LMFDB - Embedded newform 336.4.bc.f.17.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.17
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82323 - 4.36227i) q^{3} +(9.22876 + 15.9847i) q^{5} +(6.70316 - 17.2646i) q^{7} +(-11.0587 - 24.6314i) q^{9} +O(q^{10})$	\(q+(2.82323 - 4.36227i) q^{3} +(9.22876 + 15.9847i) q^{5} +(6.70316 - 17.2646i) q^{7} +(-11.0587 - 24.6314i) q^{9} +(-11.8936 - 6.86675i) q^{11} +9.57796i q^{13} +(95.7844 + 4.87012i) q^{15} +(48.2369 - 83.5487i) q^{17} +(23.2633 - 13.4311i) q^{19} +(-56.3884 - 77.9830i) q^{21} +(153.916 - 88.8636i) q^{23} +(-107.840 + 186.785i) q^{25} +(-138.670 - 21.2988i) q^{27} +131.286i q^{29} +(273.494 + 157.902i) q^{31} +(-63.5329 + 32.4965i) q^{33} +(337.832 - 52.1833i) q^{35} +(-54.7017 - 94.7462i) q^{37} +(41.7816 + 27.0408i) q^{39} +390.559 q^{41} -291.845 q^{43} +(291.666 - 404.088i) q^{45} +(-149.356 - 258.693i) q^{47} +(-253.135 - 231.455i) q^{49} +(-228.278 - 446.299i) q^{51} +(6.68211 + 3.85792i) q^{53} -253.486i q^{55} +(7.08773 - 139.400i) q^{57} +(133.833 - 231.806i) q^{59} +(195.928 - 113.119i) q^{61} +(-499.380 + 25.8171i) q^{63} +(-153.101 + 88.3927i) q^{65} +(-296.160 + 512.964i) q^{67} +(46.8943 - 922.306i) q^{69} -864.334i q^{71} +(474.644 + 274.036i) q^{73} +(510.347 + 997.763i) q^{75} +(-198.276 + 159.309i) q^{77} +(-91.1561 - 157.887i) q^{79} +(-484.408 + 544.784i) q^{81} +54.3619 q^{83} +1780.67 q^{85} +(572.705 + 370.651i) q^{87} +(-403.372 - 698.661i) q^{89} +(165.360 + 64.2026i) q^{91} +(1460.95 - 747.261i) q^{93} +(429.384 + 247.905i) q^{95} +1428.85i q^{97} +(-37.6096 + 368.892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q - 12 * q^7 + 14 * q^9	$ 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) $ 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	2.82323	−	4.36227i	0.543331	−	0.839519i
$3$	2.82323	−	4.36227i	0.543331	−	0.839519i
$4$		0			0
$5$	9.22876	+	15.9847i	0.825446	+	1.42971i	0.901578	+	0.432616i	$0.142409\pi$
$5$	9.22876	+	15.9847i	0.825446	+	1.42971i	−0.0761328	+	0.997098i	$0.524257\pi$
$6$		0			0
$7$	6.70316	−	17.2646i	0.361937	−	0.932203i
$7$	6.70316	−	17.2646i	0.361937	−	0.932203i
$8$		0			0
$9$	−11.0587	−	24.6314i	−0.409583	−	0.912273i
$10$		0			0
$11$	−11.8936	−	6.86675i	−0.326004	−	0.188218i	0.328062	−	0.944656i	$-0.393605\pi$
$11$	−11.8936	−	6.86675i	−0.326004	−	0.188218i	−0.654066	+	0.756438i	$0.726938\pi$
$12$		0			0
$13$			9.57796i			0.204342i	0.994767	+	0.102171i	$0.0325789\pi$
$13$			9.57796i			0.204342i	−0.994767	+	0.102171i	$0.967421\pi$
$14$		0			0
$15$	95.7844	+	4.87012i	1.64876	+	0.0838306i
$16$		0			0
$17$	48.2369	−	83.5487i	0.688186	−	1.19197i	−0.284239	−	0.958754i	$-0.591741\pi$
$17$	48.2369	−	83.5487i	0.688186	−	1.19197i	0.972424	−	0.233219i	$-0.0749259\pi$
$18$		0			0
$19$	23.2633	−	13.4311i	0.280893	−	0.162174i	−0.352934	−	0.935648i	$-0.614816\pi$
$19$	23.2633	−	13.4311i	0.280893	−	0.162174i	0.633828	+	0.773474i	$0.281483\pi$
$20$		0			0
$21$	−56.3884	−	77.9830i	−0.585950	−	0.810347i
$22$		0			0
$23$	153.916	−	88.8636i	1.39538	−	0.805623i	0.401476	−	0.915869i	$-0.368497\pi$
$23$	153.916	−	88.8636i	1.39538	−	0.805623i	0.993904	+	0.110246i	$0.0351639\pi$
$24$		0			0
$25$	−107.840	+	186.785i	−0.862721	+	1.49428i
$26$		0			0
$27$	−138.670	−	21.2988i	−0.988409	−	0.151813i
$28$		0			0
$29$			131.286i			0.840662i	0.907371	+	0.420331i	$0.138086\pi$
$29$			131.286i			0.840662i	−0.907371	+	0.420331i	$0.861914\pi$
$30$		0			0
$31$	273.494	+	157.902i	1.58455	+	0.914839i	0.994183	+	0.107702i	$0.0343494\pi$
$31$	273.494	+	157.902i	1.58455	+	0.914839i	0.590365	+	0.807137i	$0.298984\pi$
$32$		0			0
$33$	−63.5329	+	32.4965i	−0.335141	+	0.171421i
$34$		0			0
$35$	337.832	−	52.1833i	1.63154	−	0.252017i
$36$		0			0
$37$	−54.7017	−	94.7462i	−0.243052	−	0.420978i	0.718530	−	0.695496i	$-0.244815\pi$
$37$	−54.7017	−	94.7462i	−0.243052	−	0.420978i	−0.961582	+	0.274518i	$0.911482\pi$
$38$		0			0
$39$	41.7816	+	27.0408i	0.171549	+	0.111025i
$40$		0			0
$41$	390.559			1.48768			0.743841	−	0.668356i	$-0.233002\pi$
$41$	390.559			1.48768			0.743841	+	0.668356i	$0.233002\pi$
$42$		0			0
$43$	−291.845			−1.03502			−0.517511	−	0.855676i	$-0.673141\pi$
$43$	−291.845			−1.03502			−0.517511	+	0.855676i	$0.673141\pi$
$44$		0			0
$45$	291.666	−	404.088i	0.966200	−	1.33862i
$46$		0			0
$47$	−149.356	−	258.693i	−0.463529	−	0.802856i	0.535605	−	0.844469i	$-0.320084\pi$
$47$	−149.356	−	258.693i	−0.463529	−	0.802856i	−0.999134	+	0.0416127i	$0.986750\pi$
$48$		0			0
$49$	−253.135	−	231.455i	−0.738004	−	0.674797i
$50$		0			0
$51$	−228.278	−	446.299i	−0.626771	−	1.22538i
$52$		0			0
$53$	6.68211	+	3.85792i	0.0173181	+	0.00999860i	0.508634	−	0.860983i	$-0.330151\pi$
$53$	6.68211	+	3.85792i	0.0173181	+	0.00999860i	−0.491316	+	0.870981i	$0.663484\pi$
$54$		0			0
$55$		−	253.486i		−	0.621456i
$56$		0			0
$57$	7.08773	−	139.400i	0.0164701	−	0.323929i
$58$		0			0
$59$	133.833	−	231.806i	0.295316	−	0.511502i	−0.679743	−	0.733451i	$-0.737909\pi$
$59$	133.833	−	231.806i	0.295316	−	0.511502i	0.975058	+	0.221949i	$0.0712418\pi$
$60$		0			0
$61$	195.928	−	113.119i	0.411245	−	0.237432i	−0.280079	−	0.959977i	$-0.590361\pi$
$61$	195.928	−	113.119i	0.411245	−	0.237432i	0.691325	+	0.722544i	$0.257027\pi$
$62$		0			0
$63$	−499.380	+	25.8171i	−0.998666	+	0.0516294i
$64$		0			0
$65$	−153.101	+	88.3927i	−0.292151	+	0.168673i
$66$		0			0
$67$	−296.160	+	512.964i	−0.540026	+	0.935352i	0.458876	+	0.888500i	$0.348252\pi$
$67$	−296.160	+	512.964i	−0.540026	+	0.935352i	−0.998902	+	0.0468517i	$0.985081\pi$
$68$		0			0
$69$	46.8943	−	922.306i	0.0818175	−	1.60917i
$70$		0			0
$71$		−	864.334i		−	1.44475i	−0.691499	−	0.722377i	$-0.743050\pi$
$71$		−	864.334i		−	1.44475i	0.691499	−	0.722377i	$-0.256950\pi$
$72$		0			0
$73$	474.644	+	274.036i	0.760998	+	0.439362i	0.829654	−	0.558278i	$-0.188538\pi$
$73$	474.644	+	274.036i	0.760998	+	0.439362i	−0.0686560	+	0.997640i	$0.521871\pi$
$74$		0			0
$75$	510.347	+	997.763i	0.785730	+	1.53616i
$76$		0			0
$77$	−198.276	+	159.309i	−0.293451	+	0.235779i
$78$		0			0
$79$	−91.1561	−	157.887i	−0.129821	−	0.224857i	0.793786	−	0.608197i	$-0.208107\pi$
$79$	−91.1561	−	157.887i	−0.129821	−	0.224857i	−0.923607	+	0.383340i	$0.874774\pi$
$80$		0			0
$81$	−484.408	+	544.784i	−0.664483	+	0.747303i
$82$		0			0
$83$	54.3619			0.0718915			0.0359458	−	0.999354i	$-0.488556\pi$
$83$	54.3619			0.0718915			0.0359458	+	0.999354i	$0.488556\pi$
$84$		0			0
$85$	1780.67			2.27224
$86$		0			0
$87$	572.705	+	370.651i	0.705751	+	0.456758i
$88$		0			0
$89$	−403.372	−	698.661i	−0.480420	−	0.832111i	0.519328	−	0.854575i	$-0.326182\pi$
$89$	−403.372	−	698.661i	−0.480420	−	0.832111i	−0.999748	+	0.0224638i	$0.992849\pi$
$90$		0			0
$91$	165.360	+	64.2026i	0.190488	+	0.0739589i
$92$		0			0
$93$	1460.95	−	747.261i	1.62896	−	0.833197i
$94$		0			0
$95$	429.384	+	247.905i	0.463724	+	0.267731i
$96$		0			0
$97$			1428.85i			1.49565i	0.663897	+	0.747824i	$0.268901\pi$
$97$			1428.85i			1.49565i	−0.663897	+	0.747824i	$0.731099\pi$
$98$		0			0
$99$	−37.6096	+	368.892i	−0.0381809	+	0.374496i
$100$		0			0
$101$	−374.344	+	648.383i	−0.368799	+	0.638778i	−0.989378	−	0.145366i	$-0.953564\pi$
$101$	−374.344	+	648.383i	−0.368799	+	0.638778i	0.620579	+	0.784144i	$0.286897\pi$
$102$		0			0
$103$	−1293.50	+	746.802i	−1.23740	+	0.714413i	−0.968562	−	0.248772i	$-0.919973\pi$
$103$	−1293.50	+	746.802i	−1.23740	+	0.714413i	−0.268838	+	0.963185i	$0.586640\pi$
$104$		0			0
$105$	726.139	−	1621.04i	0.674894	−	1.50664i
$106$		0			0
$107$	−715.658	+	413.185i	−0.646591	+	0.373310i	−0.787149	−	0.616763i	$-0.788444\pi$
$107$	−715.658	+	413.185i	−0.646591	+	0.373310i	0.140558	+	0.990072i	$0.455110\pi$
$108$		0			0
$109$	−855.714	+	1482.14i	−0.751950	+	1.30242i	0.194926	+	0.980818i	$0.437553\pi$
$109$	−855.714	+	1482.14i	−0.751950	+	1.30242i	−0.946876	+	0.321598i	$0.895780\pi$
$110$		0			0
$111$	−567.744	−	28.8667i	−0.485476	−	0.0246838i
$112$		0			0
$113$			1341.89i			1.11712i	0.829465	+	0.558559i	$0.188646\pi$
$113$			1341.89i			1.11712i	−0.829465	+	0.558559i	$0.811354\pi$
$114$		0			0
$115$	2840.91	+	1640.20i	2.30362	+	1.33000i
$116$		0			0
$117$	235.918	−	105.920i	0.186416	−	0.0836951i
$118$		0			0
$119$	−1119.10	−	1392.83i	−0.862080	−	1.07295i
$120$		0			0
$121$	−571.195	−	989.340i	−0.429148	−	0.743305i
$122$		0			0
$123$	1102.64	−	1703.72i	0.808304	−	1.24894i
$124$		0			0
$125$	−1673.73			−1.19762
$126$		0			0
$127$	−609.483			−0.425849			−0.212925	−	0.977069i	$-0.568299\pi$
$127$	−609.483			−0.425849			−0.212925	+	0.977069i	$0.568299\pi$
$128$		0			0
$129$	−823.946	+	1273.11i	−0.562360	+	0.868921i
$130$		0			0
$131$	−95.9071	−	166.116i	−0.0639652	−	0.110791i	0.832269	−	0.554372i	$-0.187041\pi$
$131$	−95.9071	−	166.116i	−0.0639652	−	0.110791i	−0.896234	+	0.443581i	$0.853708\pi$
$132$		0			0
$133$	−75.9450	−	491.664i	−0.0495133	−	0.320546i
$134$		0			0
$135$	−939.297	−	2413.16i	−0.598828	−	1.53846i
$136$		0			0
$137$	1986.25	+	1146.76i	1.23866	+	0.715143i	0.968821	−	0.247761i	$-0.0796949\pi$
$137$	1986.25	+	1146.76i	1.23866	+	0.715143i	0.269843	+	0.962904i	$0.413028\pi$
$138$		0			0
$139$		−	9.00649i		−	0.00549583i	−0.999996	−	0.00274791i	$-0.999125\pi$
$139$		−	9.00649i		−	0.00549583i	0.999996	−	0.00274791i	$-0.000874689\pi$
$140$		0			0
$141$	−1550.16	−	78.8170i	−0.925863	−	0.0470751i
$142$		0			0
$143$	65.7694	−	113.916i	0.0384610	−	0.0666163i
$144$		0			0
$145$	−2098.57	+	1211.61i	−1.20191	+	0.693921i
$146$		0			0
$147$	−1724.33	+	450.792i	−0.967485	+	0.252930i
$148$		0			0
$149$	−1410.81	+	814.534i	−0.775694	+	0.447847i	−0.834902	−	0.550399i	$-0.814476\pi$
$149$	−1410.81	+	814.534i	−0.775694	+	0.447847i	0.0592083	+	0.998246i	$0.481142\pi$
$150$		0			0
$151$	963.346	−	1668.56i	0.519179	−	0.899244i	−0.480573	−	0.876955i	$-0.659571\pi$
$151$	963.346	−	1668.56i	0.519179	−	0.899244i	0.999752	−	0.0222893i	$-0.00709550\pi$
$152$		0			0
$153$	−2591.36	−	264.196i	−1.36927	−	0.139601i
$154$		0			0
$155$			5828.95i			3.02060i
$156$		0			0
$157$	−2985.71	−	1723.80i	−1.51774	−	0.876269i	−0.999782	−	0.0208632i	$-0.993359\pi$
$157$	−2985.71	−	1723.80i	−1.51774	−	0.876269i	−0.517959	−	0.855405i	$-0.673308\pi$
$158$		0			0
$159$	35.6944	−	18.2574i	0.0178035	−	0.00910631i
$160$		0			0
$161$	−502.472	−	3252.97i	−0.245965	−	1.59236i
$162$		0			0
$163$	77.3149	+	133.913i	0.0371520	+	0.0643491i	0.884004	−	0.467480i	$-0.154838\pi$
$163$	77.3149	+	133.913i	0.0371520	+	0.0643491i	−0.846852	+	0.531829i	$0.821505\pi$
$164$		0			0
$165$	−1105.78	−	715.650i	−0.521724	−	0.337656i
$166$		0			0
$167$	−1777.02			−0.823412			−0.411706	−	0.911317i	$-0.635067\pi$
$167$	−1777.02			−0.823412			−0.411706	+	0.911317i	$0.635067\pi$
$168$		0			0
$169$	2105.26			0.958244
$170$		0			0
$171$	−588.089	−	424.477i	−0.262996	−	0.189828i
$172$		0			0
$173$	1498.78	+	2595.97i	0.658673	+	1.14086i	0.980959	+	0.194213i	$0.0622152\pi$
$173$	1498.78	+	2595.97i	0.658673	+	1.14086i	−0.322286	+	0.946642i	$0.604451\pi$
$174$		0			0
$175$	2501.90	+	3113.87i	1.08072	+	1.34506i
$176$		0			0
$177$	−633.358	−	1238.26i	−0.268961	−	0.525838i
$178$		0			0
$179$	1351.00	+	780.000i	0.564125	+	0.325698i	0.754800	−	0.655956i	$-0.227734\pi$
$179$	1351.00	+	780.000i	0.564125	+	0.325698i	−0.190674	+	0.981653i	$0.561067\pi$
$180$		0			0
$181$			3334.08i			1.36917i	0.728932	+	0.684586i	$0.240017\pi$
$181$			3334.08i			1.36917i	−0.728932	+	0.684586i	$0.759983\pi$
$182$		0			0
$183$	59.6940	−	1174.05i	0.0241132	−	0.474252i
$184$		0			0
$185$	1009.66	−	1748.78i	0.401252	−	0.694989i
$186$		0			0
$187$	−1147.42	+	662.461i	−0.448703	+	0.259059i
$188$		0			0
$189$	−1297.24	+	2251.32i	−0.499262	+	0.866451i
$190$		0			0
$191$	1673.63	−	966.272i	0.634030	−	0.366058i	−0.148281	−	0.988945i	$-0.547374\pi$
$191$	1673.63	−	966.272i	0.634030	−	0.366058i	0.782311	+	0.622888i	$0.214041\pi$
$192$		0			0
$193$	−466.456	+	807.926i	−0.173970	+	0.301325i	−0.939804	−	0.341713i	$-0.888993\pi$
$193$	−466.456	+	807.926i	−0.173970	+	0.301325i	0.765834	+	0.643038i	$0.222326\pi$
$194$		0			0
$195$	−46.6458	+	917.419i	−0.0171301	+	0.336911i
$196$		0			0
$197$			70.8432i			0.0256212i	0.999918	+	0.0128106i	$0.00407785\pi$
$197$			70.8432i			0.0256212i	−0.999918	+	0.0128106i	$0.995922\pi$
$198$		0			0
$199$	−155.038	−	89.5110i	−0.0552278	−	0.0318858i	0.472132	−	0.881528i	$-0.343485\pi$
$199$	−155.038	−	89.5110i	−0.0552278	−	0.0318858i	−0.527360	+	0.849642i	$0.676818\pi$
$200$		0			0
$201$	1401.56	+	2740.15i	0.491833	+	0.961567i
$202$		0			0
$203$	2266.60	+	880.031i	0.783667	+	0.304266i
$204$		0			0
$205$	3604.37	+	6242.95i	1.22800	+	2.12696i
$206$		0			0
$207$	−3890.95	−	2808.45i	−1.30647	−	0.942998i
$208$		0			0
$209$	−368.912			−0.122096
$210$		0			0
$211$	−4212.89			−1.37454			−0.687268	−	0.726404i	$-0.741190\pi$
$211$	−4212.89			−1.37454			−0.687268	+	0.726404i	$0.741190\pi$
$212$		0			0
$213$	−3770.45	−	2440.21i	−1.21290	−	0.784979i
$214$		0			0
$215$	−2693.37	−	4665.05i	−0.854355	−	1.47979i
$216$		0			0
$217$	4559.39	−	3663.33i	1.42632	−	1.14601i
$218$		0			0
$219$	2535.45	−	1296.86i	0.782327	−	0.400153i
$220$		0			0
$221$	800.226	+	462.011i	0.243570	+	0.140625i
$222$		0			0
$223$			3209.10i			0.963665i	0.876263	+	0.481832i	$0.160029\pi$
$223$			3209.10i			0.963665i	−0.876263	+	0.481832i	$0.839971\pi$
$224$		0			0
$225$	5793.33	+	590.646i	1.71654	+	0.175006i
$226$		0			0
$227$	−2183.45	+	3781.85i	−0.638417	+	1.10577i	0.347363	+	0.937731i	$0.387077\pi$
$227$	−2183.45	+	3781.85i	−0.638417	+	1.10577i	−0.985780	+	0.168041i	$0.946256\pi$
$228$		0			0
$229$	4938.90	−	2851.47i	1.42520	−	0.822842i	0.428466	−	0.903558i	$-0.359054\pi$
$229$	4938.90	−	2851.47i	1.42520	−	0.822842i	0.996737	+	0.0807162i	$0.0257208\pi$
$230$		0			0
$231$	135.169	+	1314.70i	0.0384998	+	0.374463i
$232$		0			0
$233$	−602.128	+	347.639i	−0.169299	+	0.0977450i	−0.582255	−	0.813006i	$-0.697830\pi$
$233$	−602.128	+	347.639i	−0.169299	+	0.0977450i	0.412956	+	0.910751i	$0.364496\pi$
$234$		0			0
$235$	2756.75	−	4774.83i	0.765236	−	1.32543i
$236$		0			0
$237$	−946.099	−	48.1041i	−0.259307	−	0.0131844i
$238$		0			0
$239$			4543.15i			1.22959i	0.788687	+	0.614795i	$0.210761\pi$
$239$			4543.15i			1.22959i	−0.788687	+	0.614795i	$0.789239\pi$
$240$		0			0
$241$	−1368.50	−	790.103i	−0.365779	−	0.211183i	0.305834	−	0.952085i	$-0.401065\pi$
$241$	−1368.50	−	790.103i	−0.365779	−	0.211183i	−0.671613	+	0.740902i	$0.734398\pi$
$242$		0			0
$243$	1008.90	+	3651.17i	0.266341	+	0.963879i
$244$		0			0
$245$	1363.62	−	6182.33i	0.355584	−	1.61214i
$246$		0			0
$247$	128.642	+	222.815i	0.0331390	+	0.0573984i
$248$		0			0
$249$	153.476	−	237.141i	0.0390609	−	0.0603543i
$250$		0			0
$251$	−2564.07			−0.644792			−0.322396	−	0.946605i	$-0.604488\pi$
$251$	−2564.07			−0.644792			−0.322396	+	0.946605i	$0.604488\pi$
$252$		0			0
$253$	−2440.82			−0.606533
$254$		0			0
$255$	5027.23	−	7767.74i	1.23458	−	1.90759i
$256$		0			0
$257$	−1788.60	−	3097.94i	−0.434123	−	0.751923i	0.563101	−	0.826388i	$-0.309608\pi$
$257$	−1788.60	−	3097.94i	−0.434123	−	0.751923i	−0.997224	+	0.0744656i	$0.976275\pi$
$258$		0			0
$259$	−2002.43	+	309.307i	−0.480406	+	0.0742061i
$260$		0			0
$261$	3233.75	−	1451.86i	0.766913	−	0.344321i
$262$		0			0
$263$	1319.83	+	762.002i	0.309445	+	0.178658i	0.646678	−	0.762763i	$-0.276158\pi$
$263$	1319.83	+	762.002i	0.309445	+	0.178658i	−0.337233	+	0.941421i	$0.609491\pi$
$264$		0			0
$265$			142.415i			0.0330132i
$266$		0			0
$267$	−4186.56	−	212.864i	−0.959600	−	0.0487905i
$268$		0			0
$269$	2858.80	−	4951.58i	0.647970	−	1.12232i	−0.335637	−	0.941991i	$-0.608951\pi$
$269$	2858.80	−	4951.58i	0.647970	−	1.12232i	0.983607	−	0.180326i	$-0.0577152\pi$
$270$		0			0
$271$	−2327.04	+	1343.52i	−0.521615	+	0.301155i	−0.737595	−	0.675243i	$-0.764039\pi$
$271$	−2327.04	+	1343.52i	−0.521615	+	0.301155i	0.215980	+	0.976398i	$0.430705\pi$
$272$		0			0
$273$	746.918	−	540.085i	0.165588	−	0.119734i
$274$		0			0
$275$	2565.21	−	1481.02i	0.562501	−	0.324760i
$276$		0			0
$277$	1560.93	−	2703.62i	0.338583	−	0.586443i	−0.645584	−	0.763690i	$-0.723386\pi$
$277$	1560.93	−	2703.62i	0.338583	−	0.586443i	0.984166	+	0.177247i	$0.0567191\pi$
$278$		0			0
$279$	864.838	−	8482.73i	0.185579	−	1.82024i
$280$		0			0
$281$			1752.02i			0.371946i	0.982555	+	0.185973i	$0.0595438\pi$
$281$			1752.02i			0.371946i	−0.982555	+	0.185973i	$0.940456\pi$
$282$		0			0
$283$	−2513.35	−	1451.08i	−0.527927	−	0.304799i	0.212245	−	0.977216i	$-0.431922\pi$
$283$	−2513.35	−	1451.08i	−0.527927	−	0.304799i	−0.740172	+	0.672418i	$0.765256\pi$
$284$		0			0
$285$	2293.68	−	1173.19i	0.476721	−	0.243839i
$286$		0			0
$287$	2617.98	−	6742.85i	0.538447	−	1.38682i
$288$		0			0
$289$	−2197.09	−	3805.47i	−0.447199	−	0.774572i
$290$		0			0
$291$	6233.03	+	4033.97i	1.25562	+	0.812631i
$292$		0			0
$293$	−2276.83			−0.453973			−0.226986	−	0.973898i	$-0.572887\pi$
$293$	−2276.83			−0.453973			−0.226986	+	0.973898i	$0.572887\pi$
$294$		0			0
$295$	4940.47			0.975068
$296$		0			0
$297$	1503.03	+	1205.53i	0.293651	+	0.235529i
$298$		0			0
$299$	851.132	+	1474.20i	0.164623	+	0.285135i
$300$		0			0
$301$	−1956.29	+	5038.60i	−0.374613	+	0.964851i
$302$		0			0
$303$	1771.56	+	3463.53i	0.335886	+	0.656681i
$304$		0			0
$305$	3616.34	+	2087.89i	0.678921	+	0.391975i
$306$		0			0
$307$			7462.09i			1.38724i	0.720339	+	0.693622i	$0.243986\pi$
$307$			7462.09i			1.38724i	−0.720339	+	0.693622i	$0.756014\pi$
$308$		0			0
$309$	−394.096	+	7750.98i	−0.0725544	+	1.42698i
$310$		0			0
$311$	1299.63	−	2251.03i	0.236963	−	0.410432i	−0.722879	−	0.690975i	$-0.757181\pi$
$311$	1299.63	−	2251.03i	0.236963	−	0.410432i	0.959841	+	0.280544i	$0.0905147\pi$
$312$		0			0
$313$	−7374.60	+	4257.73i	−1.33175	+	0.768885i	−0.985568	−	0.169283i	$-0.945855\pi$
$313$	−7374.60	+	4257.73i	−1.33175	+	0.768885i	−0.346181	+	0.938168i	$0.612522\pi$
$314$		0			0
$315$	−5021.34	−	7744.17i	−0.898160	−	1.38519i
$316$		0			0
$317$	7068.63	−	4081.08i	1.25241	−	0.723079i	0.280822	−	0.959760i	$-0.409393\pi$
$317$	7068.63	−	4081.08i	1.25241	−	0.723079i	0.971588	+	0.236681i	$0.0760595\pi$
$318$		0			0
$319$	901.508	−	1561.46i	0.158228	−	0.274059i
$320$		0			0
$321$	−218.042	+	4288.41i	−0.0379126	+	0.745656i
$322$		0			0
$323$		−	2591.49i		−	0.446423i
$324$		0			0
$325$	−1789.01	−	1032.89i	−0.305344	−	0.176290i
$326$		0			0
$327$	4049.61	+	7917.28i	0.684845	+	1.33892i
$328$		0			0
$329$	−5467.40	+	844.524i	−0.916193	+	0.141520i
$330$		0			0
$331$	−1352.75	−	2343.04i	−0.224635	−	0.389079i	0.731575	−	0.681761i	$-0.238786\pi$
$331$	−1352.75	−	2343.04i	−0.224635	−	0.389079i	−0.956210	+	0.292682i	$0.905452\pi$
$332$		0			0
$333$	−1728.80	+	2395.15i	−0.284497	+	0.394155i
$334$		0			0
$335$	−10932.8			−1.78305
$336$		0			0
$337$	−5077.74			−0.820778			−0.410389	−	0.911911i	$-0.634607\pi$
$337$	−5077.74			−0.820778			−0.410389	+	0.911911i	$0.634607\pi$
$338$		0			0
$339$	5853.68	+	3788.47i	0.937842	+	0.606965i
$340$		0			0
$341$	−2168.55	−	3756.03i	−0.344379	−	0.596482i
$342$		0			0
$343$	−5692.80	+	2818.81i	−0.896158	+	0.443735i
$344$		0			0
$345$	15175.5	−	7762.15i	2.36819	−	1.21131i
$346$		0			0
$347$	3008.36	+	1736.88i	0.465409	+	0.268704i	0.714316	−	0.699823i	$-0.246738\pi$
$347$	3008.36	+	1736.88i	0.465409	+	0.268704i	−0.248907	+	0.968527i	$0.580071\pi$
$348$		0			0
$349$		−	11703.1i		−	1.79500i	−0.441018	−	0.897498i	$-0.645383\pi$
$349$		−	11703.1i		−	1.79500i	0.441018	−	0.897498i	$-0.354617\pi$
$350$		0			0
$351$	203.999	−	1328.18i	0.0310218	−	0.201974i
$352$		0			0
$353$	−572.127	+	990.953i	−0.0862642	+	0.149414i	−0.905929	−	0.423429i	$-0.860826\pi$
$353$	−572.127	+	990.953i	−0.0862642	+	0.149414i	0.819665	+	0.572843i	$0.194160\pi$
$354$		0			0
$355$	13816.1	−	7976.73i	2.06558	−	1.19257i
$356$		0			0
$357$	−9235.38	+	949.519i	−1.36915	+	0.140767i
$358$		0			0
$359$	6726.77	−	3883.71i	0.988929	−	0.570959i	0.0839752	−	0.996468i	$-0.473238\pi$
$359$	6726.77	−	3883.71i	0.988929	−	0.570959i	0.904954	+	0.425509i	$0.139905\pi$
$360$		0			0
$361$	−3068.71	+	5315.16i	−0.447399	+	0.774918i
$362$		0			0
$363$	−5928.38	−	301.426i	−0.857188	−	0.0435834i
$364$		0			0
$365$			10116.0i			1.45068i
$366$		0			0
$367$	−5758.27	−	3324.54i	−0.819017	−	0.472860i	0.0310604	−	0.999518i	$-0.490112\pi$
$367$	−5758.27	−	3324.54i	−0.819017	−	0.472860i	−0.850077	+	0.526658i	$0.823445\pi$
$368$		0			0
$369$	−4319.09	−	9619.99i	−0.609330	−	1.35717i
$370$		0			0
$371$	111.397	−	89.5040i	0.0155888	−	0.0125251i
$372$		0			0
$373$	4290.92	+	7432.09i	0.595644	+	1.03169i	0.993456	+	0.114219i	$0.0364365\pi$
$373$	4290.92	+	7432.09i	0.595644	+	1.03169i	−0.397811	+	0.917467i	$0.630230\pi$
$374$		0			0
$375$	−4725.33	+	7301.26i	−0.650707	+	1.00543i
$376$		0			0
$377$	−1257.45			−0.171783
$378$		0			0
$379$	3462.36			0.469260			0.234630	−	0.972085i	$-0.424612\pi$
$379$	3462.36			0.469260			0.234630	+	0.972085i	$0.424612\pi$
$380$		0			0
$381$	−1720.71	+	2658.73i	−0.231377	+	0.357508i
$382$		0			0
$383$	−118.825	−	205.812i	−0.0158530	−	0.0274582i	0.857990	−	0.513666i	$-0.171713\pi$
$383$	−118.825	−	205.812i	−0.0158530	−	0.0274582i	−0.873843	+	0.486208i	$0.838380\pi$
$384$		0			0
$385$	−4376.35	−	1699.16i	−0.579323	−	0.224928i
$386$		0			0
$387$	3227.44	+	7188.54i	0.423928	+	0.944223i
$388$		0			0
$389$	1989.91	+	1148.88i	0.259364	+	0.149744i	0.624044	−	0.781389i	$-0.285488\pi$
$389$	1989.91	+	1148.88i	0.259364	+	0.149744i	−0.364681	+	0.931133i	$0.618822\pi$
$390$		0			0
$391$		−	17146.0i		−	2.21767i
$392$		0			0
$393$	−995.410	−	50.6112i	−0.127765	−	0.00649618i
$394$		0			0
$395$	1682.52	−	2914.20i	0.214320	−	0.371214i
$396$		0			0
$397$	11128.7	−	6425.14i	1.40688	−	0.812264i	0.411796	−	0.911276i	$-0.364902\pi$
$397$	11128.7	−	6425.14i	1.40688	−	0.812264i	0.995086	+	0.0990120i	$0.0315682\pi$
$398$		0			0
$399$	−2359.18	−	1056.79i	−0.296007	−	0.132595i
$400$		0			0
$401$	−6083.16	+	3512.11i	−0.757553	+	0.437373i	−0.828416	−	0.560113i	$-0.810758\pi$
$401$	−6083.16	+	3512.11i	−0.757553	+	0.437373i	0.0708638	+	0.997486i	$0.477424\pi$
$402$		0			0
$403$	−1512.38	+	2619.51i	−0.186940	+	0.323790i
$404$		0			0
$405$	−13178.7	−	2715.43i	−1.61692	−	0.333163i
$406$		0			0
$407$			1502.49i			0.182987i
$408$		0			0
$409$	−851.700	−	491.729i	−0.102968	−	0.0594485i	0.447632	−	0.894218i	$-0.352268\pi$
$409$	−851.700	−	491.729i	−0.102968	−	0.0594485i	−0.550600	+	0.834769i	$0.685601\pi$
$410$		0			0
$411$	10610.1	−	5426.99i	1.27338	−	0.651322i
$412$		0			0
$413$	−3104.94	−	3864.42i	−0.369938	−	0.460425i
$414$		0			0
$415$	501.693	+	868.959i	0.0593426	+	0.102784i
$416$		0			0
$417$	−39.2887	−	25.4274i	−0.00461385	−	0.00298605i
$418$		0			0
$419$	2492.46			0.290607			0.145304	−	0.989387i	$-0.453584\pi$
$419$	2492.46			0.290607			0.145304	+	0.989387i	$0.453584\pi$
$420$		0			0
$421$	1219.53			0.141179			0.0705893	−	0.997505i	$-0.477512\pi$
$421$	1219.53			0.141179			0.0705893	+	0.997505i	$0.477512\pi$
$422$		0			0
$423$	−4720.27	+	6539.67i	−0.542570	+	0.751702i
$424$		0			0
$425$	10403.7	+	18019.8i	1.18742	+	2.05668i
$426$		0			0
$427$	−639.621	−	4140.87i	−0.0724905	−	0.469299i
$428$		0			0
$429$	−311.250	−	608.515i	−0.0350286	−	0.0684834i
$430$		0			0
$431$	7065.56	+	4079.30i	0.789643	+	0.455900i	0.839837	−	0.542839i	$-0.182651\pi$
$431$	7065.56	+	4079.30i	0.789643	+	0.455900i	−0.0501941	+	0.998739i	$0.515984\pi$
$432$		0			0
$433$		−	4779.52i		−	0.530460i	−0.964185	−	0.265230i	$-0.914552\pi$
$433$		−	4779.52i		−	0.530460i	0.964185	−	0.265230i	$-0.0854478\pi$
$434$		0			0
$435$	−639.378	+	12575.1i	−0.0704732	+	1.38605i
$436$		0			0
$437$	2387.07	−	4134.53i	0.261302	−	0.452589i
$438$		0			0
$439$	−1385.35	+	799.834i	−0.150613	+	0.0869567i	−0.573413	−	0.819267i	$-0.694381\pi$
$439$	−1385.35	+	799.834i	−0.150613	+	0.0869567i	0.422799	+	0.906223i	$0.361048\pi$
$440$		0			0
$441$	−2901.70	+	8794.67i	−0.313325	+	0.949646i
$442$		0			0
$443$	3993.15	−	2305.44i	0.428262	−	0.247257i	−0.270344	−	0.962764i	$-0.587137\pi$
$443$	3993.15	−	2305.44i	0.428262	−	0.247257i	0.698606	+	0.715507i	$0.253804\pi$
$444$		0			0
$445$	7445.25	−	12895.5i	0.793120	−	1.37373i
$446$		0			0
$447$	−429.838	+	8453.96i	−0.0454824	+	0.894538i
$448$		0			0
$449$			43.2718i			0.00454816i	0.999997	+	0.00227408i	$0.000723863\pi$
$449$			43.2718i			0.00454816i	−0.999997	+	0.00227408i	$0.999276\pi$
$450$		0			0
$451$	−4645.13	−	2681.87i	−0.484990	−	0.280009i
$452$		0			0
$453$	−4558.98	−	8913.12i	−0.472846	−	0.924448i
$454$		0			0
$455$	499.809	+	3235.74i	0.0514976	+	0.333393i
$456$		0			0
$457$	−4671.07	−	8090.53i	−0.478125	−	0.828138i	0.521560	−	0.853215i	$-0.325350\pi$
$457$	−4671.07	−	8090.53i	−0.478125	−	0.828138i	−0.999686	+	0.0250770i	$0.992017\pi$
$458$		0			0
$459$	−8468.49	+	10558.3i	−0.861166	+	1.07368i
$460$		0			0
$461$	8041.21			0.812400			0.406200	−	0.913784i	$-0.366854\pi$
$461$	8041.21			0.812400			0.406200	+	0.913784i	$0.366854\pi$
$462$		0			0
$463$	6615.17			0.664002			0.332001	−	0.943279i	$-0.392276\pi$
$463$	6615.17			0.664002			0.332001	+	0.943279i	$0.392276\pi$
$464$		0			0
$465$	25427.5	+	16456.5i	2.53585	+	1.64118i
$466$		0			0
$467$	−7002.80	−	12129.2i	−0.693899	−	1.20187i	−0.970550	−	0.240898i	$-0.922558\pi$
$467$	−7002.80	−	12129.2i	−0.693899	−	1.20187i	0.276651	−	0.960970i	$-0.410775\pi$
$468$		0			0
$469$	6870.93	+	8551.58i	0.676482	+	0.841952i
$470$		0			0
$471$	−15949.0	+	8157.77i	−1.56028	+	0.798069i
$472$		0			0
$473$	3471.08	+	2004.03i	0.337421	+	0.194810i
$474$		0			0
$475$			5793.64i			0.559643i
$476$		0			0
$477$	21.1301	−	207.253i	0.00202826	−	0.0198941i
$478$		0			0
$479$	−9340.96	+	16179.0i	−0.891021	+	1.54329i	−0.0523688	+	0.998628i	$0.516677\pi$
$479$	−9340.96	+	16179.0i	−0.891021	+	1.54329i	−0.838653	+	0.544667i	$0.816656\pi$
$480$		0			0
$481$	907.475	−	523.931i	0.0860235	−	0.0496657i
$482$		0			0
$483$	−15608.9	−	6991.98i	−1.47046	−	0.658688i
$484$		0			0
$485$	−22839.7	+	13186.5i	−2.13835	+	1.23458i
$486$		0			0
$487$	−6132.14	+	10621.2i	−0.570583	+	0.988278i	0.425923	+	0.904759i	$0.359949\pi$
$487$	−6132.14	+	10621.2i	−0.570583	+	0.988278i	−0.996506	+	0.0835191i	$0.973384\pi$
$488$		0			0
$489$	802.444	+	40.7999i	0.0742081	+	0.00377308i
$490$		0			0
$491$			4811.60i			0.442250i	0.975246	+	0.221125i	$0.0709728\pi$
$491$			4811.60i			0.442250i	−0.975246	+	0.221125i	$0.929027\pi$
$492$		0			0
$493$	10968.8	+	6332.82i	1.00205	+	0.578532i
$494$		0			0
$495$	−6243.72	+	2803.24i	−0.566938	+	0.254538i
$496$		0			0
$497$	−14922.4	−	5793.77i	−1.34680	−	0.522910i
$498$		0			0
$499$	2354.96	+	4078.91i	0.211267	+	0.365926i	0.952111	−	0.305751i	$-0.0989076\pi$
$499$	2354.96	+	4078.91i	0.211267	+	0.365926i	−0.740844	+	0.671677i	$0.765574\pi$
$500$		0			0
$501$	−5016.93	+	7751.83i	−0.447385	+	0.691270i
$502$		0			0
$503$	−12488.3			−1.10701			−0.553503	−	0.832847i	$-0.686709\pi$
$503$	−12488.3			−1.10701			−0.553503	+	0.832847i	$0.686709\pi$
$504$		0			0
$505$	−13818.9			−1.21769
$506$		0			0
$507$	5943.64	−	9183.72i	0.520644	−	0.804464i
$508$		0			0
$509$	10624.2	+	18401.6i	0.925163	+	1.60243i	0.791299	+	0.611429i	$0.209405\pi$
$509$	10624.2	+	18401.6i	0.925163	+	1.60243i	0.133864	+	0.991000i	$0.457262\pi$
$510$		0			0
$511$	7912.74	−	6357.65i	0.685008	−	0.550383i
$512$		0			0
$513$	−3511.99	+	1367.01i	−0.302258	+	0.117651i
$514$		0			0
$515$	−23874.8	−	13784.1i	−2.04281	−	1.17942i
$516$		0			0
$517$			4102.37i			0.348979i
$518$		0			0
$519$	15555.7	+	790.925i	1.31565	+	0.0668935i
$520$		0			0
$521$	14.3842	−	24.9141i	0.00120956	−	0.00209502i	−0.865420	−	0.501047i	$-0.832948\pi$
$521$	14.3842	−	24.9141i	0.00120956	−	0.00209502i	0.866630	+	0.498952i	$0.166282\pi$
$522$		0			0
$523$	−14831.5	+	8562.94i	−1.24003	+	0.715930i	−0.969100	−	0.246670i	$-0.920664\pi$
$523$	−14831.5	+	8562.94i	−1.24003	+	0.715930i	−0.270928	+	0.962600i	$0.587330\pi$
$524$		0			0
$525$	20646.9	−	2122.78i	1.71639	−	0.176468i
$526$		0			0
$527$	26385.0	−	15233.4i	2.18093	−	1.25916i
$528$		0			0
$529$	9709.97	−	16818.2i	0.798058	−	1.38228i
$530$		0			0
$531$	−7189.73	−	733.013i	−0.587586	−	0.0599060i
$532$		0			0
$533$			3740.75i			0.303996i
$534$		0			0
$535$	−13209.3	−	7626.38i	−1.06745	−	0.616293i
$536$		0			0
$537$	7216.75	−	3691.30i	0.579936	−	0.296632i
$538$		0			0
$539$	1421.33	+	4491.04i	0.113583	+	0.358892i
$540$		0			0
$541$	−7530.84	−	13043.8i	−0.598477	−	1.03659i	−0.993046	−	0.117726i	$-0.962439\pi$
$541$	−7530.84	−	13043.8i	−0.598477	−	1.03659i	0.394569	−	0.918866i	$-0.370894\pi$
$542$		0			0
$543$	14544.1	+	9412.87i	1.14944	+	0.743913i
$544$		0			0
$545$	−31588.7			−2.48278
$546$		0			0
$547$	−17531.3			−1.37035			−0.685176	−	0.728377i	$-0.740275\pi$
$547$	−17531.3			−1.37035			−0.685176	+	0.728377i	$0.740275\pi$
$548$		0			0
$549$	−4952.98	−	3575.01i	−0.385042	−	0.277919i
$550$		0			0
$551$	1763.31	+	3054.15i	0.136333	+	0.236136i
$552$		0			0
$553$	−3336.89	+	515.434i	−0.256599	+	0.0396356i
$554$		0			0
$555$	−4778.15	−	9341.61i	−0.365443	−	0.714467i
$556$		0			0
$557$	−9916.73	−	5725.43i	−0.754372	−	0.435537i	0.0728994	−	0.997339i	$-0.476775\pi$
$557$	−9916.73	−	5725.43i	−0.754372	−	0.435537i	−0.827271	+	0.561802i	$0.810108\pi$
$558$		0			0
$559$		−	2795.28i		−	0.211499i
$560$		0			0
$561$	−349.588	+	6875.61i	−0.0263095	+	0.517449i
$562$		0			0
$563$	4232.49	−	7330.90i	0.316835	−	0.548775i	−0.662990	−	0.748628i	$-0.730713\pi$
$563$	4232.49	−	7330.90i	0.316835	−	0.548775i	0.979826	+	0.199853i	$0.0640464\pi$
$564$		0			0
$565$	−21449.7	+	12384.0i	−1.59716	+	0.922121i
$566$		0			0
$567$	6158.43	+	12014.9i	0.456137	+	0.889910i
$568$		0			0
$569$	21654.5	−	12502.2i	1.59544	−	0.921126i	0.603086	−	0.797676i	$-0.293938\pi$
$569$	21654.5	−	12502.2i	1.59544	−	0.921126i	0.992351	−	0.123449i	$-0.0393957\pi$
$570$		0			0
$571$	3473.13	−	6015.64i	0.254546	−	0.440887i	−0.710226	−	0.703974i	$-0.751407\pi$
$571$	3473.13	−	6015.64i	0.254546	−	0.440887i	0.964772	+	0.263087i	$0.0847405\pi$
$572$		0			0
$573$	509.912	−	10028.8i	0.0371761	−	0.731171i
$574$		0			0
$575$			38332.2i			2.78011i
$576$		0			0
$577$	−11165.2	−	6446.23i	−0.805570	−	0.465096i	0.0398454	−	0.999206i	$-0.487313\pi$
$577$	−11165.2	−	6446.23i	−0.805570	−	0.465096i	−0.845415	+	0.534110i	$0.820647\pi$
$578$		0			0
$579$	2207.47	+	4315.77i	0.158445	+	0.309771i
$580$		0			0
$581$	364.397	−	938.539i	0.0260202	−	0.0670175i
$582$		0			0
$583$	−52.9827	−	91.7688i	−0.00376384	−	0.00651917i
$584$		0			0
$585$	3870.33	+	2793.57i	0.273536	+	0.197435i
$586$		0			0
$587$	−7903.48			−0.555727			−0.277863	−	0.960621i	$-0.589626\pi$
$587$	−7903.48			−0.555727			−0.277863	+	0.960621i	$0.589626\pi$
$588$		0			0
$589$	8483.18			0.593452
$590$		0			0
$591$	309.037	+	200.007i	0.0215095	+	0.0139208i
$592$		0			0
$593$	4196.48	+	7268.52i	0.290605	+	0.503343i	0.973953	−	0.226750i	$-0.0728100\pi$
$593$	4196.48	+	7268.52i	0.290605	+	0.503343i	−0.683348	+	0.730093i	$0.739477\pi$
$594$		0			0
$595$	11936.1	−	30742.5i	0.822407	−	2.11819i
$596$		0			0
$597$	−828.178	+	423.605i	−0.0567756	+	0.0290402i
$598$		0			0
$599$	−781.608	−	451.262i	−0.0533149	−	0.0307814i	0.473106	−	0.881006i	$-0.343133\pi$
$599$	−781.608	−	451.262i	−0.0533149	−	0.0307814i	−0.526421	+	0.850224i	$0.676466\pi$
$600$		0			0
$601$			20028.0i			1.35933i	0.733522	+	0.679665i	$0.237875\pi$
$601$			20028.0i			1.35933i	−0.733522	+	0.679665i	$0.762125\pi$
$602$		0			0
$603$	15910.2	+	1622.09i	1.07448	+	0.109546i
$604$		0			0
$605$	10542.9	−	18260.8i	0.708476	−	1.22712i
$606$		0			0
$607$	9802.72	−	5659.60i	0.655486	−	0.378445i	−0.135069	−	0.990836i	$-0.543126\pi$
$607$	9802.72	−	5659.60i	0.655486	−	0.378445i	0.790555	+	0.612391i	$0.209792\pi$
$608$		0			0
$609$	10238.1	−	7403.00i	0.681228	−	0.492586i
$610$		0			0
$611$	2477.75	−	1430.53i	0.164057	−	0.0947186i
$612$		0			0
$613$	5050.76	−	8748.18i	0.332787	−	0.576404i	−0.650270	−	0.759703i	$-0.725344\pi$
$613$	5050.76	−	8748.18i	0.332787	−	0.576404i	0.983057	+	0.183299i	$0.0586777\pi$
$614$		0			0
$615$	37409.4	+	1902.07i	2.45283	+	0.124713i
$616$		0			0
$617$		−	16367.5i		−	1.06796i	−0.845497	−	0.533981i	$-0.820696\pi$
$617$		−	16367.5i		−	1.06796i	0.845497	−	0.533981i	$-0.179304\pi$
$618$		0			0
$619$	−14160.4	−	8175.50i	−0.919473	−	0.530858i	−0.0360060	−	0.999352i	$-0.511464\pi$
$619$	−14160.4	−	8175.50i	−0.919473	−	0.530858i	−0.883467	+	0.468494i	$0.844797\pi$
$620$		0			0
$621$	−23236.3	+	9044.48i	−1.50151	+	0.584448i
$622$		0			0
$623$	−14766.0	+	2280.83i	−0.949578	+	0.146677i
$624$		0			0
$625$	−1966.46	−	3406.01i	−0.125853	−	0.217984i
$626$		0			0
$627$	−1041.52	+	1609.29i	−0.0663388	+	0.102502i
$628$		0			0
$629$	−10554.6			−0.669059
$630$		0			0
$631$	18777.1			1.18463			0.592317	−	0.805705i	$-0.298213\pi$
$631$	18777.1			1.18463			0.592317	+	0.805705i	$0.298213\pi$
$632$		0			0
$633$	−11893.9	+	18377.7i	−0.746828	+	1.15395i
$634$		0			0
$635$	−5624.77	−	9742.39i	−0.351515	−	0.608842i
$636$		0			0
$637$	2216.87	−	2424.52i	0.137889	−	0.150805i
$638$		0			0
$639$	−21289.7	+	9558.44i	−1.31801	+	0.591747i
$640$		0			0
$641$	4930.76	+	2846.78i	0.303827	+	0.175415i	0.644161	−	0.764890i	$-0.277207\pi$
$641$	4930.76	+	2846.78i	0.303827	+	0.175415i	−0.340334	+	0.940305i	$0.610540\pi$
$642$		0			0
$643$			24686.0i			1.51403i	0.653399	+	0.757014i	$0.273342\pi$
$643$			24686.0i			1.51403i	−0.653399	+	0.757014i	$0.726658\pi$
$644$		0			0
$645$	−27954.2	−	1421.32i	−1.70650	−	0.0867666i
$646$		0			0
$647$	6825.70	−	11822.5i	0.414754	−	0.718375i	−0.580649	−	0.814154i	$-0.697201\pi$
$647$	6825.70	−	11822.5i	0.414754	−	0.718375i	0.995403	+	0.0957792i	$0.0305343\pi$
$648$		0			0
$649$	−3183.51	+	1838.00i	−0.192548	+	0.111168i
$650$		0			0
$651$	−3108.22	−	30231.7i	−0.187129	−	1.82008i
$652$		0			0
$653$	12407.6	−	7163.53i	0.743563	−	0.429297i	−0.0798001	−	0.996811i	$-0.525428\pi$
$653$	12407.6	−	7163.53i	0.743563	−	0.429297i	0.823363	+	0.567514i	$0.192095\pi$
$654$		0			0
$655$	1770.21	−	3066.09i	0.105600	−	0.182904i
$656$		0			0
$657$	1500.91	−	14721.6i	0.0891264	−	0.874193i
$658$		0			0
$659$		−	32795.2i		−	1.93857i	−0.245937	−	0.969286i	$-0.579096\pi$
$659$		−	32795.2i		−	1.93857i	0.245937	−	0.969286i	$-0.420904\pi$
$660$		0			0
$661$	9352.89	+	5399.89i	0.550356	+	0.317748i	0.749266	−	0.662270i	$-0.230407\pi$
$661$	9352.89	+	5399.89i	0.550356	+	0.317748i	−0.198910	+	0.980018i	$0.563740\pi$
$662$		0			0
$663$	4274.64	−	2186.44i	0.250397	−	0.128076i
$664$		0			0
$665$	7158.21	−	5751.40i	0.417419	−	0.335383i
$666$		0			0
$667$	11666.5	+	20207.0i	0.677257	+	1.17304i
$668$		0			0
$669$	13998.9	+	9060.03i	0.809014	+	0.523589i
$670$		0			0
$671$	−3107.03			−0.178757
$672$		0			0
$673$	−7377.79			−0.422575			−0.211287	−	0.977424i	$-0.567766\pi$
$673$	−7377.79			−0.422575			−0.211287	+	0.977424i	$0.567766\pi$
$674$		0			0
$675$	18932.5	−	23604.5i	1.07957	−	1.34598i
$676$		0			0
$677$	−4387.53	−	7599.42i	−0.249079	−	0.431417i	0.714192	−	0.699950i	$-0.246794\pi$
$677$	−4387.53	−	7599.42i	−0.249079	−	0.431417i	−0.963270	+	0.268533i	$0.913461\pi$
$678$		0			0
$679$	24668.6	+	9577.82i	1.39425	+	0.541330i
$680$		0			0
$681$	10333.0	+	20201.8i	0.581444	+	1.13676i
$682$		0			0
$683$	11581.7	+	6686.67i	0.648843	+	0.374610i	0.788013	−	0.615659i	$-0.211110\pi$
$683$	11581.7	+	6686.67i	0.648843	+	0.374610i	−0.139170	+	0.990269i	$0.544443\pi$
$684$		0			0
$685$			42332.8i			2.36125i
$686$		0			0
$687$	1504.75	−	29595.2i	0.0835662	−	1.64356i
$688$		0			0
$689$	−36.9510	+	64.0010i	−0.00204314	+	0.00353881i
$690$		0			0
$691$	5884.69	−	3397.53i	0.323971	−	0.187045i	−0.329190	−	0.944264i	$-0.606776\pi$
$691$	5884.69	−	3397.53i	0.323971	−	0.187045i	0.653161	+	0.757219i	$0.273442\pi$
$692$		0			0
$693$	6116.69	+	3122.06i	0.335287	+	0.171136i
$694$		0			0
$695$	143.966	−	83.1187i	0.00785746	−	0.00453651i
$696$		0			0
$697$	18839.3	−	32630.7i	1.02380	−	1.77328i
$698$		0			0
$699$	−183.453	+	3608.11i	−0.00992679	+	0.195238i
$700$		0			0
$701$			11596.1i			0.624791i	0.949952	+	0.312395i	$0.101131\pi$
$701$			11596.1i			0.624791i	−0.949952	+	0.312395i	$0.898869\pi$
$702$		0			0
$703$	−2545.09	−	1469.41i	−0.136543	−	0.0788333i
$704$		0			0
$705$	−13046.1	−	25506.1i	−0.696945	−	1.36258i
$706$		0			0
$707$	8684.81	+	10809.1i	0.461989	+	0.574992i
$708$		0			0
$709$	−1524.48	−	2640.48i	−0.0807520	−	0.139866i	0.822821	−	0.568300i	$-0.192399\pi$
$709$	−1524.48	−	2640.48i	−0.0807520	−	0.139866i	−0.903573	+	0.428434i	$0.859065\pi$
$710$		0			0
$711$	−2880.90	+	3991.33i	−0.151958	+	0.210530i
$712$		0			0
$713$	56126.9			2.94806
$714$		0			0
$715$	2427.88			0.126990
$716$		0			0
$717$	19818.5	+	12826.4i	1.03226	+	0.668075i
$718$		0			0
$719$	15672.6	+	27145.8i	0.812922	+	1.40802i	0.910810	+	0.412825i	$0.135458\pi$
$719$	15672.6	+	27145.8i	0.812922	+	1.40802i	−0.0978884	+	0.995197i	$0.531209\pi$
$720$		0			0
$721$	4222.73	+	27337.7i	0.218117	+	1.41208i
$722$		0			0
$723$	−7310.23	+	3739.12i	−0.376031	+	0.192336i
$724$		0			0
$725$	−24522.2	−	14157.9i	−1.25618	−	0.725256i
$726$		0			0
$727$			11029.1i			0.562653i	0.959612	+	0.281326i	$0.0907743\pi$
$727$			11029.1i			0.562653i	−0.959612	+	0.281326i	$0.909226\pi$
$728$		0			0
$729$	18775.7	+	5907.01i	0.953905	+	0.300107i
$730$		0			0
$731$	−14077.7	+	24383.3i	−0.712288	+	1.23372i
$732$		0			0
$733$	−5969.98	+	3446.77i	−0.300827	+	0.173683i	−0.642814	−	0.766022i	$-0.722233\pi$
$733$	−5969.98	+	3446.77i	−0.300827	+	0.173683i	0.341987	+	0.939705i	$0.388900\pi$
$734$		0			0
$735$	−23119.2	−	23402.6i	−1.16022	−	1.17445i
$736$		0			0
$737$	7044.80	−	4067.32i	0.352101	−	0.203286i
$738$		0			0
$739$	11905.5	−	20621.0i	0.592627	−	1.02646i	−0.401250	−	0.915969i	$-0.631424\pi$
$739$	11905.5	−	20621.0i	0.592627	−	1.02646i	0.993877	−	0.110492i	$-0.0352426\pi$
$740$		0			0
$741$	1335.17	+	67.8860i	0.0661924	+	0.00336553i
$742$		0			0
$743$		−	2169.23i		−	0.107108i	−0.998565	−	0.0535541i	$-0.982945\pi$
$743$		−	2169.23i		−	0.107108i	0.998565	−	0.0535541i	$-0.0170550\pi$
$744$		0			0
$745$	−26040.1	−	15034.3i	−1.28059	−	0.739346i
$746$		0			0
$747$	−601.175	−	1339.01i	−0.0294456	−	0.0655847i
$748$		0			0
$749$	2336.32	+	15125.2i	0.113975	+	0.737868i
$750$		0			0
$751$	−4279.50	−	7412.30i	−0.207937	−	0.360158i	0.743127	−	0.669150i	$-0.233342\pi$
$751$	−4279.50	−	7412.30i	−0.207937	−	0.360158i	−0.951065	+	0.308992i	$0.900008\pi$
$752$		0			0
$753$	−7238.97	+	11185.2i	−0.350336	+	0.541315i
$754$		0			0
$755$	35562.0			1.71422
$756$		0			0
$757$	10181.6			0.488846			0.244423	−	0.969669i	$-0.421401\pi$
$757$	10181.6			0.488846			0.244423	+	0.969669i	$0.421401\pi$
$758$		0			0
$759$	−6890.99	+	10647.5i	−0.329548	+	0.509196i
$760$		0			0
$761$	−10227.7	−	17714.9i	−0.487192	−	0.843841i	0.512700	−	0.858568i	$-0.328645\pi$
$761$	−10227.7	−	17714.9i	−0.487192	−	0.843841i	−0.999892	+	0.0147269i	$0.995312\pi$
$762$		0			0
$763$	19852.6	+	24708.6i	0.941957	+	1.17236i
$764$		0			0
$765$	−19691.9	−	43860.2i	−0.930671	−	2.07290i
$766$		0			0
$767$	2220.23	+	1281.85i	0.104521	+	0.0603454i
$768$		0			0
$769$		−	20459.8i		−	0.959426i	−0.877425	−	0.479713i	$-0.840741\pi$
$769$		−	20459.8i		−	0.959426i	0.877425	−	0.479713i	$-0.159259\pi$
$770$		0			0
$771$	−18563.7	−	943.861i	−0.867125	−	0.0440886i
$772$		0			0
$773$	6789.09	−	11759.1i	0.315895	−	0.547146i	−0.663732	−	0.747970i	$-0.731029\pi$
$773$	6789.09	−	11759.1i	0.315895	−	0.547146i	0.979627	+	0.200824i	$0.0643620\pi$
$774$		0			0
$775$	−58987.2	+	34056.3i	−2.73404	+	1.57850i
$776$		0			0
$777$	−4304.05	+	9608.39i	−0.198722	+	0.443628i
$778$		0			0
$779$	9085.69	−	5245.63i	0.417880	−	0.241263i
$780$		0			0
$781$	−5935.16	+	10280.0i	−0.271929	+	0.470995i
$782$		0			0
$783$	2796.24	−	18205.4i	0.127624	−	0.830918i
$784$		0			0
$785$		−	63634.1i		−	2.89325i
$786$		0			0
$787$	11701.5	+	6755.85i	0.530003	+	0.305998i	0.741018	−	0.671485i	$-0.234343\pi$
$787$	11701.5	+	6755.85i	0.530003	+	0.305998i	−0.211015	+	0.977483i	$0.567677\pi$
$788$		0			0
$789$	7050.23	−	3606.13i	0.318118	−	0.162714i
$790$		0			0
$791$	23167.2	+	8994.91i	1.04138	+	0.404326i
$792$		0			0
$793$	1083.45	+	1876.59i	0.0485175	+	0.0840347i
$794$		0			0
$795$	621.253	+	402.071i	0.0277152	+	0.0179371i
$796$		0			0
$797$	11687.0			0.519417			0.259708	−	0.965687i	$-0.416374\pi$
$797$	11687.0			0.519417			0.259708	+	0.965687i	$0.416374\pi$
$798$		0			0
$799$	−28817.9			−1.27598
$800$		0			0
$801$	−12748.2	+	17661.9i	−0.562341	+	0.779092i
$802$		0			0
$803$	−3763.47	−	6518.52i	−0.165392	−	0.286468i
$804$		0			0
$805$	47360.6	−	38052.8i	2.07359	−	1.66607i
$806$		0			0
$807$	−13529.1	−	26450.3i	−0.590144	−	1.15377i
$808$		0			0
$809$	27747.4	+	16020.0i	1.20587	+	0.696209i	0.961854	−	0.273563i	$-0.0882022\pi$
$809$	27747.4	+	16020.0i	1.20587	+	0.696209i	0.244014	+	0.969772i	$0.421536\pi$
$810$		0			0
$811$		−	8638.65i		−	0.374037i	−0.982356	−	0.187019i	$-0.940118\pi$
$811$		−	8638.65i		−	0.374037i	0.982356	−	0.187019i	$-0.0598825\pi$
$812$		0			0
$813$	−708.990	+	13944.2i	−0.0305847	+	0.601533i
$814$		0			0
$815$	−1427.04	+	2471.71i	−0.0613339	+	0.106233i
$816$		0			0
$817$	−6789.29	+	3919.80i	−0.290731	+	0.167854i
$818$		0			0
$819$	−247.276	−	4783.04i	−0.0105501	−	0.204070i
$820$		0			0
$821$	−11198.2	+	6465.30i	−0.476031	+	0.274836i	−0.718761	−	0.695257i	$-0.755290\pi$
$821$	−11198.2	+	6465.30i	−0.476031	+	0.274836i	0.242730	+	0.970094i	$0.421957\pi$
$822$		0			0
$823$	6649.96	−	11518.1i	0.281656	−	0.487842i	−0.690137	−	0.723679i	$-0.742450\pi$
$823$	6649.96	−	11518.1i	0.281656	−	0.487842i	0.971793	+	0.235836i	$0.0757830\pi$
$824$		0			0
$825$	781.552	−	15371.4i	0.0329820	−	0.648682i
$826$		0			0
$827$		−	40780.3i		−	1.71471i	−0.514722	−	0.857357i	$-0.672105\pi$
$827$		−	40780.3i		−	1.71471i	0.514722	−	0.857357i	$-0.327895\pi$
$828$		0			0
$829$	3646.09	+	2105.07i	0.152755	+	0.0881932i	0.574429	−	0.818554i	$-0.305224\pi$
$829$	3646.09	+	2105.07i	0.152755	+	0.0881932i	−0.421674	+	0.906747i	$0.638557\pi$
$830$		0			0
$831$	−7387.03	−	14442.1i	−0.308367	−	0.602879i
$832$		0			0
$833$	−31548.2	+	9984.44i	−1.31222	+	0.415295i
$834$		0			0
$835$	−16399.7	−	28405.1i	−0.679682	−	1.17724i
$836$		0			0
$837$	−34562.3	−	27721.3i	−1.42730	−	1.14479i
$838$		0			0
$839$	−24812.4			−1.02100			−0.510499	−	0.859878i	$-0.670539\pi$
$839$	−24812.4			−1.02100			−0.510499	+	0.859878i	$0.670539\pi$
$840$		0			0
$841$	7152.99			0.293287
$842$		0			0
$843$	7642.79	+	4946.36i	0.312256	+	0.202090i
$844$		0			0
$845$	19429.0	+	33652.0i	0.790978	+	1.37001i
$846$		0			0
$847$	−20909.4	+	3229.78i	−0.848236	+	0.131023i
$848$		0			0
$849$	−13425.8	+	6867.17i	−0.542723	+	0.277598i
$850$		0			0
$851$	−16839.0	−	9721.99i	−0.678299	−	0.391616i
$852$		0			0
$853$			16088.0i			0.645770i	0.946438	+	0.322885i	$0.104653\pi$
$853$			16088.0i			0.645770i	−0.946438	+	0.322885i	$0.895347\pi$
$854$		0			0
$855$	1357.79	−	13317.8i	0.0543104	−	0.532701i
$856$		0			0
$857$	−4219.50	+	7308.39i	−0.168186	+	0.291307i	−0.937782	−	0.347224i	$-0.887124\pi$
$857$	−4219.50	+	7308.39i	−0.168186	+	0.291307i	0.769596	+	0.638531i	$0.220458\pi$
$858$		0			0
$859$	−10871.0	+	6276.35i	−0.431796	+	0.249297i	−0.700111	−	0.714034i	$-0.746866\pi$
$859$	−10871.0	+	6276.35i	−0.431796	+	0.249297i	0.268316	+	0.963331i	$0.413533\pi$
$860$		0			0
$861$	−22023.0	−	30456.9i	−0.871708	−	1.20554i
$862$		0			0
$863$	−12741.6	+	7356.38i	−0.502584	+	0.290167i	−0.729780	−	0.683682i	$-0.760377\pi$
$863$	−12741.6	+	7356.38i	−0.502584	+	0.290167i	0.227196	+	0.973849i	$0.427044\pi$
$864$		0			0
$865$	−27663.8	+	47915.2i	−1.08740	+	1.88343i
$866$		0			0
$867$	−22803.4	−	1159.43i	−0.893244	−	0.0454167i
$868$		0			0
$869$			2503.78i			0.0977388i
$870$		0			0
$871$	−4913.15	−	2836.61i	−0.191132	−	0.110350i
$872$		0			0
$873$	35194.5	−	15801.3i	1.36444	−	0.612592i
$874$		0			0
$875$	−11219.3	+	28896.4i	−0.433464	+	1.11643i
$876$		0			0
$877$	11817.2	+	20468.1i	0.455006	+	0.788093i	0.998689	−	0.0511977i	$-0.0163039\pi$
$877$	11817.2	+	20468.1i	0.455006	+	0.788093i	−0.543683	+	0.839291i	$0.682971\pi$
$878$		0			0
$879$	−6428.03	+	9932.16i	−0.246658	+	0.381119i
$880$		0			0
$881$	24798.0			0.948317			0.474158	−	0.880440i	$-0.342752\pi$
$881$	24798.0			0.948317			0.474158	+	0.880440i	$0.342752\pi$
$882$		0			0
$883$	−16328.1			−0.622291			−0.311145	−	0.950362i	$-0.600713\pi$
$883$	−16328.1			−0.622291			−0.311145	+	0.950362i	$0.600713\pi$
$884$		0			0
$885$	13948.1	−	21551.6i	0.529785	−	0.818588i
$886$		0			0
$887$	2349.70	+	4069.81i	0.0889463	+	0.154059i	0.907066	−	0.420988i	$-0.138317\pi$
$887$	2349.70	+	4069.81i	0.0889463	+	0.154059i	−0.818120	+	0.575048i	$0.804983\pi$
$888$		0			0
$889$	−4085.46	+	10522.5i	−0.154130	+	0.396978i
$890$		0			0
$891$	9502.24	−	3153.11i	0.357280	−	0.118556i
$892$		0			0
$893$	−6949.06	−	4012.04i	−0.260405	−	0.150345i
$894$		0			0
$895$			28793.7i			1.07538i
$896$		0			0
$897$	8833.81	+	449.151i	0.328821	+	0.0167188i
$898$		0			0
$899$	−20730.3	+	35905.9i	−0.769070	+	1.33207i
$900$		0			0
$901$	644.648	−	372.188i	0.0238361	−	0.0137618i
$902$		0			0
$903$	16456.7	+	22759.0i	0.606472	+	0.838727i
$904$		0			0
$905$	−53294.2	+	30769.4i	−1.95752	+	1.13018i
$906$		0			0
$907$	−20782.1	+	35995.7i	−0.760815	+	1.31777i	0.181616	+	0.983370i	$0.441867\pi$
$907$	−20782.1	+	35995.7i	−0.760815	+	1.31777i	−0.942431	+	0.334401i	$0.891466\pi$
$908$		0			0
$909$	20110.3	+	2050.31i	0.733793	+	0.0748123i
$910$		0			0
$911$			663.177i			0.0241186i	0.999927	+	0.0120593i	$0.00383869\pi$
$911$			663.177i			0.0241186i	−0.999927	+	0.0120593i	$0.996161\pi$
$912$		0			0
$913$	−646.557	−	373.290i	−0.0234369	−	0.0135313i
$914$		0			0
$915$	19317.7	−	9880.83i	0.697949	−	0.356995i
$916$		0			0
$917$	−3510.81	+	542.299i	−0.126431	+	0.0195292i
$918$		0			0
$919$	24822.2	+	42993.3i	0.890979	+	1.54322i	0.838704	+	0.544587i	$0.183314\pi$
$919$	24822.2	+	42993.3i	0.890979	+	1.54322i	0.0522743	+	0.998633i	$0.483353\pi$
$920$		0			0
$921$	32551.6	+	21067.2i	1.16462	+	0.753732i
$922$		0			0
$923$	8278.55			0.295224
$924$		0			0
$925$	23596.2			0.838743
$926$		0			0
$927$	32699.2	+	23602.0i	1.15856	+	0.836235i
$928$		0			0
$929$	−1464.21	−	2536.08i	−0.0517106	−	0.0895654i	0.839011	−	0.544114i	$-0.183134\pi$
$929$	−1464.21	−	2536.08i	−0.0517106	−	0.0895654i	−0.890722	+	0.454548i	$0.849801\pi$
$930$		0			0
$931$	−8997.47	−	1984.54i	−0.316735	−	0.0698611i
$932$		0			0
$933$	−6150.43	−	12024.5i	−0.215816	−	0.421935i
$934$		0			0
$935$	−21178.5	−	12227.4i	−0.740759	−	0.427677i
$936$		0			0
$937$		−	232.824i		−	0.00811744i	−0.999992	−	0.00405872i	$-0.998708\pi$
$937$		−	232.824i		−	0.00811744i	0.999992	−	0.00405872i	$-0.00129193\pi$
$938$		0			0
$939$	−2246.85	+	44190.5i	−0.0780865	+	1.53579i
$940$		0			0
$941$	15001.7	−	25983.8i	0.519706	−	0.900156i	−0.480032	−	0.877251i	$-0.659375\pi$
$941$	15001.7	−	25983.8i	0.519706	−	0.900156i	0.999738	−	0.0229055i	$-0.00729168\pi$
$942$		0			0
$943$	60113.3	−	34706.4i	2.07588	−	1.19851i
$944$		0			0
$945$	−47958.5	+	40.8390i	−1.65089	+	0.00140581i
$946$		0			0
$947$	−27834.2	+	16070.1i	−0.955110	+	0.551433i	−0.894665	−	0.446739i	$-0.852585\pi$
$947$	−27834.2	+	16070.1i	−0.955110	+	0.551433i	−0.0604452	+	0.998172i	$0.519252\pi$
$948$		0			0
$949$	−2624.70	+	4546.12i	−0.0897802	+	0.155504i
$950$		0			0
$951$	2153.63	−	42357.1i	0.0734345	−	1.44429i
$952$		0			0
$953$			40568.2i			1.37894i	0.724312	+	0.689472i	$0.242158\pi$
$953$			40568.2i			1.37894i	−0.724312	+	0.689472i	$0.757842\pi$
$954$		0			0
$955$	30891.1	+	17835.0i	1.04672	+	0.604321i
$956$		0			0
$957$	−4266.33	−	8340.97i	−0.144108	−	0.281740i
$958$		0			0
$959$	33112.6	−	26605.0i	1.11498	−	0.895849i
$960$		0			0
$961$	34970.5	+	60570.7i	1.17386	+	2.03319i
$962$		0			0
$963$	18091.6	+	13058.3i	0.605393	+	0.436966i
$964$		0			0
$965$	−17219.3			−0.574412
$966$		0			0
$967$	25460.9			0.846708			0.423354	−	0.905964i	$-0.360853\pi$
$967$	25460.9			0.846708			0.423354	+	0.905964i	$0.360853\pi$
$968$		0			0
$969$	−11304.8	−	7316.39i	−0.374780	−	0.242555i
$970$		0			0
$971$	−6750.18	−	11691.6i	−0.223093	−	0.386409i	0.732652	−	0.680603i	$-0.238282\pi$
$971$	−6750.18	−	11691.6i	−0.223093	−	0.386409i	−0.955746	+	0.294194i	$0.904949\pi$
$972$		0			0
$973$	−155.494	−	60.3719i	−0.00512323	−	0.00198914i
$974$		0			0
$975$	−9556.53	+	4888.08i	−0.313901	+	0.160558i
$976$		0			0
$977$	−26535.2	−	15320.1i	−0.868920	−	0.501671i	−0.00193070	−	0.999998i	$-0.500615\pi$
$977$	−26535.2	−	15320.1i	−0.868920	−	0.501671i	−0.866989	+	0.498327i	$0.833948\pi$
$978$		0			0
$979$			11079.4i			0.361695i
$980$		0			0
$981$	45970.3	+	4686.80i	1.49614	+	0.152536i
$982$		0			0
$983$	9066.36	−	15703.4i	0.294173	−	0.509522i	−0.680619	−	0.732637i	$-0.738289\pi$
$983$	9066.36	−	15703.4i	0.294173	−	0.509522i	0.974792	+	0.223115i	$0.0716225\pi$
$984$		0			0
$985$	−1132.41	+	653.795i	−0.0366309	+	0.0211489i
$986$		0			0
$987$	−11751.7	+	26234.5i	−0.378987	+	0.846053i
$988$		0			0
$989$	−44919.7	+	25934.4i	−1.44425	+	0.833838i
$990$		0			0
$991$	26549.3	−	45984.8i	0.851026	−	1.47402i	−0.0292575	−	0.999572i	$-0.509314\pi$
$991$	26549.3	−	45984.8i	0.851026	−	1.47402i	0.880283	−	0.474448i	$-0.157352\pi$
$992$		0			0
$993$	−14040.1	−	713.863i	−0.448690	−	0.0228135i
$994$		0			0
$995$		−	3304.30i		−	0.105280i
$996$		0			0
$997$	−16198.5	−	9352.21i	−0.514555	−	0.297079i	0.220149	−	0.975466i	$-0.429346\pi$
$997$	−16198.5	−	9352.21i	−0.514555	−	0.297079i	−0.734704	+	0.678388i	$0.762679\pi$
$998$		0			0
$999$	5567.51	+	14303.5i	0.176324	+	0.452997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.17		48
3.2	odd	2	inner	336.4.bc.f.17.10		48
4.3	odd	2		168.4.u.a.17.8	✓	48
7.5	odd	6	inner	336.4.bc.f.257.10		48
12.11	even	2		168.4.u.a.17.15	yes	48
21.5	even	6	inner	336.4.bc.f.257.17		48
28.19	even	6		168.4.u.a.89.15	yes	48
84.47	odd	6		168.4.u.a.89.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.8	✓	48	4.3	odd	2
168.4.u.a.17.15	yes	48	12.11	even	2
168.4.u.a.89.8	yes	48	84.47	odd	6
168.4.u.a.89.15	yes	48	28.19	even	6
336.4.bc.f.17.10		48	3.2	odd	2	inner
336.4.bc.f.17.17		48	1.1	even	1	trivial
336.4.bc.f.257.10		48	7.5	odd	6	inner
336.4.bc.f.257.17		48	21.5	even	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82323 - 4.36227i) q^{3} +(9.22876 + 15.9847i) q^{5} +(6.70316 - 17.2646i) q^{7} +(-11.0587 - 24.6314i) q^{9} +O(q^{10})\)	\(q+(2.82323 - 4.36227i) q^{3} +(9.22876 + 15.9847i) q^{5} +(6.70316 - 17.2646i) q^{7} +(-11.0587 - 24.6314i) q^{9} +(-11.8936 - 6.86675i) q^{11} +9.57796i q^{13} +(95.7844 + 4.87012i) q^{15} +(48.2369 - 83.5487i) q^{17} +(23.2633 - 13.4311i) q^{19} +(-56.3884 - 77.9830i) q^{21} +(153.916 - 88.8636i) q^{23} +(-107.840 + 186.785i) q^{25} +(-138.670 - 21.2988i) q^{27} +131.286i q^{29} +(273.494 + 157.902i) q^{31} +(-63.5329 + 32.4965i) q^{33} +(337.832 - 52.1833i) q^{35} +(-54.7017 - 94.7462i) q^{37} +(41.7816 + 27.0408i) q^{39} +390.559 q^{41} -291.845 q^{43} +(291.666 - 404.088i) q^{45} +(-149.356 - 258.693i) q^{47} +(-253.135 - 231.455i) q^{49} +(-228.278 - 446.299i) q^{51} +(6.68211 + 3.85792i) q^{53} -253.486i q^{55} +(7.08773 - 139.400i) q^{57} +(133.833 - 231.806i) q^{59} +(195.928 - 113.119i) q^{61} +(-499.380 + 25.8171i) q^{63} +(-153.101 + 88.3927i) q^{65} +(-296.160 + 512.964i) q^{67} +(46.8943 - 922.306i) q^{69} -864.334i q^{71} +(474.644 + 274.036i) q^{73} +(510.347 + 997.763i) q^{75} +(-198.276 + 159.309i) q^{77} +(-91.1561 - 157.887i) q^{79} +(-484.408 + 544.784i) q^{81} +54.3619 q^{83} +1780.67 q^{85} +(572.705 + 370.651i) q^{87} +(-403.372 - 698.661i) q^{89} +(165.360 + 64.2026i) q^{91} +(1460.95 - 747.261i) q^{93} +(429.384 + 247.905i) q^{95} +1428.85i q^{97} +(-37.6096 + 368.892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q - 12 * q^7 + 14 * q^9	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) \) 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Introduction

L-functions

Modular forms

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