LMFDB - Embedded newform 168.4.q.f.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("168.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 $ x^8 + 173x^6 + 9457x^4 + 168048*x^2 + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$8.67551i$ of defining polynomial
Character	$\chi$	$=$	168.25
Dual form			168.4.q.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(12.8033 + 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(12.8033 + 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-27.3654 + 47.3983i) q^{11} +62.0173 q^{13} +56.8741 q^{15} +(-61.2195 + 106.035i) q^{17} +(6.25288 + 10.8303i) q^{19} +(-53.9722 + 13.1910i) q^{21} +(37.2195 + 64.4661i) q^{23} +(-117.203 + 203.002i) q^{25} +27.0000 q^{27} -232.572 q^{29} +(-5.18387 + 8.97872i) q^{31} +(-82.0962 - 142.195i) q^{33} +(98.3438 - 337.053i) q^{35} +(122.993 + 213.031i) q^{37} +(-93.0260 + 161.126i) q^{39} +238.653 q^{41} -92.9718 q^{43} +(-85.3111 + 147.763i) q^{45} +(242.822 + 420.580i) q^{47} +(-15.1521 + 342.665i) q^{49} +(-183.659 - 318.106i) q^{51} +(189.278 - 327.840i) q^{53} +1037.59 q^{55} -37.5173 q^{57} +(91.3918 - 158.295i) q^{59} +(-198.235 - 343.353i) q^{61} +(46.6871 - 160.010i) q^{63} +(-587.863 - 1018.21i) q^{65} +(130.620 - 226.240i) q^{67} -223.317 q^{69} -874.523 q^{71} +(-76.2032 + 131.988i) q^{73} +(-351.610 - 609.006i) q^{75} +(-984.647 + 240.651i) q^{77} +(-286.679 - 496.542i) q^{79} +(-40.5000 + 70.1481i) q^{81} +317.754 q^{83} +2321.20 q^{85} +(348.858 - 604.240i) q^{87} +(47.5080 + 82.2863i) q^{89} +(794.025 + 829.911i) q^{91} +(-15.5516 - 26.9362i) q^{93} +(118.542 - 205.321i) q^{95} -1608.78 q^{97} +492.577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9	$ 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9} - 14 q^{11} + 44 q^{13} + 24 q^{15} - 96 q^{17} + 26 q^{19} - 36 q^{21} - 96 q^{23} - 110 q^{25} + 216 q^{27} - 152 q^{29} - 238 q^{31} - 42 q^{33} + 152 q^{35} - 562 q^{37} - 66 q^{39} + 856 q^{41} - 516 q^{43} - 36 q^{45} + 80 q^{47} + 156 q^{49} - 288 q^{51} + 2952 q^{55} - 156 q^{57} - 262 q^{59} + 276 q^{61} - 54 q^{63} - 2196 q^{65} - 150 q^{67} + 576 q^{69} - 1696 q^{71} + 218 q^{73} - 330 q^{75} - 764 q^{77} - 1762 q^{79} - 324 q^{81} + 6900 q^{83} + 2904 q^{85} + 228 q^{87} + 344 q^{89} - 2806 q^{91} - 714 q^{93} - 2004 q^{95} - 1244 q^{97} + 252 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9 - 14 * q^11 + 44 * q^13 + 24 * q^15 - 96 * q^17 + 26 * q^19 - 36 * q^21 - 96 * q^23 - 110 * q^25 + 216 * q^27 - 152 * q^29 - 238 * q^31 - 42 * q^33 + 152 * q^35 - 562 * q^37 - 66 * q^39 + 856 * q^41 - 516 * q^43 - 36 * q^45 + 80 * q^47 + 156 * q^49 - 288 * q^51 + 2952 * q^55 - 156 * q^57 - 262 * q^59 + 276 * q^61 - 54 * q^63 - 2196 * q^65 - 150 * q^67 + 576 * q^69 - 1696 * q^71 + 218 * q^73 - 330 * q^75 - 764 * q^77 - 1762 * q^79 - 324 * q^81 + 6900 * q^83 + 2904 * q^85 + 228 * q^87 + 344 * q^89 - 2806 * q^91 - 714 * q^93 - 2004 * q^95 - 1244 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$		0			0
$5$	−9.47901	−	16.4181i	−0.847828	−	1.46848i	−0.883142	−	0.469106i	$-0.844576\pi$
$5$	−9.47901	−	16.4181i	−0.847828	−	1.46848i	0.0353138	−	0.999376i	$-0.488757\pi$
$6$		0			0
$7$	12.8033	+	13.3819i	0.691312	+	0.722556i
$7$	12.8033	+	13.3819i	0.691312	+	0.722556i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	−27.3654	+	47.3983i	−0.750089	+	1.29919i	0.197690	+	0.980265i	$0.436656\pi$
$11$	−27.3654	+	47.3983i	−0.750089	+	1.29919i	−0.947779	+	0.318928i	$0.896677\pi$
$12$		0			0
$13$	62.0173			1.32312			0.661558	−	0.749894i	$-0.269896\pi$
$13$	62.0173			1.32312			0.661558	+	0.749894i	$0.269896\pi$
$14$		0			0
$15$	56.8741			0.978988
$16$		0			0
$17$	−61.2195	+	106.035i	−0.873407	+	1.51279i	−0.0149571	+	0.999888i	$0.504761\pi$
$17$	−61.2195	+	106.035i	−0.873407	+	1.51279i	−0.858450	+	0.512897i	$0.828572\pi$
$18$		0			0
$19$	6.25288	+	10.8303i	0.0755004	+	0.130771i	0.901304	−	0.433188i	$-0.142611\pi$
$19$	6.25288	+	10.8303i	0.0755004	+	0.130771i	−0.825803	+	0.563958i	$0.809278\pi$
$20$		0			0
$21$	−53.9722	+	13.1910i	−0.560843	+	0.137072i
$22$		0			0
$23$	37.2195	+	64.4661i	0.337427	+	0.584440i	0.983948	−	0.178456i	$-0.0571102\pi$
$23$	37.2195	+	64.4661i	0.337427	+	0.584440i	−0.646521	+	0.762896i	$0.723777\pi$
$24$		0			0
$25$	−117.203	+	203.002i	−0.937626	+	1.62402i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−232.572			−1.48923			−0.744613	−	0.667496i	$-0.767366\pi$
$29$	−232.572			−1.48923			−0.744613	+	0.667496i	$0.767366\pi$
$30$		0			0
$31$	−5.18387	+	8.97872i	−0.0300339	+	0.0520202i	−0.880652	−	0.473764i	$-0.842895\pi$
$31$	−5.18387	+	8.97872i	−0.0300339	+	0.0520202i	0.850618	+	0.525785i	$0.176228\pi$
$32$		0			0
$33$	−82.0962	−	142.195i	−0.433064	−	0.750089i
$34$		0			0
$35$	98.3438	−	337.053i	0.474947	−	1.62778i
$36$		0			0
$37$	122.993	+	213.031i	0.546486	+	0.946541i	0.998512	+	0.0545365i	$0.0173681\pi$
$37$	122.993	+	213.031i	0.546486	+	0.946541i	−0.452026	+	0.892005i	$0.649299\pi$
$38$		0			0
$39$	−93.0260	+	161.126i	−0.381951	+	0.661558i
$40$		0			0
$41$	238.653			0.909056			0.454528	−	0.890733i	$-0.349808\pi$
$41$	238.653			0.909056			0.454528	+	0.890733i	$0.349808\pi$
$42$		0			0
$43$	−92.9718			−0.329722			−0.164861	−	0.986317i	$-0.552718\pi$
$43$	−92.9718			−0.329722			−0.164861	+	0.986317i	$0.552718\pi$
$44$		0			0
$45$	−85.3111	+	147.763i	−0.282609	+	0.489494i
$46$		0			0
$47$	242.822	+	420.580i	0.753601	+	1.30528i	0.946067	+	0.323972i	$0.105018\pi$
$47$	242.822	+	420.580i	0.753601	+	1.30528i	−0.192465	+	0.981304i	$0.561648\pi$
$48$		0			0
$49$	−15.1521	+	342.665i	−0.0441751	+	0.999024i
$50$		0			0
$51$	−183.659	−	318.106i	−0.504262	−	0.873407i
$52$		0			0
$53$	189.278	−	327.840i	0.490555	−	0.849666i	−0.509386	−	0.860538i	$-0.670128\pi$
$53$	189.278	−	327.840i	0.490555	−	0.849666i	0.999941	+	0.0108725i	$0.00346088\pi$
$54$		0			0
$55$	1037.59			2.54379
$56$		0			0
$57$	−37.5173			−0.0871804
$58$		0			0
$59$	91.3918	−	158.295i	0.201664	−	0.349293i	−0.747400	−	0.664374i	$-0.768698\pi$
$59$	91.3918	−	158.295i	0.201664	−	0.349293i	0.949065	+	0.315081i	$0.102032\pi$
$60$		0			0
$61$	−198.235	−	343.353i	−0.416088	−	0.720686i	0.579454	−	0.815005i	$-0.303266\pi$
$61$	−198.235	−	343.353i	−0.416088	−	0.720686i	−0.995542	+	0.0943190i	$0.969933\pi$
$62$		0			0
$63$	46.6871	−	160.010i	0.0933653	−	0.319991i
$64$		0			0
$65$	−587.863	−	1018.21i	−1.12178	−	1.94297i
$66$		0			0
$67$	130.620	−	226.240i	0.238175	−	0.412531i	−0.722016	−	0.691877i	$-0.756784\pi$
$67$	130.620	−	226.240i	0.238175	−	0.412531i	0.960191	+	0.279346i	$0.0901175\pi$
$68$		0			0
$69$	−223.317			−0.389627
$70$		0			0
$71$	−874.523			−1.46179			−0.730893	−	0.682492i	$-0.760896\pi$
$71$	−874.523			−1.46179			−0.730893	+	0.682492i	$0.760896\pi$
$72$		0			0
$73$	−76.2032	+	131.988i	−0.122177	+	0.211617i	−0.920626	−	0.390446i	$-0.872321\pi$
$73$	−76.2032	+	131.988i	−0.122177	+	0.211617i	0.798449	+	0.602062i	$0.205654\pi$
$74$		0			0
$75$	−351.610	−	609.006i	−0.541339	−	0.937626i
$76$		0			0
$77$	−984.647	+	240.651i	−1.45729	+	0.356166i
$78$		0			0
$79$	−286.679	−	496.542i	−0.408277	−	0.707156i	0.586420	−	0.810007i	$-0.300537\pi$
$79$	−286.679	−	496.542i	−0.408277	−	0.707156i	−0.994697	+	0.102851i	$0.967204\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	317.754			0.420217			0.210108	−	0.977678i	$-0.432618\pi$
$83$	317.754			0.420217			0.210108	+	0.977678i	$0.432618\pi$
$84$		0			0
$85$	2321.20			2.96200
$86$		0			0
$87$	348.858	−	604.240i	0.429903	−	0.744613i
$88$		0			0
$89$	47.5080	+	82.2863i	0.0565824	+	0.0980037i	0.892929	−	0.450197i	$-0.148646\pi$
$89$	47.5080	+	82.2863i	0.0565824	+	0.0980037i	−0.836347	+	0.548201i	$0.815313\pi$
$90$		0			0
$91$	794.025	+	829.911i	0.914686	+	0.956026i
$92$		0			0
$93$	−15.5516	−	26.9362i	−0.0173401	−	0.0300339i
$94$		0			0
$95$	118.542	−	205.321i	0.128023	−	0.221742i
$96$		0			0
$97$	−1608.78			−1.68398			−0.841992	−	0.539490i	$-0.818617\pi$
$97$	−1608.78			−1.68398			−0.841992	+	0.539490i	$0.818617\pi$
$98$		0			0
$99$	492.577			0.500059
$100$		0			0
$101$	391.521	−	678.135i	0.385721	−	0.668089i	−0.606148	−	0.795352i	$-0.707286\pi$
$101$	391.521	−	678.135i	0.385721	−	0.668089i	0.991869	+	0.127263i	$0.0406194\pi$
$102$		0			0
$103$	744.805	+	1290.04i	0.712503	+	1.23409i	0.963915	+	0.266211i	$0.0857717\pi$
$103$	744.805	+	1290.04i	0.712503	+	1.23409i	−0.251412	+	0.967880i	$0.580895\pi$
$104$		0			0
$105$	728.174	+	761.085i	0.676786	+	0.707374i
$106$		0			0
$107$	−356.385	−	617.276i	−0.321991	−	0.557704i	0.658908	−	0.752223i	$-0.271019\pi$
$107$	−356.385	−	617.276i	−0.321991	−	0.557704i	−0.980899	+	0.194519i	$0.937685\pi$
$108$		0			0
$109$	−520.924	+	902.267i	−0.457757	+	0.792858i	−0.998842	−	0.0481100i	$-0.984680\pi$
$109$	−520.924	+	902.267i	−0.457757	+	0.792858i	0.541085	+	0.840968i	$0.318014\pi$
$110$		0			0
$111$	−737.960			−0.631028
$112$		0			0
$113$	352.093			0.293116			0.146558	−	0.989202i	$-0.453181\pi$
$113$	352.093			0.293116			0.146558	+	0.989202i	$0.453181\pi$
$114$		0			0
$115$	705.609	−	1222.15i	0.572160	−	0.991010i
$116$		0			0
$117$	−279.078	−	483.377i	−0.220519	−	0.381951i
$118$		0			0
$119$	−2202.77	+	538.365i	−1.69687	+	0.414721i
$120$		0			0
$121$	−832.231	−	1441.47i	−0.625267	−	1.08299i
$122$		0			0
$123$	−357.979	+	620.038i	−0.262422	+	0.454528i
$124$		0			0
$125$	2074.13			1.48413
$126$		0			0
$127$	−1093.73			−0.764194			−0.382097	−	0.924122i	$-0.624798\pi$
$127$	−1093.73			−0.764194			−0.382097	+	0.924122i	$0.624798\pi$
$128$		0			0
$129$	139.458	−	241.548i	0.0951826	−	0.164861i
$130$		0			0
$131$	1083.19	+	1876.13i	0.722430	+	1.25129i	0.960023	+	0.279921i	$0.0903083\pi$
$131$	1083.19	+	1876.13i	0.722430	+	1.25129i	−0.237593	+	0.971365i	$0.576358\pi$
$132$		0			0
$133$	−64.8730	+	222.339i	−0.0422947	+	0.144957i
$134$		0			0
$135$	−255.933	−	443.289i	−0.163165	−	0.282609i
$136$		0			0
$137$	982.461	−	1701.67i	0.612681	−	1.06119i	−0.378105	−	0.925763i	$-0.623424\pi$
$137$	982.461	−	1701.67i	0.612681	−	1.06119i	0.990787	−	0.135432i	$-0.0432424\pi$
$138$		0			0
$139$	−136.976			−0.0835840			−0.0417920	−	0.999126i	$-0.513307\pi$
$139$	−136.976			−0.0835840			−0.0417920	+	0.999126i	$0.513307\pi$
$140$		0			0
$141$	−1456.93			−0.870184
$142$		0			0
$143$	−1697.13	+	2939.51i	−0.992455	+	1.71898i
$144$		0			0
$145$	2204.55	+	3818.40i	1.26261	+	2.18690i
$146$		0			0
$147$	−867.542	−	553.364i	−0.486760	−	0.310481i
$148$		0			0
$149$	140.053	+	242.578i	0.0770037	+	0.133374i	0.901956	−	0.431828i	$-0.142131\pi$
$149$	140.053	+	242.578i	0.0770037	+	0.133374i	−0.824952	+	0.565203i	$0.808798\pi$
$150$		0			0
$151$	−1097.07	+	1900.17i	−0.591245	+	1.02407i	0.402820	+	0.915279i	$0.368030\pi$
$151$	−1097.07	+	1900.17i	−0.591245	+	1.02407i	−0.994065	+	0.108787i	$0.965303\pi$
$152$		0			0
$153$	1101.95			0.582271
$154$		0			0
$155$	196.552			0.101854
$156$		0			0
$157$	110.409	−	191.234i	0.0561248	−	0.0972111i	−0.836598	−	0.547817i	$-0.815459\pi$
$157$	110.409	−	191.234i	0.0561248	−	0.0972111i	0.892723	+	0.450606i	$0.148792\pi$
$158$		0			0
$159$	567.835	+	983.520i	0.283222	+	0.490555i
$160$		0			0
$161$	−386.149	+	1323.45i	−0.189024	+	0.647840i
$162$		0			0
$163$	−738.431	−	1279.00i	−0.354837	−	0.614596i	0.632253	−	0.774762i	$-0.282130\pi$
$163$	−738.431	−	1279.00i	−0.354837	−	0.614596i	−0.987090	+	0.160166i	$0.948797\pi$
$164$		0			0
$165$	−1556.38	+	2695.73i	−0.734328	+	1.27189i
$166$		0			0
$167$	2197.66			1.01832			0.509162	−	0.860671i	$-0.329955\pi$
$167$	2197.66			1.01832			0.509162	+	0.860671i	$0.329955\pi$
$168$		0			0
$169$	1649.15			0.750635
$170$		0			0
$171$	56.2759	−	97.4727i	0.0251668	−	0.0435902i
$172$		0			0
$173$	−1045.80	−	1811.38i	−0.459601	−	0.796052i	0.539339	−	0.842089i	$-0.318674\pi$
$173$	−1045.80	−	1811.38i	−0.459601	−	0.796052i	−0.998940	+	0.0460370i	$0.985341\pi$
$174$		0			0
$175$	−4217.14	+	1030.69i	−1.82163	+	0.445214i
$176$		0			0
$177$	274.175	+	474.886i	0.116431	+	0.201664i
$178$		0			0
$179$	−1167.27	+	2021.77i	−0.487406	+	0.844212i	−0.999895	−	0.0144814i	$-0.995390\pi$
$179$	−1167.27	+	2021.77i	−0.487406	+	0.844212i	0.512489	+	0.858694i	$0.328724\pi$
$180$		0			0
$181$	1758.40			0.722105			0.361053	−	0.932545i	$-0.382417\pi$
$181$	1758.40			0.722105			0.361053	+	0.932545i	$0.382417\pi$
$182$		0			0
$183$	1189.41			0.480457
$184$		0			0
$185$	2331.71	−	4038.64i	0.926652	−	1.60501i
$186$		0			0
$187$	−3350.60	−	5803.40i	−1.31027	−	2.26945i
$188$		0			0
$189$	345.689	+	361.312i	0.133043	+	0.139056i
$190$		0			0
$191$	1850.34	+	3204.88i	0.700973	+	1.21412i	0.968125	+	0.250467i	$0.0805841\pi$
$191$	1850.34	+	3204.88i	0.700973	+	1.21412i	−0.267152	+	0.963654i	$0.586083\pi$
$192$		0			0
$193$	−1354.22	+	2345.58i	−0.505073	+	0.874812i	0.494910	+	0.868944i	$0.335201\pi$
$193$	−1354.22	+	2345.58i	−0.505073	+	0.874812i	−0.999983	+	0.00586773i	$0.998132\pi$
$194$		0			0
$195$	3527.18			1.29531
$196$		0			0
$197$	−160.686			−0.0581138			−0.0290569	−	0.999578i	$-0.509250\pi$
$197$	−160.686			−0.0581138			−0.0290569	+	0.999578i	$0.509250\pi$
$198$		0			0
$199$	1033.00	−	1789.20i	0.367976	−	0.637353i	−0.621273	−	0.783594i	$-0.713384\pi$
$199$	1033.00	−	1789.20i	0.367976	−	0.637353i	0.989249	+	0.146241i	$0.0467176\pi$
$200$		0			0
$201$	391.859	+	678.719i	0.137510	+	0.238175i
$202$		0			0
$203$	−2977.69	−	3112.27i	−1.02952	−	1.07605i
$204$		0			0
$205$	−2262.19	−	3918.23i	−0.770723	−	1.33493i
$206$		0			0
$207$	334.976	−	580.195i	0.112476	−	0.194813i
$208$		0			0
$209$	−684.450			−0.226528
$210$		0			0
$211$	−1007.12			−0.328592			−0.164296	−	0.986411i	$-0.552535\pi$
$211$	−1007.12			−0.328592			−0.164296	+	0.986411i	$0.552535\pi$
$212$		0			0
$213$	1311.78	−	2272.08i	0.421981	−	0.730893i
$214$		0			0
$215$	881.280	+	1526.42i	0.279548	+	0.484191i
$216$		0			0
$217$	−186.523	+	45.5869i	−0.0583503	+	0.0142610i
$218$		0			0
$219$	−228.610	−	395.964i	−0.0705389	−	0.122177i
$220$		0			0
$221$	−3796.67	+	6576.03i	−1.15562	+	2.00159i
$222$		0			0
$223$	1644.83			0.493929			0.246964	−	0.969025i	$-0.420567\pi$
$223$	1644.83			0.493929			0.246964	+	0.969025i	$0.420567\pi$
$224$		0			0
$225$	2109.66			0.625084
$226$		0			0
$227$	−159.437	+	276.153i	−0.0466177	+	0.0807442i	−0.888393	−	0.459084i	$-0.848178\pi$
$227$	−159.437	+	276.153i	−0.0466177	+	0.0807442i	0.841775	+	0.539829i	$0.181511\pi$
$228$		0			0
$229$	−1268.05	−	2196.33i	−0.365918	−	0.633789i	0.623005	−	0.782218i	$-0.285912\pi$
$229$	−1268.05	−	2196.33i	−0.365918	−	0.633789i	−0.988923	+	0.148429i	$0.952578\pi$
$230$		0			0
$231$	851.740	−	2919.17i	0.242599	−	0.831459i
$232$		0			0
$233$	−1166.41	−	2020.28i	−0.327957	−	0.568038i	0.654150	−	0.756365i	$-0.273027\pi$
$233$	−1166.41	−	2020.28i	−0.327957	−	0.568038i	−0.982106	+	0.188328i	$0.939693\pi$
$234$		0			0
$235$	4603.43	−	7973.37i	1.27785	−	2.21330i
$236$		0			0
$237$	1720.07			0.471438
$238$		0			0
$239$	2713.85			0.734495			0.367248	−	0.930123i	$-0.380300\pi$
$239$	2713.85			0.734495			0.367248	+	0.930123i	$0.380300\pi$
$240$		0			0
$241$	2087.29	−	3615.30i	0.557902	−	0.966315i	−0.439769	−	0.898111i	$-0.644940\pi$
$241$	2087.29	−	3615.30i	0.557902	−	0.966315i	0.997671	−	0.0682042i	$-0.0217269\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	5769.55	−	2999.36i	1.50450	−	0.782130i
$246$		0			0
$247$	387.786	+	671.666i	0.0998958	+	0.173025i
$248$		0			0
$249$	−476.631	+	825.548i	−0.121306	+	0.210108i
$250$		0			0
$251$	6123.58			1.53991			0.769954	−	0.638099i	$-0.220279\pi$
$251$	6123.58			1.53991			0.769954	+	0.638099i	$0.220279\pi$
$252$		0			0
$253$	−4074.11			−1.01240
$254$		0			0
$255$	−3481.80	+	6030.66i	−0.855055	+	1.48100i
$256$		0			0
$257$	−2316.96	−	4013.09i	−0.562365	−	0.974045i	−0.997289	−	0.0735777i	$-0.976558\pi$
$257$	−2316.96	−	4013.09i	−0.562365	−	0.974045i	0.434925	−	0.900467i	$-0.356775\pi$
$258$		0			0
$259$	−1276.04	+	4373.38i	−0.306137	+	1.04922i
$260$		0			0
$261$	1046.58	+	1812.72i	0.248204	+	0.429903i
$262$		0			0
$263$	−1641.61	+	2843.36i	−0.384891	+	0.666650i	−0.991754	−	0.128156i	$-0.959094\pi$
$263$	−1641.61	+	2843.36i	−0.384891	+	0.666650i	0.606863	+	0.794806i	$0.292428\pi$
$264$		0			0
$265$	−7176.69			−1.66362
$266$		0			0
$267$	−285.048			−0.0653358
$268$		0			0
$269$	399.493	−	691.942i	0.0905483	−	0.156834i	−0.817194	−	0.576363i	$-0.804471\pi$
$269$	399.493	−	691.942i	0.0905483	−	0.156834i	0.907742	+	0.419529i	$0.137805\pi$
$270$		0			0
$271$	3353.04	+	5807.63i	0.751596	+	1.30180i	0.947049	+	0.321089i	$0.104049\pi$
$271$	3353.04	+	5807.63i	0.751596	+	1.30180i	−0.195453	+	0.980713i	$0.562618\pi$
$272$		0			0
$273$	−3347.21	+	818.070i	−0.742060	+	0.181362i
$274$		0			0
$275$	−6414.63	−	11110.5i	−1.40661	−	2.43631i
$276$		0			0
$277$	−581.135	+	1006.56i	−0.126054	+	0.218332i	−0.922145	−	0.386845i	$-0.873565\pi$
$277$	−581.135	+	1006.56i	−0.126054	+	0.218332i	0.796090	+	0.605178i	$0.206898\pi$
$278$		0			0
$279$	93.3096			0.0200226
$280$		0			0
$281$	2718.17			0.577055			0.288527	−	0.957472i	$-0.406834\pi$
$281$	2718.17			0.577055			0.288527	+	0.957472i	$0.406834\pi$
$282$		0			0
$283$	1504.74	−	2606.29i	0.316069	−	0.547448i	−0.663595	−	0.748092i	$-0.730970\pi$
$283$	1504.74	−	2606.29i	0.316069	−	0.547448i	0.979664	+	0.200644i	$0.0643035\pi$
$284$		0			0
$285$	355.626	+	615.963i	0.0739140	+	0.128023i
$286$		0			0
$287$	3055.54	+	3193.63i	0.628441	+	0.656844i
$288$		0			0
$289$	−5039.17	−	8728.09i	−1.02568	−	1.77653i
$290$		0			0
$291$	2413.16	−	4179.72i	0.486124	−	0.841992i
$292$		0			0
$293$	4209.15			0.839252			0.419626	−	0.907697i	$-0.362161\pi$
$293$	4209.15			0.839252			0.419626	+	0.907697i	$0.362161\pi$
$294$		0			0
$295$	−3465.21			−0.683907
$296$		0			0
$297$	−738.866	+	1279.75i	−0.144355	+	0.250030i
$298$		0			0
$299$	2308.26	+	3998.02i	0.446454	+	0.773282i
$300$		0			0
$301$	−1190.34	−	1244.14i	−0.227941	−	0.238243i
$302$		0			0
$303$	1174.56	+	2034.40i	0.222696	+	0.385721i
$304$		0			0
$305$	−3758.14	+	6509.29i	−0.705543	+	1.22204i
$306$		0			0
$307$	−3114.82			−0.579063			−0.289531	−	0.957169i	$-0.593499\pi$
$307$	−3114.82			−0.579063			−0.289531	+	0.957169i	$0.593499\pi$
$308$		0			0
$309$	−4468.83			−0.822727
$310$		0			0
$311$	4243.62	−	7350.16i	0.773741	−	1.34016i	−0.161758	−	0.986831i	$-0.551716\pi$
$311$	4243.62	−	7350.16i	0.773741	−	1.34016i	0.935499	−	0.353329i	$-0.114950\pi$
$312$		0			0
$313$	2477.46	+	4291.08i	0.447393	+	0.774908i	0.998215	−	0.0597148i	$-0.0190191\pi$
$313$	2477.46	+	4291.08i	0.447393	+	0.774908i	−0.550822	+	0.834623i	$0.685686\pi$
$314$		0			0
$315$	−3069.62	+	750.226i	−0.549058	+	0.134192i
$316$		0			0
$317$	2804.40	+	4857.36i	0.496879	+	0.860619i	0.999994	−	0.00360042i	$-0.00114605\pi$
$317$	2804.40	+	4857.36i	0.496879	+	0.860619i	−0.503115	+	0.864220i	$0.667813\pi$
$318$		0			0
$319$	6364.43	−	11023.5i	1.11705	−	1.93479i
$320$		0			0
$321$	2138.31			0.371803
$322$		0			0
$323$	−1531.19			−0.263770
$324$		0			0
$325$	−7268.63	+	12589.6i	−1.24059	+	2.14876i
$326$		0			0
$327$	−1562.77	−	2706.80i	−0.264286	−	0.457757i
$328$		0			0
$329$	−2519.26	+	8634.24i	−0.422162	+	1.44687i
$330$		0			0
$331$	3304.75	+	5723.99i	0.548777	+	0.950510i	0.998359	+	0.0572706i	$0.0182398\pi$
$331$	3304.75	+	5723.99i	0.548777	+	0.950510i	−0.449582	+	0.893239i	$0.648427\pi$
$332$		0			0
$333$	1106.94	−	1917.28i	0.182162	−	0.315514i
$334$		0			0
$335$	−4952.57			−0.807725
$336$		0			0
$337$	11455.5			1.85170			0.925850	−	0.377891i	$-0.123350\pi$
$337$	11455.5			1.85170			0.925850	+	0.377891i	$0.123350\pi$
$338$		0			0
$339$	−528.139	+	914.764i	−0.0846153	+	0.146558i
$340$		0			0
$341$	−283.717	−	491.413i	−0.0450562	−	0.0780395i
$342$		0			0
$343$	−4779.52	+	4184.47i	−0.752390	+	0.658718i
$344$		0			0
$345$	2116.83	+	3666.45i	0.330337	+	0.572160i
$346$		0			0
$347$	3022.08	−	5234.39i	0.467532	−	0.809789i	−0.531780	−	0.846883i	$-0.678477\pi$
$347$	3022.08	−	5234.39i	0.467532	−	0.809789i	0.999312	+	0.0370937i	$0.0118100\pi$
$348$		0			0
$349$	−5487.93			−0.841726			−0.420863	−	0.907124i	$-0.638273\pi$
$349$	−5487.93			−0.841726			−0.420863	+	0.907124i	$0.638273\pi$
$350$		0			0
$351$	1674.47			0.254634
$352$		0			0
$353$	−3440.08	+	5958.39i	−0.518688	+	0.898394i	0.481076	+	0.876679i	$0.340246\pi$
$353$	−3440.08	+	5958.39i	−0.518688	+	0.898394i	−0.999764	+	0.0217151i	$0.993087\pi$
$354$		0			0
$355$	8289.61	+	14358.0i	1.23934	+	2.14660i
$356$		0			0
$357$	1905.44	−	6530.51i	0.282483	−	0.968154i
$358$		0			0
$359$	1969.17	+	3410.70i	0.289495	+	0.501420i	0.973689	−	0.227880i	$-0.0731793\pi$
$359$	1969.17	+	3410.70i	0.289495	+	0.501420i	−0.684194	+	0.729300i	$0.739846\pi$
$360$		0			0
$361$	3351.30	−	5804.63i	0.488599	−	0.846279i
$362$		0			0
$363$	4993.38			0.721996
$364$		0			0
$365$	2889.32			0.414340
$366$		0			0
$367$	−719.814	+	1246.75i	−0.102381	+	0.177330i	−0.912665	−	0.408708i	$-0.865980\pi$
$367$	−719.814	+	1246.75i	−0.102381	+	0.177330i	0.810284	+	0.586038i	$0.199313\pi$
$368$		0			0
$369$	−1073.94	−	1860.11i	−0.151509	−	0.262422i
$370$		0			0
$371$	6810.52	−	1664.51i	0.953058	−	0.232931i
$372$		0			0
$373$	1247.05	+	2159.96i	0.173110	+	0.299835i	0.939506	−	0.342534i	$-0.111285\pi$
$373$	1247.05	+	2159.96i	0.173110	+	0.299835i	−0.766396	+	0.642369i	$0.777952\pi$
$374$		0			0
$375$	−3111.19	+	5388.75i	−0.428430	+	0.742063i
$376$		0			0
$377$	−14423.5			−1.97042
$378$		0			0
$379$	−1309.25			−0.177445			−0.0887225	−	0.996056i	$-0.528278\pi$
$379$	−1309.25			−0.177445			−0.0887225	+	0.996056i	$0.528278\pi$
$380$		0			0
$381$	1640.59	−	2841.59i	0.220604	−	0.382097i
$382$		0			0
$383$	−3480.90	−	6029.10i	−0.464402	−	0.804367i	0.534773	−	0.844996i	$-0.320397\pi$
$383$	−3480.90	−	6029.10i	−0.464402	−	0.804367i	−0.999174	+	0.0406289i	$0.987064\pi$
$384$		0			0
$385$	13284.5	+	13884.9i	1.75855	+	1.83803i
$386$		0			0
$387$	418.373	+	724.643i	0.0549537	+	0.0951826i
$388$		0			0
$389$	−3176.72	+	5502.25i	−0.414052	+	0.717159i	−0.995328	−	0.0965470i	$-0.969220\pi$
$389$	−3176.72	+	5502.25i	−0.414052	+	0.717159i	0.581276	+	0.813706i	$0.302554\pi$
$390$		0			0
$391$	−9114.25			−1.17884
$392$		0			0
$393$	−6499.11			−0.834191
$394$		0			0
$395$	−5434.86	+	9413.45i	−0.692297	+	1.19909i
$396$		0			0
$397$	−5752.70	−	9963.97i	−0.727254	−	1.25964i	−0.958039	−	0.286637i	$-0.907463\pi$
$397$	−5752.70	−	9963.97i	−0.727254	−	1.25964i	0.230785	−	0.973005i	$-0.425871\pi$
$398$		0			0
$399$	−480.344	−	502.053i	−0.0602689	−	0.0629927i
$400$		0			0
$401$	−826.664	−	1431.82i	−0.102947	−	0.178309i	0.809951	−	0.586498i	$-0.199494\pi$
$401$	−826.664	−	1431.82i	−0.102947	−	0.178309i	−0.912897	+	0.408189i	$0.866160\pi$
$402$		0			0
$403$	−321.489	+	556.836i	−0.0397383	+	0.0688287i
$404$		0			0
$405$	1535.60			0.188406
$406$		0			0
$407$	−13463.0			−1.63965
$408$		0			0
$409$	2447.41	−	4239.04i	0.295885	−	0.512487i	−0.679306	−	0.733855i	$-0.737719\pi$
$409$	2447.41	−	4239.04i	0.295885	−	0.512487i	0.975190	+	0.221368i	$0.0710523\pi$
$410$		0			0
$411$	2947.38	+	5105.02i	0.353732	+	0.612681i
$412$		0			0
$413$	3288.41	−	803.699i	0.391797	−	0.0957566i
$414$		0			0
$415$	−3011.99	−	5216.92i	−0.356272	−	0.617081i
$416$		0			0
$417$	205.464	−	355.875i	0.0241286	−	0.0417920i
$418$		0			0
$419$	−265.504			−0.0309563			−0.0154782	−	0.999880i	$-0.504927\pi$
$419$	−265.504			−0.0309563			−0.0154782	+	0.999880i	$0.504927\pi$
$420$		0			0
$421$	11136.8			1.28925			0.644623	−	0.764500i	$-0.277014\pi$
$421$	11136.8			1.28925			0.644623	+	0.764500i	$0.277014\pi$
$422$		0			0
$423$	2185.40	−	3785.22i	0.251200	−	0.435092i
$424$		0			0
$425$	−14350.3	−	24855.4i	−1.63786	−	2.83685i
$426$		0			0
$427$	2056.67	−	7048.81i	0.233089	−	0.798866i
$428$		0			0
$429$	−5091.39	−	8818.54i	−0.572994	−	0.992455i
$430$		0			0
$431$	−2596.71	+	4497.63i	−0.290206	+	0.502652i	−0.973858	−	0.227156i	$-0.927057\pi$
$431$	−2596.71	+	4497.63i	−0.290206	+	0.502652i	0.683652	+	0.729808i	$0.260391\pi$
$432$		0			0
$433$	6314.17			0.700785			0.350392	−	0.936603i	$-0.386048\pi$
$433$	6314.17			0.700785			0.350392	+	0.936603i	$0.386048\pi$
$434$		0			0
$435$	−13227.3			−1.45794
$436$		0			0
$437$	−465.458	+	806.198i	−0.0509517	+	0.0882509i
$438$		0			0
$439$	7711.66	+	13357.0i	0.838399	+	1.45215i	0.891232	+	0.453547i	$0.149842\pi$
$439$	7711.66	+	13357.0i	0.838399	+	1.45215i	−0.0528329	+	0.998603i	$0.516825\pi$
$440$		0			0
$441$	2738.99	−	1423.89i	0.295756	−	0.153752i
$442$		0			0
$443$	4353.06	+	7539.72i	0.466862	+	0.808629i	0.999283	−	0.0378504i	$-0.0120510\pi$
$443$	4353.06	+	7539.72i	0.466862	+	0.808629i	−0.532421	+	0.846480i	$0.678718\pi$
$444$		0			0
$445$	900.657	−	1559.98i	0.0959444	−	0.166181i
$446$		0			0
$447$	−840.315			−0.0889162
$448$		0			0
$449$	5495.91			0.577657			0.288829	−	0.957381i	$-0.406734\pi$
$449$	5495.91			0.577657			0.288829	+	0.957381i	$0.406734\pi$
$450$		0			0
$451$	−6530.83	+	11311.7i	−0.681873	+	1.18104i
$452$		0			0
$453$	−3291.20	−	5700.52i	−0.341355	−	0.591245i
$454$		0			0
$455$	6099.02	−	20903.1i	0.628409	−	2.15375i
$456$		0			0
$457$	5678.63	+	9835.67i	0.581258	+	1.00677i	0.995331	+	0.0965247i	$0.0307727\pi$
$457$	5678.63	+	9835.67i	0.581258	+	1.00677i	−0.414072	+	0.910244i	$0.635894\pi$
$458$		0			0
$459$	−1652.93	+	2862.95i	−0.168087	+	0.291136i
$460$		0			0
$461$	14514.2			1.46637			0.733184	−	0.680030i	$-0.238033\pi$
$461$	14514.2			1.46637			0.733184	+	0.680030i	$0.238033\pi$
$462$		0			0
$463$	9971.00			1.00085			0.500423	−	0.865781i	$-0.333178\pi$
$463$	9971.00			1.00085			0.500423	+	0.865781i	$0.333178\pi$
$464$		0			0
$465$	−294.828	+	510.656i	−0.0294028	+	0.0509271i
$466$		0			0
$467$	198.739	+	344.226i	0.0196928	+	0.0341089i	0.875704	−	0.482849i	$-0.160398\pi$
$467$	198.739	+	344.226i	0.0196928	+	0.0341089i	−0.856011	+	0.516957i	$0.827065\pi$
$468$		0			0
$469$	4699.88	−	1148.67i	0.462730	−	0.113093i
$470$		0			0
$471$	331.227	+	573.702i	0.0324037	+	0.0561248i
$472$		0			0
$473$	2544.21	−	4406.70i	0.247321	−	0.428373i
$474$		0			0
$475$	−2931.43			−0.283165
$476$		0			0
$477$	−3407.01			−0.327036
$478$		0			0
$479$	7030.20	−	12176.7i	0.670602	−	1.16152i	−0.307132	−	0.951667i	$-0.599369\pi$
$479$	7030.20	−	12176.7i	0.670602	−	1.16152i	0.977734	−	0.209849i	$-0.0672973\pi$
$480$		0			0
$481$	7627.71	+	13211.6i	0.723064	+	1.25238i
$482$		0			0
$483$	−2859.19	−	2988.42i	−0.269354	−	0.281527i
$484$		0			0
$485$	15249.6	+	26413.1i	1.42773	+	2.47290i
$486$		0			0
$487$	6767.34	−	11721.4i	0.629687	−	1.09065i	−0.357927	−	0.933749i	$-0.616516\pi$
$487$	6767.34	−	11721.4i	0.629687	−	1.09065i	0.987614	−	0.156900i	$-0.0501502\pi$
$488$		0			0
$489$	4430.59			0.409730
$490$		0			0
$491$	−8693.29			−0.799028			−0.399514	−	0.916727i	$-0.630821\pi$
$491$	−8693.29			−0.799028			−0.399514	+	0.916727i	$0.630821\pi$
$492$		0			0
$493$	14238.0	−	24660.9i	1.30070	−	2.25288i
$494$		0			0
$495$	−4669.14	−	8087.20i	−0.423965	−	0.734328i
$496$		0			0
$497$	−11196.8	−	11702.8i	−1.01055	−	1.05622i
$498$		0			0
$499$	−2008.97	−	3479.63i	−0.180228	−	0.312164i	0.761730	−	0.647894i	$-0.224350\pi$
$499$	−2008.97	−	3479.63i	−0.180228	−	0.312164i	−0.941958	+	0.335731i	$0.891017\pi$
$500$		0			0
$501$	−3296.49	+	5709.69i	−0.293965	+	0.509162i
$502$		0			0
$503$	52.2455			0.00463124			0.00231562	−	0.999997i	$-0.499263\pi$
$503$	52.2455			0.00463124			0.00231562	+	0.999997i	$0.499263\pi$
$504$		0			0
$505$	−14844.9			−1.30810
$506$		0			0
$507$	−2473.72	+	4284.61i	−0.216690	+	0.375318i
$508$		0			0
$509$	−4619.55	−	8001.30i	−0.402275	−	0.696761i	0.591725	−	0.806140i	$-0.298447\pi$
$509$	−4619.55	−	8001.30i	−0.402275	−	0.696761i	−0.994000	+	0.109379i	$0.965114\pi$
$510$		0			0
$511$	−2741.90	+	670.131i	−0.237367	+	0.0580134i
$512$		0			0
$513$	168.828	+	292.418i	0.0145301	+	0.0251668i
$514$		0			0
$515$	14120.0	−	24456.6i	1.20816	−	2.09259i
$516$		0			0
$517$	−26579.7			−2.26107
$518$		0			0
$519$	6274.82			0.530701
$520$		0			0
$521$	−7486.70	+	12967.3i	−0.629555	+	1.09042i	0.358086	+	0.933689i	$0.383429\pi$
$521$	−7486.70	+	12967.3i	−0.629555	+	1.09042i	−0.987641	+	0.156733i	$0.949904\pi$
$522$		0			0
$523$	−6801.76	−	11781.0i	−0.568681	−	0.984985i	−0.996697	−	0.0812134i	$-0.974120\pi$
$523$	−6801.76	−	11781.0i	−0.568681	−	0.984985i	0.428015	−	0.903771i	$-0.359213\pi$
$524$		0			0
$525$	3647.92	−	12502.5i	0.303254	−	1.03934i
$526$		0			0
$527$	−634.708	−	1099.35i	−0.0524636	−	0.0908696i
$528$		0			0
$529$	3312.91	−	5738.13i	0.272287	−	0.471614i
$530$		0			0
$531$	−1645.05			−0.134443
$532$		0			0
$533$	14800.6			1.20279
$534$		0			0
$535$	−6756.35	+	11702.3i	−0.545986	+	0.945675i
$536$		0			0
$537$	−3501.80	−	6065.30i	−0.281404	−	0.487406i
$538$		0			0
$539$	−15827.1	−	10095.4i	−1.26479	−	0.806749i
$540$		0			0
$541$	8443.19	+	14624.0i	0.670981	+	1.16217i	0.977626	+	0.210350i	$0.0674603\pi$
$541$	8443.19	+	14624.0i	0.670981	+	1.16217i	−0.306645	+	0.951824i	$0.599206\pi$
$542$		0			0
$543$	−2637.61	+	4568.47i	−0.208454	+	0.361053i
$544$		0			0
$545$	19751.4			1.55240
$546$		0			0
$547$	−5987.25			−0.468001			−0.234000	−	0.972237i	$-0.575182\pi$
$547$	−5987.25			−0.468001			−0.234000	+	0.972237i	$0.575182\pi$
$548$		0			0
$549$	−1784.11	+	3090.18i	−0.138696	+	0.240229i
$550$		0			0
$551$	−1454.25	−	2518.83i	−0.112437	−	0.194747i
$552$		0			0
$553$	2974.26	−	10193.7i	0.228713	−	0.783869i
$554$		0			0
$555$	6995.13	+	12115.9i	0.535003	+	0.926652i
$556$		0			0
$557$	−1119.35	+	1938.78i	−0.0851499	+	0.147484i	−0.905455	−	0.424442i	$-0.860470\pi$
$557$	−1119.35	+	1938.78i	−0.0851499	+	0.147484i	0.820305	+	0.571926i	$0.193804\pi$
$558$		0			0
$559$	−5765.86			−0.436261
$560$		0			0
$561$	20103.6			1.51297
$562$		0			0
$563$	−4226.42	+	7320.38i	−0.316381	+	0.547988i	−0.979730	−	0.200322i	$-0.935801\pi$
$563$	−4226.42	+	7320.38i	−0.316381	+	0.547988i	0.663349	+	0.748310i	$0.269134\pi$
$564$		0			0
$565$	−3337.49	−	5780.70i	−0.248512	−	0.430435i
$566$		0			0
$567$	−1457.25	+	356.157i	−0.107934	+	0.0263795i
$568$		0			0
$569$	−7476.78	−	12950.2i	−0.550866	−	0.954128i	−0.998212	−	0.0597671i	$-0.980964\pi$
$569$	−7476.78	−	12950.2i	−0.550866	−	0.954128i	0.447346	−	0.894361i	$-0.352369\pi$
$570$		0			0
$571$	−8010.92	+	13875.3i	−0.587122	+	1.01693i	0.407485	+	0.913212i	$0.366406\pi$
$571$	−8010.92	+	13875.3i	−0.587122	+	1.01693i	−0.994607	+	0.103713i	$0.966928\pi$
$572$		0			0
$573$	−11102.0			−0.809414
$574$		0			0
$575$	−17449.0			−1.26552
$576$		0			0
$577$	8056.54	−	13954.3i	0.581279	−	1.00681i	−0.414049	−	0.910255i	$-0.635886\pi$
$577$	8056.54	−	13954.3i	0.581279	−	1.00681i	0.995328	−	0.0965505i	$-0.0307809\pi$
$578$		0			0
$579$	−4062.67	−	7036.75i	−0.291604	−	0.505073i
$580$		0			0
$581$	4068.29	+	4252.16i	0.290501	+	0.303630i
$582$		0			0
$583$	10359.4	+	17942.9i	0.735919	+	1.27465i
$584$		0			0
$585$	−5290.76	+	9163.87i	−0.373925	+	0.647657i
$586$		0			0
$587$	−9552.04			−0.671644			−0.335822	−	0.941925i	$-0.609014\pi$
$587$	−9552.04			−0.671644			−0.335822	+	0.941925i	$0.609014\pi$
$588$		0			0
$589$	−129.656			−0.00907028
$590$		0			0
$591$	241.029	−	417.475i	0.0167760	−	0.0290569i
$592$		0			0
$593$	12083.9	+	20929.9i	0.836807	+	1.44939i	0.892551	+	0.450947i	$0.148913\pi$
$593$	12083.9	+	20929.9i	0.836807	+	1.44939i	−0.0557443	+	0.998445i	$0.517753\pi$
$594$		0			0
$595$	29719.0	+	31062.2i	2.04766	+	2.14021i
$596$		0			0
$597$	3098.99	+	5367.61i	0.212451	+	0.367976i
$598$		0			0
$599$	−410.665	+	711.293i	−0.0280122	+	0.0485186i	−0.879692	−	0.475544i	$-0.842251\pi$
$599$	−410.665	+	711.293i	−0.0280122	+	0.0485186i	0.851679	+	0.524063i	$0.175584\pi$
$600$		0			0
$601$	−14674.7			−0.995996			−0.497998	−	0.867178i	$-0.665931\pi$
$601$	−14674.7			−0.995996			−0.497998	+	0.867178i	$0.665931\pi$
$602$		0			0
$603$	−2351.15			−0.158783
$604$		0			0
$605$	−15777.4	+	27327.3i	−1.06024	+	1.83639i
$606$		0			0
$607$	−2541.56	−	4402.11i	−0.169949	−	0.294359i	0.768453	−	0.639906i	$-0.221027\pi$
$607$	−2541.56	−	4402.11i	−0.169949	−	0.294359i	−0.938402	+	0.345547i	$0.887693\pi$
$608$		0			0
$609$	12552.4	−	3067.86i	0.835222	−	0.204131i
$610$		0			0
$611$	15059.2	+	26083.3i	0.997102	+	1.72703i
$612$		0			0
$613$	11101.0	−	19227.5i	0.731428	−	1.26687i	−0.224845	−	0.974395i	$-0.572187\pi$
$613$	11101.0	−	19227.5i	0.731428	−	1.26687i	0.956273	−	0.292476i	$-0.0944792\pi$
$614$		0			0
$615$	13573.1			0.889954
$616$		0			0
$617$	−14990.6			−0.978121			−0.489060	−	0.872250i	$-0.662660\pi$
$617$	−14990.6			−0.978121			−0.489060	+	0.872250i	$0.662660\pi$
$618$		0			0
$619$	−1536.51	+	2661.32i	−0.0997700	+	0.172807i	−0.911589	−	0.411102i	$-0.865144\pi$
$619$	−1536.51	+	2661.32i	−0.0997700	+	0.172807i	0.811819	+	0.583909i	$0.198477\pi$
$620$		0			0
$621$	1004.93	+	1740.59i	0.0649378	+	0.112476i
$622$		0			0
$623$	−492.891	+	1689.28i	−0.0316970	+	0.108635i
$624$		0			0
$625$	−5010.29	−	8678.08i	−0.320659	−	0.555397i
$626$		0			0
$627$	1026.67	−	1778.25i	0.0653931	−	0.113264i
$628$		0			0
$629$	−30118.4			−1.90922
$630$		0			0
$631$	26012.7			1.64113			0.820563	−	0.571556i	$-0.193660\pi$
$631$	26012.7			1.64113			0.820563	+	0.571556i	$0.193660\pi$
$632$		0			0
$633$	1510.68	−	2616.57i	0.0948565	−	0.164296i
$634$		0			0
$635$	10367.5	+	17957.0i	0.647905	+	1.12220i
$636$		0			0
$637$	−939.691	+	21251.2i	−0.0584488	+	1.32182i
$638$		0			0
$639$	3935.35	+	6816.23i	0.243631	+	0.421981i
$640$		0			0
$641$	−4016.12	+	6956.12i	−0.247468	+	0.428627i	−0.962823	−	0.270134i	$-0.912932\pi$
$641$	−4016.12	+	6956.12i	−0.247468	+	0.428627i	0.715355	+	0.698762i	$0.246265\pi$
$642$		0			0
$643$	−24887.7			−1.52640			−0.763200	−	0.646162i	$-0.776373\pi$
$643$	−24887.7			−1.52640			−0.763200	+	0.646162i	$0.776373\pi$
$644$		0			0
$645$	−5287.68			−0.322794
$646$		0			0
$647$	10542.2	−	18259.6i	0.640580	−	1.10952i	−0.344723	−	0.938704i	$-0.612027\pi$
$647$	10542.2	−	18259.6i	0.640580	−	1.10952i	0.985303	−	0.170813i	$-0.0546395\pi$
$648$		0			0
$649$	5001.95	+	8663.62i	0.302532	+	0.524002i
$650$		0			0
$651$	161.346	−	552.982i	0.00971377	−	0.0332919i
$652$		0			0
$653$	−6583.16	−	11402.4i	−0.394516	−	0.683322i	0.598523	−	0.801106i	$-0.295754\pi$
$653$	−6583.16	−	11402.4i	−0.394516	−	0.683322i	−0.993039	+	0.117783i	$0.962421\pi$
$654$		0			0
$655$	20535.1	−	35567.8i	1.22499	−	2.12175i
$656$		0			0
$657$	1371.66			0.0814513
$658$		0			0
$659$	−13903.4			−0.821851			−0.410926	−	0.911669i	$-0.634794\pi$
$659$	−13903.4			−0.821851			−0.410926	+	0.911669i	$0.634794\pi$
$660$		0			0
$661$	−3153.30	+	5461.68i	−0.185551	+	0.321384i	−0.943762	−	0.330625i	$-0.892740\pi$
$661$	−3153.30	+	5461.68i	−0.185551	+	0.321384i	0.758211	+	0.652009i	$0.226074\pi$
$662$		0			0
$663$	−11390.0	−	19728.1i	−0.667197	−	1.15562i
$664$		0			0
$665$	4265.32	−	1042.46i	0.248725	−	0.0607892i
$666$		0			0
$667$	−8656.23	−	14993.0i	−0.502505	−	0.870364i
$668$		0			0
$669$	−2467.25	+	4273.40i	−0.142585	+	0.246964i
$670$		0			0
$671$	21699.1			1.24841
$672$		0			0
$673$	−24407.6			−1.39798			−0.698992	−	0.715129i	$-0.746368\pi$
$673$	−24407.6			−1.39798			−0.698992	+	0.715129i	$0.746368\pi$
$674$		0			0
$675$	−3164.49	+	5481.05i	−0.180446	+	0.312542i
$676$		0			0
$677$	15540.1	+	26916.3i	0.882209	+	1.52803i	0.848879	+	0.528587i	$0.177278\pi$
$677$	15540.1	+	26916.3i	0.882209	+	1.52803i	0.0333299	+	0.999444i	$0.489389\pi$
$678$		0			0
$679$	−20597.6	−	21528.5i	−1.16416	−	1.21677i
$680$		0			0
$681$	−478.312	−	828.460i	−0.0269147	−	0.0466177i
$682$		0			0
$683$	−14379.7	+	24906.4i	−0.805601	+	1.39534i	0.110283	+	0.993900i	$0.464824\pi$
$683$	−14379.7	+	24906.4i	−0.805601	+	1.39534i	−0.915885	+	0.401442i	$0.868509\pi$
$684$		0			0
$685$	−37251.0			−2.07779
$686$		0			0
$687$	7608.32			0.422526
$688$		0			0
$689$	11738.5	−	20331.7i	0.649061	−	1.12421i
$690$		0			0
$691$	−12447.7	−	21560.1i	−0.685287	−	1.18695i	−0.973346	−	0.229340i	$-0.926343\pi$
$691$	−12447.7	−	21560.1i	−0.685287	−	1.18695i	0.288059	−	0.957613i	$-0.406990\pi$
$692$		0			0
$693$	6306.60	+	6591.63i	0.345697	+	0.361321i
$694$		0			0
$695$	1298.40	+	2248.89i	0.0708649	+	0.122742i
$696$		0			0
$697$	−14610.2	+	25305.6i	−0.793976	+	1.37521i
$698$		0			0
$699$	6998.44			0.378692
$700$		0			0
$701$	−1702.74			−0.0917427			−0.0458714	−	0.998947i	$-0.514606\pi$
$701$	−1702.74			−0.0917427			−0.0458714	+	0.998947i	$0.514606\pi$
$702$		0			0
$703$	−1538.12	+	2664.11i	−0.0825198	+	0.142929i
$704$		0			0
$705$	13810.3	+	23920.1i	0.737767	+	1.27785i
$706$		0			0
$707$	14087.5	−	3443.04i	0.749385	−	0.183153i
$708$		0			0
$709$	−3261.60	−	5649.26i	−0.172767	−	0.299242i	0.766619	−	0.642102i	$-0.221938\pi$
$709$	−3261.60	−	5649.26i	−0.172767	−	0.299242i	−0.939386	+	0.342860i	$0.888604\pi$
$710$		0			0
$711$	−2580.11	+	4468.88i	−0.136092	+	0.235719i
$712$		0			0
$713$	−771.765			−0.0405369
$714$		0			0
$715$	64348.4			3.36572
$716$		0			0
$717$	−4070.77	+	7050.79i	−0.212030	+	0.367248i
$718$		0			0
$719$	12627.2	+	21871.0i	0.654959	+	1.13442i	0.981904	+	0.189379i	$0.0606476\pi$
$719$	12627.2	+	21871.0i	0.654959	+	1.13442i	−0.326945	+	0.945044i	$0.606019\pi$
$720$		0			0
$721$	−7727.27	+	26483.7i	−0.399138	+	1.36797i
$722$		0			0
$723$	6261.88	+	10845.9i	0.322105	+	0.557902i
$724$		0			0
$725$	27258.2	−	47212.6i	1.39634	−	2.41853i
$726$		0			0
$727$	−27964.9			−1.42663			−0.713316	−	0.700843i	$-0.752808\pi$
$727$	−27964.9			−1.42663			−0.713316	+	0.700843i	$0.752808\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	5691.69	−	9858.29i	0.287982	−	0.498799i
$732$		0			0
$733$	4647.19	+	8049.17i	0.234172	+	0.405597i	0.959032	−	0.283299i	$-0.0914288\pi$
$733$	4647.19	+	8049.17i	0.234172	+	0.405597i	−0.724860	+	0.688896i	$0.758096\pi$
$734$		0			0
$735$	−861.760	+	19488.8i	−0.0432469	+	0.978032i
$736$		0			0
$737$	7148.91	+	12382.3i	0.357305	+	0.618870i
$738$		0			0
$739$	−9145.60	+	15840.6i	−0.455245	+	0.788508i	−0.998702	−	0.0509292i	$-0.983782\pi$
$739$	−9145.60	+	15840.6i	−0.455245	+	0.788508i	0.543457	+	0.839437i	$0.317115\pi$
$740$		0			0
$741$	−2326.72			−0.115350
$742$		0			0
$743$	14742.4			0.727921			0.363960	−	0.931414i	$-0.381424\pi$
$743$	14742.4			0.727921			0.363960	+	0.931414i	$0.381424\pi$
$744$		0			0
$745$	2655.12	−	4598.80i	0.130572	−	0.226157i
$746$		0			0
$747$	−1429.89	−	2476.64i	−0.0700361	−	0.121306i
$748$		0			0
$749$	3697.46	−	12672.3i	0.180377	−	0.618204i
$750$		0			0
$751$	−14231.7	−	24650.0i	−0.691507	−	1.19773i	−0.971344	−	0.237678i	$-0.923614\pi$
$751$	−14231.7	−	24650.0i	−0.691507	−	1.19773i	0.279837	−	0.960048i	$-0.409720\pi$
$752$		0			0
$753$	−9185.37	+	15909.5i	−0.444533	+	0.769954i
$754$		0			0
$755$	41596.4			2.00510
$756$		0			0
$757$	−20336.7			−0.976422			−0.488211	−	0.872726i	$-0.662350\pi$
$757$	−20336.7			−0.976422			−0.488211	+	0.872726i	$0.662350\pi$
$758$		0			0
$759$	6111.17	−	10584.9i	0.292255	−	0.506200i
$760$		0			0
$761$	−19790.8	−	34278.7i	−0.942728	−	1.63285i	−0.760238	−	0.649644i	$-0.774918\pi$
$761$	−19790.8	−	34278.7i	−0.942728	−	1.63285i	−0.182489	−	0.983208i	$-0.558415\pi$
$762$		0			0
$763$	−18743.6	+	4581.01i	−0.889337	+	0.217357i
$764$		0			0
$765$	−10445.4	−	18092.0i	−0.493666	−	0.855055i
$766$		0			0
$767$	5667.87	−	9817.04i	0.266825	−	0.462155i
$768$		0			0
$769$	10580.3			0.496146			0.248073	−	0.968741i	$-0.420203\pi$
$769$	10580.3			0.496146			0.248073	+	0.968741i	$0.420203\pi$
$770$		0			0
$771$	13901.7			0.649363
$772$		0			0
$773$	−12961.1	+	22449.3i	−0.603077	+	1.04456i	0.389275	+	0.921122i	$0.372726\pi$
$773$	−12961.1	+	22449.3i	−0.603077	+	1.04456i	−0.992352	+	0.123439i	$0.960608\pi$
$774$		0			0
$775$	−1215.13	−	2104.67i	−0.0563211	−	0.0975509i
$776$		0			0
$777$	−9448.31	−	9875.33i	−0.436237	−	0.455953i
$778$		0			0
$779$	1492.27	+	2584.68i	0.0686341	+	0.118878i
$780$		0			0
$781$	23931.7	−	41450.9i	1.09647	−	1.89914i
$782$		0			0
$783$	−6279.45			−0.286602
$784$		0			0
$785$	−4186.27			−0.190337
$786$		0			0
$787$	−8610.00	+	14913.0i	−0.389979	+	0.675463i	−0.992446	−	0.122680i	$-0.960851\pi$
$787$	−8610.00	+	14913.0i	−0.389979	+	0.675463i	0.602467	+	0.798143i	$0.294184\pi$
$788$		0			0
$789$	−4924.84	−	8530.08i	−0.222217	−	0.384891i
$790$		0			0
$791$	4507.94	+	4711.68i	0.202635	+	0.211793i
$792$		0			0
$793$	−12294.0	−	21293.8i	−0.550533	−	0.953551i
$794$		0			0
$795$	10765.0	−	18645.6i	0.480247	−	0.831812i
$796$		0			0
$797$	−6275.52			−0.278909			−0.139454	−	0.990228i	$-0.544535\pi$
$797$	−6275.52			−0.278909			−0.139454	+	0.990228i	$0.544535\pi$
$798$		0			0
$799$	−59461.9			−2.63280
$800$		0			0
$801$	427.572	−	740.576i	0.0188608	−	0.0326679i
$802$		0			0
$803$	−4170.66	−	7223.80i	−0.183287	−	0.317463i
$804$		0			0
$805$	25388.8	−	6205.12i	1.11160	−	0.271679i
$806$		0			0
$807$	1198.48	+	2075.83i	0.0522781	+	0.0905483i
$808$		0			0
$809$	2302.01	−	3987.20i	0.100043	−	0.173279i	−0.811659	−	0.584131i	$-0.801435\pi$
$809$	2302.01	−	3987.20i	0.100043	−	0.173279i	0.911702	+	0.410852i	$0.134769\pi$
$810$		0			0
$811$	5104.36			0.221009			0.110505	−	0.993876i	$-0.464753\pi$
$811$	5104.36			0.221009			0.110505	+	0.993876i	$0.464753\pi$
$812$		0			0
$813$	−20118.2			−0.867868
$814$		0			0
$815$	−13999.2	+	24247.3i	−0.601682	+	1.04214i
$816$		0			0
$817$	−581.341	−	1006.91i	−0.0248942	−	0.0431180i
$818$		0			0
$819$	2895.41	−	9923.41i	0.123533	−	0.423385i
$820$		0			0
$821$	22817.7	+	39521.4i	0.969967	+	1.68003i	0.695633	+	0.718398i	$0.255124\pi$
$821$	22817.7	+	39521.4i	0.969967	+	1.68003i	0.274334	+	0.961634i	$0.411542\pi$
$822$		0			0
$823$	19688.6	−	34101.6i	0.833901	−	1.44436i	−0.0610219	−	0.998136i	$-0.519436\pi$
$823$	19688.6	−	34101.6i	0.833901	−	1.44436i	0.894922	−	0.446222i	$-0.147231\pi$
$824$		0			0
$825$	38487.8			1.62421
$826$		0			0
$827$	−30916.3			−1.29996			−0.649978	−	0.759953i	$-0.725222\pi$
$827$	−30916.3			−1.29996			−0.649978	+	0.759953i	$0.725222\pi$
$828$		0			0
$829$	1271.66	−	2202.59i	0.0532771	−	0.0922786i	−0.838157	−	0.545429i	$-0.816367\pi$
$829$	1271.66	−	2202.59i	0.0532771	−	0.0922786i	0.891434	+	0.453151i	$0.149700\pi$
$830$		0			0
$831$	−1743.41	−	3019.67i	−0.0727775	−	0.126054i
$832$		0			0
$833$	−35407.0	−	22584.5i	−1.47273	−	0.939382i
$834$		0			0
$835$	−20831.6	−	36081.5i	−0.863364	−	1.49539i
$836$		0			0
$837$	−139.964	+	242.425i	−0.00578002	+	0.0100113i
$838$		0			0
$839$	−7930.82			−0.326343			−0.163172	−	0.986598i	$-0.552172\pi$
$839$	−7930.82			−0.326343			−0.163172	+	0.986598i	$0.552172\pi$
$840$		0			0
$841$	29700.8			1.21780
$842$		0			0
$843$	−4077.25	+	7062.01i	−0.166581	+	0.288527i
$844$		0			0
$845$	−15632.3	−	27075.9i	−0.636410	−	1.10229i
$846$		0			0
$847$	8634.31	−	29592.3i	0.350270	−	1.20048i
$848$		0			0
$849$	4514.22	+	7818.87i	0.182483	+	0.316069i
$850$		0			0
$851$	−9155.51	+	15857.8i	−0.368798	+	0.638776i
$852$		0			0
$853$	41983.2			1.68520			0.842601	−	0.538538i	$-0.181023\pi$
$853$	41983.2			1.68520			0.842601	+	0.538538i	$0.181023\pi$
$854$		0			0
$855$	−2133.76			−0.0853485
$856$		0			0
$857$	5927.16	−	10266.1i	0.236252	−	0.409200i	−0.723384	−	0.690446i	$-0.757414\pi$
$857$	5927.16	−	10266.1i	0.236252	−	0.409200i	0.959636	+	0.281246i	$0.0907476\pi$
$858$		0			0
$859$	4056.94	+	7026.83i	0.161142	+	0.279106i	0.935279	−	0.353912i	$-0.115149\pi$
$859$	4056.94	+	7026.83i	0.161142	+	0.279106i	−0.774136	+	0.633019i	$0.781816\pi$
$860$		0			0
$861$	−12880.6	+	3148.07i	−0.509837	+	0.124606i
$862$		0			0
$863$	−22908.5	−	39678.7i	−0.903609	−	1.56510i	−0.822774	−	0.568369i	$-0.807575\pi$
$863$	−22908.5	−	39678.7i	−0.903609	−	1.56510i	−0.0808353	−	0.996727i	$-0.525759\pi$
$864$		0			0
$865$	−19826.3	+	34340.2i	−0.779325	+	1.34983i
$866$		0			0
$867$	30235.0			1.18435
$868$		0			0
$869$	31380.3			1.22498
$870$		0			0
$871$	8100.67	−	14030.8i	0.315133	−	0.545826i
$872$		0			0
$873$	7239.49	+	12539.2i	0.280664	+	0.486124i
$874$		0			0
$875$	26555.7	+	27755.9i	1.02599	+	1.07236i
$876$		0			0
$877$	−15906.5	−	27550.9i	−0.612456	−	1.06081i	−0.990825	−	0.135150i	$-0.956848\pi$
$877$	−15906.5	−	27550.9i	−0.612456	−	1.06081i	0.378369	−	0.925655i	$-0.376485\pi$
$878$		0			0
$879$	−6313.72	+	10935.7i	−0.242271	+	0.419626i
$880$		0			0
$881$	43551.6			1.66548			0.832742	−	0.553661i	$-0.186770\pi$
$881$	43551.6			1.66548			0.832742	+	0.553661i	$0.186770\pi$
$882$		0			0
$883$	40645.1			1.54906			0.774528	−	0.632540i	$-0.217988\pi$
$883$	40645.1			1.54906			0.774528	+	0.632540i	$0.217988\pi$
$884$		0			0
$885$	5197.82	−	9002.89i	0.197427	−	0.341953i
$886$		0			0
$887$	−17014.1	−	29469.3i	−0.644056	−	1.11554i	−0.984519	−	0.175280i	$-0.943917\pi$
$887$	−17014.1	−	29469.3i	−0.644056	−	1.11554i	0.340462	−	0.940258i	$-0.389416\pi$
$888$		0			0
$889$	−14003.3	−	14636.2i	−0.528297	−	0.552173i
$890$		0			0
$891$	−2216.60	−	3839.26i	−0.0833432	−	0.144355i
$892$		0			0
$893$	−3036.67	+	5259.68i	−0.113794	+	0.197098i
$894$		0			0
$895$	44258.2			1.65295
$896$		0			0
$897$	−13849.5			−0.515521
$898$		0			0
$899$	1205.62	−	2088.20i	0.0447272	−	0.0774699i
$900$		0			0
$901$	23175.1	+	40140.4i	0.856908	+	1.48421i
$902$		0			0
$903$	5017.89	−	1226.39i	0.184922	−	0.0451957i
$904$		0			0
$905$	−16667.9	−	28869.7i	−0.612221	−	1.06040i
$906$		0			0
$907$	−25402.4	+	43998.2i	−0.929958	+	1.61073i	−0.146571	+	0.989200i	$0.546824\pi$
$907$	−25402.4	+	43998.2i	−0.929958	+	1.61073i	−0.783387	+	0.621534i	$0.786510\pi$
$908$		0			0
$909$	−7047.38			−0.257147
$910$		0			0
$911$	28738.3			1.04516			0.522582	−	0.852589i	$-0.324969\pi$
$911$	28738.3			1.04516			0.522582	+	0.852589i	$0.324969\pi$
$912$		0			0
$913$	−8695.46	+	15061.0i	−0.315200	+	0.545943i
$914$		0			0
$915$	−11274.4	−	19527.9i	−0.407345	−	0.705543i
$916$		0			0
$917$	−11237.9	+	38515.8i	−0.404700	+	1.38703i
$918$		0			0
$919$	27371.1	+	47408.2i	0.982470	+	1.70169i	0.652680	+	0.757634i	$0.273645\pi$
$919$	27371.1	+	47408.2i	0.982470	+	1.70169i	0.329790	+	0.944054i	$0.393022\pi$
$920$		0			0
$921$	4672.23	−	8092.54i	0.167161	−	0.289531i
$922$		0			0
$923$	−54235.5			−1.93411
$924$		0			0
$925$	−57660.9			−2.04960
$926$		0			0
$927$	6703.24	−	11610.4i	0.237501	−	0.411364i
$928$		0			0
$929$	−21887.9	−	37911.0i	−0.773002	−	1.33888i	−0.935911	−	0.352238i	$-0.885421\pi$
$929$	−21887.9	−	37911.0i	−0.773002	−	1.33888i	0.162908	−	0.986641i	$-0.447912\pi$
$930$		0			0
$931$	−3805.91	+	1978.54i	−0.133978	+	0.0696499i
$932$		0			0
$933$	12730.9	+	22050.5i	0.446720	+	0.773741i
$934$		0			0
$935$	−63520.6	+	110021.i	−2.22176	+	3.84820i
$936$		0			0
$937$	35090.9			1.22345			0.611724	−	0.791071i	$-0.290476\pi$
$937$	35090.9			1.22345			0.611724	+	0.791071i	$0.290476\pi$
$938$		0			0
$939$	−14864.7			−0.516605
$940$		0			0
$941$	15892.4	−	27526.4i	0.550560	−	0.953599i	−0.447674	−	0.894197i	$-0.647747\pi$
$941$	15892.4	−	27526.4i	0.550560	−	0.953599i	0.998234	−	0.0594016i	$-0.0189193\pi$
$942$		0			0
$943$	8882.54	+	15385.0i	0.306740	+	0.531288i
$944$		0			0
$945$	2655.28	−	9100.44i	0.0914035	−	0.313267i
$946$		0			0
$947$	−28250.4	−	48931.2i	−0.969394	−	1.67904i	−0.697315	−	0.716765i	$-0.745622\pi$
$947$	−28250.4	−	48931.2i	−0.969394	−	1.67904i	−0.272079	−	0.962275i	$-0.587711\pi$
$948$		0			0
$949$	−4725.92	+	8185.53i	−0.161654	+	0.279993i
$950$		0			0
$951$	−16826.4			−0.573746
$952$		0			0
$953$	36669.1			1.24641			0.623204	−	0.782059i	$-0.285831\pi$
$953$	36669.1			1.24641			0.623204	+	0.782059i	$0.285831\pi$
$954$		0			0
$955$	35078.8	−	60758.2i	1.18861	−	2.05873i
$956$		0			0
$957$	19093.3	+	33070.6i	0.644931	+	1.11705i
$958$		0			0
$959$	35350.4	−	8639.76i	1.19033	−	0.290920i
$960$		0			0
$961$	14841.8	+	25706.7i	0.498196	+	0.862901i
$962$		0			0
$963$	−3207.46	+	5555.49i	−0.107330	+	0.185901i
$964$		0			0
$965$	51346.8			1.71286
$966$		0			0
$967$	−12012.4			−0.399474			−0.199737	−	0.979850i	$-0.564009\pi$
$967$	−12012.4			−0.399474			−0.199737	+	0.979850i	$0.564009\pi$
$968$		0			0
$969$	2296.79	−	3978.16i	0.0761440	−	0.131885i
$970$		0			0
$971$	18648.1	+	32299.5i	0.616320	+	1.06750i	0.990151	+	0.140000i	$0.0447104\pi$
$971$	18648.1	+	32299.5i	0.616320	+	1.06750i	−0.373832	+	0.927497i	$0.621956\pi$
$972$		0			0
$973$	−1753.75	−	1833.01i	−0.0577826	−	0.0603942i
$974$		0			0
$975$	−21805.9	−	37768.9i	−0.716254	−	1.24059i
$976$		0			0
$977$	−4894.22	+	8477.04i	−0.160266	+	0.277589i	−0.934964	−	0.354742i	$-0.884569\pi$
$977$	−4894.22	+	8477.04i	−0.160266	+	0.277589i	0.774698	+	0.632331i	$0.217902\pi$
$978$		0			0
$979$	−5200.30			−0.169767
$980$		0			0
$981$	9376.63			0.305171
$982$		0			0
$983$	2310.20	−	4001.39i	0.0749583	−	0.129832i	−0.826110	−	0.563509i	$-0.809451\pi$
$983$	2310.20	−	4001.39i	0.0749583	−	0.129832i	0.901068	+	0.433678i	$0.142784\pi$
$984$		0			0
$985$	1523.15	+	2638.17i	0.0492705	+	0.0853390i
$986$		0			0
$987$	−18653.5	−	19496.6i	−0.601569	−	0.628757i
$988$		0			0
$989$	−3460.37	−	5993.53i	−0.111257	−	0.192703i
$990$		0			0
$991$	−20182.7	+	34957.4i	−0.646946	+	1.12054i	0.336903	+	0.941540i	$0.390621\pi$
$991$	−20182.7	+	34957.4i	−0.646946	+	1.12054i	−0.983848	+	0.179004i	$0.942713\pi$
$992$		0			0
$993$	−19828.5			−0.633673
$994$		0			0
$995$	−39167.1			−1.24792
$996$		0			0
$997$	1497.18	−	2593.19i	0.0475587	−	0.0823742i	−0.841266	−	0.540621i	$-0.818189\pi$
$997$	1497.18	−	2593.19i	0.0475587	−	0.0823742i	0.888825	+	0.458247i	$0.151523\pi$
$998$		0			0
$999$	3320.82	+	5751.83i	0.105171	+	0.182162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.q.f.25.1	✓	8
3.2	odd	2		504.4.s.j.361.4		8
4.3	odd	2		336.4.q.m.193.1		8
7.2	even	3	inner	168.4.q.f.121.1	yes	8
7.3	odd	6		1176.4.a.ba.1.1		4
7.4	even	3		1176.4.a.bd.1.4		4
21.2	odd	6		504.4.s.j.289.4		8
28.3	even	6		2352.4.a.cp.1.1		4
28.11	odd	6		2352.4.a.cm.1.4		4
28.23	odd	6		336.4.q.m.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.f.25.1	✓	8	1.1	even	1	trivial
168.4.q.f.121.1	yes	8	7.2	even	3	inner
336.4.q.m.193.1		8	4.3	odd	2
336.4.q.m.289.1		8	28.23	odd	6
504.4.s.j.289.4		8	21.2	odd	6
504.4.s.j.361.4		8	3.2	odd	2
1176.4.a.ba.1.1		4	7.3	odd	6
1176.4.a.bd.1.4		4	7.4	even	3
2352.4.a.cm.1.4		4	28.11	odd	6
2352.4.a.cp.1.1		4	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(12.8033 + 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(12.8033 + 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-27.3654 + 47.3983i) q^{11} +62.0173 q^{13} +56.8741 q^{15} +(-61.2195 + 106.035i) q^{17} +(6.25288 + 10.8303i) q^{19} +(-53.9722 + 13.1910i) q^{21} +(37.2195 + 64.4661i) q^{23} +(-117.203 + 203.002i) q^{25} +27.0000 q^{27} -232.572 q^{29} +(-5.18387 + 8.97872i) q^{31} +(-82.0962 - 142.195i) q^{33} +(98.3438 - 337.053i) q^{35} +(122.993 + 213.031i) q^{37} +(-93.0260 + 161.126i) q^{39} +238.653 q^{41} -92.9718 q^{43} +(-85.3111 + 147.763i) q^{45} +(242.822 + 420.580i) q^{47} +(-15.1521 + 342.665i) q^{49} +(-183.659 - 318.106i) q^{51} +(189.278 - 327.840i) q^{53} +1037.59 q^{55} -37.5173 q^{57} +(91.3918 - 158.295i) q^{59} +(-198.235 - 343.353i) q^{61} +(46.6871 - 160.010i) q^{63} +(-587.863 - 1018.21i) q^{65} +(130.620 - 226.240i) q^{67} -223.317 q^{69} -874.523 q^{71} +(-76.2032 + 131.988i) q^{73} +(-351.610 - 609.006i) q^{75} +(-984.647 + 240.651i) q^{77} +(-286.679 - 496.542i) q^{79} +(-40.5000 + 70.1481i) q^{81} +317.754 q^{83} +2321.20 q^{85} +(348.858 - 604.240i) q^{87} +(47.5080 + 82.2863i) q^{89} +(794.025 + 829.911i) q^{91} +(-15.5516 - 26.9362i) q^{93} +(118.542 - 205.321i) q^{95} -1608.78 q^{97} +492.577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9	\( 8 q - 12 q^{3} - 4 q^{5} + 18 q^{7} - 36 q^{9} - 14 q^{11} + 44 q^{13} + 24 q^{15} - 96 q^{17} + 26 q^{19} - 36 q^{21} - 96 q^{23} - 110 q^{25} + 216 q^{27} - 152 q^{29} - 238 q^{31} - 42 q^{33} + 152 q^{35} - 562 q^{37} - 66 q^{39} + 856 q^{41} - 516 q^{43} - 36 q^{45} + 80 q^{47} + 156 q^{49} - 288 q^{51} + 2952 q^{55} - 156 q^{57} - 262 q^{59} + 276 q^{61} - 54 q^{63} - 2196 q^{65} - 150 q^{67} + 576 q^{69} - 1696 q^{71} + 218 q^{73} - 330 q^{75} - 764 q^{77} - 1762 q^{79} - 324 q^{81} + 6900 q^{83} + 2904 q^{85} + 228 q^{87} + 344 q^{89} - 2806 q^{91} - 714 q^{93} - 2004 q^{95} - 1244 q^{97} + 252 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 4 * q^5 + 18 * q^7 - 36 * q^9 - 14 * q^11 + 44 * q^13 + 24 * q^15 - 96 * q^17 + 26 * q^19 - 36 * q^21 - 96 * q^23 - 110 * q^25 + 216 * q^27 - 152 * q^29 - 238 * q^31 - 42 * q^33 + 152 * q^35 - 562 * q^37 - 66 * q^39 + 856 * q^41 - 516 * q^43 - 36 * q^45 + 80 * q^47 + 156 * q^49 - 288 * q^51 + 2952 * q^55 - 156 * q^57 - 262 * q^59 + 276 * q^61 - 54 * q^63 - 2196 * q^65 - 150 * q^67 + 576 * q^69 - 1696 * q^71 + 218 * q^73 - 330 * q^75 - 764 * q^77 - 1762 * q^79 - 324 * q^81 + 6900 * q^83 + 2904 * q^85 + 228 * q^87 + 344 * q^89 - 2806 * q^91 - 714 * q^93 - 2004 * q^95 - 1244 * q^97 + 252 * q^99

Introduction

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