			0.408132
$370$		0			0
$371$	−10.8176	−	18.7366i	−0.561620	−	0.972754i
$372$		0			0
$373$	18.1267	−	10.4655i	0.938566	−	0.541882i	0.0490558	−	0.998796i	$-0.484379\pi$
$373$	18.1267	−	10.4655i	0.938566	−	0.541882i	0.889511	+	0.456914i	$0.151045\pi$
$374$		0			0
$375$	−2.32524	+	1.17676i	−0.120075	+	0.0607676i
$376$		0			0
$377$	5.61396	−	6.02567i	0.289134	−	0.310338i
$378$		0			0
$379$	12.2089	−	21.1464i	0.627129	−	1.08622i	−0.360996	−	0.932567i	$-0.617563\pi$
$379$	12.2089	−	21.1464i	0.627129	−	1.08622i	0.988125	−	0.153652i	$-0.0491033\pi$
$380$		0			0
$381$	1.20961	+	2.09511i	0.0619702	+	0.107335i
$382$		0			0
$383$	25.9612	−	14.9887i	1.32656	−	0.765887i	0.341790	−	0.939776i	$-0.388967\pi$
$383$	25.9612	−	14.9887i	1.32656	−	0.765887i	0.984765	+	0.173889i	$0.0556335\pi$
$384$		0			0
$385$	−3.11491	−	9.07325i	−0.158750	−	0.462416i
$386$		0			0
$387$	17.5895	+	10.1553i	0.894123	+	0.516222i
$388$		0			0
$389$	3.80908			0.193128			0.0965640	−	0.995327i	$-0.469215\pi$
$389$	3.80908			0.193128			0.0965640	+	0.995327i	$0.469215\pi$
$390$		0			0
$391$	21.9582			1.11047
$392$		0			0
$393$	3.55990	+	2.05531i	0.179573	+	0.103677i
$394$		0			0
$395$	−24.1212	+	8.28095i	−1.21367	+	0.416660i
$396$		0			0
$397$	−10.0330	+	5.79258i	−0.503544	+	0.290721i	−0.730176	−	0.683259i	$-0.760562\pi$
$397$	−10.0330	+	5.79258i	−0.503544	+	0.290721i	0.226632	+	0.973980i	$0.427229\pi$
$398$		0			0
$399$	−1.14207	−	1.97813i	−0.0571752	−	0.0990303i
$400$		0			0
$401$	9.74302	−	16.8754i	0.486543	−	0.842717i	−0.513337	−	0.858187i	$-0.671591\pi$
$401$	9.74302	−	16.8754i	0.486543	−	0.842717i	0.999880	+	0.0154696i	$0.00492431\pi$
$402$		0			0
$403$	−21.8885	−	5.04299i	−1.09034	−	0.251209i
$404$		0			0
$405$	3.64964	−	18.6847i	0.181352	−	0.928450i
$406$		0			0
$407$	5.82679	−	3.36410i	0.288823	−	0.166752i
$408$		0			0
$409$	−2.29811	−	3.98044i	−0.113634	−	0.196820i	0.803599	−	0.595171i	$-0.202916\pi$
$409$	−2.29811	−	3.98044i	−0.113634	−	0.196820i	−0.917233	+	0.398351i	$0.869583\pi$
$410$		0			0
$411$	1.49852			0.0739167
$412$		0			0
$413$	−41.3192	−	23.8556i	−2.03318	−	1.17386i
$414$		0			0
$415$	−7.28415	−	21.2176i	−0.357565	−	1.04153i
$416$		0			0
$417$			3.49023i			0.170918i
$418$		0			0
$419$	−3.38509	+	5.86315i	−0.165373	+	0.286434i	−0.936788	−	0.349899i	$-0.886216\pi$
$419$	−3.38509	+	5.86315i	−0.165373	+	0.286434i	0.771415	+	0.636332i	$0.219549\pi$
$420$		0			0
$421$	−16.1087			−0.785088			−0.392544	−	0.919733i	$-0.628405\pi$
$421$	−16.1087			−0.785088			−0.392544	+	0.919733i	$0.628405\pi$
$422$		0			0
$423$	−16.8582	+	9.73308i	−0.819673	+	0.473238i
$424$		0			0
$425$	−7.19475	+	17.7144i	−0.348997	+	0.859276i
$426$		0			0
$427$	−15.5135	−	8.95670i	−0.750749	−	0.433445i
$428$		0			0
$429$	0.803594	−	0.246079i	0.0387979	−	0.0118808i
$430$		0			0
$431$	−1.12887	+	1.95526i	−0.0543757	+	0.0941816i	−0.891932	−	0.452169i	$-0.850650\pi$
$431$	−1.12887	+	1.95526i	−0.0543757	+	0.0941816i	0.837556	+	0.546351i	$0.183984\pi$
$432$		0			0
$433$	−8.03633	+	4.63978i	−0.386201	+	0.222974i	−0.680513	−	0.732736i	$-0.738243\pi$
$433$	−8.03633	+	4.63978i	−0.386201	+	0.222974i	0.294312	+	0.955710i	$0.404910\pi$
$434$		0			0
$435$	0.781873	−	0.897785i	0.0374879	−	0.0430455i
$436$		0			0
$437$			13.1162i			0.627432i
$438$		0			0
$439$	12.9659	−	22.4576i	0.618827	−	1.07184i	−0.370873	−	0.928684i	$-0.620941\pi$
$439$	12.9659	−	22.4576i	0.618827	−	1.07184i	0.989700	−	0.143157i	$-0.0457253\pi$
$440$		0			0
$441$	−33.5962			−1.59982
$442$		0			0
$443$			19.4318i			0.923231i	0.887080	+	0.461615i	$0.152730\pi$
$443$			19.4318i			0.923231i	−0.887080	+	0.461615i	$0.847270\pi$
$444$		0			0
$445$	4.76725	−	24.4064i	0.225990	−	1.15698i
$446$		0			0
$447$			3.65709i			0.172975i
$448$		0			0
$449$	−12.7361	−	22.0595i	−0.601052	−	1.04105i	−0.992662	−	0.120921i	$-0.961415\pi$
$449$	−12.7361	−	22.0595i	−0.601052	−	1.04105i	0.391610	−	0.920131i	$-0.371918\pi$
$450$		0			0
$451$	−1.33076	−	2.30494i	−0.0626631	−	0.108536i
$452$		0			0
$453$	0.237288	+	0.136998i	0.0111488	+	0.00643674i
$454$		0			0
$455$	27.9919	−	20.3175i	1.31228	−	0.952498i
$456$		0			0
$457$	−16.9321	−	9.77578i	−0.792053	−	0.457292i	0.0486321	−	0.998817i	$-0.484514\pi$
$457$	−16.9321	−	9.77578i	−0.792053	−	0.457292i	−0.840685	+	0.541525i	$0.817847\pi$
$458$		0			0
$459$	2.64979	+	4.58958i	0.123682	+	0.214223i
$460$		0			0
$461$	−16.1678	−	28.0034i	−0.753008	−	1.30425i	−0.946359	−	0.323118i	$-0.895269\pi$
$461$	−16.1678	−	28.0034i	−0.753008	−	1.30425i	0.193351	−	0.981130i	$-0.438064\pi$
$462$		0			0
$463$		−	28.8119i		−	1.33900i	−0.742810	−	0.669502i	$-0.766507\pi$
$463$		−	28.8119i		−	1.33900i	0.742810	−	0.669502i	$-0.233493\pi$
$464$		0			0
$465$	−3.18682	−	0.622476i	−0.147785	−	0.0288666i
$466$		0			0
$467$		−	24.8085i		−	1.14800i	−0.818856	−	0.573999i	$-0.805391\pi$
$467$		−	24.8085i		−	1.14800i	0.818856	−	0.573999i	$-0.194609\pi$
$468$		0			0
$469$	18.6351			0.860490
$470$		0			0
$471$	0.635830	−	1.10129i	0.0292975	−	0.0507448i
$472$		0			0
$473$		−	6.89506i		−	0.317035i
$474$		0			0
$475$	−10.5813	−	4.29761i	−0.485503	−	0.197188i
$476$		0			0
$477$	−12.8648	+	7.42748i	−0.589038	+	0.340081i
$478$		0			0
$479$	−3.18945	+	5.52428i	−0.145729	+	0.252411i	−0.929645	−	0.368457i	$-0.879886\pi$
$479$	−3.18945	+	5.52428i	−0.145729	+	0.252411i	0.783915	+	0.620868i	$0.213220\pi$
$480$		0			0
$481$	17.7493	+	16.5365i	0.809297	+	0.754001i
$482$		0			0
$483$	−4.97295	−	2.87113i	−0.226277	−	0.130641i
$484$		0			0
$485$	21.7964	−	25.0277i	0.989723	−	1.13645i
$486$		0			0
$487$	−15.8874	+	9.17260i	−0.719927	+	0.415650i	−0.814726	−	0.579846i	$-0.803113\pi$
$487$	−15.8874	+	9.17260i	−0.719927	+	0.415650i	0.0947988	+	0.995496i	$0.469779\pi$
$488$		0			0
$489$	1.08226			0.0489413
$490$		0			0
$491$	1.95963	−	3.39418i	0.0884369	−	0.153177i	−0.818414	−	0.574629i	$-0.805146\pi$
$491$	1.95963	−	3.39418i	0.0884369	−	0.153177i	0.906851	+	0.421452i	$0.138480\pi$
$492$		0			0
$493$		−	8.73447i		−	0.393381i
$494$		0			0
$495$	−6.22982	+	2.13874i	−0.280009	+	0.0961291i
$496$		0			0
$497$	−25.0556	−	14.4659i	−1.12390	−	0.648883i
$498$		0			0
$499$	−23.6087			−1.05687			−0.528435	−	0.848974i	$-0.677221\pi$
$499$	−23.6087			−1.05687			−0.528435	+	0.848974i	$0.677221\pi$
$500$		0			0
$501$	−0.371889	−	0.644130i	−0.0166148	−	0.0287776i
$502$		0			0
$503$	−15.9636	+	9.21658i	−0.711781	+	0.410947i	−0.811720	−	0.584047i	$-0.801469\pi$
$503$	−15.9636	+	9.21658i	−0.711781	+	0.410947i	0.0999391	+	0.994994i	$0.468135\pi$
$504$		0			0
$505$	−8.13333	+	41.6393i	−0.361928	+	1.85293i
$506$		0			0
$507$	1.69673	+	2.51063i	0.0753544	+	0.111501i
$508$		0			0
$509$	6.83848	−	11.8446i	0.303110	−	0.525002i	−0.673729	−	0.738979i	$-0.735308\pi$
$509$	6.83848	−	11.8446i	0.303110	−	0.525002i	0.976839	+	0.213977i	$0.0686416\pi$
$510$		0			0
$511$	−29.1079	−	50.4164i	−1.28766	−	2.23029i
$512$		0			0
$513$	−2.74147	+	1.58279i	−0.121039	+	0.0698819i
$514$		0			0
$515$	13.0543	+	38.0253i	0.575243	+	1.67559i
$516$		0			0
$517$	5.72304	+	3.30420i	0.251699	+	0.145319i
$518$		0			0
$519$	−0.809079			−0.0355146
$520$		0			0
$521$	25.9472			1.13677			0.568383	−	0.822764i	$-0.307569\pi$
$521$	25.9472			1.13677			0.568383	+	0.822764i	$0.307569\pi$
$522$		0			0
$523$	−28.4246	−	16.4110i	−1.24292	−	0.717601i	−0.273234	−	0.961948i	$-0.588093\pi$
$523$	−28.4246	−	16.4110i	−1.24292	−	0.717601i	−0.969688	+	0.244346i	$0.921427\pi$
$524$		0			0
$525$	3.94567	−	3.07111i	0.172203	−	0.134034i
$526$		0			0
$527$	−20.6309	+	11.9113i	−0.898697	+	0.518863i
$528$		0			0
$529$	4.98680	+	8.63738i	0.216817	+	0.375538i
$530$		0			0
$531$	−16.3796	+	28.3703i	−0.710814	+	1.23117i
$532$		0			0
$533$	6.54147	−	7.02120i	0.283342	−	0.304122i
$534$		0			0
$535$	−10.0720	−	1.96735i	−0.435451	−	0.0850558i
$536$		0			0
$537$	−1.03378	+	0.596851i	−0.0446108	+	0.0257560i
$538$		0			0
$539$	5.70265	+	9.87728i	0.245630	+	0.425444i
$540$		0			0
$541$	22.8370			0.981839			0.490920	−	0.871205i	$-0.336661\pi$
$541$	22.8370			0.981839			0.490920	+	0.871205i	$0.336661\pi$
$542$		0			0
$543$	−0.837243	−	0.483383i	−0.0359296	−	0.0207439i
$544$		0			0
$545$	−0.312072	+	0.107136i	−0.0133677	+	0.00458922i
$546$		0			0
$547$		−	31.4513i		−	1.34476i	−0.740207	−	0.672379i	$-0.765272\pi$
$547$		−	31.4513i		−	1.34476i	0.740207	−	0.672379i	$-0.234728\pi$
$548$		0			0
$549$	−6.14979	+	10.6518i	−0.262467	+	0.454606i
$550$		0			0
$551$	5.21733			0.222266
$552$		0			0
$553$	42.3749	−	24.4652i	1.80196	−	1.04036i
$554$		0			0
$555$	2.64452	+	2.30309i	0.112254	+	0.0977608i
$556$		0			0
$557$	−15.9636	−	9.21658i	−0.676399	−	0.390519i	0.122098	−	0.992518i	$-0.461038\pi$
$557$	−15.9636	−	9.21658i	−0.676399	−	0.390519i	−0.798497	+	0.601999i	$0.794371\pi$
$558$		0			0
$559$	23.7709	−	7.27920i	1.00540	−	0.307877i
$560$		0			0
$561$	0.445668	−	0.771919i	0.0188161	−	0.0325905i
$562$		0			0
$563$	8.51624	−	4.91685i	0.358917	−	0.207221i	−0.309689	−	0.950838i	$-0.600225\pi$
$563$	8.51624	−	4.91685i	0.358917	−	0.207221i	0.668605	+	0.743617i	$0.266892\pi$
$564$		0			0
$565$	23.6557	−	27.1626i	0.995202	−	1.14274i
$566$		0			0
$567$			36.5261i			1.53395i
$568$		0			0
$569$	−21.6017	+	37.4152i	−0.905591	+	1.56853i	−0.0854680	+	0.996341i	$0.527239\pi$
$569$	−21.6017	+	37.4152i	−0.905591	+	1.56853i	−0.820123	+	0.572188i	$0.806095\pi$
$570$		0			0
$571$	17.3106			0.724424			0.362212	−	0.932096i	$-0.382022\pi$
$571$	17.3106			0.724424			0.362212	+	0.932096i	$0.382022\pi$
$572$		0			0
$573$		−	0.188590i		−	0.00787847i
$574$		0			0
$575$	−28.4392	+	3.94392i	−1.18599	+	0.164473i
$576$		0			0
$577$			0.245757i			0.0102310i	0.999987	+	0.00511550i	$0.00162832\pi$
$577$			0.245757i			0.0102310i	−0.999987	+	0.00511550i	$0.998372\pi$
$578$		0			0
$579$	−1.12263	−	1.94445i	−0.0466548	−	0.0808084i
$580$		0			0
$581$	21.5202	+	37.2741i	0.892809	+	1.54639i
$582$		0			0
$583$	4.36735	+	2.52149i	0.180877	+	0.104430i
$584$		0			0
$585$	−13.9503	−	19.2196i	−0.576772	−	0.794632i
$586$		0			0
$587$	−15.9006	−	9.18021i	−0.656287	−	0.378908i	0.134573	−	0.990904i	$-0.457034\pi$
$587$	−15.9006	−	9.18021i	−0.656287	−	0.378908i	−0.790861	+	0.611996i	$0.790367\pi$
$588$		0			0
$589$	−7.11491	−	12.3234i	−0.293165	−	0.507776i
$590$		0			0
$591$	1.89281	+	3.27845i	0.0778599	+	0.134857i
$592$		0			0
$593$			20.7514i			0.852159i	0.904686	+	0.426079i	$0.140106\pi$
$593$			20.7514i			0.852159i	−0.904686	+	0.426079i	$0.859894\pi$
$594$		0			0
$595$	7.03239	−	36.0030i	0.288300	−	1.47598i
$596$		0			0
$597$		−	0.964208i		−	0.0394624i
$598$		0			0
$599$	1.80908			0.0739170			0.0369585	−	0.999317i	$-0.488233\pi$
$599$	1.80908			0.0739170			0.0369585	+	0.999317i	$0.488233\pi$
$600$		0			0
$601$	7.88585	−	13.6587i	0.321671	−	0.557150i	−0.659162	−	0.752001i	$-0.729089\pi$
$601$	7.88585	−	13.6587i	0.321671	−	0.557150i	0.980833	+	0.194851i	$0.0624223\pi$
$602$		0			0
$603$		−	12.7951i		−	0.521058i
$604$		0			0
$605$	−16.8624	−	14.6853i	−0.685555	−	0.597043i
$606$		0			0
$607$	22.3330	−	12.8939i	0.906467	−	0.523349i	0.0271746	−	0.999631i	$-0.491349\pi$
$607$	22.3330	−	12.8939i	0.906467	−	0.523349i	0.879293	+	0.476281i	$0.158016\pi$
$608$		0			0
$609$	−1.14207	+	1.97813i	−0.0462792	+	0.0801579i
$610$		0			0
$611$	−5.34945	+	23.2187i	−0.216416	+	0.939326i
$612$		0			0
$613$	5.10085	+	2.94498i	0.206021	+	0.118946i	0.599461	−	0.800404i	$-0.295382\pi$
$613$	5.10085	+	2.94498i	0.206021	+	0.118946i	−0.393440	+	0.919350i	$0.628715\pi$
$614$		0			0
$615$	0.911050	−	1.04611i	0.0367371	−	0.0421833i
$616$		0			0
$617$	−5.07106	+	2.92778i	−0.204153	+	0.117868i	−0.598591	−	0.801055i	$-0.704273\pi$
$617$	−5.07106	+	2.92778i	−0.204153	+	0.117868i	0.394438	+	0.918923i	$0.370939\pi$
$618$		0			0
$619$	29.6740			1.19270			0.596350	−	0.802725i	$-0.296617\pi$
$619$	29.6740			1.19270			0.596350	+	0.802725i	$0.296617\pi$
$620$		0			0
$621$	−3.97908	+	6.89196i	−0.159675	+	0.276565i
$622$		0			0
$623$			47.7113i			1.91151i
$624$		0			0
$625$	6.13659	−	24.2351i	0.245464	−	0.969406i
$626$		0			0
$627$	0.461087	+	0.266209i	0.0184141	+	0.0106314i
$628$		0			0
$629$	25.7283			1.02586
$630$		0			0
$631$	15.1483	+	26.2377i	0.603045	+	1.04450i	0.992357	+	0.123399i	$0.0393794\pi$
$631$	15.1483	+	26.2377i	0.603045	+	1.04450i	−0.389312	+	0.921106i	$0.627287\pi$
$632$		0			0
$633$	1.93935	−	1.11968i	0.0770821	−	0.0445034i
$634$		0			0
$635$	−22.7772	−	4.44903i	−0.903887	−	0.176554i
$636$		0			0
$637$	−28.0319	+	30.0876i	−1.11066	+	1.19212i
$638$		0			0
$639$	−9.93246	+	17.2035i	−0.392922	+	0.680561i
$640$		0			0
$641$	8.98604	+	15.5643i	0.354927	+	0.614752i	0.987105	−	0.160071i	$-0.0511723\pi$
$641$	8.98604	+	15.5643i	0.354927	+	0.614752i	−0.632178	+	0.774823i	$0.717839\pi$
$642$		0			0
$643$	−23.1517	+	13.3666i	−0.913014	+	0.527129i	−0.881400	−	0.472371i	$-0.843398\pi$
$643$	−23.1517	+	13.3666i	−0.913014	+	0.527129i	−0.0316144	+	0.999500i	$0.510065\pi$
$644$		0			0
$645$	3.39905	−	1.16692i	0.133838	−	0.0459474i
$646$		0			0
$647$	19.8974	+	11.4878i	0.782248	+	0.451631i	0.837227	−	0.546856i	$-0.184176\pi$
$647$	19.8974	+	11.4878i	0.782248	+	0.451631i	−0.0549781	+	0.998488i	$0.517509\pi$
$648$		0			0
$649$	11.1212			0.436543
$650$		0			0
$651$	6.22982			0.244166
$652$		0			0
$653$	15.4153	+	8.90006i	0.603249	+	0.348286i	0.770319	−	0.637659i	$-0.220097\pi$
$653$	15.4153	+	8.90006i	0.603249	+	0.348286i	−0.167070	+	0.985945i	$0.553430\pi$
$654$		0			0
$655$	−37.2966	+	12.8042i	−1.45730	+	0.500301i
$656$		0			0
$657$	−34.6166	+	19.9859i	−1.35052	+	0.779725i
$658$		0			0
$659$	−16.3587	−	28.3341i	−0.637244	−	1.10374i	−0.986035	−	0.166538i	$-0.946741\pi$
$659$	−16.3587	−	28.3341i	−0.637244	−	1.10374i	0.348791	−	0.937200i	$-0.386592\pi$
$660$		0			0
$661$	4.10095	−	7.10305i	0.159508	−	0.276276i	−0.775183	−	0.631737i	$-0.782342\pi$
$661$	4.10095	−	7.10305i	0.159508	−	0.276276i	0.934691	+	0.355460i	$0.115676\pi$
$662$		0			0
$663$	3.13171	+	0.721529i	0.121626	+	0.0280219i
$664$		0			0
$665$	21.5055	+	4.20063i	0.833948	+	0.162893i
$666$		0			0
$667$	11.3589	−	6.55809i	0.439820	−	0.253930i
$668$		0			0
$669$	−1.75551	−	3.04062i	−0.0678718	−	0.117557i
$670$		0			0
$671$	4.17548			0.161193
$672$		0			0
$673$	7.36805	+	4.25395i	0.284017	+	0.163978i	0.635241	−	0.772314i	$-0.280901\pi$
$673$	7.36805	+	4.25395i	0.284017	+	0.163978i	−0.351223	+	0.936292i	$0.614234\pi$
$674$		0			0
$675$	−4.25622	−	5.46827i	−0.163822	−	0.210474i
$676$		0			0
$677$		−	12.9710i		−	0.498518i	−0.968437	−	0.249259i	$-0.919813\pi$
$677$		−	12.9710i		−	0.498518i	0.968437	−	0.249259i	$-0.0801870\pi$
$678$		0			0
$679$	−31.8378	+	55.1446i	−1.22182	+	2.11626i
$680$		0			0
$681$	−4.68793			−0.179642
$682$		0			0
$683$	25.3910	−	14.6595i	0.971561	−	0.560931i	0.0718490	−	0.997416i	$-0.477110\pi$
$683$	25.3910	−	14.6595i	0.971561	−	0.560931i	0.899712	+	0.436485i	$0.143777\pi$
$684$		0			0
$685$	−9.44102	+	10.8406i	−0.360723	+	0.414200i
$686$		0			0
$687$	−2.53709	−	1.46479i	−0.0967959	−	0.0558852i
$688$		0			0
$689$	−4.08226	+	17.7186i	−0.155522	+	0.675023i
$690$		0			0
$691$	18.6079	−	32.2299i	0.707880	−	1.22608i	−0.257763	−	0.966208i	$-0.582985\pi$
$691$	18.6079	−	32.2299i	0.707880	−	1.22608i	0.965642	−	0.259875i	$-0.0836814\pi$
$692$		0			0
$693$	10.9442	−	6.31866i	0.415738	−	0.240026i
$694$		0			0
$695$	−25.2491	−	21.9892i	−0.957753	−	0.834098i
$696$		0			0
$697$		−	10.1775i		−	0.385502i
$698$		0			0
$699$	1.32528	−	2.29544i	0.0501265	−	0.0868217i
$700$		0			0
$701$	−49.9472			−1.88648			−0.943240	−	0.332113i	$-0.892238\pi$
$701$	−49.9472			−1.88648			−0.943240	+	0.332113i	$0.892238\pi$
$702$		0			0
$703$			15.3682i			0.579623i
$704$		0			0
$705$	−0.660304	+	3.38049i	−0.0248685	+	0.127317i
$706$		0			0
$707$		−	81.3994i		−	3.06134i
$708$		0			0
$709$	−15.2438	−	26.4030i	−0.572492	−	0.991585i	−0.996309	−	0.0858376i	$-0.972643\pi$
$709$	−15.2438	−	26.4030i	−0.572492	−	0.991585i	0.423817	−	0.905748i	$-0.360690\pi$
$710$		0			0
$711$	−16.7981	−	29.0952i	−0.629978	−	1.09115i
$712$		0			0
$713$	−30.9805	−	17.8866i	−1.16023	−	0.669859i
$714$		0			0
$715$	−3.28263	+	7.36372i	−0.122763	+	0.275387i
$716$		0			0
$717$	3.70440	+	2.13874i	0.138343	+	0.0798726i
$718$		0			0
$719$	0.816798	+	1.41474i	0.0304614	+	0.0527607i	0.880854	−	0.473388i	$-0.156969\pi$
$719$	0.816798	+	1.41474i	0.0304614	+	0.0527607i	−0.850393	+	0.526148i	$0.823636\pi$
$720$		0			0
$721$	−38.5676	−	66.8010i	−1.43633	−	2.48780i
$722$		0			0
$723$			0.321056i			0.0119402i
$724$		0			0
$725$	1.56881	+	11.3125i	0.0582640	+	0.420135i
$726$		0			0
$727$			17.7936i			0.659928i	0.943993	+	0.329964i	$0.107037\pi$
$727$			17.7936i			0.659928i	−0.943993	+	0.329964i	$0.892963\pi$
$728$		0			0
$729$	24.1102			0.892970
$730$		0			0
$731$	13.1832	−	22.8340i	0.487598	−	0.844545i
$732$		0			0
$733$			22.1438i			0.817901i	0.912557	+	0.408950i	$0.134105\pi$
$733$			22.1438i			0.817901i	−0.912557	+	0.408950i	$0.865895\pi$
$734$		0			0
$735$	−3.90408	+	4.48286i	−0.144004	+	0.165353i
$736$		0			0
$737$	−3.76176	+	2.17185i	−0.138566	+	0.0800013i
$738$		0			0
$739$	8.99228	−	15.5751i	0.330786	−	0.572939i	−0.651880	−	0.758322i	$-0.726019\pi$
$739$	8.99228	−	15.5751i	0.330786	−	0.572939i	0.982666	+	0.185383i	$0.0593527\pi$
$740$		0			0
$741$	−0.430988	+	1.87065i	−0.0158327	+	0.0687202i
$742$		0			0
$743$	13.2873	+	7.67144i	0.487465	+	0.281438i	0.723522	−	0.690301i	$-0.242522\pi$
$743$	13.2873	+	7.67144i	0.487465	+	0.281438i	−0.236057	+	0.971739i	$0.575855\pi$
$744$		0			0
$745$	−26.4562	−	23.0405i	−0.969280	−	0.844137i
$746$		0			0
$747$	25.5929	−	14.7761i	0.936395	−	0.540628i
$748$		0			0
$749$	19.6894			0.719437
$750$		0			0
$751$	19.1762	−	33.2142i	0.699751	−	1.21200i	−0.268802	−	0.963196i	$-0.586628\pi$
$751$	19.1762	−	33.2142i	0.699751	−	1.21200i	0.968553	−	0.248809i	$-0.0800391\pi$
$752$		0			0
$753$		−	5.88088i		−	0.214311i
$754$		0			0
$755$	−2.48604	+	0.853474i	−0.0904762	+	0.0310611i
$756$		0			0
$757$	−2.29135	−	1.32291i	−0.0832806	−	0.0480821i	0.457781	−	0.889065i	$-0.348644\pi$
$757$	−2.29135	−	1.32291i	−0.0832806	−	0.0480821i	−0.541062	+	0.840983i	$0.681978\pi$
$758$		0			0
$759$	1.33848			0.0485837
$760$		0			0
$761$	−12.3176	−	21.3346i	−0.446511	−	0.773380i	0.551645	−	0.834079i	$-0.314000\pi$
$761$	−12.3176	−	21.3346i	−0.446511	−	0.773380i	−0.998156	+	0.0606991i	$0.980667\pi$
$762$		0			0
$763$	0.548233	−	0.316523i	0.0198474	−	0.0114589i
$764$		0			0
$765$	−24.7201	−	4.82853i	−0.893758	−	0.174576i
$766$		0			0
$767$	11.7407	+	38.3405i	0.423933	+	1.38440i
$768$		0			0
$769$	−7.05509	+	12.2198i	−0.254413	+	0.440656i	−0.964736	−	0.263220i	$-0.915216\pi$
$769$	−7.05509	+	12.2198i	−0.254413	+	0.440656i	0.710323	+	0.703876i	$0.248549\pi$
$770$		0			0
$771$	3.54737	+	6.14423i	0.127755	+	0.221279i
$772$		0			0
$773$	13.1130	−	7.57081i	0.471643	−	0.272303i	−0.245284	−	0.969451i	$-0.578881\pi$
$773$	13.1130	−	7.57081i	0.471643	−	0.272303i	0.716927	+	0.697148i	$0.245548\pi$
$774$		0			0
$775$	24.5808	−	19.1324i	0.882968	−	0.687257i
$776$		0			0
$777$	−5.82679	−	3.36410i	−0.209035	−	0.120686i
$778$		0			0
$779$	6.07930			0.217814
$780$		0			0
$781$	6.74378			0.241311
$782$		0			0
$783$	2.74147	+	1.58279i	0.0979722	+	0.0565643i
$784$		0			0
$785$	3.96111	+	11.5381i	0.141378	+	0.411812i
$786$		0			0
$787$	27.7617	−	16.0282i	0.989597	−	0.571344i	0.0844431	−	0.996428i	$-0.473089\pi$
$787$	27.7617	−	16.0282i	0.989597	−	0.571344i	0.905154	+	0.425084i	$0.139756\pi$
$788$		0			0
$789$	0.378132	+	0.654944i	0.0134619	+	0.0233166i
$790$		0			0
$791$	−34.5536	+	59.8486i	−1.22859	+	2.12797i
$792$		0			0
$793$	4.40811	+	14.3951i	0.156537	+	0.511185i
$794$		0			0
$795$	−0.503889	+	2.57971i	−0.0178711	+	0.0914928i
$796$		0			0
$797$	−37.4537	+	21.6239i	−1.32668	+	0.765957i	−0.984784	−	0.173781i	$-0.944401\pi$
$797$	−37.4537	+	21.6239i	−1.32668	+	0.765957i	−0.341893	+	0.939739i	$0.611068\pi$
$798$		0			0
$799$	12.6351	+	21.8847i	0.446998	+	0.774224i
$800$		0			0
$801$	32.7592			1.15749
$802$		0			0
$803$	11.7517	+	6.78485i	0.414709	+	0.239432i
$804$		0			0
$805$	52.1010	−	17.8866i	1.83632	−	0.630421i
$806$		0			0
$807$		−	0.258422i		−	0.00909687i
$808$		0			0
$809$	−5.87737	+	10.1799i	−0.206637	+	0.357907i	−0.950653	−	0.310256i	$-0.899585\pi$
$809$	−5.87737	+	10.1799i	−0.206637	+	0.357907i	0.744016	+	0.668162i	$0.232919\pi$
$810$		0			0
$811$	−32.4068			−1.13796			−0.568979	−	0.822352i	$-0.692661\pi$
$811$	−32.4068			−1.13796			−0.568979	+	0.822352i	$0.692661\pi$
$812$		0			0
$813$	−6.09135	+	3.51684i	−0.213633	+	0.123341i
$814$		0			0
$815$	−6.81845	+	7.82928i	−0.238840	+	0.274248i
$816$		0			0
$817$	13.6393	+	7.87467i	0.477180	+	0.275500i
$818$		0			0
$819$	33.3378	+	31.0599i	1.16492	+	1.08532i
$820$		0			0
$821$	−16.0877	+	27.8648i	−0.561466	+	0.972488i	0.435903	+	0.899994i	$0.356429\pi$
$821$	−16.0877	+	27.8648i	−0.561466	+	0.972488i	−0.997369	+	0.0724940i	$0.976904\pi$
$822$		0			0
$823$	22.9608	−	13.2564i	0.800363	−	0.462090i	−0.0432348	−	0.999065i	$-0.513766\pi$
$823$	22.9608	−	13.2564i	0.800363	−	0.462090i	0.843598	+	0.536975i	$0.180433\pi$
$824$		0			0
$825$	−0.438563	+	1.07980i	−0.0152688	+	0.0375938i
$826$		0			0
$827$		−	50.5431i		−	1.75756i	−0.477229	−	0.878779i	$-0.658359\pi$
$827$		−	50.5431i		−	1.75756i	0.477229	−	0.878779i	$-0.341641\pi$
$828$		0			0
$829$	3.44567	−	5.96807i	0.119673	−	0.207280i	−0.799965	−	0.600047i	$-0.795149\pi$
$829$	3.44567	−	5.96807i	0.119673	−	0.207280i	0.919638	+	0.392767i	$0.128482\pi$
$830$		0			0
$831$	6.05433			0.210022
$832$		0			0
$833$			43.6133i			1.51111i
$834$		0			0
$835$	7.00275	+	1.36783i	0.242340	+	0.0473358i
$836$		0			0
$837$		−	8.63385i		−	0.298429i
$838$		0			0
$839$	−23.1134	−	40.0336i	−0.797964	−	1.38211i	−0.920940	−	0.389705i	$-0.872577\pi$
$839$	−23.1134	−	40.0336i	−0.797964	−	1.38211i	0.122975	−	0.992410i	$-0.460756\pi$
$840$		0			0
$841$	11.8913	+	20.5964i	0.410046	+	0.710221i
$842$		0			0
$843$	3.58968	+	2.07250i	0.123635	+	0.0713809i
$844$		0			0
$845$	−28.8522	−	3.54299i	−0.992545	−	0.121882i
$846$		0			0
$847$	37.1537	+	21.4507i	1.27662	+	0.737055i
$848$		0			0
$849$	−0.857926	−	1.48597i	−0.0294440	−	0.0509984i
$850$		0			0
$851$	19.3176	+	33.4590i	0.662197	+	1.14696i
$852$		0			0
$853$		−	17.3274i		−	0.593280i	−0.954989	−	0.296640i	$-0.904134\pi$
$853$		−	17.3274i		−	0.593280i	0.954989	−	0.296640i	$-0.0958661\pi$
$854$		0			0
$855$	2.88421	−	14.7660i	0.0986378	−	0.504986i
$856$		0			0
$857$		−	0.186033i		−	0.00635478i	−0.999995	−	0.00317739i	$-0.998989\pi$
$857$		−	0.186033i		−	0.00635478i	0.999995	−	0.00317739i	$-0.00101140\pi$
$858$		0			0
$859$	22.0947			0.753863			0.376931	−	0.926241i	$-0.376979\pi$
$859$	22.0947			0.753863			0.376931	+	0.926241i	$0.376979\pi$
$860$		0			0
$861$	−1.33076	+	2.30494i	−0.0453522	+	0.0785523i
$862$		0			0
$863$			17.5388i			0.597027i	0.954405	+	0.298514i	$0.0964908\pi$
$863$			17.5388i			0.597027i	−0.954405	+	0.298514i	$0.903509\pi$
$864$		0			0
$865$	5.09737	−	5.85305i	0.173316	−	0.199010i
$866$		0			0
$867$	−0.479906	+	0.277074i	−0.0162985	+	0.00940993i
$868$		0			0
$869$	−5.70265	+	9.87728i	−0.193449	+	0.335064i
$870$		0			0
$871$	−11.4589	−	10.6759i	−0.388269	−	0.361740i
$872$		0			0
$873$	37.8630	+	21.8602i	1.28147	+	0.739857i
$874$		0			0
$875$	−2.64148	+	47.8924i	−0.0892985	+	1.61906i
$876$		0			0
$877$	10.7590	−	6.21170i	0.363305	−	0.209754i	−0.307224	−	0.951637i	$-0.599400\pi$
$877$	10.7590	−	6.21170i	0.363305	−	0.209754i	0.670530	+	0.741883i	$0.266067\pi$
$878$		0			0
$879$	−3.91479			−0.132043
$880$		0			0
$881$	3.93171	−	6.80991i	0.132463	−	0.229432i	−0.792163	−	0.610310i	$-0.791045\pi$
$881$	3.93171	−	6.80991i	0.132463	−	0.229432i	0.924625	+	0.380878i	$0.124378\pi$
$882$		0			0
$883$		−	18.9717i		−	0.638450i	−0.947679	−	0.319225i	$-0.896577\pi$
$883$		−	18.9717i		−	0.638450i	0.947679	−	0.319225i	$-0.103423\pi$
$884$		0			0
$885$	1.88214	+	5.48239i	0.0632675	+	0.184288i
$886$		0			0
$887$	10.2459	+	5.91546i	0.344023	+	0.198622i	0.662049	−	0.749460i	$-0.269687\pi$
$887$	10.2459	+	5.91546i	0.344023	+	0.198622i	−0.318027	+	0.948082i	$0.603020\pi$
$888$		0			0
$889$	44.5264			1.49337
$890$		0			0
$891$	−4.25698	−	7.37331i	−0.142614	−	0.247015i
$892$		0			0
$893$	−13.0723	+	7.54728i	−0.437447	+	0.252560i
$894$		0			0
$895$	2.19526	−	11.2389i	0.0733795	−	0.375673i
$896$		0			0
$897$	1.41305	+	4.61445i	0.0471803	+	0.154072i
$898$		0			0
$899$	−7.11491	+	12.3234i	−0.237295	+	0.411008i
$900$		0			0
$901$	9.64207	+	16.7006i	0.321224	+	0.556376i
$902$		0			0
$903$	−5.97130	+	3.44753i	−0.198712	+	0.114727i
$904$		0			0
$905$	8.77170	−	3.01138i	0.291581	−	0.100102i
$906$		0			0
$907$	−5.16917	−	2.98442i	−0.171640	−	0.0990962i	0.411719	−	0.911311i	$-0.364928\pi$
$907$	−5.16917	−	2.98442i	−0.171640	−	0.0990962i	−0.583359	+	0.812215i	$0.698262\pi$
$908$		0			0
$909$	−55.8899			−1.85375
$910$		0			0
$911$	−29.7952			−0.987158			−0.493579	−	0.869701i	$-0.664312\pi$
$911$	−29.7952			−0.987158			−0.493579	+	0.869701i	$0.664312\pi$
$912$		0			0
$913$	−8.68832	−	5.01620i	−0.287541	−	0.166012i
$914$		0			0
$915$	0.706658	+	2.05839i	0.0233614	+	0.0680481i
$916$		0			0
$917$	65.5210	−	37.8285i	2.16369	−	1.24921i
$918$		0			0
$919$	12.0070	+	20.7967i	0.396074	+	0.686021i	0.993238	−	0.116099i	$-0.0370389\pi$
$919$	12.0070	+	20.7967i	0.396074	+	0.686021i	−0.597163	+	0.802120i	$0.703706\pi$
$920$		0			0
$921$	−0.364170	+	0.630760i	−0.0119998	+	0.0207843i
$922$		0			0
$923$	7.11949	+	23.2494i	0.234341	+	0.765263i
$924$		0			0
$925$	−33.3221	+	4.62109i	−1.09562	+	0.151940i
$926$		0			0
$927$	−45.8665	+	26.4810i	−1.50645	+	0.869751i
$928$		0			0
$929$	0.350207	+	0.606577i	0.0114899	+	0.0199011i	0.871713	−	0.490016i	$-0.163009\pi$
$929$	0.350207	+	0.606577i	0.0114899	+	0.0199011i	−0.860223	+	0.509918i	$0.829676\pi$
$930$		0			0
$931$	−26.0514			−0.853800
$932$		0			0
$933$	3.75612	+	2.16860i	0.122970	+	0.0709968i
$934$		0			0
$935$	2.77643	+	8.08731i	0.0907989	+	0.264483i
$936$		0			0
$937$		−	2.65849i		−	0.0868491i	−0.999057	−	0.0434246i	$-0.986173\pi$
$937$		−	2.65849i		−	0.0868491i	0.999057	−	0.0434246i	$-0.0138268\pi$
$938$		0			0
$939$	−2.04809	+	3.54739i	−0.0668369	+	0.115765i
$940$		0			0
$941$	−26.8370			−0.874861			−0.437431	−	0.899252i	$-0.644111\pi$
$941$	−26.8370			−0.874861			−0.437431	+	0.899252i	$0.644111\pi$
$942$		0			0
$943$	13.2356	−	7.64158i	0.431010	−	0.248844i
$944$		0			0
$945$	10.0258	+	8.73141i	0.326140	+	0.284033i
$946$		0			0
$947$	−0.0871459	−	0.0503137i	−0.00283186	−	0.00163498i	0.498583	−	0.866842i	$-0.333854\pi$
$947$	−0.0871459	−	0.0503137i	−0.00283186	−	0.00163498i	−0.501415	+	0.865207i	$0.667187\pi$
$948$		0			0
$949$	−10.9846	+	47.6772i	−0.356574	+	1.54767i
$950$		0			0
$951$	2.59470	−	4.49416i	0.0841390	−	0.145733i
$952$		0			0
$953$	47.4924	−	27.4197i	1.53843	−	0.888212i	0.539497	−	0.841987i	$-0.318614\pi$
$953$	47.4924	−	27.4197i	1.53843	−	0.888212i	0.998931	−	0.0462245i	$-0.0147190\pi$
$954$		0			0
$955$	1.36430	+	1.18816i	0.0441478	+	0.0384479i
$956$		0			0
$957$		−	0.532418i		−	0.0172106i
$958$		0			0
$959$	13.7904	−	23.8857i	0.445315	−	0.771308i
$960$		0			0
$961$	7.81060			0.251955
$962$		0			0
$963$		−	13.5190i		−	0.435645i
$964$		0			0
$965$	21.1393	+	4.12910i	0.680499	+	0.132920i
$966$		0			0
$967$			57.0788i			1.83553i	0.397123	+	0.917765i	$0.370009\pi$
$967$			57.0788i			1.83553i	−0.397123	+	0.917765i	$0.629991\pi$
$968$		0			0
$969$	1.01797	+	1.76318i	0.0327019	+	0.0566414i
$970$		0			0
$971$	−2.46735	−	4.27357i	−0.0791810	−	0.137146i	0.823716	−	0.567003i	$-0.191897\pi$
$971$	−2.46735	−	4.27357i	−0.0791810	−	0.137146i	−0.902897	+	0.429857i	$0.858564\pi$
$972$		0			0
$973$	55.6324	+	32.1194i	1.78349	+	1.02970i
$974$		0			0
$975$	−4.18564	−	0.372000i	−0.134048	−	0.0119135i
$976$		0			0
$977$	8.99957	+	5.19590i	0.287922	+	0.166232i	0.637004	−	0.770860i	$-0.280173\pi$
$977$	8.99957	+	5.19590i	0.287922	+	0.166232i	−0.349083	+	0.937092i	$0.613507\pi$
$978$		0			0
$979$	−5.56058	−	9.63120i	−0.177717	−	0.307814i
$980$		0			0
$981$	−0.217329	−	0.376424i	−0.00693877	−	0.0120183i
$982$		0			0
$983$			45.8531i			1.46249i	0.682117	+	0.731243i	$0.261059\pi$
$983$			45.8531i			1.46249i	−0.682117	+	0.731243i	$0.738941\pi$
$984$		0			0
$985$	−35.6421	−	6.96189i	−1.13565	−	0.221824i
$986$		0			0
$987$		−	6.60840i		−	0.210348i
$988$		0			0
$989$	39.5933			1.25899
$990$		0			0
$991$	−14.0070	+	24.2608i	−0.444947	+	0.770671i	−0.998049	−	0.0624430i	$-0.980111\pi$
$991$	−14.0070	+	24.2608i	−0.444947	+	0.770671i	0.553101	+	0.833114i	$0.313444\pi$
$992$		0			0
$993$			6.62107i			0.210113i
$994$		0			0
$995$	6.97529	+	6.07472i	0.221132	+	0.192581i
$996$		0			0
$997$	−10.4998	+	6.06204i	−0.332531	+	0.191987i	−0.656964	−	0.753922i	$-0.728160\pi$
$997$	−10.4998	+	6.06204i	−0.332531	+	0.191987i	0.324433	+	0.945909i	$0.394826\pi$
$998$		0			0
$999$	−4.66228	+	8.07530i	−0.147508	+	0.255491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.c.529.4		12
4.3	odd	2		260.2.ba.a.9.3	✓	12
5.4	even	2	inner	1040.2.dh.c.529.3		12
12.11	even	2		2340.2.de.a.2089.5		12
13.3	even	3	inner	1040.2.dh.c.289.3		12
20.3	even	4		1300.2.i.i.1101.4		12
20.7	even	4		1300.2.i.i.1101.3		12
20.19	odd	2		260.2.ba.a.9.4	yes	12
52.3	odd	6		260.2.ba.a.29.4	yes	12
52.7	even	12		3380.2.d.c.1689.7		12
52.19	even	12		3380.2.d.c.1689.8		12
52.35	odd	6		3380.2.c.a.2029.4		6
52.43	odd	6		3380.2.c.b.2029.4		6
60.59	even	2		2340.2.de.a.2089.6		12
65.29	even	6	inner	1040.2.dh.c.289.4		12
156.107	even	6		2340.2.de.a.289.5		12
260.3	even	12		1300.2.i.i.601.4		12
260.19	even	12		3380.2.d.c.1689.5		12
260.59	even	12		3380.2.d.c.1689.6		12
260.107	even	12		1300.2.i.i.601.3		12
260.139	odd	6		3380.2.c.a.2029.3		6
260.159	odd	6		260.2.ba.a.29.3	yes	12
260.199	odd	6		3380.2.c.b.2029.3		6
780.419	even	6		2340.2.de.a.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.ba.a.9.3	✓	12	4.3	odd	2
260.2.ba.a.9.4	yes	12	20.19	odd	2
260.2.ba.a.29.3	yes	12	260.159	odd	6
260.2.ba.a.29.4	yes	12	52.3	odd	6
1040.2.dh.c.289.3		12	13.3	even	3	inner
1040.2.dh.c.289.4		12	65.29	even	6	inner
1040.2.dh.c.529.3		12	5.4	even	2	inner
1040.2.dh.c.529.4		12	1.1	even	1	trivial
1300.2.i.i.601.3		12	260.107	even	12
1300.2.i.i.601.4		12	260.3	even	12
1300.2.i.i.1101.3		12	20.7	even	4
1300.2.i.i.1101.4		12	20.3	even	4
2340.2.de.a.289.5		12	156.107	even	6
2340.2.de.a.289.6		12	780.419	even	6
2340.2.de.a.2089.5		12	12.11	even	2
2340.2.de.a.2089.6		12	60.59	even	2
3380.2.c.a.2029.3		6	260.139	odd	6
3380.2.c.a.2029.4		6	52.35	odd	6
3380.2.c.b.2029.3		6	260.199	odd	6
3380.2.c.b.2029.4		6	52.43	odd	6
3380.2.d.c.1689.5		12	260.19	even	12
3380.2.d.c.1689.6		12	260.59	even	12
3380.2.d.c.1689.7		12	52.7	even	12
3380.2.d.c.1689.8		12	52.19	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +O(q^{10})\)	\(q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-3.51351 - 0.809492i) q^{13} +(-0.511544 - 0.0999188i) q^{15} +(-3.31164 + 1.91198i) q^{17} +(-1.14207 - 1.97813i) q^{19} +1.00000 q^{21} +(-4.97295 - 2.87113i) q^{23} +(3.94567 - 3.07111i) q^{25} -1.38589i q^{27} +(-1.14207 + 1.97813i) q^{29} +6.22982 q^{31} +(-0.201864 + 0.116546i) q^{33} +(-6.30021 + 7.23421i) q^{35} +(-5.82679 - 3.36410i) q^{37} +(-0.614908 - 0.572894i) q^{39} +(-1.33076 + 2.30494i) q^{41} +(-5.97130 + 3.44753i) q^{43} +(4.96711 + 4.32581i) q^{45} -6.60840i q^{47} +(5.70265 - 9.87728i) q^{49} -0.891336 q^{51} -5.04299i q^{53} +(0.428666 - 2.19459i) q^{55} -0.532418i q^{57} +(-5.56058 - 9.63120i) q^{59} +(-2.08774 - 3.61607i) q^{61} +(-10.9442 - 6.31866i) q^{63} +(8.01848 - 0.839022i) q^{65} +(3.76176 + 2.17185i) q^{67} +(-0.669240 - 1.15916i) q^{69} +(-3.37189 - 5.84028i) q^{71} -13.5697i q^{73} +(1.15442 - 0.160094i) q^{75} +4.29014i q^{77} +11.4053 q^{79} +(-4.25698 + 7.37331i) q^{81} +10.0324i q^{83} +(5.61560 - 6.44811i) q^{85} +(-0.461087 + 0.266209i) q^{87} +(-5.56058 + 9.63120i) q^{89} +(-14.7904 + 4.52915i) q^{91} +(1.25758 + 0.726062i) q^{93} +(3.85162 + 3.35434i) q^{95} +(-12.8538 + 7.42115i) q^{97} +2.94567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^9	\( 12 q + 4 q^{9} - 6 q^{11} - 10 q^{15} - 10 q^{19} + 12 q^{21} + 4 q^{25} - 10 q^{29} + 24 q^{31} + 6 q^{35} + 18 q^{39} + 2 q^{41} + 12 q^{45} - 4 q^{49} + 76 q^{51} + 2 q^{59} + 22 q^{61} - 40 q^{65} - 26 q^{69} + 14 q^{71} + 8 q^{75} - 8 q^{79} - 22 q^{81} + 14 q^{85} + 2 q^{89} - 58 q^{91} + 20 q^{95} - 8 q^{99}+O(q^{100}) \) 12 * q + 4 * q^9 - 6 * q^11 - 10 * q^15 - 10 * q^19 + 12 * q^21 + 4 * q^25 - 10 * q^29 + 24 * q^31 + 6 * q^35 + 18 * q^39 + 2 * q^41 + 12 * q^45 - 4 * q^49 + 76 * q^51 + 2 * q^59 + 22 * q^61 - 40 * q^65 - 26 * q^69 + 14 * q^71 + 8 * q^75 - 8 * q^79 - 22 * q^81 + 14 * q^85 + 2 * q^89 - 58 * q^91 + 20 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more