LMFDB - Embedded newform 116.2.i.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(5,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("116.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.i (of order $14$, degree $6$, 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			109.1
Root			$0.222521 + 0.974928i$ of defining polynomial
Character	$\chi$	$=$	116.109
Dual form			116.2.i.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.376510 + 0.781831i) q^{3} +(0.455927 + 1.99755i) q^{5} +(0.821552 + 0.395639i) q^{7} +(1.40097 + 1.75676i) q^{9} +O(q^{10})$	\(q+(-0.376510 + 0.781831i) q^{3} +(0.455927 + 1.99755i) q^{5} +(0.821552 + 0.395639i) q^{7} +(1.40097 + 1.75676i) q^{9} +(-1.22252 - 0.974928i) q^{11} +(1.33244 - 1.67082i) q^{13} +(-1.73341 - 0.395639i) q^{15} +0.772386i q^{17} +(-3.09030 - 6.41708i) q^{19} +(-0.618645 + 0.493353i) q^{21} +(0.297093 - 1.30165i) q^{23} +(0.722521 - 0.347948i) q^{25} +(-4.43900 + 1.01317i) q^{27} +(-3.71379 - 3.89971i) q^{29} +(0.208947 - 0.0476909i) q^{31} +(1.22252 - 0.588735i) q^{33} +(-0.415739 + 1.82147i) q^{35} +(6.38135 - 5.08896i) q^{37} +(0.804626 + 1.67082i) q^{39} +5.29150i q^{41} +(-4.53199 - 1.03440i) q^{43} +(-2.87047 + 3.59945i) q^{45} +(8.07338 + 6.43830i) q^{47} +(-3.84601 - 4.82274i) q^{49} +(-0.603875 - 0.290811i) q^{51} +(1.92812 + 8.44763i) q^{53} +(1.39008 - 2.88654i) q^{55} +6.18060 q^{57} -1.50604 q^{59} +(1.46466 - 3.04139i) q^{61} +(0.455927 + 1.99755i) q^{63} +(3.94504 + 1.89983i) q^{65} +(8.62833 + 10.8196i) q^{67} +(0.905813 + 0.722362i) q^{69} +(4.44235 - 5.57054i) q^{71} +(-7.99880 - 1.82567i) q^{73} +0.695895i q^{75} +(-0.618645 - 1.28463i) q^{77} +(4.00269 - 3.19204i) q^{79} +(-0.620801 + 2.71991i) q^{81} +(-14.2545 + 6.86461i) q^{83} +(-1.54288 + 0.352152i) q^{85} +(4.44720 - 1.43528i) q^{87} +(-14.2458 + 3.25151i) q^{89} +(1.75571 - 0.845505i) q^{91} +(-0.0413846 + 0.181318i) q^{93} +(11.4095 - 9.09874i) q^{95} +(0.0782203 + 0.162426i) q^{97} -3.51352i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9}+O(q^{10}) $ 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9	$ 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9} - 7 q^{11} + 9 q^{13} - 7 q^{15} - 7 q^{19} - 21 q^{21} + 15 q^{23} + 4 q^{25} - 7 q^{27} - 6 q^{29} + 7 q^{31} + 7 q^{33} - 33 q^{35} + 21 q^{37} - 7 q^{39} + 7 q^{43} - 3 q^{45} + 21 q^{47} - 18 q^{49} + 14 q^{51} - 5 q^{53} + 7 q^{55} + 14 q^{57} - 28 q^{59} + 21 q^{61} - q^{63} + 23 q^{65} + 25 q^{67} - 21 q^{69} + 29 q^{71} - 7 q^{73} - 21 q^{77} + 21 q^{79} - 2 q^{81} - 51 q^{83} + 28 q^{85} + 7 q^{87} - 35 q^{89} + 17 q^{91} - 7 q^{93} - 21 q^{95} - 49 q^{97}+O(q^{100}) $ 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9 - 7 * q^11 + 9 * q^13 - 7 * q^15 - 7 * q^19 - 21 * q^21 + 15 * q^23 + 4 * q^25 - 7 * q^27 - 6 * q^29 + 7 * q^31 + 7 * q^33 - 33 * q^35 + 21 * q^37 - 7 * q^39 + 7 * q^43 - 3 * q^45 + 21 * q^47 - 18 * q^49 + 14 * q^51 - 5 * q^53 + 7 * q^55 + 14 * q^57 - 28 * q^59 + 21 * q^61 - q^63 + 23 * q^65 + 25 * q^67 - 21 * q^69 + 29 * q^71 - 7 * q^73 - 21 * q^77 + 21 * q^79 - 2 * q^81 - 51 * q^83 + 28 * q^85 + 7 * q^87 - 35 * q^89 + 17 * q^91 - 7 * q^93 - 21 * q^95 - 49 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{13}{14}\right)$

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
$3$	−0.376510	+	0.781831i	−0.217378	+	0.451391i	−0.980931	−	0.194354i	$-0.937739\pi$
$3$	−0.376510	+	0.781831i	−0.217378	+	0.451391i	0.763553	+	0.645745i	$0.223453\pi$
$4$		0			0
$5$	0.455927	+	1.99755i	0.203897	+	0.893330i	0.968536	+	0.248872i	$0.0800598\pi$
$5$	0.455927	+	1.99755i	0.203897	+	0.893330i	−0.764640	+	0.644458i	$0.777083\pi$
$6$		0			0
$7$	0.821552	+	0.395639i	0.310517	+	0.149537i	0.582652	−	0.812722i	$-0.302015\pi$
$7$	0.821552	+	0.395639i	0.310517	+	0.149537i	−0.272134	+	0.962259i	$0.587729\pi$
$8$		0			0
$9$	1.40097	+	1.75676i	0.466990	+	0.585586i
$10$		0			0
$11$	−1.22252	−	0.974928i	−0.368604	−	0.293952i	0.421617	−	0.906774i	$-0.361463\pi$
$11$	−1.22252	−	0.974928i	−0.368604	−	0.293952i	−0.790221	+	0.612822i	$0.790034\pi$
$12$		0			0
$13$	1.33244	−	1.67082i	0.369552	−	0.463403i	−0.561934	−	0.827182i	$-0.689942\pi$
$13$	1.33244	−	1.67082i	0.369552	−	0.463403i	0.931485	+	0.363779i	$0.118514\pi$
$14$		0			0
$15$	−1.73341	−	0.395639i	−0.447564	−	0.102153i
$16$		0			0
$17$			0.772386i			0.187331i	0.995604	+	0.0936655i	$0.0298584\pi$
$17$			0.772386i			0.187331i	−0.995604	+	0.0936655i	$0.970142\pi$
$18$		0			0
$19$	−3.09030	−	6.41708i	−0.708964	−	1.47218i	−0.874018	−	0.485894i	$-0.838494\pi$
$19$	−3.09030	−	6.41708i	−0.708964	−	1.47218i	0.165054	−	0.986285i	$-0.447220\pi$
$20$		0			0
$21$	−0.618645	+	0.493353i	−0.135000	+	0.107659i
$22$		0			0
$23$	0.297093	−	1.30165i	0.0619483	−	0.271413i	−0.934463	−	0.356061i	$-0.884119\pi$
$23$	0.297093	−	1.30165i	0.0619483	−	0.271413i	0.996411	+	0.0846481i	$0.0269766\pi$
$24$		0			0
$25$	0.722521	−	0.347948i	0.144504	−	0.0695895i
$26$		0			0
$27$	−4.43900	+	1.01317i	−0.854286	+	0.194985i
$28$		0			0
$29$	−3.71379	−	3.89971i	−0.689634	−	0.724158i
$29$	−3.71379	−	3.89971i	−0.689634	−	0.724158i
$30$		0			0
$31$	0.208947	−	0.0476909i	0.0375281	−	0.00856553i	−0.203716	−	0.979030i	$-0.565302\pi$
$31$	0.208947	−	0.0476909i	0.0375281	−	0.00856553i	0.241244	+	0.970465i	$0.422445\pi$
$32$		0			0
$33$	1.22252	−	0.588735i	0.212814	−	0.102486i
$34$		0			0
$35$	−0.415739	+	1.82147i	−0.0702727	+	0.307885i
$36$		0			0
$37$	6.38135	−	5.08896i	1.04909	−	0.836620i	0.0622062	−	0.998063i	$-0.480186\pi$
$37$	6.38135	−	5.08896i	1.04909	−	0.836620i	0.986882	+	0.161443i	$0.0516149\pi$
$38$		0			0
$39$	0.804626	+	1.67082i	0.128843	+	0.267546i
$40$		0			0
$41$			5.29150i			0.826394i	0.910642	+	0.413197i	$0.135588\pi$
$41$			5.29150i			0.826394i	−0.910642	+	0.413197i	$0.864412\pi$
$42$		0			0
$43$	−4.53199	−	1.03440i	−0.691122	−	0.157744i	−0.137487	−	0.990504i	$-0.543903\pi$
$43$	−4.53199	−	1.03440i	−0.691122	−	0.157744i	−0.553635	+	0.832759i	$0.686760\pi$
$44$		0			0
$45$	−2.87047	+	3.59945i	−0.427904	+	0.536575i
$46$		0			0
$47$	8.07338	+	6.43830i	1.17762	+	0.939123i	0.998996	−	0.0447940i	$-0.0142631\pi$
$47$	8.07338	+	6.43830i	1.17762	+	0.939123i	0.178627	+	0.983917i	$0.442835\pi$
$48$		0			0
$49$	−3.84601	−	4.82274i	−0.549430	−	0.688964i
$50$		0			0
$51$	−0.603875	−	0.290811i	−0.0845595	−	0.0407217i
$52$		0			0
$53$	1.92812	+	8.44763i	0.264847	+	1.16037i	0.915922	+	0.401357i	$0.131461\pi$
$53$	1.92812	+	8.44763i	0.264847	+	1.16037i	−0.651075	+	0.759014i	$0.725681\pi$
$54$		0			0
$55$	1.39008	−	2.88654i	0.187439	−	0.389221i
$56$		0			0
$57$	6.18060			0.818641
$58$		0			0
$59$	−1.50604			−0.196070			−0.0980349	−	0.995183i	$-0.531256\pi$
$59$	−1.50604			−0.196070			−0.0980349	+	0.995183i	$0.531256\pi$
$60$		0			0
$61$	1.46466	−	3.04139i	0.187530	−	0.389410i	−0.785914	−	0.618336i	$-0.787807\pi$
$61$	1.46466	−	3.04139i	0.187530	−	0.389410i	0.973444	+	0.228926i	$0.0735214\pi$
$62$		0			0
$63$	0.455927	+	1.99755i	0.0574414	+	0.251667i
$64$		0			0
$65$	3.94504	+	1.89983i	0.489322	+	0.235645i
$66$		0			0
$67$	8.62833	+	10.8196i	1.05412	+	1.32182i	0.944739	+	0.327823i	$0.106315\pi$
$67$	8.62833	+	10.8196i	1.05412	+	1.32182i	0.109380	+	0.994000i	$0.465114\pi$
$68$		0			0
$69$	0.905813	+	0.722362i	0.109047	+	0.0869622i
$70$		0			0
$71$	4.44235	−	5.57054i	0.527210	−	0.661101i	−0.444912	−	0.895574i	$-0.646765\pi$
$71$	4.44235	−	5.57054i	0.527210	−	0.661101i	0.972123	+	0.234473i	$0.0753365\pi$
$72$		0			0
$73$	−7.99880	−	1.82567i	−0.936189	−	0.213679i	−0.272900	−	0.962042i	$-0.587983\pi$
$73$	−7.99880	−	1.82567i	−0.936189	−	0.213679i	−0.663289	+	0.748363i	$0.730840\pi$
$74$		0			0
$75$			0.695895i			0.0803551i
$76$		0			0
$77$	−0.618645	−	1.28463i	−0.0705012	−	0.146397i
$78$		0			0
$79$	4.00269	−	3.19204i	0.450338	−	0.359132i	−0.371904	−	0.928271i	$-0.621295\pi$
$79$	4.00269	−	3.19204i	0.450338	−	0.359132i	0.822241	+	0.569139i	$0.192723\pi$
$80$		0			0
$81$	−0.620801	+	2.71991i	−0.0689779	+	0.302212i
$82$		0			0
$83$	−14.2545	+	6.86461i	−1.56464	+	0.753489i	−0.997536	−	0.0701598i	$-0.977649\pi$
$83$	−14.2545	+	6.86461i	−1.56464	+	0.753489i	−0.567100	+	0.823649i	$0.691935\pi$
$84$		0			0
$85$	−1.54288	+	0.352152i	−0.167348	+	0.0381962i
$86$		0			0
$87$	4.44720	−	1.43528i	0.476790	−	0.153878i
$88$		0			0
$89$	−14.2458	+	3.25151i	−1.51005	+	0.344659i	−0.895802	−	0.444454i	$-0.853398\pi$
$89$	−14.2458	+	3.25151i	−1.51005	+	0.344659i	−0.614248	+	0.789113i	$0.710541\pi$
$90$		0			0
$91$	1.75571	−	0.845505i	0.184048	−	0.0886330i
$92$		0			0
$93$	−0.0413846	+	0.181318i	−0.00429138	+	0.0188018i
$94$		0			0
$95$	11.4095	−	9.09874i	1.17059	−	0.933511i
$96$		0			0
$97$	0.0782203	+	0.162426i	0.00794207	+	0.0164919i	0.904902	−	0.425620i	$-0.139944\pi$
$97$	0.0782203	+	0.162426i	0.00794207	+	0.0164919i	−0.896960	+	0.442112i	$0.854230\pi$
$98$		0			0
$99$		−	3.51352i		−	0.353122i
$100$		0			0
$101$	−10.1087	−	2.30725i	−1.00586	−	0.229580i	−0.312300	−	0.949983i	$-0.601099\pi$
$101$	−10.1087	−	2.30725i	−1.00586	−	0.229580i	−0.693555	+	0.720404i	$0.743957\pi$
$102$		0			0
$103$	2.51842	−	3.15800i	0.248147	−	0.311167i	−0.642121	−	0.766603i	$-0.721945\pi$
$103$	2.51842	−	3.15800i	0.248147	−	0.311167i	0.890268	+	0.455437i	$0.150517\pi$
$104$		0			0
$105$	−1.26755	−	1.01084i	−0.123701	−	0.0986479i
$106$		0			0
$107$	−5.59448	−	7.01526i	−0.540839	−	0.678191i	0.434048	−	0.900890i	$-0.357085\pi$
$107$	−5.59448	−	7.01526i	−0.540839	−	0.678191i	−0.974887	+	0.222699i	$0.928513\pi$
$108$		0			0
$109$	−16.4840	−	7.93829i	−1.57888	−	0.760350i	−0.580344	−	0.814371i	$-0.697082\pi$
$109$	−16.4840	−	7.93829i	−1.57888	−	0.760350i	−0.998540	+	0.0540208i	$0.982796\pi$
$110$		0			0
$111$	1.57606	+	6.90519i	0.149593	+	0.655412i
$112$		0			0
$113$	7.47972	−	15.5318i	0.703633	−	1.46111i	−0.175474	−	0.984484i	$-0.556146\pi$
$113$	7.47972	−	15.5318i	0.703633	−	1.46111i	0.879107	−	0.476625i	$-0.158140\pi$
$114$		0			0
$115$	2.73556			0.255092
$116$		0			0
$117$	4.80194			0.443939
$118$		0			0
$119$	−0.305586	+	0.634555i	−0.0280130	+	0.0581696i
$120$		0			0
$121$	−1.90366	−	8.34047i	−0.173060	−	0.758224i
$122$		0			0
$123$	−4.13706	−	1.99230i	−0.373026	−	0.179640i
$124$		0			0
$125$	7.41185	+	9.29417i	0.662936	+	0.831296i
$126$		0			0
$127$	9.76540	+	7.78764i	0.866539	+	0.691042i	0.952264	−	0.305277i	$-0.0987491\pi$
$127$	9.76540	+	7.78764i	0.866539	+	0.691042i	−0.0857246	+	0.996319i	$0.527321\pi$
$128$		0			0
$129$	2.51507	−	3.15379i	0.221439	−	0.277676i
$130$		0			0
$131$	−6.45593	−	1.47352i	−0.564057	−	0.128742i	−0.0690216	−	0.997615i	$-0.521988\pi$
$131$	−6.45593	−	1.47352i	−0.564057	−	0.128742i	−0.495035	+	0.868873i	$0.664845\pi$
$132$		0			0
$133$		−	6.49461i		−	0.563154i
$134$		0			0
$135$	−4.04772	−	8.40518i	−0.348372	−	0.723403i
$136$		0			0
$137$	−9.49665	+	7.57332i	−0.811353	+	0.647033i	−0.938665	−	0.344830i	$-0.887937\pi$
$137$	−9.49665	+	7.57332i	−0.811353	+	0.647033i	0.127312	+	0.991863i	$0.459365\pi$
$138$		0			0
$139$	−4.31886	+	18.9222i	−0.366321	+	1.60496i	0.370474	+	0.928843i	$0.379195\pi$
$139$	−4.31886	+	18.9222i	−0.366321	+	1.60496i	−0.736796	+	0.676116i	$0.763662\pi$
$140$		0			0
$141$	−8.07338	+	3.88793i	−0.679901	+	0.327423i
$142$		0			0
$143$	−3.25786	+	0.743586i	−0.272436	+	0.0621818i
$144$		0			0
$145$	6.09664	−	9.19646i	0.506298	−	0.763724i
$146$		0			0
$147$	5.21864	−	1.19112i	0.430426	−	0.0982419i
$148$		0			0
$149$	13.3741	−	6.44064i	1.09565	−	0.527637i	0.203362	−	0.979104i	$-0.434813\pi$
$149$	13.3741	−	6.44064i	1.09565	−	0.527637i	0.892288	+	0.451466i	$0.149099\pi$
$150$		0			0
$151$	−4.18718	+	18.3452i	−0.340748	+	1.49291i	0.456752	+	0.889594i	$0.349013\pi$
$151$	−4.18718	+	18.3452i	−0.340748	+	1.49291i	−0.797500	+	0.603319i	$0.793845\pi$
$152$		0			0
$153$	−1.35690	+	1.08209i	−0.109699	+	0.0874817i
$154$		0			0
$155$	0.190530	+	0.395639i	0.0153037	+	0.0317785i
$156$		0			0
$157$			15.7896i			1.26015i	0.776535	+	0.630074i	$0.216975\pi$
$157$			15.7896i			1.26015i	−0.776535	+	0.630074i	$0.783025\pi$
$158$		0			0
$159$	−7.33058	−	1.67316i	−0.581353	−	0.132690i
$160$		0			0
$161$	0.759061	−	0.951833i	0.0598224	−	0.0750149i
$162$		0			0
$163$	4.60656	+	3.67361i	0.360814	+	0.287740i	0.787071	−	0.616863i	$-0.211597\pi$
$163$	4.60656	+	3.67361i	0.360814	+	0.287740i	−0.426257	+	0.904602i	$0.640168\pi$
$164$		0			0
$165$	1.73341	+	2.17362i	0.134945	+	0.169216i
$166$		0			0
$167$	16.8584	+	8.11857i	1.30454	+	0.628234i	0.951579	−	0.307404i	$-0.0994602\pi$
$167$	16.8584	+	8.11857i	1.30454	+	0.628234i	0.352962	+	0.935638i	$0.385174\pi$
$168$		0			0
$169$	1.87651	+	8.22153i	0.144347	+	0.632425i
$170$		0			0
$171$	6.94385	−	14.4190i	0.531009	−	1.10265i
$172$		0			0
$173$	7.50604			0.570674			0.285337	−	0.958427i	$-0.407895\pi$
$173$	7.50604			0.570674			0.285337	+	0.958427i	$0.407895\pi$
$174$		0			0
$175$	0.731250			0.0552773
$176$		0			0
$177$	0.567040	−	1.17747i	0.0426213	−	0.0885041i
$178$		0			0
$179$	−1.76391	−	7.72818i	−0.131840	−	0.577631i	−0.997086	−	0.0762829i	$-0.975695\pi$
$179$	−1.76391	−	7.72818i	−0.131840	−	0.577631i	0.865246	−	0.501348i	$-0.167162\pi$
$180$		0			0
$181$	10.1271	+	4.87697i	0.752744	+	0.362503i	0.770584	−	0.637338i	$-0.219965\pi$
$181$	10.1271	+	4.87697i	0.752744	+	0.362503i	−0.0178399	+	0.999841i	$0.505679\pi$
$182$		0			0
$183$	1.82640	+	2.29023i	0.135011	+	0.169299i
$184$		0			0
$185$	13.0749	+	10.4269i	0.961283	+	0.766598i
$186$		0			0
$187$	0.753020	−	0.944258i	0.0550663	−	0.0690510i
$188$		0			0
$189$	−4.04772	−	0.923866i	−0.294428	−	0.0672014i
$190$		0			0
$191$		−	3.89971i		−	0.282173i	−0.989997	−	0.141087i	$-0.954940\pi$
$191$		−	3.89971i		−	0.282173i	0.989997	−	0.141087i	$-0.0450596\pi$
$192$		0			0
$193$	−0.442886	−	0.919662i	−0.0318796	−	0.0661987i	0.884421	−	0.466690i	$-0.154554\pi$
$193$	−0.442886	−	0.919662i	−0.0318796	−	0.0661987i	−0.916300	+	0.400491i	$0.868839\pi$
$194$		0			0
$195$	−2.97070	+	2.36905i	−0.212736	+	0.169651i
$196$		0			0
$197$	1.46130	−	6.40239i	0.104114	−	0.456151i	−0.895818	−	0.444422i	$-0.853409\pi$
$197$	1.46130	−	6.40239i	0.104114	−	0.456151i	0.999931	−	0.0117296i	$-0.00373372\pi$
$198$		0			0
$199$	−19.3523	+	9.31960i	−1.37185	+	0.660649i	−0.967246	−	0.253842i	$-0.918306\pi$
$199$	−19.3523	+	9.31960i	−1.37185	+	0.660649i	−0.404606	+	0.914491i	$0.632591\pi$
$200$		0			0
$201$	−11.7078	+	2.67222i	−0.825801	+	0.188484i
$202$		0			0
$203$	−1.50820	−	4.67314i	−0.105855	−	0.327990i
$204$		0			0
$205$	−10.5700	+	2.41254i	−0.738242	+	0.168499i
$206$		0			0
$207$	2.70291	−	1.30165i	0.187865	−	0.0904710i
$208$		0			0
$209$	−2.47823	+	10.8578i	−0.171423	+	0.751052i
$210$		0			0
$211$	9.61625	−	7.66871i	0.662010	−	0.527935i	−0.233849	−	0.972273i	$-0.575132\pi$
$211$	9.61625	−	7.66871i	0.662010	−	0.527935i	0.895860	+	0.444337i	$0.146561\pi$
$212$		0			0
$213$	2.68263	+	5.57054i	0.183811	+	0.381687i
$214$		0			0
$215$		−	9.52447i		−	0.649564i
$216$		0			0
$217$	0.190530	+	0.0434871i	0.0129340	+	0.00295210i
$218$		0			0
$219$	4.43900	−	5.56633i	0.299960	−	0.376138i
$220$		0			0
$221$	1.29052	+	1.02916i	0.0868098	+	0.0692285i
$222$		0			0
$223$	−7.66219	−	9.60808i	−0.513098	−	0.643404i	0.456030	−	0.889965i	$-0.349271\pi$
$223$	−7.66219	−	9.60808i	−0.513098	−	0.643404i	−0.969127	+	0.246560i	$0.920700\pi$
$224$		0			0
$225$	1.62349	+	0.781831i	0.108233	+	0.0521221i
$226$		0			0
$227$	−1.82251	−	7.98494i	−0.120964	−	0.529979i	−0.998706	−	0.0508461i	$-0.983808\pi$
$227$	−1.82251	−	7.98494i	−0.120964	−	0.529979i	0.877742	−	0.479133i	$-0.159049\pi$
$228$		0			0
$229$	3.84332	−	7.98074i	0.253974	−	0.527382i	−0.734530	−	0.678576i	$-0.762597\pi$
$229$	3.84332	−	7.98074i	0.253974	−	0.527382i	0.988504	+	0.151194i	$0.0483117\pi$
$230$		0			0
$231$	1.23729			0.0814078
$232$		0			0
$233$	3.90217			0.255639			0.127820	−	0.991797i	$-0.459202\pi$
$233$	3.90217			0.255639			0.127820	+	0.991797i	$0.459202\pi$
$234$		0			0
$235$	−9.17994	+	19.0623i	−0.598833	+	1.24349i
$236$		0			0
$237$	0.988582	+	4.33126i	0.0642153	+	0.281346i
$238$		0			0
$239$	−13.8409	−	6.66544i	−0.895295	−	0.431151i	−0.0711079	−	0.997469i	$-0.522653\pi$
$239$	−13.8409	−	6.66544i	−0.895295	−	0.431151i	−0.824187	+	0.566317i	$0.808368\pi$
$240$		0			0
$241$	8.35421	+	10.4758i	0.538142	+	0.674808i	0.974350	−	0.225037i	$-0.0722504\pi$
$241$	8.35421	+	10.4758i	0.538142	+	0.674808i	−0.436208	+	0.899846i	$0.643679\pi$
$242$		0			0
$243$	−12.5722	−	10.0260i	−0.806506	−	0.643167i
$244$		0			0
$245$	7.88016	−	9.88141i	0.503445	−	0.631300i
$246$		0			0
$247$	−14.8394	−	3.38700i	−0.944211	−	0.215510i
$248$		0			0
$249$		−	13.7292i		−	0.870054i
$250$		0			0
$251$	−1.88255	−	3.90916i	−0.118826	−	0.246744i	0.833069	−	0.553169i	$-0.186581\pi$
$251$	−1.88255	−	3.90916i	−0.118826	−	0.246744i	−0.951895	+	0.306425i	$0.900867\pi$
$252$		0			0
$253$	−1.63222	+	1.30165i	−0.102617	+	0.0818341i
$254$		0			0
$255$	0.305586	−	1.33886i	0.0191365	−	0.0838425i
$256$		0			0
$257$	17.0390	−	8.20555i	1.06286	−	0.511848i	0.181063	−	0.983471i	$-0.442046\pi$
$257$	17.0390	−	8.20555i	1.06286	−	0.511848i	0.881800	+	0.471624i	$0.156332\pi$
$258$		0			0
$259$	7.25600	−	1.65614i	0.450866	−	0.102907i
$260$		0			0
$261$	1.64795	−	11.9876i	0.102005	−	0.742015i
$262$		0			0
$263$	−25.9867	+	5.93130i	−1.60241	+	0.365740i	−0.927989	−	0.372608i	$-0.878464\pi$
$263$	−25.9867	+	5.93130i	−1.60241	+	0.365740i	−0.674421	+	0.738347i	$0.735607\pi$
$264$		0			0
$265$	−15.9955	+	7.70300i	−0.982593	+	0.473192i
$266$		0			0
$267$	2.82155	−	12.3620i	0.172676	−	0.756544i
$268$		0			0
$269$	−9.81863	+	7.83009i	−0.598652	+	0.477409i	−0.875312	−	0.483559i	$-0.839344\pi$
$269$	−9.81863	+	7.83009i	−0.598652	+	0.477409i	0.276660	+	0.960968i	$0.410773\pi$
$270$		0			0
$271$	0.628867	+	1.30585i	0.0382009	+	0.0793250i	0.919196	−	0.393801i	$-0.128840\pi$
$271$	0.628867	+	1.30585i	0.0382009	+	0.0793250i	−0.880995	+	0.473126i	$0.843126\pi$
$272$		0			0
$273$			1.69101i			0.102345i
$274$		0			0
$275$	−1.22252	−	0.279032i	−0.0737208	−	0.0168263i
$276$		0			0
$277$	4.95138	−	6.20883i	0.297499	−	0.373053i	−0.610505	−	0.792012i	$-0.709034\pi$
$277$	4.95138	−	6.20883i	0.297499	−	0.373053i	0.908005	+	0.418960i	$0.137605\pi$
$278$		0			0
$279$	0.376510	+	0.300257i	0.0225411	+	0.0179759i
$280$		0			0
$281$	−12.4182	−	15.5719i	−0.740807	−	0.928943i	0.258506	−	0.966010i	$-0.416770\pi$
$281$	−12.4182	−	15.5719i	−0.740807	−	0.928943i	−0.999313	+	0.0370670i	$0.988199\pi$
$282$		0			0
$283$	2.87047	+	1.38235i	0.170632	+	0.0821719i	0.517250	−	0.855834i	$-0.326956\pi$
$283$	2.87047	+	1.38235i	0.170632	+	0.0821719i	−0.346618	+	0.938006i	$0.612670\pi$
$284$		0			0
$285$	2.81790	+	12.3460i	0.166918	+	0.731317i
$286$		0			0
$287$	−2.09352	+	4.34724i	−0.123577	+	0.256610i
$288$		0			0
$289$	16.4034			0.964907
$290$		0			0
$291$	−0.156441			−0.00917072
$292$		0			0
$293$	1.01722	−	2.11228i	0.0594267	−	0.123401i	−0.869140	−	0.494566i	$-0.835327\pi$
$293$	1.01722	−	2.11228i	0.0594267	−	0.123401i	0.928567	+	0.371165i	$0.121041\pi$
$294$		0			0
$295$	−0.686645	−	3.00839i	−0.0399780	−	0.175155i
$296$		0			0
$297$	6.41454	+	3.08908i	0.372210	+	0.179247i
$298$		0			0
$299$	−1.77897	−	2.23076i	−0.102881	−	0.129008i
$300$		0			0
$301$	−3.31402	−	2.64284i	−0.191017	−	0.152331i
$302$		0			0
$303$	5.60992	−	7.03461i	0.322281	−	0.404128i
$304$		0			0
$305$	6.74309	+	1.53907i	0.386108	+	0.0881267i
$306$		0			0
$307$			34.1720i			1.95030i	0.221543	+	0.975151i	$0.428891\pi$
$307$			34.1720i			1.95030i	−0.221543	+	0.975151i	$0.571109\pi$
$308$		0			0
$309$	1.52081	+	3.15800i	0.0865159	+	0.179652i
$310$		0			0
$311$	22.1634	−	17.6748i	1.25677	−	1.00224i	0.257420	−	0.966300i	$-0.417128\pi$
$311$	22.1634	−	17.6748i	1.25677	−	1.00224i	0.999354	−	0.0359437i	$-0.0114437\pi$
$312$		0			0
$313$	0.336322	−	1.47352i	0.0190100	−	0.0832885i	−0.964533	−	0.263962i	$-0.914971\pi$
$313$	0.336322	−	1.47352i	0.0190100	−	0.0832885i	0.983543	+	0.180674i	$0.0578278\pi$
$314$		0			0
$315$	−3.78232	+	1.82147i	−0.213110	+	0.102628i
$316$		0			0
$317$	−19.5078	+	4.45253i	−1.09567	+	0.250079i	−0.731901	−	0.681411i	$-0.761367\pi$
$317$	−19.5078	+	4.45253i	−1.09567	+	0.250079i	−0.363767	+	0.931490i	$0.618510\pi$
$318$		0			0
$319$	0.738250	+	8.38816i	0.0413341	+	0.469647i
$320$		0			0
$321$	7.59113	−	1.73263i	0.423696	−	0.0967057i
$322$		0			0
$323$	4.95646	−	2.38691i	0.275785	−	0.132811i
$324$		0			0
$325$	0.381355	−	1.67082i	0.0211537	−	0.0926806i
$326$		0			0
$327$	12.4128	−	9.89889i	0.686430	−	0.547410i
$328$		0			0
$329$	4.08546	+	8.48354i	0.225239	+	0.467713i
$330$		0			0
$331$			15.9804i			0.878361i	0.898399	+	0.439180i	$0.144731\pi$
$331$			15.9804i			0.878361i	−0.898399	+	0.439180i	$0.855269\pi$
$332$		0			0
$333$	17.8802	+	4.08103i	0.979827	+	0.223639i
$334$		0			0
$335$	−17.6787	+	22.1684i	−0.965893	+	1.21119i
$336$		0			0
$337$	−5.17360	−	4.12581i	−0.281824	−	0.224747i	0.472367	−	0.881402i	$-0.343400\pi$
$337$	−5.17360	−	4.12581i	−0.281824	−	0.224747i	−0.754192	+	0.656654i	$0.771971\pi$
$338$		0			0
$339$	9.32706	+	11.6958i	0.506576	+	0.635227i
$340$		0			0
$341$	−0.301938	−	0.145406i	−0.0163508	−	0.00787415i
$342$		0			0
$343$	−2.67198	−	11.7067i	−0.144273	−	0.632103i
$344$		0			0
$345$	−1.02997	+	2.13875i	−0.0554516	+	0.115146i
$346$		0			0
$347$	19.1400			1.02749			0.513746	−	0.857942i	$-0.328257\pi$
$347$	19.1400			1.02749			0.513746	+	0.857942i	$0.328257\pi$
$348$		0			0
$349$	−6.57242			−0.351813			−0.175907	−	0.984407i	$-0.556286\pi$
$349$	−6.57242			−0.351813			−0.175907	+	0.984407i	$0.556286\pi$
$350$		0			0
$351$	−4.22186	+	8.76678i	−0.225346	+	0.467936i
$352$		0			0
$353$	3.69322	+	16.1810i	0.196570	+	0.861230i	0.972959	+	0.230976i	$0.0741920\pi$
$353$	3.69322	+	16.1810i	0.196570	+	0.861230i	−0.776389	+	0.630254i	$0.782951\pi$
$354$		0			0
$355$	13.1528	+	6.33405i	0.698078	+	0.336177i
$356$		0			0
$357$	−0.381059	−	0.477833i	−0.0201678	−	0.0252896i
$358$		0			0
$359$	2.09515	+	1.67082i	0.110578	+	0.0881827i	0.677218	−	0.735783i	$-0.263186\pi$
$359$	2.09515	+	1.67082i	0.110578	+	0.0881827i	−0.566640	+	0.823965i	$0.691757\pi$
$360$		0			0
$361$	−19.7826	+	24.8066i	−1.04119	+	1.30561i
$362$		0			0
$363$	7.23759	+	1.65193i	0.379875	+	0.0867039i
$364$		0			0
$365$		−	16.8104i		−	0.879894i
$366$		0			0
$367$	−4.63318	−	9.62089i	−0.241850	−	0.502207i	0.744345	−	0.667795i	$-0.232762\pi$
$367$	−4.63318	−	9.62089i	−0.241850	−	0.502207i	−0.986195	+	0.165589i	$0.947048\pi$
$368$		0			0
$369$	−9.29590	+	7.41323i	−0.483925	+	0.385917i
$370$		0			0
$371$	−1.75816	+	7.70300i	−0.0912791	+	0.399920i
$372$		0			0
$373$	14.1664	−	6.82216i	0.733507	−	0.353238i	−0.0295556	−	0.999563i	$-0.509409\pi$
$373$	14.1664	−	6.82216i	0.733507	−	0.353238i	0.763062	+	0.646325i	$0.223695\pi$
$374$		0			0
$375$	−10.0571	+	2.29547i	−0.519347	+	0.118538i
$376$		0			0
$377$	−11.4641	+	1.00897i	−0.590432	+	0.0519646i
$378$		0			0
$379$	34.6124	−	7.90005i	1.77792	−	0.405798i	0.797594	−	0.603194i	$-0.206106\pi$
$379$	34.6124	−	7.90005i	1.77792	−	0.405798i	0.980324	+	0.197396i	$0.0632486\pi$
$380$		0			0
$381$	−9.76540	+	4.70277i	−0.500296	+	0.240930i
$382$		0			0
$383$	−1.05980	+	4.64330i	−0.0541534	+	0.237261i	−0.994760	−	0.102237i	$-0.967400\pi$
$383$	−1.05980	+	4.64330i	−0.0541534	+	0.237261i	0.940607	+	0.339498i	$0.110257\pi$
$384$		0			0
$385$	2.28405	−	1.82147i	0.116406	−	0.0928308i
$386$		0			0
$387$	−4.53199	−	9.41078i	−0.230374	−	0.478377i
$388$		0			0
$389$		−	4.32835i		−	0.219456i	−0.993962	−	0.109728i	$-0.965002\pi$
$389$		−	4.32835i		−	0.219456i	0.993962	−	0.109728i	$-0.0349980\pi$
$390$		0			0
$391$	1.00538	+	0.229471i	0.0508441	+	0.0116048i
$392$		0			0
$393$	3.58277	−	4.49265i	0.180727	−	0.226624i
$394$		0			0
$395$	8.20118	+	6.54022i	0.412646	+	0.329074i
$396$		0			0
$397$	−6.90246	−	8.65541i	−0.346425	−	0.434403i	0.577843	−	0.816148i	$-0.303895\pi$
$397$	−6.90246	−	8.65541i	−0.346425	−	0.434403i	−0.924268	+	0.381745i	$0.875323\pi$
$398$		0			0
$399$	5.07769	+	2.44529i	0.254202	+	0.122417i
$400$		0			0
$401$	−0.577925	−	2.53205i	−0.0288602	−	0.126445i	0.958446	−	0.285275i	$-0.0920849\pi$
$401$	−0.577925	−	2.53205i	−0.0288602	−	0.126445i	−0.987306	+	0.158830i	$0.949228\pi$
$402$		0			0
$403$	0.198726	−	0.412659i	0.00989926	−	0.0205560i
$404$		0			0
$405$	−5.71618			−0.284039
$406$		0			0
$407$	−12.7627			−0.632624
$408$		0			0
$409$	8.29912	−	17.2333i	0.410365	−	0.852132i	−0.588677	−	0.808368i	$-0.700351\pi$
$409$	8.29912	−	17.2333i	0.410365	−	0.852132i	0.999042	−	0.0437633i	$-0.0139347\pi$
$410$		0			0
$411$	−2.34548	−	10.2762i	−0.115694	−	0.506888i
$412$		0			0
$413$	−1.23729	−	0.595848i	−0.0608831	−	0.0293198i
$414$		0			0
$415$	−20.2114	−	25.3443i	−0.992139	−	1.24410i
$416$		0			0
$417$	−13.1679	−	10.5010i	−0.644833	−	0.514237i
$418$		0			0
$419$	10.0274	−	12.5740i	0.489873	−	0.614281i	−0.474039	−	0.880504i	$-0.657204\pi$
$419$	10.0274	−	12.5740i	0.489873	−	0.614281i	0.963911	+	0.266223i	$0.0857758\pi$
$420$		0			0
$421$	9.92274	+	2.26480i	0.483605	+	0.110380i	0.457371	−	0.889276i	$-0.348791\pi$
$421$	9.92274	+	2.26480i	0.483605	+	0.110380i	0.0262342	+	0.999656i	$0.491648\pi$
$422$		0			0
$423$			23.2028i			1.12816i
$424$		0			0
$425$	0.268750	+	0.558065i	0.0130363	+	0.0270701i
$426$		0			0
$427$	2.40658	−	1.91919i	0.116463	−	0.0928759i
$428$		0			0
$429$	0.645260	−	2.82707i	0.0311534	−	0.136492i
$430$		0			0
$431$	18.2424	−	8.78509i	0.878707	−	0.423163i	0.0605549	−	0.998165i	$-0.480713\pi$
$431$	18.2424	−	8.78509i	0.878707	−	0.423163i	0.818152	+	0.575002i	$0.194999\pi$
$432$		0			0
$433$	8.37986	−	1.91265i	0.402710	−	0.0919160i	−0.0163680	−	0.999866i	$-0.505210\pi$
$433$	8.37986	−	1.91265i	0.402710	−	0.0919160i	0.419079	+	0.907950i	$0.362353\pi$
$434$		0			0
$435$	4.89463	+	8.22910i	0.234680	+	0.394555i
$436$		0			0
$437$	−9.27091	+	2.11602i	−0.443488	+	0.101223i
$438$		0			0
$439$	−4.15668	+	2.00175i	−0.198387	+	0.0955383i	−0.530440	−	0.847723i	$-0.677973\pi$
$439$	−4.15668	+	2.00175i	−0.198387	+	0.0955383i	0.332052	+	0.943261i	$0.392259\pi$
$440$		0			0
$441$	3.08426	−	13.5130i	0.146870	−	0.643478i
$442$		0			0
$443$	−8.62402	+	6.87743i	−0.409740	+	0.326756i	−0.806573	−	0.591134i	$-0.798680\pi$
$443$	−8.62402	+	6.87743i	−0.409740	+	0.326756i	0.396834	+	0.917891i	$0.370109\pi$
$444$		0			0
$445$	−12.9901	−	26.9742i	−0.615789	−	1.27870i
$446$		0			0
$447$			12.8813i			0.609263i
$448$		0			0
$449$	−10.0719	−	2.29884i	−0.475322	−	0.108489i	−0.0218528	−	0.999761i	$-0.506957\pi$
$449$	−10.0719	−	2.29884i	−0.475322	−	0.108489i	−0.453469	+	0.891272i	$0.649814\pi$
$450$		0			0
$451$	5.15883	−	6.46897i	0.242920	−	0.304612i
$452$		0			0
$453$	−12.7664	−	10.1808i	−0.599816	−	0.478337i
$454$		0			0
$455$	2.48941	+	3.12162i	0.116705	+	0.146344i
$456$		0			0
$457$	−23.1543	−	11.1505i	−1.08311	−	0.521599i	−0.194801	−	0.980843i	$-0.562406\pi$
$457$	−23.1543	−	11.1505i	−1.08311	−	0.521599i	−0.888310	+	0.459244i	$0.848121\pi$
$458$		0			0
$459$	−0.782560	−	3.42862i	−0.0365268	−	0.160034i
$460$		0			0
$461$	−13.5480	+	28.1327i	−0.630994	+	1.31027i	0.303002	+	0.952990i	$0.402011\pi$
$461$	−13.5480	+	28.1327i	−0.630994	+	1.31027i	−0.933996	+	0.357283i	$0.883703\pi$
$462$		0			0
$463$	−32.5241			−1.51152			−0.755761	−	0.654847i	$-0.772733\pi$
$463$	−32.5241			−1.51152			−0.755761	+	0.654847i	$0.772733\pi$
$464$		0			0
$465$	−0.381059			−0.0176712
$466$		0			0
$467$	−1.69657	+	3.52296i	−0.0785079	+	0.163023i	−0.936528	−	0.350593i	$-0.885980\pi$
$467$	−1.69657	+	3.52296i	−0.0785079	+	0.163023i	0.858020	+	0.513616i	$0.171694\pi$
$468$		0			0
$469$	2.80798	+	12.3026i	0.129660	+	0.568079i
$470$		0			0
$471$	−12.3448	−	5.94495i	−0.568819	−	0.273929i
$472$		0			0
$473$	4.53199	+	5.68294i	0.208381	+	0.261302i
$474$		0			0
$475$	−4.46562	−	3.56121i	−0.204896	−	0.163400i
$476$		0			0
$477$	−12.1392	+	15.2221i	−0.555817	+	0.696972i
$478$		0			0
$479$	−0.126178	−	0.0287994i	−0.00576523	−	0.00131588i	0.219637	−	0.975582i	$-0.429513\pi$
$479$	−0.126178	−	0.0287994i	−0.00576523	−	0.00131588i	−0.225403	+	0.974266i	$0.572370\pi$
$480$		0			0
$481$		−	17.4428i		−	0.795325i
$482$		0			0
$483$	0.458378	+	0.951833i	0.0208569	+	0.0433099i
$484$		0			0
$485$	−0.288791	+	0.230303i	−0.0131133	+	0.0104575i
$486$		0			0
$487$	3.97166	−	17.4010i	0.179973	−	0.788513i	−0.801667	−	0.597771i	$-0.796053\pi$
$487$	3.97166	−	17.4010i	0.179973	−	0.788513i	0.981640	−	0.190742i	$-0.0610895\pi$
$488$		0			0
$489$	−4.60656	+	2.21840i	−0.208316	+	0.100320i
$490$		0			0
$491$	38.5339	−	8.79511i	1.73901	−	0.396918i	0.768860	−	0.639418i	$-0.220825\pi$
$491$	38.5339	−	8.79511i	1.73901	−	0.396918i	0.970151	+	0.242500i	$0.0779674\pi$
$492$		0			0
$493$	3.01208	−	2.86848i	0.135657	−	0.129190i
$494$		0			0
$495$	7.01842	−	1.60191i	0.315454	−	0.0720004i
$496$		0			0
$497$	5.85354	−	2.81892i	0.262567	−	0.126446i
$498$		0			0
$499$	2.93051	−	12.8394i	0.131188	−	0.574770i	−0.866015	−	0.500019i	$-0.833326\pi$
$499$	2.93051	−	12.8394i	0.131188	−	0.574770i	0.997202	−	0.0747517i	$-0.0238164\pi$
$500$		0			0
$501$	−12.6947	+	10.1237i	−0.567158	+	0.452293i
$502$		0			0
$503$	13.7595	+	28.5719i	0.613505	+	1.27396i	0.943937	+	0.330127i	$0.107091\pi$
$503$	13.7595	+	28.5719i	0.613505	+	1.27396i	−0.330431	+	0.943830i	$0.607194\pi$
$504$		0			0
$505$		−	21.2446i		−	0.945371i
$506$		0			0
$507$	−7.13437	−	1.62837i	−0.316849	−	0.0723187i
$508$		0			0
$509$	9.25936	−	11.6109i	0.410414	−	0.514643i	−0.533066	−	0.846074i	$-0.678960\pi$
$509$	9.25936	−	11.6109i	0.410414	−	0.514643i	0.943479	+	0.331431i	$0.107532\pi$
$510$		0			0
$511$	−5.84913	−	4.66452i	−0.258750	−	0.206346i
$512$		0			0
$513$	20.2195	+	25.3544i	0.892711	+	1.11942i
$514$		0			0
$515$	7.45646	+	3.59084i	0.328571	+	0.158231i
$516$		0			0
$517$	−3.59299	−	15.7419i	−0.158020	−	0.692329i
$518$		0			0
$519$	−2.82610	+	5.86846i	−0.124052	+	0.257597i
$520$		0			0
$521$	−36.0495			−1.57936			−0.789679	−	0.613520i	$-0.789753\pi$
$521$	−36.0495			−1.57936			−0.789679	+	0.613520i	$0.789753\pi$
$522$		0			0
$523$	25.8974			1.13241			0.566207	−	0.824263i	$-0.308410\pi$
$523$	25.8974			1.13241			0.566207	+	0.824263i	$0.308410\pi$
$524$		0			0
$525$	−0.275323	+	0.571714i	−0.0120161	+	0.0249517i
$526$		0			0
$527$	0.0368358	+	0.161388i	0.00160459	+	0.00703017i
$528$		0			0
$529$	19.1163	+	9.20590i	0.831141	+	0.400257i
$530$		0			0
$531$	−2.10992	−	2.64575i	−0.0915626	−	0.114816i
$532$		0			0
$533$	8.84117	+	7.05059i	0.382953	+	0.305395i
$534$		0			0
$535$	11.4626	−	14.3737i	0.495573	−	0.621429i
$536$		0			0
$537$	6.70626	+	1.53066i	0.289396	+	0.0660528i
$538$		0			0
$539$			9.64549i			0.415461i
$540$		0			0
$541$	9.73878	+	20.2228i	0.418703	+	0.869446i	0.998504	+	0.0546873i	$0.0174162\pi$
$541$	9.73878	+	20.2228i	0.418703	+	0.869446i	−0.579801	+	0.814758i	$0.696870\pi$
$542$		0			0
$543$	−7.62594	+	6.08149i	−0.327260	+	0.260982i
$544$		0			0
$545$	8.34159	−	36.5469i	0.357315	−	1.56550i
$546$		0			0
$547$	−7.13922	+	3.43807i	−0.305251	+	0.147001i	−0.580238	−	0.814447i	$-0.697041\pi$
$547$	−7.13922	+	3.43807i	−0.305251	+	0.147001i	0.274987	+	0.961448i	$0.411326\pi$
$548$		0			0
$549$	7.39493	−	1.68784i	0.315608	−	0.0720354i
$550$		0			0
$551$	−13.5480	+	35.8830i	−0.577165	+	1.52867i
$552$		0			0
$553$	4.55131	−	1.03881i	0.193541	−	0.0441746i
$554$		0			0
$555$	−13.0749	+	6.29652i	−0.554997	+	0.267273i
$556$		0			0
$557$	−3.93243	+	17.2291i	−0.166622	+	0.730020i	0.820709	+	0.571347i	$0.193579\pi$
$557$	−3.93243	+	17.2291i	−0.166622	+	0.730020i	−0.987331	+	0.158673i	$0.949278\pi$
$558$		0			0
$559$	−7.76689	+	6.19389i	−0.328504	+	0.261974i
$560$		0			0
$561$	0.454731	+	0.944258i	0.0191987	+	0.0398666i
$562$		0			0
$563$		−	39.4635i		−	1.66319i	−0.555383	−	0.831595i	$-0.687428\pi$
$563$		−	39.4635i		−	1.66319i	0.555383	−	0.831595i	$-0.312572\pi$
$564$		0			0
$565$	34.4357	+	7.85973i	1.44872	+	0.330661i
$566$		0			0
$567$	−1.58612	+	1.98893i	−0.0666108	+	0.0835274i
$568$		0			0
$569$	11.2787	+	8.99449i	0.472829	+	0.377069i	0.830716	−	0.556696i	$-0.187931\pi$
$569$	11.2787	+	8.99449i	0.472829	+	0.377069i	−0.357887	+	0.933765i	$0.616503\pi$
$570$		0			0
$571$	21.9544	+	27.5299i	0.918761	+	1.15209i	0.987994	+	0.154490i	$0.0493734\pi$
$571$	21.9544	+	27.5299i	0.918761	+	1.15209i	−0.0692329	+	0.997601i	$0.522055\pi$
$572$		0			0
$573$	3.04892	+	1.46828i	0.127370	+	0.0613383i
$574$		0			0
$575$	−0.238250	−	1.04384i	−0.00993573	−	0.0435313i
$576$		0			0
$577$	−12.4321	+	25.8156i	−0.517556	+	1.07472i	0.464403	+	0.885624i	$0.346269\pi$
$577$	−12.4321	+	25.8156i	−0.517556	+	1.07472i	−0.981959	+	0.189093i	$0.939445\pi$
$578$		0			0
$579$	0.885772			0.0368114
$580$		0			0
$581$	−14.4267			−0.598522
$582$		0			0
$583$	5.87867	−	12.2072i	0.243469	−	0.505570i
$584$		0			0
$585$	2.18933	+	9.59209i	0.0905178	+	0.396584i
$586$		0			0
$587$	−31.3403	−	15.0927i	−1.29355	−	0.622941i	−0.344714	−	0.938708i	$-0.612024\pi$
$587$	−31.3403	−	15.0927i	−1.29355	−	0.622941i	−0.948837	+	0.315766i	$0.897738\pi$
$588$		0			0
$589$	−0.951747	−	1.19345i	−0.0392160	−	0.0491754i
$590$		0			0
$591$	4.45539	+	3.55306i	0.183270	+	0.146153i
$592$		0			0
$593$	−16.2962	+	20.4348i	−0.669204	+	0.839156i	−0.994310	−	0.106522i	$-0.966029\pi$
$593$	−16.2962	+	20.4348i	−0.669204	+	0.839156i	0.325106	+	0.945678i	$0.394600\pi$
$594$		0			0
$595$	−1.40688	−	0.321111i	−0.0576764	−	0.0131643i
$596$		0			0
$597$		−	18.6392i		−	0.762852i
$598$		0			0
$599$	19.9737	+	41.4758i	0.816102	+	1.69465i	0.714289	+	0.699851i	$0.246750\pi$
$599$	19.9737	+	41.4758i	0.816102	+	1.69465i	0.101813	+	0.994804i	$0.467536\pi$
$600$		0			0
$601$	0.336749	−	0.268548i	0.0137363	−	0.0109543i	−0.616598	−	0.787278i	$-0.711489\pi$
$601$	0.336749	−	0.268548i	0.0137363	−	0.0109543i	0.630334	+	0.776324i	$0.282918\pi$
$602$		0			0
$603$	−6.91939	+	30.3158i	−0.281779	+	1.23456i
$604$		0			0
$605$	15.7925	−	7.60529i	0.642058	−	0.309199i
$606$		0			0
$607$	25.0018	−	5.70649i	1.01479	−	0.231619i	0.317386	−	0.948296i	$-0.397195\pi$
$607$	25.0018	−	5.70649i	1.01479	−	0.231619i	0.697405	+	0.716677i	$0.254338\pi$
$608$		0			0
$609$	4.22146	+	0.580328i	0.171062	+	0.0235161i
$610$		0			0
$611$	21.5145	−	4.91055i	0.870385	−	0.198660i
$612$		0			0
$613$	29.3131	−	14.1165i	1.18395	−	0.570158i	0.264887	−	0.964279i	$-0.414665\pi$
$613$	29.3131	−	14.1165i	1.18395	−	0.570158i	0.919058	+	0.394121i	$0.128951\pi$
$614$		0			0
$615$	2.09352	−	9.17232i	0.0844190	−	0.369864i
$616$		0			0
$617$	−28.5300	+	22.7519i	−1.14858	+	0.915958i	−0.997365	−	0.0725432i	$-0.976888\pi$
$617$	−28.5300	+	22.7519i	−1.14858	+	0.915958i	−0.151210	+	0.988502i	$0.548317\pi$
$618$		0			0
$619$	−11.9887	−	24.8949i	−0.481868	−	1.00061i	−0.990227	−	0.139465i	$-0.955462\pi$
$619$	−11.9887	−	24.8949i	−0.481868	−	1.00061i	0.508359	−	0.861145i	$-0.330252\pi$
$620$		0			0
$621$			6.07904i			0.243943i
$622$		0			0
$623$	−12.9901	−	2.96490i	−0.520436	−	0.118786i
$624$		0			0
$625$	−12.6863	+	15.9081i	−0.507451	+	0.636323i
$626$		0			0
$627$	−7.55592	−	6.02564i	−0.301754	−	0.240641i
$628$		0			0
$629$	3.93064	+	4.92887i	0.156725	+	0.196527i
$630$		0			0
$631$	−3.46466	−	1.66849i	−0.137926	−	0.0664216i	0.363648	−	0.931536i	$-0.381531\pi$
$631$	−3.46466	−	1.66849i	−0.137926	−	0.0664216i	−0.501574	+	0.865115i	$0.667245\pi$
$632$		0			0
$633$	2.37502	+	10.4056i	0.0943985	+	0.413587i
$634$		0			0
$635$	−11.1039	+	23.0574i	−0.440644	+	0.915006i
$636$		0			0
$637$	−13.1825			−0.522311
$638$		0			0
$639$	16.0097			0.633333
$640$		0			0
$641$	18.8101	−	39.0595i	0.742953	−	1.54276i	−0.0940554	−	0.995567i	$-0.529983\pi$
$641$	18.8101	−	39.0595i	0.742953	−	1.54276i	0.837008	−	0.547190i	$-0.184303\pi$
$642$		0			0
$643$	−2.45162	−	10.7412i	−0.0966823	−	0.423593i	0.903303	−	0.429003i	$-0.141135\pi$
$643$	−2.45162	−	10.7412i	−0.0966823	−	0.423593i	−0.999985	+	0.00541025i	$0.998278\pi$
$644$		0			0
$645$	7.44653	+	3.58606i	0.293207	+	0.141201i
$646$		0			0
$647$	−30.1809	−	37.8457i	−1.18653	−	1.48787i	−0.833733	−	0.552167i	$-0.813801\pi$
$647$	−30.1809	−	37.8457i	−1.18653	−	1.48787i	−0.352800	−	0.935699i	$-0.614771\pi$
$648$		0			0
$649$	1.84117	+	1.46828i	0.0722721	+	0.0576351i
$650$		0			0
$651$	−0.105736	+	0.132589i	−0.00414412	+	0.00519656i
$652$		0			0
$653$	31.7035	+	7.23612i	1.24065	+	0.283171i	0.791993	−	0.610531i	$-0.209044\pi$
$653$	31.7035	+	7.23612i	1.24065	+	0.283171i	0.448661	+	0.893702i	$0.351901\pi$
$654$		0			0
$655$		−	13.5678i		−	0.530139i
$656$		0			0
$657$	−7.99880	−	16.6097i	−0.312063	−	0.648006i
$658$		0			0
$659$	−9.28113	+	7.40145i	−0.361541	+	0.288320i	−0.787366	−	0.616486i	$-0.788556\pi$
$659$	−9.28113	+	7.40145i	−0.361541	+	0.288320i	0.425824	+	0.904806i	$0.359984\pi$
$660$		0			0
$661$	−3.99880	+	17.5199i	−0.155535	+	0.681445i	0.835683	+	0.549212i	$0.185072\pi$
$661$	−3.99880	+	17.5199i	−0.155535	+	0.681445i	−0.991219	+	0.132233i	$0.957785\pi$
$662$		0			0
$663$	−1.29052	+	0.621482i	−0.0501196	+	0.0241364i
$664$		0			0
$665$	12.9733	−	2.96107i	0.503082	−	0.114825i
$666$		0			0
$667$	−6.17941	+	3.67548i	−0.239268	+	0.142315i
$668$		0			0
$669$	10.3968	−	2.37300i	0.401963	−	0.0917454i
$670$		0			0
$671$	−4.75571	+	2.29023i	−0.183592	+	0.0884133i
$672$		0			0
$673$	9.13049	−	40.0033i	0.351955	−	1.54201i	−0.420708	−	0.907196i	$-0.638218\pi$
$673$	9.13049	−	40.0033i	0.351955	−	1.54201i	0.772662	−	0.634817i	$-0.218925\pi$
$674$		0			0
$675$	−2.85474	+	2.27658i	−0.109879	+	0.0876256i
$676$		0			0
$677$	−0.144596	−	0.300257i	−0.00555728	−	0.0115398i	0.898172	−	0.439645i	$-0.144896\pi$
$677$	−0.144596	−	0.300257i	−0.00555728	−	0.0115398i	−0.903729	+	0.428105i	$0.859181\pi$
$678$		0			0
$679$			0.164389i			0.00630866i
$680$		0			0
$681$	6.92908	+	1.58152i	0.265523	+	0.0606038i
$682$		0			0
$683$	−15.6012	+	19.5633i	−0.596963	+	0.748568i	−0.984901	−	0.173118i	$-0.944616\pi$
$683$	−15.6012	+	19.5633i	−0.596963	+	0.748568i	0.387938	+	0.921685i	$0.373187\pi$
$684$		0			0
$685$	−19.4578	−	15.5171i	−0.743446	−	0.592878i
$686$		0			0
$687$	4.79254	+	6.00966i	0.182847	+	0.229283i
$688$		0			0
$689$	16.6836	+	8.03439i	0.635594	+	0.306086i
$690$		0			0
$691$	−5.68784	−	24.9201i	−0.216376	−	0.948004i	−0.960131	−	0.279551i	$-0.909814\pi$
$691$	−5.68784	−	24.9201i	−0.216376	−	0.948004i	0.743755	−	0.668452i	$-0.233043\pi$
$692$		0			0
$693$	1.39008	−	2.88654i	0.0528049	−	0.109651i
$694$		0			0
$695$	−39.7670			−1.50845
$696$		0			0
$697$	−4.08708			−0.154809
$698$		0			0
$699$	−1.46921	+	3.05084i	−0.0555704	+	0.115393i
$700$		0			0
$701$	−6.26862	−	27.4646i	−0.236762	−	1.03732i	−0.943896	−	0.330244i	$-0.892869\pi$
$701$	−6.26862	−	27.4646i	−0.236762	−	1.03732i	0.707133	−	0.707080i	$-0.249988\pi$
$702$		0			0
$703$	−52.3766	−	25.2232i	−1.97542	−	0.951312i
$704$		0			0
$705$	−11.4472	−	14.3543i	−0.431126	−	0.540615i
$706$		0			0
$707$	−7.39200	−	5.89493i	−0.278005	−	0.221701i
$708$		0			0
$709$	−30.3723	+	38.0856i	−1.14065	+	1.43033i	−0.254422	+	0.967093i	$0.581885\pi$
$709$	−30.3723	+	38.0856i	−1.14065	+	1.43033i	−0.886232	+	0.463242i	$0.846686\pi$
$710$		0			0
$711$	11.2153	+	2.55982i	0.420606	+	0.0960006i
$712$		0			0
$713$		−	0.286145i		−	0.0107162i
$714$		0			0
$715$	−2.97070	−	6.16872i	−0.111098	−	0.230697i
$716$		0			0
$717$	10.4225	−	8.31167i	0.389235	−	0.310405i
$718$		0			0
$719$	7.28395	−	31.9131i	0.271645	−	1.19016i	−0.636425	−	0.771339i	$-0.719588\pi$
$719$	7.28395	−	31.9131i	0.271645	−	1.19016i	0.908070	−	0.418818i	$-0.137555\pi$
$720$		0			0
$721$	3.31844	−	1.59807i	0.123585	−	0.0595154i
$722$		0			0
$723$	−11.3358	+	2.58732i	−0.421583	+	0.0962235i
$724$		0			0
$725$	−4.04019	−	1.52542i	−0.150049	−	0.0566526i
$726$		0			0
$727$	34.5960	−	7.89631i	1.28309	−	0.292858i	0.473993	−	0.880528i	$-0.342812\pi$
$727$	34.5960	−	7.89631i	1.28309	−	0.292858i	0.809100	+	0.587671i	$0.199955\pi$
$728$		0			0
$729$	5.03146	−	2.42302i	0.186350	−	0.0897416i
$730$		0			0
$731$	0.798954	−	3.50045i	0.0295504	−	0.129469i
$732$		0			0
$733$	−22.8928	+	18.2564i	−0.845564	+	0.674315i	−0.947248	−	0.320502i	$-0.896148\pi$
$733$	−22.8928	+	18.2564i	−0.845564	+	0.674315i	0.101684	+	0.994817i	$0.467577\pi$
$734$		0			0
$735$	4.75863	+	9.88141i	0.175525	+	0.364481i
$736$		0			0
$737$		−	21.6392i		−	0.797089i
$738$		0			0
$739$	15.3339	+	3.49987i	0.564068	+	0.128745i	0.495040	−	0.868870i	$-0.335153\pi$
$739$	15.3339	+	3.49987i	0.564068	+	0.128745i	0.0690274	+	0.997615i	$0.478010\pi$
$740$		0			0
$741$	8.23527	−	10.3267i	0.302530	−	0.379361i
$742$		0			0
$743$	12.3669	+	9.86226i	0.453697	+	0.361811i	0.823516	−	0.567292i	$-0.192009\pi$
$743$	12.3669	+	9.86226i	0.453697	+	0.361811i	−0.369820	+	0.929104i	$0.620581\pi$
$744$		0			0
$745$	18.9631	+	23.7790i	0.694754	+	0.871194i
$746$		0			0
$747$	−32.0296	−	15.4246i	−1.17190	−	0.564358i
$748$		0			0
$749$	−1.82065	−	7.97679i	−0.0665251	−	0.291466i
$750$		0			0
$751$	4.15801	−	8.63419i	0.151728	−	0.315066i	−0.811226	−	0.584733i	$-0.801199\pi$
$751$	4.15801	−	8.63419i	0.151728	−	0.315066i	0.962954	+	0.269667i	$0.0869136\pi$
$752$		0			0
$753$	3.76510			0.137208
$754$		0			0
$755$	−38.5545			−1.40314
$756$		0			0
$757$	2.75518	−	5.72118i	0.100139	−	0.207940i	−0.844881	−	0.534955i	$-0.820329\pi$
$757$	2.75518	−	5.72118i	0.100139	−	0.207940i	0.945019	+	0.327015i	$0.106043\pi$
$758$		0			0
$759$	−0.403125	−	1.76621i	−0.0146325	−	0.0641092i
$760$		0			0
$761$	26.9605	+	12.9835i	0.977319	+	0.470652i	0.853182	−	0.521613i	$-0.174670\pi$
$761$	26.9605	+	12.9835i	0.977319	+	0.470652i	0.124137	+	0.992265i	$0.460384\pi$
$762$		0			0
$763$	−10.4018	−	13.0434i	−0.376570	−	0.472204i
$764$		0			0
$765$	−2.78017	−	2.21711i	−0.100517	−	0.0801598i
$766$		0			0
$767$	−2.00670	+	2.51633i	−0.0724579	+	0.0908593i
$768$		0			0
$769$	30.9596	+	7.06632i	1.11643	+	0.254818i	0.740650	−	0.671891i	$-0.234518\pi$
$769$	30.9596	+	7.06632i	1.11643	+	0.254818i	0.375780	+	0.926709i	$0.377375\pi$
$770$		0			0
$771$			16.4111i			0.591031i
$772$		0			0
$773$	22.0909	+	45.8722i	0.794554	+	1.64991i	0.759486	+	0.650524i	$0.225451\pi$
$773$	22.0909	+	45.8722i	0.794554	+	1.64991i	0.0350684	+	0.999385i	$0.488835\pi$
$774$		0			0
$775$	0.134375	−	0.107160i	0.00482689	−	0.00384932i
$776$		0			0
$777$	−1.43714	+	6.29652i	−0.0515571	+	0.225887i
$778$		0			0
$779$	33.9560	−	16.3523i	1.21660	−	0.585883i
$780$		0			0
$781$	−10.8617	+	2.47912i	−0.388664	+	0.0887099i
$782$		0			0
$783$	20.4366	+	13.5481i	0.730345	+	0.484170i
$784$		0			0
$785$	−31.5405	+	7.19891i	−1.12573	+	0.256940i
$786$		0			0
$787$	−26.6386	+	12.8285i	−0.949562	+	0.457285i	−0.843533	−	0.537078i	$-0.819528\pi$
$787$	−26.6386	+	12.8285i	−0.949562	+	0.457285i	−0.106029	+	0.994363i	$0.533814\pi$
$788$		0			0
$789$	5.14699	−	22.5504i	0.183238	−	0.802817i
$790$		0			0
$791$	12.2900	−	9.80092i	0.436981	−	0.348481i
$792$		0			0
$793$	−3.13006	−	6.49964i	−0.111152	−	0.230809i
$794$		0			0
$795$		−	15.4060i		−	0.546395i
$796$		0			0
$797$	6.00849	+	1.37140i	0.212832	+	0.0485774i	0.327607	−	0.944814i	$-0.393758\pi$
$797$	6.00849	+	1.37140i	0.212832	+	0.0485774i	−0.114776	+	0.993391i	$0.536615\pi$
$798$		0			0
$799$	−4.97285	+	6.23576i	−0.175927	+	0.220605i
$800$		0			0
$801$	−25.6700	−	20.4712i	−0.907005	−	0.723313i
$802$		0			0
$803$	7.99880	+	10.0302i	0.282272	+	0.353957i
$804$		0			0
$805$	2.24741	+	1.08229i	0.0792107	+	0.0381459i
$806$		0			0
$807$	−2.42500	−	10.6246i	−0.0853641	−	0.374004i
$808$		0			0
$809$	−10.7073	+	22.2340i	−0.376449	+	0.781705i	−1.00000		7.76828e-5i	$-0.999975\pi$
$809$	−10.7073	+	22.2340i	−0.376449	+	0.781705i	0.623551	+	0.781783i	$0.285690\pi$
$810$		0			0
$811$	9.79092			0.343806			0.171903	−	0.985114i	$-0.445008\pi$
$811$	9.79092			0.343806			0.171903	+	0.985114i	$0.445008\pi$
$812$		0			0
$813$	−1.25773			−0.0441106
$814$		0			0
$815$	−5.23795	+	10.8767i	−0.183478	+	0.380995i
$816$		0			0
$817$	7.36741	+	32.2787i	0.257753	+	1.12929i
$818$		0			0
$819$	3.94504	+	1.89983i	0.137851	+	0.0663855i
$820$		0			0
$821$	−3.84518	−	4.82171i	−0.134198	−	0.168279i	0.710192	−	0.704008i	$-0.248608\pi$
$821$	−3.84518	−	4.82171i	−0.134198	−	0.168279i	−0.844390	+	0.535729i	$0.820037\pi$
$822$		0			0
$823$	−28.3408	−	22.6010i	−0.987898	−	0.787822i	−0.0106547	−	0.999943i	$-0.503392\pi$
$823$	−28.3408	−	22.6010i	−0.987898	−	0.787822i	−0.977243	+	0.212121i	$0.931963\pi$
$824$		0			0
$825$	0.678448	−	0.850747i	0.0236205	−	0.0296192i
$826$		0			0
$827$	−2.77359	−	0.633055i	−0.0964473	−	0.0220135i	0.174025	−	0.984741i	$-0.444323\pi$
$827$	−2.77359	−	0.633055i	−0.0964473	−	0.0220135i	−0.270472	+	0.962728i	$0.587180\pi$
$828$		0			0
$829$			43.5750i			1.51342i	0.653750	+	0.756711i	$0.273195\pi$
$829$			43.5750i			1.51342i	−0.653750	+	0.756711i	$0.726805\pi$
$830$		0			0
$831$	2.99002	+	6.20883i	0.103722	+	0.215382i
$832$		0			0
$833$	3.72502	−	2.97060i	0.129064	−	0.102925i
$834$		0			0
$835$	−8.53103	+	37.3769i	−0.295229	+	1.29348i
$836$		0			0
$837$	−0.879199	+	0.423400i	−0.0303895	+	0.0146348i
$838$		0			0
$839$	34.7615	−	7.93409i	1.20010	−	0.273915i	0.424670	−	0.905348i	$-0.360390\pi$
$839$	34.7615	−	7.93409i	1.20010	−	0.273915i	0.775430	+	0.631433i	$0.217533\pi$
$840$		0			0
$841$	−1.41550	+	28.9654i	−0.0488104	+	0.998808i
$842$		0			0
$843$	16.8502	−	3.84595i	0.580351	−	0.132461i
$844$		0			0
$845$	−15.5673	+	7.49683i	−0.535533	+	0.257899i
$846$		0			0
$847$	1.73586	−	7.60529i	0.0596448	−	0.261321i
$848$		0			0
$849$	−2.16152	+	1.72376i	−0.0741832	+	0.0591592i
$850$		0			0
$851$	−4.72819	−	9.81819i	−0.162080	−	0.336563i
$852$		0			0
$853$		−	14.0844i		−	0.482240i	−0.970495	−	0.241120i	$-0.922485\pi$
$853$		−	14.0844i		−	0.482240i	0.970495	−	0.241120i	$-0.0775147\pi$
$854$		0			0
$855$	31.9686	+	7.29662i	1.09330	+	0.249539i
$856$		0			0
$857$	22.1102	−	27.7253i	0.755270	−	0.947079i	−0.244475	−	0.969656i	$-0.578616\pi$
$857$	22.1102	−	27.7253i	0.755270	−	0.947079i	0.999745	+	0.0225765i	$0.00718693\pi$
$858$		0			0
$859$	−0.482647	−	0.384898i	−0.0164677	−	0.0131326i	0.615221	−	0.788354i	$-0.289067\pi$
$859$	−0.482647	−	0.384898i	−0.0164677	−	0.0131326i	−0.631689	+	0.775222i	$0.717638\pi$
$860$		0			0
$861$	−2.61058	−	3.27356i	−0.0889683	−	0.111563i
$862$		0			0
$863$	45.0323	+	21.6864i	1.53292	+	0.738214i	0.994527	−	0.104482i	$-0.0333184\pi$
$863$	45.0323	+	21.6864i	1.53292	+	0.738214i	0.538390	+	0.842696i	$0.319033\pi$
$864$		0			0
$865$	3.42221	+	14.9937i	0.116359	+	0.509800i
$866$		0			0
$867$	−6.17606	+	12.8247i	−0.209750	+	0.435550i
$868$		0			0
$869$	−8.00538			−0.271564
$870$		0			0
$871$	29.5743			1.00209
$872$		0			0
$873$	−0.175760	+	0.364968i	−0.00594856	+	0.0123523i
$874$		0			0
$875$	2.41209	+	10.5681i	0.0815436	+	0.357266i
$876$		0			0
$877$	17.1717	+	8.26948i	0.579849	+	0.279240i	0.700730	−	0.713427i	$-0.252858\pi$
$877$	17.1717	+	8.26948i	0.579849	+	0.279240i	−0.120881	+	0.992667i	$0.538572\pi$
$878$		0			0
$879$	1.26845	+	1.59059i	0.0427839	+	0.0536493i
$880$		0			0
$881$	−3.65442	−	2.91430i	−0.123120	−	0.0981853i	0.559994	−	0.828497i	$-0.310803\pi$
$881$	−3.65442	−	2.91430i	−0.123120	−	0.0981853i	−0.683114	+	0.730312i	$0.739375\pi$
$882$		0			0
$883$	8.10052	−	10.1577i	0.272604	−	0.341835i	−0.626618	−	0.779326i	$-0.715561\pi$
$883$	8.10052	−	10.1577i	0.272604	−	0.341835i	0.899223	+	0.437491i	$0.144133\pi$
$884$		0			0
$885$	2.61058	+	0.595848i	0.0877537	+	0.0200292i
$886$		0			0
$887$			1.93563i			0.0649921i	0.999472	+	0.0324960i	$0.0103456\pi$
$887$			1.93563i			0.0649921i	−0.999472	+	0.0324960i	$0.989654\pi$
$888$		0			0
$889$	4.94169	+	10.2615i	0.165739	+	0.344160i
$890$		0			0
$891$	3.41066	−	2.71991i	0.114261	−	0.0911204i
$892$		0			0
$893$	16.3659	−	71.7038i	0.547665	−	2.39948i
$894$		0			0
$895$	14.6332	−	7.04697i	0.489133	−	0.235554i
$896$		0			0
$897$	2.41388	−	0.550952i	0.0805971	−	0.0183958i
$898$		0			0
$899$	−0.961968	−	0.637721i	−0.0320834	−	0.0212692i
$900$		0			0
$901$	−6.52483	+	1.48925i	−0.217374	+	0.0496141i
$902$		0			0
$903$	3.31402	−	1.59595i	0.110284	−	0.0531098i
$904$		0			0
$905$	−5.12474	+	22.4530i	−0.170352	+	0.746362i
$906$		0			0
$907$	−37.2188	+	29.6810i	−1.23583	+	0.985542i	−0.235925	+	0.971771i	$0.575812\pi$
$907$	−37.2188	+	29.6810i	−1.23583	+	0.985542i	−0.999905	+	0.0137702i	$0.995617\pi$
$908$		0			0
$909$	−10.1087	−	20.9910i	−0.335285	−	0.696227i
$910$		0			0
$911$			44.3642i			1.46985i	0.678148	+	0.734926i	$0.262783\pi$
$911$			44.3642i			1.46985i	−0.678148	+	0.734926i	$0.737217\pi$
$912$		0			0
$913$	24.1189	+	5.50499i	0.798220	+	0.182189i
$914$		0			0
$915$	−3.74214	+	4.69249i	−0.123711	+	0.155129i
$916$		0			0
$917$	−4.72090	−	3.76479i	−0.155898	−	0.124324i
$918$		0			0
$919$	−5.86323	−	7.35226i	−0.193410	−	0.242529i	0.675665	−	0.737209i	$-0.263857\pi$
$919$	−5.86323	−	7.35226i	−0.193410	−	0.242529i	−0.869075	+	0.494680i	$0.835285\pi$
$920$		0			0
$921$	−26.7168	−	12.8661i	−0.880348	−	0.423953i
$922$		0			0
$923$	−3.38822	−	14.8448i	−0.111525	−	0.488622i
$924$		0			0
$925$	2.83997	−	5.89726i	0.0933776	−	0.193901i
$926$		0			0
$927$	9.07606			0.298097
$928$		0			0
$929$	−14.3720			−0.471529			−0.235764	−	0.971810i	$-0.575759\pi$
$929$	−14.3720			−0.471529			−0.235764	+	0.971810i	$0.575759\pi$
$930$		0			0
$931$	−19.0626	+	39.5839i	−0.624751	+	1.29731i
$932$		0			0
$933$	5.47392	+	23.9828i	0.179208	+	0.785162i
$934$		0			0
$935$	2.22952	+	1.07368i	0.0729131	+	0.0351131i
$936$		0			0
$937$	−14.6350	−	18.3518i	−0.478106	−	0.599526i	0.483029	−	0.875604i	$-0.339536\pi$
$937$	−14.6350	−	18.3518i	−0.478106	−	0.599526i	−0.961135	+	0.276078i	$0.910965\pi$
$938$		0			0
$939$	1.02542	+	0.817744i	0.0334633	+	0.0266861i
$940$		0			0
$941$	13.4725	−	16.8940i	0.439190	−	0.550727i	−0.512139	−	0.858902i	$-0.671147\pi$
$941$	13.4725	−	16.8940i	0.439190	−	0.550727i	0.951330	+	0.308175i	$0.0997183\pi$
$942$		0			0
$943$	6.88769	+	1.57207i	0.224294	+	0.0511937i
$944$		0			0
$945$		−	8.50673i		−	0.276724i
$946$		0			0
$947$	7.86403	+	16.3298i	0.255547	+	0.530648i	0.988789	−	0.149319i	$-0.0477083\pi$
$947$	7.86403	+	16.3298i	0.255547	+	0.530648i	−0.733242	+	0.679967i	$0.761994\pi$
$948$		0			0
$949$	−13.7083	+	10.9320i	−0.444990	+	0.354867i
$950$		0			0
$951$	3.86376	−	16.9283i	0.125291	−	0.548936i
$952$		0			0
$953$	28.5112	−	13.7303i	0.923568	−	0.444767i	0.0892242	−	0.996012i	$-0.471561\pi$
$953$	28.5112	−	13.7303i	0.923568	−	0.444767i	0.834344	+	0.551245i	$0.185847\pi$
$954$		0			0
$955$	7.78986	−	1.77798i	0.252074	−	0.0575342i
$956$		0			0
$957$	−6.83609	−	2.58104i	−0.220979	−	0.0834332i
$958$		0			0
$959$	−10.7983	+	2.46464i	−0.348695	+	0.0795874i
$960$		0			0
$961$	−27.8887	+	13.4305i	−0.899634	+	0.433241i
$962$		0			0
$963$	4.48643	−	19.6563i	0.144573	−	0.633416i
$964$		0			0
$965$	1.63514	−	1.30398i	0.0526372	−	0.0419767i
$966$		0			0
$967$	18.0497	+	37.4807i	0.580441	+	1.20530i	0.959966	+	0.280116i	$0.0903730\pi$
$967$	18.0497	+	37.4807i	0.580441	+	1.20530i	−0.379525	+	0.925181i	$0.623913\pi$
$968$		0			0
$969$			4.77381i			0.153357i
$970$		0			0
$971$	−51.7809	−	11.8187i	−1.66173	−	0.379279i	−0.714449	−	0.699688i	$-0.753322\pi$
$971$	−51.7809	−	11.8187i	−1.66173	−	0.379279i	−0.947279	+	0.320409i	$0.896180\pi$
$972$		0			0
$973$	−11.0345	+	13.8368i	−0.353750	+	0.443589i
$974$		0			0
$975$	1.16272	+	0.927237i	0.0372368	+	0.0296954i
$976$		0			0
$977$	−28.6735	−	35.9555i	−0.917348	−	1.15032i	−0.988252	−	0.152834i	$-0.951160\pi$
$977$	−28.6735	−	35.9555i	−0.917348	−	1.15032i	0.0709043	−	0.997483i	$-0.477412\pi$
$978$		0			0
$979$	20.5858	+	9.91358i	0.657924	+	0.316839i
$980$		0			0
$981$	−9.14795	−	40.0798i	−0.292072	−	1.27965i
$982$		0			0
$983$	−5.25750	+	10.9173i	−0.167688	+	0.348208i	−0.967831	−	0.251602i	$-0.919043\pi$
$983$	−5.25750	+	10.9173i	−0.167688	+	0.348208i	0.800143	+	0.599810i	$0.204757\pi$
$984$		0			0
$985$	13.4553			0.428722
$986$		0			0
$987$	−8.17092			−0.260083
$988$		0			0
$989$	−2.69285	+	5.59176i	−0.0856276	+	0.177808i
$990$		0			0
$991$	1.90741	+	8.35691i	0.0605909	+	0.265466i	0.996146	−	0.0877159i	$-0.0279568\pi$
$991$	1.90741	+	8.35691i	0.0605909	+	0.265466i	−0.935555	+	0.353182i	$0.885100\pi$
$992$		0			0
$993$	−12.4940	−	6.01677i	−0.396484	−	0.190937i
$994$		0			0
$995$	−27.4396	−	34.4082i	−0.869894	−	1.09081i
$996$		0			0
$997$	−12.8675	−	10.2615i	−0.407519	−	0.324986i	0.398184	−	0.917306i	$-0.369641\pi$
$997$	−12.8675	−	10.2615i	−0.407519	−	0.324986i	−0.805703	+	0.592320i	$0.798212\pi$
$998$		0			0
$999$	−23.1708	+	29.0553i	−0.733093	+	0.919270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.i.a.109.1	yes	6
3.2	odd	2		1044.2.z.b.109.1		6
4.3	odd	2		464.2.y.b.225.1		6
29.2	odd	28		3364.2.a.n.1.3		6
29.4	even	14	inner	116.2.i.a.33.1	✓	6
29.5	even	14		3364.2.c.f.1681.4		6
29.24	even	7		3364.2.c.f.1681.3		6
29.27	odd	28		3364.2.a.n.1.4		6
87.62	odd	14		1044.2.z.b.613.1		6
116.91	odd	14		464.2.y.b.33.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.i.a.33.1	✓	6	29.4	even	14	inner
116.2.i.a.109.1	yes	6	1.1	even	1	trivial
464.2.y.b.33.1		6	116.91	odd	14
464.2.y.b.225.1		6	4.3	odd	2
1044.2.z.b.109.1		6	3.2	odd	2
1044.2.z.b.613.1		6	87.62	odd	14
3364.2.a.n.1.3		6	29.2	odd	28
3364.2.a.n.1.4		6	29.27	odd	28
3364.2.c.f.1681.3		6	29.24	even	7
3364.2.c.f.1681.4		6	29.5	even	14

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.i (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376510 + 0.781831i) q^{3} +(0.455927 + 1.99755i) q^{5} +(0.821552 + 0.395639i) q^{7} +(1.40097 + 1.75676i) q^{9} +O(q^{10})\)	\(q+(-0.376510 + 0.781831i) q^{3} +(0.455927 + 1.99755i) q^{5} +(0.821552 + 0.395639i) q^{7} +(1.40097 + 1.75676i) q^{9} +(-1.22252 - 0.974928i) q^{11} +(1.33244 - 1.67082i) q^{13} +(-1.73341 - 0.395639i) q^{15} +0.772386i q^{17} +(-3.09030 - 6.41708i) q^{19} +(-0.618645 + 0.493353i) q^{21} +(0.297093 - 1.30165i) q^{23} +(0.722521 - 0.347948i) q^{25} +(-4.43900 + 1.01317i) q^{27} +(-3.71379 - 3.89971i) q^{29} +(0.208947 - 0.0476909i) q^{31} +(1.22252 - 0.588735i) q^{33} +(-0.415739 + 1.82147i) q^{35} +(6.38135 - 5.08896i) q^{37} +(0.804626 + 1.67082i) q^{39} +5.29150i q^{41} +(-4.53199 - 1.03440i) q^{43} +(-2.87047 + 3.59945i) q^{45} +(8.07338 + 6.43830i) q^{47} +(-3.84601 - 4.82274i) q^{49} +(-0.603875 - 0.290811i) q^{51} +(1.92812 + 8.44763i) q^{53} +(1.39008 - 2.88654i) q^{55} +6.18060 q^{57} -1.50604 q^{59} +(1.46466 - 3.04139i) q^{61} +(0.455927 + 1.99755i) q^{63} +(3.94504 + 1.89983i) q^{65} +(8.62833 + 10.8196i) q^{67} +(0.905813 + 0.722362i) q^{69} +(4.44235 - 5.57054i) q^{71} +(-7.99880 - 1.82567i) q^{73} +0.695895i q^{75} +(-0.618645 - 1.28463i) q^{77} +(4.00269 - 3.19204i) q^{79} +(-0.620801 + 2.71991i) q^{81} +(-14.2545 + 6.86461i) q^{83} +(-1.54288 + 0.352152i) q^{85} +(4.44720 - 1.43528i) q^{87} +(-14.2458 + 3.25151i) q^{89} +(1.75571 - 0.845505i) q^{91} +(-0.0413846 + 0.181318i) q^{93} +(11.4095 - 9.09874i) q^{95} +(0.0782203 + 0.162426i) q^{97} -3.51352i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9}+O(q^{10}) \) 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9	\( 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9} - 7 q^{11} + 9 q^{13} - 7 q^{15} - 7 q^{19} - 21 q^{21} + 15 q^{23} + 4 q^{25} - 7 q^{27} - 6 q^{29} + 7 q^{31} + 7 q^{33} - 33 q^{35} + 21 q^{37} - 7 q^{39} + 7 q^{43} - 3 q^{45} + 21 q^{47} - 18 q^{49} + 14 q^{51} - 5 q^{53} + 7 q^{55} + 14 q^{57} - 28 q^{59} + 21 q^{61} - q^{63} + 23 q^{65} + 25 q^{67} - 21 q^{69} + 29 q^{71} - 7 q^{73} - 21 q^{77} + 21 q^{79} - 2 q^{81} - 51 q^{83} + 28 q^{85} + 7 q^{87} - 35 q^{89} + 17 q^{91} - 7 q^{93} - 21 q^{95} - 49 q^{97}+O(q^{100}) \) 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9 - 7 * q^11 + 9 * q^13 - 7 * q^15 - 7 * q^19 - 21 * q^21 + 15 * q^23 + 4 * q^25 - 7 * q^27 - 6 * q^29 + 7 * q^31 + 7 * q^33 - 33 * q^35 + 21 * q^37 - 7 * q^39 + 7 * q^43 - 3 * q^45 + 21 * q^47 - 18 * q^49 + 14 * q^51 - 5 * q^53 + 7 * q^55 + 14 * q^57 - 28 * q^59 + 21 * q^61 - q^63 + 23 * q^65 + 25 * q^67 - 21 * q^69 + 29 * q^71 - 7 * q^73 - 21 * q^77 + 21 * q^79 - 2 * q^81 - 51 * q^83 + 28 * q^85 + 7 * q^87 - 35 * q^89 + 17 * q^91 - 7 * q^93 - 21 * q^95 - 49 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more