LMFDB - Embedded newform 234.2.h.d.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(55,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("234.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.2
Root			$-1.58114 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	234.55
Dual form			234.2.h.d.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +1.00000 q^{8} +(-2.08114 - 3.60464i) q^{10} +(0.581139 + 1.00656i) q^{11} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(2.58114 - 4.47066i) q^{19} +(-2.08114 + 3.60464i) q^{20} +(0.581139 - 1.00656i) q^{22} +(-3.58114 - 6.20271i) q^{23} +12.3246 q^{25} +(3.08114 - 1.87259i) q^{26} +(-1.58114 - 2.73861i) q^{28} +(0.918861 + 1.59151i) q^{29} -6.32456 q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-6.58114 + 11.3989i) q^{35} +(-1.91886 - 3.32357i) q^{37} -5.16228 q^{38} +4.16228 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-4.58114 + 7.93477i) q^{43} -1.16228 q^{44} +(-3.58114 + 6.20271i) q^{46} +4.83772 q^{47} +(-1.50000 - 2.59808i) q^{49} +(-6.16228 - 10.6734i) q^{50} +(-3.16228 - 1.73205i) q^{52} -12.4868 q^{53} +(2.41886 + 4.18959i) q^{55} +(-1.58114 + 2.73861i) q^{56} +(0.918861 - 1.59151i) q^{58} +(1.16228 - 2.01312i) q^{59} +(-0.0811388 + 0.140537i) q^{61} +(3.16228 + 5.47723i) q^{62} +1.00000 q^{64} +(0.337722 + 15.0035i) q^{65} +(1.41886 + 2.45754i) q^{67} +(1.50000 + 2.59808i) q^{68} +13.1623 q^{70} +(3.58114 - 6.20271i) q^{71} -1.00000 q^{73} +(-1.91886 + 3.32357i) q^{74} +(2.58114 + 4.47066i) q^{76} -3.67544 q^{77} -4.00000 q^{79} +(-2.08114 - 3.60464i) q^{80} +(-1.50000 + 2.59808i) q^{82} -3.48683 q^{83} +(6.24342 - 10.8139i) q^{85} +9.16228 q^{86} +(0.581139 + 1.00656i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-10.0000 - 5.47723i) q^{91} +7.16228 q^{92} +(-2.41886 - 4.18959i) q^{94} +(10.7434 - 18.6081i) q^{95} +(2.00000 - 3.46410i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} - 4 q^{22} - 8 q^{23} + 24 q^{25} + 6 q^{26} + 10 q^{29} - 2 q^{32} - 12 q^{34} - 20 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^16 + 6 * q^17 + 4 * q^19 - 2 * q^20 - 4 * q^22 - 8 * q^23 + 24 * q^25 + 6 * q^26 + 10 * q^29 - 2 * q^32 - 12 * q^34 - 20 * q^35 - 14 * q^37 - 8 * q^38 + 4 * q^40 - 6 * q^41 - 12 * q^43 + 8 * q^44 - 8 * q^46 + 32 * q^47 - 6 * q^49 - 12 * q^50 - 12 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 + 6 * q^61 + 4 * q^64 + 14 * q^65 + 12 * q^67 + 6 * q^68 + 40 * q^70 + 8 * q^71 - 4 * q^73 - 14 * q^74 + 4 * q^76 - 40 * q^77 - 16 * q^79 - 2 * q^80 - 6 * q^82 + 24 * q^83 + 6 * q^85 + 24 * q^86 - 4 * q^88 - 24 * q^89 - 40 * q^91 + 16 * q^92 - 16 * q^94 + 24 * q^95 + 8 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	4.16228			1.86143			0.930714	−	0.365749i	$-0.119187\pi$
$5$	4.16228			1.86143			0.930714	+	0.365749i	$0.119187\pi$
$6$		0			0
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	0.395558	+	0.918441i	$0.370551\pi$
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	−0.993172	+	0.116657i	$0.962782\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.08114	−	3.60464i	−0.658114	−	1.13989i
$11$	0.581139	+	1.00656i	0.175220	+	0.303490i	0.940237	−	0.340520i	$-0.110603\pi$
$11$	0.581139	+	1.00656i	0.175220	+	0.303490i	−0.765017	+	0.644010i	$0.777270\pi$
$12$		0			0
$13$	0.0811388	+	3.60464i	0.0225039	+	0.999747i
$13$	0.0811388	+	3.60464i	0.0225039	+	0.999747i
$14$	3.16228			0.845154
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	2.58114	−	4.47066i	0.592154	−	1.02564i	−0.401788	−	0.915733i	$-0.631611\pi$
$19$	2.58114	−	4.47066i	0.592154	−	1.02564i	0.993942	−	0.109908i	$-0.0350556\pi$
$20$	−2.08114	+	3.60464i	−0.465357	+	0.806022i
$21$		0			0
$22$	0.581139	−	1.00656i	0.123899	−	0.214600i
$23$	−3.58114	−	6.20271i	−0.746719	−	1.29336i	−0.949387	−	0.314108i	$-0.898295\pi$
$23$	−3.58114	−	6.20271i	−0.746719	−	1.29336i	0.202668	−	0.979247i	$-0.435039\pi$
$24$		0			0
$25$	12.3246			2.46491
$26$	3.08114	−	1.87259i	0.604261	−	0.367245i
$27$		0			0
$28$	−1.58114	−	2.73861i	−0.298807	−	0.517549i
$29$	0.918861	+	1.59151i	0.170628	+	0.295537i	0.938640	−	0.344899i	$-0.112087\pi$
$29$	0.918861	+	1.59151i	0.170628	+	0.295537i	−0.768011	+	0.640436i	$0.778754\pi$
$30$		0			0
$31$	−6.32456			−1.13592			−0.567962	−	0.823055i	$-0.692268\pi$
$31$	−6.32456			−1.13592			−0.567962	+	0.823055i	$0.692268\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$	−6.58114	+	11.3989i	−1.11242	+	1.92676i
$36$		0			0
$37$	−1.91886	−	3.32357i	−0.315459	−	0.546391i	0.664076	−	0.747665i	$-0.268825\pi$
$37$	−1.91886	−	3.32357i	−0.315459	−	0.546391i	−0.979535	+	0.201274i	$0.935492\pi$
$38$	−5.16228			−0.837432
$39$		0			0
$40$	4.16228			0.658114
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−4.58114	+	7.93477i	−0.698617	+	1.21004i	0.270329	+	0.962768i	$0.412868\pi$
$43$	−4.58114	+	7.93477i	−0.698617	+	1.21004i	−0.968946	+	0.247272i	$0.920466\pi$
$44$	−1.16228			−0.175220
$45$		0			0
$46$	−3.58114	+	6.20271i	−0.528010	+	0.914540i
$47$	4.83772			0.705654			0.352827	−	0.935689i	$-0.385220\pi$
$47$	4.83772			0.705654			0.352827	+	0.935689i	$0.385220\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−6.16228	−	10.6734i	−0.871478	−	1.50944i
$51$		0			0
$52$	−3.16228	−	1.73205i	−0.438529	−	0.240192i
$53$	−12.4868			−1.71520			−0.857599	−	0.514319i	$-0.828045\pi$
$53$	−12.4868			−1.71520			−0.857599	+	0.514319i	$0.828045\pi$
$54$		0			0
$55$	2.41886	+	4.18959i	0.326159	+	0.564924i
$56$	−1.58114	+	2.73861i	−0.211289	+	0.365963i
$57$		0			0
$58$	0.918861	−	1.59151i	0.120652	−	0.208976i
$59$	1.16228	−	2.01312i	0.151316	−	0.262086i	−0.780396	−	0.625286i	$-0.784982\pi$
$59$	1.16228	−	2.01312i	0.151316	−	0.262086i	0.931711	+	0.363200i	$0.118316\pi$
$60$		0			0
$61$	−0.0811388	+	0.140537i	−0.0103888	+	0.0179939i	−0.871173	−	0.490976i	$-0.836640\pi$
$61$	−0.0811388	+	0.140537i	−0.0103888	+	0.0179939i	0.860784	+	0.508970i	$0.169974\pi$
$62$	3.16228	+	5.47723i	0.401610	+	0.695608i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.337722	+	15.0035i	0.0418893	+	1.86096i
$66$		0			0
$67$	1.41886	+	2.45754i	0.173341	+	0.300236i	0.939586	−	0.342313i	$-0.111210\pi$
$67$	1.41886	+	2.45754i	0.173341	+	0.300236i	−0.766245	+	0.642549i	$0.777877\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	13.1623			1.57319
$71$	3.58114	−	6.20271i	0.425003	−	0.736127i	−0.571418	−	0.820659i	$-0.693606\pi$
$71$	3.58114	−	6.20271i	0.425003	−	0.736127i	0.996421	+	0.0845326i	$0.0269397\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−1.91886	+	3.32357i	−0.223063	+	0.386357i
$75$		0			0
$76$	2.58114	+	4.47066i	0.296077	+	0.512820i
$77$	−3.67544			−0.418856
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−2.08114	−	3.60464i	−0.232678	−	0.403011i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−3.48683			−0.382730			−0.191365	−	0.981519i	$-0.561291\pi$
$83$	−3.48683			−0.382730			−0.191365	+	0.981519i	$0.561291\pi$
$84$		0			0
$85$	6.24342	−	10.8139i	0.677194	−	1.17293i
$86$	9.16228			0.987994
$87$		0			0
$88$	0.581139	+	1.00656i	0.0619496	+	0.107300i
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	−10.0000	−	5.47723i	−1.04828	−	0.574169i
$92$	7.16228			0.746719
$93$		0			0
$94$	−2.41886	−	4.18959i	−0.249486	−	0.432123i
$95$	10.7434	−	18.6081i	1.10225	−	1.90916i
$96$		0			0
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	−0.746447	−	0.665445i	$-0.768242\pi$
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	0.949516	+	0.313719i	$0.101575\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$		0			0
$100$	−6.16228	+	10.6734i	−0.616228	+	1.06734i
$101$	−3.91886	−	6.78767i	−0.389941	−	0.675398i	0.602500	−	0.798119i	$-0.294171\pi$
$101$	−3.91886	−	6.78767i	−0.389941	−	0.675398i	−0.992441	+	0.122721i	$0.960838\pi$
$102$		0			0
$103$	−15.8114			−1.55794			−0.778971	−	0.627060i	$-0.784258\pi$
$103$	−15.8114			−1.55794			−0.778971	+	0.627060i	$0.784258\pi$
$104$	0.0811388	+	3.60464i	0.00795632	+	0.353464i
$105$		0			0
$106$	6.24342	+	10.8139i	0.606414	+	1.05034i
$107$	8.90569	+	15.4251i	0.860946	+	1.49120i	0.871017	+	0.491253i	$0.163461\pi$
$107$	8.90569	+	15.4251i	0.860946	+	1.49120i	−0.0100711	+	0.999949i	$0.503206\pi$
$108$		0			0
$109$	6.64911			0.636869			0.318435	−	0.947945i	$-0.396843\pi$
$109$	6.64911			0.636869			0.318435	+	0.947945i	$0.396843\pi$
$110$	2.41886	−	4.18959i	0.230629	−	0.399462i
$111$		0			0
$112$	3.16228			0.298807
$113$	−3.33772	+	5.78110i	−0.313987	+	0.543841i	−0.979222	−	0.202793i	$-0.934998\pi$
$113$	−3.33772	+	5.78110i	−0.313987	+	0.543841i	0.665235	+	0.746634i	$0.268331\pi$
$114$		0			0
$115$	−14.9057	−	25.8174i	−1.38996	−	2.40749i
$116$	−1.83772			−0.170628
$117$		0			0
$118$	−2.32456			−0.213993
$119$	4.74342	+	8.21584i	0.434828	+	0.753145i
$120$		0			0
$121$	4.82456	−	8.35637i	0.438596	−	0.759670i
$122$	0.162278			0.0146919
$123$		0			0
$124$	3.16228	−	5.47723i	0.283981	−	0.491869i
$125$	30.4868			2.72683
$126$		0			0
$127$	9.16228	+	15.8695i	0.813021	+	1.40819i	0.910740	+	0.412979i	$0.135512\pi$
$127$	9.16228	+	15.8695i	0.813021	+	1.40819i	−0.0977198	+	0.995214i	$0.531155\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	12.8246	−	7.79423i	1.12479	−	0.683599i
$131$	16.6491			1.45464			0.727320	−	0.686299i	$-0.240766\pi$
$131$	16.6491			1.45464			0.727320	+	0.686299i	$0.240766\pi$
$132$		0			0
$133$	8.16228	+	14.1375i	0.707759	+	1.22587i
$134$	1.41886	−	2.45754i	0.122571	−	0.212299i
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	3.16228	−	5.47723i	0.268221	−	0.464572i	−0.700182	−	0.713965i	$-0.746898\pi$
$139$	3.16228	−	5.47723i	0.268221	−	0.464572i	0.968402	+	0.249393i	$0.0802310\pi$
$140$	−6.58114	−	11.3989i	−0.556208	−	0.963380i
$141$		0			0
$142$	−7.16228			−0.601045
$143$	−3.58114	+	2.17647i	−0.299470	+	0.182005i
$144$		0			0
$145$	3.82456	+	6.62432i	0.317612	+	0.550120i
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$		0			0
$148$	3.83772			0.315459
$149$	−0.243416	+	0.421610i	−0.0199415	+	0.0345396i	−0.875824	−	0.482631i	$-0.839681\pi$
$149$	−0.243416	+	0.421610i	−0.0199415	+	0.0345396i	0.855882	+	0.517170i	$0.173015\pi$
$150$		0			0
$151$	0.837722			0.0681729			0.0340864	−	0.999419i	$-0.489148\pi$
$151$	0.837722			0.0681729			0.0340864	+	0.999419i	$0.489148\pi$
$152$	2.58114	−	4.47066i	0.209358	−	0.362619i
$153$		0			0
$154$	1.83772	+	3.18303i	0.148088	+	0.256496i
$155$	−26.3246			−2.11444
$156$		0			0
$157$	−10.4868			−0.836940			−0.418470	−	0.908231i	$-0.637434\pi$
$157$	−10.4868			−0.836940			−0.418470	+	0.908231i	$0.637434\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$	−2.08114	+	3.60464i	−0.164528	+	0.284972i
$161$	22.6491			1.78500
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	1.74342	+	3.01969i	0.135315	+	0.234373i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−12.9868	+	0.584952i	−0.998987	+	0.0449963i
$170$	−12.4868			−0.957696
$171$		0			0
$172$	−4.58114	−	7.93477i	−0.349309	−	0.605020i
$173$	−11.3246	+	19.6147i	−0.860990	+	1.49128i	0.00998448	+	0.999950i	$0.496822\pi$
$173$	−11.3246	+	19.6147i	−0.860990	+	1.49128i	−0.870974	+	0.491328i	$0.836512\pi$
$174$		0			0
$175$	−19.4868	+	33.7522i	−1.47307	+	2.55143i
$176$	0.581139	−	1.00656i	0.0438050	−	0.0758725i
$177$		0			0
$178$	−6.00000	+	10.3923i	−0.449719	+	0.778936i
$179$	−7.74342	−	13.4120i	−0.578770	−	1.00246i	−0.995621	−	0.0934843i	$-0.970200\pi$
$179$	−7.74342	−	13.4120i	−0.578770	−	1.00246i	0.416851	−	0.908975i	$-0.363134\pi$
$180$		0			0
$181$	3.83772			0.285256			0.142628	−	0.989776i	$-0.454445\pi$
$181$	3.83772			0.285256			0.142628	+	0.989776i	$0.454445\pi$
$182$	0.256584	+	11.3989i	0.0190192	+	0.844940i
$183$		0			0
$184$	−3.58114	−	6.20271i	−0.264005	−	0.457270i
$185$	−7.98683	−	13.8336i	−0.587204	−	1.01707i
$186$		0			0
$187$	3.48683			0.254982
$188$	−2.41886	+	4.18959i	−0.176414	+	0.305557i
$189$		0			0
$190$	−21.4868			−1.55882
$191$	−7.16228	+	12.4054i	−0.518244	+	0.897625i	0.481531	+	0.876429i	$0.340081\pi$
$191$	−7.16228	+	12.4054i	−0.518244	+	0.897625i	−0.999775	+	0.0211963i	$0.993252\pi$
$192$		0			0
$193$	9.98683	+	17.2977i	0.718868	+	1.24512i	0.961449	+	0.274985i	$0.0886728\pi$
$193$	9.98683	+	17.2977i	0.718868	+	1.24512i	−0.242581	+	0.970131i	$0.577994\pi$
$194$	−4.00000			−0.287183
$195$		0			0
$196$	3.00000			0.214286
$197$	−9.48683	−	16.4317i	−0.675909	−	1.17071i	−0.976202	−	0.216862i	$-0.930418\pi$
$197$	−9.48683	−	16.4317i	−0.675909	−	1.17071i	0.300293	−	0.953847i	$-0.402915\pi$
$198$		0			0
$199$	3.25658	−	5.64057i	0.230853	−	0.399849i	−0.727206	−	0.686419i	$-0.759182\pi$
$199$	3.25658	−	5.64057i	0.230853	−	0.399849i	0.958059	+	0.286570i	$0.0925150\pi$
$200$	12.3246			0.871478
$201$		0			0
$202$	−3.91886	+	6.78767i	−0.275730	+	0.477579i
$203$	−5.81139			−0.407879
$204$		0			0
$205$	−6.24342	−	10.8139i	−0.436059	−	0.755277i
$206$	7.90569	+	13.6931i	0.550816	+	0.954041i
$207$		0			0
$208$	3.08114	−	1.87259i	0.213639	−	0.129841i
$209$	6.00000			0.415029
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	6.24342	−	10.8139i	0.428800	−	0.742703i
$213$		0			0
$214$	8.90569	−	15.4251i	0.608781	−	1.05444i
$215$	−19.0680	+	33.0267i	−1.30042	+	2.25240i
$216$		0			0
$217$	10.0000	−	17.3205i	0.678844	−	1.17579i
$218$	−3.32456	−	5.75830i	−0.225167	−	0.390001i
$219$		0			0
$220$	−4.83772			−0.326159
$221$	9.48683	+	5.19615i	0.638153	+	0.349531i
$222$		0			0
$223$	0.837722	+	1.45098i	0.0560980	+	0.0971647i	0.892711	−	0.450630i	$-0.148801\pi$
$223$	0.837722	+	1.45098i	0.0560980	+	0.0971647i	−0.836613	+	0.547795i	$0.815467\pi$
$224$	−1.58114	−	2.73861i	−0.105644	−	0.182981i
$225$		0			0
$226$	6.67544			0.444044
$227$	7.74342	−	13.4120i	0.513949	−	0.890185i	−0.485920	−	0.874003i	$-0.661516\pi$
$227$	7.74342	−	13.4120i	0.513949	−	0.890185i	0.999869	−	0.0161821i	$-0.00515113\pi$
$228$		0			0
$229$	22.3246			1.47525			0.737624	−	0.675212i	$-0.235948\pi$
$229$	22.3246			1.47525			0.737624	+	0.675212i	$0.235948\pi$
$230$	−14.9057	+	25.8174i	−0.982852	+	1.70235i
$231$		0			0
$232$	0.918861	+	1.59151i	0.0603262	+	0.104488i
$233$	−16.6491			−1.09072			−0.545360	−	0.838202i	$-0.683607\pi$
$233$	−16.6491			−1.09072			−0.545360	+	0.838202i	$0.683607\pi$
$234$		0			0
$235$	20.1359			1.31352
$236$	1.16228	+	2.01312i	0.0756578	+	0.131043i
$237$		0			0
$238$	4.74342	−	8.21584i	0.307470	−	0.532554i
$239$	−21.4868			−1.38987			−0.694934	−	0.719074i	$-0.744566\pi$
$239$	−21.4868			−1.38987			−0.694934	+	0.719074i	$0.744566\pi$
$240$		0			0
$241$	−6.66228	+	11.5394i	−0.429155	+	0.743318i	−0.996798	−	0.0799563i	$-0.974522\pi$
$241$	−6.66228	+	11.5394i	−0.429155	+	0.743318i	0.567643	+	0.823275i	$0.307855\pi$
$242$	−9.64911			−0.620268
$243$		0			0
$244$	−0.0811388	−	0.140537i	−0.00519438	−	0.00899693i
$245$	−6.24342	−	10.8139i	−0.398877	−	0.690876i
$246$		0			0
$247$	16.3246	+	8.94133i	1.03871	+	0.568923i
$248$	−6.32456			−0.401610
$249$		0			0
$250$	−15.2434	−	26.4024i	−0.964078	−	1.66983i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$		0			0
$253$	4.16228	−	7.20928i	0.261680	−	0.453243i
$254$	9.16228	−	15.8695i	0.574892	−	0.995743i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.9868	+	19.0298i	0.685340	+	1.18704i	0.973330	+	0.229410i	$0.0736797\pi$
$257$	10.9868	+	19.0298i	0.685340	+	1.18704i	−0.287990	+	0.957633i	$0.592987\pi$
$258$		0			0
$259$	12.1359			0.754091
$260$	−13.1623	−	7.20928i	−0.816290	−	0.447100i
$261$		0			0
$262$	−8.32456	−	14.4186i	−0.514293	−	0.890781i
$263$	1.25658	+	2.17647i	0.0774843	+	0.134207i	0.902164	−	0.431393i	$-0.141978\pi$
$263$	1.25658	+	2.17647i	0.0774843	+	0.134207i	−0.824680	+	0.565600i	$0.808645\pi$
$264$		0			0
$265$	−51.9737			−3.19272
$266$	8.16228	−	14.1375i	0.500461	−	0.866824i
$267$		0			0
$268$	−2.83772			−0.173341
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	0.945944	−	0.324329i	$-0.105139\pi$
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	−0.753850	+	0.657047i	$0.771805\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−3.00000			−0.181237
$275$	7.16228	+	12.4054i	0.431902	+	0.748076i
$276$		0			0
$277$	−5.40569	+	9.36294i	−0.324797	+	0.562564i	−0.981471	−	0.191610i	$-0.938629\pi$
$277$	−5.40569	+	9.36294i	−0.324797	+	0.562564i	0.656675	+	0.754174i	$0.271963\pi$
$278$	−6.32456			−0.379322
$279$		0			0
$280$	−6.58114	+	11.3989i	−0.393298	+	0.681213i
$281$	−0.675445			−0.0402937			−0.0201468	−	0.999797i	$-0.506413\pi$
$281$	−0.675445			−0.0402937			−0.0201468	+	0.999797i	$0.506413\pi$
$282$		0			0
$283$	1.41886	+	2.45754i	0.0843425	+	0.146086i	0.905111	−	0.425176i	$-0.139788\pi$
$283$	1.41886	+	2.45754i	0.0843425	+	0.146086i	−0.820768	+	0.571261i	$0.806454\pi$
$284$	3.58114	+	6.20271i	0.212501	+	0.368063i
$285$		0			0
$286$	3.67544	+	2.01312i	0.217334	+	0.119039i
$287$	9.48683			0.559990
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	3.82456	−	6.62432i	0.224586	−	0.388994i
$291$		0			0
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$	−0.918861	+	1.59151i	−0.0536804	+	0.0929773i	−0.891617	−	0.452790i	$-0.850429\pi$
$293$	−0.918861	+	1.59151i	−0.0536804	+	0.0929773i	0.837937	+	0.545768i	$0.183762\pi$
$294$		0			0
$295$	4.83772	−	8.37918i	0.281663	−	0.487855i
$296$	−1.91886	−	3.32357i	−0.111532	−	0.193178i
$297$		0			0
$298$	0.486833			0.0282015
$299$	22.0680	−	13.4120i	1.27622	−	0.775635i
$300$		0			0
$301$	−14.4868	−	25.0919i	−0.835007	−	1.44627i
$302$	−0.418861	−	0.725489i	−0.0241028	−	0.0417472i
$303$		0			0
$304$	−5.16228			−0.296077
$305$	−0.337722	+	0.584952i	−0.0193379	+	0.0334943i
$306$		0			0
$307$	11.4868			0.655588			0.327794	−	0.944749i	$-0.393695\pi$
$307$	11.4868			0.655588			0.327794	+	0.944749i	$0.393695\pi$
$308$	1.83772	−	3.18303i	0.104714	−	0.181370i
$309$		0			0
$310$	13.1623	+	22.7977i	0.747567	+	1.29482i
$311$	21.4868			1.21841			0.609203	−	0.793014i	$-0.291489\pi$
$311$	21.4868			1.21841			0.609203	+	0.793014i	$0.291489\pi$
$312$		0			0
$313$	−4.00000			−0.226093			−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000			−0.226093			−0.113047	+	0.993590i	$0.536061\pi$
$314$	5.24342	+	9.08186i	0.295903	+	0.512519i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	12.4868			0.701330			0.350665	−	0.936501i	$-0.385956\pi$
$317$	12.4868			0.701330			0.350665	+	0.936501i	$0.385956\pi$
$318$		0			0
$319$	−1.06797	+	1.84978i	−0.0597949	+	0.103568i
$320$	4.16228			0.232678
$321$		0			0
$322$	−11.3246	−	19.6147i	−0.631093	−	1.09308i
$323$	−7.74342	−	13.4120i	−0.430855	−	0.746263i
$324$		0			0
$325$	1.00000	+	44.4256i	0.0554700	+	2.46429i
$326$	−16.0000			−0.886158
$327$		0			0
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	−7.64911	+	13.2486i	−0.421709	+	0.730422i
$330$		0			0
$331$	5.48683	−	9.50347i	0.301584	−	0.522358i	−0.674911	−	0.737899i	$-0.735818\pi$
$331$	5.48683	−	9.50347i	0.301584	−	0.522358i	0.976495	+	0.215541i	$0.0691514\pi$
$332$	1.74342	−	3.01969i	0.0956824	−	0.165727i
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	5.90569	+	10.2290i	0.322663	+	0.558868i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	7.00000	+	10.9545i	0.380750	+	0.595844i
$339$		0			0
$340$	6.24342	+	10.8139i	0.338597	+	0.586467i
$341$	−3.67544	−	6.36606i	−0.199036	−	0.344741i
$342$		0			0
$343$	−12.6491			−0.682988
$344$	−4.58114	+	7.93477i	−0.246998	+	0.427814i
$345$		0			0
$346$	22.6491			1.21762
$347$	7.74342	−	13.4120i	0.415688	−	0.719993i	−0.579812	−	0.814750i	$-0.696874\pi$
$347$	7.74342	−	13.4120i	0.415688	−	0.719993i	0.995500	+	0.0947569i	$0.0302074\pi$
$348$		0			0
$349$	2.67544	+	4.63401i	0.143213	+	0.248053i	0.928705	−	0.370820i	$-0.120923\pi$
$349$	2.67544	+	4.63401i	0.143213	+	0.248053i	−0.785492	+	0.618872i	$0.787590\pi$
$350$	38.9737			2.08323
$351$		0			0
$352$	−1.16228			−0.0619496
$353$	−14.6623	−	25.3958i	−0.780394	−	1.35168i	−0.931712	−	0.363197i	$-0.881685\pi$
$353$	−14.6623	−	25.3958i	−0.780394	−	1.35168i	0.151318	−	0.988485i	$-0.451648\pi$
$354$		0			0
$355$	14.9057	−	25.8174i	0.791112	−	1.37025i
$356$	12.0000			0.635999
$357$		0			0
$358$	−7.74342	+	13.4120i	−0.409252	+	0.708846i
$359$	28.4605			1.50209			0.751044	−	0.660252i	$-0.229551\pi$
$359$	28.4605			1.50209			0.751044	+	0.660252i	$0.229551\pi$
$360$		0			0
$361$	−3.82456	−	6.62432i	−0.201292	−	0.348649i
$362$	−1.91886	−	3.32357i	−0.100853	−	0.174683i
$363$		0			0
$364$	9.74342	−	5.92164i	0.510694	−	0.310378i
$365$	−4.16228			−0.217864
$366$		0			0
$367$	12.7434	+	22.0722i	0.665201	+	1.15216i	0.979231	+	0.202749i	$0.0649875\pi$
$367$	12.7434	+	22.0722i	0.665201	+	1.15216i	−0.314030	+	0.949413i	$0.601679\pi$
$368$	−3.58114	+	6.20271i	−0.186680	+	0.323339i
$369$		0			0
$370$	−7.98683	+	13.8336i	−0.415216	+	0.719175i
$371$	19.7434	−	34.1966i	1.02503	−	1.77540i
$372$		0			0
$373$	8.24342	−	14.2780i	0.426828	−	0.739288i	−0.569761	−	0.821810i	$-0.692964\pi$
$373$	8.24342	−	14.2780i	0.426828	−	0.739288i	0.996589	+	0.0825226i	$0.0262977\pi$
$374$	−1.74342	−	3.01969i	−0.0901499	−	0.156144i
$375$		0			0
$376$	4.83772			0.249486
$377$	−5.66228	+	3.44130i	−0.291622	+	0.177236i
$378$		0			0
$379$	−8.83772	−	15.3074i	−0.453963	−	0.786288i	0.544665	−	0.838654i	$-0.316657\pi$
$379$	−8.83772	−	15.3074i	−0.453963	−	0.786288i	−0.998628	+	0.0523664i	$0.983324\pi$
$380$	10.7434	+	18.6081i	0.551126	+	0.954578i
$381$		0			0
$382$	14.3246			0.732908
$383$	−15.4868	+	26.8240i	−0.791340	+	1.37064i	0.133797	+	0.991009i	$0.457283\pi$
$383$	−15.4868	+	26.8240i	−0.791340	+	1.37064i	−0.925137	+	0.379633i	$0.876050\pi$
$384$		0			0
$385$	−15.2982			−0.779670
$386$	9.98683	−	17.2977i	0.508316	−	0.880430i
$387$		0			0
$388$	2.00000	+	3.46410i	0.101535	+	0.175863i
$389$	12.4868			0.633108			0.316554	−	0.948575i	$-0.397474\pi$
$389$	12.4868			0.633108			0.316554	+	0.948575i	$0.397474\pi$
$390$		0			0
$391$	−21.4868			−1.08664
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$		0			0
$394$	−9.48683	+	16.4317i	−0.477940	+	0.827816i
$395$	−16.6491			−0.837708
$396$		0			0
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$	−6.51317			−0.326476
$399$		0			0
$400$	−6.16228	−	10.6734i	−0.308114	−	0.533669i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−0.513167	−	22.7977i	−0.0255627	−	1.13564i
$404$	7.83772			0.389941
$405$		0			0
$406$	2.90569	+	5.03281i	0.144207	+	0.249774i
$407$	2.23025	−	3.86291i	0.110549	−	0.191477i
$408$		0			0
$409$	−7.33772	+	12.7093i	−0.362827	+	0.628435i	−0.988425	−	0.151711i	$-0.951522\pi$
$409$	−7.33772	+	12.7093i	−0.362827	+	0.628435i	0.625598	+	0.780146i	$0.284855\pi$
$410$	−6.24342	+	10.8139i	−0.308340	+	0.534061i
$411$		0			0
$412$	7.90569	−	13.6931i	0.389486	−	0.674609i
$413$	3.67544	+	6.36606i	0.180857	+	0.313253i
$414$		0			0
$415$	−14.5132			−0.712423
$416$	−3.16228	−	1.73205i	−0.155043	−	0.0849208i
$417$		0			0
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	15.4868	+	26.8240i	0.756581	+	1.31044i	0.944584	+	0.328269i	$0.106465\pi$
$419$	15.4868	+	26.8240i	0.756581	+	1.31044i	−0.188003	+	0.982168i	$0.560201\pi$
$420$		0			0
$421$	−23.8377			−1.16178			−0.580890	−	0.813982i	$-0.697295\pi$
$421$	−23.8377			−1.16178			−0.580890	+	0.813982i	$0.697295\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$		0			0
$424$	−12.4868			−0.606414
$425$	18.4868	−	32.0201i	0.896743	−	1.55320i
$426$		0			0
$427$	−0.256584	−	0.444416i	−0.0124169	−	0.0215068i
$428$	−17.8114			−0.860946
$429$		0			0
$430$	38.1359			1.83908
$431$	4.74342	+	8.21584i	0.228482	+	0.395743i	0.957359	−	0.288903i	$-0.0932904\pi$
$431$	4.74342	+	8.21584i	0.228482	+	0.395743i	−0.728876	+	0.684646i	$0.759957\pi$
$432$		0			0
$433$	4.66228	−	8.07530i	0.224055	−	0.388074i	−0.731981	−	0.681325i	$-0.761404\pi$
$433$	4.66228	−	8.07530i	0.224055	−	0.388074i	0.956035	+	0.293251i	$0.0947372\pi$
$434$	−20.0000			−0.960031
$435$		0			0
$436$	−3.32456	+	5.75830i	−0.159217	+	0.275772i
$437$	−36.9737			−1.76869
$438$		0			0
$439$	12.7434	+	22.0722i	0.608210	+	1.05345i	0.991535	+	0.129837i	$0.0414455\pi$
$439$	12.7434	+	22.0722i	0.608210	+	1.05345i	−0.383325	+	0.923613i	$0.625221\pi$
$440$	2.41886	+	4.18959i	0.115315	+	0.199731i
$441$		0			0
$442$	−0.243416	−	10.8139i	−0.0115781	−	0.514365i
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−24.9737	−	43.2557i	−1.18387	−	2.05051i
$446$	0.837722	−	1.45098i	0.0396673	−	0.0687058i
$447$		0			0
$448$	−1.58114	+	2.73861i	−0.0747018	+	0.129387i
$449$	−3.67544	+	6.36606i	−0.173455	+	0.300433i	−0.939625	−	0.342205i	$-0.888826\pi$
$449$	−3.67544	+	6.36606i	−0.173455	+	0.300433i	0.766171	+	0.642637i	$0.222160\pi$
$450$		0			0
$451$	1.74342	−	3.01969i	0.0820943	−	0.142191i
$452$	−3.33772	−	5.78110i	−0.156993	−	0.271920i
$453$		0			0
$454$	−15.4868			−0.726833
$455$	−41.6228	−	22.7977i	−1.95131	−	1.06877i
$456$		0			0
$457$	1.66228	+	2.87915i	0.0777581	+	0.134681i	0.902282	−	0.431146i	$-0.141890\pi$
$457$	1.66228	+	2.87915i	0.0777581	+	0.134681i	−0.824524	+	0.565827i	$0.808557\pi$
$458$	−11.1623	−	19.3336i	−0.521579	−	0.903401i
$459$		0			0
$460$	29.8114			1.38996
$461$	−9.24342	+	16.0101i	−0.430509	+	0.745663i	−0.996917	−	0.0784616i	$-0.974999\pi$
$461$	−9.24342	+	16.0101i	−0.430509	+	0.745663i	0.566408	+	0.824125i	$0.308333\pi$
$462$		0			0
$463$	15.1623			0.704651			0.352325	−	0.935878i	$-0.385391\pi$
$463$	15.1623			0.704651			0.352325	+	0.935878i	$0.385391\pi$
$464$	0.918861	−	1.59151i	0.0426571	−	0.0738842i
$465$		0			0
$466$	8.32456	+	14.4186i	0.385628	+	0.667927i
$467$	6.18861			0.286375			0.143187	−	0.989696i	$-0.454265\pi$
$467$	6.18861			0.286375			0.143187	+	0.989696i	$0.454265\pi$
$468$		0			0
$469$	−8.97367			−0.414365
$470$	−10.0680	−	17.4382i	−0.464401	−	0.804366i
$471$		0			0
$472$	1.16228	−	2.01312i	0.0534982	−	0.0926615i
$473$	−10.6491			−0.489647
$474$		0			0
$475$	31.8114	−	55.0989i	1.45961	−	2.52811i
$476$	−9.48683			−0.434828
$477$		0			0
$478$	10.7434	+	18.6081i	0.491392	+	0.851117i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	11.8246	−	7.18647i	0.539153	−	0.327675i
$482$	13.3246			0.606917
$483$		0			0
$484$	4.82456	+	8.35637i	0.219298	+	0.379835i
$485$	8.32456	−	14.4186i	0.377999	−	0.654713i
$486$		0			0
$487$	6.74342	−	11.6799i	0.305573	−	0.529269i	−0.671815	−	0.740719i	$-0.734485\pi$
$487$	6.74342	−	11.6799i	0.305573	−	0.529269i	0.977389	+	0.211450i	$0.0678185\pi$
$488$	−0.0811388	+	0.140537i	−0.00367298	+	0.00636179i
$489$		0			0
$490$	−6.24342	+	10.8139i	−0.282049	+	0.488523i
$491$	−2.90569	−	5.03281i	−0.131132	−	0.227128i	0.792981	−	0.609246i	$-0.208528\pi$
$491$	−2.90569	−	5.03281i	−0.131132	−	0.227128i	−0.924113	+	0.382119i	$0.875195\pi$
$492$		0			0
$493$	5.51317			0.248301
$494$	−0.418861	−	18.6081i	−0.0188455	−	0.837220i
$495$		0			0
$496$	3.16228	+	5.47723i	0.141990	+	0.245935i
$497$	11.3246	+	19.6147i	0.507976	+	0.879840i
$498$		0			0
$499$	12.6491			0.566252			0.283126	−	0.959083i	$-0.408629\pi$
$499$	12.6491			0.566252			0.283126	+	0.959083i	$0.408629\pi$
$500$	−15.2434	+	26.4024i	−0.681706	+	1.18075i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	0.0943058	−	0.163343i	0.00420489	−	0.00728308i	−0.863915	−	0.503637i	$-0.831995\pi$
$503$	0.0943058	−	0.163343i	0.00420489	−	0.00728308i	0.868120	+	0.496354i	$0.165328\pi$
$504$		0			0
$505$	−16.3114	−	28.2522i	−0.725847	−	1.25720i
$506$	−8.32456			−0.370072
$507$		0			0
$508$	−18.3246			−0.813021
$509$	14.0811	+	24.3892i	0.624136	+	1.08103i	0.988707	+	0.149859i	$0.0478820\pi$
$509$	14.0811	+	24.3892i	0.624136	+	1.08103i	−0.364572	+	0.931175i	$0.618785\pi$
$510$		0			0
$511$	1.58114	−	2.73861i	0.0699455	−	0.121149i
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.9868	−	19.0298i	0.484608	−	0.839366i
$515$	−65.8114			−2.90000
$516$		0			0
$517$	2.81139	+	4.86947i	0.123645	+	0.214159i
$518$	−6.06797	−	10.5100i	−0.266611	−	0.461784i
$519$		0			0
$520$	0.337722	+	15.0035i	0.0148101	+	0.657947i
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	2.58114	+	4.47066i	0.112865	+	0.195488i	0.916924	−	0.399061i	$-0.130664\pi$
$523$	2.58114	+	4.47066i	0.112865	+	0.195488i	−0.804059	+	0.594549i	$0.797330\pi$
$524$	−8.32456	+	14.4186i	−0.363660	+	0.629877i
$525$		0			0
$526$	1.25658	−	2.17647i	0.0547896	−	0.0948984i
$527$	−9.48683	+	16.4317i	−0.413253	+	0.715775i
$528$		0			0
$529$	−14.1491	+	24.5070i	−0.615179	+	1.06552i
$530$	25.9868	+	45.0105i	1.12880	+	1.95513i
$531$		0			0
$532$	−16.3246			−0.707759
$533$	9.24342	−	5.61776i	0.400377	−	0.243332i
$534$		0			0
$535$	37.0680	+	64.2036i	1.60259	+	2.77576i
$536$	1.41886	+	2.45754i	0.0612855	+	0.106150i
$537$		0			0
$538$	6.00000			0.258678
$539$	1.74342	−	3.01969i	0.0750943	−	0.130067i
$540$		0			0
$541$	−15.5132			−0.666963			−0.333482	−	0.942757i	$-0.608223\pi$
$541$	−15.5132			−0.666963			−0.333482	+	0.942757i	$0.608223\pi$
$542$	3.16228	−	5.47723i	0.135831	−	0.235267i
$543$		0			0
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	27.6754			1.18549
$546$		0			0
$547$	−33.8114			−1.44567			−0.722835	−	0.691020i	$-0.757161\pi$
$547$	−33.8114			−1.44567			−0.722835	+	0.691020i	$0.757161\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$		0			0
$550$	7.16228	−	12.4054i	0.305401	−	0.528969i
$551$	9.48683			0.404153
$552$		0			0
$553$	6.32456	−	10.9545i	0.268947	−	0.465831i
$554$	10.8114			0.459332
$555$		0			0
$556$	3.16228	+	5.47723i	0.134110	+	0.232286i
$557$	9.24342	+	16.0101i	0.391656	+	0.678368i	0.992668	−	0.120872i	$-0.0385690\pi$
$557$	9.24342	+	16.0101i	0.391656	+	0.678368i	−0.601012	+	0.799240i	$0.705236\pi$
$558$		0			0
$559$	−28.9737	−	15.8695i	−1.22546	−	0.671210i
$560$	13.1623			0.556208
$561$		0			0
$562$	0.337722	+	0.584952i	0.0142460	+	0.0246747i
$563$	−20.3246	+	35.2032i	−0.856578	+	1.48364i	0.0185956	+	0.999827i	$0.494081\pi$
$563$	−20.3246	+	35.2032i	−0.856578	+	1.48364i	−0.875173	+	0.483809i	$0.839253\pi$
$564$		0			0
$565$	−13.8925	+	24.0626i	−0.584463	+	1.01232i
$566$	1.41886	−	2.45754i	0.0596392	−	0.103298i
$567$		0			0
$568$	3.58114	−	6.20271i	0.150261	−	0.260260i
$569$	−13.6491	−	23.6410i	−0.572200	−	0.991080i	−0.996340	−	0.0854833i	$-0.972757\pi$
$569$	−13.6491	−	23.6410i	−0.572200	−	0.991080i	0.424139	−	0.905597i	$-0.360577\pi$
$570$		0			0
$571$	−36.1359			−1.51224			−0.756121	−	0.654432i	$-0.772908\pi$
$571$	−36.1359			−1.51224			−0.756121	+	0.654432i	$0.772908\pi$
$572$	−0.0943058	−	4.18959i	−0.00394313	−	0.175176i
$573$		0			0
$574$	−4.74342	−	8.21584i	−0.197986	−	0.342922i
$575$	−44.1359	−	76.4457i	−1.84060	−	3.18801i
$576$		0			0
$577$	0.350889			0.0146077			0.00730386	−	0.999973i	$-0.497675\pi$
$577$	0.350889			0.0146077			0.00730386	+	0.999973i	$0.497675\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	−7.64911			−0.317612
$581$	5.51317	−	9.54909i	0.228725	−	0.396163i
$582$		0			0
$583$	−7.25658	−	12.5688i	−0.300537	−	0.520545i
$584$	−1.00000			−0.0413803
$585$		0			0
$586$	1.83772			0.0759156
$587$	−14.3246	−	24.8109i	−0.591238	−	1.02405i	−0.994066	−	0.108778i	$-0.965306\pi$
$587$	−14.3246	−	24.8109i	−0.591238	−	1.02405i	0.402828	−	0.915276i	$-0.368027\pi$
$588$		0			0
$589$	−16.3246	+	28.2750i	−0.672642	+	1.16505i
$590$	−9.67544			−0.398332
$591$		0			0
$592$	−1.91886	+	3.32357i	−0.0788647	+	0.136598i
$593$	0.675445			0.0277372			0.0138686	−	0.999904i	$-0.495585\pi$
$593$	0.675445			0.0277372			0.0138686	+	0.999904i	$0.495585\pi$
$594$		0			0
$595$	19.7434	+	34.1966i	0.809401	+	1.40192i
$596$	−0.243416	−	0.421610i	−0.00997073	−	0.0172698i
$597$		0			0
$598$	−22.6491	−	12.4054i	−0.926191	−	0.507296i
$599$	−23.6228			−0.965200			−0.482600	−	0.875841i	$-0.660308\pi$
$599$	−23.6228			−0.965200			−0.482600	+	0.875841i	$0.660308\pi$
$600$		0			0
$601$	17.1491	+	29.7031i	0.699527	+	1.21162i	0.968631	+	0.248505i	$0.0799392\pi$
$601$	17.1491	+	29.7031i	0.699527	+	1.21162i	−0.269104	+	0.963111i	$0.586727\pi$
$602$	−14.4868	+	25.0919i	−0.590439	+	1.02267i
$603$		0			0
$604$	−0.418861	+	0.725489i	−0.0170432	+	0.0295197i
$605$	20.0811	−	34.7816i	0.816414	−	1.41407i
$606$		0			0
$607$	−8.64911	+	14.9807i	−0.351057	+	0.608048i	−0.986435	−	0.164153i	$-0.947511\pi$
$607$	−8.64911	+	14.9807i	−0.351057	+	0.608048i	0.635378	+	0.772201i	$0.280844\pi$
$608$	2.58114	+	4.47066i	0.104679	+	0.181309i
$609$		0			0
$610$	0.675445			0.0273480
$611$	0.392527	+	17.4382i	0.0158799	+	0.705476i
$612$		0			0
$613$	−10.2434	−	17.7421i	−0.413728	−	0.716597i	0.581566	−	0.813499i	$-0.302440\pi$
$613$	−10.2434	−	17.7421i	−0.413728	−	0.716597i	−0.995294	+	0.0969016i	$0.969107\pi$
$614$	−5.74342	−	9.94789i	−0.231785	−	0.401464i
$615$		0			0
$616$	−3.67544			−0.148088
$617$	13.3114	−	23.0560i	0.535896	−	0.928200i	−0.463223	−	0.886242i	$-0.653307\pi$
$617$	13.3114	−	23.0560i	0.535896	−	0.928200i	0.999119	−	0.0419579i	$-0.0133595\pi$
$618$		0			0
$619$	24.6491			0.990731			0.495366	−	0.868685i	$-0.335034\pi$
$619$	24.6491			0.990731			0.495366	+	0.868685i	$0.335034\pi$
$620$	13.1623	−	22.7977i	0.528610	−	0.915579i
$621$		0			0
$622$	−10.7434	−	18.6081i	−0.430772	−	0.746119i
$623$	37.9473			1.52033
$624$		0			0
$625$	65.2719			2.61088
$626$	2.00000	+	3.46410i	0.0799361	+	0.138453i
$627$		0			0
$628$	5.24342	−	9.08186i	0.209235	−	0.362406i
$629$	−11.5132			−0.459060
$630$		0			0
$631$	12.6491	−	21.9089i	0.503553	−	0.872180i	−0.496438	−	0.868072i	$-0.665359\pi$
$631$	12.6491	−	21.9089i	0.503553	−	0.872180i	0.999992	−	0.00410769i	$-0.00130752\pi$
$632$	−4.00000			−0.159111
$633$		0			0
$634$	−6.24342	−	10.8139i	−0.247958	−	0.429475i
$635$	38.1359	+	66.0534i	1.51338	+	2.62125i
$636$		0			0
$637$	9.24342	−	5.61776i	0.366237	−	0.222584i
$638$	2.13594			0.0845628
$639$		0			0
$640$	−2.08114	−	3.60464i	−0.0822642	−	0.142486i
$641$	−8.17544	+	14.1603i	−0.322911	+	0.559298i	−0.981087	−	0.193566i	$-0.937995\pi$
$641$	−8.17544	+	14.1603i	−0.322911	+	0.559298i	0.658177	+	0.752864i	$0.271328\pi$
$642$		0			0
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$644$	−11.3246	+	19.6147i	−0.446250	+	0.772928i
$645$		0			0
$646$	−7.74342	+	13.4120i	−0.304661	+	0.527688i
$647$	20.3246	+	35.2032i	0.799041	+	1.38398i	0.920241	+	0.391351i	$0.127992\pi$
$647$	20.3246	+	35.2032i	0.799041	+	1.38398i	−0.121201	+	0.992628i	$0.538674\pi$
$648$		0			0
$649$	2.70178			0.106054
$650$	37.9737	−	23.0788i	1.48945	−	0.905225i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$	69.2982			2.70771
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$	15.2982			0.596387
$659$	2.51317	−	4.35293i	0.0978991	−	0.169566i	−0.812916	−	0.582381i	$-0.802121\pi$
$659$	2.51317	−	4.35293i	0.0978991	−	0.169566i	0.910815	+	0.412815i	$0.135454\pi$
$660$		0			0
$661$	−13.2434	−	22.9383i	−0.515109	−	0.892195i	−0.999846	−	0.0175354i	$-0.994418\pi$
$661$	−13.2434	−	22.9383i	−0.515109	−	0.892195i	0.484737	−	0.874660i	$-0.338915\pi$
$662$	−10.9737			−0.426504
$663$		0			0
$664$	−3.48683			−0.135315
$665$	33.9737	+	58.8441i	1.31744	+	2.28188i
$666$		0			0
$667$	6.58114	−	11.3989i	0.254823	−	0.441366i
$668$	12.0000			0.464294
$669$		0			0
$670$	5.90569	−	10.2290i	0.228157	−	0.395179i
$671$	−0.188612			−0.00728127
$672$		0			0
$673$	−7.33772	−	12.7093i	−0.282848	−	0.489908i	0.689237	−	0.724536i	$-0.257946\pi$
$673$	−7.33772	−	12.7093i	−0.282848	−	0.489908i	−0.972085	+	0.234628i	$0.924613\pi$
$674$	−5.50000	−	9.52628i	−0.211852	−	0.366939i
$675$		0			0
$676$	5.98683	−	11.5394i	0.230263	−	0.443823i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	6.32456	+	10.9545i	0.242714	+	0.420393i
$680$	6.24342	−	10.8139i	0.239424	−	0.414695i
$681$		0			0
$682$	−3.67544	+	6.36606i	−0.140740	+	0.243769i
$683$	17.8114	−	30.8502i	0.681534	−	1.18045i	−0.292979	−	0.956119i	$-0.594647\pi$
$683$	17.8114	−	30.8502i	0.681534	−	1.18045i	0.974513	−	0.224332i	$-0.0720201\pi$
$684$		0			0
$685$	6.24342	−	10.8139i	0.238549	−	0.413178i
$686$	6.32456	+	10.9545i	0.241473	+	0.418243i
$687$		0			0
$688$	9.16228			0.349309
$689$	−1.01317	−	45.0105i	−0.0385986	−	1.71476i
$690$		0			0
$691$	−4.58114	−	7.93477i	−0.174275	−	0.301853i	0.765635	−	0.643275i	$-0.222425\pi$
$691$	−4.58114	−	7.93477i	−0.174275	−	0.301853i	−0.939910	+	0.341422i	$0.889091\pi$
$692$	−11.3246	−	19.6147i	−0.430495	−	0.745639i
$693$		0			0
$694$	−15.4868			−0.587872
$695$	13.1623	−	22.7977i	0.499274	−	0.864767i
$696$		0			0
$697$	−9.00000			−0.340899
$698$	2.67544	−	4.63401i	0.101267	−	0.175400i
$699$		0			0
$700$	−19.4868	−	33.7522i	−0.736533	−	1.27571i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−19.8114			−0.747201
$704$	0.581139	+	1.00656i	0.0219025	+	0.0379362i
$705$		0			0
$706$	−14.6623	+	25.3958i	−0.551822	+	0.955784i
$707$	24.7851			0.932138
$708$		0			0
$709$	−22.7302	+	39.3699i	−0.853652	+	1.47857i	0.0242371	+	0.999706i	$0.492284\pi$
$709$	−22.7302	+	39.3699i	−0.853652	+	1.47857i	−0.877890	+	0.478863i	$0.841049\pi$
$710$	−29.8114			−1.11880
$711$		0			0
$712$	−6.00000	−	10.3923i	−0.224860	−	0.389468i
$713$	22.6491	+	39.2294i	0.848216	+	1.46915i
$714$		0			0
$715$	−14.9057	+	9.05906i	−0.557441	+	0.338790i
$716$	15.4868			0.578770
$717$		0			0
$718$	−14.2302	−	24.6475i	−0.531068	−	0.919837i
$719$	19.1623	−	33.1900i	0.714632	−	1.23778i	−0.248469	−	0.968640i	$-0.579927\pi$
$719$	19.1623	−	33.1900i	0.714632	−	1.23778i	0.963101	−	0.269140i	$-0.0867393\pi$
$720$		0			0
$721$	25.0000	−	43.3013i	0.931049	−	1.61262i
$722$	−3.82456	+	6.62432i	−0.142335	+	0.246532i
$723$		0			0
$724$	−1.91886	+	3.32357i	−0.0713139	+	0.123519i
$725$	11.3246	+	19.6147i	0.420583	+	0.728472i
$726$		0			0
$727$	−8.83772			−0.327773			−0.163886	−	0.986479i	$-0.552403\pi$
$727$	−8.83772			−0.327773			−0.163886	+	0.986479i	$0.552403\pi$
$728$	−10.0000	−	5.47723i	−0.370625	−	0.202999i
$729$		0			0
$730$	2.08114	+	3.60464i	0.0770264	+	0.133414i
$731$	13.7434	+	23.8043i	0.508319	+	0.880434i
$732$		0			0
$733$	21.4605			0.792662			0.396331	−	0.918108i	$-0.370283\pi$
$733$	21.4605			0.792662			0.396331	+	0.918108i	$0.370283\pi$
$734$	12.7434	−	22.0722i	0.470368	−	0.814701i
$735$		0			0
$736$	7.16228			0.264005
$737$	−1.64911	+	2.85634i	−0.0607458	+	0.105215i
$738$		0			0
$739$	19.8114	+	34.3143i	0.728774	+	1.26227i	0.957402	+	0.288759i	$0.0932427\pi$
$739$	19.8114	+	34.3143i	0.728774	+	1.26227i	−0.228628	+	0.973514i	$0.573424\pi$
$740$	15.9737			0.587204
$741$		0			0
$742$	−39.4868			−1.44961
$743$	−1.16228	−	2.01312i	−0.0426398	−	0.0738544i	0.843918	−	0.536472i	$-0.180243\pi$
$743$	−1.16228	−	2.01312i	−0.0426398	−	0.0738544i	−0.886558	+	0.462618i	$0.846910\pi$
$744$		0			0
$745$	−1.01317	+	1.75486i	−0.0371196	+	0.0642930i
$746$	−16.4868			−0.603626
$747$		0			0
$748$	−1.74342	+	3.01969i	−0.0637456	+	0.110411i
$749$	−56.3246			−2.05805
$750$		0			0
$751$	−19.3925	−	33.5888i	−0.707643	−	1.22567i	−0.965729	−	0.259552i	$-0.916425\pi$
$751$	−19.3925	−	33.5888i	−0.707643	−	1.22567i	0.258086	−	0.966122i	$-0.416908\pi$
$752$	−2.41886	−	4.18959i	−0.0882068	−	0.152779i
$753$		0			0
$754$	5.81139	+	3.18303i	0.211638	+	0.115919i
$755$	3.48683			0.126899
$756$		0			0
$757$	13.3246	+	23.0788i	0.484289	+	0.838814i	0.999837	−	0.0180472i	$-0.00574493\pi$
$757$	13.3246	+	23.0788i	0.484289	+	0.838814i	−0.515548	+	0.856861i	$0.672412\pi$
$758$	−8.83772	+	15.3074i	−0.321001	+	0.555989i
$759$		0			0
$760$	10.7434	−	18.6081i	0.389705	−	0.674988i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	−10.5132	+	18.2093i	−0.380602	+	0.659222i
$764$	−7.16228	−	12.4054i	−0.259122	−	0.448813i
$765$		0			0
$766$	30.9737			1.11912
$767$	7.35089	+	4.02625i	0.265425	+	0.145379i
$768$		0			0
$769$	−1.67544	−	2.90196i	−0.0604181	−	0.104647i	0.834234	−	0.551410i	$-0.185910\pi$
$769$	−1.67544	−	2.90196i	−0.0604181	−	0.104647i	−0.894652	+	0.446763i	$0.852577\pi$
$770$	7.64911	+	13.2486i	0.275655	+	0.477448i
$771$		0			0
$772$	−19.9737			−0.718868
$773$	−11.3246	+	19.6147i	−0.407316	+	0.705492i	−0.994588	−	0.103898i	$-0.966869\pi$
$773$	−11.3246	+	19.6147i	−0.407316	+	0.705492i	0.587272	+	0.809390i	$0.300202\pi$
$774$		0			0
$775$	−77.9473			−2.79995
$776$	2.00000	−	3.46410i	0.0717958	−	0.124354i
$777$		0			0
$778$	−6.24342	−	10.8139i	−0.223837	−	0.387698i
$779$	−15.4868			−0.554873
$780$		0			0
$781$	8.32456			0.297876
$782$	10.7434	+	18.6081i	0.384184	+	0.665426i
$783$		0			0
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$	−43.6491			−1.55790
$786$		0			0
$787$	4.51317	−	7.81703i	0.160877	−	0.278647i	−0.774306	−	0.632811i	$-0.781901\pi$
$787$	4.51317	−	7.81703i	0.160877	−	0.278647i	0.935183	+	0.354164i	$0.115234\pi$
$788$	18.9737			0.675909
$789$		0			0
$790$	8.32456	+	14.4186i	0.296174	+	0.512989i
$791$	−10.5548	−	18.2815i	−0.375286	−	0.650014i
$792$		0			0
$793$	−0.513167	−	0.281073i	−0.0182231	−	0.00998120i
$794$	26.0000			0.922705
$795$		0			0
$796$	3.25658	+	5.64057i	0.115427	+	0.199925i
$797$	9.48683	−	16.4317i	0.336041	−	0.582040i	−0.647643	−	0.761944i	$-0.724245\pi$
$797$	9.48683	−	16.4317i	0.336041	−	0.582040i	0.983684	+	0.179904i	$0.0575786\pi$
$798$		0			0
$799$	7.25658	−	12.5688i	0.256719	−	0.444651i
$800$	−6.16228	+	10.6734i	−0.217869	+	0.377361i
$801$		0			0
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	−0.581139	−	1.00656i	−0.0205079	−	0.0355208i
$804$		0			0
$805$	94.2719			3.32265
$806$	−19.4868	+	11.8433i	−0.686394	+	0.417162i
$807$		0			0
$808$	−3.91886	−	6.78767i	−0.137865	−	0.238789i
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	0.838452	−	0.544976i	$-0.183461\pi$
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	−0.891189	+	0.453632i	$0.850128\pi$
$810$		0			0
$811$	1.02633			0.0360395			0.0180197	−	0.999838i	$-0.494264\pi$
$811$	1.02633			0.0360395			0.0180197	+	0.999838i	$0.494264\pi$
$812$	2.90569	−	5.03281i	0.101970	−	0.176617i
$813$		0			0
$814$	−4.46050			−0.156340
$815$	33.2982	−	57.6742i	1.16639	−	2.02024i
$816$		0			0
$817$	23.6491	+	40.9615i	0.827378	+	1.43306i
$818$	14.6754			0.513115
$819$		0			0
$820$	12.4868			0.436059
$821$	−5.32456	−	9.22240i	−0.185828	−	0.321864i	0.758027	−	0.652223i	$-0.226163\pi$
$821$	−5.32456	−	9.22240i	−0.185828	−	0.321864i	−0.943855	+	0.330359i	$0.892830\pi$
$822$		0			0
$823$	−26.6491	+	46.1576i	−0.928930	+	1.60895i	−0.143813	+	0.989605i	$0.545936\pi$
$823$	−26.6491	+	46.1576i	−0.928930	+	1.60895i	−0.785116	+	0.619348i	$0.787397\pi$
$824$	−15.8114			−0.550816
$825$		0			0
$826$	3.67544	−	6.36606i	0.127885	−	0.221503i
$827$	−6.97367			−0.242498			−0.121249	−	0.992622i	$-0.538690\pi$
$827$	−6.97367			−0.242498			−0.121249	+	0.992622i	$0.538690\pi$
$828$		0			0
$829$	−6.08114	−	10.5328i	−0.211207	−	0.365821i	0.740886	−	0.671631i	$-0.234406\pi$
$829$	−6.08114	−	10.5328i	−0.211207	−	0.365821i	−0.952092	+	0.305810i	$0.901073\pi$
$830$	7.25658	+	12.5688i	0.251880	+	0.436268i
$831$		0			0
$832$	0.0811388	+	3.60464i	0.00281298	+	0.124968i
$833$	−9.00000			−0.311832
$834$		0			0
$835$	−24.9737	−	43.2557i	−0.864249	−	1.49692i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		0			0
$838$	15.4868	−	26.8240i	0.534984	−	0.926619i
$839$	−2.32456	+	4.02625i	−0.0802526	+	0.139002i	−0.903358	−	0.428887i	$-0.858906\pi$
$839$	−2.32456	+	4.02625i	−0.0802526	+	0.139002i	0.823106	+	0.567888i	$0.192239\pi$
$840$		0			0
$841$	12.8114	−	22.1900i	0.441772	−	0.765172i
$842$	11.9189	+	20.6441i	0.410751	+	0.711442i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−54.0548	+	2.43473i	−1.85954	+	0.0837574i
$846$		0			0
$847$	15.2566	+	26.4252i	0.524222	+	0.907980i
$848$	6.24342	+	10.8139i	0.214400	+	0.371351i
$849$		0			0
$850$	−36.9737			−1.26819
$851$	−13.7434	+	23.8043i	−0.471118	+	0.816001i
$852$		0			0
$853$	55.1359			1.88782			0.943909	−	0.330205i	$-0.107118\pi$
$853$	55.1359			1.88782			0.943909	+	0.330205i	$0.107118\pi$
$854$	−0.256584	+	0.444416i	−0.00878011	+	0.0152076i
$855$		0			0
$856$	8.90569	+	15.4251i	0.304390	+	0.527220i
$857$	−25.6491			−0.876157			−0.438078	−	0.898937i	$-0.644341\pi$
$857$	−25.6491			−0.876157			−0.438078	+	0.898937i	$0.644341\pi$
$858$		0			0
$859$	28.5132			0.972857			0.486428	−	0.873720i	$-0.338299\pi$
$859$	28.5132			0.972857			0.486428	+	0.873720i	$0.338299\pi$
$860$	−19.0680	−	33.0267i	−0.650212	−	1.12620i
$861$		0			0
$862$	4.74342	−	8.21584i	0.161561	−	0.279833i
$863$	47.8114			1.62752			0.813759	−	0.581202i	$-0.197417\pi$
$863$	47.8114			1.62752			0.813759	+	0.581202i	$0.197417\pi$
$864$		0			0
$865$	−47.1359	+	81.6418i	−1.60267	+	2.77591i
$866$	−9.32456			−0.316861
$867$		0			0
$868$	10.0000	+	17.3205i	0.339422	+	0.587896i
$869$	−2.32456	−	4.02625i	−0.0788551	−	0.136581i
$870$		0			0
$871$	−8.74342	+	5.31388i	−0.296259	+	0.180054i
$872$	6.64911			0.225167
$873$		0			0
$874$	18.4868	+	32.0201i	0.625326	+	1.08310i
$875$	−48.2039	+	83.4916i	−1.62959	+	2.82253i
$876$		0			0
$877$	22.5680	−	39.0889i	0.762066	−	1.31994i	−0.179717	−	0.983718i	$-0.557518\pi$
$877$	22.5680	−	39.0889i	0.762066	−	1.31994i	0.941784	−	0.336219i	$-0.109148\pi$
$878$	12.7434	−	22.0722i	0.430069	−	0.744902i
$879$		0			0
$880$	2.41886	−	4.18959i	0.0815398	−	0.141231i
$881$	−4.98683	−	8.63745i	−0.168011	−	0.291003i	0.769710	−	0.638394i	$-0.220401\pi$
$881$	−4.98683	−	8.63745i	−0.168011	−	0.291003i	−0.937720	+	0.347391i	$0.887068\pi$
$882$		0			0
$883$	−11.3509			−0.381988			−0.190994	−	0.981591i	$-0.561171\pi$
$883$	−11.3509			−0.381988			−0.190994	+	0.981591i	$0.561171\pi$
$884$	−9.24342	+	5.61776i	−0.310890	+	0.188946i
$885$		0			0
$886$		0			0
$887$	−19.1623	−	33.1900i	−0.643406	−	1.11441i	−0.984667	−	0.174444i	$-0.944187\pi$
$887$	−19.1623	−	33.1900i	−0.643406	−	1.11441i	0.341261	−	0.939969i	$-0.389146\pi$
$888$		0			0
$889$	−57.9473			−1.94349
$890$	−24.9737	+	43.2557i	−0.837119	+	1.44993i
$891$		0			0
$892$	−1.67544			−0.0560980
$893$	12.4868	−	21.6278i	0.417856	−	0.723748i
$894$		0			0
$895$	−32.2302	−	55.8244i	−1.07734	−	1.86600i
$896$	3.16228			0.105644
$897$		0			0
$898$	7.35089			0.245302
$899$	−5.81139	−	10.0656i	−0.193821	−	0.335707i
$900$		0			0
$901$	−18.7302	+	32.4417i	−0.623995	+	1.08079i
$902$	−3.48683			−0.116099
$903$		0			0
$904$	−3.33772	+	5.78110i	−0.111011	+	0.192277i
$905$	15.9737			0.530983
$906$		0			0
$907$	−18.1359	−	31.4124i	−0.602194	−	1.04303i	−0.992488	−	0.122341i	$-0.960960\pi$
$907$	−18.1359	−	31.4124i	−0.602194	−	1.04303i	0.390294	−	0.920690i	$-0.372373\pi$
$908$	7.74342	+	13.4120i	0.256974	+	0.445093i
$909$		0			0
$910$	1.06797	+	47.4452i	0.0354029	+	1.57279i
$911$	−49.9473			−1.65483			−0.827414	−	0.561592i	$-0.810189\pi$
$911$	−49.9473			−1.65483			−0.827414	+	0.561592i	$0.810189\pi$
$912$		0			0
$913$	−2.02633	−	3.50971i	−0.0670619	−	0.116155i
$914$	1.66228	−	2.87915i	0.0549833	−	0.0952338i
$915$		0			0
$916$	−11.1623	+	19.3336i	−0.368812	+	0.638801i
$917$	−26.3246	+	45.5955i	−0.869313	+	1.50569i
$918$		0			0
$919$	−1.67544	+	2.90196i	−0.0552678	+	0.0957267i	−0.892336	−	0.451372i	$-0.850935\pi$
$919$	−1.67544	+	2.90196i	−0.0552678	+	0.0957267i	0.837068	+	0.547099i	$0.184268\pi$
$920$	−14.9057	−	25.8174i	−0.491426	−	0.851175i
$921$		0			0
$922$	18.4868			0.608831
$923$	22.6491	+	12.4054i	0.745505	+	0.408330i
$924$		0			0
$925$	−23.6491	−	40.9615i	−0.777578	−	1.34680i
$926$	−7.58114	−	13.1309i	−0.249132	−	0.431509i
$927$		0			0
$928$	−1.83772			−0.0603262
$929$	−14.4737	+	25.0691i	−0.474866	+	0.822491i	−0.999586	−	0.0287835i	$-0.990837\pi$
$929$	−14.4737	+	25.0691i	−0.474866	+	0.822491i	0.524720	+	0.851275i	$0.324170\pi$
$930$		0			0
$931$	−15.4868			−0.507560
$932$	8.32456	−	14.4186i	0.272680	−	0.472295i
$933$		0			0
$934$	−3.09431	−	5.35949i	−0.101249	−	0.175368i
$935$	14.5132			0.474631
$936$		0			0
$937$	14.2982			0.467103			0.233551	−	0.972344i	$-0.424965\pi$
$937$	14.2982			0.467103			0.233551	+	0.972344i	$0.424965\pi$
$938$	4.48683	+	7.77142i	0.146500	+	0.253746i
$939$		0			0
$940$	−10.0680	+	17.4382i	−0.328381	+	0.568773i
$941$	−48.5964			−1.58420			−0.792099	−	0.610392i	$-0.791012\pi$
$941$	−48.5964			−1.58420			−0.792099	+	0.610392i	$0.791012\pi$
$942$		0			0
$943$	−10.7434	+	18.6081i	−0.349854	+	0.605965i
$944$	−2.32456			−0.0756578
$945$		0			0
$946$	5.32456	+	9.22240i	0.173116	+	0.299846i
$947$	−9.48683	−	16.4317i	−0.308281	−	0.533958i	0.669706	−	0.742627i	$-0.266420\pi$
$947$	−9.48683	−	16.4317i	−0.308281	−	0.533958i	−0.977986	+	0.208669i	$0.933087\pi$
$948$		0			0
$949$	−0.0811388	−	3.60464i	−0.00263388	−	0.117012i
$950$	−63.6228			−2.06420
$951$		0			0
$952$	4.74342	+	8.21584i	0.153735	+	0.266277i
$953$	13.6491	−	23.6410i	0.442138	−	0.765806i	−0.555710	−	0.831376i	$-0.687553\pi$
$953$	13.6491	−	23.6410i	0.442138	−	0.765806i	0.997848	+	0.0655707i	$0.0208868\pi$
$954$		0			0
$955$	−29.8114	+	51.6348i	−0.964674	+	1.67086i
$956$	10.7434	−	18.6081i	0.347467	−	0.601830i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	4.74342	+	8.21584i	0.153173	+	0.265303i
$960$		0			0
$961$	9.00000			0.290323
$962$	−12.1359	−	6.64713i	−0.391279	−	0.214312i
$963$		0			0
$964$	−6.66228	−	11.5394i	−0.214578	−	0.371659i
$965$	41.5680	+	71.9978i	1.33812	+	2.31769i
$966$		0			0
$967$	34.5132			1.10987			0.554934	−	0.831894i	$-0.312743\pi$
$967$	34.5132			1.10987			0.554934	+	0.831894i	$0.312743\pi$
$968$	4.82456	−	8.35637i	0.155067	−	0.268584i
$969$		0			0
$970$	−16.6491			−0.534571
$971$	9.48683	−	16.4317i	0.304447	−	0.527318i	−0.672691	−	0.739923i	$-0.734862\pi$
$971$	9.48683	−	16.4317i	0.304447	−	0.527318i	0.977138	+	0.212606i	$0.0681950\pi$
$972$		0			0
$973$	10.0000	+	17.3205i	0.320585	+	0.555270i
$974$	−13.4868			−0.432146
$975$		0			0
$976$	0.162278			0.00519438
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	0.647737	−	0.761864i	$-0.275715\pi$
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	−0.983662	+	0.180025i	$0.942382\pi$
$978$		0			0
$979$	6.97367	−	12.0787i	0.222879	−	0.386038i
$980$	12.4868			0.398877
$981$		0			0
$982$	−2.90569	+	5.03281i	−0.0927244	+	0.160603i
$983$	23.6228			0.753450			0.376725	−	0.926325i	$-0.377050\pi$
$983$	23.6228			0.753450			0.376725	+	0.926325i	$0.377050\pi$
$984$		0			0
$985$	−39.4868	−	68.3932i	−1.25816	−	2.17919i
$986$	−2.75658	−	4.77454i	−0.0877875	−	0.152052i
$987$		0			0
$988$	−15.9057	+	9.66682i	−0.506028	+	0.307542i
$989$	65.6228			2.08668
$990$		0			0
$991$	−13.3925	−	23.1965i	−0.425428	−	0.736862i	0.571033	−	0.820927i	$-0.306543\pi$
$991$	−13.3925	−	23.1965i	−0.425428	−	0.736862i	−0.996460	+	0.0840651i	$0.973210\pi$
$992$	3.16228	−	5.47723i	0.100402	−	0.173902i
$993$		0			0
$994$	11.3246	−	19.6147i	0.359193	−	0.622141i
$995$	13.5548	−	23.4776i	0.429716	−	0.744290i
$996$		0			0
$997$	29.7302	−	51.4943i	0.941566	−	1.63084i	0.179082	−	0.983834i	$-0.442687\pi$
$997$	29.7302	−	51.4943i	0.941566	−	1.63084i	0.762484	−	0.647007i	$-0.223979\pi$
$998$	−6.32456	−	10.9545i	−0.200200	−	0.346757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.h.d.55.2	✓	4
3.2	odd	2		234.2.h.e.55.1	yes	4
4.3	odd	2		1872.2.t.p.289.2		4
12.11	even	2		1872.2.t.n.289.1		4
13.2	odd	12		3042.2.b.k.1351.1		4
13.3	even	3		3042.2.a.w.1.2		2
13.9	even	3	inner	234.2.h.d.217.2	yes	4
13.10	even	6		3042.2.a.q.1.1		2
13.11	odd	12		3042.2.b.k.1351.4		4
39.2	even	12		3042.2.b.j.1351.4		4
39.11	even	12		3042.2.b.j.1351.1		4
39.23	odd	6		3042.2.a.x.1.2		2
39.29	odd	6		3042.2.a.r.1.1		2
39.35	odd	6		234.2.h.e.217.1	yes	4
52.35	odd	6		1872.2.t.p.1153.2		4
156.35	even	6		1872.2.t.n.1153.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.h.d.55.2	✓	4	1.1	even	1	trivial
234.2.h.d.217.2	yes	4	13.9	even	3	inner
234.2.h.e.55.1	yes	4	3.2	odd	2
234.2.h.e.217.1	yes	4	39.35	odd	6
1872.2.t.n.289.1		4	12.11	even	2
1872.2.t.n.1153.1		4	156.35	even	6
1872.2.t.p.289.2		4	4.3	odd	2
1872.2.t.p.1153.2		4	52.35	odd	6
3042.2.a.q.1.1		2	13.10	even	6
3042.2.a.r.1.1		2	39.29	odd	6
3042.2.a.w.1.2		2	13.3	even	3
3042.2.a.x.1.2		2	39.23	odd	6
3042.2.b.j.1351.1		4	39.11	even	12
3042.2.b.j.1351.4		4	39.2	even	12
3042.2.b.k.1351.1		4	13.2	odd	12
3042.2.b.k.1351.4		4	13.11	odd	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +1.00000 q^{8} +(-2.08114 - 3.60464i) q^{10} +(0.581139 + 1.00656i) q^{11} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(2.58114 - 4.47066i) q^{19} +(-2.08114 + 3.60464i) q^{20} +(0.581139 - 1.00656i) q^{22} +(-3.58114 - 6.20271i) q^{23} +12.3246 q^{25} +(3.08114 - 1.87259i) q^{26} +(-1.58114 - 2.73861i) q^{28} +(0.918861 + 1.59151i) q^{29} -6.32456 q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-6.58114 + 11.3989i) q^{35} +(-1.91886 - 3.32357i) q^{37} -5.16228 q^{38} +4.16228 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-4.58114 + 7.93477i) q^{43} -1.16228 q^{44} +(-3.58114 + 6.20271i) q^{46} +4.83772 q^{47} +(-1.50000 - 2.59808i) q^{49} +(-6.16228 - 10.6734i) q^{50} +(-3.16228 - 1.73205i) q^{52} -12.4868 q^{53} +(2.41886 + 4.18959i) q^{55} +(-1.58114 + 2.73861i) q^{56} +(0.918861 - 1.59151i) q^{58} +(1.16228 - 2.01312i) q^{59} +(-0.0811388 + 0.140537i) q^{61} +(3.16228 + 5.47723i) q^{62} +1.00000 q^{64} +(0.337722 + 15.0035i) q^{65} +(1.41886 + 2.45754i) q^{67} +(1.50000 + 2.59808i) q^{68} +13.1623 q^{70} +(3.58114 - 6.20271i) q^{71} -1.00000 q^{73} +(-1.91886 + 3.32357i) q^{74} +(2.58114 + 4.47066i) q^{76} -3.67544 q^{77} -4.00000 q^{79} +(-2.08114 - 3.60464i) q^{80} +(-1.50000 + 2.59808i) q^{82} -3.48683 q^{83} +(6.24342 - 10.8139i) q^{85} +9.16228 q^{86} +(0.581139 + 1.00656i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-10.0000 - 5.47723i) q^{91} +7.16228 q^{92} +(-2.41886 - 4.18959i) q^{94} +(10.7434 - 18.6081i) q^{95} +(2.00000 - 3.46410i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} - 4 q^{22} - 8 q^{23} + 24 q^{25} + 6 q^{26} + 10 q^{29} - 2 q^{32} - 12 q^{34} - 20 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^16 + 6 * q^17 + 4 * q^19 - 2 * q^20 - 4 * q^22 - 8 * q^23 + 24 * q^25 + 6 * q^26 + 10 * q^29 - 2 * q^32 - 12 * q^34 - 20 * q^35 - 14 * q^37 - 8 * q^38 + 4 * q^40 - 6 * q^41 - 12 * q^43 + 8 * q^44 - 8 * q^46 + 32 * q^47 - 6 * q^49 - 12 * q^50 - 12 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 + 6 * q^61 + 4 * q^64 + 14 * q^65 + 12 * q^67 + 6 * q^68 + 40 * q^70 + 8 * q^71 - 4 * q^73 - 14 * q^74 + 4 * q^76 - 40 * q^77 - 16 * q^79 - 2 * q^80 - 6 * q^82 + 24 * q^83 + 6 * q^85 + 24 * q^86 - 4 * q^88 - 24 * q^89 - 40 * q^91 + 16 * q^92 - 16 * q^94 + 24 * q^95 + 8 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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