LMFDB - Embedded newform 1040.2.dh.c.529.3

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			529.3
Root			$-1.75675 + 1.01426i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.201864 - 0.116546i) q^{3} +(-2.11491 - 0.726062i) q^{5} +(-3.71537 + 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +O(q^{10})$	\(q+(-0.201864 - 0.116546i) q^{3} +(-2.11491 - 0.726062i) q^{5} +(-3.71537 + 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(3.51351 + 0.809492i) q^{13} +(0.342304 + 0.393051i) q^{15} +(3.31164 - 1.91198i) q^{17} +(-1.14207 - 1.97813i) q^{19} +1.00000 q^{21} +(4.97295 + 2.87113i) q^{23} +(3.94567 + 3.07111i) q^{25} +1.38589i q^{27} +(-1.14207 + 1.97813i) q^{29} +6.22982 q^{31} +(0.201864 - 0.116546i) q^{33} +(9.41512 - 1.83904i) q^{35} +(5.82679 + 3.36410i) q^{37} +(-0.614908 - 0.572894i) q^{39} +(-1.33076 + 2.30494i) q^{41} +(5.97130 - 3.44753i) q^{43} +(1.26271 + 6.46455i) q^{45} +6.60840i q^{47} +(5.70265 - 9.87728i) q^{49} -0.891336 q^{51} +5.04299i q^{53} +(1.68624 - 1.46853i) q^{55} +0.532418i q^{57} +(-5.56058 - 9.63120i) q^{59} +(-2.08774 - 3.61607i) q^{61} +(10.9442 + 6.31866i) q^{63} +(-6.84300 - 4.26302i) q^{65} +(-3.76176 - 2.17185i) q^{67} +(-0.669240 - 1.15916i) q^{69} +(-3.37189 - 5.84028i) q^{71} +13.5697i q^{73} +(-0.438563 - 1.07980i) q^{75} -4.29014i q^{77} +11.4053 q^{79} +(-4.25698 + 7.37331i) q^{81} -10.0324i q^{83} +(-8.39203 + 1.63920i) q^{85} +(0.461087 - 0.266209i) q^{87} +(-5.56058 + 9.63120i) q^{89} +(-14.7904 + 4.52915i) q^{91} +(-1.25758 - 0.726062i) q^{93} +(0.979135 + 5.01278i) q^{95} +(12.8538 - 7.42115i) q^{97} +2.94567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.440594	−	0.897707i	$-0.354768\pi$
$3$	−0.201864	−	0.116546i	−0.116546	−	0.0672881i	−0.557140	+	0.830419i	$0.688101\pi$
$4$		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	−0.994828	−	0.101573i	$-0.967613\pi$
$7$	−3.71537	+	2.14507i	−1.40428	+	0.810760i	−0.409450	+	0.912333i	$0.634279\pi$
$8$		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
$15$	0.342304	+	0.393051i	0.0883826	+	0.101485i
$16$		0			0
$17$	3.31164	−	1.91198i	0.803191	−	0.463723i	−0.0413947	−	0.999143i	$-0.513180\pi$
$17$	3.31164	−	1.91198i	0.803191	−	0.463723i	0.844586	+	0.535420i	$0.179847\pi$
$18$		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	0.918962	−	0.394345i	$-0.129028\pi$
$23$	4.97295	+	2.87113i	1.03693	+	0.598672i	0.117968	+	0.993017i	$0.462362\pi$
$24$		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
$35$	9.41512	−	1.83904i	1.59145	−	0.310854i
$36$		0			0
$37$	5.82679	+	3.36410i	0.957919	+	0.553055i	0.895532	−	0.444997i	$-0.146795\pi$
$37$	5.82679	+	3.36410i	0.957919	+	0.553055i	0.0623871	+	0.998052i	$0.480129\pi$
$38$		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	0.0299858	−	0.999550i	$-0.490454\pi$
$43$	5.97130	−	3.44753i	0.910615	−	0.525744i	0.880629	+	0.473807i	$0.157120\pi$
$44$		0			0
$45$	1.26271	+	6.46455i	0.188233	+	0.963678i
$46$		0			0
$47$			6.60840i			0.963934i	0.876189	+	0.481967i	$0.160078\pi$
$47$			6.60840i			0.963934i	−0.876189	+	0.481967i	$0.839922\pi$
$48$		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	$0.112580\pi$
$53$			5.04299i			0.692707i	−0.938104	+	0.346354i	$0.887420\pi$
$54$		0			0
$55$	1.68624	−	1.46853i	0.227373	−	0.198017i
$56$		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
$65$	−6.84300	−	4.26302i	−0.848769	−	0.528763i
$66$		0			0
$67$	−3.76176	−	2.17185i	−0.459572	−	0.265334i	0.252292	−	0.967651i	$-0.418816\pi$
$67$	−3.76176	−	2.17185i	−0.459572	−	0.265334i	−0.711864	+	0.702317i	$0.752149\pi$
$68$		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	$0.292061\pi$
$73$			13.5697i			1.58821i	−0.607779	+	0.794106i	$0.707939\pi$
$74$		0			0
$75$	−0.438563	−	1.07980i	−0.0506408	−	0.124685i
$76$		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	$-0.814399\pi$
$83$		−	10.0324i		−	1.10120i	0.834769	−	0.550600i	$-0.185601\pi$
$84$		0			0
$85$	−8.39203	+	1.63920i	−0.910243	+	0.177796i
$86$		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
$95$	0.979135	+	5.01278i	0.100457	+	0.514300i
$96$		0			0
$97$	12.8538	−	7.42115i	1.30511	−	0.753503i	0.323831	−	0.946115i	$-0.395029\pi$
$97$	12.8538	−	7.42115i	1.30511	−	0.753503i	0.981275	+	0.192611i	$0.0616957\pi$
$98$		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	$0.346385\pi$
$103$			17.9796i			1.77159i	−0.464080	+	0.885793i	$0.653615\pi$
$104$		0			0
$105$	−2.11491	−	0.726062i	−0.206394	−	0.0708564i
$106$		0			0
$107$	−3.97459	−	2.29473i	−0.384238	−	0.221840i	0.295422	−	0.955367i	$-0.404540\pi$
$107$	−3.97459	−	2.29473i	−0.384238	−	0.221840i	−0.679661	+	0.733527i	$0.737873\pi$
$108$		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	0.329849	−	0.944034i	$-0.393002\pi$
$113$	13.9503	−	8.05419i	1.31233	−	0.757675i	0.982482	+	0.186359i	$0.0596687\pi$
$114$		0			0
$115$	−8.43270	−	9.68285i	−0.786353	−	0.902930i
$116$		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	0.0450429	−	0.998985i	$-0.485658\pi$
$127$	−8.98829	−	5.18939i	−0.797582	−	0.460484i	−0.842625	+	0.538501i	$0.818991\pi$
$128$		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	−0.718610	−	0.695413i	$-0.755221\pi$
$137$	−5.56757	+	3.21444i	−0.475670	+	0.274628i	0.242940	+	0.970041i	$0.421888\pi$
$138$		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
$145$	3.85162	−	3.35434i	0.319860	−	0.278563i
$146$		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	$0.0698562\pi$
$157$			5.45560i			0.435405i	−0.976015	+	0.217702i	$0.930144\pi$
$158$		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	−0.649138	−	0.760670i	$-0.724870\pi$
$163$	−4.02098	+	2.32152i	−0.314948	+	0.181835i	0.334191	+	0.942506i	$0.391537\pi$
$164$		0			0
$165$	−0.511544	+	0.0999188i	−0.0398236	+	0.00777867i
$166$		0			0
$167$	2.76341	+	1.59545i	0.213839	+	0.123460i	0.603094	−	0.797670i	$-0.293934\pi$
$167$	2.76341	+	1.59545i	0.213839	+	0.123460i	−0.389255	+	0.921130i	$0.627268\pi$
$168$		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	−0.381356	−	0.924428i	$-0.624543\pi$
$173$	3.00603	−	1.73553i	0.228544	−	0.131950i	0.609900	+	0.792478i	$0.291210\pi$
$174$		0			0
$175$	−21.2474	−	2.94657i	−1.60615	−	0.222740i
$176$		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
$185$	−9.88058	−	11.3454i	−0.726435	−	0.834129i
$186$		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	0.769225	−	0.638978i	$-0.220642\pi$
$193$	8.34195	+	4.81623i	0.600466	+	0.346679i	−0.168759	+	0.985657i	$0.553976\pi$
$194$		0			0
$195$	0.884516	+	1.65808i	0.0633415	+	0.118737i
$196$		0			0
$197$	−14.0650	−	8.12043i	−1.00209	−	0.578556i	−0.0932234	−	0.995645i	$-0.529717\pi$
$197$	−14.0650	−	8.12043i	−1.00209	−	0.578556i	−0.908866	+	0.417089i	$0.863050\pi$
$198$		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
$205$	4.48797	−	3.90853i	0.313453	−	0.272984i
$206$		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
$215$	−15.1319	+	2.95568i	−1.03198	+	0.201575i
$216$		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	0.868522	−	0.495650i	$-0.165070\pi$
$223$	13.0447	+	7.53136i	0.873538	+	0.504337i	0.00501557	+	0.999987i	$0.498403\pi$
$224$		0			0
$225$	2.02315	−	14.5887i	0.134877	−	0.972581i
$226$		0			0
$227$	17.4174	−	10.0559i	1.15603	−	0.667436i	0.205683	−	0.978619i	$-0.434059\pi$
$227$	17.4174	−	10.0559i	1.15603	−	0.667436i	0.950350	+	0.311183i	$0.100725\pi$
$228$		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	$0.121492\pi$
$233$			11.3712i			0.744954i	−0.928041	+	0.372477i	$0.878508\pi$
$234$		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
$245$	−19.2321	+	16.7491i	−1.22869	+	1.07006i
$246$		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	$-0.935109\pi$
$257$	−26.3596	−	15.2187i	−1.64427	−	0.949318i	−0.664974	−	0.746866i	$-0.731557\pi$
$258$		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	0.410862	−	0.911697i	$-0.365228\pi$
$263$	−2.80980	−	1.62224i	−0.173260	−	0.100032i	−0.584122	+	0.811666i	$0.698561\pi$
$264$		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
$275$	−4.63249	+	1.88149i	−0.279350	+	0.113458i
$276$		0			0
$277$	−22.4941	+	12.9870i	−1.35154	+	0.780311i	−0.988465	−	0.151449i	$-0.951606\pi$
$277$	−22.4941	+	12.9870i	−1.35154	+	0.780311i	−0.363073	+	0.931761i	$0.618273\pi$
$278$		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	0.677364	−	0.735648i	$-0.263122\pi$
$283$	6.37503	+	3.68062i	0.378956	+	0.218790i	−0.298408	+	0.954438i	$0.596456\pi$
$284$		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	−0.0108351	−	0.999941i	$-0.503449\pi$
$293$	14.5449	−	8.39750i	0.849722	−	0.490587i	0.860557	+	0.509354i	$0.170116\pi$
$294$		0			0
$295$	4.76725	+	24.4064i	0.277560	+	1.42100i
$296$		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
$305$	1.78989	+	9.16349i	0.102489	+	0.524700i
$306$		0			0
$307$		−	3.12468i		−	0.178335i	−0.996017	−	0.0891674i	$-0.971579\pi$
$307$		−	3.12468i		−	0.178335i	0.996017	−	0.0891674i	$-0.0284206\pi$
$308$		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	$-0.834564\pi$
$313$		−	17.5732i		−	0.993295i	0.867952	−	0.496647i	$-0.165436\pi$
$314$		0			0
$315$	−18.5583	−	21.3096i	−1.04564	−	1.20066i
$316$		0			0
$317$			22.2633i			1.25043i	0.780453	+	0.625215i	$0.214989\pi$
$317$			22.2633i			1.25043i	−0.780453	+	0.625215i	$0.785011\pi$
$318$		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
$325$	11.3771	+	13.9843i	0.631087	+	0.775712i
$326$		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
$335$	6.37888	+	7.32454i	0.348515	+	0.400182i
$336$		0			0
$337$		−	8.87960i		−	0.483703i	−0.970313	−	0.241851i	$-0.922245\pi$
$337$		−	8.87960i		−	0.483703i	0.970313	−	0.241851i	$-0.0777547\pi$
$338$		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
$345$	0.573760	+	2.93742i	0.0308902	+	0.158145i
$346$		0			0
$347$	−14.9652	+	8.64018i	−0.803376	+	0.463829i	−0.844650	−	0.535319i	$-0.820192\pi$
$347$	−14.9652	+	8.64018i	−0.803376	+	0.463829i	0.0412745	+	0.999148i	$0.486858\pi$
$348$		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	0.999810	−	0.0195003i	$-0.00620753\pi$
$353$	27.8598	+	16.0849i	1.48283	+	0.856111i	0.483017	+	0.875611i	$0.339541\pi$
$354$		0			0
$355$	2.89083	+	14.7999i	0.153429	+	0.785495i
$356$		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	0.848961	−	0.528456i	$-0.177229\pi$
$367$	15.6282	+	9.02293i	0.815784	+	0.470993i	−0.0331762	+	0.999450i	$0.510562\pi$
$368$		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	−0.889511	−	0.456914i	$-0.848955\pi$
$373$	−18.1267	+	10.4655i	−0.938566	+	0.541882i	−0.0490558	+	0.998796i	$0.515621\pi$
$374$		0			0
$375$	0.143518	+	2.60210i	0.00741122	+	0.134372i
$376$		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	−0.984765	−	0.173889i	$-0.944367\pi$
$383$	−25.9612	+	14.9887i	−1.32656	+	0.765887i	−0.341790	+	0.939776i	$0.611033\pi$
$384$		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	−0.226632	−	0.973980i	$-0.572771\pi$
$397$	10.0330	−	5.79258i	0.503544	−	0.290721i	0.730176	+	0.683259i	$0.239438\pi$
$398$		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
$405$	14.3566	−	12.5030i	0.713385	−	0.621281i
$406$		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
$425$	18.9385	+	2.62638i	0.918653	+	0.127398i
$426$		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	−0.294312	−	0.955710i	$-0.595090\pi$
$433$	8.03633	−	4.63978i	0.386201	−	0.222974i	0.680513	+	0.732736i	$0.261757\pi$
$434$		0			0
$435$	−1.16844	+	0.228229i	−0.0560225	+	0.0109428i
$436$		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	$-0.847270\pi$
$443$		−	19.4318i		−	0.923231i	0.887080	−	0.461615i	$-0.152730\pi$
$444$		0			0
$445$	18.7530	−	16.3318i	0.888975	−	0.774200i
$446$		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
$455$	34.5688	+	1.16000i	1.62061	+	0.0543817i
$456$		0			0
$457$	16.9321	+	9.77578i	0.792053	+	0.457292i	0.840685	−	0.541525i	$-0.182153\pi$
$457$	16.9321	+	9.77578i	0.792053	+	0.457292i	−0.0486321	+	0.998817i	$0.515486\pi$
$458$		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	$0.233493\pi$
$463$			28.8119i			1.33900i	−0.742810	+	0.669502i	$0.766507\pi$
$464$		0			0
$465$	2.13249	+	2.44863i	0.0988919	+	0.113553i
$466$		0			0
$467$			24.8085i			1.14800i	0.818856	+	0.573999i	$0.194609\pi$
$467$			24.8085i			1.14800i	−0.818856	+	0.573999i	$0.805391\pi$
$468$		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
$475$	1.56881	−	11.3125i	0.0719818	−	0.519052i
$476$		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
$485$	−32.5728	+	6.36238i	−1.47906	+	0.288901i
$486$		0			0
$487$	15.8874	−	9.17260i	0.719927	−	0.415650i	−0.0947988	−	0.995496i	$-0.530221\pi$
$487$	15.8874	−	9.17260i	0.719927	−	0.415650i	0.814726	+	0.579846i	$0.196887\pi$
$488$		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	−0.0999391	−	0.994994i	$-0.531865\pi$
$503$	15.9636	−	9.21658i	0.711781	−	0.410947i	0.811720	+	0.584047i	$0.198531\pi$
$504$		0			0
$505$	−31.9941	+	27.8633i	−1.42372	+	1.23990i
$506$		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	0.969688	−	0.244346i	$-0.0785733\pi$
$523$	28.4246	+	16.4110i	1.24292	+	0.717601i	0.273234	+	0.961948i	$0.411907\pi$
$524$		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
$535$	6.73978	+	7.73895i	0.291386	+	0.334584i
$536$		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	$0.234728\pi$
$547$			31.4513i			1.34476i	−0.740207	+	0.672379i	$0.765272\pi$
$548$		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
$555$	0.672274	+	3.44177i	0.0285364	+	0.146095i
$556$		0			0
$557$	15.9636	+	9.21658i	0.676399	+	0.390519i	0.798497	−	0.601999i	$-0.205629\pi$
$557$	15.9636	+	9.21658i	0.676399	+	0.390519i	−0.122098	+	0.992518i	$0.538962\pi$
$558$		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	−0.668605	−	0.743617i	$-0.733108\pi$
$563$	−8.51624	+	4.91685i	−0.358917	+	0.207221i	0.309689	+	0.950838i	$0.399775\pi$
$564$		0			0
$565$	−35.3514	+	6.90511i	−1.48724	+	0.290500i
$566$		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
$575$	10.8040	+	26.6010i	0.450560	+	1.10934i
$576$		0			0
$577$		−	0.245757i		−	0.0102310i	−0.999987	−	0.00511550i	$-0.998372\pi$
$577$		−	0.245757i		−	0.0102310i	0.999987	−	0.00511550i	$-0.00162832\pi$
$578$		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
$585$	−0.796473	+	23.7354i	−0.0329301	+	0.981337i
$586$		0			0
$587$	15.9006	+	9.18021i	0.656287	+	0.378908i	0.790861	−	0.611996i	$-0.209633\pi$
$587$	15.9006	+	9.18021i	0.656287	+	0.378908i	−0.134573	+	0.990904i	$0.542966\pi$
$588$		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	$-0.859894\pi$
$593$		−	20.7514i		−	0.852159i	0.904686	−	0.426079i	$-0.140106\pi$
$594$		0			0
$595$	27.6633	−	24.0917i	1.13408	−	0.987664i
$596$		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
$605$	−4.28666	−	21.9459i	−0.174277	−	0.892230i
$606$		0			0
$607$	−22.3330	+	12.8939i	−0.906467	+	0.523349i	−0.879293	−	0.476281i	$-0.841984\pi$
$607$	−22.3330	+	12.8939i	−0.906467	+	0.523349i	−0.0271746	+	0.999631i	$0.508651\pi$
$608$		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	0.393440	−	0.919350i	$-0.371285\pi$
$613$	−5.10085	−	2.94498i	−0.206021	−	0.118946i	−0.599461	+	0.800404i	$0.704618\pi$
$614$		0			0
$615$	−1.36148	+	0.265936i	−0.0549004	+	0.0107236i
$616$		0			0
$617$	5.07106	−	2.92778i	0.204153	−	0.117868i	−0.394438	−	0.918923i	$-0.629061\pi$
$617$	5.07106	−	2.92778i	0.204153	−	0.117868i	0.598591	+	0.801055i	$0.295727\pi$
$618$		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
$635$	15.2416	+	17.5011i	0.604844	+	0.694512i
$636$		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	0.0316144	−	0.999500i	$-0.489935\pi$
$643$	23.1517	−	13.3666i	0.913014	−	0.527129i	0.881400	+	0.472371i	$0.156602\pi$
$644$		0			0
$645$	3.39905	+	1.16692i	0.133838	+	0.0459474i
$646$		0			0
$647$	−19.8974	−	11.4878i	−0.782248	−	0.451631i	0.0549781	−	0.998488i	$-0.482491\pi$
$647$	−19.8974	−	11.4878i	−0.782248	−	0.451631i	−0.837227	+	0.546856i	$0.815824\pi$
$648$		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	0.167070	−	0.985945i	$-0.446570\pi$
$653$	−15.4153	−	8.90006i	−0.603249	−	0.348286i	−0.770319	+	0.637659i	$0.779903\pi$
$654$		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
$665$	−14.3906	−	16.5240i	−0.558044	−	0.640774i
$666$		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	0.351223	−	0.936292i	$-0.385766\pi$
$673$	−7.36805	−	4.25395i	−0.284017	−	0.163978i	−0.635241	+	0.772314i	$0.719099\pi$
$674$		0			0
$675$	−4.25622	+	5.46827i	−0.163822	+	0.210474i
$676$		0			0
$677$			12.9710i			0.498518i	0.968437	+	0.249259i	$0.0801870\pi$
$677$			12.9710i			0.498518i	−0.968437	+	0.249259i	$0.919813\pi$
$678$		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	−0.899712	−	0.436485i	$-0.856223\pi$
$683$	−25.3910	+	14.6595i	−0.971561	+	0.560931i	−0.0718490	+	0.997416i	$0.522890\pi$
$684$		0			0
$685$	14.1088	−	2.75584i	0.539069	−	0.105295i
$686$		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
$695$	−6.41866	−	32.8610i	−0.243474	−	1.24649i
$696$		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
$705$	−2.59744	+	2.26208i	−0.0978251	+	0.0851950i
$706$		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
$715$	7.11339	−	3.79470i	0.266026	−	0.141914i
$716$		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
$725$	−10.5813	+	4.29761i	−0.392979	+	0.159609i
$726$		0			0
$727$		−	17.7936i		−	0.659928i	−0.943993	−	0.329964i	$-0.892963\pi$
$727$		−	17.7936i		−	0.659928i	0.943993	−	0.329964i	$-0.107037\pi$
$728$		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	$-0.865895\pi$
$733$		−	22.1438i		−	0.817901i	0.912557	−	0.408950i	$-0.134105\pi$
$734$		0			0
$735$	5.83431	−	1.13960i	0.215202	−	0.0420349i
$736$		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	0.236057	−	0.971739i	$-0.424145\pi$
$743$	−13.2873	−	7.67144i	−0.487465	−	0.281438i	−0.723522	+	0.690301i	$0.757478\pi$
$744$		0			0
$745$	−6.72553	−	34.4320i	−0.246404	−	1.26149i
$746$		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	0.541062	−	0.840983i	$-0.318022\pi$
$757$	2.29135	+	1.32291i	0.0832806	+	0.0480821i	−0.457781	+	0.889065i	$0.651356\pi$
$758$		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
$765$	16.5417	+	18.9940i	0.598066	+	0.686729i
$766$		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	−0.716927	−	0.697148i	$-0.754452\pi$
$773$	−13.1130	+	7.57081i	−0.471643	+	0.272303i	0.245284	+	0.969451i	$0.421119\pi$
$774$		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	−0.905154	−	0.425084i	$-0.860244\pi$
$787$	−27.7617	+	16.0282i	−0.989597	+	0.571344i	−0.0844431	+	0.996428i	$0.526911\pi$
$788$		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
$795$	−1.98215	+	1.72624i	−0.0702996	+	0.0612232i
$796$		0			0
$797$	37.4537	−	21.6239i	1.32668	−	0.765957i	0.341893	−	0.939739i	$-0.388932\pi$
$797$	37.4537	−	21.6239i	1.32668	−	0.765957i	0.984784	+	0.173781i	$0.0555986\pi$
$798$		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
$815$	10.1896	−	1.99031i	0.356925	−	0.0697175i
$816$		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	−0.843598	−	0.536975i	$-0.819567\pi$
$823$	−22.9608	+	13.2564i	−0.800363	+	0.462090i	0.0432348	+	0.999065i	$0.486234\pi$
$824$		0			0
$825$	1.15442	+	0.160094i	0.0401916	+	0.00557374i
$826$		0			0
$827$			50.5431i			1.75756i	0.477229	+	0.878779i	$0.341641\pi$
$827$			50.5431i			1.75756i	−0.477229	+	0.878779i	$0.658359\pi$
$828$		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
$835$	−4.68595	−	5.38064i	−0.162164	−	0.186205i
$836$		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
$845$	−20.5920	−	20.5175i	−0.708387	−	0.705824i
$846$		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	$0.0958661\pi$
$853$			17.3274i			0.593280i	−0.954989	+	0.296640i	$0.904134\pi$
$854$		0			0
$855$	11.3456	−	9.88079i	0.388012	−	0.337916i
$856$		0			0
$857$			0.186033i			0.00635478i	0.999995	+	0.00317739i	$0.00101140\pi$
$857$			0.186033i			0.00635478i	−0.999995	+	0.00317739i	$0.998989\pi$
$858$		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	$-0.903509\pi$
$863$		−	17.5388i		−	0.597027i	0.954405	−	0.298514i	$-0.0964908\pi$
$864$		0			0
$865$	−7.61757	+	1.48792i	−0.259005	+	0.0505909i
$866$		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
$875$	42.7968	+	21.6586i	1.44680	+	0.732195i
$876$		0			0
$877$	−10.7590	+	6.21170i	−0.363305	+	0.209754i	−0.670530	−	0.741883i	$-0.733933\pi$
$877$	−10.7590	+	6.21170i	−0.363305	+	0.209754i	0.307224	+	0.951637i	$0.400600\pi$
$878$		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	$0.103423\pi$
$883$			18.9717i			0.638450i	−0.947679	+	0.319225i	$0.896577\pi$
$884$		0			0
$885$	1.88214	−	5.48239i	0.0632675	−	0.184288i
$886$		0			0
$887$	−10.2459	−	5.91546i	−0.344023	−	0.198622i	0.318027	−	0.948082i	$-0.396980\pi$
$887$	−10.2459	−	5.91546i	−0.344023	−	0.198622i	−0.662049	+	0.749460i	$0.730313\pi$
$888$		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
$895$	8.63550	−	7.52058i	0.288653	−	0.251385i
$896$		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	0.583359	−	0.812215i	$-0.301738\pi$
$907$	5.16917	+	2.98442i	0.171640	+	0.0990962i	−0.411719	+	0.911311i	$0.635072\pi$
$908$		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
$925$	12.6591	+	31.1683i	0.416228	+	1.02481i
$926$		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	$0.0138268\pi$
$937$			2.65849i			0.0868491i	−0.999057	+	0.0434246i	$0.986173\pi$
$938$		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
$945$	2.54870	+	13.0483i	0.0829093	+	0.424462i
$946$		0			0
$947$	0.0871459	+	0.0503137i	0.00283186	+	0.00163498i	0.501415	−	0.865207i	$-0.332813\pi$
$947$	0.0871459	+	0.0503137i	0.00283186	+	0.00163498i	−0.498583	+	0.866842i	$0.666146\pi$
$948$		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	$0.681386\pi$
$953$	−47.4924	+	27.4197i	−1.53843	+	0.888212i	−0.998931	+	0.0462245i	$0.985281\pi$
$954$		0			0
$955$	0.346824	+	1.77560i	0.0112230	+	0.0574571i
$956$		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
$965$	−14.1456	−	16.2426i	−0.455362	−	0.522869i
$966$		0			0
$967$		−	57.0788i		−	1.83553i	−0.397123	−	0.917765i	$-0.629991\pi$
$967$		−	57.0788i		−	1.83553i	0.397123	−	0.917765i	$-0.370009\pi$
$968$		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
$975$	−0.666803	−	4.14890i	−0.0213548	−	0.132871i
$976$		0			0
$977$	−8.99957	−	5.19590i	−0.287922	−	0.166232i	0.349083	−	0.937092i	$-0.386493\pi$
$977$	−8.99957	−	5.19590i	−0.287922	−	0.166232i	−0.637004	+	0.770860i	$0.719827\pi$
$978$		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	$-0.738941\pi$
$983$		−	45.8531i		−	1.46249i	0.682117	−	0.731243i	$-0.261059\pi$
$984$		0			0
$985$	23.8502	+	27.3860i	0.759931	+	0.872591i
$986$		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
$995$	1.77321	+	9.07814i	0.0562146	+	0.287796i
$996$		0			0
$997$	10.4998	−	6.06204i	0.332531	−	0.191987i	−0.324433	−	0.945909i	$-0.605174\pi$
$997$	10.4998	−	6.06204i	0.332531	−	0.191987i	0.656964	+	0.753922i	$0.271840\pi$
$998$		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.529.3		12
4.3	odd	2		260.2.ba.a.9.4	yes	12
5.4	even	2	inner	1040.2.dh.c.529.4		12
12.11	even	2		2340.2.de.a.2089.6		12
13.3	even	3	inner	1040.2.dh.c.289.4		12
20.3	even	4		1300.2.i.i.1101.3		12
20.7	even	4		1300.2.i.i.1101.4		12
20.19	odd	2		260.2.ba.a.9.3	✓	12
52.3	odd	6		260.2.ba.a.29.3	yes	12
52.7	even	12		3380.2.d.c.1689.6		12
52.19	even	12		3380.2.d.c.1689.5		12
52.35	odd	6		3380.2.c.a.2029.3		6
52.43	odd	6		3380.2.c.b.2029.3		6
60.59	even	2		2340.2.de.a.2089.5		12
65.29	even	6	inner	1040.2.dh.c.289.3		12
156.107	even	6		2340.2.de.a.289.6		12
260.3	even	12		1300.2.i.i.601.3		12
260.19	even	12		3380.2.d.c.1689.8		12
260.59	even	12		3380.2.d.c.1689.7		12
260.107	even	12		1300.2.i.i.601.4		12
260.139	odd	6		3380.2.c.a.2029.4		6
260.159	odd	6		260.2.ba.a.29.4	yes	12
260.199	odd	6		3380.2.c.b.2029.4		6
780.419	even	6		2340.2.de.a.289.5		12

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

\(f(q)\)	\(=\)	\(q+(-0.201864 - 0.116546i) q^{3} +(-2.11491 - 0.726062i) q^{5} +(-3.71537 + 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +O(q^{10})\)	\(q+(-0.201864 - 0.116546i) q^{3} +(-2.11491 - 0.726062i) q^{5} +(-3.71537 + 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(3.51351 + 0.809492i) q^{13} +(0.342304 + 0.393051i) q^{15} +(3.31164 - 1.91198i) q^{17} +(-1.14207 - 1.97813i) q^{19} +1.00000 q^{21} +(4.97295 + 2.87113i) q^{23} +(3.94567 + 3.07111i) q^{25} +1.38589i q^{27} +(-1.14207 + 1.97813i) q^{29} +6.22982 q^{31} +(0.201864 - 0.116546i) q^{33} +(9.41512 - 1.83904i) q^{35} +(5.82679 + 3.36410i) q^{37} +(-0.614908 - 0.572894i) q^{39} +(-1.33076 + 2.30494i) q^{41} +(5.97130 - 3.44753i) q^{43} +(1.26271 + 6.46455i) q^{45} +6.60840i q^{47} +(5.70265 - 9.87728i) q^{49} -0.891336 q^{51} +5.04299i q^{53} +(1.68624 - 1.46853i) q^{55} +0.532418i q^{57} +(-5.56058 - 9.63120i) q^{59} +(-2.08774 - 3.61607i) q^{61} +(10.9442 + 6.31866i) q^{63} +(-6.84300 - 4.26302i) q^{65} +(-3.76176 - 2.17185i) q^{67} +(-0.669240 - 1.15916i) q^{69} +(-3.37189 - 5.84028i) q^{71} +13.5697i q^{73} +(-0.438563 - 1.07980i) q^{75} -4.29014i q^{77} +11.4053 q^{79} +(-4.25698 + 7.37331i) q^{81} -10.0324i q^{83} +(-8.39203 + 1.63920i) q^{85} +(0.461087 - 0.266209i) q^{87} +(-5.56058 + 9.63120i) q^{89} +(-14.7904 + 4.52915i) q^{91} +(-1.25758 - 0.726062i) q^{93} +(0.979135 + 5.01278i) q^{95} +(12.8538 - 7.42115i) q^{97} +2.94567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{9}+O(q^{10}) \) 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

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