LMFDB - Embedded newform 756.2.ca.a.173.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (of order $18$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.1
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73005 - 0.0832183i) q^{3} +(0.849177 - 0.712544i) q^{5} +(-0.774464 + 2.52986i) q^{7} +(2.98615 + 0.287944i) q^{9} +O(q^{10})$	\(q+(-1.73005 - 0.0832183i) q^{3} +(0.849177 - 0.712544i) q^{5} +(-0.774464 + 2.52986i) q^{7} +(2.98615 + 0.287944i) q^{9} +(-1.67168 + 1.99223i) q^{11} +(-2.84782 - 3.39390i) q^{13} +(-1.52842 + 1.16207i) q^{15} +(1.08706 - 1.88284i) q^{17} +(-1.71304 + 0.989022i) q^{19} +(1.55039 - 4.31234i) q^{21} +(-0.488687 + 1.34266i) q^{23} +(-0.654859 + 3.71389i) q^{25} +(-5.14223 - 0.746660i) q^{27} +(-1.56472 + 1.86476i) q^{29} +(-0.907035 - 1.08096i) q^{31} +(3.05788 - 3.30754i) q^{33} +(1.14498 + 2.70014i) q^{35} -2.97188 q^{37} +(4.64444 + 6.10861i) q^{39} +(-7.49508 + 6.28912i) q^{41} +(-10.5897 + 3.85434i) q^{43} +(2.74094 - 1.88325i) q^{45} +(8.10077 + 6.79735i) q^{47} +(-5.80041 - 3.91858i) q^{49} +(-2.03735 + 3.16695i) q^{51} +(-3.97427 + 2.29454i) q^{53} +2.88290i q^{55} +(3.04594 - 1.56850i) q^{57} +(0.253027 + 1.43499i) q^{59} +(-5.34786 + 6.37333i) q^{61} +(-3.04112 + 7.33155i) q^{63} +(-4.83660 - 0.852824i) q^{65} +(-0.444834 - 0.161906i) q^{67} +(0.957186 - 2.28219i) q^{69} +(-8.36281 + 4.82827i) q^{71} -14.9642i q^{73} +(1.44200 - 6.37072i) q^{75} +(-3.74541 - 5.77203i) q^{77} +(6.35972 - 2.31475i) q^{79} +(8.83418 + 1.71969i) q^{81} +(-0.735605 - 0.617246i) q^{83} +(-0.418502 - 2.37344i) q^{85} +(2.86222 - 3.09591i) q^{87} +(8.19334 + 14.1913i) q^{89} +(10.7916 - 4.57614i) q^{91} +(1.47926 + 1.94560i) q^{93} +(-0.749949 + 2.06047i) q^{95} +(-4.74751 - 13.0437i) q^{97} +(-5.56553 + 5.46774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73005	−	0.0832183i	−0.998845	−	0.0480461i
$3$	−1.73005	−	0.0832183i	−0.998845	−	0.0480461i
$4$		0			0
$5$	0.849177	−	0.712544i	0.379763	−	0.318659i	−0.432846	−	0.901468i	$-0.642491\pi$
$5$	0.849177	−	0.712544i	0.379763	−	0.318659i	0.812610	+	0.582808i	$0.198046\pi$
$6$		0			0
$7$	−0.774464	+	2.52986i	−0.292720	+	0.956198i
$7$	−0.774464	+	2.52986i	−0.292720	+	0.956198i
$8$		0			0
$9$	2.98615	+	0.287944i	0.995383	+	0.0959813i
$10$		0			0
$11$	−1.67168	+	1.99223i	−0.504030	+	0.600679i	−0.956728	−	0.290985i	$-0.906017\pi$
$11$	−1.67168	+	1.99223i	−0.504030	+	0.600679i	0.452698	+	0.891664i	$0.350462\pi$
$12$		0			0
$13$	−2.84782	−	3.39390i	−0.789843	−	0.941298i	0.209490	−	0.977811i	$-0.432820\pi$
$13$	−2.84782	−	3.39390i	−0.789843	−	0.941298i	−0.999333	+	0.0365127i	$0.988375\pi$
$14$		0			0
$15$	−1.52842	+	1.16207i	−0.394635	+	0.300045i
$16$		0			0
$17$	1.08706	−	1.88284i	0.263650	−	0.456656i	−0.703559	−	0.710637i	$-0.748407\pi$
$17$	1.08706	−	1.88284i	0.263650	−	0.456656i	0.967209	+	0.253981i	$0.0817401\pi$
$18$		0			0
$19$	−1.71304	+	0.989022i	−0.392998	+	0.226897i	−0.683458	−	0.729990i	$-0.739525\pi$
$19$	−1.71304	+	0.989022i	−0.392998	+	0.226897i	0.290461	+	0.956887i	$0.406191\pi$
$20$		0			0
$21$	1.55039	−	4.31234i	0.338324	−	0.941030i
$22$		0			0
$23$	−0.488687	+	1.34266i	−0.101898	+	0.279963i	−0.980157	−	0.198223i	$-0.936483\pi$
$23$	−0.488687	+	1.34266i	−0.101898	+	0.279963i	0.878259	+	0.478186i	$0.158705\pi$
$24$		0			0
$25$	−0.654859	+	3.71389i	−0.130972	+	0.742777i
$26$		0			0
$27$	−5.14223	−	0.746660i	−0.989622	−	0.143695i
$28$		0			0
$29$	−1.56472	+	1.86476i	−0.290561	+	0.346277i	−0.891502	−	0.453016i	$-0.850348\pi$
$29$	−1.56472	+	1.86476i	−0.290561	+	0.346277i	0.600942	+	0.799293i	$0.294792\pi$
$30$		0			0
$31$	−0.907035	−	1.08096i	−0.162908	−	0.194147i	0.678415	−	0.734679i	$-0.262667\pi$
$31$	−0.907035	−	1.08096i	−0.162908	−	0.194147i	−0.841323	+	0.540533i	$0.818223\pi$
$32$		0			0
$33$	3.05788	−	3.30754i	0.532308	−	0.575769i
$34$		0			0
$35$	1.14498	+	2.70014i	0.193537	+	0.456407i
$36$		0			0
$37$	−2.97188			−0.488573			−0.244287	−	0.969703i	$-0.578554\pi$
$37$	−2.97188			−0.488573			−0.244287	+	0.969703i	$0.578554\pi$
$38$		0			0
$39$	4.64444	+	6.10861i	0.743705	+	0.978160i
$40$		0			0
$41$	−7.49508	+	6.28912i	−1.17054	+	0.982196i	−0.999995	−	0.00315517i	$-0.998996\pi$
$41$	−7.49508	+	6.28912i	−1.17054	+	0.982196i	−0.170540	+	0.985351i	$0.554551\pi$
$42$		0			0
$43$	−10.5897	+	3.85434i	−1.61492	+	0.587782i	−0.982404	−	0.186768i	$-0.940199\pi$
$43$	−10.5897	+	3.85434i	−1.61492	+	0.587782i	−0.632513	+	0.774550i	$0.717977\pi$
$44$		0			0
$45$	2.74094	−	1.88325i	0.408595	−	0.280738i
$46$		0			0
$47$	8.10077	+	6.79735i	1.18162	+	0.991495i	0.999967	+	0.00813245i	$0.00258867\pi$
$47$	8.10077	+	6.79735i	1.18162	+	0.991495i	0.181651	+	0.983363i	$0.441856\pi$
$48$		0			0
$49$	−5.80041	−	3.91858i	−0.828630	−	0.559797i
$50$		0			0
$51$	−2.03735	+	3.16695i	−0.285287	+	0.443461i
$52$		0			0
$53$	−3.97427	+	2.29454i	−0.545907	+	0.315180i	−0.747470	−	0.664296i	$-0.768731\pi$
$53$	−3.97427	+	2.29454i	−0.545907	+	0.315180i	0.201562	+	0.979476i	$0.435398\pi$
$54$		0			0
$55$			2.88290i			0.388730i
$56$		0			0
$57$	3.04594	−	1.56850i	0.403445	−	0.207753i
$58$		0			0
$59$	0.253027	+	1.43499i	0.0329413	+	0.186819i	0.996838	−	0.0794556i	$-0.0253182\pi$
$59$	0.253027	+	1.43499i	0.0329413	+	0.186819i	−0.963897	+	0.266275i	$0.914207\pi$
$60$		0			0
$61$	−5.34786	+	6.37333i	−0.684723	+	0.816021i	−0.990707	−	0.136016i	$-0.956570\pi$
$61$	−5.34786	+	6.37333i	−0.684723	+	0.816021i	0.305984	+	0.952037i	$0.401015\pi$
$62$		0			0
$63$	−3.04112	+	7.33155i	−0.383146	+	0.923688i
$64$		0			0
$65$	−4.83660	−	0.852824i	−0.599907	−	0.105780i
$66$		0			0
$67$	−0.444834	−	0.161906i	−0.0543451	−	0.0197800i	0.314705	−	0.949190i	$-0.398095\pi$
$67$	−0.444834	−	0.161906i	−0.0543451	−	0.0197800i	−0.369050	+	0.929410i	$0.620317\pi$
$68$		0			0
$69$	0.957186	−	2.28219i	0.115232	−	0.274744i
$70$		0			0
$71$	−8.36281	+	4.82827i	−0.992483	+	0.573010i	−0.906016	−	0.423244i	$-0.860891\pi$
$71$	−8.36281	+	4.82827i	−0.992483	+	0.573010i	−0.0864676	+	0.996255i	$0.527558\pi$
$72$		0			0
$73$		−	14.9642i		−	1.75143i	−0.482833	−	0.875713i	$-0.660392\pi$
$73$		−	14.9642i		−	1.75143i	0.482833	−	0.875713i	$-0.339608\pi$
$74$		0			0
$75$	1.44200	−	6.37072i	0.166508	−	0.735627i
$76$		0			0
$77$	−3.74541	−	5.77203i	−0.426829	−	0.657783i
$78$		0			0
$79$	6.35972	−	2.31475i	0.715525	−	0.260430i	0.0415000	−	0.999139i	$-0.486786\pi$
$79$	6.35972	−	2.31475i	0.715525	−	0.260430i	0.674025	+	0.738709i	$0.264564\pi$
$80$		0			0
$81$	8.83418	+	1.71969i	0.981575	+	0.191076i
$82$		0			0
$83$	−0.735605	−	0.617246i	−0.0807431	−	0.0677515i	0.601523	−	0.798856i	$-0.294561\pi$
$83$	−0.735605	−	0.617246i	−0.0807431	−	0.0677515i	−0.682266	+	0.731104i	$0.739005\pi$
$84$		0			0
$85$	−0.418502	−	2.37344i	−0.0453929	−	0.257436i
$86$		0			0
$87$	2.86222	−	3.09591i	0.306862	−	0.331916i
$88$		0			0
$89$	8.19334	+	14.1913i	0.868493	+	1.50427i	0.863537	+	0.504286i	$0.168244\pi$
$89$	8.19334	+	14.1913i	0.868493	+	1.50427i	0.00495596	+	0.999988i	$0.498422\pi$
$90$		0			0
$91$	10.7916	−	4.57614i	1.13127	−	0.479710i
$92$		0			0
$93$	1.47926	+	1.94560i	0.153392	+	0.201749i
$94$		0			0
$95$	−0.749949	+	2.06047i	−0.0769432	+	0.211400i
$96$		0			0
$97$	−4.74751	−	13.0437i	−0.482037	−	1.32439i	−0.907744	−	0.419525i	$-0.862197\pi$
$97$	−4.74751	−	13.0437i	−0.482037	−	1.32439i	0.425707	−	0.904861i	$-0.360026\pi$
$98$		0			0
$99$	−5.56553	+	5.46774i	−0.559357	+	0.549529i
$100$		0			0
$101$	9.77345	−	3.55725i	0.972495	−	0.353959i	0.193577	−	0.981085i	$-0.437991\pi$
$101$	9.77345	−	3.55725i	0.972495	−	0.353959i	0.778918	+	0.627126i	$0.215769\pi$
$102$		0			0
$103$	−7.59155	−	9.04725i	−0.748017	−	0.891452i	0.249010	−	0.968501i	$-0.419895\pi$
$103$	−7.59155	−	9.04725i	−0.748017	−	0.891452i	−0.997027	+	0.0770486i	$0.975450\pi$
$104$		0			0
$105$	−1.75617	−	4.76666i	−0.171385	−	0.465179i
$106$		0			0
$107$	−7.14243	−	4.12369i	−0.690485	−	0.398652i	0.113309	−	0.993560i	$-0.463855\pi$
$107$	−7.14243	−	4.12369i	−0.690485	−	0.398652i	−0.803794	+	0.594908i	$0.797188\pi$
$108$		0			0
$109$	−0.0911298	−	0.157841i	−0.00872865	−	0.0151185i	0.861628	−	0.507540i	$-0.169445\pi$
$109$	−0.0911298	−	0.157841i	−0.00872865	−	0.0151185i	−0.870357	+	0.492422i	$0.836112\pi$
$110$		0			0
$111$	5.14150	+	0.247315i	0.488009	+	0.0234741i
$112$		0			0
$113$	−2.98486	+	8.20082i	−0.280792	+	0.771469i	0.716477	+	0.697611i	$0.245753\pi$
$113$	−2.98486	+	8.20082i	−0.280792	+	0.771469i	−0.997269	+	0.0738581i	$0.976469\pi$
$114$		0			0
$115$	0.541720	+	1.48836i	0.0505156	+	0.138791i
$116$		0			0
$117$	−7.52676	−	10.9547i	−0.695849	−	1.01276i
$118$		0			0
$119$	3.92144	+	4.20830i	0.359478	+	0.385774i
$120$		0			0
$121$	0.735664	+	4.17216i	0.0668785	+	0.379287i
$122$		0			0
$123$	13.4902	−	10.2568i	1.21637	−	0.924822i
$124$		0			0
$125$	4.86152	+	8.42040i	0.434828	+	0.753144i
$126$		0			0
$127$	−1.91309	+	3.31356i	−0.169759	+	0.294031i	−0.938335	−	0.345727i	$-0.887632\pi$
$127$	−1.91309	+	3.31356i	−0.169759	+	0.294031i	0.768576	+	0.639758i	$0.220966\pi$
$128$		0			0
$129$	18.6415	−	5.78695i	1.64129	−	0.509512i
$130$		0			0
$131$	−6.52662	−	2.37550i	−0.570234	−	0.207548i	0.0407800	−	0.999168i	$-0.487016\pi$
$131$	−6.52662	−	2.37550i	−0.570234	−	0.207548i	−0.611014	+	0.791620i	$0.709238\pi$
$132$		0			0
$133$	−1.17540	−	5.09971i	−0.101920	−	0.442201i
$134$		0			0
$135$	−4.89869	+	3.03002i	−0.421612	+	0.260782i
$136$		0			0
$137$	21.2720	+	3.75082i	1.81739	+	0.320454i	0.975634	−	0.219407i	$-0.0704121\pi$
$137$	21.2720	+	3.75082i	1.81739	+	0.320454i	0.841754	+	0.539861i	$0.181523\pi$
$138$		0			0
$139$	12.3574	−	2.17894i	1.04814	−	0.184815i	0.377050	−	0.926193i	$-0.376938\pi$
$139$	12.3574	−	2.17894i	1.04814	−	0.184815i	0.671088	+	0.741378i	$0.265827\pi$
$140$		0			0
$141$	−13.4491	−	12.4339i	−1.13262	−	1.04712i
$142$		0			0
$143$	11.5221			0.963523
$144$		0			0
$145$			2.69844i			0.224093i
$146$		0			0
$147$	9.70890	+	7.26204i	0.800777	+	0.598963i
$148$		0			0
$149$	9.59865	−	1.69250i	0.786352	−	0.138655i	0.233967	−	0.972244i	$-0.424829\pi$
$149$	9.59865	−	1.69250i	0.786352	−	0.138655i	0.552385	+	0.833589i	$0.313718\pi$
$150$		0			0
$151$	2.45649	+	2.06124i	0.199906	+	0.167741i	0.737245	−	0.675625i	$-0.236126\pi$
$151$	2.45649	+	2.06124i	0.199906	+	0.167741i	−0.537339	+	0.843366i	$0.680571\pi$
$152$		0			0
$153$	3.78827	−	5.30943i	0.306264	−	0.429242i
$154$		0			0
$155$	−1.54047	−	0.271626i	−0.123733	−	0.0218175i
$156$		0			0
$157$	−3.81387	+	0.672488i	−0.304380	+	0.0536704i	−0.323752	−	0.946142i	$-0.604944\pi$
$157$	−3.81387	+	0.672488i	−0.304380	+	0.0536704i	0.0193721	+	0.999812i	$0.493833\pi$
$158$		0			0
$159$	7.06663	−	3.63894i	0.560420	−	0.288587i
$160$		0			0
$161$	−3.01826	−	2.27615i	−0.237872	−	0.179386i
$162$		0			0
$163$	1.66040	−	2.87591i	0.130053	−	0.225258i	−0.793644	−	0.608383i	$-0.791819\pi$
$163$	1.66040	−	2.87591i	0.130053	−	0.225258i	0.923697	+	0.383124i	$0.125152\pi$
$164$		0			0
$165$	0.239910	−	4.98756i	0.0186770	−	0.388281i
$166$		0			0
$167$	7.24079	+	2.63543i	0.560309	+	0.203936i	0.606621	−	0.794991i	$-0.292525\pi$
$167$	7.24079	+	2.63543i	0.560309	+	0.203936i	−0.0463118	+	0.998927i	$0.514747\pi$
$168$		0			0
$169$	−1.15105	+	6.52791i	−0.0885421	+	0.502147i
$170$		0			0
$171$	−5.40017	+	2.46011i	−0.412961	+	0.188129i
$172$		0			0
$173$	4.33485	−	24.5842i	0.329572	−	1.86910i	−0.145800	−	0.989314i	$-0.546576\pi$
$173$	4.33485	−	24.5842i	0.329572	−	1.86910i	0.475373	−	0.879784i	$-0.342313\pi$
$174$		0			0
$175$	−8.88846	−	4.53298i	−0.671904	−	0.342661i
$176$		0			0
$177$	−0.318332	−	2.50366i	−0.0239273	−	0.188186i
$178$		0			0
$179$	8.89993	+	5.13838i	0.665212	+	0.384060i	0.794260	−	0.607578i	$-0.207859\pi$
$179$	8.89993	+	5.13838i	0.665212	+	0.384060i	−0.129048	+	0.991638i	$0.541192\pi$
$180$		0			0
$181$	0.236613	+	0.136609i	0.0175873	+	0.0101540i	0.508768	−	0.860904i	$-0.330101\pi$
$181$	0.236613	+	0.136609i	0.0175873	+	0.0101540i	−0.491181	+	0.871058i	$0.663434\pi$
$182$		0			0
$183$	9.78244	−	10.5811i	0.723139	−	0.782180i
$184$		0			0
$185$	−2.52365	+	2.11759i	−0.185542	+	0.155688i
$186$		0			0
$187$	1.93384	+	5.31317i	0.141416	+	0.388538i
$188$		0			0
$189$	5.87142	−	12.4309i	0.427083	−	0.904212i
$190$		0			0
$191$	−3.56987	−	9.80814i	−0.258307	−	0.709692i	−0.999272	−	0.0381488i	$-0.987854\pi$
$191$	−3.56987	−	9.80814i	−0.258307	−	0.709692i	0.740965	−	0.671543i	$-0.234368\pi$
$192$		0			0
$193$	−2.97726	+	2.49821i	−0.214308	+	0.179825i	−0.743622	−	0.668600i	$-0.766894\pi$
$193$	−2.97726	+	2.49821i	−0.214308	+	0.179825i	0.529314	+	0.848426i	$0.322449\pi$
$194$		0			0
$195$	8.29660	+	1.87792i	0.594132	+	0.134481i
$196$		0			0
$197$	15.4374	+	8.91279i	1.09987	+	0.635010i	0.936187	−	0.351503i	$-0.114329\pi$
$197$	15.4374	+	8.91279i	1.09987	+	0.635010i	0.163683	+	0.986513i	$0.447663\pi$
$198$		0			0
$199$	−0.890033	−	0.513861i	−0.0630928	−	0.0364266i	0.468122	−	0.883664i	$-0.344931\pi$
$199$	−0.890033	−	0.513861i	−0.0630928	−	0.0364266i	−0.531215	+	0.847237i	$0.678264\pi$
$200$		0			0
$201$	0.756112	+	0.317124i	0.0533320	+	0.0223682i
$202$		0			0
$203$	−3.50576	−	5.40271i	−0.246056	−	0.379196i
$204$		0			0
$205$	−1.88337	+	10.6811i	−0.131541	+	0.746004i
$206$		0			0
$207$	−1.84590	+	3.86866i	−0.128299	+	0.268890i
$208$		0			0
$209$	0.893288	−	5.06609i	0.0617900	−	0.350429i
$210$		0			0
$211$	−12.2463	−	4.45728i	−0.843068	−	0.306852i	−0.115857	−	0.993266i	$-0.536962\pi$
$211$	−12.2463	−	4.45728i	−0.843068	−	0.306852i	−0.727211	+	0.686414i	$0.759184\pi$
$212$		0			0
$213$	14.8699	−	7.65722i	1.01887	−	0.524664i
$214$		0			0
$215$	−6.24616	+	10.8187i	−0.425984	+	0.737827i
$216$		0			0
$217$	3.43715	−	1.45751i	0.233329	−	0.0989420i
$218$		0			0
$219$	−1.24529	+	25.8888i	−0.0841492	+	1.74940i
$220$		0			0
$221$	−9.48592	+	1.67262i	−0.638092	+	0.112513i
$222$		0			0
$223$	−8.52773	−	1.50367i	−0.571059	−	0.100693i	−0.119340	−	0.992853i	$-0.538078\pi$
$223$	−8.52773	−	1.50367i	−0.571059	−	0.100693i	−0.451719	+	0.892160i	$0.649189\pi$
$224$		0			0
$225$	−3.02490	+	10.9017i	−0.201660	+	0.726777i
$226$		0			0
$227$	−22.9493	−	19.2568i	−1.52320	−	1.27812i	−0.830745	−	0.556653i	$-0.812085\pi$
$227$	−22.9493	−	19.2568i	−1.52320	−	1.27812i	−0.692454	−	0.721462i	$-0.743470\pi$
$228$		0			0
$229$	−15.6399	+	2.75774i	−1.03352	+	0.182237i	−0.664579	−	0.747218i	$-0.731389\pi$
$229$	−15.6399	+	2.75774i	−1.03352	+	0.182237i	−0.368937	+	0.929455i	$0.620278\pi$
$230$		0			0
$231$	5.99941	+	10.2976i	0.394732	+	0.677531i
$232$		0			0
$233$			4.08552i			0.267651i	0.991005	+	0.133826i	$0.0427262\pi$
$233$			4.08552i			0.267651i	−0.991005	+	0.133826i	$0.957274\pi$
$234$		0			0
$235$	11.7224			0.764685
$236$		0			0
$237$	−11.1953	+	3.47539i	−0.727211	+	0.225751i
$238$		0			0
$239$	−22.6228	+	3.98901i	−1.46335	+	0.258028i	−0.847903	−	0.530152i	$-0.822135\pi$
$239$	−22.6228	+	3.98901i	−1.46335	+	0.258028i	−0.615445	+	0.788180i	$0.711024\pi$
$240$		0			0
$241$	5.09769	+	0.898860i	0.328371	+	0.0579007i	0.335403	−	0.942075i	$-0.391127\pi$
$241$	5.09769	+	0.898860i	0.328371	+	0.0579007i	−0.00703235	+	0.999975i	$0.502238\pi$
$242$		0			0
$243$	−15.1405	−	3.71031i	−0.971261	−	0.238017i
$244$		0			0
$245$	−7.71773	+	0.805482i	−0.493068	+	0.0514604i
$246$		0			0
$247$	8.23506	+	2.99732i	0.523984	+	0.190715i
$248$		0			0
$249$	1.22127	+	1.12908i	0.0773947	+	0.0715527i
$250$		0			0
$251$	2.34715	−	4.06538i	0.148151	−	0.256604i	−0.782393	−	0.622785i	$-0.786001\pi$
$251$	2.34715	−	4.06538i	0.148151	−	0.256604i	0.930544	+	0.366180i	$0.119335\pi$
$252$		0			0
$253$	−1.85795	−	3.21806i	−0.116808	−	0.202318i
$254$		0			0
$255$	0.526515	+	4.14100i	0.0329717	+	0.259320i
$256$		0			0
$257$	−3.20377	−	18.1695i	−0.199846	−	1.13338i	−0.905347	−	0.424673i	$-0.860389\pi$
$257$	−3.20377	−	18.1695i	−0.199846	−	1.13338i	0.705501	−	0.708709i	$-0.250722\pi$
$258$		0			0
$259$	2.30161	−	7.51844i	0.143015	−	0.467173i
$260$		0			0
$261$	−5.20942	+	5.11789i	−0.322455	+	0.316790i
$262$		0			0
$263$	8.87400	+	24.3811i	0.547194	+	1.50340i	0.837483	+	0.546464i	$0.184027\pi$
$263$	8.87400	+	24.3811i	0.547194	+	1.50340i	−0.290288	+	0.956939i	$0.593751\pi$
$264$		0			0
$265$	−1.73989	+	4.78031i	−0.106881	+	0.293652i
$266$		0			0
$267$	−12.9939	−	25.2335i	−0.795215	−	1.54426i
$268$		0			0
$269$	13.5863	+	23.5321i	0.828369	+	1.43478i	0.899317	+	0.437297i	$0.144064\pi$
$269$	13.5863	+	23.5321i	0.828369	+	1.43478i	−0.0709484	+	0.997480i	$0.522603\pi$
$270$		0			0
$271$	8.32385	+	4.80578i	0.505638	+	0.291930i	0.731039	−	0.682336i	$-0.239036\pi$
$271$	8.32385	+	4.80578i	0.505638	+	0.291930i	−0.225401	+	0.974266i	$0.572369\pi$
$272$		0			0
$273$	−19.0509	+	7.01889i	−1.15301	+	0.424802i
$274$		0			0
$275$	−6.30420	−	7.51305i	−0.380157	−	0.453054i
$276$		0			0
$277$	−8.72955	+	3.17730i	−0.524508	+	0.190905i	−0.590685	−	0.806903i	$-0.701142\pi$
$277$	−8.72955	+	3.17730i	−0.524508	+	0.190905i	0.0661764	+	0.997808i	$0.478920\pi$
$278$		0			0
$279$	−2.39729	−	3.48909i	−0.143522	−	0.208886i
$280$		0			0
$281$	−5.95969	−	16.3741i	−0.355526	−	0.976798i	−0.980563	−	0.196204i	$-0.937139\pi$
$281$	−5.95969	−	16.3741i	−0.355526	−	0.976798i	0.625038	−	0.780595i	$-0.285084\pi$
$282$		0			0
$283$	3.24904	−	8.92666i	0.193135	−	0.530635i	−0.804892	−	0.593422i	$-0.797777\pi$
$283$	3.24904	−	8.92666i	0.193135	−	0.530635i	0.998027	+	0.0627870i	$0.0199989\pi$
$284$		0			0
$285$	1.46892	−	3.50230i	0.0870112	−	0.207459i
$286$		0			0
$287$	−10.1059	−	23.8322i	−0.596535	−	1.40677i
$288$		0			0
$289$	6.13661	+	10.6289i	0.360977	+	0.625230i
$290$		0			0
$291$	7.12797	+	22.9613i	0.417849	+	1.34602i
$292$		0			0
$293$	3.63421	+	20.6107i	0.212313	+	1.20409i	0.885509	+	0.464623i	$0.153810\pi$
$293$	3.63421	+	20.6107i	0.212313	+	1.20409i	−0.673196	+	0.739464i	$0.735079\pi$
$294$		0			0
$295$	1.23736	+	1.03827i	0.0720417	+	0.0604501i
$296$		0			0
$297$	10.0837	−	8.99631i	0.585114	−	0.522019i
$298$		0			0
$299$	5.94853	−	2.16509i	0.344012	−	0.125210i
$300$		0			0
$301$	−1.54960	−	29.7756i	−0.0893173	−	1.71624i
$302$		0			0
$303$	−17.2046	+	5.34088i	−0.988378	+	0.306826i
$304$		0			0
$305$			9.22266i			0.528088i
$306$		0			0
$307$	−3.82657	+	2.20927i	−0.218394	+	0.126090i	−0.605206	−	0.796069i	$-0.706909\pi$
$307$	−3.82657	+	2.20927i	−0.218394	+	0.126090i	0.386813	+	0.922158i	$0.373576\pi$
$308$		0			0
$309$	12.3809	+	16.2840i	0.704323	+	0.926362i
$310$		0			0
$311$	2.67595	+	0.973967i	0.151739	+	0.0552286i	0.416773	−	0.909010i	$-0.363161\pi$
$311$	2.67595	+	0.973967i	0.151739	+	0.0552286i	−0.265034	+	0.964239i	$0.585383\pi$
$312$		0			0
$313$	11.3800	+	2.00660i	0.643235	+	0.113420i	0.485745	−	0.874101i	$-0.338549\pi$
$313$	11.3800	+	2.00660i	0.643235	+	0.113420i	0.157490	+	0.987521i	$0.449660\pi$
$314$		0			0
$315$	2.64160	+	8.39271i	0.148837	+	0.472876i
$316$		0			0
$317$	11.9128	−	14.1971i	0.669088	−	0.797388i	−0.319571	−	0.947562i	$-0.603539\pi$
$317$	11.9128	−	14.1971i	0.669088	−	0.797388i	0.988660	+	0.150174i	$0.0479834\pi$
$318$		0			0
$319$	−1.09932	−	6.23455i	−0.0615500	−	0.349068i
$320$		0			0
$321$	12.0136	+	7.72857i	0.670534	+	0.431367i
$322$		0			0
$323$			4.30050i			0.239286i
$324$		0			0
$325$	14.4695	−	8.35395i	0.802622	−	0.463394i
$326$		0			0
$327$	0.144524	+	0.280657i	0.00799218	+	0.0155204i
$328$		0			0
$329$	−23.4701	+	15.2295i	−1.29395	+	0.839631i
$330$		0			0
$331$	22.2512	+	18.6710i	1.22304	+	1.02625i	0.998660	+	0.0517487i	$0.0164795\pi$
$331$	22.2512	+	18.6710i	1.22304	+	1.02625i	0.224378	+	0.974502i	$0.427965\pi$
$332$		0			0
$333$	−8.87447	−	0.855734i	−0.486318	−	0.0468939i
$334$		0			0
$335$	−0.493108	+	0.179477i	−0.0269414	+	0.00980586i
$336$		0			0
$337$	10.6404	−	8.92833i	0.579618	−	0.486357i	−0.305204	−	0.952287i	$-0.598725\pi$
$337$	10.6404	−	8.92833i	0.579618	−	0.486357i	0.884822	+	0.465930i	$0.154280\pi$
$338$		0			0
$339$	5.84641	−	13.9394i	0.317533	−	0.757087i
$340$		0			0
$341$	3.66979			0.198730
$342$		0			0
$343$	14.4057	−	11.6394i	0.777833	−	0.628471i
$344$		0			0
$345$	−0.813343	−	2.62002i	−0.0437889	−	0.141057i
$346$		0			0
$347$	−5.97718	−	7.12332i	−0.320872	−	0.382400i	0.581364	−	0.813644i	$-0.302519\pi$
$347$	−5.97718	−	7.12332i	−0.320872	−	0.382400i	−0.902235	+	0.431244i	$0.858075\pi$
$348$		0			0
$349$	−18.3394	+	21.8561i	−0.981686	+	1.16993i	0.00376869	+	0.999993i	$0.498800\pi$
$349$	−18.3394	+	21.8561i	−0.981686	+	1.16993i	−0.985455	+	0.169936i	$0.945644\pi$
$350$		0			0
$351$	12.1100	+	19.5785i	0.646386	+	1.04503i
$352$		0			0
$353$	−4.42204	+	25.0786i	−0.235361	+	1.33480i	0.606490	+	0.795091i	$0.292577\pi$
$353$	−4.42204	+	25.0786i	−0.235361	+	1.33480i	−0.841851	+	0.539710i	$0.818534\pi$
$354$		0			0
$355$	−3.66115	+	10.0589i	−0.194314	+	0.533872i
$356$		0			0
$357$	−6.43408	−	7.60691i	−0.340528	−	0.402600i
$358$		0			0
$359$	5.97926	−	3.45212i	0.315573	−	0.182196i	−0.333845	−	0.942628i	$-0.608346\pi$
$359$	5.97926	−	3.45212i	0.315573	−	0.182196i	0.649418	+	0.760432i	$0.275013\pi$
$360$		0			0
$361$	−7.54367	+	13.0660i	−0.397035	+	0.687685i
$362$		0			0
$363$	−0.925536	−	7.27926i	−0.0485780	−	0.382062i
$364$		0			0
$365$	−10.6626	−	12.7072i	−0.558108	−	0.665127i
$366$		0			0
$367$	−1.26692	+	1.50986i	−0.0661327	+	0.0788139i	−0.798097	−	0.602530i	$-0.794160\pi$
$367$	−1.26692	+	1.50986i	−0.0661327	+	0.0788139i	0.731964	+	0.681343i	$0.238604\pi$
$368$		0			0
$369$	−24.1923	+	16.6221i	−1.25940	+	0.865311i
$370$		0			0
$371$	−2.72695	−	11.8314i	−0.141576	−	0.614255i
$372$		0			0
$373$	−12.4218	+	10.4231i	−0.643174	+	0.539687i	−0.904991	−	0.425430i	$-0.860123\pi$
$373$	−12.4218	+	10.4231i	−0.643174	+	0.539687i	0.261817	+	0.965118i	$0.415678\pi$
$374$		0			0
$375$	−7.70994	−	14.9723i	−0.398140	−	0.773166i
$376$		0			0
$377$	10.7848			0.555447
$378$		0			0
$379$	18.2120			0.935489			0.467744	−	0.883864i	$-0.345067\pi$
$379$	18.2120			0.935489			0.467744	+	0.883864i	$0.345067\pi$
$380$		0			0
$381$	3.58549	−	5.57343i	0.183690	−	0.285535i
$382$		0			0
$383$	3.03727	−	2.54857i	0.155197	−	0.130226i	−0.561883	−	0.827217i	$-0.689923\pi$
$383$	3.03727	−	2.54857i	0.155197	−	0.130226i	0.717080	+	0.696991i	$0.245478\pi$
$384$		0			0
$385$	−7.29334	−	2.23270i	−0.371703	−	0.113789i
$386$		0			0
$387$	−32.7323	+	8.46040i	−1.66388	+	0.430066i
$388$		0			0
$389$	14.5754	−	17.3702i	0.739000	−	0.880706i	−0.257328	−	0.966324i	$-0.582842\pi$
$389$	14.5754	−	17.3702i	0.739000	−	0.880706i	0.996328	+	0.0856185i	$0.0272866\pi$
$390$		0			0
$391$	1.99678	+	2.37966i	0.100981	+	0.120345i
$392$		0			0
$393$	11.0937	+	4.65286i	0.559603	+	0.234706i
$394$		0			0
$395$	3.75117	−	6.49721i	0.188742	−	0.326910i
$396$		0			0
$397$	5.37841	−	3.10523i	0.269935	−	0.155847i	−0.358923	−	0.933367i	$-0.616856\pi$
$397$	5.37841	−	3.10523i	0.269935	−	0.155847i	0.628858	+	0.777520i	$0.283523\pi$
$398$		0			0
$399$	1.60912	+	8.92057i	0.0805567	+	0.446587i
$400$		0			0
$401$	5.11534	−	14.0543i	0.255448	−	0.701838i	−0.743986	−	0.668195i	$-0.767067\pi$
$401$	5.11534	−	14.0543i	0.255448	−	0.701838i	0.999434	−	0.0336423i	$-0.0107107\pi$
$402$		0			0
$403$	−1.08560	+	6.15677i	−0.0540778	+	0.306691i
$404$		0			0
$405$	8.72713	−	4.83442i	0.433655	−	0.240224i
$406$		0			0
$407$	4.96802	−	5.92065i	0.246256	−	0.293476i
$408$		0			0
$409$	−5.69285	−	6.78448i	−0.281493	−	0.335471i	0.606708	−	0.794925i	$-0.292490\pi$
$409$	−5.69285	−	6.78448i	−0.281493	−	0.335471i	−0.888202	+	0.459454i	$0.848045\pi$
$410$		0			0
$411$	−36.4895	−	8.25933i	−1.79989	−	0.407403i
$412$		0			0
$413$	−3.82628	−	0.471223i	−0.188279	−	0.0231874i
$414$		0			0
$415$	−1.06447			−0.0522529
$416$		0			0
$417$	−21.5602	+	2.74131i	−1.05581	+	0.134243i
$418$		0			0
$419$	1.66306	−	1.39547i	0.0812457	−	0.0681732i	−0.601260	−	0.799053i	$-0.705335\pi$
$419$	1.66306	−	1.39547i	0.0812457	−	0.0681732i	0.682506	+	0.730880i	$0.260890\pi$
$420$		0			0
$421$	−12.3900	+	4.50961i	−0.603854	+	0.219785i	−0.625812	−	0.779974i	$-0.715232\pi$
$421$	−12.3900	+	4.50961i	−0.603854	+	0.219785i	0.0219579	+	0.999759i	$0.493010\pi$
$422$		0			0
$423$	22.2328	+	22.6305i	1.08100	+	1.10033i
$424$		0			0
$425$	6.28079	+	5.27021i	0.304663	+	0.255643i
$426$		0			0
$427$	−11.9819	−	18.4653i	−0.579846	−	0.893596i
$428$		0			0
$429$	−19.9337	−	0.958846i	−0.962410	−	0.0462935i
$430$		0			0
$431$	−18.2641	+	10.5448i	−0.879749	+	0.507923i	−0.870576	−	0.492035i	$-0.836253\pi$
$431$	−18.2641	+	10.5448i	−0.879749	+	0.507923i	−0.00917317	+	0.999958i	$0.502920\pi$
$432$		0			0
$433$			24.5525i			1.17992i	0.807433	+	0.589959i	$0.200856\pi$
$433$			24.5525i			1.17992i	−0.807433	+	0.589959i	$0.799144\pi$
$434$		0			0
$435$	0.224560	−	4.66843i	0.0107668	−	0.223834i
$436$		0			0
$437$	−0.490778	−	2.78334i	−0.0234771	−	0.133145i
$438$		0			0
$439$	−23.7458	+	28.2992i	−1.13333	+	1.35064i	−0.205050	+	0.978751i	$0.565736\pi$
$439$	−23.7458	+	28.2992i	−1.13333	+	1.35064i	−0.928275	+	0.371893i	$0.878709\pi$
$440$		0			0
$441$	−16.1926	−	13.3716i	−0.771074	−	0.636745i
$442$		0			0
$443$	−22.4041	−	3.95045i	−1.06445	−	0.187692i	−0.386122	−	0.922448i	$-0.626185\pi$
$443$	−22.4041	−	3.95045i	−1.06445	−	0.187692i	−0.678331	+	0.734756i	$0.737297\pi$
$444$		0			0
$445$	17.0695	+	6.21279i	0.809173	+	0.294515i
$446$		0			0
$447$	−16.7470	+	2.12933i	−0.792106	+	0.100714i
$448$		0			0
$449$	−23.3226	+	13.4653i	−1.10066	+	0.635468i	−0.936395	−	0.350948i	$-0.885859\pi$
$449$	−23.3226	+	13.4653i	−1.10066	+	0.635468i	−0.164268	+	0.986416i	$0.552526\pi$
$450$		0			0
$451$		−	25.4453i		−	1.19817i
$452$		0			0
$453$	−4.07831	−	3.77047i	−0.191616	−	0.177152i
$454$		0			0
$455$	5.90330	−	11.5755i	0.276751	−	0.542666i
$456$		0			0
$457$	11.7898	−	4.29112i	0.551501	−	0.200730i	−0.0512121	−	0.998688i	$-0.516308\pi$
$457$	11.7898	−	4.29112i	0.551501	−	0.200730i	0.602713	+	0.797958i	$0.294086\pi$
$458$		0			0
$459$	−6.99574	+	8.87033i	−0.326533	+	0.414032i
$460$		0			0
$461$	12.3292	+	10.3454i	0.574229	+	0.481835i	0.883046	−	0.469286i	$-0.155489\pi$
$461$	12.3292	+	10.3454i	0.574229	+	0.481835i	−0.308817	+	0.951121i	$0.599933\pi$
$462$		0			0
$463$	−0.398483	−	2.25991i	−0.0185191	−	0.105027i	0.974147	−	0.225915i	$-0.0725370\pi$
$463$	−0.398483	−	2.25991i	−0.0185191	−	0.105027i	−0.992666	+	0.120888i	$0.961426\pi$
$464$		0			0
$465$	2.64248	+	0.598121i	0.122542	+	0.0277372i
$466$		0			0
$467$	1.88268	+	3.26090i	0.0871201	+	0.150896i	0.906293	−	0.422651i	$-0.138900\pi$
$467$	1.88268	+	3.26090i	0.0871201	+	0.150896i	−0.819173	+	0.573547i	$0.805567\pi$
$468$		0			0
$469$	0.754109	−	0.999978i	0.0348215	−	0.0461747i
$470$		0			0
$471$	6.65415	−	0.846055i	0.306607	−	0.0389841i
$472$		0			0
$473$	10.0239	−	27.5404i	0.460898	−	1.26631i
$474$		0			0
$475$	−2.55132	−	7.00969i	−0.117063	−	0.321627i
$476$		0			0
$477$	−12.5285	+	5.70748i	−0.573638	+	0.261328i
$478$		0			0
$479$	8.37940	−	3.04985i	0.382864	−	0.139351i	−0.143416	−	0.989663i	$-0.545809\pi$
$479$	8.37940	−	3.04985i	0.382864	−	0.139351i	0.526280	+	0.850311i	$0.323586\pi$
$480$		0			0
$481$	8.46336	+	10.0862i	0.385896	+	0.459893i
$482$		0			0
$483$	5.03233	+	4.18903i	0.228979	+	0.190607i
$484$		0			0
$485$	−13.3257	−	7.69359i	−0.605088	−	0.349348i
$486$		0			0
$487$	17.0344	+	29.5044i	0.771901	+	1.33697i	0.936520	+	0.350615i	$0.114027\pi$
$487$	17.0344	+	29.5044i	0.771901	+	1.33697i	−0.164618	+	0.986357i	$0.552639\pi$
$488$		0			0
$489$	−3.11191	+	4.83729i	−0.140726	+	0.218750i
$490$		0			0
$491$	6.27488	−	17.2401i	0.283181	−	0.778034i	−0.713797	−	0.700353i	$-0.753026\pi$
$491$	6.27488	−	17.2401i	0.283181	−	0.778034i	0.996978	−	0.0776816i	$-0.0247518\pi$
$492$		0			0
$493$	1.81010	+	4.97321i	0.0815229	+	0.223982i
$494$		0			0
$495$	−0.830113	+	8.60876i	−0.0373108	+	0.386935i
$496$		0			0
$497$	−5.73817	−	24.8961i	−0.257392	−	1.11674i
$498$		0			0
$499$	3.87321	+	21.9660i	0.173389	+	0.983335i	0.939987	+	0.341209i	$0.110836\pi$
$499$	3.87321	+	21.9660i	0.173389	+	0.983335i	−0.766599	+	0.642126i	$0.778053\pi$
$500$		0			0
$501$	−12.3076	−	5.16200i	−0.549864	−	0.230621i
$502$		0			0
$503$	3.88720	+	6.73283i	0.173322	+	0.300202i	0.939579	−	0.342331i	$-0.111217\pi$
$503$	3.88720	+	6.73283i	0.173322	+	0.300202i	−0.766257	+	0.642534i	$0.777883\pi$
$504$		0			0
$505$	5.76469	−	9.98474i	0.256526	−	0.444315i
$506$		0			0
$507$	2.53461	−	11.1978i	0.112566	−	0.497313i
$508$		0			0
$509$	−0.532804	−	0.193925i	−0.0236161	−	0.00859556i	0.330185	−	0.943916i	$-0.392889\pi$
$509$	−0.532804	−	0.193925i	−0.0236161	−	0.00859556i	−0.353801	+	0.935321i	$0.615111\pi$
$510$		0			0
$511$	37.8573	+	11.5892i	1.67471	+	0.512677i
$512$		0			0
$513$	9.54729	−	3.80672i	0.421523	−	0.168071i
$514$		0			0
$515$	−12.8931	−	2.27341i	−0.568139	−	0.100178i
$516$		0			0
$517$	−27.0837	+	4.77560i	−1.19114	+	0.210030i
$518$		0			0
$519$	−9.54536	+	42.1711i	−0.418995	+	1.85111i
$520$		0			0
$521$	−43.5123			−1.90631			−0.953155	−	0.302482i	$-0.902185\pi$
$521$	−43.5123			−1.90631			−0.953155	+	0.302482i	$0.902185\pi$
$522$		0			0
$523$			30.6289i			1.33931i	0.742673	+	0.669654i	$0.233558\pi$
$523$			30.6289i			1.33931i	−0.742673	+	0.669654i	$0.766442\pi$
$524$		0			0
$525$	15.0003	+	8.58196i	0.654665	+	0.374547i
$526$		0			0
$527$	−3.02128	+	0.532733i	−0.131609	+	0.0232062i
$528$		0			0
$529$	16.0551	+	13.4718i	0.698048	+	0.585732i
$530$		0			0
$531$	0.342381	+	4.35794i	0.0148581	+	0.189119i
$532$		0			0
$533$	42.6893	+	7.52727i	1.84908	+	0.326042i
$534$		0			0
$535$	−9.00350	+	1.58756i	−0.389255	+	0.0686362i
$536$		0			0
$537$	−14.9697	−	9.63029i	−0.645991	−	0.415578i
$538$		0			0
$539$	17.5031	−	5.00514i	0.753913	−	0.215587i
$540$		0			0
$541$	19.4663	−	33.7166i	0.836921	−	1.44959i	−0.0555351	−	0.998457i	$-0.517686\pi$
$541$	19.4663	−	33.7166i	0.836921	−	1.44959i	0.892456	−	0.451134i	$-0.148980\pi$
$542$		0			0
$543$	−0.397984	−	0.256030i	−0.0170791	−	0.0109873i
$544$		0			0
$545$	−0.189854	−	0.0691013i	−0.00813246	−	0.00295997i
$546$		0			0
$547$	7.64697	−	43.3681i	0.326961	−	1.85429i	−0.168562	−	0.985691i	$-0.553912\pi$
$547$	7.64697	−	43.3681i	0.326961	−	1.85429i	0.495523	−	0.868595i	$-0.334977\pi$
$548$		0			0
$549$	−17.8047	+	17.4918i	−0.759884	+	0.746533i
$550$		0			0
$551$	0.836131	−	4.74194i	0.0356204	−	0.202013i
$552$		0			0
$553$	0.930620	+	17.8819i	0.0395740	+	0.760416i
$554$		0			0
$555$	4.54226	−	3.45353i	0.192808	−	0.146594i
$556$		0			0
$557$	16.8215	+	9.71187i	0.712748	+	0.411505i	0.812078	−	0.583549i	$-0.198337\pi$
$557$	16.8215	+	9.71187i	0.712748	+	0.411505i	−0.0993298	+	0.995055i	$0.531670\pi$
$558$		0			0
$559$	43.2389	+	24.9640i	1.82881	+	1.05586i
$560$		0			0
$561$	−2.90348	−	9.35299i	−0.122585	−	0.394883i
$562$		0			0
$563$	−20.1901	+	16.9415i	−0.850912	+	0.714000i	−0.959990	−	0.280033i	$-0.909654\pi$
$563$	−20.1901	+	16.9415i	−0.850912	+	0.714000i	0.109079	+	0.994033i	$0.465210\pi$
$564$		0			0
$565$	3.30878	+	9.09079i	0.139201	+	0.382452i
$566$		0			0
$567$	−11.1923	+	21.0174i	−0.470034	+	0.882649i
$568$		0			0
$569$	13.0522	+	35.8606i	0.547176	+	1.50335i	0.837506	+	0.546428i	$0.184013\pi$
$569$	13.0522	+	35.8606i	0.547176	+	1.50335i	−0.290329	+	0.956927i	$0.593765\pi$
$570$		0			0
$571$	27.4086	−	22.9985i	1.14701	−	0.962459i	0.147368	−	0.989082i	$-0.452920\pi$
$571$	27.4086	−	22.9985i	1.14701	−	0.962459i	0.999646	+	0.0266227i	$0.00847528\pi$
$572$		0			0
$573$	5.35984	+	17.2657i	0.223911	+	0.721283i
$574$		0			0
$575$	−4.66645	−	2.69418i	−0.194604	−	0.112355i
$576$		0			0
$577$	−28.7395	−	16.5927i	−1.19644	−	0.690765i	−0.236680	−	0.971588i	$-0.576059\pi$
$577$	−28.7395	−	16.5927i	−1.19644	−	0.690765i	−0.959760	+	0.280822i	$0.909393\pi$
$578$		0			0
$579$	5.35870	−	4.07427i	0.222700	−	0.169321i
$580$		0			0
$581$	2.13125	−	1.38294i	0.0884190	−	0.0573742i
$582$		0			0
$583$	2.07244	−	11.7534i	0.0858316	−	0.486775i
$584$		0			0
$585$	−14.1973	−	3.93933i	−0.586984	−	0.162871i
$586$		0			0
$587$	6.48754	−	36.7927i	0.267769	−	1.51860i	−0.493262	−	0.869881i	$-0.664196\pi$
$587$	6.48754	−	36.7927i	0.267769	−	1.51860i	0.761032	−	0.648715i	$-0.224693\pi$
$588$		0			0
$589$	2.62288	+	0.954650i	0.108074	+	0.0393357i
$590$		0			0
$591$	−25.9658	−	16.7043i	−1.06809	−	0.687121i
$592$		0			0
$593$	15.3436	−	26.5758i	0.630084	−	1.09134i	−0.357450	−	0.933932i	$-0.616354\pi$
$593$	15.3436	−	26.5758i	0.630084	−	1.09134i	0.987534	−	0.157406i	$-0.0503130\pi$
$594$		0			0
$595$	6.32860	+	0.779394i	0.259447	+	0.0319520i
$596$		0			0
$597$	1.49704	+	0.963073i	0.0612698	+	0.0394159i
$598$		0			0
$599$	15.0354	−	2.65114i	0.614328	−	0.108323i	0.142178	−	0.989841i	$-0.454589\pi$
$599$	15.0354	−	2.65114i	0.614328	−	0.108323i	0.472150	+	0.881518i	$0.343478\pi$
$600$		0			0
$601$	−4.22303	−	0.744633i	−0.172261	−	0.0303742i	0.0868524	−	0.996221i	$-0.472319\pi$
$601$	−4.22303	−	0.744633i	−0.172261	−	0.0303742i	−0.259113	+	0.965847i	$0.583430\pi$
$602$		0			0
$603$	−1.28172	−	0.611564i	−0.0521957	−	0.0249048i
$604$		0			0
$605$	3.59755	+	3.01871i	0.146261	+	0.122728i
$606$		0			0
$607$	9.70430	−	1.71113i	0.393885	−	0.0694526i	0.0268022	−	0.999641i	$-0.491468\pi$
$607$	9.70430	−	1.71113i	0.393885	−	0.0694526i	0.367083	+	0.930188i	$0.380356\pi$
$608$		0			0
$609$	5.61554	+	9.63870i	0.227553	+	0.390580i
$610$		0			0
$611$		−	46.8508i		−	1.89538i
$612$		0			0
$613$	−38.3304			−1.54815			−0.774074	−	0.633095i	$-0.781784\pi$
$613$	−38.3304			−1.54815			−0.774074	+	0.633095i	$0.781784\pi$
$614$		0			0
$615$	4.14720	−	18.3222i	0.167231	−	0.738822i
$616$		0			0
$617$	−26.7808	+	4.72218i	−1.07816	+	0.190108i	−0.684399	−	0.729107i	$-0.739936\pi$
$617$	−26.7808	+	4.72218i	−1.07816	+	0.190108i	−0.393756	+	0.919215i	$0.628824\pi$
$618$		0			0
$619$	−14.3259	−	2.52604i	−0.575807	−	0.101530i	−0.121841	−	0.992550i	$-0.538880\pi$
$619$	−14.3259	−	2.52604i	−0.575807	−	0.101530i	−0.453965	+	0.891019i	$0.649991\pi$
$620$		0			0
$621$	3.51544	−	6.53936i	0.141070	−	0.262415i
$622$		0			0
$623$	−42.2475	+	9.73739i	−1.69261	+	0.390120i
$624$		0			0
$625$	−7.59055	−	2.76274i	−0.303622	−	0.110509i
$626$		0			0
$627$	−1.96702	+	8.69025i	−0.0785554	+	0.347055i
$628$		0			0
$629$	−3.23060	+	5.59557i	−0.128813	+	0.223110i
$630$		0			0
$631$	0.991846	+	1.71793i	0.0394847	+	0.0683896i	0.885092	−	0.465415i	$-0.154095\pi$
$631$	0.991846	+	1.71793i	0.0394847	+	0.0683896i	−0.845608	+	0.533805i	$0.820762\pi$
$632$		0			0
$633$	20.8157	+	8.73043i	0.827351	+	0.347003i
$634$		0			0
$635$	0.736511	+	4.17696i	0.0292275	+	0.165758i
$636$		0			0
$637$	3.21927	+	30.8454i	0.127552	+	1.22214i
$638$		0			0
$639$	−26.3629	+	12.0099i	−1.04290	+	0.475105i
$640$		0			0
$641$	1.37045	+	3.76529i	0.0541296	+	0.148720i	0.963811	−	0.266588i	$-0.0858962\pi$
$641$	1.37045	+	3.76529i	0.0541296	+	0.148720i	−0.909681	+	0.415308i	$0.863674\pi$
$642$		0			0
$643$	6.23306	−	17.1252i	0.245808	−	0.675351i	−0.754021	−	0.656850i	$-0.771888\pi$
$643$	6.23306	−	17.1252i	0.245808	−	0.675351i	0.999829	−	0.0185010i	$-0.00588939\pi$
$644$		0			0
$645$	11.7065	−	18.1970i	0.460942	−	0.716507i
$646$		0			0
$647$	13.6102	+	23.5735i	0.535072	+	0.926771i	0.999160	+	0.0409821i	$0.0130487\pi$
$647$	13.6102	+	23.5735i	0.535072	+	0.926771i	−0.464088	+	0.885789i	$0.653618\pi$
$648$		0			0
$649$	−3.28180	−	1.89475i	−0.128822	−	0.0743754i
$650$		0			0
$651$	−6.06774	+	2.23553i	−0.237813	+	0.0876172i
$652$		0			0
$653$	10.2012	+	12.1573i	0.399203	+	0.475751i	0.927777	−	0.373136i	$-0.121718\pi$
$653$	10.2012	+	12.1573i	0.399203	+	0.475751i	−0.528574	+	0.848887i	$0.677273\pi$
$654$		0			0
$655$	−7.23490	+	2.63329i	−0.282691	+	0.102891i
$656$		0			0
$657$	4.30885	−	44.6853i	0.168104	−	1.74334i
$658$		0			0
$659$	−15.1582	−	41.6467i	−0.590478	−	1.62232i	−0.769620	−	0.638502i	$-0.779554\pi$
$659$	−15.1582	−	41.6467i	−0.590478	−	1.62232i	0.179142	−	0.983823i	$-0.442668\pi$
$660$		0			0
$661$	−0.475256	+	1.30576i	−0.0184853	+	0.0507880i	−0.948592	−	0.316501i	$-0.897492\pi$
$661$	−0.475256	+	1.30576i	−0.0184853	+	0.0507880i	0.930107	+	0.367289i	$0.119714\pi$
$662$		0			0
$663$	16.5503	−	2.10432i	0.642761	−	0.0817250i
$664$		0			0
$665$	−4.63189	−	3.49303i	−0.179617	−	0.135454i
$666$		0			0
$667$	−1.73907	−	3.01216i	−0.0673371	−	0.116631i
$668$		0			0
$669$	14.6283	+	3.31109i	0.565562	+	0.128014i
$670$		0			0
$671$	−3.75723	−	21.3083i	−0.145046	−	0.822598i
$672$		0			0
$673$	−6.81767	−	5.72071i	−0.262802	−	0.220517i	0.501860	−	0.864949i	$-0.332649\pi$
$673$	−6.81767	−	5.72071i	−0.262802	−	0.220517i	−0.764662	+	0.644432i	$0.777094\pi$
$674$		0			0
$675$	6.14044	−	18.6087i	0.236346	−	0.716249i
$676$		0			0
$677$	11.3843	−	4.14353i	0.437532	−	0.159249i	−0.113856	−	0.993497i	$-0.536320\pi$
$677$	11.3843	−	4.14353i	0.437532	−	0.159249i	0.551389	+	0.834248i	$0.314098\pi$
$678$		0			0
$679$	36.6755	−	1.90869i	1.40748	−	0.0732487i
$680$		0			0
$681$	38.1009	+	35.2250i	1.46003	+	1.34982i
$682$		0			0
$683$		−	51.3039i		−	1.96309i	−0.191234	−	0.981545i	$-0.561249\pi$
$683$		−	51.3039i		−	1.96309i	0.191234	−	0.981545i	$-0.438751\pi$
$684$		0			0
$685$	20.7363	−	11.9721i	0.792293	−	0.457431i
$686$		0			0
$687$	27.2874	−	3.46950i	1.04108	−	0.132370i
$688$		0			0
$689$	19.1054	+	6.95381i	0.727859	+	0.264919i
$690$		0			0
$691$	−43.3367	−	7.64143i	−1.64861	−	0.290694i	−0.729287	−	0.684207i	$-0.760148\pi$
$691$	−43.3367	−	7.64143i	−1.64861	−	0.290694i	−0.919319	+	0.393514i	$0.871259\pi$
$692$		0			0
$693$	−9.52233	−	18.3146i	−0.361723	−	0.695714i
$694$		0			0
$695$	8.94100	−	10.6555i	0.339152	−	0.404185i
$696$		0			0
$697$	3.69382	+	20.9487i	0.139913	+	0.793488i
$698$		0			0
$699$	0.339990	−	7.06815i	0.0128596	−	0.267342i
$700$		0			0
$701$			45.5828i			1.72164i	0.508909	+	0.860820i	$0.330049\pi$
$701$			45.5828i			1.72164i	−0.508909	+	0.860820i	$0.669951\pi$
$702$		0			0
$703$	5.09093	−	2.93925i	0.192008	−	0.110856i
$704$		0			0
$705$	−20.2803	−	0.975518i	−0.763802	−	0.0367401i
$706$		0			0
$707$	1.43015	+	27.4804i	0.0537864	+	1.03351i
$708$		0			0
$709$	35.5581	+	29.8368i	1.33541	+	1.12054i	0.982780	+	0.184781i	$0.0591574\pi$
$709$	35.5581	+	29.8368i	1.33541	+	1.12054i	0.352631	+	0.935762i	$0.385287\pi$
$710$		0			0
$711$	19.6576	−	5.08094i	0.737218	−	0.190550i
$712$		0			0
$713$	1.89462	−	0.689584i	0.0709539	−	0.0258251i
$714$		0			0
$715$	9.78426	−	8.20997i	0.365911	−	0.307036i
$716$		0			0
$717$	39.4706	−	5.01856i	1.47406	−	0.187422i
$718$		0			0
$719$	30.1807			1.12555			0.562775	−	0.826610i	$-0.309734\pi$
$719$	30.1807			1.12555			0.562775	+	0.826610i	$0.309734\pi$
$720$		0			0
$721$	28.7677	−	12.1988i	1.07136	−	0.454307i
$722$		0			0
$723$	−8.74446	−	1.97930i	−0.325210	−	0.0736108i
$724$		0			0
$725$	−5.90083	−	7.03233i	−0.219151	−	0.261174i
$726$		0			0
$727$	−13.6781	+	16.3009i	−0.507293	+	0.604568i	−0.957527	−	0.288342i	$-0.906896\pi$
$727$	−13.6781	+	16.3009i	−0.507293	+	0.604568i	0.450235	+	0.892910i	$0.351340\pi$
$728$		0			0
$729$	25.8850	+	7.67899i	0.958704	+	0.284407i
$730$		0			0
$731$	−4.25453	+	24.1287i	−0.157360	+	0.892431i
$732$		0			0
$733$	−3.39264	+	9.32121i	−0.125310	+	0.344287i	−0.986446	−	0.164089i	$-0.947532\pi$
$733$	−3.39264	+	9.32121i	−0.125310	+	0.344287i	0.861135	+	0.508376i	$0.169754\pi$
$734$		0			0
$735$	13.4191	−	0.751268i	0.494971	−	0.0277110i
$736$		0			0
$737$	1.06617	−	0.615555i	0.0392730	−	0.0226743i
$738$		0			0
$739$	14.7406	−	25.5315i	0.542243	−	0.939192i	−0.456532	−	0.889707i	$-0.650909\pi$
$739$	14.7406	−	25.5315i	0.542243	−	0.939192i	0.998775	−	0.0494848i	$-0.0157579\pi$
$740$		0			0
$741$	−13.9976	−	5.87082i	−0.514216	−	0.215670i
$742$		0			0
$743$	−15.0431	−	17.9277i	−0.551879	−	0.657703i	0.415928	−	0.909397i	$-0.363457\pi$
$743$	−15.0431	−	17.9277i	−0.551879	−	0.657703i	−0.967807	+	0.251694i	$0.919012\pi$
$744$		0			0
$745$	6.94497	−	8.27669i	0.254444	−	0.303235i
$746$		0			0
$747$	−2.01889	−	2.05500i	−0.0738675	−	0.0751886i
$748$		0			0
$749$	15.9639	−	14.8757i	0.583309	−	0.543547i
$750$		0			0
$751$	25.7276	−	21.5880i	0.938813	−	0.787758i	−0.0385652	−	0.999256i	$-0.512279\pi$
$751$	25.7276	−	21.5880i	0.938813	−	0.787758i	0.977378	+	0.211498i	$0.0678343\pi$
$752$		0			0
$753$	−4.39900	+	6.83798i	−0.160308	+	0.249190i
$754$		0			0
$755$	3.55471			0.129369
$756$		0			0
$757$	−52.5640			−1.91047			−0.955235	−	0.295847i	$-0.904398\pi$
$757$	−52.5640			−1.91047			−0.955235	+	0.295847i	$0.904398\pi$
$758$		0			0
$759$	2.94654	+	5.72203i	0.106953	+	0.207696i
$760$		0			0
$761$	26.1085	−	21.9076i	0.946433	−	0.794151i	−0.0322603	−	0.999479i	$-0.510271\pi$
$761$	26.1085	−	21.9076i	0.946433	−	0.794151i	0.978693	+	0.205328i	$0.0658261\pi$
$762$		0			0
$763$	0.469894	−	0.108303i	0.0170113	−	0.00392084i
$764$		0			0
$765$	−0.566291	−	7.20796i	−0.0204743	−	0.260604i
$766$		0			0
$767$	4.14963	−	4.94533i	0.149834	−	0.178566i
$768$		0			0
$769$	−31.9548	−	38.0823i	−1.15232	−	1.37328i	−0.915789	−	0.401659i	$-0.868434\pi$
$769$	−31.9548	−	38.0823i	−1.15232	−	1.37328i	−0.236531	−	0.971624i	$-0.576011\pi$
$770$		0			0
$771$	4.03065	+	31.7008i	0.145160	+	1.14168i
$772$		0			0
$773$	1.99541	−	3.45614i	0.0717697	−	0.124309i	−0.827907	−	0.560865i	$-0.810469\pi$
$773$	1.99541	−	3.45614i	0.0717697	−	0.124309i	0.899677	+	0.436556i	$0.143802\pi$
$774$		0			0
$775$	4.60855	−	2.66075i	0.165544	−	0.0955769i
$776$		0			0
$777$	−4.60758	+	12.8157i	−0.165296	+	0.459762i
$778$		0			0
$779$	6.61927	−	18.1863i	0.237160	−	0.651592i
$780$		0			0
$781$	4.36091	−	24.7319i	0.156046	−	0.884979i
$782$		0			0
$783$	9.43847	−	8.42069i	0.337303	−	0.300931i
$784$		0			0
$785$	−2.75947	+	3.28861i	−0.0984898	+	0.117376i
$786$		0			0
$787$	−23.9842	−	28.5832i	−0.854944	−	1.01888i	−0.999568	−	0.0293960i	$-0.990642\pi$
$787$	−23.9842	−	28.5832i	−0.854944	−	1.01888i	0.144624	−	0.989487i	$-0.453803\pi$
$788$		0			0
$789$	−13.3235	−	42.9190i	−0.474329	−	1.52796i
$790$		0			0
$791$	−18.4353	−	13.9025i	−0.655484	−	0.494317i
$792$		0			0
$793$	36.8602			1.30894
$794$		0			0
$795$	3.40791	−	8.12539i	0.120866	−	0.288178i
$796$		0			0
$797$	−28.1915	+	23.6555i	−0.998594	+	0.837920i	−0.986789	−	0.162010i	$-0.948202\pi$
$797$	−28.1915	+	23.6555i	−0.998594	+	0.837920i	−0.0118051	+	0.999930i	$0.503758\pi$
$798$		0			0
$799$	21.6043	−	7.86334i	0.764307	−	0.278185i
$800$		0			0
$801$	20.3803	+	44.7365i	0.720101	+	1.58069i
$802$		0			0
$803$	29.8121	+	25.0153i	1.05205	+	0.882771i
$804$		0			0
$805$	−4.18490	+	0.217793i	−0.147498	+	0.00767618i
$806$		0			0
$807$	−21.5466	−	41.8423i	−0.758477	−	1.47292i
$808$		0			0
$809$	11.0102	−	6.35674i	0.387098	−	0.223491i	−0.293804	−	0.955866i	$-0.594921\pi$
$809$	11.0102	−	6.35674i	0.387098	−	0.223491i	0.680902	+	0.732375i	$0.261588\pi$
$810$		0			0
$811$			9.81361i			0.344603i	0.985044	+	0.172301i	$0.0551203\pi$
$811$			9.81361i			0.344603i	−0.985044	+	0.172301i	$0.944880\pi$
$812$		0			0
$813$	−14.0008	−	9.00693i	−0.491028	−	0.315887i
$814$		0			0
$815$	−0.639232	−	3.62526i	−0.0223913	−	0.126987i
$816$		0			0
$817$	14.3285	−	17.0761i	0.501292	−	0.597417i
$818$		0			0
$819$	33.5431	−	10.5576i	1.17209	−	0.368914i
$820$		0			0
$821$	−10.6712	−	1.88163i	−0.372429	−	0.0656692i	−0.0156987	−	0.999877i	$-0.504997\pi$
$821$	−10.6712	−	1.88163i	−0.372429	−	0.0656692i	−0.356730	+	0.934208i	$0.616108\pi$
$822$		0			0
$823$	−22.1136	−	8.04868i	−0.770830	−	0.280559i	−0.0734867	−	0.997296i	$-0.523413\pi$
$823$	−22.1136	−	8.04868i	−0.770830	−	0.280559i	−0.697344	+	0.716737i	$0.745635\pi$
$824$		0			0
$825$	10.2814	+	13.5226i	0.357951	+	0.470796i
$826$		0			0
$827$	4.95821	−	2.86262i	0.172414	−	0.0995432i	−0.411310	−	0.911496i	$-0.634929\pi$
$827$	4.95821	−	2.86262i	0.172414	−	0.0995432i	0.583724	+	0.811952i	$0.301595\pi$
$828$		0			0
$829$			20.9360i			0.727137i	0.931567	+	0.363569i	$0.118442\pi$
$829$			20.9360i			0.727137i	−0.931567	+	0.363569i	$0.881558\pi$
$830$		0			0
$831$	15.3670	−	4.77043i	0.533075	−	0.165484i
$832$		0			0
$833$	−13.6834	+	6.66153i	−0.474103	+	0.230808i
$834$		0			0
$835$	8.02657	−	2.92143i	0.277771	−	0.101100i
$836$		0			0
$837$	3.85707	+	6.23580i	0.133320	+	0.215541i
$838$		0			0
$839$	−9.58032	−	8.03885i	−0.330750	−	0.277532i	0.462256	−	0.886747i	$-0.347040\pi$
$839$	−9.58032	−	8.03885i	−0.330750	−	0.277532i	−0.793005	+	0.609215i	$0.791485\pi$
$840$		0			0
$841$	4.00682	+	22.7238i	0.138166	+	0.783579i
$842$		0			0
$843$	8.94794	+	28.8240i	0.308184	+	0.992752i
$844$		0			0
$845$	3.67398	+	6.36353i	0.126389	+	0.218912i
$846$		0			0
$847$	−11.1247	−	1.37006i	−0.382250	−	0.0470758i
$848$		0			0
$849$	−6.36386	+	15.1732i	−0.218407	+	0.520743i
$850$		0			0
$851$	1.45232	−	3.99021i	0.0497848	−	0.136782i
$852$		0			0
$853$	10.5214	+	28.9073i	0.360246	+	0.989768i	0.978942	+	0.204137i	$0.0654390\pi$
$853$	10.5214	+	28.9073i	0.360246	+	0.989768i	−0.618696	+	0.785630i	$0.712339\pi$
$854$		0			0
$855$	−2.83276	+	5.93692i	−0.0968783	+	0.203038i
$856$		0			0
$857$	−36.8832	+	13.4244i	−1.25991	+	0.458568i	−0.883737	−	0.467984i	$-0.844981\pi$
$857$	−36.8832	+	13.4244i	−1.25991	+	0.458568i	−0.376168	+	0.926552i	$0.622758\pi$
$858$		0			0
$859$	23.8079	+	28.3731i	0.812315	+	0.968079i	0.999900	−	0.0141696i	$-0.00451048\pi$
$859$	23.8079	+	28.3731i	0.812315	+	0.968079i	−0.187585	+	0.982248i	$0.560066\pi$
$860$		0			0
$861$	15.5005	+	42.0720i	0.528256	+	1.43381i
$862$		0			0
$863$	−34.1803	−	19.7340i	−1.16351	−	0.671754i	−0.211369	−	0.977406i	$-0.567792\pi$
$863$	−34.1803	−	19.7340i	−1.16351	−	0.671754i	−0.952143	+	0.305652i	$0.901126\pi$
$864$		0			0
$865$	−13.8362	−	23.9651i	−0.470446	−	0.814837i
$866$		0			0
$867$	−9.73212	−	18.8992i	−0.330520	−	0.641852i
$868$		0			0
$869$	−6.01990	+	16.5395i	−0.204211	+	0.561065i
$870$		0			0
$871$	0.717313	+	1.97080i	0.0243052	+	0.0667780i
$872$		0			0
$873$	−10.4209	−	40.3174i	−0.352695	−	1.36454i
$874$		0			0
$875$	−25.0675	+	5.77768i	−0.847437	+	0.195321i
$876$		0			0
$877$	4.52435	+	25.6588i	0.152776	+	0.866438i	0.960791	+	0.277275i	$0.0894313\pi$
$877$	4.52435	+	25.6588i	0.152776	+	0.866438i	−0.808014	+	0.589163i	$0.799458\pi$
$878$		0			0
$879$	−4.57219	−	35.9599i	−0.154216	−	1.21290i
$880$		0			0
$881$	2.38743	+	4.13514i	0.0804345	+	0.139317i	0.903437	−	0.428722i	$-0.141036\pi$
$881$	2.38743	+	4.13514i	0.0804345	+	0.139317i	−0.823002	+	0.568038i	$0.807703\pi$
$882$		0			0
$883$	−13.0553	+	22.6124i	−0.439345	+	0.760969i	−0.997639	−	0.0686748i	$-0.978123\pi$
$883$	−13.0553	+	22.6124i	−0.439345	+	0.760969i	0.558294	+	0.829643i	$0.311456\pi$
$884$		0			0
$885$	−2.05429	−	1.89922i	−0.0690541	−	0.0638416i
$886$		0			0
$887$	45.3711	+	16.5137i	1.52341	+	0.554476i	0.961997	−	0.273059i	$-0.0880354\pi$
$887$	45.3711	+	16.5137i	1.52341	+	0.554476i	0.561414	+	0.827535i	$0.310258\pi$
$888$		0			0
$889$	−6.90124	−	7.40608i	−0.231460	−	0.248392i
$890$		0			0
$891$	−18.1939	+	14.7249i	−0.609519	+	0.493304i
$892$		0			0
$893$	−20.5996	−	3.63227i	−0.689341	−	0.121549i
$894$		0			0
$895$	11.2189	−	1.97820i	0.375008	−	0.0661240i
$896$		0			0
$897$	−10.4714	+	3.25068i	−0.349631	+	0.108537i
$898$		0			0
$899$	3.43499			0.114563
$900$		0			0
$901$			9.97721i			0.332389i
$902$		0			0
$903$	0.203007	+	51.6422i	0.00675564	+	1.71855i
$904$		0			0
$905$	0.298266	−	0.0525923i	0.00991469	−	0.00174823i
$906$		0			0
$907$	−12.7177	−	10.6715i	−0.422286	−	0.354340i	0.406746	−	0.913541i	$-0.366663\pi$
$907$	−12.7177	−	10.6715i	−0.422286	−	0.354340i	−0.829032	+	0.559201i	$0.811108\pi$
$908$		0			0
$909$	30.2093	−	7.80826i	1.00198	−	0.258984i
$910$		0			0
$911$	39.9656	+	7.04701i	1.32412	+	0.233478i	0.790612	−	0.612317i	$-0.209762\pi$
$911$	39.9656	+	7.04701i	1.32412	+	0.233478i	0.533508	+	0.845795i	$0.320874\pi$
$912$		0			0
$913$	2.45939	−	0.433657i	0.0813939	−	0.0143519i
$914$		0			0
$915$	0.767495	−	15.9557i	0.0253726	−	0.527478i
$916$		0			0
$917$	11.0643	−	14.6717i	0.365376	−	0.484503i
$918$		0			0
$919$	−10.8765	+	18.8387i	−0.358783	+	0.621431i	−0.987758	−	0.155995i	$-0.950142\pi$
$919$	−10.8765	+	18.8387i	−0.358783	+	0.621431i	0.628975	+	0.777426i	$0.283475\pi$
$920$		0			0
$921$	6.80401	−	3.50371i	0.224200	−	0.115451i
$922$		0			0
$923$	40.2024	+	14.6325i	1.32328	+	0.481634i
$924$		0			0
$925$	1.94616	−	11.0372i	0.0639893	−	0.362901i
$926$		0			0
$927$	−20.0644	−	29.2024i	−0.659001	−	0.959132i
$928$		0			0
$929$	5.62264	−	31.8875i	0.184473	−	1.04620i	−0.742158	−	0.670225i	$-0.766198\pi$
$929$	5.62264	−	31.8875i	0.184473	−	1.04620i	0.926631	−	0.375972i	$-0.122691\pi$
$930$		0			0
$931$	13.8119	+	0.975932i	0.452666	+	0.0319849i
$932$		0			0
$933$	−4.54848	−	1.90770i	−0.148911	−	0.0624553i
$934$		0			0
$935$	5.42804	+	3.13388i	0.177516	+	0.102489i
$936$		0			0
$937$	−49.6769	−	28.6810i	−1.62287	−	0.936967i	−0.986146	−	0.165878i	$-0.946954\pi$
$937$	−49.6769	−	28.6810i	−1.62287	−	0.936967i	−0.636727	−	0.771089i	$-0.719712\pi$
$938$		0			0
$939$	−19.5210	−	4.41854i	−0.637043	−	0.144194i
$940$		0			0
$941$	−0.0695343	+	0.0583462i	−0.00226675	+	0.00190203i	−0.643920	−	0.765093i	$-0.722693\pi$
$941$	−0.0695343	+	0.0583462i	−0.00226675	+	0.00190203i	0.641654	+	0.766995i	$0.278249\pi$
$942$		0			0
$943$	−4.78138	−	13.1367i	−0.155703	−	0.427791i
$944$		0			0
$945$	−3.87167	−	14.7396i	−0.125945	−	0.479481i
$946$		0			0
$947$	9.82947	+	27.0062i	0.319415	+	0.877585i	0.990661	+	0.136350i	$0.0435372\pi$
$947$	9.82947	+	27.0062i	0.319415	+	0.877585i	−0.671246	+	0.741235i	$0.734241\pi$
$948$		0			0
$949$	−50.7869	+	42.6153i	−1.64861	+	1.38335i
$950$		0			0
$951$	−21.7912	+	23.5703i	−0.706627	+	0.764320i
$952$		0			0
$953$	50.8525	+	29.3597i	1.64727	+	0.951055i	0.978149	+	0.207905i	$0.0666646\pi$
$953$	50.8525	+	29.3597i	1.64727	+	0.951055i	0.669126	+	0.743149i	$0.266669\pi$
$954$		0			0
$955$	−10.0202	−	5.78516i	−0.324245	−	0.187203i
$956$		0			0
$957$	1.38305	+	10.8776i	0.0447076	+	0.351622i
$958$		0			0
$959$	−25.9635	+	50.9103i	−0.838404	+	1.64398i
$960$		0			0
$961$	5.03733	−	28.5681i	0.162494	−	0.921552i
$962$		0			0
$963$	−20.1410	−	14.3706i	−0.649034	−	0.463085i
$964$		0			0
$965$	−0.748129	+	4.24285i	−0.0240831	+	0.136582i
$966$		0			0
$967$	54.5281	+	19.8466i	1.75351	+	0.638224i	0.999819	−	0.0190105i	$-0.00605161\pi$
$967$	54.5281	+	19.8466i	1.75351	+	0.638224i	0.753686	+	0.657234i	$0.228274\pi$
$968$		0			0
$969$	0.357881	−	7.44008i	0.0114968	−	0.239010i
$970$		0			0
$971$	−4.34443	+	7.52477i	−0.139419	+	0.241481i	−0.927277	−	0.374376i	$-0.877857\pi$
$971$	−4.34443	+	7.52477i	−0.139419	+	0.241481i	0.787858	+	0.615857i	$0.211190\pi$
$972$		0			0
$973$	−4.05793	+	32.9500i	−0.130091	+	1.05633i
$974$		0			0
$975$	−25.7281	+	13.2486i	−0.823959	+	0.424296i
$976$		0			0
$977$	−47.3641	+	8.35156i	−1.51531	+	0.267190i	−0.868588	−	0.495535i	$-0.834972\pi$
$977$	−47.3641	+	8.35156i	−1.51531	+	0.267190i	−0.646723	+	0.762725i	$0.723861\pi$
$978$		0			0
$979$	−41.9689	−	7.40025i	−1.34133	−	0.236513i
$980$		0			0
$981$	−0.226678	−	0.497578i	−0.00723726	−	0.0158864i
$982$		0			0
$983$	−0.884960	−	0.742570i	−0.0282258	−	0.0236843i	0.628566	−	0.777757i	$-0.283642\pi$
$983$	−0.884960	−	0.742570i	−0.0282258	−	0.0236843i	−0.656791	+	0.754072i	$0.728087\pi$
$984$		0			0
$985$	19.4598	−	3.43129i	0.620042	−	0.109330i
$986$		0			0
$987$	41.8719	−	24.3947i	1.33280	−	0.776492i
$988$		0			0
$989$		−	16.1019i		−	0.512011i
$990$		0			0
$991$	−50.8896			−1.61656			−0.808281	−	0.588797i	$-0.799602\pi$
$991$	−50.8896			−1.61656			−0.808281	+	0.588797i	$0.799602\pi$
$992$		0			0
$993$	−36.9420	−	34.1535i	−1.17232	−	1.08383i
$994$		0			0
$995$	−1.12194	+	0.197829i	−0.0355680	+	0.00627160i
$996$		0			0
$997$	−26.4305	−	4.66040i	−0.837061	−	0.147596i	−0.261344	−	0.965246i	$-0.584166\pi$
$997$	−26.4305	−	4.66040i	−0.837061	−	0.147596i	−0.575717	+	0.817649i	$0.695277\pi$
$998$		0			0
$999$	15.2821	+	2.21898i	0.483503	+	0.0702054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ca.a.173.1	✓	144
7.3	odd	6		756.2.ck.a.605.8	yes	144
27.5	odd	18		756.2.ck.a.5.8	yes	144
189.59	even	18	inner	756.2.ca.a.437.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.1	✓	144	1.1	even	1	trivial
756.2.ca.a.437.1	yes	144	189.59	even	18	inner
756.2.ck.a.5.8	yes	144	27.5	odd	18
756.2.ck.a.605.8	yes	144	7.3	odd	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73005 - 0.0832183i) q^{3} +(0.849177 - 0.712544i) q^{5} +(-0.774464 + 2.52986i) q^{7} +(2.98615 + 0.287944i) q^{9} +O(q^{10})\)	\(q+(-1.73005 - 0.0832183i) q^{3} +(0.849177 - 0.712544i) q^{5} +(-0.774464 + 2.52986i) q^{7} +(2.98615 + 0.287944i) q^{9} +(-1.67168 + 1.99223i) q^{11} +(-2.84782 - 3.39390i) q^{13} +(-1.52842 + 1.16207i) q^{15} +(1.08706 - 1.88284i) q^{17} +(-1.71304 + 0.989022i) q^{19} +(1.55039 - 4.31234i) q^{21} +(-0.488687 + 1.34266i) q^{23} +(-0.654859 + 3.71389i) q^{25} +(-5.14223 - 0.746660i) q^{27} +(-1.56472 + 1.86476i) q^{29} +(-0.907035 - 1.08096i) q^{31} +(3.05788 - 3.30754i) q^{33} +(1.14498 + 2.70014i) q^{35} -2.97188 q^{37} +(4.64444 + 6.10861i) q^{39} +(-7.49508 + 6.28912i) q^{41} +(-10.5897 + 3.85434i) q^{43} +(2.74094 - 1.88325i) q^{45} +(8.10077 + 6.79735i) q^{47} +(-5.80041 - 3.91858i) q^{49} +(-2.03735 + 3.16695i) q^{51} +(-3.97427 + 2.29454i) q^{53} +2.88290i q^{55} +(3.04594 - 1.56850i) q^{57} +(0.253027 + 1.43499i) q^{59} +(-5.34786 + 6.37333i) q^{61} +(-3.04112 + 7.33155i) q^{63} +(-4.83660 - 0.852824i) q^{65} +(-0.444834 - 0.161906i) q^{67} +(0.957186 - 2.28219i) q^{69} +(-8.36281 + 4.82827i) q^{71} -14.9642i q^{73} +(1.44200 - 6.37072i) q^{75} +(-3.74541 - 5.77203i) q^{77} +(6.35972 - 2.31475i) q^{79} +(8.83418 + 1.71969i) q^{81} +(-0.735605 - 0.617246i) q^{83} +(-0.418502 - 2.37344i) q^{85} +(2.86222 - 3.09591i) q^{87} +(8.19334 + 14.1913i) q^{89} +(10.7916 - 4.57614i) q^{91} +(1.47926 + 1.94560i) q^{93} +(-0.749949 + 2.06047i) q^{95} +(-4.74751 - 13.0437i) q^{97} +(-5.56553 + 5.46774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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