LMFDB - Embedded newform 960.3.q.a.79.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(79,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("960.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.q (of order $4$, 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:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			79.20
Character	$\chi$	$=$	960.79
Dual form			960.3.q.a.559.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(-0.338767 + 4.98851i) q^{5} -7.33616i q^{7} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{3} +(-0.338767 + 4.98851i) q^{5} -7.33616i q^{7} -3.00000i q^{9} +(-1.75348 + 1.75348i) q^{11} +(5.95935 + 5.95935i) q^{13} +(-5.69475 - 6.52456i) q^{15} -11.3727i q^{17} +(20.6103 + 20.6103i) q^{19} +(8.98493 + 8.98493i) q^{21} -3.57450i q^{23} +(-24.7705 - 3.37989i) q^{25} +(3.67423 + 3.67423i) q^{27} +(28.6633 - 28.6633i) q^{29} +47.3451i q^{31} -4.29513i q^{33} +(36.5965 + 2.48525i) q^{35} +(-33.3502 + 33.3502i) q^{37} -14.5974 q^{39} +37.3695i q^{41} +(-6.45740 - 6.45740i) q^{43} +(14.9655 + 1.01630i) q^{45} +36.5378 q^{47} -4.81925 q^{49} +(13.9286 + 13.9286i) q^{51} +(8.61615 - 8.61615i) q^{53} +(-8.15323 - 9.34127i) q^{55} -50.4847 q^{57} +(-9.17960 + 9.17960i) q^{59} +(-66.1829 + 66.1829i) q^{61} -22.0085 q^{63} +(-31.7471 + 27.7094i) q^{65} +(14.8238 - 14.8238i) q^{67} +(4.37785 + 4.37785i) q^{69} -8.19449 q^{71} -100.342 q^{73} +(34.4770 - 26.1980i) q^{75} +(12.8638 + 12.8638i) q^{77} +49.4801i q^{79} -9.00000 q^{81} +(-106.446 + 106.446i) q^{83} +(56.7326 + 3.85268i) q^{85} +70.2103i q^{87} -117.584i q^{89} +(43.7187 - 43.7187i) q^{91} +(-57.9856 - 57.9856i) q^{93} +(-109.797 + 95.8326i) q^{95} +92.3995i q^{97} +(5.26044 + 5.26044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 32 q^{19} - 96 q^{35} - 672 q^{49} + 96 q^{51} - 256 q^{55} - 128 q^{59} - 32 q^{61} + 32 q^{65} - 96 q^{69} - 512 q^{71} + 192 q^{75} - 864 q^{81} + 384 q^{91}+O(q^{100}) $ 96 * q - 32 * q^19 - 96 * q^35 - 672 * q^49 + 96 * q^51 - 256 * q^55 - 128 * q^59 - 32 * q^61 + 32 * q^65 - 96 * q^69 - 512 * q^71 + 192 * q^75 - 864 * q^81 + 384 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.338767	+	4.98851i	−0.0677534	+	0.997702i
$5$	−0.338767	+	4.98851i	−0.0677534	+	0.997702i
$6$		0			0
$7$		−	7.33616i		−	1.04802i	−0.851711	−	0.524011i	$-0.824435\pi$
$7$		−	7.33616i		−	1.04802i	0.851711	−	0.524011i	$-0.175565\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−1.75348	+	1.75348i	−0.159407	+	0.159407i	−0.782304	−	0.622897i	$-0.785956\pi$
$11$	−1.75348	+	1.75348i	−0.159407	+	0.159407i	0.622897	+	0.782304i	$0.285956\pi$
$12$		0			0
$13$	5.95935	+	5.95935i	0.458411	+	0.458411i	0.898134	−	0.439722i	$-0.144923\pi$
$13$	5.95935	+	5.95935i	0.458411	+	0.458411i	−0.439722	+	0.898134i	$0.644923\pi$
$14$		0			0
$15$	−5.69475	−	6.52456i	−0.379650	−	0.434970i
$16$		0			0
$17$		−	11.3727i		−	0.668980i	−0.942399	−	0.334490i	$-0.891436\pi$
$17$		−	11.3727i		−	0.668980i	0.942399	−	0.334490i	$-0.108564\pi$
$18$		0			0
$19$	20.6103	+	20.6103i	1.08475	+	1.08475i	0.996059	+	0.0886939i	$0.0282693\pi$
$19$	20.6103	+	20.6103i	1.08475	+	1.08475i	0.0886939	+	0.996059i	$0.471731\pi$
$20$		0			0
$21$	8.98493	+	8.98493i	0.427854	+	0.427854i
$22$		0			0
$23$		−	3.57450i		−	0.155413i	−0.996976	−	0.0777065i	$-0.975240\pi$
$23$		−	3.57450i		−	0.155413i	0.996976	−	0.0777065i	$-0.0247597\pi$
$24$		0			0
$25$	−24.7705	−	3.37989i	−0.990819	−	0.135195i
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$	28.6633	−	28.6633i	0.988388	−	0.988388i	−0.0115453	−	0.999933i	$-0.503675\pi$
$29$	28.6633	−	28.6633i	0.988388	−	0.988388i	0.999933	+	0.0115453i	$0.00367507\pi$
$30$		0			0
$31$			47.3451i			1.52726i	0.645654	+	0.763630i	$0.276585\pi$
$31$			47.3451i			1.52726i	−0.645654	+	0.763630i	$0.723415\pi$
$32$		0			0
$33$		−	4.29513i		−	0.130155i
$34$		0			0
$35$	36.5965	+	2.48525i	1.04561	+	0.0710071i
$36$		0			0
$37$	−33.3502	+	33.3502i	−0.901356	+	0.901356i	−0.995553	−	0.0941979i	$-0.969971\pi$
$37$	−33.3502	+	33.3502i	−0.901356	+	0.901356i	0.0941979	+	0.995553i	$0.469971\pi$
$38$		0			0
$39$	−14.5974			−0.374291
$40$		0			0
$41$			37.3695i			0.911451i	0.890120	+	0.455725i	$0.150620\pi$
$41$			37.3695i			0.911451i	−0.890120	+	0.455725i	$0.849380\pi$
$42$		0			0
$43$	−6.45740	−	6.45740i	−0.150172	−	0.150172i	0.628023	−	0.778195i	$-0.283864\pi$
$43$	−6.45740	−	6.45740i	−0.150172	−	0.150172i	−0.778195	+	0.628023i	$0.783864\pi$
$44$		0			0
$45$	14.9655	+	1.01630i	0.332567	+	0.0225845i
$46$		0			0
$47$	36.5378			0.777401			0.388701	−	0.921364i	$-0.372924\pi$
$47$	36.5378			0.777401			0.388701	+	0.921364i	$0.372924\pi$
$48$		0			0
$49$	−4.81925			−0.0983521
$50$		0			0
$51$	13.9286	+	13.9286i	0.273110	+	0.273110i
$52$		0			0
$53$	8.61615	−	8.61615i	0.162569	−	0.162569i	−0.621135	−	0.783704i	$-0.713328\pi$
$53$	8.61615	−	8.61615i	0.162569	−	0.162569i	0.783704	+	0.621135i	$0.213328\pi$
$54$		0			0
$55$	−8.15323	−	9.34127i	−0.148240	−	0.169841i
$56$		0			0
$57$	−50.4847			−0.885697
$58$		0			0
$59$	−9.17960	+	9.17960i	−0.155587	+	0.155587i	−0.780608	−	0.625021i	$-0.785090\pi$
$59$	−9.17960	+	9.17960i	−0.155587	+	0.155587i	0.625021	+	0.780608i	$0.285090\pi$
$60$		0			0
$61$	−66.1829	+	66.1829i	−1.08497	+	1.08497i	−0.0889271	+	0.996038i	$0.528344\pi$
$61$	−66.1829	+	66.1829i	−1.08497	+	1.08497i	−0.996038	+	0.0889271i	$0.971656\pi$
$62$		0			0
$63$	−22.0085			−0.349341
$64$		0			0
$65$	−31.7471	+	27.7094i	−0.488417	+	0.426299i
$66$		0			0
$67$	14.8238	−	14.8238i	0.221251	−	0.221251i	−0.587774	−	0.809025i	$-0.699996\pi$
$67$	14.8238	−	14.8238i	0.221251	−	0.221251i	0.809025	+	0.587774i	$0.199996\pi$
$68$		0			0
$69$	4.37785	+	4.37785i	0.0634471	+	0.0634471i
$70$		0			0
$71$	−8.19449			−0.115415			−0.0577076	−	0.998334i	$-0.518379\pi$
$71$	−8.19449			−0.115415			−0.0577076	+	0.998334i	$0.518379\pi$
$72$		0			0
$73$	−100.342			−1.37455			−0.687276	−	0.726397i	$-0.741194\pi$
$73$	−100.342			−1.37455			−0.687276	+	0.726397i	$0.741194\pi$
$74$		0			0
$75$	34.4770	−	26.1980i	0.459693	−	0.349307i
$76$		0			0
$77$	12.8638	+	12.8638i	0.167062	+	0.167062i
$78$		0			0
$79$			49.4801i			0.626330i	0.949699	+	0.313165i	$0.101389\pi$
$79$			49.4801i			0.626330i	−0.949699	+	0.313165i	$0.898611\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−106.446	+	106.446i	−1.28248	+	1.28248i	−0.343235	+	0.939250i	$0.611523\pi$
$83$	−106.446	+	106.446i	−1.28248	+	1.28248i	−0.939250	+	0.343235i	$0.888477\pi$
$84$		0			0
$85$	56.7326	+	3.85268i	0.667443	+	0.0453257i
$86$		0			0
$87$			70.2103i			0.807015i
$88$		0			0
$89$		−	117.584i		−	1.32117i	−0.750751	−	0.660586i	$-0.770308\pi$
$89$		−	117.584i		−	1.32117i	0.750751	−	0.660586i	$-0.229692\pi$
$90$		0			0
$91$	43.7187	−	43.7187i	0.480426	−	0.480426i
$92$		0			0
$93$	−57.9856	−	57.9856i	−0.623501	−	0.623501i
$94$		0			0
$95$	−109.797	+	95.8326i	−1.15576	+	1.00876i
$96$		0			0
$97$			92.3995i			0.952572i	0.879290	+	0.476286i	$0.158017\pi$
$97$			92.3995i			0.952572i	−0.879290	+	0.476286i	$0.841983\pi$
$98$		0			0
$99$	5.26044	+	5.26044i	0.0531357	+	0.0531357i
$100$		0			0
$101$	50.8659	+	50.8659i	0.503623	+	0.503623i	0.912562	−	0.408939i	$-0.134101\pi$
$101$	50.8659	+	50.8659i	0.503623	+	0.503623i	−0.408939	+	0.912562i	$0.634101\pi$
$102$		0			0
$103$			186.034i			1.80615i	0.429480	+	0.903077i	$0.358697\pi$
$103$			186.034i			1.80615i	−0.429480	+	0.903077i	$0.641303\pi$
$104$		0			0
$105$	−47.8652	+	41.7776i	−0.455859	+	0.397882i
$106$		0			0
$107$	−110.979	−	110.979i	−1.03719	−	1.03719i	−0.999281	−	0.0379071i	$-0.987931\pi$
$107$	−110.979	−	110.979i	−1.03719	−	1.03719i	−0.0379071	−	0.999281i	$-0.512069\pi$
$108$		0			0
$109$	−91.4880	+	91.4880i	−0.839340	+	0.839340i	−0.988772	−	0.149432i	$-0.952255\pi$
$109$	−91.4880	+	91.4880i	−0.839340	+	0.839340i	0.149432	+	0.988772i	$0.452255\pi$
$110$		0			0
$111$		−	81.6909i		−	0.735954i
$112$		0			0
$113$			28.9812i			0.256471i	0.991744	+	0.128235i	$0.0409313\pi$
$113$			28.9812i			0.256471i	−0.991744	+	0.128235i	$0.959069\pi$
$114$		0			0
$115$	17.8314	+	1.21092i	0.155056	+	0.0105298i
$116$		0			0
$117$	17.8780	−	17.8780i	0.152804	−	0.152804i
$118$		0			0
$119$	−83.4317			−0.701106
$120$		0			0
$121$			114.851i			0.949179i
$122$		0			0
$123$	−45.7681	−	45.7681i	−0.372098	−	0.372098i
$124$		0			0
$125$	25.2520	−	122.423i	0.202016	−	0.979382i
$126$		0			0
$127$	144.324			1.13641			0.568204	−	0.822888i	$-0.307639\pi$
$127$	144.324			1.13641			0.568204	+	0.822888i	$0.307639\pi$
$128$		0			0
$129$	15.8173			0.122615
$130$		0			0
$131$	105.140	+	105.140i	0.802593	+	0.802593i	0.983500	−	0.180908i	$-0.0579035\pi$
$131$	105.140	+	105.140i	0.802593	+	0.802593i	−0.180908	+	0.983500i	$0.557903\pi$
$132$		0			0
$133$	151.200	−	151.200i	1.13685	−	1.13685i
$134$		0			0
$135$	−19.5737	+	17.0842i	−0.144990	+	0.126550i
$136$		0			0
$137$	−22.0936			−0.161267			−0.0806337	−	0.996744i	$-0.525694\pi$
$137$	−22.0936			−0.161267			−0.0806337	+	0.996744i	$0.525694\pi$
$138$		0			0
$139$	74.4843	−	74.4843i	0.535859	−	0.535859i	−0.386451	−	0.922310i	$-0.626299\pi$
$139$	74.4843	−	74.4843i	0.535859	−	0.535859i	0.922310	+	0.386451i	$0.126299\pi$
$140$		0			0
$141$	−44.7495	+	44.7495i	−0.317373	+	0.317373i
$142$		0			0
$143$	−20.8992			−0.146148
$144$		0			0
$145$	133.277	+	152.697i	0.919150	+	1.05308i
$146$		0			0
$147$	5.90236	−	5.90236i	0.0401521	−	0.0401521i
$148$		0			0
$149$	141.554	+	141.554i	0.950027	+	0.950027i	0.998809	−	0.0487822i	$-0.0155340\pi$
$149$	141.554	+	141.554i	0.950027	+	0.950027i	−0.0487822	+	0.998809i	$0.515534\pi$
$150$		0			0
$151$	27.0692			0.179266			0.0896332	−	0.995975i	$-0.471431\pi$
$151$	27.0692			0.179266			0.0896332	+	0.995975i	$0.471431\pi$
$152$		0			0
$153$	−34.1180			−0.222993
$154$		0			0
$155$	−236.181	−	16.0389i	−1.52375	−	0.103477i
$156$		0			0
$157$	185.089	+	185.089i	1.17891	+	1.17891i	0.980021	+	0.198892i	$0.0637343\pi$
$157$	185.089	+	185.089i	1.17891	+	1.17891i	0.198892	+	0.980021i	$0.436266\pi$
$158$		0			0
$159$			21.1052i			0.132737i
$160$		0			0
$161$	−26.2231			−0.162876
$162$		0			0
$163$	41.0433	−	41.0433i	0.251799	−	0.251799i	−0.569909	−	0.821708i	$-0.693021\pi$
$163$	41.0433	−	41.0433i	0.251799	−	0.251799i	0.821708	+	0.569909i	$0.193021\pi$
$164$		0			0
$165$	21.4263	+	1.45505i	0.129856	+	0.00881847i
$166$		0			0
$167$			197.932i			1.18522i	0.805488	+	0.592612i	$0.201903\pi$
$167$			197.932i			1.18522i	−0.805488	+	0.592612i	$0.798097\pi$
$168$		0			0
$169$		−	97.9723i		−	0.579718i
$170$		0			0
$171$	61.8309	−	61.8309i	0.361584	−	0.361584i
$172$		0			0
$173$	127.325	+	127.325i	0.735982	+	0.735982i	0.971798	−	0.235816i	$-0.0757762\pi$
$173$	127.325	+	127.325i	0.735982	+	0.735982i	−0.235816	+	0.971798i	$0.575776\pi$
$174$		0			0
$175$	−24.7954	+	181.720i	−0.141688	+	1.03840i
$176$		0			0
$177$		−	22.4853i		−	0.127036i
$178$		0			0
$179$	−29.4355	−	29.4355i	−0.164444	−	0.164444i	0.620088	−	0.784532i	$-0.287097\pi$
$179$	−29.4355	−	29.4355i	−0.164444	−	0.164444i	−0.784532	+	0.620088i	$0.787097\pi$
$180$		0			0
$181$	164.162	+	164.162i	0.906971	+	0.906971i	0.996027	−	0.0890559i	$-0.0283850\pi$
$181$	164.162	+	164.162i	0.906971	+	0.906971i	−0.0890559	+	0.996027i	$0.528385\pi$
$182$		0			0
$183$		−	162.114i		−	0.885870i
$184$		0			0
$185$	−155.070	−	177.666i	−0.838214	−	0.960354i
$186$		0			0
$187$	19.9417	+	19.9417i	0.106640	+	0.106640i
$188$		0			0
$189$	26.9548	−	26.9548i	0.142618	−	0.142618i
$190$		0			0
$191$		−	190.795i		−	0.998925i	−0.866336	−	0.499462i	$-0.833531\pi$
$191$		−	190.795i		−	0.998925i	0.866336	−	0.499462i	$-0.166469\pi$
$192$		0			0
$193$		−	248.223i		−	1.28613i	−0.765812	−	0.643064i	$-0.777663\pi$
$193$		−	248.223i		−	1.28613i	0.765812	−	0.643064i	$-0.222337\pi$
$194$		0			0
$195$	4.94511	−	72.8191i	0.0253595	−	0.373431i
$196$		0			0
$197$	70.1390	−	70.1390i	0.356036	−	0.356036i	−0.506314	−	0.862349i	$-0.668992\pi$
$197$	70.1390	−	70.1390i	0.356036	−	0.356036i	0.862349	+	0.506314i	$0.168992\pi$
$198$		0			0
$199$	−322.845			−1.62234			−0.811168	−	0.584813i	$-0.801168\pi$
$199$	−322.845			−1.62234			−0.811168	+	0.584813i	$0.801168\pi$
$200$		0			0
$201$			36.3107i			0.180650i
$202$		0			0
$203$	−210.278	−	210.278i	−1.03585	−	1.03585i
$204$		0			0
$205$	−186.418	−	12.6595i	−0.909356	−	0.0617539i
$206$		0			0
$207$	−10.7235			−0.0518044
$208$		0			0
$209$	−72.2795			−0.345835
$210$		0			0
$211$	−240.025	−	240.025i	−1.13756	−	1.13756i	−0.988887	−	0.148671i	$-0.952500\pi$
$211$	−240.025	−	240.025i	−1.13756	−	1.13756i	−0.148671	−	0.988887i	$-0.547500\pi$
$212$		0			0
$213$	10.0362	−	10.0362i	0.0471181	−	0.0471181i
$214$		0			0
$215$	34.4004	−	30.0253i	0.160002	−	0.139652i
$216$		0			0
$217$	347.331			1.60060
$218$		0			0
$219$	122.894	−	122.894i	0.561158	−	0.561158i
$220$		0			0
$221$	67.7737	−	67.7737i	0.306668	−	0.306668i
$222$		0			0
$223$	124.681			0.559110			0.279555	−	0.960130i	$-0.409813\pi$
$223$	124.681			0.559110			0.279555	+	0.960130i	$0.409813\pi$
$224$		0			0
$225$	−10.1397	+	74.3114i	−0.0450651	+	0.330273i
$226$		0			0
$227$	69.6686	−	69.6686i	0.306910	−	0.306910i	−0.536800	−	0.843710i	$-0.680367\pi$
$227$	69.6686	−	69.6686i	0.306910	−	0.306910i	0.843710	+	0.536800i	$0.180367\pi$
$228$		0			0
$229$	−54.3686	−	54.3686i	−0.237418	−	0.237418i	0.578362	−	0.815780i	$-0.303692\pi$
$229$	−54.3686	−	54.3686i	−0.237418	−	0.237418i	−0.815780	+	0.578362i	$0.803692\pi$
$230$		0			0
$231$	−31.5097			−0.136406
$232$		0			0
$233$	−82.3738			−0.353535			−0.176768	−	0.984253i	$-0.556564\pi$
$233$	−82.3738			−0.353535			−0.176768	+	0.984253i	$0.556564\pi$
$234$		0			0
$235$	−12.3778	+	182.269i	−0.0526716	+	0.775615i
$236$		0			0
$237$	−60.6005	−	60.6005i	−0.255698	−	0.255698i
$238$		0			0
$239$		−	270.970i		−	1.13376i	−0.823799	−	0.566882i	$-0.808150\pi$
$239$		−	270.970i		−	1.13376i	0.823799	−	0.566882i	$-0.191850\pi$
$240$		0			0
$241$	−340.081			−1.41112			−0.705562	−	0.708648i	$-0.749305\pi$
$241$	−340.081			−1.41112			−0.705562	+	0.708648i	$0.749305\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$	1.63260	−	24.0409i	0.00666369	−	0.0981261i
$246$		0			0
$247$			245.648i			0.994526i
$248$		0			0
$249$		−	260.739i		−	1.04714i
$250$		0			0
$251$	231.372	−	231.372i	0.921801	−	0.921801i	−0.0753558	−	0.997157i	$-0.524009\pi$
$251$	231.372	−	231.372i	0.921801	−	0.921801i	0.997157	+	0.0753558i	$0.0240093\pi$
$252$		0			0
$253$	6.26781	+	6.26781i	0.0247740	+	0.0247740i
$254$		0			0
$255$	−74.2016	+	64.7644i	−0.290986	+	0.253978i
$256$		0			0
$257$		−	87.9341i		−	0.342156i	−0.985257	−	0.171078i	$-0.945275\pi$
$257$		−	87.9341i		−	0.342156i	0.985257	−	0.171078i	$-0.0547250\pi$
$258$		0			0
$259$	244.662	+	244.662i	0.944641	+	0.944641i
$260$		0			0
$261$	−85.9898	−	85.9898i	−0.329463	−	0.329463i
$262$		0			0
$263$			136.621i			0.519470i	0.965680	+	0.259735i	$0.0836352\pi$
$263$			136.621i			0.519470i	−0.965680	+	0.259735i	$0.916365\pi$
$264$		0			0
$265$	40.0629	+	45.9006i	0.151181	+	0.173210i
$266$		0			0
$267$	144.011	+	144.011i	0.539366	+	0.539366i
$268$		0			0
$269$	−212.650	+	212.650i	−0.790522	+	0.790522i	−0.981579	−	0.191057i	$-0.938808\pi$
$269$	−212.650	+	212.650i	−0.790522	+	0.790522i	0.191057	+	0.981579i	$0.438808\pi$
$270$		0			0
$271$			133.721i			0.493437i	0.969087	+	0.246719i	$0.0793523\pi$
$271$			133.721i			0.493437i	−0.969087	+	0.246719i	$0.920648\pi$
$272$		0			0
$273$			107.089i			0.392266i
$274$		0			0
$275$	49.3611	−	37.5079i	0.179495	−	0.136393i
$276$		0			0
$277$	289.122	−	289.122i	1.04376	−	1.04376i	0.0447640	−	0.998998i	$-0.485746\pi$
$277$	289.122	−	289.122i	1.04376	−	1.04376i	0.998998	−	0.0447640i	$-0.0142536\pi$
$278$		0			0
$279$	142.035			0.509087
$280$		0			0
$281$		−	473.549i		−	1.68523i	−0.538519	−	0.842614i	$-0.681016\pi$
$281$		−	473.549i		−	1.68523i	0.538519	−	0.842614i	$-0.318984\pi$
$282$		0			0
$283$	179.205	+	179.205i	0.633234	+	0.633234i	0.948878	−	0.315643i	$-0.102220\pi$
$283$	179.205	+	179.205i	0.633234	+	0.633234i	−0.315643	+	0.948878i	$0.602220\pi$
$284$		0			0
$285$	17.1026	−	251.844i	0.0600090	−	0.883662i
$286$		0			0
$287$	274.148			0.955221
$288$		0			0
$289$	159.663			0.552466
$290$		0			0
$291$	−113.166	−	113.166i	−0.388886	−	0.388886i
$292$		0			0
$293$	−312.091	+	312.091i	−1.06516	+	1.06516i	−0.0674345	+	0.997724i	$0.521481\pi$
$293$	−312.091	+	312.091i	−1.06516	+	1.06516i	−0.997724	+	0.0674345i	$0.978519\pi$
$294$		0			0
$295$	−42.6828	−	48.9023i	−0.144687	−	0.165771i
$296$		0			0
$297$	−12.8854			−0.0433851
$298$		0			0
$299$	21.3017	−	21.3017i	0.0712431	−	0.0712431i
$300$		0			0
$301$	−47.3725	+	47.3725i	−0.157384	+	0.157384i
$302$		0			0
$303$	−124.595			−0.411206
$304$		0			0
$305$	−307.733	−	352.575i	−1.00896	−	1.15598i
$306$		0			0
$307$	327.818	−	327.818i	1.06781	−	1.06781i	0.0702834	−	0.997527i	$-0.477610\pi$
$307$	327.818	−	327.818i	1.06781	−	1.06781i	0.997527	−	0.0702834i	$-0.0223904\pi$
$308$		0			0
$309$	−227.844	−	227.844i	−0.737359	−	0.737359i
$310$		0			0
$311$	259.504			0.834418			0.417209	−	0.908811i	$-0.363008\pi$
$311$	259.504			0.834418			0.417209	+	0.908811i	$0.363008\pi$
$312$		0			0
$313$	−185.560			−0.592844			−0.296422	−	0.955057i	$-0.595793\pi$
$313$	−185.560			−0.592844			−0.296422	+	0.955057i	$0.595793\pi$
$314$		0			0
$315$	7.45575	−	109.790i	0.0236690	−	0.348538i
$316$		0			0
$317$	152.890	+	152.890i	0.482304	+	0.482304i	0.905867	−	0.423563i	$-0.139221\pi$
$317$	152.890	+	152.890i	0.482304	+	0.482304i	−0.423563	+	0.905867i	$0.639221\pi$
$318$		0			0
$319$			100.521i			0.315112i
$320$		0			0
$321$	271.842			0.846861
$322$		0			0
$323$	234.394	−	234.394i	0.725678	−	0.725678i
$324$		0			0
$325$	−127.474	−	167.758i	−0.392228	−	0.516178i
$326$		0			0
$327$		−	224.099i		−	0.685318i
$328$		0			0
$329$		−	268.048i		−	0.814734i
$330$		0			0
$331$	84.5870	−	84.5870i	0.255550	−	0.255550i	−0.567692	−	0.823241i	$-0.692163\pi$
$331$	84.5870	−	84.5870i	0.255550	−	0.255550i	0.823241	+	0.567692i	$0.192163\pi$
$332$		0			0
$333$	100.050	+	100.050i	0.300452	+	0.300452i
$334$		0			0
$335$	68.9269	+	78.9705i	0.205752	+	0.235733i
$336$		0			0
$337$			526.847i			1.56334i	0.623689	+	0.781672i	$0.285633\pi$
$337$			526.847i			1.56334i	−0.623689	+	0.781672i	$0.714367\pi$
$338$		0			0
$339$	−35.4946	−	35.4946i	−0.104704	−	0.104704i
$340$		0			0
$341$	−83.0185	−	83.0185i	−0.243456	−	0.243456i
$342$		0			0
$343$		−	324.117i		−	0.944948i
$344$		0			0
$345$	−23.3220	+	20.3559i	−0.0676001	+	0.0590026i
$346$		0			0
$347$	288.537	+	288.537i	0.831519	+	0.831519i	0.987725	−	0.156206i	$-0.0499262\pi$
$347$	288.537	+	288.537i	0.831519	+	0.831519i	−0.156206	+	0.987725i	$0.549926\pi$
$348$		0			0
$349$	96.2266	−	96.2266i	0.275721	−	0.275721i	−0.555677	−	0.831398i	$-0.687541\pi$
$349$	96.2266	−	96.2266i	0.275721	−	0.275721i	0.831398	+	0.555677i	$0.187541\pi$
$350$		0			0
$351$			43.7921i			0.124764i
$352$		0			0
$353$		−	271.935i		−	0.770354i	−0.922843	−	0.385177i	$-0.874140\pi$
$353$		−	271.935i		−	0.770354i	0.922843	−	0.385177i	$-0.125860\pi$
$354$		0			0
$355$	2.77602	−	40.8783i	0.00781978	−	0.115150i
$356$		0			0
$357$	102.182	−	102.182i	0.286225	−	0.286225i
$358$		0			0
$359$	−333.402			−0.928695			−0.464348	−	0.885653i	$-0.653711\pi$
$359$	−333.402			−0.928695			−0.464348	+	0.885653i	$0.653711\pi$
$360$		0			0
$361$			488.569i			1.35338i
$362$		0			0
$363$	−140.663	−	140.663i	−0.387501	−	0.387501i
$364$		0			0
$365$	33.9926	−	500.558i	0.0931305	−	1.37139i
$366$		0			0
$367$	232.602			0.633794			0.316897	−	0.948460i	$-0.397359\pi$
$367$	232.602			0.633794			0.316897	+	0.948460i	$0.397359\pi$
$368$		0			0
$369$	112.108			0.303817
$370$		0			0
$371$	−63.2095	−	63.2095i	−0.170376	−	0.170376i
$372$		0			0
$373$	−41.1698	+	41.1698i	−0.110375	+	0.110375i	−0.760137	−	0.649762i	$-0.774868\pi$
$373$	−41.1698	+	41.1698i	−0.110375	+	0.110375i	0.649762	+	0.760137i	$0.274868\pi$
$374$		0			0
$375$	119.009	+	180.864i	0.317358	+	0.482304i
$376$		0			0
$377$	341.629			0.906177
$378$		0			0
$379$	−240.873	+	240.873i	−0.635548	+	0.635548i	−0.949454	−	0.313906i	$-0.898362\pi$
$379$	−240.873	+	240.873i	−0.635548	+	0.635548i	0.313906	+	0.949454i	$0.398362\pi$
$380$		0			0
$381$	−176.760	+	176.760i	−0.463936	+	0.463936i
$382$		0			0
$383$	550.355			1.43696			0.718480	−	0.695548i	$-0.244838\pi$
$383$	550.355			1.43696			0.718480	+	0.695548i	$0.244838\pi$
$384$		0			0
$385$	−68.5290	+	59.8134i	−0.177998	+	0.155359i
$386$		0			0
$387$	−19.3722	+	19.3722i	−0.0500574	+	0.0500574i
$388$		0			0
$389$	275.527	+	275.527i	0.708296	+	0.708296i	0.966177	−	0.257881i	$-0.0830241\pi$
$389$	275.527	+	275.527i	0.708296	+	0.708296i	−0.257881	+	0.966177i	$0.583024\pi$
$390$		0			0
$391$	−40.6516			−0.103968
$392$		0			0
$393$	−257.538			−0.655314
$394$		0			0
$395$	−246.832	−	16.7622i	−0.624891	−	0.0424360i
$396$		0			0
$397$	149.150	+	149.150i	0.375692	+	0.375692i	0.869545	−	0.493853i	$-0.164412\pi$
$397$	149.150	+	149.150i	0.375692	+	0.375692i	−0.493853	+	0.869545i	$0.664412\pi$
$398$		0			0
$399$			370.364i			0.928231i
$400$		0			0
$401$	−21.7539			−0.0542492			−0.0271246	−	0.999632i	$-0.508635\pi$
$401$	−21.7539			−0.0542492			−0.0271246	+	0.999632i	$0.508635\pi$
$402$		0			0
$403$	−282.146	+	282.146i	−0.700113	+	0.700113i
$404$		0			0
$405$	3.04890	−	44.8966i	0.00752816	−	0.110856i
$406$		0			0
$407$		−	116.958i		−	0.287365i
$408$		0			0
$409$		−	366.135i		−	0.895197i	−0.894235	−	0.447598i	$-0.852279\pi$
$409$		−	366.135i		−	0.895197i	0.894235	−	0.447598i	$-0.147721\pi$
$410$		0			0
$411$	27.0591	−	27.0591i	0.0658371	−	0.0658371i
$412$		0			0
$413$	67.3431	+	67.3431i	0.163058	+	0.163058i
$414$		0			0
$415$	−494.948	−	567.068i	−1.19264	−	1.36643i
$416$		0			0
$417$			182.449i			0.437527i
$418$		0			0
$419$	102.489	+	102.489i	0.244603	+	0.244603i	0.818751	−	0.574149i	$-0.194667\pi$
$419$	102.489	+	102.489i	0.244603	+	0.244603i	−0.574149	+	0.818751i	$0.694667\pi$
$420$		0			0
$421$	−221.476	−	221.476i	−0.526071	−	0.526071i	0.393328	−	0.919398i	$-0.371324\pi$
$421$	−221.476	−	221.476i	−0.526071	−	0.526071i	−0.919398	+	0.393328i	$0.871324\pi$
$422$		0			0
$423$		−	109.614i		−	0.259134i
$424$		0			0
$425$	−38.4383	+	281.706i	−0.0904430	+	0.662838i
$426$		0			0
$427$	485.528	+	485.528i	1.13707	+	1.13707i
$428$		0			0
$429$	25.5962	−	25.5962i	0.0596647	−	0.0596647i
$430$		0			0
$431$		−	552.688i		−	1.28234i	−0.767399	−	0.641170i	$-0.778449\pi$
$431$		−	552.688i		−	1.28234i	0.767399	−	0.641170i	$-0.221551\pi$
$432$		0			0
$433$			212.203i			0.490077i	0.969513	+	0.245039i	$0.0788006\pi$
$433$			212.203i			0.490077i	−0.969513	+	0.245039i	$0.921199\pi$
$434$		0			0
$435$	−350.245	−	23.7850i	−0.805161	−	0.0546780i
$436$		0			0
$437$	73.6715	−	73.6715i	0.168585	−	0.168585i
$438$		0			0
$439$	−381.027			−0.867943			−0.433972	−	0.900927i	$-0.642888\pi$
$439$	−381.027			−0.867943			−0.433972	+	0.900927i	$0.642888\pi$
$440$		0			0
$441$			14.4578i			0.0327840i
$442$		0			0
$443$	−425.329	−	425.329i	−0.960111	−	0.960111i	0.0391237	−	0.999234i	$-0.487543\pi$
$443$	−425.329	−	425.329i	−0.960111	−	0.960111i	−0.999234	+	0.0391237i	$0.987543\pi$
$444$		0			0
$445$	586.570	+	39.8337i	1.31814	+	0.0895138i
$446$		0			0
$447$	−346.735			−0.775694
$448$		0			0
$449$	−123.003			−0.273949			−0.136975	−	0.990575i	$-0.543738\pi$
$449$	−123.003			−0.273949			−0.136975	+	0.990575i	$0.543738\pi$
$450$		0			0
$451$	−65.5266	−	65.5266i	−0.145292	−	0.145292i
$452$		0			0
$453$	−33.1529	+	33.1529i	−0.0731852	+	0.0731852i
$454$		0			0
$455$	203.281	+	232.902i	0.446771	+	0.511872i
$456$		0			0
$457$	372.714			0.815567			0.407784	−	0.913079i	$-0.366302\pi$
$457$	372.714			0.815567			0.407784	+	0.913079i	$0.366302\pi$
$458$		0			0
$459$	41.7858	−	41.7858i	0.0910366	−	0.0910366i
$460$		0			0
$461$	133.842	−	133.842i	0.290330	−	0.290330i	−0.546880	−	0.837211i	$-0.684185\pi$
$461$	133.842	−	133.842i	0.290330	−	0.290330i	0.837211	+	0.546880i	$0.184185\pi$
$462$		0			0
$463$	314.104			0.678410			0.339205	−	0.940712i	$-0.389842\pi$
$463$	314.104			0.678410			0.339205	+	0.940712i	$0.389842\pi$
$464$		0			0
$465$	308.905	−	269.618i	0.664313	−	0.579824i
$466$		0			0
$467$	−292.489	+	292.489i	−0.626314	+	0.626314i	−0.947139	−	0.320825i	$-0.896040\pi$
$467$	−292.489	+	292.489i	−0.626314	+	0.626314i	0.320825	+	0.947139i	$0.396040\pi$
$468$		0			0
$469$	−108.750	−	108.750i	−0.231876	−	0.231876i
$470$		0			0
$471$	−453.375			−0.962579
$472$		0			0
$473$	22.6458			0.0478770
$474$		0			0
$475$	−440.867	−	580.187i	−0.928140	−	1.22145i
$476$		0			0
$477$	−25.8485	−	25.8485i	−0.0541896	−	0.0541896i
$478$		0			0
$479$		−	805.123i		−	1.68084i	−0.541935	−	0.840420i	$-0.682308\pi$
$479$		−	805.123i		−	1.68084i	0.541935	−	0.840420i	$-0.317692\pi$
$480$		0			0
$481$	−397.490			−0.826383
$482$		0			0
$483$	32.1166	−	32.1166i	0.0664940	−	0.0664940i
$484$		0			0
$485$	−460.936	−	31.3019i	−0.950383	−	0.0645400i
$486$		0			0
$487$		−	39.8719i		−	0.0818724i	−0.999162	−	0.0409362i	$-0.986966\pi$
$487$		−	39.8719i		−	0.0818724i	0.999162	−	0.0409362i	$-0.0130340\pi$
$488$		0			0
$489$			100.535i			0.205593i
$490$		0			0
$491$	−605.496	+	605.496i	−1.23319	+	1.23319i	−0.270458	+	0.962732i	$0.587175\pi$
$491$	−605.496	+	605.496i	−1.23319	+	1.23319i	−0.962732	+	0.270458i	$0.912825\pi$
$492$		0			0
$493$	−325.977	−	325.977i	−0.661212	−	0.661212i
$494$		0			0
$495$	−28.0238	+	24.4597i	−0.0566137	+	0.0494135i
$496$		0			0
$497$			60.1161i			0.120958i
$498$		0			0
$499$	582.313	+	582.313i	1.16696	+	1.16696i	0.982919	+	0.184040i	$0.0589177\pi$
$499$	582.313	+	582.313i	1.16696	+	1.16696i	0.184040	+	0.982919i	$0.441082\pi$
$500$		0			0
$501$	−242.417	−	242.417i	−0.483865	−	0.483865i
$502$		0			0
$503$		−	601.274i		−	1.19537i	−0.801729	−	0.597687i	$-0.796086\pi$
$503$		−	601.274i		−	1.19537i	0.801729	−	0.597687i	$-0.203914\pi$
$504$		0			0
$505$	−270.977	+	236.513i	−0.536588	+	0.468343i
$506$		0			0
$507$	119.991	+	119.991i	0.236669	+	0.236669i
$508$		0			0
$509$	−81.2735	+	81.2735i	−0.159673	+	0.159673i	−0.782422	−	0.622749i	$-0.786016\pi$
$509$	−81.2735	+	81.2735i	−0.159673	+	0.159673i	0.622749	+	0.782422i	$0.286016\pi$
$510$		0			0
$511$			736.127i			1.44056i
$512$		0			0
$513$			151.454i			0.295232i
$514$		0			0
$515$	−928.031	−	63.0221i	−1.80200	−	0.122373i
$516$		0			0
$517$	−64.0683	+	64.0683i	−0.123923	+	0.123923i
$518$		0			0
$519$	−311.881			−0.600927
$520$		0			0
$521$			835.230i			1.60313i	0.597909	+	0.801564i	$0.295998\pi$
$521$			835.230i			1.60313i	−0.597909	+	0.801564i	$0.704002\pi$
$522$		0			0
$523$	284.226	+	284.226i	0.543453	+	0.543453i	0.924539	−	0.381086i	$-0.124450\pi$
$523$	284.226	+	284.226i	0.543453	+	0.543453i	−0.381086	+	0.924539i	$0.624450\pi$
$524$		0			0
$525$	−192.193	−	252.929i	−0.366082	−	0.481769i
$526$		0			0
$527$	538.439			1.02171
$528$		0			0
$529$	516.223			0.975847
$530$		0			0
$531$	27.5388	+	27.5388i	0.0518622	+	0.0518622i
$532$		0			0
$533$	−222.698	+	222.698i	−0.417819	+	0.417819i
$534$		0			0
$535$	591.217	−	516.025i	1.10508	−	0.964532i
$536$		0			0
$537$	72.1019			0.134268
$538$		0			0
$539$	8.45046	−	8.45046i	0.0156780	−	0.0156780i
$540$		0			0
$541$	532.928	−	532.928i	0.985080	−	0.985080i	−0.0148100	−	0.999890i	$-0.504714\pi$
$541$	532.928	−	532.928i	0.985080	−	0.985080i	0.999890	+	0.0148100i	$0.00471436\pi$
$542$		0			0
$543$	−402.112			−0.740539
$544$		0			0
$545$	−425.396	−	487.382i	−0.780543	−	0.894279i
$546$		0			0
$547$	89.4187	−	89.4187i	0.163471	−	0.163471i	−0.620631	−	0.784103i	$-0.713124\pi$
$547$	89.4187	−	89.4187i	0.163471	−	0.163471i	0.784103	+	0.620631i	$0.213124\pi$
$548$		0			0
$549$	198.549	+	198.549i	0.361655	+	0.361655i
$550$		0			0
$551$	1181.52			2.14431
$552$		0			0
$553$	362.994			0.656409
$554$		0			0
$555$	407.516	+	27.6742i	0.734263	+	0.0498634i
$556$		0			0
$557$	24.6204	+	24.6204i	0.0442018	+	0.0442018i	0.728862	−	0.684660i	$-0.240049\pi$
$557$	24.6204	+	24.6204i	0.0442018	+	0.0442018i	−0.684660	+	0.728862i	$0.740049\pi$
$558$		0			0
$559$		−	76.9638i		−	0.137681i
$560$		0			0
$561$	−48.8470			−0.0870714
$562$		0			0
$563$	−541.514	+	541.514i	−0.961836	+	0.961836i	−0.999298	−	0.0374616i	$-0.988073\pi$
$563$	−541.514	+	541.514i	−0.961836	+	0.961836i	0.0374616	+	0.999298i	$0.488073\pi$
$564$		0			0
$565$	−144.573	−	9.81788i	−0.255882	−	0.0173768i
$566$		0			0
$567$			66.0254i			0.116447i
$568$		0			0
$569$			561.664i			0.987107i	0.869715	+	0.493553i	$0.164302\pi$
$569$			561.664i			0.987107i	−0.869715	+	0.493553i	$0.835698\pi$
$570$		0			0
$571$	−178.448	+	178.448i	−0.312518	+	0.312518i	−0.845884	−	0.533366i	$-0.820927\pi$
$571$	−178.448	+	178.448i	−0.312518	+	0.312518i	0.533366	+	0.845884i	$0.320927\pi$
$572$		0			0
$573$	233.675	+	233.675i	0.407809	+	0.407809i
$574$		0			0
$575$	−12.0814	+	88.5421i	−0.0210111	+	0.153986i
$576$		0			0
$577$		−	360.111i		−	0.624109i	−0.950064	−	0.312055i	$-0.898983\pi$
$577$		−	360.111i		−	0.624109i	0.950064	−	0.312055i	$-0.101017\pi$
$578$		0			0
$579$	304.009	+	304.009i	0.525059	+	0.525059i
$580$		0			0
$581$	780.906	+	780.906i	1.34407	+	1.34407i
$582$		0			0
$583$			30.2165i			0.0518293i
$584$		0			0
$585$	83.1283	+	95.2413i	0.142100	+	0.162806i
$586$		0			0
$587$	491.499	+	491.499i	0.837306	+	0.837306i	0.988504	−	0.151197i	$-0.0483128\pi$
$587$	491.499	+	491.499i	0.837306	+	0.837306i	−0.151197	+	0.988504i	$0.548313\pi$
$588$		0			0
$589$	−975.796	+	975.796i	−1.65670	+	1.65670i
$590$		0			0
$591$			171.805i			0.290702i
$592$		0			0
$593$		−	611.202i		−	1.03070i	−0.856981	−	0.515348i	$-0.827663\pi$
$593$		−	611.202i		−	1.03070i	0.856981	−	0.515348i	$-0.172337\pi$
$594$		0			0
$595$	28.2639	−	416.200i	0.0475023	−	0.699495i
$596$		0			0
$597$	395.403	−	395.403i	0.662316	−	0.662316i
$598$		0			0
$599$	271.865			0.453864			0.226932	−	0.973911i	$-0.427130\pi$
$599$	271.865			0.453864			0.226932	+	0.973911i	$0.427130\pi$
$600$		0			0
$601$			433.691i			0.721615i	0.932640	+	0.360808i	$0.117499\pi$
$601$			433.691i			0.721615i	−0.932640	+	0.360808i	$0.882501\pi$
$602$		0			0
$603$	−44.4714	−	44.4714i	−0.0737502	−	0.0737502i
$604$		0			0
$605$	−572.934	−	38.9076i	−0.946998	−	0.0643101i
$606$		0			0
$607$	−700.912			−1.15472			−0.577358	−	0.816491i	$-0.695916\pi$
$607$	−700.912			−1.15472			−0.577358	+	0.816491i	$0.695916\pi$
$608$		0			0
$609$	515.074			0.845771
$610$		0			0
$611$	217.742	+	217.742i	0.356370	+	0.356370i
$612$		0			0
$613$	−137.968	+	137.968i	−0.225071	+	0.225071i	−0.810630	−	0.585559i	$-0.800875\pi$
$613$	−137.968	+	137.968i	−0.225071	+	0.225071i	0.585559	+	0.810630i	$0.300875\pi$
$614$		0			0
$615$	243.819	−	212.810i	0.396454	−	0.346032i
$616$		0			0
$617$	53.0611			0.0859985			0.0429993	−	0.999075i	$-0.486309\pi$
$617$	53.0611			0.0859985			0.0429993	+	0.999075i	$0.486309\pi$
$618$		0			0
$619$	472.476	−	472.476i	0.763288	−	0.763288i	−0.213627	−	0.976915i	$-0.568528\pi$
$619$	472.476	−	472.476i	0.763288	−	0.763288i	0.976915	+	0.213627i	$0.0685277\pi$
$620$		0			0
$621$	13.1336	−	13.1336i	0.0211490	−	0.0211490i
$622$		0			0
$623$	−862.617			−1.38462
$624$		0			0
$625$	602.153	+	167.443i	0.963444	+	0.267908i
$626$		0			0
$627$	88.5239	−	88.5239i	0.141186	−	0.141186i
$628$		0			0
$629$	379.280	+	379.280i	0.602989	+	0.602989i
$630$		0			0
$631$	−57.0532			−0.0904171			−0.0452086	−	0.998978i	$-0.514395\pi$
$631$	−57.0532			−0.0904171			−0.0452086	+	0.998978i	$0.514395\pi$
$632$		0			0
$633$	587.938			0.928812
$634$		0			0
$635$	−48.8921	+	719.961i	−0.0769955	+	1.13380i
$636$		0			0
$637$	−28.7196	−	28.7196i	−0.0450857	−	0.0450857i
$638$		0			0
$639$			24.5835i			0.0384718i
$640$		0			0
$641$	−67.3505			−0.105071			−0.0525355	−	0.998619i	$-0.516730\pi$
$641$	−67.3505			−0.105071			−0.0525355	+	0.998619i	$0.516730\pi$
$642$		0			0
$643$	−427.482	+	427.482i	−0.664824	+	0.664824i	−0.956513	−	0.291689i	$-0.905783\pi$
$643$	−427.482	+	427.482i	−0.664824	+	0.664824i	0.291689	+	0.956513i	$0.405783\pi$
$644$		0			0
$645$	−5.35839	+	78.9050i	−0.00830759	+	0.122333i
$646$		0			0
$647$			280.961i			0.434251i	0.976144	+	0.217126i	$0.0696682\pi$
$647$			280.961i			0.434251i	−0.976144	+	0.217126i	$0.930332\pi$
$648$		0			0
$649$		−	32.1925i		−	0.0496032i
$650$		0			0
$651$	−425.392	+	425.392i	−0.653444	+	0.653444i
$652$		0			0
$653$	−459.190	−	459.190i	−0.703201	−	0.703201i	0.261895	−	0.965096i	$-0.415652\pi$
$653$	−459.190	−	459.190i	−0.703201	−	0.703201i	−0.965096	+	0.261895i	$0.915652\pi$
$654$		0			0
$655$	−560.108	+	488.872i	−0.855127	+	0.746370i
$656$		0			0
$657$			301.027i			0.458184i
$658$		0			0
$659$	355.705	+	355.705i	0.539764	+	0.539764i	0.923460	−	0.383695i	$-0.125349\pi$
$659$	355.705	+	355.705i	0.539764	+	0.539764i	−0.383695	+	0.923460i	$0.625349\pi$
$660$		0			0
$661$	−670.134	−	670.134i	−1.01382	−	1.01382i	−0.999903	−	0.0139149i	$-0.995571\pi$
$661$	−670.134	−	670.134i	−1.01382	−	1.01382i	−0.0139149	−	0.999903i	$-0.504429\pi$
$662$		0			0
$663$			166.011i			0.250393i
$664$		0			0
$665$	703.044	+	805.487i	1.05721	+	1.21126i
$666$		0			0
$667$	−102.457	−	102.457i	−0.153608	−	0.153608i
$668$		0			0
$669$	−152.703	+	152.703i	−0.228256	+	0.228256i
$670$		0			0
$671$		−	232.101i		−	0.345902i
$672$		0			0
$673$		−	409.864i		−	0.609010i	−0.952511	−	0.304505i	$-0.901509\pi$
$673$		−	409.864i		−	0.609010i	0.952511	−	0.304505i	$-0.0984910\pi$
$674$		0			0
$675$	−78.5940	−	103.431i	−0.116436	−	0.153231i
$676$		0			0
$677$	−811.380	+	811.380i	−1.19849	+	1.19849i	−0.223875	+	0.974618i	$0.571871\pi$
$677$	−811.380	+	811.380i	−1.19849	+	1.19849i	−0.974618	+	0.223875i	$0.928129\pi$
$678$		0			0
$679$	677.857			0.998317
$680$		0			0
$681$			170.652i			0.250591i
$682$		0			0
$683$	−126.289	−	126.289i	−0.184904	−	0.184904i	0.608585	−	0.793489i	$-0.291737\pi$
$683$	−126.289	−	126.289i	−0.184904	−	0.184904i	−0.793489	+	0.608585i	$0.791737\pi$
$684$		0			0
$685$	7.48459	−	110.214i	0.0109264	−	0.160897i
$686$		0			0
$687$	133.175			0.193851
$688$		0			0
$689$	102.693			0.149047
$690$		0			0
$691$	−491.149	−	491.149i	−0.710780	−	0.710780i	0.255919	−	0.966698i	$-0.417622\pi$
$691$	−491.149	−	491.149i	−0.710780	−	0.710780i	−0.966698	+	0.255919i	$0.917622\pi$
$692$		0			0
$693$	38.5914	−	38.5914i	0.0556875	−	0.0556875i
$694$		0			0
$695$	346.333	+	396.799i	0.498321	+	0.570933i
$696$		0			0
$697$	424.990			0.609742
$698$		0			0
$699$	100.887	−	100.887i	0.144330	−	0.144330i
$700$		0			0
$701$	977.596	−	977.596i	1.39457	−	1.39457i	0.579849	−	0.814724i	$-0.303111\pi$
$701$	977.596	−	977.596i	1.39457	−	1.39457i	0.814724	−	0.579849i	$-0.196889\pi$
$702$		0			0
$703$	−1374.71			−1.95550
$704$		0			0
$705$	−208.074	−	238.393i	−0.295140	−	0.338146i
$706$		0			0
$707$	373.160	−	373.160i	0.527808	−	0.527808i
$708$		0			0
$709$	518.452	+	518.452i	0.731243	+	0.731243i	0.970866	−	0.239623i	$-0.0770238\pi$
$709$	518.452	+	518.452i	0.731243	+	0.731243i	−0.239623	+	0.970866i	$0.577024\pi$
$710$		0			0
$711$	148.440			0.208777
$712$		0			0
$713$	169.235			0.237356
$714$		0			0
$715$	7.07995	−	104.256i	0.00990203	−	0.145812i
$716$		0			0
$717$	331.869	+	331.869i	0.462857	+	0.462857i
$718$		0			0
$719$			253.428i			0.352473i	0.984348	+	0.176237i	$0.0563924\pi$
$719$			253.428i			0.352473i	−0.984348	+	0.176237i	$0.943608\pi$
$720$		0			0
$721$	1364.77			1.89289
$722$		0			0
$723$	416.512	−	416.512i	0.576089	−	0.576089i
$724$		0			0
$725$	−806.881	+	613.124i	−1.11294	+	0.845688i
$726$		0			0
$727$		−	144.550i		−	0.198830i	−0.995046	−	0.0994152i	$-0.968303\pi$
$727$		−	144.550i		−	0.198830i	0.995046	−	0.0994152i	$-0.0316972\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−73.4378	+	73.4378i	−0.100462	+	0.100462i
$732$		0			0
$733$	−634.895	−	634.895i	−0.866160	−	0.866160i	0.125885	−	0.992045i	$-0.459823\pi$
$733$	−634.895	−	634.895i	−0.866160	−	0.866160i	−0.992045	+	0.125885i	$0.959823\pi$
$734$		0			0
$735$	27.4444	+	31.4435i	0.0373394	+	0.0427803i
$736$		0			0
$737$			51.9864i			0.0705379i
$738$		0			0
$739$	−471.938	−	471.938i	−0.638617	−	0.638617i	0.311597	−	0.950214i	$-0.399136\pi$
$739$	−471.938	−	471.938i	−0.638617	−	0.638617i	−0.950214	+	0.311597i	$0.899136\pi$
$740$		0			0
$741$	−300.856	−	300.856i	−0.406014	−	0.406014i
$742$		0			0
$743$		−	268.300i		−	0.361104i	−0.983565	−	0.180552i	$-0.942212\pi$
$743$		−	268.300i		−	0.361104i	0.983565	−	0.180552i	$-0.0577884\pi$
$744$		0			0
$745$	−754.098	+	658.190i	−1.01221	+	0.883477i
$746$		0			0
$747$	319.339	+	319.339i	0.427495	+	0.427495i
$748$		0			0
$749$	−814.161	+	814.161i	−1.08700	+	1.08700i
$750$		0			0
$751$			492.801i			0.656193i	0.944644	+	0.328096i	$0.106407\pi$
$751$			492.801i			0.656193i	−0.944644	+	0.328096i	$0.893593\pi$
$752$		0			0
$753$			566.743i			0.752647i
$754$		0			0
$755$	−9.17017	+	135.035i	−0.0121459	+	0.178855i
$756$		0			0
$757$	−954.652	+	954.652i	−1.26110	+	1.26110i	−0.310538	+	0.950561i	$0.600509\pi$
$757$	−954.652	+	954.652i	−1.26110	+	1.26110i	−0.950561	+	0.310538i	$0.899491\pi$
$758$		0			0
$759$	−15.3529			−0.0202278
$760$		0			0
$761$		−	1341.34i		−	1.76260i	−0.472555	−	0.881301i	$-0.656668\pi$
$761$		−	1341.34i		−	1.76260i	0.472555	−	0.881301i	$-0.343332\pi$
$762$		0			0
$763$	671.171	+	671.171i	0.879647	+	0.879647i
$764$		0			0
$765$	11.5580	−	170.198i	0.0151086	−	0.222481i
$766$		0			0
$767$	−109.409			−0.142645
$768$		0			0
$769$	502.221			0.653084			0.326542	−	0.945183i	$-0.394117\pi$
$769$	502.221			0.653084			0.326542	+	0.945183i	$0.394117\pi$
$770$		0			0
$771$	107.697	+	107.697i	0.139685	+	0.139685i
$772$		0			0
$773$	−605.380	+	605.380i	−0.783157	+	0.783157i	−0.980362	−	0.197206i	$-0.936813\pi$
$773$	−605.380	+	605.380i	−0.783157	+	0.783157i	0.197206	+	0.980362i	$0.436813\pi$
$774$		0			0
$775$	160.021	−	1172.76i	0.206479	−	1.51324i
$776$		0			0
$777$	−599.297			−0.771296
$778$		0			0
$779$	−770.196	+	770.196i	−0.988699	+	0.988699i
$780$		0			0
$781$	14.3689	−	14.3689i	0.0183980	−	0.0183980i
$782$		0			0
$783$	210.631			0.269005
$784$		0			0
$785$	−986.023	+	860.618i	−1.25608	+	1.09633i
$786$		0			0
$787$	−232.628	+	232.628i	−0.295589	+	0.295589i	−0.839283	−	0.543694i	$-0.817025\pi$
$787$	−232.628	+	232.628i	−0.295589	+	0.295589i	0.543694	+	0.839283i	$0.317025\pi$
$788$		0			0
$789$	−167.325	−	167.325i	−0.212073	−	0.212073i
$790$		0			0
$791$	212.611			0.268787
$792$		0			0
$793$	−788.814			−0.994721
$794$		0			0
$795$	−105.283	−	7.14974i	−0.132432	−	0.00899338i
$796$		0			0
$797$	431.793	+	431.793i	0.541773	+	0.541773i	0.924049	−	0.382275i	$-0.124859\pi$
$797$	431.793	+	431.793i	0.541773	+	0.541773i	−0.382275	+	0.924049i	$0.624859\pi$
$798$		0			0
$799$		−	415.533i		−	0.520066i
$800$		0			0
$801$	−352.753			−0.440390
$802$		0			0
$803$	175.948	−	175.948i	0.219113	−	0.219113i
$804$		0			0
$805$	8.88353	−	130.814i	0.0110354	−	0.162502i
$806$		0			0
$807$		−	520.885i		−	0.645458i
$808$		0			0
$809$		−	703.625i		−	0.869746i	−0.900492	−	0.434873i	$-0.856793\pi$
$809$		−	703.625i		−	0.869746i	0.900492	−	0.434873i	$-0.143207\pi$
$810$		0			0
$811$	−856.572	+	856.572i	−1.05619	+	1.05619i	−0.0578688	+	0.998324i	$0.518430\pi$
$811$	−856.572	+	856.572i	−1.05619	+	1.05619i	−0.998324	+	0.0578688i	$0.981570\pi$
$812$		0			0
$813$	−163.775	−	163.775i	−0.201445	−	0.201445i
$814$		0			0
$815$	190.841	+	218.649i	0.234160	+	0.268281i
$816$		0			0
$817$		−	266.178i		−	0.325799i
$818$		0			0
$819$	−131.156	−	131.156i	−0.160142	−	0.160142i
$820$		0			0
$821$	−768.849	−	768.849i	−0.936479	−	0.936479i	0.0616204	−	0.998100i	$-0.480373\pi$
$821$	−768.849	−	768.849i	−0.936479	−	0.936479i	−0.998100	+	0.0616204i	$0.980373\pi$
$822$		0			0
$823$			1010.84i			1.22823i	0.789215	+	0.614117i	$0.210488\pi$
$823$			1010.84i			1.22823i	−0.789215	+	0.614117i	$0.789512\pi$
$824$		0			0
$825$	−14.5170	+	106.392i	−0.0175964	+	0.128960i
$826$		0			0
$827$	−386.667	−	386.667i	−0.467554	−	0.467554i	0.433567	−	0.901121i	$-0.357255\pi$
$827$	−386.667	−	386.667i	−0.467554	−	0.467554i	−0.901121	+	0.433567i	$0.857255\pi$
$828$		0			0
$829$	−401.742	+	401.742i	−0.484611	+	0.484611i	−0.906601	−	0.421990i	$-0.861332\pi$
$829$	−401.742	+	401.742i	−0.484611	+	0.484611i	0.421990	+	0.906601i	$0.361332\pi$
$830$		0			0
$831$			708.201i			0.852228i
$832$		0			0
$833$			54.8077i			0.0657956i
$834$		0			0
$835$	−987.387	−	67.0529i	−1.18250	−	0.0803029i
$836$		0			0
$837$	−173.957	+	173.957i	−0.207834	+	0.207834i
$838$		0			0
$839$	−1595.26			−1.90139			−0.950694	−	0.310131i	$-0.899627\pi$
$839$	−1595.26			−1.90139			−0.950694	+	0.310131i	$0.899627\pi$
$840$		0			0
$841$		−	802.164i		−	0.953822i
$842$		0			0
$843$	579.977	+	579.977i	0.687991	+	0.687991i
$844$		0			0
$845$	488.736	+	33.1898i	0.578386	+	0.0392779i
$846$		0			0
$847$	842.563			0.994761
$848$		0			0
$849$	−438.962			−0.517034
$850$		0			0
$851$	119.210	+	119.210i	0.140082	+	0.140082i
$852$		0			0
$853$	690.533	−	690.533i	0.809535	−	0.809535i	−0.175029	−	0.984563i	$-0.556002\pi$
$853$	690.533	−	690.533i	0.809535	−	0.809535i	0.984563	+	0.175029i	$0.0560018\pi$
$854$		0			0
$855$	287.498	+	329.390i	0.336255	+	0.385252i
$856$		0			0
$857$	975.642			1.13844			0.569219	−	0.822186i	$-0.307246\pi$
$857$	975.642			1.13844			0.569219	+	0.822186i	$0.307246\pi$
$858$		0			0
$859$	642.603	−	642.603i	0.748083	−	0.748083i	−0.226036	−	0.974119i	$-0.572577\pi$
$859$	642.603	−	642.603i	0.748083	−	0.748083i	0.974119	+	0.226036i	$0.0725767\pi$
$860$		0			0
$861$	−335.762	+	335.762i	−0.389967	+	0.389967i
$862$		0			0
$863$	624.600			0.723754			0.361877	−	0.932226i	$-0.382136\pi$
$863$	624.600			0.723754			0.361877	+	0.932226i	$0.382136\pi$
$864$		0			0
$865$	−678.295	+	592.028i	−0.784156	+	0.684425i
$866$		0			0
$867$	−195.546	+	195.546i	−0.225543	+	0.225543i
$868$		0			0
$869$	−86.7623	−	86.7623i	−0.0998415	−	0.0998415i
$870$		0			0
$871$	176.680			0.202848
$872$		0			0
$873$	277.198			0.317524
$874$		0			0
$875$	−898.113	−	185.253i	−1.02642	−	0.211718i
$876$		0			0
$877$	−893.631	−	893.631i	−1.01896	−	1.01896i	−0.999817	−	0.0191471i	$-0.993905\pi$
$877$	−893.631	−	893.631i	−1.01896	−	1.01896i	−0.0191471	−	0.999817i	$-0.506095\pi$
$878$		0			0
$879$		−	764.465i		−	0.869698i
$880$		0			0
$881$	1518.15			1.72321			0.861605	−	0.507579i	$-0.169459\pi$
$881$	1518.15			1.72321			0.861605	+	0.507579i	$0.169459\pi$
$882$		0			0
$883$	380.047	−	380.047i	0.430404	−	0.430404i	−0.458362	−	0.888766i	$-0.651564\pi$
$883$	380.047	−	380.047i	0.430404	−	0.430404i	0.888766	+	0.458362i	$0.151564\pi$
$884$		0			0
$885$	112.168	+	7.61729i	0.126744	+	0.00860711i
$886$		0			0
$887$		−	585.821i		−	0.660452i	−0.943902	−	0.330226i	$-0.892875\pi$
$887$		−	585.821i		−	0.660452i	0.943902	−	0.330226i	$-0.107125\pi$
$888$		0			0
$889$		−	1058.78i		−	1.19098i
$890$		0			0
$891$	15.7813	−	15.7813i	0.0177119	−	0.0177119i
$892$		0			0
$893$	753.056	+	753.056i	0.843288	+	0.843288i
$894$		0			0
$895$	156.811	−	136.867i	0.175208	−	0.152925i
$896$		0			0
$897$			52.1783i			0.0581698i
$898$		0			0
$899$	1357.06	+	1357.06i	1.50953	+	1.50953i
$900$		0			0
$901$	−97.9886	−	97.9886i	−0.108755	−	0.108755i
$902$		0			0
$903$		−	116.039i		−	0.128503i
$904$		0			0
$905$	−874.535	+	763.310i	−0.966337	+	0.843436i
$906$		0			0
$907$	−1183.59	−	1183.59i	−1.30495	−	1.30495i	−0.925011	−	0.379939i	$-0.875945\pi$
$907$	−1183.59	−	1183.59i	−1.30495	−	1.30495i	−0.379939	−	0.925011i	$-0.624055\pi$
$908$		0			0
$909$	152.598	−	152.598i	0.167874	−	0.167874i
$910$		0			0
$911$			512.773i			0.562868i	0.959581	+	0.281434i	$0.0908100\pi$
$911$			512.773i			0.562868i	−0.959581	+	0.281434i	$0.909190\pi$
$912$		0			0
$913$		−	373.302i		−	0.408874i
$914$		0			0
$915$	808.709	+	54.9190i	0.883835	+	0.0600207i
$916$		0			0
$917$	771.321	−	771.321i	0.841135	−	0.841135i
$918$		0			0
$919$	−225.492			−0.245367			−0.122684	−	0.992446i	$-0.539150\pi$
$919$	−225.492			−0.245367			−0.122684	+	0.992446i	$0.539150\pi$
$920$		0			0
$921$			802.986i			0.871864i
$922$		0			0
$923$	−48.8338	−	48.8338i	−0.0529077	−	0.0529077i
$924$		0			0
$925$	938.819	−	713.379i	1.01494	−	0.771221i
$926$		0			0
$927$	558.101			0.602051
$928$		0			0
$929$	−1624.89			−1.74907			−0.874535	−	0.484962i	$-0.838833\pi$
$929$	−1624.89			−1.74907			−0.874535	+	0.484962i	$0.838833\pi$
$930$		0			0
$931$	−99.3263	−	99.3263i	−0.106688	−	0.106688i
$932$		0			0
$933$	−317.826	+	317.826i	−0.340650	+	0.340650i
$934$		0			0
$935$	−106.235	+	92.7239i	−0.113620	+	0.0991699i
$936$		0			0
$937$	68.1189			0.0726990			0.0363495	−	0.999339i	$-0.488427\pi$
$937$	68.1189			0.0726990			0.0363495	+	0.999339i	$0.488427\pi$
$938$		0			0
$939$	227.264	−	227.264i	0.242028	−	0.242028i
$940$		0			0
$941$	771.592	−	771.592i	0.819970	−	0.819970i	−0.166133	−	0.986103i	$-0.553128\pi$
$941$	771.592	−	771.592i	0.819970	−	0.819970i	0.986103	+	0.166133i	$0.0531282\pi$
$942$		0			0
$943$	133.577			0.141651
$944$		0			0
$945$	125.333	+	143.596i	0.132627	+	0.151953i
$946$		0			0
$947$	−612.908	+	612.908i	−0.647210	+	0.647210i	−0.952318	−	0.305108i	$-0.901308\pi$
$947$	−612.908	+	612.908i	−0.647210	+	0.647210i	0.305108	+	0.952318i	$0.401308\pi$
$948$		0			0
$949$	−597.974	−	597.974i	−0.630110	−	0.630110i
$950$		0			0
$951$	−374.503			−0.393800
$952$		0			0
$953$	772.212			0.810296			0.405148	−	0.914251i	$-0.367220\pi$
$953$	772.212			0.810296			0.405148	+	0.914251i	$0.367220\pi$
$954$		0			0
$955$	951.781	+	64.6349i	0.996629	+	0.0676805i
$956$		0			0
$957$	−123.112	−	123.112i	−0.128644	−	0.128644i
$958$		0			0
$959$			162.082i			0.169012i
$960$		0			0
$961$	−1280.55			−1.33252
$962$		0			0
$963$	−332.937	+	332.937i	−0.345729	+	0.345729i
$964$		0			0
$965$	1238.26	+	84.0897i	1.28317	+	0.0871395i
$966$		0			0
$967$			737.387i			0.762551i	0.924461	+	0.381276i	$0.124515\pi$
$967$			737.387i			0.762551i	−0.924461	+	0.381276i	$0.875485\pi$
$968$		0			0
$969$			574.146i			0.592514i
$970$		0			0
$971$	357.349	−	357.349i	0.368022	−	0.368022i	−0.498734	−	0.866755i	$-0.666201\pi$
$971$	357.349	−	357.349i	0.368022	−	0.368022i	0.866755	+	0.498734i	$0.166201\pi$
$972$		0			0
$973$	−546.429	−	546.429i	−0.561592	−	0.561592i
$974$		0			0
$975$	361.584	+	49.3374i	0.370855	+	0.0506025i
$976$		0			0
$977$		−	772.087i		−	0.790263i	−0.918625	−	0.395131i	$-0.870699\pi$
$977$		−	772.087i		−	0.790263i	0.918625	−	0.395131i	$-0.129301\pi$
$978$		0			0
$979$	206.181	+	206.181i	0.210604	+	0.210604i
$980$		0			0
$981$	274.464	+	274.464i	0.279780	+	0.279780i
$982$		0			0
$983$			901.935i			0.917533i	0.888557	+	0.458767i	$0.151709\pi$
$983$			901.935i			0.917533i	−0.888557	+	0.458767i	$0.848291\pi$
$984$		0			0
$985$	326.128	+	373.650i	0.331095	+	0.379340i
$986$		0			0
$987$	328.290	+	328.290i	0.332614	+	0.332614i
$988$		0			0
$989$	−23.0820	+	23.0820i	−0.0233387	+	0.0233387i
$990$		0			0
$991$		−	783.887i		−	0.791006i	−0.918465	−	0.395503i	$-0.870570\pi$
$991$		−	783.887i		−	0.791006i	0.918465	−	0.395503i	$-0.129430\pi$
$992$		0			0
$993$			207.195i			0.208655i
$994$		0			0
$995$	109.369	−	1610.52i	0.109919	−	1.61861i
$996$		0			0
$997$	−391.218	+	391.218i	−0.392395	+	0.392395i	−0.875540	−	0.483145i	$-0.839494\pi$
$997$	−391.218	+	391.218i	−0.392395	+	0.392395i	0.483145	+	0.875540i	$0.339494\pi$
$998$		0			0
$999$	−245.073			−0.245318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.q.a.79.20		96
4.3	odd	2		240.3.q.a.139.48	yes	96
5.4	even	2	inner	960.3.q.a.79.29		96
16.3	odd	4	inner	960.3.q.a.559.29		96
16.13	even	4		240.3.q.a.19.1	✓	96
20.19	odd	2		240.3.q.a.139.1	yes	96
80.19	odd	4	inner	960.3.q.a.559.20		96
80.29	even	4		240.3.q.a.19.48	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.q.a.19.1	✓	96	16.13	even	4
240.3.q.a.19.48	yes	96	80.29	even	4
240.3.q.a.139.1	yes	96	20.19	odd	2
240.3.q.a.139.48	yes	96	4.3	odd	2
960.3.q.a.79.20		96	1.1	even	1	trivial
960.3.q.a.79.29		96	5.4	even	2	inner
960.3.q.a.559.20		96	80.19	odd	4	inner
960.3.q.a.559.29		96	16.3	odd	4	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-0.338767 + 4.98851i) q^{5} -7.33616i q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-0.338767 + 4.98851i) q^{5} -7.33616i q^{7} -3.00000i q^{9} +(-1.75348 + 1.75348i) q^{11} +(5.95935 + 5.95935i) q^{13} +(-5.69475 - 6.52456i) q^{15} -11.3727i q^{17} +(20.6103 + 20.6103i) q^{19} +(8.98493 + 8.98493i) q^{21} -3.57450i q^{23} +(-24.7705 - 3.37989i) q^{25} +(3.67423 + 3.67423i) q^{27} +(28.6633 - 28.6633i) q^{29} +47.3451i q^{31} -4.29513i q^{33} +(36.5965 + 2.48525i) q^{35} +(-33.3502 + 33.3502i) q^{37} -14.5974 q^{39} +37.3695i q^{41} +(-6.45740 - 6.45740i) q^{43} +(14.9655 + 1.01630i) q^{45} +36.5378 q^{47} -4.81925 q^{49} +(13.9286 + 13.9286i) q^{51} +(8.61615 - 8.61615i) q^{53} +(-8.15323 - 9.34127i) q^{55} -50.4847 q^{57} +(-9.17960 + 9.17960i) q^{59} +(-66.1829 + 66.1829i) q^{61} -22.0085 q^{63} +(-31.7471 + 27.7094i) q^{65} +(14.8238 - 14.8238i) q^{67} +(4.37785 + 4.37785i) q^{69} -8.19449 q^{71} -100.342 q^{73} +(34.4770 - 26.1980i) q^{75} +(12.8638 + 12.8638i) q^{77} +49.4801i q^{79} -9.00000 q^{81} +(-106.446 + 106.446i) q^{83} +(56.7326 + 3.85268i) q^{85} +70.2103i q^{87} -117.584i q^{89} +(43.7187 - 43.7187i) q^{91} +(-57.9856 - 57.9856i) q^{93} +(-109.797 + 95.8326i) q^{95} +92.3995i q^{97} +(5.26044 + 5.26044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 32 q^{19} - 96 q^{35} - 672 q^{49} + 96 q^{51} - 256 q^{55} - 128 q^{59} - 32 q^{61} + 32 q^{65} - 96 q^{69} - 512 q^{71} + 192 q^{75} - 864 q^{81} + 384 q^{91}+O(q^{100}) \) 96 * q - 32 * q^19 - 96 * q^35 - 672 * q^49 + 96 * q^51 - 256 * q^55 - 128 * q^59 - 32 * q^61 + 32 * q^65 - 96 * q^69 - 512 * q^71 + 192 * q^75 - 864 * q^81 + 384 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more